Short answer - you've missed some. Solo student flights are PIC. Afterwards, you can log pic when you're flying (including with an instructor) or acting as a required crew member (safety pilot).
Long answer - re-read FAR 61.51, part (e) in particular:
Sec. 61.51 — Pilot logbooks.
(a)
Training time and aeronautical experience. Each person must document and record the following time in a manner acceptable to the Administrator:
(1) Training and aeronautical experience used to meet the requirements for a certificate, rating, or flight review of this part.
(2) The aeronautical experience required for meeting the recent flight experience requirements of this part.
(b)
Logbook entries. For the purposes of meeting the requirements of paragraph (a) of this section, each person must enter the following information for each flight or lesson logged:
(1) General—
(i) Date.
(ii) Total flight time or lesson time.
(iii) Location where the aircraft departed and arrived, or for lessons in a flight simulator or flight training device, the location where the lesson occurred.
(iv) Type and identification of aircraft, flight simulator, flight training device, or aviation training device, as appropriate.
(v) The name of a safety pilot, if required by §91.109(b) of this chapter.
(2) Type of pilot experience or training—
(i) Solo.
(ii) Pilot in command.
(iii) Second in command.
(iv) Flight and ground training received from an authorized instructor.
(v) Training received in a flight simulator, flight training device, or aviation training device from an authorized instructor.
(3) Conditions of flight—
(i) Day or night.
(ii) Actual instrument.
(iii) Simulated instrument conditions in flight, a flight simulator, flight training device, or aviation training device.
(iv) Use of night vision goggles in an aircraft in flight, in a flight simulator, or in a flight training device.
(c)
Logging of pilot time. The pilot time described in this section may be used to:
(1) Apply for a certificate or rating issued under this part or a privilege authorized under this part; or
(2) Satisfy the recent flight experience requirements of this part.
(d)
Logging of solo flight time. Except for a student pilot performing the duties of pilot in command of an airship requiring more than one pilot flight crewmember, a pilot may log as solo flight time only that flight time when the pilot is the sole occupant of the aircraft.
(e)
Logging pilot-in-command flight time.
(1) A sport, recreational, private, commercial, or airline transport pilot may log pilot in command flight time for flights-
(i) When the pilot is the sole manipulator of the controls of an aircraft for which the pilot is rated, or has sport pilot privileges for that category and class of aircraft, if the aircraft class rating is appropriate;
(ii) When the pilot is the sole occupant in the aircraft;
(iii) When the pilot, except for a holder of a sport or recreational pilot certificate, acts as pilot in command of an aircraft for which more than one pilot is required under the type certification of the aircraft or the regulations under which the flight is conducted; or
(iv) When the pilot performs the duties of pilot in command while under the supervision of a qualified pilot in command provided—
(A) The pilot performing the duties of pilot in command holds a commercial or airline transport pilot certificate and aircraft rating that is appropriate to the category and class of aircraft being flown, if a class rating is appropriate;
(B) The pilot performing the duties of pilot in command is undergoing an approved pilot in command training program that includes ground and flight training on the following areas of operation—
( 1 ) Preflight preparation;
( 2 ) Preflight procedures;
( 3 ) Takeoff and departure;
( 4 ) In-flight maneuvers;
( 5 ) Instrument procedures;
( 6 ) Landings and approaches to landings;
( 7 ) Normal and abnormal procedures;
( 8 ) Emergency procedures; and
( 9 ) Postflight procedures;
(C) The supervising pilot in command holds—
( 1 ) A commercial pilot certificate and flight instructor certificate, and aircraft rating that is appropriate to the category, class, and type of aircraft being flown, if a class or type rating is required; or
( 2 ) An airline transport pilot certificate and aircraft rating that is appropriate to the category, class, and type of aircraft being flown, if a class or type rating is required; and
(D) The supervising pilot in command logs the pilot in command training in the pilot's logbook, certifies the pilot in command training in the pilot's logbook and attests to that certification with his or her signature, and flight instructor certificate number.
(2) If rated to act as pilot in command of the aircraft, an airline transport pilot may log all flight time while acting as pilot in command of an operation requiring an airline transport pilot certificate.
(3) A certificated flight instructor may log pilot in command flight time for all flight time while serving as the authorized instructor in an operation if the instructor is rated to act as pilot in command of that aircraft.
(4) A student pilot may log pilot-in-command time only when the student pilot—
(i) Is the sole occupant of the aircraft or is performing the duties of pilot of command of an airship requiring more than one pilot flight crewmember;
(ii) Has a solo flight endorsement as required under §61.87 of this part; and
(iii) Is undergoing training for a pilot certificate or rating.
(f)
Logging second-in-command flight time. A person may log second-in-command time only for that flight time during which that person:
(1) Is qualified in accordance with the second-in-command requirements of §61.55 of this part, and occupies a crewmember station in an aircraft that requires more than one pilot by the aircraft's type certificate; or
(2) Holds the appropriate category, class, and instrument rating (if an instrument rating is required for the flight) for the aircraft being flown, and more than one pilot is required under the type certification of the aircraft or the regulations under which the flight is being conducted.
(g)
Logging instrument time.
(1) A person may log instrument time only for that flight time when the person operates the aircraft solely by reference to instruments under actual or simulated instrument flight conditions.
(2) An authorized instructor may log instrument time when conducting instrument flight instruction in actual instrument flight conditions.
(3) For the purposes of logging instrument time to meet the recent instrument experience requirements of §61.57(c) of this part, the following information must be recorded in the person's logbook—
(i) The location and type of each instrument approach accomplished; and
(ii) The name of the safety pilot, if required.
(4) A person can use time in a flight simulator, flight training device, or aviation training device for acquiring instrument aeronautical experience for a pilot certificate, rating, or instrument recency experience, provided an authorized instructor is present to observe that time and signs the person's logbook or training record to verify the time and the content of the training session.
(h)
Logging training time.
(1) A person may log training time when that person receives training from an authorized instructor in an aircraft, flight simulator, or flight training device.
(2) The training time must be logged in a logbook and must:
(i) Be endorsed in a legible manner by the authorized instructor; and
(ii) Include a description of the training given, the length of the training lesson, and the authorized instructor's signature, certificate number, and certificate expiration date.
(i)
Presentation of required documents.
(1) Persons must present their pilot certificate, medical certificate, logbook, or any other record required by this part for inspection upon a reasonable request by—
(i) The Administrator;
(ii) An authorized representative from the National Transportation Safety Board; or
(iii) Any Federal, State, or local law enforcement officer.
(2) A student pilot must carry the following items in the aircraft on all solo cross-country flights as evidence of the required authorized instructor clearances and endorsements—
(i) Pilot logbook;
(ii) Student pilot certificate; and
(iii) Any other record required by this section.
(3) A sport pilot must carry his or her logbook or other evidence of required authorized instructor endorsements on all flights.
(4) A recreational pilot must carry his or her logbook with the required authorized instructor endorsements on all solo flights—
(i) That exceed 50 nautical miles from the airport at which training was received;
(ii) Within airspace that requires communication with air traffic control;
(iii) Conducted between sunset and sunrise; or
(iv) In an aircraft for which the pilot does not hold an appropriate category or class rating.
(5) A flight instructor with a sport pilot rating must carry his or her logbook or other evidence of required authorized instructor endorsements on all flights when providing flight training.
(j)
Aircraft requirements for logging flight time. For a person to log flight time, the time must be acquired in an aircraft that is identified as an aircraft under §61.5(b), and is—
(1) An aircraft of U.S. registry with either a standard or special airworthiness certificate;
(2) An aircraft of foreign registry with an airworthiness certificate that is approved by the aviation authority of a foreign country that is a Member State to the Convention on International Civil Aviation Organization;
(3) A military aircraft under the direct operational control of the U.S. Armed Forces; or
(4) A public aircraft under the direct operational control of a Federal, State, county, or municipal law enforcement agency, if the flight time was acquired by the pilot while engaged on an official law enforcement flight for a Federal, State, County, or Municipal law enforcement agency.
(k)
Logging night vision goggle time.
(1) A person may log night vision goggle time only for the time the person uses night vision goggles as the primary visual reference of the surface and operates:
(i) An aircraft during a night vision goggle operation; or
(ii) A flight simulator or flight training device with the lighting system adjusted to represent the period beginning 1 hour after sunset and ending 1 hour before sunrise.
(2) An authorized instructor may log night vision goggle time when that person conducts training using night vision goggles as the primary visual reference of the surface and operates:
(i) An aircraft during a night goggle operation; or
(ii) A flight simulator or flight training device with the lighting system adjusted to represent the period beginning 1 hour after sunset and ending 1 hour before sunrise.
(3) To log night vision goggle time to meet the recent night vision goggle experience requirements under §61.57(f), a person must log the information required under §61.51(b).
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