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e.g. 3,7,19 e.g. F3=1-T,F5=1+T+5T^2

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$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label Origin \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\)
2-46-1.1-c1-0-0 Elliptic curve 46.a Modular form 46.2.a.a Modular form 46.2.a.a.1.1 $1 + T$ $1 + 3 T^{2}$ $1 - 4 T + 5 T^{2}$ $1 + 4 T + 7 T^{2}$
2-84-1.1-c1-0-0 Elliptic curve 84.a Modular form 84.2.a.a Modular form 84.2.a.a.1.1 $1$ $1 + T$ $1 - 4 T + 5 T^{2}$ $1 + T$
2-99-1.1-c1-0-1 Elliptic curve 99.c Modular form 99.2.a.c Modular form 99.2.a.c.1.1 $1 - T + 2 T^{2}$ $1$ $1 - 4 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$
2-182-1.1-c1-0-0 Elliptic curve 182.a Modular form 182.2.a.a Modular form 182.2.a.a.1.1 $1 + T$ $1 - T + 3 T^{2}$ $1 - 4 T + 5 T^{2}$ $1 + T$
2-187-1.1-c1-0-7 Elliptic curve 187.b Modular form 187.2.a.b Modular form 187.2.a.b.1.1 $1 - 2 T + 2 T^{2}$ $1 + 3 T^{2}$ $1 - 4 T + 5 T^{2}$ $1 + 5 T + 7 T^{2}$
2-194-1.1-c1-0-6 Elliptic curve 194.a Modular form 194.2.a.a Modular form 194.2.a.a.1.1 $1 - T$ $1 + 3 T^{2}$ $1 - 4 T + 5 T^{2}$ $1 + 4 T + 7 T^{2}$
2-198-1.1-c1-0-1 Elliptic curve 198.c Modular form 198.2.a.c Modular form 198.2.a.c.1.1 $1 + T$ $1$ $1 - 4 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$
2-206-1.1-c1-0-5 Elliptic curve 206.a Modular form 206.2.a.a Modular form 206.2.a.a.1.1 $1 + T$ $1 - 2 T + 3 T^{2}$ $1 - 4 T + 5 T^{2}$ $1 + 7 T^{2}$
2-6e3-1.1-c1-0-2 Elliptic curve 216.d Modular form 216.2.a.d Modular form 216.2.a.d.1.1 $1$ $1$ $1 - 4 T + 5 T^{2}$ $1 + 3 T + 7 T^{2}$
2-221-1.1-c1-0-3 Elliptic curve 221.a Modular form 221.2.a.a Modular form 221.2.a.a.1.1 $1 + T + 2 T^{2}$ $1 + 3 T^{2}$ $1 - 4 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$
2-222-1.1-c1-0-3 Elliptic curve 222.c Modular form 222.2.a.c Modular form 222.2.a.c.1.1 $1 + T$ $1 - T$ $1 - 4 T + 5 T^{2}$ $1 + T + 7 T^{2}$
2-238-1.1-c1-0-3 Elliptic curve 238.b Modular form 238.2.a.b Modular form 238.2.a.b.1.1 $1 + T$ $1 - 2 T + 3 T^{2}$ $1 - 4 T + 5 T^{2}$ $1 - T$
2-2e8-1.1-c1-0-1 Elliptic curve 256.c Modular form 256.2.a.c Modular form 256.2.a.c.1.1 $1$ $1 + 3 T^{2}$ $1 - 4 T + 5 T^{2}$ $1 + 7 T^{2}$
2-259-1.1-c1-0-7 Elliptic curve 259.a Modular form 259.2.a.a Modular form 259.2.a.a.1.1 $1 - T + 2 T^{2}$ $1 + 3 T^{2}$ $1 - 4 T + 5 T^{2}$ $1 - T$
2-264-1.1-c1-0-3 Elliptic curve 264.d Modular form 264.2.a.d Modular form 264.2.a.d.1.1 $1$ $1 - T$ $1 - 4 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$
2-267-1.1-c1-0-2 Elliptic curve 267.a Modular form 267.2.a.a Modular form 267.2.a.a.1.1 $1 + 2 T^{2}$ $1 + T$ $1 - 4 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$
2-288-1.1-c1-0-2 Elliptic curve 288.e Modular form 288.2.a.e Modular form 288.2.a.e.1.1 $1$ $1$ $1 - 4 T + 5 T^{2}$ $1 + 7 T^{2}$
2-294-1.1-c1-0-1 Elliptic curve 294.b Modular form 294.2.a.b Modular form 294.2.a.b.1.1 $1 + T$ $1 + T$ $1 - 4 T + 5 T^{2}$ $1$
2-306-1.1-c1-0-6 Elliptic curve 306.d Modular form 306.2.a.d Modular form 306.2.a.d.1.1 $1 - T$ $1$ $1 - 4 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$
2-307-1.1-c1-0-6 Elliptic curve 307.a Modular form 307.2.a.a Modular form 307.2.a.a.1.1 $1 + 2 T^{2}$ $1 + 3 T^{2}$ $1 - 4 T + 5 T^{2}$ $1 + 7 T^{2}$
2-312-1.1-c1-0-1 Elliptic curve 312.c Modular form 312.2.a.c Modular form 312.2.a.c.1.1 $1$ $1 + T$ $1 - 4 T + 5 T^{2}$ $1 + 7 T^{2}$
2-318-1.1-c1-0-1 Elliptic curve 318.b Modular form 318.2.a.b Modular form 318.2.a.b.1.1 $1 + T$ $1 + T$ $1 - 4 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-336-1.1-c1-0-4 Elliptic curve 336.f Modular form 336.2.a.f Modular form 336.2.a.f.1.1 $1$ $1 - T$ $1 - 4 T + 5 T^{2}$ $1 - T$
2-342-1.1-c1-0-1 Elliptic curve 342.d Modular form 342.2.a.d Modular form 342.2.a.d.1.1 $1 + T$ $1$ $1 - 4 T + 5 T^{2}$ $1 - 3 T + 7 T^{2}$
2-354-1.1-c1-0-4 Elliptic curve 354.f Modular form 354.2.a.f Modular form 354.2.a.f.1.1 $1 - T$ $1 + T$ $1 - 4 T + 5 T^{2}$ $1 + 7 T^{2}$
2-363-1.1-c1-0-11 Elliptic curve 363.c Modular form 363.2.a.c Modular form 363.2.a.c.1.1 $1 - 2 T + 2 T^{2}$ $1 + T$ $1 - 4 T + 5 T^{2}$ $1 + T + 7 T^{2}$
2-363-1.1-c1-0-3 Elliptic curve 363.a Modular form 363.2.a.a Modular form 363.2.a.a.1.1 $1 + 2 T + 2 T^{2}$ $1 + T$ $1 - 4 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-368-1.1-c1-0-3 Elliptic curve 368.d Modular form 368.2.a.d Modular form 368.2.a.d.1.1 $1$ $1 + 3 T^{2}$ $1 - 4 T + 5 T^{2}$ $1 - 4 T + 7 T^{2}$
2-369-1.1-c1-0-11 Elliptic curve 369.b Modular form 369.2.a.b Modular form 369.2.a.b.1.1 $1 - 2 T + 2 T^{2}$ $1$ $1 - 4 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$
2-378-1.1-c1-0-5 Elliptic curve 378.h Modular form 378.2.a.h Modular form 378.2.a.h.1.1 $1 - T$ $1$ $1 - 4 T + 5 T^{2}$ $1 + T$
2-384-1.1-c1-0-2 Elliptic curve 384.d Modular form 384.2.a.d Modular form 384.2.a.d.1.1 $1$ $1 + T$ $1 - 4 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$
2-384-1.1-c1-0-5 Elliptic curve 384.h Modular form 384.2.a.h Modular form 384.2.a.h.1.1 $1$ $1 - T$ $1 - 4 T + 5 T^{2}$ $1 - 2 T + 7 T^{2}$
2-387-1.1-c1-0-13 Elliptic curve 387.e Modular form 387.2.a.e Modular form 387.2.a.e.1.1 $1 - 2 T + 2 T^{2}$ $1$ $1 - 4 T + 5 T^{2}$ $1 + 7 T^{2}$
2-392-1.1-c1-0-2 Elliptic curve 392.b Modular form 392.2.a.b Modular form 392.2.a.b.1.1 $1$ $1 + 2 T + 3 T^{2}$ $1 - 4 T + 5 T^{2}$ $1$
2-399-1.1-c1-0-8 Elliptic curve 399.b Modular form 399.2.a.b Modular form 399.2.a.b.1.1 $1 + T + 2 T^{2}$ $1 - T$ $1 - 4 T + 5 T^{2}$ $1 + T$
2-427-1.1-c1-0-12 Elliptic curve 427.b Modular form 427.2.a.b Modular form 427.2.a.b.1.1 $1 + 2 T^{2}$ $1 - 2 T + 3 T^{2}$ $1 - 4 T + 5 T^{2}$ $1 - T$
2-432-1.1-c1-0-4 Elliptic curve 432.h Modular form 432.2.a.h Modular form 432.2.a.h.1.1 $1$ $1$ $1 - 4 T + 5 T^{2}$ $1 - 3 T + 7 T^{2}$
2-442-1.1-c1-0-12 Elliptic curve 442.e Modular form 442.2.a.e Modular form 442.2.a.e.1.1 $1 - T$ $1 - 2 T + 3 T^{2}$ $1 - 4 T + 5 T^{2}$ $1 + 4 T + 7 T^{2}$
2-443-1.1-c1-0-10 Elliptic curve 443.c Modular form 443.2.a.c Modular form 443.2.a.c.1.1 $1 - T + 2 T^{2}$ $1 + 2 T + 3 T^{2}$ $1 - 4 T + 5 T^{2}$ $1 + T + 7 T^{2}$
2-448-1.1-c1-0-2 Elliptic curve 448.c Modular form 448.2.a.c Modular form 448.2.a.c.1.1 $1$ $1 + 2 T + 3 T^{2}$ $1 - 4 T + 5 T^{2}$ $1 - T$
2-448-1.1-c1-0-6 Elliptic curve 448.h Modular form 448.2.a.h Modular form 448.2.a.h.1.1 $1$ $1 - 2 T + 3 T^{2}$ $1 - 4 T + 5 T^{2}$ $1 + T$
2-456-1.1-c1-0-3 Elliptic curve 456.b Modular form 456.2.a.b Modular form 456.2.a.b.1.1 $1$ $1 + T$ $1 - 4 T + 5 T^{2}$ $1 - 4 T + 7 T^{2}$
2-459-1.1-c1-0-17 Elliptic curve 459.h Modular form 459.2.a.h Modular form 459.2.a.h.1.1 $1 - 2 T + 2 T^{2}$ $1$ $1 - 4 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-468-1.1-c1-0-2 Elliptic curve 468.d Modular form 468.2.a.d Modular form 468.2.a.d.1.1 $1$ $1$ $1 - 4 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$
2-468-1.1-c1-0-3 Elliptic curve 468.e Modular form 468.2.a.e Modular form 468.2.a.e.1.1 $1$ $1$ $1 - 4 T + 5 T^{2}$ $1 - 4 T + 7 T^{2}$
2-483-1.1-c1-0-20 Elliptic curve 483.b Modular form 483.2.a.b Modular form 483.2.a.b.1.1 $1 - 2 T + 2 T^{2}$ $1 - T$ $1 - 4 T + 5 T^{2}$ $1 + T$
2-504-1.1-c1-0-4 Elliptic curve 504.h Modular form 504.2.a.h Modular form 504.2.a.h.1.1 $1$ $1$ $1 - 4 T + 5 T^{2}$ $1 - T$
2-528-1.1-c1-0-3 Elliptic curve 528.f Modular form 528.2.a.f Modular form 528.2.a.f.1.1 $1$ $1 + T$ $1 - 4 T + 5 T^{2}$ $1 - 2 T + 7 T^{2}$
2-537-1.1-c1-0-15 Elliptic curve 537.e Modular form 537.2.a.e Modular form 537.2.a.e.1.1 $1 - T + 2 T^{2}$ $1 - T$ $1 - 4 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-544-1.1-c1-0-4 Elliptic curve 544.b Modular form 544.2.a.b Modular form 544.2.a.b.1.1 $1$ $1 + 2 T + 3 T^{2}$ $1 - 4 T + 5 T^{2}$ $1 - 4 T + 7 T^{2}$
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