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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 \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\) \(F_{ 97 }(T)\)
2-19-1.1-c1-0-0 Elliptic curve 19.a Modular form 19.2.a.a Modular form 19.2.a.a.1.1 $1 + 2 T^{2}$ $1 + 2 T + 3 T^{2}$ $1 - 3 T + 5 T^{2}$ $1 + T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-37-1.1-c1-0-0 Elliptic curve 37.b Modular form 37.2.a.b Modular form 37.2.a.b.1.1 $1 + 2 T^{2}$ $1 - T + 3 T^{2}$ $1 + 5 T^{2}$ $1 + T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-110-1.1-c1-0-4 Elliptic curve 110.c Modular form 110.2.a.c Modular form 110.2.a.c.1.1 $1 - T$ $1 - T + 3 T^{2}$ $1 + T$ $1 + T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-116-1.1-c1-0-1 Elliptic curve 116.b Modular form 116.2.a.b Modular form 116.2.a.b.1.1 $1$ $1 - T + 3 T^{2}$ $1 - 3 T + 5 T^{2}$ $1 + 4 T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-118-1.1-c1-0-1 Elliptic curve 118.c Modular form 118.2.a.c Modular form 118.2.a.c.1.1 $1 - T$ $1 + T + 3 T^{2}$ $1 - T + 5 T^{2}$ $1 - 3 T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-150-1.1-c1-0-2 Elliptic curve 150.c Modular form 150.2.a.c Modular form 150.2.a.c.1.1 $1 - T$ $1 - T$ $1$ $1 + 2 T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-153-1.1-c1-0-2 Elliptic curve 153.a Modular form 153.2.a.a Modular form 153.2.a.a.1.1 $1 + 2 T + 2 T^{2}$ $1$ $1 + T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-153-1.1-c1-0-3 Elliptic curve 153.d Modular form 153.2.a.d Modular form 153.2.a.d.1.1 $1 - 2 T + 2 T^{2}$ $1$ $1 - T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-171-1.1-c1-0-7 Elliptic curve 171.b Modular form 171.2.a.b Modular form 171.2.a.b.1.1 $1 + 2 T^{2}$ $1$ $1 + 3 T + 5 T^{2}$ $1 + T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-174-1.1-c1-0-1 Elliptic curve 174.b Modular form 174.2.a.b Modular form 174.2.a.b.1.1 $1 + T$ $1 - T$ $1 + 3 T + 5 T^{2}$ $1 - 5 T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-185-1.1-c1-0-9 Elliptic curve 185.a Modular form 185.2.a.a Modular form 185.2.a.a.1.1 $1 + 2 T + 2 T^{2}$ $1 - T + 3 T^{2}$ $1 + T$ $1 + 5 T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-254-1.1-c1-0-10 Elliptic curve 254.b Modular form 254.2.a.b Modular form 254.2.a.b.1.1 $1 - T$ $1 + 2 T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-278-1.1-c1-0-1 Elliptic curve 278.a Modular form 278.2.a.a Modular form 278.2.a.a.1.1 $1 + T$ $1 + 2 T + 3 T^{2}$ $1 - 3 T + 5 T^{2}$ $1 + T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-286-1.1-c1-0-2 Elliptic curve 286.d Modular form 286.2.a.d Modular form 286.2.a.d.1.1 $1 - T$ $1 + T + 3 T^{2}$ $1 - T + 5 T^{2}$ $1 - 3 T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-286-1.1-c1-0-6 Elliptic curve 286.b Modular form 286.2.a.b Modular form 286.2.a.b.1.1 $1 + T$ $1 + T + 3 T^{2}$ $1 + T + 5 T^{2}$ $1 - T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
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 $1 + T$ $1 + T$ $1 - 4 T + 5 T^{2}$ $1$ $1 - 8 T + 97 T^{2}$
2-300-1.1-c1-0-2 Elliptic curve 300.d Modular form 300.2.a.d Modular form 300.2.a.d.1.1 $1$ $1 - T$ $1$ $1 - 4 T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-304-1.1-c1-0-5 Elliptic curve 304.f Modular form 304.2.a.f Modular form 304.2.a.f.1.1 $1$ $1 - 2 T + 3 T^{2}$ $1 - 3 T + 5 T^{2}$ $1 - T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-325-1.1-c1-0-0 Elliptic curve 325.a Modular form 325.2.a.a Modular form 325.2.a.a.1.1 $1 + 2 T + 2 T^{2}$ $1 + T + 3 T^{2}$ $1$ $1 + 2 T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-331-1.1-c1-0-12 Elliptic curve 331.a Modular form 331.2.a.a Modular form 331.2.a.a.1.1 $1 + T + 2 T^{2}$ $1 + 2 T + 3 T^{2}$ $1 - T + 5 T^{2}$ $1 - 2 T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-333-1.1-c1-0-12 Elliptic curve 333.b Modular form 333.2.a.b Modular form 333.2.a.b.1.1 $1 + 2 T^{2}$ $1$ $1 + 5 T^{2}$ $1 + T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-357-1.1-c1-0-11 Elliptic curve 357.c Modular form 357.2.a.c Modular form 357.2.a.c.1.1 $1 + 2 T^{2}$ $1 + T$ $1 - T + 5 T^{2}$ $1 - T$ $1 - 8 T + 97 T^{2}$
2-357-1.1-c1-0-2 Elliptic curve 357.b Modular form 357.2.a.b Modular form 357.2.a.b.1.1 $1 + 2 T^{2}$ $1 + T$ $1 - T + 5 T^{2}$ $1 + T$ $1 - 8 T + 97 T^{2}$
2-378-1.1-c1-0-1 Elliptic curve 378.d Modular form 378.2.a.d Modular form 378.2.a.d.1.1 $1 + T$ $1$ $1 + 5 T^{2}$ $1 - T$ $1 - 8 T + 97 T^{2}$
2-378-1.1-c1-0-2 Elliptic curve 378.e Modular form 378.2.a.e Modular form 378.2.a.e.1.1 $1 - T$ $1$ $1 + 5 T^{2}$ $1 - T$ $1 - 8 T + 97 T^{2}$
2-378-1.1-c1-0-4 Elliptic curve 378.g Modular form 378.2.a.g Modular form 378.2.a.g.1.1 $1 - T$ $1$ $1 - 3 T + 5 T^{2}$ $1 - T$ $1 - 8 T + 97 T^{2}$
2-378-1.1-c1-0-6 Elliptic curve 378.b Modular form 378.2.a.b Modular form 378.2.a.b.1.1 $1 + T$ $1$ $1 + 3 T + 5 T^{2}$ $1 - T$ $1 - 8 T + 97 T^{2}$
2-390-1.1-c1-0-5 Elliptic curve 390.g Modular form 390.2.a.g Modular form 390.2.a.g.1.1 $1 - T$ $1 - T$ $1 + T$ $1 - 2 T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-395-1.1-c1-0-5 Elliptic curve 395.a Modular form 395.2.a.a Modular form 395.2.a.a.1.1 $1 + 2 T + 2 T^{2}$ $1 + T + 3 T^{2}$ $1 - T$ $1 - 3 T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-402-1.1-c1-0-10 Elliptic curve 402.b Modular form 402.2.a.b Modular form 402.2.a.b.1.1 $1 + T$ $1 - T$ $1 + 3 T + 5 T^{2}$ $1 + T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-406-1.1-c1-0-10 Elliptic curve 406.b Modular form 406.2.a.b Modular form 406.2.a.b.1.1 $1 + T$ $1 - T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 - T$ $1 - 8 T + 97 T^{2}$
2-415-1.1-c1-0-14 Elliptic curve 415.a Modular form 415.2.a.a Modular form 415.2.a.a.1.1 $1 - T + 2 T^{2}$ $1 - 3 T + 3 T^{2}$ $1 - T$ $1 - T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-418-1.1-c1-0-14 Elliptic curve 418.a Modular form 418.2.a.a Modular form 418.2.a.a.1.1 $1 - T$ $1 + T + 3 T^{2}$ $1 + 2 T + 5 T^{2}$ $1 + 3 T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-418-1.1-c1-0-9 Elliptic curve 418.c Modular form 418.2.a.c Modular form 418.2.a.c.1.1 $1 - T$ $1 - 3 T + 3 T^{2}$ $1 + 2 T + 5 T^{2}$ $1 - T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-420-1.1-c1-0-0 Elliptic curve 420.a Modular form 420.2.a.a Modular form 420.2.a.a.1.1 $1$ $1 + T$ $1 + T$ $1 + T$ $1 - 8 T + 97 T^{2}$
2-420-1.1-c1-0-3 Elliptic curve 420.d Modular form 420.2.a.d Modular form 420.2.a.d.1.1 $1$ $1 - T$ $1 - T$ $1 + T$ $1 - 8 T + 97 T^{2}$
2-430-1.1-c1-0-11 Elliptic curve 430.c Modular form 430.2.a.c Modular form 430.2.a.c.1.1 $1 - T$ $1 + 2 T + 3 T^{2}$ $1 + T$ $1 + T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-434-1.1-c1-0-11 Elliptic curve 434.d Modular form 434.2.a.d Modular form 434.2.a.d.1.1 $1 - T$ $1 - T + 3 T^{2}$ $1 - 3 T + 5 T^{2}$ $1 - T$ $1 - 8 T + 97 T^{2}$
2-434-1.1-c1-0-2 Elliptic curve 434.b Modular form 434.2.a.b Modular form 434.2.a.b.1.1 $1 - T$ $1 + 3 T + 3 T^{2}$ $1 + 3 T + 5 T^{2}$ $1 + T$ $1 - 8 T + 97 T^{2}$
2-450-1.1-c1-0-6 Elliptic curve 450.b Modular form 450.2.a.b Modular form 450.2.a.b.1.1 $1 + T$ $1$ $1$ $1 + 2 T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-460-1.1-c1-0-5 Elliptic curve 460.c Modular form 460.2.a.c Modular form 460.2.a.c.1.1 $1$ $1 - T + 3 T^{2}$ $1 + T$ $1 + 4 T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-464-1.1-c1-0-4 Elliptic curve 464.c Modular form 464.2.a.c Modular form 464.2.a.c.1.1 $1$ $1 + T + 3 T^{2}$ $1 - 3 T + 5 T^{2}$ $1 - 4 T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-492-1.1-c1-0-4 Elliptic curve 492.a Modular form 492.2.a.a Modular form 492.2.a.a.1.1 $1$ $1 + T$ $1 + 5 T^{2}$ $1 + 2 T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-510-1.1-c1-0-4 Elliptic curve 510.d Modular form 510.2.a.d Modular form 510.2.a.d.1.1 $1 - T$ $1 + T$ $1 + T$ $1 - 2 T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-513-1.1-c1-0-13 Elliptic curve 513.a Modular form 513.2.a.a Modular form 513.2.a.a.1.1 $1 + T + 2 T^{2}$ $1$ $1 + 5 T^{2}$ $1 + 2 T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-513-1.1-c1-0-21 Elliptic curve 513.b Modular form 513.2.a.b Modular form 513.2.a.b.1.1 $1 - T + 2 T^{2}$ $1$ $1 + 5 T^{2}$ $1 + 2 T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-522-1.1-c1-0-7 Elliptic curve 522.m Modular form 522.2.a.m Modular form 522.2.a.m.1.1 $1 - T$ $1$ $1 - 3 T + 5 T^{2}$ $1 - 5 T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-540-1.1-c1-0-3 Elliptic curve 540.a Modular form 540.2.a.a Modular form 540.2.a.a.1.1 $1$ $1$ $1 + T$ $1 + 4 T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-540-1.1-c1-0-5 Elliptic curve 540.d Modular form 540.2.a.d Modular form 540.2.a.d.1.1 $1$ $1$ $1 - T$ $1 + 4 T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
2-550-1.1-c1-0-12 Elliptic curve 550.h Modular form 550.2.a.h Modular form 550.2.a.h.1.1 $1 - T$ $1 + 3 T + 3 T^{2}$ $1$ $1 + T + 7 T^{2}$ $1 - 8 T + 97 T^{2}$
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