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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 \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\)
2-38-1.1-c1-0-1 Elliptic curve 38.b Modular form 38.2.a.b Modular form 38.2.a.b.1.1 $1 - T$ $1 + T + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 - 3 T + 7 T^{2}$
2-43-1.1-c1-0-2 Elliptic curve 43.a Modular form 43.2.a.a Modular form 43.2.a.a.1.1 $1 + 2 T + 2 T^{2}$ $1 + 2 T + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 + 7 T^{2}$
2-56-1.1-c1-0-1 Elliptic curve 56.b Modular form 56.2.a.b Modular form 56.2.a.b.1.1 $1$ $1 - 2 T + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 - T$
2-66-1.1-c1-0-2 Elliptic curve 66.c Modular form 66.2.a.c Modular form 66.2.a.c.1.1 $1 - T$ $1 - T$ $1 + 4 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$
2-99-1.1-c1-0-3 Elliptic curve 99.a Modular form 99.2.a.a Modular form 99.2.a.a.1.1 $1 + T + 2 T^{2}$ $1$ $1 + 4 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$
2-102-1.1-c1-0-2 Elliptic curve 102.a Modular form 102.2.a.a Modular form 102.2.a.a.1.1 $1 + T$ $1 + T$ $1 + 4 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$
2-106-1.1-c1-0-3 Elliptic curve 106.a Modular form 106.2.a.a Modular form 106.2.a.a.1.1 $1 + T$ $1 + T + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 + 7 T^{2}$
2-112-1.1-c1-0-2 Elliptic curve 112.a Modular form 112.2.a.a Modular form 112.2.a.a.1.1 $1$ $1 + 2 T + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 + T$
2-123-1.1-c1-0-5 Elliptic curve 123.a Modular form 123.2.a.a Modular form 123.2.a.a.1.1 $1 + 2 T + 2 T^{2}$ $1 - T$ $1 + 4 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$
2-142-1.1-c1-0-4 Elliptic curve 142.d Modular form 142.2.a.d Modular form 142.2.a.d.1.1 $1 - T$ $1 + 3 T + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 + 3 T + 7 T^{2}$
2-148-1.1-c1-0-2 Elliptic curve 148.a Modular form 148.2.a.a Modular form 148.2.a.a.1.1 $1$ $1 + T + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 + 3 T + 7 T^{2}$
2-154-1.1-c1-0-4 Elliptic curve 154.a Modular form 154.2.a.a Modular form 154.2.a.a.1.1 $1 + T$ $1 + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 + T$
2-156-1.1-c1-0-1 Elliptic curve 156.a Modular form 156.2.a.a Modular form 156.2.a.a.1.1 $1$ $1 + T$ $1 + 4 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$
2-163-1.1-c1-0-10 Elliptic curve 163.a Modular form 163.2.a.a Modular form 163.2.a.a.1.1 $1 + 2 T^{2}$ $1 + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 - 2 T + 7 T^{2}$
2-182-1.1-c1-0-4 Elliptic curve 182.e Modular form 182.2.a.e Modular form 182.2.a.e.1.1 $1 - T$ $1 - 3 T + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 + T$
2-184-1.1-c1-0-4 Elliptic curve 184.a Modular form 184.2.a.a Modular form 184.2.a.a.1.1 $1$ $1 + T + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 - 2 T + 7 T^{2}$
2-203-1.1-c1-0-0 Elliptic curve 203.a Modular form 203.2.a.a Modular form 203.2.a.a.1.1 $1 + 2 T + 2 T^{2}$ $1 + T + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 - T$
2-214-1.1-c1-0-6 Elliptic curve 214.b Modular form 214.2.a.b Modular form 214.2.a.b.1.1 $1 + T$ $1 - T + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$
2-6e3-1.1-c1-0-3 Elliptic curve 216.a Modular form 216.2.a.a Modular form 216.2.a.a.1.1 $1$ $1$ $1 + 4 T + 5 T^{2}$ $1 + 3 T + 7 T^{2}$
2-219-1.1-c1-0-11 Elliptic curve 219.c Modular form 219.2.a.c Modular form 219.2.a.c.1.1 $1 - T + 2 T^{2}$ $1 + T$ $1 + 4 T + 5 T^{2}$ $1 - 2 T + 7 T^{2}$
2-222-1.1-c1-0-0 Elliptic curve 222.a Modular form 222.2.a.a Modular form 222.2.a.a.1.1 $1 + T$ $1 + T$ $1 + 4 T + 5 T^{2}$ $1 - 3 T + 7 T^{2}$
2-226-1.1-c1-0-8 Elliptic curve 226.a Modular form 226.2.a.a Modular form 226.2.a.a.1.1 $1 - T$ $1 + 2 T + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 + 7 T^{2}$
2-238-1.1-c1-0-6 Elliptic curve 238.c Modular form 238.2.a.c Modular form 238.2.a.c.1.1 $1 - T$ $1 + 2 T + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 - T$
2-252-1.1-c1-0-1 Elliptic curve 252.a Modular form 252.2.a.a Modular form 252.2.a.a.1.1 $1$ $1$ $1 + 4 T + 5 T^{2}$ $1 + T$
2-2e8-1.1-c1-0-5 Elliptic curve 256.b Modular form 256.2.a.b Modular form 256.2.a.b.1.1 $1$ $1 + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 + 7 T^{2}$
2-282-1.1-c1-0-8 Elliptic curve 282.a Modular form 282.2.a.a Modular form 282.2.a.a.1.1 $1 - T$ $1 + T$ $1 + 4 T + 5 T^{2}$ $1 + 4 T + 7 T^{2}$
2-288-1.1-c1-0-3 Elliptic curve 288.a Modular form 288.2.a.a Modular form 288.2.a.a.1.1 $1$ $1$ $1 + 4 T + 5 T^{2}$ $1 + 7 T^{2}$
2-294-1.1-c1-0-6 Elliptic curve 294.c Modular form 294.2.a.c Modular form 294.2.a.c.1.1 $1 + T$ $1 - T$ $1 + 4 T + 5 T^{2}$ $1$
2-298-1.1-c1-0-9 Elliptic curve 298.a Modular form 298.2.a.a Modular form 298.2.a.a.1.1 $1 + T$ $1 + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 - 4 T + 7 T^{2}$
2-302-1.1-c1-0-12 Elliptic curve 302.c Modular form 302.2.a.c Modular form 302.2.a.c.1.1 $1 - T$ $1 + T + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$
2-304-1.1-c1-0-8 Elliptic curve 304.d Modular form 304.2.a.d Modular form 304.2.a.d.1.1 $1$ $1 - T + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 + 3 T + 7 T^{2}$
2-312-1.1-c1-0-5 Elliptic curve 312.d Modular form 312.2.a.d Modular form 312.2.a.d.1.1 $1$ $1 - T$ $1 + 4 T + 5 T^{2}$ $1 + 4 T + 7 T^{2}$
2-348-1.1-c1-0-3 Elliptic curve 348.c Modular form 348.2.a.c Modular form 348.2.a.c.1.1 $1$ $1 - T$ $1 + 4 T + 5 T^{2}$ $1 + 3 T + 7 T^{2}$
2-354-1.1-c1-0-10 Elliptic curve 354.d Modular form 354.2.a.d Modular form 354.2.a.d.1.1 $1 - T$ $1 + T$ $1 + 4 T + 5 T^{2}$ $1 + T + 7 T^{2}$
2-368-1.1-c1-0-9 Elliptic curve 368.e Modular form 368.2.a.e Modular form 368.2.a.e.1.1 $1$ $1 - T + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$
2-378-1.1-c1-0-0 Elliptic curve 378.a Modular form 378.2.a.a Modular form 378.2.a.a.1.1 $1 + T$ $1$ $1 + 4 T + 5 T^{2}$ $1 + T$
2-384-1.1-c1-0-0 Elliptic curve 384.a Modular form 384.2.a.a Modular form 384.2.a.a.1.1 $1$ $1 + T$ $1 + 4 T + 5 T^{2}$ $1 - 2 T + 7 T^{2}$
2-384-1.1-c1-0-7 Elliptic curve 384.e Modular form 384.2.a.e Modular form 384.2.a.e.1.1 $1$ $1 - T$ $1 + 4 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$
2-414-1.1-c1-0-9 Elliptic curve 414.b Modular form 414.2.a.b Modular form 414.2.a.b.1.1 $1 - T$ $1$ $1 + 4 T + 5 T^{2}$ $1 + 4 T + 7 T^{2}$
2-427-1.1-c1-0-30 Elliptic curve 427.c Modular form 427.2.a.c Modular form 427.2.a.c.1.1 $1 - T + 2 T^{2}$ $1 - T + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 - T$
2-432-1.1-c1-0-0 Elliptic curve 432.a Modular form 432.2.a.a Modular form 432.2.a.a.1.1 $1$ $1$ $1 + 4 T + 5 T^{2}$ $1 - 3 T + 7 T^{2}$
2-433-1.1-c1-0-33 Elliptic curve 433.a Modular form 433.2.a.a Modular form 433.2.a.a.1.1 $1 + T + 2 T^{2}$ $1 + 2 T + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 + 3 T + 7 T^{2}$
2-438-1.1-c1-0-8 Elliptic curve 438.b Modular form 438.2.a.b Modular form 438.2.a.b.1.1 $1 + T$ $1 - T$ $1 + 4 T + 5 T^{2}$ $1 + 7 T^{2}$
2-442-1.1-c1-0-14 Elliptic curve 442.b Modular form 442.2.a.b Modular form 442.2.a.b.1.1 $1 - T$ $1 + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 + 2 T + 7 T^{2}$
2-446-1.1-c1-0-18 Elliptic curve 446.a Modular form 446.2.a.a Modular form 446.2.a.a.1.1 $1 + T$ $1 + 3 T + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 + 4 T + 7 T^{2}$
2-459-1.1-c1-0-9 Elliptic curve 459.a Modular form 459.2.a.a Modular form 459.2.a.a.1.1 $1 + 2 T + 2 T^{2}$ $1$ $1 + 4 T + 5 T^{2}$ $1 - T + 7 T^{2}$
2-462-1.1-c1-0-8 Elliptic curve 462.e Modular form 462.2.a.e Modular form 462.2.a.e.1.1 $1 - T$ $1 + T$ $1 + 4 T + 5 T^{2}$ $1 - T$
2-468-1.1-c1-0-0 Elliptic curve 468.a Modular form 468.2.a.a Modular form 468.2.a.a.1.1 $1$ $1$ $1 + 4 T + 5 T^{2}$ $1 - 4 T + 7 T^{2}$
2-501-1.1-c1-0-5 Elliptic curve 501.a Modular form 501.2.a.a Modular form 501.2.a.a.1.1 $1 - T + 2 T^{2}$ $1 + T$ $1 + 4 T + 5 T^{2}$ $1 - 4 T + 7 T^{2}$
2-503-1.1-c1-0-6 Elliptic curve 503.a Modular form 503.2.a.a Modular form 503.2.a.a.1.1 $1 + T + 2 T^{2}$ $1 - T + 3 T^{2}$ $1 + 4 T + 5 T^{2}$ $1 + 3 T + 7 T^{2}$
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