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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 \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\)
4-23e2-1.1-c1e2-0-0 Genus 2 curve 529.a Modular form 23.2.a.a $1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4}$ $1 + T^{2} + 9 T^{4}$ $1 + 2 T + 6 T^{2} + 10 T^{3} + 25 T^{4}$ $1 - 2 T + 10 T^{2} - 14 T^{3} + 49 T^{4}$
4-2944-1.1-c1e2-0-2 Elliptic curve 2.2.8.1-46.1-b Elliptic curve 2.2.8.1-46.2-b Hilbert modular form 2.2.8.1-46.1-b Hilbert modular form 2.2.8.1-46.2-b $1 - T$ $1 + T^{2} + 9 T^{4}$ $1 + 7 T^{2} + 25 T^{4}$ $( 1 + 3 T + 7 T^{2} )^{2}$
4-4288-1.1-c1e2-0-0 Genus 2 curve 4288.b $1 - T$ $1 + T^{2} + 9 T^{4}$ $1 + 2 T + 6 T^{2} + 10 T^{3} + 25 T^{4}$ $( 1 - 3 T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-4432-1.1-c1e2-0-0 Bianchi modular form 2.0.4.1-277.1-a Bianchi modular form 2.0.4.1-277.2-a Elliptic curve 2.0.4.1-277.1-a Elliptic curve 2.0.4.1-277.2-a $1 + T + 2 T^{2}$ $1 + T^{2} + 9 T^{4}$ $( 1 + T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $1 + T^{2} + 49 T^{4}$
4-4889-1.1-c1e2-0-0 Genus 2 curve 4889.a $1 + T + T^{2} + 2 T^{3} + 4 T^{4}$ $1 + T^{2} + 9 T^{4}$ $1 + 5 T + 15 T^{2} + 25 T^{3} + 25 T^{4}$ $1 + T + T^{2} + 7 T^{3} + 49 T^{4}$
4-5024-1.1-c1e2-0-2 Bianchi modular form 2.0.4.1-314.1-a Bianchi modular form 2.0.4.1-314.2-a Elliptic curve 2.0.4.1-314.1-a Elliptic curve 2.0.4.1-314.2-a $1 + T$ $1 + T^{2} + 9 T^{4}$ $( 1 + 3 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $1 - 4 T^{2} + 49 T^{4}$
4-5062-1.1-c1e2-0-0 Genus 2 curve 5062.a $( 1 + T )( 1 + 2 T^{2} )$ $1 + T^{2} + 9 T^{4}$ $1 + 4 T + 11 T^{2} + 20 T^{3} + 25 T^{4}$ $( 1 - 2 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-5725-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-229.1-a Elliptic curve 2.2.5.1-229.2-a Hilbert modular form 2.2.5.1-229.1-a Hilbert modular form 2.2.5.1-229.2-a $( 1 - T + 2 T^{2} )( 1 + T + 2 T^{2} )$ $1 + T^{2} + 9 T^{4}$ $1 + 4 T + 5 T^{2}$ $( 1 - 2 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-5975-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-239.1-b Elliptic curve 2.2.5.1-239.2-b Hilbert modular form 2.2.5.1-239.1-b Hilbert modular form 2.2.5.1-239.2-b $1 - T^{2} + 4 T^{4}$ $1 + T^{2} + 9 T^{4}$ $1 - T + 5 T^{2}$ $1 + 6 T^{2} + 49 T^{4}$
4-6160-1.1-c1e2-0-0 Genus 2 curve 6160.a $1 + 2 T + 2 T^{2}$ $1 + T^{2} + 9 T^{4}$ $( 1 + T )( 1 + T + 5 T^{2} )$ $( 1 - T )( 1 + 4 T + 7 T^{2} )$
4-6203-1.1-c1e2-0-3 Genus 2 curve 6203.b $1 + 2 T + 2 T^{2} + 4 T^{3} + 4 T^{4}$ $1 + T^{2} + 9 T^{4}$ $( 1 - 3 T + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $1 + 4 T + 15 T^{2} + 28 T^{3} + 49 T^{4}$
4-6313-1.1-c1e2-0-0 Genus 2 curve 6313.a $1 + 2 T + 3 T^{2} + 4 T^{3} + 4 T^{4}$ $1 + T^{2} + 9 T^{4}$ $1 + T + 6 T^{2} + 5 T^{3} + 25 T^{4}$ $( 1 - 3 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-6512-1.1-c1e2-0-0 Genus 2 curve 6512.a $1 + 2 T + 2 T^{2}$ $1 + T^{2} + 9 T^{4}$ $1 + 3 T + 4 T^{2} + 15 T^{3} + 25 T^{4}$ $1 + T - 4 T^{2} + 7 T^{3} + 49 T^{4}$
4-6512-1.1-c1e2-0-2 Genus 2 curve 6512.b $1 + 2 T^{2}$ $1 + T^{2} + 9 T^{4}$ $( 1 + T + 5 T^{2} )( 1 + 4 T + 5 T^{2} )$ $1 - T + 10 T^{2} - 7 T^{3} + 49 T^{4}$
4-6628-1.1-c1e2-0-0 Genus 2 curve 6628.a $( 1 - T )( 1 + T )$ $1 + T^{2} + 9 T^{4}$ $1 - 2 T + 8 T^{2} - 10 T^{3} + 25 T^{4}$ $1 - 6 T^{2} + 49 T^{4}$
4-6725-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-269.1-b Elliptic curve 2.2.5.1-269.2-b Hilbert modular form 2.2.5.1-269.1-b Hilbert modular form 2.2.5.1-269.2-b $( 1 - T + 2 T^{2} )( 1 + T + 2 T^{2} )$ $1 + T^{2} + 9 T^{4}$ $1 + 3 T + 5 T^{2}$ $( 1 - 3 T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-7594-1.1-c1e2-0-0 Genus 2 curve 7594.b $( 1 + T )( 1 + T + 2 T^{2} )$ $1 + T^{2} + 9 T^{4}$ $1 + 4 T^{2} + 25 T^{4}$ $( 1 + T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-7594-1.1-c1e2-0-2 Genus 2 curve 7594.c $( 1 - T )( 1 + T + 2 T^{2} )$ $1 + T^{2} + 9 T^{4}$ $1 + 4 T + 12 T^{2} + 20 T^{3} + 25 T^{4}$ $( 1 + 7 T^{2} )( 1 + 5 T + 7 T^{2} )$
4-7705-1.1-c1e2-0-0 Genus 2 curve 7705.a $1 + T + T^{2} + 2 T^{3} + 4 T^{4}$ $1 + T^{2} + 9 T^{4}$ $( 1 + T )( 1 + 2 T + 5 T^{2} )$ $1 + T + 6 T^{2} + 7 T^{3} + 49 T^{4}$
4-7742-1.1-c1e2-0-0 Bianchi modular form 2.0.7.1-158.1-a Bianchi modular form 2.0.7.1-158.4-a Elliptic curve 2.0.7.1-158.1-a Elliptic curve 2.0.7.1-158.4-a $( 1 + T )( 1 + 2 T + 2 T^{2} )$ $1 + T^{2} + 9 T^{4}$ $1 + 3 T^{2} + 25 T^{4}$ $1 + T + 7 T^{2}$
4-7889-1.1-c1e2-0-2 Genus 2 curve 7889.b $1 + T + T^{2} + 2 T^{3} + 4 T^{4}$ $1 + T^{2} + 9 T^{4}$ $( 1 + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $1 + T$
4-7984-1.1-c1e2-0-1 Genus 2 curve 7984.b $1$ $1 + T^{2} + 9 T^{4}$ $1 + 5 T + 15 T^{2} + 25 T^{3} + 25 T^{4}$ $1 + 4 T + 16 T^{2} + 28 T^{3} + 49 T^{4}$
4-8396-1.1-c1e2-0-1 Genus 2 curve 8396.a $1 + T^{2}$ $1 + T^{2} + 9 T^{4}$ $1 + 5 T + 15 T^{2} + 25 T^{3} + 25 T^{4}$ $1 - T + 9 T^{2} - 7 T^{3} + 49 T^{4}$
4-95e2-1.1-c1e2-0-4 Elliptic curve 2.2.5.1-361.2-b Elliptic curve 2.2.5.1-361.3-b Hilbert modular form 2.2.5.1-361.2-b Hilbert modular form 2.2.5.1-361.3-b $1 + 2 T^{2} + 4 T^{4}$ $1 + T^{2} + 9 T^{4}$ $1 + 3 T + 5 T^{2}$ $( 1 - 4 T + 7 T^{2} )( 1 + 4 T + 7 T^{2} )$
4-9251-1.1-c1e2-0-0 Genus 2 curve 9251.a $( 1 - T + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $1 + T^{2} + 9 T^{4}$ $1 - 3 T^{2} + 25 T^{4}$ $1 + 2 T + 2 T^{2} + 14 T^{3} + 49 T^{4}$
4-9800-1.1-c1e2-0-0 Bianchi modular form 2.0.7.1-200.1-a Bianchi modular form 2.0.7.1-200.4-a Elliptic curve 2.0.7.1-200.1-a Elliptic curve 2.0.7.1-200.4-a $1 + 2 T + 2 T^{2}$ $1 + T^{2} + 9 T^{4}$ $1 + T^{2}$ $1 + 4 T + 7 T^{2}$
4-9967-1.1-c1e2-0-0 Genus 2 curve 9967.a $1 + 3 T + 5 T^{2} + 6 T^{3} + 4 T^{4}$ $1 + T^{2} + 9 T^{4}$ $( 1 - T + 5 T^{2} )( 1 + T + 5 T^{2} )$ $1 + 2 T + 2 T^{2} + 14 T^{3} + 49 T^{4}$
4-10150-1.1-c1e2-0-0 Genus 2 curve 10150.a $( 1 + T )( 1 - T + 2 T^{2} )$ $1 + T^{2} + 9 T^{4}$ $1 + 3 T + 5 T^{2}$ $( 1 + T )( 1 + 7 T^{2} )$
4-10688-1.1-c1e2-0-0 Elliptic curve 2.2.8.1-167.1-b Elliptic curve 2.2.8.1-167.2-b Hilbert modular form 2.2.8.1-167.1-b Hilbert modular form 2.2.8.1-167.2-b $1 + 2 T + 2 T^{2}$ $1 + T^{2} + 9 T^{4}$ $1 + 8 T^{2} + 25 T^{4}$ $( 1 + T + 7 T^{2} )( 1 + 5 T + 7 T^{2} )$
4-10688-1.1-c1e2-0-2 Elliptic curve 2.2.8.1-167.1-a Elliptic curve 2.2.8.1-167.2-a Hilbert modular form 2.2.8.1-167.1-a Hilbert modular form 2.2.8.1-167.2-a $1 + 2 T^{2}$ $1 + T^{2} + 9 T^{4}$ $1 - 4 T^{2} + 25 T^{4}$ $( 1 + T + 7 T^{2} )( 1 + 5 T + 7 T^{2} )$
4-10775-1.1-c1e2-0-3 Elliptic curve 2.2.5.1-431.1-b Elliptic curve 2.2.5.1-431.2-b Hilbert modular form 2.2.5.1-431.1-b Hilbert modular form 2.2.5.1-431.2-b $1 + 2 T^{2} + 4 T^{4}$ $1 + T^{2} + 9 T^{4}$ $1 + 2 T + 5 T^{2}$ $1 + 4 T^{2} + 49 T^{4}$
4-11776-1.1-c1e2-0-2 Elliptic curve 2.2.8.1-184.1-a Elliptic curve 2.2.8.1-184.2-a Hilbert modular form 2.2.8.1-184.1-a Hilbert modular form 2.2.8.1-184.2-a $1$ $1 + T^{2} + 9 T^{4}$ $1 + 3 T^{2} + 25 T^{4}$ $( 1 - 5 T + 7 T^{2} )( 1 - T + 7 T^{2} )$
4-12121-1.1-c1e2-0-0 Genus 2 curve 12121.a $1 + T + T^{2} + 2 T^{3} + 4 T^{4}$ $1 + T^{2} + 9 T^{4}$ $1 - 2 T^{2} + 25 T^{4}$ $1 + 2 T + 2 T^{2} + 14 T^{3} + 49 T^{4}$
4-12352-1.1-c1e2-0-0 Bianchi modular form 2.0.4.1-772.1-a Bianchi modular form 2.0.4.1-772.2-a Elliptic curve 2.0.4.1-772.1-a Elliptic curve 2.0.4.1-772.2-a $1$ $1 + T^{2} + 9 T^{4}$ $( 1 + 2 T + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $( 1 - 3 T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-12560-1.1-c1e2-0-2 Bianchi modular form 2.0.4.1-785.1-a Bianchi modular form 2.0.4.1-785.4-a Elliptic curve 2.0.4.1-785.1-a Elliptic curve 2.0.4.1-785.4-a $1 + T + 2 T^{2}$ $1 + T^{2} + 9 T^{4}$ $( 1 - T )( 1 + 3 T + 5 T^{2} )$ $( 1 - 2 T + 7 T^{2} )( 1 + 2 T + 7 T^{2} )$
4-13132-1.1-c1e2-0-1 Bianchi modular form 2.0.7.1-268.3-b Bianchi modular form 2.0.7.1-268.4-b Elliptic curve 2.0.7.1-268.3-b Elliptic curve 2.0.7.1-268.4-b $( 1 - T )^{2}$ $1 + T^{2} + 9 T^{4}$ $1 - 4 T^{2} + 25 T^{4}$ $1 + 3 T + 7 T^{2}$
4-13354-1.1-c1e2-0-0 Genus 2 curve 13354.a $( 1 - T )( 1 + T + 2 T^{2} )$ $1 + T^{2} + 9 T^{4}$ $1 + 3 T + 9 T^{2} + 15 T^{3} + 25 T^{4}$ $1 + 2 T + 7 T^{2} + 14 T^{3} + 49 T^{4}$
4-116e2-1.1-c1e2-0-1 Elliptic curve 2.2.29.1-16.1-a Hilbert modular form 2.2.29.1-16.1-a Modular form 116.2.c.a $1$ $1 + T^{2} + 9 T^{4}$ $( 1 - T + 5 T^{2} )^{2}$ $( 1 + 2 T + 7 T^{2} )^{2}$
4-116e2-1.1-c1e2-0-3 Bianchi modular form 2.0.4.1-841.1-a Bianchi modular form 2.0.4.1-841.3-a Elliptic curve 2.0.4.1-841.1-a Elliptic curve 2.0.4.1-841.3-a $1 + T + 2 T^{2}$ $1 + T^{2} + 9 T^{4}$ $( 1 + 5 T^{2} )( 1 + 2 T + 5 T^{2} )$ $1 + 9 T^{2} + 49 T^{4}$
4-13475-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-539.1-a Elliptic curve 2.2.5.1-539.2-a Hilbert modular form 2.2.5.1-539.1-a Hilbert modular form 2.2.5.1-539.2-a $1 - 3 T^{2} + 4 T^{4}$ $1 + T^{2} + 9 T^{4}$ $1 + T + 5 T^{2}$ $1 + T^{2}$
4-13475-1.1-c1e2-0-3 Elliptic curve 2.2.5.1-539.1-d Elliptic curve 2.2.5.1-539.2-d Hilbert modular form 2.2.5.1-539.1-d Hilbert modular form 2.2.5.1-539.2-d $( 1 - T + 2 T^{2} )( 1 + T + 2 T^{2} )$ $1 + T^{2} + 9 T^{4}$ $1 + T + 5 T^{2}$ $1 + T^{2}$
4-13511-1.1-c1e2-0-0 Genus 2 curve 13511.a $1 + 2 T + 3 T^{2} + 4 T^{3} + 4 T^{4}$ $1 + T^{2} + 9 T^{4}$ $1 + 5 T^{2} + 25 T^{4}$ $1 - T + 6 T^{2} - 7 T^{3} + 49 T^{4}$
4-13583-1.1-c1e2-0-0 Elliptic curve 2.2.17.1-47.1-a Elliptic curve 2.2.17.1-47.2-a Hilbert modular form 2.2.17.1-47.1-a Hilbert modular form 2.2.17.1-47.2-a $( 1 + 2 T^{2} )( 1 + 2 T + 2 T^{2} )$ $1 + T^{2} + 9 T^{4}$ $1 + 2 T^{2} + 25 T^{4}$ $( 1 - 3 T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-13622-1.1-c1e2-0-0 Genus 2 curve 13622.a $( 1 + T )( 1 + T + 2 T^{2} )$ $1 + T^{2} + 9 T^{4}$ $1 + T + 5 T^{3} + 25 T^{4}$ $1 + T + 7 T^{2}$
4-13648-1.1-c1e2-0-0 Bianchi modular form 2.0.4.1-853.1-a Bianchi modular form 2.0.4.1-853.2-a Elliptic curve 2.0.4.1-853.1-a Elliptic curve 2.0.4.1-853.2-a $1 + 2 T + 2 T^{2}$ $1 + T^{2} + 9 T^{4}$ $( 1 + 5 T^{2} )( 1 + 3 T + 5 T^{2} )$ $1 + 6 T^{2} + 49 T^{4}$
4-14275-1.1-c1e2-0-1 Elliptic curve 2.2.5.1-571.1-a Elliptic curve 2.2.5.1-571.2-a Hilbert modular form 2.2.5.1-571.1-a Hilbert modular form 2.2.5.1-571.2-a $1 + T^{2} + 4 T^{4}$ $1 + T^{2} + 9 T^{4}$ $1 + 3 T + 5 T^{2}$ $( 1 - 3 T + 7 T^{2} )( 1 + 3 T + 7 T^{2} )$
4-14383-1.1-c1e2-0-0 Genus 2 curve 14383.a $1 - T + 3 T^{2} - 2 T^{3} + 4 T^{4}$ $1 + T^{2} + 9 T^{4}$ $1 + 2 T + 8 T^{2} + 10 T^{3} + 25 T^{4}$ $1 + 2 T + 9 T^{2} + 14 T^{3} + 49 T^{4}$
4-14725-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-589.1-a Elliptic curve 2.2.5.1-589.4-a Hilbert modular form 2.2.5.1-589.1-a Hilbert modular form 2.2.5.1-589.4-a $1 - 3 T^{2} + 4 T^{4}$ $1 + T^{2} + 9 T^{4}$ $1 + 2 T + 5 T^{2}$ $( 1 - 5 T + 7 T^{2} )( 1 + 5 T + 7 T^{2} )$
4-14794-1.1-c1e2-0-0 Genus 2 curve 14794.a $( 1 - T )( 1 + 2 T + 2 T^{2} )$ $1 + T^{2} + 9 T^{4}$ $1 + 3 T + 7 T^{2} + 15 T^{3} + 25 T^{4}$ $( 1 - T + 7 T^{2} )( 1 + T + 7 T^{2} )$
4-14900-1.1-c1e2-0-0 Elliptic curve 2.2.5.1-596.1-a Elliptic curve 2.2.5.1-596.2-a Hilbert modular form 2.2.5.1-596.1-a Hilbert modular form 2.2.5.1-596.2-a $1 + T^{2}$ $1 + T^{2} + 9 T^{4}$ $1 + 2 T + 5 T^{2}$ $1 - 6 T^{2} + 49 T^{4}$
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