LMFDB - Group of Dirichlet characters of modulus 1576

sage:H = DirichletGroup(1576)

pari:g = idealstar(,1576,2)

Character group

sage:G.order() pari:g.no
Order	=	784
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{196}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{1576}(1183,\cdot)$, $\chi_{1576}(789,\cdot)$, $\chi_{1576}(593,\cdot)$

First 32 of 784 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{1576}(1,\cdot)$	1576.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1576}(3,\cdot)$	1576.bi	196	yes	$1$	$1$	$e\left(\frac{29}{196}\right)$	$e\left(\frac{135}{196}\right)$	$e\left(\frac{16}{49}\right)$	$e\left(\frac{29}{98}\right)$	$e\left(\frac{153}{196}\right)$	$e\left(\frac{115}{196}\right)$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{163}{196}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{93}{196}\right)$
$\chi_{1576}(5,\cdot)$	1576.bg	196	yes	$-1$	$1$	$e\left(\frac{135}{196}\right)$	$e\left(\frac{179}{196}\right)$	$e\left(\frac{29}{98}\right)$	$e\left(\frac{37}{98}\right)$	$e\left(\frac{131}{196}\right)$	$e\left(\frac{167}{196}\right)$	$e\left(\frac{59}{98}\right)$	$e\left(\frac{39}{196}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{193}{196}\right)$
$\chi_{1576}(7,\cdot)$	1576.be	98	no	$-1$	$1$	$e\left(\frac{16}{49}\right)$	$e\left(\frac{29}{98}\right)$	$e\left(\frac{25}{98}\right)$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{61}{98}\right)$	$e\left(\frac{61}{98}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{57}{98}\right)$
$\chi_{1576}(9,\cdot)$	1576.ba	98	no	$1$	$1$	$e\left(\frac{29}{98}\right)$	$e\left(\frac{37}{98}\right)$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{55}{98}\right)$	$e\left(\frac{17}{98}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{65}{98}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{93}{98}\right)$
$\chi_{1576}(11,\cdot)$	1576.bi	196	yes	$1$	$1$	$e\left(\frac{153}{196}\right)$	$e\left(\frac{131}{196}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{55}{98}\right)$	$e\left(\frac{57}{196}\right)$	$e\left(\frac{39}{196}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{103}{196}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{173}{196}\right)$
$\chi_{1576}(13,\cdot)$	1576.bg	196	yes	$-1$	$1$	$e\left(\frac{115}{196}\right)$	$e\left(\frac{167}{196}\right)$	$e\left(\frac{61}{98}\right)$	$e\left(\frac{17}{98}\right)$	$e\left(\frac{39}{196}\right)$	$e\left(\frac{135}{196}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{55}{196}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{41}{196}\right)$
$\chi_{1576}(15,\cdot)$	1576.be	98	no	$-1$	$1$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{59}{98}\right)$	$e\left(\frac{61}{98}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{3}{98}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{45}{98}\right)$
$\chi_{1576}(17,\cdot)$	1576.bj	196	no	$-1$	$1$	$e\left(\frac{163}{196}\right)$	$e\left(\frac{39}{196}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{65}{98}\right)$	$e\left(\frac{103}{196}\right)$	$e\left(\frac{55}{196}\right)$	$e\left(\frac{3}{98}\right)$	$e\left(\frac{193}{196}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{53}{196}\right)$
$\chi_{1576}(19,\cdot)$	1576.r	14	yes	$-1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{14}\right)$	$1$	$e\left(\frac{3}{7}\right)$
$\chi_{1576}(21,\cdot)$	1576.bg	196	yes	$-1$	$1$	$e\left(\frac{93}{196}\right)$	$e\left(\frac{193}{196}\right)$	$e\left(\frac{57}{98}\right)$	$e\left(\frac{93}{98}\right)$	$e\left(\frac{173}{196}\right)$	$e\left(\frac{41}{196}\right)$	$e\left(\frac{45}{98}\right)$	$e\left(\frac{53}{196}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{196}\right)$
$\chi_{1576}(23,\cdot)$	1576.bc	98	no	$-1$	$1$	$e\left(\frac{31}{98}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{87}{98}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{25}{98}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{79}{98}\right)$	$e\left(\frac{17}{49}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{10}{49}\right)$
$\chi_{1576}(25,\cdot)$	1576.ba	98	no	$1$	$1$	$e\left(\frac{37}{98}\right)$	$e\left(\frac{81}{98}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{33}{98}\right)$	$e\left(\frac{69}{98}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{39}{98}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{95}{98}\right)$
$\chi_{1576}(27,\cdot)$	1576.bi	196	yes	$1$	$1$	$e\left(\frac{87}{196}\right)$	$e\left(\frac{13}{196}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{87}{98}\right)$	$e\left(\frac{67}{196}\right)$	$e\left(\frac{149}{196}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{97}{196}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{83}{196}\right)$
$\chi_{1576}(29,\cdot)$	1576.bf	98	yes	$1$	$1$	$e\left(\frac{73}{98}\right)$	$e\left(\frac{83}{98}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{81}{98}\right)$	$e\left(\frac{9}{98}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{55}{98}\right)$
$\chi_{1576}(31,\cdot)$	1576.bh	196	no	$1$	$1$	$e\left(\frac{139}{196}\right)$	$e\left(\frac{5}{196}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{41}{98}\right)$	$e\left(\frac{71}{196}\right)$	$e\left(\frac{193}{196}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{75}{196}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{47}{196}\right)$
$\chi_{1576}(33,\cdot)$	1576.t	14	no	$1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{14}\right)$	$1$	$e\left(\frac{5}{14}\right)$
$\chi_{1576}(35,\cdot)$	1576.bi	196	yes	$1$	$1$	$e\left(\frac{3}{196}\right)$	$e\left(\frac{41}{196}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{3}{98}\right)$	$e\left(\frac{151}{196}\right)$	$e\left(\frac{93}{196}\right)$	$e\left(\frac{11}{49}\right)$	$e\left(\frac{125}{196}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{111}{196}\right)$
$\chi_{1576}(37,\cdot)$	1576.bf	98	yes	$1$	$1$	$e\left(\frac{79}{98}\right)$	$e\left(\frac{67}{98}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{30}{49}\right)$	$e\left(\frac{89}{98}\right)$	$e\left(\frac{97}{98}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{81}{98}\right)$
$\chi_{1576}(39,\cdot)$	1576.be	98	no	$-1$	$1$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{53}{98}\right)$	$e\left(\frac{93}{98}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{27}{98}\right)$	$e\left(\frac{27}{98}\right)$	$e\left(\frac{11}{98}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{67}{98}\right)$
$\chi_{1576}(41,\cdot)$	1576.ba	98	no	$1$	$1$	$e\left(\frac{57}{98}\right)$	$e\left(\frac{93}{98}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{27}{98}\right)$	$e\left(\frac{3}{98}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{23}{98}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{51}{98}\right)$
$\chi_{1576}(43,\cdot)$	1576.z	98	yes	$-1$	$1$	$e\left(\frac{3}{98}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{59}{98}\right)$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{53}{98}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{93}{98}\right)$	$e\left(\frac{27}{98}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{31}{49}\right)$
$\chi_{1576}(45,\cdot)$	1576.bg	196	yes	$-1$	$1$	$e\left(\frac{193}{196}\right)$	$e\left(\frac{57}{196}\right)$	$e\left(\frac{93}{98}\right)$	$e\left(\frac{95}{98}\right)$	$e\left(\frac{45}{196}\right)$	$e\left(\frac{5}{196}\right)$	$e\left(\frac{27}{98}\right)$	$e\left(\frac{169}{196}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{183}{196}\right)$
$\chi_{1576}(47,\cdot)$	1576.be	98	no	$-1$	$1$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{95}{98}\right)$	$e\left(\frac{65}{98}\right)$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{41}{98}\right)$	$e\left(\frac{41}{98}\right)$	$e\left(\frac{53}{98}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{98}\right)$
$\chi_{1576}(49,\cdot)$	1576.y	49	no	$1$	$1$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{43}{49}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{8}{49}\right)$
$\chi_{1576}(51,\cdot)$	1576.bb	98	yes	$-1$	$1$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{87}{98}\right)$	$e\left(\frac{75}{98}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{85}{98}\right)$	$e\left(\frac{85}{98}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{73}{98}\right)$
$\chi_{1576}(53,\cdot)$	1576.bf	98	yes	$1$	$1$	$e\left(\frac{97}{98}\right)$	$e\left(\frac{19}{98}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{15}{98}\right)$	$e\left(\frac{67}{98}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{20}{49}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{61}{98}\right)$
$\chi_{1576}(55,\cdot)$	1576.be	98	no	$-1$	$1$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{57}{98}\right)$	$e\left(\frac{39}{98}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{5}{98}\right)$	$e\left(\frac{5}{98}\right)$	$e\left(\frac{71}{98}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{85}{98}\right)$
$\chi_{1576}(57,\cdot)$	1576.bj	196	no	$-1$	$1$	$e\left(\frac{71}{196}\right)$	$e\left(\frac{23}{196}\right)$	$e\left(\frac{53}{98}\right)$	$e\left(\frac{71}{98}\right)$	$e\left(\frac{111}{196}\right)$	$e\left(\frac{143}{196}\right)$	$e\left(\frac{47}{98}\right)$	$e\left(\frac{149}{196}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{177}{196}\right)$
$\chi_{1576}(59,\cdot)$	1576.bb	98	yes	$-1$	$1$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{13}{98}\right)$	$e\left(\frac{45}{98}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{51}{98}\right)$	$e\left(\frac{51}{98}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{83}{98}\right)$
$\chi_{1576}(61,\cdot)$	1576.bf	98	yes	$1$	$1$	$e\left(\frac{59}{98}\right)$	$e\left(\frac{55}{98}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{95}{98}\right)$	$e\left(\frac{65}{98}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{27}{98}\right)$
$\chi_{1576}(63,\cdot)$	1576.bc	98	no	$-1$	$1$	$e\left(\frac{61}{98}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{89}{98}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{65}{98}\right)$	$e\left(\frac{39}{49}\right)$	$e\left(\frac{29}{98}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{26}{49}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Modulus	$1576$
Structure	\(C_{2}\times C_{2}\times C_{196}\)
Order	$784$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{1576}(1,\cdot)\)	1576.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1576}(3,\cdot)\)	1576.bi	196	yes	\(1\)	\(1\)	\(e\left(\frac{29}{196}\right)\)	\(e\left(\frac{135}{196}\right)\)	\(e\left(\frac{16}{49}\right)\)	\(e\left(\frac{29}{98}\right)\)	\(e\left(\frac{153}{196}\right)\)	\(e\left(\frac{115}{196}\right)\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{163}{196}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{93}{196}\right)\)
\(\chi_{1576}(5,\cdot)\)	1576.bg	196	yes	\(-1\)	\(1\)	\(e\left(\frac{135}{196}\right)\)	\(e\left(\frac{179}{196}\right)\)	\(e\left(\frac{29}{98}\right)\)	\(e\left(\frac{37}{98}\right)\)	\(e\left(\frac{131}{196}\right)\)	\(e\left(\frac{167}{196}\right)\)	\(e\left(\frac{59}{98}\right)\)	\(e\left(\frac{39}{196}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{193}{196}\right)\)
\(\chi_{1576}(7,\cdot)\)	1576.be	98	no	\(-1\)	\(1\)	\(e\left(\frac{16}{49}\right)\)	\(e\left(\frac{29}{98}\right)\)	\(e\left(\frac{25}{98}\right)\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{61}{98}\right)\)	\(e\left(\frac{61}{98}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{57}{98}\right)\)
\(\chi_{1576}(9,\cdot)\)	1576.ba	98	no	\(1\)	\(1\)	\(e\left(\frac{29}{98}\right)\)	\(e\left(\frac{37}{98}\right)\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{55}{98}\right)\)	\(e\left(\frac{17}{98}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{65}{98}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{93}{98}\right)\)
\(\chi_{1576}(11,\cdot)\)	1576.bi	196	yes	\(1\)	\(1\)	\(e\left(\frac{153}{196}\right)\)	\(e\left(\frac{131}{196}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{55}{98}\right)\)	\(e\left(\frac{57}{196}\right)\)	\(e\left(\frac{39}{196}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{103}{196}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{173}{196}\right)\)
\(\chi_{1576}(13,\cdot)\)	1576.bg	196	yes	\(-1\)	\(1\)	\(e\left(\frac{115}{196}\right)\)	\(e\left(\frac{167}{196}\right)\)	\(e\left(\frac{61}{98}\right)\)	\(e\left(\frac{17}{98}\right)\)	\(e\left(\frac{39}{196}\right)\)	\(e\left(\frac{135}{196}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{55}{196}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{41}{196}\right)\)
\(\chi_{1576}(15,\cdot)\)	1576.be	98	no	\(-1\)	\(1\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{59}{98}\right)\)	\(e\left(\frac{61}{98}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{3}{98}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{45}{98}\right)\)
\(\chi_{1576}(17,\cdot)\)	1576.bj	196	no	\(-1\)	\(1\)	\(e\left(\frac{163}{196}\right)\)	\(e\left(\frac{39}{196}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{65}{98}\right)\)	\(e\left(\frac{103}{196}\right)\)	\(e\left(\frac{55}{196}\right)\)	\(e\left(\frac{3}{98}\right)\)	\(e\left(\frac{193}{196}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{53}{196}\right)\)
\(\chi_{1576}(19,\cdot)\)	1576.r	14	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(1\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{1576}(21,\cdot)\)	1576.bg	196	yes	\(-1\)	\(1\)	\(e\left(\frac{93}{196}\right)\)	\(e\left(\frac{193}{196}\right)\)	\(e\left(\frac{57}{98}\right)\)	\(e\left(\frac{93}{98}\right)\)	\(e\left(\frac{173}{196}\right)\)	\(e\left(\frac{41}{196}\right)\)	\(e\left(\frac{45}{98}\right)\)	\(e\left(\frac{53}{196}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{196}\right)\)
\(\chi_{1576}(23,\cdot)\)	1576.bc	98	no	\(-1\)	\(1\)	\(e\left(\frac{31}{98}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{87}{98}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{25}{98}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{79}{98}\right)\)	\(e\left(\frac{17}{49}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{10}{49}\right)\)
\(\chi_{1576}(25,\cdot)\)	1576.ba	98	no	\(1\)	\(1\)	\(e\left(\frac{37}{98}\right)\)	\(e\left(\frac{81}{98}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{33}{98}\right)\)	\(e\left(\frac{69}{98}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{39}{98}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{95}{98}\right)\)
\(\chi_{1576}(27,\cdot)\)	1576.bi	196	yes	\(1\)	\(1\)	\(e\left(\frac{87}{196}\right)\)	\(e\left(\frac{13}{196}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{87}{98}\right)\)	\(e\left(\frac{67}{196}\right)\)	\(e\left(\frac{149}{196}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{97}{196}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{83}{196}\right)\)
\(\chi_{1576}(29,\cdot)\)	1576.bf	98	yes	\(1\)	\(1\)	\(e\left(\frac{73}{98}\right)\)	\(e\left(\frac{83}{98}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{81}{98}\right)\)	\(e\left(\frac{9}{98}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{55}{98}\right)\)
\(\chi_{1576}(31,\cdot)\)	1576.bh	196	no	\(1\)	\(1\)	\(e\left(\frac{139}{196}\right)\)	\(e\left(\frac{5}{196}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{41}{98}\right)\)	\(e\left(\frac{71}{196}\right)\)	\(e\left(\frac{193}{196}\right)\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{75}{196}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{47}{196}\right)\)
\(\chi_{1576}(33,\cdot)\)	1576.t	14	no	\(1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(1\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{1576}(35,\cdot)\)	1576.bi	196	yes	\(1\)	\(1\)	\(e\left(\frac{3}{196}\right)\)	\(e\left(\frac{41}{196}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{3}{98}\right)\)	\(e\left(\frac{151}{196}\right)\)	\(e\left(\frac{93}{196}\right)\)	\(e\left(\frac{11}{49}\right)\)	\(e\left(\frac{125}{196}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{111}{196}\right)\)
\(\chi_{1576}(37,\cdot)\)	1576.bf	98	yes	\(1\)	\(1\)	\(e\left(\frac{79}{98}\right)\)	\(e\left(\frac{67}{98}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{30}{49}\right)\)	\(e\left(\frac{89}{98}\right)\)	\(e\left(\frac{97}{98}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{81}{98}\right)\)
\(\chi_{1576}(39,\cdot)\)	1576.be	98	no	\(-1\)	\(1\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{53}{98}\right)\)	\(e\left(\frac{93}{98}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{27}{98}\right)\)	\(e\left(\frac{27}{98}\right)\)	\(e\left(\frac{11}{98}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{67}{98}\right)\)
\(\chi_{1576}(41,\cdot)\)	1576.ba	98	no	\(1\)	\(1\)	\(e\left(\frac{57}{98}\right)\)	\(e\left(\frac{93}{98}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{27}{98}\right)\)	\(e\left(\frac{3}{98}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{23}{98}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{51}{98}\right)\)
\(\chi_{1576}(43,\cdot)\)	1576.z	98	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{98}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{59}{98}\right)\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{53}{98}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{93}{98}\right)\)	\(e\left(\frac{27}{98}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{31}{49}\right)\)
\(\chi_{1576}(45,\cdot)\)	1576.bg	196	yes	\(-1\)	\(1\)	\(e\left(\frac{193}{196}\right)\)	\(e\left(\frac{57}{196}\right)\)	\(e\left(\frac{93}{98}\right)\)	\(e\left(\frac{95}{98}\right)\)	\(e\left(\frac{45}{196}\right)\)	\(e\left(\frac{5}{196}\right)\)	\(e\left(\frac{27}{98}\right)\)	\(e\left(\frac{169}{196}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{183}{196}\right)\)
\(\chi_{1576}(47,\cdot)\)	1576.be	98	no	\(-1\)	\(1\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{95}{98}\right)\)	\(e\left(\frac{65}{98}\right)\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{41}{98}\right)\)	\(e\left(\frac{41}{98}\right)\)	\(e\left(\frac{53}{98}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{11}{98}\right)\)
\(\chi_{1576}(49,\cdot)\)	1576.y	49	no	\(1\)	\(1\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{43}{49}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{8}{49}\right)\)
\(\chi_{1576}(51,\cdot)\)	1576.bb	98	yes	\(-1\)	\(1\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{87}{98}\right)\)	\(e\left(\frac{75}{98}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{85}{98}\right)\)	\(e\left(\frac{85}{98}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{73}{98}\right)\)
\(\chi_{1576}(53,\cdot)\)	1576.bf	98	yes	\(1\)	\(1\)	\(e\left(\frac{97}{98}\right)\)	\(e\left(\frac{19}{98}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{15}{98}\right)\)	\(e\left(\frac{67}{98}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{20}{49}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{61}{98}\right)\)
\(\chi_{1576}(55,\cdot)\)	1576.be	98	no	\(-1\)	\(1\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{57}{98}\right)\)	\(e\left(\frac{39}{98}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{5}{98}\right)\)	\(e\left(\frac{5}{98}\right)\)	\(e\left(\frac{71}{98}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{85}{98}\right)\)
\(\chi_{1576}(57,\cdot)\)	1576.bj	196	no	\(-1\)	\(1\)	\(e\left(\frac{71}{196}\right)\)	\(e\left(\frac{23}{196}\right)\)	\(e\left(\frac{53}{98}\right)\)	\(e\left(\frac{71}{98}\right)\)	\(e\left(\frac{111}{196}\right)\)	\(e\left(\frac{143}{196}\right)\)	\(e\left(\frac{47}{98}\right)\)	\(e\left(\frac{149}{196}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{177}{196}\right)\)
\(\chi_{1576}(59,\cdot)\)	1576.bb	98	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{13}{98}\right)\)	\(e\left(\frac{45}{98}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{51}{98}\right)\)	\(e\left(\frac{51}{98}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{83}{98}\right)\)
\(\chi_{1576}(61,\cdot)\)	1576.bf	98	yes	\(1\)	\(1\)	\(e\left(\frac{59}{98}\right)\)	\(e\left(\frac{55}{98}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{95}{98}\right)\)	\(e\left(\frac{65}{98}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{27}{98}\right)\)
\(\chi_{1576}(63,\cdot)\)	1576.bc	98	no	\(-1\)	\(1\)	\(e\left(\frac{61}{98}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{89}{98}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{65}{98}\right)\)	\(e\left(\frac{39}{49}\right)\)	\(e\left(\frac{29}{98}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{26}{49}\right)\)

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L-functions

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.