LMFDB - Group of Dirichlet characters of modulus 6304

sage:H = DirichletGroup(6304)

pari:g = idealstar(,6304,2)

Character group

sage:G.order() pari:g.no
Order	=	3136
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{392}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{6304}(1183,\cdot)$, $\chi_{6304}(3941,\cdot)$, $\chi_{6304}(3745,\cdot)$

First 32 of 3136 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{6304}(1,\cdot)$	6304.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6304}(3,\cdot)$	6304.dd	392	yes	$1$	$1$	$e\left(\frac{303}{392}\right)$	$e\left(\frac{221}{392}\right)$	$e\left(\frac{15}{196}\right)$	$e\left(\frac{107}{196}\right)$	$e\left(\frac{61}{392}\right)$	$e\left(\frac{279}{392}\right)$	$e\left(\frac{33}{98}\right)$	$e\left(\frac{65}{196}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{333}{392}\right)$
$\chi_{6304}(5,\cdot)$	6304.dc	392	yes	$-1$	$1$	$e\left(\frac{221}{392}\right)$	$e\left(\frac{211}{392}\right)$	$e\left(\frac{107}{196}\right)$	$e\left(\frac{25}{196}\right)$	$e\left(\frac{311}{392}\right)$	$e\left(\frac{89}{392}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{137}{196}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{43}{392}\right)$
$\chi_{6304}(7,\cdot)$	6304.cr	196	no	$-1$	$1$	$e\left(\frac{15}{196}\right)$	$e\left(\frac{107}{196}\right)$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{15}{98}\right)$	$e\left(\frac{69}{196}\right)$	$e\left(\frac{73}{196}\right)$	$e\left(\frac{61}{98}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{163}{196}\right)$
$\chi_{6304}(9,\cdot)$	6304.cp	196	no	$1$	$1$	$e\left(\frac{107}{196}\right)$	$e\left(\frac{25}{196}\right)$	$e\left(\frac{15}{98}\right)$	$e\left(\frac{9}{98}\right)$	$e\left(\frac{61}{196}\right)$	$e\left(\frac{83}{196}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{65}{98}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{137}{196}\right)$
$\chi_{6304}(11,\cdot)$	6304.df	392	yes	$1$	$1$	$e\left(\frac{61}{392}\right)$	$e\left(\frac{311}{392}\right)$	$e\left(\frac{69}{196}\right)$	$e\left(\frac{61}{196}\right)$	$e\left(\frac{359}{392}\right)$	$e\left(\frac{29}{392}\right)$	$e\left(\frac{93}{98}\right)$	$e\left(\frac{5}{196}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{199}{392}\right)$
$\chi_{6304}(13,\cdot)$	6304.de	392	yes	$-1$	$1$	$e\left(\frac{279}{392}\right)$	$e\left(\frac{89}{392}\right)$	$e\left(\frac{73}{196}\right)$	$e\left(\frac{83}{196}\right)$	$e\left(\frac{29}{392}\right)$	$e\left(\frac{123}{392}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{153}{196}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{33}{392}\right)$
$\chi_{6304}(15,\cdot)$	6304.cf	98	no	$-1$	$1$	$e\left(\frac{33}{98}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{61}{98}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{93}{98}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{3}{98}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{47}{49}\right)$
$\chi_{6304}(17,\cdot)$	6304.cm	196	no	$-1$	$1$	$e\left(\frac{65}{196}\right)$	$e\left(\frac{137}{196}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{65}{98}\right)$	$e\left(\frac{5}{196}\right)$	$e\left(\frac{153}{196}\right)$	$e\left(\frac{3}{98}\right)$	$e\left(\frac{193}{196}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{151}{196}\right)$
$\chi_{6304}(19,\cdot)$	6304.bx	56	yes	$-1$	$1$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{17}{56}\right)$
$\chi_{6304}(21,\cdot)$	6304.de	392	yes	$-1$	$1$	$e\left(\frac{333}{392}\right)$	$e\left(\frac{43}{392}\right)$	$e\left(\frac{163}{196}\right)$	$e\left(\frac{137}{196}\right)$	$e\left(\frac{199}{392}\right)$	$e\left(\frac{33}{392}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{151}{196}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{267}{392}\right)$
$\chi_{6304}(23,\cdot)$	6304.co	196	no	$-1$	$1$	$e\left(\frac{111}{196}\right)$	$e\left(\frac{47}{196}\right)$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{13}{98}\right)$	$e\left(\frac{1}{196}\right)$	$e\left(\frac{109}{196}\right)$	$e\left(\frac{79}{98}\right)$	$e\left(\frac{17}{49}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{187}{196}\right)$
$\chi_{6304}(25,\cdot)$	6304.cp	196	no	$1$	$1$	$e\left(\frac{25}{196}\right)$	$e\left(\frac{15}{196}\right)$	$e\left(\frac{9}{98}\right)$	$e\left(\frac{25}{98}\right)$	$e\left(\frac{115}{196}\right)$	$e\left(\frac{89}{196}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{39}{98}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{43}{196}\right)$
$\chi_{6304}(27,\cdot)$	6304.dd	392	yes	$1$	$1$	$e\left(\frac{125}{392}\right)$	$e\left(\frac{271}{392}\right)$	$e\left(\frac{45}{196}\right)$	$e\left(\frac{125}{196}\right)$	$e\left(\frac{183}{392}\right)$	$e\left(\frac{53}{392}\right)$	$e\left(\frac{1}{98}\right)$	$e\left(\frac{195}{196}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{215}{392}\right)$
$\chi_{6304}(29,\cdot)$	6304.da	392	yes	$1$	$1$	$e\left(\frac{145}{392}\right)$	$e\left(\frac{283}{392}\right)$	$e\left(\frac{111}{196}\right)$	$e\left(\frac{145}{196}\right)$	$e\left(\frac{79}{392}\right)$	$e\left(\frac{85}{392}\right)$	$e\left(\frac{9}{98}\right)$	$e\left(\frac{69}{98}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{367}{392}\right)$
$\chi_{6304}(31,\cdot)$	6304.cn	196	no	$1$	$1$	$e\left(\frac{139}{196}\right)$	$e\left(\frac{5}{196}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{41}{98}\right)$	$e\left(\frac{71}{196}\right)$	$e\left(\frac{193}{196}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{75}{196}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{47}{196}\right)$
$\chi_{6304}(33,\cdot)$	6304.bj	14	no	$1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{14}\right)$	$1$	$e\left(\frac{5}{14}\right)$
$\chi_{6304}(35,\cdot)$	6304.df	392	yes	$1$	$1$	$e\left(\frac{251}{392}\right)$	$e\left(\frac{33}{392}\right)$	$e\left(\frac{59}{196}\right)$	$e\left(\frac{55}{196}\right)$	$e\left(\frac{57}{392}\right)$	$e\left(\frac{235}{392}\right)$	$e\left(\frac{71}{98}\right)$	$e\left(\frac{27}{196}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{369}{392}\right)$
$\chi_{6304}(37,\cdot)$	6304.da	392	yes	$1$	$1$	$e\left(\frac{267}{392}\right)$	$e\left(\frac{121}{392}\right)$	$e\left(\frac{53}{196}\right)$	$e\left(\frac{71}{196}\right)$	$e\left(\frac{13}{392}\right)$	$e\left(\frac{143}{392}\right)$	$e\left(\frac{97}{98}\right)$	$e\left(\frac{25}{98}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{373}{392}\right)$
$\chi_{6304}(39,\cdot)$	6304.cr	196	no	$-1$	$1$	$e\left(\frac{95}{196}\right)$	$e\left(\frac{155}{196}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{95}{98}\right)$	$e\left(\frac{45}{196}\right)$	$e\left(\frac{5}{196}\right)$	$e\left(\frac{27}{98}\right)$	$e\left(\frac{11}{98}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{183}{196}\right)$
$\chi_{6304}(41,\cdot)$	6304.cp	196	no	$1$	$1$	$e\left(\frac{163}{196}\right)$	$e\left(\frac{137}{196}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{65}{98}\right)$	$e\left(\frac{5}{196}\right)$	$e\left(\frac{55}{196}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{23}{98}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{53}{196}\right)$
$\chi_{6304}(43,\cdot)$	6304.cz	392	yes	$-1$	$1$	$e\left(\frac{159}{392}\right)$	$e\left(\frac{17}{392}\right)$	$e\left(\frac{167}{196}\right)$	$e\left(\frac{159}{196}\right)$	$e\left(\frac{65}{392}\right)$	$e\left(\frac{127}{392}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{101}{392}\right)$
$\chi_{6304}(45,\cdot)$	6304.dc	392	yes	$-1$	$1$	$e\left(\frac{43}{392}\right)$	$e\left(\frac{261}{392}\right)$	$e\left(\frac{137}{196}\right)$	$e\left(\frac{43}{196}\right)$	$e\left(\frac{41}{392}\right)$	$e\left(\frac{255}{392}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{71}{196}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{317}{392}\right)$
$\chi_{6304}(47,\cdot)$	6304.cf	98	no	$-1$	$1$	$e\left(\frac{93}{98}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{65}{98}\right)$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{75}{98}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{41}{98}\right)$	$e\left(\frac{53}{98}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{30}{49}\right)$
$\chi_{6304}(49,\cdot)$	6304.cl	98	no	$1$	$1$	$e\left(\frac{15}{98}\right)$	$e\left(\frac{9}{98}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{69}{98}\right)$	$e\left(\frac{73}{98}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{43}{49}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{65}{98}\right)$
$\chi_{6304}(51,\cdot)$	6304.db	392	yes	$-1$	$1$	$e\left(\frac{41}{392}\right)$	$e\left(\frac{103}{392}\right)$	$e\left(\frac{101}{196}\right)$	$e\left(\frac{41}{196}\right)$	$e\left(\frac{71}{392}\right)$	$e\left(\frac{193}{392}\right)$	$e\left(\frac{18}{49}\right)$	$e\left(\frac{31}{98}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{243}{392}\right)$
$\chi_{6304}(53,\cdot)$	6304.da	392	yes	$1$	$1$	$e\left(\frac{143}{392}\right)$	$e\left(\frac{125}{392}\right)$	$e\left(\frac{173}{196}\right)$	$e\left(\frac{143}{196}\right)$	$e\left(\frac{305}{392}\right)$	$e\left(\frac{219}{392}\right)$	$e\left(\frac{67}{98}\right)$	$e\left(\frac{89}{98}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{97}{392}\right)$
$\chi_{6304}(55,\cdot)$	6304.cr	196	no	$-1$	$1$	$e\left(\frac{141}{196}\right)$	$e\left(\frac{65}{196}\right)$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{139}{196}\right)$	$e\left(\frac{59}{196}\right)$	$e\left(\frac{5}{98}\right)$	$e\left(\frac{71}{98}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{121}{196}\right)$
$\chi_{6304}(57,\cdot)$	6304.cs	196	no	$-1$	$1$	$e\left(\frac{11}{98}\right)$	$e\left(\frac{18}{49}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{11}{49}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{47}{98}\right)$	$e\left(\frac{47}{98}\right)$	$e\left(\frac{149}{196}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{15}{98}\right)$
$\chi_{6304}(59,\cdot)$	6304.db	392	yes	$-1$	$1$	$e\left(\frac{103}{392}\right)$	$e\left(\frac{297}{392}\right)$	$e\left(\frac{139}{196}\right)$	$e\left(\frac{103}{196}\right)$	$e\left(\frac{121}{392}\right)$	$e\left(\frac{351}{392}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{97}{98}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{381}{392}\right)$
$\chi_{6304}(61,\cdot)$	6304.da	392	yes	$1$	$1$	$e\left(\frac{89}{392}\right)$	$e\left(\frac{171}{392}\right)$	$e\left(\frac{83}{196}\right)$	$e\left(\frac{89}{196}\right)$	$e\left(\frac{135}{392}\right)$	$e\left(\frac{309}{392}\right)$	$e\left(\frac{65}{98}\right)$	$e\left(\frac{41}{98}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{255}{392}\right)$
$\chi_{6304}(63,\cdot)$	6304.ci	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	$6304$
Structure	\(C_{2}\times C_{4}\times C_{392}\)
Order	$3136$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{6304}(1,\cdot)\)	6304.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6304}(3,\cdot)\)	6304.dd	392	yes	\(1\)	\(1\)	\(e\left(\frac{303}{392}\right)\)	\(e\left(\frac{221}{392}\right)\)	\(e\left(\frac{15}{196}\right)\)	\(e\left(\frac{107}{196}\right)\)	\(e\left(\frac{61}{392}\right)\)	\(e\left(\frac{279}{392}\right)\)	\(e\left(\frac{33}{98}\right)\)	\(e\left(\frac{65}{196}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{333}{392}\right)\)
\(\chi_{6304}(5,\cdot)\)	6304.dc	392	yes	\(-1\)	\(1\)	\(e\left(\frac{221}{392}\right)\)	\(e\left(\frac{211}{392}\right)\)	\(e\left(\frac{107}{196}\right)\)	\(e\left(\frac{25}{196}\right)\)	\(e\left(\frac{311}{392}\right)\)	\(e\left(\frac{89}{392}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{137}{196}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{43}{392}\right)\)
\(\chi_{6304}(7,\cdot)\)	6304.cr	196	no	\(-1\)	\(1\)	\(e\left(\frac{15}{196}\right)\)	\(e\left(\frac{107}{196}\right)\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{15}{98}\right)\)	\(e\left(\frac{69}{196}\right)\)	\(e\left(\frac{73}{196}\right)\)	\(e\left(\frac{61}{98}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{163}{196}\right)\)
\(\chi_{6304}(9,\cdot)\)	6304.cp	196	no	\(1\)	\(1\)	\(e\left(\frac{107}{196}\right)\)	\(e\left(\frac{25}{196}\right)\)	\(e\left(\frac{15}{98}\right)\)	\(e\left(\frac{9}{98}\right)\)	\(e\left(\frac{61}{196}\right)\)	\(e\left(\frac{83}{196}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{65}{98}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{137}{196}\right)\)
\(\chi_{6304}(11,\cdot)\)	6304.df	392	yes	\(1\)	\(1\)	\(e\left(\frac{61}{392}\right)\)	\(e\left(\frac{311}{392}\right)\)	\(e\left(\frac{69}{196}\right)\)	\(e\left(\frac{61}{196}\right)\)	\(e\left(\frac{359}{392}\right)\)	\(e\left(\frac{29}{392}\right)\)	\(e\left(\frac{93}{98}\right)\)	\(e\left(\frac{5}{196}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{199}{392}\right)\)
\(\chi_{6304}(13,\cdot)\)	6304.de	392	yes	\(-1\)	\(1\)	\(e\left(\frac{279}{392}\right)\)	\(e\left(\frac{89}{392}\right)\)	\(e\left(\frac{73}{196}\right)\)	\(e\left(\frac{83}{196}\right)\)	\(e\left(\frac{29}{392}\right)\)	\(e\left(\frac{123}{392}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{153}{196}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{33}{392}\right)\)
\(\chi_{6304}(15,\cdot)\)	6304.cf	98	no	\(-1\)	\(1\)	\(e\left(\frac{33}{98}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{61}{98}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{93}{98}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{3}{98}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{47}{49}\right)\)
\(\chi_{6304}(17,\cdot)\)	6304.cm	196	no	\(-1\)	\(1\)	\(e\left(\frac{65}{196}\right)\)	\(e\left(\frac{137}{196}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{65}{98}\right)\)	\(e\left(\frac{5}{196}\right)\)	\(e\left(\frac{153}{196}\right)\)	\(e\left(\frac{3}{98}\right)\)	\(e\left(\frac{193}{196}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{151}{196}\right)\)
\(\chi_{6304}(19,\cdot)\)	6304.bx	56	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{17}{56}\right)\)
\(\chi_{6304}(21,\cdot)\)	6304.de	392	yes	\(-1\)	\(1\)	\(e\left(\frac{333}{392}\right)\)	\(e\left(\frac{43}{392}\right)\)	\(e\left(\frac{163}{196}\right)\)	\(e\left(\frac{137}{196}\right)\)	\(e\left(\frac{199}{392}\right)\)	\(e\left(\frac{33}{392}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{151}{196}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{267}{392}\right)\)
\(\chi_{6304}(23,\cdot)\)	6304.co	196	no	\(-1\)	\(1\)	\(e\left(\frac{111}{196}\right)\)	\(e\left(\frac{47}{196}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{13}{98}\right)\)	\(e\left(\frac{1}{196}\right)\)	\(e\left(\frac{109}{196}\right)\)	\(e\left(\frac{79}{98}\right)\)	\(e\left(\frac{17}{49}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{187}{196}\right)\)
\(\chi_{6304}(25,\cdot)\)	6304.cp	196	no	\(1\)	\(1\)	\(e\left(\frac{25}{196}\right)\)	\(e\left(\frac{15}{196}\right)\)	\(e\left(\frac{9}{98}\right)\)	\(e\left(\frac{25}{98}\right)\)	\(e\left(\frac{115}{196}\right)\)	\(e\left(\frac{89}{196}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{39}{98}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{43}{196}\right)\)
\(\chi_{6304}(27,\cdot)\)	6304.dd	392	yes	\(1\)	\(1\)	\(e\left(\frac{125}{392}\right)\)	\(e\left(\frac{271}{392}\right)\)	\(e\left(\frac{45}{196}\right)\)	\(e\left(\frac{125}{196}\right)\)	\(e\left(\frac{183}{392}\right)\)	\(e\left(\frac{53}{392}\right)\)	\(e\left(\frac{1}{98}\right)\)	\(e\left(\frac{195}{196}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{215}{392}\right)\)
\(\chi_{6304}(29,\cdot)\)	6304.da	392	yes	\(1\)	\(1\)	\(e\left(\frac{145}{392}\right)\)	\(e\left(\frac{283}{392}\right)\)	\(e\left(\frac{111}{196}\right)\)	\(e\left(\frac{145}{196}\right)\)	\(e\left(\frac{79}{392}\right)\)	\(e\left(\frac{85}{392}\right)\)	\(e\left(\frac{9}{98}\right)\)	\(e\left(\frac{69}{98}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{367}{392}\right)\)
\(\chi_{6304}(31,\cdot)\)	6304.cn	196	no	\(1\)	\(1\)	\(e\left(\frac{139}{196}\right)\)	\(e\left(\frac{5}{196}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{41}{98}\right)\)	\(e\left(\frac{71}{196}\right)\)	\(e\left(\frac{193}{196}\right)\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{75}{196}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{47}{196}\right)\)
\(\chi_{6304}(33,\cdot)\)	6304.bj	14	no	\(1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(1\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{6304}(35,\cdot)\)	6304.df	392	yes	\(1\)	\(1\)	\(e\left(\frac{251}{392}\right)\)	\(e\left(\frac{33}{392}\right)\)	\(e\left(\frac{59}{196}\right)\)	\(e\left(\frac{55}{196}\right)\)	\(e\left(\frac{57}{392}\right)\)	\(e\left(\frac{235}{392}\right)\)	\(e\left(\frac{71}{98}\right)\)	\(e\left(\frac{27}{196}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{369}{392}\right)\)
\(\chi_{6304}(37,\cdot)\)	6304.da	392	yes	\(1\)	\(1\)	\(e\left(\frac{267}{392}\right)\)	\(e\left(\frac{121}{392}\right)\)	\(e\left(\frac{53}{196}\right)\)	\(e\left(\frac{71}{196}\right)\)	\(e\left(\frac{13}{392}\right)\)	\(e\left(\frac{143}{392}\right)\)	\(e\left(\frac{97}{98}\right)\)	\(e\left(\frac{25}{98}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{373}{392}\right)\)
\(\chi_{6304}(39,\cdot)\)	6304.cr	196	no	\(-1\)	\(1\)	\(e\left(\frac{95}{196}\right)\)	\(e\left(\frac{155}{196}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{95}{98}\right)\)	\(e\left(\frac{45}{196}\right)\)	\(e\left(\frac{5}{196}\right)\)	\(e\left(\frac{27}{98}\right)\)	\(e\left(\frac{11}{98}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{183}{196}\right)\)
\(\chi_{6304}(41,\cdot)\)	6304.cp	196	no	\(1\)	\(1\)	\(e\left(\frac{163}{196}\right)\)	\(e\left(\frac{137}{196}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{65}{98}\right)\)	\(e\left(\frac{5}{196}\right)\)	\(e\left(\frac{55}{196}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{23}{98}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{53}{196}\right)\)
\(\chi_{6304}(43,\cdot)\)	6304.cz	392	yes	\(-1\)	\(1\)	\(e\left(\frac{159}{392}\right)\)	\(e\left(\frac{17}{392}\right)\)	\(e\left(\frac{167}{196}\right)\)	\(e\left(\frac{159}{196}\right)\)	\(e\left(\frac{65}{392}\right)\)	\(e\left(\frac{127}{392}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{101}{392}\right)\)
\(\chi_{6304}(45,\cdot)\)	6304.dc	392	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{392}\right)\)	\(e\left(\frac{261}{392}\right)\)	\(e\left(\frac{137}{196}\right)\)	\(e\left(\frac{43}{196}\right)\)	\(e\left(\frac{41}{392}\right)\)	\(e\left(\frac{255}{392}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{71}{196}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{317}{392}\right)\)
\(\chi_{6304}(47,\cdot)\)	6304.cf	98	no	\(-1\)	\(1\)	\(e\left(\frac{93}{98}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{65}{98}\right)\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{75}{98}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{41}{98}\right)\)	\(e\left(\frac{53}{98}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{30}{49}\right)\)
\(\chi_{6304}(49,\cdot)\)	6304.cl	98	no	\(1\)	\(1\)	\(e\left(\frac{15}{98}\right)\)	\(e\left(\frac{9}{98}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{69}{98}\right)\)	\(e\left(\frac{73}{98}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{43}{49}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{65}{98}\right)\)
\(\chi_{6304}(51,\cdot)\)	6304.db	392	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{392}\right)\)	\(e\left(\frac{103}{392}\right)\)	\(e\left(\frac{101}{196}\right)\)	\(e\left(\frac{41}{196}\right)\)	\(e\left(\frac{71}{392}\right)\)	\(e\left(\frac{193}{392}\right)\)	\(e\left(\frac{18}{49}\right)\)	\(e\left(\frac{31}{98}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{243}{392}\right)\)
\(\chi_{6304}(53,\cdot)\)	6304.da	392	yes	\(1\)	\(1\)	\(e\left(\frac{143}{392}\right)\)	\(e\left(\frac{125}{392}\right)\)	\(e\left(\frac{173}{196}\right)\)	\(e\left(\frac{143}{196}\right)\)	\(e\left(\frac{305}{392}\right)\)	\(e\left(\frac{219}{392}\right)\)	\(e\left(\frac{67}{98}\right)\)	\(e\left(\frac{89}{98}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{97}{392}\right)\)
\(\chi_{6304}(55,\cdot)\)	6304.cr	196	no	\(-1\)	\(1\)	\(e\left(\frac{141}{196}\right)\)	\(e\left(\frac{65}{196}\right)\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{139}{196}\right)\)	\(e\left(\frac{59}{196}\right)\)	\(e\left(\frac{5}{98}\right)\)	\(e\left(\frac{71}{98}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{121}{196}\right)\)
\(\chi_{6304}(57,\cdot)\)	6304.cs	196	no	\(-1\)	\(1\)	\(e\left(\frac{11}{98}\right)\)	\(e\left(\frac{18}{49}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{11}{49}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{47}{98}\right)\)	\(e\left(\frac{47}{98}\right)\)	\(e\left(\frac{149}{196}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{15}{98}\right)\)
\(\chi_{6304}(59,\cdot)\)	6304.db	392	yes	\(-1\)	\(1\)	\(e\left(\frac{103}{392}\right)\)	\(e\left(\frac{297}{392}\right)\)	\(e\left(\frac{139}{196}\right)\)	\(e\left(\frac{103}{196}\right)\)	\(e\left(\frac{121}{392}\right)\)	\(e\left(\frac{351}{392}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{97}{98}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{381}{392}\right)\)
\(\chi_{6304}(61,\cdot)\)	6304.da	392	yes	\(1\)	\(1\)	\(e\left(\frac{89}{392}\right)\)	\(e\left(\frac{171}{392}\right)\)	\(e\left(\frac{83}{196}\right)\)	\(e\left(\frac{89}{196}\right)\)	\(e\left(\frac{135}{392}\right)\)	\(e\left(\frac{309}{392}\right)\)	\(e\left(\frac{65}{98}\right)\)	\(e\left(\frac{41}{98}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{255}{392}\right)\)
\(\chi_{6304}(63,\cdot)\)	6304.ci	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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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.