LMFDB - Group of Dirichlet characters of modulus 1328

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1328)

pari: g = idealstar(,1328,2)

Character group

sage: G.order() pari: g.no
Order	=	656
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{164}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1328}(831,\cdot)$, $\chi_{1328}(997,\cdot)$, $\chi_{1328}(417,\cdot)$

First 32 of 656 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{1328}(1,\cdot)$	1328.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1328}(3,\cdot)$	1328.v	164	yes	$-1$	$1$	$e\left(\frac{159}{164}\right)$	$e\left(\frac{75}{164}\right)$	$e\left(\frac{1}{41}\right)$	$e\left(\frac{77}{82}\right)$	$e\left(\frac{53}{164}\right)$	$e\left(\frac{141}{164}\right)$	$e\left(\frac{35}{82}\right)$	$e\left(\frac{7}{41}\right)$	$e\left(\frac{3}{164}\right)$	$e\left(\frac{163}{164}\right)$
$\chi_{1328}(5,\cdot)$	1328.x	164	yes	$-1$	$1$	$e\left(\frac{75}{164}\right)$	$e\left(\frac{23}{164}\right)$	$e\left(\frac{11}{82}\right)$	$e\left(\frac{75}{82}\right)$	$e\left(\frac{25}{164}\right)$	$e\left(\frac{17}{164}\right)$	$e\left(\frac{49}{82}\right)$	$e\left(\frac{18}{41}\right)$	$e\left(\frac{37}{164}\right)$	$e\left(\frac{97}{164}\right)$
$\chi_{1328}(7,\cdot)$	1328.p	82	no	$-1$	$1$	$e\left(\frac{1}{41}\right)$	$e\left(\frac{11}{82}\right)$	$e\left(\frac{23}{82}\right)$	$e\left(\frac{2}{41}\right)$	$e\left(\frac{14}{41}\right)$	$e\left(\frac{1}{82}\right)$	$e\left(\frac{13}{82}\right)$	$e\left(\frac{19}{41}\right)$	$e\left(\frac{24}{41}\right)$	$e\left(\frac{25}{82}\right)$
$\chi_{1328}(9,\cdot)$	1328.s	82	no	$1$	$1$	$e\left(\frac{77}{82}\right)$	$e\left(\frac{75}{82}\right)$	$e\left(\frac{2}{41}\right)$	$e\left(\frac{36}{41}\right)$	$e\left(\frac{53}{82}\right)$	$e\left(\frac{59}{82}\right)$	$e\left(\frac{35}{41}\right)$	$e\left(\frac{14}{41}\right)$	$e\left(\frac{3}{82}\right)$	$e\left(\frac{81}{82}\right)$
$\chi_{1328}(11,\cdot)$	1328.v	164	yes	$-1$	$1$	$e\left(\frac{53}{164}\right)$	$e\left(\frac{25}{164}\right)$	$e\left(\frac{14}{41}\right)$	$e\left(\frac{53}{82}\right)$	$e\left(\frac{127}{164}\right)$	$e\left(\frac{47}{164}\right)$	$e\left(\frac{39}{82}\right)$	$e\left(\frac{16}{41}\right)$	$e\left(\frac{1}{164}\right)$	$e\left(\frac{109}{164}\right)$
$\chi_{1328}(13,\cdot)$	1328.x	164	yes	$-1$	$1$	$e\left(\frac{141}{164}\right)$	$e\left(\frac{17}{164}\right)$	$e\left(\frac{1}{82}\right)$	$e\left(\frac{59}{82}\right)$	$e\left(\frac{47}{164}\right)$	$e\left(\frac{91}{164}\right)$	$e\left(\frac{79}{82}\right)$	$e\left(\frac{24}{41}\right)$	$e\left(\frac{63}{164}\right)$	$e\left(\frac{143}{164}\right)$
$\chi_{1328}(15,\cdot)$	1328.t	82	no	$1$	$1$	$e\left(\frac{35}{82}\right)$	$e\left(\frac{49}{82}\right)$	$e\left(\frac{13}{82}\right)$	$e\left(\frac{35}{41}\right)$	$e\left(\frac{39}{82}\right)$	$e\left(\frac{79}{82}\right)$	$e\left(\frac{1}{41}\right)$	$e\left(\frac{25}{41}\right)$	$e\left(\frac{10}{41}\right)$	$e\left(\frac{24}{41}\right)$
$\chi_{1328}(17,\cdot)$	1328.m	41	no	$1$	$1$	$e\left(\frac{7}{41}\right)$	$e\left(\frac{18}{41}\right)$	$e\left(\frac{19}{41}\right)$	$e\left(\frac{14}{41}\right)$	$e\left(\frac{16}{41}\right)$	$e\left(\frac{24}{41}\right)$	$e\left(\frac{25}{41}\right)$	$e\left(\frac{10}{41}\right)$	$e\left(\frac{4}{41}\right)$	$e\left(\frac{26}{41}\right)$
$\chi_{1328}(19,\cdot)$	1328.u	164	yes	$1$	$1$	$e\left(\frac{3}{164}\right)$	$e\left(\frac{37}{164}\right)$	$e\left(\frac{24}{41}\right)$	$e\left(\frac{3}{82}\right)$	$e\left(\frac{1}{164}\right)$	$e\left(\frac{63}{164}\right)$	$e\left(\frac{10}{41}\right)$	$e\left(\frac{4}{41}\right)$	$e\left(\frac{113}{164}\right)$	$e\left(\frac{99}{164}\right)$
$\chi_{1328}(21,\cdot)$	1328.w	164	yes	$1$	$1$	$e\left(\frac{163}{164}\right)$	$e\left(\frac{97}{164}\right)$	$e\left(\frac{25}{82}\right)$	$e\left(\frac{81}{82}\right)$	$e\left(\frac{109}{164}\right)$	$e\left(\frac{143}{164}\right)$	$e\left(\frac{24}{41}\right)$	$e\left(\frac{26}{41}\right)$	$e\left(\frac{99}{164}\right)$	$e\left(\frac{49}{164}\right)$
$\chi_{1328}(23,\cdot)$	1328.p	82	no	$-1$	$1$	$e\left(\frac{28}{41}\right)$	$e\left(\frac{21}{82}\right)$	$e\left(\frac{29}{82}\right)$	$e\left(\frac{15}{41}\right)$	$e\left(\frac{23}{41}\right)$	$e\left(\frac{69}{82}\right)$	$e\left(\frac{77}{82}\right)$	$e\left(\frac{40}{41}\right)$	$e\left(\frac{16}{41}\right)$	$e\left(\frac{3}{82}\right)$
$\chi_{1328}(25,\cdot)$	1328.s	82	no	$1$	$1$	$e\left(\frac{75}{82}\right)$	$e\left(\frac{23}{82}\right)$	$e\left(\frac{11}{41}\right)$	$e\left(\frac{34}{41}\right)$	$e\left(\frac{25}{82}\right)$	$e\left(\frac{17}{82}\right)$	$e\left(\frac{8}{41}\right)$	$e\left(\frac{36}{41}\right)$	$e\left(\frac{37}{82}\right)$	$e\left(\frac{15}{82}\right)$
$\chi_{1328}(27,\cdot)$	1328.v	164	yes	$-1$	$1$	$e\left(\frac{149}{164}\right)$	$e\left(\frac{61}{164}\right)$	$e\left(\frac{3}{41}\right)$	$e\left(\frac{67}{82}\right)$	$e\left(\frac{159}{164}\right)$	$e\left(\frac{95}{164}\right)$	$e\left(\frac{23}{82}\right)$	$e\left(\frac{21}{41}\right)$	$e\left(\frac{9}{164}\right)$	$e\left(\frac{161}{164}\right)$
$\chi_{1328}(29,\cdot)$	1328.w	164	yes	$1$	$1$	$e\left(\frac{129}{164}\right)$	$e\left(\frac{115}{164}\right)$	$e\left(\frac{55}{82}\right)$	$e\left(\frac{47}{82}\right)$	$e\left(\frac{43}{164}\right)$	$e\left(\frac{85}{164}\right)$	$e\left(\frac{20}{41}\right)$	$e\left(\frac{8}{41}\right)$	$e\left(\frac{21}{164}\right)$	$e\left(\frac{75}{164}\right)$
$\chi_{1328}(31,\cdot)$	1328.r	82	no	$-1$	$1$	$e\left(\frac{71}{82}\right)$	$e\left(\frac{21}{41}\right)$	$e\left(\frac{17}{82}\right)$	$e\left(\frac{30}{41}\right)$	$e\left(\frac{51}{82}\right)$	$e\left(\frac{28}{41}\right)$	$e\left(\frac{31}{82}\right)$	$e\left(\frac{39}{41}\right)$	$e\left(\frac{23}{82}\right)$	$e\left(\frac{3}{41}\right)$
$\chi_{1328}(33,\cdot)$	1328.m	41	no	$1$	$1$	$e\left(\frac{12}{41}\right)$	$e\left(\frac{25}{41}\right)$	$e\left(\frac{15}{41}\right)$	$e\left(\frac{24}{41}\right)$	$e\left(\frac{4}{41}\right)$	$e\left(\frac{6}{41}\right)$	$e\left(\frac{37}{41}\right)$	$e\left(\frac{23}{41}\right)$	$e\left(\frac{1}{41}\right)$	$e\left(\frac{27}{41}\right)$
$\chi_{1328}(35,\cdot)$	1328.u	164	yes	$1$	$1$	$e\left(\frac{79}{164}\right)$	$e\left(\frac{45}{164}\right)$	$e\left(\frac{17}{41}\right)$	$e\left(\frac{79}{82}\right)$	$e\left(\frac{81}{164}\right)$	$e\left(\frac{19}{164}\right)$	$e\left(\frac{31}{41}\right)$	$e\left(\frac{37}{41}\right)$	$e\left(\frac{133}{164}\right)$	$e\left(\frac{147}{164}\right)$
$\chi_{1328}(37,\cdot)$	1328.w	164	yes	$1$	$1$	$e\left(\frac{51}{164}\right)$	$e\left(\frac{137}{164}\right)$	$e\left(\frac{37}{82}\right)$	$e\left(\frac{51}{82}\right)$	$e\left(\frac{17}{164}\right)$	$e\left(\frac{87}{164}\right)$	$e\left(\frac{6}{41}\right)$	$e\left(\frac{27}{41}\right)$	$e\left(\frac{35}{164}\right)$	$e\left(\frac{125}{164}\right)$
$\chi_{1328}(39,\cdot)$	1328.n	82	no	$1$	$1$	$e\left(\frac{34}{41}\right)$	$e\left(\frac{23}{41}\right)$	$e\left(\frac{3}{82}\right)$	$e\left(\frac{27}{41}\right)$	$e\left(\frac{25}{41}\right)$	$e\left(\frac{17}{41}\right)$	$e\left(\frac{16}{41}\right)$	$e\left(\frac{31}{41}\right)$	$e\left(\frac{33}{82}\right)$	$e\left(\frac{71}{82}\right)$
$\chi_{1328}(41,\cdot)$	1328.s	82	no	$1$	$1$	$e\left(\frac{51}{82}\right)$	$e\left(\frac{55}{82}\right)$	$e\left(\frac{37}{41}\right)$	$e\left(\frac{10}{41}\right)$	$e\left(\frac{17}{82}\right)$	$e\left(\frac{5}{82}\right)$	$e\left(\frac{12}{41}\right)$	$e\left(\frac{13}{41}\right)$	$e\left(\frac{35}{82}\right)$	$e\left(\frac{43}{82}\right)$
$\chi_{1328}(43,\cdot)$	1328.u	164	yes	$1$	$1$	$e\left(\frac{97}{164}\right)$	$e\left(\frac{103}{164}\right)$	$e\left(\frac{38}{41}\right)$	$e\left(\frac{15}{82}\right)$	$e\left(\frac{87}{164}\right)$	$e\left(\frac{69}{164}\right)$	$e\left(\frac{9}{41}\right)$	$e\left(\frac{20}{41}\right)$	$e\left(\frac{155}{164}\right)$	$e\left(\frac{85}{164}\right)$
$\chi_{1328}(45,\cdot)$	1328.x	164	yes	$-1$	$1$	$e\left(\frac{65}{164}\right)$	$e\left(\frac{9}{164}\right)$	$e\left(\frac{15}{82}\right)$	$e\left(\frac{65}{82}\right)$	$e\left(\frac{131}{164}\right)$	$e\left(\frac{135}{164}\right)$	$e\left(\frac{37}{82}\right)$	$e\left(\frac{32}{41}\right)$	$e\left(\frac{43}{164}\right)$	$e\left(\frac{95}{164}\right)$
$\chi_{1328}(47,\cdot)$	1328.t	82	no	$1$	$1$	$e\left(\frac{57}{82}\right)$	$e\left(\frac{47}{82}\right)$	$e\left(\frac{61}{82}\right)$	$e\left(\frac{16}{41}\right)$	$e\left(\frac{19}{82}\right)$	$e\left(\frac{49}{82}\right)$	$e\left(\frac{11}{41}\right)$	$e\left(\frac{29}{41}\right)$	$e\left(\frac{28}{41}\right)$	$e\left(\frac{18}{41}\right)$
$\chi_{1328}(49,\cdot)$	1328.m	41	no	$1$	$1$	$e\left(\frac{2}{41}\right)$	$e\left(\frac{11}{41}\right)$	$e\left(\frac{23}{41}\right)$	$e\left(\frac{4}{41}\right)$	$e\left(\frac{28}{41}\right)$	$e\left(\frac{1}{41}\right)$	$e\left(\frac{13}{41}\right)$	$e\left(\frac{38}{41}\right)$	$e\left(\frac{7}{41}\right)$	$e\left(\frac{25}{41}\right)$
$\chi_{1328}(51,\cdot)$	1328.v	164	yes	$-1$	$1$	$e\left(\frac{23}{164}\right)$	$e\left(\frac{147}{164}\right)$	$e\left(\frac{20}{41}\right)$	$e\left(\frac{23}{82}\right)$	$e\left(\frac{117}{164}\right)$	$e\left(\frac{73}{164}\right)$	$e\left(\frac{3}{82}\right)$	$e\left(\frac{17}{41}\right)$	$e\left(\frac{19}{164}\right)$	$e\left(\frac{103}{164}\right)$
$\chi_{1328}(53,\cdot)$	1328.x	164	yes	$-1$	$1$	$e\left(\frac{91}{164}\right)$	$e\left(\frac{111}{164}\right)$	$e\left(\frac{21}{82}\right)$	$e\left(\frac{9}{82}\right)$	$e\left(\frac{85}{164}\right)$	$e\left(\frac{25}{164}\right)$	$e\left(\frac{19}{82}\right)$	$e\left(\frac{12}{41}\right)$	$e\left(\frac{93}{164}\right)$	$e\left(\frac{133}{164}\right)$
$\chi_{1328}(55,\cdot)$	1328.n	82	no	$1$	$1$	$e\left(\frac{32}{41}\right)$	$e\left(\frac{12}{41}\right)$	$e\left(\frac{39}{82}\right)$	$e\left(\frac{23}{41}\right)$	$e\left(\frac{38}{41}\right)$	$e\left(\frac{16}{41}\right)$	$e\left(\frac{3}{41}\right)$	$e\left(\frac{34}{41}\right)$	$e\left(\frac{19}{82}\right)$	$e\left(\frac{21}{82}\right)$
$\chi_{1328}(57,\cdot)$	1328.q	82	no	$-1$	$1$	$e\left(\frac{81}{82}\right)$	$e\left(\frac{28}{41}\right)$	$e\left(\frac{25}{41}\right)$	$e\left(\frac{40}{41}\right)$	$e\left(\frac{27}{82}\right)$	$e\left(\frac{10}{41}\right)$	$e\left(\frac{55}{82}\right)$	$e\left(\frac{11}{41}\right)$	$e\left(\frac{29}{41}\right)$	$e\left(\frac{49}{82}\right)$
$\chi_{1328}(59,\cdot)$	1328.v	164	yes	$-1$	$1$	$e\left(\frac{17}{164}\right)$	$e\left(\frac{73}{164}\right)$	$e\left(\frac{13}{41}\right)$	$e\left(\frac{17}{82}\right)$	$e\left(\frac{115}{164}\right)$	$e\left(\frac{111}{164}\right)$	$e\left(\frac{45}{82}\right)$	$e\left(\frac{9}{41}\right)$	$e\left(\frac{121}{164}\right)$	$e\left(\frac{69}{164}\right)$
$\chi_{1328}(61,\cdot)$	1328.w	164	yes	$1$	$1$	$e\left(\frac{33}{164}\right)$	$e\left(\frac{79}{164}\right)$	$e\left(\frac{77}{82}\right)$	$e\left(\frac{33}{82}\right)$	$e\left(\frac{11}{164}\right)$	$e\left(\frac{37}{164}\right)$	$e\left(\frac{28}{41}\right)$	$e\left(\frac{3}{41}\right)$	$e\left(\frac{13}{164}\right)$	$e\left(\frac{23}{164}\right)$
$\chi_{1328}(63,\cdot)$	1328.r	82	no	$-1$	$1$	$e\left(\frac{79}{82}\right)$	$e\left(\frac{2}{41}\right)$	$e\left(\frac{27}{82}\right)$	$e\left(\frac{38}{41}\right)$	$e\left(\frac{81}{82}\right)$	$e\left(\frac{30}{41}\right)$	$e\left(\frac{1}{82}\right)$	$e\left(\frac{33}{41}\right)$	$e\left(\frac{51}{82}\right)$	$e\left(\frac{12}{41}\right)$

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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 $\F_{q}$

Modulus	$1328$
Structure	\(C_{2}\times C_{2}\times C_{164}\)
Order	$656$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{1328}(1,\cdot)\)	1328.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1328}(3,\cdot)\)	1328.v	164	yes	\(-1\)	\(1\)	\(e\left(\frac{159}{164}\right)\)	\(e\left(\frac{75}{164}\right)\)	\(e\left(\frac{1}{41}\right)\)	\(e\left(\frac{77}{82}\right)\)	\(e\left(\frac{53}{164}\right)\)	\(e\left(\frac{141}{164}\right)\)	\(e\left(\frac{35}{82}\right)\)	\(e\left(\frac{7}{41}\right)\)	\(e\left(\frac{3}{164}\right)\)	\(e\left(\frac{163}{164}\right)\)
\(\chi_{1328}(5,\cdot)\)	1328.x	164	yes	\(-1\)	\(1\)	\(e\left(\frac{75}{164}\right)\)	\(e\left(\frac{23}{164}\right)\)	\(e\left(\frac{11}{82}\right)\)	\(e\left(\frac{75}{82}\right)\)	\(e\left(\frac{25}{164}\right)\)	\(e\left(\frac{17}{164}\right)\)	\(e\left(\frac{49}{82}\right)\)	\(e\left(\frac{18}{41}\right)\)	\(e\left(\frac{37}{164}\right)\)	\(e\left(\frac{97}{164}\right)\)
\(\chi_{1328}(7,\cdot)\)	1328.p	82	no	\(-1\)	\(1\)	\(e\left(\frac{1}{41}\right)\)	\(e\left(\frac{11}{82}\right)\)	\(e\left(\frac{23}{82}\right)\)	\(e\left(\frac{2}{41}\right)\)	\(e\left(\frac{14}{41}\right)\)	\(e\left(\frac{1}{82}\right)\)	\(e\left(\frac{13}{82}\right)\)	\(e\left(\frac{19}{41}\right)\)	\(e\left(\frac{24}{41}\right)\)	\(e\left(\frac{25}{82}\right)\)
\(\chi_{1328}(9,\cdot)\)	1328.s	82	no	\(1\)	\(1\)	\(e\left(\frac{77}{82}\right)\)	\(e\left(\frac{75}{82}\right)\)	\(e\left(\frac{2}{41}\right)\)	\(e\left(\frac{36}{41}\right)\)	\(e\left(\frac{53}{82}\right)\)	\(e\left(\frac{59}{82}\right)\)	\(e\left(\frac{35}{41}\right)\)	\(e\left(\frac{14}{41}\right)\)	\(e\left(\frac{3}{82}\right)\)	\(e\left(\frac{81}{82}\right)\)
\(\chi_{1328}(11,\cdot)\)	1328.v	164	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{164}\right)\)	\(e\left(\frac{25}{164}\right)\)	\(e\left(\frac{14}{41}\right)\)	\(e\left(\frac{53}{82}\right)\)	\(e\left(\frac{127}{164}\right)\)	\(e\left(\frac{47}{164}\right)\)	\(e\left(\frac{39}{82}\right)\)	\(e\left(\frac{16}{41}\right)\)	\(e\left(\frac{1}{164}\right)\)	\(e\left(\frac{109}{164}\right)\)
\(\chi_{1328}(13,\cdot)\)	1328.x	164	yes	\(-1\)	\(1\)	\(e\left(\frac{141}{164}\right)\)	\(e\left(\frac{17}{164}\right)\)	\(e\left(\frac{1}{82}\right)\)	\(e\left(\frac{59}{82}\right)\)	\(e\left(\frac{47}{164}\right)\)	\(e\left(\frac{91}{164}\right)\)	\(e\left(\frac{79}{82}\right)\)	\(e\left(\frac{24}{41}\right)\)	\(e\left(\frac{63}{164}\right)\)	\(e\left(\frac{143}{164}\right)\)
\(\chi_{1328}(15,\cdot)\)	1328.t	82	no	\(1\)	\(1\)	\(e\left(\frac{35}{82}\right)\)	\(e\left(\frac{49}{82}\right)\)	\(e\left(\frac{13}{82}\right)\)	\(e\left(\frac{35}{41}\right)\)	\(e\left(\frac{39}{82}\right)\)	\(e\left(\frac{79}{82}\right)\)	\(e\left(\frac{1}{41}\right)\)	\(e\left(\frac{25}{41}\right)\)	\(e\left(\frac{10}{41}\right)\)	\(e\left(\frac{24}{41}\right)\)
\(\chi_{1328}(17,\cdot)\)	1328.m	41	no	\(1\)	\(1\)	\(e\left(\frac{7}{41}\right)\)	\(e\left(\frac{18}{41}\right)\)	\(e\left(\frac{19}{41}\right)\)	\(e\left(\frac{14}{41}\right)\)	\(e\left(\frac{16}{41}\right)\)	\(e\left(\frac{24}{41}\right)\)	\(e\left(\frac{25}{41}\right)\)	\(e\left(\frac{10}{41}\right)\)	\(e\left(\frac{4}{41}\right)\)	\(e\left(\frac{26}{41}\right)\)
\(\chi_{1328}(19,\cdot)\)	1328.u	164	yes	\(1\)	\(1\)	\(e\left(\frac{3}{164}\right)\)	\(e\left(\frac{37}{164}\right)\)	\(e\left(\frac{24}{41}\right)\)	\(e\left(\frac{3}{82}\right)\)	\(e\left(\frac{1}{164}\right)\)	\(e\left(\frac{63}{164}\right)\)	\(e\left(\frac{10}{41}\right)\)	\(e\left(\frac{4}{41}\right)\)	\(e\left(\frac{113}{164}\right)\)	\(e\left(\frac{99}{164}\right)\)
\(\chi_{1328}(21,\cdot)\)	1328.w	164	yes	\(1\)	\(1\)	\(e\left(\frac{163}{164}\right)\)	\(e\left(\frac{97}{164}\right)\)	\(e\left(\frac{25}{82}\right)\)	\(e\left(\frac{81}{82}\right)\)	\(e\left(\frac{109}{164}\right)\)	\(e\left(\frac{143}{164}\right)\)	\(e\left(\frac{24}{41}\right)\)	\(e\left(\frac{26}{41}\right)\)	\(e\left(\frac{99}{164}\right)\)	\(e\left(\frac{49}{164}\right)\)
\(\chi_{1328}(23,\cdot)\)	1328.p	82	no	\(-1\)	\(1\)	\(e\left(\frac{28}{41}\right)\)	\(e\left(\frac{21}{82}\right)\)	\(e\left(\frac{29}{82}\right)\)	\(e\left(\frac{15}{41}\right)\)	\(e\left(\frac{23}{41}\right)\)	\(e\left(\frac{69}{82}\right)\)	\(e\left(\frac{77}{82}\right)\)	\(e\left(\frac{40}{41}\right)\)	\(e\left(\frac{16}{41}\right)\)	\(e\left(\frac{3}{82}\right)\)
\(\chi_{1328}(25,\cdot)\)	1328.s	82	no	\(1\)	\(1\)	\(e\left(\frac{75}{82}\right)\)	\(e\left(\frac{23}{82}\right)\)	\(e\left(\frac{11}{41}\right)\)	\(e\left(\frac{34}{41}\right)\)	\(e\left(\frac{25}{82}\right)\)	\(e\left(\frac{17}{82}\right)\)	\(e\left(\frac{8}{41}\right)\)	\(e\left(\frac{36}{41}\right)\)	\(e\left(\frac{37}{82}\right)\)	\(e\left(\frac{15}{82}\right)\)
\(\chi_{1328}(27,\cdot)\)	1328.v	164	yes	\(-1\)	\(1\)	\(e\left(\frac{149}{164}\right)\)	\(e\left(\frac{61}{164}\right)\)	\(e\left(\frac{3}{41}\right)\)	\(e\left(\frac{67}{82}\right)\)	\(e\left(\frac{159}{164}\right)\)	\(e\left(\frac{95}{164}\right)\)	\(e\left(\frac{23}{82}\right)\)	\(e\left(\frac{21}{41}\right)\)	\(e\left(\frac{9}{164}\right)\)	\(e\left(\frac{161}{164}\right)\)
\(\chi_{1328}(29,\cdot)\)	1328.w	164	yes	\(1\)	\(1\)	\(e\left(\frac{129}{164}\right)\)	\(e\left(\frac{115}{164}\right)\)	\(e\left(\frac{55}{82}\right)\)	\(e\left(\frac{47}{82}\right)\)	\(e\left(\frac{43}{164}\right)\)	\(e\left(\frac{85}{164}\right)\)	\(e\left(\frac{20}{41}\right)\)	\(e\left(\frac{8}{41}\right)\)	\(e\left(\frac{21}{164}\right)\)	\(e\left(\frac{75}{164}\right)\)
\(\chi_{1328}(31,\cdot)\)	1328.r	82	no	\(-1\)	\(1\)	\(e\left(\frac{71}{82}\right)\)	\(e\left(\frac{21}{41}\right)\)	\(e\left(\frac{17}{82}\right)\)	\(e\left(\frac{30}{41}\right)\)	\(e\left(\frac{51}{82}\right)\)	\(e\left(\frac{28}{41}\right)\)	\(e\left(\frac{31}{82}\right)\)	\(e\left(\frac{39}{41}\right)\)	\(e\left(\frac{23}{82}\right)\)	\(e\left(\frac{3}{41}\right)\)
\(\chi_{1328}(33,\cdot)\)	1328.m	41	no	\(1\)	\(1\)	\(e\left(\frac{12}{41}\right)\)	\(e\left(\frac{25}{41}\right)\)	\(e\left(\frac{15}{41}\right)\)	\(e\left(\frac{24}{41}\right)\)	\(e\left(\frac{4}{41}\right)\)	\(e\left(\frac{6}{41}\right)\)	\(e\left(\frac{37}{41}\right)\)	\(e\left(\frac{23}{41}\right)\)	\(e\left(\frac{1}{41}\right)\)	\(e\left(\frac{27}{41}\right)\)
\(\chi_{1328}(35,\cdot)\)	1328.u	164	yes	\(1\)	\(1\)	\(e\left(\frac{79}{164}\right)\)	\(e\left(\frac{45}{164}\right)\)	\(e\left(\frac{17}{41}\right)\)	\(e\left(\frac{79}{82}\right)\)	\(e\left(\frac{81}{164}\right)\)	\(e\left(\frac{19}{164}\right)\)	\(e\left(\frac{31}{41}\right)\)	\(e\left(\frac{37}{41}\right)\)	\(e\left(\frac{133}{164}\right)\)	\(e\left(\frac{147}{164}\right)\)
\(\chi_{1328}(37,\cdot)\)	1328.w	164	yes	\(1\)	\(1\)	\(e\left(\frac{51}{164}\right)\)	\(e\left(\frac{137}{164}\right)\)	\(e\left(\frac{37}{82}\right)\)	\(e\left(\frac{51}{82}\right)\)	\(e\left(\frac{17}{164}\right)\)	\(e\left(\frac{87}{164}\right)\)	\(e\left(\frac{6}{41}\right)\)	\(e\left(\frac{27}{41}\right)\)	\(e\left(\frac{35}{164}\right)\)	\(e\left(\frac{125}{164}\right)\)
\(\chi_{1328}(39,\cdot)\)	1328.n	82	no	\(1\)	\(1\)	\(e\left(\frac{34}{41}\right)\)	\(e\left(\frac{23}{41}\right)\)	\(e\left(\frac{3}{82}\right)\)	\(e\left(\frac{27}{41}\right)\)	\(e\left(\frac{25}{41}\right)\)	\(e\left(\frac{17}{41}\right)\)	\(e\left(\frac{16}{41}\right)\)	\(e\left(\frac{31}{41}\right)\)	\(e\left(\frac{33}{82}\right)\)	\(e\left(\frac{71}{82}\right)\)
\(\chi_{1328}(41,\cdot)\)	1328.s	82	no	\(1\)	\(1\)	\(e\left(\frac{51}{82}\right)\)	\(e\left(\frac{55}{82}\right)\)	\(e\left(\frac{37}{41}\right)\)	\(e\left(\frac{10}{41}\right)\)	\(e\left(\frac{17}{82}\right)\)	\(e\left(\frac{5}{82}\right)\)	\(e\left(\frac{12}{41}\right)\)	\(e\left(\frac{13}{41}\right)\)	\(e\left(\frac{35}{82}\right)\)	\(e\left(\frac{43}{82}\right)\)
\(\chi_{1328}(43,\cdot)\)	1328.u	164	yes	\(1\)	\(1\)	\(e\left(\frac{97}{164}\right)\)	\(e\left(\frac{103}{164}\right)\)	\(e\left(\frac{38}{41}\right)\)	\(e\left(\frac{15}{82}\right)\)	\(e\left(\frac{87}{164}\right)\)	\(e\left(\frac{69}{164}\right)\)	\(e\left(\frac{9}{41}\right)\)	\(e\left(\frac{20}{41}\right)\)	\(e\left(\frac{155}{164}\right)\)	\(e\left(\frac{85}{164}\right)\)
\(\chi_{1328}(45,\cdot)\)	1328.x	164	yes	\(-1\)	\(1\)	\(e\left(\frac{65}{164}\right)\)	\(e\left(\frac{9}{164}\right)\)	\(e\left(\frac{15}{82}\right)\)	\(e\left(\frac{65}{82}\right)\)	\(e\left(\frac{131}{164}\right)\)	\(e\left(\frac{135}{164}\right)\)	\(e\left(\frac{37}{82}\right)\)	\(e\left(\frac{32}{41}\right)\)	\(e\left(\frac{43}{164}\right)\)	\(e\left(\frac{95}{164}\right)\)
\(\chi_{1328}(47,\cdot)\)	1328.t	82	no	\(1\)	\(1\)	\(e\left(\frac{57}{82}\right)\)	\(e\left(\frac{47}{82}\right)\)	\(e\left(\frac{61}{82}\right)\)	\(e\left(\frac{16}{41}\right)\)	\(e\left(\frac{19}{82}\right)\)	\(e\left(\frac{49}{82}\right)\)	\(e\left(\frac{11}{41}\right)\)	\(e\left(\frac{29}{41}\right)\)	\(e\left(\frac{28}{41}\right)\)	\(e\left(\frac{18}{41}\right)\)
\(\chi_{1328}(49,\cdot)\)	1328.m	41	no	\(1\)	\(1\)	\(e\left(\frac{2}{41}\right)\)	\(e\left(\frac{11}{41}\right)\)	\(e\left(\frac{23}{41}\right)\)	\(e\left(\frac{4}{41}\right)\)	\(e\left(\frac{28}{41}\right)\)	\(e\left(\frac{1}{41}\right)\)	\(e\left(\frac{13}{41}\right)\)	\(e\left(\frac{38}{41}\right)\)	\(e\left(\frac{7}{41}\right)\)	\(e\left(\frac{25}{41}\right)\)
\(\chi_{1328}(51,\cdot)\)	1328.v	164	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{164}\right)\)	\(e\left(\frac{147}{164}\right)\)	\(e\left(\frac{20}{41}\right)\)	\(e\left(\frac{23}{82}\right)\)	\(e\left(\frac{117}{164}\right)\)	\(e\left(\frac{73}{164}\right)\)	\(e\left(\frac{3}{82}\right)\)	\(e\left(\frac{17}{41}\right)\)	\(e\left(\frac{19}{164}\right)\)	\(e\left(\frac{103}{164}\right)\)
\(\chi_{1328}(53,\cdot)\)	1328.x	164	yes	\(-1\)	\(1\)	\(e\left(\frac{91}{164}\right)\)	\(e\left(\frac{111}{164}\right)\)	\(e\left(\frac{21}{82}\right)\)	\(e\left(\frac{9}{82}\right)\)	\(e\left(\frac{85}{164}\right)\)	\(e\left(\frac{25}{164}\right)\)	\(e\left(\frac{19}{82}\right)\)	\(e\left(\frac{12}{41}\right)\)	\(e\left(\frac{93}{164}\right)\)	\(e\left(\frac{133}{164}\right)\)
\(\chi_{1328}(55,\cdot)\)	1328.n	82	no	\(1\)	\(1\)	\(e\left(\frac{32}{41}\right)\)	\(e\left(\frac{12}{41}\right)\)	\(e\left(\frac{39}{82}\right)\)	\(e\left(\frac{23}{41}\right)\)	\(e\left(\frac{38}{41}\right)\)	\(e\left(\frac{16}{41}\right)\)	\(e\left(\frac{3}{41}\right)\)	\(e\left(\frac{34}{41}\right)\)	\(e\left(\frac{19}{82}\right)\)	\(e\left(\frac{21}{82}\right)\)
\(\chi_{1328}(57,\cdot)\)	1328.q	82	no	\(-1\)	\(1\)	\(e\left(\frac{81}{82}\right)\)	\(e\left(\frac{28}{41}\right)\)	\(e\left(\frac{25}{41}\right)\)	\(e\left(\frac{40}{41}\right)\)	\(e\left(\frac{27}{82}\right)\)	\(e\left(\frac{10}{41}\right)\)	\(e\left(\frac{55}{82}\right)\)	\(e\left(\frac{11}{41}\right)\)	\(e\left(\frac{29}{41}\right)\)	\(e\left(\frac{49}{82}\right)\)
\(\chi_{1328}(59,\cdot)\)	1328.v	164	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{164}\right)\)	\(e\left(\frac{73}{164}\right)\)	\(e\left(\frac{13}{41}\right)\)	\(e\left(\frac{17}{82}\right)\)	\(e\left(\frac{115}{164}\right)\)	\(e\left(\frac{111}{164}\right)\)	\(e\left(\frac{45}{82}\right)\)	\(e\left(\frac{9}{41}\right)\)	\(e\left(\frac{121}{164}\right)\)	\(e\left(\frac{69}{164}\right)\)
\(\chi_{1328}(61,\cdot)\)	1328.w	164	yes	\(1\)	\(1\)	\(e\left(\frac{33}{164}\right)\)	\(e\left(\frac{79}{164}\right)\)	\(e\left(\frac{77}{82}\right)\)	\(e\left(\frac{33}{82}\right)\)	\(e\left(\frac{11}{164}\right)\)	\(e\left(\frac{37}{164}\right)\)	\(e\left(\frac{28}{41}\right)\)	\(e\left(\frac{3}{41}\right)\)	\(e\left(\frac{13}{164}\right)\)	\(e\left(\frac{23}{164}\right)\)
\(\chi_{1328}(63,\cdot)\)	1328.r	82	no	\(-1\)	\(1\)	\(e\left(\frac{79}{82}\right)\)	\(e\left(\frac{2}{41}\right)\)	\(e\left(\frac{27}{82}\right)\)	\(e\left(\frac{38}{41}\right)\)	\(e\left(\frac{81}{82}\right)\)	\(e\left(\frac{30}{41}\right)\)	\(e\left(\frac{1}{82}\right)\)	\(e\left(\frac{33}{41}\right)\)	\(e\left(\frac{51}{82}\right)\)	\(e\left(\frac{12}{41}\right)\)

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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.