LMFDB - Group of Dirichlet characters of modulus 8450

sage:H = DirichletGroup(8450)

pari:g = idealstar(,8450,2)

Character group

sage:G.order() pari:g.no
Order	=	3120
sage:H.invariants() pari:g.cyc
Structure	=	$C_{4}\times C_{780}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{8450}(677,\cdot)$, $\chi_{8450}(3551,\cdot)$

First 32 of 3120 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	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{8450}(1,\cdot)$	8450.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8450}(3,\cdot)$	8450.cy	780	no	$-1$	$1$	$e\left(\frac{11}{780}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{11}{390}\right)$	$e\left(\frac{92}{195}\right)$	$e\left(\frac{469}{780}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{53}{65}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{11}{260}\right)$	$e\left(\frac{193}{390}\right)$
$\chi_{8450}(7,\cdot)$	8450.ck	156	no	$1$	$1$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{73}{78}\right)$
$\chi_{8450}(9,\cdot)$	8450.cu	390	no	$1$	$1$	$e\left(\frac{11}{390}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{11}{195}\right)$	$e\left(\frac{184}{195}\right)$	$e\left(\frac{79}{390}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{41}{65}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{130}\right)$	$e\left(\frac{193}{195}\right)$
$\chi_{8450}(11,\cdot)$	8450.cw	780	no	$-1$	$1$	$e\left(\frac{92}{195}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{184}{195}\right)$	$e\left(\frac{629}{780}\right)$	$e\left(\frac{311}{390}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{31}{260}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{27}{65}\right)$	$e\left(\frac{2}{195}\right)$
$\chi_{8450}(17,\cdot)$	8450.cz	780	no	$-1$	$1$	$e\left(\frac{469}{780}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{79}{390}\right)$	$e\left(\frac{311}{390}\right)$	$e\left(\frac{71}{780}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{129}{130}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{209}{260}\right)$	$e\left(\frac{287}{390}\right)$
$\chi_{8450}(19,\cdot)$	8450.bt	60	no	$-1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{8450}(21,\cdot)$	8450.cs	260	no	$-1$	$1$	$e\left(\frac{53}{65}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{41}{65}\right)$	$e\left(\frac{31}{260}\right)$	$e\left(\frac{129}{130}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{67}{260}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{29}{65}\right)$	$e\left(\frac{28}{65}\right)$
$\chi_{8450}(23,\cdot)$	8450.bv	60	no	$-1$	$1$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{8450}(27,\cdot)$	8450.cq	260	no	$-1$	$1$	$e\left(\frac{11}{260}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{11}{130}\right)$	$e\left(\frac{27}{65}\right)$	$e\left(\frac{209}{260}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{29}{65}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{33}{260}\right)$	$e\left(\frac{63}{130}\right)$
$\chi_{8450}(29,\cdot)$	8450.cu	390	no	$1$	$1$	$e\left(\frac{193}{390}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{193}{195}\right)$	$e\left(\frac{2}{195}\right)$	$e\left(\frac{287}{390}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{28}{65}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{63}{130}\right)$	$e\left(\frac{89}{195}\right)$
$\chi_{8450}(31,\cdot)$	8450.cs	260	no	$-1$	$1$	$e\left(\frac{32}{65}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{64}{65}\right)$	$e\left(\frac{69}{260}\right)$	$e\left(\frac{111}{130}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{233}{260}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{31}{65}\right)$	$e\left(\frac{12}{65}\right)$
$\chi_{8450}(33,\cdot)$	8450.cx	780	no	$1$	$1$	$e\left(\frac{379}{780}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{379}{390}\right)$	$e\left(\frac{217}{780}\right)$	$e\left(\frac{311}{780}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{243}{260}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{119}{260}\right)$	$e\left(\frac{197}{390}\right)$
$\chi_{8450}(37,\cdot)$	8450.da	780	no	$1$	$1$	$e\left(\frac{137}{780}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{137}{390}\right)$	$e\left(\frac{701}{780}\right)$	$e\left(\frac{133}{780}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{259}{260}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{137}{260}\right)$	$e\left(\frac{241}{390}\right)$
$\chi_{8450}(41,\cdot)$	8450.cw	780	no	$-1$	$1$	$e\left(\frac{188}{195}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{181}{195}\right)$	$e\left(\frac{251}{780}\right)$	$e\left(\frac{59}{390}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{69}{260}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{58}{65}\right)$	$e\left(\frac{38}{195}\right)$
$\chi_{8450}(43,\cdot)$	8450.ci	156	no	$-1$	$1$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{61}{78}\right)$
$\chi_{8450}(47,\cdot)$	8450.co	260	no	$1$	$1$	$e\left(\frac{7}{260}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{7}{130}\right)$	$e\left(\frac{51}{260}\right)$	$e\left(\frac{3}{260}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{127}{260}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{21}{260}\right)$	$e\left(\frac{111}{130}\right)$
$\chi_{8450}(49,\cdot)$	8450.cb	78	no	$1$	$1$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{34}{39}\right)$
$\chi_{8450}(51,\cdot)$	8450.bg	26	no	$1$	$1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{9}{13}\right)$	$-1$	$e\left(\frac{21}{26}\right)$	$1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{8450}(53,\cdot)$	8450.cq	260	no	$-1$	$1$	$e\left(\frac{217}{260}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{87}{130}\right)$	$e\left(\frac{54}{65}\right)$	$e\left(\frac{223}{260}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{58}{65}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{131}{260}\right)$	$e\left(\frac{61}{130}\right)$
$\chi_{8450}(57,\cdot)$	8450.br	52	no	$1$	$1$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{7}{52}\right)$	$i$	$e\left(\frac{45}{52}\right)$	$i$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{8450}(59,\cdot)$	8450.db	780	no	$-1$	$1$	$e\left(\frac{281}{390}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{86}{195}\right)$	$e\left(\frac{241}{780}\right)$	$e\left(\frac{167}{195}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{59}{260}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{21}{130}\right)$	$e\left(\frac{73}{195}\right)$
$\chi_{8450}(61,\cdot)$	8450.cm	195	no	$1$	$1$	$e\left(\frac{172}{195}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{149}{195}\right)$	$e\left(\frac{46}{195}\right)$	$e\left(\frac{83}{195}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{59}{65}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{42}{65}\right)$	$e\left(\frac{97}{195}\right)$
$\chi_{8450}(63,\cdot)$	8450.cx	780	no	$1$	$1$	$e\left(\frac{647}{780}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{257}{390}\right)$	$e\left(\frac{461}{780}\right)$	$e\left(\frac{463}{780}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{19}{260}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{127}{260}\right)$	$e\left(\frac{361}{390}\right)$
$\chi_{8450}(67,\cdot)$	8450.cx	780	no	$1$	$1$	$e\left(\frac{749}{780}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{359}{390}\right)$	$e\left(\frac{647}{780}\right)$	$e\left(\frac{61}{780}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{153}{260}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{229}{260}\right)$	$e\left(\frac{307}{390}\right)$
$\chi_{8450}(69,\cdot)$	8450.cv	390	no	$1$	$1$	$e\left(\frac{77}{390}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{77}{195}\right)$	$e\left(\frac{41}{390}\right)$	$e\left(\frac{163}{390}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{119}{130}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{77}{130}\right)$	$e\left(\frac{181}{195}\right)$
$\chi_{8450}(71,\cdot)$	8450.cw	780	no	$-1$	$1$	$e\left(\frac{19}{195}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{38}{195}\right)$	$e\left(\frac{43}{780}\right)$	$e\left(\frac{7}{390}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{17}{260}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{19}{65}\right)$	$e\left(\frac{64}{195}\right)$
$\chi_{8450}(73,\cdot)$	8450.cr	260	no	$1$	$1$	$e\left(\frac{101}{260}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{101}{130}\right)$	$e\left(\frac{123}{260}\right)$	$e\left(\frac{229}{260}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{31}{260}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{43}{260}\right)$	$e\left(\frac{23}{130}\right)$
$\chi_{8450}(77,\cdot)$	8450.cp	260	no	$-1$	$1$	$e\left(\frac{71}{260}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{71}{130}\right)$	$e\left(\frac{59}{130}\right)$	$e\left(\frac{49}{260}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{73}{130}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{213}{260}\right)$	$e\left(\frac{123}{130}\right)$
$\chi_{8450}(79,\cdot)$	8450.ce	130	no	$1$	$1$	$e\left(\frac{101}{130}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{36}{65}\right)$	$e\left(\frac{29}{65}\right)$	$e\left(\frac{99}{130}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{48}{65}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{43}{130}\right)$	$e\left(\frac{23}{65}\right)$
$\chi_{8450}(81,\cdot)$	8450.cm	195	no	$1$	$1$	$e\left(\frac{11}{195}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{22}{195}\right)$	$e\left(\frac{173}{195}\right)$	$e\left(\frac{79}{195}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{17}{65}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{65}\right)$	$e\left(\frac{191}{195}\right)$
$\chi_{8450}(83,\cdot)$	8450.co	260	no	$1$	$1$	$e\left(\frac{213}{260}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{83}{130}\right)$	$e\left(\frac{29}{260}\right)$	$e\left(\frac{17}{260}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{113}{260}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{119}{260}\right)$	$e\left(\frac{109}{130}\right)$

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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	$8450$
Structure	\(C_{4}\times C_{780}\)
Order	$3120$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{8450}(1,\cdot)\)	8450.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8450}(3,\cdot)\)	8450.cy	780	no	\(-1\)	\(1\)	\(e\left(\frac{11}{780}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{11}{390}\right)\)	\(e\left(\frac{92}{195}\right)\)	\(e\left(\frac{469}{780}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{53}{65}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{11}{260}\right)\)	\(e\left(\frac{193}{390}\right)\)
\(\chi_{8450}(7,\cdot)\)	8450.ck	156	no	\(1\)	\(1\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{73}{78}\right)\)
\(\chi_{8450}(9,\cdot)\)	8450.cu	390	no	\(1\)	\(1\)	\(e\left(\frac{11}{390}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{11}{195}\right)\)	\(e\left(\frac{184}{195}\right)\)	\(e\left(\frac{79}{390}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{41}{65}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{130}\right)\)	\(e\left(\frac{193}{195}\right)\)
\(\chi_{8450}(11,\cdot)\)	8450.cw	780	no	\(-1\)	\(1\)	\(e\left(\frac{92}{195}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{184}{195}\right)\)	\(e\left(\frac{629}{780}\right)\)	\(e\left(\frac{311}{390}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{31}{260}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{27}{65}\right)\)	\(e\left(\frac{2}{195}\right)\)
\(\chi_{8450}(17,\cdot)\)	8450.cz	780	no	\(-1\)	\(1\)	\(e\left(\frac{469}{780}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{79}{390}\right)\)	\(e\left(\frac{311}{390}\right)\)	\(e\left(\frac{71}{780}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{129}{130}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{209}{260}\right)\)	\(e\left(\frac{287}{390}\right)\)
\(\chi_{8450}(19,\cdot)\)	8450.bt	60	no	\(-1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{8450}(21,\cdot)\)	8450.cs	260	no	\(-1\)	\(1\)	\(e\left(\frac{53}{65}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{41}{65}\right)\)	\(e\left(\frac{31}{260}\right)\)	\(e\left(\frac{129}{130}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{67}{260}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{29}{65}\right)\)	\(e\left(\frac{28}{65}\right)\)
\(\chi_{8450}(23,\cdot)\)	8450.bv	60	no	\(-1\)	\(1\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{8450}(27,\cdot)\)	8450.cq	260	no	\(-1\)	\(1\)	\(e\left(\frac{11}{260}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{11}{130}\right)\)	\(e\left(\frac{27}{65}\right)\)	\(e\left(\frac{209}{260}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{29}{65}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{33}{260}\right)\)	\(e\left(\frac{63}{130}\right)\)
\(\chi_{8450}(29,\cdot)\)	8450.cu	390	no	\(1\)	\(1\)	\(e\left(\frac{193}{390}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{193}{195}\right)\)	\(e\left(\frac{2}{195}\right)\)	\(e\left(\frac{287}{390}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{28}{65}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{63}{130}\right)\)	\(e\left(\frac{89}{195}\right)\)
\(\chi_{8450}(31,\cdot)\)	8450.cs	260	no	\(-1\)	\(1\)	\(e\left(\frac{32}{65}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{64}{65}\right)\)	\(e\left(\frac{69}{260}\right)\)	\(e\left(\frac{111}{130}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{233}{260}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{31}{65}\right)\)	\(e\left(\frac{12}{65}\right)\)
\(\chi_{8450}(33,\cdot)\)	8450.cx	780	no	\(1\)	\(1\)	\(e\left(\frac{379}{780}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{379}{390}\right)\)	\(e\left(\frac{217}{780}\right)\)	\(e\left(\frac{311}{780}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{243}{260}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{119}{260}\right)\)	\(e\left(\frac{197}{390}\right)\)
\(\chi_{8450}(37,\cdot)\)	8450.da	780	no	\(1\)	\(1\)	\(e\left(\frac{137}{780}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{137}{390}\right)\)	\(e\left(\frac{701}{780}\right)\)	\(e\left(\frac{133}{780}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{259}{260}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{137}{260}\right)\)	\(e\left(\frac{241}{390}\right)\)
\(\chi_{8450}(41,\cdot)\)	8450.cw	780	no	\(-1\)	\(1\)	\(e\left(\frac{188}{195}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{181}{195}\right)\)	\(e\left(\frac{251}{780}\right)\)	\(e\left(\frac{59}{390}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{69}{260}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{58}{65}\right)\)	\(e\left(\frac{38}{195}\right)\)
\(\chi_{8450}(43,\cdot)\)	8450.ci	156	no	\(-1\)	\(1\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{61}{78}\right)\)
\(\chi_{8450}(47,\cdot)\)	8450.co	260	no	\(1\)	\(1\)	\(e\left(\frac{7}{260}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{7}{130}\right)\)	\(e\left(\frac{51}{260}\right)\)	\(e\left(\frac{3}{260}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{127}{260}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{21}{260}\right)\)	\(e\left(\frac{111}{130}\right)\)
\(\chi_{8450}(49,\cdot)\)	8450.cb	78	no	\(1\)	\(1\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{34}{39}\right)\)
\(\chi_{8450}(51,\cdot)\)	8450.bg	26	no	\(1\)	\(1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(-1\)	\(e\left(\frac{21}{26}\right)\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{8450}(53,\cdot)\)	8450.cq	260	no	\(-1\)	\(1\)	\(e\left(\frac{217}{260}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{87}{130}\right)\)	\(e\left(\frac{54}{65}\right)\)	\(e\left(\frac{223}{260}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{58}{65}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{131}{260}\right)\)	\(e\left(\frac{61}{130}\right)\)
\(\chi_{8450}(57,\cdot)\)	8450.br	52	no	\(1\)	\(1\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{41}{52}\right)\)	\(e\left(\frac{7}{52}\right)\)	\(i\)	\(e\left(\frac{45}{52}\right)\)	\(i\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{8450}(59,\cdot)\)	8450.db	780	no	\(-1\)	\(1\)	\(e\left(\frac{281}{390}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{86}{195}\right)\)	\(e\left(\frac{241}{780}\right)\)	\(e\left(\frac{167}{195}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{59}{260}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{21}{130}\right)\)	\(e\left(\frac{73}{195}\right)\)
\(\chi_{8450}(61,\cdot)\)	8450.cm	195	no	\(1\)	\(1\)	\(e\left(\frac{172}{195}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{149}{195}\right)\)	\(e\left(\frac{46}{195}\right)\)	\(e\left(\frac{83}{195}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{59}{65}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{42}{65}\right)\)	\(e\left(\frac{97}{195}\right)\)
\(\chi_{8450}(63,\cdot)\)	8450.cx	780	no	\(1\)	\(1\)	\(e\left(\frac{647}{780}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{257}{390}\right)\)	\(e\left(\frac{461}{780}\right)\)	\(e\left(\frac{463}{780}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{19}{260}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{127}{260}\right)\)	\(e\left(\frac{361}{390}\right)\)
\(\chi_{8450}(67,\cdot)\)	8450.cx	780	no	\(1\)	\(1\)	\(e\left(\frac{749}{780}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{359}{390}\right)\)	\(e\left(\frac{647}{780}\right)\)	\(e\left(\frac{61}{780}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{153}{260}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{229}{260}\right)\)	\(e\left(\frac{307}{390}\right)\)
\(\chi_{8450}(69,\cdot)\)	8450.cv	390	no	\(1\)	\(1\)	\(e\left(\frac{77}{390}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{77}{195}\right)\)	\(e\left(\frac{41}{390}\right)\)	\(e\left(\frac{163}{390}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{119}{130}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{77}{130}\right)\)	\(e\left(\frac{181}{195}\right)\)
\(\chi_{8450}(71,\cdot)\)	8450.cw	780	no	\(-1\)	\(1\)	\(e\left(\frac{19}{195}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{38}{195}\right)\)	\(e\left(\frac{43}{780}\right)\)	\(e\left(\frac{7}{390}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{17}{260}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{19}{65}\right)\)	\(e\left(\frac{64}{195}\right)\)
\(\chi_{8450}(73,\cdot)\)	8450.cr	260	no	\(1\)	\(1\)	\(e\left(\frac{101}{260}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{101}{130}\right)\)	\(e\left(\frac{123}{260}\right)\)	\(e\left(\frac{229}{260}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{31}{260}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{43}{260}\right)\)	\(e\left(\frac{23}{130}\right)\)
\(\chi_{8450}(77,\cdot)\)	8450.cp	260	no	\(-1\)	\(1\)	\(e\left(\frac{71}{260}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{71}{130}\right)\)	\(e\left(\frac{59}{130}\right)\)	\(e\left(\frac{49}{260}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{73}{130}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{213}{260}\right)\)	\(e\left(\frac{123}{130}\right)\)
\(\chi_{8450}(79,\cdot)\)	8450.ce	130	no	\(1\)	\(1\)	\(e\left(\frac{101}{130}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{36}{65}\right)\)	\(e\left(\frac{29}{65}\right)\)	\(e\left(\frac{99}{130}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{48}{65}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{43}{130}\right)\)	\(e\left(\frac{23}{65}\right)\)
\(\chi_{8450}(81,\cdot)\)	8450.cm	195	no	\(1\)	\(1\)	\(e\left(\frac{11}{195}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{22}{195}\right)\)	\(e\left(\frac{173}{195}\right)\)	\(e\left(\frac{79}{195}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{17}{65}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{65}\right)\)	\(e\left(\frac{191}{195}\right)\)
\(\chi_{8450}(83,\cdot)\)	8450.co	260	no	\(1\)	\(1\)	\(e\left(\frac{213}{260}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{83}{130}\right)\)	\(e\left(\frac{29}{260}\right)\)	\(e\left(\frac{17}{260}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{113}{260}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{119}{260}\right)\)	\(e\left(\frac{109}{130}\right)\)

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L-functions

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First 32 of 3120 characters

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