LMFDB - Group of Dirichlet characters of modulus 4225

sage:H = DirichletGroup(4225)

pari:g = idealstar(,4225,2)

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	=	$\chi_{4225}(677,\cdot)$, $\chi_{4225}(3551,\cdot)$

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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$14$
$\chi_{4225}(1,\cdot)$	4225.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4225}(2,\cdot)$	4225.cw	780	yes	$1$	$1$	$e\left(\frac{11}{195}\right)$	$e\left(\frac{113}{780}\right)$	$e\left(\frac{22}{195}\right)$	$e\left(\frac{157}{780}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{11}{65}\right)$	$e\left(\frac{113}{390}\right)$	$e\left(\frac{359}{780}\right)$	$e\left(\frac{67}{260}\right)$	$e\left(\frac{129}{130}\right)$
$\chi_{4225}(3,\cdot)$	4225.cy	780	yes	$-1$	$1$	$e\left(\frac{113}{780}\right)$	$e\left(\frac{11}{780}\right)$	$e\left(\frac{113}{390}\right)$	$e\left(\frac{31}{195}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{113}{260}\right)$	$e\left(\frac{11}{390}\right)$	$e\left(\frac{92}{195}\right)$	$e\left(\frac{79}{260}\right)$	$e\left(\frac{123}{130}\right)$
$\chi_{4225}(4,\cdot)$	4225.ct	390	yes	$1$	$1$	$e\left(\frac{22}{195}\right)$	$e\left(\frac{113}{390}\right)$	$e\left(\frac{44}{195}\right)$	$e\left(\frac{157}{390}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{22}{65}\right)$	$e\left(\frac{113}{195}\right)$	$e\left(\frac{359}{390}\right)$	$e\left(\frac{67}{130}\right)$	$e\left(\frac{64}{65}\right)$
$\chi_{4225}(6,\cdot)$	4225.cx	780	yes	$-1$	$1$	$e\left(\frac{157}{780}\right)$	$e\left(\frac{31}{195}\right)$	$e\left(\frac{157}{390}\right)$	$e\left(\frac{281}{780}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{157}{260}\right)$	$e\left(\frac{62}{195}\right)$	$e\left(\frac{727}{780}\right)$	$e\left(\frac{73}{130}\right)$	$e\left(\frac{61}{65}\right)$
$\chi_{4225}(7,\cdot)$	4225.cg	156	no	$1$	$1$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{4225}(8,\cdot)$	4225.cs	260	yes	$1$	$1$	$e\left(\frac{11}{65}\right)$	$e\left(\frac{113}{260}\right)$	$e\left(\frac{22}{65}\right)$	$e\left(\frac{157}{260}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{33}{65}\right)$	$e\left(\frac{113}{130}\right)$	$e\left(\frac{99}{260}\right)$	$e\left(\frac{201}{260}\right)$	$e\left(\frac{127}{130}\right)$
$\chi_{4225}(9,\cdot)$	4225.cv	390	yes	$1$	$1$	$e\left(\frac{113}{390}\right)$	$e\left(\frac{11}{390}\right)$	$e\left(\frac{113}{195}\right)$	$e\left(\frac{62}{195}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{113}{130}\right)$	$e\left(\frac{11}{195}\right)$	$e\left(\frac{184}{195}\right)$	$e\left(\frac{79}{130}\right)$	$e\left(\frac{58}{65}\right)$
$\chi_{4225}(11,\cdot)$	4225.cx	780	yes	$-1$	$1$	$e\left(\frac{359}{780}\right)$	$e\left(\frac{92}{195}\right)$	$e\left(\frac{359}{390}\right)$	$e\left(\frac{727}{780}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{99}{260}\right)$	$e\left(\frac{184}{195}\right)$	$e\left(\frac{629}{780}\right)$	$e\left(\frac{51}{130}\right)$	$e\left(\frac{7}{65}\right)$
$\chi_{4225}(12,\cdot)$	4225.cp	260	yes	$-1$	$1$	$e\left(\frac{67}{260}\right)$	$e\left(\frac{79}{260}\right)$	$e\left(\frac{67}{130}\right)$	$e\left(\frac{73}{130}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{201}{260}\right)$	$e\left(\frac{79}{130}\right)$	$e\left(\frac{51}{130}\right)$	$e\left(\frac{213}{260}\right)$	$e\left(\frac{121}{130}\right)$
$\chi_{4225}(14,\cdot)$	4225.cd	130	yes	$1$	$1$	$e\left(\frac{129}{130}\right)$	$e\left(\frac{123}{130}\right)$	$e\left(\frac{64}{65}\right)$	$e\left(\frac{61}{65}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{127}{130}\right)$	$e\left(\frac{58}{65}\right)$	$e\left(\frac{7}{65}\right)$	$e\left(\frac{121}{130}\right)$	$e\left(\frac{37}{65}\right)$
$\chi_{4225}(16,\cdot)$	4225.cm	195	yes	$1$	$1$	$e\left(\frac{44}{195}\right)$	$e\left(\frac{113}{195}\right)$	$e\left(\frac{88}{195}\right)$	$e\left(\frac{157}{195}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{44}{65}\right)$	$e\left(\frac{31}{195}\right)$	$e\left(\frac{164}{195}\right)$	$e\left(\frac{2}{65}\right)$	$e\left(\frac{63}{65}\right)$
$\chi_{4225}(17,\cdot)$	4225.cz	780	yes	$-1$	$1$	$e\left(\frac{457}{780}\right)$	$e\left(\frac{469}{780}\right)$	$e\left(\frac{67}{390}\right)$	$e\left(\frac{73}{390}\right)$	$e\left(\frac{61}{156}\right)$	$e\left(\frac{197}{260}\right)$	$e\left(\frac{79}{390}\right)$	$e\left(\frac{311}{390}\right)$	$e\left(\frac{201}{260}\right)$	$e\left(\frac{127}{130}\right)$
$\chi_{4225}(18,\cdot)$	4225.bs	52	no	$1$	$1$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{23}{26}\right)$
$\chi_{4225}(19,\cdot)$	4225.bu	60	no	$-1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{4225}(21,\cdot)$	4225.cr	260	yes	$-1$	$1$	$e\left(\frac{21}{260}\right)$	$e\left(\frac{53}{65}\right)$	$e\left(\frac{21}{130}\right)$	$e\left(\frac{233}{260}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{63}{260}\right)$	$e\left(\frac{41}{65}\right)$	$e\left(\frac{31}{260}\right)$	$e\left(\frac{127}{130}\right)$	$e\left(\frac{34}{65}\right)$
$\chi_{4225}(22,\cdot)$	4225.bw	60	no	$-1$	$1$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{4225}(23,\cdot)$	4225.bv	60	no	$-1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{4225}(24,\cdot)$	4225.ch	156	no	$-1$	$1$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{4225}(27,\cdot)$	4225.cq	260	yes	$-1$	$1$	$e\left(\frac{113}{260}\right)$	$e\left(\frac{11}{260}\right)$	$e\left(\frac{113}{130}\right)$	$e\left(\frac{31}{65}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{79}{260}\right)$	$e\left(\frac{11}{130}\right)$	$e\left(\frac{27}{65}\right)$	$e\left(\frac{237}{260}\right)$	$e\left(\frac{109}{130}\right)$
$\chi_{4225}(28,\cdot)$	4225.db	780	yes	$1$	$1$	$e\left(\frac{19}{390}\right)$	$e\left(\frac{71}{780}\right)$	$e\left(\frac{19}{195}\right)$	$e\left(\frac{109}{780}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{19}{130}\right)$	$e\left(\frac{71}{390}\right)$	$e\left(\frac{443}{780}\right)$	$e\left(\frac{49}{260}\right)$	$e\left(\frac{73}{130}\right)$
$\chi_{4225}(29,\cdot)$	4225.cv	390	yes	$1$	$1$	$e\left(\frac{139}{390}\right)$	$e\left(\frac{193}{390}\right)$	$e\left(\frac{139}{195}\right)$	$e\left(\frac{166}{195}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{9}{130}\right)$	$e\left(\frac{193}{195}\right)$	$e\left(\frac{2}{195}\right)$	$e\left(\frac{27}{130}\right)$	$e\left(\frac{19}{65}\right)$
$\chi_{4225}(31,\cdot)$	4225.cr	260	yes	$-1$	$1$	$e\left(\frac{139}{260}\right)$	$e\left(\frac{32}{65}\right)$	$e\left(\frac{9}{130}\right)$	$e\left(\frac{7}{260}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{157}{260}\right)$	$e\left(\frac{64}{65}\right)$	$e\left(\frac{69}{260}\right)$	$e\left(\frac{73}{130}\right)$	$e\left(\frac{61}{65}\right)$
$\chi_{4225}(32,\cdot)$	4225.cl	156	no	$1$	$1$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{4225}(33,\cdot)$	4225.cw	780	yes	$1$	$1$	$e\left(\frac{118}{195}\right)$	$e\left(\frac{379}{780}\right)$	$e\left(\frac{41}{195}\right)$	$e\left(\frac{71}{780}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{53}{65}\right)$	$e\left(\frac{379}{390}\right)$	$e\left(\frac{217}{780}\right)$	$e\left(\frac{181}{260}\right)$	$e\left(\frac{7}{130}\right)$
$\chi_{4225}(34,\cdot)$	4225.co	260	yes	$-1$	$1$	$e\left(\frac{167}{260}\right)$	$e\left(\frac{97}{130}\right)$	$e\left(\frac{37}{130}\right)$	$e\left(\frac{101}{260}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{241}{260}\right)$	$e\left(\frac{32}{65}\right)$	$e\left(\frac{67}{260}\right)$	$e\left(\frac{2}{65}\right)$	$e\left(\frac{63}{65}\right)$
$\chi_{4225}(36,\cdot)$	4225.cu	390	yes	$1$	$1$	$e\left(\frac{157}{390}\right)$	$e\left(\frac{62}{195}\right)$	$e\left(\frac{157}{195}\right)$	$e\left(\frac{281}{390}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{27}{130}\right)$	$e\left(\frac{124}{195}\right)$	$e\left(\frac{337}{390}\right)$	$e\left(\frac{8}{65}\right)$	$e\left(\frac{57}{65}\right)$
$\chi_{4225}(37,\cdot)$	4225.db	780	yes	$1$	$1$	$e\left(\frac{163}{390}\right)$	$e\left(\frac{137}{780}\right)$	$e\left(\frac{163}{195}\right)$	$e\left(\frac{463}{780}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{33}{130}\right)$	$e\left(\frac{137}{390}\right)$	$e\left(\frac{701}{780}\right)$	$e\left(\frac{3}{260}\right)$	$e\left(\frac{31}{130}\right)$
$\chi_{4225}(38,\cdot)$	4225.cp	260	yes	$-1$	$1$	$e\left(\frac{97}{260}\right)$	$e\left(\frac{29}{260}\right)$	$e\left(\frac{97}{130}\right)$	$e\left(\frac{63}{130}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{31}{260}\right)$	$e\left(\frac{29}{130}\right)$	$e\left(\frac{101}{130}\right)$	$e\left(\frac{223}{260}\right)$	$e\left(\frac{51}{130}\right)$
$\chi_{4225}(41,\cdot)$	4225.cx	780	yes	$-1$	$1$	$e\left(\frac{581}{780}\right)$	$e\left(\frac{188}{195}\right)$	$e\left(\frac{191}{390}\right)$	$e\left(\frac{553}{780}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{61}{260}\right)$	$e\left(\frac{181}{195}\right)$	$e\left(\frac{251}{780}\right)$	$e\left(\frac{59}{130}\right)$	$e\left(\frac{3}{65}\right)$
$\chi_{4225}(42,\cdot)$	4225.cy	780	yes	$-1$	$1$	$e\left(\frac{107}{780}\right)$	$e\left(\frac{749}{780}\right)$	$e\left(\frac{107}{390}\right)$	$e\left(\frac{19}{195}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{107}{260}\right)$	$e\left(\frac{359}{390}\right)$	$e\left(\frac{113}{195}\right)$	$e\left(\frac{61}{260}\right)$	$e\left(\frac{67}{130}\right)$
$\chi_{4225}(43,\cdot)$	4225.ci	156	no	$-1$	$1$	$e\left(\frac{83}{156}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{67}{156}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{25}{26}\right)$

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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	$4225$
Structure	\(C_{4}\times C_{780}\)
Order	$3120$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(14\)
\(\chi_{4225}(1,\cdot)\)	4225.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4225}(2,\cdot)\)	4225.cw	780	yes	\(1\)	\(1\)	\(e\left(\frac{11}{195}\right)\)	\(e\left(\frac{113}{780}\right)\)	\(e\left(\frac{22}{195}\right)\)	\(e\left(\frac{157}{780}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{11}{65}\right)\)	\(e\left(\frac{113}{390}\right)\)	\(e\left(\frac{359}{780}\right)\)	\(e\left(\frac{67}{260}\right)\)	\(e\left(\frac{129}{130}\right)\)
\(\chi_{4225}(3,\cdot)\)	4225.cy	780	yes	\(-1\)	\(1\)	\(e\left(\frac{113}{780}\right)\)	\(e\left(\frac{11}{780}\right)\)	\(e\left(\frac{113}{390}\right)\)	\(e\left(\frac{31}{195}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{113}{260}\right)\)	\(e\left(\frac{11}{390}\right)\)	\(e\left(\frac{92}{195}\right)\)	\(e\left(\frac{79}{260}\right)\)	\(e\left(\frac{123}{130}\right)\)
\(\chi_{4225}(4,\cdot)\)	4225.ct	390	yes	\(1\)	\(1\)	\(e\left(\frac{22}{195}\right)\)	\(e\left(\frac{113}{390}\right)\)	\(e\left(\frac{44}{195}\right)\)	\(e\left(\frac{157}{390}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{22}{65}\right)\)	\(e\left(\frac{113}{195}\right)\)	\(e\left(\frac{359}{390}\right)\)	\(e\left(\frac{67}{130}\right)\)	\(e\left(\frac{64}{65}\right)\)
\(\chi_{4225}(6,\cdot)\)	4225.cx	780	yes	\(-1\)	\(1\)	\(e\left(\frac{157}{780}\right)\)	\(e\left(\frac{31}{195}\right)\)	\(e\left(\frac{157}{390}\right)\)	\(e\left(\frac{281}{780}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{157}{260}\right)\)	\(e\left(\frac{62}{195}\right)\)	\(e\left(\frac{727}{780}\right)\)	\(e\left(\frac{73}{130}\right)\)	\(e\left(\frac{61}{65}\right)\)
\(\chi_{4225}(7,\cdot)\)	4225.cg	156	no	\(1\)	\(1\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{4225}(8,\cdot)\)	4225.cs	260	yes	\(1\)	\(1\)	\(e\left(\frac{11}{65}\right)\)	\(e\left(\frac{113}{260}\right)\)	\(e\left(\frac{22}{65}\right)\)	\(e\left(\frac{157}{260}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{33}{65}\right)\)	\(e\left(\frac{113}{130}\right)\)	\(e\left(\frac{99}{260}\right)\)	\(e\left(\frac{201}{260}\right)\)	\(e\left(\frac{127}{130}\right)\)
\(\chi_{4225}(9,\cdot)\)	4225.cv	390	yes	\(1\)	\(1\)	\(e\left(\frac{113}{390}\right)\)	\(e\left(\frac{11}{390}\right)\)	\(e\left(\frac{113}{195}\right)\)	\(e\left(\frac{62}{195}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{113}{130}\right)\)	\(e\left(\frac{11}{195}\right)\)	\(e\left(\frac{184}{195}\right)\)	\(e\left(\frac{79}{130}\right)\)	\(e\left(\frac{58}{65}\right)\)
\(\chi_{4225}(11,\cdot)\)	4225.cx	780	yes	\(-1\)	\(1\)	\(e\left(\frac{359}{780}\right)\)	\(e\left(\frac{92}{195}\right)\)	\(e\left(\frac{359}{390}\right)\)	\(e\left(\frac{727}{780}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{99}{260}\right)\)	\(e\left(\frac{184}{195}\right)\)	\(e\left(\frac{629}{780}\right)\)	\(e\left(\frac{51}{130}\right)\)	\(e\left(\frac{7}{65}\right)\)
\(\chi_{4225}(12,\cdot)\)	4225.cp	260	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{260}\right)\)	\(e\left(\frac{79}{260}\right)\)	\(e\left(\frac{67}{130}\right)\)	\(e\left(\frac{73}{130}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{201}{260}\right)\)	\(e\left(\frac{79}{130}\right)\)	\(e\left(\frac{51}{130}\right)\)	\(e\left(\frac{213}{260}\right)\)	\(e\left(\frac{121}{130}\right)\)
\(\chi_{4225}(14,\cdot)\)	4225.cd	130	yes	\(1\)	\(1\)	\(e\left(\frac{129}{130}\right)\)	\(e\left(\frac{123}{130}\right)\)	\(e\left(\frac{64}{65}\right)\)	\(e\left(\frac{61}{65}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{127}{130}\right)\)	\(e\left(\frac{58}{65}\right)\)	\(e\left(\frac{7}{65}\right)\)	\(e\left(\frac{121}{130}\right)\)	\(e\left(\frac{37}{65}\right)\)
\(\chi_{4225}(16,\cdot)\)	4225.cm	195	yes	\(1\)	\(1\)	\(e\left(\frac{44}{195}\right)\)	\(e\left(\frac{113}{195}\right)\)	\(e\left(\frac{88}{195}\right)\)	\(e\left(\frac{157}{195}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{44}{65}\right)\)	\(e\left(\frac{31}{195}\right)\)	\(e\left(\frac{164}{195}\right)\)	\(e\left(\frac{2}{65}\right)\)	\(e\left(\frac{63}{65}\right)\)
\(\chi_{4225}(17,\cdot)\)	4225.cz	780	yes	\(-1\)	\(1\)	\(e\left(\frac{457}{780}\right)\)	\(e\left(\frac{469}{780}\right)\)	\(e\left(\frac{67}{390}\right)\)	\(e\left(\frac{73}{390}\right)\)	\(e\left(\frac{61}{156}\right)\)	\(e\left(\frac{197}{260}\right)\)	\(e\left(\frac{79}{390}\right)\)	\(e\left(\frac{311}{390}\right)\)	\(e\left(\frac{201}{260}\right)\)	\(e\left(\frac{127}{130}\right)\)
\(\chi_{4225}(18,\cdot)\)	4225.bs	52	no	\(1\)	\(1\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{23}{26}\right)\)
\(\chi_{4225}(19,\cdot)\)	4225.bu	60	no	\(-1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{4225}(21,\cdot)\)	4225.cr	260	yes	\(-1\)	\(1\)	\(e\left(\frac{21}{260}\right)\)	\(e\left(\frac{53}{65}\right)\)	\(e\left(\frac{21}{130}\right)\)	\(e\left(\frac{233}{260}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{63}{260}\right)\)	\(e\left(\frac{41}{65}\right)\)	\(e\left(\frac{31}{260}\right)\)	\(e\left(\frac{127}{130}\right)\)	\(e\left(\frac{34}{65}\right)\)
\(\chi_{4225}(22,\cdot)\)	4225.bw	60	no	\(-1\)	\(1\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{4225}(23,\cdot)\)	4225.bv	60	no	\(-1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{4225}(24,\cdot)\)	4225.ch	156	no	\(-1\)	\(1\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{4225}(27,\cdot)\)	4225.cq	260	yes	\(-1\)	\(1\)	\(e\left(\frac{113}{260}\right)\)	\(e\left(\frac{11}{260}\right)\)	\(e\left(\frac{113}{130}\right)\)	\(e\left(\frac{31}{65}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{79}{260}\right)\)	\(e\left(\frac{11}{130}\right)\)	\(e\left(\frac{27}{65}\right)\)	\(e\left(\frac{237}{260}\right)\)	\(e\left(\frac{109}{130}\right)\)
\(\chi_{4225}(28,\cdot)\)	4225.db	780	yes	\(1\)	\(1\)	\(e\left(\frac{19}{390}\right)\)	\(e\left(\frac{71}{780}\right)\)	\(e\left(\frac{19}{195}\right)\)	\(e\left(\frac{109}{780}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{19}{130}\right)\)	\(e\left(\frac{71}{390}\right)\)	\(e\left(\frac{443}{780}\right)\)	\(e\left(\frac{49}{260}\right)\)	\(e\left(\frac{73}{130}\right)\)
\(\chi_{4225}(29,\cdot)\)	4225.cv	390	yes	\(1\)	\(1\)	\(e\left(\frac{139}{390}\right)\)	\(e\left(\frac{193}{390}\right)\)	\(e\left(\frac{139}{195}\right)\)	\(e\left(\frac{166}{195}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{9}{130}\right)\)	\(e\left(\frac{193}{195}\right)\)	\(e\left(\frac{2}{195}\right)\)	\(e\left(\frac{27}{130}\right)\)	\(e\left(\frac{19}{65}\right)\)
\(\chi_{4225}(31,\cdot)\)	4225.cr	260	yes	\(-1\)	\(1\)	\(e\left(\frac{139}{260}\right)\)	\(e\left(\frac{32}{65}\right)\)	\(e\left(\frac{9}{130}\right)\)	\(e\left(\frac{7}{260}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{157}{260}\right)\)	\(e\left(\frac{64}{65}\right)\)	\(e\left(\frac{69}{260}\right)\)	\(e\left(\frac{73}{130}\right)\)	\(e\left(\frac{61}{65}\right)\)
\(\chi_{4225}(32,\cdot)\)	4225.cl	156	no	\(1\)	\(1\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{4225}(33,\cdot)\)	4225.cw	780	yes	\(1\)	\(1\)	\(e\left(\frac{118}{195}\right)\)	\(e\left(\frac{379}{780}\right)\)	\(e\left(\frac{41}{195}\right)\)	\(e\left(\frac{71}{780}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{53}{65}\right)\)	\(e\left(\frac{379}{390}\right)\)	\(e\left(\frac{217}{780}\right)\)	\(e\left(\frac{181}{260}\right)\)	\(e\left(\frac{7}{130}\right)\)
\(\chi_{4225}(34,\cdot)\)	4225.co	260	yes	\(-1\)	\(1\)	\(e\left(\frac{167}{260}\right)\)	\(e\left(\frac{97}{130}\right)\)	\(e\left(\frac{37}{130}\right)\)	\(e\left(\frac{101}{260}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{241}{260}\right)\)	\(e\left(\frac{32}{65}\right)\)	\(e\left(\frac{67}{260}\right)\)	\(e\left(\frac{2}{65}\right)\)	\(e\left(\frac{63}{65}\right)\)
\(\chi_{4225}(36,\cdot)\)	4225.cu	390	yes	\(1\)	\(1\)	\(e\left(\frac{157}{390}\right)\)	\(e\left(\frac{62}{195}\right)\)	\(e\left(\frac{157}{195}\right)\)	\(e\left(\frac{281}{390}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{27}{130}\right)\)	\(e\left(\frac{124}{195}\right)\)	\(e\left(\frac{337}{390}\right)\)	\(e\left(\frac{8}{65}\right)\)	\(e\left(\frac{57}{65}\right)\)
\(\chi_{4225}(37,\cdot)\)	4225.db	780	yes	\(1\)	\(1\)	\(e\left(\frac{163}{390}\right)\)	\(e\left(\frac{137}{780}\right)\)	\(e\left(\frac{163}{195}\right)\)	\(e\left(\frac{463}{780}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{33}{130}\right)\)	\(e\left(\frac{137}{390}\right)\)	\(e\left(\frac{701}{780}\right)\)	\(e\left(\frac{3}{260}\right)\)	\(e\left(\frac{31}{130}\right)\)
\(\chi_{4225}(38,\cdot)\)	4225.cp	260	yes	\(-1\)	\(1\)	\(e\left(\frac{97}{260}\right)\)	\(e\left(\frac{29}{260}\right)\)	\(e\left(\frac{97}{130}\right)\)	\(e\left(\frac{63}{130}\right)\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{31}{260}\right)\)	\(e\left(\frac{29}{130}\right)\)	\(e\left(\frac{101}{130}\right)\)	\(e\left(\frac{223}{260}\right)\)	\(e\left(\frac{51}{130}\right)\)
\(\chi_{4225}(41,\cdot)\)	4225.cx	780	yes	\(-1\)	\(1\)	\(e\left(\frac{581}{780}\right)\)	\(e\left(\frac{188}{195}\right)\)	\(e\left(\frac{191}{390}\right)\)	\(e\left(\frac{553}{780}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{61}{260}\right)\)	\(e\left(\frac{181}{195}\right)\)	\(e\left(\frac{251}{780}\right)\)	\(e\left(\frac{59}{130}\right)\)	\(e\left(\frac{3}{65}\right)\)
\(\chi_{4225}(42,\cdot)\)	4225.cy	780	yes	\(-1\)	\(1\)	\(e\left(\frac{107}{780}\right)\)	\(e\left(\frac{749}{780}\right)\)	\(e\left(\frac{107}{390}\right)\)	\(e\left(\frac{19}{195}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{107}{260}\right)\)	\(e\left(\frac{359}{390}\right)\)	\(e\left(\frac{113}{195}\right)\)	\(e\left(\frac{61}{260}\right)\)	\(e\left(\frac{67}{130}\right)\)
\(\chi_{4225}(43,\cdot)\)	4225.ci	156	no	\(-1\)	\(1\)	\(e\left(\frac{83}{156}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{67}{156}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{25}{26}\right)\)

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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.