LMFDB - Group of Dirichlet characters of modulus 11552

sage:H = DirichletGroup(11552)

pari:g = idealstar(,11552,2)

Character group

sage:G.order() pari:g.no
Order	=	5472
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{1368}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{11552}(5055,\cdot)$, $\chi_{11552}(1445,\cdot)$, $\chi_{11552}(2529,\cdot)$

First 32 of 5472 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$21$	$23$
$\chi_{11552}(1,\cdot)$	11552.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{11552}(3,\cdot)$	11552.dq	1368	yes	$1$	$1$	$e\left(\frac{163}{1368}\right)$	$e\left(\frac{913}{1368}\right)$	$e\left(\frac{49}{228}\right)$	$e\left(\frac{163}{684}\right)$	$e\left(\frac{379}{456}\right)$	$e\left(\frac{467}{1368}\right)$	$e\left(\frac{269}{342}\right)$	$e\left(\frac{121}{342}\right)$	$e\left(\frac{457}{1368}\right)$	$e\left(\frac{61}{684}\right)$
$\chi_{11552}(5,\cdot)$	11552.dr	1368	yes	$1$	$1$	$e\left(\frac{913}{1368}\right)$	$e\left(\frac{691}{1368}\right)$	$e\left(\frac{1}{228}\right)$	$e\left(\frac{229}{684}\right)$	$e\left(\frac{373}{456}\right)$	$e\left(\frac{77}{1368}\right)$	$e\left(\frac{59}{342}\right)$	$e\left(\frac{277}{342}\right)$	$e\left(\frac{919}{1368}\right)$	$e\left(\frac{541}{684}\right)$
$\chi_{11552}(7,\cdot)$	11552.cv	228	no	$-1$	$1$	$e\left(\frac{49}{228}\right)$	$e\left(\frac{1}{228}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{37}{76}\right)$	$e\left(\frac{11}{228}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{1}{228}\right)$	$e\left(\frac{2}{57}\right)$
$\chi_{11552}(9,\cdot)$	11552.dl	684	no	$1$	$1$	$e\left(\frac{163}{684}\right)$	$e\left(\frac{229}{684}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{163}{342}\right)$	$e\left(\frac{151}{228}\right)$	$e\left(\frac{467}{684}\right)$	$e\left(\frac{98}{171}\right)$	$e\left(\frac{121}{171}\right)$	$e\left(\frac{457}{684}\right)$	$e\left(\frac{61}{342}\right)$
$\chi_{11552}(11,\cdot)$	11552.dj	456	yes	$-1$	$1$	$e\left(\frac{379}{456}\right)$	$e\left(\frac{373}{456}\right)$	$e\left(\frac{37}{76}\right)$	$e\left(\frac{151}{228}\right)$	$e\left(\frac{7}{152}\right)$	$e\left(\frac{227}{456}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{145}{456}\right)$	$e\left(\frac{181}{228}\right)$
$\chi_{11552}(13,\cdot)$	11552.do	1368	yes	$-1$	$1$	$e\left(\frac{467}{1368}\right)$	$e\left(\frac{77}{1368}\right)$	$e\left(\frac{11}{228}\right)$	$e\left(\frac{467}{684}\right)$	$e\left(\frac{227}{456}\right)$	$e\left(\frac{847}{1368}\right)$	$e\left(\frac{68}{171}\right)$	$e\left(\frac{311}{342}\right)$	$e\left(\frac{533}{1368}\right)$	$e\left(\frac{479}{684}\right)$
$\chi_{11552}(15,\cdot)$	11552.db	342	no	$1$	$1$	$e\left(\frac{269}{342}\right)$	$e\left(\frac{59}{342}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{98}{171}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{68}{171}\right)$	$e\left(\frac{164}{171}\right)$	$e\left(\frac{28}{171}\right)$	$e\left(\frac{1}{171}\right)$	$e\left(\frac{301}{342}\right)$
$\chi_{11552}(17,\cdot)$	11552.dd	342	no	$1$	$1$	$e\left(\frac{121}{342}\right)$	$e\left(\frac{277}{342}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{121}{171}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{311}{342}\right)$	$e\left(\frac{28}{171}\right)$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{163}{342}\right)$	$e\left(\frac{82}{171}\right)$
$\chi_{11552}(21,\cdot)$	11552.do	1368	yes	$-1$	$1$	$e\left(\frac{457}{1368}\right)$	$e\left(\frac{919}{1368}\right)$	$e\left(\frac{1}{228}\right)$	$e\left(\frac{457}{684}\right)$	$e\left(\frac{145}{456}\right)$	$e\left(\frac{533}{1368}\right)$	$e\left(\frac{1}{171}\right)$	$e\left(\frac{163}{342}\right)$	$e\left(\frac{463}{1368}\right)$	$e\left(\frac{85}{684}\right)$
$\chi_{11552}(23,\cdot)$	11552.dm	684	no	$-1$	$1$	$e\left(\frac{61}{684}\right)$	$e\left(\frac{541}{684}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{61}{342}\right)$	$e\left(\frac{181}{228}\right)$	$e\left(\frac{479}{684}\right)$	$e\left(\frac{301}{342}\right)$	$e\left(\frac{82}{171}\right)$	$e\left(\frac{85}{684}\right)$	$e\left(\frac{56}{171}\right)$
$\chi_{11552}(25,\cdot)$	11552.dl	684	no	$1$	$1$	$e\left(\frac{229}{684}\right)$	$e\left(\frac{7}{684}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{229}{342}\right)$	$e\left(\frac{145}{228}\right)$	$e\left(\frac{77}{684}\right)$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{106}{171}\right)$	$e\left(\frac{235}{684}\right)$	$e\left(\frac{199}{342}\right)$
$\chi_{11552}(27,\cdot)$	11552.dg	456	yes	$1$	$1$	$e\left(\frac{163}{456}\right)$	$e\left(\frac{1}{456}\right)$	$e\left(\frac{49}{76}\right)$	$e\left(\frac{163}{228}\right)$	$e\left(\frac{75}{152}\right)$	$e\left(\frac{11}{456}\right)$	$e\left(\frac{41}{114}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{1}{456}\right)$	$e\left(\frac{61}{228}\right)$
$\chi_{11552}(29,\cdot)$	11552.do	1368	yes	$-1$	$1$	$e\left(\frac{47}{1368}\right)$	$e\left(\frac{1241}{1368}\right)$	$e\left(\frac{47}{228}\right)$	$e\left(\frac{47}{684}\right)$	$e\left(\frac{431}{456}\right)$	$e\left(\frac{1339}{1368}\right)$	$e\left(\frac{161}{171}\right)$	$e\left(\frac{251}{342}\right)$	$e\left(\frac{329}{1368}\right)$	$e\left(\frac{347}{684}\right)$
$\chi_{11552}(31,\cdot)$	11552.cp	114	no	$1$	$1$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{31}{57}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{55}{114}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{97}{114}\right)$
$\chi_{11552}(33,\cdot)$	11552.df	342	no	$-1$	$1$	$e\left(\frac{325}{342}\right)$	$e\left(\frac{83}{171}\right)$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{154}{171}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{287}{342}\right)$	$e\left(\frac{149}{342}\right)$	$e\left(\frac{44}{171}\right)$	$e\left(\frac{223}{342}\right)$	$e\left(\frac{151}{171}\right)$
$\chi_{11552}(35,\cdot)$	11552.dp	1368	yes	$-1$	$1$	$e\left(\frac{1207}{1368}\right)$	$e\left(\frac{697}{1368}\right)$	$e\left(\frac{181}{228}\right)$	$e\left(\frac{523}{684}\right)$	$e\left(\frac{139}{456}\right)$	$e\left(\frac{143}{1368}\right)$	$e\left(\frac{67}{171}\right)$	$e\left(\frac{319}{342}\right)$	$e\left(\frac{925}{1368}\right)$	$e\left(\frac{565}{684}\right)$
$\chi_{11552}(37,\cdot)$	11552.cr	152	yes	$-1$	$1$	$e\left(\frac{101}{152}\right)$	$e\left(\frac{99}{152}\right)$	$e\left(\frac{75}{76}\right)$	$e\left(\frac{25}{76}\right)$	$e\left(\frac{7}{152}\right)$	$e\left(\frac{25}{152}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{99}{152}\right)$	$e\left(\frac{73}{76}\right)$
$\chi_{11552}(39,\cdot)$	11552.cg	76	no	$-1$	$1$	$e\left(\frac{35}{76}\right)$	$e\left(\frac{55}{76}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{25}{76}\right)$	$e\left(\frac{73}{76}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{55}{76}\right)$	$e\left(\frac{15}{19}\right)$
$\chi_{11552}(41,\cdot)$	11552.dk	684	no	$-1$	$1$	$e\left(\frac{329}{684}\right)$	$e\left(\frac{137}{684}\right)$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{329}{342}\right)$	$e\left(\frac{167}{228}\right)$	$e\left(\frac{481}{684}\right)$	$e\left(\frac{233}{342}\right)$	$e\left(\frac{47}{171}\right)$	$e\left(\frac{251}{684}\right)$	$e\left(\frac{35}{342}\right)$
$\chi_{11552}(43,\cdot)$	11552.dp	1368	yes	$-1$	$1$	$e\left(\frac{697}{1368}\right)$	$e\left(\frac{1231}{1368}\right)$	$e\left(\frac{127}{228}\right)$	$e\left(\frac{13}{684}\right)$	$e\left(\frac{61}{456}\right)$	$e\left(\frac{545}{1368}\right)$	$e\left(\frac{70}{171}\right)$	$e\left(\frac{295}{342}\right)$	$e\left(\frac{91}{1368}\right)$	$e\left(\frac{307}{684}\right)$
$\chi_{11552}(45,\cdot)$	11552.dh	456	yes	$1$	$1$	$e\left(\frac{413}{456}\right)$	$e\left(\frac{383}{456}\right)$	$e\left(\frac{33}{76}\right)$	$e\left(\frac{185}{228}\right)$	$e\left(\frac{73}{152}\right)$	$e\left(\frac{337}{456}\right)$	$e\left(\frac{85}{114}\right)$	$e\left(\frac{59}{114}\right)$	$e\left(\frac{155}{456}\right)$	$e\left(\frac{221}{228}\right)$
$\chi_{11552}(47,\cdot)$	11552.dc	342	no	$-1$	$1$	$e\left(\frac{97}{171}\right)$	$e\left(\frac{47}{342}\right)$	$e\left(\frac{103}{114}\right)$	$e\left(\frac{23}{171}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{175}{342}\right)$	$e\left(\frac{241}{342}\right)$	$e\left(\frac{31}{171}\right)$	$e\left(\frac{161}{342}\right)$	$e\left(\frac{205}{342}\right)$
$\chi_{11552}(49,\cdot)$	11552.cj	114	no	$1$	$1$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{11}{114}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{4}{57}\right)$
$\chi_{11552}(51,\cdot)$	11552.dq	1368	yes	$1$	$1$	$e\left(\frac{647}{1368}\right)$	$e\left(\frac{653}{1368}\right)$	$e\left(\frac{77}{228}\right)$	$e\left(\frac{647}{684}\right)$	$e\left(\frac{335}{456}\right)$	$e\left(\frac{343}{1368}\right)$	$e\left(\frac{325}{342}\right)$	$e\left(\frac{239}{342}\right)$	$e\left(\frac{1109}{1368}\right)$	$e\left(\frac{389}{684}\right)$
$\chi_{11552}(53,\cdot)$	11552.do	1368	yes	$-1$	$1$	$e\left(\frac{833}{1368}\right)$	$e\left(\frac{1271}{1368}\right)$	$e\left(\frac{149}{228}\right)$	$e\left(\frac{149}{684}\right)$	$e\left(\frac{401}{456}\right)$	$e\left(\frac{301}{1368}\right)$	$e\left(\frac{92}{171}\right)$	$e\left(\frac{119}{342}\right)$	$e\left(\frac{359}{1368}\right)$	$e\left(\frac{125}{684}\right)$
$\chi_{11552}(55,\cdot)$	11552.dm	684	no	$-1$	$1$	$e\left(\frac{341}{684}\right)$	$e\left(\frac{221}{684}\right)$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{341}{342}\right)$	$e\left(\frac{197}{228}\right)$	$e\left(\frac{379}{684}\right)$	$e\left(\frac{281}{342}\right)$	$e\left(\frac{122}{171}\right)$	$e\left(\frac{677}{684}\right)$	$e\left(\frac{100}{171}\right)$
$\chi_{11552}(59,\cdot)$	11552.dq	1368	yes	$1$	$1$	$e\left(\frac{601}{1368}\right)$	$e\left(\frac{1243}{1368}\right)$	$e\left(\frac{31}{228}\right)$	$e\left(\frac{601}{684}\right)$	$e\left(\frac{49}{456}\right)$	$e\left(\frac{1361}{1368}\right)$	$e\left(\frac{119}{342}\right)$	$e\left(\frac{37}{342}\right)$	$e\left(\frac{787}{1368}\right)$	$e\left(\frac{355}{684}\right)$
$\chi_{11552}(61,\cdot)$	11552.dr	1368	yes	$1$	$1$	$e\left(\frac{707}{1368}\right)$	$e\left(\frac{1073}{1368}\right)$	$e\left(\frac{23}{228}\right)$	$e\left(\frac{23}{684}\right)$	$e\left(\frac{143}{456}\right)$	$e\left(\frac{175}{1368}\right)$	$e\left(\frac{103}{342}\right)$	$e\left(\frac{101}{342}\right)$	$e\left(\frac{845}{1368}\right)$	$e\left(\frac{359}{684}\right)$
$\chi_{11552}(63,\cdot)$	11552.cz	342	no	$-1$	$1$	$e\left(\frac{155}{342}\right)$	$e\left(\frac{58}{171}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{155}{171}\right)$	$e\left(\frac{17}{114}\right)$	$e\left(\frac{125}{171}\right)$	$e\left(\frac{271}{342}\right)$	$e\left(\frac{142}{171}\right)$	$e\left(\frac{115}{171}\right)$	$e\left(\frac{73}{342}\right)$
$\chi_{11552}(65,\cdot)$	11552.cl	114	no	$-1$	$1$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{77}{114}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{28}{57}\right)$
$\chi_{11552}(67,\cdot)$	11552.dq	1368	yes	$1$	$1$	$e\left(\frac{1307}{1368}\right)$	$e\left(\frac{1169}{1368}\right)$	$e\left(\frac{53}{228}\right)$	$e\left(\frac{623}{684}\right)$	$e\left(\frac{275}{456}\right)$	$e\left(\frac{547}{1368}\right)$	$e\left(\frac{277}{342}\right)$	$e\left(\frac{89}{342}\right)$	$e\left(\frac{257}{1368}\right)$	$e\left(\frac{401}{684}\right)$

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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	$11552$
Structure	\(C_{2}\times C_{2}\times C_{1368}\)
Order	$5472$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)
\(\chi_{11552}(1,\cdot)\)	11552.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{11552}(3,\cdot)\)	11552.dq	1368	yes	\(1\)	\(1\)	\(e\left(\frac{163}{1368}\right)\)	\(e\left(\frac{913}{1368}\right)\)	\(e\left(\frac{49}{228}\right)\)	\(e\left(\frac{163}{684}\right)\)	\(e\left(\frac{379}{456}\right)\)	\(e\left(\frac{467}{1368}\right)\)	\(e\left(\frac{269}{342}\right)\)	\(e\left(\frac{121}{342}\right)\)	\(e\left(\frac{457}{1368}\right)\)	\(e\left(\frac{61}{684}\right)\)
\(\chi_{11552}(5,\cdot)\)	11552.dr	1368	yes	\(1\)	\(1\)	\(e\left(\frac{913}{1368}\right)\)	\(e\left(\frac{691}{1368}\right)\)	\(e\left(\frac{1}{228}\right)\)	\(e\left(\frac{229}{684}\right)\)	\(e\left(\frac{373}{456}\right)\)	\(e\left(\frac{77}{1368}\right)\)	\(e\left(\frac{59}{342}\right)\)	\(e\left(\frac{277}{342}\right)\)	\(e\left(\frac{919}{1368}\right)\)	\(e\left(\frac{541}{684}\right)\)
\(\chi_{11552}(7,\cdot)\)	11552.cv	228	no	\(-1\)	\(1\)	\(e\left(\frac{49}{228}\right)\)	\(e\left(\frac{1}{228}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{37}{76}\right)\)	\(e\left(\frac{11}{228}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{1}{228}\right)\)	\(e\left(\frac{2}{57}\right)\)
\(\chi_{11552}(9,\cdot)\)	11552.dl	684	no	\(1\)	\(1\)	\(e\left(\frac{163}{684}\right)\)	\(e\left(\frac{229}{684}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{163}{342}\right)\)	\(e\left(\frac{151}{228}\right)\)	\(e\left(\frac{467}{684}\right)\)	\(e\left(\frac{98}{171}\right)\)	\(e\left(\frac{121}{171}\right)\)	\(e\left(\frac{457}{684}\right)\)	\(e\left(\frac{61}{342}\right)\)
\(\chi_{11552}(11,\cdot)\)	11552.dj	456	yes	\(-1\)	\(1\)	\(e\left(\frac{379}{456}\right)\)	\(e\left(\frac{373}{456}\right)\)	\(e\left(\frac{37}{76}\right)\)	\(e\left(\frac{151}{228}\right)\)	\(e\left(\frac{7}{152}\right)\)	\(e\left(\frac{227}{456}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{145}{456}\right)\)	\(e\left(\frac{181}{228}\right)\)
\(\chi_{11552}(13,\cdot)\)	11552.do	1368	yes	\(-1\)	\(1\)	\(e\left(\frac{467}{1368}\right)\)	\(e\left(\frac{77}{1368}\right)\)	\(e\left(\frac{11}{228}\right)\)	\(e\left(\frac{467}{684}\right)\)	\(e\left(\frac{227}{456}\right)\)	\(e\left(\frac{847}{1368}\right)\)	\(e\left(\frac{68}{171}\right)\)	\(e\left(\frac{311}{342}\right)\)	\(e\left(\frac{533}{1368}\right)\)	\(e\left(\frac{479}{684}\right)\)
\(\chi_{11552}(15,\cdot)\)	11552.db	342	no	\(1\)	\(1\)	\(e\left(\frac{269}{342}\right)\)	\(e\left(\frac{59}{342}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{98}{171}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{68}{171}\right)\)	\(e\left(\frac{164}{171}\right)\)	\(e\left(\frac{28}{171}\right)\)	\(e\left(\frac{1}{171}\right)\)	\(e\left(\frac{301}{342}\right)\)
\(\chi_{11552}(17,\cdot)\)	11552.dd	342	no	\(1\)	\(1\)	\(e\left(\frac{121}{342}\right)\)	\(e\left(\frac{277}{342}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{121}{171}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{311}{342}\right)\)	\(e\left(\frac{28}{171}\right)\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{163}{342}\right)\)	\(e\left(\frac{82}{171}\right)\)
\(\chi_{11552}(21,\cdot)\)	11552.do	1368	yes	\(-1\)	\(1\)	\(e\left(\frac{457}{1368}\right)\)	\(e\left(\frac{919}{1368}\right)\)	\(e\left(\frac{1}{228}\right)\)	\(e\left(\frac{457}{684}\right)\)	\(e\left(\frac{145}{456}\right)\)	\(e\left(\frac{533}{1368}\right)\)	\(e\left(\frac{1}{171}\right)\)	\(e\left(\frac{163}{342}\right)\)	\(e\left(\frac{463}{1368}\right)\)	\(e\left(\frac{85}{684}\right)\)
\(\chi_{11552}(23,\cdot)\)	11552.dm	684	no	\(-1\)	\(1\)	\(e\left(\frac{61}{684}\right)\)	\(e\left(\frac{541}{684}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{61}{342}\right)\)	\(e\left(\frac{181}{228}\right)\)	\(e\left(\frac{479}{684}\right)\)	\(e\left(\frac{301}{342}\right)\)	\(e\left(\frac{82}{171}\right)\)	\(e\left(\frac{85}{684}\right)\)	\(e\left(\frac{56}{171}\right)\)
\(\chi_{11552}(25,\cdot)\)	11552.dl	684	no	\(1\)	\(1\)	\(e\left(\frac{229}{684}\right)\)	\(e\left(\frac{7}{684}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{229}{342}\right)\)	\(e\left(\frac{145}{228}\right)\)	\(e\left(\frac{77}{684}\right)\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{106}{171}\right)\)	\(e\left(\frac{235}{684}\right)\)	\(e\left(\frac{199}{342}\right)\)
\(\chi_{11552}(27,\cdot)\)	11552.dg	456	yes	\(1\)	\(1\)	\(e\left(\frac{163}{456}\right)\)	\(e\left(\frac{1}{456}\right)\)	\(e\left(\frac{49}{76}\right)\)	\(e\left(\frac{163}{228}\right)\)	\(e\left(\frac{75}{152}\right)\)	\(e\left(\frac{11}{456}\right)\)	\(e\left(\frac{41}{114}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{1}{456}\right)\)	\(e\left(\frac{61}{228}\right)\)
\(\chi_{11552}(29,\cdot)\)	11552.do	1368	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{1368}\right)\)	\(e\left(\frac{1241}{1368}\right)\)	\(e\left(\frac{47}{228}\right)\)	\(e\left(\frac{47}{684}\right)\)	\(e\left(\frac{431}{456}\right)\)	\(e\left(\frac{1339}{1368}\right)\)	\(e\left(\frac{161}{171}\right)\)	\(e\left(\frac{251}{342}\right)\)	\(e\left(\frac{329}{1368}\right)\)	\(e\left(\frac{347}{684}\right)\)
\(\chi_{11552}(31,\cdot)\)	11552.cp	114	no	\(1\)	\(1\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{31}{57}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{55}{114}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{5}{114}\right)\)	\(e\left(\frac{97}{114}\right)\)
\(\chi_{11552}(33,\cdot)\)	11552.df	342	no	\(-1\)	\(1\)	\(e\left(\frac{325}{342}\right)\)	\(e\left(\frac{83}{171}\right)\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{154}{171}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{287}{342}\right)\)	\(e\left(\frac{149}{342}\right)\)	\(e\left(\frac{44}{171}\right)\)	\(e\left(\frac{223}{342}\right)\)	\(e\left(\frac{151}{171}\right)\)
\(\chi_{11552}(35,\cdot)\)	11552.dp	1368	yes	\(-1\)	\(1\)	\(e\left(\frac{1207}{1368}\right)\)	\(e\left(\frac{697}{1368}\right)\)	\(e\left(\frac{181}{228}\right)\)	\(e\left(\frac{523}{684}\right)\)	\(e\left(\frac{139}{456}\right)\)	\(e\left(\frac{143}{1368}\right)\)	\(e\left(\frac{67}{171}\right)\)	\(e\left(\frac{319}{342}\right)\)	\(e\left(\frac{925}{1368}\right)\)	\(e\left(\frac{565}{684}\right)\)
\(\chi_{11552}(37,\cdot)\)	11552.cr	152	yes	\(-1\)	\(1\)	\(e\left(\frac{101}{152}\right)\)	\(e\left(\frac{99}{152}\right)\)	\(e\left(\frac{75}{76}\right)\)	\(e\left(\frac{25}{76}\right)\)	\(e\left(\frac{7}{152}\right)\)	\(e\left(\frac{25}{152}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{99}{152}\right)\)	\(e\left(\frac{73}{76}\right)\)
\(\chi_{11552}(39,\cdot)\)	11552.cg	76	no	\(-1\)	\(1\)	\(e\left(\frac{35}{76}\right)\)	\(e\left(\frac{55}{76}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{25}{76}\right)\)	\(e\left(\frac{73}{76}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{55}{76}\right)\)	\(e\left(\frac{15}{19}\right)\)
\(\chi_{11552}(41,\cdot)\)	11552.dk	684	no	\(-1\)	\(1\)	\(e\left(\frac{329}{684}\right)\)	\(e\left(\frac{137}{684}\right)\)	\(e\left(\frac{101}{114}\right)\)	\(e\left(\frac{329}{342}\right)\)	\(e\left(\frac{167}{228}\right)\)	\(e\left(\frac{481}{684}\right)\)	\(e\left(\frac{233}{342}\right)\)	\(e\left(\frac{47}{171}\right)\)	\(e\left(\frac{251}{684}\right)\)	\(e\left(\frac{35}{342}\right)\)
\(\chi_{11552}(43,\cdot)\)	11552.dp	1368	yes	\(-1\)	\(1\)	\(e\left(\frac{697}{1368}\right)\)	\(e\left(\frac{1231}{1368}\right)\)	\(e\left(\frac{127}{228}\right)\)	\(e\left(\frac{13}{684}\right)\)	\(e\left(\frac{61}{456}\right)\)	\(e\left(\frac{545}{1368}\right)\)	\(e\left(\frac{70}{171}\right)\)	\(e\left(\frac{295}{342}\right)\)	\(e\left(\frac{91}{1368}\right)\)	\(e\left(\frac{307}{684}\right)\)
\(\chi_{11552}(45,\cdot)\)	11552.dh	456	yes	\(1\)	\(1\)	\(e\left(\frac{413}{456}\right)\)	\(e\left(\frac{383}{456}\right)\)	\(e\left(\frac{33}{76}\right)\)	\(e\left(\frac{185}{228}\right)\)	\(e\left(\frac{73}{152}\right)\)	\(e\left(\frac{337}{456}\right)\)	\(e\left(\frac{85}{114}\right)\)	\(e\left(\frac{59}{114}\right)\)	\(e\left(\frac{155}{456}\right)\)	\(e\left(\frac{221}{228}\right)\)
\(\chi_{11552}(47,\cdot)\)	11552.dc	342	no	\(-1\)	\(1\)	\(e\left(\frac{97}{171}\right)\)	\(e\left(\frac{47}{342}\right)\)	\(e\left(\frac{103}{114}\right)\)	\(e\left(\frac{23}{171}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{175}{342}\right)\)	\(e\left(\frac{241}{342}\right)\)	\(e\left(\frac{31}{171}\right)\)	\(e\left(\frac{161}{342}\right)\)	\(e\left(\frac{205}{342}\right)\)
\(\chi_{11552}(49,\cdot)\)	11552.cj	114	no	\(1\)	\(1\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{11}{114}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{4}{57}\right)\)
\(\chi_{11552}(51,\cdot)\)	11552.dq	1368	yes	\(1\)	\(1\)	\(e\left(\frac{647}{1368}\right)\)	\(e\left(\frac{653}{1368}\right)\)	\(e\left(\frac{77}{228}\right)\)	\(e\left(\frac{647}{684}\right)\)	\(e\left(\frac{335}{456}\right)\)	\(e\left(\frac{343}{1368}\right)\)	\(e\left(\frac{325}{342}\right)\)	\(e\left(\frac{239}{342}\right)\)	\(e\left(\frac{1109}{1368}\right)\)	\(e\left(\frac{389}{684}\right)\)
\(\chi_{11552}(53,\cdot)\)	11552.do	1368	yes	\(-1\)	\(1\)	\(e\left(\frac{833}{1368}\right)\)	\(e\left(\frac{1271}{1368}\right)\)	\(e\left(\frac{149}{228}\right)\)	\(e\left(\frac{149}{684}\right)\)	\(e\left(\frac{401}{456}\right)\)	\(e\left(\frac{301}{1368}\right)\)	\(e\left(\frac{92}{171}\right)\)	\(e\left(\frac{119}{342}\right)\)	\(e\left(\frac{359}{1368}\right)\)	\(e\left(\frac{125}{684}\right)\)
\(\chi_{11552}(55,\cdot)\)	11552.dm	684	no	\(-1\)	\(1\)	\(e\left(\frac{341}{684}\right)\)	\(e\left(\frac{221}{684}\right)\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{341}{342}\right)\)	\(e\left(\frac{197}{228}\right)\)	\(e\left(\frac{379}{684}\right)\)	\(e\left(\frac{281}{342}\right)\)	\(e\left(\frac{122}{171}\right)\)	\(e\left(\frac{677}{684}\right)\)	\(e\left(\frac{100}{171}\right)\)
\(\chi_{11552}(59,\cdot)\)	11552.dq	1368	yes	\(1\)	\(1\)	\(e\left(\frac{601}{1368}\right)\)	\(e\left(\frac{1243}{1368}\right)\)	\(e\left(\frac{31}{228}\right)\)	\(e\left(\frac{601}{684}\right)\)	\(e\left(\frac{49}{456}\right)\)	\(e\left(\frac{1361}{1368}\right)\)	\(e\left(\frac{119}{342}\right)\)	\(e\left(\frac{37}{342}\right)\)	\(e\left(\frac{787}{1368}\right)\)	\(e\left(\frac{355}{684}\right)\)
\(\chi_{11552}(61,\cdot)\)	11552.dr	1368	yes	\(1\)	\(1\)	\(e\left(\frac{707}{1368}\right)\)	\(e\left(\frac{1073}{1368}\right)\)	\(e\left(\frac{23}{228}\right)\)	\(e\left(\frac{23}{684}\right)\)	\(e\left(\frac{143}{456}\right)\)	\(e\left(\frac{175}{1368}\right)\)	\(e\left(\frac{103}{342}\right)\)	\(e\left(\frac{101}{342}\right)\)	\(e\left(\frac{845}{1368}\right)\)	\(e\left(\frac{359}{684}\right)\)
\(\chi_{11552}(63,\cdot)\)	11552.cz	342	no	\(-1\)	\(1\)	\(e\left(\frac{155}{342}\right)\)	\(e\left(\frac{58}{171}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{155}{171}\right)\)	\(e\left(\frac{17}{114}\right)\)	\(e\left(\frac{125}{171}\right)\)	\(e\left(\frac{271}{342}\right)\)	\(e\left(\frac{142}{171}\right)\)	\(e\left(\frac{115}{171}\right)\)	\(e\left(\frac{73}{342}\right)\)
\(\chi_{11552}(65,\cdot)\)	11552.cl	114	no	\(-1\)	\(1\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{77}{114}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{28}{57}\right)\)
\(\chi_{11552}(67,\cdot)\)	11552.dq	1368	yes	\(1\)	\(1\)	\(e\left(\frac{1307}{1368}\right)\)	\(e\left(\frac{1169}{1368}\right)\)	\(e\left(\frac{53}{228}\right)\)	\(e\left(\frac{623}{684}\right)\)	\(e\left(\frac{275}{456}\right)\)	\(e\left(\frac{547}{1368}\right)\)	\(e\left(\frac{277}{342}\right)\)	\(e\left(\frac{89}{342}\right)\)	\(e\left(\frac{257}{1368}\right)\)	\(e\left(\frac{401}{684}\right)\)

Introduction

L-functions

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