LMFDB - Group of Dirichlet characters of modulus 2349

sage:H = DirichletGroup(2349)

pari:g = idealstar(,2349,2)

Character group

sage:G.order() pari:g.no
Order	=	1512
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{756}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{2349}(407,\cdot)$, $\chi_{2349}(1945,\cdot)$

First 32 of 1512 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{2349}(1,\cdot)$	2349.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2349}(2,\cdot)$	2349.bu	756	yes	$1$	$1$	$e\left(\frac{41}{756}\right)$	$e\left(\frac{41}{378}\right)$	$e\left(\frac{40}{189}\right)$	$e\left(\frac{137}{189}\right)$	$e\left(\frac{41}{252}\right)$	$e\left(\frac{67}{252}\right)$	$e\left(\frac{101}{756}\right)$	$e\left(\frac{299}{378}\right)$	$e\left(\frac{589}{756}\right)$	$e\left(\frac{41}{189}\right)$
$\chi_{2349}(4,\cdot)$	2349.bs	378	yes	$1$	$1$	$e\left(\frac{41}{378}\right)$	$e\left(\frac{41}{189}\right)$	$e\left(\frac{80}{189}\right)$	$e\left(\frac{85}{189}\right)$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{101}{378}\right)$	$e\left(\frac{110}{189}\right)$	$e\left(\frac{211}{378}\right)$	$e\left(\frac{82}{189}\right)$
$\chi_{2349}(5,\cdot)$	2349.bt	378	yes	$-1$	$1$	$e\left(\frac{40}{189}\right)$	$e\left(\frac{80}{189}\right)$	$e\left(\frac{31}{378}\right)$	$e\left(\frac{46}{189}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{34}{189}\right)$	$e\left(\frac{104}{189}\right)$	$e\left(\frac{86}{189}\right)$	$e\left(\frac{160}{189}\right)$
$\chi_{2349}(7,\cdot)$	2349.bo	189	yes	$1$	$1$	$e\left(\frac{137}{189}\right)$	$e\left(\frac{85}{189}\right)$	$e\left(\frac{46}{189}\right)$	$e\left(\frac{167}{189}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{107}{189}\right)$	$e\left(\frac{16}{189}\right)$	$e\left(\frac{115}{189}\right)$	$e\left(\frac{170}{189}\right)$
$\chi_{2349}(8,\cdot)$	2349.bq	252	no	$1$	$1$	$e\left(\frac{41}{252}\right)$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{101}{252}\right)$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{85}{252}\right)$	$e\left(\frac{41}{63}\right)$
$\chi_{2349}(10,\cdot)$	2349.bp	252	no	$-1$	$1$	$e\left(\frac{67}{252}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{79}{252}\right)$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{59}{252}\right)$	$e\left(\frac{4}{63}\right)$
$\chi_{2349}(11,\cdot)$	2349.bu	756	yes	$1$	$1$	$e\left(\frac{101}{756}\right)$	$e\left(\frac{101}{378}\right)$	$e\left(\frac{34}{189}\right)$	$e\left(\frac{107}{189}\right)$	$e\left(\frac{101}{252}\right)$	$e\left(\frac{79}{252}\right)$	$e\left(\frac{341}{756}\right)$	$e\left(\frac{377}{378}\right)$	$e\left(\frac{529}{756}\right)$	$e\left(\frac{101}{189}\right)$
$\chi_{2349}(13,\cdot)$	2349.bs	378	yes	$1$	$1$	$e\left(\frac{299}{378}\right)$	$e\left(\frac{110}{189}\right)$	$e\left(\frac{104}{189}\right)$	$e\left(\frac{16}{189}\right)$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{377}{378}\right)$	$e\left(\frac{143}{189}\right)$	$e\left(\frac{331}{378}\right)$	$e\left(\frac{31}{189}\right)$
$\chi_{2349}(14,\cdot)$	2349.bu	756	yes	$1$	$1$	$e\left(\frac{589}{756}\right)$	$e\left(\frac{211}{378}\right)$	$e\left(\frac{86}{189}\right)$	$e\left(\frac{115}{189}\right)$	$e\left(\frac{85}{252}\right)$	$e\left(\frac{59}{252}\right)$	$e\left(\frac{529}{756}\right)$	$e\left(\frac{331}{378}\right)$	$e\left(\frac{293}{756}\right)$	$e\left(\frac{22}{189}\right)$
$\chi_{2349}(16,\cdot)$	2349.bo	189	yes	$1$	$1$	$e\left(\frac{41}{189}\right)$	$e\left(\frac{82}{189}\right)$	$e\left(\frac{160}{189}\right)$	$e\left(\frac{170}{189}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{101}{189}\right)$	$e\left(\frac{31}{189}\right)$	$e\left(\frac{22}{189}\right)$	$e\left(\frac{164}{189}\right)$
$\chi_{2349}(17,\cdot)$	2349.y	36	no	$1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{2349}(19,\cdot)$	2349.bp	252	no	$-1$	$1$	$e\left(\frac{53}{252}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{149}{252}\right)$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{73}{252}\right)$	$e\left(\frac{53}{63}\right)$
$\chi_{2349}(20,\cdot)$	2349.br	378	yes	$-1$	$1$	$e\left(\frac{121}{378}\right)$	$e\left(\frac{121}{189}\right)$	$e\left(\frac{191}{378}\right)$	$e\left(\frac{131}{189}\right)$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{169}{378}\right)$	$e\left(\frac{25}{189}\right)$	$e\left(\frac{5}{378}\right)$	$e\left(\frac{53}{189}\right)$
$\chi_{2349}(22,\cdot)$	2349.bs	378	yes	$1$	$1$	$e\left(\frac{71}{378}\right)$	$e\left(\frac{71}{189}\right)$	$e\left(\frac{74}{189}\right)$	$e\left(\frac{55}{189}\right)$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{221}{378}\right)$	$e\left(\frac{149}{189}\right)$	$e\left(\frac{181}{378}\right)$	$e\left(\frac{142}{189}\right)$
$\chi_{2349}(23,\cdot)$	2349.br	378	yes	$-1$	$1$	$e\left(\frac{347}{378}\right)$	$e\left(\frac{158}{189}\right)$	$e\left(\frac{151}{378}\right)$	$e\left(\frac{157}{189}\right)$	$e\left(\frac{95}{126}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{191}{378}\right)$	$e\left(\frac{92}{189}\right)$	$e\left(\frac{283}{378}\right)$	$e\left(\frac{127}{189}\right)$
$\chi_{2349}(25,\cdot)$	2349.bo	189	yes	$1$	$1$	$e\left(\frac{80}{189}\right)$	$e\left(\frac{160}{189}\right)$	$e\left(\frac{31}{189}\right)$	$e\left(\frac{92}{189}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{68}{189}\right)$	$e\left(\frac{19}{189}\right)$	$e\left(\frac{172}{189}\right)$	$e\left(\frac{131}{189}\right)$
$\chi_{2349}(26,\cdot)$	2349.bi	84	no	$1$	$1$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{2349}(28,\cdot)$	2349.i	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{2349}(31,\cdot)$	2349.bv	756	yes	$-1$	$1$	$e\left(\frac{307}{756}\right)$	$e\left(\frac{307}{378}\right)$	$e\left(\frac{115}{378}\right)$	$e\left(\frac{67}{189}\right)$	$e\left(\frac{55}{252}\right)$	$e\left(\frac{179}{252}\right)$	$e\left(\frac{535}{756}\right)$	$e\left(\frac{229}{378}\right)$	$e\left(\frac{575}{756}\right)$	$e\left(\frac{118}{189}\right)$
$\chi_{2349}(32,\cdot)$	2349.bu	756	yes	$1$	$1$	$e\left(\frac{205}{756}\right)$	$e\left(\frac{205}{378}\right)$	$e\left(\frac{11}{189}\right)$	$e\left(\frac{118}{189}\right)$	$e\left(\frac{205}{252}\right)$	$e\left(\frac{83}{252}\right)$	$e\left(\frac{505}{756}\right)$	$e\left(\frac{361}{378}\right)$	$e\left(\frac{677}{756}\right)$	$e\left(\frac{16}{189}\right)$
$\chi_{2349}(34,\cdot)$	2349.bs	378	yes	$1$	$1$	$e\left(\frac{157}{378}\right)$	$e\left(\frac{157}{189}\right)$	$e\left(\frac{145}{189}\right)$	$e\left(\frac{95}{189}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{313}{378}\right)$	$e\left(\frac{34}{189}\right)$	$e\left(\frac{347}{378}\right)$	$e\left(\frac{125}{189}\right)$
$\chi_{2349}(35,\cdot)$	2349.bn	126	no	$-1$	$1$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{47}{63}\right)$
$\chi_{2349}(37,\cdot)$	2349.bp	252	no	$-1$	$1$	$e\left(\frac{223}{252}\right)$	$e\left(\frac{97}{126}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{199}{252}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{155}{252}\right)$	$e\left(\frac{34}{63}\right)$
$\chi_{2349}(38,\cdot)$	2349.bt	378	yes	$-1$	$1$	$e\left(\frac{50}{189}\right)$	$e\left(\frac{100}{189}\right)$	$e\left(\frac{275}{378}\right)$	$e\left(\frac{152}{189}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{125}{126}\right)$	$e\left(\frac{137}{189}\right)$	$e\left(\frac{130}{189}\right)$	$e\left(\frac{13}{189}\right)$	$e\left(\frac{11}{189}\right)$
$\chi_{2349}(40,\cdot)$	2349.bv	756	yes	$-1$	$1$	$e\left(\frac{283}{756}\right)$	$e\left(\frac{283}{378}\right)$	$e\left(\frac{271}{378}\right)$	$e\left(\frac{79}{189}\right)$	$e\left(\frac{31}{252}\right)$	$e\left(\frac{23}{252}\right)$	$e\left(\frac{439}{756}\right)$	$e\left(\frac{349}{378}\right)$	$e\left(\frac{599}{756}\right)$	$e\left(\frac{94}{189}\right)$
$\chi_{2349}(41,\cdot)$	2349.bk	108	yes	$1$	$1$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{25}{27}\right)$
$\chi_{2349}(43,\cdot)$	2349.bv	756	yes	$-1$	$1$	$e\left(\frac{659}{756}\right)$	$e\left(\frac{281}{378}\right)$	$e\left(\frac{221}{378}\right)$	$e\left(\frac{17}{189}\right)$	$e\left(\frac{155}{252}\right)$	$e\left(\frac{115}{252}\right)$	$e\left(\frac{683}{756}\right)$	$e\left(\frac{233}{378}\right)$	$e\left(\frac{727}{756}\right)$	$e\left(\frac{92}{189}\right)$
$\chi_{2349}(44,\cdot)$	2349.bq	252	no	$1$	$1$	$e\left(\frac{61}{252}\right)$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{181}{252}\right)$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{65}{252}\right)$	$e\left(\frac{61}{63}\right)$
$\chi_{2349}(46,\cdot)$	2349.z	36	no	$-1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{2349}(47,\cdot)$	2349.bu	756	yes	$1$	$1$	$e\left(\frac{395}{756}\right)$	$e\left(\frac{17}{378}\right)$	$e\left(\frac{118}{189}\right)$	$e\left(\frac{149}{189}\right)$	$e\left(\frac{143}{252}\right)$	$e\left(\frac{37}{252}\right)$	$e\left(\frac{383}{756}\right)$	$e\left(\frac{41}{378}\right)$	$e\left(\frac{235}{756}\right)$	$e\left(\frac{17}{189}\right)$
$\chi_{2349}(49,\cdot)$	2349.bo	189	yes	$1$	$1$	$e\left(\frac{85}{189}\right)$	$e\left(\frac{170}{189}\right)$	$e\left(\frac{92}{189}\right)$	$e\left(\frac{145}{189}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{25}{189}\right)$	$e\left(\frac{32}{189}\right)$	$e\left(\frac{41}{189}\right)$	$e\left(\frac{151}{189}\right)$

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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	$2349$
Structure	\(C_{2}\times C_{756}\)
Order	$1512$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{2349}(1,\cdot)\)	2349.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2349}(2,\cdot)\)	2349.bu	756	yes	\(1\)	\(1\)	\(e\left(\frac{41}{756}\right)\)	\(e\left(\frac{41}{378}\right)\)	\(e\left(\frac{40}{189}\right)\)	\(e\left(\frac{137}{189}\right)\)	\(e\left(\frac{41}{252}\right)\)	\(e\left(\frac{67}{252}\right)\)	\(e\left(\frac{101}{756}\right)\)	\(e\left(\frac{299}{378}\right)\)	\(e\left(\frac{589}{756}\right)\)	\(e\left(\frac{41}{189}\right)\)
\(\chi_{2349}(4,\cdot)\)	2349.bs	378	yes	\(1\)	\(1\)	\(e\left(\frac{41}{378}\right)\)	\(e\left(\frac{41}{189}\right)\)	\(e\left(\frac{80}{189}\right)\)	\(e\left(\frac{85}{189}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{101}{378}\right)\)	\(e\left(\frac{110}{189}\right)\)	\(e\left(\frac{211}{378}\right)\)	\(e\left(\frac{82}{189}\right)\)
\(\chi_{2349}(5,\cdot)\)	2349.bt	378	yes	\(-1\)	\(1\)	\(e\left(\frac{40}{189}\right)\)	\(e\left(\frac{80}{189}\right)\)	\(e\left(\frac{31}{378}\right)\)	\(e\left(\frac{46}{189}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{34}{189}\right)\)	\(e\left(\frac{104}{189}\right)\)	\(e\left(\frac{86}{189}\right)\)	\(e\left(\frac{160}{189}\right)\)
\(\chi_{2349}(7,\cdot)\)	2349.bo	189	yes	\(1\)	\(1\)	\(e\left(\frac{137}{189}\right)\)	\(e\left(\frac{85}{189}\right)\)	\(e\left(\frac{46}{189}\right)\)	\(e\left(\frac{167}{189}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{107}{189}\right)\)	\(e\left(\frac{16}{189}\right)\)	\(e\left(\frac{115}{189}\right)\)	\(e\left(\frac{170}{189}\right)\)
\(\chi_{2349}(8,\cdot)\)	2349.bq	252	no	\(1\)	\(1\)	\(e\left(\frac{41}{252}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{101}{252}\right)\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{85}{252}\right)\)	\(e\left(\frac{41}{63}\right)\)
\(\chi_{2349}(10,\cdot)\)	2349.bp	252	no	\(-1\)	\(1\)	\(e\left(\frac{67}{252}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{79}{252}\right)\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{59}{252}\right)\)	\(e\left(\frac{4}{63}\right)\)
\(\chi_{2349}(11,\cdot)\)	2349.bu	756	yes	\(1\)	\(1\)	\(e\left(\frac{101}{756}\right)\)	\(e\left(\frac{101}{378}\right)\)	\(e\left(\frac{34}{189}\right)\)	\(e\left(\frac{107}{189}\right)\)	\(e\left(\frac{101}{252}\right)\)	\(e\left(\frac{79}{252}\right)\)	\(e\left(\frac{341}{756}\right)\)	\(e\left(\frac{377}{378}\right)\)	\(e\left(\frac{529}{756}\right)\)	\(e\left(\frac{101}{189}\right)\)
\(\chi_{2349}(13,\cdot)\)	2349.bs	378	yes	\(1\)	\(1\)	\(e\left(\frac{299}{378}\right)\)	\(e\left(\frac{110}{189}\right)\)	\(e\left(\frac{104}{189}\right)\)	\(e\left(\frac{16}{189}\right)\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{377}{378}\right)\)	\(e\left(\frac{143}{189}\right)\)	\(e\left(\frac{331}{378}\right)\)	\(e\left(\frac{31}{189}\right)\)
\(\chi_{2349}(14,\cdot)\)	2349.bu	756	yes	\(1\)	\(1\)	\(e\left(\frac{589}{756}\right)\)	\(e\left(\frac{211}{378}\right)\)	\(e\left(\frac{86}{189}\right)\)	\(e\left(\frac{115}{189}\right)\)	\(e\left(\frac{85}{252}\right)\)	\(e\left(\frac{59}{252}\right)\)	\(e\left(\frac{529}{756}\right)\)	\(e\left(\frac{331}{378}\right)\)	\(e\left(\frac{293}{756}\right)\)	\(e\left(\frac{22}{189}\right)\)
\(\chi_{2349}(16,\cdot)\)	2349.bo	189	yes	\(1\)	\(1\)	\(e\left(\frac{41}{189}\right)\)	\(e\left(\frac{82}{189}\right)\)	\(e\left(\frac{160}{189}\right)\)	\(e\left(\frac{170}{189}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{101}{189}\right)\)	\(e\left(\frac{31}{189}\right)\)	\(e\left(\frac{22}{189}\right)\)	\(e\left(\frac{164}{189}\right)\)
\(\chi_{2349}(17,\cdot)\)	2349.y	36	no	\(1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{2349}(19,\cdot)\)	2349.bp	252	no	\(-1\)	\(1\)	\(e\left(\frac{53}{252}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{149}{252}\right)\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{73}{252}\right)\)	\(e\left(\frac{53}{63}\right)\)
\(\chi_{2349}(20,\cdot)\)	2349.br	378	yes	\(-1\)	\(1\)	\(e\left(\frac{121}{378}\right)\)	\(e\left(\frac{121}{189}\right)\)	\(e\left(\frac{191}{378}\right)\)	\(e\left(\frac{131}{189}\right)\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{169}{378}\right)\)	\(e\left(\frac{25}{189}\right)\)	\(e\left(\frac{5}{378}\right)\)	\(e\left(\frac{53}{189}\right)\)
\(\chi_{2349}(22,\cdot)\)	2349.bs	378	yes	\(1\)	\(1\)	\(e\left(\frac{71}{378}\right)\)	\(e\left(\frac{71}{189}\right)\)	\(e\left(\frac{74}{189}\right)\)	\(e\left(\frac{55}{189}\right)\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{221}{378}\right)\)	\(e\left(\frac{149}{189}\right)\)	\(e\left(\frac{181}{378}\right)\)	\(e\left(\frac{142}{189}\right)\)
\(\chi_{2349}(23,\cdot)\)	2349.br	378	yes	\(-1\)	\(1\)	\(e\left(\frac{347}{378}\right)\)	\(e\left(\frac{158}{189}\right)\)	\(e\left(\frac{151}{378}\right)\)	\(e\left(\frac{157}{189}\right)\)	\(e\left(\frac{95}{126}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{191}{378}\right)\)	\(e\left(\frac{92}{189}\right)\)	\(e\left(\frac{283}{378}\right)\)	\(e\left(\frac{127}{189}\right)\)
\(\chi_{2349}(25,\cdot)\)	2349.bo	189	yes	\(1\)	\(1\)	\(e\left(\frac{80}{189}\right)\)	\(e\left(\frac{160}{189}\right)\)	\(e\left(\frac{31}{189}\right)\)	\(e\left(\frac{92}{189}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{68}{189}\right)\)	\(e\left(\frac{19}{189}\right)\)	\(e\left(\frac{172}{189}\right)\)	\(e\left(\frac{131}{189}\right)\)
\(\chi_{2349}(26,\cdot)\)	2349.bi	84	no	\(1\)	\(1\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{2349}(28,\cdot)\)	2349.i	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2349}(31,\cdot)\)	2349.bv	756	yes	\(-1\)	\(1\)	\(e\left(\frac{307}{756}\right)\)	\(e\left(\frac{307}{378}\right)\)	\(e\left(\frac{115}{378}\right)\)	\(e\left(\frac{67}{189}\right)\)	\(e\left(\frac{55}{252}\right)\)	\(e\left(\frac{179}{252}\right)\)	\(e\left(\frac{535}{756}\right)\)	\(e\left(\frac{229}{378}\right)\)	\(e\left(\frac{575}{756}\right)\)	\(e\left(\frac{118}{189}\right)\)
\(\chi_{2349}(32,\cdot)\)	2349.bu	756	yes	\(1\)	\(1\)	\(e\left(\frac{205}{756}\right)\)	\(e\left(\frac{205}{378}\right)\)	\(e\left(\frac{11}{189}\right)\)	\(e\left(\frac{118}{189}\right)\)	\(e\left(\frac{205}{252}\right)\)	\(e\left(\frac{83}{252}\right)\)	\(e\left(\frac{505}{756}\right)\)	\(e\left(\frac{361}{378}\right)\)	\(e\left(\frac{677}{756}\right)\)	\(e\left(\frac{16}{189}\right)\)
\(\chi_{2349}(34,\cdot)\)	2349.bs	378	yes	\(1\)	\(1\)	\(e\left(\frac{157}{378}\right)\)	\(e\left(\frac{157}{189}\right)\)	\(e\left(\frac{145}{189}\right)\)	\(e\left(\frac{95}{189}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{313}{378}\right)\)	\(e\left(\frac{34}{189}\right)\)	\(e\left(\frac{347}{378}\right)\)	\(e\left(\frac{125}{189}\right)\)
\(\chi_{2349}(35,\cdot)\)	2349.bn	126	no	\(-1\)	\(1\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)
\(\chi_{2349}(37,\cdot)\)	2349.bp	252	no	\(-1\)	\(1\)	\(e\left(\frac{223}{252}\right)\)	\(e\left(\frac{97}{126}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{199}{252}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{155}{252}\right)\)	\(e\left(\frac{34}{63}\right)\)
\(\chi_{2349}(38,\cdot)\)	2349.bt	378	yes	\(-1\)	\(1\)	\(e\left(\frac{50}{189}\right)\)	\(e\left(\frac{100}{189}\right)\)	\(e\left(\frac{275}{378}\right)\)	\(e\left(\frac{152}{189}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{137}{189}\right)\)	\(e\left(\frac{130}{189}\right)\)	\(e\left(\frac{13}{189}\right)\)	\(e\left(\frac{11}{189}\right)\)
\(\chi_{2349}(40,\cdot)\)	2349.bv	756	yes	\(-1\)	\(1\)	\(e\left(\frac{283}{756}\right)\)	\(e\left(\frac{283}{378}\right)\)	\(e\left(\frac{271}{378}\right)\)	\(e\left(\frac{79}{189}\right)\)	\(e\left(\frac{31}{252}\right)\)	\(e\left(\frac{23}{252}\right)\)	\(e\left(\frac{439}{756}\right)\)	\(e\left(\frac{349}{378}\right)\)	\(e\left(\frac{599}{756}\right)\)	\(e\left(\frac{94}{189}\right)\)
\(\chi_{2349}(41,\cdot)\)	2349.bk	108	yes	\(1\)	\(1\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{101}{108}\right)\)	\(e\left(\frac{25}{27}\right)\)
\(\chi_{2349}(43,\cdot)\)	2349.bv	756	yes	\(-1\)	\(1\)	\(e\left(\frac{659}{756}\right)\)	\(e\left(\frac{281}{378}\right)\)	\(e\left(\frac{221}{378}\right)\)	\(e\left(\frac{17}{189}\right)\)	\(e\left(\frac{155}{252}\right)\)	\(e\left(\frac{115}{252}\right)\)	\(e\left(\frac{683}{756}\right)\)	\(e\left(\frac{233}{378}\right)\)	\(e\left(\frac{727}{756}\right)\)	\(e\left(\frac{92}{189}\right)\)
\(\chi_{2349}(44,\cdot)\)	2349.bq	252	no	\(1\)	\(1\)	\(e\left(\frac{61}{252}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{181}{252}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{65}{252}\right)\)	\(e\left(\frac{61}{63}\right)\)
\(\chi_{2349}(46,\cdot)\)	2349.z	36	no	\(-1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{2349}(47,\cdot)\)	2349.bu	756	yes	\(1\)	\(1\)	\(e\left(\frac{395}{756}\right)\)	\(e\left(\frac{17}{378}\right)\)	\(e\left(\frac{118}{189}\right)\)	\(e\left(\frac{149}{189}\right)\)	\(e\left(\frac{143}{252}\right)\)	\(e\left(\frac{37}{252}\right)\)	\(e\left(\frac{383}{756}\right)\)	\(e\left(\frac{41}{378}\right)\)	\(e\left(\frac{235}{756}\right)\)	\(e\left(\frac{17}{189}\right)\)
\(\chi_{2349}(49,\cdot)\)	2349.bo	189	yes	\(1\)	\(1\)	\(e\left(\frac{85}{189}\right)\)	\(e\left(\frac{170}{189}\right)\)	\(e\left(\frac{92}{189}\right)\)	\(e\left(\frac{145}{189}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{25}{189}\right)\)	\(e\left(\frac{32}{189}\right)\)	\(e\left(\frac{41}{189}\right)\)	\(e\left(\frac{151}{189}\right)\)

Introduction

L-functions

Modular forms

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Properties

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Character group

First 32 of 1512 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.