LMFDB - Group of Dirichlet characters of modulus 394

Show commands: PariGP / SageMath

sage: H = DirichletGroup(394)

pari: g = idealstar(,394,2)

Character group

sage: G.order() pari: g.no
Order	=	196
sage: H.invariants() pari: g.cyc
Structure	=	$C_{196}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{394}(199,\cdot)$

First 32 of 196 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{394}(1,\cdot)$	394.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{394}(3,\cdot)$	394.i	196	no	$-1$	$1$	$e\left(\frac{29}{196}\right)$	$e\left(\frac{37}{196}\right)$	$e\left(\frac{81}{98}\right)$	$e\left(\frac{29}{98}\right)$	$e\left(\frac{153}{196}\right)$	$e\left(\frac{17}{196}\right)$	$e\left(\frac{33}{98}\right)$	$e\left(\frac{163}{196}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{191}{196}\right)$
$\chi_{394}(5,\cdot)$	394.i	196	no	$-1$	$1$	$e\left(\frac{37}{196}\right)$	$e\left(\frac{81}{196}\right)$	$e\left(\frac{29}{98}\right)$	$e\left(\frac{37}{98}\right)$	$e\left(\frac{33}{196}\right)$	$e\left(\frac{69}{196}\right)$	$e\left(\frac{59}{98}\right)$	$e\left(\frac{39}{196}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{95}{196}\right)$
$\chi_{394}(7,\cdot)$	394.h	98	no	$1$	$1$	$e\left(\frac{81}{98}\right)$	$e\left(\frac{29}{98}\right)$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{59}{98}\right)$	$e\left(\frac{61}{98}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{57}{98}\right)$
$\chi_{394}(9,\cdot)$	394.h	98	no	$1$	$1$	$e\left(\frac{29}{98}\right)$	$e\left(\frac{37}{98}\right)$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{55}{98}\right)$	$e\left(\frac{17}{98}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{65}{98}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{93}{98}\right)$
$\chi_{394}(11,\cdot)$	394.i	196	no	$-1$	$1$	$e\left(\frac{153}{196}\right)$	$e\left(\frac{33}{196}\right)$	$e\left(\frac{59}{98}\right)$	$e\left(\frac{55}{98}\right)$	$e\left(\frac{57}{196}\right)$	$e\left(\frac{137}{196}\right)$	$e\left(\frac{93}{98}\right)$	$e\left(\frac{103}{196}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{75}{196}\right)$
$\chi_{394}(13,\cdot)$	394.i	196	no	$-1$	$1$	$e\left(\frac{17}{196}\right)$	$e\left(\frac{69}{196}\right)$	$e\left(\frac{61}{98}\right)$	$e\left(\frac{17}{98}\right)$	$e\left(\frac{137}{196}\right)$	$e\left(\frac{37}{196}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{55}{196}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{139}{196}\right)$
$\chi_{394}(15,\cdot)$	394.h	98	no	$1$	$1$	$e\left(\frac{33}{98}\right)$	$e\left(\frac{59}{98}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{93}{98}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{3}{98}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{45}{98}\right)$
$\chi_{394}(17,\cdot)$	394.i	196	no	$-1$	$1$	$e\left(\frac{163}{196}\right)$	$e\left(\frac{39}{196}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{65}{98}\right)$	$e\left(\frac{103}{196}\right)$	$e\left(\frac{55}{196}\right)$	$e\left(\frac{3}{98}\right)$	$e\left(\frac{193}{196}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{53}{196}\right)$
$\chi_{394}(19,\cdot)$	394.e	14	no	$1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{14}\right)$	$1$	$e\left(\frac{13}{14}\right)$
$\chi_{394}(21,\cdot)$	394.i	196	no	$-1$	$1$	$e\left(\frac{191}{196}\right)$	$e\left(\frac{95}{196}\right)$	$e\left(\frac{57}{98}\right)$	$e\left(\frac{93}{98}\right)$	$e\left(\frac{75}{196}\right)$	$e\left(\frac{139}{196}\right)$	$e\left(\frac{45}{98}\right)$	$e\left(\frac{53}{196}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{109}{196}\right)$
$\chi_{394}(23,\cdot)$	394.g	49	no	$1$	$1$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{17}{49}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{10}{49}\right)$
$\chi_{394}(25,\cdot)$	394.h	98	no	$1$	$1$	$e\left(\frac{37}{98}\right)$	$e\left(\frac{81}{98}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{33}{98}\right)$	$e\left(\frac{69}{98}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{39}{98}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{95}{98}\right)$
$\chi_{394}(27,\cdot)$	394.i	196	no	$-1$	$1$	$e\left(\frac{87}{196}\right)$	$e\left(\frac{111}{196}\right)$	$e\left(\frac{47}{98}\right)$	$e\left(\frac{87}{98}\right)$	$e\left(\frac{67}{196}\right)$	$e\left(\frac{51}{196}\right)$	$e\left(\frac{1}{98}\right)$	$e\left(\frac{97}{196}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{181}{196}\right)$
$\chi_{394}(29,\cdot)$	394.g	49	no	$1$	$1$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{17}{49}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{16}{49}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{49}\right)$
$\chi_{394}(31,\cdot)$	394.i	196	no	$-1$	$1$	$e\left(\frac{41}{196}\right)$	$e\left(\frac{5}{196}\right)$	$e\left(\frac{3}{98}\right)$	$e\left(\frac{41}{98}\right)$	$e\left(\frac{169}{196}\right)$	$e\left(\frac{193}{196}\right)$	$e\left(\frac{23}{98}\right)$	$e\left(\frac{75}{196}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{47}{196}\right)$
$\chi_{394}(33,\cdot)$	394.e	14	no	$1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{14}\right)$	$1$	$e\left(\frac{5}{14}\right)$
$\chi_{394}(35,\cdot)$	394.i	196	no	$-1$	$1$	$e\left(\frac{3}{196}\right)$	$e\left(\frac{139}{196}\right)$	$e\left(\frac{5}{98}\right)$	$e\left(\frac{3}{98}\right)$	$e\left(\frac{151}{196}\right)$	$e\left(\frac{191}{196}\right)$	$e\left(\frac{71}{98}\right)$	$e\left(\frac{125}{196}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{196}\right)$
$\chi_{394}(37,\cdot)$	394.g	49	no	$1$	$1$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{30}{49}\right)$	$e\left(\frac{20}{49}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{16}{49}\right)$
$\chi_{394}(39,\cdot)$	394.h	98	no	$1$	$1$	$e\left(\frac{23}{98}\right)$	$e\left(\frac{53}{98}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{47}{98}\right)$	$e\left(\frac{27}{98}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{11}{98}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{67}{98}\right)$
$\chi_{394}(41,\cdot)$	394.h	98	no	$1$	$1$	$e\left(\frac{57}{98}\right)$	$e\left(\frac{93}{98}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{27}{98}\right)$	$e\left(\frac{3}{98}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{23}{98}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{51}{98}\right)$
$\chi_{394}(43,\cdot)$	394.h	98	no	$1$	$1$	$e\left(\frac{3}{98}\right)$	$e\left(\frac{41}{98}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{53}{98}\right)$	$e\left(\frac{93}{98}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{27}{98}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{98}\right)$
$\chi_{394}(45,\cdot)$	394.i	196	no	$-1$	$1$	$e\left(\frac{95}{196}\right)$	$e\left(\frac{155}{196}\right)$	$e\left(\frac{93}{98}\right)$	$e\left(\frac{95}{98}\right)$	$e\left(\frac{143}{196}\right)$	$e\left(\frac{103}{196}\right)$	$e\left(\frac{27}{98}\right)$	$e\left(\frac{169}{196}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{85}{196}\right)$
$\chi_{394}(47,\cdot)$	394.h	98	no	$1$	$1$	$e\left(\frac{93}{98}\right)$	$e\left(\frac{95}{98}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{75}{98}\right)$	$e\left(\frac{41}{98}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{53}{98}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{98}\right)$
$\chi_{394}(49,\cdot)$	394.g	49	no	$1$	$1$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{43}{49}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{8}{49}\right)$
$\chi_{394}(51,\cdot)$	394.g	49	no	$1$	$1$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{13}{49}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{18}{49}\right)$	$e\left(\frac{18}{49}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{12}{49}\right)$
$\chi_{394}(53,\cdot)$	394.g	49	no	$1$	$1$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{20}{49}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{6}{49}\right)$
$\chi_{394}(55,\cdot)$	394.h	98	no	$1$	$1$	$e\left(\frac{95}{98}\right)$	$e\left(\frac{57}{98}\right)$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{45}{98}\right)$	$e\left(\frac{5}{98}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{71}{98}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{85}{98}\right)$
$\chi_{394}(57,\cdot)$	394.i	196	no	$-1$	$1$	$e\left(\frac{71}{196}\right)$	$e\left(\frac{23}{196}\right)$	$e\left(\frac{53}{98}\right)$	$e\left(\frac{71}{98}\right)$	$e\left(\frac{111}{196}\right)$	$e\left(\frac{143}{196}\right)$	$e\left(\frac{47}{98}\right)$	$e\left(\frac{149}{196}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{177}{196}\right)$
$\chi_{394}(59,\cdot)$	394.g	49	no	$1$	$1$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{17}{49}\right)$
$\chi_{394}(61,\cdot)$	394.g	49	no	$1$	$1$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{38}{49}\right)$
$\chi_{394}(63,\cdot)$	394.g	49	no	$1$	$1$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{20}{49}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{8}{49}\right)$	$e\left(\frac{39}{49}\right)$	$e\left(\frac{39}{49}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{26}{49}\right)$

Click here to search among the remaining 164 characters.

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Modulus	$394$
Structure	\(C_{196}\)
Order	$196$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{394}(1,\cdot)\)	394.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{394}(3,\cdot)\)	394.i	196	no	\(-1\)	\(1\)	\(e\left(\frac{29}{196}\right)\)	\(e\left(\frac{37}{196}\right)\)	\(e\left(\frac{81}{98}\right)\)	\(e\left(\frac{29}{98}\right)\)	\(e\left(\frac{153}{196}\right)\)	\(e\left(\frac{17}{196}\right)\)	\(e\left(\frac{33}{98}\right)\)	\(e\left(\frac{163}{196}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{191}{196}\right)\)
\(\chi_{394}(5,\cdot)\)	394.i	196	no	\(-1\)	\(1\)	\(e\left(\frac{37}{196}\right)\)	\(e\left(\frac{81}{196}\right)\)	\(e\left(\frac{29}{98}\right)\)	\(e\left(\frac{37}{98}\right)\)	\(e\left(\frac{33}{196}\right)\)	\(e\left(\frac{69}{196}\right)\)	\(e\left(\frac{59}{98}\right)\)	\(e\left(\frac{39}{196}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{95}{196}\right)\)
\(\chi_{394}(7,\cdot)\)	394.h	98	no	\(1\)	\(1\)	\(e\left(\frac{81}{98}\right)\)	\(e\left(\frac{29}{98}\right)\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{59}{98}\right)\)	\(e\left(\frac{61}{98}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{57}{98}\right)\)
\(\chi_{394}(9,\cdot)\)	394.h	98	no	\(1\)	\(1\)	\(e\left(\frac{29}{98}\right)\)	\(e\left(\frac{37}{98}\right)\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{55}{98}\right)\)	\(e\left(\frac{17}{98}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{65}{98}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{93}{98}\right)\)
\(\chi_{394}(11,\cdot)\)	394.i	196	no	\(-1\)	\(1\)	\(e\left(\frac{153}{196}\right)\)	\(e\left(\frac{33}{196}\right)\)	\(e\left(\frac{59}{98}\right)\)	\(e\left(\frac{55}{98}\right)\)	\(e\left(\frac{57}{196}\right)\)	\(e\left(\frac{137}{196}\right)\)	\(e\left(\frac{93}{98}\right)\)	\(e\left(\frac{103}{196}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{75}{196}\right)\)
\(\chi_{394}(13,\cdot)\)	394.i	196	no	\(-1\)	\(1\)	\(e\left(\frac{17}{196}\right)\)	\(e\left(\frac{69}{196}\right)\)	\(e\left(\frac{61}{98}\right)\)	\(e\left(\frac{17}{98}\right)\)	\(e\left(\frac{137}{196}\right)\)	\(e\left(\frac{37}{196}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{55}{196}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{139}{196}\right)\)
\(\chi_{394}(15,\cdot)\)	394.h	98	no	\(1\)	\(1\)	\(e\left(\frac{33}{98}\right)\)	\(e\left(\frac{59}{98}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{93}{98}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{3}{98}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{45}{98}\right)\)
\(\chi_{394}(17,\cdot)\)	394.i	196	no	\(-1\)	\(1\)	\(e\left(\frac{163}{196}\right)\)	\(e\left(\frac{39}{196}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{65}{98}\right)\)	\(e\left(\frac{103}{196}\right)\)	\(e\left(\frac{55}{196}\right)\)	\(e\left(\frac{3}{98}\right)\)	\(e\left(\frac{193}{196}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{53}{196}\right)\)
\(\chi_{394}(19,\cdot)\)	394.e	14	no	\(1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(1\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{394}(21,\cdot)\)	394.i	196	no	\(-1\)	\(1\)	\(e\left(\frac{191}{196}\right)\)	\(e\left(\frac{95}{196}\right)\)	\(e\left(\frac{57}{98}\right)\)	\(e\left(\frac{93}{98}\right)\)	\(e\left(\frac{75}{196}\right)\)	\(e\left(\frac{139}{196}\right)\)	\(e\left(\frac{45}{98}\right)\)	\(e\left(\frac{53}{196}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{109}{196}\right)\)
\(\chi_{394}(23,\cdot)\)	394.g	49	no	\(1\)	\(1\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{17}{49}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{10}{49}\right)\)
\(\chi_{394}(25,\cdot)\)	394.h	98	no	\(1\)	\(1\)	\(e\left(\frac{37}{98}\right)\)	\(e\left(\frac{81}{98}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{33}{98}\right)\)	\(e\left(\frac{69}{98}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{39}{98}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{95}{98}\right)\)
\(\chi_{394}(27,\cdot)\)	394.i	196	no	\(-1\)	\(1\)	\(e\left(\frac{87}{196}\right)\)	\(e\left(\frac{111}{196}\right)\)	\(e\left(\frac{47}{98}\right)\)	\(e\left(\frac{87}{98}\right)\)	\(e\left(\frac{67}{196}\right)\)	\(e\left(\frac{51}{196}\right)\)	\(e\left(\frac{1}{98}\right)\)	\(e\left(\frac{97}{196}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{181}{196}\right)\)
\(\chi_{394}(29,\cdot)\)	394.g	49	no	\(1\)	\(1\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{17}{49}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{16}{49}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{49}\right)\)
\(\chi_{394}(31,\cdot)\)	394.i	196	no	\(-1\)	\(1\)	\(e\left(\frac{41}{196}\right)\)	\(e\left(\frac{5}{196}\right)\)	\(e\left(\frac{3}{98}\right)\)	\(e\left(\frac{41}{98}\right)\)	\(e\left(\frac{169}{196}\right)\)	\(e\left(\frac{193}{196}\right)\)	\(e\left(\frac{23}{98}\right)\)	\(e\left(\frac{75}{196}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{47}{196}\right)\)
\(\chi_{394}(33,\cdot)\)	394.e	14	no	\(1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(1\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{394}(35,\cdot)\)	394.i	196	no	\(-1\)	\(1\)	\(e\left(\frac{3}{196}\right)\)	\(e\left(\frac{139}{196}\right)\)	\(e\left(\frac{5}{98}\right)\)	\(e\left(\frac{3}{98}\right)\)	\(e\left(\frac{151}{196}\right)\)	\(e\left(\frac{191}{196}\right)\)	\(e\left(\frac{71}{98}\right)\)	\(e\left(\frac{125}{196}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{196}\right)\)
\(\chi_{394}(37,\cdot)\)	394.g	49	no	\(1\)	\(1\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{30}{49}\right)\)	\(e\left(\frac{20}{49}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{16}{49}\right)\)
\(\chi_{394}(39,\cdot)\)	394.h	98	no	\(1\)	\(1\)	\(e\left(\frac{23}{98}\right)\)	\(e\left(\frac{53}{98}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{47}{98}\right)\)	\(e\left(\frac{27}{98}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{11}{98}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{67}{98}\right)\)
\(\chi_{394}(41,\cdot)\)	394.h	98	no	\(1\)	\(1\)	\(e\left(\frac{57}{98}\right)\)	\(e\left(\frac{93}{98}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{27}{98}\right)\)	\(e\left(\frac{3}{98}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{23}{98}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{51}{98}\right)\)
\(\chi_{394}(43,\cdot)\)	394.h	98	no	\(1\)	\(1\)	\(e\left(\frac{3}{98}\right)\)	\(e\left(\frac{41}{98}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{53}{98}\right)\)	\(e\left(\frac{93}{98}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{27}{98}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{98}\right)\)
\(\chi_{394}(45,\cdot)\)	394.i	196	no	\(-1\)	\(1\)	\(e\left(\frac{95}{196}\right)\)	\(e\left(\frac{155}{196}\right)\)	\(e\left(\frac{93}{98}\right)\)	\(e\left(\frac{95}{98}\right)\)	\(e\left(\frac{143}{196}\right)\)	\(e\left(\frac{103}{196}\right)\)	\(e\left(\frac{27}{98}\right)\)	\(e\left(\frac{169}{196}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{85}{196}\right)\)
\(\chi_{394}(47,\cdot)\)	394.h	98	no	\(1\)	\(1\)	\(e\left(\frac{93}{98}\right)\)	\(e\left(\frac{95}{98}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{75}{98}\right)\)	\(e\left(\frac{41}{98}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{53}{98}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{98}\right)\)
\(\chi_{394}(49,\cdot)\)	394.g	49	no	\(1\)	\(1\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{29}{49}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{43}{49}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{8}{49}\right)\)
\(\chi_{394}(51,\cdot)\)	394.g	49	no	\(1\)	\(1\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{13}{49}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{18}{49}\right)\)	\(e\left(\frac{18}{49}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{12}{49}\right)\)
\(\chi_{394}(53,\cdot)\)	394.g	49	no	\(1\)	\(1\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{20}{49}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{6}{49}\right)\)
\(\chi_{394}(55,\cdot)\)	394.h	98	no	\(1\)	\(1\)	\(e\left(\frac{95}{98}\right)\)	\(e\left(\frac{57}{98}\right)\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{45}{98}\right)\)	\(e\left(\frac{5}{98}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{71}{98}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{85}{98}\right)\)
\(\chi_{394}(57,\cdot)\)	394.i	196	no	\(-1\)	\(1\)	\(e\left(\frac{71}{196}\right)\)	\(e\left(\frac{23}{196}\right)\)	\(e\left(\frac{53}{98}\right)\)	\(e\left(\frac{71}{98}\right)\)	\(e\left(\frac{111}{196}\right)\)	\(e\left(\frac{143}{196}\right)\)	\(e\left(\frac{47}{98}\right)\)	\(e\left(\frac{149}{196}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{177}{196}\right)\)
\(\chi_{394}(59,\cdot)\)	394.g	49	no	\(1\)	\(1\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{17}{49}\right)\)
\(\chi_{394}(61,\cdot)\)	394.g	49	no	\(1\)	\(1\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{38}{49}\right)\)
\(\chi_{394}(63,\cdot)\)	394.g	49	no	\(1\)	\(1\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{20}{49}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{8}{49}\right)\)	\(e\left(\frac{39}{49}\right)\)	\(e\left(\frac{39}{49}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{26}{49}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 196 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.