LMFDB - Dirichlet character orbit 40310.dr

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40310, base_ring=CyclotomicField(92)) M = H._module chi = DirichletCharacter(H, M([23,46,68])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(57,40310)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$40310$
Conductor:	$20155$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$92$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 20155.dp	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{92})$
Fixed field:	Number field defined by a degree 92 polynomial

First 31 of 44 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{40310}(57,\cdot)$	$-1$	$1$	$e\left(\frac{51}{92}\right)$	$e\left(\frac{19}{92}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{5}{92}\right)$	$e\left(\frac{77}{92}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{65}{92}\right)$	$e\left(\frac{61}{92}\right)$
$\chi_{40310}(173,\cdot)$	$-1$	$1$	$e\left(\frac{77}{92}\right)$	$e\left(\frac{81}{92}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{31}{92}\right)$	$e\left(\frac{91}{92}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{35}{92}\right)$	$e\left(\frac{47}{92}\right)$
$\chi_{40310}(1797,\cdot)$	$-1$	$1$	$e\left(\frac{55}{92}\right)$	$e\left(\frac{71}{92}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{9}{92}\right)$	$e\left(\frac{65}{92}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{25}{92}\right)$	$e\left(\frac{73}{92}\right)$
$\chi_{40310}(1913,\cdot)$	$-1$	$1$	$e\left(\frac{1}{92}\right)$	$e\left(\frac{13}{92}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{47}{92}\right)$	$e\left(\frac{43}{92}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{59}{92}\right)$	$e\left(\frac{3}{92}\right)$
$\chi_{40310}(4233,\cdot)$	$-1$	$1$	$e\left(\frac{89}{92}\right)$	$e\left(\frac{53}{92}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{43}{92}\right)$	$e\left(\frac{55}{92}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{7}{92}\right)$	$e\left(\frac{83}{92}\right)$
$\chi_{40310}(6727,\cdot)$	$-1$	$1$	$e\left(\frac{35}{92}\right)$	$e\left(\frac{87}{92}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{81}{92}\right)$	$e\left(\frac{33}{92}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{41}{92}\right)$	$e\left(\frac{13}{92}\right)$
$\chi_{40310}(7133,\cdot)$	$-1$	$1$	$e\left(\frac{85}{92}\right)$	$e\left(\frac{1}{92}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{39}{92}\right)$	$e\left(\frac{67}{92}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{47}{92}\right)$	$e\left(\frac{71}{92}\right)$
$\chi_{40310}(7307,\cdot)$	$-1$	$1$	$e\left(\frac{7}{92}\right)$	$e\left(\frac{91}{92}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{53}{92}\right)$	$e\left(\frac{25}{92}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{45}{92}\right)$	$e\left(\frac{21}{92}\right)$
$\chi_{40310}(7597,\cdot)$	$-1$	$1$	$e\left(\frac{11}{92}\right)$	$e\left(\frac{51}{92}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{57}{92}\right)$	$e\left(\frac{13}{92}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{5}{92}\right)$	$e\left(\frac{33}{92}\right)$
$\chi_{40310}(8003,\cdot)$	$-1$	$1$	$e\left(\frac{45}{92}\right)$	$e\left(\frac{33}{92}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{91}{92}\right)$	$e\left(\frac{3}{92}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{79}{92}\right)$	$e\left(\frac{43}{92}\right)$
$\chi_{40310}(8873,\cdot)$	$-1$	$1$	$e\left(\frac{25}{92}\right)$	$e\left(\frac{49}{92}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{71}{92}\right)$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{3}{92}\right)$	$e\left(\frac{75}{92}\right)$
$\chi_{40310}(9627,\cdot)$	$-1$	$1$	$e\left(\frac{19}{92}\right)$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{65}{92}\right)$	$e\left(\frac{81}{92}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{17}{92}\right)$	$e\left(\frac{57}{92}\right)$
$\chi_{40310}(12933,\cdot)$	$-1$	$1$	$e\left(\frac{21}{92}\right)$	$e\left(\frac{89}{92}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{67}{92}\right)$	$e\left(\frac{75}{92}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{43}{92}\right)$	$e\left(\frac{63}{92}\right)$
$\chi_{40310}(13687,\cdot)$	$-1$	$1$	$e\left(\frac{75}{92}\right)$	$e\left(\frac{55}{92}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{29}{92}\right)$	$e\left(\frac{5}{92}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{9}{92}\right)$	$e\left(\frac{41}{92}\right)$
$\chi_{40310}(13977,\cdot)$	$-1$	$1$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{83}{92}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{17}{92}\right)$	$e\left(\frac{41}{92}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{37}{92}\right)$	$e\left(\frac{5}{92}\right)$
$\chi_{40310}(15137,\cdot)$	$-1$	$1$	$e\left(\frac{83}{92}\right)$	$e\left(\frac{67}{92}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{37}{92}\right)$	$e\left(\frac{73}{92}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{21}{92}\right)$	$e\left(\frac{65}{92}\right)$
$\chi_{40310}(16297,\cdot)$	$-1$	$1$	$e\left(\frac{31}{92}\right)$	$e\left(\frac{35}{92}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{77}{92}\right)$	$e\left(\frac{45}{92}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{81}{92}\right)$	$e\left(\frac{1}{92}\right)$
$\chi_{40310}(18037,\cdot)$	$-1$	$1$	$e\left(\frac{47}{92}\right)$	$e\left(\frac{59}{92}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{1}{92}\right)$	$e\left(\frac{89}{92}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{13}{92}\right)$	$e\left(\frac{49}{92}\right)$
$\chi_{40310}(19313,\cdot)$	$-1$	$1$	$e\left(\frac{13}{92}\right)$	$e\left(\frac{77}{92}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{59}{92}\right)$	$e\left(\frac{7}{92}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{31}{92}\right)$	$e\left(\frac{39}{92}\right)$
$\chi_{40310}(20357,\cdot)$	$-1$	$1$	$e\left(\frac{43}{92}\right)$	$e\left(\frac{7}{92}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{89}{92}\right)$	$e\left(\frac{9}{92}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{53}{92}\right)$	$e\left(\frac{37}{92}\right)$
$\chi_{40310}(20763,\cdot)$	$-1$	$1$	$e\left(\frac{33}{92}\right)$	$e\left(\frac{61}{92}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{79}{92}\right)$	$e\left(\frac{39}{92}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{15}{92}\right)$	$e\left(\frac{7}{92}\right)$
$\chi_{40310}(21053,\cdot)$	$-1$	$1$	$e\left(\frac{49}{92}\right)$	$e\left(\frac{85}{92}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{3}{92}\right)$	$e\left(\frac{83}{92}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{39}{92}\right)$	$e\left(\frac{55}{92}\right)$
$\chi_{40310}(21923,\cdot)$	$-1$	$1$	$e\left(\frac{41}{92}\right)$	$e\left(\frac{73}{92}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{87}{92}\right)$	$e\left(\frac{15}{92}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{27}{92}\right)$	$e\left(\frac{31}{92}\right)$
$\chi_{40310}(22213,\cdot)$	$-1$	$1$	$e\left(\frac{73}{92}\right)$	$e\left(\frac{29}{92}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{27}{92}\right)$	$e\left(\frac{11}{92}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{75}{92}\right)$	$e\left(\frac{35}{92}\right)$
$\chi_{40310}(23257,\cdot)$	$-1$	$1$	$e\left(\frac{39}{92}\right)$	$e\left(\frac{47}{92}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{85}{92}\right)$	$e\left(\frac{21}{92}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{1}{92}\right)$	$e\left(\frac{25}{92}\right)$
$\chi_{40310}(23953,\cdot)$	$-1$	$1$	$e\left(\frac{61}{92}\right)$	$e\left(\frac{57}{92}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{15}{92}\right)$	$e\left(\frac{47}{92}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{11}{92}\right)$	$e\left(\frac{91}{92}\right)$
$\chi_{40310}(24127,\cdot)$	$-1$	$1$	$e\left(\frac{91}{92}\right)$	$e\left(\frac{79}{92}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{45}{92}\right)$	$e\left(\frac{49}{92}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{33}{92}\right)$	$e\left(\frac{89}{92}\right)$
$\chi_{40310}(24243,\cdot)$	$-1$	$1$	$e\left(\frac{5}{92}\right)$	$e\left(\frac{65}{92}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{51}{92}\right)$	$e\left(\frac{31}{92}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{19}{92}\right)$	$e\left(\frac{15}{92}\right)$
$\chi_{40310}(24997,\cdot)$	$-1$	$1$	$e\left(\frac{71}{92}\right)$	$e\left(\frac{3}{92}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{25}{92}\right)$	$e\left(\frac{17}{92}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{49}{92}\right)$	$e\left(\frac{29}{92}\right)$
$\chi_{40310}(25983,\cdot)$	$-1$	$1$	$e\left(\frac{9}{92}\right)$	$e\left(\frac{25}{92}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{55}{92}\right)$	$e\left(\frac{19}{92}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{71}{92}\right)$	$e\left(\frac{27}{92}\right)$
$\chi_{40310}(29057,\cdot)$	$-1$	$1$	$e\left(\frac{67}{92}\right)$	$e\left(\frac{43}{92}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{21}{92}\right)$	$e\left(\frac{29}{92}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{89}{92}\right)$	$e\left(\frac{17}{92}\right)$

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

Character	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{40310}(57,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{51}{92}\right)\)	\(e\left(\frac{19}{92}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{5}{92}\right)\)	\(e\left(\frac{77}{92}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{65}{92}\right)\)	\(e\left(\frac{61}{92}\right)\)
\(\chi_{40310}(173,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{77}{92}\right)\)	\(e\left(\frac{81}{92}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{31}{92}\right)\)	\(e\left(\frac{91}{92}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{35}{92}\right)\)	\(e\left(\frac{47}{92}\right)\)
\(\chi_{40310}(1797,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{55}{92}\right)\)	\(e\left(\frac{71}{92}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{9}{92}\right)\)	\(e\left(\frac{65}{92}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{25}{92}\right)\)	\(e\left(\frac{73}{92}\right)\)
\(\chi_{40310}(1913,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{92}\right)\)	\(e\left(\frac{13}{92}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{47}{92}\right)\)	\(e\left(\frac{43}{92}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{59}{92}\right)\)	\(e\left(\frac{3}{92}\right)\)
\(\chi_{40310}(4233,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{89}{92}\right)\)	\(e\left(\frac{53}{92}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{43}{92}\right)\)	\(e\left(\frac{55}{92}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{7}{92}\right)\)	\(e\left(\frac{83}{92}\right)\)
\(\chi_{40310}(6727,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{92}\right)\)	\(e\left(\frac{87}{92}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{81}{92}\right)\)	\(e\left(\frac{33}{92}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{41}{92}\right)\)	\(e\left(\frac{13}{92}\right)\)
\(\chi_{40310}(7133,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{85}{92}\right)\)	\(e\left(\frac{1}{92}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{39}{92}\right)\)	\(e\left(\frac{67}{92}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{47}{92}\right)\)	\(e\left(\frac{71}{92}\right)\)
\(\chi_{40310}(7307,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{92}\right)\)	\(e\left(\frac{91}{92}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{53}{92}\right)\)	\(e\left(\frac{25}{92}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{45}{92}\right)\)	\(e\left(\frac{21}{92}\right)\)
\(\chi_{40310}(7597,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{92}\right)\)	\(e\left(\frac{51}{92}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{57}{92}\right)\)	\(e\left(\frac{13}{92}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{5}{92}\right)\)	\(e\left(\frac{33}{92}\right)\)
\(\chi_{40310}(8003,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{45}{92}\right)\)	\(e\left(\frac{33}{92}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{91}{92}\right)\)	\(e\left(\frac{3}{92}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{79}{92}\right)\)	\(e\left(\frac{43}{92}\right)\)
\(\chi_{40310}(8873,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{92}\right)\)	\(e\left(\frac{49}{92}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{71}{92}\right)\)	\(e\left(\frac{63}{92}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{3}{92}\right)\)	\(e\left(\frac{75}{92}\right)\)
\(\chi_{40310}(9627,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{92}\right)\)	\(e\left(\frac{63}{92}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{65}{92}\right)\)	\(e\left(\frac{81}{92}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{17}{92}\right)\)	\(e\left(\frac{57}{92}\right)\)
\(\chi_{40310}(12933,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21}{92}\right)\)	\(e\left(\frac{89}{92}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{67}{92}\right)\)	\(e\left(\frac{75}{92}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{43}{92}\right)\)	\(e\left(\frac{63}{92}\right)\)
\(\chi_{40310}(13687,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{75}{92}\right)\)	\(e\left(\frac{55}{92}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{29}{92}\right)\)	\(e\left(\frac{5}{92}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{9}{92}\right)\)	\(e\left(\frac{41}{92}\right)\)
\(\chi_{40310}(13977,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{63}{92}\right)\)	\(e\left(\frac{83}{92}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{17}{92}\right)\)	\(e\left(\frac{41}{92}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{37}{92}\right)\)	\(e\left(\frac{5}{92}\right)\)
\(\chi_{40310}(15137,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{92}\right)\)	\(e\left(\frac{67}{92}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{37}{92}\right)\)	\(e\left(\frac{73}{92}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{21}{92}\right)\)	\(e\left(\frac{65}{92}\right)\)
\(\chi_{40310}(16297,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{92}\right)\)	\(e\left(\frac{35}{92}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{77}{92}\right)\)	\(e\left(\frac{45}{92}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{81}{92}\right)\)	\(e\left(\frac{1}{92}\right)\)
\(\chi_{40310}(18037,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{92}\right)\)	\(e\left(\frac{59}{92}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{1}{92}\right)\)	\(e\left(\frac{89}{92}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{13}{92}\right)\)	\(e\left(\frac{49}{92}\right)\)
\(\chi_{40310}(19313,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{92}\right)\)	\(e\left(\frac{77}{92}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{59}{92}\right)\)	\(e\left(\frac{7}{92}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{31}{92}\right)\)	\(e\left(\frac{39}{92}\right)\)
\(\chi_{40310}(20357,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{92}\right)\)	\(e\left(\frac{7}{92}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{89}{92}\right)\)	\(e\left(\frac{9}{92}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{53}{92}\right)\)	\(e\left(\frac{37}{92}\right)\)
\(\chi_{40310}(20763,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{33}{92}\right)\)	\(e\left(\frac{61}{92}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{79}{92}\right)\)	\(e\left(\frac{39}{92}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{15}{92}\right)\)	\(e\left(\frac{7}{92}\right)\)
\(\chi_{40310}(21053,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{92}\right)\)	\(e\left(\frac{85}{92}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{3}{92}\right)\)	\(e\left(\frac{83}{92}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{39}{92}\right)\)	\(e\left(\frac{55}{92}\right)\)
\(\chi_{40310}(21923,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{92}\right)\)	\(e\left(\frac{73}{92}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{87}{92}\right)\)	\(e\left(\frac{15}{92}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{27}{92}\right)\)	\(e\left(\frac{31}{92}\right)\)
\(\chi_{40310}(22213,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{92}\right)\)	\(e\left(\frac{29}{92}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{27}{92}\right)\)	\(e\left(\frac{11}{92}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{75}{92}\right)\)	\(e\left(\frac{35}{92}\right)\)
\(\chi_{40310}(23257,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{39}{92}\right)\)	\(e\left(\frac{47}{92}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{85}{92}\right)\)	\(e\left(\frac{21}{92}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{1}{92}\right)\)	\(e\left(\frac{25}{92}\right)\)
\(\chi_{40310}(23953,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{92}\right)\)	\(e\left(\frac{57}{92}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{15}{92}\right)\)	\(e\left(\frac{47}{92}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{11}{92}\right)\)	\(e\left(\frac{91}{92}\right)\)
\(\chi_{40310}(24127,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{92}\right)\)	\(e\left(\frac{79}{92}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{45}{92}\right)\)	\(e\left(\frac{49}{92}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{33}{92}\right)\)	\(e\left(\frac{89}{92}\right)\)
\(\chi_{40310}(24243,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{92}\right)\)	\(e\left(\frac{65}{92}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{51}{92}\right)\)	\(e\left(\frac{31}{92}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{19}{92}\right)\)	\(e\left(\frac{15}{92}\right)\)
\(\chi_{40310}(24997,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{92}\right)\)	\(e\left(\frac{3}{92}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{25}{92}\right)\)	\(e\left(\frac{17}{92}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{49}{92}\right)\)	\(e\left(\frac{29}{92}\right)\)
\(\chi_{40310}(25983,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{92}\right)\)	\(e\left(\frac{25}{92}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{55}{92}\right)\)	\(e\left(\frac{19}{92}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{71}{92}\right)\)	\(e\left(\frac{27}{92}\right)\)
\(\chi_{40310}(29057,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{92}\right)\)	\(e\left(\frac{43}{92}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{21}{92}\right)\)	\(e\left(\frac{29}{92}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{89}{92}\right)\)	\(e\left(\frac{17}{92}\right)\)

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First 31 of 44 characters in Galois orbit

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

Label	40310.dr
Modulus	$40310$
Conductor	$20155$
Order	$92$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(40310\)
Conductor:	\(20155\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(92\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 20155.dp	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)