LMFDB - Dirichlet character orbit 6304.cn

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6304, base_ring=CyclotomicField(196)) M = H._module chi = DirichletCharacter(H, M([98,0,141])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(31,6304)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$6304$
Conductor:	$788$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$196$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 788.q	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{196})$
Fixed field:	Number field defined by a degree 196 polynomial (not computed)

First 31 of 84 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{6304}(31,\cdot)$	$1$	$1$	$e\left(\frac{139}{196}\right)$	$e\left(\frac{5}{196}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{41}{98}\right)$	$e\left(\frac{71}{196}\right)$	$e\left(\frac{193}{196}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{75}{196}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{47}{196}\right)$
$\chi_{6304}(95,\cdot)$	$1$	$1$	$e\left(\frac{177}{196}\right)$	$e\left(\frac{67}{196}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{79}{98}\right)$	$e\left(\frac{89}{196}\right)$	$e\left(\frac{195}{196}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{25}{196}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{81}{196}\right)$
$\chi_{6304}(159,\cdot)$	$1$	$1$	$e\left(\frac{27}{196}\right)$	$e\left(\frac{173}{196}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{27}{98}\right)$	$e\left(\frac{183}{196}\right)$	$e\left(\frac{53}{196}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{47}{196}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{19}{196}\right)$
$\chi_{6304}(255,\cdot)$	$1$	$1$	$e\left(\frac{131}{196}\right)$	$e\left(\frac{157}{196}\right)$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{33}{98}\right)$	$e\left(\frac{191}{196}\right)$	$e\left(\frac{141}{196}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{3}{196}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{143}{196}\right)$
$\chi_{6304}(319,\cdot)$	$1$	$1$	$e\left(\frac{103}{196}\right)$	$e\left(\frac{101}{196}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{5}{98}\right)$	$e\left(\frac{23}{196}\right)$	$e\left(\frac{57}{196}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{143}{196}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{87}{196}\right)$
$\chi_{6304}(383,\cdot)$	$1$	$1$	$e\left(\frac{153}{196}\right)$	$e\left(\frac{131}{196}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{55}{98}\right)$	$e\left(\frac{57}{196}\right)$	$e\left(\frac{39}{196}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{5}{196}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{173}{196}\right)$
$\chi_{6304}(415,\cdot)$	$1$	$1$	$e\left(\frac{93}{196}\right)$	$e\left(\frac{95}{196}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{93}{98}\right)$	$e\left(\frac{173}{196}\right)$	$e\left(\frac{139}{196}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{53}{196}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{109}{196}\right)$
$\chi_{6304}(511,\cdot)$	$1$	$1$	$e\left(\frac{173}{196}\right)$	$e\left(\frac{143}{196}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{75}{98}\right)$	$e\left(\frac{149}{196}\right)$	$e\left(\frac{71}{196}\right)$	$e\left(\frac{30}{49}\right)$	$e\left(\frac{185}{196}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{129}{196}\right)$
$\chi_{6304}(543,\cdot)$	$1$	$1$	$e\left(\frac{165}{196}\right)$	$e\left(\frac{99}{196}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{67}{98}\right)$	$e\left(\frac{73}{196}\right)$	$e\left(\frac{19}{196}\right)$	$e\left(\frac{17}{49}\right)$	$e\left(\frac{113}{196}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{29}{196}\right)$
$\chi_{6304}(639,\cdot)$	$1$	$1$	$e\left(\frac{67}{196}\right)$	$e\left(\frac{1}{196}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{67}{98}\right)$	$e\left(\frac{171}{196}\right)$	$e\left(\frac{117}{196}\right)$	$e\left(\frac{17}{49}\right)$	$e\left(\frac{15}{196}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{127}{196}\right)$
$\chi_{6304}(671,\cdot)$	$1$	$1$	$e\left(\frac{75}{196}\right)$	$e\left(\frac{45}{196}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{75}{98}\right)$	$e\left(\frac{51}{196}\right)$	$e\left(\frac{169}{196}\right)$	$e\left(\frac{30}{49}\right)$	$e\left(\frac{87}{196}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{31}{196}\right)$
$\chi_{6304}(767,\cdot)$	$1$	$1$	$e\left(\frac{191}{196}\right)$	$e\left(\frac{193}{196}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{93}{98}\right)$	$e\left(\frac{75}{196}\right)$	$e\left(\frac{41}{196}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{151}{196}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{196}\right)$
$\chi_{6304}(799,\cdot)$	$1$	$1$	$e\left(\frac{55}{196}\right)$	$e\left(\frac{33}{196}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{55}{98}\right)$	$e\left(\frac{155}{196}\right)$	$e\left(\frac{137}{196}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{103}{196}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{75}{196}\right)$
$\chi_{6304}(863,\cdot)$	$1$	$1$	$e\left(\frac{5}{196}\right)$	$e\left(\frac{3}{196}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{5}{98}\right)$	$e\left(\frac{121}{196}\right)$	$e\left(\frac{155}{196}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{45}{196}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{185}{196}\right)$
$\chi_{6304}(927,\cdot)$	$1$	$1$	$e\left(\frac{33}{196}\right)$	$e\left(\frac{59}{196}\right)$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{33}{98}\right)$	$e\left(\frac{93}{196}\right)$	$e\left(\frac{43}{196}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{101}{196}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{45}{196}\right)$
$\chi_{6304}(1023,\cdot)$	$1$	$1$	$e\left(\frac{125}{196}\right)$	$e\left(\frac{75}{196}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{27}{98}\right)$	$e\left(\frac{85}{196}\right)$	$e\left(\frac{151}{196}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{145}{196}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{117}{196}\right)$
$\chi_{6304}(1087,\cdot)$	$1$	$1$	$e\left(\frac{79}{196}\right)$	$e\left(\frac{165}{196}\right)$	$e\left(\frac{25}{49}\right)$	$e\left(\frac{79}{98}\right)$	$e\left(\frac{187}{196}\right)$	$e\left(\frac{97}{196}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{123}{196}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{179}{196}\right)$
$\chi_{6304}(1151,\cdot)$	$1$	$1$	$e\left(\frac{41}{196}\right)$	$e\left(\frac{103}{196}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{41}{98}\right)$	$e\left(\frac{169}{196}\right)$	$e\left(\frac{95}{196}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{173}{196}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{145}{196}\right)$
$\chi_{6304}(1503,\cdot)$	$1$	$1$	$e\left(\frac{109}{196}\right)$	$e\left(\frac{183}{196}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{11}{98}\right)$	$e\left(\frac{129}{196}\right)$	$e\left(\frac{47}{196}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{1}{196}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{113}{196}\right)$
$\chi_{6304}(1695,\cdot)$	$1$	$1$	$e\left(\frac{31}{196}\right)$	$e\left(\frac{97}{196}\right)$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{31}{98}\right)$	$e\left(\frac{123}{196}\right)$	$e\left(\frac{177}{196}\right)$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{83}{196}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{167}{196}\right)$
$\chi_{6304}(1727,\cdot)$	$1$	$1$	$e\left(\frac{145}{196}\right)$	$e\left(\frac{87}{196}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{47}{98}\right)$	$e\left(\frac{177}{196}\right)$	$e\left(\frac{183}{196}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{129}{196}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{73}{196}\right)$
$\chi_{6304}(1791,\cdot)$	$1$	$1$	$e\left(\frac{141}{196}\right)$	$e\left(\frac{163}{196}\right)$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{41}{196}\right)$	$e\left(\frac{59}{196}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{93}{196}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{121}{196}\right)$
$\chi_{6304}(1823,\cdot)$	$1$	$1$	$e\left(\frac{157}{196}\right)$	$e\left(\frac{55}{196}\right)$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{59}{98}\right)$	$e\left(\frac{193}{196}\right)$	$e\left(\frac{163}{196}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{41}{196}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{125}{196}\right)$
$\chi_{6304}(1855,\cdot)$	$1$	$1$	$e\left(\frac{1}{196}\right)$	$e\left(\frac{79}{196}\right)$	$e\left(\frac{9}{49}\right)$	$e\left(\frac{1}{98}\right)$	$e\left(\frac{181}{196}\right)$	$e\left(\frac{31}{196}\right)$	$e\left(\frac{20}{49}\right)$	$e\left(\frac{9}{196}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{37}{196}\right)$
$\chi_{6304}(1983,\cdot)$	$1$	$1$	$e\left(\frac{115}{196}\right)$	$e\left(\frac{69}{196}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{17}{98}\right)$	$e\left(\frac{39}{196}\right)$	$e\left(\frac{37}{196}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{55}{196}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{139}{196}\right)$
$\chi_{6304}(2015,\cdot)$	$1$	$1$	$e\left(\frac{193}{196}\right)$	$e\left(\frac{155}{196}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{95}{98}\right)$	$e\left(\frac{45}{196}\right)$	$e\left(\frac{103}{196}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{169}{196}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{85}{196}\right)$
$\chi_{6304}(2111,\cdot)$	$1$	$1$	$e\left(\frac{117}{196}\right)$	$e\left(\frac{31}{196}\right)$	$e\left(\frac{24}{49}\right)$	$e\left(\frac{19}{98}\right)$	$e\left(\frac{9}{196}\right)$	$e\left(\frac{99}{196}\right)$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{73}{196}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{17}{196}\right)$
$\chi_{6304}(2175,\cdot)$	$1$	$1$	$e\left(\frac{53}{196}\right)$	$e\left(\frac{71}{196}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{53}{98}\right)$	$e\left(\frac{185}{196}\right)$	$e\left(\frac{75}{196}\right)$	$e\left(\frac{31}{49}\right)$	$e\left(\frac{85}{196}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{196}\right)$
$\chi_{6304}(2239,\cdot)$	$1$	$1$	$e\left(\frac{111}{196}\right)$	$e\left(\frac{145}{196}\right)$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{13}{98}\right)$	$e\left(\frac{99}{196}\right)$	$e\left(\frac{109}{196}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{19}{196}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{187}{196}\right)$
$\chi_{6304}(2367,\cdot)$	$1$	$1$	$e\left(\frac{127}{196}\right)$	$e\left(\frac{37}{196}\right)$	$e\left(\frac{16}{49}\right)$	$e\left(\frac{29}{98}\right)$	$e\left(\frac{55}{196}\right)$	$e\left(\frac{17}{196}\right)$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{163}{196}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{191}{196}\right)$
$\chi_{6304}(2399,\cdot)$	$1$	$1$	$e\left(\frac{101}{196}\right)$	$e\left(\frac{139}{196}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{3}{98}\right)$	$e\left(\frac{53}{196}\right)$	$e\left(\frac{191}{196}\right)$	$e\left(\frac{11}{49}\right)$	$e\left(\frac{125}{196}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{196}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{6304}(31,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{196}\right)\)	\(e\left(\frac{5}{196}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{41}{98}\right)\)	\(e\left(\frac{71}{196}\right)\)	\(e\left(\frac{193}{196}\right)\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{75}{196}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{47}{196}\right)\)
\(\chi_{6304}(95,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{177}{196}\right)\)	\(e\left(\frac{67}{196}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{79}{98}\right)\)	\(e\left(\frac{89}{196}\right)\)	\(e\left(\frac{195}{196}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{25}{196}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{81}{196}\right)\)
\(\chi_{6304}(159,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{196}\right)\)	\(e\left(\frac{173}{196}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{27}{98}\right)\)	\(e\left(\frac{183}{196}\right)\)	\(e\left(\frac{53}{196}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{47}{196}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{19}{196}\right)\)
\(\chi_{6304}(255,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{196}\right)\)	\(e\left(\frac{157}{196}\right)\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{33}{98}\right)\)	\(e\left(\frac{191}{196}\right)\)	\(e\left(\frac{141}{196}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{3}{196}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{143}{196}\right)\)
\(\chi_{6304}(319,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{196}\right)\)	\(e\left(\frac{101}{196}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{5}{98}\right)\)	\(e\left(\frac{23}{196}\right)\)	\(e\left(\frac{57}{196}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{143}{196}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{87}{196}\right)\)
\(\chi_{6304}(383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{153}{196}\right)\)	\(e\left(\frac{131}{196}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{55}{98}\right)\)	\(e\left(\frac{57}{196}\right)\)	\(e\left(\frac{39}{196}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{5}{196}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{173}{196}\right)\)
\(\chi_{6304}(415,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{93}{196}\right)\)	\(e\left(\frac{95}{196}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{93}{98}\right)\)	\(e\left(\frac{173}{196}\right)\)	\(e\left(\frac{139}{196}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{53}{196}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{109}{196}\right)\)
\(\chi_{6304}(511,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{196}\right)\)	\(e\left(\frac{143}{196}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{75}{98}\right)\)	\(e\left(\frac{149}{196}\right)\)	\(e\left(\frac{71}{196}\right)\)	\(e\left(\frac{30}{49}\right)\)	\(e\left(\frac{185}{196}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{129}{196}\right)\)
\(\chi_{6304}(543,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{165}{196}\right)\)	\(e\left(\frac{99}{196}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{67}{98}\right)\)	\(e\left(\frac{73}{196}\right)\)	\(e\left(\frac{19}{196}\right)\)	\(e\left(\frac{17}{49}\right)\)	\(e\left(\frac{113}{196}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{29}{196}\right)\)
\(\chi_{6304}(639,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{196}\right)\)	\(e\left(\frac{1}{196}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{67}{98}\right)\)	\(e\left(\frac{171}{196}\right)\)	\(e\left(\frac{117}{196}\right)\)	\(e\left(\frac{17}{49}\right)\)	\(e\left(\frac{15}{196}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{127}{196}\right)\)
\(\chi_{6304}(671,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{75}{196}\right)\)	\(e\left(\frac{45}{196}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{75}{98}\right)\)	\(e\left(\frac{51}{196}\right)\)	\(e\left(\frac{169}{196}\right)\)	\(e\left(\frac{30}{49}\right)\)	\(e\left(\frac{87}{196}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{31}{196}\right)\)
\(\chi_{6304}(767,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{196}\right)\)	\(e\left(\frac{193}{196}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{93}{98}\right)\)	\(e\left(\frac{75}{196}\right)\)	\(e\left(\frac{41}{196}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{151}{196}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{196}\right)\)
\(\chi_{6304}(799,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{196}\right)\)	\(e\left(\frac{33}{196}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{55}{98}\right)\)	\(e\left(\frac{155}{196}\right)\)	\(e\left(\frac{137}{196}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{103}{196}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{75}{196}\right)\)
\(\chi_{6304}(863,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{196}\right)\)	\(e\left(\frac{3}{196}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{5}{98}\right)\)	\(e\left(\frac{121}{196}\right)\)	\(e\left(\frac{155}{196}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{45}{196}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{185}{196}\right)\)
\(\chi_{6304}(927,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{196}\right)\)	\(e\left(\frac{59}{196}\right)\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{33}{98}\right)\)	\(e\left(\frac{93}{196}\right)\)	\(e\left(\frac{43}{196}\right)\)	\(e\left(\frac{23}{49}\right)\)	\(e\left(\frac{101}{196}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{45}{196}\right)\)
\(\chi_{6304}(1023,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{196}\right)\)	\(e\left(\frac{75}{196}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{27}{98}\right)\)	\(e\left(\frac{85}{196}\right)\)	\(e\left(\frac{151}{196}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{145}{196}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{117}{196}\right)\)
\(\chi_{6304}(1087,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{196}\right)\)	\(e\left(\frac{165}{196}\right)\)	\(e\left(\frac{25}{49}\right)\)	\(e\left(\frac{79}{98}\right)\)	\(e\left(\frac{187}{196}\right)\)	\(e\left(\frac{97}{196}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{123}{196}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{179}{196}\right)\)
\(\chi_{6304}(1151,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{196}\right)\)	\(e\left(\frac{103}{196}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{41}{98}\right)\)	\(e\left(\frac{169}{196}\right)\)	\(e\left(\frac{95}{196}\right)\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{173}{196}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{145}{196}\right)\)
\(\chi_{6304}(1503,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{196}\right)\)	\(e\left(\frac{183}{196}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{11}{98}\right)\)	\(e\left(\frac{129}{196}\right)\)	\(e\left(\frac{47}{196}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{1}{196}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{113}{196}\right)\)
\(\chi_{6304}(1695,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{196}\right)\)	\(e\left(\frac{97}{196}\right)\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{31}{98}\right)\)	\(e\left(\frac{123}{196}\right)\)	\(e\left(\frac{177}{196}\right)\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{83}{196}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{167}{196}\right)\)
\(\chi_{6304}(1727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{145}{196}\right)\)	\(e\left(\frac{87}{196}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{47}{98}\right)\)	\(e\left(\frac{177}{196}\right)\)	\(e\left(\frac{183}{196}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{129}{196}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{73}{196}\right)\)
\(\chi_{6304}(1791,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{141}{196}\right)\)	\(e\left(\frac{163}{196}\right)\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{41}{196}\right)\)	\(e\left(\frac{59}{196}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{93}{196}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{121}{196}\right)\)
\(\chi_{6304}(1823,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{196}\right)\)	\(e\left(\frac{55}{196}\right)\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{59}{98}\right)\)	\(e\left(\frac{193}{196}\right)\)	\(e\left(\frac{163}{196}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{41}{196}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{125}{196}\right)\)
\(\chi_{6304}(1855,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{196}\right)\)	\(e\left(\frac{79}{196}\right)\)	\(e\left(\frac{9}{49}\right)\)	\(e\left(\frac{1}{98}\right)\)	\(e\left(\frac{181}{196}\right)\)	\(e\left(\frac{31}{196}\right)\)	\(e\left(\frac{20}{49}\right)\)	\(e\left(\frac{9}{196}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{37}{196}\right)\)
\(\chi_{6304}(1983,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{196}\right)\)	\(e\left(\frac{69}{196}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{17}{98}\right)\)	\(e\left(\frac{39}{196}\right)\)	\(e\left(\frac{37}{196}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{55}{196}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{139}{196}\right)\)
\(\chi_{6304}(2015,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{196}\right)\)	\(e\left(\frac{155}{196}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{95}{98}\right)\)	\(e\left(\frac{45}{196}\right)\)	\(e\left(\frac{103}{196}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{169}{196}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{85}{196}\right)\)
\(\chi_{6304}(2111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{117}{196}\right)\)	\(e\left(\frac{31}{196}\right)\)	\(e\left(\frac{24}{49}\right)\)	\(e\left(\frac{19}{98}\right)\)	\(e\left(\frac{9}{196}\right)\)	\(e\left(\frac{99}{196}\right)\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{73}{196}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{17}{196}\right)\)
\(\chi_{6304}(2175,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{196}\right)\)	\(e\left(\frac{71}{196}\right)\)	\(e\left(\frac{36}{49}\right)\)	\(e\left(\frac{53}{98}\right)\)	\(e\left(\frac{185}{196}\right)\)	\(e\left(\frac{75}{196}\right)\)	\(e\left(\frac{31}{49}\right)\)	\(e\left(\frac{85}{196}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{196}\right)\)
\(\chi_{6304}(2239,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{111}{196}\right)\)	\(e\left(\frac{145}{196}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{13}{98}\right)\)	\(e\left(\frac{99}{196}\right)\)	\(e\left(\frac{109}{196}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{19}{196}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{187}{196}\right)\)
\(\chi_{6304}(2367,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{196}\right)\)	\(e\left(\frac{37}{196}\right)\)	\(e\left(\frac{16}{49}\right)\)	\(e\left(\frac{29}{98}\right)\)	\(e\left(\frac{55}{196}\right)\)	\(e\left(\frac{17}{196}\right)\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{163}{196}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{191}{196}\right)\)
\(\chi_{6304}(2399,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{196}\right)\)	\(e\left(\frac{139}{196}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{3}{98}\right)\)	\(e\left(\frac{53}{196}\right)\)	\(e\left(\frac{191}{196}\right)\)	\(e\left(\frac{11}{49}\right)\)	\(e\left(\frac{125}{196}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{196}\right)\)

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First 31 of 84 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	6304.cn
Modulus	$6304$
Conductor	$788$
Order	$196$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(6304\)
Conductor:	\(788\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(196\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 788.q	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)