LMFDB - Dirichlet character orbit 6304.db

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6304, base_ring=CyclotomicField(392)) M = H._module chi = DirichletCharacter(H, M([196,343,288])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(51,6304)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$6304$
Conductor:	$6304$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$392$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	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:	$\Q(\zeta_{392})$
Fixed field:	Number field defined by a degree 392 polynomial (not computed)

First 31 of 168 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{6304}(51,\cdot)$	$-1$	$1$	$e\left(\frac{41}{392}\right)$	$e\left(\frac{103}{392}\right)$	$e\left(\frac{101}{196}\right)$	$e\left(\frac{41}{196}\right)$	$e\left(\frac{71}{392}\right)$	$e\left(\frac{193}{392}\right)$	$e\left(\frac{18}{49}\right)$	$e\left(\frac{31}{98}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{243}{392}\right)$
$\chi_{6304}(59,\cdot)$	$-1$	$1$	$e\left(\frac{103}{392}\right)$	$e\left(\frac{297}{392}\right)$	$e\left(\frac{139}{196}\right)$	$e\left(\frac{103}{196}\right)$	$e\left(\frac{121}{392}\right)$	$e\left(\frac{351}{392}\right)$	$e\left(\frac{1}{49}\right)$	$e\left(\frac{97}{98}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{381}{392}\right)$
$\chi_{6304}(171,\cdot)$	$-1$	$1$	$e\left(\frac{347}{392}\right)$	$e\left(\frac{365}{392}\right)$	$e\left(\frac{23}{196}\right)$	$e\left(\frac{151}{196}\right)$	$e\left(\frac{381}{392}\right)$	$e\left(\frac{75}{392}\right)$	$e\left(\frac{40}{49}\right)$	$e\left(\frac{9}{98}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{1}{392}\right)$
$\chi_{6304}(187,\cdot)$	$-1$	$1$	$e\left(\frac{191}{392}\right)$	$e\left(\frac{193}{392}\right)$	$e\left(\frac{155}{196}\right)$	$e\left(\frac{191}{196}\right)$	$e\left(\frac{369}{392}\right)$	$e\left(\frac{335}{392}\right)$	$e\left(\frac{48}{49}\right)$	$e\left(\frac{1}{98}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{109}{392}\right)$
$\chi_{6304}(251,\cdot)$	$-1$	$1$	$e\left(\frac{95}{392}\right)$	$e\left(\frac{57}{392}\right)$	$e\left(\frac{191}{196}\right)$	$e\left(\frac{95}{196}\right)$	$e\left(\frac{241}{392}\right)$	$e\left(\frac{103}{392}\right)$	$e\left(\frac{19}{49}\right)$	$e\left(\frac{79}{98}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{85}{392}\right)$
$\chi_{6304}(267,\cdot)$	$-1$	$1$	$e\left(\frac{123}{392}\right)$	$e\left(\frac{309}{392}\right)$	$e\left(\frac{107}{196}\right)$	$e\left(\frac{123}{196}\right)$	$e\left(\frac{213}{392}\right)$	$e\left(\frac{187}{392}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{93}{98}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{337}{392}\right)$
$\chi_{6304}(339,\cdot)$	$-1$	$1$	$e\left(\frac{233}{392}\right)$	$e\left(\frac{375}{392}\right)$	$e\left(\frac{29}{196}\right)$	$e\left(\frac{37}{196}\right)$	$e\left(\frac{327}{392}\right)$	$e\left(\frac{265}{392}\right)$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{71}{98}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{291}{392}\right)$
$\chi_{6304}(347,\cdot)$	$-1$	$1$	$e\left(\frac{127}{392}\right)$	$e\left(\frac{233}{392}\right)$	$e\left(\frac{179}{196}\right)$	$e\left(\frac{127}{196}\right)$	$e\left(\frac{153}{392}\right)$	$e\left(\frac{311}{392}\right)$	$e\left(\frac{45}{49}\right)$	$e\left(\frac{53}{98}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{93}{392}\right)$
$\chi_{6304}(355,\cdot)$	$-1$	$1$	$e\left(\frac{141}{392}\right)$	$e\left(\frac{163}{392}\right)$	$e\left(\frac{137}{196}\right)$	$e\left(\frac{141}{196}\right)$	$e\left(\frac{139}{392}\right)$	$e\left(\frac{157}{392}\right)$	$e\left(\frac{38}{49}\right)$	$e\left(\frac{11}{98}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{23}{392}\right)$
$\chi_{6304}(379,\cdot)$	$-1$	$1$	$e\left(\frac{279}{392}\right)$	$e\left(\frac{89}{392}\right)$	$e\left(\frac{171}{196}\right)$	$e\left(\frac{83}{196}\right)$	$e\left(\frac{225}{392}\right)$	$e\left(\frac{319}{392}\right)$	$e\left(\frac{46}{49}\right)$	$e\left(\frac{3}{98}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{229}{392}\right)$
$\chi_{6304}(387,\cdot)$	$-1$	$1$	$e\left(\frac{373}{392}\right)$	$e\left(\frac{67}{392}\right)$	$e\left(\frac{1}{196}\right)$	$e\left(\frac{177}{196}\right)$	$e\left(\frac{187}{392}\right)$	$e\left(\frac{293}{392}\right)$	$e\left(\frac{6}{49}\right)$	$e\left(\frac{43}{98}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{375}{392}\right)$
$\chi_{6304}(443,\cdot)$	$-1$	$1$	$e\left(\frac{207}{392}\right)$	$e\left(\frac{281}{392}\right)$	$e\left(\frac{51}{196}\right)$	$e\left(\frac{11}{196}\right)$	$e\left(\frac{129}{392}\right)$	$e\left(\frac{47}{392}\right)$	$e\left(\frac{12}{49}\right)$	$e\left(\frac{37}{98}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{309}{392}\right)$
$\chi_{6304}(475,\cdot)$	$-1$	$1$	$e\left(\frac{183}{392}\right)$	$e\left(\frac{345}{392}\right)$	$e\left(\frac{11}{196}\right)$	$e\left(\frac{183}{196}\right)$	$e\left(\frac{97}{392}\right)$	$e\left(\frac{87}{392}\right)$	$e\left(\frac{17}{49}\right)$	$e\left(\frac{81}{98}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{205}{392}\right)$
$\chi_{6304}(499,\cdot)$	$-1$	$1$	$e\left(\frac{113}{392}\right)$	$e\left(\frac{303}{392}\right)$	$e\left(\frac{25}{196}\right)$	$e\left(\frac{113}{196}\right)$	$e\left(\frac{167}{392}\right)$	$e\left(\frac{73}{392}\right)$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{95}{98}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{163}{392}\right)$
$\chi_{6304}(587,\cdot)$	$-1$	$1$	$e\left(\frac{283}{392}\right)$	$e\left(\frac{13}{392}\right)$	$e\left(\frac{47}{196}\right)$	$e\left(\frac{87}{196}\right)$	$e\left(\frac{165}{392}\right)$	$e\left(\frac{51}{392}\right)$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{61}{98}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{377}{392}\right)$
$\chi_{6304}(619,\cdot)$	$-1$	$1$	$e\left(\frac{19}{392}\right)$	$e\left(\frac{325}{392}\right)$	$e\left(\frac{195}{196}\right)$	$e\left(\frac{19}{196}\right)$	$e\left(\frac{205}{392}\right)$	$e\left(\frac{99}{392}\right)$	$e\left(\frac{43}{49}\right)$	$e\left(\frac{55}{98}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{17}{392}\right)$
$\chi_{6304}(651,\cdot)$	$-1$	$1$	$e\left(\frac{219}{392}\right)$	$e\left(\frac{53}{392}\right)$	$e\left(\frac{71}{196}\right)$	$e\left(\frac{23}{196}\right)$	$e\left(\frac{341}{392}\right)$	$e\left(\frac{27}{392}\right)$	$e\left(\frac{34}{49}\right)$	$e\left(\frac{15}{98}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{361}{392}\right)$
$\chi_{6304}(667,\cdot)$	$-1$	$1$	$e\left(\frac{367}{392}\right)$	$e\left(\frac{377}{392}\right)$	$e\left(\frac{187}{196}\right)$	$e\left(\frac{171}{196}\right)$	$e\left(\frac{81}{392}\right)$	$e\left(\frac{303}{392}\right)$	$e\left(\frac{44}{49}\right)$	$e\left(\frac{5}{98}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{349}{392}\right)$
$\chi_{6304}(691,\cdot)$	$-1$	$1$	$e\left(\frac{137}{392}\right)$	$e\left(\frac{239}{392}\right)$	$e\left(\frac{65}{196}\right)$	$e\left(\frac{137}{196}\right)$	$e\left(\frac{199}{392}\right)$	$e\left(\frac{33}{392}\right)$	$e\left(\frac{47}{49}\right)$	$e\left(\frac{51}{98}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{267}{392}\right)$
$\chi_{6304}(723,\cdot)$	$-1$	$1$	$e\left(\frac{353}{392}\right)$	$e\left(\frac{55}{392}\right)$	$e\left(\frac{33}{196}\right)$	$e\left(\frac{157}{196}\right)$	$e\left(\frac{95}{392}\right)$	$e\left(\frac{65}{392}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{47}{98}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{27}{392}\right)$
$\chi_{6304}(747,\cdot)$	$-1$	$1$	$e\left(\frac{179}{392}\right)$	$e\left(\frac{29}{392}\right)$	$e\left(\frac{135}{196}\right)$	$e\left(\frac{179}{196}\right)$	$e\left(\frac{157}{392}\right)$	$e\left(\frac{355}{392}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{23}{98}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{57}{392}\right)$
$\chi_{6304}(763,\cdot)$	$-1$	$1$	$e\left(\frac{295}{392}\right)$	$e\left(\frac{177}{392}\right)$	$e\left(\frac{67}{196}\right)$	$e\left(\frac{99}{196}\right)$	$e\left(\frac{377}{392}\right)$	$e\left(\frac{31}{392}\right)$	$e\left(\frac{10}{49}\right)$	$e\left(\frac{39}{98}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{37}{392}\right)$
$\chi_{6304}(779,\cdot)$	$-1$	$1$	$e\left(\frac{67}{392}\right)$	$e\left(\frac{197}{392}\right)$	$e\left(\frac{79}{196}\right)$	$e\left(\frac{67}{196}\right)$	$e\left(\frac{269}{392}\right)$	$e\left(\frac{19}{392}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{65}{98}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{225}{392}\right)$
$\chi_{6304}(811,\cdot)$	$-1$	$1$	$e\left(\frac{75}{392}\right)$	$e\left(\frac{45}{392}\right)$	$e\left(\frac{27}{196}\right)$	$e\left(\frac{75}{196}\right)$	$e\left(\frac{149}{392}\right)$	$e\left(\frac{267}{392}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{83}{98}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{129}{392}\right)$
$\chi_{6304}(851,\cdot)$	$-1$	$1$	$e\left(\frac{97}{392}\right)$	$e\left(\frac{215}{392}\right)$	$e\left(\frac{129}{196}\right)$	$e\left(\frac{97}{196}\right)$	$e\left(\frac{15}{392}\right)$	$e\left(\frac{361}{392}\right)$	$e\left(\frac{39}{49}\right)$	$e\left(\frac{59}{98}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{355}{392}\right)$
$\chi_{6304}(923,\cdot)$	$-1$	$1$	$e\left(\frac{199}{392}\right)$	$e\left(\frac{41}{392}\right)$	$e\left(\frac{103}{196}\right)$	$e\left(\frac{3}{196}\right)$	$e\left(\frac{249}{392}\right)$	$e\left(\frac{191}{392}\right)$	$e\left(\frac{30}{49}\right)$	$e\left(\frac{19}{98}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{13}{392}\right)$
$\chi_{6304}(963,\cdot)$	$-1$	$1$	$e\left(\frac{325}{392}\right)$	$e\left(\frac{195}{392}\right)$	$e\left(\frac{117}{196}\right)$	$e\left(\frac{129}{196}\right)$	$e\left(\frac{123}{392}\right)$	$e\left(\frac{373}{392}\right)$	$e\left(\frac{16}{49}\right)$	$e\left(\frac{33}{98}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{167}{392}\right)$
$\chi_{6304}(1019,\cdot)$	$-1$	$1$	$e\left(\frac{247}{392}\right)$	$e\left(\frac{305}{392}\right)$	$e\left(\frac{183}{196}\right)$	$e\left(\frac{51}{196}\right)$	$e\left(\frac{313}{392}\right)$	$e\left(\frac{111}{392}\right)$	$e\left(\frac{20}{49}\right)$	$e\left(\frac{29}{98}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{221}{392}\right)$
$\chi_{6304}(1027,\cdot)$	$-1$	$1$	$e\left(\frac{205}{392}\right)$	$e\left(\frac{123}{392}\right)$	$e\left(\frac{113}{196}\right)$	$e\left(\frac{9}{196}\right)$	$e\left(\frac{355}{392}\right)$	$e\left(\frac{181}{392}\right)$	$e\left(\frac{41}{49}\right)$	$e\left(\frac{57}{98}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{39}{392}\right)$
$\chi_{6304}(1075,\cdot)$	$-1$	$1$	$e\left(\frac{209}{392}\right)$	$e\left(\frac{47}{392}\right)$	$e\left(\frac{185}{196}\right)$	$e\left(\frac{13}{196}\right)$	$e\left(\frac{295}{392}\right)$	$e\left(\frac{305}{392}\right)$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{17}{98}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{187}{392}\right)$
$\chi_{6304}(1139,\cdot)$	$-1$	$1$	$e\left(\frac{257}{392}\right)$	$e\left(\frac{311}{392}\right)$	$e\left(\frac{69}{196}\right)$	$e\left(\frac{61}{196}\right)$	$e\left(\frac{359}{392}\right)$	$e\left(\frac{225}{392}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{27}{98}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{3}{392}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{6304}(51,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{392}\right)\)	\(e\left(\frac{103}{392}\right)\)	\(e\left(\frac{101}{196}\right)\)	\(e\left(\frac{41}{196}\right)\)	\(e\left(\frac{71}{392}\right)\)	\(e\left(\frac{193}{392}\right)\)	\(e\left(\frac{18}{49}\right)\)	\(e\left(\frac{31}{98}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{243}{392}\right)\)
\(\chi_{6304}(59,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{103}{392}\right)\)	\(e\left(\frac{297}{392}\right)\)	\(e\left(\frac{139}{196}\right)\)	\(e\left(\frac{103}{196}\right)\)	\(e\left(\frac{121}{392}\right)\)	\(e\left(\frac{351}{392}\right)\)	\(e\left(\frac{1}{49}\right)\)	\(e\left(\frac{97}{98}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{381}{392}\right)\)
\(\chi_{6304}(171,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{347}{392}\right)\)	\(e\left(\frac{365}{392}\right)\)	\(e\left(\frac{23}{196}\right)\)	\(e\left(\frac{151}{196}\right)\)	\(e\left(\frac{381}{392}\right)\)	\(e\left(\frac{75}{392}\right)\)	\(e\left(\frac{40}{49}\right)\)	\(e\left(\frac{9}{98}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{1}{392}\right)\)
\(\chi_{6304}(187,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{191}{392}\right)\)	\(e\left(\frac{193}{392}\right)\)	\(e\left(\frac{155}{196}\right)\)	\(e\left(\frac{191}{196}\right)\)	\(e\left(\frac{369}{392}\right)\)	\(e\left(\frac{335}{392}\right)\)	\(e\left(\frac{48}{49}\right)\)	\(e\left(\frac{1}{98}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{109}{392}\right)\)
\(\chi_{6304}(251,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{95}{392}\right)\)	\(e\left(\frac{57}{392}\right)\)	\(e\left(\frac{191}{196}\right)\)	\(e\left(\frac{95}{196}\right)\)	\(e\left(\frac{241}{392}\right)\)	\(e\left(\frac{103}{392}\right)\)	\(e\left(\frac{19}{49}\right)\)	\(e\left(\frac{79}{98}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{85}{392}\right)\)
\(\chi_{6304}(267,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{123}{392}\right)\)	\(e\left(\frac{309}{392}\right)\)	\(e\left(\frac{107}{196}\right)\)	\(e\left(\frac{123}{196}\right)\)	\(e\left(\frac{213}{392}\right)\)	\(e\left(\frac{187}{392}\right)\)	\(e\left(\frac{5}{49}\right)\)	\(e\left(\frac{93}{98}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{337}{392}\right)\)
\(\chi_{6304}(339,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{233}{392}\right)\)	\(e\left(\frac{375}{392}\right)\)	\(e\left(\frac{29}{196}\right)\)	\(e\left(\frac{37}{196}\right)\)	\(e\left(\frac{327}{392}\right)\)	\(e\left(\frac{265}{392}\right)\)	\(e\left(\frac{27}{49}\right)\)	\(e\left(\frac{71}{98}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{291}{392}\right)\)
\(\chi_{6304}(347,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{127}{392}\right)\)	\(e\left(\frac{233}{392}\right)\)	\(e\left(\frac{179}{196}\right)\)	\(e\left(\frac{127}{196}\right)\)	\(e\left(\frac{153}{392}\right)\)	\(e\left(\frac{311}{392}\right)\)	\(e\left(\frac{45}{49}\right)\)	\(e\left(\frac{53}{98}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{93}{392}\right)\)
\(\chi_{6304}(355,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{141}{392}\right)\)	\(e\left(\frac{163}{392}\right)\)	\(e\left(\frac{137}{196}\right)\)	\(e\left(\frac{141}{196}\right)\)	\(e\left(\frac{139}{392}\right)\)	\(e\left(\frac{157}{392}\right)\)	\(e\left(\frac{38}{49}\right)\)	\(e\left(\frac{11}{98}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{23}{392}\right)\)
\(\chi_{6304}(379,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{279}{392}\right)\)	\(e\left(\frac{89}{392}\right)\)	\(e\left(\frac{171}{196}\right)\)	\(e\left(\frac{83}{196}\right)\)	\(e\left(\frac{225}{392}\right)\)	\(e\left(\frac{319}{392}\right)\)	\(e\left(\frac{46}{49}\right)\)	\(e\left(\frac{3}{98}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{229}{392}\right)\)
\(\chi_{6304}(387,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{373}{392}\right)\)	\(e\left(\frac{67}{392}\right)\)	\(e\left(\frac{1}{196}\right)\)	\(e\left(\frac{177}{196}\right)\)	\(e\left(\frac{187}{392}\right)\)	\(e\left(\frac{293}{392}\right)\)	\(e\left(\frac{6}{49}\right)\)	\(e\left(\frac{43}{98}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{375}{392}\right)\)
\(\chi_{6304}(443,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{207}{392}\right)\)	\(e\left(\frac{281}{392}\right)\)	\(e\left(\frac{51}{196}\right)\)	\(e\left(\frac{11}{196}\right)\)	\(e\left(\frac{129}{392}\right)\)	\(e\left(\frac{47}{392}\right)\)	\(e\left(\frac{12}{49}\right)\)	\(e\left(\frac{37}{98}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{309}{392}\right)\)
\(\chi_{6304}(475,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{183}{392}\right)\)	\(e\left(\frac{345}{392}\right)\)	\(e\left(\frac{11}{196}\right)\)	\(e\left(\frac{183}{196}\right)\)	\(e\left(\frac{97}{392}\right)\)	\(e\left(\frac{87}{392}\right)\)	\(e\left(\frac{17}{49}\right)\)	\(e\left(\frac{81}{98}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{205}{392}\right)\)
\(\chi_{6304}(499,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{392}\right)\)	\(e\left(\frac{303}{392}\right)\)	\(e\left(\frac{25}{196}\right)\)	\(e\left(\frac{113}{196}\right)\)	\(e\left(\frac{167}{392}\right)\)	\(e\left(\frac{73}{392}\right)\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{95}{98}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{163}{392}\right)\)
\(\chi_{6304}(587,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{283}{392}\right)\)	\(e\left(\frac{13}{392}\right)\)	\(e\left(\frac{47}{196}\right)\)	\(e\left(\frac{87}{196}\right)\)	\(e\left(\frac{165}{392}\right)\)	\(e\left(\frac{51}{392}\right)\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{61}{98}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{377}{392}\right)\)
\(\chi_{6304}(619,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{392}\right)\)	\(e\left(\frac{325}{392}\right)\)	\(e\left(\frac{195}{196}\right)\)	\(e\left(\frac{19}{196}\right)\)	\(e\left(\frac{205}{392}\right)\)	\(e\left(\frac{99}{392}\right)\)	\(e\left(\frac{43}{49}\right)\)	\(e\left(\frac{55}{98}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{17}{392}\right)\)
\(\chi_{6304}(651,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{219}{392}\right)\)	\(e\left(\frac{53}{392}\right)\)	\(e\left(\frac{71}{196}\right)\)	\(e\left(\frac{23}{196}\right)\)	\(e\left(\frac{341}{392}\right)\)	\(e\left(\frac{27}{392}\right)\)	\(e\left(\frac{34}{49}\right)\)	\(e\left(\frac{15}{98}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{361}{392}\right)\)
\(\chi_{6304}(667,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{367}{392}\right)\)	\(e\left(\frac{377}{392}\right)\)	\(e\left(\frac{187}{196}\right)\)	\(e\left(\frac{171}{196}\right)\)	\(e\left(\frac{81}{392}\right)\)	\(e\left(\frac{303}{392}\right)\)	\(e\left(\frac{44}{49}\right)\)	\(e\left(\frac{5}{98}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{349}{392}\right)\)
\(\chi_{6304}(691,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{392}\right)\)	\(e\left(\frac{239}{392}\right)\)	\(e\left(\frac{65}{196}\right)\)	\(e\left(\frac{137}{196}\right)\)	\(e\left(\frac{199}{392}\right)\)	\(e\left(\frac{33}{392}\right)\)	\(e\left(\frac{47}{49}\right)\)	\(e\left(\frac{51}{98}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{267}{392}\right)\)
\(\chi_{6304}(723,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{353}{392}\right)\)	\(e\left(\frac{55}{392}\right)\)	\(e\left(\frac{33}{196}\right)\)	\(e\left(\frac{157}{196}\right)\)	\(e\left(\frac{95}{392}\right)\)	\(e\left(\frac{65}{392}\right)\)	\(e\left(\frac{2}{49}\right)\)	\(e\left(\frac{47}{98}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{27}{392}\right)\)
\(\chi_{6304}(747,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{179}{392}\right)\)	\(e\left(\frac{29}{392}\right)\)	\(e\left(\frac{135}{196}\right)\)	\(e\left(\frac{179}{196}\right)\)	\(e\left(\frac{157}{392}\right)\)	\(e\left(\frac{355}{392}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{23}{98}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{57}{392}\right)\)
\(\chi_{6304}(763,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{295}{392}\right)\)	\(e\left(\frac{177}{392}\right)\)	\(e\left(\frac{67}{196}\right)\)	\(e\left(\frac{99}{196}\right)\)	\(e\left(\frac{377}{392}\right)\)	\(e\left(\frac{31}{392}\right)\)	\(e\left(\frac{10}{49}\right)\)	\(e\left(\frac{39}{98}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{37}{392}\right)\)
\(\chi_{6304}(779,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{392}\right)\)	\(e\left(\frac{197}{392}\right)\)	\(e\left(\frac{79}{196}\right)\)	\(e\left(\frac{67}{196}\right)\)	\(e\left(\frac{269}{392}\right)\)	\(e\left(\frac{19}{392}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{65}{98}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{225}{392}\right)\)
\(\chi_{6304}(811,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{75}{392}\right)\)	\(e\left(\frac{45}{392}\right)\)	\(e\left(\frac{27}{196}\right)\)	\(e\left(\frac{75}{196}\right)\)	\(e\left(\frac{149}{392}\right)\)	\(e\left(\frac{267}{392}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{83}{98}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{129}{392}\right)\)
\(\chi_{6304}(851,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{97}{392}\right)\)	\(e\left(\frac{215}{392}\right)\)	\(e\left(\frac{129}{196}\right)\)	\(e\left(\frac{97}{196}\right)\)	\(e\left(\frac{15}{392}\right)\)	\(e\left(\frac{361}{392}\right)\)	\(e\left(\frac{39}{49}\right)\)	\(e\left(\frac{59}{98}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{355}{392}\right)\)
\(\chi_{6304}(923,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{199}{392}\right)\)	\(e\left(\frac{41}{392}\right)\)	\(e\left(\frac{103}{196}\right)\)	\(e\left(\frac{3}{196}\right)\)	\(e\left(\frac{249}{392}\right)\)	\(e\left(\frac{191}{392}\right)\)	\(e\left(\frac{30}{49}\right)\)	\(e\left(\frac{19}{98}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{13}{392}\right)\)
\(\chi_{6304}(963,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{325}{392}\right)\)	\(e\left(\frac{195}{392}\right)\)	\(e\left(\frac{117}{196}\right)\)	\(e\left(\frac{129}{196}\right)\)	\(e\left(\frac{123}{392}\right)\)	\(e\left(\frac{373}{392}\right)\)	\(e\left(\frac{16}{49}\right)\)	\(e\left(\frac{33}{98}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{167}{392}\right)\)
\(\chi_{6304}(1019,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{247}{392}\right)\)	\(e\left(\frac{305}{392}\right)\)	\(e\left(\frac{183}{196}\right)\)	\(e\left(\frac{51}{196}\right)\)	\(e\left(\frac{313}{392}\right)\)	\(e\left(\frac{111}{392}\right)\)	\(e\left(\frac{20}{49}\right)\)	\(e\left(\frac{29}{98}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{221}{392}\right)\)
\(\chi_{6304}(1027,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{205}{392}\right)\)	\(e\left(\frac{123}{392}\right)\)	\(e\left(\frac{113}{196}\right)\)	\(e\left(\frac{9}{196}\right)\)	\(e\left(\frac{355}{392}\right)\)	\(e\left(\frac{181}{392}\right)\)	\(e\left(\frac{41}{49}\right)\)	\(e\left(\frac{57}{98}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{39}{392}\right)\)
\(\chi_{6304}(1075,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{209}{392}\right)\)	\(e\left(\frac{47}{392}\right)\)	\(e\left(\frac{185}{196}\right)\)	\(e\left(\frac{13}{196}\right)\)	\(e\left(\frac{295}{392}\right)\)	\(e\left(\frac{305}{392}\right)\)	\(e\left(\frac{32}{49}\right)\)	\(e\left(\frac{17}{98}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{187}{392}\right)\)
\(\chi_{6304}(1139,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{257}{392}\right)\)	\(e\left(\frac{311}{392}\right)\)	\(e\left(\frac{69}{196}\right)\)	\(e\left(\frac{61}{196}\right)\)	\(e\left(\frac{359}{392}\right)\)	\(e\left(\frac{225}{392}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{27}{98}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{3}{392}\right)\)

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First 31 of 168 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.db
Modulus	$6304$
Conductor	$6304$
Order	$392$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(6304\)
Conductor:	\(6304\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(392\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)