LMFDB - Dirichlet character orbit 2864.u

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2864, base_ring=CyclotomicField(356)) M = H._module chi = DirichletCharacter(H, M([0,89,202])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(21,2864)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2864$
Conductor:	$2864$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$356$	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:	$\Q(\zeta_{356})$
Fixed field:	Number field defined by a degree 356 polynomial (not computed)

First 31 of 176 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{2864}(21,\cdot)$	$-1$	$1$	$e\left(\frac{11}{356}\right)$	$e\left(\frac{197}{356}\right)$	$e\left(\frac{47}{89}\right)$	$e\left(\frac{11}{178}\right)$	$e\left(\frac{271}{356}\right)$	$e\left(\frac{155}{356}\right)$	$e\left(\frac{52}{89}\right)$	$e\left(\frac{17}{89}\right)$	$e\left(\frac{139}{356}\right)$	$e\left(\frac{199}{356}\right)$
$\chi_{2864}(37,\cdot)$	$-1$	$1$	$e\left(\frac{55}{356}\right)$	$e\left(\frac{273}{356}\right)$	$e\left(\frac{57}{89}\right)$	$e\left(\frac{55}{178}\right)$	$e\left(\frac{287}{356}\right)$	$e\left(\frac{63}{356}\right)$	$e\left(\frac{82}{89}\right)$	$e\left(\frac{85}{89}\right)$	$e\left(\frac{339}{356}\right)$	$e\left(\frac{283}{356}\right)$
$\chi_{2864}(53,\cdot)$	$-1$	$1$	$e\left(\frac{59}{356}\right)$	$e\left(\frac{21}{356}\right)$	$e\left(\frac{66}{89}\right)$	$e\left(\frac{59}{178}\right)$	$e\left(\frac{159}{356}\right)$	$e\left(\frac{87}{356}\right)$	$e\left(\frac{20}{89}\right)$	$e\left(\frac{75}{89}\right)$	$e\left(\frac{163}{356}\right)$	$e\left(\frac{323}{356}\right)$
$\chi_{2864}(69,\cdot)$	$-1$	$1$	$e\left(\frac{67}{356}\right)$	$e\left(\frac{229}{356}\right)$	$e\left(\frac{84}{89}\right)$	$e\left(\frac{67}{178}\right)$	$e\left(\frac{259}{356}\right)$	$e\left(\frac{135}{356}\right)$	$e\left(\frac{74}{89}\right)$	$e\left(\frac{55}{89}\right)$	$e\left(\frac{167}{356}\right)$	$e\left(\frac{47}{356}\right)$
$\chi_{2864}(109,\cdot)$	$-1$	$1$	$e\left(\frac{121}{356}\right)$	$e\left(\frac{31}{356}\right)$	$e\left(\frac{72}{89}\right)$	$e\left(\frac{121}{178}\right)$	$e\left(\frac{133}{356}\right)$	$e\left(\frac{281}{356}\right)$	$e\left(\frac{38}{89}\right)$	$e\left(\frac{9}{89}\right)$	$e\left(\frac{105}{356}\right)$	$e\left(\frac{53}{356}\right)$
$\chi_{2864}(133,\cdot)$	$-1$	$1$	$e\left(\frac{95}{356}\right)$	$e\left(\frac{245}{356}\right)$	$e\left(\frac{58}{89}\right)$	$e\left(\frac{95}{178}\right)$	$e\left(\frac{75}{356}\right)$	$e\left(\frac{303}{356}\right)$	$e\left(\frac{85}{89}\right)$	$e\left(\frac{74}{89}\right)$	$e\left(\frac{3}{356}\right)$	$e\left(\frac{327}{356}\right)$
$\chi_{2864}(157,\cdot)$	$-1$	$1$	$e\left(\frac{341}{356}\right)$	$e\left(\frac{55}{356}\right)$	$e\left(\frac{33}{89}\right)$	$e\left(\frac{163}{178}\right)$	$e\left(\frac{213}{356}\right)$	$e\left(\frac{177}{356}\right)$	$e\left(\frac{10}{89}\right)$	$e\left(\frac{82}{89}\right)$	$e\left(\frac{37}{356}\right)$	$e\left(\frac{117}{356}\right)$
$\chi_{2864}(165,\cdot)$	$-1$	$1$	$e\left(\frac{39}{356}\right)$	$e\left(\frac{213}{356}\right)$	$e\left(\frac{21}{89}\right)$	$e\left(\frac{39}{178}\right)$	$e\left(\frac{87}{356}\right)$	$e\left(\frac{323}{356}\right)$	$e\left(\frac{63}{89}\right)$	$e\left(\frac{36}{89}\right)$	$e\left(\frac{331}{356}\right)$	$e\left(\frac{123}{356}\right)$
$\chi_{2864}(181,\cdot)$	$-1$	$1$	$e\left(\frac{127}{356}\right)$	$e\left(\frac{9}{356}\right)$	$e\left(\frac{41}{89}\right)$	$e\left(\frac{127}{178}\right)$	$e\left(\frac{119}{356}\right)$	$e\left(\frac{139}{356}\right)$	$e\left(\frac{34}{89}\right)$	$e\left(\frac{83}{89}\right)$	$e\left(\frac{19}{356}\right)$	$e\left(\frac{291}{356}\right)$
$\chi_{2864}(189,\cdot)$	$-1$	$1$	$e\left(\frac{209}{356}\right)$	$e\left(\frac{183}{356}\right)$	$e\left(\frac{3}{89}\right)$	$e\left(\frac{31}{178}\right)$	$e\left(\frac{165}{356}\right)$	$e\left(\frac{97}{356}\right)$	$e\left(\frac{9}{89}\right)$	$e\left(\frac{56}{89}\right)$	$e\left(\frac{149}{356}\right)$	$e\left(\frac{221}{356}\right)$
$\chi_{2864}(197,\cdot)$	$-1$	$1$	$e\left(\frac{147}{356}\right)$	$e\left(\frac{173}{356}\right)$	$e\left(\frac{86}{89}\right)$	$e\left(\frac{147}{178}\right)$	$e\left(\frac{191}{356}\right)$	$e\left(\frac{259}{356}\right)$	$e\left(\frac{80}{89}\right)$	$e\left(\frac{33}{89}\right)$	$e\left(\frac{207}{356}\right)$	$e\left(\frac{135}{356}\right)$
$\chi_{2864}(205,\cdot)$	$-1$	$1$	$e\left(\frac{9}{356}\right)$	$e\left(\frac{323}{356}\right)$	$e\left(\frac{87}{89}\right)$	$e\left(\frac{9}{178}\right)$	$e\left(\frac{157}{356}\right)$	$e\left(\frac{321}{356}\right)$	$e\left(\frac{83}{89}\right)$	$e\left(\frac{22}{89}\right)$	$e\left(\frac{49}{356}\right)$	$e\left(\frac{1}{356}\right)$
$\chi_{2864}(213,\cdot)$	$-1$	$1$	$e\left(\frac{27}{356}\right)$	$e\left(\frac{257}{356}\right)$	$e\left(\frac{83}{89}\right)$	$e\left(\frac{27}{178}\right)$	$e\left(\frac{115}{356}\right)$	$e\left(\frac{251}{356}\right)$	$e\left(\frac{71}{89}\right)$	$e\left(\frac{66}{89}\right)$	$e\left(\frac{147}{356}\right)$	$e\left(\frac{3}{356}\right)$
$\chi_{2864}(229,\cdot)$	$-1$	$1$	$e\left(\frac{291}{356}\right)$	$e\left(\frac{1}{356}\right)$	$e\left(\frac{54}{89}\right)$	$e\left(\frac{113}{178}\right)$	$e\left(\frac{211}{356}\right)$	$e\left(\frac{55}{356}\right)$	$e\left(\frac{73}{89}\right)$	$e\left(\frac{29}{89}\right)$	$e\left(\frac{279}{356}\right)$	$e\left(\frac{151}{356}\right)$
$\chi_{2864}(237,\cdot)$	$-1$	$1$	$e\left(\frac{161}{356}\right)$	$e\left(\frac{3}{356}\right)$	$e\left(\frac{73}{89}\right)$	$e\left(\frac{161}{178}\right)$	$e\left(\frac{277}{356}\right)$	$e\left(\frac{165}{356}\right)$	$e\left(\frac{41}{89}\right)$	$e\left(\frac{87}{89}\right)$	$e\left(\frac{125}{356}\right)$	$e\left(\frac{97}{356}\right)$
$\chi_{2864}(269,\cdot)$	$-1$	$1$	$e\left(\frac{229}{356}\right)$	$e\left(\frac{347}{356}\right)$	$e\left(\frac{48}{89}\right)$	$e\left(\frac{51}{178}\right)$	$e\left(\frac{237}{356}\right)$	$e\left(\frac{217}{356}\right)$	$e\left(\frac{55}{89}\right)$	$e\left(\frac{6}{89}\right)$	$e\left(\frac{337}{356}\right)$	$e\left(\frac{65}{356}\right)$
$\chi_{2864}(277,\cdot)$	$-1$	$1$	$e\left(\frac{307}{356}\right)$	$e\left(\frac{61}{356}\right)$	$e\left(\frac{1}{89}\right)$	$e\left(\frac{129}{178}\right)$	$e\left(\frac{55}{356}\right)$	$e\left(\frac{151}{356}\right)$	$e\left(\frac{3}{89}\right)$	$e\left(\frac{78}{89}\right)$	$e\left(\frac{287}{356}\right)$	$e\left(\frac{311}{356}\right)$
$\chi_{2864}(293,\cdot)$	$-1$	$1$	$e\left(\frac{231}{356}\right)$	$e\left(\frac{221}{356}\right)$	$e\left(\frac{8}{89}\right)$	$e\left(\frac{53}{178}\right)$	$e\left(\frac{351}{356}\right)$	$e\left(\frac{51}{356}\right)$	$e\left(\frac{24}{89}\right)$	$e\left(\frac{1}{89}\right)$	$e\left(\frac{71}{356}\right)$	$e\left(\frac{263}{356}\right)$
$\chi_{2864}(301,\cdot)$	$-1$	$1$	$e\left(\frac{193}{356}\right)$	$e\left(\frac{123}{356}\right)$	$e\left(\frac{56}{89}\right)$	$e\left(\frac{15}{178}\right)$	$e\left(\frac{321}{356}\right)$	$e\left(\frac{1}{356}\right)$	$e\left(\frac{79}{89}\right)$	$e\left(\frac{7}{89}\right)$	$e\left(\frac{141}{356}\right)$	$e\left(\frac{61}{356}\right)$
$\chi_{2864}(309,\cdot)$	$-1$	$1$	$e\left(\frac{91}{356}\right)$	$e\left(\frac{141}{356}\right)$	$e\left(\frac{49}{89}\right)$	$e\left(\frac{91}{178}\right)$	$e\left(\frac{203}{356}\right)$	$e\left(\frac{279}{356}\right)$	$e\left(\frac{58}{89}\right)$	$e\left(\frac{84}{89}\right)$	$e\left(\frac{179}{356}\right)$	$e\left(\frac{287}{356}\right)$
$\chi_{2864}(333,\cdot)$	$-1$	$1$	$e\left(\frac{253}{356}\right)$	$e\left(\frac{259}{356}\right)$	$e\left(\frac{13}{89}\right)$	$e\left(\frac{75}{178}\right)$	$e\left(\frac{181}{356}\right)$	$e\left(\frac{5}{356}\right)$	$e\left(\frac{39}{89}\right)$	$e\left(\frac{35}{89}\right)$	$e\left(\frac{349}{356}\right)$	$e\left(\frac{305}{356}\right)$
$\chi_{2864}(341,\cdot)$	$-1$	$1$	$e\left(\frac{167}{356}\right)$	$e\left(\frac{337}{356}\right)$	$e\left(\frac{42}{89}\right)$	$e\left(\frac{167}{178}\right)$	$e\left(\frac{263}{356}\right)$	$e\left(\frac{23}{356}\right)$	$e\left(\frac{37}{89}\right)$	$e\left(\frac{72}{89}\right)$	$e\left(\frac{39}{356}\right)$	$e\left(\frac{335}{356}\right)$
$\chi_{2864}(349,\cdot)$	$-1$	$1$	$e\left(\frac{109}{356}\right)$	$e\left(\frac{75}{356}\right)$	$e\left(\frac{45}{89}\right)$	$e\left(\frac{109}{178}\right)$	$e\left(\frac{161}{356}\right)$	$e\left(\frac{209}{356}\right)$	$e\left(\frac{46}{89}\right)$	$e\left(\frac{39}{89}\right)$	$e\left(\frac{277}{356}\right)$	$e\left(\frac{289}{356}\right)$
$\chi_{2864}(365,\cdot)$	$-1$	$1$	$e\left(\frac{1}{356}\right)$	$e\left(\frac{115}{356}\right)$	$e\left(\frac{69}{89}\right)$	$e\left(\frac{1}{178}\right)$	$e\left(\frac{57}{356}\right)$	$e\left(\frac{273}{356}\right)$	$e\left(\frac{29}{89}\right)$	$e\left(\frac{42}{89}\right)$	$e\left(\frac{45}{356}\right)$	$e\left(\frac{277}{356}\right)$
$\chi_{2864}(381,\cdot)$	$-1$	$1$	$e\left(\frac{57}{356}\right)$	$e\left(\frac{147}{356}\right)$	$e\left(\frac{17}{89}\right)$	$e\left(\frac{57}{178}\right)$	$e\left(\frac{45}{356}\right)$	$e\left(\frac{253}{356}\right)$	$e\left(\frac{51}{89}\right)$	$e\left(\frac{80}{89}\right)$	$e\left(\frac{73}{356}\right)$	$e\left(\frac{125}{356}\right)$
$\chi_{2864}(413,\cdot)$	$-1$	$1$	$e\left(\frac{29}{356}\right)$	$e\left(\frac{131}{356}\right)$	$e\left(\frac{43}{89}\right)$	$e\left(\frac{29}{178}\right)$	$e\left(\frac{229}{356}\right)$	$e\left(\frac{85}{356}\right)$	$e\left(\frac{40}{89}\right)$	$e\left(\frac{61}{89}\right)$	$e\left(\frac{237}{356}\right)$	$e\left(\frac{201}{356}\right)$
$\chi_{2864}(421,\cdot)$	$-1$	$1$	$e\left(\frac{199}{356}\right)$	$e\left(\frac{101}{356}\right)$	$e\left(\frac{25}{89}\right)$	$e\left(\frac{21}{178}\right)$	$e\left(\frac{307}{356}\right)$	$e\left(\frac{215}{356}\right)$	$e\left(\frac{75}{89}\right)$	$e\left(\frac{81}{89}\right)$	$e\left(\frac{55}{356}\right)$	$e\left(\frac{299}{356}\right)$
$\chi_{2864}(429,\cdot)$	$-1$	$1$	$e\left(\frac{17}{356}\right)$	$e\left(\frac{175}{356}\right)$	$e\left(\frac{16}{89}\right)$	$e\left(\frac{17}{178}\right)$	$e\left(\frac{257}{356}\right)$	$e\left(\frac{13}{356}\right)$	$e\left(\frac{48}{89}\right)$	$e\left(\frac{2}{89}\right)$	$e\left(\frac{53}{356}\right)$	$e\left(\frac{81}{356}\right)$
$\chi_{2864}(437,\cdot)$	$-1$	$1$	$e\left(\frac{151}{356}\right)$	$e\left(\frac{277}{356}\right)$	$e\left(\frac{6}{89}\right)$	$e\left(\frac{151}{178}\right)$	$e\left(\frac{63}{356}\right)$	$e\left(\frac{283}{356}\right)$	$e\left(\frac{18}{89}\right)$	$e\left(\frac{23}{89}\right)$	$e\left(\frac{31}{356}\right)$	$e\left(\frac{175}{356}\right)$
$\chi_{2864}(461,\cdot)$	$-1$	$1$	$e\left(\frac{81}{356}\right)$	$e\left(\frac{59}{356}\right)$	$e\left(\frac{71}{89}\right)$	$e\left(\frac{81}{178}\right)$	$e\left(\frac{345}{356}\right)$	$e\left(\frac{41}{356}\right)$	$e\left(\frac{35}{89}\right)$	$e\left(\frac{20}{89}\right)$	$e\left(\frac{85}{356}\right)$	$e\left(\frac{9}{356}\right)$
$\chi_{2864}(469,\cdot)$	$-1$	$1$	$e\left(\frac{243}{356}\right)$	$e\left(\frac{177}{356}\right)$	$e\left(\frac{35}{89}\right)$	$e\left(\frac{65}{178}\right)$	$e\left(\frac{323}{356}\right)$	$e\left(\frac{123}{356}\right)$	$e\left(\frac{16}{89}\right)$	$e\left(\frac{60}{89}\right)$	$e\left(\frac{255}{356}\right)$	$e\left(\frac{27}{356}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{2864}(21,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{356}\right)\)	\(e\left(\frac{197}{356}\right)\)	\(e\left(\frac{47}{89}\right)\)	\(e\left(\frac{11}{178}\right)\)	\(e\left(\frac{271}{356}\right)\)	\(e\left(\frac{155}{356}\right)\)	\(e\left(\frac{52}{89}\right)\)	\(e\left(\frac{17}{89}\right)\)	\(e\left(\frac{139}{356}\right)\)	\(e\left(\frac{199}{356}\right)\)
\(\chi_{2864}(37,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{55}{356}\right)\)	\(e\left(\frac{273}{356}\right)\)	\(e\left(\frac{57}{89}\right)\)	\(e\left(\frac{55}{178}\right)\)	\(e\left(\frac{287}{356}\right)\)	\(e\left(\frac{63}{356}\right)\)	\(e\left(\frac{82}{89}\right)\)	\(e\left(\frac{85}{89}\right)\)	\(e\left(\frac{339}{356}\right)\)	\(e\left(\frac{283}{356}\right)\)
\(\chi_{2864}(53,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{356}\right)\)	\(e\left(\frac{21}{356}\right)\)	\(e\left(\frac{66}{89}\right)\)	\(e\left(\frac{59}{178}\right)\)	\(e\left(\frac{159}{356}\right)\)	\(e\left(\frac{87}{356}\right)\)	\(e\left(\frac{20}{89}\right)\)	\(e\left(\frac{75}{89}\right)\)	\(e\left(\frac{163}{356}\right)\)	\(e\left(\frac{323}{356}\right)\)
\(\chi_{2864}(69,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{356}\right)\)	\(e\left(\frac{229}{356}\right)\)	\(e\left(\frac{84}{89}\right)\)	\(e\left(\frac{67}{178}\right)\)	\(e\left(\frac{259}{356}\right)\)	\(e\left(\frac{135}{356}\right)\)	\(e\left(\frac{74}{89}\right)\)	\(e\left(\frac{55}{89}\right)\)	\(e\left(\frac{167}{356}\right)\)	\(e\left(\frac{47}{356}\right)\)
\(\chi_{2864}(109,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{121}{356}\right)\)	\(e\left(\frac{31}{356}\right)\)	\(e\left(\frac{72}{89}\right)\)	\(e\left(\frac{121}{178}\right)\)	\(e\left(\frac{133}{356}\right)\)	\(e\left(\frac{281}{356}\right)\)	\(e\left(\frac{38}{89}\right)\)	\(e\left(\frac{9}{89}\right)\)	\(e\left(\frac{105}{356}\right)\)	\(e\left(\frac{53}{356}\right)\)
\(\chi_{2864}(133,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{95}{356}\right)\)	\(e\left(\frac{245}{356}\right)\)	\(e\left(\frac{58}{89}\right)\)	\(e\left(\frac{95}{178}\right)\)	\(e\left(\frac{75}{356}\right)\)	\(e\left(\frac{303}{356}\right)\)	\(e\left(\frac{85}{89}\right)\)	\(e\left(\frac{74}{89}\right)\)	\(e\left(\frac{3}{356}\right)\)	\(e\left(\frac{327}{356}\right)\)
\(\chi_{2864}(157,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{341}{356}\right)\)	\(e\left(\frac{55}{356}\right)\)	\(e\left(\frac{33}{89}\right)\)	\(e\left(\frac{163}{178}\right)\)	\(e\left(\frac{213}{356}\right)\)	\(e\left(\frac{177}{356}\right)\)	\(e\left(\frac{10}{89}\right)\)	\(e\left(\frac{82}{89}\right)\)	\(e\left(\frac{37}{356}\right)\)	\(e\left(\frac{117}{356}\right)\)
\(\chi_{2864}(165,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{39}{356}\right)\)	\(e\left(\frac{213}{356}\right)\)	\(e\left(\frac{21}{89}\right)\)	\(e\left(\frac{39}{178}\right)\)	\(e\left(\frac{87}{356}\right)\)	\(e\left(\frac{323}{356}\right)\)	\(e\left(\frac{63}{89}\right)\)	\(e\left(\frac{36}{89}\right)\)	\(e\left(\frac{331}{356}\right)\)	\(e\left(\frac{123}{356}\right)\)
\(\chi_{2864}(181,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{127}{356}\right)\)	\(e\left(\frac{9}{356}\right)\)	\(e\left(\frac{41}{89}\right)\)	\(e\left(\frac{127}{178}\right)\)	\(e\left(\frac{119}{356}\right)\)	\(e\left(\frac{139}{356}\right)\)	\(e\left(\frac{34}{89}\right)\)	\(e\left(\frac{83}{89}\right)\)	\(e\left(\frac{19}{356}\right)\)	\(e\left(\frac{291}{356}\right)\)
\(\chi_{2864}(189,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{209}{356}\right)\)	\(e\left(\frac{183}{356}\right)\)	\(e\left(\frac{3}{89}\right)\)	\(e\left(\frac{31}{178}\right)\)	\(e\left(\frac{165}{356}\right)\)	\(e\left(\frac{97}{356}\right)\)	\(e\left(\frac{9}{89}\right)\)	\(e\left(\frac{56}{89}\right)\)	\(e\left(\frac{149}{356}\right)\)	\(e\left(\frac{221}{356}\right)\)
\(\chi_{2864}(197,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{147}{356}\right)\)	\(e\left(\frac{173}{356}\right)\)	\(e\left(\frac{86}{89}\right)\)	\(e\left(\frac{147}{178}\right)\)	\(e\left(\frac{191}{356}\right)\)	\(e\left(\frac{259}{356}\right)\)	\(e\left(\frac{80}{89}\right)\)	\(e\left(\frac{33}{89}\right)\)	\(e\left(\frac{207}{356}\right)\)	\(e\left(\frac{135}{356}\right)\)
\(\chi_{2864}(205,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{356}\right)\)	\(e\left(\frac{323}{356}\right)\)	\(e\left(\frac{87}{89}\right)\)	\(e\left(\frac{9}{178}\right)\)	\(e\left(\frac{157}{356}\right)\)	\(e\left(\frac{321}{356}\right)\)	\(e\left(\frac{83}{89}\right)\)	\(e\left(\frac{22}{89}\right)\)	\(e\left(\frac{49}{356}\right)\)	\(e\left(\frac{1}{356}\right)\)
\(\chi_{2864}(213,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{356}\right)\)	\(e\left(\frac{257}{356}\right)\)	\(e\left(\frac{83}{89}\right)\)	\(e\left(\frac{27}{178}\right)\)	\(e\left(\frac{115}{356}\right)\)	\(e\left(\frac{251}{356}\right)\)	\(e\left(\frac{71}{89}\right)\)	\(e\left(\frac{66}{89}\right)\)	\(e\left(\frac{147}{356}\right)\)	\(e\left(\frac{3}{356}\right)\)
\(\chi_{2864}(229,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{291}{356}\right)\)	\(e\left(\frac{1}{356}\right)\)	\(e\left(\frac{54}{89}\right)\)	\(e\left(\frac{113}{178}\right)\)	\(e\left(\frac{211}{356}\right)\)	\(e\left(\frac{55}{356}\right)\)	\(e\left(\frac{73}{89}\right)\)	\(e\left(\frac{29}{89}\right)\)	\(e\left(\frac{279}{356}\right)\)	\(e\left(\frac{151}{356}\right)\)
\(\chi_{2864}(237,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{161}{356}\right)\)	\(e\left(\frac{3}{356}\right)\)	\(e\left(\frac{73}{89}\right)\)	\(e\left(\frac{161}{178}\right)\)	\(e\left(\frac{277}{356}\right)\)	\(e\left(\frac{165}{356}\right)\)	\(e\left(\frac{41}{89}\right)\)	\(e\left(\frac{87}{89}\right)\)	\(e\left(\frac{125}{356}\right)\)	\(e\left(\frac{97}{356}\right)\)
\(\chi_{2864}(269,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{229}{356}\right)\)	\(e\left(\frac{347}{356}\right)\)	\(e\left(\frac{48}{89}\right)\)	\(e\left(\frac{51}{178}\right)\)	\(e\left(\frac{237}{356}\right)\)	\(e\left(\frac{217}{356}\right)\)	\(e\left(\frac{55}{89}\right)\)	\(e\left(\frac{6}{89}\right)\)	\(e\left(\frac{337}{356}\right)\)	\(e\left(\frac{65}{356}\right)\)
\(\chi_{2864}(277,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{307}{356}\right)\)	\(e\left(\frac{61}{356}\right)\)	\(e\left(\frac{1}{89}\right)\)	\(e\left(\frac{129}{178}\right)\)	\(e\left(\frac{55}{356}\right)\)	\(e\left(\frac{151}{356}\right)\)	\(e\left(\frac{3}{89}\right)\)	\(e\left(\frac{78}{89}\right)\)	\(e\left(\frac{287}{356}\right)\)	\(e\left(\frac{311}{356}\right)\)
\(\chi_{2864}(293,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{231}{356}\right)\)	\(e\left(\frac{221}{356}\right)\)	\(e\left(\frac{8}{89}\right)\)	\(e\left(\frac{53}{178}\right)\)	\(e\left(\frac{351}{356}\right)\)	\(e\left(\frac{51}{356}\right)\)	\(e\left(\frac{24}{89}\right)\)	\(e\left(\frac{1}{89}\right)\)	\(e\left(\frac{71}{356}\right)\)	\(e\left(\frac{263}{356}\right)\)
\(\chi_{2864}(301,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{193}{356}\right)\)	\(e\left(\frac{123}{356}\right)\)	\(e\left(\frac{56}{89}\right)\)	\(e\left(\frac{15}{178}\right)\)	\(e\left(\frac{321}{356}\right)\)	\(e\left(\frac{1}{356}\right)\)	\(e\left(\frac{79}{89}\right)\)	\(e\left(\frac{7}{89}\right)\)	\(e\left(\frac{141}{356}\right)\)	\(e\left(\frac{61}{356}\right)\)
\(\chi_{2864}(309,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{356}\right)\)	\(e\left(\frac{141}{356}\right)\)	\(e\left(\frac{49}{89}\right)\)	\(e\left(\frac{91}{178}\right)\)	\(e\left(\frac{203}{356}\right)\)	\(e\left(\frac{279}{356}\right)\)	\(e\left(\frac{58}{89}\right)\)	\(e\left(\frac{84}{89}\right)\)	\(e\left(\frac{179}{356}\right)\)	\(e\left(\frac{287}{356}\right)\)
\(\chi_{2864}(333,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{253}{356}\right)\)	\(e\left(\frac{259}{356}\right)\)	\(e\left(\frac{13}{89}\right)\)	\(e\left(\frac{75}{178}\right)\)	\(e\left(\frac{181}{356}\right)\)	\(e\left(\frac{5}{356}\right)\)	\(e\left(\frac{39}{89}\right)\)	\(e\left(\frac{35}{89}\right)\)	\(e\left(\frac{349}{356}\right)\)	\(e\left(\frac{305}{356}\right)\)
\(\chi_{2864}(341,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{167}{356}\right)\)	\(e\left(\frac{337}{356}\right)\)	\(e\left(\frac{42}{89}\right)\)	\(e\left(\frac{167}{178}\right)\)	\(e\left(\frac{263}{356}\right)\)	\(e\left(\frac{23}{356}\right)\)	\(e\left(\frac{37}{89}\right)\)	\(e\left(\frac{72}{89}\right)\)	\(e\left(\frac{39}{356}\right)\)	\(e\left(\frac{335}{356}\right)\)
\(\chi_{2864}(349,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{356}\right)\)	\(e\left(\frac{75}{356}\right)\)	\(e\left(\frac{45}{89}\right)\)	\(e\left(\frac{109}{178}\right)\)	\(e\left(\frac{161}{356}\right)\)	\(e\left(\frac{209}{356}\right)\)	\(e\left(\frac{46}{89}\right)\)	\(e\left(\frac{39}{89}\right)\)	\(e\left(\frac{277}{356}\right)\)	\(e\left(\frac{289}{356}\right)\)
\(\chi_{2864}(365,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{356}\right)\)	\(e\left(\frac{115}{356}\right)\)	\(e\left(\frac{69}{89}\right)\)	\(e\left(\frac{1}{178}\right)\)	\(e\left(\frac{57}{356}\right)\)	\(e\left(\frac{273}{356}\right)\)	\(e\left(\frac{29}{89}\right)\)	\(e\left(\frac{42}{89}\right)\)	\(e\left(\frac{45}{356}\right)\)	\(e\left(\frac{277}{356}\right)\)
\(\chi_{2864}(381,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{57}{356}\right)\)	\(e\left(\frac{147}{356}\right)\)	\(e\left(\frac{17}{89}\right)\)	\(e\left(\frac{57}{178}\right)\)	\(e\left(\frac{45}{356}\right)\)	\(e\left(\frac{253}{356}\right)\)	\(e\left(\frac{51}{89}\right)\)	\(e\left(\frac{80}{89}\right)\)	\(e\left(\frac{73}{356}\right)\)	\(e\left(\frac{125}{356}\right)\)
\(\chi_{2864}(413,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{356}\right)\)	\(e\left(\frac{131}{356}\right)\)	\(e\left(\frac{43}{89}\right)\)	\(e\left(\frac{29}{178}\right)\)	\(e\left(\frac{229}{356}\right)\)	\(e\left(\frac{85}{356}\right)\)	\(e\left(\frac{40}{89}\right)\)	\(e\left(\frac{61}{89}\right)\)	\(e\left(\frac{237}{356}\right)\)	\(e\left(\frac{201}{356}\right)\)
\(\chi_{2864}(421,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{199}{356}\right)\)	\(e\left(\frac{101}{356}\right)\)	\(e\left(\frac{25}{89}\right)\)	\(e\left(\frac{21}{178}\right)\)	\(e\left(\frac{307}{356}\right)\)	\(e\left(\frac{215}{356}\right)\)	\(e\left(\frac{75}{89}\right)\)	\(e\left(\frac{81}{89}\right)\)	\(e\left(\frac{55}{356}\right)\)	\(e\left(\frac{299}{356}\right)\)
\(\chi_{2864}(429,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{356}\right)\)	\(e\left(\frac{175}{356}\right)\)	\(e\left(\frac{16}{89}\right)\)	\(e\left(\frac{17}{178}\right)\)	\(e\left(\frac{257}{356}\right)\)	\(e\left(\frac{13}{356}\right)\)	\(e\left(\frac{48}{89}\right)\)	\(e\left(\frac{2}{89}\right)\)	\(e\left(\frac{53}{356}\right)\)	\(e\left(\frac{81}{356}\right)\)
\(\chi_{2864}(437,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{151}{356}\right)\)	\(e\left(\frac{277}{356}\right)\)	\(e\left(\frac{6}{89}\right)\)	\(e\left(\frac{151}{178}\right)\)	\(e\left(\frac{63}{356}\right)\)	\(e\left(\frac{283}{356}\right)\)	\(e\left(\frac{18}{89}\right)\)	\(e\left(\frac{23}{89}\right)\)	\(e\left(\frac{31}{356}\right)\)	\(e\left(\frac{175}{356}\right)\)
\(\chi_{2864}(461,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{81}{356}\right)\)	\(e\left(\frac{59}{356}\right)\)	\(e\left(\frac{71}{89}\right)\)	\(e\left(\frac{81}{178}\right)\)	\(e\left(\frac{345}{356}\right)\)	\(e\left(\frac{41}{356}\right)\)	\(e\left(\frac{35}{89}\right)\)	\(e\left(\frac{20}{89}\right)\)	\(e\left(\frac{85}{356}\right)\)	\(e\left(\frac{9}{356}\right)\)
\(\chi_{2864}(469,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{243}{356}\right)\)	\(e\left(\frac{177}{356}\right)\)	\(e\left(\frac{35}{89}\right)\)	\(e\left(\frac{65}{178}\right)\)	\(e\left(\frac{323}{356}\right)\)	\(e\left(\frac{123}{356}\right)\)	\(e\left(\frac{16}{89}\right)\)	\(e\left(\frac{60}{89}\right)\)	\(e\left(\frac{255}{356}\right)\)	\(e\left(\frac{27}{356}\right)\)

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First 31 of 176 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	2864.u
Modulus	$2864$
Conductor	$2864$
Order	$356$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(2864\)
Conductor:	\(2864\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(356\)	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)