LMFDB - Dirichlet character orbit 1682.j

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1682, base_ring=CyclotomicField(406)) M = H._module chi = DirichletCharacter(H, M([188])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(7,1682)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$1682$
Conductor:	$841$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$203$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 841.j	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:	$\Q(\zeta_{203})$
Fixed field:	Number field defined by a degree 203 polynomial (not computed)

First 31 of 168 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{1682}(7,\cdot)$	$1$	$1$	$e\left(\frac{134}{203}\right)$	$e\left(\frac{171}{203}\right)$	$e\left(\frac{22}{203}\right)$	$e\left(\frac{65}{203}\right)$	$e\left(\frac{103}{203}\right)$	$e\left(\frac{110}{203}\right)$	$e\left(\frac{102}{203}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{83}{203}\right)$	$e\left(\frac{156}{203}\right)$
$\chi_{1682}(23,\cdot)$	$1$	$1$	$e\left(\frac{144}{203}\right)$	$e\left(\frac{5}{203}\right)$	$e\left(\frac{60}{203}\right)$	$e\left(\frac{85}{203}\right)$	$e\left(\frac{41}{203}\right)$	$e\left(\frac{97}{203}\right)$	$e\left(\frac{149}{203}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{171}{203}\right)$	$e\left(\frac{1}{203}\right)$
$\chi_{1682}(25,\cdot)$	$1$	$1$	$e\left(\frac{90}{203}\right)$	$e\left(\frac{130}{203}\right)$	$e\left(\frac{139}{203}\right)$	$e\left(\frac{180}{203}\right)$	$e\left(\frac{51}{203}\right)$	$e\left(\frac{86}{203}\right)$	$e\left(\frac{17}{203}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{183}{203}\right)$	$e\left(\frac{26}{203}\right)$
$\chi_{1682}(45,\cdot)$	$1$	$1$	$e\left(\frac{201}{203}\right)$	$e\left(\frac{155}{203}\right)$	$e\left(\frac{33}{203}\right)$	$e\left(\frac{199}{203}\right)$	$e\left(\frac{53}{203}\right)$	$e\left(\frac{165}{203}\right)$	$e\left(\frac{153}{203}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{23}{203}\right)$	$e\left(\frac{31}{203}\right)$
$\chi_{1682}(49,\cdot)$	$1$	$1$	$e\left(\frac{65}{203}\right)$	$e\left(\frac{139}{203}\right)$	$e\left(\frac{44}{203}\right)$	$e\left(\frac{130}{203}\right)$	$e\left(\frac{3}{203}\right)$	$e\left(\frac{17}{203}\right)$	$e\left(\frac{1}{203}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{166}{203}\right)$	$e\left(\frac{109}{203}\right)$
$\chi_{1682}(53,\cdot)$	$1$	$1$	$e\left(\frac{3}{203}\right)$	$e\left(\frac{72}{203}\right)$	$e\left(\frac{52}{203}\right)$	$e\left(\frac{6}{203}\right)$	$e\left(\frac{22}{203}\right)$	$e\left(\frac{57}{203}\right)$	$e\left(\frac{75}{203}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{67}{203}\right)$	$e\left(\frac{55}{203}\right)$
$\chi_{1682}(65,\cdot)$	$1$	$1$	$e\left(\frac{106}{203}\right)$	$e\left(\frac{108}{203}\right)$	$e\left(\frac{78}{203}\right)$	$e\left(\frac{9}{203}\right)$	$e\left(\frac{33}{203}\right)$	$e\left(\frac{187}{203}\right)$	$e\left(\frac{11}{203}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{202}{203}\right)$	$e\left(\frac{184}{203}\right)$
$\chi_{1682}(81,\cdot)$	$1$	$1$	$e\left(\frac{109}{203}\right)$	$e\left(\frac{180}{203}\right)$	$e\left(\frac{130}{203}\right)$	$e\left(\frac{15}{203}\right)$	$e\left(\frac{55}{203}\right)$	$e\left(\frac{41}{203}\right)$	$e\left(\frac{86}{203}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{66}{203}\right)$	$e\left(\frac{36}{203}\right)$
$\chi_{1682}(83,\cdot)$	$1$	$1$	$e\left(\frac{139}{203}\right)$	$e\left(\frac{88}{203}\right)$	$e\left(\frac{41}{203}\right)$	$e\left(\frac{75}{203}\right)$	$e\left(\frac{72}{203}\right)$	$e\left(\frac{2}{203}\right)$	$e\left(\frac{24}{203}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{127}{203}\right)$	$e\left(\frac{180}{203}\right)$
$\chi_{1682}(103,\cdot)$	$1$	$1$	$e\left(\frac{138}{203}\right)$	$e\left(\frac{64}{203}\right)$	$e\left(\frac{159}{203}\right)$	$e\left(\frac{73}{203}\right)$	$e\left(\frac{200}{203}\right)$	$e\left(\frac{186}{203}\right)$	$e\left(\frac{202}{203}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{37}{203}\right)$	$e\left(\frac{94}{203}\right)$
$\chi_{1682}(107,\cdot)$	$1$	$1$	$e\left(\frac{177}{203}\right)$	$e\left(\frac{188}{203}\right)$	$e\left(\frac{23}{203}\right)$	$e\left(\frac{151}{203}\right)$	$e\left(\frac{80}{203}\right)$	$e\left(\frac{115}{203}\right)$	$e\left(\frac{162}{203}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{96}{203}\right)$	$e\left(\frac{200}{203}\right)$
$\chi_{1682}(111,\cdot)$	$1$	$1$	$e\left(\frac{164}{203}\right)$	$e\left(\frac{79}{203}\right)$	$e\left(\frac{136}{203}\right)$	$e\left(\frac{125}{203}\right)$	$e\left(\frac{120}{203}\right)$	$e\left(\frac{71}{203}\right)$	$e\left(\frac{40}{203}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{144}{203}\right)$	$e\left(\frac{97}{203}\right)$
$\chi_{1682}(123,\cdot)$	$1$	$1$	$e\left(\frac{78}{203}\right)$	$e\left(\frac{45}{203}\right)$	$e\left(\frac{134}{203}\right)$	$e\left(\frac{156}{203}\right)$	$e\left(\frac{166}{203}\right)$	$e\left(\frac{61}{203}\right)$	$e\left(\frac{123}{203}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{118}{203}\right)$	$e\left(\frac{9}{203}\right)$
$\chi_{1682}(139,\cdot)$	$1$	$1$	$e\left(\frac{74}{203}\right)$	$e\left(\frac{152}{203}\right)$	$e\left(\frac{200}{203}\right)$	$e\left(\frac{148}{203}\right)$	$e\left(\frac{69}{203}\right)$	$e\left(\frac{188}{203}\right)$	$e\left(\frac{23}{203}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{164}{203}\right)$	$e\left(\frac{71}{203}\right)$
$\chi_{1682}(141,\cdot)$	$1$	$1$	$e\left(\frac{188}{203}\right)$	$e\left(\frac{46}{203}\right)$	$e\left(\frac{146}{203}\right)$	$e\left(\frac{173}{203}\right)$	$e\left(\frac{93}{203}\right)$	$e\left(\frac{121}{203}\right)$	$e\left(\frac{31}{203}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{71}{203}\right)$	$e\left(\frac{131}{203}\right)$
$\chi_{1682}(161,\cdot)$	$1$	$1$	$e\left(\frac{75}{203}\right)$	$e\left(\frac{176}{203}\right)$	$e\left(\frac{82}{203}\right)$	$e\left(\frac{150}{203}\right)$	$e\left(\frac{144}{203}\right)$	$e\left(\frac{4}{203}\right)$	$e\left(\frac{48}{203}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{51}{203}\right)$	$e\left(\frac{157}{203}\right)$
$\chi_{1682}(165,\cdot)$	$1$	$1$	$e\left(\frac{86}{203}\right)$	$e\left(\frac{34}{203}\right)$	$e\left(\frac{2}{203}\right)$	$e\left(\frac{172}{203}\right)$	$e\left(\frac{157}{203}\right)$	$e\left(\frac{10}{203}\right)$	$e\left(\frac{120}{203}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{26}{203}\right)$	$e\left(\frac{88}{203}\right)$
$\chi_{1682}(169,\cdot)$	$1$	$1$	$e\left(\frac{122}{203}\right)$	$e\left(\frac{86}{203}\right)$	$e\left(\frac{17}{203}\right)$	$e\left(\frac{41}{203}\right)$	$e\left(\frac{15}{203}\right)$	$e\left(\frac{85}{203}\right)$	$e\left(\frac{5}{203}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{18}{203}\right)$	$e\left(\frac{139}{203}\right)$
$\chi_{1682}(181,\cdot)$	$1$	$1$	$e\left(\frac{50}{203}\right)$	$e\left(\frac{185}{203}\right)$	$e\left(\frac{190}{203}\right)$	$e\left(\frac{100}{203}\right)$	$e\left(\frac{96}{203}\right)$	$e\left(\frac{138}{203}\right)$	$e\left(\frac{32}{203}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{34}{203}\right)$	$e\left(\frac{37}{203}\right)$
$\chi_{1682}(197,\cdot)$	$1$	$1$	$e\left(\frac{39}{203}\right)$	$e\left(\frac{124}{203}\right)$	$e\left(\frac{67}{203}\right)$	$e\left(\frac{78}{203}\right)$	$e\left(\frac{83}{203}\right)$	$e\left(\frac{132}{203}\right)$	$e\left(\frac{163}{203}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{59}{203}\right)$	$e\left(\frac{106}{203}\right)$
$\chi_{1682}(199,\cdot)$	$1$	$1$	$e\left(\frac{34}{203}\right)$	$e\left(\frac{4}{203}\right)$	$e\left(\frac{48}{203}\right)$	$e\left(\frac{68}{203}\right)$	$e\left(\frac{114}{203}\right)$	$e\left(\frac{37}{203}\right)$	$e\left(\frac{38}{203}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{15}{203}\right)$	$e\left(\frac{82}{203}\right)$
$\chi_{1682}(219,\cdot)$	$1$	$1$	$e\left(\frac{12}{203}\right)$	$e\left(\frac{85}{203}\right)$	$e\left(\frac{5}{203}\right)$	$e\left(\frac{24}{203}\right)$	$e\left(\frac{88}{203}\right)$	$e\left(\frac{25}{203}\right)$	$e\left(\frac{97}{203}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{65}{203}\right)$	$e\left(\frac{17}{203}\right)$
$\chi_{1682}(223,\cdot)$	$1$	$1$	$e\left(\frac{198}{203}\right)$	$e\left(\frac{83}{203}\right)$	$e\left(\frac{184}{203}\right)$	$e\left(\frac{193}{203}\right)$	$e\left(\frac{31}{203}\right)$	$e\left(\frac{108}{203}\right)$	$e\left(\frac{78}{203}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{159}{203}\right)$	$e\left(\frac{179}{203}\right)$
$\chi_{1682}(227,\cdot)$	$1$	$1$	$e\left(\frac{80}{203}\right)$	$e\left(\frac{93}{203}\right)$	$e\left(\frac{101}{203}\right)$	$e\left(\frac{160}{203}\right)$	$e\left(\frac{113}{203}\right)$	$e\left(\frac{99}{203}\right)$	$e\left(\frac{173}{203}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{95}{203}\right)$	$e\left(\frac{181}{203}\right)$
$\chi_{1682}(239,\cdot)$	$1$	$1$	$e\left(\frac{22}{203}\right)$	$e\left(\frac{122}{203}\right)$	$e\left(\frac{43}{203}\right)$	$e\left(\frac{44}{203}\right)$	$e\left(\frac{26}{203}\right)$	$e\left(\frac{12}{203}\right)$	$e\left(\frac{144}{203}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{153}{203}\right)$	$e\left(\frac{65}{203}\right)$
$\chi_{1682}(255,\cdot)$	$1$	$1$	$e\left(\frac{4}{203}\right)$	$e\left(\frac{96}{203}\right)$	$e\left(\frac{137}{203}\right)$	$e\left(\frac{8}{203}\right)$	$e\left(\frac{97}{203}\right)$	$e\left(\frac{76}{203}\right)$	$e\left(\frac{100}{203}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{157}{203}\right)$	$e\left(\frac{141}{203}\right)$
$\chi_{1682}(257,\cdot)$	$1$	$1$	$e\left(\frac{83}{203}\right)$	$e\left(\frac{165}{203}\right)$	$e\left(\frac{153}{203}\right)$	$e\left(\frac{166}{203}\right)$	$e\left(\frac{135}{203}\right)$	$e\left(\frac{156}{203}\right)$	$e\left(\frac{45}{203}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{162}{203}\right)$	$e\left(\frac{33}{203}\right)$
$\chi_{1682}(277,\cdot)$	$1$	$1$	$e\left(\frac{152}{203}\right)$	$e\left(\frac{197}{203}\right)$	$e\left(\frac{131}{203}\right)$	$e\left(\frac{101}{203}\right)$	$e\left(\frac{32}{203}\right)$	$e\left(\frac{46}{203}\right)$	$e\left(\frac{146}{203}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{79}{203}\right)$	$e\left(\frac{80}{203}\right)$
$\chi_{1682}(281,\cdot)$	$1$	$1$	$e\left(\frac{107}{203}\right)$	$e\left(\frac{132}{203}\right)$	$e\left(\frac{163}{203}\right)$	$e\left(\frac{11}{203}\right)$	$e\left(\frac{108}{203}\right)$	$e\left(\frac{3}{203}\right)$	$e\left(\frac{36}{203}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{89}{203}\right)$	$e\left(\frac{67}{203}\right)$
$\chi_{1682}(285,\cdot)$	$1$	$1$	$e\left(\frac{38}{203}\right)$	$e\left(\frac{100}{203}\right)$	$e\left(\frac{185}{203}\right)$	$e\left(\frac{76}{203}\right)$	$e\left(\frac{8}{203}\right)$	$e\left(\frac{113}{203}\right)$	$e\left(\frac{138}{203}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{172}{203}\right)$	$e\left(\frac{20}{203}\right)$
$\chi_{1682}(297,\cdot)$	$1$	$1$	$e\left(\frac{197}{203}\right)$	$e\left(\frac{59}{203}\right)$	$e\left(\frac{99}{203}\right)$	$e\left(\frac{191}{203}\right)$	$e\left(\frac{159}{203}\right)$	$e\left(\frac{89}{203}\right)$	$e\left(\frac{53}{203}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{69}{203}\right)$	$e\left(\frac{93}{203}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{1682}(7,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{134}{203}\right)\)	\(e\left(\frac{171}{203}\right)\)	\(e\left(\frac{22}{203}\right)\)	\(e\left(\frac{65}{203}\right)\)	\(e\left(\frac{103}{203}\right)\)	\(e\left(\frac{110}{203}\right)\)	\(e\left(\frac{102}{203}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{83}{203}\right)\)	\(e\left(\frac{156}{203}\right)\)
\(\chi_{1682}(23,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{144}{203}\right)\)	\(e\left(\frac{5}{203}\right)\)	\(e\left(\frac{60}{203}\right)\)	\(e\left(\frac{85}{203}\right)\)	\(e\left(\frac{41}{203}\right)\)	\(e\left(\frac{97}{203}\right)\)	\(e\left(\frac{149}{203}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{171}{203}\right)\)	\(e\left(\frac{1}{203}\right)\)
\(\chi_{1682}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{90}{203}\right)\)	\(e\left(\frac{130}{203}\right)\)	\(e\left(\frac{139}{203}\right)\)	\(e\left(\frac{180}{203}\right)\)	\(e\left(\frac{51}{203}\right)\)	\(e\left(\frac{86}{203}\right)\)	\(e\left(\frac{17}{203}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{183}{203}\right)\)	\(e\left(\frac{26}{203}\right)\)
\(\chi_{1682}(45,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{201}{203}\right)\)	\(e\left(\frac{155}{203}\right)\)	\(e\left(\frac{33}{203}\right)\)	\(e\left(\frac{199}{203}\right)\)	\(e\left(\frac{53}{203}\right)\)	\(e\left(\frac{165}{203}\right)\)	\(e\left(\frac{153}{203}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{23}{203}\right)\)	\(e\left(\frac{31}{203}\right)\)
\(\chi_{1682}(49,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{203}\right)\)	\(e\left(\frac{139}{203}\right)\)	\(e\left(\frac{44}{203}\right)\)	\(e\left(\frac{130}{203}\right)\)	\(e\left(\frac{3}{203}\right)\)	\(e\left(\frac{17}{203}\right)\)	\(e\left(\frac{1}{203}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{166}{203}\right)\)	\(e\left(\frac{109}{203}\right)\)
\(\chi_{1682}(53,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{203}\right)\)	\(e\left(\frac{72}{203}\right)\)	\(e\left(\frac{52}{203}\right)\)	\(e\left(\frac{6}{203}\right)\)	\(e\left(\frac{22}{203}\right)\)	\(e\left(\frac{57}{203}\right)\)	\(e\left(\frac{75}{203}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{67}{203}\right)\)	\(e\left(\frac{55}{203}\right)\)
\(\chi_{1682}(65,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{106}{203}\right)\)	\(e\left(\frac{108}{203}\right)\)	\(e\left(\frac{78}{203}\right)\)	\(e\left(\frac{9}{203}\right)\)	\(e\left(\frac{33}{203}\right)\)	\(e\left(\frac{187}{203}\right)\)	\(e\left(\frac{11}{203}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{202}{203}\right)\)	\(e\left(\frac{184}{203}\right)\)
\(\chi_{1682}(81,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{203}\right)\)	\(e\left(\frac{180}{203}\right)\)	\(e\left(\frac{130}{203}\right)\)	\(e\left(\frac{15}{203}\right)\)	\(e\left(\frac{55}{203}\right)\)	\(e\left(\frac{41}{203}\right)\)	\(e\left(\frac{86}{203}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{66}{203}\right)\)	\(e\left(\frac{36}{203}\right)\)
\(\chi_{1682}(83,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{203}\right)\)	\(e\left(\frac{88}{203}\right)\)	\(e\left(\frac{41}{203}\right)\)	\(e\left(\frac{75}{203}\right)\)	\(e\left(\frac{72}{203}\right)\)	\(e\left(\frac{2}{203}\right)\)	\(e\left(\frac{24}{203}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{127}{203}\right)\)	\(e\left(\frac{180}{203}\right)\)
\(\chi_{1682}(103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{138}{203}\right)\)	\(e\left(\frac{64}{203}\right)\)	\(e\left(\frac{159}{203}\right)\)	\(e\left(\frac{73}{203}\right)\)	\(e\left(\frac{200}{203}\right)\)	\(e\left(\frac{186}{203}\right)\)	\(e\left(\frac{202}{203}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{37}{203}\right)\)	\(e\left(\frac{94}{203}\right)\)
\(\chi_{1682}(107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{177}{203}\right)\)	\(e\left(\frac{188}{203}\right)\)	\(e\left(\frac{23}{203}\right)\)	\(e\left(\frac{151}{203}\right)\)	\(e\left(\frac{80}{203}\right)\)	\(e\left(\frac{115}{203}\right)\)	\(e\left(\frac{162}{203}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{96}{203}\right)\)	\(e\left(\frac{200}{203}\right)\)
\(\chi_{1682}(111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{164}{203}\right)\)	\(e\left(\frac{79}{203}\right)\)	\(e\left(\frac{136}{203}\right)\)	\(e\left(\frac{125}{203}\right)\)	\(e\left(\frac{120}{203}\right)\)	\(e\left(\frac{71}{203}\right)\)	\(e\left(\frac{40}{203}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{144}{203}\right)\)	\(e\left(\frac{97}{203}\right)\)
\(\chi_{1682}(123,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{78}{203}\right)\)	\(e\left(\frac{45}{203}\right)\)	\(e\left(\frac{134}{203}\right)\)	\(e\left(\frac{156}{203}\right)\)	\(e\left(\frac{166}{203}\right)\)	\(e\left(\frac{61}{203}\right)\)	\(e\left(\frac{123}{203}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{118}{203}\right)\)	\(e\left(\frac{9}{203}\right)\)
\(\chi_{1682}(139,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{74}{203}\right)\)	\(e\left(\frac{152}{203}\right)\)	\(e\left(\frac{200}{203}\right)\)	\(e\left(\frac{148}{203}\right)\)	\(e\left(\frac{69}{203}\right)\)	\(e\left(\frac{188}{203}\right)\)	\(e\left(\frac{23}{203}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{164}{203}\right)\)	\(e\left(\frac{71}{203}\right)\)
\(\chi_{1682}(141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{188}{203}\right)\)	\(e\left(\frac{46}{203}\right)\)	\(e\left(\frac{146}{203}\right)\)	\(e\left(\frac{173}{203}\right)\)	\(e\left(\frac{93}{203}\right)\)	\(e\left(\frac{121}{203}\right)\)	\(e\left(\frac{31}{203}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{71}{203}\right)\)	\(e\left(\frac{131}{203}\right)\)
\(\chi_{1682}(161,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{75}{203}\right)\)	\(e\left(\frac{176}{203}\right)\)	\(e\left(\frac{82}{203}\right)\)	\(e\left(\frac{150}{203}\right)\)	\(e\left(\frac{144}{203}\right)\)	\(e\left(\frac{4}{203}\right)\)	\(e\left(\frac{48}{203}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{51}{203}\right)\)	\(e\left(\frac{157}{203}\right)\)
\(\chi_{1682}(165,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{86}{203}\right)\)	\(e\left(\frac{34}{203}\right)\)	\(e\left(\frac{2}{203}\right)\)	\(e\left(\frac{172}{203}\right)\)	\(e\left(\frac{157}{203}\right)\)	\(e\left(\frac{10}{203}\right)\)	\(e\left(\frac{120}{203}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{26}{203}\right)\)	\(e\left(\frac{88}{203}\right)\)
\(\chi_{1682}(169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{122}{203}\right)\)	\(e\left(\frac{86}{203}\right)\)	\(e\left(\frac{17}{203}\right)\)	\(e\left(\frac{41}{203}\right)\)	\(e\left(\frac{15}{203}\right)\)	\(e\left(\frac{85}{203}\right)\)	\(e\left(\frac{5}{203}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{18}{203}\right)\)	\(e\left(\frac{139}{203}\right)\)
\(\chi_{1682}(181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{50}{203}\right)\)	\(e\left(\frac{185}{203}\right)\)	\(e\left(\frac{190}{203}\right)\)	\(e\left(\frac{100}{203}\right)\)	\(e\left(\frac{96}{203}\right)\)	\(e\left(\frac{138}{203}\right)\)	\(e\left(\frac{32}{203}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{34}{203}\right)\)	\(e\left(\frac{37}{203}\right)\)
\(\chi_{1682}(197,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{203}\right)\)	\(e\left(\frac{124}{203}\right)\)	\(e\left(\frac{67}{203}\right)\)	\(e\left(\frac{78}{203}\right)\)	\(e\left(\frac{83}{203}\right)\)	\(e\left(\frac{132}{203}\right)\)	\(e\left(\frac{163}{203}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{59}{203}\right)\)	\(e\left(\frac{106}{203}\right)\)
\(\chi_{1682}(199,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{203}\right)\)	\(e\left(\frac{4}{203}\right)\)	\(e\left(\frac{48}{203}\right)\)	\(e\left(\frac{68}{203}\right)\)	\(e\left(\frac{114}{203}\right)\)	\(e\left(\frac{37}{203}\right)\)	\(e\left(\frac{38}{203}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{15}{203}\right)\)	\(e\left(\frac{82}{203}\right)\)
\(\chi_{1682}(219,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{203}\right)\)	\(e\left(\frac{85}{203}\right)\)	\(e\left(\frac{5}{203}\right)\)	\(e\left(\frac{24}{203}\right)\)	\(e\left(\frac{88}{203}\right)\)	\(e\left(\frac{25}{203}\right)\)	\(e\left(\frac{97}{203}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{65}{203}\right)\)	\(e\left(\frac{17}{203}\right)\)
\(\chi_{1682}(223,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{198}{203}\right)\)	\(e\left(\frac{83}{203}\right)\)	\(e\left(\frac{184}{203}\right)\)	\(e\left(\frac{193}{203}\right)\)	\(e\left(\frac{31}{203}\right)\)	\(e\left(\frac{108}{203}\right)\)	\(e\left(\frac{78}{203}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{159}{203}\right)\)	\(e\left(\frac{179}{203}\right)\)
\(\chi_{1682}(227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{80}{203}\right)\)	\(e\left(\frac{93}{203}\right)\)	\(e\left(\frac{101}{203}\right)\)	\(e\left(\frac{160}{203}\right)\)	\(e\left(\frac{113}{203}\right)\)	\(e\left(\frac{99}{203}\right)\)	\(e\left(\frac{173}{203}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{95}{203}\right)\)	\(e\left(\frac{181}{203}\right)\)
\(\chi_{1682}(239,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{203}\right)\)	\(e\left(\frac{122}{203}\right)\)	\(e\left(\frac{43}{203}\right)\)	\(e\left(\frac{44}{203}\right)\)	\(e\left(\frac{26}{203}\right)\)	\(e\left(\frac{12}{203}\right)\)	\(e\left(\frac{144}{203}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{153}{203}\right)\)	\(e\left(\frac{65}{203}\right)\)
\(\chi_{1682}(255,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{203}\right)\)	\(e\left(\frac{96}{203}\right)\)	\(e\left(\frac{137}{203}\right)\)	\(e\left(\frac{8}{203}\right)\)	\(e\left(\frac{97}{203}\right)\)	\(e\left(\frac{76}{203}\right)\)	\(e\left(\frac{100}{203}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{157}{203}\right)\)	\(e\left(\frac{141}{203}\right)\)
\(\chi_{1682}(257,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{203}\right)\)	\(e\left(\frac{165}{203}\right)\)	\(e\left(\frac{153}{203}\right)\)	\(e\left(\frac{166}{203}\right)\)	\(e\left(\frac{135}{203}\right)\)	\(e\left(\frac{156}{203}\right)\)	\(e\left(\frac{45}{203}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{162}{203}\right)\)	\(e\left(\frac{33}{203}\right)\)
\(\chi_{1682}(277,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{152}{203}\right)\)	\(e\left(\frac{197}{203}\right)\)	\(e\left(\frac{131}{203}\right)\)	\(e\left(\frac{101}{203}\right)\)	\(e\left(\frac{32}{203}\right)\)	\(e\left(\frac{46}{203}\right)\)	\(e\left(\frac{146}{203}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{79}{203}\right)\)	\(e\left(\frac{80}{203}\right)\)
\(\chi_{1682}(281,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{203}\right)\)	\(e\left(\frac{132}{203}\right)\)	\(e\left(\frac{163}{203}\right)\)	\(e\left(\frac{11}{203}\right)\)	\(e\left(\frac{108}{203}\right)\)	\(e\left(\frac{3}{203}\right)\)	\(e\left(\frac{36}{203}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{89}{203}\right)\)	\(e\left(\frac{67}{203}\right)\)
\(\chi_{1682}(285,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{203}\right)\)	\(e\left(\frac{100}{203}\right)\)	\(e\left(\frac{185}{203}\right)\)	\(e\left(\frac{76}{203}\right)\)	\(e\left(\frac{8}{203}\right)\)	\(e\left(\frac{113}{203}\right)\)	\(e\left(\frac{138}{203}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{172}{203}\right)\)	\(e\left(\frac{20}{203}\right)\)
\(\chi_{1682}(297,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{203}\right)\)	\(e\left(\frac{59}{203}\right)\)	\(e\left(\frac{99}{203}\right)\)	\(e\left(\frac{191}{203}\right)\)	\(e\left(\frac{159}{203}\right)\)	\(e\left(\frac{89}{203}\right)\)	\(e\left(\frac{53}{203}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{69}{203}\right)\)	\(e\left(\frac{93}{203}\right)\)

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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	1682.j
Modulus	$1682$
Conductor	$841$
Order	$203$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(1682\)
Conductor:	\(841\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(203\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 841.j	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)