LMFDB - Dirichlet character orbit 2523.v

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2523, base_ring=CyclotomicField(406)) M = H._module chi = DirichletCharacter(H, M([203,151])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(5,2523)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2523$
Conductor:	$2523$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$406$	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:	$\Q(\zeta_{203})$
Fixed field:	Number field defined by a degree 406 polynomial (not computed)

First 31 of 168 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{2523}(5,\cdot)$	$-1$	$1$	$e\left(\frac{177}{203}\right)$	$e\left(\frac{151}{203}\right)$	$e\left(\frac{333}{406}\right)$	$e\left(\frac{171}{203}\right)$	$e\left(\frac{125}{203}\right)$	$e\left(\frac{281}{406}\right)$	$e\left(\frac{127}{203}\right)$	$e\left(\frac{43}{203}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{99}{203}\right)$
$\chi_{2523}(35,\cdot)$	$-1$	$1$	$e\left(\frac{68}{203}\right)$	$e\left(\frac{136}{203}\right)$	$e\left(\frac{269}{406}\right)$	$e\left(\frac{193}{203}\right)$	$e\left(\frac{1}{203}\right)$	$e\left(\frac{405}{406}\right)$	$e\left(\frac{27}{203}\right)$	$e\left(\frac{153}{203}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{69}{203}\right)$
$\chi_{2523}(38,\cdot)$	$-1$	$1$	$e\left(\frac{55}{203}\right)$	$e\left(\frac{110}{203}\right)$	$e\left(\frac{131}{406}\right)$	$e\left(\frac{177}{203}\right)$	$e\left(\frac{165}{203}\right)$	$e\left(\frac{241}{406}\right)$	$e\left(\frac{192}{203}\right)$	$e\left(\frac{73}{203}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{17}{203}\right)$
$\chi_{2523}(62,\cdot)$	$-1$	$1$	$e\left(\frac{4}{203}\right)$	$e\left(\frac{8}{203}\right)$	$e\left(\frac{183}{406}\right)$	$e\left(\frac{83}{203}\right)$	$e\left(\frac{12}{203}\right)$	$e\left(\frac{191}{406}\right)$	$e\left(\frac{121}{203}\right)$	$e\left(\frac{9}{203}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{16}{203}\right)$
$\chi_{2523}(71,\cdot)$	$-1$	$1$	$e\left(\frac{190}{203}\right)$	$e\left(\frac{177}{203}\right)$	$e\left(\frac{65}{406}\right)$	$e\left(\frac{187}{203}\right)$	$e\left(\frac{164}{203}\right)$	$e\left(\frac{39}{406}\right)$	$e\left(\frac{165}{203}\right)$	$e\left(\frac{123}{203}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{151}{203}\right)$
$\chi_{2523}(80,\cdot)$	$-1$	$1$	$e\left(\frac{178}{203}\right)$	$e\left(\frac{153}{203}\right)$	$e\left(\frac{125}{406}\right)$	$e\left(\frac{141}{203}\right)$	$e\left(\frac{128}{203}\right)$	$e\left(\frac{75}{406}\right)$	$e\left(\frac{5}{203}\right)$	$e\left(\frac{96}{203}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{103}{203}\right)$
$\chi_{2523}(92,\cdot)$	$-1$	$1$	$e\left(\frac{100}{203}\right)$	$e\left(\frac{200}{203}\right)$	$e\left(\frac{109}{406}\right)$	$e\left(\frac{45}{203}\right)$	$e\left(\frac{97}{203}\right)$	$e\left(\frac{309}{406}\right)$	$e\left(\frac{183}{203}\right)$	$e\left(\frac{22}{203}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{197}{203}\right)$
$\chi_{2523}(122,\cdot)$	$-1$	$1$	$e\left(\frac{173}{203}\right)$	$e\left(\frac{143}{203}\right)$	$e\left(\frac{353}{406}\right)$	$e\left(\frac{88}{203}\right)$	$e\left(\frac{113}{203}\right)$	$e\left(\frac{293}{406}\right)$	$e\left(\frac{6}{203}\right)$	$e\left(\frac{34}{203}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{83}{203}\right)$
$\chi_{2523}(125,\cdot)$	$-1$	$1$	$e\left(\frac{125}{203}\right)$	$e\left(\frac{47}{203}\right)$	$e\left(\frac{187}{406}\right)$	$e\left(\frac{107}{203}\right)$	$e\left(\frac{172}{203}\right)$	$e\left(\frac{31}{406}\right)$	$e\left(\frac{178}{203}\right)$	$e\left(\frac{129}{203}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{94}{203}\right)$
$\chi_{2523}(149,\cdot)$	$-1$	$1$	$e\left(\frac{60}{203}\right)$	$e\left(\frac{120}{203}\right)$	$e\left(\frac{309}{406}\right)$	$e\left(\frac{27}{203}\right)$	$e\left(\frac{180}{203}\right)$	$e\left(\frac{23}{406}\right)$	$e\left(\frac{191}{203}\right)$	$e\left(\frac{135}{203}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{37}{203}\right)$
$\chi_{2523}(158,\cdot)$	$-1$	$1$	$e\left(\frac{176}{203}\right)$	$e\left(\frac{149}{203}\right)$	$e\left(\frac{135}{406}\right)$	$e\left(\frac{201}{203}\right)$	$e\left(\frac{122}{203}\right)$	$e\left(\frac{81}{406}\right)$	$e\left(\frac{46}{203}\right)$	$e\left(\frac{193}{203}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{95}{203}\right)$
$\chi_{2523}(167,\cdot)$	$-1$	$1$	$e\left(\frac{59}{203}\right)$	$e\left(\frac{118}{203}\right)$	$e\left(\frac{111}{406}\right)$	$e\left(\frac{57}{203}\right)$	$e\left(\frac{177}{203}\right)$	$e\left(\frac{229}{406}\right)$	$e\left(\frac{110}{203}\right)$	$e\left(\frac{82}{203}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{33}{203}\right)$
$\chi_{2523}(179,\cdot)$	$-1$	$1$	$e\left(\frac{23}{203}\right)$	$e\left(\frac{46}{203}\right)$	$e\left(\frac{291}{406}\right)$	$e\left(\frac{122}{203}\right)$	$e\left(\frac{69}{203}\right)$	$e\left(\frac{337}{406}\right)$	$e\left(\frac{36}{203}\right)$	$e\left(\frac{1}{203}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{92}{203}\right)$
$\chi_{2523}(209,\cdot)$	$-1$	$1$	$e\left(\frac{75}{203}\right)$	$e\left(\frac{150}{203}\right)$	$e\left(\frac{31}{406}\right)$	$e\left(\frac{186}{203}\right)$	$e\left(\frac{22}{203}\right)$	$e\left(\frac{181}{406}\right)$	$e\left(\frac{188}{203}\right)$	$e\left(\frac{118}{203}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{97}{203}\right)$
$\chi_{2523}(212,\cdot)$	$-1$	$1$	$e\left(\frac{195}{203}\right)$	$e\left(\frac{187}{203}\right)$	$e\left(\frac{243}{406}\right)$	$e\left(\frac{37}{203}\right)$	$e\left(\frac{179}{203}\right)$	$e\left(\frac{227}{406}\right)$	$e\left(\frac{164}{203}\right)$	$e\left(\frac{185}{203}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{171}{203}\right)$
$\chi_{2523}(245,\cdot)$	$-1$	$1$	$e\left(\frac{162}{203}\right)$	$e\left(\frac{121}{203}\right)$	$e\left(\frac{205}{406}\right)$	$e\left(\frac{12}{203}\right)$	$e\left(\frac{80}{203}\right)$	$e\left(\frac{123}{406}\right)$	$e\left(\frac{130}{203}\right)$	$e\left(\frac{60}{203}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{39}{203}\right)$
$\chi_{2523}(254,\cdot)$	$-1$	$1$	$e\left(\frac{143}{203}\right)$	$e\left(\frac{83}{203}\right)$	$e\left(\frac{97}{406}\right)$	$e\left(\frac{176}{203}\right)$	$e\left(\frac{23}{203}\right)$	$e\left(\frac{383}{406}\right)$	$e\left(\frac{12}{203}\right)$	$e\left(\frac{68}{203}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{166}{203}\right)$
$\chi_{2523}(266,\cdot)$	$-1$	$1$	$e\left(\frac{149}{203}\right)$	$e\left(\frac{95}{203}\right)$	$e\left(\frac{67}{406}\right)$	$e\left(\frac{199}{203}\right)$	$e\left(\frac{41}{203}\right)$	$e\left(\frac{365}{406}\right)$	$e\left(\frac{92}{203}\right)$	$e\left(\frac{183}{203}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{190}{203}\right)$
$\chi_{2523}(296,\cdot)$	$-1$	$1$	$e\left(\frac{180}{203}\right)$	$e\left(\frac{157}{203}\right)$	$e\left(\frac{115}{406}\right)$	$e\left(\frac{81}{203}\right)$	$e\left(\frac{134}{203}\right)$	$e\left(\frac{69}{406}\right)$	$e\left(\frac{167}{203}\right)$	$e\left(\frac{202}{203}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{111}{203}\right)$
$\chi_{2523}(299,\cdot)$	$-1$	$1$	$e\left(\frac{62}{203}\right)$	$e\left(\frac{124}{203}\right)$	$e\left(\frac{299}{406}\right)$	$e\left(\frac{170}{203}\right)$	$e\left(\frac{186}{203}\right)$	$e\left(\frac{17}{406}\right)$	$e\left(\frac{150}{203}\right)$	$e\left(\frac{38}{203}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{45}{203}\right)$
$\chi_{2523}(323,\cdot)$	$-1$	$1$	$e\left(\frac{172}{203}\right)$	$e\left(\frac{141}{203}\right)$	$e\left(\frac{155}{406}\right)$	$e\left(\frac{118}{203}\right)$	$e\left(\frac{110}{203}\right)$	$e\left(\frac{93}{406}\right)$	$e\left(\frac{128}{203}\right)$	$e\left(\frac{184}{203}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{79}{203}\right)$
$\chi_{2523}(332,\cdot)$	$-1$	$1$	$e\left(\frac{148}{203}\right)$	$e\left(\frac{93}{203}\right)$	$e\left(\frac{275}{406}\right)$	$e\left(\frac{26}{203}\right)$	$e\left(\frac{38}{203}\right)$	$e\left(\frac{165}{406}\right)$	$e\left(\frac{11}{203}\right)$	$e\left(\frac{130}{203}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{186}{203}\right)$
$\chi_{2523}(341,\cdot)$	$-1$	$1$	$e\left(\frac{24}{203}\right)$	$e\left(\frac{48}{203}\right)$	$e\left(\frac{83}{406}\right)$	$e\left(\frac{92}{203}\right)$	$e\left(\frac{72}{203}\right)$	$e\left(\frac{131}{406}\right)$	$e\left(\frac{117}{203}\right)$	$e\left(\frac{54}{203}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{96}{203}\right)$
$\chi_{2523}(353,\cdot)$	$-1$	$1$	$e\left(\frac{72}{203}\right)$	$e\left(\frac{144}{203}\right)$	$e\left(\frac{249}{406}\right)$	$e\left(\frac{73}{203}\right)$	$e\left(\frac{13}{203}\right)$	$e\left(\frac{393}{406}\right)$	$e\left(\frac{148}{203}\right)$	$e\left(\frac{162}{203}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{85}{203}\right)$
$\chi_{2523}(383,\cdot)$	$-1$	$1$	$e\left(\frac{82}{203}\right)$	$e\left(\frac{164}{203}\right)$	$e\left(\frac{199}{406}\right)$	$e\left(\frac{179}{203}\right)$	$e\left(\frac{43}{203}\right)$	$e\left(\frac{363}{406}\right)$	$e\left(\frac{146}{203}\right)$	$e\left(\frac{83}{203}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{125}{203}\right)$
$\chi_{2523}(386,\cdot)$	$-1$	$1$	$e\left(\frac{132}{203}\right)$	$e\left(\frac{61}{203}\right)$	$e\left(\frac{355}{406}\right)$	$e\left(\frac{100}{203}\right)$	$e\left(\frac{193}{203}\right)$	$e\left(\frac{213}{406}\right)$	$e\left(\frac{136}{203}\right)$	$e\left(\frac{94}{203}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{122}{203}\right)$
$\chi_{2523}(410,\cdot)$	$-1$	$1$	$e\left(\frac{25}{203}\right)$	$e\left(\frac{50}{203}\right)$	$e\left(\frac{281}{406}\right)$	$e\left(\frac{62}{203}\right)$	$e\left(\frac{75}{203}\right)$	$e\left(\frac{331}{406}\right)$	$e\left(\frac{198}{203}\right)$	$e\left(\frac{107}{203}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{100}{203}\right)$
$\chi_{2523}(419,\cdot)$	$-1$	$1$	$e\left(\frac{134}{203}\right)$	$e\left(\frac{65}{203}\right)$	$e\left(\frac{345}{406}\right)$	$e\left(\frac{40}{203}\right)$	$e\left(\frac{199}{203}\right)$	$e\left(\frac{207}{406}\right)$	$e\left(\frac{95}{203}\right)$	$e\left(\frac{200}{203}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{130}{203}\right)$
$\chi_{2523}(428,\cdot)$	$-1$	$1$	$e\left(\frac{108}{203}\right)$	$e\left(\frac{13}{203}\right)$	$e\left(\frac{69}{406}\right)$	$e\left(\frac{8}{203}\right)$	$e\left(\frac{121}{203}\right)$	$e\left(\frac{285}{406}\right)$	$e\left(\frac{19}{203}\right)$	$e\left(\frac{40}{203}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{26}{203}\right)$
$\chi_{2523}(440,\cdot)$	$-1$	$1$	$e\left(\frac{198}{203}\right)$	$e\left(\frac{193}{203}\right)$	$e\left(\frac{25}{406}\right)$	$e\left(\frac{150}{203}\right)$	$e\left(\frac{188}{203}\right)$	$e\left(\frac{15}{406}\right)$	$e\left(\frac{1}{203}\right)$	$e\left(\frac{141}{203}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{183}{203}\right)$
$\chi_{2523}(470,\cdot)$	$-1$	$1$	$e\left(\frac{187}{203}\right)$	$e\left(\frac{171}{203}\right)$	$e\left(\frac{283}{406}\right)$	$e\left(\frac{74}{203}\right)$	$e\left(\frac{155}{203}\right)$	$e\left(\frac{251}{406}\right)$	$e\left(\frac{125}{203}\right)$	$e\left(\frac{167}{203}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{139}{203}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{2523}(5,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{177}{203}\right)\)	\(e\left(\frac{151}{203}\right)\)	\(e\left(\frac{333}{406}\right)\)	\(e\left(\frac{171}{203}\right)\)	\(e\left(\frac{125}{203}\right)\)	\(e\left(\frac{281}{406}\right)\)	\(e\left(\frac{127}{203}\right)\)	\(e\left(\frac{43}{203}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{99}{203}\right)\)
\(\chi_{2523}(35,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{68}{203}\right)\)	\(e\left(\frac{136}{203}\right)\)	\(e\left(\frac{269}{406}\right)\)	\(e\left(\frac{193}{203}\right)\)	\(e\left(\frac{1}{203}\right)\)	\(e\left(\frac{405}{406}\right)\)	\(e\left(\frac{27}{203}\right)\)	\(e\left(\frac{153}{203}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{69}{203}\right)\)
\(\chi_{2523}(38,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{55}{203}\right)\)	\(e\left(\frac{110}{203}\right)\)	\(e\left(\frac{131}{406}\right)\)	\(e\left(\frac{177}{203}\right)\)	\(e\left(\frac{165}{203}\right)\)	\(e\left(\frac{241}{406}\right)\)	\(e\left(\frac{192}{203}\right)\)	\(e\left(\frac{73}{203}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{17}{203}\right)\)
\(\chi_{2523}(62,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4}{203}\right)\)	\(e\left(\frac{8}{203}\right)\)	\(e\left(\frac{183}{406}\right)\)	\(e\left(\frac{83}{203}\right)\)	\(e\left(\frac{12}{203}\right)\)	\(e\left(\frac{191}{406}\right)\)	\(e\left(\frac{121}{203}\right)\)	\(e\left(\frac{9}{203}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{16}{203}\right)\)
\(\chi_{2523}(71,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{190}{203}\right)\)	\(e\left(\frac{177}{203}\right)\)	\(e\left(\frac{65}{406}\right)\)	\(e\left(\frac{187}{203}\right)\)	\(e\left(\frac{164}{203}\right)\)	\(e\left(\frac{39}{406}\right)\)	\(e\left(\frac{165}{203}\right)\)	\(e\left(\frac{123}{203}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{151}{203}\right)\)
\(\chi_{2523}(80,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{178}{203}\right)\)	\(e\left(\frac{153}{203}\right)\)	\(e\left(\frac{125}{406}\right)\)	\(e\left(\frac{141}{203}\right)\)	\(e\left(\frac{128}{203}\right)\)	\(e\left(\frac{75}{406}\right)\)	\(e\left(\frac{5}{203}\right)\)	\(e\left(\frac{96}{203}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{103}{203}\right)\)
\(\chi_{2523}(92,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{100}{203}\right)\)	\(e\left(\frac{200}{203}\right)\)	\(e\left(\frac{109}{406}\right)\)	\(e\left(\frac{45}{203}\right)\)	\(e\left(\frac{97}{203}\right)\)	\(e\left(\frac{309}{406}\right)\)	\(e\left(\frac{183}{203}\right)\)	\(e\left(\frac{22}{203}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{197}{203}\right)\)
\(\chi_{2523}(122,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{173}{203}\right)\)	\(e\left(\frac{143}{203}\right)\)	\(e\left(\frac{353}{406}\right)\)	\(e\left(\frac{88}{203}\right)\)	\(e\left(\frac{113}{203}\right)\)	\(e\left(\frac{293}{406}\right)\)	\(e\left(\frac{6}{203}\right)\)	\(e\left(\frac{34}{203}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{83}{203}\right)\)
\(\chi_{2523}(125,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{125}{203}\right)\)	\(e\left(\frac{47}{203}\right)\)	\(e\left(\frac{187}{406}\right)\)	\(e\left(\frac{107}{203}\right)\)	\(e\left(\frac{172}{203}\right)\)	\(e\left(\frac{31}{406}\right)\)	\(e\left(\frac{178}{203}\right)\)	\(e\left(\frac{129}{203}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{94}{203}\right)\)
\(\chi_{2523}(149,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{60}{203}\right)\)	\(e\left(\frac{120}{203}\right)\)	\(e\left(\frac{309}{406}\right)\)	\(e\left(\frac{27}{203}\right)\)	\(e\left(\frac{180}{203}\right)\)	\(e\left(\frac{23}{406}\right)\)	\(e\left(\frac{191}{203}\right)\)	\(e\left(\frac{135}{203}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{37}{203}\right)\)
\(\chi_{2523}(158,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{176}{203}\right)\)	\(e\left(\frac{149}{203}\right)\)	\(e\left(\frac{135}{406}\right)\)	\(e\left(\frac{201}{203}\right)\)	\(e\left(\frac{122}{203}\right)\)	\(e\left(\frac{81}{406}\right)\)	\(e\left(\frac{46}{203}\right)\)	\(e\left(\frac{193}{203}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{95}{203}\right)\)
\(\chi_{2523}(167,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{203}\right)\)	\(e\left(\frac{118}{203}\right)\)	\(e\left(\frac{111}{406}\right)\)	\(e\left(\frac{57}{203}\right)\)	\(e\left(\frac{177}{203}\right)\)	\(e\left(\frac{229}{406}\right)\)	\(e\left(\frac{110}{203}\right)\)	\(e\left(\frac{82}{203}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{33}{203}\right)\)
\(\chi_{2523}(179,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{203}\right)\)	\(e\left(\frac{46}{203}\right)\)	\(e\left(\frac{291}{406}\right)\)	\(e\left(\frac{122}{203}\right)\)	\(e\left(\frac{69}{203}\right)\)	\(e\left(\frac{337}{406}\right)\)	\(e\left(\frac{36}{203}\right)\)	\(e\left(\frac{1}{203}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{92}{203}\right)\)
\(\chi_{2523}(209,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{75}{203}\right)\)	\(e\left(\frac{150}{203}\right)\)	\(e\left(\frac{31}{406}\right)\)	\(e\left(\frac{186}{203}\right)\)	\(e\left(\frac{22}{203}\right)\)	\(e\left(\frac{181}{406}\right)\)	\(e\left(\frac{188}{203}\right)\)	\(e\left(\frac{118}{203}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{97}{203}\right)\)
\(\chi_{2523}(212,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{195}{203}\right)\)	\(e\left(\frac{187}{203}\right)\)	\(e\left(\frac{243}{406}\right)\)	\(e\left(\frac{37}{203}\right)\)	\(e\left(\frac{179}{203}\right)\)	\(e\left(\frac{227}{406}\right)\)	\(e\left(\frac{164}{203}\right)\)	\(e\left(\frac{185}{203}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{171}{203}\right)\)
\(\chi_{2523}(245,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{162}{203}\right)\)	\(e\left(\frac{121}{203}\right)\)	\(e\left(\frac{205}{406}\right)\)	\(e\left(\frac{12}{203}\right)\)	\(e\left(\frac{80}{203}\right)\)	\(e\left(\frac{123}{406}\right)\)	\(e\left(\frac{130}{203}\right)\)	\(e\left(\frac{60}{203}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{39}{203}\right)\)
\(\chi_{2523}(254,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{143}{203}\right)\)	\(e\left(\frac{83}{203}\right)\)	\(e\left(\frac{97}{406}\right)\)	\(e\left(\frac{176}{203}\right)\)	\(e\left(\frac{23}{203}\right)\)	\(e\left(\frac{383}{406}\right)\)	\(e\left(\frac{12}{203}\right)\)	\(e\left(\frac{68}{203}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{166}{203}\right)\)
\(\chi_{2523}(266,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{203}\right)\)	\(e\left(\frac{95}{203}\right)\)	\(e\left(\frac{67}{406}\right)\)	\(e\left(\frac{199}{203}\right)\)	\(e\left(\frac{41}{203}\right)\)	\(e\left(\frac{365}{406}\right)\)	\(e\left(\frac{92}{203}\right)\)	\(e\left(\frac{183}{203}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{190}{203}\right)\)
\(\chi_{2523}(296,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{180}{203}\right)\)	\(e\left(\frac{157}{203}\right)\)	\(e\left(\frac{115}{406}\right)\)	\(e\left(\frac{81}{203}\right)\)	\(e\left(\frac{134}{203}\right)\)	\(e\left(\frac{69}{406}\right)\)	\(e\left(\frac{167}{203}\right)\)	\(e\left(\frac{202}{203}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{111}{203}\right)\)
\(\chi_{2523}(299,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{62}{203}\right)\)	\(e\left(\frac{124}{203}\right)\)	\(e\left(\frac{299}{406}\right)\)	\(e\left(\frac{170}{203}\right)\)	\(e\left(\frac{186}{203}\right)\)	\(e\left(\frac{17}{406}\right)\)	\(e\left(\frac{150}{203}\right)\)	\(e\left(\frac{38}{203}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{45}{203}\right)\)
\(\chi_{2523}(323,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{172}{203}\right)\)	\(e\left(\frac{141}{203}\right)\)	\(e\left(\frac{155}{406}\right)\)	\(e\left(\frac{118}{203}\right)\)	\(e\left(\frac{110}{203}\right)\)	\(e\left(\frac{93}{406}\right)\)	\(e\left(\frac{128}{203}\right)\)	\(e\left(\frac{184}{203}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{79}{203}\right)\)
\(\chi_{2523}(332,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{148}{203}\right)\)	\(e\left(\frac{93}{203}\right)\)	\(e\left(\frac{275}{406}\right)\)	\(e\left(\frac{26}{203}\right)\)	\(e\left(\frac{38}{203}\right)\)	\(e\left(\frac{165}{406}\right)\)	\(e\left(\frac{11}{203}\right)\)	\(e\left(\frac{130}{203}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{186}{203}\right)\)
\(\chi_{2523}(341,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{24}{203}\right)\)	\(e\left(\frac{48}{203}\right)\)	\(e\left(\frac{83}{406}\right)\)	\(e\left(\frac{92}{203}\right)\)	\(e\left(\frac{72}{203}\right)\)	\(e\left(\frac{131}{406}\right)\)	\(e\left(\frac{117}{203}\right)\)	\(e\left(\frac{54}{203}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{96}{203}\right)\)
\(\chi_{2523}(353,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{72}{203}\right)\)	\(e\left(\frac{144}{203}\right)\)	\(e\left(\frac{249}{406}\right)\)	\(e\left(\frac{73}{203}\right)\)	\(e\left(\frac{13}{203}\right)\)	\(e\left(\frac{393}{406}\right)\)	\(e\left(\frac{148}{203}\right)\)	\(e\left(\frac{162}{203}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{85}{203}\right)\)
\(\chi_{2523}(383,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{82}{203}\right)\)	\(e\left(\frac{164}{203}\right)\)	\(e\left(\frac{199}{406}\right)\)	\(e\left(\frac{179}{203}\right)\)	\(e\left(\frac{43}{203}\right)\)	\(e\left(\frac{363}{406}\right)\)	\(e\left(\frac{146}{203}\right)\)	\(e\left(\frac{83}{203}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{125}{203}\right)\)
\(\chi_{2523}(386,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{132}{203}\right)\)	\(e\left(\frac{61}{203}\right)\)	\(e\left(\frac{355}{406}\right)\)	\(e\left(\frac{100}{203}\right)\)	\(e\left(\frac{193}{203}\right)\)	\(e\left(\frac{213}{406}\right)\)	\(e\left(\frac{136}{203}\right)\)	\(e\left(\frac{94}{203}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{122}{203}\right)\)
\(\chi_{2523}(410,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{203}\right)\)	\(e\left(\frac{50}{203}\right)\)	\(e\left(\frac{281}{406}\right)\)	\(e\left(\frac{62}{203}\right)\)	\(e\left(\frac{75}{203}\right)\)	\(e\left(\frac{331}{406}\right)\)	\(e\left(\frac{198}{203}\right)\)	\(e\left(\frac{107}{203}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{100}{203}\right)\)
\(\chi_{2523}(419,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{134}{203}\right)\)	\(e\left(\frac{65}{203}\right)\)	\(e\left(\frac{345}{406}\right)\)	\(e\left(\frac{40}{203}\right)\)	\(e\left(\frac{199}{203}\right)\)	\(e\left(\frac{207}{406}\right)\)	\(e\left(\frac{95}{203}\right)\)	\(e\left(\frac{200}{203}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{130}{203}\right)\)
\(\chi_{2523}(428,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{108}{203}\right)\)	\(e\left(\frac{13}{203}\right)\)	\(e\left(\frac{69}{406}\right)\)	\(e\left(\frac{8}{203}\right)\)	\(e\left(\frac{121}{203}\right)\)	\(e\left(\frac{285}{406}\right)\)	\(e\left(\frac{19}{203}\right)\)	\(e\left(\frac{40}{203}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{26}{203}\right)\)
\(\chi_{2523}(440,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{198}{203}\right)\)	\(e\left(\frac{193}{203}\right)\)	\(e\left(\frac{25}{406}\right)\)	\(e\left(\frac{150}{203}\right)\)	\(e\left(\frac{188}{203}\right)\)	\(e\left(\frac{15}{406}\right)\)	\(e\left(\frac{1}{203}\right)\)	\(e\left(\frac{141}{203}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{183}{203}\right)\)
\(\chi_{2523}(470,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{187}{203}\right)\)	\(e\left(\frac{171}{203}\right)\)	\(e\left(\frac{283}{406}\right)\)	\(e\left(\frac{74}{203}\right)\)	\(e\left(\frac{155}{203}\right)\)	\(e\left(\frac{251}{406}\right)\)	\(e\left(\frac{125}{203}\right)\)	\(e\left(\frac{167}{203}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{139}{203}\right)\)

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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	2523.v
Modulus	$2523$
Conductor	$2523$
Order	$406$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(2523\)
Conductor:	\(2523\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(406\)	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)