LMFDB - Dirichlet character orbit 2523.w

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2523, base_ring=CyclotomicField(812)) M = H._module chi = DirichletCharacter(H, M([0,303])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(10,2523)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2523$
Conductor:	$841$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$812$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 841.l	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:	$\Q(\zeta_{812})$
Fixed field:	Number field defined by a degree 812 polynomial (not computed)

First 31 of 336 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{2523}(10,\cdot)$	$-1$	$1$	$e\left(\frac{303}{812}\right)$	$e\left(\frac{303}{406}\right)$	$e\left(\frac{281}{406}\right)$	$e\left(\frac{62}{203}\right)$	$e\left(\frac{97}{812}\right)$	$e\left(\frac{53}{812}\right)$	$e\left(\frac{183}{812}\right)$	$e\left(\frac{11}{406}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{100}{203}\right)$
$\chi_{2523}(19,\cdot)$	$-1$	$1$	$e\left(\frac{625}{812}\right)$	$e\left(\frac{219}{406}\right)$	$e\left(\frac{183}{406}\right)$	$e\left(\frac{83}{203}\right)$	$e\left(\frac{251}{812}\right)$	$e\left(\frac{179}{812}\right)$	$e\left(\frac{281}{812}\right)$	$e\left(\frac{221}{406}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{16}{203}\right)$
$\chi_{2523}(31,\cdot)$	$-1$	$1$	$e\left(\frac{421}{812}\right)$	$e\left(\frac{15}{406}\right)$	$e\left(\frac{235}{406}\right)$	$e\left(\frac{192}{203}\right)$	$e\left(\frac{451}{812}\right)$	$e\left(\frac{79}{812}\right)$	$e\left(\frac{809}{812}\right)$	$e\left(\frac{93}{406}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{15}{203}\right)$
$\chi_{2523}(37,\cdot)$	$-1$	$1$	$e\left(\frac{311}{812}\right)$	$e\left(\frac{311}{406}\right)$	$e\left(\frac{271}{406}\right)$	$e\left(\frac{2}{203}\right)$	$e\left(\frac{121}{812}\right)$	$e\left(\frac{41}{812}\right)$	$e\left(\frac{19}{812}\right)$	$e\left(\frac{223}{406}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{108}{203}\right)$
$\chi_{2523}(40,\cdot)$	$-1$	$1$	$e\left(\frac{305}{812}\right)$	$e\left(\frac{305}{406}\right)$	$e\left(\frac{177}{406}\right)$	$e\left(\frac{47}{203}\right)$	$e\left(\frac{103}{812}\right)$	$e\left(\frac{659}{812}\right)$	$e\left(\frac{345}{812}\right)$	$e\left(\frac{267}{406}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{102}{203}\right)$
$\chi_{2523}(43,\cdot)$	$-1$	$1$	$e\left(\frac{321}{812}\right)$	$e\left(\frac{321}{406}\right)$	$e\left(\frac{157}{406}\right)$	$e\left(\frac{130}{203}\right)$	$e\left(\frac{151}{812}\right)$	$e\left(\frac{635}{812}\right)$	$e\left(\frac{17}{812}\right)$	$e\left(\frac{285}{406}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{118}{203}\right)$
$\chi_{2523}(55,\cdot)$	$-1$	$1$	$e\left(\frac{383}{812}\right)$	$e\left(\frac{383}{406}\right)$	$e\left(\frac{181}{406}\right)$	$e\left(\frac{71}{203}\right)$	$e\left(\frac{337}{812}\right)$	$e\left(\frac{745}{812}\right)$	$e\left(\frac{167}{812}\right)$	$e\left(\frac{101}{406}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{180}{203}\right)$
$\chi_{2523}(61,\cdot)$	$-1$	$1$	$e\left(\frac{285}{812}\right)$	$e\left(\frac{285}{406}\right)$	$e\left(\frac{405}{406}\right)$	$e\left(\frac{197}{203}\right)$	$e\left(\frac{43}{812}\right)$	$e\left(\frac{283}{812}\right)$	$e\left(\frac{349}{812}\right)$	$e\left(\frac{143}{406}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{82}{203}\right)$
$\chi_{2523}(73,\cdot)$	$-1$	$1$	$e\left(\frac{139}{812}\right)$	$e\left(\frac{139}{406}\right)$	$e\left(\frac{283}{406}\right)$	$e\left(\frac{74}{203}\right)$	$e\left(\frac{417}{812}\right)$	$e\left(\frac{705}{812}\right)$	$e\left(\frac{703}{812}\right)$	$e\left(\frac{131}{406}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{139}{203}\right)$
$\chi_{2523}(76,\cdot)$	$-1$	$1$	$e\left(\frac{627}{812}\right)$	$e\left(\frac{221}{406}\right)$	$e\left(\frac{79}{406}\right)$	$e\left(\frac{68}{203}\right)$	$e\left(\frac{257}{812}\right)$	$e\left(\frac{785}{812}\right)$	$e\left(\frac{443}{812}\right)$	$e\left(\frac{71}{406}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{18}{203}\right)$
$\chi_{2523}(79,\cdot)$	$-1$	$1$	$e\left(\frac{297}{812}\right)$	$e\left(\frac{297}{406}\right)$	$e\left(\frac{187}{406}\right)$	$e\left(\frac{107}{203}\right)$	$e\left(\frac{79}{812}\right)$	$e\left(\frac{671}{812}\right)$	$e\left(\frac{509}{812}\right)$	$e\left(\frac{55}{406}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{94}{203}\right)$
$\chi_{2523}(85,\cdot)$	$-1$	$1$	$e\left(\frac{771}{812}\right)$	$e\left(\frac{365}{406}\right)$	$e\left(\frac{305}{406}\right)$	$e\left(\frac{3}{203}\right)$	$e\left(\frac{689}{812}\right)$	$e\left(\frac{569}{812}\right)$	$e\left(\frac{739}{812}\right)$	$e\left(\frac{233}{406}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{162}{203}\right)$
$\chi_{2523}(97,\cdot)$	$-1$	$1$	$e\left(\frac{555}{812}\right)$	$e\left(\frac{149}{406}\right)$	$e\left(\frac{169}{406}\right)$	$e\left(\frac{202}{203}\right)$	$e\left(\frac{41}{812}\right)$	$e\left(\frac{81}{812}\right)$	$e\left(\frac{295}{812}\right)$	$e\left(\frac{193}{406}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{149}{203}\right)$
$\chi_{2523}(106,\cdot)$	$-1$	$1$	$e\left(\frac{373}{812}\right)$	$e\left(\frac{373}{406}\right)$	$e\left(\frac{295}{406}\right)$	$e\left(\frac{146}{203}\right)$	$e\left(\frac{307}{812}\right)$	$e\left(\frac{151}{812}\right)$	$e\left(\frac{169}{812}\right)$	$e\left(\frac{39}{406}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{170}{203}\right)$
$\chi_{2523}(118,\cdot)$	$-1$	$1$	$e\left(\frac{57}{812}\right)$	$e\left(\frac{57}{406}\right)$	$e\left(\frac{81}{406}\right)$	$e\left(\frac{80}{203}\right)$	$e\left(\frac{171}{812}\right)$	$e\left(\frac{219}{812}\right)$	$e\left(\frac{557}{812}\right)$	$e\left(\frac{191}{406}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{57}{203}\right)$
$\chi_{2523}(124,\cdot)$	$-1$	$1$	$e\left(\frac{423}{812}\right)$	$e\left(\frac{17}{406}\right)$	$e\left(\frac{131}{406}\right)$	$e\left(\frac{177}{203}\right)$	$e\left(\frac{457}{812}\right)$	$e\left(\frac{685}{812}\right)$	$e\left(\frac{159}{812}\right)$	$e\left(\frac{349}{406}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{17}{203}\right)$
$\chi_{2523}(127,\cdot)$	$-1$	$1$	$e\left(\frac{165}{812}\right)$	$e\left(\frac{165}{406}\right)$	$e\left(\frac{149}{406}\right)$	$e\left(\frac{82}{203}\right)$	$e\left(\frac{495}{812}\right)$	$e\left(\frac{463}{812}\right)$	$e\left(\frac{373}{812}\right)$	$e\left(\frac{211}{406}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{165}{203}\right)$
$\chi_{2523}(130,\cdot)$	$-1$	$1$	$e\left(\frac{153}{812}\right)$	$e\left(\frac{153}{406}\right)$	$e\left(\frac{367}{406}\right)$	$e\left(\frac{172}{203}\right)$	$e\left(\frac{459}{812}\right)$	$e\left(\frac{75}{812}\right)$	$e\left(\frac{213}{812}\right)$	$e\left(\frac{299}{406}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{153}{203}\right)$
$\chi_{2523}(142,\cdot)$	$-1$	$1$	$e\left(\frac{355}{812}\right)$	$e\left(\frac{355}{406}\right)$	$e\left(\frac{13}{406}\right)$	$e\left(\frac{78}{203}\right)$	$e\left(\frac{253}{812}\right)$	$e\left(\frac{381}{812}\right)$	$e\left(\frac{335}{812}\right)$	$e\left(\frac{171}{406}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{152}{203}\right)$
$\chi_{2523}(148,\cdot)$	$-1$	$1$	$e\left(\frac{313}{812}\right)$	$e\left(\frac{313}{406}\right)$	$e\left(\frac{167}{406}\right)$	$e\left(\frac{190}{203}\right)$	$e\left(\frac{127}{812}\right)$	$e\left(\frac{647}{812}\right)$	$e\left(\frac{181}{812}\right)$	$e\left(\frac{73}{406}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{110}{203}\right)$
$\chi_{2523}(160,\cdot)$	$-1$	$1$	$e\left(\frac{307}{812}\right)$	$e\left(\frac{307}{406}\right)$	$e\left(\frac{73}{406}\right)$	$e\left(\frac{32}{203}\right)$	$e\left(\frac{109}{812}\right)$	$e\left(\frac{453}{812}\right)$	$e\left(\frac{507}{812}\right)$	$e\left(\frac{117}{406}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{104}{203}\right)$
$\chi_{2523}(163,\cdot)$	$-1$	$1$	$e\left(\frac{767}{812}\right)$	$e\left(\frac{361}{406}\right)$	$e\left(\frac{107}{406}\right)$	$e\left(\frac{33}{203}\right)$	$e\left(\frac{677}{812}\right)$	$e\left(\frac{169}{812}\right)$	$e\left(\frac{415}{812}\right)$	$e\left(\frac{127}{406}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{158}{203}\right)$
$\chi_{2523}(166,\cdot)$	$-1$	$1$	$e\left(\frac{185}{812}\right)$	$e\left(\frac{185}{406}\right)$	$e\left(\frac{327}{406}\right)$	$e\left(\frac{135}{203}\right)$	$e\left(\frac{555}{812}\right)$	$e\left(\frac{27}{812}\right)$	$e\left(\frac{369}{812}\right)$	$e\left(\frac{335}{406}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{185}{203}\right)$
$\chi_{2523}(172,\cdot)$	$-1$	$1$	$e\left(\frac{323}{812}\right)$	$e\left(\frac{323}{406}\right)$	$e\left(\frac{53}{406}\right)$	$e\left(\frac{115}{203}\right)$	$e\left(\frac{157}{812}\right)$	$e\left(\frac{429}{812}\right)$	$e\left(\frac{179}{812}\right)$	$e\left(\frac{135}{406}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{120}{203}\right)$
$\chi_{2523}(184,\cdot)$	$-1$	$1$	$e\left(\frac{807}{812}\right)$	$e\left(\frac{401}{406}\right)$	$e\left(\frac{57}{406}\right)$	$e\left(\frac{139}{203}\right)$	$e\left(\frac{797}{812}\right)$	$e\left(\frac{109}{812}\right)$	$e\left(\frac{407}{812}\right)$	$e\left(\frac{375}{406}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{198}{203}\right)$
$\chi_{2523}(193,\cdot)$	$-1$	$1$	$e\left(\frac{121}{812}\right)$	$e\left(\frac{121}{406}\right)$	$e\left(\frac{1}{406}\right)$	$e\left(\frac{6}{203}\right)$	$e\left(\frac{363}{812}\right)$	$e\left(\frac{123}{812}\right)$	$e\left(\frac{57}{812}\right)$	$e\left(\frac{263}{406}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{121}{203}\right)$
$\chi_{2523}(205,\cdot)$	$-1$	$1$	$e\left(\frac{505}{812}\right)$	$e\left(\frac{99}{406}\right)$	$e\left(\frac{333}{406}\right)$	$e\left(\frac{171}{203}\right)$	$e\left(\frac{703}{812}\right)$	$e\left(\frac{359}{812}\right)$	$e\left(\frac{305}{812}\right)$	$e\left(\frac{289}{406}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{99}{203}\right)$
$\chi_{2523}(211,\cdot)$	$-1$	$1$	$e\left(\frac{535}{812}\right)$	$e\left(\frac{129}{406}\right)$	$e\left(\frac{397}{406}\right)$	$e\left(\frac{149}{203}\right)$	$e\left(\frac{793}{812}\right)$	$e\left(\frac{517}{812}\right)$	$e\left(\frac{299}{812}\right)$	$e\left(\frac{69}{406}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{129}{203}\right)$
$\chi_{2523}(214,\cdot)$	$-1$	$1$	$e\left(\frac{25}{812}\right)$	$e\left(\frac{25}{406}\right)$	$e\left(\frac{121}{406}\right)$	$e\left(\frac{117}{203}\right)$	$e\left(\frac{75}{812}\right)$	$e\left(\frac{267}{812}\right)$	$e\left(\frac{401}{812}\right)$	$e\left(\frac{155}{406}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{25}{203}\right)$
$\chi_{2523}(217,\cdot)$	$-1$	$1$	$e\left(\frac{797}{812}\right)$	$e\left(\frac{391}{406}\right)$	$e\left(\frac{171}{406}\right)$	$e\left(\frac{11}{203}\right)$	$e\left(\frac{767}{812}\right)$	$e\left(\frac{327}{812}\right)$	$e\left(\frac{409}{812}\right)$	$e\left(\frac{313}{406}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{188}{203}\right)$
$\chi_{2523}(229,\cdot)$	$-1$	$1$	$e\left(\frac{327}{812}\right)$	$e\left(\frac{327}{406}\right)$	$e\left(\frac{251}{406}\right)$	$e\left(\frac{85}{203}\right)$	$e\left(\frac{169}{812}\right)$	$e\left(\frac{17}{812}\right)$	$e\left(\frac{503}{812}\right)$	$e\left(\frac{241}{406}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{124}{203}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{2523}(10,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{303}{812}\right)\)	\(e\left(\frac{303}{406}\right)\)	\(e\left(\frac{281}{406}\right)\)	\(e\left(\frac{62}{203}\right)\)	\(e\left(\frac{97}{812}\right)\)	\(e\left(\frac{53}{812}\right)\)	\(e\left(\frac{183}{812}\right)\)	\(e\left(\frac{11}{406}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{100}{203}\right)\)
\(\chi_{2523}(19,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{625}{812}\right)\)	\(e\left(\frac{219}{406}\right)\)	\(e\left(\frac{183}{406}\right)\)	\(e\left(\frac{83}{203}\right)\)	\(e\left(\frac{251}{812}\right)\)	\(e\left(\frac{179}{812}\right)\)	\(e\left(\frac{281}{812}\right)\)	\(e\left(\frac{221}{406}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{16}{203}\right)\)
\(\chi_{2523}(31,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{421}{812}\right)\)	\(e\left(\frac{15}{406}\right)\)	\(e\left(\frac{235}{406}\right)\)	\(e\left(\frac{192}{203}\right)\)	\(e\left(\frac{451}{812}\right)\)	\(e\left(\frac{79}{812}\right)\)	\(e\left(\frac{809}{812}\right)\)	\(e\left(\frac{93}{406}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{15}{203}\right)\)
\(\chi_{2523}(37,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{311}{812}\right)\)	\(e\left(\frac{311}{406}\right)\)	\(e\left(\frac{271}{406}\right)\)	\(e\left(\frac{2}{203}\right)\)	\(e\left(\frac{121}{812}\right)\)	\(e\left(\frac{41}{812}\right)\)	\(e\left(\frac{19}{812}\right)\)	\(e\left(\frac{223}{406}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{108}{203}\right)\)
\(\chi_{2523}(40,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{305}{812}\right)\)	\(e\left(\frac{305}{406}\right)\)	\(e\left(\frac{177}{406}\right)\)	\(e\left(\frac{47}{203}\right)\)	\(e\left(\frac{103}{812}\right)\)	\(e\left(\frac{659}{812}\right)\)	\(e\left(\frac{345}{812}\right)\)	\(e\left(\frac{267}{406}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{102}{203}\right)\)
\(\chi_{2523}(43,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{321}{812}\right)\)	\(e\left(\frac{321}{406}\right)\)	\(e\left(\frac{157}{406}\right)\)	\(e\left(\frac{130}{203}\right)\)	\(e\left(\frac{151}{812}\right)\)	\(e\left(\frac{635}{812}\right)\)	\(e\left(\frac{17}{812}\right)\)	\(e\left(\frac{285}{406}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{118}{203}\right)\)
\(\chi_{2523}(55,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{383}{812}\right)\)	\(e\left(\frac{383}{406}\right)\)	\(e\left(\frac{181}{406}\right)\)	\(e\left(\frac{71}{203}\right)\)	\(e\left(\frac{337}{812}\right)\)	\(e\left(\frac{745}{812}\right)\)	\(e\left(\frac{167}{812}\right)\)	\(e\left(\frac{101}{406}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{180}{203}\right)\)
\(\chi_{2523}(61,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{285}{812}\right)\)	\(e\left(\frac{285}{406}\right)\)	\(e\left(\frac{405}{406}\right)\)	\(e\left(\frac{197}{203}\right)\)	\(e\left(\frac{43}{812}\right)\)	\(e\left(\frac{283}{812}\right)\)	\(e\left(\frac{349}{812}\right)\)	\(e\left(\frac{143}{406}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{82}{203}\right)\)
\(\chi_{2523}(73,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{139}{812}\right)\)	\(e\left(\frac{139}{406}\right)\)	\(e\left(\frac{283}{406}\right)\)	\(e\left(\frac{74}{203}\right)\)	\(e\left(\frac{417}{812}\right)\)	\(e\left(\frac{705}{812}\right)\)	\(e\left(\frac{703}{812}\right)\)	\(e\left(\frac{131}{406}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{139}{203}\right)\)
\(\chi_{2523}(76,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{627}{812}\right)\)	\(e\left(\frac{221}{406}\right)\)	\(e\left(\frac{79}{406}\right)\)	\(e\left(\frac{68}{203}\right)\)	\(e\left(\frac{257}{812}\right)\)	\(e\left(\frac{785}{812}\right)\)	\(e\left(\frac{443}{812}\right)\)	\(e\left(\frac{71}{406}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{18}{203}\right)\)
\(\chi_{2523}(79,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{297}{812}\right)\)	\(e\left(\frac{297}{406}\right)\)	\(e\left(\frac{187}{406}\right)\)	\(e\left(\frac{107}{203}\right)\)	\(e\left(\frac{79}{812}\right)\)	\(e\left(\frac{671}{812}\right)\)	\(e\left(\frac{509}{812}\right)\)	\(e\left(\frac{55}{406}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{94}{203}\right)\)
\(\chi_{2523}(85,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{771}{812}\right)\)	\(e\left(\frac{365}{406}\right)\)	\(e\left(\frac{305}{406}\right)\)	\(e\left(\frac{3}{203}\right)\)	\(e\left(\frac{689}{812}\right)\)	\(e\left(\frac{569}{812}\right)\)	\(e\left(\frac{739}{812}\right)\)	\(e\left(\frac{233}{406}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{162}{203}\right)\)
\(\chi_{2523}(97,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{555}{812}\right)\)	\(e\left(\frac{149}{406}\right)\)	\(e\left(\frac{169}{406}\right)\)	\(e\left(\frac{202}{203}\right)\)	\(e\left(\frac{41}{812}\right)\)	\(e\left(\frac{81}{812}\right)\)	\(e\left(\frac{295}{812}\right)\)	\(e\left(\frac{193}{406}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{149}{203}\right)\)
\(\chi_{2523}(106,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{373}{812}\right)\)	\(e\left(\frac{373}{406}\right)\)	\(e\left(\frac{295}{406}\right)\)	\(e\left(\frac{146}{203}\right)\)	\(e\left(\frac{307}{812}\right)\)	\(e\left(\frac{151}{812}\right)\)	\(e\left(\frac{169}{812}\right)\)	\(e\left(\frac{39}{406}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{170}{203}\right)\)
\(\chi_{2523}(118,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{57}{812}\right)\)	\(e\left(\frac{57}{406}\right)\)	\(e\left(\frac{81}{406}\right)\)	\(e\left(\frac{80}{203}\right)\)	\(e\left(\frac{171}{812}\right)\)	\(e\left(\frac{219}{812}\right)\)	\(e\left(\frac{557}{812}\right)\)	\(e\left(\frac{191}{406}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{57}{203}\right)\)
\(\chi_{2523}(124,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{423}{812}\right)\)	\(e\left(\frac{17}{406}\right)\)	\(e\left(\frac{131}{406}\right)\)	\(e\left(\frac{177}{203}\right)\)	\(e\left(\frac{457}{812}\right)\)	\(e\left(\frac{685}{812}\right)\)	\(e\left(\frac{159}{812}\right)\)	\(e\left(\frac{349}{406}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{17}{203}\right)\)
\(\chi_{2523}(127,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{165}{812}\right)\)	\(e\left(\frac{165}{406}\right)\)	\(e\left(\frac{149}{406}\right)\)	\(e\left(\frac{82}{203}\right)\)	\(e\left(\frac{495}{812}\right)\)	\(e\left(\frac{463}{812}\right)\)	\(e\left(\frac{373}{812}\right)\)	\(e\left(\frac{211}{406}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{165}{203}\right)\)
\(\chi_{2523}(130,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{153}{812}\right)\)	\(e\left(\frac{153}{406}\right)\)	\(e\left(\frac{367}{406}\right)\)	\(e\left(\frac{172}{203}\right)\)	\(e\left(\frac{459}{812}\right)\)	\(e\left(\frac{75}{812}\right)\)	\(e\left(\frac{213}{812}\right)\)	\(e\left(\frac{299}{406}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{153}{203}\right)\)
\(\chi_{2523}(142,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{355}{812}\right)\)	\(e\left(\frac{355}{406}\right)\)	\(e\left(\frac{13}{406}\right)\)	\(e\left(\frac{78}{203}\right)\)	\(e\left(\frac{253}{812}\right)\)	\(e\left(\frac{381}{812}\right)\)	\(e\left(\frac{335}{812}\right)\)	\(e\left(\frac{171}{406}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{152}{203}\right)\)
\(\chi_{2523}(148,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{313}{812}\right)\)	\(e\left(\frac{313}{406}\right)\)	\(e\left(\frac{167}{406}\right)\)	\(e\left(\frac{190}{203}\right)\)	\(e\left(\frac{127}{812}\right)\)	\(e\left(\frac{647}{812}\right)\)	\(e\left(\frac{181}{812}\right)\)	\(e\left(\frac{73}{406}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{110}{203}\right)\)
\(\chi_{2523}(160,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{307}{812}\right)\)	\(e\left(\frac{307}{406}\right)\)	\(e\left(\frac{73}{406}\right)\)	\(e\left(\frac{32}{203}\right)\)	\(e\left(\frac{109}{812}\right)\)	\(e\left(\frac{453}{812}\right)\)	\(e\left(\frac{507}{812}\right)\)	\(e\left(\frac{117}{406}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{104}{203}\right)\)
\(\chi_{2523}(163,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{767}{812}\right)\)	\(e\left(\frac{361}{406}\right)\)	\(e\left(\frac{107}{406}\right)\)	\(e\left(\frac{33}{203}\right)\)	\(e\left(\frac{677}{812}\right)\)	\(e\left(\frac{169}{812}\right)\)	\(e\left(\frac{415}{812}\right)\)	\(e\left(\frac{127}{406}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{158}{203}\right)\)
\(\chi_{2523}(166,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{185}{812}\right)\)	\(e\left(\frac{185}{406}\right)\)	\(e\left(\frac{327}{406}\right)\)	\(e\left(\frac{135}{203}\right)\)	\(e\left(\frac{555}{812}\right)\)	\(e\left(\frac{27}{812}\right)\)	\(e\left(\frac{369}{812}\right)\)	\(e\left(\frac{335}{406}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{185}{203}\right)\)
\(\chi_{2523}(172,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{323}{812}\right)\)	\(e\left(\frac{323}{406}\right)\)	\(e\left(\frac{53}{406}\right)\)	\(e\left(\frac{115}{203}\right)\)	\(e\left(\frac{157}{812}\right)\)	\(e\left(\frac{429}{812}\right)\)	\(e\left(\frac{179}{812}\right)\)	\(e\left(\frac{135}{406}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{120}{203}\right)\)
\(\chi_{2523}(184,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{807}{812}\right)\)	\(e\left(\frac{401}{406}\right)\)	\(e\left(\frac{57}{406}\right)\)	\(e\left(\frac{139}{203}\right)\)	\(e\left(\frac{797}{812}\right)\)	\(e\left(\frac{109}{812}\right)\)	\(e\left(\frac{407}{812}\right)\)	\(e\left(\frac{375}{406}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{198}{203}\right)\)
\(\chi_{2523}(193,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{121}{812}\right)\)	\(e\left(\frac{121}{406}\right)\)	\(e\left(\frac{1}{406}\right)\)	\(e\left(\frac{6}{203}\right)\)	\(e\left(\frac{363}{812}\right)\)	\(e\left(\frac{123}{812}\right)\)	\(e\left(\frac{57}{812}\right)\)	\(e\left(\frac{263}{406}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{121}{203}\right)\)
\(\chi_{2523}(205,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{505}{812}\right)\)	\(e\left(\frac{99}{406}\right)\)	\(e\left(\frac{333}{406}\right)\)	\(e\left(\frac{171}{203}\right)\)	\(e\left(\frac{703}{812}\right)\)	\(e\left(\frac{359}{812}\right)\)	\(e\left(\frac{305}{812}\right)\)	\(e\left(\frac{289}{406}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{99}{203}\right)\)
\(\chi_{2523}(211,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{535}{812}\right)\)	\(e\left(\frac{129}{406}\right)\)	\(e\left(\frac{397}{406}\right)\)	\(e\left(\frac{149}{203}\right)\)	\(e\left(\frac{793}{812}\right)\)	\(e\left(\frac{517}{812}\right)\)	\(e\left(\frac{299}{812}\right)\)	\(e\left(\frac{69}{406}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{129}{203}\right)\)
\(\chi_{2523}(214,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{812}\right)\)	\(e\left(\frac{25}{406}\right)\)	\(e\left(\frac{121}{406}\right)\)	\(e\left(\frac{117}{203}\right)\)	\(e\left(\frac{75}{812}\right)\)	\(e\left(\frac{267}{812}\right)\)	\(e\left(\frac{401}{812}\right)\)	\(e\left(\frac{155}{406}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{25}{203}\right)\)
\(\chi_{2523}(217,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{797}{812}\right)\)	\(e\left(\frac{391}{406}\right)\)	\(e\left(\frac{171}{406}\right)\)	\(e\left(\frac{11}{203}\right)\)	\(e\left(\frac{767}{812}\right)\)	\(e\left(\frac{327}{812}\right)\)	\(e\left(\frac{409}{812}\right)\)	\(e\left(\frac{313}{406}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{188}{203}\right)\)
\(\chi_{2523}(229,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{327}{812}\right)\)	\(e\left(\frac{327}{406}\right)\)	\(e\left(\frac{251}{406}\right)\)	\(e\left(\frac{85}{203}\right)\)	\(e\left(\frac{169}{812}\right)\)	\(e\left(\frac{17}{812}\right)\)	\(e\left(\frac{503}{812}\right)\)	\(e\left(\frac{241}{406}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{124}{203}\right)\)

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First 31 of 336 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.w
Modulus	$2523$
Conductor	$841$
Order	$812$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(2523\)
Conductor:	\(841\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(812\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 841.l	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)