LMFDB - Dirichlet character orbit 823586.ps

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(823586, base_ring=CyclotomicField(564)) M = H._module chi = DirichletCharacter(H, M([282,29])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(17081, 823586)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("823586.17081"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$823586$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$411793$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$564$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 411793.po	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{564})$
Fixed field:	Number field defined by a degree 564 polynomial (not computed)

First 31 of 184 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{823586}(17081,\cdot)$	$1$	$1$	$e\left(\frac{7}{282}\right)$	$e\left(\frac{40}{141}\right)$	$e\left(\frac{95}{188}\right)$	$e\left(\frac{7}{141}\right)$	$e\left(\frac{19}{141}\right)$	$e\left(\frac{38}{47}\right)$	$e\left(\frac{29}{94}\right)$	$e\left(\frac{367}{564}\right)$	$e\left(\frac{95}{282}\right)$	$e\left(\frac{299}{564}\right)$
$\chi_{823586}(18687,\cdot)$	$1$	$1$	$e\left(\frac{191}{282}\right)$	$e\left(\frac{44}{141}\right)$	$e\left(\frac{81}{188}\right)$	$e\left(\frac{50}{141}\right)$	$e\left(\frac{35}{141}\right)$	$e\left(\frac{23}{47}\right)$	$e\left(\frac{93}{94}\right)$	$e\left(\frac{305}{564}\right)$	$e\left(\frac{175}{282}\right)$	$e\left(\frac{61}{564}\right)$
$\chi_{823586}(28323,\cdot)$	$1$	$1$	$e\left(\frac{209}{282}\right)$	$e\left(\frac{26}{141}\right)$	$e\left(\frac{97}{188}\right)$	$e\left(\frac{68}{141}\right)$	$e\left(\frac{104}{141}\right)$	$e\left(\frac{20}{47}\right)$	$e\left(\frac{87}{94}\right)$	$e\left(\frac{161}{564}\right)$	$e\left(\frac{97}{282}\right)$	$e\left(\frac{145}{564}\right)$
$\chi_{823586}(31827,\cdot)$	$1$	$1$	$e\left(\frac{185}{282}\right)$	$e\left(\frac{50}{141}\right)$	$e\left(\frac{107}{188}\right)$	$e\left(\frac{44}{141}\right)$	$e\left(\frac{59}{141}\right)$	$e\left(\frac{24}{47}\right)$	$e\left(\frac{1}{94}\right)$	$e\left(\frac{71}{564}\right)$	$e\left(\frac{13}{282}\right)$	$e\left(\frac{127}{564}\right)$
$\chi_{823586}(43799,\cdot)$	$1$	$1$	$e\left(\frac{175}{282}\right)$	$e\left(\frac{13}{141}\right)$	$e\left(\frac{119}{188}\right)$	$e\left(\frac{34}{141}\right)$	$e\left(\frac{52}{141}\right)$	$e\left(\frac{10}{47}\right)$	$e\left(\frac{67}{94}\right)$	$e\left(\frac{151}{564}\right)$	$e\left(\frac{119}{282}\right)$	$e\left(\frac{143}{564}\right)$
$\chi_{823586}(45843,\cdot)$	$1$	$1$	$e\left(\frac{281}{282}\right)$	$e\left(\frac{95}{141}\right)$	$e\left(\frac{67}{188}\right)$	$e\left(\frac{140}{141}\right)$	$e\left(\frac{98}{141}\right)$	$e\left(\frac{8}{47}\right)$	$e\left(\frac{63}{94}\right)$	$e\left(\frac{431}{564}\right)$	$e\left(\frac{67}{282}\right)$	$e\left(\frac{199}{564}\right)$
$\chi_{823586}(60881,\cdot)$	$1$	$1$	$e\left(\frac{19}{282}\right)$	$e\left(\frac{28}{141}\right)$	$e\left(\frac{137}{188}\right)$	$e\left(\frac{19}{141}\right)$	$e\left(\frac{112}{141}\right)$	$e\left(\frac{36}{47}\right)$	$e\left(\frac{25}{94}\right)$	$e\left(\frac{553}{564}\right)$	$e\left(\frac{137}{282}\right)$	$e\left(\frac{449}{564}\right)$
$\chi_{823586}(62049,\cdot)$	$1$	$1$	$e\left(\frac{143}{282}\right)$	$e\left(\frac{92}{141}\right)$	$e\left(\frac{7}{188}\right)$	$e\left(\frac{2}{141}\right)$	$e\left(\frac{86}{141}\right)$	$e\left(\frac{31}{47}\right)$	$e\left(\frac{15}{94}\right)$	$e\left(\frac{407}{564}\right)$	$e\left(\frac{7}{282}\right)$	$e\left(\frac{307}{564}\right)$
$\chi_{823586}(75919,\cdot)$	$1$	$1$	$e\left(\frac{169}{282}\right)$	$e\left(\frac{19}{141}\right)$	$e\left(\frac{145}{188}\right)$	$e\left(\frac{28}{141}\right)$	$e\left(\frac{76}{141}\right)$	$e\left(\frac{11}{47}\right)$	$e\left(\frac{69}{94}\right)$	$e\left(\frac{481}{564}\right)$	$e\left(\frac{239}{282}\right)$	$e\left(\frac{209}{564}\right)$
$\chi_{823586}(77817,\cdot)$	$1$	$1$	$e\left(\frac{269}{282}\right)$	$e\left(\frac{107}{141}\right)$	$e\left(\frac{119}{188}\right)$	$e\left(\frac{128}{141}\right)$	$e\left(\frac{5}{141}\right)$	$e\left(\frac{10}{47}\right)$	$e\left(\frac{67}{94}\right)$	$e\left(\frac{527}{564}\right)$	$e\left(\frac{25}{282}\right)$	$e\left(\frac{331}{564}\right)$
$\chi_{823586}(79131,\cdot)$	$1$	$1$	$e\left(\frac{119}{282}\right)$	$e\left(\frac{116}{141}\right)$	$e\left(\frac{111}{188}\right)$	$e\left(\frac{119}{141}\right)$	$e\left(\frac{41}{141}\right)$	$e\left(\frac{35}{47}\right)$	$e\left(\frac{23}{94}\right)$	$e\left(\frac{35}{564}\right)$	$e\left(\frac{205}{282}\right)$	$e\left(\frac{7}{564}\right)$
$\chi_{823586}(83073,\cdot)$	$1$	$1$	$e\left(\frac{193}{282}\right)$	$e\left(\frac{136}{141}\right)$	$e\left(\frac{41}{188}\right)$	$e\left(\frac{52}{141}\right)$	$e\left(\frac{121}{141}\right)$	$e\left(\frac{7}{47}\right)$	$e\left(\frac{61}{94}\right)$	$e\left(\frac{289}{564}\right)$	$e\left(\frac{41}{282}\right)$	$e\left(\frac{509}{564}\right)$
$\chi_{823586}(93293,\cdot)$	$1$	$1$	$e\left(\frac{109}{282}\right)$	$e\left(\frac{79}{141}\right)$	$e\left(\frac{123}{188}\right)$	$e\left(\frac{109}{141}\right)$	$e\left(\frac{34}{141}\right)$	$e\left(\frac{21}{47}\right)$	$e\left(\frac{89}{94}\right)$	$e\left(\frac{115}{564}\right)$	$e\left(\frac{29}{282}\right)$	$e\left(\frac{23}{564}\right)$
$\chi_{823586}(97235,\cdot)$	$1$	$1$	$e\left(\frac{85}{282}\right)$	$e\left(\frac{103}{141}\right)$	$e\left(\frac{39}{188}\right)$	$e\left(\frac{85}{141}\right)$	$e\left(\frac{130}{141}\right)$	$e\left(\frac{25}{47}\right)$	$e\left(\frac{3}{94}\right)$	$e\left(\frac{307}{564}\right)$	$e\left(\frac{227}{282}\right)$	$e\left(\frac{287}{564}\right)$
$\chi_{823586}(98987,\cdot)$	$1$	$1$	$e\left(\frac{167}{282}\right)$	$e\left(\frac{68}{141}\right)$	$e\left(\frac{91}{188}\right)$	$e\left(\frac{26}{141}\right)$	$e\left(\frac{131}{141}\right)$	$e\left(\frac{27}{47}\right)$	$e\left(\frac{7}{94}\right)$	$e\left(\frac{215}{564}\right)$	$e\left(\frac{91}{282}\right)$	$e\left(\frac{43}{564}\right)$
$\chi_{823586}(112273,\cdot)$	$1$	$1$	$e\left(\frac{35}{282}\right)$	$e\left(\frac{59}{141}\right)$	$e\left(\frac{5}{188}\right)$	$e\left(\frac{35}{141}\right)$	$e\left(\frac{95}{141}\right)$	$e\left(\frac{2}{47}\right)$	$e\left(\frac{51}{94}\right)$	$e\left(\frac{425}{564}\right)$	$e\left(\frac{193}{282}\right)$	$e\left(\frac{85}{564}\right)$
$\chi_{823586}(115923,\cdot)$	$1$	$1$	$e\left(\frac{257}{282}\right)$	$e\left(\frac{119}{141}\right)$	$e\left(\frac{171}{188}\right)$	$e\left(\frac{116}{141}\right)$	$e\left(\frac{53}{141}\right)$	$e\left(\frac{12}{47}\right)$	$e\left(\frac{71}{94}\right)$	$e\left(\frac{59}{564}\right)$	$e\left(\frac{265}{282}\right)$	$e\left(\frac{463}{564}\right)$
$\chi_{823586}(123661,\cdot)$	$1$	$1$	$e\left(\frac{187}{282}\right)$	$e\left(\frac{1}{141}\right)$	$e\left(\frac{161}{188}\right)$	$e\left(\frac{46}{141}\right)$	$e\left(\frac{4}{141}\right)$	$e\left(\frac{8}{47}\right)$	$e\left(\frac{63}{94}\right)$	$e\left(\frac{337}{564}\right)$	$e\left(\frac{161}{282}\right)$	$e\left(\frac{293}{564}\right)$
$\chi_{823586}(124391,\cdot)$	$1$	$1$	$e\left(\frac{89}{282}\right)$	$e\left(\frac{5}{141}\right)$	$e\left(\frac{147}{188}\right)$	$e\left(\frac{89}{141}\right)$	$e\left(\frac{20}{141}\right)$	$e\left(\frac{40}{47}\right)$	$e\left(\frac{33}{94}\right)$	$e\left(\frac{275}{564}\right)$	$e\left(\frac{241}{282}\right)$	$e\left(\frac{55}{564}\right)$
$\chi_{823586}(128771,\cdot)$	$1$	$1$	$e\left(\frac{107}{282}\right)$	$e\left(\frac{128}{141}\right)$	$e\left(\frac{163}{188}\right)$	$e\left(\frac{107}{141}\right)$	$e\left(\frac{89}{141}\right)$	$e\left(\frac{37}{47}\right)$	$e\left(\frac{27}{94}\right)$	$e\left(\frac{131}{564}\right)$	$e\left(\frac{163}{282}\right)$	$e\left(\frac{139}{564}\right)$
$\chi_{823586}(139137,\cdot)$	$1$	$1$	$e\left(\frac{217}{282}\right)$	$e\left(\frac{112}{141}\right)$	$e\left(\frac{31}{188}\right)$	$e\left(\frac{76}{141}\right)$	$e\left(\frac{25}{141}\right)$	$e\left(\frac{3}{47}\right)$	$e\left(\frac{53}{94}\right)$	$e\left(\frac{379}{564}\right)$	$e\left(\frac{125}{282}\right)$	$e\left(\frac{527}{564}\right)$
$\chi_{823586}(140159,\cdot)$	$1$	$1$	$e\left(\frac{113}{282}\right)$	$e\left(\frac{122}{141}\right)$	$e\left(\frac{43}{188}\right)$	$e\left(\frac{113}{141}\right)$	$e\left(\frac{65}{141}\right)$	$e\left(\frac{36}{47}\right)$	$e\left(\frac{25}{94}\right)$	$e\left(\frac{83}{564}\right)$	$e\left(\frac{43}{282}\right)$	$e\left(\frac{355}{564}\right)$
$\chi_{823586}(144101,\cdot)$	$1$	$1$	$e\left(\frac{41}{282}\right)$	$e\left(\frac{53}{141}\right)$	$e\left(\frac{73}{188}\right)$	$e\left(\frac{41}{141}\right)$	$e\left(\frac{71}{141}\right)$	$e\left(\frac{1}{47}\right)$	$e\left(\frac{49}{94}\right)$	$e\left(\frac{377}{564}\right)$	$e\left(\frac{73}{282}\right)$	$e\left(\frac{301}{564}\right)$
$\chi_{823586}(148335,\cdot)$	$1$	$1$	$e\left(\frac{55}{282}\right)$	$e\left(\frac{133}{141}\right)$	$e\left(\frac{169}{188}\right)$	$e\left(\frac{55}{141}\right)$	$e\left(\frac{109}{141}\right)$	$e\left(\frac{30}{47}\right)$	$e\left(\frac{13}{94}\right)$	$e\left(\frac{265}{564}\right)$	$e\left(\frac{263}{282}\right)$	$e\left(\frac{53}{564}\right)$
$\chi_{823586}(149795,\cdot)$	$1$	$1$	$e\left(\frac{127}{282}\right)$	$e\left(\frac{61}{141}\right)$	$e\left(\frac{45}{188}\right)$	$e\left(\frac{127}{141}\right)$	$e\left(\frac{103}{141}\right)$	$e\left(\frac{18}{47}\right)$	$e\left(\frac{83}{94}\right)$	$e\left(\frac{253}{564}\right)$	$e\left(\frac{233}{282}\right)$	$e\left(\frac{389}{564}\right)$
$\chi_{823586}(160891,\cdot)$	$1$	$1$	$e\left(\frac{65}{282}\right)$	$e\left(\frac{29}{141}\right)$	$e\left(\frac{157}{188}\right)$	$e\left(\frac{65}{141}\right)$	$e\left(\frac{116}{141}\right)$	$e\left(\frac{44}{47}\right)$	$e\left(\frac{41}{94}\right)$	$e\left(\frac{185}{564}\right)$	$e\left(\frac{157}{282}\right)$	$e\left(\frac{37}{564}\right)$
$\chi_{823586}(163665,\cdot)$	$1$	$1$	$e\left(\frac{203}{282}\right)$	$e\left(\frac{32}{141}\right)$	$e\left(\frac{123}{188}\right)$	$e\left(\frac{62}{141}\right)$	$e\left(\frac{128}{141}\right)$	$e\left(\frac{21}{47}\right)$	$e\left(\frac{89}{94}\right)$	$e\left(\frac{491}{564}\right)$	$e\left(\frac{217}{282}\right)$	$e\left(\frac{211}{564}\right)$
$\chi_{823586}(164249,\cdot)$	$1$	$1$	$e\left(\frac{251}{282}\right)$	$e\left(\frac{125}{141}\right)$	$e\left(\frac{9}{188}\right)$	$e\left(\frac{110}{141}\right)$	$e\left(\frac{77}{141}\right)$	$e\left(\frac{13}{47}\right)$	$e\left(\frac{73}{94}\right)$	$e\left(\frac{389}{564}\right)$	$e\left(\frac{103}{282}\right)$	$e\left(\frac{529}{564}\right)$
$\chi_{823586}(166439,\cdot)$	$1$	$1$	$e\left(\frac{205}{282}\right)$	$e\left(\frac{124}{141}\right)$	$e\left(\frac{83}{188}\right)$	$e\left(\frac{64}{141}\right)$	$e\left(\frac{73}{141}\right)$	$e\left(\frac{5}{47}\right)$	$e\left(\frac{57}{94}\right)$	$e\left(\frac{475}{564}\right)$	$e\left(\frac{83}{282}\right)$	$e\left(\frac{95}{564}\right)$
$\chi_{823586}(167315,\cdot)$	$1$	$1$	$e\left(\frac{181}{282}\right)$	$e\left(\frac{7}{141}\right)$	$e\left(\frac{93}{188}\right)$	$e\left(\frac{40}{141}\right)$	$e\left(\frac{28}{141}\right)$	$e\left(\frac{9}{47}\right)$	$e\left(\frac{65}{94}\right)$	$e\left(\frac{385}{564}\right)$	$e\left(\frac{281}{282}\right)$	$e\left(\frac{77}{564}\right)$
$\chi_{823586}(170819,\cdot)$	$1$	$1$	$e\left(\frac{277}{282}\right)$	$e\left(\frac{52}{141}\right)$	$e\left(\frac{53}{188}\right)$	$e\left(\frac{136}{141}\right)$	$e\left(\frac{67}{141}\right)$	$e\left(\frac{40}{47}\right)$	$e\left(\frac{33}{94}\right)$	$e\left(\frac{181}{564}\right)$	$e\left(\frac{53}{282}\right)$	$e\left(\frac{149}{564}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{823586}(17081,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{282}\right)\)	\(e\left(\frac{40}{141}\right)\)	\(e\left(\frac{95}{188}\right)\)	\(e\left(\frac{7}{141}\right)\)	\(e\left(\frac{19}{141}\right)\)	\(e\left(\frac{38}{47}\right)\)	\(e\left(\frac{29}{94}\right)\)	\(e\left(\frac{367}{564}\right)\)	\(e\left(\frac{95}{282}\right)\)	\(e\left(\frac{299}{564}\right)\)
\(\chi_{823586}(18687,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{282}\right)\)	\(e\left(\frac{44}{141}\right)\)	\(e\left(\frac{81}{188}\right)\)	\(e\left(\frac{50}{141}\right)\)	\(e\left(\frac{35}{141}\right)\)	\(e\left(\frac{23}{47}\right)\)	\(e\left(\frac{93}{94}\right)\)	\(e\left(\frac{305}{564}\right)\)	\(e\left(\frac{175}{282}\right)\)	\(e\left(\frac{61}{564}\right)\)
\(\chi_{823586}(28323,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{209}{282}\right)\)	\(e\left(\frac{26}{141}\right)\)	\(e\left(\frac{97}{188}\right)\)	\(e\left(\frac{68}{141}\right)\)	\(e\left(\frac{104}{141}\right)\)	\(e\left(\frac{20}{47}\right)\)	\(e\left(\frac{87}{94}\right)\)	\(e\left(\frac{161}{564}\right)\)	\(e\left(\frac{97}{282}\right)\)	\(e\left(\frac{145}{564}\right)\)
\(\chi_{823586}(31827,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{185}{282}\right)\)	\(e\left(\frac{50}{141}\right)\)	\(e\left(\frac{107}{188}\right)\)	\(e\left(\frac{44}{141}\right)\)	\(e\left(\frac{59}{141}\right)\)	\(e\left(\frac{24}{47}\right)\)	\(e\left(\frac{1}{94}\right)\)	\(e\left(\frac{71}{564}\right)\)	\(e\left(\frac{13}{282}\right)\)	\(e\left(\frac{127}{564}\right)\)
\(\chi_{823586}(43799,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{175}{282}\right)\)	\(e\left(\frac{13}{141}\right)\)	\(e\left(\frac{119}{188}\right)\)	\(e\left(\frac{34}{141}\right)\)	\(e\left(\frac{52}{141}\right)\)	\(e\left(\frac{10}{47}\right)\)	\(e\left(\frac{67}{94}\right)\)	\(e\left(\frac{151}{564}\right)\)	\(e\left(\frac{119}{282}\right)\)	\(e\left(\frac{143}{564}\right)\)
\(\chi_{823586}(45843,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{281}{282}\right)\)	\(e\left(\frac{95}{141}\right)\)	\(e\left(\frac{67}{188}\right)\)	\(e\left(\frac{140}{141}\right)\)	\(e\left(\frac{98}{141}\right)\)	\(e\left(\frac{8}{47}\right)\)	\(e\left(\frac{63}{94}\right)\)	\(e\left(\frac{431}{564}\right)\)	\(e\left(\frac{67}{282}\right)\)	\(e\left(\frac{199}{564}\right)\)
\(\chi_{823586}(60881,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{282}\right)\)	\(e\left(\frac{28}{141}\right)\)	\(e\left(\frac{137}{188}\right)\)	\(e\left(\frac{19}{141}\right)\)	\(e\left(\frac{112}{141}\right)\)	\(e\left(\frac{36}{47}\right)\)	\(e\left(\frac{25}{94}\right)\)	\(e\left(\frac{553}{564}\right)\)	\(e\left(\frac{137}{282}\right)\)	\(e\left(\frac{449}{564}\right)\)
\(\chi_{823586}(62049,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{143}{282}\right)\)	\(e\left(\frac{92}{141}\right)\)	\(e\left(\frac{7}{188}\right)\)	\(e\left(\frac{2}{141}\right)\)	\(e\left(\frac{86}{141}\right)\)	\(e\left(\frac{31}{47}\right)\)	\(e\left(\frac{15}{94}\right)\)	\(e\left(\frac{407}{564}\right)\)	\(e\left(\frac{7}{282}\right)\)	\(e\left(\frac{307}{564}\right)\)
\(\chi_{823586}(75919,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{282}\right)\)	\(e\left(\frac{19}{141}\right)\)	\(e\left(\frac{145}{188}\right)\)	\(e\left(\frac{28}{141}\right)\)	\(e\left(\frac{76}{141}\right)\)	\(e\left(\frac{11}{47}\right)\)	\(e\left(\frac{69}{94}\right)\)	\(e\left(\frac{481}{564}\right)\)	\(e\left(\frac{239}{282}\right)\)	\(e\left(\frac{209}{564}\right)\)
\(\chi_{823586}(77817,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{269}{282}\right)\)	\(e\left(\frac{107}{141}\right)\)	\(e\left(\frac{119}{188}\right)\)	\(e\left(\frac{128}{141}\right)\)	\(e\left(\frac{5}{141}\right)\)	\(e\left(\frac{10}{47}\right)\)	\(e\left(\frac{67}{94}\right)\)	\(e\left(\frac{527}{564}\right)\)	\(e\left(\frac{25}{282}\right)\)	\(e\left(\frac{331}{564}\right)\)
\(\chi_{823586}(79131,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{282}\right)\)	\(e\left(\frac{116}{141}\right)\)	\(e\left(\frac{111}{188}\right)\)	\(e\left(\frac{119}{141}\right)\)	\(e\left(\frac{41}{141}\right)\)	\(e\left(\frac{35}{47}\right)\)	\(e\left(\frac{23}{94}\right)\)	\(e\left(\frac{35}{564}\right)\)	\(e\left(\frac{205}{282}\right)\)	\(e\left(\frac{7}{564}\right)\)
\(\chi_{823586}(83073,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{282}\right)\)	\(e\left(\frac{136}{141}\right)\)	\(e\left(\frac{41}{188}\right)\)	\(e\left(\frac{52}{141}\right)\)	\(e\left(\frac{121}{141}\right)\)	\(e\left(\frac{7}{47}\right)\)	\(e\left(\frac{61}{94}\right)\)	\(e\left(\frac{289}{564}\right)\)	\(e\left(\frac{41}{282}\right)\)	\(e\left(\frac{509}{564}\right)\)
\(\chi_{823586}(93293,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{282}\right)\)	\(e\left(\frac{79}{141}\right)\)	\(e\left(\frac{123}{188}\right)\)	\(e\left(\frac{109}{141}\right)\)	\(e\left(\frac{34}{141}\right)\)	\(e\left(\frac{21}{47}\right)\)	\(e\left(\frac{89}{94}\right)\)	\(e\left(\frac{115}{564}\right)\)	\(e\left(\frac{29}{282}\right)\)	\(e\left(\frac{23}{564}\right)\)
\(\chi_{823586}(97235,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{282}\right)\)	\(e\left(\frac{103}{141}\right)\)	\(e\left(\frac{39}{188}\right)\)	\(e\left(\frac{85}{141}\right)\)	\(e\left(\frac{130}{141}\right)\)	\(e\left(\frac{25}{47}\right)\)	\(e\left(\frac{3}{94}\right)\)	\(e\left(\frac{307}{564}\right)\)	\(e\left(\frac{227}{282}\right)\)	\(e\left(\frac{287}{564}\right)\)
\(\chi_{823586}(98987,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{167}{282}\right)\)	\(e\left(\frac{68}{141}\right)\)	\(e\left(\frac{91}{188}\right)\)	\(e\left(\frac{26}{141}\right)\)	\(e\left(\frac{131}{141}\right)\)	\(e\left(\frac{27}{47}\right)\)	\(e\left(\frac{7}{94}\right)\)	\(e\left(\frac{215}{564}\right)\)	\(e\left(\frac{91}{282}\right)\)	\(e\left(\frac{43}{564}\right)\)
\(\chi_{823586}(112273,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{282}\right)\)	\(e\left(\frac{59}{141}\right)\)	\(e\left(\frac{5}{188}\right)\)	\(e\left(\frac{35}{141}\right)\)	\(e\left(\frac{95}{141}\right)\)	\(e\left(\frac{2}{47}\right)\)	\(e\left(\frac{51}{94}\right)\)	\(e\left(\frac{425}{564}\right)\)	\(e\left(\frac{193}{282}\right)\)	\(e\left(\frac{85}{564}\right)\)
\(\chi_{823586}(115923,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{257}{282}\right)\)	\(e\left(\frac{119}{141}\right)\)	\(e\left(\frac{171}{188}\right)\)	\(e\left(\frac{116}{141}\right)\)	\(e\left(\frac{53}{141}\right)\)	\(e\left(\frac{12}{47}\right)\)	\(e\left(\frac{71}{94}\right)\)	\(e\left(\frac{59}{564}\right)\)	\(e\left(\frac{265}{282}\right)\)	\(e\left(\frac{463}{564}\right)\)
\(\chi_{823586}(123661,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{187}{282}\right)\)	\(e\left(\frac{1}{141}\right)\)	\(e\left(\frac{161}{188}\right)\)	\(e\left(\frac{46}{141}\right)\)	\(e\left(\frac{4}{141}\right)\)	\(e\left(\frac{8}{47}\right)\)	\(e\left(\frac{63}{94}\right)\)	\(e\left(\frac{337}{564}\right)\)	\(e\left(\frac{161}{282}\right)\)	\(e\left(\frac{293}{564}\right)\)
\(\chi_{823586}(124391,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{282}\right)\)	\(e\left(\frac{5}{141}\right)\)	\(e\left(\frac{147}{188}\right)\)	\(e\left(\frac{89}{141}\right)\)	\(e\left(\frac{20}{141}\right)\)	\(e\left(\frac{40}{47}\right)\)	\(e\left(\frac{33}{94}\right)\)	\(e\left(\frac{275}{564}\right)\)	\(e\left(\frac{241}{282}\right)\)	\(e\left(\frac{55}{564}\right)\)
\(\chi_{823586}(128771,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{282}\right)\)	\(e\left(\frac{128}{141}\right)\)	\(e\left(\frac{163}{188}\right)\)	\(e\left(\frac{107}{141}\right)\)	\(e\left(\frac{89}{141}\right)\)	\(e\left(\frac{37}{47}\right)\)	\(e\left(\frac{27}{94}\right)\)	\(e\left(\frac{131}{564}\right)\)	\(e\left(\frac{163}{282}\right)\)	\(e\left(\frac{139}{564}\right)\)
\(\chi_{823586}(139137,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{217}{282}\right)\)	\(e\left(\frac{112}{141}\right)\)	\(e\left(\frac{31}{188}\right)\)	\(e\left(\frac{76}{141}\right)\)	\(e\left(\frac{25}{141}\right)\)	\(e\left(\frac{3}{47}\right)\)	\(e\left(\frac{53}{94}\right)\)	\(e\left(\frac{379}{564}\right)\)	\(e\left(\frac{125}{282}\right)\)	\(e\left(\frac{527}{564}\right)\)
\(\chi_{823586}(140159,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{282}\right)\)	\(e\left(\frac{122}{141}\right)\)	\(e\left(\frac{43}{188}\right)\)	\(e\left(\frac{113}{141}\right)\)	\(e\left(\frac{65}{141}\right)\)	\(e\left(\frac{36}{47}\right)\)	\(e\left(\frac{25}{94}\right)\)	\(e\left(\frac{83}{564}\right)\)	\(e\left(\frac{43}{282}\right)\)	\(e\left(\frac{355}{564}\right)\)
\(\chi_{823586}(144101,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{282}\right)\)	\(e\left(\frac{53}{141}\right)\)	\(e\left(\frac{73}{188}\right)\)	\(e\left(\frac{41}{141}\right)\)	\(e\left(\frac{71}{141}\right)\)	\(e\left(\frac{1}{47}\right)\)	\(e\left(\frac{49}{94}\right)\)	\(e\left(\frac{377}{564}\right)\)	\(e\left(\frac{73}{282}\right)\)	\(e\left(\frac{301}{564}\right)\)
\(\chi_{823586}(148335,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{282}\right)\)	\(e\left(\frac{133}{141}\right)\)	\(e\left(\frac{169}{188}\right)\)	\(e\left(\frac{55}{141}\right)\)	\(e\left(\frac{109}{141}\right)\)	\(e\left(\frac{30}{47}\right)\)	\(e\left(\frac{13}{94}\right)\)	\(e\left(\frac{265}{564}\right)\)	\(e\left(\frac{263}{282}\right)\)	\(e\left(\frac{53}{564}\right)\)
\(\chi_{823586}(149795,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{282}\right)\)	\(e\left(\frac{61}{141}\right)\)	\(e\left(\frac{45}{188}\right)\)	\(e\left(\frac{127}{141}\right)\)	\(e\left(\frac{103}{141}\right)\)	\(e\left(\frac{18}{47}\right)\)	\(e\left(\frac{83}{94}\right)\)	\(e\left(\frac{253}{564}\right)\)	\(e\left(\frac{233}{282}\right)\)	\(e\left(\frac{389}{564}\right)\)
\(\chi_{823586}(160891,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{282}\right)\)	\(e\left(\frac{29}{141}\right)\)	\(e\left(\frac{157}{188}\right)\)	\(e\left(\frac{65}{141}\right)\)	\(e\left(\frac{116}{141}\right)\)	\(e\left(\frac{44}{47}\right)\)	\(e\left(\frac{41}{94}\right)\)	\(e\left(\frac{185}{564}\right)\)	\(e\left(\frac{157}{282}\right)\)	\(e\left(\frac{37}{564}\right)\)
\(\chi_{823586}(163665,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{203}{282}\right)\)	\(e\left(\frac{32}{141}\right)\)	\(e\left(\frac{123}{188}\right)\)	\(e\left(\frac{62}{141}\right)\)	\(e\left(\frac{128}{141}\right)\)	\(e\left(\frac{21}{47}\right)\)	\(e\left(\frac{89}{94}\right)\)	\(e\left(\frac{491}{564}\right)\)	\(e\left(\frac{217}{282}\right)\)	\(e\left(\frac{211}{564}\right)\)
\(\chi_{823586}(164249,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{251}{282}\right)\)	\(e\left(\frac{125}{141}\right)\)	\(e\left(\frac{9}{188}\right)\)	\(e\left(\frac{110}{141}\right)\)	\(e\left(\frac{77}{141}\right)\)	\(e\left(\frac{13}{47}\right)\)	\(e\left(\frac{73}{94}\right)\)	\(e\left(\frac{389}{564}\right)\)	\(e\left(\frac{103}{282}\right)\)	\(e\left(\frac{529}{564}\right)\)
\(\chi_{823586}(166439,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{205}{282}\right)\)	\(e\left(\frac{124}{141}\right)\)	\(e\left(\frac{83}{188}\right)\)	\(e\left(\frac{64}{141}\right)\)	\(e\left(\frac{73}{141}\right)\)	\(e\left(\frac{5}{47}\right)\)	\(e\left(\frac{57}{94}\right)\)	\(e\left(\frac{475}{564}\right)\)	\(e\left(\frac{83}{282}\right)\)	\(e\left(\frac{95}{564}\right)\)
\(\chi_{823586}(167315,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{181}{282}\right)\)	\(e\left(\frac{7}{141}\right)\)	\(e\left(\frac{93}{188}\right)\)	\(e\left(\frac{40}{141}\right)\)	\(e\left(\frac{28}{141}\right)\)	\(e\left(\frac{9}{47}\right)\)	\(e\left(\frac{65}{94}\right)\)	\(e\left(\frac{385}{564}\right)\)	\(e\left(\frac{281}{282}\right)\)	\(e\left(\frac{77}{564}\right)\)
\(\chi_{823586}(170819,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{277}{282}\right)\)	\(e\left(\frac{52}{141}\right)\)	\(e\left(\frac{53}{188}\right)\)	\(e\left(\frac{136}{141}\right)\)	\(e\left(\frac{67}{141}\right)\)	\(e\left(\frac{40}{47}\right)\)	\(e\left(\frac{33}{94}\right)\)	\(e\left(\frac{181}{564}\right)\)	\(e\left(\frac{53}{282}\right)\)	\(e\left(\frac{149}{564}\right)\)

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First 31 of 184 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	823586.ps
Modulus	$823586$
Conductor	$411793$
Order	$564$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(823586\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(411793\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(564\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 411793.po	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);