LMFDB - Dirichlet character orbit 23275.of

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(23275, base_ring=CyclotomicField(630)) M = H._module chi = DirichletCharacter(H, M([63,150,70])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(4, 23275)) 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("23275.4"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$23275$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$23275$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$630$	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:	yes	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:	$\Q(\zeta_{315})$
Fixed field:	Number field defined by a degree 630 polynomial (not computed)

First 31 of 144 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$8$	$9$	$11$	$12$	$13$	$16$
$\chi_{23275}(4,\cdot)$	$1$	$1$	$e\left(\frac{253}{630}\right)$	$e\left(\frac{241}{630}\right)$	$e\left(\frac{253}{315}\right)$	$e\left(\frac{247}{315}\right)$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{241}{315}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{197}{630}\right)$	$e\left(\frac{191}{315}\right)$
$\chi_{23275}(359,\cdot)$	$1$	$1$	$e\left(\frac{401}{630}\right)$	$e\left(\frac{377}{630}\right)$	$e\left(\frac{86}{315}\right)$	$e\left(\frac{74}{315}\right)$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{62}{315}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{499}{630}\right)$	$e\left(\frac{172}{315}\right)$
$\chi_{23275}(389,\cdot)$	$1$	$1$	$e\left(\frac{229}{630}\right)$	$e\left(\frac{253}{630}\right)$	$e\left(\frac{229}{315}\right)$	$e\left(\frac{241}{315}\right)$	$e\left(\frac{19}{210}\right)$	$e\left(\frac{253}{315}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{131}{630}\right)$	$e\left(\frac{143}{315}\right)$
$\chi_{23275}(669,\cdot)$	$1$	$1$	$e\left(\frac{307}{630}\right)$	$e\left(\frac{529}{630}\right)$	$e\left(\frac{307}{315}\right)$	$e\left(\frac{103}{315}\right)$	$e\left(\frac{97}{210}\right)$	$e\left(\frac{214}{315}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{503}{630}\right)$	$e\left(\frac{299}{315}\right)$
$\chi_{23275}(1054,\cdot)$	$1$	$1$	$e\left(\frac{283}{630}\right)$	$e\left(\frac{541}{630}\right)$	$e\left(\frac{283}{315}\right)$	$e\left(\frac{97}{315}\right)$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{226}{315}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{437}{630}\right)$	$e\left(\frac{251}{315}\right)$
$\chi_{23275}(1089,\cdot)$	$1$	$1$	$e\left(\frac{529}{630}\right)$	$e\left(\frac{103}{630}\right)$	$e\left(\frac{214}{315}\right)$	$e\left(\frac{1}{315}\right)$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{103}{315}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{11}{630}\right)$	$e\left(\frac{113}{315}\right)$
$\chi_{23275}(1164,\cdot)$	$1$	$1$	$e\left(\frac{629}{630}\right)$	$e\left(\frac{263}{630}\right)$	$e\left(\frac{314}{315}\right)$	$e\left(\frac{131}{315}\right)$	$e\left(\frac{209}{210}\right)$	$e\left(\frac{263}{315}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{181}{630}\right)$	$e\left(\frac{313}{315}\right)$
$\chi_{23275}(1334,\cdot)$	$1$	$1$	$e\left(\frac{361}{630}\right)$	$e\left(\frac{187}{630}\right)$	$e\left(\frac{46}{315}\right)$	$e\left(\frac{274}{315}\right)$	$e\left(\frac{151}{210}\right)$	$e\left(\frac{187}{315}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{179}{630}\right)$	$e\left(\frac{92}{315}\right)$
$\chi_{23275}(1479,\cdot)$	$1$	$1$	$e\left(\frac{353}{630}\right)$	$e\left(\frac{401}{630}\right)$	$e\left(\frac{38}{315}\right)$	$e\left(\frac{62}{315}\right)$	$e\left(\frac{143}{210}\right)$	$e\left(\frac{86}{315}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{367}{630}\right)$	$e\left(\frac{76}{315}\right)$
$\chi_{23275}(1689,\cdot)$	$1$	$1$	$e\left(\frac{239}{630}\right)$	$e\left(\frac{143}{630}\right)$	$e\left(\frac{239}{315}\right)$	$e\left(\frac{191}{315}\right)$	$e\left(\frac{29}{210}\right)$	$e\left(\frac{143}{315}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{211}{630}\right)$	$e\left(\frac{163}{315}\right)$
$\chi_{23275}(1719,\cdot)$	$1$	$1$	$e\left(\frac{337}{630}\right)$	$e\left(\frac{199}{630}\right)$	$e\left(\frac{22}{315}\right)$	$e\left(\frac{268}{315}\right)$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{199}{315}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{113}{630}\right)$	$e\left(\frac{44}{315}\right)$
$\chi_{23275}(1754,\cdot)$	$1$	$1$	$e\left(\frac{583}{630}\right)$	$e\left(\frac{391}{630}\right)$	$e\left(\frac{268}{315}\right)$	$e\left(\frac{172}{315}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{76}{315}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{317}{630}\right)$	$e\left(\frac{221}{315}\right)$
$\chi_{23275}(1829,\cdot)$	$1$	$1$	$e\left(\frac{233}{630}\right)$	$e\left(\frac{461}{630}\right)$	$e\left(\frac{233}{315}\right)$	$e\left(\frac{32}{315}\right)$	$e\left(\frac{23}{210}\right)$	$e\left(\frac{146}{315}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{37}{630}\right)$	$e\left(\frac{151}{315}\right)$
$\chi_{23275}(2144,\cdot)$	$1$	$1$	$e\left(\frac{587}{630}\right)$	$e\left(\frac{599}{630}\right)$	$e\left(\frac{272}{315}\right)$	$e\left(\frac{278}{315}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{284}{315}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{223}{630}\right)$	$e\left(\frac{229}{315}\right)$
$\chi_{23275}(2354,\cdot)$	$1$	$1$	$e\left(\frac{473}{630}\right)$	$e\left(\frac{341}{630}\right)$	$e\left(\frac{158}{315}\right)$	$e\left(\frac{92}{315}\right)$	$e\left(\frac{53}{210}\right)$	$e\left(\frac{26}{315}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{67}{630}\right)$	$e\left(\frac{1}{315}\right)$
$\chi_{23275}(2384,\cdot)$	$1$	$1$	$e\left(\frac{391}{630}\right)$	$e\left(\frac{487}{630}\right)$	$e\left(\frac{76}{315}\right)$	$e\left(\frac{124}{315}\right)$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{172}{315}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{419}{630}\right)$	$e\left(\frac{152}{315}\right)$
$\chi_{23275}(2494,\cdot)$	$1$	$1$	$e\left(\frac{467}{630}\right)$	$e\left(\frac{29}{630}\right)$	$e\left(\frac{152}{315}\right)$	$e\left(\frac{248}{315}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{29}{315}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{523}{630}\right)$	$e\left(\frac{304}{315}\right)$
$\chi_{23275}(2809,\cdot)$	$1$	$1$	$e\left(\frac{191}{630}\right)$	$e\left(\frac{167}{630}\right)$	$e\left(\frac{191}{315}\right)$	$e\left(\frac{179}{315}\right)$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{167}{315}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{79}{630}\right)$	$e\left(\frac{67}{315}\right)$
$\chi_{23275}(3084,\cdot)$	$1$	$1$	$e\left(\frac{61}{630}\right)$	$e\left(\frac{337}{630}\right)$	$e\left(\frac{61}{315}\right)$	$e\left(\frac{199}{315}\right)$	$e\left(\frac{61}{210}\right)$	$e\left(\frac{22}{315}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{299}{630}\right)$	$e\left(\frac{122}{315}\right)$
$\chi_{23275}(3159,\cdot)$	$1$	$1$	$e\left(\frac{71}{630}\right)$	$e\left(\frac{227}{630}\right)$	$e\left(\frac{71}{315}\right)$	$e\left(\frac{149}{315}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{227}{315}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{379}{630}\right)$	$e\left(\frac{142}{315}\right)$
$\chi_{23275}(3329,\cdot)$	$1$	$1$	$e\left(\frac{523}{630}\right)$	$e\left(\frac{421}{630}\right)$	$e\left(\frac{208}{315}\right)$	$e\left(\frac{157}{315}\right)$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{106}{315}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{467}{630}\right)$	$e\left(\frac{101}{315}\right)$
$\chi_{23275}(3684,\cdot)$	$1$	$1$	$e\left(\frac{311}{630}\right)$	$e\left(\frac{107}{630}\right)$	$e\left(\frac{311}{315}\right)$	$e\left(\frac{209}{315}\right)$	$e\left(\frac{101}{210}\right)$	$e\left(\frac{107}{315}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{409}{630}\right)$	$e\left(\frac{307}{315}\right)$
$\chi_{23275}(3714,\cdot)$	$1$	$1$	$e\left(\frac{499}{630}\right)$	$e\left(\frac{433}{630}\right)$	$e\left(\frac{184}{315}\right)$	$e\left(\frac{151}{315}\right)$	$e\left(\frac{79}{210}\right)$	$e\left(\frac{118}{315}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{401}{630}\right)$	$e\left(\frac{53}{315}\right)$
$\chi_{23275}(3994,\cdot)$	$1$	$1$	$e\left(\frac{577}{630}\right)$	$e\left(\frac{79}{630}\right)$	$e\left(\frac{262}{315}\right)$	$e\left(\frac{13}{315}\right)$	$e\left(\frac{157}{210}\right)$	$e\left(\frac{79}{315}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{143}{630}\right)$	$e\left(\frac{209}{315}\right)$
$\chi_{23275}(4139,\cdot)$	$1$	$1$	$e\left(\frac{29}{630}\right)$	$e\left(\frac{563}{630}\right)$	$e\left(\frac{29}{315}\right)$	$e\left(\frac{296}{315}\right)$	$e\left(\frac{29}{210}\right)$	$e\left(\frac{248}{315}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{421}{630}\right)$	$e\left(\frac{58}{315}\right)$
$\chi_{23275}(4414,\cdot)$	$1$	$1$	$e\left(\frac{169}{630}\right)$	$e\left(\frac{283}{630}\right)$	$e\left(\frac{169}{315}\right)$	$e\left(\frac{226}{315}\right)$	$e\left(\frac{169}{210}\right)$	$e\left(\frac{283}{315}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{281}{630}\right)$	$e\left(\frac{23}{315}\right)$
$\chi_{23275}(4659,\cdot)$	$1$	$1$	$e\left(\frac{1}{630}\right)$	$e\left(\frac{367}{630}\right)$	$e\left(\frac{1}{315}\right)$	$e\left(\frac{184}{315}\right)$	$e\left(\frac{1}{210}\right)$	$e\left(\frac{52}{315}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{449}{630}\right)$	$e\left(\frac{2}{315}\right)$
$\chi_{23275}(4804,\cdot)$	$1$	$1$	$e\left(\frac{263}{630}\right)$	$e\left(\frac{131}{630}\right)$	$e\left(\frac{263}{315}\right)$	$e\left(\frac{197}{315}\right)$	$e\left(\frac{53}{210}\right)$	$e\left(\frac{131}{315}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{277}{630}\right)$	$e\left(\frac{211}{315}\right)$
$\chi_{23275}(5014,\cdot)$	$1$	$1$	$e\left(\frac{149}{630}\right)$	$e\left(\frac{503}{630}\right)$	$e\left(\frac{149}{315}\right)$	$e\left(\frac{11}{315}\right)$	$e\left(\frac{149}{210}\right)$	$e\left(\frac{188}{315}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{121}{630}\right)$	$e\left(\frac{298}{315}\right)$
$\chi_{23275}(5044,\cdot)$	$1$	$1$	$e\left(\frac{607}{630}\right)$	$e\left(\frac{379}{630}\right)$	$e\left(\frac{292}{315}\right)$	$e\left(\frac{178}{315}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{64}{315}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{383}{630}\right)$	$e\left(\frac{269}{315}\right)$
$\chi_{23275}(5079,\cdot)$	$1$	$1$	$e\left(\frac{223}{630}\right)$	$e\left(\frac{571}{630}\right)$	$e\left(\frac{223}{315}\right)$	$e\left(\frac{82}{315}\right)$	$e\left(\frac{13}{210}\right)$	$e\left(\frac{256}{315}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{587}{630}\right)$	$e\left(\frac{131}{315}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)	\(16\)
\(\chi_{23275}(4,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{253}{630}\right)\)	\(e\left(\frac{241}{630}\right)\)	\(e\left(\frac{253}{315}\right)\)	\(e\left(\frac{247}{315}\right)\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{241}{315}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{197}{630}\right)\)	\(e\left(\frac{191}{315}\right)\)
\(\chi_{23275}(359,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{401}{630}\right)\)	\(e\left(\frac{377}{630}\right)\)	\(e\left(\frac{86}{315}\right)\)	\(e\left(\frac{74}{315}\right)\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{62}{315}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{499}{630}\right)\)	\(e\left(\frac{172}{315}\right)\)
\(\chi_{23275}(389,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{229}{630}\right)\)	\(e\left(\frac{253}{630}\right)\)	\(e\left(\frac{229}{315}\right)\)	\(e\left(\frac{241}{315}\right)\)	\(e\left(\frac{19}{210}\right)\)	\(e\left(\frac{253}{315}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{131}{630}\right)\)	\(e\left(\frac{143}{315}\right)\)
\(\chi_{23275}(669,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{307}{630}\right)\)	\(e\left(\frac{529}{630}\right)\)	\(e\left(\frac{307}{315}\right)\)	\(e\left(\frac{103}{315}\right)\)	\(e\left(\frac{97}{210}\right)\)	\(e\left(\frac{214}{315}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{503}{630}\right)\)	\(e\left(\frac{299}{315}\right)\)
\(\chi_{23275}(1054,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{283}{630}\right)\)	\(e\left(\frac{541}{630}\right)\)	\(e\left(\frac{283}{315}\right)\)	\(e\left(\frac{97}{315}\right)\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{226}{315}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{437}{630}\right)\)	\(e\left(\frac{251}{315}\right)\)
\(\chi_{23275}(1089,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{529}{630}\right)\)	\(e\left(\frac{103}{630}\right)\)	\(e\left(\frac{214}{315}\right)\)	\(e\left(\frac{1}{315}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{103}{315}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{11}{630}\right)\)	\(e\left(\frac{113}{315}\right)\)
\(\chi_{23275}(1164,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{629}{630}\right)\)	\(e\left(\frac{263}{630}\right)\)	\(e\left(\frac{314}{315}\right)\)	\(e\left(\frac{131}{315}\right)\)	\(e\left(\frac{209}{210}\right)\)	\(e\left(\frac{263}{315}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{181}{630}\right)\)	\(e\left(\frac{313}{315}\right)\)
\(\chi_{23275}(1334,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{361}{630}\right)\)	\(e\left(\frac{187}{630}\right)\)	\(e\left(\frac{46}{315}\right)\)	\(e\left(\frac{274}{315}\right)\)	\(e\left(\frac{151}{210}\right)\)	\(e\left(\frac{187}{315}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{179}{630}\right)\)	\(e\left(\frac{92}{315}\right)\)
\(\chi_{23275}(1479,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{353}{630}\right)\)	\(e\left(\frac{401}{630}\right)\)	\(e\left(\frac{38}{315}\right)\)	\(e\left(\frac{62}{315}\right)\)	\(e\left(\frac{143}{210}\right)\)	\(e\left(\frac{86}{315}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{367}{630}\right)\)	\(e\left(\frac{76}{315}\right)\)
\(\chi_{23275}(1689,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{239}{630}\right)\)	\(e\left(\frac{143}{630}\right)\)	\(e\left(\frac{239}{315}\right)\)	\(e\left(\frac{191}{315}\right)\)	\(e\left(\frac{29}{210}\right)\)	\(e\left(\frac{143}{315}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{211}{630}\right)\)	\(e\left(\frac{163}{315}\right)\)
\(\chi_{23275}(1719,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{337}{630}\right)\)	\(e\left(\frac{199}{630}\right)\)	\(e\left(\frac{22}{315}\right)\)	\(e\left(\frac{268}{315}\right)\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{199}{315}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{113}{630}\right)\)	\(e\left(\frac{44}{315}\right)\)
\(\chi_{23275}(1754,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{583}{630}\right)\)	\(e\left(\frac{391}{630}\right)\)	\(e\left(\frac{268}{315}\right)\)	\(e\left(\frac{172}{315}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{76}{315}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{317}{630}\right)\)	\(e\left(\frac{221}{315}\right)\)
\(\chi_{23275}(1829,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{233}{630}\right)\)	\(e\left(\frac{461}{630}\right)\)	\(e\left(\frac{233}{315}\right)\)	\(e\left(\frac{32}{315}\right)\)	\(e\left(\frac{23}{210}\right)\)	\(e\left(\frac{146}{315}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{37}{630}\right)\)	\(e\left(\frac{151}{315}\right)\)
\(\chi_{23275}(2144,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{587}{630}\right)\)	\(e\left(\frac{599}{630}\right)\)	\(e\left(\frac{272}{315}\right)\)	\(e\left(\frac{278}{315}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{284}{315}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{223}{630}\right)\)	\(e\left(\frac{229}{315}\right)\)
\(\chi_{23275}(2354,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{473}{630}\right)\)	\(e\left(\frac{341}{630}\right)\)	\(e\left(\frac{158}{315}\right)\)	\(e\left(\frac{92}{315}\right)\)	\(e\left(\frac{53}{210}\right)\)	\(e\left(\frac{26}{315}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{67}{630}\right)\)	\(e\left(\frac{1}{315}\right)\)
\(\chi_{23275}(2384,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{391}{630}\right)\)	\(e\left(\frac{487}{630}\right)\)	\(e\left(\frac{76}{315}\right)\)	\(e\left(\frac{124}{315}\right)\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{172}{315}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{419}{630}\right)\)	\(e\left(\frac{152}{315}\right)\)
\(\chi_{23275}(2494,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{467}{630}\right)\)	\(e\left(\frac{29}{630}\right)\)	\(e\left(\frac{152}{315}\right)\)	\(e\left(\frac{248}{315}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{29}{315}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{523}{630}\right)\)	\(e\left(\frac{304}{315}\right)\)
\(\chi_{23275}(2809,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{630}\right)\)	\(e\left(\frac{167}{630}\right)\)	\(e\left(\frac{191}{315}\right)\)	\(e\left(\frac{179}{315}\right)\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{167}{315}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{79}{630}\right)\)	\(e\left(\frac{67}{315}\right)\)
\(\chi_{23275}(3084,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{630}\right)\)	\(e\left(\frac{337}{630}\right)\)	\(e\left(\frac{61}{315}\right)\)	\(e\left(\frac{199}{315}\right)\)	\(e\left(\frac{61}{210}\right)\)	\(e\left(\frac{22}{315}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{299}{630}\right)\)	\(e\left(\frac{122}{315}\right)\)
\(\chi_{23275}(3159,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{630}\right)\)	\(e\left(\frac{227}{630}\right)\)	\(e\left(\frac{71}{315}\right)\)	\(e\left(\frac{149}{315}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{227}{315}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{379}{630}\right)\)	\(e\left(\frac{142}{315}\right)\)
\(\chi_{23275}(3329,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{523}{630}\right)\)	\(e\left(\frac{421}{630}\right)\)	\(e\left(\frac{208}{315}\right)\)	\(e\left(\frac{157}{315}\right)\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{106}{315}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{467}{630}\right)\)	\(e\left(\frac{101}{315}\right)\)
\(\chi_{23275}(3684,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{311}{630}\right)\)	\(e\left(\frac{107}{630}\right)\)	\(e\left(\frac{311}{315}\right)\)	\(e\left(\frac{209}{315}\right)\)	\(e\left(\frac{101}{210}\right)\)	\(e\left(\frac{107}{315}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{409}{630}\right)\)	\(e\left(\frac{307}{315}\right)\)
\(\chi_{23275}(3714,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{499}{630}\right)\)	\(e\left(\frac{433}{630}\right)\)	\(e\left(\frac{184}{315}\right)\)	\(e\left(\frac{151}{315}\right)\)	\(e\left(\frac{79}{210}\right)\)	\(e\left(\frac{118}{315}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{401}{630}\right)\)	\(e\left(\frac{53}{315}\right)\)
\(\chi_{23275}(3994,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{577}{630}\right)\)	\(e\left(\frac{79}{630}\right)\)	\(e\left(\frac{262}{315}\right)\)	\(e\left(\frac{13}{315}\right)\)	\(e\left(\frac{157}{210}\right)\)	\(e\left(\frac{79}{315}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{143}{630}\right)\)	\(e\left(\frac{209}{315}\right)\)
\(\chi_{23275}(4139,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{630}\right)\)	\(e\left(\frac{563}{630}\right)\)	\(e\left(\frac{29}{315}\right)\)	\(e\left(\frac{296}{315}\right)\)	\(e\left(\frac{29}{210}\right)\)	\(e\left(\frac{248}{315}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{421}{630}\right)\)	\(e\left(\frac{58}{315}\right)\)
\(\chi_{23275}(4414,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{630}\right)\)	\(e\left(\frac{283}{630}\right)\)	\(e\left(\frac{169}{315}\right)\)	\(e\left(\frac{226}{315}\right)\)	\(e\left(\frac{169}{210}\right)\)	\(e\left(\frac{283}{315}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{281}{630}\right)\)	\(e\left(\frac{23}{315}\right)\)
\(\chi_{23275}(4659,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{630}\right)\)	\(e\left(\frac{367}{630}\right)\)	\(e\left(\frac{1}{315}\right)\)	\(e\left(\frac{184}{315}\right)\)	\(e\left(\frac{1}{210}\right)\)	\(e\left(\frac{52}{315}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{449}{630}\right)\)	\(e\left(\frac{2}{315}\right)\)
\(\chi_{23275}(4804,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{263}{630}\right)\)	\(e\left(\frac{131}{630}\right)\)	\(e\left(\frac{263}{315}\right)\)	\(e\left(\frac{197}{315}\right)\)	\(e\left(\frac{53}{210}\right)\)	\(e\left(\frac{131}{315}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{277}{630}\right)\)	\(e\left(\frac{211}{315}\right)\)
\(\chi_{23275}(5014,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{630}\right)\)	\(e\left(\frac{503}{630}\right)\)	\(e\left(\frac{149}{315}\right)\)	\(e\left(\frac{11}{315}\right)\)	\(e\left(\frac{149}{210}\right)\)	\(e\left(\frac{188}{315}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{121}{630}\right)\)	\(e\left(\frac{298}{315}\right)\)
\(\chi_{23275}(5044,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{607}{630}\right)\)	\(e\left(\frac{379}{630}\right)\)	\(e\left(\frac{292}{315}\right)\)	\(e\left(\frac{178}{315}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{64}{315}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{383}{630}\right)\)	\(e\left(\frac{269}{315}\right)\)
\(\chi_{23275}(5079,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{223}{630}\right)\)	\(e\left(\frac{571}{630}\right)\)	\(e\left(\frac{223}{315}\right)\)	\(e\left(\frac{82}{315}\right)\)	\(e\left(\frac{13}{210}\right)\)	\(e\left(\frac{256}{315}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{587}{630}\right)\)	\(e\left(\frac{131}{315}\right)\)

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First 31 of 144 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	23275.of
Modulus	$23275$
Conductor	$23275$
Order	$630$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(23275\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(23275\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(630\)	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:	yes	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);