LMFDB - Dirichlet character orbit 5625.bq

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5625, base_ring=CyclotomicField(500)) M = H._module chi = DirichletCharacter(H, M([250,3])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(8, 5625)) 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("5625.8"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$5625$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$1875$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$500$	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 1875.x	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:	$\Q(\zeta_{500})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 500 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 200 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{5625}(8,\cdot)$	$1$	$1$	$e\left(\frac{253}{500}\right)$	$e\left(\frac{3}{250}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{259}{500}\right)$	$e\left(\frac{89}{250}\right)$	$e\left(\frac{417}{500}\right)$	$e\left(\frac{52}{125}\right)$	$e\left(\frac{3}{125}\right)$	$e\left(\frac{269}{500}\right)$	$e\left(\frac{127}{250}\right)$
$\chi_{5625}(17,\cdot)$	$1$	$1$	$e\left(\frac{423}{500}\right)$	$e\left(\frac{173}{250}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{269}{500}\right)$	$e\left(\frac{49}{250}\right)$	$e\left(\frac{47}{500}\right)$	$e\left(\frac{82}{125}\right)$	$e\left(\frac{48}{125}\right)$	$e\left(\frac{179}{500}\right)$	$e\left(\frac{157}{250}\right)$
$\chi_{5625}(53,\cdot)$	$1$	$1$	$e\left(\frac{117}{500}\right)$	$e\left(\frac{117}{250}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{351}{500}\right)$	$e\left(\frac{221}{250}\right)$	$e\left(\frac{13}{500}\right)$	$e\left(\frac{28}{125}\right)$	$e\left(\frac{117}{125}\right)$	$e\left(\frac{241}{500}\right)$	$e\left(\frac{203}{250}\right)$
$\chi_{5625}(62,\cdot)$	$1$	$1$	$e\left(\frac{299}{500}\right)$	$e\left(\frac{49}{250}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{397}{500}\right)$	$e\left(\frac{37}{250}\right)$	$e\left(\frac{311}{500}\right)$	$e\left(\frac{16}{125}\right)$	$e\left(\frac{49}{125}\right)$	$e\left(\frac{227}{500}\right)$	$e\left(\frac{241}{250}\right)$
$\chi_{5625}(98,\cdot)$	$1$	$1$	$e\left(\frac{221}{500}\right)$	$e\left(\frac{221}{250}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{163}{500}\right)$	$e\left(\frac{223}{250}\right)$	$e\left(\frac{469}{500}\right)$	$e\left(\frac{39}{125}\right)$	$e\left(\frac{96}{125}\right)$	$e\left(\frac{233}{500}\right)$	$e\left(\frac{189}{250}\right)$
$\chi_{5625}(152,\cdot)$	$1$	$1$	$e\left(\frac{171}{500}\right)$	$e\left(\frac{171}{250}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{13}{500}\right)$	$e\left(\frac{73}{250}\right)$	$e\left(\frac{19}{500}\right)$	$e\left(\frac{89}{125}\right)$	$e\left(\frac{46}{125}\right)$	$e\left(\frac{83}{500}\right)$	$e\left(\frac{239}{250}\right)$
$\chi_{5625}(188,\cdot)$	$1$	$1$	$e\left(\frac{349}{500}\right)$	$e\left(\frac{99}{250}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{47}{500}\right)$	$e\left(\frac{187}{250}\right)$	$e\left(\frac{261}{500}\right)$	$e\left(\frac{91}{125}\right)$	$e\left(\frac{99}{125}\right)$	$e\left(\frac{377}{500}\right)$	$e\left(\frac{191}{250}\right)$
$\chi_{5625}(197,\cdot)$	$1$	$1$	$e\left(\frac{67}{500}\right)$	$e\left(\frac{67}{250}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{201}{500}\right)$	$e\left(\frac{71}{250}\right)$	$e\left(\frac{63}{500}\right)$	$e\left(\frac{78}{125}\right)$	$e\left(\frac{67}{125}\right)$	$e\left(\frac{91}{500}\right)$	$e\left(\frac{3}{250}\right)$
$\chi_{5625}(233,\cdot)$	$1$	$1$	$e\left(\frac{473}{500}\right)$	$e\left(\frac{223}{250}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{419}{500}\right)$	$e\left(\frac{199}{250}\right)$	$e\left(\frac{497}{500}\right)$	$e\left(\frac{32}{125}\right)$	$e\left(\frac{98}{125}\right)$	$e\left(\frac{329}{500}\right)$	$e\left(\frac{107}{250}\right)$
$\chi_{5625}(242,\cdot)$	$1$	$1$	$e\left(\frac{203}{500}\right)$	$e\left(\frac{203}{250}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{109}{500}\right)$	$e\left(\frac{189}{250}\right)$	$e\left(\frac{467}{500}\right)$	$e\left(\frac{102}{125}\right)$	$e\left(\frac{78}{125}\right)$	$e\left(\frac{119}{500}\right)$	$e\left(\frac{177}{250}\right)$
$\chi_{5625}(278,\cdot)$	$1$	$1$	$e\left(\frac{37}{500}\right)$	$e\left(\frac{37}{250}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{111}{500}\right)$	$e\left(\frac{181}{250}\right)$	$e\left(\frac{393}{500}\right)$	$e\left(\frac{58}{125}\right)$	$e\left(\frac{37}{125}\right)$	$e\left(\frac{401}{500}\right)$	$e\left(\frac{233}{250}\right)$
$\chi_{5625}(287,\cdot)$	$1$	$1$	$e\left(\frac{279}{500}\right)$	$e\left(\frac{29}{250}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{337}{500}\right)$	$e\left(\frac{27}{250}\right)$	$e\left(\frac{31}{500}\right)$	$e\left(\frac{86}{125}\right)$	$e\left(\frac{29}{125}\right)$	$e\left(\frac{267}{500}\right)$	$e\left(\frac{61}{250}\right)$
$\chi_{5625}(323,\cdot)$	$1$	$1$	$e\left(\frac{341}{500}\right)$	$e\left(\frac{91}{250}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{23}{500}\right)$	$e\left(\frac{33}{250}\right)$	$e\left(\frac{149}{500}\right)$	$e\left(\frac{119}{125}\right)$	$e\left(\frac{91}{125}\right)$	$e\left(\frac{493}{500}\right)$	$e\left(\frac{19}{250}\right)$
$\chi_{5625}(377,\cdot)$	$1$	$1$	$e\left(\frac{51}{500}\right)$	$e\left(\frac{51}{250}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{153}{500}\right)$	$e\left(\frac{13}{250}\right)$	$e\left(\frac{339}{500}\right)$	$e\left(\frac{9}{125}\right)$	$e\left(\frac{51}{125}\right)$	$e\left(\frac{323}{500}\right)$	$e\left(\frac{159}{250}\right)$
$\chi_{5625}(413,\cdot)$	$1$	$1$	$e\left(\frac{369}{500}\right)$	$e\left(\frac{119}{250}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{107}{500}\right)$	$e\left(\frac{197}{250}\right)$	$e\left(\frac{41}{500}\right)$	$e\left(\frac{21}{125}\right)$	$e\left(\frac{119}{125}\right)$	$e\left(\frac{337}{500}\right)$	$e\left(\frac{121}{250}\right)$
$\chi_{5625}(422,\cdot)$	$1$	$1$	$e\left(\frac{147}{500}\right)$	$e\left(\frac{147}{250}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{441}{500}\right)$	$e\left(\frac{111}{250}\right)$	$e\left(\frac{183}{500}\right)$	$e\left(\frac{48}{125}\right)$	$e\left(\frac{22}{125}\right)$	$e\left(\frac{431}{500}\right)$	$e\left(\frac{223}{250}\right)$
$\chi_{5625}(458,\cdot)$	$1$	$1$	$e\left(\frac{193}{500}\right)$	$e\left(\frac{193}{250}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{79}{500}\right)$	$e\left(\frac{59}{250}\right)$	$e\left(\frac{77}{500}\right)$	$e\left(\frac{12}{125}\right)$	$e\left(\frac{68}{125}\right)$	$e\left(\frac{389}{500}\right)$	$e\left(\frac{87}{250}\right)$
$\chi_{5625}(467,\cdot)$	$1$	$1$	$e\left(\frac{483}{500}\right)$	$e\left(\frac{233}{250}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{449}{500}\right)$	$e\left(\frac{79}{250}\right)$	$e\left(\frac{387}{500}\right)$	$e\left(\frac{122}{125}\right)$	$e\left(\frac{108}{125}\right)$	$e\left(\frac{59}{500}\right)$	$e\left(\frac{197}{250}\right)$
$\chi_{5625}(503,\cdot)$	$1$	$1$	$e\left(\frac{457}{500}\right)$	$e\left(\frac{207}{250}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{371}{500}\right)$	$e\left(\frac{141}{250}\right)$	$e\left(\frac{273}{500}\right)$	$e\left(\frac{88}{125}\right)$	$e\left(\frac{82}{125}\right)$	$e\left(\frac{61}{500}\right)$	$e\left(\frac{13}{250}\right)$
$\chi_{5625}(512,\cdot)$	$1$	$1$	$e\left(\frac{259}{500}\right)$	$e\left(\frac{9}{250}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{277}{500}\right)$	$e\left(\frac{17}{250}\right)$	$e\left(\frac{251}{500}\right)$	$e\left(\frac{31}{125}\right)$	$e\left(\frac{9}{125}\right)$	$e\left(\frac{307}{500}\right)$	$e\left(\frac{131}{250}\right)$
$\chi_{5625}(548,\cdot)$	$1$	$1$	$e\left(\frac{461}{500}\right)$	$e\left(\frac{211}{250}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{383}{500}\right)$	$e\left(\frac{93}{250}\right)$	$e\left(\frac{329}{500}\right)$	$e\left(\frac{74}{125}\right)$	$e\left(\frac{86}{125}\right)$	$e\left(\frac{253}{500}\right)$	$e\left(\frac{99}{250}\right)$
$\chi_{5625}(602,\cdot)$	$1$	$1$	$e\left(\frac{431}{500}\right)$	$e\left(\frac{181}{250}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{293}{500}\right)$	$e\left(\frac{203}{250}\right)$	$e\left(\frac{159}{500}\right)$	$e\left(\frac{54}{125}\right)$	$e\left(\frac{56}{125}\right)$	$e\left(\frac{63}{500}\right)$	$e\left(\frac{79}{250}\right)$
$\chi_{5625}(638,\cdot)$	$1$	$1$	$e\left(\frac{389}{500}\right)$	$e\left(\frac{139}{250}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{167}{500}\right)$	$e\left(\frac{207}{250}\right)$	$e\left(\frac{321}{500}\right)$	$e\left(\frac{76}{125}\right)$	$e\left(\frac{14}{125}\right)$	$e\left(\frac{297}{500}\right)$	$e\left(\frac{51}{250}\right)$
$\chi_{5625}(647,\cdot)$	$1$	$1$	$e\left(\frac{227}{500}\right)$	$e\left(\frac{227}{250}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{181}{500}\right)$	$e\left(\frac{151}{250}\right)$	$e\left(\frac{303}{500}\right)$	$e\left(\frac{18}{125}\right)$	$e\left(\frac{102}{125}\right)$	$e\left(\frac{271}{500}\right)$	$e\left(\frac{193}{250}\right)$
$\chi_{5625}(683,\cdot)$	$1$	$1$	$e\left(\frac{413}{500}\right)$	$e\left(\frac{163}{250}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{239}{500}\right)$	$e\left(\frac{169}{250}\right)$	$e\left(\frac{157}{500}\right)$	$e\left(\frac{117}{125}\right)$	$e\left(\frac{38}{125}\right)$	$e\left(\frac{449}{500}\right)$	$e\left(\frac{67}{250}\right)$
$\chi_{5625}(692,\cdot)$	$1$	$1$	$e\left(\frac{263}{500}\right)$	$e\left(\frac{13}{250}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{289}{500}\right)$	$e\left(\frac{219}{250}\right)$	$e\left(\frac{307}{500}\right)$	$e\left(\frac{17}{125}\right)$	$e\left(\frac{13}{125}\right)$	$e\left(\frac{499}{500}\right)$	$e\left(\frac{217}{250}\right)$
$\chi_{5625}(728,\cdot)$	$1$	$1$	$e\left(\frac{377}{500}\right)$	$e\left(\frac{127}{250}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{131}{500}\right)$	$e\left(\frac{101}{250}\right)$	$e\left(\frac{153}{500}\right)$	$e\left(\frac{118}{125}\right)$	$e\left(\frac{2}{125}\right)$	$e\left(\frac{221}{500}\right)$	$e\left(\frac{43}{250}\right)$
$\chi_{5625}(737,\cdot)$	$1$	$1$	$e\left(\frac{239}{500}\right)$	$e\left(\frac{239}{250}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{217}{500}\right)$	$e\left(\frac{7}{250}\right)$	$e\left(\frac{471}{500}\right)$	$e\left(\frac{101}{125}\right)$	$e\left(\frac{114}{125}\right)$	$e\left(\frac{347}{500}\right)$	$e\left(\frac{201}{250}\right)$
$\chi_{5625}(773,\cdot)$	$1$	$1$	$e\left(\frac{81}{500}\right)$	$e\left(\frac{81}{250}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{243}{500}\right)$	$e\left(\frac{153}{250}\right)$	$e\left(\frac{9}{500}\right)$	$e\left(\frac{29}{125}\right)$	$e\left(\frac{81}{125}\right)$	$e\left(\frac{13}{500}\right)$	$e\left(\frac{179}{250}\right)$
$\chi_{5625}(827,\cdot)$	$1$	$1$	$e\left(\frac{311}{500}\right)$	$e\left(\frac{61}{250}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{433}{500}\right)$	$e\left(\frac{143}{250}\right)$	$e\left(\frac{479}{500}\right)$	$e\left(\frac{99}{125}\right)$	$e\left(\frac{61}{125}\right)$	$e\left(\frac{303}{500}\right)$	$e\left(\frac{249}{250}\right)$
$\chi_{5625}(863,\cdot)$	$1$	$1$	$e\left(\frac{409}{500}\right)$	$e\left(\frac{159}{250}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{227}{500}\right)$	$e\left(\frac{217}{250}\right)$	$e\left(\frac{101}{500}\right)$	$e\left(\frac{6}{125}\right)$	$e\left(\frac{34}{125}\right)$	$e\left(\frac{257}{500}\right)$	$e\left(\frac{231}{250}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{5625}(8,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{253}{500}\right)\)	\(e\left(\frac{3}{250}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{259}{500}\right)\)	\(e\left(\frac{89}{250}\right)\)	\(e\left(\frac{417}{500}\right)\)	\(e\left(\frac{52}{125}\right)\)	\(e\left(\frac{3}{125}\right)\)	\(e\left(\frac{269}{500}\right)\)	\(e\left(\frac{127}{250}\right)\)
\(\chi_{5625}(17,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{423}{500}\right)\)	\(e\left(\frac{173}{250}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{269}{500}\right)\)	\(e\left(\frac{49}{250}\right)\)	\(e\left(\frac{47}{500}\right)\)	\(e\left(\frac{82}{125}\right)\)	\(e\left(\frac{48}{125}\right)\)	\(e\left(\frac{179}{500}\right)\)	\(e\left(\frac{157}{250}\right)\)
\(\chi_{5625}(53,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{117}{500}\right)\)	\(e\left(\frac{117}{250}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{351}{500}\right)\)	\(e\left(\frac{221}{250}\right)\)	\(e\left(\frac{13}{500}\right)\)	\(e\left(\frac{28}{125}\right)\)	\(e\left(\frac{117}{125}\right)\)	\(e\left(\frac{241}{500}\right)\)	\(e\left(\frac{203}{250}\right)\)
\(\chi_{5625}(62,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{299}{500}\right)\)	\(e\left(\frac{49}{250}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{397}{500}\right)\)	\(e\left(\frac{37}{250}\right)\)	\(e\left(\frac{311}{500}\right)\)	\(e\left(\frac{16}{125}\right)\)	\(e\left(\frac{49}{125}\right)\)	\(e\left(\frac{227}{500}\right)\)	\(e\left(\frac{241}{250}\right)\)
\(\chi_{5625}(98,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{221}{500}\right)\)	\(e\left(\frac{221}{250}\right)\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{163}{500}\right)\)	\(e\left(\frac{223}{250}\right)\)	\(e\left(\frac{469}{500}\right)\)	\(e\left(\frac{39}{125}\right)\)	\(e\left(\frac{96}{125}\right)\)	\(e\left(\frac{233}{500}\right)\)	\(e\left(\frac{189}{250}\right)\)
\(\chi_{5625}(152,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{171}{500}\right)\)	\(e\left(\frac{171}{250}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{13}{500}\right)\)	\(e\left(\frac{73}{250}\right)\)	\(e\left(\frac{19}{500}\right)\)	\(e\left(\frac{89}{125}\right)\)	\(e\left(\frac{46}{125}\right)\)	\(e\left(\frac{83}{500}\right)\)	\(e\left(\frac{239}{250}\right)\)
\(\chi_{5625}(188,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{349}{500}\right)\)	\(e\left(\frac{99}{250}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{47}{500}\right)\)	\(e\left(\frac{187}{250}\right)\)	\(e\left(\frac{261}{500}\right)\)	\(e\left(\frac{91}{125}\right)\)	\(e\left(\frac{99}{125}\right)\)	\(e\left(\frac{377}{500}\right)\)	\(e\left(\frac{191}{250}\right)\)
\(\chi_{5625}(197,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{500}\right)\)	\(e\left(\frac{67}{250}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{201}{500}\right)\)	\(e\left(\frac{71}{250}\right)\)	\(e\left(\frac{63}{500}\right)\)	\(e\left(\frac{78}{125}\right)\)	\(e\left(\frac{67}{125}\right)\)	\(e\left(\frac{91}{500}\right)\)	\(e\left(\frac{3}{250}\right)\)
\(\chi_{5625}(233,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{473}{500}\right)\)	\(e\left(\frac{223}{250}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{419}{500}\right)\)	\(e\left(\frac{199}{250}\right)\)	\(e\left(\frac{497}{500}\right)\)	\(e\left(\frac{32}{125}\right)\)	\(e\left(\frac{98}{125}\right)\)	\(e\left(\frac{329}{500}\right)\)	\(e\left(\frac{107}{250}\right)\)
\(\chi_{5625}(242,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{203}{500}\right)\)	\(e\left(\frac{203}{250}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{109}{500}\right)\)	\(e\left(\frac{189}{250}\right)\)	\(e\left(\frac{467}{500}\right)\)	\(e\left(\frac{102}{125}\right)\)	\(e\left(\frac{78}{125}\right)\)	\(e\left(\frac{119}{500}\right)\)	\(e\left(\frac{177}{250}\right)\)
\(\chi_{5625}(278,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{500}\right)\)	\(e\left(\frac{37}{250}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{111}{500}\right)\)	\(e\left(\frac{181}{250}\right)\)	\(e\left(\frac{393}{500}\right)\)	\(e\left(\frac{58}{125}\right)\)	\(e\left(\frac{37}{125}\right)\)	\(e\left(\frac{401}{500}\right)\)	\(e\left(\frac{233}{250}\right)\)
\(\chi_{5625}(287,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{279}{500}\right)\)	\(e\left(\frac{29}{250}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{337}{500}\right)\)	\(e\left(\frac{27}{250}\right)\)	\(e\left(\frac{31}{500}\right)\)	\(e\left(\frac{86}{125}\right)\)	\(e\left(\frac{29}{125}\right)\)	\(e\left(\frac{267}{500}\right)\)	\(e\left(\frac{61}{250}\right)\)
\(\chi_{5625}(323,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{341}{500}\right)\)	\(e\left(\frac{91}{250}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{23}{500}\right)\)	\(e\left(\frac{33}{250}\right)\)	\(e\left(\frac{149}{500}\right)\)	\(e\left(\frac{119}{125}\right)\)	\(e\left(\frac{91}{125}\right)\)	\(e\left(\frac{493}{500}\right)\)	\(e\left(\frac{19}{250}\right)\)
\(\chi_{5625}(377,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{500}\right)\)	\(e\left(\frac{51}{250}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{153}{500}\right)\)	\(e\left(\frac{13}{250}\right)\)	\(e\left(\frac{339}{500}\right)\)	\(e\left(\frac{9}{125}\right)\)	\(e\left(\frac{51}{125}\right)\)	\(e\left(\frac{323}{500}\right)\)	\(e\left(\frac{159}{250}\right)\)
\(\chi_{5625}(413,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{369}{500}\right)\)	\(e\left(\frac{119}{250}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{107}{500}\right)\)	\(e\left(\frac{197}{250}\right)\)	\(e\left(\frac{41}{500}\right)\)	\(e\left(\frac{21}{125}\right)\)	\(e\left(\frac{119}{125}\right)\)	\(e\left(\frac{337}{500}\right)\)	\(e\left(\frac{121}{250}\right)\)
\(\chi_{5625}(422,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{147}{500}\right)\)	\(e\left(\frac{147}{250}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{441}{500}\right)\)	\(e\left(\frac{111}{250}\right)\)	\(e\left(\frac{183}{500}\right)\)	\(e\left(\frac{48}{125}\right)\)	\(e\left(\frac{22}{125}\right)\)	\(e\left(\frac{431}{500}\right)\)	\(e\left(\frac{223}{250}\right)\)
\(\chi_{5625}(458,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{500}\right)\)	\(e\left(\frac{193}{250}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{79}{500}\right)\)	\(e\left(\frac{59}{250}\right)\)	\(e\left(\frac{77}{500}\right)\)	\(e\left(\frac{12}{125}\right)\)	\(e\left(\frac{68}{125}\right)\)	\(e\left(\frac{389}{500}\right)\)	\(e\left(\frac{87}{250}\right)\)
\(\chi_{5625}(467,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{483}{500}\right)\)	\(e\left(\frac{233}{250}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{449}{500}\right)\)	\(e\left(\frac{79}{250}\right)\)	\(e\left(\frac{387}{500}\right)\)	\(e\left(\frac{122}{125}\right)\)	\(e\left(\frac{108}{125}\right)\)	\(e\left(\frac{59}{500}\right)\)	\(e\left(\frac{197}{250}\right)\)
\(\chi_{5625}(503,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{457}{500}\right)\)	\(e\left(\frac{207}{250}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{371}{500}\right)\)	\(e\left(\frac{141}{250}\right)\)	\(e\left(\frac{273}{500}\right)\)	\(e\left(\frac{88}{125}\right)\)	\(e\left(\frac{82}{125}\right)\)	\(e\left(\frac{61}{500}\right)\)	\(e\left(\frac{13}{250}\right)\)
\(\chi_{5625}(512,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{259}{500}\right)\)	\(e\left(\frac{9}{250}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{277}{500}\right)\)	\(e\left(\frac{17}{250}\right)\)	\(e\left(\frac{251}{500}\right)\)	\(e\left(\frac{31}{125}\right)\)	\(e\left(\frac{9}{125}\right)\)	\(e\left(\frac{307}{500}\right)\)	\(e\left(\frac{131}{250}\right)\)
\(\chi_{5625}(548,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{461}{500}\right)\)	\(e\left(\frac{211}{250}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{383}{500}\right)\)	\(e\left(\frac{93}{250}\right)\)	\(e\left(\frac{329}{500}\right)\)	\(e\left(\frac{74}{125}\right)\)	\(e\left(\frac{86}{125}\right)\)	\(e\left(\frac{253}{500}\right)\)	\(e\left(\frac{99}{250}\right)\)
\(\chi_{5625}(602,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{431}{500}\right)\)	\(e\left(\frac{181}{250}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{293}{500}\right)\)	\(e\left(\frac{203}{250}\right)\)	\(e\left(\frac{159}{500}\right)\)	\(e\left(\frac{54}{125}\right)\)	\(e\left(\frac{56}{125}\right)\)	\(e\left(\frac{63}{500}\right)\)	\(e\left(\frac{79}{250}\right)\)
\(\chi_{5625}(638,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{389}{500}\right)\)	\(e\left(\frac{139}{250}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{167}{500}\right)\)	\(e\left(\frac{207}{250}\right)\)	\(e\left(\frac{321}{500}\right)\)	\(e\left(\frac{76}{125}\right)\)	\(e\left(\frac{14}{125}\right)\)	\(e\left(\frac{297}{500}\right)\)	\(e\left(\frac{51}{250}\right)\)
\(\chi_{5625}(647,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{227}{500}\right)\)	\(e\left(\frac{227}{250}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{181}{500}\right)\)	\(e\left(\frac{151}{250}\right)\)	\(e\left(\frac{303}{500}\right)\)	\(e\left(\frac{18}{125}\right)\)	\(e\left(\frac{102}{125}\right)\)	\(e\left(\frac{271}{500}\right)\)	\(e\left(\frac{193}{250}\right)\)
\(\chi_{5625}(683,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{413}{500}\right)\)	\(e\left(\frac{163}{250}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{239}{500}\right)\)	\(e\left(\frac{169}{250}\right)\)	\(e\left(\frac{157}{500}\right)\)	\(e\left(\frac{117}{125}\right)\)	\(e\left(\frac{38}{125}\right)\)	\(e\left(\frac{449}{500}\right)\)	\(e\left(\frac{67}{250}\right)\)
\(\chi_{5625}(692,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{263}{500}\right)\)	\(e\left(\frac{13}{250}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{289}{500}\right)\)	\(e\left(\frac{219}{250}\right)\)	\(e\left(\frac{307}{500}\right)\)	\(e\left(\frac{17}{125}\right)\)	\(e\left(\frac{13}{125}\right)\)	\(e\left(\frac{499}{500}\right)\)	\(e\left(\frac{217}{250}\right)\)
\(\chi_{5625}(728,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{377}{500}\right)\)	\(e\left(\frac{127}{250}\right)\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{131}{500}\right)\)	\(e\left(\frac{101}{250}\right)\)	\(e\left(\frac{153}{500}\right)\)	\(e\left(\frac{118}{125}\right)\)	\(e\left(\frac{2}{125}\right)\)	\(e\left(\frac{221}{500}\right)\)	\(e\left(\frac{43}{250}\right)\)
\(\chi_{5625}(737,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{239}{500}\right)\)	\(e\left(\frac{239}{250}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{217}{500}\right)\)	\(e\left(\frac{7}{250}\right)\)	\(e\left(\frac{471}{500}\right)\)	\(e\left(\frac{101}{125}\right)\)	\(e\left(\frac{114}{125}\right)\)	\(e\left(\frac{347}{500}\right)\)	\(e\left(\frac{201}{250}\right)\)
\(\chi_{5625}(773,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{81}{500}\right)\)	\(e\left(\frac{81}{250}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{243}{500}\right)\)	\(e\left(\frac{153}{250}\right)\)	\(e\left(\frac{9}{500}\right)\)	\(e\left(\frac{29}{125}\right)\)	\(e\left(\frac{81}{125}\right)\)	\(e\left(\frac{13}{500}\right)\)	\(e\left(\frac{179}{250}\right)\)
\(\chi_{5625}(827,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{311}{500}\right)\)	\(e\left(\frac{61}{250}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{433}{500}\right)\)	\(e\left(\frac{143}{250}\right)\)	\(e\left(\frac{479}{500}\right)\)	\(e\left(\frac{99}{125}\right)\)	\(e\left(\frac{61}{125}\right)\)	\(e\left(\frac{303}{500}\right)\)	\(e\left(\frac{249}{250}\right)\)
\(\chi_{5625}(863,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{409}{500}\right)\)	\(e\left(\frac{159}{250}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{227}{500}\right)\)	\(e\left(\frac{217}{250}\right)\)	\(e\left(\frac{101}{500}\right)\)	\(e\left(\frac{6}{125}\right)\)	\(e\left(\frac{34}{125}\right)\)	\(e\left(\frac{257}{500}\right)\)	\(e\left(\frac{231}{250}\right)\)

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First 31 of 200 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	5625.bq
Modulus	$5625$
Conductor	$1875$
Order	$500$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(5625\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1875\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(500\)	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 1875.x	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);