LMFDB - Dirichlet character orbit 5625.bn

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5625, base_ring=CyclotomicField(300)) M = H._module chi = DirichletCharacter(H, M([250,3])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(32, 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("5625.32"); 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:	$1125$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$300$	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 1125.bj	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{300})$	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 300 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 80 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{5625}(32,\cdot)$	$1$	$1$	$e\left(\frac{253}{300}\right)$	$e\left(\frac{103}{150}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{89}{150}\right)$	$e\left(\frac{17}{300}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{9}{50}\right)$
$\chi_{5625}(218,\cdot)$	$1$	$1$	$e\left(\frac{83}{300}\right)$	$e\left(\frac{83}{150}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{79}{150}\right)$	$e\left(\frac{187}{300}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{49}{50}\right)$
$\chi_{5625}(257,\cdot)$	$1$	$1$	$e\left(\frac{61}{300}\right)$	$e\left(\frac{61}{150}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{29}{300}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{61}{75}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{33}{50}\right)$
$\chi_{5625}(293,\cdot)$	$1$	$1$	$e\left(\frac{247}{300}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{11}{150}\right)$	$e\left(\frac{83}{300}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{41}{50}\right)$
$\chi_{5625}(407,\cdot)$	$1$	$1$	$e\left(\frac{233}{300}\right)$	$e\left(\frac{83}{150}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{79}{150}\right)$	$e\left(\frac{37}{300}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{49}{50}\right)$
$\chi_{5625}(482,\cdot)$	$1$	$1$	$e\left(\frac{169}{300}\right)$	$e\left(\frac{19}{150}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{47}{150}\right)$	$e\left(\frac{41}{300}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{7}{50}\right)$
$\chi_{5625}(518,\cdot)$	$1$	$1$	$e\left(\frac{139}{300}\right)$	$e\left(\frac{139}{150}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{71}{300}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{17}{50}\right)$
$\chi_{5625}(632,\cdot)$	$1$	$1$	$e\left(\frac{41}{300}\right)$	$e\left(\frac{41}{150}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{133}{150}\right)$	$e\left(\frac{49}{300}\right)$	$e\left(\frac{19}{75}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{23}{50}\right)$
$\chi_{5625}(668,\cdot)$	$1$	$1$	$e\left(\frac{167}{300}\right)$	$e\left(\frac{17}{150}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{121}{150}\right)$	$e\left(\frac{163}{300}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{1}{50}\right)$
$\chi_{5625}(707,\cdot)$	$1$	$1$	$e\left(\frac{277}{300}\right)$	$e\left(\frac{127}{150}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{101}{150}\right)$	$e\left(\frac{53}{300}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{52}{75}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{31}{50}\right)$
$\chi_{5625}(743,\cdot)$	$1$	$1$	$e\left(\frac{31}{300}\right)$	$e\left(\frac{31}{150}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{53}{150}\right)$	$e\left(\frac{59}{300}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{43}{50}\right)$
$\chi_{5625}(857,\cdot)$	$1$	$1$	$e\left(\frac{149}{300}\right)$	$e\left(\frac{149}{150}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{37}{150}\right)$	$e\left(\frac{61}{300}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{47}{50}\right)$
$\chi_{5625}(893,\cdot)$	$1$	$1$	$e\left(\frac{59}{300}\right)$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{67}{150}\right)$	$e\left(\frac{151}{300}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{27}{50}\right)$
$\chi_{5625}(968,\cdot)$	$1$	$1$	$e\left(\frac{223}{300}\right)$	$e\left(\frac{73}{150}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{149}{150}\right)$	$e\left(\frac{47}{300}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{19}{50}\right)$
$\chi_{5625}(1082,\cdot)$	$1$	$1$	$e\left(\frac{257}{300}\right)$	$e\left(\frac{107}{150}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{91}{150}\right)$	$e\left(\frac{73}{300}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{32}{75}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{21}{50}\right)$
$\chi_{5625}(1118,\cdot)$	$1$	$1$	$e\left(\frac{251}{300}\right)$	$e\left(\frac{101}{150}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{13}{150}\right)$	$e\left(\frac{139}{300}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{3}{50}\right)$
$\chi_{5625}(1157,\cdot)$	$1$	$1$	$e\left(\frac{193}{300}\right)$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{77}{300}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{29}{50}\right)$
$\chi_{5625}(1343,\cdot)$	$1$	$1$	$e\left(\frac{143}{300}\right)$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{109}{150}\right)$	$e\left(\frac{127}{300}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{29}{50}\right)$
$\chi_{5625}(1382,\cdot)$	$1$	$1$	$e\left(\frac{1}{300}\right)$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{113}{150}\right)$	$e\left(\frac{89}{300}\right)$	$e\left(\frac{59}{75}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{3}{50}\right)$
$\chi_{5625}(1418,\cdot)$	$1$	$1$	$e\left(\frac{7}{300}\right)$	$e\left(\frac{7}{150}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{41}{150}\right)$	$e\left(\frac{23}{300}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{21}{50}\right)$
$\chi_{5625}(1532,\cdot)$	$1$	$1$	$e\left(\frac{173}{300}\right)$	$e\left(\frac{23}{150}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{49}{150}\right)$	$e\left(\frac{97}{300}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{23}{75}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{19}{50}\right)$
$\chi_{5625}(1607,\cdot)$	$1$	$1$	$e\left(\frac{109}{300}\right)$	$e\left(\frac{109}{150}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{17}{150}\right)$	$e\left(\frac{101}{300}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{27}{50}\right)$
$\chi_{5625}(1643,\cdot)$	$1$	$1$	$e\left(\frac{199}{300}\right)$	$e\left(\frac{49}{150}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{137}{150}\right)$	$e\left(\frac{11}{300}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{47}{50}\right)$
$\chi_{5625}(1757,\cdot)$	$1$	$1$	$e\left(\frac{281}{300}\right)$	$e\left(\frac{131}{150}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{103}{150}\right)$	$e\left(\frac{109}{300}\right)$	$e\left(\frac{4}{75}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{43}{50}\right)$
$\chi_{5625}(1793,\cdot)$	$1$	$1$	$e\left(\frac{227}{300}\right)$	$e\left(\frac{77}{150}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{103}{300}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{31}{50}\right)$
$\chi_{5625}(1832,\cdot)$	$1$	$1$	$e\left(\frac{217}{300}\right)$	$e\left(\frac{67}{150}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{71}{150}\right)$	$e\left(\frac{113}{300}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{1}{50}\right)$
$\chi_{5625}(1868,\cdot)$	$1$	$1$	$e\left(\frac{91}{300}\right)$	$e\left(\frac{91}{150}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{83}{150}\right)$	$e\left(\frac{299}{300}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{23}{50}\right)$
$\chi_{5625}(1982,\cdot)$	$1$	$1$	$e\left(\frac{89}{300}\right)$	$e\left(\frac{89}{150}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{7}{150}\right)$	$e\left(\frac{121}{300}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{17}{50}\right)$
$\chi_{5625}(2018,\cdot)$	$1$	$1$	$e\left(\frac{119}{300}\right)$	$e\left(\frac{119}{150}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{91}{300}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{7}{50}\right)$
$\chi_{5625}(2093,\cdot)$	$1$	$1$	$e\left(\frac{283}{300}\right)$	$e\left(\frac{133}{150}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{287}{300}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{49}{50}\right)$
$\chi_{5625}(2207,\cdot)$	$1$	$1$	$e\left(\frac{197}{300}\right)$	$e\left(\frac{47}{150}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{61}{150}\right)$	$e\left(\frac{133}{300}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{41}{50}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{5625}(32,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{253}{300}\right)\)	\(e\left(\frac{103}{150}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{89}{150}\right)\)	\(e\left(\frac{17}{300}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{9}{50}\right)\)
\(\chi_{5625}(218,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{300}\right)\)	\(e\left(\frac{83}{150}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{79}{150}\right)\)	\(e\left(\frac{187}{300}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{49}{50}\right)\)
\(\chi_{5625}(257,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{300}\right)\)	\(e\left(\frac{61}{150}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{29}{300}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{61}{75}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{33}{50}\right)\)
\(\chi_{5625}(293,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{247}{300}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{11}{150}\right)\)	\(e\left(\frac{83}{300}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{41}{50}\right)\)
\(\chi_{5625}(407,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{233}{300}\right)\)	\(e\left(\frac{83}{150}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{79}{150}\right)\)	\(e\left(\frac{37}{300}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{49}{50}\right)\)
\(\chi_{5625}(482,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{300}\right)\)	\(e\left(\frac{19}{150}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{47}{150}\right)\)	\(e\left(\frac{41}{300}\right)\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{7}{50}\right)\)
\(\chi_{5625}(518,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{300}\right)\)	\(e\left(\frac{139}{150}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{107}{150}\right)\)	\(e\left(\frac{71}{300}\right)\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{17}{50}\right)\)
\(\chi_{5625}(632,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{300}\right)\)	\(e\left(\frac{41}{150}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{133}{150}\right)\)	\(e\left(\frac{49}{300}\right)\)	\(e\left(\frac{19}{75}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{23}{50}\right)\)
\(\chi_{5625}(668,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{167}{300}\right)\)	\(e\left(\frac{17}{150}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{121}{150}\right)\)	\(e\left(\frac{163}{300}\right)\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{1}{50}\right)\)
\(\chi_{5625}(707,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{277}{300}\right)\)	\(e\left(\frac{127}{150}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{101}{150}\right)\)	\(e\left(\frac{53}{300}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{52}{75}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{31}{50}\right)\)
\(\chi_{5625}(743,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{300}\right)\)	\(e\left(\frac{31}{150}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{53}{150}\right)\)	\(e\left(\frac{59}{300}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{43}{50}\right)\)
\(\chi_{5625}(857,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{300}\right)\)	\(e\left(\frac{149}{150}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{37}{150}\right)\)	\(e\left(\frac{61}{300}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{47}{50}\right)\)
\(\chi_{5625}(893,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{300}\right)\)	\(e\left(\frac{59}{150}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{67}{150}\right)\)	\(e\left(\frac{151}{300}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{27}{50}\right)\)
\(\chi_{5625}(968,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{223}{300}\right)\)	\(e\left(\frac{73}{150}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{149}{150}\right)\)	\(e\left(\frac{47}{300}\right)\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{19}{50}\right)\)
\(\chi_{5625}(1082,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{257}{300}\right)\)	\(e\left(\frac{107}{150}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{91}{150}\right)\)	\(e\left(\frac{73}{300}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{32}{75}\right)\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{21}{50}\right)\)
\(\chi_{5625}(1118,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{251}{300}\right)\)	\(e\left(\frac{101}{150}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{13}{150}\right)\)	\(e\left(\frac{139}{300}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{3}{50}\right)\)
\(\chi_{5625}(1157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{300}\right)\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{59}{150}\right)\)	\(e\left(\frac{77}{300}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{29}{50}\right)\)
\(\chi_{5625}(1343,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{143}{300}\right)\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{109}{150}\right)\)	\(e\left(\frac{127}{300}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{29}{50}\right)\)
\(\chi_{5625}(1382,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{300}\right)\)	\(e\left(\frac{1}{150}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{113}{150}\right)\)	\(e\left(\frac{89}{300}\right)\)	\(e\left(\frac{59}{75}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{3}{50}\right)\)
\(\chi_{5625}(1418,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{300}\right)\)	\(e\left(\frac{7}{150}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{41}{150}\right)\)	\(e\left(\frac{23}{300}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{21}{50}\right)\)
\(\chi_{5625}(1532,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{300}\right)\)	\(e\left(\frac{23}{150}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{49}{150}\right)\)	\(e\left(\frac{97}{300}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{23}{75}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{19}{50}\right)\)
\(\chi_{5625}(1607,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{300}\right)\)	\(e\left(\frac{109}{150}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{17}{150}\right)\)	\(e\left(\frac{101}{300}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{27}{50}\right)\)
\(\chi_{5625}(1643,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{300}\right)\)	\(e\left(\frac{49}{150}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{137}{150}\right)\)	\(e\left(\frac{11}{300}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{47}{50}\right)\)
\(\chi_{5625}(1757,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{281}{300}\right)\)	\(e\left(\frac{131}{150}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{103}{150}\right)\)	\(e\left(\frac{109}{300}\right)\)	\(e\left(\frac{4}{75}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{43}{50}\right)\)
\(\chi_{5625}(1793,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{227}{300}\right)\)	\(e\left(\frac{77}{150}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{1}{150}\right)\)	\(e\left(\frac{103}{300}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{31}{50}\right)\)
\(\chi_{5625}(1832,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{217}{300}\right)\)	\(e\left(\frac{67}{150}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{71}{150}\right)\)	\(e\left(\frac{113}{300}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{1}{50}\right)\)
\(\chi_{5625}(1868,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{300}\right)\)	\(e\left(\frac{91}{150}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{83}{150}\right)\)	\(e\left(\frac{299}{300}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{23}{50}\right)\)
\(\chi_{5625}(1982,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{300}\right)\)	\(e\left(\frac{89}{150}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{7}{150}\right)\)	\(e\left(\frac{121}{300}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{17}{50}\right)\)
\(\chi_{5625}(2018,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{300}\right)\)	\(e\left(\frac{119}{150}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{91}{300}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{7}{50}\right)\)
\(\chi_{5625}(2093,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{283}{300}\right)\)	\(e\left(\frac{133}{150}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{287}{300}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{49}{50}\right)\)
\(\chi_{5625}(2207,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{300}\right)\)	\(e\left(\frac{47}{150}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{61}{150}\right)\)	\(e\left(\frac{133}{300}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{41}{50}\right)\)

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First 31 of 80 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.bn
Modulus	$5625$
Conductor	$1125$
Order	$300$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(5625\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1125\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(300\)	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 1125.bj	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);