LMFDB - Dirichlet character orbit 9025.cn

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9025, base_ring=CyclotomicField(1140)) M = H._module chi = DirichletCharacter(H, M([171,10])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(8,9025)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$9025$
Conductor:	$9025$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$1140$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{1140})$
Fixed field:	Number field defined by a degree 1140 polynomial (not computed)

First 31 of 288 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{9025}(8,\cdot)$	$1$	$1$	$e\left(\frac{181}{1140}\right)$	$e\left(\frac{307}{1140}\right)$	$e\left(\frac{181}{570}\right)$	$e\left(\frac{122}{285}\right)$	$e\left(\frac{5}{76}\right)$	$e\left(\frac{181}{380}\right)$	$e\left(\frac{307}{570}\right)$	$e\left(\frac{28}{95}\right)$	$e\left(\frac{223}{380}\right)$	$e\left(\frac{839}{1140}\right)$
$\chi_{9025}(12,\cdot)$	$1$	$1$	$e\left(\frac{983}{1140}\right)$	$e\left(\frac{521}{1140}\right)$	$e\left(\frac{413}{570}\right)$	$e\left(\frac{91}{285}\right)$	$e\left(\frac{7}{76}\right)$	$e\left(\frac{223}{380}\right)$	$e\left(\frac{521}{570}\right)$	$e\left(\frac{24}{95}\right)$	$e\left(\frac{69}{380}\right)$	$e\left(\frac{217}{1140}\right)$
$\chi_{9025}(27,\cdot)$	$1$	$1$	$e\left(\frac{307}{1140}\right)$	$e\left(\frac{949}{1140}\right)$	$e\left(\frac{307}{570}\right)$	$e\left(\frac{29}{285}\right)$	$e\left(\frac{11}{76}\right)$	$e\left(\frac{307}{380}\right)$	$e\left(\frac{379}{570}\right)$	$e\left(\frac{16}{95}\right)$	$e\left(\frac{141}{380}\right)$	$e\left(\frac{113}{1140}\right)$
$\chi_{9025}(88,\cdot)$	$1$	$1$	$e\left(\frac{293}{1140}\right)$	$e\left(\frac{371}{1140}\right)$	$e\left(\frac{293}{570}\right)$	$e\left(\frac{166}{285}\right)$	$e\left(\frac{61}{76}\right)$	$e\left(\frac{293}{380}\right)$	$e\left(\frac{371}{570}\right)$	$e\left(\frac{49}{95}\right)$	$e\left(\frac{319}{380}\right)$	$e\left(\frac{67}{1140}\right)$
$\chi_{9025}(103,\cdot)$	$1$	$1$	$e\left(\frac{469}{1140}\right)$	$e\left(\frac{1123}{1140}\right)$	$e\left(\frac{469}{570}\right)$	$e\left(\frac{113}{285}\right)$	$e\left(\frac{73}{76}\right)$	$e\left(\frac{89}{380}\right)$	$e\left(\frac{553}{570}\right)$	$e\left(\frac{82}{95}\right)$	$e\left(\frac{307}{380}\right)$	$e\left(\frac{971}{1140}\right)$
$\chi_{9025}(122,\cdot)$	$1$	$1$	$e\left(\frac{139}{1140}\right)$	$e\left(\frac{853}{1140}\right)$	$e\left(\frac{139}{570}\right)$	$e\left(\frac{248}{285}\right)$	$e\left(\frac{3}{76}\right)$	$e\left(\frac{139}{380}\right)$	$e\left(\frac{283}{570}\right)$	$e\left(\frac{32}{95}\right)$	$e\left(\frac{377}{380}\right)$	$e\left(\frac{701}{1140}\right)$
$\chi_{9025}(183,\cdot)$	$1$	$1$	$e\left(\frac{941}{1140}\right)$	$e\left(\frac{1067}{1140}\right)$	$e\left(\frac{371}{570}\right)$	$e\left(\frac{217}{285}\right)$	$e\left(\frac{5}{76}\right)$	$e\left(\frac{181}{380}\right)$	$e\left(\frac{497}{570}\right)$	$e\left(\frac{28}{95}\right)$	$e\left(\frac{223}{380}\right)$	$e\left(\frac{79}{1140}\right)$
$\chi_{9025}(198,\cdot)$	$1$	$1$	$e\left(\frac{757}{1140}\right)$	$e\left(\frac{799}{1140}\right)$	$e\left(\frac{187}{570}\right)$	$e\left(\frac{104}{285}\right)$	$e\left(\frac{65}{76}\right)$	$e\left(\frac{377}{380}\right)$	$e\left(\frac{229}{570}\right)$	$e\left(\frac{41}{95}\right)$	$e\left(\frac{11}{380}\right)$	$e\left(\frac{1103}{1140}\right)$
$\chi_{9025}(202,\cdot)$	$1$	$1$	$e\left(\frac{227}{1140}\right)$	$e\left(\frac{89}{1140}\right)$	$e\left(\frac{227}{570}\right)$	$e\left(\frac{79}{285}\right)$	$e\left(\frac{47}{76}\right)$	$e\left(\frac{227}{380}\right)$	$e\left(\frac{89}{570}\right)$	$e\left(\frac{1}{95}\right)$	$e\left(\frac{181}{380}\right)$	$e\left(\frac{13}{1140}\right)$
$\chi_{9025}(217,\cdot)$	$1$	$1$	$e\left(\frac{1111}{1140}\right)$	$e\left(\frac{757}{1140}\right)$	$e\left(\frac{541}{570}\right)$	$e\left(\frac{182}{285}\right)$	$e\left(\frac{71}{76}\right)$	$e\left(\frac{351}{380}\right)$	$e\left(\frac{187}{570}\right)$	$e\left(\frac{48}{95}\right)$	$e\left(\frac{233}{380}\right)$	$e\left(\frac{149}{1140}\right)$
$\chi_{9025}(278,\cdot)$	$1$	$1$	$e\left(\frac{449}{1140}\right)$	$e\left(\frac{623}{1140}\right)$	$e\left(\frac{449}{570}\right)$	$e\left(\frac{268}{285}\right)$	$e\left(\frac{25}{76}\right)$	$e\left(\frac{69}{380}\right)$	$e\left(\frac{53}{570}\right)$	$e\left(\frac{7}{95}\right)$	$e\left(\frac{127}{380}\right)$	$e\left(\frac{91}{1140}\right)$
$\chi_{9025}(297,\cdot)$	$1$	$1$	$e\left(\frac{419}{1140}\right)$	$e\left(\frac{1013}{1140}\right)$	$e\left(\frac{419}{570}\right)$	$e\left(\frac{73}{285}\right)$	$e\left(\frac{67}{76}\right)$	$e\left(\frac{39}{380}\right)$	$e\left(\frac{443}{570}\right)$	$e\left(\frac{37}{95}\right)$	$e\left(\frac{237}{380}\right)$	$e\left(\frac{481}{1140}\right)$
$\chi_{9025}(312,\cdot)$	$1$	$1$	$e\left(\frac{943}{1140}\right)$	$e\left(\frac{661}{1140}\right)$	$e\left(\frac{373}{570}\right)$	$e\left(\frac{116}{285}\right)$	$e\left(\frac{63}{76}\right)$	$e\left(\frac{183}{380}\right)$	$e\left(\frac{91}{570}\right)$	$e\left(\frac{64}{95}\right)$	$e\left(\frac{89}{380}\right)$	$e\left(\frac{737}{1140}\right)$
$\chi_{9025}(373,\cdot)$	$1$	$1$	$e\left(\frac{1097}{1140}\right)$	$e\left(\frac{179}{1140}\right)$	$e\left(\frac{527}{570}\right)$	$e\left(\frac{34}{285}\right)$	$e\left(\frac{45}{76}\right)$	$e\left(\frac{337}{380}\right)$	$e\left(\frac{179}{570}\right)$	$e\left(\frac{81}{95}\right)$	$e\left(\frac{31}{380}\right)$	$e\left(\frac{103}{1140}\right)$
$\chi_{9025}(388,\cdot)$	$1$	$1$	$e\left(\frac{193}{1140}\right)$	$e\left(\frac{151}{1140}\right)$	$e\left(\frac{193}{570}\right)$	$e\left(\frac{86}{285}\right)$	$e\left(\frac{49}{76}\right)$	$e\left(\frac{193}{380}\right)$	$e\left(\frac{151}{570}\right)$	$e\left(\frac{54}{95}\right)$	$e\left(\frac{179}{380}\right)$	$e\left(\frac{227}{1140}\right)$
$\chi_{9025}(392,\cdot)$	$1$	$1$	$e\left(\frac{611}{1140}\right)$	$e\left(\frac{797}{1140}\right)$	$e\left(\frac{41}{570}\right)$	$e\left(\frac{67}{285}\right)$	$e\left(\frac{11}{76}\right)$	$e\left(\frac{231}{380}\right)$	$e\left(\frac{227}{570}\right)$	$e\left(\frac{73}{95}\right)$	$e\left(\frac{293}{380}\right)$	$e\left(\frac{949}{1140}\right)$
$\chi_{9025}(483,\cdot)$	$1$	$1$	$e\left(\frac{481}{1140}\right)$	$e\left(\frac{967}{1140}\right)$	$e\left(\frac{481}{570}\right)$	$e\left(\frac{77}{285}\right)$	$e\left(\frac{41}{76}\right)$	$e\left(\frac{101}{380}\right)$	$e\left(\frac{397}{570}\right)$	$e\left(\frac{13}{95}\right)$	$e\left(\frac{263}{380}\right)$	$e\left(\frac{359}{1140}\right)$
$\chi_{9025}(487,\cdot)$	$1$	$1$	$e\left(\frac{803}{1140}\right)$	$e\left(\frac{581}{1140}\right)$	$e\left(\frac{233}{570}\right)$	$e\left(\frac{61}{285}\right)$	$e\left(\frac{31}{76}\right)$	$e\left(\frac{43}{380}\right)$	$e\left(\frac{11}{570}\right)$	$e\left(\frac{14}{95}\right)$	$e\left(\frac{349}{380}\right)$	$e\left(\frac{277}{1140}\right)$
$\chi_{9025}(502,\cdot)$	$1$	$1$	$e\left(\frac{607}{1140}\right)$	$e\left(\frac{469}{1140}\right)$	$e\left(\frac{37}{570}\right)$	$e\left(\frac{269}{285}\right)$	$e\left(\frac{47}{76}\right)$	$e\left(\frac{227}{380}\right)$	$e\left(\frac{469}{570}\right)$	$e\left(\frac{1}{95}\right)$	$e\left(\frac{181}{380}\right)$	$e\left(\frac{773}{1140}\right)$
$\chi_{9025}(563,\cdot)$	$1$	$1$	$e\left(\frac{113}{1140}\right)$	$e\left(\frac{431}{1140}\right)$	$e\left(\frac{113}{570}\right)$	$e\left(\frac{136}{285}\right)$	$e\left(\frac{9}{76}\right)$	$e\left(\frac{113}{380}\right)$	$e\left(\frac{431}{570}\right)$	$e\left(\frac{39}{95}\right)$	$e\left(\frac{219}{380}\right)$	$e\left(\frac{127}{1140}\right)$
$\chi_{9025}(578,\cdot)$	$1$	$1$	$e\left(\frac{769}{1140}\right)$	$e\left(\frac{643}{1140}\right)$	$e\left(\frac{199}{570}\right)$	$e\left(\frac{68}{285}\right)$	$e\left(\frac{33}{76}\right)$	$e\left(\frac{9}{380}\right)$	$e\left(\frac{73}{570}\right)$	$e\left(\frac{67}{95}\right)$	$e\left(\frac{347}{380}\right)$	$e\left(\frac{491}{1140}\right)$
$\chi_{9025}(597,\cdot)$	$1$	$1$	$e\left(\frac{439}{1140}\right)$	$e\left(\frac{373}{1140}\right)$	$e\left(\frac{439}{570}\right)$	$e\left(\frac{203}{285}\right)$	$e\left(\frac{39}{76}\right)$	$e\left(\frac{59}{380}\right)$	$e\left(\frac{373}{570}\right)$	$e\left(\frac{17}{95}\right)$	$e\left(\frac{37}{380}\right)$	$e\left(\frac{221}{1140}\right)$
$\chi_{9025}(658,\cdot)$	$1$	$1$	$e\left(\frac{761}{1140}\right)$	$e\left(\frac{1127}{1140}\right)$	$e\left(\frac{191}{570}\right)$	$e\left(\frac{187}{285}\right)$	$e\left(\frac{29}{76}\right)$	$e\left(\frac{1}{380}\right)$	$e\left(\frac{557}{570}\right)$	$e\left(\frac{18}{95}\right)$	$e\left(\frac{123}{380}\right)$	$e\left(\frac{139}{1140}\right)$
$\chi_{9025}(673,\cdot)$	$1$	$1$	$e\left(\frac{1057}{1140}\right)$	$e\left(\frac{319}{1140}\right)$	$e\left(\frac{487}{570}\right)$	$e\left(\frac{59}{285}\right)$	$e\left(\frac{25}{76}\right)$	$e\left(\frac{297}{380}\right)$	$e\left(\frac{319}{570}\right)$	$e\left(\frac{26}{95}\right)$	$e\left(\frac{51}{380}\right)$	$e\left(\frac{623}{1140}\right)$
$\chi_{9025}(677,\cdot)$	$1$	$1$	$e\left(\frac{47}{1140}\right)$	$e\left(\frac{149}{1140}\right)$	$e\left(\frac{47}{570}\right)$	$e\left(\frac{49}{285}\right)$	$e\left(\frac{71}{76}\right)$	$e\left(\frac{47}{380}\right)$	$e\left(\frac{149}{570}\right)$	$e\left(\frac{86}{95}\right)$	$e\left(\frac{81}{380}\right)$	$e\left(\frac{73}{1140}\right)$
$\chi_{9025}(692,\cdot)$	$1$	$1$	$e\left(\frac{271}{1140}\right)$	$e\left(\frac{277}{1140}\right)$	$e\left(\frac{271}{570}\right)$	$e\left(\frac{137}{285}\right)$	$e\left(\frac{31}{76}\right)$	$e\left(\frac{271}{380}\right)$	$e\left(\frac{277}{570}\right)$	$e\left(\frac{33}{95}\right)$	$e\left(\frac{273}{380}\right)$	$e\left(\frac{809}{1140}\right)$
$\chi_{9025}(753,\cdot)$	$1$	$1$	$e\left(\frac{269}{1140}\right)$	$e\left(\frac{683}{1140}\right)$	$e\left(\frac{269}{570}\right)$	$e\left(\frac{238}{285}\right)$	$e\left(\frac{49}{76}\right)$	$e\left(\frac{269}{380}\right)$	$e\left(\frac{113}{570}\right)$	$e\left(\frac{92}{95}\right)$	$e\left(\frac{27}{380}\right)$	$e\left(\frac{151}{1140}\right)$
$\chi_{9025}(772,\cdot)$	$1$	$1$	$e\left(\frac{239}{1140}\right)$	$e\left(\frac{1073}{1140}\right)$	$e\left(\frac{239}{570}\right)$	$e\left(\frac{43}{285}\right)$	$e\left(\frac{15}{76}\right)$	$e\left(\frac{239}{380}\right)$	$e\left(\frac{503}{570}\right)$	$e\left(\frac{27}{95}\right)$	$e\left(\frac{137}{380}\right)$	$e\left(\frac{541}{1140}\right)$
$\chi_{9025}(787,\cdot)$	$1$	$1$	$e\left(\frac{103}{1140}\right)$	$e\left(\frac{181}{1140}\right)$	$e\left(\frac{103}{570}\right)$	$e\left(\frac{71}{285}\right)$	$e\left(\frac{23}{76}\right)$	$e\left(\frac{103}{380}\right)$	$e\left(\frac{181}{570}\right)$	$e\left(\frac{49}{95}\right)$	$e\left(\frac{129}{380}\right)$	$e\left(\frac{257}{1140}\right)$
$\chi_{9025}(848,\cdot)$	$1$	$1$	$e\left(\frac{917}{1140}\right)$	$e\left(\frac{239}{1140}\right)$	$e\left(\frac{347}{570}\right)$	$e\left(\frac{4}{285}\right)$	$e\left(\frac{69}{76}\right)$	$e\left(\frac{157}{380}\right)$	$e\left(\frac{239}{570}\right)$	$e\left(\frac{71}{95}\right)$	$e\left(\frac{311}{380}\right)$	$e\left(\frac{163}{1140}\right)$
$\chi_{9025}(863,\cdot)$	$1$	$1$	$e\left(\frac{493}{1140}\right)$	$e\left(\frac{811}{1140}\right)$	$e\left(\frac{493}{570}\right)$	$e\left(\frac{41}{285}\right)$	$e\left(\frac{9}{76}\right)$	$e\left(\frac{113}{380}\right)$	$e\left(\frac{241}{570}\right)$	$e\left(\frac{39}{95}\right)$	$e\left(\frac{219}{380}\right)$	$e\left(\frac{887}{1140}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{9025}(8,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{181}{1140}\right)\)	\(e\left(\frac{307}{1140}\right)\)	\(e\left(\frac{181}{570}\right)\)	\(e\left(\frac{122}{285}\right)\)	\(e\left(\frac{5}{76}\right)\)	\(e\left(\frac{181}{380}\right)\)	\(e\left(\frac{307}{570}\right)\)	\(e\left(\frac{28}{95}\right)\)	\(e\left(\frac{223}{380}\right)\)	\(e\left(\frac{839}{1140}\right)\)
\(\chi_{9025}(12,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{983}{1140}\right)\)	\(e\left(\frac{521}{1140}\right)\)	\(e\left(\frac{413}{570}\right)\)	\(e\left(\frac{91}{285}\right)\)	\(e\left(\frac{7}{76}\right)\)	\(e\left(\frac{223}{380}\right)\)	\(e\left(\frac{521}{570}\right)\)	\(e\left(\frac{24}{95}\right)\)	\(e\left(\frac{69}{380}\right)\)	\(e\left(\frac{217}{1140}\right)\)
\(\chi_{9025}(27,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{307}{1140}\right)\)	\(e\left(\frac{949}{1140}\right)\)	\(e\left(\frac{307}{570}\right)\)	\(e\left(\frac{29}{285}\right)\)	\(e\left(\frac{11}{76}\right)\)	\(e\left(\frac{307}{380}\right)\)	\(e\left(\frac{379}{570}\right)\)	\(e\left(\frac{16}{95}\right)\)	\(e\left(\frac{141}{380}\right)\)	\(e\left(\frac{113}{1140}\right)\)
\(\chi_{9025}(88,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{293}{1140}\right)\)	\(e\left(\frac{371}{1140}\right)\)	\(e\left(\frac{293}{570}\right)\)	\(e\left(\frac{166}{285}\right)\)	\(e\left(\frac{61}{76}\right)\)	\(e\left(\frac{293}{380}\right)\)	\(e\left(\frac{371}{570}\right)\)	\(e\left(\frac{49}{95}\right)\)	\(e\left(\frac{319}{380}\right)\)	\(e\left(\frac{67}{1140}\right)\)
\(\chi_{9025}(103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{469}{1140}\right)\)	\(e\left(\frac{1123}{1140}\right)\)	\(e\left(\frac{469}{570}\right)\)	\(e\left(\frac{113}{285}\right)\)	\(e\left(\frac{73}{76}\right)\)	\(e\left(\frac{89}{380}\right)\)	\(e\left(\frac{553}{570}\right)\)	\(e\left(\frac{82}{95}\right)\)	\(e\left(\frac{307}{380}\right)\)	\(e\left(\frac{971}{1140}\right)\)
\(\chi_{9025}(122,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{1140}\right)\)	\(e\left(\frac{853}{1140}\right)\)	\(e\left(\frac{139}{570}\right)\)	\(e\left(\frac{248}{285}\right)\)	\(e\left(\frac{3}{76}\right)\)	\(e\left(\frac{139}{380}\right)\)	\(e\left(\frac{283}{570}\right)\)	\(e\left(\frac{32}{95}\right)\)	\(e\left(\frac{377}{380}\right)\)	\(e\left(\frac{701}{1140}\right)\)
\(\chi_{9025}(183,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{941}{1140}\right)\)	\(e\left(\frac{1067}{1140}\right)\)	\(e\left(\frac{371}{570}\right)\)	\(e\left(\frac{217}{285}\right)\)	\(e\left(\frac{5}{76}\right)\)	\(e\left(\frac{181}{380}\right)\)	\(e\left(\frac{497}{570}\right)\)	\(e\left(\frac{28}{95}\right)\)	\(e\left(\frac{223}{380}\right)\)	\(e\left(\frac{79}{1140}\right)\)
\(\chi_{9025}(198,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{757}{1140}\right)\)	\(e\left(\frac{799}{1140}\right)\)	\(e\left(\frac{187}{570}\right)\)	\(e\left(\frac{104}{285}\right)\)	\(e\left(\frac{65}{76}\right)\)	\(e\left(\frac{377}{380}\right)\)	\(e\left(\frac{229}{570}\right)\)	\(e\left(\frac{41}{95}\right)\)	\(e\left(\frac{11}{380}\right)\)	\(e\left(\frac{1103}{1140}\right)\)
\(\chi_{9025}(202,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{227}{1140}\right)\)	\(e\left(\frac{89}{1140}\right)\)	\(e\left(\frac{227}{570}\right)\)	\(e\left(\frac{79}{285}\right)\)	\(e\left(\frac{47}{76}\right)\)	\(e\left(\frac{227}{380}\right)\)	\(e\left(\frac{89}{570}\right)\)	\(e\left(\frac{1}{95}\right)\)	\(e\left(\frac{181}{380}\right)\)	\(e\left(\frac{13}{1140}\right)\)
\(\chi_{9025}(217,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1111}{1140}\right)\)	\(e\left(\frac{757}{1140}\right)\)	\(e\left(\frac{541}{570}\right)\)	\(e\left(\frac{182}{285}\right)\)	\(e\left(\frac{71}{76}\right)\)	\(e\left(\frac{351}{380}\right)\)	\(e\left(\frac{187}{570}\right)\)	\(e\left(\frac{48}{95}\right)\)	\(e\left(\frac{233}{380}\right)\)	\(e\left(\frac{149}{1140}\right)\)
\(\chi_{9025}(278,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{449}{1140}\right)\)	\(e\left(\frac{623}{1140}\right)\)	\(e\left(\frac{449}{570}\right)\)	\(e\left(\frac{268}{285}\right)\)	\(e\left(\frac{25}{76}\right)\)	\(e\left(\frac{69}{380}\right)\)	\(e\left(\frac{53}{570}\right)\)	\(e\left(\frac{7}{95}\right)\)	\(e\left(\frac{127}{380}\right)\)	\(e\left(\frac{91}{1140}\right)\)
\(\chi_{9025}(297,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{419}{1140}\right)\)	\(e\left(\frac{1013}{1140}\right)\)	\(e\left(\frac{419}{570}\right)\)	\(e\left(\frac{73}{285}\right)\)	\(e\left(\frac{67}{76}\right)\)	\(e\left(\frac{39}{380}\right)\)	\(e\left(\frac{443}{570}\right)\)	\(e\left(\frac{37}{95}\right)\)	\(e\left(\frac{237}{380}\right)\)	\(e\left(\frac{481}{1140}\right)\)
\(\chi_{9025}(312,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{943}{1140}\right)\)	\(e\left(\frac{661}{1140}\right)\)	\(e\left(\frac{373}{570}\right)\)	\(e\left(\frac{116}{285}\right)\)	\(e\left(\frac{63}{76}\right)\)	\(e\left(\frac{183}{380}\right)\)	\(e\left(\frac{91}{570}\right)\)	\(e\left(\frac{64}{95}\right)\)	\(e\left(\frac{89}{380}\right)\)	\(e\left(\frac{737}{1140}\right)\)
\(\chi_{9025}(373,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1097}{1140}\right)\)	\(e\left(\frac{179}{1140}\right)\)	\(e\left(\frac{527}{570}\right)\)	\(e\left(\frac{34}{285}\right)\)	\(e\left(\frac{45}{76}\right)\)	\(e\left(\frac{337}{380}\right)\)	\(e\left(\frac{179}{570}\right)\)	\(e\left(\frac{81}{95}\right)\)	\(e\left(\frac{31}{380}\right)\)	\(e\left(\frac{103}{1140}\right)\)
\(\chi_{9025}(388,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{1140}\right)\)	\(e\left(\frac{151}{1140}\right)\)	\(e\left(\frac{193}{570}\right)\)	\(e\left(\frac{86}{285}\right)\)	\(e\left(\frac{49}{76}\right)\)	\(e\left(\frac{193}{380}\right)\)	\(e\left(\frac{151}{570}\right)\)	\(e\left(\frac{54}{95}\right)\)	\(e\left(\frac{179}{380}\right)\)	\(e\left(\frac{227}{1140}\right)\)
\(\chi_{9025}(392,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{611}{1140}\right)\)	\(e\left(\frac{797}{1140}\right)\)	\(e\left(\frac{41}{570}\right)\)	\(e\left(\frac{67}{285}\right)\)	\(e\left(\frac{11}{76}\right)\)	\(e\left(\frac{231}{380}\right)\)	\(e\left(\frac{227}{570}\right)\)	\(e\left(\frac{73}{95}\right)\)	\(e\left(\frac{293}{380}\right)\)	\(e\left(\frac{949}{1140}\right)\)
\(\chi_{9025}(483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{481}{1140}\right)\)	\(e\left(\frac{967}{1140}\right)\)	\(e\left(\frac{481}{570}\right)\)	\(e\left(\frac{77}{285}\right)\)	\(e\left(\frac{41}{76}\right)\)	\(e\left(\frac{101}{380}\right)\)	\(e\left(\frac{397}{570}\right)\)	\(e\left(\frac{13}{95}\right)\)	\(e\left(\frac{263}{380}\right)\)	\(e\left(\frac{359}{1140}\right)\)
\(\chi_{9025}(487,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{803}{1140}\right)\)	\(e\left(\frac{581}{1140}\right)\)	\(e\left(\frac{233}{570}\right)\)	\(e\left(\frac{61}{285}\right)\)	\(e\left(\frac{31}{76}\right)\)	\(e\left(\frac{43}{380}\right)\)	\(e\left(\frac{11}{570}\right)\)	\(e\left(\frac{14}{95}\right)\)	\(e\left(\frac{349}{380}\right)\)	\(e\left(\frac{277}{1140}\right)\)
\(\chi_{9025}(502,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{607}{1140}\right)\)	\(e\left(\frac{469}{1140}\right)\)	\(e\left(\frac{37}{570}\right)\)	\(e\left(\frac{269}{285}\right)\)	\(e\left(\frac{47}{76}\right)\)	\(e\left(\frac{227}{380}\right)\)	\(e\left(\frac{469}{570}\right)\)	\(e\left(\frac{1}{95}\right)\)	\(e\left(\frac{181}{380}\right)\)	\(e\left(\frac{773}{1140}\right)\)
\(\chi_{9025}(563,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{1140}\right)\)	\(e\left(\frac{431}{1140}\right)\)	\(e\left(\frac{113}{570}\right)\)	\(e\left(\frac{136}{285}\right)\)	\(e\left(\frac{9}{76}\right)\)	\(e\left(\frac{113}{380}\right)\)	\(e\left(\frac{431}{570}\right)\)	\(e\left(\frac{39}{95}\right)\)	\(e\left(\frac{219}{380}\right)\)	\(e\left(\frac{127}{1140}\right)\)
\(\chi_{9025}(578,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{769}{1140}\right)\)	\(e\left(\frac{643}{1140}\right)\)	\(e\left(\frac{199}{570}\right)\)	\(e\left(\frac{68}{285}\right)\)	\(e\left(\frac{33}{76}\right)\)	\(e\left(\frac{9}{380}\right)\)	\(e\left(\frac{73}{570}\right)\)	\(e\left(\frac{67}{95}\right)\)	\(e\left(\frac{347}{380}\right)\)	\(e\left(\frac{491}{1140}\right)\)
\(\chi_{9025}(597,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{439}{1140}\right)\)	\(e\left(\frac{373}{1140}\right)\)	\(e\left(\frac{439}{570}\right)\)	\(e\left(\frac{203}{285}\right)\)	\(e\left(\frac{39}{76}\right)\)	\(e\left(\frac{59}{380}\right)\)	\(e\left(\frac{373}{570}\right)\)	\(e\left(\frac{17}{95}\right)\)	\(e\left(\frac{37}{380}\right)\)	\(e\left(\frac{221}{1140}\right)\)
\(\chi_{9025}(658,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{761}{1140}\right)\)	\(e\left(\frac{1127}{1140}\right)\)	\(e\left(\frac{191}{570}\right)\)	\(e\left(\frac{187}{285}\right)\)	\(e\left(\frac{29}{76}\right)\)	\(e\left(\frac{1}{380}\right)\)	\(e\left(\frac{557}{570}\right)\)	\(e\left(\frac{18}{95}\right)\)	\(e\left(\frac{123}{380}\right)\)	\(e\left(\frac{139}{1140}\right)\)
\(\chi_{9025}(673,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1057}{1140}\right)\)	\(e\left(\frac{319}{1140}\right)\)	\(e\left(\frac{487}{570}\right)\)	\(e\left(\frac{59}{285}\right)\)	\(e\left(\frac{25}{76}\right)\)	\(e\left(\frac{297}{380}\right)\)	\(e\left(\frac{319}{570}\right)\)	\(e\left(\frac{26}{95}\right)\)	\(e\left(\frac{51}{380}\right)\)	\(e\left(\frac{623}{1140}\right)\)
\(\chi_{9025}(677,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{1140}\right)\)	\(e\left(\frac{149}{1140}\right)\)	\(e\left(\frac{47}{570}\right)\)	\(e\left(\frac{49}{285}\right)\)	\(e\left(\frac{71}{76}\right)\)	\(e\left(\frac{47}{380}\right)\)	\(e\left(\frac{149}{570}\right)\)	\(e\left(\frac{86}{95}\right)\)	\(e\left(\frac{81}{380}\right)\)	\(e\left(\frac{73}{1140}\right)\)
\(\chi_{9025}(692,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{271}{1140}\right)\)	\(e\left(\frac{277}{1140}\right)\)	\(e\left(\frac{271}{570}\right)\)	\(e\left(\frac{137}{285}\right)\)	\(e\left(\frac{31}{76}\right)\)	\(e\left(\frac{271}{380}\right)\)	\(e\left(\frac{277}{570}\right)\)	\(e\left(\frac{33}{95}\right)\)	\(e\left(\frac{273}{380}\right)\)	\(e\left(\frac{809}{1140}\right)\)
\(\chi_{9025}(753,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{269}{1140}\right)\)	\(e\left(\frac{683}{1140}\right)\)	\(e\left(\frac{269}{570}\right)\)	\(e\left(\frac{238}{285}\right)\)	\(e\left(\frac{49}{76}\right)\)	\(e\left(\frac{269}{380}\right)\)	\(e\left(\frac{113}{570}\right)\)	\(e\left(\frac{92}{95}\right)\)	\(e\left(\frac{27}{380}\right)\)	\(e\left(\frac{151}{1140}\right)\)
\(\chi_{9025}(772,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{239}{1140}\right)\)	\(e\left(\frac{1073}{1140}\right)\)	\(e\left(\frac{239}{570}\right)\)	\(e\left(\frac{43}{285}\right)\)	\(e\left(\frac{15}{76}\right)\)	\(e\left(\frac{239}{380}\right)\)	\(e\left(\frac{503}{570}\right)\)	\(e\left(\frac{27}{95}\right)\)	\(e\left(\frac{137}{380}\right)\)	\(e\left(\frac{541}{1140}\right)\)
\(\chi_{9025}(787,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{1140}\right)\)	\(e\left(\frac{181}{1140}\right)\)	\(e\left(\frac{103}{570}\right)\)	\(e\left(\frac{71}{285}\right)\)	\(e\left(\frac{23}{76}\right)\)	\(e\left(\frac{103}{380}\right)\)	\(e\left(\frac{181}{570}\right)\)	\(e\left(\frac{49}{95}\right)\)	\(e\left(\frac{129}{380}\right)\)	\(e\left(\frac{257}{1140}\right)\)
\(\chi_{9025}(848,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{917}{1140}\right)\)	\(e\left(\frac{239}{1140}\right)\)	\(e\left(\frac{347}{570}\right)\)	\(e\left(\frac{4}{285}\right)\)	\(e\left(\frac{69}{76}\right)\)	\(e\left(\frac{157}{380}\right)\)	\(e\left(\frac{239}{570}\right)\)	\(e\left(\frac{71}{95}\right)\)	\(e\left(\frac{311}{380}\right)\)	\(e\left(\frac{163}{1140}\right)\)
\(\chi_{9025}(863,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{493}{1140}\right)\)	\(e\left(\frac{811}{1140}\right)\)	\(e\left(\frac{493}{570}\right)\)	\(e\left(\frac{41}{285}\right)\)	\(e\left(\frac{9}{76}\right)\)	\(e\left(\frac{113}{380}\right)\)	\(e\left(\frac{241}{570}\right)\)	\(e\left(\frac{39}{95}\right)\)	\(e\left(\frac{219}{380}\right)\)	\(e\left(\frac{887}{1140}\right)\)

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First 31 of 288 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	9025.cn
Modulus	$9025$
Conductor	$9025$
Order	$1140$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(9025\)
Conductor:	\(9025\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(1140\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)