LMFDB - Dirichlet character orbit 9025.cg

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9025, base_ring=CyclotomicField(380)) M = H._module chi = DirichletCharacter(H, M([171,50])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(37,9025)) 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:	$380$	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:	$\Q(\zeta_{380})$
Fixed field:	Number field defined by a degree 380 polynomial (not computed)

First 31 of 144 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{9025}(37,\cdot)$	$1$	$1$	$e\left(\frac{221}{380}\right)$	$e\left(\frac{167}{380}\right)$	$e\left(\frac{31}{190}\right)$	$e\left(\frac{2}{95}\right)$	$e\left(\frac{75}{76}\right)$	$e\left(\frac{283}{380}\right)$	$e\left(\frac{167}{190}\right)$	$e\left(\frac{59}{95}\right)$	$e\left(\frac{229}{380}\right)$	$e\left(\frac{319}{380}\right)$
$\chi_{9025}(113,\cdot)$	$1$	$1$	$e\left(\frac{131}{380}\right)$	$e\left(\frac{197}{380}\right)$	$e\left(\frac{131}{190}\right)$	$e\left(\frac{82}{95}\right)$	$e\left(\frac{73}{76}\right)$	$e\left(\frac{13}{380}\right)$	$e\left(\frac{7}{190}\right)$	$e\left(\frac{44}{95}\right)$	$e\left(\frac{79}{380}\right)$	$e\left(\frac{349}{380}\right)$
$\chi_{9025}(208,\cdot)$	$1$	$1$	$e\left(\frac{47}{380}\right)$	$e\left(\frac{149}{380}\right)$	$e\left(\frac{47}{190}\right)$	$e\left(\frac{49}{95}\right)$	$e\left(\frac{61}{76}\right)$	$e\left(\frac{141}{380}\right)$	$e\left(\frac{149}{190}\right)$	$e\left(\frac{68}{95}\right)$	$e\left(\frac{243}{380}\right)$	$e\left(\frac{73}{380}\right)$
$\chi_{9025}(227,\cdot)$	$1$	$1$	$e\left(\frac{129}{380}\right)$	$e\left(\frac{223}{380}\right)$	$e\left(\frac{129}{190}\right)$	$e\left(\frac{88}{95}\right)$	$e\left(\frac{51}{76}\right)$	$e\left(\frac{7}{380}\right)$	$e\left(\frac{33}{190}\right)$	$e\left(\frac{31}{95}\right)$	$e\left(\frac{101}{380}\right)$	$e\left(\frac{71}{380}\right)$
$\chi_{9025}(303,\cdot)$	$1$	$1$	$e\left(\frac{343}{380}\right)$	$e\left(\frac{101}{380}\right)$	$e\left(\frac{153}{190}\right)$	$e\left(\frac{16}{95}\right)$	$e\left(\frac{49}{76}\right)$	$e\left(\frac{269}{380}\right)$	$e\left(\frac{101}{190}\right)$	$e\left(\frac{92}{95}\right)$	$e\left(\frac{27}{380}\right)$	$e\left(\frac{177}{380}\right)$
$\chi_{9025}(322,\cdot)$	$1$	$1$	$e\left(\frac{273}{380}\right)$	$e\left(\frac{251}{380}\right)$	$e\left(\frac{83}{190}\right)$	$e\left(\frac{36}{95}\right)$	$e\left(\frac{39}{76}\right)$	$e\left(\frac{59}{380}\right)$	$e\left(\frac{61}{190}\right)$	$e\left(\frac{17}{95}\right)$	$e\left(\frac{37}{380}\right)$	$e\left(\frac{327}{380}\right)$
$\chi_{9025}(398,\cdot)$	$1$	$1$	$e\left(\frac{259}{380}\right)$	$e\left(\frac{53}{380}\right)$	$e\left(\frac{69}{190}\right)$	$e\left(\frac{78}{95}\right)$	$e\left(\frac{37}{76}\right)$	$e\left(\frac{17}{380}\right)$	$e\left(\frac{53}{190}\right)$	$e\left(\frac{21}{95}\right)$	$e\left(\frac{191}{380}\right)$	$e\left(\frac{281}{380}\right)$
$\chi_{9025}(417,\cdot)$	$1$	$1$	$e\left(\frac{37}{380}\right)$	$e\left(\frac{279}{380}\right)$	$e\left(\frac{37}{190}\right)$	$e\left(\frac{79}{95}\right)$	$e\left(\frac{27}{76}\right)$	$e\left(\frac{111}{380}\right)$	$e\left(\frac{89}{190}\right)$	$e\left(\frac{3}{95}\right)$	$e\left(\frac{353}{380}\right)$	$e\left(\frac{203}{380}\right)$
$\chi_{9025}(512,\cdot)$	$1$	$1$	$e\left(\frac{181}{380}\right)$	$e\left(\frac{307}{380}\right)$	$e\left(\frac{181}{190}\right)$	$e\left(\frac{27}{95}\right)$	$e\left(\frac{15}{76}\right)$	$e\left(\frac{163}{380}\right)$	$e\left(\frac{117}{190}\right)$	$e\left(\frac{84}{95}\right)$	$e\left(\frac{289}{380}\right)$	$e\left(\frac{79}{380}\right)$
$\chi_{9025}(588,\cdot)$	$1$	$1$	$e\left(\frac{91}{380}\right)$	$e\left(\frac{337}{380}\right)$	$e\left(\frac{91}{190}\right)$	$e\left(\frac{12}{95}\right)$	$e\left(\frac{13}{76}\right)$	$e\left(\frac{273}{380}\right)$	$e\left(\frac{147}{190}\right)$	$e\left(\frac{69}{95}\right)$	$e\left(\frac{139}{380}\right)$	$e\left(\frac{109}{380}\right)$
$\chi_{9025}(683,\cdot)$	$1$	$1$	$e\left(\frac{7}{380}\right)$	$e\left(\frac{289}{380}\right)$	$e\left(\frac{7}{190}\right)$	$e\left(\frac{74}{95}\right)$	$e\left(\frac{1}{76}\right)$	$e\left(\frac{21}{380}\right)$	$e\left(\frac{99}{190}\right)$	$e\left(\frac{93}{95}\right)$	$e\left(\frac{303}{380}\right)$	$e\left(\frac{213}{380}\right)$
$\chi_{9025}(702,\cdot)$	$1$	$1$	$e\left(\frac{89}{380}\right)$	$e\left(\frac{363}{380}\right)$	$e\left(\frac{89}{190}\right)$	$e\left(\frac{18}{95}\right)$	$e\left(\frac{67}{76}\right)$	$e\left(\frac{267}{380}\right)$	$e\left(\frac{173}{190}\right)$	$e\left(\frac{56}{95}\right)$	$e\left(\frac{161}{380}\right)$	$e\left(\frac{211}{380}\right)$
$\chi_{9025}(778,\cdot)$	$1$	$1$	$e\left(\frac{303}{380}\right)$	$e\left(\frac{241}{380}\right)$	$e\left(\frac{113}{190}\right)$	$e\left(\frac{41}{95}\right)$	$e\left(\frac{65}{76}\right)$	$e\left(\frac{149}{380}\right)$	$e\left(\frac{51}{190}\right)$	$e\left(\frac{22}{95}\right)$	$e\left(\frac{87}{380}\right)$	$e\left(\frac{317}{380}\right)$
$\chi_{9025}(797,\cdot)$	$1$	$1$	$e\left(\frac{233}{380}\right)$	$e\left(\frac{11}{380}\right)$	$e\left(\frac{43}{190}\right)$	$e\left(\frac{61}{95}\right)$	$e\left(\frac{55}{76}\right)$	$e\left(\frac{319}{380}\right)$	$e\left(\frac{11}{190}\right)$	$e\left(\frac{42}{95}\right)$	$e\left(\frac{97}{380}\right)$	$e\left(\frac{87}{380}\right)$
$\chi_{9025}(873,\cdot)$	$1$	$1$	$e\left(\frac{219}{380}\right)$	$e\left(\frac{193}{380}\right)$	$e\left(\frac{29}{190}\right)$	$e\left(\frac{8}{95}\right)$	$e\left(\frac{53}{76}\right)$	$e\left(\frac{277}{380}\right)$	$e\left(\frac{3}{190}\right)$	$e\left(\frac{46}{95}\right)$	$e\left(\frac{251}{380}\right)$	$e\left(\frac{41}{380}\right)$
$\chi_{9025}(892,\cdot)$	$1$	$1$	$e\left(\frac{377}{380}\right)$	$e\left(\frac{39}{380}\right)$	$e\left(\frac{187}{190}\right)$	$e\left(\frac{9}{95}\right)$	$e\left(\frac{43}{76}\right)$	$e\left(\frac{371}{380}\right)$	$e\left(\frac{39}{190}\right)$	$e\left(\frac{28}{95}\right)$	$e\left(\frac{33}{380}\right)$	$e\left(\frac{343}{380}\right)$
$\chi_{9025}(987,\cdot)$	$1$	$1$	$e\left(\frac{141}{380}\right)$	$e\left(\frac{67}{380}\right)$	$e\left(\frac{141}{190}\right)$	$e\left(\frac{52}{95}\right)$	$e\left(\frac{31}{76}\right)$	$e\left(\frac{43}{380}\right)$	$e\left(\frac{67}{190}\right)$	$e\left(\frac{14}{95}\right)$	$e\left(\frac{349}{380}\right)$	$e\left(\frac{219}{380}\right)$
$\chi_{9025}(1063,\cdot)$	$1$	$1$	$e\left(\frac{51}{380}\right)$	$e\left(\frac{97}{380}\right)$	$e\left(\frac{51}{190}\right)$	$e\left(\frac{37}{95}\right)$	$e\left(\frac{29}{76}\right)$	$e\left(\frac{153}{380}\right)$	$e\left(\frac{97}{190}\right)$	$e\left(\frac{94}{95}\right)$	$e\left(\frac{199}{380}\right)$	$e\left(\frac{249}{380}\right)$
$\chi_{9025}(1158,\cdot)$	$1$	$1$	$e\left(\frac{347}{380}\right)$	$e\left(\frac{49}{380}\right)$	$e\left(\frac{157}{190}\right)$	$e\left(\frac{4}{95}\right)$	$e\left(\frac{17}{76}\right)$	$e\left(\frac{281}{380}\right)$	$e\left(\frac{49}{190}\right)$	$e\left(\frac{23}{95}\right)$	$e\left(\frac{363}{380}\right)$	$e\left(\frac{353}{380}\right)$
$\chi_{9025}(1177,\cdot)$	$1$	$1$	$e\left(\frac{49}{380}\right)$	$e\left(\frac{123}{380}\right)$	$e\left(\frac{49}{190}\right)$	$e\left(\frac{43}{95}\right)$	$e\left(\frac{7}{76}\right)$	$e\left(\frac{147}{380}\right)$	$e\left(\frac{123}{190}\right)$	$e\left(\frac{81}{95}\right)$	$e\left(\frac{221}{380}\right)$	$e\left(\frac{351}{380}\right)$
$\chi_{9025}(1253,\cdot)$	$1$	$1$	$e\left(\frac{263}{380}\right)$	$e\left(\frac{1}{380}\right)$	$e\left(\frac{73}{190}\right)$	$e\left(\frac{66}{95}\right)$	$e\left(\frac{5}{76}\right)$	$e\left(\frac{29}{380}\right)$	$e\left(\frac{1}{190}\right)$	$e\left(\frac{47}{95}\right)$	$e\left(\frac{147}{380}\right)$	$e\left(\frac{77}{380}\right)$
$\chi_{9025}(1272,\cdot)$	$1$	$1$	$e\left(\frac{193}{380}\right)$	$e\left(\frac{151}{380}\right)$	$e\left(\frac{3}{190}\right)$	$e\left(\frac{86}{95}\right)$	$e\left(\frac{71}{76}\right)$	$e\left(\frac{199}{380}\right)$	$e\left(\frac{151}{190}\right)$	$e\left(\frac{67}{95}\right)$	$e\left(\frac{157}{380}\right)$	$e\left(\frac{227}{380}\right)$
$\chi_{9025}(1348,\cdot)$	$1$	$1$	$e\left(\frac{179}{380}\right)$	$e\left(\frac{333}{380}\right)$	$e\left(\frac{179}{190}\right)$	$e\left(\frac{33}{95}\right)$	$e\left(\frac{69}{76}\right)$	$e\left(\frac{157}{380}\right)$	$e\left(\frac{143}{190}\right)$	$e\left(\frac{71}{95}\right)$	$e\left(\frac{311}{380}\right)$	$e\left(\frac{181}{380}\right)$
$\chi_{9025}(1367,\cdot)$	$1$	$1$	$e\left(\frac{337}{380}\right)$	$e\left(\frac{179}{380}\right)$	$e\left(\frac{147}{190}\right)$	$e\left(\frac{34}{95}\right)$	$e\left(\frac{59}{76}\right)$	$e\left(\frac{251}{380}\right)$	$e\left(\frac{179}{190}\right)$	$e\left(\frac{53}{95}\right)$	$e\left(\frac{93}{380}\right)$	$e\left(\frac{103}{380}\right)$
$\chi_{9025}(1462,\cdot)$	$1$	$1$	$e\left(\frac{101}{380}\right)$	$e\left(\frac{207}{380}\right)$	$e\left(\frac{101}{190}\right)$	$e\left(\frac{77}{95}\right)$	$e\left(\frac{47}{76}\right)$	$e\left(\frac{303}{380}\right)$	$e\left(\frac{17}{190}\right)$	$e\left(\frac{39}{95}\right)$	$e\left(\frac{29}{380}\right)$	$e\left(\frac{359}{380}\right)$
$\chi_{9025}(1538,\cdot)$	$1$	$1$	$e\left(\frac{11}{380}\right)$	$e\left(\frac{237}{380}\right)$	$e\left(\frac{11}{190}\right)$	$e\left(\frac{62}{95}\right)$	$e\left(\frac{45}{76}\right)$	$e\left(\frac{33}{380}\right)$	$e\left(\frac{47}{190}\right)$	$e\left(\frac{24}{95}\right)$	$e\left(\frac{259}{380}\right)$	$e\left(\frac{9}{380}\right)$
$\chi_{9025}(1633,\cdot)$	$1$	$1$	$e\left(\frac{307}{380}\right)$	$e\left(\frac{189}{380}\right)$	$e\left(\frac{117}{190}\right)$	$e\left(\frac{29}{95}\right)$	$e\left(\frac{33}{76}\right)$	$e\left(\frac{161}{380}\right)$	$e\left(\frac{189}{190}\right)$	$e\left(\frac{48}{95}\right)$	$e\left(\frac{43}{380}\right)$	$e\left(\frac{113}{380}\right)$
$\chi_{9025}(1652,\cdot)$	$1$	$1$	$e\left(\frac{9}{380}\right)$	$e\left(\frac{263}{380}\right)$	$e\left(\frac{9}{190}\right)$	$e\left(\frac{68}{95}\right)$	$e\left(\frac{23}{76}\right)$	$e\left(\frac{27}{380}\right)$	$e\left(\frac{73}{190}\right)$	$e\left(\frac{11}{95}\right)$	$e\left(\frac{281}{380}\right)$	$e\left(\frac{111}{380}\right)$
$\chi_{9025}(1728,\cdot)$	$1$	$1$	$e\left(\frac{223}{380}\right)$	$e\left(\frac{141}{380}\right)$	$e\left(\frac{33}{190}\right)$	$e\left(\frac{91}{95}\right)$	$e\left(\frac{21}{76}\right)$	$e\left(\frac{289}{380}\right)$	$e\left(\frac{141}{190}\right)$	$e\left(\frac{72}{95}\right)$	$e\left(\frac{207}{380}\right)$	$e\left(\frac{217}{380}\right)$
$\chi_{9025}(1747,\cdot)$	$1$	$1$	$e\left(\frac{153}{380}\right)$	$e\left(\frac{291}{380}\right)$	$e\left(\frac{153}{190}\right)$	$e\left(\frac{16}{95}\right)$	$e\left(\frac{11}{76}\right)$	$e\left(\frac{79}{380}\right)$	$e\left(\frac{101}{190}\right)$	$e\left(\frac{92}{95}\right)$	$e\left(\frac{217}{380}\right)$	$e\left(\frac{367}{380}\right)$
$\chi_{9025}(1823,\cdot)$	$1$	$1$	$e\left(\frac{139}{380}\right)$	$e\left(\frac{93}{380}\right)$	$e\left(\frac{139}{190}\right)$	$e\left(\frac{58}{95}\right)$	$e\left(\frac{9}{76}\right)$	$e\left(\frac{37}{380}\right)$	$e\left(\frac{93}{190}\right)$	$e\left(\frac{1}{95}\right)$	$e\left(\frac{371}{380}\right)$	$e\left(\frac{321}{380}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{9025}(37,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{221}{380}\right)\)	\(e\left(\frac{167}{380}\right)\)	\(e\left(\frac{31}{190}\right)\)	\(e\left(\frac{2}{95}\right)\)	\(e\left(\frac{75}{76}\right)\)	\(e\left(\frac{283}{380}\right)\)	\(e\left(\frac{167}{190}\right)\)	\(e\left(\frac{59}{95}\right)\)	\(e\left(\frac{229}{380}\right)\)	\(e\left(\frac{319}{380}\right)\)
\(\chi_{9025}(113,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{380}\right)\)	\(e\left(\frac{197}{380}\right)\)	\(e\left(\frac{131}{190}\right)\)	\(e\left(\frac{82}{95}\right)\)	\(e\left(\frac{73}{76}\right)\)	\(e\left(\frac{13}{380}\right)\)	\(e\left(\frac{7}{190}\right)\)	\(e\left(\frac{44}{95}\right)\)	\(e\left(\frac{79}{380}\right)\)	\(e\left(\frac{349}{380}\right)\)
\(\chi_{9025}(208,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{380}\right)\)	\(e\left(\frac{149}{380}\right)\)	\(e\left(\frac{47}{190}\right)\)	\(e\left(\frac{49}{95}\right)\)	\(e\left(\frac{61}{76}\right)\)	\(e\left(\frac{141}{380}\right)\)	\(e\left(\frac{149}{190}\right)\)	\(e\left(\frac{68}{95}\right)\)	\(e\left(\frac{243}{380}\right)\)	\(e\left(\frac{73}{380}\right)\)
\(\chi_{9025}(227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{129}{380}\right)\)	\(e\left(\frac{223}{380}\right)\)	\(e\left(\frac{129}{190}\right)\)	\(e\left(\frac{88}{95}\right)\)	\(e\left(\frac{51}{76}\right)\)	\(e\left(\frac{7}{380}\right)\)	\(e\left(\frac{33}{190}\right)\)	\(e\left(\frac{31}{95}\right)\)	\(e\left(\frac{101}{380}\right)\)	\(e\left(\frac{71}{380}\right)\)
\(\chi_{9025}(303,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{343}{380}\right)\)	\(e\left(\frac{101}{380}\right)\)	\(e\left(\frac{153}{190}\right)\)	\(e\left(\frac{16}{95}\right)\)	\(e\left(\frac{49}{76}\right)\)	\(e\left(\frac{269}{380}\right)\)	\(e\left(\frac{101}{190}\right)\)	\(e\left(\frac{92}{95}\right)\)	\(e\left(\frac{27}{380}\right)\)	\(e\left(\frac{177}{380}\right)\)
\(\chi_{9025}(322,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{273}{380}\right)\)	\(e\left(\frac{251}{380}\right)\)	\(e\left(\frac{83}{190}\right)\)	\(e\left(\frac{36}{95}\right)\)	\(e\left(\frac{39}{76}\right)\)	\(e\left(\frac{59}{380}\right)\)	\(e\left(\frac{61}{190}\right)\)	\(e\left(\frac{17}{95}\right)\)	\(e\left(\frac{37}{380}\right)\)	\(e\left(\frac{327}{380}\right)\)
\(\chi_{9025}(398,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{259}{380}\right)\)	\(e\left(\frac{53}{380}\right)\)	\(e\left(\frac{69}{190}\right)\)	\(e\left(\frac{78}{95}\right)\)	\(e\left(\frac{37}{76}\right)\)	\(e\left(\frac{17}{380}\right)\)	\(e\left(\frac{53}{190}\right)\)	\(e\left(\frac{21}{95}\right)\)	\(e\left(\frac{191}{380}\right)\)	\(e\left(\frac{281}{380}\right)\)
\(\chi_{9025}(417,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{380}\right)\)	\(e\left(\frac{279}{380}\right)\)	\(e\left(\frac{37}{190}\right)\)	\(e\left(\frac{79}{95}\right)\)	\(e\left(\frac{27}{76}\right)\)	\(e\left(\frac{111}{380}\right)\)	\(e\left(\frac{89}{190}\right)\)	\(e\left(\frac{3}{95}\right)\)	\(e\left(\frac{353}{380}\right)\)	\(e\left(\frac{203}{380}\right)\)
\(\chi_{9025}(512,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{181}{380}\right)\)	\(e\left(\frac{307}{380}\right)\)	\(e\left(\frac{181}{190}\right)\)	\(e\left(\frac{27}{95}\right)\)	\(e\left(\frac{15}{76}\right)\)	\(e\left(\frac{163}{380}\right)\)	\(e\left(\frac{117}{190}\right)\)	\(e\left(\frac{84}{95}\right)\)	\(e\left(\frac{289}{380}\right)\)	\(e\left(\frac{79}{380}\right)\)
\(\chi_{9025}(588,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{380}\right)\)	\(e\left(\frac{337}{380}\right)\)	\(e\left(\frac{91}{190}\right)\)	\(e\left(\frac{12}{95}\right)\)	\(e\left(\frac{13}{76}\right)\)	\(e\left(\frac{273}{380}\right)\)	\(e\left(\frac{147}{190}\right)\)	\(e\left(\frac{69}{95}\right)\)	\(e\left(\frac{139}{380}\right)\)	\(e\left(\frac{109}{380}\right)\)
\(\chi_{9025}(683,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{380}\right)\)	\(e\left(\frac{289}{380}\right)\)	\(e\left(\frac{7}{190}\right)\)	\(e\left(\frac{74}{95}\right)\)	\(e\left(\frac{1}{76}\right)\)	\(e\left(\frac{21}{380}\right)\)	\(e\left(\frac{99}{190}\right)\)	\(e\left(\frac{93}{95}\right)\)	\(e\left(\frac{303}{380}\right)\)	\(e\left(\frac{213}{380}\right)\)
\(\chi_{9025}(702,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{380}\right)\)	\(e\left(\frac{363}{380}\right)\)	\(e\left(\frac{89}{190}\right)\)	\(e\left(\frac{18}{95}\right)\)	\(e\left(\frac{67}{76}\right)\)	\(e\left(\frac{267}{380}\right)\)	\(e\left(\frac{173}{190}\right)\)	\(e\left(\frac{56}{95}\right)\)	\(e\left(\frac{161}{380}\right)\)	\(e\left(\frac{211}{380}\right)\)
\(\chi_{9025}(778,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{303}{380}\right)\)	\(e\left(\frac{241}{380}\right)\)	\(e\left(\frac{113}{190}\right)\)	\(e\left(\frac{41}{95}\right)\)	\(e\left(\frac{65}{76}\right)\)	\(e\left(\frac{149}{380}\right)\)	\(e\left(\frac{51}{190}\right)\)	\(e\left(\frac{22}{95}\right)\)	\(e\left(\frac{87}{380}\right)\)	\(e\left(\frac{317}{380}\right)\)
\(\chi_{9025}(797,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{233}{380}\right)\)	\(e\left(\frac{11}{380}\right)\)	\(e\left(\frac{43}{190}\right)\)	\(e\left(\frac{61}{95}\right)\)	\(e\left(\frac{55}{76}\right)\)	\(e\left(\frac{319}{380}\right)\)	\(e\left(\frac{11}{190}\right)\)	\(e\left(\frac{42}{95}\right)\)	\(e\left(\frac{97}{380}\right)\)	\(e\left(\frac{87}{380}\right)\)
\(\chi_{9025}(873,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{219}{380}\right)\)	\(e\left(\frac{193}{380}\right)\)	\(e\left(\frac{29}{190}\right)\)	\(e\left(\frac{8}{95}\right)\)	\(e\left(\frac{53}{76}\right)\)	\(e\left(\frac{277}{380}\right)\)	\(e\left(\frac{3}{190}\right)\)	\(e\left(\frac{46}{95}\right)\)	\(e\left(\frac{251}{380}\right)\)	\(e\left(\frac{41}{380}\right)\)
\(\chi_{9025}(892,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{377}{380}\right)\)	\(e\left(\frac{39}{380}\right)\)	\(e\left(\frac{187}{190}\right)\)	\(e\left(\frac{9}{95}\right)\)	\(e\left(\frac{43}{76}\right)\)	\(e\left(\frac{371}{380}\right)\)	\(e\left(\frac{39}{190}\right)\)	\(e\left(\frac{28}{95}\right)\)	\(e\left(\frac{33}{380}\right)\)	\(e\left(\frac{343}{380}\right)\)
\(\chi_{9025}(987,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{141}{380}\right)\)	\(e\left(\frac{67}{380}\right)\)	\(e\left(\frac{141}{190}\right)\)	\(e\left(\frac{52}{95}\right)\)	\(e\left(\frac{31}{76}\right)\)	\(e\left(\frac{43}{380}\right)\)	\(e\left(\frac{67}{190}\right)\)	\(e\left(\frac{14}{95}\right)\)	\(e\left(\frac{349}{380}\right)\)	\(e\left(\frac{219}{380}\right)\)
\(\chi_{9025}(1063,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{380}\right)\)	\(e\left(\frac{97}{380}\right)\)	\(e\left(\frac{51}{190}\right)\)	\(e\left(\frac{37}{95}\right)\)	\(e\left(\frac{29}{76}\right)\)	\(e\left(\frac{153}{380}\right)\)	\(e\left(\frac{97}{190}\right)\)	\(e\left(\frac{94}{95}\right)\)	\(e\left(\frac{199}{380}\right)\)	\(e\left(\frac{249}{380}\right)\)
\(\chi_{9025}(1158,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{347}{380}\right)\)	\(e\left(\frac{49}{380}\right)\)	\(e\left(\frac{157}{190}\right)\)	\(e\left(\frac{4}{95}\right)\)	\(e\left(\frac{17}{76}\right)\)	\(e\left(\frac{281}{380}\right)\)	\(e\left(\frac{49}{190}\right)\)	\(e\left(\frac{23}{95}\right)\)	\(e\left(\frac{363}{380}\right)\)	\(e\left(\frac{353}{380}\right)\)
\(\chi_{9025}(1177,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{380}\right)\)	\(e\left(\frac{123}{380}\right)\)	\(e\left(\frac{49}{190}\right)\)	\(e\left(\frac{43}{95}\right)\)	\(e\left(\frac{7}{76}\right)\)	\(e\left(\frac{147}{380}\right)\)	\(e\left(\frac{123}{190}\right)\)	\(e\left(\frac{81}{95}\right)\)	\(e\left(\frac{221}{380}\right)\)	\(e\left(\frac{351}{380}\right)\)
\(\chi_{9025}(1253,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{263}{380}\right)\)	\(e\left(\frac{1}{380}\right)\)	\(e\left(\frac{73}{190}\right)\)	\(e\left(\frac{66}{95}\right)\)	\(e\left(\frac{5}{76}\right)\)	\(e\left(\frac{29}{380}\right)\)	\(e\left(\frac{1}{190}\right)\)	\(e\left(\frac{47}{95}\right)\)	\(e\left(\frac{147}{380}\right)\)	\(e\left(\frac{77}{380}\right)\)
\(\chi_{9025}(1272,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{380}\right)\)	\(e\left(\frac{151}{380}\right)\)	\(e\left(\frac{3}{190}\right)\)	\(e\left(\frac{86}{95}\right)\)	\(e\left(\frac{71}{76}\right)\)	\(e\left(\frac{199}{380}\right)\)	\(e\left(\frac{151}{190}\right)\)	\(e\left(\frac{67}{95}\right)\)	\(e\left(\frac{157}{380}\right)\)	\(e\left(\frac{227}{380}\right)\)
\(\chi_{9025}(1348,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{380}\right)\)	\(e\left(\frac{333}{380}\right)\)	\(e\left(\frac{179}{190}\right)\)	\(e\left(\frac{33}{95}\right)\)	\(e\left(\frac{69}{76}\right)\)	\(e\left(\frac{157}{380}\right)\)	\(e\left(\frac{143}{190}\right)\)	\(e\left(\frac{71}{95}\right)\)	\(e\left(\frac{311}{380}\right)\)	\(e\left(\frac{181}{380}\right)\)
\(\chi_{9025}(1367,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{337}{380}\right)\)	\(e\left(\frac{179}{380}\right)\)	\(e\left(\frac{147}{190}\right)\)	\(e\left(\frac{34}{95}\right)\)	\(e\left(\frac{59}{76}\right)\)	\(e\left(\frac{251}{380}\right)\)	\(e\left(\frac{179}{190}\right)\)	\(e\left(\frac{53}{95}\right)\)	\(e\left(\frac{93}{380}\right)\)	\(e\left(\frac{103}{380}\right)\)
\(\chi_{9025}(1462,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{380}\right)\)	\(e\left(\frac{207}{380}\right)\)	\(e\left(\frac{101}{190}\right)\)	\(e\left(\frac{77}{95}\right)\)	\(e\left(\frac{47}{76}\right)\)	\(e\left(\frac{303}{380}\right)\)	\(e\left(\frac{17}{190}\right)\)	\(e\left(\frac{39}{95}\right)\)	\(e\left(\frac{29}{380}\right)\)	\(e\left(\frac{359}{380}\right)\)
\(\chi_{9025}(1538,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{380}\right)\)	\(e\left(\frac{237}{380}\right)\)	\(e\left(\frac{11}{190}\right)\)	\(e\left(\frac{62}{95}\right)\)	\(e\left(\frac{45}{76}\right)\)	\(e\left(\frac{33}{380}\right)\)	\(e\left(\frac{47}{190}\right)\)	\(e\left(\frac{24}{95}\right)\)	\(e\left(\frac{259}{380}\right)\)	\(e\left(\frac{9}{380}\right)\)
\(\chi_{9025}(1633,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{307}{380}\right)\)	\(e\left(\frac{189}{380}\right)\)	\(e\left(\frac{117}{190}\right)\)	\(e\left(\frac{29}{95}\right)\)	\(e\left(\frac{33}{76}\right)\)	\(e\left(\frac{161}{380}\right)\)	\(e\left(\frac{189}{190}\right)\)	\(e\left(\frac{48}{95}\right)\)	\(e\left(\frac{43}{380}\right)\)	\(e\left(\frac{113}{380}\right)\)
\(\chi_{9025}(1652,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{380}\right)\)	\(e\left(\frac{263}{380}\right)\)	\(e\left(\frac{9}{190}\right)\)	\(e\left(\frac{68}{95}\right)\)	\(e\left(\frac{23}{76}\right)\)	\(e\left(\frac{27}{380}\right)\)	\(e\left(\frac{73}{190}\right)\)	\(e\left(\frac{11}{95}\right)\)	\(e\left(\frac{281}{380}\right)\)	\(e\left(\frac{111}{380}\right)\)
\(\chi_{9025}(1728,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{223}{380}\right)\)	\(e\left(\frac{141}{380}\right)\)	\(e\left(\frac{33}{190}\right)\)	\(e\left(\frac{91}{95}\right)\)	\(e\left(\frac{21}{76}\right)\)	\(e\left(\frac{289}{380}\right)\)	\(e\left(\frac{141}{190}\right)\)	\(e\left(\frac{72}{95}\right)\)	\(e\left(\frac{207}{380}\right)\)	\(e\left(\frac{217}{380}\right)\)
\(\chi_{9025}(1747,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{153}{380}\right)\)	\(e\left(\frac{291}{380}\right)\)	\(e\left(\frac{153}{190}\right)\)	\(e\left(\frac{16}{95}\right)\)	\(e\left(\frac{11}{76}\right)\)	\(e\left(\frac{79}{380}\right)\)	\(e\left(\frac{101}{190}\right)\)	\(e\left(\frac{92}{95}\right)\)	\(e\left(\frac{217}{380}\right)\)	\(e\left(\frac{367}{380}\right)\)
\(\chi_{9025}(1823,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{380}\right)\)	\(e\left(\frac{93}{380}\right)\)	\(e\left(\frac{139}{190}\right)\)	\(e\left(\frac{58}{95}\right)\)	\(e\left(\frac{9}{76}\right)\)	\(e\left(\frac{37}{380}\right)\)	\(e\left(\frac{93}{190}\right)\)	\(e\left(\frac{1}{95}\right)\)	\(e\left(\frac{371}{380}\right)\)	\(e\left(\frac{321}{380}\right)\)

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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	9025.cg
Modulus	$9025$
Conductor	$9025$
Order	$380$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(9025\)
Conductor:	\(9025\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(380\)	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)