LMFDB - Dirichlet character orbit 25410.gq

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(25410, base_ring=CyclotomicField(330)) M = H._module chi = DirichletCharacter(H, M([165,0,220,153])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(431,25410)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$25410$
Conductor:	$2541$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$330$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2541.cg	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:	$\Q(\zeta_{165})$
Fixed field:	Number field defined by a degree 330 polynomial (not computed)

First 31 of 80 characters in Galois orbit

Character	$-1$	$1$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$	$47$
$\chi_{25410}(431,\cdot)$	$1$	$1$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{146}{165}\right)$	$e\left(\frac{269}{330}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{89}{165}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{89}{330}\right)$
$\chi_{25410}(611,\cdot)$	$1$	$1$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{271}{330}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{151}{165}\right)$	$e\left(\frac{107}{165}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{151}{330}\right)$
$\chi_{25410}(821,\cdot)$	$1$	$1$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{127}{165}\right)$	$e\left(\frac{43}{330}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{13}{165}\right)$	$e\left(\frac{101}{165}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{13}{330}\right)$
$\chi_{25410}(1031,\cdot)$	$1$	$1$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{58}{165}\right)$	$e\left(\frac{247}{330}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{89}{165}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{67}{330}\right)$
$\chi_{25410}(1271,\cdot)$	$1$	$1$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{119}{165}\right)$	$e\left(\frac{191}{330}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{146}{165}\right)$	$e\left(\frac{157}{165}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{311}{330}\right)$
$\chi_{25410}(1481,\cdot)$	$1$	$1$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{53}{330}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{158}{165}\right)$	$e\left(\frac{136}{165}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{323}{330}\right)$
$\chi_{25410}(2081,\cdot)$	$1$	$1$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{109}{330}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{68}{165}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{79}{330}\right)$
$\chi_{25410}(2741,\cdot)$	$1$	$1$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{71}{165}\right)$	$e\left(\frac{89}{330}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{119}{165}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{119}{330}\right)$
$\chi_{25410}(2921,\cdot)$	$1$	$1$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{109}{165}\right)$	$e\left(\frac{211}{330}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{106}{165}\right)$	$e\left(\frac{62}{165}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{271}{330}\right)$
$\chi_{25410}(3131,\cdot)$	$1$	$1$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{133}{330}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{163}{330}\right)$
$\chi_{25410}(3341,\cdot)$	$1$	$1$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{37}{330}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{157}{165}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{157}{330}\right)$
$\chi_{25410}(3581,\cdot)$	$1$	$1$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{149}{165}\right)$	$e\left(\frac{131}{330}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{101}{165}\right)$	$e\left(\frac{112}{165}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{101}{330}\right)$
$\chi_{25410}(4001,\cdot)$	$1$	$1$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{83}{165}\right)$	$e\left(\frac{197}{330}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{167}{330}\right)$
$\chi_{25410}(4391,\cdot)$	$1$	$1$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{151}{165}\right)$	$e\left(\frac{259}{330}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{109}{165}\right)$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{109}{330}\right)$
$\chi_{25410}(5051,\cdot)$	$1$	$1$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{161}{165}\right)$	$e\left(\frac{239}{330}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{149}{165}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{149}{330}\right)$
$\chi_{25410}(5231,\cdot)$	$1$	$1$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{151}{330}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{17}{165}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{61}{330}\right)$
$\chi_{25410}(5441,\cdot)$	$1$	$1$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{223}{330}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{71}{165}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{313}{330}\right)$
$\chi_{25410}(5651,\cdot)$	$1$	$1$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{157}{330}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{247}{330}\right)$
$\chi_{25410}(5891,\cdot)$	$1$	$1$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{71}{330}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{56}{165}\right)$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{221}{330}\right)$
$\chi_{25410}(6101,\cdot)$	$1$	$1$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{233}{330}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{106}{165}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{293}{330}\right)$
$\chi_{25410}(6311,\cdot)$	$1$	$1$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{23}{165}\right)$	$e\left(\frac{317}{330}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{92}{165}\right)$	$e\left(\frac{4}{165}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{257}{330}\right)$
$\chi_{25410}(6701,\cdot)$	$1$	$1$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{79}{330}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{139}{330}\right)$
$\chi_{25410}(7361,\cdot)$	$1$	$1$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{59}{330}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{58}{165}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{179}{330}\right)$
$\chi_{25410}(7541,\cdot)$	$1$	$1$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{4}{165}\right)$	$e\left(\frac{91}{330}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{137}{165}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{181}{330}\right)$
$\chi_{25410}(7751,\cdot)$	$1$	$1$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{157}{165}\right)$	$e\left(\frac{313}{330}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{56}{165}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{133}{330}\right)$
$\chi_{25410}(7961,\cdot)$	$1$	$1$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{43}{165}\right)$	$e\left(\frac{277}{330}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{29}{165}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{7}{330}\right)$
$\chi_{25410}(8411,\cdot)$	$1$	$1$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{323}{330}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{113}{330}\right)$
$\chi_{25410}(8621,\cdot)$	$1$	$1$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{107}{330}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{17}{165}\right)$	$e\left(\frac{94}{165}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{17}{330}\right)$
$\chi_{25410}(9011,\cdot)$	$1$	$1$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{229}{330}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{4}{165}\right)$	$e\left(\frac{158}{165}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{169}{330}\right)$
$\chi_{25410}(9851,\cdot)$	$1$	$1$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{34}{165}\right)$	$e\left(\frac{31}{330}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{136}{165}\right)$	$e\left(\frac{92}{165}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{301}{330}\right)$
$\chi_{25410}(10061,\cdot)$	$1$	$1$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{112}{165}\right)$	$e\left(\frac{73}{330}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{118}{165}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{283}{330}\right)$

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	\(-1\)	\(1\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)	\(47\)
\(\chi_{25410}(431,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{146}{165}\right)\)	\(e\left(\frac{269}{330}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{89}{165}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{89}{330}\right)\)
\(\chi_{25410}(611,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{271}{330}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{107}{165}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{151}{330}\right)\)
\(\chi_{25410}(821,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{127}{165}\right)\)	\(e\left(\frac{43}{330}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{13}{165}\right)\)	\(e\left(\frac{101}{165}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{13}{330}\right)\)
\(\chi_{25410}(1031,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{247}{330}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{89}{165}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{67}{330}\right)\)
\(\chi_{25410}(1271,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{119}{165}\right)\)	\(e\left(\frac{191}{330}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{146}{165}\right)\)	\(e\left(\frac{157}{165}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{311}{330}\right)\)
\(\chi_{25410}(1481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{53}{330}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{158}{165}\right)\)	\(e\left(\frac{136}{165}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{323}{330}\right)\)
\(\chi_{25410}(2081,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{109}{330}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{68}{165}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{79}{330}\right)\)
\(\chi_{25410}(2741,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{71}{165}\right)\)	\(e\left(\frac{89}{330}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{119}{165}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{119}{330}\right)\)
\(\chi_{25410}(2921,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{109}{165}\right)\)	\(e\left(\frac{211}{330}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{106}{165}\right)\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{271}{330}\right)\)
\(\chi_{25410}(3131,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{133}{330}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{163}{330}\right)\)
\(\chi_{25410}(3341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{157}{165}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{157}{330}\right)\)
\(\chi_{25410}(3581,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{149}{165}\right)\)	\(e\left(\frac{131}{330}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{101}{165}\right)\)	\(e\left(\frac{112}{165}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{101}{330}\right)\)
\(\chi_{25410}(4001,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{83}{165}\right)\)	\(e\left(\frac{197}{330}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{167}{330}\right)\)
\(\chi_{25410}(4391,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{259}{330}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{109}{165}\right)\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{109}{330}\right)\)
\(\chi_{25410}(5051,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{161}{165}\right)\)	\(e\left(\frac{239}{330}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{149}{165}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{149}{330}\right)\)
\(\chi_{25410}(5231,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{151}{330}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{17}{165}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{61}{330}\right)\)
\(\chi_{25410}(5441,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{223}{330}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{71}{165}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{313}{330}\right)\)
\(\chi_{25410}(5651,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{157}{330}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{247}{330}\right)\)
\(\chi_{25410}(5891,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{71}{330}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{56}{165}\right)\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{221}{330}\right)\)
\(\chi_{25410}(6101,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{233}{330}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{106}{165}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{293}{330}\right)\)
\(\chi_{25410}(6311,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{23}{165}\right)\)	\(e\left(\frac{317}{330}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{92}{165}\right)\)	\(e\left(\frac{4}{165}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{257}{330}\right)\)
\(\chi_{25410}(6701,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{79}{330}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{139}{330}\right)\)
\(\chi_{25410}(7361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{59}{330}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{179}{330}\right)\)
\(\chi_{25410}(7541,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{4}{165}\right)\)	\(e\left(\frac{91}{330}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{137}{165}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{181}{330}\right)\)
\(\chi_{25410}(7751,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{157}{165}\right)\)	\(e\left(\frac{313}{330}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{56}{165}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{133}{330}\right)\)
\(\chi_{25410}(7961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{43}{165}\right)\)	\(e\left(\frac{277}{330}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{29}{165}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{7}{330}\right)\)
\(\chi_{25410}(8411,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{323}{330}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{113}{330}\right)\)
\(\chi_{25410}(8621,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{107}{330}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{17}{165}\right)\)	\(e\left(\frac{94}{165}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{17}{330}\right)\)
\(\chi_{25410}(9011,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{229}{330}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{4}{165}\right)\)	\(e\left(\frac{158}{165}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{169}{330}\right)\)
\(\chi_{25410}(9851,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{34}{165}\right)\)	\(e\left(\frac{31}{330}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{136}{165}\right)\)	\(e\left(\frac{92}{165}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{301}{330}\right)\)
\(\chi_{25410}(10061,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{112}{165}\right)\)	\(e\left(\frac{73}{330}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{118}{165}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{283}{330}\right)\)

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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	25410.gq
Modulus	$25410$
Conductor	$2541$
Order	$330$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(25410\)
Conductor:	\(2541\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(330\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2541.cg	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)