LMFDB - Dirichlet character orbit 5175.dq

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5175, base_ring=CyclotomicField(660)) M = H._module chi = DirichletCharacter(H, M([110,33,60])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(2,5175)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$5175$
Conductor:	$5175$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$660$	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:	$\Q(\zeta_{660})$
Fixed field:	Number field defined by a degree 660 polynomial (not computed)

First 31 of 160 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{5175}(2,\cdot)$	$1$	$1$	$e\left(\frac{263}{660}\right)$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{259}{330}\right)$	$e\left(\frac{367}{660}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{173}{220}\right)$	$e\left(\frac{29}{110}\right)$
$\chi_{5175}(77,\cdot)$	$1$	$1$	$e\left(\frac{283}{660}\right)$	$e\left(\frac{283}{330}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{29}{330}\right)$	$e\left(\frac{287}{660}\right)$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{118}{165}\right)$	$e\left(\frac{13}{220}\right)$	$e\left(\frac{109}{110}\right)$
$\chi_{5175}(128,\cdot)$	$1$	$1$	$e\left(\frac{521}{660}\right)$	$e\left(\frac{191}{330}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{163}{330}\right)$	$e\left(\frac{589}{660}\right)$	$e\left(\frac{49}{165}\right)$	$e\left(\frac{26}{165}\right)$	$e\left(\frac{111}{220}\right)$	$e\left(\frac{93}{110}\right)$
$\chi_{5175}(167,\cdot)$	$1$	$1$	$e\left(\frac{79}{660}\right)$	$e\left(\frac{79}{330}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{79}{220}\right)$	$e\left(\frac{197}{330}\right)$	$e\left(\frac{311}{660}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{107}{110}\right)$
$\chi_{5175}(173,\cdot)$	$1$	$1$	$e\left(\frac{353}{660}\right)$	$e\left(\frac{23}{330}\right)$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{49}{330}\right)$	$e\left(\frac{337}{660}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{23}{165}\right)$	$e\left(\frac{3}{220}\right)$	$e\left(\frac{59}{110}\right)$
$\chi_{5175}(248,\cdot)$	$1$	$1$	$e\left(\frac{313}{660}\right)$	$e\left(\frac{313}{330}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{179}{330}\right)$	$e\left(\frac{497}{660}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{103}{220}\right)$	$e\left(\frac{9}{110}\right)$
$\chi_{5175}(302,\cdot)$	$1$	$1$	$e\left(\frac{223}{660}\right)$	$e\left(\frac{223}{330}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{3}{220}\right)$	$e\left(\frac{59}{330}\right)$	$e\left(\frac{527}{660}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{58}{165}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{89}{110}\right)$
$\chi_{5175}(308,\cdot)$	$1$	$1$	$e\left(\frac{149}{660}\right)$	$e\left(\frac{149}{330}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{217}{330}\right)$	$e\left(\frac{361}{660}\right)$	$e\left(\frac{46}{165}\right)$	$e\left(\frac{149}{165}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{57}{110}\right)$
$\chi_{5175}(317,\cdot)$	$1$	$1$	$e\left(\frac{599}{660}\right)$	$e\left(\frac{269}{330}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{157}{330}\right)$	$e\left(\frac{211}{660}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{97}{110}\right)$
$\chi_{5175}(338,\cdot)$	$1$	$1$	$e\left(\frac{337}{660}\right)$	$e\left(\frac{7}{330}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{101}{330}\right)$	$e\left(\frac{533}{660}\right)$	$e\left(\frac{83}{165}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{87}{220}\right)$	$e\left(\frac{61}{110}\right)$
$\chi_{5175}(347,\cdot)$	$1$	$1$	$e\left(\frac{571}{660}\right)$	$e\left(\frac{241}{330}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{83}{330}\right)$	$e\left(\frac{59}{660}\right)$	$e\left(\frac{29}{165}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{73}{110}\right)$
$\chi_{5175}(353,\cdot)$	$1$	$1$	$e\left(\frac{41}{660}\right)$	$e\left(\frac{41}{330}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{73}{330}\right)$	$e\left(\frac{529}{660}\right)$	$e\left(\frac{109}{165}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{43}{110}\right)$
$\chi_{5175}(473,\cdot)$	$1$	$1$	$e\left(\frac{433}{660}\right)$	$e\left(\frac{103}{330}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{119}{330}\right)$	$e\left(\frac{17}{660}\right)$	$e\left(\frac{137}{165}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{49}{110}\right)$
$\chi_{5175}(533,\cdot)$	$1$	$1$	$e\left(\frac{449}{660}\right)$	$e\left(\frac{119}{330}\right)$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{9}{220}\right)$	$e\left(\frac{67}{330}\right)$	$e\left(\frac{481}{660}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{119}{165}\right)$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{47}{110}\right)$
$\chi_{5175}(542,\cdot)$	$1$	$1$	$e\left(\frac{59}{660}\right)$	$e\left(\frac{59}{330}\right)$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{97}{330}\right)$	$e\left(\frac{391}{660}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{59}{165}\right)$	$e\left(\frac{89}{220}\right)$	$e\left(\frac{27}{110}\right)$
$\chi_{5175}(578,\cdot)$	$1$	$1$	$e\left(\frac{641}{660}\right)$	$e\left(\frac{311}{330}\right)$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{103}{330}\right)$	$e\left(\frac{109}{660}\right)$	$e\left(\frac{34}{165}\right)$	$e\left(\frac{146}{165}\right)$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{23}{110}\right)$
$\chi_{5175}(587,\cdot)$	$1$	$1$	$e\left(\frac{287}{660}\right)$	$e\left(\frac{287}{330}\right)$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{67}{220}\right)$	$e\left(\frac{181}{330}\right)$	$e\left(\frac{403}{660}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{157}{220}\right)$	$e\left(\frac{81}{110}\right)$
$\chi_{5175}(623,\cdot)$	$1$	$1$	$e\left(\frac{593}{660}\right)$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{259}{330}\right)$	$e\left(\frac{37}{660}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{29}{110}\right)$
$\chi_{5175}(653,\cdot)$	$1$	$1$	$e\left(\frac{61}{660}\right)$	$e\left(\frac{61}{330}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{173}{330}\right)$	$e\left(\frac{449}{660}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{13}{110}\right)$
$\chi_{5175}(662,\cdot)$	$1$	$1$	$e\left(\frac{247}{660}\right)$	$e\left(\frac{247}{330}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{27}{220}\right)$	$e\left(\frac{311}{330}\right)$	$e\left(\frac{563}{660}\right)$	$e\left(\frac{53}{165}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{37}{220}\right)$	$e\left(\frac{31}{110}\right)$
$\chi_{5175}(698,\cdot)$	$1$	$1$	$e\left(\frac{613}{660}\right)$	$e\left(\frac{283}{330}\right)$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{173}{220}\right)$	$e\left(\frac{29}{330}\right)$	$e\left(\frac{617}{660}\right)$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{118}{165}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{109}{110}\right)$
$\chi_{5175}(722,\cdot)$	$1$	$1$	$e\left(\frac{611}{660}\right)$	$e\left(\frac{281}{330}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{283}{330}\right)$	$e\left(\frac{559}{660}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{13}{110}\right)$
$\chi_{5175}(752,\cdot)$	$1$	$1$	$e\left(\frac{403}{660}\right)$	$e\left(\frac{73}{330}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{299}{330}\right)$	$e\left(\frac{467}{660}\right)$	$e\left(\frac{17}{165}\right)$	$e\left(\frac{73}{165}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{39}{110}\right)$
$\chi_{5175}(767,\cdot)$	$1$	$1$	$e\left(\frac{239}{660}\right)$	$e\left(\frac{239}{330}\right)$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{7}{330}\right)$	$e\left(\frac{331}{660}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{74}{165}\right)$	$e\left(\frac{189}{220}\right)$	$e\left(\frac{87}{110}\right)$
$\chi_{5175}(788,\cdot)$	$1$	$1$	$e\left(\frac{277}{660}\right)$	$e\left(\frac{277}{330}\right)$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{131}{330}\right)$	$e\left(\frac{113}{660}\right)$	$e\left(\frac{8}{165}\right)$	$e\left(\frac{112}{165}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{41}{110}\right)$
$\chi_{5175}(878,\cdot)$	$1$	$1$	$e\left(\frac{361}{660}\right)$	$e\left(\frac{31}{330}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{23}{330}\right)$	$e\left(\frac{569}{660}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{3}{110}\right)$
$\chi_{5175}(887,\cdot)$	$1$	$1$	$e\left(\frac{367}{660}\right)$	$e\left(\frac{37}{330}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{251}{330}\right)$	$e\left(\frac{83}{660}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{71}{110}\right)$
$\chi_{5175}(923,\cdot)$	$1$	$1$	$e\left(\frac{553}{660}\right)$	$e\left(\frac{223}{330}\right)$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{59}{330}\right)$	$e\left(\frac{197}{660}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{58}{165}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{89}{110}\right)$
$\chi_{5175}(938,\cdot)$	$1$	$1$	$e\left(\frac{137}{660}\right)$	$e\left(\frac{137}{330}\right)$	$e\left(\frac{103}{132}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{91}{330}\right)$	$e\left(\frac{13}{660}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{137}{165}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{31}{110}\right)$
$\chi_{5175}(947,\cdot)$	$1$	$1$	$e\left(\frac{251}{660}\right)$	$e\left(\frac{251}{330}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{133}{330}\right)$	$e\left(\frac{19}{660}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{181}{220}\right)$	$e\left(\frac{3}{110}\right)$
$\chi_{5175}(992,\cdot)$	$1$	$1$	$e\left(\frac{179}{660}\right)$	$e\left(\frac{179}{330}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{179}{220}\right)$	$e\left(\frac{37}{330}\right)$	$e\left(\frac{571}{660}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{9}{220}\right)$	$e\left(\frac{67}{110}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{5175}(2,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{263}{660}\right)\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{259}{330}\right)\)	\(e\left(\frac{367}{660}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{173}{220}\right)\)	\(e\left(\frac{29}{110}\right)\)
\(\chi_{5175}(77,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{283}{660}\right)\)	\(e\left(\frac{283}{330}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{29}{330}\right)\)	\(e\left(\frac{287}{660}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{118}{165}\right)\)	\(e\left(\frac{13}{220}\right)\)	\(e\left(\frac{109}{110}\right)\)
\(\chi_{5175}(128,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{521}{660}\right)\)	\(e\left(\frac{191}{330}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{163}{330}\right)\)	\(e\left(\frac{589}{660}\right)\)	\(e\left(\frac{49}{165}\right)\)	\(e\left(\frac{26}{165}\right)\)	\(e\left(\frac{111}{220}\right)\)	\(e\left(\frac{93}{110}\right)\)
\(\chi_{5175}(167,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{660}\right)\)	\(e\left(\frac{79}{330}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{79}{220}\right)\)	\(e\left(\frac{197}{330}\right)\)	\(e\left(\frac{311}{660}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{107}{110}\right)\)
\(\chi_{5175}(173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{353}{660}\right)\)	\(e\left(\frac{23}{330}\right)\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{49}{330}\right)\)	\(e\left(\frac{337}{660}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{23}{165}\right)\)	\(e\left(\frac{3}{220}\right)\)	\(e\left(\frac{59}{110}\right)\)
\(\chi_{5175}(248,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{313}{660}\right)\)	\(e\left(\frac{313}{330}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{179}{330}\right)\)	\(e\left(\frac{497}{660}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{103}{220}\right)\)	\(e\left(\frac{9}{110}\right)\)
\(\chi_{5175}(302,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{223}{660}\right)\)	\(e\left(\frac{223}{330}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{3}{220}\right)\)	\(e\left(\frac{59}{330}\right)\)	\(e\left(\frac{527}{660}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{89}{110}\right)\)
\(\chi_{5175}(308,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{660}\right)\)	\(e\left(\frac{149}{330}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{217}{330}\right)\)	\(e\left(\frac{361}{660}\right)\)	\(e\left(\frac{46}{165}\right)\)	\(e\left(\frac{149}{165}\right)\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{57}{110}\right)\)
\(\chi_{5175}(317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{599}{660}\right)\)	\(e\left(\frac{269}{330}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{157}{330}\right)\)	\(e\left(\frac{211}{660}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{97}{110}\right)\)
\(\chi_{5175}(338,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{337}{660}\right)\)	\(e\left(\frac{7}{330}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{101}{330}\right)\)	\(e\left(\frac{533}{660}\right)\)	\(e\left(\frac{83}{165}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{87}{220}\right)\)	\(e\left(\frac{61}{110}\right)\)
\(\chi_{5175}(347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{571}{660}\right)\)	\(e\left(\frac{241}{330}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{83}{330}\right)\)	\(e\left(\frac{59}{660}\right)\)	\(e\left(\frac{29}{165}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{41}{220}\right)\)	\(e\left(\frac{73}{110}\right)\)
\(\chi_{5175}(353,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{660}\right)\)	\(e\left(\frac{41}{330}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{41}{220}\right)\)	\(e\left(\frac{73}{330}\right)\)	\(e\left(\frac{529}{660}\right)\)	\(e\left(\frac{109}{165}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{43}{110}\right)\)
\(\chi_{5175}(473,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{433}{660}\right)\)	\(e\left(\frac{103}{330}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{119}{330}\right)\)	\(e\left(\frac{17}{660}\right)\)	\(e\left(\frac{137}{165}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{49}{110}\right)\)
\(\chi_{5175}(533,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{449}{660}\right)\)	\(e\left(\frac{119}{330}\right)\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{9}{220}\right)\)	\(e\left(\frac{67}{330}\right)\)	\(e\left(\frac{481}{660}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{119}{165}\right)\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{47}{110}\right)\)
\(\chi_{5175}(542,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{660}\right)\)	\(e\left(\frac{59}{330}\right)\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{97}{330}\right)\)	\(e\left(\frac{391}{660}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{59}{165}\right)\)	\(e\left(\frac{89}{220}\right)\)	\(e\left(\frac{27}{110}\right)\)
\(\chi_{5175}(578,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{641}{660}\right)\)	\(e\left(\frac{311}{330}\right)\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{103}{330}\right)\)	\(e\left(\frac{109}{660}\right)\)	\(e\left(\frac{34}{165}\right)\)	\(e\left(\frac{146}{165}\right)\)	\(e\left(\frac{31}{220}\right)\)	\(e\left(\frac{23}{110}\right)\)
\(\chi_{5175}(587,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{287}{660}\right)\)	\(e\left(\frac{287}{330}\right)\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{67}{220}\right)\)	\(e\left(\frac{181}{330}\right)\)	\(e\left(\frac{403}{660}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{157}{220}\right)\)	\(e\left(\frac{81}{110}\right)\)
\(\chi_{5175}(623,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{593}{660}\right)\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{259}{330}\right)\)	\(e\left(\frac{37}{660}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{29}{110}\right)\)
\(\chi_{5175}(653,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{660}\right)\)	\(e\left(\frac{61}{330}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{173}{330}\right)\)	\(e\left(\frac{449}{660}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{13}{110}\right)\)
\(\chi_{5175}(662,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{247}{660}\right)\)	\(e\left(\frac{247}{330}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{27}{220}\right)\)	\(e\left(\frac{311}{330}\right)\)	\(e\left(\frac{563}{660}\right)\)	\(e\left(\frac{53}{165}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{37}{220}\right)\)	\(e\left(\frac{31}{110}\right)\)
\(\chi_{5175}(698,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{613}{660}\right)\)	\(e\left(\frac{283}{330}\right)\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{173}{220}\right)\)	\(e\left(\frac{29}{330}\right)\)	\(e\left(\frac{617}{660}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{118}{165}\right)\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{109}{110}\right)\)
\(\chi_{5175}(722,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{611}{660}\right)\)	\(e\left(\frac{281}{330}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{283}{330}\right)\)	\(e\left(\frac{559}{660}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{13}{110}\right)\)
\(\chi_{5175}(752,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{403}{660}\right)\)	\(e\left(\frac{73}{330}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{299}{330}\right)\)	\(e\left(\frac{467}{660}\right)\)	\(e\left(\frac{17}{165}\right)\)	\(e\left(\frac{73}{165}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{39}{110}\right)\)
\(\chi_{5175}(767,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{239}{660}\right)\)	\(e\left(\frac{239}{330}\right)\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{7}{330}\right)\)	\(e\left(\frac{331}{660}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{74}{165}\right)\)	\(e\left(\frac{189}{220}\right)\)	\(e\left(\frac{87}{110}\right)\)
\(\chi_{5175}(788,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{277}{660}\right)\)	\(e\left(\frac{277}{330}\right)\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{57}{220}\right)\)	\(e\left(\frac{131}{330}\right)\)	\(e\left(\frac{113}{660}\right)\)	\(e\left(\frac{8}{165}\right)\)	\(e\left(\frac{112}{165}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{41}{110}\right)\)
\(\chi_{5175}(878,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{361}{660}\right)\)	\(e\left(\frac{31}{330}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{23}{330}\right)\)	\(e\left(\frac{569}{660}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{3}{110}\right)\)
\(\chi_{5175}(887,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{367}{660}\right)\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{251}{330}\right)\)	\(e\left(\frac{83}{660}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{71}{110}\right)\)
\(\chi_{5175}(923,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{553}{660}\right)\)	\(e\left(\frac{223}{330}\right)\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{113}{220}\right)\)	\(e\left(\frac{59}{330}\right)\)	\(e\left(\frac{197}{660}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{89}{110}\right)\)
\(\chi_{5175}(938,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{660}\right)\)	\(e\left(\frac{137}{330}\right)\)	\(e\left(\frac{103}{132}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{91}{330}\right)\)	\(e\left(\frac{13}{660}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{137}{165}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{31}{110}\right)\)
\(\chi_{5175}(947,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{251}{660}\right)\)	\(e\left(\frac{251}{330}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{31}{220}\right)\)	\(e\left(\frac{133}{330}\right)\)	\(e\left(\frac{19}{660}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{181}{220}\right)\)	\(e\left(\frac{3}{110}\right)\)
\(\chi_{5175}(992,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{660}\right)\)	\(e\left(\frac{179}{330}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{179}{220}\right)\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{571}{660}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{9}{220}\right)\)	\(e\left(\frac{67}{110}\right)\)

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First 31 of 160 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	5175.dq
Modulus	$5175$
Conductor	$5175$
Order	$660$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(5175\)
Conductor:	\(5175\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(660\)	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)