LMFDB - Dirichlet character orbit 7865.fv

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7865, base_ring=CyclotomicField(660)) M = H._module chi = DirichletCharacter(H, M([330,498,275])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(19,7865)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$7865$
Conductor:	$7865$	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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$12$	$14$	$16$
$\chi_{7865}(19,\cdot)$	$1$	$1$	$e\left(\frac{443}{660}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{113}{330}\right)$	$e\left(\frac{157}{660}\right)$	$e\left(\frac{241}{660}\right)$	$e\left(\frac{3}{220}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{113}{165}\right)$
$\chi_{7865}(24,\cdot)$	$1$	$1$	$e\left(\frac{601}{660}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{271}{330}\right)$	$e\left(\frac{359}{660}\right)$	$e\left(\frac{467}{660}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{106}{165}\right)$
$\chi_{7865}(84,\cdot)$	$1$	$1$	$e\left(\frac{527}{660}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{197}{330}\right)$	$e\left(\frac{373}{660}\right)$	$e\left(\frac{169}{660}\right)$	$e\left(\frac{87}{220}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{32}{165}\right)$
$\chi_{7865}(149,\cdot)$	$1$	$1$	$e\left(\frac{659}{660}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{329}{330}\right)$	$e\left(\frac{241}{660}\right)$	$e\left(\frac{433}{660}\right)$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{164}{165}\right)$
$\chi_{7865}(184,\cdot)$	$1$	$1$	$e\left(\frac{163}{660}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{163}{330}\right)$	$e\left(\frac{317}{660}\right)$	$e\left(\frac{41}{660}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{163}{165}\right)$
$\chi_{7865}(189,\cdot)$	$1$	$1$	$e\left(\frac{581}{660}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{251}{330}\right)$	$e\left(\frac{559}{660}\right)$	$e\left(\frac{547}{660}\right)$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{86}{165}\right)$
$\chi_{7865}(249,\cdot)$	$1$	$1$	$e\left(\frac{427}{660}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{97}{330}\right)$	$e\left(\frac{53}{660}\right)$	$e\left(\frac{569}{660}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{97}{165}\right)$
$\chi_{7865}(314,\cdot)$	$1$	$1$	$e\left(\frac{139}{660}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{139}{330}\right)$	$e\left(\frac{161}{660}\right)$	$e\left(\frac{533}{660}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{139}{165}\right)$
$\chi_{7865}(349,\cdot)$	$1$	$1$	$e\left(\frac{433}{660}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{103}{330}\right)$	$e\left(\frac{587}{660}\right)$	$e\left(\frac{611}{660}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{103}{165}\right)$
$\chi_{7865}(409,\cdot)$	$1$	$1$	$e\left(\frac{371}{660}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{41}{330}\right)$	$e\left(\frac{349}{660}\right)$	$e\left(\frac{397}{660}\right)$	$e\left(\frac{151}{220}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{41}{165}\right)$
$\chi_{7865}(414,\cdot)$	$1$	$1$	$e\left(\frac{217}{660}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{217}{330}\right)$	$e\left(\frac{503}{660}\right)$	$e\left(\frac{419}{660}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{52}{165}\right)$
$\chi_{7865}(479,\cdot)$	$1$	$1$	$e\left(\frac{169}{660}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{169}{330}\right)$	$e\left(\frac{191}{660}\right)$	$e\left(\frac{83}{660}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{4}{165}\right)$
$\chi_{7865}(514,\cdot)$	$1$	$1$	$e\left(\frac{593}{660}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{307}{660}\right)$	$e\left(\frac{631}{660}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{98}{165}\right)$
$\chi_{7865}(574,\cdot)$	$1$	$1$	$e\left(\frac{571}{660}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{241}{330}\right)$	$e\left(\frac{329}{660}\right)$	$e\left(\frac{257}{660}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{76}{165}\right)$
$\chi_{7865}(579,\cdot)$	$1$	$1$	$e\left(\frac{557}{660}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{227}{330}\right)$	$e\left(\frac{403}{660}\right)$	$e\left(\frac{379}{660}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{62}{165}\right)$
$\chi_{7865}(644,\cdot)$	$1$	$1$	$e\left(\frac{89}{660}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{89}{330}\right)$	$e\left(\frac{331}{660}\right)$	$e\left(\frac{403}{660}\right)$	$e\left(\frac{89}{220}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{89}{165}\right)$
$\chi_{7865}(734,\cdot)$	$1$	$1$	$e\left(\frac{623}{660}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{293}{330}\right)$	$e\left(\frac{337}{660}\right)$	$e\left(\frac{181}{660}\right)$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{128}{165}\right)$
$\chi_{7865}(739,\cdot)$	$1$	$1$	$e\left(\frac{1}{660}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{419}{660}\right)$	$e\left(\frac{227}{660}\right)$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{1}{165}\right)$
$\chi_{7865}(799,\cdot)$	$1$	$1$	$e\left(\frac{167}{660}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{167}{330}\right)$	$e\left(\frac{13}{660}\right)$	$e\left(\frac{289}{660}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{2}{165}\right)$
$\chi_{7865}(864,\cdot)$	$1$	$1$	$e\left(\frac{239}{660}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{239}{330}\right)$	$e\left(\frac{481}{660}\right)$	$e\left(\frac{133}{660}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{74}{165}\right)$
$\chi_{7865}(899,\cdot)$	$1$	$1$	$e\left(\frac{343}{660}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{330}\right)$	$e\left(\frac{497}{660}\right)$	$e\left(\frac{641}{660}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{13}{165}\right)$
$\chi_{7865}(904,\cdot)$	$1$	$1$	$e\left(\frac{641}{660}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{311}{330}\right)$	$e\left(\frac{619}{660}\right)$	$e\left(\frac{307}{660}\right)$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{146}{165}\right)$
$\chi_{7865}(964,\cdot)$	$1$	$1$	$e\left(\frac{67}{660}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{67}{330}\right)$	$e\left(\frac{353}{660}\right)$	$e\left(\frac{29}{660}\right)$	$e\left(\frac{67}{220}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{67}{165}\right)$
$\chi_{7865}(1029,\cdot)$	$1$	$1$	$e\left(\frac{379}{660}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{49}{330}\right)$	$e\left(\frac{401}{660}\right)$	$e\left(\frac{233}{660}\right)$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{49}{165}\right)$
$\chi_{7865}(1064,\cdot)$	$1$	$1$	$e\left(\frac{613}{660}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{283}{330}\right)$	$e\left(\frac{107}{660}\right)$	$e\left(\frac{551}{660}\right)$	$e\left(\frac{173}{220}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{118}{165}\right)$
$\chi_{7865}(1124,\cdot)$	$1$	$1$	$e\left(\frac{431}{660}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{101}{330}\right)$	$e\left(\frac{409}{660}\right)$	$e\left(\frac{157}{660}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{101}{165}\right)$
$\chi_{7865}(1194,\cdot)$	$1$	$1$	$e\left(\frac{409}{660}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{79}{330}\right)$	$e\left(\frac{431}{660}\right)$	$e\left(\frac{443}{660}\right)$	$e\left(\frac{189}{220}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{79}{165}\right)$
$\chi_{7865}(1229,\cdot)$	$1$	$1$	$e\left(\frac{113}{660}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{113}{330}\right)$	$e\left(\frac{487}{660}\right)$	$e\left(\frac{571}{660}\right)$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{113}{165}\right)$
$\chi_{7865}(1289,\cdot)$	$1$	$1$	$e\left(\frac{631}{660}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{301}{330}\right)$	$e\left(\frac{389}{660}\right)$	$e\left(\frac{17}{660}\right)$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{136}{165}\right)$
$\chi_{7865}(1294,\cdot)$	$1$	$1$	$e\left(\frac{197}{660}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{197}{330}\right)$	$e\left(\frac{43}{660}\right)$	$e\left(\frac{499}{660}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{32}{165}\right)$
$\chi_{7865}(1359,\cdot)$	$1$	$1$	$e\left(\frac{329}{660}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{329}{330}\right)$	$e\left(\frac{571}{660}\right)$	$e\left(\frac{103}{660}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{164}{165}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(12\)	\(14\)	\(16\)
\(\chi_{7865}(19,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{443}{660}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{113}{330}\right)\)	\(e\left(\frac{157}{660}\right)\)	\(e\left(\frac{241}{660}\right)\)	\(e\left(\frac{3}{220}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{113}{165}\right)\)
\(\chi_{7865}(24,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{601}{660}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{271}{330}\right)\)	\(e\left(\frac{359}{660}\right)\)	\(e\left(\frac{467}{660}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{106}{165}\right)\)
\(\chi_{7865}(84,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{527}{660}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{197}{330}\right)\)	\(e\left(\frac{373}{660}\right)\)	\(e\left(\frac{169}{660}\right)\)	\(e\left(\frac{87}{220}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{32}{165}\right)\)
\(\chi_{7865}(149,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{659}{660}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{329}{330}\right)\)	\(e\left(\frac{241}{660}\right)\)	\(e\left(\frac{433}{660}\right)\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{164}{165}\right)\)
\(\chi_{7865}(184,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{660}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{163}{330}\right)\)	\(e\left(\frac{317}{660}\right)\)	\(e\left(\frac{41}{660}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{163}{165}\right)\)
\(\chi_{7865}(189,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{581}{660}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{251}{330}\right)\)	\(e\left(\frac{559}{660}\right)\)	\(e\left(\frac{547}{660}\right)\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{86}{165}\right)\)
\(\chi_{7865}(249,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{427}{660}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{97}{330}\right)\)	\(e\left(\frac{53}{660}\right)\)	\(e\left(\frac{569}{660}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{97}{165}\right)\)
\(\chi_{7865}(314,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{660}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{139}{330}\right)\)	\(e\left(\frac{161}{660}\right)\)	\(e\left(\frac{533}{660}\right)\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{139}{165}\right)\)
\(\chi_{7865}(349,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{433}{660}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{103}{330}\right)\)	\(e\left(\frac{587}{660}\right)\)	\(e\left(\frac{611}{660}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{103}{165}\right)\)
\(\chi_{7865}(409,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{371}{660}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{41}{330}\right)\)	\(e\left(\frac{349}{660}\right)\)	\(e\left(\frac{397}{660}\right)\)	\(e\left(\frac{151}{220}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{41}{165}\right)\)
\(\chi_{7865}(414,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{217}{660}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{217}{330}\right)\)	\(e\left(\frac{503}{660}\right)\)	\(e\left(\frac{419}{660}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{52}{165}\right)\)
\(\chi_{7865}(479,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{660}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{169}{330}\right)\)	\(e\left(\frac{191}{660}\right)\)	\(e\left(\frac{83}{660}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{4}{165}\right)\)
\(\chi_{7865}(514,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{593}{660}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{307}{660}\right)\)	\(e\left(\frac{631}{660}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{98}{165}\right)\)
\(\chi_{7865}(574,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{571}{660}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{241}{330}\right)\)	\(e\left(\frac{329}{660}\right)\)	\(e\left(\frac{257}{660}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{76}{165}\right)\)
\(\chi_{7865}(579,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{557}{660}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{227}{330}\right)\)	\(e\left(\frac{403}{660}\right)\)	\(e\left(\frac{379}{660}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{62}{165}\right)\)
\(\chi_{7865}(644,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{660}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{89}{330}\right)\)	\(e\left(\frac{331}{660}\right)\)	\(e\left(\frac{403}{660}\right)\)	\(e\left(\frac{89}{220}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{89}{165}\right)\)
\(\chi_{7865}(734,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{623}{660}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{293}{330}\right)\)	\(e\left(\frac{337}{660}\right)\)	\(e\left(\frac{181}{660}\right)\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{128}{165}\right)\)
\(\chi_{7865}(739,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{660}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{419}{660}\right)\)	\(e\left(\frac{227}{660}\right)\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{1}{165}\right)\)
\(\chi_{7865}(799,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{167}{660}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{167}{330}\right)\)	\(e\left(\frac{13}{660}\right)\)	\(e\left(\frac{289}{660}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{2}{165}\right)\)
\(\chi_{7865}(864,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{239}{660}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{239}{330}\right)\)	\(e\left(\frac{481}{660}\right)\)	\(e\left(\frac{133}{660}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{74}{165}\right)\)
\(\chi_{7865}(899,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{343}{660}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{330}\right)\)	\(e\left(\frac{497}{660}\right)\)	\(e\left(\frac{641}{660}\right)\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{13}{165}\right)\)
\(\chi_{7865}(904,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{641}{660}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{311}{330}\right)\)	\(e\left(\frac{619}{660}\right)\)	\(e\left(\frac{307}{660}\right)\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{146}{165}\right)\)
\(\chi_{7865}(964,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{660}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{67}{330}\right)\)	\(e\left(\frac{353}{660}\right)\)	\(e\left(\frac{29}{660}\right)\)	\(e\left(\frac{67}{220}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{67}{165}\right)\)
\(\chi_{7865}(1029,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{379}{660}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{49}{330}\right)\)	\(e\left(\frac{401}{660}\right)\)	\(e\left(\frac{233}{660}\right)\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{49}{165}\right)\)
\(\chi_{7865}(1064,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{613}{660}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{283}{330}\right)\)	\(e\left(\frac{107}{660}\right)\)	\(e\left(\frac{551}{660}\right)\)	\(e\left(\frac{173}{220}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{118}{165}\right)\)
\(\chi_{7865}(1124,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{431}{660}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{101}{330}\right)\)	\(e\left(\frac{409}{660}\right)\)	\(e\left(\frac{157}{660}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{101}{165}\right)\)
\(\chi_{7865}(1194,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{409}{660}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{79}{330}\right)\)	\(e\left(\frac{431}{660}\right)\)	\(e\left(\frac{443}{660}\right)\)	\(e\left(\frac{189}{220}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{79}{165}\right)\)
\(\chi_{7865}(1229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{660}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{113}{330}\right)\)	\(e\left(\frac{487}{660}\right)\)	\(e\left(\frac{571}{660}\right)\)	\(e\left(\frac{113}{220}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{113}{165}\right)\)
\(\chi_{7865}(1289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{631}{660}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{301}{330}\right)\)	\(e\left(\frac{389}{660}\right)\)	\(e\left(\frac{17}{660}\right)\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{136}{165}\right)\)
\(\chi_{7865}(1294,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{660}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{197}{330}\right)\)	\(e\left(\frac{43}{660}\right)\)	\(e\left(\frac{499}{660}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{32}{165}\right)\)
\(\chi_{7865}(1359,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{329}{660}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{329}{330}\right)\)	\(e\left(\frac{571}{660}\right)\)	\(e\left(\frac{103}{660}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{164}{165}\right)\)

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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	7865.fv
Modulus	$7865$
Conductor	$7865$
Order	$660$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(7865\)
Conductor:	\(7865\)	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)