LMFDB - Dirichlet character orbit 8954.co

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8954, base_ring=CyclotomicField(660)) M = H._module chi = DirichletCharacter(H, M([102,385])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(29,8954)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8954$
Conductor:	$4477$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$660$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4477.co	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 30 of 160 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$19$	$21$	$23$
$\chi_{8954}(29,\cdot)$	$1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{563}{660}\right)$	$e\left(\frac{247}{330}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{17}{660}\right)$	$e\left(\frac{409}{660}\right)$	$e\left(\frac{433}{660}\right)$	$e\left(\frac{161}{660}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{25}{44}\right)$
$\chi_{8954}(51,\cdot)$	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{163}{660}\right)$	$e\left(\frac{17}{330}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{577}{660}\right)$	$e\left(\frac{449}{660}\right)$	$e\left(\frac{293}{660}\right)$	$e\left(\frac{301}{660}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{41}{44}\right)$
$\chi_{8954}(171,\cdot)$	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{541}{660}\right)$	$e\left(\frac{269}{330}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{259}{660}\right)$	$e\left(\frac{563}{660}\right)$	$e\left(\frac{191}{660}\right)$	$e\left(\frac{7}{660}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{3}{44}\right)$
$\chi_{8954}(193,\cdot)$	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{221}{660}\right)$	$e\left(\frac{19}{330}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{179}{660}\right)$	$e\left(\frac{463}{660}\right)$	$e\left(\frac{211}{660}\right)$	$e\left(\frac{647}{660}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{7}{44}\right)$
$\chi_{8954}(325,\cdot)$	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{611}{660}\right)$	$e\left(\frac{169}{330}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{29}{660}\right)$	$e\left(\frac{193}{660}\right)$	$e\left(\frac{1}{660}\right)$	$e\left(\frac{197}{660}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{9}{44}\right)$
$\chi_{8954}(347,\cdot)$	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{511}{660}\right)$	$e\left(\frac{29}{330}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{169}{660}\right)$	$e\left(\frac{533}{660}\right)$	$e\left(\frac{461}{660}\right)$	$e\left(\frac{397}{660}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{13}{44}\right)$
$\chi_{8954}(393,\cdot)$	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{157}{660}\right)$	$e\left(\frac{233}{330}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{163}{660}\right)$	$e\left(\frac{311}{660}\right)$	$e\left(\frac{347}{660}\right)$	$e\left(\frac{379}{660}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{43}{44}\right)$
$\chi_{8954}(415,\cdot)$	$1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{137}{660}\right)$	$e\left(\frac{73}{330}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{323}{660}\right)$	$e\left(\frac{511}{660}\right)$	$e\left(\frac{307}{660}\right)$	$e\left(\frac{419}{660}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{35}{44}\right)$
$\chi_{8954}(541,\cdot)$	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{409}{660}\right)$	$e\left(\frac{71}{330}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{391}{660}\right)$	$e\left(\frac{167}{660}\right)$	$e\left(\frac{59}{660}\right)$	$e\left(\frac{403}{660}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{3}{44}\right)$
$\chi_{8954}(547,\cdot)$	$1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{347}{660}\right)$	$e\left(\frac{103}{330}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{293}{660}\right)$	$e\left(\frac{61}{660}\right)$	$e\left(\frac{397}{660}\right)$	$e\left(\frac{329}{660}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{9}{44}\right)$
$\chi_{8954}(563,\cdot)$	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{329}{660}\right)$	$e\left(\frac{91}{330}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{371}{660}\right)$	$e\left(\frac{307}{660}\right)$	$e\left(\frac{559}{660}\right)$	$e\left(\frac{563}{660}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{15}{44}\right)$
$\chi_{8954}(569,\cdot)$	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{547}{660}\right)$	$e\left(\frac{53}{330}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{660}\right)$	$e\left(\frac{41}{660}\right)$	$e\left(\frac{137}{660}\right)$	$e\left(\frac{589}{660}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{1}{44}\right)$
$\chi_{8954}(689,\cdot)$	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{553}{660}\right)$	$e\left(\frac{167}{330}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{427}{660}\right)$	$e\left(\frac{179}{660}\right)$	$e\left(\frac{83}{660}\right)$	$e\left(\frac{511}{660}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{43}{44}\right)$
$\chi_{8954}(695,\cdot)$	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{179}{660}\right)$	$e\left(\frac{211}{330}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{581}{660}\right)$	$e\left(\frac{157}{660}\right)$	$e\left(\frac{589}{660}\right)$	$e\left(\frac{533}{660}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{21}{44}\right)$
$\chi_{8954}(711,\cdot)$	$1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{593}{660}\right)$	$e\left(\frac{157}{330}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{107}{660}\right)$	$e\left(\frac{439}{660}\right)$	$e\left(\frac{163}{660}\right)$	$e\left(\frac{431}{660}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{15}{44}\right)$
$\chi_{8954}(843,\cdot)$	$1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{503}{660}\right)$	$e\left(\frac{97}{330}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{497}{660}\right)$	$e\left(\frac{349}{660}\right)$	$e\left(\frac{313}{660}\right)$	$e\left(\frac{281}{660}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{1}{44}\right)$
$\chi_{8954}(865,\cdot)$	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{103}{660}\right)$	$e\left(\frac{197}{330}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{397}{660}\right)$	$e\left(\frac{389}{660}\right)$	$e\left(\frac{173}{660}\right)$	$e\left(\frac{421}{660}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{17}{44}\right)$
$\chi_{8954}(985,\cdot)$	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{361}{660}\right)$	$e\left(\frac{149}{330}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{379}{660}\right)$	$e\left(\frac{383}{660}\right)$	$e\left(\frac{491}{660}\right)$	$e\left(\frac{367}{660}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{19}{44}\right)$
$\chi_{8954}(1007,\cdot)$	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{41}{660}\right)$	$e\left(\frac{229}{330}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{299}{660}\right)$	$e\left(\frac{283}{660}\right)$	$e\left(\frac{511}{660}\right)$	$e\left(\frac{347}{660}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{23}{44}\right)$
$\chi_{8954}(1139,\cdot)$	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{431}{660}\right)$	$e\left(\frac{49}{330}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{149}{660}\right)$	$e\left(\frac{13}{660}\right)$	$e\left(\frac{301}{660}\right)$	$e\left(\frac{557}{660}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{25}{44}\right)$
$\chi_{8954}(1161,\cdot)$	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{331}{660}\right)$	$e\left(\frac{239}{330}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{289}{660}\right)$	$e\left(\frac{353}{660}\right)$	$e\left(\frac{101}{660}\right)$	$e\left(\frac{97}{660}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{29}{44}\right)$
$\chi_{8954}(1229,\cdot)$	$1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{497}{660}\right)$	$e\left(\frac{313}{330}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{83}{660}\right)$	$e\left(\frac{211}{660}\right)$	$e\left(\frac{367}{660}\right)$	$e\left(\frac{359}{660}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{3}{44}\right)$
$\chi_{8954}(1355,\cdot)$	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{529}{660}\right)$	$e\left(\frac{41}{330}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{91}{660}\right)$	$e\left(\frac{287}{660}\right)$	$e\left(\frac{299}{660}\right)$	$e\left(\frac{163}{660}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{7}{44}\right)$
$\chi_{8954}(1361,\cdot)$	$1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{47}{660}\right)$	$e\left(\frac{13}{330}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{53}{660}\right)$	$e\left(\frac{421}{660}\right)$	$e\left(\frac{457}{660}\right)$	$e\left(\frac{269}{660}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{21}{44}\right)$
$\chi_{8954}(1377,\cdot)$	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{449}{660}\right)$	$e\left(\frac{61}{330}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{71}{660}\right)$	$e\left(\frac{427}{660}\right)$	$e\left(\frac{139}{660}\right)$	$e\left(\frac{323}{660}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{19}{44}\right)$
$\chi_{8954}(1383,\cdot)$	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{247}{660}\right)$	$e\left(\frac{293}{330}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{433}{660}\right)$	$e\left(\frac{401}{660}\right)$	$e\left(\frac{197}{660}\right)$	$e\left(\frac{529}{660}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{13}{44}\right)$
$\chi_{8954}(1503,\cdot)$	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{493}{660}\right)$	$e\left(\frac{17}{330}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{247}{660}\right)$	$e\left(\frac{119}{660}\right)$	$e\left(\frac{623}{660}\right)$	$e\left(\frac{631}{660}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{19}{44}\right)$
$\chi_{8954}(1509,\cdot)$	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{299}{660}\right)$	$e\left(\frac{181}{330}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{281}{660}\right)$	$e\left(\frac{277}{660}\right)$	$e\left(\frac{169}{660}\right)$	$e\left(\frac{293}{660}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{25}{44}\right)$
$\chi_{8954}(1525,\cdot)$	$1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{533}{660}\right)$	$e\left(\frac{7}{330}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{587}{660}\right)$	$e\left(\frac{379}{660}\right)$	$e\left(\frac{43}{660}\right)$	$e\left(\frac{551}{660}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{35}{44}\right)$
$\chi_{8954}(1531,\cdot)$	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{439}{660}\right)$	$e\left(\frac{311}{330}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{481}{660}\right)$	$e\left(\frac{197}{660}\right)$	$e\left(\frac{449}{660}\right)$	$e\left(\frac{13}{660}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{37}{44}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{8954}(29,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{563}{660}\right)\)	\(e\left(\frac{247}{330}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{17}{660}\right)\)	\(e\left(\frac{409}{660}\right)\)	\(e\left(\frac{433}{660}\right)\)	\(e\left(\frac{161}{660}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{25}{44}\right)\)
\(\chi_{8954}(51,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{163}{660}\right)\)	\(e\left(\frac{17}{330}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{577}{660}\right)\)	\(e\left(\frac{449}{660}\right)\)	\(e\left(\frac{293}{660}\right)\)	\(e\left(\frac{301}{660}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{41}{44}\right)\)
\(\chi_{8954}(171,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{541}{660}\right)\)	\(e\left(\frac{269}{330}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{259}{660}\right)\)	\(e\left(\frac{563}{660}\right)\)	\(e\left(\frac{191}{660}\right)\)	\(e\left(\frac{7}{660}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{3}{44}\right)\)
\(\chi_{8954}(193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{221}{660}\right)\)	\(e\left(\frac{19}{330}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{179}{660}\right)\)	\(e\left(\frac{463}{660}\right)\)	\(e\left(\frac{211}{660}\right)\)	\(e\left(\frac{647}{660}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{7}{44}\right)\)
\(\chi_{8954}(325,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{611}{660}\right)\)	\(e\left(\frac{169}{330}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{29}{660}\right)\)	\(e\left(\frac{193}{660}\right)\)	\(e\left(\frac{1}{660}\right)\)	\(e\left(\frac{197}{660}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{9}{44}\right)\)
\(\chi_{8954}(347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{511}{660}\right)\)	\(e\left(\frac{29}{330}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{169}{660}\right)\)	\(e\left(\frac{533}{660}\right)\)	\(e\left(\frac{461}{660}\right)\)	\(e\left(\frac{397}{660}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{13}{44}\right)\)
\(\chi_{8954}(393,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{157}{660}\right)\)	\(e\left(\frac{233}{330}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{163}{660}\right)\)	\(e\left(\frac{311}{660}\right)\)	\(e\left(\frac{347}{660}\right)\)	\(e\left(\frac{379}{660}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{43}{44}\right)\)
\(\chi_{8954}(415,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{137}{660}\right)\)	\(e\left(\frac{73}{330}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{323}{660}\right)\)	\(e\left(\frac{511}{660}\right)\)	\(e\left(\frac{307}{660}\right)\)	\(e\left(\frac{419}{660}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{35}{44}\right)\)
\(\chi_{8954}(541,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{409}{660}\right)\)	\(e\left(\frac{71}{330}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{391}{660}\right)\)	\(e\left(\frac{167}{660}\right)\)	\(e\left(\frac{59}{660}\right)\)	\(e\left(\frac{403}{660}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{3}{44}\right)\)
\(\chi_{8954}(547,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{347}{660}\right)\)	\(e\left(\frac{103}{330}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{293}{660}\right)\)	\(e\left(\frac{61}{660}\right)\)	\(e\left(\frac{397}{660}\right)\)	\(e\left(\frac{329}{660}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{9}{44}\right)\)
\(\chi_{8954}(563,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{329}{660}\right)\)	\(e\left(\frac{91}{330}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{371}{660}\right)\)	\(e\left(\frac{307}{660}\right)\)	\(e\left(\frac{559}{660}\right)\)	\(e\left(\frac{563}{660}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{15}{44}\right)\)
\(\chi_{8954}(569,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{547}{660}\right)\)	\(e\left(\frac{53}{330}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{660}\right)\)	\(e\left(\frac{41}{660}\right)\)	\(e\left(\frac{137}{660}\right)\)	\(e\left(\frac{589}{660}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{1}{44}\right)\)
\(\chi_{8954}(689,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{553}{660}\right)\)	\(e\left(\frac{167}{330}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{427}{660}\right)\)	\(e\left(\frac{179}{660}\right)\)	\(e\left(\frac{83}{660}\right)\)	\(e\left(\frac{511}{660}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{43}{44}\right)\)
\(\chi_{8954}(695,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{179}{660}\right)\)	\(e\left(\frac{211}{330}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{581}{660}\right)\)	\(e\left(\frac{157}{660}\right)\)	\(e\left(\frac{589}{660}\right)\)	\(e\left(\frac{533}{660}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{21}{44}\right)\)
\(\chi_{8954}(711,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{593}{660}\right)\)	\(e\left(\frac{157}{330}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{107}{660}\right)\)	\(e\left(\frac{439}{660}\right)\)	\(e\left(\frac{163}{660}\right)\)	\(e\left(\frac{431}{660}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{15}{44}\right)\)
\(\chi_{8954}(843,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{503}{660}\right)\)	\(e\left(\frac{97}{330}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{497}{660}\right)\)	\(e\left(\frac{349}{660}\right)\)	\(e\left(\frac{313}{660}\right)\)	\(e\left(\frac{281}{660}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{1}{44}\right)\)
\(\chi_{8954}(865,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{103}{660}\right)\)	\(e\left(\frac{197}{330}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{397}{660}\right)\)	\(e\left(\frac{389}{660}\right)\)	\(e\left(\frac{173}{660}\right)\)	\(e\left(\frac{421}{660}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{17}{44}\right)\)
\(\chi_{8954}(985,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{361}{660}\right)\)	\(e\left(\frac{149}{330}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{379}{660}\right)\)	\(e\left(\frac{383}{660}\right)\)	\(e\left(\frac{491}{660}\right)\)	\(e\left(\frac{367}{660}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{19}{44}\right)\)
\(\chi_{8954}(1007,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{41}{660}\right)\)	\(e\left(\frac{229}{330}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{299}{660}\right)\)	\(e\left(\frac{283}{660}\right)\)	\(e\left(\frac{511}{660}\right)\)	\(e\left(\frac{347}{660}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{23}{44}\right)\)
\(\chi_{8954}(1139,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{431}{660}\right)\)	\(e\left(\frac{49}{330}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{149}{660}\right)\)	\(e\left(\frac{13}{660}\right)\)	\(e\left(\frac{301}{660}\right)\)	\(e\left(\frac{557}{660}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{25}{44}\right)\)
\(\chi_{8954}(1161,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{331}{660}\right)\)	\(e\left(\frac{239}{330}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{289}{660}\right)\)	\(e\left(\frac{353}{660}\right)\)	\(e\left(\frac{101}{660}\right)\)	\(e\left(\frac{97}{660}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{29}{44}\right)\)
\(\chi_{8954}(1229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{497}{660}\right)\)	\(e\left(\frac{313}{330}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{83}{660}\right)\)	\(e\left(\frac{211}{660}\right)\)	\(e\left(\frac{367}{660}\right)\)	\(e\left(\frac{359}{660}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{3}{44}\right)\)
\(\chi_{8954}(1355,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{529}{660}\right)\)	\(e\left(\frac{41}{330}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{91}{660}\right)\)	\(e\left(\frac{287}{660}\right)\)	\(e\left(\frac{299}{660}\right)\)	\(e\left(\frac{163}{660}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{7}{44}\right)\)
\(\chi_{8954}(1361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{47}{660}\right)\)	\(e\left(\frac{13}{330}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{53}{660}\right)\)	\(e\left(\frac{421}{660}\right)\)	\(e\left(\frac{457}{660}\right)\)	\(e\left(\frac{269}{660}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{21}{44}\right)\)
\(\chi_{8954}(1377,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{449}{660}\right)\)	\(e\left(\frac{61}{330}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{71}{660}\right)\)	\(e\left(\frac{427}{660}\right)\)	\(e\left(\frac{139}{660}\right)\)	\(e\left(\frac{323}{660}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{19}{44}\right)\)
\(\chi_{8954}(1383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{247}{660}\right)\)	\(e\left(\frac{293}{330}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{433}{660}\right)\)	\(e\left(\frac{401}{660}\right)\)	\(e\left(\frac{197}{660}\right)\)	\(e\left(\frac{529}{660}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{13}{44}\right)\)
\(\chi_{8954}(1503,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{493}{660}\right)\)	\(e\left(\frac{17}{330}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{247}{660}\right)\)	\(e\left(\frac{119}{660}\right)\)	\(e\left(\frac{623}{660}\right)\)	\(e\left(\frac{631}{660}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{19}{44}\right)\)
\(\chi_{8954}(1509,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{299}{660}\right)\)	\(e\left(\frac{181}{330}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{281}{660}\right)\)	\(e\left(\frac{277}{660}\right)\)	\(e\left(\frac{169}{660}\right)\)	\(e\left(\frac{293}{660}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{25}{44}\right)\)
\(\chi_{8954}(1525,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{533}{660}\right)\)	\(e\left(\frac{7}{330}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{587}{660}\right)\)	\(e\left(\frac{379}{660}\right)\)	\(e\left(\frac{43}{660}\right)\)	\(e\left(\frac{551}{660}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{35}{44}\right)\)
\(\chi_{8954}(1531,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{439}{660}\right)\)	\(e\left(\frac{311}{330}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{481}{660}\right)\)	\(e\left(\frac{197}{660}\right)\)	\(e\left(\frac{449}{660}\right)\)	\(e\left(\frac{13}{660}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{37}{44}\right)\)

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First 30 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	8954.co
Modulus	$8954$
Conductor	$4477$
Order	$660$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(8954\)
Conductor:	\(4477\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(660\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4477.co	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)