LMFDB - Dirichlet character orbit 14157.il

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(14157, base_ring=CyclotomicField(330)) M = H._module chi = DirichletCharacter(H, M([165,147,55])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(17,14157)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$14157$
Conductor:	$4719$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$330$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4719.dm	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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$14$	$16$	$17$	$19$
$\chi_{14157}(17,\cdot)$	$1$	$1$	$e\left(\frac{37}{330}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{157}{165}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{74}{165}\right)$	$e\left(\frac{109}{165}\right)$	$e\left(\frac{133}{165}\right)$
$\chi_{14157}(62,\cdot)$	$1$	$1$	$e\left(\frac{41}{330}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{134}{165}\right)$
$\chi_{14157}(134,\cdot)$	$1$	$1$	$e\left(\frac{193}{330}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{43}{165}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{56}{165}\right)$	$e\left(\frac{136}{165}\right)$	$e\left(\frac{7}{165}\right)$
$\chi_{14157}(413,\cdot)$	$1$	$1$	$e\left(\frac{227}{330}\right)$	$e\left(\frac{62}{165}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{107}{165}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{89}{165}\right)$	$e\left(\frac{98}{165}\right)$
$\chi_{14157}(530,\cdot)$	$1$	$1$	$e\left(\frac{323}{330}\right)$	$e\left(\frac{158}{165}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{151}{165}\right)$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{122}{165}\right)$
$\chi_{14157}(953,\cdot)$	$1$	$1$	$e\left(\frac{211}{330}\right)$	$e\left(\frac{46}{165}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{106}{165}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{92}{165}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{94}{165}\right)$
$\chi_{14157}(998,\cdot)$	$1$	$1$	$e\left(\frac{269}{330}\right)$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{89}{165}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{43}{165}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{26}{165}\right)$
$\chi_{14157}(1349,\cdot)$	$1$	$1$	$e\left(\frac{311}{330}\right)$	$e\left(\frac{146}{165}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{71}{165}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{127}{165}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{119}{165}\right)$
$\chi_{14157}(1421,\cdot)$	$1$	$1$	$e\left(\frac{313}{330}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{106}{165}\right)$	$e\left(\frac{37}{165}\right)$
$\chi_{14157}(1700,\cdot)$	$1$	$1$	$e\left(\frac{47}{330}\right)$	$e\left(\frac{47}{165}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{137}{165}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{94}{165}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{53}{165}\right)$
$\chi_{14157}(1817,\cdot)$	$1$	$1$	$e\left(\frac{113}{330}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{101}{165}\right)$	$e\left(\frac{152}{165}\right)$
$\chi_{14157}(1889,\cdot)$	$1$	$1$	$e\left(\frac{19}{330}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{94}{165}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{46}{165}\right)$
$\chi_{14157}(2240,\cdot)$	$1$	$1$	$e\left(\frac{151}{330}\right)$	$e\left(\frac{151}{165}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{137}{165}\right)$	$e\left(\frac{97}{165}\right)$	$e\left(\frac{79}{165}\right)$
$\chi_{14157}(2285,\cdot)$	$1$	$1$	$e\left(\frac{299}{330}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{29}{165}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{116}{165}\right)$
$\chi_{14157}(2591,\cdot)$	$1$	$1$	$e\left(\frac{7}{330}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{52}{165}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{34}{165}\right)$	$e\left(\frac{43}{165}\right)$
$\chi_{14157}(2636,\cdot)$	$1$	$1$	$e\left(\frac{251}{330}\right)$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{26}{165}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{17}{165}\right)$	$e\left(\frac{104}{165}\right)$
$\chi_{14157}(2708,\cdot)$	$1$	$1$	$e\left(\frac{103}{330}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{58}{165}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{67}{165}\right)$
$\chi_{14157}(2987,\cdot)$	$1$	$1$	$e\left(\frac{197}{330}\right)$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{8}{165}\right)$
$\chi_{14157}(3104,\cdot)$	$1$	$1$	$e\left(\frac{233}{330}\right)$	$e\left(\frac{68}{165}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{136}{165}\right)$	$e\left(\frac{71}{165}\right)$	$e\left(\frac{17}{165}\right)$
$\chi_{14157}(3176,\cdot)$	$1$	$1$	$e\left(\frac{49}{330}\right)$	$e\left(\frac{49}{165}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{34}{165}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{73}{165}\right)$	$e\left(\frac{136}{165}\right)$
$\chi_{14157}(3527,\cdot)$	$1$	$1$	$e\left(\frac{91}{330}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{17}{165}\right)$	$e\left(\frac{112}{165}\right)$	$e\left(\frac{64}{165}\right)$
$\chi_{14157}(3572,\cdot)$	$1$	$1$	$e\left(\frac{329}{330}\right)$	$e\left(\frac{164}{165}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{41}{165}\right)$
$\chi_{14157}(3878,\cdot)$	$1$	$1$	$e\left(\frac{157}{330}\right)$	$e\left(\frac{157}{165}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{149}{165}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{163}{165}\right)$
$\chi_{14157}(3923,\cdot)$	$1$	$1$	$e\left(\frac{191}{330}\right)$	$e\left(\frac{26}{165}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{146}{165}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{52}{165}\right)$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{89}{165}\right)$
$\chi_{14157}(3995,\cdot)$	$1$	$1$	$e\left(\frac{223}{330}\right)$	$e\left(\frac{58}{165}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{46}{165}\right)$	$e\left(\frac{97}{165}\right)$
$\chi_{14157}(4274,\cdot)$	$1$	$1$	$e\left(\frac{17}{330}\right)$	$e\left(\frac{17}{165}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{34}{165}\right)$	$e\left(\frac{59}{165}\right)$	$e\left(\frac{128}{165}\right)$
$\chi_{14157}(4391,\cdot)$	$1$	$1$	$e\left(\frac{23}{330}\right)$	$e\left(\frac{23}{165}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{53}{165}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{46}{165}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{47}{165}\right)$
$\chi_{14157}(4463,\cdot)$	$1$	$1$	$e\left(\frac{79}{330}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{158}{165}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{61}{165}\right)$
$\chi_{14157}(4814,\cdot)$	$1$	$1$	$e\left(\frac{31}{330}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{136}{165}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{62}{165}\right)$	$e\left(\frac{127}{165}\right)$	$e\left(\frac{49}{165}\right)$
$\chi_{14157}(4859,\cdot)$	$1$	$1$	$e\left(\frac{29}{330}\right)$	$e\left(\frac{29}{165}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{74}{165}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{58}{165}\right)$	$e\left(\frac{23}{165}\right)$	$e\left(\frac{131}{165}\right)$
$\chi_{14157}(5165,\cdot)$	$1$	$1$	$e\left(\frac{307}{330}\right)$	$e\left(\frac{142}{165}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{112}{165}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{119}{165}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{118}{165}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{14157}(17,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{157}{165}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{74}{165}\right)\)	\(e\left(\frac{109}{165}\right)\)	\(e\left(\frac{133}{165}\right)\)
\(\chi_{14157}(62,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{330}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{134}{165}\right)\)
\(\chi_{14157}(134,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{330}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{43}{165}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{56}{165}\right)\)	\(e\left(\frac{136}{165}\right)\)	\(e\left(\frac{7}{165}\right)\)
\(\chi_{14157}(413,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{227}{330}\right)\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{107}{165}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{89}{165}\right)\)	\(e\left(\frac{98}{165}\right)\)
\(\chi_{14157}(530,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{323}{330}\right)\)	\(e\left(\frac{158}{165}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{122}{165}\right)\)
\(\chi_{14157}(953,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{211}{330}\right)\)	\(e\left(\frac{46}{165}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{106}{165}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{92}{165}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{94}{165}\right)\)
\(\chi_{14157}(998,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{269}{330}\right)\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{89}{165}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{43}{165}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{26}{165}\right)\)
\(\chi_{14157}(1349,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{311}{330}\right)\)	\(e\left(\frac{146}{165}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{71}{165}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{127}{165}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{119}{165}\right)\)
\(\chi_{14157}(1421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{313}{330}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{106}{165}\right)\)	\(e\left(\frac{37}{165}\right)\)
\(\chi_{14157}(1700,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{330}\right)\)	\(e\left(\frac{47}{165}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{137}{165}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{94}{165}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{53}{165}\right)\)
\(\chi_{14157}(1817,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{330}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{101}{165}\right)\)	\(e\left(\frac{152}{165}\right)\)
\(\chi_{14157}(1889,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{330}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{94}{165}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{46}{165}\right)\)
\(\chi_{14157}(2240,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{330}\right)\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{137}{165}\right)\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{79}{165}\right)\)
\(\chi_{14157}(2285,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{299}{330}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{29}{165}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{116}{165}\right)\)
\(\chi_{14157}(2591,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{330}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{52}{165}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{34}{165}\right)\)	\(e\left(\frac{43}{165}\right)\)
\(\chi_{14157}(2636,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{251}{330}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{26}{165}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{17}{165}\right)\)	\(e\left(\frac{104}{165}\right)\)
\(\chi_{14157}(2708,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{330}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{67}{165}\right)\)
\(\chi_{14157}(2987,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{330}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{8}{165}\right)\)
\(\chi_{14157}(3104,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{233}{330}\right)\)	\(e\left(\frac{68}{165}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{136}{165}\right)\)	\(e\left(\frac{71}{165}\right)\)	\(e\left(\frac{17}{165}\right)\)
\(\chi_{14157}(3176,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{330}\right)\)	\(e\left(\frac{49}{165}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{34}{165}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{73}{165}\right)\)	\(e\left(\frac{136}{165}\right)\)
\(\chi_{14157}(3527,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{330}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{17}{165}\right)\)	\(e\left(\frac{112}{165}\right)\)	\(e\left(\frac{64}{165}\right)\)
\(\chi_{14157}(3572,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{329}{330}\right)\)	\(e\left(\frac{164}{165}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{41}{165}\right)\)
\(\chi_{14157}(3878,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{330}\right)\)	\(e\left(\frac{157}{165}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{149}{165}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{163}{165}\right)\)
\(\chi_{14157}(3923,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{330}\right)\)	\(e\left(\frac{26}{165}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{146}{165}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{52}{165}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{89}{165}\right)\)
\(\chi_{14157}(3995,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{223}{330}\right)\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{46}{165}\right)\)	\(e\left(\frac{97}{165}\right)\)
\(\chi_{14157}(4274,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{330}\right)\)	\(e\left(\frac{17}{165}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{34}{165}\right)\)	\(e\left(\frac{59}{165}\right)\)	\(e\left(\frac{128}{165}\right)\)
\(\chi_{14157}(4391,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{330}\right)\)	\(e\left(\frac{23}{165}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{53}{165}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{46}{165}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{47}{165}\right)\)
\(\chi_{14157}(4463,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{330}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{158}{165}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{61}{165}\right)\)
\(\chi_{14157}(4814,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{330}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{136}{165}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{127}{165}\right)\)	\(e\left(\frac{49}{165}\right)\)
\(\chi_{14157}(4859,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{330}\right)\)	\(e\left(\frac{29}{165}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{74}{165}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{23}{165}\right)\)	\(e\left(\frac{131}{165}\right)\)
\(\chi_{14157}(5165,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{307}{330}\right)\)	\(e\left(\frac{142}{165}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{112}{165}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{119}{165}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{118}{165}\right)\)

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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	14157.il
Modulus	$14157$
Conductor	$4719$
Order	$330$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(14157\)
Conductor:	\(4719\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(330\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4719.dm	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)