LMFDB - Dirichlet character orbit 14157.iq

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(14157, base_ring=CyclotomicField(660)) M = H._module chi = DirichletCharacter(H, M([220,108,275])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(58,14157)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$14157$
Conductor:	$14157$	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:	odd	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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$14$	$16$	$17$	$19$
$\chi_{14157}(58,\cdot)$	$-1$	$1$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{347}{660}\right)$	$e\left(\frac{41}{660}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{161}{165}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{281}{330}\right)$	$e\left(\frac{439}{660}\right)$
$\chi_{14157}(115,\cdot)$	$-1$	$1$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{301}{660}\right)$	$e\left(\frac{163}{660}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{103}{330}\right)$	$e\left(\frac{377}{660}\right)$
$\chi_{14157}(223,\cdot)$	$-1$	$1$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{607}{660}\right)$	$e\left(\frac{241}{660}\right)$	$e\left(\frac{3}{220}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{211}{330}\right)$	$e\left(\frac{359}{660}\right)$
$\chi_{14157}(466,\cdot)$	$-1$	$1$	$e\left(\frac{79}{220}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{433}{660}\right)$	$e\left(\frac{559}{660}\right)$	$e\left(\frac{17}{220}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{34}{165}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{169}{330}\right)$	$e\left(\frac{641}{660}\right)$
$\chi_{14157}(526,\cdot)$	$-1$	$1$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{659}{660}\right)$	$e\left(\frac{17}{660}\right)$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{107}{165}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{197}{330}\right)$	$e\left(\frac{343}{660}\right)$
$\chi_{14157}(553,\cdot)$	$-1$	$1$	$e\left(\frac{151}{220}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{137}{660}\right)$	$e\left(\frac{311}{660}\right)$	$e\left(\frac{13}{220}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{26}{165}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{71}{330}\right)$	$e\left(\frac{529}{660}\right)$
$\chi_{14157}(643,\cdot)$	$-1$	$1$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{611}{660}\right)$	$e\left(\frac{173}{660}\right)$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{83}{330}\right)$	$e\left(\frac{307}{660}\right)$
$\chi_{14157}(691,\cdot)$	$-1$	$1$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{379}{660}\right)$	$e\left(\frac{157}{660}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{247}{330}\right)$	$e\left(\frac{23}{660}\right)$
$\chi_{14157}(808,\cdot)$	$-1$	$1$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{151}{660}\right)$	$e\left(\frac{73}{660}\right)$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{13}{165}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{283}{330}\right)$	$e\left(\frac{347}{660}\right)$
$\chi_{14157}(817,\cdot)$	$-1$	$1$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{157}{660}\right)$	$e\left(\frac{631}{660}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{91}{330}\right)$	$e\left(\frac{269}{660}\right)$
$\chi_{14157}(994,\cdot)$	$-1$	$1$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{23}{660}\right)$	$e\left(\frac{269}{660}\right)$	$e\left(\frac{7}{220}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{89}{330}\right)$	$e\left(\frac{31}{660}\right)$
$\chi_{14157}(1021,\cdot)$	$-1$	$1$	$e\left(\frac{47}{220}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{149}{660}\right)$	$e\left(\frac{107}{660}\right)$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{62}{165}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{17}{330}\right)$	$e\left(\frac{373}{660}\right)$
$\chi_{14157}(1138,\cdot)$	$-1$	$1$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{221}{660}\right)$	$e\left(\frac{203}{660}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{23}{330}\right)$	$e\left(\frac{97}{660}\right)$
$\chi_{14157}(1159,\cdot)$	$-1$	$1$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{163}{660}\right)$	$e\left(\frac{529}{660}\right)$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{49}{165}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{229}{330}\right)$	$e\left(\frac{191}{660}\right)$
$\chi_{14157}(1285,\cdot)$	$-1$	$1$	$e\left(\frac{87}{220}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{229}{660}\right)$	$e\left(\frac{67}{660}\right)$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{97}{330}\right)$	$e\left(\frac{653}{660}\right)$
$\chi_{14157}(1345,\cdot)$	$-1$	$1$	$e\left(\frac{181}{220}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{527}{660}\right)$	$e\left(\frac{281}{660}\right)$	$e\left(\frac{103}{220}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{131}{330}\right)$	$e\left(\frac{79}{660}\right)$
$\chi_{14157}(1402,\cdot)$	$-1$	$1$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{541}{660}\right)$	$e\left(\frac{43}{660}\right)$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{13}{330}\right)$	$e\left(\frac{557}{660}\right)$
$\chi_{14157}(1489,\cdot)$	$-1$	$1$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{113}{660}\right)$	$e\left(\frac{59}{660}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{119}{165}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{179}{330}\right)$	$e\left(\frac{181}{660}\right)$
$\chi_{14157}(1510,\cdot)$	$-1$	$1$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{127}{660}\right)$	$e\left(\frac{481}{660}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{106}{165}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{61}{330}\right)$	$e\left(\frac{659}{660}\right)$
$\chi_{14157}(1753,\cdot)$	$-1$	$1$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{73}{660}\right)$	$e\left(\frac{79}{660}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{109}{165}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{139}{330}\right)$	$e\left(\frac{41}{660}\right)$
$\chi_{14157}(1813,\cdot)$	$-1$	$1$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{59}{660}\right)$	$e\left(\frac{317}{660}\right)$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{257}{330}\right)$	$e\left(\frac{223}{660}\right)$
$\chi_{14157}(1840,\cdot)$	$-1$	$1$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{317}{660}\right)$	$e\left(\frac{551}{660}\right)$	$e\left(\frac{173}{220}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{71}{165}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{251}{330}\right)$	$e\left(\frac{169}{660}\right)$
$\chi_{14157}(1930,\cdot)$	$-1$	$1$	$e\left(\frac{13}{220}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{191}{660}\right)$	$e\left(\frac{53}{660}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{23}{165}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{323}{330}\right)$	$e\left(\frac{487}{660}\right)$
$\chi_{14157}(1978,\cdot)$	$-1$	$1$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{439}{660}\right)$	$e\left(\frac{457}{660}\right)$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{52}{165}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{307}{330}\right)$	$e\left(\frac{563}{660}\right)$
$\chi_{14157}(2095,\cdot)$	$-1$	$1$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{391}{660}\right)$	$e\left(\frac{613}{660}\right)$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{73}{165}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{193}{330}\right)$	$e\left(\frac{527}{660}\right)$
$\chi_{14157}(2104,\cdot)$	$-1$	$1$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{337}{660}\right)$	$e\left(\frac{211}{660}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{271}{330}\right)$	$e\left(\frac{569}{660}\right)$
$\chi_{14157}(2281,\cdot)$	$-1$	$1$	$e\left(\frac{189}{220}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{323}{660}\right)$	$e\left(\frac{449}{660}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{89}{165}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{59}{330}\right)$	$e\left(\frac{91}{660}\right)$
$\chi_{14157}(2425,\cdot)$	$-1$	$1$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{461}{660}\right)$	$e\left(\frac{83}{660}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{8}{165}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{277}{660}\right)$
$\chi_{14157}(2446,\cdot)$	$-1$	$1$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{463}{660}\right)$	$e\left(\frac{49}{660}\right)$	$e\left(\frac{7}{220}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{199}{330}\right)$	$e\left(\frac{251}{660}\right)$
$\chi_{14157}(2572,\cdot)$	$-1$	$1$	$e\left(\frac{7}{220}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{289}{660}\right)$	$e\left(\frac{367}{660}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{97}{165}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{157}{330}\right)$	$e\left(\frac{533}{660}\right)$
$\chi_{14157}(2632,\cdot)$	$-1$	$1$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{47}{660}\right)$	$e\left(\frac{521}{660}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{311}{330}\right)$	$e\left(\frac{379}{660}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{14157}(58,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{347}{660}\right)\)	\(e\left(\frac{41}{660}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{161}{165}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{281}{330}\right)\)	\(e\left(\frac{439}{660}\right)\)
\(\chi_{14157}(115,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{301}{660}\right)\)	\(e\left(\frac{163}{660}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{103}{330}\right)\)	\(e\left(\frac{377}{660}\right)\)
\(\chi_{14157}(223,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{607}{660}\right)\)	\(e\left(\frac{241}{660}\right)\)	\(e\left(\frac{3}{220}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{211}{330}\right)\)	\(e\left(\frac{359}{660}\right)\)
\(\chi_{14157}(466,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{220}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{433}{660}\right)\)	\(e\left(\frac{559}{660}\right)\)	\(e\left(\frac{17}{220}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{34}{165}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{169}{330}\right)\)	\(e\left(\frac{641}{660}\right)\)
\(\chi_{14157}(526,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{659}{660}\right)\)	\(e\left(\frac{17}{660}\right)\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{107}{165}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{197}{330}\right)\)	\(e\left(\frac{343}{660}\right)\)
\(\chi_{14157}(553,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{151}{220}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{137}{660}\right)\)	\(e\left(\frac{311}{660}\right)\)	\(e\left(\frac{13}{220}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{26}{165}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{71}{330}\right)\)	\(e\left(\frac{529}{660}\right)\)
\(\chi_{14157}(643,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{220}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{611}{660}\right)\)	\(e\left(\frac{173}{660}\right)\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{83}{330}\right)\)	\(e\left(\frac{307}{660}\right)\)
\(\chi_{14157}(691,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{379}{660}\right)\)	\(e\left(\frac{157}{660}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{247}{330}\right)\)	\(e\left(\frac{23}{660}\right)\)
\(\chi_{14157}(808,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{151}{660}\right)\)	\(e\left(\frac{73}{660}\right)\)	\(e\left(\frac{199}{220}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{13}{165}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{283}{330}\right)\)	\(e\left(\frac{347}{660}\right)\)
\(\chi_{14157}(817,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{157}{660}\right)\)	\(e\left(\frac{631}{660}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{91}{330}\right)\)	\(e\left(\frac{269}{660}\right)\)
\(\chi_{14157}(994,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{23}{660}\right)\)	\(e\left(\frac{269}{660}\right)\)	\(e\left(\frac{7}{220}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{89}{330}\right)\)	\(e\left(\frac{31}{660}\right)\)
\(\chi_{14157}(1021,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{220}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{149}{660}\right)\)	\(e\left(\frac{107}{660}\right)\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{17}{330}\right)\)	\(e\left(\frac{373}{660}\right)\)
\(\chi_{14157}(1138,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{221}{660}\right)\)	\(e\left(\frac{203}{660}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{23}{330}\right)\)	\(e\left(\frac{97}{660}\right)\)
\(\chi_{14157}(1159,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{163}{660}\right)\)	\(e\left(\frac{529}{660}\right)\)	\(e\left(\frac{107}{220}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{49}{165}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{229}{330}\right)\)	\(e\left(\frac{191}{660}\right)\)
\(\chi_{14157}(1285,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{87}{220}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{229}{660}\right)\)	\(e\left(\frac{67}{660}\right)\)	\(e\left(\frac{41}{220}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{97}{330}\right)\)	\(e\left(\frac{653}{660}\right)\)
\(\chi_{14157}(1345,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{181}{220}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{527}{660}\right)\)	\(e\left(\frac{281}{660}\right)\)	\(e\left(\frac{103}{220}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{131}{330}\right)\)	\(e\left(\frac{79}{660}\right)\)
\(\chi_{14157}(1402,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{541}{660}\right)\)	\(e\left(\frac{43}{660}\right)\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{13}{330}\right)\)	\(e\left(\frac{557}{660}\right)\)
\(\chi_{14157}(1489,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{113}{660}\right)\)	\(e\left(\frac{59}{660}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{119}{165}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{179}{330}\right)\)	\(e\left(\frac{181}{660}\right)\)
\(\chi_{14157}(1510,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{127}{660}\right)\)	\(e\left(\frac{481}{660}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{106}{165}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{61}{330}\right)\)	\(e\left(\frac{659}{660}\right)\)
\(\chi_{14157}(1753,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{73}{660}\right)\)	\(e\left(\frac{79}{660}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{109}{165}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{139}{330}\right)\)	\(e\left(\frac{41}{660}\right)\)
\(\chi_{14157}(1813,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{57}{220}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{59}{660}\right)\)	\(e\left(\frac{317}{660}\right)\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{257}{330}\right)\)	\(e\left(\frac{223}{660}\right)\)
\(\chi_{14157}(1840,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{317}{660}\right)\)	\(e\left(\frac{551}{660}\right)\)	\(e\left(\frac{173}{220}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{71}{165}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{251}{330}\right)\)	\(e\left(\frac{169}{660}\right)\)
\(\chi_{14157}(1930,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{220}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{191}{660}\right)\)	\(e\left(\frac{53}{660}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{23}{165}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{323}{330}\right)\)	\(e\left(\frac{487}{660}\right)\)
\(\chi_{14157}(1978,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{439}{660}\right)\)	\(e\left(\frac{457}{660}\right)\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{52}{165}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{307}{330}\right)\)	\(e\left(\frac{563}{660}\right)\)
\(\chi_{14157}(2095,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{220}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{391}{660}\right)\)	\(e\left(\frac{613}{660}\right)\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{73}{165}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{193}{330}\right)\)	\(e\left(\frac{527}{660}\right)\)
\(\chi_{14157}(2104,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{220}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{337}{660}\right)\)	\(e\left(\frac{211}{660}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{271}{330}\right)\)	\(e\left(\frac{569}{660}\right)\)
\(\chi_{14157}(2281,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{189}{220}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{323}{660}\right)\)	\(e\left(\frac{449}{660}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{89}{165}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{59}{330}\right)\)	\(e\left(\frac{91}{660}\right)\)
\(\chi_{14157}(2425,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{461}{660}\right)\)	\(e\left(\frac{83}{660}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{8}{165}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{277}{660}\right)\)
\(\chi_{14157}(2446,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{463}{660}\right)\)	\(e\left(\frac{49}{660}\right)\)	\(e\left(\frac{7}{220}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{199}{330}\right)\)	\(e\left(\frac{251}{660}\right)\)
\(\chi_{14157}(2572,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{220}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{289}{660}\right)\)	\(e\left(\frac{367}{660}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{157}{330}\right)\)	\(e\left(\frac{533}{660}\right)\)
\(\chi_{14157}(2632,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{47}{660}\right)\)	\(e\left(\frac{521}{660}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{311}{330}\right)\)	\(e\left(\frac{379}{660}\right)\)

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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	14157.iq
Modulus	$14157$
Conductor	$14157$
Order	$660$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(14157\)
Conductor:	\(14157\)	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:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)