LMFDB - Dirichlet character orbit 14157.jc

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(14157, base_ring=CyclotomicField(660)) M = H._module chi = DirichletCharacter(H, M([550,138,55])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(41,14157)) 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$14$	$16$	$17$	$19$
$\chi_{14157}(41,\cdot)$	$-1$	$1$	$e\left(\frac{83}{660}\right)$	$e\left(\frac{83}{330}\right)$	$e\left(\frac{257}{660}\right)$	$e\left(\frac{157}{220}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{277}{330}\right)$	$e\left(\frac{83}{165}\right)$	$e\left(\frac{301}{330}\right)$	$e\left(\frac{509}{660}\right)$
$\chi_{14157}(50,\cdot)$	$-1$	$1$	$e\left(\frac{509}{660}\right)$	$e\left(\frac{179}{330}\right)$	$e\left(\frac{431}{660}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{13}{330}\right)$	$e\left(\frac{227}{660}\right)$
$\chi_{14157}(167,\cdot)$	$-1$	$1$	$e\left(\frac{41}{660}\right)$	$e\left(\frac{41}{330}\right)$	$e\left(\frac{119}{660}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{109}{330}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{97}{330}\right)$	$e\left(\frac{323}{660}\right)$
$\chi_{14157}(227,\cdot)$	$-1$	$1$	$e\left(\frac{367}{660}\right)$	$e\left(\frac{37}{330}\right)$	$e\left(\frac{373}{660}\right)$	$e\left(\frac{13}{220}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{203}{330}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{329}{330}\right)$	$e\left(\frac{541}{660}\right)$
$\chi_{14157}(371,\cdot)$	$-1$	$1$	$e\left(\frac{73}{660}\right)$	$e\left(\frac{73}{330}\right)$	$e\left(\frac{67}{660}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{73}{220}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{17}{330}\right)$	$e\left(\frac{73}{165}\right)$	$e\left(\frac{221}{330}\right)$	$e\left(\frac{559}{660}\right)$
$\chi_{14157}(392,\cdot)$	$-1$	$1$	$e\left(\frac{47}{660}\right)$	$e\left(\frac{47}{330}\right)$	$e\left(\frac{233}{660}\right)$	$e\left(\frac{73}{220}\right)$	$e\left(\frac{47}{220}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{133}{330}\right)$	$e\left(\frac{47}{165}\right)$	$e\left(\frac{79}{330}\right)$	$e\left(\frac{161}{660}\right)$
$\chi_{14157}(635,\cdot)$	$-1$	$1$	$e\left(\frac{593}{660}\right)$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{47}{660}\right)$	$e\left(\frac{27}{220}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{7}{330}\right)$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{91}{330}\right)$	$e\left(\frac{599}{660}\right)$
$\chi_{14157}(695,\cdot)$	$-1$	$1$	$e\left(\frac{571}{660}\right)$	$e\left(\frac{241}{330}\right)$	$e\left(\frac{289}{660}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{29}{330}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{47}{330}\right)$	$e\left(\frac{313}{660}\right)$
$\chi_{14157}(722,\cdot)$	$-1$	$1$	$e\left(\frac{397}{660}\right)$	$e\left(\frac{67}{330}\right)$	$e\left(\frac{283}{660}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{323}{330}\right)$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{239}{330}\right)$	$e\left(\frac{391}{660}\right)$
$\chi_{14157}(743,\cdot)$	$-1$	$1$	$e\left(\frac{239}{660}\right)$	$e\left(\frac{239}{330}\right)$	$e\left(\frac{581}{660}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{241}{330}\right)$	$e\left(\frac{74}{165}\right)$	$e\left(\frac{163}{330}\right)$	$e\left(\frac{257}{660}\right)$
$\chi_{14157}(860,\cdot)$	$-1$	$1$	$e\left(\frac{551}{660}\right)$	$e\left(\frac{221}{330}\right)$	$e\left(\frac{569}{660}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{111}{220}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{169}{330}\right)$	$e\left(\frac{56}{165}\right)$	$e\left(\frac{217}{330}\right)$	$e\left(\frac{413}{660}\right)$
$\chi_{14157}(986,\cdot)$	$-1$	$1$	$e\left(\frac{17}{660}\right)$	$e\left(\frac{17}{330}\right)$	$e\left(\frac{323}{660}\right)$	$e\left(\frac{3}{220}\right)$	$e\left(\frac{17}{220}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{13}{330}\right)$	$e\left(\frac{17}{165}\right)$	$e\left(\frac{169}{330}\right)$	$e\left(\frac{311}{660}\right)$
$\chi_{14157}(1073,\cdot)$	$-1$	$1$	$e\left(\frac{409}{660}\right)$	$e\left(\frac{79}{330}\right)$	$e\left(\frac{511}{660}\right)$	$e\left(\frac{111}{220}\right)$	$e\left(\frac{189}{220}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{41}{330}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{203}{330}\right)$	$e\left(\frac{67}{660}\right)$
$\chi_{14157}(1163,\cdot)$	$-1$	$1$	$e\left(\frac{643}{660}\right)$	$e\left(\frac{313}{330}\right)$	$e\left(\frac{337}{660}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{317}{330}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{161}{330}\right)$	$e\left(\frac{349}{660}\right)$
$\chi_{14157}(1190,\cdot)$	$-1$	$1$	$e\left(\frac{181}{660}\right)$	$e\left(\frac{181}{330}\right)$	$e\left(\frac{139}{660}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{181}{220}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{119}{330}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{227}{330}\right)$	$e\left(\frac{283}{660}\right)$
$\chi_{14157}(1337,\cdot)$	$-1$	$1$	$e\left(\frac{149}{660}\right)$	$e\left(\frac{149}{330}\right)$	$e\left(\frac{191}{660}\right)$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{211}{330}\right)$	$e\left(\frac{149}{165}\right)$	$e\left(\frac{103}{330}\right)$	$e\left(\frac{47}{660}\right)$
$\chi_{14157}(1454,\cdot)$	$-1$	$1$	$e\left(\frac{281}{660}\right)$	$e\left(\frac{281}{330}\right)$	$e\left(\frac{59}{660}\right)$	$e\left(\frac{179}{220}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{79}{330}\right)$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{37}{330}\right)$	$e\left(\frac{443}{660}\right)$
$\chi_{14157}(1514,\cdot)$	$-1$	$1$	$e\left(\frac{247}{660}\right)$	$e\left(\frac{247}{330}\right)$	$e\left(\frac{73}{660}\right)$	$e\left(\frac{173}{220}\right)$	$e\left(\frac{27}{220}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{53}{330}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{29}{330}\right)$	$e\left(\frac{481}{660}\right)$
$\chi_{14157}(1658,\cdot)$	$-1$	$1$	$e\left(\frac{133}{660}\right)$	$e\left(\frac{133}{330}\right)$	$e\left(\frac{547}{660}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{257}{330}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{41}{330}\right)$	$e\left(\frac{259}{660}\right)$
$\chi_{14157}(1679,\cdot)$	$-1$	$1$	$e\left(\frac{587}{660}\right)$	$e\left(\frac{257}{330}\right)$	$e\left(\frac{593}{660}\right)$	$e\left(\frac{13}{220}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{313}{330}\right)$	$e\left(\frac{92}{165}\right)$	$e\left(\frac{109}{330}\right)$	$e\left(\frac{101}{660}\right)$
$\chi_{14157}(1865,\cdot)$	$-1$	$1$	$e\left(\frac{619}{660}\right)$	$e\left(\frac{289}{330}\right)$	$e\left(\frac{541}{660}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{179}{220}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{221}{330}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{233}{330}\right)$	$e\left(\frac{337}{660}\right)$
$\chi_{14157}(1922,\cdot)$	$-1$	$1$	$e\left(\frac{653}{660}\right)$	$e\left(\frac{323}{330}\right)$	$e\left(\frac{527}{660}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{247}{330}\right)$	$e\left(\frac{158}{165}\right)$	$e\left(\frac{241}{330}\right)$	$e\left(\frac{299}{660}\right)$
$\chi_{14157}(1982,\cdot)$	$-1$	$1$	$e\left(\frac{151}{660}\right)$	$e\left(\frac{151}{330}\right)$	$e\left(\frac{229}{660}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{151}{220}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{329}{330}\right)$	$e\left(\frac{151}{165}\right)$	$e\left(\frac{317}{330}\right)$	$e\left(\frac{433}{660}\right)$
$\chi_{14157}(2009,\cdot)$	$-1$	$1$	$e\left(\frac{277}{660}\right)$	$e\left(\frac{277}{330}\right)$	$e\left(\frac{643}{660}\right)$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{173}{330}\right)$	$e\left(\frac{112}{165}\right)$	$e\left(\frac{269}{330}\right)$	$e\left(\frac{331}{660}\right)$
$\chi_{14157}(2147,\cdot)$	$-1$	$1$	$e\left(\frac{131}{660}\right)$	$e\left(\frac{131}{330}\right)$	$e\left(\frac{509}{660}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{139}{330}\right)$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{157}{330}\right)$	$e\left(\frac{533}{660}\right)$
$\chi_{14157}(2273,\cdot)$	$-1$	$1$	$e\left(\frac{557}{660}\right)$	$e\left(\frac{227}{330}\right)$	$e\left(\frac{23}{660}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{193}{330}\right)$	$e\left(\frac{62}{165}\right)$	$e\left(\frac{199}{330}\right)$	$e\left(\frac{251}{660}\right)$
$\chi_{14157}(2360,\cdot)$	$-1$	$1$	$e\left(\frac{49}{660}\right)$	$e\left(\frac{49}{330}\right)$	$e\left(\frac{271}{660}\right)$	$e\left(\frac{151}{220}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{251}{330}\right)$	$e\left(\frac{49}{165}\right)$	$e\left(\frac{293}{330}\right)$	$e\left(\frac{547}{660}\right)$
$\chi_{14157}(2450,\cdot)$	$-1$	$1$	$e\left(\frac{43}{660}\right)$	$e\left(\frac{43}{330}\right)$	$e\left(\frac{157}{660}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{227}{330}\right)$	$e\left(\frac{43}{165}\right)$	$e\left(\frac{311}{330}\right)$	$e\left(\frac{49}{660}\right)$
$\chi_{14157}(2477,\cdot)$	$-1$	$1$	$e\left(\frac{421}{660}\right)$	$e\left(\frac{91}{330}\right)$	$e\left(\frac{79}{660}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{89}{330}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{167}{330}\right)$	$e\left(\frac{403}{660}\right)$
$\chi_{14157}(2615,\cdot)$	$-1$	$1$	$e\left(\frac{203}{660}\right)$	$e\left(\frac{203}{330}\right)$	$e\left(\frac{557}{660}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{97}{330}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{271}{330}\right)$	$e\left(\frac{569}{660}\right)$
$\chi_{14157}(2624,\cdot)$	$-1$	$1$	$e\left(\frac{449}{660}\right)$	$e\left(\frac{119}{330}\right)$	$e\left(\frac{611}{660}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{9}{220}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{91}{330}\right)$	$e\left(\frac{119}{165}\right)$	$e\left(\frac{193}{330}\right)$	$e\left(\frac{527}{660}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{14157}(41,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{660}\right)\)	\(e\left(\frac{83}{330}\right)\)	\(e\left(\frac{257}{660}\right)\)	\(e\left(\frac{157}{220}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{277}{330}\right)\)	\(e\left(\frac{83}{165}\right)\)	\(e\left(\frac{301}{330}\right)\)	\(e\left(\frac{509}{660}\right)\)
\(\chi_{14157}(50,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{509}{660}\right)\)	\(e\left(\frac{179}{330}\right)\)	\(e\left(\frac{431}{660}\right)\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{13}{330}\right)\)	\(e\left(\frac{227}{660}\right)\)
\(\chi_{14157}(167,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{660}\right)\)	\(e\left(\frac{41}{330}\right)\)	\(e\left(\frac{119}{660}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{41}{220}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{109}{330}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{97}{330}\right)\)	\(e\left(\frac{323}{660}\right)\)
\(\chi_{14157}(227,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{367}{660}\right)\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{373}{660}\right)\)	\(e\left(\frac{13}{220}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{203}{330}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{329}{330}\right)\)	\(e\left(\frac{541}{660}\right)\)
\(\chi_{14157}(371,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{660}\right)\)	\(e\left(\frac{73}{330}\right)\)	\(e\left(\frac{67}{660}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{73}{220}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{17}{330}\right)\)	\(e\left(\frac{73}{165}\right)\)	\(e\left(\frac{221}{330}\right)\)	\(e\left(\frac{559}{660}\right)\)
\(\chi_{14157}(392,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{660}\right)\)	\(e\left(\frac{47}{330}\right)\)	\(e\left(\frac{233}{660}\right)\)	\(e\left(\frac{73}{220}\right)\)	\(e\left(\frac{47}{220}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{133}{330}\right)\)	\(e\left(\frac{47}{165}\right)\)	\(e\left(\frac{79}{330}\right)\)	\(e\left(\frac{161}{660}\right)\)
\(\chi_{14157}(635,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{593}{660}\right)\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{47}{660}\right)\)	\(e\left(\frac{27}{220}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{7}{330}\right)\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{91}{330}\right)\)	\(e\left(\frac{599}{660}\right)\)
\(\chi_{14157}(695,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{571}{660}\right)\)	\(e\left(\frac{241}{330}\right)\)	\(e\left(\frac{289}{660}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{29}{330}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{47}{330}\right)\)	\(e\left(\frac{313}{660}\right)\)
\(\chi_{14157}(722,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{397}{660}\right)\)	\(e\left(\frac{67}{330}\right)\)	\(e\left(\frac{283}{660}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{323}{330}\right)\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{239}{330}\right)\)	\(e\left(\frac{391}{660}\right)\)
\(\chi_{14157}(743,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{239}{660}\right)\)	\(e\left(\frac{239}{330}\right)\)	\(e\left(\frac{581}{660}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{241}{330}\right)\)	\(e\left(\frac{74}{165}\right)\)	\(e\left(\frac{163}{330}\right)\)	\(e\left(\frac{257}{660}\right)\)
\(\chi_{14157}(860,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{551}{660}\right)\)	\(e\left(\frac{221}{330}\right)\)	\(e\left(\frac{569}{660}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{111}{220}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{169}{330}\right)\)	\(e\left(\frac{56}{165}\right)\)	\(e\left(\frac{217}{330}\right)\)	\(e\left(\frac{413}{660}\right)\)
\(\chi_{14157}(986,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{660}\right)\)	\(e\left(\frac{17}{330}\right)\)	\(e\left(\frac{323}{660}\right)\)	\(e\left(\frac{3}{220}\right)\)	\(e\left(\frac{17}{220}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{13}{330}\right)\)	\(e\left(\frac{17}{165}\right)\)	\(e\left(\frac{169}{330}\right)\)	\(e\left(\frac{311}{660}\right)\)
\(\chi_{14157}(1073,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{409}{660}\right)\)	\(e\left(\frac{79}{330}\right)\)	\(e\left(\frac{511}{660}\right)\)	\(e\left(\frac{111}{220}\right)\)	\(e\left(\frac{189}{220}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{41}{330}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{203}{330}\right)\)	\(e\left(\frac{67}{660}\right)\)
\(\chi_{14157}(1163,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{643}{660}\right)\)	\(e\left(\frac{313}{330}\right)\)	\(e\left(\frac{337}{660}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{317}{330}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{161}{330}\right)\)	\(e\left(\frac{349}{660}\right)\)
\(\chi_{14157}(1190,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{181}{660}\right)\)	\(e\left(\frac{181}{330}\right)\)	\(e\left(\frac{139}{660}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{181}{220}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{119}{330}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{227}{330}\right)\)	\(e\left(\frac{283}{660}\right)\)
\(\chi_{14157}(1337,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{660}\right)\)	\(e\left(\frac{149}{330}\right)\)	\(e\left(\frac{191}{660}\right)\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{211}{330}\right)\)	\(e\left(\frac{149}{165}\right)\)	\(e\left(\frac{103}{330}\right)\)	\(e\left(\frac{47}{660}\right)\)
\(\chi_{14157}(1454,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{281}{660}\right)\)	\(e\left(\frac{281}{330}\right)\)	\(e\left(\frac{59}{660}\right)\)	\(e\left(\frac{179}{220}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{79}{330}\right)\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{443}{660}\right)\)
\(\chi_{14157}(1514,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{247}{660}\right)\)	\(e\left(\frac{247}{330}\right)\)	\(e\left(\frac{73}{660}\right)\)	\(e\left(\frac{173}{220}\right)\)	\(e\left(\frac{27}{220}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{53}{330}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{29}{330}\right)\)	\(e\left(\frac{481}{660}\right)\)
\(\chi_{14157}(1658,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{133}{660}\right)\)	\(e\left(\frac{133}{330}\right)\)	\(e\left(\frac{547}{660}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{257}{330}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{41}{330}\right)\)	\(e\left(\frac{259}{660}\right)\)
\(\chi_{14157}(1679,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{587}{660}\right)\)	\(e\left(\frac{257}{330}\right)\)	\(e\left(\frac{593}{660}\right)\)	\(e\left(\frac{13}{220}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{313}{330}\right)\)	\(e\left(\frac{92}{165}\right)\)	\(e\left(\frac{109}{330}\right)\)	\(e\left(\frac{101}{660}\right)\)
\(\chi_{14157}(1865,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{619}{660}\right)\)	\(e\left(\frac{289}{330}\right)\)	\(e\left(\frac{541}{660}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{179}{220}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{221}{330}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{233}{330}\right)\)	\(e\left(\frac{337}{660}\right)\)
\(\chi_{14157}(1922,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{653}{660}\right)\)	\(e\left(\frac{323}{330}\right)\)	\(e\left(\frac{527}{660}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{247}{330}\right)\)	\(e\left(\frac{158}{165}\right)\)	\(e\left(\frac{241}{330}\right)\)	\(e\left(\frac{299}{660}\right)\)
\(\chi_{14157}(1982,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{151}{660}\right)\)	\(e\left(\frac{151}{330}\right)\)	\(e\left(\frac{229}{660}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{151}{220}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{329}{330}\right)\)	\(e\left(\frac{151}{165}\right)\)	\(e\left(\frac{317}{330}\right)\)	\(e\left(\frac{433}{660}\right)\)
\(\chi_{14157}(2009,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{277}{660}\right)\)	\(e\left(\frac{277}{330}\right)\)	\(e\left(\frac{643}{660}\right)\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{57}{220}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{173}{330}\right)\)	\(e\left(\frac{112}{165}\right)\)	\(e\left(\frac{269}{330}\right)\)	\(e\left(\frac{331}{660}\right)\)
\(\chi_{14157}(2147,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{131}{660}\right)\)	\(e\left(\frac{131}{330}\right)\)	\(e\left(\frac{509}{660}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{139}{330}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{157}{330}\right)\)	\(e\left(\frac{533}{660}\right)\)
\(\chi_{14157}(2273,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{557}{660}\right)\)	\(e\left(\frac{227}{330}\right)\)	\(e\left(\frac{23}{660}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{193}{330}\right)\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{199}{330}\right)\)	\(e\left(\frac{251}{660}\right)\)
\(\chi_{14157}(2360,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{660}\right)\)	\(e\left(\frac{49}{330}\right)\)	\(e\left(\frac{271}{660}\right)\)	\(e\left(\frac{151}{220}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{251}{330}\right)\)	\(e\left(\frac{49}{165}\right)\)	\(e\left(\frac{293}{330}\right)\)	\(e\left(\frac{547}{660}\right)\)
\(\chi_{14157}(2450,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{660}\right)\)	\(e\left(\frac{43}{330}\right)\)	\(e\left(\frac{157}{660}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{227}{330}\right)\)	\(e\left(\frac{43}{165}\right)\)	\(e\left(\frac{311}{330}\right)\)	\(e\left(\frac{49}{660}\right)\)
\(\chi_{14157}(2477,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{421}{660}\right)\)	\(e\left(\frac{91}{330}\right)\)	\(e\left(\frac{79}{660}\right)\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{89}{330}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{167}{330}\right)\)	\(e\left(\frac{403}{660}\right)\)
\(\chi_{14157}(2615,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{203}{660}\right)\)	\(e\left(\frac{203}{330}\right)\)	\(e\left(\frac{557}{660}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{97}{330}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{271}{330}\right)\)	\(e\left(\frac{569}{660}\right)\)
\(\chi_{14157}(2624,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{449}{660}\right)\)	\(e\left(\frac{119}{330}\right)\)	\(e\left(\frac{611}{660}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{9}{220}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{91}{330}\right)\)	\(e\left(\frac{119}{165}\right)\)	\(e\left(\frac{193}{330}\right)\)	\(e\left(\frac{527}{660}\right)\)

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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.jc
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)