LMFDB - Dirichlet character orbit 14157.ip

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(14157, base_ring=CyclotomicField(330)) M = H._module chi = DirichletCharacter(H, M([55,51,110])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(29,14157)) 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:	$330$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{165})$
Fixed field:	Number field defined by a degree 330 polynomial (not computed)

First 31 of 80 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$14$	$16$	$17$	$19$
$\chi_{14157}(29,\cdot)$	$1$	$1$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{89}{330}\right)$	$e\left(\frac{137}{330}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{23}{330}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{163}{330}\right)$
$\chi_{14157}(347,\cdot)$	$1$	$1$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{283}{330}\right)$	$e\left(\frac{139}{330}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{151}{330}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{281}{330}\right)$
$\chi_{14157}(380,\cdot)$	$1$	$1$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{149}{330}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{131}{330}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{164}{165}\right)$	$e\left(\frac{211}{330}\right)$
$\chi_{14157}(464,\cdot)$	$1$	$1$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{97}{330}\right)$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{229}{330}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{59}{330}\right)$
$\chi_{14157}(497,\cdot)$	$1$	$1$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{257}{330}\right)$	$e\left(\frac{251}{330}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{59}{330}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{26}{165}\right)$	$e\left(\frac{289}{330}\right)$
$\chi_{14157}(932,\cdot)$	$1$	$1$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{301}{330}\right)$	$e\left(\frac{163}{330}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{37}{330}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{47}{330}\right)$
$\chi_{14157}(1283,\cdot)$	$1$	$1$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{19}{330}\right)$	$e\left(\frac{7}{330}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{283}{330}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{52}{165}\right)$	$e\left(\frac{83}{330}\right)$
$\chi_{14157}(1316,\cdot)$	$1$	$1$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{269}{330}\right)$	$e\left(\frac{47}{330}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{203}{330}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{137}{165}\right)$	$e\left(\frac{133}{330}\right)$
$\chi_{14157}(1634,\cdot)$	$1$	$1$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{163}{330}\right)$	$e\left(\frac{199}{330}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{31}{330}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{191}{330}\right)$
$\chi_{14157}(1751,\cdot)$	$1$	$1$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{67}{330}\right)$	$e\left(\frac{181}{330}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{199}{330}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{119}{330}\right)$
$\chi_{14157}(1784,\cdot)$	$1$	$1$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{227}{330}\right)$	$e\left(\frac{101}{330}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{29}{330}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{161}{165}\right)$	$e\left(\frac{19}{330}\right)$
$\chi_{14157}(2219,\cdot)$	$1$	$1$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{211}{330}\right)$	$e\left(\frac{43}{330}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{277}{330}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{13}{165}\right)$	$e\left(\frac{227}{330}\right)$
$\chi_{14157}(2252,\cdot)$	$1$	$1$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{251}{330}\right)$	$e\left(\frac{23}{330}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{317}{330}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{53}{165}\right)$	$e\left(\frac{37}{330}\right)$
$\chi_{14157}(2570,\cdot)$	$1$	$1$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{199}{330}\right)$	$e\left(\frac{247}{330}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{133}{330}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{53}{330}\right)$
$\chi_{14157}(2603,\cdot)$	$1$	$1$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{119}{330}\right)$	$e\left(\frac{287}{330}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{53}{330}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{103}{330}\right)$
$\chi_{14157}(2921,\cdot)$	$1$	$1$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{43}{330}\right)$	$e\left(\frac{259}{330}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{241}{330}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{109}{165}\right)$	$e\left(\frac{101}{330}\right)$
$\chi_{14157}(2954,\cdot)$	$1$	$1$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{23}{330}\right)$	$e\left(\frac{269}{330}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{221}{330}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{89}{165}\right)$	$e\left(\frac{31}{330}\right)$
$\chi_{14157}(3038,\cdot)$	$1$	$1$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{37}{330}\right)$	$e\left(\frac{31}{330}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{169}{330}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{136}{165}\right)$	$e\left(\frac{179}{330}\right)$
$\chi_{14157}(3071,\cdot)$	$1$	$1$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{197}{330}\right)$	$e\left(\frac{281}{330}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{329}{330}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{79}{330}\right)$
$\chi_{14157}(3539,\cdot)$	$1$	$1$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{161}{330}\right)$	$e\left(\frac{233}{330}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{227}{330}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{217}{330}\right)$
$\chi_{14157}(3857,\cdot)$	$1$	$1$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{49}{330}\right)$	$e\left(\frac{157}{330}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{313}{330}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{23}{330}\right)$
$\chi_{14157}(3890,\cdot)$	$1$	$1$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{299}{330}\right)$	$e\left(\frac{197}{330}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{233}{330}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{73}{330}\right)$
$\chi_{14157}(4241,\cdot)$	$1$	$1$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{233}{330}\right)$	$e\left(\frac{329}{330}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{101}{330}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{271}{330}\right)$
$\chi_{14157}(4325,\cdot)$	$1$	$1$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{7}{330}\right)$	$e\left(\frac{211}{330}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{139}{330}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{106}{165}\right)$	$e\left(\frac{239}{330}\right)$
$\chi_{14157}(4358,\cdot)$	$1$	$1$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{167}{330}\right)$	$e\left(\frac{131}{330}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{299}{330}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{101}{165}\right)$	$e\left(\frac{139}{330}\right)$
$\chi_{14157}(4793,\cdot)$	$1$	$1$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{31}{330}\right)$	$e\left(\frac{133}{330}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{97}{330}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{257}{330}\right)$
$\chi_{14157}(4826,\cdot)$	$1$	$1$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{71}{330}\right)$	$e\left(\frac{113}{330}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{137}{330}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{67}{330}\right)$
$\chi_{14157}(5144,\cdot)$	$1$	$1$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{229}{330}\right)$	$e\left(\frac{67}{330}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{163}{330}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{97}{165}\right)$	$e\left(\frac{323}{330}\right)$
$\chi_{14157}(5177,\cdot)$	$1$	$1$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{149}{330}\right)$	$e\left(\frac{107}{330}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{83}{330}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{17}{165}\right)$	$e\left(\frac{43}{330}\right)$
$\chi_{14157}(5495,\cdot)$	$1$	$1$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{133}{330}\right)$	$e\left(\frac{49}{330}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{34}{165}\right)$	$e\left(\frac{251}{330}\right)$
$\chi_{14157}(5528,\cdot)$	$1$	$1$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{113}{330}\right)$	$e\left(\frac{59}{330}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{311}{330}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{181}{330}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{14157}(29,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{89}{330}\right)\)	\(e\left(\frac{137}{330}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{23}{330}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{163}{330}\right)\)
\(\chi_{14157}(347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{283}{330}\right)\)	\(e\left(\frac{139}{330}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{151}{330}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{281}{330}\right)\)
\(\chi_{14157}(380,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{149}{330}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{131}{330}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{164}{165}\right)\)	\(e\left(\frac{211}{330}\right)\)
\(\chi_{14157}(464,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{97}{330}\right)\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{229}{330}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{59}{330}\right)\)
\(\chi_{14157}(497,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{257}{330}\right)\)	\(e\left(\frac{251}{330}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{59}{330}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{26}{165}\right)\)	\(e\left(\frac{289}{330}\right)\)
\(\chi_{14157}(932,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{301}{330}\right)\)	\(e\left(\frac{163}{330}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{47}{330}\right)\)
\(\chi_{14157}(1283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{19}{330}\right)\)	\(e\left(\frac{7}{330}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{283}{330}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{52}{165}\right)\)	\(e\left(\frac{83}{330}\right)\)
\(\chi_{14157}(1316,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{269}{330}\right)\)	\(e\left(\frac{47}{330}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{203}{330}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{137}{165}\right)\)	\(e\left(\frac{133}{330}\right)\)
\(\chi_{14157}(1634,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{163}{330}\right)\)	\(e\left(\frac{199}{330}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{31}{330}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{191}{330}\right)\)
\(\chi_{14157}(1751,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{67}{330}\right)\)	\(e\left(\frac{181}{330}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{199}{330}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{119}{330}\right)\)
\(\chi_{14157}(1784,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{227}{330}\right)\)	\(e\left(\frac{101}{330}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{29}{330}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{161}{165}\right)\)	\(e\left(\frac{19}{330}\right)\)
\(\chi_{14157}(2219,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{211}{330}\right)\)	\(e\left(\frac{43}{330}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{277}{330}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{13}{165}\right)\)	\(e\left(\frac{227}{330}\right)\)
\(\chi_{14157}(2252,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{251}{330}\right)\)	\(e\left(\frac{23}{330}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{317}{330}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{53}{165}\right)\)	\(e\left(\frac{37}{330}\right)\)
\(\chi_{14157}(2570,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{199}{330}\right)\)	\(e\left(\frac{247}{330}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{133}{330}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{53}{330}\right)\)
\(\chi_{14157}(2603,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{119}{330}\right)\)	\(e\left(\frac{287}{330}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{53}{330}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{103}{330}\right)\)
\(\chi_{14157}(2921,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{43}{330}\right)\)	\(e\left(\frac{259}{330}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{241}{330}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{109}{165}\right)\)	\(e\left(\frac{101}{330}\right)\)
\(\chi_{14157}(2954,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{23}{330}\right)\)	\(e\left(\frac{269}{330}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{221}{330}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{89}{165}\right)\)	\(e\left(\frac{31}{330}\right)\)
\(\chi_{14157}(3038,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{31}{330}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{169}{330}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{136}{165}\right)\)	\(e\left(\frac{179}{330}\right)\)
\(\chi_{14157}(3071,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{197}{330}\right)\)	\(e\left(\frac{281}{330}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{329}{330}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{79}{330}\right)\)
\(\chi_{14157}(3539,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{161}{330}\right)\)	\(e\left(\frac{233}{330}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{227}{330}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{217}{330}\right)\)
\(\chi_{14157}(3857,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{49}{330}\right)\)	\(e\left(\frac{157}{330}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{313}{330}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{23}{330}\right)\)
\(\chi_{14157}(3890,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{299}{330}\right)\)	\(e\left(\frac{197}{330}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{233}{330}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{73}{330}\right)\)
\(\chi_{14157}(4241,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{233}{330}\right)\)	\(e\left(\frac{329}{330}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{101}{330}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{271}{330}\right)\)
\(\chi_{14157}(4325,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{7}{330}\right)\)	\(e\left(\frac{211}{330}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{139}{330}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{106}{165}\right)\)	\(e\left(\frac{239}{330}\right)\)
\(\chi_{14157}(4358,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{167}{330}\right)\)	\(e\left(\frac{131}{330}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{299}{330}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{101}{165}\right)\)	\(e\left(\frac{139}{330}\right)\)
\(\chi_{14157}(4793,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{31}{330}\right)\)	\(e\left(\frac{133}{330}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{97}{330}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{257}{330}\right)\)
\(\chi_{14157}(4826,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{71}{330}\right)\)	\(e\left(\frac{113}{330}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{137}{330}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{67}{330}\right)\)
\(\chi_{14157}(5144,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{229}{330}\right)\)	\(e\left(\frac{67}{330}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{163}{330}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{323}{330}\right)\)
\(\chi_{14157}(5177,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{149}{330}\right)\)	\(e\left(\frac{107}{330}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{83}{330}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{17}{165}\right)\)	\(e\left(\frac{43}{330}\right)\)
\(\chi_{14157}(5495,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{133}{330}\right)\)	\(e\left(\frac{49}{330}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{34}{165}\right)\)	\(e\left(\frac{251}{330}\right)\)
\(\chi_{14157}(5528,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{113}{330}\right)\)	\(e\left(\frac{59}{330}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{311}{330}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{181}{330}\right)\)

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

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