LMFDB - Dirichlet character orbit 14700.gp

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(14700, base_ring=CyclotomicField(210)) M = H._module chi = DirichletCharacter(H, M([0,0,168,55])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(61,14700)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$14700$
Conductor:	$1225$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$210$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1225.br	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:	$\Q(\zeta_{105})$
Fixed field:	Number field defined by a degree 210 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{14700}(61,\cdot)$	$-1$	$1$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{14700}(241,\cdot)$	$-1$	$1$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{11}{210}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{14700}(481,\cdot)$	$-1$	$1$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{14700}(661,\cdot)$	$-1$	$1$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{89}{210}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{14700}(1081,\cdot)$	$-1$	$1$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{14700}(1321,\cdot)$	$-1$	$1$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{14700}(1741,\cdot)$	$-1$	$1$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{151}{210}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{14700}(1921,\cdot)$	$-1$	$1$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{14700}(2161,\cdot)$	$-1$	$1$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{14700}(2341,\cdot)$	$-1$	$1$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{14700}(2581,\cdot)$	$-1$	$1$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{14700}(2761,\cdot)$	$-1$	$1$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{14700}(3181,\cdot)$	$-1$	$1$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{137}{210}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{14700}(3421,\cdot)$	$-1$	$1$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{14700}(4021,\cdot)$	$-1$	$1$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{83}{210}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{14700}(4261,\cdot)$	$-1$	$1$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{79}{210}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{14700}(4681,\cdot)$	$-1$	$1$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{67}{210}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{14700}(4861,\cdot)$	$-1$	$1$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{29}{210}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{14700}(5281,\cdot)$	$-1$	$1$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{107}{210}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{14700}(5521,\cdot)$	$-1$	$1$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{14700}(5941,\cdot)$	$-1$	$1$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{31}{210}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{14700}(6121,\cdot)$	$-1$	$1$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{53}{210}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{14700}(6361,\cdot)$	$-1$	$1$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{19}{210}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{14700}(6541,\cdot)$	$-1$	$1$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{131}{210}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{14700}(6961,\cdot)$	$-1$	$1$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{209}{210}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{14700}(7621,\cdot)$	$-1$	$1$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{193}{210}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{14700}(8041,\cdot)$	$-1$	$1$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{14700}(8221,\cdot)$	$-1$	$1$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{23}{210}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{14700}(8461,\cdot)$	$-1$	$1$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{169}{210}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{14700}(8641,\cdot)$	$-1$	$1$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{101}{210}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{14700}(8881,\cdot)$	$-1$	$1$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{157}{210}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{4}{7}\right)$

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	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{14700}(61,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{14700}(241,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{11}{210}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{14700}(481,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{14700}(661,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{14700}(1081,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{14700}(1321,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{14700}(1741,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{151}{210}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{14700}(1921,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{14700}(2161,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{14700}(2341,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{14700}(2581,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{14700}(2761,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{14700}(3181,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{137}{210}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{14700}(3421,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{14700}(4021,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{83}{210}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{14700}(4261,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{79}{210}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{14700}(4681,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{67}{210}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{14700}(4861,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{29}{210}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{14700}(5281,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{107}{210}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{14700}(5521,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{14700}(5941,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{31}{210}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{14700}(6121,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{53}{210}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{14700}(6361,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{19}{210}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{14700}(6541,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{131}{210}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{14700}(6961,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{209}{210}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{14700}(7621,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{193}{210}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{14700}(8041,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{14700}(8221,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{23}{210}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{14700}(8461,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{169}{210}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{14700}(8641,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{101}{210}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{14700}(8881,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{157}{210}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{4}{7}\right)\)

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Basic properties

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First 31 of 48 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	14700.gp
Modulus	$14700$
Conductor	$1225$
Order	$210$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(14700\)
Conductor:	\(1225\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(210\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1225.br	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)