LMFDB - Dirichlet character orbit 44100.pf

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(44100, base_ring=CyclotomicField(210)) M = H._module chi = DirichletCharacter(H, M([105,140,42,145])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(691,44100)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$44100$
Conductor:	$44100$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$210$	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:	$\Q(\zeta_{105})$
Fixed field:	Number field defined by a degree 210 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{44100}(691,\cdot)$	$1$	$1$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{193}{210}\right)$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{13}{42}\right)$
$\chi_{44100}(1291,\cdot)$	$1$	$1$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{23}{210}\right)$	$e\left(\frac{101}{210}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{83}{210}\right)$	$e\left(\frac{17}{42}\right)$
$\chi_{44100}(3211,\cdot)$	$1$	$1$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{25}{42}\right)$
$\chi_{44100}(3811,\cdot)$	$1$	$1$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{149}{210}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{137}{210}\right)$	$e\left(\frac{23}{42}\right)$
$\chi_{44100}(4471,\cdot)$	$1$	$1$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{79}{210}\right)$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{31}{42}\right)$
$\chi_{44100}(5071,\cdot)$	$1$	$1$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{29}{210}\right)$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{5}{42}\right)$
$\chi_{44100}(5731,\cdot)$	$1$	$1$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{37}{210}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{151}{210}\right)$	$e\left(\frac{37}{42}\right)$
$\chi_{44100}(6331,\cdot)$	$1$	$1$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{101}{210}\right)$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{29}{42}\right)$
$\chi_{44100}(6991,\cdot)$	$1$	$1$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{1}{210}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{1}{42}\right)$
$\chi_{44100}(7591,\cdot)$	$1$	$1$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{11}{210}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{11}{42}\right)$
$\chi_{44100}(9511,\cdot)$	$1$	$1$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{67}{210}\right)$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{13}{42}\right)$
$\chi_{44100}(10111,\cdot)$	$1$	$1$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{107}{210}\right)$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{17}{42}\right)$
$\chi_{44100}(10771,\cdot)$	$1$	$1$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{169}{210}\right)$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{19}{42}\right)$
$\chi_{44100}(11371,\cdot)$	$1$	$1$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{179}{210}\right)$	$e\left(\frac{83}{210}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{89}{210}\right)$	$e\left(\frac{41}{42}\right)$
$\chi_{44100}(12031,\cdot)$	$1$	$1$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{61}{210}\right)$	$e\left(\frac{67}{210}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{1}{210}\right)$	$e\left(\frac{25}{42}\right)$
$\chi_{44100}(12631,\cdot)$	$1$	$1$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{41}{210}\right)$	$e\left(\frac{107}{210}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{11}{210}\right)$	$e\left(\frac{23}{42}\right)$
$\chi_{44100}(13291,\cdot)$	$1$	$1$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{31}{210}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{13}{210}\right)$	$e\left(\frac{31}{42}\right)$
$\chi_{44100}(13891,\cdot)$	$1$	$1$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{131}{210}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{143}{210}\right)$	$e\left(\frac{5}{42}\right)$
$\chi_{44100}(15811,\cdot)$	$1$	$1$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{157}{210}\right)$	$e\left(\frac{169}{210}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{37}{210}\right)$	$e\left(\frac{1}{42}\right)$
$\chi_{44100}(16411,\cdot)$	$1$	$1$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{179}{210}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{11}{42}\right)$
$\chi_{44100}(18331,\cdot)$	$1$	$1$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{151}{210}\right)$	$e\left(\frac{97}{210}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{61}{210}\right)$	$e\left(\frac{13}{42}\right)$
$\chi_{44100}(18931,\cdot)$	$1$	$1$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{17}{210}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{41}{210}\right)$	$e\left(\frac{17}{42}\right)$
$\chi_{44100}(19591,\cdot)$	$1$	$1$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{61}{210}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{19}{42}\right)$
$\chi_{44100}(20191,\cdot)$	$1$	$1$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{53}{210}\right)$	$e\left(\frac{41}{210}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{41}{42}\right)$
$\chi_{44100}(22111,\cdot)$	$1$	$1$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{37}{210}\right)$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{97}{210}\right)$	$e\left(\frac{31}{42}\right)$
$\chi_{44100}(22711,\cdot)$	$1$	$1$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{89}{210}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{17}{210}\right)$	$e\left(\frac{5}{42}\right)$
$\chi_{44100}(23371,\cdot)$	$1$	$1$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{37}{42}\right)$
$\chi_{44100}(23971,\cdot)$	$1$	$1$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{149}{210}\right)$	$e\left(\frac{29}{42}\right)$
$\chi_{44100}(24631,\cdot)$	$1$	$1$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{31}{210}\right)$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{121}{210}\right)$	$e\left(\frac{1}{42}\right)$
$\chi_{44100}(25231,\cdot)$	$1$	$1$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{131}{210}\right)$	$e\left(\frac{137}{210}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{11}{42}\right)$
$\chi_{44100}(28411,\cdot)$	$1$	$1$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{19}{210}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{157}{210}\right)$	$e\left(\frac{19}{42}\right)$

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	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{44100}(691,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{193}{210}\right)\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{13}{42}\right)\)
\(\chi_{44100}(1291,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{23}{210}\right)\)	\(e\left(\frac{101}{210}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{83}{210}\right)\)	\(e\left(\frac{17}{42}\right)\)
\(\chi_{44100}(3211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{25}{42}\right)\)
\(\chi_{44100}(3811,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{149}{210}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{137}{210}\right)\)	\(e\left(\frac{23}{42}\right)\)
\(\chi_{44100}(4471,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{79}{210}\right)\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{31}{42}\right)\)
\(\chi_{44100}(5071,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{29}{210}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{5}{42}\right)\)
\(\chi_{44100}(5731,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{37}{210}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{151}{210}\right)\)	\(e\left(\frac{37}{42}\right)\)
\(\chi_{44100}(6331,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{101}{210}\right)\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{29}{42}\right)\)
\(\chi_{44100}(6991,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{1}{210}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{1}{42}\right)\)
\(\chi_{44100}(7591,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{11}{210}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{11}{42}\right)\)
\(\chi_{44100}(9511,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{67}{210}\right)\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{13}{42}\right)\)
\(\chi_{44100}(10111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{107}{210}\right)\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{17}{42}\right)\)
\(\chi_{44100}(10771,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{169}{210}\right)\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{19}{42}\right)\)
\(\chi_{44100}(11371,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{179}{210}\right)\)	\(e\left(\frac{83}{210}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{41}{42}\right)\)
\(\chi_{44100}(12031,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{61}{210}\right)\)	\(e\left(\frac{67}{210}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{1}{210}\right)\)	\(e\left(\frac{25}{42}\right)\)
\(\chi_{44100}(12631,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{41}{210}\right)\)	\(e\left(\frac{107}{210}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{11}{210}\right)\)	\(e\left(\frac{23}{42}\right)\)
\(\chi_{44100}(13291,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{31}{210}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{13}{210}\right)\)	\(e\left(\frac{31}{42}\right)\)
\(\chi_{44100}(13891,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{131}{210}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{143}{210}\right)\)	\(e\left(\frac{5}{42}\right)\)
\(\chi_{44100}(15811,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{157}{210}\right)\)	\(e\left(\frac{169}{210}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{37}{210}\right)\)	\(e\left(\frac{1}{42}\right)\)
\(\chi_{44100}(16411,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{179}{210}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{11}{42}\right)\)
\(\chi_{44100}(18331,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{151}{210}\right)\)	\(e\left(\frac{97}{210}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{61}{210}\right)\)	\(e\left(\frac{13}{42}\right)\)
\(\chi_{44100}(18931,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{41}{210}\right)\)	\(e\left(\frac{17}{42}\right)\)
\(\chi_{44100}(19591,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{61}{210}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{19}{42}\right)\)
\(\chi_{44100}(20191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{53}{210}\right)\)	\(e\left(\frac{41}{210}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{41}{42}\right)\)
\(\chi_{44100}(22111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{37}{210}\right)\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{97}{210}\right)\)	\(e\left(\frac{31}{42}\right)\)
\(\chi_{44100}(22711,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{5}{42}\right)\)
\(\chi_{44100}(23371,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{37}{42}\right)\)
\(\chi_{44100}(23971,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{149}{210}\right)\)	\(e\left(\frac{29}{42}\right)\)
\(\chi_{44100}(24631,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{31}{210}\right)\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{121}{210}\right)\)	\(e\left(\frac{1}{42}\right)\)
\(\chi_{44100}(25231,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{131}{210}\right)\)	\(e\left(\frac{137}{210}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{11}{42}\right)\)
\(\chi_{44100}(28411,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{19}{210}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{157}{210}\right)\)	\(e\left(\frac{19}{42}\right)\)

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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	44100.pf
Modulus	$44100$
Conductor	$44100$
Order	$210$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(44100\)
Conductor:	\(44100\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(210\)	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)