LMFDB - Dirichlet character orbit 44100.op

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(44100, base_ring=CyclotomicField(210)) M = H._module chi = DirichletCharacter(H, M([0,140,126,100])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(2221,44100)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$44100$
Conductor:	$11025$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$105$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 11025.hi	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 105 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{44100}(2221,\cdot)$	$1$	$1$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{44100}(2461,\cdot)$	$1$	$1$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{44100}(3481,\cdot)$	$1$	$1$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{44100}(3721,\cdot)$	$1$	$1$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{44100}(4741,\cdot)$	$1$	$1$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{44100}(4981,\cdot)$	$1$	$1$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{44100}(7261,\cdot)$	$1$	$1$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{44100}(8521,\cdot)$	$1$	$1$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{44100}(8761,\cdot)$	$1$	$1$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{44100}(10021,\cdot)$	$1$	$1$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{44100}(11041,\cdot)$	$1$	$1$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{44100}(11281,\cdot)$	$1$	$1$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{44100}(12541,\cdot)$	$1$	$1$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{44100}(13561,\cdot)$	$1$	$1$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{44100}(14821,\cdot)$	$1$	$1$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{44100}(16081,\cdot)$	$1$	$1$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{44100}(16321,\cdot)$	$1$	$1$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{44100}(17341,\cdot)$	$1$	$1$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{44100}(17581,\cdot)$	$1$	$1$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{44100}(18841,\cdot)$	$1$	$1$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{44100}(19861,\cdot)$	$1$	$1$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{44100}(21121,\cdot)$	$1$	$1$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{44100}(21361,\cdot)$	$1$	$1$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{44100}(22381,\cdot)$	$1$	$1$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{44100}(22621,\cdot)$	$1$	$1$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{44100}(23641,\cdot)$	$1$	$1$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{44100}(25141,\cdot)$	$1$	$1$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{44100}(26161,\cdot)$	$1$	$1$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{44100}(27661,\cdot)$	$1$	$1$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{44100}(28681,\cdot)$	$1$	$1$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{44100}(28921,\cdot)$	$1$	$1$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{1}{21}\right)$

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	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{44100}(2221,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{44100}(2461,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{44100}(3481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{44100}(3721,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{44100}(4741,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{44100}(4981,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{44100}(7261,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{44100}(8521,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{44100}(8761,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{44100}(10021,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{44100}(11041,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{44100}(11281,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{44100}(12541,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{44100}(13561,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{44100}(14821,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{44100}(16081,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{44100}(16321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{44100}(17341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{44100}(17581,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{44100}(18841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{44100}(19861,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{44100}(21121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{44100}(21361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{44100}(22381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{44100}(22621,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{44100}(23641,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{44100}(25141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{44100}(26161,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{44100}(27661,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{44100}(28681,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{44100}(28921,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{1}{21}\right)\)

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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.op
Modulus	$44100$
Conductor	$11025$
Order	$105$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(44100\)
Conductor:	\(11025\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(105\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 11025.hi	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)