LMFDB - Dirichlet character orbit 44100.rp

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(44100, base_ring=CyclotomicField(420)) M = H._module chi = DirichletCharacter(H, M([210,210,273,170])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(467,44100)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$44100$
Conductor:	$14700$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$420$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 14700.hd	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:	$\Q(\zeta_{420})$
Fixed field:	Number field defined by a degree 420 polynomial (not computed)

First 31 of 96 characters in Galois orbit

Character	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{44100}(467,\cdot)$	$1$	$1$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{29}{420}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{223}{420}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{337}{420}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{44100}(647,\cdot)$	$1$	$1$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{121}{420}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{47}{420}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{233}{420}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{44100}(1223,\cdot)$	$1$	$1$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{263}{420}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{241}{420}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{319}{420}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{13}{28}\right)$
$\chi_{44100}(1727,\cdot)$	$1$	$1$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{293}{420}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{211}{420}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{349}{420}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{23}{28}\right)$
$\chi_{44100}(2483,\cdot)$	$1$	$1$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{359}{420}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{313}{420}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{247}{420}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{17}{28}\right)$
$\chi_{44100}(2663,\cdot)$	$1$	$1$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{307}{420}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{29}{420}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{251}{420}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{44100}(2987,\cdot)$	$1$	$1$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{67}{140}\right)$	$e\left(\frac{137}{420}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{199}{420}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{361}{420}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{27}{28}\right)$
$\chi_{44100}(3923,\cdot)$	$1$	$1$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{103}{420}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{401}{420}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{299}{420}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{25}{28}\right)$
$\chi_{44100}(4247,\cdot)$	$1$	$1$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{401}{420}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{187}{420}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{373}{420}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{44100}(4427,\cdot)$	$1$	$1$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{13}{420}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{71}{420}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{209}{420}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{23}{28}\right)$
$\chi_{44100}(5003,\cdot)$	$1$	$1$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{131}{420}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{37}{420}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{103}{420}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{25}{28}\right)$
$\chi_{44100}(5183,\cdot)$	$1$	$1$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{319}{420}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{353}{420}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{347}{420}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{13}{28}\right)$
$\chi_{44100}(5687,\cdot)$	$1$	$1$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{397}{420}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{359}{420}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{341}{420}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{11}{28}\right)$
$\chi_{44100}(6263,\cdot)$	$1$	$1$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{227}{420}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{109}{420}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{31}{420}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{1}{28}\right)$
$\chi_{44100}(6767,\cdot)$	$1$	$1$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{19}{140}\right)$	$e\left(\frac{89}{420}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{163}{420}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{397}{420}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{11}{28}\right)$
$\chi_{44100}(6947,\cdot)$	$1$	$1$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{361}{420}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{227}{420}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{53}{420}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{27}{28}\right)$
$\chi_{44100}(7523,\cdot)$	$1$	$1$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{323}{420}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{181}{420}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{379}{420}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{5}{28}\right)$
$\chi_{44100}(7703,\cdot)$	$1$	$1$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{331}{420}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{257}{420}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{23}{420}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{17}{28}\right)$
$\chi_{44100}(8027,\cdot)$	$1$	$1$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{3}{140}\right)$	$e\left(\frac{353}{420}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{151}{420}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{409}{420}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{15}{28}\right)$
$\chi_{44100}(8783,\cdot)$	$1$	$1$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{69}{140}\right)$	$e\left(\frac{419}{420}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{253}{420}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{307}{420}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{44100}(8963,\cdot)$	$1$	$1$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{127}{420}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{209}{420}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{71}{420}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{5}{28}\right)$
$\chi_{44100}(9287,\cdot)$	$1$	$1$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{197}{420}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{139}{420}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{420}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{44100}(9467,\cdot)$	$1$	$1$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{289}{420}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{383}{420}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{317}{420}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{44100}(10547,\cdot)$	$1$	$1$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{41}{420}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{127}{420}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{420}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{23}{28}\right)$
$\chi_{44100}(10727,\cdot)$	$1$	$1$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{253}{420}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{251}{420}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{29}{420}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{19}{28}\right)$
$\chi_{44100}(11303,\cdot)$	$1$	$1$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{191}{420}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{397}{420}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{163}{420}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{17}{28}\right)$
$\chi_{44100}(11483,\cdot)$	$1$	$1$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{69}{140}\right)$	$e\left(\frac{139}{420}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{113}{420}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{167}{420}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{9}{28}\right)$
$\chi_{44100}(13067,\cdot)$	$1$	$1$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{149}{420}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{103}{420}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{37}{420}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{3}{28}\right)$
$\chi_{44100}(13247,\cdot)$	$1$	$1$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{181}{420}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{407}{420}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{293}{420}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{23}{28}\right)$
$\chi_{44100}(13823,\cdot)$	$1$	$1$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{383}{420}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{121}{420}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{19}{420}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{25}{28}\right)$
$\chi_{44100}(14003,\cdot)$	$1$	$1$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{151}{420}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{420}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{263}{420}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{13}{28}\right)$

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	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{44100}(467,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{29}{420}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{223}{420}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{337}{420}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{44100}(647,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{121}{420}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{47}{420}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{233}{420}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{44100}(1223,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{263}{420}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{241}{420}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{319}{420}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{44100}(1727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{293}{420}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{211}{420}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{349}{420}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{44100}(2483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{359}{420}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{313}{420}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{247}{420}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{44100}(2663,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{307}{420}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{29}{420}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{251}{420}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{44100}(2987,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{67}{140}\right)\)	\(e\left(\frac{137}{420}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{199}{420}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{361}{420}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{44100}(3923,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{103}{420}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{401}{420}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{299}{420}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{25}{28}\right)\)
\(\chi_{44100}(4247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{401}{420}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{187}{420}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{373}{420}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{44100}(4427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{13}{420}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{71}{420}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{209}{420}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{44100}(5003,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{131}{420}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{37}{420}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{103}{420}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{25}{28}\right)\)
\(\chi_{44100}(5183,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{319}{420}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{353}{420}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{347}{420}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{44100}(5687,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{397}{420}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{359}{420}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{341}{420}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{44100}(6263,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{227}{420}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{109}{420}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{31}{420}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{1}{28}\right)\)
\(\chi_{44100}(6767,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{19}{140}\right)\)	\(e\left(\frac{89}{420}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{163}{420}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{397}{420}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{44100}(6947,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{361}{420}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{227}{420}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{53}{420}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{44100}(7523,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{323}{420}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{181}{420}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{379}{420}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{5}{28}\right)\)
\(\chi_{44100}(7703,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{331}{420}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{257}{420}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{23}{420}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{44100}(8027,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{3}{140}\right)\)	\(e\left(\frac{353}{420}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{151}{420}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{409}{420}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{44100}(8783,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{69}{140}\right)\)	\(e\left(\frac{419}{420}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{253}{420}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{307}{420}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{44100}(8963,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{127}{420}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{209}{420}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{71}{420}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{5}{28}\right)\)
\(\chi_{44100}(9287,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{197}{420}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{139}{420}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{420}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{44100}(9467,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{289}{420}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{383}{420}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{317}{420}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{44100}(10547,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{41}{420}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{127}{420}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{420}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{44100}(10727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{253}{420}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{251}{420}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{29}{420}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{44100}(11303,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{191}{420}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{397}{420}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{163}{420}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{17}{28}\right)\)
\(\chi_{44100}(11483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{69}{140}\right)\)	\(e\left(\frac{139}{420}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{113}{420}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{167}{420}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{44100}(13067,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{149}{420}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{103}{420}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{37}{420}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{44100}(13247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{181}{420}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{407}{420}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{293}{420}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{44100}(13823,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{383}{420}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{121}{420}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{19}{420}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{25}{28}\right)\)
\(\chi_{44100}(14003,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{151}{420}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{17}{420}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{263}{420}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{13}{28}\right)\)

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First 31 of 96 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.rp
Modulus	$44100$
Conductor	$14700$
Order	$420$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(44100\)
Conductor:	\(14700\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(420\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 14700.hd	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)