LMFDB - Dirichlet character orbit 44100.rl

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(44100, base_ring=CyclotomicField(420)) M = H._module chi = DirichletCharacter(H, M([0,140,399,330])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(13,44100)) 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:	$420$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 11025.iw	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	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{44100}(13,\cdot)$	$1$	$1$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{271}{420}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{409}{420}\right)$	$e\left(\frac{79}{210}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{53}{210}\right)$	$e\left(\frac{25}{84}\right)$
$\chi_{44100}(517,\cdot)$	$1$	$1$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{157}{420}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{223}{420}\right)$	$e\left(\frac{193}{210}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{140}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{43}{84}\right)$
$\chi_{44100}(853,\cdot)$	$1$	$1$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{263}{420}\right)$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{197}{420}\right)$	$e\left(\frac{17}{210}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{41}{84}\right)$
$\chi_{44100}(1777,\cdot)$	$1$	$1$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{229}{420}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{31}{420}\right)$	$e\left(\frac{121}{210}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{137}{210}\right)$	$e\left(\frac{67}{84}\right)$
$\chi_{44100}(2113,\cdot)$	$1$	$1$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{251}{420}\right)$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{89}{420}\right)$	$e\left(\frac{29}{210}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{65}{84}\right)$
$\chi_{44100}(2533,\cdot)$	$1$	$1$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{247}{420}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{193}{420}\right)$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{101}{210}\right)$	$e\left(\frac{73}{84}\right)$
$\chi_{44100}(2617,\cdot)$	$1$	$1$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{137}{420}\right)$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{323}{420}\right)$	$e\left(\frac{143}{210}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{83}{84}\right)$
$\chi_{44100}(3373,\cdot)$	$1$	$1$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{239}{420}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{401}{420}\right)$	$e\left(\frac{41}{210}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{5}{84}\right)$
$\chi_{44100}(3877,\cdot)$	$1$	$1$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{209}{420}\right)$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{131}{420}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{140}\right)$	$e\left(\frac{37}{210}\right)$	$e\left(\frac{23}{84}\right)$
$\chi_{44100}(4297,\cdot)$	$1$	$1$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{373}{420}\right)$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{67}{420}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{31}{84}\right)$
$\chi_{44100}(4633,\cdot)$	$1$	$1$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{227}{420}\right)$	$e\left(\frac{103}{140}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{293}{420}\right)$	$e\left(\frac{53}{210}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{1}{210}\right)$	$e\left(\frac{29}{84}\right)$
$\chi_{44100}(5053,\cdot)$	$1$	$1$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{223}{420}\right)$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{397}{420}\right)$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{149}{210}\right)$	$e\left(\frac{37}{84}\right)$
$\chi_{44100}(5137,\cdot)$	$1$	$1$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{281}{420}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{359}{420}\right)$	$e\left(\frac{209}{210}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{67}{140}\right)$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{47}{84}\right)$
$\chi_{44100}(6313,\cdot)$	$1$	$1$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{211}{420}\right)$	$e\left(\frac{39}{140}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{289}{420}\right)$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{137}{140}\right)$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{61}{84}\right)$
$\chi_{44100}(6397,\cdot)$	$1$	$1$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{353}{420}\right)$	$e\left(\frac{117}{140}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{167}{420}\right)$	$e\left(\frac{137}{210}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{169}{210}\right)$	$e\left(\frac{71}{84}\right)$
$\chi_{44100}(6817,\cdot)$	$1$	$1$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{97}{420}\right)$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{103}{420}\right)$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{59}{140}\right)$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{79}{84}\right)$
$\chi_{44100}(7573,\cdot)$	$1$	$1$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{199}{420}\right)$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{181}{420}\right)$	$e\left(\frac{151}{210}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{1}{84}\right)$
$\chi_{44100}(8077,\cdot)$	$1$	$1$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{169}{420}\right)$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{331}{420}\right)$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{19}{84}\right)$
$\chi_{44100}(8413,\cdot)$	$1$	$1$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{191}{420}\right)$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{389}{420}\right)$	$e\left(\frac{89}{210}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{17}{84}\right)$
$\chi_{44100}(8833,\cdot)$	$1$	$1$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{187}{420}\right)$	$e\left(\frac{83}{140}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{73}{420}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{69}{140}\right)$	$e\left(\frac{11}{210}\right)$	$e\left(\frac{25}{84}\right)$
$\chi_{44100}(9337,\cdot)$	$1$	$1$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{241}{420}\right)$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{139}{420}\right)$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{43}{84}\right)$
$\chi_{44100}(9673,\cdot)$	$1$	$1$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{179}{420}\right)$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{281}{420}\right)$	$e\left(\frac{101}{210}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{97}{210}\right)$	$e\left(\frac{41}{84}\right)$
$\chi_{44100}(10177,\cdot)$	$1$	$1$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{149}{420}\right)$	$e\left(\frac{1}{140}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{420}\right)$	$e\left(\frac{131}{210}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{43}{140}\right)$	$e\left(\frac{157}{210}\right)$	$e\left(\frac{59}{84}\right)$
$\chi_{44100}(10597,\cdot)$	$1$	$1$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{313}{420}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{367}{420}\right)$	$e\left(\frac{37}{210}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{179}{210}\right)$	$e\left(\frac{67}{84}\right)$
$\chi_{44100}(10933,\cdot)$	$1$	$1$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{167}{420}\right)$	$e\left(\frac{3}{140}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{173}{420}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{129}{140}\right)$	$e\left(\frac{121}{210}\right)$	$e\left(\frac{65}{84}\right)$
$\chi_{44100}(11353,\cdot)$	$1$	$1$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{163}{420}\right)$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{277}{420}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{140}\right)$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{73}{84}\right)$
$\chi_{44100}(11437,\cdot)$	$1$	$1$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{221}{420}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{239}{420}\right)$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{13}{210}\right)$	$e\left(\frac{83}{84}\right)$
$\chi_{44100}(12613,\cdot)$	$1$	$1$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{151}{420}\right)$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{169}{420}\right)$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{83}{210}\right)$	$e\left(\frac{13}{84}\right)$
$\chi_{44100}(12697,\cdot)$	$1$	$1$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{293}{420}\right)$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{47}{420}\right)$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{31}{140}\right)$	$e\left(\frac{79}{210}\right)$	$e\left(\frac{23}{84}\right)$
$\chi_{44100}(13117,\cdot)$	$1$	$1$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{37}{420}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{403}{420}\right)$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{101}{210}\right)$	$e\left(\frac{31}{84}\right)$
$\chi_{44100}(13453,\cdot)$	$1$	$1$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{143}{420}\right)$	$e\left(\frac{47}{140}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{377}{420}\right)$	$e\left(\frac{137}{210}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{169}{210}\right)$	$e\left(\frac{29}{84}\right)$

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	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{44100}(13,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{271}{420}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{409}{420}\right)\)	\(e\left(\frac{79}{210}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{53}{210}\right)\)	\(e\left(\frac{25}{84}\right)\)
\(\chi_{44100}(517,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{157}{420}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{223}{420}\right)\)	\(e\left(\frac{193}{210}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{140}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{43}{84}\right)\)
\(\chi_{44100}(853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{263}{420}\right)\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{197}{420}\right)\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{41}{84}\right)\)
\(\chi_{44100}(1777,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{229}{420}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{31}{420}\right)\)	\(e\left(\frac{121}{210}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{137}{210}\right)\)	\(e\left(\frac{67}{84}\right)\)
\(\chi_{44100}(2113,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{251}{420}\right)\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{89}{420}\right)\)	\(e\left(\frac{29}{210}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{65}{84}\right)\)
\(\chi_{44100}(2533,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{247}{420}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{193}{420}\right)\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{101}{210}\right)\)	\(e\left(\frac{73}{84}\right)\)
\(\chi_{44100}(2617,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{137}{420}\right)\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{323}{420}\right)\)	\(e\left(\frac{143}{210}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{83}{84}\right)\)
\(\chi_{44100}(3373,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{239}{420}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{401}{420}\right)\)	\(e\left(\frac{41}{210}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{5}{84}\right)\)
\(\chi_{44100}(3877,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{209}{420}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{131}{420}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{140}\right)\)	\(e\left(\frac{37}{210}\right)\)	\(e\left(\frac{23}{84}\right)\)
\(\chi_{44100}(4297,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{373}{420}\right)\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{67}{420}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{31}{84}\right)\)
\(\chi_{44100}(4633,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{227}{420}\right)\)	\(e\left(\frac{103}{140}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{293}{420}\right)\)	\(e\left(\frac{53}{210}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{1}{210}\right)\)	\(e\left(\frac{29}{84}\right)\)
\(\chi_{44100}(5053,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{223}{420}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{397}{420}\right)\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{149}{210}\right)\)	\(e\left(\frac{37}{84}\right)\)
\(\chi_{44100}(5137,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{281}{420}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{359}{420}\right)\)	\(e\left(\frac{209}{210}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{67}{140}\right)\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{47}{84}\right)\)
\(\chi_{44100}(6313,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{211}{420}\right)\)	\(e\left(\frac{39}{140}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{289}{420}\right)\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{137}{140}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{61}{84}\right)\)
\(\chi_{44100}(6397,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{353}{420}\right)\)	\(e\left(\frac{117}{140}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{167}{420}\right)\)	\(e\left(\frac{137}{210}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{169}{210}\right)\)	\(e\left(\frac{71}{84}\right)\)
\(\chi_{44100}(6817,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{97}{420}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{103}{420}\right)\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{59}{140}\right)\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{79}{84}\right)\)
\(\chi_{44100}(7573,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{199}{420}\right)\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{181}{420}\right)\)	\(e\left(\frac{151}{210}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{1}{84}\right)\)
\(\chi_{44100}(8077,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{169}{420}\right)\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{331}{420}\right)\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{19}{84}\right)\)
\(\chi_{44100}(8413,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{191}{420}\right)\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{389}{420}\right)\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{17}{84}\right)\)
\(\chi_{44100}(8833,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{187}{420}\right)\)	\(e\left(\frac{83}{140}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{73}{420}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{69}{140}\right)\)	\(e\left(\frac{11}{210}\right)\)	\(e\left(\frac{25}{84}\right)\)
\(\chi_{44100}(9337,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{241}{420}\right)\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{139}{420}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{43}{84}\right)\)
\(\chi_{44100}(9673,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{179}{420}\right)\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{281}{420}\right)\)	\(e\left(\frac{101}{210}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{97}{210}\right)\)	\(e\left(\frac{41}{84}\right)\)
\(\chi_{44100}(10177,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{149}{420}\right)\)	\(e\left(\frac{1}{140}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{420}\right)\)	\(e\left(\frac{131}{210}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{43}{140}\right)\)	\(e\left(\frac{157}{210}\right)\)	\(e\left(\frac{59}{84}\right)\)
\(\chi_{44100}(10597,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{313}{420}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{367}{420}\right)\)	\(e\left(\frac{37}{210}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{179}{210}\right)\)	\(e\left(\frac{67}{84}\right)\)
\(\chi_{44100}(10933,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{167}{420}\right)\)	\(e\left(\frac{3}{140}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{173}{420}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{129}{140}\right)\)	\(e\left(\frac{121}{210}\right)\)	\(e\left(\frac{65}{84}\right)\)
\(\chi_{44100}(11353,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{163}{420}\right)\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{277}{420}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{140}\right)\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{73}{84}\right)\)
\(\chi_{44100}(11437,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{221}{420}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{239}{420}\right)\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{13}{210}\right)\)	\(e\left(\frac{83}{84}\right)\)
\(\chi_{44100}(12613,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{151}{420}\right)\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{169}{420}\right)\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{83}{210}\right)\)	\(e\left(\frac{13}{84}\right)\)
\(\chi_{44100}(12697,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{293}{420}\right)\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{47}{420}\right)\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{31}{140}\right)\)	\(e\left(\frac{79}{210}\right)\)	\(e\left(\frac{23}{84}\right)\)
\(\chi_{44100}(13117,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{37}{420}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{403}{420}\right)\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{101}{210}\right)\)	\(e\left(\frac{31}{84}\right)\)
\(\chi_{44100}(13453,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{143}{420}\right)\)	\(e\left(\frac{47}{140}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{377}{420}\right)\)	\(e\left(\frac{137}{210}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{169}{210}\right)\)	\(e\left(\frac{29}{84}\right)\)

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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.rl
Modulus	$44100$
Conductor	$11025$
Order	$420$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(44100\)
Conductor:	\(11025\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(420\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 11025.iw	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)