LMFDB - Dirichlet character orbit 44100.sa

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(44100, base_ring=CyclotomicField(420)) M = H._module chi = DirichletCharacter(H, M([210,140,147,290])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(103,44100)) 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:	$420$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{420})$
Fixed field:	Number field defined by a degree 420 polynomial (not computed)

First 31 of 96 characters in Galois orbit

Character	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{44100}(103,\cdot)$	$-1$	$1$	$e\left(\frac{11}{210}\right)$	$e\left(\frac{43}{420}\right)$	$e\left(\frac{341}{420}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{107}{420}\right)$	$e\left(\frac{97}{210}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{103}{420}\right)$	$e\left(\frac{89}{210}\right)$	$e\left(\frac{19}{84}\right)$
$\chi_{44100}(367,\cdot)$	$-1$	$1$	$e\left(\frac{169}{210}\right)$	$e\left(\frac{317}{420}\right)$	$e\left(\frac{199}{420}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{193}{420}\right)$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{420}\right)$	$e\left(\frac{31}{210}\right)$	$e\left(\frac{17}{84}\right)$
$\chi_{44100}(1123,\cdot)$	$-1$	$1$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{59}{420}\right)$	$e\left(\frac{253}{420}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{391}{420}\right)$	$e\left(\frac{11}{210}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{239}{420}\right)$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{71}{84}\right)$
$\chi_{44100}(1363,\cdot)$	$-1$	$1$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{331}{420}\right)$	$e\left(\frac{17}{420}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{179}{420}\right)$	$e\left(\frac{19}{210}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{31}{420}\right)$	$e\left(\frac{143}{210}\right)$	$e\left(\frac{31}{84}\right)$
$\chi_{44100}(1627,\cdot)$	$-1$	$1$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{209}{420}\right)$	$e\left(\frac{163}{420}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{61}{420}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{149}{420}\right)$	$e\left(\frac{37}{210}\right)$	$e\left(\frac{65}{84}\right)$
$\chi_{44100}(1867,\cdot)$	$-1$	$1$	$e\left(\frac{179}{210}\right)$	$e\left(\frac{337}{420}\right)$	$e\left(\frac{299}{420}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{233}{420}\right)$	$e\left(\frac{13}{210}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{397}{420}\right)$	$e\left(\frac{131}{210}\right)$	$e\left(\frac{61}{84}\right)$
$\chi_{44100}(2623,\cdot)$	$-1$	$1$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{199}{420}\right)$	$e\left(\frac{113}{420}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{251}{420}\right)$	$e\left(\frac{151}{210}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{379}{420}\right)$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{43}{84}\right)$
$\chi_{44100}(2887,\cdot)$	$-1$	$1$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{101}{420}\right)$	$e\left(\frac{127}{420}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{349}{420}\right)$	$e\left(\frac{179}{210}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{281}{420}\right)$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{29}{84}\right)$
$\chi_{44100}(3127,\cdot)$	$-1$	$1$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{289}{420}\right)$	$e\left(\frac{143}{420}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{221}{420}\right)$	$e\left(\frac{61}{210}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{409}{420}\right)$	$e\left(\frac{17}{210}\right)$	$e\left(\frac{73}{84}\right)$
$\chi_{44100}(3883,\cdot)$	$-1$	$1$	$e\left(\frac{149}{210}\right)$	$e\left(\frac{67}{420}\right)$	$e\left(\frac{209}{420}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{323}{420}\right)$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{307}{420}\right)$	$e\left(\frac{41}{210}\right)$	$e\left(\frac{55}{84}\right)$
$\chi_{44100}(4387,\cdot)$	$-1$	$1$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{241}{420}\right)$	$e\left(\frac{407}{420}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{209}{420}\right)$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{420}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{1}{84}\right)$
$\chi_{44100}(4903,\cdot)$	$-1$	$1$	$e\left(\frac{151}{210}\right)$	$e\left(\frac{323}{420}\right)$	$e\left(\frac{61}{420}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{247}{420}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{383}{420}\right)$	$e\left(\frac{19}{210}\right)$	$e\left(\frac{47}{84}\right)$
$\chi_{44100}(5647,\cdot)$	$-1$	$1$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{193}{420}\right)$	$e\left(\frac{251}{420}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{197}{420}\right)$	$e\left(\frac{157}{210}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{420}\right)$	$e\left(\frac{209}{210}\right)$	$e\left(\frac{13}{84}\right)$
$\chi_{44100}(6163,\cdot)$	$-1$	$1$	$e\left(\frac{97}{210}\right)$	$e\left(\frac{131}{420}\right)$	$e\left(\frac{277}{420}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{199}{420}\right)$	$e\left(\frac{149}{210}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{420}\right)$	$e\left(\frac{193}{210}\right)$	$e\left(\frac{11}{84}\right)$
$\chi_{44100}(6403,\cdot)$	$-1$	$1$	$e\left(\frac{101}{210}\right)$	$e\left(\frac{223}{420}\right)$	$e\left(\frac{401}{420}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{47}{420}\right)$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{163}{420}\right)$	$e\left(\frac{149}{210}\right)$	$e\left(\frac{79}{84}\right)$
$\chi_{44100}(6667,\cdot)$	$-1$	$1$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{197}{420}\right)$	$e\left(\frac{19}{420}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{373}{420}\right)$	$e\left(\frac{83}{210}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{257}{420}\right)$	$e\left(\frac{61}{210}\right)$	$e\left(\frac{5}{84}\right)$
$\chi_{44100}(7423,\cdot)$	$-1$	$1$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{359}{420}\right)$	$e\left(\frac{73}{420}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{151}{420}\right)$	$e\left(\frac{131}{210}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{59}{420}\right)$	$e\left(\frac{157}{210}\right)$	$e\left(\frac{59}{84}\right)$
$\chi_{44100}(7927,\cdot)$	$-1$	$1$	$e\left(\frac{13}{210}\right)$	$e\left(\frac{89}{420}\right)$	$e\left(\frac{403}{420}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{241}{420}\right)$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{389}{420}\right)$	$e\left(\frac{67}{210}\right)$	$e\left(\frac{53}{84}\right)$
$\chi_{44100}(8167,\cdot)$	$-1$	$1$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{97}{420}\right)$	$e\left(\frac{359}{420}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{173}{420}\right)$	$e\left(\frac{43}{210}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{37}{420}\right)$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{37}{84}\right)$
$\chi_{44100}(8683,\cdot)$	$-1$	$1$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{167}{420}\right)$	$e\left(\frac{289}{420}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{103}{420}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{107}{420}\right)$	$e\left(\frac{121}{210}\right)$	$e\left(\frac{23}{84}\right)$
$\chi_{44100}(8923,\cdot)$	$-1$	$1$	$e\left(\frac{53}{210}\right)$	$e\left(\frac{379}{420}\right)$	$e\left(\frac{173}{420}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{191}{420}\right)$	$e\left(\frac{181}{210}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{420}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{19}{84}\right)$
$\chi_{44100}(9187,\cdot)$	$-1$	$1$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{401}{420}\right)$	$e\left(\frac{367}{420}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{109}{420}\right)$	$e\left(\frac{89}{210}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{101}{420}\right)$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{17}{84}\right)$
$\chi_{44100}(10183,\cdot)$	$-1$	$1$	$e\left(\frac{29}{210}\right)$	$e\left(\frac{247}{420}\right)$	$e\left(\frac{269}{420}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{263}{420}\right)$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{367}{420}\right)$	$e\left(\frac{101}{210}\right)$	$e\left(\frac{31}{84}\right)$
$\chi_{44100}(10447,\cdot)$	$-1$	$1$	$e\left(\frac{31}{210}\right)$	$e\left(\frac{293}{420}\right)$	$e\left(\frac{331}{420}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{397}{420}\right)$	$e\left(\frac{197}{210}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{233}{420}\right)$	$e\left(\frac{79}{210}\right)$	$e\left(\frac{65}{84}\right)$
$\chi_{44100}(10687,\cdot)$	$-1$	$1$	$e\left(\frac{137}{210}\right)$	$e\left(\frac{1}{420}\right)$	$e\left(\frac{47}{420}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{149}{420}\right)$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{61}{420}\right)$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{61}{84}\right)$
$\chi_{44100}(11947,\cdot)$	$-1$	$1$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{373}{420}\right)$	$e\left(\frac{311}{420}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{137}{420}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{73}{420}\right)$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{73}{84}\right)$
$\chi_{44100}(12463,\cdot)$	$-1$	$1$	$e\left(\frac{37}{210}\right)$	$e\left(\frac{11}{420}\right)$	$e\left(\frac{97}{420}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{379}{420}\right)$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{251}{420}\right)$	$e\left(\frac{13}{210}\right)$	$e\left(\frac{83}{84}\right)$
$\chi_{44100}(12703,\cdot)$	$-1$	$1$	$e\left(\frac{191}{210}\right)$	$e\left(\frac{403}{420}\right)$	$e\left(\frac{41}{420}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{407}{420}\right)$	$e\left(\frac{157}{210}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{223}{420}\right)$	$e\left(\frac{209}{210}\right)$	$e\left(\frac{55}{84}\right)$
$\chi_{44100}(13723,\cdot)$	$-1$	$1$	$e\left(\frac{193}{210}\right)$	$e\left(\frac{239}{420}\right)$	$e\left(\frac{313}{420}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{331}{420}\right)$	$e\left(\frac{41}{210}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{299}{420}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{47}{84}\right)$
$\chi_{44100}(13963,\cdot)$	$-1$	$1$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{271}{420}\right)$	$e\left(\frac{137}{420}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{59}{420}\right)$	$e\left(\frac{79}{210}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{151}{420}\right)$	$e\left(\frac{53}{210}\right)$	$e\left(\frac{67}{84}\right)$
$\chi_{44100}(14227,\cdot)$	$-1$	$1$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{389}{420}\right)$	$e\left(\frac{223}{420}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{420}\right)$	$e\left(\frac{101}{210}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{209}{420}\right)$	$e\left(\frac{97}{210}\right)$	$e\left(\frac{41}{84}\right)$

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	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{44100}(103,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{210}\right)\)	\(e\left(\frac{43}{420}\right)\)	\(e\left(\frac{341}{420}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{107}{420}\right)\)	\(e\left(\frac{97}{210}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{103}{420}\right)\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{19}{84}\right)\)
\(\chi_{44100}(367,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{169}{210}\right)\)	\(e\left(\frac{317}{420}\right)\)	\(e\left(\frac{199}{420}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{193}{420}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{420}\right)\)	\(e\left(\frac{31}{210}\right)\)	\(e\left(\frac{17}{84}\right)\)
\(\chi_{44100}(1123,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{59}{420}\right)\)	\(e\left(\frac{253}{420}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{391}{420}\right)\)	\(e\left(\frac{11}{210}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{239}{420}\right)\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{71}{84}\right)\)
\(\chi_{44100}(1363,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{331}{420}\right)\)	\(e\left(\frac{17}{420}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{179}{420}\right)\)	\(e\left(\frac{19}{210}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{31}{420}\right)\)	\(e\left(\frac{143}{210}\right)\)	\(e\left(\frac{31}{84}\right)\)
\(\chi_{44100}(1627,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{209}{420}\right)\)	\(e\left(\frac{163}{420}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{61}{420}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{149}{420}\right)\)	\(e\left(\frac{37}{210}\right)\)	\(e\left(\frac{65}{84}\right)\)
\(\chi_{44100}(1867,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{179}{210}\right)\)	\(e\left(\frac{337}{420}\right)\)	\(e\left(\frac{299}{420}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{233}{420}\right)\)	\(e\left(\frac{13}{210}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{397}{420}\right)\)	\(e\left(\frac{131}{210}\right)\)	\(e\left(\frac{61}{84}\right)\)
\(\chi_{44100}(2623,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{199}{420}\right)\)	\(e\left(\frac{113}{420}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{251}{420}\right)\)	\(e\left(\frac{151}{210}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{379}{420}\right)\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{43}{84}\right)\)
\(\chi_{44100}(2887,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{101}{420}\right)\)	\(e\left(\frac{127}{420}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{349}{420}\right)\)	\(e\left(\frac{179}{210}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{281}{420}\right)\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{29}{84}\right)\)
\(\chi_{44100}(3127,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{289}{420}\right)\)	\(e\left(\frac{143}{420}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{221}{420}\right)\)	\(e\left(\frac{61}{210}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{409}{420}\right)\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{73}{84}\right)\)
\(\chi_{44100}(3883,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{210}\right)\)	\(e\left(\frac{67}{420}\right)\)	\(e\left(\frac{209}{420}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{323}{420}\right)\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{307}{420}\right)\)	\(e\left(\frac{41}{210}\right)\)	\(e\left(\frac{55}{84}\right)\)
\(\chi_{44100}(4387,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{241}{420}\right)\)	\(e\left(\frac{407}{420}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{209}{420}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{420}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{1}{84}\right)\)
\(\chi_{44100}(4903,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{151}{210}\right)\)	\(e\left(\frac{323}{420}\right)\)	\(e\left(\frac{61}{420}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{247}{420}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{383}{420}\right)\)	\(e\left(\frac{19}{210}\right)\)	\(e\left(\frac{47}{84}\right)\)
\(\chi_{44100}(5647,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{193}{420}\right)\)	\(e\left(\frac{251}{420}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{197}{420}\right)\)	\(e\left(\frac{157}{210}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{420}\right)\)	\(e\left(\frac{209}{210}\right)\)	\(e\left(\frac{13}{84}\right)\)
\(\chi_{44100}(6163,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{97}{210}\right)\)	\(e\left(\frac{131}{420}\right)\)	\(e\left(\frac{277}{420}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{199}{420}\right)\)	\(e\left(\frac{149}{210}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{420}\right)\)	\(e\left(\frac{193}{210}\right)\)	\(e\left(\frac{11}{84}\right)\)
\(\chi_{44100}(6403,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{101}{210}\right)\)	\(e\left(\frac{223}{420}\right)\)	\(e\left(\frac{401}{420}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{47}{420}\right)\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{163}{420}\right)\)	\(e\left(\frac{149}{210}\right)\)	\(e\left(\frac{79}{84}\right)\)
\(\chi_{44100}(6667,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{197}{420}\right)\)	\(e\left(\frac{19}{420}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{373}{420}\right)\)	\(e\left(\frac{83}{210}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{257}{420}\right)\)	\(e\left(\frac{61}{210}\right)\)	\(e\left(\frac{5}{84}\right)\)
\(\chi_{44100}(7423,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{359}{420}\right)\)	\(e\left(\frac{73}{420}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{151}{420}\right)\)	\(e\left(\frac{131}{210}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{59}{420}\right)\)	\(e\left(\frac{157}{210}\right)\)	\(e\left(\frac{59}{84}\right)\)
\(\chi_{44100}(7927,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{210}\right)\)	\(e\left(\frac{89}{420}\right)\)	\(e\left(\frac{403}{420}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{241}{420}\right)\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{389}{420}\right)\)	\(e\left(\frac{67}{210}\right)\)	\(e\left(\frac{53}{84}\right)\)
\(\chi_{44100}(8167,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{97}{420}\right)\)	\(e\left(\frac{359}{420}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{173}{420}\right)\)	\(e\left(\frac{43}{210}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{37}{420}\right)\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{37}{84}\right)\)
\(\chi_{44100}(8683,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{167}{420}\right)\)	\(e\left(\frac{289}{420}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{103}{420}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{107}{420}\right)\)	\(e\left(\frac{121}{210}\right)\)	\(e\left(\frac{23}{84}\right)\)
\(\chi_{44100}(8923,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{210}\right)\)	\(e\left(\frac{379}{420}\right)\)	\(e\left(\frac{173}{420}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{191}{420}\right)\)	\(e\left(\frac{181}{210}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{420}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{19}{84}\right)\)
\(\chi_{44100}(9187,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{401}{420}\right)\)	\(e\left(\frac{367}{420}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{109}{420}\right)\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{101}{420}\right)\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{17}{84}\right)\)
\(\chi_{44100}(10183,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{210}\right)\)	\(e\left(\frac{247}{420}\right)\)	\(e\left(\frac{269}{420}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{263}{420}\right)\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{367}{420}\right)\)	\(e\left(\frac{101}{210}\right)\)	\(e\left(\frac{31}{84}\right)\)
\(\chi_{44100}(10447,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{210}\right)\)	\(e\left(\frac{293}{420}\right)\)	\(e\left(\frac{331}{420}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{397}{420}\right)\)	\(e\left(\frac{197}{210}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{233}{420}\right)\)	\(e\left(\frac{79}{210}\right)\)	\(e\left(\frac{65}{84}\right)\)
\(\chi_{44100}(10687,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{210}\right)\)	\(e\left(\frac{1}{420}\right)\)	\(e\left(\frac{47}{420}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{149}{420}\right)\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{61}{420}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{61}{84}\right)\)
\(\chi_{44100}(11947,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{373}{420}\right)\)	\(e\left(\frac{311}{420}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{137}{420}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{73}{420}\right)\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{73}{84}\right)\)
\(\chi_{44100}(12463,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{210}\right)\)	\(e\left(\frac{11}{420}\right)\)	\(e\left(\frac{97}{420}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{379}{420}\right)\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{251}{420}\right)\)	\(e\left(\frac{13}{210}\right)\)	\(e\left(\frac{83}{84}\right)\)
\(\chi_{44100}(12703,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{191}{210}\right)\)	\(e\left(\frac{403}{420}\right)\)	\(e\left(\frac{41}{420}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{407}{420}\right)\)	\(e\left(\frac{157}{210}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{223}{420}\right)\)	\(e\left(\frac{209}{210}\right)\)	\(e\left(\frac{55}{84}\right)\)
\(\chi_{44100}(13723,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{193}{210}\right)\)	\(e\left(\frac{239}{420}\right)\)	\(e\left(\frac{313}{420}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{331}{420}\right)\)	\(e\left(\frac{41}{210}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{299}{420}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{47}{84}\right)\)
\(\chi_{44100}(13963,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{271}{420}\right)\)	\(e\left(\frac{137}{420}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{59}{420}\right)\)	\(e\left(\frac{79}{210}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{151}{420}\right)\)	\(e\left(\frac{53}{210}\right)\)	\(e\left(\frac{67}{84}\right)\)
\(\chi_{44100}(14227,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{389}{420}\right)\)	\(e\left(\frac{223}{420}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{420}\right)\)	\(e\left(\frac{101}{210}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{209}{420}\right)\)	\(e\left(\frac{97}{210}\right)\)	\(e\left(\frac{41}{84}\right)\)

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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.sa
Modulus	$44100$
Conductor	$44100$
Order	$420$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

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