LMFDB - Dirichlet character orbit 44100.rn

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(44100, base_ring=CyclotomicField(420)) M = H._module chi = DirichletCharacter(H, M([210,350,63,230])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(383,44100)) 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:	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	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{44100}(383,\cdot)$	$1$	$1$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{247}{420}\right)$	$e\left(\frac{59}{420}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{53}{420}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{367}{420}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{31}{84}\right)$
$\chi_{44100}(887,\cdot)$	$1$	$1$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{1}{420}\right)$	$e\left(\frac{257}{420}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{359}{420}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{61}{420}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{61}{84}\right)$
$\chi_{44100}(983,\cdot)$	$1$	$1$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{407}{420}\right)$	$e\left(\frac{19}{420}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{373}{420}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{47}{420}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{47}{84}\right)$
$\chi_{44100}(1487,\cdot)$	$1$	$1$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{221}{420}\right)$	$e\left(\frac{97}{420}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{379}{420}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{41}{420}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{41}{84}\right)$
$\chi_{44100}(2147,\cdot)$	$1$	$1$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{373}{420}\right)$	$e\left(\frac{101}{420}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{347}{420}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{73}{420}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{73}{84}\right)$
$\chi_{44100}(2747,\cdot)$	$1$	$1$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{113}{420}\right)$	$e\left(\frac{61}{420}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{247}{420}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{173}{420}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{5}{84}\right)$
$\chi_{44100}(2903,\cdot)$	$1$	$1$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{403}{420}\right)$	$e\left(\frac{251}{420}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{197}{420}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{223}{420}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{55}{84}\right)$
$\chi_{44100}(3503,\cdot)$	$1$	$1$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{23}{420}\right)$	$e\left(\frac{31}{420}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{277}{420}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{143}{420}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{59}{84}\right)$
$\chi_{44100}(4163,\cdot)$	$1$	$1$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{271}{420}\right)$	$e\left(\frac{347}{420}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{269}{420}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{151}{420}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{67}{84}\right)$
$\chi_{44100}(4667,\cdot)$	$1$	$1$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{277}{420}\right)$	$e\left(\frac{209}{420}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{323}{420}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{97}{420}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{13}{84}\right)$
$\chi_{44100}(4763,\cdot)$	$1$	$1$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{251}{420}\right)$	$e\left(\frac{247}{420}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{229}{420}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{191}{420}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{23}{84}\right)$
$\chi_{44100}(5267,\cdot)$	$1$	$1$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{317}{420}\right)$	$e\left(\frac{409}{420}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{403}{420}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{420}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{17}{84}\right)$
$\chi_{44100}(5423,\cdot)$	$1$	$1$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{139}{420}\right)$	$e\left(\frac{23}{420}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{341}{420}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{79}{420}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{79}{84}\right)$
$\chi_{44100}(5927,\cdot)$	$1$	$1$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{229}{420}\right)$	$e\left(\frac{53}{420}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{311}{420}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{109}{420}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{25}{84}\right)$
$\chi_{44100}(6023,\cdot)$	$1$	$1$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{59}{420}\right)$	$e\left(\frac{43}{420}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{181}{420}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{239}{420}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{71}{84}\right)$
$\chi_{44100}(6527,\cdot)$	$1$	$1$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{209}{420}\right)$	$e\left(\frac{373}{420}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{271}{420}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{149}{420}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{65}{84}\right)$
$\chi_{44100}(7187,\cdot)$	$1$	$1$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{181}{420}\right)$	$e\left(\frac{317}{420}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{299}{420}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{121}{420}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{37}{84}\right)$
$\chi_{44100}(7787,\cdot)$	$1$	$1$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{101}{420}\right)$	$e\left(\frac{337}{420}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{139}{420}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{281}{420}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{29}{84}\right)$
$\chi_{44100}(9203,\cdot)$	$1$	$1$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{163}{420}\right)$	$e\left(\frac{311}{420}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{137}{420}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{283}{420}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{31}{84}\right)$
$\chi_{44100}(9803,\cdot)$	$1$	$1$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{323}{420}\right)$	$e\left(\frac{271}{420}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{37}{420}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{383}{420}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{47}{84}\right)$
$\chi_{44100}(10463,\cdot)$	$1$	$1$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{31}{420}\right)$	$e\left(\frac{407}{420}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{209}{420}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{211}{420}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{43}{84}\right)$
$\chi_{44100}(10967,\cdot)$	$1$	$1$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{37}{420}\right)$	$e\left(\frac{269}{420}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{263}{420}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{157}{420}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{73}{84}\right)$
$\chi_{44100}(11063,\cdot)$	$1$	$1$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{131}{420}\right)$	$e\left(\frac{67}{420}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{409}{420}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{420}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{11}{84}\right)$
$\chi_{44100}(11567,\cdot)$	$1$	$1$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{197}{420}\right)$	$e\left(\frac{229}{420}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{163}{420}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{257}{420}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{5}{84}\right)$
$\chi_{44100}(11723,\cdot)$	$1$	$1$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{319}{420}\right)$	$e\left(\frac{83}{420}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{281}{420}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{139}{420}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{55}{84}\right)$
$\chi_{44100}(12227,\cdot)$	$1$	$1$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{409}{420}\right)$	$e\left(\frac{113}{420}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{251}{420}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{169}{420}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{1}{84}\right)$
$\chi_{44100}(12323,\cdot)$	$1$	$1$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{359}{420}\right)$	$e\left(\frac{283}{420}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{361}{420}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{59}{420}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{59}{84}\right)$
$\chi_{44100}(12827,\cdot)$	$1$	$1$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{89}{420}\right)$	$e\left(\frac{193}{420}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{31}{420}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{389}{420}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{53}{84}\right)$
$\chi_{44100}(12983,\cdot)$	$1$	$1$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{187}{420}\right)$	$e\left(\frac{179}{420}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{353}{420}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{67}{420}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{67}{84}\right)$
$\chi_{44100}(13487,\cdot)$	$1$	$1$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{361}{420}\right)$	$e\left(\frac{377}{420}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{239}{420}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{181}{420}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{13}{84}\right)$
$\chi_{44100}(13583,\cdot)$	$1$	$1$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{167}{420}\right)$	$e\left(\frac{79}{420}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{313}{420}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{107}{420}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{23}{84}\right)$

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	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{44100}(383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{247}{420}\right)\)	\(e\left(\frac{59}{420}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{53}{420}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{367}{420}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{31}{84}\right)\)
\(\chi_{44100}(887,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{1}{420}\right)\)	\(e\left(\frac{257}{420}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{359}{420}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{61}{420}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{61}{84}\right)\)
\(\chi_{44100}(983,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{407}{420}\right)\)	\(e\left(\frac{19}{420}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{373}{420}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{47}{420}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{47}{84}\right)\)
\(\chi_{44100}(1487,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{221}{420}\right)\)	\(e\left(\frac{97}{420}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{379}{420}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{41}{420}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{41}{84}\right)\)
\(\chi_{44100}(2147,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{373}{420}\right)\)	\(e\left(\frac{101}{420}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{347}{420}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{73}{420}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{73}{84}\right)\)
\(\chi_{44100}(2747,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{113}{420}\right)\)	\(e\left(\frac{61}{420}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{247}{420}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{173}{420}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{5}{84}\right)\)
\(\chi_{44100}(2903,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{403}{420}\right)\)	\(e\left(\frac{251}{420}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{197}{420}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{223}{420}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{55}{84}\right)\)
\(\chi_{44100}(3503,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{23}{420}\right)\)	\(e\left(\frac{31}{420}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{277}{420}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{143}{420}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{59}{84}\right)\)
\(\chi_{44100}(4163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{271}{420}\right)\)	\(e\left(\frac{347}{420}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{269}{420}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{151}{420}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{67}{84}\right)\)
\(\chi_{44100}(4667,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{277}{420}\right)\)	\(e\left(\frac{209}{420}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{323}{420}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{97}{420}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{13}{84}\right)\)
\(\chi_{44100}(4763,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{251}{420}\right)\)	\(e\left(\frac{247}{420}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{229}{420}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{191}{420}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{23}{84}\right)\)
\(\chi_{44100}(5267,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{317}{420}\right)\)	\(e\left(\frac{409}{420}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{403}{420}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{420}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{17}{84}\right)\)
\(\chi_{44100}(5423,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{139}{420}\right)\)	\(e\left(\frac{23}{420}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{341}{420}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{79}{420}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{79}{84}\right)\)
\(\chi_{44100}(5927,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{229}{420}\right)\)	\(e\left(\frac{53}{420}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{311}{420}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{109}{420}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{25}{84}\right)\)
\(\chi_{44100}(6023,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{59}{420}\right)\)	\(e\left(\frac{43}{420}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{181}{420}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{239}{420}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{71}{84}\right)\)
\(\chi_{44100}(6527,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{209}{420}\right)\)	\(e\left(\frac{373}{420}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{271}{420}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{149}{420}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{65}{84}\right)\)
\(\chi_{44100}(7187,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{181}{420}\right)\)	\(e\left(\frac{317}{420}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{299}{420}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{121}{420}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{37}{84}\right)\)
\(\chi_{44100}(7787,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{101}{420}\right)\)	\(e\left(\frac{337}{420}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{139}{420}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{281}{420}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{29}{84}\right)\)
\(\chi_{44100}(9203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{163}{420}\right)\)	\(e\left(\frac{311}{420}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{137}{420}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{283}{420}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{31}{84}\right)\)
\(\chi_{44100}(9803,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{323}{420}\right)\)	\(e\left(\frac{271}{420}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{37}{420}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{383}{420}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{47}{84}\right)\)
\(\chi_{44100}(10463,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{31}{420}\right)\)	\(e\left(\frac{407}{420}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{209}{420}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{211}{420}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{43}{84}\right)\)
\(\chi_{44100}(10967,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{37}{420}\right)\)	\(e\left(\frac{269}{420}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{263}{420}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{157}{420}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{73}{84}\right)\)
\(\chi_{44100}(11063,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{131}{420}\right)\)	\(e\left(\frac{67}{420}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{409}{420}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{420}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{11}{84}\right)\)
\(\chi_{44100}(11567,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{197}{420}\right)\)	\(e\left(\frac{229}{420}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{163}{420}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{257}{420}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{5}{84}\right)\)
\(\chi_{44100}(11723,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{319}{420}\right)\)	\(e\left(\frac{83}{420}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{281}{420}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{139}{420}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{55}{84}\right)\)
\(\chi_{44100}(12227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{409}{420}\right)\)	\(e\left(\frac{113}{420}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{251}{420}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{169}{420}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{1}{84}\right)\)
\(\chi_{44100}(12323,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{359}{420}\right)\)	\(e\left(\frac{283}{420}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{361}{420}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{59}{420}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{59}{84}\right)\)
\(\chi_{44100}(12827,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{89}{420}\right)\)	\(e\left(\frac{193}{420}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{31}{420}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{389}{420}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{53}{84}\right)\)
\(\chi_{44100}(12983,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{187}{420}\right)\)	\(e\left(\frac{179}{420}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{353}{420}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{67}{420}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{67}{84}\right)\)
\(\chi_{44100}(13487,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{361}{420}\right)\)	\(e\left(\frac{377}{420}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{239}{420}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{181}{420}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{13}{84}\right)\)
\(\chi_{44100}(13583,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{167}{420}\right)\)	\(e\left(\frac{79}{420}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{313}{420}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{107}{420}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{23}{84}\right)\)

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

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:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)