LMFDB - Dirichlet character orbit 30100.om

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(30100, base_ring=CyclotomicField(210)) M = H._module chi = DirichletCharacter(H, M([0,84,140,20])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(81, 30100)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("30100.81"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$30100$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$7525$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$105$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 7525.hh	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{105})$
Fixed field:	Number field defined by a degree 105 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$23$	$27$	$29$	$31$
$\chi_{30100}(81,\cdot)$	$1$	$1$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{11}{105}\right)$
$\chi_{30100}(541,\cdot)$	$1$	$1$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{43}{105}\right)$
$\chi_{30100}(961,\cdot)$	$1$	$1$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{82}{105}\right)$
$\chi_{30100}(2081,\cdot)$	$1$	$1$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{31}{105}\right)$
$\chi_{30100}(2181,\cdot)$	$1$	$1$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{41}{105}\right)$
$\chi_{30100}(2461,\cdot)$	$1$	$1$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{17}{105}\right)$
$\chi_{30100}(3621,\cdot)$	$1$	$1$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{79}{105}\right)$
$\chi_{30100}(3721,\cdot)$	$1$	$1$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{44}{105}\right)$
$\chi_{30100}(4281,\cdot)$	$1$	$1$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{26}{105}\right)$
$\chi_{30100}(5861,\cdot)$	$1$	$1$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{67}{105}\right)$
$\chi_{30100}(6421,\cdot)$	$1$	$1$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{34}{105}\right)$
$\chi_{30100}(6561,\cdot)$	$1$	$1$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{22}{105}\right)$
$\chi_{30100}(6981,\cdot)$	$1$	$1$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{61}{105}\right)$
$\chi_{30100}(7221,\cdot)$	$1$	$1$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{29}{105}\right)$
$\chi_{30100}(8481,\cdot)$	$1$	$1$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{101}{105}\right)$
$\chi_{30100}(9641,\cdot)$	$1$	$1$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{58}{105}\right)$
$\chi_{30100}(9741,\cdot)$	$1$	$1$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{23}{105}\right)$
$\chi_{30100}(11881,\cdot)$	$1$	$1$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{46}{105}\right)$
$\chi_{30100}(12121,\cdot)$	$1$	$1$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{74}{105}\right)$
$\chi_{30100}(12441,\cdot)$	$1$	$1$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{13}{105}\right)$
$\chi_{30100}(12581,\cdot)$	$1$	$1$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{1}{105}\right)$
$\chi_{30100}(13241,\cdot)$	$1$	$1$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{8}{105}\right)$
$\chi_{30100}(14121,\cdot)$	$1$	$1$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{94}{105}\right)$
$\chi_{30100}(14221,\cdot)$	$1$	$1$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{104}{105}\right)$
$\chi_{30100}(15661,\cdot)$	$1$	$1$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{37}{105}\right)$
$\chi_{30100}(15761,\cdot)$	$1$	$1$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{2}{105}\right)$
$\chi_{30100}(16321,\cdot)$	$1$	$1$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{89}{105}\right)$
$\chi_{30100}(18141,\cdot)$	$1$	$1$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{53}{105}\right)$
$\chi_{30100}(18461,\cdot)$	$1$	$1$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{97}{105}\right)$
$\chi_{30100}(19021,\cdot)$	$1$	$1$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{19}{105}\right)$
$\chi_{30100}(19261,\cdot)$	$1$	$1$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{92}{105}\right)$

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	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\(\chi_{30100}(81,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{11}{105}\right)\)
\(\chi_{30100}(541,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{43}{105}\right)\)
\(\chi_{30100}(961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{82}{105}\right)\)
\(\chi_{30100}(2081,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{31}{105}\right)\)
\(\chi_{30100}(2181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{41}{105}\right)\)
\(\chi_{30100}(2461,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{17}{105}\right)\)
\(\chi_{30100}(3621,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{79}{105}\right)\)
\(\chi_{30100}(3721,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{44}{105}\right)\)
\(\chi_{30100}(4281,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)
\(\chi_{30100}(5861,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{67}{105}\right)\)
\(\chi_{30100}(6421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{34}{105}\right)\)
\(\chi_{30100}(6561,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{22}{105}\right)\)
\(\chi_{30100}(6981,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{61}{105}\right)\)
\(\chi_{30100}(7221,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{29}{105}\right)\)
\(\chi_{30100}(8481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{101}{105}\right)\)
\(\chi_{30100}(9641,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{58}{105}\right)\)
\(\chi_{30100}(9741,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{23}{105}\right)\)
\(\chi_{30100}(11881,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{46}{105}\right)\)
\(\chi_{30100}(12121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{74}{105}\right)\)
\(\chi_{30100}(12441,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{13}{105}\right)\)
\(\chi_{30100}(12581,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{1}{105}\right)\)
\(\chi_{30100}(13241,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{8}{105}\right)\)
\(\chi_{30100}(14121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)
\(\chi_{30100}(14221,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{104}{105}\right)\)
\(\chi_{30100}(15661,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{37}{105}\right)\)
\(\chi_{30100}(15761,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{2}{105}\right)\)
\(\chi_{30100}(16321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{89}{105}\right)\)
\(\chi_{30100}(18141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{53}{105}\right)\)
\(\chi_{30100}(18461,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{97}{105}\right)\)
\(\chi_{30100}(19021,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{19}{105}\right)\)
\(\chi_{30100}(19261,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{92}{105}\right)\)

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First 31 of 48 characters in Galois orbit

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	30100.om
Modulus	$30100$
Conductor	$7525$
Order	$105$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(30100\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(7525\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(105\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 7525.hh	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);