LMFDB - Dirichlet character orbit 4851.fa

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4851, base_ring=CyclotomicField(210)) M = H._module chi = DirichletCharacter(H, M([70,50,42])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(4,4851)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$4851$
Conductor:	$4851$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$105$	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:	$\Q(\zeta_{105})$
Fixed field:	Number field defined by a degree 105 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$13$	$16$	$17$	$19$	$20$
$\chi_{4851}(4,\cdot)$	$1$	$1$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{86}{105}\right)$
$\chi_{4851}(16,\cdot)$	$1$	$1$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{67}{105}\right)$
$\chi_{4851}(130,\cdot)$	$1$	$1$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{68}{105}\right)$
$\chi_{4851}(256,\cdot)$	$1$	$1$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{29}{105}\right)$
$\chi_{4851}(268,\cdot)$	$1$	$1$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{16}{105}\right)$
$\chi_{4851}(394,\cdot)$	$1$	$1$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{43}{105}\right)$
$\chi_{4851}(445,\cdot)$	$1$	$1$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{105}\right)$
$\chi_{4851}(697,\cdot)$	$1$	$1$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{71}{105}\right)$
$\chi_{4851}(709,\cdot)$	$1$	$1$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{37}{105}\right)$
$\chi_{4851}(823,\cdot)$	$1$	$1$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{53}{105}\right)$
$\chi_{4851}(1087,\cdot)$	$1$	$1$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{105}\right)$
$\chi_{4851}(1138,\cdot)$	$1$	$1$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{92}{105}\right)$
$\chi_{4851}(1213,\cdot)$	$1$	$1$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{19}{105}\right)$
$\chi_{4851}(1516,\cdot)$	$1$	$1$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{38}{105}\right)$
$\chi_{4851}(1642,\cdot)$	$1$	$1$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{16}{105}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{104}{105}\right)$
$\chi_{4851}(1654,\cdot)$	$1$	$1$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{61}{105}\right)$
$\chi_{4851}(1780,\cdot)$	$1$	$1$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{32}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{88}{105}\right)$
$\chi_{4851}(1906,\cdot)$	$1$	$1$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{94}{105}\right)$
$\chi_{4851}(2083,\cdot)$	$1$	$1$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{41}{105}\right)$
$\chi_{4851}(2095,\cdot)$	$1$	$1$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{68}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{82}{105}\right)$
$\chi_{4851}(2209,\cdot)$	$1$	$1$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{37}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{23}{105}\right)$
$\chi_{4851}(2335,\cdot)$	$1$	$1$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{64}{105}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{89}{105}\right)$
$\chi_{4851}(2347,\cdot)$	$1$	$1$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{86}{105}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{31}{105}\right)$
$\chi_{4851}(2473,\cdot)$	$1$	$1$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{58}{105}\right)$
$\chi_{4851}(2524,\cdot)$	$1$	$1$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{62}{105}\right)$
$\chi_{4851}(2599,\cdot)$	$1$	$1$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{13}{105}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{64}{105}\right)$
$\chi_{4851}(2776,\cdot)$	$1$	$1$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{26}{105}\right)$
$\chi_{4851}(2788,\cdot)$	$1$	$1$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{105}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{52}{105}\right)$
$\chi_{4851}(2902,\cdot)$	$1$	$1$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{8}{105}\right)$
$\chi_{4851}(3028,\cdot)$	$1$	$1$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{74}{105}\right)$
$\chi_{4851}(3040,\cdot)$	$1$	$1$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{89}{105}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{105}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\(\chi_{4851}(4,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{86}{105}\right)\)
\(\chi_{4851}(16,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{67}{105}\right)\)
\(\chi_{4851}(130,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{68}{105}\right)\)
\(\chi_{4851}(256,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{29}{105}\right)\)
\(\chi_{4851}(268,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{16}{105}\right)\)
\(\chi_{4851}(394,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{43}{105}\right)\)
\(\chi_{4851}(445,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{105}\right)\)
\(\chi_{4851}(697,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{71}{105}\right)\)
\(\chi_{4851}(709,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{37}{105}\right)\)
\(\chi_{4851}(823,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{53}{105}\right)\)
\(\chi_{4851}(1087,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{105}\right)\)
\(\chi_{4851}(1138,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{92}{105}\right)\)
\(\chi_{4851}(1213,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{19}{105}\right)\)
\(\chi_{4851}(1516,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{38}{105}\right)\)
\(\chi_{4851}(1642,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{16}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{104}{105}\right)\)
\(\chi_{4851}(1654,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{61}{105}\right)\)
\(\chi_{4851}(1780,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{32}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{88}{105}\right)\)
\(\chi_{4851}(1906,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{94}{105}\right)\)
\(\chi_{4851}(2083,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{41}{105}\right)\)
\(\chi_{4851}(2095,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{68}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{82}{105}\right)\)
\(\chi_{4851}(2209,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{37}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{23}{105}\right)\)
\(\chi_{4851}(2335,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{64}{105}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{89}{105}\right)\)
\(\chi_{4851}(2347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{86}{105}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{31}{105}\right)\)
\(\chi_{4851}(2473,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{58}{105}\right)\)
\(\chi_{4851}(2524,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{62}{105}\right)\)
\(\chi_{4851}(2599,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{13}{105}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{64}{105}\right)\)
\(\chi_{4851}(2776,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{26}{105}\right)\)
\(\chi_{4851}(2788,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{105}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{52}{105}\right)\)
\(\chi_{4851}(2902,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{8}{105}\right)\)
\(\chi_{4851}(3028,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{74}{105}\right)\)
\(\chi_{4851}(3040,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{89}{105}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{105}\right)\)

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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	4851.fa
Modulus	$4851$
Conductor	$4851$
Order	$105$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(4851\)
Conductor:	\(4851\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(105\)	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)