LMFDB - Dirichlet character orbit 4900.dp

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4900, base_ring=CyclotomicField(420)) M = H._module chi = DirichletCharacter(H, M([0,273,250])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(17, 4900)) 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("4900.17"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$4900$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$1225$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$420$	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 1225.bu	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:	$\Q(\zeta_{420})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 420 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 96 characters in Galois orbit

Character	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$23$	$27$	$29$	$31$
$\chi_{4900}(17,\cdot)$	$1$	$1$	$e\left(\frac{61}{420}\right)$	$e\left(\frac{61}{210}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{139}{420}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{323}{420}\right)$	$e\left(\frac{61}{140}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{4900}(33,\cdot)$	$1$	$1$	$e\left(\frac{11}{420}\right)$	$e\left(\frac{11}{210}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{149}{420}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{313}{420}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{4900}(73,\cdot)$	$1$	$1$	$e\left(\frac{307}{420}\right)$	$e\left(\frac{97}{210}\right)$	$e\left(\frac{4}{105}\right)$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{73}{420}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{221}{420}\right)$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{4900}(173,\cdot)$	$1$	$1$	$e\left(\frac{107}{420}\right)$	$e\left(\frac{107}{210}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{113}{420}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{181}{420}\right)$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{4900}(213,\cdot)$	$1$	$1$	$e\left(\frac{103}{420}\right)$	$e\left(\frac{103}{210}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{97}{420}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{29}{420}\right)$	$e\left(\frac{103}{140}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{4900}(297,\cdot)$	$1$	$1$	$e\left(\frac{409}{420}\right)$	$e\left(\frac{199}{210}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{271}{420}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{107}{420}\right)$	$e\left(\frac{129}{140}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{4900}(353,\cdot)$	$1$	$1$	$e\left(\frac{319}{420}\right)$	$e\left(\frac{109}{210}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{121}{420}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{257}{420}\right)$	$e\left(\frac{39}{140}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{4900}(397,\cdot)$	$1$	$1$	$e\left(\frac{269}{420}\right)$	$e\left(\frac{59}{210}\right)$	$e\left(\frac{23}{105}\right)$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{131}{420}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{247}{420}\right)$	$e\left(\frac{129}{140}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{4900}(437,\cdot)$	$1$	$1$	$e\left(\frac{373}{420}\right)$	$e\left(\frac{163}{210}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{127}{420}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{419}{420}\right)$	$e\left(\frac{93}{140}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{4900}(453,\cdot)$	$1$	$1$	$e\left(\frac{299}{420}\right)$	$e\left(\frac{89}{210}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{41}{140}\right)$	$e\left(\frac{41}{420}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{337}{420}\right)$	$e\left(\frac{19}{140}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{4900}(537,\cdot)$	$1$	$1$	$e\left(\frac{113}{420}\right)$	$e\left(\frac{113}{210}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{67}{140}\right)$	$e\left(\frac{347}{420}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{199}{420}\right)$	$e\left(\frac{113}{140}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{4900}(577,\cdot)$	$1$	$1$	$e\left(\frac{337}{420}\right)$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{403}{420}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{311}{420}\right)$	$e\left(\frac{57}{140}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{4900}(633,\cdot)$	$1$	$1$	$e\left(\frac{331}{420}\right)$	$e\left(\frac{121}{210}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{29}{140}\right)$	$e\left(\frac{169}{420}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{293}{420}\right)$	$e\left(\frac{51}{140}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{4900}(677,\cdot)$	$1$	$1$	$e\left(\frac{377}{420}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{3}{140}\right)$	$e\left(\frac{143}{420}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{151}{420}\right)$	$e\left(\frac{97}{140}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{4900}(733,\cdot)$	$1$	$1$	$e\left(\frac{71}{420}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{109}{140}\right)$	$e\left(\frac{389}{420}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{73}{420}\right)$	$e\left(\frac{71}{140}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{4900}(773,\cdot)$	$1$	$1$	$e\left(\frac{127}{420}\right)$	$e\left(\frac{127}{210}\right)$	$e\left(\frac{94}{105}\right)$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{193}{420}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{101}{420}\right)$	$e\left(\frac{127}{140}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{4900}(817,\cdot)$	$1$	$1$	$e\left(\frac{221}{420}\right)$	$e\left(\frac{11}{210}\right)$	$e\left(\frac{47}{105}\right)$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{359}{420}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{103}{420}\right)$	$e\left(\frac{81}{140}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{4900}(873,\cdot)$	$1$	$1$	$e\left(\frac{167}{420}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{73}{140}\right)$	$e\left(\frac{353}{420}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{361}{420}\right)$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{4900}(997,\cdot)$	$1$	$1$	$e\left(\frac{229}{420}\right)$	$e\left(\frac{19}{210}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{111}{140}\right)$	$e\left(\frac{391}{420}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{407}{420}\right)$	$e\left(\frac{89}{140}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{4900}(1013,\cdot)$	$1$	$1$	$e\left(\frac{263}{420}\right)$	$e\left(\frac{53}{210}\right)$	$e\left(\frac{26}{105}\right)$	$e\left(\frac{37}{140}\right)$	$e\left(\frac{317}{420}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{229}{420}\right)$	$e\left(\frac{123}{140}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{4900}(1053,\cdot)$	$1$	$1$	$e\left(\frac{139}{420}\right)$	$e\left(\frac{139}{210}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{101}{140}\right)$	$e\left(\frac{241}{420}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{137}{420}\right)$	$e\left(\frac{139}{140}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{4900}(1137,\cdot)$	$1$	$1$	$e\left(\frac{193}{420}\right)$	$e\left(\frac{193}{210}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{107}{140}\right)$	$e\left(\frac{247}{420}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{299}{420}\right)$	$e\left(\frac{53}{140}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{4900}(1153,\cdot)$	$1$	$1$	$e\left(\frac{359}{420}\right)$	$e\left(\frac{149}{210}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{1}{140}\right)$	$e\left(\frac{281}{420}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{97}{420}\right)$	$e\left(\frac{79}{140}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{4900}(1237,\cdot)$	$1$	$1$	$e\left(\frac{173}{420}\right)$	$e\left(\frac{173}{210}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{27}{140}\right)$	$e\left(\frac{167}{420}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{379}{420}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{4900}(1277,\cdot)$	$1$	$1$	$e\left(\frac{157}{420}\right)$	$e\left(\frac{157}{210}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{103}{140}\right)$	$e\left(\frac{103}{420}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{191}{420}\right)$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{4900}(1333,\cdot)$	$1$	$1$	$e\left(\frac{151}{420}\right)$	$e\left(\frac{151}{210}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{9}{140}\right)$	$e\left(\frac{289}{420}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{173}{420}\right)$	$e\left(\frac{11}{140}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{4900}(1377,\cdot)$	$1$	$1$	$e\left(\frac{17}{420}\right)$	$e\left(\frac{17}{210}\right)$	$e\left(\frac{44}{105}\right)$	$e\left(\frac{103}{140}\right)$	$e\left(\frac{383}{420}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{331}{420}\right)$	$e\left(\frac{17}{140}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{4900}(1417,\cdot)$	$1$	$1$	$e\left(\frac{121}{420}\right)$	$e\left(\frac{121}{210}\right)$	$e\left(\frac{97}{105}\right)$	$e\left(\frac{99}{140}\right)$	$e\left(\frac{379}{420}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{83}{420}\right)$	$e\left(\frac{121}{140}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{4900}(1433,\cdot)$	$1$	$1$	$e\left(\frac{131}{420}\right)$	$e\left(\frac{131}{210}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{69}{140}\right)$	$e\left(\frac{209}{420}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{253}{420}\right)$	$e\left(\frac{131}{140}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{4900}(1473,\cdot)$	$1$	$1$	$e\left(\frac{367}{420}\right)$	$e\left(\frac{157}{210}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{33}{140}\right)$	$e\left(\frac{313}{420}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{401}{420}\right)$	$e\left(\frac{87}{140}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{4900}(1517,\cdot)$	$1$	$1$	$e\left(\frac{281}{420}\right)$	$e\left(\frac{71}{210}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{39}{140}\right)$	$e\left(\frac{179}{420}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{283}{420}\right)$	$e\left(\frac{1}{140}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{1}{30}\right)$

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	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\(\chi_{4900}(17,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{420}\right)\)	\(e\left(\frac{61}{210}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{139}{420}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{323}{420}\right)\)	\(e\left(\frac{61}{140}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{4900}(33,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{420}\right)\)	\(e\left(\frac{11}{210}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{149}{420}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{313}{420}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{4900}(73,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{307}{420}\right)\)	\(e\left(\frac{97}{210}\right)\)	\(e\left(\frac{4}{105}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{73}{420}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{221}{420}\right)\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{4900}(173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{420}\right)\)	\(e\left(\frac{107}{210}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{113}{420}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{181}{420}\right)\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{4900}(213,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{420}\right)\)	\(e\left(\frac{103}{210}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{97}{420}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{29}{420}\right)\)	\(e\left(\frac{103}{140}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{4900}(297,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{409}{420}\right)\)	\(e\left(\frac{199}{210}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{271}{420}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{107}{420}\right)\)	\(e\left(\frac{129}{140}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{4900}(353,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{319}{420}\right)\)	\(e\left(\frac{109}{210}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{121}{420}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{257}{420}\right)\)	\(e\left(\frac{39}{140}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{4900}(397,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{269}{420}\right)\)	\(e\left(\frac{59}{210}\right)\)	\(e\left(\frac{23}{105}\right)\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{131}{420}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{247}{420}\right)\)	\(e\left(\frac{129}{140}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{4900}(437,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{373}{420}\right)\)	\(e\left(\frac{163}{210}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{127}{420}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{419}{420}\right)\)	\(e\left(\frac{93}{140}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{4900}(453,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{299}{420}\right)\)	\(e\left(\frac{89}{210}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{41}{140}\right)\)	\(e\left(\frac{41}{420}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{337}{420}\right)\)	\(e\left(\frac{19}{140}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{4900}(537,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{420}\right)\)	\(e\left(\frac{113}{210}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{67}{140}\right)\)	\(e\left(\frac{347}{420}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{199}{420}\right)\)	\(e\left(\frac{113}{140}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{4900}(577,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{337}{420}\right)\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{403}{420}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{311}{420}\right)\)	\(e\left(\frac{57}{140}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{4900}(633,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{331}{420}\right)\)	\(e\left(\frac{121}{210}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{29}{140}\right)\)	\(e\left(\frac{169}{420}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{293}{420}\right)\)	\(e\left(\frac{51}{140}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{4900}(677,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{377}{420}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{3}{140}\right)\)	\(e\left(\frac{143}{420}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{151}{420}\right)\)	\(e\left(\frac{97}{140}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{4900}(733,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{420}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{109}{140}\right)\)	\(e\left(\frac{389}{420}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{73}{420}\right)\)	\(e\left(\frac{71}{140}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{4900}(773,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{420}\right)\)	\(e\left(\frac{127}{210}\right)\)	\(e\left(\frac{94}{105}\right)\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{193}{420}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{101}{420}\right)\)	\(e\left(\frac{127}{140}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{4900}(817,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{221}{420}\right)\)	\(e\left(\frac{11}{210}\right)\)	\(e\left(\frac{47}{105}\right)\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{359}{420}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{103}{420}\right)\)	\(e\left(\frac{81}{140}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{4900}(873,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{167}{420}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{73}{140}\right)\)	\(e\left(\frac{353}{420}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{361}{420}\right)\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{4900}(997,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{229}{420}\right)\)	\(e\left(\frac{19}{210}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{111}{140}\right)\)	\(e\left(\frac{391}{420}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{407}{420}\right)\)	\(e\left(\frac{89}{140}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{4900}(1013,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{263}{420}\right)\)	\(e\left(\frac{53}{210}\right)\)	\(e\left(\frac{26}{105}\right)\)	\(e\left(\frac{37}{140}\right)\)	\(e\left(\frac{317}{420}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{229}{420}\right)\)	\(e\left(\frac{123}{140}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{4900}(1053,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{420}\right)\)	\(e\left(\frac{139}{210}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{101}{140}\right)\)	\(e\left(\frac{241}{420}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{137}{420}\right)\)	\(e\left(\frac{139}{140}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{4900}(1137,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{420}\right)\)	\(e\left(\frac{193}{210}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{107}{140}\right)\)	\(e\left(\frac{247}{420}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{299}{420}\right)\)	\(e\left(\frac{53}{140}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{4900}(1153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{359}{420}\right)\)	\(e\left(\frac{149}{210}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{1}{140}\right)\)	\(e\left(\frac{281}{420}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{97}{420}\right)\)	\(e\left(\frac{79}{140}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{4900}(1237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{420}\right)\)	\(e\left(\frac{173}{210}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{27}{140}\right)\)	\(e\left(\frac{167}{420}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{379}{420}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{4900}(1277,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{420}\right)\)	\(e\left(\frac{157}{210}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{103}{140}\right)\)	\(e\left(\frac{103}{420}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{191}{420}\right)\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{4900}(1333,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{420}\right)\)	\(e\left(\frac{151}{210}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{9}{140}\right)\)	\(e\left(\frac{289}{420}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{173}{420}\right)\)	\(e\left(\frac{11}{140}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{4900}(1377,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{420}\right)\)	\(e\left(\frac{17}{210}\right)\)	\(e\left(\frac{44}{105}\right)\)	\(e\left(\frac{103}{140}\right)\)	\(e\left(\frac{383}{420}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{331}{420}\right)\)	\(e\left(\frac{17}{140}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{4900}(1417,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{420}\right)\)	\(e\left(\frac{121}{210}\right)\)	\(e\left(\frac{97}{105}\right)\)	\(e\left(\frac{99}{140}\right)\)	\(e\left(\frac{379}{420}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{83}{420}\right)\)	\(e\left(\frac{121}{140}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{4900}(1433,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{420}\right)\)	\(e\left(\frac{131}{210}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{69}{140}\right)\)	\(e\left(\frac{209}{420}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{253}{420}\right)\)	\(e\left(\frac{131}{140}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{4900}(1473,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{367}{420}\right)\)	\(e\left(\frac{157}{210}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{33}{140}\right)\)	\(e\left(\frac{313}{420}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{401}{420}\right)\)	\(e\left(\frac{87}{140}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{4900}(1517,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{281}{420}\right)\)	\(e\left(\frac{71}{210}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{39}{140}\right)\)	\(e\left(\frac{179}{420}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{283}{420}\right)\)	\(e\left(\frac{1}{140}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{1}{30}\right)\)

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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	4900.dp
Modulus	$4900$
Conductor	$1225$
Order	$420$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(4900\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1225\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(420\)	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 1225.bu	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);