LMFDB - Dirichlet character orbit 13000.hn

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13000, base_ring=CyclotomicField(100)) M = H._module chi = DirichletCharacter(H, M([50,50,44,75])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(291, 13000)) 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("13000.291"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$13000$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$13000$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$100$	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:	yes	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:	$\Q(\zeta_{100})$	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 100 polynomial	comment:Fixed field sage:chi.fixed_field()

First 31 of 40 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{13000}(291,\cdot)$	$1$	$1$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{39}{50}\right)$
$\chi_{13000}(411,\cdot)$	$1$	$1$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{21}{50}\right)$
$\chi_{13000}(811,\cdot)$	$1$	$1$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{11}{50}\right)$
$\chi_{13000}(931,\cdot)$	$1$	$1$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{3}{50}\right)$
$\chi_{13000}(1331,\cdot)$	$1$	$1$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{43}{50}\right)$
$\chi_{13000}(1971,\cdot)$	$1$	$1$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{47}{50}\right)$
$\chi_{13000}(2371,\cdot)$	$1$	$1$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{37}{50}\right)$
$\chi_{13000}(2491,\cdot)$	$1$	$1$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{9}{50}\right)$
$\chi_{13000}(2891,\cdot)$	$1$	$1$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{49}{50}\right)$
$\chi_{13000}(3011,\cdot)$	$1$	$1$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{31}{50}\right)$
$\chi_{13000}(3411,\cdot)$	$1$	$1$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{21}{50}\right)$
$\chi_{13000}(3531,\cdot)$	$1$	$1$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{13}{50}\right)$
$\chi_{13000}(3931,\cdot)$	$1$	$1$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{3}{50}\right)$
$\chi_{13000}(4571,\cdot)$	$1$	$1$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{7}{50}\right)$
$\chi_{13000}(4971,\cdot)$	$1$	$1$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{47}{50}\right)$
$\chi_{13000}(5091,\cdot)$	$1$	$1$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{19}{50}\right)$
$\chi_{13000}(5491,\cdot)$	$1$	$1$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{9}{50}\right)$
$\chi_{13000}(5611,\cdot)$	$1$	$1$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{41}{50}\right)$
$\chi_{13000}(6011,\cdot)$	$1$	$1$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{31}{50}\right)$
$\chi_{13000}(6131,\cdot)$	$1$	$1$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{23}{50}\right)$
$\chi_{13000}(6531,\cdot)$	$1$	$1$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{13}{50}\right)$
$\chi_{13000}(7171,\cdot)$	$1$	$1$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{17}{50}\right)$
$\chi_{13000}(7571,\cdot)$	$1$	$1$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{7}{50}\right)$
$\chi_{13000}(7691,\cdot)$	$1$	$1$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{29}{50}\right)$
$\chi_{13000}(8091,\cdot)$	$1$	$1$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{19}{50}\right)$
$\chi_{13000}(8211,\cdot)$	$1$	$1$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{1}{50}\right)$
$\chi_{13000}(8611,\cdot)$	$1$	$1$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{41}{50}\right)$
$\chi_{13000}(8731,\cdot)$	$1$	$1$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{33}{50}\right)$
$\chi_{13000}(9131,\cdot)$	$1$	$1$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{23}{50}\right)$
$\chi_{13000}(9771,\cdot)$	$1$	$1$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{27}{50}\right)$
$\chi_{13000}(10171,\cdot)$	$1$	$1$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{51}{100}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{17}{50}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{13000}(291,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{39}{50}\right)\)
\(\chi_{13000}(411,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{21}{50}\right)\)
\(\chi_{13000}(811,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{11}{50}\right)\)
\(\chi_{13000}(931,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{3}{50}\right)\)
\(\chi_{13000}(1331,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{43}{50}\right)\)
\(\chi_{13000}(1971,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{47}{50}\right)\)
\(\chi_{13000}(2371,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{37}{50}\right)\)
\(\chi_{13000}(2491,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{9}{50}\right)\)
\(\chi_{13000}(2891,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{49}{50}\right)\)
\(\chi_{13000}(3011,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{31}{50}\right)\)
\(\chi_{13000}(3411,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{21}{50}\right)\)
\(\chi_{13000}(3531,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{13}{50}\right)\)
\(\chi_{13000}(3931,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{3}{50}\right)\)
\(\chi_{13000}(4571,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{7}{50}\right)\)
\(\chi_{13000}(4971,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{47}{50}\right)\)
\(\chi_{13000}(5091,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{19}{50}\right)\)
\(\chi_{13000}(5491,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{9}{50}\right)\)
\(\chi_{13000}(5611,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{41}{50}\right)\)
\(\chi_{13000}(6011,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{31}{50}\right)\)
\(\chi_{13000}(6131,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{23}{50}\right)\)
\(\chi_{13000}(6531,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{13}{50}\right)\)
\(\chi_{13000}(7171,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{17}{50}\right)\)
\(\chi_{13000}(7571,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{7}{50}\right)\)
\(\chi_{13000}(7691,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{29}{50}\right)\)
\(\chi_{13000}(8091,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{19}{50}\right)\)
\(\chi_{13000}(8211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{1}{50}\right)\)
\(\chi_{13000}(8611,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{41}{50}\right)\)
\(\chi_{13000}(8731,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{33}{50}\right)\)
\(\chi_{13000}(9131,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{23}{50}\right)\)
\(\chi_{13000}(9771,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{27}{50}\right)\)
\(\chi_{13000}(10171,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{51}{100}\right)\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{17}{50}\right)\)

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Basic properties

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First 31 of 40 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	13000.hn
Modulus	$13000$
Conductor	$13000$
Order	$100$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(13000\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(13000\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(100\)	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:	yes	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);