LMFDB - Dirichlet character orbit 19951.dt

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(19951, base_ring=CyclotomicField(70)) M = H._module chi = DirichletCharacter(H, M([26,66])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(1849, 19951)) 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("19951.1849"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$19951$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$19951$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$35$	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:	$\Q(\zeta_{35})$
Fixed field:	Number field defined by a degree 35 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{19951}(1849,\cdot)$	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{2}{35}\right)$
$\chi_{19951}(1886,\cdot)$	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{17}{35}\right)$
$\chi_{19951}(2359,\cdot)$	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{18}{35}\right)$
$\chi_{19951}(4769,\cdot)$	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{11}{35}\right)$
$\chi_{19951}(5718,\cdot)$	$1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{34}{35}\right)$
$\chi_{19951}(6024,\cdot)$	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{32}{35}\right)$
$\chi_{19951}(7180,\cdot)$	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{4}{35}\right)$
$\chi_{19951}(8311,\cdot)$	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{9}{35}\right)$
$\chi_{19951}(8405,\cdot)$	$1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{6}{35}\right)$
$\chi_{19951}(9806,\cdot)$	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{31}{35}\right)$
$\chi_{19951}(10608,\cdot)$	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{16}{35}\right)$
$\chi_{19951}(10736,\cdot)$	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{23}{35}\right)$
$\chi_{19951}(13011,\cdot)$	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{26}{35}\right)$
$\chi_{19951}(13767,\cdot)$	$1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{27}{35}\right)$
$\chi_{19951}(15740,\cdot)$	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{19}{35}\right)$
$\chi_{19951}(15786,\cdot)$	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{33}{35}\right)$
$\chi_{19951}(16033,\cdot)$	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{3}{35}\right)$
$\chi_{19951}(16052,\cdot)$	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{24}{35}\right)$
$\chi_{19951}(17485,\cdot)$	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{12}{35}\right)$
$\chi_{19951}(17658,\cdot)$	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{29}{35}\right)$
$\chi_{19951}(18503,\cdot)$	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{1}{35}\right)$
$\chi_{19951}(18967,\cdot)$	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{8}{35}\right)$
$\chi_{19951}(19172,\cdot)$	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{22}{35}\right)$
$\chi_{19951}(19490,\cdot)$	$1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{13}{35}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{19951}(1849,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)
\(\chi_{19951}(1886,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)
\(\chi_{19951}(2359,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)
\(\chi_{19951}(4769,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)
\(\chi_{19951}(5718,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)
\(\chi_{19951}(6024,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)
\(\chi_{19951}(7180,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)
\(\chi_{19951}(8311,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)
\(\chi_{19951}(8405,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)
\(\chi_{19951}(9806,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)
\(\chi_{19951}(10608,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)
\(\chi_{19951}(10736,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)
\(\chi_{19951}(13011,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)
\(\chi_{19951}(13767,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)
\(\chi_{19951}(15740,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)
\(\chi_{19951}(15786,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)
\(\chi_{19951}(16033,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)
\(\chi_{19951}(16052,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)
\(\chi_{19951}(17485,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)
\(\chi_{19951}(17658,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)
\(\chi_{19951}(18503,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)
\(\chi_{19951}(18967,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)
\(\chi_{19951}(19172,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)
\(\chi_{19951}(19490,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)

Introduction

L-functions

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Varieties

Fields

Representations

Groups

Database

Properties

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Basic properties

Related number fields

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	19951.dt
Modulus	$19951$
Conductor	$19951$
Order	$35$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(19951\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(19951\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(35\)	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);