LMFDB - Dirichlet character orbit 1617.ca

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1617, base_ring=CyclotomicField(70)) M = H._module chi = DirichletCharacter(H, M([35,65,42])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(20, 1617)) 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("1617.20"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$1617$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$1617$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$70$	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 70 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$13$	$16$	$17$	$19$	$20$
$\chi_{1617}(20,\cdot)$	$1$	$1$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{35}\right)$
$\chi_{1617}(104,\cdot)$	$1$	$1$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{34}{35}\right)$
$\chi_{1617}(125,\cdot)$	$1$	$1$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{35}\right)$
$\chi_{1617}(251,\cdot)$	$1$	$1$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{6}{35}\right)$
$\chi_{1617}(335,\cdot)$	$1$	$1$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{29}{35}\right)$
$\chi_{1617}(356,\cdot)$	$1$	$1$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{12}{35}\right)$
$\chi_{1617}(377,\cdot)$	$1$	$1$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{35}\right)$
$\chi_{1617}(482,\cdot)$	$1$	$1$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{35}\right)$
$\chi_{1617}(566,\cdot)$	$1$	$1$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{24}{35}\right)$
$\chi_{1617}(608,\cdot)$	$1$	$1$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{18}{35}\right)$
$\chi_{1617}(713,\cdot)$	$1$	$1$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{31}{35}\right)$
$\chi_{1617}(797,\cdot)$	$1$	$1$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{35}\right)$
$\chi_{1617}(818,\cdot)$	$1$	$1$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{35}\right)$
$\chi_{1617}(839,\cdot)$	$1$	$1$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{35}\right)$
$\chi_{1617}(944,\cdot)$	$1$	$1$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{26}{35}\right)$
$\chi_{1617}(1049,\cdot)$	$1$	$1$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{32}{35}\right)$
$\chi_{1617}(1070,\cdot)$	$1$	$1$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{8}{35}\right)$
$\chi_{1617}(1259,\cdot)$	$1$	$1$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{35}\right)$
$\chi_{1617}(1280,\cdot)$	$1$	$1$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{27}{35}\right)$
$\chi_{1617}(1301,\cdot)$	$1$	$1$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{35}\right)$
$\chi_{1617}(1406,\cdot)$	$1$	$1$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{16}{35}\right)$
$\chi_{1617}(1490,\cdot)$	$1$	$1$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{35}\right)$
$\chi_{1617}(1511,\cdot)$	$1$	$1$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{22}{35}\right)$
$\chi_{1617}(1532,\cdot)$	$1$	$1$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{33}{35}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\(\chi_{1617}(20,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{35}\right)\)
\(\chi_{1617}(104,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{34}{35}\right)\)
\(\chi_{1617}(125,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{35}\right)\)
\(\chi_{1617}(251,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{6}{35}\right)\)
\(\chi_{1617}(335,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{29}{35}\right)\)
\(\chi_{1617}(356,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{12}{35}\right)\)
\(\chi_{1617}(377,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{35}\right)\)
\(\chi_{1617}(482,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{35}\right)\)
\(\chi_{1617}(566,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{24}{35}\right)\)
\(\chi_{1617}(608,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{18}{35}\right)\)
\(\chi_{1617}(713,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{31}{35}\right)\)
\(\chi_{1617}(797,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{35}\right)\)
\(\chi_{1617}(818,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{35}\right)\)
\(\chi_{1617}(839,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{35}\right)\)
\(\chi_{1617}(944,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{26}{35}\right)\)
\(\chi_{1617}(1049,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{32}{35}\right)\)
\(\chi_{1617}(1070,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{8}{35}\right)\)
\(\chi_{1617}(1259,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{35}\right)\)
\(\chi_{1617}(1280,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{27}{35}\right)\)
\(\chi_{1617}(1301,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{35}\right)\)
\(\chi_{1617}(1406,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{16}{35}\right)\)
\(\chi_{1617}(1490,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{35}\right)\)
\(\chi_{1617}(1511,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{22}{35}\right)\)
\(\chi_{1617}(1532,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{33}{35}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

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	1617.ca
Modulus	$1617$
Conductor	$1617$
Order	$70$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(1617\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1617\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(70\)	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);