LMFDB - Dirichlet character orbit 2552.cv

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2552, base_ring=CyclotomicField(70)) M = H._module chi = DirichletCharacter(H, M([35,35,56,5])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(91, 2552)) 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("2552.91"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$2552$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$2552$	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:	odd	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	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$19$	$21$	$23$
$\chi_{2552}(91,\cdot)$	$-1$	$1$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{2552}(179,\cdot)$	$-1$	$1$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{2552}(267,\cdot)$	$-1$	$1$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{14}\right)$
$\chi_{2552}(323,\cdot)$	$-1$	$1$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{2552}(411,\cdot)$	$-1$	$1$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{2552}(499,\cdot)$	$-1$	$1$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{14}\right)$
$\chi_{2552}(515,\cdot)$	$-1$	$1$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{31}{35}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{2552}(531,\cdot)$	$-1$	$1$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{2552}(555,\cdot)$	$-1$	$1$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{4}{35}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{2552}(643,\cdot)$	$-1$	$1$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{2552}(731,\cdot)$	$-1$	$1$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{14}\right)$
$\chi_{2552}(763,\cdot)$	$-1$	$1$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{27}{35}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{2552}(883,\cdot)$	$-1$	$1$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{2552}(995,\cdot)$	$-1$	$1$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{23}{70}\right)$	$e\left(\frac{33}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{2552}(1115,\cdot)$	$-1$	$1$	$e\left(\frac{57}{70}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{9}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{2552}(1347,\cdot)$	$-1$	$1$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{23}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{14}\right)$
$\chi_{2552}(1483,\cdot)$	$-1$	$1$	$e\left(\frac{11}{70}\right)$	$e\left(\frac{33}{70}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{2552}(1571,\cdot)$	$-1$	$1$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{13}{70}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{16}{35}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{2552}(1659,\cdot)$	$-1$	$1$	$e\left(\frac{61}{70}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{19}{70}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{14}\right)$
$\chi_{2552}(1675,\cdot)$	$-1$	$1$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{9}{70}\right)$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{3}{35}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{2552}(1907,\cdot)$	$-1$	$1$	$e\left(\frac{17}{70}\right)$	$e\left(\frac{51}{70}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{17}{35}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{34}{35}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{67}{70}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{2552}(1923,\cdot)$	$-1$	$1$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{53}{70}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{6}{35}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{2552}(2139,\cdot)$	$-1$	$1$	$e\left(\frac{59}{70}\right)$	$e\left(\frac{37}{70}\right)$	$e\left(\frac{31}{70}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{43}{70}\right)$	$e\left(\frac{13}{35}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{39}{70}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{14}\right)$
$\chi_{2552}(2275,\cdot)$	$-1$	$1$	$e\left(\frac{1}{70}\right)$	$e\left(\frac{3}{70}\right)$	$e\left(\frac{29}{70}\right)$	$e\left(\frac{1}{35}\right)$	$e\left(\frac{47}{70}\right)$	$e\left(\frac{2}{35}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{14}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{2552}(91,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{2552}(179,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{2552}(267,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{2552}(323,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{2552}(411,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{2552}(499,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{2552}(515,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{31}{35}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{2552}(531,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{2552}(555,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{4}{35}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{2552}(643,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{2552}(731,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{2552}(763,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{27}{35}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{2552}(883,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{2552}(995,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{23}{70}\right)\)	\(e\left(\frac{33}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{2552}(1115,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{57}{70}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{9}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{2552}(1347,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{23}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)
\(\chi_{2552}(1483,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{70}\right)\)	\(e\left(\frac{33}{70}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{2552}(1571,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{13}{70}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{16}{35}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{2552}(1659,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{70}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{19}{70}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{2552}(1675,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{9}{70}\right)\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{3}{35}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{2552}(1907,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{70}\right)\)	\(e\left(\frac{51}{70}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{17}{35}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{34}{35}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{67}{70}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{2552}(1923,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{53}{70}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{6}{35}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{2552}(2139,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{70}\right)\)	\(e\left(\frac{37}{70}\right)\)	\(e\left(\frac{31}{70}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{43}{70}\right)\)	\(e\left(\frac{13}{35}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{39}{70}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{2552}(2275,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{70}\right)\)	\(e\left(\frac{3}{70}\right)\)	\(e\left(\frac{29}{70}\right)\)	\(e\left(\frac{1}{35}\right)\)	\(e\left(\frac{47}{70}\right)\)	\(e\left(\frac{2}{35}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)

Introduction

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Varieties

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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	2552.cv
Modulus	$2552$
Conductor	$2552$
Order	$70$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(2552\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(2552\)	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:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);