LMFDB - Dirichlet character orbit 25410.fy

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(25410, base_ring=CyclotomicField(132)) M = H._module chi = DirichletCharacter(H, M([66,99,110,42])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(593,25410)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$25410$
Conductor:	$12705$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$132$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 12705.fy	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{132})$
Fixed field:	Number field defined by a degree 132 polynomial (not computed)

First 31 of 40 characters in Galois orbit

Character	$-1$	$1$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$	$47$
$\chi_{25410}(593,\cdot)$	$1$	$1$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{103}{132}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{79}{132}\right)$
$\chi_{25410}(857,\cdot)$	$1$	$1$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{53}{132}\right)$
$\chi_{25410}(1517,\cdot)$	$1$	$1$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{109}{132}\right)$
$\chi_{25410}(2243,\cdot)$	$1$	$1$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{131}{132}\right)$
$\chi_{25410}(3167,\cdot)$	$1$	$1$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{29}{132}\right)$
$\chi_{25410}(3827,\cdot)$	$1$	$1$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{85}{132}\right)$
$\chi_{25410}(4553,\cdot)$	$1$	$1$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{107}{132}\right)$
$\chi_{25410}(5213,\cdot)$	$1$	$1$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{31}{132}\right)$
$\chi_{25410}(5477,\cdot)$	$1$	$1$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{5}{132}\right)$
$\chi_{25410}(6137,\cdot)$	$1$	$1$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{47}{132}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{61}{132}\right)$
$\chi_{25410}(6863,\cdot)$	$1$	$1$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{83}{132}\right)$
$\chi_{25410}(7523,\cdot)$	$1$	$1$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{7}{132}\right)$
$\chi_{25410}(7787,\cdot)$	$1$	$1$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{113}{132}\right)$
$\chi_{25410}(8447,\cdot)$	$1$	$1$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{37}{132}\right)$
$\chi_{25410}(9173,\cdot)$	$1$	$1$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{107}{132}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{59}{132}\right)$
$\chi_{25410}(9833,\cdot)$	$1$	$1$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{115}{132}\right)$
$\chi_{25410}(10097,\cdot)$	$1$	$1$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{89}{132}\right)$
$\chi_{25410}(10757,\cdot)$	$1$	$1$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{13}{132}\right)$
$\chi_{25410}(11483,\cdot)$	$1$	$1$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{47}{132}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{35}{132}\right)$
$\chi_{25410}(12143,\cdot)$	$1$	$1$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{91}{132}\right)$
$\chi_{25410}(12407,\cdot)$	$1$	$1$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{65}{132}\right)$
$\chi_{25410}(14453,\cdot)$	$1$	$1$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{67}{132}\right)$
$\chi_{25410}(14717,\cdot)$	$1$	$1$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{103}{132}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{41}{132}\right)$
$\chi_{25410}(15377,\cdot)$	$1$	$1$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{97}{132}\right)$
$\chi_{25410}(16103,\cdot)$	$1$	$1$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{107}{132}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{119}{132}\right)$
$\chi_{25410}(16763,\cdot)$	$1$	$1$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{103}{132}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{43}{132}\right)$
$\chi_{25410}(17027,\cdot)$	$1$	$1$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{17}{132}\right)$
$\chi_{25410}(17687,\cdot)$	$1$	$1$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{73}{132}\right)$
$\chi_{25410}(18413,\cdot)$	$1$	$1$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{47}{132}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{95}{132}\right)$
$\chi_{25410}(19073,\cdot)$	$1$	$1$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{19}{132}\right)$
$\chi_{25410}(19337,\cdot)$	$1$	$1$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{125}{132}\right)$

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	\(-1\)	\(1\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)	\(47\)
\(\chi_{25410}(593,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{103}{132}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{79}{132}\right)\)
\(\chi_{25410}(857,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{53}{132}\right)\)
\(\chi_{25410}(1517,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{109}{132}\right)\)
\(\chi_{25410}(2243,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{131}{132}\right)\)
\(\chi_{25410}(3167,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{29}{132}\right)\)
\(\chi_{25410}(3827,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{85}{132}\right)\)
\(\chi_{25410}(4553,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{107}{132}\right)\)
\(\chi_{25410}(5213,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{31}{132}\right)\)
\(\chi_{25410}(5477,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{5}{132}\right)\)
\(\chi_{25410}(6137,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{47}{132}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{61}{132}\right)\)
\(\chi_{25410}(6863,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{83}{132}\right)\)
\(\chi_{25410}(7523,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{7}{132}\right)\)
\(\chi_{25410}(7787,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{113}{132}\right)\)
\(\chi_{25410}(8447,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{37}{132}\right)\)
\(\chi_{25410}(9173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{107}{132}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{59}{132}\right)\)
\(\chi_{25410}(9833,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{115}{132}\right)\)
\(\chi_{25410}(10097,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{89}{132}\right)\)
\(\chi_{25410}(10757,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{13}{132}\right)\)
\(\chi_{25410}(11483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{47}{132}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{35}{132}\right)\)
\(\chi_{25410}(12143,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{91}{132}\right)\)
\(\chi_{25410}(12407,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{65}{132}\right)\)
\(\chi_{25410}(14453,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{67}{132}\right)\)
\(\chi_{25410}(14717,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{103}{132}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{41}{132}\right)\)
\(\chi_{25410}(15377,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{97}{132}\right)\)
\(\chi_{25410}(16103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{107}{132}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{119}{132}\right)\)
\(\chi_{25410}(16763,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{103}{132}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{43}{132}\right)\)
\(\chi_{25410}(17027,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{17}{132}\right)\)
\(\chi_{25410}(17687,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{73}{132}\right)\)
\(\chi_{25410}(18413,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{47}{132}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{95}{132}\right)\)
\(\chi_{25410}(19073,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{19}{132}\right)\)
\(\chi_{25410}(19337,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{125}{132}\right)\)

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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	25410.fy
Modulus	$25410$
Conductor	$12705$
Order	$132$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(25410\)
Conductor:	\(12705\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(132\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 12705.fy	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)