LMFDB - Dirichlet character orbit 16830.js

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(16830, base_ring=CyclotomicField(80)) M = H._module chi = DirichletCharacter(H, M([40,20,24,25])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(107,16830)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$16830$
Conductor:	$2805$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$80$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2805.fl	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:	$\Q(\zeta_{80})$
Fixed field:	Number field defined by a degree 80 polynomial

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$7$	$13$	$19$	$23$	$29$	$31$	$37$	$41$	$43$	$47$
$\chi_{16830}(107,\cdot)$	$1$	$1$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{16830}(503,\cdot)$	$1$	$1$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{16830}(2987,\cdot)$	$1$	$1$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{16830}(3203,\cdot)$	$1$	$1$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{16830}(4193,\cdot)$	$1$	$1$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{16830}(4517,\cdot)$	$1$	$1$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{16830}(4967,\cdot)$	$1$	$1$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{16830}(5777,\cdot)$	$1$	$1$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{16830}(6047,\cdot)$	$1$	$1$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{16830}(6497,\cdot)$	$1$	$1$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{16830}(7163,\cdot)$	$1$	$1$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{16830}(7757,\cdot)$	$1$	$1$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{16830}(8027,\cdot)$	$1$	$1$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{16830}(8153,\cdot)$	$1$	$1$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{16830}(9323,\cdot)$	$1$	$1$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{16830}(10313,\cdot)$	$1$	$1$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{16830}(10853,\cdot)$	$1$	$1$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{16830}(11843,\cdot)$	$1$	$1$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{16830}(11897,\cdot)$	$1$	$1$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{16830}(12383,\cdot)$	$1$	$1$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{16830}(13283,\cdot)$	$1$	$1$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{16830}(13373,\cdot)$	$1$	$1$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{16830}(13427,\cdot)$	$1$	$1$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{16830}(13697,\cdot)$	$1$	$1$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{16830}(13877,\cdot)$	$1$	$1$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{16830}(14273,\cdot)$	$1$	$1$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{16830}(14813,\cdot)$	$1$	$1$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{16830}(14957,\cdot)$	$1$	$1$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{16830}(15407,\cdot)$	$1$	$1$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{16830}(15677,\cdot)$	$1$	$1$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{16830}(15803,\cdot)$	$1$	$1$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{5}\right)$

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	\(-1\)	\(1\)	\(7\)	\(13\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)	\(47\)
\(\chi_{16830}(107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{16830}(503,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{16830}(2987,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{16830}(3203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{16830}(4193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{16830}(4517,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{16830}(4967,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{16830}(5777,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{16830}(6047,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{16830}(6497,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{16830}(7163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{16830}(7757,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{16830}(8027,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{16830}(8153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{16830}(9323,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{16830}(10313,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{16830}(10853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{16830}(11843,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{16830}(11897,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{16830}(12383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{16830}(13283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{16830}(13373,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{16830}(13427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{16830}(13697,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{16830}(13877,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{16830}(14273,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{16830}(14813,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{16830}(14957,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{16830}(15407,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{16830}(15677,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{16830}(15803,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{5}\right)\)

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First 31 of 32 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	16830.js
Modulus	$16830$
Conductor	$2805$
Order	$80$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(16830\)
Conductor:	\(2805\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(80\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2805.fl	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)