LMFDB - Dirichlet character orbit 16830.ko

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(16830, base_ring=CyclotomicField(240)) M = H._module chi = DirichletCharacter(H, M([160,60,48,45])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(367,16830)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$16830$
Conductor:	$8415$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$240$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 8415.kp	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:	$\Q(\zeta_{240})$
Fixed field:	Number field defined by a degree 240 polynomial (not computed)

First 31 of 64 characters in Galois orbit

Character	$-1$	$1$	$7$	$13$	$19$	$23$	$29$	$31$	$37$	$41$	$43$	$47$
$\chi_{16830}(367,\cdot)$	$1$	$1$	$e\left(\frac{91}{240}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{1}{240}\right)$	$e\left(\frac{53}{240}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{239}{240}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{16830}(643,\cdot)$	$1$	$1$	$e\left(\frac{17}{240}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{227}{240}\right)$	$e\left(\frac{31}{240}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{13}{240}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{16830}(907,\cdot)$	$1$	$1$	$e\left(\frac{7}{240}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{37}{240}\right)$	$e\left(\frac{41}{240}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{203}{240}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{16830}(1093,\cdot)$	$1$	$1$	$e\left(\frac{221}{240}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{71}{240}\right)$	$e\left(\frac{163}{240}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{169}{240}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{16830}(1417,\cdot)$	$1$	$1$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{53}{240}\right)$	$e\left(\frac{169}{240}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{187}{240}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{16830}(1897,\cdot)$	$1$	$1$	$e\left(\frac{187}{240}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{97}{240}\right)$	$e\left(\frac{101}{240}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{143}{240}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{16830}(2407,\cdot)$	$1$	$1$	$e\left(\frac{203}{240}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{113}{240}\right)$	$e\left(\frac{229}{240}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{127}{240}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{16830}(2623,\cdot)$	$1$	$1$	$e\left(\frac{77}{240}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{167}{240}\right)$	$e\left(\frac{211}{240}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{73}{240}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{16830}(3067,\cdot)$	$1$	$1$	$e\left(\frac{163}{240}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{73}{240}\right)$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{167}{240}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{16830}(3193,\cdot)$	$1$	$1$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{19}{240}\right)$	$e\left(\frac{47}{240}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{221}{240}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{16830}(3463,\cdot)$	$1$	$1$	$e\left(\frac{133}{240}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{223}{240}\right)$	$e\left(\frac{59}{240}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{17}{240}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{16830}(4057,\cdot)$	$1$	$1$	$e\left(\frac{223}{240}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{13}{240}\right)$	$e\left(\frac{209}{240}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{227}{240}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{16830}(4723,\cdot)$	$1$	$1$	$e\left(\frac{1}{240}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{211}{240}\right)$	$e\left(\frac{143}{240}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{16830}(5107,\cdot)$	$1$	$1$	$e\left(\frac{179}{240}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{157}{240}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{151}{240}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{16830}(5173,\cdot)$	$1$	$1$	$e\left(\frac{109}{240}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{199}{240}\right)$	$e\left(\frac{227}{240}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{41}{240}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{16830}(5443,\cdot)$	$1$	$1$	$e\left(\frac{73}{240}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{43}{240}\right)$	$e\left(\frac{119}{240}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{197}{240}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{16830}(5503,\cdot)$	$1$	$1$	$e\left(\frac{149}{240}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{239}{240}\right)$	$e\left(\frac{187}{240}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{1}{240}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{16830}(6097,\cdot)$	$1$	$1$	$e\left(\frac{239}{240}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{97}{240}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{211}{240}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{16830}(6253,\cdot)$	$1$	$1$	$e\left(\frac{97}{240}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{67}{240}\right)$	$e\left(\frac{191}{240}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{173}{240}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{16830}(6637,\cdot)$	$1$	$1$	$e\left(\frac{131}{240}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{41}{240}\right)$	$e\left(\frac{13}{240}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{199}{240}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{16830}(6703,\cdot)$	$1$	$1$	$e\left(\frac{61}{240}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{151}{240}\right)$	$e\left(\frac{83}{240}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{16830}(6763,\cdot)$	$1$	$1$	$e\left(\frac{113}{240}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{83}{240}\right)$	$e\left(\frac{79}{240}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{157}{240}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{2}{15}\right)$
$\chi_{16830}(7027,\cdot)$	$1$	$1$	$e\left(\frac{103}{240}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{133}{240}\right)$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{107}{240}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{16830}(7033,\cdot)$	$1$	$1$	$e\left(\frac{101}{240}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{191}{240}\right)$	$e\left(\frac{43}{240}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{16830}(7483,\cdot)$	$1$	$1$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{59}{240}\right)$	$e\left(\frac{7}{240}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{181}{240}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{16830}(7627,\cdot)$	$1$	$1$	$e\left(\frac{191}{240}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{221}{240}\right)$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{19}{240}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{16830}(8017,\cdot)$	$1$	$1$	$e\left(\frac{43}{240}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{149}{240}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{47}{240}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{16830}(8167,\cdot)$	$1$	$1$	$e\left(\frac{227}{240}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{137}{240}\right)$	$e\left(\frac{61}{240}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{103}{240}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{16830}(8233,\cdot)$	$1$	$1$	$e\left(\frac{157}{240}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{7}{240}\right)$	$e\left(\frac{131}{240}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{233}{240}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{16830}(8563,\cdot)$	$1$	$1$	$e\left(\frac{197}{240}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{47}{240}\right)$	$e\left(\frac{91}{240}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{16830}(8743,\cdot)$	$1$	$1$	$e\left(\frac{173}{240}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{19}{240}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{217}{240}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{2}{15}\right)$

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	\(-1\)	\(1\)	\(7\)	\(13\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)	\(47\)
\(\chi_{16830}(367,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{240}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{1}{240}\right)\)	\(e\left(\frac{53}{240}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{239}{240}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{16830}(643,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{240}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{227}{240}\right)\)	\(e\left(\frac{31}{240}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{13}{240}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{16830}(907,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{240}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{37}{240}\right)\)	\(e\left(\frac{41}{240}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{203}{240}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{16830}(1093,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{221}{240}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{71}{240}\right)\)	\(e\left(\frac{163}{240}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{169}{240}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{16830}(1417,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{53}{240}\right)\)	\(e\left(\frac{169}{240}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{187}{240}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{16830}(1897,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{187}{240}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{97}{240}\right)\)	\(e\left(\frac{101}{240}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{143}{240}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{16830}(2407,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{203}{240}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{113}{240}\right)\)	\(e\left(\frac{229}{240}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{127}{240}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{16830}(2623,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{240}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{167}{240}\right)\)	\(e\left(\frac{211}{240}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{73}{240}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{16830}(3067,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{240}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{73}{240}\right)\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{167}{240}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{16830}(3193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{19}{240}\right)\)	\(e\left(\frac{47}{240}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{221}{240}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{16830}(3463,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{240}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{223}{240}\right)\)	\(e\left(\frac{59}{240}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{17}{240}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{16830}(4057,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{223}{240}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{13}{240}\right)\)	\(e\left(\frac{209}{240}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{227}{240}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{16830}(4723,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{240}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{211}{240}\right)\)	\(e\left(\frac{143}{240}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{16830}(5107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{240}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{157}{240}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{151}{240}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{16830}(5173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{240}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{199}{240}\right)\)	\(e\left(\frac{227}{240}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{41}{240}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{16830}(5443,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{240}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{43}{240}\right)\)	\(e\left(\frac{119}{240}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{197}{240}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{16830}(5503,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{240}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{239}{240}\right)\)	\(e\left(\frac{187}{240}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{1}{240}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{16830}(6097,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{239}{240}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{97}{240}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{211}{240}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{16830}(6253,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{240}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{67}{240}\right)\)	\(e\left(\frac{191}{240}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{173}{240}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{16830}(6637,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{240}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{41}{240}\right)\)	\(e\left(\frac{13}{240}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{199}{240}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{16830}(6703,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{240}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{151}{240}\right)\)	\(e\left(\frac{83}{240}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{16830}(6763,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{240}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{83}{240}\right)\)	\(e\left(\frac{79}{240}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{157}{240}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{2}{15}\right)\)
\(\chi_{16830}(7027,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{240}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{133}{240}\right)\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{107}{240}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{16830}(7033,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{240}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{191}{240}\right)\)	\(e\left(\frac{43}{240}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{16830}(7483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{59}{240}\right)\)	\(e\left(\frac{7}{240}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{181}{240}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{16830}(7627,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{240}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{221}{240}\right)\)	\(e\left(\frac{193}{240}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{19}{240}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{16830}(8017,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{240}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{193}{240}\right)\)	\(e\left(\frac{149}{240}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{47}{240}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{16830}(8167,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{227}{240}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{137}{240}\right)\)	\(e\left(\frac{61}{240}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{103}{240}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{16830}(8233,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{240}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{7}{240}\right)\)	\(e\left(\frac{131}{240}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{233}{240}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{16830}(8563,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{240}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{47}{240}\right)\)	\(e\left(\frac{91}{240}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{193}{240}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{16830}(8743,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{240}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{19}{240}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{217}{240}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{2}{15}\right)\)

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First 31 of 64 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.ko
Modulus	$16830$
Conductor	$8415$
Order	$240$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(16830\)
Conductor:	\(8415\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(240\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 8415.kp	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)