LMFDB - Dirichlet character orbit 15730.fb

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(15730, base_ring=CyclotomicField(220)) M = H._module chi = DirichletCharacter(H, M([165,48,55])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(203,15730)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$15730$
Conductor:	$7865$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$220$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 7865.fj	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:	$\Q(\zeta_{220})$
Fixed field:	Number field defined by a degree 220 polynomial (not computed)

First 31 of 80 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$17$	$19$	$21$	$23$	$27$	$29$	$31$
$\chi_{15730}(203,\cdot)$	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{189}{220}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{3}{220}\right)$
$\chi_{15730}(317,\cdot)$	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{193}{220}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{57}{220}\right)$
$\chi_{15730}(333,\cdot)$	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{79}{220}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{151}{220}\right)$
$\chi_{15730}(577,\cdot)$	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{173}{220}\right)$
$\chi_{15730}(707,\cdot)$	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{141}{220}\right)$
$\chi_{15730}(983,\cdot)$	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{199}{220}\right)$
$\chi_{15730}(1357,\cdot)$	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{47}{220}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{109}{220}\right)$
$\chi_{15730}(1373,\cdot)$	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{220}\right)$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{67}{220}\right)$
$\chi_{15730}(1633,\cdot)$	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{67}{220}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{103}{220}\right)$
$\chi_{15730}(1747,\cdot)$	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{137}{220}\right)$
$\chi_{15730}(1763,\cdot)$	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{171}{220}\right)$
$\chi_{15730}(2007,\cdot)$	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{53}{220}\right)$
$\chi_{15730}(2137,\cdot)$	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{161}{220}\right)$
$\chi_{15730}(2413,\cdot)$	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{159}{220}\right)$
$\chi_{15730}(2787,\cdot)$	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{69}{220}\right)$
$\chi_{15730}(2803,\cdot)$	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{147}{220}\right)$
$\chi_{15730}(3063,\cdot)$	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{203}{220}\right)$
$\chi_{15730}(3177,\cdot)$	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{220}\right)$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{217}{220}\right)$
$\chi_{15730}(3193,\cdot)$	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{191}{220}\right)$
$\chi_{15730}(3437,\cdot)$	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{179}{220}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{153}{220}\right)$
$\chi_{15730}(3567,\cdot)$	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{181}{220}\right)$
$\chi_{15730}(3843,\cdot)$	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{17}{220}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{119}{220}\right)$
$\chi_{15730}(4217,\cdot)$	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{67}{220}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{29}{220}\right)$
$\chi_{15730}(4233,\cdot)$	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{7}{220}\right)$
$\chi_{15730}(4493,\cdot)$	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{220}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{83}{220}\right)$
$\chi_{15730}(4623,\cdot)$	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{211}{220}\right)$
$\chi_{15730}(4997,\cdot)$	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{220}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{201}{220}\right)$
$\chi_{15730}(5273,\cdot)$	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{79}{220}\right)$
$\chi_{15730}(5663,\cdot)$	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{87}{220}\right)$
$\chi_{15730}(5923,\cdot)$	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{87}{220}\right)$	$e\left(\frac{89}{220}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{183}{220}\right)$
$\chi_{15730}(6037,\cdot)$	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{157}{220}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)	\(31\)
\(\chi_{15730}(203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{189}{220}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{3}{220}\right)\)
\(\chi_{15730}(317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{193}{220}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{57}{220}\right)\)
\(\chi_{15730}(333,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{79}{220}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{151}{220}\right)\)
\(\chi_{15730}(577,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{57}{220}\right)\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{173}{220}\right)\)
\(\chi_{15730}(707,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{141}{220}\right)\)
\(\chi_{15730}(983,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{199}{220}\right)\)
\(\chi_{15730}(1357,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{41}{220}\right)\)	\(e\left(\frac{47}{220}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{109}{220}\right)\)
\(\chi_{15730}(1373,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{220}\right)\)	\(e\left(\frac{41}{220}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{67}{220}\right)\)
\(\chi_{15730}(1633,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{67}{220}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{103}{220}\right)\)
\(\chi_{15730}(1747,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{137}{220}\right)\)
\(\chi_{15730}(1763,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{171}{220}\right)\)
\(\chi_{15730}(2007,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{53}{220}\right)\)
\(\chi_{15730}(2137,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{161}{220}\right)\)
\(\chi_{15730}(2413,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{159}{220}\right)\)
\(\chi_{15730}(2787,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{69}{220}\right)\)
\(\chi_{15730}(2803,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{147}{220}\right)\)
\(\chi_{15730}(3063,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{203}{220}\right)\)
\(\chi_{15730}(3177,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{220}\right)\)	\(e\left(\frac{31}{220}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{217}{220}\right)\)
\(\chi_{15730}(3193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{199}{220}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{191}{220}\right)\)
\(\chi_{15730}(3437,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{179}{220}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{153}{220}\right)\)
\(\chi_{15730}(3567,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{181}{220}\right)\)
\(\chi_{15730}(3843,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{17}{220}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{119}{220}\right)\)
\(\chi_{15730}(4217,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{67}{220}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{29}{220}\right)\)
\(\chi_{15730}(4233,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{7}{220}\right)\)
\(\chi_{15730}(4493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{220}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{83}{220}\right)\)
\(\chi_{15730}(4623,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{211}{220}\right)\)
\(\chi_{15730}(4997,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{220}\right)\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{201}{220}\right)\)
\(\chi_{15730}(5273,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{79}{220}\right)\)
\(\chi_{15730}(5663,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{87}{220}\right)\)
\(\chi_{15730}(5923,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{87}{220}\right)\)	\(e\left(\frac{89}{220}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{183}{220}\right)\)
\(\chi_{15730}(6037,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{157}{220}\right)\)

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First 31 of 80 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	15730.fb
Modulus	$15730$
Conductor	$7865$
Order	$220$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(15730\)
Conductor:	\(7865\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(220\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 7865.fj	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)