LMFDB - Dirichlet character orbit 7865.fg

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7865, base_ring=CyclotomicField(220)) M = H._module chi = DirichletCharacter(H, M([55,106,110])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(272,7865)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$7865$
Conductor:	$7865$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$220$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$12$	$14$	$16$
$\chi_{7865}(272,\cdot)$	$1$	$1$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{27}{220}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{51}{55}\right)$
$\chi_{7865}(337,\cdot)$	$1$	$1$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{39}{55}\right)$
$\chi_{7865}(402,\cdot)$	$1$	$1$	$e\left(\frac{103}{220}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{89}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{48}{55}\right)$
$\chi_{7865}(558,\cdot)$	$1$	$1$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{31}{55}\right)$
$\chi_{7865}(623,\cdot)$	$1$	$1$	$e\left(\frac{189}{220}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{24}{55}\right)$
$\chi_{7865}(662,\cdot)$	$1$	$1$	$e\left(\frac{67}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{12}{55}\right)$
$\chi_{7865}(688,\cdot)$	$1$	$1$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{3}{55}\right)$
$\chi_{7865}(948,\cdot)$	$1$	$1$	$e\left(\frac{97}{220}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{42}{55}\right)$
$\chi_{7865}(987,\cdot)$	$1$	$1$	$e\left(\frac{111}{220}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{7}{220}\right)$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{1}{55}\right)$
$\chi_{7865}(1052,\cdot)$	$1$	$1$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{29}{55}\right)$
$\chi_{7865}(1117,\cdot)$	$1$	$1$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{18}{55}\right)$
$\chi_{7865}(1273,\cdot)$	$1$	$1$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{36}{55}\right)$
$\chi_{7865}(1338,\cdot)$	$1$	$1$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{14}{55}\right)$
$\chi_{7865}(1377,\cdot)$	$1$	$1$	$e\left(\frac{87}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{32}{55}\right)$
$\chi_{7865}(1403,\cdot)$	$1$	$1$	$e\left(\frac{193}{220}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{28}{55}\right)$
$\chi_{7865}(1663,\cdot)$	$1$	$1$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{7}{55}\right)$
$\chi_{7865}(1702,\cdot)$	$1$	$1$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{73}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{6}{55}\right)$
$\chi_{7865}(1767,\cdot)$	$1$	$1$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{19}{55}\right)$
$\chi_{7865}(1832,\cdot)$	$1$	$1$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{43}{55}\right)$
$\chi_{7865}(1988,\cdot)$	$1$	$1$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{41}{55}\right)$
$\chi_{7865}(2053,\cdot)$	$1$	$1$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{193}{220}\right)$	$e\left(\frac{67}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{4}{55}\right)$
$\chi_{7865}(2092,\cdot)$	$1$	$1$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{101}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{52}{55}\right)$
$\chi_{7865}(2118,\cdot)$	$1$	$1$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{53}{55}\right)$
$\chi_{7865}(2378,\cdot)$	$1$	$1$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{189}{220}\right)$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{27}{55}\right)$
$\chi_{7865}(2482,\cdot)$	$1$	$1$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{9}{55}\right)$
$\chi_{7865}(2547,\cdot)$	$1$	$1$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{13}{55}\right)$
$\chi_{7865}(2703,\cdot)$	$1$	$1$	$e\left(\frac{101}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{157}{220}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{46}{55}\right)$
$\chi_{7865}(2768,\cdot)$	$1$	$1$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{13}{220}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{49}{55}\right)$
$\chi_{7865}(2807,\cdot)$	$1$	$1$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{17}{55}\right)$
$\chi_{7865}(2833,\cdot)$	$1$	$1$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{179}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{23}{55}\right)$
$\chi_{7865}(3093,\cdot)$	$1$	$1$	$e\left(\frac{157}{220}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{47}{55}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(12\)	\(14\)	\(16\)
\(\chi_{7865}(272,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{27}{220}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{51}{55}\right)\)
\(\chi_{7865}(337,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)
\(\chi_{7865}(402,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{220}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{89}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{48}{55}\right)\)
\(\chi_{7865}(558,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{31}{55}\right)\)
\(\chi_{7865}(623,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{189}{220}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{113}{220}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{24}{55}\right)\)
\(\chi_{7865}(662,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{12}{55}\right)\)
\(\chi_{7865}(688,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{220}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{3}{55}\right)\)
\(\chi_{7865}(948,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{220}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{42}{55}\right)\)
\(\chi_{7865}(987,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{111}{220}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{7}{220}\right)\)	\(e\left(\frac{113}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{1}{55}\right)\)
\(\chi_{7865}(1052,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{29}{55}\right)\)
\(\chi_{7865}(1117,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{18}{55}\right)\)
\(\chi_{7865}(1273,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{36}{55}\right)\)
\(\chi_{7865}(1338,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{14}{55}\right)\)
\(\chi_{7865}(1377,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{87}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{41}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{32}{55}\right)\)
\(\chi_{7865}(1403,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{220}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{28}{55}\right)\)
\(\chi_{7865}(1663,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{7}{55}\right)\)
\(\chi_{7865}(1702,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{73}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{6}{55}\right)\)
\(\chi_{7865}(1767,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{57}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{19}{55}\right)\)
\(\chi_{7865}(1832,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{43}{55}\right)\)
\(\chi_{7865}(1988,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{41}{55}\right)\)
\(\chi_{7865}(2053,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{193}{220}\right)\)	\(e\left(\frac{67}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{4}{55}\right)\)
\(\chi_{7865}(2092,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{199}{220}\right)\)	\(e\left(\frac{101}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{52}{55}\right)\)
\(\chi_{7865}(2118,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{41}{220}\right)\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{53}{55}\right)\)
\(\chi_{7865}(2378,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{189}{220}\right)\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{27}{55}\right)\)
\(\chi_{7865}(2482,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)
\(\chi_{7865}(2547,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{13}{55}\right)\)
\(\chi_{7865}(2703,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{157}{220}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{46}{55}\right)\)
\(\chi_{7865}(2768,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{13}{220}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{49}{55}\right)\)
\(\chi_{7865}(2807,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{17}{55}\right)\)
\(\chi_{7865}(2833,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{179}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{23}{55}\right)\)
\(\chi_{7865}(3093,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{220}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{31}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{47}{55}\right)\)

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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	7865.fg
Modulus	$7865$
Conductor	$7865$
Order	$220$
Real	no
Primitive	yes
Minimal	yes
Parity	even

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