LMFDB - Dirichlet character orbit 7865.fe

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7865, base_ring=CyclotomicField(220)) M = H._module chi = DirichletCharacter(H, M([165,174,0])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(183,7865)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$7865$
Conductor:	$605$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$220$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 605.w	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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$12$	$14$	$16$
$\chi_{7865}(183,\cdot)$	$1$	$1$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{9}{55}\right)$
$\chi_{7865}(222,\cdot)$	$1$	$1$	$e\left(\frac{97}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{42}{55}\right)$
$\chi_{7865}(248,\cdot)$	$1$	$1$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{13}{55}\right)$
$\chi_{7865}(508,\cdot)$	$1$	$1$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{17}{55}\right)$
$\chi_{7865}(547,\cdot)$	$1$	$1$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{36}{55}\right)$
$\chi_{7865}(612,\cdot)$	$1$	$1$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{14}{55}\right)$
$\chi_{7865}(677,\cdot)$	$1$	$1$	$e\left(\frac{193}{220}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{28}{55}\right)$
$\chi_{7865}(833,\cdot)$	$1$	$1$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{16}{55}\right)$
$\chi_{7865}(898,\cdot)$	$1$	$1$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{103}{220}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{54}{55}\right)$
$\chi_{7865}(937,\cdot)$	$1$	$1$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{7}{55}\right)$
$\chi_{7865}(963,\cdot)$	$1$	$1$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{38}{55}\right)$
$\chi_{7865}(1223,\cdot)$	$1$	$1$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{37}{55}\right)$
$\chi_{7865}(1262,\cdot)$	$1$	$1$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{41}{55}\right)$
$\chi_{7865}(1327,\cdot)$	$1$	$1$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{193}{220}\right)$	$e\left(\frac{67}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{4}{55}\right)$
$\chi_{7865}(1392,\cdot)$	$1$	$1$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{53}{55}\right)$
$\chi_{7865}(1548,\cdot)$	$1$	$1$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{173}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{21}{55}\right)$
$\chi_{7865}(1652,\cdot)$	$1$	$1$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{189}{220}\right)$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{27}{55}\right)$
$\chi_{7865}(1678,\cdot)$	$1$	$1$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{111}{220}\right)$	$e\left(\frac{189}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{8}{55}\right)$
$\chi_{7865}(1938,\cdot)$	$1$	$1$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{179}{220}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{2}{55}\right)$
$\chi_{7865}(1977,\cdot)$	$1$	$1$	$e\left(\frac{101}{220}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{157}{220}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{46}{55}\right)$
$\chi_{7865}(2042,\cdot)$	$1$	$1$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{13}{220}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{49}{55}\right)$
$\chi_{7865}(2107,\cdot)$	$1$	$1$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{179}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{23}{55}\right)$
$\chi_{7865}(2263,\cdot)$	$1$	$1$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{26}{55}\right)$
$\chi_{7865}(2328,\cdot)$	$1$	$1$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{157}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{34}{55}\right)$
$\chi_{7865}(2367,\cdot)$	$1$	$1$	$e\left(\frac{157}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{47}{55}\right)$
$\chi_{7865}(2692,\cdot)$	$1$	$1$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{51}{55}\right)$
$\chi_{7865}(2757,\cdot)$	$1$	$1$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{7}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{39}{55}\right)$
$\chi_{7865}(2822,\cdot)$	$1$	$1$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{48}{55}\right)$
$\chi_{7865}(2978,\cdot)$	$1$	$1$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{31}{55}\right)$
$\chi_{7865}(3043,\cdot)$	$1$	$1$	$e\left(\frac{79}{220}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{3}{220}\right)$	$e\left(\frac{17}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{24}{55}\right)$
$\chi_{7865}(3082,\cdot)$	$1$	$1$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{12}{55}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(12\)	\(14\)	\(16\)
\(\chi_{7865}(183,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)
\(\chi_{7865}(222,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{42}{55}\right)\)
\(\chi_{7865}(248,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{13}{55}\right)\)
\(\chi_{7865}(508,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{17}{55}\right)\)
\(\chi_{7865}(547,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{36}{55}\right)\)
\(\chi_{7865}(612,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{14}{55}\right)\)
\(\chi_{7865}(677,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{220}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{28}{55}\right)\)
\(\chi_{7865}(833,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{16}{55}\right)\)
\(\chi_{7865}(898,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{103}{220}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{54}{55}\right)\)
\(\chi_{7865}(937,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{7}{55}\right)\)
\(\chi_{7865}(963,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{38}{55}\right)\)
\(\chi_{7865}(1223,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{37}{55}\right)\)
\(\chi_{7865}(1262,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{220}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{41}{55}\right)\)
\(\chi_{7865}(1327,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{193}{220}\right)\)	\(e\left(\frac{67}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{4}{55}\right)\)
\(\chi_{7865}(1392,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{41}{220}\right)\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{53}{55}\right)\)
\(\chi_{7865}(1548,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{173}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{21}{55}\right)\)
\(\chi_{7865}(1652,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{189}{220}\right)\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{27}{55}\right)\)
\(\chi_{7865}(1678,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{111}{220}\right)\)	\(e\left(\frac{189}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{8}{55}\right)\)
\(\chi_{7865}(1938,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{179}{220}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{2}{55}\right)\)
\(\chi_{7865}(1977,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{220}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{157}{220}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{46}{55}\right)\)
\(\chi_{7865}(2042,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{13}{220}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{49}{55}\right)\)
\(\chi_{7865}(2107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{179}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{23}{55}\right)\)
\(\chi_{7865}(2263,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{26}{55}\right)\)
\(\chi_{7865}(2328,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{220}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{157}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{34}{55}\right)\)
\(\chi_{7865}(2367,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{31}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{47}{55}\right)\)
\(\chi_{7865}(2692,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{51}{55}\right)\)
\(\chi_{7865}(2757,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{7}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)
\(\chi_{7865}(2822,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{199}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{48}{55}\right)\)
\(\chi_{7865}(2978,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{107}{220}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{31}{55}\right)\)
\(\chi_{7865}(3043,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{220}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{3}{220}\right)\)	\(e\left(\frac{17}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{24}{55}\right)\)
\(\chi_{7865}(3082,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{12}{55}\right)\)

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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.fe
Modulus	$7865$
Conductor	$605$
Order	$220$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(7865\)
Conductor:	\(605\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(220\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 605.w	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)