LMFDB - Dirichlet character orbit 3025.df

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3025, base_ring=CyclotomicField(220)) M = H._module chi = DirichletCharacter(H, M([143,192])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(42,3025)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$3025$
Conductor:	$3025$	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:	odd	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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$12$	$13$	$14$
$\chi_{3025}(42,\cdot)$	$-1$	$1$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{79}{220}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{87}{220}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{97}{110}\right)$
$\chi_{3025}(48,\cdot)$	$-1$	$1$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{109}{110}\right)$
$\chi_{3025}(108,\cdot)$	$-1$	$1$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{27}{110}\right)$
$\chi_{3025}(113,\cdot)$	$-1$	$1$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{97}{220}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{67}{220}\right)$	$e\left(\frac{101}{110}\right)$
$\chi_{3025}(203,\cdot)$	$-1$	$1$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{173}{220}\right)$	$e\left(\frac{151}{220}\right)$	$e\left(\frac{93}{110}\right)$
$\chi_{3025}(212,\cdot)$	$-1$	$1$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{27}{220}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{157}{220}\right)$	$e\left(\frac{61}{110}\right)$
$\chi_{3025}(247,\cdot)$	$-1$	$1$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{53}{110}\right)$
$\chi_{3025}(317,\cdot)$	$-1$	$1$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{9}{220}\right)$	$e\left(\frac{7}{110}\right)$
$\chi_{3025}(383,\cdot)$	$-1$	$1$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{47}{110}\right)$
$\chi_{3025}(388,\cdot)$	$-1$	$1$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{37}{220}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{51}{110}\right)$
$\chi_{3025}(477,\cdot)$	$-1$	$1$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{193}{220}\right)$	$e\left(\frac{89}{110}\right)$
$\chi_{3025}(478,\cdot)$	$-1$	$1$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{63}{110}\right)$
$\chi_{3025}(522,\cdot)$	$-1$	$1$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{23}{110}\right)$
$\chi_{3025}(592,\cdot)$	$-1$	$1$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{27}{110}\right)$
$\chi_{3025}(598,\cdot)$	$-1$	$1$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{89}{110}\right)$
$\chi_{3025}(658,\cdot)$	$-1$	$1$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{220}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{67}{110}\right)$
$\chi_{3025}(663,\cdot)$	$-1$	$1$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{1}{110}\right)$
$\chi_{3025}(752,\cdot)$	$-1$	$1$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{79}{110}\right)$
$\chi_{3025}(762,\cdot)$	$-1$	$1$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{151}{220}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{71}{110}\right)$
$\chi_{3025}(797,\cdot)$	$-1$	$1$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{101}{220}\right)$	$e\left(\frac{103}{110}\right)$
$\chi_{3025}(867,\cdot)$	$-1$	$1$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{220}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{47}{110}\right)$
$\chi_{3025}(873,\cdot)$	$-1$	$1$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{89}{220}\right)$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{79}{110}\right)$
$\chi_{3025}(933,\cdot)$	$-1$	$1$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{89}{220}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{87}{110}\right)$
$\chi_{3025}(938,\cdot)$	$-1$	$1$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{47}{220}\right)$	$e\left(\frac{61}{110}\right)$
$\chi_{3025}(1027,\cdot)$	$-1$	$1$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{73}{220}\right)$	$e\left(\frac{69}{110}\right)$
$\chi_{3025}(1028,\cdot)$	$-1$	$1$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{73}{220}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{3}{110}\right)$
$\chi_{3025}(1037,\cdot)$	$-1$	$1$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{67}{220}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{21}{110}\right)$
$\chi_{3025}(1072,\cdot)$	$-1$	$1$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{73}{110}\right)$
$\chi_{3025}(1142,\cdot)$	$-1$	$1$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{67}{110}\right)$
$\chi_{3025}(1148,\cdot)$	$-1$	$1$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{173}{220}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{69}{110}\right)$
$\chi_{3025}(1208,\cdot)$	$-1$	$1$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{37}{220}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{107}{110}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(12\)	\(13\)	\(14\)
\(\chi_{3025}(42,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{79}{220}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{87}{220}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{97}{110}\right)\)
\(\chi_{3025}(48,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{109}{110}\right)\)
\(\chi_{3025}(108,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{27}{110}\right)\)
\(\chi_{3025}(113,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{97}{220}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{67}{220}\right)\)	\(e\left(\frac{101}{110}\right)\)
\(\chi_{3025}(203,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{173}{220}\right)\)	\(e\left(\frac{151}{220}\right)\)	\(e\left(\frac{93}{110}\right)\)
\(\chi_{3025}(212,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{27}{220}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{157}{220}\right)\)	\(e\left(\frac{61}{110}\right)\)
\(\chi_{3025}(247,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{53}{110}\right)\)
\(\chi_{3025}(317,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{9}{220}\right)\)	\(e\left(\frac{7}{110}\right)\)
\(\chi_{3025}(383,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{47}{110}\right)\)
\(\chi_{3025}(388,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{37}{220}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{51}{110}\right)\)
\(\chi_{3025}(477,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{193}{220}\right)\)	\(e\left(\frac{89}{110}\right)\)
\(\chi_{3025}(478,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{63}{110}\right)\)
\(\chi_{3025}(522,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{23}{110}\right)\)
\(\chi_{3025}(592,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{107}{220}\right)\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{27}{110}\right)\)
\(\chi_{3025}(598,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{89}{110}\right)\)
\(\chi_{3025}(658,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{220}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{67}{110}\right)\)
\(\chi_{3025}(663,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{1}{110}\right)\)
\(\chi_{3025}(752,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{199}{220}\right)\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{79}{110}\right)\)
\(\chi_{3025}(762,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{151}{220}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{71}{110}\right)\)
\(\chi_{3025}(797,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{101}{220}\right)\)	\(e\left(\frac{103}{110}\right)\)
\(\chi_{3025}(867,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{220}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{47}{110}\right)\)
\(\chi_{3025}(873,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{89}{220}\right)\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{79}{110}\right)\)
\(\chi_{3025}(933,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{89}{220}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{87}{110}\right)\)
\(\chi_{3025}(938,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{47}{220}\right)\)	\(e\left(\frac{61}{110}\right)\)
\(\chi_{3025}(1027,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{73}{220}\right)\)	\(e\left(\frac{69}{110}\right)\)
\(\chi_{3025}(1028,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{41}{220}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{73}{220}\right)\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{3}{110}\right)\)
\(\chi_{3025}(1037,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{67}{220}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{21}{110}\right)\)
\(\chi_{3025}(1072,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{73}{110}\right)\)
\(\chi_{3025}(1142,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{67}{110}\right)\)
\(\chi_{3025}(1148,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{173}{220}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{69}{110}\right)\)
\(\chi_{3025}(1208,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{37}{220}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{107}{110}\right)\)

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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	3025.df
Modulus	$3025$
Conductor	$3025$
Order	$220$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(3025\)
Conductor:	\(3025\)	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:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)