LMFDB - Dirichlet character orbit 3025.cx

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3025, base_ring=CyclotomicField(220)) M = H._module chi = DirichletCharacter(H, M([11,2])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(2,3025)) 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:	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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$12$	$13$	$14$
$\chi_{3025}(2,\cdot)$	$1$	$1$	$e\left(\frac{13}{220}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{41}{110}\right)$
$\chi_{3025}(8,\cdot)$	$1$	$1$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{13}{110}\right)$
$\chi_{3025}(123,\cdot)$	$1$	$1$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{179}{220}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{41}{110}\right)$
$\chi_{3025}(128,\cdot)$	$1$	$1$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{193}{220}\right)$	$e\left(\frac{17}{220}\right)$	$e\left(\frac{67}{110}\right)$
$\chi_{3025}(138,\cdot)$	$1$	$1$	$e\left(\frac{87}{220}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{9}{220}\right)$	$e\left(\frac{29}{110}\right)$
$\chi_{3025}(172,\cdot)$	$1$	$1$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{7}{110}\right)$
$\chi_{3025}(217,\cdot)$	$1$	$1$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{37}{220}\right)$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{207}{220}\right)$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{73}{110}\right)$
$\chi_{3025}(237,\cdot)$	$1$	$1$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{101}{220}\right)$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{9}{110}\right)$
$\chi_{3025}(277,\cdot)$	$1$	$1$	$e\left(\frac{173}{220}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{89}{220}\right)$	$e\left(\frac{79}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{21}{110}\right)$
$\chi_{3025}(283,\cdot)$	$1$	$1$	$e\left(\frac{79}{220}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{47}{220}\right)$	$e\left(\frac{17}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{37}{220}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{63}{110}\right)$
$\chi_{3025}(398,\cdot)$	$1$	$1$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{189}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{181}{220}\right)$	$e\left(\frac{21}{110}\right)$
$\chi_{3025}(413,\cdot)$	$1$	$1$	$e\left(\frac{67}{220}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{101}{220}\right)$	$e\left(\frac{189}{220}\right)$	$e\left(\frac{59}{110}\right)$
$\chi_{3025}(447,\cdot)$	$1$	$1$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{220}\right)$	$e\left(\frac{47}{220}\right)$	$e\left(\frac{17}{110}\right)$
$\chi_{3025}(492,\cdot)$	$1$	$1$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{97}{220}\right)$	$e\left(\frac{7}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{67}{220}\right)$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{13}{110}\right)$
$\chi_{3025}(512,\cdot)$	$1$	$1$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{181}{220}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{91}{220}\right)$	$e\left(\frac{179}{220}\right)$	$e\left(\frac{39}{110}\right)$
$\chi_{3025}(552,\cdot)$	$1$	$1$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{1}{110}\right)$
$\chi_{3025}(558,\cdot)$	$1$	$1$	$e\left(\frac{119}{220}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{73}{220}\right)$	$e\left(\frac{3}{110}\right)$
$\chi_{3025}(673,\cdot)$	$1$	$1$	$e\left(\frac{3}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{9}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{1}{110}\right)$
$\chi_{3025}(678,\cdot)$	$1$	$1$	$e\left(\frac{151}{220}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{13}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{87}{110}\right)$
$\chi_{3025}(688,\cdot)$	$1$	$1$	$e\left(\frac{47}{220}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{89}{110}\right)$
$\chi_{3025}(722,\cdot)$	$1$	$1$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{193}{220}\right)$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{27}{110}\right)$
$\chi_{3025}(767,\cdot)$	$1$	$1$	$e\left(\frac{189}{220}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{157}{220}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{103}{220}\right)$	$e\left(\frac{63}{110}\right)$
$\chi_{3025}(787,\cdot)$	$1$	$1$	$e\left(\frac{97}{220}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{41}{220}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{69}{110}\right)$
$\chi_{3025}(827,\cdot)$	$1$	$1$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{51}{220}\right)$	$e\left(\frac{91}{110}\right)$
$\chi_{3025}(833,\cdot)$	$1$	$1$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{37}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{53}{110}\right)$
$\chi_{3025}(948,\cdot)$	$1$	$1$	$e\left(\frac{163}{220}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{49}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{91}{110}\right)$
$\chi_{3025}(953,\cdot)$	$1$	$1$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{97}{110}\right)$
$\chi_{3025}(963,\cdot)$	$1$	$1$	$e\left(\frac{27}{220}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{9}{110}\right)$
$\chi_{3025}(997,\cdot)$	$1$	$1$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{73}{220}\right)$	$e\left(\frac{3}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{37}{110}\right)$
$\chi_{3025}(1042,\cdot)$	$1$	$1$	$e\left(\frac{9}{220}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{217}{220}\right)$	$e\left(\frac{27}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{220}\right)$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{3}{110}\right)$
$\chi_{3025}(1102,\cdot)$	$1$	$1$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{199}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{151}{220}\right)$	$e\left(\frac{71}{110}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(12\)	\(13\)	\(14\)
\(\chi_{3025}(2,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{220}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{41}{110}\right)\)
\(\chi_{3025}(8,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{13}{110}\right)\)
\(\chi_{3025}(123,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{179}{220}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{41}{110}\right)\)
\(\chi_{3025}(128,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{193}{220}\right)\)	\(e\left(\frac{17}{220}\right)\)	\(e\left(\frac{67}{110}\right)\)
\(\chi_{3025}(138,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{87}{220}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{41}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{9}{220}\right)\)	\(e\left(\frac{29}{110}\right)\)
\(\chi_{3025}(172,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{7}{110}\right)\)
\(\chi_{3025}(217,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{37}{220}\right)\)	\(e\left(\frac{107}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{207}{220}\right)\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{73}{110}\right)\)
\(\chi_{3025}(237,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{101}{220}\right)\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{9}{110}\right)\)
\(\chi_{3025}(277,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{173}{220}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{89}{220}\right)\)	\(e\left(\frac{79}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{21}{110}\right)\)
\(\chi_{3025}(283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{220}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{47}{220}\right)\)	\(e\left(\frac{17}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{37}{220}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{63}{110}\right)\)
\(\chi_{3025}(398,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{199}{220}\right)\)	\(e\left(\frac{189}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{181}{220}\right)\)	\(e\left(\frac{21}{110}\right)\)
\(\chi_{3025}(413,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{220}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{101}{220}\right)\)	\(e\left(\frac{189}{220}\right)\)	\(e\left(\frac{59}{110}\right)\)
\(\chi_{3025}(447,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{220}\right)\)	\(e\left(\frac{47}{220}\right)\)	\(e\left(\frac{17}{110}\right)\)
\(\chi_{3025}(492,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{97}{220}\right)\)	\(e\left(\frac{7}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{67}{220}\right)\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{13}{110}\right)\)
\(\chi_{3025}(512,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{181}{220}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{91}{220}\right)\)	\(e\left(\frac{179}{220}\right)\)	\(e\left(\frac{39}{110}\right)\)
\(\chi_{3025}(552,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{220}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{1}{110}\right)\)
\(\chi_{3025}(558,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{220}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{107}{220}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{73}{220}\right)\)	\(e\left(\frac{3}{110}\right)\)
\(\chi_{3025}(673,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{9}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{1}{110}\right)\)
\(\chi_{3025}(678,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{220}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{13}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{87}{110}\right)\)
\(\chi_{3025}(688,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{220}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{89}{110}\right)\)
\(\chi_{3025}(722,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{193}{220}\right)\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{107}{220}\right)\)	\(e\left(\frac{27}{110}\right)\)
\(\chi_{3025}(767,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{189}{220}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{157}{220}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{103}{220}\right)\)	\(e\left(\frac{63}{110}\right)\)
\(\chi_{3025}(787,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{220}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{41}{220}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{69}{110}\right)\)
\(\chi_{3025}(827,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{51}{220}\right)\)	\(e\left(\frac{91}{110}\right)\)
\(\chi_{3025}(833,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{37}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{53}{110}\right)\)
\(\chi_{3025}(948,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{220}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{49}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{91}{110}\right)\)
\(\chi_{3025}(953,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{97}{110}\right)\)
\(\chi_{3025}(963,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{220}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{9}{110}\right)\)
\(\chi_{3025}(997,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{73}{220}\right)\)	\(e\left(\frac{3}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{37}{110}\right)\)
\(\chi_{3025}(1042,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{220}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{217}{220}\right)\)	\(e\left(\frac{27}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{220}\right)\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{3}{110}\right)\)
\(\chi_{3025}(1102,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{199}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{151}{220}\right)\)	\(e\left(\frac{71}{110}\right)\)

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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.cx
Modulus	$3025$
Conductor	$3025$
Order	$220$
Real	no
Primitive	yes
Minimal	yes
Parity	even

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:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)