LMFDB - Dirichlet character orbit 6050.de

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6050, base_ring=CyclotomicField(220)) M = H._module chi = DirichletCharacter(H, M([55,14])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(7,6050)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$6050$
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	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{6050}(7,\cdot)$	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{32}{55}\right)$
$\chi_{6050}(57,\cdot)$	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{51}{55}\right)$
$\chi_{6050}(107,\cdot)$	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{55}\right)$
$\chi_{6050}(193,\cdot)$	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{55}\right)$
$\chi_{6050}(293,\cdot)$	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{103}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{220}\right)$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{37}{55}\right)$
$\chi_{6050}(343,\cdot)$	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{23}{220}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{41}{55}\right)$
$\chi_{6050}(393,\cdot)$	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{27}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{201}{220}\right)$	$e\left(\frac{79}{220}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{38}{55}\right)$
$\chi_{6050}(557,\cdot)$	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{133}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{159}{220}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{12}{55}\right)$
$\chi_{6050}(607,\cdot)$	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{69}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{153}{220}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{36}{55}\right)$
$\chi_{6050}(657,\cdot)$	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{177}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{23}{55}\right)$
$\chi_{6050}(743,\cdot)$	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{4}{55}\right)$
$\chi_{6050}(843,\cdot)$	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{31}{220}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{55}\right)$
$\chi_{6050}(893,\cdot)$	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{97}{220}\right)$	$e\left(\frac{83}{220}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{26}{55}\right)$
$\chi_{6050}(943,\cdot)$	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{39}{220}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{48}{55}\right)$
$\chi_{6050}(1007,\cdot)$	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{61}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{97}{220}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{39}{55}\right)$
$\chi_{6050}(1107,\cdot)$	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{59}{220}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{47}{55}\right)$
$\chi_{6050}(1157,\cdot)$	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{213}{220}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{21}{55}\right)$
$\chi_{6050}(1293,\cdot)$	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{131}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{193}{220}\right)$	$e\left(\frac{147}{220}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{54}{55}\right)$
$\chi_{6050}(1393,\cdot)$	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{63}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{29}{220}\right)$	$e\left(\frac{111}{220}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{52}{55}\right)$
$\chi_{6050}(1493,\cdot)$	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{47}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{81}{220}\right)$	$e\left(\frac{219}{220}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{55}\right)$
$\chi_{6050}(1557,\cdot)$	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{117}{220}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{34}{55}\right)$
$\chi_{6050}(1657,\cdot)$	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{93}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{179}{220}\right)$	$e\left(\frac{101}{220}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{27}{55}\right)$
$\chi_{6050}(1707,\cdot)$	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{107}{220}\right)$	$e\left(\frac{53}{220}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{6}{55}\right)$
$\chi_{6050}(1757,\cdot)$	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{171}{220}\right)$	$e\left(\frac{169}{220}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{43}{55}\right)$
$\chi_{6050}(1843,\cdot)$	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{49}{55}\right)$
$\chi_{6050}(1943,\cdot)$	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{43}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{149}{220}\right)$	$e\left(\frac{191}{220}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{32}{55}\right)$
$\chi_{6050}(1993,\cdot)$	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{139}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{57}{220}\right)$	$e\left(\frac{203}{220}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{51}{55}\right)$
$\chi_{6050}(2043,\cdot)$	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{21}{220}\right)$	$e\left(\frac{179}{220}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{55}\right)$
$\chi_{6050}(2107,\cdot)$	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{161}{220}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{123}{220}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{29}{55}\right)$
$\chi_{6050}(2207,\cdot)$	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{73}{220}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{79}{220}\right)$	$e\left(\frac{181}{220}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{55}\right)$
$\chi_{6050}(2257,\cdot)$	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{189}{220}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{87}{220}\right)$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{46}{55}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{6050}(7,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{32}{55}\right)\)
\(\chi_{6050}(57,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{51}{55}\right)\)
\(\chi_{6050}(107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{57}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{55}\right)\)
\(\chi_{6050}(193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{31}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{107}{220}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{55}\right)\)
\(\chi_{6050}(293,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{103}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{220}\right)\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{37}{55}\right)\)
\(\chi_{6050}(343,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{23}{220}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{41}{55}\right)\)
\(\chi_{6050}(393,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{27}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{201}{220}\right)\)	\(e\left(\frac{79}{220}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{38}{55}\right)\)
\(\chi_{6050}(557,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{133}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{159}{220}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{12}{55}\right)\)
\(\chi_{6050}(607,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{69}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{153}{220}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{36}{55}\right)\)
\(\chi_{6050}(657,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{177}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{23}{55}\right)\)
\(\chi_{6050}(743,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{4}{55}\right)\)
\(\chi_{6050}(843,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{31}{220}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{55}\right)\)
\(\chi_{6050}(893,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{97}{220}\right)\)	\(e\left(\frac{83}{220}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{26}{55}\right)\)
\(\chi_{6050}(943,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{39}{220}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{48}{55}\right)\)
\(\chi_{6050}(1007,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{61}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{97}{220}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{39}{55}\right)\)
\(\chi_{6050}(1107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{113}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{59}{220}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{47}{55}\right)\)
\(\chi_{6050}(1157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{213}{220}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{21}{55}\right)\)
\(\chi_{6050}(1293,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{131}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{193}{220}\right)\)	\(e\left(\frac{147}{220}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{54}{55}\right)\)
\(\chi_{6050}(1393,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{63}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{29}{220}\right)\)	\(e\left(\frac{111}{220}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{52}{55}\right)\)
\(\chi_{6050}(1493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{47}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{81}{220}\right)\)	\(e\left(\frac{219}{220}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{55}\right)\)
\(\chi_{6050}(1557,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{117}{220}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{34}{55}\right)\)
\(\chi_{6050}(1657,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{93}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{179}{220}\right)\)	\(e\left(\frac{101}{220}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{27}{55}\right)\)
\(\chi_{6050}(1707,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{107}{220}\right)\)	\(e\left(\frac{53}{220}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{6}{55}\right)\)
\(\chi_{6050}(1757,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{171}{220}\right)\)	\(e\left(\frac{169}{220}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{43}{55}\right)\)
\(\chi_{6050}(1843,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{113}{220}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{49}{55}\right)\)
\(\chi_{6050}(1943,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{43}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{149}{220}\right)\)	\(e\left(\frac{191}{220}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{32}{55}\right)\)
\(\chi_{6050}(1993,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{139}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{57}{220}\right)\)	\(e\left(\frac{203}{220}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{51}{55}\right)\)
\(\chi_{6050}(2043,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{21}{220}\right)\)	\(e\left(\frac{179}{220}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{55}\right)\)
\(\chi_{6050}(2107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{161}{220}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{123}{220}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{29}{55}\right)\)
\(\chi_{6050}(2207,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{73}{220}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{79}{220}\right)\)	\(e\left(\frac{181}{220}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{55}\right)\)
\(\chi_{6050}(2257,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{189}{220}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{87}{220}\right)\)	\(e\left(\frac{113}{220}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{46}{55}\right)\)

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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	6050.de
Modulus	$6050$
Conductor	$605$
Order	$220$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(6050\)
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)