LMFDB - Dirichlet character orbit 4600.cu

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4600, base_ring=CyclotomicField(110)) M = H._module chi = DirichletCharacter(H, M([0,0,22,60])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(41,4600)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$4600$
Conductor:	$575$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$55$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 575.s	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:	$\Q(\zeta_{55})$
Fixed field:	Number field defined by a degree 55 polynomial

First 31 of 40 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$27$	$29$
$\chi_{4600}(41,\cdot)$	$1$	$1$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{12}{55}\right)$
$\chi_{4600}(81,\cdot)$	$1$	$1$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{9}{55}\right)$
$\chi_{4600}(121,\cdot)$	$1$	$1$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{51}{55}\right)$
$\chi_{4600}(361,\cdot)$	$1$	$1$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{8}{55}\right)$
$\chi_{4600}(441,\cdot)$	$1$	$1$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{37}{55}\right)$
$\chi_{4600}(561,\cdot)$	$1$	$1$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{43}{55}\right)$
$\chi_{4600}(721,\cdot)$	$1$	$1$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{6}{55}\right)$
$\chi_{4600}(761,\cdot)$	$1$	$1$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{13}{55}\right)$
$\chi_{4600}(841,\cdot)$	$1$	$1$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{47}{55}\right)$
$\chi_{4600}(961,\cdot)$	$1$	$1$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{23}{55}\right)$
$\chi_{4600}(1041,\cdot)$	$1$	$1$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{7}{55}\right)$
$\chi_{4600}(1281,\cdot)$	$1$	$1$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{19}{55}\right)$
$\chi_{4600}(1361,\cdot)$	$1$	$1$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{48}{55}\right)$
$\chi_{4600}(1481,\cdot)$	$1$	$1$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{54}{55}\right)$
$\chi_{4600}(1521,\cdot)$	$1$	$1$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{16}{55}\right)$
$\chi_{4600}(1641,\cdot)$	$1$	$1$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{17}{55}\right)$
$\chi_{4600}(1681,\cdot)$	$1$	$1$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{24}{55}\right)$
$\chi_{4600}(1761,\cdot)$	$1$	$1$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{3}{55}\right)$
$\chi_{4600}(1881,\cdot)$	$1$	$1$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{34}{55}\right)$
$\chi_{4600}(1921,\cdot)$	$1$	$1$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{31}{55}\right)$
$\chi_{4600}(1961,\cdot)$	$1$	$1$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{18}{55}\right)$
$\chi_{4600}(2281,\cdot)$	$1$	$1$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{4}{55}\right)$
$\chi_{4600}(2441,\cdot)$	$1$	$1$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{27}{55}\right)$
$\chi_{4600}(2561,\cdot)$	$1$	$1$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{28}{55}\right)$
$\chi_{4600}(2681,\cdot)$	$1$	$1$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{14}{55}\right)$
$\chi_{4600}(2841,\cdot)$	$1$	$1$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{42}{55}\right)$
$\chi_{4600}(2881,\cdot)$	$1$	$1$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{29}{55}\right)$
$\chi_{4600}(3121,\cdot)$	$1$	$1$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{41}{55}\right)$
$\chi_{4600}(3321,\cdot)$	$1$	$1$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{21}{55}\right)$
$\chi_{4600}(3361,\cdot)$	$1$	$1$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{38}{55}\right)$
$\chi_{4600}(3481,\cdot)$	$1$	$1$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{39}{55}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(27\)	\(29\)
\(\chi_{4600}(41,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)
\(\chi_{4600}(81,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)
\(\chi_{4600}(121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)
\(\chi_{4600}(361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)
\(\chi_{4600}(441,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)
\(\chi_{4600}(561,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)
\(\chi_{4600}(721,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)
\(\chi_{4600}(761,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)
\(\chi_{4600}(841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)
\(\chi_{4600}(961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)
\(\chi_{4600}(1041,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)
\(\chi_{4600}(1281,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)
\(\chi_{4600}(1361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)
\(\chi_{4600}(1481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)
\(\chi_{4600}(1521,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)
\(\chi_{4600}(1641,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)
\(\chi_{4600}(1681,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)
\(\chi_{4600}(1761,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)
\(\chi_{4600}(1881,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)
\(\chi_{4600}(1921,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)
\(\chi_{4600}(1961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)
\(\chi_{4600}(2281,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)
\(\chi_{4600}(2441,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)
\(\chi_{4600}(2561,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)
\(\chi_{4600}(2681,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)
\(\chi_{4600}(2841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)
\(\chi_{4600}(2881,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)
\(\chi_{4600}(3121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)
\(\chi_{4600}(3321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)
\(\chi_{4600}(3361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)
\(\chi_{4600}(3481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)

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First 31 of 40 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	4600.cu
Modulus	$4600$
Conductor	$575$
Order	$55$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(4600\)
Conductor:	\(575\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(55\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 575.s	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)