LMFDB - Dirichlet character orbit 24200.ho

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(24200, base_ring=CyclotomicField(110)) M = H._module chi = DirichletCharacter(H, M([0,0,88,56])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(361,24200)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$24200$
Conductor:	$3025$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$55$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 3025.ca	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	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{24200}(361,\cdot)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{14}{55}\right)$
$\chi_{24200}(521,\cdot)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{38}{55}\right)$
$\chi_{24200}(841,\cdot)$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{36}{55}\right)$
$\chi_{24200}(1081,\cdot)$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{42}{55}\right)$
$\chi_{24200}(2561,\cdot)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{55}\right)$
$\chi_{24200}(2721,\cdot)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{8}{55}\right)$
$\chi_{24200}(3041,\cdot)$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{55}\right)$
$\chi_{24200}(3281,\cdot)$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{55}\right)$
$\chi_{24200}(4761,\cdot)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{24}{55}\right)$
$\chi_{24200}(5241,\cdot)$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{21}{55}\right)$
$\chi_{24200}(5481,\cdot)$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{55}\right)$
$\chi_{24200}(6961,\cdot)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{29}{55}\right)$
$\chi_{24200}(7121,\cdot)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{55}\right)$
$\chi_{24200}(7441,\cdot)$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{41}{55}\right)$
$\chi_{24200}(7681,\cdot)$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{32}{55}\right)$
$\chi_{24200}(9161,\cdot)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{34}{55}\right)$
$\chi_{24200}(9321,\cdot)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{28}{55}\right)$
$\chi_{24200}(9641,\cdot)$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{6}{55}\right)$
$\chi_{24200}(9881,\cdot)$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{47}{55}\right)$
$\chi_{24200}(11361,\cdot)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{39}{55}\right)$
$\chi_{24200}(11521,\cdot)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{53}{55}\right)$
$\chi_{24200}(11841,\cdot)$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{26}{55}\right)$
$\chi_{24200}(12081,\cdot)$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{55}\right)$
$\chi_{24200}(13721,\cdot)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{23}{55}\right)$
$\chi_{24200}(14041,\cdot)$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{46}{55}\right)$
$\chi_{24200}(15761,\cdot)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{49}{55}\right)$
$\chi_{24200}(15921,\cdot)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{48}{55}\right)$
$\chi_{24200}(16481,\cdot)$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{37}{55}\right)$
$\chi_{24200}(17961,\cdot)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{54}{55}\right)$
$\chi_{24200}(18121,\cdot)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{18}{55}\right)$
$\chi_{24200}(18441,\cdot)$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{31}{55}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{24200}(361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{14}{55}\right)\)
\(\chi_{24200}(521,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{38}{55}\right)\)
\(\chi_{24200}(841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{36}{55}\right)\)
\(\chi_{24200}(1081,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{42}{55}\right)\)
\(\chi_{24200}(2561,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{55}\right)\)
\(\chi_{24200}(2721,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{8}{55}\right)\)
\(\chi_{24200}(3041,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{55}\right)\)
\(\chi_{24200}(3281,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{55}\right)\)
\(\chi_{24200}(4761,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{24}{55}\right)\)
\(\chi_{24200}(5241,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{21}{55}\right)\)
\(\chi_{24200}(5481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{55}\right)\)
\(\chi_{24200}(6961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{29}{55}\right)\)
\(\chi_{24200}(7121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{55}\right)\)
\(\chi_{24200}(7441,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{41}{55}\right)\)
\(\chi_{24200}(7681,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{32}{55}\right)\)
\(\chi_{24200}(9161,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{34}{55}\right)\)
\(\chi_{24200}(9321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{28}{55}\right)\)
\(\chi_{24200}(9641,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{6}{55}\right)\)
\(\chi_{24200}(9881,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{47}{55}\right)\)
\(\chi_{24200}(11361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{39}{55}\right)\)
\(\chi_{24200}(11521,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{53}{55}\right)\)
\(\chi_{24200}(11841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{26}{55}\right)\)
\(\chi_{24200}(12081,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{55}\right)\)
\(\chi_{24200}(13721,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{23}{55}\right)\)
\(\chi_{24200}(14041,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{46}{55}\right)\)
\(\chi_{24200}(15761,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{49}{55}\right)\)
\(\chi_{24200}(15921,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{48}{55}\right)\)
\(\chi_{24200}(16481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{37}{55}\right)\)
\(\chi_{24200}(17961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{54}{55}\right)\)
\(\chi_{24200}(18121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{18}{55}\right)\)
\(\chi_{24200}(18441,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{31}{55}\right)\)

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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	24200.ho
Modulus	$24200$
Conductor	$3025$
Order	$55$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(24200\)
Conductor:	\(3025\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(55\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 3025.ca	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)