LMFDB - Dirichlet character orbit 9075.dx

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9075, base_ring=CyclotomicField(110)) M = H._module chi = DirichletCharacter(H, M([0,22,4])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(16,9075)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$9075$
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	$-1$	$1$	$2$	$4$	$7$	$8$	$13$	$14$	$16$	$17$	$19$	$23$
$\chi_{9075}(16,\cdot)$	$1$	$1$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{41}{55}\right)$
$\chi_{9075}(256,\cdot)$	$1$	$1$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{27}{55}\right)$
$\chi_{9075}(361,\cdot)$	$1$	$1$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{24}{55}\right)$
$\chi_{9075}(796,\cdot)$	$1$	$1$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{43}{55}\right)$
$\chi_{9075}(841,\cdot)$	$1$	$1$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{46}{55}\right)$
$\chi_{9075}(1081,\cdot)$	$1$	$1$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{17}{55}\right)$
$\chi_{9075}(1186,\cdot)$	$1$	$1$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{39}{55}\right)$
$\chi_{9075}(1621,\cdot)$	$1$	$1$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{8}{55}\right)$
$\chi_{9075}(1666,\cdot)$	$1$	$1$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{51}{55}\right)$
$\chi_{9075}(1906,\cdot)$	$1$	$1$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{7}{55}\right)$
$\chi_{9075}(2011,\cdot)$	$1$	$1$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{54}{55}\right)$
$\chi_{9075}(2446,\cdot)$	$1$	$1$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{28}{55}\right)$
$\chi_{9075}(2491,\cdot)$	$1$	$1$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{1}{55}\right)$
$\chi_{9075}(2731,\cdot)$	$1$	$1$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{52}{55}\right)$
$\chi_{9075}(2836,\cdot)$	$1$	$1$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{14}{55}\right)$
$\chi_{9075}(3271,\cdot)$	$1$	$1$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{48}{55}\right)$
$\chi_{9075}(3316,\cdot)$	$1$	$1$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{6}{55}\right)$
$\chi_{9075}(3556,\cdot)$	$1$	$1$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{42}{55}\right)$
$\chi_{9075}(3661,\cdot)$	$1$	$1$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{29}{55}\right)$
$\chi_{9075}(4096,\cdot)$	$1$	$1$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{13}{55}\right)$
$\chi_{9075}(4381,\cdot)$	$1$	$1$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{32}{55}\right)$
$\chi_{9075}(4966,\cdot)$	$1$	$1$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{16}{55}\right)$
$\chi_{9075}(5311,\cdot)$	$1$	$1$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{4}{55}\right)$
$\chi_{9075}(5746,\cdot)$	$1$	$1$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{53}{55}\right)$
$\chi_{9075}(5791,\cdot)$	$1$	$1$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{21}{55}\right)$
$\chi_{9075}(6031,\cdot)$	$1$	$1$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{12}{55}\right)$
$\chi_{9075}(6136,\cdot)$	$1$	$1$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{19}{55}\right)$
$\chi_{9075}(6571,\cdot)$	$1$	$1$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{18}{55}\right)$
$\chi_{9075}(6616,\cdot)$	$1$	$1$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{26}{55}\right)$
$\chi_{9075}(6856,\cdot)$	$1$	$1$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{2}{55}\right)$
$\chi_{9075}(6961,\cdot)$	$1$	$1$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{34}{55}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)	\(23\)
\(\chi_{9075}(16,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)
\(\chi_{9075}(256,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)
\(\chi_{9075}(361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)
\(\chi_{9075}(796,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)
\(\chi_{9075}(841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)
\(\chi_{9075}(1081,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)
\(\chi_{9075}(1186,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)
\(\chi_{9075}(1621,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)
\(\chi_{9075}(1666,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)
\(\chi_{9075}(1906,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)
\(\chi_{9075}(2011,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)
\(\chi_{9075}(2446,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)
\(\chi_{9075}(2491,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)
\(\chi_{9075}(2731,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)
\(\chi_{9075}(2836,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)
\(\chi_{9075}(3271,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)
\(\chi_{9075}(3316,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)
\(\chi_{9075}(3556,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)
\(\chi_{9075}(3661,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)
\(\chi_{9075}(4096,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)
\(\chi_{9075}(4381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)
\(\chi_{9075}(4966,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)
\(\chi_{9075}(5311,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)
\(\chi_{9075}(5746,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)
\(\chi_{9075}(5791,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)
\(\chi_{9075}(6031,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)
\(\chi_{9075}(6136,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)
\(\chi_{9075}(6571,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)
\(\chi_{9075}(6616,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)
\(\chi_{9075}(6856,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)
\(\chi_{9075}(6961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)

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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	9075.dx
Modulus	$9075$
Conductor	$3025$
Order	$55$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(9075\)
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)