LMFDB - Dirichlet character orbit 3025.cb

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3025, base_ring=CyclotomicField(110)) M = H._module chi = DirichletCharacter(H, M([88,68])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(36, 3025)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3025.36"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$3025$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$3025$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$55$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{55})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 55 polynomial	comment:Fixed field sage:chi.fixed_field()

First 31 of 40 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$12$	$13$	$14$
$\chi_{3025}(36,\cdot)$	$1$	$1$	$e\left(\frac{23}{55}\right)$	$1$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{14}{55}\right)$	$1$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{41}{55}\right)$
$\chi_{3025}(181,\cdot)$	$1$	$1$	$e\left(\frac{49}{55}\right)$	$1$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{37}{55}\right)$	$1$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{18}{55}\right)$
$\chi_{3025}(191,\cdot)$	$1$	$1$	$e\left(\frac{52}{55}\right)$	$1$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{46}{55}\right)$	$1$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{55}\right)$
$\chi_{3025}(196,\cdot)$	$1$	$1$	$e\left(\frac{41}{55}\right)$	$1$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{13}{55}\right)$	$1$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{42}{55}\right)$
$\chi_{3025}(311,\cdot)$	$1$	$1$	$e\left(\frac{13}{55}\right)$	$1$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{39}{55}\right)$	$1$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{16}{55}\right)$
$\chi_{3025}(456,\cdot)$	$1$	$1$	$e\left(\frac{54}{55}\right)$	$1$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{52}{55}\right)$	$1$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{55}\right)$
$\chi_{3025}(466,\cdot)$	$1$	$1$	$e\left(\frac{17}{55}\right)$	$1$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{51}{55}\right)$	$1$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{4}{55}\right)$
$\chi_{3025}(471,\cdot)$	$1$	$1$	$e\left(\frac{1}{55}\right)$	$1$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{3}{55}\right)$	$1$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{52}{55}\right)$
$\chi_{3025}(586,\cdot)$	$1$	$1$	$e\left(\frac{3}{55}\right)$	$1$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{9}{55}\right)$	$1$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{46}{55}\right)$
$\chi_{3025}(731,\cdot)$	$1$	$1$	$e\left(\frac{4}{55}\right)$	$1$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{12}{55}\right)$	$1$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{43}{55}\right)$
$\chi_{3025}(741,\cdot)$	$1$	$1$	$e\left(\frac{37}{55}\right)$	$1$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{1}{55}\right)$	$1$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{54}{55}\right)$
$\chi_{3025}(746,\cdot)$	$1$	$1$	$e\left(\frac{16}{55}\right)$	$1$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{48}{55}\right)$	$1$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{55}\right)$
$\chi_{3025}(861,\cdot)$	$1$	$1$	$e\left(\frac{48}{55}\right)$	$1$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{34}{55}\right)$	$1$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{21}{55}\right)$
$\chi_{3025}(1006,\cdot)$	$1$	$1$	$e\left(\frac{9}{55}\right)$	$1$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{27}{55}\right)$	$1$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{28}{55}\right)$
$\chi_{3025}(1016,\cdot)$	$1$	$1$	$e\left(\frac{2}{55}\right)$	$1$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{6}{55}\right)$	$1$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{49}{55}\right)$
$\chi_{3025}(1021,\cdot)$	$1$	$1$	$e\left(\frac{31}{55}\right)$	$1$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{38}{55}\right)$	$1$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{17}{55}\right)$
$\chi_{3025}(1136,\cdot)$	$1$	$1$	$e\left(\frac{38}{55}\right)$	$1$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{4}{55}\right)$	$1$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{51}{55}\right)$
$\chi_{3025}(1281,\cdot)$	$1$	$1$	$e\left(\frac{14}{55}\right)$	$1$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{42}{55}\right)$	$1$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{55}\right)$
$\chi_{3025}(1296,\cdot)$	$1$	$1$	$e\left(\frac{46}{55}\right)$	$1$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{28}{55}\right)$	$1$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{27}{55}\right)$
$\chi_{3025}(1411,\cdot)$	$1$	$1$	$e\left(\frac{28}{55}\right)$	$1$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{29}{55}\right)$	$1$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{26}{55}\right)$
$\chi_{3025}(1556,\cdot)$	$1$	$1$	$e\left(\frac{19}{55}\right)$	$1$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{2}{55}\right)$	$1$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{53}{55}\right)$
$\chi_{3025}(1566,\cdot)$	$1$	$1$	$e\left(\frac{42}{55}\right)$	$1$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{16}{55}\right)$	$1$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{39}{55}\right)$
$\chi_{3025}(1571,\cdot)$	$1$	$1$	$e\left(\frac{6}{55}\right)$	$1$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{18}{55}\right)$	$1$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{37}{55}\right)$
$\chi_{3025}(1686,\cdot)$	$1$	$1$	$e\left(\frac{18}{55}\right)$	$1$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{54}{55}\right)$	$1$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{55}\right)$
$\chi_{3025}(1831,\cdot)$	$1$	$1$	$e\left(\frac{24}{55}\right)$	$1$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{17}{55}\right)$	$1$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{38}{55}\right)$
$\chi_{3025}(1841,\cdot)$	$1$	$1$	$e\left(\frac{7}{55}\right)$	$1$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{21}{55}\right)$	$1$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{34}{55}\right)$
$\chi_{3025}(1846,\cdot)$	$1$	$1$	$e\left(\frac{21}{55}\right)$	$1$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{8}{55}\right)$	$1$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{47}{55}\right)$
$\chi_{3025}(1961,\cdot)$	$1$	$1$	$e\left(\frac{8}{55}\right)$	$1$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{24}{55}\right)$	$1$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{31}{55}\right)$
$\chi_{3025}(2106,\cdot)$	$1$	$1$	$e\left(\frac{29}{55}\right)$	$1$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{32}{55}\right)$	$1$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{23}{55}\right)$
$\chi_{3025}(2116,\cdot)$	$1$	$1$	$e\left(\frac{27}{55}\right)$	$1$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{26}{55}\right)$	$1$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{29}{55}\right)$
$\chi_{3025}(2121,\cdot)$	$1$	$1$	$e\left(\frac{36}{55}\right)$	$1$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{53}{55}\right)$	$1$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{55}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(12\)	\(13\)	\(14\)
\(\chi_{3025}(36,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{55}\right)\)	\(1\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(1\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{41}{55}\right)\)
\(\chi_{3025}(181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{55}\right)\)	\(1\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(1\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{18}{55}\right)\)
\(\chi_{3025}(191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{55}\right)\)	\(1\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(1\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{55}\right)\)
\(\chi_{3025}(196,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{55}\right)\)	\(1\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(1\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{42}{55}\right)\)
\(\chi_{3025}(311,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{55}\right)\)	\(1\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(1\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{16}{55}\right)\)
\(\chi_{3025}(456,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{54}{55}\right)\)	\(1\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(1\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{55}\right)\)
\(\chi_{3025}(466,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{55}\right)\)	\(1\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(1\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{4}{55}\right)\)
\(\chi_{3025}(471,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{55}\right)\)	\(1\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(1\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{52}{55}\right)\)
\(\chi_{3025}(586,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{55}\right)\)	\(1\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(1\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{46}{55}\right)\)
\(\chi_{3025}(731,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{55}\right)\)	\(1\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(1\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{43}{55}\right)\)
\(\chi_{3025}(741,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{55}\right)\)	\(1\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(1\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{54}{55}\right)\)
\(\chi_{3025}(746,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{55}\right)\)	\(1\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(1\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{55}\right)\)
\(\chi_{3025}(861,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{48}{55}\right)\)	\(1\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(1\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{21}{55}\right)\)
\(\chi_{3025}(1006,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{55}\right)\)	\(1\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(1\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{28}{55}\right)\)
\(\chi_{3025}(1016,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{55}\right)\)	\(1\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(1\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{49}{55}\right)\)
\(\chi_{3025}(1021,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{55}\right)\)	\(1\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(1\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{17}{55}\right)\)
\(\chi_{3025}(1136,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{55}\right)\)	\(1\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(1\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{51}{55}\right)\)
\(\chi_{3025}(1281,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{55}\right)\)	\(1\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(1\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{13}{55}\right)\)
\(\chi_{3025}(1296,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{46}{55}\right)\)	\(1\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(1\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{27}{55}\right)\)
\(\chi_{3025}(1411,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{55}\right)\)	\(1\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(1\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{26}{55}\right)\)
\(\chi_{3025}(1556,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{55}\right)\)	\(1\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(1\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{53}{55}\right)\)
\(\chi_{3025}(1566,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{42}{55}\right)\)	\(1\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(1\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{39}{55}\right)\)
\(\chi_{3025}(1571,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{55}\right)\)	\(1\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(1\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{37}{55}\right)\)
\(\chi_{3025}(1686,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{55}\right)\)	\(1\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(1\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{55}\right)\)
\(\chi_{3025}(1831,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{24}{55}\right)\)	\(1\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(1\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{38}{55}\right)\)
\(\chi_{3025}(1841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{55}\right)\)	\(1\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(1\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{34}{55}\right)\)
\(\chi_{3025}(1846,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{55}\right)\)	\(1\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(1\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{47}{55}\right)\)
\(\chi_{3025}(1961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{55}\right)\)	\(1\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(1\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{31}{55}\right)\)
\(\chi_{3025}(2106,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{55}\right)\)	\(1\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(1\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{23}{55}\right)\)
\(\chi_{3025}(2116,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{55}\right)\)	\(1\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(1\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{29}{55}\right)\)
\(\chi_{3025}(2121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{36}{55}\right)\)	\(1\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(1\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{55}\right)\)

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Basic properties

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

Modulus:	\(3025\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(3025\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(55\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);