LMFDB - Dirichlet character orbit 2301.bb

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2301, base_ring=CyclotomicField(58)) M = H._module chi = DirichletCharacter(H, M([0,29,27])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(103, 2301)) 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("2301.103"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$2301$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$767$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$58$	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:	no, induced from 767.n	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{29})$	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 58 polynomial	comment:Fixed field sage:chi.fixed_field()

Characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$14$	$16$	$17$
$\chi_{2301}(103,\cdot)$	$-1$	$1$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{17}{58}\right)$	$e\left(\frac{51}{58}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{49}{58}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{18}{29}\right)$
$\chi_{2301}(142,\cdot)$	$-1$	$1$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{57}{58}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{16}{29}\right)$
$\chi_{2301}(220,\cdot)$	$-1$	$1$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{57}{58}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{22}{29}\right)$
$\chi_{2301}(259,\cdot)$	$-1$	$1$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{10}{29}\right)$
$\chi_{2301}(337,\cdot)$	$-1$	$1$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{35}{58}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{17}{29}\right)$
$\chi_{2301}(415,\cdot)$	$-1$	$1$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{35}{58}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{20}{29}\right)$
$\chi_{2301}(571,\cdot)$	$-1$	$1$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{17}{58}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{6}{29}\right)$
$\chi_{2301}(688,\cdot)$	$-1$	$1$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{57}{58}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{15}{29}\right)$
$\chi_{2301}(805,\cdot)$	$-1$	$1$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{35}{58}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{45}{58}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{26}{29}\right)$
$\chi_{2301}(844,\cdot)$	$-1$	$1$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{49}{58}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{19}{29}\right)$
$\chi_{2301}(922,\cdot)$	$-1$	$1$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{27}{29}\right)$
$\chi_{2301}(1000,\cdot)$	$-1$	$1$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{39}{58}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{51}{58}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{14}{29}\right)$
$\chi_{2301}(1117,\cdot)$	$-1$	$1$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{11}{29}\right)$
$\chi_{2301}(1234,\cdot)$	$-1$	$1$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{4}{29}\right)$
$\chi_{2301}(1273,\cdot)$	$-1$	$1$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{8}{29}\right)$
$\chi_{2301}(1312,\cdot)$	$-1$	$1$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{17}{58}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{3}{29}\right)$
$\chi_{2301}(1390,\cdot)$	$-1$	$1$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{45}{58}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{21}{29}\right)$
$\chi_{2301}(1429,\cdot)$	$-1$	$1$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{1}{29}\right)$
$\chi_{2301}(1468,\cdot)$	$-1$	$1$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{39}{58}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{12}{29}\right)$
$\chi_{2301}(1507,\cdot)$	$-1$	$1$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{35}{58}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{13}{29}\right)$
$\chi_{2301}(1624,\cdot)$	$-1$	$1$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{23}{29}\right)$
$\chi_{2301}(1663,\cdot)$	$-1$	$1$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{7}{29}\right)$
$\chi_{2301}(1702,\cdot)$	$-1$	$1$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{49}{58}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{28}{29}\right)$
$\chi_{2301}(1741,\cdot)$	$-1$	$1$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{51}{58}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{39}{58}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{9}{29}\right)$
$\chi_{2301}(1780,\cdot)$	$-1$	$1$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{39}{58}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{49}{58}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{17}{58}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{24}{29}\right)$
$\chi_{2301}(2014,\cdot)$	$-1$	$1$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{57}{58}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{2}{29}\right)$
$\chi_{2301}(2053,\cdot)$	$-1$	$1$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{51}{58}\right)$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{45}{58}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{25}{29}\right)$
$\chi_{2301}(2248,\cdot)$	$-1$	$1$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{45}{58}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{5}{29}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\(\chi_{2301}(103,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{17}{58}\right)\)	\(e\left(\frac{51}{58}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{49}{58}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{18}{29}\right)\)
\(\chi_{2301}(142,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{57}{58}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{16}{29}\right)\)
\(\chi_{2301}(220,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{57}{58}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{22}{29}\right)\)
\(\chi_{2301}(259,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{3}{58}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{10}{29}\right)\)
\(\chi_{2301}(337,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{35}{58}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{17}{29}\right)\)
\(\chi_{2301}(415,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{35}{58}\right)\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{20}{29}\right)\)
\(\chi_{2301}(571,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{17}{58}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{6}{29}\right)\)
\(\chi_{2301}(688,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{57}{58}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{15}{29}\right)\)
\(\chi_{2301}(805,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{35}{58}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{45}{58}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{26}{29}\right)\)
\(\chi_{2301}(844,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{49}{58}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{19}{29}\right)\)
\(\chi_{2301}(922,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{27}{29}\right)\)
\(\chi_{2301}(1000,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{39}{58}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{51}{58}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{14}{29}\right)\)
\(\chi_{2301}(1117,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{11}{29}\right)\)
\(\chi_{2301}(1234,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{4}{29}\right)\)
\(\chi_{2301}(1273,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{8}{29}\right)\)
\(\chi_{2301}(1312,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{17}{58}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{3}{29}\right)\)
\(\chi_{2301}(1390,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{45}{58}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{3}{58}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{21}{29}\right)\)
\(\chi_{2301}(1429,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{1}{29}\right)\)
\(\chi_{2301}(1468,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{39}{58}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{12}{29}\right)\)
\(\chi_{2301}(1507,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{3}{58}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{35}{58}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{13}{29}\right)\)
\(\chi_{2301}(1624,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{3}{58}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{23}{29}\right)\)
\(\chi_{2301}(1663,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{7}{29}\right)\)
\(\chi_{2301}(1702,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{49}{58}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{28}{29}\right)\)
\(\chi_{2301}(1741,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{51}{58}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{39}{58}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{9}{29}\right)\)
\(\chi_{2301}(1780,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{39}{58}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{49}{58}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{17}{58}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{24}{29}\right)\)
\(\chi_{2301}(2014,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{57}{58}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{2}{29}\right)\)
\(\chi_{2301}(2053,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{51}{58}\right)\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{45}{58}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{25}{29}\right)\)
\(\chi_{2301}(2248,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{45}{58}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{5}{29}\right)\)

Introduction

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Properties

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Basic properties

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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	2301.bb
Modulus	$2301$
Conductor	$767$
Order	$58$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(2301\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(767\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(58\)	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:	no, induced from 767.n	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);