LMFDB - Dirichlet character orbit 2300.bk

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2300, base_ring=CyclotomicField(110)) M = H._module chi = DirichletCharacter(H, M([0,22,60])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(41, 2300)) 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("2300.41"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$2300$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$575$	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:	no, induced from 575.s	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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$27$	$29$
$\chi_{2300}(41,\cdot)$	$1$	$1$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{12}{55}\right)$
$\chi_{2300}(81,\cdot)$	$1$	$1$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{9}{55}\right)$
$\chi_{2300}(121,\cdot)$	$1$	$1$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{51}{55}\right)$
$\chi_{2300}(141,\cdot)$	$1$	$1$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{27}{55}\right)$
$\chi_{2300}(261,\cdot)$	$1$	$1$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{28}{55}\right)$
$\chi_{2300}(361,\cdot)$	$1$	$1$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{8}{55}\right)$
$\chi_{2300}(381,\cdot)$	$1$	$1$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{14}{55}\right)$
$\chi_{2300}(441,\cdot)$	$1$	$1$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{37}{55}\right)$
$\chi_{2300}(541,\cdot)$	$1$	$1$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{42}{55}\right)$
$\chi_{2300}(561,\cdot)$	$1$	$1$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{43}{55}\right)$
$\chi_{2300}(581,\cdot)$	$1$	$1$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{29}{55}\right)$
$\chi_{2300}(721,\cdot)$	$1$	$1$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{6}{55}\right)$
$\chi_{2300}(761,\cdot)$	$1$	$1$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{13}{55}\right)$
$\chi_{2300}(821,\cdot)$	$1$	$1$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{41}{55}\right)$
$\chi_{2300}(841,\cdot)$	$1$	$1$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{47}{55}\right)$
$\chi_{2300}(961,\cdot)$	$1$	$1$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{23}{55}\right)$
$\chi_{2300}(1021,\cdot)$	$1$	$1$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{21}{55}\right)$
$\chi_{2300}(1041,\cdot)$	$1$	$1$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{7}{55}\right)$
$\chi_{2300}(1061,\cdot)$	$1$	$1$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{38}{55}\right)$
$\chi_{2300}(1181,\cdot)$	$1$	$1$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{39}{55}\right)$
$\chi_{2300}(1221,\cdot)$	$1$	$1$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{46}{55}\right)$
$\chi_{2300}(1281,\cdot)$	$1$	$1$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{19}{55}\right)$
$\chi_{2300}(1361,\cdot)$	$1$	$1$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{48}{55}\right)$
$\chi_{2300}(1421,\cdot)$	$1$	$1$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{1}{55}\right)$
$\chi_{2300}(1461,\cdot)$	$1$	$1$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{53}{55}\right)$
$\chi_{2300}(1481,\cdot)$	$1$	$1$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{54}{55}\right)$
$\chi_{2300}(1521,\cdot)$	$1$	$1$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{16}{55}\right)$
$\chi_{2300}(1641,\cdot)$	$1$	$1$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{17}{55}\right)$
$\chi_{2300}(1681,\cdot)$	$1$	$1$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{24}{55}\right)$
$\chi_{2300}(1741,\cdot)$	$1$	$1$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{52}{55}\right)$
$\chi_{2300}(1761,\cdot)$	$1$	$1$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{3}{55}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(27\)	\(29\)
\(\chi_{2300}(41,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)
\(\chi_{2300}(81,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)
\(\chi_{2300}(121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)
\(\chi_{2300}(141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)
\(\chi_{2300}(261,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)
\(\chi_{2300}(361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)
\(\chi_{2300}(381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)
\(\chi_{2300}(441,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)
\(\chi_{2300}(541,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)
\(\chi_{2300}(561,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)
\(\chi_{2300}(581,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)
\(\chi_{2300}(721,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)
\(\chi_{2300}(761,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)
\(\chi_{2300}(821,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)
\(\chi_{2300}(841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)
\(\chi_{2300}(961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)
\(\chi_{2300}(1021,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)
\(\chi_{2300}(1041,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)
\(\chi_{2300}(1061,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)
\(\chi_{2300}(1181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)
\(\chi_{2300}(1221,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)
\(\chi_{2300}(1281,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)
\(\chi_{2300}(1361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)
\(\chi_{2300}(1421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)
\(\chi_{2300}(1461,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)
\(\chi_{2300}(1481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)
\(\chi_{2300}(1521,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)
\(\chi_{2300}(1641,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)
\(\chi_{2300}(1681,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)
\(\chi_{2300}(1741,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)
\(\chi_{2300}(1761,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)

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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	2300.bk
Modulus	$2300$
Conductor	$575$
Order	$55$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(2300\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(575\)	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:	no, induced from 575.s	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);