LMFDB - Dirichlet character orbit 2300.bm

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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([55,88,45])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(11, 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("2300.11"); 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:	$2300$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$110$	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 110 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 40 characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$27$	$29$
$\chi_{2300}(11,\cdot)$	$1$	$1$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{53}{55}\right)$
$\chi_{2300}(111,\cdot)$	$1$	$1$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{48}{55}\right)$
$\chi_{2300}(171,\cdot)$	$1$	$1$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{36}{55}\right)$
$\chi_{2300}(191,\cdot)$	$1$	$1$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{52}{55}\right)$
$\chi_{2300}(291,\cdot)$	$1$	$1$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{17}{55}\right)$
$\chi_{2300}(411,\cdot)$	$1$	$1$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{38}{55}\right)$
$\chi_{2300}(431,\cdot)$	$1$	$1$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{29}{55}\right)$
$\chi_{2300}(471,\cdot)$	$1$	$1$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{31}{55}\right)$
$\chi_{2300}(511,\cdot)$	$1$	$1$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{23}{55}\right)$
$\chi_{2300}(571,\cdot)$	$1$	$1$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{26}{55}\right)$
$\chi_{2300}(631,\cdot)$	$1$	$1$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{14}{55}\right)$
$\chi_{2300}(711,\cdot)$	$1$	$1$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{13}{55}\right)$
$\chi_{2300}(871,\cdot)$	$1$	$1$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{16}{55}\right)$
$\chi_{2300}(891,\cdot)$	$1$	$1$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{7}{55}\right)$
$\chi_{2300}(911,\cdot)$	$1$	$1$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{43}{55}\right)$
$\chi_{2300}(931,\cdot)$	$1$	$1$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{9}{55}\right)$
$\chi_{2300}(971,\cdot)$	$1$	$1$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{1}{55}\right)$
$\chi_{2300}(1031,\cdot)$	$1$	$1$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{4}{55}\right)$
$\chi_{2300}(1091,\cdot)$	$1$	$1$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{47}{55}\right)$
$\chi_{2300}(1111,\cdot)$	$1$	$1$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{8}{55}\right)$
$\chi_{2300}(1171,\cdot)$	$1$	$1$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{46}{55}\right)$
$\chi_{2300}(1211,\cdot)$	$1$	$1$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{28}{55}\right)$
$\chi_{2300}(1331,\cdot)$	$1$	$1$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{49}{55}\right)$
$\chi_{2300}(1371,\cdot)$	$1$	$1$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{21}{55}\right)$
$\chi_{2300}(1391,\cdot)$	$1$	$1$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{42}{55}\right)$
$\chi_{2300}(1431,\cdot)$	$1$	$1$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{34}{55}\right)$
$\chi_{2300}(1491,\cdot)$	$1$	$1$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{37}{55}\right)$
$\chi_{2300}(1571,\cdot)$	$1$	$1$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{41}{55}\right)$
$\chi_{2300}(1631,\cdot)$	$1$	$1$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{24}{55}\right)$
$\chi_{2300}(1671,\cdot)$	$1$	$1$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{6}{55}\right)$
$\chi_{2300}(1791,\cdot)$	$1$	$1$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{27}{55}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(27\)	\(29\)
\(\chi_{2300}(11,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{53}{55}\right)\)
\(\chi_{2300}(111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{48}{55}\right)\)
\(\chi_{2300}(171,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{36}{55}\right)\)
\(\chi_{2300}(191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{52}{55}\right)\)
\(\chi_{2300}(291,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{17}{55}\right)\)
\(\chi_{2300}(411,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{38}{55}\right)\)
\(\chi_{2300}(431,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{29}{55}\right)\)
\(\chi_{2300}(471,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{31}{55}\right)\)
\(\chi_{2300}(511,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{23}{55}\right)\)
\(\chi_{2300}(571,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{26}{55}\right)\)
\(\chi_{2300}(631,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{14}{55}\right)\)
\(\chi_{2300}(711,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{13}{55}\right)\)
\(\chi_{2300}(871,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{16}{55}\right)\)
\(\chi_{2300}(891,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{7}{55}\right)\)
\(\chi_{2300}(911,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{43}{55}\right)\)
\(\chi_{2300}(931,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)
\(\chi_{2300}(971,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{1}{55}\right)\)
\(\chi_{2300}(1031,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{4}{55}\right)\)
\(\chi_{2300}(1091,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{47}{55}\right)\)
\(\chi_{2300}(1111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{8}{55}\right)\)
\(\chi_{2300}(1171,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{46}{55}\right)\)
\(\chi_{2300}(1211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{28}{55}\right)\)
\(\chi_{2300}(1331,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{49}{55}\right)\)
\(\chi_{2300}(1371,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{21}{55}\right)\)
\(\chi_{2300}(1391,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{42}{55}\right)\)
\(\chi_{2300}(1431,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{34}{55}\right)\)
\(\chi_{2300}(1491,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{37}{55}\right)\)
\(\chi_{2300}(1571,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{41}{55}\right)\)
\(\chi_{2300}(1631,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{24}{55}\right)\)
\(\chi_{2300}(1671,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{6}{55}\right)\)
\(\chi_{2300}(1791,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{27}{55}\right)\)

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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	2300.bm
Modulus	$2300$
Conductor	$2300$
Order	$110$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(2300\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(2300\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(110\)	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);