LMFDB - Dirichlet character orbit 1725.bp

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1725, base_ring=CyclotomicField(110)) M = H._module chi = DirichletCharacter(H, M([55,33,105])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(14, 1725)) 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("1725.14"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$1725$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$1725$	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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{1725}(14,\cdot)$	$1$	$1$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{79}{110}\right)$
$\chi_{1725}(44,\cdot)$	$1$	$1$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{7}{110}\right)$
$\chi_{1725}(89,\cdot)$	$1$	$1$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{89}{110}\right)$
$\chi_{1725}(134,\cdot)$	$1$	$1$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{91}{110}\right)$
$\chi_{1725}(194,\cdot)$	$1$	$1$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{27}{110}\right)$
$\chi_{1725}(314,\cdot)$	$1$	$1$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{109}{110}\right)$
$\chi_{1725}(329,\cdot)$	$1$	$1$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{83}{110}\right)$
$\chi_{1725}(359,\cdot)$	$1$	$1$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{101}{110}\right)$
$\chi_{1725}(389,\cdot)$	$1$	$1$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{29}{110}\right)$
$\chi_{1725}(419,\cdot)$	$1$	$1$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{97}{110}\right)$
$\chi_{1725}(434,\cdot)$	$1$	$1$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{1}{110}\right)$
$\chi_{1725}(479,\cdot)$	$1$	$1$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{3}{110}\right)$
$\chi_{1725}(494,\cdot)$	$1$	$1$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{7}{110}\right)$	$e\left(\frac{37}{110}\right)$
$\chi_{1725}(539,\cdot)$	$1$	$1$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{49}{110}\right)$
$\chi_{1725}(569,\cdot)$	$1$	$1$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{107}{110}\right)$
$\chi_{1725}(659,\cdot)$	$1$	$1$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{21}{110}\right)$
$\chi_{1725}(704,\cdot)$	$1$	$1$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{13}{110}\right)$
$\chi_{1725}(734,\cdot)$	$1$	$1$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{51}{110}\right)$
$\chi_{1725}(764,\cdot)$	$1$	$1$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{9}{110}\right)$
$\chi_{1725}(779,\cdot)$	$1$	$1$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{43}{110}\right)$	$e\left(\frac{23}{110}\right)$
$\chi_{1725}(839,\cdot)$	$1$	$1$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{59}{110}\right)$
$\chi_{1725}(884,\cdot)$	$1$	$1$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{71}{110}\right)$
$\chi_{1725}(914,\cdot)$	$1$	$1$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{19}{110}\right)$
$\chi_{1725}(1004,\cdot)$	$1$	$1$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{43}{110}\right)$
$\chi_{1725}(1019,\cdot)$	$1$	$1$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{17}{110}\right)$
$\chi_{1725}(1079,\cdot)$	$1$	$1$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{73}{110}\right)$
$\chi_{1725}(1109,\cdot)$	$1$	$1$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{31}{110}\right)$
$\chi_{1725}(1169,\cdot)$	$1$	$1$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{47}{110}\right)$
$\chi_{1725}(1184,\cdot)$	$1$	$1$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{81}{110}\right)$
$\chi_{1725}(1229,\cdot)$	$1$	$1$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{93}{110}\right)$
$\chi_{1725}(1259,\cdot)$	$1$	$1$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{83}{110}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{41}{110}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{1725}(14,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{79}{110}\right)\)
\(\chi_{1725}(44,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{7}{110}\right)\)
\(\chi_{1725}(89,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{89}{110}\right)\)
\(\chi_{1725}(134,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{91}{110}\right)\)
\(\chi_{1725}(194,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{27}{110}\right)\)
\(\chi_{1725}(314,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{109}{110}\right)\)
\(\chi_{1725}(329,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{83}{110}\right)\)
\(\chi_{1725}(359,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{101}{110}\right)\)
\(\chi_{1725}(389,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{29}{110}\right)\)
\(\chi_{1725}(419,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{97}{110}\right)\)
\(\chi_{1725}(434,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{1}{110}\right)\)
\(\chi_{1725}(479,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{3}{110}\right)\)
\(\chi_{1725}(494,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{7}{110}\right)\)	\(e\left(\frac{37}{110}\right)\)
\(\chi_{1725}(539,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{49}{110}\right)\)
\(\chi_{1725}(569,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{107}{110}\right)\)
\(\chi_{1725}(659,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{21}{110}\right)\)
\(\chi_{1725}(704,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{13}{110}\right)\)
\(\chi_{1725}(734,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{51}{110}\right)\)
\(\chi_{1725}(764,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{9}{110}\right)\)
\(\chi_{1725}(779,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{43}{110}\right)\)	\(e\left(\frac{23}{110}\right)\)
\(\chi_{1725}(839,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{59}{110}\right)\)
\(\chi_{1725}(884,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{71}{110}\right)\)
\(\chi_{1725}(914,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{19}{110}\right)\)
\(\chi_{1725}(1004,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{43}{110}\right)\)
\(\chi_{1725}(1019,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{17}{110}\right)\)
\(\chi_{1725}(1079,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{73}{110}\right)\)
\(\chi_{1725}(1109,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{31}{110}\right)\)
\(\chi_{1725}(1169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{47}{110}\right)\)
\(\chi_{1725}(1184,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{81}{110}\right)\)
\(\chi_{1725}(1229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{93}{110}\right)\)
\(\chi_{1725}(1259,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{83}{110}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{41}{110}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

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	1725.bp
Modulus	$1725$
Conductor	$1725$
Order	$110$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(1725\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1725\)	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);