LMFDB - Dirichlet character orbit 1625.by

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1625, base_ring=CyclotomicField(100)) M = H._module chi = DirichletCharacter(H, M([3,25])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(8, 1625)) 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("1625.8"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$1625$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$1625$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$100$	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:	$\Q(\zeta_{100})$	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 100 polynomial	comment:Fixed field sage:chi.fixed_field()

First 31 of 40 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$14$
$\chi_{1625}(8,\cdot)$	$1$	$1$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{29}{50}\right)$
$\chi_{1625}(73,\cdot)$	$1$	$1$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{13}{50}\right)$
$\chi_{1625}(122,\cdot)$	$1$	$1$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{1}{50}\right)$
$\chi_{1625}(138,\cdot)$	$1$	$1$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{27}{50}\right)$
$\chi_{1625}(187,\cdot)$	$1$	$1$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{7}{50}\right)$
$\chi_{1625}(203,\cdot)$	$1$	$1$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{21}{50}\right)$
$\chi_{1625}(252,\cdot)$	$1$	$1$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{43}{50}\right)$
$\chi_{1625}(317,\cdot)$	$1$	$1$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{9}{50}\right)$
$\chi_{1625}(333,\cdot)$	$1$	$1$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{49}{50}\right)$
$\chi_{1625}(398,\cdot)$	$1$	$1$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{33}{50}\right)$
$\chi_{1625}(447,\cdot)$	$1$	$1$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{31}{50}\right)$
$\chi_{1625}(463,\cdot)$	$1$	$1$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{47}{50}\right)$
$\chi_{1625}(512,\cdot)$	$1$	$1$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{37}{50}\right)$
$\chi_{1625}(528,\cdot)$	$1$	$1$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{87}{100}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{41}{50}\right)$
$\chi_{1625}(577,\cdot)$	$1$	$1$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{23}{50}\right)$
$\chi_{1625}(642,\cdot)$	$1$	$1$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{39}{50}\right)$
$\chi_{1625}(658,\cdot)$	$1$	$1$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{19}{50}\right)$
$\chi_{1625}(723,\cdot)$	$1$	$1$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{3}{50}\right)$
$\chi_{1625}(772,\cdot)$	$1$	$1$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{11}{50}\right)$
$\chi_{1625}(788,\cdot)$	$1$	$1$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{17}{50}\right)$
$\chi_{1625}(837,\cdot)$	$1$	$1$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{17}{50}\right)$
$\chi_{1625}(853,\cdot)$	$1$	$1$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{93}{100}\right)$	$e\left(\frac{11}{50}\right)$
$\chi_{1625}(902,\cdot)$	$1$	$1$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{3}{50}\right)$
$\chi_{1625}(967,\cdot)$	$1$	$1$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{31}{100}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{39}{100}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{19}{50}\right)$
$\chi_{1625}(983,\cdot)$	$1$	$1$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{39}{50}\right)$
$\chi_{1625}(1048,\cdot)$	$1$	$1$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{23}{50}\right)$
$\chi_{1625}(1097,\cdot)$	$1$	$1$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{41}{50}\right)$
$\chi_{1625}(1113,\cdot)$	$1$	$1$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{13}{100}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{37}{50}\right)$
$\chi_{1625}(1162,\cdot)$	$1$	$1$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{3}{100}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{47}{50}\right)$
$\chi_{1625}(1178,\cdot)$	$1$	$1$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{31}{50}\right)$
$\chi_{1625}(1227,\cdot)$	$1$	$1$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{79}{100}\right)$	$e\left(\frac{33}{50}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(14\)
\(\chi_{1625}(8,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{29}{50}\right)\)
\(\chi_{1625}(73,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{13}{50}\right)\)
\(\chi_{1625}(122,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{1}{50}\right)\)
\(\chi_{1625}(138,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{27}{50}\right)\)
\(\chi_{1625}(187,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{7}{50}\right)\)
\(\chi_{1625}(203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{21}{50}\right)\)
\(\chi_{1625}(252,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{43}{50}\right)\)
\(\chi_{1625}(317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{9}{50}\right)\)
\(\chi_{1625}(333,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{49}{50}\right)\)
\(\chi_{1625}(398,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{33}{50}\right)\)
\(\chi_{1625}(447,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{31}{50}\right)\)
\(\chi_{1625}(463,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{47}{50}\right)\)
\(\chi_{1625}(512,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{37}{50}\right)\)
\(\chi_{1625}(528,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{87}{100}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{41}{50}\right)\)
\(\chi_{1625}(577,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{23}{50}\right)\)
\(\chi_{1625}(642,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{39}{50}\right)\)
\(\chi_{1625}(658,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{19}{50}\right)\)
\(\chi_{1625}(723,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{3}{50}\right)\)
\(\chi_{1625}(772,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{11}{50}\right)\)
\(\chi_{1625}(788,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{17}{50}\right)\)
\(\chi_{1625}(837,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{17}{50}\right)\)
\(\chi_{1625}(853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{93}{100}\right)\)	\(e\left(\frac{11}{50}\right)\)
\(\chi_{1625}(902,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{3}{50}\right)\)
\(\chi_{1625}(967,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{31}{100}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{39}{100}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{19}{50}\right)\)
\(\chi_{1625}(983,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{39}{50}\right)\)
\(\chi_{1625}(1048,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{23}{50}\right)\)
\(\chi_{1625}(1097,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{41}{50}\right)\)
\(\chi_{1625}(1113,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{13}{100}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{37}{50}\right)\)
\(\chi_{1625}(1162,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{3}{100}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{47}{50}\right)\)
\(\chi_{1625}(1178,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{31}{50}\right)\)
\(\chi_{1625}(1227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{79}{100}\right)\)	\(e\left(\frac{33}{50}\right)\)

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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	1625.by
Modulus	$1625$
Conductor	$1625$
Order	$100$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(1625\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1625\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(100\)	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);