LMFDB - Dirichlet character orbit 8100.de

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8100, base_ring=CyclotomicField(180)) M = H._module chi = DirichletCharacter(H, M([0,140,81])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(37, 8100)) 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("8100.37"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$8100$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$675$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$180$	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 675.bj	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{180})$	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 180 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{8100}(37,\cdot)$	$-1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{1}{45}\right)$
$\chi_{8100}(73,\cdot)$	$-1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{29}{45}\right)$
$\chi_{8100}(253,\cdot)$	$-1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{43}{45}\right)$
$\chi_{8100}(397,\cdot)$	$-1$	$1$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{38}{45}\right)$
$\chi_{8100}(577,\cdot)$	$-1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{34}{45}\right)$
$\chi_{8100}(613,\cdot)$	$-1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{26}{45}\right)$
$\chi_{8100}(937,\cdot)$	$-1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{26}{45}\right)$
$\chi_{8100}(1117,\cdot)$	$-1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{8100}(1153,\cdot)$	$-1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{23}{45}\right)$
$\chi_{8100}(1333,\cdot)$	$-1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{37}{45}\right)$
$\chi_{8100}(1477,\cdot)$	$-1$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{14}{45}\right)$
$\chi_{8100}(1873,\cdot)$	$-1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{34}{45}\right)$
$\chi_{8100}(2017,\cdot)$	$-1$	$1$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{2}{45}\right)$
$\chi_{8100}(2197,\cdot)$	$-1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{43}{45}\right)$
$\chi_{8100}(2233,\cdot)$	$-1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{17}{45}\right)$
$\chi_{8100}(2413,\cdot)$	$-1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{31}{45}\right)$
$\chi_{8100}(2737,\cdot)$	$-1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{31}{45}\right)$
$\chi_{8100}(2773,\cdot)$	$-1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{14}{45}\right)$
$\chi_{8100}(2953,\cdot)$	$-1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{28}{45}\right)$
$\chi_{8100}(3097,\cdot)$	$-1$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{23}{45}\right)$
$\chi_{8100}(3277,\cdot)$	$-1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{19}{45}\right)$
$\chi_{8100}(3313,\cdot)$	$-1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{11}{45}\right)$
$\chi_{8100}(3637,\cdot)$	$-1$	$1$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{11}{45}\right)$
$\chi_{8100}(3817,\cdot)$	$-1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{7}{45}\right)$
$\chi_{8100}(3853,\cdot)$	$-1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{8}{45}\right)$
$\chi_{8100}(4033,\cdot)$	$-1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{8100}(4177,\cdot)$	$-1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{131}{180}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{44}{45}\right)$
$\chi_{8100}(4573,\cdot)$	$-1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{19}{45}\right)$
$\chi_{8100}(4717,\cdot)$	$-1$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{32}{45}\right)$
$\chi_{8100}(4897,\cdot)$	$-1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{28}{45}\right)$
$\chi_{8100}(4933,\cdot)$	$-1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{2}{45}\right)$

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	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{8100}(37,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{1}{45}\right)\)
\(\chi_{8100}(73,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{29}{180}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{29}{45}\right)\)
\(\chi_{8100}(253,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{43}{45}\right)\)
\(\chi_{8100}(397,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{38}{45}\right)\)
\(\chi_{8100}(577,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{34}{45}\right)\)
\(\chi_{8100}(613,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{149}{180}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{26}{45}\right)\)
\(\chi_{8100}(937,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{26}{45}\right)\)
\(\chi_{8100}(1117,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{22}{45}\right)\)
\(\chi_{8100}(1153,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{23}{45}\right)\)
\(\chi_{8100}(1333,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{37}{45}\right)\)
\(\chi_{8100}(1477,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{14}{45}\right)\)
\(\chi_{8100}(1873,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{34}{45}\right)\)
\(\chi_{8100}(2017,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{2}{45}\right)\)
\(\chi_{8100}(2197,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{43}{45}\right)\)
\(\chi_{8100}(2233,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{17}{45}\right)\)
\(\chi_{8100}(2413,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{31}{45}\right)\)
\(\chi_{8100}(2737,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{31}{180}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{31}{45}\right)\)
\(\chi_{8100}(2773,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{149}{180}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{14}{45}\right)\)
\(\chi_{8100}(2953,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{28}{45}\right)\)
\(\chi_{8100}(3097,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{23}{45}\right)\)
\(\chi_{8100}(3277,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{31}{180}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{19}{45}\right)\)
\(\chi_{8100}(3313,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{11}{45}\right)\)
\(\chi_{8100}(3637,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{11}{45}\right)\)
\(\chi_{8100}(3817,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{7}{45}\right)\)
\(\chi_{8100}(3853,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{8}{45}\right)\)
\(\chi_{8100}(4033,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{22}{45}\right)\)
\(\chi_{8100}(4177,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{131}{180}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{44}{45}\right)\)
\(\chi_{8100}(4573,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{19}{45}\right)\)
\(\chi_{8100}(4717,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{167}{180}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{32}{45}\right)\)
\(\chi_{8100}(4897,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{28}{45}\right)\)
\(\chi_{8100}(4933,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{2}{45}\right)\)

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First 31 of 48 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	8100.de
Modulus	$8100$
Conductor	$675$
Order	$180$
Real	no
Primitive	no
Minimal	no
Parity	odd

Modulus:	\(8100\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(675\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(180\)	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 675.bj	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);