LMFDB - Dirichlet character orbit 8550.hi

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8550, base_ring=CyclotomicField(180)) M = H._module chi = DirichletCharacter(H, M([30,153,80])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(47,8550)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8550$
Conductor:	$4275$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$180$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4275.hi	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{180})$
Fixed field:	Number field defined by a degree 180 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$7$	$11$	$13$	$17$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{8550}(47,\cdot)$	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{8550}(137,\cdot)$	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{7}{36}\right)$
$\chi_{8550}(347,\cdot)$	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{11}{36}\right)$
$\chi_{8550}(473,\cdot)$	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{8550}(833,\cdot)$	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{5}{36}\right)$
$\chi_{8550}(1073,\cdot)$	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{8550}(1127,\cdot)$	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{31}{36}\right)$
$\chi_{8550}(1163,\cdot)$	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{8550}(1373,\cdot)$	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{97}{180}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{29}{36}\right)$
$\chi_{8550}(1517,\cdot)$	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{8550}(1847,\cdot)$	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{7}{36}\right)$
$\chi_{8550}(2153,\cdot)$	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{8550}(2183,\cdot)$	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{8550}(2783,\cdot)$	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{8550}(2837,\cdot)$	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{31}{36}\right)$
$\chi_{8550}(2867,\cdot)$	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{35}{36}\right)$
$\chi_{8550}(2873,\cdot)$	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{8550}(3083,\cdot)$	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{29}{36}\right)$
$\chi_{8550}(3227,\cdot)$	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{131}{180}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{8550}(3467,\cdot)$	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{8550}(3767,\cdot)$	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{11}{36}\right)$
$\chi_{8550}(3863,\cdot)$	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{8550}(4253,\cdot)$	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{5}{36}\right)$
$\chi_{8550}(4547,\cdot)$	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{31}{36}\right)$
$\chi_{8550}(4577,\cdot)$	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{35}{36}\right)$
$\chi_{8550}(4583,\cdot)$	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{8550}(4937,\cdot)$	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{103}{180}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{8550}(5177,\cdot)$	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{8550}(5267,\cdot)$	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{7}{36}\right)$
$\chi_{8550}(5477,\cdot)$	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{11}{36}\right)$
$\chi_{8550}(5573,\cdot)$	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{13}{36}\right)$

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	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{8550}(47,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{19}{36}\right)\)
\(\chi_{8550}(137,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{7}{36}\right)\)
\(\chi_{8550}(347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{11}{36}\right)\)
\(\chi_{8550}(473,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{17}{36}\right)\)
\(\chi_{8550}(833,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{5}{36}\right)\)
\(\chi_{8550}(1073,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{8550}(1127,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{31}{180}\right)\)	\(e\left(\frac{167}{180}\right)\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{31}{36}\right)\)
\(\chi_{8550}(1163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{25}{36}\right)\)
\(\chi_{8550}(1373,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{97}{180}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{29}{36}\right)\)
\(\chi_{8550}(1517,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{31}{180}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{23}{36}\right)\)
\(\chi_{8550}(1847,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{119}{180}\right)\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{7}{36}\right)\)
\(\chi_{8550}(2153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{149}{180}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{8550}(2183,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{167}{180}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{17}{36}\right)\)
\(\chi_{8550}(2783,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{8550}(2837,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{31}{36}\right)\)
\(\chi_{8550}(2867,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{35}{36}\right)\)
\(\chi_{8550}(2873,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{25}{36}\right)\)
\(\chi_{8550}(3083,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{29}{36}\right)\)
\(\chi_{8550}(3227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{131}{180}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{29}{180}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{23}{36}\right)\)
\(\chi_{8550}(3467,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{19}{36}\right)\)
\(\chi_{8550}(3767,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{11}{36}\right)\)
\(\chi_{8550}(3863,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{8550}(4253,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{5}{36}\right)\)
\(\chi_{8550}(4547,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{31}{36}\right)\)
\(\chi_{8550}(4577,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{149}{180}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{35}{36}\right)\)
\(\chi_{8550}(4583,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{25}{36}\right)\)
\(\chi_{8550}(4937,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{103}{180}\right)\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{23}{36}\right)\)
\(\chi_{8550}(5177,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{19}{36}\right)\)
\(\chi_{8550}(5267,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{7}{36}\right)\)
\(\chi_{8550}(5477,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{11}{36}\right)\)
\(\chi_{8550}(5573,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{13}{36}\right)\)

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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	8550.hi
Modulus	$8550$
Conductor	$4275$
Order	$180$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(8550\)
Conductor:	\(4275\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(180\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4275.hi	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)