LMFDB - Dirichlet character orbit 17550.lw

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(17550, base_ring=CyclotomicField(180)) M = H._module chi = DirichletCharacter(H, M([110,171,30])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(563, 17550)) 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("17550.563"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$17550$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$8775$	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 8775.lq	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:	$\Q(\zeta_{180})$	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	$-1$	$1$	$7$	$11$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{17550}(563,\cdot)$	$1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{17550}(797,\cdot)$	$1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{31}{36}\right)$
$\chi_{17550}(803,\cdot)$	$1$	$1$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{17550}(1037,\cdot)$	$1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{11}{36}\right)$
$\chi_{17550}(1733,\cdot)$	$1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{17550}(1967,\cdot)$	$1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{97}{180}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{17550}(1973,\cdot)$	$1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{5}{36}\right)$
$\chi_{17550}(2903,\cdot)$	$1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{17550}(3137,\cdot)$	$1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{7}{36}\right)$
$\chi_{17550}(3377,\cdot)$	$1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{17550}(4073,\cdot)$	$1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{17550}(4313,\cdot)$	$1$	$1$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{17550}(4547,\cdot)$	$1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{11}{36}\right)$
$\chi_{17550}(5477,\cdot)$	$1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{17550}(5483,\cdot)$	$1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{5}{36}\right)$
$\chi_{17550}(5717,\cdot)$	$1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{35}{36}\right)$
$\chi_{17550}(6413,\cdot)$	$1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{17550}(6647,\cdot)$	$1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{7}{36}\right)$
$\chi_{17550}(6653,\cdot)$	$1$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{29}{36}\right)$
$\chi_{17550}(6887,\cdot)$	$1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{17550}(7583,\cdot)$	$1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{17550}(7817,\cdot)$	$1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{31}{36}\right)$
$\chi_{17550}(7823,\cdot)$	$1$	$1$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{17550}(8753,\cdot)$	$1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{103}{180}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{17550}(8987,\cdot)$	$1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{17550}(9227,\cdot)$	$1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{35}{36}\right)$
$\chi_{17550}(9923,\cdot)$	$1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{17550}(10163,\cdot)$	$1$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{131}{180}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{29}{36}\right)$
$\chi_{17550}(10397,\cdot)$	$1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{17550}(11327,\cdot)$	$1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{31}{36}\right)$
$\chi_{17550}(11333,\cdot)$	$1$	$1$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{17}{36}\right)$

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	\(-1\)	\(1\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{17550}(563,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{17550}(797,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{31}{36}\right)\)
\(\chi_{17550}(803,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{17}{36}\right)\)
\(\chi_{17550}(1037,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{11}{36}\right)\)
\(\chi_{17550}(1733,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{25}{36}\right)\)
\(\chi_{17550}(1967,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{97}{180}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{19}{36}\right)\)
\(\chi_{17550}(1973,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{5}{36}\right)\)
\(\chi_{17550}(2903,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{17550}(3137,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{7}{36}\right)\)
\(\chi_{17550}(3377,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{23}{36}\right)\)
\(\chi_{17550}(4073,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{17550}(4313,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{17}{36}\right)\)
\(\chi_{17550}(4547,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{11}{36}\right)\)
\(\chi_{17550}(5477,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{19}{36}\right)\)
\(\chi_{17550}(5483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{5}{36}\right)\)
\(\chi_{17550}(5717,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{35}{36}\right)\)
\(\chi_{17550}(6413,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{17550}(6647,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{7}{36}\right)\)
\(\chi_{17550}(6653,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{29}{36}\right)\)
\(\chi_{17550}(6887,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{23}{36}\right)\)
\(\chi_{17550}(7583,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{17550}(7817,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{31}{36}\right)\)
\(\chi_{17550}(7823,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{119}{180}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{17}{36}\right)\)
\(\chi_{17550}(8753,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{103}{180}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{25}{36}\right)\)
\(\chi_{17550}(8987,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{19}{36}\right)\)
\(\chi_{17550}(9227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{29}{180}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{35}{36}\right)\)
\(\chi_{17550}(9923,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{17550}(10163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{131}{180}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{29}{36}\right)\)
\(\chi_{17550}(10397,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{23}{36}\right)\)
\(\chi_{17550}(11327,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{31}{36}\right)\)
\(\chi_{17550}(11333,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{17}{36}\right)\)

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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	17550.lw
Modulus	$17550$
Conductor	$8775$
Order	$180$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(17550\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(8775\)	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 8775.lq	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);