LMFDB - Dirichlet character orbit 18225.ci

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(18225, base_ring=CyclotomicField(810)) M = H._module chi = DirichletCharacter(H, M([475,729])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(44,18225)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$18225$
Conductor:	$6075$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$810$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 6075.ce	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{405})$
Fixed field:	Number field defined by a degree 810 polynomial (not computed)

First 19 of 216 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{18225}(44,\cdot)$	$-1$	$1$	$e\left(\frac{197}{405}\right)$	$e\left(\frac{394}{405}\right)$	$e\left(\frac{89}{162}\right)$	$e\left(\frac{62}{135}\right)$	$e\left(\frac{289}{810}\right)$	$e\left(\frac{641}{810}\right)$	$e\left(\frac{29}{810}\right)$	$e\left(\frac{383}{405}\right)$	$e\left(\frac{7}{135}\right)$	$e\left(\frac{92}{135}\right)$
$\chi_{18225}(89,\cdot)$	$-1$	$1$	$e\left(\frac{349}{405}\right)$	$e\left(\frac{293}{405}\right)$	$e\left(\frac{133}{162}\right)$	$e\left(\frac{79}{135}\right)$	$e\left(\frac{623}{810}\right)$	$e\left(\frac{157}{810}\right)$	$e\left(\frac{553}{810}\right)$	$e\left(\frac{181}{405}\right)$	$e\left(\frac{59}{135}\right)$	$e\left(\frac{4}{135}\right)$
$\chi_{18225}(179,\cdot)$	$-1$	$1$	$e\left(\frac{113}{405}\right)$	$e\left(\frac{226}{405}\right)$	$e\left(\frac{5}{162}\right)$	$e\left(\frac{113}{135}\right)$	$e\left(\frac{211}{810}\right)$	$e\left(\frac{269}{810}\right)$	$e\left(\frac{251}{810}\right)$	$e\left(\frac{47}{405}\right)$	$e\left(\frac{28}{135}\right)$	$e\left(\frac{98}{135}\right)$
$\chi_{18225}(314,\cdot)$	$-1$	$1$	$e\left(\frac{29}{405}\right)$	$e\left(\frac{58}{405}\right)$	$e\left(\frac{83}{162}\right)$	$e\left(\frac{29}{135}\right)$	$e\left(\frac{133}{810}\right)$	$e\left(\frac{707}{810}\right)$	$e\left(\frac{473}{810}\right)$	$e\left(\frac{116}{405}\right)$	$e\left(\frac{49}{135}\right)$	$e\left(\frac{104}{135}\right)$
$\chi_{18225}(359,\cdot)$	$-1$	$1$	$e\left(\frac{316}{405}\right)$	$e\left(\frac{227}{405}\right)$	$e\left(\frac{19}{162}\right)$	$e\left(\frac{46}{135}\right)$	$e\left(\frac{737}{810}\right)$	$e\left(\frac{763}{810}\right)$	$e\left(\frac{727}{810}\right)$	$e\left(\frac{49}{405}\right)$	$e\left(\frac{101}{135}\right)$	$e\left(\frac{16}{135}\right)$
$\chi_{18225}(494,\cdot)$	$-1$	$1$	$e\left(\frac{97}{405}\right)$	$e\left(\frac{194}{405}\right)$	$e\left(\frac{43}{162}\right)$	$e\left(\frac{97}{135}\right)$	$e\left(\frac{389}{810}\right)$	$e\left(\frac{661}{810}\right)$	$e\left(\frac{409}{810}\right)$	$e\left(\frac{388}{405}\right)$	$e\left(\frac{122}{135}\right)$	$e\left(\frac{22}{135}\right)$
$\chi_{18225}(584,\cdot)$	$-1$	$1$	$e\left(\frac{266}{405}\right)$	$e\left(\frac{127}{405}\right)$	$e\left(\frac{77}{162}\right)$	$e\left(\frac{131}{135}\right)$	$e\left(\frac{787}{810}\right)$	$e\left(\frac{773}{810}\right)$	$e\left(\frac{107}{810}\right)$	$e\left(\frac{254}{405}\right)$	$e\left(\frac{91}{135}\right)$	$e\left(\frac{116}{135}\right)$
$\chi_{18225}(629,\cdot)$	$-1$	$1$	$e\left(\frac{283}{405}\right)$	$e\left(\frac{161}{405}\right)$	$e\left(\frac{67}{162}\right)$	$e\left(\frac{13}{135}\right)$	$e\left(\frac{41}{810}\right)$	$e\left(\frac{559}{810}\right)$	$e\left(\frac{91}{810}\right)$	$e\left(\frac{322}{405}\right)$	$e\left(\frac{8}{135}\right)$	$e\left(\frac{28}{135}\right)$
$\chi_{18225}(719,\cdot)$	$-1$	$1$	$e\left(\frac{182}{405}\right)$	$e\left(\frac{364}{405}\right)$	$e\left(\frac{155}{162}\right)$	$e\left(\frac{47}{135}\right)$	$e\left(\frac{709}{810}\right)$	$e\left(\frac{401}{810}\right)$	$e\left(\frac{329}{810}\right)$	$e\left(\frac{323}{405}\right)$	$e\left(\frac{112}{135}\right)$	$e\left(\frac{122}{135}\right)$
$\chi_{18225}(764,\cdot)$	$-1$	$1$	$e\left(\frac{64}{405}\right)$	$e\left(\frac{128}{405}\right)$	$e\left(\frac{91}{162}\right)$	$e\left(\frac{64}{135}\right)$	$e\left(\frac{503}{810}\right)$	$e\left(\frac{457}{810}\right)$	$e\left(\frac{583}{810}\right)$	$e\left(\frac{256}{405}\right)$	$e\left(\frac{29}{135}\right)$	$e\left(\frac{34}{135}\right)$
$\chi_{18225}(854,\cdot)$	$-1$	$1$	$e\left(\frac{98}{405}\right)$	$e\left(\frac{196}{405}\right)$	$e\left(\frac{71}{162}\right)$	$e\left(\frac{98}{135}\right)$	$e\left(\frac{631}{810}\right)$	$e\left(\frac{29}{810}\right)$	$e\left(\frac{551}{810}\right)$	$e\left(\frac{392}{405}\right)$	$e\left(\frac{133}{135}\right)$	$e\left(\frac{128}{135}\right)$
$\chi_{18225}(989,\cdot)$	$-1$	$1$	$e\left(\frac{14}{405}\right)$	$e\left(\frac{28}{405}\right)$	$e\left(\frac{149}{162}\right)$	$e\left(\frac{14}{135}\right)$	$e\left(\frac{553}{810}\right)$	$e\left(\frac{467}{810}\right)$	$e\left(\frac{773}{810}\right)$	$e\left(\frac{56}{405}\right)$	$e\left(\frac{19}{135}\right)$	$e\left(\frac{134}{135}\right)$
$\chi_{18225}(1034,\cdot)$	$-1$	$1$	$e\left(\frac{31}{405}\right)$	$e\left(\frac{62}{405}\right)$	$e\left(\frac{139}{162}\right)$	$e\left(\frac{31}{135}\right)$	$e\left(\frac{617}{810}\right)$	$e\left(\frac{253}{810}\right)$	$e\left(\frac{757}{810}\right)$	$e\left(\frac{124}{405}\right)$	$e\left(\frac{71}{135}\right)$	$e\left(\frac{46}{135}\right)$
$\chi_{18225}(1169,\cdot)$	$-1$	$1$	$e\left(\frac{217}{405}\right)$	$e\left(\frac{29}{405}\right)$	$e\left(\frac{1}{162}\right)$	$e\left(\frac{82}{135}\right)$	$e\left(\frac{269}{810}\right)$	$e\left(\frac{151}{810}\right)$	$e\left(\frac{439}{810}\right)$	$e\left(\frac{58}{405}\right)$	$e\left(\frac{92}{135}\right)$	$e\left(\frac{52}{135}\right)$
$\chi_{18225}(1259,\cdot)$	$-1$	$1$	$e\left(\frac{251}{405}\right)$	$e\left(\frac{97}{405}\right)$	$e\left(\frac{143}{162}\right)$	$e\left(\frac{116}{135}\right)$	$e\left(\frac{397}{810}\right)$	$e\left(\frac{533}{810}\right)$	$e\left(\frac{407}{810}\right)$	$e\left(\frac{194}{405}\right)$	$e\left(\frac{61}{135}\right)$	$e\left(\frac{11}{135}\right)$
$\chi_{18225}(1304,\cdot)$	$-1$	$1$	$e\left(\frac{403}{405}\right)$	$e\left(\frac{401}{405}\right)$	$e\left(\frac{25}{162}\right)$	$e\left(\frac{133}{135}\right)$	$e\left(\frac{731}{810}\right)$	$e\left(\frac{49}{810}\right)$	$e\left(\frac{121}{810}\right)$	$e\left(\frac{397}{405}\right)$	$e\left(\frac{113}{135}\right)$	$e\left(\frac{58}{135}\right)$
$\chi_{18225}(1394,\cdot)$	$-1$	$1$	$e\left(\frac{167}{405}\right)$	$e\left(\frac{334}{405}\right)$	$e\left(\frac{59}{162}\right)$	$e\left(\frac{32}{135}\right)$	$e\left(\frac{319}{810}\right)$	$e\left(\frac{161}{810}\right)$	$e\left(\frac{629}{810}\right)$	$e\left(\frac{263}{405}\right)$	$e\left(\frac{82}{135}\right)$	$e\left(\frac{17}{135}\right)$
$\chi_{18225}(1439,\cdot)$	$-1$	$1$	$e\left(\frac{184}{405}\right)$	$e\left(\frac{368}{405}\right)$	$e\left(\frac{49}{162}\right)$	$e\left(\frac{49}{135}\right)$	$e\left(\frac{383}{810}\right)$	$e\left(\frac{757}{810}\right)$	$e\left(\frac{613}{810}\right)$	$e\left(\frac{331}{405}\right)$	$e\left(\frac{134}{135}\right)$	$e\left(\frac{64}{135}\right)$
$\chi_{18225}(1529,\cdot)$	$-1$	$1$	$e\left(\frac{83}{405}\right)$	$e\left(\frac{166}{405}\right)$	$e\left(\frac{137}{162}\right)$	$e\left(\frac{83}{135}\right)$	$e\left(\frac{241}{810}\right)$	$e\left(\frac{599}{810}\right)$	$e\left(\frac{41}{810}\right)$	$e\left(\frac{332}{405}\right)$	$e\left(\frac{103}{135}\right)$	$e\left(\frac{23}{135}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{18225}(44,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{197}{405}\right)\)	\(e\left(\frac{394}{405}\right)\)	\(e\left(\frac{89}{162}\right)\)	\(e\left(\frac{62}{135}\right)\)	\(e\left(\frac{289}{810}\right)\)	\(e\left(\frac{641}{810}\right)\)	\(e\left(\frac{29}{810}\right)\)	\(e\left(\frac{383}{405}\right)\)	\(e\left(\frac{7}{135}\right)\)	\(e\left(\frac{92}{135}\right)\)
\(\chi_{18225}(89,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{349}{405}\right)\)	\(e\left(\frac{293}{405}\right)\)	\(e\left(\frac{133}{162}\right)\)	\(e\left(\frac{79}{135}\right)\)	\(e\left(\frac{623}{810}\right)\)	\(e\left(\frac{157}{810}\right)\)	\(e\left(\frac{553}{810}\right)\)	\(e\left(\frac{181}{405}\right)\)	\(e\left(\frac{59}{135}\right)\)	\(e\left(\frac{4}{135}\right)\)
\(\chi_{18225}(179,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{405}\right)\)	\(e\left(\frac{226}{405}\right)\)	\(e\left(\frac{5}{162}\right)\)	\(e\left(\frac{113}{135}\right)\)	\(e\left(\frac{211}{810}\right)\)	\(e\left(\frac{269}{810}\right)\)	\(e\left(\frac{251}{810}\right)\)	\(e\left(\frac{47}{405}\right)\)	\(e\left(\frac{28}{135}\right)\)	\(e\left(\frac{98}{135}\right)\)
\(\chi_{18225}(314,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{405}\right)\)	\(e\left(\frac{58}{405}\right)\)	\(e\left(\frac{83}{162}\right)\)	\(e\left(\frac{29}{135}\right)\)	\(e\left(\frac{133}{810}\right)\)	\(e\left(\frac{707}{810}\right)\)	\(e\left(\frac{473}{810}\right)\)	\(e\left(\frac{116}{405}\right)\)	\(e\left(\frac{49}{135}\right)\)	\(e\left(\frac{104}{135}\right)\)
\(\chi_{18225}(359,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{316}{405}\right)\)	\(e\left(\frac{227}{405}\right)\)	\(e\left(\frac{19}{162}\right)\)	\(e\left(\frac{46}{135}\right)\)	\(e\left(\frac{737}{810}\right)\)	\(e\left(\frac{763}{810}\right)\)	\(e\left(\frac{727}{810}\right)\)	\(e\left(\frac{49}{405}\right)\)	\(e\left(\frac{101}{135}\right)\)	\(e\left(\frac{16}{135}\right)\)
\(\chi_{18225}(494,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{97}{405}\right)\)	\(e\left(\frac{194}{405}\right)\)	\(e\left(\frac{43}{162}\right)\)	\(e\left(\frac{97}{135}\right)\)	\(e\left(\frac{389}{810}\right)\)	\(e\left(\frac{661}{810}\right)\)	\(e\left(\frac{409}{810}\right)\)	\(e\left(\frac{388}{405}\right)\)	\(e\left(\frac{122}{135}\right)\)	\(e\left(\frac{22}{135}\right)\)
\(\chi_{18225}(584,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{266}{405}\right)\)	\(e\left(\frac{127}{405}\right)\)	\(e\left(\frac{77}{162}\right)\)	\(e\left(\frac{131}{135}\right)\)	\(e\left(\frac{787}{810}\right)\)	\(e\left(\frac{773}{810}\right)\)	\(e\left(\frac{107}{810}\right)\)	\(e\left(\frac{254}{405}\right)\)	\(e\left(\frac{91}{135}\right)\)	\(e\left(\frac{116}{135}\right)\)
\(\chi_{18225}(629,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{283}{405}\right)\)	\(e\left(\frac{161}{405}\right)\)	\(e\left(\frac{67}{162}\right)\)	\(e\left(\frac{13}{135}\right)\)	\(e\left(\frac{41}{810}\right)\)	\(e\left(\frac{559}{810}\right)\)	\(e\left(\frac{91}{810}\right)\)	\(e\left(\frac{322}{405}\right)\)	\(e\left(\frac{8}{135}\right)\)	\(e\left(\frac{28}{135}\right)\)
\(\chi_{18225}(719,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{182}{405}\right)\)	\(e\left(\frac{364}{405}\right)\)	\(e\left(\frac{155}{162}\right)\)	\(e\left(\frac{47}{135}\right)\)	\(e\left(\frac{709}{810}\right)\)	\(e\left(\frac{401}{810}\right)\)	\(e\left(\frac{329}{810}\right)\)	\(e\left(\frac{323}{405}\right)\)	\(e\left(\frac{112}{135}\right)\)	\(e\left(\frac{122}{135}\right)\)
\(\chi_{18225}(764,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{64}{405}\right)\)	\(e\left(\frac{128}{405}\right)\)	\(e\left(\frac{91}{162}\right)\)	\(e\left(\frac{64}{135}\right)\)	\(e\left(\frac{503}{810}\right)\)	\(e\left(\frac{457}{810}\right)\)	\(e\left(\frac{583}{810}\right)\)	\(e\left(\frac{256}{405}\right)\)	\(e\left(\frac{29}{135}\right)\)	\(e\left(\frac{34}{135}\right)\)
\(\chi_{18225}(854,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{98}{405}\right)\)	\(e\left(\frac{196}{405}\right)\)	\(e\left(\frac{71}{162}\right)\)	\(e\left(\frac{98}{135}\right)\)	\(e\left(\frac{631}{810}\right)\)	\(e\left(\frac{29}{810}\right)\)	\(e\left(\frac{551}{810}\right)\)	\(e\left(\frac{392}{405}\right)\)	\(e\left(\frac{133}{135}\right)\)	\(e\left(\frac{128}{135}\right)\)
\(\chi_{18225}(989,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{14}{405}\right)\)	\(e\left(\frac{28}{405}\right)\)	\(e\left(\frac{149}{162}\right)\)	\(e\left(\frac{14}{135}\right)\)	\(e\left(\frac{553}{810}\right)\)	\(e\left(\frac{467}{810}\right)\)	\(e\left(\frac{773}{810}\right)\)	\(e\left(\frac{56}{405}\right)\)	\(e\left(\frac{19}{135}\right)\)	\(e\left(\frac{134}{135}\right)\)
\(\chi_{18225}(1034,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{405}\right)\)	\(e\left(\frac{62}{405}\right)\)	\(e\left(\frac{139}{162}\right)\)	\(e\left(\frac{31}{135}\right)\)	\(e\left(\frac{617}{810}\right)\)	\(e\left(\frac{253}{810}\right)\)	\(e\left(\frac{757}{810}\right)\)	\(e\left(\frac{124}{405}\right)\)	\(e\left(\frac{71}{135}\right)\)	\(e\left(\frac{46}{135}\right)\)
\(\chi_{18225}(1169,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{217}{405}\right)\)	\(e\left(\frac{29}{405}\right)\)	\(e\left(\frac{1}{162}\right)\)	\(e\left(\frac{82}{135}\right)\)	\(e\left(\frac{269}{810}\right)\)	\(e\left(\frac{151}{810}\right)\)	\(e\left(\frac{439}{810}\right)\)	\(e\left(\frac{58}{405}\right)\)	\(e\left(\frac{92}{135}\right)\)	\(e\left(\frac{52}{135}\right)\)
\(\chi_{18225}(1259,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{251}{405}\right)\)	\(e\left(\frac{97}{405}\right)\)	\(e\left(\frac{143}{162}\right)\)	\(e\left(\frac{116}{135}\right)\)	\(e\left(\frac{397}{810}\right)\)	\(e\left(\frac{533}{810}\right)\)	\(e\left(\frac{407}{810}\right)\)	\(e\left(\frac{194}{405}\right)\)	\(e\left(\frac{61}{135}\right)\)	\(e\left(\frac{11}{135}\right)\)
\(\chi_{18225}(1304,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{403}{405}\right)\)	\(e\left(\frac{401}{405}\right)\)	\(e\left(\frac{25}{162}\right)\)	\(e\left(\frac{133}{135}\right)\)	\(e\left(\frac{731}{810}\right)\)	\(e\left(\frac{49}{810}\right)\)	\(e\left(\frac{121}{810}\right)\)	\(e\left(\frac{397}{405}\right)\)	\(e\left(\frac{113}{135}\right)\)	\(e\left(\frac{58}{135}\right)\)
\(\chi_{18225}(1394,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{167}{405}\right)\)	\(e\left(\frac{334}{405}\right)\)	\(e\left(\frac{59}{162}\right)\)	\(e\left(\frac{32}{135}\right)\)	\(e\left(\frac{319}{810}\right)\)	\(e\left(\frac{161}{810}\right)\)	\(e\left(\frac{629}{810}\right)\)	\(e\left(\frac{263}{405}\right)\)	\(e\left(\frac{82}{135}\right)\)	\(e\left(\frac{17}{135}\right)\)
\(\chi_{18225}(1439,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{184}{405}\right)\)	\(e\left(\frac{368}{405}\right)\)	\(e\left(\frac{49}{162}\right)\)	\(e\left(\frac{49}{135}\right)\)	\(e\left(\frac{383}{810}\right)\)	\(e\left(\frac{757}{810}\right)\)	\(e\left(\frac{613}{810}\right)\)	\(e\left(\frac{331}{405}\right)\)	\(e\left(\frac{134}{135}\right)\)	\(e\left(\frac{64}{135}\right)\)
\(\chi_{18225}(1529,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{405}\right)\)	\(e\left(\frac{166}{405}\right)\)	\(e\left(\frac{137}{162}\right)\)	\(e\left(\frac{83}{135}\right)\)	\(e\left(\frac{241}{810}\right)\)	\(e\left(\frac{599}{810}\right)\)	\(e\left(\frac{41}{810}\right)\)	\(e\left(\frac{332}{405}\right)\)	\(e\left(\frac{103}{135}\right)\)	\(e\left(\frac{23}{135}\right)\)

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Basic properties

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First 19 of 216 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	18225.ci
Modulus	$18225$
Conductor	$6075$
Order	$810$
Real	no
Primitive	no
Minimal	no
Parity	odd

Modulus:	\(18225\)
Conductor:	\(6075\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(810\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 6075.ce	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)