LMFDB - Dirichlet character orbit 5625.bo

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5625, base_ring=CyclotomicField(750)) M = H._module chi = DirichletCharacter(H, M([500,6])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(16, 5625)) 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("5625.16"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$5625$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$5625$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$375$	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:	$\Q(\zeta_{375})$	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 375 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 200 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{5625}(16,\cdot)$	$1$	$1$	$e\left(\frac{253}{375}\right)$	$e\left(\frac{131}{375}\right)$	$e\left(\frac{41}{75}\right)$	$e\left(\frac{3}{125}\right)$	$e\left(\frac{178}{375}\right)$	$e\left(\frac{167}{375}\right)$	$e\left(\frac{83}{375}\right)$	$e\left(\frac{262}{375}\right)$	$e\left(\frac{48}{125}\right)$	$e\left(\frac{43}{125}\right)$
$\chi_{5625}(31,\cdot)$	$1$	$1$	$e\left(\frac{161}{375}\right)$	$e\left(\frac{322}{375}\right)$	$e\left(\frac{67}{75}\right)$	$e\left(\frac{36}{125}\right)$	$e\left(\frac{11}{375}\right)$	$e\left(\frac{4}{375}\right)$	$e\left(\frac{121}{375}\right)$	$e\left(\frac{269}{375}\right)$	$e\left(\frac{76}{125}\right)$	$e\left(\frac{16}{125}\right)$
$\chi_{5625}(61,\cdot)$	$1$	$1$	$e\left(\frac{217}{375}\right)$	$e\left(\frac{59}{375}\right)$	$e\left(\frac{74}{75}\right)$	$e\left(\frac{92}{125}\right)$	$e\left(\frac{292}{375}\right)$	$e\left(\frac{38}{375}\right)$	$e\left(\frac{212}{375}\right)$	$e\left(\frac{118}{375}\right)$	$e\left(\frac{97}{125}\right)$	$e\left(\frac{27}{125}\right)$
$\chi_{5625}(106,\cdot)$	$1$	$1$	$e\left(\frac{151}{375}\right)$	$e\left(\frac{302}{375}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{26}{125}\right)$	$e\left(\frac{1}{375}\right)$	$e\left(\frac{239}{375}\right)$	$e\left(\frac{11}{375}\right)$	$e\left(\frac{229}{375}\right)$	$e\left(\frac{41}{125}\right)$	$e\left(\frac{81}{125}\right)$
$\chi_{5625}(121,\cdot)$	$1$	$1$	$e\left(\frac{89}{375}\right)$	$e\left(\frac{178}{375}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{89}{125}\right)$	$e\left(\frac{239}{375}\right)$	$e\left(\frac{121}{375}\right)$	$e\left(\frac{4}{375}\right)$	$e\left(\frac{356}{375}\right)$	$e\left(\frac{49}{125}\right)$	$e\left(\frac{109}{125}\right)$
$\chi_{5625}(166,\cdot)$	$1$	$1$	$e\left(\frac{308}{375}\right)$	$e\left(\frac{241}{375}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{58}{125}\right)$	$e\left(\frac{233}{375}\right)$	$e\left(\frac{187}{375}\right)$	$e\left(\frac{313}{375}\right)$	$e\left(\frac{107}{375}\right)$	$e\left(\frac{53}{125}\right)$	$e\left(\frac{123}{125}\right)$
$\chi_{5625}(196,\cdot)$	$1$	$1$	$e\left(\frac{229}{375}\right)$	$e\left(\frac{83}{375}\right)$	$e\left(\frac{38}{75}\right)$	$e\left(\frac{104}{125}\right)$	$e\left(\frac{4}{375}\right)$	$e\left(\frac{206}{375}\right)$	$e\left(\frac{44}{375}\right)$	$e\left(\frac{166}{375}\right)$	$e\left(\frac{39}{125}\right)$	$e\left(\frac{74}{125}\right)$
$\chi_{5625}(211,\cdot)$	$1$	$1$	$e\left(\frac{47}{375}\right)$	$e\left(\frac{94}{375}\right)$	$e\left(\frac{34}{75}\right)$	$e\left(\frac{47}{125}\right)$	$e\left(\frac{122}{375}\right)$	$e\left(\frac{283}{375}\right)$	$e\left(\frac{217}{375}\right)$	$e\left(\frac{188}{375}\right)$	$e\left(\frac{2}{125}\right)$	$e\left(\frac{7}{125}\right)$
$\chi_{5625}(241,\cdot)$	$1$	$1$	$e\left(\frac{148}{375}\right)$	$e\left(\frac{296}{375}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{23}{125}\right)$	$e\left(\frac{73}{375}\right)$	$e\left(\frac{197}{375}\right)$	$e\left(\frac{53}{375}\right)$	$e\left(\frac{217}{375}\right)$	$e\left(\frac{118}{125}\right)$	$e\left(\frac{38}{125}\right)$
$\chi_{5625}(256,\cdot)$	$1$	$1$	$e\left(\frac{131}{375}\right)$	$e\left(\frac{262}{375}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{6}{125}\right)$	$e\left(\frac{356}{375}\right)$	$e\left(\frac{334}{375}\right)$	$e\left(\frac{166}{375}\right)$	$e\left(\frac{149}{375}\right)$	$e\left(\frac{96}{125}\right)$	$e\left(\frac{86}{125}\right)$
$\chi_{5625}(286,\cdot)$	$1$	$1$	$e\left(\frac{337}{375}\right)$	$e\left(\frac{299}{375}\right)$	$e\left(\frac{14}{75}\right)$	$e\left(\frac{87}{125}\right)$	$e\left(\frac{37}{375}\right)$	$e\left(\frac{218}{375}\right)$	$e\left(\frac{32}{375}\right)$	$e\left(\frac{223}{375}\right)$	$e\left(\frac{17}{125}\right)$	$e\left(\frac{122}{125}\right)$
$\chi_{5625}(331,\cdot)$	$1$	$1$	$e\left(\frac{121}{375}\right)$	$e\left(\frac{242}{375}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{121}{125}\right)$	$e\left(\frac{346}{375}\right)$	$e\left(\frac{194}{375}\right)$	$e\left(\frac{56}{375}\right)$	$e\left(\frac{109}{375}\right)$	$e\left(\frac{61}{125}\right)$	$e\left(\frac{26}{125}\right)$
$\chi_{5625}(346,\cdot)$	$1$	$1$	$e\left(\frac{134}{375}\right)$	$e\left(\frac{268}{375}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{9}{125}\right)$	$e\left(\frac{284}{375}\right)$	$e\left(\frac{1}{375}\right)$	$e\left(\frac{124}{375}\right)$	$e\left(\frac{161}{375}\right)$	$e\left(\frac{19}{125}\right)$	$e\left(\frac{4}{125}\right)$
$\chi_{5625}(391,\cdot)$	$1$	$1$	$e\left(\frac{203}{375}\right)$	$e\left(\frac{31}{375}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{78}{125}\right)$	$e\left(\frac{128}{375}\right)$	$e\left(\frac{217}{375}\right)$	$e\left(\frac{283}{375}\right)$	$e\left(\frac{62}{375}\right)$	$e\left(\frac{123}{125}\right)$	$e\left(\frac{118}{125}\right)$
$\chi_{5625}(421,\cdot)$	$1$	$1$	$e\left(\frac{274}{375}\right)$	$e\left(\frac{173}{375}\right)$	$e\left(\frac{53}{75}\right)$	$e\left(\frac{24}{125}\right)$	$e\left(\frac{49}{375}\right)$	$e\left(\frac{86}{375}\right)$	$e\left(\frac{164}{375}\right)$	$e\left(\frac{346}{375}\right)$	$e\left(\frac{9}{125}\right)$	$e\left(\frac{94}{125}\right)$
$\chi_{5625}(436,\cdot)$	$1$	$1$	$e\left(\frac{167}{375}\right)$	$e\left(\frac{334}{375}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{42}{125}\right)$	$e\left(\frac{242}{375}\right)$	$e\left(\frac{88}{375}\right)$	$e\left(\frac{37}{375}\right)$	$e\left(\frac{293}{375}\right)$	$e\left(\frac{47}{125}\right)$	$e\left(\frac{102}{125}\right)$
$\chi_{5625}(466,\cdot)$	$1$	$1$	$e\left(\frac{43}{375}\right)$	$e\left(\frac{86}{375}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{43}{125}\right)$	$e\left(\frac{343}{375}\right)$	$e\left(\frac{227}{375}\right)$	$e\left(\frac{23}{375}\right)$	$e\left(\frac{172}{375}\right)$	$e\left(\frac{63}{125}\right)$	$e\left(\frac{33}{125}\right)$
$\chi_{5625}(481,\cdot)$	$1$	$1$	$e\left(\frac{101}{375}\right)$	$e\left(\frac{202}{375}\right)$	$e\left(\frac{22}{75}\right)$	$e\left(\frac{101}{125}\right)$	$e\left(\frac{326}{375}\right)$	$e\left(\frac{289}{375}\right)$	$e\left(\frac{211}{375}\right)$	$e\left(\frac{29}{375}\right)$	$e\left(\frac{116}{125}\right)$	$e\left(\frac{31}{125}\right)$
$\chi_{5625}(511,\cdot)$	$1$	$1$	$e\left(\frac{82}{375}\right)$	$e\left(\frac{164}{375}\right)$	$e\left(\frac{29}{75}\right)$	$e\left(\frac{82}{125}\right)$	$e\left(\frac{157}{375}\right)$	$e\left(\frac{23}{375}\right)$	$e\left(\frac{227}{375}\right)$	$e\left(\frac{328}{375}\right)$	$e\left(\frac{62}{125}\right)$	$e\left(\frac{92}{125}\right)$
$\chi_{5625}(556,\cdot)$	$1$	$1$	$e\left(\frac{91}{375}\right)$	$e\left(\frac{182}{375}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{91}{125}\right)$	$e\left(\frac{316}{375}\right)$	$e\left(\frac{149}{375}\right)$	$e\left(\frac{101}{375}\right)$	$e\left(\frac{364}{375}\right)$	$e\left(\frac{81}{125}\right)$	$e\left(\frac{96}{125}\right)$
$\chi_{5625}(571,\cdot)$	$1$	$1$	$e\left(\frac{179}{375}\right)$	$e\left(\frac{358}{375}\right)$	$e\left(\frac{13}{75}\right)$	$e\left(\frac{54}{125}\right)$	$e\left(\frac{329}{375}\right)$	$e\left(\frac{256}{375}\right)$	$e\left(\frac{244}{375}\right)$	$e\left(\frac{341}{375}\right)$	$e\left(\frac{114}{125}\right)$	$e\left(\frac{24}{125}\right)$
$\chi_{5625}(616,\cdot)$	$1$	$1$	$e\left(\frac{98}{375}\right)$	$e\left(\frac{196}{375}\right)$	$e\left(\frac{31}{75}\right)$	$e\left(\frac{98}{125}\right)$	$e\left(\frac{23}{375}\right)$	$e\left(\frac{247}{375}\right)$	$e\left(\frac{253}{375}\right)$	$e\left(\frac{17}{375}\right)$	$e\left(\frac{68}{125}\right)$	$e\left(\frac{113}{125}\right)$
$\chi_{5625}(646,\cdot)$	$1$	$1$	$e\left(\frac{319}{375}\right)$	$e\left(\frac{263}{375}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{69}{125}\right)$	$e\left(\frac{94}{375}\right)$	$e\left(\frac{341}{375}\right)$	$e\left(\frac{284}{375}\right)$	$e\left(\frac{151}{375}\right)$	$e\left(\frac{104}{125}\right)$	$e\left(\frac{114}{125}\right)$
$\chi_{5625}(661,\cdot)$	$1$	$1$	$e\left(\frac{287}{375}\right)$	$e\left(\frac{199}{375}\right)$	$e\left(\frac{64}{75}\right)$	$e\left(\frac{37}{125}\right)$	$e\left(\frac{362}{375}\right)$	$e\left(\frac{268}{375}\right)$	$e\left(\frac{232}{375}\right)$	$e\left(\frac{23}{375}\right)$	$e\left(\frac{92}{125}\right)$	$e\left(\frac{72}{125}\right)$
$\chi_{5625}(691,\cdot)$	$1$	$1$	$e\left(\frac{313}{375}\right)$	$e\left(\frac{251}{375}\right)$	$e\left(\frac{11}{75}\right)$	$e\left(\frac{63}{125}\right)$	$e\left(\frac{238}{375}\right)$	$e\left(\frac{257}{375}\right)$	$e\left(\frac{368}{375}\right)$	$e\left(\frac{127}{375}\right)$	$e\left(\frac{8}{125}\right)$	$e\left(\frac{28}{125}\right)$
$\chi_{5625}(706,\cdot)$	$1$	$1$	$e\left(\frac{71}{375}\right)$	$e\left(\frac{142}{375}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{71}{125}\right)$	$e\left(\frac{296}{375}\right)$	$e\left(\frac{244}{375}\right)$	$e\left(\frac{256}{375}\right)$	$e\left(\frac{284}{375}\right)$	$e\left(\frac{11}{125}\right)$	$e\left(\frac{101}{125}\right)$
$\chi_{5625}(736,\cdot)$	$1$	$1$	$e\left(\frac{202}{375}\right)$	$e\left(\frac{29}{375}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{77}{125}\right)$	$e\left(\frac{277}{375}\right)$	$e\left(\frac{203}{375}\right)$	$e\left(\frac{47}{375}\right)$	$e\left(\frac{58}{375}\right)$	$e\left(\frac{107}{125}\right)$	$e\left(\frac{62}{125}\right)$
$\chi_{5625}(781,\cdot)$	$1$	$1$	$e\left(\frac{61}{375}\right)$	$e\left(\frac{122}{375}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{61}{125}\right)$	$e\left(\frac{286}{375}\right)$	$e\left(\frac{104}{375}\right)$	$e\left(\frac{146}{375}\right)$	$e\left(\frac{244}{375}\right)$	$e\left(\frac{101}{125}\right)$	$e\left(\frac{41}{125}\right)$
$\chi_{5625}(796,\cdot)$	$1$	$1$	$e\left(\frac{224}{375}\right)$	$e\left(\frac{73}{375}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{99}{125}\right)$	$e\left(\frac{374}{375}\right)$	$e\left(\frac{136}{375}\right)$	$e\left(\frac{364}{375}\right)$	$e\left(\frac{146}{375}\right)$	$e\left(\frac{84}{125}\right)$	$e\left(\frac{44}{125}\right)$
$\chi_{5625}(841,\cdot)$	$1$	$1$	$e\left(\frac{368}{375}\right)$	$e\left(\frac{361}{375}\right)$	$e\left(\frac{46}{75}\right)$	$e\left(\frac{118}{125}\right)$	$e\left(\frac{293}{375}\right)$	$e\left(\frac{277}{375}\right)$	$e\left(\frac{223}{375}\right)$	$e\left(\frac{347}{375}\right)$	$e\left(\frac{13}{125}\right)$	$e\left(\frac{108}{125}\right)$
$\chi_{5625}(871,\cdot)$	$1$	$1$	$e\left(\frac{364}{375}\right)$	$e\left(\frac{353}{375}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{114}{125}\right)$	$e\left(\frac{139}{375}\right)$	$e\left(\frac{221}{375}\right)$	$e\left(\frac{29}{375}\right)$	$e\left(\frac{331}{375}\right)$	$e\left(\frac{74}{125}\right)$	$e\left(\frac{9}{125}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{5625}(16,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{253}{375}\right)\)	\(e\left(\frac{131}{375}\right)\)	\(e\left(\frac{41}{75}\right)\)	\(e\left(\frac{3}{125}\right)\)	\(e\left(\frac{178}{375}\right)\)	\(e\left(\frac{167}{375}\right)\)	\(e\left(\frac{83}{375}\right)\)	\(e\left(\frac{262}{375}\right)\)	\(e\left(\frac{48}{125}\right)\)	\(e\left(\frac{43}{125}\right)\)
\(\chi_{5625}(31,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{375}\right)\)	\(e\left(\frac{322}{375}\right)\)	\(e\left(\frac{67}{75}\right)\)	\(e\left(\frac{36}{125}\right)\)	\(e\left(\frac{11}{375}\right)\)	\(e\left(\frac{4}{375}\right)\)	\(e\left(\frac{121}{375}\right)\)	\(e\left(\frac{269}{375}\right)\)	\(e\left(\frac{76}{125}\right)\)	\(e\left(\frac{16}{125}\right)\)
\(\chi_{5625}(61,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{217}{375}\right)\)	\(e\left(\frac{59}{375}\right)\)	\(e\left(\frac{74}{75}\right)\)	\(e\left(\frac{92}{125}\right)\)	\(e\left(\frac{292}{375}\right)\)	\(e\left(\frac{38}{375}\right)\)	\(e\left(\frac{212}{375}\right)\)	\(e\left(\frac{118}{375}\right)\)	\(e\left(\frac{97}{125}\right)\)	\(e\left(\frac{27}{125}\right)\)
\(\chi_{5625}(106,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{375}\right)\)	\(e\left(\frac{302}{375}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{26}{125}\right)\)	\(e\left(\frac{1}{375}\right)\)	\(e\left(\frac{239}{375}\right)\)	\(e\left(\frac{11}{375}\right)\)	\(e\left(\frac{229}{375}\right)\)	\(e\left(\frac{41}{125}\right)\)	\(e\left(\frac{81}{125}\right)\)
\(\chi_{5625}(121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{375}\right)\)	\(e\left(\frac{178}{375}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{89}{125}\right)\)	\(e\left(\frac{239}{375}\right)\)	\(e\left(\frac{121}{375}\right)\)	\(e\left(\frac{4}{375}\right)\)	\(e\left(\frac{356}{375}\right)\)	\(e\left(\frac{49}{125}\right)\)	\(e\left(\frac{109}{125}\right)\)
\(\chi_{5625}(166,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{308}{375}\right)\)	\(e\left(\frac{241}{375}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{58}{125}\right)\)	\(e\left(\frac{233}{375}\right)\)	\(e\left(\frac{187}{375}\right)\)	\(e\left(\frac{313}{375}\right)\)	\(e\left(\frac{107}{375}\right)\)	\(e\left(\frac{53}{125}\right)\)	\(e\left(\frac{123}{125}\right)\)
\(\chi_{5625}(196,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{229}{375}\right)\)	\(e\left(\frac{83}{375}\right)\)	\(e\left(\frac{38}{75}\right)\)	\(e\left(\frac{104}{125}\right)\)	\(e\left(\frac{4}{375}\right)\)	\(e\left(\frac{206}{375}\right)\)	\(e\left(\frac{44}{375}\right)\)	\(e\left(\frac{166}{375}\right)\)	\(e\left(\frac{39}{125}\right)\)	\(e\left(\frac{74}{125}\right)\)
\(\chi_{5625}(211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{375}\right)\)	\(e\left(\frac{94}{375}\right)\)	\(e\left(\frac{34}{75}\right)\)	\(e\left(\frac{47}{125}\right)\)	\(e\left(\frac{122}{375}\right)\)	\(e\left(\frac{283}{375}\right)\)	\(e\left(\frac{217}{375}\right)\)	\(e\left(\frac{188}{375}\right)\)	\(e\left(\frac{2}{125}\right)\)	\(e\left(\frac{7}{125}\right)\)
\(\chi_{5625}(241,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{148}{375}\right)\)	\(e\left(\frac{296}{375}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{23}{125}\right)\)	\(e\left(\frac{73}{375}\right)\)	\(e\left(\frac{197}{375}\right)\)	\(e\left(\frac{53}{375}\right)\)	\(e\left(\frac{217}{375}\right)\)	\(e\left(\frac{118}{125}\right)\)	\(e\left(\frac{38}{125}\right)\)
\(\chi_{5625}(256,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{375}\right)\)	\(e\left(\frac{262}{375}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{6}{125}\right)\)	\(e\left(\frac{356}{375}\right)\)	\(e\left(\frac{334}{375}\right)\)	\(e\left(\frac{166}{375}\right)\)	\(e\left(\frac{149}{375}\right)\)	\(e\left(\frac{96}{125}\right)\)	\(e\left(\frac{86}{125}\right)\)
\(\chi_{5625}(286,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{337}{375}\right)\)	\(e\left(\frac{299}{375}\right)\)	\(e\left(\frac{14}{75}\right)\)	\(e\left(\frac{87}{125}\right)\)	\(e\left(\frac{37}{375}\right)\)	\(e\left(\frac{218}{375}\right)\)	\(e\left(\frac{32}{375}\right)\)	\(e\left(\frac{223}{375}\right)\)	\(e\left(\frac{17}{125}\right)\)	\(e\left(\frac{122}{125}\right)\)
\(\chi_{5625}(331,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{375}\right)\)	\(e\left(\frac{242}{375}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{121}{125}\right)\)	\(e\left(\frac{346}{375}\right)\)	\(e\left(\frac{194}{375}\right)\)	\(e\left(\frac{56}{375}\right)\)	\(e\left(\frac{109}{375}\right)\)	\(e\left(\frac{61}{125}\right)\)	\(e\left(\frac{26}{125}\right)\)
\(\chi_{5625}(346,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{134}{375}\right)\)	\(e\left(\frac{268}{375}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{9}{125}\right)\)	\(e\left(\frac{284}{375}\right)\)	\(e\left(\frac{1}{375}\right)\)	\(e\left(\frac{124}{375}\right)\)	\(e\left(\frac{161}{375}\right)\)	\(e\left(\frac{19}{125}\right)\)	\(e\left(\frac{4}{125}\right)\)
\(\chi_{5625}(391,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{203}{375}\right)\)	\(e\left(\frac{31}{375}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{78}{125}\right)\)	\(e\left(\frac{128}{375}\right)\)	\(e\left(\frac{217}{375}\right)\)	\(e\left(\frac{283}{375}\right)\)	\(e\left(\frac{62}{375}\right)\)	\(e\left(\frac{123}{125}\right)\)	\(e\left(\frac{118}{125}\right)\)
\(\chi_{5625}(421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{274}{375}\right)\)	\(e\left(\frac{173}{375}\right)\)	\(e\left(\frac{53}{75}\right)\)	\(e\left(\frac{24}{125}\right)\)	\(e\left(\frac{49}{375}\right)\)	\(e\left(\frac{86}{375}\right)\)	\(e\left(\frac{164}{375}\right)\)	\(e\left(\frac{346}{375}\right)\)	\(e\left(\frac{9}{125}\right)\)	\(e\left(\frac{94}{125}\right)\)
\(\chi_{5625}(436,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{167}{375}\right)\)	\(e\left(\frac{334}{375}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{42}{125}\right)\)	\(e\left(\frac{242}{375}\right)\)	\(e\left(\frac{88}{375}\right)\)	\(e\left(\frac{37}{375}\right)\)	\(e\left(\frac{293}{375}\right)\)	\(e\left(\frac{47}{125}\right)\)	\(e\left(\frac{102}{125}\right)\)
\(\chi_{5625}(466,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{375}\right)\)	\(e\left(\frac{86}{375}\right)\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{43}{125}\right)\)	\(e\left(\frac{343}{375}\right)\)	\(e\left(\frac{227}{375}\right)\)	\(e\left(\frac{23}{375}\right)\)	\(e\left(\frac{172}{375}\right)\)	\(e\left(\frac{63}{125}\right)\)	\(e\left(\frac{33}{125}\right)\)
\(\chi_{5625}(481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{375}\right)\)	\(e\left(\frac{202}{375}\right)\)	\(e\left(\frac{22}{75}\right)\)	\(e\left(\frac{101}{125}\right)\)	\(e\left(\frac{326}{375}\right)\)	\(e\left(\frac{289}{375}\right)\)	\(e\left(\frac{211}{375}\right)\)	\(e\left(\frac{29}{375}\right)\)	\(e\left(\frac{116}{125}\right)\)	\(e\left(\frac{31}{125}\right)\)
\(\chi_{5625}(511,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{82}{375}\right)\)	\(e\left(\frac{164}{375}\right)\)	\(e\left(\frac{29}{75}\right)\)	\(e\left(\frac{82}{125}\right)\)	\(e\left(\frac{157}{375}\right)\)	\(e\left(\frac{23}{375}\right)\)	\(e\left(\frac{227}{375}\right)\)	\(e\left(\frac{328}{375}\right)\)	\(e\left(\frac{62}{125}\right)\)	\(e\left(\frac{92}{125}\right)\)
\(\chi_{5625}(556,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{375}\right)\)	\(e\left(\frac{182}{375}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{91}{125}\right)\)	\(e\left(\frac{316}{375}\right)\)	\(e\left(\frac{149}{375}\right)\)	\(e\left(\frac{101}{375}\right)\)	\(e\left(\frac{364}{375}\right)\)	\(e\left(\frac{81}{125}\right)\)	\(e\left(\frac{96}{125}\right)\)
\(\chi_{5625}(571,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{375}\right)\)	\(e\left(\frac{358}{375}\right)\)	\(e\left(\frac{13}{75}\right)\)	\(e\left(\frac{54}{125}\right)\)	\(e\left(\frac{329}{375}\right)\)	\(e\left(\frac{256}{375}\right)\)	\(e\left(\frac{244}{375}\right)\)	\(e\left(\frac{341}{375}\right)\)	\(e\left(\frac{114}{125}\right)\)	\(e\left(\frac{24}{125}\right)\)
\(\chi_{5625}(616,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{98}{375}\right)\)	\(e\left(\frac{196}{375}\right)\)	\(e\left(\frac{31}{75}\right)\)	\(e\left(\frac{98}{125}\right)\)	\(e\left(\frac{23}{375}\right)\)	\(e\left(\frac{247}{375}\right)\)	\(e\left(\frac{253}{375}\right)\)	\(e\left(\frac{17}{375}\right)\)	\(e\left(\frac{68}{125}\right)\)	\(e\left(\frac{113}{125}\right)\)
\(\chi_{5625}(646,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{319}{375}\right)\)	\(e\left(\frac{263}{375}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{69}{125}\right)\)	\(e\left(\frac{94}{375}\right)\)	\(e\left(\frac{341}{375}\right)\)	\(e\left(\frac{284}{375}\right)\)	\(e\left(\frac{151}{375}\right)\)	\(e\left(\frac{104}{125}\right)\)	\(e\left(\frac{114}{125}\right)\)
\(\chi_{5625}(661,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{287}{375}\right)\)	\(e\left(\frac{199}{375}\right)\)	\(e\left(\frac{64}{75}\right)\)	\(e\left(\frac{37}{125}\right)\)	\(e\left(\frac{362}{375}\right)\)	\(e\left(\frac{268}{375}\right)\)	\(e\left(\frac{232}{375}\right)\)	\(e\left(\frac{23}{375}\right)\)	\(e\left(\frac{92}{125}\right)\)	\(e\left(\frac{72}{125}\right)\)
\(\chi_{5625}(691,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{313}{375}\right)\)	\(e\left(\frac{251}{375}\right)\)	\(e\left(\frac{11}{75}\right)\)	\(e\left(\frac{63}{125}\right)\)	\(e\left(\frac{238}{375}\right)\)	\(e\left(\frac{257}{375}\right)\)	\(e\left(\frac{368}{375}\right)\)	\(e\left(\frac{127}{375}\right)\)	\(e\left(\frac{8}{125}\right)\)	\(e\left(\frac{28}{125}\right)\)
\(\chi_{5625}(706,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{375}\right)\)	\(e\left(\frac{142}{375}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{71}{125}\right)\)	\(e\left(\frac{296}{375}\right)\)	\(e\left(\frac{244}{375}\right)\)	\(e\left(\frac{256}{375}\right)\)	\(e\left(\frac{284}{375}\right)\)	\(e\left(\frac{11}{125}\right)\)	\(e\left(\frac{101}{125}\right)\)
\(\chi_{5625}(736,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{202}{375}\right)\)	\(e\left(\frac{29}{375}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{77}{125}\right)\)	\(e\left(\frac{277}{375}\right)\)	\(e\left(\frac{203}{375}\right)\)	\(e\left(\frac{47}{375}\right)\)	\(e\left(\frac{58}{375}\right)\)	\(e\left(\frac{107}{125}\right)\)	\(e\left(\frac{62}{125}\right)\)
\(\chi_{5625}(781,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{375}\right)\)	\(e\left(\frac{122}{375}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{61}{125}\right)\)	\(e\left(\frac{286}{375}\right)\)	\(e\left(\frac{104}{375}\right)\)	\(e\left(\frac{146}{375}\right)\)	\(e\left(\frac{244}{375}\right)\)	\(e\left(\frac{101}{125}\right)\)	\(e\left(\frac{41}{125}\right)\)
\(\chi_{5625}(796,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{224}{375}\right)\)	\(e\left(\frac{73}{375}\right)\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{99}{125}\right)\)	\(e\left(\frac{374}{375}\right)\)	\(e\left(\frac{136}{375}\right)\)	\(e\left(\frac{364}{375}\right)\)	\(e\left(\frac{146}{375}\right)\)	\(e\left(\frac{84}{125}\right)\)	\(e\left(\frac{44}{125}\right)\)
\(\chi_{5625}(841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{368}{375}\right)\)	\(e\left(\frac{361}{375}\right)\)	\(e\left(\frac{46}{75}\right)\)	\(e\left(\frac{118}{125}\right)\)	\(e\left(\frac{293}{375}\right)\)	\(e\left(\frac{277}{375}\right)\)	\(e\left(\frac{223}{375}\right)\)	\(e\left(\frac{347}{375}\right)\)	\(e\left(\frac{13}{125}\right)\)	\(e\left(\frac{108}{125}\right)\)
\(\chi_{5625}(871,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{364}{375}\right)\)	\(e\left(\frac{353}{375}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{114}{125}\right)\)	\(e\left(\frac{139}{375}\right)\)	\(e\left(\frac{221}{375}\right)\)	\(e\left(\frac{29}{375}\right)\)	\(e\left(\frac{331}{375}\right)\)	\(e\left(\frac{74}{125}\right)\)	\(e\left(\frac{9}{125}\right)\)

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First 31 of 200 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	5625.bo
Modulus	$5625$
Conductor	$5625$
Order	$375$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(5625\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(5625\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(375\)	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);