LMFDB - Dirichlet character orbit 5415.cs

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5415, base_ring=CyclotomicField(684)) M = H._module chi = DirichletCharacter(H, M([0,513,658])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(13, 5415)) 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("5415.13"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$5415$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$1805$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$684$	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 1805.bi	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:	$\Q(\zeta_{684})$	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 684 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 216 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$22$
$\chi_{5415}(13,\cdot)$	$1$	$1$	$e\left(\frac{487}{684}\right)$	$e\left(\frac{145}{342}\right)$	$e\left(\frac{11}{228}\right)$	$e\left(\frac{31}{228}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{509}{684}\right)$	$e\left(\frac{130}{171}\right)$	$e\left(\frac{145}{171}\right)$	$e\left(\frac{109}{684}\right)$	$e\left(\frac{571}{684}\right)$
$\chi_{5415}(22,\cdot)$	$1$	$1$	$e\left(\frac{377}{684}\right)$	$e\left(\frac{35}{342}\right)$	$e\left(\frac{97}{228}\right)$	$e\left(\frac{149}{228}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{571}{684}\right)$	$e\left(\frac{167}{171}\right)$	$e\left(\frac{35}{171}\right)$	$e\left(\frac{215}{684}\right)$	$e\left(\frac{185}{684}\right)$
$\chi_{5415}(52,\cdot)$	$1$	$1$	$e\left(\frac{149}{684}\right)$	$e\left(\frac{149}{342}\right)$	$e\left(\frac{97}{228}\right)$	$e\left(\frac{149}{228}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{115}{684}\right)$	$e\left(\frac{110}{171}\right)$	$e\left(\frac{149}{171}\right)$	$e\left(\frac{671}{684}\right)$	$e\left(\frac{641}{684}\right)$
$\chi_{5415}(67,\cdot)$	$1$	$1$	$e\left(\frac{25}{684}\right)$	$e\left(\frac{25}{342}\right)$	$e\left(\frac{53}{228}\right)$	$e\left(\frac{25}{228}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{359}{684}\right)$	$e\left(\frac{46}{171}\right)$	$e\left(\frac{25}{171}\right)$	$e\left(\frac{7}{684}\right)$	$e\left(\frac{181}{684}\right)$
$\chi_{5415}(97,\cdot)$	$1$	$1$	$e\left(\frac{317}{684}\right)$	$e\left(\frac{317}{342}\right)$	$e\left(\frac{61}{228}\right)$	$e\left(\frac{89}{228}\right)$	$e\left(\frac{44}{57}\right)$	$e\left(\frac{667}{684}\right)$	$e\left(\frac{125}{171}\right)$	$e\left(\frac{146}{171}\right)$	$e\left(\frac{335}{684}\right)$	$e\left(\frac{161}{684}\right)$
$\chi_{5415}(148,\cdot)$	$1$	$1$	$e\left(\frac{607}{684}\right)$	$e\left(\frac{265}{342}\right)$	$e\left(\frac{83}{228}\right)$	$e\left(\frac{151}{228}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{317}{684}\right)$	$e\left(\frac{43}{171}\right)$	$e\left(\frac{94}{171}\right)$	$e\left(\frac{553}{684}\right)$	$e\left(\frac{619}{684}\right)$
$\chi_{5415}(193,\cdot)$	$1$	$1$	$e\left(\frac{71}{684}\right)$	$e\left(\frac{71}{342}\right)$	$e\left(\frac{187}{228}\right)$	$e\left(\frac{71}{228}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{445}{684}\right)$	$e\left(\frac{158}{171}\right)$	$e\left(\frac{71}{171}\right)$	$e\left(\frac{485}{684}\right)$	$e\left(\frac{131}{684}\right)$
$\chi_{5415}(223,\cdot)$	$1$	$1$	$e\left(\frac{59}{684}\right)$	$e\left(\frac{59}{342}\right)$	$e\left(\frac{43}{228}\right)$	$e\left(\frac{59}{228}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{601}{684}\right)$	$e\left(\frac{47}{171}\right)$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{509}{684}\right)$	$e\left(\frac{263}{684}\right)$
$\chi_{5415}(238,\cdot)$	$1$	$1$	$e\left(\frac{583}{684}\right)$	$e\left(\frac{241}{342}\right)$	$e\left(\frac{23}{228}\right)$	$e\left(\frac{127}{228}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{629}{684}\right)$	$e\left(\frac{163}{171}\right)$	$e\left(\frac{70}{171}\right)$	$e\left(\frac{601}{684}\right)$	$e\left(\frac{199}{684}\right)$
$\chi_{5415}(268,\cdot)$	$1$	$1$	$e\left(\frac{371}{684}\right)$	$e\left(\frac{29}{342}\right)$	$e\left(\frac{139}{228}\right)$	$e\left(\frac{143}{228}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{649}{684}\right)$	$e\left(\frac{26}{171}\right)$	$e\left(\frac{29}{171}\right)$	$e\left(\frac{569}{684}\right)$	$e\left(\frac{251}{684}\right)$
$\chi_{5415}(298,\cdot)$	$1$	$1$	$e\left(\frac{343}{684}\right)$	$e\left(\frac{1}{342}\right)$	$e\left(\frac{107}{228}\right)$	$e\left(\frac{115}{228}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{329}{684}\right)$	$e\left(\frac{166}{171}\right)$	$e\left(\frac{1}{171}\right)$	$e\left(\frac{397}{684}\right)$	$e\left(\frac{103}{684}\right)$
$\chi_{5415}(337,\cdot)$	$1$	$1$	$e\left(\frac{113}{684}\right)$	$e\left(\frac{113}{342}\right)$	$e\left(\frac{121}{228}\right)$	$e\left(\frac{113}{228}\right)$	$e\left(\frac{20}{57}\right)$	$e\left(\frac{583}{684}\right)$	$e\left(\frac{119}{171}\right)$	$e\left(\frac{113}{171}\right)$	$e\left(\frac{59}{684}\right)$	$e\left(\frac{353}{684}\right)$
$\chi_{5415}(352,\cdot)$	$1$	$1$	$e\left(\frac{385}{684}\right)$	$e\left(\frac{43}{342}\right)$	$e\left(\frac{41}{228}\right)$	$e\left(\frac{157}{228}\right)$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{467}{684}\right)$	$e\left(\frac{127}{171}\right)$	$e\left(\frac{43}{171}\right)$	$e\left(\frac{655}{684}\right)$	$e\left(\frac{325}{684}\right)$
$\chi_{5415}(382,\cdot)$	$1$	$1$	$e\left(\frac{65}{684}\right)$	$e\left(\frac{65}{342}\right)$	$e\left(\frac{1}{228}\right)$	$e\left(\frac{65}{228}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{523}{684}\right)$	$e\left(\frac{17}{171}\right)$	$e\left(\frac{65}{171}\right)$	$e\left(\frac{155}{684}\right)$	$e\left(\frac{197}{684}\right)$
$\chi_{5415}(412,\cdot)$	$1$	$1$	$e\left(\frac{217}{684}\right)$	$e\left(\frac{217}{342}\right)$	$e\left(\frac{77}{228}\right)$	$e\left(\frac{217}{228}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{599}{684}\right)$	$e\left(\frac{112}{171}\right)$	$e\left(\frac{46}{171}\right)$	$e\left(\frac{307}{684}\right)$	$e\left(\frac{121}{684}\right)$
$\chi_{5415}(433,\cdot)$	$1$	$1$	$e\left(\frac{391}{684}\right)$	$e\left(\frac{49}{342}\right)$	$e\left(\frac{227}{228}\right)$	$e\left(\frac{163}{228}\right)$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{389}{684}\right)$	$e\left(\frac{97}{171}\right)$	$e\left(\frac{49}{171}\right)$	$e\left(\frac{301}{684}\right)$	$e\left(\frac{259}{684}\right)$
$\chi_{5415}(478,\cdot)$	$1$	$1$	$e\left(\frac{359}{684}\right)$	$e\left(\frac{17}{342}\right)$	$e\left(\frac{223}{228}\right)$	$e\left(\frac{131}{228}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{121}{684}\right)$	$e\left(\frac{86}{171}\right)$	$e\left(\frac{17}{171}\right)$	$e\left(\frac{593}{684}\right)$	$e\left(\frac{383}{684}\right)$
$\chi_{5415}(508,\cdot)$	$1$	$1$	$e\left(\frac{23}{684}\right)$	$e\left(\frac{23}{342}\right)$	$e\left(\frac{67}{228}\right)$	$e\left(\frac{23}{228}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{385}{684}\right)$	$e\left(\frac{56}{171}\right)$	$e\left(\frac{23}{171}\right)$	$e\left(\frac{581}{684}\right)$	$e\left(\frac{659}{684}\right)$
$\chi_{5415}(523,\cdot)$	$1$	$1$	$e\left(\frac{259}{684}\right)$	$e\left(\frac{259}{342}\right)$	$e\left(\frac{11}{228}\right)$	$e\left(\frac{31}{228}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{53}{684}\right)$	$e\left(\frac{73}{171}\right)$	$e\left(\frac{88}{171}\right)$	$e\left(\frac{565}{684}\right)$	$e\left(\frac{343}{684}\right)$
$\chi_{5415}(547,\cdot)$	$1$	$1$	$e\left(\frac{373}{684}\right)$	$e\left(\frac{31}{342}\right)$	$e\left(\frac{125}{228}\right)$	$e\left(\frac{145}{228}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{623}{684}\right)$	$e\left(\frac{16}{171}\right)$	$e\left(\frac{31}{171}\right)$	$e\left(\frac{679}{684}\right)$	$e\left(\frac{457}{684}\right)$
$\chi_{5415}(553,\cdot)$	$1$	$1$	$e\left(\frac{119}{684}\right)$	$e\left(\frac{119}{342}\right)$	$e\left(\frac{79}{228}\right)$	$e\left(\frac{119}{228}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{505}{684}\right)$	$e\left(\frac{89}{171}\right)$	$e\left(\frac{119}{171}\right)$	$e\left(\frac{389}{684}\right)$	$e\left(\frac{287}{684}\right)$
$\chi_{5415}(583,\cdot)$	$1$	$1$	$e\left(\frac{199}{684}\right)$	$e\left(\frac{199}{342}\right)$	$e\left(\frac{203}{228}\right)$	$e\left(\frac{199}{228}\right)$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{149}{684}\right)$	$e\left(\frac{31}{171}\right)$	$e\left(\frac{28}{171}\right)$	$e\left(\frac{1}{684}\right)$	$e\left(\frac{319}{684}\right)$
$\chi_{5415}(592,\cdot)$	$1$	$1$	$e\left(\frac{269}{684}\right)$	$e\left(\frac{269}{342}\right)$	$e\left(\frac{169}{228}\right)$	$e\left(\frac{41}{228}\right)$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{607}{684}\right)$	$e\left(\frac{23}{171}\right)$	$e\left(\frac{98}{171}\right)$	$e\left(\frac{431}{684}\right)$	$e\left(\frac{5}{684}\right)$
$\chi_{5415}(622,\cdot)$	$1$	$1$	$e\left(\frac{77}{684}\right)$	$e\left(\frac{77}{342}\right)$	$e\left(\frac{145}{228}\right)$	$e\left(\frac{77}{228}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{367}{684}\right)$	$e\left(\frac{128}{171}\right)$	$e\left(\frac{77}{171}\right)$	$e\left(\frac{131}{684}\right)$	$e\left(\frac{65}{684}\right)$
$\chi_{5415}(637,\cdot)$	$1$	$1$	$e\left(\frac{61}{684}\right)$	$e\left(\frac{61}{342}\right)$	$e\left(\frac{29}{228}\right)$	$e\left(\frac{61}{228}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{575}{684}\right)$	$e\left(\frac{37}{171}\right)$	$e\left(\frac{61}{171}\right)$	$e\left(\frac{619}{684}\right)$	$e\left(\frac{469}{684}\right)$
$\chi_{5415}(667,\cdot)$	$1$	$1$	$e\left(\frac{497}{684}\right)$	$e\left(\frac{155}{342}\right)$	$e\left(\frac{169}{228}\right)$	$e\left(\frac{41}{228}\right)$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{379}{684}\right)$	$e\left(\frac{80}{171}\right)$	$e\left(\frac{155}{171}\right)$	$e\left(\frac{659}{684}\right)$	$e\left(\frac{233}{684}\right)$
$\chi_{5415}(697,\cdot)$	$1$	$1$	$e\left(\frac{73}{684}\right)$	$e\left(\frac{73}{342}\right)$	$e\left(\frac{173}{228}\right)$	$e\left(\frac{73}{228}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{419}{684}\right)$	$e\left(\frac{148}{171}\right)$	$e\left(\frac{73}{171}\right)$	$e\left(\frac{595}{684}\right)$	$e\left(\frac{337}{684}\right)$
$\chi_{5415}(718,\cdot)$	$1$	$1$	$e\left(\frac{175}{684}\right)$	$e\left(\frac{175}{342}\right)$	$e\left(\frac{143}{228}\right)$	$e\left(\frac{175}{228}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{461}{684}\right)$	$e\left(\frac{151}{171}\right)$	$e\left(\frac{4}{171}\right)$	$e\left(\frac{49}{684}\right)$	$e\left(\frac{583}{684}\right)$
$\chi_{5415}(763,\cdot)$	$1$	$1$	$e\left(\frac{647}{684}\right)$	$e\left(\frac{305}{342}\right)$	$e\left(\frac{31}{228}\right)$	$e\left(\frac{191}{228}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{481}{684}\right)$	$e\left(\frac{14}{171}\right)$	$e\left(\frac{134}{171}\right)$	$e\left(\frac{17}{684}\right)$	$e\left(\frac{635}{684}\right)$
$\chi_{5415}(793,\cdot)$	$1$	$1$	$e\left(\frac{671}{684}\right)$	$e\left(\frac{329}{342}\right)$	$e\left(\frac{91}{228}\right)$	$e\left(\frac{215}{228}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{169}{684}\right)$	$e\left(\frac{65}{171}\right)$	$e\left(\frac{158}{171}\right)$	$e\left(\frac{653}{684}\right)$	$e\left(\frac{371}{684}\right)$
$\chi_{5415}(808,\cdot)$	$1$	$1$	$e\left(\frac{619}{684}\right)$	$e\left(\frac{277}{342}\right)$	$e\left(\frac{227}{228}\right)$	$e\left(\frac{163}{228}\right)$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{161}{684}\right)$	$e\left(\frac{154}{171}\right)$	$e\left(\frac{106}{171}\right)$	$e\left(\frac{529}{684}\right)$	$e\left(\frac{487}{684}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(22\)
\(\chi_{5415}(13,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{487}{684}\right)\)	\(e\left(\frac{145}{342}\right)\)	\(e\left(\frac{11}{228}\right)\)	\(e\left(\frac{31}{228}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{509}{684}\right)\)	\(e\left(\frac{130}{171}\right)\)	\(e\left(\frac{145}{171}\right)\)	\(e\left(\frac{109}{684}\right)\)	\(e\left(\frac{571}{684}\right)\)
\(\chi_{5415}(22,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{377}{684}\right)\)	\(e\left(\frac{35}{342}\right)\)	\(e\left(\frac{97}{228}\right)\)	\(e\left(\frac{149}{228}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{571}{684}\right)\)	\(e\left(\frac{167}{171}\right)\)	\(e\left(\frac{35}{171}\right)\)	\(e\left(\frac{215}{684}\right)\)	\(e\left(\frac{185}{684}\right)\)
\(\chi_{5415}(52,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{684}\right)\)	\(e\left(\frac{149}{342}\right)\)	\(e\left(\frac{97}{228}\right)\)	\(e\left(\frac{149}{228}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{115}{684}\right)\)	\(e\left(\frac{110}{171}\right)\)	\(e\left(\frac{149}{171}\right)\)	\(e\left(\frac{671}{684}\right)\)	\(e\left(\frac{641}{684}\right)\)
\(\chi_{5415}(67,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{684}\right)\)	\(e\left(\frac{25}{342}\right)\)	\(e\left(\frac{53}{228}\right)\)	\(e\left(\frac{25}{228}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{359}{684}\right)\)	\(e\left(\frac{46}{171}\right)\)	\(e\left(\frac{25}{171}\right)\)	\(e\left(\frac{7}{684}\right)\)	\(e\left(\frac{181}{684}\right)\)
\(\chi_{5415}(97,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{317}{684}\right)\)	\(e\left(\frac{317}{342}\right)\)	\(e\left(\frac{61}{228}\right)\)	\(e\left(\frac{89}{228}\right)\)	\(e\left(\frac{44}{57}\right)\)	\(e\left(\frac{667}{684}\right)\)	\(e\left(\frac{125}{171}\right)\)	\(e\left(\frac{146}{171}\right)\)	\(e\left(\frac{335}{684}\right)\)	\(e\left(\frac{161}{684}\right)\)
\(\chi_{5415}(148,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{607}{684}\right)\)	\(e\left(\frac{265}{342}\right)\)	\(e\left(\frac{83}{228}\right)\)	\(e\left(\frac{151}{228}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{317}{684}\right)\)	\(e\left(\frac{43}{171}\right)\)	\(e\left(\frac{94}{171}\right)\)	\(e\left(\frac{553}{684}\right)\)	\(e\left(\frac{619}{684}\right)\)
\(\chi_{5415}(193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{684}\right)\)	\(e\left(\frac{71}{342}\right)\)	\(e\left(\frac{187}{228}\right)\)	\(e\left(\frac{71}{228}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{445}{684}\right)\)	\(e\left(\frac{158}{171}\right)\)	\(e\left(\frac{71}{171}\right)\)	\(e\left(\frac{485}{684}\right)\)	\(e\left(\frac{131}{684}\right)\)
\(\chi_{5415}(223,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{684}\right)\)	\(e\left(\frac{59}{342}\right)\)	\(e\left(\frac{43}{228}\right)\)	\(e\left(\frac{59}{228}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{601}{684}\right)\)	\(e\left(\frac{47}{171}\right)\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{509}{684}\right)\)	\(e\left(\frac{263}{684}\right)\)
\(\chi_{5415}(238,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{583}{684}\right)\)	\(e\left(\frac{241}{342}\right)\)	\(e\left(\frac{23}{228}\right)\)	\(e\left(\frac{127}{228}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{629}{684}\right)\)	\(e\left(\frac{163}{171}\right)\)	\(e\left(\frac{70}{171}\right)\)	\(e\left(\frac{601}{684}\right)\)	\(e\left(\frac{199}{684}\right)\)
\(\chi_{5415}(268,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{371}{684}\right)\)	\(e\left(\frac{29}{342}\right)\)	\(e\left(\frac{139}{228}\right)\)	\(e\left(\frac{143}{228}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{649}{684}\right)\)	\(e\left(\frac{26}{171}\right)\)	\(e\left(\frac{29}{171}\right)\)	\(e\left(\frac{569}{684}\right)\)	\(e\left(\frac{251}{684}\right)\)
\(\chi_{5415}(298,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{343}{684}\right)\)	\(e\left(\frac{1}{342}\right)\)	\(e\left(\frac{107}{228}\right)\)	\(e\left(\frac{115}{228}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{329}{684}\right)\)	\(e\left(\frac{166}{171}\right)\)	\(e\left(\frac{1}{171}\right)\)	\(e\left(\frac{397}{684}\right)\)	\(e\left(\frac{103}{684}\right)\)
\(\chi_{5415}(337,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{684}\right)\)	\(e\left(\frac{113}{342}\right)\)	\(e\left(\frac{121}{228}\right)\)	\(e\left(\frac{113}{228}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{583}{684}\right)\)	\(e\left(\frac{119}{171}\right)\)	\(e\left(\frac{113}{171}\right)\)	\(e\left(\frac{59}{684}\right)\)	\(e\left(\frac{353}{684}\right)\)
\(\chi_{5415}(352,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{385}{684}\right)\)	\(e\left(\frac{43}{342}\right)\)	\(e\left(\frac{41}{228}\right)\)	\(e\left(\frac{157}{228}\right)\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{467}{684}\right)\)	\(e\left(\frac{127}{171}\right)\)	\(e\left(\frac{43}{171}\right)\)	\(e\left(\frac{655}{684}\right)\)	\(e\left(\frac{325}{684}\right)\)
\(\chi_{5415}(382,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{684}\right)\)	\(e\left(\frac{65}{342}\right)\)	\(e\left(\frac{1}{228}\right)\)	\(e\left(\frac{65}{228}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{523}{684}\right)\)	\(e\left(\frac{17}{171}\right)\)	\(e\left(\frac{65}{171}\right)\)	\(e\left(\frac{155}{684}\right)\)	\(e\left(\frac{197}{684}\right)\)
\(\chi_{5415}(412,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{217}{684}\right)\)	\(e\left(\frac{217}{342}\right)\)	\(e\left(\frac{77}{228}\right)\)	\(e\left(\frac{217}{228}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{599}{684}\right)\)	\(e\left(\frac{112}{171}\right)\)	\(e\left(\frac{46}{171}\right)\)	\(e\left(\frac{307}{684}\right)\)	\(e\left(\frac{121}{684}\right)\)
\(\chi_{5415}(433,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{391}{684}\right)\)	\(e\left(\frac{49}{342}\right)\)	\(e\left(\frac{227}{228}\right)\)	\(e\left(\frac{163}{228}\right)\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{389}{684}\right)\)	\(e\left(\frac{97}{171}\right)\)	\(e\left(\frac{49}{171}\right)\)	\(e\left(\frac{301}{684}\right)\)	\(e\left(\frac{259}{684}\right)\)
\(\chi_{5415}(478,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{359}{684}\right)\)	\(e\left(\frac{17}{342}\right)\)	\(e\left(\frac{223}{228}\right)\)	\(e\left(\frac{131}{228}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{121}{684}\right)\)	\(e\left(\frac{86}{171}\right)\)	\(e\left(\frac{17}{171}\right)\)	\(e\left(\frac{593}{684}\right)\)	\(e\left(\frac{383}{684}\right)\)
\(\chi_{5415}(508,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{684}\right)\)	\(e\left(\frac{23}{342}\right)\)	\(e\left(\frac{67}{228}\right)\)	\(e\left(\frac{23}{228}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{385}{684}\right)\)	\(e\left(\frac{56}{171}\right)\)	\(e\left(\frac{23}{171}\right)\)	\(e\left(\frac{581}{684}\right)\)	\(e\left(\frac{659}{684}\right)\)
\(\chi_{5415}(523,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{259}{684}\right)\)	\(e\left(\frac{259}{342}\right)\)	\(e\left(\frac{11}{228}\right)\)	\(e\left(\frac{31}{228}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{53}{684}\right)\)	\(e\left(\frac{73}{171}\right)\)	\(e\left(\frac{88}{171}\right)\)	\(e\left(\frac{565}{684}\right)\)	\(e\left(\frac{343}{684}\right)\)
\(\chi_{5415}(547,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{373}{684}\right)\)	\(e\left(\frac{31}{342}\right)\)	\(e\left(\frac{125}{228}\right)\)	\(e\left(\frac{145}{228}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{623}{684}\right)\)	\(e\left(\frac{16}{171}\right)\)	\(e\left(\frac{31}{171}\right)\)	\(e\left(\frac{679}{684}\right)\)	\(e\left(\frac{457}{684}\right)\)
\(\chi_{5415}(553,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{684}\right)\)	\(e\left(\frac{119}{342}\right)\)	\(e\left(\frac{79}{228}\right)\)	\(e\left(\frac{119}{228}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{505}{684}\right)\)	\(e\left(\frac{89}{171}\right)\)	\(e\left(\frac{119}{171}\right)\)	\(e\left(\frac{389}{684}\right)\)	\(e\left(\frac{287}{684}\right)\)
\(\chi_{5415}(583,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{684}\right)\)	\(e\left(\frac{199}{342}\right)\)	\(e\left(\frac{203}{228}\right)\)	\(e\left(\frac{199}{228}\right)\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{149}{684}\right)\)	\(e\left(\frac{31}{171}\right)\)	\(e\left(\frac{28}{171}\right)\)	\(e\left(\frac{1}{684}\right)\)	\(e\left(\frac{319}{684}\right)\)
\(\chi_{5415}(592,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{269}{684}\right)\)	\(e\left(\frac{269}{342}\right)\)	\(e\left(\frac{169}{228}\right)\)	\(e\left(\frac{41}{228}\right)\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{607}{684}\right)\)	\(e\left(\frac{23}{171}\right)\)	\(e\left(\frac{98}{171}\right)\)	\(e\left(\frac{431}{684}\right)\)	\(e\left(\frac{5}{684}\right)\)
\(\chi_{5415}(622,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{684}\right)\)	\(e\left(\frac{77}{342}\right)\)	\(e\left(\frac{145}{228}\right)\)	\(e\left(\frac{77}{228}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{367}{684}\right)\)	\(e\left(\frac{128}{171}\right)\)	\(e\left(\frac{77}{171}\right)\)	\(e\left(\frac{131}{684}\right)\)	\(e\left(\frac{65}{684}\right)\)
\(\chi_{5415}(637,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{684}\right)\)	\(e\left(\frac{61}{342}\right)\)	\(e\left(\frac{29}{228}\right)\)	\(e\left(\frac{61}{228}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{575}{684}\right)\)	\(e\left(\frac{37}{171}\right)\)	\(e\left(\frac{61}{171}\right)\)	\(e\left(\frac{619}{684}\right)\)	\(e\left(\frac{469}{684}\right)\)
\(\chi_{5415}(667,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{497}{684}\right)\)	\(e\left(\frac{155}{342}\right)\)	\(e\left(\frac{169}{228}\right)\)	\(e\left(\frac{41}{228}\right)\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{379}{684}\right)\)	\(e\left(\frac{80}{171}\right)\)	\(e\left(\frac{155}{171}\right)\)	\(e\left(\frac{659}{684}\right)\)	\(e\left(\frac{233}{684}\right)\)
\(\chi_{5415}(697,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{684}\right)\)	\(e\left(\frac{73}{342}\right)\)	\(e\left(\frac{173}{228}\right)\)	\(e\left(\frac{73}{228}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{419}{684}\right)\)	\(e\left(\frac{148}{171}\right)\)	\(e\left(\frac{73}{171}\right)\)	\(e\left(\frac{595}{684}\right)\)	\(e\left(\frac{337}{684}\right)\)
\(\chi_{5415}(718,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{175}{684}\right)\)	\(e\left(\frac{175}{342}\right)\)	\(e\left(\frac{143}{228}\right)\)	\(e\left(\frac{175}{228}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{461}{684}\right)\)	\(e\left(\frac{151}{171}\right)\)	\(e\left(\frac{4}{171}\right)\)	\(e\left(\frac{49}{684}\right)\)	\(e\left(\frac{583}{684}\right)\)
\(\chi_{5415}(763,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{647}{684}\right)\)	\(e\left(\frac{305}{342}\right)\)	\(e\left(\frac{31}{228}\right)\)	\(e\left(\frac{191}{228}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{481}{684}\right)\)	\(e\left(\frac{14}{171}\right)\)	\(e\left(\frac{134}{171}\right)\)	\(e\left(\frac{17}{684}\right)\)	\(e\left(\frac{635}{684}\right)\)
\(\chi_{5415}(793,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{671}{684}\right)\)	\(e\left(\frac{329}{342}\right)\)	\(e\left(\frac{91}{228}\right)\)	\(e\left(\frac{215}{228}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{169}{684}\right)\)	\(e\left(\frac{65}{171}\right)\)	\(e\left(\frac{158}{171}\right)\)	\(e\left(\frac{653}{684}\right)\)	\(e\left(\frac{371}{684}\right)\)
\(\chi_{5415}(808,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{619}{684}\right)\)	\(e\left(\frac{277}{342}\right)\)	\(e\left(\frac{227}{228}\right)\)	\(e\left(\frac{163}{228}\right)\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{161}{684}\right)\)	\(e\left(\frac{154}{171}\right)\)	\(e\left(\frac{106}{171}\right)\)	\(e\left(\frac{529}{684}\right)\)	\(e\left(\frac{487}{684}\right)\)

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First 31 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	5415.cs
Modulus	$5415$
Conductor	$1805$
Order	$684$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(5415\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1805\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(684\)	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 1805.bi	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);