LMFDB - Dirichlet character orbit 836352.um

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(836352, base_ring=CyclotomicField(1056)) M = H._module chi = DirichletCharacter(H, M([0,825,176,576])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(89, 836352)) 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("836352.89"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$836352$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$139392$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$1056$	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 139392.nk	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{1056})$	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 1056 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 320 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{836352}(89,\cdot)$	$-1$	$1$	$e\left(\frac{1033}{1056}\right)$	$e\left(\frac{157}{528}\right)$	$e\left(\frac{151}{1056}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{85}{352}\right)$	$e\left(\frac{503}{528}\right)$	$e\left(\frac{505}{528}\right)$	$e\left(\frac{563}{1056}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{97}{352}\right)$
$\chi_{836352}(3257,\cdot)$	$-1$	$1$	$e\left(\frac{29}{1056}\right)$	$e\left(\frac{353}{528}\right)$	$e\left(\frac{131}{1056}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{153}{352}\right)$	$e\left(\frac{307}{528}\right)$	$e\left(\frac{29}{528}\right)$	$e\left(\frac{943}{1056}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{245}{352}\right)$
$\chi_{836352}(8009,\cdot)$	$-1$	$1$	$e\left(\frac{107}{1056}\right)$	$e\left(\frac{119}{528}\right)$	$e\left(\frac{629}{1056}\right)$	$e\left(\frac{27}{88}\right)$	$e\left(\frac{79}{352}\right)$	$e\left(\frac{277}{528}\right)$	$e\left(\frac{107}{528}\right)$	$e\left(\frac{457}{1056}\right)$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{115}{352}\right)$
$\chi_{836352}(9593,\cdot)$	$-1$	$1$	$e\left(\frac{133}{1056}\right)$	$e\left(\frac{217}{528}\right)$	$e\left(\frac{91}{1056}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{289}{352}\right)$	$e\left(\frac{443}{528}\right)$	$e\left(\frac{133}{528}\right)$	$e\left(\frac{647}{1056}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{189}{352}\right)$
$\chi_{836352}(12761,\cdot)$	$-1$	$1$	$e\left(\frac{185}{1056}\right)$	$e\left(\frac{413}{528}\right)$	$e\left(\frac{71}{1056}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{5}{352}\right)$	$e\left(\frac{247}{528}\right)$	$e\left(\frac{185}{528}\right)$	$e\left(\frac{1027}{1056}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{337}{352}\right)$
$\chi_{836352}(14345,\cdot)$	$-1$	$1$	$e\left(\frac{211}{1056}\right)$	$e\left(\frac{511}{528}\right)$	$e\left(\frac{589}{1056}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{215}{352}\right)$	$e\left(\frac{413}{528}\right)$	$e\left(\frac{211}{528}\right)$	$e\left(\frac{161}{1056}\right)$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{59}{352}\right)$
$\chi_{836352}(17513,\cdot)$	$-1$	$1$	$e\left(\frac{263}{1056}\right)$	$e\left(\frac{179}{528}\right)$	$e\left(\frac{569}{1056}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{283}{352}\right)$	$e\left(\frac{217}{528}\right)$	$e\left(\frac{263}{528}\right)$	$e\left(\frac{541}{1056}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{207}{352}\right)$
$\chi_{836352}(19097,\cdot)$	$-1$	$1$	$e\left(\frac{289}{1056}\right)$	$e\left(\frac{277}{528}\right)$	$e\left(\frac{31}{1056}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{141}{352}\right)$	$e\left(\frac{383}{528}\right)$	$e\left(\frac{289}{528}\right)$	$e\left(\frac{731}{1056}\right)$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{281}{352}\right)$
$\chi_{836352}(23849,\cdot)$	$-1$	$1$	$e\left(\frac{367}{1056}\right)$	$e\left(\frac{43}{528}\right)$	$e\left(\frac{529}{1056}\right)$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{67}{352}\right)$	$e\left(\frac{353}{528}\right)$	$e\left(\frac{367}{528}\right)$	$e\left(\frac{245}{1056}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{151}{352}\right)$
$\chi_{836352}(27017,\cdot)$	$-1$	$1$	$e\left(\frac{419}{1056}\right)$	$e\left(\frac{239}{528}\right)$	$e\left(\frac{509}{1056}\right)$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{135}{352}\right)$	$e\left(\frac{157}{528}\right)$	$e\left(\frac{419}{528}\right)$	$e\left(\frac{625}{1056}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{299}{352}\right)$
$\chi_{836352}(28601,\cdot)$	$-1$	$1$	$e\left(\frac{445}{1056}\right)$	$e\left(\frac{337}{528}\right)$	$e\left(\frac{1027}{1056}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{345}{352}\right)$	$e\left(\frac{323}{528}\right)$	$e\left(\frac{445}{528}\right)$	$e\left(\frac{815}{1056}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{21}{352}\right)$
$\chi_{836352}(31769,\cdot)$	$-1$	$1$	$e\left(\frac{497}{1056}\right)$	$e\left(\frac{5}{528}\right)$	$e\left(\frac{1007}{1056}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{61}{352}\right)$	$e\left(\frac{127}{528}\right)$	$e\left(\frac{497}{528}\right)$	$e\left(\frac{139}{1056}\right)$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{169}{352}\right)$
$\chi_{836352}(33353,\cdot)$	$-1$	$1$	$e\left(\frac{523}{1056}\right)$	$e\left(\frac{103}{528}\right)$	$e\left(\frac{469}{1056}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{271}{352}\right)$	$e\left(\frac{293}{528}\right)$	$e\left(\frac{523}{528}\right)$	$e\left(\frac{329}{1056}\right)$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{243}{352}\right)$
$\chi_{836352}(36521,\cdot)$	$-1$	$1$	$e\left(\frac{575}{1056}\right)$	$e\left(\frac{299}{528}\right)$	$e\left(\frac{449}{1056}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{339}{352}\right)$	$e\left(\frac{97}{528}\right)$	$e\left(\frac{47}{528}\right)$	$e\left(\frac{709}{1056}\right)$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{39}{352}\right)$
$\chi_{836352}(38105,\cdot)$	$-1$	$1$	$e\left(\frac{601}{1056}\right)$	$e\left(\frac{397}{528}\right)$	$e\left(\frac{967}{1056}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{197}{352}\right)$	$e\left(\frac{263}{528}\right)$	$e\left(\frac{73}{528}\right)$	$e\left(\frac{899}{1056}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{113}{352}\right)$
$\chi_{836352}(41273,\cdot)$	$-1$	$1$	$e\left(\frac{653}{1056}\right)$	$e\left(\frac{65}{528}\right)$	$e\left(\frac{947}{1056}\right)$	$e\left(\frac{85}{88}\right)$	$e\left(\frac{265}{352}\right)$	$e\left(\frac{67}{528}\right)$	$e\left(\frac{125}{528}\right)$	$e\left(\frac{223}{1056}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{261}{352}\right)$
$\chi_{836352}(42857,\cdot)$	$-1$	$1$	$e\left(\frac{679}{1056}\right)$	$e\left(\frac{163}{528}\right)$	$e\left(\frac{409}{1056}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{123}{352}\right)$	$e\left(\frac{233}{528}\right)$	$e\left(\frac{151}{528}\right)$	$e\left(\frac{413}{1056}\right)$	$e\left(\frac{107}{132}\right)$	$e\left(\frac{335}{352}\right)$
$\chi_{836352}(46025,\cdot)$	$-1$	$1$	$e\left(\frac{731}{1056}\right)$	$e\left(\frac{359}{528}\right)$	$e\left(\frac{389}{1056}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{191}{352}\right)$	$e\left(\frac{37}{528}\right)$	$e\left(\frac{203}{528}\right)$	$e\left(\frac{793}{1056}\right)$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{131}{352}\right)$
$\chi_{836352}(47609,\cdot)$	$-1$	$1$	$e\left(\frac{757}{1056}\right)$	$e\left(\frac{457}{528}\right)$	$e\left(\frac{907}{1056}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{49}{352}\right)$	$e\left(\frac{203}{528}\right)$	$e\left(\frac{229}{528}\right)$	$e\left(\frac{983}{1056}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{205}{352}\right)$
$\chi_{836352}(50777,\cdot)$	$-1$	$1$	$e\left(\frac{809}{1056}\right)$	$e\left(\frac{125}{528}\right)$	$e\left(\frac{887}{1056}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{117}{352}\right)$	$e\left(\frac{7}{528}\right)$	$e\left(\frac{281}{528}\right)$	$e\left(\frac{307}{1056}\right)$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{1}{352}\right)$
$\chi_{836352}(52361,\cdot)$	$-1$	$1$	$e\left(\frac{835}{1056}\right)$	$e\left(\frac{223}{528}\right)$	$e\left(\frac{349}{1056}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{327}{352}\right)$	$e\left(\frac{173}{528}\right)$	$e\left(\frac{307}{528}\right)$	$e\left(\frac{497}{1056}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{75}{352}\right)$
$\chi_{836352}(55529,\cdot)$	$-1$	$1$	$e\left(\frac{887}{1056}\right)$	$e\left(\frac{419}{528}\right)$	$e\left(\frac{329}{1056}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{43}{352}\right)$	$e\left(\frac{505}{528}\right)$	$e\left(\frac{359}{528}\right)$	$e\left(\frac{877}{1056}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{223}{352}\right)$
$\chi_{836352}(60281,\cdot)$	$-1$	$1$	$e\left(\frac{965}{1056}\right)$	$e\left(\frac{185}{528}\right)$	$e\left(\frac{827}{1056}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{321}{352}\right)$	$e\left(\frac{475}{528}\right)$	$e\left(\frac{437}{528}\right)$	$e\left(\frac{391}{1056}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{93}{352}\right)$
$\chi_{836352}(61865,\cdot)$	$-1$	$1$	$e\left(\frac{991}{1056}\right)$	$e\left(\frac{283}{528}\right)$	$e\left(\frac{289}{1056}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{179}{352}\right)$	$e\left(\frac{113}{528}\right)$	$e\left(\frac{463}{528}\right)$	$e\left(\frac{581}{1056}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{167}{352}\right)$
$\chi_{836352}(65033,\cdot)$	$-1$	$1$	$e\left(\frac{1043}{1056}\right)$	$e\left(\frac{479}{528}\right)$	$e\left(\frac{269}{1056}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{247}{352}\right)$	$e\left(\frac{445}{528}\right)$	$e\left(\frac{515}{528}\right)$	$e\left(\frac{961}{1056}\right)$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{315}{352}\right)$
$\chi_{836352}(66617,\cdot)$	$-1$	$1$	$e\left(\frac{13}{1056}\right)$	$e\left(\frac{49}{528}\right)$	$e\left(\frac{787}{1056}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{105}{352}\right)$	$e\left(\frac{83}{528}\right)$	$e\left(\frac{13}{528}\right)$	$e\left(\frac{95}{1056}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{37}{352}\right)$
$\chi_{836352}(69785,\cdot)$	$-1$	$1$	$e\left(\frac{65}{1056}\right)$	$e\left(\frac{245}{528}\right)$	$e\left(\frac{767}{1056}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{173}{352}\right)$	$e\left(\frac{415}{528}\right)$	$e\left(\frac{65}{528}\right)$	$e\left(\frac{475}{1056}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{185}{352}\right)$
$\chi_{836352}(71369,\cdot)$	$-1$	$1$	$e\left(\frac{91}{1056}\right)$	$e\left(\frac{343}{528}\right)$	$e\left(\frac{229}{1056}\right)$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{31}{352}\right)$	$e\left(\frac{53}{528}\right)$	$e\left(\frac{91}{528}\right)$	$e\left(\frac{665}{1056}\right)$	$e\left(\frac{47}{132}\right)$	$e\left(\frac{259}{352}\right)$
$\chi_{836352}(76121,\cdot)$	$-1$	$1$	$e\left(\frac{169}{1056}\right)$	$e\left(\frac{109}{528}\right)$	$e\left(\frac{727}{1056}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{309}{352}\right)$	$e\left(\frac{23}{528}\right)$	$e\left(\frac{169}{528}\right)$	$e\left(\frac{179}{1056}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{129}{352}\right)$
$\chi_{836352}(79289,\cdot)$	$-1$	$1$	$e\left(\frac{221}{1056}\right)$	$e\left(\frac{305}{528}\right)$	$e\left(\frac{707}{1056}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{25}{352}\right)$	$e\left(\frac{355}{528}\right)$	$e\left(\frac{221}{528}\right)$	$e\left(\frac{559}{1056}\right)$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{277}{352}\right)$
$\chi_{836352}(80873,\cdot)$	$-1$	$1$	$e\left(\frac{247}{1056}\right)$	$e\left(\frac{403}{528}\right)$	$e\left(\frac{169}{1056}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{235}{352}\right)$	$e\left(\frac{521}{528}\right)$	$e\left(\frac{247}{528}\right)$	$e\left(\frac{749}{1056}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{351}{352}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{836352}(89,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1033}{1056}\right)\)	\(e\left(\frac{157}{528}\right)\)	\(e\left(\frac{151}{1056}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{85}{352}\right)\)	\(e\left(\frac{503}{528}\right)\)	\(e\left(\frac{505}{528}\right)\)	\(e\left(\frac{563}{1056}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{97}{352}\right)\)
\(\chi_{836352}(3257,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{1056}\right)\)	\(e\left(\frac{353}{528}\right)\)	\(e\left(\frac{131}{1056}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{153}{352}\right)\)	\(e\left(\frac{307}{528}\right)\)	\(e\left(\frac{29}{528}\right)\)	\(e\left(\frac{943}{1056}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{245}{352}\right)\)
\(\chi_{836352}(8009,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{107}{1056}\right)\)	\(e\left(\frac{119}{528}\right)\)	\(e\left(\frac{629}{1056}\right)\)	\(e\left(\frac{27}{88}\right)\)	\(e\left(\frac{79}{352}\right)\)	\(e\left(\frac{277}{528}\right)\)	\(e\left(\frac{107}{528}\right)\)	\(e\left(\frac{457}{1056}\right)\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{115}{352}\right)\)
\(\chi_{836352}(9593,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{133}{1056}\right)\)	\(e\left(\frac{217}{528}\right)\)	\(e\left(\frac{91}{1056}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{289}{352}\right)\)	\(e\left(\frac{443}{528}\right)\)	\(e\left(\frac{133}{528}\right)\)	\(e\left(\frac{647}{1056}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{189}{352}\right)\)
\(\chi_{836352}(12761,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{185}{1056}\right)\)	\(e\left(\frac{413}{528}\right)\)	\(e\left(\frac{71}{1056}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{5}{352}\right)\)	\(e\left(\frac{247}{528}\right)\)	\(e\left(\frac{185}{528}\right)\)	\(e\left(\frac{1027}{1056}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{337}{352}\right)\)
\(\chi_{836352}(14345,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{211}{1056}\right)\)	\(e\left(\frac{511}{528}\right)\)	\(e\left(\frac{589}{1056}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{215}{352}\right)\)	\(e\left(\frac{413}{528}\right)\)	\(e\left(\frac{211}{528}\right)\)	\(e\left(\frac{161}{1056}\right)\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{59}{352}\right)\)
\(\chi_{836352}(17513,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{263}{1056}\right)\)	\(e\left(\frac{179}{528}\right)\)	\(e\left(\frac{569}{1056}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{283}{352}\right)\)	\(e\left(\frac{217}{528}\right)\)	\(e\left(\frac{263}{528}\right)\)	\(e\left(\frac{541}{1056}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{207}{352}\right)\)
\(\chi_{836352}(19097,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{289}{1056}\right)\)	\(e\left(\frac{277}{528}\right)\)	\(e\left(\frac{31}{1056}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{141}{352}\right)\)	\(e\left(\frac{383}{528}\right)\)	\(e\left(\frac{289}{528}\right)\)	\(e\left(\frac{731}{1056}\right)\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{281}{352}\right)\)
\(\chi_{836352}(23849,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{367}{1056}\right)\)	\(e\left(\frac{43}{528}\right)\)	\(e\left(\frac{529}{1056}\right)\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{67}{352}\right)\)	\(e\left(\frac{353}{528}\right)\)	\(e\left(\frac{367}{528}\right)\)	\(e\left(\frac{245}{1056}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{151}{352}\right)\)
\(\chi_{836352}(27017,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{419}{1056}\right)\)	\(e\left(\frac{239}{528}\right)\)	\(e\left(\frac{509}{1056}\right)\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{135}{352}\right)\)	\(e\left(\frac{157}{528}\right)\)	\(e\left(\frac{419}{528}\right)\)	\(e\left(\frac{625}{1056}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{299}{352}\right)\)
\(\chi_{836352}(28601,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{445}{1056}\right)\)	\(e\left(\frac{337}{528}\right)\)	\(e\left(\frac{1027}{1056}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{345}{352}\right)\)	\(e\left(\frac{323}{528}\right)\)	\(e\left(\frac{445}{528}\right)\)	\(e\left(\frac{815}{1056}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{21}{352}\right)\)
\(\chi_{836352}(31769,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{497}{1056}\right)\)	\(e\left(\frac{5}{528}\right)\)	\(e\left(\frac{1007}{1056}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{61}{352}\right)\)	\(e\left(\frac{127}{528}\right)\)	\(e\left(\frac{497}{528}\right)\)	\(e\left(\frac{139}{1056}\right)\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{169}{352}\right)\)
\(\chi_{836352}(33353,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{523}{1056}\right)\)	\(e\left(\frac{103}{528}\right)\)	\(e\left(\frac{469}{1056}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{271}{352}\right)\)	\(e\left(\frac{293}{528}\right)\)	\(e\left(\frac{523}{528}\right)\)	\(e\left(\frac{329}{1056}\right)\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{243}{352}\right)\)
\(\chi_{836352}(36521,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{575}{1056}\right)\)	\(e\left(\frac{299}{528}\right)\)	\(e\left(\frac{449}{1056}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{339}{352}\right)\)	\(e\left(\frac{97}{528}\right)\)	\(e\left(\frac{47}{528}\right)\)	\(e\left(\frac{709}{1056}\right)\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{39}{352}\right)\)
\(\chi_{836352}(38105,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{601}{1056}\right)\)	\(e\left(\frac{397}{528}\right)\)	\(e\left(\frac{967}{1056}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{197}{352}\right)\)	\(e\left(\frac{263}{528}\right)\)	\(e\left(\frac{73}{528}\right)\)	\(e\left(\frac{899}{1056}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{113}{352}\right)\)
\(\chi_{836352}(41273,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{653}{1056}\right)\)	\(e\left(\frac{65}{528}\right)\)	\(e\left(\frac{947}{1056}\right)\)	\(e\left(\frac{85}{88}\right)\)	\(e\left(\frac{265}{352}\right)\)	\(e\left(\frac{67}{528}\right)\)	\(e\left(\frac{125}{528}\right)\)	\(e\left(\frac{223}{1056}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{261}{352}\right)\)
\(\chi_{836352}(42857,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{679}{1056}\right)\)	\(e\left(\frac{163}{528}\right)\)	\(e\left(\frac{409}{1056}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{123}{352}\right)\)	\(e\left(\frac{233}{528}\right)\)	\(e\left(\frac{151}{528}\right)\)	\(e\left(\frac{413}{1056}\right)\)	\(e\left(\frac{107}{132}\right)\)	\(e\left(\frac{335}{352}\right)\)
\(\chi_{836352}(46025,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{731}{1056}\right)\)	\(e\left(\frac{359}{528}\right)\)	\(e\left(\frac{389}{1056}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{191}{352}\right)\)	\(e\left(\frac{37}{528}\right)\)	\(e\left(\frac{203}{528}\right)\)	\(e\left(\frac{793}{1056}\right)\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{131}{352}\right)\)
\(\chi_{836352}(47609,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{757}{1056}\right)\)	\(e\left(\frac{457}{528}\right)\)	\(e\left(\frac{907}{1056}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{49}{352}\right)\)	\(e\left(\frac{203}{528}\right)\)	\(e\left(\frac{229}{528}\right)\)	\(e\left(\frac{983}{1056}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{205}{352}\right)\)
\(\chi_{836352}(50777,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{809}{1056}\right)\)	\(e\left(\frac{125}{528}\right)\)	\(e\left(\frac{887}{1056}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{117}{352}\right)\)	\(e\left(\frac{7}{528}\right)\)	\(e\left(\frac{281}{528}\right)\)	\(e\left(\frac{307}{1056}\right)\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{1}{352}\right)\)
\(\chi_{836352}(52361,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{835}{1056}\right)\)	\(e\left(\frac{223}{528}\right)\)	\(e\left(\frac{349}{1056}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{327}{352}\right)\)	\(e\left(\frac{173}{528}\right)\)	\(e\left(\frac{307}{528}\right)\)	\(e\left(\frac{497}{1056}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{75}{352}\right)\)
\(\chi_{836352}(55529,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{887}{1056}\right)\)	\(e\left(\frac{419}{528}\right)\)	\(e\left(\frac{329}{1056}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{43}{352}\right)\)	\(e\left(\frac{505}{528}\right)\)	\(e\left(\frac{359}{528}\right)\)	\(e\left(\frac{877}{1056}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{223}{352}\right)\)
\(\chi_{836352}(60281,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{965}{1056}\right)\)	\(e\left(\frac{185}{528}\right)\)	\(e\left(\frac{827}{1056}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{321}{352}\right)\)	\(e\left(\frac{475}{528}\right)\)	\(e\left(\frac{437}{528}\right)\)	\(e\left(\frac{391}{1056}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{93}{352}\right)\)
\(\chi_{836352}(61865,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{991}{1056}\right)\)	\(e\left(\frac{283}{528}\right)\)	\(e\left(\frac{289}{1056}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{179}{352}\right)\)	\(e\left(\frac{113}{528}\right)\)	\(e\left(\frac{463}{528}\right)\)	\(e\left(\frac{581}{1056}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{167}{352}\right)\)
\(\chi_{836352}(65033,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1043}{1056}\right)\)	\(e\left(\frac{479}{528}\right)\)	\(e\left(\frac{269}{1056}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{247}{352}\right)\)	\(e\left(\frac{445}{528}\right)\)	\(e\left(\frac{515}{528}\right)\)	\(e\left(\frac{961}{1056}\right)\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{315}{352}\right)\)
\(\chi_{836352}(66617,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{1056}\right)\)	\(e\left(\frac{49}{528}\right)\)	\(e\left(\frac{787}{1056}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{105}{352}\right)\)	\(e\left(\frac{83}{528}\right)\)	\(e\left(\frac{13}{528}\right)\)	\(e\left(\frac{95}{1056}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{37}{352}\right)\)
\(\chi_{836352}(69785,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{65}{1056}\right)\)	\(e\left(\frac{245}{528}\right)\)	\(e\left(\frac{767}{1056}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{173}{352}\right)\)	\(e\left(\frac{415}{528}\right)\)	\(e\left(\frac{65}{528}\right)\)	\(e\left(\frac{475}{1056}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{185}{352}\right)\)
\(\chi_{836352}(71369,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{1056}\right)\)	\(e\left(\frac{343}{528}\right)\)	\(e\left(\frac{229}{1056}\right)\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{31}{352}\right)\)	\(e\left(\frac{53}{528}\right)\)	\(e\left(\frac{91}{528}\right)\)	\(e\left(\frac{665}{1056}\right)\)	\(e\left(\frac{47}{132}\right)\)	\(e\left(\frac{259}{352}\right)\)
\(\chi_{836352}(76121,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{169}{1056}\right)\)	\(e\left(\frac{109}{528}\right)\)	\(e\left(\frac{727}{1056}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{309}{352}\right)\)	\(e\left(\frac{23}{528}\right)\)	\(e\left(\frac{169}{528}\right)\)	\(e\left(\frac{179}{1056}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{129}{352}\right)\)
\(\chi_{836352}(79289,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{221}{1056}\right)\)	\(e\left(\frac{305}{528}\right)\)	\(e\left(\frac{707}{1056}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{25}{352}\right)\)	\(e\left(\frac{355}{528}\right)\)	\(e\left(\frac{221}{528}\right)\)	\(e\left(\frac{559}{1056}\right)\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{277}{352}\right)\)
\(\chi_{836352}(80873,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{247}{1056}\right)\)	\(e\left(\frac{403}{528}\right)\)	\(e\left(\frac{169}{1056}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{235}{352}\right)\)	\(e\left(\frac{521}{528}\right)\)	\(e\left(\frac{247}{528}\right)\)	\(e\left(\frac{749}{1056}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{351}{352}\right)\)

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First 31 of 320 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	836352.um
Modulus	$836352$
Conductor	$139392$
Order	$1056$
Real	no
Primitive	no
Minimal	no
Parity	odd

Modulus:	\(836352\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(139392\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(1056\)	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 139392.nk	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);