LMFDB - Dirichlet character orbit 987696.sn

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(987696, base_ring=CyclotomicField(4332)) M = H._module chi = DirichletCharacter(H, M([2166,3249,722,1720])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(83, 987696)) 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("987696.83"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$987696$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$987696$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$4332$	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:	$\Q(\zeta_{4332})$
Fixed field:	Number field defined by a degree 4332 polynomial (not computed)

First 31 of 1368 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$23$	$25$	$29$	$31$	$35$
$\chi_{987696}(83,\cdot)$	$1$	$1$	$e\left(\frac{3251}{4332}\right)$	$e\left(\frac{14}{1083}\right)$	$e\left(\frac{1457}{4332}\right)$	$e\left(\frac{77}{1444}\right)$	$e\left(\frac{959}{2166}\right)$	$e\left(\frac{351}{722}\right)$	$e\left(\frac{1085}{2166}\right)$	$e\left(\frac{493}{4332}\right)$	$e\left(\frac{1325}{2166}\right)$	$e\left(\frac{3307}{4332}\right)$
$\chi_{987696}(923,\cdot)$	$1$	$1$	$e\left(\frac{4033}{4332}\right)$	$e\left(\frac{73}{1083}\right)$	$e\left(\frac{403}{4332}\right)$	$e\left(\frac{943}{1444}\right)$	$e\left(\frac{127}{2166}\right)$	$e\left(\frac{51}{722}\right)$	$e\left(\frac{1867}{2166}\right)$	$e\left(\frac{3731}{4332}\right)$	$e\left(\frac{643}{2166}\right)$	$e\left(\frac{4325}{4332}\right)$
$\chi_{987696}(1451,\cdot)$	$1$	$1$	$e\left(\frac{2585}{4332}\right)$	$e\left(\frac{767}{1083}\right)$	$e\left(\frac{2543}{4332}\right)$	$e\left(\frac{67}{1444}\right)$	$e\left(\frac{1097}{2166}\right)$	$e\left(\frac{71}{722}\right)$	$e\left(\frac{419}{2166}\right)$	$e\left(\frac{2023}{4332}\right)$	$e\left(\frac{881}{2166}\right)$	$e\left(\frac{1321}{4332}\right)$
$\chi_{987696}(2291,\cdot)$	$1$	$1$	$e\left(\frac{1723}{4332}\right)$	$e\left(\frac{148}{1083}\right)$	$e\left(\frac{1633}{4332}\right)$	$e\left(\frac{453}{1444}\right)$	$e\left(\frac{391}{2166}\right)$	$e\left(\frac{49}{722}\right)$	$e\left(\frac{1723}{2166}\right)$	$e\left(\frac{725}{4332}\right)$	$e\left(\frac{547}{2166}\right)$	$e\left(\frac{2315}{4332}\right)$
$\chi_{987696}(3659,\cdot)$	$1$	$1$	$e\left(\frac{781}{4332}\right)$	$e\left(\frac{52}{1083}\right)$	$e\left(\frac{3091}{4332}\right)$	$e\left(\frac{647}{1444}\right)$	$e\left(\frac{313}{2166}\right)$	$e\left(\frac{427}{722}\right)$	$e\left(\frac{781}{2166}\right)$	$e\left(\frac{1367}{4332}\right)$	$e\left(\frac{1363}{2166}\right)$	$e\left(\frac{989}{4332}\right)$
$\chi_{987696}(4187,\cdot)$	$1$	$1$	$e\left(\frac{3077}{4332}\right)$	$e\left(\frac{962}{1083}\right)$	$e\left(\frac{3575}{4332}\right)$	$e\left(\frac{959}{1444}\right)$	$e\left(\frac{917}{2166}\right)$	$e\left(\frac{499}{722}\right)$	$e\left(\frac{911}{2166}\right)$	$e\left(\frac{4171}{4332}\right)$	$e\left(\frac{1931}{2166}\right)$	$e\left(\frac{2593}{4332}\right)$
$\chi_{987696}(5027,\cdot)$	$1$	$1$	$e\left(\frac{1207}{4332}\right)$	$e\left(\frac{868}{1083}\right)$	$e\left(\frac{445}{4332}\right)$	$e\left(\frac{81}{1444}\right)$	$e\left(\frac{2059}{2166}\right)$	$e\left(\frac{463}{722}\right)$	$e\left(\frac{1207}{2166}\right)$	$e\left(\frac{1325}{4332}\right)$	$e\left(\frac{925}{2166}\right)$	$e\left(\frac{347}{4332}\right)$
$\chi_{987696}(5555,\cdot)$	$1$	$1$	$e\left(\frac{4235}{4332}\right)$	$e\left(\frac{404}{1083}\right)$	$e\left(\frac{3521}{4332}\right)$	$e\left(\frac{417}{1444}\right)$	$e\left(\frac{599}{2166}\right)$	$e\left(\frac{485}{722}\right)$	$e\left(\frac{2069}{2166}\right)$	$e\left(\frac{457}{4332}\right)$	$e\left(\frac{1259}{2166}\right)$	$e\left(\frac{1519}{4332}\right)$
$\chi_{987696}(6395,\cdot)$	$1$	$1$	$e\left(\frac{3001}{4332}\right)$	$e\left(\frac{430}{1083}\right)$	$e\left(\frac{2359}{4332}\right)$	$e\left(\frac{199}{1444}\right)$	$e\left(\frac{1297}{2166}\right)$	$e\left(\frac{157}{722}\right)$	$e\left(\frac{835}{2166}\right)$	$e\left(\frac{599}{4332}\right)$	$e\left(\frac{1399}{2166}\right)$	$e\left(\frac{389}{4332}\right)$
$\chi_{987696}(6923,\cdot)$	$1$	$1$	$e\left(\frac{3113}{4332}\right)$	$e\left(\frac{131}{1083}\right)$	$e\left(\frac{1643}{4332}\right)$	$e\left(\frac{179}{1444}\right)$	$e\left(\frac{851}{2166}\right)$	$e\left(\frac{319}{722}\right)$	$e\left(\frac{947}{2166}\right)$	$e\left(\frac{2215}{4332}\right)$	$e\left(\frac{1955}{2166}\right)$	$e\left(\frac{3637}{4332}\right)$
$\chi_{987696}(7763,\cdot)$	$1$	$1$	$e\left(\frac{1831}{4332}\right)$	$e\left(\frac{904}{1083}\right)$	$e\left(\frac{169}{4332}\right)$	$e\left(\frac{1001}{1444}\right)$	$e\left(\frac{193}{2166}\right)$	$e\left(\frac{231}{722}\right)$	$e\left(\frac{1831}{2166}\right)$	$e\left(\frac{3521}{4332}\right)$	$e\left(\frac{619}{2166}\right)$	$e\left(\frac{1115}{4332}\right)$
$\chi_{987696}(8291,\cdot)$	$1$	$1$	$e\left(\frac{4043}{4332}\right)$	$e\left(\frac{143}{1083}\right)$	$e\left(\frac{2273}{4332}\right)$	$e\left(\frac{245}{1444}\right)$	$e\left(\frac{1673}{2166}\right)$	$e\left(\frac{1}{722}\right)$	$e\left(\frac{1877}{2166}\right)$	$e\left(\frac{781}{4332}\right)$	$e\left(\frac{1853}{2166}\right)$	$e\left(\frac{283}{4332}\right)$
$\chi_{987696}(9131,\cdot)$	$1$	$1$	$e\left(\frac{2029}{4332}\right)$	$e\left(\frac{124}{1083}\right)$	$e\left(\frac{2539}{4332}\right)$	$e\left(\frac{1043}{1444}\right)$	$e\left(\frac{913}{2166}\right)$	$e\left(\frac{685}{722}\right)$	$e\left(\frac{2029}{2166}\right)$	$e\left(\frac{1427}{4332}\right)$	$e\left(\frac{751}{2166}\right)$	$e\left(\frac{2525}{4332}\right)$
$\chi_{987696}(9659,\cdot)$	$1$	$1$	$e\left(\frac{2693}{4332}\right)$	$e\left(\frac{440}{1083}\right)$	$e\left(\frac{1079}{4332}\right)$	$e\left(\frac{615}{1444}\right)$	$e\left(\frac{899}{2166}\right)$	$e\left(\frac{253}{722}\right)$	$e\left(\frac{527}{2166}\right)$	$e\left(\frac{487}{4332}\right)$	$e\left(\frac{953}{2166}\right)$	$e\left(\frac{121}{4332}\right)$
$\chi_{987696}(10499,\cdot)$	$1$	$1$	$e\left(\frac{3595}{4332}\right)$	$e\left(\frac{256}{1083}\right)$	$e\left(\frac{805}{4332}\right)$	$e\left(\frac{325}{1444}\right)$	$e\left(\frac{1291}{2166}\right)$	$e\left(\frac{75}{722}\right)$	$e\left(\frac{1429}{2166}\right)$	$e\left(\frac{2981}{4332}\right)$	$e\left(\frac{1795}{2166}\right)$	$e\left(\frac{287}{4332}\right)$
$\chi_{987696}(11027,\cdot)$	$1$	$1$	$e\left(\frac{3395}{4332}\right)$	$e\left(\frac{1022}{1083}\right)$	$e\left(\frac{2393}{4332}\right)$	$e\left(\frac{1289}{1444}\right)$	$e\left(\frac{695}{2166}\right)$	$e\left(\frac{353}{722}\right)$	$e\left(\frac{1229}{2166}\right)$	$e\left(\frac{1333}{4332}\right)$	$e\left(\frac{1421}{2166}\right)$	$e\left(\frac{3151}{4332}\right)$
$\chi_{987696}(11867,\cdot)$	$1$	$1$	$e\left(\frac{2197}{4332}\right)$	$e\left(\frac{217}{1083}\right)$	$e\left(\frac{3631}{4332}\right)$	$e\left(\frac{291}{1444}\right)$	$e\left(\frac{1327}{2166}\right)$	$e\left(\frac{567}{722}\right)$	$e\left(\frac{31}{2166}\right)$	$e\left(\frac{3851}{4332}\right)$	$e\left(\frac{1585}{2166}\right)$	$e\left(\frac{3065}{4332}\right)$
$\chi_{987696}(12395,\cdot)$	$1$	$1$	$e\left(\frac{1817}{4332}\right)$	$e\left(\frac{806}{1083}\right)$	$e\left(\frac{1883}{4332}\right)$	$e\left(\frac{823}{1444}\right)$	$e\left(\frac{1061}{2166}\right)$	$e\left(\frac{301}{722}\right)$	$e\left(\frac{1817}{2166}\right)$	$e\left(\frac{3319}{4332}\right)$	$e\left(\frac{1091}{2166}\right)$	$e\left(\frac{709}{4332}\right)$
$\chi_{987696}(13235,\cdot)$	$1$	$1$	$e\left(\frac{2167}{4332}\right)$	$e\left(\frac{7}{1083}\right)$	$e\left(\frac{2353}{4332}\right)$	$e\left(\frac{941}{1444}\right)$	$e\left(\frac{1021}{2166}\right)$	$e\left(\frac{717}{722}\right)$	$e\left(\frac{1}{2166}\right)$	$e\left(\frac{4037}{4332}\right)$	$e\left(\frac{121}{2166}\right)$	$e\left(\frac{2195}{4332}\right)$
$\chi_{987696}(13763,\cdot)$	$1$	$1$	$e\left(\frac{2291}{4332}\right)$	$e\left(\frac{875}{1083}\right)$	$e\left(\frac{3881}{4332}\right)$	$e\left(\frac{661}{1444}\right)$	$e\left(\frac{1997}{2166}\right)$	$e\left(\frac{97}{722}\right)$	$e\left(\frac{125}{2166}\right)$	$e\left(\frac{2113}{4332}\right)$	$e\left(\frac{2129}{2166}\right)$	$e\left(\frac{1459}{4332}\right)$
$\chi_{987696}(14603,\cdot)$	$1$	$1$	$e\left(\frac{3505}{4332}\right)$	$e\left(\frac{709}{1083}\right)$	$e\left(\frac{1303}{4332}\right)$	$e\left(\frac{831}{1444}\right)$	$e\left(\frac{373}{2166}\right)$	$e\left(\frac{525}{722}\right)$	$e\left(\frac{1339}{2166}\right)$	$e\left(\frac{3539}{4332}\right)$	$e\left(\frac{1735}{2166}\right)$	$e\left(\frac{2009}{4332}\right)$
$\chi_{987696}(15131,\cdot)$	$1$	$1$	$e\left(\frac{485}{4332}\right)$	$e\left(\frac{146}{1083}\right)$	$e\left(\frac{4055}{4332}\right)$	$e\left(\frac{803}{1444}\right)$	$e\left(\frac{1337}{2166}\right)$	$e\left(\frac{463}{722}\right)$	$e\left(\frac{485}{2166}\right)$	$e\left(\frac{2047}{4332}\right)$	$e\left(\frac{203}{2166}\right)$	$e\left(\frac{1069}{4332}\right)$
$\chi_{987696}(15971,\cdot)$	$1$	$1$	$e\left(\frac{1879}{4332}\right)$	$e\left(\frac{157}{1083}\right)$	$e\left(\frac{481}{4332}\right)$	$e\left(\frac{1405}{1444}\right)$	$e\left(\frac{1549}{2166}\right)$	$e\left(\frac{713}{722}\right)$	$e\left(\frac{1879}{2166}\right)$	$e\left(\frac{2357}{4332}\right)$	$e\left(\frac{2095}{2166}\right)$	$e\left(\frac{2507}{4332}\right)$
$\chi_{987696}(16499,\cdot)$	$1$	$1$	$e\left(\frac{731}{4332}\right)$	$e\left(\frac{785}{1083}\right)$	$e\left(\frac{2405}{4332}\right)$	$e\left(\frac{1249}{1444}\right)$	$e\left(\frac{1247}{2166}\right)$	$e\left(\frac{677}{722}\right)$	$e\left(\frac{731}{2166}\right)$	$e\left(\frac{3121}{4332}\right)$	$e\left(\frac{1811}{2166}\right)$	$e\left(\frac{3871}{4332}\right)$
$\chi_{987696}(17339,\cdot)$	$1$	$1$	$e\left(\frac{1621}{4332}\right)$	$e\left(\frac{517}{1083}\right)$	$e\left(\frac{4219}{4332}\right)$	$e\left(\frac{1219}{1444}\right)$	$e\left(\frac{217}{2166}\right)$	$e\left(\frac{559}{722}\right)$	$e\left(\frac{1621}{2166}\right)$	$e\left(\frac{491}{4332}\right)$	$e\left(\frac{1201}{2166}\right)$	$e\left(\frac{3689}{4332}\right)$
$\chi_{987696}(17867,\cdot)$	$1$	$1$	$e\left(\frac{3029}{4332}\right)$	$e\left(\frac{626}{1083}\right)$	$e\left(\frac{3263}{4332}\right)$	$e\left(\frac{555}{1444}\right)$	$e\left(\frac{1727}{2166}\right)$	$e\left(\frac{17}{722}\right)$	$e\left(\frac{863}{2166}\right)$	$e\left(\frac{1003}{4332}\right)$	$e\left(\frac{455}{2166}\right)$	$e\left(\frac{1201}{4332}\right)$
$\chi_{987696}(18707,\cdot)$	$1$	$1$	$e\left(\frac{2731}{4332}\right)$	$e\left(\frac{706}{1083}\right)$	$e\left(\frac{3853}{4332}\right)$	$e\left(\frac{273}{1444}\right)$	$e\left(\frac{709}{2166}\right)$	$e\left(\frac{63}{722}\right)$	$e\left(\frac{565}{2166}\right)$	$e\left(\frac{2273}{4332}\right)$	$e\left(\frac{1219}{2166}\right)$	$e\left(\frac{1223}{4332}\right)$
$\chi_{987696}(19235,\cdot)$	$1$	$1$	$e\left(\frac{3047}{4332}\right)$	$e\left(\frac{752}{1083}\right)$	$e\left(\frac{2297}{4332}\right)$	$e\left(\frac{165}{1444}\right)$	$e\left(\frac{611}{2166}\right)$	$e\left(\frac{649}{722}\right)$	$e\left(\frac{881}{2166}\right)$	$e\left(\frac{25}{4332}\right)$	$e\left(\frac{467}{2166}\right)$	$e\left(\frac{1723}{4332}\right)$
$\chi_{987696}(20075,\cdot)$	$1$	$1$	$e\left(\frac{877}{4332}\right)$	$e\left(\frac{724}{1083}\right)$	$e\left(\frac{3715}{4332}\right)$	$e\left(\frac{11}{1444}\right)$	$e\left(\frac{859}{2166}\right)$	$e\left(\frac{669}{722}\right)$	$e\left(\frac{877}{2166}\right)$	$e\left(\frac{3371}{4332}\right)$	$e\left(\frac{2149}{2166}\right)$	$e\left(\frac{3773}{4332}\right)$
$\chi_{987696}(20603,\cdot)$	$1$	$1$	$e\left(\frac{785}{4332}\right)$	$e\left(\frac{80}{1083}\right)$	$e\left(\frac{3839}{4332}\right)$	$e\left(\frac{79}{1444}\right)$	$e\left(\frac{65}{2166}\right)$	$e\left(\frac{407}{722}\right)$	$e\left(\frac{785}{2166}\right)$	$e\left(\frac{187}{4332}\right)$	$e\left(\frac{1847}{2166}\right)$	$e\left(\frac{1105}{4332}\right)$
$\chi_{987696}(21443,\cdot)$	$1$	$1$	$e\left(\frac{391}{4332}\right)$	$e\left(\frac{571}{1083}\right)$	$e\left(\frac{3805}{4332}\right)$	$e\left(\frac{433}{1444}\right)$	$e\left(\frac{667}{2166}\right)$	$e\left(\frac{211}{722}\right)$	$e\left(\frac{391}{2166}\right)$	$e\left(\frac{3785}{4332}\right)$	$e\left(\frac{1825}{2166}\right)$	$e\left(\frac{2675}{4332}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{987696}(83,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3251}{4332}\right)\)	\(e\left(\frac{14}{1083}\right)\)	\(e\left(\frac{1457}{4332}\right)\)	\(e\left(\frac{77}{1444}\right)\)	\(e\left(\frac{959}{2166}\right)\)	\(e\left(\frac{351}{722}\right)\)	\(e\left(\frac{1085}{2166}\right)\)	\(e\left(\frac{493}{4332}\right)\)	\(e\left(\frac{1325}{2166}\right)\)	\(e\left(\frac{3307}{4332}\right)\)
\(\chi_{987696}(923,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4033}{4332}\right)\)	\(e\left(\frac{73}{1083}\right)\)	\(e\left(\frac{403}{4332}\right)\)	\(e\left(\frac{943}{1444}\right)\)	\(e\left(\frac{127}{2166}\right)\)	\(e\left(\frac{51}{722}\right)\)	\(e\left(\frac{1867}{2166}\right)\)	\(e\left(\frac{3731}{4332}\right)\)	\(e\left(\frac{643}{2166}\right)\)	\(e\left(\frac{4325}{4332}\right)\)
\(\chi_{987696}(1451,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2585}{4332}\right)\)	\(e\left(\frac{767}{1083}\right)\)	\(e\left(\frac{2543}{4332}\right)\)	\(e\left(\frac{67}{1444}\right)\)	\(e\left(\frac{1097}{2166}\right)\)	\(e\left(\frac{71}{722}\right)\)	\(e\left(\frac{419}{2166}\right)\)	\(e\left(\frac{2023}{4332}\right)\)	\(e\left(\frac{881}{2166}\right)\)	\(e\left(\frac{1321}{4332}\right)\)
\(\chi_{987696}(2291,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1723}{4332}\right)\)	\(e\left(\frac{148}{1083}\right)\)	\(e\left(\frac{1633}{4332}\right)\)	\(e\left(\frac{453}{1444}\right)\)	\(e\left(\frac{391}{2166}\right)\)	\(e\left(\frac{49}{722}\right)\)	\(e\left(\frac{1723}{2166}\right)\)	\(e\left(\frac{725}{4332}\right)\)	\(e\left(\frac{547}{2166}\right)\)	\(e\left(\frac{2315}{4332}\right)\)
\(\chi_{987696}(3659,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{781}{4332}\right)\)	\(e\left(\frac{52}{1083}\right)\)	\(e\left(\frac{3091}{4332}\right)\)	\(e\left(\frac{647}{1444}\right)\)	\(e\left(\frac{313}{2166}\right)\)	\(e\left(\frac{427}{722}\right)\)	\(e\left(\frac{781}{2166}\right)\)	\(e\left(\frac{1367}{4332}\right)\)	\(e\left(\frac{1363}{2166}\right)\)	\(e\left(\frac{989}{4332}\right)\)
\(\chi_{987696}(4187,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3077}{4332}\right)\)	\(e\left(\frac{962}{1083}\right)\)	\(e\left(\frac{3575}{4332}\right)\)	\(e\left(\frac{959}{1444}\right)\)	\(e\left(\frac{917}{2166}\right)\)	\(e\left(\frac{499}{722}\right)\)	\(e\left(\frac{911}{2166}\right)\)	\(e\left(\frac{4171}{4332}\right)\)	\(e\left(\frac{1931}{2166}\right)\)	\(e\left(\frac{2593}{4332}\right)\)
\(\chi_{987696}(5027,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1207}{4332}\right)\)	\(e\left(\frac{868}{1083}\right)\)	\(e\left(\frac{445}{4332}\right)\)	\(e\left(\frac{81}{1444}\right)\)	\(e\left(\frac{2059}{2166}\right)\)	\(e\left(\frac{463}{722}\right)\)	\(e\left(\frac{1207}{2166}\right)\)	\(e\left(\frac{1325}{4332}\right)\)	\(e\left(\frac{925}{2166}\right)\)	\(e\left(\frac{347}{4332}\right)\)
\(\chi_{987696}(5555,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4235}{4332}\right)\)	\(e\left(\frac{404}{1083}\right)\)	\(e\left(\frac{3521}{4332}\right)\)	\(e\left(\frac{417}{1444}\right)\)	\(e\left(\frac{599}{2166}\right)\)	\(e\left(\frac{485}{722}\right)\)	\(e\left(\frac{2069}{2166}\right)\)	\(e\left(\frac{457}{4332}\right)\)	\(e\left(\frac{1259}{2166}\right)\)	\(e\left(\frac{1519}{4332}\right)\)
\(\chi_{987696}(6395,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3001}{4332}\right)\)	\(e\left(\frac{430}{1083}\right)\)	\(e\left(\frac{2359}{4332}\right)\)	\(e\left(\frac{199}{1444}\right)\)	\(e\left(\frac{1297}{2166}\right)\)	\(e\left(\frac{157}{722}\right)\)	\(e\left(\frac{835}{2166}\right)\)	\(e\left(\frac{599}{4332}\right)\)	\(e\left(\frac{1399}{2166}\right)\)	\(e\left(\frac{389}{4332}\right)\)
\(\chi_{987696}(6923,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3113}{4332}\right)\)	\(e\left(\frac{131}{1083}\right)\)	\(e\left(\frac{1643}{4332}\right)\)	\(e\left(\frac{179}{1444}\right)\)	\(e\left(\frac{851}{2166}\right)\)	\(e\left(\frac{319}{722}\right)\)	\(e\left(\frac{947}{2166}\right)\)	\(e\left(\frac{2215}{4332}\right)\)	\(e\left(\frac{1955}{2166}\right)\)	\(e\left(\frac{3637}{4332}\right)\)
\(\chi_{987696}(7763,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1831}{4332}\right)\)	\(e\left(\frac{904}{1083}\right)\)	\(e\left(\frac{169}{4332}\right)\)	\(e\left(\frac{1001}{1444}\right)\)	\(e\left(\frac{193}{2166}\right)\)	\(e\left(\frac{231}{722}\right)\)	\(e\left(\frac{1831}{2166}\right)\)	\(e\left(\frac{3521}{4332}\right)\)	\(e\left(\frac{619}{2166}\right)\)	\(e\left(\frac{1115}{4332}\right)\)
\(\chi_{987696}(8291,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4043}{4332}\right)\)	\(e\left(\frac{143}{1083}\right)\)	\(e\left(\frac{2273}{4332}\right)\)	\(e\left(\frac{245}{1444}\right)\)	\(e\left(\frac{1673}{2166}\right)\)	\(e\left(\frac{1}{722}\right)\)	\(e\left(\frac{1877}{2166}\right)\)	\(e\left(\frac{781}{4332}\right)\)	\(e\left(\frac{1853}{2166}\right)\)	\(e\left(\frac{283}{4332}\right)\)
\(\chi_{987696}(9131,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2029}{4332}\right)\)	\(e\left(\frac{124}{1083}\right)\)	\(e\left(\frac{2539}{4332}\right)\)	\(e\left(\frac{1043}{1444}\right)\)	\(e\left(\frac{913}{2166}\right)\)	\(e\left(\frac{685}{722}\right)\)	\(e\left(\frac{2029}{2166}\right)\)	\(e\left(\frac{1427}{4332}\right)\)	\(e\left(\frac{751}{2166}\right)\)	\(e\left(\frac{2525}{4332}\right)\)
\(\chi_{987696}(9659,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2693}{4332}\right)\)	\(e\left(\frac{440}{1083}\right)\)	\(e\left(\frac{1079}{4332}\right)\)	\(e\left(\frac{615}{1444}\right)\)	\(e\left(\frac{899}{2166}\right)\)	\(e\left(\frac{253}{722}\right)\)	\(e\left(\frac{527}{2166}\right)\)	\(e\left(\frac{487}{4332}\right)\)	\(e\left(\frac{953}{2166}\right)\)	\(e\left(\frac{121}{4332}\right)\)
\(\chi_{987696}(10499,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3595}{4332}\right)\)	\(e\left(\frac{256}{1083}\right)\)	\(e\left(\frac{805}{4332}\right)\)	\(e\left(\frac{325}{1444}\right)\)	\(e\left(\frac{1291}{2166}\right)\)	\(e\left(\frac{75}{722}\right)\)	\(e\left(\frac{1429}{2166}\right)\)	\(e\left(\frac{2981}{4332}\right)\)	\(e\left(\frac{1795}{2166}\right)\)	\(e\left(\frac{287}{4332}\right)\)
\(\chi_{987696}(11027,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3395}{4332}\right)\)	\(e\left(\frac{1022}{1083}\right)\)	\(e\left(\frac{2393}{4332}\right)\)	\(e\left(\frac{1289}{1444}\right)\)	\(e\left(\frac{695}{2166}\right)\)	\(e\left(\frac{353}{722}\right)\)	\(e\left(\frac{1229}{2166}\right)\)	\(e\left(\frac{1333}{4332}\right)\)	\(e\left(\frac{1421}{2166}\right)\)	\(e\left(\frac{3151}{4332}\right)\)
\(\chi_{987696}(11867,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2197}{4332}\right)\)	\(e\left(\frac{217}{1083}\right)\)	\(e\left(\frac{3631}{4332}\right)\)	\(e\left(\frac{291}{1444}\right)\)	\(e\left(\frac{1327}{2166}\right)\)	\(e\left(\frac{567}{722}\right)\)	\(e\left(\frac{31}{2166}\right)\)	\(e\left(\frac{3851}{4332}\right)\)	\(e\left(\frac{1585}{2166}\right)\)	\(e\left(\frac{3065}{4332}\right)\)
\(\chi_{987696}(12395,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1817}{4332}\right)\)	\(e\left(\frac{806}{1083}\right)\)	\(e\left(\frac{1883}{4332}\right)\)	\(e\left(\frac{823}{1444}\right)\)	\(e\left(\frac{1061}{2166}\right)\)	\(e\left(\frac{301}{722}\right)\)	\(e\left(\frac{1817}{2166}\right)\)	\(e\left(\frac{3319}{4332}\right)\)	\(e\left(\frac{1091}{2166}\right)\)	\(e\left(\frac{709}{4332}\right)\)
\(\chi_{987696}(13235,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2167}{4332}\right)\)	\(e\left(\frac{7}{1083}\right)\)	\(e\left(\frac{2353}{4332}\right)\)	\(e\left(\frac{941}{1444}\right)\)	\(e\left(\frac{1021}{2166}\right)\)	\(e\left(\frac{717}{722}\right)\)	\(e\left(\frac{1}{2166}\right)\)	\(e\left(\frac{4037}{4332}\right)\)	\(e\left(\frac{121}{2166}\right)\)	\(e\left(\frac{2195}{4332}\right)\)
\(\chi_{987696}(13763,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2291}{4332}\right)\)	\(e\left(\frac{875}{1083}\right)\)	\(e\left(\frac{3881}{4332}\right)\)	\(e\left(\frac{661}{1444}\right)\)	\(e\left(\frac{1997}{2166}\right)\)	\(e\left(\frac{97}{722}\right)\)	\(e\left(\frac{125}{2166}\right)\)	\(e\left(\frac{2113}{4332}\right)\)	\(e\left(\frac{2129}{2166}\right)\)	\(e\left(\frac{1459}{4332}\right)\)
\(\chi_{987696}(14603,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3505}{4332}\right)\)	\(e\left(\frac{709}{1083}\right)\)	\(e\left(\frac{1303}{4332}\right)\)	\(e\left(\frac{831}{1444}\right)\)	\(e\left(\frac{373}{2166}\right)\)	\(e\left(\frac{525}{722}\right)\)	\(e\left(\frac{1339}{2166}\right)\)	\(e\left(\frac{3539}{4332}\right)\)	\(e\left(\frac{1735}{2166}\right)\)	\(e\left(\frac{2009}{4332}\right)\)
\(\chi_{987696}(15131,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{485}{4332}\right)\)	\(e\left(\frac{146}{1083}\right)\)	\(e\left(\frac{4055}{4332}\right)\)	\(e\left(\frac{803}{1444}\right)\)	\(e\left(\frac{1337}{2166}\right)\)	\(e\left(\frac{463}{722}\right)\)	\(e\left(\frac{485}{2166}\right)\)	\(e\left(\frac{2047}{4332}\right)\)	\(e\left(\frac{203}{2166}\right)\)	\(e\left(\frac{1069}{4332}\right)\)
\(\chi_{987696}(15971,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1879}{4332}\right)\)	\(e\left(\frac{157}{1083}\right)\)	\(e\left(\frac{481}{4332}\right)\)	\(e\left(\frac{1405}{1444}\right)\)	\(e\left(\frac{1549}{2166}\right)\)	\(e\left(\frac{713}{722}\right)\)	\(e\left(\frac{1879}{2166}\right)\)	\(e\left(\frac{2357}{4332}\right)\)	\(e\left(\frac{2095}{2166}\right)\)	\(e\left(\frac{2507}{4332}\right)\)
\(\chi_{987696}(16499,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{731}{4332}\right)\)	\(e\left(\frac{785}{1083}\right)\)	\(e\left(\frac{2405}{4332}\right)\)	\(e\left(\frac{1249}{1444}\right)\)	\(e\left(\frac{1247}{2166}\right)\)	\(e\left(\frac{677}{722}\right)\)	\(e\left(\frac{731}{2166}\right)\)	\(e\left(\frac{3121}{4332}\right)\)	\(e\left(\frac{1811}{2166}\right)\)	\(e\left(\frac{3871}{4332}\right)\)
\(\chi_{987696}(17339,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1621}{4332}\right)\)	\(e\left(\frac{517}{1083}\right)\)	\(e\left(\frac{4219}{4332}\right)\)	\(e\left(\frac{1219}{1444}\right)\)	\(e\left(\frac{217}{2166}\right)\)	\(e\left(\frac{559}{722}\right)\)	\(e\left(\frac{1621}{2166}\right)\)	\(e\left(\frac{491}{4332}\right)\)	\(e\left(\frac{1201}{2166}\right)\)	\(e\left(\frac{3689}{4332}\right)\)
\(\chi_{987696}(17867,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3029}{4332}\right)\)	\(e\left(\frac{626}{1083}\right)\)	\(e\left(\frac{3263}{4332}\right)\)	\(e\left(\frac{555}{1444}\right)\)	\(e\left(\frac{1727}{2166}\right)\)	\(e\left(\frac{17}{722}\right)\)	\(e\left(\frac{863}{2166}\right)\)	\(e\left(\frac{1003}{4332}\right)\)	\(e\left(\frac{455}{2166}\right)\)	\(e\left(\frac{1201}{4332}\right)\)
\(\chi_{987696}(18707,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2731}{4332}\right)\)	\(e\left(\frac{706}{1083}\right)\)	\(e\left(\frac{3853}{4332}\right)\)	\(e\left(\frac{273}{1444}\right)\)	\(e\left(\frac{709}{2166}\right)\)	\(e\left(\frac{63}{722}\right)\)	\(e\left(\frac{565}{2166}\right)\)	\(e\left(\frac{2273}{4332}\right)\)	\(e\left(\frac{1219}{2166}\right)\)	\(e\left(\frac{1223}{4332}\right)\)
\(\chi_{987696}(19235,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3047}{4332}\right)\)	\(e\left(\frac{752}{1083}\right)\)	\(e\left(\frac{2297}{4332}\right)\)	\(e\left(\frac{165}{1444}\right)\)	\(e\left(\frac{611}{2166}\right)\)	\(e\left(\frac{649}{722}\right)\)	\(e\left(\frac{881}{2166}\right)\)	\(e\left(\frac{25}{4332}\right)\)	\(e\left(\frac{467}{2166}\right)\)	\(e\left(\frac{1723}{4332}\right)\)
\(\chi_{987696}(20075,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{877}{4332}\right)\)	\(e\left(\frac{724}{1083}\right)\)	\(e\left(\frac{3715}{4332}\right)\)	\(e\left(\frac{11}{1444}\right)\)	\(e\left(\frac{859}{2166}\right)\)	\(e\left(\frac{669}{722}\right)\)	\(e\left(\frac{877}{2166}\right)\)	\(e\left(\frac{3371}{4332}\right)\)	\(e\left(\frac{2149}{2166}\right)\)	\(e\left(\frac{3773}{4332}\right)\)
\(\chi_{987696}(20603,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{785}{4332}\right)\)	\(e\left(\frac{80}{1083}\right)\)	\(e\left(\frac{3839}{4332}\right)\)	\(e\left(\frac{79}{1444}\right)\)	\(e\left(\frac{65}{2166}\right)\)	\(e\left(\frac{407}{722}\right)\)	\(e\left(\frac{785}{2166}\right)\)	\(e\left(\frac{187}{4332}\right)\)	\(e\left(\frac{1847}{2166}\right)\)	\(e\left(\frac{1105}{4332}\right)\)
\(\chi_{987696}(21443,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{391}{4332}\right)\)	\(e\left(\frac{571}{1083}\right)\)	\(e\left(\frac{3805}{4332}\right)\)	\(e\left(\frac{433}{1444}\right)\)	\(e\left(\frac{667}{2166}\right)\)	\(e\left(\frac{211}{722}\right)\)	\(e\left(\frac{391}{2166}\right)\)	\(e\left(\frac{3785}{4332}\right)\)	\(e\left(\frac{1825}{2166}\right)\)	\(e\left(\frac{2675}{4332}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 1368 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	987696.sn
Modulus	$987696$
Conductor	$987696$
Order	$4332$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(987696\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(987696\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(4332\)	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);