from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(140659, base_ring=CyclotomicField(140658))
M = H._module
chi = DirichletCharacter(H, M([86152]))
chi.galois_orbit()
[g,chi] = znchar(Mod(6,140659))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(140659\) | |
| Conductor: | \(140659\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70329\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | $\Q(\zeta_{70329})$ |
| Fixed field: | Number field defined by a degree 70329 polynomial (not computed) |
First 31 of 37632 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{140659}(6,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{20154}{23443}\right)\) | \(e\left(\frac{43076}{70329}\right)\) | \(e\left(\frac{16865}{23443}\right)\) | \(e\left(\frac{1432}{3349}\right)\) | \(e\left(\frac{33209}{70329}\right)\) | \(e\left(\frac{13808}{23443}\right)\) | \(e\left(\frac{13576}{23443}\right)\) | \(e\left(\frac{15823}{70329}\right)\) | \(e\left(\frac{6735}{23443}\right)\) | \(e\left(\frac{23453}{70329}\right)\) |
| \(\chi_{140659}(9,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5274}{23443}\right)\) | \(e\left(\frac{1}{70329}\right)\) | \(e\left(\frac{10548}{23443}\right)\) | \(e\left(\frac{1290}{3349}\right)\) | \(e\left(\frac{15823}{70329}\right)\) | \(e\left(\frac{18800}{23443}\right)\) | \(e\left(\frac{15822}{23443}\right)\) | \(e\left(\frac{2}{70329}\right)\) | \(e\left(\frac{14304}{23443}\right)\) | \(e\left(\frac{14275}{70329}\right)\) |
| \(\chi_{140659}(11,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{17160}{23443}\right)\) | \(e\left(\frac{42302}{70329}\right)\) | \(e\left(\frac{10877}{23443}\right)\) | \(e\left(\frac{974}{3349}\right)\) | \(e\left(\frac{23453}{70329}\right)\) | \(e\left(\frac{20711}{23443}\right)\) | \(e\left(\frac{4594}{23443}\right)\) | \(e\left(\frac{14275}{70329}\right)\) | \(e\left(\frac{535}{23443}\right)\) | \(e\left(\frac{16256}{70329}\right)\) |
| \(\chi_{140659}(13,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19668}{23443}\right)\) | \(e\left(\frac{20353}{70329}\right)\) | \(e\left(\frac{15893}{23443}\right)\) | \(e\left(\frac{2559}{3349}\right)\) | \(e\left(\frac{9028}{70329}\right)\) | \(e\left(\frac{23197}{23443}\right)\) | \(e\left(\frac{12118}{23443}\right)\) | \(e\left(\frac{40706}{70329}\right)\) | \(e\left(\frac{14138}{23443}\right)\) | \(e\left(\frac{9976}{70329}\right)\) |
| \(\chi_{140659}(19,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{835}{23443}\right)\) | \(e\left(\frac{25679}{70329}\right)\) | \(e\left(\frac{1670}{23443}\right)\) | \(e\left(\frac{951}{3349}\right)\) | \(e\left(\frac{28184}{70329}\right)\) | \(e\left(\frac{3501}{23443}\right)\) | \(e\left(\frac{2505}{23443}\right)\) | \(e\left(\frac{51358}{70329}\right)\) | \(e\left(\frac{7492}{23443}\right)\) | \(e\left(\frac{12977}{70329}\right)\) |
| \(\chi_{140659}(21,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7045}{23443}\right)\) | \(e\left(\frac{63365}{70329}\right)\) | \(e\left(\frac{14090}{23443}\right)\) | \(e\left(\frac{1807}{3349}\right)\) | \(e\left(\frac{14171}{70329}\right)\) | \(e\left(\frac{5955}{23443}\right)\) | \(e\left(\frac{21135}{23443}\right)\) | \(e\left(\frac{56401}{70329}\right)\) | \(e\left(\frac{19694}{23443}\right)\) | \(e\left(\frac{34106}{70329}\right)\) |
| \(\chi_{140659}(30,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{2220}{23443}\right)\) | \(e\left(\frac{56621}{70329}\right)\) | \(e\left(\frac{4440}{23443}\right)\) | \(e\left(\frac{2749}{3349}\right)\) | \(e\left(\frac{63281}{70329}\right)\) | \(e\left(\frac{21942}{23443}\right)\) | \(e\left(\frac{6660}{23443}\right)\) | \(e\left(\frac{42913}{70329}\right)\) | \(e\left(\frac{21463}{23443}\right)\) | \(e\left(\frac{43907}{70329}\right)\) |
| \(\chi_{140659}(36,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{16865}{23443}\right)\) | \(e\left(\frac{15823}{70329}\right)\) | \(e\left(\frac{10287}{23443}\right)\) | \(e\left(\frac{2864}{3349}\right)\) | \(e\left(\frac{66418}{70329}\right)\) | \(e\left(\frac{4173}{23443}\right)\) | \(e\left(\frac{3709}{23443}\right)\) | \(e\left(\frac{31646}{70329}\right)\) | \(e\left(\frac{13470}{23443}\right)\) | \(e\left(\frac{46906}{70329}\right)\) |
| \(\chi_{140659}(44,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5308}{23443}\right)\) | \(e\left(\frac{58124}{70329}\right)\) | \(e\left(\frac{10616}{23443}\right)\) | \(e\left(\frac{2548}{3349}\right)\) | \(e\left(\frac{3719}{70329}\right)\) | \(e\left(\frac{6084}{23443}\right)\) | \(e\left(\frac{15924}{23443}\right)\) | \(e\left(\frac{45919}{70329}\right)\) | \(e\left(\frac{23144}{23443}\right)\) | \(e\left(\frac{48887}{70329}\right)\) |
| \(\chi_{140659}(45,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{10783}{23443}\right)\) | \(e\left(\frac{13546}{70329}\right)\) | \(e\left(\frac{21566}{23443}\right)\) | \(e\left(\frac{2607}{3349}\right)\) | \(e\left(\frac{45895}{70329}\right)\) | \(e\left(\frac{3491}{23443}\right)\) | \(e\left(\frac{8906}{23443}\right)\) | \(e\left(\frac{27092}{70329}\right)\) | \(e\left(\frac{5589}{23443}\right)\) | \(e\left(\frac{34729}{70329}\right)\) |
| \(\chi_{140659}(52,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{7816}{23443}\right)\) | \(e\left(\frac{36175}{70329}\right)\) | \(e\left(\frac{15632}{23443}\right)\) | \(e\left(\frac{784}{3349}\right)\) | \(e\left(\frac{59623}{70329}\right)\) | \(e\left(\frac{8570}{23443}\right)\) | \(e\left(\frac{5}{23443}\right)\) | \(e\left(\frac{2021}{70329}\right)\) | \(e\left(\frac{13304}{23443}\right)\) | \(e\left(\frac{42607}{70329}\right)\) |
| \(\chi_{140659}(55,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{22669}{23443}\right)\) | \(e\left(\frac{55847}{70329}\right)\) | \(e\left(\frac{21895}{23443}\right)\) | \(e\left(\frac{2291}{3349}\right)\) | \(e\left(\frac{53525}{70329}\right)\) | \(e\left(\frac{5402}{23443}\right)\) | \(e\left(\frac{21121}{23443}\right)\) | \(e\left(\frac{41365}{70329}\right)\) | \(e\left(\frac{15263}{23443}\right)\) | \(e\left(\frac{36710}{70329}\right)\) |
| \(\chi_{140659}(66,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{13871}{23443}\right)\) | \(e\left(\frac{15049}{70329}\right)\) | \(e\left(\frac{4299}{23443}\right)\) | \(e\left(\frac{2406}{3349}\right)\) | \(e\left(\frac{56662}{70329}\right)\) | \(e\left(\frac{11076}{23443}\right)\) | \(e\left(\frac{18170}{23443}\right)\) | \(e\left(\frac{30098}{70329}\right)\) | \(e\left(\frac{7270}{23443}\right)\) | \(e\left(\frac{39709}{70329}\right)\) |
| \(\chi_{140659}(74,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4559}{23443}\right)\) | \(e\left(\frac{23635}{70329}\right)\) | \(e\left(\frac{9118}{23443}\right)\) | \(e\left(\frac{3203}{3349}\right)\) | \(e\left(\frac{37312}{70329}\right)\) | \(e\left(\frac{22821}{23443}\right)\) | \(e\left(\frac{13677}{23443}\right)\) | \(e\left(\frac{47270}{70329}\right)\) | \(e\left(\frac{3537}{23443}\right)\) | \(e\left(\frac{21412}{70329}\right)\) |
| \(\chi_{140659}(76,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{12426}{23443}\right)\) | \(e\left(\frac{41501}{70329}\right)\) | \(e\left(\frac{1409}{23443}\right)\) | \(e\left(\frac{2525}{3349}\right)\) | \(e\left(\frac{8450}{70329}\right)\) | \(e\left(\frac{12317}{23443}\right)\) | \(e\left(\frac{13835}{23443}\right)\) | \(e\left(\frac{12673}{70329}\right)\) | \(e\left(\frac{6658}{23443}\right)\) | \(e\left(\frac{45608}{70329}\right)\) |
| \(\chi_{140659}(81,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{10548}{23443}\right)\) | \(e\left(\frac{2}{70329}\right)\) | \(e\left(\frac{21096}{23443}\right)\) | \(e\left(\frac{2580}{3349}\right)\) | \(e\left(\frac{31646}{70329}\right)\) | \(e\left(\frac{14157}{23443}\right)\) | \(e\left(\frac{8201}{23443}\right)\) | \(e\left(\frac{4}{70329}\right)\) | \(e\left(\frac{5165}{23443}\right)\) | \(e\left(\frac{28550}{70329}\right)\) |
| \(\chi_{140659}(84,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{18636}{23443}\right)\) | \(e\left(\frac{8858}{70329}\right)\) | \(e\left(\frac{13829}{23443}\right)\) | \(e\left(\frac{32}{3349}\right)\) | \(e\left(\frac{64766}{70329}\right)\) | \(e\left(\frac{14771}{23443}\right)\) | \(e\left(\frac{9022}{23443}\right)\) | \(e\left(\frac{17716}{70329}\right)\) | \(e\left(\frac{18860}{23443}\right)\) | \(e\left(\frac{66737}{70329}\right)\) |
| \(\chi_{140659}(86,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{18014}{23443}\right)\) | \(e\left(\frac{11516}{70329}\right)\) | \(e\left(\frac{12585}{23443}\right)\) | \(e\left(\frac{2825}{3349}\right)\) | \(e\left(\frac{65558}{70329}\right)\) | \(e\left(\frac{4695}{23443}\right)\) | \(e\left(\frac{7156}{23443}\right)\) | \(e\left(\frac{23032}{70329}\right)\) | \(e\left(\frac{14346}{23443}\right)\) | \(e\left(\frac{32027}{70329}\right)\) |
| \(\chi_{140659}(95,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{6344}{23443}\right)\) | \(e\left(\frac{39224}{70329}\right)\) | \(e\left(\frac{12688}{23443}\right)\) | \(e\left(\frac{2268}{3349}\right)\) | \(e\left(\frac{58256}{70329}\right)\) | \(e\left(\frac{11635}{23443}\right)\) | \(e\left(\frac{19032}{23443}\right)\) | \(e\left(\frac{8119}{70329}\right)\) | \(e\left(\frac{22220}{23443}\right)\) | \(e\left(\frac{33431}{70329}\right)\) |
| \(\chi_{140659}(96,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{19893}{23443}\right)\) | \(e\left(\frac{4391}{70329}\right)\) | \(e\left(\frac{16343}{23443}\right)\) | \(e\left(\frac{1231}{3349}\right)\) | \(e\left(\frac{64070}{70329}\right)\) | \(e\left(\frac{7997}{23443}\right)\) | \(e\left(\frac{12793}{23443}\right)\) | \(e\left(\frac{8782}{70329}\right)\) | \(e\left(\frac{5067}{23443}\right)\) | \(e\left(\frac{18386}{70329}\right)\) |
| \(\chi_{140659}(97,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{14332}{23443}\right)\) | \(e\left(\frac{34336}{70329}\right)\) | \(e\left(\frac{5221}{23443}\right)\) | \(e\left(\frac{2915}{3349}\right)\) | \(e\left(\frac{7003}{70329}\right)\) | \(e\left(\frac{13795}{23443}\right)\) | \(e\left(\frac{19553}{23443}\right)\) | \(e\left(\frac{68672}{70329}\right)\) | \(e\left(\frac{11294}{23443}\right)\) | \(e\left(\frac{23599}{70329}\right)\) |
| \(\chi_{140659}(105,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{12554}{23443}\right)\) | \(e\left(\frac{6581}{70329}\right)\) | \(e\left(\frac{1665}{23443}\right)\) | \(e\left(\frac{3124}{3349}\right)\) | \(e\left(\frac{44243}{70329}\right)\) | \(e\left(\frac{14089}{23443}\right)\) | \(e\left(\frac{14219}{23443}\right)\) | \(e\left(\frac{13162}{70329}\right)\) | \(e\left(\frac{10979}{23443}\right)\) | \(e\left(\frac{54560}{70329}\right)\) |
| \(\chi_{140659}(106,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{12247}{23443}\right)\) | \(e\left(\frac{24401}{70329}\right)\) | \(e\left(\frac{1051}{23443}\right)\) | \(e\left(\frac{39}{3349}\right)\) | \(e\left(\frac{61142}{70329}\right)\) | \(e\left(\frac{6176}{23443}\right)\) | \(e\left(\frac{13298}{23443}\right)\) | \(e\left(\frac{48802}{70329}\right)\) | \(e\left(\frac{12520}{23443}\right)\) | \(e\left(\frac{55067}{70329}\right)\) |
| \(\chi_{140659}(109,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{6099}{23443}\right)\) | \(e\left(\frac{66503}{70329}\right)\) | \(e\left(\frac{12198}{23443}\right)\) | \(e\left(\frac{886}{3349}\right)\) | \(e\left(\frac{14471}{70329}\right)\) | \(e\left(\frac{17767}{23443}\right)\) | \(e\left(\frac{18297}{23443}\right)\) | \(e\left(\frac{62677}{70329}\right)\) | \(e\left(\frac{12301}{23443}\right)\) | \(e\left(\frac{29483}{70329}\right)\) |
| \(\chi_{140659}(113,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11483}{23443}\right)\) | \(e\left(\frac{39425}{70329}\right)\) | \(e\left(\frac{22966}{23443}\right)\) | \(e\left(\frac{336}{3349}\right)\) | \(e\left(\frac{3545}{70329}\right)\) | \(e\left(\frac{16112}{23443}\right)\) | \(e\left(\frac{11006}{23443}\right)\) | \(e\left(\frac{8521}{70329}\right)\) | \(e\left(\frac{13835}{23443}\right)\) | \(e\left(\frac{19217}{70329}\right)\) |
| \(\chi_{140659}(114,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{20989}{23443}\right)\) | \(e\left(\frac{68755}{70329}\right)\) | \(e\left(\frac{18535}{23443}\right)\) | \(e\left(\frac{2383}{3349}\right)\) | \(e\left(\frac{61393}{70329}\right)\) | \(e\left(\frac{17309}{23443}\right)\) | \(e\left(\frac{16081}{23443}\right)\) | \(e\left(\frac{67181}{70329}\right)\) | \(e\left(\frac{14227}{23443}\right)\) | \(e\left(\frac{36430}{70329}\right)\) |
| \(\chi_{140659}(117,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1499}{23443}\right)\) | \(e\left(\frac{20354}{70329}\right)\) | \(e\left(\frac{2998}{23443}\right)\) | \(e\left(\frac{500}{3349}\right)\) | \(e\left(\frac{24851}{70329}\right)\) | \(e\left(\frac{18554}{23443}\right)\) | \(e\left(\frac{4497}{23443}\right)\) | \(e\left(\frac{40708}{70329}\right)\) | \(e\left(\frac{4999}{23443}\right)\) | \(e\left(\frac{24251}{70329}\right)\) |
| \(\chi_{140659}(121,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{10877}{23443}\right)\) | \(e\left(\frac{14275}{70329}\right)\) | \(e\left(\frac{21754}{23443}\right)\) | \(e\left(\frac{1948}{3349}\right)\) | \(e\left(\frac{46906}{70329}\right)\) | \(e\left(\frac{17979}{23443}\right)\) | \(e\left(\frac{9188}{23443}\right)\) | \(e\left(\frac{28550}{70329}\right)\) | \(e\left(\frac{1070}{23443}\right)\) | \(e\left(\frac{32512}{70329}\right)\) |
| \(\chi_{140659}(122,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{6507}{23443}\right)\) | \(e\left(\frac{60689}{70329}\right)\) | \(e\left(\frac{13014}{23443}\right)\) | \(e\left(\frac{2586}{3349}\right)\) | \(e\left(\frac{9881}{70329}\right)\) | \(e\left(\frac{5833}{23443}\right)\) | \(e\left(\frac{19521}{23443}\right)\) | \(e\left(\frac{51049}{70329}\right)\) | \(e\left(\frac{1166}{23443}\right)\) | \(e\left(\frac{22853}{70329}\right)\) |
| \(\chi_{140659}(123,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{22566}{23443}\right)\) | \(e\left(\frac{431}{70329}\right)\) | \(e\left(\frac{21689}{23443}\right)\) | \(e\left(\frac{56}{3349}\right)\) | \(e\left(\frac{68129}{70329}\right)\) | \(e\left(\frac{14965}{23443}\right)\) | \(e\left(\frac{20812}{23443}\right)\) | \(e\left(\frac{862}{70329}\right)\) | \(e\left(\frac{22958}{23443}\right)\) | \(e\left(\frac{33902}{70329}\right)\) |
| \(\chi_{140659}(126,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{3756}{23443}\right)\) | \(e\left(\frac{36112}{70329}\right)\) | \(e\left(\frac{7512}{23443}\right)\) | \(e\left(\frac{3239}{3349}\right)\) | \(e\left(\frac{47380}{70329}\right)\) | \(e\left(\frac{19763}{23443}\right)\) | \(e\left(\frac{11268}{23443}\right)\) | \(e\left(\frac{1895}{70329}\right)\) | \(e\left(\frac{2986}{23443}\right)\) | \(e\left(\frac{57559}{70329}\right)\) |