from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4067, base_ring=CyclotomicField(574))
M = H._module
chi = DirichletCharacter(H, M([41,364]))
chi.galois_orbit()
[g,chi] = znchar(Mod(27,4067))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(4067\) | |
| Conductor: | \(4067\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(574\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Related number fields
| Field of values: | $\Q(\zeta_{287})$ |
| Fixed field: | Number field defined by a degree 574 polynomial (not computed) |
First 31 of 240 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{4067}(27,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{141}{287}\right)\) | \(e\left(\frac{419}{574}\right)\) | \(e\left(\frac{282}{287}\right)\) | \(e\left(\frac{111}{574}\right)\) | \(e\left(\frac{127}{574}\right)\) | \(e\left(\frac{136}{287}\right)\) | \(e\left(\frac{132}{287}\right)\) | \(e\left(\frac{393}{574}\right)\) | \(e\left(\frac{22}{287}\right)\) | \(e\left(\frac{409}{574}\right)\) |
| \(\chi_{4067}(41,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{222}{287}\right)\) | \(e\left(\frac{275}{574}\right)\) | \(e\left(\frac{157}{287}\right)\) | \(e\left(\frac{303}{574}\right)\) | \(e\left(\frac{145}{574}\right)\) | \(e\left(\frac{92}{287}\right)\) | \(e\left(\frac{275}{287}\right)\) | \(e\left(\frac{173}{574}\right)\) | \(e\left(\frac{285}{287}\right)\) | \(e\left(\frac{15}{574}\right)\) |
| \(\chi_{4067}(69,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{216}{287}\right)\) | \(e\left(\frac{477}{574}\right)\) | \(e\left(\frac{145}{287}\right)\) | \(e\left(\frac{225}{574}\right)\) | \(e\left(\frac{335}{574}\right)\) | \(e\left(\frac{74}{287}\right)\) | \(e\left(\frac{190}{287}\right)\) | \(e\left(\frac{83}{574}\right)\) | \(e\left(\frac{223}{287}\right)\) | \(e\left(\frac{193}{574}\right)\) |
| \(\chi_{4067}(90,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{110}{287}\right)\) | \(e\left(\frac{219}{574}\right)\) | \(e\left(\frac{220}{287}\right)\) | \(e\left(\frac{569}{574}\right)\) | \(e\left(\frac{439}{574}\right)\) | \(e\left(\frac{43}{287}\right)\) | \(e\left(\frac{219}{287}\right)\) | \(e\left(\frac{215}{574}\right)\) | \(e\left(\frac{180}{287}\right)\) | \(e\left(\frac{85}{574}\right)\) |
| \(\chi_{4067}(104,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{198}{287}\right)\) | \(e\left(\frac{509}{574}\right)\) | \(e\left(\frac{109}{287}\right)\) | \(e\left(\frac{565}{574}\right)\) | \(e\left(\frac{331}{574}\right)\) | \(e\left(\frac{20}{287}\right)\) | \(e\left(\frac{222}{287}\right)\) | \(e\left(\frac{387}{574}\right)\) | \(e\left(\frac{37}{287}\right)\) | \(e\left(\frac{153}{574}\right)\) |
| \(\chi_{4067}(111,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{158}{287}\right)\) | \(e\left(\frac{325}{574}\right)\) | \(e\left(\frac{29}{287}\right)\) | \(e\left(\frac{45}{574}\right)\) | \(e\left(\frac{67}{574}\right)\) | \(e\left(\frac{187}{287}\right)\) | \(e\left(\frac{38}{287}\right)\) | \(e\left(\frac{361}{574}\right)\) | \(e\left(\frac{102}{287}\right)\) | \(e\left(\frac{383}{574}\right)\) |
| \(\chi_{4067}(132,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{220}{287}\right)\) | \(e\left(\frac{151}{574}\right)\) | \(e\left(\frac{153}{287}\right)\) | \(e\left(\frac{277}{574}\right)\) | \(e\left(\frac{17}{574}\right)\) | \(e\left(\frac{86}{287}\right)\) | \(e\left(\frac{151}{287}\right)\) | \(e\left(\frac{143}{574}\right)\) | \(e\left(\frac{73}{287}\right)\) | \(e\left(\frac{457}{574}\right)\) |
| \(\chi_{4067}(153,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{44}{287}\right)\) | \(e\left(\frac{145}{574}\right)\) | \(e\left(\frac{88}{287}\right)\) | \(e\left(\frac{285}{574}\right)\) | \(e\left(\frac{233}{574}\right)\) | \(e\left(\frac{132}{287}\right)\) | \(e\left(\frac{145}{287}\right)\) | \(e\left(\frac{373}{574}\right)\) | \(e\left(\frac{72}{287}\right)\) | \(e\left(\frac{321}{574}\right)\) |
| \(\chi_{4067}(160,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{235}{287}\right)\) | \(e\left(\frac{507}{574}\right)\) | \(e\left(\frac{183}{287}\right)\) | \(e\left(\frac{185}{574}\right)\) | \(e\left(\frac{403}{574}\right)\) | \(e\left(\frac{131}{287}\right)\) | \(e\left(\frac{220}{287}\right)\) | \(e\left(\frac{81}{574}\right)\) | \(e\left(\frac{228}{287}\right)\) | \(e\left(\frac{299}{574}\right)\) |
| \(\chi_{4067}(202,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{142}{287}\right)\) | \(e\left(\frac{481}{574}\right)\) | \(e\left(\frac{284}{287}\right)\) | \(e\left(\frac{411}{574}\right)\) | \(e\left(\frac{191}{574}\right)\) | \(e\left(\frac{139}{287}\right)\) | \(e\left(\frac{194}{287}\right)\) | \(e\left(\frac{121}{574}\right)\) | \(e\left(\frac{128}{287}\right)\) | \(e\left(\frac{475}{574}\right)\) |
| \(\chi_{4067}(230,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{185}{287}\right)\) | \(e\left(\frac{277}{574}\right)\) | \(e\left(\frac{83}{287}\right)\) | \(e\left(\frac{109}{574}\right)\) | \(e\left(\frac{73}{574}\right)\) | \(e\left(\frac{268}{287}\right)\) | \(e\left(\frac{277}{287}\right)\) | \(e\left(\frac{479}{574}\right)\) | \(e\left(\frac{94}{287}\right)\) | \(e\left(\frac{443}{574}\right)\) |
| \(\chi_{4067}(258,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{53}{287}\right)\) | \(e\left(\frac{129}{574}\right)\) | \(e\left(\frac{106}{287}\right)\) | \(e\left(\frac{115}{574}\right)\) | \(e\left(\frac{235}{574}\right)\) | \(e\left(\frac{159}{287}\right)\) | \(e\left(\frac{129}{287}\right)\) | \(e\left(\frac{221}{574}\right)\) | \(e\left(\frac{165}{287}\right)\) | \(e\left(\frac{341}{574}\right)\) |
| \(\chi_{4067}(265,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{55}{287}\right)\) | \(e\left(\frac{253}{574}\right)\) | \(e\left(\frac{110}{287}\right)\) | \(e\left(\frac{141}{574}\right)\) | \(e\left(\frac{363}{574}\right)\) | \(e\left(\frac{165}{287}\right)\) | \(e\left(\frac{253}{287}\right)\) | \(e\left(\frac{251}{574}\right)\) | \(e\left(\frac{90}{287}\right)\) | \(e\left(\frac{473}{574}\right)\) |
| \(\chi_{4067}(272,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{169}{287}\right)\) | \(e\left(\frac{433}{574}\right)\) | \(e\left(\frac{51}{287}\right)\) | \(e\left(\frac{475}{574}\right)\) | \(e\left(\frac{197}{574}\right)\) | \(e\left(\frac{220}{287}\right)\) | \(e\left(\frac{146}{287}\right)\) | \(e\left(\frac{239}{574}\right)\) | \(e\left(\frac{120}{287}\right)\) | \(e\left(\frac{535}{574}\right)\) |
| \(\chi_{4067}(279,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{227}{287}\right)\) | \(e\left(\frac{11}{574}\right)\) | \(e\left(\frac{167}{287}\right)\) | \(e\left(\frac{81}{574}\right)\) | \(e\left(\frac{465}{574}\right)\) | \(e\left(\frac{107}{287}\right)\) | \(e\left(\frac{11}{287}\right)\) | \(e\left(\frac{535}{574}\right)\) | \(e\left(\frac{241}{287}\right)\) | \(e\left(\frac{345}{574}\right)\) |
| \(\chi_{4067}(286,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{152}{287}\right)\) | \(e\left(\frac{527}{574}\right)\) | \(e\left(\frac{17}{287}\right)\) | \(e\left(\frac{541}{574}\right)\) | \(e\left(\frac{257}{574}\right)\) | \(e\left(\frac{169}{287}\right)\) | \(e\left(\frac{240}{287}\right)\) | \(e\left(\frac{271}{574}\right)\) | \(e\left(\frac{40}{287}\right)\) | \(e\left(\frac{561}{574}\right)\) |
| \(\chi_{4067}(300,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{79}{287}\right)\) | \(e\left(\frac{19}{574}\right)\) | \(e\left(\frac{158}{287}\right)\) | \(e\left(\frac{453}{574}\right)\) | \(e\left(\frac{177}{574}\right)\) | \(e\left(\frac{237}{287}\right)\) | \(e\left(\frac{19}{287}\right)\) | \(e\left(\frac{37}{574}\right)\) | \(e\left(\frac{51}{287}\right)\) | \(e\left(\frac{335}{574}\right)\) |
| \(\chi_{4067}(314,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{118}{287}\right)\) | \(e\left(\frac{141}{574}\right)\) | \(e\left(\frac{236}{287}\right)\) | \(e\left(\frac{99}{574}\right)\) | \(e\left(\frac{377}{574}\right)\) | \(e\left(\frac{67}{287}\right)\) | \(e\left(\frac{141}{287}\right)\) | \(e\left(\frac{335}{574}\right)\) | \(e\left(\frac{167}{287}\right)\) | \(e\left(\frac{39}{574}\right)\) |
| \(\chi_{4067}(335,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{47}{287}\right)\) | \(e\left(\frac{331}{574}\right)\) | \(e\left(\frac{94}{287}\right)\) | \(e\left(\frac{37}{574}\right)\) | \(e\left(\frac{425}{574}\right)\) | \(e\left(\frac{141}{287}\right)\) | \(e\left(\frac{44}{287}\right)\) | \(e\left(\frac{131}{574}\right)\) | \(e\left(\frac{103}{287}\right)\) | \(e\left(\frac{519}{574}\right)\) |
| \(\chi_{4067}(349,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{114}{287}\right)\) | \(e\left(\frac{467}{574}\right)\) | \(e\left(\frac{228}{287}\right)\) | \(e\left(\frac{47}{574}\right)\) | \(e\left(\frac{121}{574}\right)\) | \(e\left(\frac{55}{287}\right)\) | \(e\left(\frac{180}{287}\right)\) | \(e\left(\frac{275}{574}\right)\) | \(e\left(\frac{30}{287}\right)\) | \(e\left(\frac{349}{574}\right)\) |
| \(\chi_{4067}(363,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{174}{287}\right)\) | \(e\left(\frac{169}{574}\right)\) | \(e\left(\frac{61}{287}\right)\) | \(e\left(\frac{253}{574}\right)\) | \(e\left(\frac{517}{574}\right)\) | \(e\left(\frac{235}{287}\right)\) | \(e\left(\frac{169}{287}\right)\) | \(e\left(\frac{27}{574}\right)\) | \(e\left(\frac{76}{287}\right)\) | \(e\left(\frac{291}{574}\right)\) |
| \(\chi_{4067}(370,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{127}{287}\right)\) | \(e\left(\frac{125}{574}\right)\) | \(e\left(\frac{254}{287}\right)\) | \(e\left(\frac{503}{574}\right)\) | \(e\left(\frac{379}{574}\right)\) | \(e\left(\frac{94}{287}\right)\) | \(e\left(\frac{125}{287}\right)\) | \(e\left(\frac{183}{574}\right)\) | \(e\left(\frac{260}{287}\right)\) | \(e\left(\frac{59}{574}\right)\) |
| \(\chi_{4067}(419,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{253}{287}\right)\) | \(e\left(\frac{475}{574}\right)\) | \(e\left(\frac{219}{287}\right)\) | \(e\left(\frac{419}{574}\right)\) | \(e\left(\frac{407}{574}\right)\) | \(e\left(\frac{185}{287}\right)\) | \(e\left(\frac{188}{287}\right)\) | \(e\left(\frac{351}{574}\right)\) | \(e\left(\frac{127}{287}\right)\) | \(e\left(\frac{339}{574}\right)\) |
| \(\chi_{4067}(426,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{248}{287}\right)\) | \(e\left(\frac{165}{574}\right)\) | \(e\left(\frac{209}{287}\right)\) | \(e\left(\frac{67}{574}\right)\) | \(e\left(\frac{87}{574}\right)\) | \(e\left(\frac{170}{287}\right)\) | \(e\left(\frac{165}{287}\right)\) | \(e\left(\frac{563}{574}\right)\) | \(e\left(\frac{171}{287}\right)\) | \(e\left(\frac{9}{574}\right)\) |
| \(\chi_{4067}(496,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{65}{287}\right)\) | \(e\left(\frac{299}{574}\right)\) | \(e\left(\frac{130}{287}\right)\) | \(e\left(\frac{271}{574}\right)\) | \(e\left(\frac{429}{574}\right)\) | \(e\left(\frac{195}{287}\right)\) | \(e\left(\frac{12}{287}\right)\) | \(e\left(\frac{401}{574}\right)\) | \(e\left(\frac{2}{287}\right)\) | \(e\left(\frac{559}{574}\right)\) |
| \(\chi_{4067}(510,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{13}{287}\right)\) | \(e\left(\frac{519}{574}\right)\) | \(e\left(\frac{26}{287}\right)\) | \(e\left(\frac{169}{574}\right)\) | \(e\left(\frac{545}{574}\right)\) | \(e\left(\frac{39}{287}\right)\) | \(e\left(\frac{232}{287}\right)\) | \(e\left(\frac{195}{574}\right)\) | \(e\left(\frac{230}{287}\right)\) | \(e\left(\frac{571}{574}\right)\) |
| \(\chi_{4067}(524,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{150}{287}\right)\) | \(e\left(\frac{403}{574}\right)\) | \(e\left(\frac{13}{287}\right)\) | \(e\left(\frac{515}{574}\right)\) | \(e\left(\frac{129}{574}\right)\) | \(e\left(\frac{163}{287}\right)\) | \(e\left(\frac{116}{287}\right)\) | \(e\left(\frac{241}{574}\right)\) | \(e\left(\frac{115}{287}\right)\) | \(e\left(\frac{429}{574}\right)\) |
| \(\chi_{4067}(531,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{131}{287}\right)\) | \(e\left(\frac{373}{574}\right)\) | \(e\left(\frac{262}{287}\right)\) | \(e\left(\frac{555}{574}\right)\) | \(e\left(\frac{61}{574}\right)\) | \(e\left(\frac{106}{287}\right)\) | \(e\left(\frac{86}{287}\right)\) | \(e\left(\frac{243}{574}\right)\) | \(e\left(\frac{110}{287}\right)\) | \(e\left(\frac{323}{574}\right)\) |
| \(\chi_{4067}(559,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{272}{287}\right)\) | \(e\left(\frac{505}{574}\right)\) | \(e\left(\frac{257}{287}\right)\) | \(e\left(\frac{379}{574}\right)\) | \(e\left(\frac{475}{574}\right)\) | \(e\left(\frac{242}{287}\right)\) | \(e\left(\frac{218}{287}\right)\) | \(e\left(\frac{349}{574}\right)\) | \(e\left(\frac{132}{287}\right)\) | \(e\left(\frac{445}{574}\right)\) |
| \(\chi_{4067}(566,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{162}{287}\right)\) | \(e\left(\frac{573}{574}\right)\) | \(e\left(\frac{37}{287}\right)\) | \(e\left(\frac{97}{574}\right)\) | \(e\left(\frac{323}{574}\right)\) | \(e\left(\frac{199}{287}\right)\) | \(e\left(\frac{286}{287}\right)\) | \(e\left(\frac{421}{574}\right)\) | \(e\left(\frac{239}{287}\right)\) | \(e\left(\frac{73}{574}\right)\) |
| \(\chi_{4067}(573,\cdot)\) | \(-1\) | \(1\) | \(e\left(\frac{31}{287}\right)\) | \(e\left(\frac{487}{574}\right)\) | \(e\left(\frac{62}{287}\right)\) | \(e\left(\frac{403}{574}\right)\) | \(e\left(\frac{549}{574}\right)\) | \(e\left(\frac{93}{287}\right)\) | \(e\left(\frac{200}{287}\right)\) | \(e\left(\frac{465}{574}\right)\) | \(e\left(\frac{129}{287}\right)\) | \(e\left(\frac{37}{574}\right)\) |