from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6017, base_ring=CyclotomicField(546))
M = H._module
chi = DirichletCharacter(H, M([0,152]))
chi.galois_orbit()
[g,chi] = znchar(Mod(34,6017))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(6017\) | |
| Conductor: | \(547\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(273\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 547.o | 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: | $\Q(\zeta_{273})$ |
| Fixed field: | Number field defined by a degree 273 polynomial (not computed) |
First 31 of 144 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{6017}(34,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{76}{273}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{152}{273}\right)\) | \(e\left(\frac{227}{273}\right)\) | \(e\left(\frac{193}{273}\right)\) | \(e\left(\frac{184}{273}\right)\) | \(e\left(\frac{76}{91}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{10}{91}\right)\) | \(e\left(\frac{269}{273}\right)\) |
| \(\chi_{6017}(56,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{53}{273}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{106}{273}\right)\) | \(e\left(\frac{205}{273}\right)\) | \(e\left(\frac{131}{273}\right)\) | \(e\left(\frac{272}{273}\right)\) | \(e\left(\frac{53}{91}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{86}{91}\right)\) | \(e\left(\frac{184}{273}\right)\) |
| \(\chi_{6017}(67,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{170}{273}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{67}{273}\right)\) | \(e\left(\frac{127}{273}\right)\) | \(e\left(\frac{209}{273}\right)\) | \(e\left(\frac{38}{273}\right)\) | \(e\left(\frac{79}{91}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{8}{91}\right)\) | \(e\left(\frac{106}{273}\right)\) |
| \(\chi_{6017}(78,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{85}{273}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{170}{273}\right)\) | \(e\left(\frac{200}{273}\right)\) | \(e\left(\frac{241}{273}\right)\) | \(e\left(\frac{19}{273}\right)\) | \(e\left(\frac{85}{91}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{4}{91}\right)\) | \(e\left(\frac{53}{273}\right)\) |
| \(\chi_{6017}(111,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{185}{273}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{97}{273}\right)\) | \(e\left(\frac{82}{273}\right)\) | \(e\left(\frac{107}{273}\right)\) | \(e\left(\frac{218}{273}\right)\) | \(e\left(\frac{3}{91}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{89}{91}\right)\) | \(e\left(\frac{19}{273}\right)\) |
| \(\chi_{6017}(122,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{118}{273}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{236}{273}\right)\) | \(e\left(\frac{101}{273}\right)\) | \(e\left(\frac{235}{273}\right)\) | \(e\left(\frac{142}{273}\right)\) | \(e\left(\frac{27}{91}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{73}{91}\right)\) | \(e\left(\frac{80}{273}\right)\) |
| \(\chi_{6017}(144,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{158}{273}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{43}{273}\right)\) | \(e\left(\frac{163}{273}\right)\) | \(e\left(\frac{236}{273}\right)\) | \(e\left(\frac{167}{273}\right)\) | \(e\left(\frac{67}{91}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{16}{91}\right)\) | \(e\left(\frac{121}{273}\right)\) |
| \(\chi_{6017}(155,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{241}{273}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{209}{273}\right)\) | \(e\left(\frac{5}{273}\right)\) | \(e\left(\frac{163}{273}\right)\) | \(e\left(\frac{253}{273}\right)\) | \(e\left(\frac{59}{91}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{82}{91}\right)\) | \(e\left(\frac{131}{273}\right)\) |
| \(\chi_{6017}(166,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{25}{273}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{50}{273}\right)\) | \(e\left(\frac{107}{273}\right)\) | \(e\left(\frac{103}{273}\right)\) | \(e\left(\frac{118}{273}\right)\) | \(e\left(\frac{25}{91}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{44}{91}\right)\) | \(e\left(\frac{128}{273}\right)\) |
| \(\chi_{6017}(177,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{197}{273}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{121}{273}\right)\) | \(e\left(\frac{46}{273}\right)\) | \(e\left(\frac{80}{273}\right)\) | \(e\left(\frac{89}{273}\right)\) | \(e\left(\frac{15}{91}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{81}{91}\right)\) | \(e\left(\frac{4}{273}\right)\) |
| \(\chi_{6017}(188,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{134}{273}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{268}{273}\right)\) | \(e\left(\frac{235}{273}\right)\) | \(e\left(\frac{17}{273}\right)\) | \(e\left(\frac{152}{273}\right)\) | \(e\left(\frac{43}{91}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{32}{91}\right)\) | \(e\left(\frac{151}{273}\right)\) |
| \(\chi_{6017}(210,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{83}{273}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{166}{273}\right)\) | \(e\left(\frac{115}{273}\right)\) | \(e\left(\frac{200}{273}\right)\) | \(e\left(\frac{86}{273}\right)\) | \(e\left(\frac{83}{91}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{66}{91}\right)\) | \(e\left(\frac{10}{273}\right)\) |
| \(\chi_{6017}(276,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{273}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{178}{273}\right)\) | \(e\left(\frac{97}{273}\right)\) | \(e\left(\frac{50}{273}\right)\) | \(e\left(\frac{158}{273}\right)\) | \(e\left(\frac{89}{91}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{62}{91}\right)\) | \(e\left(\frac{139}{273}\right)\) |
| \(\chi_{6017}(287,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{97}{273}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{194}{273}\right)\) | \(e\left(\frac{164}{273}\right)\) | \(e\left(\frac{214}{273}\right)\) | \(e\left(\frac{163}{273}\right)\) | \(e\left(\frac{6}{91}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{87}{91}\right)\) | \(e\left(\frac{38}{273}\right)\) |
| \(\chi_{6017}(452,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{68}{273}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{136}{273}\right)\) | \(e\left(\frac{160}{273}\right)\) | \(e\left(\frac{29}{273}\right)\) | \(e\left(\frac{179}{273}\right)\) | \(e\left(\frac{68}{91}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{76}{91}\right)\) | \(e\left(\frac{97}{273}\right)\) |
| \(\chi_{6017}(529,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{20}{273}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{40}{273}\right)\) | \(e\left(\frac{31}{273}\right)\) | \(e\left(\frac{137}{273}\right)\) | \(e\left(\frac{149}{273}\right)\) | \(e\left(\frac{20}{91}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{17}{91}\right)\) | \(e\left(\frac{157}{273}\right)\) |
| \(\chi_{6017}(540,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{188}{273}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{103}{273}\right)\) | \(e\left(\frac{73}{273}\right)\) | \(e\left(\frac{32}{273}\right)\) | \(e\left(\frac{254}{273}\right)\) | \(e\left(\frac{6}{91}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{87}{91}\right)\) | \(e\left(\frac{220}{273}\right)\) |
| \(\chi_{6017}(551,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{273}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{2}{273}\right)\) | \(e\left(\frac{179}{273}\right)\) | \(e\left(\frac{157}{273}\right)\) | \(e\left(\frac{103}{273}\right)\) | \(e\left(\frac{1}{91}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{60}{91}\right)\) | \(e\left(\frac{158}{273}\right)\) |
| \(\chi_{6017}(562,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{31}{273}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{62}{273}\right)\) | \(e\left(\frac{89}{273}\right)\) | \(e\left(\frac{226}{273}\right)\) | \(e\left(\frac{190}{273}\right)\) | \(e\left(\frac{31}{91}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{40}{91}\right)\) | \(e\left(\frac{257}{273}\right)\) |
| \(\chi_{6017}(705,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{164}{273}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{55}{273}\right)\) | \(e\left(\frac{145}{273}\right)\) | \(e\left(\frac{86}{273}\right)\) | \(e\left(\frac{239}{273}\right)\) | \(e\left(\frac{73}{91}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{12}{91}\right)\) | \(e\left(\frac{250}{273}\right)\) |
| \(\chi_{6017}(738,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{202}{273}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{131}{273}\right)\) | \(e\left(\frac{122}{273}\right)\) | \(e\left(\frac{46}{273}\right)\) | \(e\left(\frac{58}{273}\right)\) | \(e\left(\frac{20}{91}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{17}{91}\right)\) | \(e\left(\frac{248}{273}\right)\) |
| \(\chi_{6017}(749,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{273}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{82}{273}\right)\) | \(e\left(\frac{241}{273}\right)\) | \(e\left(\frac{158}{273}\right)\) | \(e\left(\frac{128}{273}\right)\) | \(e\left(\frac{41}{91}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{3}{91}\right)\) | \(e\left(\frac{199}{273}\right)\) |
| \(\chi_{6017}(760,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{206}{273}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{139}{273}\right)\) | \(e\left(\frac{19}{273}\right)\) | \(e\left(\frac{128}{273}\right)\) | \(e\left(\frac{197}{273}\right)\) | \(e\left(\frac{24}{91}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{75}{91}\right)\) | \(e\left(\frac{61}{273}\right)\) |
| \(\chi_{6017}(848,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{124}{273}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{248}{273}\right)\) | \(e\left(\frac{83}{273}\right)\) | \(e\left(\frac{85}{273}\right)\) | \(e\left(\frac{214}{273}\right)\) | \(e\left(\frac{33}{91}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{69}{91}\right)\) | \(e\left(\frac{209}{273}\right)\) |
| \(\chi_{6017}(859,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{86}{273}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{172}{273}\right)\) | \(e\left(\frac{106}{273}\right)\) | \(e\left(\frac{125}{273}\right)\) | \(e\left(\frac{122}{273}\right)\) | \(e\left(\frac{86}{91}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{64}{91}\right)\) | \(e\left(\frac{211}{273}\right)\) |
| \(\chi_{6017}(914,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{110}{273}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{220}{273}\right)\) | \(e\left(\frac{34}{273}\right)\) | \(e\left(\frac{71}{273}\right)\) | \(e\left(\frac{137}{273}\right)\) | \(e\left(\frac{19}{91}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{48}{91}\right)\) | \(e\left(\frac{181}{273}\right)\) |
| \(\chi_{6017}(947,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{181}{273}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{89}{273}\right)\) | \(e\left(\frac{185}{273}\right)\) | \(e\left(\frac{25}{273}\right)\) | \(e\left(\frac{79}{273}\right)\) | \(e\left(\frac{90}{91}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{31}{91}\right)\) | \(e\left(\frac{206}{273}\right)\) |
| \(\chi_{6017}(1002,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{11}{273}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{22}{273}\right)\) | \(e\left(\frac{58}{273}\right)\) | \(e\left(\frac{89}{273}\right)\) | \(e\left(\frac{41}{273}\right)\) | \(e\left(\frac{11}{91}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{23}{91}\right)\) | \(e\left(\frac{100}{273}\right)\) |
| \(\chi_{6017}(1024,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{273}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{10}{273}\right)\) | \(e\left(\frac{76}{273}\right)\) | \(e\left(\frac{239}{273}\right)\) | \(e\left(\frac{242}{273}\right)\) | \(e\left(\frac{5}{91}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{27}{91}\right)\) | \(e\left(\frac{244}{273}\right)\) |
| \(\chi_{6017}(1046,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{80}{273}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{160}{273}\right)\) | \(e\left(\frac{124}{273}\right)\) | \(e\left(\frac{2}{273}\right)\) | \(e\left(\frac{50}{273}\right)\) | \(e\left(\frac{80}{91}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{68}{91}\right)\) | \(e\left(\frac{82}{273}\right)\) |
| \(\chi_{6017}(1057,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{107}{273}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{214}{273}\right)\) | \(e\left(\frac{43}{273}\right)\) | \(e\left(\frac{146}{273}\right)\) | \(e\left(\frac{101}{273}\right)\) | \(e\left(\frac{16}{91}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{50}{91}\right)\) | \(e\left(\frac{253}{273}\right)\) |