from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2058, base_ring=CyclotomicField(294))
M = H._module
chi = DirichletCharacter(H, M([0,58]))
chi.galois_orbit()
[g,chi] = znchar(Mod(25,2058))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Basic properties
| Modulus: | \(2058\) | |
| Conductor: | \(343\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(147\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from 343.k | 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: | $\Q(\zeta_{147})$ |
| Fixed field: | Number field defined by a degree 147 polynomial (not computed) |
First 31 of 84 characters in Galois orbit
| Character | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{2058}(25,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{106}{147}\right)\) | \(e\left(\frac{5}{147}\right)\) | \(e\left(\frac{11}{49}\right)\) | \(e\left(\frac{137}{147}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{52}{147}\right)\) | \(e\left(\frac{65}{147}\right)\) | \(e\left(\frac{48}{49}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{88}{147}\right)\) |
| \(\chi_{2058}(37,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{44}{147}\right)\) | \(e\left(\frac{52}{147}\right)\) | \(e\left(\frac{36}{49}\right)\) | \(e\left(\frac{43}{147}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{41}{147}\right)\) | \(e\left(\frac{88}{147}\right)\) | \(e\left(\frac{19}{49}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{92}{147}\right)\) |
| \(\chi_{2058}(109,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{139}{147}\right)\) | \(e\left(\frac{44}{147}\right)\) | \(e\left(\frac{38}{49}\right)\) | \(e\left(\frac{59}{147}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{46}{147}\right)\) | \(e\left(\frac{131}{147}\right)\) | \(e\left(\frac{1}{49}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{10}{147}\right)\) |
| \(\chi_{2058}(121,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{5}{147}\right)\) | \(e\left(\frac{46}{147}\right)\) | \(e\left(\frac{13}{49}\right)\) | \(e\left(\frac{55}{147}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{8}{147}\right)\) | \(e\left(\frac{10}{147}\right)\) | \(e\left(\frac{30}{49}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{104}{147}\right)\) |
| \(\chi_{2058}(151,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{61}{147}\right)\) | \(e\left(\frac{32}{147}\right)\) | \(e\left(\frac{41}{49}\right)\) | \(e\left(\frac{83}{147}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{127}{147}\right)\) | \(e\left(\frac{122}{147}\right)\) | \(e\left(\frac{23}{49}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{34}{147}\right)\) |
| \(\chi_{2058}(163,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{122}{147}\right)\) | \(e\left(\frac{64}{147}\right)\) | \(e\left(\frac{33}{49}\right)\) | \(e\left(\frac{19}{147}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{107}{147}\right)\) | \(e\left(\frac{97}{147}\right)\) | \(e\left(\frac{46}{49}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{68}{147}\right)\) |
| \(\chi_{2058}(193,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{67}{147}\right)\) | \(e\left(\frac{146}{147}\right)\) | \(e\left(\frac{37}{49}\right)\) | \(e\left(\frac{2}{147}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{19}{147}\right)\) | \(e\left(\frac{134}{147}\right)\) | \(e\left(\frac{10}{49}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{100}{147}\right)\) |
| \(\chi_{2058}(205,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{134}{147}\right)\) | \(e\left(\frac{145}{147}\right)\) | \(e\left(\frac{25}{49}\right)\) | \(e\left(\frac{4}{147}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{38}{147}\right)\) | \(e\left(\frac{121}{147}\right)\) | \(e\left(\frac{20}{49}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{53}{147}\right)\) |
| \(\chi_{2058}(235,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{10}{147}\right)\) | \(e\left(\frac{92}{147}\right)\) | \(e\left(\frac{26}{49}\right)\) | \(e\left(\frac{110}{147}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{16}{147}\right)\) | \(e\left(\frac{20}{147}\right)\) | \(e\left(\frac{11}{49}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{61}{147}\right)\) |
| \(\chi_{2058}(247,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{41}{147}\right)\) | \(e\left(\frac{142}{147}\right)\) | \(e\left(\frac{38}{49}\right)\) | \(e\left(\frac{10}{147}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{95}{147}\right)\) | \(e\left(\frac{82}{147}\right)\) | \(e\left(\frac{1}{49}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{59}{147}\right)\) |
| \(\chi_{2058}(277,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{37}{147}\right)\) | \(e\left(\frac{17}{147}\right)\) | \(e\left(\frac{8}{49}\right)\) | \(e\left(\frac{113}{147}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{118}{147}\right)\) | \(e\left(\frac{74}{147}\right)\) | \(e\left(\frac{26}{49}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{64}{147}\right)\) |
| \(\chi_{2058}(289,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{137}{147}\right)\) | \(e\left(\frac{55}{147}\right)\) | \(e\left(\frac{23}{49}\right)\) | \(e\left(\frac{37}{147}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{131}{147}\right)\) | \(e\left(\frac{127}{147}\right)\) | \(e\left(\frac{38}{49}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{86}{147}\right)\) |
| \(\chi_{2058}(319,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{1}{147}\right)\) | \(e\left(\frac{68}{147}\right)\) | \(e\left(\frac{32}{49}\right)\) | \(e\left(\frac{11}{147}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{31}{147}\right)\) | \(e\left(\frac{2}{147}\right)\) | \(e\left(\frac{6}{49}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{109}{147}\right)\) |
| \(\chi_{2058}(331,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{128}{147}\right)\) | \(e\left(\frac{31}{147}\right)\) | \(e\left(\frac{29}{49}\right)\) | \(e\left(\frac{85}{147}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{146}{147}\right)\) | \(e\left(\frac{109}{147}\right)\) | \(e\left(\frac{33}{49}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{134}{147}\right)\) |
| \(\chi_{2058}(403,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{34}{147}\right)\) | \(e\left(\frac{107}{147}\right)\) | \(e\left(\frac{10}{49}\right)\) | \(e\left(\frac{80}{147}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{25}{147}\right)\) | \(e\left(\frac{68}{147}\right)\) | \(e\left(\frac{8}{49}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{31}{147}\right)\) |
| \(\chi_{2058}(415,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{89}{147}\right)\) | \(e\left(\frac{25}{147}\right)\) | \(e\left(\frac{6}{49}\right)\) | \(e\left(\frac{97}{147}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{113}{147}\right)\) | \(e\left(\frac{31}{147}\right)\) | \(e\left(\frac{44}{49}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{146}{147}\right)\) |
| \(\chi_{2058}(445,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{103}{147}\right)\) | \(e\left(\frac{95}{147}\right)\) | \(e\left(\frac{13}{49}\right)\) | \(e\left(\frac{104}{147}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{106}{147}\right)\) | \(e\left(\frac{59}{147}\right)\) | \(e\left(\frac{30}{49}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{55}{147}\right)\) |
| \(\chi_{2058}(457,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{59}{147}\right)\) | \(e\left(\frac{43}{147}\right)\) | \(e\left(\frac{26}{49}\right)\) | \(e\left(\frac{61}{147}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{65}{147}\right)\) | \(e\left(\frac{118}{147}\right)\) | \(e\left(\frac{11}{49}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{110}{147}\right)\) |
| \(\chi_{2058}(487,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{109}{147}\right)\) | \(e\left(\frac{62}{147}\right)\) | \(e\left(\frac{9}{49}\right)\) | \(e\left(\frac{23}{147}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{145}{147}\right)\) | \(e\left(\frac{71}{147}\right)\) | \(e\left(\frac{17}{49}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{121}{147}\right)\) |
| \(\chi_{2058}(499,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{71}{147}\right)\) | \(e\left(\frac{124}{147}\right)\) | \(e\left(\frac{18}{49}\right)\) | \(e\left(\frac{46}{147}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{143}{147}\right)\) | \(e\left(\frac{142}{147}\right)\) | \(e\left(\frac{34}{49}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{95}{147}\right)\) |
| \(\chi_{2058}(529,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{52}{147}\right)\) | \(e\left(\frac{8}{147}\right)\) | \(e\left(\frac{47}{49}\right)\) | \(e\left(\frac{131}{147}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{142}{147}\right)\) | \(e\left(\frac{104}{147}\right)\) | \(e\left(\frac{18}{49}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{82}{147}\right)\) |
| \(\chi_{2058}(541,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{125}{147}\right)\) | \(e\left(\frac{121}{147}\right)\) | \(e\left(\frac{31}{49}\right)\) | \(e\left(\frac{52}{147}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{53}{147}\right)\) | \(e\left(\frac{103}{147}\right)\) | \(e\left(\frac{15}{49}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{101}{147}\right)\) |
| \(\chi_{2058}(571,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{79}{147}\right)\) | \(e\left(\frac{80}{147}\right)\) | \(e\left(\frac{29}{49}\right)\) | \(e\left(\frac{134}{147}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{97}{147}\right)\) | \(e\left(\frac{11}{147}\right)\) | \(e\left(\frac{33}{49}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{85}{147}\right)\) |
| \(\chi_{2058}(583,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{74}{147}\right)\) | \(e\left(\frac{34}{147}\right)\) | \(e\left(\frac{16}{49}\right)\) | \(e\left(\frac{79}{147}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{89}{147}\right)\) | \(e\left(\frac{1}{147}\right)\) | \(e\left(\frac{3}{49}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{128}{147}\right)\) |
| \(\chi_{2058}(613,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{43}{147}\right)\) | \(e\left(\frac{131}{147}\right)\) | \(e\left(\frac{4}{49}\right)\) | \(e\left(\frac{32}{147}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{10}{147}\right)\) | \(e\left(\frac{86}{147}\right)\) | \(e\left(\frac{13}{49}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{130}{147}\right)\) |
| \(\chi_{2058}(625,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{65}{147}\right)\) | \(e\left(\frac{10}{147}\right)\) | \(e\left(\frac{22}{49}\right)\) | \(e\left(\frac{127}{147}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{104}{147}\right)\) | \(e\left(\frac{130}{147}\right)\) | \(e\left(\frac{47}{49}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{29}{147}\right)\) |
| \(\chi_{2058}(697,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{76}{147}\right)\) | \(e\left(\frac{23}{147}\right)\) | \(e\left(\frac{31}{49}\right)\) | \(e\left(\frac{101}{147}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{4}{147}\right)\) | \(e\left(\frac{5}{147}\right)\) | \(e\left(\frac{15}{49}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{52}{147}\right)\) |
| \(\chi_{2058}(709,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{26}{147}\right)\) | \(e\left(\frac{4}{147}\right)\) | \(e\left(\frac{48}{49}\right)\) | \(e\left(\frac{139}{147}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{71}{147}\right)\) | \(e\left(\frac{52}{147}\right)\) | \(e\left(\frac{9}{49}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{41}{147}\right)\) |
| \(\chi_{2058}(739,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{145}{147}\right)\) | \(e\left(\frac{11}{147}\right)\) | \(e\left(\frac{34}{49}\right)\) | \(e\left(\frac{125}{147}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{85}{147}\right)\) | \(e\left(\frac{143}{147}\right)\) | \(e\left(\frac{37}{49}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{76}{147}\right)\) |
| \(\chi_{2058}(751,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{143}{147}\right)\) | \(e\left(\frac{22}{147}\right)\) | \(e\left(\frac{19}{49}\right)\) | \(e\left(\frac{103}{147}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{23}{147}\right)\) | \(e\left(\frac{139}{147}\right)\) | \(e\left(\frac{25}{49}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{5}{147}\right)\) |
| \(\chi_{2058}(781,\cdot)\) | \(1\) | \(1\) | \(e\left(\frac{4}{147}\right)\) | \(e\left(\frac{125}{147}\right)\) | \(e\left(\frac{30}{49}\right)\) | \(e\left(\frac{44}{147}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{124}{147}\right)\) | \(e\left(\frac{8}{147}\right)\) | \(e\left(\frac{24}{49}\right)\) | \(e\left(\frac{20}{21}\right)\) | \(e\left(\frac{142}{147}\right)\) |