Basic properties
| Modulus: | \(2058\) | |
| Conductor: | \(1029\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(294\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1029}(437,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2058.x
\(\chi_{2058}(5,\cdot)\) \(\chi_{2058}(17,\cdot)\) \(\chi_{2058}(47,\cdot)\) \(\chi_{2058}(59,\cdot)\) \(\chi_{2058}(89,\cdot)\) \(\chi_{2058}(101,\cdot)\) \(\chi_{2058}(131,\cdot)\) \(\chi_{2058}(143,\cdot)\) \(\chi_{2058}(173,\cdot)\) \(\chi_{2058}(185,\cdot)\) \(\chi_{2058}(257,\cdot)\) \(\chi_{2058}(269,\cdot)\) \(\chi_{2058}(299,\cdot)\) \(\chi_{2058}(311,\cdot)\) \(\chi_{2058}(341,\cdot)\) \(\chi_{2058}(353,\cdot)\) \(\chi_{2058}(383,\cdot)\) \(\chi_{2058}(395,\cdot)\) \(\chi_{2058}(425,\cdot)\) \(\chi_{2058}(437,\cdot)\) \(\chi_{2058}(467,\cdot)\) \(\chi_{2058}(479,\cdot)\) \(\chi_{2058}(551,\cdot)\) \(\chi_{2058}(563,\cdot)\) \(\chi_{2058}(593,\cdot)\) \(\chi_{2058}(605,\cdot)\) \(\chi_{2058}(635,\cdot)\) \(\chi_{2058}(647,\cdot)\) \(\chi_{2058}(677,\cdot)\) \(\chi_{2058}(689,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{147})$ |
| Fixed field: | Number field defined by a degree 294 polynomial (not computed) |
Values on generators
\((1373,1375)\) → \((-1,e\left(\frac{115}{294}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 2058 }(437, a) \) | \(1\) | \(1\) | \(e\left(\frac{124}{147}\right)\) | \(e\left(\frac{253}{294}\right)\) | \(e\left(\frac{47}{98}\right)\) | \(e\left(\frac{41}{147}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{191}{294}\right)\) | \(e\left(\frac{101}{147}\right)\) | \(e\left(\frac{67}{98}\right)\) | \(e\left(\frac{1}{42}\right)\) | \(e\left(\frac{139}{147}\right)\) |