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 \(\chi_{343}(23,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2058.u
\(\chi_{2058}(25,\cdot)\) \(\chi_{2058}(37,\cdot)\) \(\chi_{2058}(109,\cdot)\) \(\chi_{2058}(121,\cdot)\) \(\chi_{2058}(151,\cdot)\) \(\chi_{2058}(163,\cdot)\) \(\chi_{2058}(193,\cdot)\) \(\chi_{2058}(205,\cdot)\) \(\chi_{2058}(235,\cdot)\) \(\chi_{2058}(247,\cdot)\) \(\chi_{2058}(277,\cdot)\) \(\chi_{2058}(289,\cdot)\) \(\chi_{2058}(319,\cdot)\) \(\chi_{2058}(331,\cdot)\) \(\chi_{2058}(403,\cdot)\) \(\chi_{2058}(415,\cdot)\) \(\chi_{2058}(445,\cdot)\) \(\chi_{2058}(457,\cdot)\) \(\chi_{2058}(487,\cdot)\) \(\chi_{2058}(499,\cdot)\) \(\chi_{2058}(529,\cdot)\) \(\chi_{2058}(541,\cdot)\) \(\chi_{2058}(571,\cdot)\) \(\chi_{2058}(583,\cdot)\) \(\chi_{2058}(613,\cdot)\) \(\chi_{2058}(625,\cdot)\) \(\chi_{2058}(697,\cdot)\) \(\chi_{2058}(709,\cdot)\) \(\chi_{2058}(739,\cdot)\) \(\chi_{2058}(751,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{147})$ |
| Fixed field: | Number field defined by a degree 147 polynomial (not computed) |
Values on generators
\((1373,1375)\) → \((1,e\left(\frac{82}{147}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 2058 }(709, a) \) | \(1\) | \(1\) | \(e\left(\frac{26}{147}\right)\) | \(e\left(\frac{4}{147}\right)\) | \(e\left(\frac{48}{49}\right)\) | \(e\left(\frac{139}{147}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{71}{147}\right)\) | \(e\left(\frac{52}{147}\right)\) | \(e\left(\frac{9}{49}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{41}{147}\right)\) |