Basic properties
| Modulus: | \(2012\) | |
| Conductor: | \(503\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(251\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{503}(117,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2012.e
\(\chi_{2012}(9,\cdot)\) \(\chi_{2012}(13,\cdot)\) \(\chi_{2012}(21,\cdot)\) \(\chi_{2012}(25,\cdot)\) \(\chi_{2012}(33,\cdot)\) \(\chi_{2012}(49,\cdot)\) \(\chi_{2012}(61,\cdot)\) \(\chi_{2012}(69,\cdot)\) \(\chi_{2012}(73,\cdot)\) \(\chi_{2012}(77,\cdot)\) \(\chi_{2012}(81,\cdot)\) \(\chi_{2012}(85,\cdot)\) \(\chi_{2012}(97,\cdot)\) \(\chi_{2012}(113,\cdot)\) \(\chi_{2012}(117,\cdot)\) \(\chi_{2012}(121,\cdot)\) \(\chi_{2012}(129,\cdot)\) \(\chi_{2012}(141,\cdot)\) \(\chi_{2012}(145,\cdot)\) \(\chi_{2012}(161,\cdot)\) \(\chi_{2012}(169,\cdot)\) \(\chi_{2012}(173,\cdot)\) \(\chi_{2012}(177,\cdot)\) \(\chi_{2012}(185,\cdot)\) \(\chi_{2012}(189,\cdot)\) \(\chi_{2012}(197,\cdot)\) \(\chi_{2012}(201,\cdot)\) \(\chi_{2012}(205,\cdot)\) \(\chi_{2012}(225,\cdot)\) \(\chi_{2012}(229,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{251})$ |
| Fixed field: | Number field defined by a degree 251 polynomial (not computed) |
Values on generators
\((1007,5)\) → \((1,e\left(\frac{218}{251}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 2012 }(117, a) \) | \(1\) | \(1\) | \(e\left(\frac{123}{251}\right)\) | \(e\left(\frac{218}{251}\right)\) | \(e\left(\frac{174}{251}\right)\) | \(e\left(\frac{246}{251}\right)\) | \(e\left(\frac{120}{251}\right)\) | \(e\left(\frac{175}{251}\right)\) | \(e\left(\frac{90}{251}\right)\) | \(e\left(\frac{224}{251}\right)\) | \(e\left(\frac{211}{251}\right)\) | \(e\left(\frac{46}{251}\right)\) |