Basic properties
| Modulus: | \(8013\) | |
| Conductor: | \(2671\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(267\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2671}(40,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8013.u
\(\chi_{8013}(40,\cdot)\) \(\chi_{8013}(142,\cdot)\) \(\chi_{8013}(151,\cdot)\) \(\chi_{8013}(166,\cdot)\) \(\chi_{8013}(217,\cdot)\) \(\chi_{8013}(226,\cdot)\) \(\chi_{8013}(289,\cdot)\) \(\chi_{8013}(322,\cdot)\) \(\chi_{8013}(331,\cdot)\) \(\chi_{8013}(364,\cdot)\) \(\chi_{8013}(412,\cdot)\) \(\chi_{8013}(430,\cdot)\) \(\chi_{8013}(451,\cdot)\) \(\chi_{8013}(454,\cdot)\) \(\chi_{8013}(505,\cdot)\) \(\chi_{8013}(535,\cdot)\) \(\chi_{8013}(589,\cdot)\) \(\chi_{8013}(601,\cdot)\) \(\chi_{8013}(616,\cdot)\) \(\chi_{8013}(655,\cdot)\) \(\chi_{8013}(715,\cdot)\) \(\chi_{8013}(754,\cdot)\) \(\chi_{8013}(796,\cdot)\) \(\chi_{8013}(862,\cdot)\) \(\chi_{8013}(874,\cdot)\) \(\chi_{8013}(895,\cdot)\) \(\chi_{8013}(964,\cdot)\) \(\chi_{8013}(973,\cdot)\) \(\chi_{8013}(988,\cdot)\) \(\chi_{8013}(1015,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{267})$ |
| Fixed field: | Number field defined by a degree 267 polynomial (not computed) |
Values on generators
\((2672,7)\) → \((1,e\left(\frac{154}{267}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8013 }(40, a) \) | \(1\) | \(1\) | \(e\left(\frac{52}{89}\right)\) | \(e\left(\frac{15}{89}\right)\) | \(e\left(\frac{130}{267}\right)\) | \(e\left(\frac{154}{267}\right)\) | \(e\left(\frac{67}{89}\right)\) | \(e\left(\frac{19}{267}\right)\) | \(e\left(\frac{17}{89}\right)\) | \(e\left(\frac{86}{89}\right)\) | \(e\left(\frac{43}{267}\right)\) | \(e\left(\frac{30}{89}\right)\) |