Basic properties
| Modulus: | \(8036\) | |
| Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(168\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2009}(437,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8036.eb
\(\chi_{8036}(437,\cdot)\) \(\chi_{8036}(465,\cdot)\) \(\chi_{8036}(577,\cdot)\) \(\chi_{8036}(817,\cdot)\) \(\chi_{8036}(929,\cdot)\) \(\chi_{8036}(957,\cdot)\) \(\chi_{8036}(1069,\cdot)\) \(\chi_{8036}(1473,\cdot)\) \(\chi_{8036}(1585,\cdot)\) \(\chi_{8036}(1613,\cdot)\) \(\chi_{8036}(1725,\cdot)\) \(\chi_{8036}(1965,\cdot)\) \(\chi_{8036}(2105,\cdot)\) \(\chi_{8036}(2217,\cdot)\) \(\chi_{8036}(2621,\cdot)\) \(\chi_{8036}(2733,\cdot)\) \(\chi_{8036}(2761,\cdot)\) \(\chi_{8036}(3113,\cdot)\) \(\chi_{8036}(3225,\cdot)\) \(\chi_{8036}(3365,\cdot)\) \(\chi_{8036}(3769,\cdot)\) \(\chi_{8036}(3881,\cdot)\) \(\chi_{8036}(3909,\cdot)\) \(\chi_{8036}(4021,\cdot)\) \(\chi_{8036}(4261,\cdot)\) \(\chi_{8036}(4373,\cdot)\) \(\chi_{8036}(4401,\cdot)\) \(\chi_{8036}(4513,\cdot)\) \(\chi_{8036}(4917,\cdot)\) \(\chi_{8036}(5057,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{168})$ |
| Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\((4019,493,785)\) → \((1,e\left(\frac{31}{42}\right),e\left(\frac{1}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 8036 }(437, a) \) | \(1\) | \(1\) | \(e\left(\frac{103}{168}\right)\) | \(e\left(\frac{13}{84}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{151}{168}\right)\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{43}{56}\right)\) | \(e\left(\frac{97}{168}\right)\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{13}{42}\right)\) |