Basic properties
| Modulus: | \(8024\) | |
| Conductor: | \(8024\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(116\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8024.ck
\(\chi_{8024}(21,\cdot)\) \(\chi_{8024}(285,\cdot)\) \(\chi_{8024}(293,\cdot)\) \(\chi_{8024}(429,\cdot)\) \(\chi_{8024}(557,\cdot)\) \(\chi_{8024}(829,\cdot)\) \(\chi_{8024}(965,\cdot)\) \(\chi_{8024}(973,\cdot)\) \(\chi_{8024}(1237,\cdot)\) \(\chi_{8024}(1373,\cdot)\) \(\chi_{8024}(1789,\cdot)\) \(\chi_{8024}(1917,\cdot)\) \(\chi_{8024}(2605,\cdot)\) \(\chi_{8024}(2733,\cdot)\) \(\chi_{8024}(2741,\cdot)\) \(\chi_{8024}(2877,\cdot)\) \(\chi_{8024}(3013,\cdot)\) \(\chi_{8024}(3149,\cdot)\) \(\chi_{8024}(3549,\cdot)\) \(\chi_{8024}(3557,\cdot)\) \(\chi_{8024}(3685,\cdot)\) \(\chi_{8024}(3693,\cdot)\) \(\chi_{8024}(3821,\cdot)\) \(\chi_{8024}(3829,\cdot)\) \(\chi_{8024}(3957,\cdot)\) \(\chi_{8024}(3965,\cdot)\) \(\chi_{8024}(4093,\cdot)\) \(\chi_{8024}(4237,\cdot)\) \(\chi_{8024}(4373,\cdot)\) \(\chi_{8024}(4501,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{116})$ |
| Fixed field: | Number field defined by a degree 116 polynomial (not computed) |
Values on generators
\((2007,4013,3777,3129)\) → \((1,-1,-i,e\left(\frac{5}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 8024 }(21, a) \) | \(1\) | \(1\) | \(e\left(\frac{101}{116}\right)\) | \(e\left(\frac{33}{116}\right)\) | \(e\left(\frac{41}{116}\right)\) | \(e\left(\frac{43}{58}\right)\) | \(e\left(\frac{7}{116}\right)\) | \(e\left(\frac{15}{58}\right)\) | \(e\left(\frac{9}{58}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{13}{58}\right)\) | \(e\left(\frac{97}{116}\right)\) |