Basic properties
| Modulus: | \(8034\) | |
| Conductor: | \(4017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(204\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4017}(2489,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.el
\(\chi_{8034}(41,\cdot)\) \(\chi_{8034}(119,\cdot)\) \(\chi_{8034}(431,\cdot)\) \(\chi_{8034}(509,\cdot)\) \(\chi_{8034}(773,\cdot)\) \(\chi_{8034}(839,\cdot)\) \(\chi_{8034}(1055,\cdot)\) \(\chi_{8034}(1367,\cdot)\) \(\chi_{8034}(1397,\cdot)\) \(\chi_{8034}(1475,\cdot)\) \(\chi_{8034}(1571,\cdot)\) \(\chi_{8034}(1787,\cdot)\) \(\chi_{8034}(1883,\cdot)\) \(\chi_{8034}(1913,\cdot)\) \(\chi_{8034}(2009,\cdot)\) \(\chi_{8034}(2255,\cdot)\) \(\chi_{8034}(2429,\cdot)\) \(\chi_{8034}(2489,\cdot)\) \(\chi_{8034}(2633,\cdot)\) \(\chi_{8034}(2711,\cdot)\) \(\chi_{8034}(2849,\cdot)\) \(\chi_{8034}(2879,\cdot)\) \(\chi_{8034}(3005,\cdot)\) \(\chi_{8034}(3023,\cdot)\) \(\chi_{8034}(3131,\cdot)\) \(\chi_{8034}(3209,\cdot)\) \(\chi_{8034}(3491,\cdot)\) \(\chi_{8034}(3521,\cdot)\) \(\chi_{8034}(3551,\cdot)\) \(\chi_{8034}(3599,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((-1,e\left(\frac{5}{12}\right),e\left(\frac{35}{51}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8034 }(2489, a) \) | \(1\) | \(1\) | \(e\left(\frac{191}{204}\right)\) | \(e\left(\frac{67}{204}\right)\) | \(e\left(\frac{19}{68}\right)\) | \(e\left(\frac{19}{51}\right)\) | \(e\left(\frac{67}{68}\right)\) | \(e\left(\frac{7}{51}\right)\) | \(e\left(\frac{89}{102}\right)\) | \(e\left(\frac{19}{102}\right)\) | \(e\left(\frac{59}{68}\right)\) | \(e\left(\frac{9}{34}\right)\) |