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 \(\chi_{4017}(3425,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.ea
\(\chi_{8034}(59,\cdot)\) \(\chi_{8034}(401,\cdot)\) \(\chi_{8034}(461,\cdot)\) \(\chi_{8034}(635,\cdot)\) \(\chi_{8034}(929,\cdot)\) \(\chi_{8034}(977,\cdot)\) \(\chi_{8034}(995,\cdot)\) \(\chi_{8034}(1025,\cdot)\) \(\chi_{8034}(1085,\cdot)\) \(\chi_{8034}(1151,\cdot)\) \(\chi_{8034}(1319,\cdot)\) \(\chi_{8034}(1697,\cdot)\) \(\chi_{8034}(1961,\cdot)\) \(\chi_{8034}(2039,\cdot)\) \(\chi_{8034}(2165,\cdot)\) \(\chi_{8034}(2195,\cdot)\) \(\chi_{8034}(2273,\cdot)\) \(\chi_{8034}(2321,\cdot)\) \(\chi_{8034}(2555,\cdot)\) \(\chi_{8034}(2693,\cdot)\) \(\chi_{8034}(2741,\cdot)\) \(\chi_{8034}(2819,\cdot)\) \(\chi_{8034}(2975,\cdot)\) \(\chi_{8034}(3425,\cdot)\) \(\chi_{8034}(3737,\cdot)\) \(\chi_{8034}(3863,\cdot)\) \(\chi_{8034}(4067,\cdot)\) \(\chi_{8034}(4283,\cdot)\) \(\chi_{8034}(4487,\cdot)\) \(\chi_{8034}(4565,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((-1,e\left(\frac{5}{12}\right),e\left(\frac{7}{51}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8034 }(3425, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{204}\right)\) | \(e\left(\frac{9}{68}\right)\) | \(e\left(\frac{161}{204}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{13}{204}\right)\) | \(e\left(\frac{49}{51}\right)\) | \(e\left(\frac{79}{102}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{39}{68}\right)\) | \(e\left(\frac{53}{102}\right)\) |