Basic properties
| Modulus: | \(8034\) | |
| Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(204\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1339}(197,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.ee
\(\chi_{8034}(37,\cdot)\) \(\chi_{8034}(145,\cdot)\) \(\chi_{8034}(193,\cdot)\) \(\chi_{8034}(301,\cdot)\) \(\chi_{8034}(319,\cdot)\) \(\chi_{8034}(331,\cdot)\) \(\chi_{8034}(691,\cdot)\) \(\chi_{8034}(1021,\cdot)\) \(\chi_{8034}(1033,\cdot)\) \(\chi_{8034}(1099,\cdot)\) \(\chi_{8034}(1267,\cdot)\) \(\chi_{8034}(1363,\cdot)\) \(\chi_{8034}(1567,\cdot)\) \(\chi_{8034}(1675,\cdot)\) \(\chi_{8034}(1831,\cdot)\) \(\chi_{8034}(1891,\cdot)\) \(\chi_{8034}(2047,\cdot)\) \(\chi_{8034}(2173,\cdot)\) \(\chi_{8034}(2269,\cdot)\) \(\chi_{8034}(2503,\cdot)\) \(\chi_{8034}(2767,\cdot)\) \(\chi_{8034}(2875,\cdot)\) \(\chi_{8034}(2923,\cdot)\) \(\chi_{8034}(2953,\cdot)\) \(\chi_{8034}(3127,\cdot)\) \(\chi_{8034}(3217,\cdot)\) \(\chi_{8034}(3235,\cdot)\) \(\chi_{8034}(3283,\cdot)\) \(\chi_{8034}(3391,\cdot)\) \(\chi_{8034}(3421,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((1,e\left(\frac{1}{12}\right),e\left(\frac{9}{34}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8034 }(2875, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{68}\right)\) | \(e\left(\frac{199}{204}\right)\) | \(e\left(\frac{149}{204}\right)\) | \(e\left(\frac{71}{102}\right)\) | \(e\left(\frac{121}{204}\right)\) | \(e\left(\frac{19}{102}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{5}{51}\right)\) | \(e\left(\frac{57}{68}\right)\) | \(e\left(\frac{101}{102}\right)\) |