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 \(\chi_{1339}(397,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.ed
\(\chi_{8034}(397,\cdot)\) \(\chi_{8034}(535,\cdot)\) \(\chi_{8034}(661,\cdot)\) \(\chi_{8034}(769,\cdot)\) \(\chi_{8034}(877,\cdot)\) \(\chi_{8034}(925,\cdot)\) \(\chi_{8034}(1207,\cdot)\) \(\chi_{8034}(1393,\cdot)\) \(\chi_{8034}(1519,\cdot)\) \(\chi_{8034}(1939,\cdot)\) \(\chi_{8034}(1969,\cdot)\) \(\chi_{8034}(2095,\cdot)\) \(\chi_{8034}(2113,\cdot)\) \(\chi_{8034}(2125,\cdot)\) \(\chi_{8034}(2203,\cdot)\) \(\chi_{8034}(2671,\cdot)\) \(\chi_{8034}(2749,\cdot)\) \(\chi_{8034}(2905,\cdot)\) \(\chi_{8034}(2983,\cdot)\) \(\chi_{8034}(3031,\cdot)\) \(\chi_{8034}(3205,\cdot)\) \(\chi_{8034}(3361,\cdot)\) \(\chi_{8034}(3439,\cdot)\) \(\chi_{8034}(3577,\cdot)\) \(\chi_{8034}(3625,\cdot)\) \(\chi_{8034}(3859,\cdot)\) \(\chi_{8034}(3889,\cdot)\) \(\chi_{8034}(3907,\cdot)\) \(\chi_{8034}(3919,\cdot)\) \(\chi_{8034}(3985,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((1,e\left(\frac{11}{12}\right),e\left(\frac{91}{102}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8034 }(397, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{204}\right)\) | \(e\left(\frac{133}{204}\right)\) | \(e\left(\frac{57}{68}\right)\) | \(e\left(\frac{29}{102}\right)\) | \(e\left(\frac{65}{68}\right)\) | \(e\left(\frac{59}{102}\right)\) | \(e\left(\frac{29}{102}\right)\) | \(e\left(\frac{20}{51}\right)\) | \(e\left(\frac{7}{68}\right)\) | \(e\left(\frac{27}{34}\right)\) |