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 \(\chi_{4017}(71,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.ek
\(\chi_{8034}(71,\cdot)\) \(\chi_{8034}(227,\cdot)\) \(\chi_{8034}(305,\cdot)\) \(\chi_{8034}(353,\cdot)\) \(\chi_{8034}(527,\cdot)\) \(\chi_{8034}(683,\cdot)\) \(\chi_{8034}(761,\cdot)\) \(\chi_{8034}(899,\cdot)\) \(\chi_{8034}(947,\cdot)\) \(\chi_{8034}(1181,\cdot)\) \(\chi_{8034}(1211,\cdot)\) \(\chi_{8034}(1229,\cdot)\) \(\chi_{8034}(1241,\cdot)\) \(\chi_{8034}(1307,\cdot)\) \(\chi_{8034}(1337,\cdot)\) \(\chi_{8034}(1463,\cdot)\) \(\chi_{8034}(1541,\cdot)\) \(\chi_{8034}(1631,\cdot)\) \(\chi_{8034}(1757,\cdot)\) \(\chi_{8034}(1805,\cdot)\) \(\chi_{8034}(1835,\cdot)\) \(\chi_{8034}(1865,\cdot)\) \(\chi_{8034}(2147,\cdot)\) \(\chi_{8034}(2225,\cdot)\) \(\chi_{8034}(2333,\cdot)\) \(\chi_{8034}(2351,\cdot)\) \(\chi_{8034}(2477,\cdot)\) \(\chi_{8034}(2507,\cdot)\) \(\chi_{8034}(2645,\cdot)\) \(\chi_{8034}(2723,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((-1,e\left(\frac{5}{12}\right),e\left(\frac{67}{102}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8034 }(71, a) \) | \(-1\) | \(1\) | \(e\left(\frac{185}{204}\right)\) | \(e\left(\frac{43}{204}\right)\) | \(e\left(\frac{33}{68}\right)\) | \(e\left(\frac{16}{51}\right)\) | \(e\left(\frac{43}{68}\right)\) | \(e\left(\frac{22}{51}\right)\) | \(e\left(\frac{83}{102}\right)\) | \(e\left(\frac{67}{102}\right)\) | \(e\left(\frac{13}{68}\right)\) | \(e\left(\frac{2}{17}\right)\) |