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 \(\chi_{1339}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8034.ec
\(\chi_{8034}(7,\cdot)\) \(\chi_{8034}(475,\cdot)\) \(\chi_{8034}(553,\cdot)\) \(\chi_{8034}(565,\cdot)\) \(\chi_{8034}(583,\cdot)\) \(\chi_{8034}(709,\cdot)\) \(\chi_{8034}(739,\cdot)\) \(\chi_{8034}(1159,\cdot)\) \(\chi_{8034}(1285,\cdot)\) \(\chi_{8034}(1471,\cdot)\) \(\chi_{8034}(1753,\cdot)\) \(\chi_{8034}(1801,\cdot)\) \(\chi_{8034}(1909,\cdot)\) \(\chi_{8034}(2017,\cdot)\) \(\chi_{8034}(2143,\cdot)\) \(\chi_{8034}(2281,\cdot)\) \(\chi_{8034}(2719,\cdot)\) \(\chi_{8034}(2797,\cdot)\) \(\chi_{8034}(3109,\cdot)\) \(\chi_{8034}(3187,\cdot)\) \(\chi_{8034}(3451,\cdot)\) \(\chi_{8034}(3517,\cdot)\) \(\chi_{8034}(3733,\cdot)\) \(\chi_{8034}(4045,\cdot)\) \(\chi_{8034}(4075,\cdot)\) \(\chi_{8034}(4153,\cdot)\) \(\chi_{8034}(4249,\cdot)\) \(\chi_{8034}(4465,\cdot)\) \(\chi_{8034}(4561,\cdot)\) \(\chi_{8034}(4591,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((5357,1237,5773)\) → \((1,e\left(\frac{11}{12}\right),e\left(\frac{2}{51}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8034 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{204}\right)\) | \(e\left(\frac{49}{204}\right)\) | \(e\left(\frac{55}{68}\right)\) | \(e\left(\frac{59}{102}\right)\) | \(e\left(\frac{49}{68}\right)\) | \(e\left(\frac{11}{102}\right)\) | \(e\left(\frac{59}{102}\right)\) | \(e\left(\frac{2}{51}\right)\) | \(e\left(\frac{33}{68}\right)\) | \(e\left(\frac{9}{17}\right)\) |