Basic properties
| Modulus: | \(2678\) | |
| 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 \(\chi_{1339}(11,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2678.cd
\(\chi_{2678}(11,\cdot)\) \(\chi_{2678}(67,\cdot)\) \(\chi_{2678}(85,\cdot)\) \(\chi_{2678}(115,\cdot)\) \(\chi_{2678}(123,\cdot)\) \(\chi_{2678}(241,\cdot)\) \(\chi_{2678}(271,\cdot)\) \(\chi_{2678}(293,\cdot)\) \(\chi_{2678}(349,\cdot)\) \(\chi_{2678}(357,\cdot)\) \(\chi_{2678}(371,\cdot)\) \(\chi_{2678}(379,\cdot)\) \(\chi_{2678}(383,\cdot)\) \(\chi_{2678}(405,\cdot)\) \(\chi_{2678}(457,\cdot)\) \(\chi_{2678}(479,\cdot)\) \(\chi_{2678}(483,\cdot)\) \(\chi_{2678}(487,\cdot)\) \(\chi_{2678}(513,\cdot)\) \(\chi_{2678}(639,\cdot)\) \(\chi_{2678}(695,\cdot)\) \(\chi_{2678}(717,\cdot)\) \(\chi_{2678}(791,\cdot)\) \(\chi_{2678}(799,\cdot)\) \(\chi_{2678}(817,\cdot)\) \(\chi_{2678}(869,\cdot)\) \(\chi_{2678}(895,\cdot)\) \(\chi_{2678}(981,\cdot)\) \(\chi_{2678}(1051,\cdot)\) \(\chi_{2678}(1073,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((1237,417)\) → \((e\left(\frac{7}{12}\right),e\left(\frac{61}{102}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 2678 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{102}\right)\) | \(e\left(\frac{173}{204}\right)\) | \(e\left(\frac{55}{68}\right)\) | \(e\left(\frac{16}{51}\right)\) | \(e\left(\frac{115}{204}\right)\) | \(e\left(\frac{103}{204}\right)\) | \(e\left(\frac{1}{34}\right)\) | \(e\left(\frac{155}{204}\right)\) | \(e\left(\frac{95}{204}\right)\) | \(e\left(\frac{19}{102}\right)\) |