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 \(\chi_{1339}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2678.ch
\(\chi_{2678}(5,\cdot)\) \(\chi_{2678}(21,\cdot)\) \(\chi_{2678}(99,\cdot)\) \(\chi_{2678}(109,\cdot)\) \(\chi_{2678}(151,\cdot)\) \(\chi_{2678}(177,\cdot)\) \(\chi_{2678}(187,\cdot)\) \(\chi_{2678}(281,\cdot)\) \(\chi_{2678}(291,\cdot)\) \(\chi_{2678}(307,\cdot)\) \(\chi_{2678}(395,\cdot)\) \(\chi_{2678}(447,\cdot)\) \(\chi_{2678}(463,\cdot)\) \(\chi_{2678}(489,\cdot)\) \(\chi_{2678}(499,\cdot)\) \(\chi_{2678}(577,\cdot)\) \(\chi_{2678}(593,\cdot)\) \(\chi_{2678}(603,\cdot)\) \(\chi_{2678}(629,\cdot)\) \(\chi_{2678}(671,\cdot)\) \(\chi_{2678}(733,\cdot)\) \(\chi_{2678}(775,\cdot)\) \(\chi_{2678}(889,\cdot)\) \(\chi_{2678}(967,\cdot)\) \(\chi_{2678}(1035,\cdot)\) \(\chi_{2678}(1097,\cdot)\) \(\chi_{2678}(1139,\cdot)\) \(\chi_{2678}(1217,\cdot)\) \(\chi_{2678}(1279,\cdot)\) \(\chi_{2678}(1321,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{204})$ |
| Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((1237,417)\) → \((-i,e\left(\frac{1}{102}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 2678 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{155}{204}\right)\) | \(e\left(\frac{59}{204}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{173}{204}\right)\) | \(e\left(\frac{29}{204}\right)\) | \(e\left(\frac{19}{102}\right)\) | \(e\left(\frac{109}{204}\right)\) | \(e\left(\frac{137}{204}\right)\) | \(e\left(\frac{25}{34}\right)\) |