Basic properties
| Modulus: | \(2669\) | |
| Conductor: | \(2669\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(312\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2669.cn
\(\chi_{2669}(25,\cdot)\) \(\chi_{2669}(36,\cdot)\) \(\chi_{2669}(42,\cdot)\) \(\chi_{2669}(76,\cdot)\) \(\chi_{2669}(110,\cdot)\) \(\chi_{2669}(117,\cdot)\) \(\chi_{2669}(127,\cdot)\) \(\chi_{2669}(138,\cdot)\) \(\chi_{2669}(274,\cdot)\) \(\chi_{2669}(297,\cdot)\) \(\chi_{2669}(365,\cdot)\) \(\chi_{2669}(382,\cdot)\) \(\chi_{2669}(400,\cdot)\) \(\chi_{2669}(434,\cdot)\) \(\chi_{2669}(474,\cdot)\) \(\chi_{2669}(502,\cdot)\) \(\chi_{2669}(519,\cdot)\) \(\chi_{2669}(576,\cdot)\) \(\chi_{2669}(593,\cdot)\) \(\chi_{2669}(631,\cdot)\) \(\chi_{2669}(638,\cdot)\) \(\chi_{2669}(661,\cdot)\) \(\chi_{2669}(672,\cdot)\) \(\chi_{2669}(733,\cdot)\) \(\chi_{2669}(750,\cdot)\) \(\chi_{2669}(774,\cdot)\) \(\chi_{2669}(818,\cdot)\) \(\chi_{2669}(842,\cdot)\) \(\chi_{2669}(933,\cdot)\) \(\chi_{2669}(967,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{312})$ |
| Fixed field: | Number field defined by a degree 312 polynomial (not computed) |
Values on generators
\((1414,2517)\) → \((e\left(\frac{5}{8}\right),e\left(\frac{1}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2669 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{211}{312}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{43}{312}\right)\) | \(e\left(\frac{73}{312}\right)\) | \(e\left(\frac{79}{104}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{55}{156}\right)\) | \(e\left(\frac{217}{312}\right)\) | \(e\left(\frac{229}{312}\right)\) |