Basic properties
| Modulus: | \(2678\) | |
| Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(51\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1339}(1166,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2678.bl
\(\chi_{2678}(29,\cdot)\) \(\chi_{2678}(55,\cdot)\) \(\chi_{2678}(139,\cdot)\) \(\chi_{2678}(269,\cdot)\) \(\chi_{2678}(289,\cdot)\) \(\chi_{2678}(347,\cdot)\) \(\chi_{2678}(471,\cdot)\) \(\chi_{2678}(503,\cdot)\) \(\chi_{2678}(575,\cdot)\) \(\chi_{2678}(607,\cdot)\) \(\chi_{2678}(633,\cdot)\) \(\chi_{2678}(841,\cdot)\) \(\chi_{2678}(1231,\cdot)\) \(\chi_{2678}(1277,\cdot)\) \(\chi_{2678}(1355,\cdot)\) \(\chi_{2678}(1407,\cdot)\) \(\chi_{2678}(1563,\cdot)\) \(\chi_{2678}(1595,\cdot)\) \(\chi_{2678}(1667,\cdot)\) \(\chi_{2678}(1745,\cdot)\) \(\chi_{2678}(1803,\cdot)\) \(\chi_{2678}(2109,\cdot)\) \(\chi_{2678}(2167,\cdot)\) \(\chi_{2678}(2245,\cdot)\) \(\chi_{2678}(2291,\cdot)\) \(\chi_{2678}(2395,\cdot)\) \(\chi_{2678}(2401,\cdot)\) \(\chi_{2678}(2427,\cdot)\) \(\chi_{2678}(2479,\cdot)\) \(\chi_{2678}(2505,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\((1237,417)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{50}{51}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 2678 }(2505, a) \) | \(1\) | \(1\) | \(e\left(\frac{46}{51}\right)\) | \(e\left(\frac{50}{51}\right)\) | \(e\left(\frac{13}{51}\right)\) | \(e\left(\frac{41}{51}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{49}{51}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{8}{51}\right)\) | \(e\left(\frac{10}{51}\right)\) |