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 \(\chi_{1339}(107,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2678.bk
\(\chi_{2678}(107,\cdot)\) \(\chi_{2678}(185,\cdot)\) \(\chi_{2678}(341,\cdot)\) \(\chi_{2678}(367,\cdot)\) \(\chi_{2678}(419,\cdot)\) \(\chi_{2678}(445,\cdot)\) \(\chi_{2678}(659,\cdot)\) \(\chi_{2678}(737,\cdot)\) \(\chi_{2678}(757,\cdot)\) \(\chi_{2678}(789,\cdot)\) \(\chi_{2678}(887,\cdot)\) \(\chi_{2678}(945,\cdot)\) \(\chi_{2678}(965,\cdot)\) \(\chi_{2678}(1049,\cdot)\) \(\chi_{2678}(1121,\cdot)\) \(\chi_{2678}(1127,\cdot)\) \(\chi_{2678}(1225,\cdot)\) \(\chi_{2678}(1251,\cdot)\) \(\chi_{2678}(1459,\cdot)\) \(\chi_{2678}(1491,\cdot)\) \(\chi_{2678}(1673,\cdot)\) \(\chi_{2678}(1777,\cdot)\) \(\chi_{2678}(1849,\cdot)\) \(\chi_{2678}(1959,\cdot)\) \(\chi_{2678}(1985,\cdot)\) \(\chi_{2678}(2089,\cdot)\) \(\chi_{2678}(2115,\cdot)\) \(\chi_{2678}(2213,\cdot)\) \(\chi_{2678}(2349,\cdot)\) \(\chi_{2678}(2421,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\((1237,417)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{44}{51}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 2678 }(107, a) \) | \(1\) | \(1\) | \(e\left(\frac{50}{51}\right)\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{49}{51}\right)\) | \(e\left(\frac{49}{51}\right)\) | \(e\left(\frac{43}{51}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{35}{51}\right)\) | \(e\left(\frac{5}{51}\right)\) | \(e\left(\frac{2}{51}\right)\) |