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 \(\chi_{1339}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2678.bj
\(\chi_{2678}(9,\cdot)\) \(\chi_{2678}(61,\cdot)\) \(\chi_{2678}(81,\cdot)\) \(\chi_{2678}(133,\cdot)\) \(\chi_{2678}(373,\cdot)\) \(\chi_{2678}(425,\cdot)\) \(\chi_{2678}(523,\cdot)\) \(\chi_{2678}(529,\cdot)\) \(\chi_{2678}(549,\cdot)\) \(\chi_{2678}(581,\cdot)\) \(\chi_{2678}(627,\cdot)\) \(\chi_{2678}(679,\cdot)\) \(\chi_{2678}(711,\cdot)\) \(\chi_{2678}(991,\cdot)\) \(\chi_{2678}(1043,\cdot)\) \(\chi_{2678}(1147,\cdot)\) \(\chi_{2678}(1199,\cdot)\) \(\chi_{2678}(1205,\cdot)\) \(\chi_{2678}(1329,\cdot)\) \(\chi_{2678}(1439,\cdot)\) \(\chi_{2678}(1465,\cdot)\) \(\chi_{2678}(1621,\cdot)\) \(\chi_{2678}(1823,\cdot)\) \(\chi_{2678}(1933,\cdot)\) \(\chi_{2678}(2057,\cdot)\) \(\chi_{2678}(2083,\cdot)\) \(\chi_{2678}(2141,\cdot)\) \(\chi_{2678}(2193,\cdot)\) \(\chi_{2678}(2239,\cdot)\) \(\chi_{2678}(2551,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 51 polynomial |
Values on generators
\((1237,417)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{13}{17}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 2678 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{25}{51}\right)\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{20}{51}\right)\) | \(e\left(\frac{50}{51}\right)\) | \(e\left(\frac{16}{51}\right)\) | \(e\left(\frac{13}{51}\right)\) | \(e\left(\frac{44}{51}\right)\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{15}{17}\right)\) | \(e\left(\frac{1}{51}\right)\) |