Basic properties
| Modulus: | \(2678\) | |
| Conductor: | \(1339\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(102\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1339}(23,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2678.bx
\(\chi_{2678}(23,\cdot)\) \(\chi_{2678}(179,\cdot)\) \(\chi_{2678}(381,\cdot)\) \(\chi_{2678}(491,\cdot)\) \(\chi_{2678}(615,\cdot)\) \(\chi_{2678}(641,\cdot)\) \(\chi_{2678}(699,\cdot)\) \(\chi_{2678}(751,\cdot)\) \(\chi_{2678}(797,\cdot)\) \(\chi_{2678}(1109,\cdot)\) \(\chi_{2678}(1141,\cdot)\) \(\chi_{2678}(1167,\cdot)\) \(\chi_{2678}(1245,\cdot)\) \(\chi_{2678}(1297,\cdot)\) \(\chi_{2678}(1317,\cdot)\) \(\chi_{2678}(1369,\cdot)\) \(\chi_{2678}(1609,\cdot)\) \(\chi_{2678}(1661,\cdot)\) \(\chi_{2678}(1759,\cdot)\) \(\chi_{2678}(1765,\cdot)\) \(\chi_{2678}(1785,\cdot)\) \(\chi_{2678}(1817,\cdot)\) \(\chi_{2678}(1863,\cdot)\) \(\chi_{2678}(1915,\cdot)\) \(\chi_{2678}(1947,\cdot)\) \(\chi_{2678}(2227,\cdot)\) \(\chi_{2678}(2279,\cdot)\) \(\chi_{2678}(2383,\cdot)\) \(\chi_{2678}(2435,\cdot)\) \(\chi_{2678}(2441,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((1237,417)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{4}{17}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 2678 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{11}{102}\right)\) | \(e\left(\frac{1}{51}\right)\) | \(e\left(\frac{19}{102}\right)\) | \(e\left(\frac{25}{102}\right)\) | \(e\left(\frac{7}{51}\right)\) | \(e\left(\frac{101}{102}\right)\) | \(e\left(\frac{21}{34}\right)\) | \(e\left(\frac{50}{51}\right)\) |