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 \(\chi_{1339}(25,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2678.bo
\(\chi_{2678}(25,\cdot)\) \(\chi_{2678}(129,\cdot)\) \(\chi_{2678}(155,\cdot)\) \(\chi_{2678}(311,\cdot)\) \(\chi_{2678}(337,\cdot)\) \(\chi_{2678}(441,\cdot)\) \(\chi_{2678}(467,\cdot)\) \(\chi_{2678}(519,\cdot)\) \(\chi_{2678}(597,\cdot)\) \(\chi_{2678}(701,\cdot)\) \(\chi_{2678}(753,\cdot)\) \(\chi_{2678}(779,\cdot)\) \(\chi_{2678}(831,\cdot)\) \(\chi_{2678}(857,\cdot)\) \(\chi_{2678}(883,\cdot)\) \(\chi_{2678}(987,\cdot)\) \(\chi_{2678}(1169,\cdot)\) \(\chi_{2678}(1299,\cdot)\) \(\chi_{2678}(1377,\cdot)\) \(\chi_{2678}(1533,\cdot)\) \(\chi_{2678}(1637,\cdot)\) \(\chi_{2678}(1663,\cdot)\) \(\chi_{2678}(1689,\cdot)\) \(\chi_{2678}(1767,\cdot)\) \(\chi_{2678}(1819,\cdot)\) \(\chi_{2678}(1871,\cdot)\) \(\chi_{2678}(1975,\cdot)\) \(\chi_{2678}(2079,\cdot)\) \(\chi_{2678}(2157,\cdot)\) \(\chi_{2678}(2261,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((1237,417)\) → \((-1,e\left(\frac{1}{51}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 2678 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{17}\right)\) | \(e\left(\frac{53}{102}\right)\) | \(e\left(\frac{59}{102}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{71}{102}\right)\) | \(e\left(\frac{29}{102}\right)\) | \(e\left(\frac{19}{51}\right)\) | \(e\left(\frac{7}{102}\right)\) | \(e\left(\frac{35}{102}\right)\) | \(e\left(\frac{8}{17}\right)\) |