Basic properties
| Modulus: | \(2151\) | |
| Conductor: | \(2151\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(102\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2151.x
\(\chi_{2151}(52,\cdot)\) \(\chi_{2151}(76,\cdot)\) \(\chi_{2151}(346,\cdot)\) \(\chi_{2151}(403,\cdot)\) \(\chi_{2151}(427,\cdot)\) \(\chi_{2151}(472,\cdot)\) \(\chi_{2151}(589,\cdot)\) \(\chi_{2151}(616,\cdot)\) \(\chi_{2151}(646,\cdot)\) \(\chi_{2151}(745,\cdot)\) \(\chi_{2151}(769,\cdot)\) \(\chi_{2151}(790,\cdot)\) \(\chi_{2151}(889,\cdot)\) \(\chi_{2151}(916,\cdot)\) \(\chi_{2151}(934,\cdot)\) \(\chi_{2151}(979,\cdot)\) \(\chi_{2151}(1120,\cdot)\) \(\chi_{2151}(1159,\cdot)\) \(\chi_{2151}(1363,\cdot)\) \(\chi_{2151}(1462,\cdot)\) \(\chi_{2151}(1507,\cdot)\) \(\chi_{2151}(1510,\cdot)\) \(\chi_{2151}(1606,\cdot)\) \(\chi_{2151}(1633,\cdot)\) \(\chi_{2151}(1651,\cdot)\) \(\chi_{2151}(1696,\cdot)\) \(\chi_{2151}(1780,\cdot)\) \(\chi_{2151}(1861,\cdot)\) \(\chi_{2151}(1876,\cdot)\) \(\chi_{2151}(1906,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((479,1441)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{25}{34}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2151 }(52, a) \) | \(-1\) | \(1\) | \(e\left(\frac{10}{51}\right)\) | \(e\left(\frac{20}{51}\right)\) | \(e\left(\frac{41}{51}\right)\) | \(e\left(\frac{41}{102}\right)\) | \(e\left(\frac{10}{17}\right)\) | \(1\) | \(e\left(\frac{31}{51}\right)\) | \(e\left(\frac{97}{102}\right)\) | \(e\left(\frac{61}{102}\right)\) | \(e\left(\frac{40}{51}\right)\) |