Basic properties
| Modulus: | \(959\) | |
| Conductor: | \(959\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 959.y
\(\chi_{959}(4,\cdot)\) \(\chi_{959}(18,\cdot)\) \(\chi_{959}(65,\cdot)\) \(\chi_{959}(81,\cdot)\) \(\chi_{959}(121,\cdot)\) \(\chi_{959}(151,\cdot)\) \(\chi_{959}(186,\cdot)\) \(\chi_{959}(200,\cdot)\) \(\chi_{959}(214,\cdot)\) \(\chi_{959}(240,\cdot)\) \(\chi_{959}(289,\cdot)\) \(\chi_{959}(296,\cdot)\) \(\chi_{959}(338,\cdot)\) \(\chi_{959}(352,\cdot)\) \(\chi_{959}(361,\cdot)\) \(\chi_{959}(373,\cdot)\) \(\chi_{959}(415,\cdot)\) \(\chi_{959}(429,\cdot)\) \(\chi_{959}(492,\cdot)\) \(\chi_{959}(562,\cdot)\) \(\chi_{959}(597,\cdot)\) \(\chi_{959}(611,\cdot)\) \(\chi_{959}(613,\cdot)\) \(\chi_{959}(625,\cdot)\) \(\chi_{959}(669,\cdot)\) \(\chi_{959}(772,\cdot)\) \(\chi_{959}(788,\cdot)\) \(\chi_{959}(837,\cdot)\) \(\chi_{959}(844,\cdot)\) \(\chi_{959}(886,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{51})$ |
| Fixed field: | Number field defined by a degree 102 polynomial (not computed) |
Values on generators
\((549,414)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{3}{34}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 959 }(18, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{51}\right)\) | \(e\left(\frac{77}{102}\right)\) | \(e\left(\frac{22}{51}\right)\) | \(e\left(\frac{97}{102}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{26}{51}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{22}{51}\right)\) | \(e\left(\frac{19}{102}\right)\) |