Basic properties
| Modulus: | \(163177\) | |
| Conductor: | \(163177\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(315\) | 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 163177.fi
\(\chi_{163177}(25,\cdot)\) \(\chi_{163177}(200,\cdot)\) \(\chi_{163177}(625,\cdot)\) \(\chi_{163177}(800,\cdot)\) \(\chi_{163177}(1250,\cdot)\) \(\chi_{163177}(1495,\cdot)\) \(\chi_{163177}(1600,\cdot)\) \(\chi_{163177}(2573,\cdot)\) \(\chi_{163177}(3133,\cdot)\) \(\chi_{163177}(3315,\cdot)\) \(\chi_{163177}(5000,\cdot)\) \(\chi_{163177}(6400,\cdot)\) \(\chi_{163177}(8654,\cdot)\) \(\chi_{163177}(10292,\cdot)\) \(\chi_{163177}(10469,\cdot)\) \(\chi_{163177}(11960,\cdot)\) \(\chi_{163177}(12532,\cdot)\) \(\chi_{163177}(12800,\cdot)\) \(\chi_{163177}(13218,\cdot)\) \(\chi_{163177}(17530,\cdot)\) \(\chi_{163177}(23391,\cdot)\) \(\chi_{163177}(23811,\cdot)\) \(\chi_{163177}(23951,\cdot)\) \(\chi_{163177}(25064,\cdot)\) \(\chi_{163177}(25069,\cdot)\) \(\chi_{163177}(26520,\cdot)\) \(\chi_{163177}(27311,\cdot)\) \(\chi_{163177}(27974,\cdot)\) \(\chi_{163177}(28095,\cdot)\) \(\chi_{163177}(28431,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{315})$ |
| Fixed field: | Number field defined by a degree 315 polynomial (not computed) |
Values on generators
\((46623,116558)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{23}{315}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 163177 }(625, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{128}{315}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{74}{315}\right)\) | \(e\left(\frac{289}{315}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{256}{315}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{11}{315}\right)\) | \(e\left(\frac{3}{7}\right)\) |