Basic properties
| Modulus: | \(1007\) | |
| Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(117\) | 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 1007.bc
\(\chi_{1007}(16,\cdot)\) \(\chi_{1007}(24,\cdot)\) \(\chi_{1007}(28,\cdot)\) \(\chi_{1007}(36,\cdot)\) \(\chi_{1007}(42,\cdot)\) \(\chi_{1007}(44,\cdot)\) \(\chi_{1007}(47,\cdot)\) \(\chi_{1007}(63,\cdot)\) \(\chi_{1007}(66,\cdot)\) \(\chi_{1007}(81,\cdot)\) \(\chi_{1007}(99,\cdot)\) \(\chi_{1007}(100,\cdot)\) \(\chi_{1007}(119,\cdot)\) \(\chi_{1007}(130,\cdot)\) \(\chi_{1007}(142,\cdot)\) \(\chi_{1007}(150,\cdot)\) \(\chi_{1007}(169,\cdot)\) \(\chi_{1007}(175,\cdot)\) \(\chi_{1007}(187,\cdot)\) \(\chi_{1007}(195,\cdot)\) \(\chi_{1007}(206,\cdot)\) \(\chi_{1007}(225,\cdot)\) \(\chi_{1007}(256,\cdot)\) \(\chi_{1007}(275,\cdot)\) \(\chi_{1007}(289,\cdot)\) \(\chi_{1007}(301,\cdot)\) \(\chi_{1007}(309,\cdot)\) \(\chi_{1007}(328,\cdot)\) \(\chi_{1007}(346,\cdot)\) \(\chi_{1007}(365,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 117 polynomial (not computed) |
Values on generators
\((743,267)\) → \((e\left(\frac{2}{9}\right),e\left(\frac{1}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1007 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{117}\right)\) | \(e\left(\frac{23}{117}\right)\) | \(e\left(\frac{70}{117}\right)\) | \(e\left(\frac{20}{117}\right)\) | \(e\left(\frac{58}{117}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{46}{117}\right)\) | \(e\left(\frac{55}{117}\right)\) | \(e\left(\frac{5}{39}\right)\) |