Basic properties
| Modulus: | \(1007\) | |
| Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(234\) | 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 1007.bh
\(\chi_{1007}(29,\cdot)\) \(\chi_{1007}(40,\cdot)\) \(\chi_{1007}(59,\cdot)\) \(\chi_{1007}(60,\cdot)\) \(\chi_{1007}(70,\cdot)\) \(\chi_{1007}(78,\cdot)\) \(\chi_{1007}(90,\cdot)\) \(\chi_{1007}(91,\cdot)\) \(\chi_{1007}(110,\cdot)\) \(\chi_{1007}(117,\cdot)\) \(\chi_{1007}(135,\cdot)\) \(\chi_{1007}(143,\cdot)\) \(\chi_{1007}(146,\cdot)\) \(\chi_{1007}(165,\cdot)\) \(\chi_{1007}(166,\cdot)\) \(\chi_{1007}(184,\cdot)\) \(\chi_{1007}(219,\cdot)\) \(\chi_{1007}(223,\cdot)\) \(\chi_{1007}(241,\cdot)\) \(\chi_{1007}(249,\cdot)\) \(\chi_{1007}(250,\cdot)\) \(\chi_{1007}(269,\cdot)\) \(\chi_{1007}(276,\cdot)\) \(\chi_{1007}(325,\cdot)\) \(\chi_{1007}(355,\cdot)\) \(\chi_{1007}(356,\cdot)\) \(\chi_{1007}(375,\cdot)\) \(\chi_{1007}(382,\cdot)\) \(\chi_{1007}(409,\cdot)\) \(\chi_{1007}(414,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((743,267)\) → \((e\left(\frac{11}{18}\right),e\left(\frac{19}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1007 }(91, a) \) | \(-1\) | \(1\) | \(e\left(\frac{40}{117}\right)\) | \(e\left(\frac{43}{117}\right)\) | \(e\left(\frac{80}{117}\right)\) | \(e\left(\frac{29}{234}\right)\) | \(e\left(\frac{83}{117}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{86}{117}\right)\) | \(e\left(\frac{109}{234}\right)\) | \(e\left(\frac{28}{39}\right)\) |