Basic properties
| Modulus: | \(407\) | |
| Conductor: | \(407\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | 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 407.bi
\(\chi_{407}(5,\cdot)\) \(\chi_{407}(15,\cdot)\) \(\chi_{407}(20,\cdot)\) \(\chi_{407}(42,\cdot)\) \(\chi_{407}(59,\cdot)\) \(\chi_{407}(69,\cdot)\) \(\chi_{407}(91,\cdot)\) \(\chi_{407}(92,\cdot)\) \(\chi_{407}(93,\cdot)\) \(\chi_{407}(113,\cdot)\) \(\chi_{407}(124,\cdot)\) \(\chi_{407}(126,\cdot)\) \(\chi_{407}(130,\cdot)\) \(\chi_{407}(135,\cdot)\) \(\chi_{407}(146,\cdot)\) \(\chi_{407}(163,\cdot)\) \(\chi_{407}(168,\cdot)\) \(\chi_{407}(170,\cdot)\) \(\chi_{407}(180,\cdot)\) \(\chi_{407}(190,\cdot)\) \(\chi_{407}(202,\cdot)\) \(\chi_{407}(203,\cdot)\) \(\chi_{407}(207,\cdot)\) \(\chi_{407}(224,\cdot)\) \(\chi_{407}(235,\cdot)\) \(\chi_{407}(240,\cdot)\) \(\chi_{407}(246,\cdot)\) \(\chi_{407}(257,\cdot)\) \(\chi_{407}(278,\cdot)\) \(\chi_{407}(279,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((112,298)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{17}{36}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 407 }(92, a) \) | \(-1\) | \(1\) | \(e\left(\frac{121}{180}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{119}{180}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{9}\right)\) |