Basic properties
| Modulus: | \(607\) | |
| Conductor: | \(607\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(202\) | 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 607.f
\(\chi_{607}(6,\cdot)\) \(\chi_{607}(10,\cdot)\) \(\chi_{607}(27,\cdot)\) \(\chi_{607}(33,\cdot)\) \(\chi_{607}(34,\cdot)\) \(\chi_{607}(37,\cdot)\) \(\chi_{607}(42,\cdot)\) \(\chi_{607}(45,\cdot)\) \(\chi_{607}(48,\cdot)\) \(\chi_{607}(55,\cdot)\) \(\chi_{607}(57,\cdot)\) \(\chi_{607}(58,\cdot)\) \(\chi_{607}(70,\cdot)\) \(\chi_{607}(75,\cdot)\) \(\chi_{607}(80,\cdot)\) \(\chi_{607}(83,\cdot)\) \(\chi_{607}(92,\cdot)\) \(\chi_{607}(95,\cdot)\) \(\chi_{607}(109,\cdot)\) \(\chi_{607}(118,\cdot)\) \(\chi_{607}(124,\cdot)\) \(\chi_{607}(125,\cdot)\) \(\chi_{607}(127,\cdot)\) \(\chi_{607}(129,\cdot)\) \(\chi_{607}(153,\cdot)\) \(\chi_{607}(156,\cdot)\) \(\chi_{607}(157,\cdot)\) \(\chi_{607}(159,\cdot)\) \(\chi_{607}(187,\cdot)\) \(\chi_{607}(189,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{101})$ |
| Fixed field: | Number field defined by a degree 202 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{195}{202}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 607 }(6, a) \) | \(-1\) | \(1\) | \(e\left(\frac{77}{101}\right)\) | \(e\left(\frac{195}{202}\right)\) | \(e\left(\frac{53}{101}\right)\) | \(e\left(\frac{35}{202}\right)\) | \(e\left(\frac{147}{202}\right)\) | \(e\left(\frac{10}{101}\right)\) | \(e\left(\frac{29}{101}\right)\) | \(e\left(\frac{94}{101}\right)\) | \(e\left(\frac{189}{202}\right)\) | \(e\left(\frac{55}{101}\right)\) |