Basic properties
| Modulus: | \(607\) | |
| Conductor: | \(607\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(606\) | 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.h
\(\chi_{607}(3,\cdot)\) \(\chi_{607}(5,\cdot)\) \(\chi_{607}(12,\cdot)\) \(\chi_{607}(17,\cdot)\) \(\chi_{607}(20,\cdot)\) \(\chi_{607}(21,\cdot)\) \(\chi_{607}(23,\cdot)\) \(\chi_{607}(24,\cdot)\) \(\chi_{607}(29,\cdot)\) \(\chi_{607}(31,\cdot)\) \(\chi_{607}(35,\cdot)\) \(\chi_{607}(39,\cdot)\) \(\chi_{607}(40,\cdot)\) \(\chi_{607}(46,\cdot)\) \(\chi_{607}(54,\cdot)\) \(\chi_{607}(59,\cdot)\) \(\chi_{607}(62,\cdot)\) \(\chi_{607}(65,\cdot)\) \(\chi_{607}(66,\cdot)\) \(\chi_{607}(67,\cdot)\) \(\chi_{607}(68,\cdot)\) \(\chi_{607}(74,\cdot)\) \(\chi_{607}(78,\cdot)\) \(\chi_{607}(84,\cdot)\) \(\chi_{607}(90,\cdot)\) \(\chi_{607}(96,\cdot)\) \(\chi_{607}(103,\cdot)\) \(\chi_{607}(108,\cdot)\) \(\chi_{607}(110,\cdot)\) \(\chi_{607}(113,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{303})$ |
| Fixed field: | Number field defined by a degree 606 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{557}{606}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 607 }(20, a) \) | \(-1\) | \(1\) | \(e\left(\frac{236}{303}\right)\) | \(e\left(\frac{557}{606}\right)\) | \(e\left(\frac{169}{303}\right)\) | \(e\left(\frac{245}{606}\right)\) | \(e\left(\frac{141}{202}\right)\) | \(e\left(\frac{57}{101}\right)\) | \(e\left(\frac{34}{101}\right)\) | \(e\left(\frac{254}{303}\right)\) | \(e\left(\frac{37}{202}\right)\) | \(e\left(\frac{284}{303}\right)\) |