Basic properties
| Modulus: | \(8450\) | |
| Conductor: | \(4225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(130\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4225}(79,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8450.ce
\(\chi_{8450}(79,\cdot)\) \(\chi_{8450}(209,\cdot)\) \(\chi_{8450}(469,\cdot)\) \(\chi_{8450}(729,\cdot)\) \(\chi_{8450}(859,\cdot)\) \(\chi_{8450}(989,\cdot)\) \(\chi_{8450}(1119,\cdot)\) \(\chi_{8450}(1379,\cdot)\) \(\chi_{8450}(1509,\cdot)\) \(\chi_{8450}(1639,\cdot)\) \(\chi_{8450}(1769,\cdot)\) \(\chi_{8450}(2159,\cdot)\) \(\chi_{8450}(2289,\cdot)\) \(\chi_{8450}(2419,\cdot)\) \(\chi_{8450}(2679,\cdot)\) \(\chi_{8450}(2809,\cdot)\) \(\chi_{8450}(2939,\cdot)\) \(\chi_{8450}(3069,\cdot)\) \(\chi_{8450}(3329,\cdot)\) \(\chi_{8450}(3459,\cdot)\) \(\chi_{8450}(3589,\cdot)\) \(\chi_{8450}(3979,\cdot)\) \(\chi_{8450}(4109,\cdot)\) \(\chi_{8450}(4239,\cdot)\) \(\chi_{8450}(4369,\cdot)\) \(\chi_{8450}(4629,\cdot)\) \(\chi_{8450}(4759,\cdot)\) \(\chi_{8450}(4889,\cdot)\) \(\chi_{8450}(5019,\cdot)\) \(\chi_{8450}(5279,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{65})$ |
| Fixed field: | Number field defined by a degree 130 polynomial (not computed) |
Values on generators
\((677,3551)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{2}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 8450 }(79, a) \) | \(1\) | \(1\) | \(e\left(\frac{101}{130}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{36}{65}\right)\) | \(e\left(\frac{29}{65}\right)\) | \(e\left(\frac{99}{130}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{48}{65}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{43}{130}\right)\) | \(e\left(\frac{23}{65}\right)\) |