Basic properties
| Modulus: | \(8450\) | |
| Conductor: | \(4225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(65\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4225}(131,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8450.bz
\(\chi_{8450}(131,\cdot)\) \(\chi_{8450}(261,\cdot)\) \(\chi_{8450}(391,\cdot)\) \(\chi_{8450}(521,\cdot)\) \(\chi_{8450}(781,\cdot)\) \(\chi_{8450}(911,\cdot)\) \(\chi_{8450}(1041,\cdot)\) \(\chi_{8450}(1171,\cdot)\) \(\chi_{8450}(1431,\cdot)\) \(\chi_{8450}(1561,\cdot)\) \(\chi_{8450}(1821,\cdot)\) \(\chi_{8450}(2081,\cdot)\) \(\chi_{8450}(2211,\cdot)\) \(\chi_{8450}(2341,\cdot)\) \(\chi_{8450}(2471,\cdot)\) \(\chi_{8450}(2731,\cdot)\) \(\chi_{8450}(2861,\cdot)\) \(\chi_{8450}(2991,\cdot)\) \(\chi_{8450}(3121,\cdot)\) \(\chi_{8450}(3511,\cdot)\) \(\chi_{8450}(3641,\cdot)\) \(\chi_{8450}(3771,\cdot)\) \(\chi_{8450}(4031,\cdot)\) \(\chi_{8450}(4161,\cdot)\) \(\chi_{8450}(4291,\cdot)\) \(\chi_{8450}(4421,\cdot)\) \(\chi_{8450}(4681,\cdot)\) \(\chi_{8450}(4811,\cdot)\) \(\chi_{8450}(4941,\cdot)\) \(\chi_{8450}(5331,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{65})$ |
| Fixed field: | Number field defined by a degree 65 polynomial |
Values on generators
\((677,3551)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{12}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 8450 }(131, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{65}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{34}{65}\right)\) | \(e\left(\frac{31}{65}\right)\) | \(e\left(\frac{63}{65}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{65}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{51}{65}\right)\) | \(e\left(\frac{47}{65}\right)\) |