Basic properties
| Modulus: | \(8450\) | |
| Conductor: | \(845\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{845}(399,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8450.ca
\(\chi_{8450}(399,\cdot)\) \(\chi_{8450}(549,\cdot)\) \(\chi_{8450}(1049,\cdot)\) \(\chi_{8450}(1199,\cdot)\) \(\chi_{8450}(1699,\cdot)\) \(\chi_{8450}(1849,\cdot)\) \(\chi_{8450}(2349,\cdot)\) \(\chi_{8450}(2499,\cdot)\) \(\chi_{8450}(2999,\cdot)\) \(\chi_{8450}(3149,\cdot)\) \(\chi_{8450}(3649,\cdot)\) \(\chi_{8450}(3799,\cdot)\) \(\chi_{8450}(4299,\cdot)\) \(\chi_{8450}(4449,\cdot)\) \(\chi_{8450}(4949,\cdot)\) \(\chi_{8450}(5099,\cdot)\) \(\chi_{8450}(5749,\cdot)\) \(\chi_{8450}(6249,\cdot)\) \(\chi_{8450}(6899,\cdot)\) \(\chi_{8450}(7049,\cdot)\) \(\chi_{8450}(7549,\cdot)\) \(\chi_{8450}(7699,\cdot)\) \(\chi_{8450}(8199,\cdot)\) \(\chi_{8450}(8349,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((677,3551)\) → \((-1,e\left(\frac{35}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 8450 }(399, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{78}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{35}{39}\right)\) |