Basic properties
| Modulus: | \(4225\) | |
| 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 \(\chi_{845}(74,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4225.ca
\(\chi_{4225}(74,\cdot)\) \(\chi_{4225}(224,\cdot)\) \(\chi_{4225}(399,\cdot)\) \(\chi_{4225}(549,\cdot)\) \(\chi_{4225}(724,\cdot)\) \(\chi_{4225}(874,\cdot)\) \(\chi_{4225}(1049,\cdot)\) \(\chi_{4225}(1199,\cdot)\) \(\chi_{4225}(1524,\cdot)\) \(\chi_{4225}(1699,\cdot)\) \(\chi_{4225}(1849,\cdot)\) \(\chi_{4225}(2024,\cdot)\) \(\chi_{4225}(2349,\cdot)\) \(\chi_{4225}(2499,\cdot)\) \(\chi_{4225}(2674,\cdot)\) \(\chi_{4225}(2824,\cdot)\) \(\chi_{4225}(2999,\cdot)\) \(\chi_{4225}(3149,\cdot)\) \(\chi_{4225}(3324,\cdot)\) \(\chi_{4225}(3474,\cdot)\) \(\chi_{4225}(3649,\cdot)\) \(\chi_{4225}(3799,\cdot)\) \(\chi_{4225}(3974,\cdot)\) \(\chi_{4225}(4124,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((677,3551)\) → \((-1,e\left(\frac{38}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
| \( \chi_{ 4225 }(74, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{3}{13}\right)\) |