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 \(\chi_{845}(49,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4225.cc
\(\chi_{4225}(49,\cdot)\) \(\chi_{4225}(199,\cdot)\) \(\chi_{4225}(374,\cdot)\) \(\chi_{4225}(524,\cdot)\) \(\chi_{4225}(849,\cdot)\) \(\chi_{4225}(1024,\cdot)\) \(\chi_{4225}(1174,\cdot)\) \(\chi_{4225}(1349,\cdot)\) \(\chi_{4225}(1674,\cdot)\) \(\chi_{4225}(1824,\cdot)\) \(\chi_{4225}(1999,\cdot)\) \(\chi_{4225}(2149,\cdot)\) \(\chi_{4225}(2324,\cdot)\) \(\chi_{4225}(2474,\cdot)\) \(\chi_{4225}(2649,\cdot)\) \(\chi_{4225}(2799,\cdot)\) \(\chi_{4225}(2974,\cdot)\) \(\chi_{4225}(3124,\cdot)\) \(\chi_{4225}(3299,\cdot)\) \(\chi_{4225}(3449,\cdot)\) \(\chi_{4225}(3624,\cdot)\) \(\chi_{4225}(3774,\cdot)\) \(\chi_{4225}(3949,\cdot)\) \(\chi_{4225}(4099,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((677,3551)\) → \((-1,e\left(\frac{29}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
| \( \chi_{ 4225 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{2}{13}\right)\) |