Basic properties
| Modulus: | \(4225\) | |
| Conductor: | \(169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{169}(126,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4225.bm
\(\chi_{4225}(126,\cdot)\) \(\chi_{4225}(276,\cdot)\) \(\chi_{4225}(451,\cdot)\) \(\chi_{4225}(601,\cdot)\) \(\chi_{4225}(776,\cdot)\) \(\chi_{4225}(926,\cdot)\) \(\chi_{4225}(1101,\cdot)\) \(\chi_{4225}(1251,\cdot)\) \(\chi_{4225}(1426,\cdot)\) \(\chi_{4225}(1576,\cdot)\) \(\chi_{4225}(1751,\cdot)\) \(\chi_{4225}(1901,\cdot)\) \(\chi_{4225}(2076,\cdot)\) \(\chi_{4225}(2226,\cdot)\) \(\chi_{4225}(2401,\cdot)\) \(\chi_{4225}(2551,\cdot)\) \(\chi_{4225}(2876,\cdot)\) \(\chi_{4225}(3051,\cdot)\) \(\chi_{4225}(3201,\cdot)\) \(\chi_{4225}(3376,\cdot)\) \(\chi_{4225}(3701,\cdot)\) \(\chi_{4225}(3851,\cdot)\) \(\chi_{4225}(4026,\cdot)\) \(\chi_{4225}(4176,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((677,3551)\) → \((1,e\left(\frac{11}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
| \( \chi_{ 4225 }(126, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{6}{13}\right)\) |