Basic properties
| Modulus: | \(4655\) | |
| Conductor: | \(931\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{931}(257,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4655.go
\(\chi_{4655}(136,\cdot)\) \(\chi_{4655}(376,\cdot)\) \(\chi_{4655}(451,\cdot)\) \(\chi_{4655}(591,\cdot)\) \(\chi_{4655}(621,\cdot)\) \(\chi_{4655}(801,\cdot)\) \(\chi_{4655}(1041,\cdot)\) \(\chi_{4655}(1116,\cdot)\) \(\chi_{4655}(1286,\cdot)\) \(\chi_{4655}(1321,\cdot)\) \(\chi_{4655}(1466,\cdot)\) \(\chi_{4655}(1706,\cdot)\) \(\chi_{4655}(1781,\cdot)\) \(\chi_{4655}(1921,\cdot)\) \(\chi_{4655}(1951,\cdot)\) \(\chi_{4655}(1986,\cdot)\) \(\chi_{4655}(2131,\cdot)\) \(\chi_{4655}(2446,\cdot)\) \(\chi_{4655}(2586,\cdot)\) \(\chi_{4655}(2651,\cdot)\) \(\chi_{4655}(2796,\cdot)\) \(\chi_{4655}(3036,\cdot)\) \(\chi_{4655}(3111,\cdot)\) \(\chi_{4655}(3251,\cdot)\) \(\chi_{4655}(3281,\cdot)\) \(\chi_{4655}(3316,\cdot)\) \(\chi_{4655}(3701,\cdot)\) \(\chi_{4655}(3776,\cdot)\) \(\chi_{4655}(3916,\cdot)\) \(\chi_{4655}(3946,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((932,3041,2206)\) → \((1,e\left(\frac{11}{42}\right),e\left(\frac{17}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 4655 }(3981, a) \) | \(1\) | \(1\) | \(e\left(\frac{95}{126}\right)\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{32}{63}\right)\) | \(e\left(\frac{37}{126}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{1}{63}\right)\) |