Basic properties
| Modulus: | \(8001\) | |
| Conductor: | \(8001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8001.ms
\(\chi_{8001}(248,\cdot)\) \(\chi_{8001}(374,\cdot)\) \(\chi_{8001}(425,\cdot)\) \(\chi_{8001}(677,\cdot)\) \(\chi_{8001}(803,\cdot)\) \(\chi_{8001}(1004,\cdot)\) \(\chi_{8001}(1256,\cdot)\) \(\chi_{8001}(1433,\cdot)\) \(\chi_{8001}(1622,\cdot)\) \(\chi_{8001}(1685,\cdot)\) \(\chi_{8001}(2390,\cdot)\) \(\chi_{8001}(2882,\cdot)\) \(\chi_{8001}(3083,\cdot)\) \(\chi_{8001}(3323,\cdot)\) \(\chi_{8001}(3386,\cdot)\) \(\chi_{8001}(3587,\cdot)\) \(\chi_{8001}(3638,\cdot)\) \(\chi_{8001}(3701,\cdot)\) \(\chi_{8001}(3713,\cdot)\) \(\chi_{8001}(3827,\cdot)\) \(\chi_{8001}(4217,\cdot)\) \(\chi_{8001}(4583,\cdot)\) \(\chi_{8001}(4646,\cdot)\) \(\chi_{8001}(4835,\cdot)\) \(\chi_{8001}(4898,\cdot)\) \(\chi_{8001}(5276,\cdot)\) \(\chi_{8001}(5288,\cdot)\) \(\chi_{8001}(5540,\cdot)\) \(\chi_{8001}(5603,\cdot)\) \(\chi_{8001}(5855,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((3557,1144,7750)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{1}{6}\right),e\left(\frac{5}{63}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8001 }(248, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{113}{126}\right)\) | \(e\left(\frac{79}{126}\right)\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(-1\) |