Basic properties
| Modulus: | \(8001\) | |
| Conductor: | \(2667\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2667}(410,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8001.md
\(\chi_{8001}(53,\cdot)\) \(\chi_{8001}(116,\cdot)\) \(\chi_{8001}(863,\cdot)\) \(\chi_{8001}(872,\cdot)\) \(\chi_{8001}(998,\cdot)\) \(\chi_{8001}(1061,\cdot)\) \(\chi_{8001}(1313,\cdot)\) \(\chi_{8001}(1367,\cdot)\) \(\chi_{8001}(1376,\cdot)\) \(\chi_{8001}(1493,\cdot)\) \(\chi_{8001}(1817,\cdot)\) \(\chi_{8001}(1997,\cdot)\) \(\chi_{8001}(2690,\cdot)\) \(\chi_{8001}(3014,\cdot)\) \(\chi_{8001}(3077,\cdot)\) \(\chi_{8001}(3266,\cdot)\) \(\chi_{8001}(3824,\cdot)\) \(\chi_{8001}(3896,\cdot)\) \(\chi_{8001}(4022,\cdot)\) \(\chi_{8001}(4076,\cdot)\) \(\chi_{8001}(4274,\cdot)\) \(\chi_{8001}(4706,\cdot)\) \(\chi_{8001}(4832,\cdot)\) \(\chi_{8001}(4904,\cdot)\) \(\chi_{8001}(5147,\cdot)\) \(\chi_{8001}(5210,\cdot)\) \(\chi_{8001}(5399,\cdot)\) \(\chi_{8001}(6407,\cdot)\) \(\chi_{8001}(6533,\cdot)\) \(\chi_{8001}(7226,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((3557,1144,7750)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{113}{126}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8001 }(3077, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{11}{42}\right)\) | \(e\left(\frac{19}{126}\right)\) | \(e\left(\frac{19}{63}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{31}{126}\right)\) | \(e\left(\frac{2}{3}\right)\) |