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 \(\chi_{2667}(62,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8001.oa
\(\chi_{8001}(62,\cdot)\) \(\chi_{8001}(251,\cdot)\) \(\chi_{8001}(314,\cdot)\) \(\chi_{8001}(629,\cdot)\) \(\chi_{8001}(755,\cdot)\) \(\chi_{8001}(1385,\cdot)\) \(\chi_{8001}(1637,\cdot)\) \(\chi_{8001}(1700,\cdot)\) \(\chi_{8001}(2330,\cdot)\) \(\chi_{8001}(2582,\cdot)\) \(\chi_{8001}(2708,\cdot)\) \(\chi_{8001}(2771,\cdot)\) \(\chi_{8001}(3338,\cdot)\) \(\chi_{8001}(3464,\cdot)\) \(\chi_{8001}(3527,\cdot)\) \(\chi_{8001}(3590,\cdot)\) \(\chi_{8001}(3968,\cdot)\) \(\chi_{8001}(4094,\cdot)\) \(\chi_{8001}(4598,\cdot)\) \(\chi_{8001}(4787,\cdot)\) \(\chi_{8001}(5228,\cdot)\) \(\chi_{8001}(5291,\cdot)\) \(\chi_{8001}(5543,\cdot)\) \(\chi_{8001}(5606,\cdot)\) \(\chi_{8001}(5669,\cdot)\) \(\chi_{8001}(5732,\cdot)\) \(\chi_{8001}(5921,\cdot)\) \(\chi_{8001}(5984,\cdot)\) \(\chi_{8001}(6236,\cdot)\) \(\chi_{8001}(6488,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((3557,1144,7750)\) → \((-1,-1,e\left(\frac{59}{63}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8001 }(62, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{23}{126}\right)\) | \(e\left(\frac{67}{126}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{1}{6}\right)\) |