Basic properties
| Modulus: | \(8024\) | |
| Conductor: | \(1003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(116\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1003}(81,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8024.ch
\(\chi_{8024}(81,\cdot)\) \(\chi_{8024}(225,\cdot)\) \(\chi_{8024}(361,\cdot)\) \(\chi_{8024}(489,\cdot)\) \(\chi_{8024}(497,\cdot)\) \(\chi_{8024}(625,\cdot)\) \(\chi_{8024}(761,\cdot)\) \(\chi_{8024}(897,\cdot)\) \(\chi_{8024}(905,\cdot)\) \(\chi_{8024}(1169,\cdot)\) \(\chi_{8024}(1305,\cdot)\) \(\chi_{8024}(1313,\cdot)\) \(\chi_{8024}(1441,\cdot)\) \(\chi_{8024}(1585,\cdot)\) \(\chi_{8024}(1849,\cdot)\) \(\chi_{8024}(1857,\cdot)\) \(\chi_{8024}(1993,\cdot)\) \(\chi_{8024}(2129,\cdot)\) \(\chi_{8024}(2257,\cdot)\) \(\chi_{8024}(2401,\cdot)\) \(\chi_{8024}(2529,\cdot)\) \(\chi_{8024}(2801,\cdot)\) \(\chi_{8024}(2809,\cdot)\) \(\chi_{8024}(2937,\cdot)\) \(\chi_{8024}(3073,\cdot)\) \(\chi_{8024}(3345,\cdot)\) \(\chi_{8024}(3353,\cdot)\) \(\chi_{8024}(3625,\cdot)\) \(\chi_{8024}(3753,\cdot)\) \(\chi_{8024}(3897,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{116})$ |
| Fixed field: | Number field defined by a degree 116 polynomial (not computed) |
Values on generators
\((2007,4013,3777,3129)\) → \((1,1,i,e\left(\frac{13}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 8024 }(81, a) \) | \(1\) | \(1\) | \(e\left(\frac{77}{116}\right)\) | \(e\left(\frac{109}{116}\right)\) | \(e\left(\frac{95}{116}\right)\) | \(e\left(\frac{19}{58}\right)\) | \(e\left(\frac{111}{116}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{35}{58}\right)\) | \(e\left(\frac{31}{58}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{55}{116}\right)\) |