Basic properties
| Modulus: | \(8003\) | |
| Conductor: | \(8003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(100\) | 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 8003.bp
\(\chi_{8003}(83,\cdot)\) \(\chi_{8003}(560,\cdot)\) \(\chi_{8003}(825,\cdot)\) \(\chi_{8003}(1037,\cdot)\) \(\chi_{8003}(1083,\cdot)\) \(\chi_{8003}(1136,\cdot)\) \(\chi_{8003}(1249,\cdot)\) \(\chi_{8003}(1567,\cdot)\) \(\chi_{8003}(1726,\cdot)\) \(\chi_{8003}(1885,\cdot)\) \(\chi_{8003}(1991,\cdot)\) \(\chi_{8003}(2256,\cdot)\) \(\chi_{8003}(2620,\cdot)\) \(\chi_{8003}(2627,\cdot)\) \(\chi_{8003}(2991,\cdot)\) \(\chi_{8003}(3044,\cdot)\) \(\chi_{8003}(3574,\cdot)\) \(\chi_{8003}(3627,\cdot)\) \(\chi_{8003}(3952,\cdot)\) \(\chi_{8003}(4005,\cdot)\) \(\chi_{8003}(4104,\cdot)\) \(\chi_{8003}(4899,\cdot)\) \(\chi_{8003}(5217,\cdot)\) \(\chi_{8003}(5489,\cdot)\) \(\chi_{8003}(5694,\cdot)\) \(\chi_{8003}(5860,\cdot)\) \(\chi_{8003}(5913,\cdot)\) \(\chi_{8003}(5959,\cdot)\) \(\chi_{8003}(6171,\cdot)\) \(\chi_{8003}(6383,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((4984,7103)\) → \((i,e\left(\frac{41}{50}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8003 }(83, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{67}{100}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{59}{100}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{11}{25}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{17}{50}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{29}{50}\right)\) |