Basic properties
| Modulus: | \(8003\) | |
| Conductor: | \(8003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(300\) | 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.cb
\(\chi_{8003}(30,\cdot)\) \(\chi_{8003}(129,\cdot)\) \(\chi_{8003}(507,\cdot)\) \(\chi_{8003}(712,\cdot)\) \(\chi_{8003}(719,\cdot)\) \(\chi_{8003}(818,\cdot)\) \(\chi_{8003}(977,\cdot)\) \(\chi_{8003}(1348,\cdot)\) \(\chi_{8003}(1461,\cdot)\) \(\chi_{8003}(1673,\cdot)\) \(\chi_{8003}(1772,\cdot)\) \(\chi_{8003}(1825,\cdot)\) \(\chi_{8003}(1938,\cdot)\) \(\chi_{8003}(2097,\cdot)\) \(\chi_{8003}(2196,\cdot)\) \(\chi_{8003}(2203,\cdot)\) \(\chi_{8003}(2468,\cdot)\) \(\chi_{8003}(2574,\cdot)\) \(\chi_{8003}(2673,\cdot)\) \(\chi_{8003}(2733,\cdot)\) \(\chi_{8003}(2779,\cdot)\) \(\chi_{8003}(2832,\cdot)\) \(\chi_{8003}(2998,\cdot)\) \(\chi_{8003}(3097,\cdot)\) \(\chi_{8003}(3150,\cdot)\) \(\chi_{8003}(3415,\cdot)\) \(\chi_{8003}(3468,\cdot)\) \(\chi_{8003}(3521,\cdot)\) \(\chi_{8003}(3581,\cdot)\) \(\chi_{8003}(3680,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{300})$ |
| Fixed field: | Number field defined by a degree 300 polynomial (not computed) |
Values on generators
\((4984,7103)\) → \((i,e\left(\frac{113}{150}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8003 }(30, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{27}{100}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{37}{300}\right)\) | \(e\left(\frac{19}{75}\right)\) | \(e\left(\frac{73}{75}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{27}{50}\right)\) | \(e\left(\frac{8}{75}\right)\) | \(e\left(\frac{47}{150}\right)\) |