Basic properties
| Modulus: | \(8003\) | |
| Conductor: | \(8003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1300\) | 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.cn
\(\chi_{8003}(3,\cdot)\) \(\chi_{8003}(26,\cdot)\) \(\chi_{8003}(27,\cdot)\) \(\chi_{8003}(41,\cdot)\) \(\chi_{8003}(65,\cdot)\) \(\chi_{8003}(67,\cdot)\) \(\chi_{8003}(73,\cdot)\) \(\chi_{8003}(79,\cdot)\) \(\chi_{8003}(101,\cdot)\) \(\chi_{8003}(154,\cdot)\) \(\chi_{8003}(177,\cdot)\) \(\chi_{8003}(178,\cdot)\) \(\chi_{8003}(179,\cdot)\) \(\chi_{8003}(192,\cdot)\) \(\chi_{8003}(204,\cdot)\) \(\chi_{8003}(224,\cdot)\) \(\chi_{8003}(230,\cdot)\) \(\chi_{8003}(234,\cdot)\) \(\chi_{8003}(273,\cdot)\) \(\chi_{8003}(326,\cdot)\) \(\chi_{8003}(330,\cdot)\) \(\chi_{8003}(359,\cdot)\) \(\chi_{8003}(369,\cdot)\) \(\chi_{8003}(385,\cdot)\) \(\chi_{8003}(403,\cdot)\) \(\chi_{8003}(444,\cdot)\) \(\chi_{8003}(456,\cdot)\) \(\chi_{8003}(479,\cdot)\) \(\chi_{8003}(480,\cdot)\) \(\chi_{8003}(510,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1300})$ |
| Fixed field: | Number field defined by a degree 1300 polynomial (not computed) |
Values on generators
\((4984,7103)\) → \((e\left(\frac{17}{52}\right),e\left(\frac{27}{50}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8003 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{260}\right)\) | \(e\left(\frac{387}{1300}\right)\) | \(e\left(\frac{33}{130}\right)\) | \(e\left(\frac{1099}{1300}\right)\) | \(e\left(\frac{138}{325}\right)\) | \(e\left(\frac{246}{325}\right)\) | \(e\left(\frac{99}{260}\right)\) | \(e\left(\frac{387}{650}\right)\) | \(e\left(\frac{316}{325}\right)\) | \(e\left(\frac{469}{650}\right)\) |