Basic properties
| Modulus: | \(8003\) | |
| Conductor: | \(8003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1950\) | 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.cq
\(\chi_{8003}(11,\cdot)\) \(\chi_{8003}(17,\cdot)\) \(\chi_{8003}(25,\cdot)\) \(\chi_{8003}(37,\cdot)\) \(\chi_{8003}(40,\cdot)\) \(\chi_{8003}(43,\cdot)\) \(\chi_{8003}(62,\cdot)\) \(\chi_{8003}(90,\cdot)\) \(\chi_{8003}(144,\cdot)\) \(\chi_{8003}(168,\cdot)\) \(\chi_{8003}(176,\cdot)\) \(\chi_{8003}(188,\cdot)\) \(\chi_{8003}(196,\cdot)\) \(\chi_{8003}(241,\cdot)\) \(\chi_{8003}(250,\cdot)\) \(\chi_{8003}(272,\cdot)\) \(\chi_{8003}(290,\cdot)\) \(\chi_{8003}(324,\cdot)\) \(\chi_{8003}(327,\cdot)\) \(\chi_{8003}(347,\cdot)\) \(\chi_{8003}(382,\cdot)\) \(\chi_{8003}(441,\cdot)\) \(\chi_{8003}(464,\cdot)\) \(\chi_{8003}(484,\cdot)\) \(\chi_{8003}(502,\cdot)\) \(\chi_{8003}(515,\cdot)\) \(\chi_{8003}(541,\cdot)\) \(\chi_{8003}(589,\cdot)\) \(\chi_{8003}(590,\cdot)\) \(\chi_{8003}(592,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{975})$ |
| Fixed field: | Number field defined by a degree 1950 polynomial (not computed) |
Values on generators
\((4984,7103)\) → \((e\left(\frac{3}{26}\right),e\left(\frac{47}{75}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8003 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{383}{390}\right)\) | \(e\left(\frac{469}{650}\right)\) | \(e\left(\frac{188}{195}\right)\) | \(e\left(\frac{1189}{1950}\right)\) | \(e\left(\frac{686}{975}\right)\) | \(e\left(\frac{587}{975}\right)\) | \(e\left(\frac{123}{130}\right)\) | \(e\left(\frac{144}{325}\right)\) | \(e\left(\frac{577}{975}\right)\) | \(e\left(\frac{584}{975}\right)\) |