Basic properties
Modulus: | \(2003\) | |
Conductor: | \(2003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(182\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2003.m
\(\chi_{2003}(6,\cdot)\) \(\chi_{2003}(17,\cdot)\) \(\chi_{2003}(69,\cdot)\) \(\chi_{2003}(132,\cdot)\) \(\chi_{2003}(216,\cdot)\) \(\chi_{2003}(233,\cdot)\) \(\chi_{2003}(260,\cdot)\) \(\chi_{2003}(295,\cdot)\) \(\chi_{2003}(331,\cdot)\) \(\chi_{2003}(334,\cdot)\) \(\chi_{2003}(374,\cdot)\) \(\chi_{2003}(376,\cdot)\) \(\chi_{2003}(382,\cdot)\) \(\chi_{2003}(387,\cdot)\) \(\chi_{2003}(388,\cdot)\) \(\chi_{2003}(392,\cdot)\) \(\chi_{2003}(456,\cdot)\) \(\chi_{2003}(481,\cdot)\) \(\chi_{2003}(502,\cdot)\) \(\chi_{2003}(524,\cdot)\) \(\chi_{2003}(534,\cdot)\) \(\chi_{2003}(567,\cdot)\) \(\chi_{2003}(584,\cdot)\) \(\chi_{2003}(603,\cdot)\) \(\chi_{2003}(604,\cdot)\) \(\chi_{2003}(605,\cdot)\) \(\chi_{2003}(612,\cdot)\) \(\chi_{2003}(707,\cdot)\) \(\chi_{2003}(802,\cdot)\) \(\chi_{2003}(817,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{91})$ |
Fixed field: | Number field defined by a degree 182 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{163}{182}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 2003 }(817, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{80}{91}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{163}{182}\right)\) | \(e\left(\frac{55}{182}\right)\) | \(e\left(\frac{29}{182}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{69}{91}\right)\) | \(e\left(\frac{29}{91}\right)\) | \(e\left(\frac{23}{26}\right)\) |