Basic properties
Modulus: | \(1503\) | |
Conductor: | \(1503\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(249\) | 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 1503.m
\(\chi_{1503}(4,\cdot)\) \(\chi_{1503}(7,\cdot)\) \(\chi_{1503}(16,\cdot)\) \(\chi_{1503}(22,\cdot)\) \(\chi_{1503}(25,\cdot)\) \(\chi_{1503}(31,\cdot)\) \(\chi_{1503}(49,\cdot)\) \(\chi_{1503}(58,\cdot)\) \(\chi_{1503}(61,\cdot)\) \(\chi_{1503}(76,\cdot)\) \(\chi_{1503}(85,\cdot)\) \(\chi_{1503}(88,\cdot)\) \(\chi_{1503}(94,\cdot)\) \(\chi_{1503}(97,\cdot)\) \(\chi_{1503}(112,\cdot)\) \(\chi_{1503}(115,\cdot)\) \(\chi_{1503}(121,\cdot)\) \(\chi_{1503}(124,\cdot)\) \(\chi_{1503}(130,\cdot)\) \(\chi_{1503}(133,\cdot)\) \(\chi_{1503}(157,\cdot)\) \(\chi_{1503}(169,\cdot)\) \(\chi_{1503}(175,\cdot)\) \(\chi_{1503}(178,\cdot)\) \(\chi_{1503}(196,\cdot)\) \(\chi_{1503}(205,\cdot)\) \(\chi_{1503}(211,\cdot)\) \(\chi_{1503}(214,\cdot)\) \(\chi_{1503}(223,\cdot)\) \(\chi_{1503}(229,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{249})$ |
Fixed field: | Number field defined by a degree 249 polynomial (not computed) |
Values on generators
\((335,172)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{40}{83}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 1503 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{152}{249}\right)\) | \(e\left(\frac{55}{249}\right)\) | \(e\left(\frac{37}{249}\right)\) | \(e\left(\frac{50}{249}\right)\) | \(e\left(\frac{69}{83}\right)\) | \(e\left(\frac{63}{83}\right)\) | \(e\left(\frac{206}{249}\right)\) | \(e\left(\frac{76}{249}\right)\) | \(e\left(\frac{202}{249}\right)\) | \(e\left(\frac{110}{249}\right)\) |