Basic properties
Modulus: | \(501\) | |
Conductor: | \(501\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(166\) | 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 501.h
\(\chi_{501}(2,\cdot)\) \(\chi_{501}(8,\cdot)\) \(\chi_{501}(11,\cdot)\) \(\chi_{501}(14,\cdot)\) \(\chi_{501}(29,\cdot)\) \(\chi_{501}(32,\cdot)\) \(\chi_{501}(38,\cdot)\) \(\chi_{501}(44,\cdot)\) \(\chi_{501}(47,\cdot)\) \(\chi_{501}(50,\cdot)\) \(\chi_{501}(56,\cdot)\) \(\chi_{501}(62,\cdot)\) \(\chi_{501}(65,\cdot)\) \(\chi_{501}(77,\cdot)\) \(\chi_{501}(89,\cdot)\) \(\chi_{501}(98,\cdot)\) \(\chi_{501}(107,\cdot)\) \(\chi_{501}(116,\cdot)\) \(\chi_{501}(122,\cdot)\) \(\chi_{501}(128,\cdot)\) \(\chi_{501}(137,\cdot)\) \(\chi_{501}(152,\cdot)\) \(\chi_{501}(170,\cdot)\) \(\chi_{501}(173,\cdot)\) \(\chi_{501}(176,\cdot)\) \(\chi_{501}(179,\cdot)\) \(\chi_{501}(185,\cdot)\) \(\chi_{501}(188,\cdot)\) \(\chi_{501}(191,\cdot)\) \(\chi_{501}(194,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((335,172)\) → \((-1,e\left(\frac{43}{83}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 501 }(209, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{166}\right)\) | \(e\left(\frac{37}{83}\right)\) | \(e\left(\frac{3}{166}\right)\) | \(e\left(\frac{11}{83}\right)\) | \(e\left(\frac{111}{166}\right)\) | \(e\left(\frac{20}{83}\right)\) | \(e\left(\frac{1}{166}\right)\) | \(e\left(\frac{30}{83}\right)\) | \(e\left(\frac{59}{166}\right)\) | \(e\left(\frac{74}{83}\right)\) |