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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 501.g
\(\chi_{501}(5,\cdot)\) \(\chi_{501}(17,\cdot)\) \(\chi_{501}(20,\cdot)\) \(\chi_{501}(23,\cdot)\) \(\chi_{501}(26,\cdot)\) \(\chi_{501}(35,\cdot)\) \(\chi_{501}(41,\cdot)\) \(\chi_{501}(53,\cdot)\) \(\chi_{501}(59,\cdot)\) \(\chi_{501}(68,\cdot)\) \(\chi_{501}(71,\cdot)\) \(\chi_{501}(74,\cdot)\) \(\chi_{501}(80,\cdot)\) \(\chi_{501}(83,\cdot)\) \(\chi_{501}(86,\cdot)\) \(\chi_{501}(92,\cdot)\) \(\chi_{501}(95,\cdot)\) \(\chi_{501}(101,\cdot)\) \(\chi_{501}(104,\cdot)\) \(\chi_{501}(110,\cdot)\) \(\chi_{501}(113,\cdot)\) \(\chi_{501}(119,\cdot)\) \(\chi_{501}(125,\cdot)\) \(\chi_{501}(131,\cdot)\) \(\chi_{501}(134,\cdot)\) \(\chi_{501}(140,\cdot)\) \(\chi_{501}(143,\cdot)\) \(\chi_{501}(146,\cdot)\) \(\chi_{501}(149,\cdot)\) \(\chi_{501}(155,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((335,172)\) → \((-1,e\left(\frac{53}{166}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 501 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{45}{166}\right)\) | \(e\left(\frac{45}{83}\right)\) | \(e\left(\frac{68}{83}\right)\) | \(e\left(\frac{56}{83}\right)\) | \(e\left(\frac{135}{166}\right)\) | \(e\left(\frac{15}{166}\right)\) | \(e\left(\frac{73}{166}\right)\) | \(e\left(\frac{147}{166}\right)\) | \(e\left(\frac{157}{166}\right)\) | \(e\left(\frac{7}{83}\right)\) |