Basic properties
| Modulus: | \(1013\) | |
| Conductor: | \(1013\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(506\) | 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 1013.k
\(\chi_{1013}(9,\cdot)\) \(\chi_{1013}(13,\cdot)\) \(\chi_{1013}(15,\cdot)\) \(\chi_{1013}(21,\cdot)\) \(\chi_{1013}(24,\cdot)\) \(\chi_{1013}(25,\cdot)\) \(\chi_{1013}(35,\cdot)\) \(\chi_{1013}(40,\cdot)\) \(\chi_{1013}(43,\cdot)\) \(\chi_{1013}(49,\cdot)\) \(\chi_{1013}(51,\cdot)\) \(\chi_{1013}(53,\cdot)\) \(\chi_{1013}(54,\cdot)\) \(\chi_{1013}(56,\cdot)\) \(\chi_{1013}(66,\cdot)\) \(\chi_{1013}(71,\cdot)\) \(\chi_{1013}(73,\cdot)\) \(\chi_{1013}(74,\cdot)\) \(\chi_{1013}(76,\cdot)\) \(\chi_{1013}(78,\cdot)\) \(\chi_{1013}(79,\cdot)\) \(\chi_{1013}(85,\cdot)\) \(\chi_{1013}(87,\cdot)\) \(\chi_{1013}(93,\cdot)\) \(\chi_{1013}(110,\cdot)\) \(\chi_{1013}(119,\cdot)\) \(\chi_{1013}(123,\cdot)\) \(\chi_{1013}(126,\cdot)\) \(\chi_{1013}(130,\cdot)\) \(\chi_{1013}(136,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{253})$ |
| Fixed field: | Number field defined by a degree 506 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{1}{506}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1013 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{46}\right)\) | \(e\left(\frac{1}{506}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{251}{506}\right)\) | \(e\left(\frac{182}{253}\right)\) | \(e\left(\frac{315}{506}\right)\) | \(e\left(\frac{7}{46}\right)\) | \(e\left(\frac{1}{253}\right)\) | \(e\left(\frac{54}{253}\right)\) | \(e\left(\frac{4}{23}\right)\) |