Basic properties
| Modulus: | \(1013\) | |
| Conductor: | \(1013\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(253\) | 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.j
\(\chi_{1013}(6,\cdot)\) \(\chi_{1013}(10,\cdot)\) \(\chi_{1013}(14,\cdot)\) \(\chi_{1013}(19,\cdot)\) \(\chi_{1013}(34,\cdot)\) \(\chi_{1013}(36,\cdot)\) \(\chi_{1013}(52,\cdot)\) \(\chi_{1013}(58,\cdot)\) \(\chi_{1013}(60,\cdot)\) \(\chi_{1013}(62,\cdot)\) \(\chi_{1013}(81,\cdot)\) \(\chi_{1013}(82,\cdot)\) \(\chi_{1013}(83,\cdot)\) \(\chi_{1013}(84,\cdot)\) \(\chi_{1013}(89,\cdot)\) \(\chi_{1013}(94,\cdot)\) \(\chi_{1013}(96,\cdot)\) \(\chi_{1013}(97,\cdot)\) \(\chi_{1013}(99,\cdot)\) \(\chi_{1013}(100,\cdot)\) \(\chi_{1013}(111,\cdot)\) \(\chi_{1013}(113,\cdot)\) \(\chi_{1013}(117,\cdot)\) \(\chi_{1013}(118,\cdot)\) \(\chi_{1013}(127,\cdot)\) \(\chi_{1013}(134,\cdot)\) \(\chi_{1013}(135,\cdot)\) \(\chi_{1013}(140,\cdot)\) \(\chi_{1013}(143,\cdot)\) \(\chi_{1013}(149,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{253})$ |
| Fixed field: | Number field defined by a degree 253 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{127}{253}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1013 }(1004, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{23}\right)\) | \(e\left(\frac{127}{253}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{252}{253}\right)\) | \(e\left(\frac{182}{253}\right)\) | \(e\left(\frac{31}{253}\right)\) | \(e\left(\frac{15}{23}\right)\) | \(e\left(\frac{1}{253}\right)\) | \(e\left(\frac{54}{253}\right)\) | \(e\left(\frac{4}{23}\right)\) |