Basic properties
| Modulus: | \(1014\) | |
| Conductor: | \(507\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{507}(59,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1014.x
\(\chi_{1014}(11,\cdot)\) \(\chi_{1014}(41,\cdot)\) \(\chi_{1014}(59,\cdot)\) \(\chi_{1014}(71,\cdot)\) \(\chi_{1014}(119,\cdot)\) \(\chi_{1014}(137,\cdot)\) \(\chi_{1014}(149,\cdot)\) \(\chi_{1014}(167,\cdot)\) \(\chi_{1014}(197,\cdot)\) \(\chi_{1014}(215,\cdot)\) \(\chi_{1014}(227,\cdot)\) \(\chi_{1014}(245,\cdot)\) \(\chi_{1014}(275,\cdot)\) \(\chi_{1014}(293,\cdot)\) \(\chi_{1014}(305,\cdot)\) \(\chi_{1014}(323,\cdot)\) \(\chi_{1014}(353,\cdot)\) \(\chi_{1014}(371,\cdot)\) \(\chi_{1014}(383,\cdot)\) \(\chi_{1014}(401,\cdot)\) \(\chi_{1014}(431,\cdot)\) \(\chi_{1014}(449,\cdot)\) \(\chi_{1014}(461,\cdot)\) \(\chi_{1014}(479,\cdot)\) \(\chi_{1014}(509,\cdot)\) \(\chi_{1014}(527,\cdot)\) \(\chi_{1014}(539,\cdot)\) \(\chi_{1014}(557,\cdot)\) \(\chi_{1014}(605,\cdot)\) \(\chi_{1014}(617,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((677,847)\) → \((-1,e\left(\frac{35}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 1014 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{1}{156}\right)\) | \(e\left(\frac{95}{156}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{41}{78}\right)\) |