Basic properties
| Modulus: | \(2014\) | |
| Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(468\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1007}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2014.bj
\(\chi_{2014}(5,\cdot)\) \(\chi_{2014}(35,\cdot)\) \(\chi_{2014}(55,\cdot)\) \(\chi_{2014}(61,\cdot)\) \(\chi_{2014}(73,\cdot)\) \(\chi_{2014}(85,\cdot)\) \(\chi_{2014}(101,\cdot)\) \(\chi_{2014}(111,\cdot)\) \(\chi_{2014}(137,\cdot)\) \(\chi_{2014}(139,\cdot)\) \(\chi_{2014}(157,\cdot)\) \(\chi_{2014}(161,\cdot)\) \(\chi_{2014}(177,\cdot)\) \(\chi_{2014}(207,\cdot)\) \(\chi_{2014}(215,\cdot)\) \(\chi_{2014}(233,\cdot)\) \(\chi_{2014}(245,\cdot)\) \(\chi_{2014}(251,\cdot)\) \(\chi_{2014}(253,\cdot)\) \(\chi_{2014}(263,\cdot)\) \(\chi_{2014}(283,\cdot)\) \(\chi_{2014}(291,\cdot)\) \(\chi_{2014}(313,\cdot)\) \(\chi_{2014}(321,\cdot)\) \(\chi_{2014}(339,\cdot)\) \(\chi_{2014}(351,\cdot)\) \(\chi_{2014}(359,\cdot)\) \(\chi_{2014}(385,\cdot)\) \(\chi_{2014}(389,\cdot)\) \(\chi_{2014}(397,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{468})$ |
| Fixed field: | Number field defined by a degree 468 polynomial (not computed) |
Values on generators
\((743,267)\) → \((e\left(\frac{1}{9}\right),e\left(\frac{3}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 2014 }(61, a) \) | \(-1\) | \(1\) | \(e\left(\frac{199}{468}\right)\) | \(e\left(\frac{229}{468}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{199}{234}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{110}{117}\right)\) | \(e\left(\frac{107}{117}\right)\) | \(e\left(\frac{161}{234}\right)\) | \(e\left(\frac{421}{468}\right)\) | \(e\left(\frac{17}{36}\right)\) |