Basic properties
| Modulus: | \(2014\) | |
| Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(234\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1007}(15,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2014.bg
\(\chi_{2014}(13,\cdot)\) \(\chi_{2014}(15,\cdot)\) \(\chi_{2014}(89,\cdot)\) \(\chi_{2014}(97,\cdot)\) \(\chi_{2014}(155,\cdot)\) \(\chi_{2014}(203,\cdot)\) \(\chi_{2014}(205,\cdot)\) \(\chi_{2014}(261,\cdot)\) \(\chi_{2014}(281,\cdot)\) \(\chi_{2014}(307,\cdot)\) \(\chi_{2014}(333,\cdot)\) \(\chi_{2014}(395,\cdot)\) \(\chi_{2014}(413,\cdot)\) \(\chi_{2014}(439,\cdot)\) \(\chi_{2014}(471,\cdot)\) \(\chi_{2014}(523,\cdot)\) \(\chi_{2014}(545,\cdot)\) \(\chi_{2014}(599,\cdot)\) \(\chi_{2014}(611,\cdot)\) \(\chi_{2014}(629,\cdot)\) \(\chi_{2014}(649,\cdot)\) \(\chi_{2014}(699,\cdot)\) \(\chi_{2014}(705,\cdot)\) \(\chi_{2014}(713,\cdot)\) \(\chi_{2014}(717,\cdot)\) \(\chi_{2014}(725,\cdot)\) \(\chi_{2014}(735,\cdot)\) \(\chi_{2014}(755,\cdot)\) \(\chi_{2014}(789,\cdot)\) \(\chi_{2014}(811,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((743,267)\) → \((e\left(\frac{11}{18}\right),e\left(\frac{3}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 2014 }(15, a) \) | \(-1\) | \(1\) | \(e\left(\frac{203}{234}\right)\) | \(e\left(\frac{73}{117}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{86}{117}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{139}{234}\right)\) | \(e\left(\frac{115}{234}\right)\) | \(e\left(\frac{49}{117}\right)\) | \(e\left(\frac{179}{234}\right)\) | \(e\left(\frac{2}{9}\right)\) |