Basic properties
| Modulus: | \(2014\) | |
| Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1007}(49,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2014.w
\(\chi_{2014}(49,\cdot)\) \(\chi_{2014}(121,\cdot)\) \(\chi_{2014}(201,\cdot)\) \(\chi_{2014}(311,\cdot)\) \(\chi_{2014}(387,\cdot)\) \(\chi_{2014}(501,\cdot)\) \(\chi_{2014}(505,\cdot)\) \(\chi_{2014}(543,\cdot)\) \(\chi_{2014}(577,\cdot)\) \(\chi_{2014}(619,\cdot)\) \(\chi_{2014}(733,\cdot)\) \(\chi_{2014}(805,\cdot)\) \(\chi_{2014}(1075,\cdot)\) \(\chi_{2014}(1109,\cdot)\) \(\chi_{2014}(1261,\cdot)\) \(\chi_{2014}(1265,\cdot)\) \(\chi_{2014}(1341,\cdot)\) \(\chi_{2014}(1455,\cdot)\) \(\chi_{2014}(1531,\cdot)\) \(\chi_{2014}(1565,\cdot)\) \(\chi_{2014}(1603,\cdot)\) \(\chi_{2014}(1679,\cdot)\) \(\chi_{2014}(1759,\cdot)\) \(\chi_{2014}(1793,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((743,267)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{7}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 2014 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{7}{13}\right)\) | \(e\left(\frac{25}{39}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) |