Basic properties
| Modulus: | \(371\) | |
| Conductor: | \(371\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(39\) | 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 371.q
\(\chi_{371}(16,\cdot)\) \(\chi_{371}(44,\cdot)\) \(\chi_{371}(46,\cdot)\) \(\chi_{371}(81,\cdot)\) \(\chi_{371}(95,\cdot)\) \(\chi_{371}(100,\cdot)\) \(\chi_{371}(102,\cdot)\) \(\chi_{371}(116,\cdot)\) \(\chi_{371}(121,\cdot)\) \(\chi_{371}(130,\cdot)\) \(\chi_{371}(142,\cdot)\) \(\chi_{371}(172,\cdot)\) \(\chi_{371}(205,\cdot)\) \(\chi_{371}(228,\cdot)\) \(\chi_{371}(240,\cdot)\) \(\chi_{371}(254,\cdot)\) \(\chi_{371}(256,\cdot)\) \(\chi_{371}(261,\cdot)\) \(\chi_{371}(275,\cdot)\) \(\chi_{371}(289,\cdot)\) \(\chi_{371}(312,\cdot)\) \(\chi_{371}(331,\cdot)\) \(\chi_{371}(333,\cdot)\) \(\chi_{371}(354,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 39 polynomial |
Values on generators
\((213,267)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{9}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 371 }(142, a) \) | \(1\) | \(1\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{32}{39}\right)\) |