Basic properties
| Modulus: | \(2017\) | |
| Conductor: | \(2017\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(336\) | 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 2017.bf
\(\chi_{2017}(2,\cdot)\) \(\chi_{2017}(27,\cdot)\) \(\chi_{2017}(29,\cdot)\) \(\chi_{2017}(31,\cdot)\) \(\chi_{2017}(32,\cdot)\) \(\chi_{2017}(33,\cdot)\) \(\chi_{2017}(63,\cdot)\) \(\chi_{2017}(69,\cdot)\) \(\chi_{2017}(95,\cdot)\) \(\chi_{2017}(103,\cdot)\) \(\chi_{2017}(116,\cdot)\) \(\chi_{2017}(124,\cdot)\) \(\chi_{2017}(132,\cdot)\) \(\chi_{2017}(147,\cdot)\) \(\chi_{2017}(158,\cdot)\) \(\chi_{2017}(219,\cdot)\) \(\chi_{2017}(235,\cdot)\) \(\chi_{2017}(244,\cdot)\) \(\chi_{2017}(274,\cdot)\) \(\chi_{2017}(276,\cdot)\) \(\chi_{2017}(289,\cdot)\) \(\chi_{2017}(308,\cdot)\) \(\chi_{2017}(335,\cdot)\) \(\chi_{2017}(343,\cdot)\) \(\chi_{2017}(380,\cdot)\) \(\chi_{2017}(382,\cdot)\) \(\chi_{2017}(383,\cdot)\) \(\chi_{2017}(432,\cdot)\) \(\chi_{2017}(458,\cdot)\) \(\chi_{2017}(489,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{336})$ |
| Fixed field: | Number field defined by a degree 336 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{143}{336}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2017 }(63, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{56}\right)\) | \(e\left(\frac{61}{168}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{143}{336}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{73}{168}\right)\) | \(e\left(\frac{17}{56}\right)\) | \(e\left(\frac{61}{84}\right)\) | \(e\left(\frac{65}{336}\right)\) | \(e\left(\frac{29}{42}\right)\) |