Basic properties
Modulus: | \(4029\) | |
Conductor: | \(4029\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(208\) | 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 4029.cs
\(\chi_{4029}(62,\cdot)\) \(\chi_{4029}(65,\cdot)\) \(\chi_{4029}(125,\cdot)\) \(\chi_{4029}(131,\cdot)\) \(\chi_{4029}(143,\cdot)\) \(\chi_{4029}(146,\cdot)\) \(\chi_{4029}(176,\cdot)\) \(\chi_{4029}(245,\cdot)\) \(\chi_{4029}(275,\cdot)\) \(\chi_{4029}(299,\cdot)\) \(\chi_{4029}(326,\cdot)\) \(\chi_{4029}(362,\cdot)\) \(\chi_{4029}(368,\cdot)\) \(\chi_{4029}(380,\cdot)\) \(\chi_{4029}(413,\cdot)\) \(\chi_{4029}(482,\cdot)\) \(\chi_{4029}(539,\cdot)\) \(\chi_{4029}(575,\cdot)\) \(\chi_{4029}(605,\cdot)\) \(\chi_{4029}(617,\cdot)\) \(\chi_{4029}(653,\cdot)\) \(\chi_{4029}(719,\cdot)\) \(\chi_{4029}(776,\cdot)\) \(\chi_{4029}(836,\cdot)\) \(\chi_{4029}(857,\cdot)\) \(\chi_{4029}(887,\cdot)\) \(\chi_{4029}(890,\cdot)\) \(\chi_{4029}(1010,\cdot)\) \(\chi_{4029}(1013,\cdot)\) \(\chi_{4029}(1049,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{208})$ |
Fixed field: | Number field defined by a degree 208 polynomial (not computed) |
Values on generators
\((2687,3556,3163)\) → \((-1,e\left(\frac{1}{16}\right),e\left(\frac{5}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 4029 }(836, a) \) | \(1\) | \(1\) | \(e\left(\frac{95}{104}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{137}{208}\right)\) | \(e\left(\frac{15}{208}\right)\) | \(e\left(\frac{77}{104}\right)\) | \(e\left(\frac{119}{208}\right)\) | \(e\left(\frac{19}{208}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{205}{208}\right)\) | \(e\left(\frac{17}{26}\right)\) |