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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4029.cq
\(\chi_{4029}(14,\cdot)\) \(\chi_{4029}(41,\cdot)\) \(\chi_{4029}(71,\cdot)\) \(\chi_{4029}(173,\cdot)\) \(\chi_{4029}(215,\cdot)\) \(\chi_{4029}(227,\cdot)\) \(\chi_{4029}(278,\cdot)\) \(\chi_{4029}(377,\cdot)\) \(\chi_{4029}(422,\cdot)\) \(\chi_{4029}(428,\cdot)\) \(\chi_{4029}(452,\cdot)\) \(\chi_{4029}(464,\cdot)\) \(\chi_{4029}(488,\cdot)\) \(\chi_{4029}(515,\cdot)\) \(\chi_{4029}(725,\cdot)\) \(\chi_{4029}(728,\cdot)\) \(\chi_{4029}(881,\cdot)\) \(\chi_{4029}(896,\cdot)\) \(\chi_{4029}(938,\cdot)\) \(\chi_{4029}(962,\cdot)\) \(\chi_{4029}(989,\cdot)\) \(\chi_{4029}(1085,\cdot)\) \(\chi_{4029}(1133,\cdot)\) \(\chi_{4029}(1163,\cdot)\) \(\chi_{4029}(1202,\cdot)\) \(\chi_{4029}(1355,\cdot)\) \(\chi_{4029}(1370,\cdot)\) \(\chi_{4029}(1400,\cdot)\) \(\chi_{4029}(1439,\cdot)\) \(\chi_{4029}(1493,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{208})$ |
| Fixed field: | Number field defined by a degree 208 polynomial (not computed) |
Values on generators
\((2687,3556,3163)\) → \((-1,e\left(\frac{9}{16}\right),e\left(\frac{19}{26}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 4029 }(14, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{104}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{129}{208}\right)\) | \(e\left(\frac{191}{208}\right)\) | \(e\left(\frac{93}{104}\right)\) | \(e\left(\frac{191}{208}\right)\) | \(e\left(\frac{27}{208}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{45}{208}\right)\) | \(e\left(\frac{5}{26}\right)\) |