Basic properties
| Modulus: | \(4029\) | |
| Conductor: | \(4029\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(624\) | 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.db
\(\chi_{4029}(29,\cdot)\) \(\chi_{4029}(74,\cdot)\) \(\chi_{4029}(107,\cdot)\) \(\chi_{4029}(113,\cdot)\) \(\chi_{4029}(116,\cdot)\) \(\chi_{4029}(122,\cdot)\) \(\chi_{4029}(164,\cdot)\) \(\chi_{4029}(197,\cdot)\) \(\chi_{4029}(218,\cdot)\) \(\chi_{4029}(224,\cdot)\) \(\chi_{4029}(233,\cdot)\) \(\chi_{4029}(266,\cdot)\) \(\chi_{4029}(284,\cdot)\) \(\chi_{4029}(296,\cdot)\) \(\chi_{4029}(311,\cdot)\) \(\chi_{4029}(350,\cdot)\) \(\chi_{4029}(386,\cdot)\) \(\chi_{4029}(398,\cdot)\) \(\chi_{4029}(401,\cdot)\) \(\chi_{4029}(449,\cdot)\) \(\chi_{4029}(470,\cdot)\) \(\chi_{4029}(503,\cdot)\) \(\chi_{4029}(521,\cdot)\) \(\chi_{4029}(533,\cdot)\) \(\chi_{4029}(551,\cdot)\) \(\chi_{4029}(581,\cdot)\) \(\chi_{4029}(590,\cdot)\) \(\chi_{4029}(623,\cdot)\) \(\chi_{4029}(635,\cdot)\) \(\chi_{4029}(686,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{624})$ |
| Fixed field: | Number field defined by a degree 624 polynomial (not computed) |
Values on generators
\((2687,3556,3163)\) → \((-1,e\left(\frac{13}{16}\right),e\left(\frac{11}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 4029 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{137}{312}\right)\) | \(e\left(\frac{137}{156}\right)\) | \(e\left(\frac{191}{624}\right)\) | \(e\left(\frac{257}{624}\right)\) | \(e\left(\frac{33}{104}\right)\) | \(e\left(\frac{155}{208}\right)\) | \(e\left(\frac{485}{624}\right)\) | \(e\left(\frac{7}{156}\right)\) | \(e\left(\frac{177}{208}\right)\) | \(e\left(\frac{59}{78}\right)\) |