Basic properties
| Modulus: | \(633\) | |
| Conductor: | \(633\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | 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 633.z
\(\chi_{633}(5,\cdot)\) \(\chi_{633}(11,\cdot)\) \(\chi_{633}(65,\cdot)\) \(\chi_{633}(113,\cdot)\) \(\chi_{633}(122,\cdot)\) \(\chi_{633}(125,\cdot)\) \(\chi_{633}(143,\cdot)\) \(\chi_{633}(203,\cdot)\) \(\chi_{633}(224,\cdot)\) \(\chi_{633}(236,\cdot)\) \(\chi_{633}(275,\cdot)\) \(\chi_{633}(287,\cdot)\) \(\chi_{633}(290,\cdot)\) \(\chi_{633}(293,\cdot)\) \(\chi_{633}(320,\cdot)\) \(\chi_{633}(332,\cdot)\) \(\chi_{633}(362,\cdot)\) \(\chi_{633}(380,\cdot)\) \(\chi_{633}(395,\cdot)\) \(\chi_{633}(404,\cdot)\) \(\chi_{633}(509,\cdot)\) \(\chi_{633}(518,\cdot)\) \(\chi_{633}(536,\cdot)\) \(\chi_{633}(605,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((212,424)\) → \((-1,e\left(\frac{12}{35}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 633 }(362, a) \) | \(-1\) | \(1\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(-1\) | \(e\left(\frac{13}{35}\right)\) |