Basic properties
| Modulus: | \(639\) | |
| Conductor: | \(213\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{213}(8,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 639.ba
\(\chi_{639}(8,\cdot)\) \(\chi_{639}(80,\cdot)\) \(\chi_{639}(89,\cdot)\) \(\chi_{639}(98,\cdot)\) \(\chi_{639}(107,\cdot)\) \(\chi_{639}(152,\cdot)\) \(\chi_{639}(161,\cdot)\) \(\chi_{639}(206,\cdot)\) \(\chi_{639}(215,\cdot)\) \(\chi_{639}(242,\cdot)\) \(\chi_{639}(251,\cdot)\) \(\chi_{639}(287,\cdot)\) \(\chi_{639}(296,\cdot)\) \(\chi_{639}(359,\cdot)\) \(\chi_{639}(395,\cdot)\) \(\chi_{639}(404,\cdot)\) \(\chi_{639}(413,\cdot)\) \(\chi_{639}(476,\cdot)\) \(\chi_{639}(503,\cdot)\) \(\chi_{639}(512,\cdot)\) \(\chi_{639}(521,\cdot)\) \(\chi_{639}(557,\cdot)\) \(\chi_{639}(584,\cdot)\) \(\chi_{639}(611,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((569,433)\) → \((-1,e\left(\frac{9}{35}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 639 }(8, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{6}{35}\right)\) |