Basic properties
| Modulus: | \(213\) | |
| Conductor: | \(213\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 213.n
\(\chi_{213}(11,\cdot)\) \(\chi_{213}(35,\cdot)\) \(\chi_{213}(44,\cdot)\) \(\chi_{213}(47,\cdot)\) \(\chi_{213}(53,\cdot)\) \(\chi_{213}(56,\cdot)\) \(\chi_{213}(59,\cdot)\) \(\chi_{213}(62,\cdot)\) \(\chi_{213}(65,\cdot)\) \(\chi_{213}(68,\cdot)\) \(\chi_{213}(92,\cdot)\) \(\chi_{213}(104,\cdot)\) \(\chi_{213}(113,\cdot)\) \(\chi_{213}(134,\cdot)\) \(\chi_{213}(140,\cdot)\) \(\chi_{213}(149,\cdot)\) \(\chi_{213}(155,\cdot)\) \(\chi_{213}(164,\cdot)\) \(\chi_{213}(170,\cdot)\) \(\chi_{213}(173,\cdot)\) \(\chi_{213}(194,\cdot)\) \(\chi_{213}(197,\cdot)\) \(\chi_{213}(203,\cdot)\) \(\chi_{213}(209,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((143,7)\) → \((-1,e\left(\frac{23}{70}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 213 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{31}{35}\right)\) |