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
\((143,7)\) → \((-1,e\left(\frac{9}{70}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 213 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{17}{35}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{3}{35}\right)\) |