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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 213.o
\(\chi_{213}(2,\cdot)\) \(\chi_{213}(8,\cdot)\) \(\chi_{213}(29,\cdot)\) \(\chi_{213}(38,\cdot)\) \(\chi_{213}(50,\cdot)\) \(\chi_{213}(74,\cdot)\) \(\chi_{213}(77,\cdot)\) \(\chi_{213}(80,\cdot)\) \(\chi_{213}(83,\cdot)\) \(\chi_{213}(86,\cdot)\) \(\chi_{213}(89,\cdot)\) \(\chi_{213}(95,\cdot)\) \(\chi_{213}(98,\cdot)\) \(\chi_{213}(107,\cdot)\) \(\chi_{213}(131,\cdot)\) \(\chi_{213}(146,\cdot)\) \(\chi_{213}(152,\cdot)\) \(\chi_{213}(158,\cdot)\) \(\chi_{213}(161,\cdot)\) \(\chi_{213}(182,\cdot)\) \(\chi_{213}(185,\cdot)\) \(\chi_{213}(191,\cdot)\) \(\chi_{213}(200,\cdot)\) \(\chi_{213}(206,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((143,7)\) → \((-1,e\left(\frac{9}{35}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 213 }(8, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{3}{35}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{9}{70}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{6}{35}\right)\) |