Basic properties
Modulus: | \(1075\) | |
Conductor: | \(1075\) | 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 1075.bj
\(\chi_{1075}(4,\cdot)\) \(\chi_{1075}(54,\cdot)\) \(\chi_{1075}(59,\cdot)\) \(\chi_{1075}(64,\cdot)\) \(\chi_{1075}(84,\cdot)\) \(\chi_{1075}(164,\cdot)\) \(\chi_{1075}(219,\cdot)\) \(\chi_{1075}(269,\cdot)\) \(\chi_{1075}(279,\cdot)\) \(\chi_{1075}(379,\cdot)\) \(\chi_{1075}(434,\cdot)\) \(\chi_{1075}(484,\cdot)\) \(\chi_{1075}(489,\cdot)\) \(\chi_{1075}(494,\cdot)\) \(\chi_{1075}(514,\cdot)\) \(\chi_{1075}(594,\cdot)\) \(\chi_{1075}(704,\cdot)\) \(\chi_{1075}(709,\cdot)\) \(\chi_{1075}(729,\cdot)\) \(\chi_{1075}(809,\cdot)\) \(\chi_{1075}(864,\cdot)\) \(\chi_{1075}(914,\cdot)\) \(\chi_{1075}(919,\cdot)\) \(\chi_{1075}(944,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((302,476)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{2}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 1075 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(-1\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{6}{35}\right)\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{3}{70}\right)\) |