Basic properties
Modulus: | \(946\) | |
Conductor: | \(473\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(70\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{473}(39,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 946.z
\(\chi_{946}(39,\cdot)\) \(\chi_{946}(51,\cdot)\) \(\chi_{946}(151,\cdot)\) \(\chi_{946}(161,\cdot)\) \(\chi_{946}(211,\cdot)\) \(\chi_{946}(217,\cdot)\) \(\chi_{946}(237,\cdot)\) \(\chi_{946}(303,\cdot)\) \(\chi_{946}(371,\cdot)\) \(\chi_{946}(409,\cdot)\) \(\chi_{946}(457,\cdot)\) \(\chi_{946}(469,\cdot)\) \(\chi_{946}(475,\cdot)\) \(\chi_{946}(481,\cdot)\) \(\chi_{946}(567,\cdot)\) \(\chi_{946}(591,\cdot)\) \(\chi_{946}(629,\cdot)\) \(\chi_{946}(667,\cdot)\) \(\chi_{946}(677,\cdot)\) \(\chi_{946}(733,\cdot)\) \(\chi_{946}(739,\cdot)\) \(\chi_{946}(849,\cdot)\) \(\chi_{946}(887,\cdot)\) \(\chi_{946}(899,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((431,89)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{11}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 946 }(39, a) \) | \(1\) | \(1\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{3}{70}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{67}{70}\right)\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{4}{7}\right)\) |