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 \(\chi_{473}(35,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 946.bb
\(\chi_{946}(35,\cdot)\) \(\chi_{946}(41,\cdot)\) \(\chi_{946}(107,\cdot)\) \(\chi_{946}(127,\cdot)\) \(\chi_{946}(145,\cdot)\) \(\chi_{946}(183,\cdot)\) \(\chi_{946}(193,\cdot)\) \(\chi_{946}(293,\cdot)\) \(\chi_{946}(299,\cdot)\) \(\chi_{946}(305,\cdot)\) \(\chi_{946}(365,\cdot)\) \(\chi_{946}(391,\cdot)\) \(\chi_{946}(403,\cdot)\) \(\chi_{946}(557,\cdot)\) \(\chi_{946}(563,\cdot)\) \(\chi_{946}(613,\cdot)\) \(\chi_{946}(623,\cdot)\) \(\chi_{946}(699,\cdot)\) \(\chi_{946}(723,\cdot)\) \(\chi_{946}(809,\cdot)\) \(\chi_{946}(821,\cdot)\) \(\chi_{946}(833,\cdot)\) \(\chi_{946}(871,\cdot)\) \(\chi_{946}(919,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((431,89)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{3}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 946 }(35, a) \) | \(-1\) | \(1\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{13}{70}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{6}{7}\right)\) |