Basic properties
| Modulus: | \(946\) | |
| Conductor: | \(473\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(35\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{473}(47,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 946.v
\(\chi_{946}(47,\cdot)\) \(\chi_{946}(59,\cdot)\) \(\chi_{946}(97,\cdot)\) \(\chi_{946}(207,\cdot)\) \(\chi_{946}(213,\cdot)\) \(\chi_{946}(269,\cdot)\) \(\chi_{946}(279,\cdot)\) \(\chi_{946}(317,\cdot)\) \(\chi_{946}(355,\cdot)\) \(\chi_{946}(379,\cdot)\) \(\chi_{946}(465,\cdot)\) \(\chi_{946}(471,\cdot)\) \(\chi_{946}(477,\cdot)\) \(\chi_{946}(489,\cdot)\) \(\chi_{946}(537,\cdot)\) \(\chi_{946}(575,\cdot)\) \(\chi_{946}(643,\cdot)\) \(\chi_{946}(709,\cdot)\) \(\chi_{946}(729,\cdot)\) \(\chi_{946}(735,\cdot)\) \(\chi_{946}(785,\cdot)\) \(\chi_{946}(795,\cdot)\) \(\chi_{946}(895,\cdot)\) \(\chi_{946}(907,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 35 polynomial |
Values on generators
\((431,89)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{2}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 946 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{1}{35}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) |