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 \(\chi_{473}(27,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 946.ba
\(\chi_{946}(27,\cdot)\) \(\chi_{946}(75,\cdot)\) \(\chi_{946}(113,\cdot)\) \(\chi_{946}(125,\cdot)\) \(\chi_{946}(137,\cdot)\) \(\chi_{946}(223,\cdot)\) \(\chi_{946}(247,\cdot)\) \(\chi_{946}(323,\cdot)\) \(\chi_{946}(333,\cdot)\) \(\chi_{946}(383,\cdot)\) \(\chi_{946}(389,\cdot)\) \(\chi_{946}(543,\cdot)\) \(\chi_{946}(555,\cdot)\) \(\chi_{946}(581,\cdot)\) \(\chi_{946}(641,\cdot)\) \(\chi_{946}(647,\cdot)\) \(\chi_{946}(653,\cdot)\) \(\chi_{946}(753,\cdot)\) \(\chi_{946}(763,\cdot)\) \(\chi_{946}(801,\cdot)\) \(\chi_{946}(819,\cdot)\) \(\chi_{946}(839,\cdot)\) \(\chi_{946}(905,\cdot)\) \(\chi_{946}(911,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((431,89)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{1}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 946 }(27, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{70}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{19}{35}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{11}{35}\right)\) | \(e\left(\frac{39}{70}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{1}{7}\right)\) |