Basic properties
| Modulus: | \(473\) | |
| Conductor: | \(473\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 473.ba
\(\chi_{473}(35,\cdot)\) \(\chi_{473}(41,\cdot)\) \(\chi_{473}(84,\cdot)\) \(\chi_{473}(90,\cdot)\) \(\chi_{473}(107,\cdot)\) \(\chi_{473}(127,\cdot)\) \(\chi_{473}(140,\cdot)\) \(\chi_{473}(145,\cdot)\) \(\chi_{473}(150,\cdot)\) \(\chi_{473}(183,\cdot)\) \(\chi_{473}(193,\cdot)\) \(\chi_{473}(226,\cdot)\) \(\chi_{473}(250,\cdot)\) \(\chi_{473}(293,\cdot)\) \(\chi_{473}(299,\cdot)\) \(\chi_{473}(305,\cdot)\) \(\chi_{473}(336,\cdot)\) \(\chi_{473}(348,\cdot)\) \(\chi_{473}(360,\cdot)\) \(\chi_{473}(365,\cdot)\) \(\chi_{473}(391,\cdot)\) \(\chi_{473}(398,\cdot)\) \(\chi_{473}(403,\cdot)\) \(\chi_{473}(446,\cdot)\)
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
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 473 }(35, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{1}{70}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{4}{7}\right)\) |