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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 473.bb
\(\chi_{473}(2,\cdot)\) \(\chi_{473}(8,\cdot)\) \(\chi_{473}(39,\cdot)\) \(\chi_{473}(51,\cdot)\) \(\chi_{473}(94,\cdot)\) \(\chi_{473}(118,\cdot)\) \(\chi_{473}(151,\cdot)\) \(\chi_{473}(156,\cdot)\) \(\chi_{473}(161,\cdot)\) \(\chi_{473}(194,\cdot)\) \(\chi_{473}(204,\cdot)\) \(\chi_{473}(211,\cdot)\) \(\chi_{473}(217,\cdot)\) \(\chi_{473}(237,\cdot)\) \(\chi_{473}(260,\cdot)\) \(\chi_{473}(266,\cdot)\) \(\chi_{473}(303,\cdot)\) \(\chi_{473}(371,\cdot)\) \(\chi_{473}(376,\cdot)\) \(\chi_{473}(409,\cdot)\) \(\chi_{473}(414,\cdot)\) \(\chi_{473}(426,\cdot)\) \(\chi_{473}(457,\cdot)\) \(\chi_{473}(469,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{35})$ |
| Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((431,89)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{13}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 473 }(8, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{35}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{29}{70}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{11}{14}\right)\) | \(e\left(\frac{1}{14}\right)\) |