Basic properties
| Modulus: | \(473\) | |
| Conductor: | \(473\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(210\) | 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.be
\(\chi_{473}(3,\cdot)\) \(\chi_{473}(5,\cdot)\) \(\chi_{473}(20,\cdot)\) \(\chi_{473}(26,\cdot)\) \(\chi_{473}(48,\cdot)\) \(\chi_{473}(69,\cdot)\) \(\chi_{473}(71,\cdot)\) \(\chi_{473}(91,\cdot)\) \(\chi_{473}(104,\cdot)\) \(\chi_{473}(114,\cdot)\) \(\chi_{473}(115,\cdot)\) \(\chi_{473}(119,\cdot)\) \(\chi_{473}(141,\cdot)\) \(\chi_{473}(147,\cdot)\) \(\chi_{473}(148,\cdot)\) \(\chi_{473}(157,\cdot)\) \(\chi_{473}(158,\cdot)\) \(\chi_{473}(159,\cdot)\) \(\chi_{473}(163,\cdot)\) \(\chi_{473}(190,\cdot)\) \(\chi_{473}(191,\cdot)\) \(\chi_{473}(192,\cdot)\) \(\chi_{473}(201,\cdot)\) \(\chi_{473}(202,\cdot)\) \(\chi_{473}(218,\cdot)\) \(\chi_{473}(234,\cdot)\) \(\chi_{473}(235,\cdot)\) \(\chi_{473}(245,\cdot)\) \(\chi_{473}(278,\cdot)\) \(\chi_{473}(284,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((431,89)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{1}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 473 }(3, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{89}{210}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{167}{210}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{89}{105}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{13}{42}\right)\) |