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.bd
\(\chi_{473}(13,\cdot)\) \(\chi_{473}(17,\cdot)\) \(\chi_{473}(24,\cdot)\) \(\chi_{473}(40,\cdot)\) \(\chi_{473}(52,\cdot)\) \(\chi_{473}(57,\cdot)\) \(\chi_{473}(68,\cdot)\) \(\chi_{473}(74,\cdot)\) \(\chi_{473}(83,\cdot)\) \(\chi_{473}(95,\cdot)\) \(\chi_{473}(96,\cdot)\) \(\chi_{473}(101,\cdot)\) \(\chi_{473}(117,\cdot)\) \(\chi_{473}(138,\cdot)\) \(\chi_{473}(139,\cdot)\) \(\chi_{473}(160,\cdot)\) \(\chi_{473}(167,\cdot)\) \(\chi_{473}(182,\cdot)\) \(\chi_{473}(189,\cdot)\) \(\chi_{473}(195,\cdot)\) \(\chi_{473}(228,\cdot)\) \(\chi_{473}(238,\cdot)\) \(\chi_{473}(239,\cdot)\) \(\chi_{473}(255,\cdot)\) \(\chi_{473}(271,\cdot)\) \(\chi_{473}(272,\cdot)\) \(\chi_{473}(281,\cdot)\) \(\chi_{473}(282,\cdot)\) \(\chi_{473}(283,\cdot)\) \(\chi_{473}(310,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((431,89)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{19}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 473 }(17, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{70}\right)\) | \(e\left(\frac{11}{105}\right)\) | \(e\left(\frac{23}{35}\right)\) | \(e\left(\frac{23}{105}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{69}{70}\right)\) | \(e\left(\frac{22}{105}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{16}{21}\right)\) |