Basic properties
| Modulus: | \(473\) | |
| Conductor: | \(473\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(105\) | 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.bc
\(\chi_{473}(9,\cdot)\) \(\chi_{473}(14,\cdot)\) \(\chi_{473}(15,\cdot)\) \(\chi_{473}(25,\cdot)\) \(\chi_{473}(31,\cdot)\) \(\chi_{473}(38,\cdot)\) \(\chi_{473}(53,\cdot)\) \(\chi_{473}(58,\cdot)\) \(\chi_{473}(60,\cdot)\) \(\chi_{473}(81,\cdot)\) \(\chi_{473}(103,\cdot)\) \(\chi_{473}(124,\cdot)\) \(\chi_{473}(126,\cdot)\) \(\chi_{473}(146,\cdot)\) \(\chi_{473}(152,\cdot)\) \(\chi_{473}(169,\cdot)\) \(\chi_{473}(181,\cdot)\) \(\chi_{473}(185,\cdot)\) \(\chi_{473}(196,\cdot)\) \(\chi_{473}(203,\cdot)\) \(\chi_{473}(212,\cdot)\) \(\chi_{473}(224,\cdot)\) \(\chi_{473}(225,\cdot)\) \(\chi_{473}(229,\cdot)\) \(\chi_{473}(240,\cdot)\) \(\chi_{473}(246,\cdot)\) \(\chi_{473}(267,\cdot)\) \(\chi_{473}(268,\cdot)\) \(\chi_{473}(273,\cdot)\) \(\chi_{473}(289,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 105 polynomial (not computed) |
Values on generators
\((431,89)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{19}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 473 }(103, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{35}\right)\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{44}{105}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{31}{35}\right)\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{16}{21}\right)\) |