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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 473.bf
\(\chi_{473}(18,\cdot)\) \(\chi_{473}(19,\cdot)\) \(\chi_{473}(28,\cdot)\) \(\chi_{473}(29,\cdot)\) \(\chi_{473}(30,\cdot)\) \(\chi_{473}(46,\cdot)\) \(\chi_{473}(61,\cdot)\) \(\chi_{473}(62,\cdot)\) \(\chi_{473}(63,\cdot)\) \(\chi_{473}(72,\cdot)\) \(\chi_{473}(73,\cdot)\) \(\chi_{473}(105,\cdot)\) \(\chi_{473}(106,\cdot)\) \(\chi_{473}(112,\cdot)\) \(\chi_{473}(116,\cdot)\) \(\chi_{473}(134,\cdot)\) \(\chi_{473}(149,\cdot)\) \(\chi_{473}(162,\cdot)\) \(\chi_{473}(184,\cdot)\) \(\chi_{473}(200,\cdot)\) \(\chi_{473}(205,\cdot)\) \(\chi_{473}(206,\cdot)\) \(\chi_{473}(227,\cdot)\) \(\chi_{473}(233,\cdot)\) \(\chi_{473}(244,\cdot)\) \(\chi_{473}(248,\cdot)\) \(\chi_{473}(249,\cdot)\) \(\chi_{473}(261,\cdot)\) \(\chi_{473}(270,\cdot)\) \(\chi_{473}(277,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{105})$ |
| Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((431,89)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{5}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 473 }(28, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{35}\right)\) | \(e\left(\frac{67}{210}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{121}{210}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{12}{35}\right)\) | \(e\left(\frac{67}{105}\right)\) | \(e\left(\frac{29}{42}\right)\) | \(e\left(\frac{23}{42}\right)\) |