Basic properties
Modulus: | \(4730\) | |
Conductor: | \(473\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(210\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{473}(46,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4730.dn
\(\chi_{4730}(61,\cdot)\) \(\chi_{4730}(261,\cdot)\) \(\chi_{4730}(321,\cdot)\) \(\chi_{4730}(491,\cdot)\) \(\chi_{4730}(501,\cdot)\) \(\chi_{4730}(721,\cdot)\) \(\chi_{4730}(761,\cdot)\) \(\chi_{4730}(921,\cdot)\) \(\chi_{4730}(931,\cdot)\) \(\chi_{4730}(1051,\cdot)\) \(\chi_{4730}(1151,\cdot)\) \(\chi_{4730}(1361,\cdot)\) \(\chi_{4730}(1381,\cdot)\) \(\chi_{4730}(1481,\cdot)\) \(\chi_{4730}(1491,\cdot)\) \(\chi_{4730}(1531,\cdot)\) \(\chi_{4730}(1581,\cdot)\) \(\chi_{4730}(1711,\cdot)\) \(\chi_{4730}(1811,\cdot)\) \(\chi_{4730}(1861,\cdot)\) \(\chi_{4730}(1911,\cdot)\) \(\chi_{4730}(1921,\cdot)\) \(\chi_{4730}(2041,\cdot)\) \(\chi_{4730}(2141,\cdot)\) \(\chi_{4730}(2241,\cdot)\) \(\chi_{4730}(2351,\cdot)\) \(\chi_{4730}(2411,\cdot)\) \(\chi_{4730}(2471,\cdot)\) \(\chi_{4730}(2481,\cdot)\) \(\chi_{4730}(2571,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((947,431,1981)\) → \((1,e\left(\frac{1}{10}\right),e\left(\frac{1}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 4730 }(2411, a) \) | \(1\) | \(1\) | \(e\left(\frac{173}{210}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{181}{210}\right)\) | \(e\left(\frac{169}{210}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{71}{105}\right)\) |