Basic properties
| Modulus: | \(8624\) | |
| Conductor: | \(8624\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(420\) | 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 8624.hh
\(\chi_{8624}(37,\cdot)\) \(\chi_{8624}(53,\cdot)\) \(\chi_{8624}(93,\cdot)\) \(\chi_{8624}(317,\cdot)\) \(\chi_{8624}(333,\cdot)\) \(\chi_{8624}(389,\cdot)\) \(\chi_{8624}(445,\cdot)\) \(\chi_{8624}(597,\cdot)\) \(\chi_{8624}(653,\cdot)\) \(\chi_{8624}(669,\cdot)\) \(\chi_{8624}(709,\cdot)\) \(\chi_{8624}(933,\cdot)\) \(\chi_{8624}(1005,\cdot)\) \(\chi_{8624}(1061,\cdot)\) \(\chi_{8624}(1213,\cdot)\) \(\chi_{8624}(1269,\cdot)\) \(\chi_{8624}(1285,\cdot)\) \(\chi_{8624}(1325,\cdot)\) \(\chi_{8624}(1565,\cdot)\) \(\chi_{8624}(1621,\cdot)\) \(\chi_{8624}(1677,\cdot)\) \(\chi_{8624}(1829,\cdot)\) \(\chi_{8624}(1885,\cdot)\) \(\chi_{8624}(1901,\cdot)\) \(\chi_{8624}(2165,\cdot)\) \(\chi_{8624}(2181,\cdot)\) \(\chi_{8624}(2237,\cdot)\) \(\chi_{8624}(2293,\cdot)\) \(\chi_{8624}(2445,\cdot)\) \(\chi_{8624}(2501,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{420})$ |
| Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((5391,6469,7745,3137)\) → \((1,i,e\left(\frac{16}{21}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 8624 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{420}\right)\) | \(e\left(\frac{61}{420}\right)\) | \(e\left(\frac{47}{210}\right)\) | \(e\left(\frac{13}{140}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{89}{105}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{61}{210}\right)\) | \(e\left(\frac{47}{140}\right)\) |