Basic properties
| Modulus: | \(10005\) | |
| Conductor: | \(2001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(308\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2001}(26,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 10005.fx
\(\chi_{10005}(26,\cdot)\) \(\chi_{10005}(101,\cdot)\) \(\chi_{10005}(131,\cdot)\) \(\chi_{10005}(311,\cdot)\) \(\chi_{10005}(416,\cdot)\) \(\chi_{10005}(446,\cdot)\) \(\chi_{10005}(491,\cdot)\) \(\chi_{10005}(611,\cdot)\) \(\chi_{10005}(656,\cdot)\) \(\chi_{10005}(791,\cdot)\) \(\chi_{10005}(926,\cdot)\) \(\chi_{10005}(1001,\cdot)\) \(\chi_{10005}(1076,\cdot)\) \(\chi_{10005}(1181,\cdot)\) \(\chi_{10005}(1361,\cdot)\) \(\chi_{10005}(1406,\cdot)\) \(\chi_{10005}(1481,\cdot)\) \(\chi_{10005}(1511,\cdot)\) \(\chi_{10005}(1526,\cdot)\) \(\chi_{10005}(1616,\cdot)\) \(\chi_{10005}(1751,\cdot)\) \(\chi_{10005}(1766,\cdot)\) \(\chi_{10005}(1796,\cdot)\) \(\chi_{10005}(1871,\cdot)\) \(\chi_{10005}(1961,\cdot)\) \(\chi_{10005}(1991,\cdot)\) \(\chi_{10005}(2051,\cdot)\) \(\chi_{10005}(2096,\cdot)\) \(\chi_{10005}(2201,\cdot)\) \(\chi_{10005}(2306,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{308})$ |
| Fixed field: | Number field defined by a degree 308 polynomial (not computed) |
Values on generators
\((6671,2002,9136,6556)\) → \((-1,1,e\left(\frac{8}{11}\right),e\left(\frac{19}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 10005 }(26, a) \) | \(1\) | \(1\) | \(e\left(\frac{195}{308}\right)\) | \(e\left(\frac{41}{154}\right)\) | \(e\left(\frac{74}{77}\right)\) | \(e\left(\frac{277}{308}\right)\) | \(e\left(\frac{3}{308}\right)\) | \(e\left(\frac{61}{154}\right)\) | \(e\left(\frac{183}{308}\right)\) | \(e\left(\frac{41}{77}\right)\) | \(e\left(\frac{37}{44}\right)\) | \(e\left(\frac{5}{308}\right)\) |