Basic properties
| Modulus: | \(8004\) | |
| 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 \(\chi_{2001}(77,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8004.dq
\(\chi_{8004}(77,\cdot)\) \(\chi_{8004}(101,\cdot)\) \(\chi_{8004}(269,\cdot)\) \(\chi_{8004}(305,\cdot)\) \(\chi_{8004}(317,\cdot)\) \(\chi_{8004}(449,\cdot)\) \(\chi_{8004}(485,\cdot)\) \(\chi_{8004}(533,\cdot)\) \(\chi_{8004}(653,\cdot)\) \(\chi_{8004}(785,\cdot)\) \(\chi_{8004}(809,\cdot)\) \(\chi_{8004}(1001,\cdot)\) \(\chi_{8004}(1025,\cdot)\) \(\chi_{8004}(1133,\cdot)\) \(\chi_{8004}(1145,\cdot)\) \(\chi_{8004}(1181,\cdot)\) \(\chi_{8004}(1313,\cdot)\) \(\chi_{8004}(1337,\cdot)\) \(\chi_{8004}(1361,\cdot)\) \(\chi_{8004}(1373,\cdot)\) \(\chi_{8004}(1481,\cdot)\) \(\chi_{8004}(1577,\cdot)\) \(\chi_{8004}(1613,\cdot)\) \(\chi_{8004}(1685,\cdot)\) \(\chi_{8004}(1697,\cdot)\) \(\chi_{8004}(1829,\cdot)\) \(\chi_{8004}(1853,\cdot)\) \(\chi_{8004}(1925,\cdot)\) \(\chi_{8004}(1961,\cdot)\) \(\chi_{8004}(2009,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{308})$ |
| Fixed field: | Number field defined by a degree 308 polynomial (not computed) |
Values on generators
\((4003,2669,3133,553)\) → \((1,-1,e\left(\frac{3}{11}\right),e\left(\frac{9}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 8004 }(77, a) \) | \(1\) | \(1\) | \(e\left(\frac{65}{77}\right)\) | \(e\left(\frac{3}{77}\right)\) | \(e\left(\frac{305}{308}\right)\) | \(e\left(\frac{93}{154}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{303}{308}\right)\) | \(e\left(\frac{53}{77}\right)\) | \(e\left(\frac{295}{308}\right)\) | \(e\left(\frac{68}{77}\right)\) | \(e\left(\frac{213}{308}\right)\) |