Basic properties
| Modulus: | \(8002\) | |
| Conductor: | \(4001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(160\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4001}(11,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8002.p
\(\chi_{8002}(11,\cdot)\) \(\chi_{8002}(57,\cdot)\) \(\chi_{8002}(163,\cdot)\) \(\chi_{8002}(233,\cdot)\) \(\chi_{8002}(265,\cdot)\) \(\chi_{8002}(461,\cdot)\) \(\chi_{8002}(521,\cdot)\) \(\chi_{8002}(593,\cdot)\) \(\chi_{8002}(599,\cdot)\) \(\chi_{8002}(975,\cdot)\) \(\chi_{8002}(1105,\cdot)\) \(\chi_{8002}(1147,\cdot)\) \(\chi_{8002}(1331,\cdot)\) \(\chi_{8002}(1415,\cdot)\) \(\chi_{8002}(1455,\cdot)\) \(\chi_{8002}(1649,\cdot)\) \(\chi_{8002}(1665,\cdot)\) \(\chi_{8002}(1739,\cdot)\) \(\chi_{8002}(1825,\cdot)\) \(\chi_{8002}(1887,\cdot)\) \(\chi_{8002}(2081,\cdot)\) \(\chi_{8002}(2301,\cdot)\) \(\chi_{8002}(2367,\cdot)\) \(\chi_{8002}(2501,\cdot)\) \(\chi_{8002}(2971,\cdot)\) \(\chi_{8002}(3027,\cdot)\) \(\chi_{8002}(3231,\cdot)\) \(\chi_{8002}(3695,\cdot)\) \(\chi_{8002}(3719,\cdot)\) \(\chi_{8002}(3731,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{160})$ |
| Fixed field: | Number field defined by a degree 160 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{57}{160}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8002 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{57}{160}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{21}{32}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{117}{160}\right)\) | \(e\left(\frac{127}{160}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{93}{160}\right)\) |