Basic properties
Modulus: | \(4002\) | |
Conductor: | \(667\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(308\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{667}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4002.bt
\(\chi_{4002}(31,\cdot)\) \(\chi_{4002}(55,\cdot)\) \(\chi_{4002}(73,\cdot)\) \(\chi_{4002}(85,\cdot)\) \(\chi_{4002}(127,\cdot)\) \(\chi_{4002}(163,\cdot)\) \(\chi_{4002}(193,\cdot)\) \(\chi_{4002}(211,\cdot)\) \(\chi_{4002}(259,\cdot)\) \(\chi_{4002}(271,\cdot)\) \(\chi_{4002}(301,\cdot)\) \(\chi_{4002}(403,\cdot)\) \(\chi_{4002}(409,\cdot)\) \(\chi_{4002}(427,\cdot)\) \(\chi_{4002}(445,\cdot)\) \(\chi_{4002}(541,\cdot)\) \(\chi_{4002}(565,\cdot)\) \(\chi_{4002}(577,\cdot)\) \(\chi_{4002}(583,\cdot)\) \(\chi_{4002}(601,\cdot)\) \(\chi_{4002}(607,\cdot)\) \(\chi_{4002}(685,\cdot)\) \(\chi_{4002}(715,\cdot)\) \(\chi_{4002}(739,\cdot)\) \(\chi_{4002}(775,\cdot)\) \(\chi_{4002}(823,\cdot)\) \(\chi_{4002}(859,\cdot)\) \(\chi_{4002}(901,\cdot)\) \(\chi_{4002}(913,\cdot)\) \(\chi_{4002}(949,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{308})$ |
Fixed field: | Number field defined by a degree 308 polynomial (not computed) |
Values on generators
\((2669,3133,553)\) → \((1,e\left(\frac{3}{11}\right),e\left(\frac{1}{28}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(31\) | \(35\) | \(37\) |
\( \chi_{ 4002 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{9}{154}\right)\) | \(e\left(\frac{47}{77}\right)\) | \(e\left(\frac{107}{308}\right)\) | \(e\left(\frac{71}{154}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{127}{308}\right)\) | \(e\left(\frac{9}{77}\right)\) | \(e\left(\frac{207}{308}\right)\) | \(e\left(\frac{103}{154}\right)\) | \(e\left(\frac{257}{308}\right)\) |