Basic properties
Modulus: | \(8004\) | |
Conductor: | \(2668\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(308\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{2668}(427,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8004.dk
\(\chi_{8004}(31,\cdot)\) \(\chi_{8004}(55,\cdot)\) \(\chi_{8004}(127,\cdot)\) \(\chi_{8004}(163,\cdot)\) \(\chi_{8004}(211,\cdot)\) \(\chi_{8004}(259,\cdot)\) \(\chi_{8004}(271,\cdot)\) \(\chi_{8004}(403,\cdot)\) \(\chi_{8004}(427,\cdot)\) \(\chi_{8004}(583,\cdot)\) \(\chi_{8004}(607,\cdot)\) \(\chi_{8004}(715,\cdot)\) \(\chi_{8004}(739,\cdot)\) \(\chi_{8004}(775,\cdot)\) \(\chi_{8004}(823,\cdot)\) \(\chi_{8004}(859,\cdot)\) \(\chi_{8004}(955,\cdot)\) \(\chi_{8004}(1087,\cdot)\) \(\chi_{8004}(1099,\cdot)\) \(\chi_{8004}(1255,\cdot)\) \(\chi_{8004}(1291,\cdot)\) \(\chi_{8004}(1315,\cdot)\) \(\chi_{8004}(1411,\cdot)\) \(\chi_{8004}(1435,\cdot)\) \(\chi_{8004}(1603,\cdot)\) \(\chi_{8004}(1639,\cdot)\) \(\chi_{8004}(1651,\cdot)\) \(\chi_{8004}(1783,\cdot)\) \(\chi_{8004}(1819,\cdot)\) \(\chi_{8004}(1867,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{308})$ |
Fixed field: | Number field defined by a degree 308 polynomial (not computed) |
Values on generators
\((4003,2669,3133,553)\) → \((-1,1,e\left(\frac{7}{11}\right),e\left(\frac{17}{28}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(31\) | \(35\) | \(37\) |
\( \chi_{ 8004 }(427, a) \) | \(1\) | \(1\) | \(e\left(\frac{153}{154}\right)\) | \(e\left(\frac{135}{154}\right)\) | \(e\left(\frac{125}{308}\right)\) | \(e\left(\frac{129}{154}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{157}{308}\right)\) | \(e\left(\frac{76}{77}\right)\) | \(e\left(\frac{285}{308}\right)\) | \(e\left(\frac{67}{77}\right)\) | \(e\left(\frac{57}{308}\right)\) |