Basic properties
Modulus: | \(8004\) | |
Conductor: | \(8004\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(154\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8004.cy
\(\chi_{8004}(239,\cdot)\) \(\chi_{8004}(335,\cdot)\) \(\chi_{8004}(371,\cdot)\) \(\chi_{8004}(455,\cdot)\) \(\chi_{8004}(587,\cdot)\) \(\chi_{8004}(683,\cdot)\) \(\chi_{8004}(719,\cdot)\) \(\chi_{8004}(923,\cdot)\) \(\chi_{8004}(1067,\cdot)\) \(\chi_{8004}(1271,\cdot)\) \(\chi_{8004}(1283,\cdot)\) \(\chi_{8004}(1415,\cdot)\) \(\chi_{8004}(1475,\cdot)\) \(\chi_{8004}(1499,\cdot)\) \(\chi_{8004}(1619,\cdot)\) \(\chi_{8004}(1727,\cdot)\) \(\chi_{8004}(1823,\cdot)\) \(\chi_{8004}(1967,\cdot)\) \(\chi_{8004}(2111,\cdot)\) \(\chi_{8004}(2171,\cdot)\) \(\chi_{8004}(2327,\cdot)\) \(\chi_{8004}(2423,\cdot)\) \(\chi_{8004}(2519,\cdot)\) \(\chi_{8004}(2543,\cdot)\) \(\chi_{8004}(2663,\cdot)\) \(\chi_{8004}(2891,\cdot)\) \(\chi_{8004}(3155,\cdot)\) \(\chi_{8004}(3215,\cdot)\) \(\chi_{8004}(3371,\cdot)\) \(\chi_{8004}(3707,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{77})$ |
Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((4003,2669,3133,553)\) → \((-1,-1,e\left(\frac{5}{11}\right),e\left(\frac{3}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(31\) | \(35\) | \(37\) |
\( \chi_{ 8004 }(239, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{154}\right)\) | \(e\left(\frac{43}{154}\right)\) | \(e\left(\frac{62}{77}\right)\) | \(e\left(\frac{6}{77}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{27}{154}\right)\) | \(e\left(\frac{59}{77}\right)\) | \(e\left(\frac{101}{154}\right)\) | \(e\left(\frac{51}{77}\right)\) | \(e\left(\frac{64}{77}\right)\) |