Basic properties
| Modulus: | \(8004\) | |
| Conductor: | \(2668\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(154\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2668}(67,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8004.cz
\(\chi_{8004}(67,\cdot)\) \(\chi_{8004}(283,\cdot)\) \(\chi_{8004}(295,\cdot)\) \(\chi_{8004}(631,\cdot)\) \(\chi_{8004}(787,\cdot)\) \(\chi_{8004}(847,\cdot)\) \(\chi_{8004}(1111,\cdot)\) \(\chi_{8004}(1339,\cdot)\) \(\chi_{8004}(1459,\cdot)\) \(\chi_{8004}(1483,\cdot)\) \(\chi_{8004}(1579,\cdot)\) \(\chi_{8004}(1675,\cdot)\) \(\chi_{8004}(1831,\cdot)\) \(\chi_{8004}(1891,\cdot)\) \(\chi_{8004}(2035,\cdot)\) \(\chi_{8004}(2179,\cdot)\) \(\chi_{8004}(2275,\cdot)\) \(\chi_{8004}(2383,\cdot)\) \(\chi_{8004}(2503,\cdot)\) \(\chi_{8004}(2527,\cdot)\) \(\chi_{8004}(2587,\cdot)\) \(\chi_{8004}(2719,\cdot)\) \(\chi_{8004}(2731,\cdot)\) \(\chi_{8004}(2935,\cdot)\) \(\chi_{8004}(3079,\cdot)\) \(\chi_{8004}(3283,\cdot)\) \(\chi_{8004}(3319,\cdot)\) \(\chi_{8004}(3415,\cdot)\) \(\chi_{8004}(3547,\cdot)\) \(\chi_{8004}(3631,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((4003,2669,3133,553)\) → \((-1,1,e\left(\frac{13}{22}\right),e\left(\frac{5}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 8004 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{69}{154}\right)\) | \(e\left(\frac{1}{77}\right)\) | \(e\left(\frac{115}{154}\right)\) | \(e\left(\frac{54}{77}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{89}{154}\right)\) | \(e\left(\frac{69}{77}\right)\) | \(e\left(\frac{31}{77}\right)\) | \(e\left(\frac{71}{154}\right)\) | \(e\left(\frac{37}{77}\right)\) |