Basic properties
| Modulus: | \(4002\) | |
| Conductor: | \(667\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(154\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{667}(67,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4002.bm
\(\chi_{4002}(67,\cdot)\) \(\chi_{4002}(109,\cdot)\) \(\chi_{4002}(241,\cdot)\) \(\chi_{4002}(283,\cdot)\) \(\chi_{4002}(295,\cdot)\) \(\chi_{4002}(457,\cdot)\) \(\chi_{4002}(589,\cdot)\) \(\chi_{4002}(613,\cdot)\) \(\chi_{4002}(631,\cdot)\) \(\chi_{4002}(709,\cdot)\) \(\chi_{4002}(787,\cdot)\) \(\chi_{4002}(847,\cdot)\) \(\chi_{4002}(937,\cdot)\) \(\chi_{4002}(1111,\cdot)\) \(\chi_{4002}(1165,\cdot)\) \(\chi_{4002}(1285,\cdot)\) \(\chi_{4002}(1309,\cdot)\) \(\chi_{4002}(1339,\cdot)\) \(\chi_{4002}(1459,\cdot)\) \(\chi_{4002}(1483,\cdot)\) \(\chi_{4002}(1579,\cdot)\) \(\chi_{4002}(1675,\cdot)\) \(\chi_{4002}(1717,\cdot)\) \(\chi_{4002}(1753,\cdot)\) \(\chi_{4002}(1831,\cdot)\) \(\chi_{4002}(1861,\cdot)\) \(\chi_{4002}(1891,\cdot)\) \(\chi_{4002}(2035,\cdot)\) \(\chi_{4002}(2179,\cdot)\) \(\chi_{4002}(2275,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((2669,3133,553)\) → \((1,e\left(\frac{13}{22}\right),e\left(\frac{5}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 4002 }(67, a) \) | \(-1\) | \(1\) | \(e\left(\frac{69}{154}\right)\) | \(e\left(\frac{79}{154}\right)\) | \(e\left(\frac{19}{77}\right)\) | \(e\left(\frac{54}{77}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{6}{77}\right)\) | \(e\left(\frac{69}{77}\right)\) | \(e\left(\frac{139}{154}\right)\) | \(e\left(\frac{74}{77}\right)\) | \(e\left(\frac{37}{77}\right)\) |