Basic properties
| Modulus: | \(4002\) | |
| Conductor: | \(2001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(154\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2001}(701,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4002.bp
\(\chi_{4002}(5,\cdot)\) \(\chi_{4002}(125,\cdot)\) \(\chi_{4002}(149,\cdot)\) \(\chi_{4002}(245,\cdot)\) \(\chi_{4002}(341,\cdot)\) \(\chi_{4002}(383,\cdot)\) \(\chi_{4002}(419,\cdot)\) \(\chi_{4002}(497,\cdot)\) \(\chi_{4002}(527,\cdot)\) \(\chi_{4002}(557,\cdot)\) \(\chi_{4002}(701,\cdot)\) \(\chi_{4002}(845,\cdot)\) \(\chi_{4002}(941,\cdot)\) \(\chi_{4002}(1019,\cdot)\) \(\chi_{4002}(1049,\cdot)\) \(\chi_{4002}(1079,\cdot)\) \(\chi_{4002}(1115,\cdot)\) \(\chi_{4002}(1169,\cdot)\) \(\chi_{4002}(1193,\cdot)\) \(\chi_{4002}(1211,\cdot)\) \(\chi_{4002}(1253,\cdot)\) \(\chi_{4002}(1367,\cdot)\) \(\chi_{4002}(1385,\cdot)\) \(\chi_{4002}(1397,\cdot)\) \(\chi_{4002}(1463,\cdot)\) \(\chi_{4002}(1571,\cdot)\) \(\chi_{4002}(1601,\cdot)\) \(\chi_{4002}(1745,\cdot)\) \(\chi_{4002}(1811,\cdot)\) \(\chi_{4002}(1907,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((2669,3133,553)\) → \((-1,e\left(\frac{9}{22}\right),e\left(\frac{11}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 4002 }(701, a) \) | \(1\) | \(1\) | \(e\left(\frac{15}{77}\right)\) | \(e\left(\frac{31}{154}\right)\) | \(e\left(\frac{127}{154}\right)\) | \(e\left(\frac{67}{77}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{16}{77}\right)\) | \(e\left(\frac{30}{77}\right)\) | \(e\left(\frac{37}{154}\right)\) | \(e\left(\frac{61}{154}\right)\) | \(e\left(\frac{73}{77}\right)\) |