Basic properties
| Modulus: | \(8001\) | |
| Conductor: | \(889\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{889}(649,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8001.nb
\(\chi_{8001}(649,\cdot)\) \(\chi_{8001}(901,\cdot)\) \(\chi_{8001}(1531,\cdot)\) \(\chi_{8001}(1657,\cdot)\) \(\chi_{8001}(1963,\cdot)\) \(\chi_{8001}(1972,\cdot)\) \(\chi_{8001}(2035,\cdot)\) \(\chi_{8001}(2224,\cdot)\) \(\chi_{8001}(2341,\cdot)\) \(\chi_{8001}(2404,\cdot)\) \(\chi_{8001}(2593,\cdot)\) \(\chi_{8001}(2656,\cdot)\) \(\chi_{8001}(3232,\cdot)\) \(\chi_{8001}(3358,\cdot)\) \(\chi_{8001}(3412,\cdot)\) \(\chi_{8001}(3538,\cdot)\) \(\chi_{8001}(3601,\cdot)\) \(\chi_{8001}(3853,\cdot)\) \(\chi_{8001}(3916,\cdot)\) \(\chi_{8001}(4051,\cdot)\) \(\chi_{8001}(4303,\cdot)\) \(\chi_{8001}(4357,\cdot)\) \(\chi_{8001}(4366,\cdot)\) \(\chi_{8001}(4618,\cdot)\) \(\chi_{8001}(5554,\cdot)\) \(\chi_{8001}(5617,\cdot)\) \(\chi_{8001}(5689,\cdot)\) \(\chi_{8001}(5806,\cdot)\) \(\chi_{8001}(6193,\cdot)\) \(\chi_{8001}(6319,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((3557,1144,7750)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{61}{126}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8001 }(649, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{21}\right)\) | \(e\left(\frac{1}{21}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{1}{126}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{5}{6}\right)\) |