Basic properties
Modulus: | \(8018\) | |
Conductor: | \(4009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{4009}(249,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8018.dz
\(\chi_{8018}(249,\cdot)\) \(\chi_{8018}(659,\cdot)\) \(\chi_{8018}(801,\cdot)\) \(\chi_{8018}(1001,\cdot)\) \(\chi_{8018}(1021,\cdot)\) \(\chi_{8018}(1515,\cdot)\) \(\chi_{8018}(1587,\cdot)\) \(\chi_{8018}(1865,\cdot)\) \(\chi_{8018}(2141,\cdot)\) \(\chi_{8018}(2143,\cdot)\) \(\chi_{8018}(2347,\cdot)\) \(\chi_{8018}(2359,\cdot)\) \(\chi_{8018}(2371,\cdot)\) \(\chi_{8018}(2415,\cdot)\) \(\chi_{8018}(2689,\cdot)\) \(\chi_{8018}(3681,\cdot)\) \(\chi_{8018}(3829,\cdot)\) \(\chi_{8018}(4119,\cdot)\) \(\chi_{8018}(4525,\cdot)\) \(\chi_{8018}(4879,\cdot)\) \(\chi_{8018}(4885,\cdot)\) \(\chi_{8018}(5221,\cdot)\) \(\chi_{8018}(5835,\cdot)\) \(\chi_{8018}(5941,\cdot)\) \(\chi_{8018}(6151,\cdot)\) \(\chi_{8018}(6169,\cdot)\) \(\chi_{8018}(6361,\cdot)\) \(\chi_{8018}(6709,\cdot)\) \(\chi_{8018}(6995,\cdot)\) \(\chi_{8018}(7101,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{31}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 8018 }(249, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{58}{63}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{71}{126}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{55}{126}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{11}{18}\right)\) |