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 \(\chi_{4009}(67,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8018.dv
\(\chi_{8018}(67,\cdot)\) \(\chi_{8018}(223,\cdot)\) \(\chi_{8018}(299,\cdot)\) \(\chi_{8018}(485,\cdot)\) \(\chi_{8018}(489,\cdot)\) \(\chi_{8018}(907,\cdot)\) \(\chi_{8018}(1067,\cdot)\) \(\chi_{8018}(1143,\cdot)\) \(\chi_{8018}(1333,\cdot)\) \(\chi_{8018}(1419,\cdot)\) \(\chi_{8018}(1751,\cdot)\) \(\chi_{8018}(2263,\cdot)\) \(\chi_{8018}(2333,\cdot)\) \(\chi_{8018}(2409,\cdot)\) \(\chi_{8018}(2599,\cdot)\) \(\chi_{8018}(3017,\cdot)\) \(\chi_{8018}(3107,\cdot)\) \(\chi_{8018}(3205,\cdot)\) \(\chi_{8018}(3529,\cdot)\) \(\chi_{8018}(4049,\cdot)\) \(\chi_{8018}(4373,\cdot)\) \(\chi_{8018}(4893,\cdot)\) \(\chi_{8018}(5315,\cdot)\) \(\chi_{8018}(5639,\cdot)\) \(\chi_{8018}(6131,\cdot)\) \(\chi_{8018}(6159,\cdot)\) \(\chi_{8018}(6207,\cdot)\) \(\chi_{8018}(6397,\cdot)\) \(\chi_{8018}(6815,\cdot)\) \(\chi_{8018}(6975,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((2111,1901)\) → \((e\left(\frac{17}{18}\right),e\left(\frac{13}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 8018 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{63}\right)\) | \(e\left(\frac{43}{63}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{55}{126}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{29}{126}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{7}{18}\right)\) |