Basic properties
| Modulus: | \(8023\) | |
| Conductor: | \(8023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(140\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8023.fd
\(\chi_{8023}(2,\cdot)\) \(\chi_{8023}(8,\cdot)\) \(\chi_{8023}(169,\cdot)\) \(\chi_{8023}(438,\cdot)\) \(\chi_{8023}(512,\cdot)\) \(\chi_{8023}(759,\cdot)\) \(\chi_{8023}(902,\cdot)\) \(\chi_{8023}(961,\cdot)\) \(\chi_{8023}(1003,\cdot)\) \(\chi_{8023}(1413,\cdot)\) \(\chi_{8023}(1861,\cdot)\) \(\chi_{8023}(1919,\cdot)\) \(\chi_{8023}(2048,\cdot)\) \(\chi_{8023}(2179,\cdot)\) \(\chi_{8023}(2359,\cdot)\) \(\chi_{8023}(2704,\cdot)\) \(\chi_{8023}(2772,\cdot)\) \(\chi_{8023}(2793,\cdot)\) \(\chi_{8023}(3059,\cdot)\) \(\chi_{8023}(3065,\cdot)\) \(\chi_{8023}(3224,\cdot)\) \(\chi_{8023}(3446,\cdot)\) \(\chi_{8023}(3608,\cdot)\) \(\chi_{8023}(3630,\cdot)\) \(\chi_{8023}(3844,\cdot)\) \(\chi_{8023}(3898,\cdot)\) \(\chi_{8023}(3923,\cdot)\) \(\chi_{8023}(3963,\cdot)\) \(\chi_{8023}(4012,\cdot)\) \(\chi_{8023}(4121,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{140})$ |
| Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((6894,3054)\) → \((e\left(\frac{3}{35}\right),e\left(\frac{3}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8023 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{47}{140}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{41}{140}\right)\) | \(e\left(\frac{19}{140}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{47}{70}\right)\) | \(e\left(\frac{13}{140}\right)\) | \(e\left(\frac{41}{70}\right)\) |