Basic properties
| Modulus: | \(6020\) | |
| Conductor: | \(1505\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1505}(1138,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6020.in
\(\chi_{6020}(233,\cdot)\) \(\chi_{6020}(277,\cdot)\) \(\chi_{6020}(373,\cdot)\) \(\chi_{6020}(837,\cdot)\) \(\chi_{6020}(893,\cdot)\) \(\chi_{6020}(933,\cdot)\) \(\chi_{6020}(1017,\cdot)\) \(\chi_{6020}(1173,\cdot)\) \(\chi_{6020}(1437,\cdot)\) \(\chi_{6020}(1577,\cdot)\) \(\chi_{6020}(2097,\cdot)\) \(\chi_{6020}(2137,\cdot)\) \(\chi_{6020}(2153,\cdot)\) \(\chi_{6020}(2377,\cdot)\) \(\chi_{6020}(3173,\cdot)\) \(\chi_{6020}(3273,\cdot)\) \(\chi_{6020}(3357,\cdot)\) \(\chi_{6020}(4377,\cdot)\) \(\chi_{6020}(4477,\cdot)\) \(\chi_{6020}(4713,\cdot)\) \(\chi_{6020}(5093,\cdot)\) \(\chi_{6020}(5653,\cdot)\) \(\chi_{6020}(5833,\cdot)\) \(\chi_{6020}(5917,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((3011,4817,4301,1121)\) → \((1,-i,e\left(\frac{2}{3}\right),e\left(\frac{37}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 6020 }(5653, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{84}\right)\) | \(e\left(\frac{25}{42}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{11}{28}\right)\) | \(e\left(\frac{13}{21}\right)\) | \(e\left(\frac{13}{21}\right)\) |