Basic properties
| Modulus: | \(4655\) | |
| Conductor: | \(4655\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | 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 4655.gc
\(\chi_{4655}(107,\cdot)\) \(\chi_{4655}(578,\cdot)\) \(\chi_{4655}(772,\cdot)\) \(\chi_{4655}(977,\cdot)\) \(\chi_{4655}(1038,\cdot)\) \(\chi_{4655}(1437,\cdot)\) \(\chi_{4655}(1642,\cdot)\) \(\chi_{4655}(1703,\cdot)\) \(\chi_{4655}(1908,\cdot)\) \(\chi_{4655}(2102,\cdot)\) \(\chi_{4655}(2307,\cdot)\) \(\chi_{4655}(2368,\cdot)\) \(\chi_{4655}(2573,\cdot)\) \(\chi_{4655}(2767,\cdot)\) \(\chi_{4655}(2972,\cdot)\) \(\chi_{4655}(3033,\cdot)\) \(\chi_{4655}(3238,\cdot)\) \(\chi_{4655}(3432,\cdot)\) \(\chi_{4655}(3637,\cdot)\) \(\chi_{4655}(3698,\cdot)\) \(\chi_{4655}(3903,\cdot)\) \(\chi_{4655}(4302,\cdot)\) \(\chi_{4655}(4363,\cdot)\) \(\chi_{4655}(4568,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((932,3041,2206)\) → \((i,e\left(\frac{13}{21}\right),e\left(\frac{5}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 4655 }(3432, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{17}{84}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{47}{84}\right)\) | \(e\left(\frac{29}{84}\right)\) | \(e\left(\frac{5}{7}\right)\) |