Basic properties
| Modulus: | \(8021\) | |
| Conductor: | \(8021\) | 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 8021.co
\(\chi_{8021}(120,\cdot)\) \(\chi_{8021}(217,\cdot)\) \(\chi_{8021}(497,\cdot)\) \(\chi_{8021}(581,\cdot)\) \(\chi_{8021}(653,\cdot)\) \(\chi_{8021}(737,\cdot)\) \(\chi_{8021}(1017,\cdot)\) \(\chi_{8021}(1114,\cdot)\) \(\chi_{8021}(1270,\cdot)\) \(\chi_{8021}(1615,\cdot)\) \(\chi_{8021}(1634,\cdot)\) \(\chi_{8021}(2232,\cdot)\) \(\chi_{8021}(3526,\cdot)\) \(\chi_{8021}(4007,\cdot)\) \(\chi_{8021}(4143,\cdot)\) \(\chi_{8021}(4624,\cdot)\) \(\chi_{8021}(4631,\cdot)\) \(\chi_{8021}(5112,\cdot)\) \(\chi_{8021}(5248,\cdot)\) \(\chi_{8021}(5729,\cdot)\) \(\chi_{8021}(7023,\cdot)\) \(\chi_{8021}(7621,\cdot)\) \(\chi_{8021}(7640,\cdot)\) \(\chi_{8021}(7985,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((6788,2471)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{17}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8021 }(120, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{8}{21}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{23}{42}\right)\) |