Basic properties
| Modulus: | \(8021\) | |
| Conductor: | \(8021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(56\) | 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.cc
\(\chi_{8021}(21,\cdot)\) \(\chi_{8021}(216,\cdot)\) \(\chi_{8021}(382,\cdot)\) \(\chi_{8021}(1214,\cdot)\) \(\chi_{8021}(1240,\cdot)\) \(\chi_{8021}(1412,\cdot)\) \(\chi_{8021}(1799,\cdot)\) \(\chi_{8021}(1903,\cdot)\) \(\chi_{8021}(1919,\cdot)\) \(\chi_{8021}(2400,\cdot)\) \(\chi_{8021}(2462,\cdot)\) \(\chi_{8021}(2488,\cdot)\) \(\chi_{8021}(2907,\cdot)\) \(\chi_{8021}(3320,\cdot)\) \(\chi_{8021}(4074,\cdot)\) \(\chi_{8021}(4103,\cdot)\) \(\chi_{8021}(4298,\cdot)\) \(\chi_{8021}(4389,\cdot)\) \(\chi_{8021}(4698,\cdot)\) \(\chi_{8021}(5039,\cdot)\) \(\chi_{8021}(7025,\cdot)\) \(\chi_{8021}(7301,\cdot)\) \(\chi_{8021}(7649,\cdot)\) \(\chi_{8021}(7951,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{56})$ |
| Fixed field: | Number field defined by a degree 56 polynomial |
Values on generators
\((6788,2471)\) → \((i,e\left(\frac{13}{56}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8021 }(21, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{3}{14}\right)\) | \(e\left(\frac{43}{56}\right)\) | \(e\left(\frac{47}{56}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{23}{28}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{3}{14}\right)\) |