Basic properties
| Modulus: | \(8020\) | |
| Conductor: | \(8020\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | 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 8020.cu
\(\chi_{8020}(119,\cdot)\) \(\chi_{8020}(259,\cdot)\) \(\chi_{8020}(559,\cdot)\) \(\chi_{8020}(959,\cdot)\) \(\chi_{8020}(1119,\cdot)\) \(\chi_{8020}(1279,\cdot)\) \(\chi_{8020}(1759,\cdot)\) \(\chi_{8020}(1979,\cdot)\) \(\chi_{8020}(2439,\cdot)\) \(\chi_{8020}(2559,\cdot)\) \(\chi_{8020}(2659,\cdot)\) \(\chi_{8020}(2699,\cdot)\) \(\chi_{8020}(2739,\cdot)\) \(\chi_{8020}(2759,\cdot)\) \(\chi_{8020}(3019,\cdot)\) \(\chi_{8020}(3379,\cdot)\) \(\chi_{8020}(3839,\cdot)\) \(\chi_{8020}(4199,\cdot)\) \(\chi_{8020}(4459,\cdot)\) \(\chi_{8020}(4479,\cdot)\) \(\chi_{8020}(4519,\cdot)\) \(\chi_{8020}(4559,\cdot)\) \(\chi_{8020}(4659,\cdot)\) \(\chi_{8020}(4779,\cdot)\) \(\chi_{8020}(5239,\cdot)\) \(\chi_{8020}(5459,\cdot)\) \(\chi_{8020}(5939,\cdot)\) \(\chi_{8020}(6099,\cdot)\) \(\chi_{8020}(6259,\cdot)\) \(\chi_{8020}(6659,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((4011,6417,7221)\) → \((-1,-1,e\left(\frac{9}{80}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 8020 }(119, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{47}{80}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{27}{80}\right)\) |