Basic properties
| Modulus: | \(8020\) | |
| Conductor: | \(401\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(100\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{401}(81,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8020.dc
\(\chi_{8020}(81,\cdot)\) \(\chi_{8020}(121,\cdot)\) \(\chi_{8020}(301,\cdot)\) \(\chi_{8020}(501,\cdot)\) \(\chi_{8020}(681,\cdot)\) \(\chi_{8020}(721,\cdot)\) \(\chi_{8020}(901,\cdot)\) \(\chi_{8020}(1221,\cdot)\) \(\chi_{8020}(1421,\cdot)\) \(\chi_{8020}(1661,\cdot)\) \(\chi_{8020}(1801,\cdot)\) \(\chi_{8020}(1941,\cdot)\) \(\chi_{8020}(2001,\cdot)\) \(\chi_{8020}(2121,\cdot)\) \(\chi_{8020}(2161,\cdot)\) \(\chi_{8020}(2901,\cdot)\) \(\chi_{8020}(3301,\cdot)\) \(\chi_{8020}(3321,\cdot)\) \(\chi_{8020}(3861,\cdot)\) \(\chi_{8020}(3941,\cdot)\) \(\chi_{8020}(3961,\cdot)\) \(\chi_{8020}(4301,\cdot)\) \(\chi_{8020}(4321,\cdot)\) \(\chi_{8020}(4501,\cdot)\) \(\chi_{8020}(4521,\cdot)\) \(\chi_{8020}(4861,\cdot)\) \(\chi_{8020}(4881,\cdot)\) \(\chi_{8020}(4961,\cdot)\) \(\chi_{8020}(5501,\cdot)\) \(\chi_{8020}(5521,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((4011,6417,7221)\) → \((1,1,e\left(\frac{1}{100}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 8020 }(81, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{100}\right)\) | \(e\left(\frac{31}{50}\right)\) | \(e\left(\frac{1}{50}\right)\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{19}{100}\right)\) | \(e\left(\frac{83}{100}\right)\) | \(e\left(\frac{63}{100}\right)\) | \(e\left(\frac{63}{100}\right)\) | \(e\left(\frac{91}{100}\right)\) | \(e\left(\frac{3}{100}\right)\) |