Basic properties
| Modulus: | \(8020\) | |
| Conductor: | \(8020\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(100\) | 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.di
\(\chi_{8020}(63,\cdot)\) \(\chi_{8020}(387,\cdot)\) \(\chi_{8020}(807,\cdot)\) \(\chi_{8020}(827,\cdot)\) \(\chi_{8020}(927,\cdot)\) \(\chi_{8020}(1123,\cdot)\) \(\chi_{8020}(1187,\cdot)\) \(\chi_{8020}(1427,\cdot)\) \(\chi_{8020}(1563,\cdot)\) \(\chi_{8020}(1667,\cdot)\) \(\chi_{8020}(2183,\cdot)\) \(\chi_{8020}(2483,\cdot)\) \(\chi_{8020}(2727,\cdot)\) \(\chi_{8020}(3003,\cdot)\) \(\chi_{8020}(3063,\cdot)\) \(\chi_{8020}(3167,\cdot)\) \(\chi_{8020}(3403,\cdot)\) \(\chi_{8020}(3463,\cdot)\) \(\chi_{8020}(3523,\cdot)\) \(\chi_{8020}(3787,\cdot)\) \(\chi_{8020}(4087,\cdot)\) \(\chi_{8020}(4183,\cdot)\) \(\chi_{8020}(4607,\cdot)\) \(\chi_{8020}(4667,\cdot)\) \(\chi_{8020}(4863,\cdot)\) \(\chi_{8020}(5007,\cdot)\) \(\chi_{8020}(5067,\cdot)\) \(\chi_{8020}(5127,\cdot)\) \(\chi_{8020}(5143,\cdot)\) \(\chi_{8020}(5787,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((4011,6417,7221)\) → \((-1,-i,e\left(\frac{4}{25}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 8020 }(63, a) \) | \(1\) | \(1\) | \(e\left(\frac{91}{100}\right)\) | \(e\left(\frac{17}{100}\right)\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{27}{50}\right)\) | \(e\left(\frac{29}{100}\right)\) | \(e\left(\frac{3}{100}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{31}{100}\right)\) | \(e\left(\frac{73}{100}\right)\) |