Basic properties
| Modulus: | \(8020\) | |
| Conductor: | \(8020\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(200\) | 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.ds
\(\chi_{8020}(7,\cdot)\) \(\chi_{8020}(323,\cdot)\) \(\chi_{8020}(343,\cdot)\) \(\chi_{8020}(403,\cdot)\) \(\chi_{8020}(483,\cdot)\) \(\chi_{8020}(587,\cdot)\) \(\chi_{8020}(627,\cdot)\) \(\chi_{8020}(1043,\cdot)\) \(\chi_{8020}(1063,\cdot)\) \(\chi_{8020}(1167,\cdot)\) \(\chi_{8020}(1247,\cdot)\) \(\chi_{8020}(1343,\cdot)\) \(\chi_{8020}(1363,\cdot)\) \(\chi_{8020}(1647,\cdot)\) \(\chi_{8020}(1707,\cdot)\) \(\chi_{8020}(1807,\cdot)\) \(\chi_{8020}(1867,\cdot)\) \(\chi_{8020}(1923,\cdot)\) \(\chi_{8020}(2003,\cdot)\) \(\chi_{8020}(2063,\cdot)\) \(\chi_{8020}(2083,\cdot)\) \(\chi_{8020}(2247,\cdot)\) \(\chi_{8020}(2587,\cdot)\) \(\chi_{8020}(2607,\cdot)\) \(\chi_{8020}(2627,\cdot)\) \(\chi_{8020}(2663,\cdot)\) \(\chi_{8020}(2767,\cdot)\) \(\chi_{8020}(2847,\cdot)\) \(\chi_{8020}(2983,\cdot)\) \(\chi_{8020}(2987,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{200})$ |
| Fixed field: | Number field defined by a degree 200 polynomial (not computed) |
Values on generators
\((4011,6417,7221)\) → \((-1,i,e\left(\frac{31}{200}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 8020 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{81}{200}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{81}{100}\right)\) | \(e\left(\frac{57}{100}\right)\) | \(e\left(\frac{39}{200}\right)\) | \(e\left(\frac{123}{200}\right)\) | \(e\left(\frac{53}{200}\right)\) | \(e\left(\frac{153}{200}\right)\) | \(e\left(\frac{71}{200}\right)\) | \(e\left(\frac{43}{200}\right)\) |