Basic properties
| Modulus: | \(4001\) | |
| Conductor: | \(4001\) | 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 4001.m
\(\chi_{4001}(121,\cdot)\) \(\chi_{4001}(439,\cdot)\) \(\chi_{4001}(468,\cdot)\) \(\chi_{4001}(496,\cdot)\) \(\chi_{4001}(627,\cdot)\) \(\chi_{4001}(635,\cdot)\) \(\chi_{4001}(720,\cdot)\) \(\chi_{4001}(752,\cdot)\) \(\chi_{4001}(882,\cdot)\) \(\chi_{4001}(1278,\cdot)\) \(\chi_{4001}(1289,\cdot)\) \(\chi_{4001}(1438,\cdot)\) \(\chi_{4001}(1479,\cdot)\) \(\chi_{4001}(1613,\cdot)\) \(\chi_{4001}(1725,\cdot)\) \(\chi_{4001}(1793,\cdot)\) \(\chi_{4001}(2208,\cdot)\) \(\chi_{4001}(2276,\cdot)\) \(\chi_{4001}(2388,\cdot)\) \(\chi_{4001}(2522,\cdot)\) \(\chi_{4001}(2563,\cdot)\) \(\chi_{4001}(2712,\cdot)\) \(\chi_{4001}(2723,\cdot)\) \(\chi_{4001}(3119,\cdot)\) \(\chi_{4001}(3249,\cdot)\) \(\chi_{4001}(3281,\cdot)\) \(\chi_{4001}(3366,\cdot)\) \(\chi_{4001}(3374,\cdot)\) \(\chi_{4001}(3505,\cdot)\) \(\chi_{4001}(3533,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\(3\) → \(e\left(\frac{47}{80}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4001 }(468, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{47}{80}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(i\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{3}{16}\right)\) |