Basic properties
| Modulus: | \(5950\) | |
| Conductor: | \(2975\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2975}(1686,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5950.et
\(\chi_{5950}(41,\cdot)\) \(\chi_{5950}(181,\cdot)\) \(\chi_{5950}(741,\cdot)\) \(\chi_{5950}(811,\cdot)\) \(\chi_{5950}(881,\cdot)\) \(\chi_{5950}(1091,\cdot)\) \(\chi_{5950}(1161,\cdot)\) \(\chi_{5950}(1231,\cdot)\) \(\chi_{5950}(1371,\cdot)\) \(\chi_{5950}(1791,\cdot)\) \(\chi_{5950}(1931,\cdot)\) \(\chi_{5950}(2071,\cdot)\) \(\chi_{5950}(2281,\cdot)\) \(\chi_{5950}(2421,\cdot)\) \(\chi_{5950}(2561,\cdot)\) \(\chi_{5950}(2981,\cdot)\) \(\chi_{5950}(3121,\cdot)\) \(\chi_{5950}(3191,\cdot)\) \(\chi_{5950}(3261,\cdot)\) \(\chi_{5950}(3471,\cdot)\) \(\chi_{5950}(3541,\cdot)\) \(\chi_{5950}(3611,\cdot)\) \(\chi_{5950}(4171,\cdot)\) \(\chi_{5950}(4311,\cdot)\) \(\chi_{5950}(4381,\cdot)\) \(\chi_{5950}(4661,\cdot)\) \(\chi_{5950}(4731,\cdot)\) \(\chi_{5950}(4941,\cdot)\) \(\chi_{5950}(5361,\cdot)\) \(\chi_{5950}(5571,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((477,2551,2451)\) → \((e\left(\frac{4}{5}\right),-1,e\left(\frac{1}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(33\) |
| \( \chi_{ 5950 }(4661, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{80}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{39}{80}\right)\) | \(e\left(\frac{33}{80}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{2}{5}\right)\) |