Basic properties
| Modulus: | \(4010\) | |
| Conductor: | \(2005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2005}(33,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4010.bn
\(\chi_{4010}(33,\cdot)\) \(\chi_{4010}(293,\cdot)\) \(\chi_{4010}(333,\cdot)\) \(\chi_{4010}(427,\cdot)\) \(\chi_{4010}(543,\cdot)\) \(\chi_{4010}(1177,\cdot)\) \(\chi_{4010}(1757,\cdot)\) \(\chi_{4010}(1847,\cdot)\) \(\chi_{4010}(1857,\cdot)\) \(\chi_{4010}(1863,\cdot)\) \(\chi_{4010}(1957,\cdot)\) \(\chi_{4010}(2073,\cdot)\) \(\chi_{4010}(2113,\cdot)\) \(\chi_{4010}(2217,\cdot)\) \(\chi_{4010}(2287,\cdot)\) \(\chi_{4010}(2373,\cdot)\) \(\chi_{4010}(2563,\cdot)\) \(\chi_{4010}(2577,\cdot)\) \(\chi_{4010}(2723,\cdot)\) \(\chi_{4010}(2883,\cdot)\) \(\chi_{4010}(3037,\cdot)\) \(\chi_{4010}(3053,\cdot)\) \(\chi_{4010}(3327,\cdot)\) \(\chi_{4010}(3363,\cdot)\) \(\chi_{4010}(3397,\cdot)\) \(\chi_{4010}(3533,\cdot)\) \(\chi_{4010}(3657,\cdot)\) \(\chi_{4010}(3693,\cdot)\) \(\chi_{4010}(3757,\cdot)\) \(\chi_{4010}(3767,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((2407,3211)\) → \((-i,e\left(\frac{39}{80}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 4010 }(33, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{17}{80}\right)\) |