Basic properties
| Modulus: | \(5610\) | |
| Conductor: | \(935\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{935}(299,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5610.fh
\(\chi_{5610}(79,\cdot)\) \(\chi_{5610}(139,\cdot)\) \(\chi_{5610}(469,\cdot)\) \(\chi_{5610}(589,\cdot)\) \(\chi_{5610}(1009,\cdot)\) \(\chi_{5610}(1129,\cdot)\) \(\chi_{5610}(1399,\cdot)\) \(\chi_{5610}(1459,\cdot)\) \(\chi_{5610}(1669,\cdot)\) \(\chi_{5610}(1729,\cdot)\) \(\chi_{5610}(1909,\cdot)\) \(\chi_{5610}(1999,\cdot)\) \(\chi_{5610}(2119,\cdot)\) \(\chi_{5610}(2239,\cdot)\) \(\chi_{5610}(2659,\cdot)\) \(\chi_{5610}(2989,\cdot)\) \(\chi_{5610}(3049,\cdot)\) \(\chi_{5610}(3439,\cdot)\) \(\chi_{5610}(3559,\cdot)\) \(\chi_{5610}(3649,\cdot)\) \(\chi_{5610}(3709,\cdot)\) \(\chi_{5610}(3769,\cdot)\) \(\chi_{5610}(4039,\cdot)\) \(\chi_{5610}(4219,\cdot)\) \(\chi_{5610}(4549,\cdot)\) \(\chi_{5610}(4699,\cdot)\) \(\chi_{5610}(4969,\cdot)\) \(\chi_{5610}(5029,\cdot)\) \(\chi_{5610}(5089,\cdot)\) \(\chi_{5610}(5209,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1871,3367,1531,3301)\) → \((1,-1,e\left(\frac{1}{10}\right),e\left(\frac{3}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 5610 }(4039, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{80}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{11}{80}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{71}{80}\right)\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{1}{20}\right)\) |