Basic properties
| Modulus: | \(5610\) | |
| Conductor: | \(2805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2805}(1808,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5610.ey
\(\chi_{5610}(113,\cdot)\) \(\chi_{5610}(377,\cdot)\) \(\chi_{5610}(533,\cdot)\) \(\chi_{5610}(653,\cdot)\) \(\chi_{5610}(1043,\cdot)\) \(\chi_{5610}(1127,\cdot)\) \(\chi_{5610}(1457,\cdot)\) \(\chi_{5610}(1523,\cdot)\) \(\chi_{5610}(1637,\cdot)\) \(\chi_{5610}(1643,\cdot)\) \(\chi_{5610}(1697,\cdot)\) \(\chi_{5610}(1907,\cdot)\) \(\chi_{5610}(1967,\cdot)\) \(\chi_{5610}(2033,\cdot)\) \(\chi_{5610}(2183,\cdot)\) \(\chi_{5610}(2693,\cdot)\) \(\chi_{5610}(3083,\cdot)\) \(\chi_{5610}(3173,\cdot)\) \(\chi_{5610}(3227,\cdot)\) \(\chi_{5610}(3437,\cdot)\) \(\chi_{5610}(3677,\cdot)\) \(\chi_{5610}(3683,\cdot)\) \(\chi_{5610}(3947,\cdot)\) \(\chi_{5610}(4007,\cdot)\) \(\chi_{5610}(4073,\cdot)\) \(\chi_{5610}(4613,\cdot)\) \(\chi_{5610}(4733,\cdot)\) \(\chi_{5610}(4757,\cdot)\) \(\chi_{5610}(5207,\cdot)\) \(\chi_{5610}(5267,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1871,3367,1531,3301)\) → \((-1,-i,e\left(\frac{1}{5}\right),e\left(\frac{15}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 5610 }(4613, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{80}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{47}{80}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{7}{80}\right)\) | \(e\left(\frac{33}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{3}{5}\right)\) |