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 \(\chi_{2805}(1553,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5610.fk
\(\chi_{5610}(107,\cdot)\) \(\chi_{5610}(167,\cdot)\) \(\chi_{5610}(437,\cdot)\) \(\chi_{5610}(503,\cdot)\) \(\chi_{5610}(623,\cdot)\) \(\chi_{5610}(677,\cdot)\) \(\chi_{5610}(887,\cdot)\) \(\chi_{5610}(1163,\cdot)\) \(\chi_{5610}(1553,\cdot)\) \(\chi_{5610}(2063,\cdot)\) \(\chi_{5610}(2147,\cdot)\) \(\chi_{5610}(2153,\cdot)\) \(\chi_{5610}(2207,\cdot)\) \(\chi_{5610}(2417,\cdot)\) \(\chi_{5610}(2477,\cdot)\) \(\chi_{5610}(2543,\cdot)\) \(\chi_{5610}(2657,\cdot)\) \(\chi_{5610}(2987,\cdot)\) \(\chi_{5610}(3053,\cdot)\) \(\chi_{5610}(3203,\cdot)\) \(\chi_{5610}(3593,\cdot)\) \(\chi_{5610}(3713,\cdot)\) \(\chi_{5610}(3737,\cdot)\) \(\chi_{5610}(4187,\cdot)\) \(\chi_{5610}(4193,\cdot)\) \(\chi_{5610}(4457,\cdot)\) \(\chi_{5610}(4517,\cdot)\) \(\chi_{5610}(4583,\cdot)\) \(\chi_{5610}(4703,\cdot)\) \(\chi_{5610}(4967,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((1871,3367,1531,3301)\) → \((-1,-i,e\left(\frac{1}{10}\right),e\left(\frac{15}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(13\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) | \(47\) |
| \( \chi_{ 5610 }(1553, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{71}{80}\right)\) | \(e\left(\frac{3}{80}\right)\) | \(e\left(\frac{71}{80}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{4}{5}\right)\) |