Basic properties
| Modulus: | \(3520\) | |
| Conductor: | \(3520\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3520.fi
\(\chi_{3520}(69,\cdot)\) \(\chi_{3520}(229,\cdot)\) \(\chi_{3520}(269,\cdot)\) \(\chi_{3520}(389,\cdot)\) \(\chi_{3520}(509,\cdot)\) \(\chi_{3520}(669,\cdot)\) \(\chi_{3520}(709,\cdot)\) \(\chi_{3520}(829,\cdot)\) \(\chi_{3520}(949,\cdot)\) \(\chi_{3520}(1109,\cdot)\) \(\chi_{3520}(1149,\cdot)\) \(\chi_{3520}(1269,\cdot)\) \(\chi_{3520}(1389,\cdot)\) \(\chi_{3520}(1549,\cdot)\) \(\chi_{3520}(1589,\cdot)\) \(\chi_{3520}(1709,\cdot)\) \(\chi_{3520}(1829,\cdot)\) \(\chi_{3520}(1989,\cdot)\) \(\chi_{3520}(2029,\cdot)\) \(\chi_{3520}(2149,\cdot)\) \(\chi_{3520}(2269,\cdot)\) \(\chi_{3520}(2429,\cdot)\) \(\chi_{3520}(2469,\cdot)\) \(\chi_{3520}(2589,\cdot)\) \(\chi_{3520}(2709,\cdot)\) \(\chi_{3520}(2869,\cdot)\) \(\chi_{3520}(2909,\cdot)\) \(\chi_{3520}(3029,\cdot)\) \(\chi_{3520}(3149,\cdot)\) \(\chi_{3520}(3309,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((2751,1541,2817,321)\) → \((1,e\left(\frac{15}{16}\right),-1,e\left(\frac{3}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3520 }(1549, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{13}{80}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{41}{80}\right)\) |