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.ez
\(\chi_{3520}(3,\cdot)\) \(\chi_{3520}(27,\cdot)\) \(\chi_{3520}(163,\cdot)\) \(\chi_{3520}(267,\cdot)\) \(\chi_{3520}(323,\cdot)\) \(\chi_{3520}(427,\cdot)\) \(\chi_{3520}(587,\cdot)\) \(\chi_{3520}(643,\cdot)\) \(\chi_{3520}(883,\cdot)\) \(\chi_{3520}(907,\cdot)\) \(\chi_{3520}(1043,\cdot)\) \(\chi_{3520}(1147,\cdot)\) \(\chi_{3520}(1203,\cdot)\) \(\chi_{3520}(1307,\cdot)\) \(\chi_{3520}(1467,\cdot)\) \(\chi_{3520}(1523,\cdot)\) \(\chi_{3520}(1763,\cdot)\) \(\chi_{3520}(1787,\cdot)\) \(\chi_{3520}(1923,\cdot)\) \(\chi_{3520}(2027,\cdot)\) \(\chi_{3520}(2083,\cdot)\) \(\chi_{3520}(2187,\cdot)\) \(\chi_{3520}(2347,\cdot)\) \(\chi_{3520}(2403,\cdot)\) \(\chi_{3520}(2643,\cdot)\) \(\chi_{3520}(2667,\cdot)\) \(\chi_{3520}(2803,\cdot)\) \(\chi_{3520}(2907,\cdot)\) \(\chi_{3520}(2963,\cdot)\) \(\chi_{3520}(3067,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((2751,1541,2817,321)\) → \((-1,e\left(\frac{1}{16}\right),i,e\left(\frac{4}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 3520 }(1147, a) \) | \(1\) | \(1\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{39}{80}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{41}{80}\right)\) | \(e\left(\frac{63}{80}\right)\) |