Basic properties
| Modulus: | \(9680\) | |
| Conductor: | \(605\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{605}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9680.fv
\(\chi_{9680}(17,\cdot)\) \(\chi_{9680}(193,\cdot)\) \(\chi_{9680}(337,\cdot)\) \(\chi_{9680}(497,\cdot)\) \(\chi_{9680}(513,\cdot)\) \(\chi_{9680}(657,\cdot)\) \(\chi_{9680}(673,\cdot)\) \(\chi_{9680}(833,\cdot)\) \(\chi_{9680}(897,\cdot)\) \(\chi_{9680}(1073,\cdot)\) \(\chi_{9680}(1217,\cdot)\) \(\chi_{9680}(1377,\cdot)\) \(\chi_{9680}(1393,\cdot)\) \(\chi_{9680}(1537,\cdot)\) \(\chi_{9680}(1553,\cdot)\) \(\chi_{9680}(1713,\cdot)\) \(\chi_{9680}(1777,\cdot)\) \(\chi_{9680}(1953,\cdot)\) \(\chi_{9680}(2257,\cdot)\) \(\chi_{9680}(2273,\cdot)\) \(\chi_{9680}(2433,\cdot)\) \(\chi_{9680}(2593,\cdot)\) \(\chi_{9680}(2657,\cdot)\) \(\chi_{9680}(2833,\cdot)\) \(\chi_{9680}(2977,\cdot)\) \(\chi_{9680}(3153,\cdot)\) \(\chi_{9680}(3297,\cdot)\) \(\chi_{9680}(3313,\cdot)\) \(\chi_{9680}(3473,\cdot)\) \(\chi_{9680}(3537,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((3631,2421,1937,4721)\) → \((1,1,i,e\left(\frac{49}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 9680 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{81}{220}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{163}{220}\right)\) | \(e\left(\frac{17}{220}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{7}{22}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{4}{55}\right)\) |