Basic properties
Modulus: | \(9680\) | |
Conductor: | \(4840\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4840}(2523,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9680.fr
\(\chi_{9680}(103,\cdot)\) \(\chi_{9680}(247,\cdot)\) \(\chi_{9680}(423,\cdot)\) \(\chi_{9680}(647,\cdot)\) \(\chi_{9680}(663,\cdot)\) \(\chi_{9680}(823,\cdot)\) \(\chi_{9680}(983,\cdot)\) \(\chi_{9680}(1127,\cdot)\) \(\chi_{9680}(1303,\cdot)\) \(\chi_{9680}(1367,\cdot)\) \(\chi_{9680}(1527,\cdot)\) \(\chi_{9680}(1543,\cdot)\) \(\chi_{9680}(1687,\cdot)\) \(\chi_{9680}(1863,\cdot)\) \(\chi_{9680}(2007,\cdot)\) \(\chi_{9680}(2183,\cdot)\) \(\chi_{9680}(2247,\cdot)\) \(\chi_{9680}(2407,\cdot)\) \(\chi_{9680}(2567,\cdot)\) \(\chi_{9680}(2583,\cdot)\) \(\chi_{9680}(2887,\cdot)\) \(\chi_{9680}(3063,\cdot)\) \(\chi_{9680}(3127,\cdot)\) \(\chi_{9680}(3287,\cdot)\) \(\chi_{9680}(3303,\cdot)\) \(\chi_{9680}(3447,\cdot)\) \(\chi_{9680}(3463,\cdot)\) \(\chi_{9680}(3623,\cdot)\) \(\chi_{9680}(3767,\cdot)\) \(\chi_{9680}(3943,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{220})$ |
Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((3631,2421,1937,4721)\) → \((-1,-1,-i,e\left(\frac{6}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
\( \chi_{ 9680 }(103, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{3}{220}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{169}{220}\right)\) | \(e\left(\frac{21}{220}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{47}{55}\right)\) |