Basic properties
Modulus: | \(8470\) | |
Conductor: | \(4235\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{4235}(2239,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8470.cs
\(\chi_{8470}(139,\cdot)\) \(\chi_{8470}(349,\cdot)\) \(\chi_{8470}(629,\cdot)\) \(\chi_{8470}(909,\cdot)\) \(\chi_{8470}(1119,\cdot)\) \(\chi_{8470}(1399,\cdot)\) \(\chi_{8470}(1469,\cdot)\) \(\chi_{8470}(1679,\cdot)\) \(\chi_{8470}(1889,\cdot)\) \(\chi_{8470}(2239,\cdot)\) \(\chi_{8470}(2449,\cdot)\) \(\chi_{8470}(2939,\cdot)\) \(\chi_{8470}(3009,\cdot)\) \(\chi_{8470}(3219,\cdot)\) \(\chi_{8470}(3429,\cdot)\) \(\chi_{8470}(3709,\cdot)\) \(\chi_{8470}(3779,\cdot)\) \(\chi_{8470}(3989,\cdot)\) \(\chi_{8470}(4199,\cdot)\) \(\chi_{8470}(4479,\cdot)\) \(\chi_{8470}(4549,\cdot)\) \(\chi_{8470}(4969,\cdot)\) \(\chi_{8470}(5249,\cdot)\) \(\chi_{8470}(5319,\cdot)\) \(\chi_{8470}(5529,\cdot)\) \(\chi_{8470}(5739,\cdot)\) \(\chi_{8470}(6019,\cdot)\) \(\chi_{8470}(6089,\cdot)\) \(\chi_{8470}(6299,\cdot)\) \(\chi_{8470}(6509,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((6777,6051,7141)\) → \((-1,-1,e\left(\frac{109}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 8470 }(2239, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{19}{22}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{13}{110}\right)\) |