Basic properties
Modulus: | \(8470\) | |
Conductor: | \(605\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{605}(39,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8470.cw
\(\chi_{8470}(29,\cdot)\) \(\chi_{8470}(519,\cdot)\) \(\chi_{8470}(589,\cdot)\) \(\chi_{8470}(799,\cdot)\) \(\chi_{8470}(1009,\cdot)\) \(\chi_{8470}(1289,\cdot)\) \(\chi_{8470}(1359,\cdot)\) \(\chi_{8470}(1569,\cdot)\) \(\chi_{8470}(1779,\cdot)\) \(\chi_{8470}(2059,\cdot)\) \(\chi_{8470}(2129,\cdot)\) \(\chi_{8470}(2549,\cdot)\) \(\chi_{8470}(2829,\cdot)\) \(\chi_{8470}(2899,\cdot)\) \(\chi_{8470}(3109,\cdot)\) \(\chi_{8470}(3319,\cdot)\) \(\chi_{8470}(3599,\cdot)\) \(\chi_{8470}(3669,\cdot)\) \(\chi_{8470}(3879,\cdot)\) \(\chi_{8470}(4089,\cdot)\) \(\chi_{8470}(4369,\cdot)\) \(\chi_{8470}(4439,\cdot)\) \(\chi_{8470}(4649,\cdot)\) \(\chi_{8470}(4859,\cdot)\) \(\chi_{8470}(5139,\cdot)\) \(\chi_{8470}(5209,\cdot)\) \(\chi_{8470}(5419,\cdot)\) \(\chi_{8470}(5629,\cdot)\) \(\chi_{8470}(5909,\cdot)\) \(\chi_{8470}(5979,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((6777,6051,7141)\) → \((-1,1,e\left(\frac{79}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 8470 }(3669, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{23}{110}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{73}{110}\right)\) |