Basic properties
Modulus: | \(8470\) | |
Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{121}(2,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8470.cr
\(\chi_{8470}(211,\cdot)\) \(\chi_{8470}(281,\cdot)\) \(\chi_{8470}(491,\cdot)\) \(\chi_{8470}(701,\cdot)\) \(\chi_{8470}(981,\cdot)\) \(\chi_{8470}(1051,\cdot)\) \(\chi_{8470}(1261,\cdot)\) \(\chi_{8470}(1471,\cdot)\) \(\chi_{8470}(1751,\cdot)\) \(\chi_{8470}(1821,\cdot)\) \(\chi_{8470}(2031,\cdot)\) \(\chi_{8470}(2241,\cdot)\) \(\chi_{8470}(2521,\cdot)\) \(\chi_{8470}(2591,\cdot)\) \(\chi_{8470}(2801,\cdot)\) \(\chi_{8470}(3011,\cdot)\) \(\chi_{8470}(3291,\cdot)\) \(\chi_{8470}(3571,\cdot)\) \(\chi_{8470}(3781,\cdot)\) \(\chi_{8470}(4061,\cdot)\) \(\chi_{8470}(4131,\cdot)\) \(\chi_{8470}(4341,\cdot)\) \(\chi_{8470}(4551,\cdot)\) \(\chi_{8470}(4901,\cdot)\) \(\chi_{8470}(5111,\cdot)\) \(\chi_{8470}(5601,\cdot)\) \(\chi_{8470}(5671,\cdot)\) \(\chi_{8470}(5881,\cdot)\) \(\chi_{8470}(6091,\cdot)\) \(\chi_{8470}(6371,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((6777,6051,7141)\) → \((1,1,e\left(\frac{1}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 8470 }(7141, a) \) | \(-1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{49}{110}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{21}{55}\right)\) |