Basic properties
Modulus: | \(8470\) | |
Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(55\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{121}(16,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8470.cf
\(\chi_{8470}(71,\cdot)\) \(\chi_{8470}(141,\cdot)\) \(\chi_{8470}(421,\cdot)\) \(\chi_{8470}(631,\cdot)\) \(\chi_{8470}(841,\cdot)\) \(\chi_{8470}(911,\cdot)\) \(\chi_{8470}(1191,\cdot)\) \(\chi_{8470}(1401,\cdot)\) \(\chi_{8470}(1611,\cdot)\) \(\chi_{8470}(1681,\cdot)\) \(\chi_{8470}(1961,\cdot)\) \(\chi_{8470}(2171,\cdot)\) \(\chi_{8470}(2381,\cdot)\) \(\chi_{8470}(2451,\cdot)\) \(\chi_{8470}(2731,\cdot)\) \(\chi_{8470}(2941,\cdot)\) \(\chi_{8470}(3151,\cdot)\) \(\chi_{8470}(3221,\cdot)\) \(\chi_{8470}(3501,\cdot)\) \(\chi_{8470}(3921,\cdot)\) \(\chi_{8470}(3991,\cdot)\) \(\chi_{8470}(4271,\cdot)\) \(\chi_{8470}(4481,\cdot)\) \(\chi_{8470}(4691,\cdot)\) \(\chi_{8470}(4761,\cdot)\) \(\chi_{8470}(5041,\cdot)\) \(\chi_{8470}(5251,\cdot)\) \(\chi_{8470}(5461,\cdot)\) \(\chi_{8470}(5531,\cdot)\) \(\chi_{8470}(6021,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((6777,6051,7141)\) → \((1,1,e\left(\frac{2}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 8470 }(5461, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{29}{55}\right)\) |