Basic properties
| Modulus: | \(8470\) | |
| Conductor: | \(847\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{847}(657,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8470.cx
\(\chi_{8470}(41,\cdot)\) \(\chi_{8470}(321,\cdot)\) \(\chi_{8470}(391,\cdot)\) \(\chi_{8470}(601,\cdot)\) \(\chi_{8470}(811,\cdot)\) \(\chi_{8470}(1091,\cdot)\) \(\chi_{8470}(1161,\cdot)\) \(\chi_{8470}(1581,\cdot)\) \(\chi_{8470}(1861,\cdot)\) \(\chi_{8470}(1931,\cdot)\) \(\chi_{8470}(2141,\cdot)\) \(\chi_{8470}(2351,\cdot)\) \(\chi_{8470}(2631,\cdot)\) \(\chi_{8470}(2701,\cdot)\) \(\chi_{8470}(2911,\cdot)\) \(\chi_{8470}(3121,\cdot)\) \(\chi_{8470}(3401,\cdot)\) \(\chi_{8470}(3471,\cdot)\) \(\chi_{8470}(3681,\cdot)\) \(\chi_{8470}(3891,\cdot)\) \(\chi_{8470}(4171,\cdot)\) \(\chi_{8470}(4241,\cdot)\) \(\chi_{8470}(4451,\cdot)\) \(\chi_{8470}(4661,\cdot)\) \(\chi_{8470}(4941,\cdot)\) \(\chi_{8470}(5011,\cdot)\) \(\chi_{8470}(5221,\cdot)\) \(\chi_{8470}(5431,\cdot)\) \(\chi_{8470}(5711,\cdot)\) \(\chi_{8470}(5991,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((6777,6051,7141)\) → \((1,-1,e\left(\frac{103}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 8470 }(2351, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{18}{55}\right)\) |