Basic properties
Modulus: | \(8470\) | |
Conductor: | \(847\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{847}(391,\cdot)\) | 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
\((6777,6051,7141)\) → \((1,-1,e\left(\frac{9}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 8470 }(391, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{59}{110}\right)\) | \(e\left(\frac{24}{55}\right)\) |