Basic properties
Modulus: | \(8470\) | |
Conductor: | \(4235\) | 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 \(\chi_{4235}(69,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8470.ct
\(\chi_{8470}(69,\cdot)\) \(\chi_{8470}(279,\cdot)\) \(\chi_{8470}(489,\cdot)\) \(\chi_{8470}(559,\cdot)\) \(\chi_{8470}(839,\cdot)\) \(\chi_{8470}(1259,\cdot)\) \(\chi_{8470}(1329,\cdot)\) \(\chi_{8470}(1609,\cdot)\) \(\chi_{8470}(1819,\cdot)\) \(\chi_{8470}(2029,\cdot)\) \(\chi_{8470}(2099,\cdot)\) \(\chi_{8470}(2379,\cdot)\) \(\chi_{8470}(2589,\cdot)\) \(\chi_{8470}(2799,\cdot)\) \(\chi_{8470}(2869,\cdot)\) \(\chi_{8470}(3359,\cdot)\) \(\chi_{8470}(3569,\cdot)\) \(\chi_{8470}(3919,\cdot)\) \(\chi_{8470}(4129,\cdot)\) \(\chi_{8470}(4339,\cdot)\) \(\chi_{8470}(4409,\cdot)\) \(\chi_{8470}(4689,\cdot)\) \(\chi_{8470}(4899,\cdot)\) \(\chi_{8470}(5179,\cdot)\) \(\chi_{8470}(5459,\cdot)\) \(\chi_{8470}(5669,\cdot)\) \(\chi_{8470}(5879,\cdot)\) \(\chi_{8470}(5949,\cdot)\) \(\chi_{8470}(6229,\cdot)\) \(\chi_{8470}(6439,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((6777,6051,7141)\) → \((-1,-1,e\left(\frac{24}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 8470 }(69, a) \) | \(-1\) | \(1\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{79}{110}\right)\) | \(e\left(\frac{1}{22}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{91}{110}\right)\) |