Basic properties
Modulus: | \(8550\) | |
Conductor: | \(1425\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1425}(89,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8550.gp
\(\chi_{8550}(89,\cdot)\) \(\chi_{8550}(269,\cdot)\) \(\chi_{8550}(629,\cdot)\) \(\chi_{8550}(1079,\cdot)\) \(\chi_{8550}(1169,\cdot)\) \(\chi_{8550}(1439,\cdot)\) \(\chi_{8550}(1979,\cdot)\) \(\chi_{8550}(2339,\cdot)\) \(\chi_{8550}(2789,\cdot)\) \(\chi_{8550}(2879,\cdot)\) \(\chi_{8550}(3509,\cdot)\) \(\chi_{8550}(3689,\cdot)\) \(\chi_{8550}(4589,\cdot)\) \(\chi_{8550}(4859,\cdot)\) \(\chi_{8550}(5219,\cdot)\) \(\chi_{8550}(5759,\cdot)\) \(\chi_{8550}(6209,\cdot)\) \(\chi_{8550}(6569,\cdot)\) \(\chi_{8550}(6929,\cdot)\) \(\chi_{8550}(7109,\cdot)\) \(\chi_{8550}(7469,\cdot)\) \(\chi_{8550}(7919,\cdot)\) \(\chi_{8550}(8009,\cdot)\) \(\chi_{8550}(8279,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((1901,1027,1351)\) → \((-1,e\left(\frac{3}{10}\right),e\left(\frac{5}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 8550 }(89, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{17}{18}\right)\) |