Basic properties
Modulus: | \(8550\) | |
Conductor: | \(4275\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(45\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4275}(481,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8550.fm
\(\chi_{8550}(481,\cdot)\) \(\chi_{8550}(511,\cdot)\) \(\chi_{8550}(871,\cdot)\) \(\chi_{8550}(1111,\cdot)\) \(\chi_{8550}(1411,\cdot)\) \(\chi_{8550}(2191,\cdot)\) \(\chi_{8550}(2221,\cdot)\) \(\chi_{8550}(2581,\cdot)\) \(\chi_{8550}(2821,\cdot)\) \(\chi_{8550}(2911,\cdot)\) \(\chi_{8550}(3121,\cdot)\) \(\chi_{8550}(3931,\cdot)\) \(\chi_{8550}(4291,\cdot)\) \(\chi_{8550}(4531,\cdot)\) \(\chi_{8550}(4621,\cdot)\) \(\chi_{8550}(4831,\cdot)\) \(\chi_{8550}(5611,\cdot)\) \(\chi_{8550}(5641,\cdot)\) \(\chi_{8550}(6241,\cdot)\) \(\chi_{8550}(6331,\cdot)\) \(\chi_{8550}(6541,\cdot)\) \(\chi_{8550}(7321,\cdot)\) \(\chi_{8550}(7711,\cdot)\) \(\chi_{8550}(8041,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((1901,1027,1351)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{2}{5}\right),e\left(\frac{7}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 8550 }(481, a) \) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{7}{9}\right)\) |