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 \(\chi_{4275}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8550.fk
\(\chi_{8550}(61,\cdot)\) \(\chi_{8550}(841,\cdot)\) \(\chi_{8550}(1681,\cdot)\) \(\chi_{8550}(1771,\cdot)\) \(\chi_{8550}(2011,\cdot)\) \(\chi_{8550}(2761,\cdot)\) \(\chi_{8550}(3361,\cdot)\) \(\chi_{8550}(3391,\cdot)\) \(\chi_{8550}(3481,\cdot)\) \(\chi_{8550}(3721,\cdot)\) \(\chi_{8550}(4261,\cdot)\) \(\chi_{8550}(4471,\cdot)\) \(\chi_{8550}(5071,\cdot)\) \(\chi_{8550}(5191,\cdot)\) \(\chi_{8550}(5431,\cdot)\) \(\chi_{8550}(5971,\cdot)\) \(\chi_{8550}(6181,\cdot)\) \(\chi_{8550}(6781,\cdot)\) \(\chi_{8550}(6811,\cdot)\) \(\chi_{8550}(7141,\cdot)\) \(\chi_{8550}(7681,\cdot)\) \(\chi_{8550}(7891,\cdot)\) \(\chi_{8550}(8491,\cdot)\) \(\chi_{8550}(8521,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((1901,1027,1351)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{4}{5}\right),e\left(\frac{1}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 8550 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{4}{9}\right)\) |