Basic properties
Modulus: | \(9450\) | |
Conductor: | \(4725\) | 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 \(\chi_{4725}(3481,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9450.fl
\(\chi_{9450}(331,\cdot)\) \(\chi_{9450}(571,\cdot)\) \(\chi_{9450}(961,\cdot)\) \(\chi_{9450}(1591,\cdot)\) \(\chi_{9450}(1831,\cdot)\) \(\chi_{9450}(2221,\cdot)\) \(\chi_{9450}(2461,\cdot)\) \(\chi_{9450}(3091,\cdot)\) \(\chi_{9450}(3481,\cdot)\) \(\chi_{9450}(3721,\cdot)\) \(\chi_{9450}(4111,\cdot)\) \(\chi_{9450}(4741,\cdot)\) \(\chi_{9450}(4981,\cdot)\) \(\chi_{9450}(5371,\cdot)\) \(\chi_{9450}(5611,\cdot)\) \(\chi_{9450}(6241,\cdot)\) \(\chi_{9450}(6631,\cdot)\) \(\chi_{9450}(6871,\cdot)\) \(\chi_{9450}(7261,\cdot)\) \(\chi_{9450}(7891,\cdot)\) \(\chi_{9450}(8131,\cdot)\) \(\chi_{9450}(8521,\cdot)\) \(\chi_{9450}(8761,\cdot)\) \(\chi_{9450}(9391,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((9101,6427,6751)\) → \((e\left(\frac{5}{9}\right),e\left(\frac{2}{5}\right),e\left(\frac{1}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 9450 }(3481, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{2}{9}\right)\) |