Basic properties
Modulus: | \(9450\) | |
Conductor: | \(4725\) | 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 \(\chi_{4725}(319,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9450.gn
\(\chi_{9450}(79,\cdot)\) \(\chi_{9450}(319,\cdot)\) \(\chi_{9450}(709,\cdot)\) \(\chi_{9450}(1339,\cdot)\) \(\chi_{9450}(1579,\cdot)\) \(\chi_{9450}(1969,\cdot)\) \(\chi_{9450}(2209,\cdot)\) \(\chi_{9450}(2839,\cdot)\) \(\chi_{9450}(3229,\cdot)\) \(\chi_{9450}(3469,\cdot)\) \(\chi_{9450}(3859,\cdot)\) \(\chi_{9450}(4489,\cdot)\) \(\chi_{9450}(4729,\cdot)\) \(\chi_{9450}(5119,\cdot)\) \(\chi_{9450}(5359,\cdot)\) \(\chi_{9450}(5989,\cdot)\) \(\chi_{9450}(6379,\cdot)\) \(\chi_{9450}(6619,\cdot)\) \(\chi_{9450}(7009,\cdot)\) \(\chi_{9450}(7639,\cdot)\) \(\chi_{9450}(7879,\cdot)\) \(\chi_{9450}(8269,\cdot)\) \(\chi_{9450}(8509,\cdot)\) \(\chi_{9450}(9139,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((9101,6427,6751)\) → \((e\left(\frac{7}{9}\right),e\left(\frac{9}{10}\right),e\left(\frac{2}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 9450 }(319, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{19}{45}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{11}{18}\right)\) |