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 \(\chi_{4725}(3944,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9450.gw
\(\chi_{9450}(479,\cdot)\) \(\chi_{9450}(509,\cdot)\) \(\chi_{9450}(1109,\cdot)\) \(\chi_{9450}(1139,\cdot)\) \(\chi_{9450}(1739,\cdot)\) \(\chi_{9450}(1769,\cdot)\) \(\chi_{9450}(2369,\cdot)\) \(\chi_{9450}(3029,\cdot)\) \(\chi_{9450}(3629,\cdot)\) \(\chi_{9450}(3659,\cdot)\) \(\chi_{9450}(4259,\cdot)\) \(\chi_{9450}(4289,\cdot)\) \(\chi_{9450}(4889,\cdot)\) \(\chi_{9450}(4919,\cdot)\) \(\chi_{9450}(5519,\cdot)\) \(\chi_{9450}(6179,\cdot)\) \(\chi_{9450}(6779,\cdot)\) \(\chi_{9450}(6809,\cdot)\) \(\chi_{9450}(7409,\cdot)\) \(\chi_{9450}(7439,\cdot)\) \(\chi_{9450}(8039,\cdot)\) \(\chi_{9450}(8069,\cdot)\) \(\chi_{9450}(8669,\cdot)\) \(\chi_{9450}(9329,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((9101,6427,6751)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{9}{10}\right),e\left(\frac{1}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 9450 }(8669, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{13}{18}\right)\) |