Basic properties
Modulus: | \(9450\) | |
Conductor: | \(4725\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4725}(1706,\cdot)\) | 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)
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Galois orbit 9450.gf
\(\chi_{9450}(131,\cdot)\) \(\chi_{9450}(731,\cdot)\) \(\chi_{9450}(761,\cdot)\) \(\chi_{9450}(1361,\cdot)\) \(\chi_{9450}(1391,\cdot)\) \(\chi_{9450}(1991,\cdot)\) \(\chi_{9450}(2021,\cdot)\) \(\chi_{9450}(2621,\cdot)\) \(\chi_{9450}(3281,\cdot)\) \(\chi_{9450}(3881,\cdot)\) \(\chi_{9450}(3911,\cdot)\) \(\chi_{9450}(4511,\cdot)\) \(\chi_{9450}(4541,\cdot)\) \(\chi_{9450}(5141,\cdot)\) \(\chi_{9450}(5171,\cdot)\) \(\chi_{9450}(5771,\cdot)\) \(\chi_{9450}(6431,\cdot)\) \(\chi_{9450}(7031,\cdot)\) \(\chi_{9450}(7061,\cdot)\) \(\chi_{9450}(7661,\cdot)\) \(\chi_{9450}(7691,\cdot)\) \(\chi_{9450}(8291,\cdot)\) \(\chi_{9450}(8321,\cdot)\) \(\chi_{9450}(8921,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((9101,6427,6751)\) → \((e\left(\frac{5}{18}\right),e\left(\frac{2}{5}\right),e\left(\frac{5}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 9450 }(6431, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{1}{9}\right)\) |