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 \(\chi_{4725}(146,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9450.gq
\(\chi_{9450}(41,\cdot)\) \(\chi_{9450}(461,\cdot)\) \(\chi_{9450}(671,\cdot)\) \(\chi_{9450}(1091,\cdot)\) \(\chi_{9450}(1721,\cdot)\) \(\chi_{9450}(1931,\cdot)\) \(\chi_{9450}(2561,\cdot)\) \(\chi_{9450}(2981,\cdot)\) \(\chi_{9450}(3191,\cdot)\) \(\chi_{9450}(3611,\cdot)\) \(\chi_{9450}(3821,\cdot)\) \(\chi_{9450}(4241,\cdot)\) \(\chi_{9450}(4871,\cdot)\) \(\chi_{9450}(5081,\cdot)\) \(\chi_{9450}(5711,\cdot)\) \(\chi_{9450}(6131,\cdot)\) \(\chi_{9450}(6341,\cdot)\) \(\chi_{9450}(6761,\cdot)\) \(\chi_{9450}(6971,\cdot)\) \(\chi_{9450}(7391,\cdot)\) \(\chi_{9450}(8021,\cdot)\) \(\chi_{9450}(8231,\cdot)\) \(\chi_{9450}(8861,\cdot)\) \(\chi_{9450}(9281,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((9101,6427,6751)\) → \((e\left(\frac{13}{18}\right),e\left(\frac{3}{5}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 9450 }(4871, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{8}{9}\right)\) |