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 \(\chi_{4725}(209,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9450.gh
\(\chi_{9450}(209,\cdot)\) \(\chi_{9450}(419,\cdot)\) \(\chi_{9450}(839,\cdot)\) \(\chi_{9450}(1469,\cdot)\) \(\chi_{9450}(1679,\cdot)\) \(\chi_{9450}(2309,\cdot)\) \(\chi_{9450}(2729,\cdot)\) \(\chi_{9450}(2939,\cdot)\) \(\chi_{9450}(3359,\cdot)\) \(\chi_{9450}(3569,\cdot)\) \(\chi_{9450}(3989,\cdot)\) \(\chi_{9450}(4619,\cdot)\) \(\chi_{9450}(4829,\cdot)\) \(\chi_{9450}(5459,\cdot)\) \(\chi_{9450}(5879,\cdot)\) \(\chi_{9450}(6089,\cdot)\) \(\chi_{9450}(6509,\cdot)\) \(\chi_{9450}(6719,\cdot)\) \(\chi_{9450}(7139,\cdot)\) \(\chi_{9450}(7769,\cdot)\) \(\chi_{9450}(7979,\cdot)\) \(\chi_{9450}(8609,\cdot)\) \(\chi_{9450}(9029,\cdot)\) \(\chi_{9450}(9239,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((9101,6427,6751)\) → \((e\left(\frac{7}{18}\right),e\left(\frac{7}{10}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 9450 }(209, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{79}{90}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{1}{18}\right)\) |