Basic properties
Modulus: | \(9450\) | |
Conductor: | \(4725\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{4725}(2783,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9450.hi
\(\chi_{9450}(23,\cdot)\) \(\chi_{9450}(137,\cdot)\) \(\chi_{9450}(263,\cdot)\) \(\chi_{9450}(527,\cdot)\) \(\chi_{9450}(653,\cdot)\) \(\chi_{9450}(767,\cdot)\) \(\chi_{9450}(1283,\cdot)\) \(\chi_{9450}(1397,\cdot)\) \(\chi_{9450}(1523,\cdot)\) \(\chi_{9450}(1787,\cdot)\) \(\chi_{9450}(1913,\cdot)\) \(\chi_{9450}(2027,\cdot)\) \(\chi_{9450}(2153,\cdot)\) \(\chi_{9450}(2417,\cdot)\) \(\chi_{9450}(2783,\cdot)\) \(\chi_{9450}(3047,\cdot)\) \(\chi_{9450}(3173,\cdot)\) \(\chi_{9450}(3287,\cdot)\) \(\chi_{9450}(3413,\cdot)\) \(\chi_{9450}(3677,\cdot)\) \(\chi_{9450}(3803,\cdot)\) \(\chi_{9450}(3917,\cdot)\) \(\chi_{9450}(4433,\cdot)\) \(\chi_{9450}(4547,\cdot)\) \(\chi_{9450}(4673,\cdot)\) \(\chi_{9450}(4937,\cdot)\) \(\chi_{9450}(5063,\cdot)\) \(\chi_{9450}(5177,\cdot)\) \(\chi_{9450}(5303,\cdot)\) \(\chi_{9450}(5567,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{180})$ |
Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((9101,6427,6751)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{3}{20}\right),e\left(\frac{2}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 9450 }(2783, a) \) | \(1\) | \(1\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{53}{180}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{107}{180}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{17}{36}\right)\) |