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 \(\chi_{4725}(223,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9450.hh
\(\chi_{9450}(13,\cdot)\) \(\chi_{9450}(97,\cdot)\) \(\chi_{9450}(223,\cdot)\) \(\chi_{9450}(517,\cdot)\) \(\chi_{9450}(727,\cdot)\) \(\chi_{9450}(853,\cdot)\) \(\chi_{9450}(1147,\cdot)\) \(\chi_{9450}(1273,\cdot)\) \(\chi_{9450}(1483,\cdot)\) \(\chi_{9450}(1777,\cdot)\) \(\chi_{9450}(1903,\cdot)\) \(\chi_{9450}(1987,\cdot)\) \(\chi_{9450}(2113,\cdot)\) \(\chi_{9450}(2533,\cdot)\) \(\chi_{9450}(2617,\cdot)\) \(\chi_{9450}(3037,\cdot)\) \(\chi_{9450}(3163,\cdot)\) \(\chi_{9450}(3247,\cdot)\) \(\chi_{9450}(3373,\cdot)\) \(\chi_{9450}(3667,\cdot)\) \(\chi_{9450}(3877,\cdot)\) \(\chi_{9450}(4003,\cdot)\) \(\chi_{9450}(4297,\cdot)\) \(\chi_{9450}(4423,\cdot)\) \(\chi_{9450}(4633,\cdot)\) \(\chi_{9450}(4927,\cdot)\) \(\chi_{9450}(5053,\cdot)\) \(\chi_{9450}(5137,\cdot)\) \(\chi_{9450}(5263,\cdot)\) \(\chi_{9450}(5683,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{180})$ |
Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((9101,6427,6751)\) → \((e\left(\frac{8}{9}\right),e\left(\frac{11}{20}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 9450 }(223, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{11}{180}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{149}{180}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{61}{90}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{29}{36}\right)\) |