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 \(\chi_{4725}(977,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9450.ha
\(\chi_{9450}(317,\cdot)\) \(\chi_{9450}(347,\cdot)\) \(\chi_{9450}(473,\cdot)\) \(\chi_{9450}(947,\cdot)\) \(\chi_{9450}(977,\cdot)\) \(\chi_{9450}(1073,\cdot)\) \(\chi_{9450}(1103,\cdot)\) \(\chi_{9450}(1577,\cdot)\) \(\chi_{9450}(1703,\cdot)\) \(\chi_{9450}(1733,\cdot)\) \(\chi_{9450}(2237,\cdot)\) \(\chi_{9450}(2333,\cdot)\) \(\chi_{9450}(2363,\cdot)\) \(\chi_{9450}(2837,\cdot)\) \(\chi_{9450}(2867,\cdot)\) \(\chi_{9450}(2963,\cdot)\) \(\chi_{9450}(3467,\cdot)\) \(\chi_{9450}(3497,\cdot)\) \(\chi_{9450}(3623,\cdot)\) \(\chi_{9450}(4097,\cdot)\) \(\chi_{9450}(4127,\cdot)\) \(\chi_{9450}(4223,\cdot)\) \(\chi_{9450}(4253,\cdot)\) \(\chi_{9450}(4727,\cdot)\) \(\chi_{9450}(4853,\cdot)\) \(\chi_{9450}(4883,\cdot)\) \(\chi_{9450}(5387,\cdot)\) \(\chi_{9450}(5483,\cdot)\) \(\chi_{9450}(5513,\cdot)\) \(\chi_{9450}(5987,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{180})$ |
Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((9101,6427,6751)\) → \((e\left(\frac{5}{18}\right),e\left(\frac{1}{20}\right),e\left(\frac{2}{3}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 9450 }(977, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{31}{180}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{169}{180}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{31}{36}\right)\) |