Basic properties
Modulus: | \(9450\) | |
Conductor: | \(675\) | 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 \(\chi_{675}(473,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9450.hb
\(\chi_{9450}(113,\cdot)\) \(\chi_{9450}(533,\cdot)\) \(\chi_{9450}(617,\cdot)\) \(\chi_{9450}(1037,\cdot)\) \(\chi_{9450}(1163,\cdot)\) \(\chi_{9450}(1247,\cdot)\) \(\chi_{9450}(1373,\cdot)\) \(\chi_{9450}(1667,\cdot)\) \(\chi_{9450}(1877,\cdot)\) \(\chi_{9450}(2003,\cdot)\) \(\chi_{9450}(2297,\cdot)\) \(\chi_{9450}(2423,\cdot)\) \(\chi_{9450}(2633,\cdot)\) \(\chi_{9450}(2927,\cdot)\) \(\chi_{9450}(3053,\cdot)\) \(\chi_{9450}(3137,\cdot)\) \(\chi_{9450}(3263,\cdot)\) \(\chi_{9450}(3683,\cdot)\) \(\chi_{9450}(3767,\cdot)\) \(\chi_{9450}(4187,\cdot)\) \(\chi_{9450}(4313,\cdot)\) \(\chi_{9450}(4397,\cdot)\) \(\chi_{9450}(4523,\cdot)\) \(\chi_{9450}(4817,\cdot)\) \(\chi_{9450}(5027,\cdot)\) \(\chi_{9450}(5153,\cdot)\) \(\chi_{9450}(5447,\cdot)\) \(\chi_{9450}(5573,\cdot)\) \(\chi_{9450}(5783,\cdot)\) \(\chi_{9450}(6077,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{180})$ |
Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((9101,6427,6751)\) → \((e\left(\frac{17}{18}\right),e\left(\frac{11}{20}\right),1)\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 9450 }(4523, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{1}{180}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{79}{180}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{1}{36}\right)\) |