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 \(\chi_{4725}(3883,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9450.gz
\(\chi_{9450}(103,\cdot)\) \(\chi_{9450}(367,\cdot)\) \(\chi_{9450}(733,\cdot)\) \(\chi_{9450}(997,\cdot)\) \(\chi_{9450}(1123,\cdot)\) \(\chi_{9450}(1237,\cdot)\) \(\chi_{9450}(1363,\cdot)\) \(\chi_{9450}(1627,\cdot)\) \(\chi_{9450}(1753,\cdot)\) \(\chi_{9450}(1867,\cdot)\) \(\chi_{9450}(2383,\cdot)\) \(\chi_{9450}(2497,\cdot)\) \(\chi_{9450}(2623,\cdot)\) \(\chi_{9450}(2887,\cdot)\) \(\chi_{9450}(3013,\cdot)\) \(\chi_{9450}(3127,\cdot)\) \(\chi_{9450}(3253,\cdot)\) \(\chi_{9450}(3517,\cdot)\) \(\chi_{9450}(3883,\cdot)\) \(\chi_{9450}(4147,\cdot)\) \(\chi_{9450}(4273,\cdot)\) \(\chi_{9450}(4387,\cdot)\) \(\chi_{9450}(4513,\cdot)\) \(\chi_{9450}(4777,\cdot)\) \(\chi_{9450}(4903,\cdot)\) \(\chi_{9450}(5017,\cdot)\) \(\chi_{9450}(5533,\cdot)\) \(\chi_{9450}(5647,\cdot)\) \(\chi_{9450}(5773,\cdot)\) \(\chi_{9450}(6037,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{180})$ |
Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((9101,6427,6751)\) → \((e\left(\frac{7}{9}\right),e\left(\frac{3}{20}\right),e\left(\frac{5}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 9450 }(3883, a) \) | \(1\) | \(1\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{103}{180}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{157}{180}\right)\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{13}{36}\right)\) |