Basic properties
| Modulus: | \(9450\) | |
| Conductor: | \(4725\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4725}(1202,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9450.gy
\(\chi_{9450}(227,\cdot)\) \(\chi_{9450}(353,\cdot)\) \(\chi_{9450}(383,\cdot)\) \(\chi_{9450}(887,\cdot)\) \(\chi_{9450}(983,\cdot)\) \(\chi_{9450}(1013,\cdot)\) \(\chi_{9450}(1487,\cdot)\) \(\chi_{9450}(1517,\cdot)\) \(\chi_{9450}(1613,\cdot)\) \(\chi_{9450}(2117,\cdot)\) \(\chi_{9450}(2147,\cdot)\) \(\chi_{9450}(2273,\cdot)\) \(\chi_{9450}(2747,\cdot)\) \(\chi_{9450}(2777,\cdot)\) \(\chi_{9450}(2873,\cdot)\) \(\chi_{9450}(2903,\cdot)\) \(\chi_{9450}(3377,\cdot)\) \(\chi_{9450}(3503,\cdot)\) \(\chi_{9450}(3533,\cdot)\) \(\chi_{9450}(4037,\cdot)\) \(\chi_{9450}(4133,\cdot)\) \(\chi_{9450}(4163,\cdot)\) \(\chi_{9450}(4637,\cdot)\) \(\chi_{9450}(4667,\cdot)\) \(\chi_{9450}(4763,\cdot)\) \(\chi_{9450}(5267,\cdot)\) \(\chi_{9450}(5297,\cdot)\) \(\chi_{9450}(5423,\cdot)\) \(\chi_{9450}(5897,\cdot)\) \(\chi_{9450}(5927,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((9101,6427,6751)\) → \((e\left(\frac{17}{18}\right),e\left(\frac{1}{20}\right),e\left(\frac{5}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 9450 }(5927, a) \) | \(-1\) | \(1\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{1}{180}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{109}{180}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{19}{36}\right)\) |