Basic properties
| Modulus: | \(132300\) | |
| Conductor: | \(11025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(420\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{11025}(4372,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 132300.zz
\(\chi_{132300}(37,\cdot)\) \(\chi_{132300}(613,\cdot)\) \(\chi_{132300}(3637,\cdot)\) \(\chi_{132300}(3817,\cdot)\) \(\chi_{132300}(4573,\cdot)\) \(\chi_{132300}(7597,\cdot)\) \(\chi_{132300}(8173,\cdot)\) \(\chi_{132300}(8353,\cdot)\) \(\chi_{132300}(11197,\cdot)\) \(\chi_{132300}(11377,\cdot)\) \(\chi_{132300}(11953,\cdot)\) \(\chi_{132300}(14977,\cdot)\) \(\chi_{132300}(15733,\cdot)\) \(\chi_{132300}(15913,\cdot)\) \(\chi_{132300}(18937,\cdot)\) \(\chi_{132300}(19513,\cdot)\) \(\chi_{132300}(22537,\cdot)\) \(\chi_{132300}(23473,\cdot)\) \(\chi_{132300}(26317,\cdot)\) \(\chi_{132300}(26497,\cdot)\) \(\chi_{132300}(27073,\cdot)\) \(\chi_{132300}(27253,\cdot)\) \(\chi_{132300}(30097,\cdot)\) \(\chi_{132300}(30277,\cdot)\) \(\chi_{132300}(30853,\cdot)\) \(\chi_{132300}(31033,\cdot)\) \(\chi_{132300}(34633,\cdot)\) \(\chi_{132300}(34813,\cdot)\) \(\chi_{132300}(37837,\cdot)\) \(\chi_{132300}(38413,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{420})$ |
| Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((66151,122501,15877,54001)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{17}{20}\right),e\left(\frac{20}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 132300 }(30097, a) \) | \(-1\) | \(1\) | \(e\left(\frac{38}{105}\right)\) | \(e\left(\frac{383}{420}\right)\) | \(e\left(\frac{361}{420}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{367}{420}\right)\) | \(e\left(\frac{107}{210}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{53}{420}\right)\) | \(e\left(\frac{2}{105}\right)\) | \(e\left(\frac{11}{84}\right)\) |