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 \(\chi_{11025}(5647,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 132300.bad
\(\chi_{132300}(73,\cdot)\) \(\chi_{132300}(2413,\cdot)\) \(\chi_{132300}(3097,\cdot)\) \(\chi_{132300}(5437,\cdot)\) \(\chi_{132300}(6877,\cdot)\) \(\chi_{132300}(7633,\cdot)\) \(\chi_{132300}(9217,\cdot)\) \(\chi_{132300}(9973,\cdot)\) \(\chi_{132300}(11413,\cdot)\) \(\chi_{132300}(12997,\cdot)\) \(\chi_{132300}(13753,\cdot)\) \(\chi_{132300}(17533,\cdot)\) \(\chi_{132300}(18217,\cdot)\) \(\chi_{132300}(18973,\cdot)\) \(\chi_{132300}(21313,\cdot)\) \(\chi_{132300}(21997,\cdot)\) \(\chi_{132300}(22753,\cdot)\) \(\chi_{132300}(24337,\cdot)\) \(\chi_{132300}(25777,\cdot)\) \(\chi_{132300}(26533,\cdot)\) \(\chi_{132300}(28117,\cdot)\) \(\chi_{132300}(28873,\cdot)\) \(\chi_{132300}(31897,\cdot)\) \(\chi_{132300}(33337,\cdot)\) \(\chi_{132300}(35677,\cdot)\) \(\chi_{132300}(36433,\cdot)\) \(\chi_{132300}(37117,\cdot)\) \(\chi_{132300}(37873,\cdot)\) \(\chi_{132300}(40213,\cdot)\) \(\chi_{132300}(41653,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{420})$ |
| Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((66151,122501,15877,54001)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{17}{20}\right),e\left(\frac{11}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 132300 }(12997, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{105}\right)\) | \(e\left(\frac{193}{420}\right)\) | \(e\left(\frac{251}{420}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{407}{420}\right)\) | \(e\left(\frac{157}{210}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{13}{420}\right)\) | \(e\left(\frac{209}{210}\right)\) | \(e\left(\frac{55}{84}\right)\) |