Basic properties
| Modulus: | \(6900\) | |
| Conductor: | \(575\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(55\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{575}(121,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6900.cu
\(\chi_{6900}(121,\cdot)\) \(\chi_{6900}(361,\cdot)\) \(\chi_{6900}(541,\cdot)\) \(\chi_{6900}(721,\cdot)\) \(\chi_{6900}(841,\cdot)\) \(\chi_{6900}(961,\cdot)\) \(\chi_{6900}(1021,\cdot)\) \(\chi_{6900}(1681,\cdot)\) \(\chi_{6900}(1741,\cdot)\) \(\chi_{6900}(1921,\cdot)\) \(\chi_{6900}(1981,\cdot)\) \(\chi_{6900}(2221,\cdot)\) \(\chi_{6900}(2281,\cdot)\) \(\chi_{6900}(2341,\cdot)\) \(\chi_{6900}(2881,\cdot)\) \(\chi_{6900}(3061,\cdot)\) \(\chi_{6900}(3121,\cdot)\) \(\chi_{6900}(3361,\cdot)\) \(\chi_{6900}(3481,\cdot)\) \(\chi_{6900}(3661,\cdot)\) \(\chi_{6900}(3721,\cdot)\) \(\chi_{6900}(3781,\cdot)\) \(\chi_{6900}(4261,\cdot)\) \(\chi_{6900}(4441,\cdot)\) \(\chi_{6900}(4681,\cdot)\) \(\chi_{6900}(4741,\cdot)\) \(\chi_{6900}(4861,\cdot)\) \(\chi_{6900}(4981,\cdot)\) \(\chi_{6900}(5041,\cdot)\) \(\chi_{6900}(5161,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((3451,4601,277,1201)\) → \((1,1,e\left(\frac{3}{5}\right),e\left(\frac{9}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 6900 }(121, a) \) | \(1\) | \(1\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{53}{55}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{29}{55}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{1}{11}\right)\) |