Basic properties
| Modulus: | \(6900\) | |
| Conductor: | \(1725\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1725}(1631,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6900.dj
\(\chi_{6900}(221,\cdot)\) \(\chi_{6900}(281,\cdot)\) \(\chi_{6900}(341,\cdot)\) \(\chi_{6900}(521,\cdot)\) \(\chi_{6900}(641,\cdot)\) \(\chi_{6900}(881,\cdot)\) \(\chi_{6900}(941,\cdot)\) \(\chi_{6900}(1121,\cdot)\) \(\chi_{6900}(1661,\cdot)\) \(\chi_{6900}(1721,\cdot)\) \(\chi_{6900}(1781,\cdot)\) \(\chi_{6900}(2021,\cdot)\) \(\chi_{6900}(2081,\cdot)\) \(\chi_{6900}(2261,\cdot)\) \(\chi_{6900}(2321,\cdot)\) \(\chi_{6900}(2981,\cdot)\) \(\chi_{6900}(3041,\cdot)\) \(\chi_{6900}(3161,\cdot)\) \(\chi_{6900}(3281,\cdot)\) \(\chi_{6900}(3461,\cdot)\) \(\chi_{6900}(3641,\cdot)\) \(\chi_{6900}(3881,\cdot)\) \(\chi_{6900}(4361,\cdot)\) \(\chi_{6900}(4421,\cdot)\) \(\chi_{6900}(4481,\cdot)\) \(\chi_{6900}(4541,\cdot)\) \(\chi_{6900}(4661,\cdot)\) \(\chi_{6900}(4781,\cdot)\) \(\chi_{6900}(4841,\cdot)\) \(\chi_{6900}(5021,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3451,4601,277,1201)\) → \((1,-1,e\left(\frac{2}{5}\right),e\left(\frac{13}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 6900 }(5081, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{48}{55}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{103}{110}\right)\) | \(e\left(\frac{41}{55}\right)\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{21}{110}\right)\) | \(e\left(\frac{21}{22}\right)\) |