Basic properties
| Modulus: | \(6900\) | |
| Conductor: | \(6900\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6900.dk
\(\chi_{6900}(83,\cdot)\) \(\chi_{6900}(203,\cdot)\) \(\chi_{6900}(227,\cdot)\) \(\chi_{6900}(263,\cdot)\) \(\chi_{6900}(287,\cdot)\) \(\chi_{6900}(383,\cdot)\) \(\chi_{6900}(467,\cdot)\) \(\chi_{6900}(503,\cdot)\) \(\chi_{6900}(527,\cdot)\) \(\chi_{6900}(563,\cdot)\) \(\chi_{6900}(803,\cdot)\) \(\chi_{6900}(983,\cdot)\) \(\chi_{6900}(1187,\cdot)\) \(\chi_{6900}(1247,\cdot)\) \(\chi_{6900}(1367,\cdot)\) \(\chi_{6900}(1463,\cdot)\) \(\chi_{6900}(1487,\cdot)\) \(\chi_{6900}(1523,\cdot)\) \(\chi_{6900}(1583,\cdot)\) \(\chi_{6900}(1667,\cdot)\) \(\chi_{6900}(1763,\cdot)\) \(\chi_{6900}(1847,\cdot)\) \(\chi_{6900}(1883,\cdot)\) \(\chi_{6900}(2087,\cdot)\) \(\chi_{6900}(2123,\cdot)\) \(\chi_{6900}(2183,\cdot)\) \(\chi_{6900}(2363,\cdot)\) \(\chi_{6900}(2567,\cdot)\) \(\chi_{6900}(2627,\cdot)\) \(\chi_{6900}(2687,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((3451,4601,277,1201)\) → \((-1,-1,e\left(\frac{3}{20}\right),e\left(\frac{21}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 6900 }(83, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{47}{220}\right)\) | \(e\left(\frac{29}{220}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{54}{55}\right)\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{87}{220}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{23}{44}\right)\) |