Basic properties
| Modulus: | \(6900\) | |
| Conductor: | \(6900\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | 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.da
\(\chi_{6900}(59,\cdot)\) \(\chi_{6900}(119,\cdot)\) \(\chi_{6900}(179,\cdot)\) \(\chi_{6900}(239,\cdot)\) \(\chi_{6900}(719,\cdot)\) \(\chi_{6900}(959,\cdot)\) \(\chi_{6900}(1139,\cdot)\) \(\chi_{6900}(1319,\cdot)\) \(\chi_{6900}(1439,\cdot)\) \(\chi_{6900}(1559,\cdot)\) \(\chi_{6900}(1619,\cdot)\) \(\chi_{6900}(2279,\cdot)\) \(\chi_{6900}(2339,\cdot)\) \(\chi_{6900}(2519,\cdot)\) \(\chi_{6900}(2579,\cdot)\) \(\chi_{6900}(2819,\cdot)\) \(\chi_{6900}(2879,\cdot)\) \(\chi_{6900}(2939,\cdot)\) \(\chi_{6900}(3479,\cdot)\) \(\chi_{6900}(3659,\cdot)\) \(\chi_{6900}(3719,\cdot)\) \(\chi_{6900}(3959,\cdot)\) \(\chi_{6900}(4079,\cdot)\) \(\chi_{6900}(4259,\cdot)\) \(\chi_{6900}(4319,\cdot)\) \(\chi_{6900}(4379,\cdot)\) \(\chi_{6900}(4859,\cdot)\) \(\chi_{6900}(5039,\cdot)\) \(\chi_{6900}(5279,\cdot)\) \(\chi_{6900}(5339,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3451,4601,277,1201)\) → \((-1,-1,e\left(\frac{7}{10}\right),e\left(\frac{3}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 6900 }(5459, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{13}{110}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{21}{110}\right)\) | \(e\left(\frac{89}{110}\right)\) | \(e\left(\frac{81}{110}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{63}{110}\right)\) | \(e\left(\frac{4}{11}\right)\) |