Basic properties
| Modulus: | \(6900\) | |
| Conductor: | \(2300\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2300}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6900.dh
\(\chi_{6900}(19,\cdot)\) \(\chi_{6900}(79,\cdot)\) \(\chi_{6900}(319,\cdot)\) \(\chi_{6900}(379,\cdot)\) \(\chi_{6900}(559,\cdot)\) \(\chi_{6900}(619,\cdot)\) \(\chi_{6900}(1279,\cdot)\) \(\chi_{6900}(1339,\cdot)\) \(\chi_{6900}(1459,\cdot)\) \(\chi_{6900}(1579,\cdot)\) \(\chi_{6900}(1759,\cdot)\) \(\chi_{6900}(1939,\cdot)\) \(\chi_{6900}(2179,\cdot)\) \(\chi_{6900}(2659,\cdot)\) \(\chi_{6900}(2719,\cdot)\) \(\chi_{6900}(2779,\cdot)\) \(\chi_{6900}(2839,\cdot)\) \(\chi_{6900}(2959,\cdot)\) \(\chi_{6900}(3079,\cdot)\) \(\chi_{6900}(3139,\cdot)\) \(\chi_{6900}(3319,\cdot)\) \(\chi_{6900}(3379,\cdot)\) \(\chi_{6900}(3559,\cdot)\) \(\chi_{6900}(4039,\cdot)\) \(\chi_{6900}(4159,\cdot)\) \(\chi_{6900}(4219,\cdot)\) \(\chi_{6900}(4339,\cdot)\) \(\chi_{6900}(4459,\cdot)\) \(\chi_{6900}(4519,\cdot)\) \(\chi_{6900}(4759,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((3451,4601,277,1201)\) → \((-1,1,e\left(\frac{9}{10}\right),e\left(\frac{15}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 6900 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{71}{110}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{87}{110}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{9}{22}\right)\) |