Basic properties
| Modulus: | \(6900\) | |
| Conductor: | \(575\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{575}(37,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6900.dn
\(\chi_{6900}(37,\cdot)\) \(\chi_{6900}(97,\cdot)\) \(\chi_{6900}(217,\cdot)\) \(\chi_{6900}(313,\cdot)\) \(\chi_{6900}(337,\cdot)\) \(\chi_{6900}(373,\cdot)\) \(\chi_{6900}(433,\cdot)\) \(\chi_{6900}(517,\cdot)\) \(\chi_{6900}(613,\cdot)\) \(\chi_{6900}(697,\cdot)\) \(\chi_{6900}(733,\cdot)\) \(\chi_{6900}(937,\cdot)\) \(\chi_{6900}(973,\cdot)\) \(\chi_{6900}(1033,\cdot)\) \(\chi_{6900}(1213,\cdot)\) \(\chi_{6900}(1417,\cdot)\) \(\chi_{6900}(1477,\cdot)\) \(\chi_{6900}(1537,\cdot)\) \(\chi_{6900}(1597,\cdot)\) \(\chi_{6900}(1717,\cdot)\) \(\chi_{6900}(1753,\cdot)\) \(\chi_{6900}(1813,\cdot)\) \(\chi_{6900}(1837,\cdot)\) \(\chi_{6900}(1873,\cdot)\) \(\chi_{6900}(1897,\cdot)\) \(\chi_{6900}(2077,\cdot)\) \(\chi_{6900}(2113,\cdot)\) \(\chi_{6900}(2137,\cdot)\) \(\chi_{6900}(2173,\cdot)\) \(\chi_{6900}(2317,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((3451,4601,277,1201)\) → \((1,1,e\left(\frac{9}{20}\right),e\left(\frac{21}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 6900 }(37, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{44}\right)\) | \(e\left(\frac{87}{110}\right)\) | \(e\left(\frac{201}{220}\right)\) | \(e\left(\frac{117}{220}\right)\) | \(e\left(\frac{23}{55}\right)\) | \(e\left(\frac{9}{110}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{21}{220}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{23}{44}\right)\) |