Basic properties
| Modulus: | \(5445\) | |
| Conductor: | \(1815\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1815}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5445.dg
\(\chi_{5445}(8,\cdot)\) \(\chi_{5445}(17,\cdot)\) \(\chi_{5445}(62,\cdot)\) \(\chi_{5445}(107,\cdot)\) \(\chi_{5445}(332,\cdot)\) \(\chi_{5445}(413,\cdot)\) \(\chi_{5445}(458,\cdot)\) \(\chi_{5445}(503,\cdot)\) \(\chi_{5445}(512,\cdot)\) \(\chi_{5445}(557,\cdot)\) \(\chi_{5445}(728,\cdot)\) \(\chi_{5445}(827,\cdot)\) \(\chi_{5445}(908,\cdot)\) \(\chi_{5445}(953,\cdot)\) \(\chi_{5445}(998,\cdot)\) \(\chi_{5445}(1007,\cdot)\) \(\chi_{5445}(1052,\cdot)\) \(\chi_{5445}(1097,\cdot)\) \(\chi_{5445}(1223,\cdot)\) \(\chi_{5445}(1403,\cdot)\) \(\chi_{5445}(1448,\cdot)\) \(\chi_{5445}(1493,\cdot)\) \(\chi_{5445}(1502,\cdot)\) \(\chi_{5445}(1547,\cdot)\) \(\chi_{5445}(1592,\cdot)\) \(\chi_{5445}(1718,\cdot)\) \(\chi_{5445}(1817,\cdot)\) \(\chi_{5445}(1898,\cdot)\) \(\chi_{5445}(1943,\cdot)\) \(\chi_{5445}(1988,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((3026,4357,3511)\) → \((-1,i,e\left(\frac{49}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 5445 }(17, a) \) | \(-1\) | \(1\) | \(e\left(\frac{43}{220}\right)\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{81}{220}\right)\) | \(e\left(\frac{129}{220}\right)\) | \(e\left(\frac{163}{220}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{127}{220}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{19}{44}\right)\) |