Basic properties
| Modulus: | \(1815\) | |
| Conductor: | \(1815\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1815.bv
\(\chi_{1815}(2,\cdot)\) \(\chi_{1815}(8,\cdot)\) \(\chi_{1815}(17,\cdot)\) \(\chi_{1815}(62,\cdot)\) \(\chi_{1815}(68,\cdot)\) \(\chi_{1815}(83,\cdot)\) \(\chi_{1815}(107,\cdot)\) \(\chi_{1815}(128,\cdot)\) \(\chi_{1815}(167,\cdot)\) \(\chi_{1815}(173,\cdot)\) \(\chi_{1815}(182,\cdot)\) \(\chi_{1815}(227,\cdot)\) \(\chi_{1815}(248,\cdot)\) \(\chi_{1815}(272,\cdot)\) \(\chi_{1815}(293,\cdot)\) \(\chi_{1815}(332,\cdot)\) \(\chi_{1815}(338,\cdot)\) \(\chi_{1815}(347,\cdot)\) \(\chi_{1815}(392,\cdot)\) \(\chi_{1815}(398,\cdot)\) \(\chi_{1815}(413,\cdot)\) \(\chi_{1815}(437,\cdot)\) \(\chi_{1815}(458,\cdot)\) \(\chi_{1815}(497,\cdot)\) \(\chi_{1815}(503,\cdot)\) \(\chi_{1815}(512,\cdot)\) \(\chi_{1815}(557,\cdot)\) \(\chi_{1815}(563,\cdot)\) \(\chi_{1815}(623,\cdot)\) \(\chi_{1815}(662,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((1211,727,1696)\) → \((-1,i,e\left(\frac{1}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 1815 }(2, a) \) | \(-1\) | \(1\) | \(e\left(\frac{167}{220}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{69}{220}\right)\) | \(e\left(\frac{61}{220}\right)\) | \(e\left(\frac{147}{220}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{43}{220}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{39}{44}\right)\) |