Basic properties
| Modulus: | \(1815\) | |
| Conductor: | \(605\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{605}(193,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1815.bt
\(\chi_{1815}(7,\cdot)\) \(\chi_{1815}(13,\cdot)\) \(\chi_{1815}(28,\cdot)\) \(\chi_{1815}(52,\cdot)\) \(\chi_{1815}(73,\cdot)\) \(\chi_{1815}(127,\cdot)\) \(\chi_{1815}(172,\cdot)\) \(\chi_{1815}(178,\cdot)\) \(\chi_{1815}(193,\cdot)\) \(\chi_{1815}(217,\cdot)\) \(\chi_{1815}(238,\cdot)\) \(\chi_{1815}(277,\cdot)\) \(\chi_{1815}(283,\cdot)\) \(\chi_{1815}(292,\cdot)\) \(\chi_{1815}(337,\cdot)\) \(\chi_{1815}(343,\cdot)\) \(\chi_{1815}(358,\cdot)\) \(\chi_{1815}(382,\cdot)\) \(\chi_{1815}(442,\cdot)\) \(\chi_{1815}(448,\cdot)\) \(\chi_{1815}(502,\cdot)\) \(\chi_{1815}(508,\cdot)\) \(\chi_{1815}(523,\cdot)\) \(\chi_{1815}(547,\cdot)\) \(\chi_{1815}(568,\cdot)\) \(\chi_{1815}(607,\cdot)\) \(\chi_{1815}(613,\cdot)\) \(\chi_{1815}(622,\cdot)\) \(\chi_{1815}(667,\cdot)\) \(\chi_{1815}(673,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((1211,727,1696)\) → \((1,-i,e\left(\frac{69}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 1815 }(193, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{220}\right)\) | \(e\left(\frac{83}{110}\right)\) | \(e\left(\frac{31}{220}\right)\) | \(e\left(\frac{29}{220}\right)\) | \(e\left(\frac{133}{220}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{107}{220}\right)\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{7}{44}\right)\) |