Basic properties
| Modulus: | \(1815\) | |
| Conductor: | \(605\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{605}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1815.br
\(\chi_{1815}(19,\cdot)\) \(\chi_{1815}(79,\cdot)\) \(\chi_{1815}(139,\cdot)\) \(\chi_{1815}(184,\cdot)\) \(\chi_{1815}(244,\cdot)\) \(\chi_{1815}(259,\cdot)\) \(\chi_{1815}(304,\cdot)\) \(\chi_{1815}(349,\cdot)\) \(\chi_{1815}(409,\cdot)\) \(\chi_{1815}(424,\cdot)\) \(\chi_{1815}(469,\cdot)\) \(\chi_{1815}(514,\cdot)\) \(\chi_{1815}(574,\cdot)\) \(\chi_{1815}(589,\cdot)\) \(\chi_{1815}(634,\cdot)\) \(\chi_{1815}(679,\cdot)\) \(\chi_{1815}(739,\cdot)\) \(\chi_{1815}(754,\cdot)\) \(\chi_{1815}(799,\cdot)\) \(\chi_{1815}(904,\cdot)\) \(\chi_{1815}(919,\cdot)\) \(\chi_{1815}(964,\cdot)\) \(\chi_{1815}(1009,\cdot)\) \(\chi_{1815}(1069,\cdot)\) \(\chi_{1815}(1084,\cdot)\) \(\chi_{1815}(1174,\cdot)\) \(\chi_{1815}(1234,\cdot)\) \(\chi_{1815}(1249,\cdot)\) \(\chi_{1815}(1294,\cdot)\) \(\chi_{1815}(1339,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1211,727,1696)\) → \((1,-1,e\left(\frac{83}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 1815 }(19, a) \) | \(-1\) | \(1\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{42}{55}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{69}{110}\right)\) | \(e\left(\frac{7}{22}\right)\) |