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 \(\chi_{605}(179,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1815.bm
\(\chi_{1815}(4,\cdot)\) \(\chi_{1815}(49,\cdot)\) \(\chi_{1815}(64,\cdot)\) \(\chi_{1815}(169,\cdot)\) \(\chi_{1815}(214,\cdot)\) \(\chi_{1815}(229,\cdot)\) \(\chi_{1815}(289,\cdot)\) \(\chi_{1815}(334,\cdot)\) \(\chi_{1815}(379,\cdot)\) \(\chi_{1815}(394,\cdot)\) \(\chi_{1815}(454,\cdot)\) \(\chi_{1815}(499,\cdot)\) \(\chi_{1815}(544,\cdot)\) \(\chi_{1815}(559,\cdot)\) \(\chi_{1815}(619,\cdot)\) \(\chi_{1815}(664,\cdot)\) \(\chi_{1815}(709,\cdot)\) \(\chi_{1815}(724,\cdot)\) \(\chi_{1815}(784,\cdot)\) \(\chi_{1815}(829,\cdot)\) \(\chi_{1815}(889,\cdot)\) \(\chi_{1815}(949,\cdot)\) \(\chi_{1815}(994,\cdot)\) \(\chi_{1815}(1039,\cdot)\) \(\chi_{1815}(1054,\cdot)\) \(\chi_{1815}(1114,\cdot)\) \(\chi_{1815}(1159,\cdot)\) \(\chi_{1815}(1204,\cdot)\) \(\chi_{1815}(1279,\cdot)\) \(\chi_{1815}(1324,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1211,727,1696)\) → \((1,-1,e\left(\frac{9}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 1815 }(784, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{71}{110}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{32}{55}\right)\) | \(e\left(\frac{21}{22}\right)\) |