Basic properties
| Modulus: | \(1815\) | |
| Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(55\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{121}(16,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1815.bk
\(\chi_{1815}(16,\cdot)\) \(\chi_{1815}(31,\cdot)\) \(\chi_{1815}(91,\cdot)\) \(\chi_{1815}(136,\cdot)\) \(\chi_{1815}(181,\cdot)\) \(\chi_{1815}(196,\cdot)\) \(\chi_{1815}(256,\cdot)\) \(\chi_{1815}(301,\cdot)\) \(\chi_{1815}(346,\cdot)\) \(\chi_{1815}(361,\cdot)\) \(\chi_{1815}(421,\cdot)\) \(\chi_{1815}(466,\cdot)\) \(\chi_{1815}(526,\cdot)\) \(\chi_{1815}(586,\cdot)\) \(\chi_{1815}(631,\cdot)\) \(\chi_{1815}(676,\cdot)\) \(\chi_{1815}(691,\cdot)\) \(\chi_{1815}(751,\cdot)\) \(\chi_{1815}(796,\cdot)\) \(\chi_{1815}(841,\cdot)\) \(\chi_{1815}(916,\cdot)\) \(\chi_{1815}(961,\cdot)\) \(\chi_{1815}(1006,\cdot)\) \(\chi_{1815}(1021,\cdot)\) \(\chi_{1815}(1081,\cdot)\) \(\chi_{1815}(1126,\cdot)\) \(\chi_{1815}(1171,\cdot)\) \(\chi_{1815}(1186,\cdot)\) \(\chi_{1815}(1246,\cdot)\) \(\chi_{1815}(1336,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((1211,727,1696)\) → \((1,1,e\left(\frac{2}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
| \( \chi_{ 1815 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{16}{55}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{43}{55}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{6}{11}\right)\) |