Basic properties
Modulus: | \(1815\) | |
Conductor: | \(363\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{363}(260,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1815.bp
\(\chi_{1815}(41,\cdot)\) \(\chi_{1815}(101,\cdot)\) \(\chi_{1815}(116,\cdot)\) \(\chi_{1815}(206,\cdot)\) \(\chi_{1815}(266,\cdot)\) \(\chi_{1815}(281,\cdot)\) \(\chi_{1815}(326,\cdot)\) \(\chi_{1815}(371,\cdot)\) \(\chi_{1815}(431,\cdot)\) \(\chi_{1815}(446,\cdot)\) \(\chi_{1815}(491,\cdot)\) \(\chi_{1815}(536,\cdot)\) \(\chi_{1815}(611,\cdot)\) \(\chi_{1815}(656,\cdot)\) \(\chi_{1815}(701,\cdot)\) \(\chi_{1815}(761,\cdot)\) \(\chi_{1815}(776,\cdot)\) \(\chi_{1815}(821,\cdot)\) \(\chi_{1815}(866,\cdot)\) \(\chi_{1815}(926,\cdot)\) \(\chi_{1815}(986,\cdot)\) \(\chi_{1815}(1031,\cdot)\) \(\chi_{1815}(1091,\cdot)\) \(\chi_{1815}(1106,\cdot)\) \(\chi_{1815}(1151,\cdot)\) \(\chi_{1815}(1196,\cdot)\) \(\chi_{1815}(1256,\cdot)\) \(\chi_{1815}(1271,\cdot)\) \(\chi_{1815}(1316,\cdot)\) \(\chi_{1815}(1361,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1211,727,1696)\) → \((-1,1,e\left(\frac{67}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
\( \chi_{ 1815 }(986, a) \) | \(1\) | \(1\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{29}{110}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{57}{110}\right)\) | \(e\left(\frac{41}{110}\right)\) | \(e\left(\frac{24}{55}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{61}{110}\right)\) | \(e\left(\frac{3}{22}\right)\) |