Basic properties
Modulus: | \(1815\) | |
Conductor: | \(1815\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1815.bn
\(\chi_{1815}(29,\cdot)\) \(\chi_{1815}(74,\cdot)\) \(\chi_{1815}(134,\cdot)\) \(\chi_{1815}(149,\cdot)\) \(\chi_{1815}(194,\cdot)\) \(\chi_{1815}(299,\cdot)\) \(\chi_{1815}(314,\cdot)\) \(\chi_{1815}(359,\cdot)\) \(\chi_{1815}(404,\cdot)\) \(\chi_{1815}(464,\cdot)\) \(\chi_{1815}(479,\cdot)\) \(\chi_{1815}(569,\cdot)\) \(\chi_{1815}(629,\cdot)\) \(\chi_{1815}(644,\cdot)\) \(\chi_{1815}(689,\cdot)\) \(\chi_{1815}(734,\cdot)\) \(\chi_{1815}(794,\cdot)\) \(\chi_{1815}(809,\cdot)\) \(\chi_{1815}(854,\cdot)\) \(\chi_{1815}(899,\cdot)\) \(\chi_{1815}(974,\cdot)\) \(\chi_{1815}(1019,\cdot)\) \(\chi_{1815}(1064,\cdot)\) \(\chi_{1815}(1124,\cdot)\) \(\chi_{1815}(1139,\cdot)\) \(\chi_{1815}(1184,\cdot)\) \(\chi_{1815}(1229,\cdot)\) \(\chi_{1815}(1289,\cdot)\) \(\chi_{1815}(1349,\cdot)\) \(\chi_{1815}(1394,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((1211,727,1696)\) → \((-1,-1,e\left(\frac{37}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) | \(23\) |
\( \chi_{ 1815 }(194, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{110}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{1}{110}\right)\) | \(e\left(\frac{26}{55}\right)\) | \(e\left(\frac{21}{110}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{53}{110}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{6}{11}\right)\) |