Basic properties
Modulus: | \(726\) | |
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 \(\chi_{363}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 726.n
\(\chi_{726}(17,\cdot)\) \(\chi_{726}(29,\cdot)\) \(\chi_{726}(35,\cdot)\) \(\chi_{726}(41,\cdot)\) \(\chi_{726}(83,\cdot)\) \(\chi_{726}(95,\cdot)\) \(\chi_{726}(101,\cdot)\) \(\chi_{726}(107,\cdot)\) \(\chi_{726}(149,\cdot)\) \(\chi_{726}(167,\cdot)\) \(\chi_{726}(173,\cdot)\) \(\chi_{726}(227,\cdot)\) \(\chi_{726}(281,\cdot)\) \(\chi_{726}(293,\cdot)\) \(\chi_{726}(299,\cdot)\) \(\chi_{726}(305,\cdot)\) \(\chi_{726}(347,\cdot)\) \(\chi_{726}(359,\cdot)\) \(\chi_{726}(365,\cdot)\) \(\chi_{726}(371,\cdot)\) \(\chi_{726}(413,\cdot)\) \(\chi_{726}(425,\cdot)\) \(\chi_{726}(431,\cdot)\) \(\chi_{726}(437,\cdot)\) \(\chi_{726}(479,\cdot)\) \(\chi_{726}(491,\cdot)\) \(\chi_{726}(497,\cdot)\) \(\chi_{726}(503,\cdot)\) \(\chi_{726}(545,\cdot)\) \(\chi_{726}(557,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((485,607)\) → \((-1,e\left(\frac{49}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 726 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{13}{110}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{32}{55}\right)\) |