Basic properties
Modulus: | \(363\) | |
Conductor: | \(363\) | 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 363.p
\(\chi_{363}(2,\cdot)\) \(\chi_{363}(8,\cdot)\) \(\chi_{363}(17,\cdot)\) \(\chi_{363}(29,\cdot)\) \(\chi_{363}(35,\cdot)\) \(\chi_{363}(41,\cdot)\) \(\chi_{363}(50,\cdot)\) \(\chi_{363}(62,\cdot)\) \(\chi_{363}(68,\cdot)\) \(\chi_{363}(74,\cdot)\) \(\chi_{363}(83,\cdot)\) \(\chi_{363}(95,\cdot)\) \(\chi_{363}(101,\cdot)\) \(\chi_{363}(107,\cdot)\) \(\chi_{363}(116,\cdot)\) \(\chi_{363}(128,\cdot)\) \(\chi_{363}(134,\cdot)\) \(\chi_{363}(140,\cdot)\) \(\chi_{363}(149,\cdot)\) \(\chi_{363}(167,\cdot)\) \(\chi_{363}(173,\cdot)\) \(\chi_{363}(182,\cdot)\) \(\chi_{363}(194,\cdot)\) \(\chi_{363}(200,\cdot)\) \(\chi_{363}(206,\cdot)\) \(\chi_{363}(227,\cdot)\) \(\chi_{363}(248,\cdot)\) \(\chi_{363}(260,\cdot)\) \(\chi_{363}(266,\cdot)\) \(\chi_{363}(272,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{55})$ |
Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((122,244)\) → \((-1,e\left(\frac{73}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
\( \chi_{ 363 }(305, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{55}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{71}{110}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{89}{110}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{1}{55}\right)\) |