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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 363.n
\(\chi_{363}(5,\cdot)\) \(\chi_{363}(14,\cdot)\) \(\chi_{363}(20,\cdot)\) \(\chi_{363}(26,\cdot)\) \(\chi_{363}(38,\cdot)\) \(\chi_{363}(47,\cdot)\) \(\chi_{363}(53,\cdot)\) \(\chi_{363}(59,\cdot)\) \(\chi_{363}(71,\cdot)\) \(\chi_{363}(80,\cdot)\) \(\chi_{363}(86,\cdot)\) \(\chi_{363}(92,\cdot)\) \(\chi_{363}(104,\cdot)\) \(\chi_{363}(113,\cdot)\) \(\chi_{363}(119,\cdot)\) \(\chi_{363}(125,\cdot)\) \(\chi_{363}(137,\cdot)\) \(\chi_{363}(146,\cdot)\) \(\chi_{363}(152,\cdot)\) \(\chi_{363}(158,\cdot)\) \(\chi_{363}(170,\cdot)\) \(\chi_{363}(179,\cdot)\) \(\chi_{363}(185,\cdot)\) \(\chi_{363}(191,\cdot)\) \(\chi_{363}(203,\cdot)\) \(\chi_{363}(212,\cdot)\) \(\chi_{363}(218,\cdot)\) \(\chi_{363}(224,\cdot)\) \(\chi_{363}(236,\cdot)\) \(\chi_{363}(257,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((122,244)\) → \((-1,e\left(\frac{51}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 363 }(26, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{47}{55}\right)\) | \(e\left(\frac{13}{110}\right)\) | \(e\left(\frac{27}{55}\right)\) | \(e\left(\frac{31}{110}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{36}{55}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{103}{110}\right)\) |