Basic properties
| Modulus: | \(363\) | |
| Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(55\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{121}(4,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 363.m
\(\chi_{363}(4,\cdot)\) \(\chi_{363}(16,\cdot)\) \(\chi_{363}(25,\cdot)\) \(\chi_{363}(31,\cdot)\) \(\chi_{363}(37,\cdot)\) \(\chi_{363}(49,\cdot)\) \(\chi_{363}(58,\cdot)\) \(\chi_{363}(64,\cdot)\) \(\chi_{363}(70,\cdot)\) \(\chi_{363}(82,\cdot)\) \(\chi_{363}(91,\cdot)\) \(\chi_{363}(97,\cdot)\) \(\chi_{363}(103,\cdot)\) \(\chi_{363}(115,\cdot)\) \(\chi_{363}(136,\cdot)\) \(\chi_{363}(157,\cdot)\) \(\chi_{363}(163,\cdot)\) \(\chi_{363}(169,\cdot)\) \(\chi_{363}(181,\cdot)\) \(\chi_{363}(190,\cdot)\) \(\chi_{363}(196,\cdot)\) \(\chi_{363}(214,\cdot)\) \(\chi_{363}(223,\cdot)\) \(\chi_{363}(229,\cdot)\) \(\chi_{363}(235,\cdot)\) \(\chi_{363}(247,\cdot)\) \(\chi_{363}(256,\cdot)\) \(\chi_{363}(262,\cdot)\) \(\chi_{363}(268,\cdot)\) \(\chi_{363}(280,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 55 polynomial |
Values on generators
\((122,244)\) → \((1,e\left(\frac{1}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 363 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{19}{55}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{4}{55}\right)\) | \(e\left(\frac{49}{55}\right)\) |