Basic properties
| Modulus: | \(363\) | |
| Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{121}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 363.o
\(\chi_{363}(7,\cdot)\) \(\chi_{363}(13,\cdot)\) \(\chi_{363}(19,\cdot)\) \(\chi_{363}(28,\cdot)\) \(\chi_{363}(46,\cdot)\) \(\chi_{363}(52,\cdot)\) \(\chi_{363}(61,\cdot)\) \(\chi_{363}(73,\cdot)\) \(\chi_{363}(79,\cdot)\) \(\chi_{363}(85,\cdot)\) \(\chi_{363}(106,\cdot)\) \(\chi_{363}(127,\cdot)\) \(\chi_{363}(139,\cdot)\) \(\chi_{363}(145,\cdot)\) \(\chi_{363}(151,\cdot)\) \(\chi_{363}(160,\cdot)\) \(\chi_{363}(172,\cdot)\) \(\chi_{363}(178,\cdot)\) \(\chi_{363}(184,\cdot)\) \(\chi_{363}(193,\cdot)\) \(\chi_{363}(205,\cdot)\) \(\chi_{363}(211,\cdot)\) \(\chi_{363}(217,\cdot)\) \(\chi_{363}(226,\cdot)\) \(\chi_{363}(238,\cdot)\) \(\chi_{363}(244,\cdot)\) \(\chi_{363}(250,\cdot)\) \(\chi_{363}(259,\cdot)\) \(\chi_{363}(271,\cdot)\) \(\chi_{363}(277,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((122,244)\) → \((1,e\left(\frac{7}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 363 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{39}{55}\right)\) | \(e\left(\frac{49}{110}\right)\) | \(e\left(\frac{21}{110}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{47}{110}\right)\) | \(e\left(\frac{28}{55}\right)\) | \(e\left(\frac{14}{55}\right)\) | \(e\left(\frac{13}{110}\right)\) |