Basic properties
| Modulus: | \(1936\) | |
| Conductor: | \(1936\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(220\) | 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 1936.bu
\(\chi_{1936}(59,\cdot)\) \(\chi_{1936}(75,\cdot)\) \(\chi_{1936}(91,\cdot)\) \(\chi_{1936}(115,\cdot)\) \(\chi_{1936}(147,\cdot)\) \(\chi_{1936}(163,\cdot)\) \(\chi_{1936}(179,\cdot)\) \(\chi_{1936}(203,\cdot)\) \(\chi_{1936}(235,\cdot)\) \(\chi_{1936}(267,\cdot)\) \(\chi_{1936}(291,\cdot)\) \(\chi_{1936}(339,\cdot)\) \(\chi_{1936}(355,\cdot)\) \(\chi_{1936}(379,\cdot)\) \(\chi_{1936}(411,\cdot)\) \(\chi_{1936}(427,\cdot)\) \(\chi_{1936}(443,\cdot)\) \(\chi_{1936}(467,\cdot)\) \(\chi_{1936}(499,\cdot)\) \(\chi_{1936}(515,\cdot)\) \(\chi_{1936}(531,\cdot)\) \(\chi_{1936}(555,\cdot)\) \(\chi_{1936}(587,\cdot)\) \(\chi_{1936}(603,\cdot)\) \(\chi_{1936}(619,\cdot)\) \(\chi_{1936}(643,\cdot)\) \(\chi_{1936}(675,\cdot)\) \(\chi_{1936}(691,\cdot)\) \(\chi_{1936}(707,\cdot)\) \(\chi_{1936}(731,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{220})$ |
| Fixed field: | Number field defined by a degree 220 polynomial (not computed) |
Values on generators
\((1695,485,849)\) → \((-1,-i,e\left(\frac{12}{55}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 1936 }(1171, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{197}{220}\right)\) | \(e\left(\frac{29}{55}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{63}{220}\right)\) | \(e\left(\frac{93}{110}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{189}{220}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{3}{11}\right)\) |