Basic properties
| Modulus: | \(1444\) | |
| Conductor: | \(1444\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(114\) | 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 1444.t
\(\chi_{1444}(27,\cdot)\) \(\chi_{1444}(31,\cdot)\) \(\chi_{1444}(103,\cdot)\) \(\chi_{1444}(107,\cdot)\) \(\chi_{1444}(179,\cdot)\) \(\chi_{1444}(183,\cdot)\) \(\chi_{1444}(255,\cdot)\) \(\chi_{1444}(259,\cdot)\) \(\chi_{1444}(331,\cdot)\) \(\chi_{1444}(335,\cdot)\) \(\chi_{1444}(407,\cdot)\) \(\chi_{1444}(411,\cdot)\) \(\chi_{1444}(483,\cdot)\) \(\chi_{1444}(487,\cdot)\) \(\chi_{1444}(559,\cdot)\) \(\chi_{1444}(563,\cdot)\) \(\chi_{1444}(635,\cdot)\) \(\chi_{1444}(639,\cdot)\) \(\chi_{1444}(711,\cdot)\) \(\chi_{1444}(715,\cdot)\) \(\chi_{1444}(787,\cdot)\) \(\chi_{1444}(863,\cdot)\) \(\chi_{1444}(867,\cdot)\) \(\chi_{1444}(939,\cdot)\) \(\chi_{1444}(943,\cdot)\) \(\chi_{1444}(1019,\cdot)\) \(\chi_{1444}(1091,\cdot)\) \(\chi_{1444}(1095,\cdot)\) \(\chi_{1444}(1167,\cdot)\) \(\chi_{1444}(1171,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((723,1085)\) → \((-1,e\left(\frac{101}{114}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 1444 }(31, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{33}{38}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{5}{114}\right)\) | \(e\left(\frac{97}{114}\right)\) |