Basic properties
Modulus: | \(1805\) | |
Conductor: | \(1805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(228\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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 1805.be
\(\chi_{1805}(8,\cdot)\) \(\chi_{1805}(12,\cdot)\) \(\chi_{1805}(27,\cdot)\) \(\chi_{1805}(88,\cdot)\) \(\chi_{1805}(103,\cdot)\) \(\chi_{1805}(107,\cdot)\) \(\chi_{1805}(122,\cdot)\) \(\chi_{1805}(183,\cdot)\) \(\chi_{1805}(198,\cdot)\) \(\chi_{1805}(202,\cdot)\) \(\chi_{1805}(217,\cdot)\) \(\chi_{1805}(278,\cdot)\) \(\chi_{1805}(297,\cdot)\) \(\chi_{1805}(312,\cdot)\) \(\chi_{1805}(373,\cdot)\) \(\chi_{1805}(388,\cdot)\) \(\chi_{1805}(392,\cdot)\) \(\chi_{1805}(407,\cdot)\) \(\chi_{1805}(468,\cdot)\) \(\chi_{1805}(483,\cdot)\) \(\chi_{1805}(487,\cdot)\) \(\chi_{1805}(502,\cdot)\) \(\chi_{1805}(563,\cdot)\) \(\chi_{1805}(578,\cdot)\) \(\chi_{1805}(582,\cdot)\) \(\chi_{1805}(597,\cdot)\) \(\chi_{1805}(658,\cdot)\) \(\chi_{1805}(673,\cdot)\) \(\chi_{1805}(677,\cdot)\) \(\chi_{1805}(692,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{228})$ |
Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((362,1446)\) → \((i,e\left(\frac{55}{114}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 1805 }(502, a) \) | \(1\) | \(1\) | \(e\left(\frac{167}{228}\right)\) | \(e\left(\frac{185}{228}\right)\) | \(e\left(\frac{53}{114}\right)\) | \(e\left(\frac{31}{57}\right)\) | \(e\left(\frac{47}{76}\right)\) | \(e\left(\frac{15}{76}\right)\) | \(e\left(\frac{71}{114}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{21}{76}\right)\) | \(e\left(\frac{109}{228}\right)\) |