Basic properties
Modulus: | \(4225\) | |
Conductor: | \(4225\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(780\) | 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
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4225.db
\(\chi_{4225}(28,\cdot)\) \(\chi_{4225}(37,\cdot)\) \(\chi_{4225}(58,\cdot)\) \(\chi_{4225}(72,\cdot)\) \(\chi_{4225}(102,\cdot)\) \(\chi_{4225}(123,\cdot)\) \(\chi_{4225}(137,\cdot)\) \(\chi_{4225}(158,\cdot)\) \(\chi_{4225}(167,\cdot)\) \(\chi_{4225}(202,\cdot)\) \(\chi_{4225}(223,\cdot)\) \(\chi_{4225}(253,\cdot)\) \(\chi_{4225}(267,\cdot)\) \(\chi_{4225}(288,\cdot)\) \(\chi_{4225}(297,\cdot)\) \(\chi_{4225}(353,\cdot)\) \(\chi_{4225}(362,\cdot)\) \(\chi_{4225}(383,\cdot)\) \(\chi_{4225}(397,\cdot)\) \(\chi_{4225}(448,\cdot)\) \(\chi_{4225}(462,\cdot)\) \(\chi_{4225}(483,\cdot)\) \(\chi_{4225}(492,\cdot)\) \(\chi_{4225}(513,\cdot)\) \(\chi_{4225}(527,\cdot)\) \(\chi_{4225}(548,\cdot)\) \(\chi_{4225}(578,\cdot)\) \(\chi_{4225}(592,\cdot)\) \(\chi_{4225}(613,\cdot)\) \(\chi_{4225}(622,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{780})$ |
Fixed field: | Number field defined by a degree 780 polynomial (not computed) |
Values on generators
\((677,3551)\) → \((e\left(\frac{7}{20}\right),e\left(\frac{109}{156}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(14\) |
\( \chi_{ 4225 }(28, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{390}\right)\) | \(e\left(\frac{71}{780}\right)\) | \(e\left(\frac{19}{195}\right)\) | \(e\left(\frac{109}{780}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{19}{130}\right)\) | \(e\left(\frac{71}{390}\right)\) | \(e\left(\frac{443}{780}\right)\) | \(e\left(\frac{49}{260}\right)\) | \(e\left(\frac{73}{130}\right)\) |