Basic properties
Modulus: | \(8041\) | |
Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(420\) | 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 8041.fo
\(\chi_{8041}(38,\cdot)\) \(\chi_{8041}(81,\cdot)\) \(\chi_{8041}(225,\cdot)\) \(\chi_{8041}(268,\cdot)\) \(\chi_{8041}(361,\cdot)\) \(\chi_{8041}(412,\cdot)\) \(\chi_{8041}(455,\cdot)\) \(\chi_{8041}(531,\cdot)\) \(\chi_{8041}(599,\cdot)\) \(\chi_{8041}(625,\cdot)\) \(\chi_{8041}(642,\cdot)\) \(\chi_{8041}(676,\cdot)\) \(\chi_{8041}(812,\cdot)\) \(\chi_{8041}(999,\cdot)\) \(\chi_{8041}(1092,\cdot)\) \(\chi_{8041}(1186,\cdot)\) \(\chi_{8041}(1313,\cdot)\) \(\chi_{8041}(1347,\cdot)\) \(\chi_{8041}(1356,\cdot)\) \(\chi_{8041}(1373,\cdot)\) \(\chi_{8041}(1390,\cdot)\) \(\chi_{8041}(1500,\cdot)\) \(\chi_{8041}(1543,\cdot)\) \(\chi_{8041}(1687,\cdot)\) \(\chi_{8041}(1730,\cdot)\) \(\chi_{8041}(1874,\cdot)\) \(\chi_{8041}(1917,\cdot)\) \(\chi_{8041}(2044,\cdot)\) \(\chi_{8041}(2061,\cdot)\) \(\chi_{8041}(2095,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{420})$ |
Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{1}{5}\right),i,e\left(\frac{11}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(642, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{157}{420}\right)\) | \(e\left(\frac{24}{35}\right)\) | \(e\left(\frac{61}{420}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{157}{210}\right)\) | \(e\left(\frac{83}{84}\right)\) | \(e\left(\frac{5}{84}\right)\) |