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
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8041.fp
\(\chi_{8041}(30,\cdot)\) \(\chi_{8041}(72,\cdot)\) \(\chi_{8041}(106,\cdot)\) \(\chi_{8041}(149,\cdot)\) \(\chi_{8041}(200,\cdot)\) \(\chi_{8041}(327,\cdot)\) \(\chi_{8041}(370,\cdot)\) \(\chi_{8041}(761,\cdot)\) \(\chi_{8041}(820,\cdot)\) \(\chi_{8041}(888,\cdot)\) \(\chi_{8041}(931,\cdot)\) \(\chi_{8041}(965,\cdot)\) \(\chi_{8041}(1007,\cdot)\) \(\chi_{8041}(1058,\cdot)\) \(\chi_{8041}(1152,\cdot)\) \(\chi_{8041}(1194,\cdot)\) \(\chi_{8041}(1381,\cdot)\) \(\chi_{8041}(1449,\cdot)\) \(\chi_{8041}(1492,\cdot)\) \(\chi_{8041}(1568,\cdot)\) \(\chi_{8041}(1619,\cdot)\) \(\chi_{8041}(1696,\cdot)\) \(\chi_{8041}(1789,\cdot)\) \(\chi_{8041}(1832,\cdot)\) \(\chi_{8041}(1883,\cdot)\) \(\chi_{8041}(2180,\cdot)\) \(\chi_{8041}(2350,\cdot)\) \(\chi_{8041}(2384,\cdot)\) \(\chi_{8041}(2393,\cdot)\) \(\chi_{8041}(2427,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{420})$ |
Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{9}{10}\right),i,e\left(\frac{5}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(2393, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{70}\right)\) | \(e\left(\frac{239}{420}\right)\) | \(e\left(\frac{8}{35}\right)\) | \(e\left(\frac{347}{420}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{59}{70}\right)\) | \(e\left(\frac{29}{210}\right)\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{67}{84}\right)\) |