Basic properties
Modulus: | \(8041\) | |
Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(80\) | 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.dy
\(\chi_{8041}(214,\cdot)\) \(\chi_{8041}(300,\cdot)\) \(\chi_{8041}(515,\cdot)\) \(\chi_{8041}(687,\cdot)\) \(\chi_{8041}(1246,\cdot)\) \(\chi_{8041}(1676,\cdot)\) \(\chi_{8041}(2149,\cdot)\) \(\chi_{8041}(2407,\cdot)\) \(\chi_{8041}(2579,\cdot)\) \(\chi_{8041}(2880,\cdot)\) \(\chi_{8041}(3138,\cdot)\) \(\chi_{8041}(3525,\cdot)\) \(\chi_{8041}(3611,\cdot)\) \(\chi_{8041}(3998,\cdot)\) \(\chi_{8041}(4041,\cdot)\) \(\chi_{8041}(4772,\cdot)\) \(\chi_{8041}(4944,\cdot)\) \(\chi_{8041}(4987,\cdot)\) \(\chi_{8041}(5417,\cdot)\) \(\chi_{8041}(5460,\cdot)\) \(\chi_{8041}(5503,\cdot)\) \(\chi_{8041}(5718,\cdot)\) \(\chi_{8041}(6191,\cdot)\) \(\chi_{8041}(6363,\cdot)\) \(\chi_{8041}(6406,\cdot)\) \(\chi_{8041}(6449,\cdot)\) \(\chi_{8041}(6879,\cdot)\) \(\chi_{8041}(6922,\cdot)\) \(\chi_{8041}(7137,\cdot)\) \(\chi_{8041}(7610,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{13}{16}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(4772, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{47}{80}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) |