Basic properties
Modulus: | \(8041\) | |
Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(70\) | 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.du
\(\chi_{8041}(16,\cdot)\) \(\chi_{8041}(322,\cdot)\) \(\chi_{8041}(1325,\cdot)\) \(\chi_{8041}(1478,\cdot)\) \(\chi_{8041}(2209,\cdot)\) \(\chi_{8041}(2634,\cdot)\) \(\chi_{8041}(2787,\cdot)\) \(\chi_{8041}(2940,\cdot)\) \(\chi_{8041}(3008,\cdot)\) \(\chi_{8041}(3518,\cdot)\) \(\chi_{8041}(4096,\cdot)\) \(\chi_{8041}(4249,\cdot)\) \(\chi_{8041}(4470,\cdot)\) \(\chi_{8041}(4691,\cdot)\) \(\chi_{8041}(4827,\cdot)\) \(\chi_{8041}(5201,\cdot)\) \(\chi_{8041}(5439,\cdot)\) \(\chi_{8041}(5558,\cdot)\) \(\chi_{8041}(5932,\cdot)\) \(\chi_{8041}(6153,\cdot)\) \(\chi_{8041}(6884,\cdot)\) \(\chi_{8041}(6901,\cdot)\) \(\chi_{8041}(7615,\cdot)\) \(\chi_{8041}(7632,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{35})$ |
Fixed field: | Number field defined by a degree 70 polynomial |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{1}{5}\right),-1,e\left(\frac{2}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(6153, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{29}{35}\right)\) | \(e\left(\frac{31}{70}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{26}{35}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{5}{14}\right)\) | \(e\left(\frac{3}{14}\right)\) |