Basic properties
Modulus: | \(8041\) | |
Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1680\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8041.ga
\(\chi_{8041}(28,\cdot)\) \(\chi_{8041}(29,\cdot)\) \(\chi_{8041}(46,\cdot)\) \(\chi_{8041}(61,\cdot)\) \(\chi_{8041}(62,\cdot)\) \(\chi_{8041}(63,\cdot)\) \(\chi_{8041}(73,\cdot)\) \(\chi_{8041}(105,\cdot)\) \(\chi_{8041}(112,\cdot)\) \(\chi_{8041}(116,\cdot)\) \(\chi_{8041}(184,\cdot)\) \(\chi_{8041}(227,\cdot)\) \(\chi_{8041}(233,\cdot)\) \(\chi_{8041}(244,\cdot)\) \(\chi_{8041}(248,\cdot)\) \(\chi_{8041}(249,\cdot)\) \(\chi_{8041}(261,\cdot)\) \(\chi_{8041}(277,\cdot)\) \(\chi_{8041}(292,\cdot)\) \(\chi_{8041}(347,\cdot)\) \(\chi_{8041}(413,\cdot)\) \(\chi_{8041}(415,\cdot)\) \(\chi_{8041}(420,\cdot)\) \(\chi_{8041}(435,\cdot)\) \(\chi_{8041}(448,\cdot)\) \(\chi_{8041}(464,\cdot)\) \(\chi_{8041}(503,\cdot)\) \(\chi_{8041}(534,\cdot)\) \(\chi_{8041}(585,\cdot)\) \(\chi_{8041}(589,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1680})$ |
Fixed field: | Number field defined by a degree 1680 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{15}{16}\right),e\left(\frac{1}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(3185, a) \) | \(-1\) | \(1\) | \(e\left(\frac{187}{280}\right)\) | \(e\left(\frac{271}{1680}\right)\) | \(e\left(\frac{47}{140}\right)\) | \(e\left(\frac{1483}{1680}\right)\) | \(e\left(\frac{199}{240}\right)\) | \(e\left(\frac{107}{240}\right)\) | \(e\left(\frac{1}{280}\right)\) | \(e\left(\frac{271}{840}\right)\) | \(e\left(\frac{185}{336}\right)\) | \(e\left(\frac{167}{336}\right)\) |