Basic properties
| Modulus: | \(4012\) | |
| Conductor: | \(4012\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(464\) | 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 4012.bl
\(\chi_{4012}(11,\cdot)\) \(\chi_{4012}(23,\cdot)\) \(\chi_{4012}(31,\cdot)\) \(\chi_{4012}(39,\cdot)\) \(\chi_{4012}(91,\cdot)\) \(\chi_{4012}(99,\cdot)\) \(\chi_{4012}(131,\cdot)\) \(\chi_{4012}(207,\cdot)\) \(\chi_{4012}(211,\cdot)\) \(\chi_{4012}(215,\cdot)\) \(\chi_{4012}(227,\cdot)\) \(\chi_{4012}(231,\cdot)\) \(\chi_{4012}(267,\cdot)\) \(\chi_{4012}(275,\cdot)\) \(\chi_{4012}(279,\cdot)\) \(\chi_{4012}(283,\cdot)\) \(\chi_{4012}(303,\cdot)\) \(\chi_{4012}(335,\cdot)\) \(\chi_{4012}(347,\cdot)\) \(\chi_{4012}(351,\cdot)\) \(\chi_{4012}(367,\cdot)\) \(\chi_{4012}(415,\cdot)\) \(\chi_{4012}(419,\cdot)\) \(\chi_{4012}(431,\cdot)\) \(\chi_{4012}(447,\cdot)\) \(\chi_{4012}(483,\cdot)\) \(\chi_{4012}(503,\cdot)\) \(\chi_{4012}(515,\cdot)\) \(\chi_{4012}(539,\cdot)\) \(\chi_{4012}(555,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{464})$ |
| Fixed field: | Number field defined by a degree 464 polynomial (not computed) |
Values on generators
\((2007,3777,3129)\) → \((-1,e\left(\frac{9}{16}\right),e\left(\frac{49}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 4012 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{141}{464}\right)\) | \(e\left(\frac{409}{464}\right)\) | \(e\left(\frac{415}{464}\right)\) | \(e\left(\frac{141}{232}\right)\) | \(e\left(\frac{259}{464}\right)\) | \(e\left(\frac{31}{116}\right)\) | \(e\left(\frac{43}{232}\right)\) | \(e\left(\frac{111}{232}\right)\) | \(e\left(\frac{23}{116}\right)\) | \(e\left(\frac{283}{464}\right)\) |