Basic properties
Modulus: | \(2006\) | |
Conductor: | \(1003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(464\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1003}(11,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2006.s
\(\chi_{2006}(11,\cdot)\) \(\chi_{2006}(23,\cdot)\) \(\chi_{2006}(31,\cdot)\) \(\chi_{2006}(37,\cdot)\) \(\chi_{2006}(39,\cdot)\) \(\chi_{2006}(61,\cdot)\) \(\chi_{2006}(65,\cdot)\) \(\chi_{2006}(73,\cdot)\) \(\chi_{2006}(91,\cdot)\) \(\chi_{2006}(97,\cdot)\) \(\chi_{2006}(99,\cdot)\) \(\chi_{2006}(109,\cdot)\) \(\chi_{2006}(113,\cdot)\) \(\chi_{2006}(129,\cdot)\) \(\chi_{2006}(131,\cdot)\) \(\chi_{2006}(141,\cdot)\) \(\chi_{2006}(165,\cdot)\) \(\chi_{2006}(173,\cdot)\) \(\chi_{2006}(201,\cdot)\) \(\chi_{2006}(207,\cdot)\) \(\chi_{2006}(209,\cdot)\) \(\chi_{2006}(211,\cdot)\) \(\chi_{2006}(215,\cdot)\) \(\chi_{2006}(227,\cdot)\) \(\chi_{2006}(231,\cdot)\) \(\chi_{2006}(233,\cdot)\) \(\chi_{2006}(249,\cdot)\) \(\chi_{2006}(267,\cdot)\) \(\chi_{2006}(269,\cdot)\) \(\chi_{2006}(275,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{464})$ |
Fixed field: | Number field defined by a degree 464 polynomial (not computed) |
Values on generators
\((1771,1123)\) → \((e\left(\frac{7}{16}\right),e\left(\frac{25}{58}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 2006 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{459}{464}\right)\) | \(e\left(\frac{359}{464}\right)\) | \(e\left(\frac{265}{464}\right)\) | \(e\left(\frac{227}{232}\right)\) | \(e\left(\frac{389}{464}\right)\) | \(e\left(\frac{17}{116}\right)\) | \(e\left(\frac{177}{232}\right)\) | \(e\left(\frac{117}{232}\right)\) | \(e\left(\frac{65}{116}\right)\) | \(e\left(\frac{13}{464}\right)\) |