Basic properties
Modulus: | \(2011\) | |
Conductor: | \(2011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(670\) | 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 2011.n
\(\chi_{2011}(10,\cdot)\) \(\chi_{2011}(27,\cdot)\) \(\chi_{2011}(44,\cdot)\) \(\chi_{2011}(46,\cdot)\) \(\chi_{2011}(47,\cdot)\) \(\chi_{2011}(48,\cdot)\) \(\chi_{2011}(55,\cdot)\) \(\chi_{2011}(59,\cdot)\) \(\chi_{2011}(68,\cdot)\) \(\chi_{2011}(75,\cdot)\) \(\chi_{2011}(76,\cdot)\) \(\chi_{2011}(85,\cdot)\) \(\chi_{2011}(95,\cdot)\) \(\chi_{2011}(104,\cdot)\) \(\chi_{2011}(112,\cdot)\) \(\chi_{2011}(113,\cdot)\) \(\chi_{2011}(130,\cdot)\) \(\chi_{2011}(140,\cdot)\) \(\chi_{2011}(149,\cdot)\) \(\chi_{2011}(162,\cdot)\) \(\chi_{2011}(166,\cdot)\) \(\chi_{2011}(218,\cdot)\) \(\chi_{2011}(242,\cdot)\) \(\chi_{2011}(244,\cdot)\) \(\chi_{2011}(248,\cdot)\) \(\chi_{2011}(253,\cdot)\) \(\chi_{2011}(257,\cdot)\) \(\chi_{2011}(261,\cdot)\) \(\chi_{2011}(264,\cdot)\) \(\chi_{2011}(267,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{335})$ |
Fixed field: | Number field defined by a degree 670 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{549}{670}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 2011 }(47, a) \) | \(-1\) | \(1\) | \(e\left(\frac{101}{134}\right)\) | \(e\left(\frac{549}{670}\right)\) | \(e\left(\frac{34}{67}\right)\) | \(e\left(\frac{23}{335}\right)\) | \(e\left(\frac{192}{335}\right)\) | \(e\left(\frac{443}{670}\right)\) | \(e\left(\frac{35}{134}\right)\) | \(e\left(\frac{214}{335}\right)\) | \(e\left(\frac{551}{670}\right)\) | \(e\left(\frac{483}{670}\right)\) |