Basic properties
Modulus: | \(2011\) | |
Conductor: | \(2011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(2010\) | 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.p
\(\chi_{2011}(3,\cdot)\) \(\chi_{2011}(7,\cdot)\) \(\chi_{2011}(11,\cdot)\) \(\chi_{2011}(12,\cdot)\) \(\chi_{2011}(17,\cdot)\) \(\chi_{2011}(18,\cdot)\) \(\chi_{2011}(19,\cdot)\) \(\chi_{2011}(26,\cdot)\) \(\chi_{2011}(28,\cdot)\) \(\chi_{2011}(29,\cdot)\) \(\chi_{2011}(35,\cdot)\) \(\chi_{2011}(39,\cdot)\) \(\chi_{2011}(40,\cdot)\) \(\chi_{2011}(42,\cdot)\) \(\chi_{2011}(50,\cdot)\) \(\chi_{2011}(61,\cdot)\) \(\chi_{2011}(62,\cdot)\) \(\chi_{2011}(66,\cdot)\) \(\chi_{2011}(69,\cdot)\) \(\chi_{2011}(73,\cdot)\) \(\chi_{2011}(79,\cdot)\) \(\chi_{2011}(82,\cdot)\) \(\chi_{2011}(86,\cdot)\) \(\chi_{2011}(90,\cdot)\) \(\chi_{2011}(93,\cdot)\) \(\chi_{2011}(98,\cdot)\) \(\chi_{2011}(99,\cdot)\) \(\chi_{2011}(102,\cdot)\) \(\chi_{2011}(107,\cdot)\) \(\chi_{2011}(108,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1005})$ |
Fixed field: | Number field defined by a degree 2010 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{1039}{2010}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 2011 }(99, a) \) | \(-1\) | \(1\) | \(e\left(\frac{259}{402}\right)\) | \(e\left(\frac{1039}{2010}\right)\) | \(e\left(\frac{58}{201}\right)\) | \(e\left(\frac{323}{1005}\right)\) | \(e\left(\frac{54}{335}\right)\) | \(e\left(\frac{133}{2010}\right)\) | \(e\left(\frac{125}{134}\right)\) | \(e\left(\frac{34}{1005}\right)\) | \(e\left(\frac{647}{670}\right)\) | \(e\left(\frac{83}{2010}\right)\) |