Basic properties
Modulus: | \(2011\) | |
Conductor: | \(2011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(402\) | 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.m
\(\chi_{2011}(2,\cdot)\) \(\chi_{2011}(15,\cdot)\) \(\chi_{2011}(32,\cdot)\) \(\chi_{2011}(37,\cdot)\) \(\chi_{2011}(67,\cdot)\) \(\chi_{2011}(91,\cdot)\) \(\chi_{2011}(128,\cdot)\) \(\chi_{2011}(139,\cdot)\) \(\chi_{2011}(143,\cdot)\) \(\chi_{2011}(148,\cdot)\) \(\chi_{2011}(163,\cdot)\) \(\chi_{2011}(171,\cdot)\) \(\chi_{2011}(217,\cdot)\) \(\chi_{2011}(221,\cdot)\) \(\chi_{2011}(230,\cdot)\) \(\chi_{2011}(231,\cdot)\) \(\chi_{2011}(234,\cdot)\) \(\chi_{2011}(240,\cdot)\) \(\chi_{2011}(243,\cdot)\) \(\chi_{2011}(266,\cdot)\) \(\chi_{2011}(275,\cdot)\) \(\chi_{2011}(277,\cdot)\) \(\chi_{2011}(281,\cdot)\) \(\chi_{2011}(341,\cdot)\) \(\chi_{2011}(357,\cdot)\) \(\chi_{2011}(363,\cdot)\) \(\chi_{2011}(364,\cdot)\) \(\chi_{2011}(365,\cdot)\) \(\chi_{2011}(377,\cdot)\) \(\chi_{2011}(388,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{201})$ |
Fixed field: | Number field defined by a degree 402 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{193}{402}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 2011 }(143, a) \) | \(-1\) | \(1\) | \(e\left(\frac{251}{402}\right)\) | \(e\left(\frac{193}{402}\right)\) | \(e\left(\frac{50}{201}\right)\) | \(e\left(\frac{125}{201}\right)\) | \(e\left(\frac{7}{67}\right)\) | \(e\left(\frac{217}{402}\right)\) | \(e\left(\frac{117}{134}\right)\) | \(e\left(\frac{193}{201}\right)\) | \(e\left(\frac{33}{134}\right)\) | \(e\left(\frac{347}{402}\right)\) |