Basic properties
| Modulus: | \(2011\) | |
| Conductor: | \(2011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1005\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2011.o
\(\chi_{2011}(5,\cdot)\) \(\chi_{2011}(9,\cdot)\) \(\chi_{2011}(20,\cdot)\) \(\chi_{2011}(21,\cdot)\) \(\chi_{2011}(22,\cdot)\) \(\chi_{2011}(23,\cdot)\) \(\chi_{2011}(24,\cdot)\) \(\chi_{2011}(25,\cdot)\) \(\chi_{2011}(34,\cdot)\) \(\chi_{2011}(38,\cdot)\) \(\chi_{2011}(49,\cdot)\) \(\chi_{2011}(52,\cdot)\) \(\chi_{2011}(54,\cdot)\) \(\chi_{2011}(56,\cdot)\) \(\chi_{2011}(65,\cdot)\) \(\chi_{2011}(70,\cdot)\) \(\chi_{2011}(71,\cdot)\) \(\chi_{2011}(81,\cdot)\) \(\chi_{2011}(83,\cdot)\) \(\chi_{2011}(87,\cdot)\) \(\chi_{2011}(88,\cdot)\) \(\chi_{2011}(89,\cdot)\) \(\chi_{2011}(92,\cdot)\) \(\chi_{2011}(94,\cdot)\) \(\chi_{2011}(96,\cdot)\) \(\chi_{2011}(106,\cdot)\) \(\chi_{2011}(109,\cdot)\) \(\chi_{2011}(110,\cdot)\) \(\chi_{2011}(111,\cdot)\) \(\chi_{2011}(118,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1005})$ |
| Fixed field: | Number field defined by a degree 1005 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{83}{1005}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2011 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{201}\right)\) | \(e\left(\frac{83}{1005}\right)\) | \(e\left(\frac{94}{201}\right)\) | \(e\left(\frac{572}{1005}\right)\) | \(e\left(\frac{106}{335}\right)\) | \(e\left(\frac{236}{1005}\right)\) | \(e\left(\frac{47}{67}\right)\) | \(e\left(\frac{166}{1005}\right)\) | \(e\left(\frac{269}{335}\right)\) | \(e\left(\frac{646}{1005}\right)\) |