Basic properties
| Modulus: | \(2011\) | |
| Conductor: | \(2011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(335\) | 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.l
\(\chi_{2011}(6,\cdot)\) \(\chi_{2011}(13,\cdot)\) \(\chi_{2011}(14,\cdot)\) \(\chi_{2011}(31,\cdot)\) \(\chi_{2011}(33,\cdot)\) \(\chi_{2011}(36,\cdot)\) \(\chi_{2011}(41,\cdot)\) \(\chi_{2011}(43,\cdot)\) \(\chi_{2011}(45,\cdot)\) \(\chi_{2011}(51,\cdot)\) \(\chi_{2011}(57,\cdot)\) \(\chi_{2011}(58,\cdot)\) \(\chi_{2011}(77,\cdot)\) \(\chi_{2011}(78,\cdot)\) \(\chi_{2011}(80,\cdot)\) \(\chi_{2011}(84,\cdot)\) \(\chi_{2011}(100,\cdot)\) \(\chi_{2011}(101,\cdot)\) \(\chi_{2011}(105,\cdot)\) \(\chi_{2011}(119,\cdot)\) \(\chi_{2011}(125,\cdot)\) \(\chi_{2011}(127,\cdot)\) \(\chi_{2011}(146,\cdot)\) \(\chi_{2011}(151,\cdot)\) \(\chi_{2011}(158,\cdot)\) \(\chi_{2011}(169,\cdot)\) \(\chi_{2011}(181,\cdot)\) \(\chi_{2011}(183,\cdot)\) \(\chi_{2011}(186,\cdot)\) \(\chi_{2011}(191,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{335})$ |
| Fixed field: | Number field defined by a degree 335 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{41}{335}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2011 }(6, a) \) | \(1\) | \(1\) | \(e\left(\frac{66}{67}\right)\) | \(e\left(\frac{41}{335}\right)\) | \(e\left(\frac{65}{67}\right)\) | \(e\left(\frac{109}{335}\right)\) | \(e\left(\frac{36}{335}\right)\) | \(e\left(\frac{52}{335}\right)\) | \(e\left(\frac{64}{67}\right)\) | \(e\left(\frac{82}{335}\right)\) | \(e\left(\frac{104}{335}\right)\) | \(e\left(\frac{307}{335}\right)\) |