Basic properties
Modulus: | \(4027\) | |
Conductor: | \(4027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(2013\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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 4027.o
\(\chi_{4027}(6,\cdot)\) \(\chi_{4027}(9,\cdot)\) \(\chi_{4027}(10,\cdot)\) \(\chi_{4027}(17,\cdot)\) \(\chi_{4027}(19,\cdot)\) \(\chi_{4027}(21,\cdot)\) \(\chi_{4027}(22,\cdot)\) \(\chi_{4027}(24,\cdot)\) \(\chi_{4027}(25,\cdot)\) \(\chi_{4027}(29,\cdot)\) \(\chi_{4027}(35,\cdot)\) \(\chi_{4027}(36,\cdot)\) \(\chi_{4027}(40,\cdot)\) \(\chi_{4027}(46,\cdot)\) \(\chi_{4027}(53,\cdot)\) \(\chi_{4027}(55,\cdot)\) \(\chi_{4027}(62,\cdot)\) \(\chi_{4027}(71,\cdot)\) \(\chi_{4027}(74,\cdot)\) \(\chi_{4027}(76,\cdot)\) \(\chi_{4027}(77,\cdot)\) \(\chi_{4027}(78,\cdot)\) \(\chi_{4027}(79,\cdot)\) \(\chi_{4027}(81,\cdot)\) \(\chi_{4027}(83,\cdot)\) \(\chi_{4027}(84,\cdot)\) \(\chi_{4027}(88,\cdot)\) \(\chi_{4027}(89,\cdot)\) \(\chi_{4027}(90,\cdot)\) \(\chi_{4027}(96,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{2013})$ |
Fixed field: | Number field defined by a degree 2013 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{188}{2013}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4027 }(6, a) \) | \(1\) | \(1\) | \(e\left(\frac{15}{671}\right)\) | \(e\left(\frac{188}{2013}\right)\) | \(e\left(\frac{30}{671}\right)\) | \(e\left(\frac{784}{2013}\right)\) | \(e\left(\frac{233}{2013}\right)\) | \(e\left(\frac{46}{671}\right)\) | \(e\left(\frac{45}{671}\right)\) | \(e\left(\frac{376}{2013}\right)\) | \(e\left(\frac{829}{2013}\right)\) | \(e\left(\frac{1807}{2013}\right)\) |