Basic properties
Modulus: | \(4027\) | |
Conductor: | \(4027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(61\) | 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 4027.h
\(\chi_{4027}(13,\cdot)\) \(\chi_{4027}(67,\cdot)\) \(\chi_{4027}(153,\cdot)\) \(\chi_{4027}(169,\cdot)\) \(\chi_{4027}(210,\cdot)\) \(\chi_{4027}(211,\cdot)\) \(\chi_{4027}(224,\cdot)\) \(\chi_{4027}(326,\cdot)\) \(\chi_{4027}(327,\cdot)\) \(\chi_{4027}(372,\cdot)\) \(\chi_{4027}(462,\cdot)\) \(\chi_{4027}(538,\cdot)\) \(\chi_{4027}(756,\cdot)\) \(\chi_{4027}(762,\cdot)\) \(\chi_{4027}(809,\cdot)\) \(\chi_{4027}(834,\cdot)\) \(\chi_{4027}(871,\cdot)\) \(\chi_{4027}(1142,\cdot)\) \(\chi_{4027}(1466,\cdot)\) \(\chi_{4027}(1554,\cdot)\) \(\chi_{4027}(1565,\cdot)\) \(\chi_{4027}(1574,\cdot)\) \(\chi_{4027}(1607,\cdot)\) \(\chi_{4027}(1613,\cdot)\) \(\chi_{4027}(1695,\cdot)\) \(\chi_{4027}(1707,\cdot)\) \(\chi_{4027}(1774,\cdot)\) \(\chi_{4027}(1808,\cdot)\) \(\chi_{4027}(1852,\cdot)\) \(\chi_{4027}(1900,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{61})$ |
Fixed field: | Number field defined by a degree 61 polynomial |
Values on generators
\(3\) → \(e\left(\frac{1}{61}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4027 }(13, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{61}\right)\) | \(e\left(\frac{1}{61}\right)\) | \(e\left(\frac{18}{61}\right)\) | \(e\left(\frac{47}{61}\right)\) | \(e\left(\frac{10}{61}\right)\) | \(e\left(\frac{52}{61}\right)\) | \(e\left(\frac{27}{61}\right)\) | \(e\left(\frac{2}{61}\right)\) | \(e\left(\frac{56}{61}\right)\) | \(e\left(\frac{32}{61}\right)\) |