Basic properties
Modulus: | \(6026\) | |
Conductor: | \(3013\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(715\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{3013}(59,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6026.bc
\(\chi_{6026}(3,\cdot)\) \(\chi_{6026}(9,\cdot)\) \(\chi_{6026}(13,\cdot)\) \(\chi_{6026}(25,\cdot)\) \(\chi_{6026}(27,\cdot)\) \(\chi_{6026}(35,\cdot)\) \(\chi_{6026}(41,\cdot)\) \(\chi_{6026}(49,\cdot)\) \(\chi_{6026}(55,\cdot)\) \(\chi_{6026}(59,\cdot)\) \(\chi_{6026}(75,\cdot)\) \(\chi_{6026}(77,\cdot)\) \(\chi_{6026}(81,\cdot)\) \(\chi_{6026}(101,\cdot)\) \(\chi_{6026}(105,\cdot)\) \(\chi_{6026}(117,\cdot)\) \(\chi_{6026}(121,\cdot)\) \(\chi_{6026}(123,\cdot)\) \(\chi_{6026}(147,\cdot)\) \(\chi_{6026}(151,\cdot)\) \(\chi_{6026}(165,\cdot)\) \(\chi_{6026}(167,\cdot)\) \(\chi_{6026}(169,\cdot)\) \(\chi_{6026}(177,\cdot)\) \(\chi_{6026}(179,\cdot)\) \(\chi_{6026}(225,\cdot)\) \(\chi_{6026}(233,\cdot)\) \(\chi_{6026}(239,\cdot)\) \(\chi_{6026}(265,\cdot)\) \(\chi_{6026}(269,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{715})$ |
Fixed field: | Number field defined by a degree 715 polynomial (not computed) |
Values on generators
\((787,4325)\) → \((e\left(\frac{7}{11}\right),e\left(\frac{41}{65}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 6026 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{427}{715}\right)\) | \(e\left(\frac{466}{715}\right)\) | \(e\left(\frac{461}{715}\right)\) | \(e\left(\frac{139}{715}\right)\) | \(e\left(\frac{36}{715}\right)\) | \(e\left(\frac{188}{715}\right)\) | \(e\left(\frac{178}{715}\right)\) | \(e\left(\frac{413}{715}\right)\) | \(e\left(\frac{89}{143}\right)\) | \(e\left(\frac{173}{715}\right)\) |