Basic properties
Modulus: | \(6026\) | |
Conductor: | \(3013\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(286\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3013}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6026.ba
\(\chi_{6026}(19,\cdot)\) \(\chi_{6026}(51,\cdot)\) \(\chi_{6026}(79,\cdot)\) \(\chi_{6026}(149,\cdot)\) \(\chi_{6026}(155,\cdot)\) \(\chi_{6026}(199,\cdot)\) \(\chi_{6026}(217,\cdot)\) \(\chi_{6026}(281,\cdot)\) \(\chi_{6026}(309,\cdot)\) \(\chi_{6026}(313,\cdot)\) \(\chi_{6026}(333,\cdot)\) \(\chi_{6026}(341,\cdot)\) \(\chi_{6026}(411,\cdot)\) \(\chi_{6026}(425,\cdot)\) \(\chi_{6026}(479,\cdot)\) \(\chi_{6026}(543,\cdot)\) \(\chi_{6026}(571,\cdot)\) \(\chi_{6026}(595,\cdot)\) \(\chi_{6026}(603,\cdot)\) \(\chi_{6026}(687,\cdot)\) \(\chi_{6026}(723,\cdot)\) \(\chi_{6026}(741,\cdot)\) \(\chi_{6026}(747,\cdot)\) \(\chi_{6026}(833,\cdot)\) \(\chi_{6026}(865,\cdot)\) \(\chi_{6026}(935,\cdot)\) \(\chi_{6026}(941,\cdot)\) \(\chi_{6026}(985,\cdot)\) \(\chi_{6026}(1003,\cdot)\) \(\chi_{6026}(1009,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{143})$ |
Fixed field: | Number field defined by a degree 286 polynomial (not computed) |
Values on generators
\((787,4325)\) → \((e\left(\frac{15}{22}\right),e\left(\frac{7}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 6026 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{42}{143}\right)\) | \(e\left(\frac{19}{286}\right)\) | \(e\left(\frac{229}{286}\right)\) | \(e\left(\frac{84}{143}\right)\) | \(e\left(\frac{61}{286}\right)\) | \(e\left(\frac{56}{143}\right)\) | \(e\left(\frac{103}{286}\right)\) | \(e\left(\frac{50}{143}\right)\) | \(e\left(\frac{93}{143}\right)\) | \(e\left(\frac{27}{286}\right)\) |