Basic properties
Modulus: | \(6012\) | |
Conductor: | \(668\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(166\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{668}(339,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6012.x
\(\chi_{6012}(55,\cdot)\) \(\chi_{6012}(91,\cdot)\) \(\chi_{6012}(163,\cdot)\) \(\chi_{6012}(235,\cdot)\) \(\chi_{6012}(271,\cdot)\) \(\chi_{6012}(307,\cdot)\) \(\chi_{6012}(379,\cdot)\) \(\chi_{6012}(451,\cdot)\) \(\chi_{6012}(487,\cdot)\) \(\chi_{6012}(703,\cdot)\) \(\chi_{6012}(739,\cdot)\) \(\chi_{6012}(811,\cdot)\) \(\chi_{6012}(955,\cdot)\) \(\chi_{6012}(991,\cdot)\) \(\chi_{6012}(1243,\cdot)\) \(\chi_{6012}(1279,\cdot)\) \(\chi_{6012}(1315,\cdot)\) \(\chi_{6012}(1351,\cdot)\) \(\chi_{6012}(1387,\cdot)\) \(\chi_{6012}(1459,\cdot)\) \(\chi_{6012}(1495,\cdot)\) \(\chi_{6012}(1639,\cdot)\) \(\chi_{6012}(1675,\cdot)\) \(\chi_{6012}(1711,\cdot)\) \(\chi_{6012}(1783,\cdot)\) \(\chi_{6012}(1819,\cdot)\) \(\chi_{6012}(1927,\cdot)\) \(\chi_{6012}(2071,\cdot)\) \(\chi_{6012}(2107,\cdot)\) \(\chi_{6012}(2143,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{83})$ |
Fixed field: | Number field defined by a degree 166 polynomial (not computed) |
Values on generators
\((3007,3341,4681)\) → \((-1,1,e\left(\frac{1}{166}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 6012 }(1675, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{166}\right)\) | \(e\left(\frac{35}{166}\right)\) | \(e\left(\frac{111}{166}\right)\) | \(e\left(\frac{103}{166}\right)\) | \(e\left(\frac{53}{166}\right)\) | \(e\left(\frac{141}{166}\right)\) | \(e\left(\frac{8}{83}\right)\) | \(e\left(\frac{1}{83}\right)\) | \(e\left(\frac{75}{83}\right)\) | \(e\left(\frac{7}{166}\right)\) |