Basic properties
Modulus: | \(6042\) | |
Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1007}(8,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6042.ch
\(\chi_{6042}(31,\cdot)\) \(\chi_{6042}(103,\cdot)\) \(\chi_{6042}(145,\cdot)\) \(\chi_{6042}(217,\cdot)\) \(\chi_{6042}(373,\cdot)\) \(\chi_{6042}(445,\cdot)\) \(\chi_{6042}(601,\cdot)\) \(\chi_{6042}(715,\cdot)\) \(\chi_{6042}(787,\cdot)\) \(\chi_{6042}(829,\cdot)\) \(\chi_{6042}(1015,\cdot)\) \(\chi_{6042}(1057,\cdot)\) \(\chi_{6042}(1171,\cdot)\) \(\chi_{6042}(1357,\cdot)\) \(\chi_{6042}(1399,\cdot)\) \(\chi_{6042}(1585,\cdot)\) \(\chi_{6042}(1699,\cdot)\) \(\chi_{6042}(1741,\cdot)\) \(\chi_{6042}(1927,\cdot)\) \(\chi_{6042}(1969,\cdot)\) \(\chi_{6042}(2041,\cdot)\) \(\chi_{6042}(2155,\cdot)\) \(\chi_{6042}(2311,\cdot)\) \(\chi_{6042}(2383,\cdot)\) \(\chi_{6042}(2539,\cdot)\) \(\chi_{6042}(2611,\cdot)\) \(\chi_{6042}(2653,\cdot)\) \(\chi_{6042}(2725,\cdot)\) \(\chi_{6042}(2881,\cdot)\) \(\chi_{6042}(2995,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{156})$ |
Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((2015,4771,2281)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{3}{52}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6042 }(1015, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{156}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{29}{156}\right)\) |