Basic properties
Modulus: | \(6018\) | |
Conductor: | \(1003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(464\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1003}(533,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6018.bk
\(\chi_{6018}(31,\cdot)\) \(\chi_{6018}(37,\cdot)\) \(\chi_{6018}(61,\cdot)\) \(\chi_{6018}(73,\cdot)\) \(\chi_{6018}(91,\cdot)\) \(\chi_{6018}(97,\cdot)\) \(\chi_{6018}(109,\cdot)\) \(\chi_{6018}(211,\cdot)\) \(\chi_{6018}(283,\cdot)\) \(\chi_{6018}(301,\cdot)\) \(\chi_{6018}(313,\cdot)\) \(\chi_{6018}(337,\cdot)\) \(\chi_{6018}(367,\cdot)\) \(\chi_{6018}(385,\cdot)\) \(\chi_{6018}(397,\cdot)\) \(\chi_{6018}(415,\cdot)\) \(\chi_{6018}(445,\cdot)\) \(\chi_{6018}(469,\cdot)\) \(\chi_{6018}(505,\cdot)\) \(\chi_{6018}(541,\cdot)\) \(\chi_{6018}(571,\cdot)\) \(\chi_{6018}(583,\cdot)\) \(\chi_{6018}(601,\cdot)\) \(\chi_{6018}(673,\cdot)\) \(\chi_{6018}(691,\cdot)\) \(\chi_{6018}(703,\cdot)\) \(\chi_{6018}(721,\cdot)\) \(\chi_{6018}(745,\cdot)\) \(\chi_{6018}(751,\cdot)\) \(\chi_{6018}(775,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{464})$ |
Fixed field: | Number field defined by a degree 464 polynomial (not computed) |
Values on generators
\((4013,1771,1123)\) → \((1,e\left(\frac{15}{16}\right),e\left(\frac{1}{58}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6018 }(2539, a) \) | \(1\) | \(1\) | \(e\left(\frac{367}{464}\right)\) | \(e\left(\frac{289}{464}\right)\) | \(e\left(\frac{461}{464}\right)\) | \(e\left(\frac{61}{116}\right)\) | \(e\left(\frac{181}{232}\right)\) | \(e\left(\frac{149}{464}\right)\) | \(e\left(\frac{135}{232}\right)\) | \(e\left(\frac{311}{464}\right)\) | \(e\left(\frac{131}{464}\right)\) | \(e\left(\frac{12}{29}\right)\) |