Basic properties
Modulus: | \(6042\) | |
Conductor: | \(3021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(234\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3021}(725,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6042.ck
\(\chi_{6042}(89,\cdot)\) \(\chi_{6042}(155,\cdot)\) \(\chi_{6042}(203,\cdot)\) \(\chi_{6042}(281,\cdot)\) \(\chi_{6042}(395,\cdot)\) \(\chi_{6042}(413,\cdot)\) \(\chi_{6042}(545,\cdot)\) \(\chi_{6042}(599,\cdot)\) \(\chi_{6042}(611,\cdot)\) \(\chi_{6042}(629,\cdot)\) \(\chi_{6042}(713,\cdot)\) \(\chi_{6042}(725,\cdot)\) \(\chi_{6042}(755,\cdot)\) \(\chi_{6042}(839,\cdot)\) \(\chi_{6042}(1001,\cdot)\) \(\chi_{6042}(1181,\cdot)\) \(\chi_{6042}(1229,\cdot)\) \(\chi_{6042}(1427,\cdot)\) \(\chi_{6042}(1553,\cdot)\) \(\chi_{6042}(1637,\cdot)\) \(\chi_{6042}(1667,\cdot)\) \(\chi_{6042}(1685,\cdot)\) \(\chi_{6042}(1865,\cdot)\) \(\chi_{6042}(1883,\cdot)\) \(\chi_{6042}(1997,\cdot)\) \(\chi_{6042}(2027,\cdot)\) \(\chi_{6042}(2111,\cdot)\) \(\chi_{6042}(2219,\cdot)\) \(\chi_{6042}(2321,\cdot)\) \(\chi_{6042}(2453,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{117})$ |
Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((2015,4771,2281)\) → \((-1,e\left(\frac{13}{18}\right),e\left(\frac{9}{13}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6042 }(725, a) \) | \(1\) | \(1\) | \(e\left(\frac{139}{234}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{25}{78}\right)\) | \(e\left(\frac{53}{234}\right)\) | \(e\left(\frac{151}{234}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{22}{117}\right)\) | \(e\left(\frac{73}{117}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{145}{234}\right)\) |