Basic properties
Modulus: | \(6498\) | |
Conductor: | \(3249\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3249}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6498.cl
\(\chi_{6498}(29,\cdot)\) \(\chi_{6498}(41,\cdot)\) \(\chi_{6498}(59,\cdot)\) \(\chi_{6498}(185,\cdot)\) \(\chi_{6498}(281,\cdot)\) \(\chi_{6498}(317,\cdot)\) \(\chi_{6498}(371,\cdot)\) \(\chi_{6498}(383,\cdot)\) \(\chi_{6498}(401,\cdot)\) \(\chi_{6498}(527,\cdot)\) \(\chi_{6498}(659,\cdot)\) \(\chi_{6498}(713,\cdot)\) \(\chi_{6498}(725,\cdot)\) \(\chi_{6498}(743,\cdot)\) \(\chi_{6498}(869,\cdot)\) \(\chi_{6498}(965,\cdot)\) \(\chi_{6498}(1001,\cdot)\) \(\chi_{6498}(1067,\cdot)\) \(\chi_{6498}(1085,\cdot)\) \(\chi_{6498}(1211,\cdot)\) \(\chi_{6498}(1307,\cdot)\) \(\chi_{6498}(1343,\cdot)\) \(\chi_{6498}(1397,\cdot)\) \(\chi_{6498}(1409,\cdot)\) \(\chi_{6498}(1427,\cdot)\) \(\chi_{6498}(1553,\cdot)\) \(\chi_{6498}(1649,\cdot)\) \(\chi_{6498}(1685,\cdot)\) \(\chi_{6498}(1739,\cdot)\) \(\chi_{6498}(1769,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{171})$ |
Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((3611,6139)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{17}{342}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6498 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{125}{342}\right)\) | \(e\left(\frac{7}{57}\right)\) | \(e\left(\frac{9}{38}\right)\) | \(e\left(\frac{235}{342}\right)\) | \(e\left(\frac{251}{342}\right)\) | \(e\left(\frac{31}{342}\right)\) | \(e\left(\frac{125}{171}\right)\) | \(e\left(\frac{2}{171}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{167}{342}\right)\) |