Basic properties
Modulus: | \(6498\) | |
Conductor: | \(3249\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(171\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3249}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6498.ca
\(\chi_{6498}(43,\cdot)\) \(\chi_{6498}(85,\cdot)\) \(\chi_{6498}(139,\cdot)\) \(\chi_{6498}(169,\cdot)\) \(\chi_{6498}(175,\cdot)\) \(\chi_{6498}(187,\cdot)\) \(\chi_{6498}(385,\cdot)\) \(\chi_{6498}(427,\cdot)\) \(\chi_{6498}(481,\cdot)\) \(\chi_{6498}(511,\cdot)\) \(\chi_{6498}(517,\cdot)\) \(\chi_{6498}(529,\cdot)\) \(\chi_{6498}(727,\cdot)\) \(\chi_{6498}(769,\cdot)\) \(\chi_{6498}(823,\cdot)\) \(\chi_{6498}(853,\cdot)\) \(\chi_{6498}(859,\cdot)\) \(\chi_{6498}(871,\cdot)\) \(\chi_{6498}(1069,\cdot)\) \(\chi_{6498}(1165,\cdot)\) \(\chi_{6498}(1195,\cdot)\) \(\chi_{6498}(1201,\cdot)\) \(\chi_{6498}(1213,\cdot)\) \(\chi_{6498}(1411,\cdot)\) \(\chi_{6498}(1453,\cdot)\) \(\chi_{6498}(1507,\cdot)\) \(\chi_{6498}(1537,\cdot)\) \(\chi_{6498}(1555,\cdot)\) \(\chi_{6498}(1753,\cdot)\) \(\chi_{6498}(1795,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{171})$ |
Fixed field: | Number field defined by a degree 171 polynomial (not computed) |
Values on generators
\((3611,6139)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{26}{171}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 6498 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{104}{171}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{10}{57}\right)\) | \(e\left(\frac{61}{171}\right)\) | \(e\left(\frac{62}{171}\right)\) | \(e\left(\frac{91}{171}\right)\) | \(e\left(\frac{37}{171}\right)\) | \(e\left(\frac{43}{171}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{14}{171}\right)\) |