Basic properties
Modulus: | \(6724\) | |
Conductor: | \(1681\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(410\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1681}(25,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6724.ba
\(\chi_{6724}(25,\cdot)\) \(\chi_{6724}(45,\cdot)\) \(\chi_{6724}(105,\cdot)\) \(\chi_{6724}(113,\cdot)\) \(\chi_{6724}(189,\cdot)\) \(\chi_{6724}(209,\cdot)\) \(\chi_{6724}(269,\cdot)\) \(\chi_{6724}(277,\cdot)\) \(\chi_{6724}(353,\cdot)\) \(\chi_{6724}(373,\cdot)\) \(\chi_{6724}(433,\cdot)\) \(\chi_{6724}(441,\cdot)\) \(\chi_{6724}(517,\cdot)\) \(\chi_{6724}(537,\cdot)\) \(\chi_{6724}(597,\cdot)\) \(\chi_{6724}(605,\cdot)\) \(\chi_{6724}(681,\cdot)\) \(\chi_{6724}(701,\cdot)\) \(\chi_{6724}(769,\cdot)\) \(\chi_{6724}(845,\cdot)\) \(\chi_{6724}(865,\cdot)\) \(\chi_{6724}(925,\cdot)\) \(\chi_{6724}(933,\cdot)\) \(\chi_{6724}(1009,\cdot)\) \(\chi_{6724}(1029,\cdot)\) \(\chi_{6724}(1089,\cdot)\) \(\chi_{6724}(1097,\cdot)\) \(\chi_{6724}(1173,\cdot)\) \(\chi_{6724}(1193,\cdot)\) \(\chi_{6724}(1253,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{205})$ |
Fixed field: | Number field defined by a degree 410 polynomial (not computed) |
Values on generators
\((3363,5049)\) → \((1,e\left(\frac{221}{410}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
\( \chi_{ 6724 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{82}\right)\) | \(e\left(\frac{51}{205}\right)\) | \(e\left(\frac{129}{410}\right)\) | \(e\left(\frac{6}{41}\right)\) | \(e\left(\frac{243}{410}\right)\) | \(e\left(\frac{191}{410}\right)\) | \(e\left(\frac{337}{410}\right)\) | \(e\left(\frac{93}{410}\right)\) | \(e\left(\frac{269}{410}\right)\) | \(e\left(\frac{182}{205}\right)\) |