Basic properties
Modulus: | \(987696\) | |
Conductor: | \(61731\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1083\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{61731}(43825,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 987696.pl
\(\chi_{987696}(49,\cdot)\) \(\chi_{987696}(2401,\cdot)\) \(\chi_{987696}(2785,\cdot)\) \(\chi_{987696}(5137,\cdot)\) \(\chi_{987696}(5521,\cdot)\) \(\chi_{987696}(8257,\cdot)\) \(\chi_{987696}(10609,\cdot)\) \(\chi_{987696}(10993,\cdot)\) \(\chi_{987696}(13345,\cdot)\) \(\chi_{987696}(13729,\cdot)\) \(\chi_{987696}(16081,\cdot)\) \(\chi_{987696}(16465,\cdot)\) \(\chi_{987696}(18817,\cdot)\) \(\chi_{987696}(21553,\cdot)\) \(\chi_{987696}(21937,\cdot)\) \(\chi_{987696}(24289,\cdot)\) \(\chi_{987696}(24673,\cdot)\) \(\chi_{987696}(27025,\cdot)\) \(\chi_{987696}(27409,\cdot)\) \(\chi_{987696}(29761,\cdot)\) \(\chi_{987696}(30145,\cdot)\) \(\chi_{987696}(32497,\cdot)\) \(\chi_{987696}(32881,\cdot)\) \(\chi_{987696}(35233,\cdot)\) \(\chi_{987696}(35617,\cdot)\) \(\chi_{987696}(37969,\cdot)\) \(\chi_{987696}(38353,\cdot)\) \(\chi_{987696}(40705,\cdot)\) \(\chi_{987696}(41089,\cdot)\) \(\chi_{987696}(43441,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1083})$ |
Fixed field: | Number field defined by a degree 1083 polynomial (not computed) |
Values on generators
\((617311,740773,438977,857377)\) → \((1,1,e\left(\frac{1}{3}\right),e\left(\frac{617}{1083}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 987696 }(43825, a) \) | \(1\) | \(1\) | \(e\left(\frac{682}{1083}\right)\) | \(e\left(\frac{685}{1083}\right)\) | \(e\left(\frac{823}{1083}\right)\) | \(e\left(\frac{265}{361}\right)\) | \(e\left(\frac{989}{1083}\right)\) | \(e\left(\frac{39}{361}\right)\) | \(e\left(\frac{281}{1083}\right)\) | \(e\left(\frac{248}{1083}\right)\) | \(e\left(\frac{428}{1083}\right)\) | \(e\left(\frac{284}{1083}\right)\) |