Basic properties
Modulus: | \(801\) | |
Conductor: | \(801\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 801.bc
\(\chi_{801}(5,\cdot)\) \(\chi_{801}(20,\cdot)\) \(\chi_{801}(47,\cdot)\) \(\chi_{801}(68,\cdot)\) \(\chi_{801}(110,\cdot)\) \(\chi_{801}(131,\cdot)\) \(\chi_{801}(158,\cdot)\) \(\chi_{801}(173,\cdot)\) \(\chi_{801}(218,\cdot)\) \(\chi_{801}(227,\cdot)\) \(\chi_{801}(257,\cdot)\) \(\chi_{801}(272,\cdot)\) \(\chi_{801}(284,\cdot)\) \(\chi_{801}(320,\cdot)\) \(\chi_{801}(335,\cdot)\) \(\chi_{801}(338,\cdot)\) \(\chi_{801}(347,\cdot)\) \(\chi_{801}(365,\cdot)\) \(\chi_{801}(374,\cdot)\) \(\chi_{801}(392,\cdot)\) \(\chi_{801}(398,\cdot)\) \(\chi_{801}(425,\cdot)\) \(\chi_{801}(428,\cdot)\) \(\chi_{801}(455,\cdot)\) \(\chi_{801}(524,\cdot)\) \(\chi_{801}(551,\cdot)\) \(\chi_{801}(554,\cdot)\) \(\chi_{801}(581,\cdot)\) \(\chi_{801}(587,\cdot)\) \(\chi_{801}(605,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((713,181)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{7}{44}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 801 }(20, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{73}{132}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{35}{66}\right)\) | \(e\left(\frac{131}{132}\right)\) | \(e\left(\frac{35}{132}\right)\) | \(e\left(\frac{28}{33}\right)\) |