Basic properties
Modulus: | \(1005\) | |
Conductor: | \(1005\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1005.bs
\(\chi_{1005}(17,\cdot)\) \(\chi_{1005}(23,\cdot)\) \(\chi_{1005}(47,\cdot)\) \(\chi_{1005}(77,\cdot)\) \(\chi_{1005}(83,\cdot)\) \(\chi_{1005}(122,\cdot)\) \(\chi_{1005}(167,\cdot)\) \(\chi_{1005}(173,\cdot)\) \(\chi_{1005}(188,\cdot)\) \(\chi_{1005}(218,\cdot)\) \(\chi_{1005}(227,\cdot)\) \(\chi_{1005}(248,\cdot)\) \(\chi_{1005}(257,\cdot)\) \(\chi_{1005}(272,\cdot)\) \(\chi_{1005}(278,\cdot)\) \(\chi_{1005}(287,\cdot)\) \(\chi_{1005}(317,\cdot)\) \(\chi_{1005}(323,\cdot)\) \(\chi_{1005}(368,\cdot)\) \(\chi_{1005}(428,\cdot)\) \(\chi_{1005}(437,\cdot)\) \(\chi_{1005}(458,\cdot)\) \(\chi_{1005}(467,\cdot)\) \(\chi_{1005}(473,\cdot)\) \(\chi_{1005}(488,\cdot)\) \(\chi_{1005}(518,\cdot)\) \(\chi_{1005}(542,\cdot)\) \(\chi_{1005}(557,\cdot)\) \(\chi_{1005}(572,\cdot)\) \(\chi_{1005}(638,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((671,202,136)\) → \((-1,i,e\left(\frac{32}{33}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 1005 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{95}{132}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{73}{132}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{23}{132}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{107}{132}\right)\) | \(e\left(\frac{13}{66}\right)\) |