Basic properties
Modulus: | \(2415\) | |
Conductor: | \(2415\) | 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 2415.do
\(\chi_{2415}(17,\cdot)\) \(\chi_{2415}(38,\cdot)\) \(\chi_{2415}(122,\cdot)\) \(\chi_{2415}(143,\cdot)\) \(\chi_{2415}(152,\cdot)\) \(\chi_{2415}(227,\cdot)\) \(\chi_{2415}(332,\cdot)\) \(\chi_{2415}(362,\cdot)\) \(\chi_{2415}(383,\cdot)\) \(\chi_{2415}(458,\cdot)\) \(\chi_{2415}(467,\cdot)\) \(\chi_{2415}(488,\cdot)\) \(\chi_{2415}(563,\cdot)\) \(\chi_{2415}(572,\cdot)\) \(\chi_{2415}(677,\cdot)\) \(\chi_{2415}(773,\cdot)\) \(\chi_{2415}(803,\cdot)\) \(\chi_{2415}(908,\cdot)\) \(\chi_{2415}(962,\cdot)\) \(\chi_{2415}(983,\cdot)\) \(\chi_{2415}(1088,\cdot)\) \(\chi_{2415}(1118,\cdot)\) \(\chi_{2415}(1193,\cdot)\) \(\chi_{2415}(1298,\cdot)\) \(\chi_{2415}(1307,\cdot)\) \(\chi_{2415}(1328,\cdot)\) \(\chi_{2415}(1433,\cdot)\) \(\chi_{2415}(1487,\cdot)\) \(\chi_{2415}(1538,\cdot)\) \(\chi_{2415}(1592,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((806,967,346,1891)\) → \((-1,-i,e\left(\frac{1}{6}\right),e\left(\frac{7}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(8\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) | \(22\) | \(26\) |
\( \chi_{ 2415 }(983, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{132}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{1}{33}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{85}{132}\right)\) | \(e\left(\frac{7}{66}\right)\) | \(i\) | \(e\left(\frac{14}{33}\right)\) |