Basic properties
Modulus: | \(5292\) | |
Conductor: | \(1323\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1323}(1181,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5292.eq
\(\chi_{5292}(173,\cdot)\) \(\chi_{5292}(185,\cdot)\) \(\chi_{5292}(425,\cdot)\) \(\chi_{5292}(437,\cdot)\) \(\chi_{5292}(677,\cdot)\) \(\chi_{5292}(689,\cdot)\) \(\chi_{5292}(929,\cdot)\) \(\chi_{5292}(941,\cdot)\) \(\chi_{5292}(1181,\cdot)\) \(\chi_{5292}(1193,\cdot)\) \(\chi_{5292}(1433,\cdot)\) \(\chi_{5292}(1445,\cdot)\) \(\chi_{5292}(1937,\cdot)\) \(\chi_{5292}(1949,\cdot)\) \(\chi_{5292}(2189,\cdot)\) \(\chi_{5292}(2201,\cdot)\) \(\chi_{5292}(2441,\cdot)\) \(\chi_{5292}(2453,\cdot)\) \(\chi_{5292}(2693,\cdot)\) \(\chi_{5292}(2705,\cdot)\) \(\chi_{5292}(2945,\cdot)\) \(\chi_{5292}(2957,\cdot)\) \(\chi_{5292}(3197,\cdot)\) \(\chi_{5292}(3209,\cdot)\) \(\chi_{5292}(3701,\cdot)\) \(\chi_{5292}(3713,\cdot)\) \(\chi_{5292}(3953,\cdot)\) \(\chi_{5292}(3965,\cdot)\) \(\chi_{5292}(4205,\cdot)\) \(\chi_{5292}(4217,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((2647,785,1081)\) → \((1,e\left(\frac{7}{18}\right),e\left(\frac{29}{42}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 5292 }(1181, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{63}\right)\) | \(e\left(\frac{85}{126}\right)\) | \(e\left(\frac{113}{126}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{65}{126}\right)\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{103}{126}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{3}{7}\right)\) |