Basic properties
Modulus: | \(5292\) | |
Conductor: | \(1323\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(63\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1323}(1138,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5292.eb
\(\chi_{5292}(193,\cdot)\) \(\chi_{5292}(205,\cdot)\) \(\chi_{5292}(445,\cdot)\) \(\chi_{5292}(457,\cdot)\) \(\chi_{5292}(697,\cdot)\) \(\chi_{5292}(709,\cdot)\) \(\chi_{5292}(1201,\cdot)\) \(\chi_{5292}(1213,\cdot)\) \(\chi_{5292}(1453,\cdot)\) \(\chi_{5292}(1465,\cdot)\) \(\chi_{5292}(1705,\cdot)\) \(\chi_{5292}(1717,\cdot)\) \(\chi_{5292}(1957,\cdot)\) \(\chi_{5292}(1969,\cdot)\) \(\chi_{5292}(2209,\cdot)\) \(\chi_{5292}(2221,\cdot)\) \(\chi_{5292}(2461,\cdot)\) \(\chi_{5292}(2473,\cdot)\) \(\chi_{5292}(2965,\cdot)\) \(\chi_{5292}(2977,\cdot)\) \(\chi_{5292}(3217,\cdot)\) \(\chi_{5292}(3229,\cdot)\) \(\chi_{5292}(3469,\cdot)\) \(\chi_{5292}(3481,\cdot)\) \(\chi_{5292}(3721,\cdot)\) \(\chi_{5292}(3733,\cdot)\) \(\chi_{5292}(3973,\cdot)\) \(\chi_{5292}(3985,\cdot)\) \(\chi_{5292}(4225,\cdot)\) \(\chi_{5292}(4237,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((2647,785,1081)\) → \((1,e\left(\frac{1}{9}\right),e\left(\frac{20}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 5292 }(2461, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{22}{63}\right)\) | \(e\left(\frac{16}{63}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{1}{7}\right)\) |