Basic properties
| Modulus: | \(5292\) | |
| Conductor: | \(1323\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(63\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1323}(25,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5292.ea
\(\chi_{5292}(25,\cdot)\) \(\chi_{5292}(121,\cdot)\) \(\chi_{5292}(277,\cdot)\) \(\chi_{5292}(529,\cdot)\) \(\chi_{5292}(625,\cdot)\) \(\chi_{5292}(781,\cdot)\) \(\chi_{5292}(877,\cdot)\) \(\chi_{5292}(1033,\cdot)\) \(\chi_{5292}(1129,\cdot)\) \(\chi_{5292}(1285,\cdot)\) \(\chi_{5292}(1381,\cdot)\) \(\chi_{5292}(1633,\cdot)\) \(\chi_{5292}(1789,\cdot)\) \(\chi_{5292}(1885,\cdot)\) \(\chi_{5292}(2041,\cdot)\) \(\chi_{5292}(2293,\cdot)\) \(\chi_{5292}(2389,\cdot)\) \(\chi_{5292}(2545,\cdot)\) \(\chi_{5292}(2641,\cdot)\) \(\chi_{5292}(2797,\cdot)\) \(\chi_{5292}(2893,\cdot)\) \(\chi_{5292}(3049,\cdot)\) \(\chi_{5292}(3145,\cdot)\) \(\chi_{5292}(3397,\cdot)\) \(\chi_{5292}(3553,\cdot)\) \(\chi_{5292}(3649,\cdot)\) \(\chi_{5292}(3805,\cdot)\) \(\chi_{5292}(4057,\cdot)\) \(\chi_{5292}(4153,\cdot)\) \(\chi_{5292}(4309,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 63 polynomial |
Values on generators
\((2647,785,1081)\) → \((1,e\left(\frac{5}{9}\right),e\left(\frac{8}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 5292 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{52}{63}\right)\) | \(e\left(\frac{29}{63}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{6}{7}\right)\) | \(1\) | \(e\left(\frac{37}{63}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{26}{63}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{11}{21}\right)\) |