Basic properties
| Modulus: | \(43904\) | |
| Conductor: | \(21952\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(784\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{21952}(3093,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 43904.eu
\(\chi_{43904}(41,\cdot)\) \(\chi_{43904}(153,\cdot)\) \(\chi_{43904}(265,\cdot)\) \(\chi_{43904}(377,\cdot)\) \(\chi_{43904}(601,\cdot)\) \(\chi_{43904}(713,\cdot)\) \(\chi_{43904}(825,\cdot)\) \(\chi_{43904}(937,\cdot)\) \(\chi_{43904}(1049,\cdot)\) \(\chi_{43904}(1161,\cdot)\) \(\chi_{43904}(1385,\cdot)\) \(\chi_{43904}(1497,\cdot)\) \(\chi_{43904}(1609,\cdot)\) \(\chi_{43904}(1721,\cdot)\) \(\chi_{43904}(1833,\cdot)\) \(\chi_{43904}(1945,\cdot)\) \(\chi_{43904}(2169,\cdot)\) \(\chi_{43904}(2281,\cdot)\) \(\chi_{43904}(2393,\cdot)\) \(\chi_{43904}(2505,\cdot)\) \(\chi_{43904}(2617,\cdot)\) \(\chi_{43904}(2729,\cdot)\) \(\chi_{43904}(2953,\cdot)\) \(\chi_{43904}(3065,\cdot)\) \(\chi_{43904}(3177,\cdot)\) \(\chi_{43904}(3289,\cdot)\) \(\chi_{43904}(3401,\cdot)\) \(\chi_{43904}(3513,\cdot)\) \(\chi_{43904}(3737,\cdot)\) \(\chi_{43904}(3849,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{784})$ |
| Fixed field: | Number field defined by a degree 784 polynomial (not computed) |
Values on generators
\((17151,9605,17153)\) → \((1,e\left(\frac{13}{16}\right),e\left(\frac{65}{98}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 43904 }(1721, a) \) | \(-1\) | \(1\) | \(e\left(\frac{79}{784}\right)\) | \(e\left(\frac{37}{784}\right)\) | \(e\left(\frac{79}{392}\right)\) | \(e\left(\frac{17}{784}\right)\) | \(e\left(\frac{171}{784}\right)\) | \(e\left(\frac{29}{196}\right)\) | \(e\left(\frac{65}{196}\right)\) | \(e\left(\frac{3}{16}\right)\) | \(e\left(\frac{59}{392}\right)\) | \(e\left(\frac{37}{392}\right)\) |