Basic properties
| Modulus: | \(21952\) | |
| Conductor: | \(21952\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(784\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| 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 21952.eg
\(\chi_{21952}(27,\cdot)\) \(\chi_{21952}(83,\cdot)\) \(\chi_{21952}(139,\cdot)\) \(\chi_{21952}(251,\cdot)\) \(\chi_{21952}(307,\cdot)\) \(\chi_{21952}(363,\cdot)\) \(\chi_{21952}(419,\cdot)\) \(\chi_{21952}(475,\cdot)\) \(\chi_{21952}(531,\cdot)\) \(\chi_{21952}(643,\cdot)\) \(\chi_{21952}(699,\cdot)\) \(\chi_{21952}(755,\cdot)\) \(\chi_{21952}(811,\cdot)\) \(\chi_{21952}(867,\cdot)\) \(\chi_{21952}(923,\cdot)\) \(\chi_{21952}(1035,\cdot)\) \(\chi_{21952}(1091,\cdot)\) \(\chi_{21952}(1147,\cdot)\) \(\chi_{21952}(1203,\cdot)\) \(\chi_{21952}(1259,\cdot)\) \(\chi_{21952}(1315,\cdot)\) \(\chi_{21952}(1427,\cdot)\) \(\chi_{21952}(1483,\cdot)\) \(\chi_{21952}(1539,\cdot)\) \(\chi_{21952}(1595,\cdot)\) \(\chi_{21952}(1651,\cdot)\) \(\chi_{21952}(1707,\cdot)\) \(\chi_{21952}(1819,\cdot)\) \(\chi_{21952}(1875,\cdot)\) \(\chi_{21952}(1931,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{784})$ |
| Fixed field: | Number field defined by a degree 784 polynomial (not computed) |
Values on generators
\((17151,9605,17153)\) → \((-1,e\left(\frac{13}{16}\right),e\left(\frac{9}{98}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 21952 }(21419, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{784}\right)\) | \(e\left(\frac{373}{784}\right)\) | \(e\left(\frac{23}{392}\right)\) | \(e\left(\frac{521}{784}\right)\) | \(e\left(\frac{283}{784}\right)\) | \(e\left(\frac{99}{196}\right)\) | \(e\left(\frac{9}{196}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{367}{392}\right)\) | \(e\left(\frac{373}{392}\right)\) |