Basic properties
| Modulus: | \(9747\) | |
| Conductor: | \(3249\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(171\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3249}(3103,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9747.dq
\(\chi_{9747}(226,\cdot)\) \(\chi_{9747}(289,\cdot)\) \(\chi_{9747}(370,\cdot)\) \(\chi_{9747}(424,\cdot)\) \(\chi_{9747}(442,\cdot)\) \(\chi_{9747}(739,\cdot)\) \(\chi_{9747}(802,\cdot)\) \(\chi_{9747}(883,\cdot)\) \(\chi_{9747}(928,\cdot)\) \(\chi_{9747}(937,\cdot)\) \(\chi_{9747}(955,\cdot)\) \(\chi_{9747}(1252,\cdot)\) \(\chi_{9747}(1315,\cdot)\) \(\chi_{9747}(1396,\cdot)\) \(\chi_{9747}(1441,\cdot)\) \(\chi_{9747}(1450,\cdot)\) \(\chi_{9747}(1468,\cdot)\) \(\chi_{9747}(1765,\cdot)\) \(\chi_{9747}(1828,\cdot)\) \(\chi_{9747}(1909,\cdot)\) \(\chi_{9747}(1954,\cdot)\) \(\chi_{9747}(1963,\cdot)\) \(\chi_{9747}(1981,\cdot)\) \(\chi_{9747}(2278,\cdot)\) \(\chi_{9747}(2341,\cdot)\) \(\chi_{9747}(2422,\cdot)\) \(\chi_{9747}(2467,\cdot)\) \(\chi_{9747}(2476,\cdot)\) \(\chi_{9747}(2494,\cdot)\) \(\chi_{9747}(2791,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 171 polynomial (not computed) |
Values on generators
\((6860,2890)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{142}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 9747 }(937, a) \) | \(1\) | \(1\) | \(e\left(\frac{85}{171}\right)\) | \(e\left(\frac{170}{171}\right)\) | \(e\left(\frac{169}{171}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{28}{57}\right)\) | \(e\left(\frac{83}{171}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{92}{171}\right)\) | \(e\left(\frac{124}{171}\right)\) | \(e\left(\frac{169}{171}\right)\) |