Basic properties
| Modulus: | \(3136\) | |
| Conductor: | \(1568\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(168\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1568}(1395,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3136.cu
\(\chi_{3136}(23,\cdot)\) \(\chi_{3136}(39,\cdot)\) \(\chi_{3136}(135,\cdot)\) \(\chi_{3136}(151,\cdot)\) \(\chi_{3136}(247,\cdot)\) \(\chi_{3136}(359,\cdot)\) \(\chi_{3136}(375,\cdot)\) \(\chi_{3136}(487,\cdot)\) \(\chi_{3136}(583,\cdot)\) \(\chi_{3136}(599,\cdot)\) \(\chi_{3136}(695,\cdot)\) \(\chi_{3136}(711,\cdot)\) \(\chi_{3136}(807,\cdot)\) \(\chi_{3136}(823,\cdot)\) \(\chi_{3136}(919,\cdot)\) \(\chi_{3136}(935,\cdot)\) \(\chi_{3136}(1031,\cdot)\) \(\chi_{3136}(1143,\cdot)\) \(\chi_{3136}(1159,\cdot)\) \(\chi_{3136}(1271,\cdot)\) \(\chi_{3136}(1367,\cdot)\) \(\chi_{3136}(1383,\cdot)\) \(\chi_{3136}(1479,\cdot)\) \(\chi_{3136}(1495,\cdot)\) \(\chi_{3136}(1591,\cdot)\) \(\chi_{3136}(1607,\cdot)\) \(\chi_{3136}(1703,\cdot)\) \(\chi_{3136}(1719,\cdot)\) \(\chi_{3136}(1815,\cdot)\) \(\chi_{3136}(1927,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{168})$ |
| Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\((1471,197,1473)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{19}{21}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 3136 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{5}{168}\right)\) | \(e\left(\frac{19}{168}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{11}{168}\right)\) | \(e\left(\frac{55}{56}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{11}{84}\right)\) | \(e\left(\frac{19}{84}\right)\) |