Basic properties
| Modulus: | \(7168\) | |
| Conductor: | \(3584\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(384\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3584}(2557,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7168.cp
\(\chi_{7168}(9,\cdot)\) \(\chi_{7168}(25,\cdot)\) \(\chi_{7168}(121,\cdot)\) \(\chi_{7168}(137,\cdot)\) \(\chi_{7168}(233,\cdot)\) \(\chi_{7168}(249,\cdot)\) \(\chi_{7168}(345,\cdot)\) \(\chi_{7168}(361,\cdot)\) \(\chi_{7168}(457,\cdot)\) \(\chi_{7168}(473,\cdot)\) \(\chi_{7168}(569,\cdot)\) \(\chi_{7168}(585,\cdot)\) \(\chi_{7168}(681,\cdot)\) \(\chi_{7168}(697,\cdot)\) \(\chi_{7168}(793,\cdot)\) \(\chi_{7168}(809,\cdot)\) \(\chi_{7168}(905,\cdot)\) \(\chi_{7168}(921,\cdot)\) \(\chi_{7168}(1017,\cdot)\) \(\chi_{7168}(1033,\cdot)\) \(\chi_{7168}(1129,\cdot)\) \(\chi_{7168}(1145,\cdot)\) \(\chi_{7168}(1241,\cdot)\) \(\chi_{7168}(1257,\cdot)\) \(\chi_{7168}(1353,\cdot)\) \(\chi_{7168}(1369,\cdot)\) \(\chi_{7168}(1465,\cdot)\) \(\chi_{7168}(1481,\cdot)\) \(\chi_{7168}(1577,\cdot)\) \(\chi_{7168}(1593,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{384})$ |
| Fixed field: | Number field defined by a degree 384 polynomial (not computed) |
Values on generators
\((1023,5125,1025)\) → \((1,e\left(\frac{35}{128}\right),e\left(\frac{1}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 7168 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{347}{384}\right)\) | \(e\left(\frac{361}{384}\right)\) | \(e\left(\frac{155}{192}\right)\) | \(e\left(\frac{221}{384}\right)\) | \(e\left(\frac{45}{128}\right)\) | \(e\left(\frac{27}{32}\right)\) | \(e\left(\frac{95}{96}\right)\) | \(e\left(\frac{367}{384}\right)\) | \(e\left(\frac{95}{192}\right)\) | \(e\left(\frac{169}{192}\right)\) |