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 \(\chi_{3584}(115,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7168.co
\(\chi_{7168}(87,\cdot)\) \(\chi_{7168}(103,\cdot)\) \(\chi_{7168}(199,\cdot)\) \(\chi_{7168}(215,\cdot)\) \(\chi_{7168}(311,\cdot)\) \(\chi_{7168}(327,\cdot)\) \(\chi_{7168}(423,\cdot)\) \(\chi_{7168}(439,\cdot)\) \(\chi_{7168}(535,\cdot)\) \(\chi_{7168}(551,\cdot)\) \(\chi_{7168}(647,\cdot)\) \(\chi_{7168}(663,\cdot)\) \(\chi_{7168}(759,\cdot)\) \(\chi_{7168}(775,\cdot)\) \(\chi_{7168}(871,\cdot)\) \(\chi_{7168}(887,\cdot)\) \(\chi_{7168}(983,\cdot)\) \(\chi_{7168}(999,\cdot)\) \(\chi_{7168}(1095,\cdot)\) \(\chi_{7168}(1111,\cdot)\) \(\chi_{7168}(1207,\cdot)\) \(\chi_{7168}(1223,\cdot)\) \(\chi_{7168}(1319,\cdot)\) \(\chi_{7168}(1335,\cdot)\) \(\chi_{7168}(1431,\cdot)\) \(\chi_{7168}(1447,\cdot)\) \(\chi_{7168}(1543,\cdot)\) \(\chi_{7168}(1559,\cdot)\) \(\chi_{7168}(1655,\cdot)\) \(\chi_{7168}(1671,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{384})$ |
| Fixed field: | Number field defined by a degree 384 polynomial (not computed) |
Values on generators
\((1023,5125,1025)\) → \((-1,e\left(\frac{15}{128}\right),e\left(\frac{1}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 7168 }(87, a) \) | \(1\) | \(1\) | \(e\left(\frac{295}{384}\right)\) | \(e\left(\frac{365}{384}\right)\) | \(e\left(\frac{103}{192}\right)\) | \(e\left(\frac{49}{384}\right)\) | \(e\left(\frac{65}{128}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{43}{96}\right)\) | \(e\left(\frac{11}{384}\right)\) | \(e\left(\frac{91}{192}\right)\) | \(e\left(\frac{173}{192}\right)\) |