Basic properties
Modulus: | \(7168\) | |
Conductor: | \(1792\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(192\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1792}(1699,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7168.cg
\(\chi_{7168}(47,\cdot)\) \(\chi_{7168}(143,\cdot)\) \(\chi_{7168}(271,\cdot)\) \(\chi_{7168}(367,\cdot)\) \(\chi_{7168}(495,\cdot)\) \(\chi_{7168}(591,\cdot)\) \(\chi_{7168}(719,\cdot)\) \(\chi_{7168}(815,\cdot)\) \(\chi_{7168}(943,\cdot)\) \(\chi_{7168}(1039,\cdot)\) \(\chi_{7168}(1167,\cdot)\) \(\chi_{7168}(1263,\cdot)\) \(\chi_{7168}(1391,\cdot)\) \(\chi_{7168}(1487,\cdot)\) \(\chi_{7168}(1615,\cdot)\) \(\chi_{7168}(1711,\cdot)\) \(\chi_{7168}(1839,\cdot)\) \(\chi_{7168}(1935,\cdot)\) \(\chi_{7168}(2063,\cdot)\) \(\chi_{7168}(2159,\cdot)\) \(\chi_{7168}(2287,\cdot)\) \(\chi_{7168}(2383,\cdot)\) \(\chi_{7168}(2511,\cdot)\) \(\chi_{7168}(2607,\cdot)\) \(\chi_{7168}(2735,\cdot)\) \(\chi_{7168}(2831,\cdot)\) \(\chi_{7168}(2959,\cdot)\) \(\chi_{7168}(3055,\cdot)\) \(\chi_{7168}(3183,\cdot)\) \(\chi_{7168}(3279,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{192})$ |
Fixed field: | Number field defined by a degree 192 polynomial (not computed) |
Values on generators
\((1023,5125,1025)\) → \((-1,e\left(\frac{43}{64}\right),e\left(\frac{5}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 7168 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{163}{192}\right)\) | \(e\left(\frac{161}{192}\right)\) | \(e\left(\frac{67}{96}\right)\) | \(e\left(\frac{181}{192}\right)\) | \(e\left(\frac{5}{64}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{23}{192}\right)\) | \(e\left(\frac{55}{96}\right)\) | \(e\left(\frac{65}{96}\right)\) |