Basic properties
Modulus: | \(7168\) | |
Conductor: | \(1792\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(64\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1792}(755,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7168.bv
\(\chi_{7168}(111,\cdot)\) \(\chi_{7168}(335,\cdot)\) \(\chi_{7168}(559,\cdot)\) \(\chi_{7168}(783,\cdot)\) \(\chi_{7168}(1007,\cdot)\) \(\chi_{7168}(1231,\cdot)\) \(\chi_{7168}(1455,\cdot)\) \(\chi_{7168}(1679,\cdot)\) \(\chi_{7168}(1903,\cdot)\) \(\chi_{7168}(2127,\cdot)\) \(\chi_{7168}(2351,\cdot)\) \(\chi_{7168}(2575,\cdot)\) \(\chi_{7168}(2799,\cdot)\) \(\chi_{7168}(3023,\cdot)\) \(\chi_{7168}(3247,\cdot)\) \(\chi_{7168}(3471,\cdot)\) \(\chi_{7168}(3695,\cdot)\) \(\chi_{7168}(3919,\cdot)\) \(\chi_{7168}(4143,\cdot)\) \(\chi_{7168}(4367,\cdot)\) \(\chi_{7168}(4591,\cdot)\) \(\chi_{7168}(4815,\cdot)\) \(\chi_{7168}(5039,\cdot)\) \(\chi_{7168}(5263,\cdot)\) \(\chi_{7168}(5487,\cdot)\) \(\chi_{7168}(5711,\cdot)\) \(\chi_{7168}(5935,\cdot)\) \(\chi_{7168}(6159,\cdot)\) \(\chi_{7168}(6383,\cdot)\) \(\chi_{7168}(6607,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{64})$ |
Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((1023,5125,1025)\) → \((-1,e\left(\frac{47}{64}\right),-1)\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 7168 }(111, a) \) | \(1\) | \(1\) | \(e\left(\frac{45}{64}\right)\) | \(e\left(\frac{15}{64}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{59}{64}\right)\) | \(e\left(\frac{1}{64}\right)\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{57}{64}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{15}{32}\right)\) |