Basic properties
| Modulus: | \(9600\) | |
| Conductor: | \(9600\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(160\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9600.gl
\(\chi_{9600}(59,\cdot)\) \(\chi_{9600}(179,\cdot)\) \(\chi_{9600}(419,\cdot)\) \(\chi_{9600}(539,\cdot)\) \(\chi_{9600}(659,\cdot)\) \(\chi_{9600}(779,\cdot)\) \(\chi_{9600}(1019,\cdot)\) \(\chi_{9600}(1139,\cdot)\) \(\chi_{9600}(1259,\cdot)\) \(\chi_{9600}(1379,\cdot)\) \(\chi_{9600}(1619,\cdot)\) \(\chi_{9600}(1739,\cdot)\) \(\chi_{9600}(1859,\cdot)\) \(\chi_{9600}(1979,\cdot)\) \(\chi_{9600}(2219,\cdot)\) \(\chi_{9600}(2339,\cdot)\) \(\chi_{9600}(2459,\cdot)\) \(\chi_{9600}(2579,\cdot)\) \(\chi_{9600}(2819,\cdot)\) \(\chi_{9600}(2939,\cdot)\) \(\chi_{9600}(3059,\cdot)\) \(\chi_{9600}(3179,\cdot)\) \(\chi_{9600}(3419,\cdot)\) \(\chi_{9600}(3539,\cdot)\) \(\chi_{9600}(3659,\cdot)\) \(\chi_{9600}(3779,\cdot)\) \(\chi_{9600}(4019,\cdot)\) \(\chi_{9600}(4139,\cdot)\) \(\chi_{9600}(4259,\cdot)\) \(\chi_{9600}(4379,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{160})$ |
| Fixed field: | Number field defined by a degree 160 polynomial (not computed) |
Values on generators
\((4351,901,6401,5377)\) → \((-1,e\left(\frac{17}{32}\right),-1,e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 9600 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{57}{160}\right)\) | \(e\left(\frac{43}{160}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{51}{160}\right)\) | \(e\left(\frac{11}{80}\right)\) | \(e\left(\frac{39}{160}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{93}{160}\right)\) | \(e\left(\frac{19}{80}\right)\) |