Basic properties
| Modulus: | \(9600\) | |
| Conductor: | \(3200\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(160\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3200}(163,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9600.gq
\(\chi_{9600}(163,\cdot)\) \(\chi_{9600}(187,\cdot)\) \(\chi_{9600}(403,\cdot)\) \(\chi_{9600}(427,\cdot)\) \(\chi_{9600}(667,\cdot)\) \(\chi_{9600}(883,\cdot)\) \(\chi_{9600}(1123,\cdot)\) \(\chi_{9600}(1147,\cdot)\) \(\chi_{9600}(1363,\cdot)\) \(\chi_{9600}(1387,\cdot)\) \(\chi_{9600}(1603,\cdot)\) \(\chi_{9600}(1627,\cdot)\) \(\chi_{9600}(1867,\cdot)\) \(\chi_{9600}(2083,\cdot)\) \(\chi_{9600}(2323,\cdot)\) \(\chi_{9600}(2347,\cdot)\) \(\chi_{9600}(2563,\cdot)\) \(\chi_{9600}(2587,\cdot)\) \(\chi_{9600}(2803,\cdot)\) \(\chi_{9600}(2827,\cdot)\) \(\chi_{9600}(3067,\cdot)\) \(\chi_{9600}(3283,\cdot)\) \(\chi_{9600}(3523,\cdot)\) \(\chi_{9600}(3547,\cdot)\) \(\chi_{9600}(3763,\cdot)\) \(\chi_{9600}(3787,\cdot)\) \(\chi_{9600}(4003,\cdot)\) \(\chi_{9600}(4027,\cdot)\) \(\chi_{9600}(4267,\cdot)\) \(\chi_{9600}(4483,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{160})$ |
| Fixed field: | Number field defined by a degree 160 polynomial (not computed) |
Values on generators
\((4351,901,6401,5377)\) → \((-1,e\left(\frac{11}{32}\right),1,e\left(\frac{19}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 9600 }(163, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{147}{160}\right)\) | \(e\left(\frac{33}{160}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{81}{160}\right)\) | \(e\left(\frac{61}{80}\right)\) | \(e\left(\frac{29}{160}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{23}{160}\right)\) | \(e\left(\frac{9}{80}\right)\) |