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.ge
\(\chi_{9600}(53,\cdot)\) \(\chi_{9600}(77,\cdot)\) \(\chi_{9600}(317,\cdot)\) \(\chi_{9600}(533,\cdot)\) \(\chi_{9600}(773,\cdot)\) \(\chi_{9600}(797,\cdot)\) \(\chi_{9600}(1013,\cdot)\) \(\chi_{9600}(1037,\cdot)\) \(\chi_{9600}(1253,\cdot)\) \(\chi_{9600}(1277,\cdot)\) \(\chi_{9600}(1517,\cdot)\) \(\chi_{9600}(1733,\cdot)\) \(\chi_{9600}(1973,\cdot)\) \(\chi_{9600}(1997,\cdot)\) \(\chi_{9600}(2213,\cdot)\) \(\chi_{9600}(2237,\cdot)\) \(\chi_{9600}(2453,\cdot)\) \(\chi_{9600}(2477,\cdot)\) \(\chi_{9600}(2717,\cdot)\) \(\chi_{9600}(2933,\cdot)\) \(\chi_{9600}(3173,\cdot)\) \(\chi_{9600}(3197,\cdot)\) \(\chi_{9600}(3413,\cdot)\) \(\chi_{9600}(3437,\cdot)\) \(\chi_{9600}(3653,\cdot)\) \(\chi_{9600}(3677,\cdot)\) \(\chi_{9600}(3917,\cdot)\) \(\chi_{9600}(4133,\cdot)\) \(\chi_{9600}(4373,\cdot)\) \(\chi_{9600}(4397,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{160})$ |
| Fixed field: | Number field defined by a degree 160 polynomial (not computed) |
Values on generators
\((4351,901,6401,5377)\) → \((1,e\left(\frac{5}{32}\right),-1,e\left(\frac{7}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 9600 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{61}{160}\right)\) | \(e\left(\frac{159}{160}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{143}{160}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{67}{160}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{9}{160}\right)\) | \(e\left(\frac{47}{80}\right)\) |