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.gr
\(\chi_{9600}(173,\cdot)\) \(\chi_{9600}(197,\cdot)\) \(\chi_{9600}(413,\cdot)\) \(\chi_{9600}(437,\cdot)\) \(\chi_{9600}(653,\cdot)\) \(\chi_{9600}(677,\cdot)\) \(\chi_{9600}(917,\cdot)\) \(\chi_{9600}(1133,\cdot)\) \(\chi_{9600}(1373,\cdot)\) \(\chi_{9600}(1397,\cdot)\) \(\chi_{9600}(1613,\cdot)\) \(\chi_{9600}(1637,\cdot)\) \(\chi_{9600}(1853,\cdot)\) \(\chi_{9600}(1877,\cdot)\) \(\chi_{9600}(2117,\cdot)\) \(\chi_{9600}(2333,\cdot)\) \(\chi_{9600}(2573,\cdot)\) \(\chi_{9600}(2597,\cdot)\) \(\chi_{9600}(2813,\cdot)\) \(\chi_{9600}(2837,\cdot)\) \(\chi_{9600}(3053,\cdot)\) \(\chi_{9600}(3077,\cdot)\) \(\chi_{9600}(3317,\cdot)\) \(\chi_{9600}(3533,\cdot)\) \(\chi_{9600}(3773,\cdot)\) \(\chi_{9600}(3797,\cdot)\) \(\chi_{9600}(4013,\cdot)\) \(\chi_{9600}(4037,\cdot)\) \(\chi_{9600}(4253,\cdot)\) \(\chi_{9600}(4277,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{160})$ |
| Fixed field: | Number field defined by a degree 160 polynomial (not computed) |
Values on generators
\((4351,901,6401,5377)\) → \((1,e\left(\frac{7}{32}\right),-1,e\left(\frac{11}{20}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 9600 }(173, a) \) | \(1\) | \(1\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{143}{160}\right)\) | \(e\left(\frac{117}{160}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{149}{160}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{81}{160}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{67}{160}\right)\) | \(e\left(\frac{21}{80}\right)\) |