Basic properties
Modulus: | \(4800\) | |
Conductor: | \(4800\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(80\) | 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 4800.fe
\(\chi_{4800}(11,\cdot)\) \(\chi_{4800}(131,\cdot)\) \(\chi_{4800}(371,\cdot)\) \(\chi_{4800}(491,\cdot)\) \(\chi_{4800}(611,\cdot)\) \(\chi_{4800}(731,\cdot)\) \(\chi_{4800}(971,\cdot)\) \(\chi_{4800}(1091,\cdot)\) \(\chi_{4800}(1211,\cdot)\) \(\chi_{4800}(1331,\cdot)\) \(\chi_{4800}(1571,\cdot)\) \(\chi_{4800}(1691,\cdot)\) \(\chi_{4800}(1811,\cdot)\) \(\chi_{4800}(1931,\cdot)\) \(\chi_{4800}(2171,\cdot)\) \(\chi_{4800}(2291,\cdot)\) \(\chi_{4800}(2411,\cdot)\) \(\chi_{4800}(2531,\cdot)\) \(\chi_{4800}(2771,\cdot)\) \(\chi_{4800}(2891,\cdot)\) \(\chi_{4800}(3011,\cdot)\) \(\chi_{4800}(3131,\cdot)\) \(\chi_{4800}(3371,\cdot)\) \(\chi_{4800}(3491,\cdot)\) \(\chi_{4800}(3611,\cdot)\) \(\chi_{4800}(3731,\cdot)\) \(\chi_{4800}(3971,\cdot)\) \(\chi_{4800}(4091,\cdot)\) \(\chi_{4800}(4211,\cdot)\) \(\chi_{4800}(4331,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((4351,901,1601,577)\) → \((-1,e\left(\frac{9}{16}\right),-1,e\left(\frac{4}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 4800 }(3611, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{67}{80}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{23}{80}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{21}{80}\right)\) | \(e\left(\frac{23}{40}\right)\) |