Basic properties
| Modulus: | \(6080\) | |
| Conductor: | \(1216\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(144\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1216}(51,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6080.id
\(\chi_{6080}(51,\cdot)\) \(\chi_{6080}(91,\cdot)\) \(\chi_{6080}(211,\cdot)\) \(\chi_{6080}(371,\cdot)\) \(\chi_{6080}(451,\cdot)\) \(\chi_{6080}(611,\cdot)\) \(\chi_{6080}(811,\cdot)\) \(\chi_{6080}(851,\cdot)\) \(\chi_{6080}(971,\cdot)\) \(\chi_{6080}(1131,\cdot)\) \(\chi_{6080}(1211,\cdot)\) \(\chi_{6080}(1371,\cdot)\) \(\chi_{6080}(1571,\cdot)\) \(\chi_{6080}(1611,\cdot)\) \(\chi_{6080}(1731,\cdot)\) \(\chi_{6080}(1891,\cdot)\) \(\chi_{6080}(1971,\cdot)\) \(\chi_{6080}(2131,\cdot)\) \(\chi_{6080}(2331,\cdot)\) \(\chi_{6080}(2371,\cdot)\) \(\chi_{6080}(2491,\cdot)\) \(\chi_{6080}(2651,\cdot)\) \(\chi_{6080}(2731,\cdot)\) \(\chi_{6080}(2891,\cdot)\) \(\chi_{6080}(3091,\cdot)\) \(\chi_{6080}(3131,\cdot)\) \(\chi_{6080}(3251,\cdot)\) \(\chi_{6080}(3411,\cdot)\) \(\chi_{6080}(3491,\cdot)\) \(\chi_{6080}(3651,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{144})$ |
| Fixed field: | Number field defined by a degree 144 polynomial (not computed) |
Values on generators
\((191,5701,1217,1921)\) → \((-1,e\left(\frac{15}{16}\right),1,e\left(\frac{5}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 6080 }(51, a) \) | \(1\) | \(1\) | \(e\left(\frac{133}{144}\right)\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{61}{72}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(e\left(\frac{65}{144}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{67}{144}\right)\) | \(e\left(\frac{13}{72}\right)\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{5}{144}\right)\) |