Basic properties
| Modulus: | \(1296\) | |
| Conductor: | \(1296\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(108\) | 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 1296.bs
\(\chi_{1296}(11,\cdot)\) \(\chi_{1296}(59,\cdot)\) \(\chi_{1296}(83,\cdot)\) \(\chi_{1296}(131,\cdot)\) \(\chi_{1296}(155,\cdot)\) \(\chi_{1296}(203,\cdot)\) \(\chi_{1296}(227,\cdot)\) \(\chi_{1296}(275,\cdot)\) \(\chi_{1296}(299,\cdot)\) \(\chi_{1296}(347,\cdot)\) \(\chi_{1296}(371,\cdot)\) \(\chi_{1296}(419,\cdot)\) \(\chi_{1296}(443,\cdot)\) \(\chi_{1296}(491,\cdot)\) \(\chi_{1296}(515,\cdot)\) \(\chi_{1296}(563,\cdot)\) \(\chi_{1296}(587,\cdot)\) \(\chi_{1296}(635,\cdot)\) \(\chi_{1296}(659,\cdot)\) \(\chi_{1296}(707,\cdot)\) \(\chi_{1296}(731,\cdot)\) \(\chi_{1296}(779,\cdot)\) \(\chi_{1296}(803,\cdot)\) \(\chi_{1296}(851,\cdot)\) \(\chi_{1296}(875,\cdot)\) \(\chi_{1296}(923,\cdot)\) \(\chi_{1296}(947,\cdot)\) \(\chi_{1296}(995,\cdot)\) \(\chi_{1296}(1019,\cdot)\) \(\chi_{1296}(1067,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1135,325,1217)\) → \((-1,-i,e\left(\frac{1}{54}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 1296 }(83, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{108}\right)\) | \(e\left(\frac{8}{27}\right)\) | \(e\left(\frac{53}{108}\right)\) | \(e\left(\frac{43}{108}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{23}{36}\right)\) | \(e\left(\frac{11}{54}\right)\) | \(e\left(\frac{19}{54}\right)\) | \(e\left(\frac{101}{108}\right)\) | \(e\left(\frac{47}{54}\right)\) |