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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1296.bt
\(\chi_{1296}(43,\cdot)\) \(\chi_{1296}(67,\cdot)\) \(\chi_{1296}(115,\cdot)\) \(\chi_{1296}(139,\cdot)\) \(\chi_{1296}(187,\cdot)\) \(\chi_{1296}(211,\cdot)\) \(\chi_{1296}(259,\cdot)\) \(\chi_{1296}(283,\cdot)\) \(\chi_{1296}(331,\cdot)\) \(\chi_{1296}(355,\cdot)\) \(\chi_{1296}(403,\cdot)\) \(\chi_{1296}(427,\cdot)\) \(\chi_{1296}(475,\cdot)\) \(\chi_{1296}(499,\cdot)\) \(\chi_{1296}(547,\cdot)\) \(\chi_{1296}(571,\cdot)\) \(\chi_{1296}(619,\cdot)\) \(\chi_{1296}(643,\cdot)\) \(\chi_{1296}(691,\cdot)\) \(\chi_{1296}(715,\cdot)\) \(\chi_{1296}(763,\cdot)\) \(\chi_{1296}(787,\cdot)\) \(\chi_{1296}(835,\cdot)\) \(\chi_{1296}(859,\cdot)\) \(\chi_{1296}(907,\cdot)\) \(\chi_{1296}(931,\cdot)\) \(\chi_{1296}(979,\cdot)\) \(\chi_{1296}(1003,\cdot)\) \(\chi_{1296}(1051,\cdot)\) \(\chi_{1296}(1075,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1135,325,1217)\) → \((-1,i,e\left(\frac{2}{27}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 1296 }(907, a) \) | \(-1\) | \(1\) | \(e\left(\frac{103}{108}\right)\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{77}{108}\right)\) | \(e\left(\frac{37}{108}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{22}{27}\right)\) | \(e\left(\frac{49}{54}\right)\) | \(e\left(\frac{53}{108}\right)\) | \(e\left(\frac{53}{54}\right)\) |