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.bu
\(\chi_{1296}(5,\cdot)\) \(\chi_{1296}(29,\cdot)\) \(\chi_{1296}(77,\cdot)\) \(\chi_{1296}(101,\cdot)\) \(\chi_{1296}(149,\cdot)\) \(\chi_{1296}(173,\cdot)\) \(\chi_{1296}(221,\cdot)\) \(\chi_{1296}(245,\cdot)\) \(\chi_{1296}(293,\cdot)\) \(\chi_{1296}(317,\cdot)\) \(\chi_{1296}(365,\cdot)\) \(\chi_{1296}(389,\cdot)\) \(\chi_{1296}(437,\cdot)\) \(\chi_{1296}(461,\cdot)\) \(\chi_{1296}(509,\cdot)\) \(\chi_{1296}(533,\cdot)\) \(\chi_{1296}(581,\cdot)\) \(\chi_{1296}(605,\cdot)\) \(\chi_{1296}(653,\cdot)\) \(\chi_{1296}(677,\cdot)\) \(\chi_{1296}(725,\cdot)\) \(\chi_{1296}(749,\cdot)\) \(\chi_{1296}(797,\cdot)\) \(\chi_{1296}(821,\cdot)\) \(\chi_{1296}(869,\cdot)\) \(\chi_{1296}(893,\cdot)\) \(\chi_{1296}(941,\cdot)\) \(\chi_{1296}(965,\cdot)\) \(\chi_{1296}(1013,\cdot)\) \(\chi_{1296}(1037,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1135,325,1217)\) → \((1,-i,e\left(\frac{37}{54}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 1296 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{55}{108}\right)\) | \(e\left(\frac{25}{54}\right)\) | \(e\left(\frac{71}{108}\right)\) | \(e\left(\frac{79}{108}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{1}{27}\right)\) | \(e\left(\frac{1}{54}\right)\) | \(e\left(\frac{65}{108}\right)\) | \(e\left(\frac{19}{27}\right)\) |