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.bv
\(\chi_{1296}(13,\cdot)\) \(\chi_{1296}(61,\cdot)\) \(\chi_{1296}(85,\cdot)\) \(\chi_{1296}(133,\cdot)\) \(\chi_{1296}(157,\cdot)\) \(\chi_{1296}(205,\cdot)\) \(\chi_{1296}(229,\cdot)\) \(\chi_{1296}(277,\cdot)\) \(\chi_{1296}(301,\cdot)\) \(\chi_{1296}(349,\cdot)\) \(\chi_{1296}(373,\cdot)\) \(\chi_{1296}(421,\cdot)\) \(\chi_{1296}(445,\cdot)\) \(\chi_{1296}(493,\cdot)\) \(\chi_{1296}(517,\cdot)\) \(\chi_{1296}(565,\cdot)\) \(\chi_{1296}(589,\cdot)\) \(\chi_{1296}(637,\cdot)\) \(\chi_{1296}(661,\cdot)\) \(\chi_{1296}(709,\cdot)\) \(\chi_{1296}(733,\cdot)\) \(\chi_{1296}(781,\cdot)\) \(\chi_{1296}(805,\cdot)\) \(\chi_{1296}(853,\cdot)\) \(\chi_{1296}(877,\cdot)\) \(\chi_{1296}(925,\cdot)\) \(\chi_{1296}(949,\cdot)\) \(\chi_{1296}(997,\cdot)\) \(\chi_{1296}(1021,\cdot)\) \(\chi_{1296}(1069,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1135,325,1217)\) → \((1,-i,e\left(\frac{26}{27}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 1296 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{108}\right)\) | \(e\left(\frac{49}{54}\right)\) | \(e\left(\frac{29}{108}\right)\) | \(e\left(\frac{103}{108}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{5}{54}\right)\) | \(e\left(\frac{43}{54}\right)\) | \(e\left(\frac{95}{108}\right)\) | \(e\left(\frac{7}{27}\right)\) |