Basic properties
| Modulus: | \(3888\) | |
| Conductor: | \(3888\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(324\) | 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 3888.ce
\(\chi_{3888}(13,\cdot)\) \(\chi_{3888}(61,\cdot)\) \(\chi_{3888}(85,\cdot)\) \(\chi_{3888}(133,\cdot)\) \(\chi_{3888}(157,\cdot)\) \(\chi_{3888}(205,\cdot)\) \(\chi_{3888}(229,\cdot)\) \(\chi_{3888}(277,\cdot)\) \(\chi_{3888}(301,\cdot)\) \(\chi_{3888}(349,\cdot)\) \(\chi_{3888}(373,\cdot)\) \(\chi_{3888}(421,\cdot)\) \(\chi_{3888}(445,\cdot)\) \(\chi_{3888}(493,\cdot)\) \(\chi_{3888}(517,\cdot)\) \(\chi_{3888}(565,\cdot)\) \(\chi_{3888}(589,\cdot)\) \(\chi_{3888}(637,\cdot)\) \(\chi_{3888}(661,\cdot)\) \(\chi_{3888}(709,\cdot)\) \(\chi_{3888}(733,\cdot)\) \(\chi_{3888}(781,\cdot)\) \(\chi_{3888}(805,\cdot)\) \(\chi_{3888}(853,\cdot)\) \(\chi_{3888}(877,\cdot)\) \(\chi_{3888}(925,\cdot)\) \(\chi_{3888}(949,\cdot)\) \(\chi_{3888}(997,\cdot)\) \(\chi_{3888}(1021,\cdot)\) \(\chi_{3888}(1069,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{324})$ |
| Fixed field: | Number field defined by a degree 324 polynomial (not computed) |
Values on generators
\((2431,2917,1217)\) → \((1,i,e\left(\frac{28}{81}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 3888 }(85, a) \) | \(1\) | \(1\) | \(e\left(\frac{65}{324}\right)\) | \(e\left(\frac{113}{162}\right)\) | \(e\left(\frac{25}{324}\right)\) | \(e\left(\frac{167}{324}\right)\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{73}{108}\right)\) | \(e\left(\frac{157}{162}\right)\) | \(e\left(\frac{65}{162}\right)\) | \(e\left(\frac{175}{324}\right)\) | \(e\left(\frac{74}{81}\right)\) |