Basic properties
| Modulus: | \(3484\) | |
| Conductor: | \(871\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{871}(21,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3484.ea
\(\chi_{3484}(21,\cdot)\) \(\chi_{3484}(73,\cdot)\) \(\chi_{3484}(317,\cdot)\) \(\chi_{3484}(333,\cdot)\) \(\chi_{3484}(421,\cdot)\) \(\chi_{3484}(437,\cdot)\) \(\chi_{3484}(473,\cdot)\) \(\chi_{3484}(525,\cdot)\) \(\chi_{3484}(629,\cdot)\) \(\chi_{3484}(837,\cdot)\) \(\chi_{3484}(853,\cdot)\) \(\chi_{3484}(957,\cdot)\) \(\chi_{3484}(993,\cdot)\) \(\chi_{3484}(1009,\cdot)\) \(\chi_{3484}(1061,\cdot)\) \(\chi_{3484}(1149,\cdot)\) \(\chi_{3484}(1165,\cdot)\) \(\chi_{3484}(1253,\cdot)\) \(\chi_{3484}(1357,\cdot)\) \(\chi_{3484}(1373,\cdot)\) \(\chi_{3484}(1461,\cdot)\) \(\chi_{3484}(1513,\cdot)\) \(\chi_{3484}(1529,\cdot)\) \(\chi_{3484}(1685,\cdot)\) \(\chi_{3484}(1789,\cdot)\) \(\chi_{3484}(1825,\cdot)\) \(\chi_{3484}(1893,\cdot)\) \(\chi_{3484}(1997,\cdot)\) \(\chi_{3484}(2033,\cdot)\) \(\chi_{3484}(2049,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((1743,1341,3017)\) → \((1,i,e\left(\frac{31}{33}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
| \( \chi_{ 3484 }(21, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{15}{44}\right)\) | \(e\left(\frac{47}{132}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{23}{132}\right)\) | \(e\left(\frac{43}{44}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{85}{132}\right)\) | \(e\left(\frac{131}{132}\right)\) | \(e\left(\frac{53}{66}\right)\) |