Basic properties
Modulus: | \(3312\) | |
Conductor: | \(3312\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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 3312.dm
\(\chi_{3312}(43,\cdot)\) \(\chi_{3312}(67,\cdot)\) \(\chi_{3312}(283,\cdot)\) \(\chi_{3312}(355,\cdot)\) \(\chi_{3312}(475,\cdot)\) \(\chi_{3312}(571,\cdot)\) \(\chi_{3312}(619,\cdot)\) \(\chi_{3312}(787,\cdot)\) \(\chi_{3312}(835,\cdot)\) \(\chi_{3312}(907,\cdot)\) \(\chi_{3312}(931,\cdot)\) \(\chi_{3312}(1003,\cdot)\) \(\chi_{3312}(1075,\cdot)\) \(\chi_{3312}(1123,\cdot)\) \(\chi_{3312}(1147,\cdot)\) \(\chi_{3312}(1339,\cdot)\) \(\chi_{3312}(1483,\cdot)\) \(\chi_{3312}(1555,\cdot)\) \(\chi_{3312}(1579,\cdot)\) \(\chi_{3312}(1627,\cdot)\) \(\chi_{3312}(1699,\cdot)\) \(\chi_{3312}(1723,\cdot)\) \(\chi_{3312}(1939,\cdot)\) \(\chi_{3312}(2011,\cdot)\) \(\chi_{3312}(2131,\cdot)\) \(\chi_{3312}(2227,\cdot)\) \(\chi_{3312}(2275,\cdot)\) \(\chi_{3312}(2443,\cdot)\) \(\chi_{3312}(2491,\cdot)\) \(\chi_{3312}(2563,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((415,2485,2945,2305)\) → \((-1,i,e\left(\frac{2}{3}\right),e\left(\frac{5}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(35\) |
\( \chi_{ 3312 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{107}{132}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{61}{132}\right)\) | \(e\left(\frac{35}{132}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{67}{132}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{35}{44}\right)\) |