Basic properties
Modulus: | \(3484\) | |
Conductor: | \(3484\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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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
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Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3484.ei
\(\chi_{3484}(11,\cdot)\) \(\chi_{3484}(63,\cdot)\) \(\chi_{3484}(111,\cdot)\) \(\chi_{3484}(275,\cdot)\) \(\chi_{3484}(319,\cdot)\) \(\chi_{3484}(383,\cdot)\) \(\chi_{3484}(487,\cdot)\) \(\chi_{3484}(631,\cdot)\) \(\chi_{3484}(635,\cdot)\) \(\chi_{3484}(683,\cdot)\) \(\chi_{3484}(787,\cdot)\) \(\chi_{3484}(995,\cdot)\) \(\chi_{3484}(1007,\cdot)\) \(\chi_{3484}(1051,\cdot)\) \(\chi_{3484}(1103,\cdot)\) \(\chi_{3484}(1159,\cdot)\) \(\chi_{3484}(1267,\cdot)\) \(\chi_{3484}(1419,\cdot)\) \(\chi_{3484}(1575,\cdot)\) \(\chi_{3484}(1723,\cdot)\) \(\chi_{3484}(1783,\cdot)\) \(\chi_{3484}(1827,\cdot)\) \(\chi_{3484}(1883,\cdot)\) \(\chi_{3484}(1887,\cdot)\) \(\chi_{3484}(1939,\cdot)\) \(\chi_{3484}(2255,\cdot)\) \(\chi_{3484}(2347,\cdot)\) \(\chi_{3484}(2463,\cdot)\) \(\chi_{3484}(2511,\cdot)\) \(\chi_{3484}(2607,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{132})$ |
Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((1743,1341,3017)\) → \((-1,e\left(\frac{7}{12}\right),e\left(\frac{59}{66}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(15\) | \(17\) | \(19\) | \(21\) | \(23\) |
\( \chi_{ 3484 }(11, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{33}\right)\) | \(e\left(\frac{29}{44}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{43}{132}\right)\) | \(e\left(\frac{47}{132}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{47}{132}\right)\) | \(e\left(\frac{23}{132}\right)\) | \(e\left(\frac{4}{11}\right)\) |