Basic properties
Modulus: | \(3751\) | |
Conductor: | \(3751\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(330\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3751.ee
\(\chi_{3751}(12,\cdot)\) \(\chi_{3751}(34,\cdot)\) \(\chi_{3751}(166,\cdot)\) \(\chi_{3751}(177,\cdot)\) \(\chi_{3751}(199,\cdot)\) \(\chi_{3751}(210,\cdot)\) \(\chi_{3751}(265,\cdot)\) \(\chi_{3751}(331,\cdot)\) \(\chi_{3751}(353,\cdot)\) \(\chi_{3751}(375,\cdot)\) \(\chi_{3751}(507,\cdot)\) \(\chi_{3751}(518,\cdot)\) \(\chi_{3751}(540,\cdot)\) \(\chi_{3751}(551,\cdot)\) \(\chi_{3751}(672,\cdot)\) \(\chi_{3751}(694,\cdot)\) \(\chi_{3751}(716,\cdot)\) \(\chi_{3751}(859,\cdot)\) \(\chi_{3751}(881,\cdot)\) \(\chi_{3751}(892,\cdot)\) \(\chi_{3751}(947,\cdot)\) \(\chi_{3751}(1013,\cdot)\) \(\chi_{3751}(1035,\cdot)\) \(\chi_{3751}(1057,\cdot)\) \(\chi_{3751}(1189,\cdot)\) \(\chi_{3751}(1200,\cdot)\) \(\chi_{3751}(1222,\cdot)\) \(\chi_{3751}(1233,\cdot)\) \(\chi_{3751}(1288,\cdot)\) \(\chi_{3751}(1354,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((2543,2421)\) → \((e\left(\frac{9}{11}\right),e\left(\frac{19}{30}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 3751 }(12, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{2}{55}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{76}{165}\right)\) | \(e\left(\frac{3}{55}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{38}{165}\right)\) | \(e\left(\frac{221}{330}\right)\) |