Basic properties
Modulus: | \(3751\) | |
Conductor: | \(3751\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
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.dq
\(\chi_{3751}(42,\cdot)\) \(\chi_{3751}(86,\cdot)\) \(\chi_{3751}(115,\cdot)\) \(\chi_{3751}(158,\cdot)\) \(\chi_{3751}(203,\cdot)\) \(\chi_{3751}(300,\cdot)\) \(\chi_{3751}(322,\cdot)\) \(\chi_{3751}(383,\cdot)\) \(\chi_{3751}(427,\cdot)\) \(\chi_{3751}(456,\cdot)\) \(\chi_{3751}(499,\cdot)\) \(\chi_{3751}(544,\cdot)\) \(\chi_{3751}(641,\cdot)\) \(\chi_{3751}(663,\cdot)\) \(\chi_{3751}(664,\cdot)\) \(\chi_{3751}(724,\cdot)\) \(\chi_{3751}(768,\cdot)\) \(\chi_{3751}(797,\cdot)\) \(\chi_{3751}(840,\cdot)\) \(\chi_{3751}(885,\cdot)\) \(\chi_{3751}(982,\cdot)\) \(\chi_{3751}(1004,\cdot)\) \(\chi_{3751}(1005,\cdot)\) \(\chi_{3751}(1065,\cdot)\) \(\chi_{3751}(1109,\cdot)\) \(\chi_{3751}(1138,\cdot)\) \(\chi_{3751}(1181,\cdot)\) \(\chi_{3751}(1226,\cdot)\) \(\chi_{3751}(1323,\cdot)\) \(\chi_{3751}(1345,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((2543,2421)\) → \((e\left(\frac{21}{55}\right),e\left(\frac{11}{30}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 3751 }(1005, a) \) | \(-1\) | \(1\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{4}{11}\right)\) | \(e\left(\frac{97}{165}\right)\) | \(e\left(\frac{49}{330}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{127}{165}\right)\) | \(e\left(\frac{109}{330}\right)\) |