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.dy
\(\chi_{3751}(7,\cdot)\) \(\chi_{3751}(28,\cdot)\) \(\chi_{3751}(51,\cdot)\) \(\chi_{3751}(107,\cdot)\) \(\chi_{3751}(134,\cdot)\) \(\chi_{3751}(195,\cdot)\) \(\chi_{3751}(204,\cdot)\) \(\chi_{3751}(348,\cdot)\) \(\chi_{3751}(369,\cdot)\) \(\chi_{3751}(392,\cdot)\) \(\chi_{3751}(448,\cdot)\) \(\chi_{3751}(453,\cdot)\) \(\chi_{3751}(536,\cdot)\) \(\chi_{3751}(545,\cdot)\) \(\chi_{3751}(689,\cdot)\) \(\chi_{3751}(710,\cdot)\) \(\chi_{3751}(733,\cdot)\) \(\chi_{3751}(789,\cdot)\) \(\chi_{3751}(794,\cdot)\) \(\chi_{3751}(816,\cdot)\) \(\chi_{3751}(877,\cdot)\) \(\chi_{3751}(886,\cdot)\) \(\chi_{3751}(1030,\cdot)\) \(\chi_{3751}(1051,\cdot)\) \(\chi_{3751}(1074,\cdot)\) \(\chi_{3751}(1130,\cdot)\) \(\chi_{3751}(1135,\cdot)\) \(\chi_{3751}(1157,\cdot)\) \(\chi_{3751}(1218,\cdot)\) \(\chi_{3751}(1227,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((2543,2421)\) → \((e\left(\frac{7}{110}\right),e\left(\frac{14}{15}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 3751 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{51}{55}\right)\) | \(e\left(\frac{62}{165}\right)\) | \(e\left(\frac{329}{330}\right)\) | \(e\left(\frac{191}{330}\right)\) | \(e\left(\frac{43}{110}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{277}{330}\right)\) | \(e\left(\frac{76}{165}\right)\) |