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.eb
\(\chi_{3751}(53,\cdot)\) \(\chi_{3751}(104,\cdot)\) \(\chi_{3751}(114,\cdot)\) \(\chi_{3751}(136,\cdot)\) \(\chi_{3751}(141,\cdot)\) \(\chi_{3751}(168,\cdot)\) \(\chi_{3751}(344,\cdot)\) \(\chi_{3751}(394,\cdot)\) \(\chi_{3751}(445,\cdot)\) \(\chi_{3751}(455,\cdot)\) \(\chi_{3751}(477,\cdot)\) \(\chi_{3751}(482,\cdot)\) \(\chi_{3751}(489,\cdot)\) \(\chi_{3751}(509,\cdot)\) \(\chi_{3751}(685,\cdot)\) \(\chi_{3751}(786,\cdot)\) \(\chi_{3751}(796,\cdot)\) \(\chi_{3751}(818,\cdot)\) \(\chi_{3751}(823,\cdot)\) \(\chi_{3751}(830,\cdot)\) \(\chi_{3751}(1026,\cdot)\) \(\chi_{3751}(1076,\cdot)\) \(\chi_{3751}(1127,\cdot)\) \(\chi_{3751}(1137,\cdot)\) \(\chi_{3751}(1159,\cdot)\) \(\chi_{3751}(1164,\cdot)\) \(\chi_{3751}(1171,\cdot)\) \(\chi_{3751}(1191,\cdot)\) \(\chi_{3751}(1367,\cdot)\) \(\chi_{3751}(1417,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((2543,2421)\) → \((e\left(\frac{53}{55}\right),e\left(\frac{17}{30}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 3751 }(53, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{55}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{7}{55}\right)\) | \(e\left(\frac{106}{165}\right)\) | \(e\left(\frac{307}{330}\right)\) | \(e\left(\frac{101}{165}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{34}{165}\right)\) | \(e\left(\frac{163}{330}\right)\) |