Basic properties
| Modulus: | \(3751\) | |
| Conductor: | \(121\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{121}(63,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3751.cx
\(\chi_{3751}(63,\cdot)\) \(\chi_{3751}(156,\cdot)\) \(\chi_{3751}(249,\cdot)\) \(\chi_{3751}(404,\cdot)\) \(\chi_{3751}(435,\cdot)\) \(\chi_{3751}(497,\cdot)\) \(\chi_{3751}(590,\cdot)\) \(\chi_{3751}(745,\cdot)\) \(\chi_{3751}(776,\cdot)\) \(\chi_{3751}(931,\cdot)\) \(\chi_{3751}(1117,\cdot)\) \(\chi_{3751}(1179,\cdot)\) \(\chi_{3751}(1272,\cdot)\) \(\chi_{3751}(1427,\cdot)\) \(\chi_{3751}(1458,\cdot)\) \(\chi_{3751}(1520,\cdot)\) \(\chi_{3751}(1768,\cdot)\) \(\chi_{3751}(1799,\cdot)\) \(\chi_{3751}(1861,\cdot)\) \(\chi_{3751}(1954,\cdot)\) \(\chi_{3751}(2109,\cdot)\) \(\chi_{3751}(2140,\cdot)\) \(\chi_{3751}(2202,\cdot)\) \(\chi_{3751}(2295,\cdot)\) \(\chi_{3751}(2450,\cdot)\) \(\chi_{3751}(2481,\cdot)\) \(\chi_{3751}(2543,\cdot)\) \(\chi_{3751}(2636,\cdot)\) \(\chi_{3751}(2791,\cdot)\) \(\chi_{3751}(2822,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((2543,2421)\) → \((e\left(\frac{73}{110}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 3751 }(63, a) \) | \(-1\) | \(1\) | \(e\left(\frac{73}{110}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{18}{55}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{7}{110}\right)\) | \(e\left(\frac{71}{110}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{8}{11}\right)\) |