Basic properties
| Modulus: | \(3513\) | |
| Conductor: | \(1171\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(234\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1171}(745,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3513.bn
\(\chi_{3513}(7,\cdot)\) \(\chi_{3513}(130,\cdot)\) \(\chi_{3513}(142,\cdot)\) \(\chi_{3513}(250,\cdot)\) \(\chi_{3513}(307,\cdot)\) \(\chi_{3513}(316,\cdot)\) \(\chi_{3513}(397,\cdot)\) \(\chi_{3513}(502,\cdot)\) \(\chi_{3513}(559,\cdot)\) \(\chi_{3513}(580,\cdot)\) \(\chi_{3513}(598,\cdot)\) \(\chi_{3513}(628,\cdot)\) \(\chi_{3513}(640,\cdot)\) \(\chi_{3513}(715,\cdot)\) \(\chi_{3513}(745,\cdot)\) \(\chi_{3513}(781,\cdot)\) \(\chi_{3513}(850,\cdot)\) \(\chi_{3513}(904,\cdot)\) \(\chi_{3513}(982,\cdot)\) \(\chi_{3513}(1075,\cdot)\) \(\chi_{3513}(1084,\cdot)\) \(\chi_{3513}(1090,\cdot)\) \(\chi_{3513}(1162,\cdot)\) \(\chi_{3513}(1174,\cdot)\) \(\chi_{3513}(1231,\cdot)\) \(\chi_{3513}(1234,\cdot)\) \(\chi_{3513}(1318,\cdot)\) \(\chi_{3513}(1354,\cdot)\) \(\chi_{3513}(1414,\cdot)\) \(\chi_{3513}(1429,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((1172,2344)\) → \((1,e\left(\frac{77}{234}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 3513 }(745, a) \) | \(-1\) | \(1\) | \(e\left(\frac{77}{234}\right)\) | \(e\left(\frac{77}{117}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{209}{234}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{25}{234}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{37}{117}\right)\) |