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 \(\chi_{1171}(243,\cdot)\) | 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
\((1172,2344)\) → \((1,e\left(\frac{155}{234}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 3513 }(1414, a) \) | \(-1\) | \(1\) | \(e\left(\frac{155}{234}\right)\) | \(e\left(\frac{38}{117}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{53}{234}\right)\) | \(e\left(\frac{77}{78}\right)\) | \(e\left(\frac{181}{234}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{76}{117}\right)\) |