Basic properties
Modulus: | \(87362\) | |
Conductor: | \(43681\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(3762\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{43681}(43,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 87362.dk
\(\chi_{87362}(43,\cdot)\) \(\chi_{87362}(131,\cdot)\) \(\chi_{87362}(175,\cdot)\) \(\chi_{87362}(263,\cdot)\) \(\chi_{87362}(329,\cdot)\) \(\chi_{87362}(351,\cdot)\) \(\chi_{87362}(461,\cdot)\) \(\chi_{87362}(549,\cdot)\) \(\chi_{87362}(593,\cdot)\) \(\chi_{87362}(681,\cdot)\) \(\chi_{87362}(747,\cdot)\) \(\chi_{87362}(769,\cdot)\) \(\chi_{87362}(879,\cdot)\) \(\chi_{87362}(1011,\cdot)\) \(\chi_{87362}(1099,\cdot)\) \(\chi_{87362}(1165,\cdot)\) \(\chi_{87362}(1187,\cdot)\) \(\chi_{87362}(1297,\cdot)\) \(\chi_{87362}(1385,\cdot)\) \(\chi_{87362}(1429,\cdot)\) \(\chi_{87362}(1517,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{1881})$ |
Fixed field: | Number field defined by a degree 3762 polynomial (not computed) |
Values on generators
\((21661,22023)\) → \((e\left(\frac{5}{22}\right),e\left(\frac{26}{171}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
\( \chi_{ 87362 }(43, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{171}\right)\) | \(e\left(\frac{175}{1881}\right)\) | \(e\left(\frac{499}{1254}\right)\) | \(e\left(\frac{46}{171}\right)\) | \(e\left(\frac{3679}{3762}\right)\) | \(e\left(\frac{428}{1881}\right)\) | \(e\left(\frac{1877}{3762}\right)\) | \(e\left(\frac{2003}{3762}\right)\) | \(e\left(\frac{203}{1881}\right)\) | \(e\left(\frac{350}{1881}\right)\) |