Basic properties
Modulus: | \(2888\) | |
Conductor: | \(2888\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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 2888.bs
\(\chi_{2888}(35,\cdot)\) \(\chi_{2888}(43,\cdot)\) \(\chi_{2888}(123,\cdot)\) \(\chi_{2888}(131,\cdot)\) \(\chi_{2888}(139,\cdot)\) \(\chi_{2888}(187,\cdot)\) \(\chi_{2888}(195,\cdot)\) \(\chi_{2888}(251,\cdot)\) \(\chi_{2888}(275,\cdot)\) \(\chi_{2888}(283,\cdot)\) \(\chi_{2888}(291,\cdot)\) \(\chi_{2888}(339,\cdot)\) \(\chi_{2888}(347,\cdot)\) \(\chi_{2888}(403,\cdot)\) \(\chi_{2888}(427,\cdot)\) \(\chi_{2888}(435,\cdot)\) \(\chi_{2888}(443,\cdot)\) \(\chi_{2888}(491,\cdot)\) \(\chi_{2888}(499,\cdot)\) \(\chi_{2888}(555,\cdot)\) \(\chi_{2888}(579,\cdot)\) \(\chi_{2888}(587,\cdot)\) \(\chi_{2888}(643,\cdot)\) \(\chi_{2888}(651,\cdot)\) \(\chi_{2888}(707,\cdot)\) \(\chi_{2888}(731,\cdot)\) \(\chi_{2888}(739,\cdot)\) \(\chi_{2888}(747,\cdot)\) \(\chi_{2888}(795,\cdot)\) \(\chi_{2888}(803,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{171})$ |
Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((2167,1445,2529)\) → \((-1,-1,e\left(\frac{121}{171}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 2888 }(427, a) \) | \(-1\) | \(1\) | \(e\left(\frac{61}{171}\right)\) | \(e\left(\frac{227}{342}\right)\) | \(e\left(\frac{73}{114}\right)\) | \(e\left(\frac{122}{171}\right)\) | \(e\left(\frac{10}{57}\right)\) | \(e\left(\frac{103}{342}\right)\) | \(e\left(\frac{7}{342}\right)\) | \(e\left(\frac{157}{171}\right)\) | \(e\left(\frac{341}{342}\right)\) | \(e\left(\frac{277}{342}\right)\) |