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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2888.bt
\(\chi_{2888}(5,\cdot)\) \(\chi_{2888}(61,\cdot)\) \(\chi_{2888}(85,\cdot)\) \(\chi_{2888}(93,\cdot)\) \(\chi_{2888}(101,\cdot)\) \(\chi_{2888}(149,\cdot)\) \(\chi_{2888}(157,\cdot)\) \(\chi_{2888}(213,\cdot)\) \(\chi_{2888}(237,\cdot)\) \(\chi_{2888}(253,\cdot)\) \(\chi_{2888}(301,\cdot)\) \(\chi_{2888}(309,\cdot)\) \(\chi_{2888}(365,\cdot)\) \(\chi_{2888}(397,\cdot)\) \(\chi_{2888}(405,\cdot)\) \(\chi_{2888}(453,\cdot)\) \(\chi_{2888}(461,\cdot)\) \(\chi_{2888}(517,\cdot)\) \(\chi_{2888}(541,\cdot)\) \(\chi_{2888}(549,\cdot)\) \(\chi_{2888}(557,\cdot)\) \(\chi_{2888}(605,\cdot)\) \(\chi_{2888}(613,\cdot)\) \(\chi_{2888}(669,\cdot)\) \(\chi_{2888}(693,\cdot)\) \(\chi_{2888}(701,\cdot)\) \(\chi_{2888}(709,\cdot)\) \(\chi_{2888}(757,\cdot)\) \(\chi_{2888}(765,\cdot)\) \(\chi_{2888}(845,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{171})$ |
Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((2167,1445,2529)\) → \((1,-1,e\left(\frac{46}{171}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 2888 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{305}{342}\right)\) | \(e\left(\frac{311}{342}\right)\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{134}{171}\right)\) | \(e\left(\frac{107}{114}\right)\) | \(e\left(\frac{1}{342}\right)\) | \(e\left(\frac{137}{171}\right)\) | \(e\left(\frac{136}{171}\right)\) | \(e\left(\frac{83}{342}\right)\) | \(e\left(\frac{47}{171}\right)\) |