Basic properties
Modulus: | \(2541\) | |
Conductor: | \(2541\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(330\) | 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
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2541.cg
\(\chi_{2541}(2,\cdot)\) \(\chi_{2541}(74,\cdot)\) \(\chi_{2541}(95,\cdot)\) \(\chi_{2541}(107,\cdot)\) \(\chi_{2541}(116,\cdot)\) \(\chi_{2541}(128,\cdot)\) \(\chi_{2541}(149,\cdot)\) \(\chi_{2541}(200,\cdot)\) \(\chi_{2541}(305,\cdot)\) \(\chi_{2541}(326,\cdot)\) \(\chi_{2541}(338,\cdot)\) \(\chi_{2541}(347,\cdot)\) \(\chi_{2541}(359,\cdot)\) \(\chi_{2541}(380,\cdot)\) \(\chi_{2541}(431,\cdot)\) \(\chi_{2541}(464,\cdot)\) \(\chi_{2541}(536,\cdot)\) \(\chi_{2541}(557,\cdot)\) \(\chi_{2541}(569,\cdot)\) \(\chi_{2541}(590,\cdot)\) \(\chi_{2541}(611,\cdot)\) \(\chi_{2541}(662,\cdot)\) \(\chi_{2541}(695,\cdot)\) \(\chi_{2541}(767,\cdot)\) \(\chi_{2541}(788,\cdot)\) \(\chi_{2541}(800,\cdot)\) \(\chi_{2541}(809,\cdot)\) \(\chi_{2541}(821,\cdot)\) \(\chi_{2541}(842,\cdot)\) \(\chi_{2541}(893,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((848,1816,2059)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{43}{110}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 2541 }(800, a) \) | \(1\) | \(1\) | \(e\left(\frac{92}{165}\right)\) | \(e\left(\frac{19}{165}\right)\) | \(e\left(\frac{31}{330}\right)\) | \(e\left(\frac{37}{55}\right)\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{53}{110}\right)\) | \(e\left(\frac{38}{165}\right)\) | \(e\left(\frac{163}{165}\right)\) | \(e\left(\frac{37}{330}\right)\) | \(e\left(\frac{23}{110}\right)\) |