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
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2541.ci
\(\chi_{2541}(5,\cdot)\) \(\chi_{2541}(26,\cdot)\) \(\chi_{2541}(38,\cdot)\) \(\chi_{2541}(47,\cdot)\) \(\chi_{2541}(59,\cdot)\) \(\chi_{2541}(80,\cdot)\) \(\chi_{2541}(152,\cdot)\) \(\chi_{2541}(185,\cdot)\) \(\chi_{2541}(236,\cdot)\) \(\chi_{2541}(257,\cdot)\) \(\chi_{2541}(278,\cdot)\) \(\chi_{2541}(290,\cdot)\) \(\chi_{2541}(311,\cdot)\) \(\chi_{2541}(383,\cdot)\) \(\chi_{2541}(416,\cdot)\) \(\chi_{2541}(467,\cdot)\) \(\chi_{2541}(488,\cdot)\) \(\chi_{2541}(500,\cdot)\) \(\chi_{2541}(509,\cdot)\) \(\chi_{2541}(521,\cdot)\) \(\chi_{2541}(542,\cdot)\) \(\chi_{2541}(647,\cdot)\) \(\chi_{2541}(698,\cdot)\) \(\chi_{2541}(719,\cdot)\) \(\chi_{2541}(731,\cdot)\) \(\chi_{2541}(740,\cdot)\) \(\chi_{2541}(752,\cdot)\) \(\chi_{2541}(773,\cdot)\) \(\chi_{2541}(845,\cdot)\) \(\chi_{2541}(878,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{165})$ |
Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((848,1816,2059)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{52}{55}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(13\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 2541 }(467, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{330}\right)\) | \(e\left(\frac{37}{165}\right)\) | \(e\left(\frac{104}{165}\right)\) | \(e\left(\frac{37}{110}\right)\) | \(e\left(\frac{49}{66}\right)\) | \(e\left(\frac{109}{110}\right)\) | \(e\left(\frac{74}{165}\right)\) | \(e\left(\frac{109}{165}\right)\) | \(e\left(\frac{211}{330}\right)\) | \(e\left(\frac{47}{55}\right)\) |