Basic properties
Modulus: | \(2873\) | |
Conductor: | \(2873\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(208\) | 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 2873.ck
\(\chi_{2873}(44,\cdot)\) \(\chi_{2873}(57,\cdot)\) \(\chi_{2873}(73,\cdot)\) \(\chi_{2873}(96,\cdot)\) \(\chi_{2873}(109,\cdot)\) \(\chi_{2873}(190,\cdot)\) \(\chi_{2873}(216,\cdot)\) \(\chi_{2873}(265,\cdot)\) \(\chi_{2873}(278,\cdot)\) \(\chi_{2873}(294,\cdot)\) \(\chi_{2873}(317,\cdot)\) \(\chi_{2873}(320,\cdot)\) \(\chi_{2873}(330,\cdot)\) \(\chi_{2873}(411,\cdot)\) \(\chi_{2873}(486,\cdot)\) \(\chi_{2873}(499,\cdot)\) \(\chi_{2873}(515,\cdot)\) \(\chi_{2873}(538,\cdot)\) \(\chi_{2873}(541,\cdot)\) \(\chi_{2873}(551,\cdot)\) \(\chi_{2873}(632,\cdot)\) \(\chi_{2873}(658,\cdot)\) \(\chi_{2873}(707,\cdot)\) \(\chi_{2873}(720,\cdot)\) \(\chi_{2873}(736,\cdot)\) \(\chi_{2873}(759,\cdot)\) \(\chi_{2873}(762,\cdot)\) \(\chi_{2873}(772,\cdot)\) \(\chi_{2873}(853,\cdot)\) \(\chi_{2873}(879,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{208})$ |
Fixed field: | Number field defined by a degree 208 polynomial (not computed) |
Values on generators
\((171,2536)\) → \((e\left(\frac{35}{52}\right),e\left(\frac{3}{16}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 2873 }(44, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{104}\right)\) | \(e\left(\frac{135}{208}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{207}{208}\right)\) | \(e\left(\frac{197}{208}\right)\) | \(e\left(\frac{17}{208}\right)\) | \(e\left(\frac{93}{104}\right)\) | \(e\left(\frac{31}{104}\right)\) | \(e\left(\frac{61}{208}\right)\) | \(e\left(\frac{133}{208}\right)\) |