Basic properties
Modulus: | \(2023\) | |
Conductor: | \(2023\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(204\) | 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 2023.bg
\(\chi_{2023}(4,\cdot)\) \(\chi_{2023}(30,\cdot)\) \(\chi_{2023}(72,\cdot)\) \(\chi_{2023}(81,\cdot)\) \(\chi_{2023}(123,\cdot)\) \(\chi_{2023}(149,\cdot)\) \(\chi_{2023}(191,\cdot)\) \(\chi_{2023}(200,\cdot)\) \(\chi_{2023}(242,\cdot)\) \(\chi_{2023}(268,\cdot)\) \(\chi_{2023}(310,\cdot)\) \(\chi_{2023}(319,\cdot)\) \(\chi_{2023}(361,\cdot)\) \(\chi_{2023}(387,\cdot)\) \(\chi_{2023}(429,\cdot)\) \(\chi_{2023}(438,\cdot)\) \(\chi_{2023}(480,\cdot)\) \(\chi_{2023}(506,\cdot)\) \(\chi_{2023}(548,\cdot)\) \(\chi_{2023}(557,\cdot)\) \(\chi_{2023}(599,\cdot)\) \(\chi_{2023}(625,\cdot)\) \(\chi_{2023}(667,\cdot)\) \(\chi_{2023}(676,\cdot)\) \(\chi_{2023}(718,\cdot)\) \(\chi_{2023}(744,\cdot)\) \(\chi_{2023}(786,\cdot)\) \(\chi_{2023}(795,\cdot)\) \(\chi_{2023}(837,\cdot)\) \(\chi_{2023}(863,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{204})$ |
Fixed field: | Number field defined by a degree 204 polynomial (not computed) |
Values on generators
\((290,1737)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{27}{68}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
\( \chi_{ 2023 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{102}\right)\) | \(e\left(\frac{13}{204}\right)\) | \(e\left(\frac{28}{51}\right)\) | \(e\left(\frac{53}{204}\right)\) | \(e\left(\frac{57}{68}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{13}{102}\right)\) | \(e\left(\frac{7}{204}\right)\) | \(e\left(\frac{163}{204}\right)\) | \(e\left(\frac{125}{204}\right)\) |