Basic properties
Modulus: | \(4000\) | |
Conductor: | \(4000\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(200\) | 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 4000.dd
\(\chi_{4000}(21,\cdot)\) \(\chi_{4000}(61,\cdot)\) \(\chi_{4000}(141,\cdot)\) \(\chi_{4000}(181,\cdot)\) \(\chi_{4000}(221,\cdot)\) \(\chi_{4000}(261,\cdot)\) \(\chi_{4000}(341,\cdot)\) \(\chi_{4000}(381,\cdot)\) \(\chi_{4000}(421,\cdot)\) \(\chi_{4000}(461,\cdot)\) \(\chi_{4000}(541,\cdot)\) \(\chi_{4000}(581,\cdot)\) \(\chi_{4000}(621,\cdot)\) \(\chi_{4000}(661,\cdot)\) \(\chi_{4000}(741,\cdot)\) \(\chi_{4000}(781,\cdot)\) \(\chi_{4000}(821,\cdot)\) \(\chi_{4000}(861,\cdot)\) \(\chi_{4000}(941,\cdot)\) \(\chi_{4000}(981,\cdot)\) \(\chi_{4000}(1021,\cdot)\) \(\chi_{4000}(1061,\cdot)\) \(\chi_{4000}(1141,\cdot)\) \(\chi_{4000}(1181,\cdot)\) \(\chi_{4000}(1221,\cdot)\) \(\chi_{4000}(1261,\cdot)\) \(\chi_{4000}(1341,\cdot)\) \(\chi_{4000}(1381,\cdot)\) \(\chi_{4000}(1421,\cdot)\) \(\chi_{4000}(1461,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{200})$ |
Fixed field: | Number field defined by a degree 200 polynomial (not computed) |
Values on generators
\((2751,2501,1377)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{7}{25}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 4000 }(1581, a) \) | \(1\) | \(1\) | \(e\left(\frac{117}{200}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{17}{100}\right)\) | \(e\left(\frac{131}{200}\right)\) | \(e\left(\frac{9}{200}\right)\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{33}{200}\right)\) | \(e\left(\frac{27}{200}\right)\) | \(e\left(\frac{93}{100}\right)\) | \(e\left(\frac{151}{200}\right)\) |