Basic properties
Modulus: | \(4000\) | |
Conductor: | \(1000\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(100\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1000}(933,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4000.ct
\(\chi_{4000}(17,\cdot)\) \(\chi_{4000}(113,\cdot)\) \(\chi_{4000}(177,\cdot)\) \(\chi_{4000}(273,\cdot)\) \(\chi_{4000}(337,\cdot)\) \(\chi_{4000}(433,\cdot)\) \(\chi_{4000}(497,\cdot)\) \(\chi_{4000}(753,\cdot)\) \(\chi_{4000}(817,\cdot)\) \(\chi_{4000}(913,\cdot)\) \(\chi_{4000}(977,\cdot)\) \(\chi_{4000}(1073,\cdot)\) \(\chi_{4000}(1137,\cdot)\) \(\chi_{4000}(1233,\cdot)\) \(\chi_{4000}(1297,\cdot)\) \(\chi_{4000}(1553,\cdot)\) \(\chi_{4000}(1617,\cdot)\) \(\chi_{4000}(1713,\cdot)\) \(\chi_{4000}(1777,\cdot)\) \(\chi_{4000}(1873,\cdot)\) \(\chi_{4000}(1937,\cdot)\) \(\chi_{4000}(2033,\cdot)\) \(\chi_{4000}(2097,\cdot)\) \(\chi_{4000}(2353,\cdot)\) \(\chi_{4000}(2417,\cdot)\) \(\chi_{4000}(2513,\cdot)\) \(\chi_{4000}(2577,\cdot)\) \(\chi_{4000}(2673,\cdot)\) \(\chi_{4000}(2737,\cdot)\) \(\chi_{4000}(2833,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{100})$ |
Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((2751,2501,1377)\) → \((1,-1,e\left(\frac{63}{100}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 4000 }(433, a) \) | \(-1\) | \(1\) | \(e\left(\frac{91}{100}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{19}{50}\right)\) | \(e\left(\frac{7}{100}\right)\) | \(e\left(\frac{99}{100}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{23}{50}\right)\) | \(e\left(\frac{53}{100}\right)\) | \(e\left(\frac{73}{100}\right)\) |