Basic properties
Modulus: | \(4000\) | |
Conductor: | \(2000\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(100\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{2000}(1117,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4000.cu
\(\chi_{4000}(137,\cdot)\) \(\chi_{4000}(153,\cdot)\) \(\chi_{4000}(297,\cdot)\) \(\chi_{4000}(313,\cdot)\) \(\chi_{4000}(473,\cdot)\) \(\chi_{4000}(617,\cdot)\) \(\chi_{4000}(633,\cdot)\) \(\chi_{4000}(777,\cdot)\) \(\chi_{4000}(937,\cdot)\) \(\chi_{4000}(953,\cdot)\) \(\chi_{4000}(1097,\cdot)\) \(\chi_{4000}(1113,\cdot)\) \(\chi_{4000}(1273,\cdot)\) \(\chi_{4000}(1417,\cdot)\) \(\chi_{4000}(1433,\cdot)\) \(\chi_{4000}(1577,\cdot)\) \(\chi_{4000}(1737,\cdot)\) \(\chi_{4000}(1753,\cdot)\) \(\chi_{4000}(1897,\cdot)\) \(\chi_{4000}(1913,\cdot)\) \(\chi_{4000}(2073,\cdot)\) \(\chi_{4000}(2217,\cdot)\) \(\chi_{4000}(2233,\cdot)\) \(\chi_{4000}(2377,\cdot)\) \(\chi_{4000}(2537,\cdot)\) \(\chi_{4000}(2553,\cdot)\) \(\chi_{4000}(2697,\cdot)\) \(\chi_{4000}(2713,\cdot)\) \(\chi_{4000}(2873,\cdot)\) \(\chi_{4000}(3017,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{100})$ |
Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((2751,2501,1377)\) → \((1,-i,e\left(\frac{53}{100}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 4000 }(617, a) \) | \(-1\) | \(1\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{3}{100}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{69}{100}\right)\) | \(e\left(\frac{79}{100}\right)\) | \(e\left(\frac{51}{100}\right)\) | \(e\left(\frac{93}{100}\right)\) | \(e\left(\frac{22}{25}\right)\) |