Basic properties
| Modulus: | \(4001\) | |
| Conductor: | \(4001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(100\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| 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 4001.n
\(\chi_{4001}(25,\cdot)\) \(\chi_{4001}(104,\cdot)\) \(\chi_{4001}(160,\cdot)\) \(\chi_{4001}(284,\cdot)\) \(\chi_{4001}(350,\cdot)\) \(\chi_{4001}(379,\cdot)\) \(\chi_{4001}(579,\cdot)\) \(\chi_{4001}(583,\cdot)\) \(\chi_{4001}(648,\cdot)\) \(\chi_{4001}(654,\cdot)\) \(\chi_{4001}(984,\cdot)\) \(\chi_{4001}(1024,\cdot)\) \(\chi_{4001}(1154,\cdot)\) \(\chi_{4001}(1456,\cdot)\) \(\chi_{4001}(1668,\cdot)\) \(\chi_{4001}(1735,\cdot)\) \(\chi_{4001}(1761,\cdot)\) \(\chi_{4001}(1773,\cdot)\) \(\chi_{4001}(1785,\cdot)\) \(\chi_{4001}(1873,\cdot)\) \(\chi_{4001}(2128,\cdot)\) \(\chi_{4001}(2216,\cdot)\) \(\chi_{4001}(2228,\cdot)\) \(\chi_{4001}(2240,\cdot)\) \(\chi_{4001}(2266,\cdot)\) \(\chi_{4001}(2333,\cdot)\) \(\chi_{4001}(2545,\cdot)\) \(\chi_{4001}(2847,\cdot)\) \(\chi_{4001}(2977,\cdot)\) \(\chi_{4001}(3017,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\(3\) → \(e\left(\frac{63}{100}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4001 }(1873, a) \) | \(1\) | \(1\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{63}{100}\right)\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{59}{100}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(-i\) |