Basic properties
| Modulus: | \(4000\) | |
| Conductor: | \(500\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(100\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{500}(63,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4000.cs
\(\chi_{4000}(63,\cdot)\) \(\chi_{4000}(127,\cdot)\) \(\chi_{4000}(223,\cdot)\) \(\chi_{4000}(287,\cdot)\) \(\chi_{4000}(383,\cdot)\) \(\chi_{4000}(447,\cdot)\) \(\chi_{4000}(703,\cdot)\) \(\chi_{4000}(767,\cdot)\) \(\chi_{4000}(863,\cdot)\) \(\chi_{4000}(927,\cdot)\) \(\chi_{4000}(1023,\cdot)\) \(\chi_{4000}(1087,\cdot)\) \(\chi_{4000}(1183,\cdot)\) \(\chi_{4000}(1247,\cdot)\) \(\chi_{4000}(1503,\cdot)\) \(\chi_{4000}(1567,\cdot)\) \(\chi_{4000}(1663,\cdot)\) \(\chi_{4000}(1727,\cdot)\) \(\chi_{4000}(1823,\cdot)\) \(\chi_{4000}(1887,\cdot)\) \(\chi_{4000}(1983,\cdot)\) \(\chi_{4000}(2047,\cdot)\) \(\chi_{4000}(2303,\cdot)\) \(\chi_{4000}(2367,\cdot)\) \(\chi_{4000}(2463,\cdot)\) \(\chi_{4000}(2527,\cdot)\) \(\chi_{4000}(2623,\cdot)\) \(\chi_{4000}(2687,\cdot)\) \(\chi_{4000}(2783,\cdot)\) \(\chi_{4000}(2847,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((2751,2501,1377)\) → \((-1,1,e\left(\frac{99}{100}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 4000 }(63, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{100}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{43}{50}\right)\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{61}{100}\right)\) | \(e\left(\frac{27}{100}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{19}{100}\right)\) | \(e\left(\frac{29}{100}\right)\) |