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 \(\chi_{2000}(1523,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4000.cv
\(\chi_{4000}(23,\cdot)\) \(\chi_{4000}(167,\cdot)\) \(\chi_{4000}(183,\cdot)\) \(\chi_{4000}(327,\cdot)\) \(\chi_{4000}(487,\cdot)\) \(\chi_{4000}(503,\cdot)\) \(\chi_{4000}(647,\cdot)\) \(\chi_{4000}(663,\cdot)\) \(\chi_{4000}(823,\cdot)\) \(\chi_{4000}(967,\cdot)\) \(\chi_{4000}(983,\cdot)\) \(\chi_{4000}(1127,\cdot)\) \(\chi_{4000}(1287,\cdot)\) \(\chi_{4000}(1303,\cdot)\) \(\chi_{4000}(1447,\cdot)\) \(\chi_{4000}(1463,\cdot)\) \(\chi_{4000}(1623,\cdot)\) \(\chi_{4000}(1767,\cdot)\) \(\chi_{4000}(1783,\cdot)\) \(\chi_{4000}(1927,\cdot)\) \(\chi_{4000}(2087,\cdot)\) \(\chi_{4000}(2103,\cdot)\) \(\chi_{4000}(2247,\cdot)\) \(\chi_{4000}(2263,\cdot)\) \(\chi_{4000}(2423,\cdot)\) \(\chi_{4000}(2567,\cdot)\) \(\chi_{4000}(2583,\cdot)\) \(\chi_{4000}(2727,\cdot)\) \(\chi_{4000}(2887,\cdot)\) \(\chi_{4000}(2903,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((2751,2501,1377)\) → \((-1,-i,e\left(\frac{31}{100}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 4000 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{25}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{81}{100}\right)\) | \(e\left(\frac{17}{50}\right)\) | \(e\left(\frac{63}{100}\right)\) | \(e\left(\frac{33}{100}\right)\) | \(e\left(\frac{27}{100}\right)\) | \(e\left(\frac{61}{100}\right)\) | \(e\left(\frac{19}{25}\right)\) |