Basic properties
| Modulus: | \(2000\) | |
| Conductor: | \(2000\) | 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 2000.by
\(\chi_{2000}(67,\cdot)\) \(\chi_{2000}(123,\cdot)\) \(\chi_{2000}(147,\cdot)\) \(\chi_{2000}(203,\cdot)\) \(\chi_{2000}(227,\cdot)\) \(\chi_{2000}(283,\cdot)\) \(\chi_{2000}(363,\cdot)\) \(\chi_{2000}(387,\cdot)\) \(\chi_{2000}(467,\cdot)\) \(\chi_{2000}(523,\cdot)\) \(\chi_{2000}(547,\cdot)\) \(\chi_{2000}(603,\cdot)\) \(\chi_{2000}(627,\cdot)\) \(\chi_{2000}(683,\cdot)\) \(\chi_{2000}(763,\cdot)\) \(\chi_{2000}(787,\cdot)\) \(\chi_{2000}(867,\cdot)\) \(\chi_{2000}(923,\cdot)\) \(\chi_{2000}(947,\cdot)\) \(\chi_{2000}(1003,\cdot)\) \(\chi_{2000}(1027,\cdot)\) \(\chi_{2000}(1083,\cdot)\) \(\chi_{2000}(1163,\cdot)\) \(\chi_{2000}(1187,\cdot)\) \(\chi_{2000}(1267,\cdot)\) \(\chi_{2000}(1323,\cdot)\) \(\chi_{2000}(1347,\cdot)\) \(\chi_{2000}(1403,\cdot)\) \(\chi_{2000}(1427,\cdot)\) \(\chi_{2000}(1483,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((751,501,1377)\) → \((-1,i,e\left(\frac{51}{100}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 2000 }(123, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{51}{100}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{23}{100}\right)\) | \(e\left(\frac{43}{100}\right)\) | \(e\left(\frac{17}{100}\right)\) | \(e\left(\frac{81}{100}\right)\) | \(e\left(\frac{23}{50}\right)\) |