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.bx
\(\chi_{2000}(29,\cdot)\) \(\chi_{2000}(69,\cdot)\) \(\chi_{2000}(109,\cdot)\) \(\chi_{2000}(189,\cdot)\) \(\chi_{2000}(229,\cdot)\) \(\chi_{2000}(269,\cdot)\) \(\chi_{2000}(309,\cdot)\) \(\chi_{2000}(389,\cdot)\) \(\chi_{2000}(429,\cdot)\) \(\chi_{2000}(469,\cdot)\) \(\chi_{2000}(509,\cdot)\) \(\chi_{2000}(589,\cdot)\) \(\chi_{2000}(629,\cdot)\) \(\chi_{2000}(669,\cdot)\) \(\chi_{2000}(709,\cdot)\) \(\chi_{2000}(789,\cdot)\) \(\chi_{2000}(829,\cdot)\) \(\chi_{2000}(869,\cdot)\) \(\chi_{2000}(909,\cdot)\) \(\chi_{2000}(989,\cdot)\) \(\chi_{2000}(1029,\cdot)\) \(\chi_{2000}(1069,\cdot)\) \(\chi_{2000}(1109,\cdot)\) \(\chi_{2000}(1189,\cdot)\) \(\chi_{2000}(1229,\cdot)\) \(\chi_{2000}(1269,\cdot)\) \(\chi_{2000}(1309,\cdot)\) \(\chi_{2000}(1389,\cdot)\) \(\chi_{2000}(1429,\cdot)\) \(\chi_{2000}(1469,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((751,501,1377)\) → \((1,-i,e\left(\frac{7}{50}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 2000 }(509, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{100}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{23}{50}\right)\) | \(e\left(\frac{39}{100}\right)\) | \(e\left(\frac{71}{100}\right)\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{77}{100}\right)\) | \(e\left(\frac{63}{100}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{69}{100}\right)\) |