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 \(\chi_{2000}(69,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4000.cn
\(\chi_{4000}(9,\cdot)\) \(\chi_{4000}(89,\cdot)\) \(\chi_{4000}(169,\cdot)\) \(\chi_{4000}(329,\cdot)\) \(\chi_{4000}(409,\cdot)\) \(\chi_{4000}(489,\cdot)\) \(\chi_{4000}(569,\cdot)\) \(\chi_{4000}(729,\cdot)\) \(\chi_{4000}(809,\cdot)\) \(\chi_{4000}(889,\cdot)\) \(\chi_{4000}(969,\cdot)\) \(\chi_{4000}(1129,\cdot)\) \(\chi_{4000}(1209,\cdot)\) \(\chi_{4000}(1289,\cdot)\) \(\chi_{4000}(1369,\cdot)\) \(\chi_{4000}(1529,\cdot)\) \(\chi_{4000}(1609,\cdot)\) \(\chi_{4000}(1689,\cdot)\) \(\chi_{4000}(1769,\cdot)\) \(\chi_{4000}(1929,\cdot)\) \(\chi_{4000}(2009,\cdot)\) \(\chi_{4000}(2089,\cdot)\) \(\chi_{4000}(2169,\cdot)\) \(\chi_{4000}(2329,\cdot)\) \(\chi_{4000}(2409,\cdot)\) \(\chi_{4000}(2489,\cdot)\) \(\chi_{4000}(2569,\cdot)\) \(\chi_{4000}(2729,\cdot)\) \(\chi_{4000}(2809,\cdot)\) \(\chi_{4000}(2889,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{100})$ |
Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((2751,2501,1377)\) → \((1,i,e\left(\frac{19}{50}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 4000 }(569, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{100}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{13}{100}\right)\) | \(e\left(\frac{57}{100}\right)\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{59}{100}\right)\) | \(e\left(\frac{21}{100}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{23}{100}\right)\) |