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 \(\chi_{2000}(341,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4000.cw
\(\chi_{4000}(41,\cdot)\) \(\chi_{4000}(121,\cdot)\) \(\chi_{4000}(281,\cdot)\) \(\chi_{4000}(361,\cdot)\) \(\chi_{4000}(441,\cdot)\) \(\chi_{4000}(521,\cdot)\) \(\chi_{4000}(681,\cdot)\) \(\chi_{4000}(761,\cdot)\) \(\chi_{4000}(841,\cdot)\) \(\chi_{4000}(921,\cdot)\) \(\chi_{4000}(1081,\cdot)\) \(\chi_{4000}(1161,\cdot)\) \(\chi_{4000}(1241,\cdot)\) \(\chi_{4000}(1321,\cdot)\) \(\chi_{4000}(1481,\cdot)\) \(\chi_{4000}(1561,\cdot)\) \(\chi_{4000}(1641,\cdot)\) \(\chi_{4000}(1721,\cdot)\) \(\chi_{4000}(1881,\cdot)\) \(\chi_{4000}(1961,\cdot)\) \(\chi_{4000}(2041,\cdot)\) \(\chi_{4000}(2121,\cdot)\) \(\chi_{4000}(2281,\cdot)\) \(\chi_{4000}(2361,\cdot)\) \(\chi_{4000}(2441,\cdot)\) \(\chi_{4000}(2521,\cdot)\) \(\chi_{4000}(2681,\cdot)\) \(\chi_{4000}(2761,\cdot)\) \(\chi_{4000}(2841,\cdot)\) \(\chi_{4000}(2921,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((2751,2501,1377)\) → \((1,i,e\left(\frac{6}{25}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 4000 }(2841, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{100}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{43}{50}\right)\) | \(e\left(\frac{49}{100}\right)\) | \(e\left(\frac{11}{100}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{7}{100}\right)\) | \(e\left(\frac{33}{100}\right)\) | \(e\left(\frac{47}{50}\right)\) | \(e\left(\frac{29}{100}\right)\) |