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 \(\chi_{2000}(1477,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4000.cp
\(\chi_{4000}(73,\cdot)\) \(\chi_{4000}(217,\cdot)\) \(\chi_{4000}(233,\cdot)\) \(\chi_{4000}(377,\cdot)\) \(\chi_{4000}(537,\cdot)\) \(\chi_{4000}(553,\cdot)\) \(\chi_{4000}(697,\cdot)\) \(\chi_{4000}(713,\cdot)\) \(\chi_{4000}(873,\cdot)\) \(\chi_{4000}(1017,\cdot)\) \(\chi_{4000}(1033,\cdot)\) \(\chi_{4000}(1177,\cdot)\) \(\chi_{4000}(1337,\cdot)\) \(\chi_{4000}(1353,\cdot)\) \(\chi_{4000}(1497,\cdot)\) \(\chi_{4000}(1513,\cdot)\) \(\chi_{4000}(1673,\cdot)\) \(\chi_{4000}(1817,\cdot)\) \(\chi_{4000}(1833,\cdot)\) \(\chi_{4000}(1977,\cdot)\) \(\chi_{4000}(2137,\cdot)\) \(\chi_{4000}(2153,\cdot)\) \(\chi_{4000}(2297,\cdot)\) \(\chi_{4000}(2313,\cdot)\) \(\chi_{4000}(2473,\cdot)\) \(\chi_{4000}(2617,\cdot)\) \(\chi_{4000}(2633,\cdot)\) \(\chi_{4000}(2777,\cdot)\) \(\chi_{4000}(2937,\cdot)\) \(\chi_{4000}(2953,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{100})$ |
Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((2751,2501,1377)\) → \((1,i,e\left(\frac{81}{100}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 4000 }(1977, a) \) | \(-1\) | \(1\) | \(e\left(\frac{21}{50}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{21}{25}\right)\) | \(e\left(\frac{81}{100}\right)\) | \(e\left(\frac{17}{50}\right)\) | \(e\left(\frac{13}{100}\right)\) | \(e\left(\frac{33}{100}\right)\) | \(e\left(\frac{77}{100}\right)\) | \(e\left(\frac{61}{100}\right)\) | \(e\left(\frac{13}{50}\right)\) |