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 \(\chi_{2000}(531,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4000.cm
\(\chi_{4000}(71,\cdot)\) \(\chi_{4000}(231,\cdot)\) \(\chi_{4000}(311,\cdot)\) \(\chi_{4000}(391,\cdot)\) \(\chi_{4000}(471,\cdot)\) \(\chi_{4000}(631,\cdot)\) \(\chi_{4000}(711,\cdot)\) \(\chi_{4000}(791,\cdot)\) \(\chi_{4000}(871,\cdot)\) \(\chi_{4000}(1031,\cdot)\) \(\chi_{4000}(1111,\cdot)\) \(\chi_{4000}(1191,\cdot)\) \(\chi_{4000}(1271,\cdot)\) \(\chi_{4000}(1431,\cdot)\) \(\chi_{4000}(1511,\cdot)\) \(\chi_{4000}(1591,\cdot)\) \(\chi_{4000}(1671,\cdot)\) \(\chi_{4000}(1831,\cdot)\) \(\chi_{4000}(1911,\cdot)\) \(\chi_{4000}(1991,\cdot)\) \(\chi_{4000}(2071,\cdot)\) \(\chi_{4000}(2231,\cdot)\) \(\chi_{4000}(2311,\cdot)\) \(\chi_{4000}(2391,\cdot)\) \(\chi_{4000}(2471,\cdot)\) \(\chi_{4000}(2631,\cdot)\) \(\chi_{4000}(2711,\cdot)\) \(\chi_{4000}(2791,\cdot)\) \(\chi_{4000}(2871,\cdot)\) \(\chi_{4000}(3031,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((2751,2501,1377)\) → \((-1,-i,e\left(\frac{12}{25}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 4000 }(3031, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{100}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{11}{50}\right)\) | \(e\left(\frac{73}{100}\right)\) | \(e\left(\frac{97}{100}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{39}{100}\right)\) | \(e\left(\frac{91}{100}\right)\) | \(e\left(\frac{22}{25}\right)\) | \(e\left(\frac{33}{100}\right)\) |