Basic properties
| Modulus: | \(6000\) | |
| 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 \(\chi_{2000}(683,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6000.dy
\(\chi_{6000}(67,\cdot)\) \(\chi_{6000}(283,\cdot)\) \(\chi_{6000}(523,\cdot)\) \(\chi_{6000}(547,\cdot)\) \(\chi_{6000}(763,\cdot)\) \(\chi_{6000}(787,\cdot)\) \(\chi_{6000}(1003,\cdot)\) \(\chi_{6000}(1027,\cdot)\) \(\chi_{6000}(1267,\cdot)\) \(\chi_{6000}(1483,\cdot)\) \(\chi_{6000}(1723,\cdot)\) \(\chi_{6000}(1747,\cdot)\) \(\chi_{6000}(1963,\cdot)\) \(\chi_{6000}(1987,\cdot)\) \(\chi_{6000}(2203,\cdot)\) \(\chi_{6000}(2227,\cdot)\) \(\chi_{6000}(2467,\cdot)\) \(\chi_{6000}(2683,\cdot)\) \(\chi_{6000}(2923,\cdot)\) \(\chi_{6000}(2947,\cdot)\) \(\chi_{6000}(3163,\cdot)\) \(\chi_{6000}(3187,\cdot)\) \(\chi_{6000}(3403,\cdot)\) \(\chi_{6000}(3427,\cdot)\) \(\chi_{6000}(3667,\cdot)\) \(\chi_{6000}(3883,\cdot)\) \(\chi_{6000}(4123,\cdot)\) \(\chi_{6000}(4147,\cdot)\) \(\chi_{6000}(4363,\cdot)\) \(\chi_{6000}(4387,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((751,4501,4001,5377)\) → \((-1,i,1,e\left(\frac{63}{100}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 6000 }(2683, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{63}{100}\right)\) | \(e\left(\frac{8}{25}\right)\) | \(e\left(\frac{99}{100}\right)\) | \(e\left(\frac{59}{100}\right)\) | \(e\left(\frac{53}{100}\right)\) | \(e\left(\frac{81}{100}\right)\) | \(e\left(\frac{37}{50}\right)\) | \(e\left(\frac{13}{25}\right)\) | \(e\left(\frac{11}{50}\right)\) |