Basic properties
| Modulus: | \(6040\) | |
| Conductor: | \(6040\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(100\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6040.em
\(\chi_{6040}(53,\cdot)\) \(\chi_{6040}(293,\cdot)\) \(\chi_{6040}(477,\cdot)\) \(\chi_{6040}(677,\cdot)\) \(\chi_{6040}(877,\cdot)\) \(\chi_{6040}(933,\cdot)\) \(\chi_{6040}(973,\cdot)\) \(\chi_{6040}(1013,\cdot)\) \(\chi_{6040}(1037,\cdot)\) \(\chi_{6040}(1117,\cdot)\) \(\chi_{6040}(1853,\cdot)\) \(\chi_{6040}(1877,\cdot)\) \(\chi_{6040}(2117,\cdot)\) \(\chi_{6040}(2197,\cdot)\) \(\chi_{6040}(2293,\cdot)\) \(\chi_{6040}(2517,\cdot)\) \(\chi_{6040}(2637,\cdot)\) \(\chi_{6040}(2797,\cdot)\) \(\chi_{6040}(2893,\cdot)\) \(\chi_{6040}(3077,\cdot)\) \(\chi_{6040}(3093,\cdot)\) \(\chi_{6040}(3197,\cdot)\) \(\chi_{6040}(3293,\cdot)\) \(\chi_{6040}(3453,\cdot)\) \(\chi_{6040}(3533,\cdot)\) \(\chi_{6040}(3677,\cdot)\) \(\chi_{6040}(3917,\cdot)\) \(\chi_{6040}(4293,\cdot)\) \(\chi_{6040}(4533,\cdot)\) \(\chi_{6040}(4557,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((1511,3021,2417,761)\) → \((1,-1,-i,e\left(\frac{43}{50}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 6040 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{100}\right)\) | \(e\left(\frac{37}{100}\right)\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{17}{50}\right)\) | \(e\left(\frac{1}{100}\right)\) | \(e\left(\frac{63}{100}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{23}{100}\right)\) |