Basic properties
| Modulus: | \(6040\) | |
| Conductor: | \(3020\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(100\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3020}(127,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6040.el
\(\chi_{6040}(127,\cdot)\) \(\chi_{6040}(223,\cdot)\) \(\chi_{6040}(383,\cdot)\) \(\chi_{6040}(503,\cdot)\) \(\chi_{6040}(727,\cdot)\) \(\chi_{6040}(823,\cdot)\) \(\chi_{6040}(903,\cdot)\) \(\chi_{6040}(1143,\cdot)\) \(\chi_{6040}(1167,\cdot)\) \(\chi_{6040}(1903,\cdot)\) \(\chi_{6040}(1983,\cdot)\) \(\chi_{6040}(2007,\cdot)\) \(\chi_{6040}(2047,\cdot)\) \(\chi_{6040}(2087,\cdot)\) \(\chi_{6040}(2143,\cdot)\) \(\chi_{6040}(2343,\cdot)\) \(\chi_{6040}(2543,\cdot)\) \(\chi_{6040}(2727,\cdot)\) \(\chi_{6040}(2967,\cdot)\) \(\chi_{6040}(3143,\cdot)\) \(\chi_{6040}(3447,\cdot)\) \(\chi_{6040}(3567,\cdot)\) \(\chi_{6040}(3583,\cdot)\) \(\chi_{6040}(3847,\cdot)\) \(\chi_{6040}(4007,\cdot)\) \(\chi_{6040}(4127,\cdot)\) \(\chi_{6040}(4423,\cdot)\) \(\chi_{6040}(4447,\cdot)\) \(\chi_{6040}(4463,\cdot)\) \(\chi_{6040}(4503,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((1511,3021,2417,761)\) → \((-1,1,i,e\left(\frac{11}{25}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 6040 }(127, a) \) | \(1\) | \(1\) | \(e\left(\frac{89}{100}\right)\) | \(e\left(\frac{23}{100}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{43}{50}\right)\) | \(e\left(\frac{79}{100}\right)\) | \(e\left(\frac{77}{100}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{67}{100}\right)\) |