Basic properties
| Modulus: | \(6171\) | |
| Conductor: | \(187\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{187}(40,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6171.ca
\(\chi_{6171}(40,\cdot)\) \(\chi_{6171}(112,\cdot)\) \(\chi_{6171}(403,\cdot)\) \(\chi_{6171}(481,\cdot)\) \(\chi_{6171}(838,\cdot)\) \(\chi_{6171}(844,\cdot)\) \(\chi_{6171}(1129,\cdot)\) \(\chi_{6171}(1183,\cdot)\) \(\chi_{6171}(1201,\cdot)\) \(\chi_{6171}(1570,\cdot)\) \(\chi_{6171}(1909,\cdot)\) \(\chi_{6171}(1927,\cdot)\) \(\chi_{6171}(1933,\cdot)\) \(\chi_{6171}(2272,\cdot)\) \(\chi_{6171}(2290,\cdot)\) \(\chi_{6171}(2581,\cdot)\) \(\chi_{6171}(2659,\cdot)\) \(\chi_{6171}(2944,\cdot)\) \(\chi_{6171}(2998,\cdot)\) \(\chi_{6171}(3016,\cdot)\) \(\chi_{6171}(3361,\cdot)\) \(\chi_{6171}(4087,\cdot)\) \(\chi_{6171}(4111,\cdot)\) \(\chi_{6171}(4396,\cdot)\) \(\chi_{6171}(4468,\cdot)\) \(\chi_{6171}(4474,\cdot)\) \(\chi_{6171}(4831,\cdot)\) \(\chi_{6171}(5122,\cdot)\) \(\chi_{6171}(5485,\cdot)\) \(\chi_{6171}(5539,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((4115,970,2179)\) → \((1,e\left(\frac{7}{10}\right),e\left(\frac{15}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 6171 }(40, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{39}{80}\right)\) | \(e\left(\frac{17}{80}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{3}{80}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{9}{40}\right)\) |