Basic properties
Modulus: | \(6025\) | |
Conductor: | \(6025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(80\) | 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 6025.ho
\(\chi_{6025}(377,\cdot)\) \(\chi_{6025}(697,\cdot)\) \(\chi_{6025}(863,\cdot)\) \(\chi_{6025}(1177,\cdot)\) \(\chi_{6025}(1472,\cdot)\) \(\chi_{6025}(1503,\cdot)\) \(\chi_{6025}(1708,\cdot)\) \(\chi_{6025}(1788,\cdot)\) \(\chi_{6025}(2242,\cdot)\) \(\chi_{6025}(2308,\cdot)\) \(\chi_{6025}(2317,\cdot)\) \(\chi_{6025}(2353,\cdot)\) \(\chi_{6025}(3397,\cdot)\) \(\chi_{6025}(3402,\cdot)\) \(\chi_{6025}(3467,\cdot)\) \(\chi_{6025}(3498,\cdot)\) \(\chi_{6025}(3512,\cdot)\) \(\chi_{6025}(3542,\cdot)\) \(\chi_{6025}(3598,\cdot)\) \(\chi_{6025}(3813,\cdot)\) \(\chi_{6025}(3873,\cdot)\) \(\chi_{6025}(3958,\cdot)\) \(\chi_{6025}(3973,\cdot)\) \(\chi_{6025}(4012,\cdot)\) \(\chi_{6025}(4202,\cdot)\) \(\chi_{6025}(4558,\cdot)\) \(\chi_{6025}(4797,\cdot)\) \(\chi_{6025}(4853,\cdot)\) \(\chi_{6025}(4863,\cdot)\) \(\chi_{6025}(5028,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((2652,2176)\) → \((e\left(\frac{1}{20}\right),e\left(\frac{27}{80}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 6025 }(4202, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{47}{80}\right)\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{13}{16}\right)\) |