Basic properties
Modulus: | \(6025\) | |
Conductor: | \(1205\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{1205}(1182,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6025.ha
\(\chi_{6025}(43,\cdot)\) \(\chi_{6025}(343,\cdot)\) \(\chi_{6025}(943,\cdot)\) \(\chi_{6025}(1057,\cdot)\) \(\chi_{6025}(1132,\cdot)\) \(\chi_{6025}(1182,\cdot)\) \(\chi_{6025}(1582,\cdot)\) \(\chi_{6025}(2068,\cdot)\) \(\chi_{6025}(2293,\cdot)\) \(\chi_{6025}(2307,\cdot)\) \(\chi_{6025}(2382,\cdot)\) \(\chi_{6025}(2393,\cdot)\) \(\chi_{6025}(2443,\cdot)\) \(\chi_{6025}(2618,\cdot)\) \(\chi_{6025}(2668,\cdot)\) \(\chi_{6025}(2768,\cdot)\) \(\chi_{6025}(2807,\cdot)\) \(\chi_{6025}(2993,\cdot)\) \(\chi_{6025}(3107,\cdot)\) \(\chi_{6025}(3882,\cdot)\) \(\chi_{6025}(4118,\cdot)\) \(\chi_{6025}(4182,\cdot)\) \(\chi_{6025}(4607,\cdot)\) \(\chi_{6025}(4682,\cdot)\) \(\chi_{6025}(4718,\cdot)\) \(\chi_{6025}(5018,\cdot)\) \(\chi_{6025}(5118,\cdot)\) \(\chi_{6025}(5407,\cdot)\) \(\chi_{6025}(5807,\cdot)\) \(\chi_{6025}(5857,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((2652,2176)\) → \((i,e\left(\frac{59}{80}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 6025 }(1182, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(-i\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{33}{80}\right)\) |