Basic properties
Modulus: | \(6025\) | |
Conductor: | \(6025\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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.ht
\(\chi_{6025}(213,\cdot)\) \(\chi_{6025}(508,\cdot)\) \(\chi_{6025}(1278,\cdot)\) \(\chi_{6025}(1353,\cdot)\) \(\chi_{6025}(1827,\cdot)\) \(\chi_{6025}(2433,\cdot)\) \(\chi_{6025}(2438,\cdot)\) \(\chi_{6025}(2467,\cdot)\) \(\chi_{6025}(2503,\cdot)\) \(\chi_{6025}(2548,\cdot)\) \(\chi_{6025}(2578,\cdot)\) \(\chi_{6025}(2672,\cdot)\) \(\chi_{6025}(2752,\cdot)\) \(\chi_{6025}(3048,\cdot)\) \(\chi_{6025}(3238,\cdot)\) \(\chi_{6025}(3272,\cdot)\) \(\chi_{6025}(3317,\cdot)\) \(\chi_{6025}(3833,\cdot)\) \(\chi_{6025}(4423,\cdot)\) \(\chi_{6025}(4462,\cdot)\) \(\chi_{6025}(4562,\cdot)\) \(\chi_{6025}(4777,\cdot)\) \(\chi_{6025}(4837,\cdot)\) \(\chi_{6025}(4922,\cdot)\) \(\chi_{6025}(4923,\cdot)\) \(\chi_{6025}(4937,\cdot)\) \(\chi_{6025}(5438,\cdot)\) \(\chi_{6025}(5522,\cdot)\) \(\chi_{6025}(5758,\cdot)\) \(\chi_{6025}(5817,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((2652,2176)\) → \((e\left(\frac{1}{20}\right),e\left(\frac{53}{80}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
\( \chi_{ 6025 }(2752, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{7}{80}\right)\) |