Basic properties
Modulus: | \(6400\) | |
Conductor: | \(1600\) | 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 \(\chi_{1600}(1309,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6400.dg
\(\chi_{6400}(209,\cdot)\) \(\chi_{6400}(369,\cdot)\) \(\chi_{6400}(529,\cdot)\) \(\chi_{6400}(689,\cdot)\) \(\chi_{6400}(1009,\cdot)\) \(\chi_{6400}(1169,\cdot)\) \(\chi_{6400}(1329,\cdot)\) \(\chi_{6400}(1489,\cdot)\) \(\chi_{6400}(1809,\cdot)\) \(\chi_{6400}(1969,\cdot)\) \(\chi_{6400}(2129,\cdot)\) \(\chi_{6400}(2289,\cdot)\) \(\chi_{6400}(2609,\cdot)\) \(\chi_{6400}(2769,\cdot)\) \(\chi_{6400}(2929,\cdot)\) \(\chi_{6400}(3089,\cdot)\) \(\chi_{6400}(3409,\cdot)\) \(\chi_{6400}(3569,\cdot)\) \(\chi_{6400}(3729,\cdot)\) \(\chi_{6400}(3889,\cdot)\) \(\chi_{6400}(4209,\cdot)\) \(\chi_{6400}(4369,\cdot)\) \(\chi_{6400}(4529,\cdot)\) \(\chi_{6400}(4689,\cdot)\) \(\chi_{6400}(5009,\cdot)\) \(\chi_{6400}(5169,\cdot)\) \(\chi_{6400}(5329,\cdot)\) \(\chi_{6400}(5489,\cdot)\) \(\chi_{6400}(5809,\cdot)\) \(\chi_{6400}(5969,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((4351,4101,5377)\) → \((1,e\left(\frac{11}{16}\right),e\left(\frac{7}{10}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
\( \chi_{ 6400 }(209, a) \) | \(1\) | \(1\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{49}{80}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{33}{80}\right)\) | \(e\left(\frac{27}{80}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{71}{80}\right)\) |