Basic properties
Modulus: | \(4800\) | |
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 \(\chi_{1600}(1317,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4800.fb
\(\chi_{4800}(13,\cdot)\) \(\chi_{4800}(37,\cdot)\) \(\chi_{4800}(253,\cdot)\) \(\chi_{4800}(277,\cdot)\) \(\chi_{4800}(517,\cdot)\) \(\chi_{4800}(733,\cdot)\) \(\chi_{4800}(973,\cdot)\) \(\chi_{4800}(997,\cdot)\) \(\chi_{4800}(1213,\cdot)\) \(\chi_{4800}(1237,\cdot)\) \(\chi_{4800}(1453,\cdot)\) \(\chi_{4800}(1477,\cdot)\) \(\chi_{4800}(1717,\cdot)\) \(\chi_{4800}(1933,\cdot)\) \(\chi_{4800}(2173,\cdot)\) \(\chi_{4800}(2197,\cdot)\) \(\chi_{4800}(2413,\cdot)\) \(\chi_{4800}(2437,\cdot)\) \(\chi_{4800}(2653,\cdot)\) \(\chi_{4800}(2677,\cdot)\) \(\chi_{4800}(2917,\cdot)\) \(\chi_{4800}(3133,\cdot)\) \(\chi_{4800}(3373,\cdot)\) \(\chi_{4800}(3397,\cdot)\) \(\chi_{4800}(3613,\cdot)\) \(\chi_{4800}(3637,\cdot)\) \(\chi_{4800}(3853,\cdot)\) \(\chi_{4800}(3877,\cdot)\) \(\chi_{4800}(4117,\cdot)\) \(\chi_{4800}(4333,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((4351,901,1601,577)\) → \((1,e\left(\frac{9}{16}\right),1,e\left(\frac{13}{20}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 4800 }(2917, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{17}{80}\right)\) | \(e\left(\frac{63}{80}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{51}{80}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{39}{80}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{19}{40}\right)\) |