Basic properties
Modulus: | \(9600\) | |
Conductor: | \(3200\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(160\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | no, induced from \(\chi_{3200}(1021,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 9600.gk
\(\chi_{9600}(61,\cdot)\) \(\chi_{9600}(181,\cdot)\) \(\chi_{9600}(421,\cdot)\) \(\chi_{9600}(541,\cdot)\) \(\chi_{9600}(661,\cdot)\) \(\chi_{9600}(781,\cdot)\) \(\chi_{9600}(1021,\cdot)\) \(\chi_{9600}(1141,\cdot)\) \(\chi_{9600}(1261,\cdot)\) \(\chi_{9600}(1381,\cdot)\) \(\chi_{9600}(1621,\cdot)\) \(\chi_{9600}(1741,\cdot)\) \(\chi_{9600}(1861,\cdot)\) \(\chi_{9600}(1981,\cdot)\) \(\chi_{9600}(2221,\cdot)\) \(\chi_{9600}(2341,\cdot)\) \(\chi_{9600}(2461,\cdot)\) \(\chi_{9600}(2581,\cdot)\) \(\chi_{9600}(2821,\cdot)\) \(\chi_{9600}(2941,\cdot)\) \(\chi_{9600}(3061,\cdot)\) \(\chi_{9600}(3181,\cdot)\) \(\chi_{9600}(3421,\cdot)\) \(\chi_{9600}(3541,\cdot)\) \(\chi_{9600}(3661,\cdot)\) \(\chi_{9600}(3781,\cdot)\) \(\chi_{9600}(4021,\cdot)\) \(\chi_{9600}(4141,\cdot)\) \(\chi_{9600}(4261,\cdot)\) \(\chi_{9600}(4381,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{160})$ |
Fixed field: | Number field defined by a degree 160 polynomial (not computed) |
Values on generators
\((4351,901,6401,5377)\) → \((1,e\left(\frac{3}{32}\right),1,e\left(\frac{3}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 9600 }(1021, a) \) | \(1\) | \(1\) | \(e\left(\frac{15}{16}\right)\) | \(e\left(\frac{91}{160}\right)\) | \(e\left(\frac{129}{160}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{153}{160}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{117}{160}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{119}{160}\right)\) | \(e\left(\frac{17}{80}\right)\) |