Basic properties
Modulus: | \(5600\) | |
Conductor: | \(5600\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Order: | \(120\) | 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
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Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
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Galois orbit 5600.io
\(\chi_{5600}(131,\cdot)\) \(\chi_{5600}(171,\cdot)\) \(\chi_{5600}(411,\cdot)\) \(\chi_{5600}(691,\cdot)\) \(\chi_{5600}(731,\cdot)\) \(\chi_{5600}(971,\cdot)\) \(\chi_{5600}(1011,\cdot)\) \(\chi_{5600}(1291,\cdot)\) \(\chi_{5600}(1531,\cdot)\) \(\chi_{5600}(1571,\cdot)\) \(\chi_{5600}(1811,\cdot)\) \(\chi_{5600}(2091,\cdot)\) \(\chi_{5600}(2131,\cdot)\) \(\chi_{5600}(2371,\cdot)\) \(\chi_{5600}(2411,\cdot)\) \(\chi_{5600}(2691,\cdot)\) \(\chi_{5600}(2931,\cdot)\) \(\chi_{5600}(2971,\cdot)\) \(\chi_{5600}(3211,\cdot)\) \(\chi_{5600}(3491,\cdot)\) \(\chi_{5600}(3531,\cdot)\) \(\chi_{5600}(3771,\cdot)\) \(\chi_{5600}(3811,\cdot)\) \(\chi_{5600}(4091,\cdot)\) \(\chi_{5600}(4331,\cdot)\) \(\chi_{5600}(4371,\cdot)\) \(\chi_{5600}(4611,\cdot)\) \(\chi_{5600}(4891,\cdot)\) \(\chi_{5600}(4931,\cdot)\) \(\chi_{5600}(5171,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((351,4901,5377,801)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{2}{5}\right),e\left(\frac{5}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 5600 }(131, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{29}{40}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{8}{15}\right)\) |