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.id
\(\chi_{5600}(19,\cdot)\) \(\chi_{5600}(59,\cdot)\) \(\chi_{5600}(339,\cdot)\) \(\chi_{5600}(579,\cdot)\) \(\chi_{5600}(619,\cdot)\) \(\chi_{5600}(859,\cdot)\) \(\chi_{5600}(1139,\cdot)\) \(\chi_{5600}(1179,\cdot)\) \(\chi_{5600}(1419,\cdot)\) \(\chi_{5600}(1459,\cdot)\) \(\chi_{5600}(1739,\cdot)\) \(\chi_{5600}(1979,\cdot)\) \(\chi_{5600}(2019,\cdot)\) \(\chi_{5600}(2259,\cdot)\) \(\chi_{5600}(2539,\cdot)\) \(\chi_{5600}(2579,\cdot)\) \(\chi_{5600}(2819,\cdot)\) \(\chi_{5600}(2859,\cdot)\) \(\chi_{5600}(3139,\cdot)\) \(\chi_{5600}(3379,\cdot)\) \(\chi_{5600}(3419,\cdot)\) \(\chi_{5600}(3659,\cdot)\) \(\chi_{5600}(3939,\cdot)\) \(\chi_{5600}(3979,\cdot)\) \(\chi_{5600}(4219,\cdot)\) \(\chi_{5600}(4259,\cdot)\) \(\chi_{5600}(4539,\cdot)\) \(\chi_{5600}(4779,\cdot)\) \(\chi_{5600}(4819,\cdot)\) \(\chi_{5600}(5059,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((351,4901,5377,801)\) → \((-1,e\left(\frac{7}{8}\right),e\left(\frac{3}{10}\right),e\left(\frac{1}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) |
\( \chi_{ 5600 }(339, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{120}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{1}{15}\right)\) |