Basic properties
Modulus: | \(5166\) | |
Conductor: | \(2583\) | 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: | no, induced from \(\chi_{2583}(65,\cdot)\) | 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 5166.fo
\(\chi_{5166}(65,\cdot)\) \(\chi_{5166}(95,\cdot)\) \(\chi_{5166}(317,\cdot)\) \(\chi_{5166}(347,\cdot)\) \(\chi_{5166}(473,\cdot)\) \(\chi_{5166}(725,\cdot)\) \(\chi_{5166}(977,\cdot)\) \(\chi_{5166}(1073,\cdot)\) \(\chi_{5166}(1325,\cdot)\) \(\chi_{5166}(1577,\cdot)\) \(\chi_{5166}(1703,\cdot)\) \(\chi_{5166}(1733,\cdot)\) \(\chi_{5166}(1955,\cdot)\) \(\chi_{5166}(1985,\cdot)\) \(\chi_{5166}(2207,\cdot)\) \(\chi_{5166}(2363,\cdot)\) \(\chi_{5166}(2489,\cdot)\) \(\chi_{5166}(2741,\cdot)\) \(\chi_{5166}(2963,\cdot)\) \(\chi_{5166}(3215,\cdot)\) \(\chi_{5166}(3245,\cdot)\) \(\chi_{5166}(3497,\cdot)\) \(\chi_{5166}(3593,\cdot)\) \(\chi_{5166}(3623,\cdot)\) \(\chi_{5166}(3719,\cdot)\) \(\chi_{5166}(3971,\cdot)\) \(\chi_{5166}(4001,\cdot)\) \(\chi_{5166}(4253,\cdot)\) \(\chi_{5166}(4475,\cdot)\) \(\chi_{5166}(4727,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((2297,2215,3655)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{1}{3}\right),e\left(\frac{13}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
\( \chi_{ 5166 }(65, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{49}{120}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) |