Error: 2.2.1.d655360 is not the label of a Sato-Tate group currently in the database.
Basic properties
| Modulus: | \(824\) |
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| Conductor: | \(824\) |
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| Order: | \(34\) |
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| Real: | no |
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| Primitive: | yes |
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| Minimal: | yes | |
| Parity: | odd |
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Galois orbit 824.r
\(\chi_{824}(37,\cdot)\) \(\chi_{824}(69,\cdot)\) \(\chi_{824}(125,\cdot)\) \(\chi_{824}(197,\cdot)\) \(\chi_{824}(237,\cdot)\) \(\chi_{824}(245,\cdot)\) \(\chi_{824}(301,\cdot)\) \(\chi_{824}(333,\cdot)\) \(\chi_{824}(389,\cdot)\) \(\chi_{824}(485,\cdot)\) \(\chi_{824}(501,\cdot)\) \(\chi_{824}(525,\cdot)\) \(\chi_{824}(557,\cdot)\) \(\chi_{824}(605,\cdot)\) \(\chi_{824}(621,\cdot)\) \(\chi_{824}(645,\cdot)\)
Related number fields
| Field of values: | \(\Q(\zeta_{17})\) |
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| Fixed field: | 34.0.5972527995560101978998241403889034536661667426215815029727657768716011005336879104.1 |
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Values on generators
\((207,413,417)\) → \((1,-1,e\left(\frac{25}{34}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 824 }(389, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3}{17}\right)\) | \(e\left(\frac{4}{17}\right)\) | \(e\left(\frac{16}{17}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{6}{17}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{2}{17}\right)\) |