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Degree	Signature	Class number	Class group structure	CM field
Ramified prime count	Ramified	Unramified primes	Galois group	Is Galois
Discriminant	Root discriminant	Regulator	Intermediate field	$p$-adic completions
Monogenic	Index	Ines. \(p\)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
10.0.209352647.1	x^10 - 3x^9 + 7x^8 - 11x^7 + 13x^6 - 12x^5 + 9x^4 - 5x^3 + 3x^2 - 2x + 1	$10$	[0,5]	$-\,7^{2}\cdot 23\cdot 431^{2}$	$3$	$6.79341030426$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.568036883757$
10.0.212309359.1	x^10 - 3x^9 + 5x^8 - 7x^7 + 9x^6 - 10x^5 + 9x^4 - 7x^3 + 5x^2 - 2x + 1	$10$	[0,5]	$-\,31\cdot 2617^{2}$	$2$	$6.80294428088$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.572857558707$
10.0.214816879.1	x^10 - 2x^9 + 4x^8 - 7x^7 + 9x^6 - 10x^5 + 10x^4 - 8x^3 + 6x^2 - 3x + 1	$10$	[0,5]	$-\,17^{2}\cdot 79\cdot 97^{2}$	$3$	$6.81093664096$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.577674891408$
10.0.220168975.1	x^10 - x^9 - x^8 + 2x^7 - x^6 - x^5 + 4x^4 - x^3 - 3x^2 + x + 1	$10$	[0,5]	$-\,5^{2}\cdot 13^{2}\cdot 31\cdot 41^{2}$	$4$	$6.82771857501$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.586605631071$
10.0.224198759.1	x^10 - x^9 - 2x^8 + 4x^7 - 4x^5 + 3x^4 + x^3 - 2x^2 + 1	$10$	[0,5]	$-\,71\cdot 1777^{2}$	$2$	$6.84011369338$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.59340069383$
10.0.226876987.1	x^10 - 2x^9 + 3x^8 - 3x^7 + 2x^6 + x^5 - x^4 - 3x^3 + 6x^2 - 4x + 1	$10$	[0,5]	$-\,43\cdot 2297^{2}$	$2$	$6.8482411447$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.597809920275$
10.0.262091507.1	x^10 - x^9 - 2x^6 + 3x^5 + 3x^4 - 4x^3 - 2x^2 + 2x + 1	$10$	[0,5]	$-\,83\cdot 1777^{2}$	$2$	$6.94776778804$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.656821013577$
10.0.263786699.1	x^10 - 2x^9 + 2x^8 - 2x^7 + 4x^6 - 5x^5 + 4x^4 - 2x^3 + 3x^2 - 3x + 1	$10$	[0,5]	$-\,11\cdot 59^{2}\cdot 83^{2}$	$3$	$6.95224853606$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.663236848943$
10.0.277010267.1	x^10 - 2x^9 + x^8 + 2x^7 - 3x^6 + 3x^5 - 2x^4 + 3x^2 - 3x + 1	$10$	[0,5]	$-\,107\cdot 1609^{2}$	$2$	$6.98633789626$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.679993136866$
10.0.290954507.1	x^10 - x^9 + 2x^8 + 2x^7 - x^6 + 4x^5 + 4x^4 + 2x^2 + 3x + 1	$10$	[0,5]	$-\,17^{2}\cdot 97^{2}\cdot 107$	$3$	$7.02073383839$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.702250275284$
10.0.325246087.1	x^10 - 3x^9 + 6x^8 - 10x^7 + 13x^6 - 13x^5 + 11x^4 - 8x^3 + 5x^2 - 2x + 1	$10$	[0,5]	$-\,103\cdot 1777^{2}$	$2$	$7.09939283685$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.752440468285$
10.0.328787887.1	x^10 - 2x^9 + 3x^8 - 3x^7 + 5x^6 - 6x^5 + 3x^4 - 3x^3 + 3x^2 - x + 1	$10$	[0,5]	$-\,127\cdot 1609^{2}$	$2$	$7.10708616721$			not computed	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.761759694633$
10.0.328787887.2	x^10 - 2x^9 + 3x^6 - x^5 - x^4 - 2x^3 + 2x^2 + 1	$10$	[0,5]	$-\,127\cdot 1609^{2}$	$2$	$7.10708616721$			not computed	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.76915406635$
10.0.330230659.1	x^10 - x^9 + x^8 + 2x^7 - 3x^6 + 2x^5 - 2x^3 + x^2 - x + 1	$10$	[0,5]	$-\,11^{2}\cdot 19\cdot 379^{2}$	$3$	$7.11019872499$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.770950046286$
10.0.339143411.1	x^10 - 3x^9 + 5x^8 - 6x^7 + 6x^6 - 4x^5 + x^4 + 2x^3 - 2x^2 + 1	$10$	[0,5]	$-\,131\cdot 1609^{2}$	$2$	$7.12915961712$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.777396737365$
10.0.359854459.1	x^10 - 3x^9 + 6x^8 - 9x^7 + 11x^6 - 10x^5 + 8x^4 - 5x^3 + 3x^2 - 2x + 1	$10$	[0,5]	$-\,139\cdot 1609^{2}$	$2$	$7.17154435557$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.81336454205$
10.0.364067099.1	x^10 - x^9 - 2x^6 + x^5 + 2x^4 - 2x^3 + 3x^2 - 2x + 1	$10$	[0,5]	$-\,11^{3}\cdot 523^{2}$	$2$	$7.17989583039$			not computed	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.826936802139$
10.0.370209983.1	x^10 + 2x^8 + 3x^6 - x^5 + 3x^4 + 2x^2 + 1	$10$	[0,5]	$-\,11\cdot 13\cdot 1609^{2}$	$3$	$7.19191941593$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.824223583763$
10.0.377968939.1	x^10 - 2x^9 + 4x^8 - 5x^7 + 5x^6 - 6x^5 + 7x^4 - 4x^3 + 3x^2 - 3x + 1	$10$	[0,5]	$-\,17^{2}\cdot 97^{2}\cdot 139$	$3$	$7.20685212745$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.830618920882$
10.0.379908823.1	x^10 + x^8 - x^7 - x^5 - x^3 + x^2 + 1	$10$	[0,5]	$-\,7\cdot 53^{2}\cdot 139^{2}$	$3$	$7.21054244994$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.856501846271$
10.0.386633299.1	x^10 - x^9 + 2x^8 - 2x^7 + 2x^6 - 3x^5 + 2x^4 - 2x^3 + 2x^2 - x + 1	$10$	[0,5]	$-\,13^{2}\cdot 19\cdot 347^{2}$	$3$	$7.22320474844$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.843223617742$
10.0.386864567.1	x^10 - x^9 + 3x^8 - x^7 + 4x^6 + 5x^4 + x^3 + 3x^2 + x + 1	$10$	[0,5]	$-\,19^{2}\cdot 47\cdot 151^{2}$	$3$	$7.22363669433$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.840987825694$
10.0.432343127.1	x^10 - 3x^9 + 5x^8 - 5x^7 + 5x^6 - 6x^5 + 7x^4 - 5x^3 + 3x^2 - 2x + 1	$10$	[0,5]	$-\,167\cdot 1609^{2}$	$2$	$7.30437154456$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.905139783856$
10.0.437865967.1	x^10 - x^9 - x^8 + 2x^7 + 2x^6 - 5x^5 + 2x^4 + 2x^3 - x^2 - x + 1	$10$	[0,5]	$-\,7\cdot 11^{2}\cdot 719^{2}$	$3$	$7.31364909208$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.935373385345$
10.0.437925347.1	x^10 - 3x^9 + 6x^8 - 10x^7 + 14x^6 - 15x^5 + 14x^4 - 10x^3 + 6x^2 - 3x + 1	$10$	[0,5]	$-\,83\cdot 2297^{2}$	$2$	$7.31374826808$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.904836799867$
10.0.440866291.1	x^10 - x^9 + x^8 - 3x^7 + 3x^6 - x^5 + 3x^4 - 3x^3 + x^2 - x + 1	$10$	[0,5]	$-\,19\cdot 4817^{2}$	$2$	$7.3186451295$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.924915033309$
10.0.443229763.1	x^10 - 3x^9 + 4x^8 - 4x^7 + 4x^6 - 5x^4 + 4x^3 - x + 1	$10$	[0,5]	$-\,17^{2}\cdot 97^{2}\cdot 163$	$3$	$7.32255920172$			not computed	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.943232786232$
10.0.449448427.1	x^10 - 2x^9 + 2x^8 - 3x^7 + 8x^6 - 11x^5 + 8x^4 - 3x^3 + 2x^2 - 2x + 1	$10$	[0,5]	$-\,43\cdot 53^{2}\cdot 61^{2}$	$3$	$7.33276870618$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.932430924092$
10.0.454106567.1	x^10 - 2x^9 + 2x^8 - x^7 + 2x^6 - 3x^5 + x^4 + 2x^3 - x^2 - x + 1	$10$	[0,5]	$-\,17^{2}\cdot 97^{2}\cdot 167$	$3$	$7.34033326652$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.940846654649$
10.0.476322007.1	x^10 - x^9 - 2x^8 + 4x^7 + x^6 - 5x^5 + x^4 + 4x^3 - x^2 - 2x + 1	$10$	[0,5]	$-\,7\cdot 73^{2}\cdot 113^{2}$	$3$	$7.37547617968$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$1.00383062843$
10.0.484120747.1	x^10 - x^9 + x^8 - x^7 + x^6 - 4x^5 + 3x^4 - x^3 + x + 1	$10$	[0,5]	$-\,11\cdot 17\cdot 1609^{2}$	$3$	$7.38746386304$			not computed	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.980166278371$
10.0.484176016.1	x^10 - x^8 + x^6 + 2x^2 + 1	$10$	[0,5]	$-\,2^{4}\cdot 5501^{2}$	$2$	$7.3875481967$			not computed	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$1.08216442445$
10.0.485605687.1	x^10 - 3x^9 + 5x^8 - 6x^7 + 7x^6 - 7x^5 + 6x^4 - 5x^3 + 4x^2 - 2x + 1	$10$	[0,5]	$-\,7\cdot 8329^{2}$	$2$	$7.3897266928$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$1.01495612987$
10.0.486045407.1	x^10 - x^9 + 2x^8 - 4x^7 + 5x^6 - 6x^5 + 7x^4 - 6x^3 + 5x^2 - 3x + 1	$10$	[0,5]	$-\,23\cdot 4597^{2}$	$2$	$7.3903955662$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$1.08406425262$
10.0.486736979.1	x^10 - 2x^9 + 3x^8 - 4x^7 + 7x^6 - 10x^5 + 9x^4 - 4x^3 + x^2 - x + 1	$10$	[0,5]	$-\,17^{2}\cdot 97^{2}\cdot 179$	$3$	$7.39144643944$			not computed	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.9800046881$
10.0.486736979.2	x^10 - 2x^9 - 2x^8 + 4x^7 + 4x^6 - 4x^5 - 4x^4 + x^3 + x^2 + x + 1	$10$	[0,5]	$-\,17^{2}\cdot 97^{2}\cdot 179$	$3$	$7.39144643944$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.974241656128$
10.0.501239855.1	x^10 - x^9 - x^8 + x^7 + x^5 + x^4 - 2x^3 - x^2 + x + 1	$10$	[0,5]	$-\,5\cdot 19\cdot 2297^{2}$	$3$	$7.41318024205$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$1.05729447918$
10.0.508490587.1	x^10 + 2x^8 - x^7 + 4x^6 - x^5 + 4x^4 - x^3 + 2x^2 + 1	$10$	[0,5]	$-\,11\cdot 17^{3}\cdot 97^{2}$	$3$	$7.42383467466$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.998345765058$
10.0.514709827.1	x^10 - 4x^9 + 9x^8 - 14x^7 + 16x^6 - 13x^5 + 8x^4 - 4x^3 + 2x^2 - x + 1	$10$	[0,5]	$-\,163\cdot 1777^{2}$	$2$	$7.43286501771$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$1.01758301301$
10.0.526794304.1	x^10 - 4x^9 + 8x^8 - 9x^7 + 8x^6 - 8x^5 + 8x^4 - 4x^3 + x^2 - x + 1	$10$	[0,5]	$-\,2^{6}\cdot 19^{2}\cdot 151^{2}$	$3$	$7.45013439281$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$1.13996042827$
10.0.526794304.2	x^10 + 3x^6 - x^4 + 4x^2 + 1	$10$	[0,5]	$-\,2^{6}\cdot 19^{2}\cdot 151^{2}$	$3$	$7.45013439281$			not computed	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$1.0369077211$
10.0.530439175.1	x^10 - x^9 + x^7 + x^6 - 3x^5 + x^4 + x^3 - x + 1	$10$	[0,5]	$-\,5^{2}\cdot 7\cdot 1741^{2}$	$3$	$7.4552731348$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$1.053486414$
10.0.546253891.1	x^10 - 2x^9 + 2x^8 - x^7 - 2x^6 + 2x^5 - 2x^3 + 4x^2 - 2x + 1	$10$	[0,5]	$-\,211\cdot 1609^{2}$	$2$	$7.47720786893$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$1.05442559996$
10.0.552906407.1	x^10 - x^9 + 2x^8 - 3x^7 + 3x^6 - 3x^5 + 3x^4 - 3x^3 + 2x^2 - x + 1	$10$	[0,5]	$-\,23\cdot 4903^{2}$	$2$	$7.48626441349$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$1.04972698416$
10.0.562874607.1	x^10 - 4x^9 + 8x^8 - 11x^7 + 14x^6 - 15x^5 + 11x^4 - 4x^3 + x^2 - x + 1	$10$	[0,5]	$-\,3^{2}\cdot 17^{2}\cdot 23\cdot 97^{2}$	$4$	$7.49965293275$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$1.07103275549$
10.0.562973339.1	x^10 - x^9 + 3x^8 - 2x^7 + 6x^6 - 3x^5 + 6x^4 - 2x^3 + 4x^2 + 1	$10$	[0,5]	$-\,59\cdot 3089^{2}$	$2$	$7.49978447134$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$1.0804509124$
10.0.587675987.1	x^10 - 2x^8 + 2x^6 - x^5 - 2x^4 - x^3 + x^2 + 2x + 1	$10$	[0,5]	$-\,227\cdot 1609^{2}$	$2$	$7.53206040953$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$1.11466952529$
10.0.590495323.1	x^10 - x^9 + 2x^8 - 2x^7 + 2x^6 - 3x^5 + 3x^4 - 4x^3 + 4x^2 - 2x + 1	$10$	[0,5]	$-\,11\cdot 17\cdot 1777^{2}$	$3$	$7.53566608756$			not computed	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$1.09025803881$
10.0.592440064.1	x^10 - x^9 + 3x^8 - 4x^7 + 5x^6 - 7x^5 + 7x^4 - 6x^3 + 5x^2 - 3x + 1	$10$	[0,5]	$-\,2^{8}\cdot 19\cdot 349^{2}$	$3$	$7.5381442181$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$1.22778512725$
10.0.621349399.1	x^10 - x^9 - x^8 + 3x^6 - 2x^5 - 3x^4 + 4x^3 - x + 1	$10$	[0,5]	$-\,11^{4}\cdot 31\cdot 37^{2}$	$3$	$7.57414453312$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$1.26310066768$

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