Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6019,2,Mod(1,6019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6019, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6019 = 13 \cdot 463 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6019.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.0619569766\) |
Analytic rank: | \(1\) |
Dimension: | \(108\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 6019.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.34535 | −1.65841 | −0.829205 | − | 0.558944i | \(-0.811207\pi\) | ||||
−0.829205 | + | 0.558944i | \(0.811207\pi\) | |||||||
\(3\) | −1.65067 | −0.953017 | −0.476508 | − | 0.879170i | \(-0.658098\pi\) | ||||
−0.476508 | + | 0.879170i | \(0.658098\pi\) | |||||||
\(4\) | 3.50065 | 1.75033 | ||||||||
\(5\) | −1.17678 | −0.526272 | −0.263136 | − | 0.964759i | \(-0.584757\pi\) | ||||
−0.263136 | + | 0.964759i | \(0.584757\pi\) | |||||||
\(6\) | 3.87140 | 1.58049 | ||||||||
\(7\) | 2.05341 | 0.776114 | 0.388057 | − | 0.921635i | \(-0.373146\pi\) | ||||
0.388057 | + | 0.921635i | \(0.373146\pi\) | |||||||
\(8\) | −3.51955 | −1.24435 | ||||||||
\(9\) | −0.275278 | −0.0917593 | ||||||||
\(10\) | 2.75996 | 0.872774 | ||||||||
\(11\) | 3.35882 | 1.01272 | 0.506361 | − | 0.862322i | \(-0.330990\pi\) | ||||
0.506361 | + | 0.862322i | \(0.330990\pi\) | |||||||
\(12\) | −5.77843 | −1.66809 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −4.81595 | −1.28712 | ||||||||
\(15\) | 1.94248 | 0.501546 | ||||||||
\(16\) | 1.25326 | 0.313315 | ||||||||
\(17\) | 4.47018 | 1.08418 | 0.542089 | − | 0.840321i | \(-0.317634\pi\) | ||||
0.542089 | + | 0.840321i | \(0.317634\pi\) | |||||||
\(18\) | 0.645622 | 0.152175 | ||||||||
\(19\) | 7.77434 | 1.78356 | 0.891778 | − | 0.452474i | \(-0.149458\pi\) | ||||
0.891778 | + | 0.452474i | \(0.149458\pi\) | |||||||
\(20\) | −4.11949 | −0.921147 | ||||||||
\(21\) | −3.38950 | −0.739650 | ||||||||
\(22\) | −7.87759 | −1.67951 | ||||||||
\(23\) | −7.71657 | −1.60902 | −0.804508 | − | 0.593942i | \(-0.797571\pi\) | ||||
−0.804508 | + | 0.593942i | \(0.797571\pi\) | |||||||
\(24\) | 5.80962 | 1.18588 | ||||||||
\(25\) | −3.61519 | −0.723038 | ||||||||
\(26\) | 2.34535 | 0.459960 | ||||||||
\(27\) | 5.40641 | 1.04046 | ||||||||
\(28\) | 7.18826 | 1.35845 | ||||||||
\(29\) | 1.46185 | 0.271459 | 0.135730 | − | 0.990746i | \(-0.456662\pi\) | ||||
0.135730 | + | 0.990746i | \(0.456662\pi\) | |||||||
\(30\) | −4.55578 | −0.831769 | ||||||||
\(31\) | −3.68184 | −0.661277 | −0.330639 | − | 0.943757i | \(-0.607264\pi\) | ||||
−0.330639 | + | 0.943757i | \(0.607264\pi\) | |||||||
\(32\) | 4.09977 | 0.724744 | ||||||||
\(33\) | −5.54431 | −0.965141 | ||||||||
\(34\) | −10.4841 | −1.79801 | ||||||||
\(35\) | −2.41640 | −0.408447 | ||||||||
\(36\) | −0.963653 | −0.160609 | ||||||||
\(37\) | 6.86030 | 1.12783 | 0.563913 | − | 0.825834i | \(-0.309295\pi\) | ||||
0.563913 | + | 0.825834i | \(0.309295\pi\) | |||||||
\(38\) | −18.2335 | −2.95787 | ||||||||
\(39\) | 1.65067 | 0.264319 | ||||||||
\(40\) | 4.14173 | 0.654865 | ||||||||
\(41\) | −4.73919 | −0.740136 | −0.370068 | − | 0.929005i | \(-0.620666\pi\) | ||||
−0.370068 | + | 0.929005i | \(0.620666\pi\) | |||||||
\(42\) | 7.94956 | 1.22664 | ||||||||
\(43\) | 4.69953 | 0.716671 | 0.358335 | − | 0.933593i | \(-0.383344\pi\) | ||||
0.358335 | + | 0.933593i | \(0.383344\pi\) | |||||||
\(44\) | 11.7581 | 1.77259 | ||||||||
\(45\) | 0.323941 | 0.0482903 | ||||||||
\(46\) | 18.0980 | 2.66841 | ||||||||
\(47\) | −9.86429 | −1.43885 | −0.719427 | − | 0.694568i | \(-0.755596\pi\) | ||||
−0.719427 | + | 0.694568i | \(0.755596\pi\) | |||||||
\(48\) | −2.06872 | −0.298594 | ||||||||
\(49\) | −2.78353 | −0.397646 | ||||||||
\(50\) | 8.47888 | 1.19909 | ||||||||
\(51\) | −7.37880 | −1.03324 | ||||||||
\(52\) | −3.50065 | −0.485453 | ||||||||
\(53\) | −4.33860 | −0.595952 | −0.297976 | − | 0.954573i | \(-0.596312\pi\) | ||||
−0.297976 | + | 0.954573i | \(0.596312\pi\) | |||||||
\(54\) | −12.6799 | −1.72552 | ||||||||
\(55\) | −3.95259 | −0.532967 | ||||||||
\(56\) | −7.22706 | −0.965757 | ||||||||
\(57\) | −12.8329 | −1.69976 | ||||||||
\(58\) | −3.42855 | −0.450191 | ||||||||
\(59\) | 0.235407 | 0.0306474 | 0.0153237 | − | 0.999883i | \(-0.495122\pi\) | ||||
0.0153237 | + | 0.999883i | \(0.495122\pi\) | |||||||
\(60\) | 6.79994 | 0.877868 | ||||||||
\(61\) | −0.187165 | −0.0239640 | −0.0119820 | − | 0.999928i | \(-0.503814\pi\) | ||||
−0.0119820 | + | 0.999928i | \(0.503814\pi\) | |||||||
\(62\) | 8.63518 | 1.09667 | ||||||||
\(63\) | −0.565257 | −0.0712157 | ||||||||
\(64\) | −12.1219 | −1.51524 | ||||||||
\(65\) | 1.17678 | 0.145961 | ||||||||
\(66\) | 13.0033 | 1.60060 | ||||||||
\(67\) | 1.31340 | 0.160458 | 0.0802289 | − | 0.996776i | \(-0.474435\pi\) | ||||
0.0802289 | + | 0.996776i | \(0.474435\pi\) | |||||||
\(68\) | 15.6485 | 1.89766 | ||||||||
\(69\) | 12.7375 | 1.53342 | ||||||||
\(70\) | 5.66731 | 0.677373 | ||||||||
\(71\) | −7.95224 | −0.943758 | −0.471879 | − | 0.881663i | \(-0.656424\pi\) | ||||
−0.471879 | + | 0.881663i | \(0.656424\pi\) | |||||||
\(72\) | 0.968855 | 0.114181 | ||||||||
\(73\) | −1.12431 | −0.131590 | −0.0657950 | − | 0.997833i | \(-0.520958\pi\) | ||||
−0.0657950 | + | 0.997833i | \(0.520958\pi\) | |||||||
\(74\) | −16.0898 | −1.87040 | ||||||||
\(75\) | 5.96750 | 0.689067 | ||||||||
\(76\) | 27.2153 | 3.12180 | ||||||||
\(77\) | 6.89702 | 0.785988 | ||||||||
\(78\) | −3.87140 | −0.438350 | ||||||||
\(79\) | −8.42207 | −0.947556 | −0.473778 | − | 0.880644i | \(-0.657110\pi\) | ||||
−0.473778 | + | 0.880644i | \(0.657110\pi\) | |||||||
\(80\) | −1.47481 | −0.164889 | ||||||||
\(81\) | −8.09839 | −0.899821 | ||||||||
\(82\) | 11.1150 | 1.22745 | ||||||||
\(83\) | 16.3277 | 1.79220 | 0.896100 | − | 0.443853i | \(-0.146389\pi\) | ||||
0.896100 | + | 0.443853i | \(0.146389\pi\) | |||||||
\(84\) | −11.8655 | −1.29463 | ||||||||
\(85\) | −5.26041 | −0.570572 | ||||||||
\(86\) | −11.0220 | −1.18853 | ||||||||
\(87\) | −2.41304 | −0.258705 | ||||||||
\(88\) | −11.8215 | −1.26018 | ||||||||
\(89\) | −13.9408 | −1.47772 | −0.738860 | − | 0.673859i | \(-0.764636\pi\) | ||||
−0.738860 | + | 0.673859i | \(0.764636\pi\) | |||||||
\(90\) | −0.759755 | −0.0800852 | ||||||||
\(91\) | −2.05341 | −0.215255 | ||||||||
\(92\) | −27.0130 | −2.81630 | ||||||||
\(93\) | 6.07751 | 0.630208 | ||||||||
\(94\) | 23.1352 | 2.38621 | ||||||||
\(95\) | −9.14868 | −0.938635 | ||||||||
\(96\) | −6.76738 | −0.690693 | ||||||||
\(97\) | 14.7783 | 1.50051 | 0.750257 | − | 0.661147i | \(-0.229930\pi\) | ||||
0.750257 | + | 0.661147i | \(0.229930\pi\) | |||||||
\(98\) | 6.52833 | 0.659461 | ||||||||
\(99\) | −0.924609 | −0.0929267 | ||||||||
\(100\) | −12.6555 | −1.26555 | ||||||||
\(101\) | −18.8061 | −1.87128 | −0.935640 | − | 0.352957i | \(-0.885176\pi\) | ||||
−0.935640 | + | 0.352957i | \(0.885176\pi\) | |||||||
\(102\) | 17.3059 | 1.71353 | ||||||||
\(103\) | −16.7076 | −1.64625 | −0.823124 | − | 0.567862i | \(-0.807771\pi\) | ||||
−0.823124 | + | 0.567862i | \(0.807771\pi\) | |||||||
\(104\) | 3.51955 | 0.345120 | ||||||||
\(105\) | 3.98869 | 0.389257 | ||||||||
\(106\) | 10.1755 | 0.988334 | ||||||||
\(107\) | −8.30921 | −0.803282 | −0.401641 | − | 0.915797i | \(-0.631560\pi\) | ||||
−0.401641 | + | 0.915797i | \(0.631560\pi\) | |||||||
\(108\) | 18.9260 | 1.82115 | ||||||||
\(109\) | 9.20099 | 0.881295 | 0.440648 | − | 0.897680i | \(-0.354749\pi\) | ||||
0.440648 | + | 0.897680i | \(0.354749\pi\) | |||||||
\(110\) | 9.27019 | 0.883878 | ||||||||
\(111\) | −11.3241 | −1.07484 | ||||||||
\(112\) | 2.57345 | 0.243168 | ||||||||
\(113\) | 11.6455 | 1.09551 | 0.547757 | − | 0.836638i | \(-0.315482\pi\) | ||||
0.547757 | + | 0.836638i | \(0.315482\pi\) | |||||||
\(114\) | 30.0976 | 2.81890 | ||||||||
\(115\) | 9.08069 | 0.846779 | ||||||||
\(116\) | 5.11744 | 0.475142 | ||||||||
\(117\) | 0.275278 | 0.0254495 | ||||||||
\(118\) | −0.552111 | −0.0508259 | ||||||||
\(119\) | 9.17909 | 0.841446 | ||||||||
\(120\) | −6.83664 | −0.624097 | ||||||||
\(121\) | 0.281657 | 0.0256052 | ||||||||
\(122\) | 0.438967 | 0.0397422 | ||||||||
\(123\) | 7.82285 | 0.705362 | ||||||||
\(124\) | −12.8888 | −1.15745 | ||||||||
\(125\) | 10.1382 | 0.906786 | ||||||||
\(126\) | 1.32572 | 0.118105 | ||||||||
\(127\) | −4.31315 | −0.382730 | −0.191365 | − | 0.981519i | \(-0.561291\pi\) | ||||
−0.191365 | + | 0.981519i | \(0.561291\pi\) | |||||||
\(128\) | 20.2305 | 1.78814 | ||||||||
\(129\) | −7.75738 | −0.682999 | ||||||||
\(130\) | −2.75996 | −0.242064 | ||||||||
\(131\) | −8.61452 | −0.752654 | −0.376327 | − | 0.926487i | \(-0.622813\pi\) | ||||
−0.376327 | + | 0.926487i | \(0.622813\pi\) | |||||||
\(132\) | −19.4087 | −1.68931 | ||||||||
\(133\) | 15.9639 | 1.38424 | ||||||||
\(134\) | −3.08039 | −0.266105 | ||||||||
\(135\) | −6.36215 | −0.547567 | ||||||||
\(136\) | −15.7330 | −1.34909 | ||||||||
\(137\) | −7.75851 | −0.662854 | −0.331427 | − | 0.943481i | \(-0.607530\pi\) | ||||
−0.331427 | + | 0.943481i | \(0.607530\pi\) | |||||||
\(138\) | −29.8739 | −2.54304 | ||||||||
\(139\) | 15.5249 | 1.31681 | 0.658404 | − | 0.752665i | \(-0.271232\pi\) | ||||
0.658404 | + | 0.752665i | \(0.271232\pi\) | |||||||
\(140\) | −8.45899 | −0.714915 | ||||||||
\(141\) | 16.2827 | 1.37125 | ||||||||
\(142\) | 18.6508 | 1.56514 | ||||||||
\(143\) | −3.35882 | −0.280878 | ||||||||
\(144\) | −0.344995 | −0.0287496 | ||||||||
\(145\) | −1.72028 | −0.142861 | ||||||||
\(146\) | 2.63689 | 0.218230 | ||||||||
\(147\) | 4.59469 | 0.378964 | ||||||||
\(148\) | 24.0155 | 1.97406 | ||||||||
\(149\) | 4.85569 | 0.397794 | 0.198897 | − | 0.980020i | \(-0.436264\pi\) | ||||
0.198897 | + | 0.980020i | \(0.436264\pi\) | |||||||
\(150\) | −13.9959 | −1.14276 | ||||||||
\(151\) | −16.5480 | −1.34666 | −0.673330 | − | 0.739342i | \(-0.735136\pi\) | ||||
−0.673330 | + | 0.739342i | \(0.735136\pi\) | |||||||
\(152\) | −27.3622 | −2.21936 | ||||||||
\(153\) | −1.23054 | −0.0994834 | ||||||||
\(154\) | −16.1759 | −1.30349 | ||||||||
\(155\) | 4.33271 | 0.348012 | ||||||||
\(156\) | 5.77843 | 0.462645 | ||||||||
\(157\) | −20.7001 | −1.65205 | −0.826023 | − | 0.563636i | \(-0.809402\pi\) | ||||
−0.826023 | + | 0.563636i | \(0.809402\pi\) | |||||||
\(158\) | 19.7527 | 1.57144 | ||||||||
\(159\) | 7.16161 | 0.567953 | ||||||||
\(160\) | −4.82452 | −0.381412 | ||||||||
\(161\) | −15.8452 | −1.24878 | ||||||||
\(162\) | 18.9935 | 1.49227 | ||||||||
\(163\) | 6.13774 | 0.480745 | 0.240372 | − | 0.970681i | \(-0.422730\pi\) | ||||
0.240372 | + | 0.970681i | \(0.422730\pi\) | |||||||
\(164\) | −16.5902 | −1.29548 | ||||||||
\(165\) | 6.52443 | 0.507926 | ||||||||
\(166\) | −38.2942 | −2.97220 | ||||||||
\(167\) | −16.8358 | −1.30279 | −0.651396 | − | 0.758738i | \(-0.725816\pi\) | ||||
−0.651396 | + | 0.758738i | \(0.725816\pi\) | |||||||
\(168\) | 11.9295 | 0.920382 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 12.3375 | 0.946242 | ||||||||
\(171\) | −2.14010 | −0.163658 | ||||||||
\(172\) | 16.4514 | 1.25441 | ||||||||
\(173\) | 19.0864 | 1.45111 | 0.725556 | − | 0.688164i | \(-0.241583\pi\) | ||||
0.725556 | + | 0.688164i | \(0.241583\pi\) | |||||||
\(174\) | 5.65942 | 0.429039 | ||||||||
\(175\) | −7.42345 | −0.561160 | ||||||||
\(176\) | 4.20947 | 0.317301 | ||||||||
\(177\) | −0.388580 | −0.0292074 | ||||||||
\(178\) | 32.6960 | 2.45067 | ||||||||
\(179\) | −10.3164 | −0.771082 | −0.385541 | − | 0.922691i | \(-0.625985\pi\) | ||||
−0.385541 | + | 0.922691i | \(0.625985\pi\) | |||||||
\(180\) | 1.13401 | 0.0845238 | ||||||||
\(181\) | 10.3258 | 0.767509 | 0.383755 | − | 0.923435i | \(-0.374631\pi\) | ||||
0.383755 | + | 0.923435i | \(0.374631\pi\) | |||||||
\(182\) | 4.81595 | 0.356982 | ||||||||
\(183\) | 0.308949 | 0.0228381 | ||||||||
\(184\) | 27.1588 | 2.00218 | ||||||||
\(185\) | −8.07306 | −0.593543 | ||||||||
\(186\) | −14.2539 | −1.04514 | ||||||||
\(187\) | 15.0145 | 1.09797 | ||||||||
\(188\) | −34.5314 | −2.51846 | ||||||||
\(189\) | 11.1016 | 0.807520 | ||||||||
\(190\) | 21.4568 | 1.55664 | ||||||||
\(191\) | 22.4150 | 1.62190 | 0.810948 | − | 0.585118i | \(-0.198952\pi\) | ||||
0.810948 | + | 0.585118i | \(0.198952\pi\) | |||||||
\(192\) | 20.0093 | 1.44405 | ||||||||
\(193\) | 18.3953 | 1.32412 | 0.662061 | − | 0.749450i | \(-0.269682\pi\) | ||||
0.662061 | + | 0.749450i | \(0.269682\pi\) | |||||||
\(194\) | −34.6603 | −2.48847 | ||||||||
\(195\) | −1.94248 | −0.139104 | ||||||||
\(196\) | −9.74415 | −0.696011 | ||||||||
\(197\) | −0.515714 | −0.0367431 | −0.0183715 | − | 0.999831i | \(-0.505848\pi\) | ||||
−0.0183715 | + | 0.999831i | \(0.505848\pi\) | |||||||
\(198\) | 2.16853 | 0.154111 | ||||||||
\(199\) | 0.637140 | 0.0451656 | 0.0225828 | − | 0.999745i | \(-0.492811\pi\) | ||||
0.0225828 | + | 0.999745i | \(0.492811\pi\) | |||||||
\(200\) | 12.7238 | 0.899711 | ||||||||
\(201\) | −2.16800 | −0.152919 | ||||||||
\(202\) | 44.1069 | 3.10335 | ||||||||
\(203\) | 3.00178 | 0.210683 | ||||||||
\(204\) | −25.8306 | −1.80851 | ||||||||
\(205\) | 5.57697 | 0.389513 | ||||||||
\(206\) | 39.1851 | 2.73016 | ||||||||
\(207\) | 2.12420 | 0.147642 | ||||||||
\(208\) | −1.25326 | −0.0868979 | ||||||||
\(209\) | 26.1126 | 1.80625 | ||||||||
\(210\) | −9.35487 | −0.645547 | ||||||||
\(211\) | −5.19925 | −0.357931 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(212\) | −15.1879 | −1.04311 | ||||||||
\(213\) | 13.1266 | 0.899417 | ||||||||
\(214\) | 19.4880 | 1.33217 | ||||||||
\(215\) | −5.53030 | −0.377164 | ||||||||
\(216\) | −19.0281 | −1.29470 | ||||||||
\(217\) | −7.56030 | −0.513227 | ||||||||
\(218\) | −21.5795 | −1.46155 | ||||||||
\(219\) | 1.85586 | 0.125407 | ||||||||
\(220\) | −13.8366 | −0.932865 | ||||||||
\(221\) | −4.47018 | −0.300697 | ||||||||
\(222\) | 26.5590 | 1.78252 | ||||||||
\(223\) | 10.0622 | 0.673811 | 0.336906 | − | 0.941538i | \(-0.390620\pi\) | ||||
0.336906 | + | 0.941538i | \(0.390620\pi\) | |||||||
\(224\) | 8.41849 | 0.562484 | ||||||||
\(225\) | 0.995183 | 0.0663455 | ||||||||
\(226\) | −27.3127 | −1.81681 | ||||||||
\(227\) | −4.70794 | −0.312477 | −0.156239 | − | 0.987719i | \(-0.549937\pi\) | ||||
−0.156239 | + | 0.987719i | \(0.549937\pi\) | |||||||
\(228\) | −44.9235 | −2.97513 | ||||||||
\(229\) | 20.1233 | 1.32978 | 0.664891 | − | 0.746940i | \(-0.268478\pi\) | ||||
0.664891 | + | 0.746940i | \(0.268478\pi\) | |||||||
\(230\) | −21.2974 | −1.40431 | ||||||||
\(231\) | −11.3847 | −0.749059 | ||||||||
\(232\) | −5.14506 | −0.337790 | ||||||||
\(233\) | 2.30660 | 0.151110 | 0.0755551 | − | 0.997142i | \(-0.475927\pi\) | ||||
0.0755551 | + | 0.997142i | \(0.475927\pi\) | |||||||
\(234\) | −0.645622 | −0.0422057 | ||||||||
\(235\) | 11.6081 | 0.757228 | ||||||||
\(236\) | 0.824078 | 0.0536429 | ||||||||
\(237\) | 13.9021 | 0.903037 | ||||||||
\(238\) | −21.5281 | −1.39546 | ||||||||
\(239\) | 1.72415 | 0.111526 | 0.0557630 | − | 0.998444i | \(-0.482241\pi\) | ||||
0.0557630 | + | 0.998444i | \(0.482241\pi\) | |||||||
\(240\) | 2.43443 | 0.157142 | ||||||||
\(241\) | −11.0609 | −0.712495 | −0.356247 | − | 0.934392i | \(-0.615944\pi\) | ||||
−0.356247 | + | 0.934392i | \(0.615944\pi\) | |||||||
\(242\) | −0.660584 | −0.0424640 | ||||||||
\(243\) | −2.85145 | −0.182921 | ||||||||
\(244\) | −0.655200 | −0.0419449 | ||||||||
\(245\) | 3.27559 | 0.209270 | ||||||||
\(246\) | −18.3473 | −1.16978 | ||||||||
\(247\) | −7.77434 | −0.494669 | ||||||||
\(248\) | 12.9584 | 0.822860 | ||||||||
\(249\) | −26.9517 | −1.70800 | ||||||||
\(250\) | −23.7775 | −1.50382 | ||||||||
\(251\) | −7.59593 | −0.479451 | −0.239725 | − | 0.970841i | \(-0.577057\pi\) | ||||
−0.239725 | + | 0.970841i | \(0.577057\pi\) | |||||||
\(252\) | −1.97877 | −0.124651 | ||||||||
\(253\) | −25.9185 | −1.62948 | ||||||||
\(254\) | 10.1158 | 0.634724 | ||||||||
\(255\) | 8.68322 | 0.543764 | ||||||||
\(256\) | −23.2038 | −1.45024 | ||||||||
\(257\) | 5.40333 | 0.337050 | 0.168525 | − | 0.985697i | \(-0.446100\pi\) | ||||
0.168525 | + | 0.985697i | \(0.446100\pi\) | |||||||
\(258\) | 18.1937 | 1.13269 | ||||||||
\(259\) | 14.0870 | 0.875322 | ||||||||
\(260\) | 4.11949 | 0.255480 | ||||||||
\(261\) | −0.402416 | −0.0249089 | ||||||||
\(262\) | 20.2040 | 1.24821 | ||||||||
\(263\) | −8.13411 | −0.501570 | −0.250785 | − | 0.968043i | \(-0.580689\pi\) | ||||
−0.250785 | + | 0.968043i | \(0.580689\pi\) | |||||||
\(264\) | 19.5135 | 1.20097 | ||||||||
\(265\) | 5.10557 | 0.313633 | ||||||||
\(266\) | −37.4408 | −2.29564 | ||||||||
\(267\) | 23.0117 | 1.40829 | ||||||||
\(268\) | 4.59777 | 0.280854 | ||||||||
\(269\) | −15.9763 | −0.974095 | −0.487048 | − | 0.873375i | \(-0.661926\pi\) | ||||
−0.487048 | + | 0.873375i | \(0.661926\pi\) | |||||||
\(270\) | 14.9215 | 0.908091 | ||||||||
\(271\) | 21.1591 | 1.28532 | 0.642662 | − | 0.766150i | \(-0.277830\pi\) | ||||
0.642662 | + | 0.766150i | \(0.277830\pi\) | |||||||
\(272\) | 5.60229 | 0.339689 | ||||||||
\(273\) | 3.38950 | 0.205142 | ||||||||
\(274\) | 18.1964 | 1.09928 | ||||||||
\(275\) | −12.1428 | −0.732236 | ||||||||
\(276\) | 44.5896 | 2.68398 | ||||||||
\(277\) | 1.47859 | 0.0888399 | 0.0444199 | − | 0.999013i | \(-0.485856\pi\) | ||||
0.0444199 | + | 0.999013i | \(0.485856\pi\) | |||||||
\(278\) | −36.4114 | −2.18381 | ||||||||
\(279\) | 1.01353 | 0.0606784 | ||||||||
\(280\) | 8.50465 | 0.508250 | ||||||||
\(281\) | 18.4673 | 1.10167 | 0.550834 | − | 0.834615i | \(-0.314310\pi\) | ||||
0.550834 | + | 0.834615i | \(0.314310\pi\) | |||||||
\(282\) | −38.1886 | −2.27410 | ||||||||
\(283\) | −5.32122 | −0.316314 | −0.158157 | − | 0.987414i | \(-0.550555\pi\) | ||||
−0.158157 | + | 0.987414i | \(0.550555\pi\) | |||||||
\(284\) | −27.8380 | −1.65188 | ||||||||
\(285\) | 15.1015 | 0.894534 | ||||||||
\(286\) | 7.87759 | 0.465812 | ||||||||
\(287\) | −9.73147 | −0.574430 | ||||||||
\(288\) | −1.12858 | −0.0665020 | ||||||||
\(289\) | 2.98249 | 0.175441 | ||||||||
\(290\) | 4.03465 | 0.236923 | ||||||||
\(291\) | −24.3942 | −1.43001 | ||||||||
\(292\) | −3.93580 | −0.230325 | ||||||||
\(293\) | −7.40227 | −0.432445 | −0.216223 | − | 0.976344i | \(-0.569374\pi\) | ||||
−0.216223 | + | 0.976344i | \(0.569374\pi\) | |||||||
\(294\) | −10.7761 | −0.628477 | ||||||||
\(295\) | −0.277022 | −0.0161288 | ||||||||
\(296\) | −24.1452 | −1.40341 | ||||||||
\(297\) | 18.1592 | 1.05370 | ||||||||
\(298\) | −11.3883 | −0.659705 | ||||||||
\(299\) | 7.71657 | 0.446260 | ||||||||
\(300\) | 20.8901 | 1.20609 | ||||||||
\(301\) | 9.65003 | 0.556219 | ||||||||
\(302\) | 38.8109 | 2.23331 | ||||||||
\(303\) | 31.0428 | 1.78336 | ||||||||
\(304\) | 9.74326 | 0.558814 | ||||||||
\(305\) | 0.220252 | 0.0126116 | ||||||||
\(306\) | 2.88605 | 0.164984 | ||||||||
\(307\) | 12.9999 | 0.741943 | 0.370971 | − | 0.928644i | \(-0.379025\pi\) | ||||
0.370971 | + | 0.928644i | \(0.379025\pi\) | |||||||
\(308\) | 24.1440 | 1.37573 | ||||||||
\(309\) | 27.5788 | 1.56890 | ||||||||
\(310\) | −10.1617 | −0.577146 | ||||||||
\(311\) | −20.4378 | −1.15892 | −0.579460 | − | 0.815001i | \(-0.696736\pi\) | ||||
−0.579460 | + | 0.815001i | \(0.696736\pi\) | |||||||
\(312\) | −5.80962 | −0.328905 | ||||||||
\(313\) | −3.72032 | −0.210285 | −0.105142 | − | 0.994457i | \(-0.533530\pi\) | ||||
−0.105142 | + | 0.994457i | \(0.533530\pi\) | |||||||
\(314\) | 48.5489 | 2.73977 | ||||||||
\(315\) | 0.665183 | 0.0374788 | ||||||||
\(316\) | −29.4827 | −1.65853 | ||||||||
\(317\) | −0.799939 | −0.0449291 | −0.0224645 | − | 0.999748i | \(-0.507151\pi\) | ||||
−0.0224645 | + | 0.999748i | \(0.507151\pi\) | |||||||
\(318\) | −16.7965 | −0.941898 | ||||||||
\(319\) | 4.91010 | 0.274913 | ||||||||
\(320\) | 14.2648 | 0.797427 | ||||||||
\(321\) | 13.7158 | 0.765541 | ||||||||
\(322\) | 37.1626 | 2.07099 | ||||||||
\(323\) | 34.7527 | 1.93369 | ||||||||
\(324\) | −28.3496 | −1.57498 | ||||||||
\(325\) | 3.61519 | 0.200535 | ||||||||
\(326\) | −14.3951 | −0.797273 | ||||||||
\(327\) | −15.1878 | −0.839889 | ||||||||
\(328\) | 16.6798 | 0.920988 | ||||||||
\(329\) | −20.2554 | −1.11672 | ||||||||
\(330\) | −15.3020 | −0.842350 | ||||||||
\(331\) | 8.15231 | 0.448092 | 0.224046 | − | 0.974579i | \(-0.428073\pi\) | ||||
0.224046 | + | 0.974579i | \(0.428073\pi\) | |||||||
\(332\) | 57.1576 | 3.13693 | ||||||||
\(333\) | −1.88849 | −0.103489 | ||||||||
\(334\) | 39.4857 | 2.16056 | ||||||||
\(335\) | −1.54559 | −0.0844444 | ||||||||
\(336\) | −4.24792 | −0.231743 | ||||||||
\(337\) | 27.5642 | 1.50152 | 0.750758 | − | 0.660577i | \(-0.229688\pi\) | ||||
0.750758 | + | 0.660577i | \(0.229688\pi\) | |||||||
\(338\) | −2.34535 | −0.127570 | ||||||||
\(339\) | −19.2229 | −1.04404 | ||||||||
\(340\) | −18.4149 | −0.998687 | ||||||||
\(341\) | −12.3666 | −0.669690 | ||||||||
\(342\) | 5.01929 | 0.271412 | ||||||||
\(343\) | −20.0895 | −1.08473 | ||||||||
\(344\) | −16.5402 | −0.891788 | ||||||||
\(345\) | −14.9893 | −0.806994 | ||||||||
\(346\) | −44.7642 | −2.40654 | ||||||||
\(347\) | −7.70956 | −0.413871 | −0.206935 | − | 0.978355i | \(-0.566349\pi\) | ||||
−0.206935 | + | 0.978355i | \(0.566349\pi\) | |||||||
\(348\) | −8.44722 | −0.452818 | ||||||||
\(349\) | −10.2107 | −0.546565 | −0.273283 | − | 0.961934i | \(-0.588109\pi\) | ||||
−0.273283 | + | 0.961934i | \(0.588109\pi\) | |||||||
\(350\) | 17.4106 | 0.930634 | ||||||||
\(351\) | −5.40641 | −0.288573 | ||||||||
\(352\) | 13.7704 | 0.733964 | ||||||||
\(353\) | 30.0421 | 1.59898 | 0.799491 | − | 0.600678i | \(-0.205103\pi\) | ||||
0.799491 | + | 0.600678i | \(0.205103\pi\) | |||||||
\(354\) | 0.911354 | 0.0484379 | ||||||||
\(355\) | 9.35803 | 0.496673 | ||||||||
\(356\) | −48.8018 | −2.58649 | ||||||||
\(357\) | −15.1517 | −0.801912 | ||||||||
\(358\) | 24.1955 | 1.27877 | ||||||||
\(359\) | 20.9090 | 1.10353 | 0.551767 | − | 0.833999i | \(-0.313954\pi\) | ||||
0.551767 | + | 0.833999i | \(0.313954\pi\) | |||||||
\(360\) | −1.14013 | −0.0600900 | ||||||||
\(361\) | 41.4403 | 2.18107 | ||||||||
\(362\) | −24.2175 | −1.27285 | ||||||||
\(363\) | −0.464924 | −0.0244022 | ||||||||
\(364\) | −7.18826 | −0.376767 | ||||||||
\(365\) | 1.32306 | 0.0692521 | ||||||||
\(366\) | −0.724592 | −0.0378750 | ||||||||
\(367\) | 22.4231 | 1.17048 | 0.585238 | − | 0.810862i | \(-0.301001\pi\) | ||||
0.585238 | + | 0.810862i | \(0.301001\pi\) | |||||||
\(368\) | −9.67086 | −0.504128 | ||||||||
\(369\) | 1.30459 | 0.0679144 | ||||||||
\(370\) | 18.9341 | 0.984338 | ||||||||
\(371\) | −8.90890 | −0.462527 | ||||||||
\(372\) | 21.2752 | 1.10307 | ||||||||
\(373\) | 17.8447 | 0.923963 | 0.461981 | − | 0.886890i | \(-0.347139\pi\) | ||||
0.461981 | + | 0.886890i | \(0.347139\pi\) | |||||||
\(374\) | −35.2142 | −1.82089 | ||||||||
\(375\) | −16.7348 | −0.864182 | ||||||||
\(376\) | 34.7179 | 1.79044 | ||||||||
\(377\) | −1.46185 | −0.0752892 | ||||||||
\(378\) | −26.0370 | −1.33920 | ||||||||
\(379\) | 20.2510 | 1.04023 | 0.520113 | − | 0.854098i | \(-0.325890\pi\) | ||||
0.520113 | + | 0.854098i | \(0.325890\pi\) | |||||||
\(380\) | −32.0263 | −1.64292 | ||||||||
\(381\) | 7.11960 | 0.364748 | ||||||||
\(382\) | −52.5711 | −2.68977 | ||||||||
\(383\) | −30.1757 | −1.54191 | −0.770954 | − | 0.636891i | \(-0.780220\pi\) | ||||
−0.770954 | + | 0.636891i | \(0.780220\pi\) | |||||||
\(384\) | −33.3940 | −1.70413 | ||||||||
\(385\) | −8.11626 | −0.413643 | ||||||||
\(386\) | −43.1433 | −2.19594 | ||||||||
\(387\) | −1.29368 | −0.0657613 | ||||||||
\(388\) | 51.7338 | 2.62639 | ||||||||
\(389\) | −12.7978 | −0.648875 | −0.324438 | − | 0.945907i | \(-0.605175\pi\) | ||||
−0.324438 | + | 0.945907i | \(0.605175\pi\) | |||||||
\(390\) | 4.55578 | 0.230691 | ||||||||
\(391\) | −34.4944 | −1.74446 | ||||||||
\(392\) | 9.79675 | 0.494811 | ||||||||
\(393\) | 14.2198 | 0.717292 | ||||||||
\(394\) | 1.20953 | 0.0609351 | ||||||||
\(395\) | 9.91091 | 0.498672 | ||||||||
\(396\) | −3.23673 | −0.162652 | ||||||||
\(397\) | −6.97484 | −0.350057 | −0.175029 | − | 0.984563i | \(-0.556002\pi\) | ||||
−0.175029 | + | 0.984563i | \(0.556002\pi\) | |||||||
\(398\) | −1.49431 | −0.0749032 | ||||||||
\(399\) | −26.3511 | −1.31921 | ||||||||
\(400\) | −4.53077 | −0.226539 | ||||||||
\(401\) | −32.7327 | −1.63459 | −0.817296 | − | 0.576218i | \(-0.804528\pi\) | ||||
−0.817296 | + | 0.576218i | \(0.804528\pi\) | |||||||
\(402\) | 5.08471 | 0.253602 | ||||||||
\(403\) | 3.68184 | 0.183405 | ||||||||
\(404\) | −65.8337 | −3.27535 | ||||||||
\(405\) | 9.53001 | 0.473550 | ||||||||
\(406\) | −7.04021 | −0.349400 | ||||||||
\(407\) | 23.0425 | 1.14217 | ||||||||
\(408\) | 25.9701 | 1.28571 | ||||||||
\(409\) | −34.1250 | −1.68737 | −0.843686 | − | 0.536837i | \(-0.819619\pi\) | ||||
−0.843686 | + | 0.536837i | \(0.819619\pi\) | |||||||
\(410\) | −13.0799 | −0.645972 | ||||||||
\(411\) | 12.8068 | 0.631711 | ||||||||
\(412\) | −58.4875 | −2.88147 | ||||||||
\(413\) | 0.483386 | 0.0237859 | ||||||||
\(414\) | −4.98199 | −0.244851 | ||||||||
\(415\) | −19.2141 | −0.943184 | ||||||||
\(416\) | −4.09977 | −0.201008 | ||||||||
\(417\) | −25.6266 | −1.25494 | ||||||||
\(418\) | −61.2431 | −2.99550 | ||||||||
\(419\) | −7.87824 | −0.384877 | −0.192439 | − | 0.981309i | \(-0.561640\pi\) | ||||
−0.192439 | + | 0.981309i | \(0.561640\pi\) | |||||||
\(420\) | 13.9630 | 0.681326 | ||||||||
\(421\) | −10.3585 | −0.504841 | −0.252421 | − | 0.967618i | \(-0.581227\pi\) | ||||
−0.252421 | + | 0.967618i | \(0.581227\pi\) | |||||||
\(422\) | 12.1940 | 0.593597 | ||||||||
\(423\) | 2.71542 | 0.132028 | ||||||||
\(424\) | 15.2699 | 0.741572 | ||||||||
\(425\) | −16.1605 | −0.783902 | ||||||||
\(426\) | −30.7863 | −1.49160 | ||||||||
\(427\) | −0.384326 | −0.0185988 | ||||||||
\(428\) | −29.0877 | −1.40600 | ||||||||
\(429\) | 5.54431 | 0.267682 | ||||||||
\(430\) | 12.9705 | 0.625492 | ||||||||
\(431\) | −40.9375 | −1.97189 | −0.985946 | − | 0.167066i | \(-0.946571\pi\) | ||||
−0.985946 | + | 0.167066i | \(0.946571\pi\) | |||||||
\(432\) | 6.77564 | 0.325993 | ||||||||
\(433\) | −2.56626 | −0.123326 | −0.0616632 | − | 0.998097i | \(-0.519640\pi\) | ||||
−0.0616632 | + | 0.998097i | \(0.519640\pi\) | |||||||
\(434\) | 17.7315 | 0.851141 | ||||||||
\(435\) | 2.83962 | 0.136149 | ||||||||
\(436\) | 32.2095 | 1.54255 | ||||||||
\(437\) | −59.9912 | −2.86977 | ||||||||
\(438\) | −4.35264 | −0.207977 | ||||||||
\(439\) | 11.4464 | 0.546307 | 0.273154 | − | 0.961970i | \(-0.411933\pi\) | ||||
0.273154 | + | 0.961970i | \(0.411933\pi\) | |||||||
\(440\) | 13.9113 | 0.663196 | ||||||||
\(441\) | 0.766243 | 0.0364878 | ||||||||
\(442\) | 10.4841 | 0.498679 | ||||||||
\(443\) | 38.6806 | 1.83777 | 0.918885 | − | 0.394525i | \(-0.129091\pi\) | ||||
0.918885 | + | 0.394525i | \(0.129091\pi\) | |||||||
\(444\) | −39.6418 | −1.88131 | ||||||||
\(445\) | 16.4052 | 0.777682 | ||||||||
\(446\) | −23.5992 | −1.11746 | ||||||||
\(447\) | −8.01516 | −0.379104 | ||||||||
\(448\) | −24.8912 | −1.17600 | ||||||||
\(449\) | −32.4700 | −1.53236 | −0.766178 | − | 0.642629i | \(-0.777844\pi\) | ||||
−0.766178 | + | 0.642629i | \(0.777844\pi\) | |||||||
\(450\) | −2.33405 | −0.110028 | ||||||||
\(451\) | −15.9181 | −0.749552 | ||||||||
\(452\) | 40.7667 | 1.91751 | ||||||||
\(453\) | 27.3154 | 1.28339 | ||||||||
\(454\) | 11.0418 | 0.518215 | ||||||||
\(455\) | 2.41640 | 0.113283 | ||||||||
\(456\) | 45.1660 | 2.11509 | ||||||||
\(457\) | −27.5969 | −1.29093 | −0.645465 | − | 0.763790i | \(-0.723336\pi\) | ||||
−0.645465 | + | 0.763790i | \(0.723336\pi\) | |||||||
\(458\) | −47.1960 | −2.20533 | ||||||||
\(459\) | 24.1676 | 1.12805 | ||||||||
\(460\) | 31.7883 | 1.48214 | ||||||||
\(461\) | −7.76824 | −0.361803 | −0.180902 | − | 0.983501i | \(-0.557902\pi\) | ||||
−0.180902 | + | 0.983501i | \(0.557902\pi\) | |||||||
\(462\) | 26.7011 | 1.24225 | ||||||||
\(463\) | −1.00000 | −0.0464739 | ||||||||
\(464\) | 1.83208 | 0.0850522 | ||||||||
\(465\) | −7.15189 | −0.331661 | ||||||||
\(466\) | −5.40977 | −0.250603 | ||||||||
\(467\) | 3.51723 | 0.162758 | 0.0813789 | − | 0.996683i | \(-0.474068\pi\) | ||||
0.0813789 | + | 0.996683i | \(0.474068\pi\) | |||||||
\(468\) | 0.963653 | 0.0445449 | ||||||||
\(469\) | 2.69695 | 0.124534 | ||||||||
\(470\) | −27.2250 | −1.25580 | ||||||||
\(471\) | 34.1691 | 1.57443 | ||||||||
\(472\) | −0.828526 | −0.0381360 | ||||||||
\(473\) | 15.7848 | 0.725788 | ||||||||
\(474\) | −32.6052 | −1.49761 | ||||||||
\(475\) | −28.1057 | −1.28958 | ||||||||
\(476\) | 32.1328 | 1.47280 | ||||||||
\(477\) | 1.19432 | 0.0546842 | ||||||||
\(478\) | −4.04373 | −0.184956 | ||||||||
\(479\) | −20.8676 | −0.953463 | −0.476731 | − | 0.879049i | \(-0.658179\pi\) | ||||
−0.476731 | + | 0.879049i | \(0.658179\pi\) | |||||||
\(480\) | 7.96371 | 0.363492 | ||||||||
\(481\) | −6.86030 | −0.312803 | ||||||||
\(482\) | 25.9416 | 1.18161 | ||||||||
\(483\) | 26.1553 | 1.19011 | ||||||||
\(484\) | 0.985985 | 0.0448175 | ||||||||
\(485\) | −17.3908 | −0.789678 | ||||||||
\(486\) | 6.68764 | 0.303357 | ||||||||
\(487\) | −10.6513 | −0.482656 | −0.241328 | − | 0.970444i | \(-0.577583\pi\) | ||||
−0.241328 | + | 0.970444i | \(0.577583\pi\) | |||||||
\(488\) | 0.658737 | 0.0298196 | ||||||||
\(489\) | −10.1314 | −0.458158 | ||||||||
\(490\) | −7.68240 | −0.347056 | ||||||||
\(491\) | −21.4034 | −0.965921 | −0.482960 | − | 0.875642i | \(-0.660438\pi\) | ||||
−0.482960 | + | 0.875642i | \(0.660438\pi\) | |||||||
\(492\) | 27.3851 | 1.23461 | ||||||||
\(493\) | 6.53474 | 0.294310 | ||||||||
\(494\) | 18.2335 | 0.820365 | ||||||||
\(495\) | 1.08806 | 0.0489047 | ||||||||
\(496\) | −4.61430 | −0.207188 | ||||||||
\(497\) | −16.3292 | −0.732464 | ||||||||
\(498\) | 63.2111 | 2.83256 | ||||||||
\(499\) | −16.1760 | −0.724139 | −0.362070 | − | 0.932151i | \(-0.617930\pi\) | ||||
−0.362070 | + | 0.932151i | \(0.617930\pi\) | |||||||
\(500\) | 35.4902 | 1.58717 | ||||||||
\(501\) | 27.7904 | 1.24158 | ||||||||
\(502\) | 17.8151 | 0.795126 | ||||||||
\(503\) | −36.7061 | −1.63664 | −0.818321 | − | 0.574761i | \(-0.805095\pi\) | ||||
−0.818321 | + | 0.574761i | \(0.805095\pi\) | |||||||
\(504\) | 1.98945 | 0.0886172 | ||||||||
\(505\) | 22.1307 | 0.984801 | ||||||||
\(506\) | 60.7880 | 2.70235 | ||||||||
\(507\) | −1.65067 | −0.0733090 | ||||||||
\(508\) | −15.0988 | −0.669902 | ||||||||
\(509\) | 10.0322 | 0.444670 | 0.222335 | − | 0.974970i | \(-0.428632\pi\) | ||||
0.222335 | + | 0.974970i | \(0.428632\pi\) | |||||||
\(510\) | −20.3652 | −0.901785 | ||||||||
\(511\) | −2.30866 | −0.102129 | ||||||||
\(512\) | 13.9599 | 0.616946 | ||||||||
\(513\) | 42.0313 | 1.85573 | ||||||||
\(514\) | −12.6727 | −0.558968 | ||||||||
\(515\) | 19.6611 | 0.866374 | ||||||||
\(516\) | −27.1559 | −1.19547 | ||||||||
\(517\) | −33.1324 | −1.45716 | ||||||||
\(518\) | −33.0388 | −1.45164 | ||||||||
\(519\) | −31.5054 | −1.38293 | ||||||||
\(520\) | −4.14173 | −0.181627 | ||||||||
\(521\) | −39.8464 | −1.74570 | −0.872851 | − | 0.487988i | \(-0.837731\pi\) | ||||
−0.872851 | + | 0.487988i | \(0.837731\pi\) | |||||||
\(522\) | 0.943805 | 0.0413092 | ||||||||
\(523\) | 4.33379 | 0.189503 | 0.0947516 | − | 0.995501i | \(-0.469794\pi\) | ||||
0.0947516 | + | 0.995501i | \(0.469794\pi\) | |||||||
\(524\) | −30.1564 | −1.31739 | ||||||||
\(525\) | 12.2537 | 0.534795 | ||||||||
\(526\) | 19.0773 | 0.831810 | ||||||||
\(527\) | −16.4585 | −0.716942 | ||||||||
\(528\) | −6.94846 | −0.302393 | ||||||||
\(529\) | 36.5454 | 1.58893 | ||||||||
\(530\) | −11.9743 | −0.520132 | ||||||||
\(531\) | −0.0648023 | −0.00281218 | ||||||||
\(532\) | 55.8840 | 2.42288 | ||||||||
\(533\) | 4.73919 | 0.205277 | ||||||||
\(534\) | −53.9704 | −2.33553 | ||||||||
\(535\) | 9.77811 | 0.422744 | ||||||||
\(536\) | −4.62259 | −0.199665 | ||||||||
\(537\) | 17.0290 | 0.734854 | ||||||||
\(538\) | 37.4701 | 1.61545 | ||||||||
\(539\) | −9.34935 | −0.402705 | ||||||||
\(540\) | −22.2717 | −0.958421 | ||||||||
\(541\) | −34.5042 | −1.48345 | −0.741726 | − | 0.670703i | \(-0.765993\pi\) | ||||
−0.741726 | + | 0.670703i | \(0.765993\pi\) | |||||||
\(542\) | −49.6254 | −2.13159 | ||||||||
\(543\) | −17.0445 | −0.731449 | ||||||||
\(544\) | 18.3267 | 0.785751 | ||||||||
\(545\) | −10.8275 | −0.463801 | ||||||||
\(546\) | −7.94956 | −0.340210 | ||||||||
\(547\) | 15.2149 | 0.650542 | 0.325271 | − | 0.945621i | \(-0.394545\pi\) | ||||
0.325271 | + | 0.945621i | \(0.394545\pi\) | |||||||
\(548\) | −27.1598 | −1.16021 | ||||||||
\(549\) | 0.0515225 | 0.00219893 | ||||||||
\(550\) | 28.4790 | 1.21435 | ||||||||
\(551\) | 11.3649 | 0.484163 | ||||||||
\(552\) | −44.8304 | −1.90811 | ||||||||
\(553\) | −17.2939 | −0.735412 | ||||||||
\(554\) | −3.46781 | −0.147333 | ||||||||
\(555\) | 13.3260 | 0.565656 | ||||||||
\(556\) | 54.3474 | 2.30484 | ||||||||
\(557\) | −11.6392 | −0.493170 | −0.246585 | − | 0.969121i | \(-0.579308\pi\) | ||||
−0.246585 | + | 0.969121i | \(0.579308\pi\) | |||||||
\(558\) | −2.37708 | −0.100630 | ||||||||
\(559\) | −4.69953 | −0.198769 | ||||||||
\(560\) | −3.02838 | −0.127972 | ||||||||
\(561\) | −24.7841 | −1.04638 | ||||||||
\(562\) | −43.3123 | −1.82702 | ||||||||
\(563\) | −5.24610 | −0.221097 | −0.110548 | − | 0.993871i | \(-0.535261\pi\) | ||||
−0.110548 | + | 0.993871i | \(0.535261\pi\) | |||||||
\(564\) | 57.0001 | 2.40014 | ||||||||
\(565\) | −13.7041 | −0.576538 | ||||||||
\(566\) | 12.4801 | 0.524578 | ||||||||
\(567\) | −16.6293 | −0.698364 | ||||||||
\(568\) | 27.9883 | 1.17436 | ||||||||
\(569\) | 30.3721 | 1.27326 | 0.636632 | − | 0.771168i | \(-0.280327\pi\) | ||||
0.636632 | + | 0.771168i | \(0.280327\pi\) | |||||||
\(570\) | −35.4182 | −1.48351 | ||||||||
\(571\) | 8.55417 | 0.357981 | 0.178990 | − | 0.983851i | \(-0.442717\pi\) | ||||
0.178990 | + | 0.983851i | \(0.442717\pi\) | |||||||
\(572\) | −11.7581 | −0.491629 | ||||||||
\(573\) | −36.9999 | −1.54569 | ||||||||
\(574\) | 22.8237 | 0.952642 | ||||||||
\(575\) | 27.8969 | 1.16338 | ||||||||
\(576\) | 3.33689 | 0.139037 | ||||||||
\(577\) | −16.3414 | −0.680301 | −0.340150 | − | 0.940371i | \(-0.610478\pi\) | ||||
−0.340150 | + | 0.940371i | \(0.610478\pi\) | |||||||
\(578\) | −6.99498 | −0.290953 | ||||||||
\(579\) | −30.3646 | −1.26191 | ||||||||
\(580\) | −6.02209 | −0.250054 | ||||||||
\(581\) | 33.5274 | 1.39095 | ||||||||
\(582\) | 57.2129 | 2.37155 | ||||||||
\(583\) | −14.5726 | −0.603534 | ||||||||
\(584\) | 3.95705 | 0.163744 | ||||||||
\(585\) | −0.323941 | −0.0133933 | ||||||||
\(586\) | 17.3609 | 0.717172 | ||||||||
\(587\) | 6.71206 | 0.277036 | 0.138518 | − | 0.990360i | \(-0.455766\pi\) | ||||
0.138518 | + | 0.990360i | \(0.455766\pi\) | |||||||
\(588\) | 16.0844 | 0.663310 | ||||||||
\(589\) | −28.6238 | −1.17943 | ||||||||
\(590\) | 0.649712 | 0.0267482 | ||||||||
\(591\) | 0.851275 | 0.0350168 | ||||||||
\(592\) | 8.59773 | 0.353365 | ||||||||
\(593\) | 34.6077 | 1.42117 | 0.710584 | − | 0.703612i | \(-0.248431\pi\) | ||||
0.710584 | + | 0.703612i | \(0.248431\pi\) | |||||||
\(594\) | −42.5895 | −1.74747 | ||||||||
\(595\) | −10.8018 | −0.442829 | ||||||||
\(596\) | 16.9981 | 0.696268 | ||||||||
\(597\) | −1.05171 | −0.0430436 | ||||||||
\(598\) | −18.0980 | −0.740083 | ||||||||
\(599\) | −23.5561 | −0.962476 | −0.481238 | − | 0.876590i | \(-0.659813\pi\) | ||||
−0.481238 | + | 0.876590i | \(0.659813\pi\) | |||||||
\(600\) | −21.0029 | −0.857440 | ||||||||
\(601\) | −3.39434 | −0.138458 | −0.0692289 | − | 0.997601i | \(-0.522054\pi\) | ||||
−0.0692289 | + | 0.997601i | \(0.522054\pi\) | |||||||
\(602\) | −22.6327 | −0.922439 | ||||||||
\(603\) | −0.361551 | −0.0147235 | ||||||||
\(604\) | −57.9289 | −2.35709 | ||||||||
\(605\) | −0.331449 | −0.0134753 | ||||||||
\(606\) | −72.8060 | −2.95754 | ||||||||
\(607\) | −13.2356 | −0.537217 | −0.268608 | − | 0.963249i | \(-0.586564\pi\) | ||||
−0.268608 | + | 0.963249i | \(0.586564\pi\) | |||||||
\(608\) | 31.8730 | 1.29262 | ||||||||
\(609\) | −4.95495 | −0.200785 | ||||||||
\(610\) | −0.516568 | −0.0209152 | ||||||||
\(611\) | 9.86429 | 0.399066 | ||||||||
\(612\) | −4.30770 | −0.174128 | ||||||||
\(613\) | −40.9304 | −1.65316 | −0.826581 | − | 0.562818i | \(-0.809717\pi\) | ||||
−0.826581 | + | 0.562818i | \(0.809717\pi\) | |||||||
\(614\) | −30.4892 | −1.23045 | ||||||||
\(615\) | −9.20576 | −0.371212 | ||||||||
\(616\) | −24.2744 | −0.978043 | ||||||||
\(617\) | −36.9601 | −1.48796 | −0.743978 | − | 0.668204i | \(-0.767063\pi\) | ||||
−0.743978 | + | 0.668204i | \(0.767063\pi\) | |||||||
\(618\) | −64.6818 | −2.60188 | ||||||||
\(619\) | −43.7376 | −1.75796 | −0.878982 | − | 0.476855i | \(-0.841777\pi\) | ||||
−0.878982 | + | 0.476855i | \(0.841777\pi\) | |||||||
\(620\) | 15.1673 | 0.609134 | ||||||||
\(621\) | −41.7189 | −1.67412 | ||||||||
\(622\) | 47.9337 | 1.92196 | ||||||||
\(623\) | −28.6261 | −1.14688 | ||||||||
\(624\) | 2.06872 | 0.0828151 | ||||||||
\(625\) | 6.14556 | 0.245822 | ||||||||
\(626\) | 8.72544 | 0.348739 | ||||||||
\(627\) | −43.1033 | −1.72138 | ||||||||
\(628\) | −72.4638 | −2.89162 | ||||||||
\(629\) | 30.6668 | 1.22276 | ||||||||
\(630\) | −1.56009 | −0.0621553 | ||||||||
\(631\) | 38.5065 | 1.53292 | 0.766460 | − | 0.642292i | \(-0.222016\pi\) | ||||
0.766460 | + | 0.642292i | \(0.222016\pi\) | |||||||
\(632\) | 29.6419 | 1.17909 | ||||||||
\(633\) | 8.58226 | 0.341114 | ||||||||
\(634\) | 1.87614 | 0.0745108 | ||||||||
\(635\) | 5.07562 | 0.201420 | ||||||||
\(636\) | 25.0703 | 0.994102 | ||||||||
\(637\) | 2.78353 | 0.110287 | ||||||||
\(638\) | −11.5159 | −0.455918 | ||||||||
\(639\) | 2.18908 | 0.0865986 | ||||||||
\(640\) | −23.8069 | −0.941049 | ||||||||
\(641\) | 33.1894 | 1.31090 | 0.655451 | − | 0.755238i | \(-0.272479\pi\) | ||||
0.655451 | + | 0.755238i | \(0.272479\pi\) | |||||||
\(642\) | −32.1683 | −1.26958 | ||||||||
\(643\) | 7.86750 | 0.310264 | 0.155132 | − | 0.987894i | \(-0.450420\pi\) | ||||
0.155132 | + | 0.987894i | \(0.450420\pi\) | |||||||
\(644\) | −55.4687 | −2.18577 | ||||||||
\(645\) | 9.12872 | 0.359443 | ||||||||
\(646\) | −81.5071 | −3.20685 | ||||||||
\(647\) | 14.9166 | 0.586430 | 0.293215 | − | 0.956046i | \(-0.405275\pi\) | ||||
0.293215 | + | 0.956046i | \(0.405275\pi\) | |||||||
\(648\) | 28.5027 | 1.11969 | ||||||||
\(649\) | 0.790689 | 0.0310373 | ||||||||
\(650\) | −8.47888 | −0.332569 | ||||||||
\(651\) | 12.4796 | 0.489114 | ||||||||
\(652\) | 21.4861 | 0.841460 | ||||||||
\(653\) | 1.58211 | 0.0619126 | 0.0309563 | − | 0.999521i | \(-0.490145\pi\) | ||||
0.0309563 | + | 0.999521i | \(0.490145\pi\) | |||||||
\(654\) | 35.6207 | 1.39288 | ||||||||
\(655\) | 10.1374 | 0.396100 | ||||||||
\(656\) | −5.93943 | −0.231896 | ||||||||
\(657\) | 0.309497 | 0.0120746 | ||||||||
\(658\) | 47.5059 | 1.85197 | ||||||||
\(659\) | −29.6557 | −1.15522 | −0.577612 | − | 0.816312i | \(-0.696015\pi\) | ||||
−0.577612 | + | 0.816312i | \(0.696015\pi\) | |||||||
\(660\) | 22.8398 | 0.889036 | ||||||||
\(661\) | 3.01285 | 0.117186 | 0.0585932 | − | 0.998282i | \(-0.481339\pi\) | ||||
0.0585932 | + | 0.998282i | \(0.481339\pi\) | |||||||
\(662\) | −19.1200 | −0.743120 | ||||||||
\(663\) | 7.37880 | 0.286569 | ||||||||
\(664\) | −57.4662 | −2.23012 | ||||||||
\(665\) | −18.7859 | −0.728488 | ||||||||
\(666\) | 4.42916 | 0.171627 | ||||||||
\(667\) | −11.2805 | −0.436782 | ||||||||
\(668\) | −58.9362 | −2.28031 | ||||||||
\(669\) | −16.6093 | −0.642153 | ||||||||
\(670\) | 3.62494 | 0.140043 | ||||||||
\(671\) | −0.628654 | −0.0242689 | ||||||||
\(672\) | −13.8962 | −0.536057 | ||||||||
\(673\) | 30.3291 | 1.16910 | 0.584551 | − | 0.811357i | \(-0.301271\pi\) | ||||
0.584551 | + | 0.811357i | \(0.301271\pi\) | |||||||
\(674\) | −64.6476 | −2.49013 | ||||||||
\(675\) | −19.5452 | −0.752296 | ||||||||
\(676\) | 3.50065 | 0.134640 | ||||||||
\(677\) | −23.5122 | −0.903649 | −0.451825 | − | 0.892107i | \(-0.649227\pi\) | ||||
−0.451825 | + | 0.892107i | \(0.649227\pi\) | |||||||
\(678\) | 45.0843 | 1.73145 | ||||||||
\(679\) | 30.3459 | 1.16457 | ||||||||
\(680\) | 18.5143 | 0.709990 | ||||||||
\(681\) | 7.77127 | 0.297796 | ||||||||
\(682\) | 29.0040 | 1.11062 | ||||||||
\(683\) | −26.7500 | −1.02356 | −0.511781 | − | 0.859116i | \(-0.671014\pi\) | ||||
−0.511781 | + | 0.859116i | \(0.671014\pi\) | |||||||
\(684\) | −7.49176 | −0.286455 | ||||||||
\(685\) | 9.13005 | 0.348841 | ||||||||
\(686\) | 47.1170 | 1.79893 | ||||||||
\(687\) | −33.2169 | −1.26731 | ||||||||
\(688\) | 5.88972 | 0.224544 | ||||||||
\(689\) | 4.33860 | 0.165287 | ||||||||
\(690\) | 35.1550 | 1.33833 | ||||||||
\(691\) | −4.32225 | −0.164426 | −0.0822131 | − | 0.996615i | \(-0.526199\pi\) | ||||
−0.0822131 | + | 0.996615i | \(0.526199\pi\) | |||||||
\(692\) | 66.8148 | 2.53992 | ||||||||
\(693\) | −1.89860 | −0.0721217 | ||||||||
\(694\) | 18.0816 | 0.686368 | ||||||||
\(695\) | −18.2694 | −0.692999 | ||||||||
\(696\) | 8.49282 | 0.321919 | ||||||||
\(697\) | −21.1850 | −0.802439 | ||||||||
\(698\) | 23.9476 | 0.906430 | ||||||||
\(699\) | −3.80744 | −0.144011 | ||||||||
\(700\) | −25.9869 | −0.982213 | ||||||||
\(701\) | 6.69840 | 0.252995 | 0.126498 | − | 0.991967i | \(-0.459626\pi\) | ||||
0.126498 | + | 0.991967i | \(0.459626\pi\) | |||||||
\(702\) | 12.6799 | 0.478573 | ||||||||
\(703\) | 53.3343 | 2.01154 | ||||||||
\(704\) | −40.7153 | −1.53451 | ||||||||
\(705\) | −19.1612 | −0.721651 | ||||||||
\(706\) | −70.4592 | −2.65177 | ||||||||
\(707\) | −38.6166 | −1.45233 | ||||||||
\(708\) | −1.36028 | −0.0511226 | ||||||||
\(709\) | 4.31526 | 0.162063 | 0.0810315 | − | 0.996712i | \(-0.474179\pi\) | ||||
0.0810315 | + | 0.996712i | \(0.474179\pi\) | |||||||
\(710\) | −21.9478 | −0.823688 | ||||||||
\(711\) | 2.31841 | 0.0869472 | ||||||||
\(712\) | 49.0653 | 1.83880 | ||||||||
\(713\) | 28.4111 | 1.06401 | ||||||||
\(714\) | 35.5359 | 1.32990 | ||||||||
\(715\) | 3.95259 | 0.147818 | ||||||||
\(716\) | −36.1140 | −1.34964 | ||||||||
\(717\) | −2.84601 | −0.106286 | ||||||||
\(718\) | −49.0388 | −1.83011 | ||||||||
\(719\) | 2.76799 | 0.103229 | 0.0516144 | − | 0.998667i | \(-0.483563\pi\) | ||||
0.0516144 | + | 0.998667i | \(0.483563\pi\) | |||||||
\(720\) | 0.405983 | 0.0151301 | ||||||||
\(721\) | −34.3075 | −1.27768 | ||||||||
\(722\) | −97.1920 | −3.61711 | ||||||||
\(723\) | 18.2579 | 0.679019 | ||||||||
\(724\) | 36.1470 | 1.34339 | ||||||||
\(725\) | −5.28488 | −0.196275 | ||||||||
\(726\) | 1.09041 | 0.0404689 | ||||||||
\(727\) | 7.45861 | 0.276624 | 0.138312 | − | 0.990389i | \(-0.455832\pi\) | ||||
0.138312 | + | 0.990389i | \(0.455832\pi\) | |||||||
\(728\) | 7.22706 | 0.267853 | ||||||||
\(729\) | 29.0020 | 1.07415 | ||||||||
\(730\) | −3.10303 | −0.114848 | ||||||||
\(731\) | 21.0077 | 0.776998 | ||||||||
\(732\) | 1.08152 | 0.0399742 | ||||||||
\(733\) | −16.9100 | −0.624585 | −0.312292 | − | 0.949986i | \(-0.601097\pi\) | ||||
−0.312292 | + | 0.949986i | \(0.601097\pi\) | |||||||
\(734\) | −52.5899 | −1.94113 | ||||||||
\(735\) | −5.40694 | −0.199438 | ||||||||
\(736\) | −31.6361 | −1.16612 | ||||||||
\(737\) | 4.41148 | 0.162499 | ||||||||
\(738\) | −3.05972 | −0.112630 | ||||||||
\(739\) | −23.8035 | −0.875627 | −0.437814 | − | 0.899066i | \(-0.644247\pi\) | ||||
−0.437814 | + | 0.899066i | \(0.644247\pi\) | |||||||
\(740\) | −28.2610 | −1.03889 | ||||||||
\(741\) | 12.8329 | 0.471428 | ||||||||
\(742\) | 20.8945 | 0.767060 | ||||||||
\(743\) | −37.3549 | −1.37042 | −0.685209 | − | 0.728347i | \(-0.740289\pi\) | ||||
−0.685209 | + | 0.728347i | \(0.740289\pi\) | |||||||
\(744\) | −21.3901 | −0.784199 | ||||||||
\(745\) | −5.71407 | −0.209347 | ||||||||
\(746\) | −41.8520 | −1.53231 | ||||||||
\(747\) | −4.49466 | −0.164451 | ||||||||
\(748\) | 52.5606 | 1.92181 | ||||||||
\(749\) | −17.0622 | −0.623439 | ||||||||
\(750\) | 39.2489 | 1.43317 | ||||||||
\(751\) | 35.7899 | 1.30599 | 0.652995 | − | 0.757362i | \(-0.273512\pi\) | ||||
0.652995 | + | 0.757362i | \(0.273512\pi\) | |||||||
\(752\) | −12.3625 | −0.450814 | ||||||||
\(753\) | 12.5384 | 0.456924 | ||||||||
\(754\) | 3.42855 | 0.124860 | ||||||||
\(755\) | 19.4734 | 0.708708 | ||||||||
\(756\) | 38.8627 | 1.41342 | ||||||||
\(757\) | 5.64469 | 0.205160 | 0.102580 | − | 0.994725i | \(-0.467290\pi\) | ||||
0.102580 | + | 0.994725i | \(0.467290\pi\) | |||||||
\(758\) | −47.4957 | −1.72512 | ||||||||
\(759\) | 42.7830 | 1.55293 | ||||||||
\(760\) | 32.1992 | 1.16799 | ||||||||
\(761\) | −22.2716 | −0.807343 | −0.403672 | − | 0.914904i | \(-0.632266\pi\) | ||||
−0.403672 | + | 0.914904i | \(0.632266\pi\) | |||||||
\(762\) | −16.6979 | −0.604902 | ||||||||
\(763\) | 18.8934 | 0.683986 | ||||||||
\(764\) | 78.4673 | 2.83885 | ||||||||
\(765\) | 1.44808 | 0.0523553 | ||||||||
\(766\) | 70.7726 | 2.55712 | ||||||||
\(767\) | −0.235407 | −0.00850005 | ||||||||
\(768\) | 38.3019 | 1.38210 | ||||||||
\(769\) | −32.3340 | −1.16600 | −0.582998 | − | 0.812474i | \(-0.698120\pi\) | ||||
−0.582998 | + | 0.812474i | \(0.698120\pi\) | |||||||
\(770\) | 19.0355 | 0.685990 | ||||||||
\(771\) | −8.91913 | −0.321215 | ||||||||
\(772\) | 64.3955 | 2.31765 | ||||||||
\(773\) | −24.4466 | −0.879283 | −0.439642 | − | 0.898173i | \(-0.644895\pi\) | ||||
−0.439642 | + | 0.898173i | \(0.644895\pi\) | |||||||
\(774\) | 3.03412 | 0.109059 | ||||||||
\(775\) | 13.3105 | 0.478129 | ||||||||
\(776\) | −52.0131 | −1.86716 | ||||||||
\(777\) | −23.2530 | −0.834196 | ||||||||
\(778\) | 30.0153 | 1.07610 | ||||||||
\(779\) | −36.8440 | −1.32007 | ||||||||
\(780\) | −6.79994 | −0.243477 | ||||||||
\(781\) | −26.7101 | −0.955764 | ||||||||
\(782\) | 80.9014 | 2.89303 | ||||||||
\(783\) | 7.90338 | 0.282444 | ||||||||
\(784\) | −3.48848 | −0.124589 | ||||||||
\(785\) | 24.3594 | 0.869425 | ||||||||
\(786\) | −33.3503 | −1.18956 | ||||||||
\(787\) | −13.4491 | −0.479410 | −0.239705 | − | 0.970846i | \(-0.577051\pi\) | ||||
−0.239705 | + | 0.970846i | \(0.577051\pi\) | |||||||
\(788\) | −1.80533 | −0.0643123 | ||||||||
\(789\) | 13.4268 | 0.478005 | ||||||||
\(790\) | −23.2445 | −0.827003 | ||||||||
\(791\) | 23.9129 | 0.850244 | ||||||||
\(792\) | 3.25421 | 0.115633 | ||||||||
\(793\) | 0.187165 | 0.00664643 | ||||||||
\(794\) | 16.3584 | 0.580538 | ||||||||
\(795\) | −8.42763 | −0.298897 | ||||||||
\(796\) | 2.23040 | 0.0790546 | ||||||||
\(797\) | 35.6487 | 1.26274 | 0.631370 | − | 0.775481i | \(-0.282493\pi\) | ||||
0.631370 | + | 0.775481i | \(0.282493\pi\) | |||||||
\(798\) | 61.8025 | 2.18779 | ||||||||
\(799\) | −44.0951 | −1.55997 | ||||||||
\(800\) | −14.8215 | −0.524017 | ||||||||
\(801\) | 3.83759 | 0.135595 | ||||||||
\(802\) | 76.7695 | 2.71083 | ||||||||
\(803\) | −3.77634 | −0.133264 | ||||||||
\(804\) | −7.58942 | −0.267658 | ||||||||
\(805\) | 18.6463 | 0.657197 | ||||||||
\(806\) | −8.63518 | −0.304161 | ||||||||
\(807\) | 26.3717 | 0.928329 | ||||||||
\(808\) | 66.1891 | 2.32852 | ||||||||
\(809\) | −25.3556 | −0.891455 | −0.445728 | − | 0.895169i | \(-0.647055\pi\) | ||||
−0.445728 | + | 0.895169i | \(0.647055\pi\) | |||||||
\(810\) | −22.3512 | −0.785341 | ||||||||
\(811\) | 42.3734 | 1.48793 | 0.743966 | − | 0.668217i | \(-0.232942\pi\) | ||||
0.743966 | + | 0.668217i | \(0.232942\pi\) | |||||||
\(812\) | 10.5082 | 0.368765 | ||||||||
\(813\) | −34.9268 | −1.22494 | ||||||||
\(814\) | −54.0426 | −1.89419 | ||||||||
\(815\) | −7.22276 | −0.253002 | ||||||||
\(816\) | −9.24755 | −0.323729 | ||||||||
\(817\) | 36.5357 | 1.27822 | ||||||||
\(818\) | 80.0349 | 2.79836 | ||||||||
\(819\) | 0.565257 | 0.0197517 | ||||||||
\(820\) | 19.5230 | 0.681774 | ||||||||
\(821\) | −34.9901 | −1.22116 | −0.610582 | − | 0.791953i | \(-0.709065\pi\) | ||||
−0.610582 | + | 0.791953i | \(0.709065\pi\) | |||||||
\(822\) | −30.0363 | −1.04764 | ||||||||
\(823\) | 26.2436 | 0.914794 | 0.457397 | − | 0.889263i | \(-0.348782\pi\) | ||||
0.457397 | + | 0.889263i | \(0.348782\pi\) | |||||||
\(824\) | 58.8032 | 2.04851 | ||||||||
\(825\) | 20.0437 | 0.697834 | ||||||||
\(826\) | −1.13371 | −0.0394467 | ||||||||
\(827\) | 35.8718 | 1.24739 | 0.623693 | − | 0.781670i | \(-0.285632\pi\) | ||||
0.623693 | + | 0.781670i | \(0.285632\pi\) | |||||||
\(828\) | 7.43609 | 0.258422 | ||||||||
\(829\) | 22.3899 | 0.777634 | 0.388817 | − | 0.921315i | \(-0.372884\pi\) | ||||
0.388817 | + | 0.921315i | \(0.372884\pi\) | |||||||
\(830\) | 45.0638 | 1.56419 | ||||||||
\(831\) | −2.44067 | −0.0846659 | ||||||||
\(832\) | 12.1219 | 0.420251 | ||||||||
\(833\) | −12.4429 | −0.431119 | ||||||||
\(834\) | 60.1033 | 2.08121 | ||||||||
\(835\) | 19.8120 | 0.685622 | ||||||||
\(836\) | 91.4111 | 3.16152 | ||||||||
\(837\) | −19.9055 | −0.688036 | ||||||||
\(838\) | 18.4772 | 0.638285 | ||||||||
\(839\) | −9.31199 | −0.321485 | −0.160743 | − | 0.986996i | \(-0.551389\pi\) | ||||
−0.160743 | + | 0.986996i | \(0.551389\pi\) | |||||||
\(840\) | −14.0384 | −0.484371 | ||||||||
\(841\) | −26.8630 | −0.926310 | ||||||||
\(842\) | 24.2942 | 0.837234 | ||||||||
\(843\) | −30.4835 | −1.04991 | ||||||||
\(844\) | −18.2008 | −0.626496 | ||||||||
\(845\) | −1.17678 | −0.0404824 | ||||||||
\(846\) | −6.36861 | −0.218957 | ||||||||
\(847\) | 0.578357 | 0.0198726 | ||||||||
\(848\) | −5.43739 | −0.186721 | ||||||||
\(849\) | 8.78360 | 0.301452 | ||||||||
\(850\) | 37.9021 | 1.30003 | ||||||||
\(851\) | −52.9379 | −1.81469 | ||||||||
\(852\) | 45.9515 | 1.57427 | ||||||||
\(853\) | −25.6209 | −0.877243 | −0.438621 | − | 0.898672i | \(-0.644533\pi\) | ||||
−0.438621 | + | 0.898672i | \(0.644533\pi\) | |||||||
\(854\) | 0.901378 | 0.0308445 | ||||||||
\(855\) | 2.51843 | 0.0861285 | ||||||||
\(856\) | 29.2447 | 0.999562 | ||||||||
\(857\) | 7.85009 | 0.268154 | 0.134077 | − | 0.990971i | \(-0.457193\pi\) | ||||
0.134077 | + | 0.990971i | \(0.457193\pi\) | |||||||
\(858\) | −13.0033 | −0.443926 | ||||||||
\(859\) | −18.5076 | −0.631470 | −0.315735 | − | 0.948847i | \(-0.602251\pi\) | ||||
−0.315735 | + | 0.948847i | \(0.602251\pi\) | |||||||
\(860\) | −19.3597 | −0.660159 | ||||||||
\(861\) | 16.0635 | 0.547442 | ||||||||
\(862\) | 96.0127 | 3.27021 | ||||||||
\(863\) | 5.32755 | 0.181352 | 0.0906759 | − | 0.995880i | \(-0.471097\pi\) | ||||
0.0906759 | + | 0.995880i | \(0.471097\pi\) | |||||||
\(864\) | 22.1651 | 0.754070 | ||||||||
\(865\) | −22.4605 | −0.763679 | ||||||||
\(866\) | 6.01876 | 0.204526 | ||||||||
\(867\) | −4.92312 | −0.167198 | ||||||||
\(868\) | −26.4660 | −0.898314 | ||||||||
\(869\) | −28.2882 | −0.959611 | ||||||||
\(870\) | −6.65988 | −0.225791 | ||||||||
\(871\) | −1.31340 | −0.0445030 | ||||||||
\(872\) | −32.3833 | −1.09664 | ||||||||
\(873\) | −4.06815 | −0.137686 | ||||||||
\(874\) | 140.700 | 4.75925 | ||||||||
\(875\) | 20.8178 | 0.703770 | ||||||||
\(876\) | 6.49672 | 0.219504 | ||||||||
\(877\) | −2.07870 | −0.0701926 | −0.0350963 | − | 0.999384i | \(-0.511174\pi\) | ||||
−0.0350963 | + | 0.999384i | \(0.511174\pi\) | |||||||
\(878\) | −26.8458 | −0.906002 | ||||||||
\(879\) | 12.2187 | 0.412128 | ||||||||
\(880\) | −4.95362 | −0.166986 | ||||||||
\(881\) | 11.5668 | 0.389695 | 0.194847 | − | 0.980834i | \(-0.437579\pi\) | ||||
0.194847 | + | 0.980834i | \(0.437579\pi\) | |||||||
\(882\) | −1.79711 | −0.0605117 | ||||||||
\(883\) | −11.2769 | −0.379498 | −0.189749 | − | 0.981833i | \(-0.560767\pi\) | ||||
−0.189749 | + | 0.981833i | \(0.560767\pi\) | |||||||
\(884\) | −15.6485 | −0.526317 | ||||||||
\(885\) | 0.457273 | 0.0153711 | ||||||||
\(886\) | −90.7194 | −3.04778 | ||||||||
\(887\) | −55.4726 | −1.86259 | −0.931294 | − | 0.364269i | \(-0.881319\pi\) | ||||
−0.931294 | + | 0.364269i | \(0.881319\pi\) | |||||||
\(888\) | 39.8558 | 1.33747 | ||||||||
\(889\) | −8.85664 | −0.297042 | ||||||||
\(890\) | −38.4759 | −1.28972 | ||||||||
\(891\) | −27.2010 | −0.911268 | ||||||||
\(892\) | 35.2241 | 1.17939 | ||||||||
\(893\) | −76.6883 | −2.56628 | ||||||||
\(894\) | 18.7983 | 0.628710 | ||||||||
\(895\) | 12.1401 | 0.405798 | ||||||||
\(896\) | 41.5415 | 1.38780 | ||||||||
\(897\) | −12.7375 | −0.425294 | ||||||||
\(898\) | 76.1535 | 2.54127 | ||||||||
\(899\) | −5.38230 | −0.179510 | ||||||||
\(900\) | 3.48379 | 0.116126 | ||||||||
\(901\) | −19.3943 | −0.646118 | ||||||||
\(902\) | 37.3334 | 1.24307 | ||||||||
\(903\) | −15.9290 | −0.530086 | ||||||||
\(904\) | −40.9868 | −1.36320 | ||||||||
\(905\) | −12.1512 | −0.403918 | ||||||||
\(906\) | −64.0640 | −2.12839 | ||||||||
\(907\) | −31.6157 | −1.04978 | −0.524892 | − | 0.851169i | \(-0.675894\pi\) | ||||
−0.524892 | + | 0.851169i | \(0.675894\pi\) | |||||||
\(908\) | −16.4809 | −0.546937 | ||||||||
\(909\) | 5.17691 | 0.171707 | ||||||||
\(910\) | −5.66731 | −0.187869 | ||||||||
\(911\) | 7.69749 | 0.255029 | 0.127515 | − | 0.991837i | \(-0.459300\pi\) | ||||
0.127515 | + | 0.991837i | \(0.459300\pi\) | |||||||
\(912\) | −16.0829 | −0.532559 | ||||||||
\(913\) | 54.8418 | 1.81500 | ||||||||
\(914\) | 64.7244 | 2.14089 | ||||||||
\(915\) | −0.363564 | −0.0120191 | ||||||||
\(916\) | 70.4445 | 2.32755 | ||||||||
\(917\) | −17.6891 | −0.584146 | ||||||||
\(918\) | −56.6815 | −1.87077 | ||||||||
\(919\) | −15.7089 | −0.518190 | −0.259095 | − | 0.965852i | \(-0.583424\pi\) | ||||
−0.259095 | + | 0.965852i | \(0.583424\pi\) | |||||||
\(920\) | −31.9599 | −1.05369 | ||||||||
\(921\) | −21.4586 | −0.707084 | ||||||||
\(922\) | 18.2192 | 0.600018 | ||||||||
\(923\) | 7.95224 | 0.261751 | ||||||||
\(924\) | −39.8539 | −1.31110 | ||||||||
\(925\) | −24.8013 | −0.815461 | ||||||||
\(926\) | 2.34535 | 0.0770729 | ||||||||
\(927\) | 4.59923 | 0.151059 | ||||||||
\(928\) | 5.99326 | 0.196738 | ||||||||
\(929\) | −26.0229 | −0.853784 | −0.426892 | − | 0.904303i | \(-0.640392\pi\) | ||||
−0.426892 | + | 0.904303i | \(0.640392\pi\) | |||||||
\(930\) | 16.7737 | 0.550030 | ||||||||
\(931\) | −21.6401 | −0.709225 | ||||||||
\(932\) | 8.07459 | 0.264492 | ||||||||
\(933\) | 33.7361 | 1.10447 | ||||||||
\(934\) | −8.24912 | −0.269919 | ||||||||
\(935\) | −17.6688 | −0.577830 | ||||||||
\(936\) | −0.968855 | −0.0316680 | ||||||||
\(937\) | −10.9730 | −0.358472 | −0.179236 | − | 0.983806i | \(-0.557363\pi\) | ||||
−0.179236 | + | 0.983806i | \(0.557363\pi\) | |||||||
\(938\) | −6.32529 | −0.206528 | ||||||||
\(939\) | 6.14103 | 0.200405 | ||||||||
\(940\) | 40.6359 | 1.32540 | ||||||||
\(941\) | 9.68440 | 0.315702 | 0.157851 | − | 0.987463i | \(-0.449543\pi\) | ||||
0.157851 | + | 0.987463i | \(0.449543\pi\) | |||||||
\(942\) | −80.1383 | −2.61105 | ||||||||
\(943\) | 36.5702 | 1.19089 | ||||||||
\(944\) | 0.295026 | 0.00960227 | ||||||||
\(945\) | −13.0641 | −0.424975 | ||||||||
\(946\) | −37.0209 | −1.20365 | ||||||||
\(947\) | 29.3611 | 0.954106 | 0.477053 | − | 0.878874i | \(-0.341705\pi\) | ||||
0.477053 | + | 0.878874i | \(0.341705\pi\) | |||||||
\(948\) | 48.6663 | 1.58061 | ||||||||
\(949\) | 1.12431 | 0.0364965 | ||||||||
\(950\) | 65.9177 | 2.13865 | ||||||||
\(951\) | 1.32044 | 0.0428181 | ||||||||
\(952\) | −32.3063 | −1.04705 | ||||||||
\(953\) | 32.0233 | 1.03734 | 0.518668 | − | 0.854976i | \(-0.326428\pi\) | ||||
0.518668 | + | 0.854976i | \(0.326428\pi\) | |||||||
\(954\) | −2.80110 | −0.0906889 | ||||||||
\(955\) | −26.3776 | −0.853558 | ||||||||
\(956\) | 6.03565 | 0.195207 | ||||||||
\(957\) | −8.10496 | −0.261996 | ||||||||
\(958\) | 48.9416 | 1.58123 | ||||||||
\(959\) | −15.9314 | −0.514450 | ||||||||
\(960\) | −23.5465 | −0.759961 | ||||||||
\(961\) | −17.4441 | −0.562712 | ||||||||
\(962\) | 16.0898 | 0.518755 | ||||||||
\(963\) | 2.28734 | 0.0737086 | ||||||||
\(964\) | −38.7203 | −1.24710 | ||||||||
\(965\) | −21.6472 | −0.696848 | ||||||||
\(966\) | −61.3433 | −1.97369 | ||||||||
\(967\) | −17.7899 | −0.572084 | −0.286042 | − | 0.958217i | \(-0.592340\pi\) | ||||
−0.286042 | + | 0.958217i | \(0.592340\pi\) | |||||||
\(968\) | −0.991307 | −0.0318618 | ||||||||
\(969\) | −57.3653 | −1.84284 | ||||||||
\(970\) | 40.7876 | 1.30961 | ||||||||
\(971\) | −4.79097 | −0.153749 | −0.0768747 | − | 0.997041i | \(-0.524494\pi\) | ||||
−0.0768747 | + | 0.997041i | \(0.524494\pi\) | |||||||
\(972\) | −9.98193 | −0.320171 | ||||||||
\(973\) | 31.8790 | 1.02199 | ||||||||
\(974\) | 24.9809 | 0.800441 | ||||||||
\(975\) | −5.96750 | −0.191113 | ||||||||
\(976\) | −0.234567 | −0.00750829 | ||||||||
\(977\) | −60.0639 | −1.92161 | −0.960807 | − | 0.277218i | \(-0.910588\pi\) | ||||
−0.960807 | + | 0.277218i | \(0.910588\pi\) | |||||||
\(978\) | 23.7617 | 0.759814 | ||||||||
\(979\) | −46.8246 | −1.49652 | ||||||||
\(980\) | 11.4667 | 0.366291 | ||||||||
\(981\) | −2.53283 | −0.0808671 | ||||||||
\(982\) | 50.1983 | 1.60189 | ||||||||
\(983\) | −17.7583 | −0.566403 | −0.283202 | − | 0.959060i | \(-0.591397\pi\) | ||||
−0.283202 | + | 0.959060i | \(0.591397\pi\) | |||||||
\(984\) | −27.5329 | −0.877716 | ||||||||
\(985\) | 0.606881 | 0.0193368 | ||||||||
\(986\) | −15.3262 | −0.488087 | ||||||||
\(987\) | 33.4350 | 1.06425 | ||||||||
\(988\) | −27.2153 | −0.865833 | ||||||||
\(989\) | −36.2642 | −1.15313 | ||||||||
\(990\) | −2.55188 | −0.0811040 | ||||||||
\(991\) | −24.5801 | −0.780813 | −0.390407 | − | 0.920643i | \(-0.627666\pi\) | ||||
−0.390407 | + | 0.920643i | \(0.627666\pi\) | |||||||
\(992\) | −15.0947 | −0.479257 | ||||||||
\(993\) | −13.4568 | −0.427039 | ||||||||
\(994\) | 38.2976 | 1.21473 | ||||||||
\(995\) | −0.749773 | −0.0237694 | ||||||||
\(996\) | −94.3486 | −2.98955 | ||||||||
\(997\) | −29.0419 | −0.919767 | −0.459884 | − | 0.887979i | \(-0.652109\pi\) | ||||
−0.459884 | + | 0.887979i | \(0.652109\pi\) | |||||||
\(998\) | 37.9384 | 1.20092 | ||||||||
\(999\) | 37.0896 | 1.17346 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6019.2.a.c.1.12 | ✓ | 108 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6019.2.a.c.1.12 | ✓ | 108 | 1.1 | even | 1 | trivial |