Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.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: | \(64.2077082653\) |
Analytic rank: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.30649 | −1.63094 | −0.815469 | − | 0.578801i | \(-0.803521\pi\) | ||||
−0.815469 | + | 0.578801i | \(0.803521\pi\) | |||||||
\(3\) | −1.79768 | −1.03789 | −0.518946 | − | 0.854807i | \(-0.673675\pi\) | ||||
−0.518946 | + | 0.854807i | \(0.673675\pi\) | |||||||
\(4\) | 3.31992 | 1.65996 | ||||||||
\(5\) | 3.97246 | 1.77654 | 0.888270 | − | 0.459322i | \(-0.151907\pi\) | ||||
0.888270 | + | 0.459322i | \(0.151907\pi\) | |||||||
\(6\) | 4.14634 | 1.69274 | ||||||||
\(7\) | 2.36407 | 0.893533 | 0.446767 | − | 0.894651i | \(-0.352575\pi\) | ||||
0.446767 | + | 0.894651i | \(0.352575\pi\) | |||||||
\(8\) | −3.04439 | −1.07635 | ||||||||
\(9\) | 0.231661 | 0.0772202 | ||||||||
\(10\) | −9.16247 | −2.89743 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −5.96816 | −1.72286 | ||||||||
\(13\) | 5.03650 | 1.39687 | 0.698437 | − | 0.715672i | \(-0.253879\pi\) | ||||
0.698437 | + | 0.715672i | \(0.253879\pi\) | |||||||
\(14\) | −5.45271 | −1.45730 | ||||||||
\(15\) | −7.14123 | −1.84386 | ||||||||
\(16\) | 0.382023 | 0.0955057 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −0.534324 | −0.125941 | ||||||||
\(19\) | 4.61118 | 1.05788 | 0.528938 | − | 0.848660i | \(-0.322590\pi\) | ||||
0.528938 | + | 0.848660i | \(0.322590\pi\) | |||||||
\(20\) | 13.1883 | 2.94898 | ||||||||
\(21\) | −4.24984 | −0.927391 | ||||||||
\(22\) | −2.30649 | −0.491746 | ||||||||
\(23\) | 2.01155 | 0.419437 | 0.209718 | − | 0.977762i | \(-0.432745\pi\) | ||||
0.209718 | + | 0.977762i | \(0.432745\pi\) | |||||||
\(24\) | 5.47284 | 1.11714 | ||||||||
\(25\) | 10.7805 | 2.15609 | ||||||||
\(26\) | −11.6167 | −2.27821 | ||||||||
\(27\) | 4.97659 | 0.957746 | ||||||||
\(28\) | 7.84851 | 1.48323 | ||||||||
\(29\) | 4.72977 | 0.878296 | 0.439148 | − | 0.898415i | \(-0.355280\pi\) | ||||
0.439148 | + | 0.898415i | \(0.355280\pi\) | |||||||
\(30\) | 16.4712 | 3.00722 | ||||||||
\(31\) | 2.96757 | 0.532991 | 0.266495 | − | 0.963836i | \(-0.414134\pi\) | ||||
0.266495 | + | 0.963836i | \(0.414134\pi\) | |||||||
\(32\) | 5.20764 | 0.920589 | ||||||||
\(33\) | −1.79768 | −0.312936 | ||||||||
\(34\) | −2.30649 | −0.395561 | ||||||||
\(35\) | 9.39117 | 1.58740 | ||||||||
\(36\) | 0.769095 | 0.128182 | ||||||||
\(37\) | −2.93712 | −0.482859 | −0.241430 | − | 0.970418i | \(-0.577616\pi\) | ||||
−0.241430 | + | 0.970418i | \(0.577616\pi\) | |||||||
\(38\) | −10.6357 | −1.72533 | ||||||||
\(39\) | −9.05402 | −1.44980 | ||||||||
\(40\) | −12.0937 | −1.91218 | ||||||||
\(41\) | 2.94886 | 0.460535 | 0.230268 | − | 0.973127i | \(-0.426040\pi\) | ||||
0.230268 | + | 0.973127i | \(0.426040\pi\) | |||||||
\(42\) | 9.80223 | 1.51252 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 3.31992 | 0.500497 | ||||||||
\(45\) | 0.920264 | 0.137185 | ||||||||
\(46\) | −4.63962 | −0.684075 | ||||||||
\(47\) | 0.804974 | 0.117418 | 0.0587088 | − | 0.998275i | \(-0.481302\pi\) | ||||
0.0587088 | + | 0.998275i | \(0.481302\pi\) | |||||||
\(48\) | −0.686755 | −0.0991246 | ||||||||
\(49\) | −1.41119 | −0.201599 | ||||||||
\(50\) | −24.8651 | −3.51646 | ||||||||
\(51\) | −1.79768 | −0.251726 | ||||||||
\(52\) | 16.7208 | 2.31875 | ||||||||
\(53\) | 2.26444 | 0.311045 | 0.155522 | − | 0.987832i | \(-0.450294\pi\) | ||||
0.155522 | + | 0.987832i | \(0.450294\pi\) | |||||||
\(54\) | −11.4785 | −1.56202 | ||||||||
\(55\) | 3.97246 | 0.535647 | ||||||||
\(56\) | −7.19713 | −0.961757 | ||||||||
\(57\) | −8.28943 | −1.09796 | ||||||||
\(58\) | −10.9092 | −1.43245 | ||||||||
\(59\) | −5.18744 | −0.675348 | −0.337674 | − | 0.941263i | \(-0.609640\pi\) | ||||
−0.337674 | + | 0.941263i | \(0.609640\pi\) | |||||||
\(60\) | −23.7083 | −3.06073 | ||||||||
\(61\) | −3.03068 | −0.388039 | −0.194020 | − | 0.980998i | \(-0.562153\pi\) | ||||
−0.194020 | + | 0.980998i | \(0.562153\pi\) | |||||||
\(62\) | −6.84467 | −0.869275 | ||||||||
\(63\) | 0.547661 | 0.0689988 | ||||||||
\(64\) | −12.7754 | −1.59693 | ||||||||
\(65\) | 20.0073 | 2.48160 | ||||||||
\(66\) | 4.14634 | 0.510380 | ||||||||
\(67\) | 9.82283 | 1.20005 | 0.600025 | − | 0.799981i | \(-0.295157\pi\) | ||||
0.600025 | + | 0.799981i | \(0.295157\pi\) | |||||||
\(68\) | 3.31992 | 0.402599 | ||||||||
\(69\) | −3.61612 | −0.435330 | ||||||||
\(70\) | −21.6607 | −2.58895 | ||||||||
\(71\) | 3.86568 | 0.458772 | 0.229386 | − | 0.973336i | \(-0.426328\pi\) | ||||
0.229386 | + | 0.973336i | \(0.426328\pi\) | |||||||
\(72\) | −0.705265 | −0.0831162 | ||||||||
\(73\) | 4.61176 | 0.539766 | 0.269883 | − | 0.962893i | \(-0.413015\pi\) | ||||
0.269883 | + | 0.962893i | \(0.413015\pi\) | |||||||
\(74\) | 6.77445 | 0.787514 | ||||||||
\(75\) | −19.3799 | −2.23779 | ||||||||
\(76\) | 15.3087 | 1.75603 | ||||||||
\(77\) | 2.36407 | 0.269410 | ||||||||
\(78\) | 20.8831 | 2.36454 | ||||||||
\(79\) | −12.2298 | −1.37596 | −0.687978 | − | 0.725732i | \(-0.741501\pi\) | ||||
−0.687978 | + | 0.725732i | \(0.741501\pi\) | |||||||
\(80\) | 1.51757 | 0.169670 | ||||||||
\(81\) | −9.64132 | −1.07126 | ||||||||
\(82\) | −6.80154 | −0.751105 | ||||||||
\(83\) | 0.879944 | 0.0965864 | 0.0482932 | − | 0.998833i | \(-0.484622\pi\) | ||||
0.0482932 | + | 0.998833i | \(0.484622\pi\) | |||||||
\(84\) | −14.1091 | −1.53943 | ||||||||
\(85\) | 3.97246 | 0.430874 | ||||||||
\(86\) | −2.30649 | −0.248716 | ||||||||
\(87\) | −8.50262 | −0.911577 | ||||||||
\(88\) | −3.04439 | −0.324533 | ||||||||
\(89\) | 5.21525 | 0.552815 | 0.276408 | − | 0.961040i | \(-0.410856\pi\) | ||||
0.276408 | + | 0.961040i | \(0.410856\pi\) | |||||||
\(90\) | −2.12258 | −0.223740 | ||||||||
\(91\) | 11.9066 | 1.24815 | ||||||||
\(92\) | 6.67817 | 0.696248 | ||||||||
\(93\) | −5.33474 | −0.553187 | ||||||||
\(94\) | −1.85667 | −0.191501 | ||||||||
\(95\) | 18.3177 | 1.87936 | ||||||||
\(96\) | −9.36168 | −0.955472 | ||||||||
\(97\) | −5.31064 | −0.539214 | −0.269607 | − | 0.962970i | \(-0.586894\pi\) | ||||
−0.269607 | + | 0.962970i | \(0.586894\pi\) | |||||||
\(98\) | 3.25490 | 0.328795 | ||||||||
\(99\) | 0.231661 | 0.0232828 | ||||||||
\(100\) | 35.7903 | 3.57903 | ||||||||
\(101\) | 10.9985 | 1.09439 | 0.547194 | − | 0.837006i | \(-0.315696\pi\) | ||||
0.547194 | + | 0.837006i | \(0.315696\pi\) | |||||||
\(102\) | 4.14634 | 0.410549 | ||||||||
\(103\) | 5.30396 | 0.522614 | 0.261307 | − | 0.965256i | \(-0.415846\pi\) | ||||
0.261307 | + | 0.965256i | \(0.415846\pi\) | |||||||
\(104\) | −15.3330 | −1.50353 | ||||||||
\(105\) | −16.8823 | −1.64755 | ||||||||
\(106\) | −5.22292 | −0.507295 | ||||||||
\(107\) | 3.18411 | 0.307819 | 0.153910 | − | 0.988085i | \(-0.450814\pi\) | ||||
0.153910 | + | 0.988085i | \(0.450814\pi\) | |||||||
\(108\) | 16.5219 | 1.58982 | ||||||||
\(109\) | −6.03357 | −0.577912 | −0.288956 | − | 0.957342i | \(-0.593308\pi\) | ||||
−0.288956 | + | 0.957342i | \(0.593308\pi\) | |||||||
\(110\) | −9.16247 | −0.873607 | ||||||||
\(111\) | 5.28001 | 0.501156 | ||||||||
\(112\) | 0.903127 | 0.0853375 | ||||||||
\(113\) | −2.87695 | −0.270641 | −0.135321 | − | 0.990802i | \(-0.543206\pi\) | ||||
−0.135321 | + | 0.990802i | \(0.543206\pi\) | |||||||
\(114\) | 19.1195 | 1.79071 | ||||||||
\(115\) | 7.99080 | 0.745146 | ||||||||
\(116\) | 15.7025 | 1.45794 | ||||||||
\(117\) | 1.16676 | 0.107867 | ||||||||
\(118\) | 11.9648 | 1.10145 | ||||||||
\(119\) | 2.36407 | 0.216714 | ||||||||
\(120\) | 21.7407 | 1.98464 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 6.99026 | 0.632868 | ||||||||
\(123\) | −5.30112 | −0.477986 | ||||||||
\(124\) | 9.85208 | 0.884743 | ||||||||
\(125\) | 22.9627 | 2.05385 | ||||||||
\(126\) | −1.26318 | −0.112533 | ||||||||
\(127\) | −0.497074 | −0.0441082 | −0.0220541 | − | 0.999757i | \(-0.507021\pi\) | ||||
−0.0220541 | + | 0.999757i | \(0.507021\pi\) | |||||||
\(128\) | 19.0512 | 1.68390 | ||||||||
\(129\) | −1.79768 | −0.158277 | ||||||||
\(130\) | −46.1468 | −4.04734 | ||||||||
\(131\) | 15.8516 | 1.38496 | 0.692482 | − | 0.721435i | \(-0.256517\pi\) | ||||
0.692482 | + | 0.721435i | \(0.256517\pi\) | |||||||
\(132\) | −5.96816 | −0.519461 | ||||||||
\(133\) | 10.9011 | 0.945247 | ||||||||
\(134\) | −22.6563 | −1.95721 | ||||||||
\(135\) | 19.7693 | 1.70147 | ||||||||
\(136\) | −3.04439 | −0.261054 | ||||||||
\(137\) | −3.74813 | −0.320224 | −0.160112 | − | 0.987099i | \(-0.551186\pi\) | ||||
−0.160112 | + | 0.987099i | \(0.551186\pi\) | |||||||
\(138\) | 8.34057 | 0.709996 | ||||||||
\(139\) | 9.20379 | 0.780655 | 0.390328 | − | 0.920676i | \(-0.372362\pi\) | ||||
0.390328 | + | 0.920676i | \(0.372362\pi\) | |||||||
\(140\) | 31.1779 | 2.63502 | ||||||||
\(141\) | −1.44709 | −0.121867 | ||||||||
\(142\) | −8.91618 | −0.748229 | ||||||||
\(143\) | 5.03650 | 0.421173 | ||||||||
\(144\) | 0.0884997 | 0.00737497 | ||||||||
\(145\) | 18.7888 | 1.56033 | ||||||||
\(146\) | −10.6370 | −0.880324 | ||||||||
\(147\) | 2.53687 | 0.209238 | ||||||||
\(148\) | −9.75100 | −0.801527 | ||||||||
\(149\) | −6.52470 | −0.534525 | −0.267262 | − | 0.963624i | \(-0.586119\pi\) | ||||
−0.267262 | + | 0.963624i | \(0.586119\pi\) | |||||||
\(150\) | 44.6996 | 3.64970 | ||||||||
\(151\) | 6.42473 | 0.522837 | 0.261419 | − | 0.965226i | \(-0.415810\pi\) | ||||
0.261419 | + | 0.965226i | \(0.415810\pi\) | |||||||
\(152\) | −14.0382 | −1.13865 | ||||||||
\(153\) | 0.231661 | 0.0187287 | ||||||||
\(154\) | −5.45271 | −0.439392 | ||||||||
\(155\) | 11.7885 | 0.946879 | ||||||||
\(156\) | −30.0586 | −2.40662 | ||||||||
\(157\) | −14.1635 | −1.13037 | −0.565184 | − | 0.824965i | \(-0.691195\pi\) | ||||
−0.565184 | + | 0.824965i | \(0.691195\pi\) | |||||||
\(158\) | 28.2079 | 2.24410 | ||||||||
\(159\) | −4.07075 | −0.322831 | ||||||||
\(160\) | 20.6872 | 1.63546 | ||||||||
\(161\) | 4.75543 | 0.374781 | ||||||||
\(162\) | 22.2376 | 1.74715 | ||||||||
\(163\) | 4.34203 | 0.340094 | 0.170047 | − | 0.985436i | \(-0.445608\pi\) | ||||
0.170047 | + | 0.985436i | \(0.445608\pi\) | |||||||
\(164\) | 9.78999 | 0.764470 | ||||||||
\(165\) | −7.14123 | −0.555944 | ||||||||
\(166\) | −2.02959 | −0.157526 | ||||||||
\(167\) | 7.71459 | 0.596973 | 0.298486 | − | 0.954414i | \(-0.403518\pi\) | ||||
0.298486 | + | 0.954414i | \(0.403518\pi\) | |||||||
\(168\) | 12.9382 | 0.998200 | ||||||||
\(169\) | 12.3663 | 0.951256 | ||||||||
\(170\) | −9.16247 | −0.702729 | ||||||||
\(171\) | 1.06823 | 0.0816894 | ||||||||
\(172\) | 3.31992 | 0.253141 | ||||||||
\(173\) | −21.3548 | −1.62358 | −0.811789 | − | 0.583952i | \(-0.801506\pi\) | ||||
−0.811789 | + | 0.583952i | \(0.801506\pi\) | |||||||
\(174\) | 19.6113 | 1.48673 | ||||||||
\(175\) | 25.4858 | 1.92654 | ||||||||
\(176\) | 0.382023 | 0.0287960 | ||||||||
\(177\) | 9.32537 | 0.700938 | ||||||||
\(178\) | −12.0289 | −0.901608 | ||||||||
\(179\) | 13.5048 | 1.00940 | 0.504698 | − | 0.863296i | \(-0.331604\pi\) | ||||
0.504698 | + | 0.863296i | \(0.331604\pi\) | |||||||
\(180\) | 3.05520 | 0.227721 | ||||||||
\(181\) | −13.6974 | −1.01812 | −0.509060 | − | 0.860731i | \(-0.670007\pi\) | ||||
−0.509060 | + | 0.860731i | \(0.670007\pi\) | |||||||
\(182\) | −27.4626 | −2.03566 | ||||||||
\(183\) | 5.44821 | 0.402743 | ||||||||
\(184\) | −6.12393 | −0.451462 | ||||||||
\(185\) | −11.6676 | −0.857819 | ||||||||
\(186\) | 12.3045 | 0.902213 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | 2.67245 | 0.194908 | ||||||||
\(189\) | 11.7650 | 0.855778 | ||||||||
\(190\) | −42.2497 | −3.06512 | ||||||||
\(191\) | 3.65345 | 0.264354 | 0.132177 | − | 0.991226i | \(-0.457803\pi\) | ||||
0.132177 | + | 0.991226i | \(0.457803\pi\) | |||||||
\(192\) | 22.9662 | 1.65744 | ||||||||
\(193\) | 14.9246 | 1.07430 | 0.537148 | − | 0.843488i | \(-0.319502\pi\) | ||||
0.537148 | + | 0.843488i | \(0.319502\pi\) | |||||||
\(194\) | 12.2490 | 0.879424 | ||||||||
\(195\) | −35.9668 | −2.57564 | ||||||||
\(196\) | −4.68504 | −0.334646 | ||||||||
\(197\) | −23.6293 | −1.68352 | −0.841760 | − | 0.539851i | \(-0.818481\pi\) | ||||
−0.841760 | + | 0.539851i | \(0.818481\pi\) | |||||||
\(198\) | −0.534324 | −0.0379728 | ||||||||
\(199\) | 19.9392 | 1.41345 | 0.706727 | − | 0.707486i | \(-0.250171\pi\) | ||||
0.706727 | + | 0.707486i | \(0.250171\pi\) | |||||||
\(200\) | −32.8199 | −2.32072 | ||||||||
\(201\) | −17.6583 | −1.24552 | ||||||||
\(202\) | −25.3679 | −1.78488 | ||||||||
\(203\) | 11.1815 | 0.784787 | ||||||||
\(204\) | −5.96816 | −0.417855 | ||||||||
\(205\) | 11.7143 | 0.818159 | ||||||||
\(206\) | −12.2335 | −0.852351 | ||||||||
\(207\) | 0.465997 | 0.0323890 | ||||||||
\(208\) | 1.92406 | 0.133409 | ||||||||
\(209\) | 4.61118 | 0.318962 | ||||||||
\(210\) | 38.9390 | 2.68705 | ||||||||
\(211\) | −10.3178 | −0.710304 | −0.355152 | − | 0.934809i | \(-0.615571\pi\) | ||||
−0.355152 | + | 0.934809i | \(0.615571\pi\) | |||||||
\(212\) | 7.51776 | 0.516322 | ||||||||
\(213\) | −6.94927 | −0.476156 | ||||||||
\(214\) | −7.34413 | −0.502034 | ||||||||
\(215\) | 3.97246 | 0.270920 | ||||||||
\(216\) | −15.1507 | −1.03087 | ||||||||
\(217\) | 7.01552 | 0.476245 | ||||||||
\(218\) | 13.9164 | 0.942538 | ||||||||
\(219\) | −8.29048 | −0.560219 | ||||||||
\(220\) | 13.1883 | 0.889152 | ||||||||
\(221\) | 5.03650 | 0.338792 | ||||||||
\(222\) | −12.1783 | −0.817355 | ||||||||
\(223\) | −24.3295 | −1.62922 | −0.814610 | − | 0.580009i | \(-0.803049\pi\) | ||||
−0.814610 | + | 0.580009i | \(0.803049\pi\) | |||||||
\(224\) | 12.3112 | 0.822577 | ||||||||
\(225\) | 2.49741 | 0.166494 | ||||||||
\(226\) | 6.63568 | 0.441399 | ||||||||
\(227\) | 3.67046 | 0.243617 | 0.121809 | − | 0.992554i | \(-0.461131\pi\) | ||||
0.121809 | + | 0.992554i | \(0.461131\pi\) | |||||||
\(228\) | −27.5202 | −1.82257 | ||||||||
\(229\) | −3.79206 | −0.250586 | −0.125293 | − | 0.992120i | \(-0.539987\pi\) | ||||
−0.125293 | + | 0.992120i | \(0.539987\pi\) | |||||||
\(230\) | −18.4307 | −1.21529 | ||||||||
\(231\) | −4.24984 | −0.279619 | ||||||||
\(232\) | −14.3992 | −0.945357 | ||||||||
\(233\) | −14.4413 | −0.946080 | −0.473040 | − | 0.881041i | \(-0.656843\pi\) | ||||
−0.473040 | + | 0.881041i | \(0.656843\pi\) | |||||||
\(234\) | −2.69112 | −0.175924 | ||||||||
\(235\) | 3.19773 | 0.208597 | ||||||||
\(236\) | −17.2219 | −1.12105 | ||||||||
\(237\) | 21.9852 | 1.42809 | ||||||||
\(238\) | −5.45271 | −0.353446 | ||||||||
\(239\) | 6.58703 | 0.426080 | 0.213040 | − | 0.977043i | \(-0.431664\pi\) | ||||
0.213040 | + | 0.977043i | \(0.431664\pi\) | |||||||
\(240\) | −2.72811 | −0.176099 | ||||||||
\(241\) | −15.4574 | −0.995699 | −0.497850 | − | 0.867263i | \(-0.665877\pi\) | ||||
−0.497850 | + | 0.867263i | \(0.665877\pi\) | |||||||
\(242\) | −2.30649 | −0.148267 | ||||||||
\(243\) | 2.40224 | 0.154104 | ||||||||
\(244\) | −10.0616 | −0.644130 | ||||||||
\(245\) | −5.60590 | −0.358148 | ||||||||
\(246\) | 12.2270 | 0.779566 | ||||||||
\(247\) | 23.2242 | 1.47772 | ||||||||
\(248\) | −9.03441 | −0.573686 | ||||||||
\(249\) | −1.58186 | −0.100246 | ||||||||
\(250\) | −52.9634 | −3.34970 | ||||||||
\(251\) | 1.77896 | 0.112287 | 0.0561433 | − | 0.998423i | \(-0.482120\pi\) | ||||
0.0561433 | + | 0.998423i | \(0.482120\pi\) | |||||||
\(252\) | 1.81819 | 0.114535 | ||||||||
\(253\) | 2.01155 | 0.126465 | ||||||||
\(254\) | 1.14650 | 0.0719377 | ||||||||
\(255\) | −7.14123 | −0.447201 | ||||||||
\(256\) | −18.3906 | −1.14941 | ||||||||
\(257\) | −28.2634 | −1.76302 | −0.881510 | − | 0.472165i | \(-0.843473\pi\) | ||||
−0.881510 | + | 0.472165i | \(0.843473\pi\) | |||||||
\(258\) | 4.14634 | 0.258140 | ||||||||
\(259\) | −6.94354 | −0.431451 | ||||||||
\(260\) | 66.4227 | 4.11936 | ||||||||
\(261\) | 1.09570 | 0.0678223 | ||||||||
\(262\) | −36.5617 | −2.25879 | ||||||||
\(263\) | −3.86383 | −0.238254 | −0.119127 | − | 0.992879i | \(-0.538010\pi\) | ||||
−0.119127 | + | 0.992879i | \(0.538010\pi\) | |||||||
\(264\) | 5.47284 | 0.336830 | ||||||||
\(265\) | 8.99541 | 0.552584 | ||||||||
\(266\) | −25.1434 | −1.54164 | ||||||||
\(267\) | −9.37536 | −0.573763 | ||||||||
\(268\) | 32.6110 | 1.99203 | ||||||||
\(269\) | 18.7882 | 1.14554 | 0.572768 | − | 0.819717i | \(-0.305870\pi\) | ||||
0.572768 | + | 0.819717i | \(0.305870\pi\) | |||||||
\(270\) | −45.5979 | −2.77500 | ||||||||
\(271\) | −21.7851 | −1.32335 | −0.661674 | − | 0.749791i | \(-0.730154\pi\) | ||||
−0.661674 | + | 0.749791i | \(0.730154\pi\) | |||||||
\(272\) | 0.382023 | 0.0231635 | ||||||||
\(273\) | −21.4043 | −1.29545 | ||||||||
\(274\) | 8.64504 | 0.522266 | ||||||||
\(275\) | 10.7805 | 0.650087 | ||||||||
\(276\) | −12.0052 | −0.722630 | ||||||||
\(277\) | 4.44164 | 0.266872 | 0.133436 | − | 0.991057i | \(-0.457399\pi\) | ||||
0.133436 | + | 0.991057i | \(0.457399\pi\) | |||||||
\(278\) | −21.2285 | −1.27320 | ||||||||
\(279\) | 0.687468 | 0.0411577 | ||||||||
\(280\) | −28.5903 | −1.70860 | ||||||||
\(281\) | −24.5731 | −1.46591 | −0.732956 | − | 0.680276i | \(-0.761860\pi\) | ||||
−0.732956 | + | 0.680276i | \(0.761860\pi\) | |||||||
\(282\) | 3.33770 | 0.198757 | ||||||||
\(283\) | −11.0069 | −0.654294 | −0.327147 | − | 0.944973i | \(-0.606087\pi\) | ||||
−0.327147 | + | 0.944973i | \(0.606087\pi\) | |||||||
\(284\) | 12.8338 | 0.761543 | ||||||||
\(285\) | −32.9295 | −1.95057 | ||||||||
\(286\) | −11.6167 | −0.686908 | ||||||||
\(287\) | 6.97131 | 0.411503 | ||||||||
\(288\) | 1.20641 | 0.0710881 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −43.3364 | −2.54480 | ||||||||
\(291\) | 9.54684 | 0.559646 | ||||||||
\(292\) | 15.3107 | 0.895989 | ||||||||
\(293\) | 13.3828 | 0.781834 | 0.390917 | − | 0.920426i | \(-0.372158\pi\) | ||||
0.390917 | + | 0.920426i | \(0.372158\pi\) | |||||||
\(294\) | −5.85128 | −0.341254 | ||||||||
\(295\) | −20.6069 | −1.19978 | ||||||||
\(296\) | 8.94172 | 0.519727 | ||||||||
\(297\) | 4.97659 | 0.288771 | ||||||||
\(298\) | 15.0492 | 0.871776 | ||||||||
\(299\) | 10.1312 | 0.585900 | ||||||||
\(300\) | −64.3396 | −3.71465 | ||||||||
\(301\) | 2.36407 | 0.136263 | ||||||||
\(302\) | −14.8186 | −0.852715 | ||||||||
\(303\) | −19.7717 | −1.13586 | ||||||||
\(304\) | 1.76157 | 0.101033 | ||||||||
\(305\) | −12.0393 | −0.689368 | ||||||||
\(306\) | −0.534324 | −0.0305453 | ||||||||
\(307\) | 7.62337 | 0.435089 | 0.217544 | − | 0.976050i | \(-0.430195\pi\) | ||||
0.217544 | + | 0.976050i | \(0.430195\pi\) | |||||||
\(308\) | 7.84851 | 0.447210 | ||||||||
\(309\) | −9.53482 | −0.542417 | ||||||||
\(310\) | −27.1902 | −1.54430 | ||||||||
\(311\) | −1.07712 | −0.0610777 | −0.0305388 | − | 0.999534i | \(-0.509722\pi\) | ||||
−0.0305388 | + | 0.999534i | \(0.509722\pi\) | |||||||
\(312\) | 27.5639 | 1.56050 | ||||||||
\(313\) | −6.48880 | −0.366769 | −0.183384 | − | 0.983041i | \(-0.558705\pi\) | ||||
−0.183384 | + | 0.983041i | \(0.558705\pi\) | |||||||
\(314\) | 32.6680 | 1.84356 | ||||||||
\(315\) | 2.17556 | 0.122579 | ||||||||
\(316\) | −40.6018 | −2.28403 | ||||||||
\(317\) | 8.97582 | 0.504132 | 0.252066 | − | 0.967710i | \(-0.418890\pi\) | ||||
0.252066 | + | 0.967710i | \(0.418890\pi\) | |||||||
\(318\) | 9.38916 | 0.526518 | ||||||||
\(319\) | 4.72977 | 0.264816 | ||||||||
\(320\) | −50.7500 | −2.83701 | ||||||||
\(321\) | −5.72402 | −0.319483 | ||||||||
\(322\) | −10.9684 | −0.611244 | ||||||||
\(323\) | 4.61118 | 0.256573 | ||||||||
\(324\) | −32.0084 | −1.77824 | ||||||||
\(325\) | 54.2958 | 3.01179 | ||||||||
\(326\) | −10.0149 | −0.554673 | ||||||||
\(327\) | 10.8464 | 0.599810 | ||||||||
\(328\) | −8.97748 | −0.495698 | ||||||||
\(329\) | 1.90301 | 0.104916 | ||||||||
\(330\) | 16.4712 | 0.906710 | ||||||||
\(331\) | 20.5957 | 1.13204 | 0.566022 | − | 0.824390i | \(-0.308482\pi\) | ||||
0.566022 | + | 0.824390i | \(0.308482\pi\) | |||||||
\(332\) | 2.92134 | 0.160330 | ||||||||
\(333\) | −0.680415 | −0.0372865 | ||||||||
\(334\) | −17.7937 | −0.973626 | ||||||||
\(335\) | 39.0209 | 2.13194 | ||||||||
\(336\) | −1.62354 | −0.0885711 | ||||||||
\(337\) | −30.2896 | −1.64998 | −0.824991 | − | 0.565146i | \(-0.808820\pi\) | ||||
−0.824991 | + | 0.565146i | \(0.808820\pi\) | |||||||
\(338\) | −28.5229 | −1.55144 | ||||||||
\(339\) | 5.17185 | 0.280896 | ||||||||
\(340\) | 13.1883 | 0.715234 | ||||||||
\(341\) | 2.96757 | 0.160703 | ||||||||
\(342\) | −2.46386 | −0.133230 | ||||||||
\(343\) | −19.8846 | −1.07367 | ||||||||
\(344\) | −3.04439 | −0.164142 | ||||||||
\(345\) | −14.3649 | −0.773381 | ||||||||
\(346\) | 49.2548 | 2.64795 | ||||||||
\(347\) | −16.3565 | −0.878062 | −0.439031 | − | 0.898472i | \(-0.644678\pi\) | ||||
−0.439031 | + | 0.898472i | \(0.644678\pi\) | |||||||
\(348\) | −28.2280 | −1.51318 | ||||||||
\(349\) | −35.5578 | −1.90336 | −0.951682 | − | 0.307086i | \(-0.900646\pi\) | ||||
−0.951682 | + | 0.307086i | \(0.900646\pi\) | |||||||
\(350\) | −58.7828 | −3.14207 | ||||||||
\(351\) | 25.0646 | 1.33785 | ||||||||
\(352\) | 5.20764 | 0.277568 | ||||||||
\(353\) | 12.5560 | 0.668291 | 0.334145 | − | 0.942522i | \(-0.391552\pi\) | ||||
0.334145 | + | 0.942522i | \(0.391552\pi\) | |||||||
\(354\) | −21.5089 | −1.14319 | ||||||||
\(355\) | 15.3563 | 0.815027 | ||||||||
\(356\) | 17.3142 | 0.917651 | ||||||||
\(357\) | −4.24984 | −0.224925 | ||||||||
\(358\) | −31.1487 | −1.64626 | ||||||||
\(359\) | −4.29395 | −0.226626 | −0.113313 | − | 0.993559i | \(-0.536146\pi\) | ||||
−0.113313 | + | 0.993559i | \(0.536146\pi\) | |||||||
\(360\) | −2.80164 | −0.147659 | ||||||||
\(361\) | 2.26294 | 0.119102 | ||||||||
\(362\) | 31.5930 | 1.66049 | ||||||||
\(363\) | −1.79768 | −0.0943538 | ||||||||
\(364\) | 39.5290 | 2.07188 | ||||||||
\(365\) | 18.3200 | 0.958915 | ||||||||
\(366\) | −12.5663 | −0.656849 | ||||||||
\(367\) | 1.24864 | 0.0651785 | 0.0325892 | − | 0.999469i | \(-0.489625\pi\) | ||||
0.0325892 | + | 0.999469i | \(0.489625\pi\) | |||||||
\(368\) | 0.768457 | 0.0400586 | ||||||||
\(369\) | 0.683136 | 0.0355626 | ||||||||
\(370\) | 26.9113 | 1.39905 | ||||||||
\(371\) | 5.35329 | 0.277929 | ||||||||
\(372\) | −17.7109 | −0.918267 | ||||||||
\(373\) | 30.4820 | 1.57830 | 0.789149 | − | 0.614202i | \(-0.210522\pi\) | ||||
0.789149 | + | 0.614202i | \(0.210522\pi\) | |||||||
\(374\) | −2.30649 | −0.119266 | ||||||||
\(375\) | −41.2797 | −2.13167 | ||||||||
\(376\) | −2.45065 | −0.126383 | ||||||||
\(377\) | 23.8215 | 1.22687 | ||||||||
\(378\) | −27.1359 | −1.39572 | ||||||||
\(379\) | −21.4909 | −1.10391 | −0.551957 | − | 0.833873i | \(-0.686119\pi\) | ||||
−0.551957 | + | 0.833873i | \(0.686119\pi\) | |||||||
\(380\) | 60.8134 | 3.11966 | ||||||||
\(381\) | 0.893581 | 0.0457795 | ||||||||
\(382\) | −8.42666 | −0.431146 | ||||||||
\(383\) | −12.9004 | −0.659179 | −0.329590 | − | 0.944124i | \(-0.606910\pi\) | ||||
−0.329590 | + | 0.944124i | \(0.606910\pi\) | |||||||
\(384\) | −34.2480 | −1.74771 | ||||||||
\(385\) | 9.39117 | 0.478618 | ||||||||
\(386\) | −34.4235 | −1.75211 | ||||||||
\(387\) | 0.231661 | 0.0117760 | ||||||||
\(388\) | −17.6309 | −0.895073 | ||||||||
\(389\) | −34.4946 | −1.74895 | −0.874473 | − | 0.485074i | \(-0.838793\pi\) | ||||
−0.874473 | + | 0.485074i | \(0.838793\pi\) | |||||||
\(390\) | 82.9572 | 4.20070 | ||||||||
\(391\) | 2.01155 | 0.101728 | ||||||||
\(392\) | 4.29621 | 0.216991 | ||||||||
\(393\) | −28.4962 | −1.43744 | ||||||||
\(394\) | 54.5010 | 2.74572 | ||||||||
\(395\) | −48.5823 | −2.44444 | ||||||||
\(396\) | 0.769095 | 0.0386485 | ||||||||
\(397\) | −19.8626 | −0.996875 | −0.498437 | − | 0.866926i | \(-0.666093\pi\) | ||||
−0.498437 | + | 0.866926i | \(0.666093\pi\) | |||||||
\(398\) | −45.9897 | −2.30526 | ||||||||
\(399\) | −19.5968 | −0.981065 | ||||||||
\(400\) | 4.11839 | 0.205919 | ||||||||
\(401\) | 5.32106 | 0.265721 | 0.132860 | − | 0.991135i | \(-0.457584\pi\) | ||||
0.132860 | + | 0.991135i | \(0.457584\pi\) | |||||||
\(402\) | 40.7289 | 2.03137 | ||||||||
\(403\) | 14.9461 | 0.744520 | ||||||||
\(404\) | 36.5140 | 1.81664 | ||||||||
\(405\) | −38.2998 | −1.90313 | ||||||||
\(406\) | −25.7901 | −1.27994 | ||||||||
\(407\) | −2.93712 | −0.145588 | ||||||||
\(408\) | 5.47284 | 0.270946 | ||||||||
\(409\) | 25.3552 | 1.25373 | 0.626867 | − | 0.779126i | \(-0.284337\pi\) | ||||
0.626867 | + | 0.779126i | \(0.284337\pi\) | |||||||
\(410\) | −27.0189 | −1.33437 | ||||||||
\(411\) | 6.73794 | 0.332358 | ||||||||
\(412\) | 17.6087 | 0.867518 | ||||||||
\(413\) | −12.2635 | −0.603445 | ||||||||
\(414\) | −1.07482 | −0.0528245 | ||||||||
\(415\) | 3.49555 | 0.171590 | ||||||||
\(416\) | 26.2283 | 1.28595 | ||||||||
\(417\) | −16.5455 | −0.810236 | ||||||||
\(418\) | −10.6357 | −0.520207 | ||||||||
\(419\) | −16.0949 | −0.786289 | −0.393144 | − | 0.919477i | \(-0.628613\pi\) | ||||
−0.393144 | + | 0.919477i | \(0.628613\pi\) | |||||||
\(420\) | −56.0480 | −2.73486 | ||||||||
\(421\) | 25.1303 | 1.22477 | 0.612387 | − | 0.790558i | \(-0.290209\pi\) | ||||
0.612387 | + | 0.790558i | \(0.290209\pi\) | |||||||
\(422\) | 23.7979 | 1.15846 | ||||||||
\(423\) | 0.186481 | 0.00906701 | ||||||||
\(424\) | −6.89383 | −0.334794 | ||||||||
\(425\) | 10.7805 | 0.522930 | ||||||||
\(426\) | 16.0285 | 0.776581 | ||||||||
\(427\) | −7.16474 | −0.346726 | ||||||||
\(428\) | 10.5710 | 0.510968 | ||||||||
\(429\) | −9.05402 | −0.437132 | ||||||||
\(430\) | −9.16247 | −0.441853 | ||||||||
\(431\) | −27.7556 | −1.33694 | −0.668469 | − | 0.743740i | \(-0.733050\pi\) | ||||
−0.668469 | + | 0.743740i | \(0.733050\pi\) | |||||||
\(432\) | 1.90117 | 0.0914702 | ||||||||
\(433\) | −23.4623 | −1.12753 | −0.563763 | − | 0.825937i | \(-0.690647\pi\) | ||||
−0.563763 | + | 0.825937i | \(0.690647\pi\) | |||||||
\(434\) | −16.1813 | −0.776726 | ||||||||
\(435\) | −33.7764 | −1.61945 | ||||||||
\(436\) | −20.0310 | −0.959310 | ||||||||
\(437\) | 9.27560 | 0.443712 | ||||||||
\(438\) | 19.1219 | 0.913682 | ||||||||
\(439\) | −14.9357 | −0.712842 | −0.356421 | − | 0.934326i | \(-0.616003\pi\) | ||||
−0.356421 | + | 0.934326i | \(0.616003\pi\) | |||||||
\(440\) | −12.0937 | −0.576545 | ||||||||
\(441\) | −0.326917 | −0.0155675 | ||||||||
\(442\) | −11.6167 | −0.552548 | ||||||||
\(443\) | −26.4690 | −1.25758 | −0.628789 | − | 0.777576i | \(-0.716449\pi\) | ||||
−0.628789 | + | 0.777576i | \(0.716449\pi\) | |||||||
\(444\) | 17.5292 | 0.831899 | ||||||||
\(445\) | 20.7174 | 0.982099 | ||||||||
\(446\) | 56.1158 | 2.65716 | ||||||||
\(447\) | 11.7293 | 0.554779 | ||||||||
\(448\) | −30.2020 | −1.42691 | ||||||||
\(449\) | −12.1365 | −0.572756 | −0.286378 | − | 0.958117i | \(-0.592451\pi\) | ||||
−0.286378 | + | 0.958117i | \(0.592451\pi\) | |||||||
\(450\) | −5.76027 | −0.271542 | ||||||||
\(451\) | 2.94886 | 0.138857 | ||||||||
\(452\) | −9.55125 | −0.449253 | ||||||||
\(453\) | −11.5496 | −0.542649 | ||||||||
\(454\) | −8.46591 | −0.397325 | ||||||||
\(455\) | 47.2986 | 2.21739 | ||||||||
\(456\) | 25.2362 | 1.18179 | ||||||||
\(457\) | −24.0835 | −1.12658 | −0.563290 | − | 0.826259i | \(-0.690465\pi\) | ||||
−0.563290 | + | 0.826259i | \(0.690465\pi\) | |||||||
\(458\) | 8.74636 | 0.408691 | ||||||||
\(459\) | 4.97659 | 0.232288 | ||||||||
\(460\) | 26.5288 | 1.23691 | ||||||||
\(461\) | 38.0126 | 1.77042 | 0.885211 | − | 0.465189i | \(-0.154014\pi\) | ||||
0.885211 | + | 0.465189i | \(0.154014\pi\) | |||||||
\(462\) | 9.80223 | 0.456041 | ||||||||
\(463\) | −8.42811 | −0.391688 | −0.195844 | − | 0.980635i | \(-0.562745\pi\) | ||||
−0.195844 | + | 0.980635i | \(0.562745\pi\) | |||||||
\(464\) | 1.80688 | 0.0838823 | ||||||||
\(465\) | −21.1921 | −0.982758 | ||||||||
\(466\) | 33.3088 | 1.54300 | ||||||||
\(467\) | 7.65618 | 0.354286 | 0.177143 | − | 0.984185i | \(-0.443315\pi\) | ||||
0.177143 | + | 0.984185i | \(0.443315\pi\) | |||||||
\(468\) | 3.87355 | 0.179055 | ||||||||
\(469\) | 23.2218 | 1.07228 | ||||||||
\(470\) | −7.37555 | −0.340209 | ||||||||
\(471\) | 25.4614 | 1.17320 | ||||||||
\(472\) | 15.7926 | 0.726912 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | −50.7088 | −2.32913 | ||||||||
\(475\) | 49.7106 | 2.28088 | ||||||||
\(476\) | 7.84851 | 0.359736 | ||||||||
\(477\) | 0.524582 | 0.0240190 | ||||||||
\(478\) | −15.1930 | −0.694910 | ||||||||
\(479\) | −15.8805 | −0.725600 | −0.362800 | − | 0.931867i | \(-0.618179\pi\) | ||||
−0.362800 | + | 0.931867i | \(0.618179\pi\) | |||||||
\(480\) | −37.1889 | −1.69743 | ||||||||
\(481\) | −14.7928 | −0.674494 | ||||||||
\(482\) | 35.6524 | 1.62392 | ||||||||
\(483\) | −8.54875 | −0.388982 | ||||||||
\(484\) | 3.31992 | 0.150905 | ||||||||
\(485\) | −21.0963 | −0.957935 | ||||||||
\(486\) | −5.54075 | −0.251334 | ||||||||
\(487\) | 9.58877 | 0.434509 | 0.217254 | − | 0.976115i | \(-0.430290\pi\) | ||||
0.217254 | + | 0.976115i | \(0.430290\pi\) | |||||||
\(488\) | 9.22657 | 0.417667 | ||||||||
\(489\) | −7.80559 | −0.352981 | ||||||||
\(490\) | 12.9300 | 0.584117 | ||||||||
\(491\) | 10.5643 | 0.476762 | 0.238381 | − | 0.971172i | \(-0.423383\pi\) | ||||
0.238381 | + | 0.971172i | \(0.423383\pi\) | |||||||
\(492\) | −17.5993 | −0.793437 | ||||||||
\(493\) | 4.72977 | 0.213018 | ||||||||
\(494\) | −53.5665 | −2.41007 | ||||||||
\(495\) | 0.920264 | 0.0413628 | ||||||||
\(496\) | 1.13368 | 0.0509036 | ||||||||
\(497\) | 9.13873 | 0.409928 | ||||||||
\(498\) | 3.64855 | 0.163495 | ||||||||
\(499\) | −3.31503 | −0.148401 | −0.0742006 | − | 0.997243i | \(-0.523641\pi\) | ||||
−0.0742006 | + | 0.997243i | \(0.523641\pi\) | |||||||
\(500\) | 76.2344 | 3.40930 | ||||||||
\(501\) | −13.8684 | −0.619593 | ||||||||
\(502\) | −4.10315 | −0.183133 | ||||||||
\(503\) | 5.41307 | 0.241357 | 0.120678 | − | 0.992692i | \(-0.461493\pi\) | ||||
0.120678 | + | 0.992692i | \(0.461493\pi\) | |||||||
\(504\) | −1.66729 | −0.0742671 | ||||||||
\(505\) | 43.6910 | 1.94422 | ||||||||
\(506\) | −4.63962 | −0.206256 | ||||||||
\(507\) | −22.2307 | −0.987301 | ||||||||
\(508\) | −1.65025 | −0.0732178 | ||||||||
\(509\) | 22.4941 | 0.997034 | 0.498517 | − | 0.866880i | \(-0.333878\pi\) | ||||
0.498517 | + | 0.866880i | \(0.333878\pi\) | |||||||
\(510\) | 16.4712 | 0.729357 | ||||||||
\(511\) | 10.9025 | 0.482298 | ||||||||
\(512\) | 4.31549 | 0.190719 | ||||||||
\(513\) | 22.9479 | 1.01318 | ||||||||
\(514\) | 65.1893 | 2.87538 | ||||||||
\(515\) | 21.0698 | 0.928445 | ||||||||
\(516\) | −5.96816 | −0.262734 | ||||||||
\(517\) | 0.804974 | 0.0354027 | ||||||||
\(518\) | 16.0153 | 0.703670 | ||||||||
\(519\) | 38.3892 | 1.68510 | ||||||||
\(520\) | −60.9100 | −2.67108 | ||||||||
\(521\) | 25.4152 | 1.11346 | 0.556729 | − | 0.830694i | \(-0.312056\pi\) | ||||
0.556729 | + | 0.830694i | \(0.312056\pi\) | |||||||
\(522\) | −2.52723 | −0.110614 | ||||||||
\(523\) | 5.89531 | 0.257784 | 0.128892 | − | 0.991659i | \(-0.458858\pi\) | ||||
0.128892 | + | 0.991659i | \(0.458858\pi\) | |||||||
\(524\) | 52.6261 | 2.29898 | ||||||||
\(525\) | −45.8153 | −1.99954 | ||||||||
\(526\) | 8.91190 | 0.388577 | ||||||||
\(527\) | 2.96757 | 0.129269 | ||||||||
\(528\) | −0.686755 | −0.0298872 | ||||||||
\(529\) | −18.9537 | −0.824073 | ||||||||
\(530\) | −20.7479 | −0.901230 | ||||||||
\(531\) | −1.20173 | −0.0521505 | ||||||||
\(532\) | 36.1908 | 1.56907 | ||||||||
\(533\) | 14.8520 | 0.643310 | ||||||||
\(534\) | 21.6242 | 0.935772 | ||||||||
\(535\) | 12.6488 | 0.546854 | ||||||||
\(536\) | −29.9045 | −1.29168 | ||||||||
\(537\) | −24.2773 | −1.04764 | ||||||||
\(538\) | −43.3349 | −1.86830 | ||||||||
\(539\) | −1.41119 | −0.0607843 | ||||||||
\(540\) | 65.6326 | 2.82438 | ||||||||
\(541\) | −29.8660 | −1.28404 | −0.642020 | − | 0.766688i | \(-0.721904\pi\) | ||||
−0.642020 | + | 0.766688i | \(0.721904\pi\) | |||||||
\(542\) | 50.2471 | 2.15830 | ||||||||
\(543\) | 24.6236 | 1.05670 | ||||||||
\(544\) | 5.20764 | 0.223276 | ||||||||
\(545\) | −23.9682 | −1.02668 | ||||||||
\(546\) | 49.3689 | 2.11280 | ||||||||
\(547\) | −36.5808 | −1.56408 | −0.782041 | − | 0.623227i | \(-0.785821\pi\) | ||||
−0.782041 | + | 0.623227i | \(0.785821\pi\) | |||||||
\(548\) | −12.4435 | −0.531559 | ||||||||
\(549\) | −0.702091 | −0.0299645 | ||||||||
\(550\) | −24.8651 | −1.06025 | ||||||||
\(551\) | 21.8098 | 0.929129 | ||||||||
\(552\) | 11.0089 | 0.468569 | ||||||||
\(553\) | −28.9120 | −1.22946 | ||||||||
\(554\) | −10.2446 | −0.435252 | ||||||||
\(555\) | 20.9746 | 0.890324 | ||||||||
\(556\) | 30.5558 | 1.29586 | ||||||||
\(557\) | 4.75495 | 0.201474 | 0.100737 | − | 0.994913i | \(-0.467880\pi\) | ||||
0.100737 | + | 0.994913i | \(0.467880\pi\) | |||||||
\(558\) | −1.58564 | −0.0671256 | ||||||||
\(559\) | 5.03650 | 0.213021 | ||||||||
\(560\) | 3.58764 | 0.151605 | ||||||||
\(561\) | −1.79768 | −0.0758982 | ||||||||
\(562\) | 56.6778 | 2.39081 | ||||||||
\(563\) | −28.1317 | −1.18561 | −0.592805 | − | 0.805346i | \(-0.701980\pi\) | ||||
−0.592805 | + | 0.805346i | \(0.701980\pi\) | |||||||
\(564\) | −4.80421 | −0.202294 | ||||||||
\(565\) | −11.4286 | −0.480805 | ||||||||
\(566\) | 25.3874 | 1.06711 | ||||||||
\(567\) | −22.7927 | −0.957204 | ||||||||
\(568\) | −11.7686 | −0.493801 | ||||||||
\(569\) | 3.73881 | 0.156739 | 0.0783696 | − | 0.996924i | \(-0.475029\pi\) | ||||
0.0783696 | + | 0.996924i | \(0.475029\pi\) | |||||||
\(570\) | 75.9516 | 3.18126 | ||||||||
\(571\) | −21.4103 | −0.895994 | −0.447997 | − | 0.894035i | \(-0.647863\pi\) | ||||
−0.447997 | + | 0.894035i | \(0.647863\pi\) | |||||||
\(572\) | 16.7208 | 0.699130 | ||||||||
\(573\) | −6.56774 | −0.274371 | ||||||||
\(574\) | −16.0793 | −0.671137 | ||||||||
\(575\) | 21.6854 | 0.904345 | ||||||||
\(576\) | −2.95957 | −0.123315 | ||||||||
\(577\) | 16.2220 | 0.675330 | 0.337665 | − | 0.941266i | \(-0.390363\pi\) | ||||
0.337665 | + | 0.941266i | \(0.390363\pi\) | |||||||
\(578\) | −2.30649 | −0.0959375 | ||||||||
\(579\) | −26.8297 | −1.11500 | ||||||||
\(580\) | 62.3774 | 2.59008 | ||||||||
\(581\) | 2.08025 | 0.0863032 | ||||||||
\(582\) | −22.0197 | −0.912748 | ||||||||
\(583\) | 2.26444 | 0.0937836 | ||||||||
\(584\) | −14.0400 | −0.580978 | ||||||||
\(585\) | 4.63491 | 0.191630 | ||||||||
\(586\) | −30.8675 | −1.27512 | ||||||||
\(587\) | 5.49789 | 0.226922 | 0.113461 | − | 0.993542i | \(-0.463806\pi\) | ||||
0.113461 | + | 0.993542i | \(0.463806\pi\) | |||||||
\(588\) | 8.42221 | 0.347326 | ||||||||
\(589\) | 13.6840 | 0.563838 | ||||||||
\(590\) | 47.5298 | 1.95677 | ||||||||
\(591\) | 42.4780 | 1.74731 | ||||||||
\(592\) | −1.12205 | −0.0461158 | ||||||||
\(593\) | −38.6582 | −1.58750 | −0.793751 | − | 0.608243i | \(-0.791875\pi\) | ||||
−0.793751 | + | 0.608243i | \(0.791875\pi\) | |||||||
\(594\) | −11.4785 | −0.470968 | ||||||||
\(595\) | 9.39117 | 0.385000 | ||||||||
\(596\) | −21.6615 | −0.887289 | ||||||||
\(597\) | −35.8444 | −1.46701 | ||||||||
\(598\) | −23.3675 | −0.955567 | ||||||||
\(599\) | −22.5254 | −0.920362 | −0.460181 | − | 0.887825i | \(-0.652215\pi\) | ||||
−0.460181 | + | 0.887825i | \(0.652215\pi\) | |||||||
\(600\) | 58.9998 | 2.40866 | ||||||||
\(601\) | −33.6816 | −1.37390 | −0.686951 | − | 0.726704i | \(-0.741051\pi\) | ||||
−0.686951 | + | 0.726704i | \(0.741051\pi\) | |||||||
\(602\) | −5.45271 | −0.222236 | ||||||||
\(603\) | 2.27556 | 0.0926682 | ||||||||
\(604\) | 21.3296 | 0.867888 | ||||||||
\(605\) | 3.97246 | 0.161504 | ||||||||
\(606\) | 45.6034 | 1.85251 | ||||||||
\(607\) | −17.1069 | −0.694348 | −0.347174 | − | 0.937801i | \(-0.612859\pi\) | ||||
−0.347174 | + | 0.937801i | \(0.612859\pi\) | |||||||
\(608\) | 24.0133 | 0.973869 | ||||||||
\(609\) | −20.1008 | −0.814524 | ||||||||
\(610\) | 27.7686 | 1.12432 | ||||||||
\(611\) | 4.05425 | 0.164018 | ||||||||
\(612\) | 0.769095 | 0.0310888 | ||||||||
\(613\) | −37.3777 | −1.50967 | −0.754836 | − | 0.655914i | \(-0.772283\pi\) | ||||
−0.754836 | + | 0.655914i | \(0.772283\pi\) | |||||||
\(614\) | −17.5833 | −0.709603 | ||||||||
\(615\) | −21.0585 | −0.849161 | ||||||||
\(616\) | −7.19713 | −0.289981 | ||||||||
\(617\) | 20.4256 | 0.822305 | 0.411153 | − | 0.911567i | \(-0.365126\pi\) | ||||
0.411153 | + | 0.911567i | \(0.365126\pi\) | |||||||
\(618\) | 21.9920 | 0.884649 | ||||||||
\(619\) | −9.59815 | −0.385782 | −0.192891 | − | 0.981220i | \(-0.561786\pi\) | ||||
−0.192891 | + | 0.981220i | \(0.561786\pi\) | |||||||
\(620\) | 39.1370 | 1.57178 | ||||||||
\(621\) | 10.0107 | 0.401714 | ||||||||
\(622\) | 2.48436 | 0.0996139 | ||||||||
\(623\) | 12.3292 | 0.493959 | ||||||||
\(624\) | −3.45884 | −0.138465 | ||||||||
\(625\) | 37.3162 | 1.49265 | ||||||||
\(626\) | 14.9664 | 0.598177 | ||||||||
\(627\) | −8.28943 | −0.331048 | ||||||||
\(628\) | −47.0216 | −1.87637 | ||||||||
\(629\) | −2.93712 | −0.117111 | ||||||||
\(630\) | −5.01793 | −0.199919 | ||||||||
\(631\) | −2.81773 | −0.112172 | −0.0560861 | − | 0.998426i | \(-0.517862\pi\) | ||||
−0.0560861 | + | 0.998426i | \(0.517862\pi\) | |||||||
\(632\) | 37.2321 | 1.48101 | ||||||||
\(633\) | 18.5481 | 0.737219 | ||||||||
\(634\) | −20.7027 | −0.822208 | ||||||||
\(635\) | −1.97461 | −0.0783600 | ||||||||
\(636\) | −13.5145 | −0.535887 | ||||||||
\(637\) | −7.10746 | −0.281608 | ||||||||
\(638\) | −10.9092 | −0.431899 | ||||||||
\(639\) | 0.895527 | 0.0354265 | ||||||||
\(640\) | 75.6802 | 2.99152 | ||||||||
\(641\) | 26.4632 | 1.04523 | 0.522616 | − | 0.852568i | \(-0.324956\pi\) | ||||
0.522616 | + | 0.852568i | \(0.324956\pi\) | |||||||
\(642\) | 13.2024 | 0.521058 | ||||||||
\(643\) | −10.6832 | −0.421305 | −0.210652 | − | 0.977561i | \(-0.567559\pi\) | ||||
−0.210652 | + | 0.977561i | \(0.567559\pi\) | |||||||
\(644\) | 15.7876 | 0.622120 | ||||||||
\(645\) | −7.14123 | −0.281186 | ||||||||
\(646\) | −10.6357 | −0.418454 | ||||||||
\(647\) | −27.2263 | −1.07038 | −0.535188 | − | 0.844733i | \(-0.679759\pi\) | ||||
−0.535188 | + | 0.844733i | \(0.679759\pi\) | |||||||
\(648\) | 29.3519 | 1.15305 | ||||||||
\(649\) | −5.18744 | −0.203625 | ||||||||
\(650\) | −125.233 | −4.91205 | ||||||||
\(651\) | −12.6117 | −0.494291 | ||||||||
\(652\) | 14.4152 | 0.564542 | ||||||||
\(653\) | 43.2871 | 1.69396 | 0.846978 | − | 0.531628i | \(-0.178420\pi\) | ||||
0.846978 | + | 0.531628i | \(0.178420\pi\) | |||||||
\(654\) | −25.0173 | −0.978253 | ||||||||
\(655\) | 62.9701 | 2.46044 | ||||||||
\(656\) | 1.12653 | 0.0439837 | ||||||||
\(657\) | 1.06836 | 0.0416808 | ||||||||
\(658\) | −4.38929 | −0.171112 | ||||||||
\(659\) | 39.2963 | 1.53076 | 0.765382 | − | 0.643576i | \(-0.222550\pi\) | ||||
0.765382 | + | 0.643576i | \(0.222550\pi\) | |||||||
\(660\) | −23.7083 | −0.922844 | ||||||||
\(661\) | 36.7242 | 1.42840 | 0.714202 | − | 0.699940i | \(-0.246790\pi\) | ||||
0.714202 | + | 0.699940i | \(0.246790\pi\) | |||||||
\(662\) | −47.5040 | −1.84630 | ||||||||
\(663\) | −9.05402 | −0.351629 | ||||||||
\(664\) | −2.67889 | −0.103961 | ||||||||
\(665\) | 43.3043 | 1.67927 | ||||||||
\(666\) | 1.56937 | 0.0608120 | ||||||||
\(667\) | 9.51416 | 0.368390 | ||||||||
\(668\) | 25.6118 | 0.990951 | ||||||||
\(669\) | 43.7366 | 1.69096 | ||||||||
\(670\) | −90.0014 | −3.47706 | ||||||||
\(671\) | −3.03068 | −0.116998 | ||||||||
\(672\) | −22.1316 | −0.853746 | ||||||||
\(673\) | −21.6886 | −0.836036 | −0.418018 | − | 0.908439i | \(-0.637275\pi\) | ||||
−0.418018 | + | 0.908439i | \(0.637275\pi\) | |||||||
\(674\) | 69.8629 | 2.69102 | ||||||||
\(675\) | 53.6500 | 2.06499 | ||||||||
\(676\) | 41.0552 | 1.57905 | ||||||||
\(677\) | 7.81484 | 0.300349 | 0.150174 | − | 0.988660i | \(-0.452016\pi\) | ||||
0.150174 | + | 0.988660i | \(0.452016\pi\) | |||||||
\(678\) | −11.9288 | −0.458124 | ||||||||
\(679\) | −12.5547 | −0.481805 | ||||||||
\(680\) | −12.0937 | −0.463773 | ||||||||
\(681\) | −6.59833 | −0.252848 | ||||||||
\(682\) | −6.84467 | −0.262096 | ||||||||
\(683\) | −6.99262 | −0.267565 | −0.133783 | − | 0.991011i | \(-0.542712\pi\) | ||||
−0.133783 | + | 0.991011i | \(0.542712\pi\) | |||||||
\(684\) | 3.54643 | 0.135601 | ||||||||
\(685\) | −14.8893 | −0.568891 | ||||||||
\(686\) | 45.8638 | 1.75109 | ||||||||
\(687\) | 6.81692 | 0.260082 | ||||||||
\(688\) | 0.382023 | 0.0145645 | ||||||||
\(689\) | 11.4049 | 0.434491 | ||||||||
\(690\) | 33.1326 | 1.26134 | ||||||||
\(691\) | 40.5559 | 1.54282 | 0.771409 | − | 0.636340i | \(-0.219552\pi\) | ||||
0.771409 | + | 0.636340i | \(0.219552\pi\) | |||||||
\(692\) | −70.8963 | −2.69507 | ||||||||
\(693\) | 0.547661 | 0.0208039 | ||||||||
\(694\) | 37.7261 | 1.43206 | ||||||||
\(695\) | 36.5617 | 1.38687 | ||||||||
\(696\) | 25.8853 | 0.981178 | ||||||||
\(697\) | 2.94886 | 0.111696 | ||||||||
\(698\) | 82.0138 | 3.10427 | ||||||||
\(699\) | 25.9608 | 0.981930 | ||||||||
\(700\) | 84.6106 | 3.19798 | ||||||||
\(701\) | −38.9586 | −1.47144 | −0.735722 | − | 0.677283i | \(-0.763157\pi\) | ||||
−0.735722 | + | 0.677283i | \(0.763157\pi\) | |||||||
\(702\) | −57.8114 | −2.18195 | ||||||||
\(703\) | −13.5436 | −0.510805 | ||||||||
\(704\) | −12.7754 | −0.481492 | ||||||||
\(705\) | −5.74850 | −0.216501 | ||||||||
\(706\) | −28.9604 | −1.08994 | ||||||||
\(707\) | 26.0011 | 0.977871 | ||||||||
\(708\) | 30.9595 | 1.16353 | ||||||||
\(709\) | 51.8099 | 1.94576 | 0.972881 | − | 0.231307i | \(-0.0743000\pi\) | ||||
0.972881 | + | 0.231307i | \(0.0743000\pi\) | |||||||
\(710\) | −35.4192 | −1.32926 | ||||||||
\(711\) | −2.83315 | −0.106252 | ||||||||
\(712\) | −15.8772 | −0.595024 | ||||||||
\(713\) | 5.96940 | 0.223556 | ||||||||
\(714\) | 9.80223 | 0.366839 | ||||||||
\(715\) | 20.0073 | 0.748231 | ||||||||
\(716\) | 44.8348 | 1.67556 | ||||||||
\(717\) | −11.8414 | −0.442225 | ||||||||
\(718\) | 9.90397 | 0.369613 | ||||||||
\(719\) | −1.97125 | −0.0735151 | −0.0367575 | − | 0.999324i | \(-0.511703\pi\) | ||||
−0.0367575 | + | 0.999324i | \(0.511703\pi\) | |||||||
\(720\) | 0.351562 | 0.0131019 | ||||||||
\(721\) | 12.5389 | 0.466973 | ||||||||
\(722\) | −5.21945 | −0.194248 | ||||||||
\(723\) | 27.7875 | 1.03343 | ||||||||
\(724\) | −45.4743 | −1.69004 | ||||||||
\(725\) | 50.9892 | 1.89369 | ||||||||
\(726\) | 4.14634 | 0.153885 | ||||||||
\(727\) | −19.0114 | −0.705095 | −0.352548 | − | 0.935794i | \(-0.614685\pi\) | ||||
−0.352548 | + | 0.935794i | \(0.614685\pi\) | |||||||
\(728\) | −36.2483 | −1.34345 | ||||||||
\(729\) | 24.6055 | 0.911314 | ||||||||
\(730\) | −42.2551 | −1.56393 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | 18.0876 | 0.668537 | ||||||||
\(733\) | −32.4912 | −1.20009 | −0.600046 | − | 0.799966i | \(-0.704851\pi\) | ||||
−0.600046 | + | 0.799966i | \(0.704851\pi\) | |||||||
\(734\) | −2.87998 | −0.106302 | ||||||||
\(735\) | 10.0776 | 0.371719 | ||||||||
\(736\) | 10.4754 | 0.386129 | ||||||||
\(737\) | 9.82283 | 0.361829 | ||||||||
\(738\) | −1.57565 | −0.0580005 | ||||||||
\(739\) | −6.70734 | −0.246733 | −0.123367 | − | 0.992361i | \(-0.539369\pi\) | ||||
−0.123367 | + | 0.992361i | \(0.539369\pi\) | |||||||
\(740\) | −38.7355 | −1.42394 | ||||||||
\(741\) | −41.7497 | −1.53371 | ||||||||
\(742\) | −12.3473 | −0.453285 | ||||||||
\(743\) | −11.4142 | −0.418745 | −0.209372 | − | 0.977836i | \(-0.567142\pi\) | ||||
−0.209372 | + | 0.977836i | \(0.567142\pi\) | |||||||
\(744\) | 16.2410 | 0.595424 | ||||||||
\(745\) | −25.9192 | −0.949604 | ||||||||
\(746\) | −70.3066 | −2.57411 | ||||||||
\(747\) | 0.203848 | 0.00745843 | ||||||||
\(748\) | 3.31992 | 0.121388 | ||||||||
\(749\) | 7.52744 | 0.275047 | ||||||||
\(750\) | 95.2114 | 3.47663 | ||||||||
\(751\) | 3.03628 | 0.110796 | 0.0553978 | − | 0.998464i | \(-0.482357\pi\) | ||||
0.0553978 | + | 0.998464i | \(0.482357\pi\) | |||||||
\(752\) | 0.307518 | 0.0112140 | ||||||||
\(753\) | −3.19800 | −0.116541 | ||||||||
\(754\) | −54.9441 | −2.00095 | ||||||||
\(755\) | 25.5220 | 0.928841 | ||||||||
\(756\) | 39.0588 | 1.42056 | ||||||||
\(757\) | −20.5266 | −0.746050 | −0.373025 | − | 0.927821i | \(-0.621680\pi\) | ||||
−0.373025 | + | 0.927821i | \(0.621680\pi\) | |||||||
\(758\) | 49.5686 | 1.80041 | ||||||||
\(759\) | −3.61612 | −0.131257 | ||||||||
\(760\) | −55.7662 | −2.02285 | ||||||||
\(761\) | 39.0941 | 1.41716 | 0.708579 | − | 0.705631i | \(-0.249337\pi\) | ||||
0.708579 | + | 0.705631i | \(0.249337\pi\) | |||||||
\(762\) | −2.06104 | −0.0746636 | ||||||||
\(763\) | −14.2638 | −0.516383 | ||||||||
\(764\) | 12.1292 | 0.438817 | ||||||||
\(765\) | 0.920264 | 0.0332722 | ||||||||
\(766\) | 29.7547 | 1.07508 | ||||||||
\(767\) | −26.1266 | −0.943375 | ||||||||
\(768\) | 33.0605 | 1.19297 | ||||||||
\(769\) | −10.5632 | −0.380919 | −0.190460 | − | 0.981695i | \(-0.560998\pi\) | ||||
−0.190460 | + | 0.981695i | \(0.560998\pi\) | |||||||
\(770\) | −21.6607 | −0.780597 | ||||||||
\(771\) | 50.8085 | 1.82982 | ||||||||
\(772\) | 49.5484 | 1.78329 | ||||||||
\(773\) | 2.62092 | 0.0942681 | 0.0471340 | − | 0.998889i | \(-0.484991\pi\) | ||||
0.0471340 | + | 0.998889i | \(0.484991\pi\) | |||||||
\(774\) | −0.534324 | −0.0192059 | ||||||||
\(775\) | 31.9918 | 1.14918 | ||||||||
\(776\) | 16.1676 | 0.580384 | ||||||||
\(777\) | 12.4823 | 0.447799 | ||||||||
\(778\) | 79.5616 | 2.85242 | ||||||||
\(779\) | 13.5977 | 0.487189 | ||||||||
\(780\) | −119.407 | −4.27545 | ||||||||
\(781\) | 3.86568 | 0.138325 | ||||||||
\(782\) | −4.63962 | −0.165913 | ||||||||
\(783\) | 23.5381 | 0.841185 | ||||||||
\(784\) | −0.539107 | −0.0192538 | ||||||||
\(785\) | −56.2639 | −2.00815 | ||||||||
\(786\) | 65.7263 | 2.34438 | ||||||||
\(787\) | 42.1682 | 1.50314 | 0.751568 | − | 0.659656i | \(-0.229298\pi\) | ||||
0.751568 | + | 0.659656i | \(0.229298\pi\) | |||||||
\(788\) | −78.4475 | −2.79458 | ||||||||
\(789\) | 6.94593 | 0.247282 | ||||||||
\(790\) | 112.055 | 3.98673 | ||||||||
\(791\) | −6.80131 | −0.241827 | ||||||||
\(792\) | −0.705265 | −0.0250605 | ||||||||
\(793\) | −15.2640 | −0.542042 | ||||||||
\(794\) | 45.8130 | 1.62584 | ||||||||
\(795\) | −16.1709 | −0.573523 | ||||||||
\(796\) | 66.1966 | 2.34628 | ||||||||
\(797\) | 31.4080 | 1.11253 | 0.556263 | − | 0.831006i | \(-0.312235\pi\) | ||||
0.556263 | + | 0.831006i | \(0.312235\pi\) | |||||||
\(798\) | 45.1998 | 1.60006 | ||||||||
\(799\) | 0.804974 | 0.0284779 | ||||||||
\(800\) | 56.1408 | 1.98488 | ||||||||
\(801\) | 1.20817 | 0.0426885 | ||||||||
\(802\) | −12.2730 | −0.433374 | ||||||||
\(803\) | 4.61176 | 0.162745 | ||||||||
\(804\) | −58.6242 | −2.06752 | ||||||||
\(805\) | 18.8908 | 0.665813 | ||||||||
\(806\) | −34.4732 | −1.21427 | ||||||||
\(807\) | −33.7752 | −1.18894 | ||||||||
\(808\) | −33.4835 | −1.17795 | ||||||||
\(809\) | 20.0924 | 0.706412 | 0.353206 | − | 0.935546i | \(-0.385091\pi\) | ||||
0.353206 | + | 0.935546i | \(0.385091\pi\) | |||||||
\(810\) | 88.3383 | 3.10389 | ||||||||
\(811\) | −1.68860 | −0.0592948 | −0.0296474 | − | 0.999560i | \(-0.509438\pi\) | ||||
−0.0296474 | + | 0.999560i | \(0.509438\pi\) | |||||||
\(812\) | 37.1216 | 1.30271 | ||||||||
\(813\) | 39.1626 | 1.37349 | ||||||||
\(814\) | 6.77445 | 0.237444 | ||||||||
\(815\) | 17.2486 | 0.604191 | ||||||||
\(816\) | −0.686755 | −0.0240412 | ||||||||
\(817\) | 4.61118 | 0.161325 | ||||||||
\(818\) | −58.4817 | −2.04476 | ||||||||
\(819\) | 2.75830 | 0.0963827 | ||||||||
\(820\) | 38.8904 | 1.35811 | ||||||||
\(821\) | 8.08410 | 0.282137 | 0.141068 | − | 0.990000i | \(-0.454946\pi\) | ||||
0.141068 | + | 0.990000i | \(0.454946\pi\) | |||||||
\(822\) | −15.5410 | −0.542056 | ||||||||
\(823\) | −48.9410 | −1.70597 | −0.852987 | − | 0.521931i | \(-0.825212\pi\) | ||||
−0.852987 | + | 0.521931i | \(0.825212\pi\) | |||||||
\(824\) | −16.1473 | −0.562517 | ||||||||
\(825\) | −19.3799 | −0.674720 | ||||||||
\(826\) | 28.2856 | 0.984182 | ||||||||
\(827\) | 36.6010 | 1.27274 | 0.636371 | − | 0.771384i | \(-0.280435\pi\) | ||||
0.636371 | + | 0.771384i | \(0.280435\pi\) | |||||||
\(828\) | 1.54707 | 0.0537644 | ||||||||
\(829\) | 40.4011 | 1.40319 | 0.701594 | − | 0.712577i | \(-0.252472\pi\) | ||||
0.701594 | + | 0.712577i | \(0.252472\pi\) | |||||||
\(830\) | −8.06246 | −0.279852 | ||||||||
\(831\) | −7.98465 | −0.276985 | ||||||||
\(832\) | −64.3435 | −2.23071 | ||||||||
\(833\) | −1.41119 | −0.0488949 | ||||||||
\(834\) | 38.1621 | 1.32144 | ||||||||
\(835\) | 30.6459 | 1.06055 | ||||||||
\(836\) | 15.3087 | 0.529463 | ||||||||
\(837\) | 14.7684 | 0.510470 | ||||||||
\(838\) | 37.1229 | 1.28239 | ||||||||
\(839\) | 49.1878 | 1.69815 | 0.849076 | − | 0.528270i | \(-0.177159\pi\) | ||||
0.849076 | + | 0.528270i | \(0.177159\pi\) | |||||||
\(840\) | 51.3963 | 1.77334 | ||||||||
\(841\) | −6.62927 | −0.228596 | ||||||||
\(842\) | −57.9629 | −1.99753 | ||||||||
\(843\) | 44.1747 | 1.52146 | ||||||||
\(844\) | −34.2541 | −1.17908 | ||||||||
\(845\) | 49.1248 | 1.68994 | ||||||||
\(846\) | −0.430117 | −0.0147877 | ||||||||
\(847\) | 2.36407 | 0.0812303 | ||||||||
\(848\) | 0.865068 | 0.0297066 | ||||||||
\(849\) | 19.7870 | 0.679087 | ||||||||
\(850\) | −24.8651 | −0.852866 | ||||||||
\(851\) | −5.90816 | −0.202529 | ||||||||
\(852\) | −23.0710 | −0.790400 | ||||||||
\(853\) | −8.59589 | −0.294318 | −0.147159 | − | 0.989113i | \(-0.547013\pi\) | ||||
−0.147159 | + | 0.989113i | \(0.547013\pi\) | |||||||
\(854\) | 16.5254 | 0.565489 | ||||||||
\(855\) | 4.24350 | 0.145125 | ||||||||
\(856\) | −9.69366 | −0.331322 | ||||||||
\(857\) | −6.09109 | −0.208068 | −0.104034 | − | 0.994574i | \(-0.533175\pi\) | ||||
−0.104034 | + | 0.994574i | \(0.533175\pi\) | |||||||
\(858\) | 20.8831 | 0.712936 | ||||||||
\(859\) | 21.3565 | 0.728676 | 0.364338 | − | 0.931267i | \(-0.381295\pi\) | ||||
0.364338 | + | 0.931267i | \(0.381295\pi\) | |||||||
\(860\) | 13.1883 | 0.449716 | ||||||||
\(861\) | −12.5322 | −0.427096 | ||||||||
\(862\) | 64.0181 | 2.18046 | ||||||||
\(863\) | 37.7200 | 1.28400 | 0.642002 | − | 0.766703i | \(-0.278104\pi\) | ||||
0.642002 | + | 0.766703i | \(0.278104\pi\) | |||||||
\(864\) | 25.9163 | 0.881690 | ||||||||
\(865\) | −84.8313 | −2.88435 | ||||||||
\(866\) | 54.1157 | 1.83893 | ||||||||
\(867\) | −1.79768 | −0.0610525 | ||||||||
\(868\) | 23.2910 | 0.790547 | ||||||||
\(869\) | −12.2298 | −0.414866 | ||||||||
\(870\) | 77.9050 | 2.64123 | ||||||||
\(871\) | 49.4727 | 1.67632 | ||||||||
\(872\) | 18.3685 | 0.622037 | ||||||||
\(873\) | −1.23027 | −0.0416382 | ||||||||
\(874\) | −21.3941 | −0.723667 | ||||||||
\(875\) | 54.2854 | 1.83518 | ||||||||
\(876\) | −27.5237 | −0.929940 | ||||||||
\(877\) | −22.9518 | −0.775029 | −0.387514 | − | 0.921864i | \(-0.626666\pi\) | ||||
−0.387514 | + | 0.921864i | \(0.626666\pi\) | |||||||
\(878\) | 34.4491 | 1.16260 | ||||||||
\(879\) | −24.0581 | −0.811459 | ||||||||
\(880\) | 1.51757 | 0.0511573 | ||||||||
\(881\) | −40.4541 | −1.36293 | −0.681467 | − | 0.731849i | \(-0.738658\pi\) | ||||
−0.681467 | + | 0.731849i | \(0.738658\pi\) | |||||||
\(882\) | 0.754033 | 0.0253896 | ||||||||
\(883\) | −31.5257 | −1.06092 | −0.530462 | − | 0.847708i | \(-0.677982\pi\) | ||||
−0.530462 | + | 0.847708i | \(0.677982\pi\) | |||||||
\(884\) | 16.7208 | 0.562380 | ||||||||
\(885\) | 37.0447 | 1.24524 | ||||||||
\(886\) | 61.0505 | 2.05103 | ||||||||
\(887\) | 53.9270 | 1.81069 | 0.905346 | − | 0.424676i | \(-0.139612\pi\) | ||||
0.905346 | + | 0.424676i | \(0.139612\pi\) | |||||||
\(888\) | −16.0744 | −0.539421 | ||||||||
\(889\) | −1.17512 | −0.0394121 | ||||||||
\(890\) | −47.7846 | −1.60174 | ||||||||
\(891\) | −9.64132 | −0.322996 | ||||||||
\(892\) | −80.7718 | −2.70444 | ||||||||
\(893\) | 3.71188 | 0.124213 | ||||||||
\(894\) | −27.0537 | −0.904810 | ||||||||
\(895\) | 53.6473 | 1.79323 | ||||||||
\(896\) | 45.0383 | 1.50462 | ||||||||
\(897\) | −18.2126 | −0.608101 | ||||||||
\(898\) | 27.9927 | 0.934129 | ||||||||
\(899\) | 14.0359 | 0.468124 | ||||||||
\(900\) | 8.29120 | 0.276373 | ||||||||
\(901\) | 2.26444 | 0.0754395 | ||||||||
\(902\) | −6.80154 | −0.226467 | ||||||||
\(903\) | −4.24984 | −0.141426 | ||||||||
\(904\) | 8.75856 | 0.291305 | ||||||||
\(905\) | −54.4124 | −1.80873 | ||||||||
\(906\) | 26.6391 | 0.885026 | ||||||||
\(907\) | 37.3036 | 1.23865 | 0.619323 | − | 0.785136i | \(-0.287407\pi\) | ||||
0.619323 | + | 0.785136i | \(0.287407\pi\) | |||||||
\(908\) | 12.1856 | 0.404395 | ||||||||
\(909\) | 2.54791 | 0.0845088 | ||||||||
\(910\) | −109.094 | −3.61643 | ||||||||
\(911\) | −19.4609 | −0.644769 | −0.322384 | − | 0.946609i | \(-0.604484\pi\) | ||||
−0.322384 | + | 0.946609i | \(0.604484\pi\) | |||||||
\(912\) | −3.16675 | −0.104862 | ||||||||
\(913\) | 0.879944 | 0.0291219 | ||||||||
\(914\) | 55.5485 | 1.83738 | ||||||||
\(915\) | 21.6428 | 0.715489 | ||||||||
\(916\) | −12.5893 | −0.415963 | ||||||||
\(917\) | 37.4743 | 1.23751 | ||||||||
\(918\) | −11.4785 | −0.378847 | ||||||||
\(919\) | −0.333493 | −0.0110009 | −0.00550046 | − | 0.999985i | \(-0.501751\pi\) | ||||
−0.00550046 | + | 0.999985i | \(0.501751\pi\) | |||||||
\(920\) | −24.3271 | −0.802040 | ||||||||
\(921\) | −13.7044 | −0.451575 | ||||||||
\(922\) | −87.6758 | −2.88745 | ||||||||
\(923\) | 19.4695 | 0.640847 | ||||||||
\(924\) | −14.1091 | −0.464156 | ||||||||
\(925\) | −31.6635 | −1.04109 | ||||||||
\(926\) | 19.4394 | 0.638818 | ||||||||
\(927\) | 1.22872 | 0.0403564 | ||||||||
\(928\) | 24.6309 | 0.808550 | ||||||||
\(929\) | −48.7790 | −1.60039 | −0.800194 | − | 0.599742i | \(-0.795270\pi\) | ||||
−0.800194 | + | 0.599742i | \(0.795270\pi\) | |||||||
\(930\) | 48.8794 | 1.60282 | ||||||||
\(931\) | −6.50725 | −0.213266 | ||||||||
\(932\) | −47.9439 | −1.57046 | ||||||||
\(933\) | 1.93631 | 0.0633921 | ||||||||
\(934\) | −17.6589 | −0.577818 | ||||||||
\(935\) | 3.97246 | 0.129913 | ||||||||
\(936\) | −3.55206 | −0.116103 | ||||||||
\(937\) | −13.6133 | −0.444726 | −0.222363 | − | 0.974964i | \(-0.571377\pi\) | ||||
−0.222363 | + | 0.974964i | \(0.571377\pi\) | |||||||
\(938\) | −53.5610 | −1.74883 | ||||||||
\(939\) | 11.6648 | 0.380666 | ||||||||
\(940\) | 10.6162 | 0.346263 | ||||||||
\(941\) | 1.09381 | 0.0356572 | 0.0178286 | − | 0.999841i | \(-0.494325\pi\) | ||||
0.0178286 | + | 0.999841i | \(0.494325\pi\) | |||||||
\(942\) | −58.7267 | −1.91342 | ||||||||
\(943\) | 5.93178 | 0.193165 | ||||||||
\(944\) | −1.98172 | −0.0644995 | ||||||||
\(945\) | 46.7360 | 1.52032 | ||||||||
\(946\) | −2.30649 | −0.0749906 | ||||||||
\(947\) | 17.8443 | 0.579863 | 0.289931 | − | 0.957047i | \(-0.406368\pi\) | ||||
0.289931 | + | 0.957047i | \(0.406368\pi\) | |||||||
\(948\) | 72.9891 | 2.37058 | ||||||||
\(949\) | 23.2271 | 0.753984 | ||||||||
\(950\) | −114.657 | −3.71998 | ||||||||
\(951\) | −16.1357 | −0.523235 | ||||||||
\(952\) | −7.19713 | −0.233260 | ||||||||
\(953\) | −28.7536 | −0.931420 | −0.465710 | − | 0.884937i | \(-0.654201\pi\) | ||||
−0.465710 | + | 0.884937i | \(0.654201\pi\) | |||||||
\(954\) | −1.20995 | −0.0391735 | ||||||||
\(955\) | 14.5132 | 0.469636 | ||||||||
\(956\) | 21.8684 | 0.707275 | ||||||||
\(957\) | −8.50262 | −0.274851 | ||||||||
\(958\) | 36.6284 | 1.18341 | ||||||||
\(959\) | −8.86082 | −0.286131 | ||||||||
\(960\) | 91.2323 | 2.94451 | ||||||||
\(961\) | −22.1936 | −0.715921 | ||||||||
\(962\) | 34.1195 | 1.10006 | ||||||||
\(963\) | 0.737633 | 0.0237699 | ||||||||
\(964\) | −51.3173 | −1.65282 | ||||||||
\(965\) | 59.2874 | 1.90853 | ||||||||
\(966\) | 19.7177 | 0.634405 | ||||||||
\(967\) | −34.8048 | −1.11925 | −0.559624 | − | 0.828747i | \(-0.689054\pi\) | ||||
−0.559624 | + | 0.828747i | \(0.689054\pi\) | |||||||
\(968\) | −3.04439 | −0.0978503 | ||||||||
\(969\) | −8.28943 | −0.266295 | ||||||||
\(970\) | 48.6586 | 1.56233 | ||||||||
\(971\) | −46.7985 | −1.50184 | −0.750918 | − | 0.660395i | \(-0.770389\pi\) | ||||
−0.750918 | + | 0.660395i | \(0.770389\pi\) | |||||||
\(972\) | 7.97524 | 0.255806 | ||||||||
\(973\) | 21.7584 | 0.697541 | ||||||||
\(974\) | −22.1164 | −0.708657 | ||||||||
\(975\) | −97.6067 | −3.12592 | ||||||||
\(976\) | −1.15779 | −0.0370600 | ||||||||
\(977\) | −3.80196 | −0.121635 | −0.0608177 | − | 0.998149i | \(-0.519371\pi\) | ||||
−0.0608177 | + | 0.998149i | \(0.519371\pi\) | |||||||
\(978\) | 18.0036 | 0.575690 | ||||||||
\(979\) | 5.21525 | 0.166680 | ||||||||
\(980\) | −18.6111 | −0.594511 | ||||||||
\(981\) | −1.39774 | −0.0446265 | ||||||||
\(982\) | −24.3666 | −0.777570 | ||||||||
\(983\) | −23.6880 | −0.755531 | −0.377765 | − | 0.925901i | \(-0.623307\pi\) | ||||
−0.377765 | + | 0.925901i | \(0.623307\pi\) | |||||||
\(984\) | 16.1387 | 0.514482 | ||||||||
\(985\) | −93.8667 | −2.99084 | ||||||||
\(986\) | −10.9092 | −0.347419 | ||||||||
\(987\) | −3.42101 | −0.108892 | ||||||||
\(988\) | 77.1024 | 2.45295 | ||||||||
\(989\) | 2.01155 | 0.0639635 | ||||||||
\(990\) | −2.12258 | −0.0674601 | ||||||||
\(991\) | 14.2183 | 0.451659 | 0.225830 | − | 0.974167i | \(-0.427491\pi\) | ||||
0.225830 | + | 0.974167i | \(0.427491\pi\) | |||||||
\(992\) | 15.4540 | 0.490665 | ||||||||
\(993\) | −37.0246 | −1.17494 | ||||||||
\(994\) | −21.0784 | −0.668568 | ||||||||
\(995\) | 79.2078 | 2.51106 | ||||||||
\(996\) | −5.25165 | −0.166405 | ||||||||
\(997\) | −53.4245 | −1.69197 | −0.845986 | − | 0.533206i | \(-0.820987\pi\) | ||||
−0.845986 | + | 0.533206i | \(0.820987\pi\) | |||||||
\(998\) | 7.64611 | 0.242033 | ||||||||
\(999\) | −14.6168 | −0.462457 |
(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 | 8041.2.a.j.1.10 | ✓ | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.j.1.10 | ✓ | 82 | 1.1 | even | 1 | trivial |