Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00652 | −1.41882 | −0.709412 | − | 0.704794i | \(-0.751040\pi\) | ||||
−0.709412 | + | 0.704794i | \(0.751040\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 2.02613 | 1.01306 | ||||||||
\(5\) | −1.83243 | −0.819489 | −0.409745 | − | 0.912200i | \(-0.634382\pi\) | ||||
−0.409745 | + | 0.912200i | \(0.634382\pi\) | |||||||
\(6\) | 2.00652 | 0.819159 | ||||||||
\(7\) | −1.92586 | −0.727908 | −0.363954 | − | 0.931417i | \(-0.618573\pi\) | ||||
−0.363954 | + | 0.931417i | \(0.618573\pi\) | |||||||
\(8\) | −0.0524220 | −0.0185340 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.67682 | 1.16271 | ||||||||
\(11\) | 3.86289 | 1.16471 | 0.582353 | − | 0.812936i | \(-0.302132\pi\) | ||||
0.582353 | + | 0.812936i | \(0.302132\pi\) | |||||||
\(12\) | −2.02613 | −0.584892 | ||||||||
\(13\) | 6.14415 | 1.70408 | 0.852040 | − | 0.523477i | \(-0.175365\pi\) | ||||
0.852040 | + | 0.523477i | \(0.175365\pi\) | |||||||
\(14\) | 3.86428 | 1.03277 | ||||||||
\(15\) | 1.83243 | 0.473132 | ||||||||
\(16\) | −3.94707 | −0.986766 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −2.00652 | −0.472941 | ||||||||
\(19\) | 0.890505 | 0.204296 | 0.102148 | − | 0.994769i | \(-0.467428\pi\) | ||||
0.102148 | + | 0.994769i | \(0.467428\pi\) | |||||||
\(20\) | −3.71274 | −0.830194 | ||||||||
\(21\) | 1.92586 | 0.420258 | ||||||||
\(22\) | −7.75098 | −1.65251 | ||||||||
\(23\) | −5.99726 | −1.25052 | −0.625258 | − | 0.780418i | \(-0.715006\pi\) | ||||
−0.625258 | + | 0.780418i | \(0.715006\pi\) | |||||||
\(24\) | 0.0524220 | 0.0107006 | ||||||||
\(25\) | −1.64219 | −0.328437 | ||||||||
\(26\) | −12.3284 | −2.41779 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −3.90204 | −0.737416 | ||||||||
\(29\) | 6.30206 | 1.17026 | 0.585131 | − | 0.810939i | \(-0.301043\pi\) | ||||
0.585131 | + | 0.810939i | \(0.301043\pi\) | |||||||
\(30\) | −3.67682 | −0.671292 | ||||||||
\(31\) | −6.65982 | −1.19614 | −0.598069 | − | 0.801444i | \(-0.704065\pi\) | ||||
−0.598069 | + | 0.801444i | \(0.704065\pi\) | |||||||
\(32\) | 8.02471 | 1.41858 | ||||||||
\(33\) | −3.86289 | −0.672443 | ||||||||
\(34\) | 2.00652 | 0.344115 | ||||||||
\(35\) | 3.52902 | 0.596513 | ||||||||
\(36\) | 2.02613 | 0.337688 | ||||||||
\(37\) | 3.43677 | 0.565001 | 0.282500 | − | 0.959267i | \(-0.408836\pi\) | ||||
0.282500 | + | 0.959267i | \(0.408836\pi\) | |||||||
\(38\) | −1.78682 | −0.289860 | ||||||||
\(39\) | −6.14415 | −0.983851 | ||||||||
\(40\) | 0.0960598 | 0.0151884 | ||||||||
\(41\) | 10.4479 | 1.63168 | 0.815842 | − | 0.578274i | \(-0.196274\pi\) | ||||
0.815842 | + | 0.578274i | \(0.196274\pi\) | |||||||
\(42\) | −3.86428 | −0.596272 | ||||||||
\(43\) | 9.99772 | 1.52464 | 0.762319 | − | 0.647202i | \(-0.224061\pi\) | ||||
0.762319 | + | 0.647202i | \(0.224061\pi\) | |||||||
\(44\) | 7.82671 | 1.17992 | ||||||||
\(45\) | −1.83243 | −0.273163 | ||||||||
\(46\) | 12.0336 | 1.77426 | ||||||||
\(47\) | −1.34629 | −0.196376 | −0.0981882 | − | 0.995168i | \(-0.531305\pi\) | ||||
−0.0981882 | + | 0.995168i | \(0.531305\pi\) | |||||||
\(48\) | 3.94707 | 0.569710 | ||||||||
\(49\) | −3.29105 | −0.470150 | ||||||||
\(50\) | 3.29508 | 0.465995 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 12.4488 | 1.72634 | ||||||||
\(53\) | −11.2524 | −1.54563 | −0.772817 | − | 0.634629i | \(-0.781153\pi\) | ||||
−0.772817 | + | 0.634629i | \(0.781153\pi\) | |||||||
\(54\) | 2.00652 | 0.273053 | ||||||||
\(55\) | −7.07850 | −0.954464 | ||||||||
\(56\) | 0.100958 | 0.0134910 | ||||||||
\(57\) | −0.890505 | −0.117950 | ||||||||
\(58\) | −12.6452 | −1.66040 | ||||||||
\(59\) | 2.14834 | 0.279690 | 0.139845 | − | 0.990173i | \(-0.455340\pi\) | ||||
0.139845 | + | 0.990173i | \(0.455340\pi\) | |||||||
\(60\) | 3.71274 | 0.479313 | ||||||||
\(61\) | −14.3474 | −1.83700 | −0.918501 | − | 0.395420i | \(-0.870599\pi\) | ||||
−0.918501 | + | 0.395420i | \(0.870599\pi\) | |||||||
\(62\) | 13.3631 | 1.69711 | ||||||||
\(63\) | −1.92586 | −0.242636 | ||||||||
\(64\) | −8.20762 | −1.02595 | ||||||||
\(65\) | −11.2587 | −1.39648 | ||||||||
\(66\) | 7.75098 | 0.954079 | ||||||||
\(67\) | −4.33338 | −0.529406 | −0.264703 | − | 0.964330i | \(-0.585274\pi\) | ||||
−0.264703 | + | 0.964330i | \(0.585274\pi\) | |||||||
\(68\) | −2.02613 | −0.245704 | ||||||||
\(69\) | 5.99726 | 0.721985 | ||||||||
\(70\) | −7.08105 | −0.846347 | ||||||||
\(71\) | 8.04138 | 0.954337 | 0.477168 | − | 0.878812i | \(-0.341663\pi\) | ||||
0.477168 | + | 0.878812i | \(0.341663\pi\) | |||||||
\(72\) | −0.0524220 | −0.00617799 | ||||||||
\(73\) | −0.195770 | −0.0229131 | −0.0114565 | − | 0.999934i | \(-0.503647\pi\) | ||||
−0.0114565 | + | 0.999934i | \(0.503647\pi\) | |||||||
\(74\) | −6.89594 | −0.801637 | ||||||||
\(75\) | 1.64219 | 0.189623 | ||||||||
\(76\) | 1.80428 | 0.206965 | ||||||||
\(77\) | −7.43940 | −0.847799 | ||||||||
\(78\) | 12.3284 | 1.39591 | ||||||||
\(79\) | −11.0344 | −1.24147 | −0.620736 | − | 0.784020i | \(-0.713166\pi\) | ||||
−0.620736 | + | 0.784020i | \(0.713166\pi\) | |||||||
\(80\) | 7.23274 | 0.808645 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −20.9639 | −2.31507 | ||||||||
\(83\) | −9.85496 | −1.08172 | −0.540861 | − | 0.841112i | \(-0.681902\pi\) | ||||
−0.540861 | + | 0.841112i | \(0.681902\pi\) | |||||||
\(84\) | 3.90204 | 0.425748 | ||||||||
\(85\) | 1.83243 | 0.198755 | ||||||||
\(86\) | −20.0606 | −2.16319 | ||||||||
\(87\) | −6.30206 | −0.675651 | ||||||||
\(88\) | −0.202501 | −0.0215866 | ||||||||
\(89\) | −8.91778 | −0.945283 | −0.472641 | − | 0.881255i | \(-0.656699\pi\) | ||||
−0.472641 | + | 0.881255i | \(0.656699\pi\) | |||||||
\(90\) | 3.67682 | 0.387571 | ||||||||
\(91\) | −11.8328 | −1.24041 | ||||||||
\(92\) | −12.1512 | −1.26685 | ||||||||
\(93\) | 6.65982 | 0.690591 | ||||||||
\(94\) | 2.70136 | 0.278624 | ||||||||
\(95\) | −1.63179 | −0.167418 | ||||||||
\(96\) | −8.02471 | −0.819019 | ||||||||
\(97\) | −11.5640 | −1.17415 | −0.587074 | − | 0.809534i | \(-0.699720\pi\) | ||||
−0.587074 | + | 0.809534i | \(0.699720\pi\) | |||||||
\(98\) | 6.60356 | 0.667061 | ||||||||
\(99\) | 3.86289 | 0.388235 | ||||||||
\(100\) | −3.32728 | −0.332728 | ||||||||
\(101\) | −0.668211 | −0.0664895 | −0.0332448 | − | 0.999447i | \(-0.510584\pi\) | ||||
−0.0332448 | + | 0.999447i | \(0.510584\pi\) | |||||||
\(102\) | −2.00652 | −0.198675 | ||||||||
\(103\) | 5.30849 | 0.523061 | 0.261531 | − | 0.965195i | \(-0.415773\pi\) | ||||
0.261531 | + | 0.965195i | \(0.415773\pi\) | |||||||
\(104\) | −0.322088 | −0.0315834 | ||||||||
\(105\) | −3.52902 | −0.344397 | ||||||||
\(106\) | 22.5781 | 2.19298 | ||||||||
\(107\) | −5.00162 | −0.483524 | −0.241762 | − | 0.970336i | \(-0.577725\pi\) | ||||
−0.241762 | + | 0.970336i | \(0.577725\pi\) | |||||||
\(108\) | −2.02613 | −0.194964 | ||||||||
\(109\) | −5.75725 | −0.551445 | −0.275722 | − | 0.961237i | \(-0.588917\pi\) | ||||
−0.275722 | + | 0.961237i | \(0.588917\pi\) | |||||||
\(110\) | 14.2032 | 1.35422 | ||||||||
\(111\) | −3.43677 | −0.326203 | ||||||||
\(112\) | 7.60151 | 0.718275 | ||||||||
\(113\) | 8.38572 | 0.788862 | 0.394431 | − | 0.918925i | \(-0.370942\pi\) | ||||
0.394431 | + | 0.918925i | \(0.370942\pi\) | |||||||
\(114\) | 1.78682 | 0.167351 | ||||||||
\(115\) | 10.9896 | 1.02478 | ||||||||
\(116\) | 12.7688 | 1.18555 | ||||||||
\(117\) | 6.14415 | 0.568027 | ||||||||
\(118\) | −4.31069 | −0.396831 | ||||||||
\(119\) | 1.92586 | 0.176544 | ||||||||
\(120\) | −0.0960598 | −0.00876902 | ||||||||
\(121\) | 3.92194 | 0.356540 | ||||||||
\(122\) | 28.7884 | 2.60638 | ||||||||
\(123\) | −10.4479 | −0.942054 | ||||||||
\(124\) | −13.4936 | −1.21176 | ||||||||
\(125\) | 12.1714 | 1.08864 | ||||||||
\(126\) | 3.86428 | 0.344258 | ||||||||
\(127\) | 4.29246 | 0.380894 | 0.190447 | − | 0.981697i | \(-0.439006\pi\) | ||||
0.190447 | + | 0.981697i | \(0.439006\pi\) | |||||||
\(128\) | 0.419340 | 0.0370648 | ||||||||
\(129\) | −9.99772 | −0.880250 | ||||||||
\(130\) | 22.5909 | 1.98135 | ||||||||
\(131\) | 8.79709 | 0.768605 | 0.384303 | − | 0.923207i | \(-0.374442\pi\) | ||||
0.384303 | + | 0.923207i | \(0.374442\pi\) | |||||||
\(132\) | −7.82671 | −0.681227 | ||||||||
\(133\) | −1.71499 | −0.148709 | ||||||||
\(134\) | 8.69501 | 0.751135 | ||||||||
\(135\) | 1.83243 | 0.157711 | ||||||||
\(136\) | 0.0524220 | 0.00449515 | ||||||||
\(137\) | −7.81121 | −0.667356 | −0.333678 | − | 0.942687i | \(-0.608290\pi\) | ||||
−0.333678 | + | 0.942687i | \(0.608290\pi\) | |||||||
\(138\) | −12.0336 | −1.02437 | ||||||||
\(139\) | −7.10591 | −0.602716 | −0.301358 | − | 0.953511i | \(-0.597440\pi\) | ||||
−0.301358 | + | 0.953511i | \(0.597440\pi\) | |||||||
\(140\) | 7.15023 | 0.604305 | ||||||||
\(141\) | 1.34629 | 0.113378 | ||||||||
\(142\) | −16.1352 | −1.35404 | ||||||||
\(143\) | 23.7342 | 1.98475 | ||||||||
\(144\) | −3.94707 | −0.328922 | ||||||||
\(145\) | −11.5481 | −0.959018 | ||||||||
\(146\) | 0.392816 | 0.0325096 | ||||||||
\(147\) | 3.29105 | 0.271441 | ||||||||
\(148\) | 6.96332 | 0.572381 | ||||||||
\(149\) | −6.36133 | −0.521140 | −0.260570 | − | 0.965455i | \(-0.583911\pi\) | ||||
−0.260570 | + | 0.965455i | \(0.583911\pi\) | |||||||
\(150\) | −3.29508 | −0.269042 | ||||||||
\(151\) | 23.0557 | 1.87624 | 0.938122 | − | 0.346306i | \(-0.112564\pi\) | ||||
0.938122 | + | 0.346306i | \(0.112564\pi\) | |||||||
\(152\) | −0.0466821 | −0.00378641 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 14.9273 | 1.20288 | ||||||||
\(155\) | 12.2037 | 0.980223 | ||||||||
\(156\) | −12.4488 | −0.996703 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | 22.1408 | 1.76143 | ||||||||
\(159\) | 11.2524 | 0.892372 | ||||||||
\(160\) | −14.7048 | −1.16251 | ||||||||
\(161\) | 11.5499 | 0.910260 | ||||||||
\(162\) | −2.00652 | −0.157647 | ||||||||
\(163\) | −12.4528 | −0.975380 | −0.487690 | − | 0.873017i | \(-0.662160\pi\) | ||||
−0.487690 | + | 0.873017i | \(0.662160\pi\) | |||||||
\(164\) | 21.1687 | 1.65300 | ||||||||
\(165\) | 7.07850 | 0.551060 | ||||||||
\(166\) | 19.7742 | 1.53477 | ||||||||
\(167\) | 16.1183 | 1.24727 | 0.623635 | − | 0.781716i | \(-0.285655\pi\) | ||||
0.623635 | + | 0.781716i | \(0.285655\pi\) | |||||||
\(168\) | −0.100958 | −0.00778905 | ||||||||
\(169\) | 24.7506 | 1.90389 | ||||||||
\(170\) | −3.67682 | −0.281999 | ||||||||
\(171\) | 0.890505 | 0.0680986 | ||||||||
\(172\) | 20.2566 | 1.54455 | ||||||||
\(173\) | 19.4724 | 1.48046 | 0.740230 | − | 0.672353i | \(-0.234716\pi\) | ||||
0.740230 | + | 0.672353i | \(0.234716\pi\) | |||||||
\(174\) | 12.6452 | 0.958631 | ||||||||
\(175\) | 3.16263 | 0.239072 | ||||||||
\(176\) | −15.2471 | −1.14929 | ||||||||
\(177\) | −2.14834 | −0.161479 | ||||||||
\(178\) | 17.8937 | 1.34119 | ||||||||
\(179\) | 15.4589 | 1.15545 | 0.577725 | − | 0.816231i | \(-0.303940\pi\) | ||||
0.577725 | + | 0.816231i | \(0.303940\pi\) | |||||||
\(180\) | −3.71274 | −0.276731 | ||||||||
\(181\) | 5.64307 | 0.419446 | 0.209723 | − | 0.977761i | \(-0.432744\pi\) | ||||
0.209723 | + | 0.977761i | \(0.432744\pi\) | |||||||
\(182\) | 23.7427 | 1.75993 | ||||||||
\(183\) | 14.3474 | 1.06059 | ||||||||
\(184\) | 0.314388 | 0.0231770 | ||||||||
\(185\) | −6.29765 | −0.463012 | ||||||||
\(186\) | −13.3631 | −0.979827 | ||||||||
\(187\) | −3.86289 | −0.282483 | ||||||||
\(188\) | −2.72775 | −0.198942 | ||||||||
\(189\) | 1.92586 | 0.140086 | ||||||||
\(190\) | 3.27422 | 0.237537 | ||||||||
\(191\) | 24.8861 | 1.80069 | 0.900346 | − | 0.435175i | \(-0.143313\pi\) | ||||
0.900346 | + | 0.435175i | \(0.143313\pi\) | |||||||
\(192\) | 8.20762 | 0.592334 | ||||||||
\(193\) | −6.33620 | −0.456089 | −0.228045 | − | 0.973651i | \(-0.573233\pi\) | ||||
−0.228045 | + | 0.973651i | \(0.573233\pi\) | |||||||
\(194\) | 23.2034 | 1.66591 | ||||||||
\(195\) | 11.2587 | 0.806256 | ||||||||
\(196\) | −6.66808 | −0.476292 | ||||||||
\(197\) | −25.6014 | −1.82403 | −0.912013 | − | 0.410162i | \(-0.865472\pi\) | ||||
−0.912013 | + | 0.410162i | \(0.865472\pi\) | |||||||
\(198\) | −7.75098 | −0.550838 | ||||||||
\(199\) | 5.72472 | 0.405814 | 0.202907 | − | 0.979198i | \(-0.434961\pi\) | ||||
0.202907 | + | 0.979198i | \(0.434961\pi\) | |||||||
\(200\) | 0.0860866 | 0.00608725 | ||||||||
\(201\) | 4.33338 | 0.305653 | ||||||||
\(202\) | 1.34078 | 0.0943370 | ||||||||
\(203\) | −12.1369 | −0.851843 | ||||||||
\(204\) | 2.02613 | 0.141857 | ||||||||
\(205\) | −19.1450 | −1.33715 | ||||||||
\(206\) | −10.6516 | −0.742132 | ||||||||
\(207\) | −5.99726 | −0.416838 | ||||||||
\(208\) | −24.2514 | −1.68153 | ||||||||
\(209\) | 3.43993 | 0.237945 | ||||||||
\(210\) | 7.08105 | 0.488639 | ||||||||
\(211\) | 0.0723951 | 0.00498388 | 0.00249194 | − | 0.999997i | \(-0.499207\pi\) | ||||
0.00249194 | + | 0.999997i | \(0.499207\pi\) | |||||||
\(212\) | −22.7988 | −1.56582 | ||||||||
\(213\) | −8.04138 | −0.550987 | ||||||||
\(214\) | 10.0358 | 0.686036 | ||||||||
\(215\) | −18.3202 | −1.24942 | ||||||||
\(216\) | 0.0524220 | 0.00356686 | ||||||||
\(217\) | 12.8259 | 0.870679 | ||||||||
\(218\) | 11.5520 | 0.782403 | ||||||||
\(219\) | 0.195770 | 0.0132289 | ||||||||
\(220\) | −14.3419 | −0.966932 | ||||||||
\(221\) | −6.14415 | −0.413300 | ||||||||
\(222\) | 6.89594 | 0.462825 | ||||||||
\(223\) | −22.9352 | −1.53585 | −0.767926 | − | 0.640538i | \(-0.778711\pi\) | ||||
−0.767926 | + | 0.640538i | \(0.778711\pi\) | |||||||
\(224\) | −15.4545 | −1.03260 | ||||||||
\(225\) | −1.64219 | −0.109479 | ||||||||
\(226\) | −16.8261 | −1.11926 | ||||||||
\(227\) | 24.2755 | 1.61122 | 0.805609 | − | 0.592447i | \(-0.201838\pi\) | ||||
0.805609 | + | 0.592447i | \(0.201838\pi\) | |||||||
\(228\) | −1.80428 | −0.119491 | ||||||||
\(229\) | 5.32925 | 0.352167 | 0.176083 | − | 0.984375i | \(-0.443657\pi\) | ||||
0.176083 | + | 0.984375i | \(0.443657\pi\) | |||||||
\(230\) | −22.0508 | −1.45399 | ||||||||
\(231\) | 7.43940 | 0.489477 | ||||||||
\(232\) | −0.330366 | −0.0216896 | ||||||||
\(233\) | −5.24595 | −0.343674 | −0.171837 | − | 0.985125i | \(-0.554970\pi\) | ||||
−0.171837 | + | 0.985125i | \(0.554970\pi\) | |||||||
\(234\) | −12.3284 | −0.805930 | ||||||||
\(235\) | 2.46699 | 0.160928 | ||||||||
\(236\) | 4.35281 | 0.283344 | ||||||||
\(237\) | 11.0344 | 0.716764 | ||||||||
\(238\) | −3.86428 | −0.250484 | ||||||||
\(239\) | −2.19209 | −0.141795 | −0.0708974 | − | 0.997484i | \(-0.522586\pi\) | ||||
−0.0708974 | + | 0.997484i | \(0.522586\pi\) | |||||||
\(240\) | −7.23274 | −0.466871 | ||||||||
\(241\) | 7.77245 | 0.500668 | 0.250334 | − | 0.968160i | \(-0.419460\pi\) | ||||
0.250334 | + | 0.968160i | \(0.419460\pi\) | |||||||
\(242\) | −7.86946 | −0.505868 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −29.0697 | −1.86100 | ||||||||
\(245\) | 6.03063 | 0.385283 | ||||||||
\(246\) | 20.9639 | 1.33661 | ||||||||
\(247\) | 5.47140 | 0.348137 | ||||||||
\(248\) | 0.349121 | 0.0221692 | ||||||||
\(249\) | 9.85496 | 0.624533 | ||||||||
\(250\) | −24.4221 | −1.54459 | ||||||||
\(251\) | 25.2611 | 1.59447 | 0.797234 | − | 0.603670i | \(-0.206296\pi\) | ||||
0.797234 | + | 0.603670i | \(0.206296\pi\) | |||||||
\(252\) | −3.90204 | −0.245805 | ||||||||
\(253\) | −23.1668 | −1.45648 | ||||||||
\(254\) | −8.61291 | −0.540422 | ||||||||
\(255\) | −1.83243 | −0.114751 | ||||||||
\(256\) | 15.5738 | 0.973365 | ||||||||
\(257\) | −9.97646 | −0.622314 | −0.311157 | − | 0.950358i | \(-0.600717\pi\) | ||||
−0.311157 | + | 0.950358i | \(0.600717\pi\) | |||||||
\(258\) | 20.0606 | 1.24892 | ||||||||
\(259\) | −6.61874 | −0.411268 | ||||||||
\(260\) | −22.8116 | −1.41472 | ||||||||
\(261\) | 6.30206 | 0.390088 | ||||||||
\(262\) | −17.6515 | −1.09052 | ||||||||
\(263\) | 14.1949 | 0.875293 | 0.437646 | − | 0.899147i | \(-0.355812\pi\) | ||||
0.437646 | + | 0.899147i | \(0.355812\pi\) | |||||||
\(264\) | 0.202501 | 0.0124630 | ||||||||
\(265\) | 20.6193 | 1.26663 | ||||||||
\(266\) | 3.44117 | 0.210991 | ||||||||
\(267\) | 8.91778 | 0.545759 | ||||||||
\(268\) | −8.77997 | −0.536322 | ||||||||
\(269\) | −8.01771 | −0.488849 | −0.244424 | − | 0.969668i | \(-0.578599\pi\) | ||||
−0.244424 | + | 0.969668i | \(0.578599\pi\) | |||||||
\(270\) | −3.67682 | −0.223764 | ||||||||
\(271\) | 6.63486 | 0.403039 | 0.201519 | − | 0.979485i | \(-0.435412\pi\) | ||||
0.201519 | + | 0.979485i | \(0.435412\pi\) | |||||||
\(272\) | 3.94707 | 0.239326 | ||||||||
\(273\) | 11.8328 | 0.716153 | ||||||||
\(274\) | 15.6733 | 0.946862 | ||||||||
\(275\) | −6.34359 | −0.382533 | ||||||||
\(276\) | 12.1512 | 0.731416 | ||||||||
\(277\) | 11.7417 | 0.705490 | 0.352745 | − | 0.935719i | \(-0.385248\pi\) | ||||
0.352745 | + | 0.935719i | \(0.385248\pi\) | |||||||
\(278\) | 14.2582 | 0.855148 | ||||||||
\(279\) | −6.65982 | −0.398713 | ||||||||
\(280\) | −0.184998 | −0.0110558 | ||||||||
\(281\) | −25.2715 | −1.50757 | −0.753785 | − | 0.657121i | \(-0.771774\pi\) | ||||
−0.753785 | + | 0.657121i | \(0.771774\pi\) | |||||||
\(282\) | −2.70136 | −0.160863 | ||||||||
\(283\) | −16.3299 | −0.970709 | −0.485355 | − | 0.874317i | \(-0.661309\pi\) | ||||
−0.485355 | + | 0.874317i | \(0.661309\pi\) | |||||||
\(284\) | 16.2929 | 0.966803 | ||||||||
\(285\) | 1.63179 | 0.0966590 | ||||||||
\(286\) | −47.6231 | −2.81602 | ||||||||
\(287\) | −20.1212 | −1.18772 | ||||||||
\(288\) | 8.02471 | 0.472861 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 23.1715 | 1.36068 | ||||||||
\(291\) | 11.5640 | 0.677894 | ||||||||
\(292\) | −0.396654 | −0.0232124 | ||||||||
\(293\) | 16.9866 | 0.992370 | 0.496185 | − | 0.868217i | \(-0.334734\pi\) | ||||
0.496185 | + | 0.868217i | \(0.334734\pi\) | |||||||
\(294\) | −6.60356 | −0.385128 | ||||||||
\(295\) | −3.93669 | −0.229203 | ||||||||
\(296\) | −0.180162 | −0.0104717 | ||||||||
\(297\) | −3.86289 | −0.224148 | ||||||||
\(298\) | 12.7641 | 0.739407 | ||||||||
\(299\) | −36.8481 | −2.13098 | ||||||||
\(300\) | 3.32728 | 0.192100 | ||||||||
\(301\) | −19.2542 | −1.10980 | ||||||||
\(302\) | −46.2617 | −2.66206 | ||||||||
\(303\) | 0.668211 | 0.0383877 | ||||||||
\(304\) | −3.51488 | −0.201592 | ||||||||
\(305\) | 26.2907 | 1.50540 | ||||||||
\(306\) | 2.00652 | 0.114705 | ||||||||
\(307\) | −20.3919 | −1.16382 | −0.581912 | − | 0.813251i | \(-0.697695\pi\) | ||||
−0.581912 | + | 0.813251i | \(0.697695\pi\) | |||||||
\(308\) | −15.0732 | −0.858873 | ||||||||
\(309\) | −5.30849 | −0.301990 | ||||||||
\(310\) | −24.4869 | −1.39076 | ||||||||
\(311\) | 0.253731 | 0.0143878 | 0.00719389 | − | 0.999974i | \(-0.497710\pi\) | ||||
0.00719389 | + | 0.999974i | \(0.497710\pi\) | |||||||
\(312\) | 0.322088 | 0.0182347 | ||||||||
\(313\) | −18.9071 | −1.06869 | −0.534345 | − | 0.845266i | \(-0.679442\pi\) | ||||
−0.534345 | + | 0.845266i | \(0.679442\pi\) | |||||||
\(314\) | 2.00652 | 0.113235 | ||||||||
\(315\) | 3.52902 | 0.198838 | ||||||||
\(316\) | −22.3572 | −1.25769 | ||||||||
\(317\) | −23.7699 | −1.33505 | −0.667525 | − | 0.744588i | \(-0.732646\pi\) | ||||
−0.667525 | + | 0.744588i | \(0.732646\pi\) | |||||||
\(318\) | −22.5781 | −1.26612 | ||||||||
\(319\) | 24.3442 | 1.36301 | ||||||||
\(320\) | 15.0399 | 0.840758 | ||||||||
\(321\) | 5.00162 | 0.279163 | ||||||||
\(322\) | −23.1751 | −1.29150 | ||||||||
\(323\) | −0.890505 | −0.0495490 | ||||||||
\(324\) | 2.02613 | 0.112563 | ||||||||
\(325\) | −10.0898 | −0.559683 | ||||||||
\(326\) | 24.9868 | 1.38389 | ||||||||
\(327\) | 5.75725 | 0.318377 | ||||||||
\(328\) | −0.547699 | −0.0302416 | ||||||||
\(329\) | 2.59277 | 0.142944 | ||||||||
\(330\) | −14.2032 | −0.781858 | ||||||||
\(331\) | 5.64108 | 0.310062 | 0.155031 | − | 0.987910i | \(-0.450452\pi\) | ||||
0.155031 | + | 0.987910i | \(0.450452\pi\) | |||||||
\(332\) | −19.9674 | −1.09585 | ||||||||
\(333\) | 3.43677 | 0.188334 | ||||||||
\(334\) | −32.3417 | −1.76966 | ||||||||
\(335\) | 7.94063 | 0.433843 | ||||||||
\(336\) | −7.60151 | −0.414696 | ||||||||
\(337\) | 6.97492 | 0.379948 | 0.189974 | − | 0.981789i | \(-0.439160\pi\) | ||||
0.189974 | + | 0.981789i | \(0.439160\pi\) | |||||||
\(338\) | −49.6625 | −2.70128 | ||||||||
\(339\) | −8.38572 | −0.455450 | ||||||||
\(340\) | 3.71274 | 0.201352 | ||||||||
\(341\) | −25.7262 | −1.39315 | ||||||||
\(342\) | −1.78682 | −0.0966200 | ||||||||
\(343\) | 19.8192 | 1.07013 | ||||||||
\(344\) | −0.524100 | −0.0282576 | ||||||||
\(345\) | −10.9896 | −0.591659 | ||||||||
\(346\) | −39.0718 | −2.10051 | ||||||||
\(347\) | −26.4785 | −1.42144 | −0.710720 | − | 0.703475i | \(-0.751631\pi\) | ||||
−0.710720 | + | 0.703475i | \(0.751631\pi\) | |||||||
\(348\) | −12.7688 | −0.684477 | ||||||||
\(349\) | −36.0079 | −1.92746 | −0.963729 | − | 0.266884i | \(-0.914006\pi\) | ||||
−0.963729 | + | 0.266884i | \(0.914006\pi\) | |||||||
\(350\) | −6.34587 | −0.339201 | ||||||||
\(351\) | −6.14415 | −0.327950 | ||||||||
\(352\) | 30.9986 | 1.65223 | ||||||||
\(353\) | 24.4545 | 1.30158 | 0.650790 | − | 0.759258i | \(-0.274438\pi\) | ||||
0.650790 | + | 0.759258i | \(0.274438\pi\) | |||||||
\(354\) | 4.31069 | 0.229110 | ||||||||
\(355\) | −14.7353 | −0.782069 | ||||||||
\(356\) | −18.0685 | −0.957631 | ||||||||
\(357\) | −1.92586 | −0.101927 | ||||||||
\(358\) | −31.0186 | −1.63938 | ||||||||
\(359\) | 24.7684 | 1.30722 | 0.653612 | − | 0.756830i | \(-0.273253\pi\) | ||||
0.653612 | + | 0.756830i | \(0.273253\pi\) | |||||||
\(360\) | 0.0960598 | 0.00506280 | ||||||||
\(361\) | −18.2070 | −0.958263 | ||||||||
\(362\) | −11.3229 | −0.595120 | ||||||||
\(363\) | −3.92194 | −0.205849 | ||||||||
\(364\) | −23.9747 | −1.25662 | ||||||||
\(365\) | 0.358735 | 0.0187770 | ||||||||
\(366\) | −28.7884 | −1.50480 | ||||||||
\(367\) | 22.0639 | 1.15172 | 0.575862 | − | 0.817547i | \(-0.304667\pi\) | ||||
0.575862 | + | 0.817547i | \(0.304667\pi\) | |||||||
\(368\) | 23.6716 | 1.23397 | ||||||||
\(369\) | 10.4479 | 0.543895 | ||||||||
\(370\) | 12.6364 | 0.656933 | ||||||||
\(371\) | 21.6706 | 1.12508 | ||||||||
\(372\) | 13.4936 | 0.699612 | ||||||||
\(373\) | 0.584279 | 0.0302528 | 0.0151264 | − | 0.999886i | \(-0.495185\pi\) | ||||
0.0151264 | + | 0.999886i | \(0.495185\pi\) | |||||||
\(374\) | 7.75098 | 0.400793 | ||||||||
\(375\) | −12.1714 | −0.628527 | ||||||||
\(376\) | 0.0705751 | 0.00363963 | ||||||||
\(377\) | 38.7208 | 1.99422 | ||||||||
\(378\) | −3.86428 | −0.198757 | ||||||||
\(379\) | −18.6260 | −0.956752 | −0.478376 | − | 0.878155i | \(-0.658774\pi\) | ||||
−0.478376 | + | 0.878155i | \(0.658774\pi\) | |||||||
\(380\) | −3.30622 | −0.169605 | ||||||||
\(381\) | −4.29246 | −0.219909 | ||||||||
\(382\) | −49.9344 | −2.55487 | ||||||||
\(383\) | 22.8502 | 1.16759 | 0.583796 | − | 0.811901i | \(-0.301567\pi\) | ||||
0.583796 | + | 0.811901i | \(0.301567\pi\) | |||||||
\(384\) | −0.419340 | −0.0213994 | ||||||||
\(385\) | 13.6322 | 0.694762 | ||||||||
\(386\) | 12.7137 | 0.647111 | ||||||||
\(387\) | 9.99772 | 0.508213 | ||||||||
\(388\) | −23.4301 | −1.18949 | ||||||||
\(389\) | 2.92273 | 0.148188 | 0.0740942 | − | 0.997251i | \(-0.476393\pi\) | ||||
0.0740942 | + | 0.997251i | \(0.476393\pi\) | |||||||
\(390\) | −22.5909 | −1.14394 | ||||||||
\(391\) | 5.99726 | 0.303294 | ||||||||
\(392\) | 0.172523 | 0.00871375 | ||||||||
\(393\) | −8.79709 | −0.443754 | ||||||||
\(394\) | 51.3698 | 2.58797 | ||||||||
\(395\) | 20.2199 | 1.01737 | ||||||||
\(396\) | 7.82671 | 0.393307 | ||||||||
\(397\) | −7.77571 | −0.390252 | −0.195126 | − | 0.980778i | \(-0.562512\pi\) | ||||
−0.195126 | + | 0.980778i | \(0.562512\pi\) | |||||||
\(398\) | −11.4868 | −0.575779 | ||||||||
\(399\) | 1.71499 | 0.0858570 | ||||||||
\(400\) | 6.48182 | 0.324091 | ||||||||
\(401\) | 35.4766 | 1.77162 | 0.885809 | − | 0.464050i | \(-0.153604\pi\) | ||||
0.885809 | + | 0.464050i | \(0.153604\pi\) | |||||||
\(402\) | −8.69501 | −0.433668 | ||||||||
\(403\) | −40.9189 | −2.03832 | ||||||||
\(404\) | −1.35388 | −0.0673581 | ||||||||
\(405\) | −1.83243 | −0.0910544 | ||||||||
\(406\) | 24.3529 | 1.20862 | ||||||||
\(407\) | 13.2759 | 0.658060 | ||||||||
\(408\) | −0.0524220 | −0.00259528 | ||||||||
\(409\) | −8.22238 | −0.406571 | −0.203285 | − | 0.979120i | \(-0.565162\pi\) | ||||
−0.203285 | + | 0.979120i | \(0.565162\pi\) | |||||||
\(410\) | 38.4149 | 1.89718 | ||||||||
\(411\) | 7.81121 | 0.385298 | ||||||||
\(412\) | 10.7557 | 0.529894 | ||||||||
\(413\) | −4.13741 | −0.203589 | ||||||||
\(414\) | 12.0336 | 0.591420 | ||||||||
\(415\) | 18.0586 | 0.886460 | ||||||||
\(416\) | 49.3050 | 2.41738 | ||||||||
\(417\) | 7.10591 | 0.347978 | ||||||||
\(418\) | −6.90228 | −0.337602 | ||||||||
\(419\) | −6.38908 | −0.312127 | −0.156064 | − | 0.987747i | \(-0.549880\pi\) | ||||
−0.156064 | + | 0.987747i | \(0.549880\pi\) | |||||||
\(420\) | −7.15023 | −0.348896 | ||||||||
\(421\) | −3.46000 | −0.168630 | −0.0843151 | − | 0.996439i | \(-0.526870\pi\) | ||||
−0.0843151 | + | 0.996439i | \(0.526870\pi\) | |||||||
\(422\) | −0.145262 | −0.00707126 | ||||||||
\(423\) | −1.34629 | −0.0654588 | ||||||||
\(424\) | 0.589873 | 0.0286467 | ||||||||
\(425\) | 1.64219 | 0.0796577 | ||||||||
\(426\) | 16.1352 | 0.781753 | ||||||||
\(427\) | 27.6312 | 1.33717 | ||||||||
\(428\) | −10.1339 | −0.489841 | ||||||||
\(429\) | −23.7342 | −1.14590 | ||||||||
\(430\) | 36.7598 | 1.77271 | ||||||||
\(431\) | −32.6003 | −1.57030 | −0.785152 | − | 0.619304i | \(-0.787415\pi\) | ||||
−0.785152 | + | 0.619304i | \(0.787415\pi\) | |||||||
\(432\) | 3.94707 | 0.189903 | ||||||||
\(433\) | 27.3070 | 1.31229 | 0.656145 | − | 0.754635i | \(-0.272186\pi\) | ||||
0.656145 | + | 0.754635i | \(0.272186\pi\) | |||||||
\(434\) | −25.7354 | −1.23534 | ||||||||
\(435\) | 11.5481 | 0.553689 | ||||||||
\(436\) | −11.6649 | −0.558648 | ||||||||
\(437\) | −5.34059 | −0.255475 | ||||||||
\(438\) | −0.392816 | −0.0187695 | ||||||||
\(439\) | −11.6003 | −0.553650 | −0.276825 | − | 0.960920i | \(-0.589282\pi\) | ||||
−0.276825 | + | 0.960920i | \(0.589282\pi\) | |||||||
\(440\) | 0.371069 | 0.0176900 | ||||||||
\(441\) | −3.29105 | −0.156717 | ||||||||
\(442\) | 12.3284 | 0.586400 | ||||||||
\(443\) | −24.5529 | −1.16654 | −0.583272 | − | 0.812277i | \(-0.698228\pi\) | ||||
−0.583272 | + | 0.812277i | \(0.698228\pi\) | |||||||
\(444\) | −6.96332 | −0.330465 | ||||||||
\(445\) | 16.3412 | 0.774649 | ||||||||
\(446\) | 46.0199 | 2.17910 | ||||||||
\(447\) | 6.36133 | 0.300881 | ||||||||
\(448\) | 15.8068 | 0.746799 | ||||||||
\(449\) | −21.5051 | −1.01489 | −0.507444 | − | 0.861685i | \(-0.669409\pi\) | ||||
−0.507444 | + | 0.861685i | \(0.669409\pi\) | |||||||
\(450\) | 3.29508 | 0.155332 | ||||||||
\(451\) | 40.3590 | 1.90043 | ||||||||
\(452\) | 16.9905 | 0.799167 | ||||||||
\(453\) | −23.0557 | −1.08325 | ||||||||
\(454\) | −48.7092 | −2.28604 | ||||||||
\(455\) | 21.6828 | 1.01651 | ||||||||
\(456\) | 0.0466821 | 0.00218609 | ||||||||
\(457\) | −32.7765 | −1.53322 | −0.766609 | − | 0.642114i | \(-0.778057\pi\) | ||||
−0.766609 | + | 0.642114i | \(0.778057\pi\) | |||||||
\(458\) | −10.6933 | −0.499663 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 22.2663 | 1.03817 | ||||||||
\(461\) | 20.3967 | 0.949967 | 0.474983 | − | 0.879995i | \(-0.342454\pi\) | ||||
0.474983 | + | 0.879995i | \(0.342454\pi\) | |||||||
\(462\) | −14.9273 | −0.694482 | ||||||||
\(463\) | −25.3223 | −1.17683 | −0.588414 | − | 0.808560i | \(-0.700247\pi\) | ||||
−0.588414 | + | 0.808560i | \(0.700247\pi\) | |||||||
\(464\) | −24.8746 | −1.15478 | ||||||||
\(465\) | −12.2037 | −0.565932 | ||||||||
\(466\) | 10.5261 | 0.487613 | ||||||||
\(467\) | −25.1858 | −1.16546 | −0.582730 | − | 0.812666i | \(-0.698015\pi\) | ||||
−0.582730 | + | 0.812666i | \(0.698015\pi\) | |||||||
\(468\) | 12.4488 | 0.575447 | ||||||||
\(469\) | 8.34549 | 0.385359 | ||||||||
\(470\) | −4.95006 | −0.228329 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | −0.112620 | −0.00518377 | ||||||||
\(473\) | 38.6201 | 1.77576 | ||||||||
\(474\) | −22.1408 | −1.01696 | ||||||||
\(475\) | −1.46238 | −0.0670984 | ||||||||
\(476\) | 3.90204 | 0.178850 | ||||||||
\(477\) | −11.2524 | −0.515211 | ||||||||
\(478\) | 4.39848 | 0.201182 | ||||||||
\(479\) | −2.19637 | −0.100355 | −0.0501775 | − | 0.998740i | \(-0.515979\pi\) | ||||
−0.0501775 | + | 0.998740i | \(0.515979\pi\) | |||||||
\(480\) | 14.7048 | 0.671177 | ||||||||
\(481\) | 21.1160 | 0.962807 | ||||||||
\(482\) | −15.5956 | −0.710359 | ||||||||
\(483\) | −11.5499 | −0.525539 | ||||||||
\(484\) | 7.94635 | 0.361198 | ||||||||
\(485\) | 21.1903 | 0.962201 | ||||||||
\(486\) | 2.00652 | 0.0910176 | ||||||||
\(487\) | −14.5496 | −0.659306 | −0.329653 | − | 0.944102i | \(-0.606932\pi\) | ||||
−0.329653 | + | 0.944102i | \(0.606932\pi\) | |||||||
\(488\) | 0.752121 | 0.0340469 | ||||||||
\(489\) | 12.4528 | 0.563136 | ||||||||
\(490\) | −12.1006 | −0.546649 | ||||||||
\(491\) | 38.3968 | 1.73282 | 0.866412 | − | 0.499330i | \(-0.166420\pi\) | ||||
0.866412 | + | 0.499330i | \(0.166420\pi\) | |||||||
\(492\) | −21.1687 | −0.954360 | ||||||||
\(493\) | −6.30206 | −0.283830 | ||||||||
\(494\) | −10.9785 | −0.493945 | ||||||||
\(495\) | −7.07850 | −0.318155 | ||||||||
\(496\) | 26.2867 | 1.18031 | ||||||||
\(497\) | −15.4866 | −0.694669 | ||||||||
\(498\) | −19.7742 | −0.886102 | ||||||||
\(499\) | 1.97846 | 0.0885679 | 0.0442840 | − | 0.999019i | \(-0.485899\pi\) | ||||
0.0442840 | + | 0.999019i | \(0.485899\pi\) | |||||||
\(500\) | 24.6607 | 1.10286 | ||||||||
\(501\) | −16.1183 | −0.720111 | ||||||||
\(502\) | −50.6870 | −2.26227 | ||||||||
\(503\) | −9.12840 | −0.407015 | −0.203508 | − | 0.979073i | \(-0.565234\pi\) | ||||
−0.203508 | + | 0.979073i | \(0.565234\pi\) | |||||||
\(504\) | 0.100958 | 0.00449701 | ||||||||
\(505\) | 1.22445 | 0.0544875 | ||||||||
\(506\) | 46.4846 | 2.06649 | ||||||||
\(507\) | −24.7506 | −1.09921 | ||||||||
\(508\) | 8.69706 | 0.385870 | ||||||||
\(509\) | −36.3313 | −1.61036 | −0.805179 | − | 0.593032i | \(-0.797931\pi\) | ||||
−0.805179 | + | 0.593032i | \(0.797931\pi\) | |||||||
\(510\) | 3.67682 | 0.162812 | ||||||||
\(511\) | 0.377025 | 0.0166786 | ||||||||
\(512\) | −32.0879 | −1.41810 | ||||||||
\(513\) | −0.890505 | −0.0393168 | ||||||||
\(514\) | 20.0180 | 0.882955 | ||||||||
\(515\) | −9.72746 | −0.428643 | ||||||||
\(516\) | −20.2566 | −0.891749 | ||||||||
\(517\) | −5.20057 | −0.228721 | ||||||||
\(518\) | 13.2806 | 0.583518 | ||||||||
\(519\) | −19.4724 | −0.854744 | ||||||||
\(520\) | 0.590206 | 0.0258822 | ||||||||
\(521\) | −16.0917 | −0.704991 | −0.352495 | − | 0.935814i | \(-0.614667\pi\) | ||||
−0.352495 | + | 0.935814i | \(0.614667\pi\) | |||||||
\(522\) | −12.6452 | −0.553466 | ||||||||
\(523\) | 4.30024 | 0.188036 | 0.0940182 | − | 0.995570i | \(-0.470029\pi\) | ||||
0.0940182 | + | 0.995570i | \(0.470029\pi\) | |||||||
\(524\) | 17.8240 | 0.778645 | ||||||||
\(525\) | −3.16263 | −0.138028 | ||||||||
\(526\) | −28.4823 | −1.24189 | ||||||||
\(527\) | 6.65982 | 0.290106 | ||||||||
\(528\) | 15.2471 | 0.663545 | ||||||||
\(529\) | 12.9671 | 0.563788 | ||||||||
\(530\) | −41.3730 | −1.79713 | ||||||||
\(531\) | 2.14834 | 0.0932300 | ||||||||
\(532\) | −3.47479 | −0.150651 | ||||||||
\(533\) | 64.1933 | 2.78052 | ||||||||
\(534\) | −17.8937 | −0.774336 | ||||||||
\(535\) | 9.16513 | 0.396243 | ||||||||
\(536\) | 0.227164 | 0.00981200 | ||||||||
\(537\) | −15.4589 | −0.667100 | ||||||||
\(538\) | 16.0877 | 0.693590 | ||||||||
\(539\) | −12.7130 | −0.547587 | ||||||||
\(540\) | 3.71274 | 0.159771 | ||||||||
\(541\) | 25.1234 | 1.08014 | 0.540069 | − | 0.841620i | \(-0.318398\pi\) | ||||
0.540069 | + | 0.841620i | \(0.318398\pi\) | |||||||
\(542\) | −13.3130 | −0.571841 | ||||||||
\(543\) | −5.64307 | −0.242167 | ||||||||
\(544\) | −8.02471 | −0.344057 | ||||||||
\(545\) | 10.5498 | 0.451903 | ||||||||
\(546\) | −23.7427 | −1.01610 | ||||||||
\(547\) | −37.1417 | −1.58807 | −0.794033 | − | 0.607875i | \(-0.792022\pi\) | ||||
−0.794033 | + | 0.607875i | \(0.792022\pi\) | |||||||
\(548\) | −15.8265 | −0.676074 | ||||||||
\(549\) | −14.3474 | −0.612334 | ||||||||
\(550\) | 12.7285 | 0.542747 | ||||||||
\(551\) | 5.61202 | 0.239080 | ||||||||
\(552\) | −0.314388 | −0.0133813 | ||||||||
\(553\) | 21.2508 | 0.903677 | ||||||||
\(554\) | −23.5600 | −1.00097 | ||||||||
\(555\) | 6.29765 | 0.267320 | ||||||||
\(556\) | −14.3975 | −0.610589 | ||||||||
\(557\) | −27.2639 | −1.15521 | −0.577603 | − | 0.816317i | \(-0.696012\pi\) | ||||
−0.577603 | + | 0.816317i | \(0.696012\pi\) | |||||||
\(558\) | 13.3631 | 0.565704 | ||||||||
\(559\) | 61.4275 | 2.59811 | ||||||||
\(560\) | −13.9293 | −0.588619 | ||||||||
\(561\) | 3.86289 | 0.163091 | ||||||||
\(562\) | 50.7078 | 2.13898 | ||||||||
\(563\) | −21.7338 | −0.915971 | −0.457986 | − | 0.888960i | \(-0.651429\pi\) | ||||
−0.457986 | + | 0.888960i | \(0.651429\pi\) | |||||||
\(564\) | 2.72775 | 0.114859 | ||||||||
\(565\) | −15.3663 | −0.646464 | ||||||||
\(566\) | 32.7662 | 1.37727 | ||||||||
\(567\) | −1.92586 | −0.0808786 | ||||||||
\(568\) | −0.421545 | −0.0176876 | ||||||||
\(569\) | −8.37425 | −0.351067 | −0.175533 | − | 0.984473i | \(-0.556165\pi\) | ||||
−0.175533 | + | 0.984473i | \(0.556165\pi\) | |||||||
\(570\) | −3.27422 | −0.137142 | ||||||||
\(571\) | −18.8762 | −0.789944 | −0.394972 | − | 0.918693i | \(-0.629246\pi\) | ||||
−0.394972 | + | 0.918693i | \(0.629246\pi\) | |||||||
\(572\) | 48.0885 | 2.01068 | ||||||||
\(573\) | −24.8861 | −1.03963 | ||||||||
\(574\) | 40.3736 | 1.68516 | ||||||||
\(575\) | 9.84861 | 0.410716 | ||||||||
\(576\) | −8.20762 | −0.341984 | ||||||||
\(577\) | −15.8753 | −0.660898 | −0.330449 | − | 0.943824i | \(-0.607200\pi\) | ||||
−0.330449 | + | 0.943824i | \(0.607200\pi\) | |||||||
\(578\) | −2.00652 | −0.0834603 | ||||||||
\(579\) | 6.33620 | 0.263323 | ||||||||
\(580\) | −23.3979 | −0.971545 | ||||||||
\(581\) | 18.9793 | 0.787394 | ||||||||
\(582\) | −23.2034 | −0.961813 | ||||||||
\(583\) | −43.4668 | −1.80021 | ||||||||
\(584\) | 0.0102626 | 0.000424671 0 | ||||||||
\(585\) | −11.2587 | −0.465492 | ||||||||
\(586\) | −34.0840 | −1.40800 | ||||||||
\(587\) | 5.14095 | 0.212190 | 0.106095 | − | 0.994356i | \(-0.466165\pi\) | ||||
0.106095 | + | 0.994356i | \(0.466165\pi\) | |||||||
\(588\) | 6.66808 | 0.274987 | ||||||||
\(589\) | −5.93060 | −0.244366 | ||||||||
\(590\) | 7.89905 | 0.325199 | ||||||||
\(591\) | 25.6014 | 1.05310 | ||||||||
\(592\) | −13.5651 | −0.557524 | ||||||||
\(593\) | −10.1063 | −0.415017 | −0.207509 | − | 0.978233i | \(-0.566536\pi\) | ||||
−0.207509 | + | 0.978233i | \(0.566536\pi\) | |||||||
\(594\) | 7.75098 | 0.318026 | ||||||||
\(595\) | −3.52902 | −0.144676 | ||||||||
\(596\) | −12.8889 | −0.527948 | ||||||||
\(597\) | −5.72472 | −0.234297 | ||||||||
\(598\) | 73.9364 | 3.02348 | ||||||||
\(599\) | 37.2839 | 1.52338 | 0.761688 | − | 0.647943i | \(-0.224371\pi\) | ||||
0.761688 | + | 0.647943i | \(0.224371\pi\) | |||||||
\(600\) | −0.0860866 | −0.00351447 | ||||||||
\(601\) | −44.1884 | −1.80248 | −0.901241 | − | 0.433318i | \(-0.857343\pi\) | ||||
−0.901241 | + | 0.433318i | \(0.857343\pi\) | |||||||
\(602\) | 38.6340 | 1.57461 | ||||||||
\(603\) | −4.33338 | −0.176469 | ||||||||
\(604\) | 46.7137 | 1.90075 | ||||||||
\(605\) | −7.18670 | −0.292181 | ||||||||
\(606\) | −1.34078 | −0.0544655 | ||||||||
\(607\) | −29.4875 | −1.19686 | −0.598430 | − | 0.801175i | \(-0.704209\pi\) | ||||
−0.598430 | + | 0.801175i | \(0.704209\pi\) | |||||||
\(608\) | 7.14605 | 0.289811 | ||||||||
\(609\) | 12.1369 | 0.491812 | ||||||||
\(610\) | −52.7529 | −2.13590 | ||||||||
\(611\) | −8.27180 | −0.334641 | ||||||||
\(612\) | −2.02613 | −0.0819013 | ||||||||
\(613\) | −15.9150 | −0.642802 | −0.321401 | − | 0.946943i | \(-0.604154\pi\) | ||||
−0.321401 | + | 0.946943i | \(0.604154\pi\) | |||||||
\(614\) | 40.9167 | 1.65126 | ||||||||
\(615\) | 19.1450 | 0.772003 | ||||||||
\(616\) | 0.389988 | 0.0157131 | ||||||||
\(617\) | −42.5319 | −1.71227 | −0.856134 | − | 0.516753i | \(-0.827140\pi\) | ||||
−0.856134 | + | 0.516753i | \(0.827140\pi\) | |||||||
\(618\) | 10.6516 | 0.428470 | ||||||||
\(619\) | −2.25945 | −0.0908151 | −0.0454075 | − | 0.998969i | \(-0.514459\pi\) | ||||
−0.0454075 | + | 0.998969i | \(0.514459\pi\) | |||||||
\(620\) | 24.7262 | 0.993027 | ||||||||
\(621\) | 5.99726 | 0.240662 | ||||||||
\(622\) | −0.509117 | −0.0204137 | ||||||||
\(623\) | 17.1744 | 0.688079 | ||||||||
\(624\) | 24.2514 | 0.970831 | ||||||||
\(625\) | −14.0923 | −0.563692 | ||||||||
\(626\) | 37.9374 | 1.51628 | ||||||||
\(627\) | −3.43993 | −0.137377 | ||||||||
\(628\) | −2.02613 | −0.0808512 | ||||||||
\(629\) | −3.43677 | −0.137033 | ||||||||
\(630\) | −7.08105 | −0.282116 | ||||||||
\(631\) | 12.9756 | 0.516551 | 0.258276 | − | 0.966071i | \(-0.416846\pi\) | ||||
0.258276 | + | 0.966071i | \(0.416846\pi\) | |||||||
\(632\) | 0.578447 | 0.0230094 | ||||||||
\(633\) | −0.0723951 | −0.00287745 | ||||||||
\(634\) | 47.6948 | 1.89420 | ||||||||
\(635\) | −7.86565 | −0.312139 | ||||||||
\(636\) | 22.7988 | 0.904029 | ||||||||
\(637\) | −20.2207 | −0.801174 | ||||||||
\(638\) | −48.8471 | −1.93387 | ||||||||
\(639\) | 8.04138 | 0.318112 | ||||||||
\(640\) | −0.768413 | −0.0303742 | ||||||||
\(641\) | −26.5958 | −1.05047 | −0.525235 | − | 0.850957i | \(-0.676022\pi\) | ||||
−0.525235 | + | 0.850957i | \(0.676022\pi\) | |||||||
\(642\) | −10.0358 | −0.396083 | ||||||||
\(643\) | −18.4224 | −0.726509 | −0.363254 | − | 0.931690i | \(-0.618334\pi\) | ||||
−0.363254 | + | 0.931690i | \(0.618334\pi\) | |||||||
\(644\) | 23.4016 | 0.922150 | ||||||||
\(645\) | 18.3202 | 0.721356 | ||||||||
\(646\) | 1.78682 | 0.0703014 | ||||||||
\(647\) | 29.4426 | 1.15751 | 0.578755 | − | 0.815502i | \(-0.303539\pi\) | ||||
0.578755 | + | 0.815502i | \(0.303539\pi\) | |||||||
\(648\) | −0.0524220 | −0.00205933 | ||||||||
\(649\) | 8.29881 | 0.325757 | ||||||||
\(650\) | 20.2455 | 0.794092 | ||||||||
\(651\) | −12.8259 | −0.502687 | ||||||||
\(652\) | −25.2310 | −0.988121 | ||||||||
\(653\) | 19.1072 | 0.747722 | 0.373861 | − | 0.927485i | \(-0.378034\pi\) | ||||
0.373861 | + | 0.927485i | \(0.378034\pi\) | |||||||
\(654\) | −11.5520 | −0.451721 | ||||||||
\(655\) | −16.1201 | −0.629864 | ||||||||
\(656\) | −41.2385 | −1.61009 | ||||||||
\(657\) | −0.195770 | −0.00763770 | ||||||||
\(658\) | −5.20244 | −0.202812 | ||||||||
\(659\) | 5.01331 | 0.195291 | 0.0976455 | − | 0.995221i | \(-0.468869\pi\) | ||||
0.0976455 | + | 0.995221i | \(0.468869\pi\) | |||||||
\(660\) | 14.3419 | 0.558259 | ||||||||
\(661\) | 17.5057 | 0.680893 | 0.340447 | − | 0.940264i | \(-0.389422\pi\) | ||||
0.340447 | + | 0.940264i | \(0.389422\pi\) | |||||||
\(662\) | −11.3189 | −0.439923 | ||||||||
\(663\) | 6.14415 | 0.238619 | ||||||||
\(664\) | 0.516616 | 0.0200486 | ||||||||
\(665\) | 3.14261 | 0.121865 | ||||||||
\(666\) | −6.89594 | −0.267212 | ||||||||
\(667\) | −37.7951 | −1.46343 | ||||||||
\(668\) | 32.6576 | 1.26356 | ||||||||
\(669\) | 22.9352 | 0.886725 | ||||||||
\(670\) | −15.9330 | −0.615547 | ||||||||
\(671\) | −55.4226 | −2.13957 | ||||||||
\(672\) | 15.4545 | 0.596170 | ||||||||
\(673\) | −34.2041 | −1.31847 | −0.659235 | − | 0.751937i | \(-0.729120\pi\) | ||||
−0.659235 | + | 0.751937i | \(0.729120\pi\) | |||||||
\(674\) | −13.9953 | −0.539080 | ||||||||
\(675\) | 1.64219 | 0.0632078 | ||||||||
\(676\) | 50.1477 | 1.92876 | ||||||||
\(677\) | −36.9819 | −1.42133 | −0.710664 | − | 0.703531i | \(-0.751605\pi\) | ||||
−0.710664 | + | 0.703531i | \(0.751605\pi\) | |||||||
\(678\) | 16.8261 | 0.646204 | ||||||||
\(679\) | 22.2707 | 0.854671 | ||||||||
\(680\) | −0.0960598 | −0.00368373 | ||||||||
\(681\) | −24.2755 | −0.930237 | ||||||||
\(682\) | 51.6201 | 1.97664 | ||||||||
\(683\) | −15.5900 | −0.596535 | −0.298267 | − | 0.954482i | \(-0.596409\pi\) | ||||
−0.298267 | + | 0.954482i | \(0.596409\pi\) | |||||||
\(684\) | 1.80428 | 0.0689882 | ||||||||
\(685\) | 14.3135 | 0.546891 | ||||||||
\(686\) | −39.7675 | −1.51833 | ||||||||
\(687\) | −5.32925 | −0.203324 | ||||||||
\(688\) | −39.4617 | −1.50446 | ||||||||
\(689\) | −69.1363 | −2.63388 | ||||||||
\(690\) | 22.0508 | 0.839461 | ||||||||
\(691\) | −12.4194 | −0.472457 | −0.236229 | − | 0.971698i | \(-0.575911\pi\) | ||||
−0.236229 | + | 0.971698i | \(0.575911\pi\) | |||||||
\(692\) | 39.4536 | 1.49980 | ||||||||
\(693\) | −7.43940 | −0.282600 | ||||||||
\(694\) | 53.1297 | 2.01678 | ||||||||
\(695\) | 13.0211 | 0.493919 | ||||||||
\(696\) | 0.330366 | 0.0125225 | ||||||||
\(697\) | −10.4479 | −0.395742 | ||||||||
\(698\) | 72.2505 | 2.73472 | ||||||||
\(699\) | 5.24595 | 0.198420 | ||||||||
\(700\) | 6.40788 | 0.242195 | ||||||||
\(701\) | 45.8308 | 1.73101 | 0.865504 | − | 0.500903i | \(-0.166999\pi\) | ||||
0.865504 | + | 0.500903i | \(0.166999\pi\) | |||||||
\(702\) | 12.3284 | 0.465304 | ||||||||
\(703\) | 3.06046 | 0.115427 | ||||||||
\(704\) | −31.7052 | −1.19493 | ||||||||
\(705\) | −2.46699 | −0.0929120 | ||||||||
\(706\) | −49.0684 | −1.84671 | ||||||||
\(707\) | 1.28688 | 0.0483982 | ||||||||
\(708\) | −4.35281 | −0.163588 | ||||||||
\(709\) | 12.1609 | 0.456712 | 0.228356 | − | 0.973578i | \(-0.426665\pi\) | ||||
0.228356 | + | 0.973578i | \(0.426665\pi\) | |||||||
\(710\) | 29.5667 | 1.10962 | ||||||||
\(711\) | −11.0344 | −0.413824 | ||||||||
\(712\) | 0.467488 | 0.0175198 | ||||||||
\(713\) | 39.9407 | 1.49579 | ||||||||
\(714\) | 3.86428 | 0.144617 | ||||||||
\(715\) | −43.4913 | −1.62648 | ||||||||
\(716\) | 31.3216 | 1.17054 | ||||||||
\(717\) | 2.19209 | 0.0818653 | ||||||||
\(718\) | −49.6982 | −1.85472 | ||||||||
\(719\) | 47.2832 | 1.76337 | 0.881683 | − | 0.471843i | \(-0.156411\pi\) | ||||
0.881683 | + | 0.471843i | \(0.156411\pi\) | |||||||
\(720\) | 7.23274 | 0.269548 | ||||||||
\(721\) | −10.2234 | −0.380740 | ||||||||
\(722\) | 36.5327 | 1.35961 | ||||||||
\(723\) | −7.77245 | −0.289061 | ||||||||
\(724\) | 11.4336 | 0.424925 | ||||||||
\(725\) | −10.3491 | −0.384358 | ||||||||
\(726\) | 7.86946 | 0.292063 | ||||||||
\(727\) | 10.2019 | 0.378366 | 0.189183 | − | 0.981942i | \(-0.439416\pi\) | ||||
0.189183 | + | 0.981942i | \(0.439416\pi\) | |||||||
\(728\) | 0.620298 | 0.0229898 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.719809 | −0.0266413 | ||||||||
\(731\) | −9.99772 | −0.369779 | ||||||||
\(732\) | 29.0697 | 1.07445 | ||||||||
\(733\) | −7.70062 | −0.284429 | −0.142214 | − | 0.989836i | \(-0.545422\pi\) | ||||
−0.142214 | + | 0.989836i | \(0.545422\pi\) | |||||||
\(734\) | −44.2716 | −1.63409 | ||||||||
\(735\) | −6.03063 | −0.222443 | ||||||||
\(736\) | −48.1263 | −1.77396 | ||||||||
\(737\) | −16.7394 | −0.616603 | ||||||||
\(738\) | −20.9639 | −0.771691 | ||||||||
\(739\) | −16.0844 | −0.591675 | −0.295838 | − | 0.955238i | \(-0.595599\pi\) | ||||
−0.295838 | + | 0.955238i | \(0.595599\pi\) | |||||||
\(740\) | −12.7598 | −0.469060 | ||||||||
\(741\) | −5.47140 | −0.200997 | ||||||||
\(742\) | −43.4824 | −1.59629 | ||||||||
\(743\) | 1.92699 | 0.0706943 | 0.0353471 | − | 0.999375i | \(-0.488746\pi\) | ||||
0.0353471 | + | 0.999375i | \(0.488746\pi\) | |||||||
\(744\) | −0.349121 | −0.0127994 | ||||||||
\(745\) | 11.6567 | 0.427069 | ||||||||
\(746\) | −1.17237 | −0.0429235 | ||||||||
\(747\) | −9.85496 | −0.360574 | ||||||||
\(748\) | −7.82671 | −0.286173 | ||||||||
\(749\) | 9.63243 | 0.351961 | ||||||||
\(750\) | 24.4221 | 0.891769 | ||||||||
\(751\) | 28.0063 | 1.02196 | 0.510982 | − | 0.859591i | \(-0.329282\pi\) | ||||
0.510982 | + | 0.859591i | \(0.329282\pi\) | |||||||
\(752\) | 5.31389 | 0.193778 | ||||||||
\(753\) | −25.2611 | −0.920567 | ||||||||
\(754\) | −77.6940 | −2.82945 | ||||||||
\(755\) | −42.2480 | −1.53756 | ||||||||
\(756\) | 3.90204 | 0.141916 | ||||||||
\(757\) | 7.75500 | 0.281860 | 0.140930 | − | 0.990020i | \(-0.454991\pi\) | ||||
0.140930 | + | 0.990020i | \(0.454991\pi\) | |||||||
\(758\) | 37.3734 | 1.35746 | ||||||||
\(759\) | 23.1668 | 0.840901 | ||||||||
\(760\) | 0.0855418 | 0.00310293 | ||||||||
\(761\) | 15.5413 | 0.563373 | 0.281686 | − | 0.959507i | \(-0.409106\pi\) | ||||
0.281686 | + | 0.959507i | \(0.409106\pi\) | |||||||
\(762\) | 8.61291 | 0.312013 | ||||||||
\(763\) | 11.0877 | 0.401401 | ||||||||
\(764\) | 50.4223 | 1.82421 | ||||||||
\(765\) | 1.83243 | 0.0662518 | ||||||||
\(766\) | −45.8494 | −1.65661 | ||||||||
\(767\) | 13.1997 | 0.476614 | ||||||||
\(768\) | −15.5738 | −0.561972 | ||||||||
\(769\) | −13.4400 | −0.484657 | −0.242329 | − | 0.970194i | \(-0.577911\pi\) | ||||
−0.242329 | + | 0.970194i | \(0.577911\pi\) | |||||||
\(770\) | −27.3533 | −0.985745 | ||||||||
\(771\) | 9.97646 | 0.359293 | ||||||||
\(772\) | −12.8379 | −0.462047 | ||||||||
\(773\) | −35.4138 | −1.27374 | −0.636872 | − | 0.770969i | \(-0.719772\pi\) | ||||
−0.636872 | + | 0.770969i | \(0.719772\pi\) | |||||||
\(774\) | −20.0606 | −0.721065 | ||||||||
\(775\) | 10.9367 | 0.392856 | ||||||||
\(776\) | 0.606208 | 0.0217616 | ||||||||
\(777\) | 6.61874 | 0.237446 | ||||||||
\(778\) | −5.86453 | −0.210253 | ||||||||
\(779\) | 9.30389 | 0.333347 | ||||||||
\(780\) | 22.8116 | 0.816788 | ||||||||
\(781\) | 31.0630 | 1.11152 | ||||||||
\(782\) | −12.0336 | −0.430322 | ||||||||
\(783\) | −6.30206 | −0.225217 | ||||||||
\(784\) | 12.9900 | 0.463928 | ||||||||
\(785\) | 1.83243 | 0.0654024 | ||||||||
\(786\) | 17.6515 | 0.629610 | ||||||||
\(787\) | 39.4330 | 1.40564 | 0.702818 | − | 0.711370i | \(-0.251925\pi\) | ||||
0.702818 | + | 0.711370i | \(0.251925\pi\) | |||||||
\(788\) | −51.8717 | −1.84785 | ||||||||
\(789\) | −14.1949 | −0.505351 | ||||||||
\(790\) | −40.5716 | −1.44347 | ||||||||
\(791\) | −16.1498 | −0.574219 | ||||||||
\(792\) | −0.202501 | −0.00719554 | ||||||||
\(793\) | −88.1528 | −3.13040 | ||||||||
\(794\) | 15.6021 | 0.553698 | ||||||||
\(795\) | −20.6193 | −0.731290 | ||||||||
\(796\) | 11.5990 | 0.411116 | ||||||||
\(797\) | 36.5285 | 1.29390 | 0.646952 | − | 0.762530i | \(-0.276043\pi\) | ||||
0.646952 | + | 0.762530i | \(0.276043\pi\) | |||||||
\(798\) | −3.44117 | −0.121816 | ||||||||
\(799\) | 1.34629 | 0.0476283 | ||||||||
\(800\) | −13.1781 | −0.465915 | ||||||||
\(801\) | −8.91778 | −0.315094 | ||||||||
\(802\) | −71.1846 | −2.51362 | ||||||||
\(803\) | −0.756237 | −0.0266870 | ||||||||
\(804\) | 8.77997 | 0.309646 | ||||||||
\(805\) | −21.1644 | −0.745948 | ||||||||
\(806\) | 82.1046 | 2.89201 | ||||||||
\(807\) | 8.01771 | 0.282237 | ||||||||
\(808\) | 0.0350290 | 0.00123231 | ||||||||
\(809\) | −48.4476 | −1.70333 | −0.851663 | − | 0.524090i | \(-0.824406\pi\) | ||||
−0.851663 | + | 0.524090i | \(0.824406\pi\) | |||||||
\(810\) | 3.67682 | 0.129190 | ||||||||
\(811\) | 9.64546 | 0.338698 | 0.169349 | − | 0.985556i | \(-0.445834\pi\) | ||||
0.169349 | + | 0.985556i | \(0.445834\pi\) | |||||||
\(812\) | −24.5909 | −0.862971 | ||||||||
\(813\) | −6.63486 | −0.232695 | ||||||||
\(814\) | −26.6383 | −0.933671 | ||||||||
\(815\) | 22.8190 | 0.799314 | ||||||||
\(816\) | −3.94707 | −0.138175 | ||||||||
\(817\) | 8.90302 | 0.311477 | ||||||||
\(818\) | 16.4984 | 0.576852 | ||||||||
\(819\) | −11.8328 | −0.413471 | ||||||||
\(820\) | −38.7903 | −1.35462 | ||||||||
\(821\) | 44.8788 | 1.56628 | 0.783141 | − | 0.621845i | \(-0.213616\pi\) | ||||
0.783141 | + | 0.621845i | \(0.213616\pi\) | |||||||
\(822\) | −15.6733 | −0.546671 | ||||||||
\(823\) | −21.3854 | −0.745450 | −0.372725 | − | 0.927942i | \(-0.621576\pi\) | ||||
−0.372725 | + | 0.927942i | \(0.621576\pi\) | |||||||
\(824\) | −0.278282 | −0.00969440 | ||||||||
\(825\) | 6.34359 | 0.220855 | ||||||||
\(826\) | 8.30180 | 0.288856 | ||||||||
\(827\) | 11.8470 | 0.411960 | 0.205980 | − | 0.978556i | \(-0.433962\pi\) | ||||
0.205980 | + | 0.978556i | \(0.433962\pi\) | |||||||
\(828\) | −12.1512 | −0.422283 | ||||||||
\(829\) | 2.36211 | 0.0820394 | 0.0410197 | − | 0.999158i | \(-0.486939\pi\) | ||||
0.0410197 | + | 0.999158i | \(0.486939\pi\) | |||||||
\(830\) | −36.2349 | −1.25773 | ||||||||
\(831\) | −11.7417 | −0.407315 | ||||||||
\(832\) | −50.4289 | −1.74831 | ||||||||
\(833\) | 3.29105 | 0.114028 | ||||||||
\(834\) | −14.2582 | −0.493720 | ||||||||
\(835\) | −29.5357 | −1.02212 | ||||||||
\(836\) | 6.96972 | 0.241053 | ||||||||
\(837\) | 6.65982 | 0.230197 | ||||||||
\(838\) | 12.8198 | 0.442854 | ||||||||
\(839\) | −12.0025 | −0.414373 | −0.207187 | − | 0.978301i | \(-0.566431\pi\) | ||||
−0.207187 | + | 0.978301i | \(0.566431\pi\) | |||||||
\(840\) | 0.184998 | 0.00638304 | ||||||||
\(841\) | 10.7159 | 0.369515 | ||||||||
\(842\) | 6.94257 | 0.239257 | ||||||||
\(843\) | 25.2715 | 0.870396 | ||||||||
\(844\) | 0.146682 | 0.00504899 | ||||||||
\(845\) | −45.3538 | −1.56022 | ||||||||
\(846\) | 2.70136 | 0.0928745 | ||||||||
\(847\) | −7.55313 | −0.259529 | ||||||||
\(848\) | 44.4139 | 1.52518 | ||||||||
\(849\) | 16.3299 | 0.560439 | ||||||||
\(850\) | −3.29508 | −0.113020 | ||||||||
\(851\) | −20.6112 | −0.706542 | ||||||||
\(852\) | −16.2929 | −0.558184 | ||||||||
\(853\) | 40.3937 | 1.38305 | 0.691527 | − | 0.722351i | \(-0.256938\pi\) | ||||
0.691527 | + | 0.722351i | \(0.256938\pi\) | |||||||
\(854\) | −55.4426 | −1.89721 | ||||||||
\(855\) | −1.63179 | −0.0558061 | ||||||||
\(856\) | 0.262195 | 0.00896163 | ||||||||
\(857\) | −4.99326 | −0.170566 | −0.0852832 | − | 0.996357i | \(-0.527179\pi\) | ||||
−0.0852832 | + | 0.996357i | \(0.527179\pi\) | |||||||
\(858\) | 47.6231 | 1.62583 | ||||||||
\(859\) | 45.4208 | 1.54974 | 0.774868 | − | 0.632123i | \(-0.217816\pi\) | ||||
0.774868 | + | 0.632123i | \(0.217816\pi\) | |||||||
\(860\) | −37.1190 | −1.26575 | ||||||||
\(861\) | 20.1212 | 0.685728 | ||||||||
\(862\) | 65.4133 | 2.22798 | ||||||||
\(863\) | 37.4242 | 1.27393 | 0.636967 | − | 0.770891i | \(-0.280189\pi\) | ||||
0.636967 | + | 0.770891i | \(0.280189\pi\) | |||||||
\(864\) | −8.02471 | −0.273006 | ||||||||
\(865\) | −35.6819 | −1.21322 | ||||||||
\(866\) | −54.7920 | −1.86191 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 25.9869 | 0.882052 | ||||||||
\(869\) | −42.6249 | −1.44595 | ||||||||
\(870\) | −23.1715 | −0.785588 | ||||||||
\(871\) | −26.6249 | −0.902151 | ||||||||
\(872\) | 0.301807 | 0.0102205 | ||||||||
\(873\) | −11.5640 | −0.391382 | ||||||||
\(874\) | 10.7160 | 0.362474 | ||||||||
\(875\) | −23.4404 | −0.792430 | ||||||||
\(876\) | 0.396654 | 0.0134017 | ||||||||
\(877\) | −23.0996 | −0.780018 | −0.390009 | − | 0.920811i | \(-0.627528\pi\) | ||||
−0.390009 | + | 0.920811i | \(0.627528\pi\) | |||||||
\(878\) | 23.2762 | 0.785532 | ||||||||
\(879\) | −16.9866 | −0.572945 | ||||||||
\(880\) | 27.9393 | 0.941833 | ||||||||
\(881\) | −28.8715 | −0.972705 | −0.486353 | − | 0.873763i | \(-0.661673\pi\) | ||||
−0.486353 | + | 0.873763i | \(0.661673\pi\) | |||||||
\(882\) | 6.60356 | 0.222354 | ||||||||
\(883\) | −21.2169 | −0.714004 | −0.357002 | − | 0.934104i | \(-0.616201\pi\) | ||||
−0.357002 | + | 0.934104i | \(0.616201\pi\) | |||||||
\(884\) | −12.4488 | −0.418699 | ||||||||
\(885\) | 3.93669 | 0.132330 | ||||||||
\(886\) | 49.2659 | 1.65512 | ||||||||
\(887\) | 2.45408 | 0.0823999 | 0.0412000 | − | 0.999151i | \(-0.486882\pi\) | ||||
0.0412000 | + | 0.999151i | \(0.486882\pi\) | |||||||
\(888\) | 0.180162 | 0.00604584 | ||||||||
\(889\) | −8.26669 | −0.277256 | ||||||||
\(890\) | −32.7890 | −1.09909 | ||||||||
\(891\) | 3.86289 | 0.129412 | ||||||||
\(892\) | −46.4695 | −1.55591 | ||||||||
\(893\) | −1.19888 | −0.0401189 | ||||||||
\(894\) | −12.7641 | −0.426897 | ||||||||
\(895\) | −28.3274 | −0.946880 | ||||||||
\(896\) | −0.807592 | −0.0269797 | ||||||||
\(897\) | 36.8481 | 1.23032 | ||||||||
\(898\) | 43.1504 | 1.43995 | ||||||||
\(899\) | −41.9706 | −1.39980 | ||||||||
\(900\) | −3.32728 | −0.110909 | ||||||||
\(901\) | 11.2524 | 0.374871 | ||||||||
\(902\) | −80.9813 | −2.69638 | ||||||||
\(903\) | 19.2542 | 0.640741 | ||||||||
\(904\) | −0.439596 | −0.0146208 | ||||||||
\(905\) | −10.3406 | −0.343732 | ||||||||
\(906\) | 46.2617 | 1.53694 | ||||||||
\(907\) | −1.66296 | −0.0552176 | −0.0276088 | − | 0.999619i | \(-0.508789\pi\) | ||||
−0.0276088 | + | 0.999619i | \(0.508789\pi\) | |||||||
\(908\) | 49.1851 | 1.63227 | ||||||||
\(909\) | −0.668211 | −0.0221632 | ||||||||
\(910\) | −43.5070 | −1.44224 | ||||||||
\(911\) | −35.6558 | −1.18133 | −0.590665 | − | 0.806917i | \(-0.701135\pi\) | ||||
−0.590665 | + | 0.806917i | \(0.701135\pi\) | |||||||
\(912\) | 3.51488 | 0.116389 | ||||||||
\(913\) | −38.0686 | −1.25989 | ||||||||
\(914\) | 65.7666 | 2.17537 | ||||||||
\(915\) | −26.2907 | −0.869145 | ||||||||
\(916\) | 10.7977 | 0.356767 | ||||||||
\(917\) | −16.9420 | −0.559474 | ||||||||
\(918\) | −2.00652 | −0.0662251 | ||||||||
\(919\) | 23.0236 | 0.759480 | 0.379740 | − | 0.925093i | \(-0.376014\pi\) | ||||
0.379740 | + | 0.925093i | \(0.376014\pi\) | |||||||
\(920\) | −0.576096 | −0.0189933 | ||||||||
\(921\) | 20.3919 | 0.671935 | ||||||||
\(922\) | −40.9263 | −1.34784 | ||||||||
\(923\) | 49.4075 | 1.62627 | ||||||||
\(924\) | 15.0732 | 0.495871 | ||||||||
\(925\) | −5.64381 | −0.185567 | ||||||||
\(926\) | 50.8098 | 1.66971 | ||||||||
\(927\) | 5.30849 | 0.174354 | ||||||||
\(928\) | 50.5722 | 1.66011 | ||||||||
\(929\) | 44.0824 | 1.44630 | 0.723149 | − | 0.690693i | \(-0.242694\pi\) | ||||
0.723149 | + | 0.690693i | \(0.242694\pi\) | |||||||
\(930\) | 24.4869 | 0.802958 | ||||||||
\(931\) | −2.93070 | −0.0960498 | ||||||||
\(932\) | −10.6290 | −0.348163 | ||||||||
\(933\) | −0.253731 | −0.00830679 | ||||||||
\(934\) | 50.5358 | 1.65358 | ||||||||
\(935\) | 7.07850 | 0.231492 | ||||||||
\(936\) | −0.322088 | −0.0105278 | ||||||||
\(937\) | 27.4483 | 0.896698 | 0.448349 | − | 0.893859i | \(-0.352012\pi\) | ||||
0.448349 | + | 0.893859i | \(0.352012\pi\) | |||||||
\(938\) | −16.7454 | −0.546757 | ||||||||
\(939\) | 18.9071 | 0.617009 | ||||||||
\(940\) | 4.99842 | 0.163031 | ||||||||
\(941\) | −48.8533 | −1.59257 | −0.796285 | − | 0.604921i | \(-0.793205\pi\) | ||||
−0.796285 | + | 0.604921i | \(0.793205\pi\) | |||||||
\(942\) | −2.00652 | −0.0653760 | ||||||||
\(943\) | −62.6586 | −2.04045 | ||||||||
\(944\) | −8.47964 | −0.275989 | ||||||||
\(945\) | −3.52902 | −0.114799 | ||||||||
\(946\) | −77.4921 | −2.51948 | ||||||||
\(947\) | −20.3405 | −0.660977 | −0.330488 | − | 0.943810i | \(-0.607213\pi\) | ||||
−0.330488 | + | 0.943810i | \(0.607213\pi\) | |||||||
\(948\) | 22.3572 | 0.726127 | ||||||||
\(949\) | −1.20284 | −0.0390457 | ||||||||
\(950\) | 2.93429 | 0.0952008 | ||||||||
\(951\) | 23.7699 | 0.770791 | ||||||||
\(952\) | −0.100958 | −0.00327205 | ||||||||
\(953\) | 19.8704 | 0.643667 | 0.321833 | − | 0.946796i | \(-0.395701\pi\) | ||||
0.321833 | + | 0.946796i | \(0.395701\pi\) | |||||||
\(954\) | 22.5781 | 0.730995 | ||||||||
\(955\) | −45.6021 | −1.47565 | ||||||||
\(956\) | −4.44146 | −0.143647 | ||||||||
\(957\) | −24.3442 | −0.786935 | ||||||||
\(958\) | 4.40707 | 0.142386 | ||||||||
\(959\) | 15.0433 | 0.485774 | ||||||||
\(960\) | −15.0399 | −0.485412 | ||||||||
\(961\) | 13.3532 | 0.430747 | ||||||||
\(962\) | −42.3697 | −1.36605 | ||||||||
\(963\) | −5.00162 | −0.161175 | ||||||||
\(964\) | 15.7480 | 0.507208 | ||||||||
\(965\) | 11.6107 | 0.373760 | ||||||||
\(966\) | 23.1751 | 0.745647 | ||||||||
\(967\) | −39.1328 | −1.25843 | −0.629213 | − | 0.777233i | \(-0.716623\pi\) | ||||
−0.629213 | + | 0.777233i | \(0.716623\pi\) | |||||||
\(968\) | −0.205596 | −0.00660811 | ||||||||
\(969\) | 0.890505 | 0.0286072 | ||||||||
\(970\) | −42.5187 | −1.36519 | ||||||||
\(971\) | −39.1577 | −1.25663 | −0.628315 | − | 0.777959i | \(-0.716255\pi\) | ||||
−0.628315 | + | 0.777959i | \(0.716255\pi\) | |||||||
\(972\) | −2.02613 | −0.0649880 | ||||||||
\(973\) | 13.6850 | 0.438721 | ||||||||
\(974\) | 29.1941 | 0.935440 | ||||||||
\(975\) | 10.0898 | 0.323133 | ||||||||
\(976\) | 56.6303 | 1.81269 | ||||||||
\(977\) | 6.32794 | 0.202449 | 0.101224 | − | 0.994864i | \(-0.467724\pi\) | ||||
0.101224 | + | 0.994864i | \(0.467724\pi\) | |||||||
\(978\) | −24.9868 | −0.798991 | ||||||||
\(979\) | −34.4484 | −1.10098 | ||||||||
\(980\) | 12.2188 | 0.390316 | ||||||||
\(981\) | −5.75725 | −0.183815 | ||||||||
\(982\) | −77.0440 | −2.45857 | ||||||||
\(983\) | −14.0117 | −0.446903 | −0.223451 | − | 0.974715i | \(-0.571732\pi\) | ||||
−0.223451 | + | 0.974715i | \(0.571732\pi\) | |||||||
\(984\) | 0.547699 | 0.0174600 | ||||||||
\(985\) | 46.9129 | 1.49477 | ||||||||
\(986\) | 12.6452 | 0.402706 | ||||||||
\(987\) | −2.59277 | −0.0825287 | ||||||||
\(988\) | 11.0857 | 0.352684 | ||||||||
\(989\) | −59.9589 | −1.90658 | ||||||||
\(990\) | 14.2032 | 0.451406 | ||||||||
\(991\) | −61.5751 | −1.95600 | −0.977999 | − | 0.208611i | \(-0.933106\pi\) | ||||
−0.977999 | + | 0.208611i | \(0.933106\pi\) | |||||||
\(992\) | −53.4431 | −1.69682 | ||||||||
\(993\) | −5.64108 | −0.179014 | ||||||||
\(994\) | 31.0742 | 0.985614 | ||||||||
\(995\) | −10.4902 | −0.332561 | ||||||||
\(996\) | 19.9674 | 0.632691 | ||||||||
\(997\) | 17.1467 | 0.543042 | 0.271521 | − | 0.962433i | \(-0.412473\pi\) | ||||
0.271521 | + | 0.962433i | \(0.412473\pi\) | |||||||
\(998\) | −3.96982 | −0.125662 | ||||||||
\(999\) | −3.43677 | −0.108734 |
(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 | 8007.2.a.f.1.9 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.f.1.9 | ✓ | 48 | 1.1 | even | 1 | trivial |