Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6002,2,Mod(1,6002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6002 = 2 \cdot 3001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6002.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: | \(47.9262112932\) |
Analytic rank: | \(1\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 6002.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.01653 | −1.16424 | −0.582121 | − | 0.813102i | \(-0.697777\pi\) | ||||
−0.582121 | + | 0.813102i | \(0.697777\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.99229 | −0.890977 | −0.445489 | − | 0.895288i | \(-0.646970\pi\) | ||||
−0.445489 | + | 0.895288i | \(0.646970\pi\) | |||||||
\(6\) | 2.01653 | 0.823243 | ||||||||
\(7\) | −2.17859 | −0.823431 | −0.411716 | − | 0.911312i | \(-0.635070\pi\) | ||||
−0.411716 | + | 0.911312i | \(0.635070\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.06638 | 0.355458 | ||||||||
\(10\) | 1.99229 | 0.630016 | ||||||||
\(11\) | −5.20148 | −1.56830 | −0.784152 | − | 0.620569i | \(-0.786902\pi\) | ||||
−0.784152 | + | 0.620569i | \(0.786902\pi\) | |||||||
\(12\) | −2.01653 | −0.582121 | ||||||||
\(13\) | 1.73089 | 0.480061 | 0.240031 | − | 0.970765i | \(-0.422843\pi\) | ||||
0.240031 | + | 0.970765i | \(0.422843\pi\) | |||||||
\(14\) | 2.17859 | 0.582254 | ||||||||
\(15\) | 4.01750 | 1.03731 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.01764 | −0.246813 | −0.123406 | − | 0.992356i | \(-0.539382\pi\) | ||||
−0.123406 | + | 0.992356i | \(0.539382\pi\) | |||||||
\(18\) | −1.06638 | −0.251347 | ||||||||
\(19\) | −6.14250 | −1.40919 | −0.704593 | − | 0.709612i | \(-0.748870\pi\) | ||||
−0.704593 | + | 0.709612i | \(0.748870\pi\) | |||||||
\(20\) | −1.99229 | −0.445489 | ||||||||
\(21\) | 4.39319 | 0.958673 | ||||||||
\(22\) | 5.20148 | 1.10896 | ||||||||
\(23\) | 5.36800 | 1.11931 | 0.559653 | − | 0.828727i | \(-0.310934\pi\) | ||||
0.559653 | + | 0.828727i | \(0.310934\pi\) | |||||||
\(24\) | 2.01653 | 0.411622 | ||||||||
\(25\) | −1.03080 | −0.206159 | ||||||||
\(26\) | −1.73089 | −0.339455 | ||||||||
\(27\) | 3.89920 | 0.750402 | ||||||||
\(28\) | −2.17859 | −0.411716 | ||||||||
\(29\) | 3.11531 | 0.578498 | 0.289249 | − | 0.957254i | \(-0.406594\pi\) | ||||
0.289249 | + | 0.957254i | \(0.406594\pi\) | |||||||
\(30\) | −4.01750 | −0.733491 | ||||||||
\(31\) | −3.55810 | −0.639054 | −0.319527 | − | 0.947577i | \(-0.603524\pi\) | ||||
−0.319527 | + | 0.947577i | \(0.603524\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 10.4889 | 1.82588 | ||||||||
\(34\) | 1.01764 | 0.174523 | ||||||||
\(35\) | 4.34038 | 0.733659 | ||||||||
\(36\) | 1.06638 | 0.177729 | ||||||||
\(37\) | −0.736872 | −0.121141 | −0.0605705 | − | 0.998164i | \(-0.519292\pi\) | ||||
−0.0605705 | + | 0.998164i | \(0.519292\pi\) | |||||||
\(38\) | 6.14250 | 0.996445 | ||||||||
\(39\) | −3.49037 | −0.558907 | ||||||||
\(40\) | 1.99229 | 0.315008 | ||||||||
\(41\) | 1.75227 | 0.273659 | 0.136829 | − | 0.990595i | \(-0.456309\pi\) | ||||
0.136829 | + | 0.990595i | \(0.456309\pi\) | |||||||
\(42\) | −4.39319 | −0.677884 | ||||||||
\(43\) | 6.65469 | 1.01483 | 0.507415 | − | 0.861702i | \(-0.330601\pi\) | ||||
0.507415 | + | 0.861702i | \(0.330601\pi\) | |||||||
\(44\) | −5.20148 | −0.784152 | ||||||||
\(45\) | −2.12452 | −0.316705 | ||||||||
\(46\) | −5.36800 | −0.791469 | ||||||||
\(47\) | 4.35042 | 0.634574 | 0.317287 | − | 0.948329i | \(-0.397228\pi\) | ||||
0.317287 | + | 0.948329i | \(0.397228\pi\) | |||||||
\(48\) | −2.01653 | −0.291060 | ||||||||
\(49\) | −2.25372 | −0.321961 | ||||||||
\(50\) | 1.03080 | 0.145777 | ||||||||
\(51\) | 2.05209 | 0.287350 | ||||||||
\(52\) | 1.73089 | 0.240031 | ||||||||
\(53\) | −4.05057 | −0.556389 | −0.278195 | − | 0.960525i | \(-0.589736\pi\) | ||||
−0.278195 | + | 0.960525i | \(0.589736\pi\) | |||||||
\(54\) | −3.89920 | −0.530614 | ||||||||
\(55\) | 10.3628 | 1.39732 | ||||||||
\(56\) | 2.17859 | 0.291127 | ||||||||
\(57\) | 12.3865 | 1.64063 | ||||||||
\(58\) | −3.11531 | −0.409060 | ||||||||
\(59\) | 8.76448 | 1.14104 | 0.570519 | − | 0.821284i | \(-0.306742\pi\) | ||||
0.570519 | + | 0.821284i | \(0.306742\pi\) | |||||||
\(60\) | 4.01750 | 0.518656 | ||||||||
\(61\) | 0.816696 | 0.104567 | 0.0522836 | − | 0.998632i | \(-0.483350\pi\) | ||||
0.0522836 | + | 0.998632i | \(0.483350\pi\) | |||||||
\(62\) | 3.55810 | 0.451880 | ||||||||
\(63\) | −2.32320 | −0.292696 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.44842 | −0.427724 | ||||||||
\(66\) | −10.4889 | −1.29110 | ||||||||
\(67\) | 9.86937 | 1.20574 | 0.602868 | − | 0.797841i | \(-0.294025\pi\) | ||||
0.602868 | + | 0.797841i | \(0.294025\pi\) | |||||||
\(68\) | −1.01764 | −0.123406 | ||||||||
\(69\) | −10.8247 | −1.30314 | ||||||||
\(70\) | −4.34038 | −0.518775 | ||||||||
\(71\) | −0.662399 | −0.0786123 | −0.0393061 | − | 0.999227i | \(-0.512515\pi\) | ||||
−0.0393061 | + | 0.999227i | \(0.512515\pi\) | |||||||
\(72\) | −1.06638 | −0.125674 | ||||||||
\(73\) | 7.12644 | 0.834087 | 0.417043 | − | 0.908887i | \(-0.363066\pi\) | ||||
0.417043 | + | 0.908887i | \(0.363066\pi\) | |||||||
\(74\) | 0.736872 | 0.0856597 | ||||||||
\(75\) | 2.07863 | 0.240019 | ||||||||
\(76\) | −6.14250 | −0.704593 | ||||||||
\(77\) | 11.3319 | 1.29139 | ||||||||
\(78\) | 3.49037 | 0.395207 | ||||||||
\(79\) | −4.61676 | −0.519426 | −0.259713 | − | 0.965686i | \(-0.583628\pi\) | ||||
−0.259713 | + | 0.965686i | \(0.583628\pi\) | |||||||
\(80\) | −1.99229 | −0.222744 | ||||||||
\(81\) | −11.0620 | −1.22911 | ||||||||
\(82\) | −1.75227 | −0.193506 | ||||||||
\(83\) | −16.8661 | −1.85129 | −0.925647 | − | 0.378388i | \(-0.876478\pi\) | ||||
−0.925647 | + | 0.378388i | \(0.876478\pi\) | |||||||
\(84\) | 4.39319 | 0.479337 | ||||||||
\(85\) | 2.02742 | 0.219905 | ||||||||
\(86\) | −6.65469 | −0.717593 | ||||||||
\(87\) | −6.28210 | −0.673512 | ||||||||
\(88\) | 5.20148 | 0.554479 | ||||||||
\(89\) | 18.0780 | 1.91626 | 0.958131 | − | 0.286330i | \(-0.0924354\pi\) | ||||
0.958131 | + | 0.286330i | \(0.0924354\pi\) | |||||||
\(90\) | 2.12452 | 0.223944 | ||||||||
\(91\) | −3.77090 | −0.395298 | ||||||||
\(92\) | 5.36800 | 0.559653 | ||||||||
\(93\) | 7.17501 | 0.744013 | ||||||||
\(94\) | −4.35042 | −0.448712 | ||||||||
\(95\) | 12.2376 | 1.25555 | ||||||||
\(96\) | 2.01653 | 0.205811 | ||||||||
\(97\) | 3.91078 | 0.397080 | 0.198540 | − | 0.980093i | \(-0.436380\pi\) | ||||
0.198540 | + | 0.980093i | \(0.436380\pi\) | |||||||
\(98\) | 2.25372 | 0.227661 | ||||||||
\(99\) | −5.54672 | −0.557467 | ||||||||
\(100\) | −1.03080 | −0.103080 | ||||||||
\(101\) | 11.0093 | 1.09547 | 0.547735 | − | 0.836652i | \(-0.315490\pi\) | ||||
0.547735 | + | 0.836652i | \(0.315490\pi\) | |||||||
\(102\) | −2.05209 | −0.203187 | ||||||||
\(103\) | −4.95972 | −0.488696 | −0.244348 | − | 0.969688i | \(-0.578574\pi\) | ||||
−0.244348 | + | 0.969688i | \(0.578574\pi\) | |||||||
\(104\) | −1.73089 | −0.169727 | ||||||||
\(105\) | −8.75249 | −0.854156 | ||||||||
\(106\) | 4.05057 | 0.393427 | ||||||||
\(107\) | −0.865756 | −0.0836958 | −0.0418479 | − | 0.999124i | \(-0.513324\pi\) | ||||
−0.0418479 | + | 0.999124i | \(0.513324\pi\) | |||||||
\(108\) | 3.89920 | 0.375201 | ||||||||
\(109\) | 11.9007 | 1.13988 | 0.569939 | − | 0.821687i | \(-0.306967\pi\) | ||||
0.569939 | + | 0.821687i | \(0.306967\pi\) | |||||||
\(110\) | −10.3628 | −0.988057 | ||||||||
\(111\) | 1.48592 | 0.141037 | ||||||||
\(112\) | −2.17859 | −0.205858 | ||||||||
\(113\) | −18.9162 | −1.77949 | −0.889744 | − | 0.456460i | \(-0.849117\pi\) | ||||
−0.889744 | + | 0.456460i | \(0.849117\pi\) | |||||||
\(114\) | −12.3865 | −1.16010 | ||||||||
\(115\) | −10.6946 | −0.997276 | ||||||||
\(116\) | 3.11531 | 0.289249 | ||||||||
\(117\) | 1.84577 | 0.170642 | ||||||||
\(118\) | −8.76448 | −0.806836 | ||||||||
\(119\) | 2.21702 | 0.203234 | ||||||||
\(120\) | −4.01750 | −0.366745 | ||||||||
\(121\) | 16.0553 | 1.45958 | ||||||||
\(122\) | −0.816696 | −0.0739402 | ||||||||
\(123\) | −3.53350 | −0.318605 | ||||||||
\(124\) | −3.55810 | −0.319527 | ||||||||
\(125\) | 12.0151 | 1.07466 | ||||||||
\(126\) | 2.32320 | 0.206967 | ||||||||
\(127\) | −5.89672 | −0.523249 | −0.261625 | − | 0.965170i | \(-0.584258\pi\) | ||||
−0.261625 | + | 0.965170i | \(0.584258\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −13.4193 | −1.18151 | ||||||||
\(130\) | 3.44842 | 0.302446 | ||||||||
\(131\) | 11.2970 | 0.987023 | 0.493512 | − | 0.869739i | \(-0.335713\pi\) | ||||
0.493512 | + | 0.869739i | \(0.335713\pi\) | |||||||
\(132\) | 10.4889 | 0.912942 | ||||||||
\(133\) | 13.3820 | 1.16037 | ||||||||
\(134\) | −9.86937 | −0.852584 | ||||||||
\(135\) | −7.76833 | −0.668591 | ||||||||
\(136\) | 1.01764 | 0.0872615 | ||||||||
\(137\) | 1.78132 | 0.152189 | 0.0760944 | − | 0.997101i | \(-0.475755\pi\) | ||||
0.0760944 | + | 0.997101i | \(0.475755\pi\) | |||||||
\(138\) | 10.8247 | 0.921461 | ||||||||
\(139\) | −17.6995 | −1.50125 | −0.750626 | − | 0.660728i | \(-0.770248\pi\) | ||||
−0.750626 | + | 0.660728i | \(0.770248\pi\) | |||||||
\(140\) | 4.34038 | 0.366829 | ||||||||
\(141\) | −8.77274 | −0.738798 | ||||||||
\(142\) | 0.662399 | 0.0555873 | ||||||||
\(143\) | −9.00316 | −0.752882 | ||||||||
\(144\) | 1.06638 | 0.0888646 | ||||||||
\(145\) | −6.20659 | −0.515429 | ||||||||
\(146\) | −7.12644 | −0.589788 | ||||||||
\(147\) | 4.54469 | 0.374840 | ||||||||
\(148\) | −0.736872 | −0.0605705 | ||||||||
\(149\) | 20.1669 | 1.65214 | 0.826070 | − | 0.563567i | \(-0.190572\pi\) | ||||
0.826070 | + | 0.563567i | \(0.190572\pi\) | |||||||
\(150\) | −2.07863 | −0.169719 | ||||||||
\(151\) | 0.805568 | 0.0655562 | 0.0327781 | − | 0.999463i | \(-0.489565\pi\) | ||||
0.0327781 | + | 0.999463i | \(0.489565\pi\) | |||||||
\(152\) | 6.14250 | 0.498222 | ||||||||
\(153\) | −1.08518 | −0.0877317 | ||||||||
\(154\) | −11.3319 | −0.913151 | ||||||||
\(155\) | 7.08876 | 0.569383 | ||||||||
\(156\) | −3.49037 | −0.279454 | ||||||||
\(157\) | −15.4947 | −1.23661 | −0.618306 | − | 0.785937i | \(-0.712181\pi\) | ||||
−0.618306 | + | 0.785937i | \(0.712181\pi\) | |||||||
\(158\) | 4.61676 | 0.367290 | ||||||||
\(159\) | 8.16809 | 0.647771 | ||||||||
\(160\) | 1.99229 | 0.157504 | ||||||||
\(161\) | −11.6947 | −0.921672 | ||||||||
\(162\) | 11.0620 | 0.869110 | ||||||||
\(163\) | 19.4715 | 1.52512 | 0.762562 | − | 0.646915i | \(-0.223941\pi\) | ||||
0.762562 | + | 0.646915i | \(0.223941\pi\) | |||||||
\(164\) | 1.75227 | 0.136829 | ||||||||
\(165\) | −20.8969 | −1.62682 | ||||||||
\(166\) | 16.8661 | 1.30906 | ||||||||
\(167\) | −13.2299 | −1.02376 | −0.511881 | − | 0.859057i | \(-0.671051\pi\) | ||||
−0.511881 | + | 0.859057i | \(0.671051\pi\) | |||||||
\(168\) | −4.39319 | −0.338942 | ||||||||
\(169\) | −10.0040 | −0.769541 | ||||||||
\(170\) | −2.02742 | −0.155496 | ||||||||
\(171\) | −6.55021 | −0.500907 | ||||||||
\(172\) | 6.65469 | 0.507415 | ||||||||
\(173\) | 2.90149 | 0.220596 | 0.110298 | − | 0.993899i | \(-0.464819\pi\) | ||||
0.110298 | + | 0.993899i | \(0.464819\pi\) | |||||||
\(174\) | 6.28210 | 0.476245 | ||||||||
\(175\) | 2.24569 | 0.169758 | ||||||||
\(176\) | −5.20148 | −0.392076 | ||||||||
\(177\) | −17.6738 | −1.32844 | ||||||||
\(178\) | −18.0780 | −1.35500 | ||||||||
\(179\) | −5.88100 | −0.439566 | −0.219783 | − | 0.975549i | \(-0.570535\pi\) | ||||
−0.219783 | + | 0.975549i | \(0.570535\pi\) | |||||||
\(180\) | −2.12452 | −0.158353 | ||||||||
\(181\) | 13.7437 | 1.02156 | 0.510781 | − | 0.859711i | \(-0.329356\pi\) | ||||
0.510781 | + | 0.859711i | \(0.329356\pi\) | |||||||
\(182\) | 3.77090 | 0.279518 | ||||||||
\(183\) | −1.64689 | −0.121741 | ||||||||
\(184\) | −5.36800 | −0.395734 | ||||||||
\(185\) | 1.46806 | 0.107934 | ||||||||
\(186\) | −7.17501 | −0.526097 | ||||||||
\(187\) | 5.29321 | 0.387078 | ||||||||
\(188\) | 4.35042 | 0.317287 | ||||||||
\(189\) | −8.49479 | −0.617905 | ||||||||
\(190\) | −12.2376 | −0.887810 | ||||||||
\(191\) | 24.6595 | 1.78430 | 0.892150 | − | 0.451740i | \(-0.149197\pi\) | ||||
0.892150 | + | 0.451740i | \(0.149197\pi\) | |||||||
\(192\) | −2.01653 | −0.145530 | ||||||||
\(193\) | 7.24622 | 0.521594 | 0.260797 | − | 0.965394i | \(-0.416015\pi\) | ||||
0.260797 | + | 0.965394i | \(0.416015\pi\) | |||||||
\(194\) | −3.91078 | −0.280778 | ||||||||
\(195\) | 6.95382 | 0.497974 | ||||||||
\(196\) | −2.25372 | −0.160980 | ||||||||
\(197\) | 20.9701 | 1.49406 | 0.747030 | − | 0.664790i | \(-0.231479\pi\) | ||||
0.747030 | + | 0.664790i | \(0.231479\pi\) | |||||||
\(198\) | 5.54672 | 0.394188 | ||||||||
\(199\) | −21.2249 | −1.50459 | −0.752297 | − | 0.658825i | \(-0.771054\pi\) | ||||
−0.752297 | + | 0.658825i | \(0.771054\pi\) | |||||||
\(200\) | 1.03080 | 0.0728883 | ||||||||
\(201\) | −19.9018 | −1.40377 | ||||||||
\(202\) | −11.0093 | −0.774614 | ||||||||
\(203\) | −6.78700 | −0.476354 | ||||||||
\(204\) | 2.05209 | 0.143675 | ||||||||
\(205\) | −3.49103 | −0.243824 | ||||||||
\(206\) | 4.95972 | 0.345560 | ||||||||
\(207\) | 5.72430 | 0.397867 | ||||||||
\(208\) | 1.73089 | 0.120015 | ||||||||
\(209\) | 31.9501 | 2.21003 | ||||||||
\(210\) | 8.75249 | 0.603979 | ||||||||
\(211\) | −26.5375 | −1.82692 | −0.913459 | − | 0.406930i | \(-0.866599\pi\) | ||||
−0.913459 | + | 0.406930i | \(0.866599\pi\) | |||||||
\(212\) | −4.05057 | −0.278195 | ||||||||
\(213\) | 1.33574 | 0.0915237 | ||||||||
\(214\) | 0.865756 | 0.0591819 | ||||||||
\(215\) | −13.2580 | −0.904191 | ||||||||
\(216\) | −3.89920 | −0.265307 | ||||||||
\(217\) | 7.75166 | 0.526217 | ||||||||
\(218\) | −11.9007 | −0.806015 | ||||||||
\(219\) | −14.3706 | −0.971078 | ||||||||
\(220\) | 10.3628 | 0.698662 | ||||||||
\(221\) | −1.76141 | −0.118485 | ||||||||
\(222\) | −1.48592 | −0.0997286 | ||||||||
\(223\) | 5.23517 | 0.350573 | 0.175286 | − | 0.984517i | \(-0.443915\pi\) | ||||
0.175286 | + | 0.984517i | \(0.443915\pi\) | |||||||
\(224\) | 2.17859 | 0.145563 | ||||||||
\(225\) | −1.09922 | −0.0732811 | ||||||||
\(226\) | 18.9162 | 1.25829 | ||||||||
\(227\) | −5.70185 | −0.378445 | −0.189222 | − | 0.981934i | \(-0.560597\pi\) | ||||
−0.189222 | + | 0.981934i | \(0.560597\pi\) | |||||||
\(228\) | 12.3865 | 0.820316 | ||||||||
\(229\) | 10.2629 | 0.678192 | 0.339096 | − | 0.940752i | \(-0.389879\pi\) | ||||
0.339096 | + | 0.940752i | \(0.389879\pi\) | |||||||
\(230\) | 10.6946 | 0.705181 | ||||||||
\(231\) | −22.8511 | −1.50349 | ||||||||
\(232\) | −3.11531 | −0.204530 | ||||||||
\(233\) | 22.2019 | 1.45449 | 0.727247 | − | 0.686376i | \(-0.240800\pi\) | ||||
0.727247 | + | 0.686376i | \(0.240800\pi\) | |||||||
\(234\) | −1.84577 | −0.120662 | ||||||||
\(235\) | −8.66729 | −0.565391 | ||||||||
\(236\) | 8.76448 | 0.570519 | ||||||||
\(237\) | 9.30982 | 0.604738 | ||||||||
\(238\) | −2.21702 | −0.143708 | ||||||||
\(239\) | −27.6097 | −1.78592 | −0.892961 | − | 0.450134i | \(-0.851376\pi\) | ||||
−0.892961 | + | 0.450134i | \(0.851376\pi\) | |||||||
\(240\) | 4.01750 | 0.259328 | ||||||||
\(241\) | 18.2226 | 1.17382 | 0.586910 | − | 0.809652i | \(-0.300344\pi\) | ||||
0.586910 | + | 0.809652i | \(0.300344\pi\) | |||||||
\(242\) | −16.0553 | −1.03208 | ||||||||
\(243\) | 10.6091 | 0.680576 | ||||||||
\(244\) | 0.816696 | 0.0522836 | ||||||||
\(245\) | 4.49006 | 0.286860 | ||||||||
\(246\) | 3.53350 | 0.225288 | ||||||||
\(247\) | −10.6320 | −0.676495 | ||||||||
\(248\) | 3.55810 | 0.225940 | ||||||||
\(249\) | 34.0109 | 2.15535 | ||||||||
\(250\) | −12.0151 | −0.759900 | ||||||||
\(251\) | −4.64098 | −0.292936 | −0.146468 | − | 0.989215i | \(-0.546790\pi\) | ||||
−0.146468 | + | 0.989215i | \(0.546790\pi\) | |||||||
\(252\) | −2.32320 | −0.146348 | ||||||||
\(253\) | −27.9215 | −1.75541 | ||||||||
\(254\) | 5.89672 | 0.369993 | ||||||||
\(255\) | −4.08835 | −0.256022 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.10603 | −0.193749 | −0.0968745 | − | 0.995297i | \(-0.530885\pi\) | ||||
−0.0968745 | + | 0.995297i | \(0.530885\pi\) | |||||||
\(258\) | 13.4193 | 0.835452 | ||||||||
\(259\) | 1.60535 | 0.0997514 | ||||||||
\(260\) | −3.44842 | −0.213862 | ||||||||
\(261\) | 3.32209 | 0.205632 | ||||||||
\(262\) | −11.2970 | −0.697931 | ||||||||
\(263\) | −4.91173 | −0.302870 | −0.151435 | − | 0.988467i | \(-0.548389\pi\) | ||||
−0.151435 | + | 0.988467i | \(0.548389\pi\) | |||||||
\(264\) | −10.4889 | −0.645548 | ||||||||
\(265\) | 8.06990 | 0.495730 | ||||||||
\(266\) | −13.3820 | −0.820504 | ||||||||
\(267\) | −36.4547 | −2.23099 | ||||||||
\(268\) | 9.86937 | 0.602868 | ||||||||
\(269\) | 25.0619 | 1.52805 | 0.764024 | − | 0.645187i | \(-0.223221\pi\) | ||||
0.764024 | + | 0.645187i | \(0.223221\pi\) | |||||||
\(270\) | 7.76833 | 0.472765 | ||||||||
\(271\) | 15.7737 | 0.958185 | 0.479092 | − | 0.877764i | \(-0.340966\pi\) | ||||
0.479092 | + | 0.877764i | \(0.340966\pi\) | |||||||
\(272\) | −1.01764 | −0.0617032 | ||||||||
\(273\) | 7.60411 | 0.460222 | ||||||||
\(274\) | −1.78132 | −0.107614 | ||||||||
\(275\) | 5.36167 | 0.323321 | ||||||||
\(276\) | −10.8247 | −0.651571 | ||||||||
\(277\) | −21.7596 | −1.30741 | −0.653705 | − | 0.756749i | \(-0.726786\pi\) | ||||
−0.653705 | + | 0.756749i | \(0.726786\pi\) | |||||||
\(278\) | 17.6995 | 1.06154 | ||||||||
\(279\) | −3.79427 | −0.227157 | ||||||||
\(280\) | −4.34038 | −0.259388 | ||||||||
\(281\) | −2.52287 | −0.150502 | −0.0752509 | − | 0.997165i | \(-0.523976\pi\) | ||||
−0.0752509 | + | 0.997165i | \(0.523976\pi\) | |||||||
\(282\) | 8.77274 | 0.522409 | ||||||||
\(283\) | 11.2483 | 0.668640 | 0.334320 | − | 0.942460i | \(-0.391493\pi\) | ||||
0.334320 | + | 0.942460i | \(0.391493\pi\) | |||||||
\(284\) | −0.662399 | −0.0393061 | ||||||||
\(285\) | −24.6775 | −1.46177 | ||||||||
\(286\) | 9.00316 | 0.532368 | ||||||||
\(287\) | −3.81749 | −0.225339 | ||||||||
\(288\) | −1.06638 | −0.0628368 | ||||||||
\(289\) | −15.9644 | −0.939083 | ||||||||
\(290\) | 6.20659 | 0.364463 | ||||||||
\(291\) | −7.88619 | −0.462297 | ||||||||
\(292\) | 7.12644 | 0.417043 | ||||||||
\(293\) | 16.5581 | 0.967332 | 0.483666 | − | 0.875253i | \(-0.339305\pi\) | ||||
0.483666 | + | 0.875253i | \(0.339305\pi\) | |||||||
\(294\) | −4.54469 | −0.265052 | ||||||||
\(295\) | −17.4613 | −1.01664 | ||||||||
\(296\) | 0.736872 | 0.0428298 | ||||||||
\(297\) | −20.2816 | −1.17686 | ||||||||
\(298\) | −20.1669 | −1.16824 | ||||||||
\(299\) | 9.29140 | 0.537335 | ||||||||
\(300\) | 2.07863 | 0.120010 | ||||||||
\(301\) | −14.4979 | −0.835643 | ||||||||
\(302\) | −0.805568 | −0.0463552 | ||||||||
\(303\) | −22.2006 | −1.27539 | ||||||||
\(304\) | −6.14250 | −0.352296 | ||||||||
\(305\) | −1.62709 | −0.0931670 | ||||||||
\(306\) | 1.08518 | 0.0620357 | ||||||||
\(307\) | 2.89200 | 0.165055 | 0.0825276 | − | 0.996589i | \(-0.473701\pi\) | ||||
0.0825276 | + | 0.996589i | \(0.473701\pi\) | |||||||
\(308\) | 11.3319 | 0.645695 | ||||||||
\(309\) | 10.0014 | 0.568960 | ||||||||
\(310\) | −7.08876 | −0.402614 | ||||||||
\(311\) | −30.2618 | −1.71599 | −0.857994 | − | 0.513660i | \(-0.828289\pi\) | ||||
−0.857994 | + | 0.513660i | \(0.828289\pi\) | |||||||
\(312\) | 3.49037 | 0.197604 | ||||||||
\(313\) | −13.0609 | −0.738245 | −0.369122 | − | 0.929381i | \(-0.620342\pi\) | ||||
−0.369122 | + | 0.929381i | \(0.620342\pi\) | |||||||
\(314\) | 15.4947 | 0.874417 | ||||||||
\(315\) | 4.62848 | 0.260785 | ||||||||
\(316\) | −4.61676 | −0.259713 | ||||||||
\(317\) | −3.91087 | −0.219656 | −0.109828 | − | 0.993951i | \(-0.535030\pi\) | ||||
−0.109828 | + | 0.993951i | \(0.535030\pi\) | |||||||
\(318\) | −8.16809 | −0.458044 | ||||||||
\(319\) | −16.2042 | −0.907261 | ||||||||
\(320\) | −1.99229 | −0.111372 | ||||||||
\(321\) | 1.74582 | 0.0974421 | ||||||||
\(322\) | 11.6947 | 0.651720 | ||||||||
\(323\) | 6.25083 | 0.347805 | ||||||||
\(324\) | −11.0620 | −0.614554 | ||||||||
\(325\) | −1.78419 | −0.0989691 | ||||||||
\(326\) | −19.4715 | −1.07843 | ||||||||
\(327\) | −23.9980 | −1.32709 | ||||||||
\(328\) | −1.75227 | −0.0967531 | ||||||||
\(329\) | −9.47781 | −0.522529 | ||||||||
\(330\) | 20.8969 | 1.15034 | ||||||||
\(331\) | −32.7139 | −1.79812 | −0.899058 | − | 0.437829i | \(-0.855748\pi\) | ||||
−0.899058 | + | 0.437829i | \(0.855748\pi\) | |||||||
\(332\) | −16.8661 | −0.925647 | ||||||||
\(333\) | −0.785782 | −0.0430606 | ||||||||
\(334\) | 13.2299 | 0.723908 | ||||||||
\(335\) | −19.6626 | −1.07428 | ||||||||
\(336\) | 4.39319 | 0.239668 | ||||||||
\(337\) | −32.1026 | −1.74874 | −0.874370 | − | 0.485260i | \(-0.838725\pi\) | ||||
−0.874370 | + | 0.485260i | \(0.838725\pi\) | |||||||
\(338\) | 10.0040 | 0.544148 | ||||||||
\(339\) | 38.1450 | 2.07175 | ||||||||
\(340\) | 2.02742 | 0.109952 | ||||||||
\(341\) | 18.5074 | 1.00223 | ||||||||
\(342\) | 6.55021 | 0.354195 | ||||||||
\(343\) | 20.1601 | 1.08854 | ||||||||
\(344\) | −6.65469 | −0.358797 | ||||||||
\(345\) | 21.5659 | 1.16107 | ||||||||
\(346\) | −2.90149 | −0.155985 | ||||||||
\(347\) | 14.6604 | 0.787012 | 0.393506 | − | 0.919322i | \(-0.371262\pi\) | ||||
0.393506 | + | 0.919322i | \(0.371262\pi\) | |||||||
\(348\) | −6.28210 | −0.336756 | ||||||||
\(349\) | −27.2375 | −1.45799 | −0.728995 | − | 0.684520i | \(-0.760012\pi\) | ||||
−0.728995 | + | 0.684520i | \(0.760012\pi\) | |||||||
\(350\) | −2.24569 | −0.120037 | ||||||||
\(351\) | 6.74908 | 0.360239 | ||||||||
\(352\) | 5.20148 | 0.277240 | ||||||||
\(353\) | −0.965735 | −0.0514009 | −0.0257004 | − | 0.999670i | \(-0.508182\pi\) | ||||
−0.0257004 | + | 0.999670i | \(0.508182\pi\) | |||||||
\(354\) | 17.6738 | 0.939352 | ||||||||
\(355\) | 1.31969 | 0.0700418 | ||||||||
\(356\) | 18.0780 | 0.958131 | ||||||||
\(357\) | −4.47067 | −0.236613 | ||||||||
\(358\) | 5.88100 | 0.310820 | ||||||||
\(359\) | 5.46016 | 0.288176 | 0.144088 | − | 0.989565i | \(-0.453975\pi\) | ||||
0.144088 | + | 0.989565i | \(0.453975\pi\) | |||||||
\(360\) | 2.12452 | 0.111972 | ||||||||
\(361\) | 18.7303 | 0.985804 | ||||||||
\(362\) | −13.7437 | −0.722353 | ||||||||
\(363\) | −32.3760 | −1.69930 | ||||||||
\(364\) | −3.77090 | −0.197649 | ||||||||
\(365\) | −14.1979 | −0.743152 | ||||||||
\(366\) | 1.64689 | 0.0860842 | ||||||||
\(367\) | −4.85033 | −0.253185 | −0.126592 | − | 0.991955i | \(-0.540404\pi\) | ||||
−0.126592 | + | 0.991955i | \(0.540404\pi\) | |||||||
\(368\) | 5.36800 | 0.279826 | ||||||||
\(369\) | 1.86858 | 0.0972744 | ||||||||
\(370\) | −1.46806 | −0.0763208 | ||||||||
\(371\) | 8.82456 | 0.458148 | ||||||||
\(372\) | 7.17501 | 0.372007 | ||||||||
\(373\) | 32.0711 | 1.66058 | 0.830291 | − | 0.557331i | \(-0.188174\pi\) | ||||
0.830291 | + | 0.557331i | \(0.188174\pi\) | |||||||
\(374\) | −5.29321 | −0.273705 | ||||||||
\(375\) | −24.2287 | −1.25116 | ||||||||
\(376\) | −4.35042 | −0.224356 | ||||||||
\(377\) | 5.39224 | 0.277715 | ||||||||
\(378\) | 8.49479 | 0.436925 | ||||||||
\(379\) | 16.4856 | 0.846811 | 0.423405 | − | 0.905940i | \(-0.360835\pi\) | ||||
0.423405 | + | 0.905940i | \(0.360835\pi\) | |||||||
\(380\) | 12.2376 | 0.627776 | ||||||||
\(381\) | 11.8909 | 0.609188 | ||||||||
\(382\) | −24.6595 | −1.26169 | ||||||||
\(383\) | 4.43551 | 0.226644 | 0.113322 | − | 0.993558i | \(-0.463851\pi\) | ||||
0.113322 | + | 0.993558i | \(0.463851\pi\) | |||||||
\(384\) | 2.01653 | 0.102905 | ||||||||
\(385\) | −22.5764 | −1.15060 | ||||||||
\(386\) | −7.24622 | −0.368823 | ||||||||
\(387\) | 7.09639 | 0.360730 | ||||||||
\(388\) | 3.91078 | 0.198540 | ||||||||
\(389\) | −2.80059 | −0.141995 | −0.0709977 | − | 0.997476i | \(-0.522618\pi\) | ||||
−0.0709977 | + | 0.997476i | \(0.522618\pi\) | |||||||
\(390\) | −6.95382 | −0.352121 | ||||||||
\(391\) | −5.46267 | −0.276259 | ||||||||
\(392\) | 2.25372 | 0.113830 | ||||||||
\(393\) | −22.7807 | −1.14913 | ||||||||
\(394\) | −20.9701 | −1.05646 | ||||||||
\(395\) | 9.19791 | 0.462797 | ||||||||
\(396\) | −5.54672 | −0.278733 | ||||||||
\(397\) | 13.5015 | 0.677621 | 0.338810 | − | 0.940855i | \(-0.389976\pi\) | ||||
0.338810 | + | 0.940855i | \(0.389976\pi\) | |||||||
\(398\) | 21.2249 | 1.06391 | ||||||||
\(399\) | −26.9852 | −1.35095 | ||||||||
\(400\) | −1.03080 | −0.0515398 | ||||||||
\(401\) | 16.1122 | 0.804606 | 0.402303 | − | 0.915507i | \(-0.368210\pi\) | ||||
0.402303 | + | 0.915507i | \(0.368210\pi\) | |||||||
\(402\) | 19.9018 | 0.992614 | ||||||||
\(403\) | −6.15867 | −0.306785 | ||||||||
\(404\) | 11.0093 | 0.547735 | ||||||||
\(405\) | 22.0386 | 1.09511 | ||||||||
\(406\) | 6.78700 | 0.336833 | ||||||||
\(407\) | 3.83282 | 0.189986 | ||||||||
\(408\) | −2.05209 | −0.101594 | ||||||||
\(409\) | −39.7145 | −1.96375 | −0.981877 | − | 0.189519i | \(-0.939307\pi\) | ||||
−0.981877 | + | 0.189519i | \(0.939307\pi\) | |||||||
\(410\) | 3.49103 | 0.172410 | ||||||||
\(411\) | −3.59209 | −0.177185 | ||||||||
\(412\) | −4.95972 | −0.244348 | ||||||||
\(413\) | −19.0942 | −0.939567 | ||||||||
\(414\) | −5.72430 | −0.281334 | ||||||||
\(415\) | 33.6021 | 1.64946 | ||||||||
\(416\) | −1.73089 | −0.0848636 | ||||||||
\(417\) | 35.6915 | 1.74782 | ||||||||
\(418\) | −31.9501 | −1.56273 | ||||||||
\(419\) | 34.9604 | 1.70793 | 0.853963 | − | 0.520333i | \(-0.174192\pi\) | ||||
0.853963 | + | 0.520333i | \(0.174192\pi\) | |||||||
\(420\) | −8.75249 | −0.427078 | ||||||||
\(421\) | 6.17265 | 0.300836 | 0.150418 | − | 0.988622i | \(-0.451938\pi\) | ||||
0.150418 | + | 0.988622i | \(0.451938\pi\) | |||||||
\(422\) | 26.5375 | 1.29183 | ||||||||
\(423\) | 4.63918 | 0.225565 | ||||||||
\(424\) | 4.05057 | 0.196713 | ||||||||
\(425\) | 1.04898 | 0.0508828 | ||||||||
\(426\) | −1.33574 | −0.0647170 | ||||||||
\(427\) | −1.77925 | −0.0861039 | ||||||||
\(428\) | −0.865756 | −0.0418479 | ||||||||
\(429\) | 18.1551 | 0.876536 | ||||||||
\(430\) | 13.2580 | 0.639360 | ||||||||
\(431\) | −14.0408 | −0.676322 | −0.338161 | − | 0.941088i | \(-0.609805\pi\) | ||||
−0.338161 | + | 0.941088i | \(0.609805\pi\) | |||||||
\(432\) | 3.89920 | 0.187601 | ||||||||
\(433\) | −27.5736 | −1.32510 | −0.662550 | − | 0.749017i | \(-0.730526\pi\) | ||||
−0.662550 | + | 0.749017i | \(0.730526\pi\) | |||||||
\(434\) | −7.75166 | −0.372092 | ||||||||
\(435\) | 12.5157 | 0.600084 | ||||||||
\(436\) | 11.9007 | 0.569939 | ||||||||
\(437\) | −32.9729 | −1.57731 | ||||||||
\(438\) | 14.3706 | 0.686656 | ||||||||
\(439\) | 37.7467 | 1.80155 | 0.900777 | − | 0.434282i | \(-0.142998\pi\) | ||||
0.900777 | + | 0.434282i | \(0.142998\pi\) | |||||||
\(440\) | −10.3628 | −0.494028 | ||||||||
\(441\) | −2.40332 | −0.114444 | ||||||||
\(442\) | 1.76141 | 0.0837818 | ||||||||
\(443\) | 19.8368 | 0.942476 | 0.471238 | − | 0.882006i | \(-0.343807\pi\) | ||||
0.471238 | + | 0.882006i | \(0.343807\pi\) | |||||||
\(444\) | 1.48592 | 0.0705187 | ||||||||
\(445\) | −36.0165 | −1.70735 | ||||||||
\(446\) | −5.23517 | −0.247892 | ||||||||
\(447\) | −40.6671 | −1.92349 | ||||||||
\(448\) | −2.17859 | −0.102929 | ||||||||
\(449\) | −16.3370 | −0.770990 | −0.385495 | − | 0.922710i | \(-0.625969\pi\) | ||||
−0.385495 | + | 0.922710i | \(0.625969\pi\) | |||||||
\(450\) | 1.09922 | 0.0518175 | ||||||||
\(451\) | −9.11440 | −0.429180 | ||||||||
\(452\) | −18.9162 | −0.889744 | ||||||||
\(453\) | −1.62445 | −0.0763233 | ||||||||
\(454\) | 5.70185 | 0.267601 | ||||||||
\(455\) | 7.51271 | 0.352201 | ||||||||
\(456\) | −12.3865 | −0.580051 | ||||||||
\(457\) | −36.0942 | −1.68842 | −0.844208 | − | 0.536015i | \(-0.819929\pi\) | ||||
−0.844208 | + | 0.536015i | \(0.819929\pi\) | |||||||
\(458\) | −10.2629 | −0.479554 | ||||||||
\(459\) | −3.96797 | −0.185209 | ||||||||
\(460\) | −10.6946 | −0.498638 | ||||||||
\(461\) | −4.83779 | −0.225318 | −0.112659 | − | 0.993634i | \(-0.535937\pi\) | ||||
−0.112659 | + | 0.993634i | \(0.535937\pi\) | |||||||
\(462\) | 22.8511 | 1.06313 | ||||||||
\(463\) | −25.1462 | −1.16864 | −0.584322 | − | 0.811522i | \(-0.698640\pi\) | ||||
−0.584322 | + | 0.811522i | \(0.698640\pi\) | |||||||
\(464\) | 3.11531 | 0.144625 | ||||||||
\(465\) | −14.2947 | −0.662899 | ||||||||
\(466\) | −22.2019 | −1.02848 | ||||||||
\(467\) | −32.1074 | −1.48576 | −0.742878 | − | 0.669427i | \(-0.766540\pi\) | ||||
−0.742878 | + | 0.669427i | \(0.766540\pi\) | |||||||
\(468\) | 1.84577 | 0.0853209 | ||||||||
\(469\) | −21.5014 | −0.992841 | ||||||||
\(470\) | 8.66729 | 0.399792 | ||||||||
\(471\) | 31.2455 | 1.43972 | ||||||||
\(472\) | −8.76448 | −0.403418 | ||||||||
\(473\) | −34.6142 | −1.59156 | ||||||||
\(474\) | −9.30982 | −0.427614 | ||||||||
\(475\) | 6.33167 | 0.290517 | ||||||||
\(476\) | 2.21702 | 0.101617 | ||||||||
\(477\) | −4.31943 | −0.197773 | ||||||||
\(478\) | 27.6097 | 1.26284 | ||||||||
\(479\) | 15.5845 | 0.712074 | 0.356037 | − | 0.934472i | \(-0.384128\pi\) | ||||
0.356037 | + | 0.934472i | \(0.384128\pi\) | |||||||
\(480\) | −4.01750 | −0.183373 | ||||||||
\(481\) | −1.27544 | −0.0581551 | ||||||||
\(482\) | −18.2226 | −0.830016 | ||||||||
\(483\) | 23.5827 | 1.07305 | ||||||||
\(484\) | 16.0553 | 0.729789 | ||||||||
\(485\) | −7.79140 | −0.353789 | ||||||||
\(486\) | −10.6091 | −0.481240 | ||||||||
\(487\) | −9.57076 | −0.433693 | −0.216846 | − | 0.976206i | \(-0.569577\pi\) | ||||
−0.216846 | + | 0.976206i | \(0.569577\pi\) | |||||||
\(488\) | −0.816696 | −0.0369701 | ||||||||
\(489\) | −39.2647 | −1.77561 | ||||||||
\(490\) | −4.49006 | −0.202840 | ||||||||
\(491\) | −20.4555 | −0.923145 | −0.461573 | − | 0.887102i | \(-0.652715\pi\) | ||||
−0.461573 | + | 0.887102i | \(0.652715\pi\) | |||||||
\(492\) | −3.53350 | −0.159303 | ||||||||
\(493\) | −3.17025 | −0.142781 | ||||||||
\(494\) | 10.6320 | 0.478355 | ||||||||
\(495\) | 11.0507 | 0.496690 | ||||||||
\(496\) | −3.55810 | −0.159764 | ||||||||
\(497\) | 1.44310 | 0.0647318 | ||||||||
\(498\) | −34.0109 | −1.52407 | ||||||||
\(499\) | −8.98511 | −0.402229 | −0.201114 | − | 0.979568i | \(-0.564456\pi\) | ||||
−0.201114 | + | 0.979568i | \(0.564456\pi\) | |||||||
\(500\) | 12.0151 | 0.537330 | ||||||||
\(501\) | 26.6784 | 1.19191 | ||||||||
\(502\) | 4.64098 | 0.207137 | ||||||||
\(503\) | 4.45453 | 0.198618 | 0.0993089 | − | 0.995057i | \(-0.468337\pi\) | ||||
0.0993089 | + | 0.995057i | \(0.468337\pi\) | |||||||
\(504\) | 2.32320 | 0.103484 | ||||||||
\(505\) | −21.9338 | −0.976039 | ||||||||
\(506\) | 27.9215 | 1.24126 | ||||||||
\(507\) | 20.1734 | 0.895932 | ||||||||
\(508\) | −5.89672 | −0.261625 | ||||||||
\(509\) | 19.0643 | 0.845009 | 0.422505 | − | 0.906361i | \(-0.361151\pi\) | ||||
0.422505 | + | 0.906361i | \(0.361151\pi\) | |||||||
\(510\) | 4.08835 | 0.181035 | ||||||||
\(511\) | −15.5256 | −0.686813 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −23.9509 | −1.05746 | ||||||||
\(514\) | 3.10603 | 0.137001 | ||||||||
\(515\) | 9.88118 | 0.435417 | ||||||||
\(516\) | −13.4193 | −0.590754 | ||||||||
\(517\) | −22.6286 | −0.995206 | ||||||||
\(518\) | −1.60535 | −0.0705349 | ||||||||
\(519\) | −5.85094 | −0.256828 | ||||||||
\(520\) | 3.44842 | 0.151223 | ||||||||
\(521\) | −14.7804 | −0.647542 | −0.323771 | − | 0.946136i | \(-0.604951\pi\) | ||||
−0.323771 | + | 0.946136i | \(0.604951\pi\) | |||||||
\(522\) | −3.32209 | −0.145404 | ||||||||
\(523\) | −12.3855 | −0.541581 | −0.270791 | − | 0.962638i | \(-0.587285\pi\) | ||||
−0.270791 | + | 0.962638i | \(0.587285\pi\) | |||||||
\(524\) | 11.2970 | 0.493512 | ||||||||
\(525\) | −4.52849 | −0.197639 | ||||||||
\(526\) | 4.91173 | 0.214162 | ||||||||
\(527\) | 3.62085 | 0.157727 | ||||||||
\(528\) | 10.4889 | 0.456471 | ||||||||
\(529\) | 5.81545 | 0.252846 | ||||||||
\(530\) | −8.06990 | −0.350534 | ||||||||
\(531\) | 9.34622 | 0.405591 | ||||||||
\(532\) | 13.3820 | 0.580184 | ||||||||
\(533\) | 3.03298 | 0.131373 | ||||||||
\(534\) | 36.4547 | 1.57755 | ||||||||
\(535\) | 1.72483 | 0.0745711 | ||||||||
\(536\) | −9.86937 | −0.426292 | ||||||||
\(537\) | 11.8592 | 0.511762 | ||||||||
\(538\) | −25.0619 | −1.08049 | ||||||||
\(539\) | 11.7227 | 0.504932 | ||||||||
\(540\) | −7.76833 | −0.334296 | ||||||||
\(541\) | 15.4287 | 0.663332 | 0.331666 | − | 0.943397i | \(-0.392389\pi\) | ||||
0.331666 | + | 0.943397i | \(0.392389\pi\) | |||||||
\(542\) | −15.7737 | −0.677539 | ||||||||
\(543\) | −27.7145 | −1.18934 | ||||||||
\(544\) | 1.01764 | 0.0436308 | ||||||||
\(545\) | −23.7095 | −1.01561 | ||||||||
\(546\) | −7.60411 | −0.325426 | ||||||||
\(547\) | −29.3366 | −1.25434 | −0.627171 | − | 0.778881i | \(-0.715787\pi\) | ||||
−0.627171 | + | 0.778881i | \(0.715787\pi\) | |||||||
\(548\) | 1.78132 | 0.0760944 | ||||||||
\(549\) | 0.870904 | 0.0371693 | ||||||||
\(550\) | −5.36167 | −0.228622 | ||||||||
\(551\) | −19.1358 | −0.815212 | ||||||||
\(552\) | 10.8247 | 0.460730 | ||||||||
\(553\) | 10.0581 | 0.427712 | ||||||||
\(554\) | 21.7596 | 0.924479 | ||||||||
\(555\) | −2.96038 | −0.125661 | ||||||||
\(556\) | −17.6995 | −0.750626 | ||||||||
\(557\) | 10.9988 | 0.466036 | 0.233018 | − | 0.972472i | \(-0.425140\pi\) | ||||
0.233018 | + | 0.972472i | \(0.425140\pi\) | |||||||
\(558\) | 3.79427 | 0.160624 | ||||||||
\(559\) | 11.5185 | 0.487181 | ||||||||
\(560\) | 4.34038 | 0.183415 | ||||||||
\(561\) | −10.6739 | −0.450652 | ||||||||
\(562\) | 2.52287 | 0.106421 | ||||||||
\(563\) | −9.96127 | −0.419817 | −0.209909 | − | 0.977721i | \(-0.567317\pi\) | ||||
−0.209909 | + | 0.977721i | \(0.567317\pi\) | |||||||
\(564\) | −8.77274 | −0.369399 | ||||||||
\(565\) | 37.6865 | 1.58548 | ||||||||
\(566\) | −11.2483 | −0.472800 | ||||||||
\(567\) | 24.0995 | 1.01209 | ||||||||
\(568\) | 0.662399 | 0.0277936 | ||||||||
\(569\) | 23.7346 | 0.995008 | 0.497504 | − | 0.867462i | \(-0.334250\pi\) | ||||
0.497504 | + | 0.867462i | \(0.334250\pi\) | |||||||
\(570\) | 24.6775 | 1.03362 | ||||||||
\(571\) | −42.0051 | −1.75786 | −0.878929 | − | 0.476953i | \(-0.841741\pi\) | ||||
−0.878929 | + | 0.476953i | \(0.841741\pi\) | |||||||
\(572\) | −9.00316 | −0.376441 | ||||||||
\(573\) | −49.7265 | −2.07736 | ||||||||
\(574\) | 3.81749 | 0.159339 | ||||||||
\(575\) | −5.53332 | −0.230755 | ||||||||
\(576\) | 1.06638 | 0.0444323 | ||||||||
\(577\) | −3.76406 | −0.156700 | −0.0783500 | − | 0.996926i | \(-0.524965\pi\) | ||||
−0.0783500 | + | 0.996926i | \(0.524965\pi\) | |||||||
\(578\) | 15.9644 | 0.664032 | ||||||||
\(579\) | −14.6122 | −0.607261 | ||||||||
\(580\) | −6.20659 | −0.257714 | ||||||||
\(581\) | 36.7444 | 1.52441 | ||||||||
\(582\) | 7.88619 | 0.326893 | ||||||||
\(583\) | 21.0690 | 0.872587 | ||||||||
\(584\) | −7.12644 | −0.294894 | ||||||||
\(585\) | −3.67731 | −0.152038 | ||||||||
\(586\) | −16.5581 | −0.684007 | ||||||||
\(587\) | −47.3100 | −1.95269 | −0.976346 | − | 0.216215i | \(-0.930629\pi\) | ||||
−0.976346 | + | 0.216215i | \(0.930629\pi\) | |||||||
\(588\) | 4.54469 | 0.187420 | ||||||||
\(589\) | 21.8556 | 0.900546 | ||||||||
\(590\) | 17.4613 | 0.718872 | ||||||||
\(591\) | −42.2868 | −1.73945 | ||||||||
\(592\) | −0.736872 | −0.0302853 | ||||||||
\(593\) | 19.9962 | 0.821144 | 0.410572 | − | 0.911828i | \(-0.365329\pi\) | ||||
0.410572 | + | 0.911828i | \(0.365329\pi\) | |||||||
\(594\) | 20.2816 | 0.832165 | ||||||||
\(595\) | −4.41693 | −0.181076 | ||||||||
\(596\) | 20.1669 | 0.826070 | ||||||||
\(597\) | 42.8005 | 1.75171 | ||||||||
\(598\) | −9.29140 | −0.379953 | ||||||||
\(599\) | 30.5204 | 1.24703 | 0.623515 | − | 0.781812i | \(-0.285704\pi\) | ||||
0.623515 | + | 0.781812i | \(0.285704\pi\) | |||||||
\(600\) | −2.07863 | −0.0848596 | ||||||||
\(601\) | 22.8440 | 0.931827 | 0.465914 | − | 0.884830i | \(-0.345726\pi\) | ||||
0.465914 | + | 0.884830i | \(0.345726\pi\) | |||||||
\(602\) | 14.4979 | 0.590889 | ||||||||
\(603\) | 10.5245 | 0.428589 | ||||||||
\(604\) | 0.805568 | 0.0327781 | ||||||||
\(605\) | −31.9868 | −1.30045 | ||||||||
\(606\) | 22.2006 | 0.901838 | ||||||||
\(607\) | −21.2977 | −0.864448 | −0.432224 | − | 0.901766i | \(-0.642271\pi\) | ||||
−0.432224 | + | 0.901766i | \(0.642271\pi\) | |||||||
\(608\) | 6.14250 | 0.249111 | ||||||||
\(609\) | 13.6862 | 0.554591 | ||||||||
\(610\) | 1.62709 | 0.0658790 | ||||||||
\(611\) | 7.53008 | 0.304635 | ||||||||
\(612\) | −1.08518 | −0.0438659 | ||||||||
\(613\) | −26.5985 | −1.07430 | −0.537152 | − | 0.843486i | \(-0.680500\pi\) | ||||
−0.537152 | + | 0.843486i | \(0.680500\pi\) | |||||||
\(614\) | −2.89200 | −0.116712 | ||||||||
\(615\) | 7.03975 | 0.283870 | ||||||||
\(616\) | −11.3319 | −0.456576 | ||||||||
\(617\) | 5.12203 | 0.206205 | 0.103103 | − | 0.994671i | \(-0.467123\pi\) | ||||
0.103103 | + | 0.994671i | \(0.467123\pi\) | |||||||
\(618\) | −10.0014 | −0.402315 | ||||||||
\(619\) | −0.447418 | −0.0179833 | −0.00899163 | − | 0.999960i | \(-0.502862\pi\) | ||||
−0.00899163 | + | 0.999960i | \(0.502862\pi\) | |||||||
\(620\) | 7.08876 | 0.284691 | ||||||||
\(621\) | 20.9309 | 0.839930 | ||||||||
\(622\) | 30.2618 | 1.21339 | ||||||||
\(623\) | −39.3846 | −1.57791 | ||||||||
\(624\) | −3.49037 | −0.139727 | ||||||||
\(625\) | −18.7835 | −0.751339 | ||||||||
\(626\) | 13.0609 | 0.522018 | ||||||||
\(627\) | −64.4281 | −2.57301 | ||||||||
\(628\) | −15.4947 | −0.618306 | ||||||||
\(629\) | 0.749868 | 0.0298992 | ||||||||
\(630\) | −4.62848 | −0.184403 | ||||||||
\(631\) | 16.6516 | 0.662888 | 0.331444 | − | 0.943475i | \(-0.392464\pi\) | ||||
0.331444 | + | 0.943475i | \(0.392464\pi\) | |||||||
\(632\) | 4.61676 | 0.183645 | ||||||||
\(633\) | 53.5136 | 2.12697 | ||||||||
\(634\) | 3.91087 | 0.155321 | ||||||||
\(635\) | 11.7479 | 0.466203 | ||||||||
\(636\) | 8.16809 | 0.323886 | ||||||||
\(637\) | −3.90094 | −0.154561 | ||||||||
\(638\) | 16.2042 | 0.641531 | ||||||||
\(639\) | −0.706366 | −0.0279434 | ||||||||
\(640\) | 1.99229 | 0.0787520 | ||||||||
\(641\) | 16.3382 | 0.645322 | 0.322661 | − | 0.946515i | \(-0.395423\pi\) | ||||
0.322661 | + | 0.946515i | \(0.395423\pi\) | |||||||
\(642\) | −1.74582 | −0.0689020 | ||||||||
\(643\) | −39.4221 | −1.55465 | −0.777327 | − | 0.629097i | \(-0.783425\pi\) | ||||
−0.777327 | + | 0.629097i | \(0.783425\pi\) | |||||||
\(644\) | −11.6947 | −0.460836 | ||||||||
\(645\) | 26.7352 | 1.05270 | ||||||||
\(646\) | −6.25083 | −0.245935 | ||||||||
\(647\) | −46.9144 | −1.84439 | −0.922197 | − | 0.386720i | \(-0.873608\pi\) | ||||
−0.922197 | + | 0.386720i | \(0.873608\pi\) | |||||||
\(648\) | 11.0620 | 0.434555 | ||||||||
\(649\) | −45.5882 | −1.78949 | ||||||||
\(650\) | 1.78419 | 0.0699817 | ||||||||
\(651\) | −15.6314 | −0.612644 | ||||||||
\(652\) | 19.4715 | 0.762562 | ||||||||
\(653\) | −38.8508 | −1.52035 | −0.760174 | − | 0.649720i | \(-0.774886\pi\) | ||||
−0.760174 | + | 0.649720i | \(0.774886\pi\) | |||||||
\(654\) | 23.9980 | 0.938397 | ||||||||
\(655\) | −22.5068 | −0.879415 | ||||||||
\(656\) | 1.75227 | 0.0684147 | ||||||||
\(657\) | 7.59946 | 0.296483 | ||||||||
\(658\) | 9.47781 | 0.369484 | ||||||||
\(659\) | −2.72442 | −0.106128 | −0.0530642 | − | 0.998591i | \(-0.516899\pi\) | ||||
−0.0530642 | + | 0.998591i | \(0.516899\pi\) | |||||||
\(660\) | −20.8969 | −0.813411 | ||||||||
\(661\) | 20.1897 | 0.785289 | 0.392644 | − | 0.919690i | \(-0.371560\pi\) | ||||
0.392644 | + | 0.919690i | \(0.371560\pi\) | |||||||
\(662\) | 32.7139 | 1.27146 | ||||||||
\(663\) | 3.55193 | 0.137946 | ||||||||
\(664\) | 16.8661 | 0.654531 | ||||||||
\(665\) | −26.6608 | −1.03386 | ||||||||
\(666\) | 0.785782 | 0.0304484 | ||||||||
\(667\) | 16.7230 | 0.647517 | ||||||||
\(668\) | −13.2299 | −0.511881 | ||||||||
\(669\) | −10.5569 | −0.408151 | ||||||||
\(670\) | 19.6626 | 0.759633 | ||||||||
\(671\) | −4.24802 | −0.163993 | ||||||||
\(672\) | −4.39319 | −0.169471 | ||||||||
\(673\) | −18.6030 | −0.717095 | −0.358547 | − | 0.933512i | \(-0.616728\pi\) | ||||
−0.358547 | + | 0.933512i | \(0.616728\pi\) | |||||||
\(674\) | 32.1026 | 1.23655 | ||||||||
\(675\) | −4.01929 | −0.154702 | ||||||||
\(676\) | −10.0040 | −0.384771 | ||||||||
\(677\) | 23.9407 | 0.920117 | 0.460059 | − | 0.887889i | \(-0.347828\pi\) | ||||
0.460059 | + | 0.887889i | \(0.347828\pi\) | |||||||
\(678\) | −38.1450 | −1.46495 | ||||||||
\(679\) | −8.52001 | −0.326968 | ||||||||
\(680\) | −2.02742 | −0.0777481 | ||||||||
\(681\) | 11.4979 | 0.440601 | ||||||||
\(682\) | −18.5074 | −0.708684 | ||||||||
\(683\) | 22.3650 | 0.855773 | 0.427887 | − | 0.903832i | \(-0.359258\pi\) | ||||
0.427887 | + | 0.903832i | \(0.359258\pi\) | |||||||
\(684\) | −6.55021 | −0.250453 | ||||||||
\(685\) | −3.54891 | −0.135597 | ||||||||
\(686\) | −20.1601 | −0.769717 | ||||||||
\(687\) | −20.6954 | −0.789579 | ||||||||
\(688\) | 6.65469 | 0.253708 | ||||||||
\(689\) | −7.01108 | −0.267101 | ||||||||
\(690\) | −21.5659 | −0.821001 | ||||||||
\(691\) | 4.27775 | 0.162733 | 0.0813667 | − | 0.996684i | \(-0.474072\pi\) | ||||
0.0813667 | + | 0.996684i | \(0.474072\pi\) | |||||||
\(692\) | 2.90149 | 0.110298 | ||||||||
\(693\) | 12.0841 | 0.459036 | ||||||||
\(694\) | −14.6604 | −0.556501 | ||||||||
\(695\) | 35.2624 | 1.33758 | ||||||||
\(696\) | 6.28210 | 0.238122 | ||||||||
\(697\) | −1.78317 | −0.0675426 | ||||||||
\(698\) | 27.2375 | 1.03095 | ||||||||
\(699\) | −44.7707 | −1.69338 | ||||||||
\(700\) | 2.24569 | 0.0848791 | ||||||||
\(701\) | 2.85161 | 0.107704 | 0.0538519 | − | 0.998549i | \(-0.482850\pi\) | ||||
0.0538519 | + | 0.998549i | \(0.482850\pi\) | |||||||
\(702\) | −6.74908 | −0.254727 | ||||||||
\(703\) | 4.52624 | 0.170710 | ||||||||
\(704\) | −5.20148 | −0.196038 | ||||||||
\(705\) | 17.4778 | 0.658252 | ||||||||
\(706\) | 0.965735 | 0.0363459 | ||||||||
\(707\) | −23.9849 | −0.902045 | ||||||||
\(708\) | −17.6738 | −0.664222 | ||||||||
\(709\) | −0.492083 | −0.0184806 | −0.00924028 | − | 0.999957i | \(-0.502941\pi\) | ||||
−0.00924028 | + | 0.999957i | \(0.502941\pi\) | |||||||
\(710\) | −1.31969 | −0.0495270 | ||||||||
\(711\) | −4.92320 | −0.184634 | ||||||||
\(712\) | −18.0780 | −0.677501 | ||||||||
\(713\) | −19.0999 | −0.715297 | ||||||||
\(714\) | 4.47067 | 0.167311 | ||||||||
\(715\) | 17.9369 | 0.670801 | ||||||||
\(716\) | −5.88100 | −0.219783 | ||||||||
\(717\) | 55.6756 | 2.07924 | ||||||||
\(718\) | −5.46016 | −0.203772 | ||||||||
\(719\) | 21.1879 | 0.790175 | 0.395088 | − | 0.918643i | \(-0.370714\pi\) | ||||
0.395088 | + | 0.918643i | \(0.370714\pi\) | |||||||
\(720\) | −2.12452 | −0.0791763 | ||||||||
\(721\) | 10.8052 | 0.402407 | ||||||||
\(722\) | −18.7303 | −0.697069 | ||||||||
\(723\) | −36.7463 | −1.36661 | ||||||||
\(724\) | 13.7437 | 0.510781 | ||||||||
\(725\) | −3.21125 | −0.119263 | ||||||||
\(726\) | 32.3760 | 1.20159 | ||||||||
\(727\) | 32.3848 | 1.20108 | 0.600542 | − | 0.799593i | \(-0.294952\pi\) | ||||
0.600542 | + | 0.799593i | \(0.294952\pi\) | |||||||
\(728\) | 3.77090 | 0.139759 | ||||||||
\(729\) | 11.7923 | 0.436753 | ||||||||
\(730\) | 14.1979 | 0.525488 | ||||||||
\(731\) | −6.77205 | −0.250473 | ||||||||
\(732\) | −1.64689 | −0.0608707 | ||||||||
\(733\) | 38.9051 | 1.43699 | 0.718496 | − | 0.695531i | \(-0.244831\pi\) | ||||
0.718496 | + | 0.695531i | \(0.244831\pi\) | |||||||
\(734\) | 4.85033 | 0.179029 | ||||||||
\(735\) | −9.05433 | −0.333974 | ||||||||
\(736\) | −5.36800 | −0.197867 | ||||||||
\(737\) | −51.3353 | −1.89096 | ||||||||
\(738\) | −1.86858 | −0.0687834 | ||||||||
\(739\) | −24.1775 | −0.889383 | −0.444692 | − | 0.895684i | \(-0.646687\pi\) | ||||
−0.444692 | + | 0.895684i | \(0.646687\pi\) | |||||||
\(740\) | 1.46806 | 0.0539670 | ||||||||
\(741\) | 21.4396 | 0.787604 | ||||||||
\(742\) | −8.82456 | −0.323960 | ||||||||
\(743\) | 12.4962 | 0.458440 | 0.229220 | − | 0.973375i | \(-0.426382\pi\) | ||||
0.229220 | + | 0.973375i | \(0.426382\pi\) | |||||||
\(744\) | −7.17501 | −0.263048 | ||||||||
\(745\) | −40.1783 | −1.47202 | ||||||||
\(746\) | −32.0711 | −1.17421 | ||||||||
\(747\) | −17.9856 | −0.658058 | ||||||||
\(748\) | 5.29321 | 0.193539 | ||||||||
\(749\) | 1.88613 | 0.0689178 | ||||||||
\(750\) | 24.2287 | 0.884707 | ||||||||
\(751\) | 42.2824 | 1.54291 | 0.771453 | − | 0.636286i | \(-0.219530\pi\) | ||||
0.771453 | + | 0.636286i | \(0.219530\pi\) | |||||||
\(752\) | 4.35042 | 0.158644 | ||||||||
\(753\) | 9.35864 | 0.341048 | ||||||||
\(754\) | −5.39224 | −0.196374 | ||||||||
\(755\) | −1.60492 | −0.0584091 | ||||||||
\(756\) | −8.49479 | −0.308952 | ||||||||
\(757\) | −12.3443 | −0.448661 | −0.224331 | − | 0.974513i | \(-0.572020\pi\) | ||||
−0.224331 | + | 0.974513i | \(0.572020\pi\) | |||||||
\(758\) | −16.4856 | −0.598785 | ||||||||
\(759\) | 56.3045 | 2.04372 | ||||||||
\(760\) | −12.2376 | −0.443905 | ||||||||
\(761\) | −14.1956 | −0.514592 | −0.257296 | − | 0.966333i | \(-0.582832\pi\) | ||||
−0.257296 | + | 0.966333i | \(0.582832\pi\) | |||||||
\(762\) | −11.8909 | −0.430761 | ||||||||
\(763\) | −25.9268 | −0.938611 | ||||||||
\(764\) | 24.6595 | 0.892150 | ||||||||
\(765\) | 2.16199 | 0.0781670 | ||||||||
\(766\) | −4.43551 | −0.160261 | ||||||||
\(767\) | 15.1703 | 0.547768 | ||||||||
\(768\) | −2.01653 | −0.0727651 | ||||||||
\(769\) | −18.8012 | −0.677988 | −0.338994 | − | 0.940789i | \(-0.610087\pi\) | ||||
−0.338994 | + | 0.940789i | \(0.610087\pi\) | |||||||
\(770\) | 22.5764 | 0.813597 | ||||||||
\(771\) | 6.26339 | 0.225571 | ||||||||
\(772\) | 7.24622 | 0.260797 | ||||||||
\(773\) | −43.9987 | −1.58252 | −0.791261 | − | 0.611478i | \(-0.790575\pi\) | ||||
−0.791261 | + | 0.611478i | \(0.790575\pi\) | |||||||
\(774\) | −7.09639 | −0.255075 | ||||||||
\(775\) | 3.66768 | 0.131747 | ||||||||
\(776\) | −3.91078 | −0.140389 | ||||||||
\(777\) | −3.23722 | −0.116135 | ||||||||
\(778\) | 2.80059 | 0.100406 | ||||||||
\(779\) | −10.7633 | −0.385636 | ||||||||
\(780\) | 6.95382 | 0.248987 | ||||||||
\(781\) | 3.44545 | 0.123288 | ||||||||
\(782\) | 5.46267 | 0.195345 | ||||||||
\(783\) | 12.1472 | 0.434106 | ||||||||
\(784\) | −2.25372 | −0.0804902 | ||||||||
\(785\) | 30.8699 | 1.10179 | ||||||||
\(786\) | 22.7807 | 0.812560 | ||||||||
\(787\) | 33.1121 | 1.18032 | 0.590160 | − | 0.807287i | \(-0.299065\pi\) | ||||
0.590160 | + | 0.807287i | \(0.299065\pi\) | |||||||
\(788\) | 20.9701 | 0.747030 | ||||||||
\(789\) | 9.90463 | 0.352614 | ||||||||
\(790\) | −9.19791 | −0.327247 | ||||||||
\(791\) | 41.2108 | 1.46529 | ||||||||
\(792\) | 5.54672 | 0.197094 | ||||||||
\(793\) | 1.41361 | 0.0501986 | ||||||||
\(794\) | −13.5015 | −0.479150 | ||||||||
\(795\) | −16.2732 | −0.577150 | ||||||||
\(796\) | −21.2249 | −0.752297 | ||||||||
\(797\) | −16.1632 | −0.572531 | −0.286265 | − | 0.958150i | \(-0.592414\pi\) | ||||
−0.286265 | + | 0.958150i | \(0.592414\pi\) | |||||||
\(798\) | 26.9852 | 0.955265 | ||||||||
\(799\) | −4.42715 | −0.156621 | ||||||||
\(800\) | 1.03080 | 0.0364442 | ||||||||
\(801\) | 19.2779 | 0.681151 | ||||||||
\(802\) | −16.1122 | −0.568942 | ||||||||
\(803\) | −37.0680 | −1.30810 | ||||||||
\(804\) | −19.9018 | −0.701884 | ||||||||
\(805\) | 23.2992 | 0.821189 | ||||||||
\(806\) | 6.15867 | 0.216930 | ||||||||
\(807\) | −50.5379 | −1.77902 | ||||||||
\(808\) | −11.0093 | −0.387307 | ||||||||
\(809\) | 14.3386 | 0.504117 | 0.252058 | − | 0.967712i | \(-0.418893\pi\) | ||||
0.252058 | + | 0.967712i | \(0.418893\pi\) | |||||||
\(810\) | −22.0386 | −0.774358 | ||||||||
\(811\) | 29.4702 | 1.03484 | 0.517419 | − | 0.855732i | \(-0.326893\pi\) | ||||
0.517419 | + | 0.855732i | \(0.326893\pi\) | |||||||
\(812\) | −6.78700 | −0.238177 | ||||||||
\(813\) | −31.8081 | −1.11556 | ||||||||
\(814\) | −3.83282 | −0.134340 | ||||||||
\(815\) | −38.7927 | −1.35885 | ||||||||
\(816\) | 2.05209 | 0.0718375 | ||||||||
\(817\) | −40.8764 | −1.43008 | ||||||||
\(818\) | 39.7145 | 1.38858 | ||||||||
\(819\) | −4.02119 | −0.140512 | ||||||||
\(820\) | −3.49103 | −0.121912 | ||||||||
\(821\) | −2.50677 | −0.0874870 | −0.0437435 | − | 0.999043i | \(-0.513928\pi\) | ||||
−0.0437435 | + | 0.999043i | \(0.513928\pi\) | |||||||
\(822\) | 3.59209 | 0.125288 | ||||||||
\(823\) | −35.1430 | −1.22501 | −0.612504 | − | 0.790467i | \(-0.709838\pi\) | ||||
−0.612504 | + | 0.790467i | \(0.709838\pi\) | |||||||
\(824\) | 4.95972 | 0.172780 | ||||||||
\(825\) | −10.8119 | −0.376423 | ||||||||
\(826\) | 19.0942 | 0.664374 | ||||||||
\(827\) | −33.7990 | −1.17531 | −0.587653 | − | 0.809113i | \(-0.699948\pi\) | ||||
−0.587653 | + | 0.809113i | \(0.699948\pi\) | |||||||
\(828\) | 5.72430 | 0.198933 | ||||||||
\(829\) | 25.1882 | 0.874823 | 0.437411 | − | 0.899262i | \(-0.355895\pi\) | ||||
0.437411 | + | 0.899262i | \(0.355895\pi\) | |||||||
\(830\) | −33.6021 | −1.16635 | ||||||||
\(831\) | 43.8789 | 1.52214 | ||||||||
\(832\) | 1.73089 | 0.0600077 | ||||||||
\(833\) | 2.29347 | 0.0794641 | ||||||||
\(834\) | −35.6915 | −1.23589 | ||||||||
\(835\) | 26.3578 | 0.912148 | ||||||||
\(836\) | 31.9501 | 1.10502 | ||||||||
\(837\) | −13.8738 | −0.479548 | ||||||||
\(838\) | −34.9604 | −1.20769 | ||||||||
\(839\) | 32.8691 | 1.13477 | 0.567384 | − | 0.823453i | \(-0.307956\pi\) | ||||
0.567384 | + | 0.823453i | \(0.307956\pi\) | |||||||
\(840\) | 8.75249 | 0.301990 | ||||||||
\(841\) | −19.2948 | −0.665340 | ||||||||
\(842\) | −6.17265 | −0.212723 | ||||||||
\(843\) | 5.08743 | 0.175220 | ||||||||
\(844\) | −26.5375 | −0.913459 | ||||||||
\(845\) | 19.9309 | 0.685644 | ||||||||
\(846\) | −4.63918 | −0.159498 | ||||||||
\(847\) | −34.9781 | −1.20186 | ||||||||
\(848\) | −4.05057 | −0.139097 | ||||||||
\(849\) | −22.6824 | −0.778459 | ||||||||
\(850\) | −1.04898 | −0.0359796 | ||||||||
\(851\) | −3.95553 | −0.135594 | ||||||||
\(852\) | 1.33574 | 0.0457618 | ||||||||
\(853\) | −2.04553 | −0.0700376 | −0.0350188 | − | 0.999387i | \(-0.511149\pi\) | ||||
−0.0350188 | + | 0.999387i | \(0.511149\pi\) | |||||||
\(854\) | 1.77925 | 0.0608847 | ||||||||
\(855\) | 13.0499 | 0.446297 | ||||||||
\(856\) | 0.865756 | 0.0295909 | ||||||||
\(857\) | −12.9478 | −0.442289 | −0.221145 | − | 0.975241i | \(-0.570979\pi\) | ||||
−0.221145 | + | 0.975241i | \(0.570979\pi\) | |||||||
\(858\) | −18.1551 | −0.619805 | ||||||||
\(859\) | −15.8517 | −0.540853 | −0.270426 | − | 0.962741i | \(-0.587165\pi\) | ||||
−0.270426 | + | 0.962741i | \(0.587165\pi\) | |||||||
\(860\) | −13.2580 | −0.452095 | ||||||||
\(861\) | 7.69807 | 0.262349 | ||||||||
\(862\) | 14.0408 | 0.478232 | ||||||||
\(863\) | −1.75669 | −0.0597983 | −0.0298992 | − | 0.999553i | \(-0.509519\pi\) | ||||
−0.0298992 | + | 0.999553i | \(0.509519\pi\) | |||||||
\(864\) | −3.89920 | −0.132654 | ||||||||
\(865\) | −5.78060 | −0.196546 | ||||||||
\(866\) | 27.5736 | 0.936988 | ||||||||
\(867\) | 32.1927 | 1.09332 | ||||||||
\(868\) | 7.75166 | 0.263109 | ||||||||
\(869\) | 24.0140 | 0.814618 | ||||||||
\(870\) | −12.5157 | −0.424323 | ||||||||
\(871\) | 17.0828 | 0.578827 | ||||||||
\(872\) | −11.9007 | −0.403008 | ||||||||
\(873\) | 4.17036 | 0.141145 | ||||||||
\(874\) | 32.9729 | 1.11533 | ||||||||
\(875\) | −26.1760 | −0.884909 | ||||||||
\(876\) | −14.3706 | −0.485539 | ||||||||
\(877\) | −18.9996 | −0.641570 | −0.320785 | − | 0.947152i | \(-0.603947\pi\) | ||||
−0.320785 | + | 0.947152i | \(0.603947\pi\) | |||||||
\(878\) | −37.7467 | −1.27389 | ||||||||
\(879\) | −33.3897 | −1.12621 | ||||||||
\(880\) | 10.3628 | 0.349331 | ||||||||
\(881\) | 25.1300 | 0.846652 | 0.423326 | − | 0.905978i | \(-0.360863\pi\) | ||||
0.423326 | + | 0.905978i | \(0.360863\pi\) | |||||||
\(882\) | 2.40332 | 0.0809239 | ||||||||
\(883\) | 13.5948 | 0.457500 | 0.228750 | − | 0.973485i | \(-0.426536\pi\) | ||||
0.228750 | + | 0.973485i | \(0.426536\pi\) | |||||||
\(884\) | −1.76141 | −0.0592427 | ||||||||
\(885\) | 35.2113 | 1.18361 | ||||||||
\(886\) | −19.8368 | −0.666431 | ||||||||
\(887\) | −52.5737 | −1.76525 | −0.882627 | − | 0.470075i | \(-0.844227\pi\) | ||||
−0.882627 | + | 0.470075i | \(0.844227\pi\) | |||||||
\(888\) | −1.48592 | −0.0498643 | ||||||||
\(889\) | 12.8466 | 0.430860 | ||||||||
\(890\) | 36.0165 | 1.20728 | ||||||||
\(891\) | 57.5386 | 1.92761 | ||||||||
\(892\) | 5.23517 | 0.175286 | ||||||||
\(893\) | −26.7225 | −0.894233 | ||||||||
\(894\) | 40.6671 | 1.36011 | ||||||||
\(895\) | 11.7166 | 0.391644 | ||||||||
\(896\) | 2.17859 | 0.0727817 | ||||||||
\(897\) | −18.7363 | −0.625588 | ||||||||
\(898\) | 16.3370 | 0.545173 | ||||||||
\(899\) | −11.0846 | −0.369692 | ||||||||
\(900\) | −1.09922 | −0.0366405 | ||||||||
\(901\) | 4.12201 | 0.137324 | ||||||||
\(902\) | 9.11440 | 0.303476 | ||||||||
\(903\) | 29.2353 | 0.972891 | ||||||||
\(904\) | 18.9162 | 0.629144 | ||||||||
\(905\) | −27.3814 | −0.910188 | ||||||||
\(906\) | 1.62445 | 0.0539687 | ||||||||
\(907\) | 3.92333 | 0.130272 | 0.0651360 | − | 0.997876i | \(-0.479252\pi\) | ||||
0.0651360 | + | 0.997876i | \(0.479252\pi\) | |||||||
\(908\) | −5.70185 | −0.189222 | ||||||||
\(909\) | 11.7401 | 0.389394 | ||||||||
\(910\) | −7.51271 | −0.249044 | ||||||||
\(911\) | −21.2137 | −0.702841 | −0.351420 | − | 0.936218i | \(-0.614301\pi\) | ||||
−0.351420 | + | 0.936218i | \(0.614301\pi\) | |||||||
\(912\) | 12.3865 | 0.410158 | ||||||||
\(913\) | 87.7286 | 2.90339 | ||||||||
\(914\) | 36.0942 | 1.19389 | ||||||||
\(915\) | 3.28107 | 0.108469 | ||||||||
\(916\) | 10.2629 | 0.339096 | ||||||||
\(917\) | −24.6116 | −0.812746 | ||||||||
\(918\) | 3.96797 | 0.130963 | ||||||||
\(919\) | 38.6523 | 1.27502 | 0.637510 | − | 0.770442i | \(-0.279964\pi\) | ||||
0.637510 | + | 0.770442i | \(0.279964\pi\) | |||||||
\(920\) | 10.6946 | 0.352590 | ||||||||
\(921\) | −5.83179 | −0.192164 | ||||||||
\(922\) | 4.83779 | 0.159324 | ||||||||
\(923\) | −1.14654 | −0.0377387 | ||||||||
\(924\) | −22.8511 | −0.751745 | ||||||||
\(925\) | 0.759566 | 0.0249744 | ||||||||
\(926\) | 25.1462 | 0.826356 | ||||||||
\(927\) | −5.28892 | −0.173711 | ||||||||
\(928\) | −3.11531 | −0.102265 | ||||||||
\(929\) | 26.7077 | 0.876251 | 0.438125 | − | 0.898914i | \(-0.355643\pi\) | ||||
0.438125 | + | 0.898914i | \(0.355643\pi\) | |||||||
\(930\) | 14.2947 | 0.468740 | ||||||||
\(931\) | 13.8435 | 0.453702 | ||||||||
\(932\) | 22.2019 | 0.727247 | ||||||||
\(933\) | 61.0236 | 1.99782 | ||||||||
\(934\) | 32.1074 | 1.05059 | ||||||||
\(935\) | −10.5456 | −0.344877 | ||||||||
\(936\) | −1.84577 | −0.0603310 | ||||||||
\(937\) | 51.5277 | 1.68334 | 0.841668 | − | 0.539995i | \(-0.181574\pi\) | ||||
0.841668 | + | 0.539995i | \(0.181574\pi\) | |||||||
\(938\) | 21.5014 | 0.702044 | ||||||||
\(939\) | 26.3376 | 0.859495 | ||||||||
\(940\) | −8.66729 | −0.282696 | ||||||||
\(941\) | −10.3636 | −0.337843 | −0.168921 | − | 0.985630i | \(-0.554028\pi\) | ||||
−0.168921 | + | 0.985630i | \(0.554028\pi\) | |||||||
\(942\) | −31.2455 | −1.01803 | ||||||||
\(943\) | 9.40620 | 0.306308 | ||||||||
\(944\) | 8.76448 | 0.285260 | ||||||||
\(945\) | 16.9240 | 0.550539 | ||||||||
\(946\) | 34.6142 | 1.12540 | ||||||||
\(947\) | 23.0491 | 0.748996 | 0.374498 | − | 0.927228i | \(-0.377815\pi\) | ||||
0.374498 | + | 0.927228i | \(0.377815\pi\) | |||||||
\(948\) | 9.30982 | 0.302369 | ||||||||
\(949\) | 12.3351 | 0.400413 | ||||||||
\(950\) | −6.33167 | −0.205426 | ||||||||
\(951\) | 7.88637 | 0.255733 | ||||||||
\(952\) | −2.21702 | −0.0718539 | ||||||||
\(953\) | 12.4672 | 0.403851 | 0.201925 | − | 0.979401i | \(-0.435280\pi\) | ||||
0.201925 | + | 0.979401i | \(0.435280\pi\) | |||||||
\(954\) | 4.31943 | 0.139847 | ||||||||
\(955\) | −49.1288 | −1.58977 | ||||||||
\(956\) | −27.6097 | −0.892961 | ||||||||
\(957\) | 32.6762 | 1.05627 | ||||||||
\(958\) | −15.5845 | −0.503512 | ||||||||
\(959\) | −3.88078 | −0.125317 | ||||||||
\(960\) | 4.01750 | 0.129664 | ||||||||
\(961\) | −18.3399 | −0.591610 | ||||||||
\(962\) | 1.27544 | 0.0411219 | ||||||||
\(963\) | −0.923221 | −0.0297504 | ||||||||
\(964\) | 18.2226 | 0.586910 | ||||||||
\(965\) | −14.4365 | −0.464728 | ||||||||
\(966\) | −23.5827 | −0.758760 | ||||||||
\(967\) | 43.1277 | 1.38689 | 0.693447 | − | 0.720508i | \(-0.256091\pi\) | ||||
0.693447 | + | 0.720508i | \(0.256091\pi\) | |||||||
\(968\) | −16.0553 | −0.516038 | ||||||||
\(969\) | −12.6050 | −0.404929 | ||||||||
\(970\) | 7.79140 | 0.250167 | ||||||||
\(971\) | 45.2401 | 1.45183 | 0.725913 | − | 0.687787i | \(-0.241418\pi\) | ||||
0.725913 | + | 0.687787i | \(0.241418\pi\) | |||||||
\(972\) | 10.6091 | 0.340288 | ||||||||
\(973\) | 38.5600 | 1.23618 | ||||||||
\(974\) | 9.57076 | 0.306667 | ||||||||
\(975\) | 3.59787 | 0.115224 | ||||||||
\(976\) | 0.816696 | 0.0261418 | ||||||||
\(977\) | −10.0854 | −0.322659 | −0.161329 | − | 0.986901i | \(-0.551578\pi\) | ||||
−0.161329 | + | 0.986901i | \(0.551578\pi\) | |||||||
\(978\) | 39.2647 | 1.25555 | ||||||||
\(979\) | −94.0322 | −3.00528 | ||||||||
\(980\) | 4.49006 | 0.143430 | ||||||||
\(981\) | 12.6906 | 0.405179 | ||||||||
\(982\) | 20.4555 | 0.652762 | ||||||||
\(983\) | −12.7054 | −0.405238 | −0.202619 | − | 0.979258i | \(-0.564945\pi\) | ||||
−0.202619 | + | 0.979258i | \(0.564945\pi\) | |||||||
\(984\) | 3.53350 | 0.112644 | ||||||||
\(985\) | −41.7785 | −1.33117 | ||||||||
\(986\) | 3.17025 | 0.100961 | ||||||||
\(987\) | 19.1122 | 0.608349 | ||||||||
\(988\) | −10.6320 | −0.338248 | ||||||||
\(989\) | 35.7224 | 1.13591 | ||||||||
\(990\) | −11.0507 | −0.351213 | ||||||||
\(991\) | −12.9191 | −0.410388 | −0.205194 | − | 0.978721i | \(-0.565783\pi\) | ||||
−0.205194 | + | 0.978721i | \(0.565783\pi\) | |||||||
\(992\) | 3.55810 | 0.112970 | ||||||||
\(993\) | 65.9684 | 2.09344 | ||||||||
\(994\) | −1.44310 | −0.0457723 | ||||||||
\(995\) | 42.2861 | 1.34056 | ||||||||
\(996\) | 34.0109 | 1.07768 | ||||||||
\(997\) | 60.4523 | 1.91454 | 0.957271 | − | 0.289192i | \(-0.0933865\pi\) | ||||
0.957271 | + | 0.289192i | \(0.0933865\pi\) | |||||||
\(998\) | 8.98511 | 0.284419 | ||||||||
\(999\) | −2.87322 | −0.0909045 |
(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 | 6002.2.a.b.1.15 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6002.2.a.b.1.15 | ✓ | 56 | 1.1 | even | 1 | trivial |