Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.90469 | −1.34682 | −0.673409 | − | 0.739270i | \(-0.735171\pi\) | ||||
−0.673409 | + | 0.739270i | \(0.735171\pi\) | |||||||
\(3\) | −0.920285 | −0.531327 | −0.265663 | − | 0.964066i | \(-0.585591\pi\) | ||||
−0.265663 | + | 0.964066i | \(0.585591\pi\) | |||||||
\(4\) | 1.62783 | 0.813917 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.75286 | 0.715600 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0.708859 | 0.250620 | ||||||||
\(9\) | −2.15308 | −0.717692 | ||||||||
\(10\) | 1.90469 | 0.602315 | ||||||||
\(11\) | −0.398461 | −0.120141 | −0.0600703 | − | 0.998194i | \(-0.519132\pi\) | ||||
−0.0600703 | + | 0.998194i | \(0.519132\pi\) | |||||||
\(12\) | −1.49807 | −0.432456 | ||||||||
\(13\) | 1.34448 | 0.372891 | 0.186445 | − | 0.982465i | \(-0.440303\pi\) | ||||
0.186445 | + | 0.982465i | \(0.440303\pi\) | |||||||
\(14\) | 1.90469 | 0.509049 | ||||||||
\(15\) | 0.920285 | 0.237617 | ||||||||
\(16\) | −4.60582 | −1.15146 | ||||||||
\(17\) | −0.909012 | −0.220468 | −0.110234 | − | 0.993906i | \(-0.535160\pi\) | ||||
−0.110234 | + | 0.993906i | \(0.535160\pi\) | |||||||
\(18\) | 4.10094 | 0.966600 | ||||||||
\(19\) | 2.01853 | 0.463083 | 0.231541 | − | 0.972825i | \(-0.425623\pi\) | ||||
0.231541 | + | 0.972825i | \(0.425623\pi\) | |||||||
\(20\) | −1.62783 | −0.363995 | ||||||||
\(21\) | 0.920285 | 0.200823 | ||||||||
\(22\) | 0.758945 | 0.161808 | ||||||||
\(23\) | 5.88511 | 1.22713 | 0.613565 | − | 0.789644i | \(-0.289735\pi\) | ||||
0.613565 | + | 0.789644i | \(0.289735\pi\) | |||||||
\(24\) | −0.652353 | −0.133161 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.56081 | −0.502216 | ||||||||
\(27\) | 4.74230 | 0.912656 | ||||||||
\(28\) | −1.62783 | −0.307632 | ||||||||
\(29\) | 3.75365 | 0.697035 | 0.348518 | − | 0.937302i | \(-0.386685\pi\) | ||||
0.348518 | + | 0.937302i | \(0.386685\pi\) | |||||||
\(30\) | −1.75286 | −0.320026 | ||||||||
\(31\) | 9.43024 | 1.69372 | 0.846860 | − | 0.531815i | \(-0.178490\pi\) | ||||
0.846860 | + | 0.531815i | \(0.178490\pi\) | |||||||
\(32\) | 7.35494 | 1.30018 | ||||||||
\(33\) | 0.366698 | 0.0638340 | ||||||||
\(34\) | 1.73138 | 0.296930 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −3.50485 | −0.584142 | ||||||||
\(37\) | −1.76743 | −0.290564 | −0.145282 | − | 0.989390i | \(-0.546409\pi\) | ||||
−0.145282 | + | 0.989390i | \(0.546409\pi\) | |||||||
\(38\) | −3.84467 | −0.623688 | ||||||||
\(39\) | −1.23730 | −0.198127 | ||||||||
\(40\) | −0.708859 | −0.112080 | ||||||||
\(41\) | 9.35609 | 1.46118 | 0.730588 | − | 0.682819i | \(-0.239246\pi\) | ||||
0.730588 | + | 0.682819i | \(0.239246\pi\) | |||||||
\(42\) | −1.75286 | −0.270471 | ||||||||
\(43\) | 9.16701 | 1.39796 | 0.698978 | − | 0.715143i | \(-0.253639\pi\) | ||||
0.698978 | + | 0.715143i | \(0.253639\pi\) | |||||||
\(44\) | −0.648629 | −0.0977845 | ||||||||
\(45\) | 2.15308 | 0.320962 | ||||||||
\(46\) | −11.2093 | −1.65272 | ||||||||
\(47\) | −6.01265 | −0.877035 | −0.438518 | − | 0.898723i | \(-0.644496\pi\) | ||||
−0.438518 | + | 0.898723i | \(0.644496\pi\) | |||||||
\(48\) | 4.23867 | 0.611799 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.90469 | −0.269363 | ||||||||
\(51\) | 0.836550 | 0.117140 | ||||||||
\(52\) | 2.18859 | 0.303502 | ||||||||
\(53\) | −11.2152 | −1.54053 | −0.770264 | − | 0.637725i | \(-0.779876\pi\) | ||||
−0.770264 | + | 0.637725i | \(0.779876\pi\) | |||||||
\(54\) | −9.03260 | −1.22918 | ||||||||
\(55\) | 0.398461 | 0.0537285 | ||||||||
\(56\) | −0.708859 | −0.0947253 | ||||||||
\(57\) | −1.85762 | −0.246048 | ||||||||
\(58\) | −7.14953 | −0.938779 | ||||||||
\(59\) | −12.2949 | −1.60066 | −0.800332 | − | 0.599557i | \(-0.795344\pi\) | ||||
−0.800332 | + | 0.599557i | \(0.795344\pi\) | |||||||
\(60\) | 1.49807 | 0.193400 | ||||||||
\(61\) | −9.26880 | −1.18675 | −0.593374 | − | 0.804927i | \(-0.702205\pi\) | ||||
−0.593374 | + | 0.804927i | \(0.702205\pi\) | |||||||
\(62\) | −17.9617 | −2.28113 | ||||||||
\(63\) | 2.15308 | 0.271262 | ||||||||
\(64\) | −4.79721 | −0.599651 | ||||||||
\(65\) | −1.34448 | −0.166762 | ||||||||
\(66\) | −0.698445 | −0.0859727 | ||||||||
\(67\) | −3.26366 | −0.398719 | −0.199360 | − | 0.979926i | \(-0.563886\pi\) | ||||
−0.199360 | + | 0.979926i | \(0.563886\pi\) | |||||||
\(68\) | −1.47972 | −0.179442 | ||||||||
\(69\) | −5.41598 | −0.652008 | ||||||||
\(70\) | −1.90469 | −0.227654 | ||||||||
\(71\) | −2.06582 | −0.245168 | −0.122584 | − | 0.992458i | \(-0.539118\pi\) | ||||
−0.122584 | + | 0.992458i | \(0.539118\pi\) | |||||||
\(72\) | −1.52623 | −0.179868 | ||||||||
\(73\) | −10.8291 | −1.26745 | −0.633725 | − | 0.773558i | \(-0.718475\pi\) | ||||
−0.633725 | + | 0.773558i | \(0.718475\pi\) | |||||||
\(74\) | 3.36641 | 0.391337 | ||||||||
\(75\) | −0.920285 | −0.106265 | ||||||||
\(76\) | 3.28583 | 0.376911 | ||||||||
\(77\) | 0.398461 | 0.0454089 | ||||||||
\(78\) | 2.35667 | 0.266841 | ||||||||
\(79\) | 13.4409 | 1.51221 | 0.756107 | − | 0.654448i | \(-0.227099\pi\) | ||||
0.756107 | + | 0.654448i | \(0.227099\pi\) | |||||||
\(80\) | 4.60582 | 0.514947 | ||||||||
\(81\) | 2.09496 | 0.232773 | ||||||||
\(82\) | −17.8204 | −1.96794 | ||||||||
\(83\) | 6.72692 | 0.738375 | 0.369188 | − | 0.929355i | \(-0.379636\pi\) | ||||
0.369188 | + | 0.929355i | \(0.379636\pi\) | |||||||
\(84\) | 1.49807 | 0.163453 | ||||||||
\(85\) | 0.909012 | 0.0985962 | ||||||||
\(86\) | −17.4603 | −1.88279 | ||||||||
\(87\) | −3.45443 | −0.370354 | ||||||||
\(88\) | −0.282453 | −0.0301096 | ||||||||
\(89\) | 8.30386 | 0.880208 | 0.440104 | − | 0.897947i | \(-0.354942\pi\) | ||||
0.440104 | + | 0.897947i | \(0.354942\pi\) | |||||||
\(90\) | −4.10094 | −0.432277 | ||||||||
\(91\) | −1.34448 | −0.140939 | ||||||||
\(92\) | 9.57999 | 0.998783 | ||||||||
\(93\) | −8.67851 | −0.899919 | ||||||||
\(94\) | 11.4522 | 1.18121 | ||||||||
\(95\) | −2.01853 | −0.207097 | ||||||||
\(96\) | −6.76864 | −0.690821 | ||||||||
\(97\) | 8.69125 | 0.882463 | 0.441231 | − | 0.897393i | \(-0.354542\pi\) | ||||
0.441231 | + | 0.897393i | \(0.354542\pi\) | |||||||
\(98\) | −1.90469 | −0.192402 | ||||||||
\(99\) | 0.857918 | 0.0862240 | ||||||||
\(100\) | 1.62783 | 0.162783 | ||||||||
\(101\) | −6.43641 | −0.640447 | −0.320223 | − | 0.947342i | \(-0.603758\pi\) | ||||
−0.320223 | + | 0.947342i | \(0.603758\pi\) | |||||||
\(102\) | −1.59337 | −0.157767 | ||||||||
\(103\) | 19.6516 | 1.93632 | 0.968162 | − | 0.250323i | \(-0.0805368\pi\) | ||||
0.968162 | + | 0.250323i | \(0.0805368\pi\) | |||||||
\(104\) | 0.953045 | 0.0934537 | ||||||||
\(105\) | −0.920285 | −0.0898106 | ||||||||
\(106\) | 21.3615 | 2.07481 | ||||||||
\(107\) | −0.137896 | −0.0133309 | −0.00666545 | − | 0.999978i | \(-0.502122\pi\) | ||||
−0.00666545 | + | 0.999978i | \(0.502122\pi\) | |||||||
\(108\) | 7.71968 | 0.742826 | ||||||||
\(109\) | −14.3916 | −1.37847 | −0.689234 | − | 0.724539i | \(-0.742053\pi\) | ||||
−0.689234 | + | 0.724539i | \(0.742053\pi\) | |||||||
\(110\) | −0.758945 | −0.0723625 | ||||||||
\(111\) | 1.62654 | 0.154385 | ||||||||
\(112\) | 4.60582 | 0.435209 | ||||||||
\(113\) | 5.06663 | 0.476629 | 0.238314 | − | 0.971188i | \(-0.423405\pi\) | ||||
0.238314 | + | 0.971188i | \(0.423405\pi\) | |||||||
\(114\) | 3.53819 | 0.331382 | ||||||||
\(115\) | −5.88511 | −0.548790 | ||||||||
\(116\) | 6.11032 | 0.567329 | ||||||||
\(117\) | −2.89476 | −0.267621 | ||||||||
\(118\) | 23.4180 | 2.15580 | ||||||||
\(119\) | 0.909012 | 0.0833290 | ||||||||
\(120\) | 0.652353 | 0.0595514 | ||||||||
\(121\) | −10.8412 | −0.985566 | ||||||||
\(122\) | 17.6542 | 1.59833 | ||||||||
\(123\) | −8.61027 | −0.776362 | ||||||||
\(124\) | 15.3509 | 1.37855 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −4.10094 | −0.365340 | ||||||||
\(127\) | 9.07603 | 0.805368 | 0.402684 | − | 0.915339i | \(-0.368077\pi\) | ||||
0.402684 | + | 0.915339i | \(0.368077\pi\) | |||||||
\(128\) | −5.57269 | −0.492561 | ||||||||
\(129\) | −8.43626 | −0.742771 | ||||||||
\(130\) | 2.56081 | 0.224598 | ||||||||
\(131\) | 19.6266 | 1.71479 | 0.857393 | − | 0.514662i | \(-0.172082\pi\) | ||||
0.857393 | + | 0.514662i | \(0.172082\pi\) | |||||||
\(132\) | 0.596924 | 0.0519556 | ||||||||
\(133\) | −2.01853 | −0.175029 | ||||||||
\(134\) | 6.21625 | 0.537002 | ||||||||
\(135\) | −4.74230 | −0.408152 | ||||||||
\(136\) | −0.644361 | −0.0552535 | ||||||||
\(137\) | 9.72757 | 0.831082 | 0.415541 | − | 0.909574i | \(-0.363592\pi\) | ||||
0.415541 | + | 0.909574i | \(0.363592\pi\) | |||||||
\(138\) | 10.3158 | 0.878135 | ||||||||
\(139\) | −21.3393 | −1.80997 | −0.904986 | − | 0.425442i | \(-0.860119\pi\) | ||||
−0.904986 | + | 0.425442i | \(0.860119\pi\) | |||||||
\(140\) | 1.62783 | 0.137577 | ||||||||
\(141\) | 5.53335 | 0.465992 | ||||||||
\(142\) | 3.93474 | 0.330196 | ||||||||
\(143\) | −0.535722 | −0.0447994 | ||||||||
\(144\) | 9.91669 | 0.826391 | ||||||||
\(145\) | −3.75365 | −0.311724 | ||||||||
\(146\) | 20.6261 | 1.70702 | ||||||||
\(147\) | −0.920285 | −0.0759038 | ||||||||
\(148\) | −2.87709 | −0.236495 | ||||||||
\(149\) | −9.23239 | −0.756347 | −0.378173 | − | 0.925735i | \(-0.623448\pi\) | ||||
−0.378173 | + | 0.925735i | \(0.623448\pi\) | |||||||
\(150\) | 1.75286 | 0.143120 | ||||||||
\(151\) | −8.79112 | −0.715412 | −0.357706 | − | 0.933834i | \(-0.616441\pi\) | ||||
−0.357706 | + | 0.933834i | \(0.616441\pi\) | |||||||
\(152\) | 1.43085 | 0.116058 | ||||||||
\(153\) | 1.95717 | 0.158228 | ||||||||
\(154\) | −0.758945 | −0.0611575 | ||||||||
\(155\) | −9.43024 | −0.757455 | ||||||||
\(156\) | −2.01412 | −0.161259 | ||||||||
\(157\) | −22.0034 | −1.75606 | −0.878030 | − | 0.478606i | \(-0.841142\pi\) | ||||
−0.878030 | + | 0.478606i | \(0.841142\pi\) | |||||||
\(158\) | −25.6006 | −2.03668 | ||||||||
\(159\) | 10.3212 | 0.818524 | ||||||||
\(160\) | −7.35494 | −0.581459 | ||||||||
\(161\) | −5.88511 | −0.463812 | ||||||||
\(162\) | −3.99024 | −0.313503 | ||||||||
\(163\) | 15.0074 | 1.17547 | 0.587737 | − | 0.809052i | \(-0.300019\pi\) | ||||
0.587737 | + | 0.809052i | \(0.300019\pi\) | |||||||
\(164\) | 15.2302 | 1.18928 | ||||||||
\(165\) | −0.366698 | −0.0285474 | ||||||||
\(166\) | −12.8127 | −0.994456 | ||||||||
\(167\) | −19.1886 | −1.48486 | −0.742429 | − | 0.669924i | \(-0.766326\pi\) | ||||
−0.742429 | + | 0.669924i | \(0.766326\pi\) | |||||||
\(168\) | 0.652353 | 0.0503301 | ||||||||
\(169\) | −11.1924 | −0.860952 | ||||||||
\(170\) | −1.73138 | −0.132791 | ||||||||
\(171\) | −4.34605 | −0.332351 | ||||||||
\(172\) | 14.9224 | 1.13782 | ||||||||
\(173\) | 5.28611 | 0.401896 | 0.200948 | − | 0.979602i | \(-0.435598\pi\) | ||||
0.200948 | + | 0.979602i | \(0.435598\pi\) | |||||||
\(174\) | 6.57961 | 0.498799 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 1.83524 | 0.138337 | ||||||||
\(177\) | 11.3148 | 0.850476 | ||||||||
\(178\) | −15.8163 | −1.18548 | ||||||||
\(179\) | −6.54213 | −0.488982 | −0.244491 | − | 0.969652i | \(-0.578621\pi\) | ||||
−0.244491 | + | 0.969652i | \(0.578621\pi\) | |||||||
\(180\) | 3.50485 | 0.261236 | ||||||||
\(181\) | 3.34882 | 0.248916 | 0.124458 | − | 0.992225i | \(-0.460281\pi\) | ||||
0.124458 | + | 0.992225i | \(0.460281\pi\) | |||||||
\(182\) | 2.56081 | 0.189820 | ||||||||
\(183\) | 8.52994 | 0.630551 | ||||||||
\(184\) | 4.17172 | 0.307543 | ||||||||
\(185\) | 1.76743 | 0.129944 | ||||||||
\(186\) | 16.5298 | 1.21203 | ||||||||
\(187\) | 0.362206 | 0.0264871 | ||||||||
\(188\) | −9.78760 | −0.713834 | ||||||||
\(189\) | −4.74230 | −0.344951 | ||||||||
\(190\) | 3.84467 | 0.278922 | ||||||||
\(191\) | 2.04324 | 0.147844 | 0.0739219 | − | 0.997264i | \(-0.476448\pi\) | ||||
0.0739219 | + | 0.997264i | \(0.476448\pi\) | |||||||
\(192\) | 4.41480 | 0.318611 | ||||||||
\(193\) | 25.7380 | 1.85266 | 0.926330 | − | 0.376712i | \(-0.122945\pi\) | ||||
0.926330 | + | 0.376712i | \(0.122945\pi\) | |||||||
\(194\) | −16.5541 | −1.18852 | ||||||||
\(195\) | 1.23730 | 0.0886050 | ||||||||
\(196\) | 1.62783 | 0.116274 | ||||||||
\(197\) | −0.889561 | −0.0633786 | −0.0316893 | − | 0.999498i | \(-0.510089\pi\) | ||||
−0.0316893 | + | 0.999498i | \(0.510089\pi\) | |||||||
\(198\) | −1.63406 | −0.116128 | ||||||||
\(199\) | −0.177669 | −0.0125946 | −0.00629731 | − | 0.999980i | \(-0.502005\pi\) | ||||
−0.00629731 | + | 0.999980i | \(0.502005\pi\) | |||||||
\(200\) | 0.708859 | 0.0501239 | ||||||||
\(201\) | 3.00349 | 0.211850 | ||||||||
\(202\) | 12.2593 | 0.862565 | ||||||||
\(203\) | −3.75365 | −0.263455 | ||||||||
\(204\) | 1.36176 | 0.0953426 | ||||||||
\(205\) | −9.35609 | −0.653458 | ||||||||
\(206\) | −37.4301 | −2.60788 | ||||||||
\(207\) | −12.6711 | −0.880702 | ||||||||
\(208\) | −6.19242 | −0.429367 | ||||||||
\(209\) | −0.804307 | −0.0556350 | ||||||||
\(210\) | 1.75286 | 0.120959 | ||||||||
\(211\) | −25.3607 | −1.74590 | −0.872950 | − | 0.487809i | \(-0.837796\pi\) | ||||
−0.872950 | + | 0.487809i | \(0.837796\pi\) | |||||||
\(212\) | −18.2565 | −1.25386 | ||||||||
\(213\) | 1.90114 | 0.130264 | ||||||||
\(214\) | 0.262649 | 0.0179543 | ||||||||
\(215\) | −9.16701 | −0.625185 | ||||||||
\(216\) | 3.36162 | 0.228729 | ||||||||
\(217\) | −9.43024 | −0.640166 | ||||||||
\(218\) | 27.4115 | 1.85654 | ||||||||
\(219\) | 9.96586 | 0.673430 | ||||||||
\(220\) | 0.648629 | 0.0437306 | ||||||||
\(221\) | −1.22215 | −0.0822104 | ||||||||
\(222\) | −3.09806 | −0.207928 | ||||||||
\(223\) | 17.9830 | 1.20423 | 0.602115 | − | 0.798409i | \(-0.294325\pi\) | ||||
0.602115 | + | 0.798409i | \(0.294325\pi\) | |||||||
\(224\) | −7.35494 | −0.491422 | ||||||||
\(225\) | −2.15308 | −0.143538 | ||||||||
\(226\) | −9.65035 | −0.641932 | ||||||||
\(227\) | −8.88987 | −0.590041 | −0.295021 | − | 0.955491i | \(-0.595326\pi\) | ||||
−0.295021 | + | 0.955491i | \(0.595326\pi\) | |||||||
\(228\) | −3.02390 | −0.200263 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | 11.2093 | 0.739119 | ||||||||
\(231\) | −0.366698 | −0.0241270 | ||||||||
\(232\) | 2.66081 | 0.174691 | ||||||||
\(233\) | 3.64991 | 0.239114 | 0.119557 | − | 0.992827i | \(-0.461853\pi\) | ||||
0.119557 | + | 0.992827i | \(0.461853\pi\) | |||||||
\(234\) | 5.51361 | 0.360436 | ||||||||
\(235\) | 6.01265 | 0.392222 | ||||||||
\(236\) | −20.0141 | −1.30281 | ||||||||
\(237\) | −12.3694 | −0.803480 | ||||||||
\(238\) | −1.73138 | −0.112229 | ||||||||
\(239\) | 16.1757 | 1.04632 | 0.523159 | − | 0.852235i | \(-0.324753\pi\) | ||||
0.523159 | + | 0.852235i | \(0.324753\pi\) | |||||||
\(240\) | −4.23867 | −0.273605 | ||||||||
\(241\) | 7.71156 | 0.496745 | 0.248373 | − | 0.968665i | \(-0.420104\pi\) | ||||
0.248373 | + | 0.968665i | \(0.420104\pi\) | |||||||
\(242\) | 20.6492 | 1.32738 | ||||||||
\(243\) | −16.1549 | −1.03633 | ||||||||
\(244\) | −15.0881 | −0.965915 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 16.3999 | 1.04562 | ||||||||
\(247\) | 2.71387 | 0.172679 | ||||||||
\(248\) | 6.68471 | 0.424480 | ||||||||
\(249\) | −6.19068 | −0.392318 | ||||||||
\(250\) | 1.90469 | 0.120463 | ||||||||
\(251\) | −16.6835 | −1.05305 | −0.526526 | − | 0.850159i | \(-0.676506\pi\) | ||||
−0.526526 | + | 0.850159i | \(0.676506\pi\) | |||||||
\(252\) | 3.50485 | 0.220785 | ||||||||
\(253\) | −2.34499 | −0.147428 | ||||||||
\(254\) | −17.2870 | −1.08468 | ||||||||
\(255\) | −0.836550 | −0.0523868 | ||||||||
\(256\) | 20.2087 | 1.26304 | ||||||||
\(257\) | 6.17137 | 0.384960 | 0.192480 | − | 0.981301i | \(-0.438347\pi\) | ||||
0.192480 | + | 0.981301i | \(0.438347\pi\) | |||||||
\(258\) | 16.0684 | 1.00038 | ||||||||
\(259\) | 1.76743 | 0.109823 | ||||||||
\(260\) | −2.18859 | −0.135730 | ||||||||
\(261\) | −8.08189 | −0.500256 | ||||||||
\(262\) | −37.3826 | −2.30950 | ||||||||
\(263\) | 8.12510 | 0.501015 | 0.250508 | − | 0.968115i | \(-0.419402\pi\) | ||||
0.250508 | + | 0.968115i | \(0.419402\pi\) | |||||||
\(264\) | 0.259937 | 0.0159980 | ||||||||
\(265\) | 11.2152 | 0.688945 | ||||||||
\(266\) | 3.84467 | 0.235732 | ||||||||
\(267\) | −7.64192 | −0.467678 | ||||||||
\(268\) | −5.31269 | −0.324524 | ||||||||
\(269\) | −0.627679 | −0.0382702 | −0.0191351 | − | 0.999817i | \(-0.506091\pi\) | ||||
−0.0191351 | + | 0.999817i | \(0.506091\pi\) | |||||||
\(270\) | 9.03260 | 0.549706 | ||||||||
\(271\) | 8.17038 | 0.496315 | 0.248158 | − | 0.968720i | \(-0.420175\pi\) | ||||
0.248158 | + | 0.968720i | \(0.420175\pi\) | |||||||
\(272\) | 4.18675 | 0.253859 | ||||||||
\(273\) | 1.23730 | 0.0748849 | ||||||||
\(274\) | −18.5280 | −1.11932 | ||||||||
\(275\) | −0.398461 | −0.0240281 | ||||||||
\(276\) | −8.81632 | −0.530680 | ||||||||
\(277\) | 23.8768 | 1.43462 | 0.717309 | − | 0.696756i | \(-0.245374\pi\) | ||||
0.717309 | + | 0.696756i | \(0.245374\pi\) | |||||||
\(278\) | 40.6446 | 2.43770 | ||||||||
\(279\) | −20.3040 | −1.21557 | ||||||||
\(280\) | 0.708859 | 0.0423624 | ||||||||
\(281\) | −2.41049 | −0.143798 | −0.0718988 | − | 0.997412i | \(-0.522906\pi\) | ||||
−0.0718988 | + | 0.997412i | \(0.522906\pi\) | |||||||
\(282\) | −10.5393 | −0.627607 | ||||||||
\(283\) | 11.9779 | 0.712013 | 0.356007 | − | 0.934483i | \(-0.384138\pi\) | ||||
0.356007 | + | 0.934483i | \(0.384138\pi\) | |||||||
\(284\) | −3.36281 | −0.199546 | ||||||||
\(285\) | 1.85762 | 0.110036 | ||||||||
\(286\) | 1.02038 | 0.0603365 | ||||||||
\(287\) | −9.35609 | −0.552273 | ||||||||
\(288\) | −15.8357 | −0.933130 | ||||||||
\(289\) | −16.1737 | −0.951394 | ||||||||
\(290\) | 7.14953 | 0.419835 | ||||||||
\(291\) | −7.99843 | −0.468876 | ||||||||
\(292\) | −17.6280 | −1.03160 | ||||||||
\(293\) | −14.2163 | −0.830526 | −0.415263 | − | 0.909701i | \(-0.636310\pi\) | ||||
−0.415263 | + | 0.909701i | \(0.636310\pi\) | |||||||
\(294\) | 1.75286 | 0.102229 | ||||||||
\(295\) | 12.2949 | 0.715839 | ||||||||
\(296\) | −1.25286 | −0.0728211 | ||||||||
\(297\) | −1.88962 | −0.109647 | ||||||||
\(298\) | 17.5848 | 1.01866 | ||||||||
\(299\) | 7.91240 | 0.457586 | ||||||||
\(300\) | −1.49807 | −0.0864912 | ||||||||
\(301\) | −9.16701 | −0.528377 | ||||||||
\(302\) | 16.7443 | 0.963529 | ||||||||
\(303\) | 5.92333 | 0.340287 | ||||||||
\(304\) | −9.29700 | −0.533219 | ||||||||
\(305\) | 9.26880 | 0.530730 | ||||||||
\(306\) | −3.72780 | −0.213104 | ||||||||
\(307\) | 15.2743 | 0.871750 | 0.435875 | − | 0.900007i | \(-0.356439\pi\) | ||||
0.435875 | + | 0.900007i | \(0.356439\pi\) | |||||||
\(308\) | 0.648629 | 0.0369591 | ||||||||
\(309\) | −18.0850 | −1.02882 | ||||||||
\(310\) | 17.9617 | 1.02015 | ||||||||
\(311\) | −12.3173 | −0.698452 | −0.349226 | − | 0.937038i | \(-0.613556\pi\) | ||||
−0.349226 | + | 0.937038i | \(0.613556\pi\) | |||||||
\(312\) | −0.877073 | −0.0496545 | ||||||||
\(313\) | −0.226117 | −0.0127809 | −0.00639045 | − | 0.999980i | \(-0.502034\pi\) | ||||
−0.00639045 | + | 0.999980i | \(0.502034\pi\) | |||||||
\(314\) | 41.9095 | 2.36509 | ||||||||
\(315\) | −2.15308 | −0.121312 | ||||||||
\(316\) | 21.8795 | 1.23082 | ||||||||
\(317\) | −7.51201 | −0.421916 | −0.210958 | − | 0.977495i | \(-0.567658\pi\) | ||||
−0.210958 | + | 0.977495i | \(0.567658\pi\) | |||||||
\(318\) | −19.6586 | −1.10240 | ||||||||
\(319\) | −1.49568 | −0.0837423 | ||||||||
\(320\) | 4.79721 | 0.268172 | ||||||||
\(321\) | 0.126904 | 0.00708306 | ||||||||
\(322\) | 11.2093 | 0.624670 | ||||||||
\(323\) | −1.83487 | −0.102095 | ||||||||
\(324\) | 3.41025 | 0.189458 | ||||||||
\(325\) | 1.34448 | 0.0745782 | ||||||||
\(326\) | −28.5845 | −1.58315 | ||||||||
\(327\) | 13.2444 | 0.732417 | ||||||||
\(328\) | 6.63215 | 0.366199 | ||||||||
\(329\) | 6.01265 | 0.331488 | ||||||||
\(330\) | 0.698445 | 0.0384482 | ||||||||
\(331\) | −18.5413 | −1.01912 | −0.509561 | − | 0.860434i | \(-0.670192\pi\) | ||||
−0.509561 | + | 0.860434i | \(0.670192\pi\) | |||||||
\(332\) | 10.9503 | 0.600976 | ||||||||
\(333\) | 3.80542 | 0.208536 | ||||||||
\(334\) | 36.5483 | 1.99983 | ||||||||
\(335\) | 3.26366 | 0.178313 | ||||||||
\(336\) | −4.23867 | −0.231238 | ||||||||
\(337\) | 32.0037 | 1.74335 | 0.871677 | − | 0.490081i | \(-0.163033\pi\) | ||||
0.871677 | + | 0.490081i | \(0.163033\pi\) | |||||||
\(338\) | 21.3180 | 1.15955 | ||||||||
\(339\) | −4.66275 | −0.253246 | ||||||||
\(340\) | 1.47972 | 0.0802491 | ||||||||
\(341\) | −3.75759 | −0.203485 | ||||||||
\(342\) | 8.27786 | 0.447616 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 6.49812 | 0.350355 | ||||||||
\(345\) | 5.41598 | 0.291587 | ||||||||
\(346\) | −10.0684 | −0.541280 | ||||||||
\(347\) | 12.3514 | 0.663060 | 0.331530 | − | 0.943445i | \(-0.392435\pi\) | ||||
0.331530 | + | 0.943445i | \(0.392435\pi\) | |||||||
\(348\) | −5.62324 | −0.301437 | ||||||||
\(349\) | 4.63875 | 0.248307 | 0.124153 | − | 0.992263i | \(-0.460379\pi\) | ||||
0.124153 | + | 0.992263i | \(0.460379\pi\) | |||||||
\(350\) | 1.90469 | 0.101810 | ||||||||
\(351\) | 6.37591 | 0.340321 | ||||||||
\(352\) | −2.93066 | −0.156205 | ||||||||
\(353\) | 32.9707 | 1.75485 | 0.877427 | − | 0.479710i | \(-0.159258\pi\) | ||||
0.877427 | + | 0.479710i | \(0.159258\pi\) | |||||||
\(354\) | −21.5513 | −1.14544 | ||||||||
\(355\) | 2.06582 | 0.109642 | ||||||||
\(356\) | 13.5173 | 0.716416 | ||||||||
\(357\) | −0.836550 | −0.0442749 | ||||||||
\(358\) | 12.4607 | 0.658569 | ||||||||
\(359\) | −18.5144 | −0.977152 | −0.488576 | − | 0.872521i | \(-0.662483\pi\) | ||||
−0.488576 | + | 0.872521i | \(0.662483\pi\) | |||||||
\(360\) | 1.52623 | 0.0804392 | ||||||||
\(361\) | −14.9255 | −0.785555 | ||||||||
\(362\) | −6.37846 | −0.335244 | ||||||||
\(363\) | 9.97702 | 0.523658 | ||||||||
\(364\) | −2.18859 | −0.114713 | ||||||||
\(365\) | 10.8291 | 0.566821 | ||||||||
\(366\) | −16.2469 | −0.849238 | ||||||||
\(367\) | −23.4491 | −1.22403 | −0.612017 | − | 0.790844i | \(-0.709642\pi\) | ||||
−0.612017 | + | 0.790844i | \(0.709642\pi\) | |||||||
\(368\) | −27.1058 | −1.41299 | ||||||||
\(369\) | −20.1444 | −1.04867 | ||||||||
\(370\) | −3.36641 | −0.175011 | ||||||||
\(371\) | 11.2152 | 0.582265 | ||||||||
\(372\) | −14.1272 | −0.732460 | ||||||||
\(373\) | −18.0580 | −0.935006 | −0.467503 | − | 0.883991i | \(-0.654846\pi\) | ||||
−0.467503 | + | 0.883991i | \(0.654846\pi\) | |||||||
\(374\) | −0.689890 | −0.0356733 | ||||||||
\(375\) | 0.920285 | 0.0475233 | ||||||||
\(376\) | −4.26212 | −0.219802 | ||||||||
\(377\) | 5.04670 | 0.259918 | ||||||||
\(378\) | 9.03260 | 0.464587 | ||||||||
\(379\) | −6.96985 | −0.358017 | −0.179009 | − | 0.983847i | \(-0.557289\pi\) | ||||
−0.179009 | + | 0.983847i | \(0.557289\pi\) | |||||||
\(380\) | −3.28583 | −0.168560 | ||||||||
\(381\) | −8.35254 | −0.427913 | ||||||||
\(382\) | −3.89174 | −0.199119 | ||||||||
\(383\) | −33.5228 | −1.71294 | −0.856468 | − | 0.516200i | \(-0.827346\pi\) | ||||
−0.856468 | + | 0.516200i | \(0.827346\pi\) | |||||||
\(384\) | 5.12847 | 0.261711 | ||||||||
\(385\) | −0.398461 | −0.0203075 | ||||||||
\(386\) | −49.0228 | −2.49520 | ||||||||
\(387\) | −19.7373 | −1.00330 | ||||||||
\(388\) | 14.1479 | 0.718251 | ||||||||
\(389\) | −21.8847 | −1.10960 | −0.554798 | − | 0.831985i | \(-0.687204\pi\) | ||||
−0.554798 | + | 0.831985i | \(0.687204\pi\) | |||||||
\(390\) | −2.35667 | −0.119335 | ||||||||
\(391\) | −5.34964 | −0.270543 | ||||||||
\(392\) | 0.708859 | 0.0358028 | ||||||||
\(393\) | −18.0621 | −0.911112 | ||||||||
\(394\) | 1.69434 | 0.0853594 | ||||||||
\(395\) | −13.4409 | −0.676283 | ||||||||
\(396\) | 1.39655 | 0.0701792 | ||||||||
\(397\) | 26.9346 | 1.35181 | 0.675905 | − | 0.736989i | \(-0.263753\pi\) | ||||
0.675905 | + | 0.736989i | \(0.263753\pi\) | |||||||
\(398\) | 0.338404 | 0.0169627 | ||||||||
\(399\) | 1.85762 | 0.0929975 | ||||||||
\(400\) | −4.60582 | −0.230291 | ||||||||
\(401\) | −24.8204 | −1.23947 | −0.619736 | − | 0.784810i | \(-0.712760\pi\) | ||||
−0.619736 | + | 0.784810i | \(0.712760\pi\) | |||||||
\(402\) | −5.72072 | −0.285323 | ||||||||
\(403\) | 12.6787 | 0.631573 | ||||||||
\(404\) | −10.4774 | −0.521271 | ||||||||
\(405\) | −2.09496 | −0.104099 | ||||||||
\(406\) | 7.14953 | 0.354825 | ||||||||
\(407\) | 0.704254 | 0.0349086 | ||||||||
\(408\) | 0.592996 | 0.0293577 | ||||||||
\(409\) | 9.15483 | 0.452677 | 0.226339 | − | 0.974049i | \(-0.427324\pi\) | ||||
0.226339 | + | 0.974049i | \(0.427324\pi\) | |||||||
\(410\) | 17.8204 | 0.880088 | ||||||||
\(411\) | −8.95213 | −0.441576 | ||||||||
\(412\) | 31.9895 | 1.57601 | ||||||||
\(413\) | 12.2949 | 0.604994 | ||||||||
\(414\) | 24.1345 | 1.18614 | ||||||||
\(415\) | −6.72692 | −0.330211 | ||||||||
\(416\) | 9.88854 | 0.484826 | ||||||||
\(417\) | 19.6382 | 0.961687 | ||||||||
\(418\) | 1.53195 | 0.0749303 | ||||||||
\(419\) | 5.65783 | 0.276403 | 0.138202 | − | 0.990404i | \(-0.455868\pi\) | ||||
0.138202 | + | 0.990404i | \(0.455868\pi\) | |||||||
\(420\) | −1.49807 | −0.0730984 | ||||||||
\(421\) | 27.9693 | 1.36314 | 0.681569 | − | 0.731754i | \(-0.261298\pi\) | ||||
0.681569 | + | 0.731754i | \(0.261298\pi\) | |||||||
\(422\) | 48.3041 | 2.35141 | ||||||||
\(423\) | 12.9457 | 0.629441 | ||||||||
\(424\) | −7.95001 | −0.386086 | ||||||||
\(425\) | −0.909012 | −0.0440935 | ||||||||
\(426\) | −3.62108 | −0.175442 | ||||||||
\(427\) | 9.26880 | 0.448549 | ||||||||
\(428\) | −0.224472 | −0.0108502 | ||||||||
\(429\) | 0.493017 | 0.0238031 | ||||||||
\(430\) | 17.4603 | 0.842010 | ||||||||
\(431\) | −22.3715 | −1.07760 | −0.538799 | − | 0.842434i | \(-0.681122\pi\) | ||||
−0.538799 | + | 0.842434i | \(0.681122\pi\) | |||||||
\(432\) | −21.8422 | −1.05088 | ||||||||
\(433\) | −9.00623 | −0.432812 | −0.216406 | − | 0.976303i | \(-0.569433\pi\) | ||||
−0.216406 | + | 0.976303i | \(0.569433\pi\) | |||||||
\(434\) | 17.9617 | 0.862187 | ||||||||
\(435\) | 3.45443 | 0.165627 | ||||||||
\(436\) | −23.4272 | −1.12196 | ||||||||
\(437\) | 11.8793 | 0.568263 | ||||||||
\(438\) | −18.9818 | −0.906988 | ||||||||
\(439\) | 23.2754 | 1.11087 | 0.555437 | − | 0.831559i | \(-0.312551\pi\) | ||||
0.555437 | + | 0.831559i | \(0.312551\pi\) | |||||||
\(440\) | 0.282453 | 0.0134654 | ||||||||
\(441\) | −2.15308 | −0.102527 | ||||||||
\(442\) | 2.32780 | 0.110722 | ||||||||
\(443\) | −9.18886 | −0.436576 | −0.218288 | − | 0.975884i | \(-0.570047\pi\) | ||||
−0.218288 | + | 0.975884i | \(0.570047\pi\) | |||||||
\(444\) | 2.64774 | 0.125656 | ||||||||
\(445\) | −8.30386 | −0.393641 | ||||||||
\(446\) | −34.2520 | −1.62188 | ||||||||
\(447\) | 8.49643 | 0.401867 | ||||||||
\(448\) | 4.79721 | 0.226647 | ||||||||
\(449\) | −1.68311 | −0.0794311 | −0.0397155 | − | 0.999211i | \(-0.512645\pi\) | ||||
−0.0397155 | + | 0.999211i | \(0.512645\pi\) | |||||||
\(450\) | 4.10094 | 0.193320 | ||||||||
\(451\) | −3.72804 | −0.175547 | ||||||||
\(452\) | 8.24764 | 0.387936 | ||||||||
\(453\) | 8.09034 | 0.380117 | ||||||||
\(454\) | 16.9324 | 0.794678 | ||||||||
\(455\) | 1.34448 | 0.0630301 | ||||||||
\(456\) | −1.31679 | −0.0616645 | ||||||||
\(457\) | 6.44068 | 0.301282 | 0.150641 | − | 0.988589i | \(-0.451866\pi\) | ||||
0.150641 | + | 0.988589i | \(0.451866\pi\) | |||||||
\(458\) | −1.90469 | −0.0890002 | ||||||||
\(459\) | −4.31080 | −0.201211 | ||||||||
\(460\) | −9.57999 | −0.446669 | ||||||||
\(461\) | −3.35278 | −0.156154 | −0.0780772 | − | 0.996947i | \(-0.524878\pi\) | ||||
−0.0780772 | + | 0.996947i | \(0.524878\pi\) | |||||||
\(462\) | 0.698445 | 0.0324946 | ||||||||
\(463\) | 39.1145 | 1.81781 | 0.908903 | − | 0.417007i | \(-0.136921\pi\) | ||||
0.908903 | + | 0.417007i | \(0.136921\pi\) | |||||||
\(464\) | −17.2886 | −0.802605 | ||||||||
\(465\) | 8.67851 | 0.402456 | ||||||||
\(466\) | −6.95195 | −0.322043 | ||||||||
\(467\) | 16.5803 | 0.767247 | 0.383624 | − | 0.923490i | \(-0.374676\pi\) | ||||
0.383624 | + | 0.923490i | \(0.374676\pi\) | |||||||
\(468\) | −4.71219 | −0.217821 | ||||||||
\(469\) | 3.26366 | 0.150702 | ||||||||
\(470\) | −11.4522 | −0.528251 | ||||||||
\(471\) | 20.2494 | 0.933041 | ||||||||
\(472\) | −8.71538 | −0.401158 | ||||||||
\(473\) | −3.65270 | −0.167951 | ||||||||
\(474\) | 23.5599 | 1.08214 | ||||||||
\(475\) | 2.01853 | 0.0926165 | ||||||||
\(476\) | 1.47972 | 0.0678229 | ||||||||
\(477\) | 24.1472 | 1.10562 | ||||||||
\(478\) | −30.8096 | −1.40920 | ||||||||
\(479\) | 30.9952 | 1.41621 | 0.708104 | − | 0.706108i | \(-0.249551\pi\) | ||||
0.708104 | + | 0.706108i | \(0.249551\pi\) | |||||||
\(480\) | 6.76864 | 0.308945 | ||||||||
\(481\) | −2.37627 | −0.108349 | ||||||||
\(482\) | −14.6881 | −0.669025 | ||||||||
\(483\) | 5.41598 | 0.246436 | ||||||||
\(484\) | −17.6477 | −0.802169 | ||||||||
\(485\) | −8.69125 | −0.394649 | ||||||||
\(486\) | 30.7700 | 1.39575 | ||||||||
\(487\) | 9.34362 | 0.423400 | 0.211700 | − | 0.977335i | \(-0.432100\pi\) | ||||
0.211700 | + | 0.977335i | \(0.432100\pi\) | |||||||
\(488\) | −6.57028 | −0.297422 | ||||||||
\(489\) | −13.8111 | −0.624561 | ||||||||
\(490\) | 1.90469 | 0.0860450 | ||||||||
\(491\) | −0.588749 | −0.0265699 | −0.0132849 | − | 0.999912i | \(-0.504229\pi\) | ||||
−0.0132849 | + | 0.999912i | \(0.504229\pi\) | |||||||
\(492\) | −14.0161 | −0.631894 | ||||||||
\(493\) | −3.41211 | −0.153674 | ||||||||
\(494\) | −5.16907 | −0.232567 | ||||||||
\(495\) | −0.857918 | −0.0385605 | ||||||||
\(496\) | −43.4340 | −1.95024 | ||||||||
\(497\) | 2.06582 | 0.0926646 | ||||||||
\(498\) | 11.7913 | 0.528381 | ||||||||
\(499\) | 35.2498 | 1.57800 | 0.788998 | − | 0.614395i | \(-0.210600\pi\) | ||||
0.788998 | + | 0.614395i | \(0.210600\pi\) | |||||||
\(500\) | −1.62783 | −0.0727990 | ||||||||
\(501\) | 17.6590 | 0.788945 | ||||||||
\(502\) | 31.7768 | 1.41827 | ||||||||
\(503\) | −32.7118 | −1.45855 | −0.729274 | − | 0.684222i | \(-0.760142\pi\) | ||||
−0.729274 | + | 0.684222i | \(0.760142\pi\) | |||||||
\(504\) | 1.52623 | 0.0679836 | ||||||||
\(505\) | 6.43641 | 0.286416 | ||||||||
\(506\) | 4.46647 | 0.198559 | ||||||||
\(507\) | 10.3002 | 0.457447 | ||||||||
\(508\) | 14.7743 | 0.655502 | ||||||||
\(509\) | 18.6501 | 0.826650 | 0.413325 | − | 0.910583i | \(-0.364367\pi\) | ||||
0.413325 | + | 0.910583i | \(0.364367\pi\) | |||||||
\(510\) | 1.59337 | 0.0705554 | ||||||||
\(511\) | 10.8291 | 0.479051 | ||||||||
\(512\) | −27.3458 | −1.20852 | ||||||||
\(513\) | 9.57247 | 0.422635 | ||||||||
\(514\) | −11.7545 | −0.518470 | ||||||||
\(515\) | −19.6516 | −0.865951 | ||||||||
\(516\) | −13.7328 | −0.604554 | ||||||||
\(517\) | 2.39581 | 0.105368 | ||||||||
\(518\) | −3.36641 | −0.147911 | ||||||||
\(519\) | −4.86473 | −0.213538 | ||||||||
\(520\) | −0.953045 | −0.0417938 | ||||||||
\(521\) | −4.55655 | −0.199626 | −0.0998130 | − | 0.995006i | \(-0.531824\pi\) | ||||
−0.0998130 | + | 0.995006i | \(0.531824\pi\) | |||||||
\(522\) | 15.3935 | 0.673754 | ||||||||
\(523\) | 11.7941 | 0.515720 | 0.257860 | − | 0.966182i | \(-0.416983\pi\) | ||||
0.257860 | + | 0.966182i | \(0.416983\pi\) | |||||||
\(524\) | 31.9489 | 1.39569 | ||||||||
\(525\) | 0.920285 | 0.0401645 | ||||||||
\(526\) | −15.4758 | −0.674776 | ||||||||
\(527\) | −8.57220 | −0.373411 | ||||||||
\(528\) | −1.68895 | −0.0735020 | ||||||||
\(529\) | 11.6346 | 0.505850 | ||||||||
\(530\) | −21.3615 | −0.927883 | ||||||||
\(531\) | 26.4719 | 1.14878 | ||||||||
\(532\) | −3.28583 | −0.142459 | ||||||||
\(533\) | 12.5790 | 0.544859 | ||||||||
\(534\) | 14.5555 | 0.629877 | ||||||||
\(535\) | 0.137896 | 0.00596176 | ||||||||
\(536\) | −2.31347 | −0.0999268 | ||||||||
\(537\) | 6.02062 | 0.259809 | ||||||||
\(538\) | 1.19553 | 0.0515430 | ||||||||
\(539\) | −0.398461 | −0.0171630 | ||||||||
\(540\) | −7.71968 | −0.332202 | ||||||||
\(541\) | 25.1765 | 1.08242 | 0.541211 | − | 0.840887i | \(-0.317966\pi\) | ||||
0.541211 | + | 0.840887i | \(0.317966\pi\) | |||||||
\(542\) | −15.5620 | −0.668446 | ||||||||
\(543\) | −3.08187 | −0.132256 | ||||||||
\(544\) | −6.68572 | −0.286648 | ||||||||
\(545\) | 14.3916 | 0.616469 | ||||||||
\(546\) | −2.35667 | −0.100856 | ||||||||
\(547\) | 20.4919 | 0.876170 | 0.438085 | − | 0.898934i | \(-0.355657\pi\) | ||||
0.438085 | + | 0.898934i | \(0.355657\pi\) | |||||||
\(548\) | 15.8349 | 0.676432 | ||||||||
\(549\) | 19.9564 | 0.851720 | ||||||||
\(550\) | 0.758945 | 0.0323615 | ||||||||
\(551\) | 7.57686 | 0.322785 | ||||||||
\(552\) | −3.83917 | −0.163406 | ||||||||
\(553\) | −13.4409 | −0.571563 | ||||||||
\(554\) | −45.4778 | −1.93217 | ||||||||
\(555\) | −1.62654 | −0.0690429 | ||||||||
\(556\) | −34.7368 | −1.47317 | ||||||||
\(557\) | 10.5002 | 0.444907 | 0.222454 | − | 0.974943i | \(-0.428593\pi\) | ||||
0.222454 | + | 0.974943i | \(0.428593\pi\) | |||||||
\(558\) | 38.6728 | 1.63715 | ||||||||
\(559\) | 12.3248 | 0.521285 | ||||||||
\(560\) | −4.60582 | −0.194632 | ||||||||
\(561\) | −0.333333 | −0.0140733 | ||||||||
\(562\) | 4.59122 | 0.193669 | ||||||||
\(563\) | 22.5202 | 0.949114 | 0.474557 | − | 0.880225i | \(-0.342608\pi\) | ||||
0.474557 | + | 0.880225i | \(0.342608\pi\) | |||||||
\(564\) | 9.00738 | 0.379279 | ||||||||
\(565\) | −5.06663 | −0.213155 | ||||||||
\(566\) | −22.8142 | −0.958952 | ||||||||
\(567\) | −2.09496 | −0.0879800 | ||||||||
\(568\) | −1.46437 | −0.0614438 | ||||||||
\(569\) | −34.2086 | −1.43410 | −0.717051 | − | 0.697021i | \(-0.754508\pi\) | ||||
−0.717051 | + | 0.697021i | \(0.754508\pi\) | |||||||
\(570\) | −3.53819 | −0.148199 | ||||||||
\(571\) | 24.8438 | 1.03968 | 0.519840 | − | 0.854264i | \(-0.325992\pi\) | ||||
0.519840 | + | 0.854264i | \(0.325992\pi\) | |||||||
\(572\) | −0.872067 | −0.0364630 | ||||||||
\(573\) | −1.88037 | −0.0785534 | ||||||||
\(574\) | 17.8204 | 0.743810 | ||||||||
\(575\) | 5.88511 | 0.245426 | ||||||||
\(576\) | 10.3288 | 0.430365 | ||||||||
\(577\) | −13.7575 | −0.572734 | −0.286367 | − | 0.958120i | \(-0.592448\pi\) | ||||
−0.286367 | + | 0.958120i | \(0.592448\pi\) | |||||||
\(578\) | 30.8058 | 1.28135 | ||||||||
\(579\) | −23.6863 | −0.984369 | ||||||||
\(580\) | −6.11032 | −0.253717 | ||||||||
\(581\) | −6.72692 | −0.279080 | ||||||||
\(582\) | 15.2345 | 0.631490 | ||||||||
\(583\) | 4.46883 | 0.185080 | ||||||||
\(584\) | −7.67631 | −0.317648 | ||||||||
\(585\) | 2.89476 | 0.119684 | ||||||||
\(586\) | 27.0776 | 1.11857 | ||||||||
\(587\) | 2.86817 | 0.118382 | 0.0591911 | − | 0.998247i | \(-0.481148\pi\) | ||||
0.0591911 | + | 0.998247i | \(0.481148\pi\) | |||||||
\(588\) | −1.49807 | −0.0617794 | ||||||||
\(589\) | 19.0352 | 0.784333 | ||||||||
\(590\) | −23.4180 | −0.964105 | ||||||||
\(591\) | 0.818649 | 0.0336747 | ||||||||
\(592\) | 8.14049 | 0.334572 | ||||||||
\(593\) | −13.9782 | −0.574015 | −0.287007 | − | 0.957928i | \(-0.592660\pi\) | ||||
−0.287007 | + | 0.957928i | \(0.592660\pi\) | |||||||
\(594\) | 3.59914 | 0.147675 | ||||||||
\(595\) | −0.909012 | −0.0372658 | ||||||||
\(596\) | −15.0288 | −0.615604 | ||||||||
\(597\) | 0.163506 | 0.00669186 | ||||||||
\(598\) | −15.0706 | −0.616285 | ||||||||
\(599\) | −26.0883 | −1.06594 | −0.532969 | − | 0.846135i | \(-0.678924\pi\) | ||||
−0.532969 | + | 0.846135i | \(0.678924\pi\) | |||||||
\(600\) | −0.652353 | −0.0266322 | ||||||||
\(601\) | 10.5552 | 0.430557 | 0.215278 | − | 0.976553i | \(-0.430934\pi\) | ||||
0.215278 | + | 0.976553i | \(0.430934\pi\) | |||||||
\(602\) | 17.4603 | 0.711628 | ||||||||
\(603\) | 7.02690 | 0.286157 | ||||||||
\(604\) | −14.3105 | −0.582286 | ||||||||
\(605\) | 10.8412 | 0.440759 | ||||||||
\(606\) | −11.2821 | −0.458304 | ||||||||
\(607\) | 16.1986 | 0.657482 | 0.328741 | − | 0.944420i | \(-0.393376\pi\) | ||||
0.328741 | + | 0.944420i | \(0.393376\pi\) | |||||||
\(608\) | 14.8462 | 0.602091 | ||||||||
\(609\) | 3.45443 | 0.139980 | ||||||||
\(610\) | −17.6542 | −0.714797 | ||||||||
\(611\) | −8.08387 | −0.327038 | ||||||||
\(612\) | 3.18595 | 0.128784 | ||||||||
\(613\) | 44.0509 | 1.77920 | 0.889599 | − | 0.456742i | \(-0.150984\pi\) | ||||
0.889599 | + | 0.456742i | \(0.150984\pi\) | |||||||
\(614\) | −29.0928 | −1.17409 | ||||||||
\(615\) | 8.61027 | 0.347200 | ||||||||
\(616\) | 0.282453 | 0.0113804 | ||||||||
\(617\) | −40.3143 | −1.62299 | −0.811497 | − | 0.584357i | \(-0.801347\pi\) | ||||
−0.811497 | + | 0.584357i | \(0.801347\pi\) | |||||||
\(618\) | 34.4463 | 1.38563 | ||||||||
\(619\) | 10.5871 | 0.425532 | 0.212766 | − | 0.977103i | \(-0.431753\pi\) | ||||
0.212766 | + | 0.977103i | \(0.431753\pi\) | |||||||
\(620\) | −15.3509 | −0.616506 | ||||||||
\(621\) | 27.9090 | 1.11995 | ||||||||
\(622\) | 23.4607 | 0.940688 | ||||||||
\(623\) | −8.30386 | −0.332687 | ||||||||
\(624\) | 5.69880 | 0.228134 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0.430683 | 0.0172135 | ||||||||
\(627\) | 0.740191 | 0.0295604 | ||||||||
\(628\) | −35.8178 | −1.42929 | ||||||||
\(629\) | 1.60662 | 0.0640600 | ||||||||
\(630\) | 4.10094 | 0.163385 | ||||||||
\(631\) | 41.6578 | 1.65837 | 0.829186 | − | 0.558973i | \(-0.188805\pi\) | ||||
0.829186 | + | 0.558973i | \(0.188805\pi\) | |||||||
\(632\) | 9.52767 | 0.378990 | ||||||||
\(633\) | 23.3390 | 0.927644 | ||||||||
\(634\) | 14.3080 | 0.568244 | ||||||||
\(635\) | −9.07603 | −0.360171 | ||||||||
\(636\) | 16.8012 | 0.666211 | ||||||||
\(637\) | 1.34448 | 0.0532701 | ||||||||
\(638\) | 2.84881 | 0.112786 | ||||||||
\(639\) | 4.44786 | 0.175955 | ||||||||
\(640\) | 5.57269 | 0.220280 | ||||||||
\(641\) | 39.4518 | 1.55825 | 0.779127 | − | 0.626866i | \(-0.215663\pi\) | ||||
0.779127 | + | 0.626866i | \(0.215663\pi\) | |||||||
\(642\) | −0.241712 | −0.00953959 | ||||||||
\(643\) | −37.5137 | −1.47940 | −0.739698 | − | 0.672939i | \(-0.765032\pi\) | ||||
−0.739698 | + | 0.672939i | \(0.765032\pi\) | |||||||
\(644\) | −9.57999 | −0.377504 | ||||||||
\(645\) | 8.43626 | 0.332177 | ||||||||
\(646\) | 3.49485 | 0.137503 | ||||||||
\(647\) | −15.7621 | −0.619674 | −0.309837 | − | 0.950790i | \(-0.600274\pi\) | ||||
−0.309837 | + | 0.950790i | \(0.600274\pi\) | |||||||
\(648\) | 1.48503 | 0.0583375 | ||||||||
\(649\) | 4.89906 | 0.192305 | ||||||||
\(650\) | −2.56081 | −0.100443 | ||||||||
\(651\) | 8.67851 | 0.340138 | ||||||||
\(652\) | 24.4296 | 0.956738 | ||||||||
\(653\) | −16.5984 | −0.649547 | −0.324773 | − | 0.945792i | \(-0.605288\pi\) | ||||
−0.324773 | + | 0.945792i | \(0.605288\pi\) | |||||||
\(654\) | −25.2264 | −0.986432 | ||||||||
\(655\) | −19.6266 | −0.766876 | ||||||||
\(656\) | −43.0925 | −1.68248 | ||||||||
\(657\) | 23.3159 | 0.909639 | ||||||||
\(658\) | −11.4522 | −0.446454 | ||||||||
\(659\) | 11.2084 | 0.436617 | 0.218309 | − | 0.975880i | \(-0.429946\pi\) | ||||
0.218309 | + | 0.975880i | \(0.429946\pi\) | |||||||
\(660\) | −0.596924 | −0.0232352 | ||||||||
\(661\) | −18.4365 | −0.717098 | −0.358549 | − | 0.933511i | \(-0.616728\pi\) | ||||
−0.358549 | + | 0.933511i | \(0.616728\pi\) | |||||||
\(662\) | 35.3154 | 1.37257 | ||||||||
\(663\) | 1.12472 | 0.0436806 | ||||||||
\(664\) | 4.76844 | 0.185051 | ||||||||
\(665\) | 2.01853 | 0.0782752 | ||||||||
\(666\) | −7.24813 | −0.280859 | ||||||||
\(667\) | 22.0907 | 0.855353 | ||||||||
\(668\) | −31.2359 | −1.20855 | ||||||||
\(669\) | −16.5495 | −0.639840 | ||||||||
\(670\) | −6.21625 | −0.240155 | ||||||||
\(671\) | 3.69326 | 0.142577 | ||||||||
\(672\) | 6.76864 | 0.261106 | ||||||||
\(673\) | 26.8214 | 1.03389 | 0.516945 | − | 0.856019i | \(-0.327069\pi\) | ||||
0.516945 | + | 0.856019i | \(0.327069\pi\) | |||||||
\(674\) | −60.9571 | −2.34798 | ||||||||
\(675\) | 4.74230 | 0.182531 | ||||||||
\(676\) | −18.2193 | −0.700744 | ||||||||
\(677\) | −20.1774 | −0.775480 | −0.387740 | − | 0.921769i | \(-0.626744\pi\) | ||||
−0.387740 | + | 0.921769i | \(0.626744\pi\) | |||||||
\(678\) | 8.88108 | 0.341076 | ||||||||
\(679\) | −8.69125 | −0.333540 | ||||||||
\(680\) | 0.644361 | 0.0247101 | ||||||||
\(681\) | 8.18121 | 0.313505 | ||||||||
\(682\) | 7.15703 | 0.274057 | ||||||||
\(683\) | 11.2952 | 0.432198 | 0.216099 | − | 0.976372i | \(-0.430667\pi\) | ||||
0.216099 | + | 0.976372i | \(0.430667\pi\) | |||||||
\(684\) | −7.07465 | −0.270506 | ||||||||
\(685\) | −9.72757 | −0.371671 | ||||||||
\(686\) | 1.90469 | 0.0727213 | ||||||||
\(687\) | −0.920285 | −0.0351111 | ||||||||
\(688\) | −42.2216 | −1.60968 | ||||||||
\(689\) | −15.0786 | −0.574449 | ||||||||
\(690\) | −10.3158 | −0.392714 | ||||||||
\(691\) | −11.3159 | −0.430477 | −0.215238 | − | 0.976562i | \(-0.569053\pi\) | ||||
−0.215238 | + | 0.976562i | \(0.569053\pi\) | |||||||
\(692\) | 8.60492 | 0.327110 | ||||||||
\(693\) | −0.857918 | −0.0325896 | ||||||||
\(694\) | −23.5256 | −0.893021 | ||||||||
\(695\) | 21.3393 | 0.809444 | ||||||||
\(696\) | −2.44870 | −0.0928178 | ||||||||
\(697\) | −8.50480 | −0.322142 | ||||||||
\(698\) | −8.83537 | −0.334424 | ||||||||
\(699\) | −3.35896 | −0.127048 | ||||||||
\(700\) | −1.62783 | −0.0615264 | ||||||||
\(701\) | 3.49963 | 0.132179 | 0.0660896 | − | 0.997814i | \(-0.478948\pi\) | ||||
0.0660896 | + | 0.997814i | \(0.478948\pi\) | |||||||
\(702\) | −12.1441 | −0.458350 | ||||||||
\(703\) | −3.56762 | −0.134555 | ||||||||
\(704\) | 1.91150 | 0.0720425 | ||||||||
\(705\) | −5.53335 | −0.208398 | ||||||||
\(706\) | −62.7989 | −2.36347 | ||||||||
\(707\) | 6.43641 | 0.242066 | ||||||||
\(708\) | 18.4187 | 0.692217 | ||||||||
\(709\) | −14.4654 | −0.543259 | −0.271629 | − | 0.962402i | \(-0.587562\pi\) | ||||
−0.271629 | + | 0.962402i | \(0.587562\pi\) | |||||||
\(710\) | −3.93474 | −0.147668 | ||||||||
\(711\) | −28.9392 | −1.08530 | ||||||||
\(712\) | 5.88627 | 0.220597 | ||||||||
\(713\) | 55.4980 | 2.07842 | ||||||||
\(714\) | 1.59337 | 0.0596302 | ||||||||
\(715\) | 0.535722 | 0.0200349 | ||||||||
\(716\) | −10.6495 | −0.397990 | ||||||||
\(717\) | −14.8862 | −0.555937 | ||||||||
\(718\) | 35.2641 | 1.31604 | ||||||||
\(719\) | 35.8740 | 1.33787 | 0.668937 | − | 0.743319i | \(-0.266750\pi\) | ||||
0.668937 | + | 0.743319i | \(0.266750\pi\) | |||||||
\(720\) | −9.91669 | −0.369573 | ||||||||
\(721\) | −19.6516 | −0.731862 | ||||||||
\(722\) | 28.4285 | 1.05800 | ||||||||
\(723\) | −7.09683 | −0.263934 | ||||||||
\(724\) | 5.45133 | 0.202597 | ||||||||
\(725\) | 3.75365 | 0.139407 | ||||||||
\(726\) | −19.0031 | −0.705271 | ||||||||
\(727\) | 12.3345 | 0.457461 | 0.228731 | − | 0.973490i | \(-0.426542\pi\) | ||||
0.228731 | + | 0.973490i | \(0.426542\pi\) | |||||||
\(728\) | −0.953045 | −0.0353222 | ||||||||
\(729\) | 8.58219 | 0.317859 | ||||||||
\(730\) | −20.6261 | −0.763404 | ||||||||
\(731\) | −8.33292 | −0.308204 | ||||||||
\(732\) | 13.8853 | 0.513217 | ||||||||
\(733\) | −26.3479 | −0.973180 | −0.486590 | − | 0.873630i | \(-0.661759\pi\) | ||||
−0.486590 | + | 0.873630i | \(0.661759\pi\) | |||||||
\(734\) | 44.6633 | 1.64855 | ||||||||
\(735\) | 0.920285 | 0.0339452 | ||||||||
\(736\) | 43.2846 | 1.59549 | ||||||||
\(737\) | 1.30044 | 0.0479024 | ||||||||
\(738\) | 38.3687 | 1.41237 | ||||||||
\(739\) | 29.8292 | 1.09729 | 0.548643 | − | 0.836057i | \(-0.315145\pi\) | ||||
0.548643 | + | 0.836057i | \(0.315145\pi\) | |||||||
\(740\) | 2.87709 | 0.105764 | ||||||||
\(741\) | −2.49753 | −0.0917491 | ||||||||
\(742\) | −21.3615 | −0.784204 | ||||||||
\(743\) | 26.9180 | 0.987525 | 0.493762 | − | 0.869597i | \(-0.335621\pi\) | ||||
0.493762 | + | 0.869597i | \(0.335621\pi\) | |||||||
\(744\) | −6.15184 | −0.225537 | ||||||||
\(745\) | 9.23239 | 0.338249 | ||||||||
\(746\) | 34.3948 | 1.25928 | ||||||||
\(747\) | −14.4836 | −0.529926 | ||||||||
\(748\) | 0.589612 | 0.0215583 | ||||||||
\(749\) | 0.137896 | 0.00503861 | ||||||||
\(750\) | −1.75286 | −0.0640052 | ||||||||
\(751\) | −2.07072 | −0.0755617 | −0.0377808 | − | 0.999286i | \(-0.512029\pi\) | ||||
−0.0377808 | + | 0.999286i | \(0.512029\pi\) | |||||||
\(752\) | 27.6932 | 1.00987 | ||||||||
\(753\) | 15.3536 | 0.559515 | ||||||||
\(754\) | −9.61238 | −0.350062 | ||||||||
\(755\) | 8.79112 | 0.319942 | ||||||||
\(756\) | −7.71968 | −0.280762 | ||||||||
\(757\) | −7.20119 | −0.261732 | −0.130866 | − | 0.991400i | \(-0.541776\pi\) | ||||
−0.130866 | + | 0.991400i | \(0.541776\pi\) | |||||||
\(758\) | 13.2754 | 0.482184 | ||||||||
\(759\) | 2.15806 | 0.0783326 | ||||||||
\(760\) | −1.43085 | −0.0519025 | ||||||||
\(761\) | −21.6954 | −0.786458 | −0.393229 | − | 0.919441i | \(-0.628642\pi\) | ||||
−0.393229 | + | 0.919441i | \(0.628642\pi\) | |||||||
\(762\) | 15.9090 | 0.576321 | ||||||||
\(763\) | 14.3916 | 0.521012 | ||||||||
\(764\) | 3.32606 | 0.120333 | ||||||||
\(765\) | −1.95717 | −0.0707617 | ||||||||
\(766\) | 63.8505 | 2.30701 | ||||||||
\(767\) | −16.5303 | −0.596873 | ||||||||
\(768\) | −18.5977 | −0.671087 | ||||||||
\(769\) | −18.2013 | −0.656354 | −0.328177 | − | 0.944616i | \(-0.606434\pi\) | ||||
−0.328177 | + | 0.944616i | \(0.606434\pi\) | |||||||
\(770\) | 0.758945 | 0.0273505 | ||||||||
\(771\) | −5.67942 | −0.204539 | ||||||||
\(772\) | 41.8972 | 1.50791 | ||||||||
\(773\) | 45.5355 | 1.63780 | 0.818899 | − | 0.573938i | \(-0.194585\pi\) | ||||
0.818899 | + | 0.573938i | \(0.194585\pi\) | |||||||
\(774\) | 37.5933 | 1.35126 | ||||||||
\(775\) | 9.43024 | 0.338744 | ||||||||
\(776\) | 6.16087 | 0.221162 | ||||||||
\(777\) | −1.62654 | −0.0583519 | ||||||||
\(778\) | 41.6834 | 1.49442 | ||||||||
\(779\) | 18.8856 | 0.676645 | ||||||||
\(780\) | 2.01412 | 0.0721172 | ||||||||
\(781\) | 0.823149 | 0.0294546 | ||||||||
\(782\) | 10.1894 | 0.364372 | ||||||||
\(783\) | 17.8009 | 0.636153 | ||||||||
\(784\) | −4.60582 | −0.164494 | ||||||||
\(785\) | 22.0034 | 0.785334 | ||||||||
\(786\) | 34.4027 | 1.22710 | ||||||||
\(787\) | −11.1476 | −0.397370 | −0.198685 | − | 0.980063i | \(-0.563667\pi\) | ||||
−0.198685 | + | 0.980063i | \(0.563667\pi\) | |||||||
\(788\) | −1.44806 | −0.0515849 | ||||||||
\(789\) | −7.47741 | −0.266203 | ||||||||
\(790\) | 25.6006 | 0.910829 | ||||||||
\(791\) | −5.06663 | −0.180149 | ||||||||
\(792\) | 0.608143 | 0.0216094 | ||||||||
\(793\) | −12.4617 | −0.442528 | ||||||||
\(794\) | −51.3021 | −1.82064 | ||||||||
\(795\) | −10.3212 | −0.366055 | ||||||||
\(796\) | −0.289216 | −0.0102510 | ||||||||
\(797\) | 11.2450 | 0.398319 | 0.199159 | − | 0.979967i | \(-0.436179\pi\) | ||||
0.199159 | + | 0.979967i | \(0.436179\pi\) | |||||||
\(798\) | −3.53819 | −0.125251 | ||||||||
\(799\) | 5.46557 | 0.193358 | ||||||||
\(800\) | 7.35494 | 0.260036 | ||||||||
\(801\) | −17.8788 | −0.631718 | ||||||||
\(802\) | 47.2751 | 1.66934 | ||||||||
\(803\) | 4.31498 | 0.152272 | ||||||||
\(804\) | 4.88919 | 0.172428 | ||||||||
\(805\) | 5.88511 | 0.207423 | ||||||||
\(806\) | −24.1490 | −0.850613 | ||||||||
\(807\) | 0.577643 | 0.0203340 | ||||||||
\(808\) | −4.56251 | −0.160508 | ||||||||
\(809\) | −12.3035 | −0.432568 | −0.216284 | − | 0.976331i | \(-0.569394\pi\) | ||||
−0.216284 | + | 0.976331i | \(0.569394\pi\) | |||||||
\(810\) | 3.99024 | 0.140203 | ||||||||
\(811\) | 22.7724 | 0.799648 | 0.399824 | − | 0.916592i | \(-0.369071\pi\) | ||||
0.399824 | + | 0.916592i | \(0.369071\pi\) | |||||||
\(812\) | −6.11032 | −0.214430 | ||||||||
\(813\) | −7.51908 | −0.263706 | ||||||||
\(814\) | −1.34138 | −0.0470155 | ||||||||
\(815\) | −15.0074 | −0.525688 | ||||||||
\(816\) | −3.85300 | −0.134882 | ||||||||
\(817\) | 18.5039 | 0.647369 | ||||||||
\(818\) | −17.4371 | −0.609673 | ||||||||
\(819\) | 2.89476 | 0.101151 | ||||||||
\(820\) | −15.2302 | −0.531860 | ||||||||
\(821\) | −3.96660 | −0.138435 | −0.0692176 | − | 0.997602i | \(-0.522050\pi\) | ||||
−0.0692176 | + | 0.997602i | \(0.522050\pi\) | |||||||
\(822\) | 17.0510 | 0.594723 | ||||||||
\(823\) | 47.3231 | 1.64958 | 0.824790 | − | 0.565440i | \(-0.191293\pi\) | ||||
0.824790 | + | 0.565440i | \(0.191293\pi\) | |||||||
\(824\) | 13.9302 | 0.485281 | ||||||||
\(825\) | 0.366698 | 0.0127668 | ||||||||
\(826\) | −23.4180 | −0.814817 | ||||||||
\(827\) | −0.00803216 | −0.000279306 0 | −0.000139653 | − | 1.00000i | \(-0.500044\pi\) | ||||
−0.000139653 | 1.00000i | \(0.500044\pi\) | ||||||||
\(828\) | −20.6264 | −0.716818 | ||||||||
\(829\) | 12.4919 | 0.433860 | 0.216930 | − | 0.976187i | \(-0.430396\pi\) | ||||
0.216930 | + | 0.976187i | \(0.430396\pi\) | |||||||
\(830\) | 12.8127 | 0.444734 | ||||||||
\(831\) | −21.9735 | −0.762251 | ||||||||
\(832\) | −6.44974 | −0.223604 | ||||||||
\(833\) | −0.909012 | −0.0314954 | ||||||||
\(834\) | −37.4046 | −1.29522 | ||||||||
\(835\) | 19.1886 | 0.664049 | ||||||||
\(836\) | −1.30928 | −0.0452823 | ||||||||
\(837\) | 44.7210 | 1.54578 | ||||||||
\(838\) | −10.7764 | −0.372264 | ||||||||
\(839\) | −3.90842 | −0.134933 | −0.0674667 | − | 0.997722i | \(-0.521492\pi\) | ||||
−0.0674667 | + | 0.997722i | \(0.521492\pi\) | |||||||
\(840\) | −0.652353 | −0.0225083 | ||||||||
\(841\) | −14.9101 | −0.514142 | ||||||||
\(842\) | −53.2727 | −1.83590 | ||||||||
\(843\) | 2.21833 | 0.0764035 | ||||||||
\(844\) | −41.2830 | −1.42102 | ||||||||
\(845\) | 11.1924 | 0.385030 | ||||||||
\(846\) | −24.6575 | −0.847742 | ||||||||
\(847\) | 10.8412 | 0.372509 | ||||||||
\(848\) | 51.6553 | 1.77385 | ||||||||
\(849\) | −11.0231 | −0.378312 | ||||||||
\(850\) | 1.73138 | 0.0593860 | ||||||||
\(851\) | −10.4015 | −0.356560 | ||||||||
\(852\) | 3.09474 | 0.106024 | ||||||||
\(853\) | 50.2791 | 1.72152 | 0.860761 | − | 0.509009i | \(-0.169988\pi\) | ||||
0.860761 | + | 0.509009i | \(0.169988\pi\) | |||||||
\(854\) | −17.6542 | −0.604113 | ||||||||
\(855\) | 4.34605 | 0.148632 | ||||||||
\(856\) | −0.0977488 | −0.00334098 | ||||||||
\(857\) | 48.7011 | 1.66360 | 0.831798 | − | 0.555078i | \(-0.187312\pi\) | ||||
0.831798 | + | 0.555078i | \(0.187312\pi\) | |||||||
\(858\) | −0.939044 | −0.0320584 | ||||||||
\(859\) | 27.9745 | 0.954476 | 0.477238 | − | 0.878774i | \(-0.341638\pi\) | ||||
0.477238 | + | 0.878774i | \(0.341638\pi\) | |||||||
\(860\) | −14.9224 | −0.508849 | ||||||||
\(861\) | 8.61027 | 0.293437 | ||||||||
\(862\) | 42.6107 | 1.45133 | ||||||||
\(863\) | −25.2616 | −0.859913 | −0.429957 | − | 0.902850i | \(-0.641471\pi\) | ||||
−0.429957 | + | 0.902850i | \(0.641471\pi\) | |||||||
\(864\) | 34.8793 | 1.18662 | ||||||||
\(865\) | −5.28611 | −0.179733 | ||||||||
\(866\) | 17.1541 | 0.582919 | ||||||||
\(867\) | 14.8844 | 0.505501 | ||||||||
\(868\) | −15.3509 | −0.521042 | ||||||||
\(869\) | −5.35566 | −0.181678 | ||||||||
\(870\) | −6.57961 | −0.223070 | ||||||||
\(871\) | −4.38791 | −0.148679 | ||||||||
\(872\) | −10.2016 | −0.345471 | ||||||||
\(873\) | −18.7129 | −0.633336 | ||||||||
\(874\) | −22.6263 | −0.765346 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 16.2228 | 0.548117 | ||||||||
\(877\) | −13.6423 | −0.460667 | −0.230333 | − | 0.973112i | \(-0.573982\pi\) | ||||
−0.230333 | + | 0.973112i | \(0.573982\pi\) | |||||||
\(878\) | −44.3324 | −1.49614 | ||||||||
\(879\) | 13.0831 | 0.441281 | ||||||||
\(880\) | −1.83524 | −0.0618660 | ||||||||
\(881\) | 46.3001 | 1.55989 | 0.779945 | − | 0.625848i | \(-0.215247\pi\) | ||||
0.779945 | + | 0.625848i | \(0.215247\pi\) | |||||||
\(882\) | 4.10094 | 0.138086 | ||||||||
\(883\) | −3.72856 | −0.125476 | −0.0627379 | − | 0.998030i | \(-0.519983\pi\) | ||||
−0.0627379 | + | 0.998030i | \(0.519983\pi\) | |||||||
\(884\) | −1.98945 | −0.0669124 | ||||||||
\(885\) | −11.3148 | −0.380345 | ||||||||
\(886\) | 17.5019 | 0.587988 | ||||||||
\(887\) | −50.5947 | −1.69880 | −0.849402 | − | 0.527746i | \(-0.823037\pi\) | ||||
−0.849402 | + | 0.527746i | \(0.823037\pi\) | |||||||
\(888\) | 1.15299 | 0.0386918 | ||||||||
\(889\) | −9.07603 | −0.304400 | ||||||||
\(890\) | 15.8163 | 0.530162 | ||||||||
\(891\) | −0.834761 | −0.0279655 | ||||||||
\(892\) | 29.2733 | 0.980144 | ||||||||
\(893\) | −12.1367 | −0.406140 | ||||||||
\(894\) | −16.1830 | −0.541242 | ||||||||
\(895\) | 6.54213 | 0.218679 | ||||||||
\(896\) | 5.57269 | 0.186171 | ||||||||
\(897\) | −7.28166 | −0.243128 | ||||||||
\(898\) | 3.20581 | 0.106979 | ||||||||
\(899\) | 35.3978 | 1.18058 | ||||||||
\(900\) | −3.50485 | −0.116828 | ||||||||
\(901\) | 10.1948 | 0.339637 | ||||||||
\(902\) | 7.10075 | 0.236429 | ||||||||
\(903\) | 8.43626 | 0.280741 | ||||||||
\(904\) | 3.59153 | 0.119453 | ||||||||
\(905\) | −3.34882 | −0.111319 | ||||||||
\(906\) | −15.4096 | −0.511949 | ||||||||
\(907\) | −14.2959 | −0.474686 | −0.237343 | − | 0.971426i | \(-0.576277\pi\) | ||||
−0.237343 | + | 0.971426i | \(0.576277\pi\) | |||||||
\(908\) | −14.4712 | −0.480245 | ||||||||
\(909\) | 13.8581 | 0.459643 | ||||||||
\(910\) | −2.56081 | −0.0848900 | ||||||||
\(911\) | −47.5830 | −1.57650 | −0.788248 | − | 0.615358i | \(-0.789012\pi\) | ||||
−0.788248 | + | 0.615358i | \(0.789012\pi\) | |||||||
\(912\) | 8.55589 | 0.283314 | ||||||||
\(913\) | −2.68042 | −0.0887089 | ||||||||
\(914\) | −12.2675 | −0.405772 | ||||||||
\(915\) | −8.52994 | −0.281991 | ||||||||
\(916\) | 1.62783 | 0.0537852 | ||||||||
\(917\) | −19.6266 | −0.648129 | ||||||||
\(918\) | 8.21074 | 0.270995 | ||||||||
\(919\) | 38.1996 | 1.26009 | 0.630044 | − | 0.776559i | \(-0.283037\pi\) | ||||
0.630044 | + | 0.776559i | \(0.283037\pi\) | |||||||
\(920\) | −4.17172 | −0.137537 | ||||||||
\(921\) | −14.0567 | −0.463184 | ||||||||
\(922\) | 6.38599 | 0.210311 | ||||||||
\(923\) | −2.77745 | −0.0914207 | ||||||||
\(924\) | −0.596924 | −0.0196374 | ||||||||
\(925\) | −1.76743 | −0.0581128 | ||||||||
\(926\) | −74.5010 | −2.44825 | ||||||||
\(927\) | −42.3113 | −1.38968 | ||||||||
\(928\) | 27.6079 | 0.906272 | ||||||||
\(929\) | 36.5202 | 1.19819 | 0.599095 | − | 0.800678i | \(-0.295527\pi\) | ||||
0.599095 | + | 0.800678i | \(0.295527\pi\) | |||||||
\(930\) | −16.5298 | −0.542035 | ||||||||
\(931\) | 2.01853 | 0.0661547 | ||||||||
\(932\) | 5.94146 | 0.194619 | ||||||||
\(933\) | 11.3355 | 0.371107 | ||||||||
\(934\) | −31.5804 | −1.03334 | ||||||||
\(935\) | −0.362206 | −0.0118454 | ||||||||
\(936\) | −2.05198 | −0.0670710 | ||||||||
\(937\) | 21.2960 | 0.695709 | 0.347855 | − | 0.937548i | \(-0.386910\pi\) | ||||
0.347855 | + | 0.937548i | \(0.386910\pi\) | |||||||
\(938\) | −6.21625 | −0.202968 | ||||||||
\(939\) | 0.208092 | 0.00679084 | ||||||||
\(940\) | 9.78760 | 0.319236 | ||||||||
\(941\) | 5.09091 | 0.165959 | 0.0829794 | − | 0.996551i | \(-0.473556\pi\) | ||||
0.0829794 | + | 0.996551i | \(0.473556\pi\) | |||||||
\(942\) | −38.5687 | −1.25664 | ||||||||
\(943\) | 55.0616 | 1.79305 | ||||||||
\(944\) | 56.6283 | 1.84310 | ||||||||
\(945\) | 4.74230 | 0.154267 | ||||||||
\(946\) | 6.95725 | 0.226200 | ||||||||
\(947\) | −6.81255 | −0.221378 | −0.110689 | − | 0.993855i | \(-0.535306\pi\) | ||||
−0.110689 | + | 0.993855i | \(0.535306\pi\) | |||||||
\(948\) | −20.1354 | −0.653966 | ||||||||
\(949\) | −14.5595 | −0.472621 | ||||||||
\(950\) | −3.84467 | −0.124738 | ||||||||
\(951\) | 6.91319 | 0.224175 | ||||||||
\(952\) | 0.644361 | 0.0208839 | ||||||||
\(953\) | 7.53218 | 0.243991 | 0.121996 | − | 0.992531i | \(-0.461071\pi\) | ||||
0.121996 | + | 0.992531i | \(0.461071\pi\) | |||||||
\(954\) | −45.9929 | −1.48907 | ||||||||
\(955\) | −2.04324 | −0.0661178 | ||||||||
\(956\) | 26.3313 | 0.851617 | ||||||||
\(957\) | 1.37646 | 0.0444945 | ||||||||
\(958\) | −59.0362 | −1.90737 | ||||||||
\(959\) | −9.72757 | −0.314120 | ||||||||
\(960\) | −4.41480 | −0.142487 | ||||||||
\(961\) | 57.9294 | 1.86869 | ||||||||
\(962\) | 4.52606 | 0.145926 | ||||||||
\(963\) | 0.296900 | 0.00956748 | ||||||||
\(964\) | 12.5531 | 0.404309 | ||||||||
\(965\) | −25.7380 | −0.828535 | ||||||||
\(966\) | −10.3158 | −0.331904 | ||||||||
\(967\) | −37.9642 | −1.22085 | −0.610424 | − | 0.792075i | \(-0.709001\pi\) | ||||
−0.610424 | + | 0.792075i | \(0.709001\pi\) | |||||||
\(968\) | −7.68490 | −0.247002 | ||||||||
\(969\) | 1.68860 | 0.0542457 | ||||||||
\(970\) | 16.5541 | 0.531521 | ||||||||
\(971\) | −38.0010 | −1.21951 | −0.609756 | − | 0.792590i | \(-0.708732\pi\) | ||||
−0.609756 | + | 0.792590i | \(0.708732\pi\) | |||||||
\(972\) | −26.2974 | −0.843490 | ||||||||
\(973\) | 21.3393 | 0.684105 | ||||||||
\(974\) | −17.7967 | −0.570242 | ||||||||
\(975\) | −1.23730 | −0.0396254 | ||||||||
\(976\) | 42.6905 | 1.36649 | ||||||||
\(977\) | 5.03368 | 0.161042 | 0.0805208 | − | 0.996753i | \(-0.474342\pi\) | ||||
0.0805208 | + | 0.996753i | \(0.474342\pi\) | |||||||
\(978\) | 26.3059 | 0.841169 | ||||||||
\(979\) | −3.30877 | −0.105749 | ||||||||
\(980\) | −1.62783 | −0.0519993 | ||||||||
\(981\) | 30.9862 | 0.989315 | ||||||||
\(982\) | 1.12138 | 0.0357848 | ||||||||
\(983\) | 9.52341 | 0.303749 | 0.151875 | − | 0.988400i | \(-0.451469\pi\) | ||||
0.151875 | + | 0.988400i | \(0.451469\pi\) | |||||||
\(984\) | −6.10347 | −0.194572 | ||||||||
\(985\) | 0.889561 | 0.0283438 | ||||||||
\(986\) | 6.49901 | 0.206970 | ||||||||
\(987\) | −5.53335 | −0.176129 | ||||||||
\(988\) | 4.41773 | 0.140547 | ||||||||
\(989\) | 53.9489 | 1.71547 | ||||||||
\(990\) | 1.63406 | 0.0519340 | ||||||||
\(991\) | 22.4828 | 0.714190 | 0.357095 | − | 0.934068i | \(-0.383767\pi\) | ||||
0.357095 | + | 0.934068i | \(0.383767\pi\) | |||||||
\(992\) | 69.3588 | 2.20214 | ||||||||
\(993\) | 17.0633 | 0.541487 | ||||||||
\(994\) | −3.93474 | −0.124802 | ||||||||
\(995\) | 0.177669 | 0.00563249 | ||||||||
\(996\) | −10.0774 | −0.319315 | ||||||||
\(997\) | 16.5381 | 0.523766 | 0.261883 | − | 0.965100i | \(-0.415657\pi\) | ||||
0.261883 | + | 0.965100i | \(0.415657\pi\) | |||||||
\(998\) | −67.1398 | −2.12527 | ||||||||
\(999\) | −8.38170 | −0.265185 |
(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 | 8015.2.a.l.1.12 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.12 | ✓ | 62 | 1.1 | even | 1 | trivial |