Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(1469,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.1469");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1469.10 | ||
Character | \(\chi\) | \(=\) | 1470.1469 |
Dual form | 1470.2.d.h.1469.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −1.03805 | + | 1.38652i | −0.599319 | + | 0.800510i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.98784 | − | 1.02395i | −0.888991 | − | 0.457925i | ||||
\(6\) | −1.03805 | + | 1.38652i | −0.423783 | + | 0.566046i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.844897 | − | 2.87857i | −0.281632 | − | 0.959522i | ||||
\(10\) | −1.98784 | − | 1.02395i | −0.628612 | − | 0.323802i | ||||
\(11\) | − | 1.27840i | − | 0.385451i | −0.981253 | − | 0.192726i | \(-0.938267\pi\) | ||
0.981253 | − | 0.192726i | \(-0.0617328\pi\) | |||||||
\(12\) | −1.03805 | + | 1.38652i | −0.299660 | + | 0.400255i | ||||
\(13\) | 1.32254 | 0.366805 | 0.183403 | − | 0.983038i | \(-0.441289\pi\) | ||||
0.183403 | + | 0.983038i | \(0.441289\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.48322 | − | 1.69328i | 0.899363 | − | 0.437203i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.76944i | 1.39929i | 0.714488 | + | 0.699647i | \(0.246660\pi\) | ||||
−0.714488 | + | 0.699647i | \(0.753340\pi\) | |||||||
\(18\) | −0.844897 | − | 2.87857i | −0.199144 | − | 0.678485i | ||||
\(19\) | 2.44195i | 0.560221i | 0.959968 | + | 0.280111i | \(0.0903711\pi\) | ||||
−0.959968 | + | 0.280111i | \(0.909629\pi\) | |||||||
\(20\) | −1.98784 | − | 1.02395i | −0.444496 | − | 0.228962i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 1.27840i | − | 0.272555i | ||||||
\(23\) | 0.680020 | 0.141794 | 0.0708969 | − | 0.997484i | \(-0.477414\pi\) | ||||
0.0708969 | + | 0.997484i | \(0.477414\pi\) | |||||||
\(24\) | −1.03805 | + | 1.38652i | −0.211891 | + | 0.283023i | ||||
\(25\) | 2.90305 | + | 4.07091i | 0.580610 | + | 0.814182i | ||||
\(26\) | 1.32254 | 0.259371 | ||||||||
\(27\) | 4.86825 | + | 1.81663i | 0.936895 | + | 0.349611i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.12676i | 1.13771i | 0.822437 | + | 0.568856i | \(0.192614\pi\) | ||||
−0.822437 | + | 0.568856i | \(0.807386\pi\) | |||||||
\(30\) | 3.48322 | − | 1.69328i | 0.635946 | − | 0.309149i | ||||
\(31\) | 6.94293i | 1.24699i | 0.781829 | + | 0.623493i | \(0.214287\pi\) | ||||
−0.781829 | + | 0.623493i | \(0.785713\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.77253 | + | 1.32704i | 0.308558 | + | 0.231009i | ||||
\(34\) | 5.76944i | 0.989451i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.844897 | − | 2.87857i | −0.140816 | − | 0.479761i | ||||
\(37\) | 4.67531i | 0.768616i | 0.923205 | + | 0.384308i | \(0.125560\pi\) | ||||
−0.923205 | + | 0.384308i | \(0.874440\pi\) | |||||||
\(38\) | 2.44195i | 0.396136i | ||||||||
\(39\) | −1.37286 | + | 1.83373i | −0.219834 | + | 0.293631i | ||||
\(40\) | −1.98784 | − | 1.02395i | −0.314306 | − | 0.161901i | ||||
\(41\) | −12.3285 | −1.92538 | −0.962691 | − | 0.270603i | \(-0.912777\pi\) | ||||
−0.962691 | + | 0.270603i | \(0.912777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.87753i | 0.286321i | 0.989700 | + | 0.143160i | \(0.0457265\pi\) | ||||
−0.989700 | + | 0.143160i | \(0.954274\pi\) | |||||||
\(44\) | − | 1.27840i | − | 0.192726i | ||||||
\(45\) | −1.26799 | + | 6.58728i | −0.189020 | + | 0.981973i | ||||
\(46\) | 0.680020 | 0.100263 | ||||||||
\(47\) | − | 7.97726i | − | 1.16360i | −0.813331 | − | 0.581802i | \(-0.802348\pi\) | ||
0.813331 | − | 0.581802i | \(-0.197652\pi\) | |||||||
\(48\) | −1.03805 | + | 1.38652i | −0.149830 | + | 0.200127i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.90305 | + | 4.07091i | 0.410553 | + | 0.575713i | ||||
\(51\) | −7.99947 | − | 5.98898i | −1.12015 | − | 0.838625i | ||||
\(52\) | 1.32254 | 0.183403 | ||||||||
\(53\) | 6.98682 | 0.959713 | 0.479857 | − | 0.877347i | \(-0.340689\pi\) | ||||
0.479857 | + | 0.877347i | \(0.340689\pi\) | |||||||
\(54\) | 4.86825 | + | 1.81663i | 0.662485 | + | 0.247212i | ||||
\(55\) | −1.30902 | + | 2.54126i | −0.176508 | + | 0.342663i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.38582 | − | 2.53487i | −0.448463 | − | 0.335751i | ||||
\(58\) | 6.12676i | 0.804483i | ||||||||
\(59\) | −9.65619 | −1.25713 | −0.628564 | − | 0.777758i | \(-0.716357\pi\) | ||||
−0.628564 | + | 0.777758i | \(0.716357\pi\) | |||||||
\(60\) | 3.48322 | − | 1.69328i | 0.449681 | − | 0.218602i | ||||
\(61\) | − | 4.22958i | − | 0.541542i | −0.962644 | − | 0.270771i | \(-0.912721\pi\) | ||
0.962644 | − | 0.270771i | \(-0.0872786\pi\) | |||||||
\(62\) | 6.94293i | 0.881753i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.62899 | − | 1.35421i | −0.326087 | − | 0.167969i | ||||
\(66\) | 1.77253 | + | 1.32704i | 0.218183 | + | 0.163348i | ||||
\(67\) | 12.9467i | 1.58169i | 0.612014 | + | 0.790847i | \(0.290359\pi\) | ||||
−0.612014 | + | 0.790847i | \(0.709641\pi\) | |||||||
\(68\) | 5.76944i | 0.699647i | ||||||||
\(69\) | −0.705896 | + | 0.942863i | −0.0849798 | + | 0.113507i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.09896i | 0.605135i | 0.953128 | + | 0.302567i | \(0.0978437\pi\) | ||||
−0.953128 | + | 0.302567i | \(0.902156\pi\) | |||||||
\(72\) | −0.844897 | − | 2.87857i | −0.0995721 | − | 0.339242i | ||||
\(73\) | 16.4851 | 1.92944 | 0.964720 | − | 0.263277i | \(-0.0848035\pi\) | ||||
0.964720 | + | 0.263277i | \(0.0848035\pi\) | |||||||
\(74\) | 4.67531i | 0.543493i | ||||||||
\(75\) | −8.65793 | − | 0.200664i | −0.999732 | − | 0.0231707i | ||||
\(76\) | 2.44195i | 0.280111i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.37286 | + | 1.83373i | −0.155446 | + | 0.207629i | ||||
\(79\) | −15.5370 | −1.74805 | −0.874027 | − | 0.485877i | \(-0.838500\pi\) | ||||
−0.874027 | + | 0.485877i | \(0.838500\pi\) | |||||||
\(80\) | −1.98784 | − | 1.02395i | −0.222248 | − | 0.114481i | ||||
\(81\) | −7.57230 | + | 4.86419i | −0.841366 | + | 0.540465i | ||||
\(82\) | −12.3285 | −1.36145 | ||||||||
\(83\) | 3.33498i | 0.366061i | 0.983107 | + | 0.183031i | \(0.0585907\pi\) | ||||
−0.983107 | + | 0.183031i | \(0.941409\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.90762 | − | 11.4688i | 0.640772 | − | 1.24396i | ||||
\(86\) | 1.87753i | 0.202459i | ||||||||
\(87\) | −8.49490 | − | 6.35990i | −0.910749 | − | 0.681852i | ||||
\(88\) | − | 1.27840i | − | 0.136278i | ||||||
\(89\) | 12.7400 | 1.35043 | 0.675217 | − | 0.737619i | \(-0.264050\pi\) | ||||
0.675217 | + | 0.737619i | \(0.264050\pi\) | |||||||
\(90\) | −1.26799 | + | 6.58728i | −0.133657 | + | 0.694360i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.680020 | 0.0708969 | ||||||||
\(93\) | −9.62654 | − | 7.20712i | −0.998225 | − | 0.747343i | ||||
\(94\) | − | 7.97726i | − | 0.822792i | ||||||
\(95\) | 2.50043 | − | 4.85421i | 0.256539 | − | 0.498031i | ||||
\(96\) | −1.03805 | + | 1.38652i | −0.105946 | + | 0.141512i | ||||
\(97\) | 2.90682 | 0.295142 | 0.147571 | − | 0.989051i | \(-0.452854\pi\) | ||||
0.147571 | + | 0.989051i | \(0.452854\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.67995 | + | 1.08011i | −0.369849 | + | 0.108556i | ||||
\(100\) | 2.90305 | + | 4.07091i | 0.290305 | + | 0.407091i | ||||
\(101\) | −9.02428 | −0.897949 | −0.448975 | − | 0.893544i | \(-0.648211\pi\) | ||||
−0.448975 | + | 0.893544i | \(0.648211\pi\) | |||||||
\(102\) | −7.99947 | − | 5.98898i | −0.792065 | − | 0.592997i | ||||
\(103\) | 17.4764 | 1.72200 | 0.861002 | − | 0.508602i | \(-0.169838\pi\) | ||||
0.861002 | + | 0.508602i | \(0.169838\pi\) | |||||||
\(104\) | 1.32254 | 0.129685 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.98682 | 0.678620 | ||||||||
\(107\) | −12.1115 | −1.17087 | −0.585433 | − | 0.810721i | \(-0.699075\pi\) | ||||
−0.585433 | + | 0.810721i | \(0.699075\pi\) | |||||||
\(108\) | 4.86825 | + | 1.81663i | 0.468448 | + | 0.174805i | ||||
\(109\) | 11.1753 | 1.07040 | 0.535199 | − | 0.844726i | \(-0.320237\pi\) | ||||
0.535199 | + | 0.844726i | \(0.320237\pi\) | |||||||
\(110\) | −1.30902 | + | 2.54126i | −0.124810 | + | 0.242299i | ||||
\(111\) | −6.48242 | − | 4.85321i | −0.615284 | − | 0.460646i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.00477454 | −0.000449151 | −0.000224575 | − | 1.00000i | \(-0.500071\pi\) | ||||
−0.000224575 | 1.00000i | \(0.500071\pi\) | ||||||||
\(114\) | −3.38582 | − | 2.53487i | −0.317111 | − | 0.237412i | ||||
\(115\) | −1.35177 | − | 0.696306i | −0.126053 | − | 0.0649309i | ||||
\(116\) | 6.12676i | 0.568856i | ||||||||
\(117\) | −1.11741 | − | 3.80701i | −0.103304 | − | 0.351958i | ||||
\(118\) | −9.65619 | −0.888924 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.48322 | − | 1.69328i | 0.317973 | − | 0.154575i | ||||
\(121\) | 9.36570 | 0.851427 | ||||||||
\(122\) | − | 4.22958i | − | 0.382928i | ||||||
\(123\) | 12.7976 | − | 17.0937i | 1.15392 | − | 1.54129i | ||||
\(124\) | 6.94293i | 0.623493i | ||||||||
\(125\) | −1.60240 | − | 11.0649i | −0.143323 | − | 0.989676i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.34269i | 0.651558i | 0.945446 | + | 0.325779i | \(0.105627\pi\) | ||||
−0.945446 | + | 0.325779i | \(0.894373\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −2.60324 | − | 1.94897i | −0.229203 | − | 0.171598i | ||||
\(130\) | −2.62899 | − | 1.35421i | −0.230578 | − | 0.118772i | ||||
\(131\) | −0.0771448 | −0.00674018 | −0.00337009 | − | 0.999994i | \(-0.501073\pi\) | ||||
−0.00337009 | + | 0.999994i | \(0.501073\pi\) | |||||||
\(132\) | 1.77253 | + | 1.32704i | 0.154279 | + | 0.115504i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 12.9467i | 1.11843i | ||||||||
\(135\) | −7.81718 | − | 8.59603i | −0.672796 | − | 0.739828i | ||||
\(136\) | 5.76944i | 0.494725i | ||||||||
\(137\) | −11.7831 | −1.00670 | −0.503351 | − | 0.864082i | \(-0.667900\pi\) | ||||
−0.503351 | + | 0.864082i | \(0.667900\pi\) | |||||||
\(138\) | −0.705896 | + | 0.942863i | −0.0600898 | + | 0.0802619i | ||||
\(139\) | 15.9840i | 1.35574i | 0.735181 | + | 0.677871i | \(0.237097\pi\) | ||||
−0.735181 | + | 0.677871i | \(0.762903\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.0607 | + | 8.28081i | 0.931476 | + | 0.697370i | ||||
\(142\) | 5.09896i | 0.427895i | ||||||||
\(143\) | − | 1.69073i | − | 0.141386i | ||||||
\(144\) | −0.844897 | − | 2.87857i | −0.0704081 | − | 0.239881i | ||||
\(145\) | 6.27350 | − | 12.1790i | 0.520986 | − | 1.01141i | ||||
\(146\) | 16.4851 | 1.36432 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.67531i | 0.384308i | ||||||||
\(149\) | 20.2680i | 1.66042i | 0.557449 | + | 0.830211i | \(0.311780\pi\) | ||||
−0.557449 | + | 0.830211i | \(0.688220\pi\) | |||||||
\(150\) | −8.65793 | − | 0.200664i | −0.706917 | − | 0.0163842i | ||||
\(151\) | 10.0657 | 0.819135 | 0.409568 | − | 0.912280i | \(-0.365680\pi\) | ||||
0.409568 | + | 0.912280i | \(0.365680\pi\) | |||||||
\(152\) | 2.44195i | 0.198068i | ||||||||
\(153\) | 16.6077 | − | 4.87459i | 1.34265 | − | 0.394087i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.10922 | − | 13.8015i | 0.571026 | − | 1.10856i | ||||
\(156\) | −1.37286 | + | 1.83373i | −0.109917 | + | 0.146816i | ||||
\(157\) | 9.84780 | 0.785940 | 0.392970 | − | 0.919551i | \(-0.371448\pi\) | ||||
0.392970 | + | 0.919551i | \(0.371448\pi\) | |||||||
\(158\) | −15.5370 | −1.23606 | ||||||||
\(159\) | −7.25268 | + | 9.68739i | −0.575175 | + | 0.768260i | ||||
\(160\) | −1.98784 | − | 1.02395i | −0.157153 | − | 0.0809504i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −7.57230 | + | 4.86419i | −0.594936 | + | 0.382167i | ||||
\(163\) | − | 11.4412i | − | 0.896147i | −0.893997 | − | 0.448073i | \(-0.852110\pi\) | ||
0.893997 | − | 0.448073i | \(-0.147890\pi\) | |||||||
\(164\) | −12.3285 | −0.962691 | ||||||||
\(165\) | −2.16469 | − | 4.45294i | −0.168521 | − | 0.346661i | ||||
\(166\) | 3.33498i | 0.258844i | ||||||||
\(167\) | 14.1922i | 1.09823i | 0.835748 | + | 0.549114i | \(0.185035\pi\) | ||||
−0.835748 | + | 0.549114i | \(0.814965\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.2509 | −0.865454 | ||||||||
\(170\) | 5.90762 | − | 11.4688i | 0.453094 | − | 0.879613i | ||||
\(171\) | 7.02931 | − | 2.06319i | 0.537545 | − | 0.157776i | ||||
\(172\) | 1.87753i | 0.143160i | ||||||||
\(173\) | − | 0.985415i | − | 0.0749197i | −0.999298 | − | 0.0374599i | \(-0.988073\pi\) | ||
0.999298 | − | 0.0374599i | \(-0.0119266\pi\) | |||||||
\(174\) | −8.49490 | − | 6.35990i | −0.643997 | − | 0.482142i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 1.27840i | − | 0.0963628i | ||||||
\(177\) | 10.0236 | − | 13.3885i | 0.753422 | − | 1.00634i | ||||
\(178\) | 12.7400 | 0.954901 | ||||||||
\(179\) | − | 10.2949i | − | 0.769478i | −0.923025 | − | 0.384739i | \(-0.874291\pi\) | ||
0.923025 | − | 0.384739i | \(-0.125709\pi\) | |||||||
\(180\) | −1.26799 | + | 6.58728i | −0.0945101 | + | 0.490987i | ||||
\(181\) | − | 5.05282i | − | 0.375573i | −0.982210 | − | 0.187787i | \(-0.939869\pi\) | ||
0.982210 | − | 0.187787i | \(-0.0601313\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.86441 | + | 4.39052i | 0.433510 | + | 0.324557i | ||||
\(184\) | 0.680020 | 0.0501317 | ||||||||
\(185\) | 4.78728 | − | 9.29378i | 0.351968 | − | 0.683292i | ||||
\(186\) | −9.62654 | − | 7.20712i | −0.705852 | − | 0.528452i | ||||
\(187\) | 7.37564 | 0.539360 | ||||||||
\(188\) | − | 7.97726i | − | 0.581802i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.50043 | − | 4.85421i | 0.181400 | − | 0.352161i | ||||
\(191\) | − | 9.31528i | − | 0.674030i | −0.941499 | − | 0.337015i | \(-0.890583\pi\) | ||
0.941499 | − | 0.337015i | \(-0.109417\pi\) | |||||||
\(192\) | −1.03805 | + | 1.38652i | −0.0749149 | + | 0.100064i | ||||
\(193\) | − | 2.53974i | − | 0.182814i | −0.995814 | − | 0.0914072i | \(-0.970864\pi\) | ||
0.995814 | − | 0.0914072i | \(-0.0291365\pi\) | |||||||
\(194\) | 2.90682 | 0.208697 | ||||||||
\(195\) | 4.60668 | − | 2.23942i | 0.329891 | − | 0.160368i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.65660 | −0.616757 | −0.308379 | − | 0.951264i | \(-0.599786\pi\) | ||||
−0.308379 | + | 0.951264i | \(0.599786\pi\) | |||||||
\(198\) | −3.67995 | + | 1.08011i | −0.261523 | + | 0.0767604i | ||||
\(199\) | − | 27.9233i | − | 1.97943i | −0.143062 | − | 0.989714i | \(-0.545695\pi\) | ||
0.143062 | − | 0.989714i | \(-0.454305\pi\) | |||||||
\(200\) | 2.90305 | + | 4.07091i | 0.205277 | + | 0.287857i | ||||
\(201\) | −17.9509 | − | 13.4394i | −1.26616 | − | 0.947939i | ||||
\(202\) | −9.02428 | −0.634946 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −7.99947 | − | 5.98898i | −0.560075 | − | 0.419312i | ||||
\(205\) | 24.5071 | + | 12.6237i | 1.71165 | + | 0.881680i | ||||
\(206\) | 17.4764 | 1.21764 | ||||||||
\(207\) | −0.574547 | − | 1.95748i | −0.0399338 | − | 0.136054i | ||||
\(208\) | 1.32254 | 0.0917013 | ||||||||
\(209\) | 3.12178 | 0.215938 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.5665 | −0.865116 | −0.432558 | − | 0.901606i | \(-0.642389\pi\) | ||||
−0.432558 | + | 0.901606i | \(0.642389\pi\) | |||||||
\(212\) | 6.98682 | 0.479857 | ||||||||
\(213\) | −7.06983 | − | 5.29298i | −0.484416 | − | 0.362669i | ||||
\(214\) | −12.1115 | −0.827927 | ||||||||
\(215\) | 1.92250 | − | 3.73224i | 0.131113 | − | 0.254537i | ||||
\(216\) | 4.86825 | + | 1.81663i | 0.331242 | + | 0.123606i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 11.1753 | 0.756886 | ||||||||
\(219\) | −17.1124 | + | 22.8570i | −1.15635 | + | 1.54454i | ||||
\(220\) | −1.30902 | + | 2.54126i | −0.0882538 | + | 0.171331i | ||||
\(221\) | 7.63029i | 0.513269i | ||||||||
\(222\) | −6.48242 | − | 4.85321i | −0.435072 | − | 0.325726i | ||||
\(223\) | −13.1623 | −0.881415 | −0.440708 | − | 0.897651i | \(-0.645272\pi\) | ||||
−0.440708 | + | 0.897651i | \(0.645272\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.26560 | − | 11.7961i | 0.617707 | − | 0.786408i | ||||
\(226\) | −0.00477454 | −0.000317598 | ||||||||
\(227\) | 15.5346i | 1.03107i | 0.856870 | + | 0.515533i | \(0.172406\pi\) | ||||
−0.856870 | + | 0.515533i | \(0.827594\pi\) | |||||||
\(228\) | −3.38582 | − | 2.53487i | −0.224231 | − | 0.167876i | ||||
\(229\) | − | 4.02816i | − | 0.266188i | −0.991103 | − | 0.133094i | \(-0.957509\pi\) | ||
0.991103 | − | 0.133094i | \(-0.0424912\pi\) | |||||||
\(230\) | −1.35177 | − | 0.696306i | −0.0891333 | − | 0.0459131i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.12676i | 0.402242i | ||||||||
\(233\) | 28.2529 | 1.85091 | 0.925454 | − | 0.378861i | \(-0.123684\pi\) | ||||
0.925454 | + | 0.378861i | \(0.123684\pi\) | |||||||
\(234\) | −1.11741 | − | 3.80701i | −0.0730472 | − | 0.248872i | ||||
\(235\) | −8.16832 | + | 15.8576i | −0.532843 | + | 1.03443i | ||||
\(236\) | −9.65619 | −0.628564 | ||||||||
\(237\) | 16.1283 | − | 21.5425i | 1.04764 | − | 1.39933i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.6358i | − | 0.687973i | −0.938975 | − | 0.343987i | \(-0.888223\pi\) | ||
0.938975 | − | 0.343987i | \(-0.111777\pi\) | |||||||
\(240\) | 3.48322 | − | 1.69328i | 0.224841 | − | 0.109301i | ||||
\(241\) | − | 3.42344i | − | 0.220523i | −0.993903 | − | 0.110262i | \(-0.964831\pi\) | ||
0.993903 | − | 0.110262i | \(-0.0351688\pi\) | |||||||
\(242\) | 9.36570 | 0.602050 | ||||||||
\(243\) | 1.11612 | − | 15.5484i | 0.0715994 | − | 0.997433i | ||||
\(244\) | − | 4.22958i | − | 0.270771i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 12.7976 | − | 17.0937i | 0.815944 | − | 1.08985i | ||||
\(247\) | 3.22956i | 0.205492i | ||||||||
\(248\) | 6.94293i | 0.440876i | ||||||||
\(249\) | −4.62402 | − | 3.46188i | −0.293036 | − | 0.219388i | ||||
\(250\) | −1.60240 | − | 11.0649i | −0.101345 | − | 0.699807i | ||||
\(251\) | 1.41048 | 0.0890287 | 0.0445143 | − | 0.999009i | \(-0.485826\pi\) | ||||
0.0445143 | + | 0.999009i | \(0.485826\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 0.869335i | − | 0.0546547i | ||||||
\(254\) | 7.34269i | 0.460721i | ||||||||
\(255\) | 9.76928 | + | 20.0962i | 0.611776 | + | 1.25847i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 17.8668i | − | 1.11450i | −0.830345 | − | 0.557249i | \(-0.811857\pi\) | ||
0.830345 | − | 0.557249i | \(-0.188143\pi\) | |||||||
\(258\) | −2.60324 | − | 1.94897i | −0.162071 | − | 0.121338i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.62899 | − | 1.35421i | −0.163043 | − | 0.0839846i | ||||
\(261\) | 17.6363 | − | 5.17648i | 1.09166 | − | 0.320416i | ||||
\(262\) | −0.0771448 | −0.00476602 | ||||||||
\(263\) | 1.07247 | 0.0661314 | 0.0330657 | − | 0.999453i | \(-0.489473\pi\) | ||||
0.0330657 | + | 0.999453i | \(0.489473\pi\) | |||||||
\(264\) | 1.77253 | + | 1.32704i | 0.109092 | + | 0.0816738i | ||||
\(265\) | −13.8887 | − | 7.15416i | −0.853176 | − | 0.439476i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.2247 | + | 17.6643i | −0.809341 | + | 1.08104i | ||||
\(268\) | 12.9467i | 0.790847i | ||||||||
\(269\) | 10.3792 | 0.632832 | 0.316416 | − | 0.948621i | \(-0.397520\pi\) | ||||
0.316416 | + | 0.948621i | \(0.397520\pi\) | |||||||
\(270\) | −7.81718 | − | 8.59603i | −0.475739 | − | 0.523138i | ||||
\(271\) | 9.90724i | 0.601822i | 0.953652 | + | 0.300911i | \(0.0972907\pi\) | ||||
−0.953652 | + | 0.300911i | \(0.902709\pi\) | |||||||
\(272\) | 5.76944i | 0.349824i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.7831 | −0.711846 | ||||||||
\(275\) | 5.20424 | − | 3.71125i | 0.313827 | − | 0.223797i | ||||
\(276\) | −0.705896 | + | 0.942863i | −0.0424899 | + | 0.0567537i | ||||
\(277\) | 18.3865i | 1.10474i | 0.833600 | + | 0.552368i | \(0.186276\pi\) | ||||
−0.833600 | + | 0.552368i | \(0.813724\pi\) | |||||||
\(278\) | 15.9840i | 0.958655i | ||||||||
\(279\) | 19.9857 | − | 5.86606i | 1.19651 | − | 0.351192i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 19.0144i | − | 1.13431i | −0.823612 | − | 0.567153i | \(-0.808045\pi\) | ||
0.823612 | − | 0.567153i | \(-0.191955\pi\) | |||||||
\(282\) | 11.0607 | + | 8.28081i | 0.658653 | + | 0.493115i | ||||
\(283\) | −18.6645 | −1.10949 | −0.554744 | − | 0.832021i | \(-0.687184\pi\) | ||||
−0.554744 | + | 0.832021i | \(0.687184\pi\) | |||||||
\(284\) | 5.09896i | 0.302567i | ||||||||
\(285\) | 4.13490 | + | 8.50583i | 0.244930 | + | 0.503842i | ||||
\(286\) | − | 1.69073i | − | 0.0999747i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.844897 | − | 2.87857i | −0.0497861 | − | 0.169621i | ||||
\(289\) | −16.2864 | −0.958026 | ||||||||
\(290\) | 6.27350 | − | 12.1790i | 0.368393 | − | 0.715178i | ||||
\(291\) | −3.01743 | + | 4.03037i | −0.176885 | + | 0.236264i | ||||
\(292\) | 16.4851 | 0.964720 | ||||||||
\(293\) | − | 3.41725i | − | 0.199638i | −0.995006 | − | 0.0998189i | \(-0.968174\pi\) | ||
0.995006 | − | 0.0998189i | \(-0.0318264\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.1950 | + | 9.88746i | 1.11758 | + | 0.575670i | ||||
\(296\) | 4.67531i | 0.271747i | ||||||||
\(297\) | 2.32238 | − | 6.22356i | 0.134758 | − | 0.361127i | ||||
\(298\) | 20.2680i | 1.17410i | ||||||||
\(299\) | 0.899350 | 0.0520108 | ||||||||
\(300\) | −8.65793 | − | 0.200664i | −0.499866 | − | 0.0115854i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 10.0657 | 0.579216 | ||||||||
\(303\) | 9.36767 | − | 12.5124i | 0.538158 | − | 0.718817i | ||||
\(304\) | 2.44195i | 0.140055i | ||||||||
\(305\) | −4.33088 | + | 8.40775i | −0.247985 | + | 0.481426i | ||||
\(306\) | 16.6077 | − | 4.87459i | 0.949400 | − | 0.278661i | ||||
\(307\) | −13.3096 | −0.759620 | −0.379810 | − | 0.925064i | \(-0.624011\pi\) | ||||
−0.379810 | + | 0.925064i | \(0.624011\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.1414 | + | 24.2315i | −1.03203 | + | 1.37848i | ||||
\(310\) | 7.10922 | − | 13.8015i | 0.403776 | − | 0.783870i | ||||
\(311\) | 11.7713 | 0.667487 | 0.333743 | − | 0.942664i | \(-0.391688\pi\) | ||||
0.333743 | + | 0.942664i | \(0.391688\pi\) | |||||||
\(312\) | −1.37286 | + | 1.83373i | −0.0777229 | + | 0.103814i | ||||
\(313\) | −11.2347 | −0.635022 | −0.317511 | − | 0.948255i | \(-0.602847\pi\) | ||||
−0.317511 | + | 0.948255i | \(0.602847\pi\) | |||||||
\(314\) | 9.84780 | 0.555743 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.5370 | −0.874027 | ||||||||
\(317\) | −4.68621 | −0.263204 | −0.131602 | − | 0.991303i | \(-0.542012\pi\) | ||||
−0.131602 | + | 0.991303i | \(0.542012\pi\) | |||||||
\(318\) | −7.25268 | + | 9.68739i | −0.406710 | + | 0.543242i | ||||
\(319\) | 7.83244 | 0.438532 | ||||||||
\(320\) | −1.98784 | − | 1.02395i | −0.111124 | − | 0.0572406i | ||||
\(321\) | 12.5724 | − | 16.7929i | 0.701723 | − | 0.937290i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.0887 | −0.783914 | ||||||||
\(324\) | −7.57230 | + | 4.86419i | −0.420683 | + | 0.270233i | ||||
\(325\) | 3.83939 | + | 5.38392i | 0.212971 | + | 0.298646i | ||||
\(326\) | − | 11.4412i | − | 0.633672i | ||||||
\(327\) | −11.6005 | + | 15.4948i | −0.641510 | + | 0.856864i | ||||
\(328\) | −12.3285 | −0.680725 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.16469 | − | 4.45294i | −0.119162 | − | 0.245126i | ||||
\(331\) | 26.6248 | 1.46343 | 0.731717 | − | 0.681609i | \(-0.238719\pi\) | ||||
0.731717 | + | 0.681609i | \(0.238719\pi\) | |||||||
\(332\) | 3.33498i | 0.183031i | ||||||||
\(333\) | 13.4582 | − | 3.95015i | 0.737504 | − | 0.216467i | ||||
\(334\) | 14.1922i | 0.776564i | ||||||||
\(335\) | 13.2568 | − | 25.7361i | 0.724296 | − | 1.40611i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 18.2212i | − | 0.992570i | −0.868160 | − | 0.496285i | \(-0.834697\pi\) | ||
0.868160 | − | 0.496285i | \(-0.165303\pi\) | |||||||
\(338\) | −11.2509 | −0.611968 | ||||||||
\(339\) | 0.00495622 | − | 0.00662001i | 0.000269185 | − | 0.000359550i | ||||
\(340\) | 5.90762 | − | 11.4688i | 0.320386 | − | 0.621980i | ||||
\(341\) | 8.87582 | 0.480653 | ||||||||
\(342\) | 7.02931 | − | 2.06319i | 0.380101 | − | 0.111565i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.87753i | 0.101230i | ||||||||
\(345\) | 2.36866 | − | 1.15146i | 0.127524 | − | 0.0619927i | ||||
\(346\) | − | 0.985415i | − | 0.0529762i | ||||||
\(347\) | 2.17760 | 0.116900 | 0.0584498 | − | 0.998290i | \(-0.481384\pi\) | ||||
0.0584498 | + | 0.998290i | \(0.481384\pi\) | |||||||
\(348\) | −8.49490 | − | 6.35990i | −0.455375 | − | 0.340926i | ||||
\(349\) | − | 21.1821i | − | 1.13385i | −0.823769 | − | 0.566925i | \(-0.808133\pi\) | ||
0.823769 | − | 0.566925i | \(-0.191867\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.43843 | + | 2.40256i | 0.343658 | + | 0.128239i | ||||
\(352\) | − | 1.27840i | − | 0.0681388i | ||||||
\(353\) | − | 27.1933i | − | 1.44735i | −0.690140 | − | 0.723676i | \(-0.742451\pi\) | ||
0.690140 | − | 0.723676i | \(-0.257549\pi\) | |||||||
\(354\) | 10.0236 | − | 13.3885i | 0.532749 | − | 0.711593i | ||||
\(355\) | 5.22108 | − | 10.1359i | 0.277106 | − | 0.537959i | ||||
\(356\) | 12.7400 | 0.675217 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 10.2949i | − | 0.544103i | ||||||
\(359\) | 29.0266i | 1.53197i | 0.642860 | + | 0.765984i | \(0.277748\pi\) | ||||
−0.642860 | + | 0.765984i | \(0.722252\pi\) | |||||||
\(360\) | −1.26799 | + | 6.58728i | −0.0668287 | + | 0.347180i | ||||
\(361\) | 13.0369 | 0.686152 | ||||||||
\(362\) | − | 5.05282i | − | 0.265570i | ||||||
\(363\) | −9.72208 | + | 12.9858i | −0.510277 | + | 0.681576i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −32.7699 | − | 16.8800i | −1.71526 | − | 0.883538i | ||||
\(366\) | 5.86441 | + | 4.39052i | 0.306538 | + | 0.229496i | ||||
\(367\) | −1.78381 | −0.0931141 | −0.0465570 | − | 0.998916i | \(-0.514825\pi\) | ||||
−0.0465570 | + | 0.998916i | \(0.514825\pi\) | |||||||
\(368\) | 0.680020 | 0.0354485 | ||||||||
\(369\) | 10.4163 | + | 35.4883i | 0.542250 | + | 1.84745i | ||||
\(370\) | 4.78728 | − | 9.29378i | 0.248879 | − | 0.483161i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −9.62654 | − | 7.20712i | −0.499113 | − | 0.373672i | ||||
\(373\) | 19.6625i | 1.01809i | 0.860741 | + | 0.509044i | \(0.170001\pi\) | ||||
−0.860741 | + | 0.509044i | \(0.829999\pi\) | |||||||
\(374\) | 7.37564 | 0.381385 | ||||||||
\(375\) | 17.0051 | + | 9.26418i | 0.878142 | + | 0.478400i | ||||
\(376\) | − | 7.97726i | − | 0.411396i | ||||||
\(377\) | 8.10286i | 0.417319i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.7309 | −0.859408 | −0.429704 | − | 0.902970i | \(-0.641382\pi\) | ||||
−0.429704 | + | 0.902970i | \(0.641382\pi\) | |||||||
\(380\) | 2.50043 | − | 4.85421i | 0.128269 | − | 0.249016i | ||||
\(381\) | −10.1808 | − | 7.62209i | −0.521579 | − | 0.390491i | ||||
\(382\) | − | 9.31528i | − | 0.476611i | ||||||
\(383\) | 8.48194i | 0.433407i | 0.976237 | + | 0.216704i | \(0.0695305\pi\) | ||||
−0.976237 | + | 0.216704i | \(0.930470\pi\) | |||||||
\(384\) | −1.03805 | + | 1.38652i | −0.0529729 | + | 0.0707558i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 2.53974i | − | 0.129269i | ||||||
\(387\) | 5.40460 | − | 1.58632i | 0.274731 | − | 0.0806372i | ||||
\(388\) | 2.90682 | 0.147571 | ||||||||
\(389\) | − | 22.1622i | − | 1.12367i | −0.827249 | − | 0.561835i | \(-0.810096\pi\) | ||
0.827249 | − | 0.561835i | \(-0.189904\pi\) | |||||||
\(390\) | 4.60668 | − | 2.23942i | 0.233268 | − | 0.113398i | ||||
\(391\) | 3.92333i | 0.198411i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.0800803 | − | 0.106963i | 0.00403952 | − | 0.00539558i | ||||
\(394\) | −8.65660 | −0.436113 | ||||||||
\(395\) | 30.8852 | + | 15.9092i | 1.55400 | + | 0.800477i | ||||
\(396\) | −3.67995 | + | 1.08011i | −0.184925 | + | 0.0542778i | ||||
\(397\) | −21.7809 | −1.09315 | −0.546577 | − | 0.837409i | \(-0.684069\pi\) | ||||
−0.546577 | + | 0.837409i | \(0.684069\pi\) | |||||||
\(398\) | − | 27.9233i | − | 1.39967i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.90305 | + | 4.07091i | 0.145153 | + | 0.203545i | ||||
\(401\) | − | 14.1195i | − | 0.705094i | −0.935794 | − | 0.352547i | \(-0.885316\pi\) | ||
0.935794 | − | 0.352547i | \(-0.114684\pi\) | |||||||
\(402\) | −17.9509 | − | 13.4394i | −0.895311 | − | 0.670294i | ||||
\(403\) | 9.18227i | 0.457402i | ||||||||
\(404\) | −9.02428 | −0.448975 | ||||||||
\(405\) | 20.0332 | − | 1.91559i | 0.995459 | − | 0.0951864i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.97690 | 0.296264 | ||||||||
\(408\) | −7.99947 | − | 5.98898i | −0.396033 | − | 0.296499i | ||||
\(409\) | − | 23.7751i | − | 1.17560i | −0.809005 | − | 0.587801i | \(-0.799994\pi\) | ||
0.809005 | − | 0.587801i | \(-0.200006\pi\) | |||||||
\(410\) | 24.5071 | + | 12.6237i | 1.21032 | + | 0.623442i | ||||
\(411\) | 12.2315 | − | 16.3376i | 0.603336 | − | 0.805875i | ||||
\(412\) | 17.4764 | 0.861002 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.574547 | − | 1.95748i | −0.0282374 | − | 0.0962050i | ||||
\(415\) | 3.41485 | − | 6.62941i | 0.167628 | − | 0.325425i | ||||
\(416\) | 1.32254 | 0.0648426 | ||||||||
\(417\) | −22.1622 | − | 16.5922i | −1.08529 | − | 0.812523i | ||||
\(418\) | 3.12178 | 0.152691 | ||||||||
\(419\) | 7.09712 | 0.346717 | 0.173359 | − | 0.984859i | \(-0.444538\pi\) | ||||
0.173359 | + | 0.984859i | \(0.444538\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.5901 | −0.516128 | −0.258064 | − | 0.966128i | \(-0.583085\pi\) | ||||
−0.258064 | + | 0.966128i | \(0.583085\pi\) | |||||||
\(422\) | −12.5665 | −0.611729 | ||||||||
\(423\) | −22.9631 | + | 6.73997i | −1.11650 | + | 0.327708i | ||||
\(424\) | 6.98682 | 0.339310 | ||||||||
\(425\) | −23.4869 | + | 16.7490i | −1.13928 | + | 0.812445i | ||||
\(426\) | −7.06983 | − | 5.29298i | −0.342534 | − | 0.256446i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12.1115 | −0.585433 | ||||||||
\(429\) | 2.34423 | + | 1.75506i | 0.113181 | + | 0.0847352i | ||||
\(430\) | 1.92250 | − | 3.73224i | 0.0927111 | − | 0.179985i | ||||
\(431\) | − | 30.8160i | − | 1.48435i | −0.670205 | − | 0.742176i | \(-0.733794\pi\) | ||
0.670205 | − | 0.742176i | \(-0.266206\pi\) | |||||||
\(432\) | 4.86825 | + | 1.81663i | 0.234224 | + | 0.0874027i | ||||
\(433\) | 24.3465 | 1.17002 | 0.585010 | − | 0.811026i | \(-0.301091\pi\) | ||||
0.585010 | + | 0.811026i | \(0.301091\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.3743 | + | 21.3408i | 0.497411 | + | 1.02322i | ||||
\(436\) | 11.1753 | 0.535199 | ||||||||
\(437\) | 1.66057i | 0.0794359i | ||||||||
\(438\) | −17.1124 | + | 22.8570i | −0.817664 | + | 1.09215i | ||||
\(439\) | 12.6887i | 0.605598i | 0.953054 | + | 0.302799i | \(0.0979211\pi\) | ||||
−0.953054 | + | 0.302799i | \(0.902079\pi\) | |||||||
\(440\) | −1.30902 | + | 2.54126i | −0.0624049 | + | 0.121150i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.63029i | 0.362936i | ||||||||
\(443\) | −9.71974 | −0.461799 | −0.230899 | − | 0.972978i | \(-0.574167\pi\) | ||||
−0.230899 | + | 0.972978i | \(0.574167\pi\) | |||||||
\(444\) | −6.48242 | − | 4.85321i | −0.307642 | − | 0.230323i | ||||
\(445\) | −25.3251 | − | 13.0451i | −1.20052 | − | 0.618397i | ||||
\(446\) | −13.1623 | −0.623255 | ||||||||
\(447\) | −28.1021 | − | 21.0393i | −1.32918 | − | 0.995123i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.90138i | 0.325696i | 0.986651 | + | 0.162848i | \(0.0520680\pi\) | ||||
−0.986651 | + | 0.162848i | \(0.947932\pi\) | |||||||
\(450\) | 9.26560 | − | 11.7961i | 0.436785 | − | 0.556075i | ||||
\(451\) | 15.7607i | 0.742141i | ||||||||
\(452\) | −0.00477454 | −0.000224575 | ||||||||
\(453\) | −10.4487 | + | 13.9563i | −0.490924 | + | 0.655726i | ||||
\(454\) | 15.5346i | 0.729074i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.38582 | − | 2.53487i | −0.158555 | − | 0.118706i | ||||
\(457\) | − | 4.52428i | − | 0.211637i | −0.994385 | − | 0.105818i | \(-0.966254\pi\) | ||
0.994385 | − | 0.105818i | \(-0.0337462\pi\) | |||||||
\(458\) | − | 4.02816i | − | 0.188223i | ||||||
\(459\) | −10.4809 | + | 28.0871i | −0.489209 | + | 1.31099i | ||||
\(460\) | −1.35177 | − | 0.696306i | −0.0630267 | − | 0.0324655i | ||||
\(461\) | −13.8000 | −0.642732 | −0.321366 | − | 0.946955i | \(-0.604142\pi\) | ||||
−0.321366 | + | 0.946955i | \(0.604142\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 22.5955i | − | 1.05010i | −0.851071 | − | 0.525051i | \(-0.824046\pi\) | ||
0.851071 | − | 0.525051i | \(-0.175954\pi\) | |||||||
\(464\) | 6.12676i | 0.284428i | ||||||||
\(465\) | 11.7563 | + | 24.1837i | 0.545187 | + | 1.12149i | ||||
\(466\) | 28.2529 | 1.30879 | ||||||||
\(467\) | 22.7817i | 1.05421i | 0.849799 | + | 0.527107i | \(0.176723\pi\) | ||||
−0.849799 | + | 0.527107i | \(0.823277\pi\) | |||||||
\(468\) | −1.11741 | − | 3.80701i | −0.0516521 | − | 0.175979i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −8.16832 | + | 15.8576i | −0.376777 | + | 0.731455i | ||||
\(471\) | −10.2225 | + | 13.6542i | −0.471029 | + | 0.629153i | ||||
\(472\) | −9.65619 | −0.444462 | ||||||||
\(473\) | 2.40023 | 0.110363 | ||||||||
\(474\) | 16.1283 | − | 21.5425i | 0.740795 | − | 0.989479i | ||||
\(475\) | −9.94094 | + | 7.08910i | −0.456122 | + | 0.325270i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.90314 | − | 20.1120i | −0.270286 | − | 0.920866i | ||||
\(478\) | − | 10.6358i | − | 0.486470i | ||||||
\(479\) | −31.9484 | −1.45976 | −0.729880 | − | 0.683575i | \(-0.760424\pi\) | ||||
−0.729880 | + | 0.683575i | \(0.760424\pi\) | |||||||
\(480\) | 3.48322 | − | 1.69328i | 0.158986 | − | 0.0772873i | ||||
\(481\) | 6.18326i | 0.281932i | ||||||||
\(482\) | − | 3.42344i | − | 0.155933i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.36570 | 0.425714 | ||||||||
\(485\) | −5.77830 | − | 2.97644i | −0.262379 | − | 0.135153i | ||||
\(486\) | 1.11612 | − | 15.5484i | 0.0506284 | − | 0.705292i | ||||
\(487\) | 6.93234i | 0.314135i | 0.987588 | + | 0.157067i | \(0.0502039\pi\) | ||||
−0.987588 | + | 0.157067i | \(0.949796\pi\) | |||||||
\(488\) | − | 4.22958i | − | 0.191464i | ||||||
\(489\) | 15.8635 | + | 11.8766i | 0.717374 | + | 0.537078i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 24.3178i | − | 1.09745i | −0.836004 | − | 0.548723i | \(-0.815114\pi\) | ||
0.836004 | − | 0.548723i | \(-0.184886\pi\) | |||||||
\(492\) | 12.7976 | − | 17.0937i | 0.576959 | − | 0.770644i | ||||
\(493\) | −35.3480 | −1.59199 | ||||||||
\(494\) | 3.22956i | 0.145305i | ||||||||
\(495\) | 8.42116 | + | 1.62099i | 0.378503 | + | 0.0728581i | ||||
\(496\) | 6.94293i | 0.311747i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.62402 | − | 3.46188i | −0.207207 | − | 0.155130i | ||||
\(499\) | −22.5999 | −1.01171 | −0.505854 | − | 0.862619i | \(-0.668823\pi\) | ||||
−0.505854 | + | 0.862619i | \(0.668823\pi\) | |||||||
\(500\) | −1.60240 | − | 11.0649i | −0.0716617 | − | 0.494838i | ||||
\(501\) | −19.6779 | − | 14.7323i | −0.879142 | − | 0.658189i | ||||
\(502\) | 1.41048 | 0.0629528 | ||||||||
\(503\) | 28.1932i | 1.25707i | 0.777781 | + | 0.628535i | \(0.216345\pi\) | ||||
−0.777781 | + | 0.628535i | \(0.783655\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.9389 | + | 9.24042i | 0.798269 | + | 0.411193i | ||||
\(506\) | − | 0.869335i | − | 0.0386467i | ||||||
\(507\) | 11.6790 | − | 15.5996i | 0.518683 | − | 0.692804i | ||||
\(508\) | 7.34269i | 0.325779i | ||||||||
\(509\) | 29.2730 | 1.29750 | 0.648752 | − | 0.761000i | \(-0.275291\pi\) | ||||
0.648752 | + | 0.761000i | \(0.275291\pi\) | |||||||
\(510\) | 9.76928 | + | 20.0962i | 0.432591 | + | 0.889875i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −4.43612 | + | 11.8880i | −0.195859 | + | 0.524868i | ||||
\(514\) | − | 17.8668i | − | 0.788069i | ||||||
\(515\) | −34.7404 | − | 17.8950i | −1.53085 | − | 0.788548i | ||||
\(516\) | −2.60324 | − | 1.94897i | −0.114601 | − | 0.0857988i | ||||
\(517\) | −10.1981 | −0.448513 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.36630 | + | 1.02291i | 0.0599740 | + | 0.0449008i | ||||
\(520\) | −2.62899 | − | 1.35421i | −0.115289 | − | 0.0593861i | ||||
\(521\) | −1.10870 | −0.0485729 | −0.0242865 | − | 0.999705i | \(-0.507731\pi\) | ||||
−0.0242865 | + | 0.999705i | \(0.507731\pi\) | |||||||
\(522\) | 17.6363 | − | 5.17648i | 0.771920 | − | 0.226569i | ||||
\(523\) | −38.3222 | −1.67571 | −0.837857 | − | 0.545890i | \(-0.816192\pi\) | ||||
−0.837857 | + | 0.545890i | \(0.816192\pi\) | |||||||
\(524\) | −0.0771448 | −0.00337009 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.07247 | 0.0467620 | ||||||||
\(527\) | −40.0568 | −1.74490 | ||||||||
\(528\) | 1.77253 | + | 1.32704i | 0.0771394 | + | 0.0577521i | ||||
\(529\) | −22.5376 | −0.979894 | ||||||||
\(530\) | −13.8887 | − | 7.15416i | −0.603287 | − | 0.310757i | ||||
\(531\) | 8.15849 | + | 27.7960i | 0.354048 | + | 1.20624i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.3048 | −0.706240 | ||||||||
\(534\) | −13.2247 | + | 17.6643i | −0.572291 | + | 0.764408i | ||||
\(535\) | 24.0758 | + | 12.4016i | 1.04089 | + | 0.536168i | ||||
\(536\) | 12.9467i | 0.559213i | ||||||||
\(537\) | 14.2741 | + | 10.6867i | 0.615975 | + | 0.461163i | ||||
\(538\) | 10.3792 | 0.447480 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −7.81718 | − | 8.59603i | −0.336398 | − | 0.369914i | ||||
\(541\) | 4.97661 | 0.213961 | 0.106981 | − | 0.994261i | \(-0.465882\pi\) | ||||
0.106981 | + | 0.994261i | \(0.465882\pi\) | |||||||
\(542\) | 9.90724i | 0.425552i | ||||||||
\(543\) | 7.00586 | + | 5.24509i | 0.300650 | + | 0.225088i | ||||
\(544\) | 5.76944i | 0.247363i | ||||||||
\(545\) | −22.2147 | − | 11.4429i | −0.951574 | − | 0.490162i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.0840i | 1.20079i | 0.799705 | + | 0.600393i | \(0.204989\pi\) | ||||
−0.799705 | + | 0.600393i | \(0.795011\pi\) | |||||||
\(548\) | −11.7831 | −0.503351 | ||||||||
\(549\) | −12.1751 | + | 3.57356i | −0.519622 | + | 0.152516i | ||||
\(550\) | 5.20424 | − | 3.71125i | 0.221910 | − | 0.158248i | ||||
\(551\) | −14.9612 | −0.637370 | ||||||||
\(552\) | −0.705896 | + | 0.942863i | −0.0300449 | + | 0.0401309i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 18.3865i | 0.781166i | ||||||||
\(555\) | 7.91660 | + | 16.2851i | 0.336041 | + | 0.691264i | ||||
\(556\) | 15.9840i | 0.677871i | ||||||||
\(557\) | 23.5775 | 0.999009 | 0.499504 | − | 0.866311i | \(-0.333515\pi\) | ||||
0.499504 | + | 0.866311i | \(0.333515\pi\) | |||||||
\(558\) | 19.9857 | − | 5.86606i | 0.846062 | − | 0.248330i | ||||
\(559\) | 2.48310i | 0.105024i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.65630 | + | 10.2265i | −0.323249 | + | 0.431763i | ||||
\(562\) | − | 19.0144i | − | 0.802075i | ||||||
\(563\) | − | 18.4990i | − | 0.779639i | −0.920891 | − | 0.389819i | \(-0.872537\pi\) | ||
0.920891 | − | 0.389819i | \(-0.127463\pi\) | |||||||
\(564\) | 11.0607 | + | 8.28081i | 0.465738 | + | 0.348685i | ||||
\(565\) | 0.00949104 | + | 0.00488889i | 0.000399291 | + | 0.000205677i | ||||
\(566\) | −18.6645 | −0.784526 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.09896i | 0.213947i | ||||||||
\(569\) | − | 19.5845i | − | 0.821026i | −0.911855 | − | 0.410513i | \(-0.865350\pi\) | ||
0.911855 | − | 0.410513i | \(-0.134650\pi\) | |||||||
\(570\) | 4.13490 | + | 8.50583i | 0.173192 | + | 0.356270i | ||||
\(571\) | −15.4720 | −0.647481 | −0.323741 | − | 0.946146i | \(-0.604941\pi\) | ||||
−0.323741 | + | 0.946146i | \(0.604941\pi\) | |||||||
\(572\) | − | 1.69073i | − | 0.0706928i | ||||||
\(573\) | 12.9159 | + | 9.66974i | 0.539568 | + | 0.403959i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.97413 | + | 2.76830i | 0.0823270 | + | 0.115446i | ||||
\(576\) | −0.844897 | − | 2.87857i | −0.0352041 | − | 0.119940i | ||||
\(577\) | 31.3327 | 1.30440 | 0.652199 | − | 0.758048i | \(-0.273847\pi\) | ||||
0.652199 | + | 0.758048i | \(0.273847\pi\) | |||||||
\(578\) | −16.2864 | −0.677427 | ||||||||
\(579\) | 3.52141 | + | 2.63638i | 0.146345 | + | 0.109564i | ||||
\(580\) | 6.27350 | − | 12.1790i | 0.260493 | − | 0.505707i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −3.01743 | + | 4.03037i | −0.125076 | + | 0.167064i | ||||
\(583\) | − | 8.93193i | − | 0.369923i | ||||||
\(584\) | 16.4851 | 0.682160 | ||||||||
\(585\) | −1.67696 | + | 8.71191i | −0.0693336 | + | 0.360193i | ||||
\(586\) | − | 3.41725i | − | 0.141165i | ||||||
\(587\) | 34.0806i | 1.40666i | 0.710865 | + | 0.703329i | \(0.248304\pi\) | ||||
−0.710865 | + | 0.703329i | \(0.751696\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.9543 | −0.698588 | ||||||||
\(590\) | 19.1950 | + | 9.88746i | 0.790246 | + | 0.407060i | ||||
\(591\) | 8.98600 | − | 12.0026i | 0.369635 | − | 0.493720i | ||||
\(592\) | 4.67531i | 0.192154i | ||||||||
\(593\) | − | 17.1989i | − | 0.706274i | −0.935572 | − | 0.353137i | \(-0.885115\pi\) | ||
0.935572 | − | 0.353137i | \(-0.114885\pi\) | |||||||
\(594\) | 2.32238 | − | 6.22356i | 0.0952883 | − | 0.255356i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 20.2680i | 0.830211i | ||||||||
\(597\) | 38.7163 | + | 28.9858i | 1.58455 | + | 1.18631i | ||||
\(598\) | 0.899350 | 0.0367772 | ||||||||
\(599\) | 28.4544i | 1.16262i | 0.813684 | + | 0.581308i | \(0.197459\pi\) | ||||
−0.813684 | + | 0.581308i | \(0.802541\pi\) | |||||||
\(600\) | −8.65793 | − | 0.200664i | −0.353458 | − | 0.00819209i | ||||
\(601\) | − | 2.32232i | − | 0.0947295i | −0.998878 | − | 0.0473647i | \(-0.984918\pi\) | ||
0.998878 | − | 0.0473647i | \(-0.0150823\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 37.2680 | − | 10.9386i | 1.51767 | − | 0.445456i | ||||
\(604\) | 10.0657 | 0.409568 | ||||||||
\(605\) | −18.6176 | − | 9.59001i | −0.756911 | − | 0.389889i | ||||
\(606\) | 9.36767 | − | 12.5124i | 0.380536 | − | 0.508281i | ||||
\(607\) | 32.2377 | 1.30849 | 0.654244 | − | 0.756283i | \(-0.272987\pi\) | ||||
0.654244 | + | 0.756283i | \(0.272987\pi\) | |||||||
\(608\) | 2.44195i | 0.0990340i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.33088 | + | 8.40775i | −0.175352 | + | 0.340420i | ||||
\(611\) | − | 10.5502i | − | 0.426816i | ||||||
\(612\) | 16.6077 | − | 4.87459i | 0.671327 | − | 0.197043i | ||||
\(613\) | − | 14.4301i | − | 0.582825i | −0.956597 | − | 0.291413i | \(-0.905875\pi\) | ||
0.956597 | − | 0.291413i | \(-0.0941252\pi\) | |||||||
\(614\) | −13.3096 | −0.537133 | ||||||||
\(615\) | −42.9427 | + | 20.8755i | −1.73162 | + | 0.841783i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.6916 | 1.67844 | 0.839219 | − | 0.543793i | \(-0.183012\pi\) | ||||
0.839219 | + | 0.543793i | \(0.183012\pi\) | |||||||
\(618\) | −18.1414 | + | 24.2315i | −0.729755 | + | 0.974733i | ||||
\(619\) | 7.38411i | 0.296792i | 0.988928 | + | 0.148396i | \(0.0474111\pi\) | ||||
−0.988928 | + | 0.148396i | \(0.952589\pi\) | |||||||
\(620\) | 7.10922 | − | 13.8015i | 0.285513 | − | 0.554280i | ||||
\(621\) | 3.31050 | + | 1.23534i | 0.132846 | + | 0.0495727i | ||||
\(622\) | 11.7713 | 0.471984 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.37286 | + | 1.83373i | −0.0549584 | + | 0.0734078i | ||||
\(625\) | −8.14459 | + | 23.6361i | −0.325784 | + | 0.945444i | ||||
\(626\) | −11.2347 | −0.449029 | ||||||||
\(627\) | −3.24057 | + | 4.32842i | −0.129416 | + | 0.172860i | ||||
\(628\) | 9.84780 | 0.392970 | ||||||||
\(629\) | −26.9739 | −1.07552 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.8396 | 1.74523 | 0.872613 | − | 0.488412i | \(-0.162423\pi\) | ||||
0.872613 | + | 0.488412i | \(0.162423\pi\) | |||||||
\(632\) | −15.5370 | −0.618031 | ||||||||
\(633\) | 13.0447 | − | 17.4238i | 0.518481 | − | 0.692534i | ||||
\(634\) | −4.68621 | −0.186113 | ||||||||
\(635\) | 7.51855 | − | 14.5961i | 0.298364 | − | 0.579229i | ||||
\(636\) | −7.25268 | + | 9.68739i | −0.287587 | + | 0.384130i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 7.83244 | 0.310089 | ||||||||
\(639\) | 14.6777 | − | 4.30809i | 0.580640 | − | 0.170426i | ||||
\(640\) | −1.98784 | − | 1.02395i | −0.0785764 | − | 0.0404752i | ||||
\(641\) | 15.9563i | 0.630236i | 0.949052 | + | 0.315118i | \(0.102044\pi\) | ||||
−0.949052 | + | 0.315118i | \(0.897956\pi\) | |||||||
\(642\) | 12.5724 | − | 16.7929i | 0.496193 | − | 0.662764i | ||||
\(643\) | −3.11117 | −0.122692 | −0.0613462 | − | 0.998117i | \(-0.519539\pi\) | ||||
−0.0613462 | + | 0.998117i | \(0.519539\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.17919 | + | 6.53985i | 0.125180 | + | 0.257506i | ||||
\(646\) | −14.0887 | −0.554311 | ||||||||
\(647\) | 28.0993i | 1.10470i | 0.833613 | + | 0.552350i | \(0.186269\pi\) | ||||
−0.833613 | + | 0.552350i | \(0.813731\pi\) | |||||||
\(648\) | −7.57230 | + | 4.86419i | −0.297468 | + | 0.191083i | ||||
\(649\) | 12.3444i | 0.484562i | ||||||||
\(650\) | 3.83939 | + | 5.38392i | 0.150593 | + | 0.211175i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 11.4412i | − | 0.448073i | ||||||
\(653\) | 37.3861 | 1.46303 | 0.731515 | − | 0.681825i | \(-0.238814\pi\) | ||||
0.731515 | + | 0.681825i | \(0.238814\pi\) | |||||||
\(654\) | −11.6005 | + | 15.4948i | −0.453616 | + | 0.605895i | ||||
\(655\) | 0.153352 | + | 0.0789925i | 0.00599196 | + | 0.00308649i | ||||
\(656\) | −12.3285 | −0.481345 | ||||||||
\(657\) | −13.9283 | − | 47.4536i | −0.543393 | − | 1.85134i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 15.3543i | − | 0.598119i | −0.954234 | − | 0.299059i | \(-0.903327\pi\) | ||
0.954234 | − | 0.299059i | \(-0.0966729\pi\) | |||||||
\(660\) | −2.16469 | − | 4.45294i | −0.0842603 | − | 0.173330i | ||||
\(661\) | 40.0450i | 1.55757i | 0.627291 | + | 0.778785i | \(0.284164\pi\) | ||||
−0.627291 | + | 0.778785i | \(0.715836\pi\) | |||||||
\(662\) | 26.6248 | 1.03480 | ||||||||
\(663\) | −10.5796 | − | 7.92064i | −0.410877 | − | 0.307612i | ||||
\(664\) | 3.33498i | 0.129422i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 13.4582 | − | 3.95015i | 0.521494 | − | 0.153065i | ||||
\(667\) | 4.16632i | 0.161320i | ||||||||
\(668\) | 14.1922i | 0.549114i | ||||||||
\(669\) | 13.6632 | − | 18.2499i | 0.528249 | − | 0.705582i | ||||
\(670\) | 13.2568 | − | 25.7361i | 0.512155 | − | 0.994271i | ||||
\(671\) | −5.40708 | −0.208738 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.2669i | 0.704137i | 0.935974 | + | 0.352069i | \(0.114522\pi\) | ||||
−0.935974 | + | 0.352069i | \(0.885478\pi\) | |||||||
\(674\) | − | 18.2212i | − | 0.701853i | ||||||
\(675\) | 6.73743 | + | 25.0920i | 0.259324 | + | 0.965790i | ||||
\(676\) | −11.2509 | −0.432727 | ||||||||
\(677\) | 18.1380i | 0.697098i | 0.937291 | + | 0.348549i | \(0.113326\pi\) | ||||
−0.937291 | + | 0.348549i | \(0.886674\pi\) | |||||||
\(678\) | 0.00495622 | − | 0.00662001i | 0.000190342 | − | 0.000254240i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5.90762 | − | 11.4688i | 0.226547 | − | 0.439807i | ||||
\(681\) | −21.5391 | − | 16.1257i | −0.825379 | − | 0.617938i | ||||
\(682\) | 8.87582 | 0.339873 | ||||||||
\(683\) | −6.08580 | −0.232867 | −0.116433 | − | 0.993199i | \(-0.537146\pi\) | ||||
−0.116433 | + | 0.993199i | \(0.537146\pi\) | |||||||
\(684\) | 7.02931 | − | 2.06319i | 0.268772 | − | 0.0788882i | ||||
\(685\) | 23.4231 | + | 12.0654i | 0.894949 | + | 0.460994i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.58514 | + | 4.18144i | 0.213086 | + | 0.159532i | ||||
\(688\) | 1.87753i | 0.0715802i | ||||||||
\(689\) | 9.24031 | 0.352028 | ||||||||
\(690\) | 2.36866 | − | 1.15146i | 0.0901732 | − | 0.0438355i | ||||
\(691\) | 3.60562i | 0.137164i | 0.997645 | + | 0.0685820i | \(0.0218475\pi\) | ||||
−0.997645 | + | 0.0685820i | \(0.978153\pi\) | |||||||
\(692\) | − | 0.985415i | − | 0.0374599i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.17760 | 0.0826605 | ||||||||
\(695\) | 16.3668 | − | 31.7736i | 0.620828 | − | 1.20524i | ||||
\(696\) | −8.49490 | − | 6.35990i | −0.321998 | − | 0.241071i | ||||
\(697\) | − | 71.1283i | − | 2.69418i | ||||||
\(698\) | − | 21.1821i | − | 0.801753i | ||||||
\(699\) | −29.3279 | + | 39.1733i | −1.10928 | + | 1.48167i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.6543i | 0.666794i | 0.942786 | + | 0.333397i | \(0.108195\pi\) | ||||
−0.942786 | + | 0.333397i | \(0.891805\pi\) | |||||||
\(702\) | 6.43843 | + | 2.40256i | 0.243003 | + | 0.0906788i | ||||
\(703\) | −11.4168 | −0.430595 | ||||||||
\(704\) | − | 1.27840i | − | 0.0481814i | ||||||
\(705\) | −13.5077 | − | 27.7865i | −0.508731 | − | 1.04650i | ||||
\(706\) | − | 27.1933i | − | 1.02343i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 10.0236 | − | 13.3885i | 0.376711 | − | 0.503172i | ||||
\(709\) | −28.6814 | −1.07715 | −0.538575 | − | 0.842577i | \(-0.681037\pi\) | ||||
−0.538575 | + | 0.842577i | \(0.681037\pi\) | |||||||
\(710\) | 5.22108 | − | 10.1359i | 0.195944 | − | 0.380395i | ||||
\(711\) | 13.1272 | + | 44.7244i | 0.492309 | + | 1.67730i | ||||
\(712\) | 12.7400 | 0.477451 | ||||||||
\(713\) | 4.72133i | 0.176815i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.73122 | + | 3.36090i | −0.0647440 | + | 0.125691i | ||||
\(716\) | − | 10.2949i | − | 0.384739i | ||||||
\(717\) | 14.7468 | + | 11.0405i | 0.550729 | + | 0.412316i | ||||
\(718\) | 29.0266i | 1.08326i | ||||||||
\(719\) | 12.4782 | 0.465359 | 0.232680 | − | 0.972553i | \(-0.425251\pi\) | ||||
0.232680 | + | 0.972553i | \(0.425251\pi\) | |||||||
\(720\) | −1.26799 | + | 6.58728i | −0.0472550 | + | 0.245493i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13.0369 | 0.485183 | ||||||||
\(723\) | 4.74668 | + | 3.55371i | 0.176531 | + | 0.132164i | ||||
\(724\) | − | 5.05282i | − | 0.187787i | ||||||
\(725\) | −24.9415 | + | 17.7863i | −0.926304 | + | 0.660567i | ||||
\(726\) | −9.72208 | + | 12.9858i | −0.360820 | + | 0.481947i | ||||
\(727\) | −7.85466 | −0.291313 | −0.145657 | − | 0.989335i | \(-0.546529\pi\) | ||||
−0.145657 | + | 0.989335i | \(0.546529\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.3997 | + | 17.6876i | 0.755545 | + | 0.655097i | ||||
\(730\) | −32.7699 | − | 16.8800i | −1.21287 | − | 0.624756i | ||||
\(731\) | −10.8323 | −0.400647 | ||||||||
\(732\) | 5.86441 | + | 4.39052i | 0.216755 | + | 0.162278i | ||||
\(733\) | −15.3864 | −0.568308 | −0.284154 | − | 0.958779i | \(-0.591713\pi\) | ||||
−0.284154 | + | 0.958779i | \(0.591713\pi\) | |||||||
\(734\) | −1.78381 | −0.0658416 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.680020 | 0.0250659 | ||||||||
\(737\) | 16.5511 | 0.609666 | ||||||||
\(738\) | 10.4163 | + | 35.4883i | 0.383429 | + | 1.30634i | ||||
\(739\) | 2.33784 | 0.0859990 | 0.0429995 | − | 0.999075i | \(-0.486309\pi\) | ||||
0.0429995 | + | 0.999075i | \(0.486309\pi\) | |||||||
\(740\) | 4.78728 | − | 9.29378i | 0.175984 | − | 0.341646i | ||||
\(741\) | −4.47786 | − | 3.35245i | −0.164498 | − | 0.123155i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.4896 | 0.678318 | 0.339159 | − | 0.940729i | \(-0.389858\pi\) | ||||
0.339159 | + | 0.940729i | \(0.389858\pi\) | |||||||
\(744\) | −9.62654 | − | 7.20712i | −0.352926 | − | 0.264226i | ||||
\(745\) | 20.7535 | − | 40.2897i | 0.760348 | − | 1.47610i | ||||
\(746\) | 19.6625i | 0.719897i | ||||||||
\(747\) | 9.59995 | − | 2.81771i | 0.351244 | − | 0.103095i | ||||
\(748\) | 7.37564 | 0.269680 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 17.0051 | + | 9.26418i | 0.620940 | + | 0.338280i | ||||
\(751\) | −1.91013 | −0.0697016 | −0.0348508 | − | 0.999393i | \(-0.511096\pi\) | ||||
−0.0348508 | + | 0.999393i | \(0.511096\pi\) | |||||||
\(752\) | − | 7.97726i | − | 0.290901i | ||||||
\(753\) | −1.46415 | + | 1.95566i | −0.0533566 | + | 0.0712683i | ||||
\(754\) | 8.10286i | 0.295089i | ||||||||
\(755\) | −20.0090 | − | 10.3068i | −0.728204 | − | 0.375102i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 13.3724i | − | 0.486026i | −0.970023 | − | 0.243013i | \(-0.921864\pi\) | ||
0.970023 | − | 0.243013i | \(-0.0781358\pi\) | |||||||
\(758\) | −16.7309 | −0.607693 | ||||||||
\(759\) | 1.20535 | + | 0.902415i | 0.0437516 | + | 0.0327556i | ||||
\(760\) | 2.50043 | − | 4.85421i | 0.0907002 | − | 0.176081i | ||||
\(761\) | −3.76731 | −0.136565 | −0.0682824 | − | 0.997666i | \(-0.521752\pi\) | ||||
−0.0682824 | + | 0.997666i | \(0.521752\pi\) | |||||||
\(762\) | −10.1808 | − | 7.62209i | −0.368812 | − | 0.276119i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 9.31528i | − | 0.337015i | ||||||
\(765\) | −38.0049 | − | 7.31557i | −1.37407 | − | 0.264495i | ||||
\(766\) | 8.48194i | 0.306465i | ||||||||
\(767\) | −12.7707 | −0.461121 | ||||||||
\(768\) | −1.03805 | + | 1.38652i | −0.0374575 | + | 0.0500319i | ||||
\(769\) | 11.2974i | 0.407393i | 0.979034 | + | 0.203696i | \(0.0652956\pi\) | ||||
−0.979034 | + | 0.203696i | \(0.934704\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.7727 | + | 18.5466i | 0.892167 | + | 0.667941i | ||||
\(772\) | − | 2.53974i | − | 0.0914072i | ||||||
\(773\) | − | 16.3617i | − | 0.588490i | −0.955730 | − | 0.294245i | \(-0.904932\pi\) | ||
0.955730 | − | 0.294245i | \(-0.0950682\pi\) | |||||||
\(774\) | 5.40460 | − | 1.58632i | 0.194264 | − | 0.0570191i | ||||
\(775\) | −28.2640 | + | 20.1557i | −1.01527 | + | 0.724013i | ||||
\(776\) | 2.90682 | 0.104349 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 22.1622i | − | 0.794554i | ||||||
\(779\) | − | 30.1054i | − | 1.07864i | ||||||
\(780\) | 4.60668 | − | 2.23942i | 0.164946 | − | 0.0801842i | ||||
\(781\) | 6.51849 | 0.233250 | ||||||||
\(782\) | 3.92333i | 0.140298i | ||||||||
\(783\) | −11.1301 | + | 29.8266i | −0.397756 | + | 1.06592i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19.5759 | − | 10.0837i | −0.698693 | − | 0.359901i | ||||
\(786\) | 0.0800803 | − | 0.106963i | 0.00285637 | − | 0.00381525i | ||||
\(787\) | −40.2948 | −1.43636 | −0.718178 | − | 0.695859i | \(-0.755024\pi\) | ||||
−0.718178 | + | 0.695859i | \(0.755024\pi\) | |||||||
\(788\) | −8.65660 | −0.308379 | ||||||||
\(789\) | −1.11328 | + | 1.48701i | −0.0396338 | + | 0.0529389i | ||||
\(790\) | 30.8852 | + | 15.9092i | 1.09885 | + | 0.566023i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.67995 | + | 1.08011i | −0.130761 | + | 0.0383802i | ||||
\(793\) | − | 5.59377i | − | 0.198641i | ||||||
\(794\) | −21.7809 | −0.772976 | ||||||||
\(795\) | 24.3366 | − | 11.8306i | 0.863130 | − | 0.419590i | ||||
\(796\) | − | 27.9233i | − | 0.989714i | ||||||
\(797\) | 30.0110i | 1.06304i | 0.847044 | + | 0.531522i | \(0.178380\pi\) | ||||
−0.847044 | + | 0.531522i | \(0.821620\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 46.0244 | 1.62822 | ||||||||
\(800\) | 2.90305 | + | 4.07091i | 0.102638 | + | 0.143928i | ||||
\(801\) | −10.7640 | − | 36.6729i | −0.380326 | − | 1.29577i | ||||
\(802\) | − | 14.1195i | − | 0.498577i | ||||||
\(803\) | − | 21.0746i | − | 0.743705i | ||||||
\(804\) | −17.9509 | − | 13.4394i | −0.633081 | − | 0.473970i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.18227i | 0.323432i | ||||||||
\(807\) | −10.7742 | + | 14.3910i | −0.379269 | + | 0.506588i | ||||
\(808\) | −9.02428 | −0.317473 | ||||||||
\(809\) | 27.1711i | 0.955286i | 0.878554 | + | 0.477643i | \(0.158509\pi\) | ||||
−0.878554 | + | 0.477643i | \(0.841491\pi\) | |||||||
\(810\) | 20.0332 | − | 1.91559i | 0.703896 | − | 0.0673069i | ||||
\(811\) | 6.57732i | 0.230961i | 0.993310 | + | 0.115480i | \(0.0368407\pi\) | ||||
−0.993310 | + | 0.115480i | \(0.963159\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.7366 | − | 10.2842i | −0.481764 | − | 0.360683i | ||||
\(814\) | 5.97690 | 0.209490 | ||||||||
\(815\) | −11.7153 | + | 22.7434i | −0.410368 | + | 0.796667i | ||||
\(816\) | −7.99947 | − | 5.98898i | −0.280037 | − | 0.209656i | ||||
\(817\) | −4.58483 | −0.160403 | ||||||||
\(818\) | − | 23.7751i | − | 0.831277i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 24.5071 | + | 12.6237i | 0.855824 | + | 0.440840i | ||||
\(821\) | 0.162186i | 0.00566035i | 0.999996 | + | 0.00283017i | \(0.000900873\pi\) | ||||
−0.999996 | + | 0.00283017i | \(0.999099\pi\) | |||||||
\(822\) | 12.2315 | − | 16.3376i | 0.426623 | − | 0.569840i | ||||
\(823\) | − | 53.1286i | − | 1.85195i | −0.377588 | − | 0.925974i | \(-0.623247\pi\) | ||
0.377588 | − | 0.925974i | \(-0.376753\pi\) | |||||||
\(824\) | 17.4764 | 0.608820 | ||||||||
\(825\) | −0.256529 | + | 11.0683i | −0.00893119 | + | 0.385348i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 47.5055 | 1.65193 | 0.825964 | − | 0.563723i | \(-0.190631\pi\) | ||||
0.825964 | + | 0.563723i | \(0.190631\pi\) | |||||||
\(828\) | −0.574547 | − | 1.95748i | −0.0199669 | − | 0.0680272i | ||||
\(829\) | 6.47482i | 0.224880i | 0.993659 | + | 0.112440i | \(0.0358666\pi\) | ||||
−0.993659 | + | 0.112440i | \(0.964133\pi\) | |||||||
\(830\) | 3.41485 | − | 6.62941i | 0.118531 | − | 0.230110i | ||||
\(831\) | −25.4933 | − | 19.0861i | −0.884352 | − | 0.662090i | ||||
\(832\) | 1.32254 | 0.0458507 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −22.1622 | − | 16.5922i | −0.767413 | − | 0.574540i | ||||
\(835\) | 14.5321 | − | 28.2119i | 0.502905 | − | 0.976314i | ||||
\(836\) | 3.12178 | 0.107969 | ||||||||
\(837\) | −12.6127 | + | 33.7999i | −0.435960 | + | 1.16830i | ||||
\(838\) | 7.09712 | 0.245166 | ||||||||
\(839\) | 28.7089 | 0.991142 | 0.495571 | − | 0.868567i | \(-0.334959\pi\) | ||||
0.495571 | + | 0.868567i | \(0.334959\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.53721 | −0.294386 | ||||||||
\(842\) | −10.5901 | −0.364958 | ||||||||
\(843\) | 26.3640 | + | 19.7380i | 0.908023 | + | 0.679812i | ||||
\(844\) | −12.5665 | −0.432558 | ||||||||
\(845\) | 22.3650 | + | 11.5204i | 0.769381 | + | 0.396313i | ||||
\(846\) | −22.9631 | + | 6.73997i | −0.789487 | + | 0.231725i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.98682 | 0.239928 | ||||||||
\(849\) | 19.3747 | − | 25.8787i | 0.664937 | − | 0.888156i | ||||
\(850\) | −23.4869 | + | 16.7490i | −0.805593 | + | 0.574485i | ||||
\(851\) | 3.17930i | 0.108985i | ||||||||
\(852\) | −7.06983 | − | 5.29298i | −0.242208 | − | 0.181335i | ||||
\(853\) | 41.9863 | 1.43758 | 0.718792 | − | 0.695225i | \(-0.244695\pi\) | ||||
0.718792 | + | 0.695225i | \(0.244695\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.0858 | − | 3.09635i | −0.550122 | − | 0.105893i | ||||
\(856\) | −12.1115 | −0.413964 | ||||||||
\(857\) | 26.7333i | 0.913193i | 0.889674 | + | 0.456596i | \(0.150932\pi\) | ||||
−0.889674 | + | 0.456596i | \(0.849068\pi\) | |||||||
\(858\) | 2.34423 | + | 1.75506i | 0.0800308 | + | 0.0599168i | ||||
\(859\) | − | 55.5429i | − | 1.89510i | −0.319610 | − | 0.947549i | \(-0.603552\pi\) | ||
0.319610 | − | 0.947549i | \(-0.396448\pi\) | |||||||
\(860\) | 1.92250 | − | 3.73224i | 0.0655567 | − | 0.127268i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 30.8160i | − | 1.04960i | ||||||
\(863\) | 21.2657 | 0.723892 | 0.361946 | − | 0.932199i | \(-0.382112\pi\) | ||||
0.361946 | + | 0.932199i | \(0.382112\pi\) | |||||||
\(864\) | 4.86825 | + | 1.81663i | 0.165621 | + | 0.0618030i | ||||
\(865\) | −1.00902 | + | 1.95885i | −0.0343076 | + | 0.0666030i | ||||
\(866\) | 24.3465 | 0.827329 | ||||||||
\(867\) | 16.9062 | − | 22.5816i | 0.574164 | − | 0.766910i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.8625i | 0.673790i | ||||||||
\(870\) | 10.3743 | + | 21.3408i | 0.351723 | + | 0.723522i | ||||
\(871\) | 17.1225i | 0.580174i | ||||||||
\(872\) | 11.1753 | 0.378443 | ||||||||
\(873\) | −2.45596 | − | 8.36747i | −0.0831217 | − | 0.283196i | ||||
\(874\) | 1.66057i | 0.0561697i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −17.1124 | + | 22.8570i | −0.578176 | + | 0.772268i | ||||
\(877\) | 22.3340i | 0.754166i | 0.926180 | + | 0.377083i | \(0.123073\pi\) | ||||
−0.926180 | + | 0.377083i | \(0.876927\pi\) | |||||||
\(878\) | 12.6887i | 0.428222i | ||||||||
\(879\) | 4.73810 | + | 3.54728i | 0.159812 | + | 0.119647i | ||||
\(880\) | −1.30902 | + | 2.54126i | −0.0441269 | + | 0.0856657i | ||||
\(881\) | 4.42739 | 0.149162 | 0.0745812 | − | 0.997215i | \(-0.476238\pi\) | ||||
0.0745812 | + | 0.997215i | \(0.476238\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45.9417i | 1.54606i | 0.634368 | + | 0.773031i | \(0.281260\pi\) | ||||
−0.634368 | + | 0.773031i | \(0.718740\pi\) | |||||||
\(884\) | 7.63029i | 0.256634i | ||||||||
\(885\) | −33.6346 | + | 16.3506i | −1.13061 | + | 0.549620i | ||||
\(886\) | −9.71974 | −0.326541 | ||||||||
\(887\) | 10.0111i | 0.336139i | 0.985775 | + | 0.168070i | \(0.0537533\pi\) | ||||
−0.985775 | + | 0.168070i | \(0.946247\pi\) | |||||||
\(888\) | −6.48242 | − | 4.85321i | −0.217536 | − | 0.162863i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −25.3251 | − | 13.0451i | −0.848899 | − | 0.437273i | ||||
\(891\) | 6.21837 | + | 9.68041i | 0.208323 | + | 0.324306i | ||||
\(892\) | −13.1623 | −0.440708 | ||||||||
\(893\) | 19.4801 | 0.651875 | ||||||||
\(894\) | −28.1021 | − | 21.0393i | −0.939875 | − | 0.703658i | ||||
\(895\) | −10.5415 | + | 20.4647i | −0.352363 | + | 0.684059i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.933572 | + | 1.24697i | −0.0311711 | + | 0.0416351i | ||||
\(898\) | 6.90138i | 0.230302i | ||||||||
\(899\) | −42.5377 | −1.41871 | ||||||||
\(900\) | 9.26560 | − | 11.7961i | 0.308853 | − | 0.393204i | ||||
\(901\) | 40.3100i | 1.34292i | ||||||||
\(902\) | 15.7607i | 0.524773i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.00477454 | −0.000158799 | ||||||||
\(905\) | −5.17384 | + | 10.0442i | −0.171984 | + | 0.333881i | ||||
\(906\) | −10.4487 | + | 13.9563i | −0.347135 | + | 0.463668i | ||||
\(907\) | − | 35.1538i | − | 1.16726i | −0.812019 | − | 0.583631i | \(-0.801631\pi\) | ||
0.812019 | − | 0.583631i | \(-0.198369\pi\) | |||||||
\(908\) | 15.5346i | 0.515533i | ||||||||
\(909\) | 7.62459 | + | 25.9770i | 0.252892 | + | 0.861602i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.4530i | 0.578243i | 0.957292 | + | 0.289122i | \(0.0933632\pi\) | ||||
−0.957292 | + | 0.289122i | \(0.906637\pi\) | |||||||
\(912\) | −3.38582 | − | 2.53487i | −0.112116 | − | 0.0839378i | ||||
\(913\) | 4.26342 | 0.141099 | ||||||||
\(914\) | − | 4.52428i | − | 0.149650i | ||||||
\(915\) | −7.16186 | − | 14.7325i | −0.236764 | − | 0.487043i | ||||
\(916\) | − | 4.02816i | − | 0.133094i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −10.4809 | + | 28.0871i | −0.345923 | + | 0.927012i | ||||
\(919\) | 3.80826 | 0.125623 | 0.0628114 | − | 0.998025i | \(-0.479993\pi\) | ||||
0.0628114 | + | 0.998025i | \(0.479993\pi\) | |||||||
\(920\) | −1.35177 | − | 0.696306i | −0.0445666 | − | 0.0229565i | ||||
\(921\) | 13.8161 | − | 18.4541i | 0.455255 | − | 0.608083i | ||||
\(922\) | −13.8000 | −0.454480 | ||||||||
\(923\) | 6.74355i | 0.221967i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.0327 | + | 13.5726i | −0.625793 | + | 0.446266i | ||||
\(926\) | − | 22.5955i | − | 0.742534i | ||||||
\(927\) | −14.7658 | − | 50.3071i | −0.484972 | − | 1.65230i | ||||
\(928\) | 6.12676i | 0.201121i | ||||||||
\(929\) | −4.83763 | −0.158717 | −0.0793587 | − | 0.996846i | \(-0.525287\pi\) | ||||
−0.0793587 | + | 0.996846i | \(0.525287\pi\) | |||||||
\(930\) | 11.7563 | + | 24.1837i | 0.385505 | + | 0.793016i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 28.2529 | 0.925454 | ||||||||
\(933\) | −12.2192 | + | 16.3211i | −0.400038 | + | 0.534330i | ||||
\(934\) | 22.7817i | 0.745441i | ||||||||
\(935\) | −14.6616 | − | 7.55229i | −0.479486 | − | 0.246986i | ||||
\(936\) | −1.11741 | − | 3.80701i | −0.0365236 | − | 0.124436i | ||||
\(937\) | 43.3679 | 1.41677 | 0.708384 | − | 0.705827i | \(-0.249424\pi\) | ||||
0.708384 | + | 0.705827i | \(0.249424\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.6622 | − | 15.5772i | 0.380581 | − | 0.508342i | ||||
\(940\) | −8.16832 | + | 15.8576i | −0.266421 | + | 0.517217i | ||||
\(941\) | 34.0613 | 1.11037 | 0.555183 | − | 0.831728i | \(-0.312648\pi\) | ||||
0.555183 | + | 0.831728i | \(0.312648\pi\) | |||||||
\(942\) | −10.2225 | + | 13.6542i | −0.333068 | + | 0.444878i | ||||
\(943\) | −8.38359 | −0.273007 | ||||||||
\(944\) | −9.65619 | −0.314282 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.40023 | 0.0780382 | ||||||||
\(947\) | −52.0955 | −1.69288 | −0.846438 | − | 0.532487i | \(-0.821257\pi\) | ||||
−0.846438 | + | 0.532487i | \(0.821257\pi\) | |||||||
\(948\) | 16.1283 | − | 21.5425i | 0.523821 | − | 0.699667i | ||||
\(949\) | 21.8022 | 0.707729 | ||||||||
\(950\) | −9.94094 | + | 7.08910i | −0.322527 | + | 0.230001i | ||||
\(951\) | 4.86452 | − | 6.49754i | 0.157743 | − | 0.210697i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.8965 | −0.968443 | −0.484222 | − | 0.874945i | \(-0.660897\pi\) | ||||
−0.484222 | + | 0.874945i | \(0.660897\pi\) | |||||||
\(954\) | −5.90314 | − | 20.1120i | −0.191121 | − | 0.651151i | ||||
\(955\) | −9.53839 | + | 18.5173i | −0.308655 | + | 0.599207i | ||||
\(956\) | − | 10.6358i | − | 0.343987i | ||||||
\(957\) | −8.13047 | + | 10.8599i | −0.262821 | + | 0.351049i | ||||
\(958\) | −31.9484 | −1.03221 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3.48322 | − | 1.69328i | 0.112420 | − | 0.0546504i | ||||
\(961\) | −17.2043 | −0.554976 | ||||||||
\(962\) | 6.18326i | 0.199356i | ||||||||
\(963\) | 10.2330 | + | 34.8639i | 0.329754 | + | 1.12347i | ||||
\(964\) | − | 3.42344i | − | 0.110262i | ||||||
\(965\) | −2.60057 | + | 5.04860i | −0.0837152 | + | 0.162520i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 40.6051i | − | 1.30577i | −0.757456 | − | 0.652887i | \(-0.773558\pi\) | ||
0.757456 | − | 0.652887i | \(-0.226442\pi\) | |||||||
\(968\) | 9.36570 | 0.301025 | ||||||||
\(969\) | 14.6248 | − | 19.5343i | 0.469815 | − | 0.627531i | ||||
\(970\) | −5.77830 | − | 2.97644i | −0.185530 | − | 0.0955676i | ||||
\(971\) | 40.9311 | 1.31354 | 0.656772 | − | 0.754090i | \(-0.271922\pi\) | ||||
0.656772 | + | 0.754090i | \(0.271922\pi\) | |||||||
\(972\) | 1.11612 | − | 15.5484i | 0.0357997 | − | 0.498717i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 6.93234i | 0.222127i | ||||||||
\(975\) | −11.4504 | − | 0.265386i | −0.366707 | − | 0.00849915i | ||||
\(976\) | − | 4.22958i | − | 0.135386i | ||||||
\(977\) | 5.94472 | 0.190188 | 0.0950942 | − | 0.995468i | \(-0.469685\pi\) | ||||
0.0950942 | + | 0.995468i | \(0.469685\pi\) | |||||||
\(978\) | 15.8635 | + | 11.8766i | 0.507260 | + | 0.379772i | ||||
\(979\) | − | 16.2867i | − | 0.520527i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.44197 | − | 32.1688i | −0.301459 | − | 1.02707i | ||||
\(982\) | − | 24.3178i | − | 0.776012i | ||||||
\(983\) | 23.5901i | 0.752408i | 0.926537 | + | 0.376204i | \(0.122771\pi\) | ||||
−0.926537 | + | 0.376204i | \(0.877229\pi\) | |||||||
\(984\) | 12.7976 | − | 17.0937i | 0.407972 | − | 0.544927i | ||||
\(985\) | 17.2080 | + | 8.86393i | 0.548292 | + | 0.282428i | ||||
\(986\) | −35.3480 | −1.12571 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.22956i | 0.102746i | ||||||||
\(989\) | 1.27676i | 0.0405985i | ||||||||
\(990\) | 8.42116 | + | 1.62099i | 0.267642 | + | 0.0515185i | ||||
\(991\) | 0.0743262 | 0.00236105 | 0.00118053 | − | 0.999999i | \(-0.499624\pi\) | ||||
0.00118053 | + | 0.999999i | \(0.499624\pi\) | |||||||
\(992\) | 6.94293i | 0.220438i | ||||||||
\(993\) | −27.6380 | + | 36.9160i | −0.877064 | + | 1.17149i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −28.5920 | + | 55.5071i | −0.906429 | + | 1.75969i | ||||
\(996\) | −4.62402 | − | 3.46188i | −0.146518 | − | 0.109694i | ||||
\(997\) | −11.0516 | −0.350007 | −0.175003 | − | 0.984568i | \(-0.555994\pi\) | ||||
−0.175003 | + | 0.984568i | \(0.555994\pi\) | |||||||
\(998\) | −22.5999 | −0.715386 | ||||||||
\(999\) | −8.49331 | + | 22.7606i | −0.268716 | + | 0.720112i |
(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 | 1470.2.d.h.1469.10 | yes | 24 | |
3.2 | odd | 2 | 1470.2.d.g.1469.9 | ✓ | 24 | ||
5.4 | even | 2 | 1470.2.d.g.1469.15 | yes | 24 | ||
7.6 | odd | 2 | inner | 1470.2.d.h.1469.15 | yes | 24 | |
15.14 | odd | 2 | inner | 1470.2.d.h.1469.16 | yes | 24 | |
21.20 | even | 2 | 1470.2.d.g.1469.16 | yes | 24 | ||
35.34 | odd | 2 | 1470.2.d.g.1469.10 | yes | 24 | ||
105.104 | even | 2 | inner | 1470.2.d.h.1469.9 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.d.g.1469.9 | ✓ | 24 | 3.2 | odd | 2 | ||
1470.2.d.g.1469.10 | yes | 24 | 35.34 | odd | 2 | ||
1470.2.d.g.1469.15 | yes | 24 | 5.4 | even | 2 | ||
1470.2.d.g.1469.16 | yes | 24 | 21.20 | even | 2 | ||
1470.2.d.h.1469.9 | yes | 24 | 105.104 | even | 2 | inner | |
1470.2.d.h.1469.10 | yes | 24 | 1.1 | even | 1 | trivial | |
1470.2.d.h.1469.15 | yes | 24 | 7.6 | odd | 2 | inner | |
1470.2.d.h.1469.16 | yes | 24 | 15.14 | odd | 2 | inner |