Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,2,Mod(364,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.364");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.e (of order \(3\), degree \(2\), 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: | \(8.69570878012\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 364.10 | ||
Character | \(\chi\) | \(=\) | 1089.364 |
Dual form | 1089.2.e.p.727.10 |
$q$-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 \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.245247 | + | 0.424780i | 0.173416 | + | 0.300365i | 0.939612 | − | 0.342242i | \(-0.111186\pi\) |
−0.766196 | + | 0.642607i | \(0.777853\pi\) | |||||||
\(3\) | −0.361332 | − | 1.69394i | −0.208615 | − | 0.977998i | ||||
\(4\) | 0.879708 | − | 1.52370i | 0.439854 | − | 0.761849i | ||||
\(5\) | −0.854089 | + | 1.47932i | −0.381960 | + | 0.661574i | −0.991342 | − | 0.131302i | \(-0.958084\pi\) |
0.609382 | + | 0.792876i | \(0.291417\pi\) | |||||||
\(6\) | 0.630937 | − | 0.568921i | 0.257579 | − | 0.232261i | ||||
\(7\) | −1.70526 | − | 2.95360i | −0.644528 | − | 1.11636i | −0.984410 | − | 0.175888i | \(-0.943720\pi\) |
0.339882 | − | 0.940468i | \(-0.389613\pi\) | |||||||
\(8\) | 1.84397 | 0.651942 | ||||||||
\(9\) | −2.73888 | + | 1.22415i | −0.912959 | + | 0.408051i | ||||
\(10\) | −0.837851 | −0.264952 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −2.89892 | − | 0.939612i | −0.836847 | − | 0.271243i | ||||
\(13\) | 1.99896 | − | 3.46230i | 0.554412 | − | 0.960270i | −0.443537 | − | 0.896256i | \(-0.646276\pi\) |
0.997949 | − | 0.0640140i | \(-0.0203902\pi\) | |||||||
\(14\) | 0.836420 | − | 1.44872i | 0.223543 | − | 0.387187i | ||||
\(15\) | 2.81450 | + | 0.912248i | 0.726701 | + | 0.235541i | ||||
\(16\) | −1.30719 | − | 2.26411i | −0.326797 | − | 0.566029i | ||||
\(17\) | −3.30458 | −0.801477 | −0.400739 | − | 0.916192i | \(-0.631246\pi\) | ||||
−0.400739 | + | 0.916192i | \(0.631246\pi\) | |||||||
\(18\) | −1.19170 | − | 0.863202i | −0.280886 | − | 0.203459i | ||||
\(19\) | −4.41765 | −1.01348 | −0.506739 | − | 0.862099i | \(-0.669149\pi\) | ||||
−0.506739 | + | 0.862099i | \(0.669149\pi\) | |||||||
\(20\) | 1.50270 | + | 2.60275i | 0.336013 | + | 0.581992i | ||||
\(21\) | −4.38706 | + | 3.95584i | −0.957335 | + | 0.863236i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.74601 | + | 6.48827i | −0.781096 | + | 1.35290i | 0.150208 | + | 0.988654i | \(0.452006\pi\) |
−0.931304 | + | 0.364244i | \(0.881328\pi\) | |||||||
\(24\) | −0.666286 | − | 3.12358i | −0.136005 | − | 0.637598i | ||||
\(25\) | 1.04107 | + | 1.80318i | 0.208213 | + | 0.360636i | ||||
\(26\) | 1.96096 | 0.384575 | ||||||||
\(27\) | 3.06329 | + | 4.19717i | 0.589530 | + | 0.807746i | ||||
\(28\) | −6.00053 | −1.13399 | ||||||||
\(29\) | −0.845644 | − | 1.46470i | −0.157032 | − | 0.271988i | 0.776765 | − | 0.629791i | \(-0.216859\pi\) |
−0.933797 | + | 0.357803i | \(0.883526\pi\) | |||||||
\(30\) | 0.302743 | + | 1.41927i | 0.0552730 | + | 0.259122i | ||||
\(31\) | 1.94926 | − | 3.37621i | 0.350097 | − | 0.606386i | −0.636169 | − | 0.771550i | \(-0.719482\pi\) |
0.986266 | + | 0.165164i | \(0.0528153\pi\) | |||||||
\(32\) | 2.48514 | − | 4.30439i | 0.439315 | − | 0.760915i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.810437 | − | 1.40372i | −0.138989 | − | 0.240736i | ||||
\(35\) | 5.82578 | 0.984736 | ||||||||
\(36\) | −0.544173 | + | 5.25012i | −0.0906955 | + | 0.875020i | ||||
\(37\) | 3.06553 | 0.503970 | 0.251985 | − | 0.967731i | \(-0.418917\pi\) | ||||
0.251985 | + | 0.967731i | \(0.418917\pi\) | |||||||
\(38\) | −1.08342 | − | 1.87653i | −0.175753 | − | 0.304414i | ||||
\(39\) | −6.58723 | − | 2.13508i | −1.05480 | − | 0.341887i | ||||
\(40\) | −1.57491 | + | 2.72783i | −0.249016 | + | 0.431308i | ||||
\(41\) | −0.195437 | + | 0.338507i | −0.0305222 | + | 0.0528660i | −0.880883 | − | 0.473334i | \(-0.843050\pi\) |
0.850361 | + | 0.526200i | \(0.176384\pi\) | |||||||
\(42\) | −2.75628 | − | 0.893377i | −0.425303 | − | 0.137851i | ||||
\(43\) | −4.80634 | − | 8.32483i | −0.732960 | − | 1.26952i | −0.955613 | − | 0.294626i | \(-0.904805\pi\) |
0.222652 | − | 0.974898i | \(-0.428529\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.528325 | − | 5.09722i | 0.0787581 | − | 0.759849i | ||||
\(46\) | −3.67479 | −0.541818 | ||||||||
\(47\) | 0.540129 | + | 0.935531i | 0.0787859 | + | 0.136461i | 0.902726 | − | 0.430215i | \(-0.141562\pi\) |
−0.823940 | + | 0.566676i | \(0.808229\pi\) | |||||||
\(48\) | −3.36295 | + | 3.03240i | −0.485400 | + | 0.437689i | ||||
\(49\) | −2.31583 | + | 4.01114i | −0.330833 | + | 0.573020i | ||||
\(50\) | −0.510636 | + | 0.884448i | −0.0722149 | + | 0.125080i | ||||
\(51\) | 1.19405 | + | 5.59776i | 0.167200 | + | 0.783843i | ||||
\(52\) | −3.51700 | − | 6.09163i | −0.487721 | − | 0.844757i | ||||
\(53\) | −12.5638 | −1.72577 | −0.862884 | − | 0.505402i | \(-0.831344\pi\) | ||||
−0.862884 | + | 0.505402i | \(0.831344\pi\) | |||||||
\(54\) | −1.03161 | + | 2.33057i | −0.140385 | + | 0.317150i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.14445 | − | 5.44635i | −0.420195 | − | 0.727799i | ||||
\(57\) | 1.59624 | + | 7.48324i | 0.211427 | + | 0.991180i | ||||
\(58\) | 0.414783 | − | 0.718426i | 0.0544637 | − | 0.0943339i | ||||
\(59\) | 1.82827 | − | 3.16666i | 0.238021 | − | 0.412264i | −0.722126 | − | 0.691762i | \(-0.756835\pi\) |
0.960146 | + | 0.279498i | \(0.0901681\pi\) | |||||||
\(60\) | 3.86593 | − | 3.48594i | 0.499089 | − | 0.450033i | ||||
\(61\) | 1.92659 | + | 3.33695i | 0.246674 | + | 0.427252i | 0.962601 | − | 0.270923i | \(-0.0873289\pi\) |
−0.715927 | + | 0.698175i | \(0.753996\pi\) | |||||||
\(62\) | 1.91220 | 0.242849 | ||||||||
\(63\) | 8.28616 | + | 6.00205i | 1.04396 | + | 0.756187i | ||||
\(64\) | −2.79086 | −0.348857 | ||||||||
\(65\) | 3.41458 | + | 5.91423i | 0.423527 | + | 0.733570i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.55060 | + | 2.68572i | −0.189436 | + | 0.328113i | −0.945062 | − | 0.326890i | \(-0.893999\pi\) |
0.755626 | + | 0.655003i | \(0.227333\pi\) | |||||||
\(68\) | −2.90706 | + | 5.03518i | −0.352533 | + | 0.610605i | ||||
\(69\) | 12.3443 | + | 4.00109i | 1.48608 | + | 0.481675i | ||||
\(70\) | 1.42875 | + | 2.47467i | 0.170769 | + | 0.295780i | ||||
\(71\) | 7.01715 | 0.832783 | 0.416391 | − | 0.909186i | \(-0.363295\pi\) | ||||
0.416391 | + | 0.909186i | \(0.363295\pi\) | |||||||
\(72\) | −5.05041 | + | 2.25730i | −0.595197 | + | 0.266025i | ||||
\(73\) | −15.0426 | −1.76060 | −0.880302 | − | 0.474413i | \(-0.842660\pi\) | ||||
−0.880302 | + | 0.474413i | \(0.842660\pi\) | |||||||
\(74\) | 0.751812 | + | 1.30218i | 0.0873963 | + | 0.151375i | ||||
\(75\) | 2.67831 | − | 2.41505i | 0.309264 | − | 0.278866i | ||||
\(76\) | −3.88624 | + | 6.73117i | −0.445783 | + | 0.772118i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.708557 | − | 3.32175i | −0.0802283 | − | 0.376114i | ||||
\(79\) | 1.99957 | + | 3.46335i | 0.224969 | + | 0.389657i | 0.956310 | − | 0.292354i | \(-0.0944387\pi\) |
−0.731341 | + | 0.682012i | \(0.761105\pi\) | |||||||
\(80\) | 4.46581 | 0.499293 | ||||||||
\(81\) | 6.00290 | − | 6.70561i | 0.666989 | − | 0.745067i | ||||
\(82\) | −0.191722 | −0.0211721 | ||||||||
\(83\) | 0.0624829 | + | 0.108224i | 0.00685839 | + | 0.0118791i | 0.869434 | − | 0.494049i | \(-0.164484\pi\) |
−0.862576 | + | 0.505928i | \(0.831150\pi\) | |||||||
\(84\) | 2.16818 | + | 10.1645i | 0.236568 | + | 1.10904i | ||||
\(85\) | 2.82240 | − | 4.88854i | 0.306132 | − | 0.530237i | ||||
\(86\) | 2.35748 | − | 4.08328i | 0.254214 | − | 0.440311i | ||||
\(87\) | −2.17556 | + | 1.96172i | −0.233244 | + | 0.210318i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.93327 | −0.840925 | −0.420462 | − | 0.907310i | \(-0.638132\pi\) | ||||
−0.420462 | + | 0.907310i | \(0.638132\pi\) | |||||||
\(90\) | 2.29477 | − | 1.02566i | 0.241890 | − | 0.108114i | ||||
\(91\) | −13.6350 | −1.42934 | ||||||||
\(92\) | 6.59078 | + | 11.4156i | 0.687136 | + | 1.19016i | ||||
\(93\) | −6.42344 | − | 2.08199i | −0.666080 | − | 0.215893i | ||||
\(94\) | −0.264930 | + | 0.458872i | −0.0273255 | + | 0.0473291i | ||||
\(95\) | 3.77307 | − | 6.53514i | 0.387108 | − | 0.670491i | ||||
\(96\) | −8.18934 | − | 2.65437i | −0.835821 | − | 0.270910i | ||||
\(97\) | −0.171580 | − | 0.297185i | −0.0174213 | − | 0.0301746i | 0.857183 | − | 0.515011i | \(-0.172212\pi\) |
−0.874605 | + | 0.484837i | \(0.838879\pi\) | |||||||
\(98\) | −2.27180 | −0.229487 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.66333 | 0.366333 | ||||||||
\(101\) | −3.55779 | − | 6.16228i | −0.354014 | − | 0.613169i | 0.632935 | − | 0.774205i | \(-0.281850\pi\) |
−0.986949 | + | 0.161035i | \(0.948517\pi\) | |||||||
\(102\) | −2.08498 | + | 1.88004i | −0.206444 | + | 0.186152i | ||||
\(103\) | 0.827144 | − | 1.43266i | 0.0815009 | − | 0.141164i | −0.822394 | − | 0.568918i | \(-0.807362\pi\) |
0.903895 | + | 0.427755i | \(0.140695\pi\) | |||||||
\(104\) | 3.68603 | − | 6.38439i | 0.361445 | − | 0.626041i | ||||
\(105\) | −2.10504 | − | 9.86853i | −0.205431 | − | 0.963070i | ||||
\(106\) | −3.08123 | − | 5.33685i | −0.299275 | − | 0.518360i | ||||
\(107\) | 3.30683 | 0.319683 | 0.159842 | − | 0.987143i | \(-0.448902\pi\) | ||||
0.159842 | + | 0.987143i | \(0.448902\pi\) | |||||||
\(108\) | 9.09003 | − | 0.975241i | 0.874688 | − | 0.0938426i | ||||
\(109\) | −5.50709 | −0.527484 | −0.263742 | − | 0.964593i | \(-0.584957\pi\) | ||||
−0.263742 | + | 0.964593i | \(0.584957\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.10767 | − | 5.19283i | −0.105136 | − | 0.492881i | ||||
\(112\) | −4.45819 | + | 7.72182i | −0.421260 | + | 0.729643i | ||||
\(113\) | 8.20461 | − | 14.2108i | 0.771825 | − | 1.33684i | −0.164737 | − | 0.986338i | \(-0.552677\pi\) |
0.936562 | − | 0.350503i | \(-0.113989\pi\) | |||||||
\(114\) | −2.78726 | + | 2.51329i | −0.261051 | + | 0.235392i | ||||
\(115\) | −6.39884 | − | 11.0831i | −0.596695 | − | 1.03351i | ||||
\(116\) | −2.97568 | −0.276285 | ||||||||
\(117\) | −1.23653 | + | 11.9299i | −0.114317 | + | 1.10292i | ||||
\(118\) | 1.79351 | 0.165106 | ||||||||
\(119\) | 5.63516 | + | 9.76039i | 0.516575 | + | 0.894734i | ||||
\(120\) | 5.18986 | + | 1.68216i | 0.473767 | + | 0.153559i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −0.944980 | + | 1.63675i | −0.0855545 | + | 0.148185i | ||||
\(123\) | 0.644030 | + | 0.208746i | 0.0580702 | + | 0.0188220i | ||||
\(124\) | −3.42956 | − | 5.94016i | −0.307983 | − | 0.533442i | ||||
\(125\) | −12.0975 | −1.08204 | ||||||||
\(126\) | −0.517396 | + | 4.99178i | −0.0460933 | + | 0.444703i | ||||
\(127\) | 10.7949 | 0.957894 | 0.478947 | − | 0.877844i | \(-0.341019\pi\) | ||||
0.478947 | + | 0.877844i | \(0.341019\pi\) | |||||||
\(128\) | −5.65473 | − | 9.79427i | −0.499812 | − | 0.865700i | ||||
\(129\) | −12.3651 | + | 11.1497i | −1.08869 | + | 0.981676i | ||||
\(130\) | −1.67483 | + | 2.90089i | −0.146892 | + | 0.254425i | ||||
\(131\) | 10.5778 | − | 18.3213i | 0.924189 | − | 1.60074i | 0.131329 | − | 0.991339i | \(-0.458075\pi\) |
0.792860 | − | 0.609404i | \(-0.208591\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.53325 | + | 13.0480i | 0.653216 | + | 1.13140i | ||||
\(134\) | −1.52112 | −0.131405 | ||||||||
\(135\) | −8.82530 | + | 0.946840i | −0.759561 | + | 0.0814910i | ||||
\(136\) | −6.09354 | −0.522517 | ||||||||
\(137\) | −1.60026 | − | 2.77173i | −0.136720 | − | 0.236805i | 0.789533 | − | 0.613708i | \(-0.210323\pi\) |
−0.926253 | + | 0.376902i | \(0.876989\pi\) | |||||||
\(138\) | 1.32782 | + | 6.22487i | 0.113031 | + | 0.529896i | ||||
\(139\) | 7.49682 | − | 12.9849i | 0.635872 | − | 1.10136i | −0.350457 | − | 0.936579i | \(-0.613974\pi\) |
0.986330 | − | 0.164784i | \(-0.0526928\pi\) | |||||||
\(140\) | 5.12498 | − | 8.87673i | 0.433140 | − | 0.750220i | ||||
\(141\) | 1.38957 | − | 1.25299i | 0.117023 | − | 0.105520i | ||||
\(142\) | 1.72094 | + | 2.98075i | 0.144418 | + | 0.250139i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 6.35185 | + | 4.60094i | 0.529321 | + | 0.383411i | ||||
\(145\) | 2.88902 | 0.239920 | ||||||||
\(146\) | −3.68916 | − | 6.38980i | −0.305317 | − | 0.528824i | ||||
\(147\) | 7.63142 | + | 2.47353i | 0.629429 | + | 0.204013i | ||||
\(148\) | 2.69677 | − | 4.67094i | 0.221673 | − | 0.383949i | ||||
\(149\) | −2.02556 | + | 3.50838i | −0.165940 | + | 0.287417i | −0.936989 | − | 0.349359i | \(-0.886399\pi\) |
0.771048 | + | 0.636777i | \(0.219733\pi\) | |||||||
\(150\) | 1.68271 | + | 0.545409i | 0.137393 | + | 0.0445324i | ||||
\(151\) | 3.89699 | + | 6.74979i | 0.317133 | + | 0.549290i | 0.979889 | − | 0.199546i | \(-0.0639466\pi\) |
−0.662756 | + | 0.748836i | \(0.730613\pi\) | |||||||
\(152\) | −8.14602 | −0.660729 | ||||||||
\(153\) | 9.05083 | − | 4.04530i | 0.731716 | − | 0.327043i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.32968 | + | 5.76717i | 0.267446 | + | 0.463230i | ||||
\(156\) | −9.04806 | + | 8.15870i | −0.724425 | + | 0.653219i | ||||
\(157\) | −0.154576 | + | 0.267734i | −0.0123365 | + | 0.0213675i | −0.872128 | − | 0.489278i | \(-0.837260\pi\) |
0.859791 | + | 0.510646i | \(0.170594\pi\) | |||||||
\(158\) | −0.980775 | + | 1.69875i | −0.0780262 | + | 0.135145i | ||||
\(159\) | 4.53970 | + | 21.2823i | 0.360022 | + | 1.68780i | ||||
\(160\) | 4.24506 | + | 7.35265i | 0.335601 | + | 0.581278i | ||||
\(161\) | 25.5517 | 2.01375 | ||||||||
\(162\) | 4.32060 | + | 0.905385i | 0.339459 | + | 0.0711337i | ||||
\(163\) | 10.9941 | 0.861125 | 0.430563 | − | 0.902561i | \(-0.358315\pi\) | ||||
0.430563 | + | 0.902561i | \(0.358315\pi\) | |||||||
\(164\) | 0.343855 | + | 0.595575i | 0.0268506 | + | 0.0465066i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.0306475 | + | 0.0530830i | −0.00237871 | + | 0.00412004i | ||||
\(167\) | 8.78693 | − | 15.2194i | 0.679953 | − | 1.17771i | −0.295041 | − | 0.955485i | \(-0.595333\pi\) |
0.974994 | − | 0.222229i | \(-0.0713333\pi\) | |||||||
\(168\) | −8.08961 | + | 7.29446i | −0.624127 | + | 0.562780i | ||||
\(169\) | −1.49170 | − | 2.58369i | −0.114746 | − | 0.198746i | ||||
\(170\) | 2.76874 | 0.212353 | ||||||||
\(171\) | 12.0994 | − | 5.40788i | 0.925265 | − | 0.413551i | ||||
\(172\) | −16.9127 | −1.28958 | ||||||||
\(173\) | −6.18287 | − | 10.7090i | −0.470075 | − | 0.814193i | 0.529340 | − | 0.848410i | \(-0.322440\pi\) |
−0.999414 | + | 0.0342165i | \(0.989106\pi\) | |||||||
\(174\) | −1.36685 | − | 0.443028i | −0.103620 | − | 0.0335859i | ||||
\(175\) | 3.55058 | − | 6.14978i | 0.268398 | − | 0.464880i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.02475 | − | 1.95277i | −0.452848 | − | 0.146779i | ||||
\(178\) | −1.94561 | − | 3.36990i | −0.145830 | − | 0.252584i | ||||
\(179\) | 21.8823 | 1.63556 | 0.817780 | − | 0.575531i | \(-0.195205\pi\) | ||||
0.817780 | + | 0.575531i | \(0.195205\pi\) | |||||||
\(180\) | −7.30186 | − | 5.28908i | −0.544249 | − | 0.394224i | ||||
\(181\) | −4.38018 | −0.325576 | −0.162788 | − | 0.986661i | \(-0.552049\pi\) | ||||
−0.162788 | + | 0.986661i | \(0.552049\pi\) | |||||||
\(182\) | −3.34394 | − | 5.79188i | −0.247870 | − | 0.429323i | ||||
\(183\) | 4.95646 | − | 4.46928i | 0.366392 | − | 0.330378i | ||||
\(184\) | −6.90752 | + | 11.9642i | −0.509229 | + | 0.882011i | ||||
\(185\) | −2.61823 | + | 4.53491i | −0.192496 | + | 0.333413i | ||||
\(186\) | −0.690939 | − | 3.23915i | −0.0506621 | − | 0.237506i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.90062 | 0.138617 | ||||||||
\(189\) | 7.17306 | − | 16.2050i | 0.521764 | − | 1.17874i | ||||
\(190\) | 3.70133 | 0.268523 | ||||||||
\(191\) | −6.25737 | − | 10.8381i | −0.452767 | − | 0.784216i | 0.545790 | − | 0.837922i | \(-0.316230\pi\) |
−0.998557 | + | 0.0537064i | \(0.982896\pi\) | |||||||
\(192\) | 1.00843 | + | 4.72755i | 0.0727770 | + | 0.341182i | ||||
\(193\) | 6.28286 | − | 10.8822i | 0.452250 | − | 0.783320i | −0.546276 | − | 0.837606i | \(-0.683955\pi\) |
0.998525 | + | 0.0542857i | \(0.0172882\pi\) | |||||||
\(194\) | 0.0841588 | − | 0.145767i | 0.00604225 | − | 0.0104655i | ||||
\(195\) | 8.78456 | − | 7.92110i | 0.629075 | − | 0.567242i | ||||
\(196\) | 4.07451 | + | 7.05726i | 0.291037 | + | 0.504090i | ||||
\(197\) | −10.3453 | −0.737075 | −0.368538 | − | 0.929613i | \(-0.620141\pi\) | ||||
−0.368538 | + | 0.929613i | \(0.620141\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.4773 | 1.87693 | 0.938464 | − | 0.345376i | \(-0.112249\pi\) | ||||
0.938464 | + | 0.345376i | \(0.112249\pi\) | |||||||
\(200\) | 1.91969 | + | 3.32501i | 0.135743 | + | 0.235114i | ||||
\(201\) | 5.10973 | + | 1.65619i | 0.360413 | + | 0.116819i | ||||
\(202\) | 1.74508 | − | 3.02256i | 0.122783 | − | 0.212667i | ||||
\(203\) | −2.88409 | + | 4.99539i | −0.202423 | + | 0.350608i | ||||
\(204\) | 9.57971 | + | 3.10502i | 0.670714 | + | 0.217395i | ||||
\(205\) | −0.333842 | − | 0.578231i | −0.0233165 | − | 0.0403854i | ||||
\(206\) | 0.811418 | 0.0565342 | ||||||||
\(207\) | 2.31722 | − | 22.3563i | 0.161058 | − | 1.55387i | ||||
\(208\) | −10.4521 | −0.724721 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3.67570 | − | 3.31441i | 0.253647 | − | 0.228716i | ||||
\(211\) | 3.64195 | − | 6.30804i | 0.250722 | − | 0.434264i | −0.713003 | − | 0.701161i | \(-0.752665\pi\) |
0.963725 | + | 0.266898i | \(0.0859986\pi\) | |||||||
\(212\) | −11.0525 | + | 19.1434i | −0.759086 | + | 1.31478i | ||||
\(213\) | −2.53552 | − | 11.8866i | −0.173731 | − | 0.814459i | ||||
\(214\) | 0.810990 | + | 1.40468i | 0.0554382 | + | 0.0960217i | ||||
\(215\) | 16.4202 | 1.11985 | ||||||||
\(216\) | 5.64861 | + | 7.73947i | 0.384339 | + | 0.526604i | ||||
\(217\) | −13.2960 | −0.902590 | ||||||||
\(218\) | −1.35060 | − | 2.33930i | −0.0914741 | − | 0.158438i | ||||
\(219\) | 5.43538 | + | 25.4813i | 0.367289 | + | 1.72187i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.60572 | + | 11.4414i | −0.444349 | + | 0.769635i | ||||
\(222\) | 1.93416 | − | 1.74404i | 0.129812 | − | 0.117053i | ||||
\(223\) | −11.7550 | − | 20.3603i | −0.787175 | − | 1.36343i | −0.927691 | − | 0.373349i | \(-0.878209\pi\) |
0.140516 | − | 0.990078i | \(-0.455124\pi\) | |||||||
\(224\) | −16.9512 | −1.13260 | ||||||||
\(225\) | −5.05872 | − | 3.66426i | −0.337248 | − | 0.244284i | ||||
\(226\) | 8.04863 | 0.535387 | ||||||||
\(227\) | 5.96109 | + | 10.3249i | 0.395652 | + | 0.685289i | 0.993184 | − | 0.116556i | \(-0.0371854\pi\) |
−0.597532 | + | 0.801845i | \(0.703852\pi\) | |||||||
\(228\) | 12.8064 | + | 4.15088i | 0.848127 | + | 0.274899i | ||||
\(229\) | −1.52879 | + | 2.64793i | −0.101025 | + | 0.174980i | −0.912107 | − | 0.409952i | \(-0.865546\pi\) |
0.811082 | + | 0.584932i | \(0.198879\pi\) | |||||||
\(230\) | 3.13859 | − | 5.43620i | 0.206953 | − | 0.358453i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.55934 | − | 2.70086i | −0.102376 | − | 0.177320i | ||||
\(233\) | −24.5314 | −1.60710 | −0.803552 | − | 0.595235i | \(-0.797059\pi\) | ||||
−0.803552 | + | 0.595235i | \(0.797059\pi\) | |||||||
\(234\) | −5.37082 | + | 2.40051i | −0.351102 | + | 0.156926i | ||||
\(235\) | −1.84527 | −0.120372 | ||||||||
\(236\) | −3.21669 | − | 5.57147i | −0.209389 | − | 0.362672i | ||||
\(237\) | 5.14420 | − | 4.63857i | 0.334152 | − | 0.301307i | ||||
\(238\) | −2.76401 | + | 4.78741i | −0.179164 | + | 0.310322i | ||||
\(239\) | 3.47531 | − | 6.01942i | 0.224799 | − | 0.389364i | −0.731460 | − | 0.681885i | \(-0.761161\pi\) |
0.956259 | + | 0.292521i | \(0.0944940\pi\) | |||||||
\(240\) | −1.61364 | − | 7.56483i | −0.104160 | − | 0.488308i | ||||
\(241\) | 3.88529 | + | 6.72952i | 0.250274 | + | 0.433487i | 0.963601 | − | 0.267344i | \(-0.0861461\pi\) |
−0.713327 | + | 0.700831i | \(0.752813\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.5280 | − | 7.74562i | −0.867818 | − | 0.496881i | ||||
\(244\) | 6.77934 | 0.434003 | ||||||||
\(245\) | −3.95585 | − | 6.85174i | −0.252730 | − | 0.437741i | ||||
\(246\) | 0.0692753 | + | 0.324765i | 0.00441683 | + | 0.0207063i | ||||
\(247\) | −8.83072 | + | 15.2952i | −0.561885 | + | 0.973213i | ||||
\(248\) | 3.59438 | − | 6.22564i | 0.228243 | − | 0.395329i | ||||
\(249\) | 0.160747 | − | 0.144947i | 0.0101870 | − | 0.00918565i | ||||
\(250\) | −2.96688 | − | 5.13879i | −0.187642 | − | 0.325006i | ||||
\(251\) | 0.327168 | 0.0206506 | 0.0103253 | − | 0.999947i | \(-0.496713\pi\) | ||||
0.0103253 | + | 0.999947i | \(0.496713\pi\) | |||||||
\(252\) | 16.4347 | − | 7.34556i | 1.03529 | − | 0.462727i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 2.64742 | + | 4.58547i | 0.166114 | + | 0.287718i | ||||
\(255\) | −9.30073 | − | 3.01459i | −0.582434 | − | 0.188781i | ||||
\(256\) | −0.0172493 | + | 0.0298766i | −0.00107808 | + | 0.00186729i | ||||
\(257\) | 6.86458 | − | 11.8898i | 0.428201 | − | 0.741666i | −0.568512 | − | 0.822675i | \(-0.692481\pi\) |
0.996713 | + | 0.0810088i | \(0.0258142\pi\) | |||||||
\(258\) | −7.76867 | − | 2.51802i | −0.483656 | − | 0.156765i | ||||
\(259\) | −5.22753 | − | 9.05434i | −0.324823 | − | 0.562609i | ||||
\(260\) | 12.0153 | 0.745159 | ||||||||
\(261\) | 4.10913 | + | 2.97643i | 0.254349 | + | 0.184237i | ||||
\(262\) | 10.3767 | 0.641076 | ||||||||
\(263\) | 8.42709 | + | 14.5961i | 0.519637 | + | 0.900037i | 0.999739 | + | 0.0228249i | \(0.00726603\pi\) |
−0.480103 | + | 0.877212i | \(0.659401\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.7306 | − | 18.5859i | 0.659174 | − | 1.14172i | ||||
\(266\) | −3.69501 | + | 6.39995i | −0.226556 | + | 0.392406i | ||||
\(267\) | 2.86655 | + | 13.4385i | 0.175430 | + | 0.822422i | ||||
\(268\) | 2.72815 | + | 4.72529i | 0.166648 | + | 0.288643i | ||||
\(269\) | 12.3974 | 0.755882 | 0.377941 | − | 0.925830i | \(-0.376632\pi\) | ||||
0.377941 | + | 0.925830i | \(0.376632\pi\) | |||||||
\(270\) | −2.56658 | − | 3.51660i | −0.156197 | − | 0.214014i | ||||
\(271\) | 19.2695 | 1.17054 | 0.585269 | − | 0.810839i | \(-0.300989\pi\) | ||||
0.585269 | + | 0.810839i | \(0.300989\pi\) | |||||||
\(272\) | 4.31970 | + | 7.48194i | 0.261920 | + | 0.453659i | ||||
\(273\) | 4.92677 | + | 23.0969i | 0.298182 | + | 1.39789i | ||||
\(274\) | 0.784919 | − | 1.35952i | 0.0474187 | − | 0.0821316i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 16.9558 | − | 15.2892i | 1.02062 | − | 0.920302i | ||||
\(277\) | −5.17554 | − | 8.96430i | −0.310968 | − | 0.538613i | 0.667604 | − | 0.744516i | \(-0.267320\pi\) |
−0.978572 | + | 0.205904i | \(0.933987\pi\) | |||||||
\(278\) | 7.35429 | 0.441081 | ||||||||
\(279\) | −1.20578 | + | 11.6332i | −0.0721882 | + | 0.696463i | ||||
\(280\) | 10.7426 | 0.641991 | ||||||||
\(281\) | 8.21790 | + | 14.2338i | 0.490239 | + | 0.849119i | 0.999937 | − | 0.0112348i | \(-0.00357623\pi\) |
−0.509698 | + | 0.860353i | \(0.670243\pi\) | |||||||
\(282\) | 0.873031 | + | 0.282971i | 0.0519882 | + | 0.0168507i | ||||
\(283\) | 0.632477 | − | 1.09548i | 0.0375968 | − | 0.0651197i | −0.846615 | − | 0.532206i | \(-0.821363\pi\) |
0.884212 | + | 0.467087i | \(0.154696\pi\) | |||||||
\(284\) | 6.17304 | − | 10.6920i | 0.366303 | − | 0.634455i | ||||
\(285\) | −12.4335 | − | 4.02999i | −0.736496 | − | 0.238716i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.33309 | 0.0786896 | ||||||||
\(288\) | −1.53727 | + | 14.8314i | −0.0905843 | + | 0.873947i | ||||
\(289\) | −6.07978 | −0.357634 | ||||||||
\(290\) | 0.708523 | + | 1.22720i | 0.0416059 | + | 0.0720636i | ||||
\(291\) | −0.441417 | + | 0.398029i | −0.0258763 | + | 0.0233329i | ||||
\(292\) | −13.2331 | + | 22.9204i | −0.774409 | + | 1.34132i | ||||
\(293\) | 12.0437 | − | 20.8603i | 0.703601 | − | 1.21867i | −0.263593 | − | 0.964634i | \(-0.584908\pi\) |
0.967194 | − | 0.254038i | \(-0.0817589\pi\) | |||||||
\(294\) | 0.820876 | + | 3.84830i | 0.0478745 | + | 0.224438i | ||||
\(295\) | 3.12301 | + | 5.40921i | 0.181829 | + | 0.314937i | ||||
\(296\) | 5.65274 | 0.328559 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.98705 | −0.115107 | ||||||||
\(299\) | 14.9762 | + | 25.9396i | 0.866098 | + | 1.50013i | ||||
\(300\) | −1.32368 | − | 6.20548i | −0.0764228 | − | 0.358273i | ||||
\(301\) | −16.3921 | + | 28.3920i | −0.944827 | + | 1.63649i | ||||
\(302\) | −1.91145 | + | 3.31073i | −0.109992 | + | 0.190511i | ||||
\(303\) | −9.15299 | + | 8.25332i | −0.525826 | + | 0.474141i | ||||
\(304\) | 5.77470 | + | 10.0021i | 0.331202 | + | 0.573658i | ||||
\(305\) | −6.58191 | −0.376879 | ||||||||
\(306\) | 3.93805 | + | 2.85251i | 0.225124 | + | 0.163067i | ||||
\(307\) | 16.2949 | 0.930001 | 0.465001 | − | 0.885310i | \(-0.346054\pi\) | ||||
0.465001 | + | 0.885310i | \(0.346054\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.72571 | − | 0.883469i | −0.155060 | − | 0.0502588i | ||||
\(310\) | −1.63319 | + | 2.82876i | −0.0927588 | + | 0.160663i | ||||
\(311\) | −10.6856 | + | 18.5080i | −0.605926 | + | 1.04950i | 0.385978 | + | 0.922508i | \(0.373864\pi\) |
−0.991904 | + | 0.126987i | \(0.959469\pi\) | |||||||
\(312\) | −12.1467 | − | 3.93703i | −0.687669 | − | 0.222890i | ||||
\(313\) | −1.55806 | − | 2.69864i | −0.0880669 | − | 0.152536i | 0.818627 | − | 0.574325i | \(-0.194736\pi\) |
−0.906694 | + | 0.421789i | \(0.861402\pi\) | |||||||
\(314\) | −0.151637 | −0.00855738 | ||||||||
\(315\) | −15.9561 | + | 7.13164i | −0.899024 | + | 0.401822i | ||||
\(316\) | 7.03613 | 0.395813 | ||||||||
\(317\) | 9.13242 | + | 15.8178i | 0.512928 | + | 0.888417i | 0.999888 | + | 0.0149929i | \(0.00477258\pi\) |
−0.486960 | + | 0.873425i | \(0.661894\pi\) | |||||||
\(318\) | −7.92696 | + | 7.14780i | −0.444522 | + | 0.400829i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 2.38364 | − | 4.12859i | 0.133250 | − | 0.230795i | ||||
\(321\) | −1.19487 | − | 5.60158i | −0.0666909 | − | 0.312650i | ||||
\(322\) | 6.26647 | + | 10.8538i | 0.349217 | + | 0.604861i | ||||
\(323\) | 14.5985 | 0.812280 | ||||||||
\(324\) | −4.93652 | − | 15.0456i | −0.274251 | − | 0.835866i | ||||
\(325\) | 8.32420 | 0.461744 | ||||||||
\(326\) | 2.69627 | + | 4.67008i | 0.149333 | + | 0.258652i | ||||
\(327\) | 1.98989 | + | 9.32870i | 0.110041 | + | 0.515878i | ||||
\(328\) | −0.360381 | + | 0.624198i | −0.0198987 | + | 0.0344656i | ||||
\(329\) | 1.84212 | − | 3.19065i | 0.101560 | − | 0.175906i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.88308 | − | 3.26159i | −0.103503 | − | 0.179273i | 0.809622 | − | 0.586951i | \(-0.199672\pi\) |
−0.913126 | + | 0.407678i | \(0.866339\pi\) | |||||||
\(332\) | 0.219867 | 0.0120668 | ||||||||
\(333\) | −8.39611 | + | 3.75267i | −0.460104 | + | 0.205645i | ||||
\(334\) | 8.61988 | 0.471659 | ||||||||
\(335\) | −2.64870 | − | 4.58768i | −0.144714 | − | 0.250652i | ||||
\(336\) | 14.6912 | + | 4.76178i | 0.801470 | + | 0.259776i | ||||
\(337\) | −2.98309 | + | 5.16686i | −0.162499 | + | 0.281457i | −0.935764 | − | 0.352626i | \(-0.885289\pi\) |
0.773265 | + | 0.634083i | \(0.218622\pi\) | |||||||
\(338\) | 0.731668 | − | 1.26729i | 0.0397975 | − | 0.0689313i | ||||
\(339\) | −27.0369 | − | 8.76331i | −1.46844 | − | 0.475958i | ||||
\(340\) | −4.96577 | − | 8.60097i | −0.269307 | − | 0.466453i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 5.26450 | + | 3.81332i | 0.284672 | + | 0.206201i | ||||
\(343\) | −8.07726 | −0.436131 | ||||||||
\(344\) | −8.86275 | − | 15.3507i | −0.477848 | − | 0.827656i | ||||
\(345\) | −16.4620 | + | 14.8440i | −0.886287 | + | 0.799172i | ||||
\(346\) | 3.03266 | − | 5.25272i | 0.163037 | − | 0.282388i | ||||
\(347\) | −12.1747 | + | 21.0871i | −0.653570 | + | 1.13202i | 0.328680 | + | 0.944441i | \(0.393396\pi\) |
−0.982250 | + | 0.187575i | \(0.939937\pi\) | |||||||
\(348\) | 1.07521 | + | 5.04063i | 0.0576373 | + | 0.270206i | ||||
\(349\) | −8.37089 | − | 14.4988i | −0.448083 | − | 0.776103i | 0.550178 | − | 0.835047i | \(-0.314560\pi\) |
−0.998261 | + | 0.0589445i | \(0.981227\pi\) | |||||||
\(350\) | 3.48307 | 0.186178 | ||||||||
\(351\) | 20.6553 | − | 2.21604i | 1.10250 | − | 0.118284i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.01566 | + | 6.95533i | 0.213732 | + | 0.370195i | 0.952880 | − | 0.303349i | \(-0.0981047\pi\) |
−0.739148 | + | 0.673544i | \(0.764771\pi\) | |||||||
\(354\) | −0.648054 | − | 3.03811i | −0.0344437 | − | 0.161473i | ||||
\(355\) | −5.99327 | + | 10.3806i | −0.318090 | + | 0.550947i | ||||
\(356\) | −6.97896 | + | 12.0879i | −0.369884 | + | 0.640658i | ||||
\(357\) | 14.4974 | − | 13.0724i | 0.767282 | − | 0.691864i | ||||
\(358\) | 5.36657 | + | 9.29517i | 0.283632 | + | 0.491265i | ||||
\(359\) | −28.8250 | −1.52133 | −0.760663 | − | 0.649147i | \(-0.775126\pi\) | ||||
−0.760663 | + | 0.649147i | \(0.775126\pi\) | |||||||
\(360\) | 0.974217 | − | 9.39913i | 0.0513457 | − | 0.495378i | ||||
\(361\) | 0.515640 | 0.0271390 | ||||||||
\(362\) | −1.07422 | − | 1.86061i | −0.0564600 | − | 0.0977916i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −11.9948 | + | 20.7756i | −0.628700 | + | 1.08894i | ||||
\(365\) | 12.8477 | − | 22.2529i | 0.672481 | − | 1.16477i | ||||
\(366\) | 3.11402 | + | 1.00933i | 0.162772 | + | 0.0527585i | ||||
\(367\) | −11.1717 | − | 19.3499i | −0.583158 | − | 1.01006i | −0.995102 | − | 0.0988500i | \(-0.968484\pi\) |
0.411945 | − | 0.911209i | \(-0.364850\pi\) | |||||||
\(368\) | 19.5869 | 1.02104 | ||||||||
\(369\) | 0.120894 | − | 1.16638i | 0.00629351 | − | 0.0607191i | ||||
\(370\) | −2.56845 | −0.133528 | ||||||||
\(371\) | 21.4245 | + | 37.1084i | 1.11231 | + | 1.92657i | ||||
\(372\) | −8.82308 | + | 7.95584i | −0.457456 | + | 0.412491i | ||||
\(373\) | −3.53936 | + | 6.13036i | −0.183261 | + | 0.317418i | −0.942989 | − | 0.332823i | \(-0.891999\pi\) |
0.759728 | + | 0.650241i | \(0.225332\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.37123 | + | 20.4925i | 0.225729 | + | 1.05823i | ||||
\(376\) | 0.995982 | + | 1.72509i | 0.0513639 | + | 0.0889648i | ||||
\(377\) | −6.76164 | −0.348242 | ||||||||
\(378\) | 8.64274 | − | 0.927253i | 0.444534 | − | 0.0476927i | ||||
\(379\) | −24.3461 | −1.25057 | −0.625287 | − | 0.780394i | \(-0.715018\pi\) | ||||
−0.625287 | + | 0.780394i | \(0.715018\pi\) | |||||||
\(380\) | −6.63839 | − | 11.4980i | −0.340542 | − | 0.589836i | ||||
\(381\) | −3.90055 | − | 18.2860i | −0.199831 | − | 0.936818i | ||||
\(382\) | 3.06920 | − | 5.31601i | 0.157034 | − | 0.271991i | ||||
\(383\) | 8.81894 | − | 15.2749i | 0.450627 | − | 0.780509i | −0.547798 | − | 0.836611i | \(-0.684534\pi\) |
0.998425 | + | 0.0561017i | \(0.0178671\pi\) | |||||||
\(384\) | −14.5477 | + | 13.1178i | −0.742384 | + | 0.669413i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.16341 | 0.313709 | ||||||||
\(387\) | 23.3548 | + | 16.9170i | 1.18719 | + | 0.859939i | ||||
\(388\) | −0.603760 | −0.0306513 | ||||||||
\(389\) | 8.94149 | + | 15.4871i | 0.453352 | + | 0.785228i | 0.998592 | − | 0.0530517i | \(-0.0168948\pi\) |
−0.545240 | + | 0.838280i | \(0.683561\pi\) | |||||||
\(390\) | 5.51911 | + | 1.78888i | 0.279471 | + | 0.0905835i | ||||
\(391\) | 12.3790 | − | 21.4410i | 0.626031 | − | 1.08432i | ||||
\(392\) | −4.27033 | + | 7.39642i | −0.215684 | + | 0.373576i | ||||
\(393\) | −34.8574 | − | 11.2981i | −1.75832 | − | 0.569915i | ||||
\(394\) | −2.53717 | − | 4.39450i | −0.127821 | − | 0.221392i | ||||
\(395\) | −6.83122 | −0.343716 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.9395 | −1.10111 | −0.550556 | − | 0.834798i | \(-0.685584\pi\) | ||||
−0.550556 | + | 0.834798i | \(0.685584\pi\) | |||||||
\(398\) | 6.49349 | + | 11.2471i | 0.325489 | + | 0.563764i | ||||
\(399\) | 19.3805 | − | 17.4755i | 0.970238 | − | 0.874871i | ||||
\(400\) | 2.72174 | − | 4.71418i | 0.136087 | − | 0.235709i | ||||
\(401\) | −2.70378 | + | 4.68308i | −0.135020 | + | 0.233862i | −0.925605 | − | 0.378490i | \(-0.876443\pi\) |
0.790585 | + | 0.612352i | \(0.209777\pi\) | |||||||
\(402\) | 0.549630 | + | 2.57669i | 0.0274131 | + | 0.128514i | ||||
\(403\) | −7.79298 | − | 13.4978i | −0.388196 | − | 0.672376i | ||||
\(404\) | −12.5193 | −0.622857 | ||||||||
\(405\) | 4.79276 | + | 14.6074i | 0.238154 | + | 0.725849i | ||||
\(406\) | −2.82926 | −0.140414 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 2.20179 | + | 10.3221i | 0.109005 | + | 0.511020i | ||||
\(409\) | −11.8101 | + | 20.4556i | −0.583970 | + | 1.01147i | 0.411033 | + | 0.911621i | \(0.365168\pi\) |
−0.995003 | + | 0.0998457i | \(0.968165\pi\) | |||||||
\(410\) | 0.163747 | − | 0.283619i | 0.00808690 | − | 0.0140069i | ||||
\(411\) | −4.11693 | + | 3.71227i | −0.203073 | + | 0.183113i | ||||
\(412\) | −1.45529 | − | 2.52064i | −0.0716970 | − | 0.124183i | ||||
\(413\) | −12.4707 | −0.613644 | ||||||||
\(414\) | 10.0648 | − | 4.49850i | 0.494657 | − | 0.221089i | ||||
\(415\) | −0.213464 | −0.0104785 | ||||||||
\(416\) | −9.93539 | − | 17.2086i | −0.487123 | − | 0.843721i | ||||
\(417\) | −24.7045 | − | 8.00733i | −1.20978 | − | 0.392120i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.06566 | − | 15.7022i | 0.442886 | − | 0.767102i | −0.555016 | − | 0.831840i | \(-0.687288\pi\) |
0.997902 | + | 0.0647380i | \(0.0206212\pi\) | |||||||
\(420\) | −16.8885 | − | 5.47397i | −0.824074 | − | 0.267102i | ||||
\(421\) | 6.40610 | + | 11.0957i | 0.312214 | + | 0.540771i | 0.978841 | − | 0.204620i | \(-0.0655960\pi\) |
−0.666627 | + | 0.745391i | \(0.732263\pi\) | |||||||
\(422\) | 3.57271 | 0.173917 | ||||||||
\(423\) | −2.62458 | − | 1.90111i | −0.127611 | − | 0.0924349i | ||||
\(424\) | −23.1672 | −1.12510 | ||||||||
\(425\) | −3.44028 | − | 5.95874i | −0.166878 | − | 0.289041i | ||||
\(426\) | 4.42738 | − | 3.99220i | 0.214507 | − | 0.193423i | ||||
\(427\) | 6.57067 | − | 11.3807i | 0.317977 | − | 0.550753i | ||||
\(428\) | 2.90904 | − | 5.03861i | 0.140614 | − | 0.243551i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.02700 | + | 6.97496i | 0.194199 | + | 0.336362i | ||||
\(431\) | −6.57916 | −0.316907 | −0.158453 | − | 0.987366i | \(-0.550651\pi\) | ||||
−0.158453 | + | 0.987366i | \(0.550651\pi\) | |||||||
\(432\) | 5.49859 | − | 12.4221i | 0.264551 | − | 0.597660i | ||||
\(433\) | 13.9978 | 0.672690 | 0.336345 | − | 0.941739i | \(-0.390809\pi\) | ||||
0.336345 | + | 0.941739i | \(0.390809\pi\) | |||||||
\(434\) | −3.26080 | − | 5.64787i | −0.156523 | − | 0.271106i | ||||
\(435\) | −1.04390 | − | 4.89383i | −0.0500510 | − | 0.234641i | ||||
\(436\) | −4.84463 | + | 8.39115i | −0.232016 | + | 0.401863i | ||||
\(437\) | 16.5485 | − | 28.6629i | 0.791624 | − | 1.37113i | ||||
\(438\) | −9.49095 | + | 8.55806i | −0.453495 | + | 0.408920i | ||||
\(439\) | −12.5891 | − | 21.8050i | −0.600846 | − | 1.04070i | −0.992693 | − | 0.120665i | \(-0.961497\pi\) |
0.391848 | − | 0.920030i | \(-0.371836\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.43254 | − | 13.8210i | 0.0682160 | − | 0.658141i | ||||
\(442\) | −6.48013 | −0.308228 | ||||||||
\(443\) | −13.4112 | − | 23.2289i | −0.637187 | − | 1.10364i | −0.986047 | − | 0.166466i | \(-0.946765\pi\) |
0.348860 | − | 0.937175i | \(-0.386569\pi\) | |||||||
\(444\) | −8.88673 | − | 2.88041i | −0.421746 | − | 0.136698i | ||||
\(445\) | 6.77571 | − | 11.7359i | 0.321200 | − | 0.556334i | ||||
\(446\) | 5.76577 | − | 9.98661i | 0.273017 | − | 0.472880i | ||||
\(447\) | 6.67488 | + | 2.16349i | 0.315711 | + | 0.102330i | ||||
\(448\) | 4.75914 | + | 8.24308i | 0.224848 | + | 0.389449i | ||||
\(449\) | 14.1758 | 0.668999 | 0.334499 | − | 0.942396i | \(-0.391433\pi\) | ||||
0.334499 | + | 0.942396i | \(0.391433\pi\) | |||||||
\(450\) | 0.315872 | − | 3.04749i | 0.0148903 | − | 0.143660i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −14.4353 | − | 25.0027i | −0.678981 | − | 1.17603i | ||||
\(453\) | 10.0256 | − | 9.04020i | 0.471046 | − | 0.424745i | ||||
\(454\) | −2.92388 | + | 5.06431i | −0.137225 | + | 0.237680i | ||||
\(455\) | 11.6455 | − | 20.1706i | 0.545950 | − | 0.945613i | ||||
\(456\) | 2.94342 | + | 13.7989i | 0.137838 | + | 0.646192i | ||||
\(457\) | −12.3206 | − | 21.3400i | −0.576335 | − | 0.998242i | −0.995895 | − | 0.0905145i | \(-0.971149\pi\) |
0.419560 | − | 0.907728i | \(-0.362184\pi\) | |||||||
\(458\) | −1.49972 | −0.0700773 | ||||||||
\(459\) | −10.1229 | − | 13.8699i | −0.472495 | − | 0.647390i | ||||
\(460\) | −22.5164 | −1.04983 | ||||||||
\(461\) | 13.1227 | + | 22.7292i | 0.611185 | + | 1.05860i | 0.991041 | + | 0.133558i | \(0.0426401\pi\) |
−0.379856 | + | 0.925046i | \(0.624027\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.34609 | + | 10.9917i | −0.294928 | + | 0.510830i | −0.974968 | − | 0.222345i | \(-0.928629\pi\) |
0.680040 | + | 0.733175i | \(0.261962\pi\) | |||||||
\(464\) | −2.21083 | + | 3.82927i | −0.102635 | + | 0.177769i | ||||
\(465\) | 8.56613 | − | 7.72415i | 0.397245 | − | 0.358199i | ||||
\(466\) | −6.01624 | − | 10.4204i | −0.278697 | − | 0.482718i | ||||
\(467\) | −27.7040 | −1.28199 | −0.640994 | − | 0.767546i | \(-0.721478\pi\) | ||||
−0.640994 | + | 0.767546i | \(0.721478\pi\) | |||||||
\(468\) | 17.0897 | + | 12.3789i | 0.789973 | + | 0.572214i | ||||
\(469\) | 10.5767 | 0.488387 | ||||||||
\(470\) | −0.452548 | − | 0.783835i | −0.0208745 | − | 0.0361556i | ||||
\(471\) | 0.509378 | + | 0.165102i | 0.0234709 | + | 0.00760750i | ||||
\(472\) | 3.37128 | − | 5.83923i | 0.155176 | − | 0.268772i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 3.23197 | + | 1.04756i | 0.148449 | + | 0.0481161i | ||||
\(475\) | −4.59906 | − | 7.96581i | −0.211020 | − | 0.365497i | ||||
\(476\) | 19.8292 | 0.908870 | ||||||||
\(477\) | 34.4107 | − | 15.3800i | 1.57556 | − | 0.704201i | ||||
\(478\) | 3.40924 | 0.155935 | ||||||||
\(479\) | 7.81110 | + | 13.5292i | 0.356898 | + | 0.618166i | 0.987441 | − | 0.157989i | \(-0.0505009\pi\) |
−0.630543 | + | 0.776155i | \(0.717168\pi\) | |||||||
\(480\) | 10.9211 | − | 9.84763i | 0.498477 | − | 0.449481i | ||||
\(481\) | 6.12787 | − | 10.6138i | 0.279407 | − | 0.483947i | ||||
\(482\) | −1.90571 | + | 3.30079i | −0.0868028 | + | 0.150347i | ||||
\(483\) | −9.23265 | − | 43.2830i | −0.420100 | − | 1.96945i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.586177 | 0.0266169 | ||||||||
\(486\) | −0.0275048 | − | 7.64600i | −0.00124764 | − | 0.346829i | ||||
\(487\) | 26.9270 | 1.22018 | 0.610090 | − | 0.792332i | \(-0.291133\pi\) | ||||
0.610090 | + | 0.792332i | \(0.291133\pi\) | |||||||
\(488\) | 3.55257 | + | 6.15324i | 0.160817 | + | 0.278544i | ||||
\(489\) | −3.97253 | − | 18.6234i | −0.179644 | − | 0.842178i | ||||
\(490\) | 1.94032 | − | 3.36074i | 0.0876548 | − | 0.151823i | ||||
\(491\) | −19.4999 | + | 33.7748i | −0.880017 | + | 1.52423i | −0.0286964 | + | 0.999588i | \(0.509136\pi\) |
−0.851321 | + | 0.524646i | \(0.824198\pi\) | |||||||
\(492\) | 0.884624 | − | 0.797672i | 0.0398819 | − | 0.0359618i | ||||
\(493\) | 2.79450 | + | 4.84021i | 0.125858 | + | 0.217992i | ||||
\(494\) | −8.66283 | −0.389759 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.1922 | −0.457642 | ||||||||
\(497\) | −11.9661 | − | 20.7259i | −0.536752 | − | 0.929681i | ||||
\(498\) | 0.100993 | + | 0.0327345i | 0.00452563 | + | 0.00146687i | ||||
\(499\) | 12.0176 | − | 20.8150i | 0.537980 | − | 0.931809i | −0.461033 | − | 0.887383i | \(-0.652521\pi\) |
0.999013 | − | 0.0444256i | \(-0.0141457\pi\) | |||||||
\(500\) | −10.6423 | + | 18.4330i | −0.475938 | + | 0.824349i | ||||
\(501\) | −28.9558 | − | 9.38528i | −1.29365 | − | 0.419304i | ||||
\(502\) | 0.0802369 | + | 0.138974i | 0.00358115 | + | 0.00620273i | ||||
\(503\) | −23.9865 | −1.06950 | −0.534752 | − | 0.845009i | \(-0.679595\pi\) | ||||
−0.534752 | + | 0.845009i | \(0.679595\pi\) | |||||||
\(504\) | 15.2794 | + | 11.0676i | 0.680600 | + | 0.492990i | ||||
\(505\) | 12.1547 | 0.540876 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.83763 | + | 3.46042i | −0.170435 | + | 0.153683i | ||||
\(508\) | 9.49637 | − | 16.4482i | 0.421333 | − | 0.729771i | ||||
\(509\) | −1.84943 | + | 3.20331i | −0.0819746 | + | 0.141984i | −0.904098 | − | 0.427325i | \(-0.859456\pi\) |
0.822123 | + | 0.569309i | \(0.192789\pi\) | |||||||
\(510\) | −1.00044 | − | 4.69009i | −0.0443000 | − | 0.207680i | ||||
\(511\) | 25.6516 | + | 44.4298i | 1.13476 | + | 1.96546i | ||||
\(512\) | −22.6358 | −1.00037 | ||||||||
\(513\) | −13.5325 | − | 18.5416i | −0.597476 | − | 0.818634i | ||||
\(514\) | 6.73407 | 0.297027 | ||||||||
\(515\) | 1.41291 | + | 2.44723i | 0.0622602 | + | 0.107838i | ||||
\(516\) | 6.11111 | + | 28.6491i | 0.269027 | + | 1.26121i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 2.56407 | − | 4.44110i | 0.112659 | − | 0.195131i | ||||
\(519\) | −15.9064 | + | 14.3429i | −0.698215 | + | 0.629585i | ||||
\(520\) | 6.29639 | + | 10.9057i | 0.276115 | + | 0.478245i | ||||
\(521\) | −6.41318 | −0.280966 | −0.140483 | − | 0.990083i | \(-0.544866\pi\) | ||||
−0.140483 | + | 0.990083i | \(0.544866\pi\) | |||||||
\(522\) | −0.256578 | + | 2.47544i | −0.0112301 | + | 0.108347i | ||||
\(523\) | −2.73856 | −0.119749 | −0.0598745 | − | 0.998206i | \(-0.519070\pi\) | ||||
−0.0598745 | + | 0.998206i | \(0.519070\pi\) | |||||||
\(524\) | −18.6108 | − | 32.2348i | −0.813016 | − | 1.40819i | ||||
\(525\) | −11.7003 | − | 3.79236i | −0.510643 | − | 0.165512i | ||||
\(526\) | −4.13344 | + | 7.15932i | −0.180226 | + | 0.312161i | ||||
\(527\) | −6.44147 | + | 11.1570i | −0.280595 | + | 0.486005i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.5651 | − | 28.6916i | −0.720222 | − | 1.24746i | ||||
\(530\) | 10.5266 | 0.457245 | ||||||||
\(531\) | −1.13094 | + | 10.9112i | −0.0490786 | + | 0.473505i | ||||
\(532\) | 26.5082 | 1.14928 | ||||||||
\(533\) | 0.781343 | + | 1.35333i | 0.0338437 | + | 0.0586191i | ||||
\(534\) | −5.00539 | + | 4.51340i | −0.216605 | + | 0.195314i | ||||
\(535\) | −2.82433 | + | 4.89188i | −0.122106 | + | 0.211494i | ||||
\(536\) | −2.85926 | + | 4.95239i | −0.123501 | + | 0.213910i | ||||
\(537\) | −7.90678 | − | 37.0673i | −0.341203 | − | 1.59957i | ||||
\(538\) | 3.04042 | + | 5.26617i | 0.131082 | + | 0.227041i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −6.32099 | + | 14.2800i | −0.272012 | + | 0.614515i | ||||
\(541\) | 20.9037 | 0.898719 | 0.449359 | − | 0.893351i | \(-0.351652\pi\) | ||||
0.449359 | + | 0.893351i | \(0.351652\pi\) | |||||||
\(542\) | 4.72579 | + | 8.18530i | 0.202990 | + | 0.351589i | ||||
\(543\) | 1.58270 | + | 7.41976i | 0.0679201 | + | 0.318412i | ||||
\(544\) | −8.21233 | + | 14.2242i | −0.352101 | + | 0.609856i | ||||
\(545\) | 4.70355 | − | 8.14678i | 0.201478 | − | 0.348970i | ||||
\(546\) | −8.60284 | + | 7.75724i | −0.368167 | + | 0.331979i | ||||
\(547\) | 20.9382 | + | 36.2660i | 0.895252 | + | 1.55062i | 0.833493 | + | 0.552531i | \(0.186338\pi\) |
0.0617594 | + | 0.998091i | \(0.480329\pi\) | |||||||
\(548\) | −5.63105 | −0.240547 | ||||||||
\(549\) | −9.36162 | − | 6.78106i | −0.399544 | − | 0.289408i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.73576 | + | 6.47053i | 0.159149 | + | 0.275654i | ||||
\(552\) | 22.7625 | + | 7.37790i | 0.968838 | + | 0.314024i | ||||
\(553\) | 6.81956 | − | 11.8118i | 0.289997 | − | 0.502290i | ||||
\(554\) | 2.53857 | − | 4.39693i | 0.107854 | − | 0.186808i | ||||
\(555\) | 8.62793 | + | 2.79652i | 0.366235 | + | 0.118706i | ||||
\(556\) | −13.1900 | − | 22.8458i | −0.559382 | − | 0.968878i | ||||
\(557\) | −12.5244 | −0.530675 | −0.265337 | − | 0.964156i | \(-0.585483\pi\) | ||||
−0.265337 | + | 0.964156i | \(0.585483\pi\) | |||||||
\(558\) | −5.23728 | + | 2.34082i | −0.221712 | + | 0.0990949i | ||||
\(559\) | −38.4308 | −1.62545 | ||||||||
\(560\) | −7.61538 | − | 13.1902i | −0.321809 | − | 0.557389i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.03083 | + | 6.98160i | −0.170030 | + | 0.294501i | ||||
\(563\) | 7.25437 | − | 12.5649i | 0.305735 | − | 0.529549i | −0.671690 | − | 0.740833i | \(-0.734431\pi\) |
0.977425 | + | 0.211284i | \(0.0677644\pi\) | |||||||
\(564\) | −0.686757 | − | 3.21955i | −0.0289177 | − | 0.135567i | ||||
\(565\) | 14.0149 | + | 24.2746i | 0.589613 | + | 1.02124i | ||||
\(566\) | 0.620452 | 0.0260796 | ||||||||
\(567\) | −30.0422 | − | 6.29536i | −1.26165 | − | 0.264380i | ||||
\(568\) | 12.9394 | 0.542926 | ||||||||
\(569\) | 13.9862 | + | 24.2248i | 0.586332 | + | 1.01556i | 0.994708 | + | 0.102743i | \(0.0327621\pi\) |
−0.408375 | + | 0.912814i | \(0.633905\pi\) | |||||||
\(570\) | −1.33741 | − | 6.26984i | −0.0560180 | − | 0.262615i | ||||
\(571\) | −4.52443 | + | 7.83654i | −0.189341 | + | 0.327949i | −0.945031 | − | 0.326981i | \(-0.893969\pi\) |
0.755689 | + | 0.654930i | \(0.227302\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.0981 | + | 14.5158i | −0.672507 | + | 0.606405i | ||||
\(574\) | 0.326936 | + | 0.566269i | 0.0136460 | + | 0.0236356i | ||||
\(575\) | −15.5993 | −0.650538 | ||||||||
\(576\) | 7.64382 | − | 3.41644i | 0.318493 | − | 0.142351i | ||||
\(577\) | 38.3471 | 1.59641 | 0.798204 | − | 0.602387i | \(-0.205783\pi\) | ||||
0.798204 | + | 0.602387i | \(0.205783\pi\) | |||||||
\(578\) | −1.49105 | − | 2.58257i | −0.0620194 | − | 0.107421i | ||||
\(579\) | −20.7041 | − | 6.71069i | −0.860431 | − | 0.278887i | ||||
\(580\) | 2.54149 | − | 4.40200i | 0.105530 | − | 0.182783i | ||||
\(581\) | 0.213099 | − | 0.369099i | 0.00884085 | − | 0.0153128i | ||||
\(582\) | −0.277331 | − | 0.0898897i | −0.0114957 | − | 0.00372605i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −27.7381 | −1.14781 | ||||||||
\(585\) | −16.5920 | − | 12.0184i | −0.685996 | − | 0.496899i | ||||
\(586\) | 11.8147 | 0.488062 | ||||||||
\(587\) | 0.361309 | + | 0.625805i | 0.0149128 | + | 0.0258297i | 0.873385 | − | 0.487030i | \(-0.161920\pi\) |
−0.858473 | + | 0.512859i | \(0.828586\pi\) | |||||||
\(588\) | 10.4823 | − | 9.45200i | 0.432284 | − | 0.389794i | ||||
\(589\) | −8.61114 | + | 14.9149i | −0.354816 | + | 0.614559i | ||||
\(590\) | −1.53182 | + | 2.65319i | −0.0630640 | + | 0.109230i | ||||
\(591\) | 3.73811 | + | 17.5244i | 0.153765 | + | 0.720858i | ||||
\(592\) | −4.00722 | − | 6.94071i | −0.164696 | − | 0.285261i | ||||
\(593\) | −39.6596 | −1.62863 | −0.814313 | − | 0.580426i | \(-0.802886\pi\) | ||||
−0.814313 | + | 0.580426i | \(0.802886\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.2517 | −0.789244 | ||||||||
\(596\) | 3.56380 | + | 6.17269i | 0.145979 | + | 0.252843i | ||||
\(597\) | −9.56712 | − | 44.8511i | −0.391556 | − | 1.83563i | ||||
\(598\) | −7.34576 | + | 12.7232i | −0.300390 | + | 0.520291i | ||||
\(599\) | 10.1884 | − | 17.6468i | 0.416287 | − | 0.721030i | −0.579276 | − | 0.815132i | \(-0.696665\pi\) |
0.995563 | + | 0.0941018i | \(0.0299979\pi\) | |||||||
\(600\) | 4.93872 | − | 4.45328i | 0.201623 | − | 0.181805i | ||||
\(601\) | 24.1859 | + | 41.8911i | 0.986562 | + | 1.70878i | 0.634780 | + | 0.772693i | \(0.281091\pi\) |
0.351782 | + | 0.936082i | \(0.385576\pi\) | |||||||
\(602\) | −16.0805 | −0.655392 | ||||||||
\(603\) | 0.959176 | − | 9.25402i | 0.0390607 | − | 0.376853i | ||||
\(604\) | 13.7129 | 0.557968 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5.75059 | − | 1.86391i | −0.233602 | − | 0.0757161i | ||||
\(607\) | 9.85114 | − | 17.0627i | 0.399845 | − | 0.692553i | −0.593861 | − | 0.804568i | \(-0.702397\pi\) |
0.993707 | + | 0.112015i | \(0.0357304\pi\) | |||||||
\(608\) | −10.9785 | + | 19.0153i | −0.445236 | + | 0.771171i | ||||
\(609\) | 9.50401 | + | 3.08048i | 0.385122 | + | 0.124827i | ||||
\(610\) | −1.61419 | − | 2.79586i | −0.0653568 | − | 0.113201i | ||||
\(611\) | 4.31879 | 0.174720 | ||||||||
\(612\) | 1.79826 | − | 17.3494i | 0.0726904 | − | 0.701309i | ||||
\(613\) | 5.71781 | 0.230940 | 0.115470 | − | 0.993311i | \(-0.463163\pi\) | ||||
0.115470 | + | 0.993311i | \(0.463163\pi\) | |||||||
\(614\) | 3.99629 | + | 6.92177i | 0.161277 | + | 0.279340i | ||||
\(615\) | −0.858861 | + | 0.774442i | −0.0346326 | + | 0.0312285i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.05346 | + | 5.28875i | −0.122928 | + | 0.212917i | −0.920921 | − | 0.389749i | \(-0.872562\pi\) |
0.797993 | + | 0.602666i | \(0.205895\pi\) | |||||||
\(618\) | −0.293192 | − | 1.37450i | −0.0117939 | − | 0.0552903i | ||||
\(619\) | 0.889867 | + | 1.54129i | 0.0357668 | + | 0.0619499i | 0.883355 | − | 0.468705i | \(-0.155279\pi\) |
−0.847588 | + | 0.530655i | \(0.821946\pi\) | |||||||
\(620\) | 11.7166 | 0.470549 | ||||||||
\(621\) | −38.7075 | + | 4.15281i | −1.55328 | + | 0.166646i | ||||
\(622\) | −10.4825 | −0.420309 | ||||||||
\(623\) | 13.5283 | + | 23.4317i | 0.542000 | + | 0.938771i | ||||
\(624\) | 3.77667 | + | 17.7052i | 0.151188 | + | 0.708775i | ||||
\(625\) | 5.12704 | − | 8.88029i | 0.205081 | − | 0.355212i | ||||
\(626\) | 0.764220 | − | 1.32367i | 0.0305444 | − | 0.0529044i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.271963 | + | 0.471055i | 0.0108525 | + | 0.0187971i | ||||
\(629\) | −10.1303 | −0.403920 | ||||||||
\(630\) | −6.94256 | − | 5.02882i | −0.276598 | − | 0.200353i | ||||
\(631\) | −44.8407 | −1.78508 | −0.892541 | − | 0.450966i | \(-0.851079\pi\) | ||||
−0.892541 | + | 0.450966i | \(0.851079\pi\) | |||||||
\(632\) | 3.68714 | + | 6.38631i | 0.146667 | + | 0.254034i | ||||
\(633\) | −12.0014 | − | 3.88995i | −0.477013 | − | 0.154612i | ||||
\(634\) | −4.47940 | + | 7.75855i | −0.177900 | + | 0.308131i | ||||
\(635\) | −9.21981 | + | 15.9692i | −0.365877 | + | 0.633718i | ||||
\(636\) | 36.4214 | + | 11.8051i | 1.44420 | + | 0.468102i | ||||
\(637\) | 9.25852 | + | 16.0362i | 0.366836 | + | 0.635379i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −19.2191 | + | 8.59006i | −0.760297 | + | 0.339818i | ||||
\(640\) | 19.3185 | 0.763633 | ||||||||
\(641\) | 13.5048 | + | 23.3910i | 0.533407 | + | 0.923888i | 0.999239 | + | 0.0390143i | \(0.0124218\pi\) |
−0.465832 | + | 0.884873i | \(0.654245\pi\) | |||||||
\(642\) | 2.08640 | − | 1.88133i | 0.0823438 | − | 0.0742500i | ||||
\(643\) | 16.2787 | − | 28.1955i | 0.641969 | − | 1.11192i | −0.343024 | − | 0.939327i | \(-0.611451\pi\) |
0.984993 | − | 0.172596i | \(-0.0552155\pi\) | |||||||
\(644\) | 22.4780 | − | 38.9330i | 0.885758 | − | 1.53418i | ||||
\(645\) | −5.93314 | − | 27.8148i | −0.233617 | − | 1.09521i | ||||
\(646\) | 3.58023 | + | 6.20114i | 0.140862 | + | 0.243981i | ||||
\(647\) | −31.4833 | −1.23774 | −0.618868 | − | 0.785495i | \(-0.712408\pi\) | ||||
−0.618868 | + | 0.785495i | \(0.712408\pi\) | |||||||
\(648\) | 11.0692 | − | 12.3649i | 0.434838 | − | 0.485741i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.04149 | + | 3.53596i | 0.0800736 | + | 0.138692i | ||||
\(651\) | 4.80427 | + | 22.5226i | 0.188294 | + | 0.882731i | ||||
\(652\) | 9.67160 | − | 16.7517i | 0.378769 | − | 0.656048i | ||||
\(653\) | 2.32989 | − | 4.03548i | 0.0911755 | − | 0.157921i | −0.816831 | − | 0.576878i | \(-0.804271\pi\) |
0.908006 | + | 0.418957i | \(0.137604\pi\) | |||||||
\(654\) | −3.47463 | + | 3.13310i | −0.135869 | + | 0.122514i | ||||
\(655\) | 18.0688 | + | 31.2961i | 0.706007 | + | 1.22284i | ||||
\(656\) | 1.02189 | 0.0398982 | ||||||||
\(657\) | 41.1999 | − | 18.4144i | 1.60736 | − | 0.718416i | ||||
\(658\) | 1.80710 | 0.0704481 | ||||||||
\(659\) | 16.0209 | + | 27.7490i | 0.624086 | + | 1.08095i | 0.988717 | + | 0.149797i | \(0.0478619\pi\) |
−0.364631 | + | 0.931152i | \(0.618805\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.3527 | − | 35.2519i | 0.791627 | − | 1.37114i | −0.133331 | − | 0.991072i | \(-0.542567\pi\) |
0.924959 | − | 0.380067i | \(-0.124099\pi\) | |||||||
\(662\) | 0.923639 | − | 1.59979i | 0.0358982 | − | 0.0621776i | ||||
\(663\) | 21.7680 | + | 7.05554i | 0.845399 | + | 0.274015i | ||||
\(664\) | 0.115217 | + | 0.199561i | 0.00447127 | + | 0.00774448i | ||||
\(665\) | −25.7362 | −0.998009 | ||||||||
\(666\) | −3.65318 | − | 2.64617i | −0.141558 | − | 0.102537i | ||||
\(667\) | 12.6712 | 0.490629 | ||||||||
\(668\) | −15.4599 | − | 26.7773i | −0.598160 | − | 1.03604i | ||||
\(669\) | −30.2417 | + | 27.2692i | −1.16921 | + | 1.05429i | ||||
\(670\) | 1.29917 | − | 2.25023i | 0.0501914 | − | 0.0869340i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 6.12503 | + | 28.7144i | 0.236278 | + | 1.10768i | ||||
\(673\) | 18.8818 | + | 32.7042i | 0.727838 | + | 1.26065i | 0.957795 | + | 0.287452i | \(0.0928083\pi\) |
−0.229957 | + | 0.973201i | \(0.573858\pi\) | |||||||
\(674\) | −2.92637 | −0.112720 | ||||||||
\(675\) | −4.37917 | + | 9.89319i | −0.168554 | + | 0.380789i | ||||
\(676\) | −5.24903 | −0.201886 | ||||||||
\(677\) | −9.45033 | − | 16.3685i | −0.363206 | − | 0.629091i | 0.625281 | − | 0.780400i | \(-0.284984\pi\) |
−0.988487 | + | 0.151309i | \(0.951651\pi\) | |||||||
\(678\) | −2.90823 | − | 13.6339i | −0.111690 | − | 0.523607i | ||||
\(679\) | −0.585177 | + | 1.01356i | −0.0224570 | + | 0.0388967i | ||||
\(680\) | 5.20442 | − | 9.01433i | 0.199581 | − | 0.345684i | ||||
\(681\) | 15.3359 | − | 13.8285i | 0.587672 | − | 0.529908i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.1053 | 1.19021 | 0.595105 | − | 0.803648i | \(-0.297110\pi\) | ||||
0.595105 | + | 0.803648i | \(0.297110\pi\) | |||||||
\(684\) | 2.40397 | − | 23.1932i | 0.0919180 | − | 0.886814i | ||||
\(685\) | 5.46706 | 0.208886 | ||||||||
\(686\) | −1.98092 | − | 3.43106i | −0.0756320 | − | 0.130998i | ||||
\(687\) | 5.03785 | + | 1.63289i | 0.192206 | + | 0.0622986i | ||||
\(688\) | −12.5656 | + | 21.7642i | −0.479058 | + | 0.829753i | ||||
\(689\) | −25.1145 | + | 43.4996i | −0.956787 | + | 1.65720i | ||||
\(690\) | −10.3427 | − | 3.35232i | −0.393739 | − | 0.127621i | ||||
\(691\) | −11.1057 | − | 19.2356i | −0.422481 | − | 0.731758i | 0.573701 | − | 0.819065i | \(-0.305507\pi\) |
−0.996181 | + | 0.0873068i | \(0.972174\pi\) | |||||||
\(692\) | −21.7565 | −0.827057 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.9432 | −0.453358 | ||||||||
\(695\) | 12.8059 | + | 22.1805i | 0.485756 | + | 0.841353i | ||||
\(696\) | −4.01166 | + | 3.61735i | −0.152062 | + | 0.137115i | ||||
\(697\) | 0.645837 | − | 1.11862i | 0.0244628 | − | 0.0423709i | ||||
\(698\) | 4.10587 | − | 7.11157i | 0.155409 | − | 0.269177i | ||||
\(699\) | 8.86398 | + | 41.5547i | 0.335266 | + | 1.57174i | ||||
\(700\) | −6.24694 | − | 10.8200i | −0.236112 | − | 0.408958i | ||||
\(701\) | −29.9457 | −1.13103 | −0.565517 | − | 0.824736i | \(-0.691323\pi\) | ||||
−0.565517 | + | 0.824736i | \(0.691323\pi\) | |||||||
\(702\) | 6.00698 | + | 8.23048i | 0.226719 | + | 0.310639i | ||||
\(703\) | −13.5424 | −0.510763 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.666757 | + | 3.12578i | 0.0251115 | + | 0.117724i | ||||
\(706\) | −1.96966 | + | 3.41155i | −0.0741290 | + | 0.128395i | ||||
\(707\) | −12.1339 | + | 21.0166i | −0.456343 | + | 0.790410i | ||||
\(708\) | −8.27545 | + | 7.46204i | −0.311010 | + | 0.280441i | ||||
\(709\) | −8.60286 | − | 14.9006i | −0.323087 | − | 0.559604i | 0.658036 | − | 0.752986i | \(-0.271387\pi\) |
−0.981123 | + | 0.193383i | \(0.938054\pi\) | |||||||
\(710\) | −5.87932 | −0.220647 | ||||||||
\(711\) | −9.71623 | − | 7.03792i | −0.364387 | − | 0.263942i | ||||
\(712\) | −14.6287 | −0.548234 | ||||||||
\(713\) | 14.6039 | + | 25.2946i | 0.546919 | + | 0.947291i | ||||
\(714\) | 9.10833 | + | 2.95223i | 0.340871 | + | 0.110485i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.2500 | − | 33.3420i | 0.719407 | − | 1.24605i | ||||
\(717\) | −11.4523 | − | 3.71197i | −0.427694 | − | 0.138626i | ||||
\(718\) | −7.06925 | − | 12.2443i | −0.263822 | − | 0.456953i | ||||
\(719\) | 4.72508 | 0.176216 | 0.0881079 | − | 0.996111i | \(-0.471918\pi\) | ||||
0.0881079 | + | 0.996111i | \(0.471918\pi\) | |||||||
\(720\) | −12.2313 | + | 5.46684i | −0.455834 | + | 0.203737i | ||||
\(721\) | −5.64199 | −0.210119 | ||||||||
\(722\) | 0.126459 | + | 0.219034i | 0.00470633 | + | 0.00815160i | ||||
\(723\) | 9.99554 | − | 9.01306i | 0.371738 | − | 0.335199i | ||||
\(724\) | −3.85327 | + | 6.67407i | −0.143206 | + | 0.248040i | ||||
\(725\) | 1.76074 | − | 3.04969i | 0.0653923 | − | 0.113263i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.60044 | − | 4.50410i | −0.0964450 | − | 0.167048i | 0.813766 | − | 0.581193i | \(-0.197414\pi\) |
−0.910211 | + | 0.414145i | \(0.864081\pi\) | |||||||
\(728\) | −25.1426 | −0.931845 | ||||||||
\(729\) | −8.23253 | + | 25.7143i | −0.304909 | + | 0.952382i | ||||
\(730\) | 12.6035 | 0.466475 | ||||||||
\(731\) | 15.8829 | + | 27.5100i | 0.587451 | + | 1.01749i | ||||
\(732\) | −2.44959 | − | 11.4838i | −0.0905396 | − | 0.424454i | ||||
\(733\) | 24.5316 | − | 42.4900i | 0.906095 | − | 1.56940i | 0.0866539 | − | 0.996238i | \(-0.472383\pi\) |
0.819441 | − | 0.573164i | \(-0.194284\pi\) | |||||||
\(734\) | 5.47965 | − | 9.49103i | 0.202258 | − | 0.350320i | ||||
\(735\) | −10.1771 | + | 9.17674i | −0.375387 | + | 0.338489i | ||||
\(736\) | 18.6187 | + | 32.2485i | 0.686294 | + | 1.18870i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0.525102 | − | 0.234697i | 0.0193293 | − | 0.00863930i | ||||
\(739\) | −15.5942 | −0.573641 | −0.286821 | − | 0.957984i | \(-0.592598\pi\) | ||||
−0.286821 | + | 0.957984i | \(0.592598\pi\) | |||||||
\(740\) | 4.60656 | + | 7.97879i | 0.169340 | + | 0.293306i | ||||
\(741\) | 29.1001 | + | 9.43205i | 1.06902 | + | 0.346495i | ||||
\(742\) | −10.5086 | + | 18.2014i | −0.385783 | + | 0.668196i | ||||
\(743\) | −5.56722 | + | 9.64271i | −0.204242 | + | 0.353757i | −0.949891 | − | 0.312582i | \(-0.898806\pi\) |
0.745649 | + | 0.666339i | \(0.232139\pi\) | |||||||
\(744\) | −11.8446 | − | 3.83914i | −0.434245 | − | 0.140750i | ||||
\(745\) | −3.46002 | − | 5.99293i | −0.126765 | − | 0.219564i | ||||
\(746\) | −3.47207 | −0.127122 | ||||||||
\(747\) | −0.303615 | − | 0.219923i | −0.0111087 | − | 0.00804655i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.63901 | − | 9.76705i | −0.206045 | − | 0.356880i | ||||
\(750\) | −7.63279 | + | 6.88254i | −0.278710 | + | 0.251315i | ||||
\(751\) | 4.04260 | − | 7.00199i | 0.147517 | − | 0.255506i | −0.782792 | − | 0.622283i | \(-0.786205\pi\) |
0.930309 | + | 0.366777i | \(0.119539\pi\) | |||||||
\(752\) | 1.41210 | − | 2.44583i | 0.0514940 | − | 0.0891902i | ||||
\(753\) | −0.118216 | − | 0.554203i | −0.00430804 | − | 0.0201963i | ||||
\(754\) | −1.65827 | − | 2.87221i | −0.0603907 | − | 0.104600i | ||||
\(755\) | −13.3135 | −0.484528 | ||||||||
\(756\) | −18.3813 | − | 25.1853i | −0.668523 | − | 0.915979i | ||||
\(757\) | 29.8616 | 1.08534 | 0.542669 | − | 0.839947i | \(-0.317414\pi\) | ||||
0.542669 | + | 0.839947i | \(0.317414\pi\) | |||||||
\(758\) | −5.97081 | − | 10.3417i | −0.216869 | − | 0.375629i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.95742 | − | 12.0506i | 0.252372 | − | 0.437121i | ||||
\(761\) | −17.4463 | + | 30.2179i | −0.632428 | + | 1.09540i | 0.354626 | + | 0.935008i | \(0.384608\pi\) |
−0.987054 | + | 0.160389i | \(0.948725\pi\) | |||||||
\(762\) | 6.81091 | − | 6.14145i | 0.246733 | − | 0.222481i | ||||
\(763\) | 9.39103 | + | 16.2657i | 0.339978 | + | 0.588860i | ||||
\(764\) | −22.0186 | −0.796606 | ||||||||
\(765\) | −1.74589 | + | 16.8442i | −0.0631228 | + | 0.609002i | ||||
\(766\) | 8.65128 | 0.312583 | ||||||||
\(767\) | −7.30929 | − | 12.6601i | −0.263923 | − | 0.457128i | ||||
\(768\) | 0.0568420 | + | 0.0184239i | 0.00205111 | + | 0.000664815i | ||||
\(769\) | 2.80362 | − | 4.85600i | 0.101101 | − | 0.175112i | −0.811038 | − | 0.584994i | \(-0.801097\pi\) |
0.912139 | + | 0.409882i | \(0.134430\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.6210 | − | 7.33203i | −0.814677 | − | 0.264057i | ||||
\(772\) | −11.0542 | − | 19.1464i | −0.397848 | − | 0.689093i | ||||
\(773\) | −10.8401 | −0.389893 | −0.194946 | − | 0.980814i | \(-0.562453\pi\) | ||||
−0.194946 | + | 0.980814i | \(0.562453\pi\) | |||||||
\(774\) | −1.45830 | + | 14.0695i | −0.0524175 | + | 0.505718i | ||||
\(775\) | 8.11722 | 0.291579 | ||||||||
\(776\) | −0.316388 | − | 0.548000i | −0.0113577 | − | 0.0196721i | ||||
\(777\) | −13.4487 | + | 12.1268i | −0.482468 | + | 0.435045i | ||||
\(778\) | −4.38575 | + | 7.59634i | −0.157237 | + | 0.272342i | ||||
\(779\) | 0.863374 | − | 1.49541i | 0.0309336 | − | 0.0535785i | ||||
\(780\) | −4.34153 | − | 20.3533i | −0.155452 | − | 0.728764i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 12.1436 | 0.434255 | ||||||||
\(783\) | 3.55714 | − | 8.03611i | 0.127122 | − | 0.287187i | ||||
\(784\) | 12.1089 | 0.432461 | ||||||||
\(785\) | −0.264043 | − | 0.457336i | −0.00942411 | − | 0.0163230i | ||||
\(786\) | −3.74945 | − | 17.5776i | −0.133738 | − | 0.626971i | ||||
\(787\) | 1.23822 | − | 2.14465i | 0.0441376 | − | 0.0764486i | −0.843113 | − | 0.537737i | \(-0.819279\pi\) |
0.887250 | + | 0.461288i | \(0.152613\pi\) | |||||||
\(788\) | −9.10088 | + | 15.7632i | −0.324206 | + | 0.561540i | ||||
\(789\) | 21.6800 | − | 19.5491i | 0.771830 | − | 0.695965i | ||||
\(790\) | −1.67534 | − | 2.90177i | −0.0596058 | − | 0.103240i | ||||
\(791\) | −55.9640 | −1.98985 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.4047 | 0.547037 | ||||||||
\(794\) | −5.38060 | − | 9.31947i | −0.190950 | − | 0.330735i | ||||
\(795\) | −35.3608 | − | 11.4613i | −1.25412 | − | 0.406490i | ||||
\(796\) | 23.2923 | − | 40.3435i | 0.825574 | − | 1.42994i | ||||
\(797\) | 4.83984 | − | 8.38286i | 0.171436 | − | 0.296936i | −0.767486 | − | 0.641066i | \(-0.778493\pi\) |
0.938922 | + | 0.344130i | \(0.111826\pi\) | |||||||
\(798\) | 12.1763 | + | 3.94663i | 0.431035 | + | 0.139709i | ||||
\(799\) | −1.78490 | − | 3.09153i | −0.0631451 | − | 0.109371i | ||||
\(800\) | 10.3488 | 0.365884 | ||||||||
\(801\) | 21.7282 | − | 9.71153i | 0.767730 | − | 0.343140i | ||||
\(802\) | −2.65237 | −0.0936586 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 7.01861 | − | 6.32873i | 0.247527 | − | 0.223197i | ||||
\(805\) | −21.8234 | + | 37.7992i | −0.769173 | + | 1.33225i | ||||
\(806\) | 3.82241 | − | 6.62061i | 0.134639 | − | 0.233201i | ||||
\(807\) | −4.47958 | − | 21.0005i | −0.157689 | − | 0.739251i | ||||
\(808\) | −6.56046 | − | 11.3631i | −0.230796 | − | 0.399751i | ||||
\(809\) | −7.86532 | −0.276530 | −0.138265 | − | 0.990395i | \(-0.544153\pi\) | ||||
−0.138265 | + | 0.990395i | \(0.544153\pi\) | |||||||
\(810\) | −5.02954 | + | 5.61830i | −0.176720 | + | 0.197407i | ||||
\(811\) | 39.5047 | 1.38720 | 0.693599 | − | 0.720361i | \(-0.256024\pi\) | ||||
0.693599 | + | 0.720361i | \(0.256024\pi\) | |||||||
\(812\) | 5.07431 | + | 8.78896i | 0.178073 | + | 0.308432i | ||||
\(813\) | −6.96269 | − | 32.6414i | −0.244192 | − | 1.14478i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.38994 | + | 16.2639i | −0.328915 | + | 0.569698i | ||||
\(816\) | 11.1131 | − | 10.0208i | 0.389037 | − | 0.350798i | ||||
\(817\) | 21.2327 | + | 36.7762i | 0.742839 | + | 1.28664i | ||||
\(818\) | −11.5855 | −0.405079 | ||||||||
\(819\) | 37.3446 | − | 16.6913i | 1.30493 | − | 0.583242i | ||||
\(820\) | −1.17473 | −0.0410234 | ||||||||
\(821\) | 1.67681 | + | 2.90432i | 0.0585211 | + | 0.101361i | 0.893802 | − | 0.448462i | \(-0.148028\pi\) |
−0.835281 | + | 0.549824i | \(0.814695\pi\) | |||||||
\(822\) | −2.58656 | − | 0.838368i | −0.0902167 | − | 0.0292415i | ||||
\(823\) | −8.05091 | + | 13.9446i | −0.280637 | + | 0.486078i | −0.971542 | − | 0.236868i | \(-0.923879\pi\) |
0.690905 | + | 0.722946i | \(0.257212\pi\) | |||||||
\(824\) | 1.52523 | − | 2.64177i | 0.0531339 | − | 0.0920306i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.05841 | − | 5.29732i | −0.106416 | − | 0.184317i | ||||
\(827\) | 15.2905 | 0.531702 | 0.265851 | − | 0.964014i | \(-0.414347\pi\) | ||||
0.265851 | + | 0.964014i | \(0.414347\pi\) | |||||||
\(828\) | −32.0257 | − | 23.1977i | −1.11297 | − | 0.806177i | ||||
\(829\) | −42.1463 | −1.46380 | −0.731901 | − | 0.681411i | \(-0.761367\pi\) | ||||
−0.731901 | + | 0.681411i | \(0.761367\pi\) | |||||||
\(830\) | −0.0523514 | − | 0.0906752i | −0.00181714 | − | 0.00314738i | ||||
\(831\) | −13.3149 | + | 12.0062i | −0.461889 | + | 0.416489i | ||||
\(832\) | −5.57882 | + | 9.66280i | −0.193411 | + | 0.334997i | ||||
\(833\) | 7.65284 | − | 13.2551i | 0.265155 | − | 0.459262i | ||||
\(834\) | −2.65734 | − | 12.4577i | −0.0920163 | − | 0.431376i | ||||
\(835\) | 15.0096 | + | 25.9975i | 0.519430 | + | 0.899679i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.1417 | − | 2.16094i | 0.696199 | − | 0.0746930i | ||||
\(838\) | 8.89330 | 0.307214 | ||||||||
\(839\) | −1.32370 | − | 2.29271i | −0.0456990 | − | 0.0791531i | 0.842271 | − | 0.539054i | \(-0.181218\pi\) |
−0.887970 | + | 0.459901i | \(0.847885\pi\) | |||||||
\(840\) | −3.88164 | − | 18.1973i | −0.133929 | − | 0.627866i | ||||
\(841\) | 13.0698 | − | 22.6375i | 0.450682 | − | 0.780604i | ||||
\(842\) | −3.14215 | + | 5.44237i | −0.108286 | + | 0.187556i | ||||
\(843\) | 21.1419 | − | 19.0638i | 0.728165 | − | 0.656592i | ||||
\(844\) | −6.40771 | − | 11.0985i | −0.220562 | − | 0.382025i | ||||
\(845\) | 5.09616 | 0.175313 | ||||||||
\(846\) | 0.163882 | − | 1.58111i | 0.00563436 | − | 0.0543597i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 16.4232 | + | 28.4458i | 0.563976 | + | 0.976834i | ||||
\(849\) | −2.08422 | − | 0.675546i | −0.0715302 | − | 0.0231847i | ||||
\(850\) | 1.68744 | − | 2.92273i | 0.0578786 | − | 0.100249i | ||||
\(851\) | −11.4835 | + | 19.8900i | −0.393649 | + | 0.681820i | ||||
\(852\) | −20.3422 | − | 6.59340i | −0.696912 | − | 0.225886i | ||||
\(853\) | −4.63519 | − | 8.02838i | −0.158706 | − | 0.274886i | 0.775696 | − | 0.631106i | \(-0.217399\pi\) |
−0.934402 | + | 0.356220i | \(0.884065\pi\) | |||||||
\(854\) | 6.44575 | 0.220569 | ||||||||
\(855\) | −2.33396 | + | 22.5178i | −0.0798197 | + | 0.770091i | ||||
\(856\) | 6.09770 | 0.208415 | ||||||||
\(857\) | 10.2678 | + | 17.7844i | 0.350742 | + | 0.607502i | 0.986380 | − | 0.164485i | \(-0.0525962\pi\) |
−0.635638 | + | 0.771987i | \(0.719263\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.0139 | + | 31.2010i | −0.614626 | + | 1.06456i | 0.375824 | + | 0.926691i | \(0.377360\pi\) |
−0.990450 | + | 0.137872i | \(0.955974\pi\) | |||||||
\(860\) | 14.4449 | − | 25.0194i | 0.492569 | − | 0.853154i | ||||
\(861\) | −0.481688 | − | 2.25817i | −0.0164159 | − | 0.0769583i | ||||
\(862\) | −1.61352 | − | 2.79470i | −0.0549566 | − | 0.0951877i | ||||
\(863\) | 4.31646 | 0.146934 | 0.0734670 | − | 0.997298i | \(-0.476594\pi\) | ||||
0.0734670 | + | 0.997298i | \(0.476594\pi\) | |||||||
\(864\) | 25.6789 | − | 2.75502i | 0.873616 | − | 0.0937275i | ||||
\(865\) | 21.1229 | 0.718199 | ||||||||
\(866\) | 3.43291 | + | 5.94598i | 0.116655 | + | 0.202053i | ||||
\(867\) | 2.19682 | + | 10.2988i | 0.0746080 | + | 0.349765i | ||||
\(868\) | −11.6966 | + | 20.2591i | −0.397008 | + | 0.687637i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 1.82279 | − | 1.64362i | 0.0617984 | − | 0.0557241i | ||||
\(871\) | 6.19918 | + | 10.7373i | 0.210051 | + | 0.363819i | ||||
\(872\) | −10.1549 | −0.343889 | ||||||||
\(873\) | 0.833736 | + | 0.603913i | 0.0282177 | + | 0.0204394i | ||||
\(874\) | 16.2339 | 0.549121 | ||||||||
\(875\) | 20.6295 | + | 35.7313i | 0.697403 | + | 1.20794i | ||||
\(876\) | 43.6074 | + | 14.1342i | 1.47336 | + | 0.477551i | ||||
\(877\) | −15.5580 | + | 26.9473i | −0.525356 | + | 0.909944i | 0.474207 | + | 0.880413i | \(0.342735\pi\) |
−0.999564 | + | 0.0295309i | \(0.990599\pi\) | |||||||
\(878\) | 6.17488 | − | 10.6952i | 0.208392 | − | 0.360946i | ||||
\(879\) | −39.6879 | − | 12.8638i | −1.33864 | − | 0.433886i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.9267 | 1.47993 | 0.739964 | − | 0.672647i | \(-0.234843\pi\) | ||||
0.739964 | + | 0.672647i | \(0.234843\pi\) | |||||||
\(882\) | 6.22219 | − | 2.78103i | 0.209512 | − | 0.0936423i | ||||
\(883\) | −5.87946 | −0.197860 | −0.0989298 | − | 0.995094i | \(-0.531542\pi\) | ||||
−0.0989298 | + | 0.995094i | \(0.531542\pi\) | |||||||
\(884\) | 11.6222 | + | 20.1303i | 0.390897 | + | 0.677054i | ||||
\(885\) | 8.03445 | − | 7.24472i | 0.270075 | − | 0.243529i | ||||
\(886\) | 6.57813 | − | 11.3937i | 0.220997 | − | 0.382777i | ||||
\(887\) | 3.84755 | − | 6.66416i | 0.129188 | − | 0.223760i | −0.794174 | − | 0.607690i | \(-0.792096\pi\) |
0.923362 | + | 0.383930i | \(0.125430\pi\) | |||||||
\(888\) | −2.04252 | − | 9.57542i | −0.0685425 | − | 0.321330i | ||||
\(889\) | −18.4082 | − | 31.8839i | −0.617390 | − | 1.06935i | ||||
\(890\) | 6.64689 | 0.222804 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −41.3640 | −1.38497 | ||||||||
\(893\) | −2.38610 | − | 4.13285i | −0.0798479 | − | 0.138301i | ||||
\(894\) | 0.717986 | + | 3.36595i | 0.0240130 | + | 0.112574i | ||||
\(895\) | −18.6894 | + | 32.3710i | −0.624718 | + | 1.08204i | ||||
\(896\) | −19.2856 | + | 33.4036i | −0.644286 | + | 1.11594i | ||||
\(897\) | 38.5288 | − | 34.7417i | 1.28644 | − | 1.15999i | ||||
\(898\) | 3.47658 | + | 6.02161i | 0.116015 | + | 0.200944i | ||||
\(899\) | −6.59352 | −0.219906 | ||||||||
\(900\) | −10.0334 | + | 4.48448i | −0.334447 | + | 0.149483i | ||||
\(901\) | 41.5180 | 1.38316 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 54.0174 | + | 17.5084i | 1.79759 | + | 0.582642i | ||||
\(904\) | 15.1291 | − | 26.2043i | 0.503185 | − | 0.871542i | ||||
\(905\) | 3.74106 | − | 6.47970i | 0.124357 | − | 0.215393i | ||||
\(906\) | 6.29886 | + | 2.04161i | 0.209265 | + | 0.0678281i | ||||
\(907\) | 9.49528 | + | 16.4463i | 0.315285 | + | 0.546091i | 0.979498 | − | 0.201453i | \(-0.0645664\pi\) |
−0.664213 | + | 0.747544i | \(0.731233\pi\) | |||||||
\(908\) | 20.9761 | 0.696116 | ||||||||
\(909\) | 17.2879 | + | 12.5224i | 0.573404 | + | 0.415343i | ||||
\(910\) | 11.4241 | 0.378705 | ||||||||
\(911\) | −25.0176 | − | 43.3318i | −0.828871 | − | 1.43565i | −0.898924 | − | 0.438104i | \(-0.855650\pi\) |
0.0700530 | − | 0.997543i | \(-0.477683\pi\) | |||||||
\(912\) | 14.8563 | − | 13.3961i | 0.491943 | − | 0.443588i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 6.04320 | − | 10.4671i | 0.199891 | − | 0.346222i | ||||
\(915\) | 2.37826 | + | 11.1494i | 0.0786227 | + | 0.368587i | ||||
\(916\) | 2.68977 | + | 4.65882i | 0.0888725 | + | 0.153932i | ||||
\(917\) | −72.1519 | −2.38266 | ||||||||
\(918\) | 3.40905 | − | 7.70154i | 0.112515 | − | 0.254189i | ||||
\(919\) | 3.07419 | 0.101408 | 0.0507042 | − | 0.998714i | \(-0.483853\pi\) | ||||
0.0507042 | + | 0.998714i | \(0.483853\pi\) | |||||||
\(920\) | −11.7993 | − | 20.4369i | −0.389011 | − | 0.673786i | ||||
\(921\) | −5.88789 | − | 27.6027i | −0.194013 | − | 0.909539i | ||||
\(922\) | −6.43660 | + | 11.1485i | −0.211978 | + | 0.367157i | ||||
\(923\) | 14.0270 | − | 24.2955i | 0.461705 | − | 0.799696i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.19142 | + | 5.52769i | 0.104933 | + | 0.181749i | ||||
\(926\) | −6.22544 | −0.204581 | ||||||||
\(927\) | −0.511658 | + | 4.93642i | −0.0168051 | + | 0.162133i | ||||
\(928\) | −8.40617 | −0.275946 | ||||||||
\(929\) | 0.452787 | + | 0.784250i | 0.0148555 | + | 0.0257304i | 0.873358 | − | 0.487080i | \(-0.161938\pi\) |
−0.858502 | + | 0.512810i | \(0.828605\pi\) | |||||||
\(930\) | 5.38188 | + | 1.74440i | 0.176479 | + | 0.0572011i | ||||
\(931\) | 10.2305 | − | 17.7198i | 0.335292 | − | 0.580743i | ||||
\(932\) | −21.5804 | + | 37.3784i | −0.706891 | + | 1.22437i | ||||
\(933\) | 35.2126 | + | 11.4133i | 1.15281 | + | 0.373654i | ||||
\(934\) | −6.79433 | − | 11.7681i | −0.222317 | − | 0.385065i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.28012 | + | 21.9983i | −0.0745280 | + | 0.719037i | ||||
\(937\) | −22.0542 | −0.720481 | −0.360240 | − | 0.932860i | \(-0.617305\pi\) | ||||
−0.360240 | + | 0.932860i | \(0.617305\pi\) | |||||||
\(938\) | 2.59391 | + | 4.49278i | 0.0846941 | + | 0.146694i | ||||
\(939\) | −4.00837 | + | 3.61437i | −0.130808 | + | 0.117951i | ||||
\(940\) | −1.62330 | + | 2.81164i | −0.0529462 | + | 0.0917056i | ||||
\(941\) | −2.73046 | + | 4.72930i | −0.0890105 | + | 0.154171i | −0.907093 | − | 0.420930i | \(-0.861704\pi\) |
0.818083 | + | 0.575101i | \(0.195037\pi\) | |||||||
\(942\) | 0.0547914 | + | 0.256865i | 0.00178520 | + | 0.00836910i | ||||
\(943\) | −1.46422 | − | 2.53610i | −0.0476815 | − | 0.0825868i | ||||
\(944\) | −9.55957 | −0.311138 | ||||||||
\(945\) | 17.8460 | + | 24.4518i | 0.580531 | + | 0.795417i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.2203 | − | 28.0944i | −0.527089 | − | 0.912945i | −0.999502 | − | 0.0315677i | \(-0.989950\pi\) |
0.472412 | − | 0.881378i | \(-0.343383\pi\) | |||||||
\(948\) | −2.54238 | − | 11.9188i | −0.0825728 | − | 0.387105i | ||||
\(949\) | −30.0696 | + | 52.0821i | −0.976101 | + | 1.69066i | ||||
\(950\) | 2.25581 | − | 3.90718i | 0.0731883 | − | 0.126766i | ||||
\(951\) | 23.4946 | − | 21.1853i | 0.761866 | − | 0.686980i | ||||
\(952\) | 10.3911 | + | 17.9979i | 0.336777 | + | 0.583315i | ||||
\(953\) | −53.8088 | −1.74304 | −0.871518 | − | 0.490363i | \(-0.836864\pi\) | ||||
−0.871518 | + | 0.490363i | \(0.836864\pi\) | |||||||
\(954\) | 14.9722 | + | 10.8451i | 0.484744 | + | 0.351122i | ||||
\(955\) | 21.3774 | 0.691756 | ||||||||
\(956\) | −6.11452 | − | 10.5907i | −0.197758 | − | 0.342527i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.83130 | + | 6.63600i | −0.123784 | + | 0.214400i | ||||
\(959\) | −5.45773 | + | 9.45306i | −0.176239 | + | 0.305255i | ||||
\(960\) | −7.85487 | − | 2.54596i | −0.253515 | − | 0.0821704i | ||||
\(961\) | 7.90079 | + | 13.6846i | 0.254864 | + | 0.441437i | ||||
\(962\) | 6.01137 | 0.193814 | ||||||||
\(963\) | −9.05701 | + | 4.04806i | −0.291858 | + | 0.130447i | ||||
\(964\) | 13.6717 | 0.440335 | ||||||||
\(965\) | 10.7322 | + | 18.5888i | 0.345483 | + | 0.598394i | ||||
\(966\) | 16.1215 | − | 14.5369i | 0.518701 | − | 0.467717i | ||||
\(967\) | 14.4075 | − | 24.9546i | 0.463315 | − | 0.802486i | −0.535809 | − | 0.844340i | \(-0.679993\pi\) |
0.999124 | + | 0.0418540i | \(0.0133264\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.27490 | − | 24.7289i | −0.169454 | − | 0.794408i | ||||
\(970\) | 0.143758 | + | 0.248997i | 0.00461580 | + | 0.00799480i | ||||
\(971\) | 5.39405 | 0.173103 | 0.0865517 | − | 0.996247i | \(-0.472415\pi\) | ||||
0.0865517 | + | 0.996247i | \(0.472415\pi\) | |||||||
\(972\) | −23.7026 | + | 13.7986i | −0.760262 | + | 0.442592i | ||||
\(973\) | −51.1362 | −1.63935 | ||||||||
\(974\) | 6.60377 | + | 11.4381i | 0.211598 | + | 0.366499i | ||||
\(975\) | −3.00780 | − | 14.1007i | −0.0963268 | − | 0.451584i | ||||
\(976\) | 5.03682 | − | 8.72403i | 0.161225 | − | 0.279250i | ||||
\(977\) | 1.65618 | − | 2.86859i | 0.0529859 | − | 0.0917742i | −0.838316 | − | 0.545185i | \(-0.816460\pi\) |
0.891302 | + | 0.453411i | \(0.149793\pi\) | |||||||
\(978\) | 6.93659 | − | 6.25478i | 0.221808 | − | 0.200006i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −13.9200 | −0.444657 | ||||||||
\(981\) | 15.0833 | − | 6.74152i | 0.481571 | − | 0.215240i | ||||
\(982\) | −19.1291 | −0.610435 | ||||||||
\(983\) | −16.9361 | − | 29.3341i | −0.540176 | − | 0.935613i | −0.998893 | − | 0.0470306i | \(-0.985024\pi\) |
0.458717 | − | 0.888582i | \(-0.348309\pi\) | |||||||
\(984\) | 1.18757 | + | 0.384921i | 0.0378584 | + | 0.0122708i | ||||
\(985\) | 8.83584 | − | 15.3041i | 0.281533 | − | 0.487630i | ||||
\(986\) | −1.37068 | + | 2.37409i | −0.0436514 | + | 0.0756065i | ||||
\(987\) | −6.07039 | − | 1.96756i | −0.193223 | − | 0.0626282i | ||||
\(988\) | 15.5369 | + | 26.9107i | 0.494295 | + | 0.856143i | ||||
\(989\) | 72.0183 | 2.29005 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.66640 | 0.275297 | 0.137649 | − | 0.990481i | \(-0.456046\pi\) | ||||
0.137649 | + | 0.990481i | \(0.456046\pi\) | |||||||
\(992\) | −9.68835 | − | 16.7807i | −0.307605 | − | 0.532788i | ||||
\(993\) | −4.84452 | + | 4.36834i | −0.153736 | + | 0.138625i | ||||
\(994\) | 5.86929 | − | 10.1659i | 0.186163 | − | 0.322443i | ||||
\(995\) | −22.6140 | + | 39.1686i | −0.716912 | + | 1.24173i | ||||
\(996\) | −0.0794450 | − | 0.372442i | −0.00251731 | − | 0.0118013i | ||||
\(997\) | 15.1327 | + | 26.2106i | 0.479258 | + | 0.830098i | 0.999717 | − | 0.0237880i | \(-0.00757266\pi\) |
−0.520459 | + | 0.853886i | \(0.674239\pi\) | |||||||
\(998\) | 11.7891 | 0.373177 | ||||||||
\(999\) | 9.39060 | + | 12.8666i | 0.297105 | + | 0.407080i |
(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 | 1089.2.e.p.364.10 | 36 | ||
9.4 | even | 3 | 9801.2.a.cm.1.9 | 18 | |||
9.5 | odd | 6 | 9801.2.a.cp.1.10 | 18 | |||
9.7 | even | 3 | inner | 1089.2.e.p.727.10 | 36 | ||
11.5 | even | 5 | 99.2.m.b.58.5 | yes | 72 | ||
11.9 | even | 5 | 99.2.m.b.4.5 | ✓ | 72 | ||
11.10 | odd | 2 | 1089.2.e.o.364.9 | 36 | |||
33.5 | odd | 10 | 297.2.n.b.91.5 | 72 | |||
33.20 | odd | 10 | 297.2.n.b.37.5 | 72 | |||
99.5 | odd | 30 | 891.2.f.e.487.5 | 36 | |||
99.16 | even | 15 | 99.2.m.b.25.5 | yes | 72 | ||
99.20 | odd | 30 | 297.2.n.b.235.5 | 72 | |||
99.31 | even | 15 | 891.2.f.f.730.5 | 36 | |||
99.32 | even | 6 | 9801.2.a.cn.1.9 | 18 | |||
99.38 | odd | 30 | 297.2.n.b.289.5 | 72 | |||
99.43 | odd | 6 | 1089.2.e.o.727.9 | 36 | |||
99.49 | even | 15 | 891.2.f.f.487.5 | 36 | |||
99.76 | odd | 6 | 9801.2.a.co.1.10 | 18 | |||
99.86 | odd | 30 | 891.2.f.e.730.5 | 36 | |||
99.97 | even | 15 | 99.2.m.b.70.5 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.m.b.4.5 | ✓ | 72 | 11.9 | even | 5 | ||
99.2.m.b.25.5 | yes | 72 | 99.16 | even | 15 | ||
99.2.m.b.58.5 | yes | 72 | 11.5 | even | 5 | ||
99.2.m.b.70.5 | yes | 72 | 99.97 | even | 15 | ||
297.2.n.b.37.5 | 72 | 33.20 | odd | 10 | |||
297.2.n.b.91.5 | 72 | 33.5 | odd | 10 | |||
297.2.n.b.235.5 | 72 | 99.20 | odd | 30 | |||
297.2.n.b.289.5 | 72 | 99.38 | odd | 30 | |||
891.2.f.e.487.5 | 36 | 99.5 | odd | 30 | |||
891.2.f.e.730.5 | 36 | 99.86 | odd | 30 | |||
891.2.f.f.487.5 | 36 | 99.49 | even | 15 | |||
891.2.f.f.730.5 | 36 | 99.31 | even | 15 | |||
1089.2.e.o.364.9 | 36 | 11.10 | odd | 2 | |||
1089.2.e.o.727.9 | 36 | 99.43 | odd | 6 | |||
1089.2.e.p.364.10 | 36 | 1.1 | even | 1 | trivial | ||
1089.2.e.p.727.10 | 36 | 9.7 | even | 3 | inner | ||
9801.2.a.cm.1.9 | 18 | 9.4 | even | 3 | |||
9801.2.a.cn.1.9 | 18 | 99.32 | even | 6 | |||
9801.2.a.co.1.10 | 18 | 99.76 | odd | 6 | |||
9801.2.a.cp.1.10 | 18 | 9.5 | odd | 6 |