Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(32,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([10, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.32");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.p (of order \(12\), degree \(4\), 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: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 32.12 | ||
Character | \(\chi\) | \(=\) | 225.32 |
Dual form | 225.4.p.b.218.12 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.79258 | + | 0.748271i | 0.987328 | + | 0.264554i | 0.716128 | − | 0.697969i | \(-0.245913\pi\) |
0.271200 | + | 0.962523i | \(0.412580\pi\) | |||||||
\(3\) | −5.18419 | − | 0.352314i | −0.997699 | − | 0.0678029i | ||||
\(4\) | 0.310415 | + | 0.179218i | 0.0388018 | + | 0.0224022i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −14.2137 | − | 4.86305i | −0.967118 | − | 0.330889i | ||||
\(7\) | −5.03374 | + | 18.7862i | −0.271797 | + | 1.01436i | 0.686161 | + | 0.727450i | \(0.259294\pi\) |
−0.957958 | + | 0.286909i | \(0.907372\pi\) | |||||||
\(8\) | −15.6218 | − | 15.6218i | −0.690390 | − | 0.690390i | ||||
\(9\) | 26.7517 | + | 3.65293i | 0.990806 | + | 0.135294i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 49.0377 | − | 28.3119i | 1.34413 | − | 0.776033i | 0.356718 | − | 0.934212i | \(-0.383896\pi\) |
0.987410 | + | 0.158179i | \(0.0505623\pi\) | |||||||
\(12\) | −1.54611 | − | 1.03846i | −0.0371936 | − | 0.0249816i | ||||
\(13\) | 0.616650 | + | 2.30137i | 0.0131560 | + | 0.0490988i | 0.972192 | − | 0.234186i | \(-0.0752425\pi\) |
−0.959036 | + | 0.283285i | \(0.908576\pi\) | |||||||
\(14\) | −28.1143 | + | 48.6954i | −0.536705 | + | 0.929600i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −33.3695 | − | 57.7977i | −0.521399 | − | 0.903089i | ||||
\(17\) | 92.5976 | − | 92.5976i | 1.32107 | − | 1.32107i | 0.408161 | − | 0.912910i | \(-0.366170\pi\) |
0.912910 | − | 0.408161i | \(-0.133830\pi\) | |||||||
\(18\) | 71.9731 | + | 30.2187i | 0.942457 | + | 0.395700i | ||||
\(19\) | − | 21.7774i | − | 0.262952i | −0.991319 | − | 0.131476i | \(-0.958028\pi\) | ||
0.991319 | − | 0.131476i | \(-0.0419716\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 32.7146 | − | 95.6178i | 0.339948 | − | 0.993596i | ||||
\(22\) | 158.127 | − | 42.3700i | 1.53240 | − | 0.410605i | ||||
\(23\) | 98.8952 | − | 26.4989i | 0.896569 | − | 0.240235i | 0.219027 | − | 0.975719i | \(-0.429712\pi\) |
0.677542 | + | 0.735484i | \(0.263045\pi\) | |||||||
\(24\) | 75.4824 | + | 86.4900i | 0.641991 | + | 0.735612i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.88818i | 0.0519571i | ||||||||
\(27\) | −137.399 | − | 28.3625i | −0.979352 | − | 0.202162i | ||||
\(28\) | −4.92937 | + | 4.92937i | −0.0332701 | + | 0.0332701i | ||||
\(29\) | −40.6009 | − | 70.3228i | −0.259979 | − | 0.450297i | 0.706257 | − | 0.707956i | \(-0.250382\pi\) |
−0.966236 | + | 0.257659i | \(0.917049\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.26447 | − | 7.38628i | 0.0247071 | − | 0.0427940i | −0.853407 | − | 0.521244i | \(-0.825468\pi\) |
0.878115 | + | 0.478450i | \(0.158801\pi\) | |||||||
\(32\) | −4.19518 | − | 15.6566i | −0.0231753 | − | 0.0864914i | ||||
\(33\) | −264.196 | + | 129.498i | −1.39365 | + | 0.683111i | ||||
\(34\) | 327.875 | − | 189.298i | 1.65382 | − | 0.954836i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7.64946 | + | 5.92832i | 0.0354142 | + | 0.0274459i | ||||
\(37\) | −8.92697 | − | 8.92697i | −0.0396645 | − | 0.0396645i | 0.686996 | − | 0.726661i | \(-0.258929\pi\) |
−0.726661 | + | 0.686996i | \(0.758929\pi\) | |||||||
\(38\) | 16.2954 | − | 60.8153i | 0.0695648 | − | 0.259619i | ||||
\(39\) | −2.38603 | − | 12.1480i | −0.00979667 | − | 0.0498778i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −28.1572 | − | 16.2566i | −0.107254 | − | 0.0619232i | 0.445413 | − | 0.895325i | \(-0.353057\pi\) |
−0.552668 | + | 0.833402i | \(0.686390\pi\) | |||||||
\(42\) | 162.906 | − | 242.541i | 0.598499 | − | 0.891070i | ||||
\(43\) | 428.714 | + | 114.874i | 1.52042 | + | 0.407396i | 0.919882 | − | 0.392196i | \(-0.128285\pi\) |
0.600543 | + | 0.799593i | \(0.294951\pi\) | |||||||
\(44\) | 20.2960 | 0.0695395 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 296.002 | 0.948762 | ||||||||
\(47\) | 140.159 | + | 37.5556i | 0.434986 | + | 0.116554i | 0.469666 | − | 0.882844i | \(-0.344374\pi\) |
−0.0346799 | + | 0.999398i | \(0.511041\pi\) | |||||||
\(48\) | 152.631 | + | 311.391i | 0.458967 | + | 0.936363i | ||||
\(49\) | −30.5356 | − | 17.6297i | −0.0890251 | − | 0.0513987i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −512.667 | + | 447.420i | −1.40760 | + | 1.22846i | ||||
\(52\) | −0.221029 | + | 0.824893i | −0.000589447 | + | 0.00219985i | ||||
\(53\) | −82.9808 | − | 82.9808i | −0.215062 | − | 0.215062i | 0.591352 | − | 0.806414i | \(-0.298595\pi\) |
−0.806414 | + | 0.591352i | \(0.798595\pi\) | |||||||
\(54\) | −362.476 | − | 182.017i | −0.913459 | − | 0.458691i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 372.109 | − | 214.837i | 0.887950 | − | 0.512658i | ||||
\(57\) | −7.67250 | + | 112.898i | −0.0178289 | + | 0.262347i | ||||
\(58\) | −60.7609 | − | 226.763i | −0.137557 | − | 0.513369i | ||||
\(59\) | −129.436 | + | 224.189i | −0.285612 | + | 0.494695i | −0.972757 | − | 0.231825i | \(-0.925530\pi\) |
0.687145 | + | 0.726520i | \(0.258864\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −282.613 | − | 489.500i | −0.593195 | − | 1.02744i | −0.993799 | − | 0.111192i | \(-0.964533\pi\) |
0.400604 | − | 0.916251i | \(-0.368800\pi\) | |||||||
\(62\) | 17.4358 | − | 17.4358i | 0.0357153 | − | 0.0357153i | ||||
\(63\) | −203.286 | + | 484.175i | −0.406534 | + | 0.968260i | ||||
\(64\) | 487.051i | 0.951271i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −834.688 | + | 163.944i | −1.55671 | + | 0.305759i | ||||
\(67\) | −434.879 | + | 116.526i | −0.792970 | + | 0.212476i | −0.632495 | − | 0.774564i | \(-0.717969\pi\) |
−0.160475 | + | 0.987040i | \(0.551302\pi\) | |||||||
\(68\) | 45.3388 | − | 12.1485i | 0.0808549 | − | 0.0216650i | ||||
\(69\) | −522.028 | + | 102.533i | −0.910794 | + | 0.178892i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.2978i | 0.0272422i | 0.999907 | + | 0.0136211i | \(0.00433587\pi\) | ||||
−0.999907 | + | 0.0136211i | \(0.995664\pi\) | |||||||
\(72\) | −360.844 | − | 474.974i | −0.590637 | − | 0.777448i | ||||
\(73\) | −59.2407 | + | 59.2407i | −0.0949809 | + | 0.0949809i | −0.753001 | − | 0.658020i | \(-0.771394\pi\) |
0.658020 | + | 0.753001i | \(0.271394\pi\) | |||||||
\(74\) | −18.2495 | − | 31.6091i | −0.0286684 | − | 0.0496552i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.90290 | − | 6.76003i | 0.00589071 | − | 0.0102030i | ||||
\(77\) | 285.030 | + | 1063.75i | 0.421846 | + | 1.57435i | ||||
\(78\) | 2.42681 | − | 35.7097i | 0.00352284 | − | 0.0518375i | ||||
\(79\) | 472.049 | − | 272.538i | 0.672274 | − | 0.388138i | −0.124663 | − | 0.992199i | \(-0.539785\pi\) |
0.796938 | + | 0.604061i | \(0.206452\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 702.312 | + | 195.445i | 0.963391 | + | 0.268100i | ||||
\(82\) | −66.4671 | − | 66.4671i | −0.0895129 | − | 0.0895129i | ||||
\(83\) | 260.644 | − | 972.735i | 0.344691 | − | 1.28640i | −0.548282 | − | 0.836294i | \(-0.684718\pi\) |
0.892973 | − | 0.450110i | \(-0.148615\pi\) | |||||||
\(84\) | 27.2915 | − | 23.8181i | 0.0354494 | − | 0.0309377i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1111.26 | + | 641.588i | 1.39338 | + | 0.804467i | ||||
\(87\) | 185.707 | + | 378.871i | 0.228849 | + | 0.466888i | ||||
\(88\) | −1208.34 | − | 323.773i | −1.46374 | − | 0.392208i | ||||
\(89\) | −844.831 | −1.00620 | −0.503101 | − | 0.864228i | \(-0.667808\pi\) | ||||
−0.503101 | + | 0.864228i | \(0.667808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −46.3380 | −0.0533796 | ||||||||
\(92\) | 35.4476 | + | 9.49816i | 0.0401703 | + | 0.0107636i | ||||
\(93\) | −24.7101 | + | 36.7895i | −0.0275518 | + | 0.0410203i | ||||
\(94\) | 363.305 | + | 209.754i | 0.398639 | + | 0.230154i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 16.2326 | + | 82.6450i | 0.0172576 | + | 0.0878637i | ||||
\(97\) | 105.374 | − | 393.261i | 0.110300 | − | 0.411645i | −0.888592 | − | 0.458698i | \(-0.848316\pi\) |
0.998892 | + | 0.0470524i | \(0.0149828\pi\) | |||||||
\(98\) | −72.0814 | − | 72.0814i | −0.0742992 | − | 0.0742992i | ||||
\(99\) | 1415.27 | − | 578.262i | 1.43676 | − | 0.587046i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −398.138 | + | 229.865i | −0.392240 | + | 0.226460i | −0.683130 | − | 0.730297i | \(-0.739382\pi\) |
0.290890 | + | 0.956756i | \(0.406049\pi\) | |||||||
\(102\) | −1766.46 | + | 865.845i | −1.71476 | + | 0.840504i | ||||
\(103\) | −360.103 | − | 1343.92i | −0.344485 | − | 1.28564i | −0.893212 | − | 0.449635i | \(-0.851554\pi\) |
0.548727 | − | 0.836001i | \(-0.315113\pi\) | |||||||
\(104\) | 26.3182 | − | 45.5845i | 0.0248146 | − | 0.0429801i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −169.639 | − | 293.823i | −0.155441 | − | 0.269232i | ||||
\(107\) | −319.287 | + | 319.287i | −0.288473 | + | 0.288473i | −0.836476 | − | 0.548003i | \(-0.815388\pi\) |
0.548003 | + | 0.836476i | \(0.315388\pi\) | |||||||
\(108\) | −37.5677 | − | 33.4286i | −0.0334718 | − | 0.0297839i | ||||
\(109\) | − | 1126.24i | − | 0.989672i | −0.868986 | − | 0.494836i | \(-0.835228\pi\) | ||
0.868986 | − | 0.494836i | \(-0.164772\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 43.1341 | + | 49.4243i | 0.0368838 | + | 0.0422625i | ||||
\(112\) | 1253.77 | − | 335.947i | 1.05777 | − | 0.283429i | ||||
\(113\) | 1458.69 | − | 390.853i | 1.21435 | − | 0.325384i | 0.405883 | − | 0.913925i | \(-0.366964\pi\) |
0.808467 | + | 0.588541i | \(0.200297\pi\) | |||||||
\(114\) | −105.905 | + | 309.537i | −0.0870077 | + | 0.254305i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 29.1056i | − | 0.0232965i | ||||||
\(117\) | 8.08972 | + | 63.8182i | 0.00639226 | + | 0.0504273i | ||||
\(118\) | −529.215 | + | 529.215i | −0.412866 | + | 0.412866i | ||||
\(119\) | 1273.44 | + | 2205.67i | 0.980977 | + | 1.69910i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 937.629 | − | 1624.02i | 0.704455 | − | 1.22015i | ||||
\(122\) | −422.942 | − | 1578.44i | −0.313864 | − | 1.17136i | ||||
\(123\) | 140.245 | + | 94.1974i | 0.102809 | + | 0.0690528i | ||||
\(124\) | 2.64751 | − | 1.52854i | 0.00191736 | − | 0.00110699i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −929.988 | + | 1199.99i | −0.657539 | + | 0.848440i | ||||
\(127\) | 638.135 | + | 638.135i | 0.445869 | + | 0.445869i | 0.893979 | − | 0.448110i | \(-0.147903\pi\) |
−0.448110 | + | 0.893979i | \(0.647903\pi\) | |||||||
\(128\) | −398.007 | + | 1485.38i | −0.274837 | + | 1.02571i | ||||
\(129\) | −2182.06 | − | 746.569i | −1.48930 | − | 0.509548i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2261.94 | + | 1305.93i | 1.50860 | + | 0.870992i | 0.999950 | + | 0.0100207i | \(0.00318975\pi\) |
0.508653 | + | 0.860972i | \(0.330144\pi\) | |||||||
\(132\) | −105.218 | − | 7.15058i | −0.0693795 | − | 0.00471498i | ||||
\(133\) | 409.115 | + | 109.622i | 0.266727 | + | 0.0714694i | ||||
\(134\) | −1301.63 | −0.839132 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2893.07 | −1.82411 | ||||||||
\(137\) | −942.088 | − | 252.432i | −0.587504 | − | 0.157421i | −0.0471916 | − | 0.998886i | \(-0.515027\pi\) |
−0.540312 | + | 0.841465i | \(0.681694\pi\) | |||||||
\(138\) | −1534.53 | − | 104.286i | −0.946579 | − | 0.0643288i | ||||
\(139\) | −1106.34 | − | 638.748i | −0.675099 | − | 0.389769i | 0.122907 | − | 0.992418i | \(-0.460778\pi\) |
−0.798006 | + | 0.602649i | \(0.794112\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −713.382 | − | 244.075i | −0.426082 | − | 0.145779i | ||||
\(142\) | −12.1952 | + | 45.5131i | −0.00720703 | + | 0.0268970i | ||||
\(143\) | 95.3952 | + | 95.3952i | 0.0557856 | + | 0.0557856i | ||||
\(144\) | −681.562 | − | 1668.09i | −0.394422 | − | 0.965327i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −209.763 | + | 121.107i | −0.118905 | + | 0.0686497i | ||||
\(147\) | 152.091 | + | 102.154i | 0.0853352 | + | 0.0573165i | ||||
\(148\) | −1.17119 | − | 4.37094i | −0.000650480 | − | 0.00242763i | ||||
\(149\) | 69.6092 | − | 120.567i | 0.0382725 | − | 0.0662900i | −0.846255 | − | 0.532779i | \(-0.821148\pi\) |
0.884527 | + | 0.466489i | \(0.154481\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 706.994 | + | 1224.55i | 0.381022 | + | 0.659950i | 0.991209 | − | 0.132308i | \(-0.0422388\pi\) |
−0.610186 | + | 0.792258i | \(0.708905\pi\) | |||||||
\(152\) | −340.201 | + | 340.201i | −0.181539 | + | 0.181539i | ||||
\(153\) | 2815.40 | − | 2138.89i | 1.48766 | − | 1.13019i | ||||
\(154\) | 3183.88i | 1.66600i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.43648 | − | 4.19853i | 0.000737247 | − | 0.00215482i | ||||
\(157\) | −2293.99 | + | 614.674i | −1.16612 | + | 0.312461i | −0.789407 | − | 0.613870i | \(-0.789612\pi\) |
−0.376712 | + | 0.926330i | \(0.622945\pi\) | |||||||
\(158\) | 1522.17 | − | 407.864i | 0.766438 | − | 0.205367i | ||||
\(159\) | 400.953 | + | 459.424i | 0.199985 | + | 0.229149i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1991.25i | 0.974738i | ||||||||
\(162\) | 1815.02 | + | 1071.32i | 0.880256 | + | 0.519571i | ||||
\(163\) | −940.543 | + | 940.543i | −0.451957 | + | 0.451957i | −0.896004 | − | 0.444046i | \(-0.853543\pi\) |
0.444046 | + | 0.896004i | \(0.353543\pi\) | |||||||
\(164\) | −5.82694 | − | 10.0926i | −0.00277444 | − | 0.00480547i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1455.74 | − | 2521.41i | 0.680646 | − | 1.17891i | ||||
\(167\) | 973.893 | + | 3634.62i | 0.451270 | + | 1.68416i | 0.698828 | + | 0.715290i | \(0.253705\pi\) |
−0.247558 | + | 0.968873i | \(0.579628\pi\) | |||||||
\(168\) | −2004.78 | + | 982.659i | −0.920666 | + | 0.451273i | ||||
\(169\) | 1897.74 | − | 1095.66i | 0.863788 | − | 0.498708i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 79.5514 | − | 582.584i | 0.0355757 | − | 0.260534i | ||||
\(172\) | 112.492 | + | 112.492i | 0.0498686 | + | 0.0498686i | ||||
\(173\) | −1129.62 | + | 4215.81i | −0.496437 | + | 1.85273i | 0.0253882 | + | 0.999678i | \(0.491918\pi\) |
−0.521826 | + | 0.853052i | \(0.674749\pi\) | |||||||
\(174\) | 235.105 | + | 1196.99i | 0.102432 | + | 0.521515i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3272.73 | − | 1889.51i | −1.40165 | − | 0.809245i | ||||
\(177\) | 750.006 | − | 1116.64i | 0.318497 | − | 0.474191i | ||||
\(178\) | −2359.26 | − | 632.163i | −0.993451 | − | 0.266194i | ||||
\(179\) | 2857.68 | 1.19326 | 0.596628 | − | 0.802518i | \(-0.296507\pi\) | ||||
0.596628 | + | 0.802518i | \(0.296507\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1459.11 | −0.599199 | −0.299599 | − | 0.954065i | \(-0.596853\pi\) | ||||
−0.299599 | + | 0.954065i | \(0.596853\pi\) | |||||||
\(182\) | −129.403 | − | 34.6734i | −0.0527031 | − | 0.0141218i | ||||
\(183\) | 1292.66 | + | 2637.23i | 0.522166 | + | 1.06530i | ||||
\(184\) | −1958.88 | − | 1130.96i | −0.784838 | − | 0.453127i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −96.5336 | + | 84.2478i | −0.0380548 | + | 0.0332116i | ||||
\(187\) | 1919.15 | − | 7162.38i | 0.750495 | − | 2.80088i | ||||
\(188\) | 36.7768 | + | 36.7768i | 0.0142672 | + | 0.0142672i | ||||
\(189\) | 1224.46 | − | 2438.44i | 0.471249 | − | 0.938468i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 610.123 | − | 352.255i | 0.231136 | − | 0.133446i | −0.379960 | − | 0.925003i | \(-0.624062\pi\) |
0.611096 | + | 0.791557i | \(0.290729\pi\) | |||||||
\(192\) | 171.595 | − | 2524.96i | 0.0644989 | − | 0.949081i | ||||
\(193\) | −396.828 | − | 1480.98i | −0.148001 | − | 0.552349i | −0.999603 | − | 0.0281599i | \(-0.991035\pi\) |
0.851602 | − | 0.524189i | \(-0.175631\pi\) | |||||||
\(194\) | 588.531 | − | 1019.37i | 0.217804 | − | 0.377248i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.31913 | − | 10.9451i | −0.00230289 | − | 0.00398872i | ||||
\(197\) | 989.475 | − | 989.475i | 0.357854 | − | 0.357854i | −0.505168 | − | 0.863021i | \(-0.668569\pi\) |
0.863021 | + | 0.505168i | \(0.168569\pi\) | |||||||
\(198\) | 4384.94 | − | 555.844i | 1.57386 | − | 0.199506i | ||||
\(199\) | 2035.66i | 0.725146i | 0.931955 | + | 0.362573i | \(0.118102\pi\) | ||||
−0.931955 | + | 0.362573i | \(0.881898\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2295.55 | − | 450.877i | 0.805551 | − | 0.158221i | ||||
\(202\) | −1283.84 | + | 344.003i | −0.447180 | + | 0.119822i | ||||
\(203\) | 1525.47 | − | 408.749i | 0.527424 | − | 0.141323i | ||||
\(204\) | −239.325 | + | 47.0066i | −0.0821378 | + | 0.0161330i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 4022.47i | − | 1.36048i | ||||||
\(207\) | 2742.42 | − | 347.634i | 0.920828 | − | 0.116726i | ||||
\(208\) | 112.436 | − | 112.436i | 0.0374811 | − | 0.0374811i | ||||
\(209\) | −616.560 | − | 1067.91i | −0.204059 | − | 0.353441i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −688.380 | + | 1192.31i | −0.224597 | + | 0.389014i | −0.956199 | − | 0.292719i | \(-0.905440\pi\) |
0.731601 | + | 0.681733i | \(0.238773\pi\) | |||||||
\(212\) | −10.8868 | − | 40.6301i | −0.00352693 | − | 0.0131627i | ||||
\(213\) | 5.74196 | − | 84.4912i | 0.00184710 | − | 0.0271795i | ||||
\(214\) | −1130.55 | + | 652.723i | −0.361134 | + | 0.208501i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1703.35 | + | 2589.49i | 0.536565 | + | 0.815706i | ||||
\(217\) | 117.294 | + | 117.294i | 0.0366932 | + | 0.0366932i | ||||
\(218\) | 842.733 | − | 3145.12i | 0.261821 | − | 0.977131i | ||||
\(219\) | 327.987 | − | 286.244i | 0.101202 | − | 0.0883223i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 270.201 | + | 156.001i | 0.0822430 | + | 0.0474830i | ||||
\(222\) | 83.4728 | + | 170.297i | 0.0252357 | + | 0.0514847i | ||||
\(223\) | 3795.71 | + | 1017.06i | 1.13982 | + | 0.305413i | 0.778878 | − | 0.627176i | \(-0.215789\pi\) |
0.360940 | + | 0.932589i | \(0.382456\pi\) | |||||||
\(224\) | 315.246 | 0.0940323 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4365.96 | 1.28504 | ||||||||
\(227\) | 872.812 | + | 233.869i | 0.255201 | + | 0.0683809i | 0.384151 | − | 0.923270i | \(-0.374494\pi\) |
−0.128950 | + | 0.991651i | \(0.541161\pi\) | |||||||
\(228\) | −22.6151 | + | 33.6703i | −0.00656895 | + | 0.00978012i | ||||
\(229\) | 3128.15 | + | 1806.04i | 0.902682 | + | 0.521164i | 0.878069 | − | 0.478533i | \(-0.158831\pi\) |
0.0246126 | + | 0.999697i | \(0.492165\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1102.88 | − | 5615.09i | −0.314130 | − | 1.59933i | ||||
\(232\) | −464.308 | + | 1732.82i | −0.131394 | + | 0.490368i | ||||
\(233\) | −2992.27 | − | 2992.27i | −0.841332 | − | 0.841332i | 0.147700 | − | 0.989032i | \(-0.452813\pi\) |
−0.989032 | + | 0.147700i | \(0.952813\pi\) | |||||||
\(234\) | −25.1621 | + | 184.271i | −0.00702947 | + | 0.0514794i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −80.3575 | + | 46.3945i | −0.0221645 | + | 0.0127967i | ||||
\(237\) | −2543.21 | + | 1246.58i | −0.697044 | + | 0.341662i | ||||
\(238\) | 1905.76 | + | 7112.39i | 0.519042 | + | 1.93709i | ||||
\(239\) | 1931.06 | − | 3344.69i | 0.522635 | − | 0.905230i | −0.477018 | − | 0.878893i | \(-0.658282\pi\) |
0.999653 | − | 0.0263367i | \(-0.00838419\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 858.250 | + | 1486.53i | 0.229397 | + | 0.397328i | 0.957630 | − | 0.288003i | \(-0.0929912\pi\) |
−0.728232 | + | 0.685330i | \(0.759658\pi\) | |||||||
\(242\) | 3833.62 | − | 3833.62i | 1.01832 | − | 1.01832i | ||||
\(243\) | −3572.07 | − | 1260.66i | −0.942996 | − | 0.332803i | ||||
\(244\) | − | 202.597i | − | 0.0531556i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 321.161 | + | 367.996i | 0.0832377 | + | 0.0953762i | ||||
\(247\) | 50.1178 | − | 13.4290i | 0.0129106 | − | 0.00345939i | ||||
\(248\) | −182.005 | + | 48.7681i | −0.0466021 | + | 0.0124870i | ||||
\(249\) | −1693.94 | + | 4951.02i | −0.431120 | + | 1.26007i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 2285.88i | − | 0.574836i | −0.957805 | − | 0.287418i | \(-0.907203\pi\) | ||
0.957805 | − | 0.287418i | \(-0.0927968\pi\) | |||||||
\(252\) | −149.876 | + | 113.863i | −0.0374655 | + | 0.0284630i | ||||
\(253\) | 4099.36 | − | 4099.36i | 1.01867 | − | 1.01867i | ||||
\(254\) | 1304.55 | + | 2259.54i | 0.322262 | + | 0.558175i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −274.734 | + | 475.854i | −0.0670738 | + | 0.116175i | ||||
\(257\) | −988.996 | − | 3690.98i | −0.240046 | − | 0.895865i | −0.975809 | − | 0.218625i | \(-0.929843\pi\) |
0.735763 | − | 0.677239i | \(-0.236824\pi\) | |||||||
\(258\) | −5534.96 | − | 3717.63i | −1.33563 | − | 0.897091i | ||||
\(259\) | 212.640 | − | 122.768i | 0.0510147 | − | 0.0294533i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −829.260 | − | 2029.57i | −0.196666 | − | 0.481330i | ||||
\(262\) | 5339.48 | + | 5339.48i | 1.25906 | + | 1.25906i | ||||
\(263\) | −1276.64 | + | 4764.50i | −0.299320 | + | 1.11708i | 0.638405 | + | 0.769701i | \(0.279595\pi\) |
−0.937725 | + | 0.347378i | \(0.887072\pi\) | |||||||
\(264\) | 6150.18 | + | 2104.21i | 1.43378 | + | 0.490551i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1060.46 | + | 612.257i | 0.244440 | + | 0.141127i | ||||
\(267\) | 4379.77 | + | 297.646i | 1.00389 | + | 0.0682234i | ||||
\(268\) | −155.876 | − | 41.7669i | −0.0355286 | − | 0.00951986i | ||||
\(269\) | −6569.52 | −1.48904 | −0.744518 | − | 0.667602i | \(-0.767321\pi\) | ||||
−0.744518 | + | 0.667602i | \(0.767321\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1603.65 | −0.359465 | −0.179733 | − | 0.983715i | \(-0.557523\pi\) | ||||
−0.179733 | + | 0.983715i | \(0.557523\pi\) | |||||||
\(272\) | −8441.86 | − | 2261.99i | −1.88185 | − | 0.504240i | ||||
\(273\) | 240.225 | + | 16.3255i | 0.0532567 | + | 0.00361929i | ||||
\(274\) | −2441.97 | − | 1409.87i | −0.538412 | − | 0.310852i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −180.421 | − | 61.7290i | −0.0393481 | − | 0.0134625i | ||||
\(277\) | −2276.92 | + | 8497.59i | −0.493888 | + | 1.84322i | 0.0422830 | + | 0.999106i | \(0.486537\pi\) |
−0.536171 | + | 0.844109i | \(0.680130\pi\) | |||||||
\(278\) | −2611.60 | − | 2611.60i | −0.563430 | − | 0.563430i | ||||
\(279\) | 141.064 | − | 182.018i | 0.0302697 | − | 0.0390578i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5805.61 | + | 3351.87i | −1.23250 | + | 0.711586i | −0.967551 | − | 0.252675i | \(-0.918690\pi\) |
−0.264953 | + | 0.964261i | \(0.585356\pi\) | |||||||
\(282\) | −1809.54 | − | 1215.40i | −0.382116 | − | 0.256653i | ||||
\(283\) | −295.723 | − | 1103.65i | −0.0621163 | − | 0.231821i | 0.927888 | − | 0.372859i | \(-0.121623\pi\) |
−0.990004 | + | 0.141038i | \(0.954956\pi\) | |||||||
\(284\) | −2.92087 | + | 5.05909i | −0.000610287 | + | 0.00105705i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 195.018 | + | 337.781i | 0.0403204 | + | 0.0698370i | ||||
\(287\) | 447.135 | − | 447.135i | 0.0919636 | − | 0.0919636i | ||||
\(288\) | −55.0358 | − | 434.167i | −0.0112605 | − | 0.0888316i | ||||
\(289\) | − | 12235.6i | − | 2.49046i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −684.830 | + | 2001.62i | −0.137957 | + | 0.403219i | ||||
\(292\) | −29.0062 | + | 7.77218i | −0.00581322 | + | 0.00155765i | ||||
\(293\) | −6076.51 | + | 1628.20i | −1.21158 | + | 0.324642i | −0.807382 | − | 0.590029i | \(-0.799116\pi\) |
−0.404199 | + | 0.914671i | \(0.632450\pi\) | |||||||
\(294\) | 348.289 | + | 399.080i | 0.0690905 | + | 0.0791660i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 278.910i | 0.0547679i | ||||||||
\(297\) | −7540.74 | + | 2499.20i | −1.47326 | + | 0.488278i | ||||
\(298\) | 284.606 | − | 284.606i | 0.0553248 | − | 0.0553248i | ||||
\(299\) | 121.967 | + | 211.254i | 0.0235905 | + | 0.0408599i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4316.07 | + | 7475.65i | −0.826492 | + | 1.43153i | ||||
\(302\) | 1058.05 | + | 3948.68i | 0.201602 | + | 0.752388i | ||||
\(303\) | 2145.01 | − | 1051.40i | 0.406692 | − | 0.199344i | ||||
\(304\) | −1258.68 | + | 726.702i | −0.237469 | + | 0.137103i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 9462.71 | − | 3866.36i | 1.76780 | − | 0.722304i | ||||
\(307\) | −4998.67 | − | 4998.67i | −0.929281 | − | 0.929281i | 0.0683782 | − | 0.997659i | \(-0.478218\pi\) |
−0.997659 | + | 0.0683782i | \(0.978218\pi\) | |||||||
\(308\) | −102.165 | + | 381.285i | −0.0189006 | + | 0.0705380i | ||||
\(309\) | 1393.36 | + | 7094.02i | 0.256523 | + | 1.30603i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2626.45 | − | 1516.38i | −0.478882 | − | 0.276483i | 0.241068 | − | 0.970508i | \(-0.422502\pi\) |
−0.719950 | + | 0.694025i | \(0.755835\pi\) | |||||||
\(312\) | −152.499 | + | 227.047i | −0.0276717 | + | 0.0411987i | ||||
\(313\) | 4163.08 | + | 1115.49i | 0.751793 | + | 0.201442i | 0.614313 | − | 0.789062i | \(-0.289433\pi\) |
0.137480 | + | 0.990505i | \(0.456100\pi\) | |||||||
\(314\) | −6866.12 | −1.23400 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 195.375 | 0.0347806 | ||||||||
\(317\) | 4660.18 | + | 1248.69i | 0.825684 | + | 0.221241i | 0.646830 | − | 0.762634i | \(-0.276094\pi\) |
0.178854 | + | 0.983876i | \(0.442761\pi\) | |||||||
\(318\) | 775.922 | + | 1583.00i | 0.136829 | + | 0.279152i | ||||
\(319\) | −3981.95 | − | 2298.98i | −0.698891 | − | 0.403505i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1767.74 | − | 1542.76i | 0.307369 | − | 0.268250i | ||||
\(322\) | −1490.00 | + | 5560.74i | −0.257870 | + | 0.962385i | ||||
\(323\) | −2016.54 | − | 2016.54i | −0.347378 | − | 0.347378i | ||||
\(324\) | 182.981 | + | 186.536i | 0.0313753 | + | 0.0319849i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3330.33 | + | 1922.77i | −0.565797 | + | 0.326663i | ||||
\(327\) | −396.791 | + | 5838.65i | −0.0671027 | + | 0.987395i | ||||
\(328\) | 185.909 | + | 693.821i | 0.0312960 | + | 0.116798i | ||||
\(329\) | −1411.05 | + | 2444.01i | −0.236455 | + | 0.409553i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5632.10 | + | 9755.08i | 0.935251 | + | 1.61990i | 0.774186 | + | 0.632958i | \(0.218160\pi\) |
0.161065 | + | 0.986944i | \(0.448507\pi\) | |||||||
\(332\) | 255.239 | − | 255.239i | 0.0421930 | − | 0.0421930i | ||||
\(333\) | −206.202 | − | 271.422i | −0.0339334 | − | 0.0446661i | ||||
\(334\) | 10878.7i | 1.78221i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6618.16 | + | 1299.89i | −1.07455 | + | 0.211057i | ||||
\(337\) | −2284.24 | + | 612.060i | −0.369230 | + | 0.0989348i | −0.438663 | − | 0.898652i | \(-0.644548\pi\) |
0.0694329 | + | 0.997587i | \(0.477881\pi\) | |||||||
\(338\) | 6119.46 | − | 1639.70i | 0.984777 | − | 0.263870i | ||||
\(339\) | −7699.81 | + | 1512.34i | −1.23362 | + | 0.242299i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 482.941i | − | 0.0766942i | ||||||
\(342\) | 658.085 | − | 1567.39i | 0.104050 | − | 0.247821i | ||||
\(343\) | −4232.18 | + | 4232.18i | −0.666229 | + | 0.666229i | ||||
\(344\) | −4902.73 | − | 8491.79i | −0.768424 | − | 1.33095i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6309.14 | + | 10927.7i | −0.980293 | + | 1.69792i | ||||
\(347\) | 266.565 | + | 994.834i | 0.0412391 | + | 0.153906i | 0.983475 | − | 0.181043i | \(-0.0579474\pi\) |
−0.942236 | + | 0.334950i | \(0.891281\pi\) | |||||||
\(348\) | −10.2543 | + | 150.889i | −0.00157957 | + | 0.0232429i | ||||
\(349\) | −4729.47 | + | 2730.56i | −0.725394 | + | 0.418807i | −0.816735 | − | 0.577013i | \(-0.804218\pi\) |
0.0913406 | + | 0.995820i | \(0.470885\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.4546 | − | 333.696i | −0.00295843 | − | 0.0507447i | ||||
\(352\) | −648.991 | − | 648.991i | −0.0982708 | − | 0.0982708i | ||||
\(353\) | 172.316 | − | 643.090i | 0.0259814 | − | 0.0969638i | −0.951718 | − | 0.306975i | \(-0.900683\pi\) |
0.977699 | + | 0.210011i | \(0.0673500\pi\) | |||||||
\(354\) | 2930.00 | − | 2557.10i | 0.439909 | − | 0.383922i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −262.248 | − | 151.409i | −0.0390425 | − | 0.0225412i | ||||
\(357\) | −5824.69 | − | 11883.3i | −0.863516 | − | 1.76171i | ||||
\(358\) | 7980.30 | + | 2138.31i | 1.17813 | + | 0.315680i | ||||
\(359\) | 6703.88 | 0.985563 | 0.492781 | − | 0.870153i | \(-0.335980\pi\) | ||||
0.492781 | + | 0.870153i | \(0.335980\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6384.74 | 0.930856 | ||||||||
\(362\) | −4074.69 | − | 1091.81i | −0.591605 | − | 0.158520i | ||||
\(363\) | −5433.02 | + | 8088.90i | −0.785563 | + | 1.16958i | ||||
\(364\) | −14.3840 | − | 8.30460i | −0.00207122 | − | 0.00119582i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1636.51 | + | 8331.95i | 0.233720 | + | 1.18994i | ||||
\(367\) | −845.191 | + | 3154.29i | −0.120214 | + | 0.448645i | −0.999624 | − | 0.0274202i | \(-0.991271\pi\) |
0.879410 | + | 0.476065i | \(0.157937\pi\) | |||||||
\(368\) | −4831.66 | − | 4831.66i | −0.684423 | − | 0.684423i | ||||
\(369\) | −693.871 | − | 537.748i | −0.0978901 | − | 0.0758646i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1976.60 | − | 1141.19i | 0.276603 | − | 0.159697i | ||||
\(372\) | −14.2637 | + | 6.99149i | −0.00198801 | + | 0.000974440i | ||||
\(373\) | −1093.97 | − | 4082.74i | −0.151859 | − | 0.566747i | −0.999354 | − | 0.0359425i | \(-0.988557\pi\) |
0.847495 | − | 0.530804i | \(-0.178110\pi\) | |||||||
\(374\) | 10718.8 | − | 18565.5i | 1.48197 | − | 2.56684i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1602.85 | − | 2776.22i | −0.219842 | − | 0.380778i | ||||
\(377\) | 136.802 | − | 136.802i | 0.0186888 | − | 0.0186888i | ||||
\(378\) | 5244.01 | − | 5893.32i | 0.713553 | − | 0.801904i | ||||
\(379\) | − | 2005.61i | − | 0.271824i | −0.990721 | − | 0.135912i | \(-0.956604\pi\) | ||
0.990721 | − | 0.135912i | \(-0.0433965\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3083.39 | − | 3533.04i | −0.414612 | − | 0.475074i | ||||
\(382\) | 1967.40 | − | 527.164i | 0.263511 | − | 0.0706074i | ||||
\(383\) | −1133.16 | + | 303.630i | −0.151180 | + | 0.0405085i | −0.333615 | − | 0.942709i | \(-0.608269\pi\) |
0.182435 | + | 0.983218i | \(0.441602\pi\) | |||||||
\(384\) | 2586.67 | − | 7560.29i | 0.343751 | − | 1.00471i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 4432.70i | − | 0.584504i | ||||||
\(387\) | 11049.2 | + | 4639.13i | 1.45133 | + | 0.609355i | ||||
\(388\) | 103.189 | − | 103.189i | 0.0135016 | − | 0.0135016i | ||||
\(389\) | 5874.10 | + | 10174.2i | 0.765627 | + | 1.32610i | 0.939915 | + | 0.341410i | \(0.110904\pi\) |
−0.174288 | + | 0.984695i | \(0.555762\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6703.72 | − | 11611.2i | 0.867064 | − | 1.50180i | ||||
\(392\) | 201.612 | + | 752.427i | 0.0259769 | + | 0.0969472i | ||||
\(393\) | −11266.3 | − | 7567.13i | −1.44608 | − | 0.971276i | ||||
\(394\) | 3503.59 | − | 2022.80i | 0.447990 | − | 0.258647i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 542.954 | + | 74.1400i | 0.0689001 | + | 0.00940826i | ||||
\(397\) | −10419.9 | − | 10419.9i | −1.31728 | − | 1.31728i | −0.915919 | − | 0.401363i | \(-0.868537\pi\) |
−0.401363 | − | 0.915919i | \(-0.631463\pi\) | |||||||
\(398\) | −1523.22 | + | 5684.75i | −0.191840 | + | 0.715957i | ||||
\(399\) | −2082.31 | − | 712.439i | −0.261268 | − | 0.0893898i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4827.90 | − | 2787.39i | −0.601231 | − | 0.347121i | 0.168295 | − | 0.985737i | \(-0.446174\pi\) |
−0.769526 | + | 0.638616i | \(0.779507\pi\) | |||||||
\(402\) | 6747.90 | + | 458.583i | 0.837201 | + | 0.0568956i | ||||
\(403\) | 19.6282 | + | 5.25937i | 0.00242618 | + | 0.000650093i | ||||
\(404\) | −164.784 | −0.0202928 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4565.86 | 0.558128 | ||||||||
\(407\) | −690.498 | − | 185.018i | −0.0840951 | − | 0.0225332i | ||||
\(408\) | 14998.2 | + | 1019.27i | 1.81991 | + | 0.123680i | ||||
\(409\) | 8856.21 | + | 5113.13i | 1.07069 | + | 0.618162i | 0.928369 | − | 0.371659i | \(-0.121211\pi\) |
0.142318 | + | 0.989821i | \(0.454544\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4795.03 | + | 1640.57i | 0.575478 | + | 0.196893i | ||||
\(412\) | 129.074 | − | 481.710i | 0.0154345 | − | 0.0576023i | ||||
\(413\) | −3560.12 | − | 3560.12i | −0.424169 | − | 0.424169i | ||||
\(414\) | 7918.56 | + | 1081.27i | 0.940039 | + | 0.128362i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 33.4447 | − | 19.3093i | 0.00394173 | − | 0.00227576i | ||||
\(417\) | 5510.46 | + | 3701.17i | 0.647118 | + | 0.434646i | ||||
\(418\) | −922.708 | − | 3443.59i | −0.107969 | − | 0.402947i | ||||
\(419\) | −4387.14 | + | 7598.75i | −0.511517 | + | 0.885974i | 0.488394 | + | 0.872623i | \(0.337583\pi\) |
−0.999911 | + | 0.0133505i | \(0.995750\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6005.42 | − | 10401.7i | −0.695217 | − | 1.20415i | −0.970108 | − | 0.242675i | \(-0.921975\pi\) |
0.274891 | − | 0.961475i | \(-0.411358\pi\) | |||||||
\(422\) | −2814.53 | + | 2814.53i | −0.324666 | + | 0.324666i | ||||
\(423\) | 3612.32 | + | 1516.67i | 0.415217 | + | 0.174333i | ||||
\(424\) | 2592.61i | 0.296954i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 79.2572 | − | 231.652i | 0.00901414 | − | 0.0263464i | ||||
\(427\) | 10618.4 | − | 2845.20i | 1.20342 | − | 0.322457i | ||||
\(428\) | −156.333 | + | 41.8894i | −0.0176557 | + | 0.00473084i | ||||
\(429\) | −460.938 | − | 528.156i | −0.0518748 | − | 0.0594397i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 4099.38i | − | 0.458145i | −0.973409 | − | 0.229072i | \(-0.926431\pi\) | ||
0.973409 | − | 0.229072i | \(-0.0735692\pi\) | |||||||
\(432\) | 2945.66 | + | 8887.80i | 0.328063 | + | 0.989849i | ||||
\(433\) | −4324.33 | + | 4324.33i | −0.479940 | + | 0.479940i | −0.905112 | − | 0.425172i | \(-0.860213\pi\) |
0.425172 | + | 0.905112i | \(0.360213\pi\) | |||||||
\(434\) | 239.785 | + | 415.320i | 0.0265209 | + | 0.0459355i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 201.843 | − | 349.602i | 0.0221709 | − | 0.0384011i | ||||
\(437\) | −577.078 | − | 2153.68i | −0.0631702 | − | 0.235754i | ||||
\(438\) | 1130.12 | − | 553.938i | 0.123286 | − | 0.0604296i | ||||
\(439\) | −10469.7 | + | 6044.67i | −1.13825 | + | 0.657167i | −0.945996 | − | 0.324179i | \(-0.894912\pi\) |
−0.192251 | + | 0.981346i | \(0.561579\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −752.481 | − | 583.171i | −0.0812526 | − | 0.0629706i | ||||
\(442\) | 637.829 | + | 637.829i | 0.0686390 | + | 0.0686390i | ||||
\(443\) | −2391.39 | + | 8924.79i | −0.256475 | + | 0.957177i | 0.710789 | + | 0.703405i | \(0.248338\pi\) |
−0.967264 | + | 0.253772i | \(0.918329\pi\) | |||||||
\(444\) | 4.53173 | + | 23.0724i | 0.000484383 | + | 0.00246614i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9838.80 | + | 5680.43i | 1.04458 | + | 0.603086i | ||||
\(447\) | −403.345 | + | 600.517i | −0.0426791 | + | 0.0635424i | ||||
\(448\) | −9149.82 | − | 2451.69i | −0.964930 | − | 0.258552i | ||||
\(449\) | −702.553 | −0.0738431 | −0.0369215 | − | 0.999318i | \(-0.511755\pi\) | ||||
−0.0369215 | + | 0.999318i | \(0.511755\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1841.02 | −0.192218 | ||||||||
\(452\) | 522.845 | + | 140.096i | 0.0544083 | + | 0.0145787i | ||||
\(453\) | −3233.77 | − | 6597.39i | −0.335399 | − | 0.684266i | ||||
\(454\) | 2262.40 | + | 1306.20i | 0.233876 | + | 0.135029i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1883.53 | − | 1643.81i | 0.193430 | − | 0.168813i | ||||
\(457\) | 1175.37 | − | 4386.55i | 0.120310 | − | 0.449002i | −0.879319 | − | 0.476232i | \(-0.842002\pi\) |
0.999629 | + | 0.0272303i | \(0.00866873\pi\) | |||||||
\(458\) | 7384.22 | + | 7384.22i | 0.753367 | + | 0.753367i | ||||
\(459\) | −15349.1 | + | 10096.5i | −1.56086 | + | 1.02672i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7776.73 | + | 4489.90i | −0.785680 | + | 0.453613i | −0.838440 | − | 0.544995i | \(-0.816532\pi\) |
0.0527593 | + | 0.998607i | \(0.483198\pi\) | |||||||
\(462\) | 1121.73 | − | 16505.9i | 0.112960 | − | 1.66217i | ||||
\(463\) | 1770.40 | + | 6607.21i | 0.177705 | + | 0.663204i | 0.996075 | + | 0.0885123i | \(0.0282112\pi\) |
−0.818370 | + | 0.574691i | \(0.805122\pi\) | |||||||
\(464\) | −2709.66 | + | 4693.27i | −0.271106 | + | 0.469569i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6117.14 | − | 10595.2i | −0.608093 | − | 1.05325i | ||||
\(467\) | 1646.02 | − | 1646.02i | 0.163102 | − | 0.163102i | −0.620837 | − | 0.783939i | \(-0.713207\pi\) |
0.783939 | + | 0.620837i | \(0.213207\pi\) | |||||||
\(468\) | −8.92620 | + | 21.2599i | −0.000881653 | + | 0.00209987i | ||||
\(469\) | − | 8756.28i | − | 0.862106i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12109.1 | − | 2378.38i | 1.18462 | − | 0.232675i | ||||
\(472\) | 5524.25 | − | 1480.22i | 0.538716 | − | 0.144349i | ||||
\(473\) | 24275.4 | − | 6504.58i | 2.35980 | − | 0.632306i | ||||
\(474\) | −8034.92 | + | 1578.16i | −0.778599 | + | 0.152927i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 912.895i | 0.0879044i | ||||||||
\(477\) | −1916.76 | − | 2523.00i | −0.183988 | − | 0.242181i | ||||
\(478\) | 7895.37 | − | 7895.37i | 0.755494 | − | 0.755494i | ||||
\(479\) | 7066.68 | + | 12239.8i | 0.674081 | + | 1.16754i | 0.976737 | + | 0.214442i | \(0.0687933\pi\) |
−0.302656 | + | 0.953100i | \(0.597873\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.0394 | − | 26.0491i | 0.00142565 | − | 0.00246930i | ||||
\(482\) | 1284.41 | + | 4793.47i | 0.121376 | + | 0.452980i | ||||
\(483\) | 701.547 | − | 10323.0i | 0.0660901 | − | 0.972494i | ||||
\(484\) | 582.107 | − | 336.080i | 0.0546682 | − | 0.0315627i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −9031.98 | − | 6193.36i | −0.843002 | − | 0.578059i | ||||
\(487\) | 6660.19 | + | 6660.19i | 0.619717 | + | 0.619717i | 0.945459 | − | 0.325742i | \(-0.105614\pi\) |
−0.325742 | + | 0.945459i | \(0.605614\pi\) | |||||||
\(488\) | −3231.94 | + | 12061.8i | −0.299801 | + | 1.11887i | ||||
\(489\) | 5207.33 | − | 4544.59i | 0.481561 | − | 0.420273i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4778.58 | − | 2758.92i | −0.439215 | − | 0.253581i | 0.264050 | − | 0.964509i | \(-0.414942\pi\) |
−0.703264 | + | 0.710928i | \(0.748275\pi\) | |||||||
\(492\) | 26.6522 | + | 54.3747i | 0.00244223 | + | 0.00498252i | ||||
\(493\) | −10271.3 | − | 2752.18i | −0.938325 | − | 0.251424i | ||||
\(494\) | 150.007 | 0.0136622 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −569.213 | −0.0515291 | ||||||||
\(497\) | −306.174 | − | 82.0392i | −0.0276334 | − | 0.00740435i | ||||
\(498\) | −8435.16 | + | 12558.6i | −0.759013 | + | 1.13005i | ||||
\(499\) | 4628.28 | + | 2672.14i | 0.415211 | + | 0.239722i | 0.693026 | − | 0.720913i | \(-0.256277\pi\) |
−0.277816 | + | 0.960634i | \(0.589610\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3768.32 | − | 19185.7i | −0.336040 | − | 1.71088i | ||||
\(502\) | 1710.46 | − | 6383.52i | 0.152075 | − | 0.567551i | ||||
\(503\) | 3380.78 | + | 3380.78i | 0.299685 | + | 0.299685i | 0.840890 | − | 0.541205i | \(-0.182032\pi\) |
−0.541205 | + | 0.840890i | \(0.682032\pi\) | |||||||
\(504\) | 10739.4 | − | 4387.98i | 0.949145 | − | 0.387810i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 14515.2 | − | 8380.37i | 1.27526 | − | 0.736271i | ||||
\(507\) | −10224.3 | + | 5011.52i | −0.895614 | + | 0.438993i | ||||
\(508\) | 83.7212 | + | 312.452i | 0.00731206 | + | 0.0272890i | ||||
\(509\) | 6234.51 | − | 10798.5i | 0.542908 | − | 0.940344i | −0.455828 | − | 0.890068i | \(-0.650657\pi\) |
0.998735 | − | 0.0502756i | \(-0.0160100\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −814.705 | − | 1411.11i | −0.0705292 | − | 0.122160i | ||||
\(512\) | 7575.72 | − | 7575.72i | 0.653911 | − | 0.653911i | ||||
\(513\) | −617.663 | + | 2992.20i | −0.0531588 | + | 0.257522i | ||||
\(514\) | − | 11047.4i | − | 0.948017i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −543.546 | − | 622.811i | −0.0463726 | − | 0.0531351i | ||||
\(517\) | 7936.35 | − | 2126.54i | 0.675127 | − | 0.180900i | ||||
\(518\) | 685.678 | − | 183.727i | 0.0581602 | − | 0.0155840i | ||||
\(519\) | 7341.48 | − | 21457.6i | 0.620916 | − | 1.81481i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16543.1i | 1.39111i | 0.718473 | + | 0.695555i | \(0.244841\pi\) | ||||
−0.718473 | + | 0.695555i | \(0.755159\pi\) | |||||||
\(522\) | −797.112 | − | 6288.26i | −0.0668365 | − | 0.527260i | ||||
\(523\) | 937.744 | − | 937.744i | 0.0784029 | − | 0.0784029i | −0.666818 | − | 0.745221i | \(-0.732344\pi\) |
0.745221 | + | 0.666818i | \(0.232344\pi\) | |||||||
\(524\) | 468.094 | + | 810.762i | 0.0390244 | + | 0.0675922i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7130.27 | + | 12350.0i | −0.591054 | + | 1.02374i | ||||
\(527\) | −289.072 | − | 1078.83i | −0.0238940 | − | 0.0891738i | ||||
\(528\) | 16300.7 | + | 10948.6i | 1.34356 | + | 0.902419i | ||||
\(529\) | −1458.85 | + | 842.270i | −0.119903 | + | 0.0692258i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4281.58 | + | 5524.64i | −0.349915 | + | 0.451505i | ||||
\(532\) | 107.349 | + | 107.349i | 0.00874843 | + | 0.00874843i | ||||
\(533\) | 20.0492 | − | 74.8247i | 0.00162932 | − | 0.00608071i | ||||
\(534\) | 12008.2 | + | 4108.46i | 0.973116 | + | 0.332941i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8613.91 | + | 4973.24i | 0.694150 | + | 0.400768i | ||||
\(537\) | −14814.7 | − | 1006.80i | −1.19051 | − | 0.0809062i | ||||
\(538\) | −18345.9 | − | 4915.78i | −1.47017 | − | 0.393930i | ||||
\(539\) | −1996.53 | −0.159548 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −946.946 | −0.0752540 | −0.0376270 | − | 0.999292i | \(-0.511980\pi\) | ||||
−0.0376270 | + | 0.999292i | \(0.511980\pi\) | |||||||
\(542\) | −4478.34 | − | 1199.97i | −0.354910 | − | 0.0950979i | ||||
\(543\) | 7564.32 | + | 514.066i | 0.597820 | + | 0.0406274i | ||||
\(544\) | −1838.23 | − | 1061.30i | −0.144878 | − | 0.0836451i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 658.633 | + | 225.344i | 0.0516243 | + | 0.0176627i | ||||
\(547\) | 3015.33 | − | 11253.3i | 0.235697 | − | 0.879631i | −0.742137 | − | 0.670248i | \(-0.766188\pi\) |
0.977834 | − | 0.209383i | \(-0.0671456\pi\) | |||||||
\(548\) | −247.198 | − | 247.198i | −0.0192696 | − | 0.0192696i | ||||
\(549\) | −5772.28 | − | 14127.3i | −0.448734 | − | 1.09825i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1531.45 | + | 884.183i | −0.118406 | + | 0.0683620i | ||||
\(552\) | 9756.74 | + | 6553.25i | 0.752309 | + | 0.505298i | ||||
\(553\) | 2743.77 | + | 10239.9i | 0.210989 | + | 0.787422i | ||||
\(554\) | −12717.0 | + | 22026.5i | −0.975259 | + | 1.68920i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −228.950 | − | 396.553i | −0.0174634 | − | 0.0302475i | ||||
\(557\) | 1609.11 | − | 1609.11i | 0.122406 | − | 0.122406i | −0.643250 | − | 0.765656i | \(-0.722414\pi\) |
0.765656 | + | 0.643250i | \(0.222414\pi\) | |||||||
\(558\) | 530.131 | − | 402.747i | 0.0402190 | − | 0.0305549i | ||||
\(559\) | 1057.46i | 0.0800107i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12472.7 | + | 36455.0i | −0.938676 | + | 2.74355i | ||||
\(562\) | −18720.8 | + | 5016.21i | −1.40514 | + | 0.376506i | ||||
\(563\) | −17547.6 | + | 4701.86i | −1.31357 | + | 0.351971i | −0.846567 | − | 0.532282i | \(-0.821335\pi\) |
−0.467008 | + | 0.884253i | \(0.654668\pi\) | |||||||
\(564\) | −177.701 | − | 203.615i | −0.0132670 | − | 0.0152017i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 3303.33i | − | 0.245317i | ||||||
\(567\) | −7206.92 | + | 12210.0i | −0.533796 | + | 0.904356i | ||||
\(568\) | 254.601 | − | 254.601i | 0.0188078 | − | 0.0188078i | ||||
\(569\) | −149.738 | − | 259.354i | −0.0110322 | − | 0.0191084i | 0.860457 | − | 0.509524i | \(-0.170178\pi\) |
−0.871489 | + | 0.490415i | \(0.836845\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10802.7 | − | 18710.8i | 0.791732 | − | 1.37132i | −0.133162 | − | 0.991094i | \(-0.542513\pi\) |
0.924894 | − | 0.380226i | \(-0.124154\pi\) | |||||||
\(572\) | 12.5155 | + | 46.7086i | 0.000914861 | + | 0.00341431i | ||||
\(573\) | −3287.10 | + | 1611.20i | −0.239652 | + | 0.117468i | ||||
\(574\) | 1583.24 | − | 914.085i | 0.115128 | − | 0.0664689i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1779.16 | + | 13029.5i | −0.128701 | + | 0.942524i | ||||
\(577\) | 6073.88 | + | 6073.88i | 0.438231 | + | 0.438231i | 0.891416 | − | 0.453186i | \(-0.149712\pi\) |
−0.453186 | + | 0.891416i | \(0.649712\pi\) | |||||||
\(578\) | 9155.55 | − | 34169.0i | 0.658859 | − | 2.45890i | ||||
\(579\) | 1535.46 | + | 7817.50i | 0.110210 | + | 0.561113i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16962.0 | + | 9793.00i | 1.21119 | + | 0.699281i | ||||
\(582\) | −3410.20 | + | 5077.24i | −0.242882 | + | 0.361613i | ||||
\(583\) | −6418.53 | − | 1719.84i | −0.455966 | − | 0.122176i | ||||
\(584\) | 1850.89 | 0.131148 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18187.5 | −1.28211 | ||||||||
\(587\) | 10872.4 | + | 2913.25i | 0.764484 | + | 0.204843i | 0.619933 | − | 0.784654i | \(-0.287160\pi\) |
0.144551 | + | 0.989497i | \(0.453826\pi\) | |||||||
\(588\) | 28.9035 | + | 58.9676i | 0.00202714 | + | 0.00413569i | ||||
\(589\) | −160.854 | − | 92.8691i | −0.0112528 | − | 0.00649678i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5478.24 | + | 4781.02i | −0.381294 | + | 0.332767i | ||||
\(592\) | −218.070 | + | 813.847i | −0.0151395 | + | 0.0565015i | ||||
\(593\) | 19651.0 | + | 19651.0i | 1.36082 | + | 1.36082i | 0.872870 | + | 0.487953i | \(0.162256\pi\) |
0.487953 | + | 0.872870i | \(0.337744\pi\) | |||||||
\(594\) | −22928.2 | + | 1336.72i | −1.58377 | + | 0.0923341i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 43.2154 | − | 24.9504i | 0.00297009 | − | 0.00171478i | ||||
\(597\) | 717.192 | − | 10553.3i | 0.0491670 | − | 0.723478i | ||||
\(598\) | 182.529 | + | 681.209i | 0.0124819 | + | 0.0465831i | ||||
\(599\) | −1419.69 | + | 2458.97i | −0.0968396 | + | 0.167731i | −0.910375 | − | 0.413784i | \(-0.864207\pi\) |
0.813535 | + | 0.581516i | \(0.197540\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −254.777 | − | 441.286i | −0.0172921 | − | 0.0299508i | 0.857250 | − | 0.514901i | \(-0.172171\pi\) |
−0.874542 | + | 0.484950i | \(0.838838\pi\) | |||||||
\(602\) | −17646.8 | + | 17646.8i | −1.19473 | + | 1.19473i | ||||
\(603\) | −12059.4 | + | 1528.68i | −0.814425 | + | 0.103238i | ||||
\(604\) | 506.824i | 0.0341430i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 6776.85 | − | 1331.06i | 0.454275 | − | 0.0892257i | ||||
\(607\) | −3306.40 | + | 885.947i | −0.221092 | + | 0.0592413i | −0.367664 | − | 0.929959i | \(-0.619842\pi\) |
0.146573 | + | 0.989200i | \(0.453176\pi\) | |||||||
\(608\) | −340.961 | + | 91.3602i | −0.0227431 | + | 0.00609399i | ||||
\(609\) | −8052.35 | + | 1581.59i | −0.535793 | + | 0.105237i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 345.717i | 0.0228907i | ||||||||
\(612\) | 1257.27 | − | 159.374i | 0.0830426 | − | 0.0105266i | ||||
\(613\) | 6435.77 | − | 6435.77i | 0.424043 | − | 0.424043i | −0.462550 | − | 0.886593i | \(-0.653066\pi\) |
0.886593 | + | 0.462550i | \(0.153066\pi\) | |||||||
\(614\) | −10218.9 | − | 17699.6i | −0.671660 | − | 1.16335i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12164.9 | − | 21070.2i | 0.795679 | − | 1.37816i | ||||
\(617\) | −556.352 | − | 2076.34i | −0.0363013 | − | 0.135478i | 0.945397 | − | 0.325921i | \(-0.105674\pi\) |
−0.981698 | + | 0.190443i | \(0.939008\pi\) | |||||||
\(618\) | −1417.17 | + | 20853.3i | −0.0922444 | + | 1.35735i | ||||
\(619\) | 16359.4 | − | 9445.11i | 1.06226 | − | 0.613297i | 0.136205 | − | 0.990681i | \(-0.456509\pi\) |
0.926057 | + | 0.377383i | \(0.123176\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14339.7 | + | 836.011i | −0.926623 | + | 0.0540225i | ||||
\(622\) | −6199.92 | − | 6199.92i | −0.399669 | − | 0.399669i | ||||
\(623\) | 4252.66 | − | 15871.2i | 0.273482 | − | 1.02065i | ||||
\(624\) | −622.505 | + | 543.279i | −0.0399361 | + | 0.0348535i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 10791.1 | + | 6230.22i | 0.688974 | + | 0.397779i | ||||
\(627\) | 2820.13 | + | 5753.50i | 0.179625 | + | 0.366463i | ||||
\(628\) | −822.250 | − | 220.321i | −0.0522474 | − | 0.0139996i | ||||
\(629\) | −1653.23 | −0.104799 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 865.068 | 0.0545766 | 0.0272883 | − | 0.999628i | \(-0.491313\pi\) | ||||
0.0272883 | + | 0.999628i | \(0.491313\pi\) | |||||||
\(632\) | −11631.8 | − | 3116.72i | −0.732099 | − | 0.196165i | ||||
\(633\) | 3988.77 | − | 5938.64i | 0.250457 | − | 0.372891i | ||||
\(634\) | 12079.6 | + | 6974.16i | 0.756691 | + | 0.436876i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 42.1247 | + | 214.470i | 0.00262634 | + | 0.0133715i | ||||
\(637\) | 21.7427 | − | 81.1450i | 0.00135240 | − | 0.00504723i | ||||
\(638\) | −9399.66 | − | 9399.66i | −0.583286 | − | 0.583286i | ||||
\(639\) | −59.5349 | + | 435.996i | −0.00368570 | + | 0.0269917i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6830.18 | − | 3943.41i | 0.420867 | − | 0.242988i | −0.274581 | − | 0.961564i | \(-0.588539\pi\) |
0.695448 | + | 0.718576i | \(0.255206\pi\) | |||||||
\(642\) | 6090.95 | − | 2985.53i | 0.374440 | − | 0.183535i | ||||
\(643\) | −1839.94 | − | 6866.75i | −0.112846 | − | 0.421148i | 0.886270 | − | 0.463168i | \(-0.153287\pi\) |
−0.999117 | + | 0.0420200i | \(0.986621\pi\) | |||||||
\(644\) | −356.868 | + | 618.114i | −0.0218363 | + | 0.0378216i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4122.43 | − | 7140.26i | −0.251076 | − | 0.434876i | ||||
\(647\) | 1933.74 | − | 1933.74i | 0.117501 | − | 0.117501i | −0.645911 | − | 0.763412i | \(-0.723522\pi\) |
0.763412 | + | 0.645911i | \(0.223522\pi\) | |||||||
\(648\) | −7918.16 | − | 14024.5i | −0.480023 | − | 0.850210i | ||||
\(649\) | 14658.3i | 0.886578i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −566.749 | − | 649.398i | −0.0341208 | − | 0.0390966i | ||||
\(652\) | −460.521 | + | 123.396i | −0.0276616 | + | 0.00741191i | ||||
\(653\) | 6232.28 | − | 1669.93i | 0.373488 | − | 0.100076i | −0.0671918 | − | 0.997740i | \(-0.521404\pi\) |
0.440680 | + | 0.897664i | \(0.354737\pi\) | |||||||
\(654\) | −5476.96 | + | 16008.0i | −0.327471 | + | 0.957130i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2169.90i | 0.129147i | ||||||||
\(657\) | −1801.20 | + | 1368.39i | −0.106958 | + | 0.0812572i | ||||
\(658\) | −5769.26 | + | 5769.26i | −0.341807 | + | 0.341807i | ||||
\(659\) | −3849.42 | − | 6667.40i | −0.227545 | − | 0.394120i | 0.729535 | − | 0.683944i | \(-0.239737\pi\) |
−0.957080 | + | 0.289824i | \(0.906403\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1130.78 | + | 1958.57i | −0.0665392 | + | 0.115249i | −0.897376 | − | 0.441267i | \(-0.854529\pi\) |
0.830837 | + | 0.556517i | \(0.187862\pi\) | |||||||
\(662\) | 8428.67 | + | 31456.2i | 0.494848 | + | 1.84680i | ||||
\(663\) | −1345.81 | − | 903.934i | −0.0788343 | − | 0.0529501i | ||||
\(664\) | −19267.5 | + | 11124.1i | −1.12609 | + | 0.650150i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −372.741 | − | 912.263i | −0.0216868 | − | 0.0530773i | ||||
\(667\) | −5878.71 | − | 5878.71i | −0.341266 | − | 0.341266i | ||||
\(668\) | −349.078 | + | 1302.78i | −0.0202189 | + | 0.0754581i | ||||
\(669\) | −19319.4 | − | 6609.90i | −1.11649 | − | 0.381993i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −27717.4 | − | 16002.6i | −1.59466 | − | 0.920678i | ||||
\(672\) | −1634.29 | − | 111.066i | −0.0938159 | − | 0.00637566i | ||||
\(673\) | 8335.28 | + | 2233.43i | 0.477417 | + | 0.127923i | 0.489499 | − | 0.872004i | \(-0.337180\pi\) |
−0.0120828 | + | 0.999927i | \(0.503846\pi\) | |||||||
\(674\) | −6836.92 | −0.390724 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 785.449 | 0.0446887 | ||||||||
\(677\) | 12923.2 | + | 3462.76i | 0.733646 | + | 0.196580i | 0.606252 | − | 0.795272i | \(-0.292672\pi\) |
0.127394 | + | 0.991852i | \(0.459339\pi\) | |||||||
\(678\) | −22634.0 | − | 1538.19i | −1.28209 | − | 0.0871297i | ||||
\(679\) | 6857.45 | + | 3959.15i | 0.387577 | + | 0.223768i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4442.43 | − | 1519.93i | −0.249977 | − | 0.0855269i | ||||
\(682\) | 361.371 | − | 1348.65i | 0.0202897 | − | 0.0757223i | ||||
\(683\) | −14959.7 | − | 14959.7i | −0.838091 | − | 0.838091i | 0.150516 | − | 0.988608i | \(-0.451906\pi\) |
−0.988608 | + | 0.150516i | \(0.951906\pi\) | |||||||
\(684\) | 129.103 | − | 166.586i | 0.00721695 | − | 0.00931222i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −14985.6 | + | 8651.91i | −0.834039 | + | 0.481533i | ||||
\(687\) | −15580.7 | − | 10465.0i | −0.865268 | − | 0.581169i | ||||
\(688\) | −7666.54 | − | 28611.9i | −0.424832 | − | 1.58549i | ||||
\(689\) | 139.799 | − | 242.139i | 0.00772994 | − | 0.0133886i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14446.2 | + | 25021.6i | 0.795311 | + | 1.37752i | 0.922642 | + | 0.385658i | \(0.126026\pi\) |
−0.127331 | + | 0.991860i | \(0.540641\pi\) | |||||||
\(692\) | −1106.20 | + | 1106.20i | −0.0607680 | + | 0.0607680i | ||||
\(693\) | 3739.26 | + | 29498.3i | 0.204968 | + | 1.61695i | ||||
\(694\) | 2977.62i | 0.162866i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3017.56 | − | 8819.71i | 0.164340 | − | 0.480331i | ||||
\(697\) | −4112.61 | + | 1101.97i | −0.223495 | + | 0.0598854i | ||||
\(698\) | −15250.6 | + | 4086.39i | −0.826999 | + | 0.221594i | ||||
\(699\) | 14458.3 | + | 16566.7i | 0.782351 | + | 0.896440i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4479.63i | 0.241360i | 0.992691 | + | 0.120680i | \(0.0385075\pi\) | ||||
−0.992691 | + | 0.120680i | \(0.961493\pi\) | |||||||
\(702\) | 195.366 | − | 946.432i | 0.0105037 | − | 0.0508843i | ||||
\(703\) | −194.406 | + | 194.406i | −0.0104298 | + | 0.0104298i | ||||
\(704\) | 13789.3 | + | 23883.8i | 0.738217 | + | 1.27863i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 962.411 | − | 1666.94i | 0.0513043 | − | 0.0888616i | ||||
\(707\) | −2314.17 | − | 8636.58i | −0.123102 | − | 0.459423i | ||||
\(708\) | 432.935 | − | 212.207i | 0.0229812 | − | 0.0112644i | ||||
\(709\) | 25712.6 | − | 14845.2i | 1.36200 | − | 0.786351i | 0.372110 | − | 0.928188i | \(-0.378634\pi\) |
0.989890 | + | 0.141837i | \(0.0453009\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13623.7 | − | 5566.50i | 0.718606 | − | 0.293615i | ||||
\(712\) | 13197.7 | + | 13197.7i | 0.694672 | + | 0.694672i | ||||
\(713\) | 226.007 | − | 843.471i | 0.0118710 | − | 0.0443033i | ||||
\(714\) | −7374.03 | − | 37543.5i | −0.386507 | − | 1.96783i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 887.064 | + | 512.147i | 0.0463005 | + | 0.0267316i | ||||
\(717\) | −11189.4 | + | 16659.2i | −0.582809 | + | 0.867711i | ||||
\(718\) | 18721.1 | + | 5016.31i | 0.973073 | + | 0.260734i | ||||
\(719\) | 17740.3 | 0.920171 | 0.460085 | − | 0.887875i | \(-0.347819\pi\) | ||||
0.460085 | + | 0.887875i | \(0.347819\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27059.8 | 1.39773 | ||||||||
\(722\) | 17829.9 | + | 4777.52i | 0.919060 | + | 0.246261i | ||||
\(723\) | −3925.61 | − | 8008.85i | −0.201929 | − | 0.411967i | ||||
\(724\) | −452.930 | − | 261.499i | −0.0232500 | − | 0.0134234i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −21224.8 | + | 18523.6i | −1.08502 | + | 0.946934i | ||||
\(727\) | −7841.69 | + | 29265.6i | −0.400044 | + | 1.49299i | 0.412972 | + | 0.910744i | \(0.364491\pi\) |
−0.813016 | + | 0.582242i | \(0.802176\pi\) | |||||||
\(728\) | 723.881 | + | 723.881i | 0.0368527 | + | 0.0368527i | ||||
\(729\) | 18074.1 | + | 7793.98i | 0.918261 | + | 0.395975i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 50334.8 | − | 29060.8i | 2.54679 | − | 1.47039i | ||||
\(732\) | −71.3779 | + | 1050.30i | −0.00360410 | + | 0.0530333i | ||||
\(733\) | −6548.68 | − | 24440.0i | −0.329988 | − | 1.23153i | −0.909202 | − | 0.416355i | \(-0.863307\pi\) |
0.579214 | − | 0.815175i | \(-0.303359\pi\) | |||||||
\(734\) | −4720.53 | + | 8176.20i | −0.237381 | + | 0.411157i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −829.766 | − | 1437.20i | −0.0415565 | − | 0.0719780i | ||||
\(737\) | −18026.4 | + | 18026.4i | −0.900965 | + | 0.900965i | ||||
\(738\) | −1535.31 | − | 2020.91i | −0.0765794 | − | 0.100800i | ||||
\(739\) | − | 27310.7i | − | 1.35946i | −0.733463 | − | 0.679730i | \(-0.762097\pi\) | ||
0.733463 | − | 0.679730i | \(-0.237903\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −264.552 | + | 51.9615i | −0.0131155 | + | 0.00257605i | ||||
\(742\) | 6373.73 | − | 1707.84i | 0.315346 | − | 0.0844968i | ||||
\(743\) | 9929.86 | − | 2660.70i | 0.490298 | − | 0.131375i | −0.00519568 | − | 0.999987i | \(-0.501654\pi\) |
0.495494 | + | 0.868612i | \(0.334987\pi\) | |||||||
\(744\) | 960.731 | − | 188.700i | 0.0473416 | − | 0.00929851i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 12220.0i | − | 0.599739i | ||||||
\(747\) | 10526.0 | − | 25070.2i | 0.515564 | − | 1.22794i | ||||
\(748\) | 1879.36 | − | 1879.36i | 0.0918666 | − | 0.0918666i | ||||
\(749\) | −4390.98 | − | 7605.39i | −0.214209 | − | 0.371021i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12313.5 | + | 21327.6i | −0.598302 | + | 1.03629i | 0.394770 | + | 0.918780i | \(0.370824\pi\) |
−0.993072 | + | 0.117509i | \(0.962509\pi\) | |||||||
\(752\) | −2506.42 | − | 9354.09i | −0.121542 | − | 0.453602i | ||||
\(753\) | −805.350 | + | 11850.5i | −0.0389755 | + | 0.573513i | ||||
\(754\) | 484.396 | − | 279.666i | 0.0233961 | − | 0.0135078i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 817.101 | − | 537.483i | 0.0393091 | − | 0.0258572i | ||||
\(757\) | −3491.44 | − | 3491.44i | −0.167633 | − | 0.167633i | 0.618305 | − | 0.785938i | \(-0.287820\pi\) |
−0.785938 | + | 0.618305i | \(0.787820\pi\) | |||||||
\(758\) | 1500.74 | − | 5600.84i | 0.0719121 | − | 0.268380i | ||||
\(759\) | −22696.1 | + | 19807.6i | −1.08540 | + | 0.947260i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1927.71 | + | 1112.96i | 0.0918256 | + | 0.0530155i | 0.545210 | − | 0.838300i | \(-0.316450\pi\) |
−0.453384 | + | 0.891315i | \(0.649783\pi\) | |||||||
\(762\) | −5966.96 | − | 12173.5i | −0.283675 | − | 0.578741i | ||||
\(763\) | 21157.8 | + | 5669.21i | 1.00388 | + | 0.268990i | ||||
\(764\) | 252.521 | 0.0119580 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3391.65 | −0.159981 | ||||||||
\(767\) | −595.759 | − | 159.633i | −0.0280464 | − | 0.00751502i | ||||
\(768\) | 1591.93 | − | 2370.13i | 0.0747965 | − | 0.111360i | ||||
\(769\) | −28584.4 | − | 16503.2i | −1.34042 | − | 0.773890i | −0.353548 | − | 0.935416i | \(-0.615025\pi\) |
−0.986868 | + | 0.161526i | \(0.948358\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3826.76 | + | 19483.2i | 0.178752 | + | 0.910079i | ||||
\(772\) | 142.237 | − | 530.837i | 0.00663113 | − | 0.0247477i | ||||
\(773\) | −9771.76 | − | 9771.76i | −0.454677 | − | 0.454677i | 0.442226 | − | 0.896904i | \(-0.354189\pi\) |
−0.896904 | + | 0.442226i | \(0.854189\pi\) | |||||||
\(774\) | 27384.5 | + | 21223.0i | 1.27173 | + | 0.985586i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7789.55 | + | 4497.30i | −0.360346 | + | 0.208046i | ||||
\(777\) | −1145.62 | + | 561.535i | −0.0528943 | + | 0.0259266i | ||||
\(778\) | 8790.84 | + | 32807.8i | 0.405099 | + | 1.51185i | ||||
\(779\) | −354.026 | + | 613.192i | −0.0162828 | + | 0.0282027i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 461.423 | + | 799.208i | 0.0211409 | + | 0.0366171i | ||||
\(782\) | 27409.0 | − | 27409.0i | 1.25338 | − | 1.25338i | ||||
\(783\) | 3584.00 | + | 10813.8i | 0.163578 | + | 0.493557i | ||||
\(784\) | 2353.18i | 0.107197i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −25799.7 | − | 29562.1i | −1.17080 | − | 1.34153i | ||||
\(787\) | −2450.58 | + | 656.630i | −0.110996 | + | 0.0297412i | −0.313889 | − | 0.949460i | \(-0.601632\pi\) |
0.202894 | + | 0.979201i | \(0.434965\pi\) | |||||||
\(788\) | 484.479 | − | 129.816i | 0.0219021 | − | 0.00586865i | ||||
\(789\) | 8296.97 | − | 24250.3i | 0.374373 | − | 1.09421i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29370.6i | 1.32022i | ||||||||
\(792\) | −31142.4 | − | 13075.5i | −1.39722 | − | 0.586637i | ||||
\(793\) | 952.246 | − | 952.246i | 0.0426422 | − | 0.0426422i | ||||
\(794\) | −21301.6 | − | 36895.4i | −0.952097 | − | 1.64908i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −364.827 | + | 631.899i | −0.0162449 | + | 0.0281370i | ||||
\(797\) | −7132.77 | − | 26619.9i | −0.317009 | − | 1.18309i | −0.922105 | − | 0.386940i | \(-0.873532\pi\) |
0.605096 | − | 0.796152i | \(-0.293135\pi\) | |||||||
\(798\) | −5281.93 | − | 3547.68i | −0.234308 | − | 0.157376i | ||||
\(799\) | 16456.0 | − | 9500.85i | 0.728623 | − | 0.420671i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22600.7 | − | 3086.11i | −0.996950 | − | 0.136133i | ||||
\(802\) | −11396.6 | − | 11396.6i | −0.501780 | − | 0.501780i | ||||
\(803\) | −1227.81 | + | 4582.25i | −0.0539582 | + | 0.201375i | ||||
\(804\) | 793.378 | + | 271.445i | 0.0348014 | + | 0.0119069i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 50.8780 | + | 29.3744i | 0.00222345 | + | 0.00128371i | ||||
\(807\) | 34057.7 | + | 2314.54i | 1.48561 | + | 0.100961i | ||||
\(808\) | 9810.51 | + | 2628.72i | 0.427144 | + | 0.114453i | ||||
\(809\) | −28707.4 | −1.24759 | −0.623794 | − | 0.781589i | \(-0.714409\pi\) | ||||
−0.623794 | + | 0.781589i | \(0.714409\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38280.7 | −1.65748 | −0.828741 | − | 0.559632i | \(-0.810943\pi\) | ||||
−0.828741 | + | 0.559632i | \(0.810943\pi\) | |||||||
\(812\) | 546.784 | + | 146.510i | 0.0236310 | + | 0.00633190i | ||||
\(813\) | 8313.66 | + | 564.991i | 0.358638 | + | 0.0243728i | ||||
\(814\) | −1789.83 | − | 1033.36i | −0.0770681 | − | 0.0444953i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 42967.3 | + | 14700.8i | 1.84333 | + | 0.630674i | ||||
\(817\) | 2501.65 | − | 9336.28i | 0.107126 | − | 0.399798i | ||||
\(818\) | 20905.7 | + | 20905.7i | 0.893582 | + | 0.893582i | ||||
\(819\) | −1239.62 | − | 169.270i | −0.0528888 | − | 0.00722192i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16524.5 | + | 9540.43i | −0.702447 | + | 0.405558i | −0.808258 | − | 0.588828i | \(-0.799589\pi\) |
0.105811 | + | 0.994386i | \(0.466256\pi\) | |||||||
\(822\) | 12162.9 | + | 8169.40i | 0.516096 | + | 0.346643i | ||||
\(823\) | 8758.95 | + | 32688.8i | 0.370982 | + | 1.38452i | 0.859128 | + | 0.511760i | \(0.171006\pi\) |
−0.488147 | + | 0.872762i | \(0.662327\pi\) | |||||||
\(824\) | −15369.0 | + | 26619.8i | −0.649762 | + | 1.12542i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7278.00 | − | 12605.9i | −0.306579 | − | 0.531010i | ||||
\(827\) | 20140.3 | − | 20140.3i | 0.846854 | − | 0.846854i | −0.142885 | − | 0.989739i | \(-0.545638\pi\) |
0.989739 | + | 0.142885i | \(0.0456380\pi\) | |||||||
\(828\) | 913.589 | + | 383.580i | 0.0383447 | + | 0.0160994i | ||||
\(829\) | 28979.3i | 1.21410i | 0.794662 | + | 0.607052i | \(0.207648\pi\) | ||||
−0.794662 | + | 0.607052i | \(0.792352\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14797.8 | − | 43251.0i | 0.617727 | − | 1.80549i | ||||
\(832\) | −1120.88 | + | 300.340i | −0.0467063 | + | 0.0125149i | ||||
\(833\) | −4459.99 | + | 1195.05i | −0.185510 | + | 0.0497072i | ||||
\(834\) | 12618.9 | + | 14459.2i | 0.523931 | + | 0.600335i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 441.995i | − | 0.0182855i | ||||||
\(837\) | −795.428 | + | 893.918i | −0.0328483 | + | 0.0369156i | ||||
\(838\) | −17937.4 | + | 17937.4i | −0.739423 | + | 0.739423i | ||||
\(839\) | 1123.38 | + | 1945.74i | 0.0462255 | + | 0.0800650i | 0.888212 | − | 0.459433i | \(-0.151947\pi\) |
−0.841987 | + | 0.539498i | \(0.818614\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8897.63 | − | 15411.2i | 0.364822 | − | 0.631890i | ||||
\(842\) | −8987.36 | − | 33541.3i | −0.367844 | − | 1.37281i | ||||
\(843\) | 31278.3 | − | 15331.3i | 1.27792 | − | 0.626381i | ||||
\(844\) | −427.367 | + | 246.740i | −0.0174296 | + | 0.0100630i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8952.82 | + | 6938.42i | 0.363835 | + | 0.281971i | ||||
\(847\) | 25789.4 | + | 25789.4i | 1.04620 | + | 1.04620i | ||||
\(848\) | −2027.07 | + | 7565.12i | −0.0820871 | + | 0.306353i | ||||
\(849\) | 1144.25 | + | 5825.74i | 0.0462552 | + | 0.235499i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1119.39 | − | 646.280i | −0.0450907 | − | 0.0260331i | ||||
\(852\) | 16.9247 | − | 25.1982i | 0.000680553 | − | 0.00101324i | ||||
\(853\) | −2144.34 | − | 574.575i | −0.0860738 | − | 0.0230634i | 0.215525 | − | 0.976498i | \(-0.430854\pi\) |
−0.301599 | + | 0.953435i | \(0.597520\pi\) | |||||||
\(854\) | 31781.9 | 1.27348 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9975.64 | 0.398318 | ||||||||
\(857\) | −5332.98 | − | 1428.97i | −0.212568 | − | 0.0569576i | 0.150963 | − | 0.988539i | \(-0.451762\pi\) |
−0.363532 | + | 0.931582i | \(0.618429\pi\) | |||||||
\(858\) | −892.005 | − | 1819.83i | −0.0354925 | − | 0.0724101i | ||||
\(859\) | 1162.53 | + | 671.184i | 0.0461756 | + | 0.0266595i | 0.522910 | − | 0.852388i | \(-0.324846\pi\) |
−0.476734 | + | 0.879047i | \(0.658180\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2475.57 | + | 2160.50i | −0.0979874 | + | 0.0855166i | ||||
\(862\) | 3067.45 | − | 11447.9i | 0.121204 | − | 0.452339i | ||||
\(863\) | 18896.7 | + | 18896.7i | 0.745365 | + | 0.745365i | 0.973605 | − | 0.228240i | \(-0.0732971\pi\) |
−0.228240 | + | 0.973605i | \(0.573297\pi\) | |||||||
\(864\) | 132.353 | + | 2270.19i | 0.00521151 | + | 0.0893907i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −15311.8 | + | 8840.29i | −0.600828 | + | 0.346888i | ||||
\(867\) | −4310.78 | + | 63431.8i | −0.168860 | + | 2.48473i | ||||
\(868\) | 15.3885 | + | 57.4308i | 0.000601753 | + | 0.00224577i | ||||
\(869\) | 15432.1 | − | 26729.2i | 0.602416 | − | 1.04341i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −536.336 | − | 928.962i | −0.0208646 | − | 0.0361385i | ||||
\(872\) | −17593.9 | + | 17593.9i | −0.683260 | + | 0.683260i | ||||
\(873\) | 4255.49 | − | 10135.5i | 0.164979 | − | 0.392937i | ||||
\(874\) | − | 6446.15i | − | 0.249479i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 153.112 | − | 30.0732i | 0.00590545 | − | 0.00115991i | ||||
\(877\) | 47507.6 | − | 12729.6i | 1.82921 | − | 0.490136i | 0.831365 | − | 0.555726i | \(-0.187560\pi\) |
0.997847 | + | 0.0655906i | \(0.0208931\pi\) | |||||||
\(878\) | −33760.5 | + | 9046.10i | −1.29768 | + | 0.347712i | ||||
\(879\) | 32075.4 | − | 6300.04i | 1.23080 | − | 0.241746i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 29831.9i | − | 1.14082i | −0.821360 | − | 0.570410i | \(-0.806784\pi\) | ||
0.821360 | − | 0.570410i | \(-0.193216\pi\) | |||||||
\(882\) | −1665.00 | − | 2191.61i | −0.0635639 | − | 0.0836683i | ||||
\(883\) | −12536.7 | + | 12536.7i | −0.477796 | + | 0.477796i | −0.904426 | − | 0.426630i | \(-0.859701\pi\) |
0.426630 | + | 0.904426i | \(0.359701\pi\) | |||||||
\(884\) | 55.9163 | + | 96.8498i | 0.00212745 | + | 0.00368486i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13356.3 | + | 23133.8i | −0.506449 | + | 0.877196i | ||||
\(887\) | −828.995 | − | 3093.85i | −0.0313810 | − | 0.117115i | 0.948459 | − | 0.316901i | \(-0.102642\pi\) |
−0.979840 | + | 0.199785i | \(0.935976\pi\) | |||||||
\(888\) | 98.2639 | − | 1445.92i | 0.00371343 | − | 0.0546419i | ||||
\(889\) | −15200.3 | + | 8775.92i | −0.573457 | + | 0.331085i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 39973.2 | − | 10299.7i | 1.50298 | − | 0.387263i | ||||
\(892\) | 995.968 | + | 995.968i | 0.0373851 | + | 0.0373851i | ||||
\(893\) | 817.863 | − | 3052.31i | 0.0306481 | − | 0.114380i | ||||
\(894\) | −1575.72 | + | 1375.18i | −0.0589487 | + | 0.0514463i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −25901.2 | − | 14954.1i | −0.965735 | − | 0.557568i | ||||
\(897\) | −557.875 | − | 1138.15i | −0.0207658 | − | 0.0423654i | ||||
\(898\) | −1961.94 | − | 525.700i | −0.0729073 | − | 0.0195355i | ||||
\(899\) | −692.565 | −0.0256934 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15367.6 | −0.568224 | ||||||||
\(902\) | −5141.20 | − | 1377.58i | −0.189782 | − | 0.0508519i | ||||
\(903\) | 25009.1 | − | 37234.6i | 0.921652 | − | 1.37219i | ||||
\(904\) | −28893.0 | − | 16681.4i | −1.06302 | − | 0.613734i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4093.94 | − | 20843.5i | −0.150124 | − | 0.764326i | ||||
\(907\) | −4492.30 | + | 16765.5i | −0.164459 | + | 0.613769i | 0.833650 | + | 0.552294i | \(0.186247\pi\) |
−0.998109 | + | 0.0614756i | \(0.980419\pi\) | |||||||
\(908\) | 229.020 | + | 229.020i | 0.00837037 | + | 0.00837037i | ||||
\(909\) | −11490.6 | + | 4694.92i | −0.419272 | + | 0.171310i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3395.10 | + | 1960.16i | −0.123474 | + | 0.0712877i | −0.560465 | − | 0.828178i | \(-0.689378\pi\) |
0.436991 | + | 0.899466i | \(0.356044\pi\) | |||||||
\(912\) | 6781.29 | − | 3323.91i | 0.246218 | − | 0.120686i | ||||
\(913\) | −14758.6 | − | 55080.0i | −0.534983 | − | 1.99658i | ||||
\(914\) | 6564.65 | − | 11370.3i | 0.237570 | − | 0.411484i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 647.349 | + | 1121.24i | 0.0233505 | + | 0.0404442i | ||||
\(917\) | −35919.6 | + | 35919.6i | −1.29353 | + | 1.29353i | ||||
\(918\) | −50418.7 | + | 16710.1i | −1.81271 | + | 0.600780i | ||||
\(919\) | 28637.0i | 1.02791i | 0.857818 | + | 0.513954i | \(0.171820\pi\) | ||||
−0.857818 | + | 0.513954i | \(0.828180\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24153.0 | + | 27675.2i | 0.864135 | + | 0.990151i | ||||
\(922\) | −25076.8 | + | 6719.32i | −0.895729 | + | 0.240010i | ||||
\(923\) | −37.5073 | + | 10.0501i | −0.00133756 | + | 0.000358398i | ||||
\(924\) | 663.975 | − | 1940.66i | 0.0236398 | − | 0.0690942i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 19775.9i | 0.701812i | ||||||||
\(927\) | −4724.12 | − | 37267.7i | −0.167379 | − | 1.32042i | ||||
\(928\) | −930.689 | + | 930.689i | −0.0329217 | + | 0.0329217i | ||||
\(929\) | 4966.44 | + | 8602.13i | 0.175397 | + | 0.303796i | 0.940299 | − | 0.340351i | \(-0.110546\pi\) |
−0.764902 | + | 0.644147i | \(0.777213\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −383.930 | + | 664.987i | −0.0135154 | + | 0.0234093i | ||||
\(932\) | −392.576 | − | 1465.11i | −0.0137975 | − | 0.0514929i | ||||
\(933\) | 13081.8 | + | 8786.55i | 0.459034 | + | 0.308316i | ||||
\(934\) | 5828.32 | − | 3364.98i | 0.204185 | − | 0.117886i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 870.576 | − | 1123.33i | 0.0304014 | − | 0.0392277i | ||||
\(937\) | −13440.3 | − | 13440.3i | −0.468597 | − | 0.468597i | 0.432863 | − | 0.901460i | \(-0.357503\pi\) |
−0.901460 | + | 0.432863i | \(0.857503\pi\) | |||||||
\(938\) | 6552.07 | − | 24452.7i | 0.228073 | − | 0.851181i | ||||
\(939\) | −21189.2 | − | 7249.65i | −0.736404 | − | 0.251952i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33110.5 | − | 19116.4i | −1.14705 | − | 0.662249i | −0.198882 | − | 0.980023i | \(-0.563731\pi\) |
−0.948166 | + | 0.317775i | \(0.897064\pi\) | |||||||
\(942\) | 35595.3 | + | 2419.03i | 1.23116 | + | 0.0836691i | ||||
\(943\) | −3215.40 | − | 861.563i | −0.111037 | − | 0.0297522i | ||||
\(944\) | 17276.8 | 0.595671 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 72658.3 | 2.49717 | ||||||||
\(947\) | 53216.4 | + | 14259.3i | 1.82608 | + | 0.489297i | 0.997506 | − | 0.0705807i | \(-0.0224852\pi\) |
0.828575 | + | 0.559878i | \(0.189152\pi\) | |||||||
\(948\) | −1012.86 | − | 68.8333i | −0.0347006 | − | 0.00235823i | ||||
\(949\) | −172.865 | − | 99.8039i | −0.00591301 | − | 0.00341388i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23719.4 | − | 8115.31i | −0.808784 | − | 0.276716i | ||||
\(952\) | 14563.0 | − | 54349.8i | 0.495787 | − | 1.85030i | ||||
\(953\) | 14081.7 | + | 14081.7i | 0.478647 | + | 0.478647i | 0.904699 | − | 0.426052i | \(-0.140096\pi\) |
−0.426052 | + | 0.904699i | \(0.640096\pi\) | |||||||
\(954\) | −3464.82 | − | 8479.96i | −0.117587 | − | 0.287787i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1198.86 | − | 692.160i | 0.0405584 | − | 0.0234164i | ||||
\(957\) | 19833.2 | + | 13321.2i | 0.669924 | + | 0.449963i | ||||
\(958\) | 10575.6 | + | 39468.6i | 0.356661 | + | 1.33108i | ||||
\(959\) | 9484.46 | − | 16427.6i | 0.319363 | − | 0.553153i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14859.1 | + | 25736.8i | 0.498779 | + | 0.863911i | ||||
\(962\) | 61.4906 | − | 61.4906i | 0.00206085 | − | 0.00206085i | ||||
\(963\) | −9707.82 | + | 7375.15i | −0.324850 | + | 0.246792i | ||||
\(964\) | 615.255i | 0.0205560i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 9683.56 | − | 28303.0i | 0.322529 | − | 0.942686i | ||||
\(967\) | −47533.1 | + | 12736.5i | −1.58073 | + | 0.423554i | −0.939151 | − | 0.343506i | \(-0.888385\pi\) |
−0.641575 | + | 0.767060i | \(0.721719\pi\) | |||||||
\(968\) | −40017.5 | + | 10722.6i | −1.32873 | + | 0.356032i | ||||
\(969\) | 9743.66 | + | 11164.6i | 0.323025 | + | 0.370132i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 38812.1i | − | 1.28274i | −0.767232 | − | 0.641369i | \(-0.778367\pi\) | ||
0.767232 | − | 0.641369i | \(-0.221633\pi\) | |||||||
\(972\) | −882.889 | − | 1031.50i | −0.0291344 | − | 0.0340386i | ||||
\(973\) | 17568.7 | − | 17568.7i | 0.578855 | − | 0.578855i | ||||
\(974\) | 13615.5 | + | 23582.8i | 0.447915 | + | 0.775812i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −18861.3 | + | 32668.7i | −0.618582 | + | 1.07142i | ||||
\(977\) | 4683.10 | + | 17477.6i | 0.153353 | + | 0.572320i | 0.999241 | + | 0.0389597i | \(0.0124044\pi\) |
−0.845888 | + | 0.533360i | \(0.820929\pi\) | |||||||
\(978\) | 17942.5 | − | 8794.67i | 0.586644 | − | 0.287549i | ||||
\(979\) | −41428.6 | + | 23918.8i | −1.35246 | + | 0.780846i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4114.08 | − | 30128.9i | 0.133897 | − | 0.980573i | ||||
\(982\) | −11280.2 | − | 11280.2i | −0.366563 | − | 0.366563i | ||||
\(983\) | −5531.33 | + | 20643.2i | −0.179473 | + | 0.669802i | 0.816273 | + | 0.577666i | \(0.196036\pi\) |
−0.995746 | + | 0.0921365i | \(0.970630\pi\) | |||||||
\(984\) | −719.345 | − | 3662.40i | −0.0233047 | − | 0.118652i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −26624.0 | − | 15371.4i | −0.859920 | − | 0.496475i | ||||
\(987\) | 8176.23 | − | 12173.1i | 0.263680 | − | 0.392578i | ||||
\(988\) | 17.9640 | + | 4.81345i | 0.000578454 | + | 0.000154996i | ||||
\(989\) | 45441.8 | 1.46104 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21254.8 | −0.681314 | −0.340657 | − | 0.940188i | \(-0.610650\pi\) | ||||
−0.340657 | + | 0.940188i | \(0.610650\pi\) | |||||||
\(992\) | −133.534 | − | 35.7804i | −0.00427391 | − | 0.00114519i | ||||
\(993\) | −25761.0 | − | 52556.5i | −0.823265 | − | 1.67959i | ||||
\(994\) | −793.630 | − | 458.203i | −0.0253244 | − | 0.0146210i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1413.13 | + | 1233.28i | −0.0449567 | + | 0.0392351i | ||||
\(997\) | −1350.75 | + | 5041.09i | −0.0429076 | + | 0.160133i | −0.984055 | − | 0.177862i | \(-0.943082\pi\) |
0.941148 | + | 0.337995i | \(0.109749\pi\) | |||||||
\(998\) | 10925.4 | + | 10925.4i | 0.346530 | + | 0.346530i | ||||
\(999\) | 973.368 | + | 1479.75i | 0.0308268 | + | 0.0468641i |
(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 | 225.4.p.b.32.12 | 64 | ||
5.2 | odd | 4 | 45.4.l.a.23.5 | yes | 64 | ||
5.3 | odd | 4 | inner | 225.4.p.b.68.12 | 64 | ||
5.4 | even | 2 | 45.4.l.a.32.5 | yes | 64 | ||
9.2 | odd | 6 | inner | 225.4.p.b.182.12 | 64 | ||
15.2 | even | 4 | 135.4.m.a.98.12 | 64 | |||
15.14 | odd | 2 | 135.4.m.a.17.12 | 64 | |||
45.2 | even | 12 | 45.4.l.a.38.5 | yes | 64 | ||
45.7 | odd | 12 | 135.4.m.a.8.12 | 64 | |||
45.29 | odd | 6 | 45.4.l.a.2.5 | ✓ | 64 | ||
45.34 | even | 6 | 135.4.m.a.62.12 | 64 | |||
45.38 | even | 12 | inner | 225.4.p.b.218.12 | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.l.a.2.5 | ✓ | 64 | 45.29 | odd | 6 | ||
45.4.l.a.23.5 | yes | 64 | 5.2 | odd | 4 | ||
45.4.l.a.32.5 | yes | 64 | 5.4 | even | 2 | ||
45.4.l.a.38.5 | yes | 64 | 45.2 | even | 12 | ||
135.4.m.a.8.12 | 64 | 45.7 | odd | 12 | |||
135.4.m.a.17.12 | 64 | 15.14 | odd | 2 | |||
135.4.m.a.62.12 | 64 | 45.34 | even | 6 | |||
135.4.m.a.98.12 | 64 | 15.2 | even | 4 | |||
225.4.p.b.32.12 | 64 | 1.1 | even | 1 | trivial | ||
225.4.p.b.68.12 | 64 | 5.3 | odd | 4 | inner | ||
225.4.p.b.182.12 | 64 | 9.2 | odd | 6 | inner | ||
225.4.p.b.218.12 | 64 | 45.38 | even | 12 | inner |