Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [138,4,Mod(137,138)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(138, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("138.137");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 138 = 2 \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 138.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.14226358079\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 137.3 | ||
Character | \(\chi\) | \(=\) | 138.137 |
Dual form | 138.4.d.a.137.15 |
$q$-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 \(\left(\mathbb{Z}/138\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(97\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.00000i | − | 0.707107i | ||||||
\(3\) | −3.26555 | + | 4.04180i | −0.628456 | + | 0.777845i | ||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | −6.82316 | −0.610282 | −0.305141 | − | 0.952307i | \(-0.598704\pi\) | ||||
−0.305141 | + | 0.952307i | \(0.598704\pi\) | |||||||
\(6\) | 8.08360 | + | 6.53111i | 0.550019 | + | 0.444386i | ||||
\(7\) | − | 3.09939i | − | 0.167351i | −0.996493 | − | 0.0836757i | \(-0.973334\pi\) | ||
0.996493 | − | 0.0836757i | \(-0.0266660\pi\) | |||||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | −5.67231 | − | 26.3974i | −0.210085 | − | 0.977683i | ||||
\(10\) | 13.6463i | 0.431535i | ||||||||
\(11\) | 50.4927 | 1.38401 | 0.692006 | − | 0.721892i | \(-0.256727\pi\) | ||||
0.692006 | + | 0.721892i | \(0.256727\pi\) | |||||||
\(12\) | 13.0622 | − | 16.1672i | 0.314228 | − | 0.388922i | ||||
\(13\) | 6.18710 | 0.132000 | 0.0659998 | − | 0.997820i | \(-0.478976\pi\) | ||||
0.0659998 | + | 0.997820i | \(0.478976\pi\) | |||||||
\(14\) | −6.19878 | −0.118335 | ||||||||
\(15\) | 22.2814 | − | 27.5779i | 0.383536 | − | 0.474705i | ||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 118.176 | 1.68600 | 0.843000 | − | 0.537913i | \(-0.180787\pi\) | ||||
0.843000 | + | 0.537913i | \(0.180787\pi\) | |||||||
\(18\) | −52.7949 | + | 11.3446i | −0.691326 | + | 0.148553i | ||||
\(19\) | − | 92.8440i | − | 1.12105i | −0.828139 | − | 0.560523i | \(-0.810600\pi\) | ||
0.828139 | − | 0.560523i | \(-0.189400\pi\) | |||||||
\(20\) | 27.2926 | 0.305141 | ||||||||
\(21\) | 12.5271 | + | 10.1212i | 0.130173 | + | 0.105173i | ||||
\(22\) | − | 100.985i | − | 0.978644i | ||||||
\(23\) | 109.125 | + | 16.0867i | 0.989308 | + | 0.145839i | ||||
\(24\) | −32.3344 | − | 26.1244i | −0.275010 | − | 0.222193i | ||||
\(25\) | −78.4445 | −0.627556 | ||||||||
\(26\) | − | 12.3742i | − | 0.0933377i | ||||||
\(27\) | 125.216 | + | 63.2760i | 0.892515 | + | 0.451017i | ||||
\(28\) | 12.3976i | 0.0836757i | ||||||||
\(29\) | − | 108.478i | − | 0.694618i | −0.937751 | − | 0.347309i | \(-0.887096\pi\) | ||
0.937751 | − | 0.347309i | \(-0.112904\pi\) | |||||||
\(30\) | −55.1557 | − | 44.5628i | −0.335667 | − | 0.271201i | ||||
\(31\) | −49.4045 | −0.286236 | −0.143118 | − | 0.989706i | \(-0.545713\pi\) | ||||
−0.143118 | + | 0.989706i | \(0.545713\pi\) | |||||||
\(32\) | − | 32.0000i | − | 0.176777i | ||||||
\(33\) | −164.887 | + | 204.082i | −0.869791 | + | 1.07655i | ||||
\(34\) | − | 236.353i | − | 1.19218i | ||||||
\(35\) | 21.1476i | 0.102131i | ||||||||
\(36\) | 22.6892 | + | 105.590i | 0.105043 | + | 0.488842i | ||||
\(37\) | 55.2490i | 0.245483i | 0.992439 | + | 0.122742i | \(0.0391686\pi\) | ||||
−0.992439 | + | 0.122742i | \(0.960831\pi\) | |||||||
\(38\) | −185.688 | −0.792699 | ||||||||
\(39\) | −20.2043 | + | 25.0070i | −0.0829559 | + | 0.102675i | ||||
\(40\) | − | 54.5853i | − | 0.215767i | ||||||
\(41\) | 136.636i | 0.520463i | 0.965546 | + | 0.260231i | \(0.0837989\pi\) | ||||
−0.965546 | + | 0.260231i | \(0.916201\pi\) | |||||||
\(42\) | 20.2425 | − | 25.0542i | 0.0743685 | − | 0.0920465i | ||||
\(43\) | − | 211.875i | − | 0.751411i | −0.926739 | − | 0.375706i | \(-0.877400\pi\) | ||
0.926739 | − | 0.375706i | \(-0.122600\pi\) | |||||||
\(44\) | −201.971 | −0.692006 | ||||||||
\(45\) | 38.7031 | + | 180.114i | 0.128211 | + | 0.596662i | ||||
\(46\) | 32.1734 | − | 218.250i | 0.103124 | − | 0.699547i | ||||
\(47\) | − | 451.774i | − | 1.40208i | −0.713120 | − | 0.701042i | \(-0.752719\pi\) | ||
0.713120 | − | 0.701042i | \(-0.247281\pi\) | |||||||
\(48\) | −52.2489 | + | 64.6688i | −0.157114 | + | 0.194461i | ||||
\(49\) | 333.394 | 0.971994 | ||||||||
\(50\) | 156.889i | 0.443749i | ||||||||
\(51\) | −385.912 | + | 477.646i | −1.05958 | + | 1.31145i | ||||
\(52\) | −24.7484 | −0.0659998 | ||||||||
\(53\) | 265.883 | 0.689091 | 0.344545 | − | 0.938770i | \(-0.388033\pi\) | ||||
0.344545 | + | 0.938770i | \(0.388033\pi\) | |||||||
\(54\) | 126.552 | − | 250.433i | 0.318917 | − | 0.631104i | ||||
\(55\) | −344.520 | −0.844638 | ||||||||
\(56\) | 24.7951 | 0.0591676 | ||||||||
\(57\) | 375.257 | + | 303.187i | 0.872000 | + | 0.704528i | ||||
\(58\) | −216.957 | −0.491169 | ||||||||
\(59\) | 653.373i | 1.44173i | 0.693077 | + | 0.720864i | \(0.256255\pi\) | ||||
−0.693077 | + | 0.720864i | \(0.743745\pi\) | |||||||
\(60\) | −89.1256 | + | 110.311i | −0.191768 | + | 0.237352i | ||||
\(61\) | 687.646i | 1.44335i | 0.692234 | + | 0.721673i | \(0.256626\pi\) | ||||
−0.692234 | + | 0.721673i | \(0.743374\pi\) | |||||||
\(62\) | 98.8090i | 0.202399i | ||||||||
\(63\) | −81.8160 | + | 17.5807i | −0.163617 | + | 0.0351581i | ||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | −42.2156 | −0.0805569 | ||||||||
\(66\) | 408.163 | + | 329.774i | 0.761233 | + | 0.615035i | ||||
\(67\) | − | 10.5578i | − | 0.0192513i | −0.999954 | − | 0.00962564i | \(-0.996936\pi\) | ||
0.999954 | − | 0.00962564i | \(-0.00306398\pi\) | |||||||
\(68\) | −472.706 | −0.843000 | ||||||||
\(69\) | −421.372 | + | 388.529i | −0.735177 | + | 0.677875i | ||||
\(70\) | 42.2953 | 0.0722179 | ||||||||
\(71\) | − | 314.914i | − | 0.526385i | −0.964743 | − | 0.263193i | \(-0.915224\pi\) | ||
0.964743 | − | 0.263193i | \(-0.0847755\pi\) | |||||||
\(72\) | 211.180 | − | 45.3785i | 0.345663 | − | 0.0742764i | ||||
\(73\) | 795.294 | 1.27510 | 0.637549 | − | 0.770410i | \(-0.279949\pi\) | ||||
0.637549 | + | 0.770410i | \(0.279949\pi\) | |||||||
\(74\) | 110.498 | 0.173583 | ||||||||
\(75\) | 256.165 | − | 317.057i | 0.394391 | − | 0.488141i | ||||
\(76\) | 371.376i | 0.560523i | ||||||||
\(77\) | − | 156.497i | − | 0.231616i | ||||||
\(78\) | 50.0141 | + | 40.4086i | 0.0726023 | + | 0.0586587i | ||||
\(79\) | − | 1223.44i | − | 1.74238i | −0.490949 | − | 0.871188i | \(-0.663350\pi\) | ||
0.490949 | − | 0.871188i | \(-0.336650\pi\) | |||||||
\(80\) | −109.171 | −0.152570 | ||||||||
\(81\) | −664.650 | + | 299.469i | −0.911728 | + | 0.410794i | ||||
\(82\) | 273.272 | 0.368023 | ||||||||
\(83\) | −403.836 | −0.534058 | −0.267029 | − | 0.963688i | \(-0.586042\pi\) | ||||
−0.267029 | + | 0.963688i | \(0.586042\pi\) | |||||||
\(84\) | −50.1085 | − | 40.4849i | −0.0650867 | − | 0.0525865i | ||||
\(85\) | −806.337 | −1.02894 | ||||||||
\(86\) | −423.751 | −0.531328 | ||||||||
\(87\) | 438.448 | + | 354.242i | 0.540305 | + | 0.436537i | ||||
\(88\) | 403.942i | 0.489322i | ||||||||
\(89\) | −29.6522 | −0.0353161 | −0.0176580 | − | 0.999844i | \(-0.505621\pi\) | ||||
−0.0176580 | + | 0.999844i | \(0.505621\pi\) | |||||||
\(90\) | 360.228 | − | 77.4061i | 0.421904 | − | 0.0906591i | ||||
\(91\) | − | 19.1762i | − | 0.0220903i | ||||||
\(92\) | −436.499 | − | 64.3467i | −0.494654 | − | 0.0729197i | ||||
\(93\) | 161.333 | − | 199.683i | 0.179887 | − | 0.222647i | ||||
\(94\) | −903.547 | −0.991423 | ||||||||
\(95\) | 633.489i | 0.684154i | ||||||||
\(96\) | 129.338 | + | 104.498i | 0.137505 | + | 0.111096i | ||||
\(97\) | − | 1165.71i | − | 1.22020i | −0.792324 | − | 0.610101i | \(-0.791129\pi\) | ||
0.792324 | − | 0.610101i | \(-0.208871\pi\) | |||||||
\(98\) | − | 666.788i | − | 0.687303i | ||||||
\(99\) | −286.410 | − | 1332.88i | −0.290761 | − | 1.35313i | ||||
\(100\) | 313.778 | 0.313778 | ||||||||
\(101\) | 35.8082i | 0.0352777i | 0.999844 | + | 0.0176389i | \(0.00561492\pi\) | ||||
−0.999844 | + | 0.0176389i | \(0.994385\pi\) | |||||||
\(102\) | 955.291 | + | 771.823i | 0.927333 | + | 0.749234i | ||||
\(103\) | − | 775.880i | − | 0.742230i | −0.928587 | − | 0.371115i | \(-0.878976\pi\) | ||
0.928587 | − | 0.371115i | \(-0.121024\pi\) | |||||||
\(104\) | 49.4968i | 0.0466689i | ||||||||
\(105\) | −85.4745 | − | 69.0587i | −0.0794425 | − | 0.0641852i | ||||
\(106\) | − | 531.766i | − | 0.487261i | ||||||
\(107\) | 136.147 | 0.123008 | 0.0615040 | − | 0.998107i | \(-0.480410\pi\) | ||||
0.0615040 | + | 0.998107i | \(0.480410\pi\) | |||||||
\(108\) | −500.866 | − | 253.104i | −0.446258 | − | 0.225509i | ||||
\(109\) | 352.915i | 0.310121i | 0.987905 | + | 0.155060i | \(0.0495572\pi\) | ||||
−0.987905 | + | 0.155060i | \(0.950443\pi\) | |||||||
\(110\) | 689.040i | 0.597249i | ||||||||
\(111\) | −223.305 | − | 180.419i | −0.190948 | − | 0.154275i | ||||
\(112\) | − | 49.5902i | − | 0.0418378i | ||||||
\(113\) | −713.290 | −0.593811 | −0.296906 | − | 0.954907i | \(-0.595955\pi\) | ||||
−0.296906 | + | 0.954907i | \(0.595955\pi\) | |||||||
\(114\) | 606.374 | − | 750.514i | 0.498177 | − | 0.616597i | ||||
\(115\) | −744.576 | − | 109.762i | −0.603757 | − | 0.0890031i | ||||
\(116\) | 433.913i | 0.347309i | ||||||||
\(117\) | −35.0951 | − | 163.324i | −0.0277312 | − | 0.129054i | ||||
\(118\) | 1306.75 | 1.01946 | ||||||||
\(119\) | − | 366.275i | − | 0.282154i | ||||||
\(120\) | 220.623 | + | 178.251i | 0.167833 | + | 0.135600i | ||||
\(121\) | 1218.52 | 0.915489 | ||||||||
\(122\) | 1375.29 | 1.02060 | ||||||||
\(123\) | −552.256 | − | 446.193i | −0.404839 | − | 0.327088i | ||||
\(124\) | 197.618 | 0.143118 | ||||||||
\(125\) | 1388.13 | 0.993268 | ||||||||
\(126\) | 35.1614 | + | 163.632i | 0.0248605 | + | 0.115694i | ||||
\(127\) | −2054.40 | −1.43542 | −0.717711 | − | 0.696341i | \(-0.754810\pi\) | ||||
−0.717711 | + | 0.696341i | \(0.754810\pi\) | |||||||
\(128\) | 128.000i | 0.0883883i | ||||||||
\(129\) | 856.358 | + | 691.891i | 0.584482 | + | 0.472229i | ||||
\(130\) | 84.4312i | 0.0569623i | ||||||||
\(131\) | − | 1631.00i | − | 1.08780i | −0.839151 | − | 0.543898i | \(-0.816948\pi\) | ||
0.839151 | − | 0.543898i | \(-0.183052\pi\) | |||||||
\(132\) | 659.547 | − | 816.326i | 0.434896 | − | 0.538273i | ||||
\(133\) | −287.760 | −0.187608 | ||||||||
\(134\) | −21.1155 | −0.0136127 | ||||||||
\(135\) | −854.372 | − | 431.742i | −0.544686 | − | 0.275248i | ||||
\(136\) | 945.412i | 0.596091i | ||||||||
\(137\) | 3115.35 | 1.94279 | 0.971395 | − | 0.237471i | \(-0.0763184\pi\) | ||||
0.971395 | + | 0.237471i | \(0.0763184\pi\) | |||||||
\(138\) | 777.057 | + | 842.744i | 0.479330 | + | 0.519849i | ||||
\(139\) | 1889.56 | 1.15303 | 0.576513 | − | 0.817088i | \(-0.304413\pi\) | ||||
0.576513 | + | 0.817088i | \(0.304413\pi\) | |||||||
\(140\) | − | 84.5905i | − | 0.0510657i | ||||||
\(141\) | 1825.98 | + | 1475.29i | 1.09060 | + | 0.881149i | ||||
\(142\) | −629.827 | −0.372211 | ||||||||
\(143\) | 312.404 | 0.182689 | ||||||||
\(144\) | −90.7569 | − | 422.359i | −0.0525214 | − | 0.244421i | ||||
\(145\) | 740.165i | 0.423913i | ||||||||
\(146\) | − | 1590.59i | − | 0.901630i | ||||||
\(147\) | −1088.72 | + | 1347.51i | −0.610855 | + | 0.756060i | ||||
\(148\) | − | 220.996i | − | 0.122742i | ||||||
\(149\) | −647.849 | −0.356200 | −0.178100 | − | 0.984012i | \(-0.556995\pi\) | ||||
−0.178100 | + | 0.984012i | \(0.556995\pi\) | |||||||
\(150\) | −634.114 | − | 512.330i | −0.345168 | − | 0.278877i | ||||
\(151\) | 1408.70 | 0.759195 | 0.379597 | − | 0.925152i | \(-0.376063\pi\) | ||||
0.379597 | + | 0.925152i | \(0.376063\pi\) | |||||||
\(152\) | 742.752 | 0.396349 | ||||||||
\(153\) | −670.333 | − | 3119.56i | −0.354204 | − | 1.64837i | ||||
\(154\) | −312.993 | −0.163777 | ||||||||
\(155\) | 337.095 | 0.174684 | ||||||||
\(156\) | 80.8173 | − | 100.028i | 0.0414780 | − | 0.0513376i | ||||
\(157\) | 837.809i | 0.425888i | 0.977064 | + | 0.212944i | \(0.0683053\pi\) | ||||
−0.977064 | + | 0.212944i | \(0.931695\pi\) | |||||||
\(158\) | −2446.88 | −1.23205 | ||||||||
\(159\) | −868.255 | + | 1074.65i | −0.433063 | + | 0.536006i | ||||
\(160\) | 218.341i | 0.107884i | ||||||||
\(161\) | 49.8589 | − | 338.220i | 0.0244064 | − | 0.165562i | ||||
\(162\) | 598.938 | + | 1329.30i | 0.290475 | + | 0.644689i | ||||
\(163\) | −1919.58 | −0.922410 | −0.461205 | − | 0.887294i | \(-0.652583\pi\) | ||||
−0.461205 | + | 0.887294i | \(0.652583\pi\) | |||||||
\(164\) | − | 546.544i | − | 0.260231i | ||||||
\(165\) | 1125.05 | − | 1392.48i | 0.530818 | − | 0.656997i | ||||
\(166\) | 807.673i | 0.377636i | ||||||||
\(167\) | − | 420.600i | − | 0.194892i | −0.995241 | − | 0.0974462i | \(-0.968933\pi\) | ||
0.995241 | − | 0.0974462i | \(-0.0310674\pi\) | |||||||
\(168\) | −80.9698 | + | 100.217i | −0.0371843 | + | 0.0460232i | ||||
\(169\) | −2158.72 | −0.982576 | ||||||||
\(170\) | 1612.67i | 0.727567i | ||||||||
\(171\) | −2450.84 | + | 526.639i | −1.09603 | + | 0.235515i | ||||
\(172\) | 847.501i | 0.375706i | ||||||||
\(173\) | 3160.75i | 1.38906i | 0.719464 | + | 0.694529i | \(0.244387\pi\) | ||||
−0.719464 | + | 0.694529i | \(0.755613\pi\) | |||||||
\(174\) | 708.484 | − | 876.896i | 0.308678 | − | 0.382053i | ||||
\(175\) | 243.130i | 0.105022i | ||||||||
\(176\) | 807.884 | 0.346003 | ||||||||
\(177\) | −2640.80 | − | 2133.63i | −1.12144 | − | 0.906063i | ||||
\(178\) | 59.3045i | 0.0249722i | ||||||||
\(179\) | 3316.12i | 1.38469i | 0.721569 | + | 0.692343i | \(0.243421\pi\) | ||||
−0.721569 | + | 0.692343i | \(0.756579\pi\) | |||||||
\(180\) | −154.812 | − | 720.456i | −0.0641057 | − | 0.298331i | ||||
\(181\) | 2990.38i | 1.22803i | 0.789295 | + | 0.614014i | \(0.210446\pi\) | ||||
−0.789295 | + | 0.614014i | \(0.789554\pi\) | |||||||
\(182\) | −38.3525 | −0.0156202 | ||||||||
\(183\) | −2779.33 | − | 2245.55i | −1.12270 | − | 0.907079i | ||||
\(184\) | −128.693 | + | 872.998i | −0.0515620 | + | 0.349773i | ||||
\(185\) | − | 376.973i | − | 0.149814i | ||||||
\(186\) | −399.366 | − | 322.666i | −0.157435 | − | 0.127199i | ||||
\(187\) | 5967.05 | 2.33344 | ||||||||
\(188\) | 1807.09i | 0.701042i | ||||||||
\(189\) | 196.117 | − | 388.094i | 0.0754783 | − | 0.149364i | ||||
\(190\) | 1266.98 | 0.483770 | ||||||||
\(191\) | −3767.16 | −1.42713 | −0.713565 | − | 0.700589i | \(-0.752921\pi\) | ||||
−0.713565 | + | 0.700589i | \(0.752921\pi\) | |||||||
\(192\) | 208.995 | − | 258.675i | 0.0785570 | − | 0.0972306i | ||||
\(193\) | −989.248 | −0.368951 | −0.184476 | − | 0.982837i | \(-0.559059\pi\) | ||||
−0.184476 | + | 0.982837i | \(0.559059\pi\) | |||||||
\(194\) | −2331.41 | −0.862813 | ||||||||
\(195\) | 137.857 | − | 170.627i | 0.0506265 | − | 0.0626608i | ||||
\(196\) | −1333.58 | −0.485997 | ||||||||
\(197\) | − | 2987.20i | − | 1.08035i | −0.841552 | − | 0.540176i | \(-0.818358\pi\) | ||
0.841552 | − | 0.540176i | \(-0.181642\pi\) | |||||||
\(198\) | −2665.76 | + | 572.821i | −0.956804 | + | 0.205599i | ||||
\(199\) | 2811.84i | 1.00164i | 0.865552 | + | 0.500819i | \(0.166968\pi\) | ||||
−0.865552 | + | 0.500819i | \(0.833032\pi\) | |||||||
\(200\) | − | 627.556i | − | 0.221875i | ||||||
\(201\) | 42.6724 | + | 34.4769i | 0.0149745 | + | 0.0120986i | ||||
\(202\) | 71.6164 | 0.0249451 | ||||||||
\(203\) | −336.217 | −0.116245 | ||||||||
\(204\) | 1543.65 | − | 1910.58i | 0.529789 | − | 0.655723i | ||||
\(205\) | − | 932.290i | − | 0.317629i | ||||||
\(206\) | −1551.76 | −0.524836 | ||||||||
\(207\) | −194.342 | − | 2971.86i | −0.0652546 | − | 0.997869i | ||||
\(208\) | 98.9936 | 0.0329999 | ||||||||
\(209\) | − | 4687.95i | − | 1.55154i | ||||||
\(210\) | −138.117 | + | 170.949i | −0.0453858 | + | 0.0561743i | ||||
\(211\) | 265.079 | 0.0864873 | 0.0432436 | − | 0.999065i | \(-0.486231\pi\) | ||||
0.0432436 | + | 0.999065i | \(0.486231\pi\) | |||||||
\(212\) | −1063.53 | −0.344545 | ||||||||
\(213\) | 1272.82 | + | 1028.37i | 0.409446 | + | 0.330810i | ||||
\(214\) | − | 272.295i | − | 0.0869798i | ||||||
\(215\) | 1445.66i | 0.458573i | ||||||||
\(216\) | −506.208 | + | 1001.73i | −0.159459 | + | 0.315552i | ||||
\(217\) | 153.124i | 0.0479019i | ||||||||
\(218\) | 705.830 | 0.219288 | ||||||||
\(219\) | −2597.08 | + | 3214.42i | −0.801343 | + | 0.991828i | ||||
\(220\) | 1378.08 | 0.422319 | ||||||||
\(221\) | 731.170 | 0.222551 | ||||||||
\(222\) | −360.837 | + | 446.611i | −0.109089 | + | 0.135020i | ||||
\(223\) | −3189.10 | −0.957659 | −0.478830 | − | 0.877908i | \(-0.658939\pi\) | ||||
−0.478830 | + | 0.877908i | \(0.658939\pi\) | |||||||
\(224\) | −99.1805 | −0.0295838 | ||||||||
\(225\) | 444.961 | + | 2070.73i | 0.131840 | + | 0.613551i | ||||
\(226\) | 1426.58i | 0.419888i | ||||||||
\(227\) | 4687.01 | 1.37043 | 0.685216 | − | 0.728340i | \(-0.259708\pi\) | ||||
0.685216 | + | 0.728340i | \(0.259708\pi\) | |||||||
\(228\) | −1501.03 | − | 1212.75i | −0.436000 | − | 0.352264i | ||||
\(229\) | 6067.92i | 1.75100i | 0.483216 | + | 0.875501i | \(0.339469\pi\) | ||||
−0.483216 | + | 0.875501i | \(0.660531\pi\) | |||||||
\(230\) | −219.524 | + | 1489.15i | −0.0629347 | + | 0.426921i | ||||
\(231\) | 632.528 | + | 511.048i | 0.180161 | + | 0.145561i | ||||
\(232\) | 867.827 | 0.245585 | ||||||||
\(233\) | 1827.91i | 0.513950i | 0.966418 | + | 0.256975i | \(0.0827258\pi\) | ||||
−0.966418 | + | 0.256975i | \(0.917274\pi\) | |||||||
\(234\) | −326.647 | + | 70.1903i | −0.0912547 | + | 0.0196089i | ||||
\(235\) | 3082.52i | 0.855667i | ||||||||
\(236\) | − | 2613.49i | − | 0.720864i | ||||||
\(237\) | 4944.90 | + | 3995.21i | 1.35530 | + | 1.09501i | ||||
\(238\) | −732.550 | −0.199513 | ||||||||
\(239\) | − | 3454.47i | − | 0.934942i | −0.884008 | − | 0.467471i | \(-0.845165\pi\) | ||
0.884008 | − | 0.467471i | \(-0.154835\pi\) | |||||||
\(240\) | 356.502 | − | 441.246i | 0.0958839 | − | 0.118676i | ||||
\(241\) | 780.677i | 0.208663i | 0.994543 | + | 0.104332i | \(0.0332703\pi\) | ||||
−0.994543 | + | 0.104332i | \(0.966730\pi\) | |||||||
\(242\) | − | 2437.03i | − | 0.647349i | ||||||
\(243\) | 960.057 | − | 3664.31i | 0.253447 | − | 0.967349i | ||||
\(244\) | − | 2750.58i | − | 0.721673i | ||||||
\(245\) | −2274.80 | −0.593190 | ||||||||
\(246\) | −892.385 | + | 1104.51i | −0.231286 | + | 0.286265i | ||||
\(247\) | − | 574.435i | − | 0.147977i | ||||||
\(248\) | − | 395.236i | − | 0.101200i | ||||||
\(249\) | 1318.75 | − | 1632.23i | 0.335632 | − | 0.415414i | ||||
\(250\) | − | 2776.27i | − | 0.702347i | ||||||
\(251\) | 5708.15 | 1.43544 | 0.717720 | − | 0.696332i | \(-0.245186\pi\) | ||||
0.717720 | + | 0.696332i | \(0.245186\pi\) | |||||||
\(252\) | 327.264 | − | 70.3228i | 0.0818083 | − | 0.0175790i | ||||
\(253\) | 5510.01 | + | 812.260i | 1.36921 | + | 0.201843i | ||||
\(254\) | 4108.80i | 1.01500i | ||||||||
\(255\) | 2633.14 | − | 3259.05i | 0.646641 | − | 0.800352i | ||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 5609.13i | 1.36143i | 0.732548 | + | 0.680715i | \(0.238331\pi\) | ||||
−0.732548 | + | 0.680715i | \(0.761669\pi\) | |||||||
\(258\) | 1383.78 | − | 1712.72i | 0.333916 | − | 0.413291i | ||||
\(259\) | 171.238 | 0.0410819 | ||||||||
\(260\) | 168.862 | 0.0402785 | ||||||||
\(261\) | −2863.55 | + | 615.322i | −0.679116 | + | 0.145929i | ||||
\(262\) | −3262.00 | −0.769188 | ||||||||
\(263\) | 706.383 | 0.165618 | 0.0828088 | − | 0.996565i | \(-0.473611\pi\) | ||||
0.0828088 | + | 0.996565i | \(0.473611\pi\) | |||||||
\(264\) | −1632.65 | − | 1319.09i | −0.380617 | − | 0.307518i | ||||
\(265\) | −1814.16 | −0.420540 | ||||||||
\(266\) | 575.519i | 0.132659i | ||||||||
\(267\) | 96.8310 | − | 119.848i | 0.0221946 | − | 0.0274704i | ||||
\(268\) | 42.2310i | 0.00962564i | ||||||||
\(269\) | − | 1817.30i | − | 0.411905i | −0.978562 | − | 0.205953i | \(-0.933971\pi\) | ||
0.978562 | − | 0.205953i | \(-0.0660292\pi\) | |||||||
\(270\) | −863.484 | + | 1708.74i | −0.194629 | + | 0.385151i | ||||
\(271\) | −4857.57 | −1.08884 | −0.544422 | − | 0.838812i | \(-0.683251\pi\) | ||||
−0.544422 | + | 0.838812i | \(0.683251\pi\) | |||||||
\(272\) | 1890.82 | 0.421500 | ||||||||
\(273\) | 77.5065 | + | 62.6211i | 0.0171828 | + | 0.0138828i | ||||
\(274\) | − | 6230.70i | − | 1.37376i | ||||||
\(275\) | −3960.88 | −0.868545 | ||||||||
\(276\) | 1685.49 | − | 1554.11i | 0.367589 | − | 0.338937i | ||||
\(277\) | −623.733 | −0.135294 | −0.0676471 | − | 0.997709i | \(-0.521549\pi\) | ||||
−0.0676471 | + | 0.997709i | \(0.521549\pi\) | |||||||
\(278\) | − | 3779.13i | − | 0.815313i | ||||||
\(279\) | 280.237 | + | 1304.15i | 0.0601339 | + | 0.279848i | ||||
\(280\) | −169.181 | −0.0361089 | ||||||||
\(281\) | −422.486 | −0.0896918 | −0.0448459 | − | 0.998994i | \(-0.514280\pi\) | ||||
−0.0448459 | + | 0.998994i | \(0.514280\pi\) | |||||||
\(282\) | 2950.58 | − | 3651.96i | 0.623066 | − | 0.771173i | ||||
\(283\) | − | 5963.94i | − | 1.25272i | −0.779534 | − | 0.626360i | \(-0.784544\pi\) | ||
0.779534 | − | 0.626360i | \(-0.215456\pi\) | |||||||
\(284\) | 1259.65i | 0.263193i | ||||||||
\(285\) | −2560.44 | − | 2068.69i | −0.532166 | − | 0.429961i | ||||
\(286\) | − | 624.807i | − | 0.129181i | ||||||
\(287\) | 423.489 | 0.0871001 | ||||||||
\(288\) | −844.718 | + | 181.514i | −0.172832 | + | 0.0371382i | ||||
\(289\) | 9052.68 | 1.84260 | ||||||||
\(290\) | 1480.33 | 0.299752 | ||||||||
\(291\) | 4711.55 | + | 3806.68i | 0.949127 | + | 0.766843i | ||||
\(292\) | −3181.18 | −0.637549 | ||||||||
\(293\) | −3560.06 | −0.709832 | −0.354916 | − | 0.934898i | \(-0.615491\pi\) | ||||
−0.354916 | + | 0.934898i | \(0.615491\pi\) | |||||||
\(294\) | 2695.02 | + | 2177.43i | 0.534615 | + | 0.431940i | ||||
\(295\) | − | 4458.07i | − | 0.879860i | ||||||
\(296\) | −441.992 | −0.0867914 | ||||||||
\(297\) | 6322.52 | + | 3194.98i | 1.23525 | + | 0.624213i | ||||
\(298\) | 1295.70i | 0.251872i | ||||||||
\(299\) | 675.166 | + | 99.5299i | 0.130588 | + | 0.0192507i | ||||
\(300\) | −1024.66 | + | 1268.23i | −0.197196 | + | 0.244071i | ||||
\(301\) | −656.684 | −0.125750 | ||||||||
\(302\) | − | 2817.40i | − | 0.536832i | ||||||
\(303\) | −144.730 | − | 116.934i | −0.0274406 | − | 0.0221705i | ||||
\(304\) | − | 1485.50i | − | 0.280261i | ||||||
\(305\) | − | 4691.92i | − | 0.880848i | ||||||
\(306\) | −6239.11 | + | 1340.67i | −1.16558 | + | 0.250460i | ||||
\(307\) | 1409.77 | 0.262085 | 0.131042 | − | 0.991377i | \(-0.458168\pi\) | ||||
0.131042 | + | 0.991377i | \(0.458168\pi\) | |||||||
\(308\) | 625.987i | 0.115808i | ||||||||
\(309\) | 3135.95 | + | 2533.68i | 0.577340 | + | 0.466459i | ||||
\(310\) | − | 674.189i | − | 0.123521i | ||||||
\(311\) | 9394.27i | 1.71286i | 0.516262 | + | 0.856431i | \(0.327323\pi\) | ||||
−0.516262 | + | 0.856431i | \(0.672677\pi\) | |||||||
\(312\) | −200.056 | − | 161.635i | −0.0363011 | − | 0.0293293i | ||||
\(313\) | − | 1657.79i | − | 0.299373i | −0.988734 | − | 0.149687i | \(-0.952174\pi\) | ||
0.988734 | − | 0.149687i | \(-0.0478264\pi\) | |||||||
\(314\) | 1675.62 | 0.301149 | ||||||||
\(315\) | 558.243 | − | 119.956i | 0.0998522 | − | 0.0214563i | ||||
\(316\) | 4893.76i | 0.871188i | ||||||||
\(317\) | 5647.64i | 1.00064i | 0.865840 | + | 0.500321i | \(0.166785\pi\) | ||||
−0.865840 | + | 0.500321i | \(0.833215\pi\) | |||||||
\(318\) | 2149.29 | + | 1736.51i | 0.379013 | + | 0.306222i | ||||
\(319\) | − | 5477.37i | − | 0.961360i | ||||||
\(320\) | 436.682 | 0.0762852 | ||||||||
\(321\) | −444.596 | + | 550.280i | −0.0773051 | + | 0.0956811i | ||||
\(322\) | −676.440 | − | 99.7178i | −0.117070 | − | 0.0172579i | ||||
\(323\) | − | 10972.0i | − | 1.89008i | ||||||
\(324\) | 2658.60 | − | 1197.88i | 0.455864 | − | 0.205397i | ||||
\(325\) | −485.344 | −0.0828371 | ||||||||
\(326\) | 3839.15i | 0.652242i | ||||||||
\(327\) | −1426.41 | − | 1152.46i | −0.241226 | − | 0.194897i | ||||
\(328\) | −1093.09 | −0.184011 | ||||||||
\(329\) | −1400.22 | −0.234641 | ||||||||
\(330\) | −2784.96 | − | 2250.10i | −0.464567 | − | 0.375345i | ||||
\(331\) | −7210.43 | −1.19735 | −0.598673 | − | 0.800994i | \(-0.704305\pi\) | ||||
−0.598673 | + | 0.800994i | \(0.704305\pi\) | |||||||
\(332\) | 1615.35 | 0.267029 | ||||||||
\(333\) | 1458.43 | − | 313.389i | 0.240005 | − | 0.0515724i | ||||
\(334\) | −841.201 | −0.137810 | ||||||||
\(335\) | 72.0373i | 0.0117487i | ||||||||
\(336\) | 200.434 | + | 161.940i | 0.0325433 | + | 0.0262932i | ||||
\(337\) | − | 10749.1i | − | 1.73752i | −0.495237 | − | 0.868758i | \(-0.664919\pi\) | ||
0.495237 | − | 0.868758i | \(-0.335081\pi\) | |||||||
\(338\) | 4317.44i | 0.694786i | ||||||||
\(339\) | 2329.29 | − | 2882.97i | 0.373184 | − | 0.461893i | ||||
\(340\) | 3225.35 | 0.514468 | ||||||||
\(341\) | −2494.57 | −0.396154 | ||||||||
\(342\) | 1053.28 | + | 4901.69i | 0.166534 | + | 0.775008i | ||||
\(343\) | − | 2096.41i | − | 0.330016i | ||||||
\(344\) | 1695.00 | 0.265664 | ||||||||
\(345\) | 2875.09 | − | 2650.99i | 0.448665 | − | 0.413695i | ||||
\(346\) | 6321.49 | 0.982213 | ||||||||
\(347\) | − | 5044.62i | − | 0.780431i | −0.920724 | − | 0.390215i | \(-0.872401\pi\) | ||
0.920724 | − | 0.390215i | \(-0.127599\pi\) | |||||||
\(348\) | −1753.79 | − | 1416.97i | −0.270153 | − | 0.218268i | ||||
\(349\) | −11006.0 | −1.68807 | −0.844034 | − | 0.536290i | \(-0.819825\pi\) | ||||
−0.844034 | + | 0.536290i | \(0.819825\pi\) | |||||||
\(350\) | 486.260 | 0.0742620 | ||||||||
\(351\) | 774.727 | + | 391.495i | 0.117812 | + | 0.0595340i | ||||
\(352\) | − | 1615.77i | − | 0.244661i | ||||||
\(353\) | 6049.33i | 0.912106i | 0.889953 | + | 0.456053i | \(0.150737\pi\) | ||||
−0.889953 | + | 0.456053i | \(0.849263\pi\) | |||||||
\(354\) | −4267.25 | + | 5281.61i | −0.640683 | + | 0.792978i | ||||
\(355\) | 2148.71i | 0.321244i | ||||||||
\(356\) | 118.609 | 0.0176580 | ||||||||
\(357\) | 1480.41 | + | 1196.09i | 0.219472 | + | 0.177322i | ||||
\(358\) | 6632.25 | 0.979121 | ||||||||
\(359\) | −2394.19 | −0.351979 | −0.175989 | − | 0.984392i | \(-0.556312\pi\) | ||||
−0.175989 | + | 0.984392i | \(0.556312\pi\) | |||||||
\(360\) | −1440.91 | + | 309.624i | −0.210952 | + | 0.0453296i | ||||
\(361\) | −1761.00 | −0.256743 | ||||||||
\(362\) | 5980.76 | 0.868347 | ||||||||
\(363\) | −3979.13 | + | 4925.00i | −0.575345 | + | 0.712109i | ||||
\(364\) | 76.7050i | 0.0110451i | ||||||||
\(365\) | −5426.42 | −0.778169 | ||||||||
\(366\) | −4491.09 | + | 5558.66i | −0.641402 | + | 0.793868i | ||||
\(367\) | − | 10274.1i | − | 1.46131i | −0.682744 | − | 0.730657i | \(-0.739214\pi\) | ||
0.682744 | − | 0.730657i | \(-0.260786\pi\) | |||||||
\(368\) | 1746.00 | + | 257.387i | 0.247327 | + | 0.0364598i | ||||
\(369\) | 3606.84 | − | 775.042i | 0.508848 | − | 0.109342i | ||||
\(370\) | −753.945 | −0.105934 | ||||||||
\(371\) | − | 824.074i | − | 0.115320i | ||||||
\(372\) | −645.332 | + | 798.732i | −0.0899433 | + | 0.111323i | ||||
\(373\) | − | 5217.63i | − | 0.724286i | −0.932123 | − | 0.362143i | \(-0.882045\pi\) | ||
0.932123 | − | 0.362143i | \(-0.117955\pi\) | |||||||
\(374\) | − | 11934.1i | − | 1.64999i | ||||||
\(375\) | −4533.03 | + | 5610.56i | −0.624226 | + | 0.772608i | ||||
\(376\) | 3614.19 | 0.495712 | ||||||||
\(377\) | − | 671.167i | − | 0.0916892i | ||||||
\(378\) | −776.189 | − | 392.234i | −0.105616 | − | 0.0533712i | ||||
\(379\) | 10040.7i | 1.36084i | 0.732823 | + | 0.680419i | \(0.238202\pi\) | ||||
−0.732823 | + | 0.680419i | \(0.761798\pi\) | |||||||
\(380\) | − | 2533.96i | − | 0.342077i | ||||||
\(381\) | 6708.76 | − | 8303.48i | 0.902100 | − | 1.11654i | ||||
\(382\) | 7534.31i | 1.00913i | ||||||||
\(383\) | 1660.73 | 0.221565 | 0.110782 | − | 0.993845i | \(-0.464664\pi\) | ||||
0.110782 | + | 0.993845i | \(0.464664\pi\) | |||||||
\(384\) | −517.350 | − | 417.991i | −0.0687524 | − | 0.0555482i | ||||
\(385\) | 1067.80i | 0.141351i | ||||||||
\(386\) | 1978.50i | 0.260888i | ||||||||
\(387\) | −5592.97 | + | 1201.82i | −0.734642 | + | 0.157861i | ||||
\(388\) | 4662.82i | 0.610101i | ||||||||
\(389\) | −14704.5 | −1.91658 | −0.958291 | − | 0.285796i | \(-0.907742\pi\) | ||||
−0.958291 | + | 0.285796i | \(0.907742\pi\) | |||||||
\(390\) | −341.254 | − | 275.715i | −0.0443079 | − | 0.0357983i | ||||
\(391\) | 12896.0 | + | 1901.07i | 1.66797 | + | 0.245885i | ||||
\(392\) | 2667.15i | 0.343652i | ||||||||
\(393\) | 6592.18 | + | 5326.13i | 0.846137 | + | 0.683632i | ||||
\(394\) | −5974.40 | −0.763924 | ||||||||
\(395\) | 8347.73i | 1.06334i | ||||||||
\(396\) | 1145.64 | + | 5331.52i | 0.145380 | + | 0.676563i | ||||
\(397\) | 3102.07 | 0.392162 | 0.196081 | − | 0.980588i | \(-0.437178\pi\) | ||||
0.196081 | + | 0.980588i | \(0.437178\pi\) | |||||||
\(398\) | 5623.68 | 0.708265 | ||||||||
\(399\) | 939.695 | − | 1163.07i | 0.117904 | − | 0.145930i | ||||
\(400\) | −1255.11 | −0.156889 | ||||||||
\(401\) | −10808.9 | −1.34606 | −0.673031 | − | 0.739614i | \(-0.735008\pi\) | ||||
−0.673031 | + | 0.739614i | \(0.735008\pi\) | |||||||
\(402\) | 68.9539 | − | 85.3447i | 0.00855499 | − | 0.0105886i | ||||
\(403\) | −305.671 | −0.0377830 | ||||||||
\(404\) | − | 143.233i | − | 0.0176389i | ||||||
\(405\) | 4535.01 | − | 2043.32i | 0.556411 | − | 0.250700i | ||||
\(406\) | 672.433i | 0.0821978i | ||||||||
\(407\) | 2789.67i | 0.339752i | ||||||||
\(408\) | −3821.17 | − | 3087.29i | −0.463666 | − | 0.374617i | ||||
\(409\) | −13861.0 | −1.67575 | −0.837873 | − | 0.545865i | \(-0.816201\pi\) | ||||
−0.837873 | + | 0.545865i | \(0.816201\pi\) | |||||||
\(410\) | −1864.58 | −0.224598 | ||||||||
\(411\) | −10173.3 | + | 12591.6i | −1.22096 | + | 1.51119i | ||||
\(412\) | 3103.52i | 0.371115i | ||||||||
\(413\) | 2025.06 | 0.241275 | ||||||||
\(414\) | −5943.73 | + | 388.684i | −0.705600 | + | 0.0461420i | ||||
\(415\) | 2755.44 | 0.325926 | ||||||||
\(416\) | − | 197.987i | − | 0.0233344i | ||||||
\(417\) | −6170.48 | + | 7637.24i | −0.724627 | + | 0.896876i | ||||
\(418\) | −9375.89 | −1.09710 | ||||||||
\(419\) | 8102.73 | 0.944736 | 0.472368 | − | 0.881401i | \(-0.343399\pi\) | ||||
0.472368 | + | 0.881401i | \(0.343399\pi\) | |||||||
\(420\) | 341.898 | + | 276.235i | 0.0397212 | + | 0.0320926i | ||||
\(421\) | 1825.10i | 0.211282i | 0.994404 | + | 0.105641i | \(0.0336895\pi\) | ||||
−0.994404 | + | 0.105641i | \(0.966310\pi\) | |||||||
\(422\) | − | 530.159i | − | 0.0611557i | ||||||
\(423\) | −11925.7 | + | 2562.60i | −1.37079 | + | 0.294557i | ||||
\(424\) | 2127.06i | 0.243630i | ||||||||
\(425\) | −9270.29 | −1.05806 | ||||||||
\(426\) | 2056.73 | − | 2545.64i | 0.233918 | − | 0.289522i | ||||
\(427\) | 2131.28 | 0.241546 | ||||||||
\(428\) | −544.589 | −0.0615040 | ||||||||
\(429\) | −1020.17 | + | 1262.67i | −0.114812 | + | 0.142104i | ||||
\(430\) | 2891.32 | 0.324260 | ||||||||
\(431\) | −1126.53 | −0.125901 | −0.0629504 | − | 0.998017i | \(-0.520051\pi\) | ||||
−0.0629504 | + | 0.998017i | \(0.520051\pi\) | |||||||
\(432\) | 2003.46 | + | 1012.42i | 0.223129 | + | 0.112754i | ||||
\(433\) | 6781.15i | 0.752613i | 0.926495 | + | 0.376306i | \(0.122806\pi\) | ||||
−0.926495 | + | 0.376306i | \(0.877194\pi\) | |||||||
\(434\) | 306.247 | 0.0338718 | ||||||||
\(435\) | −2991.60 | − | 2417.05i | −0.329738 | − | 0.266411i | ||||
\(436\) | − | 1411.66i | − | 0.155060i | ||||||
\(437\) | 1493.55 | − | 10131.6i | 0.163493 | − | 1.10906i | ||||
\(438\) | 6428.84 | + | 5194.15i | 0.701328 | + | 0.566635i | ||||
\(439\) | 13687.2 | 1.48806 | 0.744028 | − | 0.668149i | \(-0.232913\pi\) | ||||
0.744028 | + | 0.668149i | \(0.232913\pi\) | |||||||
\(440\) | − | 2756.16i | − | 0.298624i | ||||||
\(441\) | −1891.11 | − | 8800.74i | −0.204202 | − | 0.950302i | ||||
\(442\) | − | 1462.34i | − | 0.157367i | ||||||
\(443\) | − | 9550.89i | − | 1.02433i | −0.858888 | − | 0.512163i | \(-0.828844\pi\) | ||
0.858888 | − | 0.512163i | \(-0.171156\pi\) | |||||||
\(444\) | 893.221 | + | 721.674i | 0.0954739 | + | 0.0771377i | ||||
\(445\) | 202.322 | 0.0215528 | ||||||||
\(446\) | 6378.20i | 0.677167i | ||||||||
\(447\) | 2115.59 | − | 2618.48i | 0.223856 | − | 0.277069i | ||||
\(448\) | 198.361i | 0.0209189i | ||||||||
\(449\) | 15829.0i | 1.66373i | 0.554975 | + | 0.831867i | \(0.312728\pi\) | ||||
−0.554975 | + | 0.831867i | \(0.687272\pi\) | |||||||
\(450\) | 4141.47 | − | 889.922i | 0.433846 | − | 0.0932252i | ||||
\(451\) | 6899.13i | 0.720327i | ||||||||
\(452\) | 2853.16 | 0.296906 | ||||||||
\(453\) | −4600.19 | + | 5693.69i | −0.477121 | + | 0.590536i | ||||
\(454\) | − | 9374.03i | − | 0.969042i | ||||||
\(455\) | 130.843i | 0.0134813i | ||||||||
\(456\) | −2425.50 | + | 3002.05i | −0.249088 | + | 0.308298i | ||||
\(457\) | − | 12373.0i | − | 1.26648i | −0.773954 | − | 0.633242i | \(-0.781724\pi\) | ||
0.773954 | − | 0.633242i | \(-0.218276\pi\) | |||||||
\(458\) | 12135.8 | 1.23815 | ||||||||
\(459\) | 14797.6 | + | 7477.73i | 1.50478 | + | 0.760415i | ||||
\(460\) | 2978.30 | + | 439.048i | 0.301879 | + | 0.0445016i | ||||
\(461\) | − | 6444.45i | − | 0.651080i | −0.945528 | − | 0.325540i | \(-0.894454\pi\) | ||
0.945528 | − | 0.325540i | \(-0.105546\pi\) | |||||||
\(462\) | 1022.10 | − | 1265.06i | 0.102927 | − | 0.127393i | ||||
\(463\) | 125.291 | 0.0125762 | 0.00628808 | − | 0.999980i | \(-0.497998\pi\) | ||||
0.00628808 | + | 0.999980i | \(0.497998\pi\) | |||||||
\(464\) | − | 1735.65i | − | 0.173654i | ||||||
\(465\) | −1100.80 | + | 1362.47i | −0.109782 | + | 0.135877i | ||||
\(466\) | 3655.82 | 0.363418 | ||||||||
\(467\) | 6489.03 | 0.642990 | 0.321495 | − | 0.946911i | \(-0.395815\pi\) | ||||
0.321495 | + | 0.946911i | \(0.395815\pi\) | |||||||
\(468\) | 140.381 | + | 653.295i | 0.0138656 | + | 0.0645268i | ||||
\(469\) | −32.7226 | −0.00322173 | ||||||||
\(470\) | 6165.05 | 0.605048 | ||||||||
\(471\) | −3386.26 | − | 2735.91i | −0.331275 | − | 0.267652i | ||||
\(472\) | −5226.98 | −0.509728 | ||||||||
\(473\) | − | 10698.2i | − | 1.03996i | ||||||
\(474\) | 7990.42 | − | 9889.80i | 0.774287 | − | 0.958341i | ||||
\(475\) | 7283.10i | 0.703519i | ||||||||
\(476\) | 1465.10i | 0.141077i | ||||||||
\(477\) | −1508.17 | − | 7018.63i | −0.144768 | − | 0.673712i | ||||
\(478\) | −6908.94 | −0.661104 | ||||||||
\(479\) | 11843.7 | 1.12976 | 0.564879 | − | 0.825174i | \(-0.308923\pi\) | ||||
0.564879 | + | 0.825174i | \(0.308923\pi\) | |||||||
\(480\) | −882.491 | − | 713.005i | −0.0839167 | − | 0.0678001i | ||||
\(481\) | 341.831i | 0.0324036i | ||||||||
\(482\) | 1561.35 | 0.147547 | ||||||||
\(483\) | 1204.20 | + | 1306.00i | 0.113443 | + | 0.123033i | ||||
\(484\) | −4874.06 | −0.457745 | ||||||||
\(485\) | 7953.80i | 0.744667i | ||||||||
\(486\) | −7328.63 | − | 1920.11i | −0.684019 | − | 0.179214i | ||||
\(487\) | −14770.3 | −1.37435 | −0.687173 | − | 0.726494i | \(-0.741149\pi\) | ||||
−0.687173 | + | 0.726494i | \(0.741149\pi\) | |||||||
\(488\) | −5501.17 | −0.510300 | ||||||||
\(489\) | 6268.48 | − | 7758.54i | 0.579694 | − | 0.717492i | ||||
\(490\) | 4549.60i | 0.419449i | ||||||||
\(491\) | 89.5204i | 0.00822811i | 0.999992 | + | 0.00411405i | \(0.00130955\pi\) | ||||
−0.999992 | + | 0.00411405i | \(0.998690\pi\) | |||||||
\(492\) | 2209.02 | + | 1784.77i | 0.202420 | + | 0.163544i | ||||
\(493\) | − | 12819.6i | − | 1.17113i | ||||||
\(494\) | −1148.87 | −0.104636 | ||||||||
\(495\) | 1954.22 | + | 9094.45i | 0.177446 | + | 0.825788i | ||||
\(496\) | −790.472 | −0.0715589 | ||||||||
\(497\) | −976.040 | −0.0880913 | ||||||||
\(498\) | −3264.45 | − | 2637.50i | −0.293742 | − | 0.237328i | ||||
\(499\) | 3686.92 | 0.330760 | 0.165380 | − | 0.986230i | \(-0.447115\pi\) | ||||
0.165380 | + | 0.986230i | \(0.447115\pi\) | |||||||
\(500\) | −5552.54 | −0.496634 | ||||||||
\(501\) | 1699.98 | + | 1373.49i | 0.151596 | + | 0.122481i | ||||
\(502\) | − | 11416.3i | − | 1.01501i | ||||||
\(503\) | 12832.8 | 1.13755 | 0.568775 | − | 0.822493i | \(-0.307418\pi\) | ||||
0.568775 | + | 0.822493i | \(0.307418\pi\) | |||||||
\(504\) | −140.646 | − | 654.528i | −0.0124303 | − | 0.0578472i | ||||
\(505\) | − | 244.325i | − | 0.0215294i | ||||||
\(506\) | 1624.52 | − | 11020.0i | 0.142725 | − | 0.968181i | ||||
\(507\) | 7049.42 | − | 8725.12i | 0.617506 | − | 0.764292i | ||||
\(508\) | 8217.60 | 0.717711 | ||||||||
\(509\) | 8382.75i | 0.729978i | 0.931012 | + | 0.364989i | \(0.118927\pi\) | ||||
−0.931012 | + | 0.364989i | \(0.881073\pi\) | |||||||
\(510\) | −6518.11 | − | 5266.27i | −0.565935 | − | 0.457244i | ||||
\(511\) | − | 2464.93i | − | 0.213389i | ||||||
\(512\) | − | 512.000i | − | 0.0441942i | ||||||
\(513\) | 5874.79 | − | 11625.6i | 0.505611 | − | 1.00055i | ||||
\(514\) | 11218.3 | 0.962677 | ||||||||
\(515\) | 5293.95i | 0.452970i | ||||||||
\(516\) | −3425.43 | − | 2767.56i | −0.292241 | − | 0.236115i | ||||
\(517\) | − | 22811.3i | − | 1.94050i | ||||||
\(518\) | − | 342.476i | − | 0.0290493i | ||||||
\(519\) | −12775.1 | − | 10321.6i | −1.08047 | − | 0.872963i | ||||
\(520\) | − | 337.725i | − | 0.0284812i | ||||||
\(521\) | −8122.81 | −0.683046 | −0.341523 | − | 0.939873i | \(-0.610943\pi\) | ||||
−0.341523 | + | 0.939873i | \(0.610943\pi\) | |||||||
\(522\) | 1230.64 | + | 5727.10i | 0.103187 | + | 0.480208i | ||||
\(523\) | 21756.6i | 1.81902i | 0.415680 | + | 0.909511i | \(0.363544\pi\) | ||||
−0.415680 | + | 0.909511i | \(0.636456\pi\) | |||||||
\(524\) | 6524.01i | 0.543898i | ||||||||
\(525\) | −982.683 | − | 793.954i | −0.0816911 | − | 0.0660019i | ||||
\(526\) | − | 1412.77i | − | 0.117109i | ||||||
\(527\) | −5838.45 | −0.482593 | ||||||||
\(528\) | −2638.19 | + | 3265.31i | −0.217448 | + | 0.269137i | ||||
\(529\) | 11649.4 | + | 3510.91i | 0.957462 | + | 0.288560i | ||||
\(530\) | 3628.32i | 0.297366i | ||||||||
\(531\) | 17247.4 | − | 3706.13i | 1.40955 | − | 0.302886i | ||||
\(532\) | 1151.04 | 0.0938042 | ||||||||
\(533\) | 845.382i | 0.0687008i | ||||||||
\(534\) | −239.697 | − | 193.662i | −0.0194245 | − | 0.0156940i | ||||
\(535\) | −928.955 | −0.0750696 | ||||||||
\(536\) | 84.4621 | 0.00680635 | ||||||||
\(537\) | −13403.1 | − | 10829.0i | −1.07707 | − | 0.870214i | ||||
\(538\) | −3634.59 | −0.291261 | ||||||||
\(539\) | 16834.0 | 1.34525 | ||||||||
\(540\) | 3417.49 | + | 1726.97i | 0.272343 | + | 0.137624i | ||||
\(541\) | −2142.23 | −0.170243 | −0.0851217 | − | 0.996371i | \(-0.527128\pi\) | ||||
−0.0851217 | + | 0.996371i | \(0.527128\pi\) | |||||||
\(542\) | 9715.15i | 0.769929i | ||||||||
\(543\) | −12086.5 | − | 9765.25i | −0.955216 | − | 0.771762i | ||||
\(544\) | − | 3781.65i | − | 0.298046i | ||||||
\(545\) | − | 2408.00i | − | 0.189261i | ||||||
\(546\) | 125.242 | − | 155.013i | 0.00981661 | − | 0.0121501i | ||||
\(547\) | −19790.3 | −1.54693 | −0.773465 | − | 0.633839i | \(-0.781478\pi\) | ||||
−0.773465 | + | 0.633839i | \(0.781478\pi\) | |||||||
\(548\) | −12461.4 | −0.971395 | ||||||||
\(549\) | 18152.1 | − | 3900.54i | 1.41113 | − | 0.303226i | ||||
\(550\) | 7921.75i | 0.614154i | ||||||||
\(551\) | −10071.6 | −0.778698 | ||||||||
\(552\) | −3108.23 | − | 3370.98i | −0.239665 | − | 0.259924i | ||||
\(553\) | −3791.92 | −0.291589 | ||||||||
\(554\) | 1247.47i | 0.0956674i | ||||||||
\(555\) | 1523.65 | + | 1231.02i | 0.116532 | + | 0.0941515i | ||||
\(556\) | −7558.26 | −0.576513 | ||||||||
\(557\) | −9074.29 | −0.690287 | −0.345144 | − | 0.938550i | \(-0.612170\pi\) | ||||
−0.345144 | + | 0.938550i | \(0.612170\pi\) | |||||||
\(558\) | 2608.30 | − | 560.475i | 0.197882 | − | 0.0425211i | ||||
\(559\) | − | 1310.89i | − | 0.0991859i | ||||||
\(560\) | 338.362i | 0.0255329i | ||||||||
\(561\) | −19485.7 | + | 24117.6i | −1.46647 | + | 1.81506i | ||||
\(562\) | 844.971i | 0.0634217i | ||||||||
\(563\) | 25234.5 | 1.88900 | 0.944499 | − | 0.328514i | \(-0.106548\pi\) | ||||
0.944499 | + | 0.328514i | \(0.106548\pi\) | |||||||
\(564\) | −7303.92 | − | 5901.17i | −0.545302 | − | 0.440574i | ||||
\(565\) | 4866.89 | 0.362392 | ||||||||
\(566\) | −11927.9 | −0.885806 | ||||||||
\(567\) | 928.170 | + | 2060.01i | 0.0687469 | + | 0.152579i | ||||
\(568\) | 2519.31 | 0.186105 | ||||||||
\(569\) | 13272.6 | 0.977887 | 0.488944 | − | 0.872315i | \(-0.337382\pi\) | ||||
0.488944 | + | 0.872315i | \(0.337382\pi\) | |||||||
\(570\) | −4137.39 | + | 5120.87i | −0.304028 | + | 0.376298i | ||||
\(571\) | 17338.2i | 1.27072i | 0.772216 | + | 0.635360i | \(0.219148\pi\) | ||||
−0.772216 | + | 0.635360i | \(0.780852\pi\) | |||||||
\(572\) | −1249.61 | −0.0913445 | ||||||||
\(573\) | 12301.9 | − | 15226.1i | 0.896889 | − | 1.11009i | ||||
\(574\) | − | 846.977i | − | 0.0615891i | ||||||
\(575\) | −8560.24 | − | 1261.91i | −0.620846 | − | 0.0915223i | ||||
\(576\) | 363.028 | + | 1689.44i | 0.0262607 | + | 0.122210i | ||||
\(577\) | 18444.3 | 1.33076 | 0.665378 | − | 0.746507i | \(-0.268270\pi\) | ||||
0.665378 | + | 0.746507i | \(0.268270\pi\) | |||||||
\(578\) | − | 18105.4i | − | 1.30291i | ||||||
\(579\) | 3230.44 | − | 3998.34i | 0.231870 | − | 0.286987i | ||||
\(580\) | − | 2960.66i | − | 0.211956i | ||||||
\(581\) | 1251.65i | 0.0893753i | ||||||||
\(582\) | 7613.35 | − | 9423.10i | 0.542240 | − | 0.671134i | ||||
\(583\) | 13425.1 | 0.953710 | ||||||||
\(584\) | 6362.35i | 0.450815i | ||||||||
\(585\) | 239.460 | + | 1114.38i | 0.0169238 | + | 0.0787591i | ||||
\(586\) | 7120.12i | 0.501927i | ||||||||
\(587\) | 11823.9i | 0.831386i | 0.909505 | + | 0.415693i | \(0.136461\pi\) | ||||
−0.909505 | + | 0.415693i | \(0.863539\pi\) | |||||||
\(588\) | 4354.86 | − | 5390.05i | 0.305428 | − | 0.378030i | ||||
\(589\) | 4586.91i | 0.320883i | ||||||||
\(590\) | −8916.14 | −0.622155 | ||||||||
\(591\) | 12073.7 | + | 9754.87i | 0.840346 | + | 0.678954i | ||||
\(592\) | 883.983i | 0.0613708i | ||||||||
\(593\) | − | 18477.2i | − | 1.27954i | −0.768566 | − | 0.639770i | \(-0.779029\pi\) | ||
0.768566 | − | 0.639770i | \(-0.220971\pi\) | |||||||
\(594\) | 6389.95 | − | 12645.0i | 0.441385 | − | 0.873455i | ||||
\(595\) | 2499.15i | 0.172194i | ||||||||
\(596\) | 2591.40 | 0.178100 | ||||||||
\(597\) | −11364.9 | − | 9182.21i | −0.779119 | − | 0.629485i | ||||
\(598\) | 199.060 | − | 1350.33i | 0.0136123 | − | 0.0923398i | ||||
\(599\) | − | 21828.3i | − | 1.48895i | −0.667650 | − | 0.744475i | \(-0.732700\pi\) | ||
0.667650 | − | 0.744475i | \(-0.267300\pi\) | |||||||
\(600\) | 2536.46 | + | 2049.32i | 0.172584 | + | 0.139438i | ||||
\(601\) | −352.046 | −0.0238940 | −0.0119470 | − | 0.999929i | \(-0.503803\pi\) | ||||
−0.0119470 | + | 0.999929i | \(0.503803\pi\) | |||||||
\(602\) | 1313.37i | 0.0889185i | ||||||||
\(603\) | −278.698 | + | 59.8868i | −0.0188216 | + | 0.00404441i | ||||
\(604\) | −5634.80 | −0.379597 | ||||||||
\(605\) | −8314.13 | −0.558707 | ||||||||
\(606\) | −233.867 | + | 289.459i | −0.0156769 | + | 0.0194034i | ||||
\(607\) | −15282.5 | −1.02191 | −0.510953 | − | 0.859609i | \(-0.670707\pi\) | ||||
−0.510953 | + | 0.859609i | \(0.670707\pi\) | |||||||
\(608\) | −2971.01 | −0.198175 | ||||||||
\(609\) | 1097.93 | − | 1358.92i | 0.0730550 | − | 0.0904207i | ||||
\(610\) | −9383.84 | −0.622853 | ||||||||
\(611\) | − | 2795.17i | − | 0.185074i | ||||||
\(612\) | 2681.33 | + | 12478.2i | 0.177102 | + | 0.824187i | ||||
\(613\) | 20870.2i | 1.37511i | 0.726134 | + | 0.687553i | \(0.241315\pi\) | ||||
−0.726134 | + | 0.687553i | \(0.758685\pi\) | |||||||
\(614\) | − | 2819.55i | − | 0.185322i | ||||||
\(615\) | 3768.13 | + | 3044.44i | 0.247066 | + | 0.199616i | ||||
\(616\) | 1251.97 | 0.0818887 | ||||||||
\(617\) | 11232.5 | 0.732906 | 0.366453 | − | 0.930437i | \(-0.380572\pi\) | ||||
0.366453 | + | 0.930437i | \(0.380572\pi\) | |||||||
\(618\) | 5067.36 | − | 6271.90i | 0.329837 | − | 0.408241i | ||||
\(619\) | 11245.6i | 0.730206i | 0.930967 | + | 0.365103i | \(0.118966\pi\) | ||||
−0.930967 | + | 0.365103i | \(0.881034\pi\) | |||||||
\(620\) | −1348.38 | −0.0873422 | ||||||||
\(621\) | 12646.3 | + | 8919.29i | 0.817197 | + | 0.576359i | ||||
\(622\) | 18788.5 | 1.21118 | ||||||||
\(623\) | 91.9038i | 0.00591019i | ||||||||
\(624\) | −323.269 | + | 400.113i | −0.0207390 | + | 0.0256688i | ||||
\(625\) | 334.099 | 0.0213824 | ||||||||
\(626\) | −3315.58 | −0.211689 | ||||||||
\(627\) | 18947.7 | + | 15308.7i | 1.20686 | + | 0.975075i | ||||
\(628\) | − | 3351.24i | − | 0.212944i | ||||||
\(629\) | 6529.13i | 0.413885i | ||||||||
\(630\) | −239.912 | − | 1116.49i | −0.0151719 | − | 0.0706062i | ||||
\(631\) | 22890.2i | 1.44413i | 0.691827 | + | 0.722064i | \(0.256806\pi\) | ||||
−0.691827 | + | 0.722064i | \(0.743194\pi\) | |||||||
\(632\) | 9787.52 | 0.616023 | ||||||||
\(633\) | −865.631 | + | 1071.40i | −0.0543535 | + | 0.0672737i | ||||
\(634\) | 11295.3 | 0.707560 | ||||||||
\(635\) | 14017.5 | 0.876012 | ||||||||
\(636\) | 3473.02 | − | 4298.58i | 0.216532 | − | 0.268003i | ||||
\(637\) | 2062.74 | 0.128303 | ||||||||
\(638\) | −10954.7 | −0.679784 | ||||||||
\(639\) | −8312.91 | + | 1786.29i | −0.514638 | + | 0.110586i | ||||
\(640\) | − | 873.364i | − | 0.0539418i | ||||||
\(641\) | −18165.2 | −1.11931 | −0.559657 | − | 0.828724i | \(-0.689067\pi\) | ||||
−0.559657 | + | 0.828724i | \(0.689067\pi\) | |||||||
\(642\) | 1100.56 | + | 889.193i | 0.0676568 | + | 0.0546630i | ||||
\(643\) | 12929.0i | 0.792954i | 0.918045 | + | 0.396477i | \(0.129767\pi\) | ||||
−0.918045 | + | 0.396477i | \(0.870233\pi\) | |||||||
\(644\) | −199.436 | + | 1352.88i | −0.0122032 | + | 0.0827810i | ||||
\(645\) | −5843.07 | − | 4720.88i | −0.356699 | − | 0.288193i | ||||
\(646\) | −21943.9 | −1.33649 | ||||||||
\(647\) | − | 23926.6i | − | 1.45387i | −0.686708 | − | 0.726933i | \(-0.740945\pi\) | ||
0.686708 | − | 0.726933i | \(-0.259055\pi\) | |||||||
\(648\) | −2395.75 | − | 5317.20i | −0.145238 | − | 0.322345i | ||||
\(649\) | 32990.6i | 1.99537i | ||||||||
\(650\) | 970.688i | 0.0585747i | ||||||||
\(651\) | −618.896 | − | 500.034i | −0.0372603 | − | 0.0301043i | ||||
\(652\) | 7678.30 | 0.461205 | ||||||||
\(653\) | 16405.2i | 0.983134i | 0.870840 | + | 0.491567i | \(0.163576\pi\) | ||||
−0.870840 | + | 0.491567i | \(0.836424\pi\) | |||||||
\(654\) | −2304.93 | + | 2852.83i | −0.137813 | + | 0.170572i | ||||
\(655\) | 11128.6i | 0.663862i | ||||||||
\(656\) | 2186.18i | 0.130116i | ||||||||
\(657\) | −4511.15 | − | 20993.7i | −0.267879 | − | 1.24664i | ||||
\(658\) | 2800.44i | 0.165916i | ||||||||
\(659\) | 3748.37 | 0.221572 | 0.110786 | − | 0.993844i | \(-0.464663\pi\) | ||||
0.110786 | + | 0.993844i | \(0.464663\pi\) | |||||||
\(660\) | −4500.20 | + | 5569.92i | −0.265409 | + | 0.328499i | ||||
\(661\) | − | 20659.5i | − | 1.21568i | −0.794060 | − | 0.607839i | \(-0.792037\pi\) | ||
0.794060 | − | 0.607839i | \(-0.207963\pi\) | |||||||
\(662\) | 14420.9i | 0.846651i | ||||||||
\(663\) | −2387.68 | + | 2955.24i | −0.139864 | + | 0.173110i | ||||
\(664\) | − | 3230.69i | − | 0.188818i | ||||||
\(665\) | 1963.43 | 0.114494 | ||||||||
\(666\) | −626.778 | − | 2916.86i | −0.0364672 | − | 0.169709i | ||||
\(667\) | 1745.06 | − | 11837.7i | 0.101303 | − | 0.687191i | ||||
\(668\) | 1682.40i | 0.0974462i | ||||||||
\(669\) | 10414.2 | − | 12889.7i | 0.601847 | − | 0.744910i | ||||
\(670\) | 144.075 | 0.00830759 | ||||||||
\(671\) | 34721.1i | 1.99761i | ||||||||
\(672\) | 323.879 | − | 400.868i | 0.0185921 | − | 0.0230116i | ||||
\(673\) | 20270.8 | 1.16104 | 0.580521 | − | 0.814245i | \(-0.302849\pi\) | ||||
0.580521 | + | 0.814245i | \(0.302849\pi\) | |||||||
\(674\) | −21498.3 | −1.22861 | ||||||||
\(675\) | −9822.54 | − | 4963.65i | −0.560103 | − | 0.283038i | ||||
\(676\) | 8634.88 | 0.491288 | ||||||||
\(677\) | −15499.8 | −0.879922 | −0.439961 | − | 0.898017i | \(-0.645008\pi\) | ||||
−0.439961 | + | 0.898017i | \(0.645008\pi\) | |||||||
\(678\) | −5765.95 | − | 4658.57i | −0.326608 | − | 0.263881i | ||||
\(679\) | −3612.98 | −0.204202 | ||||||||
\(680\) | − | 6450.70i | − | 0.363784i | ||||||
\(681\) | −15305.7 | + | 18944.0i | −0.861257 | + | 1.06598i | ||||
\(682\) | 4989.13i | 0.280123i | ||||||||
\(683\) | 12938.6i | 0.724865i | 0.932010 | + | 0.362433i | \(0.118054\pi\) | ||||
−0.932010 | + | 0.362433i | \(0.881946\pi\) | |||||||
\(684\) | 9803.37 | − | 2106.56i | 0.548014 | − | 0.117758i | ||||
\(685\) | −21256.5 | −1.18565 | ||||||||
\(686\) | −4192.82 | −0.233356 | ||||||||
\(687\) | −24525.3 | − | 19815.1i | −1.36201 | − | 1.10043i | ||||
\(688\) | − | 3390.01i | − | 0.187853i | ||||||
\(689\) | 1645.04 | 0.0909596 | ||||||||
\(690\) | −5301.99 | − | 5750.18i | −0.292526 | − | 0.317254i | ||||
\(691\) | −9114.95 | −0.501807 | −0.250904 | − | 0.968012i | \(-0.580728\pi\) | ||||
−0.250904 | + | 0.968012i | \(0.580728\pi\) | |||||||
\(692\) | − | 12643.0i | − | 0.694529i | ||||||
\(693\) | −4131.11 | + | 887.697i | −0.226447 | + | 0.0486592i | ||||
\(694\) | −10089.2 | −0.551848 | ||||||||
\(695\) | −12892.8 | −0.703672 | ||||||||
\(696\) | −2833.94 | + | 3507.58i | −0.154339 | + | 0.191027i | ||||
\(697\) | 16147.2i | 0.877500i | ||||||||
\(698\) | 22011.9i | 1.19364i | ||||||||
\(699\) | −7388.05 | − | 5969.14i | −0.399774 | − | 0.322995i | ||||
\(700\) | − | 972.520i | − | 0.0525112i | ||||||
\(701\) | −10252.8 | −0.552417 | −0.276209 | − | 0.961098i | \(-0.589078\pi\) | ||||
−0.276209 | + | 0.961098i | \(0.589078\pi\) | |||||||
\(702\) | 782.990 | − | 1549.45i | 0.0420969 | − | 0.0833054i | ||||
\(703\) | 5129.53 | 0.275198 | ||||||||
\(704\) | −3231.53 | −0.173002 | ||||||||
\(705\) | −12458.9 | − | 10066.1i | −0.665576 | − | 0.537749i | ||||
\(706\) | 12098.7 | 0.644956 | ||||||||
\(707\) | 110.984 | 0.00590377 | ||||||||
\(708\) | 10563.2 | + | 8534.50i | 0.560720 | + | 0.453031i | ||||
\(709\) | − | 30842.0i | − | 1.63370i | −0.576848 | − | 0.816852i | \(-0.695717\pi\) | ||
0.576848 | − | 0.816852i | \(-0.304283\pi\) | |||||||
\(710\) | 4297.41 | 0.227153 | ||||||||
\(711\) | −32295.7 | + | 6939.73i | −1.70349 | + | 0.366048i | ||||
\(712\) | − | 237.218i | − | 0.0124861i | ||||||
\(713\) | −5391.25 | − | 794.754i | −0.283175 | − | 0.0417444i | ||||
\(714\) | 2392.18 | − | 2960.82i | 0.125385 | − | 0.155190i | ||||
\(715\) | −2131.58 | −0.111492 | ||||||||
\(716\) | − | 13264.5i | − | 0.692343i | ||||||
\(717\) | 13962.3 | + | 11280.8i | 0.727240 | + | 0.587570i | ||||
\(718\) | 4788.38i | 0.248887i | ||||||||
\(719\) | − | 14449.8i | − | 0.749496i | −0.927127 | − | 0.374748i | \(-0.877729\pi\) | ||
0.927127 | − | 0.374748i | \(-0.122271\pi\) | |||||||
\(720\) | 619.249 | + | 2881.82i | 0.0320528 | + | 0.149166i | ||||
\(721\) | −2404.75 | −0.124213 | ||||||||
\(722\) | 3522.00i | 0.181545i | ||||||||
\(723\) | −3155.34 | − | 2549.34i | −0.162308 | − | 0.131136i | ||||
\(724\) | − | 11961.5i | − | 0.614014i | ||||||
\(725\) | 8509.53i | 0.435912i | ||||||||
\(726\) | 9850.00 | + | 7958.26i | 0.503537 | + | 0.406830i | ||||
\(727\) | − | 32756.4i | − | 1.67107i | −0.549437 | − | 0.835535i | \(-0.685158\pi\) | ||
0.549437 | − | 0.835535i | \(-0.314842\pi\) | |||||||
\(728\) | 153.410 | 0.00781010 | ||||||||
\(729\) | 11675.3 | + | 15846.4i | 0.593167 | + | 0.805079i | ||||
\(730\) | 10852.8i | 0.550248i | ||||||||
\(731\) | − | 25038.7i | − | 1.26688i | ||||||
\(732\) | 11117.3 | + | 8982.18i | 0.561349 | + | 0.453540i | ||||
\(733\) | 38694.2i | 1.94980i | 0.222639 | + | 0.974901i | \(0.428533\pi\) | ||||
−0.222639 | + | 0.974901i | \(0.571467\pi\) | |||||||
\(734\) | −20548.2 | −1.03331 | ||||||||
\(735\) | 7428.48 | − | 9194.28i | 0.372794 | − | 0.461410i | ||||
\(736\) | 514.774 | − | 3491.99i | 0.0257810 | − | 0.174887i | ||||
\(737\) | − | 533.090i | − | 0.0266440i | ||||||
\(738\) | −1550.08 | − | 7213.69i | −0.0773162 | − | 0.359810i | ||||
\(739\) | 18619.1 | 0.926813 | 0.463407 | − | 0.886146i | \(-0.346627\pi\) | ||||
0.463407 | + | 0.886146i | \(0.346627\pi\) | |||||||
\(740\) | 1507.89i | 0.0749070i | ||||||||
\(741\) | 2321.75 | + | 1875.85i | 0.115104 | + | 0.0929974i | ||||
\(742\) | −1648.15 | −0.0815437 | ||||||||
\(743\) | 14237.7 | 0.703003 | 0.351502 | − | 0.936187i | \(-0.385671\pi\) | ||||
0.351502 | + | 0.936187i | \(0.385671\pi\) | |||||||
\(744\) | 1597.46 | + | 1290.66i | 0.0787176 | + | 0.0635995i | ||||
\(745\) | 4420.38 | 0.217383 | ||||||||
\(746\) | −10435.3 | −0.512147 | ||||||||
\(747\) | 2290.68 | + | 10660.2i | 0.112198 | + | 0.522139i | ||||
\(748\) | −23868.2 | −1.16672 | ||||||||
\(749\) | − | 421.973i | − | 0.0205855i | ||||||
\(750\) | 11221.1 | + | 9066.06i | 0.546317 | + | 0.441394i | ||||
\(751\) | − | 30448.9i | − | 1.47949i | −0.672887 | − | 0.739745i | \(-0.734946\pi\) | ||
0.672887 | − | 0.739745i | \(-0.265054\pi\) | |||||||
\(752\) | − | 7228.38i | − | 0.350521i | ||||||
\(753\) | −18640.3 | + | 23071.2i | −0.902111 | + | 1.11655i | ||||
\(754\) | −1342.33 | −0.0648341 | ||||||||
\(755\) | −9611.79 | −0.463323 | ||||||||
\(756\) | −784.467 | + | 1552.38i | −0.0377392 | + | 0.0746818i | ||||
\(757\) | − | 1061.16i | − | 0.0509492i | −0.999675 | − | 0.0254746i | \(-0.991890\pi\) | ||
0.999675 | − | 0.0254746i | \(-0.00810970\pi\) | |||||||
\(758\) | 20081.5 | 0.962258 | ||||||||
\(759\) | −21276.2 | + | 19617.9i | −1.01749 | + | 0.938187i | ||||
\(760\) | −5067.91 | −0.241885 | ||||||||
\(761\) | 3736.49i | 0.177986i | 0.996032 | + | 0.0889932i | \(0.0283649\pi\) | ||||
−0.996032 | + | 0.0889932i | \(0.971635\pi\) | |||||||
\(762\) | −16607.0 | − | 13417.5i | −0.789510 | − | 0.637881i | ||||
\(763\) | 1093.82 | 0.0518991 | ||||||||
\(764\) | 15068.6 | 0.713565 | ||||||||
\(765\) | 4573.79 | + | 21285.2i | 0.216164 | + | 1.00597i | ||||
\(766\) | − | 3321.46i | − | 0.156670i | ||||||
\(767\) | 4042.49i | 0.190307i | ||||||||
\(768\) | −835.982 | + | 1034.70i | −0.0392785 | + | 0.0486153i | ||||
\(769\) | − | 13779.4i | − | 0.646160i | −0.946372 | − | 0.323080i | \(-0.895282\pi\) | ||
0.946372 | − | 0.323080i | \(-0.104718\pi\) | |||||||
\(770\) | 2135.60 | 0.0999504 | ||||||||
\(771\) | −22671.0 | − | 18316.9i | −1.05898 | − | 0.855600i | ||||
\(772\) | 3956.99 | 0.184476 | ||||||||
\(773\) | 6676.82 | 0.310671 | 0.155336 | − | 0.987862i | \(-0.450354\pi\) | ||||
0.155336 | + | 0.987862i | \(0.450354\pi\) | |||||||
\(774\) | 2403.64 | + | 11185.9i | 0.111624 | + | 0.519470i | ||||
\(775\) | 3875.51 | 0.179629 | ||||||||
\(776\) | 9325.65 | 0.431406 | ||||||||
\(777\) | −559.187 | + | 692.110i | −0.0258182 | + | 0.0319554i | ||||
\(778\) | 29409.1i | 1.35523i | ||||||||
\(779\) | 12685.8 | 0.583463 | ||||||||
\(780\) | −551.429 | + | 682.508i | −0.0253132 | + | 0.0313304i | ||||
\(781\) | − | 15900.8i | − | 0.728524i | ||||||
\(782\) | 3802.13 | − | 25792.0i | 0.173867 | − | 1.17944i | ||||
\(783\) | 6864.07 | − | 13583.3i | 0.313285 | − | 0.619957i | ||||
\(784\) | 5334.30 | 0.242998 | ||||||||
\(785\) | − | 5716.51i | − | 0.259912i | ||||||
\(786\) | 10652.3 | − | 13184.4i | 0.483401 | − | 0.598309i | ||||
\(787\) | − | 36090.5i | − | 1.63467i | −0.576160 | − | 0.817337i | \(-0.695449\pi\) | ||
0.576160 | − | 0.817337i | \(-0.304551\pi\) | |||||||
\(788\) | 11948.8i | 0.540176i | ||||||||
\(789\) | −2306.73 | + | 2855.06i | −0.104083 | + | 0.128825i | ||||
\(790\) | 16695.5 | 0.751896 | ||||||||
\(791\) | 2210.76i | 0.0993750i | ||||||||
\(792\) | 10663.0 | − | 2291.28i | 0.478402 | − | 0.102799i | ||||
\(793\) | 4254.54i | 0.190521i | ||||||||
\(794\) | − | 6204.14i | − | 0.277300i | ||||||
\(795\) | 5924.24 | − | 7332.48i | 0.264291 | − | 0.327115i | ||||
\(796\) | − | 11247.4i | − | 0.500819i | ||||||
\(797\) | 34615.0 | 1.53842 | 0.769212 | − | 0.638993i | \(-0.220649\pi\) | ||||
0.769212 | + | 0.638993i | \(0.220649\pi\) | |||||||
\(798\) | −2326.13 | − | 1879.39i | −0.103188 | − | 0.0833705i | ||||
\(799\) | − | 53389.0i | − | 2.36391i | ||||||
\(800\) | 2510.22i | 0.110937i | ||||||||
\(801\) | 168.197 | + | 782.743i | 0.00741939 | + | 0.0345279i | ||||
\(802\) | 21617.8i | 0.951810i | ||||||||
\(803\) | 40156.6 | 1.76475 | ||||||||
\(804\) | −170.689 | − | 137.908i | −0.00748725 | − | 0.00604929i | ||||
\(805\) | −340.195 | + | 2307.73i | −0.0148948 | + | 0.101040i | ||||
\(806\) | 611.341i | 0.0267166i | ||||||||
\(807\) | 7345.15 | + | 5934.48i | 0.320398 | + | 0.258864i | ||||
\(808\) | −286.466 | −0.0124726 | ||||||||
\(809\) | 32639.7i | 1.41848i | 0.704966 | + | 0.709241i | \(0.250962\pi\) | ||||
−0.704966 | + | 0.709241i | \(0.749038\pi\) | |||||||
\(810\) | −4086.65 | − | 9070.02i | −0.177272 | − | 0.393442i | ||||
\(811\) | 11072.4 | 0.479413 | 0.239707 | − | 0.970845i | \(-0.422949\pi\) | ||||
0.239707 | + | 0.970845i | \(0.422949\pi\) | |||||||
\(812\) | 1344.87 | 0.0581226 | ||||||||
\(813\) | 15862.7 | − | 19633.3i | 0.684290 | − | 0.846951i | ||||
\(814\) | 5579.34 | 0.240241 | ||||||||
\(815\) | 13097.6 | 0.562930 | ||||||||
\(816\) | −6174.59 | + | 7642.33i | −0.264894 | + | 0.327862i | ||||
\(817\) | −19671.3 | −0.842366 | ||||||||
\(818\) | 27721.9i | 1.18493i | ||||||||
\(819\) | −506.204 | + | 108.774i | −0.0215973 | + | 0.00464085i | ||||
\(820\) | 3729.16i | 0.158815i | ||||||||
\(821\) | − | 36531.8i | − | 1.55295i | −0.630150 | − | 0.776473i | \(-0.717007\pi\) | ||
0.630150 | − | 0.776473i | \(-0.282993\pi\) | |||||||
\(822\) | 25183.2 | + | 20346.7i | 1.06857 | + | 0.863348i | ||||
\(823\) | −20802.7 | −0.881087 | −0.440544 | − | 0.897731i | \(-0.645214\pi\) | ||||
−0.440544 | + | 0.897731i | \(0.645214\pi\) | |||||||
\(824\) | 6207.04 | 0.262418 | ||||||||
\(825\) | 12934.5 | − | 16009.1i | 0.545843 | − | 0.675593i | ||||
\(826\) | − | 4050.11i | − | 0.170607i | ||||||
\(827\) | 6969.33 | 0.293044 | 0.146522 | − | 0.989207i | \(-0.453192\pi\) | ||||
0.146522 | + | 0.989207i | \(0.453192\pi\) | |||||||
\(828\) | 777.368 | + | 11887.5i | 0.0326273 | + | 0.498934i | ||||
\(829\) | −38446.7 | −1.61075 | −0.805374 | − | 0.592767i | \(-0.798036\pi\) | ||||
−0.805374 | + | 0.592767i | \(0.798036\pi\) | |||||||
\(830\) | − | 5510.88i | − | 0.230464i | ||||||
\(831\) | 2036.83 | − | 2521.01i | 0.0850265 | − | 0.105238i | ||||
\(832\) | −395.975 | −0.0164999 | ||||||||
\(833\) | 39399.3 | 1.63878 | ||||||||
\(834\) | 15274.5 | + | 12341.0i | 0.634187 | + | 0.512389i | ||||
\(835\) | 2869.82i | 0.118939i | ||||||||
\(836\) | 18751.8i | 0.775770i | ||||||||
\(837\) | −6186.25 | − | 3126.12i | −0.255470 | − | 0.129097i | ||||
\(838\) | − | 16205.5i | − | 0.668029i | ||||||
\(839\) | −39708.6 | −1.63396 | −0.816981 | − | 0.576665i | \(-0.804354\pi\) | ||||
−0.816981 | + | 0.576665i | \(0.804354\pi\) | |||||||
\(840\) | 552.470 | − | 683.796i | 0.0226929 | − | 0.0280871i | ||||
\(841\) | 12621.5 | 0.517506 | ||||||||
\(842\) | 3650.20 | 0.149399 | ||||||||
\(843\) | 1379.65 | − | 1707.60i | 0.0563673 | − | 0.0697663i | ||||
\(844\) | −1060.32 | −0.0432436 | ||||||||
\(845\) | 14729.3 | 0.599648 | ||||||||
\(846\) | 5125.20 | + | 23851.3i | 0.208284 | + | 0.969298i | ||||
\(847\) | − | 3776.66i | − | 0.153208i | ||||||
\(848\) | 4254.12 | 0.172273 | ||||||||
\(849\) | 24105.1 | + | 19475.6i | 0.974421 | + | 0.787279i | ||||
\(850\) | 18540.6i | 0.748161i | ||||||||
\(851\) | −888.772 | + | 6029.03i | −0.0358011 | + | 0.242858i | ||||
\(852\) | −5091.27 | − | 4113.47i | −0.204723 | − | 0.165405i | ||||
\(853\) | −32775.6 | −1.31561 | −0.657804 | − | 0.753189i | \(-0.728515\pi\) | ||||
−0.657804 | + | 0.753189i | \(0.728515\pi\) | |||||||
\(854\) | − | 4262.57i | − | 0.170799i | ||||||
\(855\) | 16722.5 | − | 3593.34i | 0.668886 | − | 0.143731i | ||||
\(856\) | 1089.18i | 0.0434899i | ||||||||
\(857\) | 3793.04i | 0.151188i | 0.997139 | + | 0.0755939i | \(0.0240852\pi\) | ||||
−0.997139 | + | 0.0755939i | \(0.975915\pi\) | |||||||
\(858\) | 2525.35 | + | 2040.34i | 0.100482 | + | 0.0811843i | ||||
\(859\) | −6491.04 | −0.257825 | −0.128912 | − | 0.991656i | \(-0.541149\pi\) | ||||
−0.128912 | + | 0.991656i | \(0.541149\pi\) | |||||||
\(860\) | − | 5782.64i | − | 0.229286i | ||||||
\(861\) | −1382.92 | + | 1711.66i | −0.0547386 | + | 0.0677504i | ||||
\(862\) | 2253.07i | 0.0890253i | ||||||||
\(863\) | 19140.0i | 0.754962i | 0.926017 | + | 0.377481i | \(0.123210\pi\) | ||||
−0.926017 | + | 0.377481i | \(0.876790\pi\) | |||||||
\(864\) | 2024.83 | − | 4006.93i | 0.0797293 | − | 0.157776i | ||||
\(865\) | − | 21566.3i | − | 0.847717i | ||||||
\(866\) | 13562.3 | 0.532178 | ||||||||
\(867\) | −29562.0 | + | 36589.1i | −1.15799 | + | 1.43325i | ||||
\(868\) | − | 612.495i | − | 0.0239510i | ||||||
\(869\) | − | 61774.8i | − | 2.41147i | ||||||
\(870\) | −4834.10 | + | 5983.20i | −0.188381 | + | 0.233160i | ||||
\(871\) | − | 65.3219i | − | 0.00254116i | ||||||
\(872\) | −2823.32 | −0.109644 | ||||||||
\(873\) | −30771.7 | + | 6612.24i | −1.19297 | + | 0.256347i | ||||
\(874\) | −20263.2 | − | 2987.10i | −0.784224 | − | 0.115607i | ||||
\(875\) | − | 4302.37i | − | 0.166225i | ||||||
\(876\) | 10388.3 | − | 12857.7i | 0.400671 | − | 0.495914i | ||||
\(877\) | 41097.4 | 1.58240 | 0.791198 | − | 0.611561i | \(-0.209458\pi\) | ||||
0.791198 | + | 0.611561i | \(0.209458\pi\) | |||||||
\(878\) | − | 27374.5i | − | 1.05221i | ||||||
\(879\) | 11625.6 | − | 14389.0i | 0.446098 | − | 0.552139i | ||||
\(880\) | −5512.32 | −0.211159 | ||||||||
\(881\) | 16022.8 | 0.612736 | 0.306368 | − | 0.951913i | \(-0.400886\pi\) | ||||
0.306368 | + | 0.951913i | \(0.400886\pi\) | |||||||
\(882\) | −17601.5 | + | 3782.22i | −0.671965 | + | 0.144392i | ||||
\(883\) | 35431.4 | 1.35035 | 0.675177 | − | 0.737656i | \(-0.264067\pi\) | ||||
0.675177 | + | 0.737656i | \(0.264067\pi\) | |||||||
\(884\) | −2924.68 | −0.111276 | ||||||||
\(885\) | 18018.6 | + | 14558.1i | 0.684395 | + | 0.552954i | ||||
\(886\) | −19101.8 | −0.724308 | ||||||||
\(887\) | 8904.23i | 0.337063i | 0.985696 | + | 0.168531i | \(0.0539024\pi\) | ||||
−0.985696 | + | 0.168531i | \(0.946098\pi\) | |||||||
\(888\) | 1443.35 | − | 1786.44i | 0.0545446 | − | 0.0675102i | ||||
\(889\) | 6367.39i | 0.240220i | ||||||||
\(890\) | − | 404.644i | − | 0.0152401i | ||||||
\(891\) | −33560.0 | + | 15121.0i | −1.26184 | + | 0.568544i | ||||
\(892\) | 12756.4 | 0.478830 | ||||||||
\(893\) | −41944.4 | −1.57180 | ||||||||
\(894\) | −5236.95 | − | 4231.17i | −0.195917 | − | 0.158290i | ||||
\(895\) | − | 22626.4i | − | 0.845049i | ||||||
\(896\) | 396.722 | 0.0147919 | ||||||||
\(897\) | −2607.07 | + | 2403.87i | −0.0970431 | + | 0.0894791i | ||||
\(898\) | 31658.0 | 1.17644 | ||||||||
\(899\) | 5359.32i | 0.198824i | ||||||||
\(900\) | −1779.84 | − | 8282.94i | −0.0659202 | − | 0.306775i | ||||
\(901\) | 31421.1 | 1.16181 | ||||||||
\(902\) | 13798.3 | 0.509348 | ||||||||
\(903\) | 2144.44 | − | 2654.19i | 0.0790282 | − | 0.0978137i | ||||
\(904\) | − | 5706.32i | − | 0.209944i | ||||||
\(905\) | − | 20403.8i | − | 0.749444i | ||||||
\(906\) | 11387.4 | + | 9200.38i | 0.417572 | + | 0.337375i | ||||
\(907\) | 431.477i | 0.0157960i | 0.999969 | + | 0.00789799i | \(0.00251404\pi\) | ||||
−0.999969 | + | 0.00789799i | \(0.997486\pi\) | |||||||
\(908\) | −18748.1 | −0.685216 | ||||||||
\(909\) | 945.245 | − | 203.115i | 0.0344904 | − | 0.00741134i | ||||
\(910\) | 261.685 | 0.00953272 | ||||||||
\(911\) | −5895.76 | −0.214418 | −0.107209 | − | 0.994236i | \(-0.534191\pi\) | ||||
−0.107209 | + | 0.994236i | \(0.534191\pi\) | |||||||
\(912\) | 6004.11 | + | 4850.99i | 0.218000 | + | 0.176132i | ||||
\(913\) | −20390.8 | −0.739143 | ||||||||
\(914\) | −24746.0 | −0.895540 | ||||||||
\(915\) | 18963.8 | + | 15321.7i | 0.685163 | + | 0.553574i | ||||
\(916\) | − | 24271.7i | − | 0.875501i | ||||||
\(917\) | −5055.11 | −0.182044 | ||||||||
\(918\) | 14955.5 | − | 29595.3i | 0.537695 | − | 1.06404i | ||||
\(919\) | − | 5190.53i | − | 0.186311i | −0.995652 | − | 0.0931555i | \(-0.970305\pi\) | ||
0.995652 | − | 0.0931555i | \(-0.0296954\pi\) | |||||||
\(920\) | 878.096 | − | 5956.61i | 0.0314674 | − | 0.213460i | ||||
\(921\) | −4603.69 | + | 5698.02i | −0.164709 | + | 0.203861i | ||||
\(922\) | −12888.9 | −0.460383 | ||||||||
\(923\) | − | 1948.40i | − | 0.0694826i | ||||||
\(924\) | −2530.11 | − | 2044.19i | −0.0900807 | − | 0.0727803i | ||||
\(925\) | − | 4333.98i | − | 0.154054i | ||||||
\(926\) | − | 250.582i | − | 0.00889269i | ||||||
\(927\) | −20481.2 | + | 4401.03i | −0.725666 | + | 0.155932i | ||||
\(928\) | −3471.31 | −0.122792 | ||||||||
\(929\) | 35347.9i | 1.24836i | 0.781280 | + | 0.624181i | \(0.214567\pi\) | ||||
−0.781280 | + | 0.624181i | \(0.785433\pi\) | |||||||
\(930\) | 2724.94 | + | 2201.60i | 0.0960799 | + | 0.0776273i | ||||
\(931\) | − | 30953.6i | − | 1.08965i | ||||||
\(932\) | − | 7311.64i | − | 0.256975i | ||||||
\(933\) | −37969.8 | − | 30677.5i | −1.33234 | − | 1.07646i | ||||
\(934\) | − | 12978.1i | − | 0.454663i | ||||||
\(935\) | −40714.2 | −1.42406 | ||||||||
\(936\) | 1306.59 | − | 280.761i | 0.0456274 | − | 0.00980445i | ||||
\(937\) | 25527.4i | 0.890016i | 0.895527 | + | 0.445008i | \(0.146799\pi\) | ||||
−0.895527 | + | 0.445008i | \(0.853201\pi\) | |||||||
\(938\) | 65.4452i | 0.00227810i | ||||||||
\(939\) | 6700.45 | + | 5413.60i | 0.232866 | + | 0.188143i | ||||
\(940\) | − | 12330.1i | − | 0.427833i | ||||||
\(941\) | −22904.6 | −0.793484 | −0.396742 | − | 0.917930i | \(-0.629859\pi\) | ||||
−0.396742 | + | 0.917930i | \(0.629859\pi\) | |||||||
\(942\) | −5471.83 | + | 6772.52i | −0.189259 | + | 0.234247i | ||||
\(943\) | −2198.02 | + | 14910.4i | −0.0759039 | + | 0.514898i | ||||
\(944\) | 10454.0i | 0.360432i | ||||||||
\(945\) | −1338.14 | + | 2648.03i | −0.0460630 | + | 0.0911539i | ||||
\(946\) | −21396.3 | −0.735364 | ||||||||
\(947\) | 41716.2i | 1.43146i | 0.698376 | + | 0.715731i | \(0.253906\pi\) | ||||
−0.698376 | + | 0.715731i | \(0.746094\pi\) | |||||||
\(948\) | −19779.6 | − | 15980.8i | −0.677649 | − | 0.547504i | ||||
\(949\) | 4920.56 | 0.168312 | ||||||||
\(950\) | 14566.2 | 0.497463 | ||||||||
\(951\) | −22826.7 | − | 18442.7i | −0.778344 | − | 0.628859i | ||||
\(952\) | 2930.20 | 0.0997566 | ||||||||
\(953\) | 31526.7 | 1.07162 | 0.535808 | − | 0.844340i | \(-0.320007\pi\) | ||||
0.535808 | + | 0.844340i | \(0.320007\pi\) | |||||||
\(954\) | −14037.3 | + | 3016.34i | −0.476387 | + | 0.102366i | ||||
\(955\) | 25703.9 | 0.870952 | ||||||||
\(956\) | 13817.9i | 0.467471i | ||||||||
\(957\) | 22138.4 | + | 17886.6i | 0.747789 | + | 0.604172i | ||||
\(958\) | − | 23687.5i | − | 0.798860i | ||||||
\(959\) | − | 9655.68i | − | 0.325128i | ||||||
\(960\) | −1426.01 | + | 1764.98i | −0.0479419 | + | 0.0593381i | ||||
\(961\) | −27350.2 | −0.918069 | ||||||||
\(962\) | 683.662 | 0.0229128 | ||||||||
\(963\) | −772.269 | − | 3593.94i | −0.0258422 | − | 0.120263i | ||||
\(964\) | − | 3122.71i | − | 0.104332i | ||||||
\(965\) | 6749.79 | 0.225164 | ||||||||
\(966\) | 2611.99 | − | 2408.40i | 0.0869974 | − | 0.0802165i | ||||
\(967\) | −22749.5 | −0.756539 | −0.378270 | − | 0.925695i | \(-0.623481\pi\) | ||||
−0.378270 | + | 0.925695i | \(0.623481\pi\) | |||||||
\(968\) | 9748.13i | 0.323674i | ||||||||
\(969\) | 44346.5 | + | 35829.6i | 1.47019 | + | 1.18783i | ||||
\(970\) | 15907.6 | 0.526559 | ||||||||
\(971\) | −37825.3 | −1.25013 | −0.625063 | − | 0.780574i | \(-0.714927\pi\) | ||||
−0.625063 | + | 0.780574i | \(0.714927\pi\) | |||||||
\(972\) | −3840.23 | + | 14657.3i | −0.126724 | + | 0.483675i | ||||
\(973\) | − | 5856.50i | − | 0.192961i | ||||||
\(974\) | 29540.6i | 0.971810i | ||||||||
\(975\) | 1584.92 | − | 1961.66i | 0.0520595 | − | 0.0644344i | ||||
\(976\) | 11002.3i | 0.360836i | ||||||||
\(977\) | −7808.43 | −0.255695 | −0.127847 | − | 0.991794i | \(-0.540807\pi\) | ||||
−0.127847 | + | 0.991794i | \(0.540807\pi\) | |||||||
\(978\) | −15517.1 | − | 12537.0i | −0.507343 | − | 0.409906i | ||||
\(979\) | −1497.22 | −0.0488779 | ||||||||
\(980\) | 9099.20 | 0.296595 | ||||||||
\(981\) | 9316.06 | − | 2001.84i | 0.303200 | − | 0.0651518i | ||||
\(982\) | 179.041 | 0.00581815 | ||||||||
\(983\) | −31418.9 | −1.01944 | −0.509719 | − | 0.860341i | \(-0.670251\pi\) | ||||
−0.509719 | + | 0.860341i | \(0.670251\pi\) | |||||||
\(984\) | 3569.54 | − | 4418.05i | 0.115643 | − | 0.143132i | ||||
\(985\) | 20382.2i | 0.659319i | ||||||||
\(986\) | −25639.2 | −0.828111 | ||||||||
\(987\) | 4572.50 | − | 5659.42i | 0.147461 | − | 0.182514i | ||||
\(988\) | 2297.74i | 0.0739887i | ||||||||
\(989\) | 3408.37 | − | 23120.9i | 0.109585 | − | 0.743378i | ||||
\(990\) | 18188.9 | − | 3908.45i | 0.583920 | − | 0.125473i | ||||
\(991\) | −22161.3 | −0.710370 | −0.355185 | − | 0.934796i | \(-0.615582\pi\) | ||||
−0.355185 | + | 0.934796i | \(0.615582\pi\) | |||||||
\(992\) | 1580.94i | 0.0505998i | ||||||||
\(993\) | 23546.1 | − | 29143.1i | 0.752479 | − | 0.931349i | ||||
\(994\) | 1952.08i | 0.0622899i | ||||||||
\(995\) | − | 19185.6i | − | 0.611281i | ||||||
\(996\) | −5275.00 | + | 6528.91i | −0.167816 | + | 0.207707i | ||||
\(997\) | −8949.91 | −0.284299 | −0.142150 | − | 0.989845i | \(-0.545401\pi\) | ||||
−0.142150 | + | 0.989845i | \(0.545401\pi\) | |||||||
\(998\) | − | 7373.83i | − | 0.233882i | ||||||
\(999\) | −3495.93 | + | 6918.08i | −0.110717 | + | 0.219097i |
(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 | 138.4.d.a.137.3 | ✓ | 24 | |
3.2 | odd | 2 | inner | 138.4.d.a.137.16 | yes | 24 | |
23.22 | odd | 2 | inner | 138.4.d.a.137.4 | yes | 24 | |
69.68 | even | 2 | inner | 138.4.d.a.137.15 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.4.d.a.137.3 | ✓ | 24 | 1.1 | even | 1 | trivial | |
138.4.d.a.137.4 | yes | 24 | 23.22 | odd | 2 | inner | |
138.4.d.a.137.15 | yes | 24 | 69.68 | even | 2 | inner | |
138.4.d.a.137.16 | yes | 24 | 3.2 | odd | 2 | inner |