Properties

Label 588.4.k.e.521.14
Level $588$
Weight $4$
Character 588.521
Analytic conductor $34.693$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 588.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(34.6931230834\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 521.14
Character \(\chi\) \(=\) 588.521
Dual form 588.4.k.e.509.14

$q$-expansion

\(f(q)\) \(=\) \(q+(1.84944 - 4.85588i) q^{3} +(1.01459 + 1.75732i) q^{5} +(-20.1591 - 17.9613i) q^{9} +O(q^{10})\) \(q+(1.84944 - 4.85588i) q^{3} +(1.01459 + 1.75732i) q^{5} +(-20.1591 - 17.9613i) q^{9} +(25.2834 + 14.5974i) q^{11} +25.7266i q^{13} +(10.4097 - 1.67666i) q^{15} +(-1.39964 + 2.42425i) q^{17} +(92.8920 - 53.6312i) q^{19} +(70.3580 - 40.6212i) q^{23} +(60.4412 - 104.687i) q^{25} +(-124.501 + 64.6720i) q^{27} -170.862i q^{29} +(22.4394 + 12.9554i) q^{31} +(117.643 - 95.7762i) q^{33} +(-90.6133 - 156.947i) q^{37} +(124.925 + 47.5798i) q^{39} -257.354 q^{41} +239.983 q^{43} +(11.1105 - 53.6493i) q^{45} +(-186.576 - 323.160i) q^{47} +(9.18329 + 11.2800i) q^{51} +(489.335 + 282.517i) q^{53} +59.2413i q^{55} +(-88.6285 - 550.260i) q^{57} +(189.642 - 328.470i) q^{59} +(-194.113 + 112.071i) q^{61} +(-45.2098 + 26.1019i) q^{65} +(-167.761 + 290.571i) q^{67} +(-67.1288 - 416.777i) q^{69} -1029.35i q^{71} +(505.848 + 292.052i) q^{73} +(-396.566 - 487.108i) q^{75} +(497.128 + 861.051i) q^{79} +(83.7817 + 724.170i) q^{81} -1281.20 q^{83} -5.68022 q^{85} +(-829.684 - 315.999i) q^{87} +(-738.927 - 1279.86i) q^{89} +(104.410 - 85.0026i) q^{93} +(188.494 + 108.827i) q^{95} -1228.85i q^{97} +(-247.504 - 748.394i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 64 q^{9} + O(q^{10}) \) \( 48 q + 64 q^{9} - 192 q^{15} - 456 q^{25} + 432 q^{37} - 688 q^{39} + 1248 q^{43} + 1536 q^{51} - 2720 q^{57} + 528 q^{67} - 3744 q^{79} - 3408 q^{81} + 13824 q^{85} + 5088 q^{93} - 15472 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(493\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.84944 4.85588i 0.355925 0.934515i
\(4\) 0 0
\(5\) 1.01459 + 1.75732i 0.0907475 + 0.157179i 0.907826 0.419347i \(-0.137741\pi\)
−0.817078 + 0.576527i \(0.804408\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −20.1591 17.9613i −0.746635 0.665234i
\(10\) 0 0
\(11\) 25.2834 + 14.5974i 0.693022 + 0.400116i 0.804743 0.593623i \(-0.202303\pi\)
−0.111721 + 0.993740i \(0.535636\pi\)
\(12\) 0 0
\(13\) 25.7266i 0.548867i 0.961606 + 0.274433i \(0.0884903\pi\)
−0.961606 + 0.274433i \(0.911510\pi\)
\(14\) 0 0
\(15\) 10.4097 1.67666i 0.179186 0.0288608i
\(16\) 0 0
\(17\) −1.39964 + 2.42425i −0.0199684 + 0.0345862i −0.875837 0.482607i \(-0.839690\pi\)
0.855869 + 0.517193i \(0.173023\pi\)
\(18\) 0 0
\(19\) 92.8920 53.6312i 1.12163 0.647571i 0.179810 0.983701i \(-0.442452\pi\)
0.941815 + 0.336130i \(0.109118\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 70.3580 40.6212i 0.637855 0.368266i −0.145933 0.989295i \(-0.546618\pi\)
0.783788 + 0.621029i \(0.213285\pi\)
\(24\) 0 0
\(25\) 60.4412 104.687i 0.483530 0.837498i
\(26\) 0 0
\(27\) −124.501 + 64.6720i −0.887417 + 0.460968i
\(28\) 0 0
\(29\) 170.862i 1.09408i −0.837107 0.547039i \(-0.815755\pi\)
0.837107 0.547039i \(-0.184245\pi\)
\(30\) 0 0
\(31\) 22.4394 + 12.9554i 0.130007 + 0.0750598i 0.563593 0.826052i \(-0.309419\pi\)
−0.433586 + 0.901112i \(0.642752\pi\)
\(32\) 0 0
\(33\) 117.643 95.7762i 0.620578 0.505227i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −90.6133 156.947i −0.402615 0.697349i 0.591426 0.806359i \(-0.298565\pi\)
−0.994041 + 0.109010i \(0.965232\pi\)
\(38\) 0 0
\(39\) 124.925 + 47.5798i 0.512924 + 0.195355i
\(40\) 0 0
\(41\) −257.354 −0.980289 −0.490145 0.871641i \(-0.663056\pi\)
−0.490145 + 0.871641i \(0.663056\pi\)
\(42\) 0 0
\(43\) 239.983 0.851095 0.425548 0.904936i \(-0.360082\pi\)
0.425548 + 0.904936i \(0.360082\pi\)
\(44\) 0 0
\(45\) 11.1105 53.6493i 0.0368058 0.177724i
\(46\) 0 0
\(47\) −186.576 323.160i −0.579041 1.00293i −0.995590 0.0938154i \(-0.970094\pi\)
0.416548 0.909114i \(-0.363240\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 9.18329 + 11.2800i 0.0252141 + 0.0309708i
\(52\) 0 0
\(53\) 489.335 + 282.517i 1.26821 + 0.732203i 0.974650 0.223737i \(-0.0718256\pi\)
0.293563 + 0.955940i \(0.405159\pi\)
\(54\) 0 0
\(55\) 59.2413i 0.145238i
\(56\) 0 0
\(57\) −88.6285 550.260i −0.205950 1.27866i
\(58\) 0 0
\(59\) 189.642 328.470i 0.418463 0.724800i −0.577322 0.816517i \(-0.695902\pi\)
0.995785 + 0.0917170i \(0.0292355\pi\)
\(60\) 0 0
\(61\) −194.113 + 112.071i −0.407436 + 0.235233i −0.689687 0.724107i \(-0.742252\pi\)
0.282251 + 0.959340i \(0.408919\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −45.2098 + 26.1019i −0.0862705 + 0.0498083i
\(66\) 0 0
\(67\) −167.761 + 290.571i −0.305900 + 0.529835i −0.977461 0.211114i \(-0.932291\pi\)
0.671561 + 0.740949i \(0.265624\pi\)
\(68\) 0 0
\(69\) −67.1288 416.777i −0.117121 0.727160i
\(70\) 0 0
\(71\) 1029.35i 1.72057i −0.509809 0.860287i \(-0.670284\pi\)
0.509809 0.860287i \(-0.329716\pi\)
\(72\) 0 0
\(73\) 505.848 + 292.052i 0.811028 + 0.468247i 0.847313 0.531094i \(-0.178219\pi\)
−0.0362846 + 0.999341i \(0.511552\pi\)
\(74\) 0 0
\(75\) −396.566 487.108i −0.610554 0.749952i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 497.128 + 861.051i 0.707991 + 1.22628i 0.965601 + 0.260027i \(0.0837316\pi\)
−0.257610 + 0.966249i \(0.582935\pi\)
\(80\) 0 0
\(81\) 83.7817 + 724.170i 0.114927 + 0.993374i
\(82\) 0 0
\(83\) −1281.20 −1.69434 −0.847171 0.531320i \(-0.821696\pi\)
−0.847171 + 0.531320i \(0.821696\pi\)
\(84\) 0 0
\(85\) −5.68022 −0.00724832
\(86\) 0 0
\(87\) −829.684 315.999i −1.02243 0.389409i
\(88\) 0 0
\(89\) −738.927 1279.86i −0.880068 1.52432i −0.851264 0.524737i \(-0.824164\pi\)
−0.0288039 0.999585i \(-0.509170\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 104.410 85.0026i 0.116417 0.0947781i
\(94\) 0 0
\(95\) 188.494 + 108.827i 0.203569 + 0.117531i
\(96\) 0 0
\(97\) 1228.85i 1.28630i −0.765742 0.643148i \(-0.777628\pi\)
0.765742 0.643148i \(-0.222372\pi\)
\(98\) 0 0
\(99\) −247.504 748.394i −0.251263 0.759762i
\(100\) 0 0
\(101\) 219.708 380.545i 0.216453 0.374907i −0.737268 0.675600i \(-0.763885\pi\)
0.953721 + 0.300693i \(0.0972179\pi\)
\(102\) 0 0
\(103\) −963.292 + 556.157i −0.921514 + 0.532037i −0.884118 0.467264i \(-0.845240\pi\)
−0.0373965 + 0.999301i \(0.511906\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 51.9337 29.9839i 0.0469217 0.0270903i −0.476356 0.879253i \(-0.658043\pi\)
0.523277 + 0.852162i \(0.324709\pi\)
\(108\) 0 0
\(109\) 119.650 207.239i 0.105141 0.182109i −0.808655 0.588283i \(-0.799804\pi\)
0.913796 + 0.406174i \(0.133137\pi\)
\(110\) 0 0
\(111\) −929.699 + 149.744i −0.794983 + 0.128045i
\(112\) 0 0
\(113\) 1701.80i 1.41674i −0.705841 0.708370i \(-0.749431\pi\)
0.705841 0.708370i \(-0.250569\pi\)
\(114\) 0 0
\(115\) 142.769 + 82.4276i 0.115767 + 0.0668384i
\(116\) 0 0
\(117\) 462.083 518.626i 0.365125 0.409803i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −239.333 414.536i −0.179814 0.311447i
\(122\) 0 0
\(123\) −475.960 + 1249.68i −0.348910 + 0.916095i
\(124\) 0 0
\(125\) 498.939 0.357011
\(126\) 0 0
\(127\) 1848.04 1.29124 0.645618 0.763661i \(-0.276600\pi\)
0.645618 + 0.763661i \(0.276600\pi\)
\(128\) 0 0
\(129\) 443.835 1165.33i 0.302926 0.795361i
\(130\) 0 0
\(131\) −149.935 259.695i −0.0999991 0.173203i 0.811685 0.584095i \(-0.198551\pi\)
−0.911684 + 0.410892i \(0.865217\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −239.967 153.173i −0.152985 0.0976519i
\(136\) 0 0
\(137\) 2035.18 + 1175.01i 1.26917 + 0.732758i 0.974832 0.222942i \(-0.0715660\pi\)
0.294342 + 0.955700i \(0.404899\pi\)
\(138\) 0 0
\(139\) 1518.73i 0.926740i 0.886165 + 0.463370i \(0.153360\pi\)
−0.886165 + 0.463370i \(0.846640\pi\)
\(140\) 0 0
\(141\) −1914.29 + 308.327i −1.14335 + 0.184155i
\(142\) 0 0
\(143\) −375.541 + 650.456i −0.219610 + 0.380377i
\(144\) 0 0
\(145\) 300.258 173.354i 0.171966 0.0992847i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 128.269 74.0563i 0.0705250 0.0407176i −0.464323 0.885666i \(-0.653702\pi\)
0.534848 + 0.844948i \(0.320369\pi\)
\(150\) 0 0
\(151\) 1246.02 2158.17i 0.671522 1.16311i −0.305950 0.952048i \(-0.598974\pi\)
0.977472 0.211063i \(-0.0676926\pi\)
\(152\) 0 0
\(153\) 71.7582 23.7313i 0.0379170 0.0125396i
\(154\) 0 0
\(155\) 52.5774i 0.0272459i
\(156\) 0 0
\(157\) 2561.86 + 1479.09i 1.30228 + 0.751874i 0.980795 0.195039i \(-0.0624834\pi\)
0.321489 + 0.946913i \(0.395817\pi\)
\(158\) 0 0
\(159\) 2276.87 1853.65i 1.13564 0.924554i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 76.2823 + 132.125i 0.0366558 + 0.0634897i 0.883771 0.467919i \(-0.154996\pi\)
−0.847115 + 0.531409i \(0.821663\pi\)
\(164\) 0 0
\(165\) 287.669 + 109.563i 0.135727 + 0.0516939i
\(166\) 0 0
\(167\) −1312.37 −0.608110 −0.304055 0.952655i \(-0.598341\pi\)
−0.304055 + 0.952655i \(0.598341\pi\)
\(168\) 0 0
\(169\) 1535.14 0.698745
\(170\) 0 0
\(171\) −2835.91 587.304i −1.26823 0.262645i
\(172\) 0 0
\(173\) 1296.27 + 2245.20i 0.569673 + 0.986703i 0.996598 + 0.0824156i \(0.0262635\pi\)
−0.426925 + 0.904287i \(0.640403\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −1244.28 1528.37i −0.528394 0.649034i
\(178\) 0 0
\(179\) −2924.92 1688.71i −1.22134 0.705138i −0.256133 0.966642i \(-0.582448\pi\)
−0.965203 + 0.261503i \(0.915782\pi\)
\(180\) 0 0
\(181\) 1525.85i 0.626606i 0.949653 + 0.313303i \(0.101436\pi\)
−0.949653 + 0.313303i \(0.898564\pi\)
\(182\) 0 0
\(183\) 185.204 + 1149.86i 0.0748122 + 0.464480i
\(184\) 0 0
\(185\) 183.870 318.473i 0.0730725 0.126565i
\(186\) 0 0
\(187\) −70.7753 + 40.8621i −0.0276770 + 0.0159793i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1311.45 757.169i 0.496825 0.286842i −0.230577 0.973054i \(-0.574061\pi\)
0.727401 + 0.686212i \(0.240728\pi\)
\(192\) 0 0
\(193\) 1487.21 2575.93i 0.554674 0.960723i −0.443255 0.896395i \(-0.646176\pi\)
0.997929 0.0643273i \(-0.0204902\pi\)
\(194\) 0 0
\(195\) 43.1348 + 267.807i 0.0158407 + 0.0983490i
\(196\) 0 0
\(197\) 2886.30i 1.04386i 0.852989 + 0.521930i \(0.174788\pi\)
−0.852989 + 0.521930i \(0.825212\pi\)
\(198\) 0 0
\(199\) 2555.15 + 1475.22i 0.910200 + 0.525504i 0.880495 0.474055i \(-0.157210\pi\)
0.0297042 + 0.999559i \(0.490543\pi\)
\(200\) 0 0
\(201\) 1100.71 + 1352.02i 0.386261 + 0.474450i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −261.108 452.252i −0.0889588 0.154081i
\(206\) 0 0
\(207\) −2147.97 444.834i −0.721228 0.149363i
\(208\) 0 0
\(209\) 3131.50 1.03641
\(210\) 0 0
\(211\) 760.988 0.248287 0.124144 0.992264i \(-0.460382\pi\)
0.124144 + 0.992264i \(0.460382\pi\)
\(212\) 0 0
\(213\) −4998.38 1903.71i −1.60790 0.612396i
\(214\) 0 0
\(215\) 243.484 + 421.727i 0.0772347 + 0.133775i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 2353.70 1916.21i 0.726249 0.591257i
\(220\) 0 0
\(221\) −62.3675 36.0079i −0.0189832 0.0109600i
\(222\) 0 0
\(223\) 575.704i 0.172879i −0.996257 0.0864395i \(-0.972451\pi\)
0.996257 0.0864395i \(-0.0275489\pi\)
\(224\) 0 0
\(225\) −3098.76 + 1024.80i −0.918153 + 0.303645i
\(226\) 0 0
\(227\) −1415.12 + 2451.05i −0.413765 + 0.716662i −0.995298 0.0968611i \(-0.969120\pi\)
0.581533 + 0.813523i \(0.302453\pi\)
\(228\) 0 0
\(229\) −3271.23 + 1888.65i −0.943969 + 0.545001i −0.891202 0.453606i \(-0.850137\pi\)
−0.0527668 + 0.998607i \(0.516804\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −4879.34 + 2817.09i −1.37192 + 0.792076i −0.991169 0.132604i \(-0.957666\pi\)
−0.380746 + 0.924680i \(0.624333\pi\)
\(234\) 0 0
\(235\) 378.596 655.747i 0.105093 0.182027i
\(236\) 0 0
\(237\) 5100.57 821.531i 1.39796 0.225165i
\(238\) 0 0
\(239\) 6082.58i 1.64623i 0.567873 + 0.823116i \(0.307767\pi\)
−0.567873 + 0.823116i \(0.692233\pi\)
\(240\) 0 0
\(241\) 2662.28 + 1537.07i 0.711587 + 0.410835i 0.811648 0.584146i \(-0.198571\pi\)
−0.100061 + 0.994981i \(0.531904\pi\)
\(242\) 0 0
\(243\) 3671.43 + 932.475i 0.969228 + 0.246166i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 1379.75 + 2389.79i 0.355430 + 0.615623i
\(248\) 0 0
\(249\) −2369.51 + 6221.37i −0.603059 + 1.58339i
\(250\) 0 0
\(251\) 2619.44 0.658715 0.329357 0.944205i \(-0.393168\pi\)
0.329357 + 0.944205i \(0.393168\pi\)
\(252\) 0 0
\(253\) 2371.86 0.589396
\(254\) 0 0
\(255\) −10.5052 + 27.5825i −0.00257986 + 0.00677366i
\(256\) 0 0
\(257\) 2128.61 + 3686.86i 0.516650 + 0.894864i 0.999813 + 0.0193338i \(0.00615452\pi\)
−0.483163 + 0.875530i \(0.660512\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −3068.90 + 3444.43i −0.727818 + 0.816876i
\(262\) 0 0
\(263\) −6041.88 3488.28i −1.41657 0.817858i −0.420575 0.907258i \(-0.638172\pi\)
−0.995996 + 0.0894000i \(0.971505\pi\)
\(264\) 0 0
\(265\) 1146.55i 0.265782i
\(266\) 0 0
\(267\) −7581.44 + 1221.12i −1.73774 + 0.279892i
\(268\) 0 0
\(269\) 2334.12 4042.81i 0.529047 0.916337i −0.470379 0.882465i \(-0.655883\pi\)
0.999426 0.0338722i \(-0.0107839\pi\)
\(270\) 0 0
\(271\) −7572.04 + 4371.72i −1.69730 + 0.979938i −0.748998 + 0.662572i \(0.769465\pi\)
−0.948303 + 0.317366i \(0.897202\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 3056.32 1764.57i 0.670193 0.386936i
\(276\) 0 0
\(277\) 300.073 519.742i 0.0650890 0.112737i −0.831644 0.555308i \(-0.812600\pi\)
0.896733 + 0.442571i \(0.145934\pi\)
\(278\) 0 0
\(279\) −219.662 664.209i −0.0471357 0.142528i
\(280\) 0 0
\(281\) 4503.57i 0.956087i 0.878336 + 0.478044i \(0.158654\pi\)
−0.878336 + 0.478044i \(0.841346\pi\)
\(282\) 0 0
\(283\) 385.112 + 222.345i 0.0808924 + 0.0467032i 0.539901 0.841729i \(-0.318462\pi\)
−0.459008 + 0.888432i \(0.651795\pi\)
\(284\) 0 0
\(285\) 877.060 714.036i 0.182290 0.148406i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 2452.58 + 4248.00i 0.499203 + 0.864644i
\(290\) 0 0
\(291\) −5967.14 2272.68i −1.20206 0.457825i
\(292\) 0 0
\(293\) 6302.01 1.25654 0.628272 0.777994i \(-0.283763\pi\)
0.628272 + 0.777994i \(0.283763\pi\)
\(294\) 0 0
\(295\) 769.635 0.151898
\(296\) 0 0
\(297\) −4091.86 182.264i −0.799440 0.0356095i
\(298\) 0 0
\(299\) 1045.05 + 1810.07i 0.202129 + 0.350097i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −1441.54 1770.67i −0.273315 0.335717i
\(304\) 0 0
\(305\) −393.889 227.412i −0.0739476 0.0426937i
\(306\) 0 0
\(307\) 7530.38i 1.39994i −0.714172 0.699970i \(-0.753197\pi\)
0.714172 0.699970i \(-0.246803\pi\)
\(308\) 0 0
\(309\) 919.080 + 5706.21i 0.169206 + 1.05053i
\(310\) 0 0
\(311\) −4683.11 + 8111.38i −0.853873 + 1.47895i 0.0238130 + 0.999716i \(0.492419\pi\)
−0.877686 + 0.479236i \(0.840914\pi\)
\(312\) 0 0
\(313\) −3393.99 + 1959.52i −0.612906 + 0.353861i −0.774102 0.633061i \(-0.781798\pi\)
0.161196 + 0.986922i \(0.448465\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −483.723 + 279.278i −0.0857054 + 0.0494820i −0.542240 0.840224i \(-0.682424\pi\)
0.456535 + 0.889706i \(0.349090\pi\)
\(318\) 0 0
\(319\) 2494.14 4319.97i 0.437758 0.758219i
\(320\) 0 0
\(321\) −49.5501 307.637i −0.00861563 0.0534911i
\(322\) 0 0
\(323\) 300.257i 0.0517237i
\(324\) 0 0
\(325\) 2693.25 + 1554.95i 0.459675 + 0.265393i
\(326\) 0 0
\(327\) −785.044 964.281i −0.132762 0.163073i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −549.892 952.441i −0.0913136 0.158160i 0.816751 0.576991i \(-0.195773\pi\)
−0.908064 + 0.418831i \(0.862440\pi\)
\(332\) 0 0
\(333\) −992.287 + 4791.45i −0.163294 + 0.788498i
\(334\) 0 0
\(335\) −680.835 −0.111039
\(336\) 0 0
\(337\) 3838.95 0.620537 0.310268 0.950649i \(-0.399581\pi\)
0.310268 + 0.950649i \(0.399581\pi\)
\(338\) 0 0
\(339\) −8263.72 3147.37i −1.32396 0.504253i
\(340\) 0 0
\(341\) 378.229 + 655.112i 0.0600652 + 0.104036i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 664.301 540.823i 0.103666 0.0843969i
\(346\) 0 0
\(347\) −4113.91 2375.17i −0.636445 0.367452i 0.146799 0.989166i \(-0.453103\pi\)
−0.783244 + 0.621715i \(0.786436\pi\)
\(348\) 0 0
\(349\) 9257.25i 1.41985i 0.704275 + 0.709927i \(0.251272\pi\)
−0.704275 + 0.709927i \(0.748728\pi\)
\(350\) 0 0
\(351\) −1663.79 3202.99i −0.253010 0.487074i
\(352\) 0 0
\(353\) 2270.09 3931.92i 0.342280 0.592847i −0.642576 0.766222i \(-0.722134\pi\)
0.984856 + 0.173376i \(0.0554675\pi\)
\(354\) 0 0
\(355\) 1808.89 1044.36i 0.270439 0.156138i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3512.47 2027.93i 0.516382 0.298133i −0.219071 0.975709i \(-0.570303\pi\)
0.735453 + 0.677575i \(0.236969\pi\)
\(360\) 0 0
\(361\) 2323.12 4023.76i 0.338696 0.586639i
\(362\) 0 0
\(363\) −2455.57 + 395.510i −0.355052 + 0.0571870i
\(364\) 0 0
\(365\) 1185.25i 0.169969i
\(366\) 0 0
\(367\) 11844.5 + 6838.44i 1.68468 + 0.972653i 0.958474 + 0.285180i \(0.0920533\pi\)
0.726210 + 0.687473i \(0.241280\pi\)
\(368\) 0 0
\(369\) 5188.03 + 4622.41i 0.731918 + 0.652122i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −84.0879 145.645i −0.0116727 0.0202177i 0.860130 0.510075i \(-0.170382\pi\)
−0.871803 + 0.489857i \(0.837049\pi\)
\(374\) 0 0
\(375\) 922.757 2422.79i 0.127069 0.333632i
\(376\) 0 0
\(377\) 4395.69 0.600503
\(378\) 0 0
\(379\) −398.381 −0.0539933 −0.0269966 0.999636i \(-0.508594\pi\)
−0.0269966 + 0.999636i \(0.508594\pi\)
\(380\) 0 0
\(381\) 3417.84 8973.85i 0.459583 1.20668i
\(382\) 0 0
\(383\) −1531.44 2652.54i −0.204316 0.353886i 0.745599 0.666395i \(-0.232164\pi\)
−0.949915 + 0.312510i \(0.898830\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −4837.85 4310.42i −0.635457 0.566178i
\(388\) 0 0
\(389\) 10631.5 + 6138.08i 1.38570 + 0.800033i 0.992827 0.119561i \(-0.0381487\pi\)
0.392871 + 0.919594i \(0.371482\pi\)
\(390\) 0 0
\(391\) 227.420i 0.0294147i
\(392\) 0 0
\(393\) −1538.34 + 247.776i −0.197453 + 0.0318031i
\(394\) 0 0
\(395\) −1008.76 + 1747.22i −0.128497 + 0.222563i
\(396\) 0 0
\(397\) 6831.34 3944.07i 0.863614 0.498608i −0.00160665 0.999999i \(-0.500511\pi\)
0.865221 + 0.501391i \(0.167178\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −4883.77 + 2819.65i −0.608189 + 0.351138i −0.772257 0.635311i \(-0.780872\pi\)
0.164067 + 0.986449i \(0.447539\pi\)
\(402\) 0 0
\(403\) −333.297 + 577.288i −0.0411978 + 0.0713567i
\(404\) 0 0
\(405\) −1187.59 + 881.965i −0.145708 + 0.108210i
\(406\) 0 0
\(407\) 5290.87i 0.644371i
\(408\) 0 0
\(409\) −2342.59 1352.49i −0.283212 0.163512i 0.351665 0.936126i \(-0.385616\pi\)
−0.634876 + 0.772614i \(0.718949\pi\)
\(410\) 0 0
\(411\) 9469.64 7709.46i 1.13650 0.925255i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −1299.89 2251.48i −0.153757 0.266315i
\(416\) 0 0
\(417\) 7374.76 + 2808.80i 0.866052 + 0.329850i
\(418\) 0 0
\(419\) −13118.4 −1.52953 −0.764766 0.644309i \(-0.777145\pi\)
−0.764766 + 0.644309i \(0.777145\pi\)
\(420\) 0 0
\(421\) 5668.08 0.656165 0.328082 0.944649i \(-0.393598\pi\)
0.328082 + 0.944649i \(0.393598\pi\)
\(422\) 0 0
\(423\) −2043.16 + 9865.77i −0.234850 + 1.13402i
\(424\) 0 0
\(425\) 169.192 + 293.049i 0.0193106 + 0.0334469i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 2463.99 + 3026.56i 0.277303 + 0.340615i
\(430\) 0 0
\(431\) 806.205 + 465.463i 0.0901010 + 0.0520199i 0.544374 0.838843i \(-0.316767\pi\)
−0.454273 + 0.890863i \(0.650101\pi\)
\(432\) 0 0
\(433\) 10673.2i 1.18458i 0.805725 + 0.592290i \(0.201776\pi\)
−0.805725 + 0.592290i \(0.798224\pi\)
\(434\) 0 0
\(435\) −286.477 1778.63i −0.0315760 0.196043i
\(436\) 0 0
\(437\) 4357.13 7546.78i 0.476956 0.826113i
\(438\) 0 0
\(439\) −2870.95 + 1657.54i −0.312125 + 0.180206i −0.647877 0.761745i \(-0.724343\pi\)
0.335752 + 0.941950i \(0.391010\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 3223.65 1861.18i 0.345734 0.199610i −0.317071 0.948402i \(-0.602699\pi\)
0.662805 + 0.748792i \(0.269366\pi\)
\(444\) 0 0
\(445\) 1499.41 2597.06i 0.159728 0.276657i
\(446\) 0 0
\(447\) −122.382 759.823i −0.0129496 0.0803991i
\(448\) 0 0
\(449\) 8582.14i 0.902041i −0.892514 0.451021i \(-0.851060\pi\)
0.892514 0.451021i \(-0.148940\pi\)
\(450\) 0 0
\(451\) −6506.78 3756.69i −0.679362 0.392230i
\(452\) 0 0
\(453\) −8175.39 10042.0i −0.847932 1.04153i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −6516.79 11287.4i −0.667052 1.15537i −0.978725 0.205178i \(-0.934223\pi\)
0.311673 0.950189i \(-0.399111\pi\)
\(458\) 0 0
\(459\) 17.4760 392.339i 0.00177714 0.0398972i
\(460\) 0 0
\(461\) −9125.03 −0.921898 −0.460949 0.887427i \(-0.652491\pi\)
−0.460949 + 0.887427i \(0.652491\pi\)
\(462\) 0 0
\(463\) 6710.20 0.673541 0.336770 0.941587i \(-0.390665\pi\)
0.336770 + 0.941587i \(0.390665\pi\)
\(464\) 0 0
\(465\) 255.310 + 97.2388i 0.0254617 + 0.00969751i
\(466\) 0 0
\(467\) −2451.93 4246.87i −0.242959 0.420818i 0.718597 0.695427i \(-0.244785\pi\)
−0.961556 + 0.274610i \(0.911451\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 11920.3 9704.59i 1.16615 0.949393i
\(472\) 0 0
\(473\) 6067.59 + 3503.13i 0.589827 + 0.340537i
\(474\) 0 0
\(475\) 12966.1i 1.25248i
\(476\) 0 0
\(477\) −4790.18 14484.4i −0.459805 1.39035i
\(478\) 0 0
\(479\) 704.962 1221.03i 0.0672454 0.116472i −0.830442 0.557104i \(-0.811912\pi\)
0.897688 + 0.440632i \(0.145246\pi\)
\(480\) 0 0
\(481\) 4037.71 2331.17i 0.382752 0.220982i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2159.48 1246.77i 0.202179 0.116728i
\(486\) 0 0
\(487\) 1007.21 1744.54i 0.0937186 0.162325i −0.815355 0.578962i \(-0.803458\pi\)
0.909073 + 0.416637i \(0.136791\pi\)
\(488\) 0 0
\(489\) 782.662 126.061i 0.0723788 0.0116578i
\(490\) 0 0
\(491\) 13955.7i 1.28271i −0.767243 0.641357i \(-0.778372\pi\)
0.767243 0.641357i \(-0.221628\pi\)
\(492\) 0 0
\(493\) 414.211 + 239.145i 0.0378400 + 0.0218469i
\(494\) 0 0
\(495\) 1064.05 1194.25i 0.0966174 0.108440i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 6464.30 + 11196.5i 0.579923 + 1.00446i 0.995487 + 0.0948930i \(0.0302509\pi\)
−0.415564 + 0.909564i \(0.636416\pi\)
\(500\) 0 0
\(501\) −2427.15 + 6372.72i −0.216441 + 0.568287i
\(502\) 0 0
\(503\) −13733.1 −1.21735 −0.608676 0.793419i \(-0.708299\pi\)
−0.608676 + 0.793419i \(0.708299\pi\)
\(504\) 0 0
\(505\) 891.651 0.0785702
\(506\) 0 0
\(507\) 2839.16 7454.47i 0.248701 0.652988i
\(508\) 0 0
\(509\) −6588.20 11411.1i −0.573707 0.993690i −0.996181 0.0873148i \(-0.972171\pi\)
0.422474 0.906375i \(-0.361162\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −8096.73 + 12684.7i −0.696841 + 1.09170i
\(514\) 0 0
\(515\) −1954.69 1128.54i −0.167250 0.0965620i
\(516\) 0 0
\(517\) 10894.1i 0.926735i
\(518\) 0 0
\(519\) 13299.8 2142.15i 1.12485 0.181176i
\(520\) 0 0
\(521\) −2649.64 + 4589.31i −0.222808 + 0.385914i −0.955659 0.294474i \(-0.904855\pi\)
0.732852 + 0.680388i \(0.238189\pi\)
\(522\) 0 0
\(523\) −3395.81 + 1960.57i −0.283917 + 0.163920i −0.635195 0.772352i \(-0.719080\pi\)
0.351278 + 0.936271i \(0.385747\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −62.8140 + 36.2657i −0.00519207 + 0.00299764i
\(528\) 0 0
\(529\) −2783.33 + 4820.87i −0.228761 + 0.396225i
\(530\) 0 0
\(531\) −9722.79 + 3215.45i −0.794601 + 0.262785i
\(532\) 0 0
\(533\) 6620.83i 0.538048i
\(534\) 0 0
\(535\) 105.383 + 60.8427i 0.00851605 + 0.00491675i
\(536\) 0 0
\(537\) −13609.6 + 11079.9i −1.09367 + 0.890379i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 2550.35 + 4417.33i 0.202676 + 0.351046i 0.949390 0.314100i \(-0.101703\pi\)
−0.746714 + 0.665146i \(0.768369\pi\)
\(542\) 0 0
\(543\) 7409.35 + 2821.97i 0.585572 + 0.223025i
\(544\) 0 0
\(545\) 485.580 0.0381651
\(546\) 0 0
\(547\) −23173.5 −1.81138 −0.905691 0.423939i \(-0.860647\pi\)
−0.905691 + 0.423939i \(0.860647\pi\)
\(548\) 0 0
\(549\) 5926.09 + 1227.27i 0.460691 + 0.0954070i
\(550\) 0 0
\(551\) −9163.53 15871.7i −0.708492 1.22714i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −1206.41 1481.85i −0.0922688 0.113335i
\(556\) 0 0
\(557\) 18408.7 + 10628.3i 1.40036 + 0.808501i 0.994430 0.105402i \(-0.0336129\pi\)
0.405934 + 0.913902i \(0.366946\pi\)
\(558\) 0 0
\(559\) 6173.95i 0.467138i
\(560\) 0 0
\(561\) 67.5269 + 419.248i 0.00508198 + 0.0315520i
\(562\) 0 0
\(563\) 4931.19 8541.07i 0.369138 0.639366i −0.620293 0.784370i \(-0.712986\pi\)
0.989431 + 0.145004i \(0.0463196\pi\)
\(564\) 0 0
\(565\) 2990.60 1726.62i 0.222682 0.128566i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −15573.7 + 8991.49i −1.14742 + 0.662466i −0.948258 0.317500i \(-0.897157\pi\)
−0.199166 + 0.979966i \(0.563823\pi\)
\(570\) 0 0
\(571\) −13285.5 + 23011.2i −0.973699 + 1.68650i −0.289537 + 0.957167i \(0.593501\pi\)
−0.684163 + 0.729330i \(0.739832\pi\)
\(572\) 0 0
\(573\) −1251.26 7768.60i −0.0912255 0.566384i
\(574\) 0 0
\(575\) 9820.79i 0.712270i
\(576\) 0 0
\(577\) 3400.09 + 1963.04i 0.245317 + 0.141634i 0.617618 0.786478i \(-0.288098\pi\)
−0.372301 + 0.928112i \(0.621431\pi\)
\(578\) 0 0
\(579\) −9757.89 11985.8i −0.700387 0.860296i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 8248.03 + 14286.0i 0.585932 + 1.01486i
\(584\) 0 0
\(585\) 1380.21 + 285.836i 0.0975467 + 0.0202015i
\(586\) 0 0
\(587\) 9284.76 0.652850 0.326425 0.945223i \(-0.394156\pi\)
0.326425 + 0.945223i \(0.394156\pi\)
\(588\) 0 0
\(589\) 2779.25 0.194426
\(590\) 0 0
\(591\) 14015.5 + 5338.04i 0.975502 + 0.371536i
\(592\) 0 0
\(593\) 2701.61 + 4679.32i 0.187085 + 0.324041i 0.944277 0.329151i \(-0.106763\pi\)
−0.757192 + 0.653193i \(0.773429\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 11889.1 9679.17i 0.815054 0.663555i
\(598\) 0 0
\(599\) −1165.84 673.101i −0.0795244 0.0459134i 0.459711 0.888069i \(-0.347953\pi\)
−0.539235 + 0.842155i \(0.681287\pi\)
\(600\) 0 0
\(601\) 15011.2i 1.01884i −0.860519 0.509418i \(-0.829861\pi\)
0.860519 0.509418i \(-0.170139\pi\)
\(602\) 0 0
\(603\) 8600.97 2844.45i 0.580860 0.192098i
\(604\) 0 0
\(605\) 485.648 841.167i 0.0326354 0.0565261i
\(606\) 0 0
\(607\) −9270.02 + 5352.05i −0.619866 + 0.357880i −0.776817 0.629727i \(-0.783167\pi\)
0.156951 + 0.987606i \(0.449834\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 8313.79 4799.97i 0.550474 0.317817i
\(612\) 0 0
\(613\) −1496.91 + 2592.72i −0.0986290 + 0.170830i −0.911117 0.412147i \(-0.864779\pi\)
0.812488 + 0.582977i \(0.198112\pi\)
\(614\) 0 0
\(615\) −2678.98 + 431.495i −0.175654 + 0.0282920i
\(616\) 0 0
\(617\) 15265.5i 0.996056i −0.867161 0.498028i \(-0.834058\pi\)
0.867161 0.498028i \(-0.165942\pi\)
\(618\) 0 0
\(619\) −19456.4 11233.2i −1.26336 0.729402i −0.289637 0.957136i \(-0.593535\pi\)
−0.973723 + 0.227735i \(0.926868\pi\)
\(620\) 0 0
\(621\) −6132.60 + 9607.58i −0.396285 + 0.620836i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −7048.94 12209.1i −0.451132 0.781383i
\(626\) 0 0
\(627\) 5791.53 15206.2i 0.368886 0.968544i
\(628\) 0 0
\(629\) 507.304 0.0321582
\(630\) 0 0
\(631\) 6614.90 0.417330 0.208665 0.977987i \(-0.433088\pi\)
0.208665 + 0.977987i \(0.433088\pi\)
\(632\) 0 0
\(633\) 1407.40 3695.27i 0.0883716 0.232028i
\(634\) 0 0
\(635\) 1875.00 + 3247.59i 0.117176 + 0.202955i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −18488.4 + 20750.7i −1.14459 + 1.28464i
\(640\) 0 0
\(641\) −10414.2 6012.64i −0.641710 0.370492i 0.143563 0.989641i \(-0.454144\pi\)
−0.785273 + 0.619150i \(0.787477\pi\)
\(642\) 0 0
\(643\) 12374.3i 0.758936i 0.925205 + 0.379468i \(0.123893\pi\)
−0.925205 + 0.379468i \(0.876107\pi\)
\(644\) 0 0
\(645\) 2498.16 402.371i 0.152504 0.0245633i
\(646\) 0 0
\(647\) −860.863 + 1491.06i −0.0523091 + 0.0906021i −0.890994 0.454014i \(-0.849991\pi\)
0.838685 + 0.544617i \(0.183325\pi\)
\(648\) 0 0
\(649\) 9589.62 5536.57i 0.580008 0.334868i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 19110.1 11033.2i 1.14523 0.661201i 0.197513 0.980300i \(-0.436714\pi\)
0.947721 + 0.319099i \(0.103380\pi\)
\(654\) 0 0
\(655\) 304.244 526.967i 0.0181493 0.0314356i
\(656\) 0 0
\(657\) −4951.83 14973.2i −0.294048 0.889134i
\(658\) 0 0
\(659\) 2582.20i 0.152638i 0.997083 + 0.0763190i \(0.0243167\pi\)
−0.997083 + 0.0763190i \(0.975683\pi\)
\(660\) 0 0
\(661\) −8695.88 5020.57i −0.511695 0.295427i 0.221835 0.975084i \(-0.428795\pi\)
−0.733530 + 0.679657i \(0.762129\pi\)
\(662\) 0 0
\(663\) −290.195 + 236.255i −0.0169989 + 0.0138392i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −6940.62 12021.5i −0.402911 0.697863i
\(668\) 0 0
\(669\) −2795.55 1064.73i −0.161558 0.0615319i
\(670\) 0 0
\(671\) −6543.78 −0.376483
\(672\) 0 0
\(673\) −15931.2 −0.912488 −0.456244 0.889855i \(-0.650806\pi\)
−0.456244 + 0.889855i \(0.650806\pi\)
\(674\) 0 0
\(675\) −754.672 + 16942.5i −0.0430331 + 0.966102i
\(676\) 0 0
\(677\) −3485.21 6036.57i −0.197855 0.342694i 0.749978 0.661463i \(-0.230064\pi\)
−0.947833 + 0.318768i \(0.896731\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 9284.85 + 11404.7i 0.522461 + 0.641747i
\(682\) 0 0
\(683\) 5897.72 + 3405.05i 0.330410 + 0.190762i 0.656023 0.754741i \(-0.272237\pi\)
−0.325613 + 0.945503i \(0.605571\pi\)
\(684\) 0 0
\(685\) 4768.60i 0.265984i
\(686\) 0 0
\(687\) 3121.09 + 19377.6i 0.173329 + 1.07613i
\(688\) 0 0
\(689\) −7268.21 + 12588.9i −0.401882 + 0.696080i
\(690\) 0 0
\(691\) 10542.5 6086.72i 0.580399 0.335094i −0.180893 0.983503i \(-0.557899\pi\)
0.761292 + 0.648409i \(0.224565\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2668.89 + 1540.88i −0.145664 + 0.0840993i
\(696\) 0 0
\(697\) 360.202 623.888i 0.0195748 0.0339045i
\(698\) 0 0
\(699\) 4655.39 + 28903.5i 0.251907 + 1.56399i
\(700\) 0 0
\(701\) 31903.7i 1.71895i 0.511176 + 0.859476i \(0.329210\pi\)
−0.511176 + 0.859476i \(0.670790\pi\)
\(702\) 0 0
\(703\) −16834.5 9719.41i −0.903166 0.521443i
\(704\) 0 0
\(705\) −2484.04 3051.18i −0.132701 0.162999i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −11558.0 20019.0i −0.612228 1.06041i −0.990864 0.134865i \(-0.956940\pi\)
0.378636 0.925546i \(-0.376393\pi\)
\(710\) 0 0
\(711\) 5443.94 26287.1i 0.287150 1.38656i
\(712\) 0 0
\(713\) 2105.05 0.110568
\(714\) 0 0
\(715\) −1524.08 −0.0797164
\(716\) 0 0
\(717\) 29536.3 + 11249.4i 1.53843 + 0.585935i
\(718\) 0 0
\(719\) 11738.3 + 20331.3i 0.608852 + 1.05456i 0.991430 + 0.130639i \(0.0417028\pi\)
−0.382578 + 0.923923i \(0.624964\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 12387.5 10085.0i 0.637203 0.518762i
\(724\) 0 0
\(725\) −17887.1 10327.1i −0.916288 0.529019i
\(726\) 0 0
\(727\) 16192.1i 0.826040i −0.910722 0.413020i \(-0.864474\pi\)
0.910722 0.413020i \(-0.135526\pi\)
\(728\) 0 0
\(729\) 11318.1 16103.5i 0.575018 0.818141i
\(730\) 0 0
\(731\) −335.890 + 581.778i −0.0169950 + 0.0294362i
\(732\) 0 0
\(733\) 31235.2 18033.7i 1.57394 0.908716i 0.578264 0.815850i \(-0.303730\pi\)
0.995679 0.0928663i \(-0.0296029\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −8483.16 + 4897.76i −0.423991 + 0.244791i
\(738\) 0 0
\(739\) −10083.4 + 17464.9i −0.501925 + 0.869360i 0.498072 + 0.867136i \(0.334041\pi\)
−0.999998 + 0.00222472i \(0.999292\pi\)
\(740\) 0 0
\(741\) 14156.3 2280.11i 0.701815 0.113039i
\(742\) 0 0
\(743\) 24217.4i 1.19576i 0.801585 + 0.597881i \(0.203991\pi\)
−0.801585 + 0.597881i \(0.796009\pi\)
\(744\) 0 0
\(745\) 260.281 + 150.273i 0.0127999 + 0.00739005i
\(746\) 0 0
\(747\) 25828.0 + 23012.1i 1.26505 + 1.12713i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 3037.56 + 5261.20i 0.147592 + 0.255638i 0.930337 0.366705i \(-0.119514\pi\)
−0.782745 + 0.622343i \(0.786181\pi\)
\(752\) 0 0
\(753\) 4844.50 12719.7i 0.234453 0.615579i
\(754\) 0 0
\(755\) 5056.80 0.243756
\(756\) 0 0
\(757\) −34408.2 −1.65203 −0.826015 0.563648i \(-0.809397\pi\)
−0.826015 + 0.563648i \(0.809397\pi\)
\(758\) 0 0
\(759\) 4386.61 11517.4i 0.209781 0.550799i
\(760\) 0 0
\(761\) 7900.11 + 13683.4i 0.376319 + 0.651804i 0.990524 0.137343i \(-0.0438563\pi\)
−0.614204 + 0.789147i \(0.710523\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 114.508 + 102.024i 0.00541184 + 0.00482183i
\(766\) 0 0
\(767\) 8450.42 + 4878.85i 0.397819 + 0.229681i
\(768\) 0 0
\(769\) 35637.1i 1.67114i 0.549383 + 0.835571i \(0.314863\pi\)
−0.549383 + 0.835571i \(0.685137\pi\)
\(770\) 0 0
\(771\) 21839.7 3517.65i 1.02015 0.164312i
\(772\) 0 0
\(773\) 8586.42 14872.1i 0.399524 0.691996i −0.594143 0.804359i \(-0.702509\pi\)
0.993667 + 0.112364i \(0.0358422\pi\)
\(774\) 0 0
\(775\) 2712.52 1566.08i 0.125725 0.0725873i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −23906.1 + 13802.2i −1.09952 + 0.634807i
\(780\) 0 0
\(781\) 15025.8 26025.4i 0.688430 1.19240i
\(782\) 0 0
\(783\) 11050.0 + 21272.5i 0.504334 + 0.970903i
\(784\) 0 0
\(785\) 6002.67i 0.272923i
\(786\) 0 0
\(787\) −9242.80 5336.33i −0.418641 0.241702i 0.275855 0.961199i \(-0.411039\pi\)
−0.694496 + 0.719497i \(0.744372\pi\)
\(788\) 0 0
\(789\) −28112.8 + 22887.3i −1.26849 + 1.03271i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −2883.20 4993.86i −0.129112 0.223628i
\(794\) 0 0
\(795\) 5567.53 + 2120.49i 0.248377 + 0.0945986i
\(796\) 0 0
\(797\) 30569.6 1.35863 0.679317 0.733845i \(-0.262276\pi\)
0.679317 + 0.733845i \(0.262276\pi\)
\(798\) 0 0