Properties

Label 108.3.k.a.5.4
Level 108
Weight 3
Character 108.5
Analytic conductor 2.943
Analytic rank 0
Dimension 36
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.k (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.94278685509\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.4
Character \(\chi\) \(=\) 108.5
Dual form 108.3.k.a.65.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.02038 + 2.82114i) q^{3} +(1.26650 + 3.47969i) q^{5} +(-0.0728181 - 0.412972i) q^{7} +(-6.91763 + 5.75729i) q^{9} +O(q^{10})\) \(q+(1.02038 + 2.82114i) q^{3} +(1.26650 + 3.47969i) q^{5} +(-0.0728181 - 0.412972i) q^{7} +(-6.91763 + 5.75729i) q^{9} +(-1.69236 + 4.64973i) q^{11} +(3.65864 + 3.06996i) q^{13} +(-8.52437 + 7.12360i) q^{15} +(20.4937 + 11.8321i) q^{17} +(-13.5371 - 23.4469i) q^{19} +(1.09075 - 0.626820i) q^{21} +(20.7690 + 3.66213i) q^{23} +(8.64689 - 7.25561i) q^{25} +(-23.3007 - 13.6409i) q^{27} +(-2.12470 - 2.53212i) q^{29} +(3.01492 - 17.0984i) q^{31} +(-14.8444 - 0.0298779i) q^{33} +(1.34479 - 0.776415i) q^{35} +(24.9593 - 43.2309i) q^{37} +(-4.92757 + 13.4541i) q^{39} +(26.0603 - 31.0575i) q^{41} +(-61.2373 - 22.2885i) q^{43} +(-28.7948 - 16.7796i) q^{45} +(-26.9440 + 4.75095i) q^{47} +(45.8797 - 16.6988i) q^{49} +(-12.4684 + 69.8889i) q^{51} +59.1590i q^{53} -18.3230 q^{55} +(52.3339 - 62.1148i) q^{57} +(-16.8092 - 46.1828i) q^{59} +(11.9824 + 67.9556i) q^{61} +(2.88133 + 2.43755i) q^{63} +(-6.04884 + 16.6191i) q^{65} +(56.4874 + 47.3986i) q^{67} +(10.8610 + 62.3289i) q^{69} +(88.6346 + 51.1732i) q^{71} +(-3.81627 - 6.60997i) q^{73} +(29.2922 + 16.9906i) q^{75} +(2.04344 + 0.360314i) q^{77} +(-99.5742 + 83.5527i) q^{79} +(14.7073 - 79.6536i) q^{81} +(-44.1227 - 52.5834i) q^{83} +(-15.2165 + 86.2972i) q^{85} +(4.97544 - 8.57780i) q^{87} +(-137.829 + 79.5758i) q^{89} +(1.00139 - 1.73447i) q^{91} +(51.3134 - 8.94149i) q^{93} +(64.4432 - 76.8005i) q^{95} +(-8.07251 - 2.93815i) q^{97} +(-15.0627 - 41.9085i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 9q^{5} + 6q^{9} + O(q^{10}) \) \( 36q - 9q^{5} + 6q^{9} + 36q^{11} + 45q^{15} + 42q^{21} - 18q^{23} - 9q^{25} - 18q^{29} + 45q^{31} - 153q^{33} - 243q^{35} - 123q^{39} - 198q^{41} + 90q^{43} - 333q^{45} - 243q^{47} + 72q^{49} - 99q^{51} + 243q^{57} + 252q^{59} - 144q^{61} + 381q^{63} + 747q^{65} + 108q^{67} + 585q^{69} + 324q^{71} - 63q^{73} + 597q^{75} + 495q^{77} + 36q^{79} - 54q^{81} - 27q^{83} - 180q^{85} - 441q^{87} - 567q^{89} + 99q^{91} - 699q^{93} - 1044q^{95} - 216q^{97} - 945q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(1\)

Coefficient data

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

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
\(3\) 1.02038 + 2.82114i 0.340128 + 0.940379i
\(4\) 0 0
\(5\) 1.26650 + 3.47969i 0.253301 + 0.695938i 0.999542 + 0.0302625i \(0.00963434\pi\)
−0.746241 + 0.665676i \(0.768143\pi\)
\(6\) 0 0
\(7\) −0.0728181 0.412972i −0.0104026 0.0589960i 0.979165 0.203068i \(-0.0650913\pi\)
−0.989567 + 0.144072i \(0.953980\pi\)
\(8\) 0 0
\(9\) −6.91763 + 5.75729i −0.768626 + 0.639699i
\(10\) 0 0
\(11\) −1.69236 + 4.64973i −0.153851 + 0.422703i −0.992542 0.121906i \(-0.961099\pi\)
0.838691 + 0.544608i \(0.183322\pi\)
\(12\) 0 0
\(13\) 3.65864 + 3.06996i 0.281434 + 0.236151i 0.772567 0.634934i \(-0.218973\pi\)
−0.491133 + 0.871085i \(0.663417\pi\)
\(14\) 0 0
\(15\) −8.52437 + 7.12360i −0.568291 + 0.474907i
\(16\) 0 0
\(17\) 20.4937 + 11.8321i 1.20551 + 0.696004i 0.961776 0.273838i \(-0.0882931\pi\)
0.243738 + 0.969841i \(0.421626\pi\)
\(18\) 0 0
\(19\) −13.5371 23.4469i −0.712478 1.23405i −0.963924 0.266177i \(-0.914240\pi\)
0.251446 0.967871i \(-0.419094\pi\)
\(20\) 0 0
\(21\) 1.09075 0.626820i 0.0519404 0.0298486i
\(22\) 0 0
\(23\) 20.7690 + 3.66213i 0.902998 + 0.159223i 0.605822 0.795600i \(-0.292844\pi\)
0.297176 + 0.954823i \(0.403955\pi\)
\(24\) 0 0
\(25\) 8.64689 7.25561i 0.345876 0.290224i
\(26\) 0 0
\(27\) −23.3007 13.6409i −0.862991 0.505220i
\(28\) 0 0
\(29\) −2.12470 2.53212i −0.0732655 0.0873144i 0.728167 0.685400i \(-0.240373\pi\)
−0.801432 + 0.598086i \(0.795928\pi\)
\(30\) 0 0
\(31\) 3.01492 17.0984i 0.0972554 0.551563i −0.896777 0.442482i \(-0.854098\pi\)
0.994033 0.109081i \(-0.0347908\pi\)
\(32\) 0 0
\(33\) −14.8444 0.0298779i −0.449830 0.000905391i
\(34\) 0 0
\(35\) 1.34479 0.776415i 0.0384226 0.0221833i
\(36\) 0 0
\(37\) 24.9593 43.2309i 0.674577 1.16840i −0.302016 0.953303i \(-0.597659\pi\)
0.976592 0.215098i \(-0.0690072\pi\)
\(38\) 0 0
\(39\) −4.92757 + 13.4541i −0.126348 + 0.344976i
\(40\) 0 0
\(41\) 26.0603 31.0575i 0.635618 0.757500i −0.348053 0.937475i \(-0.613157\pi\)
0.983671 + 0.179975i \(0.0576015\pi\)
\(42\) 0 0
\(43\) −61.2373 22.2885i −1.42412 0.518338i −0.488881 0.872350i \(-0.662595\pi\)
−0.935241 + 0.354012i \(0.884817\pi\)
\(44\) 0 0
\(45\) −28.7948 16.7796i −0.639884 0.372880i
\(46\) 0 0
\(47\) −26.9440 + 4.75095i −0.573276 + 0.101084i −0.452768 0.891628i \(-0.649564\pi\)
−0.120508 + 0.992712i \(0.538452\pi\)
\(48\) 0 0
\(49\) 45.8797 16.6988i 0.936320 0.340793i
\(50\) 0 0
\(51\) −12.4684 + 69.8889i −0.244478 + 1.37037i
\(52\) 0 0
\(53\) 59.1590i 1.11621i 0.829771 + 0.558104i \(0.188471\pi\)
−0.829771 + 0.558104i \(0.811529\pi\)
\(54\) 0 0
\(55\) −18.3230 −0.333145
\(56\) 0 0
\(57\) 52.3339 62.1148i 0.918139 1.08973i
\(58\) 0 0
\(59\) −16.8092 46.1828i −0.284901 0.782760i −0.996760 0.0804369i \(-0.974368\pi\)
0.711858 0.702323i \(-0.247854\pi\)
\(60\) 0 0
\(61\) 11.9824 + 67.9556i 0.196433 + 1.11403i 0.910364 + 0.413809i \(0.135802\pi\)
−0.713931 + 0.700216i \(0.753087\pi\)
\(62\) 0 0
\(63\) 2.88133 + 2.43755i 0.0457354 + 0.0386913i
\(64\) 0 0
\(65\) −6.04884 + 16.6191i −0.0930591 + 0.255678i
\(66\) 0 0
\(67\) 56.4874 + 47.3986i 0.843096 + 0.707441i 0.958258 0.285905i \(-0.0922943\pi\)
−0.115162 + 0.993347i \(0.536739\pi\)
\(68\) 0 0
\(69\) 10.8610 + 62.3289i 0.157405 + 0.903317i
\(70\) 0 0
\(71\) 88.6346 + 51.1732i 1.24837 + 0.720749i 0.970785 0.239951i \(-0.0771313\pi\)
0.277589 + 0.960700i \(0.410465\pi\)
\(72\) 0 0
\(73\) −3.81627 6.60997i −0.0522776 0.0905475i 0.838702 0.544590i \(-0.183315\pi\)
−0.890980 + 0.454043i \(0.849981\pi\)
\(74\) 0 0
\(75\) 29.2922 + 16.9906i 0.390563 + 0.226541i
\(76\) 0 0
\(77\) 2.04344 + 0.360314i 0.0265382 + 0.00467940i
\(78\) 0 0
\(79\) −99.5742 + 83.5527i −1.26043 + 1.05763i −0.264797 + 0.964304i \(0.585305\pi\)
−0.995636 + 0.0933246i \(0.970251\pi\)
\(80\) 0 0
\(81\) 14.7073 79.6536i 0.181571 0.983378i
\(82\) 0 0
\(83\) −44.1227 52.5834i −0.531598 0.633534i 0.431684 0.902025i \(-0.357920\pi\)
−0.963282 + 0.268491i \(0.913475\pi\)
\(84\) 0 0
\(85\) −15.2165 + 86.2972i −0.179018 + 1.01526i
\(86\) 0 0
\(87\) 4.97544 8.57780i 0.0571890 0.0985954i
\(88\) 0 0
\(89\) −137.829 + 79.5758i −1.54864 + 0.894110i −0.550399 + 0.834902i \(0.685524\pi\)
−0.998246 + 0.0592087i \(0.981142\pi\)
\(90\) 0 0
\(91\) 1.00139 1.73447i 0.0110043 0.0190601i
\(92\) 0 0
\(93\) 51.3134 8.94149i 0.551757 0.0961450i
\(94\) 0 0
\(95\) 64.4432 76.8005i 0.678350 0.808426i
\(96\) 0 0
\(97\) −8.07251 2.93815i −0.0832217 0.0302902i 0.300074 0.953916i \(-0.402989\pi\)
−0.383296 + 0.923626i \(0.625211\pi\)
\(98\) 0 0
\(99\) −15.0627 41.9085i −0.152148 0.423318i
\(100\) 0 0
\(101\) −177.614 + 31.3181i −1.75855 + 0.310080i −0.957483 0.288491i \(-0.906846\pi\)
−0.801070 + 0.598571i \(0.795735\pi\)
\(102\) 0 0
\(103\) 53.4283 19.4463i 0.518721 0.188799i −0.0693741 0.997591i \(-0.522100\pi\)
0.588095 + 0.808792i \(0.299878\pi\)
\(104\) 0 0
\(105\) 3.56258 + 3.00160i 0.0339293 + 0.0285866i
\(106\) 0 0
\(107\) 165.438i 1.54615i −0.634315 0.773074i \(-0.718718\pi\)
0.634315 0.773074i \(-0.281282\pi\)
\(108\) 0 0
\(109\) 29.6226 0.271767 0.135883 0.990725i \(-0.456613\pi\)
0.135883 + 0.990725i \(0.456613\pi\)
\(110\) 0 0
\(111\) 147.428 + 26.3017i 1.32818 + 0.236952i
\(112\) 0 0
\(113\) −33.8000 92.8649i −0.299115 0.821813i −0.994648 0.103319i \(-0.967054\pi\)
0.695533 0.718494i \(-0.255168\pi\)
\(114\) 0 0
\(115\) 13.5609 + 76.9077i 0.117921 + 0.668762i
\(116\) 0 0
\(117\) −42.9838 0.173031i −0.367383 0.00147890i
\(118\) 0 0
\(119\) 3.39400 9.32493i 0.0285210 0.0783607i
\(120\) 0 0
\(121\) 73.9355 + 62.0392i 0.611037 + 0.512721i
\(122\) 0 0
\(123\) 114.209 + 41.8292i 0.928529 + 0.340075i
\(124\) 0 0
\(125\) 116.371 + 67.1869i 0.930969 + 0.537495i
\(126\) 0 0
\(127\) −97.3125 168.550i −0.766240 1.32717i −0.939588 0.342306i \(-0.888792\pi\)
0.173348 0.984861i \(-0.444541\pi\)
\(128\) 0 0
\(129\) 0.393494 195.502i 0.00305034 1.51552i
\(130\) 0 0
\(131\) −39.4243 6.95157i −0.300949 0.0530654i 0.0211346 0.999777i \(-0.493272\pi\)
−0.322084 + 0.946711i \(0.604383\pi\)
\(132\) 0 0
\(133\) −8.69718 + 7.29780i −0.0653923 + 0.0548707i
\(134\) 0 0
\(135\) 17.9558 98.3557i 0.133006 0.728561i
\(136\) 0 0
\(137\) −122.095 145.507i −0.891201 1.06209i −0.997700 0.0677791i \(-0.978409\pi\)
0.106499 0.994313i \(-0.466036\pi\)
\(138\) 0 0
\(139\) −9.40172 + 53.3198i −0.0676383 + 0.383596i 0.932131 + 0.362121i \(0.117947\pi\)
−0.999769 + 0.0214748i \(0.993164\pi\)
\(140\) 0 0
\(141\) −40.8963 71.1649i −0.290045 0.504716i
\(142\) 0 0
\(143\) −20.4662 + 11.8162i −0.143121 + 0.0826307i
\(144\) 0 0
\(145\) 6.12004 10.6002i 0.0422072 0.0731050i
\(146\) 0 0
\(147\) 93.9247 + 112.394i 0.638943 + 0.764583i
\(148\) 0 0
\(149\) −20.0605 + 23.9072i −0.134634 + 0.160451i −0.829149 0.559028i \(-0.811175\pi\)
0.694515 + 0.719478i \(0.255619\pi\)
\(150\) 0 0
\(151\) 23.7123 + 8.63059i 0.157035 + 0.0571562i 0.419342 0.907828i \(-0.362261\pi\)
−0.262306 + 0.964985i \(0.584483\pi\)
\(152\) 0 0
\(153\) −209.889 + 36.1385i −1.37182 + 0.236199i
\(154\) 0 0
\(155\) 63.3157 11.1643i 0.408488 0.0720275i
\(156\) 0 0
\(157\) −74.4482 + 27.0969i −0.474192 + 0.172592i −0.568050 0.822994i \(-0.692302\pi\)
0.0938584 + 0.995586i \(0.470080\pi\)
\(158\) 0 0
\(159\) −166.896 + 60.3649i −1.04966 + 0.379653i
\(160\) 0 0
\(161\) 8.84367i 0.0549296i
\(162\) 0 0
\(163\) −57.7099 −0.354049 −0.177024 0.984206i \(-0.556647\pi\)
−0.177024 + 0.984206i \(0.556647\pi\)
\(164\) 0 0
\(165\) −18.6965 51.6917i −0.113312 0.313283i
\(166\) 0 0
\(167\) 33.8026 + 92.8720i 0.202411 + 0.556120i 0.998816 0.0486438i \(-0.0154899\pi\)
−0.796405 + 0.604763i \(0.793268\pi\)
\(168\) 0 0
\(169\) −25.3856 143.969i −0.150210 0.851886i
\(170\) 0 0
\(171\) 228.635 + 84.2602i 1.33705 + 0.492750i
\(172\) 0 0
\(173\) −25.1544 + 69.1111i −0.145401 + 0.399486i −0.990919 0.134461i \(-0.957070\pi\)
0.845518 + 0.533947i \(0.179292\pi\)
\(174\) 0 0
\(175\) −3.62601 3.04259i −0.0207201 0.0173862i
\(176\) 0 0
\(177\) 113.136 94.5452i 0.639188 0.534154i
\(178\) 0 0
\(179\) 149.606 + 86.3751i 0.835788 + 0.482542i 0.855830 0.517257i \(-0.173047\pi\)
−0.0200423 + 0.999799i \(0.506380\pi\)
\(180\) 0 0
\(181\) 126.841 + 219.695i 0.700778 + 1.21378i 0.968194 + 0.250201i \(0.0804968\pi\)
−0.267416 + 0.963581i \(0.586170\pi\)
\(182\) 0 0
\(183\) −179.485 + 103.145i −0.980794 + 0.563633i
\(184\) 0 0
\(185\) 182.041 + 32.0988i 0.984006 + 0.173507i
\(186\) 0 0
\(187\) −89.6987 + 75.2661i −0.479672 + 0.402493i
\(188\) 0 0
\(189\) −3.93661 + 10.6159i −0.0208286 + 0.0561686i
\(190\) 0 0
\(191\) 197.779 + 235.704i 1.03549 + 1.23405i 0.971732 + 0.236088i \(0.0758655\pi\)
0.0637623 + 0.997965i \(0.479690\pi\)
\(192\) 0 0
\(193\) 35.8393 203.255i 0.185696 1.05313i −0.739363 0.673307i \(-0.764873\pi\)
0.925058 0.379825i \(-0.124016\pi\)
\(194\) 0 0
\(195\) −53.0568 0.106790i −0.272086 0.000547639i
\(196\) 0 0
\(197\) −211.002 + 121.822i −1.07108 + 0.618386i −0.928475 0.371394i \(-0.878880\pi\)
−0.142601 + 0.989780i \(0.545546\pi\)
\(198\) 0 0
\(199\) 57.5016 99.5957i 0.288953 0.500481i −0.684607 0.728912i \(-0.740026\pi\)
0.973560 + 0.228431i \(0.0733596\pi\)
\(200\) 0 0
\(201\) −76.0790 + 207.724i −0.378503 + 1.03345i
\(202\) 0 0
\(203\) −0.890977 + 1.06183i −0.00438905 + 0.00523067i
\(204\) 0 0
\(205\) 141.076 + 51.3475i 0.688176 + 0.250476i
\(206\) 0 0
\(207\) −164.756 + 94.2396i −0.795922 + 0.455264i
\(208\) 0 0
\(209\) 131.931 23.2631i 0.631251 0.111307i
\(210\) 0 0
\(211\) 84.7742 30.8553i 0.401773 0.146234i −0.133227 0.991086i \(-0.542534\pi\)
0.535000 + 0.844852i \(0.320312\pi\)
\(212\) 0 0
\(213\) −53.9253 + 302.267i −0.253170 + 1.41909i
\(214\) 0 0
\(215\) 241.315i 1.12240i
\(216\) 0 0
\(217\) −7.28072 −0.0335517
\(218\) 0 0
\(219\) 14.7536 17.5109i 0.0673679 0.0799585i
\(220\) 0 0
\(221\) 38.6552 + 106.204i 0.174910 + 0.480562i
\(222\) 0 0
\(223\) −33.8615 192.038i −0.151845 0.861156i −0.961614 0.274407i \(-0.911518\pi\)
0.809769 0.586749i \(-0.199593\pi\)
\(224\) 0 0
\(225\) −18.0434 + 99.9743i −0.0801930 + 0.444330i
\(226\) 0 0
\(227\) 11.5741 31.7996i 0.0509873 0.140086i −0.911585 0.411112i \(-0.865141\pi\)
0.962572 + 0.271026i \(0.0873628\pi\)
\(228\) 0 0
\(229\) −198.049 166.183i −0.864842 0.725689i 0.0981633 0.995170i \(-0.468703\pi\)
−0.963006 + 0.269481i \(0.913148\pi\)
\(230\) 0 0
\(231\) 1.06860 + 6.13249i 0.00462598 + 0.0265476i
\(232\) 0 0
\(233\) 232.807 + 134.411i 0.999172 + 0.576872i 0.908003 0.418963i \(-0.137606\pi\)
0.0911690 + 0.995835i \(0.470940\pi\)
\(234\) 0 0
\(235\) −50.6565 87.7397i −0.215560 0.373360i
\(236\) 0 0
\(237\) −337.318 195.657i −1.42328 0.825556i
\(238\) 0 0
\(239\) −281.988 49.7222i −1.17987 0.208043i −0.450890 0.892580i \(-0.648893\pi\)
−0.728978 + 0.684537i \(0.760004\pi\)
\(240\) 0 0
\(241\) 203.574 170.819i 0.844707 0.708793i −0.113910 0.993491i \(-0.536338\pi\)
0.958617 + 0.284698i \(0.0918932\pi\)
\(242\) 0 0
\(243\) 239.721 39.7861i 0.986505 0.163729i
\(244\) 0 0
\(245\) 116.214 + 138.498i 0.474341 + 0.565298i
\(246\) 0 0
\(247\) 22.4539 127.342i 0.0909063 0.515555i
\(248\) 0 0
\(249\) 103.323 178.131i 0.414951 0.715387i
\(250\) 0 0
\(251\) −191.060 + 110.308i −0.761195 + 0.439476i −0.829725 0.558173i \(-0.811502\pi\)
0.0685298 + 0.997649i \(0.478169\pi\)
\(252\) 0 0
\(253\) −52.1765 + 90.3724i −0.206231 + 0.357203i
\(254\) 0 0
\(255\) −258.983 + 45.1284i −1.01562 + 0.176974i
\(256\) 0 0
\(257\) −83.9405 + 100.036i −0.326617 + 0.389246i −0.904217 0.427073i \(-0.859545\pi\)
0.577601 + 0.816320i \(0.303989\pi\)
\(258\) 0 0
\(259\) −19.6706 7.15952i −0.0759484 0.0276429i
\(260\) 0 0
\(261\) 29.2760 + 5.28375i 0.112169 + 0.0202443i
\(262\) 0 0
\(263\) 367.106 64.7307i 1.39584 0.246124i 0.575408 0.817867i \(-0.304843\pi\)
0.820433 + 0.571742i \(0.193732\pi\)
\(264\) 0 0
\(265\) −205.855 + 74.9251i −0.776811 + 0.282736i
\(266\) 0 0
\(267\) −365.133 307.638i −1.36754 1.15220i
\(268\) 0 0
\(269\) 494.470i 1.83818i −0.394050 0.919089i \(-0.628926\pi\)
0.394050 0.919089i \(-0.371074\pi\)
\(270\) 0 0
\(271\) 142.570 0.526089 0.263044 0.964784i \(-0.415273\pi\)
0.263044 + 0.964784i \(0.415273\pi\)
\(272\) 0 0
\(273\) 5.91497 + 1.05525i 0.0216666 + 0.00386538i
\(274\) 0 0
\(275\) 19.1029 + 52.4848i 0.0694651 + 0.190854i
\(276\) 0 0
\(277\) −55.8824 316.925i −0.201742 1.14413i −0.902485 0.430721i \(-0.858259\pi\)
0.700744 0.713413i \(-0.252852\pi\)
\(278\) 0 0
\(279\) 77.5846 + 135.638i 0.278081 + 0.486159i
\(280\) 0 0
\(281\) 99.5636 273.549i 0.354319 0.973483i −0.626647 0.779303i \(-0.715573\pi\)
0.980966 0.194180i \(-0.0622046\pi\)
\(282\) 0 0
\(283\) −176.969 148.495i −0.625333 0.524717i 0.274142 0.961689i \(-0.411606\pi\)
−0.899475 + 0.436972i \(0.856051\pi\)
\(284\) 0 0
\(285\) 282.422 + 103.437i 0.990953 + 0.362938i
\(286\) 0 0
\(287\) −14.7236 8.50065i −0.0513016 0.0296190i
\(288\) 0 0
\(289\) 135.495 + 234.685i 0.468842 + 0.812058i
\(290\) 0 0
\(291\) 0.0518718 25.7717i 0.000178254 0.0885625i
\(292\) 0 0
\(293\) 362.264 + 63.8769i 1.23640 + 0.218010i 0.753371 0.657596i \(-0.228427\pi\)
0.483026 + 0.875606i \(0.339538\pi\)
\(294\) 0 0
\(295\) 139.413 116.981i 0.472587 0.396547i
\(296\) 0 0
\(297\) 102.860 85.2567i 0.346330 0.287060i
\(298\) 0 0
\(299\) 64.7436 + 77.1584i 0.216534 + 0.258055i
\(300\) 0 0
\(301\) −4.74536 + 26.9123i −0.0157653 + 0.0894096i
\(302\) 0 0
\(303\) −269.587 469.116i −0.889726 1.54824i
\(304\) 0 0
\(305\) −221.289 + 127.761i −0.725536 + 0.418889i
\(306\) 0 0
\(307\) −194.279 + 336.501i −0.632831 + 1.09610i 0.354139 + 0.935193i \(0.384774\pi\)
−0.986970 + 0.160903i \(0.948559\pi\)
\(308\) 0 0
\(309\) 109.378 + 130.886i 0.353974 + 0.423579i
\(310\) 0 0
\(311\) −298.220 + 355.405i −0.958907 + 1.14278i 0.0307784 + 0.999526i \(0.490201\pi\)
−0.989686 + 0.143255i \(0.954243\pi\)
\(312\) 0 0
\(313\) 46.6231 + 16.9694i 0.148956 + 0.0542154i 0.415422 0.909629i \(-0.363634\pi\)
−0.266466 + 0.963844i \(0.585856\pi\)
\(314\) 0 0
\(315\) −4.83272 + 13.1133i −0.0153420 + 0.0416295i
\(316\) 0 0
\(317\) −125.557 + 22.1392i −0.396080 + 0.0698396i −0.368141 0.929770i \(-0.620006\pi\)
−0.0279392 + 0.999610i \(0.508894\pi\)
\(318\) 0 0
\(319\) 15.3694 5.59401i 0.0481800 0.0175361i
\(320\) 0 0
\(321\) 466.723 168.810i 1.45397 0.525889i
\(322\) 0 0
\(323\) 640.686i 1.98355i
\(324\) 0 0
\(325\) 53.9103 0.165878
\(326\) 0 0
\(327\) 30.2264 + 83.5693i 0.0924355 + 0.255564i
\(328\) 0 0
\(329\) 3.92402 + 10.7812i 0.0119271 + 0.0327695i
\(330\) 0 0
\(331\) 108.947 + 617.872i 0.329146 + 1.86668i 0.478773 + 0.877939i \(0.341082\pi\)
−0.149626 + 0.988743i \(0.547807\pi\)
\(332\) 0 0
\(333\) 76.2329 + 442.753i 0.228928 + 1.32959i
\(334\) 0 0
\(335\) −93.3909 + 256.589i −0.278779 + 0.765938i
\(336\) 0 0
\(337\) −180.611 151.551i −0.535938 0.449705i 0.334208 0.942499i \(-0.391531\pi\)
−0.870146 + 0.492794i \(0.835976\pi\)
\(338\) 0 0
\(339\) 227.496 190.112i 0.671078 0.560804i
\(340\) 0 0
\(341\) 74.4008 + 42.9553i 0.218184 + 0.125969i
\(342\) 0 0
\(343\) −20.5109 35.5260i −0.0597986 0.103574i
\(344\) 0 0
\(345\) −203.130 + 116.733i −0.588782 + 0.338355i
\(346\) 0 0
\(347\) −669.149 117.989i −1.92838 0.340026i −0.928847 0.370464i \(-0.879199\pi\)
−0.999537 + 0.0304385i \(0.990310\pi\)
\(348\) 0 0
\(349\) 330.676 277.470i 0.947496 0.795043i −0.0313783 0.999508i \(-0.509990\pi\)
0.978874 + 0.204464i \(0.0655452\pi\)
\(350\) 0 0
\(351\) −43.3719 121.440i −0.123567 0.345982i
\(352\) 0 0
\(353\) −198.688 236.787i −0.562856 0.670786i 0.407292 0.913298i \(-0.366473\pi\)
−0.970148 + 0.242512i \(0.922029\pi\)
\(354\) 0 0
\(355\) −65.8109 + 373.232i −0.185383 + 1.05136i
\(356\) 0 0
\(357\) 29.7701 + 0.0599195i 0.0833896 + 0.000167842i
\(358\) 0 0
\(359\) −110.775 + 63.9560i −0.308566 + 0.178150i −0.646284 0.763097i \(-0.723678\pi\)
0.337719 + 0.941247i \(0.390345\pi\)
\(360\) 0 0
\(361\) −186.005 + 322.170i −0.515250 + 0.892438i
\(362\) 0 0
\(363\) −99.5786 + 271.886i −0.274321 + 0.748997i
\(364\) 0 0
\(365\) 18.1673 21.6510i 0.0497735 0.0593177i
\(366\) 0 0
\(367\) 277.830 + 101.122i 0.757030 + 0.275537i 0.691561 0.722318i \(-0.256923\pi\)
0.0654694 + 0.997855i \(0.479146\pi\)
\(368\) 0 0
\(369\) −1.46883 + 364.881i −0.00398057 + 0.988838i
\(370\) 0 0
\(371\) 24.4310 4.30785i 0.0658518 0.0116114i
\(372\) 0 0
\(373\) −486.381 + 177.028i −1.30397 + 0.474607i −0.898288 0.439407i \(-0.855189\pi\)
−0.405683 + 0.914014i \(0.632966\pi\)
\(374\) 0 0
\(375\) −70.8002 + 396.855i −0.188801 + 1.05828i
\(376\) 0 0
\(377\) 15.7869i 0.0418749i
\(378\) 0 0
\(379\) −85.3566 −0.225215 −0.112608 0.993640i \(-0.535920\pi\)
−0.112608 + 0.993640i \(0.535920\pi\)
\(380\) 0 0
\(381\) 376.207 446.518i 0.987420 1.17196i
\(382\) 0 0
\(383\) 154.048 + 423.243i 0.402214 + 1.10507i 0.961189 + 0.275889i \(0.0889722\pi\)
−0.558976 + 0.829184i \(0.688806\pi\)
\(384\) 0 0
\(385\) 1.33425 + 7.56689i 0.00346558 + 0.0196543i
\(386\) 0 0
\(387\) 551.938 198.377i 1.42620 0.512601i
\(388\) 0 0
\(389\) 77.8458 213.880i 0.200118 0.549819i −0.798522 0.601966i \(-0.794384\pi\)
0.998639 + 0.0521470i \(0.0166064\pi\)
\(390\) 0 0
\(391\) 382.303 + 320.790i 0.977757 + 0.820435i
\(392\) 0 0
\(393\) −20.6166 118.315i −0.0524596 0.301055i
\(394\) 0 0
\(395\) −416.849 240.668i −1.05531 0.609285i
\(396\) 0 0
\(397\) 310.195 + 537.274i 0.781349 + 1.35334i 0.931156 + 0.364620i \(0.118801\pi\)
−0.149808 + 0.988715i \(0.547865\pi\)
\(398\) 0 0
\(399\) −29.4625 17.0894i −0.0738410 0.0428305i
\(400\) 0 0
\(401\) 78.5688 + 13.8538i 0.195932 + 0.0345481i 0.270753 0.962649i \(-0.412727\pi\)
−0.0748208 + 0.997197i \(0.523838\pi\)
\(402\) 0 0
\(403\) 63.5221 53.3014i 0.157623 0.132262i
\(404\) 0 0
\(405\) 295.797 49.7049i 0.730362 0.122728i
\(406\) 0 0
\(407\) 158.771 + 189.216i 0.390102 + 0.464905i
\(408\) 0 0
\(409\) −50.6875 + 287.463i −0.123930 + 0.702844i 0.858007 + 0.513638i \(0.171703\pi\)
−0.981937 + 0.189206i \(0.939409\pi\)
\(410\) 0 0
\(411\) 285.911 492.918i 0.695647 1.19931i
\(412\) 0 0
\(413\) −17.8482 + 10.3047i −0.0432160 + 0.0249508i
\(414\) 0 0
\(415\) 127.092 220.130i 0.306246 0.530434i
\(416\) 0 0
\(417\) −160.016 + 27.8832i −0.383731 + 0.0668661i
\(418\) 0 0
\(419\) −155.180 + 184.937i −0.370359 + 0.441376i −0.918747 0.394848i \(-0.870797\pi\)
0.548388 + 0.836224i \(0.315242\pi\)
\(420\) 0 0
\(421\) −227.236 82.7073i −0.539754 0.196454i 0.0577343 0.998332i \(-0.481612\pi\)
−0.597488 + 0.801878i \(0.703835\pi\)
\(422\) 0 0
\(423\) 159.036 187.990i 0.375972 0.444420i
\(424\) 0 0
\(425\) 263.056 46.3838i 0.618955 0.109138i
\(426\) 0 0
\(427\) 27.1912 9.89679i 0.0636797 0.0231775i
\(428\) 0 0
\(429\) −54.2185 45.6810i −0.126384 0.106483i
\(430\) 0 0
\(431\) 173.287i 0.402059i −0.979585 0.201029i \(-0.935571\pi\)
0.979585 0.201029i \(-0.0644287\pi\)
\(432\) 0 0
\(433\) −277.794 −0.641556 −0.320778 0.947154i \(-0.603944\pi\)
−0.320778 + 0.947154i \(0.603944\pi\)
\(434\) 0 0
\(435\) 36.1495 + 6.44918i 0.0831023 + 0.0148257i
\(436\) 0 0
\(437\) −195.285 536.542i −0.446878 1.22779i
\(438\) 0 0
\(439\) 8.10666 + 45.9751i 0.0184662 + 0.104727i 0.992648 0.121039i \(-0.0386226\pi\)
−0.974182 + 0.225766i \(0.927512\pi\)
\(440\) 0 0
\(441\) −221.239 + 379.659i −0.501675 + 0.860905i
\(442\) 0 0
\(443\) −13.9231 + 38.2535i −0.0314292 + 0.0863511i −0.954415 0.298483i \(-0.903519\pi\)
0.922986 + 0.384834i \(0.125741\pi\)
\(444\) 0 0
\(445\) −451.461 378.821i −1.01452 0.851282i
\(446\) 0 0
\(447\) −87.9148 32.1989i −0.196677 0.0720333i
\(448\) 0 0
\(449\) −59.6506 34.4393i −0.132852 0.0767022i 0.432101 0.901825i \(-0.357772\pi\)
−0.564953 + 0.825123i \(0.691106\pi\)
\(450\) 0 0
\(451\) 100.305 + 173.734i 0.222407 + 0.385220i
\(452\) 0 0
\(453\) −0.152369 + 75.7023i −0.000336356 + 0.167113i
\(454\) 0 0
\(455\) 7.30368 + 1.28784i 0.0160520 + 0.00283041i
\(456\) 0 0
\(457\) −285.792 + 239.808i −0.625365 + 0.524744i −0.899485 0.436952i \(-0.856058\pi\)
0.274120 + 0.961696i \(0.411614\pi\)
\(458\) 0 0
\(459\) −316.119 555.250i −0.688712 1.20969i
\(460\) 0 0
\(461\) −167.368 199.462i −0.363055 0.432672i 0.553335 0.832959i \(-0.313355\pi\)
−0.916390 + 0.400287i \(0.868910\pi\)
\(462\) 0 0
\(463\) 146.176 829.003i 0.315714 1.79050i −0.252474 0.967604i \(-0.581244\pi\)
0.568188 0.822899i \(-0.307645\pi\)
\(464\) 0 0
\(465\) 96.1023 + 167.230i 0.206672 + 0.359635i
\(466\) 0 0
\(467\) −43.5511 + 25.1442i −0.0932572 + 0.0538421i −0.545903 0.837848i \(-0.683813\pi\)
0.452646 + 0.891690i \(0.350480\pi\)
\(468\) 0 0
\(469\) 15.4610 26.7792i 0.0329658 0.0570985i
\(470\) 0 0
\(471\) −152.410 182.379i −0.323588 0.387217i
\(472\) 0 0
\(473\) 207.271 247.016i 0.438206 0.522233i
\(474\) 0 0
\(475\) −287.175 104.523i −0.604579 0.220049i
\(476\) 0 0
\(477\) −340.595 409.240i −0.714036 0.857946i
\(478\) 0 0
\(479\) −285.923 + 50.4159i −0.596917 + 0.105252i −0.463940 0.885867i \(-0.653565\pi\)
−0.132977 + 0.991119i \(0.542454\pi\)
\(480\) 0 0
\(481\) 224.034 81.5419i 0.465768 0.169526i
\(482\) 0 0
\(483\) 24.9492 9.02394i 0.0516547 0.0186831i
\(484\) 0 0
\(485\) 31.8110i 0.0655897i
\(486\) 0 0
\(487\) 211.322 0.433925 0.216963 0.976180i \(-0.430385\pi\)
0.216963 + 0.976180i \(0.430385\pi\)
\(488\) 0 0
\(489\) −58.8863 162.808i −0.120422 0.332940i
\(490\) 0 0
\(491\) −67.3176 184.954i −0.137103 0.376688i 0.852073 0.523424i \(-0.175345\pi\)
−0.989176 + 0.146736i \(0.953123\pi\)
\(492\) 0 0
\(493\) −13.5828 77.0321i −0.0275514 0.156252i
\(494\) 0 0
\(495\) 126.752 105.491i 0.256064 0.213113i
\(496\) 0 0
\(497\) 14.6789 40.3299i 0.0295350 0.0811468i
\(498\) 0 0
\(499\) 373.550 + 313.445i 0.748596 + 0.628147i 0.935131 0.354301i \(-0.115281\pi\)
−0.186535 + 0.982448i \(0.559726\pi\)
\(500\) 0 0
\(501\) −227.513 + 190.127i −0.454118 + 0.379495i
\(502\) 0 0
\(503\) 829.430 + 478.871i 1.64897 + 0.952031i 0.977484 + 0.211009i \(0.0676749\pi\)
0.671481 + 0.741022i \(0.265658\pi\)
\(504\) 0 0
\(505\) −333.926 578.377i −0.661239 1.14530i
\(506\) 0 0
\(507\) 380.252 218.520i 0.750005 0.431005i
\(508\) 0 0
\(509\) 92.3684 + 16.2870i 0.181470 + 0.0319981i 0.263645 0.964620i \(-0.415075\pi\)
−0.0821744 + 0.996618i \(0.526186\pi\)
\(510\) 0 0
\(511\) −2.45184 + 2.05734i −0.00479812 + 0.00402610i
\(512\) 0 0
\(513\) −4.41392 + 730.989i −0.00860414 + 1.42493i
\(514\) 0 0
\(515\) 135.334 + 161.285i 0.262785 + 0.313175i
\(516\) 0 0
\(517\) 23.5084 133.323i 0.0454707 0.257877i
\(518\) 0 0
\(519\) −220.639 0.444089i −0.425123 0.000855663i
\(520\) 0 0
\(521\) −463.569 + 267.642i −0.889767 + 0.513707i −0.873866 0.486166i \(-0.838395\pi\)
−0.0159010 + 0.999874i \(0.505062\pi\)
\(522\) 0 0
\(523\) 182.495 316.090i 0.348939 0.604379i −0.637123 0.770763i \(-0.719875\pi\)
0.986061 + 0.166383i \(0.0532088\pi\)
\(524\) 0 0
\(525\) 4.88363 13.3341i 0.00930215 0.0253983i
\(526\) 0 0
\(527\) 264.097 314.738i 0.501132 0.597226i
\(528\) 0 0
\(529\) −79.1589 28.8115i −0.149639 0.0544641i
\(530\) 0 0
\(531\) 382.168 + 222.701i 0.719713 + 0.419398i
\(532\) 0 0
\(533\) 190.691 33.6240i 0.357769 0.0630843i
\(534\) 0 0
\(535\) 575.673 209.528i 1.07602 0.391641i
\(536\) 0 0
\(537\) −91.0203 + 510.195i −0.169498 + 0.950084i
\(538\) 0 0
\(539\) 241.589i 0.448216i
\(540\) 0 0
\(541\) 177.907 0.328848 0.164424 0.986390i \(-0.447423\pi\)
0.164424 + 0.986390i \(0.447423\pi\)
\(542\) 0 0
\(543\) −490.362 + 582.008i −0.903062 + 1.07184i
\(544\) 0 0
\(545\) 37.5171 + 103.077i 0.0688387 + 0.189133i
\(546\) 0 0
\(547\) −25.3653 143.854i −0.0463717 0.262987i 0.952804 0.303587i \(-0.0981842\pi\)
−0.999175 + 0.0405999i \(0.987073\pi\)
\(548\) 0 0
\(549\) −474.130 401.105i −0.863624 0.730611i
\(550\) 0 0
\(551\) −30.6081 + 84.0951i −0.0555501 + 0.152623i
\(552\) 0 0
\(553\) 41.7557 + 35.0372i 0.0755077 + 0.0633584i
\(554\) 0 0
\(555\) 95.1969 + 546.316i 0.171526 + 0.984353i
\(556\) 0 0
\(557\) 310.962 + 179.534i 0.558280 + 0.322323i 0.752455 0.658644i \(-0.228870\pi\)
−0.194175 + 0.980967i \(0.562203\pi\)
\(558\) 0 0
\(559\) −155.620 269.542i −0.278390 0.482186i
\(560\) 0 0
\(561\) −303.863 176.252i −0.541646 0.314175i
\(562\) 0 0
\(563\) 88.7692 + 15.6524i 0.157672 + 0.0278018i 0.251927 0.967746i \(-0.418936\pi\)
−0.0942550 + 0.995548i \(0.530047\pi\)
\(564\) 0 0
\(565\) 280.333 235.227i 0.496165 0.416332i
\(566\) 0 0
\(567\) −33.9657 0.273462i −0.0599042 0.000482296i
\(568\) 0 0
\(569\) 55.8825 + 66.5981i 0.0982117 + 0.117044i 0.812912 0.582387i \(-0.197881\pi\)
−0.714700 + 0.699431i \(0.753437\pi\)
\(570\) 0 0
\(571\) −53.7562 + 304.867i −0.0941440 + 0.533917i 0.900862 + 0.434105i \(0.142935\pi\)
−0.995006 + 0.0998121i \(0.968176\pi\)
\(572\) 0 0
\(573\) −463.143 + 798.472i −0.808278 + 1.39349i
\(574\) 0 0
\(575\) 206.158 119.025i 0.358536 0.207001i
\(576\) 0 0
\(577\) −0.428109 + 0.741507i −0.000741957 + 0.00128511i −0.866396 0.499357i \(-0.833570\pi\)
0.865654 + 0.500642i \(0.166903\pi\)
\(578\) 0 0
\(579\) 609.979 106.290i 1.05350 0.183576i
\(580\) 0 0
\(581\) −18.5025 + 22.0505i −0.0318460 + 0.0379526i
\(582\) 0 0
\(583\) −275.073 100.118i −0.471824 0.171730i
\(584\) 0 0
\(585\) −53.8371 149.789i −0.0920292 0.256050i
\(586\) 0 0
\(587\) −145.579 + 25.6695i −0.248005 + 0.0437300i −0.296269 0.955105i \(-0.595742\pi\)
0.0482634 + 0.998835i \(0.484631\pi\)
\(588\) 0 0
\(589\) −441.719 + 160.773i −0.749947 + 0.272958i
\(590\) 0 0
\(591\) −558.980 470.960i −0.945820 0.796887i
\(592\) 0 0
\(593\) 1100.38i 1.85562i 0.373053 + 0.927810i \(0.378311\pi\)
−0.373053 + 0.927810i \(0.621689\pi\)
\(594\) 0 0
\(595\) 36.7464 0.0617586
\(596\) 0 0
\(597\) 339.647 + 60.5940i 0.568923 + 0.101498i
\(598\) 0 0
\(599\) 278.390 + 764.871i 0.464758 + 1.27691i 0.921869 + 0.387503i \(0.126662\pi\)
−0.457110 + 0.889410i \(0.651116\pi\)
\(600\) 0 0
\(601\) 29.8172 + 169.102i 0.0496127 + 0.281367i 0.999514 0.0311835i \(-0.00992763\pi\)
−0.949901 + 0.312551i \(0.898817\pi\)
\(602\) 0 0
\(603\) −663.646 2.67151i −1.10057 0.00443036i
\(604\) 0 0
\(605\) −122.238 + 335.846i −0.202046 + 0.555117i
\(606\) 0 0
\(607\) 228.821 + 192.003i 0.376970 + 0.316315i 0.811512 0.584336i \(-0.198645\pi\)
−0.434542 + 0.900652i \(0.643090\pi\)
\(608\) 0 0
\(609\) −3.90469 1.43010i −0.00641165 0.00234827i
\(610\) 0 0
\(611\) −113.164 65.3351i −0.185211 0.106931i
\(612\) 0 0
\(613\) −531.261 920.171i −0.866657 1.50109i −0.865392 0.501096i \(-0.832931\pi\)
−0.00126544 0.999999i \(-0.500403\pi\)
\(614\) 0 0
\(615\) −0.906517 + 450.389i −0.00147401 + 0.732340i
\(616\) 0 0
\(617\) 1155.37 + 203.722i 1.87255 + 0.330182i 0.990116 0.140248i \(-0.0447900\pi\)
0.882437 + 0.470430i \(0.155901\pi\)
\(618\) 0 0
\(619\) −830.742 + 697.075i −1.34207 + 1.12613i −0.360983 + 0.932572i \(0.617559\pi\)
−0.981089 + 0.193559i \(0.937997\pi\)
\(620\) 0 0
\(621\) −433.977 368.638i −0.698836 0.593621i
\(622\) 0 0
\(623\) 42.8991 + 51.1251i 0.0688589 + 0.0820628i
\(624\) 0 0
\(625\) −37.4029 + 212.122i −0.0598446 + 0.339395i
\(626\) 0 0
\(627\) 200.249 + 348.459i 0.319376 + 0.555757i
\(628\) 0 0
\(629\) 1023.02 590.641i 1.62642 0.939016i
\(630\) 0 0
\(631\) 224.052 388.070i 0.355075 0.615008i −0.632056 0.774923i \(-0.717789\pi\)
0.987131 + 0.159915i \(0.0511220\pi\)
\(632\) 0 0
\(633\) 173.549 + 207.675i 0.274169 + 0.328081i
\(634\) 0 0
\(635\) 463.256 552.087i 0.729537 0.869428i
\(636\) 0 0
\(637\) 219.122 + 79.7540i 0.343991 + 0.125202i
\(638\) 0 0
\(639\) −907.760 + 156.297i −1.42059 + 0.244597i
\(640\) 0 0
\(641\) −1055.80 + 186.166i −1.64711 + 0.290430i −0.918773 0.394787i \(-0.870818\pi\)
−0.728339 + 0.685217i \(0.759707\pi\)
\(642\) 0 0
\(643\) 567.428 206.527i 0.882469 0.321193i 0.139263 0.990255i \(-0.455527\pi\)
0.743206 + 0.669063i \(0.233304\pi\)
\(644\) 0 0
\(645\) 680.784 246.234i 1.05548 0.381759i
\(646\) 0 0
\(647\) 666.631i 1.03034i 0.857087 + 0.515171i \(0.172272\pi\)
−0.857087 + 0.515171i \(0.827728\pi\)
\(648\) 0 0
\(649\) 243.185 0.374707
\(650\) 0 0
\(651\) −7.42913 20.5399i −0.0114119 0.0315513i
\(652\) 0 0
\(653\) −331.003 909.424i −0.506896 1.39269i −0.884422 0.466687i \(-0.845447\pi\)
0.377526 0.925999i \(-0.376775\pi\)
\(654\) 0 0
\(655\) −25.7417 145.989i −0.0393004 0.222883i
\(656\) 0 0
\(657\) 64.4550 + 23.7540i 0.0981050 + 0.0361552i
\(658\) 0 0
\(659\) −80.4022 + 220.903i −0.122006 + 0.335210i −0.985628 0.168931i \(-0.945969\pi\)
0.863621 + 0.504141i \(0.168191\pi\)
\(660\) 0 0
\(661\) 217.996 + 182.920i 0.329797 + 0.276732i 0.792617 0.609720i \(-0.208718\pi\)
−0.462820 + 0.886452i \(0.653162\pi\)
\(662\) 0 0
\(663\) −260.174 + 217.421i −0.392419 + 0.327935i
\(664\) 0 0
\(665\) −36.4091 21.0208i −0.0547505 0.0316102i
\(666\) 0 0
\(667\) −34.8548 60.3703i −0.0522561 0.0905103i
\(668\) 0 0
\(669\) 507.213 291.480i 0.758167 0.435695i
\(670\) 0 0
\(671\) −336.253 59.2906i −0.501123 0.0883615i
\(672\) 0 0
\(673\) −456.711 + 383.226i −0.678620 + 0.569430i −0.915603 0.402084i \(-0.868286\pi\)
0.236983 + 0.971514i \(0.423841\pi\)
\(674\) 0 0
\(675\) −300.452 + 51.1092i −0.445115 + 0.0757174i
\(676\) 0 0
\(677\) −193.259 230.317i −0.285464 0.340203i 0.604188 0.796842i \(-0.293498\pi\)
−0.889652 + 0.456639i \(0.849053\pi\)
\(678\) 0 0
\(679\) −0.625550 + 3.54767i −0.000921282 + 0.00522485i
\(680\) 0 0
\(681\) 101.521 + 0.204336i 0.149076 + 0.000300052i
\(682\) 0 0
\(683\) 690.441 398.626i 1.01089 0.583640i 0.0994413 0.995043i \(-0.468294\pi\)
0.911454 + 0.411403i \(0.134961\pi\)
\(684\) 0 0
\(685\) 351.685 609.136i 0.513408 0.889249i
\(686\) 0 0
\(687\) 266.738 728.293i 0.388265 1.06011i
\(688\) 0 0
\(689\) −181.616 + 216.442i −0.263594 + 0.314139i
\(690\) 0 0
\(691\) 571.492 + 208.006i 0.827050 + 0.301022i 0.720648 0.693301i \(-0.243845\pi\)
0.106403 + 0.994323i \(0.466067\pi\)
\(692\) 0 0
\(693\) −16.2102 + 9.27217i −0.0233914 + 0.0133798i
\(694\) 0 0
\(695\) −197.444 + 34.8147i −0.284092 + 0.0500931i
\(696\) 0 0
\(697\) 901.548 328.137i 1.29347 0.470784i
\(698\) 0 0
\(699\) −141.640 + 793.932i −0.202632 + 1.13581i
\(700\) 0 0
\(701\) 722.930i 1.03128i 0.856804 + 0.515642i \(0.172446\pi\)
−0.856804 + 0.515642i \(0.827554\pi\)
\(702\) 0 0
\(703\) −1351.51 −1.92248
\(704\) 0 0
\(705\) 195.837 232.437i 0.277782 0.329698i
\(706\) 0 0
\(707\) 25.8670 + 71.0690i 0.0365870 + 0.100522i
\(708\) 0 0
\(709\) −109.152 619.033i −0.153952 0.873108i −0.959737 0.280899i \(-0.909367\pi\)
0.805785 0.592208i \(-0.201744\pi\)
\(710\) 0 0
\(711\) 207.781 1151.26i 0.292237 1.61922i
\(712\) 0 0
\(713\) 125.233 344.076i 0.175643 0.482575i
\(714\) 0 0
\(715\) −67.0373 56.2510i −0.0937584 0.0786727i
\(716\) 0 0
\(717\) −147.463 846.264i −0.205667 1.18028i
\(718\) 0 0
\(719\) −594.383 343.167i −0.826680 0.477284i 0.0260347 0.999661i \(-0.491712\pi\)
−0.852714 + 0.522377i \(0.825045\pi\)
\(720\) 0 0
\(721\) −11.9213 20.6484i −0.0165344 0.0286385i
\(722\) 0 0
\(723\) 689.629 + 400.010i 0.953843 + 0.553264i
\(724\) 0 0
\(725\) −36.7441 6.47897i −0.0506815 0.00893651i
\(726\) 0 0
\(727\) −178.673 + 149.924i −0.245767 + 0.206223i −0.757347 0.653012i \(-0.773505\pi\)
0.511580 + 0.859236i \(0.329060\pi\)
\(728\) 0 0
\(729\) 356.849 + 635.688i 0.489505 + 0.872000i
\(730\) 0 0
\(731\) −991.261 1181.34i −1.35603 1.61606i
\(732\) 0 0
\(733\) −32.0772 + 181.919i −0.0437615 + 0.248184i −0.998839 0.0481722i \(-0.984660\pi\)
0.955078 + 0.296356i \(0.0957715\pi\)
\(734\) 0 0
\(735\) −272.139 + 469.176i −0.370258 + 0.638334i
\(736\) 0 0
\(737\) −315.988 + 182.436i −0.428749 + 0.247538i
\(738\) 0 0
\(739\) 117.640 203.758i 0.159188 0.275721i −0.775388 0.631485i \(-0.782446\pi\)
0.934576 + 0.355763i \(0.115779\pi\)
\(740\) 0 0
\(741\) 382.161 66.5925i 0.515737 0.0898685i
\(742\) 0 0
\(743\) 808.583 963.631i 1.08827 1.29695i 0.136327 0.990664i \(-0.456470\pi\)
0.951941 0.306283i \(-0.0990853\pi\)
\(744\) 0 0
\(745\) −108.596 39.5258i −0.145767 0.0530547i
\(746\) 0 0
\(747\) 607.962 + 109.725i 0.813871 + 0.146888i
\(748\) 0 0
\(749\) −68.3213 + 12.0469i −0.0912166 + 0.0160840i
\(750\) 0 0
\(751\) −611.586 + 222.599i −0.814363 + 0.296404i −0.715425 0.698690i \(-0.753767\pi\)
−0.0989379 + 0.995094i \(0.531545\pi\)
\(752\) 0 0
\(753\) −506.150 426.449i −0.672178 0.566333i
\(754\) 0 0
\(755\) 93.4423i 0.123765i
\(756\) 0 0
\(757\) 802.442 1.06003 0.530015 0.847988i \(-0.322186\pi\)
0.530015 + 0.847988i \(0.322186\pi\)
\(758\) 0 0
\(759\) −308.193 54.9826i −0.406051 0.0724408i
\(760\) 0 0
\(761\) −242.179 665.380i −0.318237 0.874350i −0.990924 0.134422i \(-0.957082\pi\)
0.672687 0.739927i \(-0.265140\pi\)
\(762\) 0 0
\(763\) −2.15706 12.2333i −0.00282708 0.0160332i
\(764\) 0 0
\(765\) −391.576 684.578i −0.511863 0.894873i
\(766\) 0 0
\(767\) 80.2809 220.570i 0.104669 0.287575i
\(768\) 0 0
\(769\) 840.006 + 704.848i 1.09233 + 0.916578i 0.996886 0.0788564i \(-0.0251269\pi\)
0.0954490 + 0.995434i \(0.469571\pi\)
\(770\) 0 0
\(771\) −367.868 134.732i −0.477131 0.174750i
\(772\) 0 0
\(773\) −218.368 126.075i −0.282495 0.163098i 0.352058 0.935978i \(-0.385482\pi\)
−0.634552 + 0.772880i \(0.718815\pi\)
\(774\) 0 0
\(775\) −97.9899 169.723i −0.126439 0.218998i
\(776\) 0 0
\(777\) 0.126398 62.7990i 0.000162675 0.0808224i
\(778\) 0 0
\(779\) −1080.98 190.607i −1.38766 0.244681i
\(780\) 0 0
\(781\) −387.943 + 325.523i −0.496726 + 0.416803i
\(782\) 0 0
\(783\) 14.9666 + 87.9831i 0.0191144 + 0.112367i