Properties

Label 1148.2.ba.a.113.5
Level $1148$
Weight $2$
Character 1148.113
Analytic conductor $9.167$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.ba (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 113.5
Character \(\chi\) \(=\) 1148.113
Dual form 1148.2.ba.a.701.16

$q$-expansion

\(f(q)\) \(=\) \(q-1.92602i q^{3} +(-0.139283 - 0.428669i) q^{5} +(0.587785 + 0.809017i) q^{7} -0.709536 q^{9} +O(q^{10})\) \(q-1.92602i q^{3} +(-0.139283 - 0.428669i) q^{5} +(0.587785 + 0.809017i) q^{7} -0.709536 q^{9} +(-2.10233 - 0.683089i) q^{11} +(-0.972224 + 1.33815i) q^{13} +(-0.825623 + 0.268261i) q^{15} +(-2.14323 - 0.696377i) q^{17} +(-5.11495 - 7.04013i) q^{19} +(1.55818 - 1.13208i) q^{21} +(-3.19690 - 2.32268i) q^{23} +(3.88073 - 2.81951i) q^{25} -4.41147i q^{27} +(0.718030 - 0.233302i) q^{29} +(-1.81584 + 5.58857i) q^{31} +(-1.31564 + 4.04912i) q^{33} +(0.264932 - 0.364648i) q^{35} +(-2.05784 - 6.33339i) q^{37} +(2.57730 + 1.87252i) q^{39} +(-1.14365 - 6.30016i) q^{41} +(0.280406 + 0.203727i) q^{43} +(0.0988263 + 0.304156i) q^{45} +(-5.20384 + 7.16247i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(-1.34123 + 4.12789i) q^{51} +(1.15547 - 0.375434i) q^{53} +0.996346i q^{55} +(-13.5594 + 9.85147i) q^{57} +(-2.93755 - 2.13426i) q^{59} +(-7.32118 + 5.31915i) q^{61} +(-0.417055 - 0.574027i) q^{63} +(0.709038 + 0.230381i) q^{65} +(11.0803 - 3.60019i) q^{67} +(-4.47353 + 6.15728i) q^{69} +(-1.00436 - 0.326337i) q^{71} +9.55551 q^{73} +(-5.43043 - 7.47434i) q^{75} +(-0.683089 - 2.10233i) q^{77} -6.59667i q^{79} -10.6252 q^{81} -17.0599 q^{83} +1.01573i q^{85} +(-0.449343 - 1.38294i) q^{87} +(0.654613 + 0.900998i) q^{89} -1.65405 q^{91} +(10.7637 + 3.49733i) q^{93} +(-2.30546 + 3.17319i) q^{95} +(14.0674 - 4.57079i) q^{97} +(1.49168 + 0.484676i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{5} - 60q^{9} + O(q^{10}) \) \( 80q - 4q^{5} - 60q^{9} + 10q^{11} + 20q^{15} - 10q^{17} - 30q^{19} - 4q^{21} - 20q^{25} + 2q^{31} + 10q^{33} + 10q^{37} + 36q^{39} - 14q^{41} + 30q^{43} + 44q^{45} - 60q^{47} + 20q^{49} - 32q^{51} + 16q^{57} - 60q^{59} + 44q^{61} - 10q^{65} - 10q^{67} - 40q^{71} - 88q^{73} - 70q^{75} - 8q^{77} - 40q^{81} + 28q^{83} - 24q^{87} + 24q^{91} - 100q^{93} + 120q^{97} - 100q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\)

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
\(3\) 1.92602i 1.11199i −0.831187 0.555993i \(-0.812338\pi\)
0.831187 0.555993i \(-0.187662\pi\)
\(4\) 0 0
\(5\) −0.139283 0.428669i −0.0622892 0.191707i 0.915069 0.403297i \(-0.132136\pi\)
−0.977358 + 0.211590i \(0.932136\pi\)
\(6\) 0 0
\(7\) 0.587785 + 0.809017i 0.222162 + 0.305780i
\(8\) 0 0
\(9\) −0.709536 −0.236512
\(10\) 0 0
\(11\) −2.10233 0.683089i −0.633877 0.205959i −0.0255851 0.999673i \(-0.508145\pi\)
−0.608292 + 0.793714i \(0.708145\pi\)
\(12\) 0 0
\(13\) −0.972224 + 1.33815i −0.269647 + 0.371137i −0.922270 0.386546i \(-0.873668\pi\)
0.652624 + 0.757682i \(0.273668\pi\)
\(14\) 0 0
\(15\) −0.825623 + 0.268261i −0.213175 + 0.0692647i
\(16\) 0 0
\(17\) −2.14323 0.696377i −0.519809 0.168896i 0.0373496 0.999302i \(-0.488108\pi\)
−0.557159 + 0.830406i \(0.688108\pi\)
\(18\) 0 0
\(19\) −5.11495 7.04013i −1.17345 1.61512i −0.635294 0.772270i \(-0.719121\pi\)
−0.538156 0.842845i \(-0.680879\pi\)
\(20\) 0 0
\(21\) 1.55818 1.13208i 0.340023 0.247041i
\(22\) 0 0
\(23\) −3.19690 2.32268i −0.666600 0.484313i 0.202286 0.979327i \(-0.435163\pi\)
−0.868885 + 0.495014i \(0.835163\pi\)
\(24\) 0 0
\(25\) 3.88073 2.81951i 0.776146 0.563903i
\(26\) 0 0
\(27\) 4.41147i 0.848988i
\(28\) 0 0
\(29\) 0.718030 0.233302i 0.133335 0.0433231i −0.241589 0.970379i \(-0.577669\pi\)
0.374924 + 0.927055i \(0.377669\pi\)
\(30\) 0 0
\(31\) −1.81584 + 5.58857i −0.326134 + 1.00374i 0.644792 + 0.764358i \(0.276944\pi\)
−0.970926 + 0.239379i \(0.923056\pi\)
\(32\) 0 0
\(33\) −1.31564 + 4.04912i −0.229023 + 0.704862i
\(34\) 0 0
\(35\) 0.264932 0.364648i 0.0447817 0.0616367i
\(36\) 0 0
\(37\) −2.05784 6.33339i −0.338308 1.04120i −0.965070 0.261993i \(-0.915620\pi\)
0.626762 0.779211i \(-0.284380\pi\)
\(38\) 0 0
\(39\) 2.57730 + 1.87252i 0.412699 + 0.299843i
\(40\) 0 0
\(41\) −1.14365 6.30016i −0.178608 0.983920i
\(42\) 0 0
\(43\) 0.280406 + 0.203727i 0.0427616 + 0.0310681i 0.608961 0.793200i \(-0.291587\pi\)
−0.566199 + 0.824268i \(0.691587\pi\)
\(44\) 0 0
\(45\) 0.0988263 + 0.304156i 0.0147322 + 0.0453409i
\(46\) 0 0
\(47\) −5.20384 + 7.16247i −0.759058 + 1.04475i 0.238234 + 0.971208i \(0.423432\pi\)
−0.997292 + 0.0735459i \(0.976568\pi\)
\(48\) 0 0
\(49\) −0.309017 + 0.951057i −0.0441453 + 0.135865i
\(50\) 0 0
\(51\) −1.34123 + 4.12789i −0.187810 + 0.578020i
\(52\) 0 0
\(53\) 1.15547 0.375434i 0.158715 0.0515698i −0.228582 0.973525i \(-0.573409\pi\)
0.387297 + 0.921955i \(0.373409\pi\)
\(54\) 0 0
\(55\) 0.996346i 0.134347i
\(56\) 0 0
\(57\) −13.5594 + 9.85147i −1.79599 + 1.30486i
\(58\) 0 0
\(59\) −2.93755 2.13426i −0.382437 0.277857i 0.379912 0.925022i \(-0.375954\pi\)
−0.762349 + 0.647166i \(0.775954\pi\)
\(60\) 0 0
\(61\) −7.32118 + 5.31915i −0.937381 + 0.681047i −0.947789 0.318899i \(-0.896687\pi\)
0.0104081 + 0.999946i \(0.496687\pi\)
\(62\) 0 0
\(63\) −0.417055 0.574027i −0.0525440 0.0723206i
\(64\) 0 0
\(65\) 0.709038 + 0.230381i 0.0879454 + 0.0285752i
\(66\) 0 0
\(67\) 11.0803 3.60019i 1.35367 0.439834i 0.459745 0.888051i \(-0.347941\pi\)
0.893925 + 0.448217i \(0.147941\pi\)
\(68\) 0 0
\(69\) −4.47353 + 6.15728i −0.538549 + 0.741249i
\(70\) 0 0
\(71\) −1.00436 0.326337i −0.119196 0.0387291i 0.248812 0.968552i \(-0.419960\pi\)
−0.368008 + 0.929823i \(0.619960\pi\)
\(72\) 0 0
\(73\) 9.55551 1.11839 0.559194 0.829037i \(-0.311111\pi\)
0.559194 + 0.829037i \(0.311111\pi\)
\(74\) 0 0
\(75\) −5.43043 7.47434i −0.627052 0.863063i
\(76\) 0 0
\(77\) −0.683089 2.10233i −0.0778452 0.239583i
\(78\) 0 0
\(79\) 6.59667i 0.742183i −0.928596 0.371092i \(-0.878984\pi\)
0.928596 0.371092i \(-0.121016\pi\)
\(80\) 0 0
\(81\) −10.6252 −1.18057
\(82\) 0 0
\(83\) −17.0599 −1.87256 −0.936282 0.351249i \(-0.885757\pi\)
−0.936282 + 0.351249i \(0.885757\pi\)
\(84\) 0 0
\(85\) 1.01573i 0.110171i
\(86\) 0 0
\(87\) −0.449343 1.38294i −0.0481747 0.148266i
\(88\) 0 0
\(89\) 0.654613 + 0.900998i 0.0693888 + 0.0955056i 0.842301 0.539008i \(-0.181201\pi\)
−0.772912 + 0.634513i \(0.781201\pi\)
\(90\) 0 0
\(91\) −1.65405 −0.173391
\(92\) 0 0
\(93\) 10.7637 + 3.49733i 1.11614 + 0.362656i
\(94\) 0 0
\(95\) −2.30546 + 3.17319i −0.236535 + 0.325562i
\(96\) 0 0
\(97\) 14.0674 4.57079i 1.42833 0.464093i 0.510093 0.860119i \(-0.329611\pi\)
0.918240 + 0.396026i \(0.129611\pi\)
\(98\) 0 0
\(99\) 1.49168 + 0.484676i 0.149920 + 0.0487118i
\(100\) 0 0
\(101\) 8.75730 + 12.0534i 0.871384 + 1.19936i 0.978734 + 0.205136i \(0.0657635\pi\)
−0.107350 + 0.994221i \(0.534236\pi\)
\(102\) 0 0
\(103\) −8.73706 + 6.34785i −0.860888 + 0.625472i −0.928126 0.372265i \(-0.878581\pi\)
0.0672382 + 0.997737i \(0.478581\pi\)
\(104\) 0 0
\(105\) −0.702317 0.510263i −0.0685391 0.0497966i
\(106\) 0 0
\(107\) 7.71510 5.60535i 0.745847 0.541890i −0.148690 0.988884i \(-0.547506\pi\)
0.894537 + 0.446994i \(0.147506\pi\)
\(108\) 0 0
\(109\) 5.26522i 0.504316i 0.967686 + 0.252158i \(0.0811403\pi\)
−0.967686 + 0.252158i \(0.918860\pi\)
\(110\) 0 0
\(111\) −12.1982 + 3.96344i −1.15780 + 0.376193i
\(112\) 0 0
\(113\) −4.54679 + 13.9936i −0.427726 + 1.31641i 0.472633 + 0.881259i \(0.343303\pi\)
−0.900360 + 0.435147i \(0.856697\pi\)
\(114\) 0 0
\(115\) −0.550389 + 1.69392i −0.0513240 + 0.157959i
\(116\) 0 0
\(117\) 0.689829 0.949468i 0.0637747 0.0877783i
\(118\) 0 0
\(119\) −0.696377 2.14323i −0.0638368 0.196469i
\(120\) 0 0
\(121\) −4.94600 3.59348i −0.449636 0.326680i
\(122\) 0 0
\(123\) −12.1342 + 2.20269i −1.09411 + 0.198610i
\(124\) 0 0
\(125\) −3.57239 2.59550i −0.319525 0.232148i
\(126\) 0 0
\(127\) 0.115096 + 0.354230i 0.0102131 + 0.0314328i 0.956033 0.293258i \(-0.0947396\pi\)
−0.945820 + 0.324691i \(0.894740\pi\)
\(128\) 0 0
\(129\) 0.392382 0.540067i 0.0345473 0.0475502i
\(130\) 0 0
\(131\) 6.21892 19.1399i 0.543350 1.67226i −0.181531 0.983385i \(-0.558105\pi\)
0.724881 0.688874i \(-0.241895\pi\)
\(132\) 0 0
\(133\) 2.68909 8.27616i 0.233174 0.717634i
\(134\) 0 0
\(135\) −1.89106 + 0.614442i −0.162756 + 0.0528828i
\(136\) 0 0
\(137\) 10.3062i 0.880514i 0.897872 + 0.440257i \(0.145113\pi\)
−0.897872 + 0.440257i \(0.854887\pi\)
\(138\) 0 0
\(139\) 2.15444 1.56529i 0.182737 0.132766i −0.492656 0.870224i \(-0.663974\pi\)
0.675393 + 0.737458i \(0.263974\pi\)
\(140\) 0 0
\(141\) 13.7950 + 10.0227i 1.16175 + 0.844062i
\(142\) 0 0
\(143\) 2.95801 2.14912i 0.247362 0.179719i
\(144\) 0 0
\(145\) −0.200019 0.275302i −0.0166106 0.0228626i
\(146\) 0 0
\(147\) 1.83175 + 0.595172i 0.151080 + 0.0490889i
\(148\) 0 0
\(149\) 9.36952 3.04434i 0.767581 0.249402i 0.101052 0.994881i \(-0.467779\pi\)
0.666529 + 0.745479i \(0.267779\pi\)
\(150\) 0 0
\(151\) 12.4149 17.0876i 1.01031 1.39057i 0.0915286 0.995802i \(-0.470825\pi\)
0.918781 0.394769i \(-0.129175\pi\)
\(152\) 0 0
\(153\) 1.52070 + 0.494105i 0.122941 + 0.0399460i
\(154\) 0 0
\(155\) 2.64856 0.212738
\(156\) 0 0
\(157\) −2.86206 3.93928i −0.228417 0.314389i 0.679390 0.733778i \(-0.262245\pi\)
−0.907807 + 0.419388i \(0.862245\pi\)
\(158\) 0 0
\(159\) −0.723091 2.22545i −0.0573449 0.176489i
\(160\) 0 0
\(161\) 3.95159i 0.311429i
\(162\) 0 0
\(163\) 3.29317 0.257941 0.128971 0.991648i \(-0.458833\pi\)
0.128971 + 0.991648i \(0.458833\pi\)
\(164\) 0 0
\(165\) 1.91898 0.149392
\(166\) 0 0
\(167\) 18.8829i 1.46120i −0.682804 0.730602i \(-0.739240\pi\)
0.682804 0.730602i \(-0.260760\pi\)
\(168\) 0 0
\(169\) 3.17179 + 9.76177i 0.243984 + 0.750905i
\(170\) 0 0
\(171\) 3.62924 + 4.99523i 0.277535 + 0.381994i
\(172\) 0 0
\(173\) −20.7077 −1.57438 −0.787188 0.616714i \(-0.788464\pi\)
−0.787188 + 0.616714i \(0.788464\pi\)
\(174\) 0 0
\(175\) 4.56207 + 1.48231i 0.344860 + 0.112052i
\(176\) 0 0
\(177\) −4.11061 + 5.65777i −0.308973 + 0.425264i
\(178\) 0 0
\(179\) 8.31791 2.70265i 0.621710 0.202006i 0.0188107 0.999823i \(-0.494012\pi\)
0.602899 + 0.797817i \(0.294012\pi\)
\(180\) 0 0
\(181\) 15.2537 + 4.95623i 1.13380 + 0.368394i 0.815019 0.579435i \(-0.196727\pi\)
0.318781 + 0.947828i \(0.396727\pi\)
\(182\) 0 0
\(183\) 10.2448 + 14.1007i 0.757314 + 1.04235i
\(184\) 0 0
\(185\) −2.42831 + 1.76427i −0.178533 + 0.129712i
\(186\) 0 0
\(187\) 4.03009 + 2.92803i 0.294709 + 0.214119i
\(188\) 0 0
\(189\) 3.56895 2.59300i 0.259603 0.188613i
\(190\) 0 0
\(191\) 7.15899i 0.518006i 0.965876 + 0.259003i \(0.0833940\pi\)
−0.965876 + 0.259003i \(0.916606\pi\)
\(192\) 0 0
\(193\) 23.9479 7.78113i 1.72380 0.560098i 0.731273 0.682085i \(-0.238926\pi\)
0.992532 + 0.121987i \(0.0389265\pi\)
\(194\) 0 0
\(195\) 0.443717 1.36562i 0.0317752 0.0977940i
\(196\) 0 0
\(197\) 7.66918 23.6033i 0.546407 1.68167i −0.171215 0.985234i \(-0.554769\pi\)
0.717622 0.696433i \(-0.245231\pi\)
\(198\) 0 0
\(199\) 6.41021 8.82289i 0.454408 0.625438i −0.518930 0.854817i \(-0.673669\pi\)
0.973337 + 0.229379i \(0.0736694\pi\)
\(200\) 0 0
\(201\) −6.93403 21.3408i −0.489089 1.50526i
\(202\) 0 0
\(203\) 0.610792 + 0.443767i 0.0428692 + 0.0311463i
\(204\) 0 0
\(205\) −2.54139 + 1.36775i −0.177499 + 0.0955280i
\(206\) 0 0
\(207\) 2.26832 + 1.64803i 0.157659 + 0.114546i
\(208\) 0 0
\(209\) 5.94429 + 18.2946i 0.411175 + 1.26547i
\(210\) 0 0
\(211\) −6.54725 + 9.01151i −0.450731 + 0.620378i −0.972554 0.232675i \(-0.925252\pi\)
0.521823 + 0.853054i \(0.325252\pi\)
\(212\) 0 0
\(213\) −0.628530 + 1.93442i −0.0430662 + 0.132544i
\(214\) 0 0
\(215\) 0.0482756 0.148577i 0.00329237 0.0101329i
\(216\) 0 0
\(217\) −5.58857 + 1.81584i −0.379377 + 0.123267i
\(218\) 0 0
\(219\) 18.4041i 1.24363i
\(220\) 0 0
\(221\) 3.01556 2.19093i 0.202848 0.147378i
\(222\) 0 0
\(223\) −2.86057 2.07833i −0.191558 0.139175i 0.487872 0.872915i \(-0.337773\pi\)
−0.679431 + 0.733740i \(0.737773\pi\)
\(224\) 0 0
\(225\) −2.75352 + 2.00055i −0.183568 + 0.133370i
\(226\) 0 0
\(227\) −12.6120 17.3590i −0.837091 1.15216i −0.986561 0.163391i \(-0.947757\pi\)
0.149470 0.988766i \(-0.452243\pi\)
\(228\) 0 0
\(229\) −0.122283 0.0397321i −0.00808067 0.00262557i 0.304974 0.952361i \(-0.401352\pi\)
−0.313055 + 0.949735i \(0.601352\pi\)
\(230\) 0 0
\(231\) −4.04912 + 1.31564i −0.266413 + 0.0865627i
\(232\) 0 0
\(233\) 3.12780 4.30505i 0.204909 0.282033i −0.694178 0.719804i \(-0.744232\pi\)
0.899087 + 0.437771i \(0.144232\pi\)
\(234\) 0 0
\(235\) 3.79513 + 1.23311i 0.247567 + 0.0804395i
\(236\) 0 0
\(237\) −12.7053 −0.825297
\(238\) 0 0
\(239\) 11.0216 + 15.1699i 0.712925 + 0.981257i 0.999729 + 0.0232681i \(0.00740713\pi\)
−0.286804 + 0.957989i \(0.592593\pi\)
\(240\) 0 0
\(241\) 3.26751 + 10.0564i 0.210479 + 0.647787i 0.999444 + 0.0333489i \(0.0106173\pi\)
−0.788965 + 0.614438i \(0.789383\pi\)
\(242\) 0 0
\(243\) 7.22983i 0.463794i
\(244\) 0 0
\(245\) 0.450729 0.0287960
\(246\) 0 0
\(247\) 14.3936 0.915845
\(248\) 0 0
\(249\) 32.8576i 2.08226i
\(250\) 0 0
\(251\) −4.36736 13.4413i −0.275665 0.848410i −0.989043 0.147630i \(-0.952835\pi\)
0.713377 0.700780i \(-0.247165\pi\)
\(252\) 0 0
\(253\) 5.13434 + 7.06682i 0.322793 + 0.444287i
\(254\) 0 0
\(255\) 1.95631 0.122509
\(256\) 0 0
\(257\) −11.4037 3.70529i −0.711344 0.231130i −0.0690779 0.997611i \(-0.522006\pi\)
−0.642266 + 0.766482i \(0.722006\pi\)
\(258\) 0 0
\(259\) 3.91425 5.38751i 0.243220 0.334763i
\(260\) 0 0
\(261\) −0.509468 + 0.165536i −0.0315353 + 0.0102464i
\(262\) 0 0
\(263\) 19.9964 + 6.49722i 1.23303 + 0.400636i 0.851811 0.523849i \(-0.175504\pi\)
0.381219 + 0.924485i \(0.375504\pi\)
\(264\) 0 0
\(265\) −0.321873 0.443021i −0.0197725 0.0272146i
\(266\) 0 0
\(267\) 1.73534 1.26080i 0.106201 0.0771594i
\(268\) 0 0
\(269\) 16.6790 + 12.1180i 1.01694 + 0.738848i 0.965653 0.259836i \(-0.0836684\pi\)
0.0512846 + 0.998684i \(0.483668\pi\)
\(270\) 0 0
\(271\) 1.66117 1.20691i 0.100909 0.0733146i −0.536187 0.844099i \(-0.680136\pi\)
0.637096 + 0.770785i \(0.280136\pi\)
\(272\) 0 0
\(273\) 3.18572i 0.192809i
\(274\) 0 0
\(275\) −10.0846 + 3.27667i −0.608121 + 0.197591i
\(276\) 0 0
\(277\) −2.96520 + 9.12593i −0.178161 + 0.548324i −0.999764 0.0217368i \(-0.993080\pi\)
0.821602 + 0.570061i \(0.193080\pi\)
\(278\) 0 0
\(279\) 1.28840 3.96529i 0.0771346 0.237396i
\(280\) 0 0
\(281\) −7.07083 + 9.73217i −0.421810 + 0.580572i −0.966049 0.258358i \(-0.916819\pi\)
0.544239 + 0.838930i \(0.316819\pi\)
\(282\) 0 0
\(283\) 7.99148 + 24.5952i 0.475044 + 1.46204i 0.845898 + 0.533344i \(0.179065\pi\)
−0.370854 + 0.928691i \(0.620935\pi\)
\(284\) 0 0
\(285\) 6.11161 + 4.44035i 0.362021 + 0.263023i
\(286\) 0 0
\(287\) 4.42472 4.62838i 0.261183 0.273204i
\(288\) 0 0
\(289\) −9.64480 7.00736i −0.567341 0.412198i
\(290\) 0 0
\(291\) −8.80341 27.0941i −0.516065 1.58829i
\(292\) 0 0
\(293\) 14.0447 19.3309i 0.820500 1.12932i −0.169118 0.985596i \(-0.554092\pi\)
0.989618 0.143725i \(-0.0459082\pi\)
\(294\) 0 0
\(295\) −0.505738 + 1.55650i −0.0294452 + 0.0906231i
\(296\) 0 0
\(297\) −3.01342 + 9.27437i −0.174857 + 0.538153i
\(298\) 0 0
\(299\) 6.21621 2.01977i 0.359493 0.116806i
\(300\) 0 0
\(301\) 0.346601i 0.0199778i
\(302\) 0 0
\(303\) 23.2150 16.8667i 1.33367 0.968966i
\(304\) 0 0
\(305\) 3.29987 + 2.39749i 0.188950 + 0.137280i
\(306\) 0 0
\(307\) 21.0299 15.2791i 1.20024 0.872026i 0.205932 0.978566i \(-0.433977\pi\)
0.994308 + 0.106541i \(0.0339774\pi\)
\(308\) 0 0
\(309\) 12.2261 + 16.8277i 0.695516 + 0.957295i
\(310\) 0 0
\(311\) −18.8804 6.13462i −1.07061 0.347862i −0.279885 0.960033i \(-0.590296\pi\)
−0.790725 + 0.612171i \(0.790296\pi\)
\(312\) 0 0
\(313\) −5.77610 + 1.87677i −0.326484 + 0.106081i −0.467673 0.883901i \(-0.654908\pi\)
0.141189 + 0.989983i \(0.454908\pi\)
\(314\) 0 0
\(315\) −0.187979 + 0.258731i −0.0105914 + 0.0145778i
\(316\) 0 0
\(317\) −8.94765 2.90727i −0.502550 0.163288i 0.0467613 0.998906i \(-0.485110\pi\)
−0.549312 + 0.835618i \(0.685110\pi\)
\(318\) 0 0
\(319\) −1.66890 −0.0934406
\(320\) 0 0
\(321\) −10.7960 14.8594i −0.602573 0.829371i
\(322\) 0 0
\(323\) 6.05992 + 18.6505i 0.337183 + 1.03774i
\(324\) 0 0
\(325\) 7.93420i 0.440110i
\(326\) 0 0
\(327\) 10.1409 0.560792
\(328\) 0 0
\(329\) −8.85330 −0.488098
\(330\) 0 0
\(331\) 0.605520i 0.0332824i 0.999862 + 0.0166412i \(0.00529730\pi\)
−0.999862 + 0.0166412i \(0.994703\pi\)
\(332\) 0 0
\(333\) 1.46012 + 4.49377i 0.0800138 + 0.246257i
\(334\) 0 0
\(335\) −3.08658 4.24832i −0.168638 0.232110i
\(336\) 0 0
\(337\) 9.68438 0.527542 0.263771 0.964585i \(-0.415034\pi\)
0.263771 + 0.964585i \(0.415034\pi\)
\(338\) 0 0
\(339\) 26.9519 + 8.75719i 1.46382 + 0.475625i
\(340\) 0 0
\(341\) 7.63498 10.5086i 0.413457 0.569075i
\(342\) 0 0
\(343\) −0.951057 + 0.309017i −0.0513522 + 0.0166853i
\(344\) 0 0
\(345\) 3.26252 + 1.06006i 0.175648 + 0.0570715i
\(346\) 0 0
\(347\) −14.9107 20.5228i −0.800446 1.10172i −0.992728 0.120380i \(-0.961589\pi\)
0.192282 0.981340i \(-0.438411\pi\)
\(348\) 0 0
\(349\) −6.92358 + 5.03027i −0.370611 + 0.269264i −0.757464 0.652877i \(-0.773562\pi\)
0.386853 + 0.922141i \(0.373562\pi\)
\(350\) 0 0
\(351\) 5.90322 + 4.28894i 0.315090 + 0.228927i
\(352\) 0 0
\(353\) 17.1474 12.4583i 0.912665 0.663090i −0.0290225 0.999579i \(-0.509239\pi\)
0.941687 + 0.336489i \(0.109239\pi\)
\(354\) 0 0
\(355\) 0.475992i 0.0252630i
\(356\) 0 0
\(357\) −4.12789 + 1.34123i −0.218471 + 0.0709856i
\(358\) 0 0
\(359\) −11.2362 + 34.5813i −0.593022 + 1.82513i −0.0286860 + 0.999588i \(0.509132\pi\)
−0.564336 + 0.825545i \(0.690868\pi\)
\(360\) 0 0
\(361\) −17.5293 + 53.9497i −0.922596 + 2.83946i
\(362\) 0 0
\(363\) −6.92110 + 9.52608i −0.363264 + 0.499989i
\(364\) 0 0
\(365\) −1.33092 4.09615i −0.0696635 0.214402i
\(366\) 0 0
\(367\) 12.5308 + 9.10414i 0.654101 + 0.475232i 0.864666 0.502347i \(-0.167530\pi\)
−0.210564 + 0.977580i \(0.567530\pi\)
\(368\) 0 0
\(369\) 0.811461 + 4.47020i 0.0422430 + 0.232709i
\(370\) 0 0
\(371\) 0.982898 + 0.714117i 0.0510295 + 0.0370751i
\(372\) 0 0
\(373\) −4.24556 13.0665i −0.219827 0.676558i −0.998776 0.0494701i \(-0.984247\pi\)
0.778949 0.627088i \(-0.215753\pi\)
\(374\) 0 0
\(375\) −4.99897 + 6.88049i −0.258146 + 0.355307i
\(376\) 0 0
\(377\) −0.385892 + 1.18765i −0.0198745 + 0.0611673i
\(378\) 0 0
\(379\) −2.10986 + 6.49347i −0.108376 + 0.333547i −0.990508 0.137455i \(-0.956108\pi\)
0.882132 + 0.471002i \(0.156108\pi\)
\(380\) 0 0
\(381\) 0.682252 0.221677i 0.0349528 0.0113569i
\(382\) 0 0
\(383\) 6.69312i 0.342002i 0.985271 + 0.171001i \(0.0547002\pi\)
−0.985271 + 0.171001i \(0.945300\pi\)
\(384\) 0 0
\(385\) −0.806061 + 0.585638i −0.0410807 + 0.0298469i
\(386\) 0 0
\(387\) −0.198958 0.144552i −0.0101136 0.00734798i
\(388\) 0 0
\(389\) −0.403781 + 0.293364i −0.0204725 + 0.0148742i −0.597974 0.801515i \(-0.704028\pi\)
0.577502 + 0.816389i \(0.304028\pi\)
\(390\) 0 0
\(391\) 5.23422 + 7.20429i 0.264706 + 0.364337i
\(392\) 0 0
\(393\) −36.8637 11.9777i −1.85953 0.604197i
\(394\) 0 0
\(395\) −2.82779 + 0.918803i −0.142281 + 0.0462300i
\(396\) 0 0
\(397\) 20.3359 27.9900i 1.02063 1.40478i 0.108869 0.994056i \(-0.465277\pi\)
0.911761 0.410720i \(-0.134723\pi\)
\(398\) 0 0
\(399\) −15.9400 5.17923i −0.797999 0.259286i
\(400\) 0 0
\(401\) −20.3228 −1.01487 −0.507437 0.861689i \(-0.669407\pi\)
−0.507437 + 0.861689i \(0.669407\pi\)
\(402\) 0 0
\(403\) −5.71296 7.86321i −0.284583 0.391694i
\(404\) 0 0
\(405\) 1.47990 + 4.55468i 0.0735371 + 0.226324i
\(406\) 0 0
\(407\) 14.7206i 0.729672i
\(408\) 0 0
\(409\) −1.61976 −0.0800918 −0.0400459 0.999198i \(-0.512750\pi\)
−0.0400459 + 0.999198i \(0.512750\pi\)
\(410\) 0 0
\(411\) 19.8498 0.979119
\(412\) 0 0
\(413\) 3.63101i 0.178671i
\(414\) 0 0
\(415\) 2.37615 + 7.31304i 0.116641 + 0.358983i
\(416\) 0 0
\(417\) −3.01478 4.14949i −0.147634 0.203201i
\(418\) 0 0
\(419\) −24.1276 −1.17871 −0.589354 0.807875i \(-0.700618\pi\)
−0.589354 + 0.807875i \(0.700618\pi\)
\(420\) 0 0
\(421\) 17.5365 + 5.69795i 0.854676 + 0.277701i 0.703403 0.710791i \(-0.251663\pi\)
0.151273 + 0.988492i \(0.451663\pi\)
\(422\) 0 0
\(423\) 3.69231 5.08203i 0.179526 0.247097i
\(424\) 0 0
\(425\) −10.2807 + 3.34041i −0.498689 + 0.162034i
\(426\) 0 0
\(427\) −8.60656 2.79644i −0.416501 0.135329i
\(428\) 0 0
\(429\) −4.13924 5.69718i −0.199845 0.275062i
\(430\) 0 0
\(431\) 3.52675 2.56233i 0.169878 0.123423i −0.499598 0.866257i \(-0.666519\pi\)
0.669476 + 0.742834i \(0.266519\pi\)
\(432\) 0 0
\(433\) 4.66687 + 3.39068i 0.224275 + 0.162946i 0.694249 0.719735i \(-0.255737\pi\)
−0.469974 + 0.882680i \(0.655737\pi\)
\(434\) 0 0
\(435\) −0.530236 + 0.385239i −0.0254229 + 0.0184708i
\(436\) 0 0
\(437\) 34.3870i 1.64495i
\(438\) 0 0
\(439\) 28.7707 9.34816i 1.37315 0.446163i 0.472738 0.881203i \(-0.343266\pi\)
0.900411 + 0.435040i \(0.143266\pi\)
\(440\) 0 0
\(441\) 0.219259 0.674809i 0.0104409 0.0321338i
\(442\) 0 0
\(443\) 4.33994 13.3570i 0.206197 0.634609i −0.793465 0.608616i \(-0.791725\pi\)
0.999662 0.0259932i \(-0.00827483\pi\)
\(444\) 0 0
\(445\) 0.295053 0.406106i 0.0139869 0.0192513i
\(446\) 0 0
\(447\) −5.86345 18.0458i −0.277332 0.853539i
\(448\) 0 0
\(449\) −3.25616 2.36574i −0.153668 0.111646i 0.508295 0.861183i \(-0.330276\pi\)
−0.661962 + 0.749537i \(0.730276\pi\)
\(450\) 0 0
\(451\) −1.89924 + 14.0262i −0.0894317 + 0.660470i
\(452\) 0 0
\(453\) −32.9110 23.9113i −1.54630 1.12345i
\(454\) 0 0
\(455\) 0.230381 + 0.709038i 0.0108004 + 0.0332402i
\(456\) 0 0
\(457\) 8.77548 12.0784i 0.410500 0.565004i −0.552841 0.833287i \(-0.686456\pi\)
0.963340 + 0.268283i \(0.0864561\pi\)
\(458\) 0 0
\(459\) −3.07205 + 9.45478i −0.143391 + 0.441311i
\(460\) 0 0
\(461\) −1.42179 + 4.37582i −0.0662194 + 0.203802i −0.978691 0.205337i \(-0.934171\pi\)
0.912472 + 0.409139i \(0.134171\pi\)
\(462\) 0 0
\(463\) 8.03576 2.61098i 0.373453 0.121342i −0.116276 0.993217i \(-0.537096\pi\)
0.489729 + 0.871875i \(0.337096\pi\)
\(464\) 0 0
\(465\) 5.10117i 0.236561i
\(466\) 0 0
\(467\) 6.01936 4.37332i 0.278543 0.202373i −0.439739 0.898126i \(-0.644929\pi\)
0.718282 + 0.695753i \(0.244929\pi\)
\(468\) 0 0
\(469\) 9.42543 + 6.84798i 0.435226 + 0.316210i
\(470\) 0 0
\(471\) −7.58712 + 5.51237i −0.349596 + 0.253997i
\(472\) 0 0
\(473\) −0.450343 0.619844i −0.0207068 0.0285005i
\(474\) 0 0
\(475\) −39.6995 12.8991i −1.82154 0.591853i
\(476\) 0 0
\(477\) −0.819845 + 0.266384i −0.0375381 + 0.0121969i
\(478\) 0 0
\(479\) −4.77228 + 6.56847i −0.218051 + 0.300121i −0.904004 0.427525i \(-0.859386\pi\)
0.685953 + 0.727646i \(0.259386\pi\)
\(480\) 0 0
\(481\) 10.4757 + 3.40377i 0.477652 + 0.155199i
\(482\) 0 0
\(483\) −7.61082 −0.346304
\(484\) 0 0
\(485\) −3.91871 5.39364i −0.177940 0.244913i
\(486\) 0 0
\(487\) −6.04231 18.5963i −0.273803 0.842679i −0.989534 0.144303i \(-0.953906\pi\)
0.715731 0.698377i \(-0.246094\pi\)
\(488\) 0 0
\(489\) 6.34270i 0.286827i
\(490\) 0 0
\(491\) 16.2184 0.731926 0.365963 0.930629i \(-0.380740\pi\)
0.365963 + 0.930629i \(0.380740\pi\)
\(492\) 0 0
\(493\) −1.70137 −0.0766257
\(494\) 0 0
\(495\) 0.706944i 0.0317748i
\(496\) 0 0
\(497\) −0.326337 1.00436i −0.0146382 0.0450518i
\(498\) 0 0
\(499\) −20.4446 28.1396i −0.915226 1.25970i −0.965350 0.260958i \(-0.915962\pi\)
0.0501240 0.998743i \(-0.484038\pi\)
\(500\) 0 0
\(501\) −36.3688 −1.62484
\(502\) 0 0
\(503\) 3.86840 + 1.25692i 0.172483 + 0.0560433i 0.393986 0.919117i \(-0.371096\pi\)
−0.221502 + 0.975160i \(0.571096\pi\)
\(504\) 0 0
\(505\) 3.94717 5.43281i 0.175647 0.241757i
\(506\) 0 0
\(507\) 18.8013 6.10892i 0.834996 0.271307i
\(508\) 0 0
\(509\) 12.9517 + 4.20828i 0.574076 + 0.186529i 0.581645 0.813443i \(-0.302409\pi\)
−0.00756907 + 0.999971i \(0.502409\pi\)
\(510\) 0 0
\(511\) 5.61659 + 7.73057i 0.248463 + 0.341980i
\(512\) 0 0
\(513\) −31.0573 + 22.5644i −1.37121 + 0.996245i
\(514\) 0 0
\(515\) 3.93805 + 2.86116i 0.173531 + 0.126078i
\(516\) 0 0
\(517\) 15.8328 11.5032i 0.696326 0.505910i
\(518\) 0 0
\(519\) 39.8833i 1.75068i
\(520\) 0 0
\(521\) −37.9858 + 12.3423i −1.66419 + 0.540728i −0.981744 0.190208i \(-0.939084\pi\)
−0.682446 + 0.730936i \(0.739084\pi\)
\(522\) 0 0
\(523\) −1.48048 + 4.55646i −0.0647371 + 0.199240i −0.978193 0.207697i \(-0.933403\pi\)
0.913456 + 0.406937i \(0.133403\pi\)
\(524\) 0 0
\(525\) 2.85494 8.78662i 0.124600 0.383479i
\(526\) 0 0
\(527\) 7.78350 10.7131i 0.339055 0.466669i
\(528\) 0 0
\(529\) −2.28208 7.02353i −0.0992210 0.305371i
\(530\) 0 0
\(531\) 2.08430 + 1.51433i 0.0904509 + 0.0657165i
\(532\) 0 0
\(533\) 9.54246 + 4.59480i 0.413330 + 0.199023i
\(534\) 0 0
\(535\) −3.47742 2.52649i −0.150342 0.109230i
\(536\) 0 0
\(537\) −5.20535 16.0204i −0.224628 0.691333i
\(538\) 0 0
\(539\) 1.29931 1.78835i 0.0559653 0.0770297i
\(540\) 0 0
\(541\) −4.33937 + 13.3552i −0.186564 + 0.574185i −0.999972 0.00750878i \(-0.997610\pi\)
0.813408 + 0.581694i \(0.197610\pi\)
\(542\) 0 0
\(543\) 9.54578 29.3789i 0.409649 1.26077i
\(544\) 0 0
\(545\) 2.25703 0.733355i 0.0966807 0.0314135i
\(546\) 0 0
\(547\) 29.2085i 1.24886i 0.781079 + 0.624432i \(0.214670\pi\)
−0.781079 + 0.624432i \(0.785330\pi\)
\(548\) 0 0
\(549\) 5.19464 3.77413i 0.221702 0.161076i
\(550\) 0 0
\(551\) −5.31516 3.86169i −0.226433 0.164514i
\(552\) 0 0
\(553\) 5.33682 3.87742i 0.226944 0.164885i
\(554\) 0 0
\(555\) 3.39801 + 4.67696i 0.144237 + 0.198526i
\(556\) 0 0
\(557\) −18.1699 5.90377i −0.769885 0.250151i −0.102369 0.994746i \(-0.532642\pi\)
−0.667516 + 0.744596i \(0.732642\pi\)
\(558\) 0 0
\(559\) −0.545236 + 0.177158i −0.0230610 + 0.00749297i
\(560\) 0 0
\(561\) 5.63943 7.76201i 0.238097 0.327712i
\(562\) 0 0
\(563\) −29.4374 9.56479i −1.24064 0.403108i −0.386081 0.922465i \(-0.626171\pi\)
−0.854557 + 0.519357i \(0.826171\pi\)
\(564\) 0 0
\(565\) 6.63191 0.279006
\(566\) 0 0
\(567\) −6.24532 8.59594i −0.262279 0.360996i
\(568\) 0 0
\(569\) −1.23356 3.79651i −0.0517136 0.159158i 0.921865 0.387512i \(-0.126666\pi\)
−0.973578 + 0.228354i \(0.926666\pi\)
\(570\) 0 0
\(571\) 32.2310i 1.34882i 0.738355 + 0.674412i \(0.235603\pi\)
−0.738355 + 0.674412i \(0.764397\pi\)
\(572\) 0 0
\(573\) 13.7883 0.576016
\(574\) 0 0
\(575\) −18.9551 −0.790484
\(576\) 0 0
\(577\) 40.0742i 1.66831i −0.551530 0.834155i \(-0.685956\pi\)
0.551530 0.834155i \(-0.314044\pi\)
\(578\) 0 0
\(579\) −14.9866 46.1240i −0.622821 1.91685i
\(580\) 0 0
\(581\) −10.0275 13.8017i −0.416013 0.572592i
\(582\) 0 0
\(583\) −2.68563 −0.111227
\(584\) 0 0
\(585\) −0.503089 0.163463i −0.0208002 0.00675838i
\(586\) 0 0
\(587\) 5.69573 7.83950i 0.235088 0.323571i −0.675131 0.737698i \(-0.735913\pi\)
0.910219 + 0.414127i \(0.135913\pi\)
\(588\) 0 0
\(589\) 48.6322 15.8015i 2.00385 0.651091i
\(590\) 0 0
\(591\) −45.4604 14.7710i −1.86999 0.607596i
\(592\) 0 0
\(593\) −11.7409 16.1600i −0.482142 0.663611i 0.496773 0.867880i \(-0.334518\pi\)
−0.978915 + 0.204270i \(0.934518\pi\)
\(594\) 0 0
\(595\) −0.821742 + 0.597030i −0.0336881 + 0.0244759i
\(596\) 0 0
\(597\) −16.9930 12.3462i −0.695478 0.505295i
\(598\) 0 0
\(599\) −25.1345 + 18.2613i −1.02697 + 0.746135i −0.967699 0.252107i \(-0.918876\pi\)
−0.0592674 + 0.998242i \(0.518876\pi\)
\(600\) 0 0
\(601\) 1.38917i 0.0566655i 0.999599 + 0.0283327i \(0.00901980\pi\)
−0.999599 + 0.0283327i \(0.990980\pi\)
\(602\) 0 0
\(603\) −7.86185 + 2.55447i −0.320159 + 0.104026i
\(604\) 0 0
\(605\) −0.851519 + 2.62071i −0.0346192 + 0.106547i
\(606\) 0 0
\(607\) 9.24189 28.4436i 0.375117 1.15449i −0.568283 0.822833i \(-0.692392\pi\)
0.943400 0.331657i \(-0.107608\pi\)
\(608\) 0 0
\(609\) 0.854702 1.17640i 0.0346343 0.0476700i
\(610\) 0 0
\(611\) −4.52518 13.9271i −0.183069 0.563428i
\(612\) 0 0
\(613\) −5.70143 4.14233i −0.230278 0.167307i 0.466663 0.884435i \(-0.345456\pi\)
−0.696941 + 0.717128i \(0.745456\pi\)
\(614\) 0 0
\(615\) 2.63431 + 4.89476i 0.106226 + 0.197376i
\(616\) 0 0
\(617\) 3.80328 + 2.76324i 0.153114 + 0.111244i 0.661705 0.749765i \(-0.269833\pi\)
−0.508590 + 0.861009i \(0.669833\pi\)
\(618\) 0 0
\(619\) 11.8899 + 36.5934i 0.477896 + 1.47081i 0.842012 + 0.539459i \(0.181371\pi\)
−0.364116 + 0.931354i \(0.618629\pi\)
\(620\) 0 0
\(621\) −10.2464 + 14.1030i −0.411176 + 0.565935i
\(622\) 0 0
\(623\) −0.344150 + 1.05919i −0.0137881 + 0.0424354i
\(624\) 0 0
\(625\) 6.79650 20.9175i 0.271860 0.836698i
\(626\) 0 0
\(627\) 35.2358 11.4488i 1.40718 0.457221i
\(628\) 0 0
\(629\) 15.0069i 0.598366i
\(630\) 0 0
\(631\) 1.02881 0.747472i 0.0409562 0.0297564i −0.567119 0.823636i \(-0.691942\pi\)
0.608075 + 0.793880i \(0.291942\pi\)
\(632\) 0 0
\(633\) 17.3563 + 12.6101i 0.689852 + 0.501207i
\(634\) 0 0
\(635\) 0.135816 0.0986763i 0.00538971 0.00391585i
\(636\) 0 0
\(637\) −0.972224 1.33815i −0.0385209 0.0530195i
\(638\) 0 0
\(639\) 0.712632 + 0.231548i 0.0281913 + 0.00915990i
\(640\) 0 0
\(641\) −2.23897 + 0.727487i −0.0884342 + 0.0287340i −0.352900 0.935661i \(-0.614804\pi\)
0.264466 + 0.964395i \(0.414804\pi\)
\(642\) 0 0
\(643\) 3.06309 4.21599i 0.120797 0.166262i −0.744336 0.667805i \(-0.767234\pi\)
0.865133 + 0.501543i \(0.167234\pi\)
\(644\) 0 0
\(645\) −0.286162 0.0929796i −0.0112676 0.00366107i
\(646\) 0 0
\(647\) −29.1066 −1.14430 −0.572149 0.820150i \(-0.693890\pi\)
−0.572149 + 0.820150i \(0.693890\pi\)
\(648\) 0 0
\(649\) 4.71782 + 6.49352i 0.185191 + 0.254893i
\(650\) 0 0
\(651\) 3.49733 + 10.7637i 0.137071 + 0.421862i
\(652\) 0 0
\(653\) 25.9950i 1.01726i 0.860984 + 0.508631i \(0.169848\pi\)
−0.860984 + 0.508631i \(0.830152\pi\)
\(654\) 0 0
\(655\) −9.07086 −0.354428
\(656\) 0 0
\(657\) −6.77998 −0.264512
\(658\) 0 0
\(659\) 49.8227i 1.94082i −0.241470 0.970408i \(-0.577630\pi\)
0.241470 0.970408i \(-0.422370\pi\)
\(660\) 0 0
\(661\) −5.90574 18.1760i −0.229707 0.706965i −0.997780 0.0666022i \(-0.978784\pi\)
0.768073 0.640362i \(-0.221216\pi\)
\(662\) 0 0
\(663\) −4.21977 5.80801i −0.163882 0.225564i
\(664\) 0 0
\(665\) −3.92228 −0.152099
\(666\) 0 0
\(667\) −2.83736 0.921913i −0.109863 0.0356966i
\(668\) 0 0
\(669\) −4.00289 + 5.50951i −0.154761 + 0.213010i
\(670\) 0 0
\(671\) 19.0250 6.18159i 0.734451 0.238638i
\(672\) 0 0
\(673\) 25.2612 + 8.20785i 0.973746 + 0.316389i 0.752327 0.658790i \(-0.228931\pi\)
0.221419 + 0.975179i \(0.428931\pi\)
\(674\) 0 0
\(675\) −12.4382 17.1197i −0.478746 0.658938i
\(676\) 0 0
\(677\) 7.30645 5.30845i 0.280810 0.204020i −0.438461 0.898750i \(-0.644476\pi\)
0.719270 + 0.694730i \(0.244476\pi\)
\(678\) 0 0
\(679\) 11.9665 + 8.69416i 0.459232 + 0.333651i
\(680\) 0 0
\(681\) −33.4337 + 24.2910i −1.28118 + 0.930833i
\(682\) 0 0
\(683\) 12.7724i 0.488721i 0.969684 + 0.244361i \(0.0785780\pi\)
−0.969684 + 0.244361i \(0.921422\pi\)
\(684\) 0 0
\(685\) 4.41793 1.43547i 0.168800 0.0548465i
\(686\) 0 0
\(687\) −0.0765246 + 0.235519i −0.00291960 + 0.00898559i
\(688\) 0 0
\(689\) −0.620985 + 1.91119i −0.0236576 + 0.0728107i
\(690\) 0 0
\(691\) −19.6788 + 27.0856i −0.748618 + 1.03038i 0.249458 + 0.968386i \(0.419748\pi\)
−0.998076 + 0.0619989i \(0.980252\pi\)
\(692\) 0 0
\(693\) 0.484676 + 1.49168i 0.0184113 + 0.0566643i
\(694\) 0 0
\(695\) −0.971069 0.705523i −0.0368347 0.0267620i
\(696\) 0 0
\(697\) −1.93619 + 14.2991i −0.0733383 + 0.541617i
\(698\) 0 0
\(699\) −8.29159 6.02419i −0.313617 0.227856i
\(700\) 0 0
\(701\) −6.97042 21.4527i −0.263269 0.810259i −0.992087 0.125551i \(-0.959930\pi\)
0.728818 0.684707i \(-0.240070\pi\)
\(702\) 0 0
\(703\) −34.0621 + 46.8825i −1.28468 + 1.76821i
\(704\) 0 0
\(705\) 2.37500 7.30949i 0.0894476 0.275291i
\(706\) 0 0
\(707\) −4.60398 + 14.1696i −0.173151 + 0.532903i
\(708\) 0 0
\(709\) 39.6349 12.8781i 1.48852 0.483649i 0.551873 0.833928i \(-0.313913\pi\)
0.936645 + 0.350279i \(0.113913\pi\)
\(710\) 0 0
\(711\) 4.68058i 0.175535i
\(712\) 0 0
\(713\) 18.7855 13.6485i 0.703524 0.511140i
\(714\) 0 0
\(715\) −1.33326 0.968672i −0.0498612 0.0362263i
\(716\) 0 0
\(717\) 29.2174 21.2277i 1.09114 0.792763i
\(718\) 0 0
\(719\) −25.8899 35.6344i −0.965530 1.32894i −0.944273 0.329164i \(-0.893233\pi\)
−0.0212573 0.999774i \(-0.506767\pi\)
\(720\) 0 0
\(721\) −10.2710 3.33726i −0.382513 0.124286i
\(722\) 0 0
\(723\) 19.3687 6.29327i 0.720330 0.234049i
\(724\) 0 0
\(725\) 2.12868 2.92988i 0.0790572 0.108813i
\(726\) 0 0
\(727\) −31.3662 10.1915i −1.16331 0.377982i −0.337168 0.941445i \(-0.609469\pi\)
−0.826142 + 0.563462i \(0.809469\pi\)
\(728\) 0 0
\(729\) −17.9507 −0.664842
\(730\) 0 0
\(731\) −0.459104 0.631902i −0.0169806 0.0233717i
\(732\) 0 0
\(733\) 11.1282 + 34.2489i 0.411028 + 1.26501i 0.915756 + 0.401735i \(0.131593\pi\)
−0.504728 + 0.863278i \(0.668407\pi\)
\(734\) 0 0
\(735\) 0.868111i 0.0320208i
\(736\) 0 0
\(737\) −25.7536 −0.948647
\(738\) 0 0
\(739\) 26.9701 0.992110 0.496055 0.868291i \(-0.334781\pi\)
0.496055 + 0.868291i \(0.334781\pi\)
\(740\) 0 0
\(741\) 27.7224i 1.01841i
\(742\) 0 0
\(743\) 6.66286 + 20.5062i 0.244437 + 0.752299i 0.995729 + 0.0923289i \(0.0294311\pi\)
−0.751292 + 0.659970i \(0.770569\pi\)
\(744\) 0 0
\(745\) −2.61003 3.59240i −0.0956241 0.131615i
\(746\) 0 0
\(747\) 12.1046 0.442884
\(748\) 0 0
\(749\) 9.06965 + 2.94691i 0.331398 + 0.107678i
\(750\) 0 0
\(751\) −26.0233 + 35.8180i −0.949603 + 1.30702i 0.00210110 + 0.999998i \(0.499331\pi\)
−0.951704 + 0.307018i \(0.900669\pi\)
\(752\) 0 0
\(753\) −25.8882 + 8.41160i −0.943420 + 0.306536i
\(754\) 0 0
\(755\) −9.05411 2.94186i −0.329513 0.107065i
\(756\) 0 0
\(757\) −4.15546 5.71950i −0.151033 0.207879i 0.726796 0.686853i \(-0.241009\pi\)
−0.877829 + 0.478975i \(0.841009\pi\)
\(758\) 0 0
\(759\) 13.6108 9.88882i 0.494041 0.358942i
\(760\) 0 0
\(761\) 25.6482 + 18.6345i 0.929747 + 0.675501i 0.945931 0.324368i \(-0.105152\pi\)
−0.0161835 + 0.999869i \(0.505152\pi\)
\(762\) 0 0
\(763\) −4.25965 + 3.09482i −0.154210 + 0.112040i
\(764\) 0 0
\(765\) 0.720696i 0.0260568i
\(766\) 0 0
\(767\) 5.71192 1.85592i 0.206245 0.0670132i
\(768\) 0 0
\(769\) −2.92490 + 9.00191i −0.105474 + 0.324617i −0.989842 0.142175i \(-0.954590\pi\)
0.884367 + 0.466792i \(0.154590\pi\)
\(770\) 0 0
\(771\) −7.13645 + 21.9637i −0.257013 + 0.791005i
\(772\) 0 0
\(773\) −1.83069 + 2.51973i −0.0658453 + 0.0906282i −0.840670 0.541548i \(-0.817838\pi\)
0.774824 + 0.632177i \(0.217838\pi\)
\(774\) 0 0
\(775\) 8.71028 + 26.8075i 0.312883 + 0.962954i
\(776\) 0 0
\(777\) −10.3764 7.53891i −0.372252 0.270457i
\(778\) 0 0
\(779\) −38.5042 + 40.2765i −1.37956 + 1.44305i
\(780\) 0 0
\(781\) 1.88859 + 1.37214i 0.0675789 + 0.0490989i
\(782\) 0 0
\(783\) −1.02920 3.16757i −0.0367808 0.113200i
\(784\) 0 0
\(785\) −1.29001 + 1.77555i −0.0460425 + 0.0633721i
\(786\) 0 0
\(787\) −4.96058 + 15.2671i −0.176826 + 0.544213i −0.999712 0.0239924i \(-0.992362\pi\)
0.822887 + 0.568206i \(0.192362\pi\)
\(788\) 0 0
\(789\) 12.5138 38.5134i 0.445501 1.37111i
\(790\) 0 0
\(791\) −13.9936 + 4.54679i −0.497555 + 0.161665i
\(792\) 0 0
\(793\) 14.9682i 0.531538i
\(794\) 0 0
\(795\) −0.853265 + 0.619933i −0.0302622 + 0.0219868i
\(796\) 0 0
\(797\) 36.3590 + 26.4164i