Properties

Label 1183.2.e.j.170.5
Level $1183$
Weight $2$
Character 1183.170
Analytic conductor $9.446$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 170.5
Character \(\chi\) \(=\) 1183.170
Dual form 1183.2.e.j.508.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.249993 + 0.433001i) q^{2} +(-0.424801 - 0.735776i) q^{3} +(0.875007 + 1.51556i) q^{4} +(0.521238 - 0.902810i) q^{5} +0.424789 q^{6} +(-2.40155 + 1.11021i) q^{7} -1.87496 q^{8} +(1.13909 - 1.97296i) q^{9} +O(q^{10})\) \(q+(-0.249993 + 0.433001i) q^{2} +(-0.424801 - 0.735776i) q^{3} +(0.875007 + 1.51556i) q^{4} +(0.521238 - 0.902810i) q^{5} +0.424789 q^{6} +(-2.40155 + 1.11021i) q^{7} -1.87496 q^{8} +(1.13909 - 1.97296i) q^{9} +(0.260612 + 0.451393i) q^{10} +(-1.98365 - 3.43579i) q^{11} +(0.743407 - 1.28762i) q^{12} +(0.119647 - 1.31742i) q^{14} -0.885688 q^{15} +(-1.28129 + 2.21925i) q^{16} +(0.0710177 + 0.123006i) q^{17} +(0.569529 + 0.986453i) q^{18} +(-2.75488 + 4.77160i) q^{19} +1.82435 q^{20} +(1.83705 + 1.29538i) q^{21} +1.98360 q^{22} +(-2.19549 + 3.80270i) q^{23} +(0.796483 + 1.37955i) q^{24} +(1.95662 + 3.38897i) q^{25} -4.48435 q^{27} +(-3.78396 - 2.66823i) q^{28} -8.39759 q^{29} +(0.221416 - 0.383504i) q^{30} +(1.42326 + 2.46516i) q^{31} +(-2.51558 - 4.35712i) q^{32} +(-1.68531 + 2.91905i) q^{33} -0.0710158 q^{34} +(-0.249465 + 2.74683i) q^{35} +3.98684 q^{36} +(-0.421593 + 0.730221i) q^{37} +(-1.37740 - 2.38574i) q^{38} +(-0.977298 + 1.69273i) q^{40} -12.0974 q^{41} +(-1.02015 + 0.471607i) q^{42} +4.82323 q^{43} +(3.47142 - 6.01267i) q^{44} +(-1.18747 - 2.05676i) q^{45} +(-1.09772 - 1.90130i) q^{46} +(-2.27824 + 3.94602i) q^{47} +2.17717 q^{48} +(4.53485 - 5.33246i) q^{49} -1.95657 q^{50} +(0.0603367 - 0.104506i) q^{51} +(0.139800 + 0.242141i) q^{53} +(1.12106 - 1.94173i) q^{54} -4.13582 q^{55} +(4.50280 - 2.08160i) q^{56} +4.68111 q^{57} +(2.09934 - 3.63617i) q^{58} +(-5.39075 - 9.33705i) q^{59} +(-0.774983 - 1.34231i) q^{60} +(2.93177 - 5.07797i) q^{61} -1.42322 q^{62} +(-0.545169 + 6.00279i) q^{63} -2.60963 q^{64} +(-0.842634 - 1.45949i) q^{66} +(2.57223 + 4.45524i) q^{67} +(-0.124282 + 0.215263i) q^{68} +3.73058 q^{69} +(-1.12701 - 0.794706i) q^{70} -3.69880 q^{71} +(-2.13574 + 3.69921i) q^{72} +(-3.30640 - 5.72686i) q^{73} +(-0.210791 - 0.365101i) q^{74} +(1.66235 - 2.87927i) q^{75} -9.64216 q^{76} +(8.57829 + 6.04892i) q^{77} +(-5.96135 + 10.3254i) q^{79} +(1.33571 + 2.31352i) q^{80} +(-1.51231 - 2.61940i) q^{81} +(3.02426 - 5.23818i) q^{82} -2.87321 q^{83} +(-0.355795 + 3.91762i) q^{84} +0.148068 q^{85} +(-1.20578 + 2.08846i) q^{86} +(3.56730 + 6.17875i) q^{87} +(3.71926 + 6.44195i) q^{88} +(0.873824 - 1.51351i) q^{89} +1.18744 q^{90} -7.68427 q^{92} +(1.20921 - 2.09440i) q^{93} +(-1.13909 - 1.97296i) q^{94} +(2.87190 + 4.97427i) q^{95} +(-2.13724 + 3.70181i) q^{96} +2.70291 q^{97} +(1.17528 + 3.29668i) q^{98} -9.03822 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 6q^{3} - 8q^{4} - 2q^{9} + O(q^{10}) \) \( 24q - 6q^{3} - 8q^{4} - 2q^{9} - 24q^{10} + 2q^{12} + 8q^{14} - 16q^{16} - 34q^{17} + 60q^{22} - 6q^{23} + 10q^{25} + 24q^{27} + 4q^{29} - 22q^{30} - 24q^{35} - 52q^{36} - 38q^{38} - 2q^{40} + 32q^{42} + 44q^{43} - 76q^{48} + 12q^{49} - 8q^{51} - 16q^{53} + 60q^{55} + 54q^{56} + 10q^{61} + 164q^{62} - 4q^{64} - 68q^{66} - 22q^{68} + 28q^{69} - 66q^{74} - 2q^{75} + 38q^{77} - 70q^{79} + 28q^{81} - 10q^{82} + 20q^{87} + 28q^{88} - 132q^{92} + 2q^{94} - 4q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.249993 + 0.433001i −0.176772 + 0.306178i −0.940773 0.339037i \(-0.889899\pi\)
0.764001 + 0.645215i \(0.223232\pi\)
\(3\) −0.424801 0.735776i −0.245259 0.424801i 0.716946 0.697129i \(-0.245540\pi\)
−0.962204 + 0.272328i \(0.912206\pi\)
\(4\) 0.875007 + 1.51556i 0.437503 + 0.757778i
\(5\) 0.521238 0.902810i 0.233105 0.403749i −0.725616 0.688100i \(-0.758445\pi\)
0.958720 + 0.284351i \(0.0917782\pi\)
\(6\) 0.424789 0.173420
\(7\) −2.40155 + 1.11021i −0.907699 + 0.419621i
\(8\) −1.87496 −0.662897
\(9\) 1.13909 1.97296i 0.379696 0.657653i
\(10\) 0.260612 + 0.451393i 0.0824127 + 0.142743i
\(11\) −1.98365 3.43579i −0.598094 1.03593i −0.993102 0.117251i \(-0.962592\pi\)
0.395009 0.918677i \(-0.370742\pi\)
\(12\) 0.743407 1.28762i 0.214603 0.371703i
\(13\) 0 0
\(14\) 0.119647 1.31742i 0.0319770 0.352095i
\(15\) −0.885688 −0.228684
\(16\) −1.28129 + 2.21925i −0.320322 + 0.554813i
\(17\) 0.0710177 + 0.123006i 0.0172243 + 0.0298334i 0.874509 0.485009i \(-0.161184\pi\)
−0.857285 + 0.514843i \(0.827850\pi\)
\(18\) 0.569529 + 0.986453i 0.134239 + 0.232509i
\(19\) −2.75488 + 4.77160i −0.632014 + 1.09468i 0.355126 + 0.934818i \(0.384438\pi\)
−0.987140 + 0.159861i \(0.948895\pi\)
\(20\) 1.82435 0.407936
\(21\) 1.83705 + 1.29538i 0.400877 + 0.282676i
\(22\) 1.98360 0.422905
\(23\) −2.19549 + 3.80270i −0.457791 + 0.792917i −0.998844 0.0480711i \(-0.984693\pi\)
0.541053 + 0.840989i \(0.318026\pi\)
\(24\) 0.796483 + 1.37955i 0.162581 + 0.281599i
\(25\) 1.95662 + 3.38897i 0.391325 + 0.677794i
\(26\) 0 0
\(27\) −4.48435 −0.863013
\(28\) −3.78396 2.66823i −0.715101 0.504249i
\(29\) −8.39759 −1.55939 −0.779697 0.626157i \(-0.784627\pi\)
−0.779697 + 0.626157i \(0.784627\pi\)
\(30\) 0.221416 0.383504i 0.0404249 0.0700179i
\(31\) 1.42326 + 2.46516i 0.255625 + 0.442756i 0.965065 0.262010i \(-0.0843853\pi\)
−0.709440 + 0.704766i \(0.751052\pi\)
\(32\) −2.51558 4.35712i −0.444696 0.770237i
\(33\) −1.68531 + 2.91905i −0.293376 + 0.508141i
\(34\) −0.0710158 −0.0121791
\(35\) −0.249465 + 2.74683i −0.0421672 + 0.464298i
\(36\) 3.98684 0.664473
\(37\) −0.421593 + 0.730221i −0.0693095 + 0.120048i −0.898598 0.438774i \(-0.855413\pi\)
0.829288 + 0.558821i \(0.188746\pi\)
\(38\) −1.37740 2.38574i −0.223445 0.387017i
\(39\) 0 0
\(40\) −0.977298 + 1.69273i −0.154524 + 0.267644i
\(41\) −12.0974 −1.88929 −0.944647 0.328089i \(-0.893595\pi\)
−0.944647 + 0.328089i \(0.893595\pi\)
\(42\) −1.02015 + 0.471607i −0.157413 + 0.0727705i
\(43\) 4.82323 0.735536 0.367768 0.929918i \(-0.380122\pi\)
0.367768 + 0.929918i \(0.380122\pi\)
\(44\) 3.47142 6.01267i 0.523336 0.906444i
\(45\) −1.18747 2.05676i −0.177018 0.306604i
\(46\) −1.09772 1.90130i −0.161849 0.280331i
\(47\) −2.27824 + 3.94602i −0.332315 + 0.575587i −0.982965 0.183791i \(-0.941163\pi\)
0.650650 + 0.759378i \(0.274496\pi\)
\(48\) 2.17717 0.314247
\(49\) 4.53485 5.33246i 0.647836 0.761780i
\(50\) −1.95657 −0.276701
\(51\) 0.0603367 0.104506i 0.00844883 0.0146338i
\(52\) 0 0
\(53\) 0.139800 + 0.242141i 0.0192030 + 0.0332606i 0.875467 0.483278i \(-0.160554\pi\)
−0.856264 + 0.516538i \(0.827220\pi\)
\(54\) 1.12106 1.94173i 0.152557 0.264236i
\(55\) −4.13582 −0.557673
\(56\) 4.50280 2.08160i 0.601711 0.278166i
\(57\) 4.68111 0.620028
\(58\) 2.09934 3.63617i 0.275657 0.477452i
\(59\) −5.39075 9.33705i −0.701815 1.21558i −0.967829 0.251611i \(-0.919040\pi\)
0.266013 0.963969i \(-0.414294\pi\)
\(60\) −0.774983 1.34231i −0.100050 0.173292i
\(61\) 2.93177 5.07797i 0.375374 0.650168i −0.615009 0.788520i \(-0.710847\pi\)
0.990383 + 0.138353i \(0.0441808\pi\)
\(62\) −1.42322 −0.180750
\(63\) −0.545169 + 6.00279i −0.0686848 + 0.756280i
\(64\) −2.60963 −0.326204
\(65\) 0 0
\(66\) −0.842634 1.45949i −0.103721 0.179650i
\(67\) 2.57223 + 4.45524i 0.314248 + 0.544294i 0.979277 0.202523i \(-0.0649142\pi\)
−0.665029 + 0.746818i \(0.731581\pi\)
\(68\) −0.124282 + 0.215263i −0.0150714 + 0.0261044i
\(69\) 3.73058 0.449109
\(70\) −1.12701 0.794706i −0.134704 0.0949856i
\(71\) −3.69880 −0.438967 −0.219484 0.975616i \(-0.570437\pi\)
−0.219484 + 0.975616i \(0.570437\pi\)
\(72\) −2.13574 + 3.69921i −0.251700 + 0.435956i
\(73\) −3.30640 5.72686i −0.386985 0.670278i 0.605057 0.796182i \(-0.293150\pi\)
−0.992042 + 0.125904i \(0.959817\pi\)
\(74\) −0.210791 0.365101i −0.0245040 0.0424421i
\(75\) 1.66235 2.87927i 0.191952 0.332470i
\(76\) −9.64216 −1.10603
\(77\) 8.57829 + 6.04892i 0.977587 + 0.689339i
\(78\) 0 0
\(79\) −5.96135 + 10.3254i −0.670705 + 1.16169i 0.307000 + 0.951710i \(0.400675\pi\)
−0.977705 + 0.209985i \(0.932658\pi\)
\(80\) 1.33571 + 2.31352i 0.149337 + 0.258659i
\(81\) −1.51231 2.61940i −0.168035 0.291045i
\(82\) 3.02426 5.23818i 0.333974 0.578460i
\(83\) −2.87321 −0.315376 −0.157688 0.987489i \(-0.550404\pi\)
−0.157688 + 0.987489i \(0.550404\pi\)
\(84\) −0.355795 + 3.91762i −0.0388204 + 0.427447i
\(85\) 0.148068 0.0160603
\(86\) −1.20578 + 2.08846i −0.130022 + 0.225205i
\(87\) 3.56730 + 6.17875i 0.382455 + 0.662432i
\(88\) 3.71926 + 6.44195i 0.396475 + 0.686714i
\(89\) 0.873824 1.51351i 0.0926252 0.160432i −0.815990 0.578066i \(-0.803807\pi\)
0.908615 + 0.417635i \(0.137141\pi\)
\(90\) 1.18744 0.125167
\(91\) 0 0
\(92\) −7.68427 −0.801141
\(93\) 1.20921 2.09440i 0.125389 0.217180i
\(94\) −1.13909 1.97296i −0.117488 0.203495i
\(95\) 2.87190 + 4.97427i 0.294650 + 0.510350i
\(96\) −2.13724 + 3.70181i −0.218131 + 0.377815i
\(97\) 2.70291 0.274438 0.137219 0.990541i \(-0.456184\pi\)
0.137219 + 0.990541i \(0.456184\pi\)
\(98\) 1.17528 + 3.29668i 0.118721 + 0.333014i
\(99\) −9.03822 −0.908376
\(100\) −3.42412 + 5.93074i −0.342412 + 0.593074i
\(101\) −5.73612 9.93524i −0.570765 0.988594i −0.996488 0.0837401i \(-0.973313\pi\)
0.425723 0.904854i \(-0.360020\pi\)
\(102\) 0.0301676 + 0.0522517i 0.00298703 + 0.00517369i
\(103\) −2.08475 + 3.61090i −0.205417 + 0.355792i −0.950265 0.311441i \(-0.899188\pi\)
0.744849 + 0.667233i \(0.232522\pi\)
\(104\) 0 0
\(105\) 2.12702 0.983303i 0.207576 0.0959606i
\(106\) −0.139796 −0.0135782
\(107\) −4.24371 + 7.35032i −0.410255 + 0.710583i −0.994917 0.100694i \(-0.967894\pi\)
0.584662 + 0.811277i \(0.301227\pi\)
\(108\) −3.92383 6.79628i −0.377571 0.653972i
\(109\) 3.21518 + 5.56886i 0.307958 + 0.533400i 0.977916 0.209000i \(-0.0670209\pi\)
−0.669957 + 0.742400i \(0.733688\pi\)
\(110\) 1.03393 1.79081i 0.0985810 0.170747i
\(111\) 0.716373 0.0679951
\(112\) 0.613225 6.75214i 0.0579443 0.638018i
\(113\) 10.9633 1.03134 0.515670 0.856788i \(-0.327543\pi\)
0.515670 + 0.856788i \(0.327543\pi\)
\(114\) −1.17025 + 2.02692i −0.109603 + 0.189839i
\(115\) 2.28874 + 3.96422i 0.213426 + 0.369665i
\(116\) −7.34795 12.7270i −0.682240 1.18167i
\(117\) 0 0
\(118\) 5.39060 0.496245
\(119\) −0.307115 0.216560i −0.0281532 0.0198521i
\(120\) 1.66063 0.151594
\(121\) −2.36975 + 4.10453i −0.215432 + 0.373139i
\(122\) 1.46584 + 2.53892i 0.132711 + 0.229863i
\(123\) 5.13898 + 8.90097i 0.463366 + 0.802573i
\(124\) −2.49073 + 4.31406i −0.223674 + 0.387414i
\(125\) 9.29184 0.831087
\(126\) −2.46292 1.73671i −0.219415 0.154719i
\(127\) −2.00787 −0.178170 −0.0890849 0.996024i \(-0.528394\pi\)
−0.0890849 + 0.996024i \(0.528394\pi\)
\(128\) 5.68356 9.84421i 0.502360 0.870113i
\(129\) −2.04891 3.54882i −0.180397 0.312456i
\(130\) 0 0
\(131\) 6.22511 10.7822i 0.543890 0.942046i −0.454785 0.890601i \(-0.650284\pi\)
0.998676 0.0514449i \(-0.0163826\pi\)
\(132\) −5.89864 −0.513411
\(133\) 1.31849 14.5177i 0.114328 1.25885i
\(134\) −2.57217 −0.222201
\(135\) −2.33741 + 4.04851i −0.201172 + 0.348441i
\(136\) −0.133155 0.230631i −0.0114180 0.0197765i
\(137\) −2.62259 4.54246i −0.224063 0.388088i 0.731975 0.681332i \(-0.238599\pi\)
−0.956038 + 0.293243i \(0.905265\pi\)
\(138\) −0.932620 + 1.61535i −0.0793899 + 0.137507i
\(139\) −20.7385 −1.75902 −0.879510 0.475881i \(-0.842129\pi\)
−0.879510 + 0.475881i \(0.842129\pi\)
\(140\) −4.38125 + 2.02541i −0.370283 + 0.171179i
\(141\) 3.87119 0.326013
\(142\) 0.924676 1.60159i 0.0775971 0.134402i
\(143\) 0 0
\(144\) 2.91900 + 5.05585i 0.243250 + 0.421321i
\(145\) −4.37714 + 7.58143i −0.363502 + 0.629604i
\(146\) 3.30631 0.273633
\(147\) −5.84991 1.07141i −0.482492 0.0883681i
\(148\) −1.47559 −0.121293
\(149\) 0.00568799 0.00985188i 0.000465978 0.000807098i −0.865792 0.500403i \(-0.833185\pi\)
0.866258 + 0.499596i \(0.166518\pi\)
\(150\) 0.831153 + 1.43960i 0.0678633 + 0.117543i
\(151\) 9.45271 + 16.3726i 0.769251 + 1.33238i 0.937970 + 0.346717i \(0.112704\pi\)
−0.168719 + 0.985664i \(0.553963\pi\)
\(152\) 5.16529 8.94654i 0.418960 0.725660i
\(153\) 0.323582 0.0261600
\(154\) −4.76371 + 2.20222i −0.383870 + 0.177460i
\(155\) 2.96743 0.238350
\(156\) 0 0
\(157\) −9.89687 17.1419i −0.789856 1.36807i −0.926054 0.377390i \(-0.876822\pi\)
0.136198 0.990682i \(-0.456512\pi\)
\(158\) −2.98060 5.16255i −0.237124 0.410710i
\(159\) 0.118774 0.205723i 0.00941942 0.0163149i
\(160\) −5.24486 −0.414643
\(161\) 1.05076 11.5698i 0.0828117 0.911830i
\(162\) 1.51227 0.118815
\(163\) −4.46627 + 7.73581i −0.349825 + 0.605915i −0.986218 0.165450i \(-0.947092\pi\)
0.636393 + 0.771365i \(0.280426\pi\)
\(164\) −10.5853 18.3343i −0.826572 1.43167i
\(165\) 1.75690 + 3.04304i 0.136774 + 0.236900i
\(166\) 0.718284 1.24410i 0.0557496 0.0965612i
\(167\) 6.13469 0.474716 0.237358 0.971422i \(-0.423719\pi\)
0.237358 + 0.971422i \(0.423719\pi\)
\(168\) −3.44438 2.42879i −0.265740 0.187385i
\(169\) 0 0
\(170\) −0.0370161 + 0.0641138i −0.00283900 + 0.00491730i
\(171\) 6.27611 + 10.8705i 0.479946 + 0.831291i
\(172\) 4.22036 + 7.30987i 0.321799 + 0.557373i
\(173\) −12.1314 + 21.0122i −0.922332 + 1.59753i −0.126535 + 0.991962i \(0.540386\pi\)
−0.795797 + 0.605563i \(0.792948\pi\)
\(174\) −3.56721 −0.270429
\(175\) −8.46140 5.96650i −0.639622 0.451025i
\(176\) 10.1665 0.766330
\(177\) −4.57999 + 7.93277i −0.344253 + 0.596263i
\(178\) 0.436901 + 0.756734i 0.0327471 + 0.0567196i
\(179\) 2.06838 + 3.58253i 0.154598 + 0.267771i 0.932912 0.360103i \(-0.117259\pi\)
−0.778315 + 0.627874i \(0.783925\pi\)
\(180\) 2.07809 3.59936i 0.154892 0.268280i
\(181\) 7.86568 0.584651 0.292326 0.956319i \(-0.405571\pi\)
0.292326 + 0.956319i \(0.405571\pi\)
\(182\) 0 0
\(183\) −4.98167 −0.368256
\(184\) 4.11645 7.12989i 0.303468 0.525623i
\(185\) 0.439501 + 0.761237i 0.0323127 + 0.0559673i
\(186\) 0.604586 + 1.04717i 0.0443304 + 0.0767825i
\(187\) 0.281749 0.488003i 0.0206035 0.0356863i
\(188\) −7.97389 −0.581556
\(189\) 10.7694 4.97858i 0.783356 0.362139i
\(190\) −2.87182 −0.208344
\(191\) 3.23933 5.61069i 0.234390 0.405975i −0.724705 0.689059i \(-0.758024\pi\)
0.959095 + 0.283084i \(0.0913574\pi\)
\(192\) 1.10857 + 1.92011i 0.0800044 + 0.138572i
\(193\) 2.41464 + 4.18228i 0.173810 + 0.301047i 0.939749 0.341866i \(-0.111059\pi\)
−0.765939 + 0.642913i \(0.777726\pi\)
\(194\) −0.675708 + 1.17036i −0.0485130 + 0.0840270i
\(195\) 0 0
\(196\) 12.0497 + 2.20689i 0.860690 + 0.157635i
\(197\) 25.8362 1.84075 0.920377 0.391032i \(-0.127882\pi\)
0.920377 + 0.391032i \(0.127882\pi\)
\(198\) 2.25950 3.91356i 0.160575 0.278125i
\(199\) −8.55731 14.8217i −0.606612 1.05068i −0.991795 0.127842i \(-0.959195\pi\)
0.385183 0.922840i \(-0.374138\pi\)
\(200\) −3.66858 6.35417i −0.259408 0.449308i
\(201\) 2.18537 3.78518i 0.154144 0.266986i
\(202\) 5.73596 0.403581
\(203\) 20.1672 9.32312i 1.41546 0.654355i
\(204\) 0.211180 0.0147856
\(205\) −6.30561 + 10.9216i −0.440403 + 0.762800i
\(206\) −1.04235 1.80540i −0.0726238 0.125788i
\(207\) 5.00171 + 8.66322i 0.347643 + 0.602136i
\(208\) 0 0
\(209\) 21.8589 1.51201
\(210\) −0.105970 + 1.16682i −0.00731262 + 0.0805184i
\(211\) 18.2911 1.25921 0.629607 0.776914i \(-0.283216\pi\)
0.629607 + 0.776914i \(0.283216\pi\)
\(212\) −0.244652 + 0.423750i −0.0168028 + 0.0291032i
\(213\) 1.57125 + 2.72149i 0.107661 + 0.186474i
\(214\) −2.12180 3.67506i −0.145043 0.251222i
\(215\) 2.51405 4.35446i 0.171457 0.296972i
\(216\) 8.40796 0.572089
\(217\) −6.15488 4.34008i −0.417821 0.294624i
\(218\) −3.21509 −0.217754
\(219\) −2.80912 + 4.86555i −0.189823 + 0.328783i
\(220\) −3.61887 6.26806i −0.243984 0.422593i
\(221\) 0 0
\(222\) −0.179088 + 0.310190i −0.0120196 + 0.0208186i
\(223\) 11.5087 0.770679 0.385340 0.922775i \(-0.374084\pi\)
0.385340 + 0.922775i \(0.374084\pi\)
\(224\) 10.8786 + 7.67099i 0.726858 + 0.512539i
\(225\) 8.91507 0.594338
\(226\) −2.74075 + 4.74711i −0.182312 + 0.315773i
\(227\) 8.95223 + 15.5057i 0.594181 + 1.02915i 0.993662 + 0.112410i \(0.0358569\pi\)
−0.399481 + 0.916741i \(0.630810\pi\)
\(228\) 4.09600 + 7.09448i 0.271264 + 0.469843i
\(229\) −1.93175 + 3.34589i −0.127654 + 0.221103i −0.922767 0.385358i \(-0.874078\pi\)
0.795113 + 0.606461i \(0.207411\pi\)
\(230\) −2.28868 −0.150911
\(231\) 0.806593 8.88129i 0.0530699 0.584346i
\(232\) 15.7451 1.03372
\(233\) −12.5321 + 21.7062i −0.821004 + 1.42202i 0.0839312 + 0.996472i \(0.473252\pi\)
−0.904935 + 0.425549i \(0.860081\pi\)
\(234\) 0 0
\(235\) 2.37501 + 4.11363i 0.154928 + 0.268344i
\(236\) 9.43388 16.3400i 0.614093 1.06364i
\(237\) 10.1295 0.657985
\(238\) 0.170548 0.0788427i 0.0110550 0.00511061i
\(239\) −7.80462 −0.504839 −0.252419 0.967618i \(-0.581226\pi\)
−0.252419 + 0.967618i \(0.581226\pi\)
\(240\) 1.13482 1.96557i 0.0732524 0.126877i
\(241\) −10.8826 18.8493i −0.701012 1.21419i −0.968112 0.250519i \(-0.919399\pi\)
0.267100 0.963669i \(-0.413935\pi\)
\(242\) −1.18484 2.05221i −0.0761647 0.131921i
\(243\) −8.01138 + 13.8761i −0.513930 + 0.890154i
\(244\) 10.2613 0.656910
\(245\) −2.45046 6.87359i −0.156554 0.439137i
\(246\) −5.13884 −0.327640
\(247\) 0 0
\(248\) −2.66855 4.62207i −0.169453 0.293502i
\(249\) 1.22054 + 2.11404i 0.0773488 + 0.133972i
\(250\) −2.32290 + 4.02338i −0.146913 + 0.254461i
\(251\) 7.67980 0.484745 0.242372 0.970183i \(-0.422074\pi\)
0.242372 + 0.970183i \(0.422074\pi\)
\(252\) −9.57458 + 4.42624i −0.603142 + 0.278827i
\(253\) 17.4203 1.09521
\(254\) 0.501955 0.869411i 0.0314954 0.0545517i
\(255\) −0.0628995 0.108945i −0.00393892 0.00682241i
\(256\) 0.232070 + 0.401958i 0.0145044 + 0.0251224i
\(257\) −6.81187 + 11.7985i −0.424913 + 0.735971i −0.996412 0.0846316i \(-0.973029\pi\)
0.571499 + 0.820603i \(0.306362\pi\)
\(258\) 2.04886 0.127556
\(259\) 0.201775 2.22172i 0.0125377 0.138051i
\(260\) 0 0
\(261\) −9.56560 + 16.5681i −0.592096 + 1.02554i
\(262\) 3.11247 + 5.39096i 0.192289 + 0.333055i
\(263\) 5.86158 + 10.1525i 0.361440 + 0.626033i 0.988198 0.153181i \(-0.0489518\pi\)
−0.626758 + 0.779214i \(0.715618\pi\)
\(264\) 3.15989 5.47309i 0.194478 0.336845i
\(265\) 0.291476 0.0179052
\(266\) 5.95658 + 4.20024i 0.365221 + 0.257533i
\(267\) −1.48481 −0.0908686
\(268\) −4.50144 + 7.79673i −0.274970 + 0.476261i
\(269\) −4.59938 7.96636i −0.280429 0.485717i 0.691061 0.722796i \(-0.257143\pi\)
−0.971490 + 0.237079i \(0.923810\pi\)
\(270\) −1.16867 2.02420i −0.0711232 0.123189i
\(271\) 1.28184 2.22022i 0.0778665 0.134869i −0.824463 0.565916i \(-0.808523\pi\)
0.902329 + 0.431048i \(0.141856\pi\)
\(272\) −0.363976 −0.0220693
\(273\) 0 0
\(274\) 2.62252 0.158432
\(275\) 7.76252 13.4451i 0.468097 0.810769i
\(276\) 3.26428 + 5.65391i 0.196487 + 0.340325i
\(277\) 0.466941 + 0.808765i 0.0280558 + 0.0485940i 0.879712 0.475506i \(-0.157735\pi\)
−0.851657 + 0.524100i \(0.824402\pi\)
\(278\) 5.18450 8.97981i 0.310945 0.538573i
\(279\) 6.48488 0.388240
\(280\) 0.467736 5.15018i 0.0279525 0.307782i
\(281\) 6.45288 0.384947 0.192473 0.981302i \(-0.438349\pi\)
0.192473 + 0.981302i \(0.438349\pi\)
\(282\) −0.967771 + 1.67623i −0.0576299 + 0.0998180i
\(283\) −11.0873 19.2037i −0.659071 1.14154i −0.980857 0.194731i \(-0.937616\pi\)
0.321786 0.946812i \(-0.395717\pi\)
\(284\) −3.23648 5.60575i −0.192050 0.332640i
\(285\) 2.43997 4.22615i 0.144531 0.250335i
\(286\) 0 0
\(287\) 29.0524 13.4307i 1.71491 0.792788i
\(288\) −11.4619 −0.675398
\(289\) 8.48991 14.7050i 0.499407 0.864998i
\(290\) −2.18851 3.79061i −0.128514 0.222593i
\(291\) −1.14820 1.98873i −0.0673085 0.116582i
\(292\) 5.78625 10.0221i 0.338615 0.586498i
\(293\) 24.2026 1.41393 0.706964 0.707249i \(-0.250064\pi\)
0.706964 + 0.707249i \(0.250064\pi\)
\(294\) 1.92636 2.26517i 0.112347 0.132107i
\(295\) −11.2394 −0.654385
\(296\) 0.790469 1.36913i 0.0459451 0.0795792i
\(297\) 8.89539 + 15.4073i 0.516163 + 0.894020i
\(298\) 0.00284392 + 0.00492581i 0.000164744 + 0.000285345i
\(299\) 0 0
\(300\) 5.81827 0.335918
\(301\) −11.5832 + 5.35481i −0.667645 + 0.308646i
\(302\) −9.45246 −0.543928
\(303\) −4.87341 + 8.44100i −0.279970 + 0.484923i
\(304\) −7.05959 12.2276i −0.404895 0.701299i
\(305\) −3.05630 5.29366i −0.175003 0.303114i
\(306\) −0.0808933 + 0.140111i −0.00462436 + 0.00800963i
\(307\) 24.2924 1.38644 0.693220 0.720726i \(-0.256191\pi\)
0.693220 + 0.720726i \(0.256191\pi\)
\(308\) −1.66142 + 18.2937i −0.0946684 + 1.04238i
\(309\) 3.54242 0.201521
\(310\) −0.741837 + 1.28490i −0.0421335 + 0.0729774i
\(311\) −1.99355 3.45294i −0.113044 0.195798i 0.803952 0.594694i \(-0.202727\pi\)
−0.916996 + 0.398896i \(0.869393\pi\)
\(312\) 0 0
\(313\) −14.2377 + 24.6604i −0.804763 + 1.39389i 0.111688 + 0.993743i \(0.464374\pi\)
−0.916451 + 0.400147i \(0.868959\pi\)
\(314\) 9.89661 0.558498
\(315\) 5.13521 + 3.62106i 0.289336 + 0.204024i
\(316\) −20.8649 −1.17374
\(317\) 8.40806 14.5632i 0.472244 0.817950i −0.527252 0.849709i \(-0.676778\pi\)
0.999496 + 0.0317591i \(0.0101109\pi\)
\(318\) 0.0593856 + 0.102859i 0.00333018 + 0.00576804i
\(319\) 16.6579 + 28.8523i 0.932664 + 1.61542i
\(320\) −1.36024 + 2.35600i −0.0760396 + 0.131704i
\(321\) 7.21093 0.402475
\(322\) 4.74706 + 3.34736i 0.264543 + 0.186541i
\(323\) −0.782582 −0.0435440
\(324\) 2.64657 4.58399i 0.147031 0.254666i
\(325\) 0 0
\(326\) −2.23308 3.86780i −0.123679 0.214218i
\(327\) 2.73162 4.73131i 0.151059 0.261642i
\(328\) 22.6821 1.25241
\(329\) 1.09037 12.0059i 0.0601139 0.661906i
\(330\) −1.75685 −0.0967115
\(331\) 3.10459 5.37730i 0.170644 0.295563i −0.768002 0.640448i \(-0.778749\pi\)
0.938645 + 0.344885i \(0.112082\pi\)
\(332\) −2.51408 4.35451i −0.137978 0.238985i
\(333\) 0.960464 + 1.66357i 0.0526331 + 0.0911632i
\(334\) −1.53363 + 2.65633i −0.0839165 + 0.145348i
\(335\) 5.36298 0.293011
\(336\) −5.22857 + 2.41712i −0.285242 + 0.131865i
\(337\) −7.69650 −0.419255 −0.209628 0.977781i \(-0.567225\pi\)
−0.209628 + 0.977781i \(0.567225\pi\)
\(338\) 0 0
\(339\) −4.65721 8.06653i −0.252945 0.438114i
\(340\) 0.129561 + 0.224406i 0.00702642 + 0.0121701i
\(341\) 5.64651 9.78005i 0.305776 0.529619i
\(342\) −6.27594 −0.339364
\(343\) −4.97049 + 17.8408i −0.268381 + 0.963313i
\(344\) −9.04335 −0.487585
\(345\) 1.94452 3.36801i 0.104689 0.181327i
\(346\) −6.06553 10.5058i −0.326085 0.564795i
\(347\) −15.2047 26.3353i −0.816231 1.41375i −0.908440 0.418015i \(-0.862726\pi\)
0.0922088 0.995740i \(-0.470607\pi\)
\(348\) −6.24283 + 10.8129i −0.334651 + 0.579632i
\(349\) −16.1581 −0.864924 −0.432462 0.901652i \(-0.642355\pi\)
−0.432462 + 0.901652i \(0.642355\pi\)
\(350\) 4.69880 2.17221i 0.251161 0.116110i
\(351\) 0 0
\(352\) −9.98008 + 17.2860i −0.531940 + 0.921347i
\(353\) 5.92119 + 10.2558i 0.315153 + 0.545861i 0.979470 0.201590i \(-0.0646108\pi\)
−0.664317 + 0.747451i \(0.731277\pi\)
\(354\) −2.28993 3.96628i −0.121709 0.210805i
\(355\) −1.92796 + 3.33932i −0.102325 + 0.177233i
\(356\) 3.05841 0.162095
\(357\) −0.0288772 + 0.317963i −0.00152834 + 0.0168284i
\(358\) −2.06832 −0.109314
\(359\) −15.6826 + 27.1631i −0.827698 + 1.43362i 0.0721417 + 0.997394i \(0.477017\pi\)
−0.899840 + 0.436221i \(0.856317\pi\)
\(360\) 2.22646 + 3.85634i 0.117345 + 0.203247i
\(361\) −5.67876 9.83591i −0.298882 0.517679i
\(362\) −1.96637 + 3.40585i −0.103350 + 0.179007i
\(363\) 4.02669 0.211346
\(364\) 0 0
\(365\) −6.89369 −0.360832
\(366\) 1.24538 2.15707i 0.0650973 0.112752i
\(367\) −12.0387 20.8517i −0.628415 1.08845i −0.987870 0.155285i \(-0.950370\pi\)
0.359454 0.933163i \(-0.382963\pi\)
\(368\) −5.62610 9.74470i −0.293281 0.507977i
\(369\) −13.7800 + 23.8676i −0.717358 + 1.24250i
\(370\) −0.439489 −0.0228479
\(371\) −0.604564 0.426305i −0.0313874 0.0221326i
\(372\) 4.23225 0.219432
\(373\) 9.19612 15.9281i 0.476157 0.824728i −0.523470 0.852044i \(-0.675363\pi\)
0.999627 + 0.0273160i \(0.00869604\pi\)
\(374\) 0.140871 + 0.243995i 0.00728425 + 0.0126167i
\(375\) −3.94718 6.83672i −0.203831 0.353046i
\(376\) 4.27160 7.39862i 0.220291 0.381555i
\(377\) 0 0
\(378\) −0.536539 + 5.90776i −0.0275966 + 0.303862i
\(379\) 8.13740 0.417990 0.208995 0.977917i \(-0.432981\pi\)
0.208995 + 0.977917i \(0.432981\pi\)
\(380\) −5.02586 + 8.70504i −0.257821 + 0.446559i
\(381\) 0.852946 + 1.47735i 0.0436977 + 0.0756867i
\(382\) 1.61962 + 2.80527i 0.0828671 + 0.143530i
\(383\) −11.1856 + 19.3739i −0.571555 + 0.989962i 0.424852 + 0.905263i \(0.360326\pi\)
−0.996407 + 0.0846992i \(0.973007\pi\)
\(384\) −9.65752 −0.492833
\(385\) 9.93236 4.59164i 0.506200 0.234012i
\(386\) −2.41458 −0.122899
\(387\) 5.49409 9.51604i 0.279280 0.483727i
\(388\) 2.36506 + 4.09641i 0.120068 + 0.207963i
\(389\) 10.6973 + 18.5283i 0.542374 + 0.939420i 0.998767 + 0.0496415i \(0.0158079\pi\)
−0.456393 + 0.889778i \(0.650859\pi\)
\(390\) 0 0
\(391\) −0.623674 −0.0315406
\(392\) −8.50265 + 9.99813i −0.429449 + 0.504982i
\(393\) −10.5777 −0.533576
\(394\) −6.45888 + 11.1871i −0.325394 + 0.563599i
\(395\) 6.21456 + 10.7639i 0.312689 + 0.541592i
\(396\) −7.90851 13.6979i −0.397417 0.688347i
\(397\) −0.598365 + 1.03640i −0.0300311 + 0.0520154i −0.880650 0.473767i \(-0.842894\pi\)
0.850619 + 0.525782i \(0.176227\pi\)
\(398\) 8.55708 0.428928
\(399\) −11.2419 + 5.19703i −0.562799 + 0.260177i
\(400\) −10.0280 −0.501399
\(401\) 18.1375 31.4150i 0.905741 1.56879i 0.0858220 0.996310i \(-0.472648\pi\)
0.819919 0.572479i \(-0.194018\pi\)
\(402\) 1.09266 + 1.89254i 0.0544968 + 0.0943913i
\(403\) 0 0
\(404\) 10.0383 17.3868i 0.499423 0.865026i
\(405\) −3.15309 −0.156679
\(406\) −1.00475 + 11.0631i −0.0498647 + 0.549055i
\(407\) 3.34518 0.165814
\(408\) −0.113129 + 0.195945i −0.00560071 + 0.00970071i
\(409\) −7.33616 12.7066i −0.362750 0.628301i 0.625662 0.780094i \(-0.284829\pi\)
−0.988412 + 0.151793i \(0.951495\pi\)
\(410\) −3.15272 5.46067i −0.155702 0.269683i
\(411\) −2.22816 + 3.85928i −0.109907 + 0.190364i
\(412\) −7.29669 −0.359482
\(413\) 23.3122 + 16.4385i 1.14712 + 0.808884i
\(414\) −5.00158 −0.245814
\(415\) −1.49763 + 2.59397i −0.0735156 + 0.127333i
\(416\) 0 0
\(417\) 8.80975 + 15.2589i 0.431415 + 0.747233i
\(418\) −5.46458 + 9.46494i −0.267282 + 0.462945i
\(419\) −5.93348 −0.289870 −0.144935 0.989441i \(-0.546297\pi\)
−0.144935 + 0.989441i \(0.546297\pi\)
\(420\) 3.35141 + 2.36322i 0.163532 + 0.115314i
\(421\) 2.63174 0.128263 0.0641317 0.997941i \(-0.479572\pi\)
0.0641317 + 0.997941i \(0.479572\pi\)
\(422\) −4.57266 + 7.92008i −0.222594 + 0.385544i
\(423\) 5.19023 + 8.98974i 0.252358 + 0.437096i
\(424\) −0.262119 0.454004i −0.0127296 0.0220484i
\(425\) −0.277910 + 0.481354i −0.0134806 + 0.0233491i
\(426\) −1.57121 −0.0761255
\(427\) −1.40315 + 15.4499i −0.0679030 + 0.747672i
\(428\) −14.8531 −0.717952
\(429\) 0 0
\(430\) 1.25699 + 2.17717i 0.0606175 + 0.104993i
\(431\) −9.41883 16.3139i −0.453689 0.785812i 0.544923 0.838486i \(-0.316559\pi\)
−0.998612 + 0.0526738i \(0.983226\pi\)
\(432\) 5.74573 9.95190i 0.276442 0.478811i
\(433\) 19.1355 0.919591 0.459796 0.888025i \(-0.347923\pi\)
0.459796 + 0.888025i \(0.347923\pi\)
\(434\) 3.41794 1.58008i 0.164066 0.0758463i
\(435\) 7.43765 0.356608
\(436\) −5.62661 + 9.74557i −0.269466 + 0.466728i
\(437\) −12.0966 20.9520i −0.578660 1.00227i
\(438\) −1.40452 2.43271i −0.0671108 0.116239i
\(439\) 0.632554 1.09561i 0.0301901 0.0522908i −0.850536 0.525918i \(-0.823722\pi\)
0.880726 + 0.473627i \(0.157055\pi\)
\(440\) 7.75448 0.369680
\(441\) −5.35512 15.0212i −0.255006 0.715296i
\(442\) 0 0
\(443\) 10.4696 18.1339i 0.497426 0.861568i −0.502569 0.864537i \(-0.667612\pi\)
0.999996 + 0.00296930i \(0.000945159\pi\)
\(444\) 0.626831 + 1.08570i 0.0297481 + 0.0515252i
\(445\) −0.910940 1.57779i −0.0431827 0.0747946i
\(446\) −2.87710 + 4.98328i −0.136234 + 0.235965i
\(447\) −0.00966505 −0.000457141
\(448\) 6.26715 2.89725i 0.296095 0.136882i
\(449\) −17.8632 −0.843018 −0.421509 0.906824i \(-0.638499\pi\)
−0.421509 + 0.906824i \(0.638499\pi\)
\(450\) −2.22871 + 3.86023i −0.105062 + 0.181973i
\(451\) 23.9970 + 41.5640i 1.12997 + 1.95717i
\(452\) 9.59295 + 16.6155i 0.451214 + 0.781526i
\(453\) 8.03104 13.9102i 0.377331 0.653557i
\(454\) −8.95199 −0.420138
\(455\) 0 0
\(456\) −8.77687 −0.411015
\(457\) 3.28298 5.68629i 0.153571 0.265994i −0.778966 0.627066i \(-0.784256\pi\)
0.932538 + 0.361072i \(0.117589\pi\)
\(458\) −0.965850 1.67290i −0.0451312 0.0781695i
\(459\) −0.318468 0.551603i −0.0148648 0.0257466i
\(460\) −4.00533 + 6.93744i −0.186749 + 0.323460i
\(461\) −5.11364 −0.238166 −0.119083 0.992884i \(-0.537995\pi\)
−0.119083 + 0.992884i \(0.537995\pi\)
\(462\) 3.64397 + 2.56952i 0.169533 + 0.119545i
\(463\) −33.3239 −1.54869 −0.774347 0.632761i \(-0.781921\pi\)
−0.774347 + 0.632761i \(0.781921\pi\)
\(464\) 10.7597 18.6364i 0.499508 0.865173i
\(465\) −1.26057 2.18336i −0.0584574 0.101251i
\(466\) −6.26587 10.8528i −0.290261 0.502747i
\(467\) 6.47472 11.2145i 0.299614 0.518947i −0.676433 0.736504i \(-0.736475\pi\)
0.976048 + 0.217557i \(0.0698087\pi\)
\(468\) 0 0
\(469\) −11.1236 7.84374i −0.513641 0.362190i
\(470\) −2.37494 −0.109548
\(471\) −8.40840 + 14.5638i −0.387439 + 0.671063i
\(472\) 10.1074 + 17.5066i 0.465231 + 0.805805i
\(473\) −9.56761 16.5716i −0.439919 0.761962i
\(474\) −2.53232 + 4.38611i −0.116313 + 0.201461i
\(475\) −21.5611 −0.989290
\(476\) 0.0594814 0.654942i 0.00272633 0.0300192i
\(477\) 0.636979 0.0291652
\(478\) 1.95110 3.37941i 0.0892414 0.154571i
\(479\) 13.5060 + 23.3930i 0.617104 + 1.06885i 0.990012 + 0.140987i \(0.0450274\pi\)
−0.372908 + 0.927868i \(0.621639\pi\)
\(480\) 2.22802 + 3.85905i 0.101695 + 0.176141i
\(481\) 0 0
\(482\) 10.8823 0.495677
\(483\) −8.95917 + 4.14174i −0.407656 + 0.188456i
\(484\) −8.29420 −0.377009
\(485\) 1.40886 2.44021i 0.0639729 0.110804i
\(486\) −4.00558 6.93788i −0.181697 0.314708i
\(487\) 16.0419 + 27.7854i 0.726928 + 1.25908i 0.958175 + 0.286182i \(0.0923862\pi\)
−0.231247 + 0.972895i \(0.574280\pi\)
\(488\) −5.49694 + 9.52097i −0.248835 + 0.430994i
\(489\) 7.58910 0.343191
\(490\) 3.58887 + 0.657299i 0.162129 + 0.0296937i
\(491\) −28.6040 −1.29088 −0.645440 0.763811i \(-0.723326\pi\)
−0.645440 + 0.763811i \(0.723326\pi\)
\(492\) −8.99328 + 15.5768i −0.405448 + 0.702257i
\(493\) −0.596378 1.03296i −0.0268595 0.0465220i
\(494\) 0 0
\(495\) −4.71106 + 8.15980i −0.211746 + 0.366756i
\(496\) −7.29442 −0.327529
\(497\) 8.88285 4.10646i 0.398450 0.184200i
\(498\) −1.22051 −0.0546924
\(499\) −0.899082 + 1.55726i −0.0402484 + 0.0697123i −0.885448 0.464739i \(-0.846148\pi\)
0.845199 + 0.534451i \(0.179482\pi\)
\(500\) 8.13042 + 14.0823i 0.363603 + 0.629780i
\(501\) −2.60602 4.51376i −0.116428 0.201660i
\(502\) −1.91990 + 3.32536i −0.0856893 + 0.148418i
\(503\) 29.0772 1.29649 0.648245 0.761432i \(-0.275503\pi\)
0.648245 + 0.761432i \(0.275503\pi\)
\(504\) 1.02217 11.2550i 0.0455310 0.501336i
\(505\) −11.9595 −0.532191
\(506\) −4.35497 + 7.54303i −0.193602 + 0.335329i
\(507\) 0 0
\(508\) −1.75690 3.04304i −0.0779499 0.135013i
\(509\) −11.5957 + 20.0843i −0.513969 + 0.890220i 0.485900 + 0.874014i \(0.338492\pi\)
−0.999869 + 0.0162054i \(0.994841\pi\)
\(510\) 0.0628979 0.00278516
\(511\) 14.2985 + 10.0825i 0.632529 + 0.446024i
\(512\) 22.5022 0.994464
\(513\) 12.3539 21.3975i 0.545436 0.944723i
\(514\) −3.40585 5.89910i −0.150225 0.260198i
\(515\) 2.17330 + 3.76427i 0.0957671 + 0.165874i
\(516\) 3.58562 6.21048i 0.157848 0.273401i
\(517\) 18.0769 0.795022
\(518\) 0.911564 + 0.642783i 0.0400518 + 0.0282423i
\(519\) 20.6137 0.904840
\(520\) 0 0
\(521\) −16.6255 28.7962i −0.728376 1.26158i −0.957569 0.288203i \(-0.906942\pi\)
0.229193 0.973381i \(-0.426391\pi\)
\(522\) −4.78267 8.28383i −0.209332 0.362574i
\(523\) −19.3560 + 33.5256i −0.846380 + 1.46597i 0.0380367 + 0.999276i \(0.487890\pi\)
−0.884417 + 0.466697i \(0.845444\pi\)
\(524\) 21.7881 0.951816
\(525\) −0.795602 + 8.76027i −0.0347229 + 0.382330i
\(526\) −5.86142 −0.255570
\(527\) −0.202153 + 0.350140i −0.00880594 + 0.0152523i
\(528\) −4.31874 7.48028i −0.187949 0.325537i
\(529\) 1.85966 + 3.22102i 0.0808546 + 0.140044i
\(530\) −0.0728671 + 0.126210i −0.00316514 + 0.00548219i
\(531\) −24.5622 −1.06591
\(532\) 23.1561 10.7049i 1.00394 0.464115i
\(533\) 0 0
\(534\) 0.371191 0.642922i 0.0160630 0.0278220i
\(535\) 4.42396 + 7.66253i 0.191265 + 0.331280i
\(536\) −4.82283 8.35338i −0.208314 0.360811i
\(537\) 1.75730 3.04372i 0.0758329 0.131346i
\(538\) 4.59926 0.198288
\(539\) −27.3168 5.00304i −1.17662 0.215496i
\(540\) −8.18100 −0.352054
\(541\) −11.3337 + 19.6306i −0.487275 + 0.843986i −0.999893 0.0146313i \(-0.995343\pi\)
0.512618 + 0.858617i \(0.328676\pi\)
\(542\) 0.640905 + 1.11008i 0.0275292 + 0.0476820i
\(543\) −3.34135 5.78738i −0.143391 0.248360i
\(544\) 0.357302 0.618865i 0.0153192 0.0265336i
\(545\) 6.70349 0.287146
\(546\) 0 0
\(547\) −9.21134 −0.393848 −0.196924 0.980419i \(-0.563095\pi\)
−0.196924 + 0.980419i \(0.563095\pi\)
\(548\) 4.58957 7.94936i 0.196057 0.339580i
\(549\) −6.67909 11.5685i −0.285056 0.493732i
\(550\) 3.88116 + 6.72236i 0.165493 + 0.286642i
\(551\) 23.1344 40.0699i 0.985558 1.70704i
\(552\) −6.99468 −0.297713
\(553\) 2.85311 31.4152i 0.121327 1.33591i
\(554\) −0.466928 −0.0198379
\(555\) 0.373400 0.646748i 0.0158500 0.0274529i
\(556\) −18.1464 31.4304i −0.769577 1.33295i
\(557\) 5.66403 + 9.81039i 0.239993 + 0.415680i 0.960712 0.277547i \(-0.0895216\pi\)
−0.720719 + 0.693227i \(0.756188\pi\)
\(558\) −1.62118 + 2.80796i −0.0686299 + 0.118871i
\(559\) 0 0
\(560\) −5.77627 4.07310i −0.244092 0.172120i
\(561\) −0.478748 −0.0202128
\(562\) −1.61318 + 2.79411i −0.0680478 + 0.117862i
\(563\) −16.3193 28.2659i −0.687777 1.19127i −0.972555 0.232672i \(-0.925253\pi\)
0.284778 0.958594i \(-0.408080\pi\)
\(564\) 3.38732 + 5.86700i 0.142632 + 0.247045i
\(565\) 5.71448 9.89776i 0.240410 0.416402i
\(566\) 11.0870 0.466021
\(567\) 6.53998 + 4.61162i 0.274653 + 0.193670i
\(568\) 6.93510 0.290990
\(569\) −17.5045 + 30.3188i −0.733829 + 1.27103i 0.221407 + 0.975182i \(0.428935\pi\)
−0.955235 + 0.295847i \(0.904398\pi\)
\(570\) 1.21995 + 2.11302i 0.0510981 + 0.0885046i
\(571\) −13.1273 22.7371i −0.549360 0.951519i −0.998319 0.0579663i \(-0.981538\pi\)
0.448959 0.893552i \(-0.351795\pi\)
\(572\) 0 0
\(573\) −5.50428 −0.229945
\(574\) −1.44742 + 15.9373i −0.0604140 + 0.665211i
\(575\) −17.1830 −0.716580
\(576\) −2.97260 + 5.14870i −0.123858 + 0.214529i
\(577\) 12.2863 + 21.2806i 0.511487 + 0.885922i 0.999911 + 0.0133154i \(0.00423855\pi\)
−0.488424 + 0.872606i \(0.662428\pi\)
\(578\) 4.24484 + 7.35228i 0.176562 + 0.305815i
\(579\) 2.05148 3.55327i 0.0852567 0.147669i
\(580\) −15.3201 −0.636133
\(581\) 6.90015 3.18988i 0.286267 0.132338i
\(582\) 1.14817 0.0475930
\(583\) 0.554629 0.960646i 0.0229704 0.0397859i
\(584\) 6.19936 + 10.7376i 0.256531 + 0.444325i
\(585\) 0 0
\(586\) −6.05048 + 10.4797i −0.249943 + 0.432914i
\(587\) −20.5279 −0.847279 −0.423639 0.905831i \(-0.639248\pi\)
−0.423639 + 0.905831i \(0.639248\pi\)
\(588\) −3.49493 9.80335i −0.144129 0.404283i
\(589\) −15.6837 −0.646235
\(590\) 2.80978 4.86669i 0.115677 0.200358i
\(591\) −10.9752 19.0097i −0.451461 0.781954i
\(592\) −1.08036 1.87124i −0.0444027 0.0769077i
\(593\) 19.1417 33.1545i 0.786057 1.36149i −0.142308 0.989822i \(-0.545452\pi\)
0.928365 0.371669i \(-0.121214\pi\)
\(594\) −8.89515 −0.364972
\(595\) −0.355593 + 0.164387i −0.0145779 + 0.00673923i
\(596\) 0.0199081 0.000815468
\(597\) −7.27030 + 12.5925i −0.297554 + 0.515378i
\(598\) 0 0
\(599\) −7.03567 12.1861i −0.287470 0.497912i 0.685735 0.727851i \(-0.259481\pi\)
−0.973205 + 0.229939i \(0.926147\pi\)
\(600\) −3.11683 + 5.39851i −0.127244 + 0.220393i
\(601\) −20.2342 −0.825369 −0.412685 0.910874i \(-0.635409\pi\)
−0.412685 + 0.910874i \(0.635409\pi\)
\(602\) 0.577085 6.35421i 0.0235202 0.258978i
\(603\) 11.7200 0.477276
\(604\) −16.5424 + 28.6522i −0.673099 + 1.16584i
\(605\) 2.47041 + 4.27887i 0.100436 + 0.173961i
\(606\) −2.43664 4.22039i −0.0989818 0.171441i
\(607\) −3.27563 + 5.67356i −0.132954 + 0.230283i −0.924814 0.380420i \(-0.875780\pi\)
0.791860 + 0.610703i \(0.209113\pi\)
\(608\) 27.7205 1.12422
\(609\) −15.4268 10.8781i −0.625125 0.440803i
\(610\) 3.05621 0.123742
\(611\) 0 0
\(612\) 0.283136 + 0.490406i 0.0114451 + 0.0198235i
\(613\) −16.6622 28.8598i −0.672980 1.16564i −0.977055 0.212988i \(-0.931681\pi\)
0.304075 0.952648i \(-0.401653\pi\)
\(614\) −6.07294 + 10.5186i −0.245084 + 0.424498i
\(615\) 10.7145 0.432051
\(616\) −16.0839 11.3415i −0.648040 0.456961i
\(617\) 6.76038 0.272162 0.136081 0.990698i \(-0.456549\pi\)
0.136081 + 0.990698i \(0.456549\pi\)
\(618\) −0.885581 + 1.53387i −0.0356233 + 0.0617013i
\(619\) −8.80931 15.2582i −0.354076 0.613278i 0.632883 0.774247i \(-0.281871\pi\)
−0.986959 + 0.160970i \(0.948538\pi\)
\(620\) 2.59652 + 4.49731i 0.104279 + 0.180616i
\(621\) 9.84534 17.0526i 0.395080 0.684298i
\(622\) 1.99350 0.0799321
\(623\) −0.418213 + 4.60489i −0.0167554 + 0.184491i
\(624\) 0 0
\(625\) −4.93986 + 8.55609i −0.197594 + 0.342244i
\(626\) −7.11866 12.3299i −0.284519 0.492801i
\(627\) −9.28569 16.0833i −0.370835 0.642304i
\(628\) 17.3197 29.9985i 0.691130 1.19707i
\(629\) −0.119762 −0.00477524
\(630\) −2.85169 + 1.31831i −0.113614 + 0.0525228i
\(631\) −15.7519 −0.627074 −0.313537 0.949576i \(-0.601514\pi\)
−0.313537 + 0.949576i \(0.601514\pi\)
\(632\) 11.1773 19.3596i 0.444608 0.770084i
\(633\) −7.77009 13.4582i −0.308833 0.534915i
\(634\) 4.20392 + 7.28140i 0.166959 + 0.289181i
\(635\) −1.04658 + 1.81273i −0.0415322 + 0.0719359i
\(636\) 0.415713 0.0164841
\(637\) 0 0
\(638\) −16.6575 −0.659475
\(639\) −4.21327 + 7.29759i −0.166674 + 0.288688i
\(640\) −5.92497 10.2623i −0.234205 0.405655i
\(641\) 10.4702 + 18.1350i 0.413550 + 0.716289i 0.995275 0.0970962i \(-0.0309554\pi\)
−0.581725 + 0.813385i \(0.697622\pi\)
\(642\) −1.80268 + 3.12234i −0.0711463 + 0.123229i
\(643\) −18.9315 −0.746586 −0.373293 0.927713i \(-0.621771\pi\)
−0.373293 + 0.927713i \(0.621771\pi\)
\(644\) 18.4541 8.53118i 0.727195 0.336176i
\(645\) −4.27188 −0.168205
\(646\) 0.195640 0.338859i 0.00769736 0.0133322i
\(647\) 18.8384 + 32.6291i 0.740614 + 1.28278i 0.952216 + 0.305426i \(0.0987988\pi\)
−0.211601 + 0.977356i \(0.567868\pi\)
\(648\) 2.83552 + 4.91126i 0.111390 + 0.192933i
\(649\) −21.3867 + 37.0429i −0.839503 + 1.45406i
\(650\) 0 0
\(651\) −0.578727 + 6.37229i −0.0226821 + 0.249750i
\(652\) −15.6321 −0.612199
\(653\) −14.5163 + 25.1430i −0.568066 + 0.983920i 0.428691 + 0.903451i \(0.358975\pi\)
−0.996757 + 0.0804686i \(0.974358\pi\)
\(654\) 1.36577 + 2.36559i 0.0534060 + 0.0925019i
\(655\) −6.48952 11.2402i −0.253567 0.439190i
\(656\) 15.5002 26.8472i 0.605182 1.04821i
\(657\) −15.0651 −0.587747
\(658\) 4.92598 + 3.47352i 0.192035 + 0.135412i
\(659\) −1.41830 −0.0552493 −0.0276247 0.999618i \(-0.508794\pi\)
−0.0276247 + 0.999618i \(0.508794\pi\)
\(660\) −3.07459 + 5.32535i −0.119678 + 0.207289i
\(661\) −2.29649 3.97764i −0.0893231 0.154712i 0.817902 0.575357i \(-0.195137\pi\)
−0.907225 + 0.420645i \(0.861804\pi\)
\(662\) 1.55225 + 2.68858i 0.0603300 + 0.104495i
\(663\) 0 0
\(664\) 5.38715 0.209062
\(665\) −12.4195 8.75753i −0.481607 0.339602i
\(666\) −0.960439 −0.0372162
\(667\) 18.4368 31.9335i 0.713877 1.23647i
\(668\) 5.36789 + 9.29746i 0.207690 + 0.359730i
\(669\) −4.88890 8.46782i −0.189016 0.327385i
\(670\) −1.34071 + 2.32218i −0.0517961 + 0.0897135i
\(671\) −23.2624 −0.898036
\(672\) 1.02289 11.2629i 0.0394587 0.434475i
\(673\) −4.20223 −0.161984 −0.0809920 0.996715i \(-0.525809\pi\)
−0.0809920 + 0.996715i \(0.525809\pi\)
\(674\) 1.92407 3.33259i 0.0741126 0.128367i
\(675\) −8.77418 15.1973i −0.337718 0.584945i
\(676\) 0 0
\(677\) −4.04354 + 7.00361i −0.155406 + 0.269171i −0.933207 0.359340i \(-0.883002\pi\)
0.777801 + 0.628511i \(0.216335\pi\)
\(678\) 4.65709 0.178854
\(679\) −6.49115 + 3.00080i −0.249108 + 0.115160i
\(680\) −0.277622 −0.0106463
\(681\) 7.60583 13.1737i 0.291456 0.504817i
\(682\) 2.82318 + 4.88989i 0.108105 + 0.187244i
\(683\) −12.3433 21.3792i −0.472302 0.818051i 0.527196 0.849744i \(-0.323243\pi\)
−0.999498 + 0.0316929i \(0.989910\pi\)
\(684\) −10.9833 + 19.0236i −0.419956 + 0.727386i
\(685\) −5.46797 −0.208920
\(686\) −6.48250 6.61231i −0.247503 0.252459i
\(687\) 3.28244 0.125233
\(688\) −6.17994 + 10.7040i −0.235608 + 0.408085i
\(689\) 0 0
\(690\) 0.972234 + 1.68396i 0.0370123 + 0.0641072i
\(691\) 5.62835 9.74859i 0.214113 0.370854i −0.738885 0.673831i \(-0.764647\pi\)
0.952998 + 0.302978i \(0.0979807\pi\)
\(692\) −42.4602 −1.61409
\(693\) 21.7057 10.0344i 0.824532 0.381174i
\(694\) 15.2043 0.577147
\(695\) −10.8097 + 18.7230i −0.410035 + 0.710202i
\(696\) −6.68854 11.5849i −0.253528 0.439124i
\(697\) −0.859128 1.48805i −0.0325418 0.0563640i
\(698\) 4.03942 6.99648i 0.152894 0.264821i
\(699\) 21.2946 0.805434
\(700\) 1.63878 18.0445i 0.0619402 0.682016i
\(701\) −22.2305 −0.839635 −0.419818 0.907608i \(-0.637906\pi\)
−0.419818 + 0.907608i \(0.637906\pi\)
\(702\) 0 0
\(703\) −2.32288 4.02335i −0.0876091 0.151743i
\(704\) 5.17660 + 8.96614i 0.195101 + 0.337924i
\(705\) 2.01781 3.49495i 0.0759951 0.131627i
\(706\) −5.92103 −0.222841
\(707\) 24.8058 + 17.4916i 0.932918 + 0.657841i
\(708\) −16.0301 −0.602447
\(709\) −11.8870 + 20.5889i −0.446427 + 0.773234i −0.998150 0.0607929i \(-0.980637\pi\)
0.551723 + 0.834027i \(0.313970\pi\)
\(710\) −0.963952 1.66961i −0.0361765 0.0626595i
\(711\) 13.5810 + 23.5230i 0.509328 + 0.882182i
\(712\) −1.63838 + 2.83776i −0.0614010 + 0.106350i
\(713\) −12.4990 −0.468092
\(714\) −0.130459 0.0919926i −0.00488232 0.00344274i
\(715\) 0 0
\(716\) −3.61969 + 6.26948i −0.135274 + 0.234301i
\(717\) 3.31541 + 5.74246i 0.123816 + 0.214456i
\(718\) −7.84111 13.5812i −0.292628 0.506846i
\(719\) −10.3904 + 17.9967i −0.387496 + 0.671163i −0.992112 0.125354i \(-0.959993\pi\)
0.604616 + 0.796517i \(0.293327\pi\)
\(720\) 6.08597 0.226811
\(721\) 0.997764 10.9863i 0.0371587 0.409150i
\(722\) 5.67861 0.211336
\(723\) −9.24589 + 16.0144i −0.343859 + 0.595580i
\(724\) 6.88252 + 11.9209i 0.255787 + 0.443036i
\(725\) −16.4309 28.4592i −0.610229 1.05695i
\(726\) −1.00665 + 1.74356i −0.0373601 + 0.0647097i
\(727\) 26.7719 0.992915 0.496457 0.868061i \(-0.334634\pi\)
0.496457 + 0.868061i \(0.334634\pi\)
\(728\) 0 0
\(729\) 4.53910 0.168115
\(730\) 1.72338 2.98497i 0.0637850 0.110479i
\(731\) 0.342535 + 0.593287i 0.0126691 + 0.0219435i
\(732\) −4.35899 7.55000i −0.161113 0.279056i
\(733\) −2.62824 + 4.55224i −0.0970761 + 0.168141i −0.910473 0.413568i \(-0.864282\pi\)
0.813397 + 0.581709i \(0.197616\pi\)
\(734\) 12.0384 0.444345
\(735\) −4.01647 + 4.72290i −0.148150 + 0.174207i
\(736\) 22.0917 0.814312
\(737\) 10.2048 17.6753i 0.375900 0.651078i
\(738\) −6.88981 11.9335i −0.253617 0.439278i
\(739\) 3.57501 + 6.19209i 0.131509 + 0.227780i 0.924258 0.381768i \(-0.124685\pi\)
−0.792750 + 0.609547i \(0.791351\pi\)
\(740\) −0.769132 + 1.33218i −0.0282738 + 0.0489717i
\(741\) 0 0
\(742\) 0.335727 0.155204i 0.0123249 0.00569771i
\(743\) 0.713641 0.0261810 0.0130905 0.999914i \(-0.495833\pi\)
0.0130905 + 0.999914i \(0.495833\pi\)
\(744\) −2.26721 + 3.92692i −0.0831198 + 0.143968i
\(745\) −0.00592959 0.0102703i −0.000217243 0.000376276i
\(746\) 4.59794 + 7.96386i 0.168342 + 0.291578i
\(747\) −3.27284 + 5.66873i −0.119747 + 0.207408i
\(748\) 0.986128 0.0360564
\(749\) 2.03104 22.3636i 0.0742127 0.817147i
\(750\) 3.94707 0.144127
\(751\) 12.8507 22.2580i 0.468927 0.812205i −0.530442 0.847721i \(-0.677974\pi\)
0.999369 + 0.0355158i \(0.0113074\pi\)
\(752\) −5.83815 10.1120i −0.212896 0.368746i
\(753\) −3.26238 5.65062i −0.118888 0.205920i
\(754\) 0 0
\(755\) 19.7084 0.717263
\(756\) 16.9686 + 11.9653i 0.617142 + 0.435173i
\(757\) 16.3885 0.595650 0.297825 0.954621i \(-0.403739\pi\)
0.297825 + 0.954621i \(0.403739\pi\)
\(758\) −2.03430 + 3.52350i −0.0738889 + 0.127979i
\(759\) −7.40018 12.8175i −0.268609 0.465245i
\(760\) −5.38468 9.32654i −0.195323 0.338309i
\(761\) −4.15999 + 7.20531i −0.150800 + 0.261192i −0.931522 0.363686i \(-0.881518\pi\)
0.780722 + 0.624878i \(0.214851\pi\)
\(762\) −0.852923 −0.0308981
\(763\) −13.9040 9.80433i −0.503359 0.354941i
\(764\) 11.3378 0.410185
\(765\) 0.168663 0.292133i 0.00609802 0.0105621i
\(766\) −5.59263 9.68671i −0.202070 0.349995i
\(767\) 0 0
\(768\) 0.197167 0.341504i 0.00711466 0.0123230i
\(769\) −25.5588 −0.921675 −0.460838 0.887485i \(-0.652451\pi\)
−0.460838 + 0.887485i \(0.652451\pi\)
\(770\) −0.494838 + 5.44860i −0.0178327 + 0.196354i
\(771\) 11.5748 0.416855
\(772\) −4.22565 + 7.31905i −0.152085 + 0.263418i
\(773\) 4.20038 + 7.27528i 0.151077 + 0.261674i 0.931624 0.363424i \(-0.118392\pi\)
−0.780546 + 0.625098i \(0.785059\pi\)
\(774\) 2.74697 + 4.75789i 0.0987378 + 0.171019i
\(775\) −5.56957 + 9.64678i −0.200065 + 0.346523i
\(776\) −5.06783 −0.181925
\(777\) −1.72040 + 0.795326i −0.0617191 + 0.0285322i
\(778\) −10.6970 −0.383506
\(779\) 33.3269 57.7238i 1.19406 2.06817i
\(780\) 0 0
\(781\) 7.33714 + 12.7083i 0.262544 + 0.454739i