Properties

Label 1183.2.e.j.508.8
Level $1183$
Weight $2$
Character 1183.508
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 508.8
Character \(\chi\) \(=\) 1183.508
Dual form 1183.2.e.j.170.8

$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 \(-0.110101\pi\)
−0.764001 + 0.645215i \(0.776768\pi\)
\(3\) −0.424801 + 0.735776i −0.245259 + 0.424801i −0.962204 0.272328i \(-0.912206\pi\)
0.716946 + 0.697129i \(0.245540\pi\)
\(4\) 0.875007 1.51556i 0.437503 0.757778i
\(5\) −0.521238 0.902810i −0.233105 0.403749i 0.725616 0.688100i \(-0.241555\pi\)
−0.958720 + 0.284351i \(0.908222\pi\)
\(6\) −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 −0.395009 0.918677i \(-0.629258\pi\)
0.993102 0.117251i \(-0.0374083\pi\)
\(12\) 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 −0.857285 0.514843i \(-0.827850\pi\)
0.874509 + 0.485009i \(0.161184\pi\)
\(18\) −0.569529 + 0.986453i −0.134239 + 0.232509i
\(19\) 2.75488 + 4.77160i 0.632014 + 1.09468i 0.987140 + 0.159861i \(0.0511046\pi\)
−0.355126 + 0.934818i \(0.615562\pi\)
\(20\) −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 0.541053 0.840989i \(-0.318026\pi\)
−0.998844 + 0.0480711i \(0.984693\pi\)
\(24\) −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 \(-0.915615\pi\)
0.709440 + 0.704766i \(0.248948\pi\)
\(32\) 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 \(-0.144587\pi\)
−0.829288 + 0.558821i \(0.811254\pi\)
\(38\) −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 \(-0.106405\pi\)
0.944647 + 0.328089i \(0.106405\pi\)
\(42\) −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 \(-0.0588369\pi\)
−0.650650 + 0.759378i \(0.725504\pi\)
\(48\) 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 −0.856264 0.516538i \(-0.827220\pi\)
0.875467 + 0.483278i \(0.160554\pi\)
\(54\) −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 −0.266013 0.963969i \(-0.585706\pi\)
0.967829 0.251611i \(-0.0809602\pi\)
\(60\) 0.774983 1.34231i 0.100050 0.173292i
\(61\) 2.93177 + 5.07797i 0.375374 + 0.650168i 0.990383 0.138353i \(-0.0441808\pi\)
−0.615009 + 0.788520i \(0.710847\pi\)
\(62\) −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 \(-0.935086\pi\)
0.665029 + 0.746818i \(0.268419\pi\)
\(68\) −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 \(-0.429563\pi\)
0.219484 + 0.975616i \(0.429563\pi\)
\(72\) 2.13574 + 3.69921i 0.251700 + 0.435956i
\(73\) 3.30640 5.72686i 0.386985 0.670278i −0.605057 0.796182i \(-0.706850\pi\)
0.992042 + 0.125904i \(0.0401831\pi\)
\(74\) −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 −0.977705 0.209985i \(-0.932658\pi\)
0.307000 0.951710i \(-0.400675\pi\)
\(80\) −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 \(-0.449596\pi\)
0.157688 + 0.987489i \(0.449596\pi\)
\(84\) 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 \(-0.196193\pi\)
−0.908615 + 0.417635i \(0.862859\pi\)
\(90\) 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 \(-0.543816\pi\)
−0.137219 + 0.990541i \(0.543816\pi\)
\(98\) −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 0.425723 + 0.904854i \(0.360020\pi\)
−0.996488 + 0.0837401i \(0.973313\pi\)
\(102\) −0.0301676 + 0.0522517i −0.00298703 + 0.00517369i
\(103\) −2.08475 3.61090i −0.205417 0.355792i 0.744849 0.667233i \(-0.232522\pi\)
−0.950265 + 0.311441i \(0.899188\pi\)
\(104\) 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 0.584662 0.811277i \(-0.301227\pi\)
−0.994917 + 0.100694i \(0.967894\pi\)
\(108\) −3.92383 + 6.79628i −0.377571 + 0.653972i
\(109\) −3.21518 + 5.56886i −0.307958 + 0.533400i −0.977916 0.209000i \(-0.932979\pi\)
0.669957 + 0.742400i \(0.266312\pi\)
\(110\) −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 0.998676 + 0.0514449i \(0.0163826\pi\)
−0.454785 + 0.890601i \(0.650284\pi\)
\(132\) 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 \(-0.761401\pi\)
0.956038 + 0.293243i \(0.0947346\pi\)
\(138\) 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 \(-0.166815\pi\)
−0.866258 + 0.499596i \(0.833482\pi\)
\(150\) −0.831153 + 1.43960i −0.0678633 + 0.117543i
\(151\) −9.45271 + 16.3726i −0.769251 + 1.33238i 0.168719 + 0.985664i \(0.446037\pi\)
−0.937970 + 0.346717i \(0.887296\pi\)
\(152\) 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 0.136198 + 0.990682i \(0.456512\pi\)
−0.926054 + 0.377390i \(0.876822\pi\)
\(158\) 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 \(-0.0529076\pi\)
−0.636393 + 0.771365i \(0.719574\pi\)
\(164\) 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 \(-0.576281\pi\)
−0.237358 + 0.971422i \(0.576281\pi\)
\(168\) −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 −0.795797 0.605563i \(-0.792948\pi\)
−0.126535 0.991962i \(-0.540386\pi\)
\(174\) 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 −0.778315 0.627874i \(-0.783925\pi\)
0.932912 + 0.360103i \(0.117259\pi\)
\(180\) −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 0.959095 0.283084i \(-0.0913574\pi\)
−0.724705 + 0.689059i \(0.758024\pi\)
\(192\) 1.10857 1.92011i 0.0800044 0.138572i
\(193\) −2.41464 + 4.18228i −0.173810 + 0.301047i −0.939749 0.341866i \(-0.888941\pi\)
0.765939 + 0.642913i \(0.222274\pi\)
\(194\) −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 \(-0.872118\pi\)
−0.920377 + 0.391032i \(0.872118\pi\)
\(198\) 2.25950 + 3.91356i 0.160575 + 0.278125i
\(199\) −8.55731 + 14.8217i −0.606612 + 1.05068i 0.385183 + 0.922840i \(0.374138\pi\)
−0.991795 + 0.127842i \(0.959195\pi\)
\(200\) 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 \(-0.625916\pi\)
−0.385340 + 0.922775i \(0.625916\pi\)
\(224\) 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 0.399481 + 0.916741i \(0.369190\pi\)
−0.993662 + 0.112410i \(0.964143\pi\)
\(228\) −4.09600 + 7.09448i −0.271264 + 0.469843i
\(229\) 1.93175 + 3.34589i 0.127654 + 0.221103i 0.922767 0.385358i \(-0.125922\pi\)
−0.795113 + 0.606461i \(0.792589\pi\)
\(230\) −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 −0.904935 0.425549i \(-0.860081\pi\)
0.0839312 0.996472i \(-0.473252\pi\)
\(234\) 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 \(-0.418774\pi\)
0.252419 + 0.967618i \(0.418774\pi\)
\(240\) −1.13482 1.96557i −0.0732524 0.126877i
\(241\) 10.8826 18.8493i 0.701012 1.21419i −0.267100 0.963669i \(-0.586065\pi\)
0.968112 0.250519i \(-0.0806012\pi\)
\(242\) 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 0.571499 0.820603i \(-0.306362\pi\)
−0.996412 + 0.0846316i \(0.973029\pi\)
\(258\) −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 −0.626758 0.779214i \(-0.715618\pi\)
0.988198 + 0.153181i \(0.0489518\pi\)
\(264\) 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 −0.971490 0.237079i \(-0.923810\pi\)
0.691061 + 0.722796i \(0.257143\pi\)
\(270\) −1.16867 + 2.02420i −0.0711232 + 0.123189i
\(271\) −1.28184 2.22022i −0.0778665 0.134869i 0.824463 0.565916i \(-0.191477\pi\)
−0.902329 + 0.431048i \(0.858144\pi\)
\(272\) −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 −0.851657 0.524100i \(-0.824402\pi\)
0.879712 + 0.475506i \(0.157735\pi\)
\(278\) −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 \(-0.561651\pi\)
−0.192473 + 0.981302i \(0.561651\pi\)
\(282\) −0.967771 1.67623i −0.0576299 0.0998180i
\(283\) −11.0873 + 19.2037i −0.659071 + 1.14154i 0.321786 + 0.946812i \(0.395717\pi\)
−0.980857 + 0.194731i \(0.937616\pi\)
\(284\) 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 \(-0.749936\pi\)
−0.706964 + 0.707249i \(0.749936\pi\)
\(294\) −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 \(-0.743809\pi\)
−0.693220 + 0.720726i \(0.743809\pi\)
\(308\) −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 −0.916996 0.398896i \(-0.869393\pi\)
0.803952 + 0.594694i \(0.202727\pi\)
\(312\) 0 0
\(313\) −14.2377 24.6604i −0.804763 1.39389i −0.916451 0.400147i \(-0.868959\pi\)
0.111688 0.993743i \(-0.464374\pi\)
\(314\) −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 \(-0.323222\pi\)
−0.999496 + 0.0317591i \(0.989889\pi\)
\(318\) −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 \(-0.221251\pi\)
−0.938645 + 0.344885i \(0.887918\pi\)
\(332\) 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 0.0922088 + 0.995740i \(0.470607\pi\)
−0.908440 + 0.418015i \(0.862726\pi\)
\(348\) −6.24283 10.8129i −0.334651 0.579632i
\(349\) 16.1581 0.864924 0.432462 0.901652i \(-0.357645\pi\)
0.432462 + 0.901652i \(0.357645\pi\)
\(350\) 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 \(-0.935389\pi\)
0.664317 + 0.747451i \(0.268723\pi\)
\(354\) −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 0.899840 + 0.436221i \(0.143683\pi\)
−0.0721417 + 0.997394i \(0.522983\pi\)
\(360\) 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 0.359454 + 0.933163i \(0.382963\pi\)
−0.987870 + 0.155285i \(0.950370\pi\)
\(368\) −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 0.999627 0.0273160i \(-0.00869604\pi\)
−0.523470 + 0.852044i \(0.675363\pi\)
\(374\) 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 \(-0.567019\pi\)
−0.208995 + 0.977917i \(0.567019\pi\)
\(380\) −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 0.996407 + 0.0846992i \(0.0269929\pi\)
−0.424852 + 0.905263i \(0.639674\pi\)
\(384\) 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 −0.456393 0.889778i \(-0.650859\pi\)
0.998767 0.0496415i \(-0.0158079\pi\)
\(390\) 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 \(-0.157106\pi\)
−0.850619 + 0.525782i \(0.823773\pi\)
\(398\) −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 −0.819919 0.572479i \(-0.805982\pi\)
−0.0858220 0.996310i \(-0.527352\pi\)
\(402\) 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 \(-0.715171\pi\)
0.988412 + 0.151793i \(0.0485046\pi\)
\(410\) 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 \(-0.520428\pi\)
−0.0641317 + 0.997941i \(0.520428\pi\)
\(422\) 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 \(-0.683441\pi\)
0.998612 + 0.0526738i \(0.0167744\pi\)
\(432\) 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 0.880726 0.473627i \(-0.157055\pi\)
−0.850536 + 0.525918i \(0.823722\pi\)
\(440\) −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 0.999996 0.00296930i \(-0.000945159\pi\)
−0.502569 + 0.864537i \(0.667612\pi\)
\(444\) −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 \(-0.361501\pi\)
0.421509 + 0.906824i \(0.361501\pi\)
\(450\) 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 \(-0.215744\pi\)
−0.932538 + 0.361072i \(0.882411\pi\)
\(458\) −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 \(-0.462005\pi\)
0.119083 + 0.992884i \(0.462005\pi\)
\(462\) −3.64397 + 2.56952i −0.169533 + 0.119545i
\(463\) 33.3239 1.54869 0.774347 0.632761i \(-0.218079\pi\)
0.774347 + 0.632761i \(0.218079\pi\)
\(464\) 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 0.976048 0.217557i \(-0.0698087\pi\)
−0.676433 + 0.736504i \(0.736475\pi\)
\(468\) 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 0.372908 + 0.927868i \(0.378361\pi\)
−0.990012 + 0.140987i \(0.954973\pi\)
\(480\) 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 0.231247 + 0.972895i \(0.425720\pi\)
−0.958175 + 0.286182i \(0.907614\pi\)
\(488\) 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 \(-0.153852\pi\)
−0.845199 + 0.534451i \(0.820518\pi\)
\(500\) −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 0.999869 + 0.0162054i \(0.00515855\pi\)
−0.485900 + 0.874014i \(0.661508\pi\)
\(510\) 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 0.229193 + 0.973381i \(0.426391\pi\)
−0.957569 + 0.288203i \(0.906942\pi\)
\(522\) 4.78267 8.28383i 0.209332 0.362574i
\(523\) −19.3560 33.5256i −0.846380 1.46597i −0.884417 0.466697i \(-0.845444\pi\)
0.0380367 0.999276i \(-0.487890\pi\)
\(524\) 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 \(-0.00465746\pi\)
−0.512618 + 0.858617i \(0.671324\pi\)
\(542\) 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 \(-0.910478\pi\)
0.720719 + 0.693227i \(0.243812\pi\)
\(558\) −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 0.284778 + 0.958594i \(0.408080\pi\)
−0.972555 + 0.232672i \(0.925253\pi\)
\(564\) −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 −0.955235 0.295847i \(-0.904398\pi\)
0.221407 0.975182i \(-0.428935\pi\)
\(570\) −1.21995 + 2.11302i −0.0510981 + 0.0885046i
\(571\) −13.1273 + 22.7371i −0.549360 + 0.951519i 0.448959 + 0.893552i \(0.351795\pi\)
−0.998319 + 0.0579663i \(0.981538\pi\)
\(572\) 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 0.488424 + 0.872606i \(0.337572\pi\)
−0.999911 + 0.0133154i \(0.995761\pi\)
\(578\) −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 \(-0.360752\pi\)
0.423639 + 0.905831i \(0.360752\pi\)
\(588\) −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 −0.928365 0.371669i \(-0.878786\pi\)
0.142308 0.989822i \(-0.454548\pi\)
\(594\) −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 −0.973205 0.229939i \(-0.926147\pi\)
0.685735 + 0.727851i \(0.259481\pi\)
\(600\) 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 0.791860 0.610703i \(-0.209113\pi\)
−0.924814 + 0.380420i \(0.875780\pi\)
\(608\) 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 −0.304075 0.952648i \(-0.598347\pi\)
0.977055 0.212988i \(-0.0683195\pi\)
\(614\) −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 \(-0.543451\pi\)
−0.136081 + 0.990698i \(0.543451\pi\)
\(618\) 0.885581 + 1.53387i 0.0356233 + 0.0617013i
\(619\) 8.80931 15.2582i 0.354076 0.613278i −0.632883 0.774247i \(-0.718129\pi\)
0.986959 + 0.160970i \(0.0514621\pi\)
\(620\) 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 \(-0.398486\pi\)
0.313537 + 0.949576i \(0.398486\pi\)
\(632\) −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 −0.581725 0.813385i \(-0.697622\pi\)
0.995275 + 0.0970962i \(0.0309554\pi\)
\(642\) 1.80268 + 3.12234i 0.0711463 + 0.123229i
\(643\) 18.9315 0.746586 0.373293 0.927713i \(-0.378229\pi\)
0.373293 + 0.927713i \(0.378229\pi\)
\(644\) −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 −0.211601 0.977356i \(-0.567868\pi\)
0.952216 0.305426i \(-0.0987988\pi\)
\(648\) −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 −0.996757 0.0804686i \(-0.974358\pi\)
0.428691 0.903451i \(-0.358975\pi\)
\(654\) 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 \(-0.804863\pi\)
0.907225 + 0.420645i \(0.138196\pi\)
\(662\) 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 0.777801 0.628511i \(-0.216335\pi\)
−0.933207 + 0.359340i \(0.883002\pi\)
\(678\) −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 \(-0.676757\pi\)
0.999498 + 0.0316929i \(0.0100898\pi\)
\(684\) 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 \(-0.235353\pi\)
−0.952998 + 0.302978i \(0.902019\pi\)
\(692\) −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 \(-0.0193629\pi\)
−0.551723 + 0.834027i \(0.686030\pi\)
\(710\) 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 0.604616 0.796517i \(-0.293327\pi\)
−0.992112 + 0.125354i \(0.959993\pi\)
\(720\) −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 \(-0.135718\pi\)
−0.813397 + 0.581709i \(0.802384\pi\)
\(734\) −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 \(-0.875315\pi\)
0.792750 + 0.609547i \(0.208649\pi\)
\(740\) −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 \(-0.504167\pi\)
−0.0130905 + 0.999914i \(0.504167\pi\)
\(744\) −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 0.999369 0.0355158i \(-0.0113074\pi\)
−0.530442 + 0.847721i \(0.677974\pi\)
\(752\) 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 \(-0.118482\pi\)
−0.780722 + 0.624878i \(0.785149\pi\)
\(762\) 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 \(-0.347549\pi\)
0.460838 + 0.887485i \(0.347549\pi\)
\(770\) −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 \(-0.881608\pi\)
0.780546 + 0.625098i \(0.214941\pi\)
\(774\) −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
\(782\) −0.155914 0.270052i <