Properties

Label 804.2.ba.b.41.11
Level 804
Weight 2
Character 804.41
Analytic conductor 6.420
Analytic rank 0
Dimension 440
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.ba (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(440\)
Relative dimension: \(22\) over \(\Q(\zeta_{66})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label 41.11
Character \(\chi\) = 804.41
Dual form 804.2.ba.b.353.11

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.313881 + 1.70337i) q^{3} +(0.391534 - 2.72318i) q^{5} +(0.116340 + 1.21837i) q^{7} +(-2.80296 - 1.06931i) q^{9} +O(q^{10})\) \(q+(-0.313881 + 1.70337i) q^{3} +(0.391534 - 2.72318i) q^{5} +(0.116340 + 1.21837i) q^{7} +(-2.80296 - 1.06931i) q^{9} +(1.23209 - 0.493254i) q^{11} +(-0.385910 - 0.404731i) q^{13} +(4.51569 + 1.52168i) q^{15} +(2.29296 - 0.793601i) q^{17} +(4.71345 + 0.450080i) q^{19} +(-2.11185 - 0.184253i) q^{21} +(5.02418 - 0.239331i) q^{23} +(-2.46494 - 0.723772i) q^{25} +(2.70124 - 4.43884i) q^{27} +(2.38566 - 1.37736i) q^{29} +(3.24107 - 3.39914i) q^{31} +(0.453466 + 2.25353i) q^{33} +(3.36339 + 0.160218i) q^{35} +(-3.40187 + 5.89222i) q^{37} +(0.810537 - 0.530311i) q^{39} +(-0.873683 - 0.168389i) q^{41} +(-0.960559 - 0.832329i) q^{43} +(-4.00939 + 7.21428i) q^{45} +(0.522344 - 1.01321i) q^{47} +(5.40261 - 1.04127i) q^{49} +(0.632081 + 4.15486i) q^{51} +(-1.34190 - 1.54863i) q^{53} +(-0.860814 - 3.54832i) q^{55} +(-2.24612 + 7.88750i) q^{57} +(0.531959 + 1.81168i) q^{59} +(2.74049 - 6.84541i) q^{61} +(0.976722 - 3.53944i) q^{63} +(-1.25325 + 0.892436i) q^{65} +(6.90314 + 4.39849i) q^{67} +(-1.16932 + 8.63317i) q^{69} +(1.94404 + 0.672840i) q^{71} +(4.71011 + 1.88564i) q^{73} +(2.00655 - 3.97154i) q^{75} +(0.744306 + 1.44375i) q^{77} +(7.34631 - 1.78219i) q^{79} +(6.71314 + 5.99448i) q^{81} +(-6.30692 + 8.01990i) q^{83} +(-1.26335 - 6.55486i) q^{85} +(1.59735 + 4.49599i) q^{87} +(-7.62896 + 11.8709i) q^{89} +(0.448214 - 0.517267i) q^{91} +(4.77269 + 6.58768i) q^{93} +(3.07113 - 12.6594i) q^{95} +(-16.2625 - 9.38917i) q^{97} +(-3.98094 + 0.0650804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 440q - 12q^{7} + 4q^{9} + O(q^{10}) \) \( 440q - 12q^{7} + 4q^{9} - 2q^{15} - 10q^{19} + 22q^{21} - 68q^{25} + 50q^{31} + 11q^{33} - 22q^{37} - 45q^{39} + 22q^{43} + 22q^{45} - 18q^{49} - 6q^{51} + 126q^{55} - 183q^{57} - 56q^{61} - 141q^{63} - 12q^{67} + 33q^{69} + 356q^{73} + 165q^{75} + 228q^{79} + 24q^{81} - 6q^{85} + 75q^{87} - 4q^{91} - 75q^{93} + 12q^{97} + 88q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{53}{66}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.313881 + 1.70337i −0.181219 + 0.983443i
\(4\) 0 0
\(5\) 0.391534 2.72318i 0.175099 1.21784i −0.692810 0.721120i \(-0.743628\pi\)
0.867909 0.496723i \(-0.165463\pi\)
\(6\) 0 0
\(7\) 0.116340 + 1.21837i 0.0439724 + 0.460500i 0.990464 + 0.137772i \(0.0439940\pi\)
−0.946492 + 0.322728i \(0.895400\pi\)
\(8\) 0 0
\(9\) −2.80296 1.06931i −0.934319 0.356438i
\(10\) 0 0
\(11\) 1.23209 0.493254i 0.371489 0.148722i −0.178403 0.983957i \(-0.557093\pi\)
0.549892 + 0.835236i \(0.314669\pi\)
\(12\) 0 0
\(13\) −0.385910 0.404731i −0.107032 0.112252i 0.668038 0.744127i \(-0.267134\pi\)
−0.775071 + 0.631875i \(0.782286\pi\)
\(14\) 0 0
\(15\) 4.51569 + 1.52168i 1.16595 + 0.392897i
\(16\) 0 0
\(17\) 2.29296 0.793601i 0.556124 0.192476i −0.0345265 0.999404i \(-0.510992\pi\)
0.590651 + 0.806927i \(0.298871\pi\)
\(18\) 0 0
\(19\) 4.71345 + 0.450080i 1.08134 + 0.103255i 0.620484 0.784219i \(-0.286936\pi\)
0.460856 + 0.887475i \(0.347542\pi\)
\(20\) 0 0
\(21\) −2.11185 0.184253i −0.460844 0.0402072i
\(22\) 0 0
\(23\) 5.02418 0.239331i 1.04761 0.0499040i 0.483292 0.875459i \(-0.339441\pi\)
0.564321 + 0.825555i \(0.309138\pi\)
\(24\) 0 0
\(25\) −2.46494 0.723772i −0.492988 0.144754i
\(26\) 0 0
\(27\) 2.70124 4.43884i 0.519853 0.854256i
\(28\) 0 0
\(29\) 2.38566 1.37736i 0.443006 0.255770i −0.261866 0.965104i \(-0.584338\pi\)
0.704872 + 0.709335i \(0.251005\pi\)
\(30\) 0 0
\(31\) 3.24107 3.39914i 0.582114 0.610503i −0.365154 0.930947i \(-0.618984\pi\)
0.947267 + 0.320444i \(0.103832\pi\)
\(32\) 0 0
\(33\) 0.453466 + 2.25353i 0.0789383 + 0.392289i
\(34\) 0 0
\(35\) 3.36339 + 0.160218i 0.568516 + 0.0270818i
\(36\) 0 0
\(37\) −3.40187 + 5.89222i −0.559264 + 0.968674i 0.438294 + 0.898832i \(0.355583\pi\)
−0.997558 + 0.0698426i \(0.977750\pi\)
\(38\) 0 0
\(39\) 0.810537 0.530311i 0.129790 0.0849177i
\(40\) 0 0
\(41\) −0.873683 0.168389i −0.136446 0.0262979i 0.120571 0.992705i \(-0.461528\pi\)
−0.257017 + 0.966407i \(0.582740\pi\)
\(42\) 0 0
\(43\) −0.960559 0.832329i −0.146484 0.126929i 0.578536 0.815657i \(-0.303624\pi\)
−0.725020 + 0.688728i \(0.758170\pi\)
\(44\) 0 0
\(45\) −4.00939 + 7.21428i −0.597684 + 1.07544i
\(46\) 0 0
\(47\) 0.522344 1.01321i 0.0761917 0.147791i −0.847663 0.530536i \(-0.821991\pi\)
0.923854 + 0.382745i \(0.125021\pi\)
\(48\) 0 0
\(49\) 5.40261 1.04127i 0.771802 0.148753i
\(50\) 0 0
\(51\) 0.632081 + 4.15486i 0.0885091 + 0.581797i
\(52\) 0 0
\(53\) −1.34190 1.54863i −0.184324 0.212721i 0.656066 0.754704i \(-0.272219\pi\)
−0.840390 + 0.541983i \(0.817674\pi\)
\(54\) 0 0
\(55\) −0.860814 3.54832i −0.116072 0.478456i
\(56\) 0 0
\(57\) −2.24612 + 7.88750i −0.297506 + 1.04472i
\(58\) 0 0
\(59\) 0.531959 + 1.81168i 0.0692551 + 0.235861i 0.986846 0.161666i \(-0.0516867\pi\)
−0.917590 + 0.397527i \(0.869868\pi\)
\(60\) 0 0
\(61\) 2.74049 6.84541i 0.350884 0.876465i −0.642983 0.765881i \(-0.722303\pi\)
0.993867 0.110585i \(-0.0352724\pi\)
\(62\) 0 0
\(63\) 0.976722 3.53944i 0.123055 0.445927i
\(64\) 0 0
\(65\) −1.25325 + 0.892436i −0.155447 + 0.110693i
\(66\) 0 0
\(67\) 6.90314 + 4.39849i 0.843352 + 0.537361i
\(68\) 0 0
\(69\) −1.16932 + 8.63317i −0.140770 + 1.03931i
\(70\) 0 0
\(71\) 1.94404 + 0.672840i 0.230716 + 0.0798515i 0.439980 0.898008i \(-0.354986\pi\)
−0.209264 + 0.977859i \(0.567107\pi\)
\(72\) 0 0
\(73\) 4.71011 + 1.88564i 0.551276 + 0.220698i 0.630541 0.776156i \(-0.282833\pi\)
−0.0792648 + 0.996854i \(0.525257\pi\)
\(74\) 0 0
\(75\) 2.00655 3.97154i 0.231697 0.458593i
\(76\) 0 0
\(77\) 0.744306 + 1.44375i 0.0848216 + 0.164531i
\(78\) 0 0
\(79\) 7.34631 1.78219i 0.826524 0.200513i 0.199882 0.979820i \(-0.435944\pi\)
0.626642 + 0.779307i \(0.284429\pi\)
\(80\) 0 0
\(81\) 6.71314 + 5.99448i 0.745904 + 0.666053i
\(82\) 0 0
\(83\) −6.30692 + 8.01990i −0.692274 + 0.880298i −0.997404 0.0720127i \(-0.977058\pi\)
0.305130 + 0.952311i \(0.401300\pi\)
\(84\) 0 0
\(85\) −1.26335 6.55486i −0.137029 0.710974i
\(86\) 0 0
\(87\) 1.59735 + 4.49599i 0.171253 + 0.482021i
\(88\) 0 0
\(89\) −7.62896 + 11.8709i −0.808668 + 1.25831i 0.154119 + 0.988052i \(0.450746\pi\)
−0.962787 + 0.270260i \(0.912890\pi\)
\(90\) 0 0
\(91\) 0.448214 0.517267i 0.0469856 0.0542243i
\(92\) 0 0
\(93\) 4.77269 + 6.58768i 0.494905 + 0.683111i
\(94\) 0 0
\(95\) 3.07113 12.6594i 0.315091 1.29882i
\(96\) 0 0
\(97\) −16.2625 9.38917i −1.65121 0.953326i −0.976576 0.215172i \(-0.930969\pi\)
−0.674632 0.738154i \(-0.735698\pi\)
\(98\) 0 0
\(99\) −3.98094 + 0.0650804i −0.400099 + 0.00654083i
\(100\) 0 0
\(101\) −0.376368 + 0.528535i −0.0374500 + 0.0525912i −0.832876 0.553459i \(-0.813308\pi\)
0.795426 + 0.606050i \(0.207247\pi\)
\(102\) 0 0
\(103\) 6.94853 + 6.62541i 0.684659 + 0.652821i 0.950331 0.311243i \(-0.100745\pi\)
−0.265671 + 0.964064i \(0.585594\pi\)
\(104\) 0 0
\(105\) −1.32861 + 5.67881i −0.129660 + 0.554195i
\(106\) 0 0
\(107\) −16.4738 + 2.36858i −1.59259 + 0.228979i −0.880825 0.473443i \(-0.843011\pi\)
−0.711761 + 0.702422i \(0.752102\pi\)
\(108\) 0 0
\(109\) 1.09834 3.74061i 0.105202 0.358286i −0.890020 0.455921i \(-0.849310\pi\)
0.995222 + 0.0976356i \(0.0311280\pi\)
\(110\) 0 0
\(111\) −8.96886 7.64411i −0.851286 0.725547i
\(112\) 0 0
\(113\) 5.10511 4.01470i 0.480248 0.377671i −0.348486 0.937314i \(-0.613304\pi\)
0.828734 + 0.559643i \(0.189062\pi\)
\(114\) 0 0
\(115\) 1.31539 13.7754i 0.122661 1.28457i
\(116\) 0 0
\(117\) 0.648905 + 1.54710i 0.0599913 + 0.143030i
\(118\) 0 0
\(119\) 1.23366 + 2.70134i 0.113090 + 0.247632i
\(120\) 0 0
\(121\) −6.68633 + 6.37540i −0.607848 + 0.579582i
\(122\) 0 0
\(123\) 0.561061 1.43535i 0.0505892 0.129421i
\(124\) 0 0
\(125\) 2.77834 6.08372i 0.248502 0.544145i
\(126\) 0 0
\(127\) −3.22444 + 0.307896i −0.286122 + 0.0273214i −0.237131 0.971478i \(-0.576207\pi\)
−0.0489919 + 0.998799i \(0.515601\pi\)
\(128\) 0 0
\(129\) 1.71927 1.37494i 0.151373 0.121057i
\(130\) 0 0
\(131\) −9.66705 15.0422i −0.844614 1.31424i −0.947567 0.319558i \(-0.896465\pi\)
0.102953 0.994686i \(-0.467171\pi\)
\(132\) 0 0
\(133\) 5.79509i 0.502498i
\(134\) 0 0
\(135\) −11.0301 9.09391i −0.949323 0.782679i
\(136\) 0 0
\(137\) −3.60970 + 2.31981i −0.308397 + 0.198195i −0.685680 0.727903i \(-0.740495\pi\)
0.377283 + 0.926098i \(0.376859\pi\)
\(138\) 0 0
\(139\) 2.32375 + 0.334105i 0.197098 + 0.0283384i 0.240157 0.970734i \(-0.422801\pi\)
−0.0430588 + 0.999073i \(0.513710\pi\)
\(140\) 0 0
\(141\) 1.56191 + 1.20777i 0.131537 + 0.101713i
\(142\) 0 0
\(143\) −0.675110 0.308312i −0.0564555 0.0257824i
\(144\) 0 0
\(145\) −2.81673 7.03586i −0.233917 0.584297i
\(146\) 0 0
\(147\) 0.0778891 + 9.52950i 0.00642418 + 0.785980i
\(148\) 0 0
\(149\) −0.945908 + 0.431982i −0.0774918 + 0.0353893i −0.453784 0.891112i \(-0.649926\pi\)
0.376292 + 0.926501i \(0.377199\pi\)
\(150\) 0 0
\(151\) −3.82320 11.0464i −0.311128 0.898945i −0.986829 0.161769i \(-0.948280\pi\)
0.675701 0.737176i \(-0.263841\pi\)
\(152\) 0 0
\(153\) −7.27567 0.227463i −0.588203 0.0183893i
\(154\) 0 0
\(155\) −7.98747 10.1569i −0.641569 0.815822i
\(156\) 0 0
\(157\) −0.761451 15.9848i −0.0607704 1.27573i −0.799063 0.601247i \(-0.794671\pi\)
0.738293 0.674480i \(-0.235632\pi\)
\(158\) 0 0
\(159\) 3.05910 1.79967i 0.242602 0.142723i
\(160\) 0 0
\(161\) 0.876106 + 6.09345i 0.0690469 + 0.480231i
\(162\) 0 0
\(163\) −4.69557 8.13297i −0.367786 0.637023i 0.621433 0.783467i \(-0.286551\pi\)
−0.989219 + 0.146444i \(0.953217\pi\)
\(164\) 0 0
\(165\) 6.31431 0.352535i 0.491569 0.0274448i
\(166\) 0 0
\(167\) −1.98924 1.41653i −0.153932 0.109615i 0.500496 0.865739i \(-0.333151\pi\)
−0.654428 + 0.756124i \(0.727090\pi\)
\(168\) 0 0
\(169\) 0.603684 12.6729i 0.0464373 0.974838i
\(170\) 0 0
\(171\) −12.7303 6.30171i −0.973513 0.481904i
\(172\) 0 0
\(173\) 5.71849 + 1.38729i 0.434769 + 0.105474i 0.447169 0.894449i \(-0.352432\pi\)
−0.0124006 + 0.999923i \(0.503947\pi\)
\(174\) 0 0
\(175\) 0.595050 3.08741i 0.0449815 0.233386i
\(176\) 0 0
\(177\) −3.25295 + 0.337470i −0.244506 + 0.0253658i
\(178\) 0 0
\(179\) −5.21601 3.35213i −0.389863 0.250550i 0.330995 0.943633i \(-0.392616\pi\)
−0.720858 + 0.693083i \(0.756252\pi\)
\(180\) 0 0
\(181\) −14.7417 7.59988i −1.09574 0.564895i −0.187046 0.982351i \(-0.559891\pi\)
−0.908697 + 0.417457i \(0.862922\pi\)
\(182\) 0 0
\(183\) 10.8001 + 6.81672i 0.798367 + 0.503907i
\(184\) 0 0
\(185\) 14.7136 + 11.5709i 1.08177 + 0.850710i
\(186\) 0 0
\(187\) 2.43368 2.10880i 0.177968 0.154211i
\(188\) 0 0
\(189\) 5.72241 + 2.77468i 0.416244 + 0.201829i
\(190\) 0 0
\(191\) −9.03973 + 4.66031i −0.654092 + 0.337208i −0.753126 0.657876i \(-0.771455\pi\)
0.0990340 + 0.995084i \(0.468425\pi\)
\(192\) 0 0
\(193\) −13.2949 + 3.90374i −0.956989 + 0.280997i −0.722694 0.691168i \(-0.757096\pi\)
−0.234295 + 0.972165i \(0.575278\pi\)
\(194\) 0 0
\(195\) −1.12678 2.41487i −0.0806903 0.172933i
\(196\) 0 0
\(197\) −1.26789 + 3.66332i −0.0903332 + 0.261001i −0.981113 0.193434i \(-0.938037\pi\)
0.890780 + 0.454435i \(0.150159\pi\)
\(198\) 0 0
\(199\) 0.123476 + 0.173398i 0.00875298 + 0.0122918i 0.818929 0.573894i \(-0.194568\pi\)
−0.810176 + 0.586186i \(0.800629\pi\)
\(200\) 0 0
\(201\) −9.65903 + 10.3780i −0.681296 + 0.732008i
\(202\) 0 0
\(203\) 1.95568 + 2.74637i 0.137262 + 0.192757i
\(204\) 0 0
\(205\) −0.800629 + 2.31327i −0.0559184 + 0.161565i
\(206\) 0 0
\(207\) −14.3385 4.70158i −0.996593 0.326783i
\(208\) 0 0
\(209\) 6.02940 1.77039i 0.417062 0.122460i
\(210\) 0 0
\(211\) 10.1272 5.22092i 0.697183 0.359423i −0.0729238 0.997338i \(-0.523233\pi\)
0.770107 + 0.637915i \(0.220203\pi\)
\(212\) 0 0
\(213\) −1.75630 + 3.10024i −0.120339 + 0.212425i
\(214\) 0 0
\(215\) −2.64267 + 2.28989i −0.180229 + 0.156169i
\(216\) 0 0
\(217\) 4.51847 + 3.55336i 0.306734 + 0.241218i
\(218\) 0 0
\(219\) −4.69037 + 7.43120i −0.316946 + 0.502154i
\(220\) 0 0
\(221\) −1.20607 0.621772i −0.0811290 0.0418249i
\(222\) 0 0
\(223\) 11.9839 + 7.70158i 0.802501 + 0.515736i 0.876431 0.481528i \(-0.159918\pi\)
−0.0739303 + 0.997263i \(0.523554\pi\)
\(224\) 0 0
\(225\) 6.13519 + 4.66450i 0.409012 + 0.310967i
\(226\) 0 0
\(227\) −5.18582 + 26.9066i −0.344195 + 1.78585i 0.236397 + 0.971657i \(0.424033\pi\)
−0.580592 + 0.814195i \(0.697179\pi\)
\(228\) 0 0
\(229\) −1.41830 0.344077i −0.0937242 0.0227372i 0.188623 0.982050i \(-0.439598\pi\)
−0.282347 + 0.959312i \(0.591113\pi\)
\(230\) 0 0
\(231\) −2.69287 + 0.814664i −0.177178 + 0.0536010i
\(232\) 0 0
\(233\) −1.05818 + 22.2139i −0.0693235 + 1.45528i 0.649646 + 0.760237i \(0.274917\pi\)
−0.718969 + 0.695042i \(0.755386\pi\)
\(234\) 0 0
\(235\) −2.55463 1.81914i −0.166645 0.118668i
\(236\) 0 0
\(237\) 0.729874 + 13.0729i 0.0474104 + 0.849176i
\(238\) 0 0
\(239\) 4.21922 + 7.30790i 0.272919 + 0.472709i 0.969608 0.244664i \(-0.0786777\pi\)
−0.696689 + 0.717373i \(0.745344\pi\)
\(240\) 0 0
\(241\) −0.999176 6.94942i −0.0643626 0.447651i −0.996364 0.0851972i \(-0.972848\pi\)
0.932002 0.362454i \(-0.118061\pi\)
\(242\) 0 0
\(243\) −12.3180 + 9.55342i −0.790198 + 0.612852i
\(244\) 0 0
\(245\) −0.720253 15.1200i −0.0460153 0.965980i
\(246\) 0 0
\(247\) −1.63681 2.08137i −0.104148 0.132434i
\(248\) 0 0
\(249\) −11.6813 13.2603i −0.740269 0.840339i
\(250\) 0 0
\(251\) −1.04387 3.01606i −0.0658885 0.190372i 0.907251 0.420591i \(-0.138177\pi\)
−0.973139 + 0.230218i \(0.926056\pi\)
\(252\) 0 0
\(253\) 6.07218 2.77307i 0.381755 0.174342i
\(254\) 0 0
\(255\) 11.5619 0.0945009i 0.724035 0.00591788i
\(256\) 0 0
\(257\) 7.84302 + 19.5909i 0.489234 + 1.22205i 0.943557 + 0.331210i \(0.107457\pi\)
−0.454323 + 0.890837i \(0.650119\pi\)
\(258\) 0 0
\(259\) −7.57467 3.45923i −0.470667 0.214946i
\(260\) 0 0
\(261\) −8.15973 + 1.30967i −0.505075 + 0.0810663i
\(262\) 0 0
\(263\) 14.4057 + 2.07122i 0.888291 + 0.127717i 0.571329 0.820721i \(-0.306428\pi\)
0.316962 + 0.948438i \(0.397337\pi\)
\(264\) 0 0
\(265\) −4.74260 + 3.04789i −0.291336 + 0.187230i
\(266\) 0 0
\(267\) −17.8260 16.7210i −1.09093 1.02331i
\(268\) 0 0
\(269\) 2.11390i 0.128887i 0.997921 + 0.0644433i \(0.0205272\pi\)
−0.997921 + 0.0644433i \(0.979473\pi\)
\(270\) 0 0
\(271\) 14.4161 + 22.4319i 0.875715 + 1.36264i 0.931326 + 0.364186i \(0.118653\pi\)
−0.0556111 + 0.998453i \(0.517711\pi\)
\(272\) 0 0
\(273\) 0.740412 + 0.925836i 0.0448118 + 0.0560341i
\(274\) 0 0
\(275\) −3.39403 + 0.324091i −0.204668 + 0.0195434i
\(276\) 0 0
\(277\) −7.66671 + 16.7878i −0.460648 + 1.00868i 0.526691 + 0.850057i \(0.323432\pi\)
−0.987339 + 0.158622i \(0.949295\pi\)
\(278\) 0 0
\(279\) −12.7193 + 6.06192i −0.761486 + 0.362918i
\(280\) 0 0
\(281\) −12.0772 + 11.5156i −0.720465 + 0.686962i −0.958756 0.284232i \(-0.908261\pi\)
0.238291 + 0.971194i \(0.423413\pi\)
\(282\) 0 0
\(283\) 8.00553 + 17.5297i 0.475879 + 1.04203i 0.983576 + 0.180494i \(0.0577697\pi\)
−0.507697 + 0.861536i \(0.669503\pi\)
\(284\) 0 0
\(285\) 20.5996 + 9.20481i 1.22022 + 0.545246i
\(286\) 0 0
\(287\) 0.103515 1.08406i 0.00611030 0.0639899i
\(288\) 0 0
\(289\) −8.73504 + 6.86931i −0.513826 + 0.404077i
\(290\) 0 0
\(291\) 21.0978 24.7540i 1.23677 1.45111i
\(292\) 0 0
\(293\) 7.87807 26.8302i 0.460242 1.56744i −0.323423 0.946254i \(-0.604834\pi\)
0.783665 0.621184i \(-0.213348\pi\)
\(294\) 0 0
\(295\) 5.14182 0.739283i 0.299369 0.0430427i
\(296\) 0 0
\(297\) 1.13868 6.80144i 0.0660732 0.394660i
\(298\) 0 0
\(299\) −2.03574 1.94108i −0.117730 0.112255i
\(300\) 0 0
\(301\) 0.902332 1.26715i 0.0520096 0.0730372i
\(302\) 0 0
\(303\) −0.782157 0.806992i −0.0449338 0.0463605i
\(304\) 0 0
\(305\) −17.5683 10.1431i −1.00596 0.580790i
\(306\) 0 0
\(307\) 1.28221 5.28532i 0.0731793 0.301649i −0.923447 0.383727i \(-0.874640\pi\)
0.996626 + 0.0820776i \(0.0261555\pi\)
\(308\) 0 0
\(309\) −13.4666 + 9.75635i −0.766086 + 0.555019i
\(310\) 0 0
\(311\) 17.5738 20.2813i 0.996519 1.15004i 0.00784489 0.999969i \(-0.497503\pi\)
0.988675 0.150075i \(-0.0479517\pi\)
\(312\) 0 0
\(313\) −6.64992 + 10.3475i −0.375876 + 0.584874i −0.976727 0.214487i \(-0.931192\pi\)
0.600851 + 0.799361i \(0.294828\pi\)
\(314\) 0 0
\(315\) −9.25611 4.04560i −0.521523 0.227944i
\(316\) 0 0
\(317\) 4.27531 + 22.1824i 0.240126 + 1.24589i 0.879091 + 0.476654i \(0.158151\pi\)
−0.638965 + 0.769236i \(0.720637\pi\)
\(318\) 0 0
\(319\) 2.25996 2.87377i 0.126533 0.160900i
\(320\) 0 0
\(321\) 1.13625 28.8045i 0.0634195 1.60771i
\(322\) 0 0
\(323\) 11.1649 2.70858i 0.621234 0.150710i
\(324\) 0 0
\(325\) 0.658312 + 1.27695i 0.0365166 + 0.0708323i
\(326\) 0 0
\(327\) 6.02691 + 3.04500i 0.333289 + 0.168389i
\(328\) 0 0
\(329\) 1.29523 + 0.518531i 0.0714082 + 0.0285875i
\(330\) 0 0
\(331\) −14.2369 4.92743i −0.782529 0.270836i −0.0935477 0.995615i \(-0.529821\pi\)
−0.688982 + 0.724779i \(0.741942\pi\)
\(332\) 0 0
\(333\) 15.8359 12.8780i 0.867804 0.705708i
\(334\) 0 0
\(335\) 14.6807 17.0763i 0.802092 0.932979i
\(336\) 0 0
\(337\) −0.383661 + 0.273204i −0.0208993 + 0.0148824i −0.590459 0.807068i \(-0.701053\pi\)
0.569560 + 0.821950i \(0.307114\pi\)
\(338\) 0 0
\(339\) 5.23613 + 9.95604i 0.284388 + 0.540738i
\(340\) 0 0
\(341\) 2.31665 5.78671i 0.125454 0.313368i
\(342\) 0 0
\(343\) 4.31090 + 14.6816i 0.232767 + 0.792730i
\(344\) 0 0
\(345\) 23.0518 + 6.56446i 1.24107 + 0.353419i
\(346\) 0 0
\(347\) −6.14122 25.3145i −0.329678 1.35895i −0.859627 0.510922i \(-0.829304\pi\)
0.529949 0.848029i \(-0.322211\pi\)
\(348\) 0 0
\(349\) −6.63358 7.65556i −0.355088 0.409793i 0.549900 0.835230i \(-0.314666\pi\)
−0.904988 + 0.425437i \(0.860120\pi\)
\(350\) 0 0
\(351\) −2.83897 + 0.619721i −0.151533 + 0.0330782i
\(352\) 0 0
\(353\) 18.5420 3.57367i 0.986889 0.190207i 0.329825 0.944042i \(-0.393010\pi\)
0.657064 + 0.753835i \(0.271798\pi\)
\(354\) 0 0
\(355\) 2.59342 5.03054i 0.137645 0.266993i
\(356\) 0 0
\(357\) −4.98861 + 1.25348i −0.264025 + 0.0663414i
\(358\) 0 0
\(359\) 23.8703 + 20.6837i 1.25983 + 1.09165i 0.991742 + 0.128250i \(0.0409361\pi\)
0.268085 + 0.963395i \(0.413609\pi\)
\(360\) 0 0
\(361\) 3.35742 + 0.647090i 0.176706 + 0.0340574i
\(362\) 0 0
\(363\) −8.76097 13.3904i −0.459832 0.702815i
\(364\) 0 0
\(365\) 6.97911 12.0882i 0.365303 0.632724i
\(366\) 0 0
\(367\) 5.04928 + 0.240527i 0.263570 + 0.0125554i 0.178951 0.983858i \(-0.442730\pi\)
0.0846192 + 0.996413i \(0.473033\pi\)
\(368\) 0 0
\(369\) 2.26884 + 1.40623i 0.118111 + 0.0732053i
\(370\) 0 0
\(371\) 1.73069 1.81509i 0.0898529 0.0942350i
\(372\) 0 0
\(373\) 10.8855 6.28474i 0.563630 0.325412i −0.190971 0.981596i \(-0.561164\pi\)
0.754601 + 0.656184i \(0.227830\pi\)
\(374\) 0 0
\(375\) 9.49077 + 6.64212i 0.490101 + 0.342998i
\(376\) 0 0
\(377\) −1.47811 0.434012i −0.0761265 0.0223528i
\(378\) 0 0
\(379\) 22.0364 1.04972i 1.13194 0.0539207i 0.526761 0.850014i \(-0.323406\pi\)
0.605174 + 0.796093i \(0.293103\pi\)
\(380\) 0 0
\(381\) 0.487628 5.58906i 0.0249819 0.286336i
\(382\) 0 0
\(383\) −14.1261 1.34888i −0.721811 0.0689246i −0.272317 0.962208i \(-0.587790\pi\)
−0.449495 + 0.893283i \(0.648396\pi\)
\(384\) 0 0
\(385\) 4.22302 1.46160i 0.215225 0.0744901i
\(386\) 0 0
\(387\) 1.80239 + 3.36012i 0.0916204 + 0.170805i
\(388\) 0 0
\(389\) −24.8341 26.0452i −1.25914 1.32055i −0.925931 0.377692i \(-0.876718\pi\)
−0.333206 0.942854i \(-0.608131\pi\)
\(390\) 0 0
\(391\) 11.3303 4.53597i 0.572998 0.229394i
\(392\) 0 0
\(393\) 28.6568 11.7451i 1.44554 0.592463i
\(394\) 0 0
\(395\) −1.97691 20.7031i −0.0994689 1.04169i
\(396\) 0 0
\(397\) 0.691067 4.80647i 0.0346836 0.241230i −0.965103 0.261869i \(-0.915661\pi\)
0.999787 + 0.0206393i \(0.00657015\pi\)
\(398\) 0 0
\(399\) −9.87119 1.81897i −0.494178 0.0910623i
\(400\) 0 0
\(401\) −12.6244 −0.630431 −0.315215 0.949020i \(-0.602077\pi\)
−0.315215 + 0.949020i \(0.602077\pi\)
\(402\) 0 0
\(403\) −2.62650 −0.130835
\(404\) 0 0
\(405\) 18.9525 15.9340i 0.941756 0.791768i
\(406\) 0 0
\(407\) −1.28505 + 8.93772i −0.0636976 + 0.443026i
\(408\) 0 0
\(409\) 2.55467 + 26.7538i 0.126321 + 1.32289i 0.807106 + 0.590406i \(0.201032\pi\)
−0.680786 + 0.732482i \(0.738362\pi\)
\(410\) 0 0
\(411\) −2.81849 6.87680i −0.139026 0.339208i
\(412\) 0 0
\(413\) −2.14541 + 0.858893i −0.105569 + 0.0422634i
\(414\) 0 0
\(415\) 19.3702 + 20.3149i 0.950848 + 0.997221i
\(416\) 0 0
\(417\) −1.29849 + 3.85334i −0.0635872 + 0.188699i
\(418\) 0 0
\(419\) −2.18948 + 0.757785i −0.106963 + 0.0370202i −0.380025 0.924976i \(-0.624085\pi\)
0.273062 + 0.961996i \(0.411963\pi\)
\(420\) 0 0
\(421\) −17.5179 1.67276i −0.853771 0.0815253i −0.341013 0.940059i \(-0.610770\pi\)
−0.512758 + 0.858533i \(0.671376\pi\)
\(422\) 0 0
\(423\) −2.54754 + 2.28142i −0.123866 + 0.110927i
\(424\) 0 0
\(425\) −6.22640 + 0.296600i −0.302025 + 0.0143872i
\(426\) 0 0
\(427\) 8.65907 + 2.54253i 0.419042 + 0.123042i
\(428\) 0 0
\(429\) 0.737075 1.05319i 0.0355863 0.0508485i
\(430\) 0 0
\(431\) 5.42894 3.13440i 0.261503 0.150979i −0.363517 0.931588i \(-0.618424\pi\)
0.625020 + 0.780609i \(0.285091\pi\)
\(432\) 0 0
\(433\) −27.1057 + 28.4277i −1.30262 + 1.36615i −0.412140 + 0.911121i \(0.635218\pi\)
−0.890478 + 0.455026i \(0.849630\pi\)
\(434\) 0 0
\(435\) 12.8688 2.58952i 0.617012 0.124158i
\(436\) 0 0
\(437\) 23.7889 + 1.13321i 1.13798 + 0.0542086i
\(438\) 0 0
\(439\) −19.9893 + 34.6225i −0.954037 + 1.65244i −0.217480 + 0.976065i \(0.569784\pi\)
−0.736557 + 0.676376i \(0.763549\pi\)
\(440\) 0 0
\(441\) −16.2567 2.85846i −0.774130 0.136117i
\(442\) 0 0
\(443\) −18.8957 3.64184i −0.897760 0.173029i −0.280561 0.959836i \(-0.590521\pi\)
−0.617199 + 0.786807i \(0.711733\pi\)
\(444\) 0 0
\(445\) 29.3396 + 25.4229i 1.39083 + 1.20516i
\(446\) 0 0
\(447\) −0.438923 1.74682i −0.0207603 0.0826220i
\(448\) 0 0
\(449\) 13.2613 25.7233i 0.625839 1.21396i −0.336391 0.941722i \(-0.609206\pi\)
0.962230 0.272236i \(-0.0877632\pi\)
\(450\) 0 0
\(451\) −1.15951 + 0.223478i −0.0545994 + 0.0105232i
\(452\) 0 0
\(453\) 20.0162 3.04508i 0.940444 0.143070i
\(454\) 0 0
\(455\) −1.23312 1.42310i −0.0578095 0.0667157i
\(456\) 0 0
\(457\) −4.23176 17.4436i −0.197954 0.815975i −0.980999 0.194011i \(-0.937850\pi\)
0.783046 0.621964i \(-0.213665\pi\)
\(458\) 0 0
\(459\) 2.67115 12.3218i 0.124679 0.575132i
\(460\) 0 0
\(461\) −7.60647 25.9052i −0.354268 1.20653i −0.923257 0.384182i \(-0.874483\pi\)
0.568989 0.822345i \(-0.307335\pi\)
\(462\) 0 0
\(463\) −15.6598 + 39.1164i −0.727774 + 1.81789i −0.174985 + 0.984571i \(0.555988\pi\)
−0.552789 + 0.833321i \(0.686436\pi\)
\(464\) 0 0
\(465\) 19.8081 10.4176i 0.918579 0.483104i
\(466\) 0 0
\(467\) 0.478506 0.340743i 0.0221426 0.0157677i −0.568932 0.822385i \(-0.692643\pi\)
0.591075 + 0.806617i \(0.298704\pi\)
\(468\) 0 0
\(469\) −4.55587 + 8.92228i −0.210370 + 0.411993i
\(470\) 0 0
\(471\) 27.4671 + 3.72030i 1.26562 + 0.171422i
\(472\) 0 0
\(473\) −1.59404 0.551704i −0.0732942 0.0253674i
\(474\) 0 0
\(475\) −11.2926 4.52089i −0.518141 0.207433i
\(476\) 0 0
\(477\) 2.10531 + 5.77566i 0.0963955 + 0.264449i
\(478\) 0 0
\(479\) 9.48141 + 18.3914i 0.433217 + 0.840323i 0.999866 + 0.0163640i \(0.00520905\pi\)
−0.566650 + 0.823959i \(0.691761\pi\)
\(480\) 0 0
\(481\) 3.69758 0.897022i 0.168595 0.0409007i
\(482\) 0 0
\(483\) −10.6544 0.420285i −0.484793 0.0191236i
\(484\) 0 0
\(485\) −31.9357 + 40.6096i −1.45013 + 1.84399i
\(486\) 0 0
\(487\) 2.22781 + 11.5590i 0.100952 + 0.523787i 0.996835 + 0.0794976i \(0.0253316\pi\)
−0.895883 + 0.444289i \(0.853456\pi\)
\(488\) 0 0
\(489\) 15.3273 5.44552i 0.693126 0.246255i
\(490\) 0 0
\(491\) −14.6960 + 22.8674i −0.663222 + 1.03199i 0.332810 + 0.942994i \(0.392003\pi\)
−0.996032 + 0.0889991i \(0.971633\pi\)
\(492\) 0 0
\(493\) 4.37714 5.05149i 0.197137 0.227508i
\(494\) 0 0
\(495\) −1.38145 + 10.8663i −0.0620914 + 0.488403i
\(496\) 0 0
\(497\) −0.593597 + 2.44684i −0.0266265 + 0.109756i
\(498\) 0 0
\(499\) −10.1839 5.87965i −0.455892 0.263209i 0.254423 0.967093i \(-0.418114\pi\)
−0.710315 + 0.703884i \(0.751448\pi\)
\(500\) 0 0
\(501\) 3.03727 2.94380i 0.135695 0.131519i
\(502\) 0 0
\(503\) 0.482854 0.678074i 0.0215294 0.0302338i −0.803671 0.595074i \(-0.797123\pi\)
0.825200 + 0.564840i \(0.191062\pi\)
\(504\) 0 0
\(505\) 1.29193 + 1.23186i 0.0574903 + 0.0548169i
\(506\) 0 0
\(507\) 21.3972 + 5.00608i 0.950282 + 0.222328i
\(508\) 0 0
\(509\) −21.3596 + 3.07105i −0.946749 + 0.136122i −0.598359 0.801228i \(-0.704180\pi\)
−0.348390 + 0.937350i \(0.613271\pi\)
\(510\) 0 0
\(511\) −1.74943 + 5.95802i −0.0773904 + 0.263567i
\(512\) 0 0
\(513\) 14.7300 19.7065i 0.650345 0.870064i
\(514\) 0 0
\(515\) 20.7628 16.3280i 0.914917 0.719499i
\(516\) 0 0
\(517\) 0.143806 1.50601i 0.00632460 0.0662342i
\(518\) 0 0
\(519\) −4.15800 + 9.30527i −0.182516 + 0.408456i
\(520\) 0 0
\(521\) 11.9834 + 26.2401i 0.525004 + 1.14960i 0.967510 + 0.252833i \(0.0813624\pi\)
−0.442506 + 0.896766i \(0.645910\pi\)
\(522\) 0 0
\(523\) 18.3875 17.5325i 0.804031 0.766642i −0.171808 0.985130i \(-0.554961\pi\)
0.975840 + 0.218488i \(0.0701125\pi\)
\(524\) 0 0
\(525\) 5.07224 + 1.98267i 0.221371 + 0.0865309i
\(526\) 0 0
\(527\) 4.73409 10.3662i 0.206220 0.451559i
\(528\) 0 0
\(529\) 2.28921 0.218593i 0.0995309 0.00950405i
\(530\) 0 0
\(531\) 0.446202 5.64691i 0.0193635 0.245055i
\(532\) 0 0
\(533\) 0.269011 + 0.418589i 0.0116522 + 0.0181311i
\(534\) 0 0
\(535\) 45.7886i 1.97961i
\(536\) 0 0
\(537\) 7.34713 7.83264i 0.317052 0.338004i
\(538\) 0 0
\(539\) 6.14289 3.94780i 0.264593 0.170044i
\(540\) 0 0
\(541\) 21.6401 + 3.11138i 0.930382 + 0.133769i 0.590809 0.806811i \(-0.298809\pi\)
0.339572 + 0.940580i \(0.389718\pi\)
\(542\) 0 0
\(543\) 17.5726 22.7252i 0.754111 0.975230i
\(544\) 0 0
\(545\) −9.75632 4.45556i −0.417915 0.190855i
\(546\) 0 0
\(547\) −10.0117 25.0080i −0.428070 1.06927i −0.973004 0.230788i \(-0.925870\pi\)
0.544934 0.838479i \(-0.316555\pi\)
\(548\) 0 0
\(549\) −15.0014 + 16.2570i −0.640243 + 0.693830i
\(550\) 0 0
\(551\) 11.8646 5.41839i 0.505450 0.230831i
\(552\) 0 0
\(553\) 3.02604 + 8.74317i 0.128680 + 0.371797i
\(554\) 0 0
\(555\) −24.3279 + 21.4309i −1.03266 + 0.909690i
\(556\) 0 0
\(557\) 0.432284 + 0.549693i 0.0183164 + 0.0232913i 0.795125 0.606446i \(-0.207405\pi\)
−0.776809 + 0.629737i \(0.783163\pi\)
\(558\) 0 0
\(559\) 0.0338201 + 0.709972i 0.00143044 + 0.0300286i
\(560\) 0 0
\(561\) 2.82818 + 4.80738i 0.119406 + 0.202968i
\(562\) 0 0
\(563\) 2.63758 + 18.3448i 0.111161 + 0.773141i 0.966794 + 0.255558i \(0.0822590\pi\)
−0.855633 + 0.517583i \(0.826832\pi\)
\(564\) 0 0
\(565\) −8.93392 15.4740i −0.375853 0.650996i
\(566\) 0 0
\(567\) −6.52248 + 8.87647i −0.273918 + 0.372777i
\(568\) 0 0
\(569\) −13.6750 9.73792i −0.573285 0.408235i 0.256314 0.966594i \(-0.417492\pi\)
−0.829600 + 0.558359i \(0.811431\pi\)
\(570\) 0 0
\(571\) −0.974025 + 20.4473i −0.0407617 + 0.855693i 0.882217 + 0.470842i \(0.156050\pi\)
−0.922979 + 0.384850i \(0.874253\pi\)
\(572\) 0 0
\(573\) −5.10084 16.8608i −0.213091 0.704371i
\(574\) 0 0
\(575\) −12.5575 3.04642i −0.523685 0.127045i
\(576\) 0 0
\(577\) 0.506839 2.62973i 0.0211000 0.109477i −0.969852 0.243696i \(-0.921640\pi\)
0.990952 + 0.134218i \(0.0428524\pi\)
\(578\) 0 0
\(579\) −2.47650 23.8715i −0.102920 0.992066i
\(580\) 0 0
\(581\) −10.5049 6.75111i −0.435818 0.280083i
\(582\) 0 0
\(583\) −2.41721 1.24616i −0.100110 0.0516105i
\(584\) 0 0
\(585\) 4.46710 1.16134i 0.184692 0.0480156i
\(586\) 0 0
\(587\) 32.5963 + 25.6340i 1.34539 + 1.05803i 0.992484 + 0.122371i \(0.0390496\pi\)
0.352908 + 0.935658i \(0.385193\pi\)
\(588\) 0 0
\(589\) 16.8065 14.5629i 0.692501 0.600055i
\(590\) 0 0
\(591\) −5.84203 3.30953i −0.240309 0.136136i
\(592\) 0 0
\(593\) 36.1310 18.6268i 1.48372 0.764912i 0.489474 0.872018i \(-0.337189\pi\)
0.994248 + 0.107106i \(0.0341584\pi\)
\(594\) 0 0
\(595\) 7.83926 2.30181i 0.321378 0.0943652i
\(596\) 0 0
\(597\) −0.334118 + 0.155899i −0.0136745 + 0.00638054i
\(598\) 0 0
\(599\) −5.35408 + 15.4696i −0.218762 + 0.632071i 0.781208 + 0.624271i \(0.214604\pi\)
−0.999970 + 0.00779958i \(0.997517\pi\)
\(600\) 0 0
\(601\) −16.4721 23.1319i −0.671912 0.943569i 0.328087 0.944647i \(-0.393596\pi\)
−0.999999 + 0.00107875i \(0.999657\pi\)
\(602\) 0 0
\(603\) −14.6458 19.7104i −0.596424 0.802669i
\(604\) 0 0
\(605\) 14.7434 + 20.7043i 0.599406 + 0.841748i
\(606\) 0 0
\(607\) −3.91860 + 11.3220i −0.159051 + 0.459548i −0.996166 0.0874786i \(-0.972119\pi\)
0.837115 + 0.547026i \(0.184240\pi\)
\(608\) 0 0
\(609\) −5.29194 + 2.46922i −0.214440 + 0.100058i
\(610\) 0 0
\(611\) −0.611653 + 0.179598i −0.0247448 + 0.00726574i
\(612\) 0 0
\(613\) 10.0645 5.18862i 0.406502 0.209566i −0.242834 0.970068i \(-0.578077\pi\)
0.649336 + 0.760501i \(0.275047\pi\)
\(614\) 0 0
\(615\) −3.68905 2.08986i −0.148757 0.0842713i
\(616\) 0 0
\(617\) −9.49940 + 8.23127i −0.382431 + 0.331379i −0.824769 0.565470i \(-0.808695\pi\)
0.442338 + 0.896849i \(0.354149\pi\)
\(618\) 0 0
\(619\) −27.4773 21.6084i −1.10441 0.868515i −0.112270 0.993678i \(-0.535812\pi\)
−0.992136 + 0.125163i \(0.960055\pi\)
\(620\) 0 0
\(621\) 12.5091 22.9480i 0.501974 0.920872i
\(622\) 0 0
\(623\) −15.3507 7.91382i −0.615012 0.317061i
\(624\) 0 0
\(625\) −26.2852 16.8925i −1.05141 0.675698i
\(626\) 0 0
\(627\) 1.12312 + 10.8260i 0.0448531 + 0.432349i
\(628\) 0 0
\(629\) −3.12429 + 16.2103i −0.124573 + 0.646349i
\(630\) 0 0
\(631\) −11.0020 2.66905i −0.437982 0.106253i 0.0107043 0.999943i \(-0.496593\pi\)
−0.448686 + 0.893690i \(0.648108\pi\)
\(632\) 0 0
\(633\) 5.71444 + 18.8891i 0.227129 + 0.750774i
\(634\) 0 0
\(635\) −0.424020 + 8.90127i −0.0168267 + 0.353236i
\(636\) 0 0
\(637\) −2.50635 1.78477i −0.0993054 0.0707151i
\(638\) 0 0
\(639\) −4.72960 3.96474i −0.187100 0.156843i
\(640\) 0 0
\(641\) −4.78783 8.29276i −0.189108 0.327544i 0.755845 0.654750i \(-0.227226\pi\)
−0.944953 + 0.327206i \(0.893893\pi\)
\(642\) 0 0
\(643\) 5.98513 + 41.6275i 0.236031 + 1.64163i 0.671197 + 0.741279i \(0.265780\pi\)
−0.435167 + 0.900350i \(0.643311\pi\)
\(644\) 0 0
\(645\) −3.07105 5.22021i −0.120922 0.205546i
\(646\) 0 0
\(647\) −1.36358 28.6251i −0.0536079 1.12537i −0.852106 0.523370i \(-0.824675\pi\)
0.798498 0.601998i \(-0.205628\pi\)
\(648\) 0 0
\(649\) 1.54904 + 1.96977i 0.0608052 + 0.0773201i
\(650\) 0 0
\(651\) −7.47097 + 6.58130i −0.292810 + 0.257942i
\(652\) 0 0
\(653\) 3.80338 + 10.9891i 0.148838 + 0.430038i 0.994633 0.103470i \(-0.0329946\pi\)
−0.845795 + 0.533508i \(0.820873\pi\)
\(654\) 0 0
\(655\) −44.7476 + 20.4356i −1.74843 + 0.798483i
\(656\) 0 0
\(657\) −11.1859 10.3220i −0.436403 0.402698i
\(658\) 0 0
\(659\) 11.3100 + 28.2510i 0.440575 + 1.10050i 0.968011 + 0.250908i \(0.0807291\pi\)
−0.527436 + 0.849595i \(0.676847\pi\)
\(660\) 0 0
\(661\) −22.5536 10.2999i −0.877234 0.400619i −0.0746864 0.997207i \(-0.523796\pi\)
−0.802548 + 0.596588i \(0.796523\pi\)
\(662\) 0 0
\(663\) 1.43767 1.85922i 0.0558346 0.0722063i
\(664\) 0 0
\(665\) 15.7811 + 2.26897i 0.611963 + 0.0879870i
\(666\) 0 0
\(667\) 11.6563 7.49107i 0.451335 0.290055i
\(668\) 0 0
\(669\) −16.8802 + 17.9957i −0.652625 + 0.695752i
\(670\) 0 0
\(671\) 9.78592i 0.377781i
\(672\) 0 0
\(673\) −7.02204 10.9265i −0.270680 0.421186i 0.679128 0.734020i \(-0.262358\pi\)
−0.949808 + 0.312834i \(0.898722\pi\)
\(674\) 0 0
\(675\) −9.87110 + 8.98641i −0.379939 + 0.345887i
\(676\) 0 0
\(677\) −31.8794 + 3.04411i −1.22522 + 0.116995i −0.687537 0.726149i \(-0.741308\pi\)
−0.537688 + 0.843144i \(0.680702\pi\)
\(678\) 0 0
\(679\) 9.54748 20.9061i 0.366399 0.802302i
\(680\) 0 0
\(681\) −44.2042 17.2788i −1.69391 0.662127i
\(682\) 0 0
\(683\) 8.13714 7.75874i 0.311359 0.296880i −0.518245 0.855232i \(-0.673415\pi\)
0.829604 + 0.558352i \(0.188566\pi\)
\(684\) 0 0
\(685\) 4.90394 + 10.7381i 0.187370 + 0.410283i
\(686\) 0 0
\(687\) 1.03127 2.30790i 0.0393454 0.0880519i
\(688\) 0 0
\(689\) −0.108927 + 1.14074i −0.00414980 + 0.0434587i
\(690\) 0 0
\(691\) −20.8296 + 16.3806i −0.792395 + 0.623147i −0.930092 0.367328i \(-0.880273\pi\)
0.137696 + 0.990475i \(0.456030\pi\)
\(692\) 0 0
\(693\) −0.542434 4.84267i −0.0206054 0.183958i
\(694\) 0 0
\(695\) 1.81965 6.19718i 0.0690234 0.235072i
\(696\) 0 0
\(697\) −2.13695 + 0.307247i −0.0809429 + 0.0116378i
\(698\) 0 0
\(699\) −37.5064 8.77499i −1.41862 0.331901i
\(700\) 0 0
\(701\) −23.1230 22.0477i −0.873344 0.832732i 0.113645 0.993521i \(-0.463747\pi\)
−0.986989 + 0.160790i \(0.948596\pi\)
\(702\) 0 0
\(703\) −18.6865 + 26.2416i −0.704776 + 0.989720i
\(704\) 0 0
\(705\) 3.90052 3.78049i 0.146902 0.142381i
\(706\) 0 0
\(707\) −0.687737 0.397065i −0.0258650 0.0149332i
\(708\) 0 0
\(709\) 9.35642 38.5677i 0.351388 1.44844i −0.472321 0.881427i \(-0.656584\pi\)
0.823709 0.567013i \(-0.191901\pi\)
\(710\) 0 0
\(711\) −22.4971 2.86009i −0.843707 0.107262i
\(712\) 0 0
\(713\) 15.4702 17.8536i 0.579363 0.668621i
\(714\) 0 0
\(715\) −1.10392 + 1.71773i −0.0412842 + 0.0642395i
\(716\) 0 0
\(717\) −13.7724 + 4.89309i −0.514340 + 0.182736i
\(718\) 0 0
\(719\) 9.00803 + 46.7381i 0.335943 + 1.74304i 0.620343 + 0.784331i \(0.286993\pi\)
−0.284400 + 0.958706i \(0.591795\pi\)
\(720\) 0 0
\(721\) −7.26380 + 9.23667i −0.270518 + 0.343992i
\(722\) 0 0
\(723\) 12.1511 + 0.479324i 0.451903 + 0.0178263i
\(724\) 0 0
\(725\) −6.87741 + 1.66844i −0.255420 + 0.0619643i
\(726\) 0 0
\(727\) −6.14806 11.9256i −0.228019 0.442295i 0.746875 0.664964i \(-0.231553\pi\)
−0.974894 + 0.222669i \(0.928523\pi\)
\(728\) 0 0
\(729\) −12.4067 23.9807i −0.459506 0.888175i
\(730\) 0 0
\(731\) −2.86306 1.14620i −0.105894 0.0423936i
\(732\) 0 0
\(733\) 40.6330 + 14.0632i 1.50081 + 0.519437i 0.949203 0.314664i \(-0.101892\pi\)
0.551612 + 0.834101i \(0.314013\pi\)
\(734\) 0 0
\(735\) 25.9810 + 3.51902i 0.958325 + 0.129801i
\(736\) 0 0
\(737\) 10.6748 + 2.01433i 0.393213 + 0.0741988i
\(738\) 0 0
\(739\) 10.6843 7.60824i 0.393028 0.279874i −0.366410 0.930453i \(-0.619413\pi\)
0.759438 + 0.650580i \(0.225474\pi\)
\(740\) 0 0
\(741\) 4.05911 2.13479i 0.149115 0.0784234i
\(742\) 0 0
\(743\) 7.58373 18.9432i 0.278220 0.694960i −0.721776 0.692127i \(-0.756674\pi\)
0.999996 0.00283325i \(-0.000901852\pi\)
\(744\) 0 0
\(745\) 0.806008 + 2.74501i 0.0295299 + 0.100569i
\(746\) 0 0
\(747\) 26.2538 15.7354i 0.960576 0.575727i
\(748\) 0 0
\(749\) −4.80237 19.7956i −0.175475 0.723317i
\(750\) 0 0
\(751\) −9.68114 11.1726i −0.353270 0.407695i 0.551104 0.834437i \(-0.314207\pi\)
−0.904374 + 0.426742i \(0.859661\pi\)
\(752\) 0 0
\(753\) 5.46513 0.831413i 0.199160 0.0302984i
\(754\) 0 0
\(755\) −31.5783 + 6.08622i −1.14925 + 0.221500i
\(756\) 0 0
\(757\) −4.18141 + 8.11081i −0.151976 + 0.294792i −0.952517 0.304486i \(-0.901515\pi\)
0.800541 + 0.599278i \(0.204546\pi\)
\(758\) 0 0
\(759\) 2.81763 + 11.2136i 0.102274 + 0.407028i
\(760\) 0 0
\(761\) 34.8272 + 30.1779i 1.26248 + 1.09395i 0.991328 + 0.131413i \(0.0419515\pi\)
0.271156 + 0.962535i \(0.412594\pi\)
\(762\) 0 0
\(763\) 4.68523 + 0.903004i 0.169617 + 0.0326909i
\(764\) 0 0
\(765\) −3.46810 + 19.7239i −0.125389 + 0.713119i
\(766\) 0 0
\(767\) 0.527956 0.914447i 0.0190634 0.0330188i
\(768\) 0 0
\(769\) 44.5794 + 2.12358i 1.60758 + 0.0765783i 0.832036 0.554721i \(-0.187175\pi\)
0.775539 + 0.631299i \(0.217478\pi\)
\(770\) 0 0
\(771\) −35.8324 + 7.21036i −1.29047 + 0.259675i
\(772\) 0 0
\(773\) 9.12213 9.56701i 0.328100 0.344102i −0.538936 0.842347i \(-0.681174\pi\)
0.867036 + 0.498245i \(0.166022\pi\)