Properties

Label 1323.2.g.h.361.3
Level $1323$
Weight $2$
Character 1323.361
Analytic conductor $10.564$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.3
Character \(\chi\) \(=\) 1323.361
Dual form 1323.2.g.h.667.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.863305 + 1.49529i) q^{2} +(-0.490592 - 0.849731i) q^{4} -3.51231 q^{5} -1.75910 q^{8} +O(q^{10})\) \(q+(-0.863305 + 1.49529i) q^{2} +(-0.490592 - 0.849731i) q^{4} -3.51231 q^{5} -1.75910 q^{8} +(3.03220 - 5.25192i) q^{10} +6.09064 q^{11} +(0.560139 - 0.970190i) q^{13} +(2.49982 - 4.32982i) q^{16} +(0.601978 - 1.04266i) q^{17} +(1.10269 + 1.90991i) q^{19} +(1.72311 + 2.98452i) q^{20} +(-5.25808 + 9.10727i) q^{22} +1.27339 q^{23} +7.33633 q^{25} +(0.967143 + 1.67514i) q^{26} +(3.10262 + 5.37390i) q^{29} +(0.0942019 + 0.163162i) q^{31} +(2.55712 + 4.42907i) q^{32} +(1.03938 + 1.80026i) q^{34} +(-1.78835 - 3.09752i) q^{37} -3.80782 q^{38} +6.17850 q^{40} +(-1.68320 + 2.91538i) q^{41} +(-1.90276 - 3.29567i) q^{43} +(-2.98802 - 5.17540i) q^{44} +(-1.09932 + 1.90408i) q^{46} +(-2.86035 + 4.95427i) q^{47} +(-6.33349 + 10.9699i) q^{50} -1.09920 q^{52} +(-4.16913 + 7.22115i) q^{53} -21.3922 q^{55} -10.7140 q^{58} +(-5.63427 - 9.75883i) q^{59} +(-6.00109 + 10.3942i) q^{61} -0.325300 q^{62} +1.16898 q^{64} +(-1.96738 + 3.40761i) q^{65} +(3.95652 + 6.85289i) q^{67} -1.18130 q^{68} +12.2052 q^{71} +(2.65737 - 4.60269i) q^{73} +6.17557 q^{74} +(1.08194 - 1.87397i) q^{76} +(-4.60855 + 7.98225i) q^{79} +(-8.78016 + 15.2077i) q^{80} +(-2.90623 - 5.03373i) q^{82} +(-0.624950 - 1.08245i) q^{83} +(-2.11433 + 3.66213i) q^{85} +6.57064 q^{86} -10.7140 q^{88} +(2.77066 + 4.79892i) q^{89} +(-0.624715 - 1.08204i) q^{92} +(-4.93871 - 8.55409i) q^{94} +(-3.87298 - 6.70820i) q^{95} +(8.24277 + 14.2769i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 4q^{2} - 12q^{4} + 24q^{8} + O(q^{10}) \) \( 24q - 4q^{2} - 12q^{4} + 24q^{8} + 40q^{11} - 12q^{16} + 64q^{23} + 24q^{25} - 16q^{29} - 48q^{32} - 12q^{37} - 56q^{44} + 24q^{46} + 4q^{50} - 32q^{53} + 96q^{64} - 60q^{65} - 12q^{67} + 112q^{71} + 136q^{74} + 12q^{79} + 12q^{85} + 152q^{86} - 16q^{92} - 64q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.863305 + 1.49529i −0.610449 + 1.05733i 0.380716 + 0.924692i \(0.375678\pi\)
−0.991165 + 0.132637i \(0.957656\pi\)
\(3\) 0 0
\(4\) −0.490592 0.849731i −0.245296 0.424865i
\(5\) −3.51231 −1.57075 −0.785377 0.619018i \(-0.787531\pi\)
−0.785377 + 0.619018i \(0.787531\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.75910 −0.621935
\(9\) 0 0
\(10\) 3.03220 5.25192i 0.958865 1.66080i
\(11\) 6.09064 1.83640 0.918199 0.396120i \(-0.129644\pi\)
0.918199 + 0.396120i \(0.129644\pi\)
\(12\) 0 0
\(13\) 0.560139 0.970190i 0.155355 0.269082i −0.777833 0.628471i \(-0.783681\pi\)
0.933188 + 0.359388i \(0.117015\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 2.49982 4.32982i 0.624956 1.08246i
\(17\) 0.601978 1.04266i 0.146001 0.252881i −0.783745 0.621083i \(-0.786693\pi\)
0.929746 + 0.368202i \(0.120026\pi\)
\(18\) 0 0
\(19\) 1.10269 + 1.90991i 0.252974 + 0.438163i 0.964343 0.264655i \(-0.0852581\pi\)
−0.711370 + 0.702818i \(0.751925\pi\)
\(20\) 1.72311 + 2.98452i 0.385300 + 0.667359i
\(21\) 0 0
\(22\) −5.25808 + 9.10727i −1.12103 + 1.94168i
\(23\) 1.27339 0.265520 0.132760 0.991148i \(-0.457616\pi\)
0.132760 + 0.991148i \(0.457616\pi\)
\(24\) 0 0
\(25\) 7.33633 1.46727
\(26\) 0.967143 + 1.67514i 0.189672 + 0.328522i
\(27\) 0 0
\(28\) 0 0
\(29\) 3.10262 + 5.37390i 0.576142 + 0.997907i 0.995917 + 0.0902789i \(0.0287758\pi\)
−0.419774 + 0.907628i \(0.637891\pi\)
\(30\) 0 0
\(31\) 0.0942019 + 0.163162i 0.0169192 + 0.0293048i 0.874361 0.485276i \(-0.161281\pi\)
−0.857442 + 0.514581i \(0.827948\pi\)
\(32\) 2.55712 + 4.42907i 0.452040 + 0.782956i
\(33\) 0 0
\(34\) 1.03938 + 1.80026i 0.178252 + 0.308742i
\(35\) 0 0
\(36\) 0 0
\(37\) −1.78835 3.09752i −0.294003 0.509228i 0.680749 0.732516i \(-0.261654\pi\)
−0.974753 + 0.223288i \(0.928321\pi\)
\(38\) −3.80782 −0.617710
\(39\) 0 0
\(40\) 6.17850 0.976907
\(41\) −1.68320 + 2.91538i −0.262871 + 0.455307i −0.967004 0.254762i \(-0.918003\pi\)
0.704132 + 0.710069i \(0.251336\pi\)
\(42\) 0 0
\(43\) −1.90276 3.29567i −0.290168 0.502585i 0.683681 0.729781i \(-0.260378\pi\)
−0.973849 + 0.227195i \(0.927044\pi\)
\(44\) −2.98802 5.17540i −0.450461 0.780221i
\(45\) 0 0
\(46\) −1.09932 + 1.90408i −0.162086 + 0.280742i
\(47\) −2.86035 + 4.95427i −0.417225 + 0.722654i −0.995659 0.0930746i \(-0.970331\pi\)
0.578434 + 0.815729i \(0.303664\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −6.33349 + 10.9699i −0.895691 + 1.55138i
\(51\) 0 0
\(52\) −1.09920 −0.152432
\(53\) −4.16913 + 7.22115i −0.572675 + 0.991901i 0.423615 + 0.905842i \(0.360761\pi\)
−0.996290 + 0.0860593i \(0.972573\pi\)
\(54\) 0 0
\(55\) −21.3922 −2.88453
\(56\) 0 0
\(57\) 0 0
\(58\) −10.7140 −1.40682
\(59\) −5.63427 9.75883i −0.733519 1.27049i −0.955370 0.295411i \(-0.904543\pi\)
0.221851 0.975081i \(-0.428790\pi\)
\(60\) 0 0
\(61\) −6.00109 + 10.3942i −0.768361 + 1.33084i 0.170091 + 0.985428i \(0.445594\pi\)
−0.938451 + 0.345411i \(0.887739\pi\)
\(62\) −0.325300 −0.0413131
\(63\) 0 0
\(64\) 1.16898 0.146123
\(65\) −1.96738 + 3.40761i −0.244024 + 0.422662i
\(66\) 0 0
\(67\) 3.95652 + 6.85289i 0.483366 + 0.837214i 0.999818 0.0191025i \(-0.00608088\pi\)
−0.516452 + 0.856316i \(0.672748\pi\)
\(68\) −1.18130 −0.143254
\(69\) 0 0
\(70\) 0 0
\(71\) 12.2052 1.44850 0.724248 0.689540i \(-0.242187\pi\)
0.724248 + 0.689540i \(0.242187\pi\)
\(72\) 0 0
\(73\) 2.65737 4.60269i 0.311021 0.538704i −0.667563 0.744554i \(-0.732662\pi\)
0.978584 + 0.205849i \(0.0659957\pi\)
\(74\) 6.17557 0.717896
\(75\) 0 0
\(76\) 1.08194 1.87397i 0.124107 0.214959i
\(77\) 0 0
\(78\) 0 0
\(79\) −4.60855 + 7.98225i −0.518503 + 0.898073i 0.481266 + 0.876575i \(0.340177\pi\)
−0.999769 + 0.0214988i \(0.993156\pi\)
\(80\) −8.78016 + 15.2077i −0.981651 + 1.70027i
\(81\) 0 0
\(82\) −2.90623 5.03373i −0.320939 0.555883i
\(83\) −0.624950 1.08245i −0.0685972 0.118814i 0.829687 0.558229i \(-0.188519\pi\)
−0.898284 + 0.439415i \(0.855186\pi\)
\(84\) 0 0
\(85\) −2.11433 + 3.66213i −0.229332 + 0.397214i
\(86\) 6.57064 0.708531
\(87\) 0 0
\(88\) −10.7140 −1.14212
\(89\) 2.77066 + 4.79892i 0.293689 + 0.508684i 0.974679 0.223608i \(-0.0717837\pi\)
−0.680990 + 0.732293i \(0.738450\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.624715 1.08204i −0.0651310 0.112810i
\(93\) 0 0
\(94\) −4.93871 8.55409i −0.509389 0.882287i
\(95\) −3.87298 6.70820i −0.397359 0.688246i
\(96\) 0 0
\(97\) 8.24277 + 14.2769i 0.836926 + 1.44960i 0.892452 + 0.451142i \(0.148983\pi\)
−0.0555261 + 0.998457i \(0.517684\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −3.59915 6.23391i −0.359915 0.623391i
\(101\) 12.9638 1.28995 0.644975 0.764203i \(-0.276868\pi\)
0.644975 + 0.764203i \(0.276868\pi\)
\(102\) 0 0
\(103\) 2.70182 0.266218 0.133109 0.991101i \(-0.457504\pi\)
0.133109 + 0.991101i \(0.457504\pi\)
\(104\) −0.985340 + 1.70666i −0.0966205 + 0.167352i
\(105\) 0 0
\(106\) −7.19847 12.4681i −0.699177 1.21101i
\(107\) −0.0892402 0.154569i −0.00862718 0.0149427i 0.861680 0.507453i \(-0.169413\pi\)
−0.870307 + 0.492510i \(0.836079\pi\)
\(108\) 0 0
\(109\) −4.67927 + 8.10473i −0.448192 + 0.776292i −0.998268 0.0588226i \(-0.981265\pi\)
0.550076 + 0.835115i \(0.314599\pi\)
\(110\) 18.4680 31.9876i 1.76086 3.04989i
\(111\) 0 0
\(112\) 0 0
\(113\) −4.21019 + 7.29226i −0.396061 + 0.685998i −0.993236 0.116113i \(-0.962957\pi\)
0.597175 + 0.802111i \(0.296290\pi\)
\(114\) 0 0
\(115\) −4.47254 −0.417067
\(116\) 3.04424 5.27278i 0.282651 0.489565i
\(117\) 0 0
\(118\) 19.4564 1.79110
\(119\) 0 0
\(120\) 0 0
\(121\) 26.0959 2.37235
\(122\) −10.3615 17.9467i −0.938090 1.62482i
\(123\) 0 0
\(124\) 0.0924294 0.160092i 0.00830040 0.0143767i
\(125\) −8.20593 −0.733960
\(126\) 0 0
\(127\) −9.92438 −0.880647 −0.440323 0.897839i \(-0.645136\pi\)
−0.440323 + 0.897839i \(0.645136\pi\)
\(128\) −6.12343 + 10.6061i −0.541240 + 0.937455i
\(129\) 0 0
\(130\) −3.39691 5.88361i −0.297928 0.516027i
\(131\) 15.2467 1.33211 0.666055 0.745902i \(-0.267981\pi\)
0.666055 + 0.745902i \(0.267981\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −13.6627 −1.18028
\(135\) 0 0
\(136\) −1.05894 + 1.83413i −0.0908032 + 0.157276i
\(137\) −6.14700 −0.525174 −0.262587 0.964908i \(-0.584576\pi\)
−0.262587 + 0.964908i \(0.584576\pi\)
\(138\) 0 0
\(139\) 0.438687 0.759829i 0.0372090 0.0644478i −0.846821 0.531878i \(-0.821487\pi\)
0.884030 + 0.467430i \(0.154820\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −10.5368 + 18.2504i −0.884233 + 1.53154i
\(143\) 3.41161 5.90908i 0.285293 0.494142i
\(144\) 0 0
\(145\) −10.8974 18.8748i −0.904977 1.56747i
\(146\) 4.58824 + 7.94706i 0.379725 + 0.657703i
\(147\) 0 0
\(148\) −1.75470 + 3.03923i −0.144236 + 0.249823i
\(149\) −5.77553 −0.473150 −0.236575 0.971613i \(-0.576025\pi\)
−0.236575 + 0.971613i \(0.576025\pi\)
\(150\) 0 0
\(151\) −2.02643 −0.164908 −0.0824541 0.996595i \(-0.526276\pi\)
−0.0824541 + 0.996595i \(0.526276\pi\)
\(152\) −1.93973 3.35972i −0.157333 0.272509i
\(153\) 0 0
\(154\) 0 0
\(155\) −0.330866 0.573077i −0.0265758 0.0460307i
\(156\) 0 0
\(157\) 1.52378 + 2.63927i 0.121611 + 0.210636i 0.920403 0.390971i \(-0.127861\pi\)
−0.798792 + 0.601607i \(0.794527\pi\)
\(158\) −7.95718 13.7822i −0.633039 1.09646i
\(159\) 0 0
\(160\) −8.98141 15.5563i −0.710043 1.22983i
\(161\) 0 0
\(162\) 0 0
\(163\) 2.69445 + 4.66693i 0.211046 + 0.365542i 0.952042 0.305967i \(-0.0989797\pi\)
−0.740996 + 0.671509i \(0.765646\pi\)
\(164\) 3.30306 0.257925
\(165\) 0 0
\(166\) 2.15809 0.167500
\(167\) 8.30480 14.3843i 0.642645 1.11309i −0.342196 0.939629i \(-0.611171\pi\)
0.984840 0.173464i \(-0.0554961\pi\)
\(168\) 0 0
\(169\) 5.87249 + 10.1714i 0.451730 + 0.782419i
\(170\) −3.65063 6.32308i −0.279991 0.484958i
\(171\) 0 0
\(172\) −1.86696 + 3.23366i −0.142354 + 0.246564i
\(173\) −8.82516 + 15.2856i −0.670965 + 1.16214i 0.306666 + 0.951817i \(0.400786\pi\)
−0.977631 + 0.210328i \(0.932547\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 15.2255 26.3714i 1.14767 1.98782i
\(177\) 0 0
\(178\) −9.56769 −0.717128
\(179\) 1.31422 2.27630i 0.0982294 0.170138i −0.812722 0.582651i \(-0.802015\pi\)
0.910952 + 0.412513i \(0.135349\pi\)
\(180\) 0 0
\(181\) 3.97391 0.295378 0.147689 0.989034i \(-0.452816\pi\)
0.147689 + 0.989034i \(0.452816\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −2.24002 −0.165136
\(185\) 6.28125 + 10.8794i 0.461806 + 0.799872i
\(186\) 0 0
\(187\) 3.66643 6.35045i 0.268116 0.464391i
\(188\) 5.61306 0.409374
\(189\) 0 0
\(190\) 13.3743 0.970270
\(191\) −9.10295 + 15.7668i −0.658666 + 1.14084i 0.322295 + 0.946639i \(0.395546\pi\)
−0.980961 + 0.194204i \(0.937787\pi\)
\(192\) 0 0
\(193\) 0.101193 + 0.175271i 0.00728401 + 0.0126163i 0.869644 0.493679i \(-0.164348\pi\)
−0.862360 + 0.506295i \(0.831015\pi\)
\(194\) −28.4641 −2.04360
\(195\) 0 0
\(196\) 0 0
\(197\) 1.63136 0.116229 0.0581147 0.998310i \(-0.481491\pi\)
0.0581147 + 0.998310i \(0.481491\pi\)
\(198\) 0 0
\(199\) −3.14605 + 5.44912i −0.223018 + 0.386278i −0.955723 0.294268i \(-0.904924\pi\)
0.732705 + 0.680546i \(0.238257\pi\)
\(200\) −12.9053 −0.912544
\(201\) 0 0
\(202\) −11.1918 + 19.3847i −0.787449 + 1.36390i
\(203\) 0 0
\(204\) 0 0
\(205\) 5.91192 10.2397i 0.412906 0.715174i
\(206\) −2.33249 + 4.04000i −0.162512 + 0.281480i
\(207\) 0 0
\(208\) −2.80050 4.85061i −0.194180 0.336329i
\(209\) 6.71607 + 11.6326i 0.464560 + 0.804642i
\(210\) 0 0
\(211\) 8.14368 14.1053i 0.560634 0.971046i −0.436807 0.899555i \(-0.643891\pi\)
0.997441 0.0714912i \(-0.0227758\pi\)
\(212\) 8.18138 0.561899
\(213\) 0 0
\(214\) 0.308166 0.0210658
\(215\) 6.68308 + 11.5754i 0.455782 + 0.789438i
\(216\) 0 0
\(217\) 0 0
\(218\) −8.07927 13.9937i −0.547197 0.947773i
\(219\) 0 0
\(220\) 10.4949 + 18.1776i 0.707563 + 1.22554i
\(221\) −0.674383 1.16807i −0.0453639 0.0785726i
\(222\) 0 0
\(223\) −9.98472 17.2940i −0.668626 1.15809i −0.978288 0.207248i \(-0.933549\pi\)
0.309662 0.950847i \(-0.399784\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −7.26936 12.5909i −0.483551 0.837534i
\(227\) −3.61283 −0.239792 −0.119896 0.992786i \(-0.538256\pi\)
−0.119896 + 0.992786i \(0.538256\pi\)
\(228\) 0 0
\(229\) 13.7147 0.906290 0.453145 0.891437i \(-0.350302\pi\)
0.453145 + 0.891437i \(0.350302\pi\)
\(230\) 3.86117 6.68774i 0.254598 0.440976i
\(231\) 0 0
\(232\) −5.45781 9.45321i −0.358323 0.620634i
\(233\) −12.6271 21.8707i −0.827227 1.43280i −0.900205 0.435466i \(-0.856583\pi\)
0.0729776 0.997334i \(-0.476750\pi\)
\(234\) 0 0
\(235\) 10.0464 17.4009i 0.655357 1.13511i
\(236\) −5.52825 + 9.57521i −0.359859 + 0.623293i
\(237\) 0 0
\(238\) 0 0
\(239\) 4.49495 7.78549i 0.290754 0.503601i −0.683234 0.730200i \(-0.739427\pi\)
0.973988 + 0.226598i \(0.0727604\pi\)
\(240\) 0 0
\(241\) 9.25724 0.596311 0.298156 0.954517i \(-0.403629\pi\)
0.298156 + 0.954517i \(0.403629\pi\)
\(242\) −22.5287 + 39.0209i −1.44820 + 2.50836i
\(243\) 0 0
\(244\) 11.7763 0.753903
\(245\) 0 0
\(246\) 0 0
\(247\) 2.47063 0.157203
\(248\) −0.165710 0.287019i −0.0105226 0.0182257i
\(249\) 0 0
\(250\) 7.08422 12.2702i 0.448045 0.776037i
\(251\) −20.6517 −1.30353 −0.651763 0.758422i \(-0.725970\pi\)
−0.651763 + 0.758422i \(0.725970\pi\)
\(252\) 0 0
\(253\) 7.75576 0.487600
\(254\) 8.56777 14.8398i 0.537590 0.931133i
\(255\) 0 0
\(256\) −9.40380 16.2879i −0.587738 1.01799i
\(257\) 2.44579 0.152564 0.0762819 0.997086i \(-0.475695\pi\)
0.0762819 + 0.997086i \(0.475695\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 3.86073 0.239432
\(261\) 0 0
\(262\) −13.1626 + 22.7982i −0.813186 + 1.40848i
\(263\) 24.5628 1.51460 0.757302 0.653065i \(-0.226517\pi\)
0.757302 + 0.653065i \(0.226517\pi\)
\(264\) 0 0
\(265\) 14.6433 25.3629i 0.899531 1.55803i
\(266\) 0 0
\(267\) 0 0
\(268\) 3.88207 6.72395i 0.237135 0.410730i
\(269\) −14.7851 + 25.6086i −0.901466 + 1.56139i −0.0758746 + 0.997117i \(0.524175\pi\)
−0.825592 + 0.564268i \(0.809158\pi\)
\(270\) 0 0
\(271\) 12.3958 + 21.4701i 0.752989 + 1.30421i 0.946368 + 0.323090i \(0.104722\pi\)
−0.193380 + 0.981124i \(0.561945\pi\)
\(272\) −3.00968 5.21291i −0.182488 0.316079i
\(273\) 0 0
\(274\) 5.30674 9.19154i 0.320592 0.555281i
\(275\) 44.6830 2.69448
\(276\) 0 0
\(277\) 1.87850 0.112868 0.0564340 0.998406i \(-0.482027\pi\)
0.0564340 + 0.998406i \(0.482027\pi\)
\(278\) 0.757442 + 1.31193i 0.0454284 + 0.0786842i
\(279\) 0 0
\(280\) 0 0
\(281\) −6.03965 10.4610i −0.360295 0.624049i 0.627714 0.778444i \(-0.283991\pi\)
−0.988009 + 0.154395i \(0.950657\pi\)
\(282\) 0 0
\(283\) 13.9859 + 24.2244i 0.831378 + 1.43999i 0.896946 + 0.442140i \(0.145781\pi\)
−0.0655680 + 0.997848i \(0.520886\pi\)
\(284\) −5.98779 10.3712i −0.355310 0.615415i
\(285\) 0 0
\(286\) 5.89052 + 10.2027i 0.348314 + 0.603297i
\(287\) 0 0
\(288\) 0 0
\(289\) 7.77524 + 13.4671i 0.457367 + 0.792183i
\(290\) 37.6310 2.20977
\(291\) 0 0
\(292\) −5.21473 −0.305169
\(293\) 4.41163 7.64117i 0.257730 0.446402i −0.707903 0.706309i \(-0.750359\pi\)
0.965634 + 0.259908i \(0.0836921\pi\)
\(294\) 0 0
\(295\) 19.7893 + 34.2761i 1.15218 + 1.99563i
\(296\) 3.14589 + 5.44883i 0.182851 + 0.316707i
\(297\) 0 0
\(298\) 4.98604 8.63608i 0.288834 0.500275i
\(299\) 0.713276 1.23543i 0.0412498 0.0714467i
\(300\) 0 0
\(301\) 0 0
\(302\) 1.74942 3.03009i 0.100668 0.174362i
\(303\) 0 0
\(304\) 11.0261 0.632389
\(305\) 21.0777 36.5076i 1.20691 2.09042i
\(306\) 0 0
\(307\) 1.05532 0.0602304 0.0301152 0.999546i \(-0.490413\pi\)
0.0301152 + 0.999546i \(0.490413\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 1.14255 0.0648927
\(311\) 1.53608 + 2.66056i 0.0871029 + 0.150867i 0.906285 0.422666i \(-0.138906\pi\)
−0.819182 + 0.573533i \(0.805572\pi\)
\(312\) 0 0
\(313\) −14.0810 + 24.3891i −0.795907 + 1.37855i 0.126355 + 0.991985i \(0.459672\pi\)
−0.922262 + 0.386566i \(0.873661\pi\)
\(314\) −5.26196 −0.296949
\(315\) 0 0
\(316\) 9.04368 0.508747
\(317\) 6.42324 11.1254i 0.360765 0.624863i −0.627322 0.778760i \(-0.715849\pi\)
0.988087 + 0.153897i \(0.0491823\pi\)
\(318\) 0 0
\(319\) 18.8969 + 32.7305i 1.05803 + 1.83255i
\(320\) −4.10582 −0.229523
\(321\) 0 0
\(322\) 0 0
\(323\) 2.65517 0.147738
\(324\) 0 0
\(325\) 4.10937 7.11763i 0.227947 0.394815i
\(326\) −9.30454 −0.515331
\(327\) 0 0
\(328\) 2.96091 5.12845i 0.163489 0.283171i
\(329\) 0 0
\(330\) 0 0
\(331\) 10.7780 18.6681i 0.592413 1.02609i −0.401493 0.915862i \(-0.631509\pi\)
0.993906 0.110228i \(-0.0351581\pi\)
\(332\) −0.613191 + 1.06208i −0.0336532 + 0.0582891i
\(333\) 0 0
\(334\) 14.3392 + 24.8361i 0.784604 + 1.35897i
\(335\) −13.8965 24.0695i −0.759248 1.31506i
\(336\) 0 0
\(337\) 6.30340 10.9178i 0.343368 0.594731i −0.641688 0.766966i \(-0.721766\pi\)
0.985056 + 0.172235i \(0.0550989\pi\)
\(338\) −20.2790 −1.10303
\(339\) 0 0
\(340\) 4.14910 0.225017
\(341\) 0.573750 + 0.993764i 0.0310703 + 0.0538153i
\(342\) 0 0
\(343\) 0 0
\(344\) 3.34714 + 5.79741i 0.180466 + 0.312575i
\(345\) 0 0
\(346\) −15.2376 26.3923i −0.819179 1.41886i
\(347\) 11.5683 + 20.0369i 0.621020 + 1.07564i 0.989296 + 0.145922i \(0.0466147\pi\)
−0.368276 + 0.929716i \(0.620052\pi\)
\(348\) 0 0
\(349\) 8.24346 + 14.2781i 0.441262 + 0.764289i 0.997783 0.0665448i \(-0.0211975\pi\)
−0.556521 + 0.830833i \(0.687864\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 15.5745 + 26.9759i 0.830124 + 1.43782i
\(353\) 24.4875 1.30334 0.651669 0.758503i \(-0.274069\pi\)
0.651669 + 0.758503i \(0.274069\pi\)
\(354\) 0 0
\(355\) −42.8686 −2.27523
\(356\) 2.71852 4.70862i 0.144081 0.249556i
\(357\) 0 0
\(358\) 2.26915 + 3.93028i 0.119928 + 0.207722i
\(359\) 10.2389 + 17.7342i 0.540386 + 0.935977i 0.998882 + 0.0472797i \(0.0150552\pi\)
−0.458495 + 0.888697i \(0.651611\pi\)
\(360\) 0 0
\(361\) 7.06816 12.2424i 0.372009 0.644338i
\(362\) −3.43070 + 5.94214i −0.180313 + 0.312312i
\(363\) 0 0
\(364\) 0 0
\(365\) −9.33349 + 16.1661i −0.488537 + 0.846172i
\(366\) 0 0
\(367\) 22.2539 1.16164 0.580821 0.814031i \(-0.302732\pi\)
0.580821 + 0.814031i \(0.302732\pi\)
\(368\) 3.18325 5.51355i 0.165938 0.287414i
\(369\) 0 0
\(370\) −21.6905 −1.12764
\(371\) 0 0
\(372\) 0 0
\(373\) −32.5369 −1.68469 −0.842347 0.538935i \(-0.818827\pi\)
−0.842347 + 0.538935i \(0.818827\pi\)
\(374\) 6.33050 + 10.9647i 0.327342 + 0.566974i
\(375\) 0 0
\(376\) 5.03163 8.71504i 0.259487 0.449444i
\(377\) 6.95160 0.358026
\(378\) 0 0
\(379\) 1.54440 0.0793306 0.0396653 0.999213i \(-0.487371\pi\)
0.0396653 + 0.999213i \(0.487371\pi\)
\(380\) −3.80011 + 6.58198i −0.194941 + 0.337648i
\(381\) 0 0
\(382\) −15.7173 27.2231i −0.804165 1.39285i
\(383\) −31.6294 −1.61619 −0.808093 0.589055i \(-0.799500\pi\)
−0.808093 + 0.589055i \(0.799500\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −0.349441 −0.0177861
\(387\) 0 0
\(388\) 8.08767 14.0083i 0.410589 0.711162i
\(389\) 5.24626 0.265996 0.132998 0.991116i \(-0.457540\pi\)
0.132998 + 0.991116i \(0.457540\pi\)
\(390\) 0 0
\(391\) 0.766552 1.32771i 0.0387662 0.0671451i
\(392\) 0 0
\(393\) 0 0
\(394\) −1.40836 + 2.43935i −0.0709521 + 0.122893i
\(395\) 16.1867 28.0362i 0.814440 1.41065i
\(396\) 0 0
\(397\) −0.0138175 0.0239325i −0.000693478 0.00120114i 0.865678 0.500600i \(-0.166887\pi\)
−0.866372 + 0.499399i \(0.833554\pi\)
\(398\) −5.43201 9.40851i −0.272282 0.471606i
\(399\) 0 0
\(400\) 18.3395 31.7650i 0.916977 1.58825i
\(401\) −12.1377 −0.606127 −0.303064 0.952970i \(-0.598009\pi\)
−0.303064 + 0.952970i \(0.598009\pi\)
\(402\) 0 0
\(403\) 0.211065 0.0105139
\(404\) −6.35996 11.0158i −0.316420 0.548055i
\(405\) 0 0
\(406\) 0 0
\(407\) −10.8922 18.8659i −0.539907 0.935146i
\(408\) 0 0
\(409\) −15.6726 27.1458i −0.774963 1.34227i −0.934816 0.355134i \(-0.884435\pi\)
0.159853 0.987141i \(-0.448898\pi\)
\(410\) 10.2076 + 17.6800i 0.504116 + 0.873155i
\(411\) 0 0
\(412\) −1.32549 2.29582i −0.0653022 0.113107i
\(413\) 0 0
\(414\) 0 0
\(415\) 2.19502 + 3.80189i 0.107749 + 0.186627i
\(416\) 5.72938 0.280906
\(417\) 0 0
\(418\) −23.1921 −1.13436
\(419\) −7.44319 + 12.8920i −0.363623 + 0.629814i −0.988554 0.150866i \(-0.951794\pi\)
0.624931 + 0.780680i \(0.285127\pi\)
\(420\) 0 0
\(421\) −4.54213 7.86721i −0.221370 0.383424i 0.733854 0.679307i \(-0.237720\pi\)
−0.955224 + 0.295883i \(0.904386\pi\)
\(422\) 14.0610 + 24.3543i 0.684477 + 1.18555i
\(423\) 0 0
\(424\) 7.33392 12.7027i 0.356166 0.616898i
\(425\) 4.41631 7.64927i 0.214223 0.371044i
\(426\) 0 0
\(427\) 0 0
\(428\) −0.0875611 + 0.151660i −0.00423243 + 0.00733078i
\(429\) 0 0
\(430\) −23.0781 −1.11293
\(431\) −8.31776 + 14.4068i −0.400652 + 0.693950i −0.993805 0.111140i \(-0.964550\pi\)
0.593152 + 0.805090i \(0.297883\pi\)
\(432\) 0 0
\(433\) 19.7423 0.948756 0.474378 0.880321i \(-0.342673\pi\)
0.474378 + 0.880321i \(0.342673\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 9.18244 0.439759
\(437\) 1.40415 + 2.43206i 0.0671696 + 0.116341i
\(438\) 0 0
\(439\) 3.36757 5.83280i 0.160725 0.278384i −0.774404 0.632692i \(-0.781950\pi\)
0.935129 + 0.354307i \(0.115283\pi\)
\(440\) 37.6310 1.79399
\(441\) 0 0
\(442\) 2.32879 0.110769
\(443\) 14.3202 24.8033i 0.680372 1.17844i −0.294496 0.955653i \(-0.595152\pi\)
0.974867 0.222786i \(-0.0715150\pi\)
\(444\) 0 0
\(445\) −9.73141 16.8553i −0.461313 0.799017i
\(446\) 34.4794 1.63265
\(447\) 0 0
\(448\) 0 0
\(449\) 6.66872 0.314716 0.157358 0.987542i \(-0.449702\pi\)
0.157358 + 0.987542i \(0.449702\pi\)
\(450\) 0 0
\(451\) −10.2518 + 17.7566i −0.482736 + 0.836124i
\(452\) 8.26194 0.388609
\(453\) 0 0
\(454\) 3.11898 5.40223i 0.146381 0.253539i
\(455\) 0 0
\(456\) 0 0
\(457\) 14.3287 24.8180i 0.670266 1.16093i −0.307563 0.951528i \(-0.599513\pi\)
0.977829 0.209407i \(-0.0671533\pi\)
\(458\) −11.8399 + 20.5074i −0.553244 + 0.958246i
\(459\) 0 0
\(460\) 2.19419 + 3.80045i 0.102305 + 0.177197i
\(461\) 10.0087 + 17.3355i 0.466150 + 0.807395i 0.999253 0.0386554i \(-0.0123075\pi\)
−0.533103 + 0.846050i \(0.678974\pi\)
\(462\) 0 0
\(463\) −4.95789 + 8.58731i −0.230413 + 0.399086i −0.957930 0.287003i \(-0.907341\pi\)
0.727517 + 0.686090i \(0.240674\pi\)
\(464\) 31.0240 1.44025
\(465\) 0 0
\(466\) 43.6041 2.01992
\(467\) −8.04035 13.9263i −0.372063 0.644432i 0.617820 0.786320i \(-0.288016\pi\)
−0.989883 + 0.141888i \(0.954683\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 17.3463 + 30.0446i 0.800124 + 1.38586i
\(471\) 0 0
\(472\) 9.91123 + 17.1667i 0.456201 + 0.790164i
\(473\) −11.5890 20.0728i −0.532863 0.922946i
\(474\) 0 0
\(475\) 8.08967 + 14.0117i 0.371180 + 0.642902i
\(476\) 0 0
\(477\) 0 0
\(478\) 7.76103 + 13.4425i 0.354981 + 0.614846i
\(479\) −8.20255 −0.374784 −0.187392 0.982285i \(-0.560003\pi\)
−0.187392 + 0.982285i \(0.560003\pi\)
\(480\) 0 0
\(481\) −4.00690 −0.182699
\(482\) −7.99183 + 13.8423i −0.364018 + 0.630497i
\(483\) 0 0
\(484\) −12.8024 22.1745i −0.581929 1.00793i
\(485\) −28.9512 50.1449i −1.31460 2.27696i
\(486\) 0 0
\(487\) −1.36840 + 2.37014i −0.0620081 + 0.107401i −0.895363 0.445337i \(-0.853084\pi\)
0.833355 + 0.552738i \(0.186417\pi\)
\(488\) 10.5565 18.2844i 0.477871 0.827696i
\(489\) 0 0
\(490\) 0 0
\(491\) −9.85482 + 17.0690i −0.444742 + 0.770315i −0.998034 0.0626719i \(-0.980038\pi\)
0.553293 + 0.832987i \(0.313371\pi\)
\(492\) 0 0
\(493\) 7.47084 0.336470
\(494\) −2.13291 + 3.69431i −0.0959642 + 0.166215i
\(495\) 0 0
\(496\) 0.941952 0.0422949
\(497\) 0 0
\(498\) 0 0
\(499\) −33.0960 −1.48158 −0.740789 0.671737i \(-0.765548\pi\)
−0.740789 + 0.671737i \(0.765548\pi\)
\(500\) 4.02576 + 6.97283i 0.180038 + 0.311834i
\(501\) 0 0
\(502\) 17.8288 30.8803i 0.795737 1.37826i
\(503\) 12.1860 0.543346 0.271673 0.962390i \(-0.412423\pi\)
0.271673 + 0.962390i \(0.412423\pi\)
\(504\) 0 0
\(505\) −45.5331 −2.02619
\(506\) −6.69559 + 11.5971i −0.297655 + 0.515554i
\(507\) 0 0
\(508\) 4.86882 + 8.43305i 0.216019 + 0.374156i
\(509\) 13.6393 0.604551 0.302276 0.953221i \(-0.402254\pi\)
0.302276 + 0.953221i \(0.402254\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 7.97968 0.352656
\(513\) 0 0
\(514\) −2.11146 + 3.65715i −0.0931325 + 0.161310i
\(515\) −9.48962 −0.418163
\(516\) 0 0
\(517\) −17.4214 + 30.1747i −0.766190 + 1.32708i
\(518\) 0 0
\(519\) 0 0
\(520\) 3.46082 5.99432i 0.151767 0.262868i
\(521\) 17.7745 30.7863i 0.778714 1.34877i −0.153969 0.988076i \(-0.549206\pi\)
0.932683 0.360697i \(-0.117461\pi\)
\(522\) 0 0
\(523\) 13.3593 + 23.1391i 0.584163 + 1.01180i 0.994979 + 0.100082i \(0.0319105\pi\)
−0.410816 + 0.911718i \(0.634756\pi\)
\(524\) −7.47991 12.9556i −0.326761 0.565967i
\(525\) 0 0
\(526\) −21.2052 + 36.7284i −0.924589 + 1.60143i
\(527\) 0.226830 0.00988086
\(528\) 0 0
\(529\) −21.3785 −0.929499
\(530\) 25.2833 + 43.7919i 1.09824 + 1.90220i
\(531\) 0 0
\(532\) 0 0
\(533\) 1.88565 + 3.26604i 0.0816766 + 0.141468i
\(534\) 0 0
\(535\) 0.313440 + 0.542893i 0.0135512 + 0.0234713i
\(536\) −6.95990 12.0549i −0.300622 0.520693i
\(537\) 0 0
\(538\) −25.5282 44.2161i −1.10060 1.90629i
\(539\) 0 0
\(540\) 0 0
\(541\) −18.7927 32.5500i −0.807963 1.39943i −0.914272 0.405100i \(-0.867237\pi\)
0.106309 0.994333i \(-0.466097\pi\)
\(542\) −42.8053 −1.83864
\(543\) 0 0
\(544\) 6.15733 0.263993
\(545\) 16.4350 28.4663i 0.704000 1.21936i
\(546\) 0 0
\(547\) −9.13381 15.8202i −0.390533 0.676424i 0.601986 0.798506i \(-0.294376\pi\)
−0.992520 + 0.122082i \(0.961043\pi\)
\(548\) 3.01567 + 5.22329i 0.128823 + 0.223128i
\(549\) 0 0
\(550\) −38.5750 + 66.8139i −1.64485 + 2.84896i
\(551\) −6.84243 + 11.8514i −0.291498 + 0.504889i
\(552\) 0 0
\(553\) 0 0
\(554\) −1.62172 + 2.80890i −0.0689002 + 0.119339i
\(555\) 0 0
\(556\) −0.860866 −0.0365089
\(557\) −1.94636 + 3.37119i −0.0824698 + 0.142842i −0.904310 0.426876i \(-0.859614\pi\)
0.821840 + 0.569718i \(0.192947\pi\)
\(558\) 0 0
\(559\) −4.26324 −0.180316
\(560\) 0 0
\(561\) 0 0
\(562\) 20.8562 0.879767
\(563\) 1.66428 + 2.88261i 0.0701409 + 0.121488i 0.898963 0.438025i \(-0.144322\pi\)
−0.828822 + 0.559512i \(0.810988\pi\)
\(564\) 0 0
\(565\) 14.7875 25.6127i 0.622115 1.07753i
\(566\) −48.2965 −2.03006
\(567\) 0 0
\(568\) −21.4702 −0.900870
\(569\) −18.3122 + 31.7177i −0.767688 + 1.32967i 0.171126 + 0.985249i \(0.445259\pi\)
−0.938814 + 0.344425i \(0.888074\pi\)
\(570\) 0 0
\(571\) 11.2912 + 19.5569i 0.472522 + 0.818432i 0.999506 0.0314435i \(-0.0100104\pi\)
−0.526984 + 0.849875i \(0.676677\pi\)
\(572\) −6.69483 −0.279925
\(573\) 0 0
\(574\) 0 0
\(575\) 9.34201 0.389589
\(576\) 0 0
\(577\) −11.2725 + 19.5245i −0.469279 + 0.812815i −0.999383 0.0351177i \(-0.988819\pi\)
0.530104 + 0.847932i \(0.322153\pi\)
\(578\) −26.8496 −1.11680
\(579\) 0 0
\(580\) −10.6923 + 18.5197i −0.443975 + 0.768987i
\(581\) 0 0
\(582\) 0 0
\(583\) −25.3927 + 43.9814i −1.05166 + 1.82152i
\(584\) −4.67457 + 8.09659i −0.193435 + 0.335039i
\(585\) 0 0
\(586\) 7.61717 + 13.1933i 0.314662 + 0.545011i
\(587\) 12.1198 + 20.9921i 0.500237 + 0.866436i 1.00000 0.000273884i \(8.71801e-5\pi\)
−0.499763 + 0.866162i \(0.666579\pi\)
\(588\) 0 0
\(589\) −0.207750 + 0.359834i −0.00856020 + 0.0148267i
\(590\) −68.3368 −2.81338
\(591\) 0 0
\(592\) −17.8822 −0.734956
\(593\) −22.8663 39.6056i −0.939007 1.62641i −0.767328 0.641255i \(-0.778414\pi\)
−0.171680 0.985153i \(-0.554919\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 2.83343 + 4.90764i 0.116062 + 0.201025i
\(597\) 0 0
\(598\) 1.23155 + 2.13311i 0.0503618 + 0.0872292i
\(599\) −15.0834 26.1252i −0.616290 1.06745i −0.990157 0.139963i \(-0.955302\pi\)
0.373866 0.927483i \(-0.378032\pi\)
\(600\) 0 0
\(601\) 7.36933 + 12.7641i 0.300601 + 0.520657i 0.976272 0.216547i \(-0.0694794\pi\)
−0.675671 + 0.737203i \(0.736146\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0.994149 + 1.72192i 0.0404513 + 0.0700638i
\(605\) −91.6569 −3.72638
\(606\) 0 0
\(607\) −6.07836 −0.246713 −0.123356 0.992362i \(-0.539366\pi\)
−0.123356 + 0.992362i \(0.539366\pi\)
\(608\) −5.63941 + 9.76774i −0.228708 + 0.396134i
\(609\) 0 0
\(610\) 36.3930 + 63.0345i 1.47351 + 2.55219i
\(611\) 3.20439 + 5.55016i 0.129636 + 0.224535i
\(612\) 0 0
\(613\) −5.88668 + 10.1960i −0.237761 + 0.411814i −0.960071 0.279755i \(-0.909747\pi\)
0.722311 + 0.691569i \(0.243080\pi\)
\(614\) −0.911065 + 1.57801i −0.0367676 + 0.0636833i
\(615\) 0 0
\(616\) 0 0
\(617\) 16.0319 27.7680i 0.645418 1.11790i −0.338786 0.940863i \(-0.610016\pi\)
0.984205 0.177034i \(-0.0566503\pi\)
\(618\) 0 0
\(619\) −12.5518 −0.504498 −0.252249 0.967662i \(-0.581170\pi\)
−0.252249 + 0.967662i \(0.581170\pi\)
\(620\) −0.324641 + 0.562294i −0.0130379 + 0.0225823i
\(621\) 0 0
\(622\) −5.30441 −0.212688
\(623\) 0 0
\(624\) 0 0
\(625\) −7.85989 −0.314396
\(626\) −24.3125 42.1104i −0.971721 1.68307i
\(627\) 0 0
\(628\) 1.49511 2.58961i 0.0596614 0.103337i
\(629\) −4.30619 −0.171699
\(630\) 0 0
\(631\) 33.4642 1.33219 0.666095 0.745867i \(-0.267964\pi\)
0.666095 + 0.745867i \(0.267964\pi\)
\(632\) 8.10690 14.0416i 0.322475 0.558543i
\(633\) 0 0
\(634\) 11.0904 + 19.2092i 0.440457 + 0.762894i
\(635\) 34.8575 1.38328
\(636\) 0 0
\(637\) 0 0
\(638\) −65.2553 −2.58348
\(639\) 0 0
\(640\) 21.5074 37.2519i 0.850155 1.47251i
\(641\) 18.9837 0.749809 0.374905 0.927063i \(-0.377675\pi\)
0.374905 + 0.927063i \(0.377675\pi\)
\(642\) 0 0
\(643\) 4.81347 8.33718i 0.189825 0.328786i −0.755367 0.655302i \(-0.772541\pi\)
0.945192 + 0.326516i \(0.105875\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −2.29222 + 3.97025i −0.0901864 + 0.156207i
\(647\) −3.90607 + 6.76551i −0.153564 + 0.265980i −0.932535 0.361079i \(-0.882408\pi\)
0.778972 + 0.627059i \(0.215742\pi\)
\(648\) 0 0
\(649\) −34.3163 59.4375i −1.34703 2.33313i
\(650\) 7.09528 + 12.2894i 0.278300 + 0.482029i
\(651\) 0 0
\(652\) 2.64376 4.57912i 0.103537 0.179332i
\(653\) −31.7429 −1.24219 −0.621097 0.783734i \(-0.713313\pi\)
−0.621097 + 0.783734i \(0.713313\pi\)
\(654\) 0 0
\(655\) −53.5512 −2.09242
\(656\) 8.41540 + 14.5759i 0.328566 + 0.569093i
\(657\) 0 0
\(658\) 0 0
\(659\) −3.10685 5.38122i −0.121026 0.209623i 0.799147 0.601136i \(-0.205285\pi\)
−0.920172 + 0.391513i \(0.871952\pi\)
\(660\) 0 0
\(661\) −13.7631 23.8384i −0.535324 0.927208i −0.999148 0.0412802i \(-0.986856\pi\)
0.463824 0.885927i \(-0.346477\pi\)
\(662\) 18.6094 + 32.2325i 0.723276 + 1.25275i
\(663\) 0 0
\(664\) 1.09935 + 1.90413i 0.0426630 + 0.0738945i
\(665\) 0 0
\(666\) 0 0
\(667\) 3.95084 + 6.84306i 0.152977 + 0.264964i
\(668\) −16.2971 −0.630553
\(669\) 0 0
\(670\) 47.9878 1.85393
\(671\) −36.5505 + 63.3073i −1.41102 + 2.44395i
\(672\) 0 0
\(673\) −8.10894 14.0451i −0.312577 0.541399i 0.666343 0.745646i \(-0.267859\pi\)
−0.978919 + 0.204247i \(0.934526\pi\)
\(674\) 10.8835 + 18.8508i 0.419217 + 0.726106i
\(675\) 0 0
\(676\) 5.76199 9.98006i 0.221615 0.383849i
\(677\) −10.2545 + 17.7613i −0.394112 + 0.682623i −0.992987 0.118220i \(-0.962281\pi\)
0.598875 + 0.800842i \(0.295615\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 3.71932 6.44205i 0.142629 0.247041i
\(681\) 0 0
\(682\) −1.98128 −0.0758673
\(683\) −0.0561542 + 0.0972618i −0.00214868 + 0.00372162i −0.867098 0.498138i \(-0.834017\pi\)
0.864949 + 0.501860i \(0.167351\pi\)
\(684\) 0 0
\(685\) 21.5902 0.824918
\(686\) 0 0
\(687\) 0 0
\(688\) −19.0262 −0.725368
\(689\) 4.67059 + 8.08970i 0.177935 + 0.308193i
\(690\) 0 0
\(691\) −9.43351 + 16.3393i −0.358868 + 0.621577i −0.987772 0.155906i \(-0.950170\pi\)
0.628904 + 0.777483i \(0.283504\pi\)
\(692\) 17.3182 0.658340
\(693\) 0 0
\(694\) −39.9480 −1.51640
\(695\) −1.54081 + 2.66876i −0.0584461 + 0.101232i
\(696\) 0 0
\(697\) 2.02650 + 3.51000i 0.0767590 + 0.132951i
\(698\) −28.4665 −1.07747
\(699\) 0 0
\(700\) 0 0
\(701\) 3.16006 0.119354 0.0596770 0.998218i \(-0.480993\pi\)
0.0596770 + 0.998218i \(0.480993\pi\)
\(702\) 0 0
\(703\) 3.94398 6.83118i 0.148750 0.257643i
\(704\) 7.11984 0.268339
\(705\) 0 0
\(706\) −21.1402 + 36.6159i −0.795622 + 1.37806i
\(707\) 0 0
\(708\) 0 0
\(709\) 10.7606 18.6378i 0.404121 0.699959i −0.590097 0.807332i \(-0.700911\pi\)
0.994219 + 0.107373i \(0.0342440\pi\)
\(710\) 37.0087 64.1009i 1.38891 2.40567i
\(711\) 0 0
\(712\) −4.87385 8.44176i −0.182655 0.316368i
\(713\) 0.119956 + 0.207769i 0.00449237 + 0.00778102i
\(714\) 0 0
\(715\) −11.9826 + 20.7545i −0.448125 + 0.776175i
\(716\) −2.57898 −0.0963812
\(717\) 0 0
\(718\) −35.3570 −1.31951
\(719\) −9.41508 16.3074i −0.351123 0.608163i 0.635323 0.772246i \(-0.280867\pi\)
−0.986447 + 0.164083i \(0.947533\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 12.2040 + 21.1379i 0.454185 + 0.786671i
\(723\) 0 0
\(724\) −1.94957 3.37675i −0.0724551 0.125496i
\(725\) 22.7618 + 39.4247i 0.845354 + 1.46420i
\(726\) 0 0
\(727\) −19.5426 33.8489i −0.724797 1.25538i −0.959058 0.283211i \(-0.908600\pi\)
0.234261 0.972174i \(-0.424733\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −16.1153 27.9125i −0.596454 1.03309i
\(731\) −4.58167 −0.169459
\(732\) 0 0
\(733\) 18.5985 0.686951 0.343475 0.939162i \(-0.388396\pi\)
0.343475 + 0.939162i \(0.388396\pi\)
\(734\) −19.2119 + 33.2759i −0.709123 + 1.22824i
\(735\) 0 0
\(736\) 3.25621 + 5.63993i 0.120026 + 0.207890i
\(737\) 24.0977 + 41.7385i 0.887651 + 1.53746i
\(738\) 0 0
\(739\) −2.75068 + 4.76432i −0.101185 + 0.175258i −0.912173 0.409805i \(-0.865597\pi\)
0.810988 + 0.585063i \(0.198930\pi\)
\(740\) 6.16306 10.6747i 0.226559 0.392411i
\(741\) 0 0
\(742\) 0 0
\(743\) −10.2326 + 17.7234i −0.375399 + 0.650210i −0.990387 0.138327i \(-0.955828\pi\)
0.614988 + 0.788537i \(0.289161\pi\)
\(744\) 0 0
\(745\) 20.2855 0.743201
\(746\) 28.0892 48.6520i 1.02842 1.78128i
\(747\) 0 0
\(748\) −7.19489 −0.263071
\(749\) 0 0
\(750\) 0 0
\(751\) 38.0460 1.38832 0.694159 0.719822i \(-0.255777\pi\)
0.694159 + 0.719822i \(0.255777\pi\)
\(752\) 14.3007 + 24.7696i 0.521494 + 0.903254i
\(753\) 0 0
\(754\) −6.00135 + 10.3946i −0.218556 + 0.378551i
\(755\) 7.11744 0.259030
\(756\) 0 0
\(757\) −51.0780 −1.85646 −0.928230 0.372006i \(-0.878670\pi\)
−0.928230 + 0.372006i \(0.878670\pi\)
\(758\) −1.33329 + 2.30933i −0.0484273 + 0.0838786i
\(759\) 0 0
\(760\) 6.81295 + 11.8004i 0.247132 + 0.428045i
\(761\) 40.0749 1.45271 0.726357 0.687317i \(-0.241212\pi\)
0.726357 + 0.687317i \(0.241212\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 17.8633 0.646273
\(765\) 0 0
\(766\) 27.3058 47.2951i 0.986599 1.70884i
\(767\) −12.6239 −0.455822
\(768\) 0 0
\(769\) 22.4828 38.9414i 0.810751 1.40426i −0.101587 0.994827i \(-0.532392\pi\)
0.912339 0.409436i \(-0.134274\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.0992886 0.171973i 0.00357348 0.00618944i
\(773\) −12.1781 + 21.0930i −0.438014 + 0.758663i −0.997536 0.0701524i \(-0.977651\pi\)
0.559522 + 0.828816i \(0.310985\pi\)
\(774\) 0 0
\(775\) 0.691096 + 1.19701i 0.0248249 + 0.0429980i
\(776\) −14.4998 25.1145i −0.520514 0.901556i
\(777\) 0 0
\(778\) −4.52913 + 7.84468i −0.162377 + 0.281245i
\(779\) −7.42416 −0.265998
\(780\) 0 0
\(781\) 74.3377 2.66001
\(782\) 1.32354 + 2.29243i 0.0473296 + 0.0819773i
\(783\) 0 0
\(784\) 0 0
\(785\) −5.35200 9.26993i −0.191021 0.330858i
\(786\) 0 0
\(787\) −20.7617 35.9603i −0.740073 1.28184i −0.952461 0.304659i \(-0.901457\pi\)
0.212388 0.977185i \(-0.431876\pi\)
\(788\) −0.800331 1.38621i −0.0285106 0.0493818i
\(789\) 0 0
\(790\) 27.9481 + 48.4075i 0.994349 + 1.72226i
\(791\) 0 0
\(792\) 0 0
\(793\) 6.72289 + 11.6444i 0.238737 + 0.413504i
\(794\) 0.0477147 0.00169333
\(795\) 0 0
\(796\) 6.17372 0.218822
\(797\)