Properties

Label 1323.2.o.e.440.3
Level $1323$
Weight $2$
Character 1323.440
Analytic conductor $10.564$
Analytic rank $0$
Dimension $48$
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.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 440.3
Character \(\chi\) \(=\) 1323.440
Dual form 1323.2.o.e.881.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.80506 - 1.04215i) q^{2} +(1.17216 + 2.03024i) q^{4} +(-1.65233 - 2.86191i) q^{5} -0.717672i q^{8} +O(q^{10})\) \(q+(-1.80506 - 1.04215i) q^{2} +(1.17216 + 2.03024i) q^{4} +(-1.65233 - 2.86191i) q^{5} -0.717672i q^{8} +6.88790i q^{10} +(-2.30482 - 1.33069i) q^{11} +(2.11249 - 1.21964i) q^{13} +(1.59640 - 2.76504i) q^{16} +7.18034 q^{17} -4.90454i q^{19} +(3.87358 - 6.70924i) q^{20} +(2.77356 + 4.80394i) q^{22} +(4.32174 - 2.49516i) q^{23} +(-2.96036 + 5.12749i) q^{25} -5.08422 q^{26} +(-5.50701 - 3.17947i) q^{29} +(2.30833 - 1.33271i) q^{31} +(-7.00624 + 4.04505i) q^{32} +(-12.9609 - 7.48301i) q^{34} -1.68957 q^{37} +(-5.11128 + 8.85299i) q^{38} +(-2.05391 + 1.18583i) q^{40} +(-0.553137 - 0.958062i) q^{41} +(2.93481 - 5.08323i) q^{43} -6.23912i q^{44} -10.4013 q^{46} +(-2.44098 + 4.22790i) q^{47} +(10.6873 - 6.17029i) q^{50} +(4.95235 + 2.85924i) q^{52} -10.3232i q^{53} +8.79491i q^{55} +(6.62698 + 11.4783i) q^{58} +(2.56820 + 4.44826i) q^{59} +(4.44613 + 2.56698i) q^{61} -5.55556 q^{62} +10.4766 q^{64} +(-6.98103 - 4.03050i) q^{65} +(-4.16544 - 7.21476i) q^{67} +(8.41652 + 14.5778i) q^{68} +2.07026i q^{71} +8.01491i q^{73} +(3.04978 + 1.76079i) q^{74} +(9.95741 - 5.74891i) q^{76} +(-2.50501 + 4.33881i) q^{79} -10.5511 q^{80} +2.30581i q^{82} +(-1.04482 + 1.80968i) q^{83} +(-11.8643 - 20.5495i) q^{85} +(-10.5950 + 6.11703i) q^{86} +(-0.954997 + 1.65410i) q^{88} -1.08253 q^{89} +(10.1315 + 5.84945i) q^{92} +(8.81223 - 5.08774i) q^{94} +(-14.0364 + 8.10390i) q^{95} +(-9.47203 - 5.46868i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 24q^{4} + O(q^{10}) \) \( 48q + 24q^{4} + 24q^{11} - 24q^{16} + 48q^{23} - 24q^{25} - 120q^{32} - 48q^{50} - 48q^{64} - 120q^{65} + 168q^{74} - 24q^{79} - 24q^{85} - 24q^{86} + 144q^{92} - 96q^{95} + O(q^{100}) \)

Character values

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

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.80506 1.04215i −1.27637 0.736913i −0.300191 0.953879i \(-0.597050\pi\)
−0.976179 + 0.216966i \(0.930384\pi\)
\(3\) 0 0
\(4\) 1.17216 + 2.03024i 0.586081 + 1.01512i
\(5\) −1.65233 2.86191i −0.738942 1.27989i −0.952972 0.303059i \(-0.901992\pi\)
0.214029 0.976827i \(-0.431341\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0.717672i 0.253735i
\(9\) 0 0
\(10\) 6.88790i 2.17814i
\(11\) −2.30482 1.33069i −0.694929 0.401217i 0.110527 0.993873i \(-0.464746\pi\)
−0.805456 + 0.592656i \(0.798079\pi\)
\(12\) 0 0
\(13\) 2.11249 1.21964i 0.585899 0.338269i −0.177576 0.984107i \(-0.556825\pi\)
0.763474 + 0.645839i \(0.223492\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.59640 2.76504i 0.399100 0.691261i
\(17\) 7.18034 1.74149 0.870744 0.491736i \(-0.163637\pi\)
0.870744 + 0.491736i \(0.163637\pi\)
\(18\) 0 0
\(19\) 4.90454i 1.12518i −0.826736 0.562589i \(-0.809805\pi\)
0.826736 0.562589i \(-0.190195\pi\)
\(20\) 3.87358 6.70924i 0.866160 1.50023i
\(21\) 0 0
\(22\) 2.77356 + 4.80394i 0.591324 + 1.02420i
\(23\) 4.32174 2.49516i 0.901145 0.520276i 0.0235732 0.999722i \(-0.492496\pi\)
0.877571 + 0.479446i \(0.159162\pi\)
\(24\) 0 0
\(25\) −2.96036 + 5.12749i −0.592072 + 1.02550i
\(26\) −5.08422 −0.997098
\(27\) 0 0
\(28\) 0 0
\(29\) −5.50701 3.17947i −1.02263 0.590413i −0.107762 0.994177i \(-0.534368\pi\)
−0.914863 + 0.403764i \(0.867702\pi\)
\(30\) 0 0
\(31\) 2.30833 1.33271i 0.414588 0.239362i −0.278171 0.960531i \(-0.589728\pi\)
0.692759 + 0.721169i \(0.256395\pi\)
\(32\) −7.00624 + 4.04505i −1.23854 + 0.715071i
\(33\) 0 0
\(34\) −12.9609 7.48301i −2.22278 1.28333i
\(35\) 0 0
\(36\) 0 0
\(37\) −1.68957 −0.277764 −0.138882 0.990309i \(-0.544351\pi\)
−0.138882 + 0.990309i \(0.544351\pi\)
\(38\) −5.11128 + 8.85299i −0.829159 + 1.43614i
\(39\) 0 0
\(40\) −2.05391 + 1.18583i −0.324752 + 0.187496i
\(41\) −0.553137 0.958062i −0.0863855 0.149624i 0.819595 0.572943i \(-0.194198\pi\)
−0.905981 + 0.423319i \(0.860865\pi\)
\(42\) 0 0
\(43\) 2.93481 5.08323i 0.447554 0.775186i −0.550672 0.834721i \(-0.685629\pi\)
0.998226 + 0.0595356i \(0.0189620\pi\)
\(44\) 6.23912i 0.940582i
\(45\) 0 0
\(46\) −10.4013 −1.53359
\(47\) −2.44098 + 4.22790i −0.356053 + 0.616703i −0.987298 0.158881i \(-0.949211\pi\)
0.631244 + 0.775584i \(0.282545\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 10.6873 6.17029i 1.51141 0.872610i
\(51\) 0 0
\(52\) 4.95235 + 2.85924i 0.686767 + 0.396505i
\(53\) 10.3232i 1.41800i −0.705210 0.708999i \(-0.749147\pi\)
0.705210 0.708999i \(-0.250853\pi\)
\(54\) 0 0
\(55\) 8.79491i 1.18591i
\(56\) 0 0
\(57\) 0 0
\(58\) 6.62698 + 11.4783i 0.870166 + 1.50717i
\(59\) 2.56820 + 4.44826i 0.334351 + 0.579114i 0.983360 0.181667i \(-0.0581494\pi\)
−0.649009 + 0.760781i \(0.724816\pi\)
\(60\) 0 0
\(61\) 4.44613 + 2.56698i 0.569269 + 0.328668i 0.756857 0.653580i \(-0.226734\pi\)
−0.187588 + 0.982248i \(0.560067\pi\)
\(62\) −5.55556 −0.705556
\(63\) 0 0
\(64\) 10.4766 1.30958
\(65\) −6.98103 4.03050i −0.865891 0.499922i
\(66\) 0 0
\(67\) −4.16544 7.21476i −0.508890 0.881423i −0.999947 0.0102956i \(-0.996723\pi\)
0.491057 0.871127i \(-0.336611\pi\)
\(68\) 8.41652 + 14.5778i 1.02065 + 1.76782i
\(69\) 0 0
\(70\) 0 0
\(71\) 2.07026i 0.245695i 0.992426 + 0.122848i \(0.0392026\pi\)
−0.992426 + 0.122848i \(0.960797\pi\)
\(72\) 0 0
\(73\) 8.01491i 0.938075i 0.883178 + 0.469037i \(0.155399\pi\)
−0.883178 + 0.469037i \(0.844601\pi\)
\(74\) 3.04978 + 1.76079i 0.354530 + 0.204688i
\(75\) 0 0
\(76\) 9.95741 5.74891i 1.14219 0.659445i
\(77\) 0 0
\(78\) 0 0
\(79\) −2.50501 + 4.33881i −0.281836 + 0.488155i −0.971837 0.235654i \(-0.924277\pi\)
0.690001 + 0.723809i \(0.257610\pi\)
\(80\) −10.5511 −1.17965
\(81\) 0 0
\(82\) 2.30581i 0.254634i
\(83\) −1.04482 + 1.80968i −0.114684 + 0.198638i −0.917653 0.397382i \(-0.869919\pi\)
0.802970 + 0.596020i \(0.203252\pi\)
\(84\) 0 0
\(85\) −11.8643 20.5495i −1.28686 2.22891i
\(86\) −10.5950 + 6.11703i −1.14249 + 0.659616i
\(87\) 0 0
\(88\) −0.954997 + 1.65410i −0.101803 + 0.176328i
\(89\) −1.08253 −0.114748 −0.0573741 0.998353i \(-0.518273\pi\)
−0.0573741 + 0.998353i \(0.518273\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 10.1315 + 5.84945i 1.05629 + 0.609847i
\(93\) 0 0
\(94\) 8.81223 5.08774i 0.908912 0.524761i
\(95\) −14.0364 + 8.10390i −1.44010 + 0.831442i
\(96\) 0 0
\(97\) −9.47203 5.46868i −0.961739 0.555260i −0.0650310 0.997883i \(-0.520715\pi\)
−0.896708 + 0.442623i \(0.854048\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −13.8801 −1.38801
\(101\) 0.263957 0.457188i 0.0262647 0.0454919i −0.852594 0.522573i \(-0.824972\pi\)
0.878859 + 0.477082i \(0.158305\pi\)
\(102\) 0 0
\(103\) 0.678733 0.391867i 0.0668775 0.0386118i −0.466188 0.884685i \(-0.654373\pi\)
0.533066 + 0.846074i \(0.321040\pi\)
\(104\) −0.875305 1.51607i −0.0858308 0.148663i
\(105\) 0 0
\(106\) −10.7583 + 18.6340i −1.04494 + 1.80989i
\(107\) 5.35086i 0.517288i 0.965973 + 0.258644i \(0.0832756\pi\)
−0.965973 + 0.258644i \(0.916724\pi\)
\(108\) 0 0
\(109\) 5.96522 0.571364 0.285682 0.958324i \(-0.407780\pi\)
0.285682 + 0.958324i \(0.407780\pi\)
\(110\) 9.16563 15.8753i 0.873909 1.51365i
\(111\) 0 0
\(112\) 0 0
\(113\) −10.0024 + 5.77487i −0.940944 + 0.543254i −0.890256 0.455461i \(-0.849475\pi\)
−0.0506876 + 0.998715i \(0.516141\pi\)
\(114\) 0 0
\(115\) −14.2818 8.24562i −1.33179 0.768908i
\(116\) 14.9074i 1.38412i
\(117\) 0 0
\(118\) 10.7058i 0.985551i
\(119\) 0 0
\(120\) 0 0
\(121\) −1.95854 3.39230i −0.178049 0.308391i
\(122\) −5.35036 9.26709i −0.484399 0.839003i
\(123\) 0 0
\(124\) 5.41146 + 3.12431i 0.485963 + 0.280571i
\(125\) 3.04265 0.272143
\(126\) 0 0
\(127\) −19.0954 −1.69444 −0.847221 0.531241i \(-0.821726\pi\)
−0.847221 + 0.531241i \(0.821726\pi\)
\(128\) −4.89849 2.82815i −0.432970 0.249975i
\(129\) 0 0
\(130\) 8.40079 + 14.5506i 0.736798 + 1.27617i
\(131\) −2.07563 3.59509i −0.181349 0.314105i 0.760991 0.648762i \(-0.224713\pi\)
−0.942340 + 0.334657i \(0.891380\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 17.3641i 1.50003i
\(135\) 0 0
\(136\) 5.15313i 0.441877i
\(137\) 5.45092 + 3.14709i 0.465704 + 0.268874i 0.714440 0.699697i \(-0.246682\pi\)
−0.248736 + 0.968571i \(0.580015\pi\)
\(138\) 0 0
\(139\) 1.32575 0.765423i 0.112449 0.0649223i −0.442721 0.896660i \(-0.645987\pi\)
0.555170 + 0.831737i \(0.312653\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 2.15753 3.73695i 0.181056 0.313598i
\(143\) −6.49186 −0.542877
\(144\) 0 0
\(145\) 21.0141i 1.74513i
\(146\) 8.35276 14.4674i 0.691279 1.19733i
\(147\) 0 0
\(148\) −1.98045 3.43025i −0.162792 0.281965i
\(149\) 4.63163 2.67407i 0.379438 0.219069i −0.298136 0.954523i \(-0.596365\pi\)
0.677574 + 0.735455i \(0.263031\pi\)
\(150\) 0 0
\(151\) −5.74384 + 9.94862i −0.467427 + 0.809607i −0.999307 0.0372121i \(-0.988152\pi\)
0.531880 + 0.846820i \(0.321486\pi\)
\(152\) −3.51985 −0.285498
\(153\) 0 0
\(154\) 0 0
\(155\) −7.62821 4.40415i −0.612713 0.353750i
\(156\) 0 0
\(157\) 5.77243 3.33271i 0.460690 0.265979i −0.251644 0.967820i \(-0.580971\pi\)
0.712334 + 0.701840i \(0.247638\pi\)
\(158\) 9.04340 5.22121i 0.719454 0.415377i
\(159\) 0 0
\(160\) 23.1532 + 13.3675i 1.83042 + 1.05679i
\(161\) 0 0
\(162\) 0 0
\(163\) −23.0921 −1.80871 −0.904356 0.426778i \(-0.859649\pi\)
−0.904356 + 0.426778i \(0.859649\pi\)
\(164\) 1.29673 2.24601i 0.101258 0.175384i
\(165\) 0 0
\(166\) 3.77192 2.17772i 0.292757 0.169024i
\(167\) 7.95418 + 13.7770i 0.615513 + 1.06610i 0.990294 + 0.138986i \(0.0443844\pi\)
−0.374782 + 0.927113i \(0.622282\pi\)
\(168\) 0 0
\(169\) −3.52493 + 6.10536i −0.271149 + 0.469643i
\(170\) 49.4575i 3.79321i
\(171\) 0 0
\(172\) 13.7603 1.04921
\(173\) 9.33097 16.1617i 0.709421 1.22875i −0.255651 0.966769i \(-0.582290\pi\)
0.965072 0.261984i \(-0.0843767\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −7.35882 + 4.24861i −0.554692 + 0.320251i
\(177\) 0 0
\(178\) 1.95404 + 1.12816i 0.146461 + 0.0845595i
\(179\) 22.0307i 1.64665i 0.567568 + 0.823326i \(0.307884\pi\)
−0.567568 + 0.823326i \(0.692116\pi\)
\(180\) 0 0
\(181\) 17.6986i 1.31552i 0.753226 + 0.657762i \(0.228497\pi\)
−0.753226 + 0.657762i \(0.771503\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1.79070 3.10159i −0.132012 0.228652i
\(185\) 2.79173 + 4.83541i 0.205252 + 0.355507i
\(186\) 0 0
\(187\) −16.5494 9.55479i −1.21021 0.698715i
\(188\) −11.4449 −0.834704
\(189\) 0 0
\(190\) 33.7820 2.45080
\(191\) −13.2711 7.66209i −0.960265 0.554409i −0.0640104 0.997949i \(-0.520389\pi\)
−0.896255 + 0.443540i \(0.853722\pi\)
\(192\) 0 0
\(193\) −12.9333 22.4012i −0.930962 1.61247i −0.781681 0.623678i \(-0.785638\pi\)
−0.149280 0.988795i \(-0.547696\pi\)
\(194\) 11.3984 + 19.7426i 0.818356 + 1.41744i
\(195\) 0 0
\(196\) 0 0
\(197\) 4.18301i 0.298027i −0.988835 0.149014i \(-0.952390\pi\)
0.988835 0.149014i \(-0.0476098\pi\)
\(198\) 0 0
\(199\) 22.0077i 1.56008i −0.625729 0.780041i \(-0.715198\pi\)
0.625729 0.780041i \(-0.284802\pi\)
\(200\) 3.67986 + 2.12457i 0.260205 + 0.150230i
\(201\) 0 0
\(202\) −0.952918 + 0.550168i −0.0670471 + 0.0387097i
\(203\) 0 0
\(204\) 0 0
\(205\) −1.82793 + 3.16606i −0.127668 + 0.221127i
\(206\) −1.63354 −0.113814
\(207\) 0 0
\(208\) 7.78816i 0.540012i
\(209\) −6.52641 + 11.3041i −0.451441 + 0.781919i
\(210\) 0 0
\(211\) 12.2926 + 21.2914i 0.846257 + 1.46576i 0.884525 + 0.466493i \(0.154483\pi\)
−0.0382677 + 0.999268i \(0.512184\pi\)
\(212\) 20.9586 12.1004i 1.43944 0.831061i
\(213\) 0 0
\(214\) 5.57641 9.65863i 0.381196 0.660250i
\(215\) −19.3970 −1.32287
\(216\) 0 0
\(217\) 0 0
\(218\) −10.7676 6.21666i −0.729272 0.421045i
\(219\) 0 0
\(220\) −17.8558 + 10.3091i −1.20384 + 0.695036i
\(221\) 15.1684 8.75747i 1.02034 0.589091i
\(222\) 0 0
\(223\) −7.31908 4.22567i −0.490122 0.282972i 0.234503 0.972115i \(-0.424654\pi\)
−0.724625 + 0.689143i \(0.757987\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 24.0732 1.60132
\(227\) 2.91475 5.04849i 0.193458 0.335080i −0.752936 0.658094i \(-0.771363\pi\)
0.946394 + 0.323014i \(0.104696\pi\)
\(228\) 0 0
\(229\) 4.15541 2.39913i 0.274597 0.158539i −0.356378 0.934342i \(-0.615988\pi\)
0.630975 + 0.775803i \(0.282655\pi\)
\(230\) 17.1864 + 29.7677i 1.13324 + 1.96282i
\(231\) 0 0
\(232\) −2.28182 + 3.95223i −0.149809 + 0.259476i
\(233\) 23.0463i 1.50981i −0.655831 0.754907i \(-0.727682\pi\)
0.655831 0.754907i \(-0.272318\pi\)
\(234\) 0 0
\(235\) 16.1332 1.05241
\(236\) −6.02069 + 10.4281i −0.391914 + 0.678815i
\(237\) 0 0
\(238\) 0 0
\(239\) −5.91972 + 3.41775i −0.382915 + 0.221076i −0.679086 0.734059i \(-0.737624\pi\)
0.296171 + 0.955135i \(0.404290\pi\)
\(240\) 0 0
\(241\) −3.89112 2.24654i −0.250649 0.144712i 0.369412 0.929266i \(-0.379559\pi\)
−0.620061 + 0.784553i \(0.712892\pi\)
\(242\) 8.16440i 0.524828i
\(243\) 0 0
\(244\) 12.0356i 0.770503i
\(245\) 0 0
\(246\) 0 0
\(247\) −5.98180 10.3608i −0.380613 0.659241i
\(248\) −0.956451 1.65662i −0.0607347 0.105196i
\(249\) 0 0
\(250\) −5.49217 3.17091i −0.347355 0.200546i
\(251\) 0.467438 0.0295044 0.0147522 0.999891i \(-0.495304\pi\)
0.0147522 + 0.999891i \(0.495304\pi\)
\(252\) 0 0
\(253\) −13.2811 −0.834975
\(254\) 34.4683 + 19.9003i 2.16273 + 1.24866i
\(255\) 0 0
\(256\) −4.58192 7.93613i −0.286370 0.496008i
\(257\) 10.7433 + 18.6079i 0.670146 + 1.16073i 0.977862 + 0.209249i \(0.0671020\pi\)
−0.307716 + 0.951478i \(0.599565\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 18.8976i 1.17198i
\(261\) 0 0
\(262\) 8.65248i 0.534552i
\(263\) −9.60394 5.54484i −0.592205 0.341909i 0.173764 0.984787i \(-0.444407\pi\)
−0.765969 + 0.642878i \(0.777740\pi\)
\(264\) 0 0
\(265\) −29.5440 + 17.0572i −1.81487 + 1.04782i
\(266\) 0 0
\(267\) 0 0
\(268\) 9.76514 16.9137i 0.596501 1.03317i
\(269\) 22.0575 1.34487 0.672435 0.740156i \(-0.265248\pi\)
0.672435 + 0.740156i \(0.265248\pi\)
\(270\) 0 0
\(271\) 4.74436i 0.288199i −0.989563 0.144100i \(-0.953971\pi\)
0.989563 0.144100i \(-0.0460286\pi\)
\(272\) 11.4627 19.8540i 0.695028 1.20382i
\(273\) 0 0
\(274\) −6.55950 11.3614i −0.396274 0.686366i
\(275\) 13.6462 7.87862i 0.822895 0.475099i
\(276\) 0 0
\(277\) 3.21329 5.56558i 0.193068 0.334404i −0.753197 0.657794i \(-0.771490\pi\)
0.946265 + 0.323391i \(0.104823\pi\)
\(278\) −3.19075 −0.191368
\(279\) 0 0
\(280\) 0 0
\(281\) 17.0883 + 9.86595i 1.01940 + 0.588553i 0.913931 0.405869i \(-0.133031\pi\)
0.105473 + 0.994422i \(0.466364\pi\)
\(282\) 0 0
\(283\) 4.85087 2.80065i 0.288354 0.166481i −0.348845 0.937180i \(-0.613426\pi\)
0.637199 + 0.770699i \(0.280093\pi\)
\(284\) −4.20314 + 2.42668i −0.249410 + 0.143997i
\(285\) 0 0
\(286\) 11.7182 + 6.76551i 0.692912 + 0.400053i
\(287\) 0 0
\(288\) 0 0
\(289\) 34.5573 2.03278
\(290\) 21.8999 37.9317i 1.28600 2.22743i
\(291\) 0 0
\(292\) −16.2722 + 9.39477i −0.952260 + 0.549787i
\(293\) −15.0393 26.0488i −0.878603 1.52178i −0.852875 0.522115i \(-0.825143\pi\)
−0.0257278 0.999669i \(-0.508190\pi\)
\(294\) 0 0
\(295\) 8.48701 14.6999i 0.494133 0.855863i
\(296\) 1.21256i 0.0704787i
\(297\) 0 0
\(298\) −11.1472 −0.645738
\(299\) 6.08641 10.5420i 0.351986 0.609658i
\(300\) 0 0
\(301\) 0 0
\(302\) 20.7360 11.9719i 1.19322 0.688906i
\(303\) 0 0
\(304\) −13.5613 7.82960i −0.777792 0.449059i
\(305\) 16.9659i 0.971466i
\(306\) 0 0
\(307\) 23.4497i 1.33835i −0.743106 0.669173i \(-0.766648\pi\)
0.743106 0.669173i \(-0.233352\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 9.17959 + 15.8995i 0.521366 + 0.903032i
\(311\) −8.35507 14.4714i −0.473773 0.820599i 0.525776 0.850623i \(-0.323775\pi\)
−0.999549 + 0.0300243i \(0.990442\pi\)
\(312\) 0 0
\(313\) 12.8757 + 7.43377i 0.727776 + 0.420182i 0.817608 0.575775i \(-0.195300\pi\)
−0.0898319 + 0.995957i \(0.528633\pi\)
\(314\) −13.8928 −0.784014
\(315\) 0 0
\(316\) −11.7451 −0.660715
\(317\) −1.96761 1.13600i −0.110512 0.0638040i 0.443725 0.896163i \(-0.353657\pi\)
−0.554237 + 0.832359i \(0.686990\pi\)
\(318\) 0 0
\(319\) 8.46176 + 14.6562i 0.473768 + 0.820590i
\(320\) −17.3108 29.9832i −0.967704 1.67611i
\(321\) 0 0
\(322\) 0 0
\(323\) 35.2163i 1.95949i
\(324\) 0 0
\(325\) 14.4423i 0.801117i
\(326\) 41.6826 + 24.0655i 2.30859 + 1.33286i
\(327\) 0 0
\(328\) −0.687575 + 0.396971i −0.0379650 + 0.0219191i
\(329\) 0 0
\(330\) 0 0
\(331\) 5.97440 10.3480i 0.328383 0.568775i −0.653808 0.756660i \(-0.726830\pi\)
0.982191 + 0.187885i \(0.0601631\pi\)
\(332\) −4.89878 −0.268855
\(333\) 0 0
\(334\) 33.1578i 1.81432i
\(335\) −13.7653 + 23.8423i −0.752080 + 1.30264i
\(336\) 0 0
\(337\) 2.34636 + 4.06402i 0.127815 + 0.221381i 0.922830 0.385208i \(-0.125870\pi\)
−0.795015 + 0.606590i \(0.792537\pi\)
\(338\) 12.7254 7.34703i 0.692172 0.399626i
\(339\) 0 0
\(340\) 27.8137 48.1747i 1.50841 2.61264i
\(341\) −7.09369 −0.384145
\(342\) 0 0
\(343\) 0 0
\(344\) −3.64810 2.10623i −0.196692 0.113560i
\(345\) 0 0
\(346\) −33.6859 + 19.4486i −1.81097 + 1.04556i
\(347\) −6.40529 + 3.69809i −0.343854 + 0.198524i −0.661975 0.749526i \(-0.730281\pi\)
0.318121 + 0.948050i \(0.396948\pi\)
\(348\) 0 0
\(349\) 18.0496 + 10.4209i 0.966171 + 0.557819i 0.898067 0.439859i \(-0.144972\pi\)
0.0681042 + 0.997678i \(0.478305\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 21.5308 1.14760
\(353\) −3.54953 + 6.14797i −0.188923 + 0.327224i −0.944891 0.327384i \(-0.893833\pi\)
0.755969 + 0.654608i \(0.227166\pi\)
\(354\) 0 0
\(355\) 5.92491 3.42075i 0.314462 0.181554i
\(356\) −1.26890 2.19780i −0.0672517 0.116483i
\(357\) 0 0
\(358\) 22.9593 39.7668i 1.21344 2.10174i
\(359\) 9.89233i 0.522097i −0.965326 0.261049i \(-0.915932\pi\)
0.965326 0.261049i \(-0.0840683\pi\)
\(360\) 0 0
\(361\) −5.05452 −0.266027
\(362\) 18.4446 31.9470i 0.969426 1.67910i
\(363\) 0 0
\(364\) 0 0
\(365\) 22.9380 13.2432i 1.20063 0.693183i
\(366\) 0 0
\(367\) 27.0321 + 15.6070i 1.41107 + 0.814680i 0.995489 0.0948779i \(-0.0302461\pi\)
0.415578 + 0.909558i \(0.363579\pi\)
\(368\) 15.9331i 0.830568i
\(369\) 0 0
\(370\) 11.6376i 0.605011i
\(371\) 0 0
\(372\) 0 0
\(373\) −14.5232 25.1549i −0.751981 1.30247i −0.946861 0.321642i \(-0.895765\pi\)
0.194881 0.980827i \(-0.437568\pi\)
\(374\) 19.9151 + 34.4939i 1.02978 + 1.78364i
\(375\) 0 0
\(376\) 3.03425 + 1.75182i 0.156479 + 0.0903434i
\(377\) −15.5113 −0.798873
\(378\) 0 0
\(379\) −0.518354 −0.0266261 −0.0133130 0.999911i \(-0.504238\pi\)
−0.0133130 + 0.999911i \(0.504238\pi\)
\(380\) −32.9058 18.9981i −1.68803 0.974584i
\(381\) 0 0
\(382\) 15.9701 + 27.6611i 0.817102 + 1.41526i
\(383\) −6.60511 11.4404i −0.337505 0.584576i 0.646458 0.762950i \(-0.276250\pi\)
−0.983963 + 0.178374i \(0.942916\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 53.9140i 2.74415i
\(387\) 0 0
\(388\) 25.6407i 1.30171i
\(389\) 29.2921 + 16.9118i 1.48517 + 0.857461i 0.999857 0.0168815i \(-0.00537382\pi\)
0.485309 + 0.874343i \(0.338707\pi\)
\(390\) 0 0
\(391\) 31.0316 17.9161i 1.56933 0.906055i
\(392\) 0 0
\(393\) 0 0
\(394\) −4.35933 + 7.55059i −0.219620 + 0.380393i
\(395\) 16.5564 0.833043
\(396\) 0 0
\(397\) 8.57345i 0.430289i 0.976582 + 0.215145i \(0.0690223\pi\)
−0.976582 + 0.215145i \(0.930978\pi\)
\(398\) −22.9353 + 39.7251i −1.14964 + 1.99124i
\(399\) 0 0
\(400\) 9.45183 + 16.3710i 0.472591 + 0.818552i
\(401\) −13.9743 + 8.06808i −0.697844 + 0.402900i −0.806544 0.591174i \(-0.798665\pi\)
0.108700 + 0.994075i \(0.465331\pi\)
\(402\) 0 0
\(403\) 3.25087 5.63068i 0.161938 0.280484i
\(404\) 1.23760 0.0615730
\(405\) 0 0
\(406\) 0 0
\(407\) 3.89416 + 2.24830i 0.193026 + 0.111444i
\(408\) 0 0
\(409\) 14.1364 8.16165i 0.699000 0.403568i −0.107975 0.994154i \(-0.534437\pi\)
0.806975 + 0.590586i \(0.201103\pi\)
\(410\) 6.59903 3.80995i 0.325903 0.188160i
\(411\) 0 0
\(412\) 1.59117 + 0.918662i 0.0783913 + 0.0452592i
\(413\) 0 0
\(414\) 0 0
\(415\) 6.90551 0.338978
\(416\) −9.86706 + 17.0902i −0.483772 + 0.837918i
\(417\) 0 0
\(418\) 23.5611 13.6030i 1.15241 0.665345i
\(419\) 0.589031 + 1.02023i 0.0287760 + 0.0498415i 0.880055 0.474872i \(-0.157506\pi\)
−0.851279 + 0.524714i \(0.824172\pi\)
\(420\) 0 0
\(421\) 3.43544 5.95035i 0.167433 0.290002i −0.770084 0.637943i \(-0.779786\pi\)
0.937517 + 0.347941i \(0.113119\pi\)
\(422\) 51.2430i 2.49447i
\(423\) 0 0
\(424\) −7.40866 −0.359796
\(425\) −21.2564 + 36.8172i −1.03109 + 1.78589i
\(426\) 0 0
\(427\) 0 0
\(428\) −10.8636 + 6.27208i −0.525110 + 0.303172i
\(429\) 0 0
\(430\) 35.0128 + 20.2146i 1.68847 + 0.974837i
\(431\) 0.811164i 0.0390724i 0.999809 + 0.0195362i \(0.00621896\pi\)
−0.999809 + 0.0195362i \(0.993781\pi\)
\(432\) 0 0
\(433\) 8.59662i 0.413127i −0.978433 0.206564i \(-0.933772\pi\)
0.978433 0.206564i \(-0.0662280\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 6.99219 + 12.1108i 0.334865 + 0.580004i
\(437\) −12.2376 21.1961i −0.585404 1.01395i
\(438\) 0 0
\(439\) −23.8968 13.7968i −1.14053 0.658486i −0.193969 0.981008i \(-0.562136\pi\)
−0.946562 + 0.322522i \(0.895470\pi\)
\(440\) 6.31186 0.300906
\(441\) 0 0
\(442\) −36.5065 −1.73643
\(443\) 10.6051 + 6.12286i 0.503864 + 0.290906i 0.730308 0.683118i \(-0.239377\pi\)
−0.226444 + 0.974024i \(0.572710\pi\)
\(444\) 0 0
\(445\) 1.78870 + 3.09811i 0.0847924 + 0.146865i
\(446\) 8.80759 + 15.2552i 0.417051 + 0.722354i
\(447\) 0 0
\(448\) 0 0
\(449\) 22.0163i 1.03901i −0.854466 0.519507i \(-0.826116\pi\)
0.854466 0.519507i \(-0.173884\pi\)
\(450\) 0 0
\(451\) 2.94421i 0.138637i
\(452\) −23.4488 13.5382i −1.10294 0.636781i
\(453\) 0 0
\(454\) −10.5226 + 6.07522i −0.493849 + 0.285124i
\(455\) 0 0
\(456\) 0 0
\(457\) −12.0780 + 20.9196i −0.564983 + 0.978579i 0.432069 + 0.901841i \(0.357784\pi\)
−0.997051 + 0.0767380i \(0.975550\pi\)
\(458\) −10.0010 −0.467317
\(459\) 0 0
\(460\) 38.6608i 1.80257i
\(461\) 16.3899 28.3881i 0.763352 1.32216i −0.177762 0.984074i \(-0.556886\pi\)
0.941114 0.338091i \(-0.109781\pi\)
\(462\) 0 0
\(463\) 15.7659 + 27.3074i 0.732704 + 1.26908i 0.955723 + 0.294266i \(0.0950753\pi\)
−0.223020 + 0.974814i \(0.571591\pi\)
\(464\) −17.5828 + 10.1514i −0.816259 + 0.471267i
\(465\) 0 0
\(466\) −24.0178 + 41.6000i −1.11260 + 1.92708i
\(467\) −33.1531 −1.53414 −0.767070 0.641563i \(-0.778286\pi\)
−0.767070 + 0.641563i \(0.778286\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −29.1213 16.8132i −1.34327 0.775536i
\(471\) 0 0
\(472\) 3.19239 1.84313i 0.146942 0.0848368i
\(473\) −13.5284 + 7.81062i −0.622036 + 0.359133i
\(474\) 0 0
\(475\) 25.1480 + 14.5192i 1.15387 + 0.666187i
\(476\) 0 0
\(477\) 0 0
\(478\) 14.2473 0.651655
\(479\) −11.3972 + 19.7406i −0.520754 + 0.901972i 0.478955 + 0.877839i \(0.341016\pi\)
−0.999709 + 0.0241323i \(0.992318\pi\)
\(480\) 0 0
\(481\) −3.56921 + 2.06068i −0.162742 + 0.0939590i
\(482\) 4.68247 + 8.11027i 0.213281 + 0.369413i
\(483\) 0 0
\(484\) 4.59146 7.95264i 0.208703 0.361484i
\(485\) 36.1441i 1.64122i
\(486\) 0 0
\(487\) −2.73119 −0.123762 −0.0618811 0.998084i \(-0.519710\pi\)
−0.0618811 + 0.998084i \(0.519710\pi\)
\(488\) 1.84225 3.19087i 0.0833946 0.144444i
\(489\) 0 0
\(490\) 0 0
\(491\) −21.6775 + 12.5155i −0.978291 + 0.564817i −0.901754 0.432250i \(-0.857720\pi\)
−0.0765375 + 0.997067i \(0.524387\pi\)
\(492\) 0 0
\(493\) −39.5422 22.8297i −1.78089 1.02820i
\(494\) 24.9358i 1.12191i
\(495\) 0 0
\(496\) 8.51016i 0.382118i
\(497\) 0 0
\(498\) 0 0
\(499\) −4.29981 7.44749i −0.192486 0.333395i 0.753588 0.657348i \(-0.228322\pi\)
−0.946073 + 0.323952i \(0.894988\pi\)
\(500\) 3.56648 + 6.17732i 0.159498 + 0.276258i
\(501\) 0 0
\(502\) −0.843754 0.487141i −0.0376586 0.0217422i
\(503\) 39.0362 1.74054 0.870269 0.492577i \(-0.163945\pi\)
0.870269 + 0.492577i \(0.163945\pi\)
\(504\) 0 0
\(505\) −1.74457 −0.0776325
\(506\) 23.9732 + 13.8409i 1.06574 + 0.615304i
\(507\) 0 0
\(508\) −22.3829 38.7683i −0.993079 1.72006i
\(509\) −16.2909 28.2167i −0.722083 1.25068i −0.960163 0.279439i \(-0.909851\pi\)
0.238080 0.971245i \(-0.423482\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 30.4128i 1.34407i
\(513\) 0 0
\(514\) 44.7844i 1.97536i
\(515\) −2.24298 1.29498i −0.0988373 0.0570638i
\(516\) 0 0
\(517\) 11.2520 6.49636i 0.494864 0.285710i
\(518\) 0 0
\(519\) 0 0
\(520\) −2.89258 + 5.01009i −0.126848 + 0.219707i
\(521\) −7.36912 −0.322847 −0.161424 0.986885i \(-0.551609\pi\)
−0.161424 + 0.986885i \(0.551609\pi\)
\(522\) 0 0
\(523\) 43.4157i 1.89843i 0.314622 + 0.949217i \(0.398122\pi\)
−0.314622 + 0.949217i \(0.601878\pi\)
\(524\) 4.86594 8.42806i 0.212570 0.368181i
\(525\) 0 0
\(526\) 11.5571 + 20.0175i 0.503915 + 0.872806i
\(527\) 16.5746 9.56933i 0.722000 0.416847i
\(528\) 0 0
\(529\) 0.951610 1.64824i 0.0413744 0.0716625i
\(530\) 71.1050 3.08860
\(531\) 0 0
\(532\) 0 0
\(533\) −2.33699 1.34926i −0.101226 0.0584430i
\(534\) 0 0
\(535\) 15.3137 8.84137i 0.662069 0.382246i
\(536\) −5.17783 + 2.98942i −0.223648 + 0.129123i
\(537\) 0 0
\(538\) −39.8151 22.9873i −1.71655 0.991052i
\(539\) 0 0
\(540\) 0 0
\(541\) −21.6442 −0.930555 −0.465278 0.885165i \(-0.654045\pi\)
−0.465278 + 0.885165i \(0.654045\pi\)
\(542\) −4.94434 + 8.56385i −0.212378 + 0.367849i
\(543\) 0 0
\(544\) −50.3072 + 29.0449i −2.15690 + 1.24529i
\(545\) −9.85648 17.0719i −0.422205 0.731281i
\(546\) 0 0
\(547\) −11.9092 + 20.6273i −0.509200 + 0.881960i 0.490743 + 0.871304i \(0.336725\pi\)
−0.999943 + 0.0106561i \(0.996608\pi\)
\(548\) 14.7556i 0.630328i
\(549\) 0 0
\(550\) −32.8429 −1.40043
\(551\) −15.5938 + 27.0093i −0.664320 + 1.15064i
\(552\) 0 0
\(553\) 0 0
\(554\) −11.6004 + 6.69748i −0.492852 + 0.284548i
\(555\) 0 0
\(556\) 3.10799 + 1.79440i 0.131808 + 0.0760994i
\(557\) 10.8777i 0.460905i 0.973084 + 0.230452i \(0.0740206\pi\)
−0.973084 + 0.230452i \(0.925979\pi\)
\(558\) 0 0
\(559\) 14.3177i 0.605574i
\(560\) 0 0
\(561\) 0 0
\(562\) −20.5636 35.6173i −0.867425 1.50242i
\(563\) −6.67759 11.5659i −0.281427 0.487445i 0.690310 0.723514i \(-0.257474\pi\)
−0.971736 + 0.236069i \(0.924141\pi\)
\(564\) 0 0
\(565\) 33.0543 + 19.0839i 1.39061 + 0.802867i
\(566\) −11.6748 −0.490729
\(567\) 0 0
\(568\) 1.48577 0.0623415
\(569\) −8.34729 4.81931i −0.349937 0.202036i 0.314721 0.949184i \(-0.398089\pi\)
−0.664657 + 0.747148i \(0.731422\pi\)
\(570\) 0 0
\(571\) 17.2031 + 29.7966i 0.719926 + 1.24695i 0.961028 + 0.276449i \(0.0891578\pi\)
−0.241102 + 0.970500i \(0.577509\pi\)
\(572\) −7.60951 13.1801i −0.318170 0.551086i
\(573\) 0 0
\(574\) 0 0
\(575\) 29.5462i 1.23216i
\(576\) 0 0
\(577\) 24.1352i 1.00476i 0.864647 + 0.502381i \(0.167542\pi\)
−0.864647 + 0.502381i \(0.832458\pi\)
\(578\) −62.3780 36.0140i −2.59458 1.49798i
\(579\) 0 0
\(580\) −42.6637 + 24.6319i −1.77151 + 1.02278i
\(581\) 0 0
\(582\) 0 0
\(583\) −13.7369 + 23.7930i −0.568925 + 0.985407i
\(584\) 5.75208 0.238023
\(585\) 0 0
\(586\) 62.6928i 2.58981i
\(587\) 3.96848 6.87362i 0.163797 0.283704i −0.772431 0.635099i \(-0.780959\pi\)
0.936227 + 0.351395i \(0.114293\pi\)
\(588\) 0 0
\(589\) −6.53634 11.3213i −0.269325 0.466485i
\(590\) −30.6391 + 17.6895i −1.26139 + 0.728266i
\(591\) 0 0
\(592\) −2.69724 + 4.67175i −0.110856 + 0.192008i
\(593\) 41.8293 1.71772 0.858862 0.512207i \(-0.171172\pi\)
0.858862 + 0.512207i \(0.171172\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 10.8580 + 6.26889i 0.444763 + 0.256784i
\(597\) 0 0
\(598\) −21.9727 + 12.6859i −0.898529 + 0.518766i
\(599\) 7.57344 4.37253i 0.309442 0.178657i −0.337235 0.941421i \(-0.609492\pi\)
0.646677 + 0.762764i \(0.276158\pi\)
\(600\) 0 0
\(601\) 12.6427 + 7.29924i 0.515705 + 0.297742i 0.735176 0.677877i \(-0.237100\pi\)
−0.219471 + 0.975619i \(0.570433\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −26.9308 −1.09580
\(605\) −6.47230 + 11.2104i −0.263137 + 0.455766i
\(606\) 0 0
\(607\) −9.51436 + 5.49312i −0.386176 + 0.222959i −0.680502 0.732746i \(-0.738238\pi\)
0.294326 + 0.955705i \(0.404905\pi\)
\(608\) 19.8391 + 34.3624i 0.804583 + 1.39358i
\(609\) 0 0
\(610\) −17.6811 + 30.6245i −0.715885 + 1.23995i
\(611\) 11.9085i 0.481767i
\(612\) 0 0
\(613\) 23.8135 0.961818 0.480909 0.876770i \(-0.340307\pi\)
0.480909 + 0.876770i \(0.340307\pi\)
\(614\) −24.4382 + 42.3282i −0.986244 + 1.70823i
\(615\) 0 0
\(616\) 0 0
\(617\) 36.5255 21.0880i 1.47046 0.848971i 0.471011 0.882127i \(-0.343889\pi\)
0.999450 + 0.0331557i \(0.0105557\pi\)
\(618\) 0 0
\(619\) 22.6532 + 13.0789i 0.910511 + 0.525683i 0.880595 0.473869i \(-0.157143\pi\)
0.0299151 + 0.999552i \(0.490476\pi\)
\(620\) 20.6495i 0.829304i
\(621\) 0 0
\(622\) 34.8290i 1.39652i
\(623\) 0 0
\(624\) 0 0
\(625\) 9.77434 + 16.9297i 0.390974 + 0.677186i
\(626\) −15.4942 26.8368i −0.619274 1.07261i
\(627\) 0 0
\(628\) 13.5324 + 7.81295i 0.540003 + 0.311771i
\(629\) −12.1317 −0.483724
\(630\) 0 0
\(631\) −19.2419 −0.766009 −0.383004 0.923746i \(-0.625111\pi\)
−0.383004 + 0.923746i \(0.625111\pi\)
\(632\) 3.11385 + 1.79778i 0.123862 + 0.0715118i
\(633\) 0 0
\(634\) 2.36776 + 4.10109i 0.0940359 + 0.162875i
\(635\) 31.5518 + 54.6493i 1.25209 + 2.16869i
\(636\) 0 0
\(637\) 0 0
\(638\) 35.2738i 1.39650i
\(639\) 0 0
\(640\) 18.6921i 0.738869i
\(641\) −15.2483 8.80362i −0.602272 0.347722i 0.167663 0.985844i \(-0.446378\pi\)
−0.769935 + 0.638122i \(0.779711\pi\)
\(642\) 0 0
\(643\) −43.1158 + 24.8929i −1.70032 + 0.981680i −0.754893 + 0.655848i \(0.772311\pi\)
−0.945428 + 0.325832i \(0.894355\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −36.7007 + 63.5675i −1.44397 + 2.50103i
\(647\) 11.5407 0.453712 0.226856 0.973928i \(-0.427155\pi\)
0.226856 + 0.973928i \(0.427155\pi\)
\(648\) 0 0
\(649\) 13.6699i 0.536590i
\(650\) 15.0511 26.0693i 0.590354 1.02252i
\(651\) 0 0
\(652\) −27.0677 46.8826i −1.06005 1.83606i
\(653\) −18.2249 + 10.5222i −0.713197 + 0.411765i −0.812244 0.583318i \(-0.801754\pi\)
0.0990464 + 0.995083i \(0.468421\pi\)
\(654\) 0 0
\(655\) −6.85923 + 11.8805i −0.268012 + 0.464211i
\(656\) −3.53211 −0.137906
\(657\) 0 0
\(658\) 0 0
\(659\) 31.8016 + 18.3607i 1.23881 + 0.715230i 0.968852 0.247641i \(-0.0796555\pi\)
0.269962 + 0.962871i \(0.412989\pi\)
\(660\) 0 0
\(661\) 19.9819 11.5365i 0.777205 0.448719i −0.0582339 0.998303i \(-0.518547\pi\)
0.835439 + 0.549583i \(0.185214\pi\)
\(662\) −21.5683 + 12.4525i −0.838276 + 0.483979i
\(663\) 0 0
\(664\) 1.29875 + 0.749836i 0.0504015 + 0.0290993i
\(665\) 0 0
\(666\) 0 0
\(667\) −31.7331 −1.22871
\(668\) −18.6472 + 32.2978i −0.721480 + 1.24964i
\(669\) 0 0
\(670\) 49.6945 28.6911i 1.91987 1.10844i
\(671\) −6.83168 11.8328i −0.263734 0.456801i
\(672\) 0 0
\(673\) 24.7594 42.8846i 0.954406 1.65308i 0.218684 0.975796i \(-0.429824\pi\)
0.735722 0.677284i \(-0.236843\pi\)
\(674\) 9.78107i 0.376753i
\(675\) 0 0
\(676\) −16.5272 −0.635660
\(677\) 14.9077 25.8208i 0.572948 0.992374i −0.423314 0.905983i \(-0.639133\pi\)
0.996261 0.0863911i \(-0.0275335\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −14.7478 + 8.51465i −0.565553 + 0.326522i
\(681\) 0 0
\(682\) 12.8045 + 7.39271i 0.490311 + 0.283081i
\(683\) 30.2348i 1.15690i −0.815717 0.578451i \(-0.803658\pi\)
0.815717 0.578451i \(-0.196342\pi\)
\(684\) 0 0
\(685\) 20.8001i 0.794731i
\(686\) 0 0
\(687\) 0 0
\(688\) −9.37024 16.2297i −0.357237 0.618753i
\(689\) −12.5906 21.8076i −0.479664 0.830802i
\(690\) 0 0
\(691\) −26.7555 15.4473i −1.01783 0.587642i −0.104352 0.994540i \(-0.533277\pi\)
−0.913473 + 0.406899i \(0.866610\pi\)
\(692\) 43.7496 1.66311
\(693\) 0 0
\(694\) 15.4159 0.585180
\(695\) −4.38115 2.52946i −0.166186 0.0959478i
\(696\) 0 0
\(697\) −3.97172 6.87921i −0.150439 0.260569i
\(698\) −21.7204 37.6208i −0.822128 1.42397i
\(699\) 0 0
\(700\) 0 0
\(701\) 0.757329i 0.0286039i 0.999898 + 0.0143020i \(0.00455261\pi\)
−0.999898 + 0.0143020i \(0.995447\pi\)
\(702\) 0 0
\(703\) 8.28659i 0.312535i
\(704\) −24.1467 13.9411i −0.910065 0.525426i
\(705\) 0 0
\(706\) 12.8142 7.39831i 0.482270 0.278439i
\(707\) 0 0
\(708\) 0 0
\(709\) 10.7544 18.6271i 0.403889 0.699556i −0.590303 0.807182i \(-0.700992\pi\)
0.994191 + 0.107626i \(0.0343249\pi\)
\(710\) −14.2598 −0.535159
\(711\) 0 0
\(712\) 0.776904i 0.0291157i
\(713\) 6.65065 11.5193i 0.249069 0.431400i
\(714\) 0 0
\(715\) 10.7267 + 18.5791i 0.401155 + 0.694820i
\(716\) −44.7277 + 25.8235i −1.67155 + 0.965071i
\(717\) 0 0
\(718\) −10.3093 + 17.8562i −0.384740 + 0.666389i
\(719\) 44.2509 1.65028 0.825140 0.564929i \(-0.191096\pi\)
0.825140 + 0.564929i \(0.191096\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 9.12371 + 5.26758i 0.339549 + 0.196039i
\(723\) 0 0
\(724\) −35.9324 + 20.7456i −1.33542 + 0.771003i
\(725\) 32.6054 18.8248i 1.21094 0.699134i
\(726\) 0 0
\(727\) 2.95166 + 1.70414i 0.109471 + 0.0632031i 0.553736 0.832692i \(-0.313202\pi\)
−0.444265 + 0.895895i \(0.646535\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −55.2059 −2.04326
\(731\) 21.0729 36.4994i 0.779410 1.34998i
\(732\) 0 0
\(733\) 5.46407 3.15468i 0.201820 0.116521i −0.395684 0.918387i \(-0.629492\pi\)
0.597504 + 0.801866i \(0.296159\pi\)
\(734\) −32.5298 56.3432i −1.20070 2.07967i
\(735\) 0 0
\(736\) −20.1861 + 34.9633i −0.744069 + 1.28876i
\(737\) 22.1716i 0.816701i
\(738\) 0 0
\(739\) −4.90776 −0.180535 −0.0902674 0.995918i \(-0.528772\pi\)
−0.0902674 + 0.995918i \(0.528772\pi\)
\(740\) −6.54471 + 11.3358i −0.240588 + 0.416711i
\(741\) 0 0
\(742\) 0 0
\(743\) −26.1921 + 15.1220i −0.960895 + 0.554773i −0.896448 0.443148i \(-0.853862\pi\)
−0.0644465 + 0.997921i \(0.520528\pi\)
\(744\) 0 0
\(745\) −15.3059 8.83688i −0.560766 0.323758i
\(746\) 60.5414i 2.21658i
\(747\) 0 0
\(748\) 44.7990i 1.63801i
\(749\) 0 0
\(750\) 0 0
\(751\) 25.0321 + 43.3569i 0.913435 + 1.58212i 0.809177 + 0.587565i \(0.199913\pi\)
0.104257 + 0.994550i \(0.466753\pi\)
\(752\) 7.79355 + 13.4988i 0.284202 + 0.492252i
\(753\) 0 0
\(754\) 27.9988 + 16.1651i 1.01966 + 0.588700i
\(755\) 37.9628 1.38161
\(756\) 0 0
\(757\) 37.2695 1.35458 0.677291 0.735716i \(-0.263154\pi\)
0.677291 + 0.735716i \(0.263154\pi\)
\(758\) 0.935660 + 0.540204i 0.0339847 + 0.0196211i
\(759\) 0 0
\(760\) 5.81594 + 10.0735i 0.210966 + 0.365405i
\(761\) 5.27174 + 9.13092i 0.191100 + 0.330996i 0.945615 0.325287i \(-0.105461\pi\)
−0.754515 + 0.656283i \(0.772128\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 35.9248i 1.29971i
\(765\) 0 0
\(766\) 27.5341i 0.994848i
\(767\) 10.8506 + 6.26459i 0.391792 + 0.226201i
\(768\) 0 0
\(769\) −12.4720 + 7.20070i −0.449751 + 0.259664i −0.707725 0.706488i \(-0.750278\pi\)
0.257974 + 0.966152i \(0.416945\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 30.3199 52.5156i 1.09124 1.89008i
\(773\) −21.8771 −0.786866 −0.393433 0.919353i \(-0.628713\pi\)
−0.393433 + 0.919353i \(0.628713\pi\)
\(774\) 0 0
\(775\) 15.7812i 0.566879i
\(776\) −3.92472 + 6.79781i −0.140889 + 0.244027i
\(777\) 0 0
\(778\) −35.2493 61.0536i −1.26375 2.18888i
\(779\) −4.69885 + 2.71288i −0.168354 + 0.0971992i
\(780\) 0 0
\(781\) 2.75487 4.77158i 0.0985771 0.170740i
\(782\) −74.6851 −2.67073
\(783\) 0 0
\(784\) 0 0
\(785\) −19.0759 11.0135i −0.680847 0.393087i
\(786\) 0 0
\(787\) −23.9804 + 13.8451i −0.854807 + 0.493523i −0.862270 0.506449i \(-0.830958\pi\)
0.00746275 + 0.999972i \(0.497625\pi\)
\(788\) 8.49253 4.90316i 0.302534 0.174668i
\(789\) 0 0
\(790\) −29.8853 17.2543i −1.06327 0.613880i
\(791\) 0 0
\(792\) 0 0
\(793\) 12.5232 0.444712
\(794\) 8.93484 15.4756i 0.317086 0.549208i
\(795\) 0 0
\(796\) 44.6809 25.7965i 1.58367 0.914334i