Properties

Label 804.2.s.b.5.3
Level 804
Weight 2
Character 804.5
Analytic conductor 6.420
Analytic rank 0
Dimension 200
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.s (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(200\)
Relative dimension: \(20\) over \(\Q(\zeta_{22})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 5.3
Character \(\chi\) = 804.5
Dual form 804.2.s.b.161.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.57919 - 0.711443i) q^{3} +(-0.583807 + 0.171421i) q^{5} +(-0.967947 - 0.838730i) q^{7} +(1.98770 + 2.24701i) q^{9} +O(q^{10})\) \(q+(-1.57919 - 0.711443i) q^{3} +(-0.583807 + 0.171421i) q^{5} +(-0.967947 - 0.838730i) q^{7} +(1.98770 + 2.24701i) q^{9} +(1.09908 - 0.322720i) q^{11} +(-1.75990 - 2.73846i) q^{13} +(1.04390 + 0.144638i) q^{15} +(6.02227 + 0.865872i) q^{17} +(-3.63947 - 4.20017i) q^{19} +(0.931865 + 2.01316i) q^{21} +(-8.45963 + 3.86338i) q^{23} +(-3.89482 + 2.50305i) q^{25} +(-1.54033 - 4.96260i) q^{27} -1.03707i q^{29} +(-4.67082 + 7.26794i) q^{31} +(-1.96526 - 0.272298i) q^{33} +(0.708870 + 0.323730i) q^{35} -7.68565 q^{37} +(0.830965 + 5.57663i) q^{39} +(-0.975368 + 6.78383i) q^{41} +(6.37193 + 0.916145i) q^{43} +(-1.54562 - 0.971087i) q^{45} +(1.82570 - 0.833771i) q^{47} +(-0.762752 - 5.30506i) q^{49} +(-8.89431 - 5.65188i) q^{51} +(0.719704 + 5.00565i) q^{53} +(-0.586331 + 0.376812i) q^{55} +(2.75924 + 9.22215i) q^{57} +(-4.32558 + 6.73073i) q^{59} +(-2.70183 + 9.20160i) q^{61} +(-0.0393469 - 3.84213i) q^{63} +(1.49687 + 1.29705i) q^{65} +(-6.99330 - 4.25368i) q^{67} +(16.1080 - 0.0824778i) q^{69} +(-12.4132 + 1.78475i) q^{71} +(-2.27484 - 0.667954i) q^{73} +(7.93145 - 1.18185i) q^{75} +(-1.33453 - 0.609459i) q^{77} +(-8.54411 - 13.2949i) q^{79} +(-1.09812 + 8.93276i) q^{81} +(-3.58147 - 12.1974i) q^{83} +(-3.66427 + 0.526843i) q^{85} +(-0.737815 + 1.63773i) q^{87} +(1.31786 + 0.601845i) q^{89} +(-0.593340 + 4.12677i) q^{91} +(12.5468 - 8.15445i) q^{93} +(2.84474 + 1.82820i) q^{95} -10.2951i q^{97} +(2.90980 + 1.82818i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 200q - 10q^{9} + O(q^{10}) \) \( 200q - 10q^{9} + 2q^{15} + 6q^{19} - 10q^{21} - 20q^{25} - 44q^{31} - 5q^{33} + 78q^{39} - 22q^{43} - 22q^{45} - 16q^{49} + 36q^{55} + 66q^{57} + 176q^{61} + 132q^{63} + 46q^{67} - 26q^{73} - 165q^{75} - 44q^{79} + 42q^{81} - 66q^{87} - 20q^{91} + 84q^{93} - 55q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{22}\right)\) \(1\)

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
\(3\) −1.57919 0.711443i −0.911747 0.410752i
\(4\) 0 0
\(5\) −0.583807 + 0.171421i −0.261086 + 0.0766618i −0.409656 0.912240i \(-0.634351\pi\)
0.148570 + 0.988902i \(0.452533\pi\)
\(6\) 0 0
\(7\) −0.967947 0.838730i −0.365849 0.317010i 0.452464 0.891783i \(-0.350545\pi\)
−0.818313 + 0.574772i \(0.805091\pi\)
\(8\) 0 0
\(9\) 1.98770 + 2.24701i 0.662566 + 0.749004i
\(10\) 0 0
\(11\) 1.09908 0.322720i 0.331386 0.0973037i −0.111807 0.993730i \(-0.535664\pi\)
0.443193 + 0.896426i \(0.353846\pi\)
\(12\) 0 0
\(13\) −1.75990 2.73846i −0.488109 0.759513i 0.506607 0.862177i \(-0.330900\pi\)
−0.994716 + 0.102664i \(0.967263\pi\)
\(14\) 0 0
\(15\) 1.04390 + 0.144638i 0.269534 + 0.0373455i
\(16\) 0 0
\(17\) 6.02227 + 0.865872i 1.46062 + 0.210005i 0.826370 0.563127i \(-0.190402\pi\)
0.634245 + 0.773132i \(0.281311\pi\)
\(18\) 0 0
\(19\) −3.63947 4.20017i −0.834951 0.963585i 0.164790 0.986329i \(-0.447305\pi\)
−0.999741 + 0.0227439i \(0.992760\pi\)
\(20\) 0 0
\(21\) 0.931865 + 2.01316i 0.203350 + 0.439307i
\(22\) 0 0
\(23\) −8.45963 + 3.86338i −1.76395 + 0.805571i −0.780323 + 0.625377i \(0.784945\pi\)
−0.983631 + 0.180194i \(0.942327\pi\)
\(24\) 0 0
\(25\) −3.89482 + 2.50305i −0.778965 + 0.500610i
\(26\) 0 0
\(27\) −1.54033 4.96260i −0.296437 0.955052i
\(28\) 0 0
\(29\) 1.03707i 0.192579i −0.995353 0.0962894i \(-0.969303\pi\)
0.995353 0.0962894i \(-0.0306974\pi\)
\(30\) 0 0
\(31\) −4.67082 + 7.26794i −0.838904 + 1.30536i 0.111318 + 0.993785i \(0.464493\pi\)
−0.950222 + 0.311575i \(0.899143\pi\)
\(32\) 0 0
\(33\) −1.96526 0.272298i −0.342108 0.0474011i
\(34\) 0 0
\(35\) 0.708870 + 0.323730i 0.119821 + 0.0547203i
\(36\) 0 0
\(37\) −7.68565 −1.26351 −0.631756 0.775167i \(-0.717666\pi\)
−0.631756 + 0.775167i \(0.717666\pi\)
\(38\) 0 0
\(39\) 0.830965 + 5.57663i 0.133061 + 0.892976i
\(40\) 0 0
\(41\) −0.975368 + 6.78383i −0.152327 + 1.05946i 0.759979 + 0.649947i \(0.225209\pi\)
−0.912306 + 0.409509i \(0.865700\pi\)
\(42\) 0 0
\(43\) 6.37193 + 0.916145i 0.971710 + 0.139711i 0.609846 0.792520i \(-0.291231\pi\)
0.361864 + 0.932231i \(0.382140\pi\)
\(44\) 0 0
\(45\) −1.54562 0.971087i −0.230407 0.144761i
\(46\) 0 0
\(47\) 1.82570 0.833771i 0.266306 0.121618i −0.277787 0.960643i \(-0.589601\pi\)
0.544093 + 0.839025i \(0.316874\pi\)
\(48\) 0 0
\(49\) −0.762752 5.30506i −0.108965 0.757865i
\(50\) 0 0
\(51\) −8.89431 5.65188i −1.24545 0.791422i
\(52\) 0 0
\(53\) 0.719704 + 5.00565i 0.0988589 + 0.687579i 0.977630 + 0.210334i \(0.0674552\pi\)
−0.878771 + 0.477244i \(0.841636\pi\)
\(54\) 0 0
\(55\) −0.586331 + 0.376812i −0.0790608 + 0.0508093i
\(56\) 0 0
\(57\) 2.75924 + 9.22215i 0.365470 + 1.22150i
\(58\) 0 0
\(59\) −4.32558 + 6.73073i −0.563142 + 0.876266i −0.999726 0.0233972i \(-0.992552\pi\)
0.436584 + 0.899663i \(0.356188\pi\)
\(60\) 0 0
\(61\) −2.70183 + 9.20160i −0.345934 + 1.17814i 0.584410 + 0.811458i \(0.301326\pi\)
−0.930345 + 0.366686i \(0.880492\pi\)
\(62\) 0 0
\(63\) −0.0393469 3.84213i −0.00495724 0.484063i
\(64\) 0 0
\(65\) 1.49687 + 1.29705i 0.185664 + 0.160879i
\(66\) 0 0
\(67\) −6.99330 4.25368i −0.854367 0.519669i
\(68\) 0 0
\(69\) 16.1080 0.0824778i 1.93917 0.00992916i
\(70\) 0 0
\(71\) −12.4132 + 1.78475i −1.47318 + 0.211811i −0.831656 0.555291i \(-0.812607\pi\)
−0.641524 + 0.767103i \(0.721698\pi\)
\(72\) 0 0
\(73\) −2.27484 0.667954i −0.266250 0.0781781i 0.145883 0.989302i \(-0.453398\pi\)
−0.412133 + 0.911124i \(0.635216\pi\)
\(74\) 0 0
\(75\) 7.93145 1.18185i 0.915845 0.136469i
\(76\) 0 0
\(77\) −1.33453 0.609459i −0.152084 0.0694542i
\(78\) 0 0
\(79\) −8.54411 13.2949i −0.961288 1.49579i −0.865817 0.500361i \(-0.833201\pi\)
−0.0954710 0.995432i \(-0.530436\pi\)
\(80\) 0 0
\(81\) −1.09812 + 8.93276i −0.122014 + 0.992528i
\(82\) 0 0
\(83\) −3.58147 12.1974i −0.393118 1.33884i −0.883950 0.467582i \(-0.845125\pi\)
0.490832 0.871254i \(-0.336693\pi\)
\(84\) 0 0
\(85\) −3.66427 + 0.526843i −0.397446 + 0.0571441i
\(86\) 0 0
\(87\) −0.737815 + 1.63773i −0.0791021 + 0.175583i
\(88\) 0 0
\(89\) 1.31786 + 0.601845i 0.139692 + 0.0637954i 0.484035 0.875049i \(-0.339171\pi\)
−0.344342 + 0.938844i \(0.611898\pi\)
\(90\) 0 0
\(91\) −0.593340 + 4.12677i −0.0621989 + 0.432603i
\(92\) 0 0
\(93\) 12.5468 8.15445i 1.30105 0.845577i
\(94\) 0 0
\(95\) 2.84474 + 1.82820i 0.291864 + 0.187570i
\(96\) 0 0
\(97\) 10.2951i 1.04531i −0.852545 0.522654i \(-0.824942\pi\)
0.852545 0.522654i \(-0.175058\pi\)
\(98\) 0 0
\(99\) 2.90980 + 1.82818i 0.292446 + 0.183739i
\(100\) 0 0
\(101\) 11.0980 + 12.8078i 1.10430 + 1.27443i 0.958494 + 0.285113i \(0.0920311\pi\)
0.145803 + 0.989314i \(0.453423\pi\)
\(102\) 0 0
\(103\) 6.87710 + 4.41965i 0.677621 + 0.435481i 0.833666 0.552269i \(-0.186238\pi\)
−0.156045 + 0.987750i \(0.549874\pi\)
\(104\) 0 0
\(105\) −0.889126 1.01555i −0.0867698 0.0991078i
\(106\) 0 0
\(107\) 4.41018 15.0197i 0.426348 1.45201i −0.414158 0.910205i \(-0.635924\pi\)
0.840506 0.541802i \(-0.182258\pi\)
\(108\) 0 0
\(109\) 4.47433 + 6.96219i 0.428563 + 0.666857i 0.986637 0.162934i \(-0.0520959\pi\)
−0.558074 + 0.829791i \(0.688460\pi\)
\(110\) 0 0
\(111\) 12.1371 + 5.46790i 1.15200 + 0.518990i
\(112\) 0 0
\(113\) −8.56513 2.51495i −0.805740 0.236587i −0.147175 0.989110i \(-0.547018\pi\)
−0.658565 + 0.752524i \(0.728836\pi\)
\(114\) 0 0
\(115\) 4.27652 3.70563i 0.398788 0.345551i
\(116\) 0 0
\(117\) 2.65521 9.39776i 0.245474 0.868823i
\(118\) 0 0
\(119\) −5.10300 5.88918i −0.467792 0.539860i
\(120\) 0 0
\(121\) −8.14995 + 5.23766i −0.740905 + 0.476151i
\(122\) 0 0
\(123\) 6.36660 10.0191i 0.574057 0.903388i
\(124\) 0 0
\(125\) 3.83701 4.42814i 0.343192 0.396065i
\(126\) 0 0
\(127\) −11.6912 + 13.4924i −1.03743 + 1.19725i −0.0574060 + 0.998351i \(0.518283\pi\)
−0.980019 + 0.198902i \(0.936262\pi\)
\(128\) 0 0
\(129\) −9.41071 5.98003i −0.828567 0.526513i
\(130\) 0 0
\(131\) 12.8076 5.84904i 1.11901 0.511033i 0.231966 0.972724i \(-0.425484\pi\)
0.887041 + 0.461691i \(0.152757\pi\)
\(132\) 0 0
\(133\) 7.11807i 0.617215i
\(134\) 0 0
\(135\) 1.74995 + 2.63315i 0.150612 + 0.226626i
\(136\) 0 0
\(137\) −2.05122 4.49155i −0.175248 0.383739i 0.801542 0.597938i \(-0.204013\pi\)
−0.976790 + 0.214199i \(0.931286\pi\)
\(138\) 0 0
\(139\) 4.82451 + 16.4308i 0.409210 + 1.39364i 0.864202 + 0.503145i \(0.167824\pi\)
−0.454992 + 0.890496i \(0.650358\pi\)
\(140\) 0 0
\(141\) −3.47632 + 0.0177998i −0.292759 + 0.00149902i
\(142\) 0 0
\(143\) −2.81804 2.44184i −0.235656 0.204197i
\(144\) 0 0
\(145\) 0.177775 + 0.605447i 0.0147634 + 0.0502797i
\(146\) 0 0
\(147\) −2.56972 + 8.92036i −0.211947 + 0.735739i
\(148\) 0 0
\(149\) 7.26172 6.29231i 0.594903 0.515486i −0.304554 0.952495i \(-0.598508\pi\)
0.899457 + 0.437009i \(0.143962\pi\)
\(150\) 0 0
\(151\) 2.84904 19.8155i 0.231852 1.61256i −0.458231 0.888833i \(-0.651517\pi\)
0.690082 0.723731i \(-0.257574\pi\)
\(152\) 0 0
\(153\) 10.0248 + 15.2532i 0.810459 + 1.23315i
\(154\) 0 0
\(155\) 1.48098 5.04375i 0.118955 0.405123i
\(156\) 0 0
\(157\) −2.80627 6.14488i −0.223965 0.490414i 0.763976 0.645244i \(-0.223244\pi\)
−0.987941 + 0.154830i \(0.950517\pi\)
\(158\) 0 0
\(159\) 2.42468 8.41691i 0.192290 0.667504i
\(160\) 0 0
\(161\) 11.4288 + 3.35580i 0.900716 + 0.264474i
\(162\) 0 0
\(163\) 0.764311 0.0598654 0.0299327 0.999552i \(-0.490471\pi\)
0.0299327 + 0.999552i \(0.490471\pi\)
\(164\) 0 0
\(165\) 1.19401 0.177917i 0.0929535 0.0138508i
\(166\) 0 0
\(167\) 12.8888 11.1682i 0.997362 0.864219i 0.00661997 0.999978i \(-0.497893\pi\)
0.990742 + 0.135759i \(0.0433473\pi\)
\(168\) 0 0
\(169\) 0.998474 2.18635i 0.0768057 0.168181i
\(170\) 0 0
\(171\) 2.20367 16.5266i 0.168519 1.26382i
\(172\) 0 0
\(173\) 4.09433 6.37090i 0.311286 0.484371i −0.649996 0.759938i \(-0.725229\pi\)
0.961282 + 0.275567i \(0.0888657\pi\)
\(174\) 0 0
\(175\) 5.86937 + 0.843887i 0.443682 + 0.0637919i
\(176\) 0 0
\(177\) 11.6194 7.55171i 0.873371 0.567621i
\(178\) 0 0
\(179\) −2.25923 + 4.94702i −0.168863 + 0.369758i −0.975077 0.221865i \(-0.928785\pi\)
0.806214 + 0.591623i \(0.201513\pi\)
\(180\) 0 0
\(181\) −4.41394 9.66518i −0.328085 0.718407i 0.671662 0.740857i \(-0.265581\pi\)
−0.999748 + 0.0224503i \(0.992853\pi\)
\(182\) 0 0
\(183\) 10.8131 12.6089i 0.799330 0.932077i
\(184\) 0 0
\(185\) 4.48693 1.31748i 0.329886 0.0968632i
\(186\) 0 0
\(187\) 6.89841 0.991841i 0.504462 0.0725306i
\(188\) 0 0
\(189\) −2.67132 + 6.09545i −0.194310 + 0.443379i
\(190\) 0 0
\(191\) −10.4922 + 22.9746i −0.759185 + 1.66238i −0.0100657 + 0.999949i \(0.503204\pi\)
−0.749120 + 0.662435i \(0.769523\pi\)
\(192\) 0 0
\(193\) 13.0421 + 8.38163i 0.938789 + 0.603323i 0.918051 0.396462i \(-0.129762\pi\)
0.0207378 + 0.999785i \(0.493398\pi\)
\(194\) 0 0
\(195\) −1.44107 3.11323i −0.103198 0.222943i
\(196\) 0 0
\(197\) −2.51254 17.4751i −0.179011 1.24505i −0.859056 0.511881i \(-0.828949\pi\)
0.680045 0.733170i \(-0.261960\pi\)
\(198\) 0 0
\(199\) −2.27947 + 2.63064i −0.161587 + 0.186481i −0.830769 0.556617i \(-0.812099\pi\)
0.669182 + 0.743098i \(0.266645\pi\)
\(200\) 0 0
\(201\) 8.01751 + 11.6927i 0.565512 + 0.824740i
\(202\) 0 0
\(203\) −0.869821 + 1.00383i −0.0610494 + 0.0704548i
\(204\) 0 0
\(205\) −0.593465 4.12764i −0.0414494 0.288287i
\(206\) 0 0
\(207\) −25.4962 11.3296i −1.77211 0.787465i
\(208\) 0 0
\(209\) −5.35555 3.44180i −0.370451 0.238075i
\(210\) 0 0
\(211\) 0.718721 1.57378i 0.0494788 0.108343i −0.883278 0.468849i \(-0.844669\pi\)
0.932757 + 0.360506i \(0.117396\pi\)
\(212\) 0 0
\(213\) 20.8726 + 6.01285i 1.43017 + 0.411993i
\(214\) 0 0
\(215\) −3.87702 + 0.557431i −0.264411 + 0.0380165i
\(216\) 0 0
\(217\) 10.6169 3.11742i 0.720725 0.211624i
\(218\) 0 0
\(219\) 3.11720 + 2.67325i 0.210641 + 0.180642i
\(220\) 0 0
\(221\) −8.22746 18.0156i −0.553439 1.21186i
\(222\) 0 0
\(223\) 1.72185 3.77033i 0.115304 0.252480i −0.843178 0.537635i \(-0.819318\pi\)
0.958481 + 0.285155i \(0.0920451\pi\)
\(224\) 0 0
\(225\) −13.3661 3.77641i −0.891074 0.251760i
\(226\) 0 0
\(227\) −18.7033 2.68913i −1.24138 0.178484i −0.509833 0.860273i \(-0.670293\pi\)
−0.731548 + 0.681789i \(0.761202\pi\)
\(228\) 0 0
\(229\) −5.93670 + 9.23768i −0.392308 + 0.610443i −0.980085 0.198580i \(-0.936367\pi\)
0.587777 + 0.809023i \(0.300003\pi\)
\(230\) 0 0
\(231\) 1.67388 + 1.91189i 0.110133 + 0.125793i
\(232\) 0 0
\(233\) 0.376373 0.824142i 0.0246570 0.0539913i −0.896903 0.442228i \(-0.854188\pi\)
0.921560 + 0.388236i \(0.126916\pi\)
\(234\) 0 0
\(235\) −0.922932 + 0.799725i −0.0602054 + 0.0521683i
\(236\) 0 0
\(237\) 4.03423 + 27.0739i 0.262051 + 1.75864i
\(238\) 0 0
\(239\) 4.03610 0.261074 0.130537 0.991443i \(-0.458330\pi\)
0.130537 + 0.991443i \(0.458330\pi\)
\(240\) 0 0
\(241\) −4.39067 1.28922i −0.282828 0.0830458i 0.137242 0.990538i \(-0.456176\pi\)
−0.420070 + 0.907492i \(0.637994\pi\)
\(242\) 0 0
\(243\) 8.08930 13.3253i 0.518929 0.854817i
\(244\) 0 0
\(245\) 1.35470 + 2.96638i 0.0865485 + 0.189515i
\(246\) 0 0
\(247\) −5.09690 + 17.3584i −0.324308 + 1.10449i
\(248\) 0 0
\(249\) −3.02191 + 21.8100i −0.191506 + 1.38215i
\(250\) 0 0
\(251\) −3.39552 + 23.6163i −0.214323 + 1.49065i 0.544173 + 0.838973i \(0.316843\pi\)
−0.758496 + 0.651677i \(0.774066\pi\)
\(252\) 0 0
\(253\) −8.05104 + 6.97626i −0.506164 + 0.438594i
\(254\) 0 0
\(255\) 6.16141 + 1.77494i 0.385842 + 0.111151i
\(256\) 0 0
\(257\) 5.18032 + 17.6425i 0.323139 + 1.10051i 0.947601 + 0.319456i \(0.103500\pi\)
−0.624462 + 0.781055i \(0.714682\pi\)
\(258\) 0 0
\(259\) 7.43930 + 6.44619i 0.462255 + 0.400547i
\(260\) 0 0
\(261\) 2.33030 2.06138i 0.144242 0.127596i
\(262\) 0 0
\(263\) 2.34820 + 7.99724i 0.144796 + 0.493131i 0.999670 0.0257060i \(-0.00818338\pi\)
−0.854873 + 0.518837i \(0.826365\pi\)
\(264\) 0 0
\(265\) −1.27824 2.79896i −0.0785217 0.171939i
\(266\) 0 0
\(267\) −1.65297 1.88801i −0.101160 0.115544i
\(268\) 0 0
\(269\) 11.6474i 0.710157i 0.934837 + 0.355078i \(0.115546\pi\)
−0.934837 + 0.355078i \(0.884454\pi\)
\(270\) 0 0
\(271\) 9.86330 4.50442i 0.599153 0.273624i −0.0926633 0.995697i \(-0.529538\pi\)
0.691816 + 0.722073i \(0.256811\pi\)
\(272\) 0 0
\(273\) 3.87296 6.09484i 0.234402 0.368876i
\(274\) 0 0
\(275\) −3.47295 + 4.00800i −0.209427 + 0.241691i
\(276\) 0 0
\(277\) −1.64801 + 1.90191i −0.0990196 + 0.114275i −0.803096 0.595849i \(-0.796816\pi\)
0.704077 + 0.710124i \(0.251361\pi\)
\(278\) 0 0
\(279\) −25.6153 + 3.95107i −1.53355 + 0.236544i
\(280\) 0 0
\(281\) 7.41890 4.76784i 0.442574 0.284425i −0.300314 0.953840i \(-0.597092\pi\)
0.742889 + 0.669415i \(0.233455\pi\)
\(282\) 0 0
\(283\) −9.32066 10.7566i −0.554056 0.639415i 0.407767 0.913086i \(-0.366307\pi\)
−0.961823 + 0.273671i \(0.911762\pi\)
\(284\) 0 0
\(285\) −3.19173 4.91096i −0.189062 0.290900i
\(286\) 0 0
\(287\) 6.63391 5.74831i 0.391587 0.339312i
\(288\) 0 0
\(289\) 19.2066 + 5.63958i 1.12980 + 0.331740i
\(290\) 0 0
\(291\) −7.32437 + 16.2579i −0.429362 + 0.953057i
\(292\) 0 0
\(293\) −10.1776 15.8366i −0.594582 0.925187i −0.999939 0.0110287i \(-0.996489\pi\)
0.405358 0.914158i \(-0.367147\pi\)
\(294\) 0 0
\(295\) 1.37151 4.67094i 0.0798525 0.271953i
\(296\) 0 0
\(297\) −3.29448 4.95721i −0.191165 0.287646i
\(298\) 0 0
\(299\) 25.4679 + 16.3672i 1.47284 + 0.946539i
\(300\) 0 0
\(301\) −5.39929 6.23111i −0.311210 0.359155i
\(302\) 0 0
\(303\) −8.41390 28.1217i −0.483366 1.61555i
\(304\) 0 0
\(305\) 5.83511i 0.334117i
\(306\) 0 0
\(307\) −1.02503 0.658746i −0.0585015 0.0375966i 0.511063 0.859543i \(-0.329252\pi\)
−0.569565 + 0.821947i \(0.692888\pi\)
\(308\) 0 0
\(309\) −7.71594 11.8721i −0.438945 0.675382i
\(310\) 0 0
\(311\) −0.910675 + 6.33389i −0.0516397 + 0.359162i 0.947575 + 0.319534i \(0.103526\pi\)
−0.999215 + 0.0396278i \(0.987383\pi\)
\(312\) 0 0
\(313\) −18.0740 8.25412i −1.02160 0.466550i −0.167068 0.985945i \(-0.553430\pi\)
−0.854534 + 0.519395i \(0.826157\pi\)
\(314\) 0 0
\(315\) 0.681593 + 2.23632i 0.0384034 + 0.126002i
\(316\) 0 0
\(317\) −7.47147 + 1.07423i −0.419639 + 0.0603350i −0.348900 0.937160i \(-0.613445\pi\)
−0.0707391 + 0.997495i \(0.522536\pi\)
\(318\) 0 0
\(319\) −0.334682 1.13982i −0.0187386 0.0638179i
\(320\) 0 0
\(321\) −17.6502 + 20.5814i −0.985136 + 1.14874i
\(322\) 0 0
\(323\) −18.2810 28.4459i −1.01718 1.58277i
\(324\) 0 0
\(325\) 13.7090 + 6.26070i 0.760440 + 0.347281i
\(326\) 0 0
\(327\) −2.11262 14.1779i −0.116828 0.784038i
\(328\) 0 0
\(329\) −2.46649 0.724228i −0.135982 0.0399280i
\(330\) 0 0
\(331\) 20.9135 3.00691i 1.14951 0.165275i 0.458891 0.888493i \(-0.348247\pi\)
0.690620 + 0.723218i \(0.257338\pi\)
\(332\) 0 0
\(333\) −15.2767 17.2697i −0.837160 0.946376i
\(334\) 0 0
\(335\) 4.81190 + 1.28453i 0.262902 + 0.0701812i
\(336\) 0 0
\(337\) −8.27804 7.17296i −0.450934 0.390736i 0.399572 0.916702i \(-0.369159\pi\)
−0.850506 + 0.525966i \(0.823704\pi\)
\(338\) 0 0
\(339\) 11.7367 + 10.0652i 0.637453 + 0.546666i
\(340\) 0 0
\(341\) −2.78811 + 9.49543i −0.150985 + 0.514206i
\(342\) 0 0
\(343\) −8.55829 + 13.3170i −0.462104 + 0.719048i
\(344\) 0 0
\(345\) −9.38979 + 2.80939i −0.505529 + 0.151253i
\(346\) 0 0
\(347\) 8.52778 5.48047i 0.457795 0.294207i −0.291346 0.956618i \(-0.594103\pi\)
0.749141 + 0.662411i \(0.230467\pi\)
\(348\) 0 0
\(349\) −3.83309 26.6597i −0.205181 1.42706i −0.788608 0.614897i \(-0.789198\pi\)
0.583427 0.812166i \(-0.301711\pi\)
\(350\) 0 0
\(351\) −10.8791 + 12.9518i −0.580681 + 0.691318i
\(352\) 0 0
\(353\) 4.00838 + 27.8789i 0.213344 + 1.48384i 0.761882 + 0.647716i \(0.224276\pi\)
−0.548537 + 0.836126i \(0.684815\pi\)
\(354\) 0 0
\(355\) 6.94098 3.16984i 0.368389 0.168238i
\(356\) 0 0
\(357\) 3.86881 + 12.9306i 0.204759 + 0.684362i
\(358\) 0 0
\(359\) 13.9546 + 2.00637i 0.736496 + 0.105892i 0.500347 0.865825i \(-0.333206\pi\)
0.236149 + 0.971717i \(0.424115\pi\)
\(360\) 0 0
\(361\) −1.69171 + 11.7661i −0.0890376 + 0.619270i
\(362\) 0 0
\(363\) 16.5966 2.47304i 0.871098 0.129801i
\(364\) 0 0
\(365\) 1.44257 0.0755076
\(366\) 0 0
\(367\) 10.4511 + 4.77287i 0.545544 + 0.249142i 0.669070 0.743200i \(-0.266693\pi\)
−0.123526 + 0.992341i \(0.539420\pi\)
\(368\) 0 0
\(369\) −17.1821 + 11.2925i −0.894463 + 0.587866i
\(370\) 0 0
\(371\) 3.50175 5.44884i 0.181802 0.282890i
\(372\) 0 0
\(373\) 12.8632i 0.666030i −0.942922 0.333015i \(-0.891934\pi\)
0.942922 0.333015i \(-0.108066\pi\)
\(374\) 0 0
\(375\) −9.20975 + 4.26308i −0.475589 + 0.220144i
\(376\) 0 0
\(377\) −2.83997 + 1.82514i −0.146266 + 0.0939995i
\(378\) 0 0
\(379\) −16.1756 + 7.38714i −0.830884 + 0.379452i −0.785001 0.619495i \(-0.787337\pi\)
−0.0458831 + 0.998947i \(0.514610\pi\)
\(380\) 0 0
\(381\) 28.0617 12.9894i 1.43764 0.665467i
\(382\) 0 0
\(383\) 9.24502 + 10.6693i 0.472398 + 0.545177i 0.941077 0.338192i \(-0.109815\pi\)
−0.468679 + 0.883369i \(0.655270\pi\)
\(384\) 0 0
\(385\) 0.883580 + 0.127040i 0.0450314 + 0.00647454i
\(386\) 0 0
\(387\) 10.6069 + 16.1388i 0.539178 + 0.820382i
\(388\) 0 0
\(389\) −20.1160 31.3011i −1.01992 1.58703i −0.789322 0.613979i \(-0.789568\pi\)
−0.230599 0.973049i \(-0.574068\pi\)
\(390\) 0 0
\(391\) −54.2914 + 15.9414i −2.74563 + 0.806190i
\(392\) 0 0
\(393\) −24.3870 + 0.124869i −1.23016 + 0.00629880i
\(394\) 0 0
\(395\) 7.26714 + 6.29701i 0.365649 + 0.316837i
\(396\) 0 0
\(397\) 0.849895 0.249552i 0.0426550 0.0125246i −0.260335 0.965518i \(-0.583833\pi\)
0.302990 + 0.952994i \(0.402015\pi\)
\(398\) 0 0
\(399\) 5.06410 11.2408i 0.253522 0.562744i
\(400\) 0 0
\(401\) −30.6446 −1.53032 −0.765160 0.643840i \(-0.777340\pi\)
−0.765160 + 0.643840i \(0.777340\pi\)
\(402\) 0 0
\(403\) 28.1232 1.40091
\(404\) 0 0
\(405\) −0.890170 5.40324i −0.0442329 0.268489i
\(406\) 0 0
\(407\) −8.44716 + 2.48031i −0.418710 + 0.122944i
\(408\) 0 0
\(409\) −3.99205 3.45913i −0.197394 0.171043i 0.550555 0.834799i \(-0.314416\pi\)
−0.747949 + 0.663756i \(0.768961\pi\)
\(410\) 0 0
\(411\) 0.0437907 + 8.55235i 0.00216004 + 0.421856i
\(412\) 0 0
\(413\) 9.83219 2.88699i 0.483811 0.142060i
\(414\) 0 0
\(415\) 4.18178 + 6.50697i 0.205275 + 0.319415i
\(416\) 0 0
\(417\) 4.07074 29.3797i 0.199345 1.43873i
\(418\) 0 0
\(419\) −31.2307 4.49030i −1.52572 0.219366i −0.672179 0.740389i \(-0.734641\pi\)
−0.853543 + 0.521023i \(0.825551\pi\)
\(420\) 0 0
\(421\) −9.84377 11.3603i −0.479756 0.553668i 0.463343 0.886179i \(-0.346650\pi\)
−0.943099 + 0.332511i \(0.892104\pi\)
\(422\) 0 0
\(423\) 5.50244 + 2.44509i 0.267538 + 0.118885i
\(424\) 0 0
\(425\) −25.6230 + 11.7016i −1.24290 + 0.567613i
\(426\) 0 0
\(427\) 10.3329 6.64055i 0.500044 0.321359i
\(428\) 0 0
\(429\) 2.71299 + 5.86101i 0.130984 + 0.282972i
\(430\) 0 0
\(431\) 34.5012i 1.66187i 0.556373 + 0.830933i \(0.312192\pi\)
−0.556373 + 0.830933i \(0.687808\pi\)
\(432\) 0 0
\(433\) 8.95964 13.9415i 0.430573 0.669985i −0.556392 0.830920i \(-0.687815\pi\)
0.986965 + 0.160935i \(0.0514510\pi\)
\(434\) 0 0
\(435\) 0.150000 1.08259i 0.00719195 0.0519064i
\(436\) 0 0
\(437\) 47.0154 + 21.4712i 2.24905 + 1.02711i
\(438\) 0 0
\(439\) −0.732575 −0.0349639 −0.0174819 0.999847i \(-0.505565\pi\)
−0.0174819 + 0.999847i \(0.505565\pi\)
\(440\) 0 0
\(441\) 10.4044 12.2588i 0.495448 0.583750i
\(442\) 0 0
\(443\) 5.09060 35.4059i 0.241862 1.68218i −0.400903 0.916120i \(-0.631304\pi\)
0.642765 0.766064i \(-0.277787\pi\)
\(444\) 0 0
\(445\) −0.872542 0.125453i −0.0413624 0.00594702i
\(446\) 0 0
\(447\) −15.9443 + 4.77047i −0.754138 + 0.225636i
\(448\) 0 0
\(449\) 0.701077 0.320171i 0.0330859 0.0151098i −0.398803 0.917036i \(-0.630574\pi\)
0.431889 + 0.901927i \(0.357847\pi\)
\(450\) 0 0
\(451\) 1.11727 + 7.77076i 0.0526100 + 0.365911i
\(452\) 0 0
\(453\) −18.5968 + 29.2656i −0.873754 + 1.37502i
\(454\) 0 0
\(455\) −0.361020 2.51095i −0.0169249 0.117715i
\(456\) 0 0
\(457\) 22.2164 14.2776i 1.03924 0.667879i 0.0944416 0.995530i \(-0.469893\pi\)
0.944799 + 0.327651i \(0.106257\pi\)
\(458\) 0 0
\(459\) −4.97933 31.2198i −0.232415 1.45722i
\(460\) 0 0
\(461\) −13.8050 + 21.4810i −0.642964 + 1.00047i 0.354885 + 0.934910i \(0.384520\pi\)
−0.997849 + 0.0655610i \(0.979116\pi\)
\(462\) 0 0
\(463\) −2.08357 + 7.09599i −0.0968317 + 0.329779i −0.993635 0.112652i \(-0.964065\pi\)
0.896803 + 0.442431i \(0.145884\pi\)
\(464\) 0 0
\(465\) −5.92709 + 6.91141i −0.274862 + 0.320509i
\(466\) 0 0
\(467\) −8.29179 7.18487i −0.383698 0.332476i 0.441560 0.897232i \(-0.354425\pi\)
−0.825258 + 0.564755i \(0.808971\pi\)
\(468\) 0 0
\(469\) 3.20145 + 9.98283i 0.147829 + 0.460964i
\(470\) 0 0
\(471\) 0.0599100 + 11.7004i 0.00276051 + 0.539128i
\(472\) 0 0
\(473\) 7.29893 1.04943i 0.335605 0.0482528i
\(474\) 0 0
\(475\) 24.6883 + 7.24914i 1.13278 + 0.332613i
\(476\) 0 0
\(477\) −9.81720 + 11.5669i −0.449499 + 0.529612i
\(478\) 0 0
\(479\) 26.7907 + 12.2349i 1.22410 + 0.559027i 0.919363 0.393409i \(-0.128704\pi\)
0.304736 + 0.952437i \(0.401432\pi\)
\(480\) 0 0
\(481\) 13.5260 + 21.0469i 0.616732 + 0.959654i
\(482\) 0 0
\(483\) −15.6608 13.4304i −0.712592 0.611104i
\(484\) 0 0
\(485\) 1.76480 + 6.01034i 0.0801352 + 0.272916i
\(486\) 0 0
\(487\) −21.4636 + 3.08600i −0.972607 + 0.139840i −0.610258 0.792203i \(-0.708934\pi\)
−0.362349 + 0.932042i \(0.618025\pi\)
\(488\) 0 0
\(489\) −1.20699 0.543764i −0.0545821 0.0245898i
\(490\) 0 0
\(491\) −10.3451 4.72447i −0.466870 0.213212i 0.168068 0.985775i \(-0.446247\pi\)
−0.634938 + 0.772563i \(0.718974\pi\)
\(492\) 0 0
\(493\) 0.897968 6.24551i 0.0404425 0.281283i
\(494\) 0 0
\(495\) −2.01215 0.568504i −0.0904393 0.0255524i
\(496\) 0 0
\(497\) 13.5123 + 8.68381i 0.606108 + 0.389522i
\(498\) 0 0
\(499\) 33.0070i 1.47760i −0.673927 0.738798i \(-0.735394\pi\)
0.673927 0.738798i \(-0.264606\pi\)
\(500\) 0 0
\(501\) −28.2993 + 8.46707i −1.26432 + 0.378281i
\(502\) 0 0
\(503\) −14.5907 16.8386i −0.650567 0.750795i 0.330639 0.943757i \(-0.392736\pi\)
−0.981206 + 0.192963i \(0.938190\pi\)
\(504\) 0 0
\(505\) −8.67464 5.57485i −0.386017 0.248078i
\(506\) 0 0
\(507\) −3.13225 + 2.74231i −0.139108 + 0.121790i
\(508\) 0 0
\(509\) −0.629879 + 2.14517i −0.0279189 + 0.0950831i −0.972274 0.233845i \(-0.924869\pi\)
0.944355 + 0.328928i \(0.106687\pi\)
\(510\) 0 0
\(511\) 1.64169 + 2.55453i 0.0726242 + 0.113006i
\(512\) 0 0
\(513\) −15.2378 + 24.5309i −0.672763 + 1.08306i
\(514\) 0 0
\(515\) −4.77252 1.40134i −0.210302 0.0617503i
\(516\) 0 0
\(517\) 1.73752 1.50557i 0.0764163 0.0662151i
\(518\) 0 0
\(519\) −10.9983 + 7.14799i −0.482770 + 0.313762i
\(520\) 0 0
\(521\) 12.0476 + 13.9037i 0.527817 + 0.609133i 0.955571 0.294762i \(-0.0952404\pi\)
−0.427754 + 0.903895i \(0.640695\pi\)
\(522\) 0 0
\(523\) −5.28647 + 3.39741i −0.231161 + 0.148558i −0.651094 0.758997i \(-0.725690\pi\)
0.419933 + 0.907555i \(0.362053\pi\)
\(524\) 0 0
\(525\) −8.66848 5.50838i −0.378323 0.240405i
\(526\) 0 0
\(527\) −34.4220 + 39.7252i −1.49945 + 1.73046i
\(528\) 0 0
\(529\) 41.5778 47.9833i 1.80773 2.08623i
\(530\) 0 0
\(531\) −23.7220 + 3.65902i −1.02945 + 0.158788i
\(532\) 0 0
\(533\) 20.2938 9.26788i 0.879023 0.401436i
\(534\) 0 0
\(535\) 9.52458i 0.411784i
\(536\) 0 0
\(537\) 7.08729 6.20499i 0.305839 0.267765i
\(538\) 0 0
\(539\) −2.55037 5.58454i −0.109852 0.240543i
\(540\) 0 0
\(541\) −7.79124 26.5345i −0.334972 1.14081i −0.939020 0.343861i \(-0.888265\pi\)
0.604049 0.796947i \(-0.293553\pi\)
\(542\) 0 0
\(543\) 0.0942314 + 18.4034i 0.00404386 + 0.789767i
\(544\) 0 0
\(545\) −3.80561 3.29758i −0.163014 0.141253i
\(546\) 0 0
\(547\) 9.77075 + 33.2761i 0.417767 + 1.42278i 0.852737 + 0.522340i \(0.174941\pi\)
−0.434970 + 0.900445i \(0.643241\pi\)
\(548\) 0 0
\(549\) −26.0465 + 12.2189i −1.11164 + 0.521492i
\(550\) 0 0
\(551\) −4.35586 + 3.77437i −0.185566 + 0.160794i
\(552\) 0 0
\(553\) −2.88059 + 20.0350i −0.122495 + 0.851973i
\(554\) 0 0
\(555\) −8.02304 1.11164i −0.340559 0.0471865i
\(556\) 0 0
\(557\) −3.66286 + 12.4745i −0.155200 + 0.528563i −0.999979 0.00655314i \(-0.997914\pi\)
0.844778 + 0.535116i \(0.179732\pi\)
\(558\) 0 0
\(559\) −8.70515 19.0616i −0.368189 0.806220i
\(560\) 0 0
\(561\) −11.5996 3.34152i −0.489733 0.141079i
\(562\) 0 0
\(563\) 7.56202 + 2.22041i 0.318701 + 0.0935791i 0.437171 0.899379i \(-0.355981\pi\)
−0.118469 + 0.992958i \(0.537799\pi\)
\(564\) 0 0
\(565\) 5.43150 0.228505
\(566\) 0 0
\(567\) 8.55510 7.72540i 0.359280 0.324436i
\(568\) 0 0
\(569\) 24.4567 21.1919i 1.02528 0.888409i 0.0314691 0.999505i \(-0.489981\pi\)
0.993810 + 0.111096i \(0.0354360\pi\)
\(570\) 0 0
\(571\) −11.7884 + 25.8130i −0.493330 + 1.08024i 0.485250 + 0.874376i \(0.338729\pi\)
−0.978580 + 0.205867i \(0.933999\pi\)
\(572\) 0 0
\(573\) 32.9143 28.8167i 1.37501 1.20384i
\(574\) 0 0
\(575\) 23.2785 36.2221i 0.970781 1.51056i
\(576\) 0 0
\(577\) −13.5436 1.94728i −0.563828 0.0810663i −0.145494 0.989359i \(-0.546477\pi\)
−0.418335 + 0.908293i \(0.637386\pi\)
\(578\) 0 0
\(579\) −14.6329 22.5149i −0.608122 0.935688i
\(580\) 0 0
\(581\) −6.76364 + 14.8103i −0.280603 + 0.614435i
\(582\) 0 0
\(583\) 2.40643 + 5.26936i 0.0996644 + 0.218234i
\(584\) 0 0
\(585\) 0.0608476 + 5.94163i 0.00251574 + 0.245656i
\(586\) 0 0
\(587\) 15.3714 4.51344i 0.634444 0.186290i 0.0513323 0.998682i \(-0.483653\pi\)
0.583112 + 0.812392i \(0.301835\pi\)
\(588\) 0 0
\(589\) 47.5258 6.83319i 1.95827 0.281556i
\(590\) 0 0
\(591\) −8.46477 + 29.3841i −0.348194 + 1.20870i
\(592\) 0 0
\(593\) −0.420135 + 0.919968i −0.0172529 + 0.0377786i −0.918062 0.396436i \(-0.870247\pi\)
0.900809 + 0.434215i \(0.142974\pi\)
\(594\) 0 0
\(595\) 3.98870 + 2.56338i 0.163521 + 0.105088i
\(596\) 0 0
\(597\) 5.47127 2.53258i 0.223924 0.103652i
\(598\) 0 0
\(599\) 1.01345 + 7.04867i 0.0414083 + 0.288001i 0.999995 + 0.00319963i \(0.00101847\pi\)
−0.958587 + 0.284801i \(0.908072\pi\)
\(600\) 0 0
\(601\) 9.23676 10.6598i 0.376775 0.434822i −0.535415 0.844589i \(-0.679845\pi\)
0.912190 + 0.409767i \(0.134390\pi\)
\(602\) 0 0
\(603\) −4.34249 24.1690i −0.176840 0.984240i
\(604\) 0 0
\(605\) 3.86015 4.45485i 0.156937 0.181116i
\(606\) 0 0
\(607\) 2.12560 + 14.7839i 0.0862754 + 0.600059i 0.986392 + 0.164410i \(0.0525720\pi\)
−0.900117 + 0.435649i \(0.856519\pi\)
\(608\) 0 0
\(609\) 2.08778 0.966407i 0.0846011 0.0391608i
\(610\) 0 0
\(611\) −5.49631 3.53227i −0.222357 0.142900i
\(612\) 0 0
\(613\) −1.00616 + 2.20318i −0.0406384 + 0.0889857i −0.928862 0.370425i \(-0.879212\pi\)
0.888224 + 0.459411i \(0.151939\pi\)
\(614\) 0 0
\(615\) −1.99939 + 6.94056i −0.0806231 + 0.279870i
\(616\) 0 0
\(617\) −33.8862 + 4.87210i −1.36421 + 0.196144i −0.785232 0.619201i \(-0.787456\pi\)
−0.578976 + 0.815345i \(0.696547\pi\)
\(618\) 0 0
\(619\) 18.7221 5.49730i 0.752504 0.220955i 0.117084 0.993122i \(-0.462645\pi\)
0.635420 + 0.772167i \(0.280827\pi\)
\(620\) 0 0
\(621\) 32.2031 + 36.0308i 1.29226 + 1.44587i
\(622\) 0 0
\(623\) −0.770829 1.68788i −0.0308826 0.0676235i
\(624\) 0 0
\(625\) 8.13542 17.8141i 0.325417 0.712563i
\(626\) 0 0
\(627\) 6.00880 + 9.24544i 0.239968 + 0.369227i
\(628\) 0 0
\(629\) −46.2851 6.65479i −1.84551 0.265344i
\(630\) 0 0
\(631\) 18.6285 28.9865i 0.741589 1.15394i −0.241427 0.970419i \(-0.577616\pi\)
0.983017 0.183517i \(-0.0587481\pi\)
\(632\) 0 0
\(633\) −2.25465 + 1.97397i −0.0896144 + 0.0784583i
\(634\) 0 0
\(635\) 4.51252 9.88104i 0.179074 0.392117i
\(636\) 0 0
\(637\) −13.1853 + 11.4252i −0.522422 + 0.452681i
\(638\) 0 0
\(639\) −28.6841 24.3451i −1.13473 0.963079i
\(640\) 0 0
\(641\) −39.9842 −1.57928 −0.789641 0.613570i \(-0.789733\pi\)
−0.789641 + 0.613570i \(0.789733\pi\)
\(642\) 0 0
\(643\) 35.2776 + 10.3584i 1.39121 + 0.408497i 0.889658 0.456628i \(-0.150943\pi\)
0.501556 + 0.865125i \(0.332761\pi\)
\(644\) 0 0
\(645\) 6.51914 + 1.87799i 0.256691 + 0.0739457i
\(646\) 0 0
\(647\) 6.01849 + 13.1787i 0.236611 + 0.518106i 0.990270 0.139160i \(-0.0444401\pi\)
−0.753659 + 0.657266i \(0.771713\pi\)
\(648\) 0 0
\(649\) −2.58203 + 8.79357i −0.101353 + 0.345178i
\(650\) 0 0
\(651\) −18.9841 2.63036i −0.744044 0.103092i
\(652\) 0 0
\(653\) 0.548182 3.81269i 0.0214520 0.149202i −0.976280 0.216511i \(-0.930532\pi\)
0.997732 + 0.0673090i \(0.0214413\pi\)
\(654\) 0 0
\(655\) −6.47452 + 5.61021i −0.252981 + 0.219209i
\(656\) 0 0
\(657\) −3.02080 6.43929i −0.117853 0.251221i
\(658\) 0 0
\(659\) −1.69144 5.76053i −0.0658893 0.224398i 0.919966 0.391999i \(-0.128216\pi\)
−0.985855 + 0.167601i \(0.946398\pi\)
\(660\) 0 0
\(661\) −9.68627 8.39320i −0.376752 0.326458i 0.445815 0.895125i \(-0.352914\pi\)
−0.822568 + 0.568667i \(0.807459\pi\)
\(662\) 0 0
\(663\) 0.175645 + 34.3035i 0.00682148 + 1.33224i
\(664\) 0 0
\(665\) −1.22019 4.15558i −0.0473168 0.161146i
\(666\) 0 0
\(667\) 4.00659 + 8.77321i 0.155136 + 0.339700i
\(668\) 0 0
\(669\) −5.40151 + 4.72907i −0.208834 + 0.182836i
\(670\) 0 0
\(671\) 10.9853i 0.424081i
\(672\) 0 0
\(673\) 32.8059 14.9819i 1.26457 0.577511i 0.333640 0.942701i \(-0.391723\pi\)
0.930933 + 0.365190i \(0.118996\pi\)
\(674\) 0 0
\(675\) 18.4210 + 15.4729i 0.709023 + 0.595552i
\(676\) 0 0
\(677\) −6.41707 + 7.40570i −0.246628 + 0.284624i −0.865544 0.500834i \(-0.833027\pi\)
0.618915 + 0.785458i \(0.287572\pi\)
\(678\) 0 0
\(679\) −8.63481 + 9.96510i −0.331373 + 0.382425i
\(680\) 0 0
\(681\) 27.6229 + 17.5530i 1.05851 + 0.672632i
\(682\) 0 0
\(683\) −13.6651 + 8.78203i −0.522881 + 0.336035i −0.775311 0.631580i \(-0.782407\pi\)
0.252430 + 0.967615i \(0.418770\pi\)
\(684\) 0 0
\(685\) 1.96746 + 2.27057i 0.0751729 + 0.0867542i
\(686\) 0 0
\(687\) 15.9473 10.3644i 0.608426 0.395428i
\(688\) 0 0
\(689\) 12.4412 10.7803i 0.473971 0.410698i
\(690\) 0 0
\(691\) −5.07491 1.49013i −0.193059 0.0566872i 0.183774 0.982969i \(-0.441169\pi\)
−0.376833 + 0.926281i \(0.622987\pi\)
\(692\) 0 0
\(693\) −1.28318 4.21012i −0.0487438 0.159929i
\(694\) 0 0
\(695\) −5.63317 8.76538i −0.213678 0.332490i
\(696\) 0 0
\(697\) −11.7479 + 40.0095i −0.444982 + 1.51547i
\(698\) 0 0
\(699\) −1.18070 + 1.03371i −0.0446580 + 0.0390985i
\(700\) 0 0
\(701\) 18.4569 + 11.8615i 0.697108 + 0.448004i 0.840606 0.541647i \(-0.182199\pi\)
−0.143499 + 0.989651i \(0.545835\pi\)
\(702\) 0 0
\(703\) 27.9717 + 32.2810i 1.05497 + 1.21750i
\(704\) 0 0
\(705\) 2.02645 0.606306i 0.0763204 0.0228348i
\(706\) 0 0
\(707\) 21.7056i 0.816322i
\(708\) 0 0
\(709\) −16.7714 10.7783i −0.629865 0.404789i 0.186395 0.982475i \(-0.440320\pi\)
−0.816259 + 0.577686i \(0.803956\pi\)
\(710\) 0 0
\(711\) 12.8907 45.6250i 0.483439 1.71107i
\(712\) 0 0
\(713\) 11.4346 79.5292i 0.428228 2.97839i
\(714\) 0 0
\(715\) 2.06377 + 0.942492i 0.0771806 + 0.0352472i
\(716\) 0 0
\(717\) −6.37379 2.87146i −0.238033 0.107237i
\(718\) 0 0
\(719\) 20.6253 2.96548i 0.769195 0.110594i 0.253465 0.967345i \(-0.418430\pi\)
0.515730 + 0.856751i \(0.327521\pi\)
\(720\) 0 0
\(721\) −2.94978 10.0460i −0.109855 0.374133i
\(722\) 0 0
\(723\) 6.01651 + 5.15964i 0.223756 + 0.191889i
\(724\) 0 0
\(725\) 2.59583 + 4.03920i 0.0964069 + 0.150012i
\(726\) 0 0
\(727\) 14.7024 + 6.71435i 0.545281 + 0.249021i 0.668957 0.743301i \(-0.266741\pi\)
−0.123676 + 0.992323i \(0.539468\pi\)
\(728\) 0 0
\(729\) −22.2547 + 15.2881i −0.824250 + 0.566226i
\(730\) 0 0
\(731\) 37.5802 + 11.0345i 1.38995 + 0.408127i
\(732\) 0 0
\(733\) −6.02305 + 0.865984i −0.222467 + 0.0319859i −0.252647 0.967559i \(-0.581301\pi\)
0.0301801 + 0.999544i \(0.490392\pi\)
\(734\) 0 0
\(735\) −0.0289209 5.64827i −0.00106676 0.208340i
\(736\) 0 0
\(737\) −9.05896 2.41827i −0.333691 0.0890780i
\(738\) 0 0
\(739\) 16.3473 + 14.1650i 0.601345 + 0.521068i 0.901476 0.432830i \(-0.142485\pi\)
−0.300131 + 0.953898i \(0.597030\pi\)
\(740\) 0 0
\(741\) 20.3985 23.7862i 0.749359 0.873806i
\(742\) 0 0
\(743\) 2.90477 9.89274i 0.106566 0.362929i −0.888894 0.458113i \(-0.848526\pi\)
0.995460 + 0.0951835i \(0.0303438\pi\)
\(744\) 0 0
\(745\) −3.16080 + 4.91830i −0.115803 + 0.180193i
\(746\) 0 0
\(747\) 20.2888 32.2923i 0.742328 1.18151i
\(748\) 0 0
\(749\) −16.8663 + 10.8393i −0.616280 + 0.396059i
\(750\) 0 0
\(751\) 5.38440 + 37.4493i 0.196480 + 1.36654i 0.814400 + 0.580304i \(0.197066\pi\)
−0.617920 + 0.786241i \(0.712025\pi\)
\(752\) 0 0
\(753\) 22.1639 34.8790i 0.807696 1.27106i
\(754\) 0 0
\(755\) 1.73351 + 12.0568i 0.0630888 + 0.438792i
\(756\) 0 0
\(757\) −34.1999 + 15.6186i −1.24302 + 0.567667i −0.924837 0.380363i \(-0.875799\pi\)
−0.318180 + 0.948030i \(0.603072\pi\)
\(758\) 0 0
\(759\) 17.6774 5.28900i 0.641647 0.191979i
\(760\) 0 0
\(761\) 36.7723 + 5.28706i 1.33300 + 0.191656i 0.771714 0.635969i \(-0.219400\pi\)
0.561281 + 0.827625i \(0.310309\pi\)
\(762\) 0 0
\(763\) 1.50849 10.4918i 0.0546110 0.379828i
\(764\) 0 0
\(765\) −8.46728 7.18646i −0.306135 0.259827i
\(766\) 0 0
\(767\) 26.0445 0.940411
\(768\) 0 0
\(769\) −24.3703 11.1296i −0.878817 0.401342i −0.0756767 0.997132i \(-0.524112\pi\)
−0.803140 + 0.595790i \(0.796839\pi\)
\(770\) 0 0
\(771\) 4.37095 31.5465i 0.157416 1.13612i
\(772\) 0 0
\(773\) 13.4086 20.8642i 0.482273 0.750432i −0.511805 0.859102i \(-0.671023\pi\)
0.994078 + 0.108670i \(0.0346592\pi\)
\(774\) 0 0
\(775\) 39.9986i 1.43679i
\(776\) 0 0