Properties

Label 108.4.i.a.49.9
Level $108$
Weight $4$
Character 108.49
Analytic conductor $6.372$
Analytic rank $0$
Dimension $54$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.i (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.37220628062\)
Analytic rank: \(0\)
Dimension: \(54\)
Relative dimension: \(9\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 49.9
Character \(\chi\) \(=\) 108.49
Dual form 108.4.i.a.97.9

$q$-expansion

\(f(q)\) \(=\) \(q+(5.17716 - 0.443910i) q^{3} +(-4.80495 + 1.74886i) q^{5} +(5.74341 + 32.5725i) q^{7} +(26.6059 - 4.59638i) q^{9} +O(q^{10})\) \(q+(5.17716 - 0.443910i) q^{3} +(-4.80495 + 1.74886i) q^{5} +(5.74341 + 32.5725i) q^{7} +(26.6059 - 4.59638i) q^{9} +(28.2317 + 10.2755i) q^{11} +(7.59849 + 6.37589i) q^{13} +(-24.0996 + 11.1871i) q^{15} +(44.7319 - 77.4779i) q^{17} +(-29.6509 - 51.3568i) q^{19} +(44.1938 + 166.083i) q^{21} +(-17.0562 + 96.7304i) q^{23} +(-75.7266 + 63.5421i) q^{25} +(135.702 - 35.6068i) q^{27} +(108.085 - 90.6938i) q^{29} +(4.10141 - 23.2603i) q^{31} +(150.721 + 40.6655i) q^{33} +(-84.5615 - 146.465i) q^{35} +(-114.087 + 197.604i) q^{37} +(42.1689 + 29.6359i) q^{39} +(-357.814 - 300.241i) q^{41} +(-10.1135 - 3.68102i) q^{43} +(-119.801 + 68.6153i) q^{45} +(-66.0561 - 374.623i) q^{47} +(-705.667 + 256.842i) q^{49} +(197.191 - 420.972i) q^{51} -202.984 q^{53} -153.622 q^{55} +(-176.305 - 252.720i) q^{57} +(766.955 - 279.149i) q^{59} +(-109.702 - 622.151i) q^{61} +(302.524 + 840.222i) q^{63} +(-47.6609 - 17.3471i) q^{65} +(-466.269 - 391.246i) q^{67} +(-45.3629 + 508.360i) q^{69} +(140.376 - 243.138i) q^{71} +(608.806 + 1054.48i) q^{73} +(-363.841 + 362.583i) q^{75} +(-172.552 + 978.592i) q^{77} +(278.680 - 233.841i) q^{79} +(686.746 - 244.582i) q^{81} +(453.825 - 380.804i) q^{83} +(-79.4366 + 450.507i) q^{85} +(519.311 - 517.516i) q^{87} +(-359.138 - 622.046i) q^{89} +(-164.037 + 284.121i) q^{91} +(10.9082 - 122.243i) q^{93} +(232.286 + 194.911i) q^{95} +(776.386 + 282.581i) q^{97} +(798.358 + 143.625i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54q + 12q^{5} - 48q^{9} + O(q^{10}) \) \( 54q + 12q^{5} - 48q^{9} - 87q^{11} + 234q^{15} + 204q^{17} - 12q^{21} + 96q^{23} - 216q^{25} + 27q^{27} + 318q^{29} - 54q^{31} + 63q^{33} + 6q^{35} + 66q^{39} + 867q^{41} - 513q^{43} - 306q^{45} - 1548q^{47} + 594q^{49} - 1368q^{51} - 1068q^{53} - 1269q^{57} - 1218q^{59} - 54q^{61} + 30q^{63} + 96q^{65} - 2997q^{67} + 1476q^{69} - 120q^{71} - 216q^{73} + 732q^{75} + 3480q^{77} + 2808q^{79} + 3348q^{81} + 4464q^{83} + 2160q^{85} + 4824q^{87} + 4029q^{89} + 270q^{91} + 1164q^{93} - 1650q^{95} - 3483q^{97} - 5076q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\) \(1\)

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
\(3\) 5.17716 0.443910i 0.996344 0.0854306i
\(4\) 0 0
\(5\) −4.80495 + 1.74886i −0.429767 + 0.156423i −0.547841 0.836582i \(-0.684550\pi\)
0.118074 + 0.993005i \(0.462328\pi\)
\(6\) 0 0
\(7\) 5.74341 + 32.5725i 0.310115 + 1.75875i 0.598392 + 0.801203i \(0.295806\pi\)
−0.288277 + 0.957547i \(0.593082\pi\)
\(8\) 0 0
\(9\) 26.6059 4.59638i 0.985403 0.170236i
\(10\) 0 0
\(11\) 28.2317 + 10.2755i 0.773833 + 0.281652i 0.698599 0.715514i \(-0.253807\pi\)
0.0752344 + 0.997166i \(0.476029\pi\)
\(12\) 0 0
\(13\) 7.59849 + 6.37589i 0.162111 + 0.136027i 0.720235 0.693731i \(-0.244034\pi\)
−0.558124 + 0.829758i \(0.688479\pi\)
\(14\) 0 0
\(15\) −24.0996 + 11.1871i −0.414833 + 0.192566i
\(16\) 0 0
\(17\) 44.7319 77.4779i 0.638181 1.10536i −0.347650 0.937624i \(-0.613020\pi\)
0.985832 0.167738i \(-0.0536463\pi\)
\(18\) 0 0
\(19\) −29.6509 51.3568i −0.358020 0.620108i 0.629610 0.776911i \(-0.283215\pi\)
−0.987630 + 0.156803i \(0.949881\pi\)
\(20\) 0 0
\(21\) 44.1938 + 166.083i 0.459232 + 1.72583i
\(22\) 0 0
\(23\) −17.0562 + 96.7304i −0.154629 + 0.876943i 0.804496 + 0.593958i \(0.202436\pi\)
−0.959124 + 0.282984i \(0.908676\pi\)
\(24\) 0 0
\(25\) −75.7266 + 63.5421i −0.605812 + 0.508337i
\(26\) 0 0
\(27\) 135.702 35.6068i 0.967257 0.253798i
\(28\) 0 0
\(29\) 108.085 90.6938i 0.692097 0.580738i −0.227416 0.973798i \(-0.573028\pi\)
0.919513 + 0.393059i \(0.128583\pi\)
\(30\) 0 0
\(31\) 4.10141 23.2603i 0.0237624 0.134764i −0.970619 0.240623i \(-0.922648\pi\)
0.994381 + 0.105859i \(0.0337594\pi\)
\(32\) 0 0
\(33\) 150.721 + 40.6655i 0.795066 + 0.214514i
\(34\) 0 0
\(35\) −84.5615 146.465i −0.408386 0.707345i
\(36\) 0 0
\(37\) −114.087 + 197.604i −0.506912 + 0.877997i 0.493056 + 0.869998i \(0.335880\pi\)
−0.999968 + 0.00799976i \(0.997454\pi\)
\(38\) 0 0
\(39\) 42.1689 + 29.6359i 0.173139 + 0.121681i
\(40\) 0 0
\(41\) −357.814 300.241i −1.36295 1.14365i −0.975058 0.221951i \(-0.928758\pi\)
−0.387896 0.921703i \(-0.626798\pi\)
\(42\) 0 0
\(43\) −10.1135 3.68102i −0.0358673 0.0130546i 0.324024 0.946049i \(-0.394964\pi\)
−0.359892 + 0.932994i \(0.617186\pi\)
\(44\) 0 0
\(45\) −119.801 + 68.6153i −0.396865 + 0.227301i
\(46\) 0 0
\(47\) −66.0561 374.623i −0.205006 1.16265i −0.897430 0.441156i \(-0.854569\pi\)
0.692424 0.721490i \(-0.256543\pi\)
\(48\) 0 0
\(49\) −705.667 + 256.842i −2.05734 + 0.748810i
\(50\) 0 0
\(51\) 197.191 420.972i 0.541417 1.15584i
\(52\) 0 0
\(53\) −202.984 −0.526076 −0.263038 0.964786i \(-0.584724\pi\)
−0.263038 + 0.964786i \(0.584724\pi\)
\(54\) 0 0
\(55\) −153.622 −0.376625
\(56\) 0 0
\(57\) −176.305 252.720i −0.409687 0.587255i
\(58\) 0 0
\(59\) 766.955 279.149i 1.69236 0.615967i 0.697437 0.716646i \(-0.254324\pi\)
0.994919 + 0.100678i \(0.0321013\pi\)
\(60\) 0 0
\(61\) −109.702 622.151i −0.230261 1.30587i −0.852368 0.522942i \(-0.824835\pi\)
0.622108 0.782932i \(-0.286277\pi\)
\(62\) 0 0
\(63\) 302.524 + 840.222i 0.604992 + 1.68029i
\(64\) 0 0
\(65\) −47.6609 17.3471i −0.0909477 0.0331023i
\(66\) 0 0
\(67\) −466.269 391.246i −0.850206 0.713408i 0.109629 0.993973i \(-0.465034\pi\)
−0.959835 + 0.280565i \(0.909478\pi\)
\(68\) 0 0
\(69\) −45.3629 + 508.360i −0.0791457 + 0.886947i
\(70\) 0 0
\(71\) 140.376 243.138i 0.234642 0.406411i −0.724527 0.689247i \(-0.757942\pi\)
0.959168 + 0.282835i \(0.0912750\pi\)
\(72\) 0 0
\(73\) 608.806 + 1054.48i 0.976101 + 1.69066i 0.676252 + 0.736671i \(0.263603\pi\)
0.299849 + 0.953987i \(0.403064\pi\)
\(74\) 0 0
\(75\) −363.841 + 362.583i −0.560170 + 0.558233i
\(76\) 0 0
\(77\) −172.552 + 978.592i −0.255379 + 1.44832i
\(78\) 0 0
\(79\) 278.680 233.841i 0.396886 0.333027i −0.422402 0.906408i \(-0.638813\pi\)
0.819289 + 0.573381i \(0.194369\pi\)
\(80\) 0 0
\(81\) 686.746 244.582i 0.942039 0.335503i
\(82\) 0 0
\(83\) 453.825 380.804i 0.600166 0.503599i −0.291333 0.956622i \(-0.594099\pi\)
0.891499 + 0.453023i \(0.149654\pi\)
\(84\) 0 0
\(85\) −79.4366 + 450.507i −0.101366 + 0.574875i
\(86\) 0 0
\(87\) 519.311 517.516i 0.639954 0.637741i
\(88\) 0 0
\(89\) −359.138 622.046i −0.427737 0.740862i 0.568935 0.822383i \(-0.307356\pi\)
−0.996672 + 0.0815204i \(0.974022\pi\)
\(90\) 0 0
\(91\) −164.037 + 284.121i −0.188965 + 0.327297i
\(92\) 0 0
\(93\) 10.9082 122.243i 0.0121626 0.136301i
\(94\) 0 0
\(95\) 232.286 + 194.911i 0.250864 + 0.210500i
\(96\) 0 0
\(97\) 776.386 + 282.581i 0.812681 + 0.295792i 0.714731 0.699400i \(-0.246549\pi\)
0.0979501 + 0.995191i \(0.468771\pi\)
\(98\) 0 0
\(99\) 798.358 + 143.625i 0.810485 + 0.145806i
\(100\) 0 0
\(101\) 171.883 + 974.796i 0.169336 + 0.960355i 0.944480 + 0.328569i \(0.106566\pi\)
−0.775143 + 0.631785i \(0.782322\pi\)
\(102\) 0 0
\(103\) 645.975 235.116i 0.617959 0.224919i −0.0140232 0.999902i \(-0.504464\pi\)
0.631982 + 0.774983i \(0.282242\pi\)
\(104\) 0 0
\(105\) −502.805 720.733i −0.467321 0.669870i
\(106\) 0 0
\(107\) −1298.75 −1.17341 −0.586706 0.809800i \(-0.699576\pi\)
−0.586706 + 0.809800i \(0.699576\pi\)
\(108\) 0 0
\(109\) 576.373 0.506482 0.253241 0.967403i \(-0.418503\pi\)
0.253241 + 0.967403i \(0.418503\pi\)
\(110\) 0 0
\(111\) −502.926 + 1073.67i −0.430051 + 0.918093i
\(112\) 0 0
\(113\) −1844.78 + 671.443i −1.53577 + 0.558974i −0.965026 0.262155i \(-0.915567\pi\)
−0.570743 + 0.821129i \(0.693345\pi\)
\(114\) 0 0
\(115\) −87.2136 494.613i −0.0707193 0.401069i
\(116\) 0 0
\(117\) 231.471 + 134.711i 0.182901 + 0.106444i
\(118\) 0 0
\(119\) 2780.57 + 1012.04i 2.14197 + 0.779612i
\(120\) 0 0
\(121\) −328.164 275.362i −0.246555 0.206884i
\(122\) 0 0
\(123\) −1985.74 1395.56i −1.45567 1.02303i
\(124\) 0 0
\(125\) 572.318 991.284i 0.409518 0.709305i
\(126\) 0 0
\(127\) −245.983 426.055i −0.171870 0.297687i 0.767204 0.641403i \(-0.221647\pi\)
−0.939073 + 0.343716i \(0.888314\pi\)
\(128\) 0 0
\(129\) −53.9933 14.5677i −0.0368515 0.00994275i
\(130\) 0 0
\(131\) −377.965 + 2143.55i −0.252084 + 1.42964i 0.551365 + 0.834264i \(0.314107\pi\)
−0.803449 + 0.595374i \(0.797004\pi\)
\(132\) 0 0
\(133\) 1502.52 1260.77i 0.979588 0.821972i
\(134\) 0 0
\(135\) −589.772 + 408.413i −0.375996 + 0.260375i
\(136\) 0 0
\(137\) 1065.12 893.740i 0.664228 0.557353i −0.247123 0.968984i \(-0.579485\pi\)
0.911351 + 0.411631i \(0.135041\pi\)
\(138\) 0 0
\(139\) 191.282 1084.82i 0.116722 0.661963i −0.869161 0.494529i \(-0.835341\pi\)
0.985883 0.167435i \(-0.0535483\pi\)
\(140\) 0 0
\(141\) −508.282 1910.16i −0.303582 1.14088i
\(142\) 0 0
\(143\) 149.003 + 258.080i 0.0871344 + 0.150921i
\(144\) 0 0
\(145\) −360.730 + 624.803i −0.206600 + 0.357842i
\(146\) 0 0
\(147\) −3539.33 + 1642.96i −1.98585 + 0.921832i
\(148\) 0 0
\(149\) 1499.38 + 1258.13i 0.824388 + 0.691744i 0.953995 0.299821i \(-0.0969271\pi\)
−0.129607 + 0.991565i \(0.541372\pi\)
\(150\) 0 0
\(151\) 617.466 + 224.739i 0.332773 + 0.121119i 0.503002 0.864285i \(-0.332229\pi\)
−0.170230 + 0.985404i \(0.554451\pi\)
\(152\) 0 0
\(153\) 834.014 2266.97i 0.440693 1.19787i
\(154\) 0 0
\(155\) 20.9718 + 118.937i 0.0108677 + 0.0616339i
\(156\) 0 0
\(157\) −1247.25 + 453.962i −0.634022 + 0.230765i −0.638981 0.769222i \(-0.720644\pi\)
0.00495878 + 0.999988i \(0.498422\pi\)
\(158\) 0 0
\(159\) −1050.88 + 90.1067i −0.524152 + 0.0449429i
\(160\) 0 0
\(161\) −3248.71 −1.59028
\(162\) 0 0
\(163\) 2562.11 1.23116 0.615582 0.788073i \(-0.288921\pi\)
0.615582 + 0.788073i \(0.288921\pi\)
\(164\) 0 0
\(165\) −795.325 + 68.1943i −0.375248 + 0.0321753i
\(166\) 0 0
\(167\) −3356.67 + 1221.73i −1.55537 + 0.566109i −0.969670 0.244417i \(-0.921404\pi\)
−0.585703 + 0.810526i \(0.699181\pi\)
\(168\) 0 0
\(169\) −364.420 2066.73i −0.165872 0.940705i
\(170\) 0 0
\(171\) −1024.94 1230.11i −0.458359 0.550109i
\(172\) 0 0
\(173\) −2140.09 778.930i −0.940510 0.342318i −0.174143 0.984720i \(-0.555715\pi\)
−0.766367 + 0.642403i \(0.777938\pi\)
\(174\) 0 0
\(175\) −2504.66 2101.66i −1.08191 0.907830i
\(176\) 0 0
\(177\) 3846.73 1785.66i 1.63355 0.758294i
\(178\) 0 0
\(179\) 577.965 1001.07i 0.241336 0.418006i −0.719759 0.694224i \(-0.755748\pi\)
0.961095 + 0.276218i \(0.0890811\pi\)
\(180\) 0 0
\(181\) 1786.92 + 3095.03i 0.733815 + 1.27100i 0.955241 + 0.295827i \(0.0955952\pi\)
−0.221427 + 0.975177i \(0.571071\pi\)
\(182\) 0 0
\(183\) −844.124 3172.27i −0.340980 1.28143i
\(184\) 0 0
\(185\) 202.599 1149.00i 0.0805157 0.456627i
\(186\) 0 0
\(187\) 2058.98 1727.69i 0.805174 0.675621i
\(188\) 0 0
\(189\) 1939.20 + 4215.67i 0.746328 + 1.62246i
\(190\) 0 0
\(191\) −615.799 + 516.717i −0.233286 + 0.195750i −0.751935 0.659237i \(-0.770880\pi\)
0.518649 + 0.854987i \(0.326435\pi\)
\(192\) 0 0
\(193\) −155.121 + 879.737i −0.0578543 + 0.328108i −0.999974 0.00716788i \(-0.997718\pi\)
0.942120 + 0.335276i \(0.108829\pi\)
\(194\) 0 0
\(195\) −254.448 68.6517i −0.0934432 0.0252115i
\(196\) 0 0
\(197\) 1162.98 + 2014.35i 0.420605 + 0.728509i 0.995999 0.0893676i \(-0.0284846\pi\)
−0.575394 + 0.817876i \(0.695151\pi\)
\(198\) 0 0
\(199\) 158.416 274.384i 0.0564311 0.0977415i −0.836430 0.548074i \(-0.815361\pi\)
0.892861 + 0.450333i \(0.148695\pi\)
\(200\) 0 0
\(201\) −2587.63 1818.56i −0.908045 0.638166i
\(202\) 0 0
\(203\) 3574.90 + 2999.70i 1.23600 + 1.03713i
\(204\) 0 0
\(205\) 2244.35 + 816.878i 0.764646 + 0.278309i
\(206\) 0 0
\(207\) −9.18465 + 2652.00i −0.00308395 + 0.890466i
\(208\) 0 0
\(209\) −309.377 1754.56i −0.102393 0.580697i
\(210\) 0 0
\(211\) −3958.48 + 1440.77i −1.29153 + 0.470079i −0.894229 0.447609i \(-0.852276\pi\)
−0.397302 + 0.917688i \(0.630054\pi\)
\(212\) 0 0
\(213\) 618.816 1321.08i 0.199064 0.424971i
\(214\) 0 0
\(215\) 55.0324 0.0174567
\(216\) 0 0
\(217\) 781.202 0.244384
\(218\) 0 0
\(219\) 3619.98 + 5188.97i 1.11697 + 1.60109i
\(220\) 0 0
\(221\) 833.886 303.510i 0.253816 0.0923813i
\(222\) 0 0
\(223\) −92.7029 525.744i −0.0278379 0.157876i 0.967720 0.252028i \(-0.0810974\pi\)
−0.995558 + 0.0941513i \(0.969986\pi\)
\(224\) 0 0
\(225\) −1722.71 + 2038.66i −0.510432 + 0.604048i
\(226\) 0 0
\(227\) 5420.84 + 1973.03i 1.58500 + 0.576891i 0.976283 0.216500i \(-0.0694640\pi\)
0.608713 + 0.793391i \(0.291686\pi\)
\(228\) 0 0
\(229\) 1142.36 + 958.554i 0.329647 + 0.276607i 0.792556 0.609799i \(-0.208750\pi\)
−0.462909 + 0.886406i \(0.653194\pi\)
\(230\) 0 0
\(231\) −458.923 + 5142.92i −0.130714 + 1.46485i
\(232\) 0 0
\(233\) 225.811 391.116i 0.0634908 0.109969i −0.832533 0.553976i \(-0.813110\pi\)
0.896024 + 0.444007i \(0.146443\pi\)
\(234\) 0 0
\(235\) 972.558 + 1684.52i 0.269969 + 0.467600i
\(236\) 0 0
\(237\) 1338.97 1334.34i 0.366984 0.365716i
\(238\) 0 0
\(239\) 537.820 3050.13i 0.145559 0.825508i −0.821357 0.570414i \(-0.806783\pi\)
0.966916 0.255093i \(-0.0821062\pi\)
\(240\) 0 0
\(241\) 427.852 359.010i 0.114358 0.0959580i −0.583815 0.811886i \(-0.698441\pi\)
0.698174 + 0.715928i \(0.253996\pi\)
\(242\) 0 0
\(243\) 3446.82 1571.09i 0.909933 0.414756i
\(244\) 0 0
\(245\) 2941.51 2468.22i 0.767046 0.643628i
\(246\) 0 0
\(247\) 102.143 579.285i 0.0263127 0.149227i
\(248\) 0 0
\(249\) 2180.48 2172.94i 0.554949 0.553030i
\(250\) 0 0
\(251\) −315.189 545.923i −0.0792612 0.137284i 0.823670 0.567069i \(-0.191923\pi\)
−0.902931 + 0.429785i \(0.858589\pi\)
\(252\) 0 0
\(253\) −1475.48 + 2555.60i −0.366650 + 0.635056i
\(254\) 0 0
\(255\) −211.271 + 2367.61i −0.0518835 + 0.581433i
\(256\) 0 0
\(257\) −1711.18 1435.85i −0.415333 0.348506i 0.411051 0.911612i \(-0.365162\pi\)
−0.826384 + 0.563106i \(0.809606\pi\)
\(258\) 0 0
\(259\) −7091.71 2581.17i −1.70138 0.619251i
\(260\) 0 0
\(261\) 2458.82 2909.79i 0.583132 0.690081i
\(262\) 0 0
\(263\) 115.370 + 654.298i 0.0270496 + 0.153406i 0.995341 0.0964178i \(-0.0307385\pi\)
−0.968291 + 0.249824i \(0.919627\pi\)
\(264\) 0 0
\(265\) 975.328 354.990i 0.226090 0.0822901i
\(266\) 0 0
\(267\) −2135.45 3061.00i −0.489466 0.701612i
\(268\) 0 0
\(269\) −6952.64 −1.57587 −0.787936 0.615757i \(-0.788850\pi\)
−0.787936 + 0.615757i \(0.788850\pi\)
\(270\) 0 0
\(271\) −8783.48 −1.96885 −0.984426 0.175802i \(-0.943748\pi\)
−0.984426 + 0.175802i \(0.943748\pi\)
\(272\) 0 0
\(273\) −723.123 + 1543.76i −0.160313 + 0.342244i
\(274\) 0 0
\(275\) −2790.81 + 1015.77i −0.611972 + 0.222740i
\(276\) 0 0
\(277\) 1226.41 + 6955.33i 0.266021 + 1.50868i 0.766111 + 0.642709i \(0.222189\pi\)
−0.500089 + 0.865974i \(0.666699\pi\)
\(278\) 0 0
\(279\) 2.20859 637.712i 0.000473924 0.136842i
\(280\) 0 0
\(281\) −6216.63 2262.67i −1.31976 0.480354i −0.416379 0.909191i \(-0.636701\pi\)
−0.903382 + 0.428837i \(0.858923\pi\)
\(282\) 0 0
\(283\) 4086.69 + 3429.14i 0.858405 + 0.720288i 0.961624 0.274371i \(-0.0884696\pi\)
−0.103218 + 0.994659i \(0.532914\pi\)
\(284\) 0 0
\(285\) 1289.11 + 905.973i 0.267930 + 0.188299i
\(286\) 0 0
\(287\) 7724.54 13379.3i 1.58873 2.75176i
\(288\) 0 0
\(289\) −1545.39 2676.69i −0.314551 0.544818i
\(290\) 0 0
\(291\) 4144.91 + 1118.32i 0.834980 + 0.225283i
\(292\) 0 0
\(293\) −50.5304 + 286.572i −0.0100751 + 0.0571390i −0.989431 0.145006i \(-0.953680\pi\)
0.979356 + 0.202145i \(0.0647911\pi\)
\(294\) 0 0
\(295\) −3196.99 + 2682.59i −0.630968 + 0.529445i
\(296\) 0 0
\(297\) 4196.98 + 389.168i 0.819979 + 0.0760332i
\(298\) 0 0
\(299\) −746.344 + 626.257i −0.144355 + 0.121128i
\(300\) 0 0
\(301\) 61.8139 350.564i 0.0118369 0.0671302i
\(302\) 0 0
\(303\) 1322.59 + 4970.37i 0.250761 + 0.942377i
\(304\) 0 0
\(305\) 1615.17 + 2797.55i 0.303227 + 0.525204i
\(306\) 0 0
\(307\) 572.764 992.056i 0.106480 0.184429i −0.807862 0.589372i \(-0.799375\pi\)
0.914342 + 0.404943i \(0.132709\pi\)
\(308\) 0 0
\(309\) 3239.94 1503.98i 0.596485 0.276889i
\(310\) 0 0
\(311\) −7195.48 6037.72i −1.31196 1.10086i −0.987945 0.154808i \(-0.950524\pi\)
−0.324011 0.946053i \(-0.605031\pi\)
\(312\) 0 0
\(313\) −2912.59 1060.10i −0.525972 0.191438i 0.0653667 0.997861i \(-0.479178\pi\)
−0.591339 + 0.806423i \(0.701401\pi\)
\(314\) 0 0
\(315\) −2923.04 3508.15i −0.522840 0.627498i
\(316\) 0 0
\(317\) 116.213 + 659.077i 0.0205905 + 0.116774i 0.993371 0.114956i \(-0.0366726\pi\)
−0.972780 + 0.231730i \(0.925561\pi\)
\(318\) 0 0
\(319\) 3983.33 1449.81i 0.699134 0.254464i
\(320\) 0 0
\(321\) −6723.84 + 576.529i −1.16912 + 0.100245i
\(322\) 0 0
\(323\) −5305.36 −0.913926
\(324\) 0 0
\(325\) −980.545 −0.167356
\(326\) 0 0
\(327\) 2983.97 255.858i 0.504630 0.0432690i
\(328\) 0 0
\(329\) 11823.0 4303.23i 1.98123 0.721109i
\(330\) 0 0
\(331\) 50.4286 + 285.995i 0.00837404 + 0.0474915i 0.988708 0.149852i \(-0.0478797\pi\)
−0.980334 + 0.197343i \(0.936769\pi\)
\(332\) 0 0
\(333\) −2127.11 + 5781.82i −0.350046 + 0.951476i
\(334\) 0 0
\(335\) 2924.63 + 1064.48i 0.476984 + 0.173608i
\(336\) 0 0
\(337\) −6338.56 5318.68i −1.02458 0.859724i −0.0343831 0.999409i \(-0.510947\pi\)
−0.990196 + 0.139685i \(0.955391\pi\)
\(338\) 0 0
\(339\) −9252.63 + 4295.08i −1.48240 + 0.688132i
\(340\) 0 0
\(341\) 354.800 614.532i 0.0563446 0.0975917i
\(342\) 0 0
\(343\) −6746.56 11685.4i −1.06204 1.83951i
\(344\) 0 0
\(345\) −671.083 2521.97i −0.104724 0.393561i
\(346\) 0 0
\(347\) −698.081 + 3959.02i −0.107997 + 0.612482i 0.881984 + 0.471280i \(0.156208\pi\)
−0.989981 + 0.141202i \(0.954903\pi\)
\(348\) 0 0
\(349\) −6291.10 + 5278.86i −0.964914 + 0.809659i −0.981745 0.190200i \(-0.939086\pi\)
0.0168317 + 0.999858i \(0.494642\pi\)
\(350\) 0 0
\(351\) 1258.16 + 594.666i 0.191326 + 0.0904299i
\(352\) 0 0
\(353\) −3542.55 + 2972.56i −0.534139 + 0.448196i −0.869528 0.493884i \(-0.835577\pi\)
0.335389 + 0.942080i \(0.391132\pi\)
\(354\) 0 0
\(355\) −249.285 + 1413.76i −0.0372694 + 0.211366i
\(356\) 0 0
\(357\) 14844.7 + 4005.18i 2.20074 + 0.593772i
\(358\) 0 0
\(359\) 6159.42 + 10668.4i 0.905521 + 1.56841i 0.820217 + 0.572053i \(0.193853\pi\)
0.0853041 + 0.996355i \(0.472814\pi\)
\(360\) 0 0
\(361\) 1671.15 2894.52i 0.243644 0.422004i
\(362\) 0 0
\(363\) −1821.19 1279.92i −0.263327 0.185064i
\(364\) 0 0
\(365\) −4769.42 4002.02i −0.683953 0.573905i
\(366\) 0 0
\(367\) 8080.39 + 2941.02i 1.14930 + 0.418311i 0.845263 0.534350i \(-0.179444\pi\)
0.304036 + 0.952661i \(0.401666\pi\)
\(368\) 0 0
\(369\) −10900.0 6343.54i −1.53775 0.894936i
\(370\) 0 0
\(371\) −1165.82 6611.70i −0.163144 0.925236i
\(372\) 0 0
\(373\) −2385.97 + 868.421i −0.331208 + 0.120550i −0.502271 0.864710i \(-0.667502\pi\)
0.171063 + 0.985260i \(0.445280\pi\)
\(374\) 0 0
\(375\) 2522.94 5386.09i 0.347424 0.741697i
\(376\) 0 0
\(377\) 1399.53 0.191193
\(378\) 0 0
\(379\) 11211.7 1.51955 0.759774 0.650187i \(-0.225309\pi\)
0.759774 + 0.650187i \(0.225309\pi\)
\(380\) 0 0
\(381\) −1462.62 2096.56i −0.196673 0.281916i
\(382\) 0 0
\(383\) 7480.47 2722.67i 0.998001 0.363243i 0.209188 0.977876i \(-0.432918\pi\)
0.788813 + 0.614633i \(0.210696\pi\)
\(384\) 0 0
\(385\) −882.314 5003.85i −0.116797 0.662389i
\(386\) 0 0
\(387\) −285.998 51.4511i −0.0375662 0.00675816i
\(388\) 0 0
\(389\) −12432.6 4525.09i −1.62045 0.589797i −0.636986 0.770875i \(-0.719819\pi\)
−0.983469 + 0.181078i \(0.942041\pi\)
\(390\) 0 0
\(391\) 6731.52 + 5648.41i 0.870659 + 0.730569i
\(392\) 0 0
\(393\) −1005.24 + 11265.3i −0.129027 + 1.44595i
\(394\) 0 0
\(395\) −930.091 + 1610.96i −0.118476 + 0.205206i
\(396\) 0 0
\(397\) 6065.99 + 10506.6i 0.766859 + 1.32824i 0.939258 + 0.343212i \(0.111515\pi\)
−0.172399 + 0.985027i \(0.555152\pi\)
\(398\) 0 0
\(399\) 7219.13 7194.17i 0.905785 0.902654i
\(400\) 0 0
\(401\) 533.798 3027.32i 0.0664753 0.377000i −0.933362 0.358938i \(-0.883139\pi\)
0.999837 0.0180626i \(-0.00574981\pi\)
\(402\) 0 0
\(403\) 179.469 150.593i 0.0221837 0.0186143i
\(404\) 0 0
\(405\) −2872.04 + 2376.22i −0.352377 + 0.291544i
\(406\) 0 0
\(407\) −5251.33 + 4406.39i −0.639555 + 0.536651i
\(408\) 0 0
\(409\) −1787.94 + 10139.9i −0.216156 + 1.22588i 0.662733 + 0.748856i \(0.269396\pi\)
−0.878889 + 0.477026i \(0.841715\pi\)
\(410\) 0 0
\(411\) 5117.54 5099.85i 0.614184 0.612061i
\(412\) 0 0
\(413\) 13497.5 + 23378.4i 1.60816 + 2.78541i
\(414\) 0 0
\(415\) −1514.63 + 2623.42i −0.179157 + 0.310310i
\(416\) 0 0
\(417\) 508.738 5701.18i 0.0597434 0.669515i
\(418\) 0 0
\(419\) 3312.78 + 2779.75i 0.386252 + 0.324104i 0.815151 0.579248i \(-0.196654\pi\)
−0.428899 + 0.903353i \(0.641098\pi\)
\(420\) 0 0
\(421\) −5518.54 2008.58i −0.638853 0.232523i 0.00222710 0.999998i \(-0.499291\pi\)
−0.641080 + 0.767474i \(0.721513\pi\)
\(422\) 0 0
\(423\) −3479.39 9663.56i −0.399938 1.11078i
\(424\) 0 0
\(425\) 1535.72 + 8709.50i 0.175278 + 0.994054i
\(426\) 0 0
\(427\) 19635.0 7146.54i 2.22530 0.809942i
\(428\) 0 0
\(429\) 885.974 + 1269.98i 0.0997092 + 0.142926i
\(430\) 0 0
\(431\) −187.346 −0.0209377 −0.0104688 0.999945i \(-0.503332\pi\)
−0.0104688 + 0.999945i \(0.503332\pi\)
\(432\) 0 0
\(433\) −313.829 −0.0348307 −0.0174153 0.999848i \(-0.505544\pi\)
−0.0174153 + 0.999848i \(0.505544\pi\)
\(434\) 0 0
\(435\) −1590.20 + 3394.84i −0.175274 + 0.374184i
\(436\) 0 0
\(437\) 5473.49 1992.19i 0.599159 0.218076i
\(438\) 0 0
\(439\) 2543.97 + 14427.5i 0.276576 + 1.56854i 0.733911 + 0.679246i \(0.237693\pi\)
−0.457335 + 0.889295i \(0.651196\pi\)
\(440\) 0 0
\(441\) −17594.4 + 10077.0i −1.89983 + 1.08811i
\(442\) 0 0
\(443\) −3295.46 1199.45i −0.353436 0.128640i 0.159200 0.987246i \(-0.449109\pi\)
−0.512636 + 0.858606i \(0.671331\pi\)
\(444\) 0 0
\(445\) 2813.51 + 2360.82i 0.299715 + 0.251491i
\(446\) 0 0
\(447\) 8321.01 + 5847.94i 0.880471 + 0.618787i
\(448\) 0 0
\(449\) −905.931 + 1569.12i −0.0952194 + 0.164925i −0.909700 0.415266i \(-0.863689\pi\)
0.814481 + 0.580191i \(0.197022\pi\)
\(450\) 0 0
\(451\) −7016.55 12153.0i −0.732586 1.26888i
\(452\) 0 0
\(453\) 3296.48 + 889.411i 0.341904 + 0.0922477i
\(454\) 0 0
\(455\) 291.304 1652.07i 0.0300143 0.170220i
\(456\) 0 0
\(457\) 11433.8 9594.07i 1.17035 0.982039i 0.170354 0.985383i \(-0.445509\pi\)
0.999994 + 0.00334372i \(0.00106434\pi\)
\(458\) 0 0
\(459\) 3311.49 12106.7i 0.336747 1.23114i
\(460\) 0 0
\(461\) −6096.59 + 5115.65i −0.615936 + 0.516832i −0.896523 0.442997i \(-0.853915\pi\)
0.280587 + 0.959829i \(0.409471\pi\)
\(462\) 0 0
\(463\) 2533.18 14366.4i 0.254270 1.44204i −0.543669 0.839300i \(-0.682965\pi\)
0.797939 0.602738i \(-0.205924\pi\)
\(464\) 0 0
\(465\) 161.372 + 606.447i 0.0160934 + 0.0604802i
\(466\) 0 0
\(467\) 4109.70 + 7118.22i 0.407226 + 0.705336i 0.994578 0.103996i \(-0.0331629\pi\)
−0.587352 + 0.809332i \(0.699830\pi\)
\(468\) 0 0
\(469\) 10065.9 17434.6i 0.991044 1.71654i
\(470\) 0 0
\(471\) −6255.70 + 2903.90i −0.611990 + 0.284086i
\(472\) 0 0
\(473\) −247.697 207.842i −0.0240785 0.0202042i
\(474\) 0 0
\(475\) 5508.68 + 2004.99i 0.532117 + 0.193675i
\(476\) 0 0
\(477\) −5400.57 + 932.993i −0.518397 + 0.0895573i
\(478\) 0 0
\(479\) 729.906 + 4139.50i 0.0696247 + 0.394861i 0.999627 + 0.0273078i \(0.00869343\pi\)
−0.930002 + 0.367554i \(0.880195\pi\)
\(480\) 0 0
\(481\) −2126.79 + 774.088i −0.201607 + 0.0733791i
\(482\) 0 0
\(483\) −16819.1 + 1442.14i −1.58446 + 0.135858i
\(484\) 0 0
\(485\) −4224.69 −0.395532
\(486\) 0 0
\(487\) −13008.8 −1.21044 −0.605219 0.796059i \(-0.706914\pi\)
−0.605219 + 0.796059i \(0.706914\pi\)
\(488\) 0 0
\(489\) 13264.4 1137.34i 1.22666 0.105179i
\(490\) 0 0
\(491\) −13256.1 + 4824.83i −1.21841 + 0.443465i −0.869614 0.493733i \(-0.835632\pi\)
−0.348797 + 0.937198i \(0.613410\pi\)
\(492\) 0 0
\(493\) −2191.93 12431.1i −0.200243 1.13563i
\(494\) 0 0
\(495\) −4087.25 + 706.106i −0.371128 + 0.0641153i
\(496\) 0 0
\(497\) 8725.86 + 3175.95i 0.787542 + 0.286642i
\(498\) 0 0
\(499\) 7229.72 + 6066.46i 0.648591 + 0.544232i 0.906643 0.421899i \(-0.138636\pi\)
−0.258052 + 0.966131i \(0.583081\pi\)
\(500\) 0 0
\(501\) −16835.7 + 7815.15i −1.50132 + 0.696916i
\(502\) 0 0
\(503\) 4547.85 7877.10i 0.403138 0.698256i −0.590965 0.806697i \(-0.701253\pi\)
0.994103 + 0.108442i \(0.0345861\pi\)
\(504\) 0 0
\(505\) −2530.67 4383.24i −0.222996 0.386241i
\(506\) 0 0
\(507\) −2804.10 10538.0i −0.245630 0.923095i
\(508\) 0 0
\(509\) 1245.45 7063.30i 0.108455 0.615079i −0.881329 0.472503i \(-0.843350\pi\)
0.989784 0.142576i \(-0.0455384\pi\)
\(510\) 0 0
\(511\) −30850.6 + 25886.7i −2.67074 + 2.24102i
\(512\) 0 0
\(513\) −5852.35 5913.47i −0.503679 0.508940i
\(514\) 0 0
\(515\) −2692.69 + 2259.43i −0.230396 + 0.193325i
\(516\) 0 0
\(517\) 1984.56 11255.0i 0.168822 0.957435i
\(518\) 0 0
\(519\) −11425.4 3082.63i −0.966316 0.260718i
\(520\) 0 0
\(521\) 4043.78 + 7004.04i 0.340041 + 0.588968i 0.984440 0.175721i \(-0.0562257\pi\)
−0.644399 + 0.764689i \(0.722892\pi\)
\(522\) 0 0
\(523\) 7678.53 13299.6i 0.641986 1.11195i −0.343003 0.939334i \(-0.611444\pi\)
0.984989 0.172618i \(-0.0552226\pi\)
\(524\) 0 0
\(525\) −13899.9 9768.76i −1.15551 0.812083i
\(526\) 0 0
\(527\) −1618.69 1358.25i −0.133798 0.112270i
\(528\) 0 0
\(529\) 2367.38 + 861.657i 0.194574 + 0.0708192i
\(530\) 0 0
\(531\) 19122.4 10952.2i 1.56279 0.895077i
\(532\) 0 0
\(533\) −804.538 4562.76i −0.0653816 0.370798i
\(534\) 0 0
\(535\) 6240.43 2271.33i 0.504294 0.183548i
\(536\) 0 0
\(537\) 2547.83 5439.24i 0.204743 0.437096i
\(538\) 0 0
\(539\) −22561.3 −1.80294
\(540\) 0 0
\(541\) 2309.43 0.183531 0.0917654 0.995781i \(-0.470749\pi\)
0.0917654 + 0.995781i \(0.470749\pi\)
\(542\) 0 0
\(543\) 10625.1 + 15230.2i 0.839714 + 1.20367i
\(544\) 0 0
\(545\) −2769.44 + 1007.99i −0.217669 + 0.0792252i
\(546\) 0 0
\(547\) 2461.77 + 13961.4i 0.192427 + 1.09131i 0.916035 + 0.401098i \(0.131371\pi\)
−0.723608 + 0.690212i \(0.757517\pi\)
\(548\) 0 0
\(549\) −5778.36 16048.6i −0.449207 1.24761i
\(550\) 0 0
\(551\) −7862.54 2861.73i −0.607905 0.221259i
\(552\) 0 0
\(553\) 9217.36 + 7734.28i 0.708792 + 0.594747i
\(554\) 0 0
\(555\) 538.837 6038.48i 0.0412114 0.461836i
\(556\) 0 0
\(557\) 11430.0 19797.4i 0.869489 1.50600i 0.00697005 0.999976i \(-0.497781\pi\)
0.862519 0.506024i \(-0.168885\pi\)
\(558\) 0 0
\(559\) −53.3776 92.4528i −0.00403870 0.00699524i
\(560\) 0 0
\(561\) 9892.72 9858.52i 0.744511 0.741937i
\(562\) 0 0
\(563\) 1033.46 5861.04i 0.0773626 0.438745i −0.921382 0.388658i \(-0.872939\pi\)
0.998745 0.0500875i \(-0.0159500\pi\)
\(564\) 0 0
\(565\) 7689.79 6452.50i 0.572587 0.480458i
\(566\) 0 0
\(567\) 11910.9 + 20964.3i 0.882207 + 1.55277i
\(568\) 0 0
\(569\) −8500.63 + 7132.88i −0.626301 + 0.525529i −0.899777 0.436350i \(-0.856271\pi\)
0.273476 + 0.961879i \(0.411826\pi\)
\(570\) 0 0
\(571\) −1804.91 + 10236.2i −0.132282 + 0.750211i 0.844431 + 0.535664i \(0.179939\pi\)
−0.976714 + 0.214547i \(0.931173\pi\)
\(572\) 0 0
\(573\) −2958.71 + 2948.48i −0.215710 + 0.214964i
\(574\) 0 0
\(575\) −4854.85 8408.85i −0.352106 0.609866i
\(576\) 0 0
\(577\) −10062.0 + 17427.8i −0.725971 + 1.25742i 0.232602 + 0.972572i \(0.425276\pi\)
−0.958573 + 0.284846i \(0.908057\pi\)
\(578\) 0 0
\(579\) −412.563 + 4623.39i −0.0296123 + 0.331851i
\(580\) 0 0
\(581\) 15010.3 + 12595.1i 1.07183 + 0.899368i
\(582\) 0 0
\(583\) −5730.58 2085.76i −0.407095 0.148170i
\(584\) 0 0
\(585\) −1347.79 242.468i −0.0952554 0.0171365i
\(586\) 0 0
\(587\) 2679.51 + 15196.3i 0.188408 + 1.06851i 0.921498 + 0.388382i \(0.126966\pi\)
−0.733091 + 0.680131i \(0.761923\pi\)
\(588\) 0 0
\(589\) −1316.18 + 479.052i −0.0920754 + 0.0335127i
\(590\) 0 0
\(591\) 6915.14 + 9912.32i 0.481304 + 0.689913i
\(592\) 0 0
\(593\) 8549.53 0.592052 0.296026 0.955180i \(-0.404338\pi\)
0.296026 + 0.955180i \(0.404338\pi\)
\(594\) 0 0
\(595\) −15130.4 −1.04250
\(596\) 0 0
\(597\) 698.340 1490.85i 0.0478746 0.102205i
\(598\) 0 0
\(599\) −15101.5 + 5496.51i −1.03010 + 0.374927i −0.801120 0.598504i \(-0.795762\pi\)
−0.228983 + 0.973430i \(0.573540\pi\)
\(600\) 0 0
\(601\) −1363.83 7734.68i −0.0925656 0.524966i −0.995466 0.0951161i \(-0.969678\pi\)
0.902901 0.429849i \(-0.141433\pi\)
\(602\) 0 0
\(603\) −14203.8 8266.30i −0.959244 0.558258i
\(604\) 0 0
\(605\) 2058.38 + 749.189i 0.138322 + 0.0503453i
\(606\) 0 0
\(607\) 1421.95 + 1193.16i 0.0950829 + 0.0797840i 0.689090 0.724676i \(-0.258010\pi\)
−0.594007 + 0.804460i \(0.702455\pi\)
\(608\) 0 0
\(609\) 19839.4 + 13943.0i 1.32009 + 0.927746i
\(610\) 0 0
\(611\) 1886.63 3267.74i 0.124918 0.216364i
\(612\) 0 0
\(613\) −3861.72 6688.70i −0.254443 0.440708i 0.710301 0.703898i \(-0.248559\pi\)
−0.964744 + 0.263190i \(0.915225\pi\)
\(614\) 0 0
\(615\) 11982.0 + 3232.81i 0.785627 + 0.211967i
\(616\) 0 0
\(617\) 3164.80 17948.4i 0.206499 1.17111i −0.688564 0.725175i \(-0.741759\pi\)
0.895063 0.445939i \(-0.147130\pi\)
\(618\) 0 0
\(619\) 1605.52 1347.19i 0.104251 0.0874770i −0.589172 0.808007i \(-0.700546\pi\)
0.693423 + 0.720530i \(0.256102\pi\)
\(620\) 0 0
\(621\) 1129.70 + 13733.9i 0.0730003 + 0.887474i
\(622\) 0 0
\(623\) 18198.9 15270.7i 1.17034 0.982035i
\(624\) 0 0
\(625\) 1129.38 6405.05i 0.0722806 0.409923i
\(626\) 0 0
\(627\) −2380.56 8946.32i −0.151628 0.569827i
\(628\) 0 0
\(629\) 10206.6 + 17678.4i 0.647004 + 1.12064i
\(630\) 0 0
\(631\) −9208.35 + 15949.3i −0.580948 + 1.00623i 0.414419 + 0.910086i \(0.363985\pi\)
−0.995367 + 0.0961459i \(0.969348\pi\)
\(632\) 0 0
\(633\) −19854.1 + 9216.30i −1.24665 + 0.578697i
\(634\) 0 0
\(635\) 1927.04 + 1616.98i 0.120429 + 0.101052i
\(636\) 0 0
\(637\) −6999.60 2547.65i −0.435376 0.158464i
\(638\) 0 0
\(639\) 2617.27 7114.13i 0.162031 0.440423i
\(640\) 0 0
\(641\) −4147.90 23523.9i −0.255589 1.44951i −0.794557 0.607189i \(-0.792297\pi\)
0.538969 0.842326i \(-0.318814\pi\)
\(642\) 0 0
\(643\) −3014.06 + 1097.03i −0.184857 + 0.0672824i −0.432790 0.901495i \(-0.642471\pi\)
0.247933 + 0.968777i \(0.420249\pi\)
\(644\) 0 0
\(645\) 284.912 24.4295i 0.0173928 0.00149133i
\(646\) 0 0
\(647\) −8439.89 −0.512838 −0.256419 0.966566i \(-0.582543\pi\)
−0.256419 + 0.966566i \(0.582543\pi\)
\(648\) 0 0
\(649\) 24520.8 1.48309
\(650\) 0 0
\(651\) 4044.40 346.783i 0.243491 0.0208779i
\(652\) 0 0
\(653\) 26279.5 9564.97i 1.57488 0.573210i 0.600798 0.799401i \(-0.294849\pi\)
0.974083 + 0.226191i \(0.0726272\pi\)
\(654\) 0 0
\(655\) −1932.66 10960.6i −0.115290 0.653844i
\(656\) 0 0
\(657\) 21044.6 + 25257.2i 1.24966 + 1.49981i
\(658\) 0 0
\(659\) −4419.19 1608.45i −0.261225 0.0950781i 0.208088 0.978110i \(-0.433276\pi\)
−0.469313 + 0.883032i \(0.655498\pi\)
\(660\) 0 0
\(661\) −24298.4 20388.8i −1.42980 1.19975i −0.945829 0.324664i \(-0.894749\pi\)
−0.483973 0.875083i \(-0.660807\pi\)
\(662\) 0 0
\(663\) 4182.43 1941.49i 0.244995 0.113727i
\(664\) 0 0
\(665\) −5014.64 + 8685.61i −0.292420 + 0.506486i
\(666\) 0 0
\(667\) 6929.33 + 12002.0i 0.402256 + 0.696728i
\(668\) 0 0
\(669\) −713.320 2680.71i −0.0412236 0.154921i
\(670\) 0 0
\(671\) 3295.83 18691.6i 0.189619 1.07538i
\(672\) 0 0
\(673\) 1397.36 1172.52i 0.0800358 0.0671580i −0.601892 0.798577i \(-0.705586\pi\)
0.681928 + 0.731419i \(0.261142\pi\)
\(674\) 0 0
\(675\) −8013.75 + 11319.2i −0.456962 + 0.645446i
\(676\) 0 0
\(677\) 7383.95 6195.87i 0.419185 0.351738i −0.408668 0.912683i \(-0.634007\pi\)
0.827853 + 0.560945i \(0.189562\pi\)
\(678\) 0 0
\(679\) −4745.28 + 26911.8i −0.268199 + 1.52103i
\(680\) 0 0
\(681\) 28940.4 + 7808.29i 1.62849 + 0.439375i
\(682\) 0 0
\(683\) 3985.79 + 6903.58i 0.223297 + 0.386762i 0.955807 0.293994i \(-0.0949847\pi\)
−0.732510 + 0.680756i \(0.761651\pi\)
\(684\) 0 0
\(685\) −3554.81 + 6157.11i −0.198281 + 0.343432i
\(686\) 0 0
\(687\) 6339.69 + 4455.48i 0.352073 + 0.247434i
\(688\) 0 0
\(689\) −1542.37 1294.20i −0.0852826 0.0715606i
\(690\) 0 0
\(691\) 18824.4 + 6851.54i 1.03635 + 0.377199i 0.803494 0.595313i \(-0.202972\pi\)
0.232853 + 0.972512i \(0.425194\pi\)
\(692\) 0 0
\(693\) −92.9184 + 26829.4i −0.00509333 + 1.47066i
\(694\) 0 0
\(695\) 978.087 + 5547.01i 0.0533827 + 0.302748i
\(696\) 0 0
\(697\) −39267.8 + 14292.3i −2.13396 + 0.776699i
\(698\) 0 0
\(699\) 995.437 2125.11i 0.0538639 0.114991i
\(700\) 0 0
\(701\) −14959.1 −0.805987 −0.402993 0.915203i \(-0.632030\pi\)
−0.402993 + 0.915203i \(0.632030\pi\)
\(702\) 0 0
\(703\) 13531.1 0.725938
\(704\) 0 0
\(705\) 5782.86 + 8289.30i 0.308929 + 0.442827i
\(706\) 0 0
\(707\) −30764.4 + 11197.3i −1.63651 + 0.595641i
\(708\) 0 0
\(709\) −1068.39 6059.12i −0.0565925 0.320952i 0.943349 0.331803i \(-0.107657\pi\)
−0.999941 + 0.0108511i \(0.996546\pi\)
\(710\) 0 0
\(711\) 6339.72 7502.46i 0.334400 0.395730i
\(712\) 0 0
\(713\) 2180.02 + 793.463i 0.114506 + 0.0416766i
\(714\) 0 0
\(715\) −1167.29 979.477i −0.0610550 0.0512313i
\(716\) 0 0
\(717\) 1430.39 16029.7i 0.0745036 0.834925i
\(718\) 0 0
\(719\) 10762.6 18641.4i 0.558244 0.966908i −0.439399 0.898292i \(-0.644809\pi\)
0.997643 0.0686155i \(-0.0218582\pi\)
\(720\) 0 0
\(721\) 11368.4 + 19690.7i 0.587214 + 1.01708i
\(722\) 0 0
\(723\) 2055.69 2048.58i 0.105743 0.105377i
\(724\) 0 0
\(725\) −2422.00 + 13735.9i −0.124070 + 0.703637i
\(726\) 0 0
\(727\) 9630.04 8080.56i 0.491277 0.412230i −0.363207 0.931709i \(-0.618318\pi\)
0.854484 + 0.519478i \(0.173874\pi\)
\(728\) 0 0
\(729\) 17147.3 9663.87i 0.871173 0.490975i
\(730\) 0 0
\(731\) −737.594 + 618.915i −0.0373200 + 0.0313152i
\(732\) 0 0
\(733\) −644.806 + 3656.88i −0.0324918 + 0.184270i −0.996734 0.0807515i \(-0.974268\pi\)
0.964242 + 0.265022i \(0.0853791\pi\)
\(734\) 0 0
\(735\) 14133.0 14084.1i 0.709257 0.706805i
\(736\) 0 0
\(737\) −9143.30 15836.7i −0.456985 0.791521i
\(738\) 0 0
\(739\) −2061.21 + 3570.13i −0.102602 + 0.177712i −0.912756 0.408505i \(-0.866050\pi\)
0.810154 + 0.586217i \(0.199384\pi\)
\(740\) 0 0
\(741\) 271.662 3044.39i 0.0134680 0.150929i
\(742\) 0 0
\(743\) 7603.08 + 6379.74i 0.375411 + 0.315007i 0.810898 0.585188i \(-0.198979\pi\)
−0.435487 + 0.900195i \(0.643424\pi\)
\(744\) 0 0
\(745\) −9404.72 3423.04i −0.462500 0.168336i
\(746\) 0 0
\(747\) 10324.1 12217.6i 0.505674 0.598418i
\(748\) 0 0
\(749\) −7459.27 42303.6i −0.363893 2.06374i
\(750\) 0 0
\(751\) −10461.9 + 3807.83i −0.508337 + 0.185020i −0.583440 0.812156i \(-0.698294\pi\)
0.0751030 + 0.997176i \(0.476071\pi\)
\(752\) 0 0
\(753\) −1874.12 2686.41i −0.0906997 0.130011i
\(754\) 0 0
\(755\) −3359.93 −0.161961
\(756\) 0 0
\(757\) −32325.4 −1.55203 −0.776015 0.630715i \(-0.782762\pi\)
−0.776015 + 0.630715i \(0.782762\pi\)
\(758\) 0 0
\(759\) −6504.31 + 13885.7i −0.311056 + 0.664057i
\(760\) 0 0
\(761\) 13060.1 4753.49i 0.622114 0.226431i −0.0116814 0.999932i \(-0.503718\pi\)
0.633795 + 0.773501i \(0.281496\pi\)
\(762\) 0 0
\(763\) 3310.35 + 18773.9i 0.157068 + 0.890775i
\(764\) 0 0
\(765\) −42.7761 + 12351.3i −0.00202167 + 0.583740i
\(766\) 0 0
\(767\) 7607.52 + 2768.91i 0.358138 + 0.130351i
\(768\) 0 0
\(769\) −7019.28 5889.88i −0.329157 0.276196i 0.463199 0.886254i \(-0.346701\pi\)
−0.792356 + 0.610059i \(0.791146\pi\)
\(770\) 0 0
\(771\) −9496.45 6674.02i −0.443588 0.311750i
\(772\) 0 0
\(773\) −1545.03 + 2676.06i −0.0718897 + 0.124517i −0.899729 0.436448i \(-0.856236\pi\)
0.827840 + 0.560965i \(0.189570\pi\)
\(774\) 0 0
\(775\) 1167.42 + 2022.03i 0.0541097 + 0.0937207i
\(776\) 0 0
\(777\) −37860.7 10215.0i −1.74806 0.471638i
\(778\) 0 0
\(779\) −4809.95 + 27278.6i −0.221225 + 1.25463i
\(780\) 0 0
\(781\) 6461.41 5421.76i 0.296040 0.248407i
\(782\) 0 0
\(783\) 11438.0 16155.9i 0.522046 0.737376i