Properties

Label 324.4.i.a.37.6
Level 324
Weight 4
Character 324.37
Analytic conductor 19.117
Analytic rank 0
Dimension 54
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 324.i (of order \(9\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.1166188419\)
Analytic rank: \(0\)
Dimension: \(54\)
Relative dimension: \(9\) over \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 108)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 37.6
Character \(\chi\) \(=\) 324.37
Dual form 324.4.i.a.289.6

$q$-expansion

\(f(q)\) \(=\) \(q+(4.80495 - 1.74886i) q^{5} +(5.74341 + 32.5725i) q^{7} +O(q^{10})\) \(q+(4.80495 - 1.74886i) q^{5} +(5.74341 + 32.5725i) q^{7} +(-28.2317 - 10.2755i) q^{11} +(7.59849 + 6.37589i) q^{13} +(-44.7319 + 77.4779i) q^{17} +(-29.6509 - 51.3568i) q^{19} +(17.0562 - 96.7304i) q^{23} +(-75.7266 + 63.5421i) q^{25} +(-108.085 + 90.6938i) q^{29} +(4.10141 - 23.2603i) q^{31} +(84.5615 + 146.465i) q^{35} +(-114.087 + 197.604i) q^{37} +(357.814 + 300.241i) q^{41} +(-10.1135 - 3.68102i) q^{43} +(66.0561 + 374.623i) q^{47} +(-705.667 + 256.842i) q^{49} +202.984 q^{53} -153.622 q^{55} +(-766.955 + 279.149i) q^{59} +(-109.702 - 622.151i) q^{61} +(47.6609 + 17.3471i) q^{65} +(-466.269 - 391.246i) q^{67} +(-140.376 + 243.138i) q^{71} +(608.806 + 1054.48i) q^{73} +(172.552 - 978.592i) q^{77} +(278.680 - 233.841i) q^{79} +(-453.825 + 380.804i) q^{83} +(-79.4366 + 450.507i) q^{85} +(359.138 + 622.046i) q^{89} +(-164.037 + 284.121i) q^{91} +(-232.286 - 194.911i) q^{95} +(776.386 + 282.581i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54q - 12q^{5} + O(q^{10}) \) \( 54q - 12q^{5} + 87q^{11} - 204q^{17} - 96q^{23} - 216q^{25} - 318q^{29} - 54q^{31} - 6q^{35} - 867q^{41} - 513q^{43} + 1548q^{47} + 594q^{49} + 1068q^{53} + 1218q^{59} - 54q^{61} - 96q^{65} - 2997q^{67} + 120q^{71} - 216q^{73} - 3480q^{77} + 2808q^{79} - 4464q^{83} + 2160q^{85} - 4029q^{89} + 270q^{91} + 1650q^{95} - 3483q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{9}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 4.80495 1.74886i 0.429767 0.156423i −0.118074 0.993005i \(-0.537672\pi\)
0.547841 + 0.836582i \(0.315450\pi\)
\(6\) 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
\(9\) 0 0
\(10\) 0 0
\(11\) −28.2317 10.2755i −0.773833 0.281652i −0.0752344 0.997166i \(-0.523971\pi\)
−0.698599 + 0.715514i \(0.746193\pi\)
\(12\) 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
\(15\) 0 0
\(16\) 0 0
\(17\) −44.7319 + 77.4779i −0.638181 + 1.10536i 0.347650 + 0.937624i \(0.386980\pi\)
−0.985832 + 0.167738i \(0.946354\pi\)
\(18\) 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
\(21\) 0 0
\(22\) 0 0
\(23\) 17.0562 96.7304i 0.154629 0.876943i −0.804496 0.593958i \(-0.797564\pi\)
0.959124 0.282984i \(-0.0913245\pi\)
\(24\) 0 0
\(25\) −75.7266 + 63.5421i −0.605812 + 0.508337i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −108.085 + 90.6938i −0.692097 + 0.580738i −0.919513 0.393059i \(-0.871417\pi\)
0.227416 + 0.973798i \(0.426972\pi\)
\(30\) 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
\(33\) 0 0
\(34\) 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
\(39\) 0 0
\(40\) 0 0
\(41\) 357.814 + 300.241i 1.36295 + 1.14365i 0.975058 + 0.221951i \(0.0712424\pi\)
0.387896 + 0.921703i \(0.373202\pi\)
\(42\) 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
\(45\) 0 0
\(46\) 0 0
\(47\) 66.0561 + 374.623i 0.205006 + 1.16265i 0.897430 + 0.441156i \(0.145431\pi\)
−0.692424 + 0.721490i \(0.743457\pi\)
\(48\) 0 0
\(49\) −705.667 + 256.842i −2.05734 + 0.748810i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 202.984 0.526076 0.263038 0.964786i \(-0.415276\pi\)
0.263038 + 0.964786i \(0.415276\pi\)
\(54\) 0 0
\(55\) −153.622 −0.376625
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −766.955 + 279.149i −1.69236 + 0.615967i −0.994919 0.100678i \(-0.967899\pi\)
−0.697437 + 0.716646i \(0.745676\pi\)
\(60\) 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
\(63\) 0 0
\(64\) 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
\(69\) 0 0
\(70\) 0 0
\(71\) −140.376 + 243.138i −0.234642 + 0.406411i −0.959168 0.282835i \(-0.908725\pi\)
0.724527 + 0.689247i \(0.242058\pi\)
\(72\) 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
\(75\) 0 0
\(76\) 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
\(81\) 0 0
\(82\) 0 0
\(83\) −453.825 + 380.804i −0.600166 + 0.503599i −0.891499 0.453023i \(-0.850346\pi\)
0.291333 + 0.956622i \(0.405901\pi\)
\(84\) 0 0
\(85\) −79.4366 + 450.507i −0.101366 + 0.574875i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 359.138 + 622.046i 0.427737 + 0.740862i 0.996672 0.0815204i \(-0.0259776\pi\)
−0.568935 + 0.822383i \(0.692644\pi\)
\(90\) 0 0
\(91\) −164.037 + 284.121i −0.188965 + 0.327297i
\(92\) 0 0
\(93\) 0 0
\(94\) 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
\(99\) 0 0
\(100\) 0 0
\(101\) −171.883 974.796i −0.169336 0.960355i −0.944480 0.328569i \(-0.893434\pi\)
0.775143 0.631785i \(-0.217678\pi\)
\(102\) 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
\(105\) 0 0
\(106\) 0 0
\(107\) 1298.75 1.17341 0.586706 0.809800i \(-0.300424\pi\)
0.586706 + 0.809800i \(0.300424\pi\)
\(108\) 0 0
\(109\) 576.373 0.506482 0.253241 0.967403i \(-0.418503\pi\)
0.253241 + 0.967403i \(0.418503\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1844.78 671.443i 1.53577 0.558974i 0.570743 0.821129i \(-0.306655\pi\)
0.965026 + 0.262155i \(0.0844331\pi\)
\(114\) 0 0
\(115\) −87.2136 494.613i −0.0707193 0.401069i
\(116\) 0 0
\(117\) 0 0
\(118\) 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
\(123\) 0 0
\(124\) 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
\(129\) 0 0
\(130\) 0 0
\(131\) 377.965 2143.55i 0.252084 1.42964i −0.551365 0.834264i \(-0.685893\pi\)
0.803449 0.595374i \(-0.202996\pi\)
\(132\) 0 0
\(133\) 1502.52 1260.77i 0.979588 0.821972i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1065.12 + 893.740i −0.664228 + 0.557353i −0.911351 0.411631i \(-0.864959\pi\)
0.247123 + 0.968984i \(0.420515\pi\)
\(138\) 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
\(141\) 0 0
\(142\) 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
\(147\) 0 0
\(148\) 0 0
\(149\) −1499.38 1258.13i −0.824388 0.691744i 0.129607 0.991565i \(-0.458628\pi\)
−0.953995 + 0.299821i \(0.903073\pi\)
\(150\) 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
\(153\) 0 0
\(154\) 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
\(159\) 0 0
\(160\) 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
\(165\) 0 0
\(166\) 0 0
\(167\) 3356.67 1221.73i 1.55537 0.566109i 0.585703 0.810526i \(-0.300819\pi\)
0.969670 + 0.244417i \(0.0785965\pi\)
\(168\) 0 0
\(169\) −364.420 2066.73i −0.165872 0.940705i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 2140.09 + 778.930i 0.940510 + 0.342318i 0.766367 0.642403i \(-0.222062\pi\)
0.174143 + 0.984720i \(0.444285\pi\)
\(174\) 0 0
\(175\) −2504.66 2101.66i −1.08191 0.907830i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −577.965 + 1001.07i −0.241336 + 0.418006i −0.961095 0.276218i \(-0.910919\pi\)
0.719759 + 0.694224i \(0.244252\pi\)
\(180\) 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
\(183\) 0 0
\(184\) 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
\(189\) 0 0
\(190\) 0 0
\(191\) 615.799 516.717i 0.233286 0.195750i −0.518649 0.854987i \(-0.673565\pi\)
0.751935 + 0.659237i \(0.229120\pi\)
\(192\) 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
\(195\) 0 0
\(196\) 0 0
\(197\) −1162.98 2014.35i −0.420605 0.728509i 0.575394 0.817876i \(-0.304849\pi\)
−0.995999 + 0.0893676i \(0.971515\pi\)
\(198\) 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
\(201\) 0 0
\(202\) 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
\(207\) 0 0
\(208\) 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
\(213\) 0 0
\(214\) 0 0
\(215\) −55.0324 −0.0174567
\(216\) 0 0
\(217\) 781.202 0.244384
\(218\) 0 0
\(219\) 0 0
\(220\) 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
\(225\) 0 0
\(226\) 0 0
\(227\) −5420.84 1973.03i −1.58500 0.576891i −0.608713 0.793391i \(-0.708314\pi\)
−0.976283 + 0.216500i \(0.930536\pi\)
\(228\) 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
\(231\) 0 0
\(232\) 0 0
\(233\) −225.811 + 391.116i −0.0634908 + 0.109969i −0.896024 0.444007i \(-0.853557\pi\)
0.832533 + 0.553976i \(0.186890\pi\)
\(234\) 0 0
\(235\) 972.558 + 1684.52i 0.269969 + 0.467600i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −537.820 + 3050.13i −0.145559 + 0.825508i 0.821357 + 0.570414i \(0.193217\pi\)
−0.966916 + 0.255093i \(0.917894\pi\)
\(240\) 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
\(243\) 0 0
\(244\) 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
\(249\) 0 0
\(250\) 0 0
\(251\) 315.189 + 545.923i 0.0792612 + 0.137284i 0.902931 0.429785i \(-0.141411\pi\)
−0.823670 + 0.567069i \(0.808077\pi\)
\(252\) 0 0
\(253\) −1475.48 + 2555.60i −0.366650 + 0.635056i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1711.18 + 1435.85i 0.415333 + 0.348506i 0.826384 0.563106i \(-0.190394\pi\)
−0.411051 + 0.911612i \(0.634838\pi\)
\(258\) 0 0
\(259\) −7091.71 2581.17i −1.70138 0.619251i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −115.370 654.298i −0.0270496 0.153406i 0.968291 0.249824i \(-0.0803726\pi\)
−0.995341 + 0.0964178i \(0.969262\pi\)
\(264\) 0 0
\(265\) 975.328 354.990i 0.226090 0.0822901i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 6952.64 1.57587 0.787936 0.615757i \(-0.211150\pi\)
0.787936 + 0.615757i \(0.211150\pi\)
\(270\) 0 0
\(271\) −8783.48 −1.96885 −0.984426 0.175802i \(-0.943748\pi\)
−0.984426 + 0.175802i \(0.943748\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 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
\(279\) 0 0
\(280\) 0 0
\(281\) 6216.63 + 2262.67i 1.31976 + 0.480354i 0.903382 0.428837i \(-0.141077\pi\)
0.416379 + 0.909191i \(0.363299\pi\)
\(282\) 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
\(285\) 0 0
\(286\) 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
\(291\) 0 0
\(292\) 0 0
\(293\) 50.5304 286.572i 0.0100751 0.0571390i −0.979356 0.202145i \(-0.935209\pi\)
0.989431 + 0.145006i \(0.0463200\pi\)
\(294\) 0 0
\(295\) −3196.99 + 2682.59i −0.630968 + 0.529445i
\(296\) 0 0
\(297\) 0 0
\(298\) 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
\(303\) 0 0
\(304\) 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
\(309\) 0 0
\(310\) 0 0
\(311\) 7195.48 + 6037.72i 1.31196 + 1.10086i 0.987945 + 0.154808i \(0.0494759\pi\)
0.324011 + 0.946053i \(0.394969\pi\)
\(312\) 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
\(315\) 0 0
\(316\) 0 0
\(317\) −116.213 659.077i −0.0205905 0.116774i 0.972780 0.231730i \(-0.0744385\pi\)
−0.993371 + 0.114956i \(0.963327\pi\)
\(318\) 0 0
\(319\) 3983.33 1449.81i 0.699134 0.254464i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 5305.36 0.913926
\(324\) 0 0
\(325\) −980.545 −0.167356
\(326\) 0 0
\(327\) 0 0
\(328\) 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
\(333\) 0 0
\(334\) 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
\(339\) 0 0
\(340\) 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
\(345\) 0 0
\(346\) 0 0
\(347\) 698.081 3959.02i 0.107997 0.612482i −0.881984 0.471280i \(-0.843792\pi\)
0.989981 0.141202i \(-0.0450967\pi\)
\(348\) 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
\(351\) 0 0
\(352\) 0 0
\(353\) 3542.55 2972.56i 0.534139 0.448196i −0.335389 0.942080i \(-0.608868\pi\)
0.869528 + 0.493884i \(0.164423\pi\)
\(354\) 0 0
\(355\) −249.285 + 1413.76i −0.0372694 + 0.211366i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −6159.42 10668.4i −0.905521 1.56841i −0.820217 0.572053i \(-0.806147\pi\)
−0.0853041 0.996355i \(-0.527186\pi\)
\(360\) 0 0
\(361\) 1671.15 2894.52i 0.243644 0.422004i
\(362\) 0 0
\(363\) 0 0
\(364\) 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
\(369\) 0 0
\(370\) 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
\(375\) 0 0
\(376\) 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
\(381\) 0 0
\(382\) 0 0
\(383\) −7480.47 + 2722.67i −0.998001 + 0.363243i −0.788813 0.614633i \(-0.789304\pi\)
−0.209188 + 0.977876i \(0.567082\pi\)
\(384\) 0 0
\(385\) −882.314 5003.85i −0.116797 0.662389i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 12432.6 + 4525.09i 1.62045 + 0.589797i 0.983469 0.181078i \(-0.0579586\pi\)
0.636986 + 0.770875i \(0.280181\pi\)
\(390\) 0 0
\(391\) 6731.52 + 5648.41i 0.870659 + 0.730569i
\(392\) 0 0
\(393\) 0 0
\(394\) 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
\(399\) 0 0
\(400\) 0 0
\(401\) −533.798 + 3027.32i −0.0664753 + 0.377000i 0.933362 + 0.358938i \(0.116861\pi\)
−0.999837 + 0.0180626i \(0.994250\pi\)
\(402\) 0 0
\(403\) 179.469 150.593i 0.0221837 0.0186143i
\(404\) 0 0
\(405\) 0 0
\(406\) 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
\(411\) 0 0
\(412\) 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
\(417\) 0 0
\(418\) 0 0
\(419\) −3312.78 2779.75i −0.386252 0.324104i 0.428899 0.903353i \(-0.358902\pi\)
−0.815151 + 0.579248i \(0.803346\pi\)
\(420\) 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
\(423\) 0 0
\(424\) 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
\(429\) 0 0
\(430\) 0 0
\(431\) 187.346 0.0209377 0.0104688 0.999945i \(-0.496668\pi\)
0.0104688 + 0.999945i \(0.496668\pi\)
\(432\) 0 0
\(433\) −313.829 −0.0348307 −0.0174153 0.999848i \(-0.505544\pi\)
−0.0174153 + 0.999848i \(0.505544\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 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
\(441\) 0 0
\(442\) 0 0
\(443\) 3295.46 + 1199.45i 0.353436 + 0.128640i 0.512636 0.858606i \(-0.328669\pi\)
−0.159200 + 0.987246i \(0.550891\pi\)
\(444\) 0 0
\(445\) 2813.51 + 2360.82i 0.299715 + 0.251491i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 905.931 1569.12i 0.0952194 0.164925i −0.814481 0.580191i \(-0.802978\pi\)
0.909700 + 0.415266i \(0.136311\pi\)
\(450\) 0 0
\(451\) −7016.55 12153.0i −0.732586 1.26888i
\(452\) 0 0
\(453\) 0 0
\(454\) 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
\(459\) 0 0
\(460\) 0 0
\(461\) 6096.59 5115.65i 0.615936 0.516832i −0.280587 0.959829i \(-0.590529\pi\)
0.896523 + 0.442997i \(0.146085\pi\)
\(462\) 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
\(465\) 0 0
\(466\) 0 0
\(467\) −4109.70 7118.22i −0.407226 0.705336i 0.587352 0.809332i \(-0.300170\pi\)
−0.994578 + 0.103996i \(0.966837\pi\)
\(468\) 0 0
\(469\) 10065.9 17434.6i 0.991044 1.71654i
\(470\) 0 0
\(471\) 0 0
\(472\) 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
\(477\) 0 0
\(478\) 0 0
\(479\) −729.906 4139.50i −0.0696247 0.394861i −0.999627 0.0273078i \(-0.991307\pi\)
0.930002 0.367554i \(-0.119805\pi\)
\(480\) 0 0
\(481\) −2126.79 + 774.088i −0.201607 + 0.0733791i
\(482\) 0 0
\(483\) 0 0
\(484\) 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
\(489\) 0 0
\(490\) 0 0
\(491\) 13256.1 4824.83i 1.21841 0.443465i 0.348797 0.937198i \(-0.386590\pi\)
0.869614 + 0.493733i \(0.164368\pi\)
\(492\) 0 0
\(493\) −2191.93 12431.1i −0.200243 1.13563i
\(494\) 0 0
\(495\) 0 0
\(496\) 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
\(501\) 0 0
\(502\) 0 0
\(503\) −4547.85 + 7877.10i −0.403138 + 0.698256i −0.994103 0.108442i \(-0.965414\pi\)
0.590965 + 0.806697i \(0.298747\pi\)
\(504\) 0 0
\(505\) −2530.67 4383.24i −0.222996 0.386241i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1245.45 + 7063.30i −0.108455 + 0.615079i 0.881329 + 0.472503i \(0.156650\pi\)
−0.989784 + 0.142576i \(0.954462\pi\)
\(510\) 0 0
\(511\) −30850.6 + 25886.7i −2.67074 + 2.24102i
\(512\) 0 0
\(513\) 0 0
\(514\) 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
\(519\) 0 0
\(520\) 0 0
\(521\) −4043.78 7004.04i −0.340041 0.588968i 0.644399 0.764689i \(-0.277108\pi\)
−0.984440 + 0.175721i \(0.943774\pi\)
\(522\) 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
\(525\) 0 0
\(526\) 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
\(531\) 0 0
\(532\) 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
\(537\) 0 0
\(538\) 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
\(543\) 0 0
\(544\) 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
\(549\) 0 0
\(550\) 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
\(555\) 0 0
\(556\) 0 0
\(557\) −11430.0 + 19797.4i −0.869489 + 1.50600i −0.00697005 + 0.999976i \(0.502219\pi\)
−0.862519 + 0.506024i \(0.831115\pi\)
\(558\) 0 0
\(559\) −53.3776 92.4528i −0.00403870 0.00699524i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1033.46 + 5861.04i −0.0773626 + 0.438745i 0.921382 + 0.388658i \(0.127061\pi\)
−0.998745 + 0.0500875i \(0.984050\pi\)
\(564\) 0 0
\(565\) 7689.79 6452.50i 0.572587 0.480458i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 8500.63 7132.88i 0.626301 0.525529i −0.273476 0.961879i \(-0.588174\pi\)
0.899777 + 0.436350i \(0.143729\pi\)
\(570\) 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
\(573\) 0 0
\(574\) 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
\(579\) 0 0
\(580\) 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
\(585\) 0 0
\(586\) 0 0
\(587\) −2679.51 15196.3i −0.188408 1.06851i −0.921498 0.388382i \(-0.873034\pi\)
0.733091 0.680131i \(-0.238077\pi\)
\(588\) 0 0
\(589\) −1316.18 + 479.052i −0.0920754 + 0.0335127i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −8549.53 −0.592052 −0.296026 0.955180i \(-0.595662\pi\)
−0.296026 + 0.955180i \(0.595662\pi\)
\(594\) 0 0
\(595\) −15130.4 −1.04250
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 15101.5 5496.51i 1.03010 0.374927i 0.228983 0.973430i \(-0.426460\pi\)
0.801120 + 0.598504i \(0.204238\pi\)
\(600\) 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
\(603\) 0 0
\(604\) 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
\(609\) 0 0
\(610\) 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
\(615\) 0 0
\(616\) 0 0
\(617\) −3164.80 + 17948.4i −0.206499 + 1.17111i 0.688564 + 0.725175i \(0.258241\pi\)
−0.895063 + 0.445939i \(0.852870\pi\)
\(618\) 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
\(621\) 0 0
\(622\) 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
\(627\) 0 0
\(628\) 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
\(633\) 0 0
\(634\) 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
\(639\) 0 0
\(640\) 0 0
\(641\) 4147.90 + 23523.9i 0.255589 + 1.44951i 0.794557 + 0.607189i \(0.207703\pi\)
−0.538969 + 0.842326i \(0.681186\pi\)
\(642\) 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
\(645\) 0 0
\(646\) 0 0
\(647\) 8439.89 0.512838 0.256419 0.966566i \(-0.417457\pi\)
0.256419 + 0.966566i \(0.417457\pi\)
\(648\) 0 0
\(649\) 24520.8 1.48309
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −26279.5 + 9564.97i −1.57488 + 0.573210i −0.974083 0.226191i \(-0.927373\pi\)
−0.600798 + 0.799401i \(0.705151\pi\)
\(654\) 0 0
\(655\) −1932.66 10960.6i −0.115290 0.653844i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 4419.19 + 1608.45i 0.261225 + 0.0950781i 0.469313 0.883032i \(-0.344502\pi\)
−0.208088 + 0.978110i \(0.566724\pi\)
\(660\) 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
\(663\) 0 0
\(664\) 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
\(669\) 0 0
\(670\) 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
\(675\) 0 0
\(676\) 0 0
\(677\) −7383.95 + 6195.87i −0.419185 + 0.351738i −0.827853 0.560945i \(-0.810438\pi\)
0.408668 + 0.912683i \(0.365993\pi\)
\(678\) 0 0
\(679\) −4745.28 + 26911.8i −0.268199 + 1.52103i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −3985.79 6903.58i −0.223297 0.386762i 0.732510 0.680756i \(-0.238349\pi\)
−0.955807 + 0.293994i \(0.905015\pi\)
\(684\) 0 0
\(685\) −3554.81 + 6157.11i −0.198281 + 0.343432i
\(686\) 0 0
\(687\) 0 0
\(688\) 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
\(693\) 0 0
\(694\) 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
\(699\) 0 0
\(700\) 0 0
\(701\) 14959.1 0.805987 0.402993 0.915203i \(-0.367970\pi\)
0.402993 + 0.915203i \(0.367970\pi\)
\(702\) 0 0
\(703\) 13531.1 0.725938
\(704\) 0 0
\(705\) 0 0
\(706\) 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
\(711\) 0 0
\(712\) 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
\(717\) 0 0
\(718\) 0 0
\(719\) −10762.6 + 18641.4i −0.558244 + 0.966908i 0.439399 + 0.898292i \(0.355191\pi\)
−0.997643 + 0.0686155i \(0.978142\pi\)
\(720\) 0 0
\(721\) 11368.4 + 19690.7i 0.587214 + 1.01708i
\(722\) 0 0
\(723\) 0 0
\(724\) 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
\(729\) 0 0
\(730\) 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
\(735\) 0 0
\(736\) 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
\(741\) 0 0
\(742\) 0 0
\(743\) −7603.08 6379.74i −0.375411 0.315007i 0.435487 0.900195i \(-0.356576\pi\)
−0.810898 + 0.585188i \(0.801021\pi\)
\(744\) 0 0
\(745\) −9404.72 3423.04i −0.462500 0.168336i
\(746\) 0 0
\(747\) 0 0
\(748\) 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
\(753\) 0 0
\(754\) 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
\(759\) 0 0
\(760\) 0 0
\(761\) −13060.1 + 4753.49i −0.622114 + 0.226431i −0.633795 0.773501i \(-0.718504\pi\)
0.0116814 + 0.999932i \(0.496282\pi\)
\(762\) 0 0
\(763\) 3310.35 + 18773.9i 0.157068 + 0.890775i
\(764\) 0 0
\(765\) 0 0
\(766\) 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
\(771\) 0 0
\(772\) 0 0
\(773\) 1545.03 2676.06i 0.0718897 0.124517i −0.827840 0.560965i \(-0.810430\pi\)
0.899729 + 0.436448i \(0.143764\pi\)
\(774\) 0 0
\(775\) 1167.42 + 2022.03i 0.0541097 + 0.0937207i
\(776\) 0 0
\(777\) 0 0
\(778\) 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
\(783\) 0 0
\(784\) 0 0
\(785\) −5199.06 + 4362.53i −0.236385 + 0.198351i
\(786\) 0 0
\(787\) 3688.64 20919.3i 0.167072 0.947512i −0.779830 0.625991i \(-0.784695\pi\)
0.946902 0.321521i \(-0.104194\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 32465.9 + 56232.6i 1.45936