Properties

Label 324.4.i.a.37.2
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 37.2
Character \(\chi\) \(=\) 324.37
Dual form 324.4.i.a.289.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-13.2490 + 4.82225i) q^{5} +(3.17294 + 17.9946i) q^{7} +O(q^{10})\) \(q+(-13.2490 + 4.82225i) q^{5} +(3.17294 + 17.9946i) q^{7} +(-33.5576 - 12.2140i) q^{11} +(-6.15848 - 5.16757i) q^{13} +(58.3572 - 101.078i) q^{17} +(39.9112 + 69.1281i) q^{19} +(15.4931 - 87.8657i) q^{23} +(56.5267 - 47.4316i) q^{25} +(-85.5671 + 71.7993i) q^{29} +(47.1052 - 267.147i) q^{31} +(-128.813 - 223.110i) q^{35} +(180.562 - 312.742i) q^{37} +(10.5230 + 8.82981i) q^{41} +(-383.698 - 139.655i) q^{43} +(-14.3445 - 81.3518i) q^{47} +(8.57561 - 3.12127i) q^{49} +28.8354 q^{53} +503.503 q^{55} +(-629.134 + 228.986i) q^{59} +(-16.7704 - 95.1097i) q^{61} +(106.513 + 38.7676i) q^{65} +(514.271 + 431.525i) q^{67} +(47.7773 - 82.7527i) q^{71} +(-502.908 - 871.062i) q^{73} +(113.309 - 642.610i) q^{77} +(780.366 - 654.805i) q^{79} +(547.955 - 459.789i) q^{83} +(-285.754 + 1620.59i) q^{85} +(-314.627 - 544.950i) q^{89} +(73.4481 - 127.216i) q^{91} +(-862.136 - 723.418i) q^{95} +(-1544.58 - 562.179i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54q - 12q^{5} + O(q^{10}) \) \( 54q - 12q^{5} + 87q^{11} - 204q^{17} - 96q^{23} - 216q^{25} - 318q^{29} - 54q^{31} - 6q^{35} - 867q^{41} - 513q^{43} + 1548q^{47} + 594q^{49} + 1068q^{53} + 1218q^{59} - 54q^{61} - 96q^{65} - 2997q^{67} + 120q^{71} - 216q^{73} - 3480q^{77} + 2808q^{79} - 4464q^{83} + 2160q^{85} - 4029q^{89} + 270q^{91} + 1650q^{95} - 3483q^{97} + O(q^{100}) \)

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
\(5\) −13.2490 + 4.82225i −1.18503 + 0.431315i −0.857975 0.513691i \(-0.828278\pi\)
−0.327053 + 0.945006i \(0.606055\pi\)
\(6\) 0 0
\(7\) 3.17294 + 17.9946i 0.171323 + 0.971618i 0.942303 + 0.334760i \(0.108655\pi\)
−0.770981 + 0.636858i \(0.780234\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −33.5576 12.2140i −0.919817 0.334786i −0.161651 0.986848i \(-0.551682\pi\)
−0.758166 + 0.652062i \(0.773904\pi\)
\(12\) 0 0
\(13\) −6.15848 5.16757i −0.131389 0.110248i 0.574725 0.818346i \(-0.305109\pi\)
−0.706114 + 0.708098i \(0.749553\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 58.3572 101.078i 0.832570 1.44205i −0.0634231 0.997987i \(-0.520202\pi\)
0.895993 0.444067i \(-0.146465\pi\)
\(18\) 0 0
\(19\) 39.9112 + 69.1281i 0.481908 + 0.834689i 0.999784 0.0207667i \(-0.00661072\pi\)
−0.517877 + 0.855455i \(0.673277\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 15.4931 87.8657i 0.140458 0.796576i −0.830445 0.557101i \(-0.811914\pi\)
0.970903 0.239475i \(-0.0769753\pi\)
\(24\) 0 0
\(25\) 56.5267 47.4316i 0.452214 0.379453i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −85.5671 + 71.7993i −0.547911 + 0.459752i −0.874233 0.485507i \(-0.838635\pi\)
0.326322 + 0.945259i \(0.394191\pi\)
\(30\) 0 0
\(31\) 47.1052 267.147i 0.272914 1.54777i −0.472596 0.881279i \(-0.656683\pi\)
0.745511 0.666494i \(-0.232206\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −128.813 223.110i −0.622095 1.07750i
\(36\) 0 0
\(37\) 180.562 312.742i 0.802275 1.38958i −0.115841 0.993268i \(-0.536956\pi\)
0.918115 0.396313i \(-0.129710\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 10.5230 + 8.82981i 0.0400832 + 0.0336338i 0.662609 0.748965i \(-0.269449\pi\)
−0.622526 + 0.782599i \(0.713894\pi\)
\(42\) 0 0
\(43\) −383.698 139.655i −1.36078 0.495282i −0.444482 0.895788i \(-0.646612\pi\)
−0.916294 + 0.400506i \(0.868834\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −14.3445 81.3518i −0.0445184 0.252476i 0.954424 0.298454i \(-0.0964709\pi\)
−0.998942 + 0.0459775i \(0.985360\pi\)
\(48\) 0 0
\(49\) 8.57561 3.12127i 0.0250018 0.00909990i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 28.8354 0.0747329 0.0373665 0.999302i \(-0.488103\pi\)
0.0373665 + 0.999302i \(0.488103\pi\)
\(54\) 0 0
\(55\) 503.503 1.23441
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −629.134 + 228.986i −1.38824 + 0.505279i −0.924666 0.380779i \(-0.875656\pi\)
−0.463575 + 0.886058i \(0.653434\pi\)
\(60\) 0 0
\(61\) −16.7704 95.1097i −0.0352005 0.199632i 0.962136 0.272570i \(-0.0878736\pi\)
−0.997336 + 0.0729379i \(0.976763\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 106.513 + 38.7676i 0.203251 + 0.0739773i
\(66\) 0 0
\(67\) 514.271 + 431.525i 0.937735 + 0.786853i 0.977190 0.212368i \(-0.0681176\pi\)
−0.0394546 + 0.999221i \(0.512562\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 47.7773 82.7527i 0.0798609 0.138323i −0.823329 0.567565i \(-0.807886\pi\)
0.903190 + 0.429241i \(0.141219\pi\)
\(72\) 0 0
\(73\) −502.908 871.062i −0.806314 1.39658i −0.915400 0.402545i \(-0.868126\pi\)
0.109086 0.994032i \(-0.465207\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 113.309 642.610i 0.167699 0.951068i
\(78\) 0 0
\(79\) 780.366 654.805i 1.11137 0.932548i 0.113231 0.993569i \(-0.463880\pi\)
0.998137 + 0.0610203i \(0.0194355\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 547.955 459.789i 0.724650 0.608053i −0.204018 0.978967i \(-0.565400\pi\)
0.928667 + 0.370914i \(0.120956\pi\)
\(84\) 0 0
\(85\) −285.754 + 1620.59i −0.364640 + 2.06797i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −314.627 544.950i −0.374724 0.649041i 0.615562 0.788089i \(-0.288929\pi\)
−0.990286 + 0.139048i \(0.955596\pi\)
\(90\) 0 0
\(91\) 73.4481 127.216i 0.0846094 0.146548i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −862.136 723.418i −0.931088 0.781275i
\(96\) 0 0
\(97\) −1544.58 562.179i −1.61678 0.588461i −0.634017 0.773319i \(-0.718595\pi\)
−0.982765 + 0.184858i \(0.940817\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 221.812 + 1257.96i 0.218526 + 1.23932i 0.874683 + 0.484696i \(0.161070\pi\)
−0.656157 + 0.754624i \(0.727819\pi\)
\(102\) 0 0
\(103\) −47.4842 + 17.2828i −0.0454248 + 0.0165333i −0.364633 0.931151i \(-0.618805\pi\)
0.319208 + 0.947685i \(0.396583\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1585.17 1.43219 0.716095 0.698003i \(-0.245928\pi\)
0.716095 + 0.698003i \(0.245928\pi\)
\(108\) 0 0
\(109\) 201.612 0.177164 0.0885821 0.996069i \(-0.471766\pi\)
0.0885821 + 0.996069i \(0.471766\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1453.68 + 529.095i −1.21018 + 0.440470i −0.866766 0.498715i \(-0.833806\pi\)
−0.343414 + 0.939184i \(0.611583\pi\)
\(114\) 0 0
\(115\) 218.442 + 1238.84i 0.177129 + 1.00455i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2004.02 + 729.403i 1.54376 + 0.561884i
\(120\) 0 0
\(121\) −42.6753 35.8088i −0.0320626 0.0269037i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 361.010 625.287i 0.258318 0.447419i
\(126\) 0 0
\(127\) 1112.61 + 1927.10i 0.777387 + 1.34647i 0.933443 + 0.358725i \(0.116788\pi\)
−0.156056 + 0.987748i \(0.549878\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −215.838 + 1224.08i −0.143953 + 0.816397i 0.824249 + 0.566227i \(0.191598\pi\)
−0.968202 + 0.250170i \(0.919514\pi\)
\(132\) 0 0
\(133\) −1117.30 + 937.525i −0.728437 + 0.611231i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2055.53 + 1724.79i −1.28187 + 1.07561i −0.288883 + 0.957364i \(0.593284\pi\)
−0.992984 + 0.118250i \(0.962272\pi\)
\(138\) 0 0
\(139\) −261.289 + 1481.85i −0.159441 + 0.904234i 0.795172 + 0.606384i \(0.207381\pi\)
−0.954613 + 0.297850i \(0.903731\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 143.547 + 248.631i 0.0839440 + 0.145395i
\(144\) 0 0
\(145\) 787.445 1363.90i 0.450992 0.781140i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 172.536 + 144.775i 0.0948639 + 0.0796003i 0.688986 0.724774i \(-0.258056\pi\)
−0.594122 + 0.804375i \(0.702500\pi\)
\(150\) 0 0
\(151\) −2151.99 783.262i −1.15978 0.422126i −0.310761 0.950488i \(-0.600584\pi\)
−0.849019 + 0.528362i \(0.822806\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 664.150 + 3766.58i 0.344167 + 1.95187i
\(156\) 0 0
\(157\) −1002.97 + 365.052i −0.509846 + 0.185569i −0.584117 0.811669i \(-0.698559\pi\)
0.0742710 + 0.997238i \(0.476337\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1630.27 0.798032
\(162\) 0 0
\(163\) 565.717 0.271843 0.135921 0.990720i \(-0.456601\pi\)
0.135921 + 0.990720i \(0.456601\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1411.33 513.682i 0.653964 0.238023i 0.00633579 0.999980i \(-0.497983\pi\)
0.647628 + 0.761956i \(0.275761\pi\)
\(168\) 0 0
\(169\) −370.282 2099.97i −0.168540 0.955837i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 388.119 + 141.264i 0.170567 + 0.0620814i 0.425892 0.904774i \(-0.359960\pi\)
−0.255325 + 0.966855i \(0.582182\pi\)
\(174\) 0 0
\(175\) 1032.87 + 866.680i 0.446158 + 0.374371i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 699.370 1211.34i 0.292030 0.505811i −0.682260 0.731110i \(-0.739003\pi\)
0.974290 + 0.225299i \(0.0723360\pi\)
\(180\) 0 0
\(181\) −807.914 1399.35i −0.331778 0.574656i 0.651083 0.759007i \(-0.274315\pi\)
−0.982860 + 0.184351i \(0.940982\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −884.145 + 5014.24i −0.351371 + 1.99272i
\(186\) 0 0
\(187\) −3192.88 + 2679.15i −1.24859 + 1.04769i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1340.95 1125.19i 0.507998 0.426261i −0.352426 0.935840i \(-0.614643\pi\)
0.860424 + 0.509579i \(0.170199\pi\)
\(192\) 0 0
\(193\) −212.711 + 1206.35i −0.0793331 + 0.449920i 0.919103 + 0.394017i \(0.128915\pi\)
−0.998436 + 0.0559032i \(0.982196\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2719.89 4710.98i −0.983675 1.70377i −0.647683 0.761910i \(-0.724262\pi\)
−0.335992 0.941865i \(-0.609071\pi\)
\(198\) 0 0
\(199\) 1103.11 1910.64i 0.392951 0.680611i −0.599886 0.800085i \(-0.704788\pi\)
0.992837 + 0.119474i \(0.0381209\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1563.50 1311.93i −0.540572 0.453594i
\(204\) 0 0
\(205\) −181.998 66.2420i −0.0620064 0.0225685i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −494.993 2807.25i −0.163825 0.929097i
\(210\) 0 0
\(211\) −445.805 + 162.260i −0.145453 + 0.0529404i −0.413721 0.910404i \(-0.635771\pi\)
0.268268 + 0.963344i \(0.413549\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 5757.06 1.82618
\(216\) 0 0
\(217\) 4956.67 1.55060
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −881.717 + 320.919i −0.268374 + 0.0976803i
\(222\) 0 0
\(223\) −257.186 1458.57i −0.0772306 0.437996i −0.998764 0.0496981i \(-0.984174\pi\)
0.921534 0.388298i \(-0.126937\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1055.78 384.271i −0.308697 0.112357i 0.183026 0.983108i \(-0.441411\pi\)
−0.491723 + 0.870751i \(0.663633\pi\)
\(228\) 0 0
\(229\) 2643.38 + 2218.06i 0.762793 + 0.640059i 0.938852 0.344321i \(-0.111891\pi\)
−0.176060 + 0.984380i \(0.556335\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3359.46 + 5818.75i −0.944572 + 1.63605i −0.187967 + 0.982175i \(0.560190\pi\)
−0.756605 + 0.653872i \(0.773143\pi\)
\(234\) 0 0
\(235\) 582.350 + 1008.66i 0.161652 + 0.279990i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1084.54 6150.74i 0.293528 1.66468i −0.379598 0.925152i \(-0.623938\pi\)
0.673126 0.739528i \(-0.264951\pi\)
\(240\) 0 0
\(241\) −644.213 + 540.559i −0.172189 + 0.144483i −0.724809 0.688949i \(-0.758072\pi\)
0.552621 + 0.833433i \(0.313628\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −98.5668 + 82.7074i −0.0257029 + 0.0215673i
\(246\) 0 0
\(247\) 111.433 631.968i 0.0287057 0.162798i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −2582.47 4472.97i −0.649419 1.12483i −0.983262 0.182198i \(-0.941679\pi\)
0.333843 0.942629i \(-0.391654\pi\)
\(252\) 0 0
\(253\) −1593.10 + 2759.33i −0.395878 + 0.685681i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −3334.32 2797.83i −0.809297 0.679081i 0.141143 0.989989i \(-0.454922\pi\)
−0.950440 + 0.310909i \(0.899367\pi\)
\(258\) 0 0
\(259\) 6200.59 + 2256.83i 1.48759 + 0.541438i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 267.218 + 1515.47i 0.0626517 + 0.355315i 0.999976 + 0.00685846i \(0.00218313\pi\)
−0.937325 + 0.348457i \(0.886706\pi\)
\(264\) 0 0
\(265\) −382.041 + 139.051i −0.0885606 + 0.0322334i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −3281.40 −0.743757 −0.371878 0.928281i \(-0.621286\pi\)
−0.371878 + 0.928281i \(0.621286\pi\)
\(270\) 0 0
\(271\) −4649.81 −1.04227 −0.521136 0.853474i \(-0.674492\pi\)
−0.521136 + 0.853474i \(0.674492\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2476.23 + 901.273i −0.542990 + 0.197632i
\(276\) 0 0
\(277\) −1143.21 6483.47i −0.247974 1.40633i −0.813482 0.581590i \(-0.802431\pi\)
0.565508 0.824743i \(-0.308680\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 4066.26 + 1480.00i 0.863249 + 0.314197i 0.735430 0.677601i \(-0.236980\pi\)
0.127819 + 0.991798i \(0.459202\pi\)
\(282\) 0 0
\(283\) −954.503 800.923i −0.200492 0.168233i 0.537014 0.843573i \(-0.319552\pi\)
−0.737506 + 0.675340i \(0.763997\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −125.500 + 217.373i −0.0258120 + 0.0447078i
\(288\) 0 0
\(289\) −4354.62 7542.42i −0.886347 1.53520i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 584.021 3312.15i 0.116447 0.660402i −0.869577 0.493797i \(-0.835608\pi\)
0.986024 0.166605i \(-0.0532804\pi\)
\(294\) 0 0
\(295\) 7231.18 6067.68i 1.42717 1.19754i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −549.466 + 461.057i −0.106276 + 0.0891759i
\(300\) 0 0
\(301\) 1295.58 7347.61i 0.248093 1.40701i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 680.834 + 1179.24i 0.127818 + 0.221387i
\(306\) 0 0
\(307\) 1343.07 2326.27i 0.249685 0.432467i −0.713753 0.700397i \(-0.753006\pi\)
0.963438 + 0.267930i \(0.0863396\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −607.838 510.037i −0.110827 0.0929953i 0.585690 0.810535i \(-0.300824\pi\)
−0.696517 + 0.717540i \(0.745268\pi\)
\(312\) 0 0
\(313\) 1948.47 + 709.186i 0.351866 + 0.128069i 0.511905 0.859042i \(-0.328940\pi\)
−0.160039 + 0.987111i \(0.551162\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1177.45 6677.64i −0.208619 1.18314i −0.891643 0.452739i \(-0.850447\pi\)
0.683024 0.730396i \(-0.260664\pi\)
\(318\) 0 0
\(319\) 3748.38 1364.30i 0.657896 0.239455i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 9316.41 1.60489
\(324\) 0 0
\(325\) −593.225 −0.101250
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1418.38 516.249i 0.237684 0.0865098i
\(330\) 0 0
\(331\) −300.134 1702.14i −0.0498394 0.282653i 0.949695 0.313178i \(-0.101393\pi\)
−0.999534 + 0.0305241i \(0.990282\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −8894.51 3237.34i −1.45062 0.527984i
\(336\) 0 0
\(337\) −4592.96 3853.95i −0.742417 0.622962i 0.191069 0.981577i \(-0.438805\pi\)
−0.933486 + 0.358615i \(0.883249\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −4843.65 + 8389.45i −0.769204 + 1.33230i
\(342\) 0 0
\(343\) 3217.06 + 5572.11i 0.506429 + 0.877160i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −550.059 + 3119.54i −0.0850971 + 0.482610i 0.912238 + 0.409660i \(0.134352\pi\)
−0.997336 + 0.0729501i \(0.976759\pi\)
\(348\) 0 0
\(349\) −5745.12 + 4820.73i −0.881173 + 0.739392i −0.966420 0.256968i \(-0.917276\pi\)
0.0852471 + 0.996360i \(0.472832\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 6735.79 5652.00i 1.01561 0.852197i 0.0265392 0.999648i \(-0.491551\pi\)
0.989069 + 0.147451i \(0.0471069\pi\)
\(354\) 0 0
\(355\) −233.948 + 1326.79i −0.0349766 + 0.198362i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −3196.24 5536.04i −0.469891 0.813875i 0.529516 0.848300i \(-0.322374\pi\)
−0.999407 + 0.0344245i \(0.989040\pi\)
\(360\) 0 0
\(361\) 243.700 422.101i 0.0355300 0.0615397i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 10863.5 + 9115.57i 1.55787 + 1.30721i
\(366\) 0 0
\(367\) 10794.5 + 3928.89i 1.53534 + 0.558819i 0.964922 0.262535i \(-0.0845585\pi\)
0.570419 + 0.821354i \(0.306781\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 91.4929 + 518.882i 0.0128034 + 0.0726119i
\(372\) 0 0
\(373\) 2603.65 947.652i 0.361426 0.131548i −0.154923 0.987927i \(-0.549513\pi\)
0.516349 + 0.856378i \(0.327291\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 897.991 0.122676
\(378\) 0 0
\(379\) −8765.55 −1.18801 −0.594005 0.804461i \(-0.702454\pi\)
−0.594005 + 0.804461i \(0.702454\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 3592.97 1307.73i 0.479353 0.174470i −0.0910317 0.995848i \(-0.529016\pi\)
0.570384 + 0.821378i \(0.306794\pi\)
\(384\) 0 0
\(385\) 1597.59 + 9060.36i 0.211482 + 1.19937i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −8013.33 2916.61i −1.04445 0.380149i −0.237886 0.971293i \(-0.576454\pi\)
−0.806566 + 0.591144i \(0.798677\pi\)
\(390\) 0 0
\(391\) −7977.12 6693.60i −1.03176 0.865754i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −7181.45 + 12438.6i −0.914780 + 1.58445i
\(396\) 0 0
\(397\) 6081.30 + 10533.1i 0.768796 + 1.33159i 0.938216 + 0.346050i \(0.112477\pi\)
−0.169420 + 0.985544i \(0.554190\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1077.38 6110.10i 0.134168 0.760907i −0.841267 0.540620i \(-0.818190\pi\)
0.975435 0.220287i \(-0.0706993\pi\)
\(402\) 0 0
\(403\) −1670.60 + 1401.80i −0.206497 + 0.173272i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −9879.03 + 8289.49i −1.20316 + 1.00957i
\(408\) 0 0
\(409\) −773.536 + 4386.94i −0.0935181 + 0.530367i 0.901673 + 0.432418i \(0.142339\pi\)
−0.995191 + 0.0979494i \(0.968772\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −6116.72 10594.5i −0.728775 1.26228i
\(414\) 0 0
\(415\) −5042.65 + 8734.13i −0.596467 + 1.03311i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 9991.52 + 8383.88i 1.16496 + 0.977517i 0.999961 0.00877723i \(-0.00279391\pi\)
0.164998 + 0.986294i \(0.447238\pi\)
\(420\) 0 0
\(421\) −15259.8 5554.12i −1.76655 0.642972i −1.00000 0.000788484i \(-0.999749\pi\)
−0.766551 0.642183i \(-0.778029\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1495.53 8481.56i −0.170691 0.968038i
\(426\) 0 0
\(427\) 1658.25 603.555i 0.187936 0.0684029i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 506.152 0.0565672 0.0282836 0.999600i \(-0.490996\pi\)
0.0282836 + 0.999600i \(0.490996\pi\)
\(432\) 0 0
\(433\) 3810.53 0.422916 0.211458 0.977387i \(-0.432179\pi\)
0.211458 + 0.977387i \(0.432179\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6692.34 2435.81i 0.732581 0.266638i
\(438\) 0 0
\(439\) 2784.60 + 15792.2i 0.302737 + 1.71691i 0.633969 + 0.773358i \(0.281425\pi\)
−0.331232 + 0.943549i \(0.607464\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 7142.68 + 2599.72i 0.766048 + 0.278819i 0.695342 0.718679i \(-0.255253\pi\)
0.0707054 + 0.997497i \(0.477475\pi\)
\(444\) 0 0
\(445\) 6796.38 + 5702.84i 0.723999 + 0.607507i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −7613.88 + 13187.6i −0.800270 + 1.38611i 0.119168 + 0.992874i \(0.461977\pi\)
−0.919438 + 0.393234i \(0.871356\pi\)
\(450\) 0 0
\(451\) −245.278 424.834i −0.0256091 0.0443562i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −359.649 + 2039.67i −0.0370562 + 0.210156i
\(456\) 0 0
\(457\) 2349.87 1971.78i 0.240531 0.201829i −0.514551 0.857460i \(-0.672042\pi\)
0.755082 + 0.655630i \(0.227597\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4161.68 3492.06i 0.420453 0.352802i −0.407883 0.913034i \(-0.633733\pi\)
0.828335 + 0.560233i \(0.189288\pi\)
\(462\) 0 0
\(463\) 3055.02 17325.9i 0.306650 1.73910i −0.308986 0.951067i \(-0.599989\pi\)
0.615635 0.788031i \(-0.288899\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −761.856 1319.57i −0.0754914 0.130755i 0.825808 0.563951i \(-0.190719\pi\)
−0.901300 + 0.433196i \(0.857386\pi\)
\(468\) 0 0
\(469\) −6133.38 + 10623.3i −0.603866 + 1.04593i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 11170.2 + 9372.93i 1.08585 + 0.911137i
\(474\) 0 0
\(475\) 5534.90 + 2014.54i 0.534650 + 0.194597i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −17.9267 101.668i −0.00171001 0.00969793i 0.983941 0.178495i \(-0.0571228\pi\)
−0.985651 + 0.168797i \(0.946012\pi\)
\(480\) 0 0
\(481\) −2728.10 + 992.948i −0.258609 + 0.0941259i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 23175.1 2.16974
\(486\) 0 0
\(487\) −6424.90 −0.597823 −0.298912 0.954281i \(-0.596624\pi\)
−0.298912 + 0.954281i \(0.596624\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 9033.50 3287.92i 0.830297 0.302203i 0.108316 0.994116i \(-0.465454\pi\)
0.721981 + 0.691913i \(0.243232\pi\)
\(492\) 0 0
\(493\) 2263.85 + 12838.9i 0.206813 + 1.17289i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1640.70 + 597.166i 0.148079 + 0.0538964i
\(498\) 0 0
\(499\) −15561.9 13058.0i −1.39608 1.17145i −0.962806 0.270192i \(-0.912913\pi\)
−0.433277 0.901261i \(-0.642643\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −4198.74 + 7272.42i −0.372192 + 0.644655i −0.989902 0.141751i \(-0.954727\pi\)
0.617711 + 0.786405i \(0.288060\pi\)
\(504\) 0 0
\(505\) −9004.96 15597.0i −0.793496 1.37438i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1856.65 + 10529.6i −0.161679 + 0.916926i 0.790744 + 0.612147i \(0.209694\pi\)
−0.952423 + 0.304779i \(0.901417\pi\)
\(510\) 0 0
\(511\) 14078.7 11813.5i 1.21880 1.02269i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 545.777 457.961i 0.0466986 0.0391848i
\(516\) 0 0
\(517\) −512.261 + 2905.17i −0.0435768 + 0.247136i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 8883.34 + 15386.4i 0.746998 + 1.29384i 0.949255 + 0.314506i \(0.101839\pi\)
−0.202257 + 0.979332i \(0.564828\pi\)
\(522\) 0 0
\(523\) −9911.83 + 17167.8i −0.828708 + 1.43536i 0.0703449 + 0.997523i \(0.477590\pi\)
−0.899052 + 0.437841i \(0.855743\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −24253.6 20351.2i −2.00475 1.68219i
\(528\) 0 0
\(529\) 3952.90 + 1438.74i 0.324887 + 0.118249i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −19.1767 108.756i −0.00155841 0.00883820i
\(534\) 0 0
\(535\) −21002.0 + 7644.09i −1.69719 + 0.617725i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −325.899 −0.0260436
\(540\) 0 0
\(541\) 879.526 0.0698960 0.0349480 0.999389i \(-0.488873\pi\)
0.0349480 + 0.999389i \(0.488873\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −2671.16 + 972.221i −0.209944 + 0.0764135i
\(546\) 0 0
\(547\) −1578.98 8954.82i −0.123423 0.699964i −0.982232 0.187670i \(-0.939907\pi\)
0.858810 0.512295i \(-0.171205\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −8378.43 3049.50i −0.647792 0.235777i
\(552\) 0 0
\(553\) 14259.0 + 11964.7i 1.09648 + 0.920059i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −11427.3 + 19792.7i −0.869283 + 1.50564i −0.00655273 + 0.999979i \(0.502086\pi\)
−0.862730 + 0.505664i \(0.831248\pi\)
\(558\) 0 0
\(559\) 1641.32 + 2842.85i 0.124187 + 0.215098i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −999.815 + 5670.23i −0.0748440 + 0.424462i 0.924245 + 0.381799i \(0.124695\pi\)
−0.999090 + 0.0426629i \(0.986416\pi\)
\(564\) 0 0
\(565\) 16708.4 14020.0i 1.24412 1.04394i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 912.392 765.588i 0.0672223 0.0564062i −0.608557 0.793510i \(-0.708252\pi\)
0.675780 + 0.737104i \(0.263807\pi\)
\(570\) 0 0
\(571\) 1268.54 7194.23i 0.0929713 0.527267i −0.902379 0.430944i \(-0.858181\pi\)
0.995350 0.0963229i \(-0.0307081\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −3291.83 5701.62i −0.238746 0.413520i
\(576\) 0 0
\(577\) 5516.75 9555.29i 0.398033 0.689414i −0.595450 0.803393i \(-0.703026\pi\)
0.993483 + 0.113978i \(0.0363594\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 10012.4 + 8401.37i 0.714944 + 0.599910i
\(582\) 0 0
\(583\) −967.646 352.194i −0.0687406 0.0250195i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1937.43 + 10987.7i 0.136229 + 0.772593i 0.973996 + 0.226565i \(0.0727496\pi\)
−0.837767 + 0.546028i \(0.816139\pi\)
\(588\) 0 0
\(589\) 20347.4 7405.84i 1.42343 0.518085i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −9356.50 −0.647935 −0.323967 0.946068i \(-0.605017\pi\)
−0.323967 + 0.946068i \(0.605017\pi\)
\(594\) 0 0
\(595\) −30068.6 −2.07175
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −2260.98 + 822.930i −0.154226 + 0.0561335i −0.417979 0.908457i \(-0.637262\pi\)
0.263754 + 0.964590i \(0.415039\pi\)
\(600\) 0 0
\(601\) 1862.04 + 10560.2i 0.126380 + 0.716736i 0.980479 + 0.196625i \(0.0629983\pi\)
−0.854099 + 0.520111i \(0.825891\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 738.084 + 268.641i 0.0495990 + 0.0180526i
\(606\) 0 0
\(607\) 6535.29 + 5483.76i 0.437000 + 0.366687i 0.834585 0.550879i \(-0.185707\pi\)
−0.397585 + 0.917565i \(0.630152\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −332.051 + 575.130i −0.0219859 + 0.0380806i
\(612\) 0 0
\(613\) 2670.34 + 4625.17i 0.175945 + 0.304745i 0.940488 0.339827i \(-0.110369\pi\)
−0.764543 + 0.644573i \(0.777035\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3028.80 17177.2i 0.197625 1.12079i −0.711005 0.703187i \(-0.751760\pi\)
0.908630 0.417601i \(-0.137129\pi\)
\(618\) 0 0
\(619\) −6065.97 + 5089.96i −0.393881 + 0.330505i −0.818123 0.575044i \(-0.804985\pi\)
0.424242 + 0.905549i \(0.360541\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 8807.88 7390.69i 0.566421 0.475284i
\(624\) 0 0
\(625\) −3369.43 + 19109.0i −0.215644 + 1.22298i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −21074.1 36501.5i −1.33590 2.31385i
\(630\) 0 0
\(631\) 8251.31 14291.7i 0.520570 0.901653i −0.479144 0.877736i \(-0.659053\pi\)
0.999714 0.0239171i \(-0.00761378\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −24033.9 20166.8i −1.50198 1.26031i
\(636\) 0 0
\(637\) −68.9420 25.0928i −0.00428820 0.00156078i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −3265.74 18520.9i −0.201231 1.14124i −0.903262 0.429089i \(-0.858835\pi\)
0.702031 0.712146i \(-0.252277\pi\)
\(642\) 0 0
\(643\) −955.782 + 347.876i −0.0586195 + 0.0213358i −0.371163 0.928568i \(-0.621041\pi\)
0.312544 + 0.949903i \(0.398819\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 20407.3 1.24002 0.620011 0.784593i \(-0.287128\pi\)
0.620011 + 0.784593i \(0.287128\pi\)
\(648\) 0 0
\(649\) 23909.0 1.44609
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 24273.6 8834.88i 1.45467 0.529457i 0.510780 0.859711i \(-0.329357\pi\)
0.943892 + 0.330254i \(0.107134\pi\)
\(654\) 0 0
\(655\) −3043.16 17258.6i −0.181536 1.02954i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 11124.7 + 4049.07i 0.657599 + 0.239347i 0.649199 0.760618i \(-0.275104\pi\)
0.00839966 + 0.999965i \(0.497326\pi\)
\(660\) 0 0
\(661\) −5401.80 4532.65i −0.317860 0.266717i 0.469871 0.882735i \(-0.344300\pi\)
−0.787732 + 0.616018i \(0.788745\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 10282.1 17809.2i 0.599585 1.03851i
\(666\) 0 0
\(667\) 4982.99 + 8630.80i 0.289269 + 0.501028i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −598.892 + 3396.48i −0.0344560 + 0.195410i
\(672\) 0 0
\(673\) −17454.9 + 14646.4i −0.999756 + 0.838895i −0.986951 0.161023i \(-0.948521\pi\)
−0.0128057 + 0.999918i \(0.504076\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 8712.25 7310.45i 0.494592 0.415012i −0.361076 0.932536i \(-0.617591\pi\)
0.855669 + 0.517524i \(0.173146\pi\)
\(678\) 0 0
\(679\) 5215.37 29577.8i 0.294768 1.67171i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 5758.82 + 9974.56i 0.322628 + 0.558808i 0.981029 0.193859i \(-0.0621003\pi\)
−0.658401 + 0.752667i \(0.728767\pi\)
\(684\) 0 0
\(685\) 18916.4 32764.1i 1.05512 1.82752i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −177.582 149.009i −0.00981907 0.00823918i
\(690\) 0 0
\(691\) −13056.2 4752.05i −0.718784 0.261616i −0.0433746 0.999059i \(-0.513811\pi\)
−0.675410 + 0.737443i \(0.736033\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −3684.00 20893.0i −0.201068 1.14031i
\(696\) 0 0
\(697\) 1506.59 548.352i 0.0818738 0.0297996i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −25381.5 −1.36754 −0.683771 0.729696i \(-0.739661\pi\)
−0.683771 + 0.729696i \(0.739661\pi\)
\(702\) 0 0
\(703\) 28825.7 1.54649
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −21932.7 + 7982.83i −1.16671 + 0.424647i
\(708\) 0 0
\(709\) −3197.43 18133.5i −0.169368 0.960535i −0.944445 0.328668i \(-0.893400\pi\)
0.775077 0.631867i \(-0.217711\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −22743.2 8277.85i −1.19459 0.434794i
\(714\) 0 0
\(715\) −3100.81 2601.89i −0.162187 0.136091i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 4178.46 7237.30i 0.216732 0.375391i −0.737075 0.675811i \(-0.763794\pi\)
0.953807 + 0.300420i \(0.0971269\pi\)
\(720\) 0 0
\(721\) −461.662 799.623i −0.0238463 0.0413031i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1431.27 + 8117.16i −0.0733189 + 0.415812i
\(726\) 0 0
\(727\) −2910.27 + 2442.01i −0.148468 + 0.124579i −0.713996 0.700149i \(-0.753117\pi\)
0.565528 + 0.824729i \(0.308672\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −36507.5 + 30633.4i −1.84716 + 1.54996i
\(732\) 0 0
\(733\) −3398.64 + 19274.7i −0.171257 + 0.971249i 0.771118 + 0.636692i \(0.219698\pi\)
−0.942375 + 0.334557i \(0.891413\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −11987.1 20762.2i −0.599117 1.03770i
\(738\) 0 0
\(739\) −3828.18 + 6630.60i −0.190557 + 0.330055i −0.945435 0.325811i \(-0.894363\pi\)
0.754878 + 0.655866i \(0.227696\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 8817.80 + 7399.01i 0.435388 + 0.365334i 0.833980 0.551794i \(-0.186057\pi\)
−0.398592 + 0.917128i \(0.630501\pi\)
\(744\) 0 0
\(745\) −2984.08 1086.12i −0.146749 0.0534123i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 5029.65 + 28524.6i 0.245366 + 1.39154i
\(750\) 0 0
\(751\) 21813.3 7939.39i 1.05989 0.385769i 0.247504 0.968887i \(-0.420390\pi\)
0.812387 + 0.583118i \(0.198168\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 32288.9 1.55644
\(756\) 0 0
\(757\) −2092.13 −0.100449 −0.0502244 0.998738i \(-0.515994\pi\)
−0.0502244 + 0.998738i \(0.515994\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −22912.8 + 8339.57i −1.09144 + 0.397253i −0.824155 0.566364i \(-0.808350\pi\)
−0.267288 + 0.963617i \(0.586127\pi\)
\(762\) 0 0
\(763\) 639.701 + 3627.93i 0.0303522 + 0.172136i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 5057.81 + 1840.89i 0.238105 + 0.0866633i
\(768\) 0 0
\(769\) 3200.87 + 2685.85i 0.150099 + 0.125948i 0.714745 0.699385i \(-0.246543\pi\)
−0.564646 + 0.825333i \(0.690987\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 7133.99 12356.4i 0.331943 0.574942i −0.650950 0.759121i \(-0.725629\pi\)
0.982893 + 0.184179i \(0.0589625\pi\)
\(774\) 0 0
\(775\) −10008.5 17335.2i −0.463891 0.803482i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −190.405 + 1079.84i −0.00875734 + 0.0496653i
\(780\) 0 0
\(781\) −2614.03 + 2193.43i −0.119766 + 0.100496i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 11528.0 9673.16i 0.524143 0.439809i
\(786\) 0 0
\(787\) −3425.45 + 19426.7i −0.155151 + 0.879908i 0.803496 + 0.595310i \(0.202971\pi\)
−0.958647 + 0.284597i \(0.908140\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −14133.3 24479.6i