Properties

Label 324.4.i.a.37.9
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 37.9
Character \(\chi\) \(=\) 324.37
Dual form 324.4.i.a.289.9

$q$-expansion

\(f(q)\) \(=\) \(q+(13.0875 - 4.76347i) q^{5} +(-0.689494 - 3.91032i) q^{7} +O(q^{10})\) \(q+(13.0875 - 4.76347i) q^{5} +(-0.689494 - 3.91032i) q^{7} +(41.0823 + 14.9527i) q^{11} +(4.04425 + 3.39352i) q^{13} +(3.06285 - 5.30501i) q^{17} +(-7.42787 - 12.8654i) q^{19} +(21.3706 - 121.199i) q^{23} +(52.8371 - 44.3356i) q^{25} +(108.223 - 90.8101i) q^{29} +(-46.8412 + 265.650i) q^{31} +(-27.6504 - 47.8920i) q^{35} +(100.261 - 173.657i) q^{37} +(-239.406 - 200.886i) q^{41} +(462.032 + 168.166i) q^{43} +(10.6113 + 60.1798i) q^{47} +(307.499 - 111.921i) q^{49} +380.159 q^{53} +608.892 q^{55} +(154.748 - 56.3238i) q^{59} +(-149.877 - 849.997i) q^{61} +(69.0941 + 25.1482i) q^{65} +(159.359 + 133.718i) q^{67} +(451.411 - 781.866i) q^{71} +(353.597 + 612.447i) q^{73} +(30.1439 - 170.954i) q^{77} +(-847.858 + 711.438i) q^{79} +(-652.401 + 547.430i) q^{83} +(14.8148 - 84.0192i) q^{85} +(-214.477 - 371.485i) q^{89} +(10.4813 - 18.1541i) q^{91} +(-158.497 - 132.994i) q^{95} +(-1166.45 - 424.552i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54q - 12q^{5} + O(q^{10}) \) \( 54q - 12q^{5} + 87q^{11} - 204q^{17} - 96q^{23} - 216q^{25} - 318q^{29} - 54q^{31} - 6q^{35} - 867q^{41} - 513q^{43} + 1548q^{47} + 594q^{49} + 1068q^{53} + 1218q^{59} - 54q^{61} - 96q^{65} - 2997q^{67} + 120q^{71} - 216q^{73} - 3480q^{77} + 2808q^{79} - 4464q^{83} + 2160q^{85} - 4029q^{89} + 270q^{91} + 1650q^{95} - 3483q^{97} + O(q^{100}) \)

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
\(5\) 13.0875 4.76347i 1.17058 0.426058i 0.317717 0.948186i \(-0.397084\pi\)
0.852867 + 0.522128i \(0.174862\pi\)
\(6\) 0 0
\(7\) −0.689494 3.91032i −0.0372292 0.211137i 0.960518 0.278216i \(-0.0897432\pi\)
−0.997748 + 0.0670790i \(0.978632\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 41.0823 + 14.9527i 1.12607 + 0.409856i 0.836864 0.547411i \(-0.184387\pi\)
0.289206 + 0.957267i \(0.406609\pi\)
\(12\) 0 0
\(13\) 4.04425 + 3.39352i 0.0862825 + 0.0723996i 0.684909 0.728629i \(-0.259842\pi\)
−0.598626 + 0.801028i \(0.704287\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.06285 5.30501i 0.0436970 0.0756855i −0.843350 0.537365i \(-0.819420\pi\)
0.887047 + 0.461680i \(0.152753\pi\)
\(18\) 0 0
\(19\) −7.42787 12.8654i −0.0896879 0.155344i 0.817691 0.575657i \(-0.195254\pi\)
−0.907379 + 0.420313i \(0.861920\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 21.3706 121.199i 0.193743 1.09877i −0.720455 0.693502i \(-0.756067\pi\)
0.914198 0.405268i \(-0.132822\pi\)
\(24\) 0 0
\(25\) 52.8371 44.3356i 0.422697 0.354685i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 108.223 90.8101i 0.692985 0.581483i −0.226784 0.973945i \(-0.572821\pi\)
0.919768 + 0.392462i \(0.128377\pi\)
\(30\) 0 0
\(31\) −46.8412 + 265.650i −0.271385 + 1.53910i 0.478831 + 0.877907i \(0.341061\pi\)
−0.750216 + 0.661193i \(0.770050\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −27.6504 47.8920i −0.133537 0.231292i
\(36\) 0 0
\(37\) 100.261 173.657i 0.445481 0.771595i −0.552605 0.833443i \(-0.686366\pi\)
0.998086 + 0.0618483i \(0.0196995\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −239.406 200.886i −0.911927 0.765197i 0.0605578 0.998165i \(-0.480712\pi\)
−0.972485 + 0.232967i \(0.925156\pi\)
\(42\) 0 0
\(43\) 462.032 + 168.166i 1.63859 + 0.596397i 0.986791 0.161998i \(-0.0517939\pi\)
0.651795 + 0.758395i \(0.274016\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10.6113 + 60.1798i 0.0329323 + 0.186769i 0.996836 0.0794815i \(-0.0253264\pi\)
−0.963904 + 0.266250i \(0.914215\pi\)
\(48\) 0 0
\(49\) 307.499 111.921i 0.896500 0.326299i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 380.159 0.985262 0.492631 0.870238i \(-0.336035\pi\)
0.492631 + 0.870238i \(0.336035\pi\)
\(54\) 0 0
\(55\) 608.892 1.49278
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 154.748 56.3238i 0.341467 0.124284i −0.165594 0.986194i \(-0.552954\pi\)
0.507061 + 0.861910i \(0.330732\pi\)
\(60\) 0 0
\(61\) −149.877 849.997i −0.314588 1.78411i −0.574523 0.818488i \(-0.694812\pi\)
0.259935 0.965626i \(-0.416299\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 69.0941 + 25.1482i 0.131847 + 0.0479885i
\(66\) 0 0
\(67\) 159.359 + 133.718i 0.290579 + 0.243825i 0.776410 0.630228i \(-0.217039\pi\)
−0.485831 + 0.874053i \(0.661483\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 451.411 781.866i 0.754543 1.30691i −0.191058 0.981579i \(-0.561192\pi\)
0.945601 0.325329i \(-0.105475\pi\)
\(72\) 0 0
\(73\) 353.597 + 612.447i 0.566923 + 0.981939i 0.996868 + 0.0790840i \(0.0251995\pi\)
−0.429945 + 0.902855i \(0.641467\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 30.1439 170.954i 0.0446132 0.253014i
\(78\) 0 0
\(79\) −847.858 + 711.438i −1.20749 + 1.01320i −0.208104 + 0.978107i \(0.566729\pi\)
−0.999384 + 0.0350955i \(0.988826\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −652.401 + 547.430i −0.862775 + 0.723954i −0.962564 0.271054i \(-0.912628\pi\)
0.0997890 + 0.995009i \(0.468183\pi\)
\(84\) 0 0
\(85\) 14.8148 84.0192i 0.0189047 0.107214i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −214.477 371.485i −0.255444 0.442442i 0.709572 0.704633i \(-0.248888\pi\)
−0.965016 + 0.262191i \(0.915555\pi\)
\(90\) 0 0
\(91\) 10.4813 18.1541i 0.0120740 0.0209128i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −158.497 132.994i −0.171173 0.143631i
\(96\) 0 0
\(97\) −1166.45 424.552i −1.22098 0.444400i −0.350480 0.936570i \(-0.613981\pi\)
−0.870499 + 0.492171i \(0.836204\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 142.775 + 809.715i 0.140659 + 0.797719i 0.970750 + 0.240091i \(0.0771773\pi\)
−0.830091 + 0.557628i \(0.811712\pi\)
\(102\) 0 0
\(103\) −1713.66 + 623.722i −1.63934 + 0.596672i −0.986924 0.161187i \(-0.948468\pi\)
−0.652418 + 0.757859i \(0.726245\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2093.70 1.89164 0.945819 0.324695i \(-0.105262\pi\)
0.945819 + 0.324695i \(0.105262\pi\)
\(108\) 0 0
\(109\) 785.096 0.689895 0.344947 0.938622i \(-0.387897\pi\)
0.344947 + 0.938622i \(0.387897\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1484.56 + 540.337i −1.23589 + 0.449828i −0.875612 0.483015i \(-0.839542\pi\)
−0.360281 + 0.932844i \(0.617319\pi\)
\(114\) 0 0
\(115\) −297.638 1687.99i −0.241347 1.36875i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −22.8561 8.31893i −0.0176068 0.00640836i
\(120\) 0 0
\(121\) 444.562 + 373.032i 0.334006 + 0.280265i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −390.150 + 675.760i −0.279169 + 0.483534i
\(126\) 0 0
\(127\) −197.197 341.555i −0.137783 0.238646i 0.788874 0.614554i \(-0.210664\pi\)
−0.926657 + 0.375908i \(0.877331\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −104.311 + 591.579i −0.0695704 + 0.394553i 0.930061 + 0.367405i \(0.119754\pi\)
−0.999631 + 0.0271482i \(0.991357\pi\)
\(132\) 0 0
\(133\) −45.1865 + 37.9160i −0.0294599 + 0.0247198i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −875.032 + 734.239i −0.545686 + 0.457885i −0.873477 0.486865i \(-0.838140\pi\)
0.327791 + 0.944750i \(0.393696\pi\)
\(138\) 0 0
\(139\) −359.669 + 2039.78i −0.219473 + 1.24469i 0.653501 + 0.756926i \(0.273300\pi\)
−0.872974 + 0.487767i \(0.837812\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 115.404 + 199.886i 0.0674867 + 0.116890i
\(144\) 0 0
\(145\) 983.804 1704.00i 0.563451 0.975926i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2383.51 2000.00i −1.31050 1.09964i −0.988227 0.152997i \(-0.951108\pi\)
−0.322276 0.946646i \(-0.604448\pi\)
\(150\) 0 0
\(151\) −35.5500 12.9391i −0.0191590 0.00697332i 0.332423 0.943130i \(-0.392134\pi\)
−0.351582 + 0.936157i \(0.614356\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 652.379 + 3699.82i 0.338067 + 1.91727i
\(156\) 0 0
\(157\) −2170.17 + 789.878i −1.10318 + 0.401523i −0.828486 0.560010i \(-0.810797\pi\)
−0.274689 + 0.961533i \(0.588575\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −488.661 −0.239204
\(162\) 0 0
\(163\) 232.306 0.111630 0.0558148 0.998441i \(-0.482224\pi\)
0.0558148 + 0.998441i \(0.482224\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1530.58 + 557.084i −0.709218 + 0.258134i −0.671342 0.741148i \(-0.734282\pi\)
−0.0378768 + 0.999282i \(0.512059\pi\)
\(168\) 0 0
\(169\) −376.665 2136.17i −0.171445 0.972314i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1144.54 + 416.577i 0.502992 + 0.183074i 0.581039 0.813876i \(-0.302646\pi\)
−0.0780474 + 0.996950i \(0.524869\pi\)
\(174\) 0 0
\(175\) −209.797 176.041i −0.0906238 0.0760424i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1158.73 + 2006.98i −0.483842 + 0.838039i −0.999828 0.0185580i \(-0.994092\pi\)
0.515986 + 0.856597i \(0.327426\pi\)
\(180\) 0 0
\(181\) −77.3428 133.962i −0.0317616 0.0550127i 0.849708 0.527254i \(-0.176778\pi\)
−0.881469 + 0.472241i \(0.843445\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 484.957 2750.33i 0.192728 1.09302i
\(186\) 0 0
\(187\) 205.153 172.144i 0.0802260 0.0673176i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2149.29 + 1803.47i −0.814227 + 0.683217i −0.951613 0.307300i \(-0.900574\pi\)
0.137386 + 0.990518i \(0.456130\pi\)
\(192\) 0 0
\(193\) −475.369 + 2695.95i −0.177294 + 1.00549i 0.758168 + 0.652060i \(0.226095\pi\)
−0.935462 + 0.353427i \(0.885016\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1571.62 2722.12i −0.568391 0.984482i −0.996725 0.0808620i \(-0.974233\pi\)
0.428334 0.903620i \(-0.359101\pi\)
\(198\) 0 0
\(199\) −935.924 + 1621.07i −0.333396 + 0.577459i −0.983175 0.182664i \(-0.941528\pi\)
0.649779 + 0.760123i \(0.274861\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −429.716 360.574i −0.148572 0.124667i
\(204\) 0 0
\(205\) −4090.15 1488.69i −1.39350 0.507194i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −112.780 639.608i −0.0373262 0.211687i
\(210\) 0 0
\(211\) 238.052 86.6438i 0.0776691 0.0282692i −0.302893 0.953024i \(-0.597953\pi\)
0.380562 + 0.924755i \(0.375730\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 6847.91 2.17220
\(216\) 0 0
\(217\) 1071.07 0.335065
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 30.3896 11.0609i 0.00924988 0.00336668i
\(222\) 0 0
\(223\) 600.687 + 3406.66i 0.180381 + 1.02299i 0.931748 + 0.363106i \(0.118284\pi\)
−0.751367 + 0.659885i \(0.770605\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1925.67 + 700.886i 0.563044 + 0.204931i 0.607833 0.794065i \(-0.292039\pi\)
−0.0447883 + 0.998997i \(0.514261\pi\)
\(228\) 0 0
\(229\) −693.662 582.052i −0.200168 0.167961i 0.537194 0.843459i \(-0.319484\pi\)
−0.737362 + 0.675498i \(0.763929\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 696.488 1206.35i 0.195830 0.339188i −0.751342 0.659913i \(-0.770593\pi\)
0.947172 + 0.320725i \(0.103927\pi\)
\(234\) 0 0
\(235\) 425.540 + 737.057i 0.118124 + 0.204597i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 43.4332 246.322i 0.0117551 0.0666663i −0.978366 0.206882i \(-0.933668\pi\)
0.990121 + 0.140216i \(0.0447795\pi\)
\(240\) 0 0
\(241\) 3775.11 3167.70i 1.00903 0.846677i 0.0208208 0.999783i \(-0.493372\pi\)
0.988210 + 0.153106i \(0.0489276\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3491.28 2929.53i 0.910406 0.763921i
\(246\) 0 0
\(247\) 13.6191 77.2377i 0.00350835 0.0198968i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −557.386 965.420i −0.140167 0.242776i 0.787392 0.616452i \(-0.211431\pi\)
−0.927559 + 0.373676i \(0.878097\pi\)
\(252\) 0 0
\(253\) 2690.21 4659.57i 0.668505 1.15788i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 2365.04 + 1984.51i 0.574037 + 0.481674i 0.882983 0.469406i \(-0.155532\pi\)
−0.308946 + 0.951080i \(0.599976\pi\)
\(258\) 0 0
\(259\) −748.183 272.316i −0.179497 0.0653317i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −187.667 1064.32i −0.0440003 0.249538i 0.954872 0.297018i \(-0.0959921\pi\)
−0.998872 + 0.0474799i \(0.984881\pi\)
\(264\) 0 0
\(265\) 4975.34 1810.88i 1.15333 0.419778i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 5507.29 1.24827 0.624137 0.781315i \(-0.285451\pi\)
0.624137 + 0.781315i \(0.285451\pi\)
\(270\) 0 0
\(271\) 4075.64 0.913570 0.456785 0.889577i \(-0.349001\pi\)
0.456785 + 0.889577i \(0.349001\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2833.61 1031.35i 0.621356 0.226155i
\(276\) 0 0
\(277\) 615.311 + 3489.60i 0.133467 + 0.756931i 0.975915 + 0.218152i \(0.0700029\pi\)
−0.842447 + 0.538779i \(0.818886\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −6900.33 2511.51i −1.46491 0.533183i −0.518195 0.855262i \(-0.673396\pi\)
−0.946713 + 0.322080i \(0.895618\pi\)
\(282\) 0 0
\(283\) −102.360 85.8899i −0.0215005 0.0180411i 0.631974 0.774990i \(-0.282245\pi\)
−0.653475 + 0.756948i \(0.726689\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −620.458 + 1074.66i −0.127611 + 0.221029i
\(288\) 0 0
\(289\) 2437.74 + 4222.29i 0.496181 + 0.859411i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −710.916 + 4031.81i −0.141748 + 0.803893i 0.828173 + 0.560473i \(0.189381\pi\)
−0.969921 + 0.243420i \(0.921731\pi\)
\(294\) 0 0
\(295\) 1756.98 1474.28i 0.346763 0.290969i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 497.719 417.636i 0.0962671 0.0807777i
\(300\) 0 0
\(301\) 339.013 1922.64i 0.0649183 0.368170i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −6010.46 10410.4i −1.12839 1.95442i
\(306\) 0 0
\(307\) −4191.33 + 7259.59i −0.779191 + 1.34960i 0.153217 + 0.988192i \(0.451037\pi\)
−0.932409 + 0.361406i \(0.882297\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1493.12 1252.88i −0.272242 0.228438i 0.496437 0.868073i \(-0.334641\pi\)
−0.768679 + 0.639635i \(0.779086\pi\)
\(312\) 0 0
\(313\) −1191.53 433.681i −0.215173 0.0783165i 0.232185 0.972672i \(-0.425413\pi\)
−0.447358 + 0.894355i \(0.647635\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1155.38 6552.49i −0.204709 1.16096i −0.897898 0.440204i \(-0.854906\pi\)
0.693189 0.720756i \(-0.256205\pi\)
\(318\) 0 0
\(319\) 5803.91 2112.45i 1.01867 0.370767i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −91.0017 −0.0156764
\(324\) 0 0
\(325\) 364.140 0.0621504
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 228.005 82.9872i 0.0382077 0.0139065i
\(330\) 0 0
\(331\) 988.638 + 5606.85i 0.164171 + 0.931058i 0.949915 + 0.312507i \(0.101169\pi\)
−0.785745 + 0.618551i \(0.787720\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2722.58 + 990.936i 0.444030 + 0.161614i
\(336\) 0 0
\(337\) 4026.87 + 3378.95i 0.650913 + 0.546181i 0.907348 0.420381i \(-0.138103\pi\)
−0.256435 + 0.966561i \(0.582548\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −5896.53 + 10213.1i −0.936407 + 1.62190i
\(342\) 0 0
\(343\) −1330.63 2304.72i −0.209467 0.362808i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1204.18 6829.25i 0.186293 1.05652i −0.737989 0.674813i \(-0.764224\pi\)
0.924282 0.381710i \(-0.124665\pi\)
\(348\) 0 0
\(349\) −362.713 + 304.352i −0.0556320 + 0.0466808i −0.670180 0.742199i \(-0.733783\pi\)
0.614548 + 0.788880i \(0.289339\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1133.07 + 950.758i −0.170842 + 0.143353i −0.724200 0.689590i \(-0.757791\pi\)
0.553358 + 0.832944i \(0.313346\pi\)
\(354\) 0 0
\(355\) 2183.45 12383.0i 0.326438 1.85132i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1718.27 2976.14i −0.252610 0.437534i 0.711634 0.702551i \(-0.247956\pi\)
−0.964244 + 0.265017i \(0.914622\pi\)
\(360\) 0 0
\(361\) 3319.15 5748.94i 0.483912 0.838160i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 7545.08 + 6331.07i 1.08199 + 0.907900i
\(366\) 0 0
\(367\) 8040.63 + 2926.55i 1.14364 + 0.416253i 0.843228 0.537556i \(-0.180652\pi\)
0.300416 + 0.953808i \(0.402874\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −262.117 1486.54i −0.0366805 0.208025i
\(372\) 0 0
\(373\) −8918.15 + 3245.94i −1.23797 + 0.450586i −0.876321 0.481727i \(-0.840010\pi\)
−0.361653 + 0.932313i \(0.617787\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 745.848 0.101892
\(378\) 0 0
\(379\) −11784.3 −1.59714 −0.798572 0.601899i \(-0.794411\pi\)
−0.798572 + 0.601899i \(0.794411\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 8550.92 3112.28i 1.14081 0.415222i 0.298606 0.954376i \(-0.403478\pi\)
0.842207 + 0.539155i \(0.181256\pi\)
\(384\) 0 0
\(385\) −419.827 2380.96i −0.0555750 0.315182i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 8567.80 + 3118.43i 1.11672 + 0.406454i 0.833455 0.552587i \(-0.186359\pi\)
0.283267 + 0.959041i \(0.408582\pi\)
\(390\) 0 0
\(391\) −577.506 484.585i −0.0746949 0.0626765i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −7707.46 + 13349.7i −0.981783 + 1.70050i
\(396\) 0 0
\(397\) −4029.27 6978.90i −0.509378 0.882269i −0.999941 0.0108631i \(-0.996542\pi\)
0.490563 0.871406i \(-0.336791\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2031.54 + 11521.4i −0.252993 + 1.43479i 0.548180 + 0.836361i \(0.315321\pi\)
−0.801173 + 0.598433i \(0.795790\pi\)
\(402\) 0 0
\(403\) −1090.93 + 915.396i −0.134846 + 0.113149i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 6715.58 5635.04i 0.817885 0.686287i
\(408\) 0 0
\(409\) −489.847 + 2778.06i −0.0592210 + 0.335859i −0.999995 0.00317545i \(-0.998989\pi\)
0.940774 + 0.339034i \(0.110100\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −326.942 566.281i −0.0389535 0.0674694i
\(414\) 0 0
\(415\) −5930.65 + 10272.2i −0.701504 + 1.21504i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −7349.28 6166.78i −0.856887 0.719014i 0.104408 0.994535i \(-0.466705\pi\)
−0.961295 + 0.275521i \(0.911150\pi\)
\(420\) 0 0
\(421\) 11950.5 + 4349.63i 1.38345 + 0.503535i 0.923222 0.384266i \(-0.125545\pi\)
0.460228 + 0.887801i \(0.347768\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −73.3687 416.094i −0.00837389 0.0474907i
\(426\) 0 0
\(427\) −3220.42 + 1172.14i −0.364981 + 0.132842i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 7867.05 0.879216 0.439608 0.898190i \(-0.355117\pi\)
0.439608 + 0.898190i \(0.355117\pi\)
\(432\) 0 0
\(433\) −17294.1 −1.91940 −0.959702 0.281018i \(-0.909328\pi\)
−0.959702 + 0.281018i \(0.909328\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1718.02 + 625.306i −0.188064 + 0.0684496i
\(438\) 0 0
\(439\) 578.944 + 3283.35i 0.0629418 + 0.356961i 0.999970 + 0.00770790i \(0.00245352\pi\)
−0.937028 + 0.349253i \(0.886435\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −12292.3 4474.02i −1.31834 0.479836i −0.415413 0.909633i \(-0.636363\pi\)
−0.902925 + 0.429797i \(0.858585\pi\)
\(444\) 0 0
\(445\) −4576.53 3840.17i −0.487525 0.409082i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −9483.66 + 16426.2i −0.996796 + 1.72650i −0.429132 + 0.903242i \(0.641180\pi\)
−0.567665 + 0.823260i \(0.692153\pi\)
\(450\) 0 0
\(451\) −6831.56 11832.6i −0.713272 1.23542i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 50.6974 287.519i 0.00522359 0.0296244i
\(456\) 0 0
\(457\) −10486.3 + 8799.07i −1.07337 + 0.900664i −0.995353 0.0962885i \(-0.969303\pi\)
−0.0780156 + 0.996952i \(0.524858\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 7991.70 6705.83i 0.807398 0.677488i −0.142587 0.989782i \(-0.545542\pi\)
0.949985 + 0.312295i \(0.101098\pi\)
\(462\) 0 0
\(463\) 848.557 4812.41i 0.0851745 0.483048i −0.912144 0.409869i \(-0.865574\pi\)
0.997319 0.0731793i \(-0.0233145\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −3003.39 5202.03i −0.297602 0.515463i 0.677984 0.735076i \(-0.262854\pi\)
−0.975587 + 0.219614i \(0.929520\pi\)
\(468\) 0 0
\(469\) 413.003 715.341i 0.0406624 0.0704294i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 16466.8 + 13817.3i 1.60073 + 1.34317i
\(474\) 0 0
\(475\) −962.864 350.454i −0.0930089 0.0338525i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −529.337 3002.02i −0.0504928 0.286359i 0.949097 0.314982i \(-0.101999\pi\)
−0.999590 + 0.0286237i \(0.990888\pi\)
\(480\) 0 0
\(481\) 994.788 362.073i 0.0943003 0.0343225i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −17288.3 −1.61860
\(486\) 0 0
\(487\) −1795.38 −0.167056 −0.0835281 0.996505i \(-0.526619\pi\)
−0.0835281 + 0.996505i \(0.526619\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −11759.8 + 4280.20i −1.08088 + 0.393407i −0.820234 0.572028i \(-0.806157\pi\)
−0.260643 + 0.965435i \(0.583935\pi\)
\(492\) 0 0
\(493\) −150.277 852.262i −0.0137285 0.0778580i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −3368.59 1226.07i −0.304028 0.110657i
\(498\) 0 0
\(499\) −10407.7 8733.06i −0.933688 0.783458i 0.0427875 0.999084i \(-0.486376\pi\)
−0.976476 + 0.215627i \(0.930821\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −6402.30 + 11089.1i −0.567523 + 0.982979i 0.429287 + 0.903168i \(0.358765\pi\)
−0.996810 + 0.0798111i \(0.974568\pi\)
\(504\) 0 0
\(505\) 5725.62 + 9917.06i 0.504528 + 0.873868i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −14.7863 + 83.8573i −0.00128761 + 0.00730237i −0.985445 0.169996i \(-0.945625\pi\)
0.984157 + 0.177298i \(0.0567357\pi\)
\(510\) 0 0
\(511\) 2151.06 1804.95i 0.186218 0.156255i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −19456.5 + 16326.0i −1.66477 + 1.39691i
\(516\) 0 0
\(517\) −463.914 + 2630.99i −0.0394641 + 0.223812i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −8164.42 14141.2i −0.686545 1.18913i −0.972949 0.231021i \(-0.925793\pi\)
0.286404 0.958109i \(-0.407540\pi\)
\(522\) 0 0
\(523\) −5508.00 + 9540.13i −0.460512 + 0.797630i −0.998986 0.0450116i \(-0.985668\pi\)
0.538474 + 0.842642i \(0.319001\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1265.81 + 1062.14i 0.104629 + 0.0877940i
\(528\) 0 0
\(529\) −2799.22 1018.83i −0.230067 0.0837374i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −286.507 1624.86i −0.0232833 0.132046i
\(534\) 0 0
\(535\) 27401.3 9973.26i 2.21432 0.805947i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 14306.3 1.14326
\(540\) 0 0
\(541\) 8618.57 0.684919 0.342460 0.939533i \(-0.388740\pi\)
0.342460 + 0.939533i \(0.388740\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 10275.0 3739.78i 0.807580 0.293935i
\(546\) 0 0
\(547\) −118.470 671.876i −0.00926034 0.0525180i 0.979827 0.199845i \(-0.0640440\pi\)
−0.989088 + 0.147327i \(0.952933\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1972.18 717.815i −0.152482 0.0554990i
\(552\) 0 0
\(553\) 3366.54 + 2824.86i 0.258878 + 0.217225i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 706.450 1223.61i 0.0537401 0.0930806i −0.837904 0.545818i \(-0.816219\pi\)
0.891644 + 0.452737i \(0.149552\pi\)
\(558\) 0 0
\(559\) 1297.90 + 2248.02i 0.0982024 + 0.170092i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −3353.19 + 19016.9i −0.251013 + 1.42356i 0.555092 + 0.831789i \(0.312683\pi\)
−0.806104 + 0.591774i \(0.798428\pi\)
\(564\) 0 0
\(565\) −16855.4 + 14143.3i −1.25506 + 1.05312i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 10023.8 8410.99i 0.738525 0.619696i −0.193916 0.981018i \(-0.562119\pi\)
0.932441 + 0.361322i \(0.117675\pi\)
\(570\) 0 0
\(571\) 3569.22 20242.1i 0.261589 1.48354i −0.516987 0.855993i \(-0.672946\pi\)
0.778576 0.627551i \(-0.215943\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −4244.26 7351.28i −0.307823 0.533164i
\(576\) 0 0
\(577\) 1699.26 2943.21i 0.122602 0.212352i −0.798191 0.602404i \(-0.794210\pi\)
0.920793 + 0.390052i \(0.127543\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 2590.45 + 2173.65i 0.184974 + 0.155212i
\(582\) 0 0
\(583\) 15617.8 + 5684.41i 1.10947 + 0.403815i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −2010.20 11400.4i −0.141346 0.801612i −0.970229 0.242190i \(-0.922134\pi\)
0.828883 0.559422i \(-0.188977\pi\)
\(588\) 0 0
\(589\) 3765.63 1370.58i 0.263430 0.0958806i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 20424.8 1.41441 0.707205 0.707008i \(-0.249956\pi\)
0.707205 + 0.707008i \(0.249956\pi\)
\(594\) 0 0
\(595\) −338.756 −0.0233406
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 15491.8 5638.56i 1.05672 0.384616i 0.245528 0.969389i \(-0.421039\pi\)
0.811197 + 0.584773i \(0.198816\pi\)
\(600\) 0 0
\(601\) −3430.04 19452.7i −0.232803 1.32029i −0.847192 0.531286i \(-0.821709\pi\)
0.614390 0.789003i \(-0.289402\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 7595.15 + 2764.41i 0.510391 + 0.185767i
\(606\) 0 0
\(607\) −3232.28 2712.21i −0.216136 0.181359i 0.528291 0.849063i \(-0.322833\pi\)
−0.744427 + 0.667704i \(0.767277\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −161.307 + 279.391i −0.0106805 + 0.0184991i
\(612\) 0 0
\(613\) 5986.71 + 10369.3i 0.394455 + 0.683216i 0.993031 0.117850i \(-0.0376001\pi\)
−0.598577 + 0.801066i \(0.704267\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 766.653 4347.91i 0.0500232 0.283695i −0.949527 0.313685i \(-0.898436\pi\)
0.999550 + 0.0299897i \(0.00954746\pi\)
\(618\) 0 0
\(619\) 4277.74 3589.45i 0.277766 0.233073i −0.493252 0.869886i \(-0.664192\pi\)
0.771018 + 0.636813i \(0.219748\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1304.74 + 1094.81i −0.0839061 + 0.0704055i
\(624\) 0 0
\(625\) −3384.29 + 19193.3i −0.216594 + 1.22837i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −614.167 1063.77i −0.0389324 0.0674328i
\(630\) 0 0
\(631\) 6743.30 11679.7i 0.425431 0.736867i −0.571030 0.820929i \(-0.693456\pi\)
0.996461 + 0.0840619i \(0.0267893\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −4207.80 3530.77i −0.262963 0.220652i
\(636\) 0 0
\(637\) 1623.41 + 590.872i 0.100976 + 0.0367523i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1301.91 7383.47i −0.0802218 0.454960i −0.998286 0.0585281i \(-0.981359\pi\)
0.918064 0.396432i \(-0.129752\pi\)
\(642\) 0 0
\(643\) −18909.9 + 6882.64i −1.15977 + 0.422122i −0.849016 0.528367i \(-0.822804\pi\)
−0.310756 + 0.950490i \(0.600582\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 13603.1 0.826575 0.413288 0.910601i \(-0.364380\pi\)
0.413288 + 0.910601i \(0.364380\pi\)
\(648\) 0 0
\(649\) 7199.61 0.435454
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −21556.3 + 7845.87i −1.29183 + 0.470188i −0.894327 0.447413i \(-0.852345\pi\)
−0.397503 + 0.917601i \(0.630123\pi\)
\(654\) 0 0
\(655\) 1452.79 + 8239.19i 0.0866645 + 0.491499i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −15226.4 5541.95i −0.900054 0.327593i −0.149779 0.988719i \(-0.547856\pi\)
−0.750274 + 0.661127i \(0.770079\pi\)
\(660\) 0 0
\(661\) 8534.64 + 7161.41i 0.502207 + 0.421402i 0.858377 0.513019i \(-0.171473\pi\)
−0.356170 + 0.934421i \(0.615918\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −410.768 + 711.470i −0.0239532 + 0.0414882i
\(666\) 0 0
\(667\) −8693.28 15057.2i −0.504655 0.874089i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 6552.46 37160.9i 0.376982 2.13797i
\(672\) 0 0
\(673\) 972.493 816.019i 0.0557011 0.0467388i −0.614512 0.788907i \(-0.710647\pi\)
0.670213 + 0.742169i \(0.266203\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 15101.6 12671.8i 0.857315 0.719372i −0.104073 0.994570i \(-0.533188\pi\)
0.961388 + 0.275197i \(0.0887431\pi\)
\(678\) 0 0
\(679\) −855.875 + 4853.91i −0.0483733 + 0.274339i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −4391.39 7606.11i −0.246020 0.426120i 0.716398 0.697692i \(-0.245790\pi\)
−0.962418 + 0.271572i \(0.912456\pi\)
\(684\) 0 0
\(685\) −7954.48 + 13777.6i −0.443686 + 0.768487i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1537.46 + 1290.08i 0.0850108 + 0.0713325i
\(690\) 0 0
\(691\) 9374.91 + 3412.19i 0.516119 + 0.187852i 0.586930 0.809638i \(-0.300336\pi\)
−0.0708107 + 0.997490i \(0.522559\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 5009.27 + 28409.0i 0.273399 + 1.55053i
\(696\) 0 0
\(697\) −1798.97 + 654.770i −0.0977628 + 0.0355828i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 4822.63 0.259841 0.129920 0.991524i \(-0.458528\pi\)
0.129920 + 0.991524i \(0.458528\pi\)
\(702\) 0 0
\(703\) −2978.90 −0.159817
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3067.80 1116.59i 0.163192 0.0593969i
\(708\) 0 0
\(709\) 2404.44 + 13636.3i 0.127363 + 0.722314i 0.979876 + 0.199607i \(0.0639666\pi\)
−0.852513 + 0.522707i \(0.824922\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 31195.4 + 11354.2i 1.63854 + 0.596379i
\(714\) 0 0
\(715\) 2462.51 + 2066.29i 0.128801 + 0.108077i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 17247.7 29874.0i 0.894621 1.54953i 0.0603471 0.998177i \(-0.480779\pi\)
0.834273 0.551351i \(-0.185887\pi\)
\(720\) 0 0
\(721\) 3620.51 + 6270.91i 0.187011 + 0.323913i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1692.08 9596.29i 0.0866792 0.491582i
\(726\) 0 0
\(727\) 28116.6 23592.6i 1.43437 1.20358i 0.491295 0.870993i \(-0.336524\pi\)
0.943073 0.332585i \(-0.107921\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 2307.25 1936.02i 0.116740 0.0979564i
\(732\) 0 0
\(733\) −2455.96 + 13928.4i −0.123756 + 0.701854i 0.858283 + 0.513176i \(0.171531\pi\)
−0.982039 + 0.188678i \(0.939580\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4547.38 + 7876.28i 0.227279 + 0.393659i
\(738\) 0 0
\(739\) 17248.4 29875.1i 0.858583 1.48711i −0.0146980 0.999892i \(-0.504679\pi\)
0.873281 0.487217i \(-0.161988\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −29161.7 24469.5i −1.43989 1.20821i −0.939564 0.342373i \(-0.888769\pi\)
−0.500326 0.865837i \(-0.666786\pi\)
\(744\) 0 0
\(745\) −40721.2 14821.3i −2.00256 0.728874i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1443.59 8187.01i −0.0704241 0.399395i
\(750\) 0 0
\(751\) −4734.32 + 1723.15i −0.230037 + 0.0837266i −0.454467 0.890764i \(-0.650170\pi\)
0.224430 + 0.974490i \(0.427948\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −526.896 −0.0253983
\(756\) 0 0
\(757\) 39695.9 1.90591 0.952954 0.303115i \(-0.0980266\pi\)
0.952954 + 0.303115i \(0.0980266\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 6617.71 2408.65i 0.315233 0.114735i −0.179558 0.983747i \(-0.557467\pi\)
0.494791 + 0.869012i \(0.335245\pi\)
\(762\) 0 0
\(763\) −541.319 3069.97i −0.0256842 0.145662i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 816.977 + 297.355i 0.0384607 + 0.0139985i
\(768\) 0 0
\(769\) 30249.5 + 25382.4i 1.41850 + 1.19026i 0.952138 + 0.305669i \(0.0988802\pi\)
0.466362 + 0.884594i \(0.345564\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −15979.4 + 27677.1i −0.743516 + 1.28781i 0.207369 + 0.978263i \(0.433510\pi\)
−0.950885 + 0.309545i \(0.899823\pi\)
\(774\) 0 0
\(775\) 9302.79 + 16112.9i 0.431182 + 0.746829i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −806.206 + 4572.22i −0.0370800 + 0.210291i
\(780\) 0 0
\(781\) 30236.0 25371.0i 1.38531 1.16241i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −24639.6 + 20675.1i −1.12029 + 0.940033i
\(786\) 0 0
\(787\) 787.039 4463.52i 0.0356479 0.202169i −0.961782 0.273816i \(-0.911714\pi\)
0.997430 + 0.0716463i \(0.0228253\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 3136.48 +