Properties

Label 108.4.i.a.13.8
Level 108
Weight 4
Character 108.13
Analytic conductor 6.372
Analytic rank 0
Dimension 54
CM no
Inner twists 2

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 13.8
Character \(\chi\) \(=\) 108.13
Dual form 108.4.i.a.25.8

$q$-expansion

\(f(q)\) \(=\) \(q+(5.14478 + 0.728858i) q^{3} +(-5.18194 - 4.34817i) q^{5} +(16.8240 + 6.12342i) q^{7} +(25.9375 + 7.49962i) q^{9} +O(q^{10})\) \(q+(5.14478 + 0.728858i) q^{3} +(-5.18194 - 4.34817i) q^{5} +(16.8240 + 6.12342i) q^{7} +(25.9375 + 7.49962i) q^{9} +(45.5667 - 38.2350i) q^{11} +(-5.02544 + 28.5007i) q^{13} +(-23.4908 - 26.1473i) q^{15} +(-14.6698 + 25.4089i) q^{17} +(13.7884 + 23.8822i) q^{19} +(82.0925 + 43.7660i) q^{21} +(-0.946050 + 0.344334i) q^{23} +(-13.7600 - 78.0370i) q^{25} +(127.977 + 57.4887i) q^{27} +(-15.4827 - 87.8069i) q^{29} +(-11.6374 + 4.23566i) q^{31} +(262.299 - 163.499i) q^{33} +(-60.5552 - 104.885i) q^{35} +(-186.599 + 323.199i) q^{37} +(-46.6278 + 142.967i) q^{39} +(38.3921 - 217.733i) q^{41} +(-415.169 + 348.368i) q^{43} +(-101.797 - 151.643i) q^{45} +(-575.029 - 209.294i) q^{47} +(-17.2036 - 14.4355i) q^{49} +(-93.9924 + 120.031i) q^{51} -51.1253 q^{53} -402.376 q^{55} +(53.5316 + 132.919i) q^{57} +(-326.874 - 274.280i) q^{59} +(488.734 + 177.884i) q^{61} +(390.449 + 285.000i) q^{63} +(149.967 - 125.838i) q^{65} +(38.0132 - 215.584i) q^{67} +(-5.11819 + 1.08199i) q^{69} +(-99.9846 + 173.178i) q^{71} +(-398.711 - 690.588i) q^{73} +(-13.9145 - 411.513i) q^{75} +(1000.74 - 364.240i) q^{77} +(227.171 + 1288.35i) q^{79} +(616.511 + 389.044i) q^{81} +(-11.1689 - 63.3422i) q^{83} +(186.500 - 67.8805i) q^{85} +(-15.6565 - 463.032i) q^{87} +(466.341 + 807.726i) q^{89} +(-259.070 + 448.722i) q^{91} +(-62.9590 + 13.3096i) q^{93} +(32.3931 - 183.711i) q^{95} +(915.498 - 768.194i) q^{97} +(1468.64 - 649.989i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54q + 12q^{5} - 48q^{9} + O(q^{10}) \) \( 54q + 12q^{5} - 48q^{9} - 87q^{11} + 234q^{15} + 204q^{17} - 12q^{21} + 96q^{23} - 216q^{25} + 27q^{27} + 318q^{29} - 54q^{31} + 63q^{33} + 6q^{35} + 66q^{39} + 867q^{41} - 513q^{43} - 306q^{45} - 1548q^{47} + 594q^{49} - 1368q^{51} - 1068q^{53} - 1269q^{57} - 1218q^{59} - 54q^{61} + 30q^{63} + 96q^{65} - 2997q^{67} + 1476q^{69} - 120q^{71} - 216q^{73} + 732q^{75} + 3480q^{77} + 2808q^{79} + 3348q^{81} + 4464q^{83} + 2160q^{85} + 4824q^{87} + 4029q^{89} + 270q^{91} + 1164q^{93} - 1650q^{95} - 3483q^{97} - 5076q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 5.14478 + 0.728858i 0.990113 + 0.140269i
\(4\) 0 0
\(5\) −5.18194 4.34817i −0.463487 0.388912i 0.380925 0.924606i \(-0.375606\pi\)
−0.844412 + 0.535694i \(0.820050\pi\)
\(6\) 0 0
\(7\) 16.8240 + 6.12342i 0.908409 + 0.330634i 0.753617 0.657313i \(-0.228307\pi\)
0.154792 + 0.987947i \(0.450529\pi\)
\(8\) 0 0
\(9\) 25.9375 + 7.49962i 0.960649 + 0.277764i
\(10\) 0 0
\(11\) 45.5667 38.2350i 1.24899 1.04803i 0.252223 0.967669i \(-0.418838\pi\)
0.996766 0.0803571i \(-0.0256061\pi\)
\(12\) 0 0
\(13\) −5.02544 + 28.5007i −0.107216 + 0.608052i 0.883096 + 0.469192i \(0.155455\pi\)
−0.990312 + 0.138860i \(0.955656\pi\)
\(14\) 0 0
\(15\) −23.4908 26.1473i −0.404353 0.450080i
\(16\) 0 0
\(17\) −14.6698 + 25.4089i −0.209291 + 0.362503i −0.951491 0.307675i \(-0.900449\pi\)
0.742200 + 0.670178i \(0.233782\pi\)
\(18\) 0 0
\(19\) 13.7884 + 23.8822i 0.166488 + 0.288366i 0.937183 0.348839i \(-0.113424\pi\)
−0.770695 + 0.637205i \(0.780091\pi\)
\(20\) 0 0
\(21\) 82.0925 + 43.7660i 0.853050 + 0.454786i
\(22\) 0 0
\(23\) −0.946050 + 0.344334i −0.00857674 + 0.00312168i −0.346305 0.938122i \(-0.612564\pi\)
0.337728 + 0.941244i \(0.390342\pi\)
\(24\) 0 0
\(25\) −13.7600 78.0370i −0.110080 0.624296i
\(26\) 0 0
\(27\) 127.977 + 57.4887i 0.912190 + 0.409767i
\(28\) 0 0
\(29\) −15.4827 87.8069i −0.0991404 0.562253i −0.993400 0.114704i \(-0.963408\pi\)
0.894259 0.447549i \(-0.147703\pi\)
\(30\) 0 0
\(31\) −11.6374 + 4.23566i −0.0674238 + 0.0245402i −0.375512 0.926818i \(-0.622533\pi\)
0.308088 + 0.951358i \(0.400311\pi\)
\(32\) 0 0
\(33\) 262.299 163.499i 1.38365 0.862471i
\(34\) 0 0
\(35\) −60.5552 104.885i −0.292448 0.506536i
\(36\) 0 0
\(37\) −186.599 + 323.199i −0.829100 + 1.43604i 0.0696442 + 0.997572i \(0.477814\pi\)
−0.898745 + 0.438472i \(0.855520\pi\)
\(38\) 0 0
\(39\) −46.6278 + 142.967i −0.191447 + 0.587001i
\(40\) 0 0
\(41\) 38.3921 217.733i 0.146240 0.829369i −0.820123 0.572187i \(-0.806095\pi\)
0.966363 0.257182i \(-0.0827939\pi\)
\(42\) 0 0
\(43\) −415.169 + 348.368i −1.47239 + 1.23548i −0.558505 + 0.829501i \(0.688625\pi\)
−0.913882 + 0.405979i \(0.866931\pi\)
\(44\) 0 0
\(45\) −101.797 151.643i −0.337223 0.502348i
\(46\) 0 0
\(47\) −575.029 209.294i −1.78461 0.649545i −0.999546 0.0301286i \(-0.990408\pi\)
−0.785063 0.619416i \(-0.787369\pi\)
\(48\) 0 0
\(49\) −17.2036 14.4355i −0.0501562 0.0420861i
\(50\) 0 0
\(51\) −93.9924 + 120.031i −0.258070 + 0.329562i
\(52\) 0 0
\(53\) −51.1253 −0.132502 −0.0662509 0.997803i \(-0.521104\pi\)
−0.0662509 + 0.997803i \(0.521104\pi\)
\(54\) 0 0
\(55\) −402.376 −0.986480
\(56\) 0 0
\(57\) 53.5316 + 132.919i 0.124394 + 0.308868i
\(58\) 0 0
\(59\) −326.874 274.280i −0.721278 0.605224i 0.206460 0.978455i \(-0.433806\pi\)
−0.927739 + 0.373231i \(0.878250\pi\)
\(60\) 0 0
\(61\) 488.734 + 177.884i 1.02583 + 0.373373i 0.799493 0.600675i \(-0.205101\pi\)
0.226341 + 0.974048i \(0.427324\pi\)
\(62\) 0 0
\(63\) 390.449 + 285.000i 0.780824 + 0.569946i
\(64\) 0 0
\(65\) 149.967 125.838i 0.286172 0.240127i
\(66\) 0 0
\(67\) 38.0132 215.584i 0.0693143 0.393101i −0.930337 0.366705i \(-0.880486\pi\)
0.999652 0.0263958i \(-0.00840303\pi\)
\(68\) 0 0
\(69\) −5.11819 + 1.08199i −0.00892982 + 0.00188777i
\(70\) 0 0
\(71\) −99.9846 + 173.178i −0.167127 + 0.289472i −0.937408 0.348232i \(-0.886782\pi\)
0.770282 + 0.637704i \(0.220116\pi\)
\(72\) 0 0
\(73\) −398.711 690.588i −0.639255 1.10722i −0.985597 0.169113i \(-0.945910\pi\)
0.346342 0.938108i \(-0.387424\pi\)
\(74\) 0 0
\(75\) −13.9145 411.513i −0.0214227 0.633565i
\(76\) 0 0
\(77\) 1000.74 364.240i 1.48111 0.539078i
\(78\) 0 0
\(79\) 227.171 + 1288.35i 0.323529 + 1.83482i 0.519819 + 0.854277i \(0.326000\pi\)
−0.196290 + 0.980546i \(0.562889\pi\)
\(80\) 0 0
\(81\) 616.511 + 389.044i 0.845694 + 0.533667i
\(82\) 0 0
\(83\) −11.1689 63.3422i −0.0147705 0.0837675i 0.976531 0.215375i \(-0.0690973\pi\)
−0.991302 + 0.131607i \(0.957986\pi\)
\(84\) 0 0
\(85\) 186.500 67.8805i 0.237986 0.0866197i
\(86\) 0 0
\(87\) −15.6565 463.032i −0.0192937 0.570601i
\(88\) 0 0
\(89\) 466.341 + 807.726i 0.555416 + 0.962009i 0.997871 + 0.0652184i \(0.0207744\pi\)
−0.442455 + 0.896791i \(0.645892\pi\)
\(90\) 0 0
\(91\) −259.070 + 448.722i −0.298439 + 0.516911i
\(92\) 0 0
\(93\) −62.9590 + 13.3096i −0.0701994 + 0.0148402i
\(94\) 0 0
\(95\) 32.3931 183.711i 0.0349839 0.198403i
\(96\) 0 0
\(97\) 915.498 768.194i 0.958296 0.804106i −0.0223792 0.999750i \(-0.507124\pi\)
0.980675 + 0.195644i \(0.0626797\pi\)
\(98\) 0 0
\(99\) 1468.64 649.989i 1.49094 0.659862i
\(100\) 0 0
\(101\) −934.108 339.987i −0.920269 0.334951i −0.161924 0.986803i \(-0.551770\pi\)
−0.758346 + 0.651853i \(0.773992\pi\)
\(102\) 0 0
\(103\) −252.152 211.581i −0.241216 0.202405i 0.514163 0.857693i \(-0.328103\pi\)
−0.755379 + 0.655288i \(0.772547\pi\)
\(104\) 0 0
\(105\) −235.097 583.745i −0.218506 0.542549i
\(106\) 0 0
\(107\) −321.330 −0.290319 −0.145159 0.989408i \(-0.546369\pi\)
−0.145159 + 0.989408i \(0.546369\pi\)
\(108\) 0 0
\(109\) 379.701 0.333658 0.166829 0.985986i \(-0.446647\pi\)
0.166829 + 0.985986i \(0.446647\pi\)
\(110\) 0 0
\(111\) −1195.58 + 1526.79i −1.02234 + 1.30555i
\(112\) 0 0
\(113\) 1463.88 + 1228.34i 1.21867 + 1.02259i 0.998893 + 0.0470391i \(0.0149785\pi\)
0.219780 + 0.975549i \(0.429466\pi\)
\(114\) 0 0
\(115\) 6.39960 + 2.32926i 0.00518927 + 0.00188874i
\(116\) 0 0
\(117\) −344.092 + 701.549i −0.271892 + 0.554344i
\(118\) 0 0
\(119\) −402.394 + 337.648i −0.309978 + 0.260102i
\(120\) 0 0
\(121\) 383.283 2173.71i 0.287966 1.63314i
\(122\) 0 0
\(123\) 356.215 1092.20i 0.261129 0.800657i
\(124\) 0 0
\(125\) −690.799 + 1196.50i −0.494295 + 0.856145i
\(126\) 0 0
\(127\) −84.0772 145.626i −0.0587453 0.101750i 0.835157 0.550011i \(-0.185377\pi\)
−0.893902 + 0.448262i \(0.852043\pi\)
\(128\) 0 0
\(129\) −2389.86 + 1489.68i −1.63113 + 1.01674i
\(130\) 0 0
\(131\) 1884.63 685.949i 1.25695 0.457493i 0.374207 0.927345i \(-0.377915\pi\)
0.882745 + 0.469852i \(0.155693\pi\)
\(132\) 0 0
\(133\) 85.7348 + 486.226i 0.0558958 + 0.317001i
\(134\) 0 0
\(135\) −413.198 854.368i −0.263425 0.544683i
\(136\) 0 0
\(137\) −160.622 910.931i −0.100167 0.568073i −0.993041 0.117768i \(-0.962426\pi\)
0.892874 0.450306i \(-0.148685\pi\)
\(138\) 0 0
\(139\) 2389.86 869.838i 1.45831 0.530782i 0.513412 0.858142i \(-0.328381\pi\)
0.944900 + 0.327360i \(0.106159\pi\)
\(140\) 0 0
\(141\) −2805.85 1495.88i −1.67585 0.893448i
\(142\) 0 0
\(143\) 860.732 + 1490.83i 0.503343 + 0.871815i
\(144\) 0 0
\(145\) −301.569 + 522.332i −0.172717 + 0.299154i
\(146\) 0 0
\(147\) −77.9873 86.8066i −0.0437570 0.0487054i
\(148\) 0 0
\(149\) −353.990 + 2007.58i −0.194631 + 1.10381i 0.718313 + 0.695720i \(0.244915\pi\)
−0.912943 + 0.408086i \(0.866196\pi\)
\(150\) 0 0
\(151\) 631.192 529.633i 0.340170 0.285437i −0.456658 0.889642i \(-0.650954\pi\)
0.796829 + 0.604205i \(0.206509\pi\)
\(152\) 0 0
\(153\) −571.056 + 549.025i −0.301746 + 0.290105i
\(154\) 0 0
\(155\) 78.7217 + 28.6523i 0.0407940 + 0.0148478i
\(156\) 0 0
\(157\) −721.515 605.423i −0.366772 0.307758i 0.440711 0.897649i \(-0.354726\pi\)
−0.807483 + 0.589891i \(0.799171\pi\)
\(158\) 0 0
\(159\) −263.028 37.2631i −0.131192 0.0185859i
\(160\) 0 0
\(161\) −18.0248 −0.00882332
\(162\) 0 0
\(163\) −3395.63 −1.63169 −0.815847 0.578267i \(-0.803729\pi\)
−0.815847 + 0.578267i \(0.803729\pi\)
\(164\) 0 0
\(165\) −2070.14 293.275i −0.976728 0.138372i
\(166\) 0 0
\(167\) −2218.43 1861.48i −1.02795 0.862550i −0.0373420 0.999303i \(-0.511889\pi\)
−0.990605 + 0.136752i \(0.956334\pi\)
\(168\) 0 0
\(169\) 1277.47 + 464.961i 0.581461 + 0.211634i
\(170\) 0 0
\(171\) 178.530 + 722.854i 0.0798392 + 0.323263i
\(172\) 0 0
\(173\) −1595.10 + 1338.45i −0.701002 + 0.588211i −0.922059 0.387050i \(-0.873494\pi\)
0.221056 + 0.975261i \(0.429050\pi\)
\(174\) 0 0
\(175\) 246.355 1397.15i 0.106416 0.603513i
\(176\) 0 0
\(177\) −1481.79 1649.36i −0.629253 0.700414i
\(178\) 0 0
\(179\) −2179.06 + 3774.24i −0.909890 + 1.57598i −0.0956752 + 0.995413i \(0.530501\pi\)
−0.814215 + 0.580563i \(0.802832\pi\)
\(180\) 0 0
\(181\) −1347.22 2333.45i −0.553248 0.958254i −0.998038 0.0626187i \(-0.980055\pi\)
0.444789 0.895635i \(-0.353279\pi\)
\(182\) 0 0
\(183\) 2384.77 + 1271.39i 0.963320 + 0.513574i
\(184\) 0 0
\(185\) 2372.27 863.436i 0.942772 0.343141i
\(186\) 0 0
\(187\) 303.053 + 1718.70i 0.118510 + 0.672105i
\(188\) 0 0
\(189\) 1801.05 + 1750.84i 0.693159 + 0.673837i
\(190\) 0 0
\(191\) −523.862 2970.97i −0.198457 1.12551i −0.907408 0.420250i \(-0.861942\pi\)
0.708951 0.705258i \(-0.249169\pi\)
\(192\) 0 0
\(193\) 1388.37 505.325i 0.517808 0.188467i −0.0698784 0.997556i \(-0.522261\pi\)
0.587686 + 0.809089i \(0.300039\pi\)
\(194\) 0 0
\(195\) 863.267 538.102i 0.317025 0.197612i
\(196\) 0 0
\(197\) 1889.39 + 3272.53i 0.683318 + 1.18354i 0.973962 + 0.226711i \(0.0727973\pi\)
−0.290644 + 0.956831i \(0.593869\pi\)
\(198\) 0 0
\(199\) 160.647 278.248i 0.0572258 0.0991180i −0.835993 0.548740i \(-0.815108\pi\)
0.893219 + 0.449622i \(0.148441\pi\)
\(200\) 0 0
\(201\) 352.700 1081.43i 0.123769 0.379492i
\(202\) 0 0
\(203\) 277.198 1572.07i 0.0958399 0.543535i
\(204\) 0 0
\(205\) −1145.68 + 961.343i −0.390332 + 0.327527i
\(206\) 0 0
\(207\) −27.1206 + 1.83616i −0.00910633 + 0.000616530i
\(208\) 0 0
\(209\) 1541.43 + 561.034i 0.510157 + 0.185682i
\(210\) 0 0
\(211\) 973.780 + 817.098i 0.317714 + 0.266594i 0.787672 0.616095i \(-0.211286\pi\)
−0.469957 + 0.882689i \(0.655731\pi\)
\(212\) 0 0
\(213\) −640.621 + 818.090i −0.206078 + 0.263167i
\(214\) 0 0
\(215\) 3666.15 1.16293
\(216\) 0 0
\(217\) −221.724 −0.0693622
\(218\) 0 0
\(219\) −1547.94 3843.53i −0.477626 1.18594i
\(220\) 0 0
\(221\) −650.448 545.791i −0.197981 0.166126i
\(222\) 0 0
\(223\) 4698.03 + 1709.94i 1.41078 + 0.513481i 0.931358 0.364104i \(-0.118625\pi\)
0.479420 + 0.877585i \(0.340847\pi\)
\(224\) 0 0
\(225\) 228.347 2127.28i 0.0676584 0.630306i
\(226\) 0 0
\(227\) −907.775 + 761.713i −0.265423 + 0.222717i −0.765780 0.643103i \(-0.777647\pi\)
0.500356 + 0.865820i \(0.333202\pi\)
\(228\) 0 0
\(229\) 321.039 1820.70i 0.0926412 0.525394i −0.902803 0.430053i \(-0.858495\pi\)
0.995445 0.0953410i \(-0.0303941\pi\)
\(230\) 0 0
\(231\) 5414.08 1144.54i 1.54208 0.325996i
\(232\) 0 0
\(233\) 1585.36 2745.93i 0.445754 0.772068i −0.552351 0.833612i \(-0.686269\pi\)
0.998104 + 0.0615437i \(0.0196024\pi\)
\(234\) 0 0
\(235\) 2069.73 + 3584.87i 0.574528 + 0.995111i
\(236\) 0 0
\(237\) 229.721 + 6793.87i 0.0629620 + 1.86206i
\(238\) 0 0
\(239\) 5573.01 2028.41i 1.50832 0.548983i 0.550119 0.835086i \(-0.314582\pi\)
0.958199 + 0.286104i \(0.0923602\pi\)
\(240\) 0 0
\(241\) −517.453 2934.62i −0.138307 0.784380i −0.972499 0.232906i \(-0.925177\pi\)
0.834192 0.551474i \(-0.185935\pi\)
\(242\) 0 0
\(243\) 2888.26 + 2450.89i 0.762477 + 0.647016i
\(244\) 0 0
\(245\) 26.3800 + 149.608i 0.00687900 + 0.0390127i
\(246\) 0 0
\(247\) −749.953 + 272.961i −0.193192 + 0.0703161i
\(248\) 0 0
\(249\) −11.2943 334.022i −0.00287448 0.0850112i
\(250\) 0 0
\(251\) −3456.30 5986.49i −0.869162 1.50543i −0.862854 0.505453i \(-0.831326\pi\)
−0.00630772 0.999980i \(-0.502008\pi\)
\(252\) 0 0
\(253\) −29.9428 + 51.8624i −0.00744066 + 0.0128876i
\(254\) 0 0
\(255\) 1008.98 213.298i 0.247783 0.0523814i
\(256\) 0 0
\(257\) −882.257 + 5003.53i −0.214139 + 1.21444i 0.668256 + 0.743931i \(0.267041\pi\)
−0.882395 + 0.470510i \(0.844070\pi\)
\(258\) 0 0
\(259\) −5118.43 + 4294.87i −1.22797 + 1.03039i
\(260\) 0 0
\(261\) 256.935 2393.61i 0.0609344 0.567666i
\(262\) 0 0
\(263\) −7196.97 2619.48i −1.68739 0.614160i −0.693099 0.720843i \(-0.743755\pi\)
−0.994293 + 0.106682i \(0.965977\pi\)
\(264\) 0 0
\(265\) 264.928 + 222.301i 0.0614129 + 0.0515316i
\(266\) 0 0
\(267\) 1810.50 + 4495.47i 0.414985 + 1.03041i
\(268\) 0 0
\(269\) −6884.46 −1.56042 −0.780210 0.625518i \(-0.784888\pi\)
−0.780210 + 0.625518i \(0.784888\pi\)
\(270\) 0 0
\(271\) −3232.55 −0.724588 −0.362294 0.932064i \(-0.618006\pi\)
−0.362294 + 0.932064i \(0.618006\pi\)
\(272\) 0 0
\(273\) −1659.91 + 2119.75i −0.367994 + 0.469939i
\(274\) 0 0
\(275\) −3610.75 3029.78i −0.791768 0.664372i
\(276\) 0 0
\(277\) −2971.80 1081.65i −0.644615 0.234621i −0.00103476 0.999999i \(-0.500329\pi\)
−0.643580 + 0.765379i \(0.722552\pi\)
\(278\) 0 0
\(279\) −333.611 + 22.5866i −0.0715870 + 0.00484668i
\(280\) 0 0
\(281\) 3251.44 2728.28i 0.690266 0.579202i −0.228720 0.973492i \(-0.573454\pi\)
0.918986 + 0.394290i \(0.129009\pi\)
\(282\) 0 0
\(283\) −927.955 + 5262.69i −0.194916 + 1.10542i 0.717623 + 0.696432i \(0.245230\pi\)
−0.912538 + 0.408991i \(0.865881\pi\)
\(284\) 0 0
\(285\) 300.555 921.541i 0.0624678 0.191535i
\(286\) 0 0
\(287\) 1979.18 3428.04i 0.407063 0.705054i
\(288\) 0 0
\(289\) 2026.09 + 3509.30i 0.412394 + 0.714288i
\(290\) 0 0
\(291\) 5269.94 3284.92i 1.06161 0.661737i
\(292\) 0 0
\(293\) 2133.39 776.490i 0.425372 0.154823i −0.120459 0.992718i \(-0.538437\pi\)
0.545830 + 0.837896i \(0.316214\pi\)
\(294\) 0 0
\(295\) 501.229 + 2842.61i 0.0989243 + 0.561028i
\(296\) 0 0
\(297\) 8029.56 2273.62i 1.56876 0.444205i
\(298\) 0 0
\(299\) −5.05944 28.6935i −0.000978579 0.00554980i
\(300\) 0 0
\(301\) −9118.00 + 3318.68i −1.74602 + 0.635500i
\(302\) 0 0
\(303\) −4557.98 2429.99i −0.864188 0.460724i
\(304\) 0 0
\(305\) −1759.12 3046.88i −0.330252 0.572013i
\(306\) 0 0
\(307\) −324.386 + 561.853i −0.0603052 + 0.104452i −0.894602 0.446864i \(-0.852541\pi\)
0.834297 + 0.551316i \(0.185874\pi\)
\(308\) 0 0
\(309\) −1143.05 1272.32i −0.210440 0.234239i
\(310\) 0 0
\(311\) −990.109 + 5615.19i −0.180527 + 1.02382i 0.751042 + 0.660255i \(0.229552\pi\)
−0.931569 + 0.363565i \(0.881559\pi\)
\(312\) 0 0
\(313\) 3737.23 3135.91i 0.674890 0.566300i −0.239618 0.970867i \(-0.577022\pi\)
0.914508 + 0.404567i \(0.132578\pi\)
\(314\) 0 0
\(315\) −784.057 3174.59i −0.140243 0.567835i
\(316\) 0 0
\(317\) 6695.08 + 2436.81i 1.18623 + 0.431751i 0.858397 0.512987i \(-0.171461\pi\)
0.327829 + 0.944737i \(0.393683\pi\)
\(318\) 0 0
\(319\) −4062.80 3409.09i −0.713081 0.598346i
\(320\) 0 0
\(321\) −1653.17 234.203i −0.287448 0.0407226i
\(322\) 0 0
\(323\) −809.093 −0.139378
\(324\) 0 0
\(325\) 2293.26 0.391407
\(326\) 0 0
\(327\) 1953.48 + 276.748i 0.330359 + 0.0468018i
\(328\) 0 0
\(329\) −8392.68 7042.30i −1.40639 1.18010i
\(330\) 0 0
\(331\) −4873.32 1773.74i −0.809250 0.294543i −0.0959363 0.995387i \(-0.530584\pi\)
−0.713314 + 0.700844i \(0.752807\pi\)
\(332\) 0 0
\(333\) −7263.80 + 6983.57i −1.19536 + 1.14924i
\(334\) 0 0
\(335\) −1134.38 + 951.855i −0.185008 + 0.155240i
\(336\) 0 0
\(337\) −1266.75 + 7184.10i −0.204760 + 1.16125i 0.693056 + 0.720884i \(0.256264\pi\)
−0.897816 + 0.440370i \(0.854847\pi\)
\(338\) 0 0
\(339\) 6636.05 + 7386.50i 1.06319 + 1.18342i
\(340\) 0 0
\(341\) −368.327 + 637.961i −0.0584927 + 0.101312i
\(342\) 0 0
\(343\) −3271.52 5666.44i −0.515002 0.892009i
\(344\) 0 0
\(345\) 31.2268 + 16.6480i 0.00487303 + 0.00259796i
\(346\) 0 0
\(347\) −3010.74 + 1095.82i −0.465777 + 0.169529i −0.564239 0.825612i \(-0.690830\pi\)
0.0984612 + 0.995141i \(0.468608\pi\)
\(348\) 0 0
\(349\) −322.003 1826.17i −0.0493881 0.280094i 0.950105 0.311930i \(-0.100976\pi\)
−0.999493 + 0.0318364i \(0.989864\pi\)
\(350\) 0 0
\(351\) −2281.61 + 3358.52i −0.346961 + 0.510726i
\(352\) 0 0
\(353\) 57.4469 + 325.798i 0.00866173 + 0.0491231i 0.988832 0.149033i \(-0.0476159\pi\)
−0.980171 + 0.198156i \(0.936505\pi\)
\(354\) 0 0
\(355\) 1271.12 462.651i 0.190040 0.0691689i
\(356\) 0 0
\(357\) −2316.32 + 1443.84i −0.343397 + 0.214051i
\(358\) 0 0
\(359\) 2668.13 + 4621.33i 0.392251 + 0.679399i 0.992746 0.120229i \(-0.0383630\pi\)
−0.600495 + 0.799629i \(0.705030\pi\)
\(360\) 0 0
\(361\) 3049.26 5281.47i 0.444563 0.770006i
\(362\) 0 0
\(363\) 3556.23 10903.9i 0.514198 1.57660i
\(364\) 0 0
\(365\) −936.693 + 5312.25i −0.134325 + 0.761797i
\(366\) 0 0
\(367\) 1992.63 1672.02i 0.283418 0.237816i −0.489984 0.871731i \(-0.662998\pi\)
0.773403 + 0.633915i \(0.218553\pi\)
\(368\) 0 0
\(369\) 2628.71 5359.52i 0.370854 0.756113i
\(370\) 0 0
\(371\) −860.130 313.062i −0.120366 0.0438096i
\(372\) 0 0
\(373\) 4976.72 + 4175.97i 0.690844 + 0.579687i 0.919153 0.393902i \(-0.128875\pi\)
−0.228308 + 0.973589i \(0.573319\pi\)
\(374\) 0 0
\(375\) −4426.08 + 5652.23i −0.609499 + 0.778346i
\(376\) 0 0
\(377\) 2580.37 0.352508
\(378\) 0 0
\(379\) 5410.32 0.733271 0.366635 0.930365i \(-0.380510\pi\)
0.366635 + 0.930365i \(0.380510\pi\)
\(380\) 0 0
\(381\) −326.418 810.494i −0.0438922 0.108984i
\(382\) 0 0
\(383\) −6463.74 5423.72i −0.862354 0.723601i 0.100120 0.994975i \(-0.468077\pi\)
−0.962474 + 0.271374i \(0.912522\pi\)
\(384\) 0 0
\(385\) −6769.57 2463.92i −0.896128 0.326164i
\(386\) 0 0
\(387\) −13381.1 + 5922.20i −1.75762 + 0.777887i
\(388\) 0 0
\(389\) 8970.57 7527.21i 1.16922 0.981091i 0.169229 0.985577i \(-0.445872\pi\)
0.999990 + 0.00448556i \(0.00142780\pi\)
\(390\) 0 0
\(391\) 5.12924 29.0894i 0.000663419 0.00376244i
\(392\) 0 0
\(393\) 10196.0 2155.43i 1.30870 0.276659i
\(394\) 0 0
\(395\) 4424.78 7663.95i 0.563633 0.976241i
\(396\) 0 0
\(397\) 6759.21 + 11707.3i 0.854496 + 1.48003i 0.877112 + 0.480286i \(0.159467\pi\)
−0.0226159 + 0.999744i \(0.507199\pi\)
\(398\) 0 0
\(399\) 86.6970 + 2564.01i 0.0108779 + 0.321707i
\(400\) 0 0
\(401\) 6064.01 2207.12i 0.755168 0.274859i 0.0643893 0.997925i \(-0.479490\pi\)
0.690779 + 0.723066i \(0.257268\pi\)
\(402\) 0 0
\(403\) −62.2364 352.960i −0.00769284 0.0436283i
\(404\) 0 0
\(405\) −1503.10 4696.70i −0.184419 0.576249i
\(406\) 0 0
\(407\) 3854.82 + 21861.7i 0.469475 + 2.66252i
\(408\) 0 0
\(409\) 5073.67 1846.66i 0.613390 0.223256i −0.0165958 0.999862i \(-0.505283\pi\)
0.629986 + 0.776606i \(0.283061\pi\)
\(410\) 0 0
\(411\) −162.424 4803.61i −0.0194934 0.576507i
\(412\) 0 0
\(413\) −3819.79 6616.07i −0.455108 0.788270i
\(414\) 0 0
\(415\) −217.546 + 376.800i −0.0257323 + 0.0445696i
\(416\) 0 0
\(417\) 12929.3 2733.26i 1.51835 0.320979i
\(418\) 0 0
\(419\) −1598.37 + 9064.78i −0.186361 + 1.05691i 0.737833 + 0.674983i \(0.235849\pi\)
−0.924194 + 0.381923i \(0.875262\pi\)
\(420\) 0 0
\(421\) 6648.55 5578.80i 0.769669 0.645829i −0.170955 0.985279i \(-0.554685\pi\)
0.940624 + 0.339450i \(0.110241\pi\)
\(422\) 0 0
\(423\) −13345.2 9741.06i −1.53396 1.11968i
\(424\) 0 0
\(425\) 2184.69 + 795.162i 0.249348 + 0.0907553i
\(426\) 0 0
\(427\) 7133.18 + 5985.45i 0.808428 + 0.678351i
\(428\) 0 0
\(429\) 3341.67 + 8297.35i 0.376078 + 0.933799i
\(430\) 0 0
\(431\) 13477.8 1.50628 0.753138 0.657862i \(-0.228539\pi\)
0.753138 + 0.657862i \(0.228539\pi\)
\(432\) 0 0
\(433\) 12659.9 1.40507 0.702533 0.711651i \(-0.252052\pi\)
0.702533 + 0.711651i \(0.252052\pi\)
\(434\) 0 0
\(435\) −1932.21 + 2467.48i −0.212971 + 0.271970i
\(436\) 0 0
\(437\) −21.2680 17.8460i −0.00232811 0.00195352i
\(438\) 0 0
\(439\) −8751.79 3185.39i −0.951480 0.346311i −0.180791 0.983522i \(-0.557866\pi\)
−0.770689 + 0.637211i \(0.780088\pi\)
\(440\) 0 0
\(441\) −337.958 503.442i −0.0364926 0.0543616i
\(442\) 0 0
\(443\) −3512.25 + 2947.12i −0.376686 + 0.316077i −0.811400 0.584492i \(-0.801294\pi\)
0.434714 + 0.900569i \(0.356850\pi\)
\(444\) 0 0
\(445\) 1095.58 6213.32i 0.116709 0.661887i
\(446\) 0 0
\(447\) −3284.44 + 10070.5i −0.347536 + 1.06559i
\(448\) 0 0
\(449\) 530.524 918.895i 0.0557616 0.0965820i −0.836797 0.547513i \(-0.815575\pi\)
0.892559 + 0.450931i \(0.148908\pi\)
\(450\) 0 0
\(451\) −6575.61 11389.3i −0.686548 1.18914i
\(452\) 0 0
\(453\) 3633.37 2264.80i 0.376845 0.234899i
\(454\) 0 0
\(455\) 3293.61 1198.77i 0.339355 0.123515i
\(456\) 0 0
\(457\) −2136.23 12115.2i −0.218662 1.24009i −0.874437 0.485139i \(-0.838769\pi\)
0.655775 0.754956i \(-0.272342\pi\)
\(458\) 0 0
\(459\) −3338.12 + 2408.39i −0.339455 + 0.244911i
\(460\) 0 0
\(461\) −30.2863 171.762i −0.00305981 0.0173531i 0.983240 0.182318i \(-0.0583600\pi\)
−0.986299 + 0.164965i \(0.947249\pi\)
\(462\) 0 0
\(463\) 8366.64 3045.21i 0.839808 0.305665i 0.113930 0.993489i \(-0.463656\pi\)
0.725878 + 0.687824i \(0.241434\pi\)
\(464\) 0 0
\(465\) 384.122 + 204.787i 0.0383080 + 0.0204232i
\(466\) 0 0
\(467\) 1326.26 + 2297.15i 0.131418 + 0.227622i 0.924223 0.381853i \(-0.124714\pi\)
−0.792806 + 0.609475i \(0.791380\pi\)
\(468\) 0 0
\(469\) 1959.64 3394.20i 0.192938 0.334179i
\(470\) 0 0
\(471\) −3270.77 3640.65i −0.319977 0.356162i
\(472\) 0 0
\(473\) −5598.02 + 31748.0i −0.544181 + 3.08620i
\(474\) 0 0
\(475\) 1673.97 1404.63i 0.161699 0.135681i
\(476\) 0 0
\(477\) −1326.06 383.420i −0.127288 0.0368042i
\(478\) 0 0
\(479\) 18164.9 + 6611.48i 1.73272 + 0.630660i 0.998819 0.0485928i \(-0.0154736\pi\)
0.733905 + 0.679252i \(0.237696\pi\)
\(480\) 0 0
\(481\) −8273.67 6942.43i −0.784297 0.658103i
\(482\) 0 0
\(483\) −92.7337 13.1375i −0.00873609 0.00123764i
\(484\) 0 0
\(485\) −8084.29 −0.756884
\(486\) 0 0
\(487\) 6386.49 0.594249 0.297125 0.954839i \(-0.403972\pi\)
0.297125 + 0.954839i \(0.403972\pi\)
\(488\) 0 0
\(489\) −17469.8 2474.93i −1.61556 0.228876i
\(490\) 0 0
\(491\) −13082.9 10977.9i −1.20249 1.00901i −0.999555 0.0298176i \(-0.990507\pi\)
−0.202936 0.979192i \(-0.565048\pi\)
\(492\) 0 0
\(493\) 2458.20 + 894.712i 0.224568 + 0.0817359i
\(494\) 0 0
\(495\) −10436.7 3017.67i −0.947662 0.274009i
\(496\) 0 0
\(497\) −2742.58 + 2301.30i −0.247528 + 0.207701i
\(498\) 0 0
\(499\) −1145.21 + 6494.83i −0.102739 + 0.582662i 0.889360 + 0.457207i \(0.151150\pi\)
−0.992099 + 0.125455i \(0.959961\pi\)
\(500\) 0 0
\(501\) −10056.6 11193.8i −0.896796 0.998211i
\(502\) 0 0
\(503\) −3417.70 + 5919.63i −0.302958 + 0.524738i −0.976805 0.214133i \(-0.931307\pi\)
0.673847 + 0.738871i \(0.264641\pi\)
\(504\) 0 0
\(505\) 3362.17 + 5823.45i 0.296267 + 0.513149i
\(506\) 0 0
\(507\) 6233.41 + 3323.21i 0.546026 + 0.291103i
\(508\) 0 0
\(509\) −435.292 + 158.433i −0.0379056 + 0.0137965i −0.360903 0.932603i \(-0.617532\pi\)
0.322998 + 0.946400i \(0.395309\pi\)
\(510\) 0 0
\(511\) −2479.14 14059.9i −0.214620 1.21717i
\(512\) 0 0
\(513\) 391.638 + 3849.05i 0.0337061 + 0.331266i
\(514\) 0 0
\(515\) 386.650 + 2192.80i 0.0330831 + 0.187624i
\(516\) 0 0
\(517\) −34204.5 + 12449.4i −2.90970 + 1.05904i
\(518\) 0 0
\(519\) −9181.99 + 5723.43i −0.776579 + 0.484067i
\(520\) 0 0
\(521\) −5085.58 8808.49i −0.427646 0.740704i 0.569018 0.822325i \(-0.307324\pi\)
−0.996663 + 0.0816212i \(0.973990\pi\)
\(522\) 0 0
\(523\) 4957.61 8586.84i 0.414496 0.717928i −0.580879 0.813990i \(-0.697291\pi\)
0.995375 + 0.0960616i \(0.0306246\pi\)
\(524\) 0 0
\(525\) 2285.77 7008.48i 0.190017 0.582619i
\(526\) 0 0
\(527\) 63.0949 357.829i 0.00521529 0.0295774i
\(528\) 0 0
\(529\) −9319.69 + 7820.15i −0.765981 + 0.642734i
\(530\) 0 0
\(531\) −6421.32 9565.59i −0.524786 0.781754i
\(532\) 0 0
\(533\) 6012.60 + 2188.41i 0.488620 + 0.177843i
\(534\) 0 0
\(535\) 1665.11 + 1397.19i 0.134559 + 0.112908i
\(536\) 0 0
\(537\) −13961.6 + 17829.4i −1.12195 + 1.43277i
\(538\) 0 0
\(539\) −1335.85 −0.106752
\(540\) 0 0
\(541\) 12272.1 0.975264 0.487632 0.873049i \(-0.337861\pi\)
0.487632 + 0.873049i \(0.337861\pi\)
\(542\) 0 0
\(543\) −5230.39 12987.0i −0.413365 1.02638i
\(544\) 0 0
\(545\) −1967.59 1651.00i −0.154646 0.129764i
\(546\) 0 0
\(547\) 17044.4 + 6203.64i 1.33229 + 0.484915i 0.907377 0.420318i \(-0.138082\pi\)
0.424915 + 0.905233i \(0.360304\pi\)
\(548\) 0 0
\(549\) 11342.5 + 8279.20i 0.881758 + 0.643621i
\(550\) 0 0
\(551\) 1883.54 1580.48i 0.145629 0.122197i
\(552\) 0 0
\(553\) −4067.21 + 23066.3i −0.312758 + 1.77374i
\(554\) 0 0
\(555\) 12834.1 2713.14i 0.981583 0.207507i
\(556\) 0 0
\(557\) 1502.66 2602.69i 0.114309 0.197988i −0.803195 0.595717i \(-0.796868\pi\)
0.917503 + 0.397729i \(0.130201\pi\)
\(558\) 0 0
\(559\) −7842.33 13583.3i −0.593373 1.02775i
\(560\) 0 0
\(561\) 306.454 + 9063.21i 0.0230633 + 0.682084i
\(562\) 0 0
\(563\) 2205.13 802.602i 0.165071 0.0600811i −0.258163 0.966101i \(-0.583117\pi\)
0.423234 + 0.906020i \(0.360895\pi\)
\(564\) 0 0
\(565\) −2244.71 12730.4i −0.167143 0.947913i
\(566\) 0 0
\(567\) 7989.89 + 10320.4i 0.591788 + 0.764403i
\(568\) 0 0
\(569\) −3585.08 20332.0i −0.264138 1.49800i −0.771479 0.636255i \(-0.780483\pi\)
0.507341 0.861745i \(-0.330628\pi\)
\(570\) 0 0
\(571\) 10022.8 3648.01i 0.734575 0.267363i 0.0524748 0.998622i \(-0.483289\pi\)
0.682100 + 0.731259i \(0.261067\pi\)
\(572\) 0 0
\(573\) −529.742 15666.8i −0.0386218 1.14222i
\(574\) 0 0
\(575\) 39.8885 + 69.0889i 0.00289298 + 0.00501079i
\(576\) 0 0
\(577\) −5276.40 + 9138.99i −0.380692 + 0.659378i −0.991161 0.132662i \(-0.957648\pi\)
0.610469 + 0.792040i \(0.290981\pi\)
\(578\) 0 0
\(579\) 7511.16 1587.86i 0.539125 0.113971i
\(580\) 0 0
\(581\) 199.965 1134.06i 0.0142787 0.0809788i
\(582\) 0 0
\(583\) −2329.61 + 1954.78i −0.165493 + 0.138865i
\(584\) 0 0
\(585\) 4833.52 2139.22i 0.341609 0.151189i
\(586\) 0 0
\(587\) −5519.40 2008.90i −0.388092 0.141254i 0.140602 0.990066i \(-0.455096\pi\)
−0.528695 + 0.848812i \(0.677318\pi\)
\(588\) 0 0
\(589\) −261.618 219.524i −0.0183018 0.0153571i
\(590\) 0 0
\(591\) 7335.31 + 18213.5i 0.510549 + 1.26769i
\(592\) 0 0
\(593\) −10619.0 −0.735360 −0.367680 0.929952i \(-0.619848\pi\)
−0.367680 + 0.929952i \(0.619848\pi\)
\(594\) 0 0
\(595\) 3553.33 0.244828
\(596\) 0 0
\(597\) 1029.29 1314.44i 0.0705632 0.0901111i
\(598\) 0 0
\(599\) −291.282 244.414i −0.0198689 0.0166719i 0.632799 0.774316i \(-0.281906\pi\)
−0.652668 + 0.757644i \(0.726350\pi\)
\(600\) 0 0
\(601\) −2760.03 1004.57i −0.187327 0.0681816i 0.246653 0.969104i \(-0.420669\pi\)
−0.433981 + 0.900922i \(0.642891\pi\)
\(602\) 0 0
\(603\) 2602.77 5306.63i 0.175776 0.358379i
\(604\) 0 0
\(605\) −11437.8 + 9597.45i −0.768616 + 0.644945i
\(606\) 0 0
\(607\) 4004.42 22710.2i 0.267766 1.51858i −0.493274 0.869874i \(-0.664200\pi\)
0.761040 0.648705i \(-0.224689\pi\)
\(608\) 0 0
\(609\) 2571.94 7885.91i 0.171133 0.524718i
\(610\) 0 0
\(611\) 8854.79 15336.9i 0.586295 1.01549i
\(612\) 0 0
\(613\) 7919.71 + 13717.3i 0.521818 + 0.903814i 0.999678 + 0.0253787i \(0.00807915\pi\)
−0.477860 + 0.878436i \(0.658588\pi\)
\(614\) 0 0
\(615\) −6594.98 + 4110.86i −0.432415 + 0.269538i
\(616\) 0 0
\(617\) 7369.88 2682.42i 0.480875 0.175024i −0.0901973 0.995924i \(-0.528750\pi\)
0.571072 + 0.820900i \(0.306528\pi\)
\(618\) 0 0
\(619\) 3859.29 + 21887.1i 0.250594 + 1.42119i 0.807133 + 0.590369i \(0.201018\pi\)
−0.556539 + 0.830821i \(0.687871\pi\)
\(620\) 0 0
\(621\) −140.868 10.3204i −0.00910278 0.000666899i
\(622\) 0 0
\(623\) 2899.66 + 16444.8i 0.186472 + 1.05754i
\(624\) 0 0
\(625\) −525.504 + 191.268i −0.0336323 + 0.0122411i
\(626\) 0 0
\(627\) 7521.40 + 4009.88i 0.479068 + 0.255405i
\(628\) 0 0
\(629\) −5474.75 9482.54i −0.347047 0.601103i
\(630\) 0 0
\(631\) −2964.46 + 5134.59i −0.187026 + 0.323938i −0.944257 0.329209i \(-0.893218\pi\)
0.757232 + 0.653146i \(0.226551\pi\)
\(632\) 0 0
\(633\) 4414.33 + 4913.54i 0.277179 + 0.308524i
\(634\) 0 0
\(635\) −197.523 + 1120.21i −0.0123440 + 0.0700065i
\(636\) 0 0
\(637\) 497.879 417.770i 0.0309681 0.0259853i
\(638\) 0 0
\(639\) −3892.13 + 3741.97i −0.240955 + 0.231659i
\(640\) 0 0
\(641\) 3853.21 + 1402.45i 0.237430 + 0.0864175i 0.457995 0.888955i \(-0.348568\pi\)
−0.220565 + 0.975372i \(0.570790\pi\)
\(642\) 0 0
\(643\) 237.689 + 199.444i 0.0145778 + 0.0122322i 0.650047 0.759894i \(-0.274749\pi\)
−0.635470 + 0.772126i \(0.719193\pi\)
\(644\) 0 0
\(645\) 18861.5 + 2672.10i 1.15143 + 0.163122i
\(646\) 0 0
\(647\) 17190.2 1.04454 0.522268 0.852781i \(-0.325086\pi\)
0.522268 + 0.852781i \(0.325086\pi\)
\(648\) 0 0
\(649\) −25381.7 −1.53516
\(650\) 0 0
\(651\) −1140.72 161.605i −0.0686764 0.00972934i
\(652\) 0 0
\(653\) −5085.19 4266.98i −0.304746 0.255712i 0.477571 0.878593i \(-0.341518\pi\)
−0.782316 + 0.622881i \(0.785962\pi\)
\(654\) 0 0
\(655\) −12748.7 4640.13i −0.760506 0.276802i
\(656\) 0 0
\(657\) −5162.43 20902.3i −0.306554 1.24121i
\(658\) 0 0
\(659\) −1245.58 + 1045.16i −0.0736279 + 0.0617812i −0.678859 0.734269i \(-0.737525\pi\)
0.605231 + 0.796050i \(0.293081\pi\)
\(660\) 0 0
\(661\) −1371.31 + 7777.07i −0.0806924 + 0.457629i 0.917511 + 0.397711i \(0.130195\pi\)
−0.998203 + 0.0599185i \(0.980916\pi\)
\(662\) 0 0
\(663\) −2948.61 3282.06i −0.172722 0.192254i
\(664\) 0 0
\(665\) 1669.92 2892.39i 0.0973785 0.168665i
\(666\) 0 0
\(667\) 44.8823 + 77.7385i 0.00260547 + 0.00451281i
\(668\) 0 0
\(669\) 22924.0 + 12221.5i 1.32481 + 0.706293i
\(670\) 0 0
\(671\) 29071.4 10581.1i 1.67256 0.608763i
\(672\) 0 0
\(673\) 2739.40 + 15535.9i 0.156904 + 0.889846i 0.957025 + 0.290007i \(0.0936576\pi\)
−0.800121 + 0.599839i \(0.795231\pi\)
\(674\) 0 0
\(675\) 2725.28 10778.0i 0.155402 0.614584i
\(676\) 0 0
\(677\) −5133.84 29115.5i −0.291447 1.65288i −0.681303 0.732002i \(-0.738586\pi\)
0.389856 0.920876i \(-0.372525\pi\)
\(678\) 0 0
\(679\) 20106.3 7318.09i 1.13639 0.413612i
\(680\) 0 0
\(681\) −5225.48 + 3257.21i −0.294039 + 0.183284i
\(682\) 0 0
\(683\) 12777.3 + 22131.0i 0.715829 + 1.23985i 0.962639 + 0.270788i \(0.0872843\pi\)
−0.246810 + 0.969064i \(0.579382\pi\)
\(684\) 0 0
\(685\) −3128.55 + 5418.80i −0.174505 + 0.302251i
\(686\) 0 0
\(687\) 2978.71 9133.12i 0.165422 0.507205i
\(688\) 0 0
\(689\) 256.927 1457.11i 0.0142063 0.0805680i
\(690\) 0 0
\(691\) −16424.3 + 13781.6i −0.904212 + 0.758724i −0.971009 0.239042i \(-0.923166\pi\)
0.0667969 + 0.997767i \(0.478722\pi\)
\(692\) 0 0
\(693\) 28688.4 1942.31i 1.57256 0.106468i
\(694\) 0 0
\(695\) −16166.3 5884.06i −0.882336 0.321144i
\(696\) 0 0
\(697\) 4969.13 + 4169.60i 0.270042 + 0.226592i
\(698\) 0 0
\(699\) 10157.7 12971.7i 0.549644 0.701910i
\(700\) 0 0
\(701\) −11587.1 −0.624308 −0.312154 0.950031i \(-0.601051\pi\)
−0.312154 + 0.950031i \(0.601051\pi\)
\(702\) 0 0
\(703\) −10291.6 −0.552142
\(704\) 0 0
\(705\) 8035.43 + 19951.9i 0.429265 + 1.06586i
\(706\) 0 0
\(707\) −13633.5 11439.9i −0.725235 0.608544i
\(708\) 0 0
\(709\) 8347.62 + 3038.29i 0.442174 + 0.160938i 0.553506 0.832845i \(-0.313289\pi\)
−0.111332 + 0.993783i \(0.535512\pi\)
\(710\) 0 0
\(711\) −3769.90 + 35120.4i −0.198850 + 1.85249i
\(712\) 0 0
\(713\) 9.55107 8.01430i 0.000501669 0.000420951i
\(714\) 0 0
\(715\) 2022.12 11468.0i 0.105766 0.599831i
\(716\) 0 0
\(717\) 30150.3 6373.79i 1.57041 0.331985i
\(718\) 0 0
\(719\) −4391.89 + 7606.97i −0.227802 + 0.394565i −0.957156 0.289571i \(-0.906487\pi\)
0.729354 + 0.684136i \(0.239821\pi\)
\(720\) 0 0
\(721\) −2946.60 5103.66i −0.152201 0.263620i
\(722\) 0 0
\(723\) −523.261 15475.1i −0.0269160 0.796026i
\(724\) 0 0
\(725\) −6639.15 + 2416.45i −0.340099 + 0.123786i
\(726\) 0 0
\(727\) 2189.91 + 12419.6i 0.111718 + 0.633587i 0.988323 + 0.152375i \(0.0486921\pi\)
−0.876604 + 0.481212i \(0.840197\pi\)
\(728\) 0 0
\(729\) 13073.1 + 14714.4i 0.664182 + 0.747571i
\(730\) 0 0
\(731\) −2761.19 15659.5i −0.139707 0.792320i
\(732\) 0 0
\(733\) 5389.52 1961.62i 0.271578 0.0988462i −0.202642 0.979253i \(-0.564953\pi\)
0.474219 + 0.880407i \(0.342730\pi\)
\(734\) 0 0
\(735\) 26.6760 + 788.929i 0.00133872 + 0.0395919i
\(736\) 0 0
\(737\) −6510.71 11276.9i −0.325407 0.563622i
\(738\) 0 0
\(739\) −6949.01 + 12036.0i −0.345904 + 0.599124i −0.985518 0.169573i \(-0.945761\pi\)
0.639613 + 0.768697i \(0.279095\pi\)
\(740\) 0 0
\(741\) −4057.29 + 857.713i −0.201145 + 0.0425221i
\(742\) 0 0
\(743\) 2458.80 13944.6i 0.121406 0.688528i −0.861972 0.506956i \(-0.830770\pi\)
0.983378 0.181572i \(-0.0581184\pi\)
\(744\) 0 0
\(745\) 10563.6 8863.95i 0.519492 0.435906i
\(746\) 0 0
\(747\) 185.348 1726.70i 0.00907835 0.0845739i
\(748\) 0 0
\(749\) −5406.04 1967.64i −0.263728 0.0959892i
\(750\) 0 0
\(751\) −8216.97 6894.86i −0.399256 0.335016i 0.420950 0.907084i \(-0.361697\pi\)
−0.820206 + 0.572068i \(0.806141\pi\)
\(752\) 0 0
\(753\) −13418.6 33318.3i −0.649404 1.61247i
\(754\) 0 0
\(755\) −5573.74 −0.268674
\(756\) 0 0
\(757\) −12941.7 −0.621366 −0.310683 0.950514i \(-0.600558\pi\)
−0.310683 + 0.950514i \(0.600558\pi\)
\(758\) 0 0
\(759\) −191.849 + 244.997i −0.00917482 + 0.0117165i
\(760\) 0 0
\(761\) −16885.2 14168.4i −0.804323 0.674907i 0.144923 0.989443i \(-0.453707\pi\)
−0.949245 + 0.314536i \(0.898151\pi\)
\(762\) 0 0
\(763\) 6388.07 + 2325.07i 0.303098 + 0.110319i
\(764\) 0 0
\(765\) 5346.43 361.972i 0.252681 0.0171073i
\(766\) 0 0
\(767\) 9459.87 7937.77i 0.445340 0.373685i
\(768\) 0 0
\(769\) −2620.50 + 14861.6i −0.122884 + 0.696908i 0.859659 + 0.510869i \(0.170676\pi\)
−0.982542 + 0.186039i \(0.940435\pi\)
\(770\) 0 0
\(771\) −8185.88 + 25099.0i −0.382370 + 1.17240i
\(772\) 0 0
\(773\) −16889.2 + 29253.0i −0.785852 + 1.36113i 0.142637 + 0.989775i \(0.454442\pi\)
−0.928489 + 0.371360i \(0.878892\pi\)
\(774\) 0 0
\(775\) 490.669 + 849.864i 0.0227424 + 0.0393910i
\(776\) 0 0
\(777\) −29463.5 + 18365.6i −1.36036 + 0.847954i
\(778\) 0 0
\(779\) 5729.31 2085.30i 0.263509 0.0959095i
\(780\) 0 0
\(781\) 2065.51 + 11714.1i 0.0946347 + 0.536700i
\(782\) 0 0
\(783\) 3066.48 12127.3i 0.139958 0.553506i