Properties

Label 108.4.i.a.25.8
Level 108
Weight 4
Character 108.25
Analytic conductor 6.372
Analytic rank 0
Dimension 54
CM no
Inner twists 2

Related objects

Downloads

Learn more about

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 25.8
Character \(\chi\) \(=\) 108.25
Dual form 108.4.i.a.13.8

$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\) \(1\)

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 −0.844412 0.535694i \(-0.820050\pi\)
0.380925 + 0.924606i \(0.375606\pi\)
\(6\) 0 0
\(7\) 16.8240 6.12342i 0.908409 0.330634i 0.154792 0.987947i \(-0.450529\pi\)
0.753617 + 0.657313i \(0.228307\pi\)
\(8\) 0 0
\(9\) 25.9375 7.49962i 0.960649 0.277764i
\(10\) 0 0
\(11\) 45.5667 + 38.2350i 1.24899 + 1.04803i 0.996766 + 0.0803571i \(0.0256061\pi\)
0.252223 + 0.967669i \(0.418838\pi\)
\(12\) 0 0
\(13\) −5.02544 28.5007i −0.107216 0.608052i −0.990312 0.138860i \(-0.955656\pi\)
0.883096 0.469192i \(-0.155455\pi\)
\(14\) 0 0
\(15\) −23.4908 + 26.1473i −0.404353 + 0.450080i
\(16\) 0 0
\(17\) −14.6698 25.4089i −0.209291 0.362503i 0.742200 0.670178i \(-0.233782\pi\)
−0.951491 + 0.307675i \(0.900449\pi\)
\(18\) 0 0
\(19\) 13.7884 23.8822i 0.166488 0.288366i −0.770695 0.637205i \(-0.780091\pi\)
0.937183 + 0.348839i \(0.113424\pi\)
\(20\) 0 0
\(21\) 82.0925 43.7660i 0.853050 0.454786i
\(22\) 0 0
\(23\) −0.946050 0.344334i −0.00857674 0.00312168i 0.337728 0.941244i \(-0.390342\pi\)
−0.346305 + 0.938122i \(0.612564\pi\)
\(24\) 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 0.894259 + 0.447549i \(0.147703\pi\)
−0.993400 + 0.114704i \(0.963408\pi\)
\(30\) 0 0
\(31\) −11.6374 4.23566i −0.0674238 0.0245402i 0.308088 0.951358i \(-0.400311\pi\)
−0.375512 + 0.926818i \(0.622533\pi\)
\(32\) 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 −0.898745 0.438472i \(-0.855520\pi\)
0.0696442 0.997572i \(-0.477814\pi\)
\(38\) 0 0
\(39\) −46.6278 142.967i −0.191447 0.587001i
\(40\) 0 0
\(41\) 38.3921 + 217.733i 0.146240 + 0.829369i 0.966363 + 0.257182i \(0.0827939\pi\)
−0.820123 + 0.572187i \(0.806095\pi\)
\(42\) 0 0
\(43\) −415.169 348.368i −1.47239 1.23548i −0.913882 0.405979i \(-0.866931\pi\)
−0.558505 0.829501i \(-0.688625\pi\)
\(44\) 0 0
\(45\) −101.797 + 151.643i −0.337223 + 0.502348i
\(46\) 0 0
\(47\) −575.029 + 209.294i −1.78461 + 0.649545i −0.785063 + 0.619416i \(0.787369\pi\)
−0.999546 + 0.0301286i \(0.990408\pi\)
\(48\) 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 −0.927739 0.373231i \(-0.878250\pi\)
0.206460 + 0.978455i \(0.433806\pi\)
\(60\) 0 0
\(61\) 488.734 177.884i 1.02583 0.373373i 0.226341 0.974048i \(-0.427324\pi\)
0.799493 + 0.600675i \(0.205101\pi\)
\(62\) 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 0.999652 + 0.0263958i \(0.00840303\pi\)
−0.930337 + 0.366705i \(0.880486\pi\)
\(68\) 0 0
\(69\) −5.11819 1.08199i −0.00892982 0.00188777i
\(70\) 0 0
\(71\) −99.9846 173.178i −0.167127 0.289472i 0.770282 0.637704i \(-0.220116\pi\)
−0.937408 + 0.348232i \(0.886782\pi\)
\(72\) 0 0
\(73\) −398.711 + 690.588i −0.639255 + 1.10722i 0.346342 + 0.938108i \(0.387424\pi\)
−0.985597 + 0.169113i \(0.945910\pi\)
\(74\) 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 −0.196290 0.980546i \(-0.562889\pi\)
0.519819 0.854277i \(-0.326000\pi\)
\(80\) 0 0
\(81\) 616.511 389.044i 0.845694 0.533667i
\(82\) 0 0
\(83\) −11.1689 + 63.3422i −0.0147705 + 0.0837675i −0.991302 0.131607i \(-0.957986\pi\)
0.976531 + 0.215375i \(0.0690973\pi\)
\(84\) 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 −0.442455 0.896791i \(-0.645892\pi\)
0.997871 0.0652184i \(-0.0207744\pi\)
\(90\) 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 0.980675 0.195644i \(-0.0626797\pi\)
−0.0223792 + 0.999750i \(0.507124\pi\)
\(98\) 0 0
\(99\) 1468.64 + 649.989i 1.49094 + 0.659862i
\(100\) 0 0
\(101\) −934.108 + 339.987i −0.920269 + 0.334951i −0.758346 0.651853i \(-0.773992\pi\)
−0.161924 + 0.986803i \(0.551770\pi\)
\(102\) 0 0
\(103\) −252.152 + 211.581i −0.241216 + 0.202405i −0.755379 0.655288i \(-0.772547\pi\)
0.514163 + 0.857693i \(0.328103\pi\)
\(104\) 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 0.219780 0.975549i \(-0.429466\pi\)
0.998893 0.0470391i \(-0.0149785\pi\)
\(114\) 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 −0.893902 0.448262i \(-0.852043\pi\)
0.835157 + 0.550011i \(0.185377\pi\)
\(128\) 0 0
\(129\) −2389.86 1489.68i −1.63113 1.01674i
\(130\) 0 0
\(131\) 1884.63 + 685.949i 1.25695 + 0.457493i 0.882745 0.469852i \(-0.155693\pi\)
0.374207 + 0.927345i \(0.377915\pi\)
\(132\) 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 0.892874 + 0.450306i \(0.148685\pi\)
−0.993041 + 0.117768i \(0.962426\pi\)
\(138\) 0 0
\(139\) 2389.86 + 869.838i 1.45831 + 0.530782i 0.944900 0.327360i \(-0.106159\pi\)
0.513412 + 0.858142i \(0.328381\pi\)
\(140\) 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 −0.912943 0.408086i \(-0.866196\pi\)
0.718313 0.695720i \(-0.244915\pi\)
\(150\) 0 0
\(151\) 631.192 + 529.633i 0.340170 + 0.285437i 0.796829 0.604205i \(-0.206509\pi\)
−0.456658 + 0.889642i \(0.650954\pi\)
\(152\) 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 −0.807483 0.589891i \(-0.799171\pi\)
0.440711 + 0.897649i \(0.354726\pi\)
\(158\) 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 −0.990605 0.136752i \(-0.956334\pi\)
−0.0373420 + 0.999303i \(0.511889\pi\)
\(168\) 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 0.221056 0.975261i \(-0.429050\pi\)
−0.922059 + 0.387050i \(0.873494\pi\)
\(174\) 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 −0.814215 0.580563i \(-0.802832\pi\)
−0.0956752 0.995413i \(-0.530501\pi\)
\(180\) 0 0
\(181\) −1347.22 + 2333.45i −0.553248 + 0.958254i 0.444789 + 0.895635i \(0.353279\pi\)
−0.998038 + 0.0626187i \(0.980055\pi\)
\(182\) 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 0.708951 + 0.705258i \(0.249169\pi\)
−0.907408 + 0.420250i \(0.861942\pi\)
\(192\) 0 0
\(193\) 1388.37 + 505.325i 0.517808 + 0.188467i 0.587686 0.809089i \(-0.300039\pi\)
−0.0698784 + 0.997556i \(0.522261\pi\)
\(194\) 0 0
\(195\) 863.267 + 538.102i 0.317025 + 0.197612i
\(196\) 0 0
\(197\) 1889.39 3272.53i 0.683318 1.18354i −0.290644 0.956831i \(-0.593869\pi\)
0.973962 0.226711i \(-0.0727973\pi\)
\(198\) 0 0
\(199\) 160.647 + 278.248i 0.0572258 + 0.0991180i 0.893219 0.449622i \(-0.148441\pi\)
−0.835993 + 0.548740i \(0.815108\pi\)
\(200\) 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 −0.469957 0.882689i \(-0.655731\pi\)
0.787672 + 0.616095i \(0.211286\pi\)
\(212\) 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 0.479420 0.877585i \(-0.340847\pi\)
0.931358 + 0.364104i \(0.118625\pi\)
\(224\) 0 0
\(225\) 228.347 + 2127.28i 0.0676584 + 0.630306i
\(226\) 0 0
\(227\) −907.775 761.713i −0.265423 0.222717i 0.500356 0.865820i \(-0.333202\pi\)
−0.765780 + 0.643103i \(0.777647\pi\)
\(228\) 0 0
\(229\) 321.039 + 1820.70i 0.0926412 + 0.525394i 0.995445 + 0.0953410i \(0.0303941\pi\)
−0.902803 + 0.430053i \(0.858495\pi\)
\(230\) 0 0
\(231\) 5414.08 + 1144.54i 1.54208 + 0.325996i
\(232\) 0 0
\(233\) 1585.36 + 2745.93i 0.445754 + 0.772068i 0.998104 0.0615437i \(-0.0196024\pi\)
−0.552351 + 0.833612i \(0.686269\pi\)
\(234\) 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 0.958199 0.286104i \(-0.0923602\pi\)
0.550119 + 0.835086i \(0.314582\pi\)
\(240\) 0 0
\(241\) −517.453 + 2934.62i −0.138307 + 0.784380i 0.834192 + 0.551474i \(0.185935\pi\)
−0.972499 + 0.232906i \(0.925177\pi\)
\(242\) 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 −0.00630772 + 0.999980i \(0.502008\pi\)
−0.862854 + 0.505453i \(0.831326\pi\)
\(252\) 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 −0.882395 0.470510i \(-0.844070\pi\)
0.668256 0.743931i \(-0.267041\pi\)
\(258\) 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 −0.994293 0.106682i \(-0.965977\pi\)
−0.693099 + 0.720843i \(0.743755\pi\)
\(264\) 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 −0.643580 0.765379i \(-0.722552\pi\)
−0.00103476 + 0.999999i \(0.500329\pi\)
\(278\) 0 0
\(279\) −333.611 22.5866i −0.0715870 0.00484668i
\(280\) 0 0
\(281\) 3251.44 + 2728.28i 0.690266 + 0.579202i 0.918986 0.394290i \(-0.129009\pi\)
−0.228720 + 0.973492i \(0.573454\pi\)
\(282\) 0 0
\(283\) −927.955 5262.69i −0.194916 1.10542i −0.912538 0.408991i \(-0.865881\pi\)
0.717623 0.696432i \(-0.245230\pi\)
\(284\) 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 0.545830 0.837896i \(-0.316214\pi\)
−0.120459 + 0.992718i \(0.538437\pi\)
\(294\) 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 0.834297 0.551316i \(-0.185874\pi\)
−0.894602 + 0.446864i \(0.852541\pi\)
\(308\) 0 0
\(309\) −1143.05 + 1272.32i −0.210440 + 0.234239i
\(310\) 0 0
\(311\) −990.109 5615.19i −0.180527 1.02382i −0.931569 0.363565i \(-0.881559\pi\)
0.751042 0.660255i \(-0.229552\pi\)
\(312\) 0 0
\(313\) 3737.23 + 3135.91i 0.674890 + 0.566300i 0.914508 0.404567i \(-0.132578\pi\)
−0.239618 + 0.970867i \(0.577022\pi\)
\(314\) 0 0
\(315\) −784.057 + 3174.59i −0.140243 + 0.567835i
\(316\) 0 0
\(317\) 6695.08 2436.81i 1.18623 0.431751i 0.327829 0.944737i \(-0.393683\pi\)
0.858397 + 0.512987i \(0.171461\pi\)
\(318\) 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 −0.713314 0.700844i \(-0.752807\pi\)
−0.0959363 + 0.995387i \(0.530584\pi\)
\(332\) 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 −0.897816 0.440370i \(-0.854847\pi\)
0.693056 0.720884i \(-0.256264\pi\)
\(338\) 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 0.0984612 0.995141i \(-0.468608\pi\)
−0.564239 + 0.825612i \(0.690830\pi\)
\(348\) 0 0
\(349\) −322.003 + 1826.17i −0.0493881 + 0.280094i −0.999493 0.0318364i \(-0.989864\pi\)
0.950105 + 0.311930i \(0.100976\pi\)
\(350\) 0 0
\(351\) −2281.61 3358.52i −0.346961 0.510726i
\(352\) 0 0
\(353\) 57.4469 325.798i 0.00866173 0.0491231i −0.980171 0.198156i \(-0.936505\pi\)
0.988832 + 0.149033i \(0.0476159\pi\)
\(354\) 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 −0.600495 0.799629i \(-0.705030\pi\)
0.992746 + 0.120229i \(0.0383630\pi\)
\(360\) 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 0.773403 0.633915i \(-0.218553\pi\)
−0.489984 + 0.871731i \(0.662998\pi\)
\(368\) 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 −0.228308 0.973589i \(-0.573319\pi\)
0.919153 + 0.393902i \(0.128875\pi\)
\(374\) 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 −0.962474 0.271374i \(-0.912522\pi\)
0.100120 + 0.994975i \(0.468077\pi\)
\(384\) 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 0.999990 0.00448556i \(-0.00142780\pi\)
0.169229 + 0.985577i \(0.445872\pi\)
\(390\) 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 −0.0226159 0.999744i \(-0.507199\pi\)
0.877112 0.480286i \(-0.159467\pi\)
\(398\) 0 0
\(399\) 86.6970 2564.01i 0.0108779 0.321707i
\(400\) 0 0
\(401\) 6064.01 + 2207.12i 0.755168 + 0.274859i 0.690779 0.723066i \(-0.257268\pi\)
0.0643893 + 0.997925i \(0.479490\pi\)
\(402\) 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 0.629986 0.776606i \(-0.283061\pi\)
−0.0165958 + 0.999862i \(0.505283\pi\)
\(410\) 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 −0.924194 0.381923i \(-0.875262\pi\)
0.737833 0.674983i \(-0.235849\pi\)
\(420\) 0 0
\(421\) 6648.55 + 5578.80i 0.769669 + 0.645829i 0.940624 0.339450i \(-0.110241\pi\)
−0.170955 + 0.985279i \(0.554685\pi\)
\(422\) 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 −0.770689 0.637211i \(-0.780088\pi\)
−0.180791 + 0.983522i \(0.557866\pi\)
\(440\) 0 0
\(441\) −337.958 + 503.442i −0.0364926 + 0.0543616i
\(442\) 0 0
\(443\) −3512.25 2947.12i −0.376686 0.316077i 0.434714 0.900569i \(-0.356850\pi\)
−0.811400 + 0.584492i \(0.801294\pi\)
\(444\) 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 0.892559 0.450931i \(-0.148908\pi\)
−0.836797 + 0.547513i \(0.815575\pi\)
\(450\) 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 0.655775 + 0.754956i \(0.272342\pi\)
−0.874437 + 0.485139i \(0.838769\pi\)
\(458\) 0 0
\(459\) −3338.12 2408.39i −0.339455 0.244911i
\(460\) 0 0
\(461\) −30.2863 + 171.762i −0.00305981 + 0.0173531i −0.986299 0.164965i \(-0.947249\pi\)
0.983240 + 0.182318i \(0.0583600\pi\)
\(462\) 0 0
\(463\) 8366.64 + 3045.21i 0.839808 + 0.305665i 0.725878 0.687824i \(-0.241434\pi\)
0.113930 + 0.993489i \(0.463656\pi\)
\(464\) 0 0
\(465\) 384.122 204.787i 0.0383080 0.0204232i
\(466\) 0 0
\(467\) 1326.26 2297.15i 0.131418 0.227622i −0.792806 0.609475i \(-0.791380\pi\)
0.924223 + 0.381853i \(0.124714\pi\)
\(468\) 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 0.733905 0.679252i \(-0.237696\pi\)
0.998819 + 0.0485928i \(0.0154736\pi\)
\(480\) 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 −0.202936 + 0.979192i \(0.565048\pi\)
−0.999555 + 0.0298176i \(0.990507\pi\)
\(492\) 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 −0.992099 0.125455i \(-0.959961\pi\)
0.889360 0.457207i \(-0.151150\pi\)
\(500\) 0 0
\(501\) −10056.6 + 11193.8i −0.896796 + 0.998211i
\(502\) 0 0
\(503\) −3417.70 5919.63i −0.302958 0.524738i 0.673847 0.738871i \(-0.264641\pi\)
−0.976805 + 0.214133i \(0.931307\pi\)
\(504\) 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 0.322998 0.946400i \(-0.395309\pi\)
−0.360903 + 0.932603i \(0.617532\pi\)
\(510\) 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 −0.996663 0.0816212i \(-0.973990\pi\)
0.569018 + 0.822325i \(0.307324\pi\)
\(522\) 0 0
\(523\) 4957.61 + 8586.84i 0.414496 + 0.717928i 0.995375 0.0960616i \(-0.0306246\pi\)
−0.580879 + 0.813990i \(0.697291\pi\)
\(524\) 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 0.424915 0.905233i \(-0.360304\pi\)
0.907377 + 0.420318i \(0.138082\pi\)
\(548\) 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 0.917503 0.397729i \(-0.130201\pi\)
−0.803195 + 0.595717i \(0.796868\pi\)
\(558\) 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 0.423234 0.906020i \(-0.360895\pi\)
−0.258163 + 0.966101i \(0.583117\pi\)
\(564\) 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 0.507341 + 0.861745i \(0.330628\pi\)
−0.771479 + 0.636255i \(0.780483\pi\)
\(570\) 0 0
\(571\) 10022.8 + 3648.01i 0.734575 + 0.267363i 0.682100 0.731259i \(-0.261067\pi\)
0.0524748 + 0.998622i \(0.483289\pi\)
\(572\) 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 0.610469 0.792040i \(-0.290981\pi\)
−0.991161 + 0.132662i \(0.957648\pi\)
\(578\) 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 −0.528695 0.848812i \(-0.677318\pi\)
0.140602 + 0.990066i \(0.455096\pi\)
\(588\) 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 −0.652668 0.757644i \(-0.726350\pi\)
0.632799 + 0.774316i \(0.281906\pi\)
\(600\) 0 0
\(601\) −2760.03 + 1004.57i −0.187327 + 0.0681816i −0.433981 0.900922i \(-0.642891\pi\)
0.246653 + 0.969104i \(0.420669\pi\)
\(602\) 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 0.761040 + 0.648705i \(0.224689\pi\)
−0.493274 + 0.869874i \(0.664200\pi\)
\(608\) 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 −0.477860 0.878436i \(-0.658588\pi\)
0.999678 0.0253787i \(-0.00807915\pi\)
\(614\) 0 0
\(615\) −6594.98 4110.86i −0.432415 0.269538i
\(616\) 0 0
\(617\) 7369.88 + 2682.42i 0.480875 + 0.175024i 0.571072 0.820900i \(-0.306528\pi\)
−0.0901973 + 0.995924i \(0.528750\pi\)
\(618\) 0 0
\(619\) 3859.29 21887.1i 0.250594 1.42119i −0.556539 0.830821i \(-0.687871\pi\)
0.807133 0.590369i \(-0.201018\pi\)
\(620\) 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 0.757232 0.653146i \(-0.226551\pi\)
−0.944257 + 0.329209i \(0.893218\pi\)
\(632\) 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 −0.220565 0.975372i \(-0.570790\pi\)
0.457995 + 0.888955i \(0.348568\pi\)
\(642\) 0 0
\(643\) 237.689 199.444i 0.0145778 0.0122322i −0.635470 0.772126i \(-0.719193\pi\)
0.650047 + 0.759894i \(0.274749\pi\)
\(644\) 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 −0.782316 0.622881i \(-0.785962\pi\)
0.477571 + 0.878593i \(0.341518\pi\)
\(654\) 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 0.605231 0.796050i \(-0.293081\pi\)
−0.678859 + 0.734269i \(0.737525\pi\)
\(660\) 0 0
\(661\) −1371.31 7777.07i −0.0806924 0.457629i −0.998203 0.0599185i \(-0.980916\pi\)
0.917511 0.397711i \(-0.130195\pi\)
\(662\) 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 −0.800121 0.599839i \(-0.795231\pi\)
0.957025 0.290007i \(-0.0936576\pi\)
\(674\) 0 0
\(675\) 2725.28 + 10778.0i 0.155402 + 0.614584i
\(676\) 0 0
\(677\) −5133.84 + 29115.5i −0.291447 + 1.65288i 0.389856 + 0.920876i \(0.372525\pi\)
−0.681303 + 0.732002i \(0.738586\pi\)
\(678\) 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 −0.246810 0.969064i \(-0.579382\pi\)
0.962639 0.270788i \(-0.0872843\pi\)
\(684\) 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 0.0667969 0.997767i \(-0.478722\pi\)
−0.971009 + 0.239042i \(0.923166\pi\)
\(692\) 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 −0.111332 0.993783i \(-0.535512\pi\)
0.553506 + 0.832845i \(0.313289\pi\)
\(710\) 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 0.729354 0.684136i \(-0.239821\pi\)
−0.957156 + 0.289571i \(0.906487\pi\)
\(720\) 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 −0.876604 0.481212i \(-0.840197\pi\)
0.988323 0.152375i \(-0.0486921\pi\)
\(728\) 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 0.474219 0.880407i \(-0.342730\pi\)
−0.202642 + 0.979253i \(0.564953\pi\)
\(734\) 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 0.639613 0.768697i \(-0.279095\pi\)
−0.985518 + 0.169573i \(0.945761\pi\)
\(740\) 0 0
\(741\) −4057.29 857.713i −0.201145 0.0425221i
\(742\) 0 0
\(743\) 2458.80 + 13944.6i 0.121406 + 0.688528i 0.983378 + 0.181572i \(0.0581184\pi\)
−0.861972 + 0.506956i \(0.830770\pi\)
\(744\) 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 −0.820206 0.572068i \(-0.806141\pi\)
0.420950 + 0.907084i \(0.361697\pi\)
\(752\) 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 −0.949245 0.314536i \(-0.898151\pi\)
0.144923 + 0.989443i \(0.453707\pi\)
\(762\) 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 −0.982542 0.186039i \(-0.940435\pi\)
0.859659 0.510869i \(-0.170676\pi\)
\(770\) 0 0
\(771\) −8185.88 25099.0i −0.382370 1.17240i
\(772\) 0 0
\(773\) −16889.2 29253.0i −0.785852 1.36113i −0.928489 0.371360i \(-0.878892\pi\)
0.142637 0.989775i \(-0.454442\pi\)
\(774\) 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