Properties

Label 117.4.q.d.10.2
Level $117$
Weight $4$
Character 117.10
Analytic conductor $6.903$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 117.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.90322347067\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-17})\)
Defining polynomial: \( x^{4} - 17x^{2} + 289 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 10.2
Root \(3.57071 - 2.06155i\) of defining polynomial
Character \(\chi\) \(=\) 117.10
Dual form 117.4.q.d.82.2

$q$-expansion

\(f(q)\) \(=\) \(q+(3.57071 - 2.06155i) q^{2} +(4.50000 - 7.79423i) q^{4} -13.4424i q^{5} +(-27.2121 - 15.7109i) q^{7} -4.12311i q^{8} +O(q^{10})\) \(q+(3.57071 - 2.06155i) q^{2} +(4.50000 - 7.79423i) q^{4} -13.4424i q^{5} +(-27.2121 - 15.7109i) q^{7} -4.12311i q^{8} +(-27.7121 - 47.9988i) q^{10} +(35.0707 - 20.2481i) q^{11} +(42.1364 + 20.5310i) q^{13} -129.556 q^{14} +(27.5000 + 47.6314i) q^{16} +(21.5707 - 37.3616i) q^{17} +(23.3636 + 13.4890i) q^{19} +(-104.773 - 60.4906i) q^{20} +(83.4850 - 144.600i) q^{22} +(9.50500 + 16.4631i) q^{23} -55.6971 q^{25} +(192.783 - 13.5562i) q^{26} +(-244.909 + 141.398i) q^{28} +(-77.0557 - 133.464i) q^{29} +308.270i q^{31} +(224.955 + 129.878i) q^{32} -177.877i q^{34} +(-211.192 + 365.796i) q^{35} +(-37.6821 + 21.7558i) q^{37} +111.233 q^{38} -55.4243 q^{40} +(-41.4293 + 23.9192i) q^{41} +(171.061 - 296.286i) q^{43} -364.466i q^{44} +(67.8793 + 39.1901i) q^{46} +133.468i q^{47} +(322.167 + 558.010i) q^{49} +(-198.879 + 114.823i) q^{50} +(349.637 - 236.032i) q^{52} +438.454 q^{53} +(-272.182 - 471.433i) q^{55} +(-64.7779 + 112.199i) q^{56} +(-550.288 - 317.709i) q^{58} +(-511.434 - 295.277i) q^{59} +(270.652 - 468.783i) q^{61} +(635.516 + 1100.75i) q^{62} +631.000 q^{64} +(275.985 - 566.413i) q^{65} +(-199.485 + 115.173i) q^{67} +(-194.136 - 336.254i) q^{68} +1741.54i q^{70} +(389.202 + 224.706i) q^{71} +389.711i q^{73} +(-89.7014 + 155.367i) q^{74} +(210.272 - 121.401i) q^{76} -1272.47 q^{77} -897.820 q^{79} +(640.279 - 369.665i) q^{80} +(-98.6214 + 170.817i) q^{82} +1300.24i q^{83} +(-502.228 - 289.961i) q^{85} -1410.60i q^{86} +(-83.4850 - 144.600i) q^{88} +(-801.113 + 462.523i) q^{89} +(-824.061 - 1220.69i) q^{91} +171.090 q^{92} +(275.151 + 476.575i) q^{94} +(181.324 - 314.062i) q^{95} +(1351.43 + 780.247i) q^{97} +(2300.73 + 1328.33i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 18 q^{4} - 66 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 18 q^{4} - 66 q^{7} - 68 q^{10} + 126 q^{11} + 40 q^{13} - 204 q^{14} + 110 q^{16} + 72 q^{17} + 222 q^{19} - 162 q^{20} + 34 q^{22} + 138 q^{23} + 120 q^{25} + 714 q^{26} - 594 q^{28} + 6 q^{29} - 402 q^{35} + 492 q^{37} - 612 q^{38} - 136 q^{40} - 180 q^{41} + 470 q^{43} - 714 q^{46} + 346 q^{49} - 1224 q^{50} - 144 q^{52} + 2268 q^{53} - 446 q^{55} - 102 q^{56} - 2244 q^{58} - 2160 q^{59} - 160 q^{61} + 1428 q^{62} + 2524 q^{64} + 804 q^{65} - 498 q^{67} - 648 q^{68} + 1314 q^{71} - 1530 q^{74} + 1998 q^{76} - 2976 q^{77} + 8 q^{79} + 990 q^{80} + 34 q^{82} - 852 q^{85} - 34 q^{88} + 252 q^{89} - 1668 q^{91} + 2484 q^{92} + 2686 q^{94} + 54 q^{95} - 336 q^{97} + 6732 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.57071 2.06155i 1.26244 0.728869i 0.288892 0.957362i \(-0.406713\pi\)
0.973546 + 0.228493i \(0.0733797\pi\)
\(3\) 0 0
\(4\) 4.50000 7.79423i 0.562500 0.974279i
\(5\) 13.4424i 1.20232i −0.799128 0.601161i \(-0.794705\pi\)
0.799128 0.601161i \(-0.205295\pi\)
\(6\) 0 0
\(7\) −27.2121 15.7109i −1.46932 0.848311i −0.469910 0.882715i \(-0.655713\pi\)
−0.999408 + 0.0344037i \(0.989047\pi\)
\(8\) 4.12311i 0.182217i
\(9\) 0 0
\(10\) −27.7121 47.9988i −0.876335 1.51786i
\(11\) 35.0707 20.2481i 0.961293 0.555003i 0.0647219 0.997903i \(-0.479384\pi\)
0.896571 + 0.442901i \(0.146051\pi\)
\(12\) 0 0
\(13\) 42.1364 + 20.5310i 0.898965 + 0.438021i
\(14\) −129.556 −2.47323
\(15\) 0 0
\(16\) 27.5000 + 47.6314i 0.429688 + 0.744241i
\(17\) 21.5707 37.3616i 0.307745 0.533030i −0.670124 0.742249i \(-0.733759\pi\)
0.977869 + 0.209219i \(0.0670923\pi\)
\(18\) 0 0
\(19\) 23.3636 + 13.4890i 0.282104 + 0.162873i 0.634375 0.773025i \(-0.281257\pi\)
−0.352272 + 0.935898i \(0.614591\pi\)
\(20\) −104.773 60.4906i −1.17140 0.676306i
\(21\) 0 0
\(22\) 83.4850 144.600i 0.809048 1.40131i
\(23\) 9.50500 + 16.4631i 0.0861709 + 0.149252i 0.905890 0.423514i \(-0.139204\pi\)
−0.819719 + 0.572766i \(0.805870\pi\)
\(24\) 0 0
\(25\) −55.6971 −0.445577
\(26\) 192.783 13.5562i 1.45415 0.102253i
\(27\) 0 0
\(28\) −244.909 + 141.398i −1.65298 + 0.954350i
\(29\) −77.0557 133.464i −0.493410 0.854611i 0.506561 0.862204i \(-0.330916\pi\)
−0.999971 + 0.00759297i \(0.997583\pi\)
\(30\) 0 0
\(31\) 308.270i 1.78603i 0.450025 + 0.893016i \(0.351415\pi\)
−0.450025 + 0.893016i \(0.648585\pi\)
\(32\) 224.955 + 129.878i 1.24271 + 0.717480i
\(33\) 0 0
\(34\) 177.877i 0.897223i
\(35\) −211.192 + 365.796i −1.01994 + 1.76659i
\(36\) 0 0
\(37\) −37.6821 + 21.7558i −0.167430 + 0.0966657i −0.581373 0.813637i \(-0.697484\pi\)
0.413944 + 0.910303i \(0.364151\pi\)
\(38\) 111.233 0.474851
\(39\) 0 0
\(40\) −55.4243 −0.219084
\(41\) −41.4293 + 23.9192i −0.157809 + 0.0911110i −0.576825 0.816868i \(-0.695708\pi\)
0.419016 + 0.907979i \(0.362375\pi\)
\(42\) 0 0
\(43\) 171.061 296.286i 0.606663 1.05077i −0.385123 0.922865i \(-0.625841\pi\)
0.991786 0.127906i \(-0.0408256\pi\)
\(44\) 364.466i 1.24876i
\(45\) 0 0
\(46\) 67.8793 + 39.1901i 0.217571 + 0.125615i
\(47\) 133.468i 0.414218i 0.978318 + 0.207109i \(0.0664055\pi\)
−0.978318 + 0.207109i \(0.933594\pi\)
\(48\) 0 0
\(49\) 322.167 + 558.010i 0.939263 + 1.62685i
\(50\) −198.879 + 114.823i −0.562514 + 0.324767i
\(51\) 0 0
\(52\) 349.637 236.032i 0.932422 0.629455i
\(53\) 438.454 1.13635 0.568173 0.822909i \(-0.307650\pi\)
0.568173 + 0.822909i \(0.307650\pi\)
\(54\) 0 0
\(55\) −272.182 471.433i −0.667291 1.15578i
\(56\) −64.7779 + 112.199i −0.154577 + 0.267735i
\(57\) 0 0
\(58\) −550.288 317.709i −1.24580 0.719262i
\(59\) −511.434 295.277i −1.12853 0.651555i −0.184963 0.982746i \(-0.559216\pi\)
−0.943564 + 0.331190i \(0.892550\pi\)
\(60\) 0 0
\(61\) 270.652 468.783i 0.568089 0.983960i −0.428665 0.903463i \(-0.641016\pi\)
0.996755 0.0804965i \(-0.0256506\pi\)
\(62\) 635.516 + 1100.75i 1.30178 + 2.25476i
\(63\) 0 0
\(64\) 631.000 1.23242
\(65\) 275.985 566.413i 0.526642 1.08084i
\(66\) 0 0
\(67\) −199.485 + 115.173i −0.363746 + 0.210009i −0.670723 0.741708i \(-0.734016\pi\)
0.306977 + 0.951717i \(0.400683\pi\)
\(68\) −194.136 336.254i −0.346213 0.599659i
\(69\) 0 0
\(70\) 1741.54i 2.97362i
\(71\) 389.202 + 224.706i 0.650561 + 0.375601i 0.788671 0.614816i \(-0.210770\pi\)
−0.138110 + 0.990417i \(0.544103\pi\)
\(72\) 0 0
\(73\) 389.711i 0.624826i 0.949946 + 0.312413i \(0.101137\pi\)
−0.949946 + 0.312413i \(0.898863\pi\)
\(74\) −89.7014 + 155.367i −0.140913 + 0.244069i
\(75\) 0 0
\(76\) 210.272 121.401i 0.317367 0.183232i
\(77\) −1272.47 −1.88326
\(78\) 0 0
\(79\) −897.820 −1.27864 −0.639321 0.768940i \(-0.720784\pi\)
−0.639321 + 0.768940i \(0.720784\pi\)
\(80\) 640.279 369.665i 0.894816 0.516623i
\(81\) 0 0
\(82\) −98.6214 + 170.817i −0.132816 + 0.230044i
\(83\) 1300.24i 1.71952i 0.510700 + 0.859759i \(0.329386\pi\)
−0.510700 + 0.859759i \(0.670614\pi\)
\(84\) 0 0
\(85\) −502.228 289.961i −0.640874 0.370009i
\(86\) 1410.60i 1.76871i
\(87\) 0 0
\(88\) −83.4850 144.600i −0.101131 0.175164i
\(89\) −801.113 + 462.523i −0.954132 + 0.550869i −0.894362 0.447344i \(-0.852370\pi\)
−0.0597703 + 0.998212i \(0.519037\pi\)
\(90\) 0 0
\(91\) −824.061 1220.69i −0.949287 1.40619i
\(92\) 171.090 0.193884
\(93\) 0 0
\(94\) 275.151 + 476.575i 0.301911 + 0.522925i
\(95\) 181.324 314.062i 0.195825 0.339179i
\(96\) 0 0
\(97\) 1351.43 + 780.247i 1.41460 + 0.816722i 0.995818 0.0913623i \(-0.0291221\pi\)
0.418787 + 0.908085i \(0.362455\pi\)
\(98\) 2300.73 + 1328.33i 2.37152 + 1.36920i
\(99\) 0 0
\(100\) −250.637 + 434.116i −0.250637 + 0.434116i
\(101\) −479.420 830.380i −0.472318 0.818078i 0.527181 0.849753i \(-0.323249\pi\)
−0.999498 + 0.0316752i \(0.989916\pi\)
\(102\) 0 0
\(103\) −635.153 −0.607606 −0.303803 0.952735i \(-0.598257\pi\)
−0.303803 + 0.952735i \(0.598257\pi\)
\(104\) 84.6514 173.733i 0.0798150 0.163807i
\(105\) 0 0
\(106\) 1565.59 903.897i 1.43457 0.828247i
\(107\) −724.162 1254.29i −0.654275 1.13324i −0.982075 0.188490i \(-0.939641\pi\)
0.327800 0.944747i \(-0.393693\pi\)
\(108\) 0 0
\(109\) 331.084i 0.290937i −0.989363 0.145468i \(-0.953531\pi\)
0.989363 0.145468i \(-0.0464689\pi\)
\(110\) −1943.77 1122.24i −1.68483 0.972736i
\(111\) 0 0
\(112\) 1728.20i 1.45803i
\(113\) 347.602 602.065i 0.289378 0.501217i −0.684284 0.729216i \(-0.739885\pi\)
0.973661 + 0.227999i \(0.0732184\pi\)
\(114\) 0 0
\(115\) 221.304 127.770i 0.179449 0.103605i
\(116\) −1387.00 −1.11017
\(117\) 0 0
\(118\) −2434.91 −1.89959
\(119\) −1173.97 + 677.792i −0.904351 + 0.522127i
\(120\) 0 0
\(121\) 154.470 267.550i 0.116056 0.201014i
\(122\) 2231.85i 1.65625i
\(123\) 0 0
\(124\) 2402.73 + 1387.22i 1.74009 + 1.00464i
\(125\) 931.594i 0.666595i
\(126\) 0 0
\(127\) 123.577 + 214.042i 0.0863441 + 0.149552i 0.905963 0.423357i \(-0.139148\pi\)
−0.819619 + 0.572909i \(0.805815\pi\)
\(128\) 453.481 261.817i 0.313144 0.180794i
\(129\) 0 0
\(130\) −182.227 2591.46i −0.122941 1.74835i
\(131\) −472.243 −0.314962 −0.157481 0.987522i \(-0.550337\pi\)
−0.157481 + 0.987522i \(0.550337\pi\)
\(132\) 0 0
\(133\) −423.849 734.127i −0.276333 0.478623i
\(134\) −474.869 + 822.498i −0.306138 + 0.530246i
\(135\) 0 0
\(136\) −154.046 88.9383i −0.0971273 0.0560765i
\(137\) 1585.43 + 915.349i 0.988704 + 0.570829i 0.904887 0.425652i \(-0.139955\pi\)
0.0838175 + 0.996481i \(0.473289\pi\)
\(138\) 0 0
\(139\) 50.0000 86.6025i 0.0305104 0.0528456i −0.850367 0.526190i \(-0.823620\pi\)
0.880877 + 0.473344i \(0.156953\pi\)
\(140\) 1900.73 + 3292.16i 1.14744 + 1.98742i
\(141\) 0 0
\(142\) 1852.97 1.09506
\(143\) 1893.47 133.146i 1.10727 0.0778615i
\(144\) 0 0
\(145\) −1794.08 + 1035.81i −1.02752 + 0.593237i
\(146\) 803.411 + 1391.55i 0.455416 + 0.788804i
\(147\) 0 0
\(148\) 391.604i 0.217498i
\(149\) 129.520 + 74.7784i 0.0712127 + 0.0411147i 0.535184 0.844736i \(-0.320242\pi\)
−0.463971 + 0.885850i \(0.653576\pi\)
\(150\) 0 0
\(151\) 800.032i 0.431163i 0.976486 + 0.215582i \(0.0691647\pi\)
−0.976486 + 0.215582i \(0.930835\pi\)
\(152\) 55.6164 96.3305i 0.0296782 0.0514042i
\(153\) 0 0
\(154\) −4543.61 + 2623.26i −2.37750 + 1.37265i
\(155\) 4143.88 2.14739
\(156\) 0 0
\(157\) −2706.16 −1.37564 −0.687818 0.725884i \(-0.741431\pi\)
−0.687818 + 0.725884i \(0.741431\pi\)
\(158\) −3205.86 + 1850.90i −1.61421 + 0.931962i
\(159\) 0 0
\(160\) 1745.86 3023.93i 0.862642 1.49414i
\(161\) 597.330i 0.292399i
\(162\) 0 0
\(163\) 3185.46 + 1839.12i 1.53070 + 0.883750i 0.999330 + 0.0366108i \(0.0116562\pi\)
0.531371 + 0.847139i \(0.321677\pi\)
\(164\) 430.546i 0.205000i
\(165\) 0 0
\(166\) 2680.52 + 4642.79i 1.25330 + 2.17079i
\(167\) −2791.30 + 1611.56i −1.29339 + 0.746742i −0.979254 0.202635i \(-0.935050\pi\)
−0.314140 + 0.949377i \(0.601716\pi\)
\(168\) 0 0
\(169\) 1353.96 + 1730.20i 0.616275 + 0.787531i
\(170\) −2391.08 −1.07875
\(171\) 0 0
\(172\) −1539.55 2666.57i −0.682496 1.18212i
\(173\) 1344.77 2329.21i 0.590988 1.02362i −0.403111 0.915151i \(-0.632071\pi\)
0.994100 0.108471i \(-0.0345954\pi\)
\(174\) 0 0
\(175\) 1515.64 + 875.054i 0.654694 + 0.377988i
\(176\) 1928.89 + 1113.64i 0.826111 + 0.476955i
\(177\) 0 0
\(178\) −1907.03 + 3303.07i −0.803022 + 1.39088i
\(179\) 762.021 + 1319.86i 0.318191 + 0.551122i 0.980111 0.198452i \(-0.0635915\pi\)
−0.661920 + 0.749574i \(0.730258\pi\)
\(180\) 0 0
\(181\) −476.881 −0.195836 −0.0979180 0.995194i \(-0.531218\pi\)
−0.0979180 + 0.995194i \(0.531218\pi\)
\(182\) −5459.01 2659.91i −2.22335 1.08333i
\(183\) 0 0
\(184\) 67.8793 39.1901i 0.0271963 0.0157018i
\(185\) 292.449 + 506.537i 0.116223 + 0.201305i
\(186\) 0 0
\(187\) 1747.06i 0.683197i
\(188\) 1040.28 + 600.605i 0.403564 + 0.232998i
\(189\) 0 0
\(190\) 1495.23i 0.570924i
\(191\) −684.871 + 1186.23i −0.259453 + 0.449386i −0.966096 0.258185i \(-0.916876\pi\)
0.706642 + 0.707571i \(0.250209\pi\)
\(192\) 0 0
\(193\) 1857.38 1072.36i 0.692732 0.399949i −0.111903 0.993719i \(-0.535695\pi\)
0.804635 + 0.593770i \(0.202361\pi\)
\(194\) 6434.08 2.38113
\(195\) 0 0
\(196\) 5799.01 2.11334
\(197\) 207.620 119.869i 0.0750879 0.0433520i −0.461986 0.886887i \(-0.652863\pi\)
0.537074 + 0.843535i \(0.319530\pi\)
\(198\) 0 0
\(199\) −794.969 + 1376.93i −0.283185 + 0.490491i −0.972167 0.234287i \(-0.924724\pi\)
0.688982 + 0.724778i \(0.258058\pi\)
\(200\) 229.645i 0.0811918i
\(201\) 0 0
\(202\) −3423.74 1976.70i −1.19254 0.688515i
\(203\) 4842.47i 1.67426i
\(204\) 0 0
\(205\) 321.531 + 556.908i 0.109545 + 0.189737i
\(206\) −2267.95 + 1309.40i −0.767066 + 0.442866i
\(207\) 0 0
\(208\) 180.832 + 2571.62i 0.0602810 + 0.857258i
\(209\) 1092.50 0.361579
\(210\) 0 0
\(211\) 936.427 + 1621.94i 0.305527 + 0.529189i 0.977379 0.211497i \(-0.0678339\pi\)
−0.671851 + 0.740686i \(0.734501\pi\)
\(212\) 1973.04 3417.41i 0.639195 1.10712i
\(213\) 0 0
\(214\) −5171.55 2985.80i −1.65196 0.953761i
\(215\) −3982.78 2299.46i −1.26337 0.729404i
\(216\) 0 0
\(217\) 4843.22 8388.70i 1.51511 2.62425i
\(218\) −682.547 1182.21i −0.212055 0.367290i
\(219\) 0 0
\(220\) −4899.28 −1.50141
\(221\) 1675.98 1131.42i 0.510130 0.344377i
\(222\) 0 0
\(223\) −48.6085 + 28.0642i −0.0145967 + 0.00842742i −0.507281 0.861781i \(-0.669349\pi\)
0.492684 + 0.870208i \(0.336016\pi\)
\(224\) −4081.00 7068.51i −1.21729 2.10841i
\(225\) 0 0
\(226\) 2866.40i 0.843673i
\(227\) −577.976 333.695i −0.168994 0.0975687i 0.413117 0.910678i \(-0.364440\pi\)
−0.582111 + 0.813109i \(0.697773\pi\)
\(228\) 0 0
\(229\) 723.299i 0.208720i −0.994540 0.104360i \(-0.966721\pi\)
0.994540 0.104360i \(-0.0332795\pi\)
\(230\) 526.808 912.458i 0.151029 0.261590i
\(231\) 0 0
\(232\) −550.288 + 317.709i −0.155725 + 0.0899078i
\(233\) −275.451 −0.0774482 −0.0387241 0.999250i \(-0.512329\pi\)
−0.0387241 + 0.999250i \(0.512329\pi\)
\(234\) 0 0
\(235\) 1794.12 0.498024
\(236\) −4602.91 + 2657.49i −1.26959 + 0.733000i
\(237\) 0 0
\(238\) −2794.61 + 4840.41i −0.761124 + 1.31831i
\(239\) 1529.39i 0.413925i 0.978349 + 0.206963i \(0.0663579\pi\)
−0.978349 + 0.206963i \(0.933642\pi\)
\(240\) 0 0
\(241\) 844.830 + 487.763i 0.225810 + 0.130372i 0.608638 0.793448i \(-0.291716\pi\)
−0.382827 + 0.923820i \(0.625050\pi\)
\(242\) 1273.79i 0.338357i
\(243\) 0 0
\(244\) −2435.87 4219.05i −0.639101 1.10695i
\(245\) 7500.97 4330.69i 1.95600 1.12930i
\(246\) 0 0
\(247\) 707.516 + 1048.05i 0.182260 + 0.269984i
\(248\) 1271.03 0.325446
\(249\) 0 0
\(250\) −1920.53 3326.46i −0.485860 0.841534i
\(251\) 937.070 1623.05i 0.235647 0.408152i −0.723814 0.689995i \(-0.757613\pi\)
0.959460 + 0.281843i \(0.0909458\pi\)
\(252\) 0 0
\(253\) 666.694 + 384.916i 0.165671 + 0.0956501i
\(254\) 882.517 + 509.522i 0.218008 + 0.125867i
\(255\) 0 0
\(256\) −1444.50 + 2501.95i −0.352661 + 0.610827i
\(257\) 909.094 + 1574.60i 0.220653 + 0.382181i 0.955006 0.296586i \(-0.0958480\pi\)
−0.734354 + 0.678767i \(0.762515\pi\)
\(258\) 0 0
\(259\) 1367.22 0.328010
\(260\) −3172.82 4699.95i −0.756808 1.12107i
\(261\) 0 0
\(262\) −1686.24 + 973.554i −0.397620 + 0.229566i
\(263\) 336.899 + 583.527i 0.0789890 + 0.136813i 0.902814 0.430031i \(-0.141497\pi\)
−0.823825 + 0.566844i \(0.808164\pi\)
\(264\) 0 0
\(265\) 5893.86i 1.36625i
\(266\) −3026.88 1747.57i −0.697707 0.402822i
\(267\) 0 0
\(268\) 2073.11i 0.472520i
\(269\) −1678.20 + 2906.73i −0.380378 + 0.658834i −0.991116 0.132998i \(-0.957540\pi\)
0.610738 + 0.791833i \(0.290873\pi\)
\(270\) 0 0
\(271\) −7721.09 + 4457.77i −1.73071 + 0.999227i −0.845699 + 0.533660i \(0.820816\pi\)
−0.885013 + 0.465567i \(0.845850\pi\)
\(272\) 2372.78 0.528937
\(273\) 0 0
\(274\) 7548.16 1.66424
\(275\) −1953.34 + 1127.76i −0.428330 + 0.247296i
\(276\) 0 0
\(277\) 2008.65 3479.09i 0.435698 0.754651i −0.561654 0.827372i \(-0.689835\pi\)
0.997352 + 0.0727208i \(0.0231682\pi\)
\(278\) 412.311i 0.0889523i
\(279\) 0 0
\(280\) 1508.21 + 870.768i 0.321904 + 0.185851i
\(281\) 1841.12i 0.390860i 0.980718 + 0.195430i \(0.0626103\pi\)
−0.980718 + 0.195430i \(0.937390\pi\)
\(282\) 0 0
\(283\) 2424.70 + 4199.70i 0.509305 + 0.882143i 0.999942 + 0.0107784i \(0.00343094\pi\)
−0.490637 + 0.871364i \(0.663236\pi\)
\(284\) 3502.82 2022.35i 0.731881 0.422551i
\(285\) 0 0
\(286\) 6486.55 4378.91i 1.34111 0.905351i
\(287\) 1503.17 0.309162
\(288\) 0 0
\(289\) 1525.91 + 2642.95i 0.310586 + 0.537951i
\(290\) −4270.76 + 7397.17i −0.864785 + 1.49785i
\(291\) 0 0
\(292\) 3037.50 + 1753.70i 0.608754 + 0.351464i
\(293\) 1224.43 + 706.927i 0.244137 + 0.140953i 0.617077 0.786903i \(-0.288317\pi\)
−0.372940 + 0.927856i \(0.621650\pi\)
\(294\) 0 0
\(295\) −3969.22 + 6874.89i −0.783379 + 1.35685i
\(296\) 89.7014 + 155.367i 0.0176142 + 0.0305086i
\(297\) 0 0
\(298\) 616.639 0.119869
\(299\) 62.5022 + 888.845i 0.0120889 + 0.171917i
\(300\) 0 0
\(301\) −9309.86 + 5375.05i −1.78276 + 1.02928i
\(302\) 1649.31 + 2856.68i 0.314262 + 0.544317i
\(303\) 0 0
\(304\) 1483.79i 0.279937i
\(305\) −6301.55 3638.20i −1.18304 0.683026i
\(306\) 0 0
\(307\) 4625.64i 0.859932i 0.902845 + 0.429966i \(0.141474\pi\)
−0.902845 + 0.429966i \(0.858526\pi\)
\(308\) −5726.10 + 9917.89i −1.05933 + 1.83482i
\(309\) 0 0
\(310\) 14796.6 8542.83i 2.71094 1.56516i
\(311\) −6060.79 −1.10507 −0.552534 0.833490i \(-0.686339\pi\)
−0.552534 + 0.833490i \(0.686339\pi\)
\(312\) 0 0
\(313\) 969.946 0.175158 0.0875792 0.996158i \(-0.472087\pi\)
0.0875792 + 0.996158i \(0.472087\pi\)
\(314\) −9662.91 + 5578.88i −1.73665 + 1.00266i
\(315\) 0 0
\(316\) −4040.19 + 6997.81i −0.719236 + 1.24575i
\(317\) 8741.63i 1.54883i −0.632679 0.774414i \(-0.718045\pi\)
0.632679 0.774414i \(-0.281955\pi\)
\(318\) 0 0
\(319\) −5404.80 3120.46i −0.948623 0.547687i
\(320\) 8482.13i 1.48177i
\(321\) 0 0
\(322\) −1231.43 2132.89i −0.213120 0.369135i
\(323\) 1007.94 581.933i 0.173632 0.100247i
\(324\) 0 0
\(325\) −2346.88 1143.52i −0.400558 0.195172i
\(326\) 15165.8 2.57655
\(327\) 0 0
\(328\) 98.6214 + 170.817i 0.0166020 + 0.0287555i
\(329\) 2096.90 3631.94i 0.351386 0.608618i
\(330\) 0 0
\(331\) −6051.57 3493.88i −1.00491 0.580184i −0.0952114 0.995457i \(-0.530353\pi\)
−0.909697 + 0.415273i \(0.863686\pi\)
\(332\) 10134.4 + 5851.09i 1.67529 + 0.967229i
\(333\) 0 0
\(334\) −6644.61 + 11508.8i −1.08855 + 1.88543i
\(335\) 1548.19 + 2681.55i 0.252498 + 0.437339i
\(336\) 0 0
\(337\) 4156.59 0.671881 0.335940 0.941883i \(-0.390946\pi\)
0.335940 + 0.941883i \(0.390946\pi\)
\(338\) 8401.50 + 3386.81i 1.35202 + 0.545025i
\(339\) 0 0
\(340\) −4520.05 + 2609.65i −0.720983 + 0.416260i
\(341\) 6241.89 + 10811.3i 0.991252 + 1.71690i
\(342\) 0 0
\(343\) 9468.49i 1.49053i
\(344\) −1221.62 705.301i −0.191469 0.110544i
\(345\) 0 0
\(346\) 11089.3i 1.72301i
\(347\) −156.256 + 270.644i −0.0241737 + 0.0418701i −0.877859 0.478919i \(-0.841029\pi\)
0.853685 + 0.520789i \(0.174362\pi\)
\(348\) 0 0
\(349\) 3861.39 2229.37i 0.592251 0.341936i −0.173736 0.984792i \(-0.555584\pi\)
0.765987 + 0.642856i \(0.222251\pi\)
\(350\) 7215.88 1.10201
\(351\) 0 0
\(352\) 10519.1 1.59281
\(353\) 1947.84 1124.59i 0.293692 0.169563i −0.345914 0.938266i \(-0.612431\pi\)
0.639605 + 0.768703i \(0.279098\pi\)
\(354\) 0 0
\(355\) 3020.58 5231.80i 0.451594 0.782183i
\(356\) 8325.41i 1.23945i
\(357\) 0 0
\(358\) 5441.92 + 3141.89i 0.803392 + 0.463838i
\(359\) 7842.79i 1.15300i −0.817098 0.576499i \(-0.804418\pi\)
0.817098 0.576499i \(-0.195582\pi\)
\(360\) 0 0
\(361\) −3065.60 5309.77i −0.446945 0.774131i
\(362\) −1702.81 + 983.116i −0.247231 + 0.142739i
\(363\) 0 0
\(364\) −13222.7 + 929.796i −1.90400 + 0.133886i
\(365\) 5238.64 0.751241
\(366\) 0 0
\(367\) −3330.12 5767.94i −0.473653 0.820392i 0.525892 0.850552i \(-0.323732\pi\)
−0.999545 + 0.0301597i \(0.990398\pi\)
\(368\) −522.775 + 905.473i −0.0740531 + 0.128264i
\(369\) 0 0
\(370\) 2088.51 + 1205.80i 0.293449 + 0.169423i
\(371\) −11931.3 6888.53i −1.66965 0.963975i
\(372\) 0 0
\(373\) 18.4936 32.0319i 0.00256720 0.00444651i −0.864739 0.502222i \(-0.832516\pi\)
0.867306 + 0.497775i \(0.165850\pi\)
\(374\) −3601.66 6238.26i −0.497961 0.862494i
\(375\) 0 0
\(376\) 550.301 0.0754777
\(377\) −506.696 7205.74i −0.0692207 0.984389i
\(378\) 0 0
\(379\) 10461.5 6039.93i 1.41786 0.818603i 0.421751 0.906712i \(-0.361416\pi\)
0.996111 + 0.0881092i \(0.0280825\pi\)
\(380\) −1631.91 2826.55i −0.220303 0.381577i
\(381\) 0 0
\(382\) 5647.59i 0.756429i
\(383\) −9151.63 5283.69i −1.22096 0.704919i −0.255835 0.966721i \(-0.582350\pi\)
−0.965122 + 0.261801i \(0.915684\pi\)
\(384\) 0 0
\(385\) 17104.9i 2.26428i
\(386\) 4421.45 7658.18i 0.583021 1.00982i
\(387\) 0 0
\(388\) 12162.8 7022.22i 1.59143 0.918813i
\(389\) −9757.49 −1.27179 −0.635893 0.771778i \(-0.719368\pi\)
−0.635893 + 0.771778i \(0.719368\pi\)
\(390\) 0 0
\(391\) 820.119 0.106075
\(392\) 2300.73 1328.33i 0.296440 0.171150i
\(393\) 0 0
\(394\) 494.234 856.039i 0.0631959 0.109458i
\(395\) 12068.8i 1.53734i
\(396\) 0 0
\(397\) −12298.0 7100.26i −1.55471 0.897612i −0.997748 0.0670737i \(-0.978634\pi\)
−0.556962 0.830538i \(-0.688033\pi\)
\(398\) 6555.48i 0.825620i
\(399\) 0 0
\(400\) −1531.67 2652.93i −0.191459 0.331617i
\(401\) −10978.1 + 6338.19i −1.36713 + 0.789313i −0.990561 0.137076i \(-0.956230\pi\)
−0.376569 + 0.926389i \(0.622896\pi\)
\(402\) 0 0
\(403\) −6329.10 + 12989.4i −0.782319 + 1.60558i
\(404\) −8629.56 −1.06271
\(405\) 0 0
\(406\) 9983.01 + 17291.1i 1.22032 + 2.11365i
\(407\) −881.026 + 1525.98i −0.107299 + 0.185848i
\(408\) 0 0
\(409\) −1328.20 766.838i −0.160576 0.0927083i 0.417559 0.908650i \(-0.362886\pi\)
−0.578134 + 0.815942i \(0.696219\pi\)
\(410\) 2296.19 + 1325.71i 0.276587 + 0.159688i
\(411\) 0 0
\(412\) −2858.19 + 4950.53i −0.341779 + 0.591978i
\(413\) 9278.15 + 16070.2i 1.10544 + 1.91468i
\(414\) 0 0
\(415\) 17478.3 2.06741
\(416\) 6812.28 + 10091.1i 0.802883 + 1.18932i
\(417\) 0 0
\(418\) 3901.02 2252.25i 0.456471 0.263544i
\(419\) −1082.95 1875.72i −0.126266 0.218699i 0.795961 0.605348i \(-0.206966\pi\)
−0.922227 + 0.386649i \(0.873633\pi\)
\(420\) 0 0
\(421\) 734.575i 0.0850380i 0.999096 + 0.0425190i \(0.0135383\pi\)
−0.999096 + 0.0425190i \(0.986462\pi\)
\(422\) 6687.43 + 3860.99i 0.771419 + 0.445379i
\(423\) 0 0
\(424\) 1807.79i 0.207062i
\(425\) −1201.43 + 2080.93i −0.137124 + 0.237506i
\(426\) 0 0
\(427\) −14730.0 + 8504.40i −1.66941 + 0.963833i
\(428\) −13034.9 −1.47212
\(429\) 0 0
\(430\) −18961.8 −2.12656
\(431\) 11872.6 6854.66i 1.32688 0.766073i 0.342061 0.939678i \(-0.388875\pi\)
0.984815 + 0.173605i \(0.0555416\pi\)
\(432\) 0 0
\(433\) 5024.97 8703.50i 0.557701 0.965967i −0.439987 0.898004i \(-0.645017\pi\)
0.997688 0.0679624i \(-0.0216498\pi\)
\(434\) 39938.2i 4.41727i
\(435\) 0 0
\(436\) −2580.54 1489.88i −0.283453 0.163652i
\(437\) 512.850i 0.0561395i
\(438\) 0 0
\(439\) −4066.73 7043.79i −0.442129 0.765790i 0.555718 0.831371i \(-0.312443\pi\)
−0.997847 + 0.0655807i \(0.979110\pi\)
\(440\) −1943.77 + 1122.24i −0.210604 + 0.121592i
\(441\) 0 0
\(442\) 3651.98 7495.09i 0.393003 0.806572i
\(443\) 2370.78 0.254264 0.127132 0.991886i \(-0.459423\pi\)
0.127132 + 0.991886i \(0.459423\pi\)
\(444\) 0 0
\(445\) 6217.40 + 10768.9i 0.662321 + 1.14717i
\(446\) −115.711 + 200.418i −0.0122850 + 0.0212782i
\(447\) 0 0
\(448\) −17170.9 9913.60i −1.81082 1.04548i
\(449\) −11191.8 6461.60i −1.17634 0.679158i −0.221172 0.975235i \(-0.570988\pi\)
−0.955164 + 0.296077i \(0.904322\pi\)
\(450\) 0 0
\(451\) −968.636 + 1677.73i −0.101134 + 0.175169i
\(452\) −3128.42 5418.58i −0.325550 0.563869i
\(453\) 0 0
\(454\) −2751.72 −0.284459
\(455\) −16409.0 + 11077.3i −1.69070 + 1.14135i
\(456\) 0 0
\(457\) 7275.71 4200.63i 0.744734 0.429972i −0.0790543 0.996870i \(-0.525190\pi\)
0.823788 + 0.566898i \(0.191857\pi\)
\(458\) −1491.12 2582.70i −0.152130 0.263497i
\(459\) 0 0
\(460\) 2299.85i 0.233111i
\(461\) 15265.7 + 8813.67i 1.54229 + 0.890441i 0.998694 + 0.0510940i \(0.0162708\pi\)
0.543596 + 0.839347i \(0.317063\pi\)
\(462\) 0 0
\(463\) 5461.81i 0.548233i 0.961697 + 0.274116i \(0.0883853\pi\)
−0.961697 + 0.274116i \(0.911615\pi\)
\(464\) 4238.06 7340.54i 0.424024 0.734431i
\(465\) 0 0
\(466\) −983.558 + 567.858i −0.0977735 + 0.0564496i
\(467\) 8262.19 0.818691 0.409345 0.912379i \(-0.365757\pi\)
0.409345 + 0.912379i \(0.365757\pi\)
\(468\) 0 0
\(469\) 7237.89 0.712611
\(470\) 6406.29 3698.68i 0.628724 0.362994i
\(471\) 0 0
\(472\) −1217.46 + 2108.70i −0.118725 + 0.205637i
\(473\) 13854.6i 1.34680i
\(474\) 0 0
\(475\) −1301.28 751.297i −0.125699 0.0725723i
\(476\) 12200.3i 1.17479i
\(477\) 0 0
\(478\) 3152.92 + 5461.02i 0.301697 + 0.522555i
\(479\) −1364.74 + 787.935i −0.130181 + 0.0751601i −0.563676 0.825996i \(-0.690613\pi\)
0.433495 + 0.901156i \(0.357280\pi\)
\(480\) 0 0
\(481\) −2034.46 + 143.060i −0.192855 + 0.0135613i
\(482\) 4022.20 0.380095
\(483\) 0 0
\(484\) −1390.23 2407.95i −0.130563 0.226141i
\(485\) 10488.4 18166.4i 0.981963 1.70081i
\(486\) 0 0
\(487\) 10908.2 + 6297.84i 1.01498 + 0.586001i 0.912647 0.408749i \(-0.134035\pi\)
0.102337 + 0.994750i \(0.467368\pi\)
\(488\) −1932.84 1115.93i −0.179294 0.103516i
\(489\) 0 0
\(490\) 17855.9 30927.3i 1.64622 2.85133i
\(491\) 535.606 + 927.697i 0.0492293 + 0.0852676i 0.889590 0.456760i \(-0.150990\pi\)
−0.840361 + 0.542028i \(0.817657\pi\)
\(492\) 0 0
\(493\) −6648.59 −0.607378
\(494\) 4686.96 + 2283.72i 0.426875 + 0.207995i
\(495\) 0 0
\(496\) −14683.3 + 8477.44i −1.32924 + 0.767436i
\(497\) −7060.68 12229.5i −0.637253 1.10376i
\(498\) 0 0
\(499\) 1422.30i 0.127597i −0.997963 0.0637985i \(-0.979678\pi\)
0.997963 0.0637985i \(-0.0203215\pi\)
\(500\) −7261.06 4192.17i −0.649449 0.374959i
\(501\) 0 0
\(502\) 7727.28i 0.687022i
\(503\) −4674.67 + 8096.76i −0.414380 + 0.717727i −0.995363 0.0961884i \(-0.969335\pi\)
0.580983 + 0.813916i \(0.302668\pi\)
\(504\) 0 0
\(505\) −11162.3 + 6444.54i −0.983593 + 0.567878i
\(506\) 3174.10 0.278866
\(507\) 0 0
\(508\) 2224.39 0.194274
\(509\) −11896.0 + 6868.15i −1.03591 + 0.598086i −0.918673 0.395018i \(-0.870738\pi\)
−0.117241 + 0.993103i \(0.537405\pi\)
\(510\) 0 0
\(511\) 6122.73 10604.9i 0.530046 0.918067i
\(512\) 16100.7i 1.38976i
\(513\) 0 0
\(514\) 6492.23 + 3748.29i 0.557120 + 0.321654i
\(515\) 8537.96i 0.730538i
\(516\) 0 0
\(517\) 2702.47 + 4680.81i 0.229892 + 0.398185i
\(518\) 4881.94 2818.59i 0.414093 0.239076i
\(519\) 0 0
\(520\) −2335.38 1137.92i −0.196949 0.0959632i
\(521\) −11052.3 −0.929386 −0.464693 0.885472i \(-0.653835\pi\)
−0.464693 + 0.885472i \(0.653835\pi\)
\(522\) 0 0
\(523\) −3238.52 5609.28i −0.270766 0.468980i 0.698292 0.715813i \(-0.253944\pi\)
−0.969058 + 0.246832i \(0.920610\pi\)
\(524\) −2125.09 + 3680.77i −0.177166 + 0.306861i
\(525\) 0 0
\(526\) 2405.94 + 1389.07i 0.199437 + 0.115145i
\(527\) 11517.5 + 6649.61i 0.952009 + 0.549643i
\(528\) 0 0
\(529\) 5902.81 10224.0i 0.485149 0.840303i
\(530\) −12150.5 21045.3i −0.995819 1.72481i
\(531\) 0 0
\(532\) −7629.27 −0.621750
\(533\) −2236.77 + 157.286i −0.181773 + 0.0127820i
\(534\) 0 0
\(535\) −16860.6 + 9734.45i −1.36252 + 0.786649i
\(536\) 474.869 + 822.498i 0.0382672 + 0.0662808i
\(537\) 0 0
\(538\) 13838.8i 1.10898i
\(539\) 22597.3 + 13046.5i 1.80581 + 1.04259i
\(540\) 0 0
\(541\) 18341.5i 1.45761i −0.684723 0.728803i \(-0.740077\pi\)
0.684723 0.728803i \(-0.259923\pi\)
\(542\) −18379.9 + 31834.9i −1.45661 + 2.52292i
\(543\) 0 0
\(544\) 9704.88 5603.11i 0.764877 0.441602i
\(545\) −4450.55 −0.349799
\(546\) 0 0
\(547\) −18943.1 −1.48071 −0.740356 0.672215i \(-0.765343\pi\)
−0.740356 + 0.672215i \(0.765343\pi\)
\(548\) 14268.9 8238.14i 1.11229 0.642182i
\(549\) 0 0
\(550\) −4649.88 + 8053.82i −0.360493 + 0.624393i
\(551\) 4157.61i 0.321452i
\(552\) 0 0
\(553\) 24431.6 + 14105.6i 1.87873 + 1.08469i
\(554\) 16563.8i 1.27027i
\(555\) 0 0
\(556\) −450.000 779.423i −0.0343242 0.0594512i
\(557\) 359.861 207.766i 0.0273749 0.0158049i −0.486250 0.873820i \(-0.661636\pi\)
0.513625 + 0.858015i \(0.328302\pi\)
\(558\) 0 0
\(559\) 13290.9 8972.38i 1.00563 0.678875i
\(560\) −23231.1 −1.75303
\(561\) 0 0
\(562\) 3795.56 + 6574.10i 0.284886 + 0.493437i
\(563\) −9145.90 + 15841.2i −0.684643 + 1.18584i 0.288907 + 0.957357i \(0.406708\pi\)
−0.973549 + 0.228478i \(0.926625\pi\)
\(564\) 0 0
\(565\) −8093.17 4672.59i −0.602623 0.347925i
\(566\) 17315.8 + 9997.29i 1.28593 + 0.742434i
\(567\) 0 0
\(568\) 926.486 1604.72i 0.0684410 0.118543i
\(569\) −2173.73 3765.02i −0.160154 0.277395i 0.774770 0.632244i \(-0.217866\pi\)
−0.934924 + 0.354848i \(0.884532\pi\)
\(570\) 0 0
\(571\) 16756.0 1.22805 0.614024 0.789288i \(-0.289550\pi\)
0.614024 + 0.789288i \(0.289550\pi\)
\(572\) 7482.84 15357.3i 0.546981 1.12259i
\(573\) 0 0
\(574\) 5367.40 3098.87i 0.390298 0.225339i
\(575\) −529.401 916.950i −0.0383958 0.0665034i
\(576\) 0 0
\(577\) 19974.7i 1.44117i 0.693364 + 0.720587i \(0.256128\pi\)
−0.693364 + 0.720587i \(0.743872\pi\)
\(578\) 10897.2 + 6291.48i 0.784191 + 0.452753i
\(579\) 0 0
\(580\) 18644.6i 1.33478i
\(581\) 20428.0 35382.4i 1.45869 2.52652i
\(582\) 0 0
\(583\) 15376.9 8877.86i 1.09236 0.630675i
\(584\) 1606.82 0.113854
\(585\) 0 0
\(586\) 5829.47 0.410944
\(587\) 13638.7 7874.33i 0.958996 0.553677i 0.0631321 0.998005i \(-0.479891\pi\)
0.895864 + 0.444329i \(0.146558\pi\)
\(588\) 0 0
\(589\) −4158.25 + 7202.30i −0.290896 + 0.503846i
\(590\) 32731.0i 2.28392i
\(591\) 0 0
\(592\) −2072.52 1196.57i −0.143885 0.0830721i
\(593\) 13318.4i 0.922297i 0.887323 + 0.461148i \(0.152562\pi\)
−0.887323 + 0.461148i \(0.847438\pi\)
\(594\) 0 0
\(595\) 9111.13 + 15780.9i 0.627765 + 1.08732i
\(596\) 1165.68 673.006i 0.0801143 0.0462540i
\(597\) 0 0
\(598\) 2055.58 + 3044.96i 0.140567 + 0.208224i
\(599\) −2970.80 −0.202644 −0.101322 0.994854i \(-0.532307\pi\)
−0.101322 + 0.994854i \(0.532307\pi\)
\(600\) 0 0
\(601\) −5316.31 9208.13i −0.360827 0.624971i 0.627270 0.778802i \(-0.284172\pi\)
−0.988097 + 0.153831i \(0.950839\pi\)
\(602\) −22161.9 + 38385.5i −1.50042 + 2.59880i
\(603\) 0 0
\(604\) 6235.63 + 3600.14i 0.420073 + 0.242529i
\(605\) −3596.50 2076.44i −0.241684 0.139536i
\(606\) 0 0
\(607\) −5793.94 + 10035.4i −0.387428 + 0.671045i −0.992103 0.125428i \(-0.959970\pi\)
0.604675 + 0.796472i \(0.293303\pi\)
\(608\) 3503.83 + 6068.82i 0.233716 + 0.404808i
\(609\) 0 0
\(610\) −30001.4 −1.99135
\(611\) −2740.22 + 5623.85i −0.181436 + 0.372368i
\(612\) 0 0
\(613\) 18006.7 10396.2i 1.18643 0.684988i 0.228939 0.973441i \(-0.426474\pi\)
0.957494 + 0.288453i \(0.0931409\pi\)
\(614\) 9536.00 + 16516.8i 0.626778 + 1.08561i
\(615\) 0 0
\(616\) 5246.51i 0.343162i
\(617\) −1353.40 781.388i −0.0883079 0.0509846i 0.455196 0.890391i \(-0.349569\pi\)
−0.543504 + 0.839407i \(0.682903\pi\)
\(618\) 0 0
\(619\) 758.406i 0.0492454i −0.999697 0.0246227i \(-0.992162\pi\)
0.999697 0.0246227i \(-0.00783844\pi\)
\(620\) 18647.5 32298.4i 1.20790 2.09215i
\(621\) 0 0
\(622\) −21641.4 + 12494.6i −1.39508 + 0.805450i
\(623\) 29066.7 1.86923
\(624\) 0 0
\(625\) −19485.0 −1.24704
\(626\) 3463.40 1999.59i 0.221127 0.127668i
\(627\) 0 0
\(628\) −12177.7 + 21092.4i −0.773795 + 1.34025i
\(629\) 1877.15i 0.118994i
\(630\) 0 0
\(631\) −12354.0 7132.59i −0.779406 0.449990i 0.0568136 0.998385i \(-0.481906\pi\)
−0.836220 + 0.548394i \(0.815239\pi\)
\(632\) 3701.81i 0.232990i
\(633\) 0 0
\(634\) −18021.3 31213.9i −1.12889 1.95530i
\(635\) 2877.23 1661.17i 0.179810 0.103813i
\(636\) 0 0
\(637\) 2118.48 + 30127.0i 0.131770 + 1.87390i
\(638\) −25732.0 −1.59677
\(639\) 0 0
\(640\) −3519.44 6095.85i −0.217372 0.376500i
\(641\) −1992.82 + 3451.67i −0.122795 + 0.212688i −0.920869 0.389872i \(-0.872519\pi\)
0.798074 + 0.602560i \(0.205853\pi\)
\(642\) 0 0
\(643\) 7063.78 + 4078.28i 0.433232 + 0.250127i 0.700723 0.713434i \(-0.252861\pi\)
−0.267490 + 0.963561i \(0.586194\pi\)
\(644\) −4655.73 2687.98i −0.284878 0.164474i
\(645\) 0 0
\(646\) 2399.37 4155.83i 0.146133 0.253110i
\(647\) −5639.62 9768.11i −0.342684 0.593546i 0.642246 0.766498i \(-0.278003\pi\)
−0.984930 + 0.172953i \(0.944669\pi\)
\(648\) 0 0
\(649\) −23915.2 −1.44646
\(650\) −10737.5 + 755.041i −0.647935 + 0.0455617i
\(651\) 0 0
\(652\) 28669.1 16552.1i 1.72204 0.994219i
\(653\) 3282.88 + 5686.11i 0.196736 + 0.340757i 0.947468 0.319850i \(-0.103632\pi\)
−0.750732 + 0.660607i \(0.770299\pi\)
\(654\) 0 0
\(655\) 6348.06i 0.378686i
\(656\) −2278.61 1315.56i −0.135617 0.0782986i
\(657\) 0 0
\(658\) 17291.5i 1.02446i
\(659\) 2399.67 4156.36i 0.141848 0.245688i −0.786344 0.617788i \(-0.788029\pi\)
0.928193 + 0.372100i \(0.121362\pi\)
\(660\) 0 0
\(661\) −13504.5 + 7796.80i −0.794648 + 0.458790i −0.841596 0.540107i \(-0.818384\pi\)
0.0469482 + 0.998897i \(0.485050\pi\)
\(662\) −28811.3 −1.69151
\(663\) 0 0
\(664\) 5361.03 0.313326
\(665\) −9868.41 + 5697.53i −0.575459 + 0.332242i
\(666\) 0 0
\(667\) 1464.83 2537.16i 0.0850351 0.147285i
\(668\) 29008.0i 1.68017i
\(669\) 0 0
\(670\) 11056.3 + 6383.37i 0.637526 + 0.368076i
\(671\) 21920.8i 1.26116i
\(672\) 0 0
\(673\) −1102.77 1910.06i −0.0631630 0.109402i 0.832715 0.553702i \(-0.186785\pi\)
−0.895878 + 0.444301i \(0.853452\pi\)
\(674\) 14842.0 8569.03i 0.848208 0.489713i
\(675\) 0 0
\(676\) 19578.4 2767.13i 1.11393 0.157438i
\(677\) 15046.4 0.854182 0.427091 0.904209i \(-0.359538\pi\)
0.427091 + 0.904209i \(0.359538\pi\)
\(678\) 0 0
\(679\) −24516.8 42464.4i −1.38567 2.40005i
\(680\) −1195.54 + 2070.74i −0.0674219 + 0.116778i
\(681\) 0 0
\(682\) 44576.0 + 25736.0i 2.50279 + 1.44499i
\(683\) −26528.5 15316.3i −1.48622 0.858068i −0.486340 0.873770i \(-0.661668\pi\)
−0.999877 + 0.0157020i \(0.995002\pi\)
\(684\) 0 0
\(685\) 12304.5 21311.9i 0.686320 1.18874i
\(686\) −19519.8 33809.3i −1.08640 1.88170i
\(687\) 0 0
\(688\) 18816.7 1.04270
\(689\) 18474.9 + 9001.90i 1.02153 + 0.497743i
\(690\) 0 0
\(691\) 1884.22 1087.86i 0.103733 0.0598901i −0.447236 0.894416i \(-0.647592\pi\)
0.550969 + 0.834526i \(0.314258\pi\)
\(692\) −12102.9 20962.9i −0.664862 1.15157i
\(693\) 0 0
\(694\) 1288.52i 0.0704780i
\(695\) −1164.14 672.118i −0.0635373 0.0366833i
\(696\) 0 0
\(697\) 2063.82i 0.112156i
\(698\) 9191.95 15920.9i 0.498453 0.863346i
\(699\) 0 0
\(700\) 13640.7 7875.49i 0.736531 0.425236i
\(701\) −32718.2 −1.76284 −0.881419 0.472335i \(-0.843411\pi\)
−0.881419 + 0.472335i \(0.843411\pi\)
\(702\) 0 0
\(703\) −1173.85 −0.0629768
\(704\) 22129.6 12776.5i 1.18472 0.683997i
\(705\) 0 0
\(706\) 4636.79 8031.15i 0.247178 0.428125i
\(707\) 30128.6i 1.60269i
\(708\) 0 0
\(709\) −21840.9 12609.8i −1.15691 0.667945i −0.206352 0.978478i \(-0.566159\pi\)
−0.950563 + 0.310533i \(0.899492\pi\)
\(710\) 24908.3i 1.31661i
\(711\) 0 0
\(712\) 1907.03 + 3303.07i 0.100378 + 0.173859i
\(713\) −5075.10 + 2930.11i −0.266569 + 0.153904i
\(714\) 0 0
\(715\) −1789.79 25452.7i −0.0936146 1.33130i
\(716\) 13716.4 0.715929
\(717\) 0 0
\(718\) −16168.3 28004.4i −0.840385 1.45559i
\(719\) 17733.1 30714.6i 0.919796 1.59313i 0.120071 0.992765i \(-0.461688\pi\)
0.799724 0.600368i \(-0.204979\pi\)
\(720\) 0 0
\(721\) 17283.9 + 9978.85i 0.892767 + 0.515439i
\(722\) −21892.7 12639.8i −1.12848 0.651529i
\(723\) 0 0
\(724\) −2145.97 + 3716.92i −0.110158 + 0.190799i
\(725\) 4291.78 + 7433.59i 0.219852 + 0.380795i
\(726\) 0 0
\(727\) 14262.2 0.727588 0.363794 0.931479i \(-0.381481\pi\)
0.363794 + 0.931479i \(0.381481\pi\)
\(728\) −5033.05 + 3397.69i −0.256233 + 0.172976i
\(729\) 0 0
\(730\) 18705.7 10799.7i 0.948396 0.547557i
\(731\) −7379.80 12782.2i −0.373395 0.646739i
\(732\) 0 0
\(733\) 16022.5i 0.807371i 0.914898 + 0.403685i \(0.132271\pi\)
−0.914898 + 0.403685i \(0.867729\pi\)
\(734\) −23781.8 13730.4i −1.19592 0.690463i
\(735\) 0 0
\(736\) 4937.96i 0.247304i
\(737\) −4664.05 + 8078.38i −0.233111 + 0.403760i
\(738\) 0 0
\(739\) −3287.61 + 1898.11i −0.163649 + 0.0944830i −0.579588 0.814910i \(-0.696786\pi\)
0.415939 + 0.909393i \(0.363453\pi\)
\(740\) 5264.09 0.261502
\(741\) 0 0
\(742\) −56804.3 −2.81044
\(743\) 26266.0 15164.7i 1.29691 0.748772i 0.317042 0.948412i \(-0.397310\pi\)
0.979869 + 0.199639i \(0.0639771\pi\)
\(744\) 0 0
\(745\) 1005.20 1741.05i 0.0494331 0.0856206i
\(746\) 152.502i 0.00748460i
\(747\) 0 0
\(748\) −13617.0 7861.78i −0.665624 0.384298i
\(749\) 45509.1i 2.22011i
\(750\) 0 0
\(751\) 10775.9 + 18664.5i 0.523595 + 0.906893i 0.999623 + 0.0274629i \(0.00874280\pi\)
−0.476028 + 0.879430i \(0.657924\pi\)
\(752\) −6357.25 + 3670.36i −0.308278 + 0.177984i
\(753\) 0 0
\(754\) −16664.3 24685.1i −0.804877 1.19228i
\(755\) 10754.3 0.518397
\(756\) 0 0
\(757\) 10208.8 + 17682.2i 0.490153 + 0.848970i 0.999936 0.0113335i \(-0.00360764\pi\)
−0.509783 + 0.860303i \(0.670274\pi\)
\(758\) 24903.3 43133.7i 1.19331 2.06687i
\(759\) 0 0
\(760\) −1294.91 747.616i −0.0618043 0.0356828i
\(761\) 27171.9 + 15687.7i 1.29432 + 0.747278i 0.979417 0.201845i \(-0.0646937\pi\)
0.314906 + 0.949123i \(0.398027\pi\)
\(762\) 0 0
\(763\) −5201.64 + 9009.50i −0.246805 + 0.427478i
\(764\) 6163.84 + 10676.1i 0.291885 + 0.505559i
\(765\) 0 0
\(766\) −43570.5 −2.05518
\(767\) −15487.7 22942.2i −0.729111 1.08004i
\(768\) 0 0
\(769\) 10784.3 6226.33i 0.505712 0.291973i −0.225357 0.974276i \(-0.572355\pi\)
0.731069 + 0.682303i \(0.239022\pi\)
\(770\) 35262.8 + 61076.9i 1.65037 + 2.85852i
\(771\) 0 0
\(772\) 19302.5i 0.899885i
\(773\) −32432.4 18724.9i −1.50907 0.871264i −0.999944 0.0105740i \(-0.996634\pi\)
−0.509129 0.860690i \(-0.670033\pi\)
\(774\) 0 0
\(775\) 17169.8i 0.795815i
\(776\) 3217.04 5572.08i 0.148821 0.257765i
\(777\) 0 0
\(778\) −34841.2 + 20115.6i −1.60555 + 0.926965i
\(779\) −1290.58 −0.0593580
\(780\) 0 0
\(781\) 18199.5 0.833839
\(782\) 2928.41 1690.72i 0.133913 0.0773145i
\(783\) 0