Properties

Label 117.4.q.d.82.2
Level $117$
Weight $4$
Character 117.82
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 82.2
Root \(3.57071 + 2.06155i\) of defining polynomial
Character \(\chi\) \(=\) 117.82
Dual form 117.4.q.d.10.2

$q$-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 \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

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

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 0.973546 0.228493i \(-0.0733797\pi\)
0.288892 + 0.957362i \(0.406713\pi\)
\(3\) 0 0
\(4\) 4.50000 + 7.79423i 0.562500 + 0.974279i
\(5\) 13.4424i 1.20232i 0.799128 + 0.601161i \(0.205295\pi\)
−0.799128 + 0.601161i \(0.794705\pi\)
\(6\) 0 0
\(7\) −27.2121 + 15.7109i −1.46932 + 0.848311i −0.999408 0.0344037i \(-0.989047\pi\)
−0.469910 + 0.882715i \(0.655713\pi\)
\(8\) 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 0.896571 0.442901i \(-0.146051\pi\)
0.0647219 + 0.997903i \(0.479384\pi\)
\(12\) 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 0.977869 0.209219i \(-0.0670923\pi\)
−0.670124 + 0.742249i \(0.733759\pi\)
\(18\) 0 0
\(19\) 23.3636 13.4890i 0.282104 0.162873i −0.352272 0.935898i \(-0.614591\pi\)
0.634375 + 0.773025i \(0.281257\pi\)
\(20\) −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 −0.819719 0.572766i \(-0.805870\pi\)
0.905890 + 0.423514i \(0.139204\pi\)
\(24\) 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 −0.999971 0.00759297i \(-0.997583\pi\)
0.506561 + 0.862204i \(0.330916\pi\)
\(30\) 0 0
\(31\) 308.270i 1.78603i −0.450025 0.893016i \(-0.648585\pi\)
0.450025 0.893016i \(-0.351415\pi\)
\(32\) 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 0.413944 0.910303i \(-0.364151\pi\)
−0.581373 + 0.813637i \(0.697484\pi\)
\(38\) 111.233 0.474851
\(39\) 0 0
\(40\) −55.4243 −0.219084
\(41\) −41.4293 23.9192i −0.157809 0.0911110i 0.419016 0.907979i \(-0.362375\pi\)
−0.576825 + 0.816868i \(0.695708\pi\)
\(42\) 0 0
\(43\) 171.061 + 296.286i 0.606663 + 1.05077i 0.991786 + 0.127906i \(0.0408256\pi\)
−0.385123 + 0.922865i \(0.625841\pi\)
\(44\) 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 \(-0.933594\pi\)
0.978318 0.207109i \(-0.0664055\pi\)
\(48\) 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 −0.943564 0.331190i \(-0.892550\pi\)
−0.184963 + 0.982746i \(0.559216\pi\)
\(60\) 0 0
\(61\) 270.652 + 468.783i 0.568089 + 0.983960i 0.996755 + 0.0804965i \(0.0256506\pi\)
−0.428665 + 0.903463i \(0.641016\pi\)
\(62\) 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 0.306977 0.951717i \(-0.400683\pi\)
−0.670723 + 0.741708i \(0.734016\pi\)
\(68\) −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 −0.138110 0.990417i \(-0.544103\pi\)
0.788671 + 0.614816i \(0.210770\pi\)
\(72\) 0 0
\(73\) 389.711i 0.624826i −0.949946 0.312413i \(-0.898863\pi\)
0.949946 0.312413i \(-0.101137\pi\)
\(74\) −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 \(-0.670614\pi\)
0.510700 0.859759i \(-0.329386\pi\)
\(84\) 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 −0.0597703 0.998212i \(-0.519037\pi\)
−0.894362 + 0.447344i \(0.852370\pi\)
\(90\) 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 0.418787 0.908085i \(-0.362455\pi\)
0.995818 + 0.0913623i \(0.0291221\pi\)
\(98\) 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 −0.999498 0.0316752i \(-0.989916\pi\)
0.527181 + 0.849753i \(0.323249\pi\)
\(102\) 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 0.327800 + 0.944747i \(0.393693\pi\)
−0.982075 + 0.188490i \(0.939641\pi\)
\(108\) 0 0
\(109\) 331.084i 0.290937i 0.989363 + 0.145468i \(0.0464689\pi\)
−0.989363 + 0.145468i \(0.953531\pi\)
\(110\) −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 0.973661 0.227999i \(-0.0732184\pi\)
−0.684284 + 0.729216i \(0.739885\pi\)
\(114\) 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 −0.819619 0.572909i \(-0.805815\pi\)
0.905963 + 0.423357i \(0.139148\pi\)
\(128\) 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 0.0838175 0.996481i \(-0.473289\pi\)
0.904887 + 0.425652i \(0.139955\pi\)
\(138\) 0 0
\(139\) 50.0000 + 86.6025i 0.0305104 + 0.0528456i 0.880877 0.473344i \(-0.156953\pi\)
−0.850367 + 0.526190i \(0.823620\pi\)
\(140\) 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 −0.463971 0.885850i \(-0.653576\pi\)
0.535184 + 0.844736i \(0.320242\pi\)
\(150\) 0 0
\(151\) 800.032i 0.431163i −0.976486 0.215582i \(-0.930835\pi\)
0.976486 0.215582i \(-0.0691647\pi\)
\(152\) 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 0.531371 0.847139i \(-0.321677\pi\)
0.999330 0.0366108i \(-0.0116562\pi\)
\(164\) 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 −0.314140 0.949377i \(-0.601716\pi\)
−0.979254 + 0.202635i \(0.935050\pi\)
\(168\) 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 0.994100 + 0.108471i \(0.0345954\pi\)
−0.403111 + 0.915151i \(0.632071\pi\)
\(174\) 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 −0.661920 0.749574i \(-0.730258\pi\)
0.980111 + 0.198452i \(0.0635915\pi\)
\(180\) 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 0.706642 0.707571i \(-0.250209\pi\)
−0.966096 + 0.258185i \(0.916876\pi\)
\(192\) 0 0
\(193\) 1857.38 + 1072.36i 0.692732 + 0.399949i 0.804635 0.593770i \(-0.202361\pi\)
−0.111903 + 0.993719i \(0.535695\pi\)
\(194\) 6434.08 2.38113
\(195\) 0 0
\(196\) 5799.01 2.11334
\(197\) 207.620 + 119.869i 0.0750879 + 0.0433520i 0.537074 0.843535i \(-0.319530\pi\)
−0.461986 + 0.886887i \(0.652863\pi\)
\(198\) 0 0
\(199\) −794.969 1376.93i −0.283185 0.490491i 0.688982 0.724778i \(-0.258058\pi\)
−0.972167 + 0.234287i \(0.924724\pi\)
\(200\) 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 −0.671851 0.740686i \(-0.734501\pi\)
0.977379 + 0.211497i \(0.0678339\pi\)
\(212\) 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 0.492684 0.870208i \(-0.336016\pi\)
−0.507281 + 0.861781i \(0.669349\pi\)
\(224\) −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 −0.582111 0.813109i \(-0.697773\pi\)
0.413117 + 0.910678i \(0.364440\pi\)
\(228\) 0 0
\(229\) 723.299i 0.208720i 0.994540 + 0.104360i \(0.0332795\pi\)
−0.994540 + 0.104360i \(0.966721\pi\)
\(230\) 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 \(-0.933642\pi\)
0.978349 0.206963i \(-0.0663579\pi\)
\(240\) 0 0
\(241\) 844.830 487.763i 0.225810 0.130372i −0.382827 0.923820i \(-0.625050\pi\)
0.608638 + 0.793448i \(0.291716\pi\)
\(242\) 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 0.959460 0.281843i \(-0.0909458\pi\)
−0.723814 + 0.689995i \(0.757613\pi\)
\(252\) 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 −0.734354 0.678767i \(-0.762515\pi\)
0.955006 + 0.296586i \(0.0958480\pi\)
\(258\) 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 −0.823825 0.566844i \(-0.808164\pi\)
0.902814 + 0.430031i \(0.141497\pi\)
\(264\) 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 0.610738 0.791833i \(-0.290873\pi\)
−0.991116 + 0.132998i \(0.957540\pi\)
\(270\) 0 0
\(271\) −7721.09 4457.77i −1.73071 0.999227i −0.885013 0.465567i \(-0.845850\pi\)
−0.845699 0.533660i \(-0.820816\pi\)
\(272\) 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 0.997352 0.0727208i \(-0.0231682\pi\)
−0.561654 + 0.827372i \(0.689835\pi\)
\(278\) 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 \(-0.937390\pi\)
0.980718 0.195430i \(-0.0626103\pi\)
\(282\) 0 0
\(283\) 2424.70 4199.70i 0.509305 0.882143i −0.490637 0.871364i \(-0.663236\pi\)
0.999942 0.0107784i \(-0.00343094\pi\)
\(284\) 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 −0.372940 0.927856i \(-0.621650\pi\)
0.617077 + 0.786903i \(0.288317\pi\)
\(294\) 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 \(-0.858526\pi\)
0.902845 0.429966i \(-0.141474\pi\)
\(308\) −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 \(0.281955\pi\)
−0.632679 + 0.774414i \(0.718045\pi\)
\(318\) 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 −0.909697 0.415273i \(-0.863686\pi\)
−0.0952114 + 0.995457i \(0.530353\pi\)
\(332\) 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 0.853685 0.520789i \(-0.174362\pi\)
−0.877859 + 0.478919i \(0.841029\pi\)
\(348\) 0 0
\(349\) 3861.39 + 2229.37i 0.592251 + 0.341936i 0.765987 0.642856i \(-0.222251\pi\)
−0.173736 + 0.984792i \(0.555584\pi\)
\(350\) 7215.88 1.10201
\(351\) 0 0
\(352\) 10519.1 1.59281
\(353\) 1947.84 + 1124.59i 0.293692 + 0.169563i 0.639605 0.768703i \(-0.279098\pi\)
−0.345914 + 0.938266i \(0.612431\pi\)
\(354\) 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 \(0.195582\pi\)
−0.817098 + 0.576499i \(0.804418\pi\)
\(360\) 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 −0.999545 0.0301597i \(-0.990398\pi\)
0.525892 + 0.850552i \(0.323732\pi\)
\(368\) −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 0.867306 0.497775i \(-0.165850\pi\)
−0.864739 + 0.502222i \(0.832516\pi\)
\(374\) −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 0.996111 0.0881092i \(-0.0280825\pi\)
0.421751 + 0.906712i \(0.361416\pi\)
\(380\) −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 −0.965122 0.261801i \(-0.915684\pi\)
−0.255835 + 0.966721i \(0.582350\pi\)
\(384\) 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 −0.556962 + 0.830538i \(0.688033\pi\)
−0.997748 + 0.0670737i \(0.978634\pi\)
\(398\) 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 −0.376569 0.926389i \(-0.622896\pi\)
−0.990561 + 0.137076i \(0.956230\pi\)
\(402\) 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 −0.578134 0.815942i \(-0.696219\pi\)
0.417559 + 0.908650i \(0.362886\pi\)
\(410\) 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 −0.922227 0.386649i \(-0.873633\pi\)
0.795961 + 0.605348i \(0.206966\pi\)
\(420\) 0 0
\(421\) 734.575i 0.0850380i −0.999096 0.0425190i \(-0.986462\pi\)
0.999096 0.0425190i \(-0.0135383\pi\)
\(422\) 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 0.984815 0.173605i \(-0.0555416\pi\)
0.342061 + 0.939678i \(0.388875\pi\)
\(432\) 0 0
\(433\) 5024.97 + 8703.50i 0.557701 + 0.965967i 0.997688 + 0.0679624i \(0.0216498\pi\)
−0.439987 + 0.898004i \(0.645017\pi\)
\(434\) 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 −0.997847 0.0655807i \(-0.979110\pi\)
0.555718 + 0.831371i \(0.312443\pi\)
\(440\) −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 −0.955164 0.296077i \(-0.904322\pi\)
−0.221172 + 0.975235i \(0.570988\pi\)
\(450\) 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 0.823788 0.566898i \(-0.191857\pi\)
−0.0790543 + 0.996870i \(0.525190\pi\)
\(458\) −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 0.543596 0.839347i \(-0.317063\pi\)
0.998694 0.0510940i \(-0.0162708\pi\)
\(462\) 0 0
\(463\) 5461.81i 0.548233i −0.961697 0.274116i \(-0.911615\pi\)
0.961697 0.274116i \(-0.0883853\pi\)
\(464\) 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 0.433495 0.901156i \(-0.357280\pi\)
−0.563676 + 0.825996i \(0.690613\pi\)
\(480\) 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 0.102337 0.994750i \(-0.467368\pi\)
0.912647 + 0.408749i \(0.134035\pi\)
\(488\) −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 −0.840361 0.542028i \(-0.817657\pi\)
0.889590 + 0.456760i \(0.150990\pi\)
\(492\) 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 \(0.0203215\pi\)
−0.997963 + 0.0637985i \(0.979678\pi\)
\(500\) −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 0.580983 0.813916i \(-0.302668\pi\)
−0.995363 + 0.0961884i \(0.969335\pi\)
\(504\) 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 −0.117241 0.993103i \(-0.537405\pi\)
−0.918673 + 0.395018i \(0.870738\pi\)
\(510\) 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 −0.969058 0.246832i \(-0.920610\pi\)
0.698292 + 0.715813i \(0.253944\pi\)
\(524\) −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 \(0.259923\pi\)
−0.684723 + 0.728803i \(0.740077\pi\)
\(542\) −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 0.513625 0.858015i \(-0.328302\pi\)
−0.486250 + 0.873820i \(0.661636\pi\)
\(558\) 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 −0.973549 0.228478i \(-0.926625\pi\)
0.288907 0.957357i \(-0.406708\pi\)
\(564\) 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 −0.934924 0.354848i \(-0.884532\pi\)
0.774770 + 0.632244i \(0.217866\pi\)
\(570\) 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 \(-0.743872\pi\)
0.693364 0.720587i \(-0.256128\pi\)
\(578\) 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 0.895864 0.444329i \(-0.146558\pi\)
0.0631321 + 0.998005i \(0.479891\pi\)
\(588\) 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 \(-0.847438\pi\)
0.887323 0.461148i \(-0.152562\pi\)
\(594\) 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 −0.988097 0.153831i \(-0.950839\pi\)
0.627270 + 0.778802i \(0.284172\pi\)
\(602\) −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 0.604675 0.796472i \(-0.293303\pi\)
−0.992103 + 0.125428i \(0.959970\pi\)
\(608\) 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 0.957494 0.288453i \(-0.0931409\pi\)
0.228939 + 0.973441i \(0.426474\pi\)
\(614\) 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 −0.543504 0.839407i \(-0.682903\pi\)
0.455196 + 0.890391i \(0.349569\pi\)
\(618\) 0 0
\(619\) 758.406i 0.0492454i 0.999697 + 0.0246227i \(0.00783844\pi\)
−0.999697 + 0.0246227i \(0.992162\pi\)
\(620\) 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 −0.836220 0.548394i \(-0.815239\pi\)
0.0568136 + 0.998385i \(0.481906\pi\)
\(632\) 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 0.798074 0.602560i \(-0.205853\pi\)
−0.920869 + 0.389872i \(0.872519\pi\)
\(642\) 0 0
\(643\) 7063.78 4078.28i 0.433232 0.250127i −0.267490 0.963561i \(-0.586194\pi\)
0.700723 + 0.713434i \(0.252861\pi\)
\(644\) −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 −0.984930 0.172953i \(-0.944669\pi\)
0.642246 + 0.766498i \(0.278003\pi\)
\(648\) 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 −0.750732 0.660607i \(-0.770299\pi\)
0.947468 + 0.319850i \(0.103632\pi\)
\(654\) 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 0.928193 0.372100i \(-0.121362\pi\)
−0.786344 + 0.617788i \(0.788029\pi\)
\(660\) 0 0
\(661\) −13504.5 7796.80i −0.794648 0.458790i 0.0469482 0.998897i \(-0.485050\pi\)
−0.841596 + 0.540107i \(0.818384\pi\)
\(662\) −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 −0.895878 0.444301i \(-0.853452\pi\)
0.832715 + 0.553702i \(0.186785\pi\)
\(674\) 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 −0.999877 0.0157020i \(-0.995002\pi\)
−0.486340 + 0.873770i \(0.661668\pi\)
\(684\) 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 0.550969 0.834526i \(-0.314258\pi\)
−0.447236 + 0.894416i \(0.647592\pi\)
\(692\) −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 −0.950563 0.310533i \(-0.899492\pi\)
−0.206352 + 0.978478i \(0.566159\pi\)
\(710\) 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 0.799724 + 0.600368i \(0.204979\pi\)
0.120071 + 0.992765i \(0.461688\pi\)
\(720\) 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 \(-0.867729\pi\)
0.914898 0.403685i \(-0.132271\pi\)
\(734\) −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 0.415939 0.909393i \(-0.363453\pi\)
−0.579588 + 0.814910i \(0.696786\pi\)
\(740\) 5264.09 0.261502
\(741\) 0 0
\(742\) −56804.3 −2.81044
\(743\) 26266.0 + 15164.7i 1.29691 + 0.748772i 0.979869 0.199639i \(-0.0639771\pi\)
0.317042 + 0.948412i \(0.397310\pi\)
\(744\) 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 −0.476028 0.879430i \(-0.657924\pi\)
0.999623 0.0274629i \(-0.00874280\pi\)
\(752\) −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 −0.509783 0.860303i \(-0.670274\pi\)
0.999936 + 0.0113335i \(0.00360764\pi\)
\(758\) 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 0.314906 0.949123i \(-0.398027\pi\)
0.979417 + 0.201845i \(0.0646937\pi\)
\(762\) 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 0.731069 0.682303i \(-0.239022\pi\)
−0.225357 + 0.974276i \(0.572355\pi\)
\(770\) 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 −0.509129 + 0.860690i \(0.670033\pi\)
−0.999944 + 0.0105740i \(0.996634\pi\)
\(774\) 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