Properties

Label 128.4.g.a.49.2
Level $128$
Weight $4$
Character 128.49
Analytic conductor $7.552$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 128.g (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.55224448073\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(11\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 49.2
Character \(\chi\) \(=\) 128.49
Dual form 128.4.g.a.81.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-6.97998 + 2.89120i) q^{3} +(1.57150 - 3.79394i) q^{5} +(-15.6607 - 15.6607i) q^{7} +(21.2692 - 21.2692i) q^{9} +O(q^{10})\) \(q+(-6.97998 + 2.89120i) q^{3} +(1.57150 - 3.79394i) q^{5} +(-15.6607 - 15.6607i) q^{7} +(21.2692 - 21.2692i) q^{9} +(56.0992 + 23.2370i) q^{11} +(14.0971 + 34.0334i) q^{13} +31.0252i q^{15} -26.6088i q^{17} +(30.7752 + 74.2979i) q^{19} +(154.590 + 64.0332i) q^{21} +(141.584 - 141.584i) q^{23} +(76.4640 + 76.4640i) q^{25} +(-8.90248 + 21.4925i) q^{27} +(-11.9990 + 4.97014i) q^{29} +128.572 q^{31} -458.754 q^{33} +(-84.0267 + 34.8050i) q^{35} +(85.1234 - 205.506i) q^{37} +(-196.795 - 196.795i) q^{39} +(-32.3348 + 32.3348i) q^{41} +(-314.016 - 130.070i) q^{43} +(-47.2695 - 114.119i) q^{45} +184.040i q^{47} +147.516i q^{49} +(76.9314 + 185.729i) q^{51} +(277.346 + 114.881i) q^{53} +(176.320 - 176.320i) q^{55} +(-429.620 - 429.620i) q^{57} +(-241.099 + 582.065i) q^{59} +(297.419 - 123.195i) q^{61} -666.181 q^{63} +151.275 q^{65} +(605.866 - 250.958i) q^{67} +(-578.904 + 1397.60i) q^{69} +(-163.321 - 163.321i) q^{71} +(624.709 - 624.709i) q^{73} +(-754.790 - 312.644i) q^{75} +(-514.644 - 1242.46i) q^{77} -139.919i q^{79} +636.381i q^{81} +(226.003 + 545.620i) q^{83} +(-100.952 - 41.8158i) q^{85} +(69.3829 - 69.3829i) q^{87} +(231.313 + 231.313i) q^{89} +(312.217 - 753.759i) q^{91} +(-897.429 + 371.727i) q^{93} +330.245 q^{95} -594.442 q^{97} +(1687.42 - 698.950i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 4q^{19} - 4q^{21} - 324q^{23} - 4q^{25} + 268q^{27} - 4q^{29} + 752q^{31} - 8q^{33} + 460q^{35} - 4q^{37} - 596q^{39} - 4q^{41} - 804q^{43} + 104q^{45} + 1384q^{51} + 748q^{53} + 292q^{55} - 4q^{57} - 1372q^{59} - 1828q^{61} - 2512q^{63} - 8q^{65} - 2036q^{67} - 1060q^{69} - 220q^{71} - 4q^{73} + 1712q^{75} + 1900q^{77} - 2436q^{83} + 496q^{85} + 1292q^{87} - 4q^{89} + 3604q^{91} - 112q^{93} + 6088q^{95} - 8q^{97} + 5424q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(1\)

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
\(3\) −6.97998 + 2.89120i −1.34330 + 0.556412i −0.934419 0.356177i \(-0.884080\pi\)
−0.408879 + 0.912589i \(0.634080\pi\)
\(4\) 0 0
\(5\) 1.57150 3.79394i 0.140559 0.339340i −0.837886 0.545845i \(-0.816209\pi\)
0.978446 + 0.206504i \(0.0662088\pi\)
\(6\) 0 0
\(7\) −15.6607 15.6607i −0.845599 0.845599i 0.143981 0.989580i \(-0.454009\pi\)
−0.989580 + 0.143981i \(0.954009\pi\)
\(8\) 0 0
\(9\) 21.2692 21.2692i 0.787747 0.787747i
\(10\) 0 0
\(11\) 56.0992 + 23.2370i 1.53768 + 0.636930i 0.981037 0.193819i \(-0.0620874\pi\)
0.556647 + 0.830749i \(0.312087\pi\)
\(12\) 0 0
\(13\) 14.0971 + 34.0334i 0.300757 + 0.726091i 0.999938 + 0.0111463i \(0.00354805\pi\)
−0.699181 + 0.714944i \(0.746452\pi\)
\(14\) 0 0
\(15\) 31.0252i 0.534044i
\(16\) 0 0
\(17\) 26.6088i 0.379622i −0.981821 0.189811i \(-0.939212\pi\)
0.981821 0.189811i \(-0.0607876\pi\)
\(18\) 0 0
\(19\) 30.7752 + 74.2979i 0.371595 + 0.897110i 0.993481 + 0.114002i \(0.0363670\pi\)
−0.621885 + 0.783108i \(0.713633\pi\)
\(20\) 0 0
\(21\) 154.590 + 64.0332i 1.60639 + 0.665390i
\(22\) 0 0
\(23\) 141.584 141.584i 1.28358 1.28358i 0.344957 0.938618i \(-0.387893\pi\)
0.938618 0.344957i \(-0.112107\pi\)
\(24\) 0 0
\(25\) 76.4640 + 76.4640i 0.611712 + 0.611712i
\(26\) 0 0
\(27\) −8.90248 + 21.4925i −0.0634549 + 0.153194i
\(28\) 0 0
\(29\) −11.9990 + 4.97014i −0.0768329 + 0.0318252i −0.420769 0.907168i \(-0.638240\pi\)
0.343936 + 0.938993i \(0.388240\pi\)
\(30\) 0 0
\(31\) 128.572 0.744909 0.372455 0.928050i \(-0.378516\pi\)
0.372455 + 0.928050i \(0.378516\pi\)
\(32\) 0 0
\(33\) −458.754 −2.41996
\(34\) 0 0
\(35\) −84.0267 + 34.8050i −0.405803 + 0.168089i
\(36\) 0 0
\(37\) 85.1234 205.506i 0.378222 0.913108i −0.614078 0.789246i \(-0.710472\pi\)
0.992299 0.123863i \(-0.0395282\pi\)
\(38\) 0 0
\(39\) −196.795 196.795i −0.808011 0.808011i
\(40\) 0 0
\(41\) −32.3348 + 32.3348i −0.123167 + 0.123167i −0.766004 0.642836i \(-0.777758\pi\)
0.642836 + 0.766004i \(0.277758\pi\)
\(42\) 0 0
\(43\) −314.016 130.070i −1.11365 0.461289i −0.251457 0.967868i \(-0.580910\pi\)
−0.862193 + 0.506579i \(0.830910\pi\)
\(44\) 0 0
\(45\) −47.2695 114.119i −0.156589 0.378040i
\(46\) 0 0
\(47\) 184.040i 0.571169i 0.958353 + 0.285585i \(0.0921878\pi\)
−0.958353 + 0.285585i \(0.907812\pi\)
\(48\) 0 0
\(49\) 147.516i 0.430076i
\(50\) 0 0
\(51\) 76.9314 + 185.729i 0.211227 + 0.509946i
\(52\) 0 0
\(53\) 277.346 + 114.881i 0.718801 + 0.297737i 0.711941 0.702239i \(-0.247816\pi\)
0.00685997 + 0.999976i \(0.497816\pi\)
\(54\) 0 0
\(55\) 176.320 176.320i 0.432272 0.432272i
\(56\) 0 0
\(57\) −429.620 429.620i −0.998326 0.998326i
\(58\) 0 0
\(59\) −241.099 + 582.065i −0.532008 + 1.28438i 0.398184 + 0.917306i \(0.369641\pi\)
−0.930192 + 0.367075i \(0.880359\pi\)
\(60\) 0 0
\(61\) 297.419 123.195i 0.624271 0.258582i −0.0480457 0.998845i \(-0.515299\pi\)
0.672317 + 0.740264i \(0.265299\pi\)
\(62\) 0 0
\(63\) −666.181 −1.33224
\(64\) 0 0
\(65\) 151.275 0.288666
\(66\) 0 0
\(67\) 605.866 250.958i 1.10475 0.457603i 0.245624 0.969365i \(-0.421007\pi\)
0.859127 + 0.511763i \(0.171007\pi\)
\(68\) 0 0
\(69\) −578.904 + 1397.60i −1.01003 + 2.43842i
\(70\) 0 0
\(71\) −163.321 163.321i −0.272994 0.272994i 0.557310 0.830304i \(-0.311833\pi\)
−0.830304 + 0.557310i \(0.811833\pi\)
\(72\) 0 0
\(73\) 624.709 624.709i 1.00160 1.00160i 0.00159983 0.999999i \(-0.499491\pi\)
0.999999 0.00159983i \(-0.000509242\pi\)
\(74\) 0 0
\(75\) −754.790 312.644i −1.16207 0.481347i
\(76\) 0 0
\(77\) −514.644 1242.46i −0.761678 1.83885i
\(78\) 0 0
\(79\) 139.919i 0.199267i −0.995024 0.0996336i \(-0.968233\pi\)
0.995024 0.0996336i \(-0.0317671\pi\)
\(80\) 0 0
\(81\) 636.381i 0.872951i
\(82\) 0 0
\(83\) 226.003 + 545.620i 0.298881 + 0.721562i 0.999964 + 0.00848231i \(0.00270004\pi\)
−0.701083 + 0.713079i \(0.747300\pi\)
\(84\) 0 0
\(85\) −100.952 41.8158i −0.128821 0.0533595i
\(86\) 0 0
\(87\) 69.3829 69.3829i 0.0855015 0.0855015i
\(88\) 0 0
\(89\) 231.313 + 231.313i 0.275496 + 0.275496i 0.831308 0.555812i \(-0.187593\pi\)
−0.555812 + 0.831308i \(0.687593\pi\)
\(90\) 0 0
\(91\) 312.217 753.759i 0.359662 0.868301i
\(92\) 0 0
\(93\) −897.429 + 371.727i −1.00063 + 0.414476i
\(94\) 0 0
\(95\) 330.245 0.356657
\(96\) 0 0
\(97\) −594.442 −0.622231 −0.311116 0.950372i \(-0.600703\pi\)
−0.311116 + 0.950372i \(0.600703\pi\)
\(98\) 0 0
\(99\) 1687.42 698.950i 1.71305 0.709567i
\(100\) 0 0
\(101\) 164.682 397.578i 0.162242 0.391688i −0.821762 0.569831i \(-0.807009\pi\)
0.984005 + 0.178143i \(0.0570088\pi\)
\(102\) 0 0
\(103\) 718.153 + 718.153i 0.687007 + 0.687007i 0.961569 0.274563i \(-0.0885330\pi\)
−0.274563 + 0.961569i \(0.588533\pi\)
\(104\) 0 0
\(105\) 485.876 485.876i 0.451587 0.451587i
\(106\) 0 0
\(107\) −367.941 152.406i −0.332432 0.137698i 0.210223 0.977653i \(-0.432581\pi\)
−0.542655 + 0.839956i \(0.682581\pi\)
\(108\) 0 0
\(109\) 177.769 + 429.173i 0.156213 + 0.377131i 0.982538 0.186062i \(-0.0595726\pi\)
−0.826325 + 0.563193i \(0.809573\pi\)
\(110\) 0 0
\(111\) 1680.54i 1.43702i
\(112\) 0 0
\(113\) 323.520i 0.269329i 0.990891 + 0.134665i \(0.0429957\pi\)
−0.990891 + 0.134665i \(0.957004\pi\)
\(114\) 0 0
\(115\) −314.661 759.659i −0.255150 0.615988i
\(116\) 0 0
\(117\) 1023.70 + 424.029i 0.808896 + 0.335056i
\(118\) 0 0
\(119\) −416.713 + 416.713i −0.321008 + 0.321008i
\(120\) 0 0
\(121\) 1666.00 + 1666.00i 1.25169 + 1.25169i
\(122\) 0 0
\(123\) 132.210 319.183i 0.0969185 0.233982i
\(124\) 0 0
\(125\) 884.506 366.374i 0.632901 0.262156i
\(126\) 0 0
\(127\) 1147.19 0.801550 0.400775 0.916177i \(-0.368741\pi\)
0.400775 + 0.916177i \(0.368741\pi\)
\(128\) 0 0
\(129\) 2567.88 1.75263
\(130\) 0 0
\(131\) −1429.33 + 592.049i −0.953293 + 0.394867i −0.804468 0.593997i \(-0.797549\pi\)
−0.148825 + 0.988863i \(0.547549\pi\)
\(132\) 0 0
\(133\) 681.596 1645.52i 0.444375 1.07282i
\(134\) 0 0
\(135\) 67.5509 + 67.5509i 0.0430656 + 0.0430656i
\(136\) 0 0
\(137\) −247.558 + 247.558i −0.154382 + 0.154382i −0.780072 0.625690i \(-0.784817\pi\)
0.625690 + 0.780072i \(0.284817\pi\)
\(138\) 0 0
\(139\) 599.777 + 248.436i 0.365989 + 0.151598i 0.558096 0.829776i \(-0.311532\pi\)
−0.192107 + 0.981374i \(0.561532\pi\)
\(140\) 0 0
\(141\) −532.096 1284.59i −0.317806 0.767250i
\(142\) 0 0
\(143\) 2236.82i 1.30806i
\(144\) 0 0
\(145\) 53.3340i 0.0305458i
\(146\) 0 0
\(147\) −426.499 1029.66i −0.239299 0.577720i
\(148\) 0 0
\(149\) −1776.52 735.857i −0.976765 0.404589i −0.163539 0.986537i \(-0.552291\pi\)
−0.813226 + 0.581948i \(0.802291\pi\)
\(150\) 0 0
\(151\) 1331.94 1331.94i 0.717827 0.717827i −0.250333 0.968160i \(-0.580540\pi\)
0.968160 + 0.250333i \(0.0805401\pi\)
\(152\) 0 0
\(153\) −565.947 565.947i −0.299047 0.299047i
\(154\) 0 0
\(155\) 202.051 487.794i 0.104704 0.252778i
\(156\) 0 0
\(157\) −2417.43 + 1001.33i −1.22887 + 0.509013i −0.900218 0.435440i \(-0.856593\pi\)
−0.328647 + 0.944453i \(0.606593\pi\)
\(158\) 0 0
\(159\) −2268.01 −1.13123
\(160\) 0 0
\(161\) −4434.60 −2.17078
\(162\) 0 0
\(163\) −1823.96 + 755.507i −0.876462 + 0.363042i −0.775124 0.631810i \(-0.782312\pi\)
−0.101338 + 0.994852i \(0.532312\pi\)
\(164\) 0 0
\(165\) −720.933 + 1740.49i −0.340149 + 0.821191i
\(166\) 0 0
\(167\) −2602.55 2602.55i −1.20594 1.20594i −0.972332 0.233605i \(-0.924948\pi\)
−0.233605 0.972332i \(-0.575052\pi\)
\(168\) 0 0
\(169\) 593.967 593.967i 0.270354 0.270354i
\(170\) 0 0
\(171\) 2234.82 + 925.692i 0.999420 + 0.413973i
\(172\) 0 0
\(173\) 1666.31 + 4022.82i 0.732295 + 1.76792i 0.634794 + 0.772681i \(0.281085\pi\)
0.0975011 + 0.995235i \(0.468915\pi\)
\(174\) 0 0
\(175\) 2394.96i 1.03453i
\(176\) 0 0
\(177\) 4759.87i 2.02132i
\(178\) 0 0
\(179\) 317.180 + 765.739i 0.132442 + 0.319743i 0.976163 0.217039i \(-0.0696398\pi\)
−0.843721 + 0.536782i \(0.819640\pi\)
\(180\) 0 0
\(181\) −1556.05 644.538i −0.639008 0.264686i 0.0395667 0.999217i \(-0.487402\pi\)
−0.678575 + 0.734531i \(0.737402\pi\)
\(182\) 0 0
\(183\) −1719.79 + 1719.79i −0.694704 + 0.694704i
\(184\) 0 0
\(185\) −645.907 645.907i −0.256692 0.256692i
\(186\) 0 0
\(187\) 618.309 1492.73i 0.241793 0.583740i
\(188\) 0 0
\(189\) 476.007 197.168i 0.183198 0.0758830i
\(190\) 0 0
\(191\) 582.225 0.220567 0.110283 0.993900i \(-0.464824\pi\)
0.110283 + 0.993900i \(0.464824\pi\)
\(192\) 0 0
\(193\) 2115.34 0.788941 0.394471 0.918909i \(-0.370928\pi\)
0.394471 + 0.918909i \(0.370928\pi\)
\(194\) 0 0
\(195\) −1055.89 + 437.365i −0.387764 + 0.160617i
\(196\) 0 0
\(197\) 1017.56 2456.60i 0.368009 0.888453i −0.626067 0.779769i \(-0.715336\pi\)
0.994076 0.108684i \(-0.0346637\pi\)
\(198\) 0 0
\(199\) 260.073 + 260.073i 0.0926437 + 0.0926437i 0.751910 0.659266i \(-0.229133\pi\)
−0.659266 + 0.751910i \(0.729133\pi\)
\(200\) 0 0
\(201\) −3503.36 + 3503.36i −1.22939 + 1.22939i
\(202\) 0 0
\(203\) 265.748 + 110.077i 0.0918812 + 0.0380584i
\(204\) 0 0
\(205\) 71.8622 + 173.491i 0.0244833 + 0.0591079i
\(206\) 0 0
\(207\) 6022.74i 2.02227i
\(208\) 0 0
\(209\) 4883.17i 1.61615i
\(210\) 0 0
\(211\) 594.857 + 1436.11i 0.194084 + 0.468560i 0.990723 0.135895i \(-0.0433910\pi\)
−0.796640 + 0.604455i \(0.793391\pi\)
\(212\) 0 0
\(213\) 1612.17 + 667.781i 0.518610 + 0.214815i
\(214\) 0 0
\(215\) −986.953 + 986.953i −0.313068 + 0.313068i
\(216\) 0 0
\(217\) −2013.53 2013.53i −0.629895 0.629895i
\(218\) 0 0
\(219\) −2554.30 + 6166.62i −0.788143 + 1.90275i
\(220\) 0 0
\(221\) 905.589 375.107i 0.275640 0.114174i
\(222\) 0 0
\(223\) 1890.38 0.567663 0.283832 0.958874i \(-0.408394\pi\)
0.283832 + 0.958874i \(0.408394\pi\)
\(224\) 0 0
\(225\) 3252.65 0.963749
\(226\) 0 0
\(227\) 711.120 294.556i 0.207924 0.0861248i −0.276291 0.961074i \(-0.589105\pi\)
0.484215 + 0.874949i \(0.339105\pi\)
\(228\) 0 0
\(229\) 90.4906 218.464i 0.0261126 0.0630414i −0.910285 0.413981i \(-0.864138\pi\)
0.936398 + 0.350940i \(0.114138\pi\)
\(230\) 0 0
\(231\) 7184.41 + 7184.41i 2.04632 + 2.04632i
\(232\) 0 0
\(233\) −2838.71 + 2838.71i −0.798155 + 0.798155i −0.982804 0.184650i \(-0.940885\pi\)
0.184650 + 0.982804i \(0.440885\pi\)
\(234\) 0 0
\(235\) 698.236 + 289.219i 0.193821 + 0.0802832i
\(236\) 0 0
\(237\) 404.534 + 976.631i 0.110875 + 0.267675i
\(238\) 0 0
\(239\) 7044.27i 1.90651i −0.302168 0.953255i \(-0.597710\pi\)
0.302168 0.953255i \(-0.402290\pi\)
\(240\) 0 0
\(241\) 5909.62i 1.57955i −0.613395 0.789776i \(-0.710197\pi\)
0.613395 0.789776i \(-0.289803\pi\)
\(242\) 0 0
\(243\) −2080.27 5022.23i −0.549176 1.32583i
\(244\) 0 0
\(245\) 559.667 + 231.822i 0.145942 + 0.0604512i
\(246\) 0 0
\(247\) −2094.77 + 2094.77i −0.539624 + 0.539624i
\(248\) 0 0
\(249\) −3155.00 3155.00i −0.802971 0.802971i
\(250\) 0 0
\(251\) −431.008 + 1040.55i −0.108386 + 0.261668i −0.968762 0.247993i \(-0.920229\pi\)
0.860375 + 0.509661i \(0.170229\pi\)
\(252\) 0 0
\(253\) 11232.7 4652.74i 2.79128 1.15619i
\(254\) 0 0
\(255\) 825.542 0.202735
\(256\) 0 0
\(257\) −225.266 −0.0546759 −0.0273380 0.999626i \(-0.508703\pi\)
−0.0273380 + 0.999626i \(0.508703\pi\)
\(258\) 0 0
\(259\) −4551.47 + 1885.28i −1.09195 + 0.452299i
\(260\) 0 0
\(261\) −149.498 + 360.919i −0.0354547 + 0.0855951i
\(262\) 0 0
\(263\) −3244.94 3244.94i −0.760803 0.760803i 0.215664 0.976468i \(-0.430808\pi\)
−0.976468 + 0.215664i \(0.930808\pi\)
\(264\) 0 0
\(265\) 871.700 871.700i 0.202068 0.202068i
\(266\) 0 0
\(267\) −2283.34 945.789i −0.523363 0.216784i
\(268\) 0 0
\(269\) 83.5926 + 201.810i 0.0189470 + 0.0457420i 0.933070 0.359695i \(-0.117119\pi\)
−0.914123 + 0.405437i \(0.867119\pi\)
\(270\) 0 0
\(271\) 4103.79i 0.919880i 0.887950 + 0.459940i \(0.152129\pi\)
−0.887950 + 0.459940i \(0.847871\pi\)
\(272\) 0 0
\(273\) 6163.91i 1.36651i
\(274\) 0 0
\(275\) 2512.77 + 6066.36i 0.551002 + 1.33024i
\(276\) 0 0
\(277\) −775.002 321.016i −0.168106 0.0696318i 0.297043 0.954864i \(-0.403999\pi\)
−0.465149 + 0.885232i \(0.653999\pi\)
\(278\) 0 0
\(279\) 2734.62 2734.62i 0.586800 0.586800i
\(280\) 0 0
\(281\) 1856.75 + 1856.75i 0.394180 + 0.394180i 0.876174 0.481994i \(-0.160087\pi\)
−0.481994 + 0.876174i \(0.660087\pi\)
\(282\) 0 0
\(283\) 2964.83 7157.74i 0.622760 1.50348i −0.225689 0.974199i \(-0.572463\pi\)
0.848449 0.529277i \(-0.177537\pi\)
\(284\) 0 0
\(285\) −2305.10 + 954.805i −0.479096 + 0.198448i
\(286\) 0 0
\(287\) 1012.77 0.208300
\(288\) 0 0
\(289\) 4204.97 0.855887
\(290\) 0 0
\(291\) 4149.19 1718.65i 0.835842 0.346217i
\(292\) 0 0
\(293\) 316.687 764.550i 0.0631435 0.152442i −0.889158 0.457600i \(-0.848709\pi\)
0.952302 + 0.305158i \(0.0987092\pi\)
\(294\) 0 0
\(295\) 1829.43 + 1829.43i 0.361063 + 0.361063i
\(296\) 0 0
\(297\) −998.843 + 998.843i −0.195147 + 0.195147i
\(298\) 0 0
\(299\) 6814.50 + 2822.66i 1.31804 + 0.545949i
\(300\) 0 0
\(301\) 2880.73 + 6954.70i 0.551636 + 1.33177i
\(302\) 0 0
\(303\) 3251.22i 0.616427i
\(304\) 0 0
\(305\) 1321.99i 0.248186i
\(306\) 0 0
\(307\) −1040.36 2511.64i −0.193408 0.466928i 0.797191 0.603727i \(-0.206318\pi\)
−0.990599 + 0.136799i \(0.956318\pi\)
\(308\) 0 0
\(309\) −7089.02 2936.37i −1.30511 0.540596i
\(310\) 0 0
\(311\) 520.010 520.010i 0.0948138 0.0948138i −0.658109 0.752923i \(-0.728643\pi\)
0.752923 + 0.658109i \(0.228643\pi\)
\(312\) 0 0
\(313\) 1970.33 + 1970.33i 0.355814 + 0.355814i 0.862267 0.506454i \(-0.169044\pi\)
−0.506454 + 0.862267i \(0.669044\pi\)
\(314\) 0 0
\(315\) −1046.90 + 2527.45i −0.187258 + 0.452082i
\(316\) 0 0
\(317\) −6426.24 + 2661.83i −1.13859 + 0.471620i −0.870693 0.491827i \(-0.836329\pi\)
−0.267898 + 0.963447i \(0.586329\pi\)
\(318\) 0 0
\(319\) −788.624 −0.138415
\(320\) 0 0
\(321\) 3008.86 0.523172
\(322\) 0 0
\(323\) 1976.98 818.890i 0.340563 0.141066i
\(324\) 0 0
\(325\) −1524.41 + 3680.25i −0.260182 + 0.628135i
\(326\) 0 0
\(327\) −2481.65 2481.65i −0.419681 0.419681i
\(328\) 0 0
\(329\) 2882.19 2882.19i 0.482980 0.482980i
\(330\) 0 0
\(331\) 7122.25 + 2950.13i 1.18270 + 0.489891i 0.885372 0.464884i \(-0.153904\pi\)
0.297330 + 0.954775i \(0.403904\pi\)
\(332\) 0 0
\(333\) −2560.44 6181.45i −0.421355 1.01724i
\(334\) 0 0
\(335\) 2693.00i 0.439207i
\(336\) 0 0
\(337\) 8124.62i 1.31328i −0.754203 0.656641i \(-0.771977\pi\)
0.754203 0.656641i \(-0.228023\pi\)
\(338\) 0 0
\(339\) −935.361 2258.16i −0.149858 0.361789i
\(340\) 0 0
\(341\) 7212.77 + 2987.63i 1.14544 + 0.474455i
\(342\) 0 0
\(343\) −3061.42 + 3061.42i −0.481927 + 0.481927i
\(344\) 0 0
\(345\) 4392.66 + 4392.66i 0.685486 + 0.685486i
\(346\) 0 0
\(347\) −226.606 + 547.076i −0.0350572 + 0.0846356i −0.940438 0.339964i \(-0.889585\pi\)
0.905381 + 0.424600i \(0.139585\pi\)
\(348\) 0 0
\(349\) −10769.6 + 4460.93i −1.65182 + 0.684206i −0.997409 0.0719343i \(-0.977083\pi\)
−0.654410 + 0.756140i \(0.727083\pi\)
\(350\) 0 0
\(351\) −856.962 −0.130317
\(352\) 0 0
\(353\) −8090.20 −1.21982 −0.609912 0.792469i \(-0.708795\pi\)
−0.609912 + 0.792469i \(0.708795\pi\)
\(354\) 0 0
\(355\) −876.287 + 362.970i −0.131010 + 0.0542660i
\(356\) 0 0
\(357\) 1703.85 4113.45i 0.252597 0.609823i
\(358\) 0 0
\(359\) −2606.68 2606.68i −0.383218 0.383218i 0.489042 0.872260i \(-0.337346\pi\)
−0.872260 + 0.489042i \(0.837346\pi\)
\(360\) 0 0
\(361\) 276.986 276.986i 0.0403828 0.0403828i
\(362\) 0 0
\(363\) −16445.4 6811.89i −2.37784 0.984935i
\(364\) 0 0
\(365\) −1388.38 3351.84i −0.199099 0.480667i
\(366\) 0 0
\(367\) 8063.18i 1.14685i 0.819258 + 0.573426i \(0.194386\pi\)
−0.819258 + 0.573426i \(0.805614\pi\)
\(368\) 0 0
\(369\) 1375.47i 0.194049i
\(370\) 0 0
\(371\) −2544.33 6142.55i −0.356051 0.859584i
\(372\) 0 0
\(373\) −7668.37 3176.34i −1.06449 0.440924i −0.219444 0.975625i \(-0.570424\pi\)
−0.845042 + 0.534701i \(0.820424\pi\)
\(374\) 0 0
\(375\) −5114.57 + 5114.57i −0.704307 + 0.704307i
\(376\) 0 0
\(377\) −338.302 338.302i −0.0462160 0.0462160i
\(378\) 0 0
\(379\) 3822.52 9228.39i 0.518073 1.25074i −0.421012 0.907055i \(-0.638325\pi\)
0.939085 0.343685i \(-0.111675\pi\)
\(380\) 0 0
\(381\) −8007.38 + 3316.76i −1.07672 + 0.445992i
\(382\) 0 0
\(383\) −9953.63 −1.32795 −0.663977 0.747753i \(-0.731133\pi\)
−0.663977 + 0.747753i \(0.731133\pi\)
\(384\) 0 0
\(385\) −5522.59 −0.731058
\(386\) 0 0
\(387\) −9445.34 + 3912.39i −1.24065 + 0.513896i
\(388\) 0 0
\(389\) 3176.18 7667.98i 0.413982 0.999440i −0.570076 0.821592i \(-0.693086\pi\)
0.984058 0.177848i \(-0.0569136\pi\)
\(390\) 0 0
\(391\) −3767.37 3767.37i −0.487274 0.487274i
\(392\) 0 0
\(393\) 8264.98 8264.98i 1.06085 1.06085i
\(394\) 0 0
\(395\) −530.844 219.883i −0.0676194 0.0280089i
\(396\) 0 0
\(397\) −60.6257 146.363i −0.00766427 0.0185032i 0.920001 0.391916i \(-0.128188\pi\)
−0.927665 + 0.373413i \(0.878188\pi\)
\(398\) 0 0
\(399\) 13456.3i 1.68837i
\(400\) 0 0
\(401\) 3474.14i 0.432644i 0.976322 + 0.216322i \(0.0694062\pi\)
−0.976322 + 0.216322i \(0.930594\pi\)
\(402\) 0 0
\(403\) 1812.49 + 4375.74i 0.224036 + 0.540872i
\(404\) 0 0
\(405\) 2414.39 + 1000.07i 0.296228 + 0.122701i
\(406\) 0 0
\(407\) 9550.71 9550.71i 1.16317 1.16317i
\(408\) 0 0
\(409\) 4584.30 + 4584.30i 0.554228 + 0.554228i 0.927658 0.373430i \(-0.121819\pi\)
−0.373430 + 0.927658i \(0.621819\pi\)
\(410\) 0 0
\(411\) 1012.21 2443.69i 0.121481 0.293280i
\(412\) 0 0
\(413\) 12891.3 5339.77i 1.53594 0.636206i
\(414\) 0 0
\(415\) 2425.22 0.286865
\(416\) 0 0
\(417\) −4904.71 −0.575983
\(418\) 0 0
\(419\) 10250.7 4245.97i 1.19517 0.495058i 0.305738 0.952116i \(-0.401097\pi\)
0.889437 + 0.457058i \(0.151097\pi\)
\(420\) 0 0
\(421\) −3016.30 + 7282.00i −0.349182 + 0.843000i 0.647535 + 0.762036i \(0.275800\pi\)
−0.996717 + 0.0809641i \(0.974200\pi\)
\(422\) 0 0
\(423\) 3914.37 + 3914.37i 0.449937 + 0.449937i
\(424\) 0 0
\(425\) 2034.61 2034.61i 0.232220 0.232220i
\(426\) 0 0
\(427\) −6587.10 2728.47i −0.746539 0.309227i
\(428\) 0 0
\(429\) −6467.11 15613.0i −0.727820 1.75711i
\(430\) 0 0
\(431\) 14216.7i 1.58885i 0.607365 + 0.794423i \(0.292227\pi\)
−0.607365 + 0.794423i \(0.707773\pi\)
\(432\) 0 0
\(433\) 14011.6i 1.55509i 0.628830 + 0.777543i \(0.283534\pi\)
−0.628830 + 0.777543i \(0.716466\pi\)
\(434\) 0 0
\(435\) −154.199 372.270i −0.0169961 0.0410321i
\(436\) 0 0
\(437\) 14876.6 + 6162.10i 1.62848 + 0.674538i
\(438\) 0 0
\(439\) 1061.27 1061.27i 0.115380 0.115380i −0.647060 0.762439i \(-0.724002\pi\)
0.762439 + 0.647060i \(0.224002\pi\)
\(440\) 0 0
\(441\) 3137.54 + 3137.54i 0.338791 + 0.338791i
\(442\) 0 0
\(443\) −2529.77 + 6107.40i −0.271316 + 0.655014i −0.999540 0.0303248i \(-0.990346\pi\)
0.728224 + 0.685339i \(0.240346\pi\)
\(444\) 0 0
\(445\) 1241.10 514.080i 0.132211 0.0547634i
\(446\) 0 0
\(447\) 14527.6 1.53720
\(448\) 0 0
\(449\) 1260.27 0.132463 0.0662313 0.997804i \(-0.478902\pi\)
0.0662313 + 0.997804i \(0.478902\pi\)
\(450\) 0 0
\(451\) −2565.32 + 1062.59i −0.267841 + 0.110943i
\(452\) 0 0
\(453\) −5446.01 + 13147.8i −0.564847 + 1.36366i
\(454\) 0 0
\(455\) −2369.07 2369.07i −0.244096 0.244096i
\(456\) 0 0
\(457\) −7126.17 + 7126.17i −0.729427 + 0.729427i −0.970506 0.241078i \(-0.922499\pi\)
0.241078 + 0.970506i \(0.422499\pi\)
\(458\) 0 0
\(459\) 571.889 + 236.884i 0.0581558 + 0.0240889i
\(460\) 0 0
\(461\) −429.245 1036.29i −0.0433665 0.104696i 0.900712 0.434417i \(-0.143045\pi\)
−0.944079 + 0.329721i \(0.893045\pi\)
\(462\) 0 0
\(463\) 18501.7i 1.85712i −0.371178 0.928562i \(-0.621046\pi\)
0.371178 0.928562i \(-0.378954\pi\)
\(464\) 0 0
\(465\) 3988.96i 0.397814i
\(466\) 0 0
\(467\) 5016.56 + 12111.1i 0.497085 + 1.20007i 0.951046 + 0.309049i \(0.100011\pi\)
−0.453961 + 0.891022i \(0.649989\pi\)
\(468\) 0 0
\(469\) −13418.5 5558.11i −1.32112 0.547228i
\(470\) 0 0
\(471\) 13978.5 13978.5i 1.36751 1.36751i
\(472\) 0 0
\(473\) −14593.6 14593.6i −1.41863 1.41863i
\(474\) 0 0
\(475\) −3327.92 + 8034.30i −0.321464 + 0.776082i
\(476\) 0 0
\(477\) 8342.34 3455.51i 0.800775 0.331692i
\(478\) 0 0
\(479\) −4560.24 −0.434995 −0.217497 0.976061i \(-0.569789\pi\)
−0.217497 + 0.976061i \(0.569789\pi\)
\(480\) 0 0
\(481\) 8194.08 0.776752
\(482\) 0 0
\(483\) 30953.4 12821.3i 2.91601 1.20785i
\(484\) 0 0
\(485\) −934.167 + 2255.28i −0.0874605 + 0.211148i
\(486\) 0 0
\(487\) 14926.4 + 14926.4i 1.38887 + 1.38887i 0.827706 + 0.561162i \(0.189646\pi\)
0.561162 + 0.827706i \(0.310354\pi\)
\(488\) 0 0
\(489\) 10546.9 10546.9i 0.975348 0.975348i
\(490\) 0 0
\(491\) 1750.78 + 725.196i 0.160920 + 0.0666551i 0.461689 0.887042i \(-0.347244\pi\)
−0.300770 + 0.953697i \(0.597244\pi\)
\(492\) 0 0
\(493\) 132.249 + 319.278i 0.0120816 + 0.0291675i
\(494\) 0 0
\(495\) 7500.36i 0.681042i
\(496\) 0 0
\(497\) 5115.43i 0.461687i
\(498\) 0 0
\(499\) −1646.59 3975.23i −0.147719 0.356625i 0.832649 0.553801i \(-0.186823\pi\)
−0.980368 + 0.197176i \(0.936823\pi\)
\(500\) 0 0
\(501\) 25690.2 + 10641.2i 2.29093 + 0.948934i
\(502\) 0 0
\(503\) −11968.8 + 11968.8i −1.06096 + 1.06096i −0.0629447 + 0.998017i \(0.520049\pi\)
−0.998017 + 0.0629447i \(0.979951\pi\)
\(504\) 0 0
\(505\) −1249.59 1249.59i −0.110111 0.110111i
\(506\) 0 0
\(507\) −2428.60 + 5863.15i −0.212737 + 0.513593i
\(508\) 0 0
\(509\) −1912.55 + 792.203i −0.166546 + 0.0689858i −0.464399 0.885626i \(-0.653730\pi\)
0.297853 + 0.954612i \(0.403730\pi\)
\(510\) 0 0
\(511\) −19566.8 −1.69390
\(512\) 0 0
\(513\) −1870.82 −0.161011
\(514\) 0 0
\(515\) 3853.21 1596.05i 0.329694 0.136564i
\(516\) 0 0
\(517\) −4276.54 + 10324.5i −0.363795 + 0.878278i
\(518\) 0 0
\(519\) −23261.6 23261.6i −1.96738 1.96738i
\(520\) 0 0
\(521\) −1713.04 + 1713.04i −0.144049 + 0.144049i −0.775454 0.631405i \(-0.782479\pi\)
0.631405 + 0.775454i \(0.282479\pi\)
\(522\) 0 0
\(523\) −12429.1 5148.29i −1.03917 0.430438i −0.203155 0.979147i \(-0.565120\pi\)
−0.836014 + 0.548709i \(0.815120\pi\)
\(524\) 0 0
\(525\) 6924.32 + 16716.8i 0.575623 + 1.38968i
\(526\) 0 0
\(527\) 3421.14i 0.282784i
\(528\) 0 0
\(529\) 27924.9i 2.29513i
\(530\) 0 0
\(531\) 7252.06 + 17508.0i 0.592679 + 1.43085i
\(532\) 0 0
\(533\) −1556.29 644.638i −0.126474 0.0523872i
\(534\) 0 0
\(535\) −1156.44 + 1156.44i −0.0934528 + 0.0934528i
\(536\) 0 0
\(537\) −4427.81 4427.81i −0.355818 0.355818i
\(538\) 0 0
\(539\) −3427.83 + 8275.52i −0.273928 + 0.661321i
\(540\) 0 0
\(541\) 5533.67 2292.12i 0.439762 0.182155i −0.151806 0.988410i \(-0.548509\pi\)
0.591568 + 0.806255i \(0.298509\pi\)
\(542\) 0 0
\(543\) 12724.7 1.00565
\(544\) 0 0
\(545\) 1907.62 0.149933
\(546\) 0 0
\(547\) −11530.9 + 4776.23i −0.901323 + 0.373340i −0.784729 0.619840i \(-0.787198\pi\)
−0.116594 + 0.993180i \(0.537198\pi\)
\(548\) 0 0
\(549\) 3705.60 8946.10i 0.288071 0.695465i
\(550\) 0 0
\(551\) −738.541 738.541i −0.0571015 0.0571015i
\(552\) 0 0
\(553\) −2191.23 + 2191.23i −0.168500 + 0.168500i
\(554\) 0 0
\(555\) 6375.86 + 2640.97i 0.487640 + 0.201987i
\(556\) 0 0
\(557\) −6605.12 15946.2i −0.502456 1.21304i −0.948142 0.317847i \(-0.897040\pi\)
0.445686 0.895189i \(-0.352960\pi\)
\(558\) 0 0
\(559\) 12520.7i 0.947347i
\(560\) 0 0
\(561\) 12206.9i 0.918673i
\(562\) 0 0
\(563\) 3621.28 + 8742.53i 0.271081 + 0.654447i 0.999530 0.0306525i \(-0.00975852\pi\)
−0.728449 + 0.685100i \(0.759759\pi\)
\(564\) 0 0
\(565\) 1227.42 + 508.412i 0.0913943 + 0.0378567i
\(566\) 0 0
\(567\) 9966.19 9966.19i 0.738167 0.738167i
\(568\) 0 0
\(569\) 4482.37 + 4482.37i 0.330247 + 0.330247i 0.852680 0.522433i \(-0.174976\pi\)
−0.522433 + 0.852680i \(0.674976\pi\)
\(570\) 0 0
\(571\) −2954.21 + 7132.09i −0.216515 + 0.522712i −0.994399 0.105696i \(-0.966293\pi\)
0.777884 + 0.628408i \(0.216293\pi\)
\(572\) 0 0
\(573\) −4063.92 + 1683.33i −0.296287 + 0.122726i
\(574\) 0 0
\(575\) 21652.1 1.57036
\(576\) 0 0
\(577\) −25355.5 −1.82940 −0.914699 0.404136i \(-0.867572\pi\)
−0.914699 + 0.404136i \(0.867572\pi\)
\(578\) 0 0
\(579\) −14765.0 + 6115.88i −1.05978 + 0.438976i
\(580\) 0 0
\(581\) 5005.43 12084.2i 0.357419 0.862885i
\(582\) 0 0
\(583\) 12889.4 + 12889.4i 0.915651 + 0.915651i
\(584\) 0 0
\(585\) 3217.48 3217.48i 0.227396 0.227396i
\(586\) 0 0
\(587\) −11437.3 4737.49i −0.804206 0.333113i −0.0575663 0.998342i \(-0.518334\pi\)
−0.746640 + 0.665229i \(0.768334\pi\)
\(588\) 0 0
\(589\) 3956.82 + 9552.61i 0.276805 + 0.668266i
\(590\) 0 0
\(591\) 20089.0i 1.39822i
\(592\) 0 0
\(593\) 2914.83i 0.201851i 0.994894 + 0.100925i \(0.0321804\pi\)
−0.994894 + 0.100925i \(0.967820\pi\)
\(594\) 0 0
\(595\) 926.119 + 2235.85i 0.0638104 + 0.154052i
\(596\) 0 0
\(597\) −2567.23 1063.38i −0.175996 0.0729000i
\(598\) 0 0
\(599\) 8115.44 8115.44i 0.553569 0.553569i −0.373900 0.927469i \(-0.621980\pi\)
0.927469 + 0.373900i \(0.121980\pi\)
\(600\) 0 0
\(601\) 9424.82 + 9424.82i 0.639678 + 0.639678i 0.950476 0.310798i \(-0.100596\pi\)
−0.310798 + 0.950476i \(0.600596\pi\)
\(602\) 0 0
\(603\) 7548.60 18223.9i 0.509789 1.23074i
\(604\) 0 0
\(605\) 8938.81 3702.58i 0.600685 0.248812i
\(606\) 0 0
\(607\) −29374.9 −1.96423 −0.982117 0.188274i \(-0.939711\pi\)
−0.982117 + 0.188274i \(0.939711\pi\)
\(608\) 0 0
\(609\) −2173.17 −0.144600
\(610\) 0 0
\(611\) −6263.51 + 2594.43i −0.414721 + 0.171783i
\(612\) 0 0
\(613\) −137.019 + 330.794i −0.00902800 + 0.0217955i −0.928329 0.371759i \(-0.878755\pi\)
0.919301 + 0.393555i \(0.128755\pi\)
\(614\) 0 0
\(615\) −1003.19 1003.19i −0.0657767 0.0657767i
\(616\) 0 0
\(617\) −2046.11 + 2046.11i −0.133506 + 0.133506i −0.770702 0.637196i \(-0.780094\pi\)
0.637196 + 0.770702i \(0.280094\pi\)
\(618\) 0 0
\(619\) 15046.6 + 6232.49i 0.977014 + 0.404693i 0.813319 0.581818i \(-0.197659\pi\)
0.163696 + 0.986511i \(0.447659\pi\)
\(620\) 0 0
\(621\) 1782.54 + 4303.43i 0.115187 + 0.278085i
\(622\) 0 0
\(623\) 7245.06i 0.465919i
\(624\) 0 0
\(625\) 9585.53i 0.613474i
\(626\) 0 0
\(627\) −14118.2 34084.4i −0.899247 2.17097i
\(628\) 0 0
\(629\) −5468.27 2265.03i −0.346636 0.143581i
\(630\) 0 0
\(631\) −16948.0 + 16948.0i −1.06924 + 1.06924i −0.0718201 + 0.997418i \(0.522881\pi\)
−0.997418 + 0.0718201i \(0.977119\pi\)
\(632\) 0 0
\(633\) −8304.18 8304.18i −0.521424 0.521424i
\(634\) 0 0
\(635\) 1802.81 4352.38i 0.112665 0.271998i
\(636\) 0 0
\(637\) −5020.48 + 2079.55i −0.312274 + 0.129348i
\(638\) 0 0
\(639\) −6947.39 −0.430101
\(640\) 0 0
\(641\) −1901.61 −0.117175 −0.0585876 0.998282i \(-0.518660\pi\)
−0.0585876 + 0.998282i \(0.518660\pi\)
\(642\) 0 0
\(643\) −23668.9 + 9803.96i −1.45165 + 0.601291i −0.962590 0.270961i \(-0.912659\pi\)
−0.489056 + 0.872253i \(0.662659\pi\)
\(644\) 0 0
\(645\) 4035.43 9742.39i 0.246349 0.594739i
\(646\) 0 0
\(647\) −15183.7 15183.7i −0.922619 0.922619i 0.0745946 0.997214i \(-0.476234\pi\)
−0.997214 + 0.0745946i \(0.976234\pi\)
\(648\) 0 0
\(649\) −27050.9 + 27050.9i −1.63612 + 1.63612i
\(650\) 0 0
\(651\) 19875.9 + 8232.86i 1.19662 + 0.495655i
\(652\) 0 0
\(653\) −4239.30 10234.6i −0.254053 0.613338i 0.744471 0.667655i \(-0.232702\pi\)
−0.998524 + 0.0543169i \(0.982702\pi\)
\(654\) 0 0
\(655\) 6353.21i 0.378993i
\(656\) 0 0
\(657\) 26574.1i 1.57801i
\(658\) 0 0
\(659\) −7838.85 18924.7i −0.463366 1.11866i −0.967007 0.254751i \(-0.918006\pi\)
0.503641 0.863913i \(-0.331994\pi\)
\(660\) 0 0
\(661\) −2051.85 849.906i −0.120738 0.0500114i 0.321497 0.946911i \(-0.395814\pi\)
−0.442235 + 0.896899i \(0.645814\pi\)
\(662\) 0 0
\(663\) −5236.48 + 5236.48i −0.306739 + 0.306739i
\(664\) 0 0
\(665\) −5171.87 5171.87i −0.301589 0.301589i
\(666\) 0 0
\(667\) −995.169 + 2402.55i −0.0577707 + 0.139471i
\(668\) 0 0
\(669\) −13194.8 + 5465.46i −0.762541 + 0.315855i
\(670\) 0 0
\(671\) 19547.6 1.12463
\(672\) 0 0
\(673\) 17511.0 1.00297 0.501486 0.865166i \(-0.332787\pi\)
0.501486 + 0.865166i \(0.332787\pi\)
\(674\) 0 0
\(675\) −2324.12 + 962.682i −0.132527 + 0.0548943i
\(676\) 0 0
\(677\) −2390.19 + 5770.44i −0.135691 + 0.327586i −0.977090 0.212828i \(-0.931733\pi\)
0.841399 + 0.540414i \(0.181733\pi\)
\(678\) 0 0
\(679\) 9309.39 + 9309.39i 0.526158 + 0.526158i
\(680\) 0 0
\(681\) −4111.98 + 4111.98i −0.231383 + 0.231383i
\(682\) 0 0
\(683\) 1674.92 + 693.777i 0.0938349 + 0.0388677i 0.429107 0.903254i \(-0.358828\pi\)
−0.335272 + 0.942121i \(0.608828\pi\)
\(684\) 0 0
\(685\) 550.182 + 1328.26i 0.0306882 + 0.0740878i
\(686\) 0 0
\(687\) 1786.50i 0.0992128i
\(688\) 0 0
\(689\) 11058.5i 0.611461i
\(690\) 0 0
\(691\) −8855.39 21378.8i −0.487518 1.17697i −0.955965 0.293481i \(-0.905186\pi\)
0.468447 0.883492i \(-0.344814\pi\)
\(692\) 0 0
\(693\) −37372.2 15480.1i −2.04856 0.848542i
\(694\) 0 0
\(695\) 1885.10 1885.10i 0.102886 0.102886i
\(696\) 0 0
\(697\) 860.391 + 860.391i 0.0467570 + 0.0467570i
\(698\) 0 0
\(699\) 11606.9 28021.4i 0.628056 1.51626i
\(700\) 0 0
\(701\) −31059.0 + 12865.1i −1.67344 + 0.693163i −0.998980 0.0451460i \(-0.985625\pi\)
−0.674463 + 0.738309i \(0.735625\pi\)
\(702\) 0 0
\(703\) 17888.4 0.959704
\(704\) 0 0
\(705\) −5709.86 −0.305030
\(706\) 0 0
\(707\) −8805.40 + 3647.31i −0.468403 + 0.194019i
\(708\) 0 0
\(709\) 9260.32 22356.4i 0.490520 1.18422i −0.463936 0.885869i \(-0.653563\pi\)
0.954456 0.298352i \(-0.0964368\pi\)
\(710\) 0 0
\(711\) −2975.96 2975.96i −0.156972 0.156972i
\(712\) 0 0
\(713\) 18203.7 18203.7i 0.956147 0.956147i
\(714\) 0 0
\(715\) 8486.37 + 3515.17i 0.443877 + 0.183860i
\(716\) 0 0
\(717\) 20366.4 + 49168.8i 1.06080 + 2.56101i
\(718\) 0 0
\(719\) 2669.74i 0.138476i −0.997600 0.0692381i \(-0.977943\pi\)
0.997600 0.0692381i \(-0.0220568\pi\)
\(720\) 0 0
\(721\) 22493.6i 1.16186i
\(722\) 0 0
\(723\) 17085.9 + 41249.0i 0.878882 + 2.12181i
\(724\) 0 0
\(725\) −1297.53 537.453i −0.0664674 0.0275317i
\(726\) 0 0
\(727\) 16054.1 16054.1i 0.818999 0.818999i −0.166964 0.985963i \(-0.553396\pi\)
0.985963 + 0.166964i \(0.0533962\pi\)
\(728\) 0 0
\(729\) 16890.8 + 16890.8i 0.858143 + 0.858143i
\(730\) 0 0
\(731\) −3461.00 + 8355.59i −0.175116 + 0.422767i
\(732\) 0 0
\(733\) 20176.5 8357.40i 1.01670 0.421129i 0.188802 0.982015i \(-0.439539\pi\)
0.827893 + 0.560886i \(0.189539\pi\)
\(734\) 0 0
\(735\) −4576.71 −0.229679
\(736\) 0 0
\(737\) 39820.1 1.99022
\(738\) 0 0
\(739\) 16792.0 6955.46i 0.835862 0.346225i 0.0766414 0.997059i \(-0.475580\pi\)
0.759221 + 0.650833i \(0.225580\pi\)
\(740\) 0 0
\(741\) 8565.05 20677.9i 0.424622 1.02513i
\(742\) 0 0
\(743\) 17381.8 + 17381.8i 0.858243 + 0.858243i 0.991131 0.132888i \(-0.0424250\pi\)
−0.132888 + 0.991131i \(0.542425\pi\)
\(744\) 0 0
\(745\) −5583.60 + 5583.60i −0.274587 + 0.274587i
\(746\) 0 0
\(747\) 16411.8 + 6797.99i 0.803851 + 0.332966i
\(748\) 0 0
\(749\) 3375.43 + 8149.01i 0.164667 + 0.397541i
\(750\) 0 0
\(751\) 17302.5i 0.840717i −0.907358 0.420358i \(-0.861904\pi\)
0.907358 0.420358i \(-0.138096\pi\)
\(752\) 0 0
\(753\) 8509.12i 0.411806i
\(754\) 0 0
\(755\) −2960.16 7146.45i −0.142690 0.344485i
\(756\) 0 0
\(757\) −15089.7 6250.38i −0.724499 0.300097i −0.0102100 0.999948i \(-0.503250\pi\)
−0.714289 + 0.699850i \(0.753250\pi\)
\(758\) 0 0
\(759\) −64952.1 + 64952.1i −3.10621 + 3.10621i
\(760\) 0 0
\(761\) 21880.6 + 21880.6i 1.04227 + 1.04227i 0.999066 + 0.0432084i \(0.0137579\pi\)
0.0432084 + 0.999066i \(0.486242\pi\)
\(762\) 0 0
\(763\) 3937.16 9505.14i 0.186808 0.450995i
\(764\) 0 0
\(765\) −3036.56 + 1257.78i −0.143512 + 0.0594448i
\(766\) 0 0
\(767\) −23208.5 −1.09258
\(768\) 0 0
\(769\) 33208.8 1.55727 0.778634 0.627479i \(-0.215913\pi\)
0.778634 + 0.627479i \(0.215913\pi\)
\(770\) 0 0
\(771\) 1572.35 651.290i 0.0734460 0.0304223i
\(772\) 0 0
\(773\) −14567.1 + 35168.2i −0.677805 + 1.63637i 0.0902005 + 0.995924i \(0.471249\pi\)
−0.768006 + 0.640443i \(0.778751\pi\)
\(774\) 0 0
\(775\) 9831.11 + 9831.11i 0.455670 + 0.455670i
\(776\) 0 0
\(777\) 26318.4 26318.4i 1.21515 1.21515i
\(778\) 0 0
\(779\) −3397.52 1407.30i −0.156263 0.0647262i
\(780\) 0 0
\(781\) −5367.06 12957.2i −0.245901 0.593657i
\(782\) 0 0
\(783\) 302.134i 0.0137898i
\(784\) 0 0
\(785\) 10745.2i 0.488550i
\(786\) 0 0