Properties

Label 39.4.b.b.25.2
Level $39$
Weight $4$
Character 39.25
Analytic conductor $2.301$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 39 = 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 39.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.30107449022\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.1362828.1
Defining polynomial: \( x^{4} + 23x^{2} + 48 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 25.2
Root \(-1.52356i\) of defining polynomial
Character \(\chi\) \(=\) 39.25
Dual form 39.4.b.b.25.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.52356i q^{2} +3.00000 q^{3} +5.67878 q^{4} +9.65841i q^{5} -4.57067i q^{6} -22.3639i q^{7} -20.8404i q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-1.52356i q^{2} +3.00000 q^{3} +5.67878 q^{4} +9.65841i q^{5} -4.57067i q^{6} -22.3639i q^{7} -20.8404i q^{8} +9.00000 q^{9} +14.7151 q^{10} +50.3050i q^{11} +17.0363 q^{12} +(-39.7151 - 24.8940i) q^{13} -34.0727 q^{14} +28.9752i q^{15} +13.6788 q^{16} -86.1454 q^{17} -13.7120i q^{18} +116.880i q^{19} +54.8480i q^{20} -67.0918i q^{21} +76.6424 q^{22} -72.0000 q^{23} -62.5211i q^{24} +31.7151 q^{25} +(-37.9273 + 60.5082i) q^{26} +27.0000 q^{27} -127.000i q^{28} +14.1454 q^{29} +44.1454 q^{30} -196.215i q^{31} -187.563i q^{32} +150.915i q^{33} +131.247i q^{34} +216.000 q^{35} +51.1090 q^{36} +154.424i q^{37} +178.073 q^{38} +(-119.145 - 74.6819i) q^{39} +201.285 q^{40} -265.726i q^{41} -102.218 q^{42} -211.855 q^{43} +285.671i q^{44} +86.9257i q^{45} +109.696i q^{46} -67.5535i q^{47} +41.0363 q^{48} -157.145 q^{49} -48.3197i q^{50} -258.436 q^{51} +(-225.533 - 141.367i) q^{52} +686.581 q^{53} -41.1360i q^{54} -485.866 q^{55} -466.073 q^{56} +350.639i q^{57} -21.5512i q^{58} +91.9304i q^{59} +164.544i q^{60} +329.006 q^{61} -298.945 q^{62} -201.275i q^{63} -176.333 q^{64} +(240.436 - 383.585i) q^{65} +229.927 q^{66} +768.370i q^{67} -489.201 q^{68} -216.000 q^{69} -329.088i q^{70} +264.969i q^{71} -187.563i q^{72} -771.306i q^{73} +235.273 q^{74} +95.1454 q^{75} +663.734i q^{76} +1125.02 q^{77} +(-113.782 + 181.525i) q^{78} +1226.86 q^{79} +132.115i q^{80} +81.0000 q^{81} -404.849 q^{82} -514.019i q^{83} -381.000i q^{84} -832.027i q^{85} +322.772i q^{86} +42.4361 q^{87} +1048.38 q^{88} -527.889i q^{89} +132.436 q^{90} +(-556.727 + 888.186i) q^{91} -408.872 q^{92} -588.646i q^{93} -102.921 q^{94} -1128.87 q^{95} -562.690i q^{96} -74.2755i q^{97} +239.420i q^{98} +452.745i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 12 q^{3} - 14 q^{4} + 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 12 q^{3} - 14 q^{4} + 36 q^{9} - 88 q^{10} - 42 q^{12} - 12 q^{13} + 84 q^{14} + 18 q^{16} + 96 q^{17} + 380 q^{22} - 288 q^{23} - 20 q^{25} - 372 q^{26} + 108 q^{27} - 384 q^{29} - 264 q^{30} + 864 q^{35} - 126 q^{36} + 492 q^{38} - 36 q^{39} + 952 q^{40} + 252 q^{42} - 1288 q^{43} + 54 q^{48} - 188 q^{49} + 288 q^{51} - 1306 q^{52} + 984 q^{53} - 328 q^{55} - 1644 q^{56} + 288 q^{61} + 1668 q^{62} + 1314 q^{64} - 360 q^{65} + 1140 q^{66} - 4380 q^{68} - 864 q^{69} + 3144 q^{74} - 60 q^{75} + 1416 q^{77} - 1116 q^{78} + 4320 q^{79} + 324 q^{81} - 3088 q^{82} - 1152 q^{87} + 1036 q^{88} - 792 q^{90} - 24 q^{91} + 1008 q^{92} - 1660 q^{94} - 1872 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).

\(n\) \(14\) \(28\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.52356i 0.538658i −0.963048 0.269329i \(-0.913198\pi\)
0.963048 0.269329i \(-0.0868019\pi\)
\(3\) 3.00000 0.577350
\(4\) 5.67878 0.709847
\(5\) 9.65841i 0.863874i 0.901904 + 0.431937i \(0.142170\pi\)
−0.901904 + 0.431937i \(0.857830\pi\)
\(6\) 4.57067i 0.310994i
\(7\) 22.3639i 1.20754i −0.797159 0.603769i \(-0.793665\pi\)
0.797159 0.603769i \(-0.206335\pi\)
\(8\) 20.8404i 0.921023i
\(9\) 9.00000 0.333333
\(10\) 14.7151 0.465333
\(11\) 50.3050i 1.37887i 0.724349 + 0.689433i \(0.242140\pi\)
−0.724349 + 0.689433i \(0.757860\pi\)
\(12\) 17.0363 0.409831
\(13\) −39.7151 24.8940i −0.847307 0.531103i
\(14\) −34.0727 −0.650450
\(15\) 28.9752i 0.498758i
\(16\) 13.6788 0.213731
\(17\) −86.1454 −1.22902 −0.614509 0.788910i \(-0.710646\pi\)
−0.614509 + 0.788910i \(0.710646\pi\)
\(18\) 13.7120i 0.179553i
\(19\) 116.880i 1.41127i 0.708578 + 0.705633i \(0.249337\pi\)
−0.708578 + 0.705633i \(0.750663\pi\)
\(20\) 54.8480i 0.613219i
\(21\) 67.0918i 0.697173i
\(22\) 76.6424 0.742737
\(23\) −72.0000 −0.652741 −0.326370 0.945242i \(-0.605826\pi\)
−0.326370 + 0.945242i \(0.605826\pi\)
\(24\) 62.5211i 0.531753i
\(25\) 31.7151 0.253721
\(26\) −37.9273 + 60.5082i −0.286083 + 0.456409i
\(27\) 27.0000 0.192450
\(28\) 127.000i 0.857168i
\(29\) 14.1454 0.0905768 0.0452884 0.998974i \(-0.485579\pi\)
0.0452884 + 0.998974i \(0.485579\pi\)
\(30\) 44.1454 0.268660
\(31\) 196.215i 1.13682i −0.822747 0.568408i \(-0.807559\pi\)
0.822747 0.568408i \(-0.192441\pi\)
\(32\) 187.563i 1.03615i
\(33\) 150.915i 0.796089i
\(34\) 131.247i 0.662021i
\(35\) 216.000 1.04316
\(36\) 51.1090 0.236616
\(37\) 154.424i 0.686138i 0.939310 + 0.343069i \(0.111467\pi\)
−0.939310 + 0.343069i \(0.888533\pi\)
\(38\) 178.073 0.760190
\(39\) −119.145 74.6819i −0.489193 0.306633i
\(40\) 201.285 0.795648
\(41\) 265.726i 1.01218i −0.862480 0.506091i \(-0.831090\pi\)
0.862480 0.506091i \(-0.168910\pi\)
\(42\) −102.218 −0.375538
\(43\) −211.855 −0.751338 −0.375669 0.926754i \(-0.622587\pi\)
−0.375669 + 0.926754i \(0.622587\pi\)
\(44\) 285.671i 0.978785i
\(45\) 86.9257i 0.287958i
\(46\) 109.696i 0.351604i
\(47\) 67.5535i 0.209653i −0.994491 0.104827i \(-0.966571\pi\)
0.994491 0.104827i \(-0.0334287\pi\)
\(48\) 41.0363 0.123398
\(49\) −157.145 −0.458150
\(50\) 48.3197i 0.136669i
\(51\) −258.436 −0.709574
\(52\) −225.533 141.367i −0.601459 0.377002i
\(53\) 686.581 1.77942 0.889710 0.456527i \(-0.150907\pi\)
0.889710 + 0.456527i \(0.150907\pi\)
\(54\) 41.1360i 0.103665i
\(55\) −485.866 −1.19117
\(56\) −466.073 −1.11217
\(57\) 350.639i 0.814795i
\(58\) 21.5512i 0.0487899i
\(59\) 91.9304i 0.202853i 0.994843 + 0.101426i \(0.0323406\pi\)
−0.994843 + 0.101426i \(0.967659\pi\)
\(60\) 164.544i 0.354042i
\(61\) 329.006 0.690572 0.345286 0.938498i \(-0.387782\pi\)
0.345286 + 0.938498i \(0.387782\pi\)
\(62\) −298.945 −0.612355
\(63\) 201.275i 0.402513i
\(64\) −176.333 −0.344400
\(65\) 240.436 383.585i 0.458807 0.731967i
\(66\) 229.927 0.428820
\(67\) 768.370i 1.40106i 0.713621 + 0.700532i \(0.247054\pi\)
−0.713621 + 0.700532i \(0.752946\pi\)
\(68\) −489.201 −0.872416
\(69\) −216.000 −0.376860
\(70\) 329.088i 0.561908i
\(71\) 264.969i 0.442902i 0.975171 + 0.221451i \(0.0710793\pi\)
−0.975171 + 0.221451i \(0.928921\pi\)
\(72\) 187.563i 0.307008i
\(73\) 771.306i 1.23664i −0.785927 0.618319i \(-0.787814\pi\)
0.785927 0.618319i \(-0.212186\pi\)
\(74\) 235.273 0.369594
\(75\) 95.1454 0.146486
\(76\) 663.734i 1.00178i
\(77\) 1125.02 1.66503
\(78\) −113.782 + 181.525i −0.165170 + 0.263508i
\(79\) 1226.86 1.74725 0.873624 0.486602i \(-0.161764\pi\)
0.873624 + 0.486602i \(0.161764\pi\)
\(80\) 132.115i 0.184637i
\(81\) 81.0000 0.111111
\(82\) −404.849 −0.545220
\(83\) 514.019i 0.679771i −0.940467 0.339885i \(-0.889612\pi\)
0.940467 0.339885i \(-0.110388\pi\)
\(84\) 381.000i 0.494886i
\(85\) 832.027i 1.06172i
\(86\) 322.772i 0.404714i
\(87\) 42.4361 0.0522945
\(88\) 1048.38 1.26997
\(89\) 527.889i 0.628720i −0.949304 0.314360i \(-0.898210\pi\)
0.949304 0.314360i \(-0.101790\pi\)
\(90\) 132.436 0.155111
\(91\) −556.727 + 888.186i −0.641328 + 1.02316i
\(92\) −408.872 −0.463346
\(93\) 588.646i 0.656341i
\(94\) −102.921 −0.112931
\(95\) −1128.87 −1.21916
\(96\) 562.690i 0.598222i
\(97\) 74.2755i 0.0777478i −0.999244 0.0388739i \(-0.987623\pi\)
0.999244 0.0388739i \(-0.0123771\pi\)
\(98\) 239.420i 0.246786i
\(99\) 452.745i 0.459622i
\(100\) 180.103 0.180103
\(101\) −609.419 −0.600390 −0.300195 0.953878i \(-0.597052\pi\)
−0.300195 + 0.953878i \(0.597052\pi\)
\(102\) 393.742i 0.382218i
\(103\) 32.4361 0.0310293 0.0155147 0.999880i \(-0.495061\pi\)
0.0155147 + 0.999880i \(0.495061\pi\)
\(104\) −518.799 + 827.678i −0.489158 + 0.780389i
\(105\) 648.000 0.602270
\(106\) 1046.04i 0.958498i
\(107\) −1725.45 −1.55893 −0.779467 0.626444i \(-0.784510\pi\)
−0.779467 + 0.626444i \(0.784510\pi\)
\(108\) 153.327 0.136610
\(109\) 1273.43i 1.11902i 0.828825 + 0.559508i \(0.189010\pi\)
−0.828825 + 0.559508i \(0.810990\pi\)
\(110\) 740.244i 0.641632i
\(111\) 463.271i 0.396142i
\(112\) 305.911i 0.258088i
\(113\) 1114.73 0.928006 0.464003 0.885834i \(-0.346413\pi\)
0.464003 + 0.885834i \(0.346413\pi\)
\(114\) 534.218 0.438896
\(115\) 695.406i 0.563886i
\(116\) 80.3284 0.0642957
\(117\) −357.436 224.046i −0.282436 0.177034i
\(118\) 140.061 0.109268
\(119\) 1926.55i 1.48409i
\(120\) 603.855 0.459368
\(121\) −1199.59 −0.901272
\(122\) 501.259i 0.371982i
\(123\) 797.179i 0.584384i
\(124\) 1114.26i 0.806966i
\(125\) 1513.62i 1.08306i
\(126\) −306.654 −0.216817
\(127\) −1174.01 −0.820289 −0.410144 0.912021i \(-0.634522\pi\)
−0.410144 + 0.912021i \(0.634522\pi\)
\(128\) 1231.85i 0.850637i
\(129\) −635.564 −0.433785
\(130\) −584.413 366.318i −0.394280 0.247140i
\(131\) −1445.16 −0.963851 −0.481925 0.876212i \(-0.660062\pi\)
−0.481925 + 0.876212i \(0.660062\pi\)
\(132\) 857.013i 0.565102i
\(133\) 2613.89 1.70416
\(134\) 1170.65 0.754695
\(135\) 260.777i 0.166253i
\(136\) 1795.30i 1.13195i
\(137\) 508.793i 0.317293i −0.987335 0.158646i \(-0.949287\pi\)
0.987335 0.158646i \(-0.0507130\pi\)
\(138\) 329.088i 0.202999i
\(139\) −757.018 −0.461938 −0.230969 0.972961i \(-0.574190\pi\)
−0.230969 + 0.972961i \(0.574190\pi\)
\(140\) 1226.62 0.740486
\(141\) 202.661i 0.121043i
\(142\) 403.695 0.238573
\(143\) 1252.29 1997.87i 0.732320 1.16832i
\(144\) 123.109 0.0712436
\(145\) 136.622i 0.0782470i
\(146\) −1175.13 −0.666125
\(147\) −471.436 −0.264513
\(148\) 876.939i 0.487054i
\(149\) 3247.79i 1.78570i −0.450352 0.892851i \(-0.648702\pi\)
0.450352 0.892851i \(-0.351298\pi\)
\(150\) 144.959i 0.0789058i
\(151\) 795.296i 0.428611i −0.976767 0.214305i \(-0.931251\pi\)
0.976767 0.214305i \(-0.0687488\pi\)
\(152\) 2435.82 1.29981
\(153\) −775.308 −0.409673
\(154\) 1714.03i 0.896884i
\(155\) 1895.13 0.982067
\(156\) −676.600 424.102i −0.347252 0.217662i
\(157\) −65.2732 −0.0331807 −0.0165903 0.999862i \(-0.505281\pi\)
−0.0165903 + 0.999862i \(0.505281\pi\)
\(158\) 1869.19i 0.941169i
\(159\) 2059.74 1.02735
\(160\) 1811.56 0.895104
\(161\) 1610.20i 0.788210i
\(162\) 123.408i 0.0598509i
\(163\) 1855.39i 0.891568i 0.895140 + 0.445784i \(0.147075\pi\)
−0.895140 + 0.445784i \(0.852925\pi\)
\(164\) 1509.00i 0.718495i
\(165\) −1457.60 −0.687721
\(166\) −783.137 −0.366164
\(167\) 3532.54i 1.63686i 0.574604 + 0.818432i \(0.305156\pi\)
−0.574604 + 0.818432i \(0.694844\pi\)
\(168\) −1398.22 −0.642112
\(169\) 957.581 + 1977.33i 0.435859 + 0.900015i
\(170\) −1267.64 −0.571903
\(171\) 1051.92i 0.470422i
\(172\) −1203.08 −0.533335
\(173\) 3178.36 1.39680 0.698400 0.715708i \(-0.253896\pi\)
0.698400 + 0.715708i \(0.253896\pi\)
\(174\) 64.6537i 0.0281689i
\(175\) 709.275i 0.306378i
\(176\) 688.111i 0.294706i
\(177\) 275.791i 0.117117i
\(178\) −804.267 −0.338665
\(179\) −2741.16 −1.14460 −0.572302 0.820043i \(-0.693950\pi\)
−0.572302 + 0.820043i \(0.693950\pi\)
\(180\) 493.632i 0.204406i
\(181\) −3871.09 −1.58970 −0.794850 0.606806i \(-0.792450\pi\)
−0.794850 + 0.606806i \(0.792450\pi\)
\(182\) 1353.20 + 848.204i 0.551131 + 0.345456i
\(183\) 987.018 0.398702
\(184\) 1500.51i 0.601189i
\(185\) −1491.49 −0.592737
\(186\) −896.834 −0.353544
\(187\) 4333.54i 1.69465i
\(188\) 383.621i 0.148822i
\(189\) 603.826i 0.232391i
\(190\) 1719.90i 0.656708i
\(191\) −928.291 −0.351669 −0.175834 0.984420i \(-0.556262\pi\)
−0.175834 + 0.984420i \(0.556262\pi\)
\(192\) −528.999 −0.198840
\(193\) 2261.51i 0.843456i 0.906722 + 0.421728i \(0.138576\pi\)
−0.906722 + 0.421728i \(0.861424\pi\)
\(194\) −113.163 −0.0418795
\(195\) 721.308 1150.75i 0.264892 0.422601i
\(196\) −892.394 −0.325216
\(197\) 2265.59i 0.819374i −0.912226 0.409687i \(-0.865638\pi\)
0.912226 0.409687i \(-0.134362\pi\)
\(198\) 689.782 0.247579
\(199\) 260.895 0.0929366 0.0464683 0.998920i \(-0.485203\pi\)
0.0464683 + 0.998920i \(0.485203\pi\)
\(200\) 660.955i 0.233683i
\(201\) 2305.11i 0.808905i
\(202\) 928.483i 0.323405i
\(203\) 316.346i 0.109375i
\(204\) −1467.60 −0.503690
\(205\) 2566.49 0.874399
\(206\) 49.4181i 0.0167142i
\(207\) −648.000 −0.217580
\(208\) −543.254 340.519i −0.181096 0.113513i
\(209\) −5879.63 −1.94595
\(210\) 987.264i 0.324417i
\(211\) 5851.22 1.90907 0.954537 0.298092i \(-0.0963502\pi\)
0.954537 + 0.298092i \(0.0963502\pi\)
\(212\) 3898.94 1.26312
\(213\) 794.907i 0.255710i
\(214\) 2628.82i 0.839732i
\(215\) 2046.18i 0.649062i
\(216\) 562.690i 0.177251i
\(217\) −4388.15 −1.37275
\(218\) 1940.15 0.602767
\(219\) 2313.92i 0.713973i
\(220\) −2759.13 −0.845547
\(221\) 3421.27 + 2144.50i 1.04136 + 0.652736i
\(222\) 705.820 0.213385
\(223\) 3463.60i 1.04009i −0.854139 0.520045i \(-0.825915\pi\)
0.854139 0.520045i \(-0.174085\pi\)
\(224\) −4194.65 −1.25119
\(225\) 285.436 0.0845737
\(226\) 1698.35i 0.499878i
\(227\) 5329.15i 1.55819i 0.626908 + 0.779093i \(0.284320\pi\)
−0.626908 + 0.779093i \(0.715680\pi\)
\(228\) 1991.20i 0.578380i
\(229\) 4773.95i 1.37761i −0.724949 0.688803i \(-0.758137\pi\)
0.724949 0.688803i \(-0.241863\pi\)
\(230\) −1059.49 −0.303742
\(231\) 3375.05 0.961308
\(232\) 294.795i 0.0834233i
\(233\) 4813.78 1.35348 0.676741 0.736221i \(-0.263392\pi\)
0.676741 + 0.736221i \(0.263392\pi\)
\(234\) −341.346 + 544.574i −0.0953610 + 0.152136i
\(235\) 652.459 0.181114
\(236\) 522.052i 0.143995i
\(237\) 3680.58 1.00877
\(238\) 2935.20 0.799416
\(239\) 1683.19i 0.455549i 0.973714 + 0.227775i \(0.0731449\pi\)
−0.973714 + 0.227775i \(0.926855\pi\)
\(240\) 396.346i 0.106600i
\(241\) 664.861i 0.177707i 0.996045 + 0.0888537i \(0.0283204\pi\)
−0.996045 + 0.0888537i \(0.971680\pi\)
\(242\) 1827.65i 0.485477i
\(243\) 243.000 0.0641500
\(244\) 1868.35 0.490201
\(245\) 1517.77i 0.395784i
\(246\) −1214.55 −0.314783
\(247\) 2909.60 4641.89i 0.749528 1.19578i
\(248\) −4089.20 −1.04703
\(249\) 1542.06i 0.392466i
\(250\) 2306.08 0.583398
\(251\) −2142.04 −0.538662 −0.269331 0.963048i \(-0.586802\pi\)
−0.269331 + 0.963048i \(0.586802\pi\)
\(252\) 1143.00i 0.285723i
\(253\) 3621.96i 0.900042i
\(254\) 1788.67i 0.441855i
\(255\) 2496.08i 0.612983i
\(256\) −3287.46 −0.802603
\(257\) −3152.62 −0.765194 −0.382597 0.923915i \(-0.624970\pi\)
−0.382597 + 0.923915i \(0.624970\pi\)
\(258\) 968.317i 0.233662i
\(259\) 3453.52 0.828539
\(260\) 1365.38 2178.29i 0.325683 0.519585i
\(261\) 127.308 0.0301923
\(262\) 2201.79i 0.519186i
\(263\) −2167.71 −0.508238 −0.254119 0.967173i \(-0.581786\pi\)
−0.254119 + 0.967173i \(0.581786\pi\)
\(264\) 3145.13 0.733216
\(265\) 6631.28i 1.53719i
\(266\) 3982.40i 0.917958i
\(267\) 1583.67i 0.362992i
\(268\) 4363.40i 0.994542i
\(269\) −3248.98 −0.736409 −0.368204 0.929745i \(-0.620027\pi\)
−0.368204 + 0.929745i \(0.620027\pi\)
\(270\) 397.308 0.0895534
\(271\) 4897.70i 1.09784i 0.835876 + 0.548919i \(0.184960\pi\)
−0.835876 + 0.548919i \(0.815040\pi\)
\(272\) −1178.36 −0.262679
\(273\) −1670.18 + 2664.56i −0.370271 + 0.590719i
\(274\) −775.175 −0.170912
\(275\) 1595.43i 0.349847i
\(276\) −1226.62 −0.267513
\(277\) −2900.33 −0.629111 −0.314555 0.949239i \(-0.601855\pi\)
−0.314555 + 0.949239i \(0.601855\pi\)
\(278\) 1153.36i 0.248827i
\(279\) 1765.94i 0.378939i
\(280\) 4501.52i 0.960776i
\(281\) 4396.53i 0.933364i −0.884425 0.466682i \(-0.845449\pi\)
0.884425 0.466682i \(-0.154551\pi\)
\(282\) −308.764 −0.0652009
\(283\) 559.151 0.117449 0.0587245 0.998274i \(-0.481297\pi\)
0.0587245 + 0.998274i \(0.481297\pi\)
\(284\) 1504.70i 0.314393i
\(285\) −3386.62 −0.703880
\(286\) −3043.86 1907.93i −0.629327 0.394470i
\(287\) −5942.69 −1.22225
\(288\) 1688.07i 0.345384i
\(289\) 2508.02 0.510487
\(290\) 208.151 0.0421484
\(291\) 222.827i 0.0448877i
\(292\) 4380.08i 0.877825i
\(293\) 6918.65i 1.37950i 0.724050 + 0.689748i \(0.242278\pi\)
−0.724050 + 0.689748i \(0.757722\pi\)
\(294\) 718.259i 0.142482i
\(295\) −887.901 −0.175239
\(296\) 3218.25 0.631949
\(297\) 1358.24i 0.265363i
\(298\) −4948.19 −0.961883
\(299\) 2859.49 + 1792.37i 0.553072 + 0.346673i
\(300\) 540.310 0.103983
\(301\) 4737.90i 0.907270i
\(302\) −1211.68 −0.230875
\(303\) −1828.26 −0.346635
\(304\) 1598.77i 0.301631i
\(305\) 3177.67i 0.596567i
\(306\) 1181.22i 0.220674i
\(307\) 8980.94i 1.66961i 0.550548 + 0.834803i \(0.314419\pi\)
−0.550548 + 0.834803i \(0.685581\pi\)
\(308\) 6388.73 1.18192
\(309\) 97.3082 0.0179148
\(310\) 2887.33i 0.528998i
\(311\) 7943.13 1.44827 0.724137 0.689656i \(-0.242238\pi\)
0.724137 + 0.689656i \(0.242238\pi\)
\(312\) −1556.40 + 2483.03i −0.282416 + 0.450558i
\(313\) −5059.57 −0.913686 −0.456843 0.889547i \(-0.651020\pi\)
−0.456843 + 0.889547i \(0.651020\pi\)
\(314\) 99.4473i 0.0178730i
\(315\) 1944.00 0.347721
\(316\) 6967.07 1.24028
\(317\) 8702.12i 1.54183i −0.636939 0.770914i \(-0.719800\pi\)
0.636939 0.770914i \(-0.280200\pi\)
\(318\) 3138.13i 0.553389i
\(319\) 711.582i 0.124893i
\(320\) 1703.10i 0.297519i
\(321\) −5176.36 −0.900051
\(322\) 2453.23 0.424576
\(323\) 10068.6i 1.73447i
\(324\) 459.981 0.0788719
\(325\) −1259.57 789.515i −0.214980 0.134752i
\(326\) 2826.79 0.480250
\(327\) 3820.30i 0.646064i
\(328\) −5537.84 −0.932244
\(329\) −1510.76 −0.253164
\(330\) 2220.73i 0.370446i
\(331\) 1737.65i 0.288549i −0.989538 0.144275i \(-0.953915\pi\)
0.989538 0.144275i \(-0.0460848\pi\)
\(332\) 2919.00i 0.482533i
\(333\) 1389.81i 0.228713i
\(334\) 5382.02 0.881710
\(335\) −7421.23 −1.21034
\(336\) 917.734i 0.149007i
\(337\) −2917.47 −0.471586 −0.235793 0.971803i \(-0.575769\pi\)
−0.235793 + 0.971803i \(0.575769\pi\)
\(338\) 3012.58 1458.93i 0.484800 0.234779i
\(339\) 3344.18 0.535785
\(340\) 4724.90i 0.753658i
\(341\) 9870.61 1.56752
\(342\) 1602.65 0.253397
\(343\) 4156.44i 0.654305i
\(344\) 4415.13i 0.692000i
\(345\) 2086.22i 0.325560i
\(346\) 4842.41i 0.752397i
\(347\) 5081.23 0.786095 0.393047 0.919518i \(-0.371421\pi\)
0.393047 + 0.919518i \(0.371421\pi\)
\(348\) 240.985 0.0371211
\(349\) 4266.14i 0.654330i −0.944967 0.327165i \(-0.893907\pi\)
0.944967 0.327165i \(-0.106093\pi\)
\(350\) −1080.62 −0.165033
\(351\) −1072.31 672.137i −0.163064 0.102211i
\(352\) 9435.38 1.42871
\(353\) 3264.49i 0.492213i 0.969243 + 0.246106i \(0.0791513\pi\)
−0.969243 + 0.246106i \(0.920849\pi\)
\(354\) 420.183 0.0630861
\(355\) −2559.18 −0.382612
\(356\) 2997.76i 0.446295i
\(357\) 5779.65i 0.856838i
\(358\) 4176.31i 0.616550i
\(359\) 4416.98i 0.649357i 0.945824 + 0.324679i \(0.105256\pi\)
−0.945824 + 0.324679i \(0.894744\pi\)
\(360\) 1811.56 0.265216
\(361\) −6801.87 −0.991670
\(362\) 5897.82i 0.856305i
\(363\) −3598.78 −0.520350
\(364\) −3161.53 + 5043.81i −0.455245 + 0.726285i
\(365\) 7449.59 1.06830
\(366\) 1503.78i 0.214764i
\(367\) −1740.22 −0.247516 −0.123758 0.992312i \(-0.539495\pi\)
−0.123758 + 0.992312i \(0.539495\pi\)
\(368\) −984.872 −0.139511
\(369\) 2391.54i 0.337394i
\(370\) 2272.37i 0.319283i
\(371\) 15354.7i 2.14872i
\(372\) 3342.79i 0.465902i
\(373\) 1176.28 0.163285 0.0816427 0.996662i \(-0.473983\pi\)
0.0816427 + 0.996662i \(0.473983\pi\)
\(374\) −6602.39 −0.912838
\(375\) 4540.86i 0.625304i
\(376\) −1407.84 −0.193095
\(377\) −561.785 352.134i −0.0767464 0.0481056i
\(378\) −919.962 −0.125179
\(379\) 7135.54i 0.967092i −0.875319 0.483546i \(-0.839349\pi\)
0.875319 0.483546i \(-0.160651\pi\)
\(380\) −6410.62 −0.865415
\(381\) −3522.04 −0.473594
\(382\) 1414.30i 0.189429i
\(383\) 1942.87i 0.259207i 0.991566 + 0.129603i \(0.0413704\pi\)
−0.991566 + 0.129603i \(0.958630\pi\)
\(384\) 3695.56i 0.491116i
\(385\) 10865.9i 1.43838i
\(386\) 3445.53 0.454334
\(387\) −1906.69 −0.250446
\(388\) 421.794i 0.0551891i
\(389\) 7545.92 0.983531 0.491766 0.870728i \(-0.336352\pi\)
0.491766 + 0.870728i \(0.336352\pi\)
\(390\) −1753.24 1098.95i −0.227638 0.142686i
\(391\) 6202.47 0.802231
\(392\) 3274.97i 0.421967i
\(393\) −4335.49 −0.556480
\(394\) −3451.75 −0.441362
\(395\) 11849.5i 1.50940i
\(396\) 2571.04i 0.326262i
\(397\) 415.922i 0.0525806i 0.999654 + 0.0262903i \(0.00836943\pi\)
−0.999654 + 0.0262903i \(0.991631\pi\)
\(398\) 397.489i 0.0500611i
\(399\) 7841.67 0.983896
\(400\) 433.824 0.0542280
\(401\) 958.178i 0.119324i −0.998219 0.0596622i \(-0.980998\pi\)
0.998219 0.0596622i \(-0.0190024\pi\)
\(402\) 3511.96 0.435723
\(403\) −4884.58 + 7792.71i −0.603767 + 0.963233i
\(404\) −3460.75 −0.426185
\(405\) 782.331i 0.0959860i
\(406\) −481.970 −0.0589157
\(407\) −7768.29 −0.946093
\(408\) 5385.90i 0.653534i
\(409\) 4284.83i 0.518022i −0.965874 0.259011i \(-0.916603\pi\)
0.965874 0.259011i \(-0.0833966\pi\)
\(410\) 3910.20i 0.471002i
\(411\) 1526.38i 0.183189i
\(412\) 184.197 0.0220261
\(413\) 2055.92 0.244953
\(414\) 987.264i 0.117201i
\(415\) 4964.61 0.587236
\(416\) −4669.20 + 7449.10i −0.550303 + 0.877938i
\(417\) −2271.05 −0.266700
\(418\) 8957.95i 1.04820i
\(419\) −9949.01 −1.16000 −0.580001 0.814616i \(-0.696948\pi\)
−0.580001 + 0.814616i \(0.696948\pi\)
\(420\) 3679.85 0.427520
\(421\) 377.250i 0.0436724i 0.999762 + 0.0218362i \(0.00695122\pi\)
−0.999762 + 0.0218362i \(0.993049\pi\)
\(422\) 8914.66i 1.02834i
\(423\) 607.982i 0.0698843i
\(424\) 14308.6i 1.63889i
\(425\) −2732.11 −0.311828
\(426\) 1211.08 0.137740
\(427\) 7357.86i 0.833892i
\(428\) −9798.47 −1.10661
\(429\) 3756.87 5993.61i 0.422805 0.674532i
\(430\) −3117.47 −0.349622
\(431\) 2437.13i 0.272373i −0.990683 0.136186i \(-0.956515\pi\)
0.990683 0.136186i \(-0.0434846\pi\)
\(432\) 369.327 0.0411325
\(433\) −11215.1 −1.24471 −0.622357 0.782733i \(-0.713825\pi\)
−0.622357 + 0.782733i \(0.713825\pi\)
\(434\) 6685.58i 0.739443i
\(435\) 409.865i 0.0451759i
\(436\) 7231.55i 0.794331i
\(437\) 8415.34i 0.921191i
\(438\) −3525.38 −0.384588
\(439\) 1835.19 0.199519 0.0997596 0.995012i \(-0.468193\pi\)
0.0997596 + 0.995012i \(0.468193\pi\)
\(440\) 10125.6i 1.09709i
\(441\) −1414.31 −0.152717
\(442\) 3267.26 5212.50i 0.351601 0.560935i
\(443\) 11610.1 1.24518 0.622588 0.782550i \(-0.286081\pi\)
0.622588 + 0.782550i \(0.286081\pi\)
\(444\) 2630.82i 0.281201i
\(445\) 5098.56 0.543135
\(446\) −5276.99 −0.560253
\(447\) 9743.38i 1.03098i
\(448\) 3943.50i 0.415877i
\(449\) 14087.0i 1.48064i 0.672255 + 0.740319i \(0.265326\pi\)
−0.672255 + 0.740319i \(0.734674\pi\)
\(450\) 434.878i 0.0455563i
\(451\) 13367.4 1.39566
\(452\) 6330.29 0.658743
\(453\) 2385.89i 0.247459i
\(454\) 8119.26 0.839330
\(455\) −8578.47 5377.10i −0.883878 0.554027i
\(456\) 7307.45 0.750445
\(457\) 2375.01i 0.243103i 0.992585 + 0.121552i \(0.0387870\pi\)
−0.992585 + 0.121552i \(0.961213\pi\)
\(458\) −7273.38 −0.742058
\(459\) −2325.92 −0.236525
\(460\) 3949.05i 0.400273i
\(461\) 6372.06i 0.643766i −0.946779 0.321883i \(-0.895684\pi\)
0.946779 0.321883i \(-0.104316\pi\)
\(462\) 5142.08i 0.517816i
\(463\) 63.4732i 0.00637117i 0.999995 + 0.00318558i \(0.00101400\pi\)
−0.999995 + 0.00318558i \(0.998986\pi\)
\(464\) 193.491 0.0193591
\(465\) 5685.38 0.566996
\(466\) 7334.06i 0.729064i
\(467\) 7855.78 0.778420 0.389210 0.921149i \(-0.372748\pi\)
0.389210 + 0.921149i \(0.372748\pi\)
\(468\) −2029.80 1272.31i −0.200486 0.125667i
\(469\) 17183.8 1.69184
\(470\) 994.058i 0.0975584i
\(471\) −195.820 −0.0191569
\(472\) 1915.86 0.186832
\(473\) 10657.3i 1.03599i
\(474\) 5607.57i 0.543384i
\(475\) 3706.85i 0.358068i
\(476\) 10940.4i 1.05348i
\(477\) 6179.23 0.593140
\(478\) 2564.43 0.245385
\(479\) 13033.3i 1.24323i 0.783324 + 0.621613i \(0.213523\pi\)
−0.783324 + 0.621613i \(0.786477\pi\)
\(480\) 5434.69 0.516789
\(481\) 3844.22 6132.96i 0.364410 0.581370i
\(482\) 1012.95 0.0957235
\(483\) 4830.61i 0.455073i
\(484\) −6812.23 −0.639766
\(485\) 717.384 0.0671643
\(486\) 370.224i 0.0345549i
\(487\) 69.8976i 0.00650383i −0.999995 0.00325191i \(-0.998965\pi\)
0.999995 0.00325191i \(-0.00103512\pi\)
\(488\) 6856.60i 0.636033i
\(489\) 5566.18i 0.514747i
\(490\) −2312.41 −0.213192
\(491\) 2625.66 0.241333 0.120667 0.992693i \(-0.461497\pi\)
0.120667 + 0.992693i \(0.461497\pi\)
\(492\) 4527.01i 0.414823i
\(493\) −1218.56 −0.111321
\(494\) −7072.18 4432.93i −0.644114 0.403739i
\(495\) −4372.80 −0.397056
\(496\) 2683.99i 0.242973i
\(497\) 5925.75 0.534821
\(498\) −2349.41 −0.211405
\(499\) 7631.34i 0.684621i 0.939587 + 0.342310i \(0.111209\pi\)
−0.939587 + 0.342310i \(0.888791\pi\)
\(500\) 8595.51i 0.768806i
\(501\) 10597.6i 0.945044i
\(502\) 3263.51i 0.290154i
\(503\) −4320.14 −0.382953 −0.191477 0.981497i \(-0.561328\pi\)
−0.191477 + 0.981497i \(0.561328\pi\)
\(504\) −4194.65 −0.370724
\(505\) 5886.01i 0.518662i
\(506\) −5518.26 −0.484815
\(507\) 2872.74 + 5932.00i 0.251643 + 0.519624i
\(508\) −6666.95 −0.582280
\(509\) 12450.7i 1.08422i −0.840308 0.542109i \(-0.817626\pi\)
0.840308 0.542109i \(-0.182374\pi\)
\(510\) −3802.92 −0.330188
\(511\) −17249.4 −1.49329
\(512\) 4846.21i 0.418309i
\(513\) 3155.75i 0.271598i
\(514\) 4803.18i 0.412178i
\(515\) 313.281i 0.0268054i
\(516\) −3609.23 −0.307921
\(517\) 3398.28 0.289083
\(518\) 5261.63i 0.446299i
\(519\) 9535.08 0.806443
\(520\) −7994.05 5010.78i −0.674158 0.422571i
\(521\) 14373.1 1.20863 0.604314 0.796746i \(-0.293447\pi\)
0.604314 + 0.796746i \(0.293447\pi\)
\(522\) 193.961i 0.0162633i
\(523\) −16946.7 −1.41688 −0.708439 0.705772i \(-0.750600\pi\)
−0.708439 + 0.705772i \(0.750600\pi\)
\(524\) −8206.76 −0.684187
\(525\) 2127.82i 0.176887i
\(526\) 3302.62i 0.273767i
\(527\) 16903.0i 1.39717i
\(528\) 2064.33i 0.170149i
\(529\) −6983.00 −0.573929
\(530\) 10103.1 0.828022
\(531\) 827.373i 0.0676176i
\(532\) 14843.7 1.20969
\(533\) −6614.98 + 10553.4i −0.537574 + 0.857630i
\(534\) −2412.80 −0.195528
\(535\) 16665.1i 1.34672i
\(536\) 16013.1 1.29041
\(537\) −8223.49 −0.660837
\(538\) 4950.00i 0.396673i
\(539\) 7905.20i 0.631727i
\(540\) 1480.90i 0.118014i
\(541\) 815.667i 0.0648212i −0.999475 0.0324106i \(-0.989682\pi\)
0.999475 0.0324106i \(-0.0103184\pi\)
\(542\) 7461.92 0.591359
\(543\) −11613.3 −0.917814
\(544\) 16157.7i 1.27345i
\(545\) −12299.3 −0.966689
\(546\) 4059.60 + 2544.61i 0.318196 + 0.199449i
\(547\) −17971.4 −1.40476 −0.702378 0.711804i \(-0.747878\pi\)
−0.702378 + 0.711804i \(0.747878\pi\)
\(548\) 2889.32i 0.225230i
\(549\) 2961.05 0.230191
\(550\) 2430.72 0.188448
\(551\) 1653.31i 0.127828i
\(552\) 4501.52i 0.347097i
\(553\) 27437.4i 2.10987i
\(554\) 4418.81i 0.338876i
\(555\) −4474.47 −0.342217
\(556\) −4298.94 −0.327906
\(557\) 6760.83i 0.514301i −0.966371 0.257151i \(-0.917216\pi\)
0.966371 0.257151i \(-0.0827836\pi\)
\(558\) −2690.50 −0.204118
\(559\) 8413.83 + 5273.90i 0.636614 + 0.399038i
\(560\) 2954.62 0.222956
\(561\) 13000.6i 0.978408i
\(562\) −6698.36 −0.502764
\(563\) 12962.7 0.970359 0.485179 0.874415i \(-0.338754\pi\)
0.485179 + 0.874415i \(0.338754\pi\)
\(564\) 1150.86i 0.0859222i
\(565\) 10766.5i 0.801681i
\(566\) 851.898i 0.0632649i
\(567\) 1811.48i 0.134171i
\(568\) 5522.05 0.407923
\(569\) 164.757 0.0121388 0.00606938 0.999982i \(-0.498068\pi\)
0.00606938 + 0.999982i \(0.498068\pi\)
\(570\) 5159.70i 0.379151i
\(571\) −5216.55 −0.382322 −0.191161 0.981559i \(-0.561225\pi\)
−0.191161 + 0.981559i \(0.561225\pi\)
\(572\) 7111.48 11345.5i 0.519836 0.829331i
\(573\) −2784.87 −0.203036
\(574\) 9054.01i 0.658375i
\(575\) −2283.49 −0.165614
\(576\) −1587.00 −0.114800
\(577\) 12753.3i 0.920151i 0.887880 + 0.460076i \(0.152178\pi\)
−0.887880 + 0.460076i \(0.847822\pi\)
\(578\) 3821.11i 0.274978i
\(579\) 6784.53i 0.486970i
\(580\) 775.844i 0.0555434i
\(581\) −11495.5 −0.820849
\(582\) −339.489 −0.0241791
\(583\) 34538.5i 2.45358i
\(584\) −16074.3 −1.13897
\(585\) 2163.92 3452.26i 0.152936 0.243989i
\(586\) 10540.9 0.743076
\(587\) 1575.38i 0.110771i 0.998465 + 0.0553857i \(0.0176388\pi\)
−0.998465 + 0.0553857i \(0.982361\pi\)
\(588\) −2677.18 −0.187764
\(589\) 22933.6 1.60435
\(590\) 1352.77i 0.0943941i
\(591\) 6796.77i 0.473066i
\(592\) 2112.33i 0.146649i
\(593\) 3845.95i 0.266331i −0.991094 0.133165i \(-0.957486\pi\)
0.991094 0.133165i \(-0.0425142\pi\)
\(594\) 2069.35 0.142940
\(595\) −18607.4 −1.28207
\(596\) 18443.5i 1.26758i
\(597\) 782.686 0.0536570
\(598\) 2730.77 4356.59i 0.186738 0.297917i
\(599\) 6107.20 0.416583 0.208292 0.978067i \(-0.433210\pi\)
0.208292 + 0.978067i \(0.433210\pi\)
\(600\) 1982.86i 0.134917i
\(601\) 9638.90 0.654208 0.327104 0.944988i \(-0.393927\pi\)
0.327104 + 0.944988i \(0.393927\pi\)
\(602\) 7218.46 0.488708
\(603\) 6915.33i 0.467022i
\(604\) 4516.31i 0.304248i
\(605\) 11586.2i 0.778586i
\(606\) 2785.45i 0.186718i
\(607\) 11821.7 0.790489 0.395244 0.918576i \(-0.370660\pi\)
0.395244 + 0.918576i \(0.370660\pi\)
\(608\) 21922.4 1.46228
\(609\) 949.037i 0.0631477i
\(610\) 4841.36 0.321346
\(611\) −1681.67 + 2682.90i −0.111347 + 0.177640i
\(612\) −4402.80 −0.290805
\(613\) 8107.86i 0.534214i 0.963667 + 0.267107i \(0.0860677\pi\)
−0.963667 + 0.267107i \(0.913932\pi\)
\(614\) 13683.0 0.899347
\(615\) 7699.48 0.504834
\(616\) 23445.8i 1.53354i
\(617\) 27647.6i 1.80397i 0.431768 + 0.901985i \(0.357890\pi\)
−0.431768 + 0.901985i \(0.642110\pi\)
\(618\) 148.254i 0.00964995i
\(619\) 29181.9i 1.89486i −0.319956 0.947432i \(-0.603668\pi\)
0.319956 0.947432i \(-0.396332\pi\)
\(620\) 10762.0 0.697118
\(621\) −1944.00 −0.125620
\(622\) 12101.8i 0.780125i
\(623\) −11805.7 −0.759204
\(624\) −1629.76 1021.56i −0.104556 0.0655369i
\(625\) −10654.8 −0.681905
\(626\) 7708.53i 0.492165i
\(627\) −17638.9 −1.12349
\(628\) −370.672 −0.0235532
\(629\) 13302.9i 0.843277i
\(630\) 2961.79i 0.187303i
\(631\) 2209.34i 0.139386i 0.997569 + 0.0696928i \(0.0222019\pi\)
−0.997569 + 0.0696928i \(0.977798\pi\)
\(632\) 25568.2i 1.60926i
\(633\) 17553.7 1.10220
\(634\) −13258.2 −0.830518
\(635\) 11339.1i 0.708627i
\(636\) 11696.8 0.729260
\(637\) 6241.05 + 3911.97i 0.388194 + 0.243325i
\(638\) 1084.13 0.0672748
\(639\) 2384.72i 0.147634i
\(640\) 11897.8 0.734844
\(641\) 18256.0 1.12491 0.562455 0.826828i \(-0.309857\pi\)
0.562455 + 0.826828i \(0.309857\pi\)
\(642\) 7886.47i 0.484820i
\(643\) 1281.61i 0.0786033i 0.999227 + 0.0393016i \(0.0125133\pi\)
−0.999227 + 0.0393016i \(0.987487\pi\)
\(644\) 9143.99i 0.559509i
\(645\) 6138.54i 0.374736i
\(646\) −15340.1 −0.934287
\(647\) −16393.2 −0.996107 −0.498054 0.867146i \(-0.665952\pi\)
−0.498054 + 0.867146i \(0.665952\pi\)
\(648\) 1688.07i 0.102336i
\(649\) −4624.56 −0.279707
\(650\) −1202.87 + 1919.02i −0.0725853 + 0.115800i
\(651\) −13164.4 −0.792557
\(652\) 10536.4i 0.632878i
\(653\) 16759.2 1.00434 0.502172 0.864768i \(-0.332534\pi\)
0.502172 + 0.864768i \(0.332534\pi\)
\(654\) 5820.44 0.348008
\(655\) 13958.0i 0.832646i
\(656\) 3634.81i 0.216335i
\(657\) 6941.76i 0.412213i
\(658\) 2301.73i 0.136369i
\(659\) −29659.3 −1.75320 −0.876601 0.481217i \(-0.840195\pi\)
−0.876601 + 0.481217i \(0.840195\pi\)
\(660\) −8277.38 −0.488177
\(661\) 10386.0i 0.611147i 0.952169 + 0.305573i \(0.0988481\pi\)
−0.952169 + 0.305573i \(0.901152\pi\)
\(662\) −2647.40 −0.155429
\(663\) 10263.8 + 6433.50i 0.601227 + 0.376857i
\(664\) −10712.4 −0.626084
\(665\) 25246.0i 1.47218i
\(666\) 2117.46 0.123198
\(667\) −1018.47 −0.0591232
\(668\) 20060.5i 1.16192i
\(669\) 10390.8i 0.600496i
\(670\) 11306.7i 0.651962i
\(671\) 16550.6i 0.952206i
\(672\) −12584.0 −0.722376
\(673\) 19449.6 1.11400 0.557002 0.830511i \(-0.311951\pi\)
0.557002 + 0.830511i \(0.311951\pi\)
\(674\) 4444.92i 0.254024i
\(675\) 856.308 0.0488286
\(676\) 5437.89 + 11228.8i 0.309393 + 0.638873i
\(677\) −6629.48 −0.376354 −0.188177 0.982135i \(-0.560258\pi\)
−0.188177 + 0.982135i \(0.560258\pi\)
\(678\) 5095.04i 0.288605i
\(679\) −1661.09 −0.0938835
\(680\) −17339.8 −0.977867
\(681\) 15987.5i 0.899619i
\(682\) 15038.4i 0.844356i
\(683\) 2526.40i 0.141537i 0.997493 + 0.0707687i \(0.0225452\pi\)
−0.997493 + 0.0707687i \(0.977455\pi\)
\(684\) 5973.61i 0.333928i
\(685\) 4914.13 0.274101
\(686\) −6332.57 −0.352447
\(687\) 14321.9i 0.795361i
\(688\) −2897.91 −0.160584
\(689\) −27267.7 17091.7i −1.50771 0.945055i
\(690\) −3178.47 −0.175365
\(691\) 3808.76i 0.209685i 0.994489 + 0.104842i \(0.0334338\pi\)
−0.994489 + 0.104842i \(0.966566\pi\)
\(692\) 18049.2 0.991515
\(693\) 10125.2 0.555011
\(694\) 7741.54i 0.423436i
\(695\) 7311.59i 0.399056i
\(696\) 884.384i 0.0481645i
\(697\) 22891.1i 1.24399i
\(698\) −6499.69 −0.352460
\(699\) 14441.3 0.781433
\(700\) 4027.81i 0.217482i
\(701\) −33617.8 −1.81131 −0.905655 0.424015i \(-0.860620\pi\)
−0.905655 + 0.424015i \(0.860620\pi\)
\(702\) −1024.04 + 1633.72i −0.0550567 + 0.0878359i
\(703\) −18049.0 −0.968323
\(704\) 8870.43i 0.474882i
\(705\) 1957.38 0.104566
\(706\) 4973.63 0.265134
\(707\) 13629.0i 0.724994i
\(708\) 1566.16i 0.0831353i
\(709\) 26606.5i 1.40935i −0.709530 0.704675i \(-0.751093\pi\)
0.709530 0.704675i \(-0.248907\pi\)
\(710\) 3899.05i 0.206097i
\(711\) 11041.7 0.582416
\(712\) −11001.4 −0.579066
\(713\) 14127.5i 0.742046i
\(714\) 8805.61 0.461543
\(715\) 19296.2 + 12095.1i 1.00928 + 0.632633i
\(716\) −15566.5 −0.812494
\(717\) 5049.56i 0.263011i
\(718\) 6729.51 0.349781
\(719\) 16539.3 0.857877 0.428939 0.903334i \(-0.358888\pi\)
0.428939 + 0.903334i \(0.358888\pi\)
\(720\) 1189.04i 0.0615456i
\(721\) 725.398i 0.0374691i
\(722\) 10363.0i 0.534171i
\(723\) 1994.58i 0.102599i
\(724\) −21983.1 −1.12844
\(725\) 448.622 0.0229812
\(726\) 5482.94i 0.280291i
\(727\) 12757.5 0.650823 0.325411 0.945573i \(-0.394497\pi\)
0.325411 + 0.945573i \(0.394497\pi\)
\(728\) 18510.1 + 11602.4i 0.942350 + 0.590678i
\(729\) 729.000 0.0370370
\(730\) 11349.9i 0.575448i
\(731\) 18250.3 0.923408
\(732\) 5605.06 0.283017
\(733\) 20523.4i 1.03417i −0.855933 0.517087i \(-0.827016\pi\)
0.855933 0.517087i \(-0.172984\pi\)
\(734\) 2651.31i 0.133327i
\(735\) 4553.32i 0.228506i
\(736\) 13504.6i 0.676338i
\(737\) −38652.9 −1.93188
\(738\) −3643.64 −0.181740
\(739\) 7462.66i 0.371473i −0.982600 0.185736i \(-0.940533\pi\)
0.982600 0.185736i \(-0.0594670\pi\)
\(740\) −8469.84 −0.420753
\(741\) 8728.80 13925.7i 0.432740 0.690381i
\(742\) −23393.7 −1.15742
\(743\) 18847.8i 0.930632i −0.885145 0.465316i \(-0.845941\pi\)
0.885145 0.465316i \(-0.154059\pi\)
\(744\) −12267.6 −0.604506
\(745\) 31368.5 1.54262
\(746\) 1792.13i 0.0879549i
\(747\) 4626.17i 0.226590i
\(748\) 24609.2i 1.20294i
\(749\) 38587.9i 1.88247i
\(750\) 6918.25 0.336825
\(751\) 20832.6 1.01224 0.506119 0.862464i \(-0.331080\pi\)
0.506119 + 0.862464i \(0.331080\pi\)
\(752\) 924.050i 0.0448093i
\(753\) −6426.11 −0.310996
\(754\) −536.496 + 855.910i −0.0259125 + 0.0413400i
\(755\) 7681.29 0.370266
\(756\) 3429.00i 0.164962i
\(757\) −20860.9 −1.00159 −0.500795 0.865566i \(-0.666959\pi\)
−0.500795 + 0.865566i \(0.666959\pi\)
\(758\) −10871.4 −0.520932
\(759\) 10865.9i 0.519640i
\(760\) 23526.1i 1.12287i
\(761\) 4464.86i 0.212682i −0.994330 0.106341i \(-0.966086\pi\)
0.994330 0.106341i \(-0.0339135\pi\)
\(762\) 5366.01i 0.255105i
\(763\) 28479.0 1.35126
\(764\) −5271.56 −0.249631
\(765\) 7488.24i 0.353906i
\(766\) 2960.08 0.139624
\(767\) 2288.51 3651.03i 0.107736 0.171879i
\(768\) −9862.38 −0.463383
\(769\) 23797.7i 1.11595i −0.829857 0.557977i \(-0.811578\pi\)
0.829857 0.557977i \(-0.188422\pi\)
\(770\) 16554.8 0.774795
\(771\) −9457.85 −0.441785
\(772\) 12842.6i 0.598725i
\(773\) 29418.7i 1.36885i −0.729085 0.684423i \(-0.760054\pi\)
0.729085 0.684423i \(-0.239946\pi\)
\(774\) 2904.95i 0.134905i
\(775\) 6222.99i 0.288434i
\(776\) −1547.93 −0.0716075
\(777\) 10360.6 0.478357
\(778\) 11496.6i 0.529787i
\(779\) 31058.0 1.42846
\(780\) 4096.15 6534.88i 0.188033 0.299982i
\(781\) −13329.3 −0.610703
\(782\) 9449.80i 0.432128i
\(783\) 381.925 0.0174315
\(784\) −2149.56 −0.0979208
\(785\) 630.435i 0.0286640i
\(786\)