Properties

Label 690.3.b.a.599.17
Level $690$
Weight $3$
Character 690.599
Analytic conductor $18.801$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(88\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 599.17
Character \(\chi\) \(=\) 690.599
Dual form 690.3.b.a.599.18

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} +(-1.23483 - 2.73408i) q^{3} +2.00000 q^{4} +(4.77075 - 1.49664i) q^{5} +(1.74631 + 3.86657i) q^{6} +2.54772i q^{7} -2.82843 q^{8} +(-5.95040 + 6.75224i) q^{9} +O(q^{10})\) \(q-1.41421 q^{2} +(-1.23483 - 2.73408i) q^{3} +2.00000 q^{4} +(4.77075 - 1.49664i) q^{5} +(1.74631 + 3.86657i) q^{6} +2.54772i q^{7} -2.82843 q^{8} +(-5.95040 + 6.75224i) q^{9} +(-6.74686 + 2.11656i) q^{10} -15.8694i q^{11} +(-2.46966 - 5.46816i) q^{12} +23.6018i q^{13} -3.60302i q^{14} +(-9.98298 - 11.1955i) q^{15} +4.00000 q^{16} +32.3944 q^{17} +(8.41514 - 9.54911i) q^{18} +2.70349 q^{19} +(9.54151 - 2.99327i) q^{20} +(6.96567 - 3.14599i) q^{21} +22.4428i q^{22} -4.79583 q^{23} +(3.49262 + 7.73315i) q^{24} +(20.5202 - 14.2802i) q^{25} -33.3780i q^{26} +(25.8089 + 7.93103i) q^{27} +5.09544i q^{28} -13.8764i q^{29} +(14.1181 + 15.8329i) q^{30} +16.4061 q^{31} -5.65685 q^{32} +(-43.3883 + 19.5960i) q^{33} -45.8126 q^{34} +(3.81301 + 12.1545i) q^{35} +(-11.9008 + 13.5045i) q^{36} +8.63454i q^{37} -3.82331 q^{38} +(64.5293 - 29.1442i) q^{39} +(-13.4937 + 4.23313i) q^{40} +59.3900i q^{41} +(-9.85095 + 4.44911i) q^{42} +51.2988i q^{43} -31.7389i q^{44} +(-18.2822 + 41.1188i) q^{45} +6.78233 q^{46} -38.9126 q^{47} +(-4.93931 - 10.9363i) q^{48} +42.5091 q^{49} +(-29.0199 + 20.1952i) q^{50} +(-40.0015 - 88.5689i) q^{51} +47.2036i q^{52} +85.0310 q^{53} +(-36.4993 - 11.2162i) q^{54} +(-23.7508 - 75.7091i) q^{55} -7.20604i q^{56} +(-3.33834 - 7.39155i) q^{57} +19.6241i q^{58} -78.7364i q^{59} +(-19.9660 - 22.3911i) q^{60} -68.8771 q^{61} -23.2018 q^{62} +(-17.2028 - 15.1600i) q^{63} +8.00000 q^{64} +(35.3233 + 112.598i) q^{65} +(61.3604 - 27.7130i) q^{66} -66.3843i q^{67} +64.7888 q^{68} +(5.92203 + 13.1122i) q^{69} +(-5.39241 - 17.1891i) q^{70} -88.6614i q^{71} +(16.8303 - 19.0982i) q^{72} -37.1977i q^{73} -12.2111i q^{74} +(-64.3820 - 38.4702i) q^{75} +5.40697 q^{76} +40.4309 q^{77} +(-91.2581 + 41.2161i) q^{78} +104.696 q^{79} +(19.0830 - 5.98654i) q^{80} +(-10.1854 - 80.3571i) q^{81} -83.9902i q^{82} +76.6784 q^{83} +(13.9313 - 6.29199i) q^{84} +(154.546 - 48.4826i) q^{85} -72.5475i q^{86} +(-37.9391 + 17.1349i) q^{87} +44.8855i q^{88} -76.2385i q^{89} +(25.8550 - 58.1508i) q^{90} -60.1308 q^{91} -9.59166 q^{92} +(-20.2588 - 44.8557i) q^{93} +55.0308 q^{94} +(12.8977 - 4.04613i) q^{95} +(6.98524 + 15.4663i) q^{96} -73.6041i q^{97} -60.1170 q^{98} +(107.154 + 94.4295i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88q + 176q^{4} + 8q^{9} + O(q^{10}) \) \( 88q + 176q^{4} + 8q^{9} + 32q^{10} - 12q^{15} + 352q^{16} - 16q^{19} - 176q^{21} + 72q^{25} - 72q^{30} + 32q^{31} + 160q^{34} + 16q^{36} + 144q^{39} + 64q^{40} + 92q^{45} - 360q^{49} + 48q^{51} - 144q^{54} + 16q^{55} - 24q^{60} + 208q^{61} + 704q^{64} + 512q^{66} + 304q^{70} + 536q^{75} - 32q^{76} + 448q^{79} - 24q^{81} - 352q^{84} - 96q^{85} + 32q^{90} - 64q^{91} + 160q^{94} + 296q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 −0.707107
\(3\) −1.23483 2.73408i −0.411609 0.911360i
\(4\) 2.00000 0.500000
\(5\) 4.77075 1.49664i 0.954151 0.299327i
\(6\) 1.74631 + 3.86657i 0.291052 + 0.644429i
\(7\) 2.54772i 0.363960i 0.983302 + 0.181980i \(0.0582506\pi\)
−0.983302 + 0.181980i \(0.941749\pi\)
\(8\) −2.82843 −0.353553
\(9\) −5.95040 + 6.75224i −0.661156 + 0.750249i
\(10\) −6.74686 + 2.11656i −0.674686 + 0.211656i
\(11\) 15.8694i 1.44268i −0.692583 0.721338i \(-0.743527\pi\)
0.692583 0.721338i \(-0.256473\pi\)
\(12\) −2.46966 5.46816i −0.205805 0.455680i
\(13\) 23.6018i 1.81552i 0.419486 + 0.907762i \(0.362210\pi\)
−0.419486 + 0.907762i \(0.637790\pi\)
\(14\) 3.60302i 0.257358i
\(15\) −9.98298 11.1955i −0.665532 0.746369i
\(16\) 4.00000 0.250000
\(17\) 32.3944 1.90555 0.952776 0.303673i \(-0.0982131\pi\)
0.952776 + 0.303673i \(0.0982131\pi\)
\(18\) 8.41514 9.54911i 0.467508 0.530506i
\(19\) 2.70349 0.142289 0.0711444 0.997466i \(-0.477335\pi\)
0.0711444 + 0.997466i \(0.477335\pi\)
\(20\) 9.54151 2.99327i 0.477075 0.149664i
\(21\) 6.96567 3.14599i 0.331699 0.149809i
\(22\) 22.4428i 1.02013i
\(23\) −4.79583 −0.208514
\(24\) 3.49262 + 7.73315i 0.145526 + 0.322215i
\(25\) 20.5202 14.2802i 0.820806 0.571206i
\(26\) 33.3780i 1.28377i
\(27\) 25.8089 + 7.93103i 0.955885 + 0.293742i
\(28\) 5.09544i 0.181980i
\(29\) 13.8764i 0.478495i −0.970959 0.239248i \(-0.923099\pi\)
0.970959 0.239248i \(-0.0769008\pi\)
\(30\) 14.1181 + 15.8329i 0.470602 + 0.527763i
\(31\) 16.4061 0.529230 0.264615 0.964354i \(-0.414755\pi\)
0.264615 + 0.964354i \(0.414755\pi\)
\(32\) −5.65685 −0.176777
\(33\) −43.3883 + 19.5960i −1.31480 + 0.593819i
\(34\) −45.8126 −1.34743
\(35\) 3.81301 + 12.1545i 0.108943 + 0.347272i
\(36\) −11.9008 + 13.5045i −0.330578 + 0.375124i
\(37\) 8.63454i 0.233366i 0.993169 + 0.116683i \(0.0372261\pi\)
−0.993169 + 0.116683i \(0.962774\pi\)
\(38\) −3.82331 −0.100613
\(39\) 64.5293 29.1442i 1.65460 0.747286i
\(40\) −13.4937 + 4.23313i −0.337343 + 0.105828i
\(41\) 59.3900i 1.44854i 0.689518 + 0.724269i \(0.257822\pi\)
−0.689518 + 0.724269i \(0.742178\pi\)
\(42\) −9.85095 + 4.44911i −0.234546 + 0.105931i
\(43\) 51.2988i 1.19300i 0.802615 + 0.596498i \(0.203442\pi\)
−0.802615 + 0.596498i \(0.796558\pi\)
\(44\) 31.7389i 0.721338i
\(45\) −18.2822 + 41.1188i −0.406272 + 0.913752i
\(46\) 6.78233 0.147442
\(47\) −38.9126 −0.827928 −0.413964 0.910293i \(-0.635856\pi\)
−0.413964 + 0.910293i \(0.635856\pi\)
\(48\) −4.93931 10.9363i −0.102902 0.227840i
\(49\) 42.5091 0.867533
\(50\) −29.0199 + 20.1952i −0.580398 + 0.403904i
\(51\) −40.0015 88.5689i −0.784343 1.73665i
\(52\) 47.2036i 0.907762i
\(53\) 85.0310 1.60436 0.802180 0.597083i \(-0.203674\pi\)
0.802180 + 0.597083i \(0.203674\pi\)
\(54\) −36.4993 11.2162i −0.675913 0.207707i
\(55\) −23.7508 75.7091i −0.431832 1.37653i
\(56\) 7.20604i 0.128679i
\(57\) −3.33834 7.39155i −0.0585674 0.129676i
\(58\) 19.6241i 0.338347i
\(59\) 78.7364i 1.33452i −0.744827 0.667258i \(-0.767468\pi\)
0.744827 0.667258i \(-0.232532\pi\)
\(60\) −19.9660 22.3911i −0.332766 0.373185i
\(61\) −68.8771 −1.12913 −0.564567 0.825387i \(-0.690957\pi\)
−0.564567 + 0.825387i \(0.690957\pi\)
\(62\) −23.2018 −0.374222
\(63\) −17.2028 15.1600i −0.273060 0.240634i
\(64\) 8.00000 0.125000
\(65\) 35.3233 + 112.598i 0.543436 + 1.73228i
\(66\) 61.3604 27.7130i 0.929702 0.419893i
\(67\) 66.3843i 0.990810i −0.868662 0.495405i \(-0.835020\pi\)
0.868662 0.495405i \(-0.164980\pi\)
\(68\) 64.7888 0.952776
\(69\) 5.92203 + 13.1122i 0.0858265 + 0.190032i
\(70\) −5.39241 17.1891i −0.0770344 0.245559i
\(71\) 88.6614i 1.24875i −0.781124 0.624376i \(-0.785353\pi\)
0.781124 0.624376i \(-0.214647\pi\)
\(72\) 16.8303 19.0982i 0.233754 0.265253i
\(73\) 37.1977i 0.509557i −0.966999 0.254778i \(-0.917997\pi\)
0.966999 0.254778i \(-0.0820025\pi\)
\(74\) 12.2111i 0.165015i
\(75\) −64.3820 38.4702i −0.858426 0.512937i
\(76\) 5.40697 0.0711444
\(77\) 40.4309 0.525076
\(78\) −91.2581 + 41.2161i −1.16998 + 0.528411i
\(79\) 104.696 1.32526 0.662631 0.748946i \(-0.269440\pi\)
0.662631 + 0.748946i \(0.269440\pi\)
\(80\) 19.0830 5.98654i 0.238538 0.0748318i
\(81\) −10.1854 80.3571i −0.125746 0.992062i
\(82\) 83.9902i 1.02427i
\(83\) 76.6784 0.923836 0.461918 0.886923i \(-0.347161\pi\)
0.461918 + 0.886923i \(0.347161\pi\)
\(84\) 13.9313 6.29199i 0.165849 0.0749046i
\(85\) 154.546 48.4826i 1.81818 0.570384i
\(86\) 72.5475i 0.843575i
\(87\) −37.9391 + 17.1349i −0.436082 + 0.196953i
\(88\) 44.8855i 0.510063i
\(89\) 76.2385i 0.856612i −0.903634 0.428306i \(-0.859111\pi\)
0.903634 0.428306i \(-0.140889\pi\)
\(90\) 25.8550 58.1508i 0.287278 0.646120i
\(91\) −60.1308 −0.660778
\(92\) −9.59166 −0.104257
\(93\) −20.2588 44.8557i −0.217836 0.482320i
\(94\) 55.0308 0.585434
\(95\) 12.8977 4.04613i 0.135765 0.0425909i
\(96\) 6.98524 + 15.4663i 0.0727629 + 0.161107i
\(97\) 73.6041i 0.758805i −0.925232 0.379403i \(-0.876130\pi\)
0.925232 0.379403i \(-0.123870\pi\)
\(98\) −60.1170 −0.613439
\(99\) 107.154 + 94.4295i 1.08237 + 0.953833i
\(100\) 41.0403 28.5603i 0.410403 0.285603i
\(101\) 4.51645i 0.0447173i −0.999750 0.0223587i \(-0.992882\pi\)
0.999750 0.0223587i \(-0.00711758\pi\)
\(102\) 56.5707 + 125.255i 0.554614 + 1.22799i
\(103\) 45.2000i 0.438835i −0.975631 0.219417i \(-0.929584\pi\)
0.975631 0.219417i \(-0.0704156\pi\)
\(104\) 66.7560i 0.641884i
\(105\) 28.5231 25.4338i 0.271648 0.242227i
\(106\) −120.252 −1.13445
\(107\) 25.9543 0.242563 0.121282 0.992618i \(-0.461300\pi\)
0.121282 + 0.992618i \(0.461300\pi\)
\(108\) 51.6178 + 15.8621i 0.477942 + 0.146871i
\(109\) 53.8738 0.494255 0.247128 0.968983i \(-0.420513\pi\)
0.247128 + 0.968983i \(0.420513\pi\)
\(110\) 33.5887 + 107.069i 0.305351 + 0.973354i
\(111\) 23.6075 10.6622i 0.212680 0.0960556i
\(112\) 10.1909i 0.0909900i
\(113\) −82.8476 −0.733165 −0.366582 0.930386i \(-0.619472\pi\)
−0.366582 + 0.930386i \(0.619472\pi\)
\(114\) 4.72112 + 10.4532i 0.0414134 + 0.0916950i
\(115\) −22.8797 + 7.17762i −0.198954 + 0.0624140i
\(116\) 27.7527i 0.239248i
\(117\) −159.365 140.440i −1.36209 1.20034i
\(118\) 111.350i 0.943645i
\(119\) 82.5318i 0.693545i
\(120\) 28.2361 + 31.6658i 0.235301 + 0.263881i
\(121\) −130.839 −1.08131
\(122\) 97.4070 0.798418
\(123\) 162.377 73.3365i 1.32014 0.596231i
\(124\) 32.8123 0.264615
\(125\) 76.5244 98.8383i 0.612195 0.790707i
\(126\) 24.3284 + 21.4394i 0.193083 + 0.170154i
\(127\) 90.0823i 0.709310i 0.934997 + 0.354655i \(0.115402\pi\)
−0.934997 + 0.354655i \(0.884598\pi\)
\(128\) −11.3137 −0.0883883
\(129\) 140.255 63.3452i 1.08725 0.491048i
\(130\) −49.9547 159.238i −0.384267 1.22491i
\(131\) 135.317i 1.03296i 0.856300 + 0.516478i \(0.172757\pi\)
−0.856300 + 0.516478i \(0.827243\pi\)
\(132\) −86.7767 + 39.1920i −0.657399 + 0.296909i
\(133\) 6.88772i 0.0517874i
\(134\) 93.8815i 0.700609i
\(135\) 134.998 0.789532i 0.999983 0.00584839i
\(136\) −91.6252 −0.673715
\(137\) 117.874 0.860392 0.430196 0.902736i \(-0.358444\pi\)
0.430196 + 0.902736i \(0.358444\pi\)
\(138\) −8.37501 18.5434i −0.0606885 0.134373i
\(139\) −183.405 −1.31946 −0.659729 0.751504i \(-0.729329\pi\)
−0.659729 + 0.751504i \(0.729329\pi\)
\(140\) 7.62602 + 24.3091i 0.0544715 + 0.173636i
\(141\) 48.0504 + 106.390i 0.340783 + 0.754541i
\(142\) 125.386i 0.883001i
\(143\) 374.547 2.61921
\(144\) −23.8016 + 27.0090i −0.165289 + 0.187562i
\(145\) −20.7679 66.2007i −0.143227 0.456556i
\(146\) 52.6054i 0.360311i
\(147\) −52.4914 116.223i −0.357085 0.790635i
\(148\) 17.2691i 0.116683i
\(149\) 24.5997i 0.165099i −0.996587 0.0825493i \(-0.973694\pi\)
0.996587 0.0825493i \(-0.0263062\pi\)
\(150\) 91.0499 + 54.4051i 0.606999 + 0.362701i
\(151\) −32.5412 −0.215505 −0.107752 0.994178i \(-0.534365\pi\)
−0.107752 + 0.994178i \(0.534365\pi\)
\(152\) −7.64661 −0.0503067
\(153\) −192.760 + 218.735i −1.25987 + 1.42964i
\(154\) −57.1779 −0.371285
\(155\) 78.2696 24.5540i 0.504965 0.158413i
\(156\) 129.059 58.2883i 0.827298 0.373643i
\(157\) 3.81607i 0.0243062i −0.999926 0.0121531i \(-0.996131\pi\)
0.999926 0.0121531i \(-0.00386855\pi\)
\(158\) −148.062 −0.937101
\(159\) −104.999 232.482i −0.660369 1.46215i
\(160\) −26.9875 + 8.46625i −0.168672 + 0.0529141i
\(161\) 12.2184i 0.0758909i
\(162\) 14.4044 + 113.642i 0.0889160 + 0.701494i
\(163\) 176.476i 1.08268i 0.840805 + 0.541338i \(0.182082\pi\)
−0.840805 + 0.541338i \(0.817918\pi\)
\(164\) 118.780i 0.724269i
\(165\) −177.667 + 158.424i −1.07677 + 0.960147i
\(166\) −108.440 −0.653251
\(167\) −157.350 −0.942215 −0.471107 0.882076i \(-0.656146\pi\)
−0.471107 + 0.882076i \(0.656146\pi\)
\(168\) −19.7019 + 8.89821i −0.117273 + 0.0529656i
\(169\) −388.045 −2.29613
\(170\) −218.561 + 68.5648i −1.28565 + 0.403322i
\(171\) −16.0868 + 18.2546i −0.0940750 + 0.106752i
\(172\) 102.598i 0.596498i
\(173\) −248.801 −1.43815 −0.719077 0.694930i \(-0.755435\pi\)
−0.719077 + 0.694930i \(0.755435\pi\)
\(174\) 53.6540 24.2324i 0.308356 0.139267i
\(175\) 36.3818 + 52.2796i 0.207896 + 0.298741i
\(176\) 63.4777i 0.360669i
\(177\) −215.272 + 97.2259i −1.21622 + 0.549299i
\(178\) 107.817i 0.605716i
\(179\) 111.059i 0.620442i −0.950664 0.310221i \(-0.899597\pi\)
0.950664 0.310221i \(-0.100403\pi\)
\(180\) −36.5645 + 82.2377i −0.203136 + 0.456876i
\(181\) 219.405 1.21218 0.606092 0.795395i \(-0.292736\pi\)
0.606092 + 0.795395i \(0.292736\pi\)
\(182\) 85.0377 0.467240
\(183\) 85.0514 + 188.316i 0.464762 + 1.02905i
\(184\) 13.5647 0.0737210
\(185\) 12.9228 + 41.1933i 0.0698528 + 0.222666i
\(186\) 28.6502 + 63.4356i 0.154033 + 0.341051i
\(187\) 514.081i 2.74909i
\(188\) −77.8252 −0.413964
\(189\) −20.2060 + 65.7538i −0.106910 + 0.347904i
\(190\) −18.2400 + 5.72210i −0.0960003 + 0.0301163i
\(191\) 23.6963i 0.124065i 0.998074 + 0.0620323i \(0.0197582\pi\)
−0.998074 + 0.0620323i \(0.980242\pi\)
\(192\) −9.87862 21.8727i −0.0514512 0.113920i
\(193\) 98.0811i 0.508192i −0.967179 0.254096i \(-0.918222\pi\)
0.967179 0.254096i \(-0.0817780\pi\)
\(194\) 104.092i 0.536556i
\(195\) 264.235 235.616i 1.35505 1.20829i
\(196\) 85.0183 0.433767
\(197\) 316.042 1.60428 0.802138 0.597139i \(-0.203696\pi\)
0.802138 + 0.597139i \(0.203696\pi\)
\(198\) −151.539 133.543i −0.765348 0.674462i
\(199\) 168.719 0.847835 0.423918 0.905701i \(-0.360655\pi\)
0.423918 + 0.905701i \(0.360655\pi\)
\(200\) −58.0398 + 40.3904i −0.290199 + 0.201952i
\(201\) −181.500 + 81.9731i −0.902985 + 0.407827i
\(202\) 6.38723i 0.0316199i
\(203\) 35.3531 0.174153
\(204\) −80.0030 177.138i −0.392171 0.868323i
\(205\) 88.8853 + 283.335i 0.433587 + 1.38212i
\(206\) 63.9224i 0.310303i
\(207\) 28.5371 32.3826i 0.137860 0.156438i
\(208\) 94.4072i 0.453881i
\(209\) 42.9028i 0.205277i
\(210\) −40.3377 + 35.9689i −0.192084 + 0.171280i
\(211\) 168.980 0.800852 0.400426 0.916329i \(-0.368862\pi\)
0.400426 + 0.916329i \(0.368862\pi\)
\(212\) 170.062 0.802180
\(213\) −242.408 + 109.482i −1.13806 + 0.513998i
\(214\) −36.7049 −0.171518
\(215\) 76.7756 + 244.734i 0.357096 + 1.13830i
\(216\) −72.9986 22.4323i −0.337956 0.103853i
\(217\) 41.7982i 0.192619i
\(218\) −76.1891 −0.349491
\(219\) −101.701 + 45.9327i −0.464390 + 0.209738i
\(220\) −47.5015 151.418i −0.215916 0.688265i
\(221\) 764.566i 3.45958i
\(222\) −33.3861 + 15.0786i −0.150388 + 0.0679215i
\(223\) 256.517i 1.15030i −0.818048 0.575151i \(-0.804943\pi\)
0.818048 0.575151i \(-0.195057\pi\)
\(224\) 14.4121i 0.0643396i
\(225\) −25.6801 + 223.530i −0.114134 + 0.993465i
\(226\) 117.164 0.518426
\(227\) 319.013 1.40534 0.702672 0.711514i \(-0.251990\pi\)
0.702672 + 0.711514i \(0.251990\pi\)
\(228\) −6.67668 14.7831i −0.0292837 0.0648382i
\(229\) 88.2037 0.385169 0.192584 0.981280i \(-0.438313\pi\)
0.192584 + 0.981280i \(0.438313\pi\)
\(230\) 32.3568 10.1507i 0.140682 0.0441334i
\(231\) −49.9251 110.541i −0.216126 0.478534i
\(232\) 39.2483i 0.169174i
\(233\) −442.366 −1.89857 −0.949283 0.314423i \(-0.898189\pi\)
−0.949283 + 0.314423i \(0.898189\pi\)
\(234\) 225.376 + 198.612i 0.963146 + 0.848771i
\(235\) −185.642 + 58.2380i −0.789968 + 0.247821i
\(236\) 157.473i 0.667258i
\(237\) −129.281 286.246i −0.545490 1.20779i
\(238\) 116.718i 0.490410i
\(239\) 69.6082i 0.291248i 0.989340 + 0.145624i \(0.0465189\pi\)
−0.989340 + 0.145624i \(0.953481\pi\)
\(240\) −39.9319 44.7822i −0.166383 0.186592i
\(241\) −37.8588 −0.157090 −0.0785452 0.996911i \(-0.525028\pi\)
−0.0785452 + 0.996911i \(0.525028\pi\)
\(242\) 185.034 0.764604
\(243\) −207.125 + 127.075i −0.852368 + 0.522942i
\(244\) −137.754 −0.564567
\(245\) 202.801 63.6207i 0.827757 0.259676i
\(246\) −229.636 + 103.713i −0.933480 + 0.421599i
\(247\) 63.8071i 0.258329i
\(248\) −46.4036 −0.187111
\(249\) −94.6846 209.645i −0.380260 0.841948i
\(250\) −108.222 + 139.779i −0.432887 + 0.559114i
\(251\) 38.2880i 0.152542i 0.997087 + 0.0762709i \(0.0243014\pi\)
−0.997087 + 0.0762709i \(0.975699\pi\)
\(252\) −34.4056 30.3199i −0.136530 0.120317i
\(253\) 76.1071i 0.300819i
\(254\) 127.396i 0.501558i
\(255\) −323.393 362.673i −1.26821 1.42225i
\(256\) 16.0000 0.0625000
\(257\) −5.46616 −0.0212691 −0.0106346 0.999943i \(-0.503385\pi\)
−0.0106346 + 0.999943i \(0.503385\pi\)
\(258\) −198.351 + 89.5836i −0.768801 + 0.347223i
\(259\) −21.9984 −0.0849358
\(260\) 70.6466 + 225.197i 0.271718 + 0.866141i
\(261\) 93.6965 + 82.5699i 0.358990 + 0.316360i
\(262\) 191.368i 0.730411i
\(263\) −485.162 −1.84472 −0.922361 0.386329i \(-0.873743\pi\)
−0.922361 + 0.386329i \(0.873743\pi\)
\(264\) 122.721 55.4259i 0.464851 0.209947i
\(265\) 405.662 127.261i 1.53080 0.480228i
\(266\) 9.74071i 0.0366192i
\(267\) −208.442 + 94.1414i −0.780682 + 0.352589i
\(268\) 132.769i 0.495405i
\(269\) 268.151i 0.996844i 0.866935 + 0.498422i \(0.166087\pi\)
−0.866935 + 0.498422i \(0.833913\pi\)
\(270\) −190.916 + 1.11657i −0.707095 + 0.00413544i
\(271\) 129.334 0.477246 0.238623 0.971112i \(-0.423304\pi\)
0.238623 + 0.971112i \(0.423304\pi\)
\(272\) 129.578 0.476388
\(273\) 74.2511 + 164.402i 0.271982 + 0.602207i
\(274\) −166.699 −0.608389
\(275\) −226.618 325.643i −0.824066 1.18416i
\(276\) 11.8441 + 26.2244i 0.0429132 + 0.0950159i
\(277\) 403.297i 1.45595i 0.685605 + 0.727974i \(0.259538\pi\)
−0.685605 + 0.727974i \(0.740462\pi\)
\(278\) 259.373 0.932997
\(279\) −97.6231 + 110.778i −0.349904 + 0.397054i
\(280\) −10.7848 34.3782i −0.0385172 0.122779i
\(281\) 128.348i 0.456755i −0.973573 0.228378i \(-0.926658\pi\)
0.973573 0.228378i \(-0.0733421\pi\)
\(282\) −67.9535 150.459i −0.240970 0.533541i
\(283\) 351.650i 1.24258i 0.783581 + 0.621289i \(0.213391\pi\)
−0.783581 + 0.621289i \(0.786609\pi\)
\(284\) 177.323i 0.624376i
\(285\) −26.9889 30.2670i −0.0946977 0.106200i
\(286\) −529.690 −1.85206
\(287\) −151.309 −0.527209
\(288\) 33.6606 38.1964i 0.116877 0.132626i
\(289\) 760.397 2.63113
\(290\) 29.3702 + 93.6219i 0.101277 + 0.322834i
\(291\) −201.240 + 90.8884i −0.691545 + 0.312331i
\(292\) 74.3953i 0.254778i
\(293\) 246.993 0.842979 0.421489 0.906833i \(-0.361507\pi\)
0.421489 + 0.906833i \(0.361507\pi\)
\(294\) 74.2341 + 164.365i 0.252497 + 0.559064i
\(295\) −117.840 375.632i −0.399457 1.27333i
\(296\) 24.4222i 0.0825073i
\(297\) 125.861 409.572i 0.423774 1.37903i
\(298\) 34.7892i 0.116742i
\(299\) 113.190i 0.378563i
\(300\) −128.764 76.9405i −0.429213 0.256468i
\(301\) −130.695 −0.434202
\(302\) 46.0202 0.152385
\(303\) −12.3483 + 5.57704i −0.0407536 + 0.0184061i
\(304\) 10.8139 0.0355722
\(305\) −328.596 + 103.084i −1.07736 + 0.337980i
\(306\) 272.603 309.338i 0.890860 1.01091i
\(307\) 322.299i 1.04983i −0.851154 0.524917i \(-0.824097\pi\)
0.851154 0.524917i \(-0.175903\pi\)
\(308\) 80.8617 0.262538
\(309\) −123.580 + 55.8142i −0.399936 + 0.180628i
\(310\) −110.690 + 34.7246i −0.357064 + 0.112015i
\(311\) 197.270i 0.634308i 0.948374 + 0.317154i \(0.102727\pi\)
−0.948374 + 0.317154i \(0.897273\pi\)
\(312\) −182.516 + 82.4321i −0.584988 + 0.264206i
\(313\) 542.137i 1.73207i 0.499987 + 0.866033i \(0.333338\pi\)
−0.499987 + 0.866033i \(0.666662\pi\)
\(314\) 5.39674i 0.0171871i
\(315\) −104.759 46.5780i −0.332569 0.147867i
\(316\) 209.391 0.662631
\(317\) −96.0108 −0.302873 −0.151437 0.988467i \(-0.548390\pi\)
−0.151437 + 0.988467i \(0.548390\pi\)
\(318\) 148.491 + 328.779i 0.466951 + 1.03390i
\(319\) −220.210 −0.690314
\(320\) 38.1660 11.9731i 0.119269 0.0374159i
\(321\) −32.0490 70.9611i −0.0998413 0.221063i
\(322\) 17.2795i 0.0536630i
\(323\) 87.5778 0.271139
\(324\) −20.3709 160.714i −0.0628731 0.496031i
\(325\) 337.038 + 484.313i 1.03704 + 1.49019i
\(326\) 249.575i 0.765567i
\(327\) −66.5249 147.295i −0.203440 0.450444i
\(328\) 167.980i 0.512135i
\(329\) 99.1384i 0.301333i
\(330\) 251.259 224.046i 0.761391 0.678927i
\(331\) 246.600 0.745016 0.372508 0.928029i \(-0.378498\pi\)
0.372508 + 0.928029i \(0.378498\pi\)
\(332\) 153.357 0.461918
\(333\) −58.3025 51.3790i −0.175083 0.154291i
\(334\) 222.526 0.666246
\(335\) −99.3531 316.703i −0.296576 0.945382i
\(336\) 27.8627 12.5840i 0.0829247 0.0374523i
\(337\) 136.820i 0.405994i 0.979179 + 0.202997i \(0.0650682\pi\)
−0.979179 + 0.202997i \(0.934932\pi\)
\(338\) 548.779 1.62361
\(339\) 102.303 + 226.512i 0.301777 + 0.668177i
\(340\) 309.091 96.9652i 0.909092 0.285192i
\(341\) 260.356i 0.763508i
\(342\) 22.7502 25.8159i 0.0665211 0.0754850i
\(343\) 233.140i 0.679707i
\(344\) 145.095i 0.421788i
\(345\) 47.8767 + 53.6919i 0.138773 + 0.155629i
\(346\) 351.857 1.01693
\(347\) 351.266 1.01229 0.506147 0.862447i \(-0.331069\pi\)
0.506147 + 0.862447i \(0.331069\pi\)
\(348\) −75.8782 + 34.2698i −0.218041 + 0.0984765i
\(349\) −210.440 −0.602979 −0.301489 0.953470i \(-0.597484\pi\)
−0.301489 + 0.953470i \(0.597484\pi\)
\(350\) −51.4517 73.9345i −0.147005 0.211241i
\(351\) −187.187 + 609.136i −0.533295 + 1.73543i
\(352\) 89.7711i 0.255031i
\(353\) −479.609 −1.35867 −0.679333 0.733830i \(-0.737731\pi\)
−0.679333 + 0.733830i \(0.737731\pi\)
\(354\) 304.440 137.498i 0.860001 0.388413i
\(355\) −132.694 422.982i −0.373786 1.19150i
\(356\) 152.477i 0.428306i
\(357\) 225.649 101.913i 0.632069 0.285469i
\(358\) 157.061i 0.438719i
\(359\) 666.963i 1.85783i 0.370288 + 0.928917i \(0.379259\pi\)
−0.370288 + 0.928917i \(0.620741\pi\)
\(360\) 51.7100 116.302i 0.143639 0.323060i
\(361\) −353.691 −0.979754
\(362\) −310.286 −0.857143
\(363\) 161.564 + 357.724i 0.445079 + 0.985467i
\(364\) −120.262 −0.330389
\(365\) −55.6714 177.461i −0.152524 0.486194i
\(366\) −120.281 266.319i −0.328636 0.727647i
\(367\) 503.975i 1.37323i −0.727022 0.686614i \(-0.759096\pi\)
0.727022 0.686614i \(-0.240904\pi\)
\(368\) −19.1833 −0.0521286
\(369\) −401.016 353.395i −1.08676 0.957709i
\(370\) −18.2756 58.2561i −0.0493934 0.157449i
\(371\) 216.635i 0.583922i
\(372\) −40.5175 89.7114i −0.108918 0.241160i
\(373\) 632.077i 1.69458i 0.531133 + 0.847288i \(0.321766\pi\)
−0.531133 + 0.847288i \(0.678234\pi\)
\(374\) 727.020i 1.94390i
\(375\) −364.726 87.1756i −0.972604 0.232468i
\(376\) 110.062 0.292717
\(377\) 327.507 0.868719
\(378\) 28.5757 92.9899i 0.0755970 0.246005i
\(379\) 567.452 1.49724 0.748618 0.663002i \(-0.230718\pi\)
0.748618 + 0.663002i \(0.230718\pi\)
\(380\) 25.7953 8.09227i 0.0678824 0.0212954i
\(381\) 246.292 111.236i 0.646437 0.291958i
\(382\) 33.5117i 0.0877269i
\(383\) −75.9370 −0.198269 −0.0991345 0.995074i \(-0.531607\pi\)
−0.0991345 + 0.995074i \(0.531607\pi\)
\(384\) 13.9705 + 30.9326i 0.0363815 + 0.0805536i
\(385\) 192.886 60.5103i 0.501002 0.157170i
\(386\) 138.708i 0.359346i
\(387\) −346.382 305.248i −0.895043 0.788756i
\(388\) 147.208i 0.379403i
\(389\) 216.366i 0.556210i 0.960551 + 0.278105i \(0.0897063\pi\)
−0.960551 + 0.278105i \(0.910294\pi\)
\(390\) −373.685 + 333.212i −0.958166 + 0.854390i
\(391\) −155.358 −0.397335
\(392\) −120.234 −0.306719
\(393\) 369.969 167.094i 0.941396 0.425175i
\(394\) −446.951 −1.13439
\(395\) 499.477 156.691i 1.26450 0.396687i
\(396\) 214.308 + 188.859i 0.541183 + 0.476917i
\(397\) 723.583i 1.82263i 0.411712 + 0.911314i \(0.364931\pi\)
−0.411712 + 0.911314i \(0.635069\pi\)
\(398\) −238.605 −0.599510
\(399\) 18.8316 8.50515i 0.0471970 0.0213162i
\(400\) 82.0806 57.1206i 0.205202 0.142802i
\(401\) 258.627i 0.644955i −0.946577 0.322478i \(-0.895484\pi\)
0.946577 0.322478i \(-0.104516\pi\)
\(402\) 256.680 115.928i 0.638507 0.288377i
\(403\) 387.215i 0.960830i
\(404\) 9.03290i 0.0223587i
\(405\) −168.858 368.120i −0.416932 0.908938i
\(406\) −49.9968 −0.123145
\(407\) 137.025 0.336671
\(408\) 113.141 + 250.511i 0.277307 + 0.613997i
\(409\) −399.257 −0.976178 −0.488089 0.872794i \(-0.662306\pi\)
−0.488089 + 0.872794i \(0.662306\pi\)
\(410\) −125.703 400.696i −0.306592 0.977308i
\(411\) −145.554 322.276i −0.354145 0.784127i
\(412\) 90.3999i 0.219417i
\(413\) 200.598 0.485710
\(414\) −40.3576 + 45.7959i −0.0974821 + 0.110618i
\(415\) 365.814 114.760i 0.881479 0.276529i
\(416\) 133.512i 0.320942i
\(417\) 226.473 + 501.443i 0.543101 + 1.20250i
\(418\) 60.6737i 0.145152i
\(419\) 447.017i 1.06687i −0.845842 0.533434i \(-0.820901\pi\)
0.845842 0.533434i \(-0.179099\pi\)
\(420\) 57.0462 50.8677i 0.135824 0.121113i
\(421\) 272.776 0.647923 0.323962 0.946070i \(-0.394985\pi\)
0.323962 + 0.946070i \(0.394985\pi\)
\(422\) −238.973 −0.566288
\(423\) 231.546 262.747i 0.547389 0.621152i
\(424\) −240.504 −0.567227
\(425\) 664.738 462.597i 1.56409 1.08846i
\(426\) 342.816 154.830i 0.804732 0.363451i
\(427\) 175.480i 0.410959i
\(428\) 51.9085 0.121282
\(429\) −462.501 1024.04i −1.07809 2.38705i
\(430\) −108.577 346.106i −0.252505 0.804898i
\(431\) 436.879i 1.01364i 0.862052 + 0.506820i \(0.169179\pi\)
−0.862052 + 0.506820i \(0.830821\pi\)
\(432\) 103.236 + 31.7241i 0.238971 + 0.0734355i
\(433\) 81.5626i 0.188366i 0.995555 + 0.0941832i \(0.0300239\pi\)
−0.995555 + 0.0941832i \(0.969976\pi\)
\(434\) 59.1116i 0.136202i
\(435\) −155.353 + 138.527i −0.357134 + 0.318454i
\(436\) 107.748 0.247128
\(437\) −12.9655 −0.0296693
\(438\) 143.828 64.9586i 0.328373 0.148307i
\(439\) −459.523 −1.04675 −0.523375 0.852103i \(-0.675327\pi\)
−0.523375 + 0.852103i \(0.675327\pi\)
\(440\) 67.1773 + 214.138i 0.152676 + 0.486677i
\(441\) −252.946 + 287.032i −0.573575 + 0.650866i
\(442\) 1081.26i 2.44629i
\(443\) 341.453 0.770773 0.385387 0.922755i \(-0.374068\pi\)
0.385387 + 0.922755i \(0.374068\pi\)
\(444\) 47.2151 21.3243i 0.106340 0.0480278i
\(445\) −114.101 363.715i −0.256407 0.817337i
\(446\) 362.770i 0.813386i
\(447\) −67.2575 + 30.3764i −0.150464 + 0.0679561i
\(448\) 20.3818i 0.0454950i
\(449\) 51.7486i 0.115253i −0.998338 0.0576264i \(-0.981647\pi\)
0.998338 0.0576264i \(-0.0183532\pi\)
\(450\) 36.3172 316.119i 0.0807049 0.702486i
\(451\) 942.486 2.08977
\(452\) −165.695 −0.366582
\(453\) 40.1828 + 88.9703i 0.0887037 + 0.196402i
\(454\) −451.152 −0.993728
\(455\) −286.869 + 89.9939i −0.630481 + 0.197789i
\(456\) 9.44225 + 20.9065i 0.0207067 + 0.0458475i
\(457\) 408.775i 0.894474i −0.894416 0.447237i \(-0.852408\pi\)
0.894416 0.447237i \(-0.147592\pi\)
\(458\) −124.739 −0.272356
\(459\) 836.063 + 256.921i 1.82149 + 0.559741i
\(460\) −45.7595 + 14.3552i −0.0994771 + 0.0312070i
\(461\) 274.701i 0.595882i 0.954584 + 0.297941i \(0.0962998\pi\)
−0.954584 + 0.297941i \(0.903700\pi\)
\(462\) 70.6048 + 156.329i 0.152824 + 0.338374i
\(463\) 25.3001i 0.0546439i 0.999627 + 0.0273219i \(0.00869793\pi\)
−0.999627 + 0.0273219i \(0.991302\pi\)
\(464\) 55.5054i 0.119624i
\(465\) −163.782 183.676i −0.352220 0.395001i
\(466\) 625.600 1.34249
\(467\) −745.058 −1.59541 −0.797706 0.603046i \(-0.793953\pi\)
−0.797706 + 0.603046i \(0.793953\pi\)
\(468\) −318.730 280.880i −0.681047 0.600172i
\(469\) 169.128 0.360615
\(470\) 262.538 82.3610i 0.558592 0.175236i
\(471\) −10.4335 + 4.71219i −0.0221517 + 0.0100047i
\(472\) 222.700i 0.471822i
\(473\) 814.083 1.72111
\(474\) 182.831 + 404.814i 0.385720 + 0.854037i
\(475\) 55.4760 38.6062i 0.116791 0.0812762i
\(476\) 165.064i 0.346772i
\(477\) −505.969 + 574.150i −1.06073 + 1.20367i
\(478\) 98.4409i 0.205943i
\(479\) 168.038i 0.350810i −0.984496 0.175405i \(-0.943876\pi\)
0.984496 0.175405i \(-0.0561235\pi\)
\(480\) 56.4723 + 63.3315i 0.117651 + 0.131941i
\(481\) −203.791 −0.423681
\(482\) 53.5404 0.111080
\(483\) −33.4062 + 15.0877i −0.0691639 + 0.0312374i
\(484\) −261.678 −0.540657
\(485\) −110.159 351.147i −0.227131 0.724014i
\(486\) 292.920 179.711i 0.602715 0.369776i
\(487\) 256.289i 0.526261i 0.964760 + 0.263131i \(0.0847550\pi\)
−0.964760 + 0.263131i \(0.915245\pi\)
\(488\) 194.814 0.399209
\(489\) 482.500 217.918i 0.986707 0.445639i
\(490\) −286.803 + 89.9733i −0.585313 + 0.183619i
\(491\) 631.851i 1.28686i −0.765503 0.643432i \(-0.777510\pi\)
0.765503 0.643432i \(-0.222490\pi\)
\(492\) 324.754 146.673i 0.660070 0.298116i
\(493\) 449.516i 0.911798i
\(494\) 90.2369i 0.182666i
\(495\) 652.533 + 290.129i 1.31825 + 0.586119i
\(496\) 65.6246 0.132308
\(497\) 225.884 0.454496
\(498\) 133.904 + 296.483i 0.268884 + 0.595347i
\(499\) 539.468 1.08110 0.540550 0.841312i \(-0.318216\pi\)
0.540550 + 0.841312i \(0.318216\pi\)
\(500\) 153.049 197.677i 0.306098 0.395353i
\(501\) 194.300 + 430.207i 0.387824 + 0.858697i
\(502\) 54.1474i 0.107863i
\(503\) −294.962 −0.586406 −0.293203 0.956050i \(-0.594721\pi\)
−0.293203 + 0.956050i \(0.594721\pi\)
\(504\) 48.6569 + 42.8788i 0.0965414 + 0.0850770i
\(505\) −6.75949 21.5469i −0.0133851 0.0426671i
\(506\) 107.632i 0.212711i
\(507\) 479.169 + 1060.95i 0.945106 + 2.09260i
\(508\) 180.165i 0.354655i
\(509\) 145.947i 0.286733i −0.989670 0.143367i \(-0.954207\pi\)
0.989670 0.143367i \(-0.0457928\pi\)
\(510\) 457.346 + 512.897i 0.896757 + 1.00568i
\(511\) 94.7692 0.185458
\(512\) −22.6274 −0.0441942
\(513\) 69.7740 + 21.4414i 0.136012 + 0.0417962i
\(514\) 7.73032 0.0150395
\(515\) −67.6479 215.638i −0.131355 0.418714i
\(516\) 280.510 126.690i 0.543624 0.245524i
\(517\) 617.521i 1.19443i
\(518\) 31.1104 0.0600587
\(519\) 307.226 + 680.241i 0.591958 + 1.31068i
\(520\) −99.9094 318.476i −0.192134 0.612454i
\(521\) 699.345i 1.34231i −0.741316 0.671156i \(-0.765798\pi\)
0.741316 0.671156i \(-0.234202\pi\)
\(522\) −132.507 116.772i −0.253845 0.223700i
\(523\) 807.343i 1.54368i 0.635819 + 0.771839i \(0.280663\pi\)
−0.635819 + 0.771839i \(0.719337\pi\)
\(524\) 270.635i 0.516478i
\(525\) 98.0114 164.027i 0.186688 0.312433i
\(526\) 686.123 1.30442
\(527\) 531.467 1.00848
\(528\) −173.553 + 78.3841i −0.328699 + 0.148455i
\(529\) 23.0000 0.0434783
\(530\) −573.693 + 179.974i −1.08244 + 0.339573i
\(531\) 531.647 + 468.513i 1.00122 + 0.882323i
\(532\) 13.7754i 0.0258937i
\(533\) −1401.71 −2.62985
\(534\) 294.782 133.136i 0.552026 0.249318i
\(535\) 123.821 38.8441i 0.231442 0.0726058i
\(536\) 187.763i 0.350304i
\(537\) −303.645 + 137.139i −0.565446 + 0.255380i
\(538\) 379.223i 0.704875i
\(539\) 674.596i 1.25157i
\(540\) 269.995 1.57906i 0.499991 0.00292419i
\(541\) −91.7399 −0.169575 −0.0847873 0.996399i \(-0.527021\pi\)
−0.0847873 + 0.996399i \(0.527021\pi\)
\(542\) −182.906 −0.337464
\(543\) −270.928 599.872i −0.498946 1.10474i
\(544\) −183.250 −0.336857
\(545\) 257.019 80.6295i 0.471594 0.147944i
\(546\) −105.007 232.500i −0.192320 0.425824i
\(547\) 865.481i 1.58223i −0.611666 0.791116i \(-0.709500\pi\)
0.611666 0.791116i \(-0.290500\pi\)
\(548\) 235.747 0.430196
\(549\) 409.847 465.075i 0.746533 0.847131i
\(550\) 320.486 + 460.529i 0.582703 + 0.837326i
\(551\) 37.5145i 0.0680845i
\(552\) −16.7500 37.0869i −0.0303442 0.0671864i
\(553\) 266.735i 0.482342i
\(554\) 570.349i 1.02951i
\(555\) 96.6683 86.1985i 0.174177 0.155313i
\(556\) −366.809 −0.659729
\(557\) −399.268 −0.716819 −0.358410 0.933564i \(-0.616681\pi\)
−0.358410 + 0.933564i \(0.616681\pi\)
\(558\) 138.060 156.664i 0.247419 0.280760i
\(559\) −1210.74 −2.16591
\(560\) 15.2520 + 48.6181i 0.0272358 + 0.0868181i
\(561\) −1405.54 + 634.801i −2.50542 + 1.13155i
\(562\) 181.512i 0.322975i
\(563\) −766.176 −1.36088 −0.680440 0.732804i \(-0.738211\pi\)
−0.680440 + 0.732804i \(0.738211\pi\)
\(564\) 96.1008 + 212.781i 0.170391 + 0.377270i
\(565\) −395.246 + 123.993i −0.699550 + 0.219456i
\(566\) 497.308i 0.878636i
\(567\) 204.727 25.9497i 0.361071 0.0457666i
\(568\) 250.772i 0.441501i
\(569\) 783.307i 1.37664i −0.725408 0.688319i \(-0.758349\pi\)
0.725408 0.688319i \(-0.241651\pi\)
\(570\) 38.1680 + 42.8040i 0.0669614 + 0.0750947i
\(571\) 88.9855 0.155841 0.0779207 0.996960i \(-0.475172\pi\)
0.0779207 + 0.996960i \(0.475172\pi\)
\(572\) 749.095 1.30961
\(573\) 64.7877 29.2609i 0.113068 0.0510661i
\(574\) 213.983 0.372793
\(575\) −98.4112 + 68.4853i −0.171150 + 0.119105i
\(576\) −47.6032 + 54.0179i −0.0826445 + 0.0937811i
\(577\) 459.789i 0.796861i −0.917199 0.398431i \(-0.869555\pi\)
0.917199 0.398431i \(-0.130445\pi\)
\(578\) −1075.36 −1.86049
\(579\) −268.162 + 121.113i −0.463147 + 0.209177i
\(580\) −41.5357 132.401i −0.0716133 0.228278i
\(581\) 195.355i 0.336239i
\(582\) 284.596 128.536i 0.488996 0.220852i
\(583\) 1349.39i 2.31457i
\(584\) 105.211i 0.180156i
\(585\) −970.479 431.494i −1.65894 0.737597i
\(586\) −349.301 −0.596076
\(587\) 294.716 0.502072 0.251036 0.967978i \(-0.419229\pi\)
0.251036 + 0.967978i \(0.419229\pi\)
\(588\) −104.983 232.447i −0.178542 0.395318i
\(589\) 44.3538 0.0753035
\(590\) 166.651 + 531.224i 0.282459 + 0.900379i
\(591\) −390.258 864.085i −0.660334 1.46207i
\(592\) 34.5382i 0.0583415i
\(593\) −882.001 −1.48735 −0.743677 0.668539i \(-0.766920\pi\)
−0.743677 + 0.668539i \(0.766920\pi\)
\(594\) −177.994 + 579.223i −0.299654 + 0.975123i
\(595\) 123.520 + 393.739i 0.207597 + 0.661746i
\(596\) 49.1994i 0.0825493i
\(597\) −208.339 461.292i −0.348977 0.772683i
\(598\) 160.075i 0.267684i
\(599\) 615.514i 1.02757i −0.857919 0.513785i \(-0.828243\pi\)
0.857919 0.513785i \(-0.171757\pi\)
\(600\) 182.100 + 108.810i 0.303500 + 0.181350i
\(601\) −16.1189 −0.0268201 −0.0134101 0.999910i \(-0.504269\pi\)
−0.0134101 + 0.999910i \(0.504269\pi\)
\(602\) 184.831 0.307027
\(603\) 448.242 + 395.013i 0.743354 + 0.655080i
\(604\) −65.0824 −0.107752
\(605\) −624.200 + 195.818i −1.03174 + 0.323667i
\(606\) 17.4632 7.88712i 0.0288172 0.0130151i
\(607\) 189.949i 0.312931i −0.987683 0.156465i \(-0.949990\pi\)
0.987683 0.156465i \(-0.0500100\pi\)
\(608\) −15.2932 −0.0251533
\(609\) −43.6549 96.6582i −0.0716830 0.158716i
\(610\) 464.705 145.783i 0.761811 0.238988i
\(611\) 918.408i 1.50312i
\(612\) −385.519 + 437.469i −0.629933 + 0.714819i
\(613\) 448.071i 0.730947i 0.930822 + 0.365474i \(0.119093\pi\)
−0.930822 + 0.365474i \(0.880907\pi\)
\(614\) 455.799i 0.742344i
\(615\) 664.903 592.890i 1.08114 0.964048i
\(616\) −114.356 −0.185642
\(617\) −884.688 −1.43385 −0.716927 0.697148i \(-0.754452\pi\)
−0.716927 + 0.697148i \(0.754452\pi\)
\(618\) 174.769 78.9331i 0.282798 0.127724i
\(619\) −869.748 −1.40509 −0.702543 0.711641i \(-0.747952\pi\)
−0.702543 + 0.711641i \(0.747952\pi\)
\(620\) 156.539 49.1080i 0.252483 0.0792065i
\(621\) −123.775 38.0359i −0.199316 0.0612494i
\(622\) 278.981i 0.448523i
\(623\) 194.234 0.311772
\(624\) 258.117 116.577i 0.413649 0.186822i
\(625\) 217.154 586.062i 0.347446 0.937700i
\(626\) 766.697i 1.22476i
\(627\) −117.300 + 52.9776i −0.187081 + 0.0844937i
\(628\) 7.63215i 0.0121531i
\(629\) 279.711i 0.444691i
\(630\) 148.152 + 65.8713i 0.235162 + 0.104558i
\(631\) 326.782 0.517880 0.258940 0.965893i \(-0.416627\pi\)
0.258940 + 0.965893i \(0.416627\pi\)
\(632\) −296.124 −0.468551
\(633\) −208.661 462.004i −0.329638 0.729865i
\(634\) 135.780 0.214164
\(635\) 134.820 + 429.761i 0.212316 + 0.676788i
\(636\) −209.997 464.964i −0.330185 0.731075i
\(637\) 1003.29i 1.57503i
\(638\) 311.424 0.488125
\(639\) 598.663 + 527.571i 0.936875 + 0.825620i
\(640\) −53.9749 + 16.9325i −0.0843358 + 0.0264570i
\(641\) 219.166i 0.341913i −0.985279 0.170957i \(-0.945314\pi\)
0.985279 0.170957i \(-0.0546858\pi\)
\(642\) 45.3242 + 100.354i 0.0705984 + 0.156315i
\(643\) 707.067i 1.09964i 0.835284 + 0.549819i \(0.185303\pi\)
−0.835284 + 0.549819i \(0.814697\pi\)
\(644\) 24.4369i 0.0379454i
\(645\) 574.318 512.115i 0.890415 0.793977i
\(646\) −123.854 −0.191724
\(647\) 127.046 0.196361 0.0981807 0.995169i \(-0.468698\pi\)
0.0981807 + 0.995169i \(0.468698\pi\)
\(648\) 28.8088 + 227.284i 0.0444580 + 0.350747i
\(649\) −1249.50 −1.92527
\(650\) −476.643 684.922i −0.733297 1.05373i
\(651\) 114.280 51.6136i 0.175545 0.0792836i
\(652\) 352.952i 0.541338i
\(653\) 35.8607 0.0549169 0.0274585 0.999623i \(-0.491259\pi\)
0.0274585 + 0.999623i \(0.491259\pi\)
\(654\) 94.0804 + 208.307i 0.143854 + 0.318512i
\(655\) 202.521 + 645.566i 0.309192 + 0.985596i
\(656\) 237.560i 0.362134i
\(657\) 251.167 + 221.341i 0.382294 + 0.336896i
\(658\) 140.203i 0.213074i
\(659\) 152.748i 0.231788i 0.993262 + 0.115894i \(0.0369733\pi\)
−0.993262 + 0.115894i \(0.963027\pi\)
\(660\) −355.334 + 316.849i −0.538384 + 0.480074i
\(661\) −96.2217 −0.145570 −0.0727850 0.997348i \(-0.523189\pi\)
−0.0727850 + 0.997348i \(0.523189\pi\)
\(662\) −348.746 −0.526806
\(663\) 2090.39 944.107i 3.15292 1.42399i
\(664\) −216.879 −0.326625
\(665\) 10.3084 + 32.8596i 0.0155014 + 0.0494130i
\(666\) 82.4521 + 72.6609i 0.123802 + 0.109100i
\(667\) 66.5487i 0.0997732i
\(668\) −314.700 −0.471107
\(669\) −701.339 + 316.755i −1.04834 + 0.473475i
\(670\) 140.507 + 447.886i 0.209711 + 0.668486i
\(671\) 1093.04i 1.62897i
\(672\) −39.4038 + 17.7964i −0.0586366 + 0.0264828i
\(673\) 1060.82i 1.57626i 0.615508 + 0.788130i \(0.288951\pi\)
−0.615508 + 0.788130i \(0.711049\pi\)
\(674\) 193.493i 0.287081i
\(675\) 642.859 205.809i 0.952384 0.304902i
\(676\) −776.090 −1.14806
\(677\) 1107.81 1.63634 0.818172 0.574973i \(-0.194987\pi\)
0.818172 + 0.574973i \(0.194987\pi\)
\(678\) −144.678 320.337i −0.213389 0.472473i
\(679\) 187.523 0.276175
\(680\) −437.121 + 137.130i −0.642825 + 0.201661i
\(681\) −393.926 872.207i −0.578452 1.28077i
\(682\) 368.199i 0.539882i
\(683\) −637.718 −0.933701 −0.466850 0.884336i \(-0.654611\pi\)
−0.466850 + 0.884336i \(0.654611\pi\)
\(684\) −32.1737 + 36.5092i −0.0470375 + 0.0533760i
\(685\) 562.346 176.414i 0.820943 0.257539i
\(686\) 329.709i 0.480626i
\(687\) −108.916 241.156i −0.158539 0.351028i
\(688\) 205.195i 0.298249i
\(689\) 2006.89i 2.91275i
\(690\) −67.7079 75.9318i −0.0981274 0.110046i
\(691\) −1182.13 −1.71075 −0.855376 0.518008i \(-0.826674\pi\)
−0.855376 + 0.518008i \(0.826674\pi\)
\(692\) −497.601 −0.719077
\(693\) −240.580 + 272.999i −0.347157 + 0.393938i
\(694\) −496.765 −0.715800
\(695\) −874.978 + 274.490i −1.25896 + 0.394950i
\(696\) 107.308 48.4649i 0.154178 0.0696334i
\(697\) 1923.90i 2.76026i
\(698\) 297.607 0.426370
\(699\) 546.246 + 1209.46i 0.781467 + 1.73028i
\(700\) 72.7637 + 104.559i 0.103948 + 0.149370i
\(701\) 245.292i 0.349917i 0.984576 + 0.174958i \(0.0559791\pi\)
−0.984576 + 0.174958i \(0.944021\pi\)
\(702\) 264.722 861.449i 0.377097 1.22714i
\(703\) 23.3434i 0.0332053i
\(704\) 126.955i 0.180334i
\(705\) 388.464 + 435.648i 0.551013 + 0.617940i
\(706\) 678.269 0.960721
\(707\) 11.5066 0.0162753
\(708\) −430.544 + 194.452i −0.608112 + 0.274649i
\(709\) 1079.15 1.52207 0.761034 0.648712i \(-0.224692\pi\)
0.761034 + 0.648712i \(0.224692\pi\)
\(710\) 187.657 + 598.186i 0.264306 + 0.842516i
\(711\) −622.981 + 706.930i −0.876204 + 0.994276i
\(712\) 215.635i 0.302858i
\(713\) −78.6811 −0.110352
\(714\) −319.115 + 144.126i −0.446940 + 0.201857i
\(715\) 1786.87 560.561i 2.49912 0.784002i
\(716\) 222.118i 0.310221i
\(717\) 190.315 85.9542i 0.265432 0.119880i
\(718\) 943.227i 1.31369i
\(719\) 111.651i 0.155287i 0.996981 + 0.0776433i \(0.0247395\pi\)
−0.996981 + 0.0776433i \(0.975260\pi\)
\(720\) −73.1290 + 164.475i −0.101568 + 0.228438i
\(721\) 115.157 0.159718
\(722\) 500.195 0.692791
\(723\) 46.7491 + 103.509i 0.0646599 + 0.143166i
\(724\) 438.810 0.606092
\(725\) −198.157 284.745i −0.273320 0.392752i
\(726\) −228.485 505.899i −0.314718 0.696830i
\(727\) 699.812i 0.962602i −0.876555 0.481301i \(-0.840164\pi\)
0.876555 0.481301i \(-0.159836\pi\)
\(728\) 170.075 0.233620
\(729\) 603.198 + 409.382i 0.827431 + 0.561567i
\(730\) 78.7312 + 250.967i 0.107851 + 0.343791i
\(731\) 1661.79i 2.27332i
\(732\) 170.103 + 376.631i 0.232381 + 0.514524i
\(733\) 1137.24i 1.55148i −0.631052 0.775740i \(-0.717377\pi\)
0.631052 0.775740i \(-0.282623\pi\)
\(734\) 712.728i 0.971019i
\(735\) −424.368 475.913i −0.577371 0.647500i
\(736\) 27.1293 0.0368605
\(737\) −1053.48 −1.42942
\(738\) 567.122 + 499.775i 0.768458 + 0.677202i
\(739\) −143.147 −0.193704 −0.0968519 0.995299i \(-0.530877\pi\)
−0.0968519 + 0.995299i \(0.530877\pi\)
\(740\) 25.8455 + 82.3865i 0.0349264 + 0.111333i
\(741\) 174.454 78.7908i 0.235430 0.106330i
\(742\) 306.368i 0.412895i
\(743\) −516.019 −0.694508 −0.347254 0.937771i \(-0.612886\pi\)
−0.347254 + 0.937771i \(0.612886\pi\)
\(744\) 57.3004 + 126.871i 0.0770167 + 0.170526i
\(745\) −36.8168 117.359i −0.0494185 0.157529i
\(746\) 893.892i 1.19825i
\(747\) −456.267 + 517.751i −0.610800 + 0.693107i
\(748\) 1028.16i 1.37455i
\(749\) 66.1242i 0.0882833i
\(750\) 515.801 + 123.285i 0.687735 + 0.164380i
\(751\) 456.997 0.608518 0.304259 0.952589i \(-0.401591\pi\)
0.304259 + 0.952589i \(0.401591\pi\)
\(752\) −155.650 −0.206982
\(753\) 104.683 47.2791i 0.139021 0.0627876i
\(754\) −463.165 −0.614277
\(755\) −155.246 + 48.7024i −0.205624 + 0.0645064i
\(756\) −40.4121 + 131.508i −0.0534551 + 0.173952i
\(757\) 1156.06i 1.52716i −0.645711 0.763582i \(-0.723439\pi\)
0.645711 0.763582i \(-0.276561\pi\)
\(758\) −802.499 −1.05871
\(759\) 208.083 93.9792i 0.274154 0.123820i
\(760\) −36.4801 + 11.4442i −0.0480001 + 0.0150582i
\(761\) 146.174i 0.192081i 0.995377 + 0.0960405i \(0.0306178\pi\)
−0.995377 + 0.0960405i \(0.969382\pi\)
\(762\) −348.310 + 157.312i −0.457100 + 0.206446i
\(763\) 137.255i 0.179889i
\(764\) 47.3927i 0.0620323i
\(765\) −592.242 + 1332.02i −0.774173 + 1.74120i
\(766\) 107.391 0.140197
\(767\) 1858.32 2.42284
\(768\) −19.7572 43.7453i −0.0257256 0.0569600i
\(769\) 292.979 0.380986 0.190493 0.981689i \(-0.438991\pi\)
0.190493 + 0.981689i \(0.438991\pi\)
\(770\) −272.781 + 85.5745i −0.354262 + 0.111136i
\(771\) 6.74977 + 14.9449i 0.00875457 + 0.0193838i
\(772\) 196.162i 0.254096i
\(773\) 43.2864 0.0559979 0.0279990 0.999608i \(-0.491086\pi\)
0.0279990 + 0.999608i \(0.491086\pi\)
\(774\) 489.858 + 431.687i 0.632891 + 0.557735i
\(775\) 336.657 234.282i 0.434396 0.302300i
\(776\) 208.184i 0.268278i
\(777\) 27.1642 + 60.1454i 0.0349604 + 0.0774072i
\(778\) 305.987i 0.393300i
\(779\) 160.560i 0.206111i
\(780\) 528.470 471.233i 0.677525 0.604145i
\(781\) −1407.01 −1.80154
\(782\) 219.709 0.280958
\(783\) 110.054 358.133i 0.140554