Properties

Label 690.3.g.a.461.16
Level $690$
Weight $3$
Character 690.461
Analytic conductor $18.801$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(56\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 461.16
Character \(\chi\) \(=\) 690.461
Dual form 690.3.g.a.461.15

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421i q^{2} +(0.880203 + 2.86797i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(-4.05592 + 1.24480i) q^{6} -3.20877 q^{7} -2.82843i q^{8} +(-7.45049 + 5.04879i) q^{9} +O(q^{10})\) \(q+1.41421i q^{2} +(0.880203 + 2.86797i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(-4.05592 + 1.24480i) q^{6} -3.20877 q^{7} -2.82843i q^{8} +(-7.45049 + 5.04879i) q^{9} +3.16228 q^{10} -14.6872i q^{11} +(-1.76041 - 5.73594i) q^{12} +18.4837 q^{13} -4.53789i q^{14} +(6.41297 - 1.96819i) q^{15} +4.00000 q^{16} -27.0341i q^{17} +(-7.14007 - 10.5366i) q^{18} -5.52980 q^{19} +4.47214i q^{20} +(-2.82437 - 9.20266i) q^{21} +20.7708 q^{22} +4.79583i q^{23} +(8.11184 - 2.48959i) q^{24} -5.00000 q^{25} +26.1399i q^{26} +(-21.0377 - 16.9238i) q^{27} +6.41754 q^{28} +8.45614i q^{29} +(2.78345 + 9.06931i) q^{30} +49.6101 q^{31} +5.65685i q^{32} +(42.1224 - 12.9277i) q^{33} +38.2320 q^{34} +7.17503i q^{35} +(14.9010 - 10.0976i) q^{36} +42.6353 q^{37} -7.82032i q^{38} +(16.2694 + 53.0108i) q^{39} -6.32456 q^{40} -20.1288i q^{41} +(13.0145 - 3.99426i) q^{42} -17.0418 q^{43} +29.3744i q^{44} +(11.2894 + 16.6598i) q^{45} -6.78233 q^{46} -52.7239i q^{47} +(3.52081 + 11.4719i) q^{48} -38.7038 q^{49} -7.07107i q^{50} +(77.5330 - 23.7955i) q^{51} -36.9675 q^{52} -3.72931i q^{53} +(23.9339 - 29.7518i) q^{54} -32.8416 q^{55} +9.07578i q^{56} +(-4.86735 - 15.8593i) q^{57} -11.9588 q^{58} -29.1113i q^{59} +(-12.8259 + 3.93639i) q^{60} +8.31060 q^{61} +70.1592i q^{62} +(23.9069 - 16.2004i) q^{63} -8.00000 q^{64} -41.3309i q^{65} +(18.2825 + 59.5701i) q^{66} +0.327172 q^{67} +54.0683i q^{68} +(-13.7543 + 4.22131i) q^{69} -10.1470 q^{70} +69.2777i q^{71} +(14.2801 + 21.0732i) q^{72} +22.6543 q^{73} +60.2955i q^{74} +(-4.40102 - 14.3398i) q^{75} +11.0596 q^{76} +47.1278i q^{77} +(-74.9685 + 23.0085i) q^{78} +68.6785 q^{79} -8.94427i q^{80} +(30.0195 - 75.2319i) q^{81} +28.4664 q^{82} -73.2079i q^{83} +(5.64874 + 18.4053i) q^{84} -60.4501 q^{85} -24.1008i q^{86} +(-24.2519 + 7.44312i) q^{87} -41.5416 q^{88} +72.4059i q^{89} +(-23.5605 + 15.9657i) q^{90} -59.3101 q^{91} -9.59166i q^{92} +(43.6669 + 142.280i) q^{93} +74.5628 q^{94} +12.3650i q^{95} +(-16.2237 + 4.97918i) q^{96} +89.0797 q^{97} -54.7354i q^{98} +(74.1525 + 109.427i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q - 8q^{3} - 112q^{4} + 16q^{6} - 16q^{7} + O(q^{10}) \) \( 56q - 8q^{3} - 112q^{4} + 16q^{6} - 16q^{7} + 16q^{12} + 80q^{13} - 40q^{15} + 224q^{16} - 32q^{18} - 64q^{19} + 56q^{21} - 96q^{22} - 32q^{24} - 280q^{25} + 40q^{27} + 32q^{28} - 80q^{31} + 32q^{33} + 192q^{34} + 240q^{37} - 56q^{39} - 144q^{43} - 32q^{48} + 72q^{49} - 24q^{51} - 160q^{52} + 16q^{54} - 16q^{57} + 80q^{60} + 112q^{61} - 64q^{63} - 448q^{64} + 160q^{66} + 832q^{67} + 64q^{72} - 608q^{73} + 40q^{75} + 128q^{76} - 320q^{78} + 48q^{79} - 32q^{81} - 448q^{82} - 112q^{84} + 240q^{85} + 200q^{87} + 192q^{88} + 80q^{91} - 232q^{93} + 160q^{94} + 64q^{96} - 448q^{97} + 464q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) 0.880203 + 2.86797i 0.293401 + 0.955989i
\(4\) −2.00000 −0.500000
\(5\) 2.23607i 0.447214i
\(6\) −4.05592 + 1.24480i −0.675987 + 0.207466i
\(7\) −3.20877 −0.458396 −0.229198 0.973380i \(-0.573610\pi\)
−0.229198 + 0.973380i \(0.573610\pi\)
\(8\) 2.82843i 0.353553i
\(9\) −7.45049 + 5.04879i −0.827832 + 0.560977i
\(10\) 3.16228 0.316228
\(11\) 14.6872i 1.33520i −0.744521 0.667599i \(-0.767322\pi\)
0.744521 0.667599i \(-0.232678\pi\)
\(12\) −1.76041 5.73594i −0.146701 0.477995i
\(13\) 18.4837 1.42183 0.710913 0.703280i \(-0.248282\pi\)
0.710913 + 0.703280i \(0.248282\pi\)
\(14\) 4.53789i 0.324135i
\(15\) 6.41297 1.96819i 0.427531 0.131213i
\(16\) 4.00000 0.250000
\(17\) 27.0341i 1.59024i −0.606450 0.795121i \(-0.707407\pi\)
0.606450 0.795121i \(-0.292593\pi\)
\(18\) −7.14007 10.5366i −0.396670 0.585365i
\(19\) −5.52980 −0.291042 −0.145521 0.989355i \(-0.546486\pi\)
−0.145521 + 0.989355i \(0.546486\pi\)
\(20\) 4.47214i 0.223607i
\(21\) −2.82437 9.20266i −0.134494 0.438222i
\(22\) 20.7708 0.944128
\(23\) 4.79583i 0.208514i
\(24\) 8.11184 2.48959i 0.337993 0.103733i
\(25\) −5.00000 −0.200000
\(26\) 26.1399i 1.00538i
\(27\) −21.0377 16.9238i −0.779174 0.626807i
\(28\) 6.41754 0.229198
\(29\) 8.45614i 0.291591i 0.989315 + 0.145796i \(0.0465742\pi\)
−0.989315 + 0.145796i \(0.953426\pi\)
\(30\) 2.78345 + 9.06931i 0.0927816 + 0.302310i
\(31\) 49.6101 1.60032 0.800162 0.599783i \(-0.204747\pi\)
0.800162 + 0.599783i \(0.204747\pi\)
\(32\) 5.65685i 0.176777i
\(33\) 42.1224 12.9277i 1.27644 0.391749i
\(34\) 38.2320 1.12447
\(35\) 7.17503i 0.205001i
\(36\) 14.9010 10.0976i 0.413916 0.280488i
\(37\) 42.6353 1.15231 0.576153 0.817342i \(-0.304553\pi\)
0.576153 + 0.817342i \(0.304553\pi\)
\(38\) 7.82032i 0.205798i
\(39\) 16.2694 + 53.0108i 0.417165 + 1.35925i
\(40\) −6.32456 −0.158114
\(41\) 20.1288i 0.490946i −0.969403 0.245473i \(-0.921057\pi\)
0.969403 0.245473i \(-0.0789432\pi\)
\(42\) 13.0145 3.99426i 0.309870 0.0951015i
\(43\) −17.0418 −0.396321 −0.198161 0.980170i \(-0.563497\pi\)
−0.198161 + 0.980170i \(0.563497\pi\)
\(44\) 29.3744i 0.667599i
\(45\) 11.2894 + 16.6598i 0.250876 + 0.370218i
\(46\) −6.78233 −0.147442
\(47\) 52.7239i 1.12178i −0.827889 0.560892i \(-0.810458\pi\)
0.827889 0.560892i \(-0.189542\pi\)
\(48\) 3.52081 + 11.4719i 0.0733503 + 0.238997i
\(49\) −38.7038 −0.789873
\(50\) 7.07107i 0.141421i
\(51\) 77.5330 23.7955i 1.52026 0.466579i
\(52\) −36.9675 −0.710913
\(53\) 3.72931i 0.0703643i −0.999381 0.0351821i \(-0.988799\pi\)
0.999381 0.0351821i \(-0.0112011\pi\)
\(54\) 23.9339 29.7518i 0.443220 0.550959i
\(55\) −32.8416 −0.597119
\(56\) 9.07578i 0.162067i
\(57\) −4.86735 15.8593i −0.0853921 0.278233i
\(58\) −11.9588 −0.206186
\(59\) 29.1113i 0.493412i −0.969090 0.246706i \(-0.920652\pi\)
0.969090 0.246706i \(-0.0793481\pi\)
\(60\) −12.8259 + 3.93639i −0.213766 + 0.0656065i
\(61\) 8.31060 0.136239 0.0681196 0.997677i \(-0.478300\pi\)
0.0681196 + 0.997677i \(0.478300\pi\)
\(62\) 70.1592i 1.13160i
\(63\) 23.9069 16.2004i 0.379475 0.257149i
\(64\) −8.00000 −0.125000
\(65\) 41.3309i 0.635860i
\(66\) 18.2825 + 59.5701i 0.277008 + 0.902577i
\(67\) 0.327172 0.00488317 0.00244158 0.999997i \(-0.499223\pi\)
0.00244158 + 0.999997i \(0.499223\pi\)
\(68\) 54.0683i 0.795121i
\(69\) −13.7543 + 4.22131i −0.199338 + 0.0611783i
\(70\) −10.1470 −0.144958
\(71\) 69.2777i 0.975742i 0.872916 + 0.487871i \(0.162226\pi\)
−0.872916 + 0.487871i \(0.837774\pi\)
\(72\) 14.2801 + 21.0732i 0.198335 + 0.292683i
\(73\) 22.6543 0.310333 0.155166 0.987888i \(-0.450409\pi\)
0.155166 + 0.987888i \(0.450409\pi\)
\(74\) 60.2955i 0.814804i
\(75\) −4.40102 14.3398i −0.0586802 0.191198i
\(76\) 11.0596 0.145521
\(77\) 47.1278i 0.612050i
\(78\) −74.9685 + 23.0085i −0.961135 + 0.294980i
\(79\) 68.6785 0.869348 0.434674 0.900588i \(-0.356864\pi\)
0.434674 + 0.900588i \(0.356864\pi\)
\(80\) 8.94427i 0.111803i
\(81\) 30.0195 75.2319i 0.370611 0.928788i
\(82\) 28.4664 0.347151
\(83\) 73.2079i 0.882022i −0.897502 0.441011i \(-0.854620\pi\)
0.897502 0.441011i \(-0.145380\pi\)
\(84\) 5.64874 + 18.4053i 0.0672469 + 0.219111i
\(85\) −60.4501 −0.711178
\(86\) 24.1008i 0.280242i
\(87\) −24.2519 + 7.44312i −0.278758 + 0.0855531i
\(88\) −41.5416 −0.472064
\(89\) 72.4059i 0.813550i 0.913528 + 0.406775i \(0.133347\pi\)
−0.913528 + 0.406775i \(0.866653\pi\)
\(90\) −23.5605 + 15.9657i −0.261783 + 0.177396i
\(91\) −59.3101 −0.651759
\(92\) 9.59166i 0.104257i
\(93\) 43.6669 + 142.280i 0.469537 + 1.52989i
\(94\) 74.5628 0.793222
\(95\) 12.3650i 0.130158i
\(96\) −16.2237 + 4.97918i −0.168997 + 0.0518665i
\(97\) 89.0797 0.918348 0.459174 0.888346i \(-0.348145\pi\)
0.459174 + 0.888346i \(0.348145\pi\)
\(98\) 54.7354i 0.558525i
\(99\) 74.1525 + 109.427i 0.749015 + 1.10532i
\(100\) 10.0000 0.100000
\(101\) 84.9463i 0.841052i −0.907280 0.420526i \(-0.861845\pi\)
0.907280 0.420526i \(-0.138155\pi\)
\(102\) 33.6520 + 109.648i 0.329921 + 1.07498i
\(103\) −161.088 −1.56396 −0.781981 0.623303i \(-0.785791\pi\)
−0.781981 + 0.623303i \(0.785791\pi\)
\(104\) 52.2799i 0.502691i
\(105\) −20.5778 + 6.31548i −0.195979 + 0.0601475i
\(106\) 5.27404 0.0497551
\(107\) 27.8404i 0.260191i 0.991501 + 0.130095i \(0.0415284\pi\)
−0.991501 + 0.130095i \(0.958472\pi\)
\(108\) 42.0754 + 33.8476i 0.389587 + 0.313404i
\(109\) 213.350 1.95734 0.978672 0.205431i \(-0.0658596\pi\)
0.978672 + 0.205431i \(0.0658596\pi\)
\(110\) 46.4450i 0.422227i
\(111\) 37.5278 + 122.277i 0.338088 + 1.10159i
\(112\) −12.8351 −0.114599
\(113\) 33.6988i 0.298219i −0.988821 0.149110i \(-0.952359\pi\)
0.988821 0.149110i \(-0.0476408\pi\)
\(114\) 22.4284 6.88347i 0.196741 0.0603813i
\(115\) 10.7238 0.0932505
\(116\) 16.9123i 0.145796i
\(117\) −137.713 + 93.3205i −1.17703 + 0.797611i
\(118\) 41.1696 0.348895
\(119\) 86.7463i 0.728961i
\(120\) −5.56689 18.1386i −0.0463908 0.151155i
\(121\) −94.7135 −0.782756
\(122\) 11.7530i 0.0963357i
\(123\) 57.7287 17.7174i 0.469339 0.144044i
\(124\) −99.2201 −0.800162
\(125\) 11.1803i 0.0894427i
\(126\) 22.9108 + 33.8095i 0.181832 + 0.268329i
\(127\) −150.876 −1.18800 −0.593999 0.804466i \(-0.702452\pi\)
−0.593999 + 0.804466i \(0.702452\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) −15.0003 48.8754i −0.116281 0.378879i
\(130\) 58.4507 0.449621
\(131\) 132.703i 1.01300i −0.862239 0.506501i \(-0.830939\pi\)
0.862239 0.506501i \(-0.169061\pi\)
\(132\) −84.2448 + 25.8554i −0.638218 + 0.195874i
\(133\) 17.7439 0.133413
\(134\) 0.462692i 0.00345292i
\(135\) −37.8428 + 47.0417i −0.280317 + 0.348457i
\(136\) −76.4641 −0.562236
\(137\) 41.0423i 0.299579i −0.988718 0.149789i \(-0.952140\pi\)
0.988718 0.149789i \(-0.0478596\pi\)
\(138\) −5.96983 19.4515i −0.0432596 0.140953i
\(139\) −100.667 −0.724219 −0.362110 0.932135i \(-0.617943\pi\)
−0.362110 + 0.932135i \(0.617943\pi\)
\(140\) 14.3501i 0.102500i
\(141\) 151.210 46.4077i 1.07241 0.329133i
\(142\) −97.9734 −0.689954
\(143\) 271.474i 1.89842i
\(144\) −29.8019 + 20.1952i −0.206958 + 0.140244i
\(145\) 18.9085 0.130403
\(146\) 32.0380i 0.219438i
\(147\) −34.0672 111.001i −0.231750 0.755110i
\(148\) −85.2707 −0.576153
\(149\) 54.7479i 0.367435i −0.982979 0.183718i \(-0.941187\pi\)
0.982979 0.183718i \(-0.0588132\pi\)
\(150\) 20.2796 6.22398i 0.135197 0.0414932i
\(151\) 91.6265 0.606798 0.303399 0.952864i \(-0.401879\pi\)
0.303399 + 0.952864i \(0.401879\pi\)
\(152\) 15.6406i 0.102899i
\(153\) 136.490 + 201.417i 0.892089 + 1.31645i
\(154\) −66.6488 −0.432785
\(155\) 110.931i 0.715687i
\(156\) −32.5389 106.022i −0.208583 0.679625i
\(157\) 76.9201 0.489937 0.244968 0.969531i \(-0.421222\pi\)
0.244968 + 0.969531i \(0.421222\pi\)
\(158\) 97.1261i 0.614722i
\(159\) 10.6955 3.28255i 0.0672675 0.0206450i
\(160\) 12.6491 0.0790569
\(161\) 15.3887i 0.0955822i
\(162\) 106.394 + 42.4539i 0.656753 + 0.262061i
\(163\) −28.7684 −0.176493 −0.0882465 0.996099i \(-0.528126\pi\)
−0.0882465 + 0.996099i \(0.528126\pi\)
\(164\) 40.2575i 0.245473i
\(165\) −28.9072 94.1885i −0.175195 0.570840i
\(166\) 103.532 0.623684
\(167\) 61.3209i 0.367191i 0.983002 + 0.183595i \(0.0587737\pi\)
−0.983002 + 0.183595i \(0.941226\pi\)
\(168\) −26.0290 + 7.98853i −0.154935 + 0.0475508i
\(169\) 172.648 1.02159
\(170\) 85.4894i 0.502879i
\(171\) 41.1997 27.9188i 0.240934 0.163268i
\(172\) 34.0836 0.198161
\(173\) 267.085i 1.54385i −0.635716 0.771923i \(-0.719295\pi\)
0.635716 0.771923i \(-0.280705\pi\)
\(174\) −10.5262 34.2974i −0.0604952 0.197112i
\(175\) 16.0439 0.0916792
\(176\) 58.7488i 0.333800i
\(177\) 83.4903 25.6238i 0.471696 0.144767i
\(178\) −102.397 −0.575266
\(179\) 49.4363i 0.276180i 0.990420 + 0.138090i \(0.0440964\pi\)
−0.990420 + 0.138090i \(0.955904\pi\)
\(180\) −22.5789 33.3196i −0.125438 0.185109i
\(181\) 285.987 1.58004 0.790019 0.613082i \(-0.210070\pi\)
0.790019 + 0.613082i \(0.210070\pi\)
\(182\) 83.8771i 0.460863i
\(183\) 7.31501 + 23.8345i 0.0399727 + 0.130243i
\(184\) 13.5647 0.0737210
\(185\) 95.3355i 0.515327i
\(186\) −201.214 + 61.7544i −1.08180 + 0.332013i
\(187\) −397.055 −2.12329
\(188\) 105.448i 0.560892i
\(189\) 67.5052 + 54.3046i 0.357170 + 0.287326i
\(190\) −17.4868 −0.0920356
\(191\) 265.836i 1.39181i −0.718133 0.695906i \(-0.755003\pi\)
0.718133 0.695906i \(-0.244997\pi\)
\(192\) −7.04162 22.9437i −0.0366751 0.119499i
\(193\) −229.353 −1.18836 −0.594178 0.804333i \(-0.702523\pi\)
−0.594178 + 0.804333i \(0.702523\pi\)
\(194\) 125.978i 0.649370i
\(195\) 118.536 36.3796i 0.607875 0.186562i
\(196\) 77.4076 0.394937
\(197\) 79.4445i 0.403272i 0.979461 + 0.201636i \(0.0646258\pi\)
−0.979461 + 0.201636i \(0.935374\pi\)
\(198\) −154.753 + 104.867i −0.781579 + 0.529634i
\(199\) −216.050 −1.08568 −0.542840 0.839836i \(-0.682651\pi\)
−0.542840 + 0.839836i \(0.682651\pi\)
\(200\) 14.1421i 0.0707107i
\(201\) 0.287978 + 0.938320i 0.00143273 + 0.00466826i
\(202\) 120.132 0.594714
\(203\) 27.1338i 0.133664i
\(204\) −155.066 + 47.5910i −0.760128 + 0.233289i
\(205\) −45.0093 −0.219558
\(206\) 227.813i 1.10589i
\(207\) −24.2131 35.7313i −0.116972 0.172615i
\(208\) 73.9349 0.355456
\(209\) 81.2172i 0.388599i
\(210\) −8.93144 29.1014i −0.0425307 0.138578i
\(211\) 111.332 0.527640 0.263820 0.964572i \(-0.415017\pi\)
0.263820 + 0.964572i \(0.415017\pi\)
\(212\) 7.45861i 0.0351821i
\(213\) −198.686 + 60.9784i −0.932799 + 0.286284i
\(214\) −39.3723 −0.183983
\(215\) 38.1067i 0.177240i
\(216\) −47.8677 + 59.5036i −0.221610 + 0.275480i
\(217\) −159.187 −0.733582
\(218\) 301.723i 1.38405i
\(219\) 19.9404 + 64.9717i 0.0910519 + 0.296675i
\(220\) 65.6831 0.298560
\(221\) 499.692i 2.26105i
\(222\) −172.926 + 53.0723i −0.778944 + 0.239064i
\(223\) −257.455 −1.15451 −0.577254 0.816565i \(-0.695876\pi\)
−0.577254 + 0.816565i \(0.695876\pi\)
\(224\) 18.1516i 0.0810337i
\(225\) 37.2524 25.2439i 0.165566 0.112195i
\(226\) 47.6573 0.210873
\(227\) 2.14581i 0.00945290i −0.999989 0.00472645i \(-0.998496\pi\)
0.999989 0.00472645i \(-0.00150448\pi\)
\(228\) 9.73470 + 31.7186i 0.0426960 + 0.139117i
\(229\) −107.929 −0.471305 −0.235653 0.971837i \(-0.575723\pi\)
−0.235653 + 0.971837i \(0.575723\pi\)
\(230\) 15.1658i 0.0659380i
\(231\) −135.161 + 41.4821i −0.585113 + 0.179576i
\(232\) 23.9176 0.103093
\(233\) 155.714i 0.668300i −0.942520 0.334150i \(-0.891551\pi\)
0.942520 0.334150i \(-0.108449\pi\)
\(234\) −131.975 194.755i −0.563996 0.832287i
\(235\) −117.894 −0.501677
\(236\) 58.2226i 0.246706i
\(237\) 60.4510 + 196.968i 0.255068 + 0.831088i
\(238\) −122.678 −0.515453
\(239\) 435.813i 1.82349i 0.410761 + 0.911743i \(0.365263\pi\)
−0.410761 + 0.911743i \(0.634737\pi\)
\(240\) 25.6519 7.87278i 0.106883 0.0328032i
\(241\) 449.437 1.86488 0.932442 0.361320i \(-0.117674\pi\)
0.932442 + 0.361320i \(0.117674\pi\)
\(242\) 133.945i 0.553492i
\(243\) 242.186 + 19.8755i 0.996649 + 0.0817923i
\(244\) −16.6212 −0.0681196
\(245\) 86.5443i 0.353242i
\(246\) 25.0562 + 81.6407i 0.101854 + 0.331873i
\(247\) −102.211 −0.413811
\(248\) 140.318i 0.565800i
\(249\) 209.958 64.4378i 0.843204 0.258786i
\(250\) −15.8114 −0.0632456
\(251\) 273.849i 1.09103i −0.838100 0.545517i \(-0.816333\pi\)
0.838100 0.545517i \(-0.183667\pi\)
\(252\) −47.8138 + 32.4008i −0.189737 + 0.128575i
\(253\) 70.4373 0.278408
\(254\) 213.370i 0.840041i
\(255\) −53.2084 173.369i −0.208660 0.679879i
\(256\) 16.0000 0.0625000
\(257\) 381.933i 1.48612i 0.669225 + 0.743059i \(0.266626\pi\)
−0.669225 + 0.743059i \(0.733374\pi\)
\(258\) 69.1203 21.2136i 0.267908 0.0822232i
\(259\) −136.807 −0.528213
\(260\) 82.6618i 0.317930i
\(261\) −42.6933 63.0024i −0.163576 0.241388i
\(262\) 187.671 0.716301
\(263\) 80.3574i 0.305541i −0.988262 0.152771i \(-0.951180\pi\)
0.988262 0.152771i \(-0.0488196\pi\)
\(264\) −36.5651 119.140i −0.138504 0.451288i
\(265\) −8.33898 −0.0314679
\(266\) 25.0936i 0.0943369i
\(267\) −207.658 + 63.7319i −0.777745 + 0.238696i
\(268\) −0.654345 −0.00244158
\(269\) 387.384i 1.44009i −0.693928 0.720045i \(-0.744121\pi\)
0.693928 0.720045i \(-0.255879\pi\)
\(270\) −66.5271 53.5177i −0.246397 0.198214i
\(271\) −456.085 −1.68297 −0.841485 0.540280i \(-0.818318\pi\)
−0.841485 + 0.540280i \(0.818318\pi\)
\(272\) 108.137i 0.397561i
\(273\) −52.2049 170.099i −0.191227 0.623075i
\(274\) 58.0426 0.211834
\(275\) 73.4359i 0.267040i
\(276\) 27.5086 8.44261i 0.0996688 0.0305892i
\(277\) 250.843 0.905570 0.452785 0.891620i \(-0.350430\pi\)
0.452785 + 0.891620i \(0.350430\pi\)
\(278\) 142.364i 0.512101i
\(279\) −369.619 + 250.471i −1.32480 + 0.897745i
\(280\) 20.2941 0.0724788
\(281\) 0.440087i 0.00156615i −1.00000 0.000783073i \(-0.999751\pi\)
1.00000 0.000783073i \(-0.000249260\pi\)
\(282\) 65.6304 + 213.844i 0.232732 + 0.758311i
\(283\) −131.628 −0.465118 −0.232559 0.972582i \(-0.574710\pi\)
−0.232559 + 0.972582i \(0.574710\pi\)
\(284\) 138.555i 0.487871i
\(285\) −35.4625 + 10.8837i −0.124430 + 0.0381885i
\(286\) 383.922 1.34239
\(287\) 64.5886i 0.225048i
\(288\) −28.5603 42.1463i −0.0991676 0.146341i
\(289\) −441.844 −1.52887
\(290\) 26.7407i 0.0922092i
\(291\) 78.4083 + 255.478i 0.269444 + 0.877931i
\(292\) −45.3085 −0.155166
\(293\) 94.8962i 0.323878i −0.986801 0.161939i \(-0.948225\pi\)
0.986801 0.161939i \(-0.0517748\pi\)
\(294\) 156.979 48.1783i 0.533944 0.163872i
\(295\) −65.0948 −0.220660
\(296\) 120.591i 0.407402i
\(297\) −248.563 + 308.985i −0.836912 + 1.04035i
\(298\) 77.4252 0.259816
\(299\) 88.6449i 0.296471i
\(300\) 8.80203 + 28.6797i 0.0293401 + 0.0955989i
\(301\) 54.6833 0.181672
\(302\) 129.579i 0.429071i
\(303\) 243.623 74.7700i 0.804037 0.246766i
\(304\) −22.1192 −0.0727605
\(305\) 18.5831i 0.0609281i
\(306\) −284.847 + 193.025i −0.930873 + 0.630802i
\(307\) 21.3796 0.0696403 0.0348202 0.999394i \(-0.488914\pi\)
0.0348202 + 0.999394i \(0.488914\pi\)
\(308\) 94.2557i 0.306025i
\(309\) −141.790 461.995i −0.458868 1.49513i
\(310\) 156.881 0.506067
\(311\) 401.801i 1.29196i 0.763353 + 0.645982i \(0.223552\pi\)
−0.763353 + 0.645982i \(0.776448\pi\)
\(312\) 149.937 46.0169i 0.480567 0.147490i
\(313\) −430.198 −1.37443 −0.687217 0.726452i \(-0.741168\pi\)
−0.687217 + 0.726452i \(0.741168\pi\)
\(314\) 108.781i 0.346438i
\(315\) −36.2252 53.4575i −0.115001 0.169706i
\(316\) −137.357 −0.434674
\(317\) 268.540i 0.847129i −0.905866 0.423564i \(-0.860779\pi\)
0.905866 0.423564i \(-0.139221\pi\)
\(318\) 4.64222 + 15.1258i 0.0145982 + 0.0475653i
\(319\) 124.197 0.389332
\(320\) 17.8885i 0.0559017i
\(321\) −79.8454 + 24.5052i −0.248740 + 0.0763403i
\(322\) 21.7629 0.0675868
\(323\) 149.493i 0.462828i
\(324\) −60.0389 + 150.464i −0.185305 + 0.464394i
\(325\) −92.4187 −0.284365
\(326\) 40.6846i 0.124799i
\(327\) 187.792 + 611.882i 0.574287 + 1.87120i
\(328\) −56.9328 −0.173576
\(329\) 169.179i 0.514222i
\(330\) 133.203 40.8810i 0.403645 0.123882i
\(331\) 284.638 0.859935 0.429967 0.902844i \(-0.358525\pi\)
0.429967 + 0.902844i \(0.358525\pi\)
\(332\) 146.416i 0.441011i
\(333\) −317.654 + 215.257i −0.953916 + 0.646417i
\(334\) −86.7208 −0.259643
\(335\) 0.731580i 0.00218382i
\(336\) −11.2975 36.8106i −0.0336235 0.109555i
\(337\) 210.916 0.625864 0.312932 0.949776i \(-0.398689\pi\)
0.312932 + 0.949776i \(0.398689\pi\)
\(338\) 244.162i 0.722371i
\(339\) 96.6471 29.6618i 0.285095 0.0874979i
\(340\) 120.900 0.355589
\(341\) 728.632i 2.13675i
\(342\) 39.4831 + 58.2652i 0.115448 + 0.170366i
\(343\) 281.421 0.820471
\(344\) 48.2016i 0.140121i
\(345\) 9.43913 + 30.7555i 0.0273598 + 0.0891465i
\(346\) 377.716 1.09166
\(347\) 469.776i 1.35382i 0.736065 + 0.676911i \(0.236682\pi\)
−0.736065 + 0.676911i \(0.763318\pi\)
\(348\) 48.5039 14.8862i 0.139379 0.0427766i
\(349\) −533.718 −1.52928 −0.764639 0.644459i \(-0.777083\pi\)
−0.764639 + 0.644459i \(0.777083\pi\)
\(350\) 22.6894i 0.0648270i
\(351\) −388.855 312.815i −1.10785 0.891210i
\(352\) 83.0833 0.236032
\(353\) 213.137i 0.603788i 0.953341 + 0.301894i \(0.0976189\pi\)
−0.953341 + 0.301894i \(0.902381\pi\)
\(354\) 36.2376 + 118.073i 0.102366 + 0.333540i
\(355\) 154.910 0.436365
\(356\) 144.812i 0.406775i
\(357\) −248.786 + 76.3544i −0.696879 + 0.213878i
\(358\) −69.9135 −0.195289
\(359\) 606.042i 1.68814i −0.536233 0.844070i \(-0.680153\pi\)
0.536233 0.844070i \(-0.319847\pi\)
\(360\) 47.1210 31.9313i 0.130892 0.0886982i
\(361\) −330.421 −0.915294
\(362\) 404.447i 1.11726i
\(363\) −83.3671 271.635i −0.229661 0.748307i
\(364\) 118.620 0.325880
\(365\) 50.6565i 0.138785i
\(366\) −33.7071 + 10.3450i −0.0920959 + 0.0282650i
\(367\) 379.037 1.03280 0.516399 0.856348i \(-0.327272\pi\)
0.516399 + 0.856348i \(0.327272\pi\)
\(368\) 19.1833i 0.0521286i
\(369\) 101.626 + 149.969i 0.275409 + 0.406420i
\(370\) 134.825 0.364391
\(371\) 11.9665i 0.0322547i
\(372\) −87.3339 284.560i −0.234768 0.764947i
\(373\) −88.5064 −0.237283 −0.118641 0.992937i \(-0.537854\pi\)
−0.118641 + 0.992937i \(0.537854\pi\)
\(374\) 561.521i 1.50139i
\(375\) −32.0649 + 9.84097i −0.0855063 + 0.0262426i
\(376\) −149.126 −0.396611
\(377\) 156.301i 0.414592i
\(378\) −76.7983 + 95.4668i −0.203170 + 0.252558i
\(379\) 565.323 1.49162 0.745809 0.666160i \(-0.232063\pi\)
0.745809 + 0.666160i \(0.232063\pi\)
\(380\) 24.7300i 0.0650790i
\(381\) −132.801 432.707i −0.348560 1.13571i
\(382\) 375.949 0.984160
\(383\) 592.968i 1.54822i 0.633051 + 0.774110i \(0.281802\pi\)
−0.633051 + 0.774110i \(0.718198\pi\)
\(384\) 32.4474 9.95836i 0.0844983 0.0259332i
\(385\) 105.381 0.273717
\(386\) 324.354i 0.840295i
\(387\) 126.970 86.0406i 0.328087 0.222327i
\(388\) −178.159 −0.459174
\(389\) 626.639i 1.61090i 0.592666 + 0.805448i \(0.298075\pi\)
−0.592666 + 0.805448i \(0.701925\pi\)
\(390\) 51.4485 + 167.635i 0.131919 + 0.429833i
\(391\) 129.651 0.331589
\(392\) 109.471i 0.279262i
\(393\) 380.589 116.806i 0.968419 0.297216i
\(394\) −112.352 −0.285156
\(395\) 153.570i 0.388784i
\(396\) −148.305 218.853i −0.374508 0.552660i
\(397\) −29.5114 −0.0743361 −0.0371681 0.999309i \(-0.511834\pi\)
−0.0371681 + 0.999309i \(0.511834\pi\)
\(398\) 305.541i 0.767691i
\(399\) 15.6182 + 50.8889i 0.0391434 + 0.127541i
\(400\) −20.0000 −0.0500000
\(401\) 467.472i 1.16576i −0.812557 0.582882i \(-0.801925\pi\)
0.812557 0.582882i \(-0.198075\pi\)
\(402\) −1.32698 + 0.407263i −0.00330096 + 0.00101309i
\(403\) 916.979 2.27538
\(404\) 169.893i 0.420526i
\(405\) −168.224 67.1255i −0.415367 0.165742i
\(406\) 38.3730 0.0945148
\(407\) 626.193i 1.53856i
\(408\) −67.3039 219.297i −0.164961 0.537491i
\(409\) −397.499 −0.971880 −0.485940 0.873992i \(-0.661523\pi\)
−0.485940 + 0.873992i \(0.661523\pi\)
\(410\) 63.6528i 0.155251i
\(411\) 117.708 36.1256i 0.286394 0.0878968i
\(412\) 322.176 0.781981
\(413\) 93.4115i 0.226178i
\(414\) 50.5316 34.2426i 0.122057 0.0827115i
\(415\) −163.698 −0.394452
\(416\) 104.560i 0.251346i
\(417\) −88.6070 288.708i −0.212487 0.692346i
\(418\) −114.859 −0.274781
\(419\) 456.925i 1.09051i 0.838269 + 0.545257i \(0.183568\pi\)
−0.838269 + 0.545257i \(0.816432\pi\)
\(420\) 41.1555 12.6310i 0.0979893 0.0300737i
\(421\) −312.034 −0.741174 −0.370587 0.928798i \(-0.620843\pi\)
−0.370587 + 0.928798i \(0.620843\pi\)
\(422\) 157.447i 0.373098i
\(423\) 266.192 + 392.818i 0.629295 + 0.928649i
\(424\) −10.5481 −0.0248775
\(425\) 135.171i 0.318049i
\(426\) −86.2365 280.985i −0.202433 0.659588i
\(427\) −26.6668 −0.0624515
\(428\) 55.6808i 0.130095i
\(429\) 778.579 238.952i 1.81487 0.556998i
\(430\) −53.8910 −0.125328
\(431\) 572.063i 1.32729i 0.748046 + 0.663647i \(0.230992\pi\)
−0.748046 + 0.663647i \(0.769008\pi\)
\(432\) −84.1508 67.6952i −0.194794 0.156702i
\(433\) 565.137 1.30517 0.652583 0.757717i \(-0.273685\pi\)
0.652583 + 0.757717i \(0.273685\pi\)
\(434\) 225.125i 0.518721i
\(435\) 16.6433 + 54.2290i 0.0382605 + 0.124664i
\(436\) −426.701 −0.978672
\(437\) 26.5200i 0.0606865i
\(438\) −91.8839 + 28.1999i −0.209781 + 0.0643834i
\(439\) 752.081 1.71317 0.856584 0.516008i \(-0.172582\pi\)
0.856584 + 0.516008i \(0.172582\pi\)
\(440\) 92.8899i 0.211113i
\(441\) 288.362 195.407i 0.653882 0.443100i
\(442\) 706.671 1.59880
\(443\) 761.734i 1.71949i 0.510724 + 0.859745i \(0.329378\pi\)
−0.510724 + 0.859745i \(0.670622\pi\)
\(444\) −75.0555 244.554i −0.169044 0.550797i
\(445\) 161.905 0.363830
\(446\) 364.097i 0.816360i
\(447\) 157.015 48.1892i 0.351264 0.107806i
\(448\) 25.6702 0.0572995
\(449\) 149.930i 0.333920i 0.985964 + 0.166960i \(0.0533951\pi\)
−0.985964 + 0.166960i \(0.946605\pi\)
\(450\) 35.7003 + 52.6829i 0.0793341 + 0.117073i
\(451\) −295.635 −0.655510
\(452\) 67.3976i 0.149110i
\(453\) 80.6499 + 262.782i 0.178035 + 0.580092i
\(454\) 3.03463 0.00668421
\(455\) 132.621i 0.291475i
\(456\) −44.8569 + 13.7669i −0.0983703 + 0.0301907i
\(457\) 415.935 0.910143 0.455071 0.890455i \(-0.349614\pi\)
0.455071 + 0.890455i \(0.349614\pi\)
\(458\) 152.635i 0.333263i
\(459\) −457.520 + 568.736i −0.996776 + 1.23908i
\(460\) −21.4476 −0.0466252
\(461\) 798.234i 1.73153i 0.500454 + 0.865763i \(0.333167\pi\)
−0.500454 + 0.865763i \(0.666833\pi\)
\(462\) −58.6645 191.147i −0.126979 0.413737i
\(463\) −566.084 −1.22264 −0.611322 0.791382i \(-0.709362\pi\)
−0.611322 + 0.791382i \(0.709362\pi\)
\(464\) 33.8246i 0.0728978i
\(465\) 318.148 97.6422i 0.684189 0.209983i
\(466\) 220.213 0.472560
\(467\) 704.756i 1.50911i 0.656234 + 0.754557i \(0.272148\pi\)
−0.656234 + 0.754557i \(0.727852\pi\)
\(468\) 275.426 186.641i 0.588516 0.398805i
\(469\) −1.04982 −0.00223843
\(470\) 166.728i 0.354739i
\(471\) 67.7053 + 220.604i 0.143748 + 0.468374i
\(472\) −82.3392 −0.174447
\(473\) 250.296i 0.529168i
\(474\) −278.555 + 85.4907i −0.587668 + 0.180360i
\(475\) 27.6490 0.0582084
\(476\) 173.493i 0.364480i
\(477\) 18.8285 + 27.7851i 0.0394727 + 0.0582498i
\(478\) −616.333 −1.28940
\(479\) 464.409i 0.969539i −0.874642 0.484770i \(-0.838903\pi\)
0.874642 0.484770i \(-0.161097\pi\)
\(480\) 11.1338 + 36.2772i 0.0231954 + 0.0755776i
\(481\) 788.060 1.63838
\(482\) 635.600i 1.31867i
\(483\) 44.1344 13.5452i 0.0913755 0.0280439i
\(484\) 189.427 0.391378
\(485\) 199.188i 0.410698i
\(486\) −28.1083 + 342.502i −0.0578359 + 0.704738i
\(487\) −764.898 −1.57063 −0.785316 0.619095i \(-0.787500\pi\)
−0.785316 + 0.619095i \(0.787500\pi\)
\(488\) 23.5059i 0.0481679i
\(489\) −25.3220 82.5067i −0.0517832 0.168725i
\(490\) −122.392 −0.249780
\(491\) 739.524i 1.50616i 0.657930 + 0.753079i \(0.271432\pi\)
−0.657930 + 0.753079i \(0.728568\pi\)
\(492\) −115.457 + 35.4348i −0.234669 + 0.0720220i
\(493\) 228.604 0.463701
\(494\) 144.549i 0.292609i
\(495\) 244.685 165.810i 0.494314 0.334970i
\(496\) 198.440 0.400081
\(497\) 222.296i 0.447276i
\(498\) 91.1288 + 296.925i 0.182990 + 0.596235i
\(499\) 622.508 1.24751 0.623756 0.781619i \(-0.285606\pi\)
0.623756 + 0.781619i \(0.285606\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) −175.866 + 53.9748i −0.351031 + 0.107734i
\(502\) 387.281 0.771477
\(503\) 736.196i 1.46361i −0.681514 0.731805i \(-0.738678\pi\)
0.681514 0.731805i \(-0.261322\pi\)
\(504\) −45.8217 67.6189i −0.0909160 0.134165i
\(505\) −189.946 −0.376130
\(506\) 99.6134i 0.196864i
\(507\) 151.966 + 495.150i 0.299735 + 0.976627i
\(508\) 301.751 0.593999
\(509\) 618.281i 1.21470i 0.794435 + 0.607349i \(0.207767\pi\)
−0.794435 + 0.607349i \(0.792233\pi\)
\(510\) 245.181 75.2481i 0.480747 0.147545i
\(511\) −72.6924 −0.142255
\(512\) 22.6274i 0.0441942i
\(513\) 116.334 + 93.5852i 0.226773 + 0.182427i
\(514\) −540.134 −1.05084
\(515\) 360.204i 0.699425i
\(516\) 30.0005 + 97.7508i 0.0581406 + 0.189440i
\(517\) −774.366 −1.49781
\(518\) 193.474i 0.373503i
\(519\) 765.992 235.089i 1.47590 0.452966i
\(520\) −116.901 −0.224810
\(521\) 141.633i 0.271848i 0.990719 + 0.135924i \(0.0434003\pi\)
−0.990719 + 0.135924i \(0.956600\pi\)
\(522\) 89.0988 60.3774i 0.170687 0.115666i
\(523\) −582.032 −1.11287 −0.556435 0.830891i \(-0.687831\pi\)
−0.556435 + 0.830891i \(0.687831\pi\)
\(524\) 265.407i 0.506501i
\(525\) 14.1219 + 46.0133i 0.0268988 + 0.0876443i
\(526\) 113.642 0.216050
\(527\) 1341.16i 2.54490i
\(528\) 168.490 51.7108i 0.319109 0.0979372i
\(529\) −23.0000 −0.0434783
\(530\) 11.7931i 0.0222511i
\(531\) 146.977 + 216.893i 0.276792 + 0.408462i
\(532\) −35.4877 −0.0667063
\(533\) 372.055i 0.698039i
\(534\) −90.1305 293.673i −0.168784 0.549949i
\(535\) 62.2531 0.116361
\(536\) 0.925383i 0.00172646i
\(537\) −141.782 + 43.5140i −0.264026 + 0.0810316i
\(538\) 547.844 1.01830
\(539\) 568.450i 1.05464i
\(540\) 75.6855 94.0835i 0.140158 0.174229i
\(541\) 687.177 1.27020 0.635099 0.772431i \(-0.280959\pi\)
0.635099 + 0.772431i \(0.280959\pi\)
\(542\) 645.002i 1.19004i
\(543\) 251.727 + 820.202i 0.463585 + 1.51050i
\(544\) 152.928 0.281118
\(545\) 477.066i 0.875351i
\(546\) 240.557 73.8289i 0.440580 0.135218i
\(547\) −751.639 −1.37411 −0.687055 0.726605i \(-0.741097\pi\)
−0.687055 + 0.726605i \(0.741097\pi\)
\(548\) 82.0846i 0.149789i
\(549\) −61.9180 + 41.9584i −0.112783 + 0.0764270i
\(550\) −103.854 −0.188826
\(551\) 46.7608i 0.0848653i
\(552\) 11.9397 + 38.9030i 0.0216298 + 0.0704765i
\(553\) −220.374 −0.398506
\(554\) 354.745i 0.640335i
\(555\) 273.419 83.9146i 0.492647 0.151198i
\(556\) 201.333 0.362110
\(557\) 486.059i 0.872638i 0.899792 + 0.436319i \(0.143718\pi\)
−0.899792 + 0.436319i \(0.856282\pi\)
\(558\) −354.219 522.720i −0.634801 0.936775i
\(559\) −314.996 −0.563500
\(560\) 28.7001i 0.0512502i
\(561\) −349.489 1138.74i −0.622976 2.02984i
\(562\) 0.622377 0.00110743
\(563\) 677.685i 1.20370i 0.798608 + 0.601852i \(0.205570\pi\)
−0.798608 + 0.601852i \(0.794430\pi\)
\(564\) −302.421 + 92.8154i −0.536207 + 0.164566i
\(565\) −75.3528 −0.133368
\(566\) 186.151i 0.328888i
\(567\) −96.3256 + 241.402i −0.169886 + 0.425753i
\(568\) 195.947 0.344977
\(569\) 1092.44i 1.91992i 0.280130 + 0.959962i \(0.409623\pi\)
−0.280130 + 0.959962i \(0.590377\pi\)
\(570\) −15.3919 50.1515i −0.0270033 0.0879851i
\(571\) −985.455 −1.72584 −0.862920 0.505340i \(-0.831367\pi\)
−0.862920 + 0.505340i \(0.831367\pi\)
\(572\) 542.948i 0.949210i
\(573\) 762.410 233.990i 1.33056 0.408359i
\(574\) −91.3421 −0.159133
\(575\) 23.9792i 0.0417029i
\(576\) 59.6039 40.3903i 0.103479 0.0701221i
\(577\) 756.257 1.31067 0.655335 0.755338i \(-0.272527\pi\)
0.655335 + 0.755338i \(0.272527\pi\)
\(578\) 624.862i 1.08108i
\(579\) −201.877 657.777i −0.348665 1.13606i
\(580\) −37.8170 −0.0652017
\(581\) 234.907i 0.404315i
\(582\) −361.300 + 110.886i −0.620791 + 0.190526i
\(583\) −54.7730 −0.0939503
\(584\) 64.0760i 0.109719i
\(585\) 208.671 + 307.935i 0.356702 + 0.526385i
\(586\) 134.204 0.229016
\(587\) 41.9003i 0.0713804i 0.999363 + 0.0356902i \(0.0113630\pi\)
−0.999363 + 0.0356902i \(0.988637\pi\)
\(588\) 68.1344 + 222.002i 0.115875 + 0.377555i
\(589\) −274.334 −0.465762
\(590\) 92.0580i 0.156030i
\(591\) −227.844 + 69.9273i −0.385524 + 0.118320i
\(592\) 170.541 0.288077
\(593\) 959.818i 1.61858i −0.587410 0.809290i \(-0.699852\pi\)
0.587410 0.809290i \(-0.300148\pi\)
\(594\) −436.970 351.521i −0.735640 0.591786i
\(595\) 193.971 0.326001
\(596\) 109.496i 0.183718i
\(597\) −190.168 619.625i −0.318539 1.03790i
\(598\) −125.363 −0.209637
\(599\) 705.255i 1.17739i 0.808356 + 0.588694i \(0.200358\pi\)
−0.808356 + 0.588694i \(0.799642\pi\)
\(600\) −40.5592 + 12.4480i −0.0675987 + 0.0207466i
\(601\) 598.282 0.995478 0.497739 0.867327i \(-0.334164\pi\)
0.497739 + 0.867327i \(0.334164\pi\)
\(602\) 77.3339i 0.128462i
\(603\) −2.43759 + 1.65182i −0.00404244 + 0.00273934i
\(604\) −183.253 −0.303399
\(605\) 211.786i 0.350059i
\(606\) 105.741 + 344.535i 0.174490 + 0.568540i
\(607\) −394.189 −0.649405 −0.324702 0.945816i \(-0.605264\pi\)
−0.324702 + 0.945816i \(0.605264\pi\)
\(608\) 31.2813i 0.0514495i
\(609\) 77.8190 23.8833i 0.127782 0.0392172i
\(610\) 26.2804 0.0430826
\(611\) 974.534i 1.59498i
\(612\) −272.979 402.835i −0.446044 0.658227i
\(613\) −369.754 −0.603187 −0.301594 0.953437i \(-0.597519\pi\)
−0.301594 + 0.953437i \(0.597519\pi\)
\(614\) 30.2353i 0.0492431i
\(615\) −39.6173 129.085i −0.0644184 0.209895i
\(616\) 133.298 0.216392
\(617\) 171.624i 0.278158i 0.990281 + 0.139079i \(0.0444143\pi\)
−0.990281 + 0.139079i \(0.955586\pi\)
\(618\) 653.360 200.522i 1.05722 0.324469i
\(619\) 690.409 1.11536 0.557681 0.830055i \(-0.311691\pi\)
0.557681 + 0.830055i \(0.311691\pi\)
\(620\) 221.863i 0.357843i
\(621\) 81.1637 100.893i 0.130698 0.162469i
\(622\) −568.232 −0.913556
\(623\) 232.334i 0.372928i
\(624\) 65.0777 + 212.043i 0.104291 + 0.339813i
\(625\) 25.0000 0.0400000
\(626\) 608.392i 0.971872i
\(627\) −232.928 + 71.4877i −0.371497 + 0.114015i
\(628\) −153.840 −0.244968
\(629\) 1152.61i 1.83245i
\(630\) 75.6003 51.2302i 0.120000 0.0813178i
\(631\) 912.234 1.44570 0.722848 0.691007i \(-0.242833\pi\)
0.722848 + 0.691007i \(0.242833\pi\)
\(632\) 194.252i 0.307361i
\(633\) 97.9948 + 319.297i 0.154810 + 0.504418i
\(634\) 379.773 0.599011
\(635\) 337.368i 0.531289i
\(636\) −21.3911 + 6.56510i −0.0336338 + 0.0103225i
\(637\) −715.390 −1.12306
\(638\) 175.641i 0.275299i
\(639\) −349.768 516.152i −0.547368 0.807750i
\(640\) −25.2982 −0.0395285
\(641\) 249.344i 0.388993i 0.980903 + 0.194496i \(0.0623072\pi\)
−0.980903 + 0.194496i \(0.937693\pi\)
\(642\) −34.6556 112.919i −0.0539807 0.175886i
\(643\) 46.5166 0.0723431 0.0361715 0.999346i \(-0.488484\pi\)
0.0361715 + 0.999346i \(0.488484\pi\)
\(644\) 30.7775i 0.0477911i
\(645\) −109.289 + 33.5416i −0.169440 + 0.0520025i
\(646\) −211.416 −0.327269
\(647\) 334.980i 0.517744i 0.965912 + 0.258872i \(0.0833507\pi\)
−0.965912 + 0.258872i \(0.916649\pi\)
\(648\) −212.788 84.9078i −0.328376 0.131031i
\(649\) −427.563 −0.658803
\(650\) 130.700i 0.201076i
\(651\) −140.117 456.544i −0.215234 0.701297i
\(652\) 57.5367 0.0882465
\(653\) 767.471i 1.17530i −0.809115 0.587650i \(-0.800053\pi\)
0.809115 0.587650i \(-0.199947\pi\)
\(654\) −865.332 + 265.578i −1.32314 + 0.406082i
\(655\) −296.734 −0.453028
\(656\) 80.5151i 0.122736i
\(657\) −168.785 + 114.377i −0.256903 + 0.174089i
\(658\) −239.255 −0.363610
\(659\) 515.713i 0.782569i 0.920270 + 0.391285i \(0.127969\pi\)
−0.920270 + 0.391285i \(0.872031\pi\)
\(660\) 57.8145 + 188.377i 0.0875977 + 0.285420i
\(661\) −392.863 −0.594346 −0.297173 0.954824i \(-0.596044\pi\)
−0.297173 + 0.954824i \(0.596044\pi\)
\(662\) 402.540i 0.608066i
\(663\) 1433.10 439.830i 2.16154 0.663394i
\(664\) −207.063 −0.311842
\(665\) 39.6765i 0.0596639i
\(666\) −304.419 449.231i −0.457086 0.674520i
\(667\) −40.5542 −0.0608009
\(668\) 122.642i 0.183595i
\(669\) −226.613 738.374i −0.338734 1.10370i
\(670\) 1.03461 0.00154419
\(671\) 122.059i 0.181907i
\(672\) 52.0581 15.9771i 0.0774674 0.0237754i
\(673\) 817.428 1.21460 0.607302 0.794471i \(-0.292252\pi\)
0.607302 + 0.794471i \(0.292252\pi\)
\(674\) 298.280i 0.442553i
\(675\) 105.189 + 84.6190i 0.155835 + 0.125361i
\(676\) −345.297 −0.510794
\(677\) 78.0109i 0.115230i −0.998339 0.0576151i \(-0.981650\pi\)
0.998339 0.0576151i \(-0.0183496\pi\)
\(678\) 41.9481 + 136.680i 0.0618703 + 0.201592i
\(679\) −285.837 −0.420967
\(680\) 170.979i 0.251439i
\(681\) 6.15411 1.88875i 0.00903687 0.00277349i
\(682\) 1030.44 1.51091
\(683\) 1048.62i 1.53532i 0.640857 + 0.767661i \(0.278579\pi\)
−0.640857 + 0.767661i \(0.721421\pi\)
\(684\) −82.3994 + 55.8376i −0.120467 + 0.0816339i
\(685\) −91.7734 −0.133976
\(686\) 397.990i 0.580160i
\(687\) −94.9993 309.537i −0.138281 0.450563i
\(688\) −68.1673 −0.0990804
\(689\) 68.9315i 0.100046i
\(690\) −43.4949 + 13.3489i −0.0630361 + 0.0193463i
\(691\) −1164.83 −1.68571 −0.842855 0.538141i \(-0.819127\pi\)
−0.842855 + 0.538141i \(0.819127\pi\)
\(692\) 534.171i 0.771923i
\(693\) −237.938 351.125i −0.343346 0.506674i
\(694\) −664.364 −0.957297
\(695\) 225.097i 0.323881i
\(696\) 21.0523 + 68.5949i 0.0302476 + 0.0985558i
\(697\) −544.164 −0.780723
\(698\) 754.791i 1.08136i
\(699\) 446.583 137.060i 0.638888 0.196080i
\(700\) −32.0877 −0.0458396
\(701\) 522.136i 0.744845i −0.928063 0.372423i \(-0.878527\pi\)
0.928063 0.372423i \(-0.121473\pi\)
\(702\) 442.387 549.924i 0.630181 0.783368i
\(703\) −235.765 −0.335370
\(704\) 117.498i 0.166900i
\(705\) −103.771 338.117i −0.147193 0.479598i
\(706\) −301.422 −0.426943
\(707\) 272.573i 0.385535i
\(708\) −166.981 + 51.2477i −0.235848 + 0.0723837i
\(709\) 1140.17 1.60813 0.804066 0.594540i \(-0.202666\pi\)
0.804066 + 0.594540i \(0.202666\pi\)
\(710\) 219.075i 0.308557i
\(711\) −511.688 + 346.743i −0.719674 + 0.487684i
\(712\) 204.795 0.287633
\(713\) 237.922i 0.333691i
\(714\) −107.981 351.836i −0.151234 0.492768i
\(715\) −607.034 −0.848999
\(716\) 98.8726i 0.138090i
\(717\) −1249.90 + 383.604i −1.74323 + 0.535013i
\(718\) 857.073 1.19370
\(719\) 398.568i 0.554336i −0.960821 0.277168i \(-0.910604\pi\)
0.960821 0.277168i \(-0.0893959\pi\)
\(720\) 45.1577 + 66.6392i 0.0627191 + 0.0925544i
\(721\) 516.895 0.716914
\(722\) 467.286i 0.647211i
\(723\) 395.596 + 1288.97i 0.547159 + 1.78281i
\(724\) −571.974 −0.790019
\(725\) 42.2807i 0.0583182i
\(726\) 384.150 117.899i 0.529133 0.162395i
\(727\) 541.732 0.745161 0.372581 0.928000i \(-0.378473\pi\)
0.372581 + 0.928000i \(0.378473\pi\)
\(728\) 167.754i 0.230432i
\(729\) 156.170 + 712.076i 0.214225 + 0.976784i
\(730\) 71.6391 0.0981358
\(731\) 460.711i 0.630247i
\(732\) −14.6300 47.6690i −0.0199864 0.0651216i
\(733\) −93.0260 −0.126911 −0.0634556 0.997985i \(-0.520212\pi\)
−0.0634556 + 0.997985i \(0.520212\pi\)
\(734\) 536.039i 0.730298i
\(735\) −248.206 + 76.1766i −0.337696 + 0.103642i
\(736\) −27.1293 −0.0368605
\(737\) 4.80524i 0.00652000i
\(738\) −212.088 + 143.721i −0.287383 + 0.194744i
\(739\) 1323.24 1.79058 0.895290 0.445483i \(-0.146968\pi\)
0.895290 + 0.445483i \(0.146968\pi\)
\(740\) 190.671i 0.257664i
\(741\) −89.9667 293.139i −0.121413 0.395599i
\(742\) −16.9232 −0.0228075
\(743\) 219.461i 0.295371i 0.989034 + 0.147686i \(0.0471824\pi\)
−0.989034 + 0.147686i \(0.952818\pi\)
\(744\) 402.429 123.509i 0.540899 0.166006i
\(745\) −122.420 −0.164322
\(746\) 125.167i 0.167784i
\(747\) 369.611 + 545.434i 0.494794 + 0.730166i
\(748\) 794.111 1.06165
\(749\) 89.3336i 0.119270i
\(750\) −13.9172 45.3466i −0.0185563 0.0604621i
\(751\) −249.205 −0.331830 −0.165915 0.986140i \(-0.553058\pi\)
−0.165915 + 0.986140i \(0.553058\pi\)
\(752\) 210.896i 0.280446i
\(753\) 785.391 241.043i 1.04302 0.320110i
\(754\) −221.043 −0.293161
\(755\) 204.883i 0.271368i
\(756\) −135.010 108.609i −0.178585 0.143663i
\(757\) −1195.89 −1.57978 −0.789889 0.613249i \(-0.789862\pi\)
−0.789889 + 0.613249i \(0.789862\pi\)
\(758\) 799.488i 1.05473i
\(759\) 61.9991 + 202.012i 0.0816853 + 0.266155i
\(760\) 34.9735 0.0460178
\(761\) 267.295i 0.351241i −0.984458 0.175621i \(-0.943807\pi\)
0.984458 0.175621i \(-0.0561932\pi\)
\(762\) 611.940 187.809i 0.803071 0.246469i
\(763\) −684.593 −0.897238
\(764\) 531.672i 0.695906i
\(765\) 450.383 305.200i 0.588736 0.398954i
\(766\) −838.584 −1.09476
\(767\) 538.085i 0.701545i
\(768\) 14.0832 + 45.8875i 0.0183376 + 0.0597493i
\(769\) 758.937 0.986914 0.493457 0.869770i \(-0.335733\pi\)
0.493457 + 0.869770i \(0.335733\pi\)
\(770\) 149.031i 0.193547i
\(771\) −1095.37 + 336.178i −1.42071 + 0.436029i
\(772\) 458.706 0.594178
\(773\) 669.855i 0.866565i −0.901258 0.433282i \(-0.857355\pi\)
0.901258 0.433282i \(-0.142645\pi\)
\(774\) 121.680 + 179.562i 0.157209 + 0.231993i
\(775\) −248.050 −0.320065
\(776\) 251.956i 0.324685i
\(777\) −120.418 392.358i −0.154978 0.504966i
\(778\) −886.201 −1.13908
\(779\) 111.308i 0.142886i
\(780\) −237.071 + 72.7591i −0.303938 + 0.0932809i
\(781\) 1017.49 1.30281
\(782\) 183.354i 0.234469i
\(783\) 143.110 177.898i 0.182771 0.227200i
\(784\) −154.815 −0.197468
\(785\) 171.999i 0.219106i
\(786\) 165.188 + 538.234i