Properties

Label 690.3.g.a.461.12
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 461.12
Character \(\chi\) \(=\) 690.461
Dual form 690.3.g.a.461.11

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421i q^{2} +(-1.59356 + 2.54176i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(-3.59459 - 2.25364i) q^{6} +10.3156 q^{7} -2.82843i q^{8} +(-3.92110 - 8.10092i) q^{9} +O(q^{10})\) \(q+1.41421i q^{2} +(-1.59356 + 2.54176i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(-3.59459 - 2.25364i) q^{6} +10.3156 q^{7} -2.82843i q^{8} +(-3.92110 - 8.10092i) q^{9} -3.16228 q^{10} +14.4101i q^{11} +(3.18713 - 5.08352i) q^{12} +14.5857 q^{13} +14.5885i q^{14} +(-5.68355 - 3.56332i) q^{15} +4.00000 q^{16} -0.438401i q^{17} +(11.4564 - 5.54528i) q^{18} +30.5080 q^{19} -4.47214i q^{20} +(-16.4387 + 26.2199i) q^{21} -20.3790 q^{22} +4.79583i q^{23} +(7.18919 + 4.50728i) q^{24} -5.00000 q^{25} +20.6274i q^{26} +(26.8391 + 2.94284i) q^{27} -20.6313 q^{28} +23.6165i q^{29} +(5.03929 - 8.03776i) q^{30} +37.8103 q^{31} +5.65685i q^{32} +(-36.6271 - 22.9635i) q^{33} +0.619993 q^{34} +23.0665i q^{35} +(7.84220 + 16.2018i) q^{36} +3.95366 q^{37} +43.1448i q^{38} +(-23.2433 + 37.0735i) q^{39} +6.32456 q^{40} +0.897806i q^{41} +(-37.0806 - 23.2478i) q^{42} -47.5033 q^{43} -28.8203i q^{44} +(18.1142 - 8.76785i) q^{45} -6.78233 q^{46} +39.9836i q^{47} +(-6.37426 + 10.1670i) q^{48} +57.4126 q^{49} -7.07107i q^{50} +(1.11431 + 0.698620i) q^{51} -29.1715 q^{52} -67.0896i q^{53} +(-4.16180 + 37.9563i) q^{54} -32.2221 q^{55} -29.1771i q^{56} +(-48.6164 + 77.5440i) q^{57} -33.3988 q^{58} -43.7546i q^{59} +(11.3671 + 7.12664i) q^{60} -69.1629 q^{61} +53.4719i q^{62} +(-40.4487 - 83.5663i) q^{63} -8.00000 q^{64} +32.6147i q^{65} +(32.4753 - 51.7986i) q^{66} +15.9838 q^{67} +0.876802i q^{68} +(-12.1899 - 7.64247i) q^{69} -32.6209 q^{70} -32.7189i q^{71} +(-22.9129 + 11.0906i) q^{72} -136.933 q^{73} +5.59132i q^{74} +(7.96782 - 12.7088i) q^{75} -61.0159 q^{76} +148.650i q^{77} +(-52.4298 - 32.8710i) q^{78} -117.203 q^{79} +8.94427i q^{80} +(-50.2499 + 63.5291i) q^{81} -1.26969 q^{82} -72.3768i q^{83} +(32.8773 - 52.4398i) q^{84} +0.980294 q^{85} -67.1798i q^{86} +(-60.0276 - 37.6345i) q^{87} +40.7580 q^{88} +48.7209i q^{89} +(12.3996 + 25.6174i) q^{90} +150.461 q^{91} -9.59166i q^{92} +(-60.2532 + 96.1048i) q^{93} -56.5454 q^{94} +68.2179i q^{95} +(-14.3784 - 9.01456i) q^{96} +128.346 q^{97} +81.1936i q^{98} +(116.735 - 56.5036i) 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
\(3\) −1.59356 + 2.54176i −0.531188 + 0.847254i
\(4\) −2.00000 −0.500000
\(5\) 2.23607i 0.447214i
\(6\) −3.59459 2.25364i −0.599099 0.375607i
\(7\) 10.3156 1.47366 0.736832 0.676076i \(-0.236321\pi\)
0.736832 + 0.676076i \(0.236321\pi\)
\(8\) 2.82843i 0.353553i
\(9\) −3.92110 8.10092i −0.435678 0.900103i
\(10\) −3.16228 −0.316228
\(11\) 14.4101i 1.31001i 0.755623 + 0.655006i \(0.227334\pi\)
−0.755623 + 0.655006i \(0.772666\pi\)
\(12\) 3.18713 5.08352i 0.265594 0.423627i
\(13\) 14.5857 1.12198 0.560990 0.827822i \(-0.310421\pi\)
0.560990 + 0.827822i \(0.310421\pi\)
\(14\) 14.5885i 1.04204i
\(15\) −5.68355 3.56332i −0.378903 0.237555i
\(16\) 4.00000 0.250000
\(17\) 0.438401i 0.0257883i −0.999917 0.0128941i \(-0.995896\pi\)
0.999917 0.0128941i \(-0.00410445\pi\)
\(18\) 11.4564 5.54528i 0.636469 0.308071i
\(19\) 30.5080 1.60568 0.802841 0.596193i \(-0.203321\pi\)
0.802841 + 0.596193i \(0.203321\pi\)
\(20\) 4.47214i 0.223607i
\(21\) −16.4387 + 26.2199i −0.782793 + 1.24857i
\(22\) −20.3790 −0.926319
\(23\) 4.79583i 0.208514i
\(24\) 7.18919 + 4.50728i 0.299549 + 0.187803i
\(25\) −5.00000 −0.200000
\(26\) 20.6274i 0.793360i
\(27\) 26.8391 + 2.94284i 0.994042 + 0.108994i
\(28\) −20.6313 −0.736832
\(29\) 23.6165i 0.814363i 0.913347 + 0.407182i \(0.133488\pi\)
−0.913347 + 0.407182i \(0.866512\pi\)
\(30\) 5.03929 8.03776i 0.167976 0.267925i
\(31\) 37.8103 1.21969 0.609844 0.792522i \(-0.291232\pi\)
0.609844 + 0.792522i \(0.291232\pi\)
\(32\) 5.65685i 0.176777i
\(33\) −36.6271 22.9635i −1.10991 0.695863i
\(34\) 0.619993 0.0182351
\(35\) 23.0665i 0.659043i
\(36\) 7.84220 + 16.2018i 0.217839 + 0.450051i
\(37\) 3.95366 0.106856 0.0534278 0.998572i \(-0.482985\pi\)
0.0534278 + 0.998572i \(0.482985\pi\)
\(38\) 43.1448i 1.13539i
\(39\) −23.2433 + 37.0735i −0.595983 + 0.950602i
\(40\) 6.32456 0.158114
\(41\) 0.897806i 0.0218977i 0.999940 + 0.0109488i \(0.00348520\pi\)
−0.999940 + 0.0109488i \(0.996515\pi\)
\(42\) −37.0806 23.2478i −0.882870 0.553518i
\(43\) −47.5033 −1.10473 −0.552364 0.833603i \(-0.686274\pi\)
−0.552364 + 0.833603i \(0.686274\pi\)
\(44\) 28.8203i 0.655006i
\(45\) 18.1142 8.76785i 0.402538 0.194841i
\(46\) −6.78233 −0.147442
\(47\) 39.9836i 0.850716i 0.905025 + 0.425358i \(0.139852\pi\)
−0.905025 + 0.425358i \(0.860148\pi\)
\(48\) −6.37426 + 10.1670i −0.132797 + 0.211813i
\(49\) 57.4126 1.17169
\(50\) 7.07107i 0.141421i
\(51\) 1.11431 + 0.698620i 0.0218492 + 0.0136984i
\(52\) −29.1715 −0.560990
\(53\) 67.0896i 1.26584i −0.774217 0.632920i \(-0.781856\pi\)
0.774217 0.632920i \(-0.218144\pi\)
\(54\) −4.16180 + 37.9563i −0.0770704 + 0.702894i
\(55\) −32.2221 −0.585856
\(56\) 29.1771i 0.521019i
\(57\) −48.6164 + 77.5440i −0.852920 + 1.36042i
\(58\) −33.3988 −0.575842
\(59\) 43.7546i 0.741604i −0.928712 0.370802i \(-0.879083\pi\)
0.928712 0.370802i \(-0.120917\pi\)
\(60\) 11.3671 + 7.12664i 0.189452 + 0.118777i
\(61\) −69.1629 −1.13382 −0.566909 0.823781i \(-0.691861\pi\)
−0.566909 + 0.823781i \(0.691861\pi\)
\(62\) 53.4719i 0.862449i
\(63\) −40.4487 83.5663i −0.642043 1.32645i
\(64\) −8.00000 −0.125000
\(65\) 32.6147i 0.501765i
\(66\) 32.4753 51.7986i 0.492050 0.784827i
\(67\) 15.9838 0.238565 0.119282 0.992860i \(-0.461941\pi\)
0.119282 + 0.992860i \(0.461941\pi\)
\(68\) 0.876802i 0.0128941i
\(69\) −12.1899 7.64247i −0.176665 0.110760i
\(70\) −32.6209 −0.466013
\(71\) 32.7189i 0.460830i −0.973092 0.230415i \(-0.925992\pi\)
0.973092 0.230415i \(-0.0740084\pi\)
\(72\) −22.9129 + 11.0906i −0.318234 + 0.154035i
\(73\) −136.933 −1.87580 −0.937900 0.346906i \(-0.887232\pi\)
−0.937900 + 0.346906i \(0.887232\pi\)
\(74\) 5.59132i 0.0755584i
\(75\) 7.96782 12.7088i 0.106238 0.169451i
\(76\) −61.0159 −0.802841
\(77\) 148.650i 1.93052i
\(78\) −52.4298 32.8710i −0.672177 0.421423i
\(79\) −117.203 −1.48359 −0.741793 0.670629i \(-0.766024\pi\)
−0.741793 + 0.670629i \(0.766024\pi\)
\(80\) 8.94427i 0.111803i
\(81\) −50.2499 + 63.5291i −0.620369 + 0.784310i
\(82\) −1.26969 −0.0154840
\(83\) 72.3768i 0.872009i −0.899944 0.436005i \(-0.856393\pi\)
0.899944 0.436005i \(-0.143607\pi\)
\(84\) 32.8773 52.4398i 0.391396 0.624284i
\(85\) 0.980294 0.0115329
\(86\) 67.1798i 0.781161i
\(87\) −60.0276 37.6345i −0.689973 0.432580i
\(88\) 40.7580 0.463159
\(89\) 48.7209i 0.547426i 0.961811 + 0.273713i \(0.0882519\pi\)
−0.961811 + 0.273713i \(0.911748\pi\)
\(90\) 12.3996 + 25.6174i 0.137773 + 0.284637i
\(91\) 150.461 1.65342
\(92\) 9.59166i 0.104257i
\(93\) −60.2532 + 96.1048i −0.647884 + 1.03339i
\(94\) −56.5454 −0.601547
\(95\) 68.2179i 0.718083i
\(96\) −14.3784 9.01456i −0.149775 0.0939017i
\(97\) 128.346 1.32316 0.661579 0.749876i \(-0.269887\pi\)
0.661579 + 0.749876i \(0.269887\pi\)
\(98\) 81.1936i 0.828507i
\(99\) 116.735 56.5036i 1.17915 0.570744i
\(100\) 10.0000 0.100000
\(101\) 97.9145i 0.969450i −0.874666 0.484725i \(-0.838920\pi\)
0.874666 0.484725i \(-0.161080\pi\)
\(102\) −0.987998 + 1.57587i −0.00968626 + 0.0154497i
\(103\) 99.4761 0.965787 0.482894 0.875679i \(-0.339586\pi\)
0.482894 + 0.875679i \(0.339586\pi\)
\(104\) 41.2547i 0.396680i
\(105\) −58.6295 36.7579i −0.558376 0.350076i
\(106\) 94.8790 0.895085
\(107\) 155.354i 1.45191i 0.687742 + 0.725956i \(0.258602\pi\)
−0.687742 + 0.725956i \(0.741398\pi\)
\(108\) −53.6783 5.88568i −0.497021 0.0544970i
\(109\) 44.8327 0.411309 0.205655 0.978625i \(-0.434068\pi\)
0.205655 + 0.978625i \(0.434068\pi\)
\(110\) 45.5689i 0.414262i
\(111\) −6.30041 + 10.0493i −0.0567605 + 0.0905339i
\(112\) 41.2626 0.368416
\(113\) 180.557i 1.59785i 0.601428 + 0.798927i \(0.294599\pi\)
−0.601428 + 0.798927i \(0.705401\pi\)
\(114\) −109.664 68.7540i −0.961963 0.603105i
\(115\) −10.7238 −0.0932505
\(116\) 47.2331i 0.407182i
\(117\) −57.1922 118.158i −0.488822 1.00990i
\(118\) 61.8784 0.524393
\(119\) 4.52239i 0.0380033i
\(120\) −10.0786 + 16.0755i −0.0839882 + 0.133963i
\(121\) −86.6522 −0.716134
\(122\) 97.8111i 0.801730i
\(123\) −2.28201 1.43071i −0.0185529 0.0116318i
\(124\) −75.6206 −0.609844
\(125\) 11.1803i 0.0894427i
\(126\) 118.181 57.2031i 0.937941 0.453993i
\(127\) −180.797 −1.42360 −0.711800 0.702382i \(-0.752120\pi\)
−0.711800 + 0.702382i \(0.752120\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) 75.6996 120.742i 0.586818 0.935985i
\(130\) −46.1242 −0.354801
\(131\) 102.689i 0.783889i −0.919989 0.391944i \(-0.871803\pi\)
0.919989 0.391944i \(-0.128197\pi\)
\(132\) 73.2543 + 45.9270i 0.554957 + 0.347932i
\(133\) 314.709 2.36624
\(134\) 22.6045i 0.168691i
\(135\) −6.58039 + 60.0142i −0.0487436 + 0.444549i
\(136\) −1.23999 −0.00911754
\(137\) 63.7156i 0.465077i −0.972587 0.232539i \(-0.925297\pi\)
0.972587 0.232539i \(-0.0747032\pi\)
\(138\) 10.8081 17.2391i 0.0783194 0.124921i
\(139\) 198.895 1.43090 0.715451 0.698663i \(-0.246221\pi\)
0.715451 + 0.698663i \(0.246221\pi\)
\(140\) 46.1330i 0.329521i
\(141\) −101.629 63.7165i −0.720772 0.451890i
\(142\) 46.2715 0.325856
\(143\) 210.183i 1.46981i
\(144\) −15.6844 32.4037i −0.108920 0.225026i
\(145\) −52.8082 −0.364194
\(146\) 193.653i 1.32639i
\(147\) −91.4907 + 145.929i −0.622385 + 0.992715i
\(148\) −7.90732 −0.0534278
\(149\) 77.1700i 0.517919i 0.965888 + 0.258960i \(0.0833797\pi\)
−0.965888 + 0.258960i \(0.916620\pi\)
\(150\) 17.9730 + 11.2682i 0.119820 + 0.0751214i
\(151\) −122.875 −0.813741 −0.406871 0.913486i \(-0.633380\pi\)
−0.406871 + 0.913486i \(0.633380\pi\)
\(152\) 86.2896i 0.567694i
\(153\) −3.55145 + 1.71901i −0.0232121 + 0.0112354i
\(154\) −210.223 −1.36508
\(155\) 84.5464i 0.545461i
\(156\) 46.4867 74.1470i 0.297991 0.475301i
\(157\) 190.139 1.21108 0.605538 0.795817i \(-0.292958\pi\)
0.605538 + 0.795817i \(0.292958\pi\)
\(158\) 165.750i 1.04905i
\(159\) 170.526 + 106.912i 1.07249 + 0.672400i
\(160\) −12.6491 −0.0790569
\(161\) 49.4721i 0.307280i
\(162\) −89.8437 71.0641i −0.554591 0.438667i
\(163\) 41.0811 0.252031 0.126016 0.992028i \(-0.459781\pi\)
0.126016 + 0.992028i \(0.459781\pi\)
\(164\) 1.79561i 0.0109488i
\(165\) 51.3479 81.9008i 0.311200 0.496368i
\(166\) 102.356 0.616604
\(167\) 173.319i 1.03784i 0.854823 + 0.518920i \(0.173666\pi\)
−0.854823 + 0.518920i \(0.826334\pi\)
\(168\) 74.1611 + 46.4955i 0.441435 + 0.276759i
\(169\) 43.7439 0.258840
\(170\) 1.38635i 0.00815497i
\(171\) −119.625 247.143i −0.699561 1.44528i
\(172\) 95.0066 0.552364
\(173\) 50.1795i 0.290055i 0.989428 + 0.145027i \(0.0463270\pi\)
−0.989428 + 0.145027i \(0.953673\pi\)
\(174\) 53.2232 84.8919i 0.305880 0.487884i
\(175\) −51.5782 −0.294733
\(176\) 57.6406i 0.327503i
\(177\) 111.214 + 69.7258i 0.628327 + 0.393931i
\(178\) −68.9018 −0.387089
\(179\) 192.115i 1.07327i 0.843816 + 0.536633i \(0.180304\pi\)
−0.843816 + 0.536633i \(0.819696\pi\)
\(180\) −36.2284 + 17.5357i −0.201269 + 0.0974206i
\(181\) 89.0532 0.492007 0.246003 0.969269i \(-0.420883\pi\)
0.246003 + 0.969269i \(0.420883\pi\)
\(182\) 212.785i 1.16915i
\(183\) 110.216 175.796i 0.602271 0.960631i
\(184\) 13.5647 0.0737210
\(185\) 8.84065i 0.0477873i
\(186\) −135.913 85.2109i −0.730714 0.458123i
\(187\) 6.31742 0.0337830
\(188\) 79.9673i 0.425358i
\(189\) 276.863 + 30.3573i 1.46488 + 0.160621i
\(190\) −96.4747 −0.507761
\(191\) 288.927i 1.51271i −0.654163 0.756354i \(-0.726979\pi\)
0.654163 0.756354i \(-0.273021\pi\)
\(192\) 12.7485 20.3341i 0.0663985 0.105907i
\(193\) −315.184 −1.63308 −0.816539 0.577291i \(-0.804110\pi\)
−0.816539 + 0.577291i \(0.804110\pi\)
\(194\) 181.509i 0.935613i
\(195\) −82.8988 51.9737i −0.425122 0.266532i
\(196\) −114.825 −0.585843
\(197\) 177.931i 0.903202i 0.892220 + 0.451601i \(0.149147\pi\)
−0.892220 + 0.451601i \(0.850853\pi\)
\(198\) 79.9082 + 165.089i 0.403577 + 0.833782i
\(199\) −232.143 −1.16655 −0.583275 0.812275i \(-0.698229\pi\)
−0.583275 + 0.812275i \(0.698229\pi\)
\(200\) 14.1421i 0.0707107i
\(201\) −25.4713 + 40.6271i −0.126723 + 0.202125i
\(202\) 138.472 0.685505
\(203\) 243.620i 1.20010i
\(204\) −2.22862 1.39724i −0.0109246 0.00684922i
\(205\) −2.00755 −0.00979295
\(206\) 140.680i 0.682915i
\(207\) 38.8507 18.8049i 0.187684 0.0908452i
\(208\) 58.3430 0.280495
\(209\) 439.624i 2.10346i
\(210\) 51.9836 82.9146i 0.247541 0.394832i
\(211\) 240.137 1.13809 0.569045 0.822307i \(-0.307313\pi\)
0.569045 + 0.822307i \(0.307313\pi\)
\(212\) 134.179i 0.632920i
\(213\) 83.1637 + 52.1397i 0.390440 + 0.244787i
\(214\) −219.704 −1.02666
\(215\) 106.221i 0.494049i
\(216\) 8.32361 75.9126i 0.0385352 0.351447i
\(217\) 390.038 1.79741
\(218\) 63.4030i 0.290840i
\(219\) 218.212 348.052i 0.996403 1.58928i
\(220\) 64.4441 0.292928
\(221\) 6.39440i 0.0289340i
\(222\) −14.2118 8.91013i −0.0640171 0.0401357i
\(223\) −43.0954 −0.193253 −0.0966265 0.995321i \(-0.530805\pi\)
−0.0966265 + 0.995321i \(0.530805\pi\)
\(224\) 58.3541i 0.260509i
\(225\) 19.6055 + 40.5046i 0.0871356 + 0.180021i
\(226\) −255.347 −1.12985
\(227\) 261.201i 1.15066i −0.817920 0.575332i \(-0.804873\pi\)
0.817920 0.575332i \(-0.195127\pi\)
\(228\) 97.2328 155.088i 0.426460 0.680210i
\(229\) 306.887 1.34012 0.670060 0.742307i \(-0.266268\pi\)
0.670060 + 0.742307i \(0.266268\pi\)
\(230\) 15.1658i 0.0659380i
\(231\) −377.833 236.883i −1.63564 1.02547i
\(232\) 66.7977 0.287921
\(233\) 14.3031i 0.0613867i 0.999529 + 0.0306934i \(0.00977154\pi\)
−0.999529 + 0.0306934i \(0.990228\pi\)
\(234\) 167.101 80.8820i 0.714105 0.345649i
\(235\) −89.4061 −0.380452
\(236\) 87.5092i 0.370802i
\(237\) 186.771 297.903i 0.788063 1.25697i
\(238\) 6.39562 0.0268724
\(239\) 170.994i 0.715456i −0.933826 0.357728i \(-0.883551\pi\)
0.933826 0.357728i \(-0.116449\pi\)
\(240\) −22.7342 14.2533i −0.0947259 0.0593887i
\(241\) 206.779 0.858003 0.429002 0.903304i \(-0.358865\pi\)
0.429002 + 0.903304i \(0.358865\pi\)
\(242\) 122.545i 0.506383i
\(243\) −81.3993 228.961i −0.334977 0.942226i
\(244\) 138.326 0.566909
\(245\) 128.378i 0.523994i
\(246\) 2.02333 3.22725i 0.00822492 0.0131189i
\(247\) 444.981 1.80154
\(248\) 106.944i 0.431225i
\(249\) 183.965 + 115.337i 0.738813 + 0.463201i
\(250\) 15.8114 0.0632456
\(251\) 288.871i 1.15088i −0.817844 0.575439i \(-0.804831\pi\)
0.817844 0.575439i \(-0.195169\pi\)
\(252\) 80.8974 + 167.133i 0.321021 + 0.663224i
\(253\) −69.1086 −0.273157
\(254\) 255.686i 1.00664i
\(255\) −1.56216 + 2.49167i −0.00612613 + 0.00977127i
\(256\) 16.0000 0.0625000
\(257\) 383.396i 1.49181i 0.666050 + 0.745907i \(0.267984\pi\)
−0.666050 + 0.745907i \(0.732016\pi\)
\(258\) 170.755 + 107.055i 0.661841 + 0.414943i
\(259\) 40.7846 0.157469
\(260\) 65.2294i 0.250882i
\(261\) 191.316 92.6029i 0.733011 0.354800i
\(262\) 145.225 0.554293
\(263\) 214.097i 0.814056i −0.913416 0.407028i \(-0.866565\pi\)
0.913416 0.407028i \(-0.133435\pi\)
\(264\) −64.9506 + 103.597i −0.246025 + 0.392414i
\(265\) 150.017 0.566101
\(266\) 445.066i 1.67318i
\(267\) −123.837 77.6400i −0.463809 0.290786i
\(268\) −31.9677 −0.119282
\(269\) 251.023i 0.933173i −0.884476 0.466586i \(-0.845484\pi\)
0.884476 0.466586i \(-0.154516\pi\)
\(270\) −84.8728 9.30607i −0.314344 0.0344669i
\(271\) 228.635 0.843673 0.421837 0.906672i \(-0.361386\pi\)
0.421837 + 0.906672i \(0.361386\pi\)
\(272\) 1.75360i 0.00644707i
\(273\) −239.770 + 382.437i −0.878278 + 1.40087i
\(274\) 90.1075 0.328859
\(275\) 72.0507i 0.262003i
\(276\) 24.3797 + 15.2849i 0.0883323 + 0.0553802i
\(277\) −509.608 −1.83974 −0.919870 0.392223i \(-0.871706\pi\)
−0.919870 + 0.392223i \(0.871706\pi\)
\(278\) 281.280i 1.01180i
\(279\) −148.258 306.298i −0.531391 1.09784i
\(280\) 65.2419 0.233007
\(281\) 16.5755i 0.0589876i 0.999565 + 0.0294938i \(0.00938953\pi\)
−0.999565 + 0.0294938i \(0.990610\pi\)
\(282\) 90.1088 143.725i 0.319535 0.509663i
\(283\) −125.782 −0.444461 −0.222230 0.974994i \(-0.571334\pi\)
−0.222230 + 0.974994i \(0.571334\pi\)
\(284\) 65.4378i 0.230415i
\(285\) −173.394 108.710i −0.608399 0.381437i
\(286\) −297.243 −1.03931
\(287\) 9.26145i 0.0322698i
\(288\) 45.8257 22.1811i 0.159117 0.0770177i
\(289\) 288.808 0.999335
\(290\) 74.6821i 0.257524i
\(291\) −204.528 + 326.226i −0.702845 + 1.12105i
\(292\) 273.867 0.937900
\(293\) 52.6345i 0.179640i −0.995958 0.0898200i \(-0.971371\pi\)
0.995958 0.0898200i \(-0.0286292\pi\)
\(294\) −206.375 129.387i −0.701955 0.440093i
\(295\) 97.8383 0.331655
\(296\) 11.1826i 0.0377792i
\(297\) −42.4067 + 386.756i −0.142784 + 1.30221i
\(298\) −109.135 −0.366224
\(299\) 69.9508i 0.233949i
\(300\) −15.9356 + 25.4176i −0.0531188 + 0.0847254i
\(301\) −490.027 −1.62800
\(302\) 173.771i 0.575402i
\(303\) 248.875 + 156.033i 0.821371 + 0.514961i
\(304\) 122.032 0.401421
\(305\) 154.653i 0.507059i
\(306\) −2.43105 5.02251i −0.00794462 0.0164134i
\(307\) −584.003 −1.90229 −0.951146 0.308742i \(-0.900092\pi\)
−0.951146 + 0.308742i \(0.900092\pi\)
\(308\) 297.300i 0.965259i
\(309\) −158.522 + 252.845i −0.513015 + 0.818267i
\(310\) −119.567 −0.385699
\(311\) 612.766i 1.97031i −0.171668 0.985155i \(-0.554916\pi\)
0.171668 0.985155i \(-0.445084\pi\)
\(312\) 104.860 + 65.7421i 0.336089 + 0.210712i
\(313\) −448.197 −1.43194 −0.715970 0.698131i \(-0.754015\pi\)
−0.715970 + 0.698131i \(0.754015\pi\)
\(314\) 268.897i 0.856360i
\(315\) 186.860 90.4461i 0.593206 0.287130i
\(316\) 234.407 0.741793
\(317\) 375.651i 1.18502i −0.805563 0.592509i \(-0.798137\pi\)
0.805563 0.592509i \(-0.201863\pi\)
\(318\) −151.196 + 241.160i −0.475458 + 0.758364i
\(319\) −340.318 −1.06683
\(320\) 17.8885i 0.0559017i
\(321\) −394.874 247.567i −1.23014 0.771238i
\(322\) −69.9641 −0.217280
\(323\) 13.3747i 0.0414078i
\(324\) 100.500 127.058i 0.310185 0.392155i
\(325\) −72.9287 −0.224396
\(326\) 58.0974i 0.178213i
\(327\) −71.4438 + 113.954i −0.218483 + 0.348483i
\(328\) 2.53938 0.00774200
\(329\) 412.457i 1.25367i
\(330\) 115.825 + 72.6169i 0.350985 + 0.220051i
\(331\) 257.176 0.776967 0.388483 0.921456i \(-0.372999\pi\)
0.388483 + 0.921456i \(0.372999\pi\)
\(332\) 144.754i 0.436005i
\(333\) −15.5027 32.0283i −0.0465547 0.0961811i
\(334\) −245.110 −0.733864
\(335\) 35.7409i 0.106689i
\(336\) −65.7546 + 104.880i −0.195698 + 0.312142i
\(337\) 622.010 1.84573 0.922863 0.385128i \(-0.125843\pi\)
0.922863 + 0.385128i \(0.125843\pi\)
\(338\) 61.8633i 0.183027i
\(339\) −458.934 287.730i −1.35379 0.848761i
\(340\) −1.96059 −0.00576644
\(341\) 544.852i 1.59781i
\(342\) 349.513 169.175i 1.02197 0.494664i
\(343\) 86.7811 0.253006
\(344\) 134.360i 0.390580i
\(345\) 17.0891 27.2574i 0.0495336 0.0790068i
\(346\) −70.9645 −0.205100
\(347\) 50.3108i 0.144988i 0.997369 + 0.0724939i \(0.0230958\pi\)
−0.997369 + 0.0724939i \(0.976904\pi\)
\(348\) 120.055 + 75.2690i 0.344986 + 0.216290i
\(349\) 479.971 1.37528 0.687638 0.726054i \(-0.258648\pi\)
0.687638 + 0.726054i \(0.258648\pi\)
\(350\) 72.9426i 0.208408i
\(351\) 391.469 + 42.9235i 1.11530 + 0.122289i
\(352\) −81.5161 −0.231580
\(353\) 415.132i 1.17601i 0.808857 + 0.588005i \(0.200086\pi\)
−0.808857 + 0.588005i \(0.799914\pi\)
\(354\) −98.6072 + 157.280i −0.278551 + 0.444294i
\(355\) 73.1617 0.206089
\(356\) 97.4419i 0.273713i
\(357\) 11.4948 + 7.20672i 0.0321984 + 0.0201869i
\(358\) −271.691 −0.758913
\(359\) 3.52584i 0.00982129i 0.999988 + 0.00491064i \(0.00156311\pi\)
−0.999988 + 0.00491064i \(0.998437\pi\)
\(360\) −24.7992 51.2347i −0.0688867 0.142319i
\(361\) 569.736 1.57822
\(362\) 125.940i 0.347901i
\(363\) 138.086 220.249i 0.380402 0.606747i
\(364\) −300.923 −0.826711
\(365\) 306.192i 0.838883i
\(366\) 248.612 + 155.868i 0.679269 + 0.425870i
\(367\) −64.7408 −0.176406 −0.0882028 0.996103i \(-0.528112\pi\)
−0.0882028 + 0.996103i \(0.528112\pi\)
\(368\) 19.1833i 0.0521286i
\(369\) 7.27305 3.52039i 0.0197102 0.00954035i
\(370\) −12.5026 −0.0337907
\(371\) 692.072i 1.86542i
\(372\) 120.506 192.210i 0.323942 0.516693i
\(373\) −209.857 −0.562618 −0.281309 0.959617i \(-0.590769\pi\)
−0.281309 + 0.959617i \(0.590769\pi\)
\(374\) 8.93418i 0.0238882i
\(375\) 28.4178 + 17.8166i 0.0757807 + 0.0475109i
\(376\) 113.091 0.300773
\(377\) 344.465i 0.913700i
\(378\) −42.9317 + 391.544i −0.113576 + 1.03583i
\(379\) 27.5758 0.0727593 0.0363797 0.999338i \(-0.488417\pi\)
0.0363797 + 0.999338i \(0.488417\pi\)
\(380\) 136.436i 0.359042i
\(381\) 288.112 459.544i 0.756200 1.20615i
\(382\) 408.605 1.06965
\(383\) 626.105i 1.63474i −0.576113 0.817370i \(-0.695431\pi\)
0.576113 0.817370i \(-0.304569\pi\)
\(384\) 28.7567 + 18.0291i 0.0748874 + 0.0469509i
\(385\) −332.391 −0.863354
\(386\) 445.737i 1.15476i
\(387\) 186.265 + 384.821i 0.481306 + 0.994368i
\(388\) −256.692 −0.661579
\(389\) 214.358i 0.551048i −0.961294 0.275524i \(-0.911149\pi\)
0.961294 0.275524i \(-0.0888514\pi\)
\(390\) 73.5019 117.237i 0.188466 0.300607i
\(391\) 2.10250 0.00537723
\(392\) 162.387i 0.414253i
\(393\) 261.012 + 163.642i 0.664153 + 0.416392i
\(394\) −251.632 −0.638661
\(395\) 262.074i 0.663480i
\(396\) −233.471 + 113.007i −0.589573 + 0.285372i
\(397\) −106.021 −0.267055 −0.133528 0.991045i \(-0.542631\pi\)
−0.133528 + 0.991045i \(0.542631\pi\)
\(398\) 328.300i 0.824875i
\(399\) −501.510 + 799.916i −1.25692 + 2.00480i
\(400\) −20.0000 −0.0500000
\(401\) 594.192i 1.48178i 0.671629 + 0.740888i \(0.265595\pi\)
−0.671629 + 0.740888i \(0.734405\pi\)
\(402\) −57.4554 36.0218i −0.142924 0.0896065i
\(403\) 551.492 1.36847
\(404\) 195.829i 0.484725i
\(405\) −142.055 112.362i −0.350754 0.277438i
\(406\) −344.531 −0.848597
\(407\) 56.9728i 0.139982i
\(408\) 1.97600 3.15175i 0.00484313 0.00772487i
\(409\) 152.159 0.372028 0.186014 0.982547i \(-0.440443\pi\)
0.186014 + 0.982547i \(0.440443\pi\)
\(410\) 2.83911i 0.00692466i
\(411\) 161.950 + 101.535i 0.394039 + 0.247044i
\(412\) −198.952 −0.482894
\(413\) 451.357i 1.09287i
\(414\) 26.5942 + 54.9431i 0.0642372 + 0.132713i
\(415\) 161.839 0.389974
\(416\) 82.5094i 0.198340i
\(417\) −316.953 + 505.544i −0.760078 + 1.21234i
\(418\) −621.722 −1.48737
\(419\) 156.542i 0.373608i 0.982397 + 0.186804i \(0.0598130\pi\)
−0.982397 + 0.186804i \(0.940187\pi\)
\(420\) 117.259 + 73.5159i 0.279188 + 0.175038i
\(421\) −407.584 −0.968134 −0.484067 0.875031i \(-0.660841\pi\)
−0.484067 + 0.875031i \(0.660841\pi\)
\(422\) 339.605i 0.804751i
\(423\) 323.904 156.780i 0.765731 0.370638i
\(424\) −189.758 −0.447542
\(425\) 2.19200i 0.00515766i
\(426\) −73.7367 + 117.611i −0.173091 + 0.276083i
\(427\) −713.460 −1.67087
\(428\) 310.709i 0.725956i
\(429\) −534.234 334.940i −1.24530 0.780745i
\(430\) 150.219 0.349346
\(431\) 439.199i 1.01902i −0.860464 0.509511i \(-0.829826\pi\)
0.860464 0.509511i \(-0.170174\pi\)
\(432\) 107.357 + 11.7714i 0.248511 + 0.0272485i
\(433\) −27.2770 −0.0629954 −0.0314977 0.999504i \(-0.510028\pi\)
−0.0314977 + 0.999504i \(0.510028\pi\)
\(434\) 551.597i 1.27096i
\(435\) 84.1533 134.226i 0.193456 0.308565i
\(436\) −89.6654 −0.205655
\(437\) 146.311i 0.334808i
\(438\) 492.220 + 308.599i 1.12379 + 0.704563i
\(439\) −230.229 −0.524441 −0.262220 0.965008i \(-0.584455\pi\)
−0.262220 + 0.965008i \(0.584455\pi\)
\(440\) 91.1377i 0.207131i
\(441\) −225.121 465.095i −0.510478 1.05464i
\(442\) 9.04305 0.0204594
\(443\) 396.205i 0.894369i −0.894442 0.447184i \(-0.852427\pi\)
0.894442 0.447184i \(-0.147573\pi\)
\(444\) 12.6008 20.0985i 0.0283802 0.0452669i
\(445\) −108.943 −0.244816
\(446\) 60.9461i 0.136650i
\(447\) −196.148 122.975i −0.438809 0.275113i
\(448\) −82.5252 −0.184208
\(449\) 256.272i 0.570762i 0.958414 + 0.285381i \(0.0921202\pi\)
−0.958414 + 0.285381i \(0.907880\pi\)
\(450\) −57.2822 + 27.7264i −0.127294 + 0.0616142i
\(451\) −12.9375 −0.0286863
\(452\) 361.115i 0.798927i
\(453\) 195.809 312.319i 0.432250 0.689445i
\(454\) 369.394 0.813643
\(455\) 336.442i 0.739433i
\(456\) 219.327 + 137.508i 0.480981 + 0.301553i
\(457\) 0.112362 0.000245868 0.000122934 1.00000i \(-0.499961\pi\)
0.000122934 1.00000i \(0.499961\pi\)
\(458\) 434.004i 0.947608i
\(459\) 1.29014 11.7663i 0.00281077 0.0256347i
\(460\) 21.4476 0.0466252
\(461\) 61.9220i 0.134321i −0.997742 0.0671606i \(-0.978606\pi\)
0.997742 0.0671606i \(-0.0213940\pi\)
\(462\) 335.004 534.336i 0.725116 1.15657i
\(463\) −327.777 −0.707941 −0.353971 0.935257i \(-0.615169\pi\)
−0.353971 + 0.935257i \(0.615169\pi\)
\(464\) 94.4662i 0.203591i
\(465\) −214.897 134.730i −0.462144 0.289742i
\(466\) −20.2276 −0.0434070
\(467\) 686.322i 1.46964i −0.678262 0.734820i \(-0.737267\pi\)
0.678262 0.734820i \(-0.262733\pi\)
\(468\) 114.384 + 236.316i 0.244411 + 0.504949i
\(469\) 164.884 0.351564
\(470\) 126.439i 0.269020i
\(471\) −302.999 + 483.288i −0.643309 + 1.02609i
\(472\) −123.757 −0.262196
\(473\) 684.529i 1.44721i
\(474\) 421.298 + 264.134i 0.888815 + 0.557245i
\(475\) −152.540 −0.321136
\(476\) 9.04478i 0.0190016i
\(477\) −543.487 + 263.065i −1.13939 + 0.551499i
\(478\) 241.822 0.505904
\(479\) 130.191i 0.271798i 0.990723 + 0.135899i \(0.0433922\pi\)
−0.990723 + 0.135899i \(0.956608\pi\)
\(480\) 20.1572 32.1510i 0.0419941 0.0669813i
\(481\) 57.6671 0.119890
\(482\) 292.429i 0.606700i
\(483\) −125.746 78.8370i −0.260344 0.163224i
\(484\) 173.304 0.358067
\(485\) 286.991i 0.591734i
\(486\) 323.800 115.116i 0.666255 0.236864i
\(487\) 138.291 0.283966 0.141983 0.989869i \(-0.454652\pi\)
0.141983 + 0.989869i \(0.454652\pi\)
\(488\) 195.622i 0.400865i
\(489\) −65.4654 + 104.418i −0.133876 + 0.213534i
\(490\) −181.554 −0.370519
\(491\) 642.931i 1.30943i 0.755875 + 0.654716i \(0.227212\pi\)
−0.755875 + 0.654716i \(0.772788\pi\)
\(492\) 4.56402 + 2.86142i 0.00927645 + 0.00581590i
\(493\) 10.3535 0.0210010
\(494\) 629.299i 1.27388i
\(495\) 126.346 + 261.028i 0.255244 + 0.527330i
\(496\) 151.241 0.304922
\(497\) 337.517i 0.679108i
\(498\) −163.111 + 260.165i −0.327533 + 0.522420i
\(499\) 139.535 0.279630 0.139815 0.990178i \(-0.455349\pi\)
0.139815 + 0.990178i \(0.455349\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) −440.536 276.195i −0.879314 0.551288i
\(502\) 408.525 0.813794
\(503\) 887.770i 1.76495i 0.470358 + 0.882475i \(0.344125\pi\)
−0.470358 + 0.882475i \(0.655875\pi\)
\(504\) −236.361 + 114.406i −0.468970 + 0.226996i
\(505\) 218.943 0.433551
\(506\) 97.7343i 0.193151i
\(507\) −69.7088 + 111.187i −0.137493 + 0.219303i
\(508\) 361.595 0.711800
\(509\) 436.679i 0.857916i −0.903325 0.428958i \(-0.858881\pi\)
0.903325 0.428958i \(-0.141119\pi\)
\(510\) −3.52376 2.20923i −0.00690933 0.00433183i
\(511\) −1412.56 −2.76430
\(512\) 22.6274i 0.0441942i
\(513\) 818.808 + 89.7800i 1.59612 + 0.175010i
\(514\) −542.204 −1.05487
\(515\) 222.435i 0.431913i
\(516\) −151.399 + 241.484i −0.293409 + 0.467992i
\(517\) −576.170 −1.11445
\(518\) 57.6781i 0.111348i
\(519\) −127.544 79.9643i −0.245750 0.154074i
\(520\) 92.2483 0.177401
\(521\) 188.925i 0.362620i 0.983426 + 0.181310i \(0.0580338\pi\)
−0.983426 + 0.181310i \(0.941966\pi\)
\(522\) 130.960 + 270.561i 0.250882 + 0.518317i
\(523\) 193.538 0.370053 0.185027 0.982733i \(-0.440763\pi\)
0.185027 + 0.982733i \(0.440763\pi\)
\(524\) 205.379i 0.391944i
\(525\) 82.1933 131.100i 0.156559 0.249713i
\(526\) 302.778 0.575624
\(527\) 16.5761i 0.0314537i
\(528\) −146.509 91.8540i −0.277478 0.173966i
\(529\) −23.0000 −0.0434783
\(530\) 212.156i 0.400294i
\(531\) −354.453 + 171.566i −0.667519 + 0.323100i
\(532\) −629.419 −1.18312
\(533\) 13.0952i 0.0245688i
\(534\) 109.799 175.132i 0.205617 0.327962i
\(535\) −347.383 −0.649314
\(536\) 45.2091i 0.0843453i
\(537\) −488.309 306.147i −0.909328 0.570106i
\(538\) 355.001 0.659853
\(539\) 827.323i 1.53492i
\(540\) 13.1608 120.028i 0.0243718 0.222275i
\(541\) −224.735 −0.415407 −0.207704 0.978192i \(-0.566599\pi\)
−0.207704 + 0.978192i \(0.566599\pi\)
\(542\) 323.339i 0.596567i
\(543\) −141.912 + 226.352i −0.261348 + 0.416855i
\(544\) 2.47997 0.00455877
\(545\) 100.249i 0.183943i
\(546\) −540.848 339.086i −0.990563 0.621037i
\(547\) 926.193 1.69322 0.846611 0.532212i \(-0.178639\pi\)
0.846611 + 0.532212i \(0.178639\pi\)
\(548\) 127.431i 0.232539i
\(549\) 271.195 + 560.283i 0.493979 + 1.02055i
\(550\) 101.895 0.185264
\(551\) 720.493i 1.30761i
\(552\) −21.6162 + 34.4781i −0.0391597 + 0.0624604i
\(553\) −1209.03 −2.18631
\(554\) 720.695i 1.30089i
\(555\) −22.4708 14.0882i −0.0404880 0.0253841i
\(556\) −397.791 −0.715451
\(557\) 367.940i 0.660575i 0.943880 + 0.330288i \(0.107146\pi\)
−0.943880 + 0.330288i \(0.892854\pi\)
\(558\) 433.171 209.669i 0.776293 0.375750i
\(559\) −692.871 −1.23948
\(560\) 92.2660i 0.164761i
\(561\) −10.0672 + 16.0574i −0.0179451 + 0.0286228i
\(562\) −23.4413 −0.0417105
\(563\) 480.071i 0.852701i −0.904558 0.426351i \(-0.859799\pi\)
0.904558 0.426351i \(-0.140201\pi\)
\(564\) 203.258 + 127.433i 0.360386 + 0.225945i
\(565\) −403.739 −0.714582
\(566\) 177.883i 0.314281i
\(567\) −518.360 + 655.344i −0.914216 + 1.15581i
\(568\) −92.5431 −0.162928
\(569\) 723.376i 1.27131i −0.771973 0.635655i \(-0.780730\pi\)
0.771973 0.635655i \(-0.219270\pi\)
\(570\) 153.739 245.216i 0.269717 0.430203i
\(571\) −811.310 −1.42086 −0.710429 0.703769i \(-0.751499\pi\)
−0.710429 + 0.703769i \(0.751499\pi\)
\(572\) 420.365i 0.734904i
\(573\) 734.384 + 460.424i 1.28165 + 0.803533i
\(574\) −13.0977 −0.0228182
\(575\) 23.9792i 0.0417029i
\(576\) 31.3688 + 64.8074i 0.0544598 + 0.112513i
\(577\) 110.169 0.190934 0.0954672 0.995433i \(-0.469566\pi\)
0.0954672 + 0.995433i \(0.469566\pi\)
\(578\) 408.436i 0.706637i
\(579\) 502.266 801.122i 0.867471 1.38363i
\(580\) 105.616 0.182097
\(581\) 746.613i 1.28505i
\(582\) −461.353 289.246i −0.792702 0.496987i
\(583\) 966.770 1.65827
\(584\) 387.306i 0.663195i
\(585\) 264.209 127.886i 0.451640 0.218608i
\(586\) 74.4365 0.127025
\(587\) 758.107i 1.29149i 0.763551 + 0.645747i \(0.223454\pi\)
−0.763551 + 0.645747i \(0.776546\pi\)
\(588\) 182.981 291.858i 0.311193 0.496357i
\(589\) 1153.52 1.95843
\(590\) 138.364i 0.234516i
\(591\) −452.258 283.544i −0.765242 0.479771i
\(592\) 15.8146 0.0267139
\(593\) 634.205i 1.06949i 0.845015 + 0.534743i \(0.179591\pi\)
−0.845015 + 0.534743i \(0.820409\pi\)
\(594\) −546.955 59.9722i −0.920800 0.100963i
\(595\) 10.1124 0.0169956
\(596\) 154.340i 0.258960i
\(597\) 369.935 590.053i 0.619657 0.988363i
\(598\) −98.9253 −0.165427
\(599\) 346.330i 0.578180i −0.957302 0.289090i \(-0.906647\pi\)
0.957302 0.289090i \(-0.0933527\pi\)
\(600\) −35.9459 22.5364i −0.0599099 0.0375607i
\(601\) −746.606 −1.24227 −0.621137 0.783702i \(-0.713329\pi\)
−0.621137 + 0.783702i \(0.713329\pi\)
\(602\) 693.003i 1.15117i
\(603\) −62.6742 129.484i −0.103937 0.214733i
\(604\) 245.750 0.406871
\(605\) 193.760i 0.320265i
\(606\) −220.664 + 351.963i −0.364132 + 0.580797i
\(607\) 907.294 1.49472 0.747359 0.664420i \(-0.231321\pi\)
0.747359 + 0.664420i \(0.231321\pi\)
\(608\) 172.579i 0.283847i
\(609\) −619.224 388.224i −1.01679 0.637478i
\(610\) 218.712 0.358545
\(611\) 583.191i 0.954486i
\(612\) 7.10290 3.43803i 0.0116061 0.00561770i
\(613\) −361.864 −0.590316 −0.295158 0.955448i \(-0.595372\pi\)
−0.295158 + 0.955448i \(0.595372\pi\)
\(614\) 825.906i 1.34512i
\(615\) 3.19917 5.10272i 0.00520190 0.00829711i
\(616\) 420.446 0.682541
\(617\) 3.49792i 0.00566925i 0.999996 + 0.00283462i \(0.000902290\pi\)
−0.999996 + 0.00283462i \(0.999098\pi\)
\(618\) −357.576 224.183i −0.578602 0.362756i
\(619\) 48.8766 0.0789606 0.0394803 0.999220i \(-0.487430\pi\)
0.0394803 + 0.999220i \(0.487430\pi\)
\(620\) 169.093i 0.272730i
\(621\) −14.1134 + 128.716i −0.0227268 + 0.207272i
\(622\) 866.582 1.39322
\(623\) 502.588i 0.806722i
\(624\) −92.9733 + 148.294i −0.148996 + 0.237651i
\(625\) 25.0000 0.0400000
\(626\) 633.847i 1.01253i
\(627\) −1117.42 700.570i −1.78217 1.11734i
\(628\) −380.278 −0.605538
\(629\) 1.73329i 0.00275562i
\(630\) 127.910 + 264.260i 0.203032 + 0.419460i
\(631\) 1130.12 1.79101 0.895503 0.445056i \(-0.146816\pi\)
0.895503 + 0.445056i \(0.146816\pi\)
\(632\) 331.501i 0.524527i
\(633\) −382.674 + 610.370i −0.604540 + 0.964250i
\(634\) 531.251 0.837935
\(635\) 404.275i 0.636654i
\(636\) −341.051 213.823i −0.536244 0.336200i
\(637\) 837.405 1.31461
\(638\) 481.282i 0.754360i
\(639\) −265.053 + 128.294i −0.414794 + 0.200773i
\(640\) 25.2982 0.0395285
\(641\) 1010.87i 1.57702i −0.615023 0.788510i \(-0.710853\pi\)
0.615023 0.788510i \(-0.289147\pi\)
\(642\) 350.113 558.436i 0.545348 0.869838i
\(643\) −979.174 −1.52282 −0.761410 0.648270i \(-0.775493\pi\)
−0.761410 + 0.648270i \(0.775493\pi\)
\(644\) 98.9442i 0.153640i
\(645\) 269.987 + 169.269i 0.418585 + 0.262433i
\(646\) 18.9147 0.0292797
\(647\) 426.288i 0.658869i −0.944178 0.329435i \(-0.893142\pi\)
0.944178 0.329435i \(-0.106858\pi\)
\(648\) 179.687 + 142.128i 0.277295 + 0.219334i
\(649\) 630.510 0.971510
\(650\) 103.137i 0.158672i
\(651\) −621.551 + 991.383i −0.954763 + 1.52286i
\(652\) −82.1622 −0.126016
\(653\) 903.600i 1.38377i −0.722009 0.691884i \(-0.756781\pi\)
0.722009 0.691884i \(-0.243219\pi\)
\(654\) −161.155 101.037i −0.246415 0.154491i
\(655\) 229.621 0.350566
\(656\) 3.59122i 0.00547442i
\(657\) 536.930 + 1109.29i 0.817245 + 1.68841i
\(658\) −583.302 −0.886478
\(659\) 1085.47i 1.64715i −0.567210 0.823573i \(-0.691977\pi\)
0.567210 0.823573i \(-0.308023\pi\)
\(660\) −102.696 + 163.802i −0.155600 + 0.248184i
\(661\) −180.375 −0.272883 −0.136441 0.990648i \(-0.543567\pi\)
−0.136441 + 0.990648i \(0.543567\pi\)
\(662\) 363.702i 0.549398i
\(663\) 16.2530 + 10.1899i 0.0245144 + 0.0153694i
\(664\) −204.712 −0.308302
\(665\) 703.712i 1.05821i
\(666\) 45.2948 21.9241i 0.0680103 0.0329191i
\(667\) −113.261 −0.169807
\(668\) 346.638i 0.518920i
\(669\) 68.6753 109.538i 0.102654 0.163734i
\(670\) −50.5453 −0.0754408
\(671\) 996.647i 1.48532i
\(672\) −148.322 92.9911i −0.220718 0.138380i
\(673\) 1106.01 1.64341 0.821704 0.569914i \(-0.193024\pi\)
0.821704 + 0.569914i \(0.193024\pi\)
\(674\) 879.655i 1.30513i
\(675\) −134.196 14.7142i −0.198808 0.0217988i
\(676\) −87.4879 −0.129420
\(677\) 1216.03i 1.79621i 0.439781 + 0.898105i \(0.355056\pi\)
−0.439781 + 0.898105i \(0.644944\pi\)
\(678\) 406.912 649.031i 0.600165 0.957273i
\(679\) 1323.97 1.94989
\(680\) 2.77269i 0.00407749i
\(681\) 663.910 + 416.240i 0.974905 + 0.611220i
\(682\) −770.537 −1.12982
\(683\) 737.028i 1.07910i −0.841952 0.539552i \(-0.818594\pi\)
0.841952 0.539552i \(-0.181406\pi\)
\(684\) 239.250 + 494.285i 0.349780 + 0.722639i
\(685\) 142.472 0.207989
\(686\) 122.727i 0.178902i
\(687\) −489.045 + 780.035i −0.711856 + 1.13542i
\(688\) −190.013 −0.276182
\(689\) 978.551i 1.42025i
\(690\) 38.5477 + 24.1676i 0.0558663 + 0.0350255i
\(691\) 507.773 0.734838 0.367419 0.930055i \(-0.380241\pi\)
0.367419 + 0.930055i \(0.380241\pi\)
\(692\) 100.359i 0.145027i
\(693\) 1204.20 582.872i 1.73766 0.841085i
\(694\) −71.1502 −0.102522
\(695\) 444.743i 0.639919i
\(696\) −106.446 + 169.784i −0.152940 + 0.243942i
\(697\) 0.393599 0.000564704
\(698\) 678.782i 0.972466i
\(699\) −36.3551 22.7929i −0.0520101 0.0326079i
\(700\) 103.156 0.147366
\(701\) 891.513i 1.27177i −0.771783 0.635886i \(-0.780635\pi\)
0.771783 0.635886i \(-0.219365\pi\)
\(702\) −60.7030 + 553.621i −0.0864715 + 0.788633i
\(703\) 120.618 0.171576
\(704\) 115.281i 0.163752i
\(705\) 142.474 227.249i 0.202091 0.322339i
\(706\) −587.085 −0.831565
\(707\) 1010.05i 1.42864i
\(708\) −222.428 139.452i −0.314163 0.196966i
\(709\) 668.547 0.942944 0.471472 0.881881i \(-0.343723\pi\)
0.471472 + 0.881881i \(0.343723\pi\)
\(710\) 103.466i 0.145727i
\(711\) 459.566 + 949.455i 0.646366 + 1.33538i
\(712\) 137.804 0.193544
\(713\) 181.332i 0.254322i
\(714\) −10.1918 + 16.2562i −0.0142743 + 0.0227677i
\(715\) −469.983 −0.657318
\(716\) 384.229i 0.536633i
\(717\) 434.626 + 272.490i 0.606173 + 0.380042i
\(718\) −4.98629 −0.00694470
\(719\) 501.263i 0.697167i 0.937278 + 0.348583i \(0.113337\pi\)
−0.937278 + 0.348583i \(0.886663\pi\)
\(720\) 72.4569 35.0714i 0.100635 0.0487103i
\(721\) 1026.16 1.42325
\(722\) 805.728i 1.11597i
\(723\) −329.515 + 525.582i −0.455761 + 0.726946i
\(724\) −178.106 −0.246003
\(725\) 118.083i 0.162873i
\(726\) 311.479 + 195.283i 0.429035 + 0.268985i
\(727\) −462.615 −0.636334 −0.318167 0.948035i \(-0.603067\pi\)
−0.318167 + 0.948035i \(0.603067\pi\)
\(728\) 425.569i 0.584573i
\(729\) 711.679 + 157.967i 0.976241 + 0.216689i
\(730\) 433.021 0.593180
\(731\) 20.8255i 0.0284890i
\(732\) −220.431 + 351.591i −0.301135 + 0.480316i
\(733\) 445.512 0.607792 0.303896 0.952705i \(-0.401712\pi\)
0.303896 + 0.952705i \(0.401712\pi\)
\(734\) 91.5574i 0.124738i
\(735\) −326.307 204.579i −0.443956 0.278339i
\(736\) −27.1293 −0.0368605
\(737\) 230.329i 0.312523i
\(738\) 4.97858 + 10.2857i 0.00674604 + 0.0139372i
\(739\) −861.893 −1.16630 −0.583148 0.812366i \(-0.698179\pi\)
−0.583148 + 0.812366i \(0.698179\pi\)
\(740\) 17.6813i 0.0238937i
\(741\) −709.107 + 1131.04i −0.956959 + 1.52637i
\(742\) 978.738 1.31905
\(743\) 1095.60i 1.47456i −0.675587 0.737280i \(-0.736110\pi\)
0.675587 0.737280i \(-0.263890\pi\)
\(744\) 271.825 + 170.422i 0.365357 + 0.229062i
\(745\) −172.557 −0.231621
\(746\) 296.782i 0.397831i
\(747\) −586.319 + 283.797i −0.784898 + 0.379915i
\(748\) −12.6348 −0.0168915
\(749\) 1602.58i 2.13963i
\(750\) −25.1965 + 40.1888i −0.0335953 + 0.0535850i
\(751\) 1272.16 1.69396 0.846979 0.531626i \(-0.178419\pi\)
0.846979 + 0.531626i \(0.178419\pi\)
\(752\) 159.935i 0.212679i
\(753\) 734.240 + 460.334i 0.975086 + 0.611333i
\(754\) −487.147 −0.646083
\(755\) 274.757i 0.363916i
\(756\) −553.726 60.7146i −0.732442 0.0803103i
\(757\) −361.418 −0.477435 −0.238718 0.971089i \(-0.576727\pi\)
−0.238718 + 0.971089i \(0.576727\pi\)
\(758\) 38.9980i 0.0514486i
\(759\) 110.129 175.658i 0.145098 0.231433i
\(760\) 192.949 0.253881
\(761\) 917.813i 1.20606i −0.797718 0.603031i \(-0.793960\pi\)
0.797718 0.603031i \(-0.206040\pi\)
\(762\) 649.893 + 407.452i 0.852878 + 0.534714i
\(763\) 462.478 0.606132
\(764\) 577.854i 0.756354i
\(765\) −3.84383 7.94129i −0.00502462 0.0103808i
\(766\) 885.447 1.15594
\(767\) 638.194i 0.832065i
\(768\) −25.4970 + 40.6682i −0.0331993 + 0.0529534i
\(769\) 692.243 0.900186 0.450093 0.892982i \(-0.351391\pi\)
0.450093 + 0.892982i \(0.351391\pi\)
\(770\) 470.072i 0.610484i
\(771\) −974.502 610.967i −1.26395 0.792434i
\(772\) 630.368 0.816539
\(773\) 996.702i 1.28939i 0.764438 + 0.644697i \(0.223017\pi\)
−0.764438 + 0.644697i \(0.776983\pi\)
\(774\) −544.218 + 263.419i −0.703125 + 0.340334i
\(775\) −189.052 −0.243938
\(776\) 363.018i 0.467807i
\(777\) −64.9928 + 103.665i −0.0836459 + 0.133416i
\(778\) 303.148 0.389650
\(779\) 27.3902i 0.0351607i
\(780\) 165.798 + 103.947i 0.212561 + 0.133266i
\(781\) 471.484 0.603693
\(782\) 2.97338i 0.00380228i
\(783\) −69.4997 + 633.848i −0.0887608 + 0.809512i
\(784\) 229.650 0.292921
\(785\) 425.163i 0.541610i
\(786\)