Properties

Label 690.3.g.a.461.8
Level $690$
Weight $3$
Character 690.461
Analytic conductor $18.801$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

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 461.8
Character \(\chi\) \(=\) 690.461
Dual form 690.3.g.a.461.7

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421i q^{2} +(1.56849 - 2.55731i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(3.61658 + 2.21819i) q^{6} -1.76788 q^{7} -2.82843i q^{8} +(-4.07965 - 8.02225i) q^{9} +O(q^{10})\) \(q+1.41421i q^{2} +(1.56849 - 2.55731i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(3.61658 + 2.21819i) q^{6} -1.76788 q^{7} -2.82843i q^{8} +(-4.07965 - 8.02225i) q^{9} +3.16228 q^{10} +17.7224i q^{11} +(-3.13699 + 5.11462i) q^{12} -20.6890 q^{13} -2.50016i q^{14} +(-5.71832 - 3.50726i) q^{15} +4.00000 q^{16} +0.0288786i q^{17} +(11.3452 - 5.76950i) q^{18} -5.91750 q^{19} +4.47214i q^{20} +(-2.77291 + 4.52102i) q^{21} -25.0633 q^{22} +4.79583i q^{23} +(-7.23316 - 4.43637i) q^{24} -5.00000 q^{25} -29.2586i q^{26} +(-26.9143 - 2.14992i) q^{27} +3.53576 q^{28} +45.1942i q^{29} +(4.96001 - 8.08692i) q^{30} +41.1755 q^{31} +5.65685i q^{32} +(45.3217 + 27.7975i) q^{33} -0.0408405 q^{34} +3.95310i q^{35} +(8.15930 + 16.0445i) q^{36} -70.8841 q^{37} -8.36861i q^{38} +(-32.4505 + 52.9081i) q^{39} -6.32456 q^{40} +18.6543i q^{41} +(-6.39369 - 3.92149i) q^{42} +60.4201 q^{43} -35.4448i q^{44} +(-17.9383 + 9.12238i) q^{45} -6.78233 q^{46} +51.6509i q^{47} +(6.27398 - 10.2292i) q^{48} -45.8746 q^{49} -7.07107i q^{50} +(0.0738515 + 0.0452959i) q^{51} +41.3780 q^{52} +21.7689i q^{53} +(3.04045 - 38.0625i) q^{54} +39.6285 q^{55} +5.00033i q^{56} +(-9.28156 + 15.1329i) q^{57} -63.9142 q^{58} -68.2581i q^{59} +(11.4366 + 7.01452i) q^{60} +1.38027 q^{61} +58.2310i q^{62} +(7.21234 + 14.1824i) q^{63} -8.00000 q^{64} +46.2620i q^{65} +(-39.3116 + 64.0945i) q^{66} -100.715 q^{67} -0.0577572i q^{68} +(12.2644 + 7.52223i) q^{69} -5.59053 q^{70} +56.2569i q^{71} +(-22.6903 + 11.5390i) q^{72} -73.9837 q^{73} -100.245i q^{74} +(-7.84247 + 12.7865i) q^{75} +11.8350 q^{76} -31.3311i q^{77} +(-74.8233 - 45.8920i) q^{78} +4.47024 q^{79} -8.94427i q^{80} +(-47.7129 + 65.4559i) q^{81} -26.3811 q^{82} +21.0356i q^{83} +(5.54583 - 9.04204i) q^{84} +0.0645745 q^{85} +85.4469i q^{86} +(115.575 + 70.8868i) q^{87} +50.1266 q^{88} -28.2078i q^{89} +(-12.9010 - 25.3686i) q^{90} +36.5757 q^{91} -9.59166i q^{92} +(64.5835 - 105.298i) q^{93} -73.0455 q^{94} +13.2319i q^{95} +(14.4663 + 8.87274i) q^{96} +57.7059 q^{97} -64.8765i q^{98} +(142.174 - 72.3013i) 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
\(3\) 1.56849 2.55731i 0.522831 0.852436i
\(4\) −2.00000 −0.500000
\(5\) 2.23607i 0.447214i
\(6\) 3.61658 + 2.21819i 0.602763 + 0.369698i
\(7\) −1.76788 −0.252555 −0.126277 0.991995i \(-0.540303\pi\)
−0.126277 + 0.991995i \(0.540303\pi\)
\(8\) 2.82843i 0.353553i
\(9\) −4.07965 8.02225i −0.453295 0.891361i
\(10\) 3.16228 0.316228
\(11\) 17.7224i 1.61113i 0.592508 + 0.805564i \(0.298138\pi\)
−0.592508 + 0.805564i \(0.701862\pi\)
\(12\) −3.13699 + 5.11462i −0.261416 + 0.426218i
\(13\) −20.6890 −1.59146 −0.795730 0.605652i \(-0.792913\pi\)
−0.795730 + 0.605652i \(0.792913\pi\)
\(14\) 2.50016i 0.178583i
\(15\) −5.71832 3.50726i −0.381221 0.233817i
\(16\) 4.00000 0.250000
\(17\) 0.0288786i 0.00169874i 1.00000 0.000849371i \(0.000270363\pi\)
−1.00000 0.000849371i \(0.999730\pi\)
\(18\) 11.3452 5.76950i 0.630287 0.320528i
\(19\) −5.91750 −0.311447 −0.155724 0.987801i \(-0.549771\pi\)
−0.155724 + 0.987801i \(0.549771\pi\)
\(20\) 4.47214i 0.223607i
\(21\) −2.77291 + 4.52102i −0.132043 + 0.215287i
\(22\) −25.0633 −1.13924
\(23\) 4.79583i 0.208514i
\(24\) −7.23316 4.43637i −0.301382 0.184849i
\(25\) −5.00000 −0.200000
\(26\) 29.2586i 1.12533i
\(27\) −26.9143 2.14992i −0.996825 0.0796268i
\(28\) 3.53576 0.126277
\(29\) 45.1942i 1.55842i 0.626763 + 0.779210i \(0.284379\pi\)
−0.626763 + 0.779210i \(0.715621\pi\)
\(30\) 4.96001 8.08692i 0.165334 0.269564i
\(31\) 41.1755 1.32824 0.664121 0.747625i \(-0.268806\pi\)
0.664121 + 0.747625i \(0.268806\pi\)
\(32\) 5.65685i 0.176777i
\(33\) 45.3217 + 27.7975i 1.37338 + 0.842349i
\(34\) −0.0408405 −0.00120119
\(35\) 3.95310i 0.112946i
\(36\) 8.15930 + 16.0445i 0.226647 + 0.445680i
\(37\) −70.8841 −1.91579 −0.957893 0.287125i \(-0.907300\pi\)
−0.957893 + 0.287125i \(0.907300\pi\)
\(38\) 8.36861i 0.220226i
\(39\) −32.4505 + 52.9081i −0.832065 + 1.35662i
\(40\) −6.32456 −0.158114
\(41\) 18.6543i 0.454982i 0.973780 + 0.227491i \(0.0730522\pi\)
−0.973780 + 0.227491i \(0.926948\pi\)
\(42\) −6.39369 3.92149i −0.152231 0.0933688i
\(43\) 60.4201 1.40512 0.702559 0.711625i \(-0.252041\pi\)
0.702559 + 0.711625i \(0.252041\pi\)
\(44\) 35.4448i 0.805564i
\(45\) −17.9383 + 9.12238i −0.398629 + 0.202719i
\(46\) −6.78233 −0.147442
\(47\) 51.6509i 1.09896i 0.835508 + 0.549478i \(0.185173\pi\)
−0.835508 + 0.549478i \(0.814827\pi\)
\(48\) 6.27398 10.2292i 0.130708 0.213109i
\(49\) −45.8746 −0.936216
\(50\) 7.07107i 0.141421i
\(51\) 0.0738515 + 0.0452959i 0.00144807 + 0.000888155i
\(52\) 41.3780 0.795730
\(53\) 21.7689i 0.410734i 0.978685 + 0.205367i \(0.0658388\pi\)
−0.978685 + 0.205367i \(0.934161\pi\)
\(54\) 3.04045 38.0625i 0.0563046 0.704862i
\(55\) 39.6285 0.720519
\(56\) 5.00033i 0.0892915i
\(57\) −9.28156 + 15.1329i −0.162834 + 0.265489i
\(58\) −63.9142 −1.10197
\(59\) 68.2581i 1.15692i −0.815712 0.578458i \(-0.803655\pi\)
0.815712 0.578458i \(-0.196345\pi\)
\(60\) 11.4366 + 7.01452i 0.190611 + 0.116909i
\(61\) 1.38027 0.0226273 0.0113136 0.999936i \(-0.496399\pi\)
0.0113136 + 0.999936i \(0.496399\pi\)
\(62\) 58.2310i 0.939209i
\(63\) 7.21234 + 14.1824i 0.114482 + 0.225117i
\(64\) −8.00000 −0.125000
\(65\) 46.2620i 0.711722i
\(66\) −39.3116 + 64.0945i −0.595631 + 0.971129i
\(67\) −100.715 −1.50322 −0.751608 0.659610i \(-0.770721\pi\)
−0.751608 + 0.659610i \(0.770721\pi\)
\(68\) 0.0577572i 0.000849371i
\(69\) 12.2644 + 7.52223i 0.177745 + 0.109018i
\(70\) −5.59053 −0.0798648
\(71\) 56.2569i 0.792350i 0.918175 + 0.396175i \(0.129663\pi\)
−0.918175 + 0.396175i \(0.870337\pi\)
\(72\) −22.6903 + 11.5390i −0.315144 + 0.160264i
\(73\) −73.9837 −1.01348 −0.506738 0.862100i \(-0.669149\pi\)
−0.506738 + 0.862100i \(0.669149\pi\)
\(74\) 100.245i 1.35467i
\(75\) −7.84247 + 12.7865i −0.104566 + 0.170487i
\(76\) 11.8350 0.155724
\(77\) 31.3311i 0.406898i
\(78\) −74.8233 45.8920i −0.959274 0.588359i
\(79\) 4.47024 0.0565854 0.0282927 0.999600i \(-0.490993\pi\)
0.0282927 + 0.999600i \(0.490993\pi\)
\(80\) 8.94427i 0.111803i
\(81\) −47.7129 + 65.4559i −0.589048 + 0.808098i
\(82\) −26.3811 −0.321721
\(83\) 21.0356i 0.253441i 0.991938 + 0.126721i \(0.0404451\pi\)
−0.991938 + 0.126721i \(0.959555\pi\)
\(84\) 5.54583 9.04204i 0.0660217 0.107643i
\(85\) 0.0645745 0.000759700
\(86\) 85.4469i 0.993569i
\(87\) 115.575 + 70.8868i 1.32845 + 0.814791i
\(88\) 50.1266 0.569620
\(89\) 28.2078i 0.316942i −0.987364 0.158471i \(-0.949344\pi\)
0.987364 0.158471i \(-0.0506564\pi\)
\(90\) −12.9010 25.3686i −0.143344 0.281873i
\(91\) 36.5757 0.401930
\(92\) 9.59166i 0.104257i
\(93\) 64.5835 105.298i 0.694447 1.13224i
\(94\) −73.0455 −0.777079
\(95\) 13.2319i 0.139283i
\(96\) 14.4663 + 8.87274i 0.150691 + 0.0924244i
\(97\) 57.7059 0.594906 0.297453 0.954736i \(-0.403863\pi\)
0.297453 + 0.954736i \(0.403863\pi\)
\(98\) 64.8765i 0.662005i
\(99\) 142.174 72.3013i 1.43610 0.730316i
\(100\) 10.0000 0.100000
\(101\) 68.2488i 0.675730i −0.941195 0.337865i \(-0.890295\pi\)
0.941195 0.337865i \(-0.109705\pi\)
\(102\) −0.0640581 + 0.104442i −0.000628021 + 0.00102394i
\(103\) −61.1415 −0.593607 −0.296803 0.954939i \(-0.595921\pi\)
−0.296803 + 0.954939i \(0.595921\pi\)
\(104\) 58.5173i 0.562666i
\(105\) 10.1093 + 6.20042i 0.0962791 + 0.0590516i
\(106\) −30.7859 −0.290433
\(107\) 146.342i 1.36769i −0.729629 0.683843i \(-0.760307\pi\)
0.729629 0.683843i \(-0.239693\pi\)
\(108\) 53.8285 + 4.29985i 0.498412 + 0.0398134i
\(109\) 48.8918 0.448549 0.224274 0.974526i \(-0.427999\pi\)
0.224274 + 0.974526i \(0.427999\pi\)
\(110\) 56.0432i 0.509484i
\(111\) −111.181 + 181.272i −1.00163 + 1.63309i
\(112\) −7.07153 −0.0631386
\(113\) 127.489i 1.12822i 0.825698 + 0.564112i \(0.190781\pi\)
−0.825698 + 0.564112i \(0.809219\pi\)
\(114\) −21.4011 13.1261i −0.187729 0.115141i
\(115\) 10.7238 0.0932505
\(116\) 90.3884i 0.779210i
\(117\) 84.4038 + 165.972i 0.721400 + 1.41856i
\(118\) 96.5315 0.818064
\(119\) 0.0510540i 0.000429025i
\(120\) −9.92003 + 16.1738i −0.0826669 + 0.134782i
\(121\) −193.084 −1.59574
\(122\) 1.95199i 0.0159999i
\(123\) 47.7047 + 29.2591i 0.387843 + 0.237879i
\(124\) −82.3510 −0.664121
\(125\) 11.1803i 0.0894427i
\(126\) −20.0569 + 10.1998i −0.159182 + 0.0809507i
\(127\) −230.507 −1.81501 −0.907506 0.420038i \(-0.862017\pi\)
−0.907506 + 0.420038i \(0.862017\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) 94.7685 154.513i 0.734640 1.19777i
\(130\) −65.4243 −0.503264
\(131\) 65.2731i 0.498268i −0.968469 0.249134i \(-0.919854\pi\)
0.968469 0.249134i \(-0.0801460\pi\)
\(132\) −90.6434 55.5950i −0.686692 0.421174i
\(133\) 10.4614 0.0786574
\(134\) 142.433i 1.06293i
\(135\) −4.80737 + 60.1821i −0.0356102 + 0.445794i
\(136\) 0.0816810 0.000600596
\(137\) 123.243i 0.899587i −0.893133 0.449793i \(-0.851498\pi\)
0.893133 0.449793i \(-0.148502\pi\)
\(138\) −10.6380 + 17.3445i −0.0770873 + 0.125685i
\(139\) −219.172 −1.57678 −0.788389 0.615177i \(-0.789085\pi\)
−0.788389 + 0.615177i \(0.789085\pi\)
\(140\) 7.90621i 0.0564729i
\(141\) 132.087 + 81.0142i 0.936790 + 0.574569i
\(142\) −79.5592 −0.560276
\(143\) 366.659i 2.56405i
\(144\) −16.3186 32.0890i −0.113324 0.222840i
\(145\) 101.057 0.696947
\(146\) 104.629i 0.716635i
\(147\) −71.9540 + 117.315i −0.489483 + 0.798064i
\(148\) 141.768 0.957893
\(149\) 84.6070i 0.567832i −0.958849 0.283916i \(-0.908366\pi\)
0.958849 0.283916i \(-0.0916337\pi\)
\(150\) −18.0829 11.0909i −0.120553 0.0739395i
\(151\) −29.2120 −0.193457 −0.0967284 0.995311i \(-0.530838\pi\)
−0.0967284 + 0.995311i \(0.530838\pi\)
\(152\) 16.7372i 0.110113i
\(153\) 0.231671 0.117815i 0.00151419 0.000770030i
\(154\) 44.3089 0.287720
\(155\) 92.0712i 0.594008i
\(156\) 64.9011 105.816i 0.416033 0.678309i
\(157\) 269.251 1.71498 0.857488 0.514503i \(-0.172024\pi\)
0.857488 + 0.514503i \(0.172024\pi\)
\(158\) 6.32188i 0.0400119i
\(159\) 55.6698 + 34.1444i 0.350125 + 0.214745i
\(160\) 12.6491 0.0790569
\(161\) 8.47846i 0.0526613i
\(162\) −92.5687 67.4762i −0.571412 0.416520i
\(163\) −296.191 −1.81712 −0.908561 0.417752i \(-0.862818\pi\)
−0.908561 + 0.417752i \(0.862818\pi\)
\(164\) 37.3085i 0.227491i
\(165\) 62.1571 101.342i 0.376710 0.614196i
\(166\) −29.7488 −0.179210
\(167\) 139.977i 0.838188i −0.907943 0.419094i \(-0.862348\pi\)
0.907943 0.419094i \(-0.137652\pi\)
\(168\) 12.7874 + 7.84298i 0.0761153 + 0.0466844i
\(169\) 259.034 1.53274
\(170\) 0.0913222i 0.000537189i
\(171\) 24.1413 + 47.4716i 0.141177 + 0.277612i
\(172\) −120.840 −0.702559
\(173\) 2.23761i 0.0129342i −0.999979 0.00646708i \(-0.997941\pi\)
0.999979 0.00646708i \(-0.00205855\pi\)
\(174\) −100.249 + 163.448i −0.576144 + 0.939359i
\(175\) 8.83941 0.0505109
\(176\) 70.8897i 0.402782i
\(177\) −174.557 107.062i −0.986198 0.604872i
\(178\) 39.8919 0.224112
\(179\) 86.0465i 0.480707i 0.970685 + 0.240353i \(0.0772633\pi\)
−0.970685 + 0.240353i \(0.922737\pi\)
\(180\) 35.8766 18.2448i 0.199314 0.101360i
\(181\) 43.5809 0.240778 0.120389 0.992727i \(-0.461586\pi\)
0.120389 + 0.992727i \(0.461586\pi\)
\(182\) 51.7258i 0.284208i
\(183\) 2.16494 3.52976i 0.0118303 0.0192883i
\(184\) 13.5647 0.0737210
\(185\) 158.502i 0.856766i
\(186\) 148.914 + 91.3349i 0.800616 + 0.491048i
\(187\) −0.511799 −0.00273689
\(188\) 103.302i 0.549478i
\(189\) 47.5812 + 3.80081i 0.251753 + 0.0201101i
\(190\) −18.7128 −0.0984883
\(191\) 195.043i 1.02117i 0.859828 + 0.510584i \(0.170571\pi\)
−0.859828 + 0.510584i \(0.829429\pi\)
\(192\) −12.5480 + 20.4585i −0.0653539 + 0.106555i
\(193\) 330.591 1.71290 0.856452 0.516226i \(-0.172664\pi\)
0.856452 + 0.516226i \(0.172664\pi\)
\(194\) 81.6085i 0.420662i
\(195\) 118.306 + 72.5616i 0.606698 + 0.372111i
\(196\) 91.7492 0.468108
\(197\) 91.7002i 0.465483i −0.972539 0.232742i \(-0.925230\pi\)
0.972539 0.232742i \(-0.0747697\pi\)
\(198\) 102.249 + 201.064i 0.516411 + 1.01547i
\(199\) 6.18236 0.0310671 0.0155336 0.999879i \(-0.495055\pi\)
0.0155336 + 0.999879i \(0.495055\pi\)
\(200\) 14.1421i 0.0707107i
\(201\) −157.972 + 257.560i −0.785928 + 1.28140i
\(202\) 96.5183 0.477813
\(203\) 79.8980i 0.393586i
\(204\) −0.147703 0.0905919i −0.000724034 0.000444078i
\(205\) 41.7122 0.203474
\(206\) 86.4671i 0.419743i
\(207\) 38.4733 19.5653i 0.185862 0.0945185i
\(208\) −82.7559 −0.397865
\(209\) 104.872i 0.501782i
\(210\) −8.76872 + 14.2967i −0.0417558 + 0.0680796i
\(211\) 312.639 1.48170 0.740851 0.671670i \(-0.234423\pi\)
0.740851 + 0.671670i \(0.234423\pi\)
\(212\) 43.5378i 0.205367i
\(213\) 143.866 + 88.2386i 0.675428 + 0.414266i
\(214\) 206.959 0.967100
\(215\) 135.103i 0.628388i
\(216\) −6.08090 + 76.1250i −0.0281523 + 0.352431i
\(217\) −72.7934 −0.335454
\(218\) 69.1435i 0.317172i
\(219\) −116.043 + 189.199i −0.529877 + 0.863923i
\(220\) −79.2571 −0.360259
\(221\) 0.597469i 0.00270348i
\(222\) −256.358 157.234i −1.15477 0.708262i
\(223\) 73.3202 0.328790 0.164395 0.986395i \(-0.447433\pi\)
0.164395 + 0.986395i \(0.447433\pi\)
\(224\) 10.0007i 0.0446458i
\(225\) 20.3983 + 40.1112i 0.0906589 + 0.178272i
\(226\) −180.297 −0.797775
\(227\) 54.4085i 0.239685i 0.992793 + 0.119843i \(0.0382390\pi\)
−0.992793 + 0.119843i \(0.961761\pi\)
\(228\) 18.5631 30.2657i 0.0814172 0.132744i
\(229\) −104.576 −0.456662 −0.228331 0.973584i \(-0.573327\pi\)
−0.228331 + 0.973584i \(0.573327\pi\)
\(230\) 15.1658i 0.0659380i
\(231\) −80.1234 49.1427i −0.346854 0.212739i
\(232\) 127.828 0.550985
\(233\) 72.9504i 0.313092i −0.987671 0.156546i \(-0.949964\pi\)
0.987671 0.156546i \(-0.0500359\pi\)
\(234\) −234.720 + 119.365i −1.00308 + 0.510107i
\(235\) 115.495 0.491468
\(236\) 136.516i 0.578458i
\(237\) 7.01155 11.4318i 0.0295846 0.0482354i
\(238\) 0.0722012 0.000303366
\(239\) 401.263i 1.67892i 0.543418 + 0.839462i \(0.317130\pi\)
−0.543418 + 0.839462i \(0.682870\pi\)
\(240\) −22.8733 14.0290i −0.0953053 0.0584543i
\(241\) −75.2115 −0.312081 −0.156041 0.987751i \(-0.549873\pi\)
−0.156041 + 0.987751i \(0.549873\pi\)
\(242\) 273.062i 1.12836i
\(243\) 92.5536 + 224.684i 0.380879 + 0.924625i
\(244\) −2.76053 −0.0113136
\(245\) 102.579i 0.418689i
\(246\) −41.3786 + 67.4646i −0.168206 + 0.274246i
\(247\) 122.427 0.495656
\(248\) 116.462i 0.469604i
\(249\) 53.7945 + 32.9942i 0.216042 + 0.132507i
\(250\) −15.8114 −0.0632456
\(251\) 95.2872i 0.379630i −0.981820 0.189815i \(-0.939211\pi\)
0.981820 0.189815i \(-0.0607889\pi\)
\(252\) −14.4247 28.3648i −0.0572408 0.112559i
\(253\) −84.9937 −0.335944
\(254\) 325.986i 1.28341i
\(255\) 0.101285 0.165137i 0.000397195 0.000647596i
\(256\) 16.0000 0.0625000
\(257\) 110.044i 0.428188i 0.976813 + 0.214094i \(0.0686799\pi\)
−0.976813 + 0.214094i \(0.931320\pi\)
\(258\) 218.514 + 134.023i 0.846954 + 0.519469i
\(259\) 125.315 0.483840
\(260\) 92.5239i 0.355861i
\(261\) 362.559 184.377i 1.38911 0.706423i
\(262\) 92.3101 0.352329
\(263\) 372.584i 1.41667i −0.705876 0.708335i \(-0.749446\pi\)
0.705876 0.708335i \(-0.250554\pi\)
\(264\) 78.6232 128.189i 0.297815 0.485565i
\(265\) 48.6767 0.183686
\(266\) 14.7947i 0.0556192i
\(267\) −72.1361 44.2438i −0.270173 0.165707i
\(268\) 201.431 0.751608
\(269\) 61.0243i 0.226856i 0.993546 + 0.113428i \(0.0361831\pi\)
−0.993546 + 0.113428i \(0.963817\pi\)
\(270\) −85.1104 6.79865i −0.315224 0.0251802i
\(271\) 489.007 1.80445 0.902227 0.431262i \(-0.141932\pi\)
0.902227 + 0.431262i \(0.141932\pi\)
\(272\) 0.115514i 0.000424685i
\(273\) 57.3687 93.5353i 0.210142 0.342620i
\(274\) 174.292 0.636104
\(275\) 88.6121i 0.322226i
\(276\) −24.5288 15.0445i −0.0888726 0.0545089i
\(277\) 319.748 1.15432 0.577162 0.816630i \(-0.304160\pi\)
0.577162 + 0.816630i \(0.304160\pi\)
\(278\) 309.956i 1.11495i
\(279\) −167.982 330.320i −0.602085 1.18394i
\(280\) 11.1811 0.0399324
\(281\) 244.012i 0.868371i 0.900824 + 0.434185i \(0.142964\pi\)
−0.900824 + 0.434185i \(0.857036\pi\)
\(282\) −114.571 + 186.800i −0.406282 + 0.662410i
\(283\) −312.536 −1.10437 −0.552183 0.833723i \(-0.686205\pi\)
−0.552183 + 0.833723i \(0.686205\pi\)
\(284\) 112.514i 0.396175i
\(285\) 33.8381 + 20.7542i 0.118730 + 0.0728218i
\(286\) 518.534 1.81305
\(287\) 32.9785i 0.114908i
\(288\) 45.3807 23.0780i 0.157572 0.0801319i
\(289\) 288.999 0.999997
\(290\) 142.917i 0.492816i
\(291\) 90.5114 147.572i 0.311036 0.507120i
\(292\) 147.967 0.506738
\(293\) 439.469i 1.49989i −0.661498 0.749947i \(-0.730079\pi\)
0.661498 0.749947i \(-0.269921\pi\)
\(294\) −165.909 101.758i −0.564317 0.346117i
\(295\) −152.630 −0.517389
\(296\) 200.490i 0.677333i
\(297\) 38.1018 476.986i 0.128289 1.60601i
\(298\) 119.652 0.401518
\(299\) 99.2209i 0.331842i
\(300\) 15.6849 25.5731i 0.0522831 0.0852436i
\(301\) −106.816 −0.354869
\(302\) 41.3120i 0.136795i
\(303\) −174.533 107.048i −0.576017 0.353293i
\(304\) −23.6700 −0.0778618
\(305\) 3.08637i 0.0101192i
\(306\) 0.166615 + 0.327633i 0.000544494 + 0.00107070i
\(307\) −147.088 −0.479115 −0.239557 0.970882i \(-0.577002\pi\)
−0.239557 + 0.970882i \(0.577002\pi\)
\(308\) 62.6623i 0.203449i
\(309\) −95.9001 + 156.358i −0.310356 + 0.506012i
\(310\) 130.208 0.420027
\(311\) 601.613i 1.93445i 0.253930 + 0.967223i \(0.418277\pi\)
−0.253930 + 0.967223i \(0.581723\pi\)
\(312\) 149.647 + 91.7840i 0.479637 + 0.294179i
\(313\) −88.4556 −0.282606 −0.141303 0.989966i \(-0.545129\pi\)
−0.141303 + 0.989966i \(0.545129\pi\)
\(314\) 380.779i 1.21267i
\(315\) 31.7128 16.1273i 0.100675 0.0511977i
\(316\) −8.94049 −0.0282927
\(317\) 435.939i 1.37520i 0.726089 + 0.687601i \(0.241336\pi\)
−0.726089 + 0.687601i \(0.758664\pi\)
\(318\) −48.2875 + 78.7290i −0.151847 + 0.247575i
\(319\) −800.950 −2.51082
\(320\) 17.8885i 0.0559017i
\(321\) −374.243 229.537i −1.16586 0.715069i
\(322\) 11.9904 0.0372371
\(323\) 0.170889i 0.000529068i
\(324\) 95.4258 130.912i 0.294524 0.404049i
\(325\) 103.445 0.318292
\(326\) 418.877i 1.28490i
\(327\) 76.6865 125.031i 0.234515 0.382359i
\(328\) 52.7622 0.160860
\(329\) 91.3128i 0.277546i
\(330\) 143.320 + 87.9034i 0.434302 + 0.266374i
\(331\) 305.202 0.922060 0.461030 0.887384i \(-0.347480\pi\)
0.461030 + 0.887384i \(0.347480\pi\)
\(332\) 42.0712i 0.126721i
\(333\) 289.182 + 568.650i 0.868415 + 1.70766i
\(334\) 197.958 0.592688
\(335\) 225.207i 0.672258i
\(336\) −11.0917 + 18.0841i −0.0330109 + 0.0538217i
\(337\) 222.147 0.659189 0.329594 0.944123i \(-0.393088\pi\)
0.329594 + 0.944123i \(0.393088\pi\)
\(338\) 366.329i 1.08381i
\(339\) 326.029 + 199.966i 0.961739 + 0.589871i
\(340\) −0.129149 −0.000379850
\(341\) 729.729i 2.13997i
\(342\) −67.1350 + 34.1410i −0.196301 + 0.0998275i
\(343\) 167.727 0.489000
\(344\) 170.894i 0.496784i
\(345\) 16.8202 27.4241i 0.0487543 0.0794901i
\(346\) 3.16446 0.00914583
\(347\) 656.982i 1.89332i −0.322235 0.946660i \(-0.604434\pi\)
0.322235 0.946660i \(-0.395566\pi\)
\(348\) −231.151 141.774i −0.664227 0.407396i
\(349\) −409.550 −1.17350 −0.586748 0.809769i \(-0.699592\pi\)
−0.586748 + 0.809769i \(0.699592\pi\)
\(350\) 12.5008i 0.0357166i
\(351\) 556.829 + 44.4797i 1.58641 + 0.126723i
\(352\) −100.253 −0.284810
\(353\) 249.433i 0.706609i −0.935508 0.353304i \(-0.885058\pi\)
0.935508 0.353304i \(-0.114942\pi\)
\(354\) 151.409 246.861i 0.427709 0.697347i
\(355\) 125.794 0.354350
\(356\) 56.4156i 0.158471i
\(357\) −0.130561 0.0800778i −0.000365716 0.000224308i
\(358\) −121.688 −0.339911
\(359\) 333.458i 0.928851i 0.885612 + 0.464426i \(0.153739\pi\)
−0.885612 + 0.464426i \(0.846261\pi\)
\(360\) 25.8020 + 50.7371i 0.0716722 + 0.140937i
\(361\) −325.983 −0.903001
\(362\) 61.6327i 0.170256i
\(363\) −302.851 + 493.775i −0.834301 + 1.36026i
\(364\) −73.1513 −0.200965
\(365\) 165.433i 0.453240i
\(366\) 4.99184 + 3.06168i 0.0136389 + 0.00836526i
\(367\) −144.077 −0.392581 −0.196290 0.980546i \(-0.562889\pi\)
−0.196290 + 0.980546i \(0.562889\pi\)
\(368\) 19.1833i 0.0521286i
\(369\) 149.649 76.1029i 0.405553 0.206241i
\(370\) −224.155 −0.605825
\(371\) 38.4849i 0.103733i
\(372\) −129.167 + 210.597i −0.347223 + 0.566121i
\(373\) −494.074 −1.32459 −0.662297 0.749241i \(-0.730418\pi\)
−0.662297 + 0.749241i \(0.730418\pi\)
\(374\) 0.723793i 0.00193527i
\(375\) 28.5916 + 17.5363i 0.0762442 + 0.0467635i
\(376\) 146.091 0.388540
\(377\) 935.021i 2.48016i
\(378\) −5.37516 + 67.2900i −0.0142200 + 0.178016i
\(379\) −533.662 −1.40808 −0.704040 0.710160i \(-0.748622\pi\)
−0.704040 + 0.710160i \(0.748622\pi\)
\(380\) 26.4639i 0.0696417i
\(381\) −361.548 + 589.476i −0.948946 + 1.54718i
\(382\) −275.833 −0.722075
\(383\) 245.335i 0.640563i −0.947322 0.320281i \(-0.896223\pi\)
0.947322 0.320281i \(-0.103777\pi\)
\(384\) −28.9326 17.7455i −0.0753454 0.0462122i
\(385\) −70.0586 −0.181970
\(386\) 467.526i 1.21121i
\(387\) −246.493 484.705i −0.636932 1.25247i
\(388\) −115.412 −0.297453
\(389\) 119.365i 0.306852i 0.988160 + 0.153426i \(0.0490306\pi\)
−0.988160 + 0.153426i \(0.950969\pi\)
\(390\) −102.618 + 167.310i −0.263122 + 0.429000i
\(391\) −0.138497 −0.000354212
\(392\) 129.753i 0.331002i
\(393\) −166.923 102.380i −0.424742 0.260510i
\(394\) 129.684 0.329147
\(395\) 9.99577i 0.0253057i
\(396\) −284.347 + 144.603i −0.718049 + 0.365158i
\(397\) 424.026 1.06808 0.534038 0.845461i \(-0.320674\pi\)
0.534038 + 0.845461i \(0.320674\pi\)
\(398\) 8.74317i 0.0219678i
\(399\) 16.4087 26.7531i 0.0411246 0.0670504i
\(400\) −20.0000 −0.0500000
\(401\) 787.894i 1.96482i −0.186731 0.982411i \(-0.559789\pi\)
0.186731 0.982411i \(-0.440211\pi\)
\(402\) −364.245 223.406i −0.906083 0.555735i
\(403\) −851.879 −2.11384
\(404\) 136.498i 0.337865i
\(405\) 146.364 + 106.689i 0.361392 + 0.263430i
\(406\) 112.993 0.278307
\(407\) 1256.24i 3.08658i
\(408\) 0.128116 0.208884i 0.000314010 0.000511970i
\(409\) −9.78449 −0.0239230 −0.0119615 0.999928i \(-0.503808\pi\)
−0.0119615 + 0.999928i \(0.503808\pi\)
\(410\) 58.9900i 0.143878i
\(411\) −315.171 193.307i −0.766840 0.470332i
\(412\) 122.283 0.296803
\(413\) 120.672i 0.292185i
\(414\) 27.6695 + 54.4095i 0.0668346 + 0.131424i
\(415\) 47.0371 0.113342
\(416\) 117.035i 0.281333i
\(417\) −343.770 + 560.491i −0.824389 + 1.34410i
\(418\) 148.312 0.354813
\(419\) 542.817i 1.29551i −0.761850 0.647753i \(-0.775709\pi\)
0.761850 0.647753i \(-0.224291\pi\)
\(420\) −20.2186 12.4008i −0.0481396 0.0295258i
\(421\) −675.751 −1.60511 −0.802555 0.596578i \(-0.796527\pi\)
−0.802555 + 0.596578i \(0.796527\pi\)
\(422\) 442.138i 1.04772i
\(423\) 414.357 210.718i 0.979566 0.498151i
\(424\) 61.5718 0.145216
\(425\) 0.144393i 0.000339748i
\(426\) −124.788 + 203.457i −0.292930 + 0.477600i
\(427\) −2.44015 −0.00571463
\(428\) 292.685i 0.683843i
\(429\) −937.659 575.102i −2.18569 1.34056i
\(430\) 191.065 0.444337
\(431\) 357.378i 0.829184i 0.910007 + 0.414592i \(0.136076\pi\)
−0.910007 + 0.414592i \(0.863924\pi\)
\(432\) −107.657 8.59969i −0.249206 0.0199067i
\(433\) −59.5104 −0.137437 −0.0687187 0.997636i \(-0.521891\pi\)
−0.0687187 + 0.997636i \(0.521891\pi\)
\(434\) 102.945i 0.237201i
\(435\) 158.508 258.435i 0.364386 0.594102i
\(436\) −97.7836 −0.224274
\(437\) 28.3793i 0.0649412i
\(438\) −267.568 164.110i −0.610886 0.374679i
\(439\) 292.816 0.667006 0.333503 0.942749i \(-0.391769\pi\)
0.333503 + 0.942749i \(0.391769\pi\)
\(440\) 112.086i 0.254742i
\(441\) 187.152 + 368.017i 0.424382 + 0.834506i
\(442\) 0.844948 0.00191165
\(443\) 70.1379i 0.158325i −0.996862 0.0791624i \(-0.974775\pi\)
0.996862 0.0791624i \(-0.0252246\pi\)
\(444\) 222.363 362.545i 0.500817 0.816543i
\(445\) −63.0746 −0.141741
\(446\) 103.690i 0.232490i
\(447\) −216.366 132.706i −0.484040 0.296880i
\(448\) 14.1431 0.0315693
\(449\) 751.278i 1.67323i 0.547795 + 0.836613i \(0.315468\pi\)
−0.547795 + 0.836613i \(0.684532\pi\)
\(450\) −56.7259 + 28.8475i −0.126057 + 0.0641055i
\(451\) −330.599 −0.733035
\(452\) 254.979i 0.564112i
\(453\) −45.8188 + 74.7040i −0.101145 + 0.164910i
\(454\) −76.9453 −0.169483
\(455\) 81.7857i 0.179749i
\(456\) 42.8022 + 26.2522i 0.0938645 + 0.0575707i
\(457\) −296.898 −0.649666 −0.324833 0.945771i \(-0.605308\pi\)
−0.324833 + 0.945771i \(0.605308\pi\)
\(458\) 147.892i 0.322909i
\(459\) 0.0620868 0.777247i 0.000135265 0.00169335i
\(460\) −21.4476 −0.0466252
\(461\) 44.6191i 0.0967875i 0.998828 + 0.0483938i \(0.0154102\pi\)
−0.998828 + 0.0483938i \(0.984590\pi\)
\(462\) 69.4983 113.312i 0.150429 0.245263i
\(463\) −652.545 −1.40938 −0.704692 0.709513i \(-0.748915\pi\)
−0.704692 + 0.709513i \(0.748915\pi\)
\(464\) 180.777i 0.389605i
\(465\) −235.454 144.413i −0.506354 0.310566i
\(466\) 103.167 0.221389
\(467\) 614.730i 1.31634i −0.752870 0.658169i \(-0.771331\pi\)
0.752870 0.658169i \(-0.228669\pi\)
\(468\) −168.808 331.944i −0.360700 0.709282i
\(469\) 178.053 0.379644
\(470\) 163.335i 0.347520i
\(471\) 422.319 688.559i 0.896644 1.46191i
\(472\) −193.063 −0.409032
\(473\) 1070.79i 2.26383i
\(474\) 16.1670 + 9.91583i 0.0341076 + 0.0209195i
\(475\) 29.5875 0.0622895
\(476\) 0.102108i 0.000214512i
\(477\) 174.636 88.8095i 0.366112 0.186184i
\(478\) −567.471 −1.18718
\(479\) 633.184i 1.32189i 0.750436 + 0.660944i \(0.229844\pi\)
−0.750436 + 0.660944i \(0.770156\pi\)
\(480\) 19.8401 32.3477i 0.0413335 0.0673910i
\(481\) 1466.52 3.04890
\(482\) 106.365i 0.220675i
\(483\) −21.6820 13.2984i −0.0448904 0.0275330i
\(484\) 386.168 0.797868
\(485\) 129.034i 0.266050i
\(486\) −317.751 + 130.891i −0.653809 + 0.269322i
\(487\) −169.555 −0.348163 −0.174081 0.984731i \(-0.555696\pi\)
−0.174081 + 0.984731i \(0.555696\pi\)
\(488\) 3.90398i 0.00799996i
\(489\) −464.574 + 757.451i −0.950049 + 1.54898i
\(490\) −145.068 −0.296058
\(491\) 694.164i 1.41378i 0.707325 + 0.706888i \(0.249902\pi\)
−0.707325 + 0.706888i \(0.750098\pi\)
\(492\) −95.4094 58.5182i −0.193922 0.118939i
\(493\) −1.30514 −0.00264735
\(494\) 173.138i 0.350482i
\(495\) −161.671 317.910i −0.326607 0.642242i
\(496\) 164.702 0.332060
\(497\) 99.4555i 0.200112i
\(498\) −46.6609 + 76.0770i −0.0936966 + 0.152765i
\(499\) 155.122 0.310865 0.155433 0.987847i \(-0.450323\pi\)
0.155433 + 0.987847i \(0.450323\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) −357.965 219.554i −0.714502 0.438231i
\(502\) 134.756 0.268439
\(503\) 460.543i 0.915593i 0.889057 + 0.457796i \(0.151361\pi\)
−0.889057 + 0.457796i \(0.848639\pi\)
\(504\) 40.1138 20.3996i 0.0795910 0.0404754i
\(505\) −152.609 −0.302196
\(506\) 120.199i 0.237548i
\(507\) 406.293 662.429i 0.801367 1.30657i
\(508\) 461.013 0.907506
\(509\) 720.090i 1.41472i 0.706856 + 0.707358i \(0.250113\pi\)
−0.706856 + 0.707358i \(0.749887\pi\)
\(510\) 0.233539 + 0.143238i 0.000457919 + 0.000280859i
\(511\) 130.794 0.255958
\(512\) 22.6274i 0.0441942i
\(513\) 159.265 + 12.7222i 0.310458 + 0.0247995i
\(514\) −155.626 −0.302775
\(515\) 136.717i 0.265469i
\(516\) −189.537 + 309.026i −0.367320 + 0.598887i
\(517\) −915.379 −1.77056
\(518\) 177.222i 0.342127i
\(519\) −5.72226 3.50968i −0.0110255 0.00676238i
\(520\) 130.849 0.251632
\(521\) 139.098i 0.266983i −0.991050 0.133491i \(-0.957381\pi\)
0.991050 0.133491i \(-0.0426188\pi\)
\(522\) 260.748 + 512.736i 0.499517 + 0.982252i
\(523\) −665.486 −1.27244 −0.636220 0.771508i \(-0.719503\pi\)
−0.636220 + 0.771508i \(0.719503\pi\)
\(524\) 130.546i 0.249134i
\(525\) 13.8646 22.6051i 0.0264087 0.0430573i
\(526\) 526.914 1.00174
\(527\) 1.18909i 0.00225634i
\(528\) 181.287 + 111.190i 0.343346 + 0.210587i
\(529\) −23.0000 −0.0434783
\(530\) 68.8393i 0.129886i
\(531\) −547.583 + 278.469i −1.03123 + 0.524424i
\(532\) −20.9229 −0.0393287
\(533\) 385.938i 0.724086i
\(534\) 62.5702 102.016i 0.117173 0.191041i
\(535\) −327.232 −0.611648
\(536\) 284.866i 0.531467i
\(537\) 220.048 + 134.963i 0.409772 + 0.251329i
\(538\) −86.3014 −0.160412
\(539\) 813.009i 1.50836i
\(540\) 9.61475 120.364i 0.0178051 0.222897i
\(541\) 673.074 1.24413 0.622065 0.782966i \(-0.286294\pi\)
0.622065 + 0.782966i \(0.286294\pi\)
\(542\) 691.560i 1.27594i
\(543\) 68.3564 111.450i 0.125887 0.205248i
\(544\) −0.163362 −0.000300298
\(545\) 109.325i 0.200597i
\(546\) 132.279 + 81.1316i 0.242269 + 0.148593i
\(547\) −298.530 −0.545759 −0.272880 0.962048i \(-0.587976\pi\)
−0.272880 + 0.962048i \(0.587976\pi\)
\(548\) 246.487i 0.449793i
\(549\) −5.63100 11.0728i −0.0102568 0.0201691i
\(550\) 125.316 0.227848
\(551\) 267.437i 0.485366i
\(552\) 21.2761 34.6890i 0.0385436 0.0628424i
\(553\) −7.90286 −0.0142909
\(554\) 452.191i 0.816230i
\(555\) 405.338 + 248.609i 0.730338 + 0.447944i
\(556\) 438.344 0.788389
\(557\) 152.164i 0.273185i 0.990627 + 0.136592i \(0.0436150\pi\)
−0.990627 + 0.136592i \(0.956385\pi\)
\(558\) 467.143 237.562i 0.837174 0.425738i
\(559\) −1250.03 −2.23619
\(560\) 15.8124i 0.0282365i
\(561\) −0.802753 + 1.30883i −0.00143093 + 0.00233302i
\(562\) −345.085 −0.614031
\(563\) 216.421i 0.384407i 0.981355 + 0.192203i \(0.0615633\pi\)
−0.981355 + 0.192203i \(0.938437\pi\)
\(564\) −264.175 162.028i −0.468395 0.287284i
\(565\) 285.075 0.504557
\(566\) 441.992i 0.780905i
\(567\) 84.3508 115.718i 0.148767 0.204089i
\(568\) 159.118 0.280138
\(569\) 168.117i 0.295460i −0.989028 0.147730i \(-0.952803\pi\)
0.989028 0.147730i \(-0.0471966\pi\)
\(570\) −29.3509 + 47.8543i −0.0514928 + 0.0839550i
\(571\) 17.0074 0.0297853 0.0148926 0.999889i \(-0.495259\pi\)
0.0148926 + 0.999889i \(0.495259\pi\)
\(572\) 733.317i 1.28202i
\(573\) 498.785 + 305.924i 0.870480 + 0.533899i
\(574\) 46.6387 0.0812521
\(575\) 23.9792i 0.0417029i
\(576\) 32.6372 + 64.1780i 0.0566618 + 0.111420i
\(577\) 955.512 1.65600 0.828000 0.560728i \(-0.189478\pi\)
0.828000 + 0.560728i \(0.189478\pi\)
\(578\) 408.707i 0.707105i
\(579\) 518.530 845.422i 0.895560 1.46014i
\(580\) −202.115 −0.348473
\(581\) 37.1885i 0.0640077i
\(582\) 208.698 + 128.002i 0.358588 + 0.219935i
\(583\) −385.798 −0.661745
\(584\) 209.257i 0.358318i
\(585\) 371.125 188.733i 0.634401 0.322620i
\(586\) 621.503 1.06059
\(587\) 727.196i 1.23883i 0.785062 + 0.619417i \(0.212631\pi\)
−0.785062 + 0.619417i \(0.787369\pi\)
\(588\) 143.908 234.631i 0.244742 0.399032i
\(589\) −243.656 −0.413677
\(590\) 215.851i 0.365849i
\(591\) −234.506 143.831i −0.396795 0.243369i
\(592\) −283.536 −0.478947
\(593\) 335.046i 0.565002i 0.959267 + 0.282501i \(0.0911641\pi\)
−0.959267 + 0.282501i \(0.908836\pi\)
\(594\) 674.560 + 53.8841i 1.13562 + 0.0907140i
\(595\) −0.114160 −0.000191866
\(596\) 169.214i 0.283916i
\(597\) 9.69699 15.8102i 0.0162429 0.0264827i
\(598\) 140.319 0.234648
\(599\) 228.357i 0.381230i −0.981665 0.190615i \(-0.938952\pi\)
0.981665 0.190615i \(-0.0610482\pi\)
\(600\) 36.1658 + 22.1819i 0.0602763 + 0.0369698i
\(601\) 710.722 1.18257 0.591283 0.806464i \(-0.298622\pi\)
0.591283 + 0.806464i \(0.298622\pi\)
\(602\) 151.060i 0.250930i
\(603\) 410.884 + 807.964i 0.681399 + 1.33991i
\(604\) 58.4239 0.0967284
\(605\) 431.749i 0.713635i
\(606\) 151.388 246.827i 0.249816 0.407305i
\(607\) 690.106 1.13691 0.568456 0.822713i \(-0.307541\pi\)
0.568456 + 0.822713i \(0.307541\pi\)
\(608\) 33.4744i 0.0550566i
\(609\) −204.324 125.320i −0.335507 0.205779i
\(610\) 4.36478 0.00715538
\(611\) 1068.61i 1.74894i
\(612\) −0.463343 + 0.235629i −0.000757096 + 0.000385015i
\(613\) −812.071 −1.32475 −0.662374 0.749173i \(-0.730451\pi\)
−0.662374 + 0.749173i \(0.730451\pi\)
\(614\) 208.014i 0.338785i
\(615\) 65.4253 106.671i 0.106383 0.173449i
\(616\) −88.6178 −0.143860
\(617\) 1026.40i 1.66354i 0.555120 + 0.831770i \(0.312672\pi\)
−0.555120 + 0.831770i \(0.687328\pi\)
\(618\) −221.123 135.623i −0.357804 0.219455i
\(619\) −682.233 −1.10215 −0.551077 0.834455i \(-0.685783\pi\)
−0.551077 + 0.834455i \(0.685783\pi\)
\(620\) 184.142i 0.297004i
\(621\) 10.3107 129.076i 0.0166033 0.207852i
\(622\) −850.809 −1.36786
\(623\) 49.8681i 0.0800451i
\(624\) −129.802 + 211.632i −0.208016 + 0.339154i
\(625\) 25.0000 0.0400000
\(626\) 125.095i 0.199833i
\(627\) −268.191 164.492i −0.427737 0.262347i
\(628\) −538.503 −0.857488
\(629\) 2.04703i 0.00325443i
\(630\) 22.8074 + 44.8486i 0.0362023 + 0.0711883i
\(631\) 19.9854 0.0316726 0.0158363 0.999875i \(-0.494959\pi\)
0.0158363 + 0.999875i \(0.494959\pi\)
\(632\) 12.6438i 0.0200059i
\(633\) 490.373 799.514i 0.774680 1.26306i
\(634\) −616.511 −0.972415
\(635\) 515.428i 0.811698i
\(636\) −111.340 68.2888i −0.175062 0.107372i
\(637\) 949.098 1.48995
\(638\) 1132.71i 1.77541i
\(639\) 451.306 229.508i 0.706270 0.359168i
\(640\) −25.2982 −0.0395285
\(641\) 78.5394i 0.122526i 0.998122 + 0.0612632i \(0.0195129\pi\)
−0.998122 + 0.0612632i \(0.980487\pi\)
\(642\) 324.615 529.259i 0.505630 0.824391i
\(643\) 947.424 1.47344 0.736722 0.676196i \(-0.236373\pi\)
0.736722 + 0.676196i \(0.236373\pi\)
\(644\) 16.9569i 0.0263306i
\(645\) −345.501 211.909i −0.535661 0.328541i
\(646\) 0.241674 0.000374108
\(647\) 405.423i 0.626619i −0.949651 0.313310i \(-0.898562\pi\)
0.949651 0.313310i \(-0.101438\pi\)
\(648\) 185.137 + 134.952i 0.285706 + 0.208260i
\(649\) 1209.70 1.86394
\(650\) 146.293i 0.225066i
\(651\) −114.176 + 186.155i −0.175386 + 0.285953i
\(652\) 592.382 0.908561
\(653\) 953.530i 1.46023i 0.683325 + 0.730115i \(0.260533\pi\)
−0.683325 + 0.730115i \(0.739467\pi\)
\(654\) 176.821 + 108.451i 0.270369 + 0.165827i
\(655\) −145.955 −0.222832
\(656\) 74.6170i 0.113746i
\(657\) 301.828 + 593.515i 0.459403 + 0.903372i
\(658\) 129.136 0.196255
\(659\) 784.567i 1.19054i −0.803525 0.595271i \(-0.797045\pi\)
0.803525 0.595271i \(-0.202955\pi\)
\(660\) −124.314 + 202.685i −0.188355 + 0.307098i
\(661\) −525.618 −0.795186 −0.397593 0.917562i \(-0.630154\pi\)
−0.397593 + 0.917562i \(0.630154\pi\)
\(662\) 431.621i 0.651995i
\(663\) −1.52791 0.937126i −0.00230454 0.00141346i
\(664\) 59.4977 0.0896050
\(665\) 23.3925i 0.0351767i
\(666\) −804.192 + 408.966i −1.20750 + 0.614062i
\(667\) −216.744 −0.324953
\(668\) 279.955i 0.419094i
\(669\) 115.002 187.502i 0.171902 0.280273i
\(670\) −318.490 −0.475358
\(671\) 24.4616i 0.0364555i
\(672\) −25.5747 15.6860i −0.0380577 0.0233422i
\(673\) 124.971 0.185693 0.0928465 0.995680i \(-0.470403\pi\)
0.0928465 + 0.995680i \(0.470403\pi\)
\(674\) 314.163i 0.466117i
\(675\) 134.571 + 10.7496i 0.199365 + 0.0159254i
\(676\) −518.068 −0.766372
\(677\) 867.241i 1.28101i 0.767956 + 0.640503i \(0.221274\pi\)
−0.767956 + 0.640503i \(0.778726\pi\)
\(678\) −282.795 + 461.075i −0.417102 + 0.680052i
\(679\) −102.017 −0.150246
\(680\) 0.182644i 0.000268595i
\(681\) 139.139 + 85.3395i 0.204316 + 0.125315i
\(682\) −1031.99 −1.51319
\(683\) 765.086i 1.12018i 0.828430 + 0.560092i \(0.189234\pi\)
−0.828430 + 0.560092i \(0.810766\pi\)
\(684\) −48.2827 94.9433i −0.0705887 0.138806i
\(685\) −275.581 −0.402307
\(686\) 237.202i 0.345775i
\(687\) −164.026 + 267.432i −0.238757 + 0.389275i
\(688\) 241.680 0.351280
\(689\) 450.376i 0.653667i
\(690\) 38.7835 + 23.7874i 0.0562080 + 0.0344745i
\(691\) 896.181 1.29693 0.648467 0.761243i \(-0.275411\pi\)
0.648467 + 0.761243i \(0.275411\pi\)
\(692\) 4.47522i 0.00646708i
\(693\) −251.346 + 127.820i −0.362693 + 0.184445i
\(694\) 929.113 1.33878
\(695\) 490.084i 0.705157i
\(696\) 200.498 326.897i 0.288072 0.469679i
\(697\) −0.538709 −0.000772897
\(698\) 579.191i 0.829787i
\(699\) −186.557 114.422i −0.266891 0.163694i
\(700\) −17.6788 −0.0252555
\(701\) 90.6113i 0.129260i −0.997909 0.0646300i \(-0.979413\pi\)
0.997909 0.0646300i \(-0.0205867\pi\)
\(702\) −62.9038 + 787.475i −0.0896066 + 1.12176i
\(703\) 419.456 0.596666
\(704\) 141.779i 0.201391i
\(705\) 181.153 295.356i 0.256955 0.418945i
\(706\) 352.751 0.499648
\(707\) 120.656i 0.170659i
\(708\) 349.114 + 214.125i 0.493099 + 0.302436i
\(709\) −393.144 −0.554505 −0.277253 0.960797i \(-0.589424\pi\)
−0.277253 + 0.960797i \(0.589424\pi\)
\(710\) 177.900i 0.250563i
\(711\) −18.2370 35.8614i −0.0256498 0.0504380i
\(712\) −79.7838 −0.112056
\(713\) 197.471i 0.276958i
\(714\) 0.113247 0.184641i 0.000158609 0.000258600i
\(715\) −819.874 −1.14668
\(716\) 172.093i 0.240353i
\(717\) 1026.15 + 629.379i 1.43118 + 0.877794i
\(718\) −471.580 −0.656797
\(719\) 924.192i 1.28539i −0.766124 0.642693i \(-0.777817\pi\)
0.766124 0.642693i \(-0.222183\pi\)
\(720\) −71.7532 + 36.4895i −0.0996572 + 0.0506799i
\(721\) 108.091 0.149918
\(722\) 461.010i 0.638518i
\(723\) −117.969 + 192.339i −0.163166 + 0.266029i
\(724\) −87.1618 −0.120389
\(725\) 225.971i 0.311684i
\(726\) −698.304 428.296i −0.961851 0.589940i
\(727\) 1152.02 1.58463 0.792314 0.610114i \(-0.208876\pi\)
0.792314 + 0.610114i \(0.208876\pi\)
\(728\) 103.452i 0.142104i
\(729\) 719.756 + 115.727i 0.987319 + 0.158748i
\(730\) −233.957 −0.320489
\(731\) 1.74485i 0.00238693i
\(732\) −4.32988 + 7.05953i −0.00591513 + 0.00964416i
\(733\) −624.542 −0.852035 −0.426017 0.904715i \(-0.640084\pi\)
−0.426017 + 0.904715i \(0.640084\pi\)
\(734\) 203.756i 0.277596i
\(735\) 262.325 + 160.894i 0.356905 + 0.218904i
\(736\) −27.1293 −0.0368605
\(737\) 1784.92i 2.42187i
\(738\) 107.626 + 211.636i 0.145834 + 0.286769i
\(739\) −858.733 −1.16202 −0.581010 0.813896i \(-0.697342\pi\)
−0.581010 + 0.813896i \(0.697342\pi\)
\(740\) 317.003i 0.428383i
\(741\) 192.026 313.084i 0.259144 0.422515i
\(742\) 54.4258 0.0733501
\(743\) 1376.70i 1.85289i −0.376429 0.926445i \(-0.622848\pi\)
0.376429 0.926445i \(-0.377152\pi\)
\(744\) −297.829 182.670i −0.400308 0.245524i
\(745\) −189.187 −0.253942
\(746\) 698.726i 0.936630i
\(747\) 168.753 85.8180i 0.225907 0.114883i
\(748\) 1.02360 0.00136845
\(749\) 258.716i 0.345415i
\(750\) −24.8001 + 40.4346i −0.0330668 + 0.0539128i
\(751\) −841.206 −1.12011 −0.560057 0.828454i \(-0.689221\pi\)
−0.560057 + 0.828454i \(0.689221\pi\)
\(752\) 206.604i 0.274739i
\(753\) −243.679 149.457i −0.323610 0.198483i
\(754\) 1322.32 1.75374
\(755\) 65.3199i 0.0865165i
\(756\) −95.1625 7.60162i −0.125876 0.0100551i
\(757\) 21.0572 0.0278167 0.0139083 0.999903i \(-0.495573\pi\)
0.0139083 + 0.999903i \(0.495573\pi\)
\(758\) 754.713i 0.995663i
\(759\) −133.312 + 217.355i −0.175642 + 0.286370i
\(760\) 37.4255 0.0492441
\(761\) 209.778i 0.275661i 0.990456 + 0.137830i \(0.0440129\pi\)
−0.990456 + 0.137830i \(0.955987\pi\)
\(762\) −833.646 511.307i −1.09402 0.671006i
\(763\) −86.4350 −0.113283
\(764\) 390.086i 0.510584i
\(765\) −0.263442 0.518033i −0.000344368 0.000677167i
\(766\) 346.957 0.452946
\(767\) 1412.19i 1.84119i
\(768\) 25.0959 40.9169i 0.0326770 0.0532773i
\(769\) −217.912 −0.283370 −0.141685 0.989912i \(-0.545252\pi\)
−0.141685 + 0.989912i \(0.545252\pi\)
\(770\) 99.0778i 0.128672i
\(771\) 281.417 + 172.604i 0.365003 + 0.223870i
\(772\) −661.181 −0.856452
\(773\) 1256.63i 1.62565i 0.582507 + 0.812826i \(0.302072\pi\)
−0.582507 + 0.812826i \(0.697928\pi\)
\(774\) 685.476 348.594i 0.885628 0.450379i
\(775\) −205.878 −0.265648
\(776\) 163.217i 0.210331i
\(777\) 196.555 320.468i 0.252967 0.412443i
\(778\) −168.808 −0.216977
\(779\) 110.387i 0.141703i
\(780\) −236.612 145.123i −0.303349 0.186055i
\(781\) −997.007 −1.27658
\(782\) 0.195864i 0.000250466i
\(783\) 97.1640 1216.37i 0.124092 1.55347i
\(784\) −183.498 −0.234054
\(785\) 602.064i 0.766961i
\(786\) 144.788