Properties

Label 105.4.g.b.104.11
Level $105$
Weight $4$
Character 105.104
Analytic conductor $6.195$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.19520055060\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 104.11
Character \(\chi\) \(=\) 105.104
Dual form 105.4.g.b.104.12

$q$-expansion

\(f(q)\) \(=\) \(q-3.23327 q^{2} +(3.88311 - 3.45274i) q^{3} +2.45405 q^{4} +(-8.12252 + 7.68276i) q^{5} +(-12.5552 + 11.1637i) q^{6} +(17.9067 - 4.72745i) q^{7} +17.9316 q^{8} +(3.15713 - 26.8148i) q^{9} +O(q^{10})\) \(q-3.23327 q^{2} +(3.88311 - 3.45274i) q^{3} +2.45405 q^{4} +(-8.12252 + 7.68276i) q^{5} +(-12.5552 + 11.1637i) q^{6} +(17.9067 - 4.72745i) q^{7} +17.9316 q^{8} +(3.15713 - 26.8148i) q^{9} +(26.2623 - 24.8404i) q^{10} +0.605380i q^{11} +(9.52936 - 8.47321i) q^{12} -12.8386 q^{13} +(-57.8974 + 15.2851i) q^{14} +(-5.01406 + 57.8780i) q^{15} -77.6100 q^{16} -117.765i q^{17} +(-10.2079 + 86.6995i) q^{18} -98.5363i q^{19} +(-19.9331 + 18.8539i) q^{20} +(53.2112 - 80.1846i) q^{21} -1.95736i q^{22} +136.085 q^{23} +(69.6303 - 61.9131i) q^{24} +(6.95051 - 124.807i) q^{25} +41.5106 q^{26} +(-80.3251 - 115.026i) q^{27} +(43.9440 - 11.6014i) q^{28} +77.5484i q^{29} +(16.2118 - 187.135i) q^{30} -131.050i q^{31} +107.482 q^{32} +(2.09022 + 2.35076i) q^{33} +380.766i q^{34} +(-109.128 + 175.972i) q^{35} +(7.74776 - 65.8048i) q^{36} -260.419i q^{37} +318.595i q^{38} +(-49.8536 + 44.3283i) q^{39} +(-145.649 + 137.764i) q^{40} +58.0698 q^{41} +(-172.046 + 259.259i) q^{42} +519.487i q^{43} +1.48563i q^{44} +(180.368 + 242.059i) q^{45} -440.001 q^{46} +104.603i q^{47} +(-301.369 + 267.968i) q^{48} +(298.302 - 169.306i) q^{49} +(-22.4729 + 403.534i) q^{50} +(-406.612 - 457.294i) q^{51} -31.5065 q^{52} +550.436 q^{53} +(259.713 + 371.909i) q^{54} +(-4.65099 - 4.91721i) q^{55} +(321.096 - 84.7705i) q^{56} +(-340.221 - 382.628i) q^{57} -250.735i q^{58} -498.426 q^{59} +(-12.3048 + 142.035i) q^{60} +172.038i q^{61} +423.720i q^{62} +(-70.2315 - 495.090i) q^{63} +273.362 q^{64} +(104.282 - 98.6356i) q^{65} +(-6.75826 - 7.60065i) q^{66} +622.829i q^{67} -289.001i q^{68} +(528.435 - 469.868i) q^{69} +(352.840 - 568.965i) q^{70} +151.768i q^{71} +(56.6123 - 480.831i) q^{72} -242.271 q^{73} +842.005i q^{74} +(-403.936 - 508.636i) q^{75} -241.813i q^{76} +(2.86190 + 10.8404i) q^{77} +(161.190 - 143.325i) q^{78} +94.6776 q^{79} +(630.389 - 596.259i) q^{80} +(-709.065 - 169.316i) q^{81} -187.756 q^{82} -779.959i q^{83} +(130.583 - 196.777i) q^{84} +(904.759 + 956.547i) q^{85} -1679.64i q^{86} +(267.755 + 301.129i) q^{87} +10.8554i q^{88} -1000.67 q^{89} +(-583.178 - 782.643i) q^{90} +(-229.897 + 60.6937i) q^{91} +333.961 q^{92} +(-452.482 - 508.882i) q^{93} -338.211i q^{94} +(757.030 + 800.363i) q^{95} +(417.364 - 371.107i) q^{96} +1127.53 q^{97} +(-964.493 + 547.413i) q^{98} +(16.2331 + 1.91126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q + 184q^{4} + 4q^{9} + O(q^{10}) \) \( 40q + 184q^{4} + 4q^{9} - 188q^{15} + 184q^{16} + 148q^{21} + 712q^{25} - 336q^{30} - 1520q^{36} + 644q^{39} - 1488q^{46} - 1496q^{49} - 220q^{51} + 1984q^{60} + 40q^{64} - 3000q^{70} - 1192q^{79} + 4636q^{81} - 2192q^{84} + 4808q^{85} - 4408q^{91} + 5276q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.23327 −1.14313 −0.571567 0.820555i \(-0.693664\pi\)
−0.571567 + 0.820555i \(0.693664\pi\)
\(3\) 3.88311 3.45274i 0.747305 0.664481i
\(4\) 2.45405 0.306756
\(5\) −8.12252 + 7.68276i −0.726500 + 0.687167i
\(6\) −12.5552 + 11.1637i −0.854271 + 0.759591i
\(7\) 17.9067 4.72745i 0.966873 0.255258i
\(8\) 17.9316 0.792471
\(9\) 3.15713 26.8148i 0.116931 0.993140i
\(10\) 26.2623 24.8404i 0.830487 0.785524i
\(11\) 0.605380i 0.0165935i 0.999966 + 0.00829677i \(0.00264098\pi\)
−0.999966 + 0.00829677i \(0.997359\pi\)
\(12\) 9.52936 8.47321i 0.229241 0.203834i
\(13\) −12.8386 −0.273906 −0.136953 0.990578i \(-0.543731\pi\)
−0.136953 + 0.990578i \(0.543731\pi\)
\(14\) −57.8974 + 15.2851i −1.10527 + 0.291794i
\(15\) −5.01406 + 57.8780i −0.0863083 + 0.996268i
\(16\) −77.6100 −1.21266
\(17\) 117.765i 1.68013i −0.542487 0.840064i \(-0.682517\pi\)
0.542487 0.840064i \(-0.317483\pi\)
\(18\) −10.2079 + 86.6995i −0.133668 + 1.13529i
\(19\) 98.5363i 1.18978i −0.803808 0.594889i \(-0.797196\pi\)
0.803808 0.594889i \(-0.202804\pi\)
\(20\) −19.9331 + 18.8539i −0.222858 + 0.210793i
\(21\) 53.2112 80.1846i 0.552935 0.833224i
\(22\) 1.95736i 0.0189687i
\(23\) 136.085 1.23373 0.616865 0.787069i \(-0.288403\pi\)
0.616865 + 0.787069i \(0.288403\pi\)
\(24\) 69.6303 61.9131i 0.592218 0.526581i
\(25\) 6.95051 124.807i 0.0556040 0.998453i
\(26\) 41.5106 0.313112
\(27\) −80.3251 115.026i −0.572539 0.819877i
\(28\) 43.9440 11.6014i 0.296594 0.0783021i
\(29\) 77.5484i 0.496565i 0.968688 + 0.248283i \(0.0798661\pi\)
−0.968688 + 0.248283i \(0.920134\pi\)
\(30\) 16.2118 187.135i 0.0986620 1.13887i
\(31\) 131.050i 0.759267i −0.925137 0.379633i \(-0.876050\pi\)
0.925137 0.379633i \(-0.123950\pi\)
\(32\) 107.482 0.593759
\(33\) 2.09022 + 2.35076i 0.0110261 + 0.0124004i
\(34\) 380.766i 1.92061i
\(35\) −109.128 + 175.972i −0.527028 + 0.849848i
\(36\) 7.74776 65.8048i 0.0358693 0.304652i
\(37\) 260.419i 1.15710i −0.815648 0.578548i \(-0.803619\pi\)
0.815648 0.578548i \(-0.196381\pi\)
\(38\) 318.595i 1.36008i
\(39\) −49.8536 + 44.3283i −0.204692 + 0.182005i
\(40\) −145.649 + 137.764i −0.575730 + 0.544559i
\(41\) 58.0698 0.221195 0.110597 0.993865i \(-0.464724\pi\)
0.110597 + 0.993865i \(0.464724\pi\)
\(42\) −172.046 + 259.259i −0.632079 + 0.952487i
\(43\) 519.487i 1.84235i 0.389150 + 0.921174i \(0.372769\pi\)
−0.389150 + 0.921174i \(0.627231\pi\)
\(44\) 1.48563i 0.00509018i
\(45\) 180.368 + 242.059i 0.597503 + 0.801867i
\(46\) −440.001 −1.41032
\(47\) 104.603i 0.324638i 0.986738 + 0.162319i \(0.0518973\pi\)
−0.986738 + 0.162319i \(0.948103\pi\)
\(48\) −301.369 + 267.968i −0.906225 + 0.805787i
\(49\) 298.302 169.306i 0.869687 0.493604i
\(50\) −22.4729 + 403.534i −0.0635629 + 1.14137i
\(51\) −406.612 457.294i −1.11641 1.25557i
\(52\) −31.5065 −0.0840225
\(53\) 550.436 1.42657 0.713285 0.700874i \(-0.247206\pi\)
0.713285 + 0.700874i \(0.247206\pi\)
\(54\) 259.713 + 371.909i 0.654490 + 0.937230i
\(55\) −4.65099 4.91721i −0.0114025 0.0120552i
\(56\) 321.096 84.7705i 0.766218 0.202285i
\(57\) −340.221 382.628i −0.790584 0.889127i
\(58\) 250.735i 0.567641i
\(59\) −498.426 −1.09982 −0.549911 0.835223i \(-0.685338\pi\)
−0.549911 + 0.835223i \(0.685338\pi\)
\(60\) −12.3048 + 142.035i −0.0264756 + 0.305612i
\(61\) 172.038i 0.361101i 0.983566 + 0.180551i \(0.0577880\pi\)
−0.983566 + 0.180551i \(0.942212\pi\)
\(62\) 423.720i 0.867944i
\(63\) −70.2315 495.090i −0.140450 0.990088i
\(64\) 273.362 0.533910
\(65\) 104.282 98.6356i 0.198993 0.188219i
\(66\) −6.75826 7.60065i −0.0126043 0.0141754i
\(67\) 622.829i 1.13568i 0.823139 + 0.567840i \(0.192221\pi\)
−0.823139 + 0.567840i \(0.807779\pi\)
\(68\) 289.001i 0.515390i
\(69\) 528.435 469.868i 0.921973 0.819789i
\(70\) 352.840 568.965i 0.602464 0.971490i
\(71\) 151.768i 0.253684i 0.991923 + 0.126842i \(0.0404842\pi\)
−0.991923 + 0.126842i \(0.959516\pi\)
\(72\) 56.6123 480.831i 0.0926642 0.787034i
\(73\) −242.271 −0.388435 −0.194217 0.980959i \(-0.562217\pi\)
−0.194217 + 0.980959i \(0.562217\pi\)
\(74\) 842.005i 1.32272i
\(75\) −403.936 508.636i −0.621899 0.783097i
\(76\) 241.813i 0.364972i
\(77\) 2.86190 + 10.8404i 0.00423564 + 0.0160439i
\(78\) 161.190 143.325i 0.233990 0.208057i
\(79\) 94.6776 0.134836 0.0674181 0.997725i \(-0.478524\pi\)
0.0674181 + 0.997725i \(0.478524\pi\)
\(80\) 630.389 596.259i 0.880995 0.833297i
\(81\) −709.065 169.316i −0.972654 0.232257i
\(82\) −187.756 −0.252855
\(83\) 779.959i 1.03147i −0.856750 0.515733i \(-0.827520\pi\)
0.856750 0.515733i \(-0.172480\pi\)
\(84\) 130.583 196.777i 0.169616 0.255597i
\(85\) 904.759 + 956.547i 1.15453 + 1.22061i
\(86\) 1679.64i 2.10605i
\(87\) 267.755 + 301.129i 0.329958 + 0.371086i
\(88\) 10.8554i 0.0131499i
\(89\) −1000.67 −1.19180 −0.595902 0.803057i \(-0.703205\pi\)
−0.595902 + 0.803057i \(0.703205\pi\)
\(90\) −583.178 782.643i −0.683026 0.916642i
\(91\) −229.897 + 60.6937i −0.264832 + 0.0699168i
\(92\) 333.961 0.378454
\(93\) −452.482 508.882i −0.504518 0.567404i
\(94\) 338.211i 0.371104i
\(95\) 757.030 + 800.363i 0.817576 + 0.864373i
\(96\) 417.364 371.107i 0.443720 0.394542i
\(97\) 1127.53 1.18024 0.590120 0.807316i \(-0.299080\pi\)
0.590120 + 0.807316i \(0.299080\pi\)
\(98\) −964.493 + 547.413i −0.994169 + 0.564256i
\(99\) 16.2331 + 1.91126i 0.0164797 + 0.00194030i
\(100\) 17.0569 306.282i 0.0170569 0.306282i
\(101\) −485.611 −0.478416 −0.239208 0.970968i \(-0.576888\pi\)
−0.239208 + 0.970968i \(0.576888\pi\)
\(102\) 1314.69 + 1478.56i 1.27621 + 1.43528i
\(103\) 1560.10 1.49244 0.746218 0.665702i \(-0.231868\pi\)
0.746218 + 0.665702i \(0.231868\pi\)
\(104\) −230.216 −0.217063
\(105\) 183.830 + 1060.11i 0.170856 + 0.985296i
\(106\) −1779.71 −1.63076
\(107\) −756.538 −0.683526 −0.341763 0.939786i \(-0.611024\pi\)
−0.341763 + 0.939786i \(0.611024\pi\)
\(108\) −197.122 282.279i −0.175630 0.251503i
\(109\) −795.599 −0.699124 −0.349562 0.936913i \(-0.613670\pi\)
−0.349562 + 0.936913i \(0.613670\pi\)
\(110\) 15.0379 + 15.8987i 0.0130346 + 0.0137807i
\(111\) −899.159 1011.24i −0.768868 0.864704i
\(112\) −1389.74 + 366.897i −1.17249 + 0.309541i
\(113\) −391.491 −0.325915 −0.162957 0.986633i \(-0.552103\pi\)
−0.162957 + 0.986633i \(0.552103\pi\)
\(114\) 1100.03 + 1237.14i 0.903744 + 1.01639i
\(115\) −1105.36 + 1045.51i −0.896304 + 0.847778i
\(116\) 190.308i 0.152324i
\(117\) −40.5331 + 344.264i −0.0320281 + 0.272027i
\(118\) 1611.55 1.25724
\(119\) −556.727 2108.78i −0.428866 1.62447i
\(120\) −89.9099 + 1037.84i −0.0683968 + 0.789514i
\(121\) 1330.63 0.999725
\(122\) 556.245i 0.412788i
\(123\) 225.492 200.500i 0.165300 0.146980i
\(124\) 321.603i 0.232910i
\(125\) 902.403 + 1067.14i 0.645707 + 0.763585i
\(126\) 227.078 + 1600.76i 0.160553 + 1.13180i
\(127\) 1360.11i 0.950314i −0.879901 0.475157i \(-0.842391\pi\)
0.879901 0.475157i \(-0.157609\pi\)
\(128\) −1743.71 −1.20409
\(129\) 1793.65 + 2017.23i 1.22421 + 1.37680i
\(130\) −337.171 + 318.916i −0.227475 + 0.215160i
\(131\) 1235.28 0.823871 0.411935 0.911213i \(-0.364853\pi\)
0.411935 + 0.911213i \(0.364853\pi\)
\(132\) 5.12951 + 5.76888i 0.00338232 + 0.00380392i
\(133\) −465.825 1764.46i −0.303700 1.15036i
\(134\) 2013.77i 1.29824i
\(135\) 1536.16 + 317.179i 0.979342 + 0.202211i
\(136\) 2111.71i 1.33145i
\(137\) 141.306 0.0881213 0.0440606 0.999029i \(-0.485971\pi\)
0.0440606 + 0.999029i \(0.485971\pi\)
\(138\) −1708.57 + 1519.21i −1.05394 + 0.937130i
\(139\) 894.717i 0.545963i 0.962019 + 0.272982i \(0.0880098\pi\)
−0.962019 + 0.272982i \(0.911990\pi\)
\(140\) −267.806 + 431.844i −0.161669 + 0.260696i
\(141\) 361.168 + 406.187i 0.215715 + 0.242603i
\(142\) 490.709i 0.289995i
\(143\) 7.77222i 0.00454507i
\(144\) −245.025 + 2081.10i −0.141797 + 1.20434i
\(145\) −595.786 629.888i −0.341223 0.360754i
\(146\) 783.330 0.444033
\(147\) 573.771 1687.40i 0.321931 0.946763i
\(148\) 639.081i 0.354947i
\(149\) 2252.95i 1.23872i 0.785108 + 0.619359i \(0.212608\pi\)
−0.785108 + 0.619359i \(0.787392\pi\)
\(150\) 1306.03 + 1644.56i 0.710915 + 0.895185i
\(151\) −835.424 −0.450237 −0.225119 0.974331i \(-0.572277\pi\)
−0.225119 + 0.974331i \(0.572277\pi\)
\(152\) 1766.91i 0.942864i
\(153\) −3157.84 371.799i −1.66860 0.196459i
\(154\) −9.25331 35.0499i −0.00484190 0.0183403i
\(155\) 1006.82 + 1064.46i 0.521743 + 0.551607i
\(156\) −122.343 + 108.784i −0.0627904 + 0.0558313i
\(157\) −2999.64 −1.52483 −0.762413 0.647091i \(-0.775986\pi\)
−0.762413 + 0.647091i \(0.775986\pi\)
\(158\) −306.118 −0.154136
\(159\) 2137.41 1900.52i 1.06608 0.947929i
\(160\) −873.023 + 825.757i −0.431366 + 0.408012i
\(161\) 2436.85 643.337i 1.19286 0.314919i
\(162\) 2292.60 + 547.443i 1.11187 + 0.265501i
\(163\) 802.994i 0.385861i 0.981212 + 0.192930i \(0.0617992\pi\)
−0.981212 + 0.192930i \(0.938201\pi\)
\(164\) 142.506 0.0678529
\(165\) −35.0382 3.03541i −0.0165316 0.00143216i
\(166\) 2521.82i 1.17910i
\(167\) 1489.38i 0.690129i 0.938579 + 0.345065i \(0.112143\pi\)
−0.938579 + 0.345065i \(0.887857\pi\)
\(168\) 954.160 1437.83i 0.438185 0.660306i
\(169\) −2032.17 −0.924975
\(170\) −2925.33 3092.78i −1.31978 1.39532i
\(171\) −2642.23 311.092i −1.18162 0.139122i
\(172\) 1274.85i 0.565152i
\(173\) 263.075i 0.115614i −0.998328 0.0578069i \(-0.981589\pi\)
0.998328 0.0578069i \(-0.0184108\pi\)
\(174\) −865.724 973.633i −0.377186 0.424201i
\(175\) −465.556 2267.74i −0.201101 0.979570i
\(176\) 46.9836i 0.0201223i
\(177\) −1935.44 + 1720.94i −0.821903 + 0.730811i
\(178\) 3235.43 1.36239
\(179\) 347.625i 0.145155i −0.997363 0.0725774i \(-0.976878\pi\)
0.997363 0.0725774i \(-0.0231224\pi\)
\(180\) 442.631 + 594.025i 0.183288 + 0.245978i
\(181\) 2556.58i 1.04988i 0.851138 + 0.524942i \(0.175913\pi\)
−0.851138 + 0.524942i \(0.824087\pi\)
\(182\) 743.320 196.239i 0.302739 0.0799243i
\(183\) 594.002 + 668.042i 0.239945 + 0.269853i
\(184\) 2440.22 0.977694
\(185\) 2000.73 + 2115.25i 0.795118 + 0.840630i
\(186\) 1463.00 + 1645.35i 0.576732 + 0.648619i
\(187\) 71.2925 0.0278793
\(188\) 256.702i 0.0995846i
\(189\) −1982.14 1680.00i −0.762853 0.646572i
\(190\) −2447.69 2587.79i −0.934599 0.988095i
\(191\) 2990.51i 1.13291i 0.824093 + 0.566455i \(0.191685\pi\)
−0.824093 + 0.566455i \(0.808315\pi\)
\(192\) 1061.50 943.849i 0.398994 0.354773i
\(193\) 3949.63i 1.47306i 0.676406 + 0.736529i \(0.263537\pi\)
−0.676406 + 0.736529i \(0.736463\pi\)
\(194\) −3645.61 −1.34917
\(195\) 64.3734 743.071i 0.0236404 0.272884i
\(196\) 732.050 415.486i 0.266782 0.151416i
\(197\) −1583.28 −0.572610 −0.286305 0.958139i \(-0.592427\pi\)
−0.286305 + 0.958139i \(0.592427\pi\)
\(198\) −52.4862 6.17964i −0.0188385 0.00221802i
\(199\) 101.664i 0.0362151i −0.999836 0.0181075i \(-0.994236\pi\)
0.999836 0.0181075i \(-0.00576413\pi\)
\(200\) 124.633 2237.98i 0.0440646 0.791245i
\(201\) 2150.47 + 2418.51i 0.754638 + 0.848700i
\(202\) 1570.11 0.546894
\(203\) 366.606 + 1388.64i 0.126752 + 0.480115i
\(204\) −997.846 1122.22i −0.342467 0.385154i
\(205\) −471.673 + 446.136i −0.160698 + 0.151998i
\(206\) −5044.22 −1.70605
\(207\) 429.640 3649.10i 0.144261 1.22527i
\(208\) 996.402 0.332154
\(209\) 59.6519 0.0197426
\(210\) −594.371 3427.62i −0.195312 1.12633i
\(211\) 5047.18 1.64674 0.823370 0.567506i \(-0.192091\pi\)
0.823370 + 0.567506i \(0.192091\pi\)
\(212\) 1350.80 0.437610
\(213\) 524.017 + 589.334i 0.168568 + 0.189580i
\(214\) 2446.09 0.781362
\(215\) −3991.09 4219.54i −1.26600 1.33847i
\(216\) −1440.35 2062.59i −0.453721 0.649729i
\(217\) −619.532 2346.68i −0.193809 0.734114i
\(218\) 2572.39 0.799193
\(219\) −940.768 + 836.501i −0.290279 + 0.258107i
\(220\) −11.4138 12.0671i −0.00349780 0.00369801i
\(221\) 1511.93i 0.460197i
\(222\) 2907.23 + 3269.60i 0.878920 + 0.988473i
\(223\) 1866.03 0.560353 0.280177 0.959948i \(-0.409607\pi\)
0.280177 + 0.959948i \(0.409607\pi\)
\(224\) 1924.65 508.115i 0.574090 0.151562i
\(225\) −3324.72 580.407i −0.985102 0.171972i
\(226\) 1265.80 0.372565
\(227\) 2270.46i 0.663857i −0.943305 0.331929i \(-0.892301\pi\)
0.943305 0.331929i \(-0.107699\pi\)
\(228\) −834.919 938.988i −0.242517 0.272745i
\(229\) 998.351i 0.288091i 0.989571 + 0.144046i \(0.0460112\pi\)
−0.989571 + 0.144046i \(0.953989\pi\)
\(230\) 3573.92 3380.42i 1.02460 0.969124i
\(231\) 48.5422 + 32.2130i 0.0138261 + 0.00917516i
\(232\) 1390.56i 0.393513i
\(233\) 4098.89 1.15248 0.576238 0.817282i \(-0.304520\pi\)
0.576238 + 0.817282i \(0.304520\pi\)
\(234\) 131.054 1113.10i 0.0366124 0.310964i
\(235\) −803.642 849.642i −0.223080 0.235849i
\(236\) −1223.16 −0.337377
\(237\) 367.644 326.897i 0.100764 0.0895961i
\(238\) 1800.05 + 6818.28i 0.490252 + 1.85699i
\(239\) 4118.06i 1.11454i −0.830332 0.557270i \(-0.811849\pi\)
0.830332 0.557270i \(-0.188151\pi\)
\(240\) 389.141 4491.91i 0.104662 1.20813i
\(241\) 6644.14i 1.77588i −0.459961 0.887939i \(-0.652137\pi\)
0.459961 0.887939i \(-0.347863\pi\)
\(242\) −4302.30 −1.14282
\(243\) −3337.98 + 1790.75i −0.881200 + 0.472743i
\(244\) 422.190i 0.110770i
\(245\) −1122.23 + 3666.98i −0.292639 + 0.956223i
\(246\) −729.076 + 648.272i −0.188960 + 0.168017i
\(247\) 1265.07i 0.325887i
\(248\) 2349.93i 0.601697i
\(249\) −2693.00 3028.67i −0.685389 0.770820i
\(250\) −2917.72 3450.36i −0.738130 0.872880i
\(251\) −160.793 −0.0404349 −0.0202174 0.999796i \(-0.506436\pi\)
−0.0202174 + 0.999796i \(0.506436\pi\)
\(252\) −172.352 1214.98i −0.0430839 0.303716i
\(253\) 82.3834i 0.0204719i
\(254\) 4397.59i 1.08634i
\(255\) 6815.99 + 590.480i 1.67386 + 0.145009i
\(256\) 3450.99 0.842527
\(257\) 587.416i 0.142576i 0.997456 + 0.0712879i \(0.0227109\pi\)
−0.997456 + 0.0712879i \(0.977289\pi\)
\(258\) −5799.37 6522.24i −1.39943 1.57386i
\(259\) −1231.12 4663.25i −0.295358 1.11877i
\(260\) 255.912 242.057i 0.0610423 0.0577374i
\(261\) 2079.44 + 244.831i 0.493159 + 0.0580637i
\(262\) −3994.00 −0.941795
\(263\) 4760.99 1.11626 0.558128 0.829755i \(-0.311520\pi\)
0.558128 + 0.829755i \(0.311520\pi\)
\(264\) 37.4810 + 42.1528i 0.00873785 + 0.00982699i
\(265\) −4470.93 + 4228.87i −1.03640 + 0.980292i
\(266\) 1506.14 + 5704.99i 0.347170 + 1.31502i
\(267\) −3885.70 + 3455.05i −0.890641 + 0.791930i
\(268\) 1528.45i 0.348377i
\(269\) 5639.75 1.27830 0.639148 0.769084i \(-0.279287\pi\)
0.639148 + 0.769084i \(0.279287\pi\)
\(270\) −4966.81 1025.53i −1.11952 0.231154i
\(271\) 2250.90i 0.504547i 0.967656 + 0.252274i \(0.0811783\pi\)
−0.967656 + 0.252274i \(0.918822\pi\)
\(272\) 9139.74i 2.03742i
\(273\) −683.156 + 1029.46i −0.151452 + 0.228225i
\(274\) −456.882 −0.100734
\(275\) 75.5555 + 4.20770i 0.0165679 + 0.000922668i
\(276\) 1296.81 1153.08i 0.282821 0.251476i
\(277\) 6323.83i 1.37170i −0.727741 0.685852i \(-0.759430\pi\)
0.727741 0.685852i \(-0.240570\pi\)
\(278\) 2892.86i 0.624109i
\(279\) −3514.08 413.742i −0.754058 0.0887816i
\(280\) −1956.83 + 3155.45i −0.417654 + 0.673479i
\(281\) 7909.21i 1.67909i 0.543291 + 0.839544i \(0.317178\pi\)
−0.543291 + 0.839544i \(0.682822\pi\)
\(282\) −1167.76 1313.31i −0.246592 0.277328i
\(283\) 1364.88 0.286692 0.143346 0.989673i \(-0.454214\pi\)
0.143346 + 0.989673i \(0.454214\pi\)
\(284\) 372.447i 0.0778193i
\(285\) 5703.08 + 494.067i 1.18534 + 0.102688i
\(286\) 25.1297i 0.00519563i
\(287\) 1039.84 274.522i 0.213867 0.0564617i
\(288\) 339.334 2882.10i 0.0694287 0.589686i
\(289\) −8955.57 −1.82283
\(290\) 1926.34 + 2036.60i 0.390064 + 0.412391i
\(291\) 4378.32 3893.07i 0.882000 0.784246i
\(292\) −594.547 −0.119155
\(293\) 6158.77i 1.22798i 0.789312 + 0.613992i \(0.210437\pi\)
−0.789312 + 0.613992i \(0.789563\pi\)
\(294\) −1855.16 + 5455.82i −0.368010 + 1.08228i
\(295\) 4048.47 3829.28i 0.799021 0.755761i
\(296\) 4669.71i 0.916965i
\(297\) 69.6342 48.6272i 0.0136047 0.00950046i
\(298\) 7284.41i 1.41602i
\(299\) −1747.14 −0.337926
\(300\) −991.279 1248.22i −0.190772 0.240220i
\(301\) 2455.85 + 9302.31i 0.470274 + 1.78132i
\(302\) 2701.15 0.514682
\(303\) −1885.68 + 1676.69i −0.357523 + 0.317898i
\(304\) 7647.41i 1.44279i
\(305\) −1321.72 1397.38i −0.248137 0.262340i
\(306\) 10210.2 + 1202.13i 1.90744 + 0.224579i
\(307\) 7256.37 1.34900 0.674500 0.738275i \(-0.264359\pi\)
0.674500 + 0.738275i \(0.264359\pi\)
\(308\) 7.02326 + 26.6029i 0.00129931 + 0.00492155i
\(309\) 6058.03 5386.61i 1.11530 0.991694i
\(310\) −3255.34 3441.67i −0.596422 0.630561i
\(311\) −8404.97 −1.53248 −0.766241 0.642553i \(-0.777875\pi\)
−0.766241 + 0.642553i \(0.777875\pi\)
\(312\) −893.954 + 794.876i −0.162212 + 0.144234i
\(313\) 3012.62 0.544035 0.272018 0.962292i \(-0.412309\pi\)
0.272018 + 0.962292i \(0.412309\pi\)
\(314\) 9698.67 1.74308
\(315\) 4374.12 + 3481.81i 0.782392 + 0.622786i
\(316\) 232.344 0.0413619
\(317\) 8375.12 1.48389 0.741946 0.670459i \(-0.233903\pi\)
0.741946 + 0.670459i \(0.233903\pi\)
\(318\) −6910.82 + 6144.88i −1.21868 + 1.08361i
\(319\) −46.9463 −0.00823977
\(320\) −2220.39 + 2100.17i −0.387886 + 0.366885i
\(321\) −2937.72 + 2612.13i −0.510803 + 0.454190i
\(322\) −7878.99 + 2080.08i −1.36360 + 0.359995i
\(323\) −11604.1 −1.99898
\(324\) −1740.08 415.509i −0.298368 0.0712464i
\(325\) −89.2346 + 1602.34i −0.0152303 + 0.273482i
\(326\) 2596.30i 0.441091i
\(327\) −3089.40 + 2747.00i −0.522459 + 0.464555i
\(328\) 1041.28 0.175290
\(329\) 494.507 + 1873.10i 0.0828664 + 0.313883i
\(330\) 113.288 + 9.81432i 0.0188979 + 0.00163715i
\(331\) −7389.43 −1.22707 −0.613535 0.789668i \(-0.710253\pi\)
−0.613535 + 0.789668i \(0.710253\pi\)
\(332\) 1914.06i 0.316409i
\(333\) −6983.07 822.176i −1.14916 0.135300i
\(334\) 4815.57i 0.788911i
\(335\) −4785.04 5058.93i −0.780402 0.825072i
\(336\) −4129.73 + 6223.13i −0.670521 + 1.01042i
\(337\) 7612.87i 1.23056i 0.788308 + 0.615281i \(0.210957\pi\)
−0.788308 + 0.615281i \(0.789043\pi\)
\(338\) 6570.56 1.05737
\(339\) −1520.20 + 1351.72i −0.243558 + 0.216564i
\(340\) 2220.32 + 2347.42i 0.354159 + 0.374431i
\(341\) 79.3350 0.0125989
\(342\) 8543.05 + 1005.85i 1.35075 + 0.159035i
\(343\) 4541.24 4441.93i 0.714880 0.699247i
\(344\) 9315.21i 1.46001i
\(345\) −682.340 + 7876.35i −0.106481 + 1.22913i
\(346\) 850.592i 0.132162i
\(347\) −2248.77 −0.347898 −0.173949 0.984755i \(-0.555653\pi\)
−0.173949 + 0.984755i \(0.555653\pi\)
\(348\) 657.084 + 738.987i 0.101217 + 0.113833i
\(349\) 4137.50i 0.634600i −0.948325 0.317300i \(-0.897224\pi\)
0.948325 0.317300i \(-0.102776\pi\)
\(350\) 1505.27 + 7332.21i 0.229886 + 1.11978i
\(351\) 1031.26 + 1476.76i 0.156822 + 0.224569i
\(352\) 65.0674i 0.00985257i
\(353\) 4970.30i 0.749412i 0.927144 + 0.374706i \(0.122256\pi\)
−0.927144 + 0.374706i \(0.877744\pi\)
\(354\) 6257.82 5564.26i 0.939546 0.835415i
\(355\) −1166.00 1232.74i −0.174323 0.184302i
\(356\) −2455.69 −0.365593
\(357\) −9442.93 6266.41i −1.39992 0.929002i
\(358\) 1123.97i 0.165932i
\(359\) 2942.19i 0.432543i −0.976333 0.216271i \(-0.930610\pi\)
0.976333 0.216271i \(-0.0693896\pi\)
\(360\) 3234.27 + 4340.50i 0.473503 + 0.635456i
\(361\) −2850.40 −0.415571
\(362\) 8266.11i 1.20016i
\(363\) 5167.00 4594.34i 0.747100 0.664298i
\(364\) −564.179 + 148.945i −0.0812390 + 0.0214474i
\(365\) 1967.85 1861.31i 0.282198 0.266919i
\(366\) −1920.57 2159.96i −0.274289 0.308478i
\(367\) −2416.72 −0.343738 −0.171869 0.985120i \(-0.554981\pi\)
−0.171869 + 0.985120i \(0.554981\pi\)
\(368\) −10561.6 −1.49609
\(369\) 183.334 1557.13i 0.0258645 0.219677i
\(370\) −6468.92 6839.19i −0.908927 0.960954i
\(371\) 9856.52 2602.16i 1.37931 0.364144i
\(372\) −1110.41 1248.82i −0.154764 0.174055i
\(373\) 4691.02i 0.651185i −0.945510 0.325592i \(-0.894436\pi\)
0.945510 0.325592i \(-0.105564\pi\)
\(374\) −230.508 −0.0318698
\(375\) 7188.70 + 1028.07i 0.989928 + 0.141571i
\(376\) 1875.70i 0.257266i
\(377\) 995.612i 0.136012i
\(378\) 6408.79 + 5431.90i 0.872044 + 0.739118i
\(379\) 736.245 0.0997846 0.0498923 0.998755i \(-0.484112\pi\)
0.0498923 + 0.998755i \(0.484112\pi\)
\(380\) 1857.79 + 1964.13i 0.250797 + 0.265152i
\(381\) −4696.10 5281.45i −0.631465 0.710175i
\(382\) 9669.14i 1.29507i
\(383\) 11813.2i 1.57605i −0.615641 0.788027i \(-0.711103\pi\)
0.615641 0.788027i \(-0.288897\pi\)
\(384\) −6771.02 + 6020.58i −0.899823 + 0.800095i
\(385\) −106.530 66.0639i −0.0141020 0.00874527i
\(386\) 12770.2i 1.68390i
\(387\) 13929.9 + 1640.09i 1.82971 + 0.215427i
\(388\) 2767.01 0.362046
\(389\) 3748.94i 0.488635i −0.969695 0.244318i \(-0.921436\pi\)
0.969695 0.244318i \(-0.0785639\pi\)
\(390\) −208.137 + 2402.55i −0.0270241 + 0.311943i
\(391\) 16026.1i 2.07282i
\(392\) 5349.03 3035.93i 0.689201 0.391167i
\(393\) 4796.74 4265.11i 0.615683 0.547446i
\(394\) 5119.18 0.654570
\(395\) −769.020 + 727.385i −0.0979585 + 0.0926549i
\(396\) 39.8370 + 4.69034i 0.00505526 + 0.000595198i
\(397\) 5770.01 0.729443 0.364721 0.931117i \(-0.381164\pi\)
0.364721 + 0.931117i \(0.381164\pi\)
\(398\) 328.709i 0.0413987i
\(399\) −7901.09 5243.24i −0.991352 0.657870i
\(400\) −539.429 + 9686.25i −0.0674286 + 1.21078i
\(401\) 6380.54i 0.794586i 0.917692 + 0.397293i \(0.130050\pi\)
−0.917692 + 0.397293i \(0.869950\pi\)
\(402\) −6953.05 7819.71i −0.862653 0.970179i
\(403\) 1682.49i 0.207968i
\(404\) −1191.71 −0.146757
\(405\) 7060.20 4072.31i 0.866233 0.499641i
\(406\) −1185.34 4489.85i −0.144895 0.548836i
\(407\) 157.652 0.0192003
\(408\) −7291.19 8200.00i −0.884724 0.995002i
\(409\) 5529.03i 0.668443i −0.942495 0.334221i \(-0.891527\pi\)
0.942495 0.334221i \(-0.108473\pi\)
\(410\) 1525.05 1442.48i 0.183699 0.173754i
\(411\) 548.708 487.894i 0.0658535 0.0585549i
\(412\) 3828.56 0.457814
\(413\) −8925.18 + 2356.28i −1.06339 + 0.280739i
\(414\) −1389.14 + 11798.5i −0.164910 + 1.40064i
\(415\) 5992.24 + 6335.23i 0.708789 + 0.749359i
\(416\) −1379.91 −0.162634
\(417\) 3089.23 + 3474.29i 0.362782 + 0.408001i
\(418\) −192.871 −0.0225685
\(419\) 4493.27 0.523892 0.261946 0.965083i \(-0.415636\pi\)
0.261946 + 0.965083i \(0.415636\pi\)
\(420\) 451.127 + 2601.56i 0.0524113 + 0.302246i
\(421\) −99.8897 −0.0115637 −0.00578186 0.999983i \(-0.501840\pi\)
−0.00578186 + 0.999983i \(0.501840\pi\)
\(422\) −16318.9 −1.88244
\(423\) 2804.92 + 330.246i 0.322411 + 0.0379601i
\(424\) 9870.18 1.13052
\(425\) −14697.8 818.525i −1.67753 0.0934219i
\(426\) −1694.29 1905.48i −0.192696 0.216715i
\(427\) 813.300 + 3080.64i 0.0921741 + 0.349139i
\(428\) −1856.58 −0.209676
\(429\) −26.8355 30.1804i −0.00302011 0.00339656i
\(430\) 12904.3 + 13642.9i 1.44721 + 1.53005i
\(431\) 13563.7i 1.51588i −0.652327 0.757938i \(-0.726207\pi\)
0.652327 0.757938i \(-0.273793\pi\)
\(432\) 6234.03 + 8927.14i 0.694294 + 0.994230i
\(433\) −10400.5 −1.15431 −0.577155 0.816634i \(-0.695837\pi\)
−0.577155 + 0.816634i \(0.695837\pi\)
\(434\) 2003.11 + 7587.45i 0.221550 + 0.839191i
\(435\) −4488.35 388.833i −0.494712 0.0428577i
\(436\) −1952.44 −0.214461
\(437\) 13409.4i 1.46786i
\(438\) 3041.76 2704.64i 0.331828 0.295051i
\(439\) 6478.07i 0.704286i 0.935946 + 0.352143i \(0.114547\pi\)
−0.935946 + 0.352143i \(0.885453\pi\)
\(440\) −83.3995 88.1733i −0.00903617 0.00955340i
\(441\) −3598.13 8533.44i −0.388525 0.921438i
\(442\) 4888.49i 0.526068i
\(443\) 8331.80 0.893579 0.446790 0.894639i \(-0.352567\pi\)
0.446790 + 0.894639i \(0.352567\pi\)
\(444\) −2206.58 2481.62i −0.235855 0.265254i
\(445\) 8127.93 7687.88i 0.865845 0.818968i
\(446\) −6033.39 −0.640559
\(447\) 7778.87 + 8748.47i 0.823105 + 0.925701i
\(448\) 4895.02 1292.30i 0.516223 0.136285i
\(449\) 5571.92i 0.585646i −0.956167 0.292823i \(-0.905405\pi\)
0.956167 0.292823i \(-0.0945947\pi\)
\(450\) 10749.7 + 1876.61i 1.12610 + 0.196588i
\(451\) 35.1543i 0.00367040i
\(452\) −960.739 −0.0999765
\(453\) −3244.05 + 2884.50i −0.336465 + 0.299174i
\(454\) 7341.01i 0.758878i
\(455\) 1401.05 2259.23i 0.144356 0.232779i
\(456\) −6100.69 6861.11i −0.626515 0.704607i
\(457\) 9668.94i 0.989702i 0.868978 + 0.494851i \(0.164777\pi\)
−0.868978 + 0.494851i \(0.835223\pi\)
\(458\) 3227.94i 0.329327i
\(459\) −13546.0 + 9459.47i −1.37750 + 0.961940i
\(460\) −2712.60 + 2565.74i −0.274947 + 0.260061i
\(461\) 9540.16 0.963838 0.481919 0.876216i \(-0.339940\pi\)
0.481919 + 0.876216i \(0.339940\pi\)
\(462\) −156.950 104.153i −0.0158051 0.0104884i
\(463\) 291.188i 0.0292282i 0.999893 + 0.0146141i \(0.00465198\pi\)
−0.999893 + 0.0146141i \(0.995348\pi\)
\(464\) 6018.54i 0.602163i
\(465\) 7584.90 + 657.092i 0.756433 + 0.0655310i
\(466\) −13252.8 −1.31744
\(467\) 12431.2i 1.23180i 0.787825 + 0.615899i \(0.211207\pi\)
−0.787825 + 0.615899i \(0.788793\pi\)
\(468\) −99.4702 + 844.840i −0.00982481 + 0.0834461i
\(469\) 2944.39 + 11152.8i 0.289892 + 1.09806i
\(470\) 2598.39 + 2747.12i 0.255011 + 0.269607i
\(471\) −11648.0 + 10357.0i −1.13951 + 1.01322i
\(472\) −8937.55 −0.871577
\(473\) −314.487 −0.0305711
\(474\) −1188.69 + 1056.95i −0.115187 + 0.102420i
\(475\) −12298.0 684.877i −1.18794 0.0661565i
\(476\) −1366.24 5175.07i −0.131558 0.498317i
\(477\) 1737.80 14759.8i 0.166810 1.41678i
\(478\) 13314.8i 1.27407i
\(479\) −2250.43 −0.214665 −0.107333 0.994223i \(-0.534231\pi\)
−0.107333 + 0.994223i \(0.534231\pi\)
\(480\) −538.921 + 6220.83i −0.0512464 + 0.591544i
\(481\) 3343.40i 0.316936i
\(482\) 21482.3i 2.03007i
\(483\) 7241.27 10912.0i 0.682173 1.02797i
\(484\) 3265.44 0.306672
\(485\) −9158.37 + 8662.53i −0.857444 + 0.811021i
\(486\) 10792.6 5789.98i 1.00733 0.540409i
\(487\) 18863.6i 1.75522i 0.479380 + 0.877608i \(0.340862\pi\)
−0.479380 + 0.877608i \(0.659138\pi\)
\(488\) 3084.91i 0.286162i
\(489\) 2772.53 + 3118.12i 0.256397 + 0.288356i
\(490\) 3628.47 11856.3i 0.334525 1.09309i
\(491\) 10861.4i 0.998309i −0.866513 0.499155i \(-0.833644\pi\)
0.866513 0.499155i \(-0.166356\pi\)
\(492\) 553.368 492.038i 0.0507068 0.0450869i
\(493\) 9132.48 0.834293
\(494\) 4090.30i 0.372533i
\(495\) −146.538 + 109.191i −0.0133058 + 0.00991469i
\(496\) 10170.8i 0.920730i
\(497\) 717.477 + 2717.68i 0.0647550 + 0.245281i
\(498\) 8707.20 + 9792.51i 0.783492 + 0.881151i
\(499\) 1749.79 0.156977 0.0784883 0.996915i \(-0.474991\pi\)
0.0784883 + 0.996915i \(0.474991\pi\)
\(500\) 2214.54 + 2618.82i 0.198075 + 0.234235i
\(501\) 5142.44 + 5783.43i 0.458578 + 0.515737i
\(502\) 519.887 0.0462225
\(503\) 12989.4i 1.15143i −0.817651 0.575715i \(-0.804724\pi\)
0.817651 0.575715i \(-0.195276\pi\)
\(504\) −1259.36 8877.75i −0.111302 0.784616i
\(505\) 3944.38 3730.83i 0.347569 0.328752i
\(506\) 266.368i 0.0234022i
\(507\) −7891.15 + 7016.56i −0.691239 + 0.614628i
\(508\) 3337.77i 0.291515i
\(509\) 4913.86 0.427904 0.213952 0.976844i \(-0.431366\pi\)
0.213952 + 0.976844i \(0.431366\pi\)
\(510\) −22038.0 1909.18i −1.91345 0.165765i
\(511\) −4338.29 + 1145.33i −0.375567 + 0.0991511i
\(512\) 2791.68 0.240969
\(513\) −11334.2 + 7914.93i −0.975472 + 0.681195i
\(514\) 1899.27i 0.162983i
\(515\) −12671.9 + 11985.8i −1.08425 + 1.02555i
\(516\) 4401.72 + 4950.38i 0.375533 + 0.422341i
\(517\) −63.3248 −0.00538689
\(518\) 3980.53 + 15077.6i 0.337634 + 1.27890i
\(519\) −908.329 1021.55i −0.0768231 0.0863988i
\(520\) 1869.93 1768.69i 0.157696 0.149158i
\(521\) 6450.02 0.542381 0.271190 0.962526i \(-0.412583\pi\)
0.271190 + 0.962526i \(0.412583\pi\)
\(522\) −6723.41 791.604i −0.563747 0.0663747i
\(523\) −21041.2 −1.75921 −0.879606 0.475702i \(-0.842194\pi\)
−0.879606 + 0.475702i \(0.842194\pi\)
\(524\) 3031.44 0.252728
\(525\) −9637.72 7198.44i −0.801190 0.598410i
\(526\) −15393.6 −1.27603
\(527\) −15433.1 −1.27567
\(528\) −162.222 182.443i −0.0133709 0.0150375i
\(529\) 6352.25 0.522088
\(530\) 14455.7 13673.1i 1.18475 1.12061i
\(531\) −1573.60 + 13365.2i −0.128603 + 1.09228i
\(532\) −1143.16 4330.08i −0.0931620 0.352881i
\(533\) −745.534 −0.0605866
\(534\) 12563.5 11171.1i 1.01812 0.905283i
\(535\) 6144.99 5812.30i 0.496582 0.469696i
\(536\) 11168.3i 0.899994i
\(537\) −1200.26 1349.87i −0.0964526 0.108475i
\(538\) −18234.9 −1.46126
\(539\) 102.495 + 180.586i 0.00819065 + 0.0144312i
\(540\) 3769.80 + 778.374i 0.300419 + 0.0620294i
\(541\) 16947.6 1.34683 0.673415 0.739264i \(-0.264827\pi\)
0.673415 + 0.739264i \(0.264827\pi\)
\(542\) 7277.77i 0.576765i
\(543\) 8827.20 + 9927.47i 0.697627 + 0.784583i
\(544\) 12657.6i 0.997592i
\(545\) 6462.27 6112.39i 0.507914 0.480415i
\(546\) 2208.83 3328.51i 0.173130 0.260892i
\(547\) 23736.9i 1.85542i −0.373298 0.927712i \(-0.621773\pi\)
0.373298 0.927712i \(-0.378227\pi\)
\(548\) 346.773 0.0270318
\(549\) 4613.16 + 543.146i 0.358624 + 0.0422239i
\(550\) −244.291 13.6046i −0.0189393 0.00105473i
\(551\) 7641.34 0.590802
\(552\) 9475.67 8425.47i 0.730636 0.649659i
\(553\) 1695.37 447.583i 0.130369 0.0344180i
\(554\) 20446.7i 1.56804i
\(555\) 15072.5 + 1305.75i 1.15278 + 0.0998670i
\(556\) 2195.68i 0.167478i
\(557\) 8025.91 0.610537 0.305268 0.952266i \(-0.401254\pi\)
0.305268 + 0.952266i \(0.401254\pi\)
\(558\) 11362.0 + 1337.74i 0.861990 + 0.101489i
\(559\) 6669.47i 0.504631i
\(560\) 8469.42 13657.2i 0.639104 1.03057i
\(561\) 276.837 246.155i 0.0208343 0.0185252i
\(562\) 25572.6i 1.91942i
\(563\) 8553.71i 0.640313i 0.947365 + 0.320156i \(0.103735\pi\)
−0.947365 + 0.320156i \(0.896265\pi\)
\(564\) 886.326 + 996.803i 0.0661721 + 0.0744201i
\(565\) 3179.89 3007.73i 0.236777 0.223958i
\(566\) −4413.04 −0.327728
\(567\) −13497.5 + 320.178i −0.999719 + 0.0237146i
\(568\) 2721.44i 0.201037i
\(569\) 8983.39i 0.661868i −0.943654 0.330934i \(-0.892636\pi\)
0.943654 0.330934i \(-0.107364\pi\)
\(570\) −18439.6 1597.45i −1.35500 0.117386i
\(571\) −8976.45 −0.657886 −0.328943 0.944350i \(-0.606692\pi\)
−0.328943 + 0.944350i \(0.606692\pi\)
\(572\) 19.0734i 0.00139423i
\(573\) 10325.5 + 11612.5i 0.752797 + 0.846630i
\(574\) −3362.09 + 887.604i −0.244479 + 0.0645434i
\(575\) 945.863 16984.4i 0.0686003 1.23182i
\(576\) 863.040 7330.14i 0.0624305 0.530248i
\(577\) −1444.10 −0.104192 −0.0520958 0.998642i \(-0.516590\pi\)
−0.0520958 + 0.998642i \(0.516590\pi\)
\(578\) 28955.8 2.08374
\(579\) 13637.0 + 15336.8i 0.978819 + 1.10082i
\(580\) −1462.09 1545.78i −0.104672 0.110664i
\(581\) −3687.21 13966.5i −0.263290 0.997296i
\(582\) −14156.3 + 12587.4i −1.00824 + 0.896499i
\(583\) 333.223i 0.0236719i
\(584\) −4344.31 −0.307823
\(585\) −2315.66 3107.69i −0.163660 0.219636i
\(586\) 19913.0i 1.40375i
\(587\) 21411.0i 1.50549i 0.658310 + 0.752747i \(0.271272\pi\)
−0.658310 + 0.752747i \(0.728728\pi\)
\(588\) 1408.06 4140.96i 0.0987544 0.290426i
\(589\) −12913.2 −0.903358
\(590\) −13089.8 + 12381.1i −0.913388 + 0.863937i
\(591\) −6148.06 + 5466.67i −0.427915 + 0.380488i
\(592\) 20211.1i 1.40316i
\(593\) 2596.21i 0.179787i −0.995951 0.0898935i \(-0.971347\pi\)
0.995951 0.0898935i \(-0.0286527\pi\)
\(594\) −225.146 + 157.225i −0.0155520 + 0.0108603i
\(595\) 20723.3 + 12851.4i 1.42785 + 0.885475i
\(596\) 5528.86i 0.379985i
\(597\) −351.021 394.775i −0.0240642 0.0270637i
\(598\) 5648.99 0.386295
\(599\) 13043.3i 0.889709i 0.895603 + 0.444854i \(0.146745\pi\)
−0.895603 + 0.444854i \(0.853255\pi\)
\(600\) −7243.20 9120.65i −0.492837 0.620581i
\(601\) 320.380i 0.0217447i −0.999941 0.0108724i \(-0.996539\pi\)
0.999941 0.0108724i \(-0.00346085\pi\)
\(602\) −7940.42 30076.9i −0.537587 2.03628i
\(603\) 16701.0 + 1966.35i 1.12789 + 0.132796i
\(604\) −2050.17 −0.138113
\(605\) −10808.1 + 10222.9i −0.726300 + 0.686977i
\(606\) 6096.92 5421.19i 0.408697 0.363401i
\(607\) 9539.65 0.637895 0.318948 0.947772i \(-0.396671\pi\)
0.318948 + 0.947772i \(0.396671\pi\)
\(608\) 10590.9i 0.706442i
\(609\) 6218.19 + 4126.45i 0.413750 + 0.274568i
\(610\) 4273.50 + 4518.11i 0.283654 + 0.299890i
\(611\) 1342.96i 0.0889202i
\(612\) −7749.50 912.414i −0.511855 0.0602650i
\(613\) 10566.9i 0.696235i 0.937451 + 0.348118i \(0.113179\pi\)
−0.937451 + 0.348118i \(0.886821\pi\)
\(614\) −23461.8 −1.54209
\(615\) −291.165 + 3360.96i −0.0190909 + 0.220369i
\(616\) 51.3184 + 194.385i 0.00335662 + 0.0127143i
\(617\) 10459.5 0.682467 0.341233 0.939979i \(-0.389155\pi\)
0.341233 + 0.939979i \(0.389155\pi\)
\(618\) −19587.3 + 17416.4i −1.27494 + 1.13364i
\(619\) 12347.7i 0.801768i 0.916129 + 0.400884i \(0.131297\pi\)
−0.916129 + 0.400884i \(0.868703\pi\)
\(620\) 2470.80 + 2612.23i 0.160048 + 0.169209i
\(621\) −10931.1 15653.3i −0.706359 1.01151i
\(622\) 27175.6 1.75183
\(623\) −17918.7 + 4730.60i −1.15232 + 0.304217i
\(624\) 3869.14 3440.32i 0.248221 0.220710i
\(625\) −15528.4 1734.94i −0.993816 0.111036i
\(626\) −9740.61 −0.621906
\(627\) 231.635 205.963i 0.0147538 0.0131186i
\(628\) −7361.28 −0.467750
\(629\) −30668.2 −1.94407
\(630\) −14142.7 11257.6i −0.894379 0.711928i
\(631\) −7403.86 −0.467105 −0.233552 0.972344i \(-0.575035\pi\)
−0.233552 + 0.972344i \(0.575035\pi\)
\(632\) 1697.72 0.106854
\(633\) 19598.8 17426.6i 1.23062 1.09423i
\(634\) −27079.1 −1.69629
\(635\) 10449.4 + 11047.5i 0.653024 + 0.690403i
\(636\) 5245.30 4663.96i 0.327028 0.290783i
\(637\) −3829.78 + 2173.65i −0.238212 + 0.135201i
\(638\) 151.790 0.00941917
\(639\) 4069.64 + 479.153i 0.251944 + 0.0296635i
\(640\) 14163.3 13396.5i 0.874772 0.827411i
\(641\) 24209.2i 1.49174i 0.666089 + 0.745872i \(0.267967\pi\)
−0.666089 + 0.745872i \(0.732033\pi\)
\(642\) 9498.46 8445.74i 0.583916 0.519200i
\(643\) −11848.9 −0.726712 −0.363356 0.931650i \(-0.618369\pi\)
−0.363356 + 0.931650i \(0.618369\pi\)
\(644\) 5980.15 1578.78i 0.365917 0.0966036i
\(645\) −30066.8 2604.74i −1.83547 0.159010i
\(646\) 37519.3 2.28510
\(647\) 6193.88i 0.376362i −0.982134 0.188181i \(-0.939741\pi\)
0.982134 0.188181i \(-0.0602592\pi\)
\(648\) −12714.6 3036.09i −0.770800 0.184057i
\(649\) 301.737i 0.0182500i
\(650\) 288.520 5180.80i 0.0174103 0.312627i
\(651\) −10508.2 6973.33i −0.632639 0.419825i
\(652\) 1970.59i 0.118365i
\(653\) 27763.0 1.66378 0.831892 0.554938i \(-0.187258\pi\)
0.831892 + 0.554938i \(0.187258\pi\)
\(654\) 9988.87 8881.80i 0.597241 0.531048i
\(655\) −10033.6 + 9490.37i −0.598542 + 0.566136i
\(656\) −4506.80 −0.268233
\(657\) −764.883 + 6496.46i −0.0454200 + 0.385770i
\(658\) −1598.87 6056.26i −0.0947274 0.358811i
\(659\) 6793.61i 0.401581i −0.979634 0.200790i \(-0.935649\pi\)
0.979634 0.200790i \(-0.0643510\pi\)
\(660\) −85.9855 7.44906i −0.00507118 0.000439324i
\(661\) 11194.7i 0.658732i 0.944202 + 0.329366i \(0.106835\pi\)
−0.944202 + 0.329366i \(0.893165\pi\)
\(662\) 23892.1 1.40271
\(663\) 5220.32 + 5871.01i 0.305792 + 0.343908i
\(664\) 13985.9i 0.817406i
\(665\) 17339.6 + 10753.1i 1.01113 + 0.627046i
\(666\) 22578.2 + 2658.32i 1.31364 + 0.154666i
\(667\) 10553.2i 0.612627i
\(668\) 3655.01i 0.211702i
\(669\) 7246.01 6442.93i 0.418755 0.372344i
\(670\) 15471.3 + 16356.9i 0.892104 + 0.943168i
\(671\) −104.148 −0.00599195
\(672\) 5719.24 8618.39i 0.328310 0.494735i
\(673\) 9778.19i 0.560062i −0.959991 0.280031i \(-0.909655\pi\)
0.959991 0.280031i \(-0.0903447\pi\)
\(674\) 24614.5i 1.40670i
\(675\) −14914.3 + 9225.61i −0.850444 + 0.526065i
\(676\) −4987.05 −0.283742
\(677\) 18617.5i 1.05691i −0.848961 0.528455i \(-0.822772\pi\)
0.848961 0.528455i \(-0.177228\pi\)
\(678\) 4915.23 4370.47i 0.278419 0.247562i
\(679\) 20190.4 5330.33i 1.14114 0.301266i
\(680\) 16223.7 + 17152.4i 0.914930 + 0.967300i
\(681\) −7839.31 8816.44i −0.441120 0.496104i
\(682\) −256.512 −0.0144023
\(683\) −7222.59 −0.404634 −0.202317 0.979320i \(-0.564847\pi\)
−0.202317 + 0.979320i \(0.564847\pi\)
\(684\) −6484.17 763.436i −0.362468 0.0426765i
\(685\) −1147.76 + 1085.62i −0.0640201 + 0.0605540i
\(686\) −14683.1 + 14362.0i −0.817204 + 0.799334i
\(687\) 3447.05 + 3876.71i 0.191431 + 0.215292i
\(688\) 40317.4i 2.23414i
\(689\) −7066.82 −0.390746
\(690\) 2206.19 25466.4i 0.121722 1.40506i
\(691\) 10418.8i 0.573589i 0.957992 + 0.286795i \(0.0925898\pi\)
−0.957992 + 0.286795i \(0.907410\pi\)
\(692\) 645.598i 0.0354653i
\(693\) 299.718 42.5168i 0.0164291 0.00233056i
\(694\) 7270.90 0.397694
\(695\) −6873.89 7267.35i −0.375168 0.396642i
\(696\) 4801.26 + 5399.72i 0.261482 + 0.294075i
\(697\) 6838.58i 0.371635i
\(698\) 13377.7i 0.725433i
\(699\) 15916.4 14152.4i 0.861252 0.765799i
\(700\) −1142.50 5565.14i −0.0616891 0.300490i
\(701\) 30401.8i 1.63803i 0.573772 + 0.819015i \(0.305480\pi\)
−0.573772 + 0.819015i \(0.694520\pi\)
\(702\) −3334.34 4774.78i −0.179269 0.256713i
\(703\) −25660.7 −1.37669
\(704\) 165.488i 0.00885946i
\(705\) −6054.23 524.487i −0.323426 0.0280189i
\(706\) 16070.3i 0.856678i
\(707\) −8695.70 + 2295.70i −0.462568 + 0.122120i
\(708\) −4749.68 + 4223.27i −0.252124 + 0.224181i
\(709\) −20621.4 −1.09232 −0.546159 0.837682i \(-0.683911\pi\)
−0.546159 + 0.837682i \(0.683911\pi\)
\(710\) 3769.99 + 3985.79i 0.199275 + 0.210682i
\(711\) 298.910 2538.76i 0.0157665 0.133911i
\(712\) −17943.5 −0.944469
\(713\) 17834.0i 0.936730i
\(714\) 30531.6 + 20261.0i 1.60030 + 1.06197i
\(715\) 59.7121 + 63.1300i 0.00312322 + 0.00330200i
\(716\) 853.090i 0.0445272i
\(717\) −14218.6 15990.9i −0.740590 0.832901i
\(718\) 9512.91i 0.494455i
\(719\) 12233.8 0.634555 0.317278 0.948333i \(-0.397231\pi\)
0.317278 + 0.948333i \(0.397231\pi\)
\(720\) −13998.3 18786.2i −0.724566 0.972390i
\(721\) 27936.2 7375.27i 1.44300 0.380956i
\(722\) 9216.13 0.475054
\(723\) −22940.5 25799.9i −1.18004 1.32712i
\(724\) 6273.97i 0.322058i
\(725\) 9678.56 + 539.001i 0.495797 + 0.0276110i
\(726\) −16706.3 + 14854.7i −0.854035 + 0.759382i
\(727\) 27169.3 1.38604 0.693021 0.720918i \(-0.256279\pi\)
0.693021 + 0.720918i \(0.256279\pi\)
\(728\) −4122.41 + 1088.33i −0.209872 + 0.0554070i
\(729\) −6778.77 + 18478.9i −0.344397 + 0.938824i
\(730\) −6362.61 + 6018.13i −0.322590 + 0.305125i
\(731\) 61177.3 3.09538
\(732\) 1457.71 + 1639.41i 0.0736046 + 0.0827792i
\(733\) 13215.7 0.665937 0.332968 0.942938i \(-0.391950\pi\)
0.332968 + 0.942938i \(0.391950\pi\)
\(734\) 7813.92 0.392939
\(735\) 8303.40 + 18114.1i 0.416701 + 0.909043i
\(736\) 14626.7 0.732538
\(737\) −377.048 −0.0188450
\(738\) −592.769 + 5034.62i −0.0295666 + 0.251121i
\(739\) 12158.0 0.605194 0.302597 0.953119i \(-0.402146\pi\)
0.302597 + 0.953119i \(0.402146\pi\)
\(740\) 4909.90 + 5190.94i 0.243908 + 0.257869i
\(741\) 4367.95 + 4912.39i 0.216546 + 0.243537i
\(742\) −31868.8 + 8413.49i −1.57674 + 0.416265i
\(743\) −28694.3 −1.41681 −0.708406 0.705805i \(-0.750586\pi\)
−0.708406 + 0.705805i \(0.750586\pi\)
\(744\) −8113.71 9125.05i −0.399816 0.449651i
\(745\) −17308.9 18299.6i −0.851206 0.899929i
\(746\) 15167.4i 0.744392i
\(747\) −20914.4 2462.43i −1.02439 0.120610i
\(748\) 174.956 0.00855215
\(749\) −13547.1 + 3576.49i −0.660883 + 0.174476i
\(750\) −23243.0 3324.03i −1.13162 0.161835i
\(751\) −5141.82 −0.249837 −0.124919 0.992167i \(-0.539867\pi\)
−0.124919 + 0.992167i \(0.539867\pi\)
\(752\) 8118.27i 0.393674i
\(753\) −624.376 + 555.176i −0.0302172 + 0.0268682i
\(754\) 3219.08i 0.155480i
\(755\) 6785.75 6418.36i 0.327097 0.309388i
\(756\) −4864.27 4122.81i −0.234010 0.198340i
\(757\) 23836.1i 1.14444i 0.820102 + 0.572218i \(0.193917\pi\)
−0.820102 + 0.572218i \(0.806083\pi\)
\(758\) −2380.48 −0.114067
\(759\) 284.449 + 319.904i 0.0136032 + 0.0152988i
\(760\) 13574.7 + 14351.8i 0.647905 + 0.684990i
\(761\) −29237.9 −1.39274 −0.696369 0.717684i \(-0.745202\pi\)
−0.696369 + 0.717684i \(0.745202\pi\)
\(762\) 15183.8 + 17076.4i 0.721850 + 0.811825i
\(763\) −14246.6 + 3761.15i −0.675965 + 0.178457i
\(764\) 7338.87i 0.347527i
\(765\) 28506.0 21241.0i 1.34724 1.00388i
\(766\) 38195.4i 1.80164i
\(767\) 6399.08 0.301248
\(768\) 13400.6 11915.4i 0.629625 0.559843i
\(769\) 11924.6i 0.559185i −0.960119 0.279592i \(-0.909801\pi\)
0.960119 0.279592i \(-0.0901993\pi\)
\(770\) 344.440 + 213.603i 0.0161205 + 0.00999702i
\(771\) 2028.20 + 2281.00i 0.0947389 + 0.106548i
\(772\) 9692.58i 0.451870i
\(773\) 16127.3i 0.750400i 0.926944 + 0.375200i \(0.122426\pi\)
−0.926944 + 0.375200i \(0.877574\pi\)
\(774\) −45039.2 5302.85i −2.09160 0.246262i
\(775\) −16355.9 910.863i −0.758092 0.0422183i
\(776\) 20218.4 0.935305
\(777\) −20881.6 13857.2i −0.964121 0.639799i
\(778\) 12121.4i 0.558576i
\(779\) 5721.98<