Properties

Label 105.4.g.b.104.9
Level $105$
Weight $4$
Character 105.104
Analytic conductor $6.195$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $8$

Related objects

Downloads

Learn more about

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 104.9
Character \(\chi\) \(=\) 105.104
Dual form 105.4.g.b.104.10

$q$-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} +(85.8565 + 43.4702i) 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} +(-181.768 - 99.1743i) 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} +(-277.598 - 140.551i) 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} +(-183.299 - 465.240i) 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} +(587.704 + 320.658i) 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} +(210.696 + 106.678i) 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 \(-0.997359\pi\)
0.999966 0.00829677i \(-0.00264098\pi\)
\(12\) −9.52936 8.47321i −0.229241 0.203834i
\(13\) 12.8386 0.273906 0.136953 0.990578i \(-0.456269\pi\)
0.136953 + 0.990578i \(0.456269\pi\)
\(14\) 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
\(21\) 85.8565 + 43.4702i 0.892163 + 0.451713i
\(22\) 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 \(-0.920134\pi\)
0.968688 0.248283i \(-0.0798661\pi\)
\(30\) 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
\(35\) −181.768 99.1743i −0.877838 0.478958i
\(36\) 7.74776 + 65.8048i 0.0358693 + 0.304652i
\(37\) 260.419i 1.15710i 0.815648 + 0.578548i \(0.196381\pi\)
−0.815648 + 0.578548i \(0.803619\pi\)
\(38\) 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 \(-0.535276\pi\)
−0.110597 + 0.993865i \(0.535276\pi\)
\(42\) −277.598 140.551i −1.01986 0.516368i
\(43\) 519.487i 1.84235i −0.389150 0.921174i \(-0.627231\pi\)
0.389150 0.921174i \(-0.372769\pi\)
\(44\) 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 \(-0.314662\pi\)
0.549911 + 0.835223i \(0.314662\pi\)
\(60\) −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
\(63\) −183.299 465.240i −0.366564 0.930393i
\(64\) 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 \(-0.807779\pi\)
0.823139 0.567840i \(-0.192221\pi\)
\(68\) 289.001i 0.515390i
\(69\) −528.435 469.868i −0.921973 0.819789i
\(70\) 587.704 + 320.658i 1.00349 + 0.547513i
\(71\) 151.768i 0.253684i −0.991923 0.126842i \(-0.959516\pi\)
0.991923 0.126842i \(-0.0404842\pi\)
\(72\) 56.6123 + 480.831i 0.0926642 + 0.787034i
\(73\) 242.271 0.388435 0.194217 0.980959i \(-0.437783\pi\)
0.194217 + 0.980959i \(0.437783\pi\)
\(74\) 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 \(-0.172480\pi\)
\(84\) 210.696 + 106.678i 0.273677 + 0.138566i
\(85\) 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 \(-0.296795\pi\)
0.595902 + 0.803057i \(0.296795\pi\)
\(90\) 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 \(-0.700920\pi\)
−0.590120 + 0.807316i \(0.700920\pi\)
\(98\) −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 \(-0.423112\pi\)
0.239208 + 0.970968i \(0.423112\pi\)
\(102\) 1314.69 1478.56i 1.27621 1.43528i
\(103\) −1560.10 −1.49244 −0.746218 0.665702i \(-0.768132\pi\)
−0.746218 + 0.665702i \(0.768132\pi\)
\(104\) 230.216 0.217063
\(105\) 363.400 + 1012.70i 0.337755 + 0.941234i
\(106\) −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
\(126\) 592.657 + 1504.25i 0.419032 + 1.06356i
\(127\) 1360.11i 0.950314i 0.879901 + 0.475157i \(0.157609\pi\)
−0.879901 + 0.475157i \(0.842391\pi\)
\(128\) −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 \(-0.635147\pi\)
−0.411935 + 0.911213i \(0.635147\pi\)
\(132\) −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 \(0.911990\pi\)
\(140\) −446.067 243.379i −0.269282 0.146923i
\(141\) 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
\(147\) −1742.91 372.526i −0.977912 0.209017i
\(148\) 639.081i 0.354947i
\(149\) 2252.95i 1.23872i −0.785108 0.619359i \(-0.787392\pi\)
0.785108 0.619359i \(-0.212608\pi\)
\(150\) −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 \(-0.224014\pi\)
0.762413 + 0.647091i \(0.224014\pi\)
\(158\) −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 \(-0.938201\pi\)
0.981212 0.192930i \(-0.0617992\pi\)
\(164\) −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 \(0.887857\pi\)
\(168\) 1539.54 + 779.488i 0.707013 + 0.357969i
\(169\) −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
\(175\) −714.477 2202.02i −0.308625 0.951184i
\(176\) 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 \(0.0231224\pi\)
−0.997363 + 0.0725774i \(0.976878\pi\)
\(180\) −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
\(189\) −894.582 + 2439.47i −0.344293 + 0.938862i
\(190\) −2447.69 + 2587.79i −0.934599 + 0.988095i
\(191\) 2990.51i 1.13291i −0.824093 0.566455i \(-0.808315\pi\)
0.824093 0.566455i \(-0.191685\pi\)
\(192\) −1061.50 943.849i −0.398994 0.354773i
\(193\) 3949.63i 1.47306i −0.676406 0.736529i \(-0.736463\pi\)
0.676406 0.736529i \(-0.263537\pi\)
\(194\) 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
\(210\) −1174.97 3274.34i −0.386099 1.07596i
\(211\) 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 \(-0.590393\pi\)
−0.280177 + 0.959948i \(0.590393\pi\)
\(224\) −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
\(231\) 26.3160 51.9759i 0.00749551 0.0148042i
\(232\) 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 \(0.188151\pi\)
−0.830332 + 0.557270i \(0.811849\pi\)
\(240\) 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
\(245\) 3723.71 + 916.593i 0.971016 + 0.239016i
\(246\) −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 \(-0.493564\pi\)
0.0202174 + 0.999796i \(0.493564\pi\)
\(252\) −449.826 1141.72i −0.112446 0.285404i
\(253\) 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 \(-0.720713\pi\)
−0.639148 + 0.769084i \(0.720713\pi\)
\(270\) −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
\(273\) 1102.28 + 558.095i 0.244369 + 0.123727i
\(274\) −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 \(0.240570\pi\)
−0.727741 + 0.685852i \(0.759430\pi\)
\(278\) 2892.86i 0.624109i
\(279\) 3514.08 413.742i 0.754058 0.0887816i
\(280\) −3259.38 1778.35i −0.695661 0.379560i
\(281\) 7909.21i 1.67909i −0.543291 0.839544i \(-0.682822\pi\)
0.543291 0.839544i \(-0.317178\pi\)
\(282\) −1167.76 + 1313.31i −0.246592 + 0.277328i
\(283\) −1364.88 −0.286692 −0.143346 0.989673i \(-0.545786\pi\)
−0.143346 + 0.989673i \(0.545786\pi\)
\(284\) 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 \(0.789563\pi\)
\(294\) 5635.31 + 1204.48i 1.11788 + 0.238934i
\(295\) 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 \(-0.735641\pi\)
−0.674500 + 0.738275i \(0.735641\pi\)
\(308\) 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 \(-0.222125\pi\)
0.766241 + 0.642553i \(0.222125\pi\)
\(312\) −893.954 794.876i −0.162212 0.144234i
\(313\) −3012.62 −0.544035 −0.272018 0.962292i \(-0.587691\pi\)
−0.272018 + 0.962292i \(0.587691\pi\)
\(314\) −9698.67 −1.74308
\(315\) 2085.47 5187.16i 0.373026 0.927821i
\(316\) 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
\(336\) −6663.33 3373.72i −1.08189 0.547772i
\(337\) 7612.87i 1.23056i −0.788308 0.615281i \(-0.789043\pi\)
0.788308 0.615281i \(-0.210957\pi\)
\(338\) 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 \(-0.102776\pi\)
\(350\) 2310.10 + 7119.73i 0.352800 + 1.08733i
\(351\) 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
\(357\) 5119.26 10110.9i 0.758935 1.49895i
\(358\) 1123.97i 0.165932i
\(359\) 2942.19i 0.432543i 0.976333 + 0.216271i \(0.0693896\pi\)
−0.976333 + 0.216271i \(0.930610\pi\)
\(360\) −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 \(-0.445019\pi\)
0.171869 + 0.985120i \(0.445019\pi\)
\(368\) −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 \(0.105564\pi\)
−0.945510 + 0.325592i \(0.894436\pi\)
\(374\) 230.508 0.0318698
\(375\) 7188.70 1028.07i 0.989928 0.141571i
\(376\) 1875.70i 0.257266i
\(377\) 995.612i 0.136012i
\(378\) 2892.43 7887.46i 0.393573 1.07325i
\(379\) 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
\(385\) −60.0382 + 110.038i −0.00794761 + 0.0145664i
\(386\) 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 \(0.0785639\pi\)
−0.969695 + 0.244318i \(0.921436\pi\)
\(390\) 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 \(-0.618836\pi\)
−0.364721 + 0.931117i \(0.618836\pi\)
\(398\) 328.709i 0.0413987i
\(399\) 4283.39 8459.99i 0.537438 1.06148i
\(400\) −539.429 9686.25i −0.0674286 1.21078i
\(401\) 6380.54i 0.794586i −0.917692 0.397293i \(-0.869950\pi\)
0.917692 0.397293i \(-0.130050\pi\)
\(402\) 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 \(-0.584364\pi\)
−0.261946 + 0.965083i \(0.584364\pi\)
\(420\) 891.803 + 2485.22i 0.103608 + 0.288730i
\(421\) −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 \(0.273793\pi\)
−0.652327 + 0.757938i \(0.726207\pi\)
\(432\) −6234.03 + 8927.14i −0.694294 + 0.994230i
\(433\) 10400.5 1.15431 0.577155 0.816634i \(-0.304163\pi\)
0.577155 + 0.816634i \(0.304163\pi\)
\(434\) −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
\(441\) 5481.69 + 7464.39i 0.591911 + 0.806003i
\(442\) 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 \(0.0945947\pi\)
−0.956167 + 0.292823i \(0.905405\pi\)
\(450\) 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
\(455\) −2333.64 1273.26i −0.240445 0.131189i
\(456\) −6100.69 + 6861.11i −0.626515 + 0.704607i
\(457\) 9668.94i 0.989702i −0.868978 0.494851i \(-0.835223\pi\)
0.868978 0.494851i \(-0.164777\pi\)
\(458\) 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 \(-0.660060\pi\)
−0.481919 + 0.876216i \(0.660060\pi\)
\(462\) −85.0867 + 168.052i −0.00856838 + 0.0169231i
\(463\) 291.188i 0.0292282i −0.999893 0.0146141i \(-0.995348\pi\)
0.999893 0.0146141i \(-0.00465198\pi\)
\(464\) 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 \(-0.465769\pi\)
0.107333 + 0.994223i \(0.465769\pi\)
\(480\) −538.921 6220.83i −0.0512464 0.591544i
\(481\) 3343.40i 0.316936i
\(482\) 21482.3i 2.03007i
\(483\) 11683.8 + 5915.66i 1.10069 + 0.557291i
\(484\) 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 \(-0.659138\pi\)
0.479380 0.877608i \(-0.340862\pi\)
\(488\) 3084.91i 0.286162i
\(489\) −2772.53 + 3118.12i −0.256397 + 0.288356i
\(490\) −12039.8 2963.59i −1.11000 0.273228i
\(491\) 10861.4i 0.998309i 0.866513 + 0.499155i \(0.166356\pi\)
−0.866513 + 0.499155i \(0.833644\pi\)
\(492\) 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 \(-0.195276\pi\)
\(504\) −3286.84 8342.48i −0.290491 0.737309i
\(505\) 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 \(-0.568634\pi\)
−0.213952 + 0.976844i \(0.568634\pi\)
\(510\) 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 \(-0.587417\pi\)
−0.271190 + 0.962526i \(0.587417\pi\)
\(522\) −6723.41 + 791.604i −0.563747 + 0.0663747i
\(523\) 21041.2 1.75921 0.879606 0.475702i \(-0.157806\pi\)
0.879606 + 0.475702i \(0.157806\pi\)
\(524\) −3031.44 −0.252728
\(525\) −4828.62 + 11017.6i −0.401406 + 0.915900i
\(526\) −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
\(546\) −3563.96 1804.47i −0.279347 0.141436i
\(547\) 23736.9i 1.85542i 0.373298 + 0.927712i \(0.378227\pi\)
−0.373298 + 0.927712i \(0.621773\pi\)
\(548\) 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
\(560\) 14107.0 + 7696.93i 1.06452 + 0.580812i
\(561\) 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
\(567\) 11896.6 6383.96i 0.881148 0.472841i
\(568\) 2721.44i 0.201037i
\(569\) 8983.39i 0.661868i 0.943654 + 0.330934i \(0.107364\pi\)
−0.943654 + 0.330934i \(0.892636\pi\)
\(570\) 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 \(-0.483410\pi\)
0.0520958 + 0.998642i \(0.483410\pi\)
\(578\) 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 \(0.728728\pi\)
\(588\) −4277.20 914.199i −0.299981 0.0641172i
\(589\) −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
\(595\) −11679.3 + 21405.8i −0.804711 + 1.47488i
\(596\) 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 \(-0.853255\pi\)
0.895603 0.444854i \(-0.146745\pi\)
\(600\) 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 \(-0.603329\pi\)
−0.318948 + 0.947772i \(0.603329\pi\)
\(608\) 10590.9i 0.706442i
\(609\) 3371.04 6658.04i 0.224305 0.443017i
\(610\) 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 \(-0.886821\pi\)
0.937451 0.348118i \(-0.113179\pi\)
\(614\) 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
\(630\) −6742.91 + 16771.5i −0.426419 + 1.06062i
\(631\) −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 \(-0.732033\pi\)
0.666089 0.745872i \(-0.267967\pi\)
\(642\) −9498.46 8445.74i −0.583916 0.519200i
\(643\) 11848.9 0.726712 0.363356 0.931650i \(-0.381631\pi\)
0.363356 + 0.931650i \(0.381631\pi\)
\(644\) −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
\(651\) 5696.76 11251.5i 0.342970 0.677390i
\(652\) 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 \(0.0643510\pi\)
−0.979634 + 0.200790i \(0.935649\pi\)
\(660\) −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
\(665\) −9772.27 + 17910.7i −0.569853 + 1.04443i
\(666\) 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
\(672\) 9228.02 + 4672.25i 0.529730 + 0.268209i
\(673\) 9778.19i 0.560062i 0.959991 + 0.280031i \(0.0903447\pi\)
−0.959991 + 0.280031i \(0.909655\pi\)
\(674\) 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
\(693\) −281.647 + 110.966i −0.0154385 + 0.00608260i
\(694\) 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
\(700\) −1753.36 5403.87i −0.0946728 0.291782i
\(701\) 30401.8i 1.63803i −0.573772 0.819015i \(-0.694520\pi\)
0.573772 0.819015i \(-0.305480\pi\)
\(702\) −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
\(714\) −16552.0 + 32691.2i −0.867565 + 1.71350i
\(715\) 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 \(-0.602769\pi\)
−0.317278 + 0.948333i \(0.602769\pi\)
\(720\) 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 \(-0.743721\pi\)
−0.693021 + 0.720918i \(0.743721\pi\)
\(728\) −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 \(-0.608050\pi\)
−0.332968 + 0.942938i \(0.608050\pi\)
\(734\) −7813.92 −0.392939
\(735\) −11294.8 16416.2i −0.566824 0.823839i
\(736\) 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
\(756\) −2195.35 + 5986.57i −0.105614 + 0.288002i
\(757\) 23836.1i 1.14444i −0.820102 0.572218i \(-0.806083\pi\)
0.820102 0.572218i \(-0.193917\pi\)
\(758\) −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 \(-0.254798\pi\)
0.696369 + 0.717684i \(0.254798\pi\)
\(762\) −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 \(-0.0901993\pi\)
\(770\) 194.120 355.784i 0.00908519 0.0166514i
\(771\) 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
\(777\) −11320.4 + 22358.6i −0.522675 + 1.03232i
\(778\) 12121.4i 0.558576i
\(779\) 5721.98i