Properties

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

$q$-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 \(0.00264098\pi\)
−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 \(-0.456269\pi\)
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 \(0.317483\pi\)
−0.542487 + 0.840064i \(0.682517\pi\)
\(18\) −10.2079 + 86.6995i −0.133668 + 1.13529i
\(19\) 98.5363i 1.18978i 0.803808 + 0.594889i \(0.202804\pi\)
−0.803808 + 0.594889i \(0.797196\pi\)
\(20\) 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 \(0.0798661\pi\)
−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 \(0.123950\pi\)
−0.925137 + 0.379633i \(0.876050\pi\)
\(32\) 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 \(-0.803619\pi\)
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 \(-0.535276\pi\)
−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 \(0.372769\pi\)
−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 \(-0.948103\pi\)
0.986738 0.162319i \(-0.0518973\pi\)
\(48\) 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 \(-0.942212\pi\)
0.983566 0.180551i \(-0.0577880\pi\)
\(62\) 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 \(0.192221\pi\)
−0.823139 + 0.567840i \(0.807779\pi\)
\(68\) 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 \(0.0404842\pi\)
−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 \(-0.437783\pi\)
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 \(0.172480\pi\)
−0.856750 + 0.515733i \(0.827520\pi\)
\(84\) 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 \(-0.842391\pi\)
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 \(-0.635147\pi\)
−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 \(-0.911990\pi\)
0.962019 0.272982i \(-0.0880098\pi\)
\(140\) −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 \(0.212608\pi\)
−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 \(-0.224014\pi\)
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 \(0.0617992\pi\)
−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 \(-0.887857\pi\)
0.938579 0.345065i \(-0.112143\pi\)
\(168\) 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 \(0.0184108\pi\)
−0.998328 + 0.0578069i \(0.981589\pi\)
\(174\) 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 \(-0.976878\pi\)
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 \(-0.824087\pi\)
0.851138 0.524942i \(-0.175913\pi\)
\(182\) 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 \(0.191685\pi\)
−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 \(0.00576413\pi\)
−0.999836 + 0.0181075i \(0.994236\pi\)
\(200\) 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 \(0.107699\pi\)
−0.943305 + 0.331929i \(0.892301\pi\)
\(228\) −834.919 938.988i −0.242517 0.272745i
\(229\) 998.351i 0.288091i −0.989571 0.144046i \(-0.953989\pi\)
0.989571 0.144046i \(-0.0460112\pi\)
\(230\) −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 \(-0.811849\pi\)
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 \(0.347863\pi\)
−0.459961 + 0.887939i \(0.652137\pi\)
\(242\) −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 \(-0.977289\pi\)
0.997456 0.0712879i \(-0.0227109\pi\)
\(258\) 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 \(-0.918822\pi\)
0.967656 0.252274i \(-0.0811783\pi\)
\(272\) 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 \(-0.759430\pi\)
0.727741 0.685852i \(-0.240570\pi\)
\(278\) 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 \(0.317178\pi\)
−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 \(-0.545786\pi\)
−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 \(-0.789563\pi\)
0.789312 0.613992i \(-0.210437\pi\)
\(294\) 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 \(0.210957\pi\)
−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 \(0.102776\pi\)
−0.948325 + 0.317300i \(0.897224\pi\)
\(350\) 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 \(-0.877744\pi\)
0.927144 0.374706i \(-0.122256\pi\)
\(354\) 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 \(-0.930610\pi\)
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 \(-0.445019\pi\)
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 \(-0.894436\pi\)
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
\(378\) 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 \(0.288897\pi\)
−0.615641 + 0.788027i \(0.711103\pi\)
\(384\) 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 \(-0.921436\pi\)
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 \(-0.618836\pi\)
−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 \(0.130050\pi\)
−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 \(0.108473\pi\)
−0.942495 + 0.334221i \(0.891527\pi\)
\(410\) 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 \(-0.726207\pi\)
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 \(-0.304163\pi\)
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 \(-0.885453\pi\)
0.935946 0.352143i \(-0.114547\pi\)
\(440\) 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 \(-0.905405\pi\)
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
\(455\) −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 \(0.164777\pi\)
−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 \(-0.660060\pi\)
−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 \(0.00465198\pi\)
−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 \(-0.788793\pi\)
0.787825 0.615899i \(-0.211207\pi\)
\(468\) 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 \(0.340862\pi\)
−0.479380 + 0.877608i \(0.659138\pi\)
\(488\) 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 \(-0.833644\pi\)
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 \(0.195276\pi\)
−0.817651 + 0.575715i \(0.804724\pi\)
\(504\) −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 \(-0.621773\pi\)
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
\(560\) 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 \(-0.896265\pi\)
0.947365 0.320156i \(-0.103735\pi\)
\(564\) 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 \(-0.892636\pi\)
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 \(-0.483410\pi\)
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 \(-0.728728\pi\)
0.658310 0.752747i \(-0.271272\pi\)
\(588\) −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 \(0.0286527\pi\)
−0.995951 + 0.0898935i \(0.971347\pi\)
\(594\) 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 \(0.146745\pi\)
−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 \(0.00346085\pi\)
−0.999941 + 0.0108724i \(0.996539\pi\)
\(602\) −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 \(0.113179\pi\)
−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 \(-0.868703\pi\)
0.916129 0.400884i \(-0.131297\pi\)
\(620\) 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 \(0.267967\pi\)
−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 \(-0.381631\pi\)
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 \(0.0602592\pi\)
−0.982134 + 0.188181i \(0.939741\pi\)
\(648\) −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 \(-0.935649\pi\)
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 \(-0.893165\pi\)
0.944202 0.329366i \(-0.106835\pi\)
\(662\) 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 \(-0.909655\pi\)
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 \(0.177228\pi\)
−0.848961 + 0.528455i \(0.822772\pi\)
\(678\) −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 \(-0.907410\pi\)
0.957992 0.286795i \(-0.0925898\pi\)
\(692\) 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 \(0.305480\pi\)
−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
\(714\) −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 \(0.193917\pi\)
−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 \(-0.254798\pi\)
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 \(0.0901993\pi\)
−0.960119 + 0.279592i \(0.909801\pi\)
\(770\) 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 \(-0.877574\pi\)
0.926944 0.375200i \(-0.122426\pi\)
\(774\) −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
\(779\) 5721.98<