Properties

Label 147.4.c.b.146.18
Level $147$
Weight $4$
Character 147.146
Analytic conductor $8.673$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 147.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.67328077084\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 146.18
Character \(\chi\) \(=\) 147.146
Dual form 147.4.c.b.146.8

$q$-expansion

\(f(q)\) \(=\) \(q+2.86969i q^{2} +(2.76278 + 4.40080i) q^{3} -0.235115 q^{4} +5.57059 q^{5} +(-12.6289 + 7.92832i) q^{6} +22.2828i q^{8} +(-11.7341 + 24.3169i) q^{9} +O(q^{10})\) \(q+2.86969i q^{2} +(2.76278 + 4.40080i) q^{3} -0.235115 q^{4} +5.57059 q^{5} +(-12.6289 + 7.92832i) q^{6} +22.2828i q^{8} +(-11.7341 + 24.3169i) q^{9} +15.9859i q^{10} -42.7198i q^{11} +(-0.649571 - 1.03469i) q^{12} +69.8357i q^{13} +(15.3903 + 24.5151i) q^{15} -65.8256 q^{16} +67.5034 q^{17} +(-69.7819 - 33.6732i) q^{18} +79.3413i q^{19} -1.30973 q^{20} +122.593 q^{22} -208.831i q^{23} +(-98.0622 + 61.5625i) q^{24} -93.9685 q^{25} -200.407 q^{26} +(-139.432 + 15.5429i) q^{27} +5.72587i q^{29} +(-70.3506 + 44.1655i) q^{30} -193.293i q^{31} -10.6367i q^{32} +(188.001 - 118.025i) q^{33} +193.714i q^{34} +(2.75886 - 5.71727i) q^{36} +163.609 q^{37} -227.685 q^{38} +(-307.333 + 192.941i) q^{39} +124.128i q^{40} +58.1164 q^{41} +58.9508 q^{43} +10.0441i q^{44} +(-65.3658 + 135.460i) q^{45} +599.280 q^{46} +148.572 q^{47} +(-181.862 - 289.685i) q^{48} -269.660i q^{50} +(186.497 + 297.069i) q^{51} -16.4194i q^{52} -100.642i q^{53} +(-44.6034 - 400.128i) q^{54} -237.975i q^{55} +(-349.165 + 219.203i) q^{57} -16.4315 q^{58} +738.690 q^{59} +(-3.61850 - 5.76386i) q^{60} +356.946i q^{61} +554.692 q^{62} -496.081 q^{64} +389.026i q^{65} +(338.696 + 539.505i) q^{66} +721.159 q^{67} -15.8711 q^{68} +(919.024 - 576.955i) q^{69} +308.915i q^{71} +(-541.849 - 261.468i) q^{72} -827.134i q^{73} +469.506i q^{74} +(-259.614 - 413.537i) q^{75} -18.6543i q^{76} +(-553.680 - 881.950i) q^{78} +467.203 q^{79} -366.688 q^{80} +(-453.623 - 570.673i) q^{81} +166.776i q^{82} -274.704 q^{83} +376.034 q^{85} +169.170i q^{86} +(-25.1984 + 15.8193i) q^{87} +951.917 q^{88} +541.074 q^{89} +(-388.727 - 187.579i) q^{90} +49.0993i q^{92} +(850.645 - 534.027i) q^{93} +426.355i q^{94} +441.978i q^{95} +(46.8099 - 29.3868i) q^{96} +41.4658i q^{97} +(1038.81 + 501.277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 96 q^{4} - 64 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 96 q^{4} - 64 q^{9} + 256 q^{15} + 864 q^{16} - 32 q^{18} - 384 q^{22} + 744 q^{25} - 1704 q^{30} + 584 q^{36} + 432 q^{37} - 2368 q^{39} - 624 q^{43} + 3744 q^{46} - 2160 q^{51} + 2032 q^{57} + 6384 q^{58} - 5832 q^{60} - 3504 q^{64} + 3792 q^{67} - 7472 q^{72} + 2248 q^{78} + 2784 q^{79} - 1968 q^{81} - 3744 q^{85} - 624 q^{88} - 3232 q^{93} + 1320 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.86969i 1.01459i 0.861773 + 0.507294i \(0.169354\pi\)
−0.861773 + 0.507294i \(0.830646\pi\)
\(3\) 2.76278 + 4.40080i 0.531698 + 0.846934i
\(4\) −0.235115 −0.0293894
\(5\) 5.57059 0.498249 0.249124 0.968471i \(-0.419857\pi\)
0.249124 + 0.968471i \(0.419857\pi\)
\(6\) −12.6289 + 7.92832i −0.859290 + 0.539454i
\(7\) 0 0
\(8\) 22.2828i 0.984770i
\(9\) −11.7341 + 24.3169i −0.434596 + 0.900626i
\(10\) 15.9859i 0.505517i
\(11\) 42.7198i 1.17095i −0.810689 0.585477i \(-0.800907\pi\)
0.810689 0.585477i \(-0.199093\pi\)
\(12\) −0.649571 1.03469i −0.0156263 0.0248909i
\(13\) 69.8357i 1.48992i 0.667110 + 0.744959i \(0.267531\pi\)
−0.667110 + 0.744959i \(0.732469\pi\)
\(14\) 0 0
\(15\) 15.3903 + 24.5151i 0.264918 + 0.421984i
\(16\) −65.8256 −1.02853
\(17\) 67.5034 0.963058 0.481529 0.876430i \(-0.340082\pi\)
0.481529 + 0.876430i \(0.340082\pi\)
\(18\) −69.7819 33.6732i −0.913764 0.440936i
\(19\) 79.3413i 0.958008i 0.877813 + 0.479004i \(0.159002\pi\)
−0.877813 + 0.479004i \(0.840998\pi\)
\(20\) −1.30973 −0.0146432
\(21\) 0 0
\(22\) 122.593 1.18804
\(23\) 208.831i 1.89323i −0.322365 0.946615i \(-0.604478\pi\)
0.322365 0.946615i \(-0.395522\pi\)
\(24\) −98.0622 + 61.5625i −0.834036 + 0.523600i
\(25\) −93.9685 −0.751748
\(26\) −200.407 −1.51165
\(27\) −139.432 + 15.5429i −0.993844 + 0.110787i
\(28\) 0 0
\(29\) 5.72587i 0.0366644i 0.999832 + 0.0183322i \(0.00583564\pi\)
−0.999832 + 0.0183322i \(0.994164\pi\)
\(30\) −70.3506 + 44.1655i −0.428140 + 0.268782i
\(31\) 193.293i 1.11989i −0.828531 0.559944i \(-0.810823\pi\)
0.828531 0.559944i \(-0.189177\pi\)
\(32\) 10.6367i 0.0587599i
\(33\) 188.001 118.025i 0.991722 0.622594i
\(34\) 193.714i 0.977108i
\(35\) 0 0
\(36\) 2.75886 5.71727i 0.0127725 0.0264688i
\(37\) 163.609 0.726949 0.363474 0.931604i \(-0.381590\pi\)
0.363474 + 0.931604i \(0.381590\pi\)
\(38\) −227.685 −0.971983
\(39\) −307.333 + 192.941i −1.26186 + 0.792186i
\(40\) 124.128i 0.490661i
\(41\) 58.1164 0.221372 0.110686 0.993855i \(-0.464695\pi\)
0.110686 + 0.993855i \(0.464695\pi\)
\(42\) 0 0
\(43\) 58.9508 0.209068 0.104534 0.994521i \(-0.466665\pi\)
0.104534 + 0.994521i \(0.466665\pi\)
\(44\) 10.0441i 0.0344136i
\(45\) −65.3658 + 135.460i −0.216537 + 0.448736i
\(46\) 599.280 1.92085
\(47\) 148.572 0.461094 0.230547 0.973061i \(-0.425948\pi\)
0.230547 + 0.973061i \(0.425948\pi\)
\(48\) −181.862 289.685i −0.546865 0.871094i
\(49\) 0 0
\(50\) 269.660i 0.762715i
\(51\) 186.497 + 297.069i 0.512056 + 0.815647i
\(52\) 16.4194i 0.0437878i
\(53\) 100.642i 0.260834i −0.991459 0.130417i \(-0.958368\pi\)
0.991459 0.130417i \(-0.0416316\pi\)
\(54\) −44.6034 400.128i −0.112403 1.00834i
\(55\) 237.975i 0.583427i
\(56\) 0 0
\(57\) −349.165 + 219.203i −0.811370 + 0.509370i
\(58\) −16.4315 −0.0371993
\(59\) 738.690 1.62999 0.814994 0.579469i \(-0.196740\pi\)
0.814994 + 0.579469i \(0.196740\pi\)
\(60\) −3.61850 5.76386i −0.00778577 0.0124019i
\(61\) 356.946i 0.749218i 0.927183 + 0.374609i \(0.122223\pi\)
−0.927183 + 0.374609i \(0.877777\pi\)
\(62\) 554.692 1.13622
\(63\) 0 0
\(64\) −496.081 −0.968909
\(65\) 389.026i 0.742350i
\(66\) 338.696 + 539.505i 0.631676 + 1.00619i
\(67\) 721.159 1.31498 0.657489 0.753464i \(-0.271619\pi\)
0.657489 + 0.753464i \(0.271619\pi\)
\(68\) −15.8711 −0.0283037
\(69\) 919.024 576.955i 1.60344 1.00663i
\(70\) 0 0
\(71\) 308.915i 0.516359i 0.966097 + 0.258180i \(0.0831226\pi\)
−0.966097 + 0.258180i \(0.916877\pi\)
\(72\) −541.849 261.468i −0.886909 0.427977i
\(73\) 827.134i 1.32615i −0.748555 0.663073i \(-0.769252\pi\)
0.748555 0.663073i \(-0.230748\pi\)
\(74\) 469.506i 0.737554i
\(75\) −259.614 413.537i −0.399703 0.636681i
\(76\) 18.6543i 0.0281552i
\(77\) 0 0
\(78\) −553.680 881.950i −0.803743 1.28027i
\(79\) 467.203 0.665373 0.332686 0.943038i \(-0.392045\pi\)
0.332686 + 0.943038i \(0.392045\pi\)
\(80\) −366.688 −0.512462
\(81\) −453.623 570.673i −0.622253 0.782816i
\(82\) 166.776i 0.224602i
\(83\) −274.704 −0.363285 −0.181643 0.983365i \(-0.558141\pi\)
−0.181643 + 0.983365i \(0.558141\pi\)
\(84\) 0 0
\(85\) 376.034 0.479843
\(86\) 169.170i 0.212118i
\(87\) −25.1984 + 15.8193i −0.0310523 + 0.0194944i
\(88\) 951.917 1.15312
\(89\) 541.074 0.644424 0.322212 0.946668i \(-0.395574\pi\)
0.322212 + 0.946668i \(0.395574\pi\)
\(90\) −388.727 187.579i −0.455282 0.219696i
\(91\) 0 0
\(92\) 49.0993i 0.0556409i
\(93\) 850.645 534.027i 0.948471 0.595441i
\(94\) 426.355i 0.467821i
\(95\) 441.978i 0.477326i
\(96\) 46.8099 29.3868i 0.0497658 0.0312425i
\(97\) 41.4658i 0.0434042i 0.999764 + 0.0217021i \(0.00690854\pi\)
−0.999764 + 0.0217021i \(0.993091\pi\)
\(98\) 0 0
\(99\) 1038.81 + 501.277i 1.05459 + 0.508892i
\(100\) 22.0934 0.0220934
\(101\) −1263.68 −1.24496 −0.622479 0.782637i \(-0.713874\pi\)
−0.622479 + 0.782637i \(0.713874\pi\)
\(102\) −852.496 + 535.189i −0.827546 + 0.519526i
\(103\) 309.423i 0.296003i 0.988987 + 0.148001i \(0.0472840\pi\)
−0.988987 + 0.148001i \(0.952716\pi\)
\(104\) −1556.14 −1.46723
\(105\) 0 0
\(106\) 288.810 0.264639
\(107\) 895.715i 0.809272i 0.914478 + 0.404636i \(0.132602\pi\)
−0.914478 + 0.404636i \(0.867398\pi\)
\(108\) 32.7827 3.65438i 0.0292085 0.00325595i
\(109\) −1590.61 −1.39773 −0.698865 0.715254i \(-0.746311\pi\)
−0.698865 + 0.715254i \(0.746311\pi\)
\(110\) 682.913 0.591938
\(111\) 452.015 + 720.009i 0.386517 + 0.615678i
\(112\) 0 0
\(113\) 859.839i 0.715812i −0.933758 0.357906i \(-0.883491\pi\)
0.933758 0.357906i \(-0.116509\pi\)
\(114\) −629.044 1002.00i −0.516801 0.823206i
\(115\) 1163.31i 0.943300i
\(116\) 1.34624i 0.00107754i
\(117\) −1698.19 819.458i −1.34186 0.647512i
\(118\) 2119.81i 1.65377i
\(119\) 0 0
\(120\) −546.264 + 342.940i −0.415557 + 0.260883i
\(121\) −493.980 −0.371135
\(122\) −1024.32 −0.760147
\(123\) 160.563 + 255.759i 0.117703 + 0.187488i
\(124\) 45.4462i 0.0329128i
\(125\) −1219.78 −0.872807
\(126\) 0 0
\(127\) 1382.66 0.966075 0.483038 0.875600i \(-0.339533\pi\)
0.483038 + 0.875600i \(0.339533\pi\)
\(128\) 1508.69i 1.04180i
\(129\) 162.868 + 259.431i 0.111161 + 0.177067i
\(130\) −1116.38 −0.753180
\(131\) −879.895 −0.586846 −0.293423 0.955983i \(-0.594794\pi\)
−0.293423 + 0.955983i \(0.594794\pi\)
\(132\) −44.2019 + 27.7496i −0.0291461 + 0.0182976i
\(133\) 0 0
\(134\) 2069.50i 1.33416i
\(135\) −776.721 + 86.5833i −0.495182 + 0.0551993i
\(136\) 1504.17i 0.948391i
\(137\) 3037.41i 1.89419i −0.320958 0.947093i \(-0.604005\pi\)
0.320958 0.947093i \(-0.395995\pi\)
\(138\) 1655.68 + 2637.31i 1.02131 + 1.62683i
\(139\) 652.162i 0.397954i −0.980004 0.198977i \(-0.936238\pi\)
0.980004 0.198977i \(-0.0637620\pi\)
\(140\) 0 0
\(141\) 410.472 + 653.835i 0.245163 + 0.390517i
\(142\) −886.491 −0.523892
\(143\) 2983.37 1.74463
\(144\) 772.403 1600.68i 0.446993 0.926317i
\(145\) 31.8965i 0.0182680i
\(146\) 2373.62 1.34549
\(147\) 0 0
\(148\) −38.4669 −0.0213646
\(149\) 395.474i 0.217440i 0.994072 + 0.108720i \(0.0346752\pi\)
−0.994072 + 0.108720i \(0.965325\pi\)
\(150\) 1186.72 745.013i 0.645969 0.405534i
\(151\) −705.128 −0.380017 −0.190008 0.981782i \(-0.560852\pi\)
−0.190008 + 0.981782i \(0.560852\pi\)
\(152\) −1767.95 −0.943417
\(153\) −792.091 + 1641.47i −0.418541 + 0.867355i
\(154\) 0 0
\(155\) 1076.76i 0.557983i
\(156\) 72.2586 45.3633i 0.0370854 0.0232819i
\(157\) 1597.79i 0.812214i 0.913825 + 0.406107i \(0.133114\pi\)
−0.913825 + 0.406107i \(0.866886\pi\)
\(158\) 1340.73i 0.675079i
\(159\) 442.903 278.051i 0.220909 0.138685i
\(160\) 59.2526i 0.0292771i
\(161\) 0 0
\(162\) 1637.65 1301.76i 0.794236 0.631331i
\(163\) −2736.42 −1.31493 −0.657463 0.753487i \(-0.728370\pi\)
−0.657463 + 0.753487i \(0.728370\pi\)
\(164\) −13.6640 −0.00650599
\(165\) 1047.28 657.472i 0.494124 0.310207i
\(166\) 788.315i 0.368585i
\(167\) −24.6732 −0.0114328 −0.00571638 0.999984i \(-0.501820\pi\)
−0.00571638 + 0.999984i \(0.501820\pi\)
\(168\) 0 0
\(169\) −2680.03 −1.21986
\(170\) 1079.10i 0.486843i
\(171\) −1929.33 930.997i −0.862806 0.416346i
\(172\) −13.8602 −0.00614437
\(173\) 1403.61 0.616847 0.308424 0.951249i \(-0.400199\pi\)
0.308424 + 0.951249i \(0.400199\pi\)
\(174\) −45.3965 72.3116i −0.0197787 0.0315053i
\(175\) 0 0
\(176\) 2812.06i 1.20436i
\(177\) 2040.84 + 3250.83i 0.866661 + 1.38049i
\(178\) 1552.71i 0.653825i
\(179\) 1714.52i 0.715919i 0.933737 + 0.357959i \(0.116527\pi\)
−0.933737 + 0.357959i \(0.883473\pi\)
\(180\) 15.3685 31.8486i 0.00636388 0.0131881i
\(181\) 2046.41i 0.840377i −0.907437 0.420189i \(-0.861964\pi\)
0.907437 0.420189i \(-0.138036\pi\)
\(182\) 0 0
\(183\) −1570.85 + 986.164i −0.634538 + 0.398357i
\(184\) 4653.34 1.86440
\(185\) 911.397 0.362201
\(186\) 1532.49 + 2441.09i 0.604128 + 0.962307i
\(187\) 2883.73i 1.12770i
\(188\) −34.9315 −0.0135513
\(189\) 0 0
\(190\) −1268.34 −0.484290
\(191\) 3373.11i 1.27785i −0.769268 0.638926i \(-0.779379\pi\)
0.769268 0.638926i \(-0.220621\pi\)
\(192\) −1370.56 2183.15i −0.515166 0.820602i
\(193\) −424.928 −0.158482 −0.0792409 0.996855i \(-0.525250\pi\)
−0.0792409 + 0.996855i \(0.525250\pi\)
\(194\) −118.994 −0.0440374
\(195\) −1712.03 + 1074.79i −0.628722 + 0.394706i
\(196\) 0 0
\(197\) 4420.59i 1.59875i −0.600832 0.799375i \(-0.705164\pi\)
0.600832 0.799375i \(-0.294836\pi\)
\(198\) −1438.51 + 2981.07i −0.516316 + 1.06998i
\(199\) 1577.80i 0.562046i −0.959701 0.281023i \(-0.909326\pi\)
0.959701 0.281023i \(-0.0906737\pi\)
\(200\) 2093.88i 0.740299i
\(201\) 1992.40 + 3173.67i 0.699171 + 1.11370i
\(202\) 3626.36i 1.26312i
\(203\) 0 0
\(204\) −43.8483 69.8454i −0.0150490 0.0239714i
\(205\) 323.743 0.110298
\(206\) −887.946 −0.300321
\(207\) 5078.13 + 2450.44i 1.70509 + 0.822790i
\(208\) 4596.98i 1.53242i
\(209\) 3389.44 1.12178
\(210\) 0 0
\(211\) 911.064 0.297252 0.148626 0.988893i \(-0.452515\pi\)
0.148626 + 0.988893i \(0.452515\pi\)
\(212\) 23.6623i 0.00766574i
\(213\) −1359.47 + 853.465i −0.437322 + 0.274547i
\(214\) −2570.42 −0.821078
\(215\) 328.391 0.104168
\(216\) −346.340 3106.95i −0.109099 0.978708i
\(217\) 0 0
\(218\) 4564.55i 1.41812i
\(219\) 3640.05 2285.19i 1.12316 0.705109i
\(220\) 55.9514i 0.0171466i
\(221\) 4714.15i 1.43488i
\(222\) −2066.20 + 1297.14i −0.624659 + 0.392155i
\(223\) 3070.23i 0.921964i −0.887410 0.460982i \(-0.847497\pi\)
0.887410 0.460982i \(-0.152503\pi\)
\(224\) 0 0
\(225\) 1102.63 2285.02i 0.326706 0.677044i
\(226\) 2467.47 0.726255
\(227\) −3352.67 −0.980284 −0.490142 0.871643i \(-0.663055\pi\)
−0.490142 + 0.871643i \(0.663055\pi\)
\(228\) 82.0940 51.5378i 0.0238456 0.0149701i
\(229\) 4353.50i 1.25628i 0.778102 + 0.628138i \(0.216183\pi\)
−0.778102 + 0.628138i \(0.783817\pi\)
\(230\) 3338.35 0.957061
\(231\) 0 0
\(232\) −127.588 −0.0361060
\(233\) 3683.52i 1.03569i −0.855475 0.517844i \(-0.826735\pi\)
0.855475 0.517844i \(-0.173265\pi\)
\(234\) 2351.59 4873.27i 0.656958 1.36143i
\(235\) 827.633 0.229740
\(236\) −173.677 −0.0479043
\(237\) 1290.78 + 2056.07i 0.353777 + 0.563527i
\(238\) 0 0
\(239\) 4537.46i 1.22805i 0.789287 + 0.614025i \(0.210451\pi\)
−0.789287 + 0.614025i \(0.789549\pi\)
\(240\) −1013.08 1613.72i −0.272475 0.434021i
\(241\) 2221.10i 0.593666i 0.954929 + 0.296833i \(0.0959305\pi\)
−0.954929 + 0.296833i \(0.904069\pi\)
\(242\) 1417.57i 0.376549i
\(243\) 1258.16 3572.95i 0.332143 0.943229i
\(244\) 83.9234i 0.0220190i
\(245\) 0 0
\(246\) −733.948 + 460.766i −0.190223 + 0.119420i
\(247\) −5540.86 −1.42735
\(248\) 4307.12 1.10283
\(249\) −758.947 1208.92i −0.193158 0.307679i
\(250\) 3500.40i 0.885539i
\(251\) −652.142 −0.163995 −0.0819976 0.996633i \(-0.526130\pi\)
−0.0819976 + 0.996633i \(0.526130\pi\)
\(252\) 0 0
\(253\) −8921.22 −2.21689
\(254\) 3967.82i 0.980169i
\(255\) 1038.90 + 1654.85i 0.255131 + 0.406395i
\(256\) 360.828 0.0880927
\(257\) −6873.84 −1.66840 −0.834199 0.551464i \(-0.814069\pi\)
−0.834199 + 0.551464i \(0.814069\pi\)
\(258\) −744.485 + 467.381i −0.179650 + 0.112782i
\(259\) 0 0
\(260\) 91.4659i 0.0218172i
\(261\) −139.235 67.1878i −0.0330209 0.0159342i
\(262\) 2525.03i 0.595407i
\(263\) 3285.60i 0.770337i −0.922846 0.385169i \(-0.874143\pi\)
0.922846 0.385169i \(-0.125857\pi\)
\(264\) 2629.94 + 4189.20i 0.613112 + 0.976618i
\(265\) 560.633i 0.129960i
\(266\) 0 0
\(267\) 1494.87 + 2381.16i 0.342638 + 0.545785i
\(268\) −169.555 −0.0386464
\(269\) 1257.58 0.285040 0.142520 0.989792i \(-0.454479\pi\)
0.142520 + 0.989792i \(0.454479\pi\)
\(270\) −248.467 2228.95i −0.0560046 0.502406i
\(271\) 370.755i 0.0831061i 0.999136 + 0.0415530i \(0.0132306\pi\)
−0.999136 + 0.0415530i \(0.986769\pi\)
\(272\) −4443.46 −0.990530
\(273\) 0 0
\(274\) 8716.43 1.92182
\(275\) 4014.31i 0.880263i
\(276\) −216.076 + 135.651i −0.0471242 + 0.0295841i
\(277\) −1540.16 −0.334078 −0.167039 0.985950i \(-0.553421\pi\)
−0.167039 + 0.985950i \(0.553421\pi\)
\(278\) 1871.50 0.403760
\(279\) 4700.29 + 2268.12i 1.00860 + 0.486698i
\(280\) 0 0
\(281\) 3782.78i 0.803066i 0.915845 + 0.401533i \(0.131522\pi\)
−0.915845 + 0.401533i \(0.868478\pi\)
\(282\) −1876.30 + 1177.93i −0.396214 + 0.248739i
\(283\) 9263.07i 1.94570i 0.231441 + 0.972849i \(0.425656\pi\)
−0.231441 + 0.972849i \(0.574344\pi\)
\(284\) 72.6306i 0.0151755i
\(285\) −1945.06 + 1221.09i −0.404264 + 0.253793i
\(286\) 8561.34i 1.77008i
\(287\) 0 0
\(288\) 258.651 + 124.812i 0.0529207 + 0.0255368i
\(289\) −356.285 −0.0725187
\(290\) −91.5330 −0.0185345
\(291\) −182.482 + 114.561i −0.0367605 + 0.0230779i
\(292\) 194.472i 0.0389746i
\(293\) −7316.39 −1.45880 −0.729399 0.684089i \(-0.760200\pi\)
−0.729399 + 0.684089i \(0.760200\pi\)
\(294\) 0 0
\(295\) 4114.94 0.812140
\(296\) 3645.66i 0.715877i
\(297\) 663.991 + 5956.53i 0.129726 + 1.16375i
\(298\) −1134.89 −0.220612
\(299\) 14583.9 2.82076
\(300\) 61.0393 + 97.2287i 0.0117470 + 0.0187117i
\(301\) 0 0
\(302\) 2023.50i 0.385561i
\(303\) −3491.27 5561.20i −0.661941 1.05440i
\(304\) 5222.69i 0.985335i
\(305\) 1988.40i 0.373297i
\(306\) −4710.52 2273.05i −0.880008 0.424647i
\(307\) 4347.69i 0.808260i 0.914701 + 0.404130i \(0.132426\pi\)
−0.914701 + 0.404130i \(0.867574\pi\)
\(308\) 0 0
\(309\) −1361.71 + 854.867i −0.250695 + 0.157384i
\(310\) 3089.96 0.566123
\(311\) −4550.35 −0.829667 −0.414833 0.909897i \(-0.636160\pi\)
−0.414833 + 0.909897i \(0.636160\pi\)
\(312\) −4299.26 6848.24i −0.780121 1.24265i
\(313\) 8447.73i 1.52554i 0.646670 + 0.762770i \(0.276161\pi\)
−0.646670 + 0.762770i \(0.723839\pi\)
\(314\) −4585.17 −0.824063
\(315\) 0 0
\(316\) −109.846 −0.0195549
\(317\) 3333.54i 0.590632i 0.955400 + 0.295316i \(0.0954249\pi\)
−0.955400 + 0.295316i \(0.904575\pi\)
\(318\) 797.919 + 1271.00i 0.140708 + 0.224132i
\(319\) 244.608 0.0429323
\(320\) −2763.47 −0.482758
\(321\) −3941.86 + 2474.67i −0.685400 + 0.430288i
\(322\) 0 0
\(323\) 5355.81i 0.922617i
\(324\) 106.654 + 134.174i 0.0182876 + 0.0230065i
\(325\) 6562.36i 1.12004i
\(326\) 7852.67i 1.33411i
\(327\) −4394.50 6999.94i −0.743169 1.18379i
\(328\) 1295.00i 0.218001i
\(329\) 0 0
\(330\) 1886.74 + 3005.36i 0.314732 + 0.501333i
\(331\) −7496.89 −1.24491 −0.622457 0.782654i \(-0.713865\pi\)
−0.622457 + 0.782654i \(0.713865\pi\)
\(332\) 64.5870 0.0106767
\(333\) −1919.80 + 3978.46i −0.315929 + 0.654709i
\(334\) 70.8045i 0.0115996i
\(335\) 4017.28 0.655186
\(336\) 0 0
\(337\) 5107.78 0.825633 0.412817 0.910814i \(-0.364545\pi\)
0.412817 + 0.910814i \(0.364545\pi\)
\(338\) 7690.84i 1.23765i
\(339\) 3783.98 2375.55i 0.606246 0.380596i
\(340\) −88.4113 −0.0141023
\(341\) −8257.45 −1.31134
\(342\) 2671.67 5536.59i 0.422420 0.875393i
\(343\) 0 0
\(344\) 1313.59i 0.205884i
\(345\) 5119.51 3213.98i 0.798913 0.501550i
\(346\) 4027.93i 0.625846i
\(347\) 2966.35i 0.458910i 0.973319 + 0.229455i \(0.0736944\pi\)
−0.973319 + 0.229455i \(0.926306\pi\)
\(348\) 5.92452 3.71936i 0.000912608 0.000572927i
\(349\) 2869.90i 0.440178i 0.975480 + 0.220089i \(0.0706348\pi\)
−0.975480 + 0.220089i \(0.929365\pi\)
\(350\) 0 0
\(351\) −1085.45 9737.37i −0.165063 1.48075i
\(352\) −454.397 −0.0688052
\(353\) −12653.2 −1.90783 −0.953913 0.300083i \(-0.902986\pi\)
−0.953913 + 0.300083i \(0.902986\pi\)
\(354\) −9328.87 + 5856.58i −1.40063 + 0.879304i
\(355\) 1720.84i 0.257275i
\(356\) −127.215 −0.0189392
\(357\) 0 0
\(358\) −4920.15 −0.726363
\(359\) 6591.26i 0.969006i −0.874790 0.484503i \(-0.839000\pi\)
0.874790 0.484503i \(-0.161000\pi\)
\(360\) −3018.42 1456.53i −0.441902 0.213239i
\(361\) 563.957 0.0822214
\(362\) 5872.55 0.852637
\(363\) −1364.76 2173.91i −0.197331 0.314327i
\(364\) 0 0
\(365\) 4607.62i 0.660751i
\(366\) −2829.98 4507.85i −0.404168 0.643795i
\(367\) 10286.0i 1.46301i −0.681836 0.731505i \(-0.738818\pi\)
0.681836 0.731505i \(-0.261182\pi\)
\(368\) 13746.4i 1.94724i
\(369\) −681.943 + 1413.21i −0.0962074 + 0.199373i
\(370\) 2615.43i 0.367485i
\(371\) 0 0
\(372\) −199.999 + 125.558i −0.0278750 + 0.0174996i
\(373\) 4411.01 0.612314 0.306157 0.951981i \(-0.400957\pi\)
0.306157 + 0.951981i \(0.400957\pi\)
\(374\) 8275.42 1.14415
\(375\) −3370.00 5368.03i −0.464069 0.739210i
\(376\) 3310.60i 0.454072i
\(377\) −399.870 −0.0546269
\(378\) 0 0
\(379\) 3838.27 0.520207 0.260103 0.965581i \(-0.416243\pi\)
0.260103 + 0.965581i \(0.416243\pi\)
\(380\) 103.916i 0.0140283i
\(381\) 3820.00 + 6084.83i 0.513660 + 0.818202i
\(382\) 9679.78 1.29649
\(383\) −2126.75 −0.283739 −0.141869 0.989885i \(-0.545311\pi\)
−0.141869 + 0.989885i \(0.545311\pi\)
\(384\) 6639.45 4168.19i 0.882339 0.553924i
\(385\) 0 0
\(386\) 1219.41i 0.160794i
\(387\) −691.733 + 1433.50i −0.0908598 + 0.188292i
\(388\) 9.74922i 0.00127562i
\(389\) 7218.57i 0.940864i −0.882436 0.470432i \(-0.844098\pi\)
0.882436 0.470432i \(-0.155902\pi\)
\(390\) −3084.33 4912.98i −0.400464 0.637894i
\(391\) 14096.8i 1.82329i
\(392\) 0 0
\(393\) −2430.96 3872.24i −0.312025 0.497020i
\(394\) 12685.7 1.62207
\(395\) 2602.60 0.331521
\(396\) −244.240 117.858i −0.0309938 0.0149560i
\(397\) 115.449i 0.0145950i −0.999973 0.00729750i \(-0.997677\pi\)
0.999973 0.00729750i \(-0.00232289\pi\)
\(398\) 4527.79 0.570245
\(399\) 0 0
\(400\) 6185.54 0.773192
\(401\) 8905.68i 1.10905i 0.832168 + 0.554524i \(0.187100\pi\)
−0.832168 + 0.554524i \(0.812900\pi\)
\(402\) −9107.46 + 5717.58i −1.12995 + 0.709370i
\(403\) 13498.8 1.66854
\(404\) 297.110 0.0365885
\(405\) −2526.95 3178.99i −0.310037 0.390037i
\(406\) 0 0
\(407\) 6989.33i 0.851224i
\(408\) −6619.53 + 4155.68i −0.803225 + 0.504257i
\(409\) 6752.61i 0.816370i −0.912899 0.408185i \(-0.866162\pi\)
0.912899 0.408185i \(-0.133838\pi\)
\(410\) 929.041i 0.111908i
\(411\) 13367.0 8391.70i 1.60425 1.00713i
\(412\) 72.7499i 0.00869934i
\(413\) 0 0
\(414\) −7032.00 + 14572.6i −0.834793 + 1.72997i
\(415\) −1530.26 −0.181007
\(416\) 742.820 0.0875475
\(417\) 2870.04 1801.78i 0.337041 0.211591i
\(418\) 9726.65i 1.13815i
\(419\) 888.062 0.103543 0.0517717 0.998659i \(-0.483513\pi\)
0.0517717 + 0.998659i \(0.483513\pi\)
\(420\) 0 0
\(421\) −14976.0 −1.73369 −0.866847 0.498574i \(-0.833857\pi\)
−0.866847 + 0.498574i \(0.833857\pi\)
\(422\) 2614.47i 0.301589i
\(423\) −1743.35 + 3612.81i −0.200390 + 0.415273i
\(424\) 2242.58 0.256861
\(425\) −6343.20 −0.723977
\(426\) −2449.18 3901.27i −0.278552 0.443702i
\(427\) 0 0
\(428\) 210.596i 0.0237840i
\(429\) 8242.39 + 13129.2i 0.927614 + 1.47758i
\(430\) 942.379i 0.105687i
\(431\) 1095.38i 0.122419i 0.998125 + 0.0612095i \(0.0194958\pi\)
−0.998125 + 0.0612095i \(0.980504\pi\)
\(432\) 9178.23 1023.12i 1.02219 0.113947i
\(433\) 12688.2i 1.40822i 0.710093 + 0.704108i \(0.248653\pi\)
−0.710093 + 0.704108i \(0.751347\pi\)
\(434\) 0 0
\(435\) −140.370 + 88.1230i −0.0154718 + 0.00971304i
\(436\) 373.976 0.0410784
\(437\) 16568.9 1.81373
\(438\) 6557.78 + 10445.8i 0.715395 + 1.13954i
\(439\) 13445.2i 1.46175i −0.682513 0.730873i \(-0.739113\pi\)
0.682513 0.730873i \(-0.260887\pi\)
\(440\) 5302.74 0.574541
\(441\) 0 0
\(442\) −13528.1 −1.45581
\(443\) 2276.97i 0.244204i 0.992518 + 0.122102i \(0.0389634\pi\)
−0.992518 + 0.122102i \(0.961037\pi\)
\(444\) −106.276 169.285i −0.0113595 0.0180944i
\(445\) 3014.10 0.321083
\(446\) 8810.61 0.935414
\(447\) −1740.40 + 1092.61i −0.184157 + 0.115612i
\(448\) 0 0
\(449\) 1685.89i 0.177198i 0.996067 + 0.0885991i \(0.0282390\pi\)
−0.996067 + 0.0885991i \(0.971761\pi\)
\(450\) 6557.30 + 3164.22i 0.686921 + 0.331472i
\(451\) 2482.72i 0.259217i
\(452\) 202.161i 0.0210373i
\(453\) −1948.12 3103.13i −0.202054 0.321849i
\(454\) 9621.12i 0.994585i
\(455\) 0 0
\(456\) −4884.45 7780.38i −0.501613 0.799013i
\(457\) −2083.59 −0.213275 −0.106637 0.994298i \(-0.534008\pi\)
−0.106637 + 0.994298i \(0.534008\pi\)
\(458\) −12493.2 −1.27460
\(459\) −9412.17 + 1049.20i −0.957130 + 0.106694i
\(460\) 273.512i 0.0277230i
\(461\) 14128.1 1.42736 0.713679 0.700473i \(-0.247028\pi\)
0.713679 + 0.700473i \(0.247028\pi\)
\(462\) 0 0
\(463\) 16141.5 1.62021 0.810106 0.586283i \(-0.199409\pi\)
0.810106 + 0.586283i \(0.199409\pi\)
\(464\) 376.909i 0.0377103i
\(465\) 4738.60 2974.85i 0.472575 0.296678i
\(466\) 10570.6 1.05080
\(467\) −6249.38 −0.619244 −0.309622 0.950860i \(-0.600203\pi\)
−0.309622 + 0.950860i \(0.600203\pi\)
\(468\) 399.269 + 192.667i 0.0394364 + 0.0190300i
\(469\) 0 0
\(470\) 2375.05i 0.233091i
\(471\) −7031.56 + 4414.35i −0.687892 + 0.431852i
\(472\) 16460.1i 1.60516i
\(473\) 2518.36i 0.244809i
\(474\) −5900.27 + 3704.14i −0.571748 + 0.358938i
\(475\) 7455.58i 0.720180i
\(476\) 0 0
\(477\) 2447.29 + 1180.94i 0.234914 + 0.113357i
\(478\) −13021.1 −1.24597
\(479\) 10624.2 1.01343 0.506713 0.862115i \(-0.330860\pi\)
0.506713 + 0.862115i \(0.330860\pi\)
\(480\) 260.759 163.702i 0.0247957 0.0155665i
\(481\) 11425.7i 1.08309i
\(482\) −6373.86 −0.602327
\(483\) 0 0
\(484\) 116.142 0.0109074
\(485\) 230.989i 0.0216261i
\(486\) 10253.2 + 3610.52i 0.956989 + 0.336988i
\(487\) −3970.15 −0.369414 −0.184707 0.982794i \(-0.559134\pi\)
−0.184707 + 0.982794i \(0.559134\pi\)
\(488\) −7953.76 −0.737807
\(489\) −7560.13 12042.4i −0.699143 1.11366i
\(490\) 0 0
\(491\) 4184.69i 0.384628i 0.981333 + 0.192314i \(0.0615993\pi\)
−0.981333 + 0.192314i \(0.938401\pi\)
\(492\) −37.7508 60.1327i −0.00345922 0.00551015i
\(493\) 386.516i 0.0353099i
\(494\) 15900.5i 1.44818i
\(495\) 5786.80 + 2792.41i 0.525449 + 0.253555i
\(496\) 12723.7i 1.15183i
\(497\) 0 0
\(498\) 3469.22 2177.94i 0.312167 0.195976i
\(499\) 18462.3 1.65628 0.828141 0.560520i \(-0.189399\pi\)
0.828141 + 0.560520i \(0.189399\pi\)
\(500\) 286.790 0.0256512
\(501\) −68.1668 108.582i −0.00607877 0.00968280i
\(502\) 1871.44i 0.166388i
\(503\) 11828.5 1.04853 0.524263 0.851557i \(-0.324341\pi\)
0.524263 + 0.851557i \(0.324341\pi\)
\(504\) 0 0
\(505\) −7039.44 −0.620299
\(506\) 25601.1i 2.24923i
\(507\) −7404.33 11794.3i −0.648595 1.03314i
\(508\) −325.085 −0.0283924
\(509\) −797.139 −0.0694157 −0.0347078 0.999398i \(-0.511050\pi\)
−0.0347078 + 0.999398i \(0.511050\pi\)
\(510\) −4748.91 + 2981.32i −0.412324 + 0.258853i
\(511\) 0 0
\(512\) 11034.1i 0.952425i
\(513\) −1233.20 11062.8i −0.106134 0.952110i
\(514\) 19725.8i 1.69274i
\(515\) 1723.67i 0.147483i
\(516\) −38.2927 60.9960i −0.00326694 0.00520388i
\(517\) 6346.96i 0.539921i
\(518\) 0 0
\(519\) 3877.87 + 6177.01i 0.327976 + 0.522429i
\(520\) −8668.60 −0.731044
\(521\) −8365.75 −0.703475 −0.351737 0.936099i \(-0.614409\pi\)
−0.351737 + 0.936099i \(0.614409\pi\)
\(522\) 192.808 399.562i 0.0161666 0.0335026i
\(523\) 3623.04i 0.302915i −0.988464 0.151457i \(-0.951603\pi\)
0.988464 0.151457i \(-0.0483966\pi\)
\(524\) 206.877 0.0172470
\(525\) 0 0
\(526\) 9428.65 0.781575
\(527\) 13048.0i 1.07852i
\(528\) −12375.3 + 7769.10i −1.02001 + 0.640354i
\(529\) −31443.4 −2.58432
\(530\) 1608.84 0.131856
\(531\) −8667.85 + 17962.7i −0.708386 + 1.46801i
\(532\) 0 0
\(533\) 4058.60i 0.329827i
\(534\) −6833.18 + 4289.81i −0.553747 + 0.347637i
\(535\) 4989.66i 0.403219i
\(536\) 16069.4i 1.29495i
\(537\) −7545.27 + 4736.85i −0.606336 + 0.380652i
\(538\) 3608.86i 0.289199i
\(539\) 0 0
\(540\) 182.619 20.3570i 0.0145531 0.00162227i
\(541\) 2220.96 0.176500 0.0882501 0.996098i \(-0.471873\pi\)
0.0882501 + 0.996098i \(0.471873\pi\)
\(542\) −1063.95 −0.0843185
\(543\) 9005.83 5653.78i 0.711744 0.446826i
\(544\) 718.012i 0.0565892i
\(545\) −8860.62 −0.696417
\(546\) 0 0
\(547\) 10592.4 0.827969 0.413985 0.910284i \(-0.364137\pi\)
0.413985 + 0.910284i \(0.364137\pi\)
\(548\) 714.141i 0.0556690i
\(549\) −8679.82 4188.43i −0.674765 0.325607i
\(550\) −11519.8 −0.893104
\(551\) −454.298 −0.0351248
\(552\) 12856.2 + 20478.4i 0.991295 + 1.57902i
\(553\) 0 0
\(554\) 4419.79i 0.338951i
\(555\) 2517.99 + 4010.88i 0.192582 + 0.306761i
\(556\) 153.333i 0.0116956i
\(557\) 989.584i 0.0752783i 0.999291 + 0.0376392i \(0.0119837\pi\)
−0.999291 + 0.0376392i \(0.988016\pi\)
\(558\) −6508.80 + 13488.4i −0.493798 + 1.02331i
\(559\) 4116.87i 0.311494i
\(560\) 0 0
\(561\) 12690.7 7967.12i 0.955086 0.599594i
\(562\) −10855.4 −0.814781
\(563\) −16789.7 −1.25684 −0.628422 0.777872i \(-0.716299\pi\)
−0.628422 + 0.777872i \(0.716299\pi\)
\(564\) −96.5080 153.726i −0.00720518 0.0114770i
\(565\) 4789.81i 0.356653i
\(566\) −26582.1 −1.97408
\(567\) 0 0
\(568\) −6883.50 −0.508495
\(569\) 11077.7i 0.816174i 0.912943 + 0.408087i \(0.133804\pi\)
−0.912943 + 0.408087i \(0.866196\pi\)
\(570\) −3504.14 5581.71i −0.257496 0.410161i
\(571\) −4213.19 −0.308785 −0.154393 0.988010i \(-0.549342\pi\)
−0.154393 + 0.988010i \(0.549342\pi\)
\(572\) −701.434 −0.0512735
\(573\) 14844.4 9319.17i 1.08226 0.679431i
\(574\) 0 0
\(575\) 19623.6i 1.42323i
\(576\) 5821.06 12063.2i 0.421083 0.872624i
\(577\) 1676.34i 0.120948i −0.998170 0.0604738i \(-0.980739\pi\)
0.998170 0.0604738i \(-0.0192612\pi\)
\(578\) 1022.43i 0.0735767i
\(579\) −1173.98 1870.02i −0.0842644 0.134224i
\(580\) 7.49934i 0.000536885i
\(581\) 0 0
\(582\) −328.754 523.668i −0.0234146 0.0372968i
\(583\) −4299.39 −0.305424
\(584\) 18430.9 1.30595
\(585\) −9459.91 4564.86i −0.668580 0.322622i
\(586\) 20995.8i 1.48008i
\(587\) −22687.3 −1.59524 −0.797620 0.603161i \(-0.793908\pi\)
−0.797620 + 0.603161i \(0.793908\pi\)
\(588\) 0 0
\(589\) 15336.1 1.07286
\(590\) 11808.6i 0.823988i
\(591\) 19454.1 12213.1i 1.35404 0.850052i
\(592\) −10769.6 −0.747685
\(593\) 17961.5 1.24383 0.621916 0.783084i \(-0.286355\pi\)
0.621916 + 0.783084i \(0.286355\pi\)
\(594\) −17093.4 + 1905.45i −1.18072 + 0.131619i
\(595\) 0 0
\(596\) 92.9820i 0.00639042i
\(597\) 6943.57 4359.11i 0.476016 0.298838i
\(598\) 41851.2i 2.86191i
\(599\) 6899.45i 0.470624i −0.971920 0.235312i \(-0.924389\pi\)
0.971920 0.235312i \(-0.0756112\pi\)
\(600\) 9214.76 5784.94i 0.626985 0.393615i
\(601\) 19792.8i 1.34337i 0.740838 + 0.671684i \(0.234429\pi\)
−0.740838 + 0.671684i \(0.765571\pi\)
\(602\) 0 0
\(603\) −8462.13 + 17536.3i −0.571484 + 1.18430i
\(604\) 165.786 0.0111685
\(605\) −2751.76 −0.184918
\(606\) 15958.9 10018.9i 1.06978 0.671597i
\(607\) 17838.2i 1.19280i 0.802688 + 0.596399i \(0.203402\pi\)
−0.802688 + 0.596399i \(0.796598\pi\)
\(608\) 843.928 0.0562924
\(609\) 0 0
\(610\) −5706.09 −0.378743
\(611\) 10375.6i 0.686993i
\(612\) 186.232 385.935i 0.0123007 0.0254910i
\(613\) 6785.09 0.447059 0.223530 0.974697i \(-0.428242\pi\)
0.223530 + 0.974697i \(0.428242\pi\)
\(614\) −12476.5 −0.820052
\(615\) 894.431 + 1424.73i 0.0586454 + 0.0934155i
\(616\) 0 0
\(617\) 3472.07i 0.226549i 0.993564 + 0.113274i \(0.0361339\pi\)
−0.993564 + 0.113274i \(0.963866\pi\)
\(618\) −2453.20 3907.67i −0.159680 0.254352i
\(619\) 7359.94i 0.477901i 0.971032 + 0.238951i \(0.0768034\pi\)
−0.971032 + 0.238951i \(0.923197\pi\)
\(620\) 253.162i 0.0163988i
\(621\) 3245.85 + 29117.8i 0.209745 + 1.88158i
\(622\) 13058.1i 0.841770i
\(623\) 0 0
\(624\) 20230.4 12700.5i 1.29786 0.814784i
\(625\) 4951.14 0.316873
\(626\) −24242.4 −1.54780
\(627\) 9364.29 + 14916.3i 0.596449 + 0.950077i
\(628\) 375.665i 0.0238705i
\(629\) 11044.2 0.700094
\(630\) 0 0
\(631\) −14566.0 −0.918957 −0.459479 0.888189i \(-0.651964\pi\)
−0.459479 + 0.888189i \(0.651964\pi\)
\(632\) 10410.6i 0.655239i
\(633\) 2517.07 + 4009.41i 0.158048 + 0.251753i
\(634\) −9566.23 −0.599248
\(635\) 7702.26 0.481346
\(636\) −104.133 + 65.3739i −0.00649238 + 0.00407585i
\(637\) 0 0
\(638\) 701.949i 0.0435586i
\(639\) −7511.86 3624.84i −0.465046 0.224407i
\(640\) 8404.31i 0.519077i
\(641\) 2089.00i 0.128722i 0.997927 + 0.0643609i \(0.0205009\pi\)
−0.997927 + 0.0643609i \(0.979499\pi\)
\(642\) −7101.52 11311.9i −0.436565 0.695399i
\(643\) 9732.76i 0.596925i −0.954421 0.298462i \(-0.903526\pi\)
0.954421 0.298462i \(-0.0964737\pi\)
\(644\) 0 0
\(645\) 907.272 + 1445.18i 0.0553857 + 0.0882232i
\(646\) −15369.5 −0.936077
\(647\) 18491.0 1.12358 0.561790 0.827280i \(-0.310113\pi\)
0.561790 + 0.827280i \(0.310113\pi\)
\(648\) 12716.2 10108.0i 0.770894 0.612777i
\(649\) 31556.7i 1.90864i
\(650\) 18831.9 1.13638
\(651\) 0 0
\(652\) 643.373 0.0386449
\(653\) 5592.68i 0.335158i 0.985859 + 0.167579i \(0.0535950\pi\)
−0.985859 + 0.167579i \(0.946405\pi\)
\(654\) 20087.7 12610.8i 1.20105 0.754011i
\(655\) −4901.54 −0.292395
\(656\) −3825.55 −0.227687
\(657\) 20113.3 + 9705.65i 1.19436 + 0.576337i
\(658\) 0 0
\(659\) 9543.49i 0.564130i −0.959395 0.282065i \(-0.908981\pi\)
0.959395 0.282065i \(-0.0910193\pi\)
\(660\) −246.231 + 154.581i −0.0145220 + 0.00911678i
\(661\) 6778.91i 0.398894i 0.979909 + 0.199447i \(0.0639146\pi\)
−0.979909 + 0.199447i \(0.936085\pi\)
\(662\) 21513.7i 1.26307i
\(663\) −20746.0 + 13024.2i −1.21525 + 0.762921i
\(664\) 6121.18i 0.357753i
\(665\) 0 0
\(666\) −11416.9 5509.22i −0.664260 0.320538i
\(667\) 1195.74 0.0694141
\(668\) 5.80105 0.000336002
\(669\) 13511.5 8482.38i 0.780843 0.490206i
\(670\) 11528.3i 0.664744i
\(671\) 15248.7 0.877300
\(672\) 0 0
\(673\) −25094.5 −1.43733 −0.718663 0.695359i \(-0.755246\pi\)
−0.718663 + 0.695359i \(0.755246\pi\)
\(674\) 14657.7i 0.837678i
\(675\) 13102.3 1460.55i 0.747120 0.0832836i
\(676\) 630.114 0.0358508
\(677\) 26332.2 1.49487 0.747435 0.664335i \(-0.231285\pi\)
0.747435 + 0.664335i \(0.231285\pi\)
\(678\) 6817.08 + 10858.8i 0.386148 + 0.615090i
\(679\) 0 0
\(680\) 8379.10i 0.472535i
\(681\) −9262.69 14754.4i −0.521214 0.830236i
\(682\) 23696.3i 1.33047i
\(683\) 2346.73i 0.131472i 0.997837 + 0.0657359i \(0.0209395\pi\)
−0.997837 + 0.0657359i \(0.979061\pi\)
\(684\) 453.615 + 218.891i 0.0253573 + 0.0122361i
\(685\) 16920.2i 0.943777i
\(686\) 0 0
\(687\) −19158.9 + 12027.8i −1.06398 + 0.667959i
\(688\) −3880.47 −0.215031
\(689\) 7028.38 0.388621
\(690\) 9223.12 + 14691.4i 0.508867 + 0.810568i
\(691\) 11233.2i 0.618421i −0.950994 0.309211i \(-0.899935\pi\)
0.950994 0.309211i \(-0.100065\pi\)
\(692\) −330.010 −0.0181288
\(693\) 0 0
\(694\) −8512.50 −0.465605
\(695\) 3632.93i 0.198280i
\(696\) −352.499 561.491i −0.0191975 0.0305794i
\(697\) 3923.06 0.213194
\(698\) −8235.72 −0.446600
\(699\) 16210.4 10176.8i 0.877160 0.550673i
\(700\) 0 0
\(701\) 17277.2i 0.930887i −0.885078 0.465443i \(-0.845895\pi\)
0.885078 0.465443i \(-0.154105\pi\)
\(702\) 27943.2 3114.91i 1.50235 0.167471i
\(703\) 12980.9i 0.696422i
\(704\) 21192.5i 1.13455i
\(705\) 2286.57 + 3642.25i 0.122152 + 0.194574i
\(706\) 36310.8i 1.93566i
\(707\) 0 0
\(708\) −479.832 764.319i −0.0254706 0.0405718i
\(709\) 18839.1 0.997910 0.498955 0.866628i \(-0.333717\pi\)
0.498955 + 0.866628i \(0.333717\pi\)
\(710\) −4938.28 −0.261029
\(711\) −5482.20 + 11360.9i −0.289168 + 0.599252i
\(712\) 12056.6i 0.634609i
\(713\) −40365.7 −2.12020
\(714\) 0 0
\(715\) 16619.1 0.869259
\(716\) 403.110i 0.0210404i
\(717\) −19968.5 + 12536.0i −1.04008 + 0.652951i
\(718\) 18914.9 0.983142
\(719\) −10519.4 −0.545630 −0.272815 0.962067i \(-0.587955\pi\)
−0.272815 + 0.962067i \(0.587955\pi\)
\(720\) 4302.74 8916.71i 0.222714 0.461536i
\(721\) 0 0
\(722\) 1618.38i 0.0834209i
\(723\) −9774.61 + 6136.41i −0.502796 + 0.315651i
\(724\) 481.141i 0.0246982i
\(725\) 538.051i 0.0275624i
\(726\) 6238.44 3916.44i 0.318912 0.200210i
\(727\) 1692.44i 0.0863401i 0.999068 + 0.0431700i \(0.0137457\pi\)
−0.999068 + 0.0431700i \(0.986254\pi\)
\(728\) 0 0
\(729\) 19199.8 4334.38i 0.975453 0.220209i
\(730\) 13222.5 0.670390
\(731\) 3979.38 0.201344
\(732\) 369.330 231.862i 0.0186487 0.0117075i
\(733\) 30431.1i 1.53342i −0.641991 0.766712i \(-0.721892\pi\)
0.641991 0.766712i \(-0.278108\pi\)
\(734\) 29517.6 1.48435
\(735\) 0 0
\(736\) −2221.27 −0.111246
\(737\) 30807.7i 1.53978i
\(738\) −4055.48 1956.96i −0.202282 0.0976109i
\(739\) 4913.38 0.244576 0.122288 0.992495i \(-0.460977\pi\)
0.122288 + 0.992495i \(0.460977\pi\)
\(740\) −214.283 −0.0106449
\(741\) −15308.2 24384.2i −0.758920 1.20887i
\(742\) 0 0
\(743\) 27101.5i 1.33816i −0.743188 0.669082i \(-0.766687\pi\)
0.743188 0.669082i \(-0.233313\pi\)
\(744\) 11899.6 + 18954.8i 0.586373 + 0.934026i
\(745\) 2203.03i 0.108339i
\(746\) 12658.2i 0.621247i
\(747\) 3223.40 6679.95i 0.157882 0.327184i
\(748\) 678.009i 0.0331423i
\(749\) 0 0
\(750\) 15404.6 9670.84i 0.749994 0.470839i
\(751\) 16616.9 0.807403 0.403701 0.914891i \(-0.367723\pi\)
0.403701 + 0.914891i \(0.367723\pi\)
\(752\) −9779.84 −0.474247
\(753\) −1801.72 2869.94i −0.0871959 0.138893i
\(754\) 1147.50i 0.0554239i
\(755\) −3927.98 −0.189343
\(756\) 0 0
\(757\) −29748.9 −1.42833 −0.714163 0.699980i \(-0.753192\pi\)
−0.714163 + 0.699980i \(0.753192\pi\)
\(758\) 11014.6i 0.527796i
\(759\) −24647.4 39260.5i −1.17871 1.87756i
\(760\) −9848.51 −0.470057
\(761\) −4756.16 −0.226558 −0.113279 0.993563i \(-0.536135\pi\)
−0.113279 + 0.993563i \(0.536135\pi\)
\(762\) −17461.6 + 10962.2i −0.830139 + 0.521153i
\(763\) 0 0
\(764\) 793.069i 0.0375553i
\(765\) −4412.41 + 9143.98i −0.208538 + 0.432159i
\(766\) 6103.12i 0.287878i
\(767\) 51587.0i 2.42855i
\(768\) 996.888 + 1587.93i 0.0468387 + 0.0746088i
\(769\) 9226.71i 0.432671i 0.976319 + 0.216335i \(0.0694104\pi\)
−0.976319 + 0.216335i \(0.930590\pi\)
\(770\) 0 0
\(771\) −18990.9 30250.4i −0.887083 1.41302i
\(772\) 99.9070 0.00465768
\(773\) −4745.02 −0.220785 −0.110392 0.993888i \(-0.535211\pi\)
−0.110392 + 0.993888i \(0.535211\pi\)
\(774\) −4113.70 1985.06i −0.191039 0.0921853i
\(775\) 18163.5i 0.841873i
\(776\) −923.973 −0.0427432
\(777\) 0 0
\(778\) 20715.1 0.954590
\(779\) 4611.03i 0.212076i
\(780\) 402.523 252.700i 0.0184777 0.0116002i
\(781\) 13196.8 0.604633
\(782\) 40453.5 1.84989
\(783\) −88.9968 798.372i −0.00406192 0.0364387i
\(784\) 0 0
\(785\) 8900.65i 0.404685i
\(786\) 11112.1 6976.09i