Properties

Label 147.4.c.b.146.7
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 146.7
Character \(\chi\) \(=\) 147.146
Dual form 147.4.c.b.146.17

$q$-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 \(-0.830646\pi\)
0.861773 0.507294i \(-0.169354\pi\)
\(3\) −2.76278 + 4.40080i −0.531698 + 0.846934i
\(4\) −0.235115 −0.0293894
\(5\) −5.57059 −0.498249 −0.249124 0.968471i \(-0.580143\pi\)
−0.249124 + 0.968471i \(0.580143\pi\)
\(6\) 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 \(0.199093\pi\)
−0.810689 + 0.585477i \(0.800907\pi\)
\(12\) 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 \(-0.659918\pi\)
−0.481529 + 0.876430i \(0.659918\pi\)
\(18\) −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 \(0.395522\pi\)
−0.322365 + 0.946615i \(0.604478\pi\)
\(24\) 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 \(-0.994164\pi\)
0.999832 0.0183322i \(-0.00583564\pi\)
\(30\) −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 \(-0.535305\pi\)
−0.110686 + 0.993855i \(0.535305\pi\)
\(42\) 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 \(-0.574052\pi\)
−0.230547 + 0.973061i \(0.574052\pi\)
\(48\) 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 \(0.0416316\pi\)
−0.991459 + 0.130417i \(0.958368\pi\)
\(54\) 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 \(-0.803260\pi\)
−0.814994 + 0.579469i \(0.803260\pi\)
\(60\) −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 \(-0.916877\pi\)
0.966097 0.258180i \(-0.0831226\pi\)
\(72\) −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 \(-0.441859\pi\)
0.181643 + 0.983365i \(0.441859\pi\)
\(84\) 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 \(-0.604426\pi\)
−0.322212 + 0.946668i \(0.604426\pi\)
\(90\) 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 \(-0.286126\pi\)
0.622479 + 0.782637i \(0.286126\pi\)
\(102\) −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 \(-0.867398\pi\)
0.914478 0.404636i \(-0.132602\pi\)
\(108\) −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 \(0.116509\pi\)
−0.933758 + 0.357906i \(0.883491\pi\)
\(114\) −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 \(-0.405206\pi\)
0.293423 + 0.955983i \(0.405206\pi\)
\(132\) 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 \(0.395995\pi\)
−0.320958 + 0.947093i \(0.604005\pi\)
\(138\) −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 \(-0.965325\pi\)
0.994072 0.108720i \(-0.0346752\pi\)
\(150\) −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 \(-0.498180\pi\)
0.00571638 + 0.999984i \(0.498180\pi\)
\(168\) 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 \(-0.599801\pi\)
−0.308424 + 0.951249i \(0.599801\pi\)
\(174\) 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 \(-0.883473\pi\)
0.933737 0.357959i \(-0.116527\pi\)
\(180\) −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 \(0.220621\pi\)
−0.769268 + 0.638926i \(0.779379\pi\)
\(192\) 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 \(0.294836\pi\)
−0.600832 + 0.799375i \(0.705164\pi\)
\(198\) −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 \(-0.336945\pi\)
0.490142 + 0.871643i \(0.336945\pi\)
\(228\) 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 \(0.173265\pi\)
−0.855475 + 0.517844i \(0.826735\pi\)
\(234\) −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 \(-0.789549\pi\)
0.789287 0.614025i \(-0.210451\pi\)
\(240\) −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 \(-0.473870\pi\)
0.0819976 + 0.996633i \(0.473870\pi\)
\(252\) 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 \(-0.185931\pi\)
0.834199 + 0.551464i \(0.185931\pi\)
\(258\) 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 \(0.125857\pi\)
−0.922846 + 0.385169i \(0.874143\pi\)
\(264\) −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 \(-0.545521\pi\)
−0.142520 + 0.989792i \(0.545521\pi\)
\(270\) −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 \(-0.868478\pi\)
0.915845 0.401533i \(-0.131522\pi\)
\(282\) −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 \(-0.239800\pi\)
0.729399 + 0.684089i \(0.239800\pi\)
\(294\) 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 \(-0.363840\pi\)
0.414833 + 0.909897i \(0.363840\pi\)
\(312\) −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 \(-0.904575\pi\)
0.955400 0.295316i \(-0.0954249\pi\)
\(318\) −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 \(-0.926306\pi\)
0.973319 0.229455i \(-0.0736944\pi\)
\(348\) −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 \(-0.0970143\pi\)
0.953913 + 0.300083i \(0.0970143\pi\)
\(354\) −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 \(0.161000\pi\)
−0.874790 + 0.484503i \(0.839000\pi\)
\(360\) 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 \(-0.454689\pi\)
0.141869 + 0.989885i \(0.454689\pi\)
\(384\) −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 \(0.155902\pi\)
−0.882436 + 0.470432i \(0.844098\pi\)
\(390\) 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 \(-0.812900\pi\)
0.832168 0.554524i \(-0.187100\pi\)
\(402\) 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 \(-0.516487\pi\)
−0.0517717 + 0.998659i \(0.516487\pi\)
\(420\) 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 \(-0.980504\pi\)
0.998125 0.0612095i \(-0.0194958\pi\)
\(432\) −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 \(-0.961037\pi\)
0.992518 0.122102i \(-0.0389634\pi\)
\(444\) 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 \(-0.971761\pi\)
0.996067 0.0885991i \(-0.0282390\pi\)
\(450\) 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 \(-0.752972\pi\)
−0.713679 + 0.700473i \(0.752972\pi\)
\(462\) 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 \(-0.399797\pi\)
0.309622 + 0.950860i \(0.399797\pi\)
\(468\) −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 \(-0.669140\pi\)
−0.506713 + 0.862115i \(0.669140\pi\)
\(480\) 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 \(-0.938401\pi\)
0.981333 0.192314i \(-0.0615993\pi\)
\(492\) −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 \(-0.675659\pi\)
−0.524263 + 0.851557i \(0.675659\pi\)
\(504\) 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 \(-0.488950\pi\)
0.0347078 + 0.999398i \(0.488950\pi\)
\(510\) 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 \(-0.385591\pi\)
0.351737 + 0.936099i \(0.385591\pi\)
\(522\) 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 \(-0.988016\pi\)
0.999291 0.0376392i \(-0.0119837\pi\)
\(558\) 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 \(-0.283701\pi\)
0.628422 + 0.777872i \(0.283701\pi\)
\(564\) −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 \(-0.866196\pi\)
0.912943 0.408087i \(-0.133804\pi\)
\(570\) 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 \(-0.206092\pi\)
0.797620 + 0.603161i \(0.206092\pi\)
\(588\) 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 \(-0.713645\pi\)
−0.621916 + 0.783084i \(0.713645\pi\)
\(594\) 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 \(0.0756112\pi\)
−0.971920 + 0.235312i \(0.924389\pi\)
\(600\) −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 \(-0.963866\pi\)
0.993564 0.113274i \(-0.0361339\pi\)
\(618\) −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 \(-0.979499\pi\)
0.997927 0.0643609i \(-0.0205009\pi\)
\(642\) 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 \(-0.689887\pi\)
−0.561790 + 0.827280i \(0.689887\pi\)
\(648\) 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 \(-0.946405\pi\)
0.985859 0.167579i \(-0.0535950\pi\)
\(654\) −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 \(0.0910193\pi\)
−0.959395 + 0.282065i \(0.908981\pi\)
\(660\) −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 \(-0.768715\pi\)
−0.747435 + 0.664335i \(0.768715\pi\)
\(678\) −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 \(-0.979061\pi\)
0.997837 0.0657359i \(-0.0209395\pi\)
\(684\) −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 \(0.154105\pi\)
−0.885078 + 0.465443i \(0.845895\pi\)
\(702\) 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 \(-0.412045\pi\)
0.272815 + 0.962067i \(0.412045\pi\)
\(720\) −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 \(0.233313\pi\)
−0.743188 + 0.669082i \(0.766687\pi\)
\(744\) 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 \(-0.463865\pi\)
0.113279 + 0.993563i \(0.463865\pi\)
\(762\) 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 \(-0.464789\pi\)
0.110392 + 0.993888i \(0.464789\pi\)
\(774\) −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 0.504271 +