Properties

Label 147.4.c.b.146.20
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 146.20
Character \(\chi\) \(=\) 147.146
Dual form 147.4.c.b.146.6

$q$-expansion

\(f(q)\) \(=\) \(q+3.20022i q^{2} +(0.930073 - 5.11224i) q^{3} -2.24142 q^{4} -11.9763 q^{5} +(16.3603 + 2.97644i) q^{6} +18.4287i q^{8} +(-25.2699 - 9.50951i) q^{9} +O(q^{10})\) \(q+3.20022i q^{2} +(0.930073 - 5.11224i) q^{3} -2.24142 q^{4} -11.9763 q^{5} +(16.3603 + 2.97644i) q^{6} +18.4287i q^{8} +(-25.2699 - 9.50951i) q^{9} -38.3267i q^{10} +60.3470i q^{11} +(-2.08468 + 11.4587i) q^{12} +3.46204i q^{13} +(-11.1388 + 61.2255i) q^{15} -76.9074 q^{16} -32.4937 q^{17} +(30.4325 - 80.8694i) q^{18} +142.952i q^{19} +26.8438 q^{20} -193.124 q^{22} +89.8989i q^{23} +(94.2120 + 17.1401i) q^{24} +18.4309 q^{25} -11.0793 q^{26} +(-72.1177 + 120.341i) q^{27} -247.795i q^{29} +(-195.935 - 35.6466i) q^{30} -207.886i q^{31} -98.6909i q^{32} +(308.508 + 56.1271i) q^{33} -103.987i q^{34} +(56.6405 + 21.3148i) q^{36} +98.3044 q^{37} -457.477 q^{38} +(17.6988 + 3.21995i) q^{39} -220.707i q^{40} -150.249 q^{41} +59.4615 q^{43} -135.263i q^{44} +(302.639 + 113.888i) q^{45} -287.696 q^{46} -232.849 q^{47} +(-71.5295 + 393.169i) q^{48} +58.9830i q^{50} +(-30.2215 + 166.115i) q^{51} -7.75989i q^{52} +292.851i q^{53} +(-385.119 - 230.793i) q^{54} -722.731i q^{55} +(730.803 + 132.956i) q^{57} +792.998 q^{58} +465.699 q^{59} +(24.9667 - 137.232i) q^{60} +13.1309i q^{61} +665.282 q^{62} -299.427 q^{64} -41.4623i q^{65} +(-179.619 + 987.294i) q^{66} +481.684 q^{67} +72.8320 q^{68} +(459.584 + 83.6125i) q^{69} +550.199i q^{71} +(175.248 - 465.693i) q^{72} +372.298i q^{73} +314.596i q^{74} +(17.1421 - 94.2231i) q^{75} -320.415i q^{76} +(-10.3046 + 56.6400i) q^{78} +879.193 q^{79} +921.063 q^{80} +(548.139 + 480.609i) q^{81} -480.832i q^{82} -1119.54 q^{83} +389.153 q^{85} +190.290i q^{86} +(-1266.78 - 230.467i) q^{87} -1112.12 q^{88} +21.2955 q^{89} +(-364.468 + 968.513i) q^{90} -201.501i q^{92} +(-1062.76 - 193.349i) q^{93} -745.169i q^{94} -1712.03i q^{95} +(-504.531 - 91.7897i) q^{96} -612.931i q^{97} +(573.870 - 1524.96i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 96 q^{4} - 64 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.20022i 1.13145i 0.824594 + 0.565725i \(0.191403\pi\)
−0.824594 + 0.565725i \(0.808597\pi\)
\(3\) 0.930073 5.11224i 0.178993 0.983850i
\(4\) −2.24142 −0.280177
\(5\) −11.9763 −1.07119 −0.535595 0.844475i \(-0.679913\pi\)
−0.535595 + 0.844475i \(0.679913\pi\)
\(6\) 16.3603 + 2.97644i 1.11318 + 0.202521i
\(7\) 0 0
\(8\) 18.4287i 0.814443i
\(9\) −25.2699 9.50951i −0.935923 0.352204i
\(10\) 38.3267i 1.21200i
\(11\) 60.3470i 1.65412i 0.562115 + 0.827059i \(0.309988\pi\)
−0.562115 + 0.827059i \(0.690012\pi\)
\(12\) −2.08468 + 11.4587i −0.0501497 + 0.275653i
\(13\) 3.46204i 0.0738613i 0.999318 + 0.0369307i \(0.0117581\pi\)
−0.999318 + 0.0369307i \(0.988242\pi\)
\(14\) 0 0
\(15\) −11.1388 + 61.2255i −0.191735 + 1.05389i
\(16\) −76.9074 −1.20168
\(17\) −32.4937 −0.463581 −0.231790 0.972766i \(-0.574458\pi\)
−0.231790 + 0.972766i \(0.574458\pi\)
\(18\) 30.4325 80.8694i 0.398501 1.05895i
\(19\) 142.952i 1.72607i 0.505142 + 0.863036i \(0.331440\pi\)
−0.505142 + 0.863036i \(0.668560\pi\)
\(20\) 26.8438 0.300123
\(21\) 0 0
\(22\) −193.124 −1.87155
\(23\) 89.8989i 0.815009i 0.913203 + 0.407505i \(0.133601\pi\)
−0.913203 + 0.407505i \(0.866399\pi\)
\(24\) 94.2120 + 17.1401i 0.801290 + 0.145779i
\(25\) 18.4309 0.147447
\(26\) −11.0793 −0.0835703
\(27\) −72.1177 + 120.341i −0.514039 + 0.857767i
\(28\) 0 0
\(29\) 247.795i 1.58670i −0.608766 0.793350i \(-0.708335\pi\)
0.608766 0.793350i \(-0.291665\pi\)
\(30\) −195.935 35.6466i −1.19242 0.216938i
\(31\) 207.886i 1.20443i −0.798332 0.602217i \(-0.794284\pi\)
0.798332 0.602217i \(-0.205716\pi\)
\(32\) 98.6909i 0.545195i
\(33\) 308.508 + 56.1271i 1.62740 + 0.296075i
\(34\) 103.987i 0.524518i
\(35\) 0 0
\(36\) 56.6405 + 21.3148i 0.262225 + 0.0986796i
\(37\) 98.3044 0.436787 0.218394 0.975861i \(-0.429918\pi\)
0.218394 + 0.975861i \(0.429918\pi\)
\(38\) −457.477 −1.95296
\(39\) 17.6988 + 3.21995i 0.0726685 + 0.0132206i
\(40\) 220.707i 0.872423i
\(41\) −150.249 −0.572318 −0.286159 0.958182i \(-0.592378\pi\)
−0.286159 + 0.958182i \(0.592378\pi\)
\(42\) 0 0
\(43\) 59.4615 0.210879 0.105439 0.994426i \(-0.466375\pi\)
0.105439 + 0.994426i \(0.466375\pi\)
\(44\) 135.263i 0.463447i
\(45\) 302.639 + 113.888i 1.00255 + 0.377277i
\(46\) −287.696 −0.922142
\(47\) −232.849 −0.722649 −0.361325 0.932440i \(-0.617675\pi\)
−0.361325 + 0.932440i \(0.617675\pi\)
\(48\) −71.5295 + 393.169i −0.215092 + 1.18227i
\(49\) 0 0
\(50\) 58.9830i 0.166829i
\(51\) −30.2215 + 166.115i −0.0829775 + 0.456094i
\(52\) 7.75989i 0.0206943i
\(53\) 292.851i 0.758984i 0.925195 + 0.379492i \(0.123901\pi\)
−0.925195 + 0.379492i \(0.876099\pi\)
\(54\) −385.119 230.793i −0.970519 0.581609i
\(55\) 722.731i 1.77187i
\(56\) 0 0
\(57\) 730.803 + 132.956i 1.69820 + 0.308954i
\(58\) 792.998 1.79527
\(59\) 465.699 1.02761 0.513804 0.857908i \(-0.328236\pi\)
0.513804 + 0.857908i \(0.328236\pi\)
\(60\) 24.9667 137.232i 0.0537198 0.295276i
\(61\) 13.1309i 0.0275612i 0.999905 + 0.0137806i \(0.00438664\pi\)
−0.999905 + 0.0137806i \(0.995613\pi\)
\(62\) 665.282 1.36276
\(63\) 0 0
\(64\) −299.427 −0.584817
\(65\) 41.4623i 0.0791195i
\(66\) −179.619 + 987.294i −0.334994 + 1.84133i
\(67\) 481.684 0.878315 0.439157 0.898410i \(-0.355277\pi\)
0.439157 + 0.898410i \(0.355277\pi\)
\(68\) 72.8320 0.129885
\(69\) 459.584 + 83.6125i 0.801847 + 0.145881i
\(70\) 0 0
\(71\) 550.199i 0.919671i 0.888004 + 0.459836i \(0.152092\pi\)
−0.888004 + 0.459836i \(0.847908\pi\)
\(72\) 175.248 465.693i 0.286850 0.762256i
\(73\) 372.298i 0.596907i 0.954424 + 0.298453i \(0.0964707\pi\)
−0.954424 + 0.298453i \(0.903529\pi\)
\(74\) 314.596i 0.494203i
\(75\) 17.1421 94.2231i 0.0263920 0.145066i
\(76\) 320.415i 0.483607i
\(77\) 0 0
\(78\) −10.3046 + 56.6400i −0.0149585 + 0.0822207i
\(79\) 879.193 1.25211 0.626056 0.779778i \(-0.284668\pi\)
0.626056 + 0.779778i \(0.284668\pi\)
\(80\) 921.063 1.28723
\(81\) 548.139 + 480.609i 0.751905 + 0.659272i
\(82\) 480.832i 0.647548i
\(83\) −1119.54 −1.48055 −0.740275 0.672304i \(-0.765305\pi\)
−0.740275 + 0.672304i \(0.765305\pi\)
\(84\) 0 0
\(85\) 389.153 0.496583
\(86\) 190.290i 0.238599i
\(87\) −1266.78 230.467i −1.56108 0.284008i
\(88\) −1112.12 −1.34718
\(89\) 21.2955 0.0253631 0.0126816 0.999920i \(-0.495963\pi\)
0.0126816 + 0.999920i \(0.495963\pi\)
\(90\) −364.468 + 968.513i −0.426870 + 1.13434i
\(91\) 0 0
\(92\) 201.501i 0.228347i
\(93\) −1062.76 193.349i −1.18498 0.215585i
\(94\) 745.169i 0.817641i
\(95\) 1712.03i 1.84895i
\(96\) −504.531 91.7897i −0.536390 0.0975859i
\(97\) 612.931i 0.641585i −0.947150 0.320792i \(-0.896051\pi\)
0.947150 0.320792i \(-0.103949\pi\)
\(98\) 0 0
\(99\) 573.870 1524.96i 0.582587 1.54813i
\(100\) −41.3114 −0.0413114
\(101\) −341.044 −0.335992 −0.167996 0.985788i \(-0.553730\pi\)
−0.167996 + 0.985788i \(0.553730\pi\)
\(102\) −531.606 96.7155i −0.516047 0.0938849i
\(103\) 595.559i 0.569730i 0.958568 + 0.284865i \(0.0919488\pi\)
−0.958568 + 0.284865i \(0.908051\pi\)
\(104\) −63.8010 −0.0601558
\(105\) 0 0
\(106\) −937.188 −0.858752
\(107\) 27.6358i 0.0249687i −0.999922 0.0124844i \(-0.996026\pi\)
0.999922 0.0124844i \(-0.00397400\pi\)
\(108\) 161.646 269.735i 0.144022 0.240327i
\(109\) 362.610 0.318640 0.159320 0.987227i \(-0.449070\pi\)
0.159320 + 0.987227i \(0.449070\pi\)
\(110\) 2312.90 2.00479
\(111\) 91.4302 502.555i 0.0781817 0.429734i
\(112\) 0 0
\(113\) 557.806i 0.464371i −0.972672 0.232186i \(-0.925412\pi\)
0.972672 0.232186i \(-0.0745876\pi\)
\(114\) −425.487 + 2338.73i −0.349566 + 1.92142i
\(115\) 1076.65i 0.873030i
\(116\) 555.412i 0.444558i
\(117\) 32.9223 87.4855i 0.0260142 0.0691285i
\(118\) 1490.34i 1.16269i
\(119\) 0 0
\(120\) −1128.31 205.274i −0.858333 0.156157i
\(121\) −2310.76 −1.73611
\(122\) −42.0217 −0.0311841
\(123\) −139.743 + 768.111i −0.102441 + 0.563075i
\(124\) 465.960i 0.337455i
\(125\) 1276.30 0.913246
\(126\) 0 0
\(127\) −1038.78 −0.725804 −0.362902 0.931827i \(-0.618214\pi\)
−0.362902 + 0.931827i \(0.618214\pi\)
\(128\) 1747.76i 1.20689i
\(129\) 55.3035 303.981i 0.0377458 0.207473i
\(130\) 132.689 0.0895197
\(131\) −825.411 −0.550508 −0.275254 0.961372i \(-0.588762\pi\)
−0.275254 + 0.961372i \(0.588762\pi\)
\(132\) −691.496 125.804i −0.455962 0.0829535i
\(133\) 0 0
\(134\) 1541.50i 0.993769i
\(135\) 863.701 1441.24i 0.550634 0.918831i
\(136\) 598.817i 0.377560i
\(137\) 1890.23i 1.17878i −0.807847 0.589392i \(-0.799367\pi\)
0.807847 0.589392i \(-0.200633\pi\)
\(138\) −267.579 + 1470.77i −0.165057 + 0.907250i
\(139\) 201.550i 0.122987i −0.998107 0.0614936i \(-0.980414\pi\)
0.998107 0.0614936i \(-0.0195864\pi\)
\(140\) 0 0
\(141\) −216.567 + 1190.38i −0.129349 + 0.710979i
\(142\) −1760.76 −1.04056
\(143\) −208.924 −0.122175
\(144\) 1943.44 + 731.351i 1.12468 + 0.423236i
\(145\) 2967.65i 1.69966i
\(146\) −1191.44 −0.675369
\(147\) 0 0
\(148\) −220.341 −0.122378
\(149\) 2151.81i 1.18311i 0.806265 + 0.591554i \(0.201485\pi\)
−0.806265 + 0.591554i \(0.798515\pi\)
\(150\) 301.535 + 54.8585i 0.164135 + 0.0298612i
\(151\) 1803.04 0.971718 0.485859 0.874037i \(-0.338507\pi\)
0.485859 + 0.874037i \(0.338507\pi\)
\(152\) −2634.42 −1.40579
\(153\) 821.113 + 308.999i 0.433876 + 0.163275i
\(154\) 0 0
\(155\) 2489.70i 1.29018i
\(156\) −39.6704 7.21726i −0.0203601 0.00370412i
\(157\) 2626.82i 1.33531i 0.744472 + 0.667654i \(0.232701\pi\)
−0.744472 + 0.667654i \(0.767299\pi\)
\(158\) 2813.61i 1.41670i
\(159\) 1497.12 + 272.373i 0.746727 + 0.135853i
\(160\) 1181.95i 0.584007i
\(161\) 0 0
\(162\) −1538.06 + 1754.17i −0.745933 + 0.850742i
\(163\) 1445.35 0.694531 0.347265 0.937767i \(-0.387110\pi\)
0.347265 + 0.937767i \(0.387110\pi\)
\(164\) 336.772 0.160350
\(165\) −3694.77 672.193i −1.74326 0.317152i
\(166\) 3582.78i 1.67517i
\(167\) 2634.85 1.22090 0.610452 0.792054i \(-0.290988\pi\)
0.610452 + 0.792054i \(0.290988\pi\)
\(168\) 0 0
\(169\) 2185.01 0.994545
\(170\) 1245.38i 0.561858i
\(171\) 1359.40 3612.38i 0.607930 1.61547i
\(172\) −133.278 −0.0590835
\(173\) −593.511 −0.260831 −0.130416 0.991459i \(-0.541631\pi\)
−0.130416 + 0.991459i \(0.541631\pi\)
\(174\) 737.546 4053.99i 0.321340 1.76628i
\(175\) 0 0
\(176\) 4641.13i 1.98772i
\(177\) 433.134 2380.76i 0.183934 1.01101i
\(178\) 68.1503i 0.0286971i
\(179\) 2639.12i 1.10199i 0.834508 + 0.550996i \(0.185752\pi\)
−0.834508 + 0.550996i \(0.814248\pi\)
\(180\) −678.342 255.272i −0.280892 0.105705i
\(181\) 1778.65i 0.730421i 0.930925 + 0.365211i \(0.119003\pi\)
−0.930925 + 0.365211i \(0.880997\pi\)
\(182\) 0 0
\(183\) 67.1281 + 12.2127i 0.0271161 + 0.00493326i
\(184\) −1656.72 −0.663778
\(185\) −1177.32 −0.467882
\(186\) 618.761 3401.08i 0.243923 1.34075i
\(187\) 1960.89i 0.766817i
\(188\) 521.912 0.202470
\(189\) 0 0
\(190\) 5478.87 2.09199
\(191\) 1407.33i 0.533147i −0.963815 0.266574i \(-0.914108\pi\)
0.963815 0.266574i \(-0.0858916\pi\)
\(192\) −278.489 + 1530.74i −0.104678 + 0.575373i
\(193\) −1993.13 −0.743362 −0.371681 0.928360i \(-0.621219\pi\)
−0.371681 + 0.928360i \(0.621219\pi\)
\(194\) 1961.52 0.725921
\(195\) −211.965 38.5630i −0.0778417 0.0141618i
\(196\) 0 0
\(197\) 3336.46i 1.20666i −0.797490 0.603332i \(-0.793840\pi\)
0.797490 0.603332i \(-0.206160\pi\)
\(198\) 4880.22 + 1836.51i 1.75163 + 0.659167i
\(199\) 2628.45i 0.936312i 0.883646 + 0.468156i \(0.155082\pi\)
−0.883646 + 0.468156i \(0.844918\pi\)
\(200\) 339.658i 0.120087i
\(201\) 448.001 2462.48i 0.157212 0.864130i
\(202\) 1091.42i 0.380158i
\(203\) 0 0
\(204\) 67.7390 372.334i 0.0232484 0.127787i
\(205\) 1799.43 0.613061
\(206\) −1905.92 −0.644621
\(207\) 854.894 2271.74i 0.287050 0.762786i
\(208\) 266.256i 0.0887575i
\(209\) −8626.71 −2.85513
\(210\) 0 0
\(211\) −2000.49 −0.652698 −0.326349 0.945249i \(-0.605818\pi\)
−0.326349 + 0.945249i \(0.605818\pi\)
\(212\) 656.402i 0.212650i
\(213\) 2812.75 + 511.726i 0.904819 + 0.164614i
\(214\) 88.4406 0.0282508
\(215\) −712.126 −0.225891
\(216\) −2217.74 1329.04i −0.698602 0.418656i
\(217\) 0 0
\(218\) 1160.43i 0.360525i
\(219\) 1903.28 + 346.264i 0.587267 + 0.106842i
\(220\) 1619.94i 0.496439i
\(221\) 112.494i 0.0342407i
\(222\) 1608.29 + 292.597i 0.486222 + 0.0884587i
\(223\) 5476.01i 1.64440i 0.569200 + 0.822199i \(0.307253\pi\)
−0.569200 + 0.822199i \(0.692747\pi\)
\(224\) 0 0
\(225\) −465.748 175.269i −0.137999 0.0519315i
\(226\) 1785.10 0.525412
\(227\) −3873.17 −1.13247 −0.566236 0.824243i \(-0.691601\pi\)
−0.566236 + 0.824243i \(0.691601\pi\)
\(228\) −1638.04 298.009i −0.475797 0.0865621i
\(229\) 1923.73i 0.555124i −0.960708 0.277562i \(-0.910474\pi\)
0.960708 0.277562i \(-0.0895265\pi\)
\(230\) 3445.53 0.987789
\(231\) 0 0
\(232\) 4566.54 1.29228
\(233\) 1976.75i 0.555800i 0.960610 + 0.277900i \(0.0896383\pi\)
−0.960610 + 0.277900i \(0.910362\pi\)
\(234\) 279.973 + 105.359i 0.0782154 + 0.0294338i
\(235\) 2788.66 0.774095
\(236\) −1043.83 −0.287913
\(237\) 817.713 4494.64i 0.224119 1.23189i
\(238\) 0 0
\(239\) 1168.46i 0.316241i −0.987420 0.158121i \(-0.949457\pi\)
0.987420 0.158121i \(-0.0505434\pi\)
\(240\) 856.656 4708.69i 0.230404 1.26644i
\(241\) 6244.92i 1.66917i 0.550877 + 0.834587i \(0.314293\pi\)
−0.550877 + 0.834587i \(0.685707\pi\)
\(242\) 7394.93i 1.96432i
\(243\) 2966.80 2355.21i 0.783210 0.621757i
\(244\) 29.4318i 0.00772204i
\(245\) 0 0
\(246\) −2458.12 447.208i −0.637091 0.115906i
\(247\) −494.905 −0.127490
\(248\) 3831.08 0.980943
\(249\) −1041.26 + 5723.36i −0.265007 + 1.45664i
\(250\) 4084.44i 1.03329i
\(251\) 3590.31 0.902862 0.451431 0.892306i \(-0.350914\pi\)
0.451431 + 0.892306i \(0.350914\pi\)
\(252\) 0 0
\(253\) −5425.13 −1.34812
\(254\) 3324.34i 0.821211i
\(255\) 361.941 1989.44i 0.0888847 0.488563i
\(256\) 3197.80 0.780713
\(257\) −952.226 −0.231121 −0.115561 0.993300i \(-0.536866\pi\)
−0.115561 + 0.993300i \(0.536866\pi\)
\(258\) 972.807 + 176.984i 0.234745 + 0.0427074i
\(259\) 0 0
\(260\) 92.9344i 0.0221675i
\(261\) −2356.40 + 6261.75i −0.558842 + 1.48503i
\(262\) 2641.50i 0.622871i
\(263\) 5149.06i 1.20724i 0.797271 + 0.603621i \(0.206276\pi\)
−0.797271 + 0.603621i \(0.793724\pi\)
\(264\) −1034.35 + 5685.41i −0.241136 + 1.32543i
\(265\) 3507.26i 0.813016i
\(266\) 0 0
\(267\) 19.8064 108.868i 0.00453981 0.0249535i
\(268\) −1079.66 −0.246084
\(269\) 7121.96 1.61425 0.807126 0.590380i \(-0.201022\pi\)
0.807126 + 0.590380i \(0.201022\pi\)
\(270\) 4612.29 + 2764.03i 1.03961 + 0.623014i
\(271\) 806.788i 0.180845i −0.995904 0.0904223i \(-0.971178\pi\)
0.995904 0.0904223i \(-0.0288217\pi\)
\(272\) 2499.00 0.557075
\(273\) 0 0
\(274\) 6049.16 1.33373
\(275\) 1112.25i 0.243895i
\(276\) −1030.12 187.411i −0.224660 0.0408725i
\(277\) −5533.95 −1.20037 −0.600185 0.799861i \(-0.704906\pi\)
−0.600185 + 0.799861i \(0.704906\pi\)
\(278\) 645.003 0.139154
\(279\) −1976.90 + 5253.27i −0.424207 + 1.12726i
\(280\) 0 0
\(281\) 8052.89i 1.70959i 0.518965 + 0.854796i \(0.326318\pi\)
−0.518965 + 0.854796i \(0.673682\pi\)
\(282\) −3809.48 693.061i −0.804437 0.146352i
\(283\) 4273.39i 0.897622i −0.893627 0.448811i \(-0.851848\pi\)
0.893627 0.448811i \(-0.148152\pi\)
\(284\) 1233.23i 0.257671i
\(285\) −8752.29 1592.31i −1.81909 0.330949i
\(286\) 668.602i 0.138235i
\(287\) 0 0
\(288\) −938.501 + 2493.91i −0.192020 + 0.510261i
\(289\) −3857.16 −0.785093
\(290\) −9497.15 −1.92308
\(291\) −3133.45 570.071i −0.631223 0.114839i
\(292\) 834.476i 0.167240i
\(293\) 5195.28 1.03588 0.517938 0.855418i \(-0.326700\pi\)
0.517938 + 0.855418i \(0.326700\pi\)
\(294\) 0 0
\(295\) −5577.34 −1.10076
\(296\) 1811.62i 0.355738i
\(297\) −7262.23 4352.09i −1.41885 0.850282i
\(298\) −6886.27 −1.33863
\(299\) −311.234 −0.0601977
\(300\) −38.4226 + 211.194i −0.00739443 + 0.0406442i
\(301\) 0 0
\(302\) 5770.13i 1.09945i
\(303\) −317.196 + 1743.50i −0.0601401 + 0.330566i
\(304\) 10994.0i 2.07418i
\(305\) 157.259i 0.0295233i
\(306\) −988.865 + 2627.74i −0.184737 + 0.490909i
\(307\) 5359.28i 0.996320i 0.867085 + 0.498160i \(0.165991\pi\)
−0.867085 + 0.498160i \(0.834009\pi\)
\(308\) 0 0
\(309\) 3044.64 + 553.914i 0.560529 + 0.101977i
\(310\) −7967.59 −1.45977
\(311\) 9042.99 1.64881 0.824406 0.565998i \(-0.191509\pi\)
0.824406 + 0.565998i \(0.191509\pi\)
\(312\) −59.3396 + 326.166i −0.0107674 + 0.0591843i
\(313\) 4146.30i 0.748764i 0.927275 + 0.374382i \(0.122145\pi\)
−0.927275 + 0.374382i \(0.877855\pi\)
\(314\) −8406.42 −1.51083
\(315\) 0 0
\(316\) −1970.64 −0.350814
\(317\) 6742.06i 1.19455i −0.802037 0.597274i \(-0.796250\pi\)
0.802037 0.597274i \(-0.203750\pi\)
\(318\) −871.653 + 4791.12i −0.153710 + 0.844883i
\(319\) 14953.7 2.62459
\(320\) 3586.01 0.626450
\(321\) −141.281 25.7033i −0.0245655 0.00446922i
\(322\) 0 0
\(323\) 4645.03i 0.800174i
\(324\) −1228.61 1077.25i −0.210667 0.184713i
\(325\) 63.8085i 0.0108906i
\(326\) 4625.44i 0.785826i
\(327\) 337.254 1853.75i 0.0570342 0.313494i
\(328\) 2768.91i 0.466120i
\(329\) 0 0
\(330\) 2151.17 11824.1i 0.358842 1.97241i
\(331\) 1435.92 0.238445 0.119223 0.992868i \(-0.461960\pi\)
0.119223 + 0.992868i \(0.461960\pi\)
\(332\) 2509.36 0.414817
\(333\) −2484.14 934.826i −0.408800 0.153838i
\(334\) 8432.10i 1.38139i
\(335\) −5768.78 −0.940842
\(336\) 0 0
\(337\) −10555.0 −1.70613 −0.853066 0.521804i \(-0.825259\pi\)
−0.853066 + 0.521804i \(0.825259\pi\)
\(338\) 6992.53i 1.12528i
\(339\) −2851.63 518.800i −0.456872 0.0831190i
\(340\) −872.255 −0.139131
\(341\) 12545.3 1.99228
\(342\) 11560.4 + 4350.38i 1.82782 + 0.687842i
\(343\) 0 0
\(344\) 1095.80i 0.171749i
\(345\) −5504.10 1001.37i −0.858930 0.156266i
\(346\) 1899.37i 0.295117i
\(347\) 10123.3i 1.56614i −0.621936 0.783068i \(-0.713654\pi\)
0.621936 0.783068i \(-0.286346\pi\)
\(348\) 2839.40 + 516.573i 0.437378 + 0.0795725i
\(349\) 8986.21i 1.37828i −0.724627 0.689141i \(-0.757988\pi\)
0.724627 0.689141i \(-0.242012\pi\)
\(350\) 0 0
\(351\) −416.626 249.674i −0.0633558 0.0379676i
\(352\) 5955.69 0.901817
\(353\) −121.541 −0.0183257 −0.00916286 0.999958i \(-0.502917\pi\)
−0.00916286 + 0.999958i \(0.502917\pi\)
\(354\) 7618.97 + 1386.13i 1.14391 + 0.208112i
\(355\) 6589.33i 0.985142i
\(356\) −47.7321 −0.00710617
\(357\) 0 0
\(358\) −8445.75 −1.24685
\(359\) 1227.13i 0.180405i 0.995923 + 0.0902025i \(0.0287514\pi\)
−0.995923 + 0.0902025i \(0.971249\pi\)
\(360\) −2098.82 + 5577.26i −0.307271 + 0.816521i
\(361\) −13576.2 −1.97933
\(362\) −5692.08 −0.826434
\(363\) −2149.17 + 11813.1i −0.310750 + 1.70807i
\(364\) 0 0
\(365\) 4458.74i 0.639400i
\(366\) −39.0832 + 214.825i −0.00558173 + 0.0306805i
\(367\) 4743.63i 0.674702i 0.941379 + 0.337351i \(0.109531\pi\)
−0.941379 + 0.337351i \(0.890469\pi\)
\(368\) 6913.89i 0.979379i
\(369\) 3796.79 + 1428.80i 0.535645 + 0.201572i
\(370\) 3767.68i 0.529385i
\(371\) 0 0
\(372\) 2382.10 + 433.377i 0.332006 + 0.0604020i
\(373\) 3990.87 0.553993 0.276996 0.960871i \(-0.410661\pi\)
0.276996 + 0.960871i \(0.410661\pi\)
\(374\) 6275.30 0.867615
\(375\) 1187.05 6524.75i 0.163464 0.898497i
\(376\) 4291.11i 0.588557i
\(377\) 857.875 0.117196
\(378\) 0 0
\(379\) 11239.6 1.52332 0.761659 0.647978i \(-0.224385\pi\)
0.761659 + 0.647978i \(0.224385\pi\)
\(380\) 3837.37i 0.518035i
\(381\) −966.145 + 5310.51i −0.129914 + 0.714083i
\(382\) 4503.78 0.603229
\(383\) −2856.23 −0.381061 −0.190530 0.981681i \(-0.561021\pi\)
−0.190530 + 0.981681i \(0.561021\pi\)
\(384\) −8934.95 1625.54i −1.18740 0.216024i
\(385\) 0 0
\(386\) 6378.47i 0.841077i
\(387\) −1502.59 565.449i −0.197366 0.0742724i
\(388\) 1373.84i 0.179758i
\(389\) 5117.16i 0.666967i 0.942756 + 0.333483i \(0.108224\pi\)
−0.942756 + 0.333483i \(0.891776\pi\)
\(390\) 123.410 678.335i 0.0160234 0.0880740i
\(391\) 2921.15i 0.377823i
\(392\) 0 0
\(393\) −767.692 + 4219.70i −0.0985368 + 0.541617i
\(394\) 10677.4 1.36528
\(395\) −10529.4 −1.34125
\(396\) −1286.28 + 3418.08i −0.163228 + 0.433750i
\(397\) 11770.8i 1.48806i 0.668145 + 0.744031i \(0.267089\pi\)
−0.668145 + 0.744031i \(0.732911\pi\)
\(398\) −8411.63 −1.05939
\(399\) 0 0
\(400\) −1417.47 −0.177184
\(401\) 7064.59i 0.879773i −0.898053 0.439886i \(-0.855019\pi\)
0.898053 0.439886i \(-0.144981\pi\)
\(402\) 7880.49 + 1433.70i 0.977720 + 0.177877i
\(403\) 719.711 0.0889611
\(404\) 764.424 0.0941374
\(405\) −6564.65 5755.90i −0.805433 0.706205i
\(406\) 0 0
\(407\) 5932.37i 0.722498i
\(408\) −3061.30 556.944i −0.371463 0.0675805i
\(409\) 116.430i 0.0140760i −0.999975 0.00703800i \(-0.997760\pi\)
0.999975 0.00703800i \(-0.00224028\pi\)
\(410\) 5758.57i 0.693647i
\(411\) −9663.31 1758.05i −1.15975 0.210994i
\(412\) 1334.90i 0.159626i
\(413\) 0 0
\(414\) 7270.07 + 2735.85i 0.863054 + 0.324782i
\(415\) 13407.9 1.58595
\(416\) 341.672 0.0402688
\(417\) −1030.37 187.456i −0.121001 0.0220138i
\(418\) 27607.4i 3.23043i
\(419\) 15827.8 1.84544 0.922721 0.385469i \(-0.125960\pi\)
0.922721 + 0.385469i \(0.125960\pi\)
\(420\) 0 0
\(421\) 9126.46 1.05652 0.528262 0.849082i \(-0.322844\pi\)
0.528262 + 0.849082i \(0.322844\pi\)
\(422\) 6402.00i 0.738494i
\(423\) 5884.08 + 2214.28i 0.676344 + 0.254520i
\(424\) −5396.87 −0.618149
\(425\) −598.888 −0.0683537
\(426\) −1637.64 + 9001.42i −0.186253 + 1.02376i
\(427\) 0 0
\(428\) 61.9434i 0.00699567i
\(429\) −194.314 + 1068.07i −0.0218685 + 0.120202i
\(430\) 2278.96i 0.255584i
\(431\) 7030.17i 0.785688i 0.919605 + 0.392844i \(0.128509\pi\)
−0.919605 + 0.392844i \(0.871491\pi\)
\(432\) 5546.39 9255.14i 0.617710 1.03076i
\(433\) 3219.72i 0.357344i −0.983909 0.178672i \(-0.942820\pi\)
0.983909 0.178672i \(-0.0571801\pi\)
\(434\) 0 0
\(435\) 15171.3 + 2760.13i 1.67221 + 0.304226i
\(436\) −812.762 −0.0892758
\(437\) −12851.2 −1.40677
\(438\) −1108.12 + 6090.90i −0.120886 + 0.664463i
\(439\) 8192.20i 0.890643i 0.895371 + 0.445322i \(0.146911\pi\)
−0.895371 + 0.445322i \(0.853089\pi\)
\(440\) 13319.0 1.44309
\(441\) 0 0
\(442\) 360.007 0.0387416
\(443\) 8513.16i 0.913030i −0.889716 0.456515i \(-0.849097\pi\)
0.889716 0.456515i \(-0.150903\pi\)
\(444\) −204.934 + 1126.44i −0.0219048 + 0.120402i
\(445\) −255.040 −0.0271687
\(446\) −17524.5 −1.86055
\(447\) 11000.6 + 2001.34i 1.16400 + 0.211768i
\(448\) 0 0
\(449\) 7522.13i 0.790627i −0.918546 0.395313i \(-0.870636\pi\)
0.918546 0.395313i \(-0.129364\pi\)
\(450\) 560.899 1490.50i 0.0587578 0.156139i
\(451\) 9067.10i 0.946681i
\(452\) 1250.28i 0.130106i
\(453\) 1676.96 9217.57i 0.173930 0.956025i
\(454\) 12395.0i 1.28133i
\(455\) 0 0
\(456\) −2450.20 + 13467.8i −0.251626 + 1.38308i
\(457\) 2743.19 0.280790 0.140395 0.990096i \(-0.455163\pi\)
0.140395 + 0.990096i \(0.455163\pi\)
\(458\) 6156.35 0.628095
\(459\) 2343.37 3910.33i 0.238299 0.397644i
\(460\) 2413.23i 0.244603i
\(461\) 5771.24 0.583066 0.291533 0.956561i \(-0.405835\pi\)
0.291533 + 0.956561i \(0.405835\pi\)
\(462\) 0 0
\(463\) −7850.41 −0.787990 −0.393995 0.919113i \(-0.628907\pi\)
−0.393995 + 0.919113i \(0.628907\pi\)
\(464\) 19057.2i 1.90670i
\(465\) 12727.9 + 2315.60i 1.26934 + 0.230932i
\(466\) −6326.04 −0.628859
\(467\) −8750.90 −0.867117 −0.433558 0.901125i \(-0.642742\pi\)
−0.433558 + 0.901125i \(0.642742\pi\)
\(468\) −73.7927 + 196.092i −0.00728861 + 0.0193683i
\(469\) 0 0
\(470\) 8924.34i 0.875849i
\(471\) 13428.9 + 2443.14i 1.31374 + 0.239010i
\(472\) 8582.25i 0.836928i
\(473\) 3588.32i 0.348818i
\(474\) 14383.8 + 2616.86i 1.39382 + 0.253579i
\(475\) 2634.73i 0.254505i
\(476\) 0 0
\(477\) 2784.87 7400.32i 0.267317 0.710351i
\(478\) 3739.34 0.357811
\(479\) −3902.82 −0.372285 −0.186143 0.982523i \(-0.559599\pi\)
−0.186143 + 0.982523i \(0.559599\pi\)
\(480\) 6042.40 + 1099.30i 0.574576 + 0.104533i
\(481\) 340.334i 0.0322617i
\(482\) −19985.1 −1.88858
\(483\) 0 0
\(484\) 5179.38 0.486418
\(485\) 7340.62i 0.687259i
\(486\) 7537.20 + 9494.41i 0.703487 + 0.886163i
\(487\) 9800.27 0.911895 0.455947 0.890007i \(-0.349300\pi\)
0.455947 + 0.890007i \(0.349300\pi\)
\(488\) −241.985 −0.0224470
\(489\) 1344.28 7388.97i 0.124316 0.683314i
\(490\) 0 0
\(491\) 4021.32i 0.369612i −0.982775 0.184806i \(-0.940834\pi\)
0.982775 0.184806i \(-0.0591657\pi\)
\(492\) 313.223 1721.66i 0.0287016 0.157761i
\(493\) 8051.76i 0.735564i
\(494\) 1583.81i 0.144248i
\(495\) −6872.82 + 18263.4i −0.624061 + 1.65834i
\(496\) 15988.0i 1.44734i
\(497\) 0 0
\(498\) −18316.0 3332.25i −1.64811 0.299842i
\(499\) −14860.6 −1.33317 −0.666585 0.745429i \(-0.732245\pi\)
−0.666585 + 0.745429i \(0.732245\pi\)
\(500\) −2860.72 −0.255871
\(501\) 2450.60 13470.0i 0.218533 1.20119i
\(502\) 11489.8i 1.02154i
\(503\) −12436.1 −1.10238 −0.551191 0.834379i \(-0.685826\pi\)
−0.551191 + 0.834379i \(0.685826\pi\)
\(504\) 0 0
\(505\) 4084.44 0.359911
\(506\) 17361.6i 1.52533i
\(507\) 2032.22 11170.3i 0.178016 0.978483i
\(508\) 2328.35 0.203354
\(509\) 1508.79 0.131387 0.0656935 0.997840i \(-0.479074\pi\)
0.0656935 + 0.997840i \(0.479074\pi\)
\(510\) 6366.65 + 1158.29i 0.552785 + 0.100569i
\(511\) 0 0
\(512\) 3748.39i 0.323549i
\(513\) −17203.0 10309.4i −1.48057 0.887269i
\(514\) 3047.33i 0.261502i
\(515\) 7132.57i 0.610289i
\(516\) −123.958 + 681.349i −0.0105755 + 0.0581293i
\(517\) 14051.7i 1.19535i
\(518\) 0 0
\(519\) −552.008 + 3034.17i −0.0466869 + 0.256619i
\(520\) 764.098 0.0644383
\(521\) −5041.89 −0.423971 −0.211986 0.977273i \(-0.567993\pi\)
−0.211986 + 0.977273i \(0.567993\pi\)
\(522\) −20039.0 7541.02i −1.68024 0.632301i
\(523\) 11320.9i 0.946520i −0.880923 0.473260i \(-0.843077\pi\)
0.880923 0.473260i \(-0.156923\pi\)
\(524\) 1850.09 0.154240
\(525\) 0 0
\(526\) −16478.1 −1.36593
\(527\) 6754.99i 0.558353i
\(528\) −23726.5 4316.59i −1.95562 0.355787i
\(529\) 4085.19 0.335760
\(530\) 11224.0 0.919886
\(531\) −11768.2 4428.57i −0.961762 0.361928i
\(532\) 0 0
\(533\) 520.170i 0.0422721i
\(534\) 348.400 + 63.3847i 0.0282336 + 0.00513657i
\(535\) 330.973i 0.0267462i
\(536\) 8876.83i 0.715337i
\(537\) 13491.8 + 2454.57i 1.08420 + 0.197249i
\(538\) 22791.9i 1.82644i
\(539\) 0 0
\(540\) −1935.92 + 3230.42i −0.154275 + 0.257436i
\(541\) −2725.44 −0.216591 −0.108295 0.994119i \(-0.534539\pi\)
−0.108295 + 0.994119i \(0.534539\pi\)
\(542\) 2581.90 0.204616
\(543\) 9092.89 + 1654.28i 0.718625 + 0.130740i
\(544\) 3206.83i 0.252742i
\(545\) −4342.72 −0.341324
\(546\) 0 0
\(547\) −2794.16 −0.218409 −0.109204 0.994019i \(-0.534830\pi\)
−0.109204 + 0.994019i \(0.534830\pi\)
\(548\) 4236.80i 0.330269i
\(549\) 124.868 331.816i 0.00970717 0.0257952i
\(550\) −3559.44 −0.275955
\(551\) 35422.7 2.73876
\(552\) −1540.87 + 8469.56i −0.118811 + 0.653059i
\(553\) 0 0
\(554\) 17709.9i 1.35816i
\(555\) −1094.99 + 6018.73i −0.0837475 + 0.460326i
\(556\) 451.757i 0.0344582i
\(557\) 9812.66i 0.746455i 0.927740 + 0.373228i \(0.121749\pi\)
−0.927740 + 0.373228i \(0.878251\pi\)
\(558\) −16811.6 6326.50i −1.27544 0.479968i
\(559\) 205.858i 0.0155758i
\(560\) 0 0
\(561\) −10024.6 1823.78i −0.754433 0.137255i
\(562\) −25771.0 −1.93432
\(563\) 7765.81 0.581332 0.290666 0.956825i \(-0.406123\pi\)
0.290666 + 0.956825i \(0.406123\pi\)
\(564\) 485.417 2668.14i 0.0362407 0.199200i
\(565\) 6680.43i 0.497429i
\(566\) 13675.8 1.01561
\(567\) 0 0
\(568\) −10139.5 −0.749020
\(569\) 17119.1i 1.26128i 0.776074 + 0.630642i \(0.217208\pi\)
−0.776074 + 0.630642i \(0.782792\pi\)
\(570\) 5095.75 28009.3i 0.374452 2.05821i
\(571\) 9591.66 0.702974 0.351487 0.936193i \(-0.385676\pi\)
0.351487 + 0.936193i \(0.385676\pi\)
\(572\) 468.286 0.0342308
\(573\) −7194.63 1308.92i −0.524537 0.0954295i
\(574\) 0 0
\(575\) 1656.92i 0.120171i
\(576\) 7566.49 + 2847.40i 0.547344 + 0.205975i
\(577\) 12488.1i 0.901015i −0.892773 0.450508i \(-0.851243\pi\)
0.892773 0.450508i \(-0.148757\pi\)
\(578\) 12343.8i 0.888293i
\(579\) −1853.76 + 10189.4i −0.133056 + 0.731357i
\(580\) 6651.76i 0.476206i
\(581\) 0 0
\(582\) 1824.35 10027.7i 0.129934 0.714197i
\(583\) −17672.7 −1.25545
\(584\) −6860.98 −0.486146
\(585\) −394.286 + 1047.75i −0.0278662 + 0.0740498i
\(586\) 16626.0i 1.17204i
\(587\) −7385.70 −0.519319 −0.259660 0.965700i \(-0.583610\pi\)
−0.259660 + 0.965700i \(0.583610\pi\)
\(588\) 0 0
\(589\) 29717.7 2.07894
\(590\) 17848.7i 1.24546i
\(591\) −17056.8 3103.15i −1.18718 0.215984i
\(592\) −7560.33 −0.524878
\(593\) −26052.0 −1.80409 −0.902047 0.431638i \(-0.857936\pi\)
−0.902047 + 0.431638i \(0.857936\pi\)
\(594\) 13927.6 23240.8i 0.962051 1.60535i
\(595\) 0 0
\(596\) 4823.11i 0.331480i
\(597\) 13437.3 + 2444.65i 0.921191 + 0.167593i
\(598\) 996.016i 0.0681106i
\(599\) 15788.5i 1.07696i −0.842638 0.538480i \(-0.818999\pi\)
0.842638 0.538480i \(-0.181001\pi\)
\(600\) 1736.41 + 315.907i 0.118148 + 0.0214947i
\(601\) 27175.5i 1.84445i 0.386658 + 0.922223i \(0.373629\pi\)
−0.386658 + 0.922223i \(0.626371\pi\)
\(602\) 0 0
\(603\) −12172.1 4580.58i −0.822035 0.309346i
\(604\) −4041.37 −0.272253
\(605\) 27674.2 1.85970
\(606\) −5579.59 1015.10i −0.374019 0.0680455i
\(607\) 17900.4i 1.19696i −0.801138 0.598480i \(-0.795772\pi\)
0.801138 0.598480i \(-0.204228\pi\)
\(608\) 14108.0 0.941047
\(609\) 0 0
\(610\) 503.263 0.0334041
\(611\) 806.133i 0.0533758i
\(612\) −1840.46 692.596i −0.121562 0.0457460i
\(613\) −14607.7 −0.962478 −0.481239 0.876589i \(-0.659813\pi\)
−0.481239 + 0.876589i \(0.659813\pi\)
\(614\) −17150.9 −1.12729
\(615\) 1673.60 9199.10i 0.109733 0.603160i
\(616\) 0 0
\(617\) 23934.5i 1.56170i 0.624721 + 0.780848i \(0.285213\pi\)
−0.624721 + 0.780848i \(0.714787\pi\)
\(618\) −1772.65 + 9743.52i −0.115382 + 0.634210i
\(619\) 20858.7i 1.35441i −0.735793 0.677207i \(-0.763190\pi\)
0.735793 0.677207i \(-0.236810\pi\)
\(620\) 5580.46i 0.361479i
\(621\) −10818.6 6483.30i −0.699088 0.418947i
\(622\) 28939.6i 1.86555i
\(623\) 0 0
\(624\) −1361.17 247.638i −0.0873241 0.0158869i
\(625\) −17589.2 −1.12571
\(626\) −13269.1 −0.847188
\(627\) −8023.47 + 44101.8i −0.511047 + 2.80902i
\(628\) 5887.82i 0.374123i
\(629\) −3194.27 −0.202486
\(630\) 0 0
\(631\) 2986.73 0.188431 0.0942155 0.995552i \(-0.469966\pi\)
0.0942155 + 0.995552i \(0.469966\pi\)
\(632\) 16202.4i 1.01977i
\(633\) −1860.60 + 10227.0i −0.116828 + 0.642157i
\(634\) 21576.1 1.35157
\(635\) 12440.8 0.777474
\(636\) −3355.68 610.501i −0.209216 0.0380628i
\(637\) 0 0
\(638\) 47855.0i 2.96959i
\(639\) 5232.13 13903.5i 0.323912 0.860742i
\(640\) 20931.6i 1.29280i
\(641\) 64.5977i 0.00398043i 0.999998 + 0.00199021i \(0.000633505\pi\)
−0.999998 + 0.00199021i \(0.999366\pi\)
\(642\) 82.2562 452.129i 0.00505669 0.0277946i
\(643\) 18370.0i 1.12666i −0.826232 0.563330i \(-0.809520\pi\)
0.826232 0.563330i \(-0.190480\pi\)
\(644\) 0 0
\(645\) −662.329 + 3640.56i −0.0404329 + 0.222243i
\(646\) 14865.1 0.905357
\(647\) 13583.6 0.825389 0.412694 0.910870i \(-0.364588\pi\)
0.412694 + 0.910870i \(0.364588\pi\)
\(648\) −8857.02 + 10101.5i −0.536939 + 0.612383i
\(649\) 28103.5i 1.69978i
\(650\) −204.201 −0.0123222
\(651\) 0 0
\(652\) −3239.63 −0.194592
\(653\) 18842.8i 1.12922i −0.825359 0.564608i \(-0.809028\pi\)
0.825359 0.564608i \(-0.190972\pi\)
\(654\) 5932.41 + 1079.29i 0.354703 + 0.0645313i
\(655\) 9885.34 0.589698
\(656\) 11555.3 0.687741
\(657\) 3540.37 9407.94i 0.210233 0.558659i
\(658\) 0 0
\(659\) 7348.15i 0.434360i −0.976132 0.217180i \(-0.930314\pi\)
0.976132 0.217180i \(-0.0696859\pi\)
\(660\) 8281.54 + 1506.67i 0.488422 + 0.0888590i
\(661\) 24656.9i 1.45090i 0.688276 + 0.725449i \(0.258368\pi\)
−0.688276 + 0.725449i \(0.741632\pi\)
\(662\) 4595.27i 0.269789i
\(663\) −575.098 104.628i −0.0336877 0.00612883i
\(664\) 20631.7i 1.20582i
\(665\) 0 0
\(666\) 2991.65 7949.81i 0.174060 0.462536i
\(667\) 22276.5 1.29318
\(668\) −5905.80 −0.342070
\(669\) 27994.7 + 5093.09i 1.61784 + 0.294335i
\(670\) 18461.4i 1.06451i
\(671\) −792.408 −0.0455895
\(672\) 0 0
\(673\) 4465.46 0.255767 0.127883 0.991789i \(-0.459182\pi\)
0.127883 + 0.991789i \(0.459182\pi\)
\(674\) 33778.3i 1.93040i
\(675\) −1329.19 + 2218.00i −0.0757937 + 0.126475i
\(676\) −4897.53 −0.278649
\(677\) −12986.1 −0.737218 −0.368609 0.929585i \(-0.620166\pi\)
−0.368609 + 0.929585i \(0.620166\pi\)
\(678\) 1660.27 9125.86i 0.0940449 0.516927i
\(679\) 0 0
\(680\) 7171.59i 0.404438i
\(681\) −3602.33 + 19800.5i −0.202704 + 1.11418i
\(682\) 40147.8i 2.25416i
\(683\) 6369.97i 0.356867i 0.983952 + 0.178433i \(0.0571029\pi\)
−0.983952 + 0.178433i \(0.942897\pi\)
\(684\) −3046.99 + 8096.86i −0.170328 + 0.452619i
\(685\) 22637.9i 1.26270i
\(686\) 0 0
\(687\) −9834.55 1789.21i −0.546159 0.0993632i
\(688\) −4573.03 −0.253408
\(689\) −1013.86 −0.0560596
\(690\) 3204.59 17614.4i 0.176807 0.971836i
\(691\) 5802.65i 0.319455i −0.987161 0.159727i \(-0.948938\pi\)
0.987161 0.159727i \(-0.0510615\pi\)
\(692\) 1330.31 0.0730790
\(693\) 0 0
\(694\) 32396.9 1.77200
\(695\) 2413.81i 0.131743i
\(696\) 4247.22 23345.2i 0.231308 1.27141i
\(697\) 4882.16 0.265315
\(698\) 28757.9 1.55946
\(699\) 10105.6 + 1838.52i 0.546824 + 0.0994840i
\(700\) 0 0
\(701\) 1479.34i 0.0797058i 0.999206 + 0.0398529i \(0.0126889\pi\)
−0.999206 + 0.0398529i \(0.987311\pi\)
\(702\) 799.014 1333.30i 0.0429584 0.0716838i
\(703\) 14052.8i 0.753927i
\(704\) 18069.5i 0.967357i
\(705\) 2593.66 14256.3i 0.138557 0.761593i
\(706\) 388.958i 0.0207346i
\(707\) 0 0
\(708\) −970.836 + 5336.29i −0.0515342 + 0.283263i
\(709\) 20247.8 1.07253 0.536264 0.844050i \(-0.319835\pi\)
0.536264 + 0.844050i \(0.319835\pi\)
\(710\) 21087.3 1.11464
\(711\) −22217.1 8360.69i −1.17188 0.440999i
\(712\) 392.449i 0.0206568i
\(713\) 18688.7 0.981625
\(714\) 0 0
\(715\) 2502.12 0.130873
\(716\) 5915.37i 0.308754i
\(717\) −5973.46 1086.76i −0.311134 0.0566048i
\(718\) −3927.08 −0.204119
\(719\) −20722.0 −1.07482 −0.537412 0.843320i \(-0.680598\pi\)
−0.537412 + 0.843320i \(0.680598\pi\)
\(720\) −23275.2 8758.86i −1.20474 0.453366i
\(721\) 0 0
\(722\) 43446.9i 2.23951i
\(723\) 31925.5 + 5808.23i 1.64222 + 0.298770i
\(724\) 3986.71i 0.204648i
\(725\) 4567.08i 0.233954i
\(726\) −37804.7 6877.83i −1.93259 0.351598i
\(727\) 6251.88i 0.318940i −0.987203 0.159470i \(-0.949021\pi\)
0.987203 0.159470i \(-0.0509785\pi\)
\(728\) 0 0
\(729\) −9281.07 17357.5i −0.471527 0.881852i
\(730\) 14269.0 0.723449
\(731\) −1932.12 −0.0977594
\(732\) −150.462 27.3737i −0.00759733 0.00138219i
\(733\) 36709.5i 1.84979i −0.380220 0.924896i \(-0.624152\pi\)
0.380220 0.924896i \(-0.375848\pi\)
\(734\) −15180.7 −0.763391
\(735\) 0 0
\(736\) 8872.20 0.444339
\(737\) 29068.2i 1.45284i
\(738\) −4572.47 + 12150.6i −0.228069 + 0.606055i
\(739\) −26973.7 −1.34268 −0.671341 0.741148i \(-0.734282\pi\)
−0.671341 + 0.741148i \(0.734282\pi\)
\(740\) 2638.87 0.131090
\(741\) −460.298 + 2530.07i −0.0228198 + 0.125431i
\(742\) 0 0
\(743\) 14303.4i 0.706246i −0.935577 0.353123i \(-0.885120\pi\)
0.935577 0.353123i \(-0.114880\pi\)
\(744\) 3563.18 19585.4i 0.175582 0.965101i
\(745\) 25770.6i 1.26733i
\(746\) 12771.7i 0.626815i
\(747\) 28290.7 + 10646.3i 1.38568 + 0.521455i
\(748\) 4395.19i 0.214845i
\(749\) 0 0
\(750\) 20880.6 + 3798.83i 1.01660 + 0.184952i
\(751\) −3720.67 −0.180784 −0.0903921 0.995906i \(-0.528812\pi\)
−0.0903921 + 0.995906i \(0.528812\pi\)
\(752\) 17907.8 0.868392
\(753\) 3339.25 18354.5i 0.161606 0.888281i
\(754\) 2745.39i 0.132601i
\(755\) −21593.7 −1.04089
\(756\) 0 0
\(757\) 107.033 0.00513896 0.00256948 0.999997i \(-0.499182\pi\)
0.00256948 + 0.999997i \(0.499182\pi\)
\(758\) 35969.1i 1.72356i
\(759\) −5045.76 + 27734.5i −0.241304 + 1.32635i
\(760\) 31550.5 1.50586
\(761\) 15183.9 0.723279 0.361639 0.932318i \(-0.382217\pi\)
0.361639 + 0.932318i \(0.382217\pi\)
\(762\) −16994.8 3091.88i −0.807949 0.146991i
\(763\) 0 0
\(764\) 3154.43i 0.149376i
\(765\) −9833.86 3700.65i −0.464764 0.174898i
\(766\) 9140.55i 0.431151i
\(767\) 1612.27i 0.0759005i
\(768\) 2974.19 16347.9i 0.139742 0.768105i
\(769\) 23780.6i 1.11515i 0.830126 + 0.557576i \(0.188268\pi\)
−0.830126 + 0.557576i \(0.811732\pi\)
\(770\) 0 0
\(771\) −885.639 + 4868.00i −0.0413690 + 0.227389i
\(772\) 4467.45 0.208273
\(773\) −24377.3 −1.13427 −0.567135 0.823625i \(-0.691948\pi\)
−0.567135 + 0.823625i \(0.691948\pi\)
\(774\) 1809.56 4808.61i 0.0840354 0.223310i
\(775\) 3831.53i 0.177591i
\(776\) 11295.5 0.522534
\(777\) 0 0
\(778\) −16376.0 −0.754639
\(779\) 21478.4i 0.987862i
\(780\) 475.103 + 86.4358i 0.0218095 + 0.00396782i
\(781\) −33202.9 −1.52124
\(782\) 9348.31 0.427487
\(783\) 29819.9 + 17870.4i 1.36102 + 0.815626i
\(784\) 0 0
\(785\) 31459.5i 1.43037i
\(786\) −13504.0 2456.79i