Properties

Label 441.4.e.p.361.1
Level $441$
Weight $4$
Character 441.361
Analytic conductor $26.020$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(26.0198423125\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-19})\)
Defining polynomial: \(x^{4} - x^{3} - 4 x^{2} - 5 x + 25\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(2.13746 + 0.656712i\) of defining polynomial
Character \(\chi\) \(=\) 441.361
Dual form 441.4.e.p.226.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.63746 - 4.56821i) q^{2} +(-9.91238 + 17.1687i) q^{4} +(-5.27492 - 9.13642i) q^{5} +62.3746 q^{8} +O(q^{10})\) \(q+(-2.63746 - 4.56821i) q^{2} +(-9.91238 + 17.1687i) q^{4} +(-5.27492 - 9.13642i) q^{5} +62.3746 q^{8} +(-27.8248 + 48.1939i) q^{10} +(17.3746 - 30.0937i) q^{11} +37.2990 q^{13} +(-85.2114 - 147.590i) q^{16} +(5.27492 - 9.13642i) q^{17} +(-29.2990 - 50.7474i) q^{19} +209.148 q^{20} -183.299 q^{22} +(-62.6736 - 108.554i) q^{23} +(6.85050 - 11.8654i) q^{25} +(-98.3746 - 170.390i) q^{26} +35.4020 q^{29} +(145.897 - 252.701i) q^{31} +(-199.985 + 346.384i) q^{32} -55.6495 q^{34} +(129.949 + 225.077i) q^{37} +(-154.550 + 267.688i) q^{38} +(-329.021 - 569.881i) q^{40} -338.248 q^{41} +6.80397 q^{43} +(344.447 + 596.599i) q^{44} +(-330.598 + 572.613i) q^{46} +(-125.347 - 217.108i) q^{47} -72.2716 q^{50} +(-369.722 + 640.377i) q^{52} +(-268.450 + 464.969i) q^{53} -366.598 q^{55} +(-93.3713 - 161.724i) q^{58} +(17.9452 - 31.0820i) q^{59} +(28.8970 + 50.0511i) q^{61} -1539.19 q^{62} +746.423 q^{64} +(-196.749 - 340.780i) q^{65} +(-240.846 + 417.157i) q^{67} +(104.574 + 181.127i) q^{68} -363.752 q^{71} +(290.650 - 503.420i) q^{73} +(685.468 - 1187.26i) q^{74} +1161.69 q^{76} +(346.846 + 600.754i) q^{79} +(-898.966 + 1557.05i) q^{80} +(892.114 + 1545.19i) q^{82} +1334.39 q^{83} -111.299 q^{85} +(-17.9452 - 31.0820i) q^{86} +(1083.73 - 1877.08i) q^{88} +(176.519 + 305.740i) q^{89} +2484.98 q^{92} +(-661.196 + 1145.23i) q^{94} +(-309.100 + 535.376i) q^{95} -1445.88 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 3q^{2} - 17q^{4} - 6q^{5} + 174q^{8} + O(q^{10}) \) \( 4q - 3q^{2} - 17q^{4} - 6q^{5} + 174q^{8} - 66q^{10} - 6q^{11} - 32q^{13} - 137q^{16} + 6q^{17} + 64q^{19} + 444q^{20} - 552q^{22} + 6q^{23} + 118q^{25} - 318q^{26} + 504q^{29} + 40q^{31} - 279q^{32} - 132q^{34} + 248q^{37} - 588q^{38} - 546q^{40} - 900q^{41} + 752q^{43} + 804q^{44} - 960q^{46} + 12q^{47} + 330q^{50} - 890q^{52} - 1104q^{53} - 1104q^{55} + 306q^{58} - 804q^{59} - 428q^{61} - 4224q^{62} + 2578q^{64} - 636q^{65} - 148q^{67} + 222q^{68} - 1908q^{71} + 1072q^{73} + 1398q^{74} + 3016q^{76} + 572q^{79} - 1950q^{80} + 1530q^{82} + 3888q^{83} - 264q^{85} + 804q^{86} + 1164q^{88} - 366q^{89} + 5712q^{92} - 1920q^{94} - 1176q^{95} - 1616q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.63746 4.56821i −0.932482 1.61511i −0.779063 0.626946i \(-0.784305\pi\)
−0.153420 0.988161i \(-0.549029\pi\)
\(3\) 0 0
\(4\) −9.91238 + 17.1687i −1.23905 + 2.14609i
\(5\) −5.27492 9.13642i −0.471803 0.817187i 0.527677 0.849445i \(-0.323063\pi\)
−0.999480 + 0.0322587i \(0.989730\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 62.3746 2.75659
\(9\) 0 0
\(10\) −27.8248 + 48.1939i −0.879896 + 1.52402i
\(11\) 17.3746 30.0937i 0.476240 0.824871i −0.523390 0.852093i \(-0.675333\pi\)
0.999629 + 0.0272223i \(0.00866619\pi\)
\(12\) 0 0
\(13\) 37.2990 0.795760 0.397880 0.917437i \(-0.369746\pi\)
0.397880 + 0.917437i \(0.369746\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −85.2114 147.590i −1.33143 2.30610i
\(17\) 5.27492 9.13642i 0.0752562 0.130348i −0.825941 0.563756i \(-0.809356\pi\)
0.901198 + 0.433408i \(0.142689\pi\)
\(18\) 0 0
\(19\) −29.2990 50.7474i −0.353771 0.612750i 0.633136 0.774041i \(-0.281768\pi\)
−0.986907 + 0.161291i \(0.948434\pi\)
\(20\) 209.148 2.33834
\(21\) 0 0
\(22\) −183.299 −1.77634
\(23\) −62.6736 108.554i −0.568189 0.984132i −0.996745 0.0806171i \(-0.974311\pi\)
0.428556 0.903515i \(-0.359022\pi\)
\(24\) 0 0
\(25\) 6.85050 11.8654i 0.0548040 0.0949233i
\(26\) −98.3746 170.390i −0.742032 1.28524i
\(27\) 0 0
\(28\) 0 0
\(29\) 35.4020 0.226689 0.113345 0.993556i \(-0.463844\pi\)
0.113345 + 0.993556i \(0.463844\pi\)
\(30\) 0 0
\(31\) 145.897 252.701i 0.845286 1.46408i −0.0400859 0.999196i \(-0.512763\pi\)
0.885372 0.464883i \(-0.153904\pi\)
\(32\) −199.985 + 346.384i −1.10477 + 1.91352i
\(33\) 0 0
\(34\) −55.6495 −0.280700
\(35\) 0 0
\(36\) 0 0
\(37\) 129.949 + 225.077i 0.577389 + 1.00007i 0.995778 + 0.0917993i \(0.0292618\pi\)
−0.418388 + 0.908268i \(0.637405\pi\)
\(38\) −154.550 + 267.688i −0.659771 + 1.14276i
\(39\) 0 0
\(40\) −329.021 569.881i −1.30057 2.25265i
\(41\) −338.248 −1.28842 −0.644212 0.764847i \(-0.722815\pi\)
−0.644212 + 0.764847i \(0.722815\pi\)
\(42\) 0 0
\(43\) 6.80397 0.0241301 0.0120651 0.999927i \(-0.496159\pi\)
0.0120651 + 0.999927i \(0.496159\pi\)
\(44\) 344.447 + 596.599i 1.18017 + 2.04411i
\(45\) 0 0
\(46\) −330.598 + 572.613i −1.05965 + 1.83537i
\(47\) −125.347 217.108i −0.389016 0.673796i 0.603301 0.797513i \(-0.293852\pi\)
−0.992317 + 0.123717i \(0.960518\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −72.2716 −0.204415
\(51\) 0 0
\(52\) −369.722 + 640.377i −0.985984 + 1.70777i
\(53\) −268.450 + 464.969i −0.695745 + 1.20507i 0.274184 + 0.961677i \(0.411592\pi\)
−0.969929 + 0.243388i \(0.921741\pi\)
\(54\) 0 0
\(55\) −366.598 −0.898765
\(56\) 0 0
\(57\) 0 0
\(58\) −93.3713 161.724i −0.211384 0.366127i
\(59\) 17.9452 31.0820i 0.0395977 0.0685853i −0.845547 0.533900i \(-0.820726\pi\)
0.885145 + 0.465315i \(0.154059\pi\)
\(60\) 0 0
\(61\) 28.8970 + 50.0511i 0.0606538 + 0.105056i 0.894758 0.446552i \(-0.147348\pi\)
−0.834104 + 0.551607i \(0.814015\pi\)
\(62\) −1539.19 −3.15286
\(63\) 0 0
\(64\) 746.423 1.45786
\(65\) −196.749 340.780i −0.375442 0.650285i
\(66\) 0 0
\(67\) −240.846 + 417.157i −0.439164 + 0.760654i −0.997625 0.0688767i \(-0.978059\pi\)
0.558462 + 0.829530i \(0.311392\pi\)
\(68\) 104.574 + 181.127i 0.186492 + 0.323013i
\(69\) 0 0
\(70\) 0 0
\(71\) −363.752 −0.608021 −0.304010 0.952669i \(-0.598326\pi\)
−0.304010 + 0.952669i \(0.598326\pi\)
\(72\) 0 0
\(73\) 290.650 503.420i 0.465999 0.807135i −0.533247 0.845960i \(-0.679028\pi\)
0.999246 + 0.0388253i \(0.0123616\pi\)
\(74\) 685.468 1187.26i 1.07681 1.86509i
\(75\) 0 0
\(76\) 1161.69 1.75336
\(77\) 0 0
\(78\) 0 0
\(79\) 346.846 + 600.754i 0.493964 + 0.855571i 0.999976 0.00695559i \(-0.00221405\pi\)
−0.506012 + 0.862527i \(0.668881\pi\)
\(80\) −898.966 + 1557.05i −1.25634 + 2.17605i
\(81\) 0 0
\(82\) 892.114 + 1545.19i 1.20143 + 2.08094i
\(83\) 1334.39 1.76468 0.882341 0.470611i \(-0.155967\pi\)
0.882341 + 0.470611i \(0.155967\pi\)
\(84\) 0 0
\(85\) −111.299 −0.142024
\(86\) −17.9452 31.0820i −0.0225009 0.0389728i
\(87\) 0 0
\(88\) 1083.73 1877.08i 1.31280 2.27383i
\(89\) 176.519 + 305.740i 0.210236 + 0.364139i 0.951788 0.306756i \(-0.0992435\pi\)
−0.741552 + 0.670895i \(0.765910\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 2484.98 2.81605
\(93\) 0 0
\(94\) −661.196 + 1145.23i −0.725502 + 1.25661i
\(95\) −309.100 + 535.376i −0.333821 + 0.578194i
\(96\) 0 0
\(97\) −1445.88 −1.51347 −0.756735 0.653722i \(-0.773207\pi\)
−0.756735 + 0.653722i \(0.773207\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 135.809 + 235.229i 0.135809 + 0.235229i
\(101\) −237.426 + 411.234i −0.233909 + 0.405142i −0.958955 0.283558i \(-0.908485\pi\)
0.725046 + 0.688700i \(0.241818\pi\)
\(102\) 0 0
\(103\) −999.794 1731.69i −0.956433 1.65659i −0.731053 0.682320i \(-0.760971\pi\)
−0.225380 0.974271i \(-0.572362\pi\)
\(104\) 2326.51 2.19359
\(105\) 0 0
\(106\) 2832.10 2.59508
\(107\) 583.368 + 1010.42i 0.527068 + 0.912909i 0.999502 + 0.0315431i \(0.0100421\pi\)
−0.472434 + 0.881366i \(0.656625\pi\)
\(108\) 0 0
\(109\) 668.588 1158.03i 0.587515 1.01761i −0.407042 0.913410i \(-0.633440\pi\)
0.994557 0.104196i \(-0.0332270\pi\)
\(110\) 966.887 + 1674.70i 0.838082 + 1.45160i
\(111\) 0 0
\(112\) 0 0
\(113\) −906.578 −0.754723 −0.377361 0.926066i \(-0.623169\pi\)
−0.377361 + 0.926066i \(0.623169\pi\)
\(114\) 0 0
\(115\) −661.196 + 1145.23i −0.536146 + 0.928633i
\(116\) −350.918 + 607.807i −0.280878 + 0.486496i
\(117\) 0 0
\(118\) −189.319 −0.147697
\(119\) 0 0
\(120\) 0 0
\(121\) 61.7475 + 106.950i 0.0463918 + 0.0803530i
\(122\) 152.429 264.015i 0.113117 0.195925i
\(123\) 0 0
\(124\) 2892.37 + 5009.74i 2.09470 + 3.62813i
\(125\) −1463.27 −1.04703
\(126\) 0 0
\(127\) −1714.89 −1.19820 −0.599101 0.800674i \(-0.704475\pi\)
−0.599101 + 0.800674i \(0.704475\pi\)
\(128\) −368.782 638.749i −0.254656 0.441078i
\(129\) 0 0
\(130\) −1037.84 + 1797.58i −0.700186 + 1.21276i
\(131\) −235.306 407.561i −0.156937 0.271823i 0.776826 0.629716i \(-0.216829\pi\)
−0.933763 + 0.357893i \(0.883495\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 2540.88 1.63805
\(135\) 0 0
\(136\) 329.021 569.881i 0.207451 0.359315i
\(137\) −221.955 + 384.438i −0.138415 + 0.239742i −0.926897 0.375316i \(-0.877534\pi\)
0.788482 + 0.615058i \(0.210868\pi\)
\(138\) 0 0
\(139\) −1669.98 −1.01904 −0.509518 0.860460i \(-0.670176\pi\)
−0.509518 + 0.860460i \(0.670176\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 959.382 + 1661.70i 0.566969 + 0.982019i
\(143\) 648.055 1122.46i 0.378972 0.656400i
\(144\) 0 0
\(145\) −186.743 323.448i −0.106953 0.185247i
\(146\) −3066.30 −1.73814
\(147\) 0 0
\(148\) −5152.39 −2.86165
\(149\) 371.935 + 644.211i 0.204497 + 0.354200i 0.949973 0.312334i \(-0.101111\pi\)
−0.745475 + 0.666534i \(0.767777\pi\)
\(150\) 0 0
\(151\) −303.382 + 525.473i −0.163503 + 0.283195i −0.936123 0.351674i \(-0.885613\pi\)
0.772620 + 0.634869i \(0.218946\pi\)
\(152\) −1827.51 3165.35i −0.975203 1.68910i
\(153\) 0 0
\(154\) 0 0
\(155\) −3078.38 −1.59523
\(156\) 0 0
\(157\) 1557.39 2697.48i 0.791678 1.37123i −0.133250 0.991083i \(-0.542541\pi\)
0.924927 0.380144i \(-0.124125\pi\)
\(158\) 1829.58 3168.93i 0.921226 1.59561i
\(159\) 0 0
\(160\) 4219.61 2.08493
\(161\) 0 0
\(162\) 0 0
\(163\) −1206.54 2089.78i −0.579774 1.00420i −0.995505 0.0947109i \(-0.969807\pi\)
0.415730 0.909488i \(-0.363526\pi\)
\(164\) 3352.84 5807.28i 1.59642 2.76508i
\(165\) 0 0
\(166\) −3519.40 6095.79i −1.64553 2.85015i
\(167\) −610.475 −0.282874 −0.141437 0.989947i \(-0.545172\pi\)
−0.141437 + 0.989947i \(0.545172\pi\)
\(168\) 0 0
\(169\) −805.784 −0.366766
\(170\) 293.547 + 508.437i 0.132435 + 0.229385i
\(171\) 0 0
\(172\) −67.4435 + 116.816i −0.0298984 + 0.0517855i
\(173\) −1896.90 3285.54i −0.833636 1.44390i −0.895136 0.445792i \(-0.852922\pi\)
0.0615006 0.998107i \(-0.480411\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −5922.05 −2.53631
\(177\) 0 0
\(178\) 931.124 1612.75i 0.392082 0.679107i
\(179\) −1402.34 + 2428.92i −0.585562 + 1.01422i 0.409243 + 0.912426i \(0.365793\pi\)
−0.994805 + 0.101798i \(0.967540\pi\)
\(180\) 0 0
\(181\) −3106.04 −1.27553 −0.637763 0.770232i \(-0.720140\pi\)
−0.637763 + 0.770232i \(0.720140\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −3909.24 6771.00i −1.56627 2.71285i
\(185\) 1370.94 2374.53i 0.544828 0.943670i
\(186\) 0 0
\(187\) −183.299 317.483i −0.0716800 0.124153i
\(188\) 4969.95 1.92804
\(189\) 0 0
\(190\) 3260.95 1.24513
\(191\) 130.976 + 226.857i 0.0496182 + 0.0859413i 0.889768 0.456413i \(-0.150866\pi\)
−0.840150 + 0.542355i \(0.817533\pi\)
\(192\) 0 0
\(193\) −2025.54 + 3508.33i −0.755447 + 1.30847i 0.189704 + 0.981841i \(0.439247\pi\)
−0.945152 + 0.326632i \(0.894086\pi\)
\(194\) 3813.44 + 6605.07i 1.41128 + 2.44442i
\(195\) 0 0
\(196\) 0 0
\(197\) 2874.83 1.03971 0.519855 0.854254i \(-0.325986\pi\)
0.519855 + 0.854254i \(0.325986\pi\)
\(198\) 0 0
\(199\) −1533.49 + 2656.07i −0.546261 + 0.946151i 0.452266 + 0.891883i \(0.350616\pi\)
−0.998526 + 0.0542680i \(0.982717\pi\)
\(200\) 427.297 740.100i 0.151072 0.261665i
\(201\) 0 0
\(202\) 2504.81 0.872463
\(203\) 0 0
\(204\) 0 0
\(205\) 1784.23 + 3090.37i 0.607882 + 1.05288i
\(206\) −5273.83 + 9134.54i −1.78371 + 3.08948i
\(207\) 0 0
\(208\) −3178.30 5504.98i −1.05950 1.83510i
\(209\) −2036.23 −0.673919
\(210\) 0 0
\(211\) 595.422 0.194268 0.0971340 0.995271i \(-0.469032\pi\)
0.0971340 + 0.995271i \(0.469032\pi\)
\(212\) −5321.96 9217.90i −1.72412 2.98626i
\(213\) 0 0
\(214\) 3077.22 5329.90i 0.982964 1.70254i
\(215\) −35.8904 62.1640i −0.0113847 0.0197188i
\(216\) 0 0
\(217\) 0 0
\(218\) −7053.49 −2.19139
\(219\) 0 0
\(220\) 3633.86 6294.03i 1.11361 1.92883i
\(221\) 196.749 340.780i 0.0598859 0.103725i
\(222\) 0 0
\(223\) 3779.79 1.13504 0.567520 0.823360i \(-0.307903\pi\)
0.567520 + 0.823360i \(0.307903\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 2391.06 + 4141.44i 0.703766 + 1.21896i
\(227\) −913.809 + 1582.76i −0.267188 + 0.462783i −0.968135 0.250431i \(-0.919428\pi\)
0.700947 + 0.713214i \(0.252761\pi\)
\(228\) 0 0
\(229\) −425.125 736.338i −0.122677 0.212483i 0.798146 0.602465i \(-0.205815\pi\)
−0.920823 + 0.389982i \(0.872481\pi\)
\(230\) 6975.51 1.99979
\(231\) 0 0
\(232\) 2208.18 0.624890
\(233\) −3295.55 5708.06i −0.926604 1.60492i −0.788962 0.614443i \(-0.789381\pi\)
−0.137642 0.990482i \(-0.543952\pi\)
\(234\) 0 0
\(235\) −1322.39 + 2290.45i −0.367078 + 0.635798i
\(236\) 355.759 + 616.193i 0.0981269 + 0.169961i
\(237\) 0 0
\(238\) 0 0
\(239\) 182.556 0.0494083 0.0247042 0.999695i \(-0.492136\pi\)
0.0247042 + 0.999695i \(0.492136\pi\)
\(240\) 0 0
\(241\) 761.949 1319.73i 0.203657 0.352745i −0.746047 0.665894i \(-0.768050\pi\)
0.949704 + 0.313149i \(0.101384\pi\)
\(242\) 325.713 564.152i 0.0865191 0.149856i
\(243\) 0 0
\(244\) −1145.75 −0.300612
\(245\) 0 0
\(246\) 0 0
\(247\) −1092.82 1892.83i −0.281517 0.487602i
\(248\) 9100.27 15762.1i 2.33011 4.03587i
\(249\) 0 0
\(250\) 3859.32 + 6684.54i 0.976339 + 1.69107i
\(251\) 2357.73 0.592903 0.296451 0.955048i \(-0.404197\pi\)
0.296451 + 0.955048i \(0.404197\pi\)
\(252\) 0 0
\(253\) −4355.71 −1.08238
\(254\) 4522.94 + 7833.97i 1.11730 + 1.93522i
\(255\) 0 0
\(256\) 1040.40 1802.02i 0.254003 0.439946i
\(257\) −1391.27 2409.76i −0.337686 0.584890i 0.646311 0.763074i \(-0.276311\pi\)
−0.983997 + 0.178185i \(0.942978\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 7801.01 1.86076
\(261\) 0 0
\(262\) −1241.22 + 2149.85i −0.292682 + 0.506940i
\(263\) 1021.89 1769.97i 0.239591 0.414984i −0.721006 0.692929i \(-0.756320\pi\)
0.960597 + 0.277945i \(0.0896532\pi\)
\(264\) 0 0
\(265\) 5664.21 1.31302
\(266\) 0 0
\(267\) 0 0
\(268\) −4774.70 8270.03i −1.08829 1.88497i
\(269\) −1726.42 + 2990.24i −0.391307 + 0.677763i −0.992622 0.121248i \(-0.961310\pi\)
0.601315 + 0.799012i \(0.294644\pi\)
\(270\) 0 0
\(271\) 1322.15 + 2290.02i 0.296364 + 0.513318i 0.975301 0.220879i \(-0.0708925\pi\)
−0.678937 + 0.734196i \(0.737559\pi\)
\(272\) −1797.93 −0.400793
\(273\) 0 0
\(274\) 2341.59 0.516280
\(275\) −238.049 412.313i −0.0521996 0.0904124i
\(276\) 0 0
\(277\) −1339.74 + 2320.50i −0.290604 + 0.503341i −0.973953 0.226751i \(-0.927190\pi\)
0.683349 + 0.730092i \(0.260523\pi\)
\(278\) 4404.50 + 7628.82i 0.950232 + 1.64585i
\(279\) 0 0
\(280\) 0 0
\(281\) 1019.69 0.216476 0.108238 0.994125i \(-0.465479\pi\)
0.108238 + 0.994125i \(0.465479\pi\)
\(282\) 0 0
\(283\) 216.103 374.301i 0.0453922 0.0786216i −0.842437 0.538795i \(-0.818880\pi\)
0.887829 + 0.460174i \(0.152213\pi\)
\(284\) 3605.65 6245.17i 0.753366 1.30487i
\(285\) 0 0
\(286\) −6836.87 −1.41354
\(287\) 0 0
\(288\) 0 0
\(289\) 2400.85 + 4158.40i 0.488673 + 0.846406i
\(290\) −985.051 + 1706.16i −0.199463 + 0.345480i
\(291\) 0 0
\(292\) 5762.05 + 9980.17i 1.15479 + 2.00016i
\(293\) −2245.92 −0.447809 −0.223904 0.974611i \(-0.571880\pi\)
−0.223904 + 0.974611i \(0.571880\pi\)
\(294\) 0 0
\(295\) −378.638 −0.0747293
\(296\) 8105.48 + 14039.1i 1.59163 + 2.75678i
\(297\) 0 0
\(298\) 1961.93 3398.16i 0.381381 0.660571i
\(299\) −2337.66 4048.95i −0.452142 0.783133i
\(300\) 0 0
\(301\) 0 0
\(302\) 3200.63 0.609853
\(303\) 0 0
\(304\) −4993.22 + 8648.51i −0.942042 + 1.63166i
\(305\) 304.859 528.031i 0.0572333 0.0991310i
\(306\) 0 0
\(307\) 3197.08 0.594354 0.297177 0.954822i \(-0.403955\pi\)
0.297177 + 0.954822i \(0.403955\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 8119.10 + 14062.7i 1.48753 + 2.57647i
\(311\) 1677.80 2906.04i 0.305915 0.529860i −0.671550 0.740959i \(-0.734371\pi\)
0.977465 + 0.211100i \(0.0677045\pi\)
\(312\) 0 0
\(313\) −1128.20 1954.09i −0.203736 0.352881i 0.745993 0.665954i \(-0.231975\pi\)
−0.949729 + 0.313072i \(0.898642\pi\)
\(314\) −16430.2 −2.95290
\(315\) 0 0
\(316\) −13752.3 −2.44818
\(317\) −3069.59 5316.69i −0.543866 0.942004i −0.998677 0.0514158i \(-0.983627\pi\)
0.454811 0.890588i \(-0.349707\pi\)
\(318\) 0 0
\(319\) 615.095 1065.38i 0.107958 0.186989i
\(320\) −3937.32 6819.64i −0.687821 1.19134i
\(321\) 0 0
\(322\) 0 0
\(323\) −618.199 −0.106494
\(324\) 0 0
\(325\) 255.517 442.568i 0.0436108 0.0755362i
\(326\) −6364.38 + 11023.4i −1.08126 + 1.87280i
\(327\) 0 0
\(328\) −21098.0 −3.55166
\(329\) 0 0
\(330\) 0 0
\(331\) −3514.91 6088.00i −0.583676 1.01096i −0.995039 0.0994849i \(-0.968280\pi\)
0.411363 0.911472i \(-0.365053\pi\)
\(332\) −13227.0 + 22909.8i −2.18652 + 3.78717i
\(333\) 0 0
\(334\) 1610.10 + 2788.78i 0.263775 + 0.456872i
\(335\) 5081.76 0.828795
\(336\) 0 0
\(337\) 10328.4 1.66951 0.834757 0.550619i \(-0.185608\pi\)
0.834757 + 0.550619i \(0.185608\pi\)
\(338\) 2125.22 + 3680.99i 0.342003 + 0.592366i
\(339\) 0 0
\(340\) 1103.24 1910.86i 0.175975 0.304797i
\(341\) −5069.80 8781.15i −0.805118 1.39450i
\(342\) 0 0
\(343\) 0 0
\(344\) 424.395 0.0665170
\(345\) 0 0
\(346\) −10006.0 + 17330.9i −1.55470 + 2.69282i
\(347\) 983.768 1703.94i 0.152194 0.263608i −0.779840 0.625980i \(-0.784699\pi\)
0.932034 + 0.362371i \(0.118033\pi\)
\(348\) 0 0
\(349\) 4365.46 0.669564 0.334782 0.942296i \(-0.391337\pi\)
0.334782 + 0.942296i \(0.391337\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 6949.30 + 12036.5i 1.05227 + 1.82258i
\(353\) 3035.79 5258.15i 0.457731 0.792813i −0.541110 0.840952i \(-0.681996\pi\)
0.998841 + 0.0481389i \(0.0153290\pi\)
\(354\) 0 0
\(355\) 1918.76 + 3323.40i 0.286866 + 0.496866i
\(356\) −6998.90 −1.04197
\(357\) 0 0
\(358\) 14794.4 2.18411
\(359\) 4819.02 + 8346.79i 0.708463 + 1.22709i 0.965427 + 0.260673i \(0.0839443\pi\)
−0.256965 + 0.966421i \(0.582722\pi\)
\(360\) 0 0
\(361\) 1712.64 2966.37i 0.249692 0.432479i
\(362\) 8192.06 + 14189.1i 1.18941 + 2.06011i
\(363\) 0 0
\(364\) 0 0
\(365\) −6132.61 −0.879439
\(366\) 0 0
\(367\) 261.362 452.693i 0.0371744 0.0643879i −0.846840 0.531848i \(-0.821498\pi\)
0.884014 + 0.467460i \(0.154831\pi\)
\(368\) −10681.0 + 18500.0i −1.51301 + 2.62060i
\(369\) 0 0
\(370\) −14463.1 −2.03217
\(371\) 0 0
\(372\) 0 0
\(373\) −1614.92 2797.12i −0.224175 0.388283i 0.731896 0.681416i \(-0.238636\pi\)
−0.956072 + 0.293133i \(0.905302\pi\)
\(374\) −966.887 + 1674.70i −0.133681 + 0.231542i
\(375\) 0 0
\(376\) −7818.48 13542.0i −1.07236 1.85738i
\(377\) 1320.46 0.180390
\(378\) 0 0
\(379\) 6639.71 0.899892 0.449946 0.893056i \(-0.351443\pi\)
0.449946 + 0.893056i \(0.351443\pi\)
\(380\) −6127.82 10613.7i −0.827239 1.43282i
\(381\) 0 0
\(382\) 690.887 1196.65i 0.0925363 0.160278i
\(383\) 7112.22 + 12318.7i 0.948871 + 1.64349i 0.747809 + 0.663914i \(0.231106\pi\)
0.201063 + 0.979578i \(0.435561\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 21369.1 2.81777
\(387\) 0 0
\(388\) 14332.1 24823.9i 1.87526 3.24805i
\(389\) 1460.91 2530.37i 0.190414 0.329807i −0.754973 0.655755i \(-0.772350\pi\)
0.945388 + 0.325948i \(0.105684\pi\)
\(390\) 0 0
\(391\) −1322.39 −0.171039
\(392\) 0 0
\(393\) 0 0
\(394\) −7582.24 13132.8i −0.969512 1.67924i
\(395\) 3659.16 6337.86i 0.466108 0.807322i
\(396\) 0 0
\(397\) 405.970 + 703.161i 0.0513226 + 0.0888933i 0.890545 0.454894i \(-0.150323\pi\)
−0.839223 + 0.543788i \(0.816990\pi\)
\(398\) 16178.0 2.03751
\(399\) 0 0
\(400\) −2334.96 −0.291870
\(401\) 1169.32 + 2025.32i 0.145618 + 0.252218i 0.929603 0.368561i \(-0.120150\pi\)
−0.783985 + 0.620780i \(0.786816\pi\)
\(402\) 0 0
\(403\) 5441.81 9425.50i 0.672645 1.16506i
\(404\) −4706.91 8152.61i −0.579648 1.00398i
\(405\) 0 0
\(406\) 0 0
\(407\) 9031.21 1.09990
\(408\) 0 0
\(409\) −1363.79 + 2362.15i −0.164877 + 0.285576i −0.936612 0.350369i \(-0.886056\pi\)
0.771734 + 0.635945i \(0.219390\pi\)
\(410\) 9411.65 16301.5i 1.13368 1.96359i
\(411\) 0 0
\(412\) 39641.3 4.74026
\(413\) 0 0
\(414\) 0 0
\(415\) −7038.81 12191.6i −0.832582 1.44207i
\(416\) −7459.23 + 12919.8i −0.879132 + 1.52270i
\(417\) 0 0
\(418\) 5370.48 + 9301.94i 0.628418 + 1.08845i
\(419\) 13306.3 1.55144 0.775721 0.631076i \(-0.217386\pi\)
0.775721 + 0.631076i \(0.217386\pi\)
\(420\) 0 0
\(421\) −11007.5 −1.27428 −0.637138 0.770750i \(-0.719882\pi\)
−0.637138 + 0.770750i \(0.719882\pi\)
\(422\) −1570.40 2720.01i −0.181151 0.313763i
\(423\) 0 0
\(424\) −16744.5 + 29002.3i −1.91789 + 3.32187i
\(425\) −72.2716 125.178i −0.00824868 0.0142871i
\(426\) 0 0
\(427\) 0 0
\(428\) −23130.2 −2.61225
\(429\) 0 0
\(430\) −189.319 + 327.910i −0.0212320 + 0.0367749i
\(431\) −3262.81 + 5651.36i −0.364650 + 0.631592i −0.988720 0.149776i \(-0.952145\pi\)
0.624070 + 0.781368i \(0.285478\pi\)
\(432\) 0 0
\(433\) 11716.3 1.30034 0.650171 0.759788i \(-0.274697\pi\)
0.650171 + 0.759788i \(0.274697\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 13254.6 + 22957.6i 1.45592 + 2.52172i
\(437\) −3672.55 + 6361.04i −0.402018 + 0.696315i
\(438\) 0 0
\(439\) −7305.69 12653.8i −0.794264 1.37571i −0.923306 0.384066i \(-0.874524\pi\)
0.129042 0.991639i \(-0.458810\pi\)
\(440\) −22866.4 −2.47753
\(441\) 0 0
\(442\) −2075.67 −0.223370
\(443\) −7619.89 13198.0i −0.817228 1.41548i −0.907717 0.419583i \(-0.862176\pi\)
0.0904888 0.995897i \(-0.471157\pi\)
\(444\) 0 0
\(445\) 1862.25 3225.51i 0.198380 0.343604i
\(446\) −9969.05 17266.9i −1.05840 1.83321i
\(447\) 0 0
\(448\) 0 0
\(449\) −10678.8 −1.12241 −0.561206 0.827676i \(-0.689662\pi\)
−0.561206 + 0.827676i \(0.689662\pi\)
\(450\) 0 0
\(451\) −5876.91 + 10179.1i −0.613598 + 1.06278i
\(452\) 8986.34 15564.8i 0.935137 1.61971i
\(453\) 0 0
\(454\) 9640.53 0.996592
\(455\) 0 0
\(456\) 0 0
\(457\) −2114.12 3661.76i −0.216399 0.374814i 0.737306 0.675559i \(-0.236098\pi\)
−0.953704 + 0.300746i \(0.902764\pi\)
\(458\) −2242.50 + 3884.12i −0.228788 + 0.396273i
\(459\) 0 0
\(460\) −13108.0 22703.8i −1.32862 2.30124i
\(461\) 910.121 0.0919492 0.0459746 0.998943i \(-0.485361\pi\)
0.0459746 + 0.998943i \(0.485361\pi\)
\(462\) 0 0
\(463\) 4456.16 0.447290 0.223645 0.974671i \(-0.428204\pi\)
0.223645 + 0.974671i \(0.428204\pi\)
\(464\) −3016.65 5224.99i −0.301820 0.522768i
\(465\) 0 0
\(466\) −17383.8 + 30109.5i −1.72808 + 2.99313i
\(467\) 2214.71 + 3835.99i 0.219453 + 0.380104i 0.954641 0.297759i \(-0.0962393\pi\)
−0.735188 + 0.677864i \(0.762906\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 13951.0 1.36918
\(471\) 0 0
\(472\) 1119.32 1938.73i 0.109155 0.189062i
\(473\) 118.216 204.757i 0.0114917 0.0199043i
\(474\) 0 0
\(475\) −802.851 −0.0775523
\(476\) 0 0
\(477\) 0 0
\(478\) −481.485 833.957i −0.0460724 0.0797998i
\(479\) −1376.43 + 2384.04i −0.131296 + 0.227411i −0.924176 0.381966i \(-0.875247\pi\)
0.792881 + 0.609377i \(0.208580\pi\)
\(480\) 0 0
\(481\) 4846.95 + 8395.16i 0.459463 + 0.795814i
\(482\) −8038.43 −0.759628
\(483\) 0 0
\(484\) −2448.26 −0.229927
\(485\) 7626.88 + 13210.1i 0.714060 + 1.23679i
\(486\) 0 0
\(487\) 335.299 580.755i 0.0311989 0.0540380i −0.850004 0.526776i \(-0.823401\pi\)
0.881203 + 0.472738i \(0.156734\pi\)
\(488\) 1802.44 + 3121.92i 0.167198 + 0.289595i
\(489\) 0 0
\(490\) 0 0
\(491\) 8244.70 0.757797 0.378898 0.925438i \(-0.376303\pi\)
0.378898 + 0.925438i \(0.376303\pi\)
\(492\) 0 0
\(493\) 186.743 323.448i 0.0170598 0.0295484i
\(494\) −5764.56 + 9984.50i −0.525019 + 0.909360i
\(495\) 0 0
\(496\) −49728.3 −4.50175
\(497\) 0 0
\(498\) 0 0
\(499\) −4082.46 7071.02i −0.366244 0.634353i 0.622731 0.782436i \(-0.286023\pi\)
−0.988975 + 0.148083i \(0.952690\pi\)
\(500\) 14504.5 25122.5i 1.29732 2.24703i
\(501\) 0 0
\(502\) −6218.42 10770.6i −0.552872 0.957602i
\(503\) 8175.59 0.724715 0.362357 0.932039i \(-0.381972\pi\)
0.362357 + 0.932039i \(0.381972\pi\)
\(504\) 0 0
\(505\) 5009.61 0.441435
\(506\) 11488.0 + 19897.8i 1.00930 + 1.74815i
\(507\) 0 0
\(508\) 16998.6 29442.4i 1.48463 2.57145i
\(509\) 439.224 + 760.758i 0.0382480 + 0.0662475i 0.884516 0.466510i \(-0.154489\pi\)
−0.846268 + 0.532758i \(0.821156\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −16876.5 −1.45673
\(513\) 0 0
\(514\) −7338.86 + 12711.3i −0.629773 + 1.09080i
\(515\) −10547.7 + 18269.1i −0.902496 + 1.56317i
\(516\) 0 0
\(517\) −8711.42 −0.741060
\(518\) 0 0
\(519\) 0 0
\(520\) −12272.1 21256.0i −1.03494 1.79257i
\(521\) −5856.30 + 10143.4i −0.492455 + 0.852957i −0.999962 0.00869048i \(-0.997234\pi\)
0.507507 + 0.861647i \(0.330567\pi\)
\(522\) 0 0
\(523\) −3670.91 6358.20i −0.306917 0.531596i 0.670769 0.741666i \(-0.265964\pi\)
−0.977686 + 0.210070i \(0.932631\pi\)
\(524\) 9329.75 0.777809
\(525\) 0 0
\(526\) −10780.8 −0.893659
\(527\) −1539.19 2665.95i −0.127226 0.220362i
\(528\) 0 0
\(529\) −1772.46 + 3069.99i −0.145678 + 0.252321i
\(530\) −14939.1 25875.3i −1.22437 2.12066i
\(531\) 0 0
\(532\) 0 0
\(533\) −12616.3 −1.02528
\(534\) 0 0
\(535\) 6154.44 10659.8i 0.497345 0.861426i
\(536\) −15022.6 + 26020.0i −1.21060 + 2.09681i
\(537\) 0 0
\(538\) 18213.4 1.45955
\(539\) 0 0
\(540\) 0 0
\(541\) 7934.36 + 13742.7i 0.630545 + 1.09214i 0.987440 + 0.157992i \(0.0505020\pi\)
−0.356895 + 0.934144i \(0.616165\pi\)
\(542\) 6974.21 12079.7i 0.552709 0.957319i
\(543\) 0 0
\(544\) 2109.80 + 3654.29i 0.166282 + 0.288008i
\(545\) −14107.0 −1.10877
\(546\) 0 0
\(547\) 2315.26 0.180975 0.0904875 0.995898i \(-0.471157\pi\)
0.0904875 + 0.995898i \(0.471157\pi\)
\(548\) −4400.21 7621.38i −0.343006 0.594104i
\(549\) 0 0
\(550\) −1255.69 + 2174.92i −0.0973505 + 0.168616i
\(551\) −1037.24 1796.56i −0.0801961 0.138904i
\(552\) 0 0
\(553\) 0 0
\(554\) 14134.1 1.08393
\(555\) 0 0
\(556\) 16553.5 28671.5i 1.26263 2.18694i
\(557\) −2409.52 + 4173.42i −0.183294 + 0.317475i −0.943000 0.332792i \(-0.892009\pi\)
0.759706 + 0.650266i \(0.225343\pi\)
\(558\) 0 0
\(559\) 253.781 0.0192018
\(560\) 0 0
\(561\) 0 0
\(562\) −2689.39 4658.17i −0.201860 0.349631i
\(563\) −1270.43 + 2200.45i −0.0951017 + 0.164721i −0.909651 0.415373i \(-0.863651\pi\)
0.814549 + 0.580094i \(0.196984\pi\)
\(564\) 0 0
\(565\) 4782.12 + 8282.88i 0.356081 + 0.616750i
\(566\) −2279.85 −0.169310
\(567\) 0 0
\(568\) −22688.9 −1.67607
\(569\) −12110.0 20975.1i −0.892227 1.54538i −0.837200 0.546898i \(-0.815809\pi\)
−0.0550275 0.998485i \(-0.517525\pi\)
\(570\) 0 0
\(571\) 5886.04 10194.9i 0.431389 0.747188i −0.565604 0.824677i \(-0.691357\pi\)
0.996993 + 0.0774891i \(0.0246903\pi\)
\(572\) 12847.5 + 22252.6i 0.939129 + 1.62662i
\(573\) 0 0
\(574\) 0 0
\(575\) −1717.38 −0.124556
\(576\) 0 0
\(577\) 5292.13 9166.24i 0.381827 0.661344i −0.609496 0.792789i \(-0.708628\pi\)
0.991324 + 0.131445i \(0.0419616\pi\)
\(578\) 12664.3 21935.2i 0.911358 1.57852i
\(579\) 0 0
\(580\) 7404.25 0.530077
\(581\) 0 0
\(582\) 0 0
\(583\) 9328.42 + 16157.3i 0.662682 + 1.14780i
\(584\) 18129.1 31400.6i 1.28457 2.22494i
\(585\) 0 0
\(586\) 5923.52 + 10259.8i 0.417574 + 0.723259i
\(587\) −8712.63 −0.612621 −0.306311 0.951932i \(-0.599095\pi\)
−0.306311 + 0.951932i \(0.599095\pi\)
\(588\) 0 0
\(589\) −17098.6 −1.19615
\(590\) 998.641 + 1729.70i 0.0696838 + 0.120696i
\(591\) 0 0
\(592\) 22146.2 38358.3i 1.53750 2.66304i
\(593\) 7681.43 + 13304.6i 0.531937 + 0.921341i 0.999305 + 0.0372786i \(0.0118689\pi\)
−0.467368 + 0.884063i \(0.654798\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −14747.0 −1.01353
\(597\) 0 0
\(598\) −12331.0 + 21357.9i −0.843229 + 1.46052i
\(599\) 13001.9 22519.9i 0.886883 1.53613i 0.0433430 0.999060i \(-0.486199\pi\)
0.843540 0.537066i \(-0.180467\pi\)
\(600\) 0 0
\(601\) −20567.7 −1.39596 −0.697982 0.716115i \(-0.745918\pi\)
−0.697982 + 0.716115i \(0.745918\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −6014.48 10417.4i −0.405175 0.701783i
\(605\) 651.426 1128.30i 0.0437756 0.0758216i
\(606\) 0 0
\(607\) 9821.04 + 17010.5i 0.656711 + 1.13746i 0.981462 + 0.191657i \(0.0613862\pi\)
−0.324751 + 0.945800i \(0.605280\pi\)
\(608\) 23437.4 1.56334
\(609\) 0 0
\(610\) −3216.21 −0.213476
\(611\) −4675.33 8097.90i −0.309564 0.536180i
\(612\) 0 0
\(613\) −4227.29 + 7321.89i −0.278530 + 0.482428i −0.971020 0.239000i \(-0.923180\pi\)
0.692490 + 0.721428i \(0.256514\pi\)
\(614\) −8432.16 14604.9i −0.554225 0.959946i
\(615\) 0 0
\(616\) 0 0
\(617\) 24168.4 1.57696 0.788479 0.615061i \(-0.210869\pi\)
0.788479 + 0.615061i \(0.210869\pi\)
\(618\) 0 0
\(619\) −1018.78 + 1764.58i −0.0661523 + 0.114579i −0.897205 0.441615i \(-0.854406\pi\)
0.831052 + 0.556194i \(0.187739\pi\)
\(620\) 30514.0 52851.9i 1.97657 3.42352i
\(621\) 0 0
\(622\) −17700.5 −1.14104
\(623\) 0 0
\(624\) 0 0
\(625\) 6862.33 + 11885.9i 0.439189 + 0.760698i
\(626\) −5951.14 + 10307.7i −0.379961 + 0.658111i
\(627\) 0 0
\(628\) 30874.9 + 53476.9i 1.96185 + 3.39803i
\(629\) 2741.87 0.173808
\(630\) 0 0
\(631\) 12339.5 0.778489 0.389244 0.921135i \(-0.372736\pi\)
0.389244 + 0.921135i \(0.372736\pi\)
\(632\) 21634.3 + 37471.8i 1.36166 + 2.35846i
\(633\) 0 0
\(634\) −16191.9 + 28045.1i −1.01429 + 1.75680i
\(635\) 9045.89 + 15667.9i 0.565315 + 0.979154i
\(636\) 0 0
\(637\) 0 0
\(638\) −6489.15 −0.402677
\(639\) 0 0
\(640\) −3890.59 + 6738.70i −0.240295 + 0.416204i
\(641\) −5111.32 + 8853.06i −0.314953 + 0.545515i −0.979428 0.201796i \(-0.935322\pi\)
0.664474 + 0.747311i \(0.268655\pi\)
\(642\) 0 0
\(643\) 1211.75 0.0743187 0.0371594 0.999309i \(-0.488169\pi\)
0.0371594 + 0.999309i \(0.488169\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 1630.48 + 2824.07i 0.0993037 + 0.171999i
\(647\) 1408.61 2439.78i 0.0855922 0.148250i −0.820051 0.572290i \(-0.806055\pi\)
0.905643 + 0.424040i \(0.139388\pi\)
\(648\) 0 0
\(649\) −623.581 1080.07i −0.0377160 0.0653260i
\(650\) −2695.66 −0.162665
\(651\) 0 0
\(652\) 47838.6 2.87347
\(653\) 10493.1 + 18174.6i 0.628831 + 1.08917i 0.987787 + 0.155812i \(0.0497995\pi\)
−0.358956 + 0.933355i \(0.616867\pi\)
\(654\) 0 0
\(655\) −2482.44 + 4299.70i −0.148087 + 0.256494i
\(656\) 28822.5 + 49922.1i 1.71544 + 2.97124i
\(657\) 0 0
\(658\) 0 0
\(659\) 2384.09 0.140927 0.0704635 0.997514i \(-0.477552\pi\)
0.0704635 + 0.997514i \(0.477552\pi\)
\(660\) 0 0
\(661\) −3788.55 + 6561.96i −0.222931 + 0.386128i −0.955697 0.294353i \(-0.904896\pi\)
0.732766 + 0.680481i \(0.238229\pi\)
\(662\) −18540.8 + 32113.7i −1.08854 + 1.88540i
\(663\) 0 0
\(664\) 83232.2 4.86451
\(665\) 0 0
\(666\) 0 0
\(667\) −2218.77 3843.02i −0.128802 0.223092i
\(668\) 6051.26 10481.1i 0.350494 0.607074i
\(669\) 0 0
\(670\) −13402.9 23214.6i −0.772837 1.33859i
\(671\) 2008.30 0.115543
\(672\) 0 0
\(673\) 11724.6 0.671547 0.335774 0.941943i \(-0.391002\pi\)
0.335774 + 0.941943i \(0.391002\pi\)
\(674\) −27240.8 47182.5i −1.55679 2.69644i
\(675\) 0 0
\(676\) 7987.23 13834.3i 0.454440 0.787113i
\(677\) −16152.1 27976.3i −0.916952 1.58821i −0.804018 0.594606i \(-0.797308\pi\)
−0.112935 0.993602i \(-0.536025\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −6942.23 −0.391503
\(681\) 0 0
\(682\) −26742.8 + 46319.9i −1.50152 + 2.60070i
\(683\) 16683.6 28896.8i 0.934669 1.61889i 0.159446 0.987207i \(-0.449029\pi\)
0.775223 0.631687i \(-0.217637\pi\)
\(684\) 0 0
\(685\) 4683.18 0.261219
\(686\) 0 0
\(687\) 0 0
\(688\) −579.776 1004.20i −0.0321275 0.0556465i
\(689\) −10012.9 + 17342.9i −0.553646 + 0.958943i
\(690\) 0 0
\(691\) −521.837 903.849i −0.0287288 0.0497598i 0.851304 0.524674i \(-0.175813\pi\)
−0.880032 + 0.474914i \(0.842479\pi\)
\(692\) 75211.3 4.13166
\(693\) 0 0
\(694\) −10378.6 −0.567674
\(695\) 8809.01 + 15257.6i 0.480784 + 0.832742i
\(696\) 0 0
\(697\) −1784.23 + 3090.37i −0.0969619 + 0.167943i
\(698\) −11513.7 19942.4i −0.624357 1.08142i
\(699\) 0 0
\(700\) 0 0
\(701\) 11305.7 0.609143 0.304572 0.952489i \(-0.401487\pi\)
0.304572 + 0.952489i \(0.401487\pi\)
\(702\) 0 0
\(703\) 7614.72 13189.1i 0.408527 0.707590i
\(704\) 12968.8 22462.6i 0.694289 1.20254i
\(705\) 0 0
\(706\) −32027.1 −1.70730
\(707\) 0 0
\(708\) 0 0
\(709\) 6653.38 + 11524.0i 0.352430 + 0.610427i 0.986675 0.162706i \(-0.0520221\pi\)
−0.634245 + 0.773132i \(0.718689\pi\)
\(710\) 10121.3 17530.6i 0.534995 0.926639i
\(711\) 0 0
\(712\) 11010.3 + 19070.4i 0.579535 + 1.00378i
\(713\) −36575.6 −1.92113
\(714\) 0 0
\(715\) −13673.7 −0.715201
\(716\) −27801.0 48152.8i −1.45108 2.51334i
\(717\) 0 0
\(718\) 25419.9 44028.6i 1.32126 2.28849i
\(719\) −5350.62 9267.55i −0.277531 0.480697i 0.693240 0.720707i \(-0.256183\pi\)
−0.970770 + 0.240010i \(0.922849\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −18068.0 −0.931333
\(723\) 0 0
\(724\) 30788.3 53326.8i 1.58044 2.73740i
\(725\) 242.521 420.059i 0.0124235 0.0215181i
\(726\) 0 0
\(727\) 2121.14 0.108210 0.0541051 0.998535i \(-0.482769\pi\)
0.0541051 + 0.998535i \(0.482769\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 16174.5 + 28015.1i 0.820062 + 1.42039i
\(731\) 35.8904 62.1640i 0.00181594 0.00314531i
\(732\) 0 0
\(733\) −10792.0 18692.3i −0.543809 0.941906i −0.998681 0.0513484i \(-0.983648\pi\)
0.454871 0.890557i \(-0.349685\pi\)
\(734\) −2757.33 −0.138658
\(735\) 0 0
\(736\) 50135.0 2.51087
\(737\) 8369.18 + 14495.8i 0.418294 + 0.724507i
\(738\) 0 0
\(739\) 4972.61 8612.81i 0.247524 0.428724i −0.715314 0.698803i \(-0.753716\pi\)
0.962838 + 0.270079i \(0.0870497\pi\)
\(740\) 27178.5 + 47074.5i 1.35013 + 2.33850i
\(741\) 0 0
\(742\) 0 0
\(743\) −2867.01 −0.141562 −0.0707808 0.997492i \(-0.522549\pi\)
−0.0707808 + 0.997492i \(0.522549\pi\)
\(744\) 0 0
\(745\) 3923.86 6796.32i 0.192965 0.334225i
\(746\) −8518.57 + 14754.6i −0.418079 + 0.724134i
\(747\) 0 0
\(748\) 7267.71 0.355259
\(749\) 0 0
\(750\) 0 0
\(751\) 5412.05 + 9373.94i 0.262967 + 0.455473i 0.967029 0.254666i \(-0.0819655\pi\)
−0.704062 + 0.710139i \(0.748632\pi\)
\(752\) −21362.0 + 37000.1i −1.03589 + 1.79422i
\(753\) 0 0
\(754\) −3482.66 6032.14i −0.168211 0.291349i
\(755\) 6401.26 0.308564
\(756\) 0 0
\(757\) −14512.0 −0.696761 −0.348381 0.937353i \(-0.613268\pi\)
−0.348381 + 0.937353i \(0.613268\pi\)
\(758\) −17512.0 30331.6i −0.839134 1.45342i
\(759\) 0 0
\(760\) −19280.0 + 33393.9i −0.920208 + 1.59385i
\(761\) 16537.9 + 28644.5i 0.787778 + 1.36447i 0.927325 + 0.374256i \(0.122102\pi\)
−0.139547 + 0.990215i \(0.544565\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −5193.13 −0.245917
\(765\) 0 0
\(766\) 37516.4 64980.3i 1.76961 3.06506i
\(767\) 669.338 1159.33i 0.0315103 0.0545774i
\(768\) 0 0
\(769\) −6728.44 −0.315518 −0.157759 0.987478i \(-0.550427\pi\)
−0.157759 + 0.987478i \(0.550427\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −40155.8 69551.8i −1.87207 3.24252i
\(773\) 12116.6 20986.6i 0.563784 0.976503i −0.433377 0.901213i \(-0.642678\pi\)
0.997162 0.0752907i \(-0.0239885\pi\)
\(774\) 0 0
\(775\) −1998.93 3462.26i −0.0926501 0.160475i
\(776\) −90186.0 −4.17202
\(777\) 0 0
\(778\) −15412.4 −0.710231
\(779\) 9910.32 + 17165.2i 0.455807 + 0.789481i
\(780\) 0 0
\(781\) −6320.05 + 10946.6i −0.289564 + 0.501539i
\(782\) 3487.75 + 6040.97i 0.159491 + 0.276246i
\(783\) 0 0
\(784\) 0 0
\(785\) −32860.5 −1.49406
\(786\) 0 0
\(787\) −8600.19 + 14896.0i −0.389535 + 0.674694i −0.992387 0.123159i \(-0.960697\pi\)
0.602852 + 0.797853i \(0.294031\pi\)
\(788\) −28496.4 + 49357.2i −1.28825 + 2.23131i
\(789\) 0 0