Properties

Label 441.4.e.q.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.q.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 0.999480 0.0322587i \(-0.0102700\pi\)
−0.527677 + 0.849445i \(0.676937\pi\)
\(6\) 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 \(-0.630254\pi\)
−0.397880 + 0.917437i \(0.630254\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −85.2114 147.590i −1.33143 2.30610i
\(17\) −5.27492 + 9.13642i −0.0752562 + 0.130348i −0.901198 0.433408i \(-0.857311\pi\)
0.825941 + 0.563756i \(0.190644\pi\)
\(18\) 0 0
\(19\) 29.2990 + 50.7474i 0.353771 + 0.612750i 0.986907 0.161291i \(-0.0515658\pi\)
−0.633136 + 0.774041i \(0.718232\pi\)
\(20\) −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 \(0.487237\pi\)
−0.885372 + 0.464883i \(0.846096\pi\)
\(32\) −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 \(-0.277185\pi\)
0.644212 + 0.764847i \(0.277185\pi\)
\(42\) 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 0.992317 0.123717i \(-0.0394816\pi\)
−0.603301 + 0.797513i \(0.706148\pi\)
\(48\) 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 −0.885145 0.465315i \(-0.845941\pi\)
0.845547 + 0.533900i \(0.179274\pi\)
\(60\) 0 0
\(61\) −28.8970 50.0511i −0.0606538 0.105056i 0.834104 0.551607i \(-0.185985\pi\)
−0.894758 + 0.446552i \(0.852652\pi\)
\(62\) 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 −0.999246 0.0388253i \(-0.987638\pi\)
0.533247 + 0.845960i \(0.320972\pi\)
\(74\) 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 \(-0.844033\pi\)
−0.882341 + 0.470611i \(0.844033\pi\)
\(84\) 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 0.741552 0.670895i \(-0.234090\pi\)
−0.951788 + 0.306756i \(0.900757\pi\)
\(90\) 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 \(-0.226793\pi\)
0.756735 + 0.653722i \(0.226793\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 135.809 + 235.229i 0.135809 + 0.235229i
\(101\) 237.426 411.234i 0.233909 0.405142i −0.725046 0.688700i \(-0.758182\pi\)
0.958955 + 0.283558i \(0.0915150\pi\)
\(102\) 0 0
\(103\) 999.794 + 1731.69i 0.956433 + 1.65659i 0.731053 + 0.682320i \(0.239029\pi\)
0.225380 + 0.974271i \(0.427638\pi\)
\(104\) −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 0.933763 0.357893i \(-0.116505\pi\)
−0.776826 + 0.629716i \(0.783171\pi\)
\(132\) 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 \(-0.329824\pi\)
0.509518 + 0.860460i \(0.329824\pi\)
\(140\) 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 \(0.457459\pi\)
−0.924927 + 0.380144i \(0.875875\pi\)
\(158\) 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 \(-0.454828\pi\)
0.141437 + 0.989947i \(0.454828\pi\)
\(168\) 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 \(0.147078\pi\)
−0.0615006 + 0.998107i \(0.519589\pi\)
\(174\) 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 \(-0.279860\pi\)
0.637763 + 0.770232i \(0.279860\pi\)
\(182\) 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 \(-0.649384\pi\)
0.998526 0.0542680i \(-0.0172825\pi\)
\(200\) 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 \(-0.692097\pi\)
−0.567520 + 0.823360i \(0.692097\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 2391.06 + 4141.44i 0.703766 + 1.21896i
\(227\) 913.809 1582.76i 0.267188 0.462783i −0.700947 0.713214i \(-0.747239\pi\)
0.968135 + 0.250431i \(0.0805722\pi\)
\(228\) 0 0
\(229\) 425.125 + 736.338i 0.122677 + 0.212483i 0.920823 0.389982i \(-0.127519\pi\)
−0.798146 + 0.602465i \(0.794185\pi\)
\(230\) −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 −0.949704 0.313149i \(-0.898616\pi\)
0.746047 + 0.665894i \(0.231950\pi\)
\(242\) 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 \(-0.595803\pi\)
−0.296451 + 0.955048i \(0.595803\pi\)
\(252\) 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 0.983997 0.178185i \(-0.0570224\pi\)
−0.646311 + 0.763074i \(0.723689\pi\)
\(258\) 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 −0.601315 0.799012i \(-0.705356\pi\)
0.992622 + 0.121248i \(0.0386898\pi\)
\(270\) 0 0
\(271\) −1322.15 2290.02i −0.296364 0.513318i 0.678937 0.734196i \(-0.262441\pi\)
−0.975301 + 0.220879i \(0.929108\pi\)
\(272\) 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 −0.887829 0.460174i \(-0.847787\pi\)
0.842437 + 0.538795i \(0.181120\pi\)
\(284\) 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 \(-0.428120\pi\)
0.223904 + 0.974611i \(0.428120\pi\)
\(294\) 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 \(-0.596045\pi\)
−0.297177 + 0.954822i \(0.596045\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 8119.10 + 14062.7i 1.48753 + 2.57647i
\(311\) −1677.80 + 2906.04i −0.305915 + 0.529860i −0.977465 0.211100i \(-0.932296\pi\)
0.671550 + 0.740959i \(0.265629\pi\)
\(312\) 0 0
\(313\) 1128.20 + 1954.09i 0.203736 + 0.352881i 0.949729 0.313072i \(-0.101358\pi\)
−0.745993 + 0.665954i \(0.768025\pi\)
\(314\) 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 \(-0.608663\pi\)
−0.334782 + 0.942296i \(0.608663\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 6949.30 + 12036.5i 1.05227 + 1.82258i
\(353\) −3035.79 + 5258.15i −0.457731 + 0.792813i −0.998841 0.0481389i \(-0.984671\pi\)
0.541110 + 0.840952i \(0.318004\pi\)
\(354\) 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 −0.884014 0.467460i \(-0.845169\pi\)
0.846840 + 0.531848i \(0.178502\pi\)
\(368\) −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 \(-0.768894\pi\)
−0.201063 0.979578i \(-0.564439\pi\)
\(384\) 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 0.839223 0.543788i \(-0.183010\pi\)
−0.890545 + 0.454894i \(0.849677\pi\)
\(398\) −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 −0.771734 0.635945i \(-0.780610\pi\)
0.936612 + 0.350369i \(0.113944\pi\)
\(410\) 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 \(-0.782614\pi\)
−0.775721 + 0.631076i \(0.782614\pi\)
\(420\) 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 \(-0.725303\pi\)
−0.650171 + 0.759788i \(0.725303\pi\)
\(434\) 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 \(0.125476\pi\)
−0.129042 + 0.991639i \(0.541190\pi\)
\(440\) 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 \(-0.514639\pi\)
−0.0459746 + 0.998943i \(0.514639\pi\)
\(462\) 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 0.735188 0.677864i \(-0.237094\pi\)
−0.954641 + 0.297759i \(0.903761\pi\)
\(468\) 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 −0.792881 0.609377i \(-0.791420\pi\)
0.924176 + 0.381966i \(0.124753\pi\)
\(480\) 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 \(-0.618028\pi\)
−0.362357 + 0.932039i \(0.618028\pi\)
\(504\) 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 0.846268 0.532758i \(-0.178844\pi\)
−0.884516 + 0.466510i \(0.845511\pi\)
\(510\) 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 −0.507507 0.861647i \(-0.669433\pi\)
0.999962 + 0.00869048i \(0.00276630\pi\)
\(522\) 0 0
\(523\) 3670.91 + 6358.20i 0.306917 + 0.531596i 0.977686 0.210070i \(-0.0673692\pi\)
−0.670769 + 0.741666i \(0.734036\pi\)
\(524\) −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 −0.814549 0.580094i \(-0.803016\pi\)
0.909651 + 0.415373i \(0.136349\pi\)
\(564\) 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 −0.991324 0.131445i \(-0.958038\pi\)
0.609496 + 0.792789i \(0.291372\pi\)
\(578\) 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 \(-0.400905\pi\)
0.306311 + 0.951932i \(0.400905\pi\)
\(588\) 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 \(-0.988131\pi\)
0.467368 0.884063i \(-0.345202\pi\)
\(594\) 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 \(-0.254082\pi\)
0.697982 + 0.716115i \(0.254082\pi\)
\(602\) 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 \(-0.938614\pi\)
0.324751 0.945800i \(-0.394720\pi\)
\(608\) −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 −0.831052 0.556194i \(-0.812261\pi\)
0.897205 + 0.441615i \(0.145594\pi\)
\(620\) 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 \(-0.511831\pi\)
−0.0371594 + 0.999309i \(0.511831\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 1630.48 + 2824.07i 0.0993037 + 0.171999i
\(647\) −1408.61 + 2439.78i −0.0855922 + 0.148250i −0.905643 0.424040i \(-0.860612\pi\)
0.820051 + 0.572290i \(0.193945\pi\)
\(648\) 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 −0.732766 0.680481i \(-0.761771\pi\)
0.955697 + 0.294353i \(0.0951042\pi\)
\(662\) −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 \(0.202692\pi\)
0.112935 + 0.993602i \(0.463975\pi\)
\(678\) 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 0.880032 0.474914i \(-0.157521\pi\)
−0.851304 + 0.524674i \(0.824187\pi\)
\(692\) −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 0.970770 0.240010i \(-0.0771506\pi\)
−0.693240 + 0.720707i \(0.743817\pi\)
\(720\) 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 \(-0.517231\pi\)
−0.0541051 + 0.998535i \(0.517231\pi\)
\(728\) 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 \(0.0163519\pi\)
−0.454871 + 0.890557i \(0.650315\pi\)
\(734\) 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 \(-0.877898\pi\)
0.139547 0.990215i \(-0.455435\pi\)
\(762\) 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 \(-0.449573\pi\)
0.157759 + 0.987478i \(0.449573\pi\)
\(770\) 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 \(0.357322\pi\)
−0.997162 + 0.0752907i \(0.976012\pi\)
\(774\) 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 −0.602852 0.797853i \(-0.705969\pi\)
0.992387 + 0.123159i \(0.0393026\pi\)
\(788\) −28496.4 + 49357.2i −1.28825 + 2.23131i
\(789\) 0 0
\(790\) 3860