Properties

Label 147.4.e.l.67.2
Level $147$
Weight $4$
Character 147.67
Analytic conductor $8.673$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 147.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.67328077084\)
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: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.2
Root \(2.13746 + 0.656712i\) of defining polynomial
Character \(\chi\) \(=\) 147.67
Dual form 147.4.e.l.79.2

$q$-expansion

\(f(q)\) \(=\) \(q+(2.63746 + 4.56821i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-9.91238 + 17.1687i) q^{4} +(-5.27492 - 9.13642i) q^{5} -15.8248 q^{6} -62.3746 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(2.63746 + 4.56821i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-9.91238 + 17.1687i) q^{4} +(-5.27492 - 9.13642i) q^{5} -15.8248 q^{6} -62.3746 q^{8} +(-4.50000 - 7.79423i) q^{9} +(27.8248 - 48.1939i) q^{10} +(-17.3746 + 30.0937i) q^{11} +(-29.7371 - 51.5062i) q^{12} -37.2990 q^{13} +31.6495 q^{15} +(-85.2114 - 147.590i) q^{16} +(5.27492 - 9.13642i) q^{17} +(23.7371 - 41.1139i) q^{18} +(29.2990 + 50.7474i) q^{19} +209.148 q^{20} -183.299 q^{22} +(62.6736 + 108.554i) q^{23} +(93.5619 - 162.054i) q^{24} +(6.85050 - 11.8654i) q^{25} +(-98.3746 - 170.390i) q^{26} +27.0000 q^{27} -35.4020 q^{29} +(83.4743 + 144.582i) q^{30} +(-145.897 + 252.701i) q^{31} +(199.985 - 346.384i) q^{32} +(-52.1238 - 90.2810i) q^{33} +55.6495 q^{34} +178.423 q^{36} +(129.949 + 225.077i) q^{37} +(-154.550 + 267.688i) q^{38} +(55.9485 - 96.9057i) q^{39} +(329.021 + 569.881i) q^{40} -338.248 q^{41} +6.80397 q^{43} +(-344.447 - 596.599i) q^{44} +(-47.4743 + 82.2278i) q^{45} +(-330.598 + 572.613i) q^{46} +(-125.347 - 217.108i) q^{47} +511.268 q^{48} +72.2716 q^{50} +(15.8248 + 27.4093i) q^{51} +(369.722 - 640.377i) q^{52} +(268.450 - 464.969i) q^{53} +(71.2114 + 123.342i) q^{54} +366.598 q^{55} -175.794 q^{57} +(-93.3713 - 161.724i) q^{58} +(17.9452 - 31.0820i) q^{59} +(-313.722 + 543.382i) q^{60} +(-28.8970 - 50.0511i) q^{61} -1539.19 q^{62} +746.423 q^{64} +(196.749 + 340.780i) q^{65} +(274.949 - 476.225i) q^{66} +(-240.846 + 417.157i) q^{67} +(104.574 + 181.127i) q^{68} -376.042 q^{69} +363.752 q^{71} +(280.686 + 486.162i) q^{72} +(-290.650 + 503.420i) q^{73} +(-685.468 + 1187.26i) q^{74} +(20.5515 + 35.5962i) q^{75} -1161.69 q^{76} +590.248 q^{78} +(346.846 + 600.754i) q^{79} +(-898.966 + 1557.05i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-892.114 - 1545.19i) q^{82} +1334.39 q^{83} -111.299 q^{85} +(17.9452 + 31.0820i) q^{86} +(53.1030 - 91.9771i) q^{87} +(1083.73 - 1877.08i) q^{88} +(176.519 + 305.740i) q^{89} -500.846 q^{90} -2484.98 q^{92} +(-437.691 - 758.103i) q^{93} +(661.196 - 1145.23i) q^{94} +(309.100 - 535.376i) q^{95} +(599.954 + 1039.15i) q^{96} +1445.88 q^{97} +312.743 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 3q^{2} - 6q^{3} - 17q^{4} - 6q^{5} - 18q^{6} - 174q^{8} - 18q^{9} + O(q^{10}) \) \( 4q + 3q^{2} - 6q^{3} - 17q^{4} - 6q^{5} - 18q^{6} - 174q^{8} - 18q^{9} + 66q^{10} + 6q^{11} - 51q^{12} + 32q^{13} + 36q^{15} - 137q^{16} + 6q^{17} + 27q^{18} - 64q^{19} + 444q^{20} - 552q^{22} - 6q^{23} + 261q^{24} + 118q^{25} - 318q^{26} + 108q^{27} - 504q^{29} + 198q^{30} - 40q^{31} + 279q^{32} + 18q^{33} + 132q^{34} + 306q^{36} + 248q^{37} - 588q^{38} - 48q^{39} + 546q^{40} - 900q^{41} + 752q^{43} - 804q^{44} - 54q^{45} - 960q^{46} + 12q^{47} + 822q^{48} - 330q^{50} + 18q^{51} + 890q^{52} + 1104q^{53} + 81q^{54} + 1104q^{55} + 384q^{57} + 306q^{58} - 804q^{59} - 666q^{60} + 428q^{61} - 4224q^{62} + 2578q^{64} + 636q^{65} + 828q^{66} - 148q^{67} + 222q^{68} + 36q^{69} + 1908q^{71} + 783q^{72} - 1072q^{73} - 1398q^{74} + 354q^{75} - 3016q^{76} + 1908q^{78} + 572q^{79} - 1950q^{80} - 162q^{81} - 1530q^{82} + 3888q^{83} - 264q^{85} - 804q^{86} + 756q^{87} + 1164q^{88} - 366q^{89} - 1188q^{90} - 5712q^{92} - 120q^{93} + 1920q^{94} + 1176q^{95} + 837q^{96} + 1616q^{97} - 108q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(50\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 \(0.215695\pi\)
0.153420 + 0.988161i \(0.450971\pi\)
\(3\) −1.50000 + 2.59808i −0.288675 + 0.500000i
\(4\) −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 \(0.989730\pi\)
\(6\) −15.8248 −1.07674
\(7\) 0 0
\(8\) −62.3746 −2.75659
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) 27.8248 48.1939i 0.879896 1.52402i
\(11\) −17.3746 + 30.0937i −0.476240 + 0.824871i −0.999629 0.0272223i \(-0.991334\pi\)
0.523390 + 0.852093i \(0.324667\pi\)
\(12\) −29.7371 51.5062i −0.715364 1.23905i
\(13\) −37.2990 −0.795760 −0.397880 0.917437i \(-0.630254\pi\)
−0.397880 + 0.917437i \(0.630254\pi\)
\(14\) 0 0
\(15\) 31.6495 0.544791
\(16\) −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 \(0.142689\pi\)
\(18\) 23.7371 41.1139i 0.310827 0.538369i
\(19\) 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 \(0.0256891\pi\)
−0.428556 + 0.903515i \(0.640978\pi\)
\(24\) 93.5619 162.054i 0.795760 1.37830i
\(25\) 6.85050 11.8654i 0.0548040 0.0949233i
\(26\) −98.3746 170.390i −0.742032 1.28524i
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) −35.4020 −0.226689 −0.113345 0.993556i \(-0.536156\pi\)
−0.113345 + 0.993556i \(0.536156\pi\)
\(30\) 83.4743 + 144.582i 0.508008 + 0.879896i
\(31\) −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
\(33\) −52.1238 90.2810i −0.274957 0.476240i
\(34\) 55.6495 0.280700
\(35\) 0 0
\(36\) 178.423 0.826031
\(37\) 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
\(39\) 55.9485 96.9057i 0.229716 0.397880i
\(40\) 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
\(45\) −47.4743 + 82.2278i −0.157268 + 0.272396i
\(46\) −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 \(0.960518\pi\)
\(48\) 511.268 1.53740
\(49\) 0 0
\(50\) 72.2716 0.204415
\(51\) 15.8248 + 27.4093i 0.0434492 + 0.0752562i
\(52\) 369.722 640.377i 0.985984 1.70777i
\(53\) 268.450 464.969i 0.695745 1.20507i −0.274184 0.961677i \(-0.588408\pi\)
0.969929 0.243388i \(-0.0782588\pi\)
\(54\) 71.2114 + 123.342i 0.179456 + 0.310827i
\(55\) 366.598 0.898765
\(56\) 0 0
\(57\) −175.794 −0.408500
\(58\) −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 \(0.154059\pi\)
\(60\) −313.722 + 543.382i −0.675022 + 1.16917i
\(61\) −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
\(66\) 274.949 476.225i 0.512785 0.888170i
\(67\) −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
\(69\) −376.042 −0.656088
\(70\) 0 0
\(71\) 363.752 0.608021 0.304010 0.952669i \(-0.401674\pi\)
0.304010 + 0.952669i \(0.401674\pi\)
\(72\) 280.686 + 486.162i 0.459432 + 0.795760i
\(73\) −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
\(75\) 20.5515 + 35.5962i 0.0316411 + 0.0548040i
\(76\) −1161.69 −1.75336
\(77\) 0 0
\(78\) 590.248 0.856825
\(79\) 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
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) −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
\(87\) 53.1030 91.9771i 0.0654395 0.113345i
\(88\) 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 \(0.765910\pi\)
\(90\) −500.846 −0.586597
\(91\) 0 0
\(92\) −2484.98 −2.81605
\(93\) −437.691 758.103i −0.488026 0.845286i
\(94\) 661.196 1145.23i 0.725502 1.25661i
\(95\) 309.100 535.376i 0.333821 0.578194i
\(96\) 599.954 + 1039.15i 0.637839 + 1.10477i
\(97\) 1445.88 1.51347 0.756735 0.653722i \(-0.226793\pi\)
0.756735 + 0.653722i \(0.226793\pi\)
\(98\) 0 0
\(99\) 312.743 0.317493
\(100\) 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 \(0.241818\pi\)
\(102\) −83.4743 + 144.582i −0.0810312 + 0.140350i
\(103\) 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 \(-0.989958\pi\)
0.472434 0.881366i \(-0.343375\pi\)
\(108\) −267.634 + 463.556i −0.238455 + 0.413016i
\(109\) 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
\(111\) −779.691 −0.666712
\(112\) 0 0
\(113\) 906.578 0.754723 0.377361 0.926066i \(-0.376831\pi\)
0.377361 + 0.926066i \(0.376831\pi\)
\(114\) −463.650 803.064i −0.380919 0.659771i
\(115\) 661.196 1145.23i 0.536146 0.928633i
\(116\) 350.918 607.807i 0.280878 0.486496i
\(117\) 167.846 + 290.717i 0.132627 + 0.229716i
\(118\) 189.319 0.147697
\(119\) 0 0
\(120\) −1974.12 −1.50177
\(121\) 61.7475 + 106.950i 0.0463918 + 0.0803530i
\(122\) 152.429 264.015i 0.113117 0.195925i
\(123\) 507.371 878.793i 0.371936 0.644212i
\(124\) −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
\(129\) −10.2060 + 17.6772i −0.00696577 + 0.0120651i
\(130\) −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 \(0.883495\pi\)
\(132\) 2066.68 1.36274
\(133\) 0 0
\(134\) −2540.88 −1.63805
\(135\) −142.423 246.683i −0.0907985 0.157268i
\(136\) −329.021 + 569.881i −0.207451 + 0.359315i
\(137\) 221.955 384.438i 0.138415 0.239742i −0.788482 0.615058i \(-0.789132\pi\)
0.926897 + 0.375316i \(0.122466\pi\)
\(138\) −991.794 1717.84i −0.611791 1.05965i
\(139\) 1669.98 1.01904 0.509518 0.860460i \(-0.329824\pi\)
0.509518 + 0.860460i \(0.329824\pi\)
\(140\) 0 0
\(141\) 752.083 0.449197
\(142\) 959.382 + 1661.70i 0.566969 + 0.982019i
\(143\) 648.055 1122.46i 0.378972 0.656400i
\(144\) −766.902 + 1328.31i −0.443809 + 0.768700i
\(145\) 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 0.745475 0.666534i \(-0.232223\pi\)
−0.949973 + 0.312334i \(0.898889\pi\)
\(150\) −108.407 + 187.767i −0.0590095 + 0.102207i
\(151\) −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
\(153\) −94.9485 −0.0501708
\(154\) 0 0
\(155\) 3078.38 1.59523
\(156\) 1109.17 + 1921.13i 0.569258 + 0.985984i
\(157\) −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
\(159\) 805.350 + 1394.91i 0.401688 + 0.695745i
\(160\) −4219.61 −2.08493
\(161\) 0 0
\(162\) −427.268 −0.207218
\(163\) −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
\(165\) −549.897 + 952.450i −0.259451 + 0.449382i
\(166\) 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
\(171\) 263.691 456.726i 0.117924 0.204250i
\(172\) −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 \(-0.480411\pi\)
\(174\) 560.228 0.244085
\(175\) 0 0
\(176\) 5922.05 2.53631
\(177\) 53.8356 + 93.2460i 0.0228618 + 0.0395977i
\(178\) −931.124 + 1612.75i −0.392082 + 0.679107i
\(179\) 1402.34 2428.92i 0.585562 1.01422i −0.409243 0.912426i \(-0.634207\pi\)
0.994805 0.101798i \(-0.0324596\pi\)
\(180\) −941.165 1630.15i −0.389724 0.675022i
\(181\) 3106.04 1.27553 0.637763 0.770232i \(-0.279860\pi\)
0.637763 + 0.770232i \(0.279860\pi\)
\(182\) 0 0
\(183\) 173.382 0.0700370
\(184\) −3909.24 6771.00i −1.56627 2.71285i
\(185\) 1370.94 2374.53i 0.544828 0.943670i
\(186\) 2308.78 3998.93i 0.910152 1.57643i
\(187\) 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 0.840150 0.542355i \(-0.182467\pi\)
−0.889768 + 0.456413i \(0.849134\pi\)
\(192\) −1119.63 + 1939.26i −0.420847 + 0.728928i
\(193\) −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
\(195\) −1180.50 −0.433523
\(196\) 0 0
\(197\) −2874.83 −1.03971 −0.519855 0.854254i \(-0.674014\pi\)
−0.519855 + 0.854254i \(0.674014\pi\)
\(198\) 824.846 + 1428.67i 0.296057 + 0.512785i
\(199\) 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
\(201\) −722.537 1251.47i −0.253551 0.439164i
\(202\) −2504.81 −0.872463
\(203\) 0 0
\(204\) −627.444 −0.215342
\(205\) 1784.23 + 3090.37i 0.607882 + 1.05288i
\(206\) −5273.83 + 9134.54i −1.78371 + 3.08948i
\(207\) 564.062 976.985i 0.189396 0.328044i
\(208\) 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
\(213\) −545.629 + 945.057i −0.175520 + 0.304010i
\(214\) 3077.22 5329.90i 0.982964 1.70254i
\(215\) −35.8904 62.1640i −0.0113847 0.0197188i
\(216\) −1684.11 −0.530507
\(217\) 0 0
\(218\) 7053.49 2.19139
\(219\) −871.949 1510.26i −0.269045 0.465999i
\(220\) −3633.86 + 6294.03i −1.11361 + 1.92883i
\(221\) −196.749 + 340.780i −0.0598859 + 0.103725i
\(222\) −2056.40 3561.79i −0.621697 1.07681i
\(223\) −3779.79 −1.13504 −0.567520 0.823360i \(-0.692097\pi\)
−0.567520 + 0.823360i \(0.692097\pi\)
\(224\) 0 0
\(225\) −123.309 −0.0365360
\(226\) 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 \(0.252761\pi\)
\(228\) 1742.54 3018.16i 0.506150 0.876678i
\(229\) 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 \(0.210619\pi\)
0.137642 + 0.990482i \(0.456048\pi\)
\(234\) −885.371 + 1533.51i −0.247344 + 0.428413i
\(235\) −1322.39 + 2290.45i −0.367078 + 0.635798i
\(236\) 355.759 + 616.193i 0.0981269 + 0.169961i
\(237\) −2081.07 −0.570381
\(238\) 0 0
\(239\) −182.556 −0.0494083 −0.0247042 0.999695i \(-0.507864\pi\)
−0.0247042 + 0.999695i \(0.507864\pi\)
\(240\) −2696.90 4671.16i −0.725350 1.25634i
\(241\) −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
\(243\) −121.500 210.444i −0.0320750 0.0555556i
\(244\) 1145.75 0.300612
\(245\) 0 0
\(246\) 5352.68 1.38730
\(247\) −1092.82 1892.83i −0.281517 0.487602i
\(248\) 9100.27 15762.1i 2.33011 4.03587i
\(249\) −2001.59 + 3466.85i −0.509420 + 0.882341i
\(250\) −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
\(255\) 166.949 289.163i 0.0409989 0.0710122i
\(256\) 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 \(0.942978\pi\)
\(258\) −107.671 −0.0259818
\(259\) 0 0
\(260\) −7801.01 −1.86076
\(261\) 159.309 + 275.931i 0.0377815 + 0.0654395i
\(262\) 1241.22 2149.85i 0.292682 0.506940i
\(263\) −1021.89 + 1769.97i −0.239591 + 0.414984i −0.960597 0.277945i \(-0.910347\pi\)
0.721006 + 0.692929i \(0.243680\pi\)
\(264\) 3251.20 + 5631.24i 0.757945 + 1.31280i
\(265\) −5664.21 −1.31302
\(266\) 0 0
\(267\) −1059.11 −0.242759
\(268\) −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 \(0.294644\pi\)
\(270\) 751.268 1301.23i 0.169336 0.293299i
\(271\) −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
\(276\) 3727.47 6456.16i 0.812924 1.40803i
\(277\) −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
\(279\) 2626.15 0.563524
\(280\) 0 0
\(281\) −1019.69 −0.216476 −0.108238 0.994125i \(-0.534521\pi\)
−0.108238 + 0.994125i \(0.534521\pi\)
\(282\) 1983.59 + 3435.68i 0.418869 + 0.725502i
\(283\) −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
\(285\) 927.299 + 1606.13i 0.192731 + 0.333821i
\(286\) 6836.87 1.41354
\(287\) 0 0
\(288\) −3599.72 −0.736513
\(289\) 2400.85 + 4158.40i 0.488673 + 0.846406i
\(290\) −985.051 + 1706.16i −0.199463 + 0.345480i
\(291\) −2168.82 + 3756.50i −0.436901 + 0.756735i
\(292\) −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
\(297\) −469.114 + 812.529i −0.0916523 + 0.158747i
\(298\) 1961.93 3398.16i 0.381381 0.660571i
\(299\) −2337.66 4048.95i −0.452142 0.783133i
\(300\) −814.856 −0.156819
\(301\) 0 0
\(302\) −3200.63 −0.609853
\(303\) −712.278 1233.70i −0.135047 0.233909i
\(304\) 4993.22 8648.51i 0.942042 1.63166i
\(305\) −304.859 + 528.031i −0.0572333 + 0.0991310i
\(306\) −250.423 433.745i −0.0467834 0.0810312i
\(307\) −3197.08 −0.594354 −0.297177 0.954822i \(-0.596045\pi\)
−0.297177 + 0.954822i \(0.596045\pi\)
\(308\) 0 0
\(309\) −5998.76 −1.10439
\(310\) 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 \(0.0677045\pi\)
\(312\) −3489.77 + 6044.45i −0.633234 + 1.09679i
\(313\) 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 \(0.0163734\pi\)
−0.454811 + 0.890588i \(0.650293\pi\)
\(318\) −4248.16 + 7358.02i −0.749135 + 1.29754i
\(319\) 615.095 1065.38i 0.107958 0.186989i
\(320\) −3937.32 6819.64i −0.687821 1.19134i
\(321\) 3500.21 0.608606
\(322\) 0 0
\(323\) 618.199 0.106494
\(324\) −802.902 1390.67i −0.137672 0.238455i
\(325\) −255.517 + 442.568i −0.0436108 + 0.0755362i
\(326\) 6364.38 11023.4i 1.08126 1.87280i
\(327\) 2005.76 + 3474.09i 0.339202 + 0.587515i
\(328\) 21098.0 3.55166
\(329\) 0 0
\(330\) −5801.32 −0.967734
\(331\) −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
\(333\) 1169.54 2025.70i 0.192463 0.333356i
\(334\) −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
\(339\) −1359.87 + 2355.36i −0.217870 + 0.377361i
\(340\) 1103.24 1910.86i 0.175975 0.304797i
\(341\) −5069.80 8781.15i −0.805118 1.39450i
\(342\) 2781.90 0.439847
\(343\) 0 0
\(344\) −424.395 −0.0665170
\(345\) 1983.59 + 3435.68i 0.309544 + 0.536146i
\(346\) 10006.0 17330.9i 1.55470 2.69282i
\(347\) −983.768 + 1703.94i −0.152194 + 0.263608i −0.932034 0.362371i \(-0.881967\pi\)
0.779840 + 0.625980i \(0.215301\pi\)
\(348\) 1052.75 + 1823.42i 0.162165 + 0.280878i
\(349\) −4365.46 −0.669564 −0.334782 0.942296i \(-0.608663\pi\)
−0.334782 + 0.942296i \(0.608663\pi\)
\(350\) 0 0
\(351\) −1007.07 −0.153144
\(352\) 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 \(0.0153290\pi\)
\(354\) −283.978 + 491.865i −0.0426364 + 0.0738484i
\(355\) −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 \(-0.916056\pi\)
0.256965 0.966421i \(-0.417278\pi\)
\(360\) 2961.19 5128.93i 0.433523 0.750884i
\(361\) 1712.64 2966.37i 0.249692 0.432479i
\(362\) 8192.06 + 14189.1i 1.18941 + 2.06011i
\(363\) −370.485 −0.0535687
\(364\) 0 0
\(365\) 6132.61 0.879439
\(366\) 457.288 + 792.046i 0.0653083 + 0.113117i
\(367\) −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
\(369\) 1522.11 + 2636.38i 0.214737 + 0.371936i
\(370\) 14463.1 2.03217
\(371\) 0 0
\(372\) 17354.2 2.41875
\(373\) −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
\(375\) 2194.91 3801.69i 0.302252 0.523516i
\(376\) 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
\(381\) 2572.33 4455.41i 0.345891 0.599101i
\(382\) 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 \(0.435561\pi\)
\(384\) −2212.69 −0.294052
\(385\) 0 0
\(386\) −21369.1 −2.81777
\(387\) −30.6179 53.0317i −0.00402169 0.00696577i
\(388\) −14332.1 + 24823.9i −1.87526 + 3.24805i
\(389\) −1460.91 + 2530.37i −0.190414 + 0.329807i −0.945388 0.325948i \(-0.894316\pi\)
0.754973 + 0.655755i \(0.227650\pi\)
\(390\) −3113.51 5392.75i −0.404253 0.700186i
\(391\) 1322.39 0.171039
\(392\) 0 0
\(393\) 1411.83 0.181215
\(394\) −7582.24 13132.8i −0.969512 1.67924i
\(395\) 3659.16 6337.86i 0.466108 0.807322i
\(396\) −3100.02 + 5369.40i −0.393389 + 0.681369i
\(397\) −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 0.783985 0.620780i \(-0.213184\pi\)
−0.929603 + 0.368561i \(0.879850\pi\)
\(402\) 3811.32 6601.40i 0.472864 0.819025i
\(403\) 5441.81 9425.50i 0.672645 1.16506i
\(404\) −4706.91 8152.61i −0.579648 1.00398i
\(405\) 854.537 0.104845
\(406\) 0 0
\(407\) −9031.21 −1.09990
\(408\) −987.062 1709.64i −0.119772 0.207451i
\(409\) 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
\(411\) 665.865 + 1153.31i 0.0799142 + 0.138415i
\(412\) −39641.3 −4.74026
\(413\) 0 0
\(414\) 5950.76 0.706435
\(415\) −7038.81 12191.6i −0.832582 1.44207i
\(416\) −7459.23 + 12919.8i −0.879132 + 1.52270i
\(417\) −2504.97 + 4338.74i −0.294170 + 0.509518i
\(418\) −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
\(423\) −1128.12 + 1953.97i −0.129672 + 0.224599i
\(424\) −16744.5 + 29002.3i −1.91789 + 3.32187i
\(425\) −72.2716 125.178i −0.00824868 0.0142871i
\(426\) −5756.29 −0.654679
\(427\) 0 0
\(428\) 23130.2 2.61225
\(429\) 1944.16 + 3367.39i 0.218800 + 0.378972i
\(430\) 189.319 327.910i 0.0212320 0.0367749i
\(431\) 3262.81 5651.36i 0.364650 0.631592i −0.624070 0.781368i \(-0.714522\pi\)
0.988720 + 0.149776i \(0.0478553\pi\)
\(432\) −2300.71 3984.94i −0.256233 0.443809i
\(433\) −11716.3 −1.30034 −0.650171 0.759788i \(-0.725303\pi\)
−0.650171 + 0.759788i \(0.725303\pi\)
\(434\) 0 0
\(435\) −1120.46 −0.123498
\(436\) 13254.6 + 22957.6i 1.45592 + 2.52172i
\(437\) −3672.55 + 6361.04i −0.402018 + 0.696315i
\(438\) 4599.46 7966.49i 0.501759 0.869072i
\(439\) 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 \(0.137824\pi\)
−0.0904888 + 0.995897i \(0.528843\pi\)
\(444\) 7728.59 13386.3i 0.826087 1.43082i
\(445\) 1862.25 3225.51i 0.198380 0.343604i
\(446\) −9969.05 17266.9i −1.05840 1.83321i
\(447\) 2231.61 0.236133
\(448\) 0 0
\(449\) 10678.8 1.12241 0.561206 0.827676i \(-0.310338\pi\)
0.561206 + 0.827676i \(0.310338\pi\)
\(450\) −325.222 563.301i −0.0340692 0.0590095i
\(451\) 5876.91 10179.1i 0.613598 1.06278i
\(452\) −8986.34 + 15564.8i −0.935137 + 1.61971i
\(453\) −910.146 1576.42i −0.0943982 0.163503i
\(454\) −9640.53 −0.996592
\(455\) 0 0
\(456\) 10965.1 1.12607
\(457\) −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
\(459\) 142.423 246.683i 0.0144831 0.0250854i
\(460\) 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
\(465\) −4617.57 + 7997.86i −0.460505 + 0.797617i
\(466\) −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 \(0.762906\pi\)
\(468\) −6654.99 −0.657323
\(469\) 0 0
\(470\) −13951.0 −1.36918
\(471\) −4672.18 8092.45i −0.457075 0.791678i
\(472\) −1119.32 + 1938.73i −0.109155 + 0.189062i
\(473\) −118.216 + 204.757i −0.0114917 + 0.0199043i
\(474\) −5488.74 9506.78i −0.531870 0.921226i
\(475\) 802.851 0.0775523
\(476\) 0 0
\(477\) −4832.10 −0.463830
\(478\) −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 \(0.208580\pi\)
\(480\) 6329.41 10962.9i 0.601869 1.04247i
\(481\) −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
\(486\) 640.902 1110.08i 0.0598188 0.103609i
\(487\) 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
\(489\) 7239.22 0.669466
\(490\) 0 0
\(491\) −8244.70 −0.757797 −0.378898 0.925438i \(-0.623697\pi\)
−0.378898 + 0.925438i \(0.623697\pi\)
\(492\) 10058.5 + 17421.8i 0.921692 + 1.59642i
\(493\) −186.743 + 323.448i −0.0170598 + 0.0295484i
\(494\) 5764.56 9984.50i 0.525019 0.909360i
\(495\) −1649.69 2857.35i −0.149794 0.259451i
\(496\) 49728.3 4.50175
\(497\) 0 0
\(498\) −21116.4 −1.90010
\(499\) −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
\(501\) 915.713 1586.06i 0.0816587 0.141437i
\(502\) 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
\(507\) 1208.68 2093.49i 0.105876 0.183383i
\(508\) 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 \(0.821156\pi\)
\(510\) 1761.28 0.152923
\(511\) 0 0
\(512\) 16876.5 1.45673
\(513\) 791.073 + 1370.18i 0.0680833 + 0.117924i
\(514\) 7338.86 12711.3i 0.629773 1.09080i
\(515\) 10547.7 18269.1i 0.902496 1.56317i
\(516\) −202.331 350.447i −0.0172618 0.0298984i
\(517\) 8711.42 0.741060
\(518\) 0 0
\(519\) 11381.4 0.962600
\(520\) −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 \(0.330567\pi\)
\(522\) −840.341 + 1455.51i −0.0704612 + 0.122042i
\(523\) 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
\(528\) −8883.07 + 15385.9i −0.732171 + 1.26816i
\(529\) −1772.46 + 3069.99i −0.145678 + 0.252321i
\(530\) −14939.1 25875.3i −1.22437 2.12066i
\(531\) −323.014 −0.0263985
\(532\) 0 0
\(533\) 12616.3 1.02528
\(534\) −2793.37 4838.26i −0.226369 0.392082i
\(535\) −6154.44 + 10659.8i −0.497345 + 0.861426i
\(536\) 15022.6 26020.0i 1.21060 2.09681i
\(537\) 4207.01 + 7286.76i 0.338075 + 0.585562i
\(538\) −18213.4 −1.45955
\(539\) 0 0
\(540\) 5646.99 0.450015
\(541\) 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
\(543\) −4659.07 + 8069.74i −0.368213 + 0.637763i
\(544\) −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
\(549\) −260.073 + 450.460i −0.0202179 + 0.0350185i
\(550\) −1255.69 + 2174.92i −0.0973505 + 0.168616i
\(551\) −1037.24 1796.56i −0.0801961 0.138904i
\(552\) 23455.4 1.80857
\(553\) 0 0
\(554\) −14134.1 −1.08393
\(555\) 4112.81 + 7123.59i 0.314557 + 0.544828i
\(556\) −16553.5 + 28671.5i −1.26263 + 2.18694i
\(557\) 2409.52 4173.42i 0.183294 0.317475i −0.759706 0.650266i \(-0.774657\pi\)
0.943000 + 0.332792i \(0.107991\pi\)
\(558\) 6926.35 + 11996.8i 0.525476 + 0.910152i
\(559\) −253.781 −0.0192018
\(560\) 0 0
\(561\) −1099.79 −0.0827689
\(562\) −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 \(0.196984\pi\)
\(564\) −7454.93 + 12912.3i −0.556577 + 0.964019i
\(565\) −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 \(0.184191\pi\)
0.0550275 + 0.998485i \(0.482475\pi\)
\(570\) −4891.43 + 8472.20i −0.359437 + 0.622564i
\(571\) 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
\(573\) 785.855 0.0572942
\(574\) 0 0
\(575\) 1717.38 0.124556
\(576\) −3358.90 5817.79i −0.242976 0.420847i
\(577\) −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
\(579\) −6076.61 10525.0i −0.436158 0.755447i
\(580\) −7404.25 −0.530077
\(581\) 0 0
\(582\) −22880.6 −1.62961
\(583\) 9328.42 + 16157.3i 0.662682 + 1.14780i
\(584\) 18129.1 31400.6i 1.28457 2.22494i
\(585\) 1770.74 3067.02i 0.125147 0.216762i
\(586\) −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
\(591\) 4312.24 7469.02i 0.300139 0.519855i
\(592\) 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 \(0.654798\pi\)
\(594\) −4949.07 −0.341857
\(595\) 0 0
\(596\) 14747.0 1.01353
\(597\) 4600.46 + 7968.22i 0.315384 + 0.546261i
\(598\) 12331.0 21357.9i 0.843229 1.46052i
\(599\) −13001.9 + 22519.9i −0.886883 + 1.53613i −0.0433430 + 0.999060i \(0.513801\pi\)
−0.843540 + 0.537066i \(0.819533\pi\)
\(600\) −1281.89 2220.30i −0.0872216 0.151072i
\(601\) 20567.7 1.39596 0.697982 0.716115i \(-0.254082\pi\)
0.697982 + 0.716115i \(0.254082\pi\)
\(602\) 0 0
\(603\) 4335.22 0.292776
\(604\) −6014.48 10417.4i −0.405175 0.701783i
\(605\) 651.426 1128.30i 0.0437756 0.0758216i
\(606\) 3757.21 6507.68i 0.251858 0.436231i
\(607\) −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
\(612\) 941.165 1630.15i 0.0621640 0.107671i
\(613\) −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
\(615\) −10705.4 −0.701922
\(616\) 0 0
\(617\) −24168.4 −1.57696 −0.788479 0.615061i \(-0.789131\pi\)
−0.788479 + 0.615061i \(0.789131\pi\)
\(618\) −15821.5 27403.6i −1.02983 1.78371i
\(619\) 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
\(621\) 1692.19 + 2930.95i 0.109348 + 0.189396i
\(622\) 17700.5 1.14104
\(623\) 0 0
\(624\) −19069.8 −1.22340
\(625\) 6862.33 + 11885.9i 0.439189 + 0.760698i
\(626\) −5951.14 + 10307.7i −0.379961 + 0.658111i
\(627\) 3054.35 5290.29i 0.194544 0.336960i
\(628\) −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
\(633\) −893.133 + 1546.95i −0.0560803 + 0.0971340i
\(634\) −16191.9 + 28045.1i −1.01429 + 1.75680i
\(635\) 9045.89 + 15667.9i 0.565315 + 0.979154i
\(636\) −31931.7 −1.99084
\(637\) 0 0
\(638\) 6489.15 0.402677
\(639\) −1636.89 2835.17i −0.101337 0.175520i
\(640\) 3890.59 6738.70i 0.240295 0.416204i
\(641\) 5111.32 8853.06i 0.314953 0.545515i −0.664474 0.747311i \(-0.731345\pi\)
0.979428 + 0.201796i \(0.0646779\pi\)
\(642\) 9231.65 + 15989.7i 0.567514 + 0.982964i
\(643\) −1211.75 −0.0743187 −0.0371594 0.999309i \(-0.511831\pi\)
−0.0371594 + 0.999309i \(0.511831\pi\)
\(644\) 0 0
\(645\) 215.342 0.0131459
\(646\) 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 \(0.139388\pi\)
\(648\) 2526.17 4375.46i 0.153144 0.265253i
\(649\) 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 \(-0.950201\pi\)
0.358956 0.933355i \(-0.383133\pi\)
\(654\) −10580.2 + 18325.5i −0.632600 + 1.09569i
\(655\) −2482.44 + 4299.70i −0.148087 + 0.256494i
\(656\) 28822.5 + 49922.1i 1.71544 + 2.97124i
\(657\) 5231.69 0.310666
\(658\) 0 0
\(659\) −2384.09 −0.140927 −0.0704635 0.997514i \(-0.522448\pi\)
−0.0704635 + 0.997514i \(0.522448\pi\)
\(660\) −10901.6 18882.1i −0.642944 1.11361i
\(661\) 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
\(663\) −590.248 1022.34i −0.0345751 0.0598859i
\(664\) −83232.2 −4.86451
\(665\) 0 0
\(666\) 12338.4 0.717874
\(667\) −2218.77 3843.02i −0.128802 0.223092i
\(668\) 6051.26 10481.1i 0.350494 0.607074i
\(669\) 5669.69 9820.19i 0.327658 0.567520i
\(670\) 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
\(675\) 184.963 320.366i 0.0105470 0.0182680i
\(676\) 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 \(-0.536025\pi\)
\(678\) −14346.4 −0.812639
\(679\) 0 0
\(680\) 6942.23 0.391503
\(681\) −2741.43 4748.29i −0.154261 0.267188i
\(682\) 26742.8 46319.9i 1.50152 2.60070i
\(683\) −16683.6 + 28896.8i −0.934669 + 1.61889i −0.159446 + 0.987207i \(0.550971\pi\)
−0.775223 + 0.631687i \(0.782363\pi\)
\(684\) 5227.61 + 9054.49i 0.292226 + 0.506150i
\(685\) −4683.18 −0.261219
\(686\) 0 0
\(687\) −2550.75 −0.141655
\(688\) −579.776 1004.20i −0.0321275 0.0556465i
\(689\) −10012.9 + 17342.9i −0.553646 + 0.958943i
\(690\) −10463.3 + 18122.9i −0.577289 + 0.999894i
\(691\) 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
\(696\) −3312.28 + 5737.03i −0.180390 + 0.312445i
\(697\) −1784.23 + 3090.37i −0.0969619 + 0.167943i
\(698\) −11513.7 19942.4i −0.624357 1.08142i
\(699\) −19773.3 −1.06995
\(700\) 0 0
\(701\) −11305.7 −0.609143 −0.304572 0.952489i \(-0.598513\pi\)
−0.304572 + 0.952489i \(0.598513\pi\)
\(702\) −2656.11 4600.52i −0.142804 0.247344i
\(703\) −7614.72 + 13189.1i −0.408527 + 0.707590i
\(704\) −12968.8 + 22462.6i −0.694289 + 1.20254i
\(705\) −3967.18 6871.35i −0.211933 0.367078i
\(706\) 32027.1 1.70730
\(707\) 0 0
\(708\) −2134.55 −0.113307
\(709\) 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
\(711\) 3121.61 5406.79i 0.164655 0.285190i
\(712\) −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
\(717\) 273.835 474.296i 0.0142630 0.0247042i
\(718\) 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 \(0.922849\pi\)
\(720\) 16181.4 0.837562
\(721\) 0 0
\(722\) 18068.0 0.931333
\(723\) −2285.85 3959.20i −0.117582 0.203657i
\(724\) −30788.3 + 53326.8i −1.58044 + 2.73740i
\(725\) −242.521 + 420.059i −0.0124235 + 0.0215181i
\(726\) −977.139 1692.45i −0.0499518 0.0865191i
\(727\) −2121.14 −0.108210 −0.0541051 0.998535i \(-0.517231\pi\)
−0.0541051 + 0.998535i \(0.517231\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 16174.5 + 28015.1i 0.820062 + 1.42039i
\(731\) 35.8904 62.1640i 0.00181594 0.00314531i
\(732\) −1718.63 + 2976.75i −0.0867792 + 0.150306i
\(733\) 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
\(738\) −8029.02 + 13906.7i −0.400478 + 0.693648i
\(739\) 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
\(741\) 6556.94 0.325068
\(742\) 0 0
\(743\) 2867.01 0.141562 0.0707808 0.997492i \(-0.477451\pi\)
0.0707808 + 0.997492i \(0.477451\pi\)
\(744\) 27300.8 + 47286.4i 1.34529 + 2.33011i
\(745\) −3923.86 + 6796.32i −0.192965 + 0.334225i
\(746\) 8518.57 14754.6i 0.418079 0.724134i
\(747\) −6004.76 10400.6i −0.294114 0.509420i
\(748\) −7267.71 −0.355259
\(749\) 0 0
\(750\) 23155.9 1.12738
\(751\) 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
\(753\) −3536.60 + 6125.56i −0.171156 + 0.296451i
\(754\) 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
\(759\) 6533.57 11316.5i 0.312455 0.541188i
\(760\) −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 \(0.544565\pi\)
\(762\) 27137.7 1.29015
\(763\) 0 0
\(764\) 5193.13 0.245917
\(765\) 500.846 + 867.490i 0.0236707 + 0.0409989i
\(766\) −37516.4 + 64980.3i −1.76961 + 3.06506i
\(767\) −669.338 + 1159.33i −0.0315103 + 0.0545774i
\(768\) 3121.19 + 5406.06i 0.146649 + 0.254003i
\(769\) 6728.44 0.315518 0.157759 0.987478i \(-0.449573\pi\)
0.157759 + 0.987478i \(0.449573\pi\)
\(770\) 0 0
\(771\) 8347.65 0.389926
\(772\) −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 \(-0.0239885\pi\)
\(774\) 161.507 279.738i 0.00750031 0.0129909i
\(775\) 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