Properties

Label 128.4.g.a.49.9
Level $128$
Weight $4$
Character 128.49
Analytic conductor $7.552$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 128.g (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.55224448073\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(11\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 49.9
Character \(\chi\) \(=\) 128.49
Dual form 128.4.g.a.81.9

$q$-expansion

\(f(q)\) \(=\) \(q+(5.56908 - 2.30679i) q^{3} +(6.28381 - 15.1704i) q^{5} +(16.6573 + 16.6573i) q^{7} +(6.60151 - 6.60151i) q^{9} +O(q^{10})\) \(q+(5.56908 - 2.30679i) q^{3} +(6.28381 - 15.1704i) q^{5} +(16.6573 + 16.6573i) q^{7} +(6.60151 - 6.60151i) q^{9} +(-3.11257 - 1.28927i) q^{11} +(-28.8862 - 69.7374i) q^{13} -98.9809i q^{15} +66.2302i q^{17} +(12.5299 + 30.2498i) q^{19} +(131.191 + 54.3410i) q^{21} +(63.7309 - 63.7309i) q^{23} +(-102.268 - 102.268i) q^{25} +(-40.7473 + 98.3726i) q^{27} +(190.908 - 79.0767i) q^{29} -123.811 q^{31} -20.3082 q^{33} +(357.370 - 148.028i) q^{35} +(-46.0901 + 111.271i) q^{37} +(-321.739 - 321.739i) q^{39} +(-100.187 + 100.187i) q^{41} +(-27.5836 - 11.4255i) q^{43} +(-58.6652 - 141.630i) q^{45} +394.293i q^{47} +211.932i q^{49} +(152.779 + 368.841i) q^{51} +(135.196 + 56.0002i) q^{53} +(-39.1175 + 39.1175i) q^{55} +(139.560 + 139.560i) q^{57} +(-297.070 + 717.190i) q^{59} +(-548.826 + 227.331i) q^{61} +219.927 q^{63} -1239.46 q^{65} +(-163.352 + 67.6626i) q^{67} +(207.909 - 501.937i) q^{69} +(-194.022 - 194.022i) q^{71} +(547.142 - 547.142i) q^{73} +(-805.449 - 333.628i) q^{75} +(-30.3713 - 73.3227i) q^{77} +715.813i q^{79} +893.911i q^{81} +(-54.6375 - 131.907i) q^{83} +(1004.74 + 416.178i) q^{85} +(880.769 - 880.769i) q^{87} +(220.576 + 220.576i) q^{89} +(680.471 - 1642.80i) q^{91} +(-689.512 + 285.605i) q^{93} +537.638 q^{95} +1364.39 q^{97} +(-29.0587 + 12.0365i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 4q^{19} - 4q^{21} - 324q^{23} - 4q^{25} + 268q^{27} - 4q^{29} + 752q^{31} - 8q^{33} + 460q^{35} - 4q^{37} - 596q^{39} - 4q^{41} - 804q^{43} + 104q^{45} + 1384q^{51} + 748q^{53} + 292q^{55} - 4q^{57} - 1372q^{59} - 1828q^{61} - 2512q^{63} - 8q^{65} - 2036q^{67} - 1060q^{69} - 220q^{71} - 4q^{73} + 1712q^{75} + 1900q^{77} - 2436q^{83} + 496q^{85} + 1292q^{87} - 4q^{89} + 3604q^{91} - 112q^{93} + 6088q^{95} - 8q^{97} + 5424q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 5.56908 2.30679i 1.07177 0.443942i 0.224155 0.974553i \(-0.428038\pi\)
0.847615 + 0.530612i \(0.178038\pi\)
\(4\) 0 0
\(5\) 6.28381 15.1704i 0.562041 1.35689i −0.346091 0.938201i \(-0.612491\pi\)
0.908131 0.418685i \(-0.137509\pi\)
\(6\) 0 0
\(7\) 16.6573 + 16.6573i 0.899411 + 0.899411i 0.995384 0.0959733i \(-0.0305963\pi\)
−0.0959733 + 0.995384i \(0.530596\pi\)
\(8\) 0 0
\(9\) 6.60151 6.60151i 0.244500 0.244500i
\(10\) 0 0
\(11\) −3.11257 1.28927i −0.0853158 0.0353390i 0.339617 0.940564i \(-0.389702\pi\)
−0.424933 + 0.905225i \(0.639702\pi\)
\(12\) 0 0
\(13\) −28.8862 69.7374i −0.616275 1.48782i −0.855998 0.516979i \(-0.827057\pi\)
0.239723 0.970841i \(-0.422943\pi\)
\(14\) 0 0
\(15\) 98.9809i 1.70378i
\(16\) 0 0
\(17\) 66.2302i 0.944893i 0.881359 + 0.472447i \(0.156629\pi\)
−0.881359 + 0.472447i \(0.843371\pi\)
\(18\) 0 0
\(19\) 12.5299 + 30.2498i 0.151292 + 0.365251i 0.981296 0.192507i \(-0.0616617\pi\)
−0.830004 + 0.557758i \(0.811662\pi\)
\(20\) 0 0
\(21\) 131.191 + 54.3410i 1.36325 + 0.564676i
\(22\) 0 0
\(23\) 63.7309 63.7309i 0.577775 0.577775i −0.356515 0.934290i \(-0.616035\pi\)
0.934290 + 0.356515i \(0.116035\pi\)
\(24\) 0 0
\(25\) −102.268 102.268i −0.818143 0.818143i
\(26\) 0 0
\(27\) −40.7473 + 98.3726i −0.290438 + 0.701178i
\(28\) 0 0
\(29\) 190.908 79.0767i 1.22244 0.506351i 0.324255 0.945970i \(-0.394887\pi\)
0.898184 + 0.439619i \(0.144887\pi\)
\(30\) 0 0
\(31\) −123.811 −0.717325 −0.358662 0.933467i \(-0.616767\pi\)
−0.358662 + 0.933467i \(0.616767\pi\)
\(32\) 0 0
\(33\) −20.3082 −0.107127
\(34\) 0 0
\(35\) 357.370 148.028i 1.72590 0.714892i
\(36\) 0 0
\(37\) −46.0901 + 111.271i −0.204788 + 0.494403i −0.992588 0.121529i \(-0.961220\pi\)
0.787799 + 0.615932i \(0.211220\pi\)
\(38\) 0 0
\(39\) −321.739 321.739i −1.32101 1.32101i
\(40\) 0 0
\(41\) −100.187 + 100.187i −0.381624 + 0.381624i −0.871687 0.490063i \(-0.836974\pi\)
0.490063 + 0.871687i \(0.336974\pi\)
\(42\) 0 0
\(43\) −27.5836 11.4255i −0.0978246 0.0405203i 0.333234 0.942844i \(-0.391860\pi\)
−0.431059 + 0.902324i \(0.641860\pi\)
\(44\) 0 0
\(45\) −58.6652 141.630i −0.194340 0.469178i
\(46\) 0 0
\(47\) 394.293i 1.22369i 0.790976 + 0.611847i \(0.209573\pi\)
−0.790976 + 0.611847i \(0.790427\pi\)
\(48\) 0 0
\(49\) 211.932i 0.617879i
\(50\) 0 0
\(51\) 152.779 + 368.841i 0.419478 + 1.01271i
\(52\) 0 0
\(53\) 135.196 + 56.0002i 0.350390 + 0.145136i 0.550935 0.834548i \(-0.314271\pi\)
−0.200545 + 0.979684i \(0.564271\pi\)
\(54\) 0 0
\(55\) −39.1175 + 39.1175i −0.0959019 + 0.0959019i
\(56\) 0 0
\(57\) 139.560 + 139.560i 0.324301 + 0.324301i
\(58\) 0 0
\(59\) −297.070 + 717.190i −0.655512 + 1.58254i 0.149152 + 0.988814i \(0.452346\pi\)
−0.804664 + 0.593731i \(0.797654\pi\)
\(60\) 0 0
\(61\) −548.826 + 227.331i −1.15197 + 0.477160i −0.875193 0.483775i \(-0.839265\pi\)
−0.276774 + 0.960935i \(0.589265\pi\)
\(62\) 0 0
\(63\) 219.927 0.439812
\(64\) 0 0
\(65\) −1239.46 −2.36517
\(66\) 0 0
\(67\) −163.352 + 67.6626i −0.297860 + 0.123378i −0.526609 0.850108i \(-0.676537\pi\)
0.228749 + 0.973486i \(0.426537\pi\)
\(68\) 0 0
\(69\) 207.909 501.937i 0.362743 0.875740i
\(70\) 0 0
\(71\) −194.022 194.022i −0.324312 0.324312i 0.526107 0.850419i \(-0.323651\pi\)
−0.850419 + 0.526107i \(0.823651\pi\)
\(72\) 0 0
\(73\) 547.142 547.142i 0.877235 0.877235i −0.116013 0.993248i \(-0.537011\pi\)
0.993248 + 0.116013i \(0.0370113\pi\)
\(74\) 0 0
\(75\) −805.449 333.628i −1.24007 0.513654i
\(76\) 0 0
\(77\) −30.3713 73.3227i −0.0449497 0.108518i
\(78\) 0 0
\(79\) 715.813i 1.01943i 0.860342 + 0.509717i \(0.170250\pi\)
−0.860342 + 0.509717i \(0.829750\pi\)
\(80\) 0 0
\(81\) 893.911i 1.22621i
\(82\) 0 0
\(83\) −54.6375 131.907i −0.0722560 0.174441i 0.883625 0.468195i \(-0.155096\pi\)
−0.955881 + 0.293754i \(0.905096\pi\)
\(84\) 0 0
\(85\) 1004.74 + 416.178i 1.28211 + 0.531068i
\(86\) 0 0
\(87\) 880.769 880.769i 1.08538 1.08538i
\(88\) 0 0
\(89\) 220.576 + 220.576i 0.262708 + 0.262708i 0.826153 0.563445i \(-0.190524\pi\)
−0.563445 + 0.826153i \(0.690524\pi\)
\(90\) 0 0
\(91\) 680.471 1642.80i 0.783877 1.89245i
\(92\) 0 0
\(93\) −689.512 + 285.605i −0.768807 + 0.318450i
\(94\) 0 0
\(95\) 537.638 0.580637
\(96\) 0 0
\(97\) 1364.39 1.42817 0.714087 0.700057i \(-0.246842\pi\)
0.714087 + 0.700057i \(0.246842\pi\)
\(98\) 0 0
\(99\) −29.0587 + 12.0365i −0.0295001 + 0.0122194i
\(100\) 0 0
\(101\) −349.311 + 843.310i −0.344136 + 0.830817i 0.653153 + 0.757226i \(0.273446\pi\)
−0.997289 + 0.0735909i \(0.976554\pi\)
\(102\) 0 0
\(103\) −273.149 273.149i −0.261302 0.261302i 0.564281 0.825583i \(-0.309154\pi\)
−0.825583 + 0.564281i \(0.809154\pi\)
\(104\) 0 0
\(105\) 1648.76 1648.76i 1.53240 1.53240i
\(106\) 0 0
\(107\) 675.362 + 279.744i 0.610185 + 0.252747i 0.666307 0.745677i \(-0.267874\pi\)
−0.0561229 + 0.998424i \(0.517874\pi\)
\(108\) 0 0
\(109\) −602.506 1454.58i −0.529446 1.27820i −0.931887 0.362749i \(-0.881838\pi\)
0.402441 0.915446i \(-0.368162\pi\)
\(110\) 0 0
\(111\) 726.000i 0.620801i
\(112\) 0 0
\(113\) 315.691i 0.262812i −0.991329 0.131406i \(-0.958051\pi\)
0.991329 0.131406i \(-0.0419491\pi\)
\(114\) 0 0
\(115\) −566.354 1367.30i −0.459242 1.10871i
\(116\) 0 0
\(117\) −651.064 269.679i −0.514452 0.213093i
\(118\) 0 0
\(119\) −1103.22 + 1103.22i −0.849847 + 0.849847i
\(120\) 0 0
\(121\) −933.133 933.133i −0.701077 0.701077i
\(122\) 0 0
\(123\) −326.839 + 789.060i −0.239594 + 0.578432i
\(124\) 0 0
\(125\) −297.776 + 123.343i −0.213071 + 0.0882569i
\(126\) 0 0
\(127\) −356.698 −0.249227 −0.124613 0.992205i \(-0.539769\pi\)
−0.124613 + 0.992205i \(0.539769\pi\)
\(128\) 0 0
\(129\) −179.971 −0.122834
\(130\) 0 0
\(131\) 2481.91 1028.04i 1.65531 0.685652i 0.657606 0.753362i \(-0.271569\pi\)
0.997705 + 0.0677095i \(0.0215691\pi\)
\(132\) 0 0
\(133\) −295.166 + 712.594i −0.192437 + 0.464585i
\(134\) 0 0
\(135\) 1236.31 + 1236.31i 0.788181 + 0.788181i
\(136\) 0 0
\(137\) −811.069 + 811.069i −0.505798 + 0.505798i −0.913234 0.407436i \(-0.866423\pi\)
0.407436 + 0.913234i \(0.366423\pi\)
\(138\) 0 0
\(139\) −2505.86 1037.96i −1.52910 0.633373i −0.549709 0.835356i \(-0.685261\pi\)
−0.979389 + 0.201984i \(0.935261\pi\)
\(140\) 0 0
\(141\) 909.552 + 2195.85i 0.543249 + 1.31152i
\(142\) 0 0
\(143\) 254.304i 0.148713i
\(144\) 0 0
\(145\) 3393.06i 1.94330i
\(146\) 0 0
\(147\) 488.883 + 1180.27i 0.274302 + 0.662224i
\(148\) 0 0
\(149\) −610.519 252.885i −0.335676 0.139041i 0.208478 0.978027i \(-0.433149\pi\)
−0.544154 + 0.838986i \(0.683149\pi\)
\(150\) 0 0
\(151\) 1314.56 1314.56i 0.708457 0.708457i −0.257753 0.966211i \(-0.582982\pi\)
0.966211 + 0.257753i \(0.0829822\pi\)
\(152\) 0 0
\(153\) 437.219 + 437.219i 0.231027 + 0.231027i
\(154\) 0 0
\(155\) −778.003 + 1878.26i −0.403166 + 0.973328i
\(156\) 0 0
\(157\) 2290.74 948.857i 1.16447 0.482338i 0.285107 0.958496i \(-0.407971\pi\)
0.879360 + 0.476158i \(0.157971\pi\)
\(158\) 0 0
\(159\) 882.101 0.439969
\(160\) 0 0
\(161\) 2123.17 1.03931
\(162\) 0 0
\(163\) 26.3934 10.9325i 0.0126828 0.00525338i −0.376333 0.926484i \(-0.622815\pi\)
0.389016 + 0.921231i \(0.372815\pi\)
\(164\) 0 0
\(165\) −127.613 + 308.085i −0.0602100 + 0.145360i
\(166\) 0 0
\(167\) 111.233 + 111.233i 0.0515415 + 0.0515415i 0.732408 0.680866i \(-0.238397\pi\)
−0.680866 + 0.732408i \(0.738397\pi\)
\(168\) 0 0
\(169\) −2475.38 + 2475.38i −1.12671 + 1.12671i
\(170\) 0 0
\(171\) 282.410 + 116.978i 0.126295 + 0.0523131i
\(172\) 0 0
\(173\) −835.349 2016.71i −0.367112 0.886287i −0.994221 0.107355i \(-0.965762\pi\)
0.627109 0.778932i \(-0.284238\pi\)
\(174\) 0 0
\(175\) 3407.02i 1.47169i
\(176\) 0 0
\(177\) 4679.37i 1.98713i
\(178\) 0 0
\(179\) −539.124 1301.56i −0.225117 0.543481i 0.770454 0.637496i \(-0.220030\pi\)
−0.995571 + 0.0940151i \(0.970030\pi\)
\(180\) 0 0
\(181\) −702.054 290.800i −0.288305 0.119420i 0.233844 0.972274i \(-0.424870\pi\)
−0.522149 + 0.852854i \(0.674870\pi\)
\(182\) 0 0
\(183\) −2532.05 + 2532.05i −1.02281 + 1.02281i
\(184\) 0 0
\(185\) 1398.42 + 1398.42i 0.555749 + 0.555749i
\(186\) 0 0
\(187\) 85.3885 206.146i 0.0333916 0.0806144i
\(188\) 0 0
\(189\) −2317.36 + 959.883i −0.891870 + 0.369425i
\(190\) 0 0
\(191\) −2407.52 −0.912052 −0.456026 0.889966i \(-0.650728\pi\)
−0.456026 + 0.889966i \(0.650728\pi\)
\(192\) 0 0
\(193\) −1721.96 −0.642224 −0.321112 0.947041i \(-0.604057\pi\)
−0.321112 + 0.947041i \(0.604057\pi\)
\(194\) 0 0
\(195\) −6902.66 + 2859.18i −2.53492 + 1.05000i
\(196\) 0 0
\(197\) 160.639 387.816i 0.0580966 0.140258i −0.892166 0.451708i \(-0.850815\pi\)
0.950262 + 0.311451i \(0.100815\pi\)
\(198\) 0 0
\(199\) 854.977 + 854.977i 0.304562 + 0.304562i 0.842795 0.538234i \(-0.180908\pi\)
−0.538234 + 0.842795i \(0.680908\pi\)
\(200\) 0 0
\(201\) −753.637 + 753.637i −0.264465 + 0.264465i
\(202\) 0 0
\(203\) 4497.22 + 1862.81i 1.55489 + 0.644057i
\(204\) 0 0
\(205\) 890.326 + 2149.44i 0.303332 + 0.732308i
\(206\) 0 0
\(207\) 841.441i 0.282532i
\(208\) 0 0
\(209\) 110.309i 0.0365082i
\(210\) 0 0
\(211\) 819.136 + 1977.57i 0.267259 + 0.645221i 0.999352 0.0359838i \(-0.0114565\pi\)
−0.732093 + 0.681204i \(0.761456\pi\)
\(212\) 0 0
\(213\) −1528.09 632.956i −0.491563 0.203612i
\(214\) 0 0
\(215\) −346.660 + 346.660i −0.109963 + 0.109963i
\(216\) 0 0
\(217\) −2062.36 2062.36i −0.645170 0.645170i
\(218\) 0 0
\(219\) 1784.94 4309.22i 0.550753 1.32964i
\(220\) 0 0
\(221\) 4618.72 1913.14i 1.40583 0.582314i
\(222\) 0 0
\(223\) −3155.56 −0.947587 −0.473793 0.880636i \(-0.657116\pi\)
−0.473793 + 0.880636i \(0.657116\pi\)
\(224\) 0 0
\(225\) −1350.24 −0.400073
\(226\) 0 0
\(227\) −329.052 + 136.298i −0.0962112 + 0.0398520i −0.430270 0.902700i \(-0.641582\pi\)
0.334059 + 0.942552i \(0.391582\pi\)
\(228\) 0 0
\(229\) 1834.29 4428.38i 0.529317 1.27788i −0.402654 0.915352i \(-0.631912\pi\)
0.931971 0.362532i \(-0.118088\pi\)
\(230\) 0 0
\(231\) −338.280 338.280i −0.0963515 0.0963515i
\(232\) 0 0
\(233\) −2068.42 + 2068.42i −0.581573 + 0.581573i −0.935335 0.353762i \(-0.884902\pi\)
0.353762 + 0.935335i \(0.384902\pi\)
\(234\) 0 0
\(235\) 5981.61 + 2477.66i 1.66041 + 0.687766i
\(236\) 0 0
\(237\) 1651.23 + 3986.42i 0.452569 + 1.09260i
\(238\) 0 0
\(239\) 1635.41i 0.442620i −0.975204 0.221310i \(-0.928967\pi\)
0.975204 0.221310i \(-0.0710332\pi\)
\(240\) 0 0
\(241\) 3798.84i 1.01537i −0.861542 0.507686i \(-0.830501\pi\)
0.861542 0.507686i \(-0.169499\pi\)
\(242\) 0 0
\(243\) 961.887 + 2322.20i 0.253930 + 0.613042i
\(244\) 0 0
\(245\) 3215.11 + 1331.74i 0.838391 + 0.347273i
\(246\) 0 0
\(247\) 1747.60 1747.60i 0.450191 0.450191i
\(248\) 0 0
\(249\) −608.562 608.562i −0.154884 0.154884i
\(250\) 0 0
\(251\) 641.114 1547.79i 0.161222 0.389224i −0.822539 0.568709i \(-0.807443\pi\)
0.983761 + 0.179485i \(0.0574430\pi\)
\(252\) 0 0
\(253\) −280.533 + 116.201i −0.0697113 + 0.0288754i
\(254\) 0 0
\(255\) 6555.52 1.60989
\(256\) 0 0
\(257\) −576.329 −0.139885 −0.0699424 0.997551i \(-0.522282\pi\)
−0.0699424 + 0.997551i \(0.522282\pi\)
\(258\) 0 0
\(259\) −2621.22 + 1085.75i −0.628860 + 0.260482i
\(260\) 0 0
\(261\) 738.255 1782.31i 0.175084 0.422690i
\(262\) 0 0
\(263\) −5045.11 5045.11i −1.18287 1.18287i −0.978997 0.203873i \(-0.934647\pi\)
−0.203873 0.978997i \(-0.565353\pi\)
\(264\) 0 0
\(265\) 1699.10 1699.10i 0.393867 0.393867i
\(266\) 0 0
\(267\) 1737.23 + 719.583i 0.398190 + 0.164936i
\(268\) 0 0
\(269\) 555.865 + 1341.98i 0.125991 + 0.304170i 0.974271 0.225378i \(-0.0723616\pi\)
−0.848280 + 0.529548i \(0.822362\pi\)
\(270\) 0 0
\(271\) 6517.54i 1.46093i −0.682950 0.730465i \(-0.739303\pi\)
0.682950 0.730465i \(-0.260697\pi\)
\(272\) 0 0
\(273\) 10718.6i 2.37626i
\(274\) 0 0
\(275\) 186.465 + 450.166i 0.0408882 + 0.0987129i
\(276\) 0 0
\(277\) −5983.48 2478.44i −1.29788 0.537599i −0.376555 0.926394i \(-0.622891\pi\)
−0.921324 + 0.388795i \(0.872891\pi\)
\(278\) 0 0
\(279\) −817.338 + 817.338i −0.175386 + 0.175386i
\(280\) 0 0
\(281\) 3663.87 + 3663.87i 0.777822 + 0.777822i 0.979460 0.201638i \(-0.0646264\pi\)
−0.201638 + 0.979460i \(0.564626\pi\)
\(282\) 0 0
\(283\) −1065.93 + 2573.38i −0.223897 + 0.540535i −0.995413 0.0956751i \(-0.969499\pi\)
0.771516 + 0.636210i \(0.219499\pi\)
\(284\) 0 0
\(285\) 2994.15 1240.22i 0.622309 0.257769i
\(286\) 0 0
\(287\) −3337.69 −0.686473
\(288\) 0 0
\(289\) 526.558 0.107177
\(290\) 0 0
\(291\) 7598.40 3147.36i 1.53067 0.634026i
\(292\) 0 0
\(293\) 1873.89 4523.96i 0.373630 0.902023i −0.619499 0.784997i \(-0.712664\pi\)
0.993129 0.117025i \(-0.0373358\pi\)
\(294\) 0 0
\(295\) 9013.36 + 9013.36i 1.77891 + 1.77891i
\(296\) 0 0
\(297\) 253.657 253.657i 0.0495578 0.0495578i
\(298\) 0 0
\(299\) −6285.37 2603.49i −1.21569 0.503557i
\(300\) 0 0
\(301\) −269.151 649.787i −0.0515401 0.124429i
\(302\) 0 0
\(303\) 5502.25i 1.04322i
\(304\) 0 0
\(305\) 9754.44i 1.83127i
\(306\) 0 0
\(307\) −3251.76 7850.45i −0.604521 1.45944i −0.868882 0.495019i \(-0.835161\pi\)
0.264361 0.964424i \(-0.414839\pi\)
\(308\) 0 0
\(309\) −2151.28 891.091i −0.396059 0.164053i
\(310\) 0 0
\(311\) −1620.08 + 1620.08i −0.295389 + 0.295389i −0.839205 0.543815i \(-0.816979\pi\)
0.543815 + 0.839205i \(0.316979\pi\)
\(312\) 0 0
\(313\) 4904.15 + 4904.15i 0.885620 + 0.885620i 0.994099 0.108479i \(-0.0345979\pi\)
−0.108479 + 0.994099i \(0.534598\pi\)
\(314\) 0 0
\(315\) 1381.98 3336.39i 0.247192 0.596775i
\(316\) 0 0
\(317\) −1326.36 + 549.398i −0.235003 + 0.0973415i −0.497077 0.867706i \(-0.665593\pi\)
0.262074 + 0.965048i \(0.415593\pi\)
\(318\) 0 0
\(319\) −696.165 −0.122187
\(320\) 0 0
\(321\) 4406.46 0.766182
\(322\) 0 0
\(323\) −2003.45 + 829.856i −0.345124 + 0.142955i
\(324\) 0 0
\(325\) −4177.77 + 10086.0i −0.713049 + 1.72145i
\(326\) 0 0
\(327\) −6710.81 6710.81i −1.13489 1.13489i
\(328\) 0 0
\(329\) −6567.87 + 6567.87i −1.10060 + 1.10060i
\(330\) 0 0
\(331\) −3808.89 1577.69i −0.632494 0.261988i 0.0433183 0.999061i \(-0.486207\pi\)
−0.675812 + 0.737074i \(0.736207\pi\)
\(332\) 0 0
\(333\) 430.295 + 1038.82i 0.0708109 + 0.170953i
\(334\) 0 0
\(335\) 2903.30i 0.473505i
\(336\) 0 0
\(337\) 528.946i 0.0855000i −0.999086 0.0427500i \(-0.986388\pi\)
0.999086 0.0427500i \(-0.0136119\pi\)
\(338\) 0 0
\(339\) −728.232 1758.11i −0.116673 0.281674i
\(340\) 0 0
\(341\) 385.369 + 159.625i 0.0611992 + 0.0253495i
\(342\) 0 0
\(343\) 2183.23 2183.23i 0.343684 0.343684i
\(344\) 0 0
\(345\) −6308.14 6308.14i −0.984403 0.984403i
\(346\) 0 0
\(347\) −2777.92 + 6706.49i −0.429759 + 1.03753i 0.549605 + 0.835425i \(0.314778\pi\)
−0.979364 + 0.202105i \(0.935222\pi\)
\(348\) 0 0
\(349\) −2949.74 + 1221.82i −0.452424 + 0.187400i −0.597247 0.802058i \(-0.703739\pi\)
0.144823 + 0.989458i \(0.453739\pi\)
\(350\) 0 0
\(351\) 8037.28 1.22222
\(352\) 0 0
\(353\) 9005.55 1.35784 0.678919 0.734213i \(-0.262449\pi\)
0.678919 + 0.734213i \(0.262449\pi\)
\(354\) 0 0
\(355\) −4162.59 + 1724.20i −0.622331 + 0.257778i
\(356\) 0 0
\(357\) −3599.02 + 8688.80i −0.533558 + 1.28812i
\(358\) 0 0
\(359\) 7280.93 + 7280.93i 1.07040 + 1.07040i 0.997327 + 0.0730705i \(0.0232798\pi\)
0.0730705 + 0.997327i \(0.476720\pi\)
\(360\) 0 0
\(361\) 4091.99 4091.99i 0.596588 0.596588i
\(362\) 0 0
\(363\) −7349.24 3044.15i −1.06263 0.440156i
\(364\) 0 0
\(365\) −4862.26 11738.5i −0.697266 1.68335i
\(366\) 0 0
\(367\) 2730.08i 0.388308i 0.980971 + 0.194154i \(0.0621961\pi\)
−0.980971 + 0.194154i \(0.937804\pi\)
\(368\) 0 0
\(369\) 1322.77i 0.186614i
\(370\) 0 0
\(371\) 1319.20 + 3184.82i 0.184607 + 0.445681i
\(372\) 0 0
\(373\) 807.251 + 334.374i 0.112059 + 0.0464162i 0.438008 0.898971i \(-0.355684\pi\)
−0.325950 + 0.945387i \(0.605684\pi\)
\(374\) 0 0
\(375\) −1373.81 + 1373.81i −0.189182 + 0.189182i
\(376\) 0 0
\(377\) −11029.2 11029.2i −1.50672 1.50672i
\(378\) 0 0
\(379\) 511.994 1236.06i 0.0693914 0.167526i −0.885379 0.464870i \(-0.846101\pi\)
0.954770 + 0.297344i \(0.0961010\pi\)
\(380\) 0 0
\(381\) −1986.48 + 822.826i −0.267114 + 0.110642i
\(382\) 0 0
\(383\) −7830.32 −1.04468 −0.522338 0.852739i \(-0.674940\pi\)
−0.522338 + 0.852739i \(0.674940\pi\)
\(384\) 0 0
\(385\) −1303.19 −0.172510
\(386\) 0 0
\(387\) −257.519 + 106.668i −0.0338254 + 0.0140109i
\(388\) 0 0
\(389\) 1347.70 3253.64i 0.175659 0.424077i −0.811389 0.584507i \(-0.801288\pi\)
0.987047 + 0.160430i \(0.0512880\pi\)
\(390\) 0 0
\(391\) 4220.91 + 4220.91i 0.545936 + 0.545936i
\(392\) 0 0
\(393\) 11450.5 11450.5i 1.46972 1.46972i
\(394\) 0 0
\(395\) 10859.2 + 4498.03i 1.38326 + 0.572963i
\(396\) 0 0
\(397\) −23.4283 56.5609i −0.00296180 0.00715041i 0.922392 0.386256i \(-0.126232\pi\)
−0.925354 + 0.379105i \(0.876232\pi\)
\(398\) 0 0
\(399\) 4649.38i 0.583359i
\(400\) 0 0
\(401\) 12034.3i 1.49866i 0.662195 + 0.749332i \(0.269625\pi\)
−0.662195 + 0.749332i \(0.730375\pi\)
\(402\) 0 0
\(403\) 3576.42 + 8634.24i 0.442070 + 1.06725i
\(404\) 0 0
\(405\) 13561.0 + 5617.16i 1.66383 + 0.689183i
\(406\) 0 0
\(407\) 286.917 286.917i 0.0349434 0.0349434i
\(408\) 0 0
\(409\) 8440.37 + 8440.37i 1.02041 + 1.02041i 0.999787 + 0.0206265i \(0.00656608\pi\)
0.0206265 + 0.999787i \(0.493434\pi\)
\(410\) 0 0
\(411\) −2645.94 + 6387.87i −0.317554 + 0.766644i
\(412\) 0 0
\(413\) −16894.8 + 6998.07i −2.01293 + 0.833784i
\(414\) 0 0
\(415\) −2344.41 −0.277308
\(416\) 0 0
\(417\) −16349.7 −1.92002
\(418\) 0 0
\(419\) 14617.4 6054.71i 1.70431 0.705947i 0.704315 0.709887i \(-0.251254\pi\)
0.999992 + 0.00393979i \(0.00125408\pi\)
\(420\) 0 0
\(421\) −5214.86 + 12589.8i −0.603697 + 1.45745i 0.266051 + 0.963959i \(0.414281\pi\)
−0.869749 + 0.493495i \(0.835719\pi\)
\(422\) 0 0
\(423\) 2602.93 + 2602.93i 0.299194 + 0.299194i
\(424\) 0 0
\(425\) 6773.23 6773.23i 0.773058 0.773058i
\(426\) 0 0
\(427\) −12928.7 5355.24i −1.46525 0.606928i
\(428\) 0 0
\(429\) 586.626 + 1416.24i 0.0660200 + 0.159386i
\(430\) 0 0
\(431\) 3490.31i 0.390075i −0.980796 0.195037i \(-0.937517\pi\)
0.980796 0.195037i \(-0.0624828\pi\)
\(432\) 0 0
\(433\) 11691.1i 1.29755i −0.760980 0.648775i \(-0.775282\pi\)
0.760980 0.648775i \(-0.224718\pi\)
\(434\) 0 0
\(435\) −7827.08 18896.2i −0.862712 2.08277i
\(436\) 0 0
\(437\) 2726.39 + 1129.31i 0.298446 + 0.123620i
\(438\) 0 0
\(439\) −6721.98 + 6721.98i −0.730804 + 0.730804i −0.970779 0.239975i \(-0.922861\pi\)
0.239975 + 0.970779i \(0.422861\pi\)
\(440\) 0 0
\(441\) 1399.07 + 1399.07i 0.151072 + 0.151072i
\(442\) 0 0
\(443\) 3951.12 9538.86i 0.423755 1.02304i −0.557475 0.830194i \(-0.688230\pi\)
0.981230 0.192842i \(-0.0617704\pi\)
\(444\) 0 0
\(445\) 4732.29 1960.18i 0.504117 0.208812i
\(446\) 0 0
\(447\) −3983.39 −0.421494
\(448\) 0 0
\(449\) −3683.45 −0.387155 −0.193578 0.981085i \(-0.562009\pi\)
−0.193578 + 0.981085i \(0.562009\pi\)
\(450\) 0 0
\(451\) 441.006 182.671i 0.0460448 0.0190724i
\(452\) 0 0
\(453\) 4288.47 10353.3i 0.444790 1.07382i
\(454\) 0 0
\(455\) −20646.1 20646.1i −2.12726 2.12726i
\(456\) 0 0
\(457\) −6693.56 + 6693.56i −0.685146 + 0.685146i −0.961155 0.276009i \(-0.910988\pi\)
0.276009 + 0.961155i \(0.410988\pi\)
\(458\) 0 0
\(459\) −6515.24 2698.70i −0.662539 0.274432i
\(460\) 0 0
\(461\) −2097.99 5065.00i −0.211959 0.511715i 0.781765 0.623573i \(-0.214320\pi\)
−0.993724 + 0.111858i \(0.964320\pi\)
\(462\) 0 0
\(463\) 17006.8i 1.70707i 0.521038 + 0.853534i \(0.325545\pi\)
−0.521038 + 0.853534i \(0.674455\pi\)
\(464\) 0 0
\(465\) 12254.9i 1.22217i
\(466\) 0 0
\(467\) 7003.63 + 16908.3i 0.693981 + 1.67542i 0.736601 + 0.676328i \(0.236430\pi\)
−0.0426191 + 0.999091i \(0.513570\pi\)
\(468\) 0 0
\(469\) −3848.08 1593.93i −0.378866 0.156931i
\(470\) 0 0
\(471\) 10568.5 10568.5i 1.03391 1.03391i
\(472\) 0 0
\(473\) 71.1253 + 71.1253i 0.00691404 + 0.00691404i
\(474\) 0 0
\(475\) 1812.18 4374.99i 0.175049 0.422607i
\(476\) 0 0
\(477\) 1262.19 522.815i 0.121156 0.0501846i
\(478\) 0 0
\(479\) 12250.2 1.16853 0.584263 0.811564i \(-0.301384\pi\)
0.584263 + 0.811564i \(0.301384\pi\)
\(480\) 0 0
\(481\) 9091.14 0.861789
\(482\) 0 0
\(483\) 11824.1 4897.71i 1.11391 0.461395i
\(484\) 0 0
\(485\) 8573.56 20698.4i 0.802691 1.93787i
\(486\) 0 0
\(487\) −6781.49 6781.49i −0.631003 0.631003i 0.317317 0.948320i \(-0.397218\pi\)
−0.948320 + 0.317317i \(0.897218\pi\)
\(488\) 0 0
\(489\) 121.768 121.768i 0.0112608 0.0112608i
\(490\) 0 0
\(491\) 2990.34 + 1238.64i 0.274851 + 0.113847i 0.515852 0.856678i \(-0.327476\pi\)
−0.241000 + 0.970525i \(0.577476\pi\)
\(492\) 0 0
\(493\) 5237.27 + 12643.9i 0.478447 + 1.15507i
\(494\) 0 0
\(495\) 516.469i 0.0468961i
\(496\) 0 0
\(497\) 6463.76i 0.583379i
\(498\) 0 0
\(499\) −672.528 1623.63i −0.0603336 0.145658i 0.890838 0.454322i \(-0.150118\pi\)
−0.951171 + 0.308663i \(0.900118\pi\)
\(500\) 0 0
\(501\) 876.053 + 362.873i 0.0781221 + 0.0323592i
\(502\) 0 0
\(503\) 14586.7 14586.7i 1.29302 1.29302i 0.360107 0.932911i \(-0.382740\pi\)
0.932911 0.360107i \(-0.117260\pi\)
\(504\) 0 0
\(505\) 10598.4 + 10598.4i 0.933906 + 0.933906i
\(506\) 0 0
\(507\) −8075.40 + 19495.7i −0.707379 + 1.70776i
\(508\) 0 0
\(509\) 10300.8 4266.74i 0.897005 0.371552i 0.113937 0.993488i \(-0.463654\pi\)
0.783068 + 0.621936i \(0.213654\pi\)
\(510\) 0 0
\(511\) 18227.8 1.57799
\(512\) 0 0
\(513\) −3486.31 −0.300047
\(514\) 0 0
\(515\) −5860.20 + 2427.38i −0.501420 + 0.207695i
\(516\) 0 0
\(517\) 508.350 1227.26i 0.0432441 0.104400i
\(518\) 0 0
\(519\) −9304.25 9304.25i −0.786919 0.786919i
\(520\) 0 0
\(521\) 10841.1 10841.1i 0.911623 0.911623i −0.0847773 0.996400i \(-0.527018\pi\)
0.996400 + 0.0847773i \(0.0270179\pi\)
\(522\) 0 0
\(523\) 7489.02 + 3102.05i 0.626142 + 0.259356i 0.673113 0.739540i \(-0.264957\pi\)
−0.0469711 + 0.998896i \(0.514957\pi\)
\(524\) 0 0
\(525\) −7859.27 18974.0i −0.653346 1.57732i
\(526\) 0 0
\(527\) 8200.01i 0.677795i
\(528\) 0 0
\(529\) 4043.73i 0.332352i
\(530\) 0 0
\(531\) 2773.43 + 6695.64i 0.226660 + 0.547205i
\(532\) 0 0
\(533\) 9880.79 + 4092.76i 0.802973 + 0.332602i
\(534\) 0 0
\(535\) 8487.69 8487.69i 0.685897 0.685897i
\(536\) 0 0
\(537\) −6004.85 6004.85i −0.482548 0.482548i
\(538\) 0 0
\(539\) 273.238 659.654i 0.0218352 0.0527149i
\(540\) 0 0
\(541\) 20246.0 8386.17i 1.60895 0.666451i 0.616308 0.787505i \(-0.288628\pi\)
0.992646 + 0.121054i \(0.0386276\pi\)
\(542\) 0 0
\(543\) −4580.61 −0.362013
\(544\) 0 0
\(545\) −25852.6 −2.03194
\(546\) 0 0
\(547\) −10328.3 + 4278.13i −0.807325 + 0.334405i −0.747886 0.663827i \(-0.768931\pi\)
−0.0594388 + 0.998232i \(0.518931\pi\)
\(548\) 0 0
\(549\) −2122.35 + 5123.81i −0.164990 + 0.398322i
\(550\) 0 0
\(551\) 4784.11 + 4784.11i 0.369891 + 0.369891i
\(552\) 0 0
\(553\) −11923.5 + 11923.5i −0.916890 + 0.916890i
\(554\) 0 0
\(555\) 11013.7 + 4562.04i 0.842356 + 0.348915i
\(556\) 0 0
\(557\) 1262.85 + 3048.78i 0.0960657 + 0.231923i 0.964606 0.263696i \(-0.0849414\pi\)
−0.868540 + 0.495619i \(0.834941\pi\)
\(558\) 0 0
\(559\) 2253.65i 0.170517i
\(560\) 0 0
\(561\) 1345.02i 0.101224i
\(562\) 0 0
\(563\) −3354.10 8097.52i −0.251081 0.606163i 0.747211 0.664587i \(-0.231393\pi\)
−0.998292 + 0.0584237i \(0.981393\pi\)
\(564\) 0 0
\(565\) −4789.17 1983.74i −0.356605 0.147711i
\(566\) 0 0
\(567\) −14890.2 + 14890.2i −1.10287 + 1.10287i
\(568\) 0 0
\(569\) −8264.07 8264.07i −0.608872 0.608872i 0.333780 0.942651i \(-0.391676\pi\)
−0.942651 + 0.333780i \(0.891676\pi\)
\(570\) 0 0
\(571\) 2298.13 5548.17i 0.168430 0.406626i −0.817016 0.576615i \(-0.804373\pi\)
0.985446 + 0.169989i \(0.0543732\pi\)
\(572\) 0 0
\(573\) −13407.7 + 5553.64i −0.977510 + 0.404898i
\(574\) 0 0
\(575\) −13035.3 −0.945405
\(576\) 0 0
\(577\) −7818.78 −0.564125 −0.282062 0.959396i \(-0.591019\pi\)
−0.282062 + 0.959396i \(0.591019\pi\)
\(578\) 0 0
\(579\) −9589.72 + 3972.19i −0.688317 + 0.285110i
\(580\) 0 0
\(581\) 1287.10 3107.33i 0.0919067 0.221882i
\(582\) 0 0
\(583\) −348.609 348.609i −0.0247648 0.0247648i
\(584\) 0 0
\(585\) −8182.32 + 8182.32i −0.578286 + 0.578286i
\(586\) 0 0
\(587\) −12603.6 5220.58i −0.886211 0.367081i −0.107309 0.994226i \(-0.534223\pi\)
−0.778902 + 0.627145i \(0.784223\pi\)
\(588\) 0 0
\(589\) −1551.33 3745.25i −0.108526 0.262004i
\(590\) 0 0
\(591\) 2530.34i 0.176116i
\(592\) 0 0
\(593\) 22972.2i 1.59081i 0.606075 + 0.795407i \(0.292743\pi\)
−0.606075 + 0.795407i \(0.707257\pi\)
\(594\) 0 0
\(595\) 9803.90 + 23668.7i 0.675497 + 1.63079i
\(596\) 0 0
\(597\) 6733.69 + 2789.19i 0.461628 + 0.191212i
\(598\) 0 0
\(599\) −7947.99 + 7947.99i −0.542147 + 0.542147i −0.924158 0.382011i \(-0.875232\pi\)
0.382011 + 0.924158i \(0.375232\pi\)
\(600\) 0 0
\(601\) −10055.8 10055.8i −0.682506 0.682506i 0.278058 0.960564i \(-0.410309\pi\)
−0.960564 + 0.278058i \(0.910309\pi\)
\(602\) 0 0
\(603\) −631.694 + 1525.04i −0.0426610 + 0.102993i
\(604\) 0 0
\(605\) −20019.7 + 8292.42i −1.34532 + 0.557248i
\(606\) 0 0
\(607\) −24716.9 −1.65277 −0.826383 0.563109i \(-0.809605\pi\)
−0.826383 + 0.563109i \(0.809605\pi\)
\(608\) 0 0
\(609\) 29342.5 1.95241
\(610\) 0 0
\(611\) 27497.0 11389.6i 1.82064 0.754132i
\(612\) 0 0
\(613\) −5388.03 + 13007.9i −0.355009 + 0.857067i 0.640977 + 0.767560i \(0.278529\pi\)
−0.995986 + 0.0895074i \(0.971471\pi\)
\(614\) 0 0
\(615\) 9916.59 + 9916.59i 0.650204 + 0.650204i
\(616\) 0 0
\(617\) −1763.96 + 1763.96i −0.115096 + 0.115096i −0.762309 0.647213i \(-0.775934\pi\)
0.647213 + 0.762309i \(0.275934\pi\)
\(618\) 0 0
\(619\) 21023.8 + 8708.35i 1.36513 + 0.565457i 0.940465 0.339891i \(-0.110390\pi\)
0.424670 + 0.905348i \(0.360390\pi\)
\(620\) 0 0
\(621\) 3672.52 + 8866.24i 0.237316 + 0.572931i
\(622\) 0 0
\(623\) 7348.41i 0.472565i
\(624\) 0 0
\(625\) 12786.1i 0.818312i
\(626\) 0 0
\(627\) −254.459 614.319i −0.0162075 0.0391284i
\(628\) 0 0
\(629\) −7369.53 3052.56i −0.467158 0.193503i
\(630\) 0 0
\(631\) −20760.0 + 20760.0i −1.30973 + 1.30973i −0.388129 + 0.921605i \(0.626878\pi\)
−0.921605 + 0.388129i \(0.873122\pi\)
\(632\) 0 0
\(633\) 9123.67 + 9123.67i 0.572881 + 0.572881i
\(634\) 0 0
\(635\) −2241.42 + 5411.26i −0.140076 + 0.338172i
\(636\) 0 0
\(637\) 14779.6 6121.92i 0.919293 0.380784i
\(638\) 0 0
\(639\) −2561.67 −0.158589
\(640\) 0 0
\(641\) 16062.4 0.989745 0.494872 0.868966i \(-0.335215\pi\)
0.494872 + 0.868966i \(0.335215\pi\)
\(642\) 0 0
\(643\) −24877.7 + 10304.7i −1.52579 + 0.632001i −0.978741 0.205101i \(-0.934248\pi\)
−0.547046 + 0.837103i \(0.684248\pi\)
\(644\) 0 0
\(645\) −1130.91 + 2730.25i −0.0690378 + 0.166672i
\(646\) 0 0
\(647\) 11101.6 + 11101.6i 0.674572 + 0.674572i 0.958767 0.284195i \(-0.0917262\pi\)
−0.284195 + 0.958767i \(0.591726\pi\)
\(648\) 0 0
\(649\) 1849.30 1849.30i 0.111851 0.111851i
\(650\) 0 0
\(651\) −16242.8 6728.01i −0.977891 0.405056i
\(652\) 0 0
\(653\) 1485.55 + 3586.44i 0.0890262 + 0.214928i 0.962121 0.272622i \(-0.0878907\pi\)
−0.873095 + 0.487550i \(0.837891\pi\)
\(654\) 0 0
\(655\) 44111.8i 2.63143i
\(656\) 0 0
\(657\) 7223.93i 0.428968i
\(658\) 0 0
\(659\) −10740.4 25929.6i −0.634881 1.53274i −0.833417 0.552644i \(-0.813619\pi\)
0.198537 0.980093i \(-0.436381\pi\)
\(660\) 0 0
\(661\) −1477.94 612.182i −0.0869670 0.0360229i 0.338776 0.940867i \(-0.389987\pi\)
−0.425743 + 0.904844i \(0.639987\pi\)
\(662\) 0 0
\(663\) 21308.8 21308.8i 1.24821 1.24821i
\(664\) 0 0
\(665\) 8955.61 + 8955.61i 0.522231 + 0.522231i
\(666\) 0 0
\(667\) 7127.12 17206.4i 0.413738 0.998851i
\(668\) 0 0
\(669\) −17573.6 + 7279.21i −1.01560 + 0.420673i
\(670\) 0 0
\(671\) 2001.35 0.115143
\(672\) 0 0
\(673\) −25713.9 −1.47281 −0.736404 0.676543i \(-0.763478\pi\)
−0.736404 + 0.676543i \(0.763478\pi\)
\(674\) 0 0
\(675\) 14227.5 5893.22i 0.811284 0.336045i
\(676\) 0 0
\(677\) −4314.50 + 10416.1i −0.244933 + 0.591321i −0.997760 0.0668981i \(-0.978690\pi\)
0.752827 + 0.658219i \(0.228690\pi\)
\(678\) 0 0
\(679\) 22727.1 + 22727.1i 1.28451 + 1.28451i
\(680\) 0 0
\(681\) −1518.11 + 1518.11i −0.0854244 + 0.0854244i
\(682\) 0 0
\(683\) 1854.70 + 768.242i 0.103907 + 0.0430395i 0.434031 0.900898i \(-0.357091\pi\)
−0.330125 + 0.943937i \(0.607091\pi\)
\(684\) 0 0
\(685\) 7207.68 + 17400.9i 0.402031 + 0.970589i
\(686\) 0 0
\(687\) 28893.3i 1.60458i
\(688\) 0 0
\(689\) 11045.9i 0.610761i
\(690\) 0 0
\(691\) 2881.88 + 6957.49i 0.158657 + 0.383032i 0.983140 0.182855i \(-0.0585338\pi\)
−0.824483 + 0.565887i \(0.808534\pi\)
\(692\) 0 0
\(693\) −684.537 283.544i −0.0375230 0.0155425i
\(694\) 0 0
\(695\) −31492.7 + 31492.7i −1.71883 + 1.71883i
\(696\) 0 0
\(697\) −6635.41 6635.41i −0.360594 0.360594i
\(698\) 0 0
\(699\) −6747.78 + 16290.6i −0.365128 + 0.881497i
\(700\) 0 0
\(701\) 26418.3 10942.8i 1.42340 0.589592i 0.467688 0.883893i \(-0.345087\pi\)
0.955713 + 0.294302i \(0.0950870\pi\)
\(702\) 0 0
\(703\) −3943.44 −0.211564
\(704\) 0 0
\(705\) 39027.5 2.08491
\(706\) 0 0
\(707\) −19865.9 + 8228.71i −1.05676 + 0.437726i
\(708\) 0 0
\(709\) −1886.73 + 4554.97i −0.0999404 + 0.241277i −0.965939 0.258768i \(-0.916683\pi\)
0.865999 + 0.500046i \(0.166683\pi\)
\(710\) 0 0
\(711\) 4725.45 + 4725.45i 0.249252 + 0.249252i
\(712\) 0 0
\(713\) −7890.58 + 7890.58i −0.414452 + 0.414452i
\(714\) 0 0
\(715\) 3857.91 + 1598.00i 0.201787 + 0.0835828i
\(716\) 0 0
\(717\) −3772.55 9107.75i −0.196497 0.474387i
\(718\) 0 0
\(719\) 29695.2i 1.54026i 0.637889 + 0.770129i \(0.279808\pi\)
−0.637889 + 0.770129i \(0.720192\pi\)
\(720\) 0 0
\(721\) 9099.85i 0.470036i
\(722\) 0 0
\(723\) −8763.12 21156.0i −0.450766 1.08825i
\(724\) 0 0
\(725\) −27610.8 11436.8i −1.41440 0.585863i
\(726\) 0 0
\(727\) 26485.0 26485.0i 1.35113 1.35113i 0.466739 0.884395i \(-0.345429\pi\)
0.884395 0.466739i \(-0.154571\pi\)
\(728\) 0 0
\(729\) −6352.78 6352.78i −0.322755 0.322755i
\(730\) 0 0
\(731\) 756.713 1826.87i 0.0382873 0.0924338i
\(732\) 0 0
\(733\) 3763.54 1558.91i 0.189645 0.0785534i −0.285840 0.958277i \(-0.592273\pi\)
0.475485 + 0.879724i \(0.342273\pi\)
\(734\) 0 0
\(735\) 20977.3 1.05273
\(736\) 0 0
\(737\) 595.679 0.0297722
\(738\) 0 0
\(739\) −14266.3 + 5909.30i −0.710142 + 0.294150i −0.708363 0.705848i \(-0.750566\pi\)
−0.00177857 + 0.999998i \(0.500566\pi\)
\(740\) 0 0
\(741\) 5701.18 13763.9i 0.282643 0.682360i
\(742\) 0 0
\(743\) −17888.3 17888.3i −0.883253 0.883253i 0.110611 0.993864i \(-0.464719\pi\)
−0.993864 + 0.110611i \(0.964719\pi\)
\(744\) 0 0
\(745\) −7672.77 + 7672.77i −0.377327 + 0.377327i
\(746\) 0 0
\(747\) −1231.47 510.093i −0.0603176 0.0249844i
\(748\) 0 0
\(749\) 6589.94 + 15909.5i 0.321483 + 0.776130i
\(750\) 0 0
\(751\) 20239.7i 0.983432i 0.870756 + 0.491716i \(0.163630\pi\)
−0.870756 + 0.491716i \(0.836370\pi\)
\(752\) 0 0
\(753\) 10098.7i 0.488732i
\(754\) 0 0
\(755\) −11682.0 28202.8i −0.563114 1.35948i
\(756\) 0 0
\(757\) −15064.3 6239.82i −0.723275 0.299591i −0.00949004 0.999955i \(-0.503021\pi\)
−0.713785 + 0.700364i \(0.753021\pi\)
\(758\) 0 0
\(759\) −1294.26 + 1294.26i −0.0618955 + 0.0618955i
\(760\) 0 0
\(761\) −3008.89 3008.89i −0.143328 0.143328i 0.631802 0.775130i \(-0.282316\pi\)
−0.775130 + 0.631802i \(0.782316\pi\)
\(762\) 0 0
\(763\) 14193.2 34265.5i 0.673433 1.62581i
\(764\) 0 0
\(765\) 9380.21 3885.41i 0.443323 0.183631i
\(766\) 0 0
\(767\) 58596.1 2.75852
\(768\) 0 0
\(769\) 33250.5 1.55923 0.779613 0.626261i \(-0.215416\pi\)
0.779613 + 0.626261i \(0.215416\pi\)
\(770\) 0 0
\(771\) −3209.62 + 1329.47i −0.149924 + 0.0621007i
\(772\) 0 0
\(773\) −6032.84 + 14564.6i −0.280707 + 0.677686i −0.999853 0.0171732i \(-0.994533\pi\)
0.719146 + 0.694859i \(0.244533\pi\)
\(774\) 0 0
\(775\) 12661.9 + 12661.9i 0.586875 + 0.586875i
\(776\) 0 0
\(777\) −12093.2 + 12093.2i −0.558355 + 0.558355i
\(778\) 0 0
\(779\) −4285.96 1775.30i −0.197125 0.0816520i
\(780\) 0 0
\(781\) 353.760 + 854.052i 0.0162081 + 0.0391298i
\(782\) 0 0
\(783\) 22002.3i 1.00421i
\(784\) 0 0
\(785\) 40714.0i 1.85114i
\(786\) 0 0