Properties

Label 108.4.i.a.49.1
Level 108
Weight 4
Character 108.49
Analytic conductor 6.372
Analytic rank 0
Dimension 54
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.i (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.37220628062\)
Analytic rank: \(0\)
Dimension: \(54\)
Relative dimension: \(9\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 49.1
Character \(\chi\) \(=\) 108.49
Dual form 108.4.i.a.97.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-5.16735 + 0.546343i) q^{3} +(5.21695 - 1.89881i) q^{5} +(1.58868 + 9.00985i) q^{7} +(26.4030 - 5.64629i) q^{9} +O(q^{10})\) \(q+(-5.16735 + 0.546343i) q^{3} +(5.21695 - 1.89881i) q^{5} +(1.58868 + 9.00985i) q^{7} +(26.4030 - 5.64629i) q^{9} +(-67.4972 - 24.5670i) q^{11} +(-63.1985 - 53.0298i) q^{13} +(-25.9204 + 12.6621i) q^{15} +(21.0212 - 36.4097i) q^{17} +(-22.5218 - 39.0089i) q^{19} +(-13.1317 - 45.6891i) q^{21} +(12.1174 - 68.7214i) q^{23} +(-72.1445 + 60.5364i) q^{25} +(-133.349 + 43.6014i) q^{27} +(142.727 - 119.762i) q^{29} +(-46.3221 + 262.706i) q^{31} +(362.204 + 90.0696i) q^{33} +(25.3961 + 43.9873i) q^{35} +(-40.4209 + 70.0111i) q^{37} +(355.541 + 239.496i) q^{39} +(-216.792 - 181.910i) q^{41} +(-249.820 - 90.9271i) q^{43} +(127.022 - 79.5908i) q^{45} +(-10.5496 - 59.8299i) q^{47} +(243.661 - 88.6854i) q^{49} +(-88.7316 + 199.627i) q^{51} +206.241 q^{53} -398.778 q^{55} +(137.690 + 189.268i) q^{57} +(558.381 - 203.234i) q^{59} +(124.554 + 706.379i) q^{61} +(92.8181 + 228.917i) q^{63} +(-430.397 - 156.652i) q^{65} +(23.6459 + 19.8412i) q^{67} +(-25.0696 + 361.728i) q^{69} +(155.414 - 269.185i) q^{71} +(-263.889 - 457.070i) q^{73} +(339.722 - 352.229i) q^{75} +(114.113 - 647.169i) q^{77} +(-500.648 + 420.094i) q^{79} +(665.239 - 298.158i) q^{81} +(-883.108 + 741.015i) q^{83} +(40.5310 - 229.863i) q^{85} +(-672.091 + 696.832i) q^{87} +(240.988 + 417.404i) q^{89} +(377.389 - 653.656i) q^{91} +(95.8352 - 1382.80i) q^{93} +(-191.566 - 160.743i) q^{95} +(-858.230 - 312.370i) q^{97} +(-1920.84 - 267.534i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54q + 12q^{5} - 48q^{9} + O(q^{10}) \) \( 54q + 12q^{5} - 48q^{9} - 87q^{11} + 234q^{15} + 204q^{17} - 12q^{21} + 96q^{23} - 216q^{25} + 27q^{27} + 318q^{29} - 54q^{31} + 63q^{33} + 6q^{35} + 66q^{39} + 867q^{41} - 513q^{43} - 306q^{45} - 1548q^{47} + 594q^{49} - 1368q^{51} - 1068q^{53} - 1269q^{57} - 1218q^{59} - 54q^{61} + 30q^{63} + 96q^{65} - 2997q^{67} + 1476q^{69} - 120q^{71} - 216q^{73} + 732q^{75} + 3480q^{77} + 2808q^{79} + 3348q^{81} + 4464q^{83} + 2160q^{85} + 4824q^{87} + 4029q^{89} + 270q^{91} + 1164q^{93} - 1650q^{95} - 3483q^{97} - 5076q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\) \(1\)

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
\(3\) −5.16735 + 0.546343i −0.994457 + 0.105144i
\(4\) 0 0
\(5\) 5.21695 1.89881i 0.466618 0.169835i −0.0980017 0.995186i \(-0.531245\pi\)
0.564620 + 0.825351i \(0.309023\pi\)
\(6\) 0 0
\(7\) 1.58868 + 9.00985i 0.0857806 + 0.486486i 0.997185 + 0.0749750i \(0.0238877\pi\)
−0.911405 + 0.411511i \(0.865001\pi\)
\(8\) 0 0
\(9\) 26.4030 5.64629i 0.977890 0.209122i
\(10\) 0 0
\(11\) −67.4972 24.5670i −1.85011 0.673384i −0.985189 0.171472i \(-0.945148\pi\)
−0.864918 0.501912i \(-0.832630\pi\)
\(12\) 0 0
\(13\) −63.1985 53.0298i −1.34832 1.13137i −0.979405 0.201907i \(-0.935286\pi\)
−0.368911 0.929465i \(-0.620269\pi\)
\(14\) 0 0
\(15\) −25.9204 + 12.6621i −0.446175 + 0.217956i
\(16\) 0 0
\(17\) 21.0212 36.4097i 0.299905 0.519450i −0.676209 0.736710i \(-0.736378\pi\)
0.976114 + 0.217259i \(0.0697117\pi\)
\(18\) 0 0
\(19\) −22.5218 39.0089i −0.271940 0.471013i 0.697419 0.716664i \(-0.254332\pi\)
−0.969358 + 0.245650i \(0.920998\pi\)
\(20\) 0 0
\(21\) −13.1317 45.6891i −0.136456 0.474770i
\(22\) 0 0
\(23\) 12.1174 68.7214i 0.109855 0.623018i −0.879315 0.476241i \(-0.841999\pi\)
0.989170 0.146777i \(-0.0468899\pi\)
\(24\) 0 0
\(25\) −72.1445 + 60.5364i −0.577156 + 0.484291i
\(26\) 0 0
\(27\) −133.349 + 43.6014i −0.950481 + 0.310782i
\(28\) 0 0
\(29\) 142.727 119.762i 0.913924 0.766873i −0.0589376 0.998262i \(-0.518771\pi\)
0.972861 + 0.231388i \(0.0743268\pi\)
\(30\) 0 0
\(31\) −46.3221 + 262.706i −0.268377 + 1.52204i 0.490866 + 0.871235i \(0.336680\pi\)
−0.759243 + 0.650807i \(0.774431\pi\)
\(32\) 0 0
\(33\) 362.204 + 90.0696i 1.91065 + 0.475124i
\(34\) 0 0
\(35\) 25.3961 + 43.9873i 0.122649 + 0.212435i
\(36\) 0 0
\(37\) −40.4209 + 70.0111i −0.179599 + 0.311074i −0.941743 0.336333i \(-0.890813\pi\)
0.762144 + 0.647407i \(0.224147\pi\)
\(38\) 0 0
\(39\) 355.541 + 239.496i 1.45980 + 0.983334i
\(40\) 0 0
\(41\) −216.792 181.910i −0.825787 0.692918i 0.128533 0.991705i \(-0.458973\pi\)
−0.954320 + 0.298788i \(0.903418\pi\)
\(42\) 0 0
\(43\) −249.820 90.9271i −0.885982 0.322471i −0.141361 0.989958i \(-0.545148\pi\)
−0.744621 + 0.667487i \(0.767370\pi\)
\(44\) 0 0
\(45\) 127.022 79.5908i 0.420785 0.263660i
\(46\) 0 0
\(47\) −10.5496 59.8299i −0.0327409 0.185683i 0.964051 0.265716i \(-0.0856084\pi\)
−0.996792 + 0.0800335i \(0.974497\pi\)
\(48\) 0 0
\(49\) 243.661 88.6854i 0.710382 0.258558i
\(50\) 0 0
\(51\) −88.7316 + 199.627i −0.243626 + 0.548104i
\(52\) 0 0
\(53\) 206.241 0.534517 0.267258 0.963625i \(-0.413882\pi\)
0.267258 + 0.963625i \(0.413882\pi\)
\(54\) 0 0
\(55\) −398.778 −0.977658
\(56\) 0 0
\(57\) 137.690 + 189.268i 0.319956 + 0.439810i
\(58\) 0 0
\(59\) 558.381 203.234i 1.23212 0.448455i 0.357797 0.933800i \(-0.383528\pi\)
0.874323 + 0.485345i \(0.161306\pi\)
\(60\) 0 0
\(61\) 124.554 + 706.379i 0.261434 + 1.48266i 0.779002 + 0.627022i \(0.215726\pi\)
−0.517568 + 0.855642i \(0.673163\pi\)
\(62\) 0 0
\(63\) 92.8181 + 228.917i 0.185619 + 0.457791i
\(64\) 0 0
\(65\) −430.397 156.652i −0.821295 0.298927i
\(66\) 0 0
\(67\) 23.6459 + 19.8412i 0.0431164 + 0.0361790i 0.664091 0.747652i \(-0.268819\pi\)
−0.620975 + 0.783831i \(0.713263\pi\)
\(68\) 0 0
\(69\) −25.0696 + 361.728i −0.0437395 + 0.631115i
\(70\) 0 0
\(71\) 155.414 269.185i 0.259779 0.449950i −0.706404 0.707809i \(-0.749684\pi\)
0.966182 + 0.257859i \(0.0830171\pi\)
\(72\) 0 0
\(73\) −263.889 457.070i −0.423094 0.732821i 0.573146 0.819453i \(-0.305723\pi\)
−0.996240 + 0.0866322i \(0.972389\pi\)
\(74\) 0 0
\(75\) 339.722 352.229i 0.523037 0.542291i
\(76\) 0 0
\(77\) 114.113 647.169i 0.168889 0.957815i
\(78\) 0 0
\(79\) −500.648 + 420.094i −0.713004 + 0.598281i −0.925440 0.378893i \(-0.876305\pi\)
0.212436 + 0.977175i \(0.431860\pi\)
\(80\) 0 0
\(81\) 665.239 298.158i 0.912536 0.408996i
\(82\) 0 0
\(83\) −883.108 + 741.015i −1.16788 + 0.979964i −0.999983 0.00584137i \(-0.998141\pi\)
−0.167893 + 0.985805i \(0.553696\pi\)
\(84\) 0 0
\(85\) 40.5310 229.863i 0.0517201 0.293319i
\(86\) 0 0
\(87\) −672.091 + 696.832i −0.828226 + 0.858716i
\(88\) 0 0
\(89\) 240.988 + 417.404i 0.287019 + 0.497132i 0.973097 0.230397i \(-0.0740023\pi\)
−0.686078 + 0.727528i \(0.740669\pi\)
\(90\) 0 0
\(91\) 377.389 653.656i 0.434737 0.752987i
\(92\) 0 0
\(93\) 95.8352 1382.80i 0.106856 1.54182i
\(94\) 0 0
\(95\) −191.566 160.743i −0.206887 0.173598i
\(96\) 0 0
\(97\) −858.230 312.370i −0.898351 0.326973i −0.148759 0.988873i \(-0.547528\pi\)
−0.749592 + 0.661901i \(0.769750\pi\)
\(98\) 0 0
\(99\) −1920.84 267.534i −1.95002 0.271598i
\(100\) 0 0
\(101\) −92.4446 524.279i −0.0910750 0.516512i −0.995880 0.0906852i \(-0.971094\pi\)
0.904805 0.425827i \(-0.140017\pi\)
\(102\) 0 0
\(103\) 303.355 110.412i 0.290199 0.105624i −0.192819 0.981234i \(-0.561763\pi\)
0.483017 + 0.875611i \(0.339541\pi\)
\(104\) 0 0
\(105\) −155.263 213.423i −0.144305 0.198361i
\(106\) 0 0
\(107\) −209.423 −0.189212 −0.0946062 0.995515i \(-0.530159\pi\)
−0.0946062 + 0.995515i \(0.530159\pi\)
\(108\) 0 0
\(109\) −196.115 −0.172334 −0.0861672 0.996281i \(-0.527462\pi\)
−0.0861672 + 0.996281i \(0.527462\pi\)
\(110\) 0 0
\(111\) 170.619 383.855i 0.145896 0.328234i
\(112\) 0 0
\(113\) 203.446 74.0482i 0.169368 0.0616448i −0.255945 0.966691i \(-0.582386\pi\)
0.425312 + 0.905047i \(0.360164\pi\)
\(114\) 0 0
\(115\) −67.2731 381.525i −0.0545500 0.309368i
\(116\) 0 0
\(117\) −1968.05 1043.31i −1.55510 0.824394i
\(118\) 0 0
\(119\) 361.442 + 131.554i 0.278431 + 0.101341i
\(120\) 0 0
\(121\) 2932.73 + 2460.86i 2.20341 + 1.84888i
\(122\) 0 0
\(123\) 1219.63 + 821.552i 0.894066 + 0.602251i
\(124\) 0 0
\(125\) −608.412 + 1053.80i −0.435344 + 0.754038i
\(126\) 0 0
\(127\) −611.723 1059.53i −0.427414 0.740303i 0.569228 0.822180i \(-0.307242\pi\)
−0.996642 + 0.0818763i \(0.973909\pi\)
\(128\) 0 0
\(129\) 1340.59 + 333.365i 0.914977 + 0.227528i
\(130\) 0 0
\(131\) 194.741 1104.43i 0.129882 0.736599i −0.848405 0.529347i \(-0.822437\pi\)
0.978288 0.207252i \(-0.0664519\pi\)
\(132\) 0 0
\(133\) 315.684 264.891i 0.205814 0.172699i
\(134\) 0 0
\(135\) −612.883 + 480.671i −0.390730 + 0.306441i
\(136\) 0 0
\(137\) −1967.06 + 1650.56i −1.22670 + 1.02932i −0.228252 + 0.973602i \(0.573301\pi\)
−0.998446 + 0.0557200i \(0.982255\pi\)
\(138\) 0 0
\(139\) 434.934 2466.63i 0.265400 1.50516i −0.502494 0.864581i \(-0.667584\pi\)
0.767894 0.640577i \(-0.221305\pi\)
\(140\) 0 0
\(141\) 87.2012 + 303.398i 0.0520827 + 0.181211i
\(142\) 0 0
\(143\) 2962.94 + 5131.96i 1.73268 + 3.00109i
\(144\) 0 0
\(145\) 517.194 895.807i 0.296211 0.513053i
\(146\) 0 0
\(147\) −1210.63 + 591.391i −0.679259 + 0.331817i
\(148\) 0 0
\(149\) 88.5089 + 74.2678i 0.0486640 + 0.0408339i 0.666795 0.745241i \(-0.267666\pi\)
−0.618131 + 0.786075i \(0.712110\pi\)
\(150\) 0 0
\(151\) 1464.39 + 532.995i 0.789209 + 0.287249i 0.705007 0.709200i \(-0.250944\pi\)
0.0842019 + 0.996449i \(0.473166\pi\)
\(152\) 0 0
\(153\) 349.443 1080.02i 0.184645 0.570682i
\(154\) 0 0
\(155\) 257.169 + 1458.48i 0.133267 + 0.755792i
\(156\) 0 0
\(157\) 1712.19 623.186i 0.870367 0.316788i 0.132052 0.991243i \(-0.457844\pi\)
0.738316 + 0.674455i \(0.235621\pi\)
\(158\) 0 0
\(159\) −1065.72 + 112.678i −0.531554 + 0.0562011i
\(160\) 0 0
\(161\) 638.420 0.312513
\(162\) 0 0
\(163\) 1785.32 0.857897 0.428948 0.903329i \(-0.358884\pi\)
0.428948 + 0.903329i \(0.358884\pi\)
\(164\) 0 0
\(165\) 2060.62 217.869i 0.972239 0.102795i
\(166\) 0 0
\(167\) 1097.06 399.298i 0.508343 0.185022i −0.0751000 0.997176i \(-0.523928\pi\)
0.583442 + 0.812154i \(0.301705\pi\)
\(168\) 0 0
\(169\) 800.382 + 4539.19i 0.364307 + 2.06609i
\(170\) 0 0
\(171\) −814.899 902.788i −0.364426 0.403731i
\(172\) 0 0
\(173\) −3928.51 1429.86i −1.72647 0.628383i −0.728100 0.685471i \(-0.759596\pi\)
−0.998369 + 0.0570873i \(0.981819\pi\)
\(174\) 0 0
\(175\) −660.038 553.838i −0.285110 0.239235i
\(176\) 0 0
\(177\) −2774.32 + 1355.25i −1.17814 + 0.575519i
\(178\) 0 0
\(179\) 918.530 1590.94i 0.383543 0.664316i −0.608023 0.793919i \(-0.708037\pi\)
0.991566 + 0.129604i \(0.0413705\pi\)
\(180\) 0 0
\(181\) −1157.45 2004.76i −0.475318 0.823275i 0.524282 0.851544i \(-0.324334\pi\)
−0.999600 + 0.0282697i \(0.991000\pi\)
\(182\) 0 0
\(183\) −1029.54 3582.06i −0.415877 1.44696i
\(184\) 0 0
\(185\) −77.9358 + 441.996i −0.0309727 + 0.175655i
\(186\) 0 0
\(187\) −2313.35 + 1941.13i −0.904646 + 0.759088i
\(188\) 0 0
\(189\) −604.691 1132.18i −0.232724 0.435737i
\(190\) 0 0
\(191\) 1309.35 1098.67i 0.496027 0.416216i −0.360153 0.932893i \(-0.617276\pi\)
0.856180 + 0.516677i \(0.172831\pi\)
\(192\) 0 0
\(193\) −538.413 + 3053.49i −0.200808 + 1.13884i 0.703095 + 0.711096i \(0.251801\pi\)
−0.903902 + 0.427740i \(0.859310\pi\)
\(194\) 0 0
\(195\) 2309.60 + 574.330i 0.848173 + 0.210916i
\(196\) 0 0
\(197\) −269.298 466.438i −0.0973943 0.168692i 0.813211 0.581969i \(-0.197717\pi\)
−0.910605 + 0.413277i \(0.864384\pi\)
\(198\) 0 0
\(199\) 1847.26 3199.55i 0.658035 1.13975i −0.323089 0.946369i \(-0.604721\pi\)
0.981124 0.193381i \(-0.0619454\pi\)
\(200\) 0 0
\(201\) −133.027 89.6078i −0.0466814 0.0314450i
\(202\) 0 0
\(203\) 1305.79 + 1095.69i 0.451470 + 0.378828i
\(204\) 0 0
\(205\) −1476.41 537.369i −0.503009 0.183080i
\(206\) 0 0
\(207\) −68.0839 1882.87i −0.0228607 0.632216i
\(208\) 0 0
\(209\) 561.828 + 3186.28i 0.185945 + 1.05455i
\(210\) 0 0
\(211\) 3344.47 1217.29i 1.09120 0.397164i 0.267134 0.963660i \(-0.413924\pi\)
0.824065 + 0.566496i \(0.191701\pi\)
\(212\) 0 0
\(213\) −656.012 + 1475.88i −0.211029 + 0.474770i
\(214\) 0 0
\(215\) −1475.95 −0.468182
\(216\) 0 0
\(217\) −2440.53 −0.763474
\(218\) 0 0
\(219\) 1613.32 + 2217.66i 0.497801 + 0.684273i
\(220\) 0 0
\(221\) −3259.31 + 1186.29i −0.992058 + 0.361080i
\(222\) 0 0
\(223\) −932.642 5289.28i −0.280064 1.58832i −0.722401 0.691474i \(-0.756962\pi\)
0.442337 0.896849i \(-0.354150\pi\)
\(224\) 0 0
\(225\) −1563.03 + 2005.69i −0.463119 + 0.594279i
\(226\) 0 0
\(227\) −1788.67 651.023i −0.522988 0.190352i 0.0670166 0.997752i \(-0.478652\pi\)
−0.590005 + 0.807400i \(0.700874\pi\)
\(228\) 0 0
\(229\) −1969.18 1652.34i −0.568240 0.476810i 0.312821 0.949812i \(-0.398726\pi\)
−0.881061 + 0.473002i \(0.843170\pi\)
\(230\) 0 0
\(231\) −236.088 + 3406.49i −0.0672443 + 0.970263i
\(232\) 0 0
\(233\) 1769.64 3065.11i 0.497567 0.861811i −0.502429 0.864618i \(-0.667560\pi\)
0.999996 + 0.00280750i \(0.000893656\pi\)
\(234\) 0 0
\(235\) −168.643 292.098i −0.0468129 0.0810823i
\(236\) 0 0
\(237\) 2357.51 2444.30i 0.646146 0.669933i
\(238\) 0 0
\(239\) 1060.55 6014.68i 0.287035 1.62786i −0.410890 0.911685i \(-0.634782\pi\)
0.697925 0.716171i \(-0.254107\pi\)
\(240\) 0 0
\(241\) −2459.06 + 2063.40i −0.657270 + 0.551515i −0.909267 0.416213i \(-0.863357\pi\)
0.251997 + 0.967728i \(0.418913\pi\)
\(242\) 0 0
\(243\) −3274.63 + 1904.14i −0.864475 + 0.502676i
\(244\) 0 0
\(245\) 1102.77 925.334i 0.287565 0.241296i
\(246\) 0 0
\(247\) −645.292 + 3659.63i −0.166230 + 0.942740i
\(248\) 0 0
\(249\) 4158.48 4311.57i 1.05837 1.09733i
\(250\) 0 0
\(251\) 1804.49 + 3125.47i 0.453778 + 0.785967i 0.998617 0.0525736i \(-0.0167424\pi\)
−0.544839 + 0.838541i \(0.683409\pi\)
\(252\) 0 0
\(253\) −2506.17 + 4340.82i −0.622773 + 1.07868i
\(254\) 0 0
\(255\) −83.8542 + 1209.93i −0.0205928 + 0.297131i
\(256\) 0 0
\(257\) −4944.99 4149.34i −1.20023 1.00712i −0.999623 0.0274439i \(-0.991263\pi\)
−0.200610 0.979671i \(-0.564292\pi\)
\(258\) 0 0
\(259\) −695.005 252.961i −0.166739 0.0606882i
\(260\) 0 0
\(261\) 3092.22 3967.97i 0.733347 0.941039i
\(262\) 0 0
\(263\) −1324.95 7514.17i −0.310646 1.76176i −0.595657 0.803239i \(-0.703108\pi\)
0.285011 0.958524i \(-0.408003\pi\)
\(264\) 0 0
\(265\) 1075.95 391.613i 0.249415 0.0907797i
\(266\) 0 0
\(267\) −1473.32 2025.21i −0.337698 0.464198i
\(268\) 0 0
\(269\) −7418.04 −1.68136 −0.840681 0.541531i \(-0.817845\pi\)
−0.840681 + 0.541531i \(0.817845\pi\)
\(270\) 0 0
\(271\) −5946.94 −1.33303 −0.666515 0.745492i \(-0.732215\pi\)
−0.666515 + 0.745492i \(0.732215\pi\)
\(272\) 0 0
\(273\) −1592.98 + 3583.85i −0.353156 + 0.794523i
\(274\) 0 0
\(275\) 6356.75 2313.67i 1.39391 0.507343i
\(276\) 0 0
\(277\) 105.510 + 598.379i 0.0228863 + 0.129795i 0.994110 0.108373i \(-0.0345642\pi\)
−0.971224 + 0.238168i \(0.923453\pi\)
\(278\) 0 0
\(279\) 260.268 + 7197.77i 0.0558489 + 1.54451i
\(280\) 0 0
\(281\) 6387.32 + 2324.79i 1.35600 + 0.493543i 0.914815 0.403874i \(-0.132336\pi\)
0.441184 + 0.897417i \(0.354559\pi\)
\(282\) 0 0
\(283\) −56.9781 47.8103i −0.0119682 0.0100425i 0.636784 0.771042i \(-0.280264\pi\)
−0.648752 + 0.761000i \(0.724709\pi\)
\(284\) 0 0
\(285\) 1077.71 + 725.953i 0.223993 + 0.150883i
\(286\) 0 0
\(287\) 1294.57 2242.26i 0.266258 0.461173i
\(288\) 0 0
\(289\) 1572.72 + 2724.03i 0.320114 + 0.554454i
\(290\) 0 0
\(291\) 4605.43 + 1145.24i 0.927750 + 0.230705i
\(292\) 0 0
\(293\) −17.3041 + 98.1364i −0.00345023 + 0.0195672i −0.986484 0.163856i \(-0.947607\pi\)
0.983034 + 0.183423i \(0.0587179\pi\)
\(294\) 0 0
\(295\) 2527.14 2120.52i 0.498766 0.418514i
\(296\) 0 0
\(297\) 10071.8 + 333.002i 1.96777 + 0.0650598i
\(298\) 0 0
\(299\) −4410.09 + 3700.50i −0.852983 + 0.715738i
\(300\) 0 0
\(301\) 422.355 2395.30i 0.0808776 0.458680i
\(302\) 0 0
\(303\) 764.130 + 2658.63i 0.144878 + 0.504073i
\(304\) 0 0
\(305\) 1991.07 + 3448.64i 0.373798 + 0.647437i
\(306\) 0 0
\(307\) −2496.99 + 4324.91i −0.464204 + 0.804024i −0.999165 0.0408521i \(-0.986993\pi\)
0.534962 + 0.844876i \(0.320326\pi\)
\(308\) 0 0
\(309\) −1507.22 + 736.274i −0.277484 + 0.135551i
\(310\) 0 0
\(311\) 5733.38 + 4810.88i 1.04537 + 0.877170i 0.992599 0.121437i \(-0.0387502\pi\)
0.0527712 + 0.998607i \(0.483195\pi\)
\(312\) 0 0
\(313\) 4171.87 + 1518.44i 0.753380 + 0.274208i 0.690027 0.723783i \(-0.257599\pi\)
0.0633524 + 0.997991i \(0.479821\pi\)
\(314\) 0 0
\(315\) 918.898 + 1018.00i 0.164362 + 0.182089i
\(316\) 0 0
\(317\) −299.891 1700.77i −0.0531342 0.301339i 0.946647 0.322273i \(-0.104447\pi\)
−0.999781 + 0.0209343i \(0.993336\pi\)
\(318\) 0 0
\(319\) −12575.9 + 4577.25i −2.20726 + 0.803376i
\(320\) 0 0
\(321\) 1082.16 114.417i 0.188164 0.0198945i
\(322\) 0 0
\(323\) −1893.74 −0.326224
\(324\) 0 0
\(325\) 7769.66 1.32610
\(326\) 0 0
\(327\) 1013.40 107.146i 0.171379 0.0181199i
\(328\) 0 0
\(329\) 522.298 190.101i 0.0875235 0.0318559i
\(330\) 0 0
\(331\) −146.572 831.251i −0.0243393 0.138035i 0.970217 0.242239i \(-0.0778818\pi\)
−0.994556 + 0.104204i \(0.966771\pi\)
\(332\) 0 0
\(333\) −671.932 + 2076.73i −0.110575 + 0.341754i
\(334\) 0 0
\(335\) 161.034 + 58.6116i 0.0262634 + 0.00955908i
\(336\) 0 0
\(337\) 25.8927 + 21.7265i 0.00418536 + 0.00351193i 0.644878 0.764286i \(-0.276908\pi\)
−0.640693 + 0.767798i \(0.721353\pi\)
\(338\) 0 0
\(339\) −1010.82 + 493.784i −0.161947 + 0.0791111i
\(340\) 0 0
\(341\) 9580.49 16593.9i 1.52145 2.63522i
\(342\) 0 0
\(343\) 2755.17 + 4772.09i 0.433717 + 0.751220i
\(344\) 0 0
\(345\) 556.067 + 1934.72i 0.0867758 + 0.301918i
\(346\) 0 0
\(347\) −1785.27 + 10124.8i −0.276191 + 1.56636i 0.458963 + 0.888455i \(0.348221\pi\)
−0.735154 + 0.677900i \(0.762890\pi\)
\(348\) 0 0
\(349\) −5099.40 + 4278.91i −0.782134 + 0.656289i −0.943785 0.330559i \(-0.892763\pi\)
0.161651 + 0.986848i \(0.448318\pi\)
\(350\) 0 0
\(351\) 10739.6 + 4315.92i 1.63316 + 0.656316i
\(352\) 0 0
\(353\) 6159.61 5168.53i 0.928734 0.779300i −0.0468557 0.998902i \(-0.514920\pi\)
0.975590 + 0.219601i \(0.0704756\pi\)
\(354\) 0 0
\(355\) 299.655 1699.43i 0.0448001 0.254074i
\(356\) 0 0
\(357\) −1939.57 482.315i −0.287543 0.0715037i
\(358\) 0 0
\(359\) −1712.40 2965.97i −0.251747 0.436039i 0.712260 0.701916i \(-0.247672\pi\)
−0.964007 + 0.265877i \(0.914338\pi\)
\(360\) 0 0
\(361\) 2415.04 4182.97i 0.352098 0.609851i
\(362\) 0 0
\(363\) −16498.9 11113.8i −2.38559 1.60696i
\(364\) 0 0
\(365\) −2244.59 1883.43i −0.321882 0.270091i
\(366\) 0 0
\(367\) −3402.99 1238.59i −0.484018 0.176168i 0.0884742 0.996078i \(-0.471801\pi\)
−0.572492 + 0.819910i \(0.694023\pi\)
\(368\) 0 0
\(369\) −6751.09 3578.91i −0.952433 0.504907i
\(370\) 0 0
\(371\) 327.651 + 1858.20i 0.0458512 + 0.260035i
\(372\) 0 0
\(373\) −1812.31 + 659.627i −0.251576 + 0.0915662i −0.464730 0.885452i \(-0.653849\pi\)
0.213154 + 0.977019i \(0.431626\pi\)
\(374\) 0 0
\(375\) 2568.14 5777.76i 0.353649 0.795632i
\(376\) 0 0
\(377\) −15371.1 −2.09988
\(378\) 0 0
\(379\) 4403.13 0.596763 0.298382 0.954447i \(-0.403553\pi\)
0.298382 + 0.954447i \(0.403553\pi\)
\(380\) 0 0
\(381\) 3739.85 + 5140.78i 0.502883 + 0.691260i
\(382\) 0 0
\(383\) −10231.3 + 3723.88i −1.36500 + 0.496819i −0.917596 0.397515i \(-0.869873\pi\)
−0.447402 + 0.894333i \(0.647651\pi\)
\(384\) 0 0
\(385\) −633.530 3592.93i −0.0838641 0.475617i
\(386\) 0 0
\(387\) −7109.41 990.194i −0.933828 0.130063i
\(388\) 0 0
\(389\) 7053.47 + 2567.25i 0.919345 + 0.334614i 0.757978 0.652280i \(-0.226187\pi\)
0.161367 + 0.986894i \(0.448410\pi\)
\(390\) 0 0
\(391\) −2247.41 1885.80i −0.290681 0.243910i
\(392\) 0 0
\(393\) −402.897 + 5813.37i −0.0517136 + 0.746172i
\(394\) 0 0
\(395\) −1814.18 + 3142.25i −0.231091 + 0.400262i
\(396\) 0 0
\(397\) −3635.79 6297.37i −0.459635 0.796111i 0.539307 0.842110i \(-0.318686\pi\)
−0.998942 + 0.0459984i \(0.985353\pi\)
\(398\) 0 0
\(399\) −1486.53 + 1541.25i −0.186515 + 0.193381i
\(400\) 0 0
\(401\) −2014.16 + 11422.9i −0.250828 + 1.42252i 0.555729 + 0.831363i \(0.312439\pi\)
−0.806558 + 0.591155i \(0.798672\pi\)
\(402\) 0 0
\(403\) 16858.7 14146.1i 2.08385 1.74856i
\(404\) 0 0
\(405\) 2904.37 2818.64i 0.356344 0.345826i
\(406\) 0 0
\(407\) 4448.26 3732.53i 0.541750 0.454582i
\(408\) 0 0
\(409\) 1420.37 8055.31i 0.171718 0.973862i −0.770146 0.637868i \(-0.779817\pi\)
0.941864 0.335994i \(-0.109072\pi\)
\(410\) 0 0
\(411\) 9262.74 9603.73i 1.11167 1.15260i
\(412\) 0 0
\(413\) 2718.20 + 4708.06i 0.323859 + 0.560940i
\(414\) 0 0
\(415\) −3200.08 + 5542.70i −0.378520 + 0.655615i
\(416\) 0 0
\(417\) −899.829 + 12983.6i −0.105671 + 1.52472i
\(418\) 0 0
\(419\) −6454.20 5415.71i −0.752525 0.631444i 0.183644 0.982993i \(-0.441211\pi\)
−0.936169 + 0.351549i \(0.885655\pi\)
\(420\) 0 0
\(421\) 4401.68 + 1602.08i 0.509560 + 0.185465i 0.583989 0.811762i \(-0.301491\pi\)
−0.0744290 + 0.997226i \(0.523713\pi\)
\(422\) 0 0
\(423\) −616.358 1520.12i −0.0708472 0.174730i
\(424\) 0 0
\(425\) 687.553 + 3899.31i 0.0784735 + 0.445045i
\(426\) 0 0
\(427\) −6166.49 + 2244.42i −0.698869 + 0.254368i
\(428\) 0 0
\(429\) −18114.4 24899.9i −2.03862 2.80228i
\(430\) 0 0
\(431\) −8784.41 −0.981740 −0.490870 0.871233i \(-0.663321\pi\)
−0.490870 + 0.871233i \(0.663321\pi\)
\(432\) 0 0
\(433\) −6469.85 −0.718063 −0.359031 0.933325i \(-0.616893\pi\)
−0.359031 + 0.933325i \(0.616893\pi\)
\(434\) 0 0
\(435\) −2183.11 + 4911.51i −0.240625 + 0.541354i
\(436\) 0 0
\(437\) −2953.65 + 1075.04i −0.323323 + 0.117680i
\(438\) 0 0
\(439\) −148.990 844.963i −0.0161979 0.0918631i 0.975637 0.219391i \(-0.0704070\pi\)
−0.991835 + 0.127528i \(0.959296\pi\)
\(440\) 0 0
\(441\) 5932.65 3717.34i 0.640605 0.401398i
\(442\) 0 0
\(443\) 412.777 + 150.239i 0.0442701 + 0.0161130i 0.364060 0.931375i \(-0.381390\pi\)
−0.319790 + 0.947488i \(0.603612\pi\)
\(444\) 0 0
\(445\) 2049.80 + 1719.98i 0.218359 + 0.183225i
\(446\) 0 0
\(447\) −497.932 335.412i −0.0526877 0.0354909i
\(448\) 0 0
\(449\) 1510.09 2615.54i 0.158720 0.274911i −0.775687 0.631117i \(-0.782597\pi\)
0.934407 + 0.356206i \(0.115930\pi\)
\(450\) 0 0
\(451\) 10163.9 + 17604.4i 1.06120 + 1.83804i
\(452\) 0 0
\(453\) −7858.23 1954.11i −0.815037 0.202676i
\(454\) 0 0
\(455\) 727.645 4126.68i 0.0749726 0.425191i
\(456\) 0 0
\(457\) 5728.39 4806.69i 0.586352 0.492008i −0.300674 0.953727i \(-0.597212\pi\)
0.887026 + 0.461719i \(0.152767\pi\)
\(458\) 0 0
\(459\) −1215.63 + 5771.75i −0.123618 + 0.586933i
\(460\) 0 0
\(461\) 4559.80 3826.13i 0.460675 0.386552i −0.382705 0.923871i \(-0.625007\pi\)
0.843379 + 0.537319i \(0.180563\pi\)
\(462\) 0 0
\(463\) 299.450 1698.27i 0.0300575 0.170465i −0.966084 0.258229i \(-0.916861\pi\)
0.996141 + 0.0877642i \(0.0279722\pi\)
\(464\) 0 0
\(465\) −2125.71 7395.97i −0.211995 0.737591i
\(466\) 0 0
\(467\) 7069.94 + 12245.5i 0.700552 + 1.21339i 0.968273 + 0.249895i \(0.0803961\pi\)
−0.267721 + 0.963496i \(0.586271\pi\)
\(468\) 0 0
\(469\) −141.201 + 244.567i −0.0139020 + 0.0240790i
\(470\) 0 0
\(471\) −8507.02 + 4155.67i −0.832235 + 0.406546i
\(472\) 0 0
\(473\) 14628.4 + 12274.7i 1.42202 + 1.19321i
\(474\) 0 0
\(475\) 3986.28 + 1450.89i 0.385059 + 0.140150i
\(476\) 0 0
\(477\) 5445.39 1164.50i 0.522698 0.111779i
\(478\) 0 0
\(479\) 467.551 + 2651.62i 0.0445991 + 0.252934i 0.998953 0.0457434i \(-0.0145656\pi\)
−0.954354 + 0.298677i \(0.903455\pi\)
\(480\) 0 0
\(481\) 6267.22 2281.08i 0.594097 0.216234i
\(482\) 0 0
\(483\) −3298.94 + 348.796i −0.310781 + 0.0328587i
\(484\) 0 0
\(485\) −5070.47 −0.474718
\(486\) 0 0
\(487\) 12687.7 1.18056 0.590280 0.807199i \(-0.299017\pi\)
0.590280 + 0.807199i \(0.299017\pi\)
\(488\) 0 0
\(489\) −9225.38 + 975.397i −0.853142 + 0.0902024i
\(490\) 0 0
\(491\) −5094.55 + 1854.26i −0.468256 + 0.170431i −0.565362 0.824843i \(-0.691264\pi\)
0.0971061 + 0.995274i \(0.469041\pi\)
\(492\) 0 0
\(493\) −1360.22 7714.21i −0.124262 0.704727i
\(494\) 0 0
\(495\) −10528.9 + 2251.61i −0.956041 + 0.204450i
\(496\) 0 0
\(497\) 2672.22 + 972.609i 0.241178 + 0.0877817i
\(498\) 0 0
\(499\) −10451.5 8769.82i −0.937619 0.786756i 0.0395506 0.999218i \(-0.487407\pi\)
−0.977169 + 0.212462i \(0.931852\pi\)
\(500\) 0 0
\(501\) −5450.75 + 2662.68i −0.486071 + 0.237445i
\(502\) 0 0
\(503\) 3966.78 6870.66i 0.351630 0.609041i −0.634905 0.772590i \(-0.718961\pi\)
0.986535 + 0.163549i \(0.0522942\pi\)
\(504\) 0 0
\(505\) −1477.79 2559.60i −0.130219 0.225546i
\(506\) 0 0
\(507\) −6615.80 23018.3i −0.579523 2.01633i
\(508\) 0 0
\(509\) −3183.90 + 18056.8i −0.277257 + 1.57240i 0.454443 + 0.890776i \(0.349838\pi\)
−0.731700 + 0.681627i \(0.761273\pi\)
\(510\) 0 0
\(511\) 3698.89 3103.74i 0.320214 0.268691i
\(512\) 0 0
\(513\) 4704.10 + 4219.81i 0.404856 + 0.363176i
\(514\) 0 0
\(515\) 1372.94 1152.03i 0.117473 0.0985718i
\(516\) 0 0
\(517\) −757.769 + 4297.52i −0.0644616 + 0.365580i
\(518\) 0 0
\(519\) 21081.2 + 5242.28i 1.78297 + 0.443373i
\(520\) 0 0
\(521\) −3020.36 5231.43i −0.253982 0.439910i 0.710637 0.703559i \(-0.248407\pi\)
−0.964618 + 0.263650i \(0.915074\pi\)
\(522\) 0 0
\(523\) 2909.21 5038.90i 0.243233 0.421292i −0.718400 0.695630i \(-0.755125\pi\)
0.961633 + 0.274338i \(0.0884586\pi\)
\(524\) 0 0
\(525\) 3713.23 + 2501.27i 0.308684 + 0.207932i
\(526\) 0 0
\(527\) 8591.29 + 7208.95i 0.710138 + 0.595876i
\(528\) 0 0
\(529\) 6857.44 + 2495.90i 0.563610 + 0.205137i
\(530\) 0 0
\(531\) 13595.4 8518.78i 1.11110 0.696202i
\(532\) 0 0
\(533\) 4054.27 + 22992.9i 0.329475 + 1.86854i
\(534\) 0 0
\(535\) −1092.55 + 397.656i −0.0882899 + 0.0321349i
\(536\) 0 0
\(537\) −3877.17 + 8722.78i −0.311568 + 0.700960i
\(538\) 0 0
\(539\) −18625.2 −1.48839
\(540\) 0 0
\(541\) 6742.32 0.535813 0.267907 0.963445i \(-0.413668\pi\)
0.267907 + 0.963445i \(0.413668\pi\)
\(542\) 0 0
\(543\) 7076.23 + 9726.94i 0.559245 + 0.768735i
\(544\) 0 0
\(545\) −1023.12 + 372.387i −0.0804144 + 0.0292684i
\(546\) 0 0
\(547\) 996.065 + 5648.96i 0.0778586 + 0.441558i 0.998670 + 0.0515507i \(0.0164164\pi\)
−0.920812 + 0.390007i \(0.872473\pi\)
\(548\) 0 0
\(549\) 7277.01 + 17947.3i 0.565711 + 1.39521i
\(550\) 0 0
\(551\) −7886.27 2870.37i −0.609740 0.221927i
\(552\) 0 0
\(553\) −4580.35 3843.37i −0.352217 0.295546i
\(554\) 0 0
\(555\) 161.240 2326.53i 0.0123320 0.177938i
\(556\) 0 0
\(557\) 11916.4 20639.9i 0.906492 1.57009i 0.0875890 0.996157i \(-0.472084\pi\)
0.818902 0.573933i \(-0.194583\pi\)
\(558\) 0 0
\(559\) 10966.4 + 18994.4i 0.829749 + 1.43717i
\(560\) 0 0
\(561\) 10893.4 11294.4i 0.819818 0.849998i
\(562\) 0 0
\(563\) 143.937 816.308i 0.0107748 0.0611070i −0.978946 0.204118i \(-0.934567\pi\)
0.989721 + 0.143011i \(0.0456785\pi\)
\(564\) 0 0
\(565\) 920.762 772.611i 0.0685606 0.0575292i
\(566\) 0 0
\(567\) 3743.21 + 5520.02i 0.277249 + 0.408852i
\(568\) 0 0
\(569\) 809.884 679.573i 0.0596698 0.0500689i −0.612465 0.790498i \(-0.709822\pi\)
0.672135 + 0.740429i \(0.265378\pi\)
\(570\) 0 0
\(571\) −4496.33 + 25499.9i −0.329537 + 1.86890i 0.146124 + 0.989266i \(0.453320\pi\)
−0.475661 + 0.879629i \(0.657791\pi\)
\(572\) 0 0
\(573\) −6165.62 + 6392.59i −0.449515 + 0.466063i
\(574\) 0 0
\(575\) 3285.94 + 5691.42i 0.238319 + 0.412780i
\(576\) 0 0
\(577\) −1489.92 + 2580.62i −0.107498 + 0.186192i −0.914756 0.404007i \(-0.867617\pi\)
0.807258 + 0.590199i \(0.200951\pi\)
\(578\) 0 0
\(579\) 1113.92 16072.6i 0.0799530 1.15364i
\(580\) 0 0
\(581\) −8079.41 6779.43i −0.576920 0.484093i
\(582\) 0 0
\(583\) −13920.7 5066.72i −0.988913 0.359935i
\(584\) 0 0
\(585\) −12248.3 1705.93i −0.865648 0.120567i
\(586\) 0 0
\(587\) −3085.89 17501.0i −0.216982 1.23057i −0.877434 0.479698i \(-0.840746\pi\)
0.660452 0.750868i \(-0.270365\pi\)
\(588\) 0 0
\(589\) 11291.1 4109.63i 0.789884 0.287494i
\(590\) 0 0
\(591\) 1646.39 + 2263.12i 0.114591 + 0.157516i
\(592\) 0 0
\(593\) −3329.70 −0.230581 −0.115290 0.993332i \(-0.536780\pi\)
−0.115290 + 0.993332i \(0.536780\pi\)
\(594\) 0 0
\(595\) 2135.42 0.147132
\(596\) 0 0
\(597\) −7797.40 + 17542.4i −0.534550 + 1.20262i
\(598\) 0 0
\(599\) 12799.7 4658.71i 0.873090 0.317779i 0.133672 0.991026i \(-0.457323\pi\)
0.739418 + 0.673247i \(0.235101\pi\)
\(600\) 0 0
\(601\) 447.186 + 2536.12i 0.0303513 + 0.172131i 0.996215 0.0869185i \(-0.0277020\pi\)
−0.965864 + 0.259049i \(0.916591\pi\)
\(602\) 0 0
\(603\) 736.351 + 390.357i 0.0497289 + 0.0263625i
\(604\) 0 0
\(605\) 19972.6 + 7269.45i 1.34215 + 0.488504i
\(606\) 0 0
\(607\) −8011.80 6722.70i −0.535731 0.449532i 0.334344 0.942451i \(-0.391485\pi\)
−0.870075 + 0.492919i \(0.835930\pi\)
\(608\) 0 0
\(609\) −7346.09 4948.39i −0.488799 0.329259i
\(610\) 0 0
\(611\) −2506.05 + 4340.60i −0.165931 + 0.287401i
\(612\) 0 0
\(613\) −12357.4 21403.7i −0.814211 1.41025i −0.909893 0.414842i \(-0.863837\pi\)
0.0956826 0.995412i \(-0.469497\pi\)
\(614\) 0 0
\(615\) 7922.71 + 1970.15i 0.519470 + 0.129177i
\(616\) 0 0
\(617\) 1578.77 8953.67i 0.103013 0.584216i −0.888982 0.457942i \(-0.848587\pi\)
0.991995 0.126274i \(-0.0403020\pi\)
\(618\) 0 0
\(619\) 7255.84 6088.37i 0.471142 0.395335i −0.376069 0.926592i \(-0.622725\pi\)
0.847211 + 0.531257i \(0.178280\pi\)
\(620\) 0 0
\(621\) 1380.51 + 9692.26i 0.0892074 + 0.626308i
\(622\) 0 0
\(623\) −3377.89 + 2834.39i −0.217227 + 0.182275i
\(624\) 0 0
\(625\) 871.146 4940.52i 0.0557534 0.316193i
\(626\) 0 0
\(627\) −4643.97 16157.7i −0.295793 1.02915i
\(628\) 0 0
\(629\) 1699.39 + 2943.43i 0.107725 + 0.186585i
\(630\) 0 0
\(631\) −7345.25 + 12722.3i −0.463407 + 0.802644i −0.999128 0.0417505i \(-0.986707\pi\)
0.535721 + 0.844395i \(0.320040\pi\)
\(632\) 0 0
\(633\) −16617.0 + 8117.38i −1.04339 + 0.509695i
\(634\) 0 0
\(635\) −5203.19 4365.99i −0.325169 0.272849i
\(636\) 0 0
\(637\) −20102.0 7316.53i −1.25035 0.455088i
\(638\) 0 0
\(639\) 2583.51 7984.82i 0.159940 0.494326i
\(640\) 0 0
\(641\) −4526.38 25670.4i −0.278910 1.58178i −0.726261 0.687419i \(-0.758744\pi\)
0.447351 0.894359i \(-0.352368\pi\)
\(642\) 0 0
\(643\) 2079.34 756.817i 0.127529 0.0464167i −0.277467 0.960735i \(-0.589495\pi\)
0.404996 + 0.914318i \(0.367273\pi\)
\(644\) 0 0
\(645\) 7626.77 806.376i 0.465587 0.0492264i
\(646\) 0 0
\(647\) −13758.7 −0.836027 −0.418013 0.908441i \(-0.637273\pi\)
−0.418013 + 0.908441i \(0.637273\pi\)
\(648\) 0 0
\(649\) −42682.0 −2.58154
\(650\) 0 0
\(651\) 12611.1 1333.36i 0.759242 0.0802744i
\(652\) 0 0
\(653\) −15288.2 + 5564.44i −0.916191 + 0.333466i −0.756722 0.653737i \(-0.773200\pi\)
−0.159469 + 0.987203i \(0.550978\pi\)
\(654\) 0 0
\(655\) −1081.15 6131.53i −0.0644949 0.365769i
\(656\) 0 0
\(657\) −9548.22 10578.0i −0.566988 0.628140i
\(658\) 0 0
\(659\) −10222.0 3720.52i −0.604240 0.219925i 0.0217411 0.999764i \(-0.493079\pi\)
−0.625981 + 0.779838i \(0.715301\pi\)
\(660\) 0 0
\(661\) 316.290 + 265.399i 0.0186116 + 0.0156170i 0.652046 0.758179i \(-0.273911\pi\)
−0.633434 + 0.773796i \(0.718355\pi\)
\(662\) 0 0
\(663\) 16193.9 7910.68i 0.948594 0.463387i
\(664\) 0 0
\(665\) 1143.93 1981.35i 0.0667063 0.115539i
\(666\) 0 0
\(667\) −6500.75 11259.6i −0.377377 0.653635i
\(668\) 0 0
\(669\) 7709.04 + 26822.0i 0.445514 + 1.55007i
\(670\) 0 0
\(671\) 8946.57 50738.5i 0.514722 2.91913i
\(672\) 0 0
\(673\) −18608.4 + 15614.3i −1.06582 + 0.894333i −0.994668 0.103133i \(-0.967113\pi\)
−0.0711564 + 0.997465i \(0.522669\pi\)
\(674\) 0 0
\(675\) 6980.91 11218.1i 0.398067 0.639679i
\(676\) 0 0
\(677\) −8328.43 + 6988.38i −0.472803 + 0.396729i −0.847816 0.530291i \(-0.822083\pi\)
0.375013 + 0.927020i \(0.377638\pi\)
\(678\) 0 0
\(679\) 1450.95 8228.77i 0.0820067 0.465083i
\(680\) 0 0
\(681\) 9598.38 + 2386.84i 0.540104 + 0.134308i
\(682\) 0 0
\(683\) 6279.52 + 10876.5i 0.351800 + 0.609335i 0.986565 0.163370i \(-0.0522365\pi\)
−0.634765 + 0.772705i \(0.718903\pi\)
\(684\) 0 0
\(685\) −7127.96 + 12346.0i −0.397585 + 0.688637i
\(686\) 0 0
\(687\) 11078.2 + 7462.36i 0.615224 + 0.414420i
\(688\) 0 0
\(689\) −13034.1 10936.9i −0.720698 0.604737i
\(690\) 0 0
\(691\) 16718.3 + 6084.96i 0.920396 + 0.334997i 0.758396 0.651794i \(-0.225983\pi\)
0.162000 + 0.986791i \(0.448206\pi\)
\(692\) 0 0
\(693\) −641.165 17731.5i −0.0351455 0.971955i
\(694\) 0 0
\(695\) −2414.65 13694.2i −0.131788 0.747408i
\(696\) 0 0
\(697\) −11180.5 + 4069.38i −0.607594 + 0.221146i
\(698\) 0 0
\(699\) −7469.76 + 16805.3i −0.404195 + 0.909350i
\(700\) 0 0
\(701\) 21646.4 1.16629 0.583147 0.812367i \(-0.301821\pi\)
0.583147 + 0.812367i \(0.301821\pi\)
\(702\) 0 0
\(703\) 3641.41 0.195360
\(704\) 0 0
\(705\) 1031.02 + 1417.23i 0.0550787 + 0.0757108i
\(706\) 0 0
\(707\) 4576.81 1665.82i 0.243463 0.0886135i
\(708\) 0 0
\(709\) 3459.28 + 19618.5i 0.183238 + 1.03920i 0.928198 + 0.372086i \(0.121357\pi\)
−0.744960 + 0.667109i \(0.767532\pi\)
\(710\) 0 0
\(711\) −10846.7 + 13918.5i −0.572126 + 0.734158i
\(712\) 0 0
\(713\) 17492.2 + 6366.64i 0.918777 + 0.334407i
\(714\) 0 0
\(715\) 25202.2 + 21147.1i 1.31819 + 1.10609i
\(716\) 0 0
\(717\) −2194.16 + 31659.4i −0.114285 + 1.64901i
\(718\) 0 0
\(719\) 10932.0 18934.8i 0.567031 0.982126i −0.429827 0.902911i \(-0.641425\pi\)
0.996858 0.0792148i \(-0.0252413\pi\)
\(720\) 0 0
\(721\) 1476.73 + 2557.77i 0.0762779 + 0.132117i
\(722\) 0 0
\(723\) 11579.5 12005.8i 0.595639 0.617566i
\(724\) 0 0
\(725\) −3047.00 + 17280.4i −0.156087 + 0.885211i
\(726\) 0 0
\(727\) −25330.4 + 21254.7i −1.29223 + 1.08431i −0.300799 + 0.953688i \(0.597253\pi\)
−0.991432 + 0.130623i \(0.958302\pi\)
\(728\) 0 0
\(729\) 15880.8 11628.4i 0.806830 0.590784i
\(730\) 0 0
\(731\) −8562.15 + 7184.49i −0.433218 + 0.363513i
\(732\) 0 0
\(733\) 2985.32 16930.6i 0.150430 0.853131i −0.812416 0.583079i \(-0.801848\pi\)
0.962846 0.270052i \(-0.0870410\pi\)
\(734\) 0 0
\(735\) −5192.85 + 5384.02i −0.260600 + 0.270194i
\(736\) 0 0
\(737\) −1108.59 1920.14i −0.0554077 0.0959689i
\(738\) 0 0
\(739\) 9649.35 16713.2i 0.480321 0.831940i −0.519424 0.854516i \(-0.673854\pi\)
0.999745 + 0.0225766i \(0.00718696\pi\)
\(740\) 0 0
\(741\) 1335.04 19263.1i 0.0661859 0.954992i
\(742\) 0 0
\(743\) 20573.9 + 17263.5i 1.01586 + 0.852405i 0.989101 0.147237i \(-0.0470380\pi\)
0.0267555 + 0.999642i \(0.491482\pi\)
\(744\) 0 0
\(745\) 602.767 + 219.389i 0.0296425 + 0.0107890i
\(746\) 0 0
\(747\) −19132.7 + 24551.3i −0.937122 + 1.20252i
\(748\) 0 0
\(749\) −332.707 1886.87i −0.0162308 0.0920492i
\(750\) 0 0
\(751\) −27645.8 + 10062.2i −1.34329 + 0.488916i −0.910846 0.412746i \(-0.864570\pi\)
−0.432440 + 0.901663i \(0.642347\pi\)
\(752\) 0 0
\(753\) −11032.0 15164.5i −0.533903 0.733899i
\(754\) 0 0
\(755\) 8651.72 0.417044
\(756\) 0 0
\(757\) 24191.8 1.16151 0.580756 0.814077i \(-0.302757\pi\)
0.580756 + 0.814077i \(0.302757\pi\)
\(758\) 0 0
\(759\) 10578.7 23799.7i 0.505905 1.13818i
\(760\) 0 0
\(761\) 12610.5 4589.85i 0.600698 0.218636i −0.0237304 0.999718i \(-0.507554\pi\)
0.624428 + 0.781082i \(0.285332\pi\)
\(762\) 0 0
\(763\) −311.565 1766.97i −0.0147830 0.0838383i
\(764\) 0 0
\(765\) −227.730 6297.93i −0.0107629 0.297650i
\(766\) 0 0
\(767\) −46066.3 16766.8i −2.16866 0.789326i
\(768\) 0 0
\(769\) 16690.9 + 14005.3i 0.782689 + 0.656754i 0.943924 0.330162i \(-0.107103\pi\)
−0.161235 + 0.986916i \(0.551548\pi\)
\(770\) 0 0
\(771\) 27819.4 + 18739.4i 1.29947 + 0.875336i
\(772\) 0 0
\(773\) −670.497 + 1161.34i −0.0311981 + 0.0540367i −0.881203 0.472738i \(-0.843266\pi\)
0.850005 + 0.526775i \(0.176599\pi\)
\(774\) 0 0
\(775\) −12561.4 21756.9i −0.582216 1.00843i
\(776\) 0 0
\(777\) 3729.54 + 927.428i 0.172196 + 0.0428202i
\(778\) 0 0
\(779\) −2213.57 + 12553.8i −0.101809 + 0.577389i
\(780\) 0 0
\(781\) −17103.1 + 14351.2i −0.783607 + 0.657524i
\(782\) 0