Properties

Label 108.4.i.a.97.1
Level 108
Weight 4
Character 108.97
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 97.1
Character \(\chi\) \(=\) 108.97
Dual form 108.4.i.a.49.1

$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{2}{9}\right)\) \(1\)

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 0.564620 0.825351i \(-0.309023\pi\)
−0.0980017 + 0.995186i \(0.531245\pi\)
\(6\) 0 0
\(7\) 1.58868 9.00985i 0.0857806 0.486486i −0.911405 0.411511i \(-0.865001\pi\)
0.997185 0.0749750i \(-0.0238877\pi\)
\(8\) 0 0
\(9\) 26.4030 + 5.64629i 0.977890 + 0.209122i
\(10\) 0 0
\(11\) −67.4972 + 24.5670i −1.85011 + 0.673384i −0.864918 + 0.501912i \(0.832630\pi\)
−0.985189 + 0.171472i \(0.945148\pi\)
\(12\) 0 0
\(13\) −63.1985 + 53.0298i −1.34832 + 1.13137i −0.368911 + 0.929465i \(0.620269\pi\)
−0.979405 + 0.201907i \(0.935286\pi\)
\(14\) 0 0
\(15\) −25.9204 12.6621i −0.446175 0.217956i
\(16\) 0 0
\(17\) 21.0212 + 36.4097i 0.299905 + 0.519450i 0.976114 0.217259i \(-0.0697117\pi\)
−0.676209 + 0.736710i \(0.736378\pi\)
\(18\) 0 0
\(19\) −22.5218 + 39.0089i −0.271940 + 0.471013i −0.969358 0.245650i \(-0.920998\pi\)
0.697419 + 0.716664i \(0.254332\pi\)
\(20\) 0 0
\(21\) −13.1317 + 45.6891i −0.136456 + 0.474770i
\(22\) 0 0
\(23\) 12.1174 + 68.7214i 0.109855 + 0.623018i 0.989170 + 0.146777i \(0.0468899\pi\)
−0.879315 + 0.476241i \(0.841999\pi\)
\(24\) 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 0.972861 0.231388i \(-0.0743268\pi\)
−0.0589376 + 0.998262i \(0.518771\pi\)
\(30\) 0 0
\(31\) −46.3221 262.706i −0.268377 1.52204i −0.759243 0.650807i \(-0.774431\pi\)
0.490866 0.871235i \(-0.336680\pi\)
\(32\) 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 0.762144 0.647407i \(-0.224147\pi\)
−0.941743 + 0.336333i \(0.890813\pi\)
\(38\) 0 0
\(39\) 355.541 239.496i 1.45980 0.983334i
\(40\) 0 0
\(41\) −216.792 + 181.910i −0.825787 + 0.692918i −0.954320 0.298788i \(-0.903418\pi\)
0.128533 + 0.991705i \(0.458973\pi\)
\(42\) 0 0
\(43\) −249.820 + 90.9271i −0.885982 + 0.322471i −0.744621 0.667487i \(-0.767370\pi\)
−0.141361 + 0.989958i \(0.545148\pi\)
\(44\) 0 0
\(45\) 127.022 + 79.5908i 0.420785 + 0.263660i
\(46\) 0 0
\(47\) −10.5496 + 59.8299i −0.0327409 + 0.185683i −0.996792 0.0800335i \(-0.974497\pi\)
0.964051 + 0.265716i \(0.0856084\pi\)
\(48\) 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 0.874323 0.485345i \(-0.161306\pi\)
0.357797 + 0.933800i \(0.383528\pi\)
\(60\) 0 0
\(61\) 124.554 706.379i 0.261434 1.48266i −0.517568 0.855642i \(-0.673163\pi\)
0.779002 0.627022i \(-0.215726\pi\)
\(62\) 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 −0.620975 0.783831i \(-0.713263\pi\)
0.664091 + 0.747652i \(0.268819\pi\)
\(68\) 0 0
\(69\) −25.0696 361.728i −0.0437395 0.631115i
\(70\) 0 0
\(71\) 155.414 + 269.185i 0.259779 + 0.449950i 0.966182 0.257859i \(-0.0830171\pi\)
−0.706404 + 0.707809i \(0.749684\pi\)
\(72\) 0 0
\(73\) −263.889 + 457.070i −0.423094 + 0.732821i −0.996240 0.0866322i \(-0.972389\pi\)
0.573146 + 0.819453i \(0.305723\pi\)
\(74\) 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 0.212436 0.977175i \(-0.431860\pi\)
−0.925440 + 0.378893i \(0.876305\pi\)
\(80\) 0 0
\(81\) 665.239 + 298.158i 0.912536 + 0.408996i
\(82\) 0 0
\(83\) −883.108 741.015i −1.16788 0.979964i −0.167893 0.985805i \(-0.553696\pi\)
−0.999983 + 0.00584137i \(0.998141\pi\)
\(84\) 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 −0.686078 0.727528i \(-0.740669\pi\)
0.973097 + 0.230397i \(0.0740023\pi\)
\(90\) 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 −0.749592 0.661901i \(-0.769750\pi\)
−0.148759 + 0.988873i \(0.547528\pi\)
\(98\) 0 0
\(99\) −1920.84 + 267.534i −1.95002 + 0.271598i
\(100\) 0 0
\(101\) −92.4446 + 524.279i −0.0910750 + 0.516512i 0.904805 + 0.425827i \(0.140017\pi\)
−0.995880 + 0.0906852i \(0.971094\pi\)
\(102\) 0 0
\(103\) 303.355 + 110.412i 0.290199 + 0.105624i 0.483017 0.875611i \(-0.339541\pi\)
−0.192819 + 0.981234i \(0.561763\pi\)
\(104\) 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 0.425312 0.905047i \(-0.360164\pi\)
−0.255945 + 0.966691i \(0.582386\pi\)
\(114\) 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 −0.996642 0.0818763i \(-0.973909\pi\)
0.569228 + 0.822180i \(0.307242\pi\)
\(128\) 0 0
\(129\) 1340.59 333.365i 0.914977 0.227528i
\(130\) 0 0
\(131\) 194.741 + 1104.43i 0.129882 + 0.736599i 0.978288 + 0.207252i \(0.0664519\pi\)
−0.848405 + 0.529347i \(0.822437\pi\)
\(132\) 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 −0.998446 0.0557200i \(-0.982255\pi\)
−0.228252 0.973602i \(-0.573301\pi\)
\(138\) 0 0
\(139\) 434.934 + 2466.63i 0.265400 + 1.50516i 0.767894 + 0.640577i \(0.221305\pi\)
−0.502494 + 0.864581i \(0.667584\pi\)
\(140\) 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 −0.618131 0.786075i \(-0.712110\pi\)
0.666795 + 0.745241i \(0.267666\pi\)
\(150\) 0 0
\(151\) 1464.39 532.995i 0.789209 0.287249i 0.0842019 0.996449i \(-0.473166\pi\)
0.705007 + 0.709200i \(0.250944\pi\)
\(152\) 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 0.738316 0.674455i \(-0.235621\pi\)
0.132052 + 0.991243i \(0.457844\pi\)
\(158\) 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 0.583442 0.812154i \(-0.301705\pi\)
−0.0751000 + 0.997176i \(0.523928\pi\)
\(168\) 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 −0.998369 0.0570873i \(-0.981819\pi\)
−0.728100 + 0.685471i \(0.759596\pi\)
\(174\) 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 0.991566 0.129604i \(-0.0413705\pi\)
−0.608023 + 0.793919i \(0.708037\pi\)
\(180\) 0 0
\(181\) −1157.45 + 2004.76i −0.475318 + 0.823275i −0.999600 0.0282697i \(-0.991000\pi\)
0.524282 + 0.851544i \(0.324334\pi\)
\(182\) 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 0.856180 0.516677i \(-0.172831\pi\)
−0.360153 + 0.932893i \(0.617276\pi\)
\(192\) 0 0
\(193\) −538.413 3053.49i −0.200808 1.13884i −0.903902 0.427740i \(-0.859310\pi\)
0.703095 0.711096i \(-0.251801\pi\)
\(194\) 0 0
\(195\) 2309.60 574.330i 0.848173 0.210916i
\(196\) 0 0
\(197\) −269.298 + 466.438i −0.0973943 + 0.168692i −0.910605 0.413277i \(-0.864384\pi\)
0.813211 + 0.581969i \(0.197717\pi\)
\(198\) 0 0
\(199\) 1847.26 + 3199.55i 0.658035 + 1.13975i 0.981124 + 0.193381i \(0.0619454\pi\)
−0.323089 + 0.946369i \(0.604721\pi\)
\(200\) 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 0.824065 0.566496i \(-0.191701\pi\)
0.267134 + 0.963660i \(0.413924\pi\)
\(212\) 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 0.442337 + 0.896849i \(0.354150\pi\)
−0.722401 + 0.691474i \(0.756962\pi\)
\(224\) 0 0
\(225\) −1563.03 2005.69i −0.463119 0.594279i
\(226\) 0 0
\(227\) −1788.67 + 651.023i −0.522988 + 0.190352i −0.590005 0.807400i \(-0.700874\pi\)
0.0670166 + 0.997752i \(0.478652\pi\)
\(228\) 0 0
\(229\) −1969.18 + 1652.34i −0.568240 + 0.476810i −0.881061 0.473002i \(-0.843170\pi\)
0.312821 + 0.949812i \(0.398726\pi\)
\(230\) 0 0
\(231\) −236.088 3406.49i −0.0672443 0.970263i
\(232\) 0 0
\(233\) 1769.64 + 3065.11i 0.497567 + 0.861811i 0.999996 0.00280750i \(-0.000893656\pi\)
−0.502429 + 0.864618i \(0.667560\pi\)
\(234\) 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 0.697925 + 0.716171i \(0.254107\pi\)
−0.410890 + 0.911685i \(0.634782\pi\)
\(240\) 0 0
\(241\) −2459.06 2063.40i −0.657270 0.551515i 0.251997 0.967728i \(-0.418913\pi\)
−0.909267 + 0.416213i \(0.863357\pi\)
\(242\) 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 −0.544839 0.838541i \(-0.683409\pi\)
0.998617 + 0.0525736i \(0.0167424\pi\)
\(252\) 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 −0.200610 + 0.979671i \(0.564292\pi\)
−0.999623 + 0.0274439i \(0.991263\pi\)
\(258\) 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 0.285011 + 0.958524i \(0.408003\pi\)
−0.595657 + 0.803239i \(0.703108\pi\)
\(264\) 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 −0.971224 0.238168i \(-0.923453\pi\)
0.994110 + 0.108373i \(0.0345642\pi\)
\(278\) 0 0
\(279\) 260.268 7197.77i 0.0558489 1.54451i
\(280\) 0 0
\(281\) 6387.32 2324.79i 1.35600 0.493543i 0.441184 0.897417i \(-0.354559\pi\)
0.914815 + 0.403874i \(0.132336\pi\)
\(282\) 0 0
\(283\) −56.9781 + 47.8103i −0.0119682 + 0.0100425i −0.648752 0.761000i \(-0.724709\pi\)
0.636784 + 0.771042i \(0.280264\pi\)
\(284\) 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 0.983034 0.183423i \(-0.0587179\pi\)
−0.986484 + 0.163856i \(0.947607\pi\)
\(294\) 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 0.534962 0.844876i \(-0.320326\pi\)
−0.999165 + 0.0408521i \(0.986993\pi\)
\(308\) 0 0
\(309\) −1507.22 736.274i −0.277484 0.135551i
\(310\) 0 0
\(311\) 5733.38 4810.88i 1.04537 0.877170i 0.0527712 0.998607i \(-0.483195\pi\)
0.992599 + 0.121437i \(0.0387502\pi\)
\(312\) 0 0
\(313\) 4171.87 1518.44i 0.753380 0.274208i 0.0633524 0.997991i \(-0.479821\pi\)
0.690027 + 0.723783i \(0.257599\pi\)
\(314\) 0 0
\(315\) 918.898 1018.00i 0.164362 0.182089i
\(316\) 0 0
\(317\) −299.891 + 1700.77i −0.0531342 + 0.301339i −0.999781 0.0209343i \(-0.993336\pi\)
0.946647 + 0.322273i \(0.104447\pi\)
\(318\) 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 −0.994556 0.104204i \(-0.966771\pi\)
0.970217 + 0.242239i \(0.0778818\pi\)
\(332\) 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 −0.640693 0.767798i \(-0.721353\pi\)
0.644878 + 0.764286i \(0.276908\pi\)
\(338\) 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 −0.735154 0.677900i \(-0.762890\pi\)
0.458963 0.888455i \(-0.348221\pi\)
\(348\) 0 0
\(349\) −5099.40 4278.91i −0.782134 0.656289i 0.161651 0.986848i \(-0.448318\pi\)
−0.943785 + 0.330559i \(0.892763\pi\)
\(350\) 0 0
\(351\) 10739.6 4315.92i 1.63316 0.656316i
\(352\) 0 0
\(353\) 6159.61 + 5168.53i 0.928734 + 0.779300i 0.975590 0.219601i \(-0.0704756\pi\)
−0.0468557 + 0.998902i \(0.514920\pi\)
\(354\) 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 −0.964007 0.265877i \(-0.914338\pi\)
0.712260 + 0.701916i \(0.247672\pi\)
\(360\) 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 −0.572492 0.819910i \(-0.694023\pi\)
0.0884742 + 0.996078i \(0.471801\pi\)
\(368\) 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 0.213154 0.977019i \(-0.431626\pi\)
−0.464730 + 0.885452i \(0.653849\pi\)
\(374\) 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 −0.447402 0.894333i \(-0.647651\pi\)
−0.917596 + 0.397515i \(0.869873\pi\)
\(384\) 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 0.161367 0.986894i \(-0.448410\pi\)
0.757978 + 0.652280i \(0.226187\pi\)
\(390\) 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 −0.998942 0.0459984i \(-0.985353\pi\)
0.539307 + 0.842110i \(0.318686\pi\)
\(398\) 0 0
\(399\) −1486.53 1541.25i −0.186515 0.193381i
\(400\) 0 0
\(401\) −2014.16 11422.9i −0.250828 1.42252i −0.806558 0.591155i \(-0.798672\pi\)
0.555729 0.831363i \(-0.312439\pi\)
\(402\) 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 0.941864 + 0.335994i \(0.109072\pi\)
−0.770146 + 0.637868i \(0.779817\pi\)
\(410\) 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 −0.936169 0.351549i \(-0.885655\pi\)
0.183644 + 0.982993i \(0.441211\pi\)
\(420\) 0 0
\(421\) 4401.68 1602.08i 0.509560 0.185465i −0.0744290 0.997226i \(-0.523713\pi\)
0.583989 + 0.811762i \(0.301491\pi\)
\(422\) 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 −0.991835 0.127528i \(-0.959296\pi\)
0.975637 + 0.219391i \(0.0704070\pi\)
\(440\) 0 0
\(441\) 5932.65 + 3717.34i 0.640605 + 0.401398i
\(442\) 0 0
\(443\) 412.777 150.239i 0.0442701 0.0161130i −0.319790 0.947488i \(-0.603612\pi\)
0.364060 + 0.931375i \(0.381390\pi\)
\(444\) 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 0.934407 0.356206i \(-0.115930\pi\)
−0.775687 + 0.631117i \(0.782597\pi\)
\(450\) 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 0.887026 0.461719i \(-0.152767\pi\)
−0.300674 + 0.953727i \(0.597212\pi\)
\(458\) 0 0
\(459\) −1215.63 5771.75i −0.123618 0.586933i
\(460\) 0 0
\(461\) 4559.80 + 3826.13i 0.460675 + 0.386552i 0.843379 0.537319i \(-0.180563\pi\)
−0.382705 + 0.923871i \(0.625007\pi\)
\(462\) 0 0
\(463\) 299.450 + 1698.27i 0.0300575 + 0.170465i 0.996141 0.0877642i \(-0.0279722\pi\)
−0.966084 + 0.258229i \(0.916861\pi\)
\(464\) 0 0
\(465\) −2125.71 + 7395.97i −0.211995 + 0.737591i
\(466\) 0 0
\(467\) 7069.94 12245.5i 0.700552 1.21339i −0.267721 0.963496i \(-0.586271\pi\)
0.968273 0.249895i \(-0.0803961\pi\)
\(468\) 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 −0.954354 0.298677i \(-0.903455\pi\)
0.998953 + 0.0457434i \(0.0145656\pi\)
\(480\) 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 0.0971061 0.995274i \(-0.469041\pi\)
−0.565362 + 0.824843i \(0.691264\pi\)
\(492\) 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 −0.977169 0.212462i \(-0.931852\pi\)
0.0395506 + 0.999218i \(0.487407\pi\)
\(500\) 0 0
\(501\) −5450.75 2662.68i −0.486071 0.237445i
\(502\) 0 0
\(503\) 3966.78 + 6870.66i 0.351630 + 0.609041i 0.986535 0.163549i \(-0.0522942\pi\)
−0.634905 + 0.772590i \(0.718961\pi\)
\(504\) 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 −0.731700 0.681627i \(-0.761273\pi\)
0.454443 0.890776i \(-0.349838\pi\)
\(510\) 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 −0.964618 0.263650i \(-0.915074\pi\)
0.710637 + 0.703559i \(0.248407\pi\)
\(522\) 0 0
\(523\) 2909.21 + 5038.90i 0.243233 + 0.421292i 0.961633 0.274338i \(-0.0884586\pi\)
−0.718400 + 0.695630i \(0.755125\pi\)
\(524\) 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 −0.920812 0.390007i \(-0.872473\pi\)
0.998670 0.0515507i \(-0.0164164\pi\)
\(548\) 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 0.818902 + 0.573933i \(0.194583\pi\)
0.0875890 + 0.996157i \(0.472084\pi\)
\(558\) 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 0.989721 0.143011i \(-0.0456785\pi\)
−0.978946 + 0.204118i \(0.934567\pi\)
\(564\) 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 0.672135 0.740429i \(-0.265378\pi\)
−0.612465 + 0.790498i \(0.709822\pi\)
\(570\) 0 0
\(571\) −4496.33 25499.9i −0.329537 1.86890i −0.475661 0.879629i \(-0.657791\pi\)
0.146124 0.989266i \(-0.453320\pi\)
\(572\) 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 0.807258 0.590199i \(-0.200951\pi\)
−0.914756 + 0.404007i \(0.867617\pi\)
\(578\) 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 0.660452 + 0.750868i \(0.270365\pi\)
−0.877434 + 0.479698i \(0.840746\pi\)
\(588\) 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 0.739418 0.673247i \(-0.235101\pi\)
0.133672 + 0.991026i \(0.457323\pi\)
\(600\) 0 0
\(601\) 447.186 2536.12i 0.0303513 0.172131i −0.965864 0.259049i \(-0.916591\pi\)
0.996215 + 0.0869185i \(0.0277020\pi\)
\(602\) 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 −0.870075 0.492919i \(-0.835930\pi\)
0.334344 + 0.942451i \(0.391485\pi\)
\(608\) 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 0.0956826 + 0.995412i \(0.469497\pi\)
−0.909893 + 0.414842i \(0.863837\pi\)
\(614\) 0 0
\(615\) 7922.71 1970.15i 0.519470 0.129177i
\(616\) 0 0
\(617\) 1578.77 + 8953.67i 0.103013 + 0.584216i 0.991995 + 0.126274i \(0.0403020\pi\)
−0.888982 + 0.457942i \(0.848587\pi\)
\(618\) 0 0
\(619\) 7255.84 + 6088.37i 0.471142 + 0.395335i 0.847211 0.531257i \(-0.178280\pi\)
−0.376069 + 0.926592i \(0.622725\pi\)
\(620\) 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 0.535721 0.844395i \(-0.320040\pi\)
−0.999128 + 0.0417505i \(0.986707\pi\)
\(632\) 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 0.447351 + 0.894359i \(0.352368\pi\)
−0.726261 + 0.687419i \(0.758744\pi\)
\(642\) 0 0
\(643\) 2079.34 + 756.817i 0.127529 + 0.0464167i 0.404996 0.914318i \(-0.367273\pi\)
−0.277467 + 0.960735i \(0.589495\pi\)
\(644\) 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 −0.159469 0.987203i \(-0.550978\pi\)
−0.756722 + 0.653737i \(0.773200\pi\)
\(654\) 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 −0.625981 0.779838i \(-0.715301\pi\)
0.0217411 + 0.999764i \(0.493079\pi\)
\(660\) 0 0
\(661\) 316.290 265.399i 0.0186116 0.0156170i −0.633434 0.773796i \(-0.718355\pi\)
0.652046 + 0.758179i \(0.273911\pi\)
\(662\) 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 −0.0711564 0.997465i \(-0.522669\pi\)
−0.994668 + 0.103133i \(0.967113\pi\)
\(674\) 0 0
\(675\) 6980.91 + 11218.1i 0.398067 + 0.639679i
\(676\) 0 0
\(677\) −8328.43 6988.38i −0.472803 0.396729i 0.375013 0.927020i \(-0.377638\pi\)
−0.847816 + 0.530291i \(0.822083\pi\)
\(678\) 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 −0.634765 0.772705i \(-0.718903\pi\)
0.986565 + 0.163370i \(0.0522365\pi\)
\(684\) 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 0.162000 0.986791i \(-0.448206\pi\)
0.758396 + 0.651794i \(0.225983\pi\)
\(692\) 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 −0.744960 0.667109i \(-0.767532\pi\)
0.928198 0.372086i \(-0.121357\pi\)
\(710\) 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 0.996858 + 0.0792148i \(0.0252413\pi\)
−0.429827 + 0.902911i \(0.641425\pi\)
\(720\) 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 −0.991432 0.130623i \(-0.958302\pi\)
−0.300799 0.953688i \(-0.597253\pi\)
\(728\) 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 0.962846 + 0.270052i \(0.0870410\pi\)
−0.812416 + 0.583079i \(0.801848\pi\)
\(734\) 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 0.999745 0.0225766i \(-0.00718696\pi\)
−0.519424 + 0.854516i \(0.673854\pi\)
\(740\) 0 0
\(741\) 1335.04 + 19263.1i 0.0661859 + 0.954992i
\(742\) 0 0
\(743\) 20573.9 17263.5i 1.01586 0.852405i 0.0267555 0.999642i \(-0.491482\pi\)
0.989101 + 0.147237i \(0.0470380\pi\)
\(744\) 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 −0.432440 0.901663i \(-0.642347\pi\)
−0.910846 + 0.412746i \(0.864570\pi\)
\(752\) 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 0.624428 0.781082i \(-0.285332\pi\)
−0.0237304 + 0.999718i \(0.507554\pi\)
\(762\) 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 −0.161235 0.986916i \(-0.551548\pi\)
0.943924 + 0.330162i \(0.107103\pi\)
\(770\) 0 0
\(771\) 27819.4 18739.4i 1.29947 0.875336i
\(772\) 0 0
\(773\) −670.497 1161.34i −0.0311981 0.0540367i 0.850005 0.526775i \(-0.176599\pi\)
−0.881203 + 0.472738i \(0.843266\pi\)
\(774\) 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 0
\(783\) −13810.7 22193.3i −0.630338 1.01293i