Properties

Label 128.4.g.a.17.4
Level $128$
Weight $4$
Character 128.17
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 17.4
Character \(\chi\) \(=\) 128.17
Dual form 128.4.g.a.113.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.64064 + 3.96085i) q^{3} +(-11.8087 + 4.89132i) q^{5} +(5.11236 - 5.11236i) q^{7} +(6.09524 + 6.09524i) q^{9} +O(q^{10})\) \(q+(-1.64064 + 3.96085i) q^{3} +(-11.8087 + 4.89132i) q^{5} +(5.11236 - 5.11236i) q^{7} +(6.09524 + 6.09524i) q^{9} +(-15.2446 - 36.8038i) q^{11} +(-73.4903 - 30.4407i) q^{13} -54.7973i q^{15} -66.8708i q^{17} +(37.0353 + 15.3405i) q^{19} +(11.8618 + 28.6368i) q^{21} +(-30.1143 - 30.1143i) q^{23} +(27.1316 - 27.1316i) q^{25} +(-141.085 + 58.4395i) q^{27} +(64.4434 - 155.580i) q^{29} -219.132 q^{31} +170.785 q^{33} +(-35.3641 + 85.3765i) q^{35} +(-286.081 + 118.499i) q^{37} +(241.142 - 241.142i) q^{39} +(64.2737 + 64.2737i) q^{41} +(200.870 + 484.942i) q^{43} +(-101.791 - 42.1630i) q^{45} -392.444i q^{47} +290.727i q^{49} +(264.865 + 109.711i) q^{51} +(107.214 + 258.838i) q^{53} +(360.038 + 360.038i) q^{55} +(-121.523 + 121.523i) q^{57} +(-237.764 + 98.4852i) q^{59} +(-43.9101 + 106.008i) q^{61} +62.3222 q^{63} +1016.72 q^{65} +(333.028 - 804.000i) q^{67} +(168.685 - 69.8717i) q^{69} +(-387.445 + 387.445i) q^{71} +(-518.132 - 518.132i) q^{73} +(62.9512 + 151.978i) q^{75} +(-266.091 - 110.218i) q^{77} +214.985i q^{79} -421.957i q^{81} +(-436.657 - 180.869i) q^{83} +(327.086 + 789.656i) q^{85} +(510.501 + 510.501i) q^{87} +(-877.926 + 877.926i) q^{89} +(-531.333 + 220.085i) q^{91} +(359.517 - 867.951i) q^{93} -512.374 q^{95} +43.7563 q^{97} +(131.408 - 317.248i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 4q^{19} - 4q^{21} - 324q^{23} - 4q^{25} + 268q^{27} - 4q^{29} + 752q^{31} - 8q^{33} + 460q^{35} - 4q^{37} - 596q^{39} - 4q^{41} - 804q^{43} + 104q^{45} + 1384q^{51} + 748q^{53} + 292q^{55} - 4q^{57} - 1372q^{59} - 1828q^{61} - 2512q^{63} - 8q^{65} - 2036q^{67} - 1060q^{69} - 220q^{71} - 4q^{73} + 1712q^{75} + 1900q^{77} - 2436q^{83} + 496q^{85} + 1292q^{87} - 4q^{89} + 3604q^{91} - 112q^{93} + 6088q^{95} - 8q^{97} + 5424q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\)

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
\(3\) −1.64064 + 3.96085i −0.315741 + 0.762266i 0.683730 + 0.729735i \(0.260357\pi\)
−0.999471 + 0.0325307i \(0.989643\pi\)
\(4\) 0 0
\(5\) −11.8087 + 4.89132i −1.05620 + 0.437493i −0.842101 0.539319i \(-0.818682\pi\)
−0.214099 + 0.976812i \(0.568682\pi\)
\(6\) 0 0
\(7\) 5.11236 5.11236i 0.276042 0.276042i −0.555485 0.831527i \(-0.687467\pi\)
0.831527 + 0.555485i \(0.187467\pi\)
\(8\) 0 0
\(9\) 6.09524 + 6.09524i 0.225750 + 0.225750i
\(10\) 0 0
\(11\) −15.2446 36.8038i −0.417858 1.00880i −0.982967 0.183781i \(-0.941166\pi\)
0.565110 0.825016i \(-0.308834\pi\)
\(12\) 0 0
\(13\) −73.4903 30.4407i −1.56789 0.649440i −0.581450 0.813582i \(-0.697515\pi\)
−0.986437 + 0.164142i \(0.947515\pi\)
\(14\) 0 0
\(15\) 54.7973i 0.943240i
\(16\) 0 0
\(17\) 66.8708i 0.954033i −0.878894 0.477016i \(-0.841718\pi\)
0.878894 0.477016i \(-0.158282\pi\)
\(18\) 0 0
\(19\) 37.0353 + 15.3405i 0.447184 + 0.185230i 0.594899 0.803800i \(-0.297192\pi\)
−0.147715 + 0.989030i \(0.547192\pi\)
\(20\) 0 0
\(21\) 11.8618 + 28.6368i 0.123260 + 0.297575i
\(22\) 0 0
\(23\) −30.1143 30.1143i −0.273012 0.273012i 0.557300 0.830311i \(-0.311837\pi\)
−0.830311 + 0.557300i \(0.811837\pi\)
\(24\) 0 0
\(25\) 27.1316 27.1316i 0.217053 0.217053i
\(26\) 0 0
\(27\) −141.085 + 58.4395i −1.00563 + 0.416544i
\(28\) 0 0
\(29\) 64.4434 155.580i 0.412649 0.996224i −0.571774 0.820411i \(-0.693745\pi\)
0.984424 0.175813i \(-0.0562553\pi\)
\(30\) 0 0
\(31\) −219.132 −1.26959 −0.634796 0.772680i \(-0.718916\pi\)
−0.634796 + 0.772680i \(0.718916\pi\)
\(32\) 0 0
\(33\) 170.785 0.900907
\(34\) 0 0
\(35\) −35.3641 + 85.3765i −0.170789 + 0.412322i
\(36\) 0 0
\(37\) −286.081 + 118.499i −1.27112 + 0.526515i −0.913305 0.407277i \(-0.866478\pi\)
−0.357816 + 0.933792i \(0.616478\pi\)
\(38\) 0 0
\(39\) 241.142 241.142i 0.990092 0.990092i
\(40\) 0 0
\(41\) 64.2737 + 64.2737i 0.244826 + 0.244826i 0.818843 0.574017i \(-0.194616\pi\)
−0.574017 + 0.818843i \(0.694616\pi\)
\(42\) 0 0
\(43\) 200.870 + 484.942i 0.712380 + 1.71984i 0.693967 + 0.720006i \(0.255861\pi\)
0.0184123 + 0.999830i \(0.494139\pi\)
\(44\) 0 0
\(45\) −101.791 42.1630i −0.337201 0.139673i
\(46\) 0 0
\(47\) 392.444i 1.21795i −0.793188 0.608977i \(-0.791580\pi\)
0.793188 0.608977i \(-0.208420\pi\)
\(48\) 0 0
\(49\) 290.727i 0.847602i
\(50\) 0 0
\(51\) 264.865 + 109.711i 0.727227 + 0.301227i
\(52\) 0 0
\(53\) 107.214 + 258.838i 0.277868 + 0.670833i 0.999776 0.0211562i \(-0.00673472\pi\)
−0.721908 + 0.691989i \(0.756735\pi\)
\(54\) 0 0
\(55\) 360.038 + 360.038i 0.882683 + 0.882683i
\(56\) 0 0
\(57\) −121.523 + 121.523i −0.282388 + 0.282388i
\(58\) 0 0
\(59\) −237.764 + 98.4852i −0.524649 + 0.217317i −0.629258 0.777197i \(-0.716641\pi\)
0.104609 + 0.994513i \(0.466641\pi\)
\(60\) 0 0
\(61\) −43.9101 + 106.008i −0.0921658 + 0.222508i −0.963239 0.268645i \(-0.913424\pi\)
0.871074 + 0.491153i \(0.163424\pi\)
\(62\) 0 0
\(63\) 62.3222 0.124633
\(64\) 0 0
\(65\) 1016.72 1.94013
\(66\) 0 0
\(67\) 333.028 804.000i 0.607251 1.46603i −0.258727 0.965951i \(-0.583303\pi\)
0.865978 0.500083i \(-0.166697\pi\)
\(68\) 0 0
\(69\) 168.685 69.8717i 0.294309 0.121907i
\(70\) 0 0
\(71\) −387.445 + 387.445i −0.647624 + 0.647624i −0.952418 0.304794i \(-0.901412\pi\)
0.304794 + 0.952418i \(0.401412\pi\)
\(72\) 0 0
\(73\) −518.132 518.132i −0.830723 0.830723i 0.156892 0.987616i \(-0.449852\pi\)
−0.987616 + 0.156892i \(0.949852\pi\)
\(74\) 0 0
\(75\) 62.9512 + 151.978i 0.0969197 + 0.233985i
\(76\) 0 0
\(77\) −266.091 110.218i −0.393816 0.163124i
\(78\) 0 0
\(79\) 214.985i 0.306173i 0.988213 + 0.153086i \(0.0489213\pi\)
−0.988213 + 0.153086i \(0.951079\pi\)
\(80\) 0 0
\(81\) 421.957i 0.578816i
\(82\) 0 0
\(83\) −436.657 180.869i −0.577462 0.239193i 0.0747842 0.997200i \(-0.476173\pi\)
−0.652246 + 0.758007i \(0.726173\pi\)
\(84\) 0 0
\(85\) 327.086 + 789.656i 0.417382 + 1.00765i
\(86\) 0 0
\(87\) 510.501 + 510.501i 0.629097 + 0.629097i
\(88\) 0 0
\(89\) −877.926 + 877.926i −1.04562 + 1.04562i −0.0467087 + 0.998909i \(0.514873\pi\)
−0.998909 + 0.0467087i \(0.985127\pi\)
\(90\) 0 0
\(91\) −531.333 + 220.085i −0.612075 + 0.253530i
\(92\) 0 0
\(93\) 359.517 867.951i 0.400862 0.967767i
\(94\) 0 0
\(95\) −512.374 −0.553352
\(96\) 0 0
\(97\) 43.7563 0.0458019 0.0229009 0.999738i \(-0.492710\pi\)
0.0229009 + 0.999738i \(0.492710\pi\)
\(98\) 0 0
\(99\) 131.408 317.248i 0.133404 0.322067i
\(100\) 0 0
\(101\) 427.453 177.057i 0.421120 0.174434i −0.162052 0.986782i \(-0.551811\pi\)
0.583172 + 0.812349i \(0.301811\pi\)
\(102\) 0 0
\(103\) −570.431 + 570.431i −0.545691 + 0.545691i −0.925192 0.379500i \(-0.876096\pi\)
0.379500 + 0.925192i \(0.376096\pi\)
\(104\) 0 0
\(105\) −280.144 280.144i −0.260374 0.260374i
\(106\) 0 0
\(107\) −398.490 962.041i −0.360033 0.869196i −0.995294 0.0968989i \(-0.969108\pi\)
0.635261 0.772297i \(-0.280892\pi\)
\(108\) 0 0
\(109\) −129.224 53.5263i −0.113554 0.0470357i 0.325183 0.945651i \(-0.394574\pi\)
−0.438737 + 0.898615i \(0.644574\pi\)
\(110\) 0 0
\(111\) 1327.54i 1.13517i
\(112\) 0 0
\(113\) 772.521i 0.643121i −0.946889 0.321561i \(-0.895793\pi\)
0.946889 0.321561i \(-0.104207\pi\)
\(114\) 0 0
\(115\) 502.909 + 208.312i 0.407796 + 0.168915i
\(116\) 0 0
\(117\) −262.398 633.484i −0.207339 0.500561i
\(118\) 0 0
\(119\) −341.868 341.868i −0.263353 0.263353i
\(120\) 0 0
\(121\) −180.963 + 180.963i −0.135960 + 0.135960i
\(122\) 0 0
\(123\) −360.028 + 149.129i −0.263924 + 0.109321i
\(124\) 0 0
\(125\) 423.735 1022.99i 0.303200 0.731990i
\(126\) 0 0
\(127\) −485.865 −0.339477 −0.169738 0.985489i \(-0.554292\pi\)
−0.169738 + 0.985489i \(0.554292\pi\)
\(128\) 0 0
\(129\) −2250.34 −1.53590
\(130\) 0 0
\(131\) 764.762 1846.30i 0.510058 1.23139i −0.433792 0.901013i \(-0.642825\pi\)
0.943850 0.330375i \(-0.107175\pi\)
\(132\) 0 0
\(133\) 267.765 110.912i 0.174572 0.0723103i
\(134\) 0 0
\(135\) 1380.19 1380.19i 0.879908 0.879908i
\(136\) 0 0
\(137\) −1360.64 1360.64i −0.848519 0.848519i 0.141430 0.989948i \(-0.454830\pi\)
−0.989948 + 0.141430i \(0.954830\pi\)
\(138\) 0 0
\(139\) −76.8204 185.461i −0.0468764 0.113170i 0.898707 0.438550i \(-0.144508\pi\)
−0.945583 + 0.325380i \(0.894508\pi\)
\(140\) 0 0
\(141\) 1554.41 + 643.859i 0.928405 + 0.384558i
\(142\) 0 0
\(143\) 3168.78i 1.85305i
\(144\) 0 0
\(145\) 2152.41i 1.23274i
\(146\) 0 0
\(147\) −1151.53 476.978i −0.646098 0.267623i
\(148\) 0 0
\(149\) 687.916 + 1660.78i 0.378230 + 0.913128i 0.992298 + 0.123875i \(0.0395321\pi\)
−0.614068 + 0.789253i \(0.710468\pi\)
\(150\) 0 0
\(151\) 1133.92 + 1133.92i 0.611107 + 0.611107i 0.943235 0.332128i \(-0.107766\pi\)
−0.332128 + 0.943235i \(0.607766\pi\)
\(152\) 0 0
\(153\) 407.594 407.594i 0.215373 0.215373i
\(154\) 0 0
\(155\) 2587.67 1071.85i 1.34094 0.555437i
\(156\) 0 0
\(157\) −368.347 + 889.267i −0.187244 + 0.452046i −0.989427 0.145032i \(-0.953672\pi\)
0.802183 + 0.597078i \(0.203672\pi\)
\(158\) 0 0
\(159\) −1201.12 −0.599087
\(160\) 0 0
\(161\) −307.911 −0.150725
\(162\) 0 0
\(163\) −988.667 + 2386.85i −0.475082 + 1.14695i 0.486807 + 0.873509i \(0.338161\pi\)
−0.961889 + 0.273440i \(0.911839\pi\)
\(164\) 0 0
\(165\) −2016.75 + 835.365i −0.951538 + 0.394140i
\(166\) 0 0
\(167\) −373.791 + 373.791i −0.173202 + 0.173202i −0.788385 0.615182i \(-0.789082\pi\)
0.615182 + 0.788385i \(0.289082\pi\)
\(168\) 0 0
\(169\) 2920.67 + 2920.67i 1.32939 + 1.32939i
\(170\) 0 0
\(171\) 132.235 + 319.244i 0.0591361 + 0.142767i
\(172\) 0 0
\(173\) −71.8748 29.7715i −0.0315870 0.0130837i 0.366834 0.930286i \(-0.380442\pi\)
−0.398421 + 0.917203i \(0.630442\pi\)
\(174\) 0 0
\(175\) 277.414i 0.119831i
\(176\) 0 0
\(177\) 1103.33i 0.468538i
\(178\) 0 0
\(179\) 1660.73 + 687.899i 0.693459 + 0.287240i 0.701440 0.712728i \(-0.252541\pi\)
−0.00798155 + 0.999968i \(0.502541\pi\)
\(180\) 0 0
\(181\) −757.224 1828.10i −0.310962 0.750728i −0.999670 0.0256892i \(-0.991822\pi\)
0.688708 0.725038i \(-0.258178\pi\)
\(182\) 0 0
\(183\) −347.843 347.843i −0.140510 0.140510i
\(184\) 0 0
\(185\) 2798.63 2798.63i 1.11221 1.11221i
\(186\) 0 0
\(187\) −2461.10 + 1019.42i −0.962426 + 0.398650i
\(188\) 0 0
\(189\) −422.516 + 1020.04i −0.162611 + 0.392578i
\(190\) 0 0
\(191\) 3023.78 1.14551 0.572757 0.819725i \(-0.305874\pi\)
0.572757 + 0.819725i \(0.305874\pi\)
\(192\) 0 0
\(193\) 2155.34 0.803860 0.401930 0.915670i \(-0.368339\pi\)
0.401930 + 0.915670i \(0.368339\pi\)
\(194\) 0 0
\(195\) −1668.07 + 4027.07i −0.612578 + 1.47889i
\(196\) 0 0
\(197\) 2832.03 1173.07i 1.02423 0.424251i 0.193606 0.981079i \(-0.437982\pi\)
0.830628 + 0.556828i \(0.187982\pi\)
\(198\) 0 0
\(199\) −751.482 + 751.482i −0.267694 + 0.267694i −0.828171 0.560476i \(-0.810618\pi\)
0.560476 + 0.828171i \(0.310618\pi\)
\(200\) 0 0
\(201\) 2638.15 + 2638.15i 0.925774 + 0.925774i
\(202\) 0 0
\(203\) −465.924 1124.84i −0.161091 0.388908i
\(204\) 0 0
\(205\) −1073.37 444.605i −0.365695 0.151476i
\(206\) 0 0
\(207\) 367.108i 0.123265i
\(208\) 0 0
\(209\) 1596.90i 0.528517i
\(210\) 0 0
\(211\) 469.343 + 194.408i 0.153132 + 0.0634295i 0.457933 0.888987i \(-0.348590\pi\)
−0.304801 + 0.952416i \(0.598590\pi\)
\(212\) 0 0
\(213\) −898.956 2170.27i −0.289180 0.698143i
\(214\) 0 0
\(215\) −4744.01 4744.01i −1.50483 1.50483i
\(216\) 0 0
\(217\) −1120.29 + 1120.29i −0.350460 + 0.350460i
\(218\) 0 0
\(219\) 2902.31 1202.18i 0.895525 0.370939i
\(220\) 0 0
\(221\) −2035.59 + 4914.35i −0.619587 + 1.49582i
\(222\) 0 0
\(223\) 6411.24 1.92524 0.962619 0.270857i \(-0.0873072\pi\)
0.962619 + 0.270857i \(0.0873072\pi\)
\(224\) 0 0
\(225\) 330.748 0.0979993
\(226\) 0 0
\(227\) −139.729 + 337.336i −0.0408553 + 0.0986334i −0.942990 0.332821i \(-0.891999\pi\)
0.902135 + 0.431455i \(0.141999\pi\)
\(228\) 0 0
\(229\) −2169.11 + 898.477i −0.625935 + 0.259271i −0.673025 0.739620i \(-0.735005\pi\)
0.0470898 + 0.998891i \(0.485005\pi\)
\(230\) 0 0
\(231\) 873.117 873.117i 0.248688 0.248688i
\(232\) 0 0
\(233\) −1442.89 1442.89i −0.405696 0.405696i 0.474539 0.880235i \(-0.342615\pi\)
−0.880235 + 0.474539i \(0.842615\pi\)
\(234\) 0 0
\(235\) 1919.57 + 4634.25i 0.532846 + 1.28640i
\(236\) 0 0
\(237\) −851.522 352.712i −0.233385 0.0966713i
\(238\) 0 0
\(239\) 2049.94i 0.554811i −0.960753 0.277406i \(-0.910525\pi\)
0.960753 0.277406i \(-0.0894746\pi\)
\(240\) 0 0
\(241\) 3964.18i 1.05956i 0.848134 + 0.529782i \(0.177726\pi\)
−0.848134 + 0.529782i \(0.822274\pi\)
\(242\) 0 0
\(243\) −2138.00 885.588i −0.564414 0.233788i
\(244\) 0 0
\(245\) −1422.04 3433.11i −0.370820 0.895238i
\(246\) 0 0
\(247\) −2254.76 2254.76i −0.580838 0.580838i
\(248\) 0 0
\(249\) 1432.79 1432.79i 0.364657 0.364657i
\(250\) 0 0
\(251\) 3653.50 1513.33i 0.918754 0.380560i 0.127353 0.991858i \(-0.459352\pi\)
0.791401 + 0.611297i \(0.209352\pi\)
\(252\) 0 0
\(253\) −649.240 + 1567.41i −0.161334 + 0.389494i
\(254\) 0 0
\(255\) −3664.34 −0.899882
\(256\) 0 0
\(257\) −6137.79 −1.48975 −0.744873 0.667206i \(-0.767490\pi\)
−0.744873 + 0.667206i \(0.767490\pi\)
\(258\) 0 0
\(259\) −856.743 + 2068.36i −0.205542 + 0.496223i
\(260\) 0 0
\(261\) 1341.10 555.500i 0.318053 0.131742i
\(262\) 0 0
\(263\) −1379.24 + 1379.24i −0.323374 + 0.323374i −0.850060 0.526686i \(-0.823434\pi\)
0.526686 + 0.850060i \(0.323434\pi\)
\(264\) 0 0
\(265\) −2532.12 2532.12i −0.586969 0.586969i
\(266\) 0 0
\(267\) −2036.97 4917.69i −0.466894 1.12718i
\(268\) 0 0
\(269\) 136.201 + 56.4164i 0.0308711 + 0.0127872i 0.398066 0.917357i \(-0.369682\pi\)
−0.367194 + 0.930144i \(0.619682\pi\)
\(270\) 0 0
\(271\) 1576.16i 0.353302i −0.984274 0.176651i \(-0.943474\pi\)
0.984274 0.176651i \(-0.0565264\pi\)
\(272\) 0 0
\(273\) 2465.61i 0.546614i
\(274\) 0 0
\(275\) −1412.16 584.936i −0.309660 0.128265i
\(276\) 0 0
\(277\) −1137.39 2745.89i −0.246711 0.595613i 0.751210 0.660063i \(-0.229471\pi\)
−0.997921 + 0.0644505i \(0.979471\pi\)
\(278\) 0 0
\(279\) −1335.67 1335.67i −0.286610 0.286610i
\(280\) 0 0
\(281\) 346.910 346.910i 0.0736474 0.0736474i −0.669324 0.742971i \(-0.733416\pi\)
0.742971 + 0.669324i \(0.233416\pi\)
\(282\) 0 0
\(283\) −2926.90 + 1212.36i −0.614791 + 0.254655i −0.668275 0.743914i \(-0.732967\pi\)
0.0534844 + 0.998569i \(0.482967\pi\)
\(284\) 0 0
\(285\) 840.620 2029.44i 0.174716 0.421802i
\(286\) 0 0
\(287\) 657.181 0.135164
\(288\) 0 0
\(289\) 441.294 0.0898217
\(290\) 0 0
\(291\) −71.7883 + 173.312i −0.0144615 + 0.0349132i
\(292\) 0 0
\(293\) 551.934 228.618i 0.110049 0.0455837i −0.326980 0.945031i \(-0.606031\pi\)
0.437029 + 0.899448i \(0.356031\pi\)
\(294\) 0 0
\(295\) 2325.96 2325.96i 0.459060 0.459060i
\(296\) 0 0
\(297\) 4301.59 + 4301.59i 0.840416 + 0.840416i
\(298\) 0 0
\(299\) 1296.41 + 3129.81i 0.250747 + 0.605357i
\(300\) 0 0
\(301\) 3506.12 + 1452.28i 0.671393 + 0.278100i
\(302\) 0 0
\(303\) 1983.56i 0.376081i
\(304\) 0 0
\(305\) 1466.60i 0.275335i
\(306\) 0 0
\(307\) −3795.75 1572.25i −0.705651 0.292290i 0.000852873 1.00000i \(-0.499729\pi\)
−0.706503 + 0.707710i \(0.749729\pi\)
\(308\) 0 0
\(309\) −1323.52 3195.26i −0.243665 0.588259i
\(310\) 0 0
\(311\) 2922.48 + 2922.48i 0.532857 + 0.532857i 0.921421 0.388565i \(-0.127029\pi\)
−0.388565 + 0.921421i \(0.627029\pi\)
\(312\) 0 0
\(313\) 4410.61 4410.61i 0.796493 0.796493i −0.186048 0.982541i \(-0.559568\pi\)
0.982541 + 0.186048i \(0.0595678\pi\)
\(314\) 0 0
\(315\) −735.943 + 304.838i −0.131637 + 0.0545259i
\(316\) 0 0
\(317\) −823.383 + 1987.82i −0.145886 + 0.352199i −0.979884 0.199568i \(-0.936046\pi\)
0.833998 + 0.551767i \(0.186046\pi\)
\(318\) 0 0
\(319\) −6708.36 −1.17742
\(320\) 0 0
\(321\) 4464.28 0.776236
\(322\) 0 0
\(323\) 1025.83 2476.58i 0.176715 0.426628i
\(324\) 0 0
\(325\) −2819.82 + 1168.01i −0.481278 + 0.199352i
\(326\) 0 0
\(327\) 424.019 424.019i 0.0717074 0.0717074i
\(328\) 0 0
\(329\) −2006.32 2006.32i −0.336206 0.336206i
\(330\) 0 0
\(331\) −2294.33 5539.00i −0.380990 0.919791i −0.991775 0.127995i \(-0.959146\pi\)
0.610785 0.791797i \(-0.290854\pi\)
\(332\) 0 0
\(333\) −2466.01 1021.46i −0.405816 0.168094i
\(334\) 0 0
\(335\) 11123.1i 1.81409i
\(336\) 0 0
\(337\) 4177.18i 0.675209i 0.941288 + 0.337604i \(0.109617\pi\)
−0.941288 + 0.337604i \(0.890383\pi\)
\(338\) 0 0
\(339\) 3059.84 + 1267.43i 0.490229 + 0.203060i
\(340\) 0 0
\(341\) 3340.60 + 8064.91i 0.530509 + 1.28076i
\(342\) 0 0
\(343\) 3239.85 + 3239.85i 0.510015 + 0.510015i
\(344\) 0 0
\(345\) −1650.18 + 1650.18i −0.257516 + 0.257516i
\(346\) 0 0
\(347\) 6068.09 2513.48i 0.938767 0.388850i 0.139769 0.990184i \(-0.455364\pi\)
0.798998 + 0.601334i \(0.205364\pi\)
\(348\) 0 0
\(349\) 3219.82 7773.32i 0.493848 1.19225i −0.458899 0.888488i \(-0.651756\pi\)
0.952747 0.303765i \(-0.0982438\pi\)
\(350\) 0 0
\(351\) 12147.3 1.84723
\(352\) 0 0
\(353\) −10007.7 −1.50895 −0.754473 0.656331i \(-0.772107\pi\)
−0.754473 + 0.656331i \(0.772107\pi\)
\(354\) 0 0
\(355\) 2680.10 6470.34i 0.400690 0.967352i
\(356\) 0 0
\(357\) 1914.97 793.206i 0.283896 0.117594i
\(358\) 0 0
\(359\) −3853.86 + 3853.86i −0.566572 + 0.566572i −0.931166 0.364595i \(-0.881208\pi\)
0.364595 + 0.931166i \(0.381208\pi\)
\(360\) 0 0
\(361\) −3713.76 3713.76i −0.541443 0.541443i
\(362\) 0 0
\(363\) −419.873 1013.66i −0.0607097 0.146566i
\(364\) 0 0
\(365\) 8652.81 + 3584.11i 1.24085 + 0.513975i
\(366\) 0 0
\(367\) 2274.12i 0.323456i −0.986835 0.161728i \(-0.948293\pi\)
0.986835 0.161728i \(-0.0517067\pi\)
\(368\) 0 0
\(369\) 783.528i 0.110539i
\(370\) 0 0
\(371\) 1871.39 + 775.156i 0.261881 + 0.108475i
\(372\) 0 0
\(373\) 4974.80 + 12010.2i 0.690577 + 1.66720i 0.743615 + 0.668608i \(0.233109\pi\)
−0.0530384 + 0.998592i \(0.516891\pi\)
\(374\) 0 0
\(375\) 3356.70 + 3356.70i 0.462238 + 0.462238i
\(376\) 0 0
\(377\) −9471.92 + 9471.92i −1.29398 + 1.29398i
\(378\) 0 0
\(379\) −10078.6 + 4174.70i −1.36597 + 0.565805i −0.940694 0.339257i \(-0.889824\pi\)
−0.425280 + 0.905062i \(0.639824\pi\)
\(380\) 0 0
\(381\) 797.128 1924.44i 0.107187 0.258771i
\(382\) 0 0
\(383\) −14593.3 −1.94695 −0.973477 0.228784i \(-0.926525\pi\)
−0.973477 + 0.228784i \(0.926525\pi\)
\(384\) 0 0
\(385\) 3681.29 0.487314
\(386\) 0 0
\(387\) −1731.49 + 4180.19i −0.227433 + 0.549072i
\(388\) 0 0
\(389\) 5607.97 2322.90i 0.730939 0.302765i 0.0140014 0.999902i \(-0.495543\pi\)
0.716938 + 0.697137i \(0.245543\pi\)
\(390\) 0 0
\(391\) −2013.77 + 2013.77i −0.260462 + 0.260462i
\(392\) 0 0
\(393\) 6058.21 + 6058.21i 0.777599 + 0.777599i
\(394\) 0 0
\(395\) −1051.56 2538.69i −0.133948 0.323380i
\(396\) 0 0
\(397\) −1428.80 591.828i −0.180628 0.0748187i 0.290536 0.956864i \(-0.406166\pi\)
−0.471165 + 0.882045i \(0.656166\pi\)
\(398\) 0 0
\(399\) 1242.54i 0.155902i
\(400\) 0 0
\(401\) 7265.44i 0.904786i −0.891819 0.452393i \(-0.850571\pi\)
0.891819 0.452393i \(-0.149429\pi\)
\(402\) 0 0
\(403\) 16104.1 + 6670.54i 1.99058 + 0.824524i
\(404\) 0 0
\(405\) 2063.92 + 4982.75i 0.253228 + 0.611346i
\(406\) 0 0
\(407\) 8722.41 + 8722.41i 1.06229 + 1.06229i
\(408\) 0 0
\(409\) −7223.12 + 7223.12i −0.873252 + 0.873252i −0.992825 0.119573i \(-0.961847\pi\)
0.119573 + 0.992825i \(0.461847\pi\)
\(410\) 0 0
\(411\) 7621.59 3156.97i 0.914709 0.378885i
\(412\) 0 0
\(413\) −712.046 + 1719.03i −0.0848365 + 0.204813i
\(414\) 0 0
\(415\) 6041.03 0.714561
\(416\) 0 0
\(417\) 860.618 0.101066
\(418\) 0 0
\(419\) 3225.87 7787.95i 0.376120 0.908034i −0.616566 0.787304i \(-0.711476\pi\)
0.992685 0.120730i \(-0.0385235\pi\)
\(420\) 0 0
\(421\) 1956.30 810.327i 0.226471 0.0938074i −0.266563 0.963818i \(-0.585888\pi\)
0.493034 + 0.870010i \(0.335888\pi\)
\(422\) 0 0
\(423\) 2392.04 2392.04i 0.274953 0.274953i
\(424\) 0 0
\(425\) −1814.31 1814.31i −0.207076 0.207076i
\(426\) 0 0
\(427\) 317.469 + 766.438i 0.0359799 + 0.0868631i
\(428\) 0 0
\(429\) −12551.1 5198.82i −1.41252 0.585085i
\(430\) 0 0
\(431\) 10185.7i 1.13835i −0.822216 0.569175i \(-0.807263\pi\)
0.822216 0.569175i \(-0.192737\pi\)
\(432\) 0 0
\(433\) 4456.20i 0.494576i −0.968942 0.247288i \(-0.920461\pi\)
0.968942 0.247288i \(-0.0795394\pi\)
\(434\) 0 0
\(435\) −8525.37 3531.32i −0.939678 0.389227i
\(436\) 0 0
\(437\) −653.325 1577.27i −0.0715166 0.172656i
\(438\) 0 0
\(439\) −2494.47 2494.47i −0.271195 0.271195i 0.558386 0.829581i \(-0.311421\pi\)
−0.829581 + 0.558386i \(0.811421\pi\)
\(440\) 0 0
\(441\) −1772.05 + 1772.05i −0.191346 + 0.191346i
\(442\) 0 0
\(443\) −13843.2 + 5734.06i −1.48468 + 0.614974i −0.970151 0.242501i \(-0.922032\pi\)
−0.514526 + 0.857475i \(0.672032\pi\)
\(444\) 0 0
\(445\) 6072.93 14661.4i 0.646932 1.56183i
\(446\) 0 0
\(447\) −7706.71 −0.815469
\(448\) 0 0
\(449\) 6724.60 0.706801 0.353400 0.935472i \(-0.385025\pi\)
0.353400 + 0.935472i \(0.385025\pi\)
\(450\) 0 0
\(451\) 1385.69 3345.35i 0.144677 0.349282i
\(452\) 0 0
\(453\) −6351.64 + 2630.94i −0.658778 + 0.272875i
\(454\) 0 0
\(455\) 5197.83 5197.83i 0.535556 0.535556i
\(456\) 0 0
\(457\) −12569.7 12569.7i −1.28662 1.28662i −0.936826 0.349795i \(-0.886251\pi\)
−0.349795 0.936826i \(-0.613749\pi\)
\(458\) 0 0
\(459\) 3907.90 + 9434.49i 0.397396 + 0.959400i
\(460\) 0 0
\(461\) 5822.39 + 2411.71i 0.588234 + 0.243654i 0.656891 0.753986i \(-0.271871\pi\)
−0.0686568 + 0.997640i \(0.521871\pi\)
\(462\) 0 0
\(463\) 15045.1i 1.51016i −0.655634 0.755079i \(-0.727598\pi\)
0.655634 0.755079i \(-0.272402\pi\)
\(464\) 0 0
\(465\) 12007.9i 1.19753i
\(466\) 0 0
\(467\) −12797.5 5300.90i −1.26809 0.525260i −0.355708 0.934597i \(-0.615760\pi\)
−0.912383 + 0.409337i \(0.865760\pi\)
\(468\) 0 0
\(469\) −2407.78 5812.90i −0.237060 0.572313i
\(470\) 0 0
\(471\) −2917.93 2917.93i −0.285459 0.285459i
\(472\) 0 0
\(473\) 14785.5 14785.5i 1.43729 1.43729i
\(474\) 0 0
\(475\) 1421.04 588.616i 0.137267 0.0568580i
\(476\) 0 0
\(477\) −924.184 + 2231.18i −0.0887117 + 0.214169i
\(478\) 0 0
\(479\) −5991.54 −0.571525 −0.285762 0.958301i \(-0.592247\pi\)
−0.285762 + 0.958301i \(0.592247\pi\)
\(480\) 0 0
\(481\) 24631.4 2.33491
\(482\) 0 0
\(483\) 505.170 1219.59i 0.0475902 0.114893i
\(484\) 0 0
\(485\) −516.705 + 214.026i −0.0483760 + 0.0200380i
\(486\) 0 0
\(487\) −6120.86 + 6120.86i −0.569534 + 0.569534i −0.931998 0.362464i \(-0.881936\pi\)
0.362464 + 0.931998i \(0.381936\pi\)
\(488\) 0 0
\(489\) −7831.92 7831.92i −0.724278 0.724278i
\(490\) 0 0
\(491\) 7107.17 + 17158.2i 0.653242 + 1.57707i 0.808045 + 0.589121i \(0.200526\pi\)
−0.154803 + 0.987945i \(0.549474\pi\)
\(492\) 0 0
\(493\) −10403.8 4309.38i −0.950430 0.393681i
\(494\) 0 0
\(495\) 4389.04i 0.398531i
\(496\) 0 0
\(497\) 3961.52i 0.357543i
\(498\) 0 0
\(499\) −276.250 114.426i −0.0247828 0.0102654i 0.370258 0.928929i \(-0.379269\pi\)
−0.395040 + 0.918664i \(0.629269\pi\)
\(500\) 0 0
\(501\) −867.274 2093.78i −0.0773392 0.186713i
\(502\) 0 0
\(503\) −3966.95 3966.95i −0.351645 0.351645i 0.509076 0.860721i \(-0.329987\pi\)
−0.860721 + 0.509076i \(0.829987\pi\)
\(504\) 0 0
\(505\) −4181.61 + 4181.61i −0.368474 + 0.368474i
\(506\) 0 0
\(507\) −16360.1 + 6776.58i −1.43309 + 0.593606i
\(508\) 0 0
\(509\) −4067.11 + 9818.87i −0.354168 + 0.855037i 0.641928 + 0.766765i \(0.278135\pi\)
−0.996096 + 0.0882726i \(0.971865\pi\)
\(510\) 0 0
\(511\) −5297.76 −0.458629
\(512\) 0 0
\(513\) −6121.64 −0.526856
\(514\) 0 0
\(515\) 3945.88 9526.19i 0.337624 0.815095i
\(516\) 0 0
\(517\) −14443.4 + 5982.67i −1.22867 + 0.508931i
\(518\) 0 0
\(519\) 235.841 235.841i 0.0199466 0.0199466i
\(520\) 0 0
\(521\) 9171.85 + 9171.85i 0.771259 + 0.771259i 0.978327 0.207067i \(-0.0663919\pi\)
−0.207067 + 0.978327i \(0.566392\pi\)
\(522\) 0 0
\(523\) −6048.17 14601.6i −0.505675 1.22081i −0.946351 0.323140i \(-0.895261\pi\)
0.440676 0.897666i \(-0.354739\pi\)
\(524\) 0 0
\(525\) 1098.79 + 455.135i 0.0913434 + 0.0378357i
\(526\) 0 0
\(527\) 14653.6i 1.21123i
\(528\) 0 0
\(529\) 10353.3i 0.850929i
\(530\) 0 0
\(531\) −2049.52 848.940i −0.167499 0.0693802i
\(532\) 0 0
\(533\) −2766.96 6680.03i −0.224860 0.542860i
\(534\) 0 0
\(535\) 9411.29 + 9411.29i 0.760534 + 0.760534i
\(536\) 0 0
\(537\) −5449.33 + 5449.33i −0.437907 + 0.437907i
\(538\) 0 0
\(539\) 10699.9 4432.04i 0.855059 0.354177i
\(540\) 0 0
\(541\) 1872.33 4520.21i 0.148795 0.359222i −0.831855 0.554993i \(-0.812721\pi\)
0.980650 + 0.195771i \(0.0627210\pi\)
\(542\) 0 0
\(543\) 8483.17 0.670437
\(544\) 0 0
\(545\) 1787.78 0.140514
\(546\) 0 0
\(547\) 1131.56 2731.83i 0.0884499 0.213537i −0.873464 0.486888i \(-0.838132\pi\)
0.961914 + 0.273351i \(0.0881320\pi\)
\(548\) 0 0
\(549\) −913.789 + 378.504i −0.0710375 + 0.0294247i
\(550\) 0 0
\(551\) 4773.36 4773.36i 0.369060 0.369060i
\(552\) 0 0
\(553\) 1099.08 + 1099.08i 0.0845165 + 0.0845165i
\(554\) 0 0
\(555\) 6493.41 + 15676.5i 0.496630 + 1.19897i
\(556\) 0 0
\(557\) −4125.91 1709.01i −0.313861 0.130005i 0.220192 0.975457i \(-0.429332\pi\)
−0.534053 + 0.845451i \(0.679332\pi\)
\(558\) 0 0
\(559\) 41753.1i 3.15916i
\(560\) 0 0
\(561\) 11420.6i 0.859494i
\(562\) 0 0
\(563\) 13629.3 + 5645.44i 1.02026 + 0.422605i 0.829187 0.558971i \(-0.188804\pi\)
0.191072 + 0.981576i \(0.438804\pi\)
\(564\) 0 0
\(565\) 3778.65 + 9122.46i 0.281361 + 0.679265i
\(566\) 0 0
\(567\) −2157.20 2157.20i −0.159777 0.159777i
\(568\) 0 0
\(569\) −1198.17 + 1198.17i −0.0882777 + 0.0882777i −0.749867 0.661589i \(-0.769882\pi\)
0.661589 + 0.749867i \(0.269882\pi\)
\(570\) 0 0
\(571\) −1981.86 + 820.913i −0.145251 + 0.0601649i −0.454125 0.890938i \(-0.650048\pi\)
0.308874 + 0.951103i \(0.400048\pi\)
\(572\) 0 0
\(573\) −4960.93 + 11976.7i −0.361685 + 0.873186i
\(574\) 0 0
\(575\) −1634.10 −0.118516
\(576\) 0 0
\(577\) 1653.54 0.119303 0.0596515 0.998219i \(-0.481001\pi\)
0.0596515 + 0.998219i \(0.481001\pi\)
\(578\) 0 0
\(579\) −3536.14 + 8536.99i −0.253812 + 0.612755i
\(580\) 0 0
\(581\) −3157.02 + 1307.68i −0.225431 + 0.0933765i
\(582\) 0 0
\(583\) 7891.78 7891.78i 0.560625 0.560625i
\(584\) 0 0
\(585\) 6197.14 + 6197.14i 0.437983 + 0.437983i
\(586\) 0 0
\(587\) −5748.28 13877.6i −0.404186 0.975790i −0.986638 0.162926i \(-0.947907\pi\)
0.582453 0.812865i \(-0.302093\pi\)
\(588\) 0 0
\(589\) −8115.65 3361.61i −0.567741 0.235166i
\(590\) 0 0
\(591\) 13141.8i 0.914692i
\(592\) 0 0
\(593\) 10098.5i 0.699322i 0.936876 + 0.349661i \(0.113703\pi\)
−0.936876 + 0.349661i \(0.886297\pi\)
\(594\) 0 0
\(595\) 5709.19 + 2364.83i 0.393368 + 0.162938i
\(596\) 0 0
\(597\) −1743.60 4209.42i −0.119532 0.288576i
\(598\) 0 0
\(599\) −15005.1 15005.1i −1.02353 1.02353i −0.999716 0.0238107i \(-0.992420\pi\)
−0.0238107 0.999716i \(-0.507580\pi\)
\(600\) 0 0
\(601\) 11177.5 11177.5i 0.758632 0.758632i −0.217442 0.976073i \(-0.569771\pi\)
0.976073 + 0.217442i \(0.0697712\pi\)
\(602\) 0 0
\(603\) 6930.46 2870.69i 0.468043 0.193870i
\(604\) 0 0
\(605\) 1251.79 3022.08i 0.0841197 0.203083i
\(606\) 0 0
\(607\) 16418.5 1.09787 0.548935 0.835865i \(-0.315033\pi\)
0.548935 + 0.835865i \(0.315033\pi\)
\(608\) 0 0
\(609\) 5219.73 0.347314
\(610\) 0 0
\(611\) −11946.3 + 28840.8i −0.790989 + 1.90962i
\(612\) 0 0
\(613\) −954.545 + 395.385i −0.0628935 + 0.0260513i −0.413908 0.910319i \(-0.635837\pi\)
0.351015 + 0.936370i \(0.385837\pi\)
\(614\) 0 0
\(615\) 3522.03 3522.03i 0.230930 0.230930i
\(616\) 0 0
\(617\) 7933.23 + 7933.23i 0.517633 + 0.517633i 0.916855 0.399221i \(-0.130719\pi\)
−0.399221 + 0.916855i \(0.630719\pi\)
\(618\) 0 0
\(619\) 5475.77 + 13219.7i 0.355557 + 0.858391i 0.995913 + 0.0903128i \(0.0287867\pi\)
−0.640356 + 0.768078i \(0.721213\pi\)
\(620\) 0 0
\(621\) 6008.56 + 2488.83i 0.388269 + 0.160826i
\(622\) 0 0
\(623\) 8976.55i 0.577268i
\(624\) 0 0
\(625\) 18949.0i 1.21274i
\(626\) 0 0
\(627\) 6325.10 + 2619.94i 0.402871 + 0.166875i
\(628\) 0 0
\(629\) 7924.11 + 19130.5i 0.502313 + 1.21269i
\(630\) 0 0
\(631\) 14339.1 + 14339.1i 0.904647 + 0.904647i 0.995834 0.0911870i \(-0.0290661\pi\)
−0.0911870 + 0.995834i \(0.529066\pi\)
\(632\) 0 0
\(633\) −1540.04 + 1540.04i −0.0967002 + 0.0967002i
\(634\) 0 0
\(635\) 5737.42 2376.52i 0.358555 0.148519i
\(636\) 0 0
\(637\) 8849.94 21365.6i 0.550467 1.32894i
\(638\) 0 0
\(639\) −4723.15 −0.292402
\(640\) 0 0
\(641\) −8662.28 −0.533759 −0.266879 0.963730i \(-0.585993\pi\)
−0.266879 + 0.963730i \(0.585993\pi\)
\(642\) 0 0
\(643\) −3070.12 + 7411.92i −0.188295 + 0.454584i −0.989632 0.143630i \(-0.954123\pi\)
0.801337 + 0.598214i \(0.204123\pi\)
\(644\) 0 0
\(645\) 26573.5 11007.1i 1.62222 0.671945i
\(646\) 0 0
\(647\) −16839.6 + 16839.6i −1.02323 + 1.02323i −0.0235089 + 0.999724i \(0.507484\pi\)
−0.999724 + 0.0235089i \(0.992516\pi\)
\(648\) 0 0
\(649\) 7249.27 + 7249.27i 0.438457 + 0.438457i
\(650\) 0 0
\(651\) −2599.30 6275.26i −0.156489 0.377799i
\(652\) 0 0
\(653\) 5431.53 + 2249.81i 0.325501 + 0.134827i 0.539449 0.842018i \(-0.318632\pi\)
−0.213948 + 0.976845i \(0.568632\pi\)
\(654\) 0 0
\(655\) 25543.0i 1.52374i
\(656\) 0 0
\(657\) 6316.28i 0.375071i
\(658\) 0 0
\(659\) −6283.92 2602.88i −0.371452 0.153860i 0.189145 0.981949i \(-0.439428\pi\)
−0.560597 + 0.828089i \(0.689428\pi\)
\(660\) 0 0
\(661\) −6288.29 15181.3i −0.370024 0.893318i −0.993745 0.111671i \(-0.964380\pi\)
0.623721 0.781647i \(-0.285620\pi\)
\(662\) 0 0
\(663\) −16125.4 16125.4i −0.944580 0.944580i
\(664\) 0 0
\(665\) −2619.44 + 2619.44i −0.152748 + 0.152748i
\(666\) 0 0
\(667\) −6625.86 + 2744.52i −0.384639 + 0.159323i
\(668\) 0 0
\(669\) −10518.5 + 25394.0i −0.607877 + 1.46754i
\(670\) 0 0
\(671\) 4570.91 0.262978
\(672\) 0 0
\(673\) −22750.9 −1.30309 −0.651546 0.758609i \(-0.725879\pi\)
−0.651546 + 0.758609i \(0.725879\pi\)
\(674\) 0 0
\(675\) −2242.32 + 5413.44i −0.127862 + 0.308686i
\(676\) 0 0
\(677\) 18090.7 7493.42i 1.02701 0.425400i 0.195375 0.980729i \(-0.437408\pi\)
0.831631 + 0.555329i \(0.187408\pi\)
\(678\) 0 0
\(679\) 223.698 223.698i 0.0126432 0.0126432i
\(680\) 0 0
\(681\) −1106.89 1106.89i −0.0622852 0.0622852i
\(682\) 0 0
\(683\) −4949.33 11948.7i −0.277278 0.669408i 0.722481 0.691391i \(-0.243002\pi\)
−0.999758 + 0.0219835i \(0.993002\pi\)
\(684\) 0 0
\(685\) 22722.6 + 9412.02i 1.26743 + 0.524985i
\(686\) 0 0
\(687\) 10065.6i 0.558991i
\(688\) 0 0
\(689\) 22285.7i 1.23225i
\(690\) 0 0
\(691\) 8985.78 + 3722.03i 0.494696 + 0.204910i 0.616062 0.787698i \(-0.288727\pi\)
−0.121365 + 0.992608i \(0.538727\pi\)
\(692\) 0 0
\(693\) −950.080 2293.69i −0.0520787 0.125729i
\(694\) 0 0
\(695\) 1814.30 + 1814.30i 0.0990218 + 0.0990218i
\(696\) 0 0
\(697\) 4298.04 4298.04i 0.233572 0.233572i
\(698\) 0 0
\(699\) 8082.35 3347.82i 0.437343 0.181153i
\(700\) 0 0
\(701\) −5041.79 + 12172.0i −0.271649 + 0.655818i −0.999554 0.0298593i \(-0.990494\pi\)
0.727905 + 0.685678i \(0.240494\pi\)
\(702\) 0 0
\(703\) −12413.0 −0.665951
\(704\) 0 0
\(705\) −21504.9 −1.14882
\(706\) 0 0
\(707\) 1280.12 3090.47i 0.0680958 0.164398i
\(708\) 0 0
\(709\) −29815.3 + 12349.9i −1.57932 + 0.654176i −0.988306 0.152486i \(-0.951272\pi\)
−0.591014 + 0.806661i \(0.701272\pi\)
\(710\) 0 0
\(711\) −1310.38 + 1310.38i −0.0691185 + 0.0691185i
\(712\) 0 0
\(713\) 6599.03 + 6599.03i 0.346614 + 0.346614i
\(714\) 0 0
\(715\) −15499.5 37419.1i −0.810697 1.95720i
\(716\) 0 0
\(717\) 8119.52 + 3363.22i 0.422914 + 0.175177i
\(718\) 0 0
\(719\) 35519.5i 1.84236i 0.389141 + 0.921178i \(0.372772\pi\)
−0.389141 + 0.921178i \(0.627228\pi\)
\(720\) 0 0
\(721\) 5832.50i 0.301267i
\(722\) 0 0
\(723\) −15701.5 6503.78i −0.807670 0.334548i
\(724\) 0 0
\(725\) −2472.69 5969.60i −0.126667 0.305800i
\(726\) 0 0
\(727\) 6873.52 + 6873.52i 0.350653 + 0.350653i 0.860353 0.509699i \(-0.170243\pi\)
−0.509699 + 0.860353i \(0.670243\pi\)
\(728\) 0 0
\(729\) 15071.3 15071.3i 0.765702 0.765702i
\(730\) 0 0
\(731\) 32428.5 13432.3i 1.64078 0.679634i
\(732\) 0 0
\(733\) 6189.58 14943.0i 0.311893 0.752975i −0.687742 0.725955i \(-0.741398\pi\)
0.999635 0.0270204i \(-0.00860190\pi\)
\(734\) 0 0
\(735\) 15931.1 0.799492
\(736\) 0 0
\(737\) −34667.2 −1.73268
\(738\) 0 0
\(739\) 8349.16 20156.7i 0.415601 1.00335i −0.568007 0.823024i \(-0.692285\pi\)
0.983607 0.180325i \(-0.0577148\pi\)
\(740\) 0 0
\(741\) 12630.0 5231.53i 0.626148 0.259359i
\(742\) 0 0
\(743\) 6318.96 6318.96i 0.312006 0.312006i −0.533680 0.845686i \(-0.679191\pi\)
0.845686 + 0.533680i \(0.179191\pi\)
\(744\) 0 0
\(745\) −16246.8 16246.8i −0.798974 0.798974i
\(746\) 0 0
\(747\) −1559.09 3763.97i −0.0763642 0.184360i
\(748\) 0 0
\(749\) −6955.53 2881.07i −0.339318 0.140550i
\(750\) 0 0
\(751\) 4475.99i 0.217485i −0.994070 0.108742i \(-0.965318\pi\)
0.994070 0.108742i \(-0.0346824\pi\)
\(752\) 0 0
\(753\) 16953.8i 0.820493i
\(754\) 0 0
\(755\) −18936.5 7843.74i −0.912806 0.378097i
\(756\) 0 0
\(757\) −8674.08 20941.1i −0.416466 1.00544i −0.983363 0.181650i \(-0.941856\pi\)
0.566897 0.823788i \(-0.308144\pi\)
\(758\) 0 0
\(759\) −5143.09 5143.09i −0.245958 0.245958i
\(760\) 0 0
\(761\) −6136.35 + 6136.35i −0.292303 + 0.292303i −0.837989 0.545686i \(-0.816269\pi\)
0.545686 + 0.837989i \(0.316269\pi\)
\(762\) 0 0
\(763\) −934.286 + 386.994i −0.0443295 + 0.0183619i
\(764\) 0 0
\(765\) −2819.48 + 6806.82i −0.133253 + 0.321701i
\(766\) 0 0
\(767\) 20471.3 0.963725
\(768\) 0 0
\(769\) 13154.1 0.616838 0.308419 0.951251i \(-0.400200\pi\)
0.308419 + 0.951251i \(0.400200\pi\)
\(770\) 0 0
\(771\) 10069.9 24310.9i 0.470374 1.13558i
\(772\) 0 0
\(773\) −14475.7 + 5996.05i −0.673552 + 0.278995i −0.693129 0.720814i \(-0.743768\pi\)
0.0195763 + 0.999808i \(0.493768\pi\)
\(774\) 0 0
\(775\) −5945.42 + 5945.42i −0.275569 + 0.275569i
\(776\) 0 0
\(777\) −6786.86 6786.86i −0.313356 0.313356i
\(778\) 0 0
\(779\) 1394.41 + 3366.39i 0.0641332 + 0.154831i
\(780\) 0 0
\(781\) 20165.9 + 8353.00i 0.923936 + 0.382707i
\(782\) 0 0
\(783\) 25716.1i 1.17371i
\(784\) 0 0
\(785\) 12302.8i 0.559369i
\(786\) 0 0