Properties

Label 76.2.i.a.5.2
Level $76$
Weight $2$
Character 76.5
Analytic conductor $0.607$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 76.i (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.606863055362\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 6 x^{11} - 3 x^{10} + 70 x^{9} - 15 x^{8} - 426 x^{7} + 64 x^{6} + 1659 x^{5} + 267 x^{4} - 3969 x^{3} - 2088 x^{2} + 4446 x + 4161\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 5.2
Root \(-1.75227 - 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 76.5
Dual form 76.2.i.a.61.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.314751 - 1.78504i) q^{3} +(0.216181 + 0.181398i) q^{5} +(-0.579936 - 1.00448i) q^{7} +(-0.268219 - 0.0976237i) q^{9} +O(q^{10})\) \(q+(0.314751 - 1.78504i) q^{3} +(0.216181 + 0.181398i) q^{5} +(-0.579936 - 1.00448i) q^{7} +(-0.268219 - 0.0976237i) q^{9} +(-0.622469 + 1.07815i) q^{11} +(0.977096 + 5.54139i) q^{13} +(0.391845 - 0.328797i) q^{15} +(-6.25251 + 2.27573i) q^{17} +(3.09208 - 3.07231i) q^{19} +(-1.97557 + 0.719049i) q^{21} +(-4.65029 + 3.90205i) q^{23} +(-0.854412 - 4.84561i) q^{25} +(2.46018 - 4.26116i) q^{27} +(3.64892 + 1.32810i) q^{29} +(-0.0400606 - 0.0693870i) q^{31} +(1.72862 + 1.45048i) q^{33} +(0.0568388 - 0.322349i) q^{35} +3.71365 q^{37} +10.1991 q^{39} +(1.11697 - 6.33464i) q^{41} +(0.189407 + 0.158931i) q^{43} +(-0.0402752 - 0.0697587i) q^{45} +(-10.8939 - 3.96505i) q^{47} +(2.82735 - 4.89711i) q^{49} +(2.09428 + 11.8773i) q^{51} +(3.50255 - 2.93899i) q^{53} +(-0.330140 + 0.120161i) q^{55} +(-4.51095 - 6.48649i) q^{57} +(-9.32947 + 3.39565i) q^{59} +(-4.27534 + 3.58744i) q^{61} +(0.0574889 + 0.326036i) q^{63} +(-0.793965 + 1.37519i) q^{65} +(-3.47734 - 1.26565i) q^{67} +(5.50164 + 9.52912i) q^{69} +(7.14016 + 5.99131i) q^{71} +(0.191208 - 1.08439i) q^{73} -8.91853 q^{75} +1.44397 q^{77} +(-1.50923 + 8.55928i) q^{79} +(-7.48795 - 6.28314i) q^{81} +(5.77114 + 9.99591i) q^{83} +(-1.76449 - 0.642221i) q^{85} +(3.51920 - 6.09544i) q^{87} +(-0.418534 - 2.37362i) q^{89} +(4.99955 - 4.19512i) q^{91} +(-0.136468 + 0.0496702i) q^{93} +(1.22576 - 0.103280i) q^{95} +(-13.4638 + 4.90042i) q^{97} +(0.272211 - 0.228412i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 3q^{3} + 3q^{7} - 3q^{9} + O(q^{10}) \) \( 12q - 3q^{3} + 3q^{7} - 3q^{9} + 3q^{11} - 9q^{13} - 15q^{15} - 3q^{17} - 12q^{19} - 15q^{21} - 12q^{23} - 18q^{25} - 9q^{27} + 27q^{29} + 6q^{31} + 48q^{33} + 33q^{35} - 12q^{37} + 60q^{39} + 3q^{41} + 27q^{43} + 24q^{45} - 15q^{47} + 9q^{49} - 33q^{51} - 21q^{53} - 27q^{55} - 42q^{57} - 48q^{59} - 6q^{61} - 9q^{63} - 33q^{65} + 24q^{67} - 33q^{69} + 30q^{73} + 42q^{75} + 24q^{77} + 3q^{79} + 3q^{81} + 3q^{83} - 42q^{85} - 18q^{87} - 18q^{89} - 24q^{91} - 78q^{93} + 9q^{95} + 12q^{97} - 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\) \(1\)

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
\(3\) 0.314751 1.78504i 0.181721 1.03059i −0.748375 0.663276i \(-0.769165\pi\)
0.930096 0.367317i \(-0.119723\pi\)
\(4\) 0 0
\(5\) 0.216181 + 0.181398i 0.0966793 + 0.0811235i 0.689846 0.723956i \(-0.257678\pi\)
−0.593167 + 0.805079i \(0.702123\pi\)
\(6\) 0 0
\(7\) −0.579936 1.00448i −0.219195 0.379657i 0.735367 0.677669i \(-0.237010\pi\)
−0.954562 + 0.298012i \(0.903677\pi\)
\(8\) 0 0
\(9\) −0.268219 0.0976237i −0.0894063 0.0325412i
\(10\) 0 0
\(11\) −0.622469 + 1.07815i −0.187682 + 0.325074i −0.944477 0.328578i \(-0.893431\pi\)
0.756795 + 0.653652i \(0.226764\pi\)
\(12\) 0 0
\(13\) 0.977096 + 5.54139i 0.270998 + 1.53690i 0.751395 + 0.659853i \(0.229381\pi\)
−0.480397 + 0.877051i \(0.659508\pi\)
\(14\) 0 0
\(15\) 0.391845 0.328797i 0.101174 0.0848951i
\(16\) 0 0
\(17\) −6.25251 + 2.27573i −1.51646 + 0.551945i −0.960260 0.279106i \(-0.909962\pi\)
−0.556196 + 0.831051i \(0.687740\pi\)
\(18\) 0 0
\(19\) 3.09208 3.07231i 0.709371 0.704835i
\(20\) 0 0
\(21\) −1.97557 + 0.719049i −0.431105 + 0.156909i
\(22\) 0 0
\(23\) −4.65029 + 3.90205i −0.969652 + 0.813635i −0.982496 0.186283i \(-0.940356\pi\)
0.0128443 + 0.999918i \(0.495911\pi\)
\(24\) 0 0
\(25\) −0.854412 4.84561i −0.170882 0.969122i
\(26\) 0 0
\(27\) 2.46018 4.26116i 0.473462 0.820060i
\(28\) 0 0
\(29\) 3.64892 + 1.32810i 0.677587 + 0.246621i 0.657811 0.753183i \(-0.271483\pi\)
0.0197756 + 0.999804i \(0.493705\pi\)
\(30\) 0 0
\(31\) −0.0400606 0.0693870i −0.00719510 0.0124623i 0.862405 0.506218i \(-0.168957\pi\)
−0.869601 + 0.493756i \(0.835624\pi\)
\(32\) 0 0
\(33\) 1.72862 + 1.45048i 0.300913 + 0.252496i
\(34\) 0 0
\(35\) 0.0568388 0.322349i 0.00960751 0.0544869i
\(36\) 0 0
\(37\) 3.71365 0.610521 0.305260 0.952269i \(-0.401256\pi\)
0.305260 + 0.952269i \(0.401256\pi\)
\(38\) 0 0
\(39\) 10.1991 1.63317
\(40\) 0 0
\(41\) 1.11697 6.33464i 0.174441 0.989305i −0.764346 0.644806i \(-0.776938\pi\)
0.938787 0.344498i \(-0.111951\pi\)
\(42\) 0 0
\(43\) 0.189407 + 0.158931i 0.0288842 + 0.0242368i 0.657115 0.753790i \(-0.271776\pi\)
−0.628231 + 0.778027i \(0.716221\pi\)
\(44\) 0 0
\(45\) −0.0402752 0.0697587i −0.00600387 0.0103990i
\(46\) 0 0
\(47\) −10.8939 3.96505i −1.58904 0.578362i −0.611893 0.790940i \(-0.709592\pi\)
−0.977144 + 0.212578i \(0.931814\pi\)
\(48\) 0 0
\(49\) 2.82735 4.89711i 0.403907 0.699587i
\(50\) 0 0
\(51\) 2.09428 + 11.8773i 0.293258 + 1.66315i
\(52\) 0 0
\(53\) 3.50255 2.93899i 0.481113 0.403702i −0.369716 0.929145i \(-0.620545\pi\)
0.850829 + 0.525443i \(0.176100\pi\)
\(54\) 0 0
\(55\) −0.330140 + 0.120161i −0.0445161 + 0.0162025i
\(56\) 0 0
\(57\) −4.51095 6.48649i −0.597490 0.859156i
\(58\) 0 0
\(59\) −9.32947 + 3.39565i −1.21459 + 0.442076i −0.868295 0.496049i \(-0.834784\pi\)
−0.346298 + 0.938124i \(0.612562\pi\)
\(60\) 0 0
\(61\) −4.27534 + 3.58744i −0.547401 + 0.459324i −0.874060 0.485818i \(-0.838522\pi\)
0.326659 + 0.945142i \(0.394077\pi\)
\(62\) 0 0
\(63\) 0.0574889 + 0.326036i 0.00724292 + 0.0410766i
\(64\) 0 0
\(65\) −0.793965 + 1.37519i −0.0984792 + 0.170571i
\(66\) 0 0
\(67\) −3.47734 1.26565i −0.424824 0.154623i 0.120756 0.992682i \(-0.461468\pi\)
−0.545580 + 0.838059i \(0.683691\pi\)
\(68\) 0 0
\(69\) 5.50164 + 9.52912i 0.662319 + 1.14717i
\(70\) 0 0
\(71\) 7.14016 + 5.99131i 0.847382 + 0.711038i 0.959211 0.282690i \(-0.0912267\pi\)
−0.111830 + 0.993727i \(0.535671\pi\)
\(72\) 0 0
\(73\) 0.191208 1.08439i 0.0223792 0.126919i −0.971571 0.236747i \(-0.923919\pi\)
0.993951 + 0.109828i \(0.0350300\pi\)
\(74\) 0 0
\(75\) −8.91853 −1.02982
\(76\) 0 0
\(77\) 1.44397 0.164556
\(78\) 0 0
\(79\) −1.50923 + 8.55928i −0.169802 + 0.962994i 0.774172 + 0.632975i \(0.218166\pi\)
−0.943974 + 0.330019i \(0.892945\pi\)
\(80\) 0 0
\(81\) −7.48795 6.28314i −0.831995 0.698126i
\(82\) 0 0
\(83\) 5.77114 + 9.99591i 0.633465 + 1.09719i 0.986838 + 0.161711i \(0.0517014\pi\)
−0.353373 + 0.935483i \(0.614965\pi\)
\(84\) 0 0
\(85\) −1.76449 0.642221i −0.191386 0.0696587i
\(86\) 0 0
\(87\) 3.51920 6.09544i 0.377298 0.653500i
\(88\) 0 0
\(89\) −0.418534 2.37362i −0.0443645 0.251603i 0.954557 0.298027i \(-0.0963286\pi\)
−0.998922 + 0.0464239i \(0.985218\pi\)
\(90\) 0 0
\(91\) 4.99955 4.19512i 0.524095 0.439768i
\(92\) 0 0
\(93\) −0.136468 + 0.0496702i −0.0141510 + 0.00515056i
\(94\) 0 0
\(95\) 1.22576 0.103280i 0.125760 0.0105963i
\(96\) 0 0
\(97\) −13.4638 + 4.90042i −1.36704 + 0.497562i −0.918224 0.396062i \(-0.870376\pi\)
−0.448816 + 0.893624i \(0.648154\pi\)
\(98\) 0 0
\(99\) 0.272211 0.228412i 0.0273582 0.0229563i
\(100\) 0 0
\(101\) −2.97288 16.8600i −0.295813 1.67764i −0.663881 0.747838i \(-0.731092\pi\)
0.368068 0.929799i \(-0.380019\pi\)
\(102\) 0 0
\(103\) 6.64081 11.5022i 0.654339 1.13335i −0.327720 0.944775i \(-0.606280\pi\)
0.982059 0.188573i \(-0.0603863\pi\)
\(104\) 0 0
\(105\) −0.557515 0.202919i −0.0544079 0.0198029i
\(106\) 0 0
\(107\) −0.494870 0.857140i −0.0478409 0.0828628i 0.841113 0.540859i \(-0.181901\pi\)
−0.888954 + 0.457996i \(0.848567\pi\)
\(108\) 0 0
\(109\) 10.3519 + 8.68625i 0.991529 + 0.831991i 0.985788 0.167992i \(-0.0537283\pi\)
0.00574045 + 0.999984i \(0.498173\pi\)
\(110\) 0 0
\(111\) 1.16887 6.62902i 0.110945 0.629198i
\(112\) 0 0
\(113\) 16.5369 1.55566 0.777829 0.628476i \(-0.216321\pi\)
0.777829 + 0.628476i \(0.216321\pi\)
\(114\) 0 0
\(115\) −1.71313 −0.159750
\(116\) 0 0
\(117\) 0.278895 1.58169i 0.0257838 0.146227i
\(118\) 0 0
\(119\) 5.91198 + 4.96074i 0.541950 + 0.454750i
\(120\) 0 0
\(121\) 4.72506 + 8.18405i 0.429551 + 0.744005i
\(122\) 0 0
\(123\) −10.9560 3.98766i −0.987871 0.359555i
\(124\) 0 0
\(125\) 1.39979 2.42450i 0.125201 0.216854i
\(126\) 0 0
\(127\) −0.388935 2.20576i −0.0345124 0.195729i 0.962677 0.270653i \(-0.0872397\pi\)
−0.997189 + 0.0749239i \(0.976129\pi\)
\(128\) 0 0
\(129\) 0.343314 0.288075i 0.0302271 0.0253636i
\(130\) 0 0
\(131\) 16.5173 6.01181i 1.44313 0.525255i 0.502463 0.864599i \(-0.332427\pi\)
0.940662 + 0.339344i \(0.110205\pi\)
\(132\) 0 0
\(133\) −4.87927 1.32418i −0.423087 0.114821i
\(134\) 0 0
\(135\) 1.30481 0.474912i 0.112300 0.0408739i
\(136\) 0 0
\(137\) 4.36728 3.66458i 0.373122 0.313086i −0.436873 0.899523i \(-0.643914\pi\)
0.809995 + 0.586437i \(0.199470\pi\)
\(138\) 0 0
\(139\) 0.891090 + 5.05362i 0.0755813 + 0.428643i 0.998994 + 0.0448352i \(0.0142763\pi\)
−0.923413 + 0.383808i \(0.874613\pi\)
\(140\) 0 0
\(141\) −10.5066 + 18.1980i −0.884818 + 1.53255i
\(142\) 0 0
\(143\) −6.58265 2.39589i −0.550469 0.200354i
\(144\) 0 0
\(145\) 0.547914 + 0.949015i 0.0455018 + 0.0788114i
\(146\) 0 0
\(147\) −7.85162 6.58829i −0.647591 0.543393i
\(148\) 0 0
\(149\) −2.06723 + 11.7238i −0.169354 + 0.960454i 0.775107 + 0.631830i \(0.217696\pi\)
−0.944461 + 0.328624i \(0.893415\pi\)
\(150\) 0 0
\(151\) −14.8628 −1.20952 −0.604759 0.796409i \(-0.706731\pi\)
−0.604759 + 0.796409i \(0.706731\pi\)
\(152\) 0 0
\(153\) 1.89921 0.153542
\(154\) 0 0
\(155\) 0.00392629 0.0222671i 0.000315367 0.00178854i
\(156\) 0 0
\(157\) −8.45258 7.09255i −0.674589 0.566047i 0.239831 0.970815i \(-0.422908\pi\)
−0.914420 + 0.404767i \(0.867353\pi\)
\(158\) 0 0
\(159\) −4.14379 7.17725i −0.328624 0.569193i
\(160\) 0 0
\(161\) 6.61640 + 2.40817i 0.521446 + 0.189791i
\(162\) 0 0
\(163\) −1.99237 + 3.45089i −0.156055 + 0.270295i −0.933443 0.358727i \(-0.883211\pi\)
0.777388 + 0.629021i \(0.216544\pi\)
\(164\) 0 0
\(165\) 0.110581 + 0.627134i 0.00860869 + 0.0488223i
\(166\) 0 0
\(167\) −6.19785 + 5.20061i −0.479604 + 0.402436i −0.850283 0.526325i \(-0.823569\pi\)
0.370679 + 0.928761i \(0.379125\pi\)
\(168\) 0 0
\(169\) −17.5362 + 6.38267i −1.34894 + 0.490974i
\(170\) 0 0
\(171\) −1.12928 + 0.522190i −0.0863584 + 0.0399329i
\(172\) 0 0
\(173\) 6.13327 2.23233i 0.466304 0.169721i −0.0981735 0.995169i \(-0.531300\pi\)
0.564477 + 0.825449i \(0.309078\pi\)
\(174\) 0 0
\(175\) −4.37181 + 3.66838i −0.330478 + 0.277304i
\(176\) 0 0
\(177\) 3.12491 + 17.7222i 0.234883 + 1.33209i
\(178\) 0 0
\(179\) 4.91617 8.51506i 0.367452 0.636445i −0.621715 0.783244i \(-0.713564\pi\)
0.989166 + 0.146799i \(0.0468969\pi\)
\(180\) 0 0
\(181\) 12.9463 + 4.71208i 0.962293 + 0.350246i 0.774932 0.632045i \(-0.217784\pi\)
0.187361 + 0.982291i \(0.440007\pi\)
\(182\) 0 0
\(183\) 5.05805 + 8.76080i 0.373902 + 0.647617i
\(184\) 0 0
\(185\) 0.802823 + 0.673648i 0.0590247 + 0.0495276i
\(186\) 0 0
\(187\) 1.43842 8.15771i 0.105188 0.596551i
\(188\) 0 0
\(189\) −5.70699 −0.415123
\(190\) 0 0
\(191\) 1.03137 0.0746275 0.0373137 0.999304i \(-0.488120\pi\)
0.0373137 + 0.999304i \(0.488120\pi\)
\(192\) 0 0
\(193\) −0.407183 + 2.30925i −0.0293097 + 0.166224i −0.995949 0.0899169i \(-0.971340\pi\)
0.966640 + 0.256140i \(0.0824510\pi\)
\(194\) 0 0
\(195\) 2.20486 + 1.85010i 0.157893 + 0.132488i
\(196\) 0 0
\(197\) −7.78406 13.4824i −0.554592 0.960581i −0.997935 0.0642291i \(-0.979541\pi\)
0.443344 0.896352i \(-0.353792\pi\)
\(198\) 0 0
\(199\) 12.8701 + 4.68434i 0.912339 + 0.332064i 0.755186 0.655510i \(-0.227546\pi\)
0.157153 + 0.987574i \(0.449769\pi\)
\(200\) 0 0
\(201\) −3.35372 + 5.80882i −0.236553 + 0.409722i
\(202\) 0 0
\(203\) −0.782093 4.43547i −0.0548922 0.311309i
\(204\) 0 0
\(205\) 1.39056 1.16682i 0.0971207 0.0814940i
\(206\) 0 0
\(207\) 1.62823 0.592626i 0.113170 0.0411904i
\(208\) 0 0
\(209\) 1.38768 + 5.24614i 0.0959878 + 0.362883i
\(210\) 0 0
\(211\) 20.2595 7.37386i 1.39472 0.507638i 0.468116 0.883667i \(-0.344933\pi\)
0.926608 + 0.376030i \(0.122711\pi\)
\(212\) 0 0
\(213\) 12.9421 10.8597i 0.886778 0.744095i
\(214\) 0 0
\(215\) 0.0121165 + 0.0687159i 0.000826336 + 0.00468638i
\(216\) 0 0
\(217\) −0.0464652 + 0.0804801i −0.00315426 + 0.00546335i
\(218\) 0 0
\(219\) −1.87550 0.682627i −0.126735 0.0461276i
\(220\) 0 0
\(221\) −18.7200 32.4240i −1.25924 2.18107i
\(222\) 0 0
\(223\) −19.9848 16.7693i −1.33828 1.12295i −0.982063 0.188551i \(-0.939621\pi\)
−0.356220 0.934402i \(-0.615935\pi\)
\(224\) 0 0
\(225\) −0.243877 + 1.38309i −0.0162585 + 0.0922063i
\(226\) 0 0
\(227\) 21.7357 1.44265 0.721325 0.692596i \(-0.243533\pi\)
0.721325 + 0.692596i \(0.243533\pi\)
\(228\) 0 0
\(229\) −20.1255 −1.32993 −0.664964 0.746875i \(-0.731553\pi\)
−0.664964 + 0.746875i \(0.731553\pi\)
\(230\) 0 0
\(231\) 0.454491 2.57754i 0.0299033 0.169590i
\(232\) 0 0
\(233\) 16.8667 + 14.1529i 1.10498 + 0.927184i 0.997750 0.0670504i \(-0.0213588\pi\)
0.107226 + 0.994235i \(0.465803\pi\)
\(234\) 0 0
\(235\) −1.63581 2.83330i −0.106708 0.184824i
\(236\) 0 0
\(237\) 14.8036 + 5.38808i 0.961598 + 0.349993i
\(238\) 0 0
\(239\) −2.18637 + 3.78691i −0.141425 + 0.244955i −0.928033 0.372497i \(-0.878502\pi\)
0.786609 + 0.617452i \(0.211835\pi\)
\(240\) 0 0
\(241\) −2.60506 14.7740i −0.167807 0.951679i −0.946123 0.323807i \(-0.895037\pi\)
0.778317 0.627872i \(-0.216074\pi\)
\(242\) 0 0
\(243\) −2.26484 + 1.90042i −0.145289 + 0.121912i
\(244\) 0 0
\(245\) 1.49954 0.545790i 0.0958024 0.0348692i
\(246\) 0 0
\(247\) 20.0461 + 14.1325i 1.27550 + 0.899226i
\(248\) 0 0
\(249\) 19.6596 7.15550i 1.24587 0.453461i
\(250\) 0 0
\(251\) −17.9754 + 15.0832i −1.13460 + 0.952042i −0.999249 0.0387556i \(-0.987661\pi\)
−0.135351 + 0.990798i \(0.543216\pi\)
\(252\) 0 0
\(253\) −1.31233 7.44261i −0.0825057 0.467913i
\(254\) 0 0
\(255\) −1.70176 + 2.94754i −0.106569 + 0.184582i
\(256\) 0 0
\(257\) −0.0996901 0.0362842i −0.00621850 0.00226335i 0.338909 0.940819i \(-0.389942\pi\)
−0.345128 + 0.938556i \(0.612164\pi\)
\(258\) 0 0
\(259\) −2.15368 3.73029i −0.133823 0.231789i
\(260\) 0 0
\(261\) −0.849054 0.712441i −0.0525551 0.0440990i
\(262\) 0 0
\(263\) −2.70397 + 15.3350i −0.166734 + 0.945594i 0.780525 + 0.625124i \(0.214952\pi\)
−0.947259 + 0.320469i \(0.896159\pi\)
\(264\) 0 0
\(265\) 1.29031 0.0792633
\(266\) 0 0
\(267\) −4.36874 −0.267363
\(268\) 0 0
\(269\) 2.43886 13.8315i 0.148700 0.843321i −0.815621 0.578586i \(-0.803605\pi\)
0.964321 0.264734i \(-0.0852843\pi\)
\(270\) 0 0
\(271\) 8.77391 + 7.36218i 0.532977 + 0.447221i 0.869128 0.494587i \(-0.164681\pi\)
−0.336151 + 0.941808i \(0.609125\pi\)
\(272\) 0 0
\(273\) −5.91485 10.2448i −0.357983 0.620044i
\(274\) 0 0
\(275\) 5.75613 + 2.09506i 0.347108 + 0.126337i
\(276\) 0 0
\(277\) −12.8642 + 22.2814i −0.772932 + 1.33876i 0.163017 + 0.986623i \(0.447878\pi\)
−0.935949 + 0.352135i \(0.885456\pi\)
\(278\) 0 0
\(279\) 0.00397120 + 0.0225218i 0.000237749 + 0.00134834i
\(280\) 0 0
\(281\) −20.6252 + 17.3066i −1.23039 + 1.03242i −0.232181 + 0.972673i \(0.574586\pi\)
−0.998213 + 0.0597510i \(0.980969\pi\)
\(282\) 0 0
\(283\) −2.78007 + 1.01186i −0.165258 + 0.0601491i −0.423324 0.905978i \(-0.639137\pi\)
0.258066 + 0.966127i \(0.416915\pi\)
\(284\) 0 0
\(285\) 0.201450 2.22053i 0.0119329 0.131533i
\(286\) 0 0
\(287\) −7.01078 + 2.55172i −0.413834 + 0.150623i
\(288\) 0 0
\(289\) 20.8922 17.5306i 1.22895 1.03121i
\(290\) 0 0
\(291\) 4.50970 + 25.5758i 0.264363 + 1.49928i
\(292\) 0 0
\(293\) −5.01204 + 8.68111i −0.292807 + 0.507156i −0.974472 0.224508i \(-0.927923\pi\)
0.681666 + 0.731664i \(0.261256\pi\)
\(294\) 0 0
\(295\) −2.63282 0.958268i −0.153289 0.0557925i
\(296\) 0 0
\(297\) 3.06277 + 5.30488i 0.177720 + 0.307820i
\(298\) 0 0
\(299\) −26.1666 21.9564i −1.51325 1.26977i
\(300\) 0 0
\(301\) 0.0497991 0.282425i 0.00287037 0.0162787i
\(302\) 0 0
\(303\) −31.0316 −1.78272
\(304\) 0 0
\(305\) −1.57500 −0.0901844
\(306\) 0 0
\(307\) −2.87822 + 16.3232i −0.164269 + 0.931614i 0.785547 + 0.618802i \(0.212382\pi\)
−0.949815 + 0.312811i \(0.898729\pi\)
\(308\) 0 0
\(309\) −18.4417 15.4744i −1.04911 0.880310i
\(310\) 0 0
\(311\) −0.215620 0.373465i −0.0122267 0.0211772i 0.859847 0.510551i \(-0.170559\pi\)
−0.872074 + 0.489374i \(0.837225\pi\)
\(312\) 0 0
\(313\) 13.0841 + 4.76223i 0.739557 + 0.269177i 0.684205 0.729290i \(-0.260149\pi\)
0.0553527 + 0.998467i \(0.482372\pi\)
\(314\) 0 0
\(315\) −0.0467141 + 0.0809112i −0.00263204 + 0.00455883i
\(316\) 0 0
\(317\) −2.87712 16.3170i −0.161595 0.916452i −0.952506 0.304521i \(-0.901504\pi\)
0.790911 0.611932i \(-0.209607\pi\)
\(318\) 0 0
\(319\) −3.70322 + 3.10737i −0.207341 + 0.173980i
\(320\) 0 0
\(321\) −1.68579 + 0.613577i −0.0940915 + 0.0342465i
\(322\) 0 0
\(323\) −12.3415 + 26.2463i −0.686700 + 1.46039i
\(324\) 0 0
\(325\) 26.0165 9.46925i 1.44314 0.525259i
\(326\) 0 0
\(327\) 18.7635 15.7445i 1.03763 0.870672i
\(328\) 0 0
\(329\) 2.33495 + 13.2422i 0.128730 + 0.730064i
\(330\) 0 0
\(331\) −4.74773 + 8.22332i −0.260959 + 0.451994i −0.966497 0.256678i \(-0.917372\pi\)
0.705538 + 0.708672i \(0.250705\pi\)
\(332\) 0 0
\(333\) −0.996072 0.362540i −0.0545844 0.0198671i
\(334\) 0 0
\(335\) −0.522150 0.904390i −0.0285281 0.0494121i
\(336\) 0 0
\(337\) 9.65934 + 8.10515i 0.526178 + 0.441515i 0.866779 0.498692i \(-0.166186\pi\)
−0.340601 + 0.940208i \(0.610631\pi\)
\(338\) 0 0
\(339\) 5.20499 29.5190i 0.282696 1.60325i
\(340\) 0 0
\(341\) 0.0997461 0.00540155
\(342\) 0 0
\(343\) −14.6778 −0.792529
\(344\) 0 0
\(345\) −0.539208 + 3.05800i −0.0290300 + 0.164637i
\(346\) 0 0
\(347\) 8.36688 + 7.02065i 0.449158 + 0.376888i 0.839123 0.543941i \(-0.183069\pi\)
−0.389965 + 0.920830i \(0.627513\pi\)
\(348\) 0 0
\(349\) −4.20032 7.27517i −0.224838 0.389431i 0.731433 0.681913i \(-0.238852\pi\)
−0.956271 + 0.292483i \(0.905519\pi\)
\(350\) 0 0
\(351\) 26.0165 + 9.46925i 1.38866 + 0.505431i
\(352\) 0 0
\(353\) −6.69379 + 11.5940i −0.356274 + 0.617086i −0.987335 0.158648i \(-0.949287\pi\)
0.631061 + 0.775733i \(0.282620\pi\)
\(354\) 0 0
\(355\) 0.456761 + 2.59042i 0.0242423 + 0.137485i
\(356\) 0 0
\(357\) 10.7159 8.99172i 0.567146 0.475892i
\(358\) 0 0
\(359\) 26.6099 9.68521i 1.40442 0.511166i 0.474931 0.880023i \(-0.342473\pi\)
0.929486 + 0.368857i \(0.120251\pi\)
\(360\) 0 0
\(361\) 0.121876 18.9996i 0.00641452 0.999979i
\(362\) 0 0
\(363\) 16.0961 5.85849i 0.844824 0.307491i
\(364\) 0 0
\(365\) 0.238042 0.199741i 0.0124597 0.0104549i
\(366\) 0 0
\(367\) 0.0720091 + 0.408384i 0.00375884 + 0.0213175i 0.986629 0.162979i \(-0.0521104\pi\)
−0.982871 + 0.184297i \(0.940999\pi\)
\(368\) 0 0
\(369\) −0.918003 + 1.59003i −0.0477893 + 0.0827735i
\(370\) 0 0
\(371\) −4.98342 1.81381i −0.258726 0.0941686i
\(372\) 0 0
\(373\) 2.01032 + 3.48198i 0.104090 + 0.180290i 0.913366 0.407139i \(-0.133474\pi\)
−0.809276 + 0.587429i \(0.800140\pi\)
\(374\) 0 0
\(375\) −3.88725 3.26179i −0.200737 0.168438i
\(376\) 0 0
\(377\) −3.79416 + 21.5177i −0.195409 + 1.10822i
\(378\) 0 0
\(379\) 14.1791 0.728332 0.364166 0.931334i \(-0.381354\pi\)
0.364166 + 0.931334i \(0.381354\pi\)
\(380\) 0 0
\(381\) −4.05978 −0.207989
\(382\) 0 0
\(383\) 1.88738 10.7039i 0.0964407 0.546943i −0.897856 0.440290i \(-0.854876\pi\)
0.994296 0.106653i \(-0.0340133\pi\)
\(384\) 0 0
\(385\) 0.312160 + 0.261933i 0.0159091 + 0.0133493i
\(386\) 0 0
\(387\) −0.0352870 0.0611189i −0.00179374 0.00310685i
\(388\) 0 0
\(389\) −24.0167 8.74136i −1.21769 0.443205i −0.348328 0.937373i \(-0.613251\pi\)
−0.869367 + 0.494168i \(0.835473\pi\)
\(390\) 0 0
\(391\) 20.1960 34.9804i 1.02135 1.76904i
\(392\) 0 0
\(393\) −5.53249 31.3763i −0.279077 1.58272i
\(394\) 0 0
\(395\) −1.87890 + 1.57659i −0.0945378 + 0.0793267i
\(396\) 0 0
\(397\) 16.1594 5.88155i 0.811018 0.295186i 0.0969735 0.995287i \(-0.469084\pi\)
0.714044 + 0.700101i \(0.246862\pi\)
\(398\) 0 0
\(399\) −3.89948 + 8.29291i −0.195218 + 0.415165i
\(400\) 0 0
\(401\) −14.4376 + 5.25485i −0.720979 + 0.262415i −0.676341 0.736588i \(-0.736436\pi\)
−0.0446377 + 0.999003i \(0.514213\pi\)
\(402\) 0 0
\(403\) 0.345357 0.289789i 0.0172035 0.0144354i
\(404\) 0 0
\(405\) −0.479009 2.71659i −0.0238021 0.134989i
\(406\) 0 0
\(407\) −2.31164 + 4.00387i −0.114584 + 0.198465i
\(408\) 0 0
\(409\) −13.4638 4.90042i −0.665741 0.242310i −0.0130280 0.999915i \(-0.504147\pi\)
−0.652713 + 0.757605i \(0.726369\pi\)
\(410\) 0 0
\(411\) −5.16682 8.94920i −0.254860 0.441431i
\(412\) 0 0
\(413\) 8.82135 + 7.40200i 0.434070 + 0.364228i
\(414\) 0 0
\(415\) −0.565622 + 3.20780i −0.0277653 + 0.157465i
\(416\) 0 0
\(417\) 9.30139 0.455491
\(418\) 0 0
\(419\) −17.2723 −0.843805 −0.421902 0.906641i \(-0.638637\pi\)
−0.421902 + 0.906641i \(0.638637\pi\)
\(420\) 0 0
\(421\) −4.83458 + 27.4183i −0.235623 + 1.33629i 0.605674 + 0.795713i \(0.292903\pi\)
−0.841297 + 0.540573i \(0.818208\pi\)
\(422\) 0 0
\(423\) 2.53486 + 2.12700i 0.123249 + 0.103418i
\(424\) 0 0
\(425\) 16.3695 + 28.3528i 0.794038 + 1.37531i
\(426\) 0 0
\(427\) 6.08293 + 2.21401i 0.294374 + 0.107143i
\(428\) 0 0
\(429\) −6.34865 + 10.9962i −0.306516 + 0.530901i
\(430\) 0 0
\(431\) −6.57872 37.3098i −0.316886 1.79715i −0.561444 0.827515i \(-0.689754\pi\)
0.244558 0.969635i \(-0.421357\pi\)
\(432\) 0 0
\(433\) 5.76405 4.83661i 0.277003 0.232433i −0.493693 0.869636i \(-0.664353\pi\)
0.770696 + 0.637204i \(0.219909\pi\)
\(434\) 0 0
\(435\) 1.86648 0.679345i 0.0894911 0.0325721i
\(436\) 0 0
\(437\) −2.39074 + 26.3526i −0.114365 + 1.26061i
\(438\) 0 0
\(439\) −19.9813 + 7.27259i −0.953655 + 0.347102i −0.771544 0.636176i \(-0.780515\pi\)
−0.182111 + 0.983278i \(0.558293\pi\)
\(440\) 0 0
\(441\) −1.23642 + 1.03748i −0.0588772 + 0.0494039i
\(442\) 0 0
\(443\) −2.59412 14.7120i −0.123250 0.698988i −0.982332 0.187149i \(-0.940075\pi\)
0.859081 0.511839i \(-0.171036\pi\)
\(444\) 0 0
\(445\) 0.340090 0.589054i 0.0161218 0.0279238i
\(446\) 0 0
\(447\) 20.2768 + 7.38017i 0.959062 + 0.349070i
\(448\) 0 0
\(449\) −8.47286 14.6754i −0.399859 0.692576i 0.593849 0.804576i \(-0.297608\pi\)
−0.993708 + 0.112000i \(0.964274\pi\)
\(450\) 0 0
\(451\) 6.13441 + 5.14738i 0.288858 + 0.242381i
\(452\) 0 0
\(453\) −4.67808 + 26.5307i −0.219795 + 1.24652i
\(454\) 0 0
\(455\) 1.84180 0.0863447
\(456\) 0 0
\(457\) −10.2922 −0.481448 −0.240724 0.970594i \(-0.577385\pi\)
−0.240724 + 0.970594i \(0.577385\pi\)
\(458\) 0 0
\(459\) −5.68507 + 32.2416i −0.265356 + 1.50491i
\(460\) 0 0
\(461\) 4.59397 + 3.85480i 0.213962 + 0.179536i 0.743470 0.668770i \(-0.233179\pi\)
−0.529507 + 0.848305i \(0.677623\pi\)
\(462\) 0 0
\(463\) −1.69033 2.92774i −0.0785563 0.136063i 0.824071 0.566487i \(-0.191698\pi\)
−0.902627 + 0.430423i \(0.858364\pi\)
\(464\) 0 0
\(465\) −0.0385118 0.0140172i −0.00178594 0.000650030i
\(466\) 0 0
\(467\) −1.03045 + 1.78480i −0.0476837 + 0.0825906i −0.888882 0.458136i \(-0.848517\pi\)
0.841198 + 0.540727i \(0.181851\pi\)
\(468\) 0 0
\(469\) 0.745318 + 4.22691i 0.0344156 + 0.195180i
\(470\) 0 0
\(471\) −15.3209 + 12.8558i −0.705952 + 0.592364i
\(472\) 0 0
\(473\) −0.289251 + 0.105279i −0.0132998 + 0.00484073i
\(474\) 0 0
\(475\) −17.5291 12.3580i −0.804290 0.567023i
\(476\) 0 0
\(477\) −1.22637 + 0.446361i −0.0561515 + 0.0204375i
\(478\) 0 0
\(479\) −4.53663 + 3.80668i −0.207284 + 0.173932i −0.740519 0.672035i \(-0.765420\pi\)
0.533235 + 0.845967i \(0.320976\pi\)
\(480\) 0 0
\(481\) 3.62860 + 20.5788i 0.165450 + 0.938312i
\(482\) 0 0
\(483\) 6.38120 11.0526i 0.290355 0.502909i
\(484\) 0 0
\(485\) −3.79954 1.38292i −0.172528 0.0627952i
\(486\) 0 0
\(487\) 13.3232 + 23.0764i 0.603731 + 1.04569i 0.992251 + 0.124252i \(0.0396532\pi\)
−0.388520 + 0.921440i \(0.627013\pi\)
\(488\) 0 0
\(489\) 5.53287 + 4.64263i 0.250205 + 0.209947i
\(490\) 0 0
\(491\) 6.15100 34.8841i 0.277591 1.57430i −0.453019 0.891501i \(-0.649653\pi\)
0.730610 0.682795i \(-0.239236\pi\)
\(492\) 0 0
\(493\) −25.8373 −1.16365
\(494\) 0 0
\(495\) 0.100280 0.00450727
\(496\) 0 0
\(497\) 1.87730 10.6467i 0.0842086 0.477571i
\(498\) 0 0
\(499\) −26.5322 22.2631i −1.18774 0.996634i −0.999896 0.0144356i \(-0.995405\pi\)
−0.187846 0.982198i \(-0.560151\pi\)
\(500\) 0 0
\(501\) 7.33252 + 12.7003i 0.327593 + 0.567408i
\(502\) 0 0
\(503\) −29.0173 10.5614i −1.29382 0.470912i −0.398840 0.917020i \(-0.630587\pi\)
−0.894979 + 0.446109i \(0.852810\pi\)
\(504\) 0 0
\(505\) 2.41569 4.18410i 0.107497 0.186190i
\(506\) 0 0
\(507\) 5.87377 + 33.3118i 0.260863 + 1.47943i
\(508\) 0 0
\(509\) 11.9255 10.0067i 0.528590 0.443540i −0.339024 0.940778i \(-0.610097\pi\)
0.867614 + 0.497238i \(0.165652\pi\)
\(510\) 0 0
\(511\) −1.20014 + 0.436815i −0.0530910 + 0.0193235i
\(512\) 0 0
\(513\) −5.48451 20.7343i −0.242147 0.915440i
\(514\) 0 0
\(515\) 3.52210 1.28194i 0.155202 0.0564890i
\(516\) 0 0
\(517\) 11.0560 9.27711i 0.486244 0.408007i
\(518\) 0 0
\(519\) −2.05434 11.6507i −0.0901756 0.511411i
\(520\) 0 0
\(521\) −11.1132 + 19.2486i −0.486877 + 0.843295i −0.999886 0.0150876i \(-0.995197\pi\)
0.513009 + 0.858383i \(0.328531\pi\)
\(522\) 0 0
\(523\) −10.1135 3.68103i −0.442234 0.160960i 0.111299 0.993787i \(-0.464499\pi\)
−0.553534 + 0.832827i \(0.686721\pi\)
\(524\) 0 0
\(525\) 5.17218 + 8.95848i 0.225732 + 0.390980i
\(526\) 0 0
\(527\) 0.408385 + 0.342676i 0.0177895 + 0.0149272i
\(528\) 0 0
\(529\) 2.40523 13.6408i 0.104575 0.593077i
\(530\) 0 0
\(531\) 2.83383 0.122978
\(532\) 0 0
\(533\) 36.1941 1.56774
\(534\) 0 0
\(535\) 0.0485015 0.275066i 0.00209690 0.0118921i
\(536\) 0 0
\(537\) −13.6523 11.4557i −0.589142 0.494349i
\(538\) 0 0
\(539\) 3.51988 + 6.09660i 0.151612 + 0.262599i
\(540\) 0 0
\(541\) 11.5235 + 4.19422i 0.495435 + 0.180323i 0.577639 0.816292i \(-0.303974\pi\)
−0.0822049 + 0.996615i \(0.526196\pi\)
\(542\) 0 0
\(543\) 12.4861 21.6266i 0.535830 0.928085i
\(544\) 0 0
\(545\) 0.662215 + 3.75561i 0.0283662 + 0.160873i
\(546\) 0 0
\(547\) 14.2562 11.9624i 0.609552 0.511475i −0.284948 0.958543i \(-0.591976\pi\)
0.894500 + 0.447068i \(0.147532\pi\)
\(548\) 0 0
\(549\) 1.49695 0.544844i 0.0638881 0.0232534i
\(550\) 0 0
\(551\) 15.3630 7.10401i 0.654488 0.302641i
\(552\) 0 0
\(553\) 9.47288 3.44785i 0.402828 0.146617i
\(554\) 0 0
\(555\) 1.45518 1.22104i 0.0617688 0.0518302i
\(556\) 0 0
\(557\) −0.706865 4.00883i −0.0299508 0.169860i 0.966163 0.257931i \(-0.0830407\pi\)
−0.996114 + 0.0880715i \(0.971930\pi\)
\(558\) 0 0
\(559\) −0.695630 + 1.20487i −0.0294220 + 0.0509604i
\(560\) 0 0
\(561\) −14.1091 5.13529i −0.595686 0.216812i
\(562\) 0 0
\(563\) 12.4377 + 21.5428i 0.524188 + 0.907920i 0.999603 + 0.0281586i \(0.00896435\pi\)
−0.475416 + 0.879761i \(0.657702\pi\)
\(564\) 0 0
\(565\) 3.57496 + 2.99975i 0.150400 + 0.126201i
\(566\) 0 0
\(567\) −1.96875 + 11.1653i −0.0826795 + 0.468899i
\(568\) 0 0
\(569\) 19.2420 0.806667 0.403334 0.915053i \(-0.367851\pi\)
0.403334 + 0.915053i \(0.367851\pi\)
\(570\) 0 0
\(571\) 13.5395 0.566612 0.283306 0.959030i \(-0.408569\pi\)
0.283306 + 0.959030i \(0.408569\pi\)
\(572\) 0 0
\(573\) 0.324625 1.84104i 0.0135614 0.0769106i
\(574\) 0 0
\(575\) 22.8811 + 19.1995i 0.954207 + 0.800675i
\(576\) 0 0
\(577\) −12.8402 22.2398i −0.534543 0.925855i −0.999185 0.0403567i \(-0.987151\pi\)
0.464643 0.885498i \(-0.346183\pi\)
\(578\) 0 0
\(579\) 3.99394 + 1.45368i 0.165983 + 0.0604127i
\(580\) 0 0
\(581\) 6.69379 11.5940i 0.277705 0.481000i
\(582\) 0 0
\(583\) 0.988438 + 5.60571i 0.0409369 + 0.232165i
\(584\) 0 0
\(585\) 0.347207 0.291341i 0.0143552 0.0120455i
\(586\) 0 0
\(587\) 17.4378 6.34683i 0.719734 0.261962i 0.0439211 0.999035i \(-0.486015\pi\)
0.675813 + 0.737073i \(0.263793\pi\)
\(588\) 0 0
\(589\) −0.337049 0.0914715i −0.0138878 0.00376902i
\(590\) 0 0
\(591\) −26.5166 + 9.65127i −1.09075 + 0.397000i
\(592\) 0 0
\(593\) 2.75772 2.31400i 0.113246 0.0950248i −0.584406 0.811461i \(-0.698673\pi\)
0.697652 + 0.716437i \(0.254228\pi\)
\(594\) 0 0
\(595\) 0.378193 + 2.14484i 0.0155044 + 0.0879298i
\(596\) 0 0
\(597\) 12.4126 21.4993i 0.508014 0.879907i
\(598\) 0 0
\(599\) 12.3328 + 4.48878i 0.503905 + 0.183407i 0.581450 0.813582i \(-0.302486\pi\)
−0.0775443 + 0.996989i \(0.524708\pi\)
\(600\) 0 0
\(601\) −6.78825 11.7576i −0.276898 0.479602i 0.693714 0.720251i \(-0.255973\pi\)
−0.970612 + 0.240649i \(0.922640\pi\)
\(602\) 0 0
\(603\) 0.809130 + 0.678941i 0.0329503 + 0.0276486i
\(604\) 0 0
\(605\) −0.463097 + 2.62635i −0.0188276 + 0.106777i
\(606\) 0 0
\(607\) −18.3633 −0.745343 −0.372672 0.927963i \(-0.621558\pi\)
−0.372672 + 0.927963i \(0.621558\pi\)
\(608\) 0 0
\(609\) −8.16365 −0.330808
\(610\) 0 0
\(611\) 11.3275 64.2415i 0.458262 2.59893i
\(612\) 0 0
\(613\) 4.42518 + 3.71316i 0.178731 + 0.149973i 0.727764 0.685827i \(-0.240559\pi\)
−0.549033 + 0.835801i \(0.685004\pi\)
\(614\) 0 0
\(615\) −1.64513 2.84945i −0.0663382 0.114901i
\(616\) 0 0
\(617\) −39.3443 14.3201i −1.58394 0.576507i −0.607885 0.794025i \(-0.707982\pi\)
−0.976056 + 0.217518i \(0.930204\pi\)
\(618\) 0 0
\(619\) −18.0480 + 31.2601i −0.725412 + 1.25645i 0.233392 + 0.972383i \(0.425017\pi\)
−0.958804 + 0.284068i \(0.908316\pi\)
\(620\) 0 0
\(621\) 5.18672 + 29.4154i 0.208136 + 1.18040i
\(622\) 0 0
\(623\) −2.14153 + 1.79696i −0.0857986 + 0.0719936i
\(624\) 0 0
\(625\) −22.3757 + 8.14410i −0.895029 + 0.325764i
\(626\) 0 0
\(627\) 9.80133 0.825838i 0.391427 0.0329808i
\(628\) 0 0
\(629\) −23.2197 + 8.45126i −0.925828 + 0.336974i
\(630\) 0 0
\(631\) −29.6886 + 24.9117i −1.18188 + 0.991717i −0.181918 + 0.983314i \(0.558231\pi\)
−0.999965 + 0.00840360i \(0.997325\pi\)
\(632\) 0 0
\(633\) −6.78594 38.4850i −0.269717 1.52964i
\(634\) 0 0
\(635\) 0.316039 0.547396i 0.0125416 0.0217227i
\(636\) 0 0
\(637\) 29.8994 + 10.8825i 1.18466 + 0.431179i
\(638\) 0 0
\(639\) −1.33023 2.30403i −0.0526232 0.0911461i
\(640\) 0 0
\(641\) 5.24003 + 4.39691i 0.206969 + 0.173667i 0.740380 0.672189i \(-0.234646\pi\)
−0.533411 + 0.845856i \(0.679090\pi\)
\(642\) 0 0
\(643\) −2.89363 + 16.4106i −0.114114 + 0.647171i 0.873072 + 0.487592i \(0.162125\pi\)
−0.987185 + 0.159579i \(0.948986\pi\)
\(644\) 0 0
\(645\) 0.126474 0.00497992
\(646\) 0 0
\(647\) 36.1664 1.42185 0.710924 0.703269i \(-0.248277\pi\)
0.710924 + 0.703269i \(0.248277\pi\)
\(648\) 0 0
\(649\) 2.14629 12.1722i 0.0842494 0.477802i
\(650\) 0 0
\(651\) 0.129035 + 0.108273i 0.00505729 + 0.00424357i
\(652\) 0 0
\(653\) 4.83426 + 8.37319i 0.189179 + 0.327668i 0.944977 0.327137i \(-0.106084\pi\)
−0.755798 + 0.654805i \(0.772751\pi\)
\(654\) 0 0
\(655\) 4.66127 + 1.69656i 0.182131 + 0.0662902i
\(656\) 0 0
\(657\) −0.157148 + 0.272188i −0.00613093 + 0.0106191i
\(658\) 0 0
\(659\) 4.94409 + 28.0393i 0.192594 + 1.09226i 0.915803 + 0.401627i \(0.131555\pi\)
−0.723209 + 0.690629i \(0.757334\pi\)
\(660\) 0 0
\(661\) −19.5360 + 16.3927i −0.759863 + 0.637601i −0.938091 0.346388i \(-0.887408\pi\)
0.178228 + 0.983989i \(0.442964\pi\)
\(662\) 0 0
\(663\) −63.7702 + 23.2104i −2.47663 + 0.901419i
\(664\) 0 0
\(665\) −0.814604 1.17135i −0.0315890 0.0454231i
\(666\) 0 0
\(667\) −22.1508 + 8.06223i −0.857683 + 0.312171i
\(668\) 0 0
\(669\) −36.2240 + 30.3956i −1.40050 + 1.17516i
\(670\) 0 0
\(671\) −1.20652 6.84252i −0.0465772 0.264153i
\(672\) 0 0
\(673\) 20.3192 35.1938i 0.783246 1.35662i −0.146795 0.989167i \(-0.546896\pi\)
0.930041 0.367456i \(-0.119771\pi\)
\(674\) 0 0
\(675\) −22.7499 8.28029i −0.875644 0.318708i
\(676\) 0 0
\(677\) −10.2220 17.7050i −0.392862 0.680457i 0.599964 0.800027i \(-0.295182\pi\)
−0.992826 + 0.119570i \(0.961848\pi\)
\(678\) 0 0
\(679\) 12.7305 + 10.6822i 0.488552 + 0.409944i
\(680\) 0 0
\(681\) 6.84133 38.7991i 0.262160 1.48679i
\(682\) 0 0
\(683\) 39.8318 1.52412 0.762061 0.647505i \(-0.224187\pi\)
0.762061 + 0.647505i \(0.224187\pi\)
\(684\) 0 0
\(685\) 1.60887 0.0614718
\(686\) 0 0
\(687\) −6.33450 + 35.9247i −0.241676 + 1.37061i
\(688\) 0 0
\(689\) 19.7084 + 16.5373i 0.750831 + 0.630022i
\(690\) 0 0
\(691\) 14.0389 + 24.3160i 0.534064 + 0.925025i 0.999208 + 0.0397906i \(0.0126691\pi\)
−0.465144 + 0.885235i \(0.653998\pi\)
\(692\) 0 0
\(693\) −0.387300 0.140966i −0.0147123 0.00535484i
\(694\) 0 0
\(695\) −0.724079 + 1.25414i −0.0274659 + 0.0475723i
\(696\) 0 0
\(697\) 7.43206 + 42.1493i 0.281509 + 1.59652i
\(698\) 0 0
\(699\) 30.5722 25.6531i 1.15635 0.970290i
\(700\) 0 0
\(701\) −4.02822 + 1.46615i −0.152144 + 0.0553757i −0.416969 0.908921i \(-0.636908\pi\)
0.264826 + 0.964296i \(0.414686\pi\)
\(702\) 0 0
\(703\) 11.4829 11.4095i 0.433086 0.430317i
\(704\) 0 0
\(705\) −5.57242 + 2.02819i −0.209869 + 0.0763862i
\(706\) 0 0
\(707\) −15.2115 + 12.7639i −0.572087 + 0.480038i
\(708\) 0 0
\(709\) −0.715927 4.06022i −0.0268872 0.152485i 0.968408 0.249369i \(-0.0802234\pi\)
−0.995296 + 0.0968845i \(0.969112\pi\)
\(710\) 0 0
\(711\) 1.24039 2.14842i 0.0465184 0.0805722i
\(712\) 0 0
\(713\) 0.457045 + 0.166351i 0.0171165 + 0.00622989i
\(714\) 0 0
\(715\) −0.988438 1.71202i −0.0369655 0.0640261i
\(716\) 0 0
\(717\) 6.07162 + 5.09469i 0.226749 + 0.190265i
\(718\) 0 0
\(719\) −7.79796 + 44.2244i −0.290815 + 1.64929i 0.392927 + 0.919570i \(0.371462\pi\)
−0.683742 + 0.729724i \(0.739649\pi\)
\(720\) 0 0
\(721\) −15.4050 −0.573712
\(722\) 0 0
\(723\) −27.1922 −1.01129
\(724\) 0 0
\(725\) 3.31776 18.8160i 0.123219 0.698807i
\(726\) 0 0
\(727\) −26.7341 22.4326i −0.991514 0.831979i −0.00572754 0.999984i \(-0.501823\pi\)
−0.985786 + 0.168005i \(0.946268\pi\)
\(728\) 0 0
\(729\) −11.9828 20.7548i −0.443806 0.768695i
\(730\) 0 0
\(731\) −1.54595 0.562680i −0.0571791 0.0208115i
\(732\) 0 0
\(733\) 0.524006 0.907605i 0.0193546 0.0335232i −0.856186 0.516668i \(-0.827172\pi\)
0.875540 + 0.483145i \(0.160506\pi\)
\(734\) 0 0
\(735\) −0.502273 2.84853i −0.0185266 0.105070i
\(736\) 0 0
\(737\) 3.52909 2.96126i 0.129996 0.109079i
\(738\) 0 0
\(739\) −20.8426 + 7.58607i −0.766706 + 0.279058i −0.695618 0.718412i \(-0.744869\pi\)
−0.0710882 + 0.997470i \(0.522647\pi\)
\(740\) 0 0
\(741\) 31.5365 31.3348i 1.15852 1.15111i
\(742\) 0 0
\(743\) 35.7965 13.0288i 1.31325 0.477982i 0.411957 0.911203i \(-0.364845\pi\)
0.901288 + 0.433221i \(0.142623\pi\)
\(744\) 0 0
\(745\) −2.57357 + 2.15948i −0.0942884 + 0.0791174i
\(746\) 0 0
\(747\) −0.572091 3.24449i −0.0209317 0.118710i
\(748\) 0 0
\(749\) −0.573986 + 0.994173i −0.0209730 + 0.0363263i
\(750\) 0 0
\(751\) 11.9657 + 4.35515i 0.436634 + 0.158922i 0.550979 0.834519i \(-0.314255\pi\)
−0.114345 + 0.993441i \(0.536477\pi\)
\(752\) 0 0
\(753\) 21.2663 + 36.8343i 0.774987 + 1.34232i
\(754\) 0 0
\(755\) −3.21306 2.69608i −0.116935 0.0981203i
\(756\) 0 0
\(757\) 7.21125 40.8970i 0.262097 1.48643i −0.515078 0.857143i \(-0.672237\pi\)
0.777175 0.629284i \(-0.216652\pi\)
\(758\) 0 0
\(759\) −13.6984 −0.497221
\(760\) 0 0
\(761\) 36.4398 1.32094 0.660471 0.750851i \(-0.270357\pi\)
0.660471 + 0.750851i \(0.270357\pi\)
\(762\) 0 0
\(763\) 2.72173 15.4357i 0.0985333 0.558810i
\(764\) 0 0
\(765\) 0.410573 + 0.344512i 0.0148443 + 0.0124558i
\(766\) 0 0
\(767\) −27.9324 48.3803i −1.00858 1.74691i
\(768\) 0 0
\(769\) −11.0091 4.00697i −0.396997 0.144495i 0.135804 0.990736i \(-0.456638\pi\)
−0.532801 + 0.846241i \(0.678860\pi\)
\(770\) 0 0
\(771\) −0.0961463 + 0.166530i −0.00346263 + 0.00599744i
\(772\) 0 0
\(773\) 6.22310 + 35.2929i 0.223829 + 1.26940i 0.864911 + 0.501926i \(0.167375\pi\)
−0.641081 + 0.767473i \(0.721514\pi\)
\(774\) 0 0
\(775\) −0.301994 + 0.253403i −0.0108480 + 0.00910251i
\(776\) 0 0
\(777\) −7.33658 + 2.67030i −0.263198 + 0.0957964i
\(778\) 0 0
\(779\) −16.0082 23.0189i −0.573553 0.824736i
\(780\) 0 0
\(781\) −10.9041 + 3.96875i −0.390178 + 0.142013i
\(782\) 0 0
\(783\) 14.6362 12.2812i 0.523056 0.438896i
\(784\) 0 0
\(785\) −0.540717 3.06656i −0.0192990 0.109450i
\(786\) 0 0
\(787\) −1.05573 + 1.82858i −0.0376328 + 0.0651819i −0.884228 0.467055i \(-0.845315\pi\)
0.846596 + 0.532237i \(0.178648\pi\)
\(788\) 0 0
\(789\) 26.5224 + 9.65337i 0.944223 + 0.343669i
\(790\) 0 0
\(791\) −9.59033 16.6109i −0.340993 0.590617i
\(792\) 0 0
\(793\) −24.0568 20.1860i −0.854282 0.716827i
\(794\) 0