Properties

Label 576.2.bb.e.49.7
Level $576$
Weight $2$
Character 576.49
Analytic conductor $4.599$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bb (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 49.7
Character \(\chi\) \(=\) 576.49
Dual form 576.2.bb.e.529.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.841300 + 1.51401i) q^{3} +(-0.0691269 + 0.0185225i) q^{5} +(-1.28192 + 0.740118i) q^{7} +(-1.58443 - 2.54747i) q^{9} +O(q^{10})\) \(q+(-0.841300 + 1.51401i) q^{3} +(-0.0691269 + 0.0185225i) q^{5} +(-1.28192 + 0.740118i) q^{7} +(-1.58443 - 2.54747i) q^{9} +(-0.587070 + 2.19098i) q^{11} +(0.104109 + 0.388539i) q^{13} +(0.0301133 - 0.120242i) q^{15} -0.851000 q^{17} +(-3.75230 + 3.75230i) q^{19} +(-0.0420615 - 2.56350i) q^{21} +(-7.44629 - 4.29912i) q^{23} +(-4.32569 + 2.49744i) q^{25} +(5.18986 - 0.255647i) q^{27} +(-4.77230 - 1.27873i) q^{29} +(4.50318 - 7.79974i) q^{31} +(-2.82325 - 2.73210i) q^{33} +(0.0749065 - 0.0749065i) q^{35} +(4.13315 + 4.13315i) q^{37} +(-0.675837 - 0.169257i) q^{39} +(-2.05305 - 1.18533i) q^{41} +(0.669562 - 2.49884i) q^{43} +(0.156712 + 0.146751i) q^{45} +(-3.42005 - 5.92370i) q^{47} +(-2.40445 + 4.16463i) q^{49} +(0.715947 - 1.28842i) q^{51} +(3.95421 + 3.95421i) q^{53} -0.162329i q^{55} +(-2.52419 - 8.83782i) q^{57} +(-13.7811 + 3.69264i) q^{59} +(-3.28936 - 0.881382i) q^{61} +(3.91654 + 2.09299i) q^{63} +(-0.0143934 - 0.0249301i) q^{65} +(1.73506 + 6.47532i) q^{67} +(12.7735 - 7.65687i) q^{69} +0.362864i q^{71} +15.8744i q^{73} +(-0.141931 - 8.65022i) q^{75} +(-0.869003 - 3.24316i) q^{77} +(5.45338 + 9.44553i) q^{79} +(-3.97918 + 8.07255i) q^{81} +(5.37105 + 1.43917i) q^{83} +(0.0588270 - 0.0157627i) q^{85} +(5.95094 - 6.14948i) q^{87} -13.1832i q^{89} +(-0.421024 - 0.421024i) q^{91} +(8.02033 + 13.3798i) q^{93} +(0.189883 - 0.328887i) q^{95} +(-0.627593 - 1.08702i) q^{97} +(6.51161 - 1.97590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q - 2q^{3} + 4q^{5} + O(q^{10}) \) \( 72q - 2q^{3} + 4q^{5} + 2q^{11} - 16q^{13} + 20q^{15} - 16q^{17} - 28q^{19} - 16q^{21} - 8q^{27} + 4q^{29} - 28q^{31} - 32q^{33} + 16q^{35} + 16q^{37} + 10q^{43} + 40q^{45} + 56q^{47} + 4q^{49} + 54q^{51} - 8q^{53} + 14q^{59} - 32q^{61} + 108q^{63} - 64q^{65} + 18q^{67} + 32q^{69} - 86q^{75} - 36q^{77} - 44q^{79} - 44q^{81} - 20q^{83} - 8q^{85} + 80q^{91} - 4q^{93} - 48q^{95} + 40q^{97} - 28q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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
\(3\) −0.841300 + 1.51401i −0.485725 + 0.874112i
\(4\) 0 0
\(5\) −0.0691269 + 0.0185225i −0.0309145 + 0.00828352i −0.274243 0.961660i \(-0.588427\pi\)
0.243329 + 0.969944i \(0.421761\pi\)
\(6\) 0 0
\(7\) −1.28192 + 0.740118i −0.484521 + 0.279738i −0.722299 0.691581i \(-0.756914\pi\)
0.237778 + 0.971320i \(0.423581\pi\)
\(8\) 0 0
\(9\) −1.58443 2.54747i −0.528142 0.849156i
\(10\) 0 0
\(11\) −0.587070 + 2.19098i −0.177008 + 0.660604i 0.819192 + 0.573519i \(0.194422\pi\)
−0.996201 + 0.0870855i \(0.972245\pi\)
\(12\) 0 0
\(13\) 0.104109 + 0.388539i 0.0288745 + 0.107761i 0.978859 0.204535i \(-0.0655684\pi\)
−0.949985 + 0.312297i \(0.898902\pi\)
\(14\) 0 0
\(15\) 0.0301133 0.120242i 0.00777523 0.0310462i
\(16\) 0 0
\(17\) −0.851000 −0.206398 −0.103199 0.994661i \(-0.532908\pi\)
−0.103199 + 0.994661i \(0.532908\pi\)
\(18\) 0 0
\(19\) −3.75230 + 3.75230i −0.860837 + 0.860837i −0.991435 0.130598i \(-0.958310\pi\)
0.130598 + 0.991435i \(0.458310\pi\)
\(20\) 0 0
\(21\) −0.0420615 2.56350i −0.00917857 0.559401i
\(22\) 0 0
\(23\) −7.44629 4.29912i −1.55266 0.896428i −0.997924 0.0643999i \(-0.979487\pi\)
−0.554734 0.832028i \(-0.687180\pi\)
\(24\) 0 0
\(25\) −4.32569 + 2.49744i −0.865138 + 0.499488i
\(26\) 0 0
\(27\) 5.18986 0.255647i 0.998789 0.0491992i
\(28\) 0 0
\(29\) −4.77230 1.27873i −0.886193 0.237455i −0.213116 0.977027i \(-0.568361\pi\)
−0.673077 + 0.739572i \(0.735028\pi\)
\(30\) 0 0
\(31\) 4.50318 7.79974i 0.808796 1.40088i −0.104902 0.994483i \(-0.533453\pi\)
0.913698 0.406393i \(-0.133214\pi\)
\(32\) 0 0
\(33\) −2.82325 2.73210i −0.491464 0.475597i
\(34\) 0 0
\(35\) 0.0749065 0.0749065i 0.0126615 0.0126615i
\(36\) 0 0
\(37\) 4.13315 + 4.13315i 0.679485 + 0.679485i 0.959884 0.280399i \(-0.0904666\pi\)
−0.280399 + 0.959884i \(0.590467\pi\)
\(38\) 0 0
\(39\) −0.675837 0.169257i −0.108220 0.0271028i
\(40\) 0 0
\(41\) −2.05305 1.18533i −0.320633 0.185118i 0.331042 0.943616i \(-0.392600\pi\)
−0.651675 + 0.758499i \(0.725933\pi\)
\(42\) 0 0
\(43\) 0.669562 2.49884i 0.102107 0.381070i −0.895894 0.444269i \(-0.853464\pi\)
0.998001 + 0.0631989i \(0.0201303\pi\)
\(44\) 0 0
\(45\) 0.156712 + 0.146751i 0.0233613 + 0.0218764i
\(46\) 0 0
\(47\) −3.42005 5.92370i −0.498865 0.864060i 0.501134 0.865370i \(-0.332916\pi\)
−0.999999 + 0.00130966i \(0.999583\pi\)
\(48\) 0 0
\(49\) −2.40445 + 4.16463i −0.343493 + 0.594947i
\(50\) 0 0
\(51\) 0.715947 1.28842i 0.100253 0.180415i
\(52\) 0 0
\(53\) 3.95421 + 3.95421i 0.543152 + 0.543152i 0.924452 0.381300i \(-0.124523\pi\)
−0.381300 + 0.924452i \(0.624523\pi\)
\(54\) 0 0
\(55\) 0.162329i 0.0218885i
\(56\) 0 0
\(57\) −2.52419 8.83782i −0.334338 1.17060i
\(58\) 0 0
\(59\) −13.7811 + 3.69264i −1.79415 + 0.480741i −0.993040 0.117777i \(-0.962423\pi\)
−0.801109 + 0.598518i \(0.795756\pi\)
\(60\) 0 0
\(61\) −3.28936 0.881382i −0.421160 0.112849i 0.0420139 0.999117i \(-0.486623\pi\)
−0.463173 + 0.886268i \(0.653289\pi\)
\(62\) 0 0
\(63\) 3.91654 + 2.09299i 0.493438 + 0.263692i
\(64\) 0 0
\(65\) −0.0143934 0.0249301i −0.00178528 0.00309220i
\(66\) 0 0
\(67\) 1.73506 + 6.47532i 0.211971 + 0.791086i 0.987211 + 0.159419i \(0.0509622\pi\)
−0.775240 + 0.631667i \(0.782371\pi\)
\(68\) 0 0
\(69\) 12.7735 7.65687i 1.53774 0.921779i
\(70\) 0 0
\(71\) 0.362864i 0.0430640i 0.999768 + 0.0215320i \(0.00685439\pi\)
−0.999768 + 0.0215320i \(0.993146\pi\)
\(72\) 0 0
\(73\) 15.8744i 1.85796i 0.370128 + 0.928981i \(0.379314\pi\)
−0.370128 + 0.928981i \(0.620686\pi\)
\(74\) 0 0
\(75\) −0.141931 8.65022i −0.0163888 0.998841i
\(76\) 0 0
\(77\) −0.869003 3.24316i −0.0990321 0.369593i
\(78\) 0 0
\(79\) 5.45338 + 9.44553i 0.613553 + 1.06271i 0.990637 + 0.136526i \(0.0435937\pi\)
−0.377083 + 0.926179i \(0.623073\pi\)
\(80\) 0 0
\(81\) −3.97918 + 8.07255i −0.442131 + 0.896950i
\(82\) 0 0
\(83\) 5.37105 + 1.43917i 0.589549 + 0.157969i 0.541247 0.840863i \(-0.317952\pi\)
0.0483022 + 0.998833i \(0.484619\pi\)
\(84\) 0 0
\(85\) 0.0588270 0.0157627i 0.00638069 0.00170970i
\(86\) 0 0
\(87\) 5.95094 6.14948i 0.638008 0.659294i
\(88\) 0 0
\(89\) 13.1832i 1.39741i −0.715408 0.698707i \(-0.753759\pi\)
0.715408 0.698707i \(-0.246241\pi\)
\(90\) 0 0
\(91\) −0.421024 0.421024i −0.0441353 0.0441353i
\(92\) 0 0
\(93\) 8.02033 + 13.3798i 0.831669 + 1.38742i
\(94\) 0 0
\(95\) 0.189883 0.328887i 0.0194816 0.0337431i
\(96\) 0 0
\(97\) −0.627593 1.08702i −0.0637224 0.110370i 0.832404 0.554169i \(-0.186964\pi\)
−0.896127 + 0.443799i \(0.853631\pi\)
\(98\) 0 0
\(99\) 6.51161 1.97590i 0.654442 0.198585i
\(100\) 0 0
\(101\) −1.43047 + 5.33858i −0.142337 + 0.531209i 0.857522 + 0.514446i \(0.172003\pi\)
−0.999860 + 0.0167625i \(0.994664\pi\)
\(102\) 0 0
\(103\) 9.59933 + 5.54217i 0.945850 + 0.546087i 0.891789 0.452451i \(-0.149450\pi\)
0.0540605 + 0.998538i \(0.482784\pi\)
\(104\) 0 0
\(105\) 0.0503900 + 0.176428i 0.00491756 + 0.0172176i
\(106\) 0 0
\(107\) 6.90288 + 6.90288i 0.667327 + 0.667327i 0.957096 0.289770i \(-0.0935787\pi\)
−0.289770 + 0.957096i \(0.593579\pi\)
\(108\) 0 0
\(109\) 9.39169 9.39169i 0.899560 0.899560i −0.0958367 0.995397i \(-0.530553\pi\)
0.995397 + 0.0958367i \(0.0305527\pi\)
\(110\) 0 0
\(111\) −9.73483 + 2.78039i −0.923989 + 0.263903i
\(112\) 0 0
\(113\) −5.81166 + 10.0661i −0.546715 + 0.946938i 0.451782 + 0.892128i \(0.350789\pi\)
−0.998497 + 0.0548097i \(0.982545\pi\)
\(114\) 0 0
\(115\) 0.594369 + 0.159261i 0.0554252 + 0.0148511i
\(116\) 0 0
\(117\) 0.824837 0.880825i 0.0762562 0.0814323i
\(118\) 0 0
\(119\) 1.09092 0.629841i 0.100004 0.0577374i
\(120\) 0 0
\(121\) 5.07055 + 2.92749i 0.460959 + 0.266135i
\(122\) 0 0
\(123\) 3.52183 2.11111i 0.317553 0.190353i
\(124\) 0 0
\(125\) 0.505785 0.505785i 0.0452388 0.0452388i
\(126\) 0 0
\(127\) 10.1965 0.904796 0.452398 0.891816i \(-0.350569\pi\)
0.452398 + 0.891816i \(0.350569\pi\)
\(128\) 0 0
\(129\) 3.21996 + 3.11600i 0.283501 + 0.274348i
\(130\) 0 0
\(131\) 1.82077 + 6.79522i 0.159082 + 0.593701i 0.998721 + 0.0505571i \(0.0160997\pi\)
−0.839639 + 0.543144i \(0.817234\pi\)
\(132\) 0 0
\(133\) 2.03301 7.58731i 0.176285 0.657903i
\(134\) 0 0
\(135\) −0.354024 + 0.113801i −0.0304695 + 0.00979445i
\(136\) 0 0
\(137\) 12.5671 7.25564i 1.07368 0.619891i 0.144497 0.989505i \(-0.453843\pi\)
0.929185 + 0.369614i \(0.120510\pi\)
\(138\) 0 0
\(139\) −5.09570 + 1.36539i −0.432212 + 0.115811i −0.468364 0.883535i \(-0.655157\pi\)
0.0361523 + 0.999346i \(0.488490\pi\)
\(140\) 0 0
\(141\) 11.8458 0.194364i 0.997596 0.0163684i
\(142\) 0 0
\(143\) −0.912398 −0.0762986
\(144\) 0 0
\(145\) 0.353579 0.0293632
\(146\) 0 0
\(147\) −4.28241 7.14406i −0.353207 0.589232i
\(148\) 0 0
\(149\) −19.3330 + 5.18027i −1.58382 + 0.424384i −0.940107 0.340879i \(-0.889275\pi\)
−0.643717 + 0.765264i \(0.722609\pi\)
\(150\) 0 0
\(151\) −11.0910 + 6.40336i −0.902569 + 0.521098i −0.878033 0.478601i \(-0.841144\pi\)
−0.0245362 + 0.999699i \(0.507811\pi\)
\(152\) 0 0
\(153\) 1.34835 + 2.16790i 0.109007 + 0.175264i
\(154\) 0 0
\(155\) −0.166821 + 0.622583i −0.0133993 + 0.0500070i
\(156\) 0 0
\(157\) 1.98067 + 7.39195i 0.158074 + 0.589942i 0.998822 + 0.0485153i \(0.0154490\pi\)
−0.840748 + 0.541427i \(0.817884\pi\)
\(158\) 0 0
\(159\) −9.31337 + 2.66002i −0.738598 + 0.210953i
\(160\) 0 0
\(161\) 12.7274 1.00306
\(162\) 0 0
\(163\) −10.3989 + 10.3989i −0.814504 + 0.814504i −0.985305 0.170802i \(-0.945364\pi\)
0.170802 + 0.985305i \(0.445364\pi\)
\(164\) 0 0
\(165\) 0.245768 + 0.136568i 0.0191330 + 0.0106318i
\(166\) 0 0
\(167\) 5.44443 + 3.14334i 0.421302 + 0.243239i 0.695634 0.718396i \(-0.255123\pi\)
−0.274332 + 0.961635i \(0.588457\pi\)
\(168\) 0 0
\(169\) 11.1182 6.41910i 0.855247 0.493777i
\(170\) 0 0
\(171\) 15.5041 + 3.61362i 1.18563 + 0.276340i
\(172\) 0 0
\(173\) −11.3578 3.04333i −0.863521 0.231380i −0.200237 0.979748i \(-0.564171\pi\)
−0.663284 + 0.748368i \(0.730838\pi\)
\(174\) 0 0
\(175\) 3.69680 6.40305i 0.279452 0.484025i
\(176\) 0 0
\(177\) 6.00338 23.9713i 0.451242 1.80179i
\(178\) 0 0
\(179\) 9.21801 9.21801i 0.688986 0.688986i −0.273021 0.962008i \(-0.588023\pi\)
0.962008 + 0.273021i \(0.0880230\pi\)
\(180\) 0 0
\(181\) −11.5919 11.5919i −0.861621 0.861621i 0.129905 0.991526i \(-0.458533\pi\)
−0.991526 + 0.129905i \(0.958533\pi\)
\(182\) 0 0
\(183\) 4.10176 4.23861i 0.303211 0.313327i
\(184\) 0 0
\(185\) −0.362268 0.209155i −0.0266345 0.0153774i
\(186\) 0 0
\(187\) 0.499597 1.86452i 0.0365341 0.136347i
\(188\) 0 0
\(189\) −6.46379 + 4.16883i −0.470171 + 0.303238i
\(190\) 0 0
\(191\) −11.1864 19.3755i −0.809423 1.40196i −0.913264 0.407368i \(-0.866447\pi\)
0.103842 0.994594i \(-0.466887\pi\)
\(192\) 0 0
\(193\) 7.17911 12.4346i 0.516764 0.895061i −0.483047 0.875594i \(-0.660470\pi\)
0.999811 0.0194663i \(-0.00619671\pi\)
\(194\) 0 0
\(195\) 0.0498536 0.000817989i 0.00357009 5.85774e-5i
\(196\) 0 0
\(197\) 1.57538 + 1.57538i 0.112241 + 0.112241i 0.760997 0.648756i \(-0.224710\pi\)
−0.648756 + 0.760997i \(0.724710\pi\)
\(198\) 0 0
\(199\) 1.72755i 0.122463i −0.998124 0.0612313i \(-0.980497\pi\)
0.998124 0.0612313i \(-0.0195027\pi\)
\(200\) 0 0
\(201\) −11.2634 2.82080i −0.794457 0.198964i
\(202\) 0 0
\(203\) 7.06413 1.89283i 0.495804 0.132850i
\(204\) 0 0
\(205\) 0.163877 + 0.0439106i 0.0114456 + 0.00306685i
\(206\) 0 0
\(207\) 0.846243 + 25.7808i 0.0588179 + 1.79189i
\(208\) 0 0
\(209\) −6.01834 10.4241i −0.416297 0.721048i
\(210\) 0 0
\(211\) −3.19942 11.9404i −0.220257 0.822011i −0.984249 0.176785i \(-0.943430\pi\)
0.763992 0.645225i \(-0.223236\pi\)
\(212\) 0 0
\(213\) −0.549378 0.305278i −0.0376428 0.0209173i
\(214\) 0 0
\(215\) 0.185139i 0.0126264i
\(216\) 0 0
\(217\) 13.3316i 0.905005i
\(218\) 0 0
\(219\) −24.0340 13.3552i −1.62407 0.902458i
\(220\) 0 0
\(221\) −0.0885965 0.330647i −0.00595964 0.0222417i
\(222\) 0 0
\(223\) 7.22081 + 12.5068i 0.483541 + 0.837518i 0.999821 0.0189019i \(-0.00601703\pi\)
−0.516280 + 0.856420i \(0.672684\pi\)
\(224\) 0 0
\(225\) 13.2159 + 7.06255i 0.881059 + 0.470837i
\(226\) 0 0
\(227\) 1.61577 + 0.432945i 0.107243 + 0.0287356i 0.312041 0.950069i \(-0.398987\pi\)
−0.204799 + 0.978804i \(0.565654\pi\)
\(228\) 0 0
\(229\) −19.6207 + 5.25735i −1.29657 + 0.347416i −0.840153 0.542349i \(-0.817535\pi\)
−0.456420 + 0.889765i \(0.650868\pi\)
\(230\) 0 0
\(231\) 5.64126 + 1.41280i 0.371168 + 0.0929553i
\(232\) 0 0
\(233\) 23.5814i 1.54487i 0.635094 + 0.772435i \(0.280961\pi\)
−0.635094 + 0.772435i \(0.719039\pi\)
\(234\) 0 0
\(235\) 0.346139 + 0.346139i 0.0225796 + 0.0225796i
\(236\) 0 0
\(237\) −18.8885 + 0.309920i −1.22694 + 0.0201315i
\(238\) 0 0
\(239\) −4.28400 + 7.42011i −0.277109 + 0.479967i −0.970665 0.240436i \(-0.922710\pi\)
0.693556 + 0.720403i \(0.256043\pi\)
\(240\) 0 0
\(241\) 3.69013 + 6.39149i 0.237702 + 0.411712i 0.960055 0.279813i \(-0.0902725\pi\)
−0.722352 + 0.691525i \(0.756939\pi\)
\(242\) 0 0
\(243\) −8.87421 12.8159i −0.569281 0.822143i
\(244\) 0 0
\(245\) 0.0890729 0.332424i 0.00569066 0.0212378i
\(246\) 0 0
\(247\) −1.84856 1.06727i −0.117621 0.0679086i
\(248\) 0 0
\(249\) −6.69758 + 6.92103i −0.424442 + 0.438602i
\(250\) 0 0
\(251\) 8.74661 + 8.74661i 0.552081 + 0.552081i 0.927041 0.374960i \(-0.122343\pi\)
−0.374960 + 0.927041i \(0.622343\pi\)
\(252\) 0 0
\(253\) 13.7908 13.7908i 0.867017 0.867017i
\(254\) 0 0
\(255\) −0.0256265 + 0.102326i −0.00160479 + 0.00640788i
\(256\) 0 0
\(257\) 2.21071 3.82905i 0.137900 0.238850i −0.788802 0.614648i \(-0.789298\pi\)
0.926702 + 0.375798i \(0.122631\pi\)
\(258\) 0 0
\(259\) −8.35739 2.23936i −0.519303 0.139147i
\(260\) 0 0
\(261\) 4.30383 + 14.1833i 0.266400 + 0.877926i
\(262\) 0 0
\(263\) 9.48601 5.47675i 0.584932 0.337711i −0.178159 0.984002i \(-0.557014\pi\)
0.763091 + 0.646291i \(0.223681\pi\)
\(264\) 0 0
\(265\) −0.346584 0.200100i −0.0212905 0.0122921i
\(266\) 0 0
\(267\) 19.9594 + 11.0910i 1.22150 + 0.678759i
\(268\) 0 0
\(269\) −10.6376 + 10.6376i −0.648586 + 0.648586i −0.952651 0.304065i \(-0.901656\pi\)
0.304065 + 0.952651i \(0.401656\pi\)
\(270\) 0 0
\(271\) −19.1209 −1.16151 −0.580757 0.814077i \(-0.697243\pi\)
−0.580757 + 0.814077i \(0.697243\pi\)
\(272\) 0 0
\(273\) 0.991640 0.283225i 0.0600168 0.0171416i
\(274\) 0 0
\(275\) −2.93235 10.9437i −0.176827 0.659928i
\(276\) 0 0
\(277\) 2.70176 10.0831i 0.162333 0.605835i −0.836032 0.548680i \(-0.815130\pi\)
0.998365 0.0571550i \(-0.0182029\pi\)
\(278\) 0 0
\(279\) −27.0046 + 0.886412i −1.61672 + 0.0530681i
\(280\) 0 0
\(281\) 12.1779 7.03092i 0.726473 0.419429i −0.0906576 0.995882i \(-0.528897\pi\)
0.817130 + 0.576453i \(0.195564\pi\)
\(282\) 0 0
\(283\) −24.6641 + 6.60872i −1.46613 + 0.392848i −0.901601 0.432568i \(-0.857608\pi\)
−0.564526 + 0.825415i \(0.690941\pi\)
\(284\) 0 0
\(285\) 0.338188 + 0.564177i 0.0200325 + 0.0334190i
\(286\) 0 0
\(287\) 3.50914 0.207138
\(288\) 0 0
\(289\) −16.2758 −0.957400
\(290\) 0 0
\(291\) 2.17375 0.0356666i 0.127428 0.00209081i
\(292\) 0 0
\(293\) −13.2569 + 3.55218i −0.774476 + 0.207520i −0.624348 0.781146i \(-0.714635\pi\)
−0.150128 + 0.988667i \(0.547969\pi\)
\(294\) 0 0
\(295\) 0.884250 0.510522i 0.0514830 0.0297237i
\(296\) 0 0
\(297\) −2.48670 + 11.5209i −0.144293 + 0.668513i
\(298\) 0 0
\(299\) 0.895150 3.34075i 0.0517679 0.193200i
\(300\) 0 0
\(301\) 0.991111 + 3.69888i 0.0571267 + 0.213200i
\(302\) 0 0
\(303\) −6.87919 6.65709i −0.395199 0.382440i
\(304\) 0 0
\(305\) 0.243709 0.0139547
\(306\) 0 0
\(307\) 14.1122 14.1122i 0.805426 0.805426i −0.178512 0.983938i \(-0.557128\pi\)
0.983938 + 0.178512i \(0.0571283\pi\)
\(308\) 0 0
\(309\) −16.4668 + 9.87080i −0.936763 + 0.561530i
\(310\) 0 0
\(311\) 11.2914 + 6.51907i 0.640274 + 0.369662i 0.784720 0.619850i \(-0.212807\pi\)
−0.144446 + 0.989513i \(0.546140\pi\)
\(312\) 0 0
\(313\) −6.50512 + 3.75573i −0.367691 + 0.212287i −0.672449 0.740143i \(-0.734758\pi\)
0.304758 + 0.952430i \(0.401424\pi\)
\(314\) 0 0
\(315\) −0.309506 0.0721380i −0.0174387 0.00406451i
\(316\) 0 0
\(317\) 1.45660 + 0.390294i 0.0818107 + 0.0219211i 0.299492 0.954099i \(-0.403183\pi\)
−0.217682 + 0.976020i \(0.569849\pi\)
\(318\) 0 0
\(319\) 5.60335 9.70528i 0.313727 0.543391i
\(320\) 0 0
\(321\) −16.2584 + 4.64361i −0.907456 + 0.259181i
\(322\) 0 0
\(323\) 3.19321 3.19321i 0.177675 0.177675i
\(324\) 0 0
\(325\) −1.42069 1.42069i −0.0788059 0.0788059i
\(326\) 0 0
\(327\) 6.31784 + 22.1203i 0.349377 + 1.22326i
\(328\) 0 0
\(329\) 8.76847 + 5.06248i 0.483422 + 0.279104i
\(330\) 0 0
\(331\) 5.29948 19.7779i 0.291286 1.08709i −0.652837 0.757499i \(-0.726421\pi\)
0.944122 0.329595i \(-0.106912\pi\)
\(332\) 0 0
\(333\) 3.98039 17.0777i 0.218124 0.935854i
\(334\) 0 0
\(335\) −0.239878 0.415481i −0.0131059 0.0227002i
\(336\) 0 0
\(337\) 4.81432 8.33864i 0.262253 0.454235i −0.704588 0.709617i \(-0.748868\pi\)
0.966840 + 0.255382i \(0.0822013\pi\)
\(338\) 0 0
\(339\) −10.3508 17.2675i −0.562177 0.937842i
\(340\) 0 0
\(341\) 14.4454 + 14.4454i 0.782261 + 0.782261i
\(342\) 0 0
\(343\) 17.4800i 0.943829i
\(344\) 0 0
\(345\) −0.741165 + 0.765892i −0.0399030 + 0.0412343i
\(346\) 0 0
\(347\) −8.72145 + 2.33691i −0.468192 + 0.125452i −0.485199 0.874404i \(-0.661253\pi\)
0.0170070 + 0.999855i \(0.494586\pi\)
\(348\) 0 0
\(349\) −26.4971 7.09989i −1.41836 0.380048i −0.533458 0.845826i \(-0.679108\pi\)
−0.884902 + 0.465778i \(0.845775\pi\)
\(350\) 0 0
\(351\) 0.639638 + 1.98985i 0.0341413 + 0.106210i
\(352\) 0 0
\(353\) −2.21080 3.82922i −0.117669 0.203809i 0.801174 0.598431i \(-0.204209\pi\)
−0.918844 + 0.394622i \(0.870876\pi\)
\(354\) 0 0
\(355\) −0.00672115 0.0250837i −0.000356722 0.00133130i
\(356\) 0 0
\(357\) 0.0357943 + 2.18154i 0.00189444 + 0.115459i
\(358\) 0 0
\(359\) 21.7288i 1.14680i 0.819275 + 0.573400i \(0.194376\pi\)
−0.819275 + 0.573400i \(0.805624\pi\)
\(360\) 0 0
\(361\) 9.15954i 0.482081i
\(362\) 0 0
\(363\) −8.69809 + 5.21395i −0.456531 + 0.273662i
\(364\) 0 0
\(365\) −0.294034 1.09735i −0.0153905 0.0574380i
\(366\) 0 0
\(367\) −1.28705 2.22924i −0.0671835 0.116365i 0.830477 0.557053i \(-0.188068\pi\)
−0.897660 + 0.440688i \(0.854735\pi\)
\(368\) 0 0
\(369\) 0.233322 + 7.10816i 0.0121462 + 0.370036i
\(370\) 0 0
\(371\) −7.99556 2.14241i −0.415109 0.111228i
\(372\) 0 0
\(373\) 1.42780 0.382578i 0.0739287 0.0198091i −0.221665 0.975123i \(-0.571149\pi\)
0.295594 + 0.955314i \(0.404483\pi\)
\(374\) 0 0
\(375\) 0.340244 + 1.19128i 0.0175701 + 0.0615174i
\(376\) 0 0
\(377\) 1.98735i 0.102354i
\(378\) 0 0
\(379\) −4.66662 4.66662i −0.239708 0.239708i 0.577021 0.816729i \(-0.304215\pi\)
−0.816729 + 0.577021i \(0.804215\pi\)
\(380\) 0 0
\(381\) −8.57835 + 15.4376i −0.439482 + 0.790893i
\(382\) 0 0
\(383\) 1.48376 2.56995i 0.0758165 0.131318i −0.825625 0.564220i \(-0.809177\pi\)
0.901441 + 0.432902i \(0.142510\pi\)
\(384\) 0 0
\(385\) 0.120143 + 0.208094i 0.00612305 + 0.0106054i
\(386\) 0 0
\(387\) −7.42659 + 2.25354i −0.377515 + 0.114554i
\(388\) 0 0
\(389\) 7.85632 29.3202i 0.398331 1.48659i −0.417700 0.908585i \(-0.637164\pi\)
0.816031 0.578008i \(-0.196170\pi\)
\(390\) 0 0
\(391\) 6.33679 + 3.65855i 0.320465 + 0.185021i
\(392\) 0 0
\(393\) −11.8198 2.96016i −0.596231 0.149320i
\(394\) 0 0
\(395\) −0.551930 0.551930i −0.0277706 0.0277706i
\(396\) 0 0
\(397\) 11.6823 11.6823i 0.586319 0.586319i −0.350314 0.936632i \(-0.613925\pi\)
0.936632 + 0.350314i \(0.113925\pi\)
\(398\) 0 0
\(399\) 9.77685 + 9.46120i 0.489455 + 0.473652i
\(400\) 0 0
\(401\) 0.390756 0.676809i 0.0195134 0.0337982i −0.856104 0.516804i \(-0.827122\pi\)
0.875617 + 0.483006i \(0.160455\pi\)
\(402\) 0 0
\(403\) 3.49932 + 0.937641i 0.174314 + 0.0467072i
\(404\) 0 0
\(405\) 0.125545 0.631735i 0.00623836 0.0313912i
\(406\) 0 0
\(407\) −11.4821 + 6.62918i −0.569145 + 0.328596i
\(408\) 0 0
\(409\) −26.9864 15.5806i −1.33439 0.770412i −0.348423 0.937338i \(-0.613283\pi\)
−0.985969 + 0.166926i \(0.946616\pi\)
\(410\) 0 0
\(411\) 0.412344 + 25.1309i 0.0203394 + 1.23962i
\(412\) 0 0
\(413\) 14.9333 14.9333i 0.734822 0.734822i
\(414\) 0 0
\(415\) −0.397941 −0.0195342
\(416\) 0 0
\(417\) 2.21981 8.86363i 0.108705 0.434054i
\(418\) 0 0
\(419\) 5.93759 + 22.1594i 0.290070 + 1.08256i 0.945054 + 0.326914i \(0.106009\pi\)
−0.654984 + 0.755643i \(0.727325\pi\)
\(420\) 0 0
\(421\) −6.71096 + 25.0456i −0.327072 + 1.22065i 0.585140 + 0.810932i \(0.301039\pi\)
−0.912212 + 0.409718i \(0.865627\pi\)
\(422\) 0 0
\(423\) −9.67161 + 18.0981i −0.470250 + 0.879961i
\(424\) 0 0
\(425\) 3.68116 2.12532i 0.178563 0.103093i
\(426\) 0 0
\(427\) 4.86903 1.30465i 0.235629 0.0631366i
\(428\) 0 0
\(429\) 0.767601 1.38138i 0.0370601 0.0666935i
\(430\) 0 0
\(431\) −8.53959 −0.411338 −0.205669 0.978622i \(-0.565937\pi\)
−0.205669 + 0.978622i \(0.565937\pi\)
\(432\) 0 0
\(433\) −9.28283 −0.446104 −0.223052 0.974807i \(-0.571602\pi\)
−0.223052 + 0.974807i \(0.571602\pi\)
\(434\) 0 0
\(435\) −0.297467 + 0.535321i −0.0142624 + 0.0256667i
\(436\) 0 0
\(437\) 44.0723 11.8091i 2.10826 0.564908i
\(438\) 0 0
\(439\) 12.0947 6.98286i 0.577247 0.333274i −0.182792 0.983152i \(-0.558513\pi\)
0.760038 + 0.649878i \(0.225180\pi\)
\(440\) 0 0
\(441\) 14.4189 0.473295i 0.686616 0.0225378i
\(442\) 0 0
\(443\) 3.19925 11.9398i 0.152001 0.567276i −0.847343 0.531047i \(-0.821799\pi\)
0.999344 0.0362287i \(-0.0115345\pi\)
\(444\) 0 0
\(445\) 0.244185 + 0.911312i 0.0115755 + 0.0432004i
\(446\) 0 0
\(447\) 8.42193 33.6285i 0.398344 1.59057i
\(448\) 0 0
\(449\) 15.5226 0.732554 0.366277 0.930506i \(-0.380632\pi\)
0.366277 + 0.930506i \(0.380632\pi\)
\(450\) 0 0
\(451\) 3.80232 3.80232i 0.179044 0.179044i
\(452\) 0 0
\(453\) −0.363908 22.1789i −0.0170979 1.04206i
\(454\) 0 0
\(455\) 0.0369025 + 0.0213057i 0.00173002 + 0.000998825i
\(456\) 0 0
\(457\) 23.3712 13.4934i 1.09326 0.631194i 0.158817 0.987308i \(-0.449232\pi\)
0.934442 + 0.356114i \(0.115899\pi\)
\(458\) 0 0
\(459\) −4.41657 + 0.217555i −0.206148 + 0.0101546i
\(460\) 0 0
\(461\) 22.8014 + 6.10962i 1.06197 + 0.284554i 0.747189 0.664611i \(-0.231403\pi\)
0.314779 + 0.949165i \(0.398070\pi\)
\(462\) 0 0
\(463\) −11.7055 + 20.2745i −0.544001 + 0.942238i 0.454668 + 0.890661i \(0.349758\pi\)
−0.998669 + 0.0515769i \(0.983575\pi\)
\(464\) 0 0
\(465\) −0.802248 0.776346i −0.0372033 0.0360022i
\(466\) 0 0
\(467\) −17.4581 + 17.4581i −0.807865 + 0.807865i −0.984310 0.176446i \(-0.943540\pi\)
0.176446 + 0.984310i \(0.443540\pi\)
\(468\) 0 0
\(469\) −7.01671 7.01671i −0.324001 0.324001i
\(470\) 0 0
\(471\) −12.8578 3.22011i −0.592456 0.148375i
\(472\) 0 0
\(473\) 5.08182 + 2.93399i 0.233662 + 0.134905i
\(474\) 0 0
\(475\) 6.86016 25.6024i 0.314766 1.17472i
\(476\) 0 0
\(477\) 3.80806 16.3384i 0.174359 0.748082i
\(478\) 0 0
\(479\) 9.62715 + 16.6747i 0.439876 + 0.761887i 0.997679 0.0680859i \(-0.0216892\pi\)
−0.557804 + 0.829973i \(0.688356\pi\)
\(480\) 0 0
\(481\) −1.17559 + 2.03618i −0.0536023 + 0.0928420i
\(482\) 0 0
\(483\) −10.7076 + 19.2694i −0.487212 + 0.876787i
\(484\) 0 0
\(485\) 0.0635180 + 0.0635180i 0.00288420 + 0.00288420i
\(486\) 0 0
\(487\) 15.8010i 0.716012i −0.933719 0.358006i \(-0.883457\pi\)
0.933719 0.358006i \(-0.116543\pi\)
\(488\) 0 0
\(489\) −6.99539 24.4926i −0.316342 1.10759i
\(490\) 0 0
\(491\) 10.9388 2.93103i 0.493659 0.132276i −0.00339642 0.999994i \(-0.501081\pi\)
0.497056 + 0.867719i \(0.334414\pi\)
\(492\) 0 0
\(493\) 4.06122 + 1.08820i 0.182908 + 0.0490101i
\(494\) 0 0
\(495\) −0.413529 + 0.257199i −0.0185867 + 0.0115602i
\(496\) 0 0
\(497\) −0.268562 0.465164i −0.0120467 0.0208654i
\(498\) 0 0
\(499\) 1.04051 + 3.88323i 0.0465796 + 0.173837i 0.985297 0.170850i \(-0.0546515\pi\)
−0.938717 + 0.344688i \(0.887985\pi\)
\(500\) 0 0
\(501\) −9.33943 + 5.59840i −0.417255 + 0.250118i
\(502\) 0 0
\(503\) 24.1846i 1.07834i −0.842198 0.539169i \(-0.818739\pi\)
0.842198 0.539169i \(-0.181261\pi\)
\(504\) 0 0
\(505\) 0.395536i 0.0176011i
\(506\) 0 0
\(507\) 0.364802 + 22.2334i 0.0162014 + 0.987421i
\(508\) 0 0
\(509\) 3.36446 + 12.5563i 0.149127 + 0.556550i 0.999537 + 0.0304290i \(0.00968734\pi\)
−0.850410 + 0.526121i \(0.823646\pi\)
\(510\) 0 0
\(511\) −11.7490 20.3498i −0.519743 0.900222i
\(512\) 0 0
\(513\) −18.5147 + 20.4332i −0.817442 + 0.902147i
\(514\) 0 0
\(515\) −0.766227 0.205310i −0.0337640 0.00904703i
\(516\) 0 0
\(517\) 14.9865 4.01562i 0.659105 0.176607i
\(518\) 0 0
\(519\) 14.1630 14.6355i 0.621685 0.642427i
\(520\) 0 0
\(521\) 3.39592i 0.148778i 0.997229 + 0.0743889i \(0.0237006\pi\)
−0.997229 + 0.0743889i \(0.976299\pi\)
\(522\) 0 0
\(523\) 21.4956 + 21.4956i 0.939938 + 0.939938i 0.998296 0.0583574i \(-0.0185863\pi\)
−0.0583574 + 0.998296i \(0.518586\pi\)
\(524\) 0 0
\(525\) 6.58413 + 10.9839i 0.287355 + 0.479375i
\(526\) 0 0
\(527\) −3.83221 + 6.63758i −0.166934 + 0.289138i
\(528\) 0 0
\(529\) 25.4648 + 44.1063i 1.10716 + 1.91767i
\(530\) 0 0
\(531\) 31.2421 + 29.2562i 1.35579 + 1.26961i
\(532\) 0 0
\(533\) 0.246806 0.921094i 0.0106904 0.0398970i
\(534\) 0 0
\(535\) −0.605034 0.349316i −0.0261579 0.0151023i
\(536\) 0 0
\(537\) 6.20101 + 21.7112i 0.267593 + 0.936909i
\(538\) 0 0
\(539\) −7.71302 7.71302i −0.332223 0.332223i
\(540\) 0 0
\(541\) −14.7438 + 14.7438i −0.633886 + 0.633886i −0.949041 0.315154i \(-0.897944\pi\)
0.315154 + 0.949041i \(0.397944\pi\)
\(542\) 0 0
\(543\) 27.3025 7.79795i 1.17166 0.334642i
\(544\) 0 0
\(545\) −0.475261 + 0.823176i −0.0203579 + 0.0352610i
\(546\) 0 0
\(547\) 30.6555 + 8.21413i 1.31074 + 0.351211i 0.845500 0.533976i \(-0.179303\pi\)
0.465236 + 0.885186i \(0.345969\pi\)
\(548\) 0 0
\(549\) 2.96646 + 9.77603i 0.126606 + 0.417231i
\(550\) 0 0
\(551\) 22.7053 13.1089i 0.967278 0.558458i
\(552\) 0 0
\(553\) −13.9816 8.07229i −0.594559 0.343269i
\(554\) 0 0
\(555\) 0.621439 0.372513i 0.0263786 0.0158123i
\(556\) 0 0
\(557\) −16.6150 + 16.6150i −0.704002 + 0.704002i −0.965267 0.261265i \(-0.915860\pi\)
0.261265 + 0.965267i \(0.415860\pi\)
\(558\) 0 0
\(559\) 1.04060 0.0440129
\(560\) 0 0
\(561\) 2.40259 + 2.32502i 0.101437 + 0.0981622i
\(562\) 0 0
\(563\) 0.625738 + 2.33528i 0.0263717 + 0.0984205i 0.977857 0.209273i \(-0.0671096\pi\)
−0.951486 + 0.307693i \(0.900443\pi\)
\(564\) 0 0
\(565\) 0.215293 0.803484i 0.00905745 0.0338028i
\(566\) 0 0
\(567\) −0.873644 13.2935i −0.0366896 0.558272i
\(568\) 0 0
\(569\) −8.83926 + 5.10335i −0.370561 + 0.213943i −0.673703 0.739002i \(-0.735297\pi\)
0.303143 + 0.952945i \(0.401964\pi\)
\(570\) 0 0
\(571\) −20.9394 + 5.61069i −0.876285 + 0.234800i −0.668804 0.743439i \(-0.733193\pi\)
−0.207481 + 0.978239i \(0.566527\pi\)
\(572\) 0 0
\(573\) 38.7458 0.635734i 1.61863 0.0265582i
\(574\) 0 0
\(575\) 42.9471 1.79102
\(576\) 0 0
\(577\) −17.0725 −0.710737 −0.355369 0.934726i \(-0.615645\pi\)
−0.355369 + 0.934726i \(0.615645\pi\)
\(578\) 0 0
\(579\) 12.7862 + 21.3304i 0.531378 + 0.886462i
\(580\) 0 0
\(581\) −7.95043 + 2.13031i −0.329839 + 0.0883802i
\(582\) 0 0
\(583\) −10.9850 + 6.34217i −0.454951 + 0.262666i
\(584\) 0 0
\(585\) −0.0407034 + 0.0761668i −0.00168288 + 0.00314911i
\(586\) 0 0
\(587\) 3.63287 13.5581i 0.149945 0.559602i −0.849541 0.527523i \(-0.823121\pi\)
0.999485 0.0320783i \(-0.0102126\pi\)
\(588\) 0 0
\(589\) 12.3697 + 46.1643i 0.509684 + 1.90217i
\(590\) 0 0
\(591\) −3.71049 + 1.05976i −0.152629 + 0.0435928i
\(592\) 0 0
\(593\) −27.5850 −1.13278 −0.566390 0.824137i \(-0.691660\pi\)
−0.566390 + 0.824137i \(0.691660\pi\)
\(594\) 0 0
\(595\) −0.0637455 + 0.0637455i −0.00261331 + 0.00261331i
\(596\) 0 0
\(597\) 2.61552 + 1.45339i 0.107046 + 0.0594832i
\(598\) 0 0
\(599\) −34.8788 20.1373i −1.42511 0.822788i −0.428380 0.903598i \(-0.640916\pi\)
−0.996729 + 0.0808109i \(0.974249\pi\)
\(600\) 0 0
\(601\) 5.90297 3.40808i 0.240787 0.139018i −0.374751 0.927125i \(-0.622272\pi\)
0.615538 + 0.788107i \(0.288939\pi\)
\(602\) 0 0
\(603\) 13.7466 14.6797i 0.559804 0.597802i
\(604\) 0 0
\(605\) −0.404736 0.108449i −0.0164549 0.00440907i
\(606\) 0 0
\(607\) 1.09235 1.89200i 0.0443370 0.0767939i −0.843005 0.537905i \(-0.819216\pi\)
0.887342 + 0.461111i \(0.152549\pi\)
\(608\) 0 0
\(609\) −3.07730 + 12.2876i −0.124699 + 0.497917i
\(610\) 0 0
\(611\) 1.94553 1.94553i 0.0787077 0.0787077i
\(612\) 0 0
\(613\) 15.3068 + 15.3068i 0.618236 + 0.618236i 0.945079 0.326843i \(-0.105985\pi\)
−0.326843 + 0.945079i \(0.605985\pi\)
\(614\) 0 0
\(615\) −0.204350 + 0.211168i −0.00824020 + 0.00851512i
\(616\) 0 0
\(617\) −10.1056 5.83447i −0.406836 0.234887i 0.282593 0.959240i \(-0.408805\pi\)
−0.689429 + 0.724353i \(0.742139\pi\)
\(618\) 0 0
\(619\) 1.13744 4.24500i 0.0457178 0.170621i −0.939292 0.343118i \(-0.888517\pi\)
0.985010 + 0.172497i \(0.0551835\pi\)
\(620\) 0 0
\(621\) −39.7442 20.4082i −1.59488 0.818952i
\(622\) 0 0
\(623\) 9.75711 + 16.8998i 0.390910 + 0.677076i
\(624\) 0 0
\(625\) 12.4616 21.5841i 0.498464 0.863365i
\(626\) 0 0
\(627\) 20.8453 0.342027i 0.832483 0.0136592i
\(628\) 0 0
\(629\) −3.51731 3.51731i −0.140244 0.140244i
\(630\) 0 0
\(631\) 31.5374i 1.25548i −0.778422 0.627742i \(-0.783979\pi\)
0.778422 0.627742i \(-0.216021\pi\)
\(632\) 0 0
\(633\) 20.7695 + 5.20152i 0.825513 + 0.206742i
\(634\) 0 0
\(635\) −0.704855 + 0.188865i −0.0279713 + 0.00749489i
\(636\) 0 0
\(637\) −1.86844 0.500648i −0.0740304 0.0198364i
\(638\) 0 0
\(639\) 0.924384 0.574932i 0.0365681 0.0227439i
\(640\) 0 0
\(641\) 9.38996 + 16.2639i 0.370881 + 0.642385i 0.989701 0.143148i \(-0.0457225\pi\)
−0.618820 + 0.785533i \(0.712389\pi\)
\(642\) 0 0
\(643\) 6.94427 + 25.9164i 0.273855 + 1.02204i 0.956605 + 0.291389i \(0.0941175\pi\)
−0.682749 + 0.730653i \(0.739216\pi\)
\(644\) 0 0
\(645\) −0.280302 0.155758i −0.0110369 0.00613295i
\(646\) 0 0
\(647\) 16.5176i 0.649373i 0.945822 + 0.324686i \(0.105259\pi\)
−0.945822 + 0.324686i \(0.894741\pi\)
\(648\) 0 0
\(649\) 32.3620i 1.27032i
\(650\) 0 0
\(651\) −20.1841 11.2158i −0.791075 0.439584i
\(652\) 0 0
\(653\) 10.8252 + 40.4003i 0.423624 + 1.58099i 0.766909 + 0.641756i \(0.221794\pi\)
−0.343285 + 0.939231i \(0.611540\pi\)
\(654\) 0 0
\(655\) −0.251729 0.436008i −0.00983587 0.0170362i
\(656\) 0 0
\(657\) 40.4396 25.1519i 1.57770 0.981268i
\(658\) 0 0
\(659\) 11.3797 + 3.04918i 0.443290 + 0.118779i 0.473558 0.880763i \(-0.342969\pi\)
−0.0302682 + 0.999542i \(0.509636\pi\)
\(660\) 0 0
\(661\) 39.1808 10.4985i 1.52396 0.408343i 0.602913 0.797807i \(-0.294006\pi\)
0.921042 + 0.389464i \(0.127340\pi\)
\(662\) 0 0
\(663\) 0.575137 + 0.144037i 0.0223365 + 0.00559395i
\(664\) 0 0
\(665\) 0.562144i 0.0217990i
\(666\) 0 0
\(667\) 30.0385 + 30.0385i 1.16309 + 1.16309i
\(668\) 0 0
\(669\) −25.0102 + 0.410364i −0.966952 + 0.0158656i
\(670\) 0 0
\(671\) 3.86217 6.68948i 0.149098 0.258245i
\(672\) 0 0
\(673\) −6.73175 11.6597i −0.259490 0.449450i 0.706615 0.707598i \(-0.250221\pi\)
−0.966105 + 0.258148i \(0.916888\pi\)
\(674\) 0 0
\(675\) −21.8113 + 14.0672i −0.839516 + 0.541447i
\(676\) 0 0
\(677\) 2.56756 9.58227i 0.0986794 0.368277i −0.898872 0.438211i \(-0.855612\pi\)
0.997552 + 0.0699343i \(0.0222790\pi\)
\(678\) 0 0
\(679\) 1.60905 + 0.928986i 0.0617497 + 0.0356512i
\(680\) 0 0
\(681\) −2.01483 + 2.08205i −0.0772085 + 0.0797844i
\(682\) 0 0
\(683\) −4.48800 4.48800i −0.171728 0.171728i 0.616010 0.787738i \(-0.288748\pi\)
−0.787738 + 0.616010i \(0.788748\pi\)
\(684\) 0 0
\(685\) −0.734335 + 0.734335i −0.0280575 + 0.0280575i
\(686\) 0 0
\(687\) 8.54725 34.1289i 0.326098 1.30210i
\(688\) 0 0
\(689\) −1.12470 + 1.94803i −0.0428475 + 0.0742140i
\(690\) 0 0
\(691\) −35.9149 9.62336i −1.36627 0.366090i −0.500153 0.865937i \(-0.666723\pi\)
−0.866114 + 0.499847i \(0.833390\pi\)
\(692\) 0 0
\(693\) −6.88498 + 7.35231i −0.261539 + 0.279291i
\(694\) 0 0
\(695\) 0.326960 0.188770i 0.0124023 0.00716047i
\(696\) 0 0
\(697\) 1.74715 + 1.00872i 0.0661780 + 0.0382079i
\(698\) 0 0
\(699\) −35.7024 19.8391i −1.35039 0.750382i
\(700\) 0 0
\(701\) 36.9558 36.9558i 1.39580 1.39580i 0.584175 0.811628i \(-0.301418\pi\)
0.811628 0.584175i \(-0.198582\pi\)
\(702\) 0 0
\(703\) −31.0176 −1.16985
\(704\) 0 0
\(705\) −0.815264 + 0.232850i −0.0307046 + 0.00876963i
\(706\) 0 0
\(707\) −2.11743 7.90237i −0.0796343 0.297199i
\(708\) 0 0
\(709\) −1.53529 + 5.72979i −0.0576591 + 0.215187i −0.988744 0.149615i \(-0.952197\pi\)
0.931085 + 0.364802i \(0.118863\pi\)
\(710\) 0 0
\(711\) 15.4217 28.8581i 0.578359 1.08226i
\(712\) 0 0
\(713\) −67.0640 + 38.7194i −2.51157 + 1.45005i
\(714\) 0 0
\(715\) 0.0630713 0.0168999i 0.00235873 0.000632021i
\(716\) 0 0
\(717\) −7.62996 12.7285i −0.284946 0.475356i
\(718\) 0 0
\(719\) −9.58462 −0.357446 −0.178723 0.983899i \(-0.557197\pi\)
−0.178723 + 0.983899i \(0.557197\pi\)
\(720\) 0 0
\(721\) −16.4075 −0.611046
\(722\) 0 0
\(723\) −12.7813 + 0.209713i −0.475340 + 0.00779931i
\(724\) 0 0
\(725\) 23.8370 6.38711i 0.885285 0.237211i
\(726\) 0 0
\(727\) −34.4374 + 19.8824i −1.27721 + 0.737399i −0.976335 0.216264i \(-0.930613\pi\)
−0.300877 + 0.953663i \(0.597279\pi\)
\(728\) 0 0
\(729\) 26.8693 2.65354i 0.995159 0.0982793i
\(730\) 0 0
\(731\) −0.569798 + 2.12651i −0.0210747 + 0.0786520i
\(732\) 0 0
\(733\) −9.37557 34.9901i −0.346295 1.29239i −0.891092 0.453822i \(-0.850060\pi\)
0.544798 0.838567i \(-0.316606\pi\)
\(734\) 0 0
\(735\) 0.428356 + 0.414526i 0.0158001 + 0.0152900i
\(736\) 0 0
\(737\) −15.2059 −0.560115
\(738\) 0 0
\(739\) 7.78860 7.78860i 0.286508 0.286508i −0.549190 0.835698i \(-0.685064\pi\)
0.835698 + 0.549190i \(0.185064\pi\)
\(740\) 0 0
\(741\) 3.17105 1.90084i 0.116491 0.0698291i
\(742\) 0 0
\(743\) 3.75539 + 2.16817i 0.137772 + 0.0795426i 0.567302 0.823510i \(-0.307987\pi\)
−0.429530 + 0.903053i \(0.641321\pi\)
\(744\) 0 0
\(745\) 1.24048 0.716193i 0.0454477 0.0262393i
\(746\) 0 0
\(747\) −4.84380 15.9628i −0.177226 0.584050i
\(748\) 0 0
\(749\) −13.9579 3.74001i −0.510011 0.136657i
\(750\) 0 0
\(751\) 6.74026 11.6745i 0.245956 0.426008i −0.716444 0.697644i \(-0.754232\pi\)
0.962400 + 0.271637i \(0.0875649\pi\)
\(752\) 0 0
\(753\) −20.6010 + 5.88389i −0.750741 + 0.214421i
\(754\) 0 0
\(755\) 0.648077 0.648077i 0.0235859 0.0235859i
\(756\) 0 0
\(757\) 25.9901 + 25.9901i 0.944625 + 0.944625i 0.998545 0.0539205i \(-0.0171718\pi\)
−0.0539205 + 0.998545i \(0.517172\pi\)
\(758\) 0 0
\(759\) 9.27712 + 32.4815i 0.336738 + 1.17900i
\(760\) 0 0
\(761\) −29.3955 16.9715i −1.06558 0.615216i −0.138613 0.990347i \(-0.544264\pi\)
−0.926972 + 0.375131i \(0.877598\pi\)
\(762\) 0 0
\(763\) −5.08845 + 18.9904i −0.184214 + 0.687498i
\(764\) 0 0
\(765\) −0.133362 0.124885i −0.00482171 0.00451523i
\(766\) 0 0
\(767\) −2.86947 4.97006i −0.103610 0.179459i
\(768\) 0 0
\(769\) 2.38011 4.12248i 0.0858291 0.148660i −0.819915 0.572485i \(-0.805979\pi\)
0.905744 + 0.423825i \(0.139313\pi\)
\(770\) 0 0
\(771\) 3.93734 + 6.56840i 0.141800 + 0.236555i
\(772\) 0 0
\(773\) −38.1267 38.1267i −1.37132 1.37132i −0.858486 0.512837i \(-0.828595\pi\)
−0.512837 0.858486i \(-0.671405\pi\)
\(774\) 0 0
\(775\) 44.9857i 1.61593i
\(776\) 0 0
\(777\) 10.4215 10.7692i 0.373868 0.386342i
\(778\) 0 0
\(779\) 12.1514 3.25596i 0.435369 0.116657i
\(780\) 0 0
\(781\) −0.795027 0.213027i −0.0284483 0.00762270i
\(782\) 0 0
\(783\) −25.0944 5.41642i −0.896802 0.193567i
\(784\) 0 0
\(785\) −0.273835 0.474296i −0.00977359 0.0169284i
\(786\) 0 0
\(787\) −6.10176 22.7721i −0.217504 0.811736i −0.985270 0.171006i \(-0.945298\pi\)
0.767766 0.640730i \(-0.221368\pi\)
\(788\) 0 0
\(789\) 0.311248 + 18.9695i 0.0110807 + 0.675331i
\(790\) 0 0
\(791\) 17.2053i 0.611749i
\(792\) 0 0
\(793\) 1.36980i 0.0486432i
\(794\) 0 0
\(795\) 0.594534 0.356386i 0.0210860 0.0126397i
\(796\) 0 0