Properties

Label 980.2.c.e.979.7
Level $980$
Weight $2$
Character 980.979
Analytic conductor $7.825$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.82533939809\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 979.7
Character \(\chi\) \(=\) 980.979
Dual form 980.2.c.e.979.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.36075 + 0.385185i) q^{2} -0.423388i q^{3} +(1.70326 - 1.04828i) q^{4} +(-1.74517 - 1.39799i) q^{5} +(0.163083 + 0.576124i) q^{6} +(-1.91393 + 2.08252i) q^{8} +2.82074 q^{9} +O(q^{10})\) \(q+(-1.36075 + 0.385185i) q^{2} -0.423388i q^{3} +(1.70326 - 1.04828i) q^{4} +(-1.74517 - 1.39799i) q^{5} +(0.163083 + 0.576124i) q^{6} +(-1.91393 + 2.08252i) q^{8} +2.82074 q^{9} +(2.91323 + 1.23009i) q^{10} +4.89551i q^{11} +(-0.443829 - 0.721142i) q^{12} -2.54664 q^{13} +(-0.591890 + 0.738886i) q^{15} +(1.80222 - 3.57099i) q^{16} +5.11429 q^{17} +(-3.83832 + 1.08651i) q^{18} -6.26601 q^{19} +(-4.43797 - 0.551709i) q^{20} +(-1.88568 - 6.66155i) q^{22} -4.63109 q^{23} +(0.881712 + 0.810335i) q^{24} +(1.09127 + 4.87946i) q^{25} +(3.46533 - 0.980929i) q^{26} -2.46443i q^{27} -1.88958 q^{29} +(0.520805 - 1.23342i) q^{30} +1.47756 q^{31} +(-1.07687 + 5.55341i) q^{32} +2.07270 q^{33} +(-6.95926 + 1.96995i) q^{34} +(4.80447 - 2.95693i) q^{36} +2.35920i q^{37} +(8.52645 - 2.41357i) q^{38} +1.07822i q^{39} +(6.25147 - 0.958707i) q^{40} +7.05393i q^{41} +10.7790 q^{43} +(5.13187 + 8.33835i) q^{44} +(-4.92269 - 3.94336i) q^{45} +(6.30175 - 1.78383i) q^{46} +12.2145i q^{47} +(-1.51192 - 0.763038i) q^{48} +(-3.36444 - 6.21937i) q^{50} -2.16533i q^{51} +(-4.33760 + 2.66959i) q^{52} +2.23621i q^{53} +(0.949263 + 3.35347i) q^{54} +(6.84386 - 8.54352i) q^{55} +2.65295i q^{57} +(2.57124 - 0.727837i) q^{58} +5.69000 q^{59} +(-0.233587 + 1.87899i) q^{60} -3.87005i q^{61} +(-2.01059 + 0.569136i) q^{62} +(-0.673743 - 7.97158i) q^{64} +(4.44433 + 3.56017i) q^{65} +(-2.82042 + 0.798374i) q^{66} -0.889310 q^{67} +(8.71100 - 5.36121i) q^{68} +1.96075i q^{69} +14.3310i q^{71} +(-5.39870 + 5.87424i) q^{72} +7.87187 q^{73} +(-0.908729 - 3.21027i) q^{74} +(2.06590 - 0.462031i) q^{75} +(-10.6727 + 6.56853i) q^{76} +(-0.415314 - 1.46718i) q^{78} +4.63973i q^{79} +(-8.13739 + 3.71253i) q^{80} +7.41882 q^{81} +(-2.71707 - 9.59861i) q^{82} -4.32876i q^{83} +(-8.92534 - 7.14971i) q^{85} +(-14.6675 + 4.15191i) q^{86} +0.800024i q^{87} +(-10.1950 - 9.36967i) q^{88} +2.18254i q^{89} +(8.21746 + 3.46977i) q^{90} +(-7.88798 + 4.85468i) q^{92} -0.625583i q^{93} +(-4.70485 - 16.6208i) q^{94} +(10.9353 + 8.75979i) q^{95} +(2.35125 + 0.455934i) q^{96} -3.42330 q^{97} +13.8090i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 16q^{4} - 64q^{9} + O(q^{10}) \) \( 48q + 16q^{4} - 64q^{9} + 16q^{16} - 16q^{25} - 48q^{29} - 8q^{30} + 176q^{36} - 48q^{44} - 32q^{46} + 32q^{50} + 24q^{60} - 80q^{64} - 16q^{65} - 112q^{74} - 48q^{81} - 64q^{85} - 112q^{86} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\) \(491\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36075 + 0.385185i −0.962193 + 0.272367i
\(3\) 0.423388i 0.244443i −0.992503 0.122222i \(-0.960998\pi\)
0.992503 0.122222i \(-0.0390019\pi\)
\(4\) 1.70326 1.04828i 0.851632 0.524140i
\(5\) −1.74517 1.39799i −0.780466 0.625198i
\(6\) 0.163083 + 0.576124i 0.0665783 + 0.235202i
\(7\) 0 0
\(8\) −1.91393 + 2.08252i −0.676676 + 0.736280i
\(9\) 2.82074 0.940248
\(10\) 2.91323 + 1.23009i 0.921243 + 0.388988i
\(11\) 4.89551i 1.47605i 0.674772 + 0.738026i \(0.264242\pi\)
−0.674772 + 0.738026i \(0.735758\pi\)
\(12\) −0.443829 0.721142i −0.128122 0.208176i
\(13\) −2.54664 −0.706311 −0.353156 0.935565i \(-0.614891\pi\)
−0.353156 + 0.935565i \(0.614891\pi\)
\(14\) 0 0
\(15\) −0.591890 + 0.738886i −0.152825 + 0.190780i
\(16\) 1.80222 3.57099i 0.450555 0.892749i
\(17\) 5.11429 1.24040 0.620199 0.784444i \(-0.287052\pi\)
0.620199 + 0.784444i \(0.287052\pi\)
\(18\) −3.83832 + 1.08651i −0.904700 + 0.256093i
\(19\) −6.26601 −1.43752 −0.718760 0.695258i \(-0.755290\pi\)
−0.718760 + 0.695258i \(0.755290\pi\)
\(20\) −4.43797 0.551709i −0.992361 0.123366i
\(21\) 0 0
\(22\) −1.88568 6.66155i −0.402028 1.42025i
\(23\) −4.63109 −0.965650 −0.482825 0.875717i \(-0.660389\pi\)
−0.482825 + 0.875717i \(0.660389\pi\)
\(24\) 0.881712 + 0.810335i 0.179979 + 0.165409i
\(25\) 1.09127 + 4.87946i 0.218254 + 0.975892i
\(26\) 3.46533 0.980929i 0.679608 0.192376i
\(27\) 2.46443i 0.474280i
\(28\) 0 0
\(29\) −1.88958 −0.350886 −0.175443 0.984490i \(-0.556136\pi\)
−0.175443 + 0.984490i \(0.556136\pi\)
\(30\) 0.520805 1.23342i 0.0950856 0.225191i
\(31\) 1.47756 0.265378 0.132689 0.991158i \(-0.457639\pi\)
0.132689 + 0.991158i \(0.457639\pi\)
\(32\) −1.07687 + 5.55341i −0.190366 + 0.981713i
\(33\) 2.07270 0.360811
\(34\) −6.95926 + 1.96995i −1.19350 + 0.337844i
\(35\) 0 0
\(36\) 4.80447 2.95693i 0.800745 0.492821i
\(37\) 2.35920i 0.387850i 0.981016 + 0.193925i \(0.0621218\pi\)
−0.981016 + 0.193925i \(0.937878\pi\)
\(38\) 8.52645 2.41357i 1.38317 0.391533i
\(39\) 1.07822i 0.172653i
\(40\) 6.25147 0.958707i 0.988444 0.151585i
\(41\) 7.05393i 1.10164i 0.834624 + 0.550819i \(0.185685\pi\)
−0.834624 + 0.550819i \(0.814315\pi\)
\(42\) 0 0
\(43\) 10.7790 1.64378 0.821890 0.569646i \(-0.192920\pi\)
0.821890 + 0.569646i \(0.192920\pi\)
\(44\) 5.13187 + 8.33835i 0.773658 + 1.25705i
\(45\) −4.92269 3.94336i −0.733831 0.587841i
\(46\) 6.30175 1.78383i 0.929142 0.263011i
\(47\) 12.2145i 1.78167i 0.454329 + 0.890834i \(0.349879\pi\)
−0.454329 + 0.890834i \(0.650121\pi\)
\(48\) −1.51192 0.763038i −0.218226 0.110135i
\(49\) 0 0
\(50\) −3.36444 6.21937i −0.475804 0.879552i
\(51\) 2.16533i 0.303207i
\(52\) −4.33760 + 2.66959i −0.601517 + 0.370206i
\(53\) 2.23621i 0.307167i 0.988136 + 0.153583i \(0.0490813\pi\)
−0.988136 + 0.153583i \(0.950919\pi\)
\(54\) 0.949263 + 3.35347i 0.129178 + 0.456349i
\(55\) 6.84386 8.54352i 0.922825 1.15201i
\(56\) 0 0
\(57\) 2.65295i 0.351392i
\(58\) 2.57124 0.727837i 0.337620 0.0955697i
\(59\) 5.69000 0.740774 0.370387 0.928877i \(-0.379225\pi\)
0.370387 + 0.928877i \(0.379225\pi\)
\(60\) −0.233587 + 1.87899i −0.0301559 + 0.242576i
\(61\) 3.87005i 0.495509i −0.968823 0.247754i \(-0.920307\pi\)
0.968823 0.247754i \(-0.0796926\pi\)
\(62\) −2.01059 + 0.569136i −0.255345 + 0.0722803i
\(63\) 0 0
\(64\) −0.673743 7.97158i −0.0842179 0.996447i
\(65\) 4.44433 + 3.56017i 0.551252 + 0.441585i
\(66\) −2.82042 + 0.798374i −0.347170 + 0.0982731i
\(67\) −0.889310 −0.108646 −0.0543232 0.998523i \(-0.517300\pi\)
−0.0543232 + 0.998523i \(0.517300\pi\)
\(68\) 8.71100 5.36121i 1.05636 0.650142i
\(69\) 1.96075i 0.236046i
\(70\) 0 0
\(71\) 14.3310i 1.70078i 0.526152 + 0.850391i \(0.323634\pi\)
−0.526152 + 0.850391i \(0.676366\pi\)
\(72\) −5.39870 + 5.87424i −0.636243 + 0.692286i
\(73\) 7.87187 0.921333 0.460667 0.887573i \(-0.347610\pi\)
0.460667 + 0.887573i \(0.347610\pi\)
\(74\) −0.908729 3.21027i −0.105638 0.373187i
\(75\) 2.06590 0.462031i 0.238550 0.0533507i
\(76\) −10.6727 + 6.56853i −1.22424 + 0.753462i
\(77\) 0 0
\(78\) −0.415314 1.46718i −0.0470250 0.166126i
\(79\) 4.63973i 0.522010i 0.965337 + 0.261005i \(0.0840540\pi\)
−0.965337 + 0.261005i \(0.915946\pi\)
\(80\) −8.13739 + 3.71253i −0.909788 + 0.415074i
\(81\) 7.41882 0.824313
\(82\) −2.71707 9.59861i −0.300050 1.05999i
\(83\) 4.32876i 0.475143i −0.971370 0.237571i \(-0.923649\pi\)
0.971370 0.237571i \(-0.0763514\pi\)
\(84\) 0 0
\(85\) −8.92534 7.14971i −0.968089 0.775495i
\(86\) −14.6675 + 4.15191i −1.58163 + 0.447712i
\(87\) 0.800024i 0.0857716i
\(88\) −10.1950 9.36967i −1.08679 0.998810i
\(89\) 2.18254i 0.231349i 0.993287 + 0.115674i \(0.0369029\pi\)
−0.993287 + 0.115674i \(0.963097\pi\)
\(90\) 8.21746 + 3.46977i 0.866196 + 0.365745i
\(91\) 0 0
\(92\) −7.88798 + 4.85468i −0.822378 + 0.506135i
\(93\) 0.625583i 0.0648699i
\(94\) −4.70485 16.6208i −0.485268 1.71431i
\(95\) 10.9353 + 8.75979i 1.12194 + 0.898735i
\(96\) 2.35125 + 0.455934i 0.239973 + 0.0465336i
\(97\) −3.42330 −0.347584 −0.173792 0.984782i \(-0.555602\pi\)
−0.173792 + 0.984782i \(0.555602\pi\)
\(98\) 0 0
\(99\) 13.8090i 1.38785i
\(100\) 6.97376 + 7.16705i 0.697376 + 0.716705i
\(101\) 7.30698i 0.727072i 0.931580 + 0.363536i \(0.118431\pi\)
−0.931580 + 0.363536i \(0.881569\pi\)
\(102\) 0.834054 + 2.94647i 0.0825836 + 0.291744i
\(103\) 6.75072i 0.665168i −0.943074 0.332584i \(-0.892079\pi\)
0.943074 0.332584i \(-0.107921\pi\)
\(104\) 4.87409 5.30342i 0.477944 0.520043i
\(105\) 0 0
\(106\) −0.861354 3.04291i −0.0836621 0.295554i
\(107\) 9.82994 0.950296 0.475148 0.879906i \(-0.342395\pi\)
0.475148 + 0.879906i \(0.342395\pi\)
\(108\) −2.58341 4.19758i −0.248589 0.403912i
\(109\) −9.41221 −0.901526 −0.450763 0.892644i \(-0.648848\pi\)
−0.450763 + 0.892644i \(0.648848\pi\)
\(110\) −6.02192 + 14.2617i −0.574167 + 1.35980i
\(111\) 0.998857 0.0948073
\(112\) 0 0
\(113\) 15.9261i 1.49820i 0.662455 + 0.749102i \(0.269515\pi\)
−0.662455 + 0.749102i \(0.730485\pi\)
\(114\) −1.02188 3.61000i −0.0957077 0.338107i
\(115\) 8.08207 + 6.47420i 0.753657 + 0.603722i
\(116\) −3.21845 + 1.98080i −0.298826 + 0.183913i
\(117\) −7.18342 −0.664107
\(118\) −7.74264 + 2.19170i −0.712768 + 0.201763i
\(119\) 0 0
\(120\) −0.405905 2.64680i −0.0370539 0.241618i
\(121\) −12.9660 −1.17873
\(122\) 1.49069 + 5.26615i 0.134960 + 0.476775i
\(123\) 2.98655 0.269288
\(124\) 2.51668 1.54890i 0.226005 0.139095i
\(125\) 4.91696 10.0411i 0.439786 0.898103i
\(126\) 0 0
\(127\) 12.2192 1.08428 0.542138 0.840290i \(-0.317615\pi\)
0.542138 + 0.840290i \(0.317615\pi\)
\(128\) 3.98733 + 10.5878i 0.352433 + 0.935837i
\(129\) 4.56369i 0.401811i
\(130\) −7.41894 3.13260i −0.650684 0.274747i
\(131\) −9.85060 −0.860651 −0.430325 0.902674i \(-0.641601\pi\)
−0.430325 + 0.902674i \(0.641601\pi\)
\(132\) 3.53036 2.17277i 0.307278 0.189115i
\(133\) 0 0
\(134\) 1.21013 0.342549i 0.104539 0.0295917i
\(135\) −3.44524 + 4.30087i −0.296519 + 0.370160i
\(136\) −9.78840 + 10.6506i −0.839348 + 0.913281i
\(137\) 4.69484i 0.401107i 0.979683 + 0.200554i \(0.0642741\pi\)
−0.979683 + 0.200554i \(0.935726\pi\)
\(138\) −0.755252 2.66808i −0.0642913 0.227122i
\(139\) 13.8745 1.17682 0.588409 0.808564i \(-0.299755\pi\)
0.588409 + 0.808564i \(0.299755\pi\)
\(140\) 0 0
\(141\) 5.17147 0.435516
\(142\) −5.52011 19.5009i −0.463237 1.63648i
\(143\) 12.4671i 1.04255i
\(144\) 5.08360 10.0729i 0.423633 0.839405i
\(145\) 3.29764 + 2.64160i 0.273854 + 0.219373i
\(146\) −10.7116 + 3.03213i −0.886501 + 0.250941i
\(147\) 0 0
\(148\) 2.47310 + 4.01834i 0.203288 + 0.330306i
\(149\) −5.46359 −0.447595 −0.223797 0.974636i \(-0.571845\pi\)
−0.223797 + 0.974636i \(0.571845\pi\)
\(150\) −2.63321 + 1.42446i −0.215000 + 0.116307i
\(151\) 1.49611i 0.121751i 0.998145 + 0.0608757i \(0.0193893\pi\)
−0.998145 + 0.0608757i \(0.980611\pi\)
\(152\) 11.9927 13.0491i 0.972736 1.05842i
\(153\) 14.4261 1.16628
\(154\) 0 0
\(155\) −2.57861 2.06561i −0.207119 0.165914i
\(156\) 1.13027 + 1.83649i 0.0904943 + 0.147037i
\(157\) −22.9035 −1.82790 −0.913948 0.405831i \(-0.866982\pi\)
−0.913948 + 0.405831i \(0.866982\pi\)
\(158\) −1.78716 6.31350i −0.142179 0.502275i
\(159\) 0.946783 0.0750848
\(160\) 9.64291 8.18622i 0.762339 0.647178i
\(161\) 0 0
\(162\) −10.0951 + 2.85762i −0.793148 + 0.224516i
\(163\) −1.93051 −0.151209 −0.0756047 0.997138i \(-0.524089\pi\)
−0.0756047 + 0.997138i \(0.524089\pi\)
\(164\) 7.39449 + 12.0147i 0.577413 + 0.938191i
\(165\) −3.61723 2.89761i −0.281601 0.225578i
\(166\) 1.66737 + 5.89034i 0.129413 + 0.457179i
\(167\) 16.9677i 1.31300i 0.754327 + 0.656499i \(0.227963\pi\)
−0.754327 + 0.656499i \(0.772037\pi\)
\(168\) 0 0
\(169\) −6.51462 −0.501124
\(170\) 14.8991 + 6.29104i 1.14271 + 0.482501i
\(171\) −17.6748 −1.35163
\(172\) 18.3595 11.2994i 1.39990 0.861570i
\(173\) 10.0363 0.763047 0.381524 0.924359i \(-0.375399\pi\)
0.381524 + 0.924359i \(0.375399\pi\)
\(174\) −0.308158 1.08863i −0.0233614 0.0825289i
\(175\) 0 0
\(176\) 17.4818 + 8.82279i 1.31774 + 0.665043i
\(177\) 2.40908i 0.181077i
\(178\) −0.840682 2.96988i −0.0630118 0.222602i
\(179\) 3.55282i 0.265550i 0.991146 + 0.132775i \(0.0423888\pi\)
−0.991146 + 0.132775i \(0.957611\pi\)
\(180\) −12.5184 1.55623i −0.933065 0.115994i
\(181\) 22.2716i 1.65543i 0.561148 + 0.827716i \(0.310360\pi\)
−0.561148 + 0.827716i \(0.689640\pi\)
\(182\) 0 0
\(183\) −1.63853 −0.121124
\(184\) 8.86359 9.64432i 0.653432 0.710989i
\(185\) 3.29813 4.11722i 0.242483 0.302704i
\(186\) 0.240965 + 0.851260i 0.0176684 + 0.0624174i
\(187\) 25.0371i 1.83089i
\(188\) 12.8042 + 20.8045i 0.933843 + 1.51733i
\(189\) 0 0
\(190\) −18.2543 7.70775i −1.32431 0.559179i
\(191\) 17.8460i 1.29129i −0.763636 0.645647i \(-0.776588\pi\)
0.763636 0.645647i \(-0.223412\pi\)
\(192\) −3.37507 + 0.285255i −0.243575 + 0.0205865i
\(193\) 18.2331i 1.31245i −0.754567 0.656223i \(-0.772153\pi\)
0.754567 0.656223i \(-0.227847\pi\)
\(194\) 4.65825 1.31861i 0.334443 0.0946703i
\(195\) 1.50733 1.88168i 0.107942 0.134750i
\(196\) 0 0
\(197\) 11.3569i 0.809148i −0.914505 0.404574i \(-0.867420\pi\)
0.914505 0.404574i \(-0.132580\pi\)
\(198\) −5.31902 18.7905i −0.378006 1.33538i
\(199\) −9.02829 −0.639998 −0.319999 0.947418i \(-0.603683\pi\)
−0.319999 + 0.947418i \(0.603683\pi\)
\(200\) −12.2502 7.06636i −0.866218 0.499667i
\(201\) 0.376523i 0.0265579i
\(202\) −2.81454 9.94295i −0.198030 0.699584i
\(203\) 0 0
\(204\) −2.26987 3.68813i −0.158923 0.258221i
\(205\) 9.86129 12.3103i 0.688743 0.859792i
\(206\) 2.60028 + 9.18602i 0.181170 + 0.640021i
\(207\) −13.0631 −0.907950
\(208\) −4.58961 + 9.09404i −0.318232 + 0.630558i
\(209\) 30.6753i 2.12186i
\(210\) 0 0
\(211\) 4.40164i 0.303021i −0.988456 0.151511i \(-0.951586\pi\)
0.988456 0.151511i \(-0.0484138\pi\)
\(212\) 2.34417 + 3.80885i 0.160998 + 0.261593i
\(213\) 6.06759 0.415744
\(214\) −13.3761 + 3.78635i −0.914369 + 0.258829i
\(215\) −18.8112 15.0689i −1.28291 1.02769i
\(216\) 5.13222 + 4.71675i 0.349203 + 0.320934i
\(217\) 0 0
\(218\) 12.8076 3.62544i 0.867442 0.245546i
\(219\) 3.33286i 0.225214i
\(220\) 2.70090 21.7262i 0.182094 1.46478i
\(221\) −13.0243 −0.876107
\(222\) −1.35919 + 0.384745i −0.0912230 + 0.0258224i
\(223\) 14.1103i 0.944899i −0.881358 0.472449i \(-0.843370\pi\)
0.881358 0.472449i \(-0.156630\pi\)
\(224\) 0 0
\(225\) 3.07819 + 13.7637i 0.205213 + 0.917580i
\(226\) −6.13451 21.6714i −0.408062 1.44156i
\(227\) 10.9976i 0.729936i −0.931020 0.364968i \(-0.881080\pi\)
0.931020 0.364968i \(-0.118920\pi\)
\(228\) 2.78104 + 4.51868i 0.184179 + 0.299257i
\(229\) 8.10937i 0.535883i −0.963435 0.267941i \(-0.913657\pi\)
0.963435 0.267941i \(-0.0863433\pi\)
\(230\) −13.4914 5.69666i −0.889598 0.375626i
\(231\) 0 0
\(232\) 3.61652 3.93507i 0.237436 0.258350i
\(233\) 15.8742i 1.03995i −0.854180 0.519977i \(-0.825941\pi\)
0.854180 0.519977i \(-0.174059\pi\)
\(234\) 9.77482 2.76695i 0.639000 0.180881i
\(235\) 17.0757 21.3164i 1.11390 1.39053i
\(236\) 9.69157 5.96471i 0.630867 0.388269i
\(237\) 1.96441 0.127602
\(238\) 0 0
\(239\) 24.4934i 1.58435i −0.610295 0.792174i \(-0.708949\pi\)
0.610295 0.792174i \(-0.291051\pi\)
\(240\) 1.57184 + 3.44527i 0.101462 + 0.222391i
\(241\) 19.1862i 1.23589i 0.786222 + 0.617945i \(0.212034\pi\)
−0.786222 + 0.617945i \(0.787966\pi\)
\(242\) 17.6435 4.99433i 1.13417 0.321048i
\(243\) 10.5343i 0.675778i
\(244\) −4.05689 6.59171i −0.259716 0.421991i
\(245\) 0 0
\(246\) −4.06394 + 1.15038i −0.259107 + 0.0733452i
\(247\) 15.9573 1.01534
\(248\) −2.82795 + 3.07705i −0.179575 + 0.195393i
\(249\) −1.83274 −0.116145
\(250\) −2.82305 + 15.5573i −0.178546 + 0.983932i
\(251\) −21.1323 −1.33386 −0.666929 0.745121i \(-0.732392\pi\)
−0.666929 + 0.745121i \(0.732392\pi\)
\(252\) 0 0
\(253\) 22.6716i 1.42535i
\(254\) −16.6272 + 4.70664i −1.04328 + 0.295321i
\(255\) −3.02710 + 3.77888i −0.189564 + 0.236643i
\(256\) −9.50401 12.8714i −0.594000 0.804465i
\(257\) −25.6520 −1.60013 −0.800064 0.599915i \(-0.795201\pi\)
−0.800064 + 0.599915i \(0.795201\pi\)
\(258\) 1.75787 + 6.21003i 0.109440 + 0.386620i
\(259\) 0 0
\(260\) 11.3019 + 1.40500i 0.700916 + 0.0871346i
\(261\) −5.33001 −0.329919
\(262\) 13.4042 3.79431i 0.828113 0.234413i
\(263\) 10.0198 0.617845 0.308922 0.951087i \(-0.400032\pi\)
0.308922 + 0.951087i \(0.400032\pi\)
\(264\) −3.96701 + 4.31643i −0.244152 + 0.265658i
\(265\) 3.12619 3.90257i 0.192040 0.239733i
\(266\) 0 0
\(267\) 0.924061 0.0565516
\(268\) −1.51473 + 0.932245i −0.0925269 + 0.0569459i
\(269\) 13.6945i 0.834966i 0.908685 + 0.417483i \(0.137088\pi\)
−0.908685 + 0.417483i \(0.862912\pi\)
\(270\) 3.03147 7.17945i 0.184490 0.436927i
\(271\) 15.3609 0.933107 0.466554 0.884493i \(-0.345495\pi\)
0.466554 + 0.884493i \(0.345495\pi\)
\(272\) 9.21708 18.2631i 0.558868 1.10736i
\(273\) 0 0
\(274\) −1.80838 6.38849i −0.109249 0.385943i
\(275\) −23.8875 + 5.34233i −1.44047 + 0.322155i
\(276\) 2.05541 + 3.33967i 0.123721 + 0.201025i
\(277\) 17.8089i 1.07004i −0.844841 0.535018i \(-0.820305\pi\)
0.844841 0.535018i \(-0.179695\pi\)
\(278\) −18.8796 + 5.34424i −1.13233 + 0.320526i
\(279\) 4.16783 0.249521
\(280\) 0 0
\(281\) 29.6169 1.76680 0.883398 0.468624i \(-0.155250\pi\)
0.883398 + 0.468624i \(0.155250\pi\)
\(282\) −7.03706 + 1.99198i −0.419051 + 0.118620i
\(283\) 3.57827i 0.212706i −0.994328 0.106353i \(-0.966083\pi\)
0.994328 0.106353i \(-0.0339174\pi\)
\(284\) 15.0229 + 24.4095i 0.891447 + 1.44844i
\(285\) 3.70879 4.62987i 0.219690 0.274250i
\(286\) 4.80215 + 16.9646i 0.283957 + 1.00314i
\(287\) 0 0
\(288\) −3.03757 + 15.6647i −0.178991 + 0.923053i
\(289\) 9.15600 0.538588
\(290\) −5.50476 2.32435i −0.323251 0.136490i
\(291\) 1.44938i 0.0849644i
\(292\) 13.4079 8.25192i 0.784637 0.482907i
\(293\) −17.7739 −1.03836 −0.519180 0.854665i \(-0.673763\pi\)
−0.519180 + 0.854665i \(0.673763\pi\)
\(294\) 0 0
\(295\) −9.93004 7.95453i −0.578149 0.463131i
\(296\) −4.91307 4.51534i −0.285566 0.262449i
\(297\) 12.0647 0.700063
\(298\) 7.43456 2.10449i 0.430673 0.121910i
\(299\) 11.7937 0.682049
\(300\) 3.03444 2.95261i 0.175194 0.170469i
\(301\) 0 0
\(302\) −0.576278 2.03582i −0.0331611 0.117148i
\(303\) 3.09369 0.177728
\(304\) −11.2927 + 22.3759i −0.647682 + 1.28334i
\(305\) −5.41027 + 6.75391i −0.309791 + 0.386728i
\(306\) −19.6303 + 5.55672i −1.12219 + 0.317657i
\(307\) 32.8923i 1.87726i 0.344923 + 0.938631i \(0.387905\pi\)
−0.344923 + 0.938631i \(0.612095\pi\)
\(308\) 0 0
\(309\) −2.85818 −0.162596
\(310\) 4.30447 + 1.81753i 0.244478 + 0.103229i
\(311\) 19.8748 1.12700 0.563499 0.826117i \(-0.309455\pi\)
0.563499 + 0.826117i \(0.309455\pi\)
\(312\) −2.24540 2.06363i −0.127121 0.116830i
\(313\) −6.37144 −0.360135 −0.180068 0.983654i \(-0.557632\pi\)
−0.180068 + 0.983654i \(0.557632\pi\)
\(314\) 31.1658 8.82208i 1.75879 0.497859i
\(315\) 0 0
\(316\) 4.86373 + 7.90269i 0.273606 + 0.444561i
\(317\) 17.0023i 0.954942i 0.878648 + 0.477471i \(0.158446\pi\)
−0.878648 + 0.477471i \(0.841554\pi\)
\(318\) −1.28833 + 0.364687i −0.0722461 + 0.0204506i
\(319\) 9.25045i 0.517926i
\(320\) −9.96835 + 14.8537i −0.557248 + 0.830346i
\(321\) 4.16188i 0.232293i
\(322\) 0 0
\(323\) −32.0462 −1.78310
\(324\) 12.6362 7.77699i 0.702011 0.432055i
\(325\) −2.77908 12.4262i −0.154155 0.689283i
\(326\) 2.62694 0.743605i 0.145493 0.0411845i
\(327\) 3.98502i 0.220372i
\(328\) −14.6899 13.5007i −0.811115 0.745453i
\(329\) 0 0
\(330\) 6.03824 + 2.54961i 0.332394 + 0.140351i
\(331\) 14.6613i 0.805857i 0.915231 + 0.402929i \(0.132008\pi\)
−0.915231 + 0.402929i \(0.867992\pi\)
\(332\) −4.53775 7.37302i −0.249041 0.404647i
\(333\) 6.65469i 0.364675i
\(334\) −6.53570 23.0887i −0.357618 1.26336i
\(335\) 1.55200 + 1.24324i 0.0847949 + 0.0679256i
\(336\) 0 0
\(337\) 15.2435i 0.830368i 0.909738 + 0.415184i \(0.136283\pi\)
−0.909738 + 0.415184i \(0.863717\pi\)
\(338\) 8.86475 2.50934i 0.482179 0.136490i
\(339\) 6.74293 0.366226
\(340\) −22.6971 2.82160i −1.23092 0.153023i
\(341\) 7.23343i 0.391712i
\(342\) 24.0509 6.80807i 1.30052 0.368138i
\(343\) 0 0
\(344\) −20.6302 + 22.4474i −1.11231 + 1.21028i
\(345\) 2.74110 3.42185i 0.147576 0.184226i
\(346\) −13.6569 + 3.86584i −0.734199 + 0.207829i
\(347\) −33.4194 −1.79405 −0.897024 0.441983i \(-0.854275\pi\)
−0.897024 + 0.441983i \(0.854275\pi\)
\(348\) 0.838649 + 1.36265i 0.0449563 + 0.0730459i
\(349\) 16.1586i 0.864951i 0.901646 + 0.432476i \(0.142360\pi\)
−0.901646 + 0.432476i \(0.857640\pi\)
\(350\) 0 0
\(351\) 6.27603i 0.334990i
\(352\) −27.1868 5.27183i −1.44906 0.280990i
\(353\) −22.6854 −1.20742 −0.603711 0.797203i \(-0.706312\pi\)
−0.603711 + 0.797203i \(0.706312\pi\)
\(354\) 0.927941 + 3.27814i 0.0493195 + 0.174231i
\(355\) 20.0346 25.0102i 1.06333 1.32740i
\(356\) 2.28791 + 3.71744i 0.121259 + 0.197024i
\(357\) 0 0
\(358\) −1.36850 4.83449i −0.0723272 0.255511i
\(359\) 16.7678i 0.884971i −0.896776 0.442486i \(-0.854097\pi\)
0.896776 0.442486i \(-0.145903\pi\)
\(360\) 17.6338 2.70427i 0.929382 0.142527i
\(361\) 20.2628 1.06647
\(362\) −8.57867 30.3059i −0.450885 1.59285i
\(363\) 5.48966i 0.288133i
\(364\) 0 0
\(365\) −13.7378 11.0048i −0.719069 0.576016i
\(366\) 2.22963 0.631138i 0.116544 0.0329901i
\(367\) 15.6432i 0.816567i 0.912855 + 0.408284i \(0.133873\pi\)
−0.912855 + 0.408284i \(0.866127\pi\)
\(368\) −8.34625 + 16.5376i −0.435078 + 0.862082i
\(369\) 19.8973i 1.03581i
\(370\) −2.90203 + 6.87288i −0.150869 + 0.357304i
\(371\) 0 0
\(372\) −0.655785 1.06553i −0.0340009 0.0552453i
\(373\) 17.1045i 0.885637i 0.896611 + 0.442819i \(0.146021\pi\)
−0.896611 + 0.442819i \(0.853979\pi\)
\(374\) −9.64392 34.0691i −0.498675 1.76167i
\(375\) −4.25128 2.08178i −0.219535 0.107503i
\(376\) −25.4369 23.3777i −1.31181 1.20561i
\(377\) 4.81207 0.247834
\(378\) 0 0
\(379\) 10.3762i 0.532990i −0.963836 0.266495i \(-0.914134\pi\)
0.963836 0.266495i \(-0.0858655\pi\)
\(380\) 27.8084 + 3.45701i 1.42654 + 0.177341i
\(381\) 5.17345i 0.265044i
\(382\) 6.87403 + 24.2839i 0.351706 + 1.24247i
\(383\) 9.23779i 0.472029i −0.971750 0.236015i \(-0.924159\pi\)
0.971750 0.236015i \(-0.0758413\pi\)
\(384\) 4.48274 1.68819i 0.228759 0.0861500i
\(385\) 0 0
\(386\) 7.02311 + 24.8106i 0.357467 + 1.26283i
\(387\) 30.4047 1.54556
\(388\) −5.83079 + 3.58858i −0.296013 + 0.182182i
\(389\) 17.0843 0.866208 0.433104 0.901344i \(-0.357418\pi\)
0.433104 + 0.901344i \(0.357418\pi\)
\(390\) −1.32630 + 3.14109i −0.0671600 + 0.159055i
\(391\) −23.6848 −1.19779
\(392\) 0 0
\(393\) 4.17063i 0.210380i
\(394\) 4.37452 + 15.4539i 0.220385 + 0.778557i
\(395\) 6.48628 8.09714i 0.326360 0.407411i
\(396\) 14.4757 + 23.5203i 0.727430 + 1.18194i
\(397\) 33.5365 1.68315 0.841573 0.540143i \(-0.181630\pi\)
0.841573 + 0.540143i \(0.181630\pi\)
\(398\) 12.2852 3.47756i 0.615802 0.174315i
\(399\) 0 0
\(400\) 19.3912 + 4.89694i 0.969562 + 0.244847i
\(401\) −12.8286 −0.640627 −0.320314 0.947312i \(-0.603788\pi\)
−0.320314 + 0.947312i \(0.603788\pi\)
\(402\) −0.145031 0.512353i −0.00723350 0.0255538i
\(403\) −3.76282 −0.187440
\(404\) 7.65976 + 12.4457i 0.381087 + 0.619198i
\(405\) −12.9471 10.3714i −0.643348 0.515359i
\(406\) 0 0
\(407\) −11.5495 −0.572487
\(408\) 4.50934 + 4.14429i 0.223245 + 0.205173i
\(409\) 21.5972i 1.06791i −0.845511 0.533957i \(-0.820704\pi\)
0.845511 0.533957i \(-0.179296\pi\)
\(410\) −8.67696 + 20.5497i −0.428525 + 1.01488i
\(411\) 1.98774 0.0980480
\(412\) −7.07664 11.4983i −0.348641 0.566479i
\(413\) 0 0
\(414\) 17.7756 5.03172i 0.873623 0.247296i
\(415\) −6.05154 + 7.55444i −0.297058 + 0.370833i
\(416\) 2.74240 14.1425i 0.134457 0.693395i
\(417\) 5.87429i 0.287665i
\(418\) 11.8157 + 41.7413i 0.577924 + 2.04164i
\(419\) −18.7281 −0.914929 −0.457464 0.889228i \(-0.651242\pi\)
−0.457464 + 0.889228i \(0.651242\pi\)
\(420\) 0 0
\(421\) −18.9665 −0.924371 −0.462186 0.886783i \(-0.652935\pi\)
−0.462186 + 0.886783i \(0.652935\pi\)
\(422\) 1.69545 + 5.98951i 0.0825330 + 0.291565i
\(423\) 34.4540i 1.67521i
\(424\) −4.65694 4.27994i −0.226161 0.207852i
\(425\) 5.58108 + 24.9550i 0.270722 + 1.21049i
\(426\) −8.25645 + 2.33715i −0.400026 + 0.113235i
\(427\) 0 0
\(428\) 16.7430 10.3045i 0.809303 0.498088i
\(429\) −5.27843 −0.254845
\(430\) 31.4016 + 13.2591i 1.51432 + 0.639411i
\(431\) 27.0242i 1.30171i −0.759203 0.650854i \(-0.774411\pi\)
0.759203 0.650854i \(-0.225589\pi\)
\(432\) −8.80048 4.44145i −0.423413 0.213689i
\(433\) 15.0015 0.720928 0.360464 0.932773i \(-0.382618\pi\)
0.360464 + 0.932773i \(0.382618\pi\)
\(434\) 0 0
\(435\) 1.11842 1.39618i 0.0536243 0.0669418i
\(436\) −16.0315 + 9.86662i −0.767769 + 0.472526i
\(437\) 29.0185 1.38814
\(438\) 1.28377 + 4.53517i 0.0613408 + 0.216699i
\(439\) 18.4380 0.879997 0.439998 0.897999i \(-0.354979\pi\)
0.439998 + 0.897999i \(0.354979\pi\)
\(440\) 4.69336 + 30.6041i 0.223747 + 1.45900i
\(441\) 0 0
\(442\) 17.7227 5.01676i 0.842985 0.238623i
\(443\) −20.8595 −0.991067 −0.495533 0.868589i \(-0.665027\pi\)
−0.495533 + 0.868589i \(0.665027\pi\)
\(444\) 1.70132 1.04708i 0.0807410 0.0496923i
\(445\) 3.05116 3.80891i 0.144639 0.180560i
\(446\) 5.43510 + 19.2006i 0.257359 + 0.909175i
\(447\) 2.31322i 0.109411i
\(448\) 0 0
\(449\) 14.6483 0.691298 0.345649 0.938364i \(-0.387659\pi\)
0.345649 + 0.938364i \(0.387659\pi\)
\(450\) −9.49022 17.5432i −0.447373 0.826996i
\(451\) −34.5326 −1.62608
\(452\) 16.6950 + 27.1264i 0.785268 + 1.27592i
\(453\) 0.633433 0.0297613
\(454\) 4.23611 + 14.9649i 0.198811 + 0.702339i
\(455\) 0 0
\(456\) −5.52481 5.07756i −0.258723 0.237779i
\(457\) 1.19001i 0.0556663i 0.999613 + 0.0278331i \(0.00886070\pi\)
−0.999613 + 0.0278331i \(0.991139\pi\)
\(458\) 3.12361 + 11.0348i 0.145957 + 0.515623i
\(459\) 12.6038i 0.588297i
\(460\) 20.5527 + 2.55501i 0.958273 + 0.119128i
\(461\) 14.5645i 0.678336i 0.940726 + 0.339168i \(0.110146\pi\)
−0.940726 + 0.339168i \(0.889854\pi\)
\(462\) 0 0
\(463\) −4.69391 −0.218145 −0.109072 0.994034i \(-0.534788\pi\)
−0.109072 + 0.994034i \(0.534788\pi\)
\(464\) −3.40543 + 6.74767i −0.158093 + 0.313253i
\(465\) −0.874556 + 1.09175i −0.0405565 + 0.0506287i
\(466\) 6.11451 + 21.6008i 0.283249 + 1.00064i
\(467\) 25.2818i 1.16990i 0.811068 + 0.584952i \(0.198887\pi\)
−0.811068 + 0.584952i \(0.801113\pi\)
\(468\) −12.2353 + 7.53023i −0.565575 + 0.348085i
\(469\) 0 0
\(470\) −15.0249 + 35.5836i −0.693048 + 1.64135i
\(471\) 9.69706i 0.446817i
\(472\) −10.8903 + 11.8495i −0.501265 + 0.545418i
\(473\) 52.7686i 2.42631i
\(474\) −2.67306 + 0.756661i −0.122778 + 0.0347546i
\(475\) −6.83791 30.5747i −0.313745 1.40286i
\(476\) 0 0
\(477\) 6.30776i 0.288813i
\(478\) 9.43451 + 33.3294i 0.431525 + 1.52445i
\(479\) 4.10286 0.187464 0.0937322 0.995597i \(-0.470120\pi\)
0.0937322 + 0.995597i \(0.470120\pi\)
\(480\) −3.46595 4.08269i −0.158198 0.186349i
\(481\) 6.00804i 0.273943i
\(482\) −7.39023 26.1075i −0.336616 1.18916i
\(483\) 0 0
\(484\) −22.0846 + 13.5920i −1.00385 + 0.617820i
\(485\) 5.97426 + 4.78573i 0.271277 + 0.217309i
\(486\) 4.05767 + 14.3346i 0.184060 + 0.650229i
\(487\) −33.8115 −1.53215 −0.766073 0.642754i \(-0.777792\pi\)
−0.766073 + 0.642754i \(0.777792\pi\)
\(488\) 8.05943 + 7.40700i 0.364833 + 0.335299i
\(489\) 0.817356i 0.0369621i
\(490\) 0 0
\(491\) 25.9116i 1.16937i −0.811259 0.584686i \(-0.801218\pi\)
0.811259 0.584686i \(-0.198782\pi\)
\(492\) 5.08688 3.13074i 0.229334 0.141145i
\(493\) −9.66385 −0.435238
\(494\) −21.7138 + 6.14651i −0.976950 + 0.276544i
\(495\) 19.3048 24.0991i 0.867684 1.08317i
\(496\) 2.66289 5.27637i 0.119567 0.236916i
\(497\) 0 0
\(498\) 2.49390 0.705946i 0.111754 0.0316342i
\(499\) 24.3024i 1.08792i 0.839110 + 0.543962i \(0.183077\pi\)
−0.839110 + 0.543962i \(0.816923\pi\)
\(500\) −2.15099 22.2570i −0.0961953 0.995362i
\(501\) 7.18391 0.320953
\(502\) 28.7557 8.13985i 1.28343 0.363299i
\(503\) 11.5222i 0.513750i 0.966445 + 0.256875i \(0.0826928\pi\)
−0.966445 + 0.256875i \(0.917307\pi\)
\(504\) 0 0
\(505\) 10.2151 12.7520i 0.454564 0.567455i
\(506\) 8.73276 + 30.8503i 0.388218 + 1.37146i
\(507\) 2.75821i 0.122496i
\(508\) 20.8125 12.8091i 0.923404 0.568312i
\(509\) 27.1315i 1.20258i −0.799031 0.601290i \(-0.794653\pi\)
0.799031 0.601290i \(-0.205347\pi\)
\(510\) 2.66355 6.30810i 0.117944 0.279327i
\(511\) 0 0
\(512\) 17.8904 + 13.8540i 0.790653 + 0.612264i
\(513\) 15.4422i 0.681788i
\(514\) 34.9059 9.88077i 1.53963 0.435822i
\(515\) −9.43741 + 11.7812i −0.415862 + 0.519141i
\(516\) −4.78403 7.77318i −0.210605 0.342195i
\(517\) −59.7962 −2.62983
\(518\) 0 0
\(519\) 4.24926i 0.186522i
\(520\) −15.9203 + 2.44148i −0.698149 + 0.107066i
\(521\) 17.2809i 0.757090i −0.925583 0.378545i \(-0.876424\pi\)
0.925583 0.378545i \(-0.123576\pi\)
\(522\) 7.25279 2.05304i 0.317446 0.0898592i
\(523\) 19.0461i 0.832828i −0.909175 0.416414i \(-0.863287\pi\)
0.909175 0.416414i \(-0.136713\pi\)
\(524\) −16.7782 + 10.3262i −0.732958 + 0.451101i
\(525\) 0 0
\(526\) −13.6344 + 3.85946i −0.594486 + 0.168281i
\(527\) 7.55669 0.329175
\(528\) 3.73546 7.40160i 0.162565 0.322114i
\(529\) −1.55298 −0.0675209
\(530\) −2.75073 + 6.51457i −0.119484 + 0.282975i
\(531\) 16.0500 0.696511
\(532\) 0 0
\(533\) 17.9638i 0.778100i
\(534\) −1.25741 + 0.355935i −0.0544136 + 0.0154028i
\(535\) −17.1550 13.7421i −0.741674 0.594123i
\(536\) 1.70208 1.85200i 0.0735185 0.0799943i
\(537\) 1.50422 0.0649120
\(538\) −5.27490 18.6347i −0.227417 0.803399i
\(539\) 0 0
\(540\) −1.35965 + 10.9371i −0.0585100 + 0.470657i
\(541\) 18.3881 0.790564 0.395282 0.918560i \(-0.370647\pi\)
0.395282 + 0.918560i \(0.370647\pi\)
\(542\) −20.9023 + 5.91679i −0.897830 + 0.254148i
\(543\) 9.42951 0.404659
\(544\) −5.50743 + 28.4018i −0.236129 + 1.21772i
\(545\) 16.4259 + 13.1581i 0.703610 + 0.563632i
\(546\) 0 0
\(547\) 18.9519 0.810323 0.405161 0.914245i \(-0.367215\pi\)
0.405161 + 0.914245i \(0.367215\pi\)
\(548\) 4.92151 + 7.99656i 0.210236 + 0.341596i
\(549\) 10.9164i 0.465901i
\(550\) 30.4470 16.4707i 1.29826 0.702311i
\(551\) 11.8401 0.504405
\(552\) −4.08329 3.75274i −0.173796 0.159727i
\(553\) 0 0
\(554\) 6.85974 + 24.2335i 0.291443 + 1.02958i
\(555\) −1.74318 1.39639i −0.0739939 0.0592734i
\(556\) 23.6319 14.5443i 1.00222 0.616817i
\(557\) 25.5109i 1.08093i −0.841365 0.540467i \(-0.818248\pi\)
0.841365 0.540467i \(-0.181752\pi\)
\(558\) −5.67136 + 1.60539i −0.240088 + 0.0679614i
\(559\) −27.4502 −1.16102
\(560\) 0 0
\(561\) 10.6004 0.447549
\(562\) −40.3011 + 11.4080i −1.70000 + 0.481217i
\(563\) 31.4612i 1.32593i 0.748650 + 0.662965i \(0.230702\pi\)
−0.748650 + 0.662965i \(0.769298\pi\)
\(564\) 8.80838 5.42115i 0.370900 0.228272i
\(565\) 22.2645 27.7939i 0.936675 1.16930i
\(566\) 1.37830 + 4.86912i 0.0579342 + 0.204665i
\(567\) 0 0
\(568\) −29.8446 27.4286i −1.25225 1.15088i
\(569\) 16.4346 0.688972 0.344486 0.938791i \(-0.388053\pi\)
0.344486 + 0.938791i \(0.388053\pi\)
\(570\) −3.26337 + 7.72865i −0.136687 + 0.323717i
\(571\) 15.0067i 0.628011i 0.949421 + 0.314005i \(0.101671\pi\)
−0.949421 + 0.314005i \(0.898329\pi\)
\(572\) −13.0690 21.2348i −0.546443 0.887871i
\(573\) −7.55580 −0.315648
\(574\) 0 0
\(575\) −5.05378 22.5972i −0.210757 0.942370i
\(576\) −1.90046 22.4858i −0.0791857 0.936907i
\(577\) 2.49932 0.104048 0.0520240 0.998646i \(-0.483433\pi\)
0.0520240 + 0.998646i \(0.483433\pi\)
\(578\) −12.4590 + 3.52676i −0.518226 + 0.146694i
\(579\) −7.71967 −0.320818
\(580\) 8.38589 + 1.04250i 0.348205 + 0.0432873i
\(581\) 0 0
\(582\) −0.558282 1.97225i −0.0231415 0.0817522i
\(583\) −10.9474 −0.453394
\(584\) −15.0662 + 16.3933i −0.623444 + 0.678360i
\(585\) 12.5363 + 10.0423i 0.518313 + 0.415199i
\(586\) 24.1857 6.84624i 0.999104 0.282815i
\(587\) 22.1562i 0.914482i 0.889343 + 0.457241i \(0.151162\pi\)
−0.889343 + 0.457241i \(0.848838\pi\)
\(588\) 0 0
\(589\) −9.25842 −0.381487
\(590\) 16.5762 + 6.99920i 0.682433 + 0.288153i
\(591\) −4.80839 −0.197791
\(592\) 8.42469 + 4.25180i 0.346253 + 0.174748i
\(593\) −28.6502 −1.17652 −0.588262 0.808670i \(-0.700188\pi\)
−0.588262 + 0.808670i \(0.700188\pi\)
\(594\) −16.4169 + 4.64713i −0.673596 + 0.190674i
\(595\) 0 0
\(596\) −9.30594 + 5.72737i −0.381186 + 0.234602i
\(597\) 3.82247i 0.156443i
\(598\) −16.0483 + 4.54277i −0.656263 + 0.185768i
\(599\) 16.4006i 0.670110i 0.942199 + 0.335055i \(0.108755\pi\)
−0.942199 + 0.335055i \(0.891245\pi\)
\(600\) −2.99181 + 5.18657i −0.122140 + 0.211741i
\(601\) 22.1672i 0.904220i −0.891962 0.452110i \(-0.850671\pi\)
0.891962 0.452110i \(-0.149329\pi\)
\(602\) 0 0
\(603\) −2.50851 −0.102155
\(604\) 1.56834 + 2.54826i 0.0638147 + 0.103687i
\(605\) 22.6280 + 18.1263i 0.919959 + 0.736940i
\(606\) −4.20973 + 1.19164i −0.171008 + 0.0484072i
\(607\) 28.7504i 1.16694i 0.812133 + 0.583472i \(0.198306\pi\)
−0.812133 + 0.583472i \(0.801694\pi\)
\(608\) 6.74768 34.7977i 0.273654 1.41123i
\(609\) 0 0
\(610\) 4.76050 11.2743i 0.192747 0.456484i
\(611\) 31.1059i 1.25841i
\(612\) 24.5715 15.1226i 0.993243 0.611295i
\(613\) 12.1472i 0.490620i −0.969445 0.245310i \(-0.921110\pi\)
0.969445 0.245310i \(-0.0788898\pi\)
\(614\) −12.6696 44.7581i −0.511305 1.80629i
\(615\) −5.21205 4.17515i −0.210170 0.168358i
\(616\) 0 0
\(617\) 15.9265i 0.641175i 0.947219 + 0.320588i \(0.103880\pi\)
−0.947219 + 0.320588i \(0.896120\pi\)
\(618\) 3.88925 1.10093i 0.156449 0.0442858i
\(619\) −3.88335 −0.156085 −0.0780424 0.996950i \(-0.524867\pi\)
−0.0780424 + 0.996950i \(0.524867\pi\)
\(620\) −6.55739 0.815184i −0.263351 0.0327386i
\(621\) 11.4130i 0.457989i
\(622\) −27.0446 + 7.65549i −1.08439 + 0.306957i
\(623\) 0 0
\(624\) 3.85031 + 1.94319i 0.154136 + 0.0777897i
\(625\) −22.6183 + 10.6496i −0.904730 + 0.425985i
\(626\) 8.66992 2.45419i 0.346520 0.0980890i
\(627\) −12.9876 −0.518673
\(628\) −39.0107 + 24.0092i −1.55670 + 0.958073i
\(629\) 12.0656i 0.481089i
\(630\) 0 0
\(631\) 12.2743i 0.488633i −0.969696 0.244316i \(-0.921436\pi\)
0.969696 0.244316i \(-0.0785636\pi\)
\(632\) −9.66231 8.88012i −0.384346 0.353232i
\(633\) −1.86360 −0.0740715
\(634\) −6.54902 23.1358i −0.260095 0.918838i
\(635\) −21.3246 17.0822i −0.846240 0.677887i
\(636\) 1.61262 0.992493i 0.0639446 0.0393549i
\(637\) 0 0
\(638\) 3.56314 + 12.5875i 0.141066 + 0.498345i
\(639\) 40.4242i 1.59916i
\(640\) 7.84299 24.0518i 0.310021 0.950730i
\(641\) 14.8270 0.585631 0.292816 0.956169i \(-0.405408\pi\)
0.292816 + 0.956169i \(0.405408\pi\)
\(642\) 1.60309 + 5.66326i 0.0632691 + 0.223511i
\(643\) 11.8058i 0.465577i −0.972527 0.232789i \(-0.925215\pi\)
0.972527 0.232789i \(-0.0747850\pi\)
\(644\) 0 0
\(645\) −6.37998 + 7.96444i −0.251211 + 0.313600i
\(646\) 43.6068 12.3437i 1.71569 0.485657i
\(647\) 34.6071i 1.36054i −0.732960 0.680272i \(-0.761862\pi\)
0.732960 0.680272i \(-0.238138\pi\)
\(648\) −14.1991 + 15.4498i −0.557793 + 0.606926i
\(649\) 27.8554i 1.09342i
\(650\) 8.56802 + 15.8385i 0.336065 + 0.621237i
\(651\) 0 0
\(652\) −3.28817 + 2.02372i −0.128775 + 0.0792549i
\(653\) 28.1875i 1.10306i −0.834155 0.551531i \(-0.814044\pi\)
0.834155 0.551531i \(-0.185956\pi\)
\(654\) −1.53497 5.42260i −0.0600221 0.212040i
\(655\) 17.1910 + 13.7710i 0.671709 + 0.538077i
\(656\) 25.1895 + 12.7127i 0.983487 + 0.496349i
\(657\) 22.2045 0.866281
\(658\) 0 0
\(659\) 9.79123i 0.381412i −0.981647 0.190706i \(-0.938922\pi\)
0.981647 0.190706i \(-0.0610777\pi\)
\(660\) −9.19859 1.14353i −0.358055 0.0445117i
\(661\) 0.817006i 0.0317779i 0.999874 + 0.0158889i \(0.00505782\pi\)
−0.999874 + 0.0158889i \(0.994942\pi\)
\(662\) −5.64731 19.9503i −0.219489 0.775391i
\(663\) 5.51432i 0.214158i
\(664\) 9.01470 + 8.28494i 0.349838 + 0.321518i
\(665\) 0 0
\(666\) −2.56329 9.05536i −0.0993255 0.350888i
\(667\) 8.75081 0.338833
\(668\) 17.7869 + 28.9004i 0.688194 + 1.11819i
\(669\) −5.97415 −0.230974
\(670\) −2.59076 1.09393i −0.100090 0.0422622i
\(671\) 18.9459 0.731397
\(672\) 0 0
\(673\) 9.43129i 0.363550i −0.983340 0.181775i \(-0.941816\pi\)
0.983340 0.181775i \(-0.0581842\pi\)
\(674\) −5.87158 20.7426i −0.226165 0.798974i
\(675\) 12.0251 2.68936i 0.462846 0.103514i
\(676\) −11.0961 + 6.82914i −0.426774 + 0.262659i
\(677\) −2.47400 −0.0950837 −0.0475418 0.998869i \(-0.515139\pi\)
−0.0475418 + 0.998869i \(0.515139\pi\)
\(678\) −9.17542 + 2.59728i −0.352380 + 0.0997479i
\(679\) 0 0
\(680\) 31.9719 4.90311i 1.22606 0.188026i
\(681\) −4.65625 −0.178428
\(682\) −2.78621 9.84287i −0.106690 0.376903i
\(683\) 18.7560 0.717679 0.358840 0.933399i \(-0.383173\pi\)
0.358840 + 0.933399i \(0.383173\pi\)
\(684\) −30.1048 + 18.5281i −1.15109 + 0.708440i
\(685\) 6.56332 8.19332i 0.250772 0.313051i
\(686\) 0 0
\(687\) −3.43341 −0.130993
\(688\) 19.4261 38.4917i 0.740613 1.46748i
\(689\) 5.69482i 0.216955i
\(690\) −2.41190 + 5.71210i −0.0918193 + 0.217456i
\(691\) 4.22127 0.160585 0.0802923 0.996771i \(-0.474415\pi\)
0.0802923 + 0.996771i \(0.474415\pi\)
\(692\) 17.0945 10.5209i 0.649836 0.399943i
\(693\) 0 0
\(694\) 45.4753 12.8727i 1.72622 0.488640i
\(695\) −24.2134 19.3963i −0.918466 0.735744i
\(696\) −1.66606 1.53119i −0.0631520 0.0580396i
\(697\) 36.0759i 1.36647i
\(698\) −6.22406 21.9878i −0.235584 0.832250i
\(699\) −6.72095 −0.254210
\(700\) 0 0
\(701\) −12.2843 −0.463971 −0.231985 0.972719i \(-0.574522\pi\)
−0.231985 + 0.972719i \(0.574522\pi\)
\(702\) −2.41743 8.54008i −0.0912401 0.322325i
\(703\) 14.7828i 0.557542i
\(704\) 39.0250 3.29832i 1.47081 0.124310i
\(705\) −9.02512 7.22964i −0.339906 0.272284i
\(706\) 30.8691 8.73809i 1.16177 0.328862i
\(707\) 0 0
\(708\) −2.52539 4.10329i −0.0949098 0.154211i
\(709\) 2.93616 0.110270 0.0551348 0.998479i \(-0.482441\pi\)
0.0551348 + 0.998479i \(0.482441\pi\)
\(710\) −17.6285 + 41.7495i −0.661584 + 1.56683i
\(711\) 13.0875i 0.490819i
\(712\) −4.54517 4.17723i −0.170337 0.156548i
\(713\) −6.84273 −0.256262
\(714\) 0 0
\(715\) −17.4288 + 21.7573i −0.651802 + 0.813677i
\(716\) 3.72435 + 6.05140i 0.139186 + 0.226151i
\(717\) −10.3702 −0.387283
\(718\) 6.45872 + 22.8168i 0.241037 + 0.851514i
\(719\) −47.5276 −1.77248 −0.886240 0.463226i \(-0.846692\pi\)
−0.886240 + 0.463226i \(0.846692\pi\)
\(720\) −22.9535 + 10.4721i −0.855426 + 0.390272i
\(721\) 0 0
\(722\) −27.5726 + 7.80495i −1.02615 + 0.290470i
\(723\) 8.12319 0.302105
\(724\) 23.3468 + 37.9343i 0.867677 + 1.40982i
\(725\) −2.06204 9.22011i −0.0765823 0.342426i
\(726\) −2.11454 7.47004i −0.0784779 0.277239i
\(727\) 8.28795i 0.307383i 0.988119 + 0.153692i \(0.0491162\pi\)
−0.988119 + 0.153692i \(0.950884\pi\)
\(728\) 0 0
\(729\) 17.7963 0.659124
\(730\) 22.9325 + 9.68311i 0.848771 + 0.358388i
\(731\) 55.1269 2.03894
\(732\) −2.79085 + 1.71764i −0.103153 + 0.0634858i
\(733\) 41.9860 1.55079 0.775395 0.631477i \(-0.217551\pi\)
0.775395 + 0.631477i \(0.217551\pi\)
\(734\) −6.02552 21.2864i −0.222406 0.785696i
\(735\) 0 0
\(736\) 4.98709 25.7184i 0.183826 0.947991i
\(737\) 4.35363i 0.160368i
\(738\) −7.66416 27.0752i −0.282121 0.996653i
\(739\) 25.9230i 0.953593i −0.879014 0.476796i \(-0.841798\pi\)
0.879014 0.476796i \(-0.158202\pi\)
\(740\) 1.30159 10.4701i 0.0478474 0.384887i
\(741\) 6.75612i 0.248192i
\(742\) 0 0
\(743\) −11.2976 −0.414470 −0.207235 0.978291i \(-0.566446\pi\)
−0.207235 + 0.978291i \(0.566446\pi\)
\(744\) 1.30279 + 1.19732i 0.0477624 + 0.0438959i
\(745\) 9.53492 + 7.63802i 0.349332 + 0.279835i
\(746\) −6.58840 23.2749i −0.241219 0.852155i
\(747\) 12.2103i 0.446752i
\(748\) 26.2459 + 42.6448i 0.959644 + 1.55925i
\(749\) 0 0
\(750\) 6.58679 + 1.19525i 0.240515 + 0.0436442i
\(751\) 5.61823i 0.205012i 0.994732 + 0.102506i \(0.0326861\pi\)
−0.994732 + 0.102506i \(0.967314\pi\)
\(752\) 43.6179 + 22.0132i 1.59058 + 0.802739i
\(753\) 8.94716i 0.326053i
\(754\) −6.54802 + 1.85354i −0.238465 + 0.0675020i
\(755\) 2.09153 2.61097i 0.0761187 0.0950228i
\(756\) 0 0
\(757\) 27.0456i 0.982990i −0.870880 0.491495i \(-0.836451\pi\)
0.870880 0.491495i \(-0.163549\pi\)
\(758\) 3.99676 + 14.1194i 0.145169 + 0.512839i
\(759\) −9.59887 −0.348417
\(760\) −39.1718 + 6.00726i −1.42091 + 0.217906i
\(761\) 25.8142i 0.935765i −0.883791 0.467883i \(-0.845017\pi\)
0.883791 0.467883i \(-0.154983\pi\)
\(762\) 1.99274 + 7.03975i 0.0721892 + 0.255023i
\(763\) 0 0
\(764\) −18.7076 30.3965i −0.676818 1.09971i
\(765\) −25.1761 20.1675i −0.910243 0.729157i
\(766\) 3.55826 + 12.5703i 0.128565 + 0.454183i
\(767\) −14.4904 −0.523217
\(768\) −5.44961 + 4.02388i −0.196646 + 0.145199i
\(769\) 5.58909i 0.201548i 0.994909 + 0.100774i \(0.0321319\pi\)
−0.994909 + 0.100774i \(0.967868\pi\)
\(770\) 0 0
\(771\) 10.8608i 0.391140i
\(772\) −19.1134 31.0557i −0.687905 1.11772i
\(773\) −8.77216 −0.315513 −0.157756 0.987478i \(-0.550426\pi\)
−0.157756 + 0.987478i \(0.550426\pi\)
\(774\) −41.3732 + 11.7115i −1.48713 + 0.420960i
\(775\) 1.61242 + 7.20971i 0.0579199 + 0.258980i
\(776\) 6.55196 7.12908i 0.235202 0.255919i
\(777\) 0 0
\(778\) −23.2474 + 6.58062i −0.833459 + 0.235927i
\(779\) 44.2000i 1.58363i
\(780\) 0.594862 4.78510i 0.0212995 0.171334i
\(781\) −70.1578 −2.51044
\(782\) 32.2290 9.12303i 1.15251 0.326239i
\(783\) 4.65674i 0.166418i
\(784\) 0 0
\(785\) 39.9706 + 32.0187i 1.42661 + 1.14280i
\(786\) −1.60646 5.67517i