Properties

Label 405.2.r.a.368.1
Level $405$
Weight $2$
Character 405.368
Analytic conductor $3.234$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.r (of order \(36\), degree \(12\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(16\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 368.1
Character \(\chi\) \(=\) 405.368
Dual form 405.2.r.a.197.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.44518 - 0.213925i) q^{2} +(3.96351 + 0.698873i) q^{4} +(-1.02222 - 1.98874i) q^{5} +(-3.87397 - 2.71258i) q^{7} +(-4.80021 - 1.28621i) q^{8} +O(q^{10})\) \(q+(-2.44518 - 0.213925i) q^{2} +(3.96351 + 0.698873i) q^{4} +(-1.02222 - 1.98874i) q^{5} +(-3.87397 - 2.71258i) q^{7} +(-4.80021 - 1.28621i) q^{8} +(2.07406 + 5.08149i) q^{10} +(-0.927704 + 2.54885i) q^{11} +(0.0885504 + 1.01214i) q^{13} +(8.89224 + 7.46148i) q^{14} +(3.89833 + 1.41887i) q^{16} +(1.15325 - 0.309013i) q^{17} +(0.507294 - 0.292886i) q^{19} +(-2.66169 - 8.59677i) q^{20} +(2.81366 - 6.03392i) q^{22} +(0.750556 + 1.07190i) q^{23} +(-2.91015 + 4.06584i) q^{25} -2.49379i q^{26} +(-13.4587 - 13.4587i) q^{28} +(0.185521 - 0.155671i) q^{29} +(-0.978463 + 5.54914i) q^{31} +(-0.220700 - 0.102914i) q^{32} +(-2.88601 + 0.508881i) q^{34} +(-1.43458 + 10.4771i) q^{35} +(-0.227764 - 0.850028i) q^{37} +(-1.30308 + 0.607636i) q^{38} +(2.34891 + 10.8611i) q^{40} +(2.80103 - 3.33813i) q^{41} +(4.67013 + 10.0151i) q^{43} +(-5.45828 + 9.45402i) q^{44} +(-1.60593 - 2.78156i) q^{46} +(-3.77551 + 5.39198i) q^{47} +(5.25539 + 14.4391i) q^{49} +(7.98561 - 9.31914i) q^{50} +(-0.356385 + 4.07349i) q^{52} +(-6.73617 + 6.73617i) q^{53} +(6.01730 - 0.760513i) q^{55} +(15.1069 + 18.0037i) q^{56} +(-0.486933 + 0.340954i) q^{58} +(-11.1903 + 4.07292i) q^{59} +(-1.40842 - 7.98754i) q^{61} +(3.57962 - 13.3593i) q^{62} +(-6.66780 - 3.84966i) q^{64} +(1.92235 - 1.21073i) q^{65} +(-7.77347 + 0.680090i) q^{67} +(4.78688 - 0.418798i) q^{68} +(5.74912 - 25.3116i) q^{70} +(-1.13442 - 0.654959i) q^{71} +(-0.567144 + 2.11661i) q^{73} +(0.375082 + 2.12719i) q^{74} +(2.21535 - 0.806323i) q^{76} +(10.5078 - 7.35767i) q^{77} +(2.17780 + 2.59540i) q^{79} +(-1.16316 - 9.20314i) q^{80} +(-7.56311 + 7.56311i) q^{82} +(0.839279 - 9.59300i) q^{83} +(-1.79342 - 1.97763i) q^{85} +(-9.27680 - 25.4878i) q^{86} +(7.73153 - 11.0418i) q^{88} +(1.54112 + 2.66930i) q^{89} +(2.40246 - 4.16118i) q^{91} +(2.22571 + 4.77305i) q^{92} +(10.3853 - 12.3767i) q^{94} +(-1.10104 - 0.709481i) q^{95} +(-3.04230 + 1.41865i) q^{97} +(-9.76147 - 36.4303i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.44518 0.213925i −1.72900 0.151268i −0.821192 0.570652i \(-0.806690\pi\)
−0.907809 + 0.419384i \(0.862246\pi\)
\(3\) 0 0
\(4\) 3.96351 + 0.698873i 1.98175 + 0.349437i
\(5\) −1.02222 1.98874i −0.457149 0.889390i
\(6\) 0 0
\(7\) −3.87397 2.71258i −1.46422 1.02526i −0.989406 0.145174i \(-0.953626\pi\)
−0.474816 0.880085i \(-0.657485\pi\)
\(8\) −4.80021 1.28621i −1.69713 0.454744i
\(9\) 0 0
\(10\) 2.07406 + 5.08149i 0.655875 + 1.60691i
\(11\) −0.927704 + 2.54885i −0.279713 + 0.768506i 0.717682 + 0.696371i \(0.245203\pi\)
−0.997395 + 0.0721346i \(0.977019\pi\)
\(12\) 0 0
\(13\) 0.0885504 + 1.01214i 0.0245595 + 0.280716i 0.998537 + 0.0540717i \(0.0172200\pi\)
−0.973978 + 0.226644i \(0.927224\pi\)
\(14\) 8.89224 + 7.46148i 2.37655 + 1.99416i
\(15\) 0 0
\(16\) 3.89833 + 1.41887i 0.974582 + 0.354719i
\(17\) 1.15325 0.309013i 0.279704 0.0749466i −0.116240 0.993221i \(-0.537084\pi\)
0.395944 + 0.918275i \(0.370417\pi\)
\(18\) 0 0
\(19\) 0.507294 0.292886i 0.116381 0.0671927i −0.440679 0.897665i \(-0.645262\pi\)
0.557061 + 0.830472i \(0.311929\pi\)
\(20\) −2.66169 8.59677i −0.595171 1.92230i
\(21\) 0 0
\(22\) 2.81366 6.03392i 0.599875 1.28644i
\(23\) 0.750556 + 1.07190i 0.156502 + 0.223508i 0.889744 0.456460i \(-0.150883\pi\)
−0.733242 + 0.679967i \(0.761994\pi\)
\(24\) 0 0
\(25\) −2.91015 + 4.06584i −0.582030 + 0.813168i
\(26\) 2.49379i 0.489073i
\(27\) 0 0
\(28\) −13.4587 13.4587i −2.54346 2.54346i
\(29\) 0.185521 0.155671i 0.0344504 0.0289073i −0.625400 0.780304i \(-0.715064\pi\)
0.659850 + 0.751397i \(0.270620\pi\)
\(30\) 0 0
\(31\) −0.978463 + 5.54914i −0.175737 + 0.996655i 0.761552 + 0.648103i \(0.224438\pi\)
−0.937290 + 0.348552i \(0.886674\pi\)
\(32\) −0.220700 0.102914i −0.0390146 0.0181928i
\(33\) 0 0
\(34\) −2.88601 + 0.508881i −0.494946 + 0.0872724i
\(35\) −1.43458 + 10.4771i −0.242488 + 1.77096i
\(36\) 0 0
\(37\) −0.227764 0.850028i −0.0374442 0.139744i 0.944673 0.328013i \(-0.106379\pi\)
−0.982117 + 0.188269i \(0.939712\pi\)
\(38\) −1.30308 + 0.607636i −0.211387 + 0.0985715i
\(39\) 0 0
\(40\) 2.34891 + 10.8611i 0.371396 + 1.71730i
\(41\) 2.80103 3.33813i 0.437447 0.521329i −0.501609 0.865095i \(-0.667258\pi\)
0.939055 + 0.343766i \(0.111703\pi\)
\(42\) 0 0
\(43\) 4.67013 + 10.0151i 0.712188 + 1.52729i 0.844191 + 0.536043i \(0.180082\pi\)
−0.132002 + 0.991249i \(0.542141\pi\)
\(44\) −5.45828 + 9.45402i −0.822867 + 1.42525i
\(45\) 0 0
\(46\) −1.60593 2.78156i −0.236782 0.410118i
\(47\) −3.77551 + 5.39198i −0.550714 + 0.786501i −0.993942 0.109908i \(-0.964944\pi\)
0.443228 + 0.896409i \(0.353833\pi\)
\(48\) 0 0
\(49\) 5.25539 + 14.4391i 0.750770 + 2.06272i
\(50\) 7.98561 9.31914i 1.12934 1.31793i
\(51\) 0 0
\(52\) −0.356385 + 4.07349i −0.0494217 + 0.564892i
\(53\) −6.73617 + 6.73617i −0.925284 + 0.925284i −0.997397 0.0721125i \(-0.977026\pi\)
0.0721125 + 0.997397i \(0.477026\pi\)
\(54\) 0 0
\(55\) 6.01730 0.760513i 0.811372 0.102548i
\(56\) 15.1069 + 18.0037i 2.01874 + 2.40584i
\(57\) 0 0
\(58\) −0.486933 + 0.340954i −0.0639375 + 0.0447695i
\(59\) −11.1903 + 4.07292i −1.45685 + 0.530250i −0.944495 0.328525i \(-0.893449\pi\)
−0.512354 + 0.858775i \(0.671226\pi\)
\(60\) 0 0
\(61\) −1.40842 7.98754i −0.180330 1.02270i −0.931811 0.362945i \(-0.881771\pi\)
0.751481 0.659755i \(-0.229340\pi\)
\(62\) 3.57962 13.3593i 0.454612 1.69663i
\(63\) 0 0
\(64\) −6.66780 3.84966i −0.833475 0.481207i
\(65\) 1.92235 1.21073i 0.238439 0.150172i
\(66\) 0 0
\(67\) −7.77347 + 0.680090i −0.949680 + 0.0830863i −0.551458 0.834203i \(-0.685928\pi\)
−0.398222 + 0.917289i \(0.630373\pi\)
\(68\) 4.78688 0.418798i 0.580494 0.0507867i
\(69\) 0 0
\(70\) 5.74912 25.3116i 0.687151 3.02531i
\(71\) −1.13442 0.654959i −0.134631 0.0777293i 0.431172 0.902270i \(-0.358100\pi\)
−0.565803 + 0.824541i \(0.691434\pi\)
\(72\) 0 0
\(73\) −0.567144 + 2.11661i −0.0663792 + 0.247730i −0.991141 0.132817i \(-0.957598\pi\)
0.924761 + 0.380547i \(0.124264\pi\)
\(74\) 0.375082 + 2.12719i 0.0436024 + 0.247281i
\(75\) 0 0
\(76\) 2.21535 0.806323i 0.254119 0.0924916i
\(77\) 10.5078 7.35767i 1.19748 0.838485i
\(78\) 0 0
\(79\) 2.17780 + 2.59540i 0.245022 + 0.292006i 0.874513 0.485002i \(-0.161181\pi\)
−0.629491 + 0.777008i \(0.716737\pi\)
\(80\) −1.16316 9.20314i −0.130046 1.02894i
\(81\) 0 0
\(82\) −7.56311 + 7.56311i −0.835206 + 0.835206i
\(83\) 0.839279 9.59300i 0.0921228 1.05297i −0.799644 0.600474i \(-0.794979\pi\)
0.891767 0.452495i \(-0.149466\pi\)
\(84\) 0 0
\(85\) −1.79342 1.97763i −0.194523 0.214505i
\(86\) −9.27680 25.4878i −1.00034 2.74842i
\(87\) 0 0
\(88\) 7.73153 11.0418i 0.824183 1.17706i
\(89\) 1.54112 + 2.66930i 0.163359 + 0.282945i 0.936071 0.351811i \(-0.114434\pi\)
−0.772713 + 0.634756i \(0.781101\pi\)
\(90\) 0 0
\(91\) 2.40246 4.16118i 0.251846 0.436211i
\(92\) 2.22571 + 4.77305i 0.232046 + 0.497624i
\(93\) 0 0
\(94\) 10.3853 12.3767i 1.07116 1.27656i
\(95\) −1.10104 0.709481i −0.112964 0.0727912i
\(96\) 0 0
\(97\) −3.04230 + 1.41865i −0.308899 + 0.144042i −0.570886 0.821030i \(-0.693400\pi\)
0.261987 + 0.965071i \(0.415622\pi\)
\(98\) −9.76147 36.4303i −0.986057 3.68002i
\(99\) 0 0
\(100\) −14.3759 + 14.0812i −1.43759 + 1.40812i
\(101\) 7.00303 1.23482i 0.696828 0.122870i 0.185996 0.982550i \(-0.440449\pi\)
0.510831 + 0.859681i \(0.329338\pi\)
\(102\) 0 0
\(103\) −13.2831 6.19401i −1.30882 0.610314i −0.362032 0.932166i \(-0.617917\pi\)
−0.946790 + 0.321852i \(0.895695\pi\)
\(104\) 0.876761 4.97236i 0.0859735 0.487580i
\(105\) 0 0
\(106\) 17.9122 15.0301i 1.73978 1.45985i
\(107\) 6.31758 + 6.31758i 0.610743 + 0.610743i 0.943140 0.332397i \(-0.107857\pi\)
−0.332397 + 0.943140i \(0.607857\pi\)
\(108\) 0 0
\(109\) 8.92248i 0.854618i −0.904106 0.427309i \(-0.859462\pi\)
0.904106 0.427309i \(-0.140538\pi\)
\(110\) −14.8760 + 0.572336i −1.41838 + 0.0545701i
\(111\) 0 0
\(112\) −11.2532 16.0712i −1.06333 1.51859i
\(113\) −1.37886 + 2.95698i −0.129713 + 0.278169i −0.960428 0.278527i \(-0.910154\pi\)
0.830716 + 0.556697i \(0.187931\pi\)
\(114\) 0 0
\(115\) 1.36451 2.58838i 0.127241 0.241367i
\(116\) 0.844108 0.487346i 0.0783734 0.0452489i
\(117\) 0 0
\(118\) 28.2335 7.56514i 2.59910 0.696427i
\(119\) −5.30588 1.93118i −0.486389 0.177031i
\(120\) 0 0
\(121\) 2.79051 + 2.34151i 0.253683 + 0.212865i
\(122\) 1.73510 + 19.8322i 0.157088 + 1.79553i
\(123\) 0 0
\(124\) −7.75629 + 21.3102i −0.696536 + 1.91372i
\(125\) 11.0607 + 1.63135i 0.989298 + 0.145912i
\(126\) 0 0
\(127\) 12.7720 + 3.42225i 1.13333 + 0.303676i 0.776267 0.630404i \(-0.217111\pi\)
0.357065 + 0.934079i \(0.383777\pi\)
\(128\) 15.8794 + 11.1188i 1.40355 + 0.982777i
\(129\) 0 0
\(130\) −4.95950 + 2.54920i −0.434977 + 0.223579i
\(131\) 0.581695 + 0.102569i 0.0508229 + 0.00896145i 0.199002 0.979999i \(-0.436230\pi\)
−0.148179 + 0.988961i \(0.547341\pi\)
\(132\) 0 0
\(133\) −2.75972 0.241444i −0.239298 0.0209359i
\(134\) 19.1530 1.65457
\(135\) 0 0
\(136\) −5.93330 −0.508776
\(137\) −17.1355 1.49916i −1.46398 0.128082i −0.672875 0.739756i \(-0.734941\pi\)
−0.791110 + 0.611674i \(0.790496\pi\)
\(138\) 0 0
\(139\) −11.8215 2.08444i −1.00268 0.176800i −0.351878 0.936046i \(-0.614457\pi\)
−0.650804 + 0.759246i \(0.725568\pi\)
\(140\) −13.0082 + 40.5237i −1.09939 + 3.42487i
\(141\) 0 0
\(142\) 2.63375 + 1.84417i 0.221019 + 0.154759i
\(143\) −2.66193 0.713261i −0.222602 0.0596459i
\(144\) 0 0
\(145\) −0.499230 0.209823i −0.0414588 0.0174249i
\(146\) 1.83956 5.05416i 0.152243 0.418285i
\(147\) 0 0
\(148\) −0.308684 3.52827i −0.0253737 0.290022i
\(149\) −7.50454 6.29706i −0.614796 0.515875i 0.281367 0.959600i \(-0.409212\pi\)
−0.896163 + 0.443725i \(0.853657\pi\)
\(150\) 0 0
\(151\) −14.4897 5.27382i −1.17916 0.429178i −0.323252 0.946313i \(-0.604776\pi\)
−0.855904 + 0.517135i \(0.826998\pi\)
\(152\) −2.81183 + 0.753427i −0.228069 + 0.0611110i
\(153\) 0 0
\(154\) −27.2675 + 15.7429i −2.19728 + 1.26860i
\(155\) 12.0360 3.72652i 0.966753 0.299321i
\(156\) 0 0
\(157\) 7.14630 15.3253i 0.570337 1.22309i −0.383716 0.923451i \(-0.625356\pi\)
0.954052 0.299640i \(-0.0968664\pi\)
\(158\) −4.76989 6.81211i −0.379472 0.541942i
\(159\) 0 0
\(160\) 0.0209341 + 0.544114i 0.00165498 + 0.0430160i
\(161\) 6.18847i 0.487720i
\(162\) 0 0
\(163\) 7.64324 + 7.64324i 0.598665 + 0.598665i 0.939957 0.341293i \(-0.110865\pi\)
−0.341293 + 0.939957i \(0.610865\pi\)
\(164\) 13.4348 11.2731i 1.04908 0.880285i
\(165\) 0 0
\(166\) −4.10437 + 23.2770i −0.318561 + 1.80665i
\(167\) 0.952493 + 0.444155i 0.0737061 + 0.0343697i 0.459122 0.888373i \(-0.348164\pi\)
−0.385416 + 0.922743i \(0.625942\pi\)
\(168\) 0 0
\(169\) 11.7859 2.07818i 0.906609 0.159860i
\(170\) 3.96215 + 5.21932i 0.303883 + 0.400304i
\(171\) 0 0
\(172\) 11.5108 + 42.9589i 0.877690 + 3.27558i
\(173\) −16.6052 + 7.74314i −1.26247 + 0.588700i −0.934492 0.355985i \(-0.884145\pi\)
−0.327979 + 0.944685i \(0.606368\pi\)
\(174\) 0 0
\(175\) 22.3027 7.85691i 1.68593 0.593927i
\(176\) −7.23299 + 8.61994i −0.545207 + 0.649752i
\(177\) 0 0
\(178\) −3.19728 6.85659i −0.239646 0.513923i
\(179\) −4.22807 + 7.32323i −0.316021 + 0.547364i −0.979654 0.200694i \(-0.935680\pi\)
0.663633 + 0.748058i \(0.269014\pi\)
\(180\) 0 0
\(181\) 0.511902 + 0.886641i 0.0380494 + 0.0659035i 0.884423 0.466686i \(-0.154552\pi\)
−0.846374 + 0.532590i \(0.821219\pi\)
\(182\) −6.76462 + 9.66088i −0.501427 + 0.716112i
\(183\) 0 0
\(184\) −2.22413 6.11074i −0.163965 0.450489i
\(185\) −1.45766 + 1.32188i −0.107169 + 0.0971863i
\(186\) 0 0
\(187\) −0.282250 + 3.22613i −0.0206402 + 0.235918i
\(188\) −18.7326 + 18.7326i −1.36621 + 1.36621i
\(189\) 0 0
\(190\) 2.54046 + 1.97035i 0.184304 + 0.142944i
\(191\) −2.57471 3.06842i −0.186300 0.222023i 0.664808 0.747014i \(-0.268513\pi\)
−0.851108 + 0.524991i \(0.824069\pi\)
\(192\) 0 0
\(193\) 0.199928 0.139991i 0.0143911 0.0100768i −0.566359 0.824159i \(-0.691648\pi\)
0.580750 + 0.814082i \(0.302759\pi\)
\(194\) 7.74244 2.81802i 0.555875 0.202322i
\(195\) 0 0
\(196\) 10.7387 + 60.9022i 0.767050 + 4.35015i
\(197\) 2.46125 9.18550i 0.175357 0.654440i −0.821134 0.570735i \(-0.806658\pi\)
0.996491 0.0837043i \(-0.0266751\pi\)
\(198\) 0 0
\(199\) 4.26708 + 2.46360i 0.302486 + 0.174640i 0.643559 0.765397i \(-0.277457\pi\)
−0.341073 + 0.940037i \(0.610790\pi\)
\(200\) 19.1988 15.7738i 1.35756 1.11538i
\(201\) 0 0
\(202\) −17.3878 + 1.52124i −1.22340 + 0.107034i
\(203\) −1.14097 + 0.0998220i −0.0800805 + 0.00700613i
\(204\) 0 0
\(205\) −9.50192 2.15821i −0.663643 0.150736i
\(206\) 31.1544 + 17.9870i 2.17063 + 1.25322i
\(207\) 0 0
\(208\) −1.09090 + 4.07128i −0.0756400 + 0.282292i
\(209\) 0.275903 + 1.56473i 0.0190846 + 0.108234i
\(210\) 0 0
\(211\) −24.7804 + 9.01933i −1.70595 + 0.620916i −0.996481 0.0838177i \(-0.973289\pi\)
−0.709472 + 0.704734i \(0.751066\pi\)
\(212\) −31.4066 + 21.9911i −2.15701 + 1.51036i
\(213\) 0 0
\(214\) −14.0961 16.7991i −0.963589 1.14836i
\(215\) 15.1436 19.5253i 1.03278 1.33161i
\(216\) 0 0
\(217\) 18.8430 18.8430i 1.27915 1.27915i
\(218\) −1.90874 + 21.8170i −0.129276 + 1.47764i
\(219\) 0 0
\(220\) 24.3811 + 1.19103i 1.64377 + 0.0802993i
\(221\) 0.414884 + 1.13988i 0.0279081 + 0.0766769i
\(222\) 0 0
\(223\) −1.66646 + 2.37995i −0.111594 + 0.159373i −0.871064 0.491169i \(-0.836570\pi\)
0.759470 + 0.650543i \(0.225459\pi\)
\(224\) 0.575821 + 0.997351i 0.0384737 + 0.0666383i
\(225\) 0 0
\(226\) 4.00414 6.93537i 0.266351 0.461334i
\(227\) 5.72184 + 12.2705i 0.379772 + 0.814424i 0.999560 + 0.0296545i \(0.00944070\pi\)
−0.619788 + 0.784769i \(0.712782\pi\)
\(228\) 0 0
\(229\) −6.17868 + 7.36346i −0.408298 + 0.486591i −0.930532 0.366212i \(-0.880655\pi\)
0.522233 + 0.852803i \(0.325099\pi\)
\(230\) −3.89018 + 6.03713i −0.256511 + 0.398077i
\(231\) 0 0
\(232\) −1.09076 + 0.508632i −0.0716122 + 0.0333933i
\(233\) 4.61537 + 17.2248i 0.302363 + 1.12843i 0.935192 + 0.354142i \(0.115227\pi\)
−0.632829 + 0.774292i \(0.718106\pi\)
\(234\) 0 0
\(235\) 14.5826 + 1.99672i 0.951265 + 0.130251i
\(236\) −47.1992 + 8.32249i −3.07240 + 0.541748i
\(237\) 0 0
\(238\) 12.5607 + 5.85714i 0.814188 + 0.379662i
\(239\) 4.22324 23.9512i 0.273179 1.54927i −0.471510 0.881861i \(-0.656291\pi\)
0.744688 0.667412i \(-0.232598\pi\)
\(240\) 0 0
\(241\) 5.17529 4.34259i 0.333370 0.279731i −0.460701 0.887555i \(-0.652402\pi\)
0.794071 + 0.607825i \(0.207958\pi\)
\(242\) −6.32237 6.32237i −0.406418 0.406418i
\(243\) 0 0
\(244\) 32.6430i 2.08975i
\(245\) 23.3433 25.2114i 1.49135 1.61070i
\(246\) 0 0
\(247\) 0.341362 + 0.487515i 0.0217203 + 0.0310199i
\(248\) 11.8342 25.3785i 0.751472 1.61154i
\(249\) 0 0
\(250\) −26.6963 6.35510i −1.68842 0.401932i
\(251\) −22.8066 + 13.1674i −1.43954 + 0.831118i −0.997817 0.0660346i \(-0.978965\pi\)
−0.441721 + 0.897152i \(0.645632\pi\)
\(252\) 0 0
\(253\) −3.42841 + 0.918641i −0.215543 + 0.0577544i
\(254\) −30.4977 11.1003i −1.91360 0.696492i
\(255\) 0 0
\(256\) −24.6532 20.6865i −1.54083 1.29291i
\(257\) −1.41734 16.2002i −0.0884111 1.01054i −0.902753 0.430158i \(-0.858458\pi\)
0.814342 0.580385i \(-0.197098\pi\)
\(258\) 0 0
\(259\) −1.42342 + 3.91081i −0.0884470 + 0.243006i
\(260\) 8.46541 3.45524i 0.525003 0.214285i
\(261\) 0 0
\(262\) −1.40040 0.375237i −0.0865173 0.0231822i
\(263\) −5.48334 3.83947i −0.338117 0.236752i 0.392170 0.919893i \(-0.371725\pi\)
−0.730287 + 0.683141i \(0.760613\pi\)
\(264\) 0 0
\(265\) 20.2823 + 6.51065i 1.24593 + 0.399946i
\(266\) 6.69635 + 1.18075i 0.410579 + 0.0723962i
\(267\) 0 0
\(268\) −31.2855 2.73713i −1.91107 0.167197i
\(269\) −3.20425 −0.195366 −0.0976832 0.995218i \(-0.531143\pi\)
−0.0976832 + 0.995218i \(0.531143\pi\)
\(270\) 0 0
\(271\) −29.5892 −1.79742 −0.898709 0.438546i \(-0.855494\pi\)
−0.898709 + 0.438546i \(0.855494\pi\)
\(272\) 4.93420 + 0.431686i 0.299180 + 0.0261748i
\(273\) 0 0
\(274\) 41.5786 + 7.33143i 2.51186 + 0.442908i
\(275\) −7.66344 11.1894i −0.462123 0.674747i
\(276\) 0 0
\(277\) 7.72074 + 5.40612i 0.463895 + 0.324822i 0.782050 0.623216i \(-0.214174\pi\)
−0.318155 + 0.948039i \(0.603063\pi\)
\(278\) 28.4596 + 7.62573i 1.70689 + 0.457361i
\(279\) 0 0
\(280\) 20.3621 48.4473i 1.21687 2.89528i
\(281\) −0.877392 + 2.41061i −0.0523408 + 0.143805i −0.963108 0.269115i \(-0.913269\pi\)
0.910767 + 0.412920i \(0.135491\pi\)
\(282\) 0 0
\(283\) 1.56435 + 17.8806i 0.0929908 + 1.06289i 0.889093 + 0.457727i \(0.151336\pi\)
−0.796102 + 0.605163i \(0.793108\pi\)
\(284\) −4.03856 3.38875i −0.239644 0.201085i
\(285\) 0 0
\(286\) 6.35630 + 2.31350i 0.375856 + 0.136800i
\(287\) −19.9060 + 5.33381i −1.17502 + 0.314845i
\(288\) 0 0
\(289\) −13.4879 + 7.78726i −0.793408 + 0.458074i
\(290\) 1.17582 + 0.619853i 0.0690465 + 0.0363990i
\(291\) 0 0
\(292\) −3.72712 + 7.99284i −0.218113 + 0.467745i
\(293\) 14.0808 + 20.1095i 0.822609 + 1.17481i 0.982240 + 0.187630i \(0.0600807\pi\)
−0.159631 + 0.987177i \(0.551030\pi\)
\(294\) 0 0
\(295\) 19.5389 + 18.0911i 1.13760 + 1.05330i
\(296\) 4.37326i 0.254191i
\(297\) 0 0
\(298\) 17.0028 + 17.0028i 0.984947 + 0.984947i
\(299\) −1.01845 + 0.854582i −0.0588986 + 0.0494218i
\(300\) 0 0
\(301\) 9.07491 51.4664i 0.523069 2.96647i
\(302\) 34.3017 + 15.9951i 1.97384 + 0.920417i
\(303\) 0 0
\(304\) 2.39317 0.421980i 0.137258 0.0242022i
\(305\) −14.4454 + 10.9660i −0.827142 + 0.627910i
\(306\) 0 0
\(307\) −5.03134 18.7772i −0.287154 1.07167i −0.947251 0.320493i \(-0.896151\pi\)
0.660097 0.751180i \(-0.270515\pi\)
\(308\) 46.7900 21.8185i 2.66611 1.24323i
\(309\) 0 0
\(310\) −30.2273 + 6.53719i −1.71680 + 0.371287i
\(311\) 3.69580 4.40448i 0.209569 0.249755i −0.651013 0.759067i \(-0.725656\pi\)
0.860582 + 0.509312i \(0.170100\pi\)
\(312\) 0 0
\(313\) 4.98349 + 10.6871i 0.281683 + 0.604072i 0.995340 0.0964234i \(-0.0307403\pi\)
−0.713657 + 0.700495i \(0.752963\pi\)
\(314\) −20.7524 + 35.9442i −1.17113 + 2.02845i
\(315\) 0 0
\(316\) 6.81788 + 11.8089i 0.383536 + 0.664303i
\(317\) 7.97058 11.3832i 0.447672 0.639342i −0.530366 0.847769i \(-0.677945\pi\)
0.978038 + 0.208427i \(0.0668343\pi\)
\(318\) 0 0
\(319\) 0.224672 + 0.617281i 0.0125792 + 0.0345611i
\(320\) −0.840019 + 17.1957i −0.0469585 + 0.961268i
\(321\) 0 0
\(322\) −1.32387 + 15.1319i −0.0737763 + 0.843268i
\(323\) 0.494532 0.494532i 0.0275165 0.0275165i
\(324\) 0 0
\(325\) −4.37288 2.58543i −0.242564 0.143414i
\(326\) −17.0540 20.3241i −0.944533 1.12565i
\(327\) 0 0
\(328\) −17.7390 + 12.4210i −0.979475 + 0.685836i
\(329\) 29.2524 10.6470i 1.61274 0.586988i
\(330\) 0 0
\(331\) 5.48482 + 31.1060i 0.301473 + 1.70974i 0.639658 + 0.768659i \(0.279076\pi\)
−0.338185 + 0.941080i \(0.609813\pi\)
\(332\) 10.0308 37.4354i 0.550511 2.05453i
\(333\) 0 0
\(334\) −2.23400 1.28980i −0.122239 0.0705747i
\(335\) 9.29869 + 14.7642i 0.508041 + 0.806653i
\(336\) 0 0
\(337\) 3.38108 0.295807i 0.184179 0.0161136i 0.00530714 0.999986i \(-0.498311\pi\)
0.178872 + 0.983872i \(0.442755\pi\)
\(338\) −29.2632 + 2.56020i −1.59171 + 0.139257i
\(339\) 0 0
\(340\) −5.72610 9.09174i −0.310542 0.493069i
\(341\) −13.2362 7.64191i −0.716779 0.413833i
\(342\) 0 0
\(343\) 10.2398 38.2154i 0.552897 2.06344i
\(344\) −9.53602 54.0814i −0.514148 2.91588i
\(345\) 0 0
\(346\) 42.2591 15.3811i 2.27186 0.826891i
\(347\) −28.6368 + 20.0517i −1.53730 + 1.07643i −0.570376 + 0.821384i \(0.693202\pi\)
−0.966928 + 0.255048i \(0.917909\pi\)
\(348\) 0 0
\(349\) −14.2588 16.9930i −0.763258 0.909615i 0.234792 0.972046i \(-0.424559\pi\)
−0.998049 + 0.0624307i \(0.980115\pi\)
\(350\) −56.2149 + 14.4404i −3.00481 + 0.771873i
\(351\) 0 0
\(352\) 0.467056 0.467056i 0.0248942 0.0248942i
\(353\) 2.38887 27.3049i 0.127147 1.45330i −0.617886 0.786268i \(-0.712011\pi\)
0.745033 0.667028i \(-0.232434\pi\)
\(354\) 0 0
\(355\) −0.142916 + 2.92558i −0.00758520 + 0.155274i
\(356\) 4.24274 + 11.6568i 0.224865 + 0.617811i
\(357\) 0 0
\(358\) 11.9050 17.0021i 0.629199 0.898589i
\(359\) 1.15564 + 2.00162i 0.0609923 + 0.105642i 0.894909 0.446248i \(-0.147240\pi\)
−0.833917 + 0.551890i \(0.813907\pi\)
\(360\) 0 0
\(361\) −9.32844 + 16.1573i −0.490970 + 0.850385i
\(362\) −1.06202 2.27750i −0.0558184 0.119703i
\(363\) 0 0
\(364\) 12.4303 14.8139i 0.651525 0.776458i
\(365\) 4.78912 1.03573i 0.250674 0.0542128i
\(366\) 0 0
\(367\) 28.2899 13.1918i 1.47672 0.688607i 0.493288 0.869866i \(-0.335795\pi\)
0.983435 + 0.181259i \(0.0580172\pi\)
\(368\) 1.40501 + 5.24358i 0.0732414 + 0.273340i
\(369\) 0 0
\(370\) 3.84701 2.92039i 0.199997 0.151824i
\(371\) 44.3681 7.82330i 2.30348 0.406165i
\(372\) 0 0
\(373\) −29.3777 13.6991i −1.52112 0.709310i −0.530721 0.847547i \(-0.678079\pi\)
−0.990399 + 0.138237i \(0.955857\pi\)
\(374\) 1.38030 7.82808i 0.0713737 0.404780i
\(375\) 0 0
\(376\) 25.0584 21.0265i 1.29229 1.08436i
\(377\) 0.173988 + 0.173988i 0.00896083 + 0.00896083i
\(378\) 0 0
\(379\) 4.84696i 0.248972i 0.992221 + 0.124486i \(0.0397282\pi\)
−0.992221 + 0.124486i \(0.960272\pi\)
\(380\) −3.86814 3.58152i −0.198431 0.183728i
\(381\) 0 0
\(382\) 5.63921 + 8.05362i 0.288527 + 0.412059i
\(383\) −5.21058 + 11.1741i −0.266248 + 0.570971i −0.993294 0.115618i \(-0.963115\pi\)
0.727046 + 0.686589i \(0.240893\pi\)
\(384\) 0 0
\(385\) −25.3738 13.3762i −1.29317 0.681715i
\(386\) −0.518806 + 0.299533i −0.0264065 + 0.0152458i
\(387\) 0 0
\(388\) −13.0496 + 3.49664i −0.662495 + 0.177515i
\(389\) 11.2960 + 4.11142i 0.572732 + 0.208457i 0.612118 0.790767i \(-0.290318\pi\)
−0.0393859 + 0.999224i \(0.512540\pi\)
\(390\) 0 0
\(391\) 1.19681 + 1.00424i 0.0605253 + 0.0507868i
\(392\) −6.65526 76.0700i −0.336141 3.84211i
\(393\) 0 0
\(394\) −7.98319 + 21.9336i −0.402187 + 1.10500i
\(395\) 2.93539 6.98414i 0.147696 0.351410i
\(396\) 0 0
\(397\) −16.1554 4.32882i −0.810815 0.217257i −0.170488 0.985360i \(-0.554534\pi\)
−0.640327 + 0.768103i \(0.721201\pi\)
\(398\) −9.90675 6.93678i −0.496580 0.347709i
\(399\) 0 0
\(400\) −17.1136 + 11.7208i −0.855681 + 0.586042i
\(401\) −15.5955 2.74991i −0.778803 0.137324i −0.229905 0.973213i \(-0.573841\pi\)
−0.548898 + 0.835889i \(0.684953\pi\)
\(402\) 0 0
\(403\) −5.70313 0.498959i −0.284093 0.0248549i
\(404\) 28.6196 1.42388
\(405\) 0 0
\(406\) 2.81123 0.139519
\(407\) 2.37789 + 0.208038i 0.117868 + 0.0103121i
\(408\) 0 0
\(409\) −6.67646 1.17724i −0.330130 0.0582108i 0.00612663 0.999981i \(-0.498050\pi\)
−0.336257 + 0.941770i \(0.609161\pi\)
\(410\) 22.7722 + 7.30990i 1.12464 + 0.361010i
\(411\) 0 0
\(412\) −48.3188 33.8332i −2.38050 1.66684i
\(413\) 54.3989 + 14.5761i 2.67679 + 0.717245i
\(414\) 0 0
\(415\) −19.9359 + 8.13702i −0.978614 + 0.399431i
\(416\) 0.0846199 0.232491i 0.00414883 0.0113988i
\(417\) 0 0
\(418\) −0.339898 3.88505i −0.0166250 0.190024i
\(419\) 20.0804 + 16.8495i 0.980992 + 0.823150i 0.984239 0.176845i \(-0.0565892\pi\)
−0.00324717 + 0.999995i \(0.501034\pi\)
\(420\) 0 0
\(421\) −8.48131 3.08694i −0.413354 0.150448i 0.126968 0.991907i \(-0.459475\pi\)
−0.540322 + 0.841458i \(0.681698\pi\)
\(422\) 62.5219 16.7527i 3.04352 0.815508i
\(423\) 0 0
\(424\) 40.9991 23.6709i 1.99109 1.14956i
\(425\) −2.09973 + 5.58820i −0.101852 + 0.271068i
\(426\) 0 0
\(427\) −16.2107 + 34.7639i −0.784490 + 1.68234i
\(428\) 20.6246 + 29.4549i 0.996926 + 1.42376i
\(429\) 0 0
\(430\) −41.2056 + 44.5032i −1.98711 + 2.14613i
\(431\) 26.9295i 1.29715i 0.761151 + 0.648575i \(0.224635\pi\)
−0.761151 + 0.648575i \(0.775365\pi\)
\(432\) 0 0
\(433\) −0.461356 0.461356i −0.0221714 0.0221714i 0.695934 0.718106i \(-0.254991\pi\)
−0.718106 + 0.695934i \(0.754991\pi\)
\(434\) −50.1055 + 42.0435i −2.40514 + 2.01815i
\(435\) 0 0
\(436\) 6.23568 35.3643i 0.298635 1.69364i
\(437\) 0.694699 + 0.323943i 0.0332319 + 0.0154963i
\(438\) 0 0
\(439\) 1.32806 0.234172i 0.0633847 0.0111764i −0.141866 0.989886i \(-0.545310\pi\)
0.205251 + 0.978709i \(0.434199\pi\)
\(440\) −29.8624 4.08890i −1.42364 0.194931i
\(441\) 0 0
\(442\) −0.770614 2.87597i −0.0366544 0.136796i
\(443\) −28.2741 + 13.1844i −1.34334 + 0.626410i −0.955411 0.295278i \(-0.904588\pi\)
−0.387930 + 0.921689i \(0.626810\pi\)
\(444\) 0 0
\(445\) 3.73318 5.79349i 0.176970 0.274638i
\(446\) 4.58392 5.46290i 0.217055 0.258676i
\(447\) 0 0
\(448\) 15.3883 + 33.0004i 0.727031 + 1.55912i
\(449\) 9.91012 17.1648i 0.467688 0.810059i −0.531631 0.846976i \(-0.678421\pi\)
0.999318 + 0.0369176i \(0.0117539\pi\)
\(450\) 0 0
\(451\) 5.90986 + 10.2362i 0.278285 + 0.482003i
\(452\) −7.53169 + 10.7564i −0.354261 + 0.505937i
\(453\) 0 0
\(454\) −11.3659 31.2276i −0.533430 1.46559i
\(455\) −10.7313 0.524232i −0.503093 0.0245764i
\(456\) 0 0
\(457\) −1.15032 + 13.1482i −0.0538096 + 0.615046i 0.920636 + 0.390422i \(0.127671\pi\)
−0.974446 + 0.224624i \(0.927885\pi\)
\(458\) 16.6832 16.6832i 0.779554 0.779554i
\(459\) 0 0
\(460\) 7.21718 9.30543i 0.336503 0.433868i
\(461\) 3.71376 + 4.42589i 0.172967 + 0.206134i 0.845563 0.533876i \(-0.179265\pi\)
−0.672596 + 0.740010i \(0.734821\pi\)
\(462\) 0 0
\(463\) −12.0734 + 8.45389i −0.561099 + 0.392885i −0.819437 0.573169i \(-0.805714\pi\)
0.258339 + 0.966054i \(0.416825\pi\)
\(464\) 0.944098 0.343624i 0.0438287 0.0159523i
\(465\) 0 0
\(466\) −7.60057 43.1050i −0.352090 1.99680i
\(467\) 5.81437 21.6995i 0.269057 1.00413i −0.690663 0.723177i \(-0.742681\pi\)
0.959720 0.280958i \(-0.0906522\pi\)
\(468\) 0 0
\(469\) 31.9590 + 18.4515i 1.47573 + 0.852012i
\(470\) −35.2299 8.00191i −1.62503 0.369101i
\(471\) 0 0
\(472\) 58.9542 5.15783i 2.71359 0.237408i
\(473\) −29.8595 + 2.61237i −1.37294 + 0.120117i
\(474\) 0 0
\(475\) −0.285472 + 2.91492i −0.0130984 + 0.133746i
\(476\) −19.6802 11.3624i −0.902042 0.520794i
\(477\) 0 0
\(478\) −15.4503 + 57.6614i −0.706682 + 2.63737i
\(479\) 3.89318 + 22.0793i 0.177884 + 1.00883i 0.934762 + 0.355274i \(0.115613\pi\)
−0.756878 + 0.653556i \(0.773276\pi\)
\(480\) 0 0
\(481\) 0.840176 0.305799i 0.0383087 0.0139432i
\(482\) −13.5835 + 9.51126i −0.618711 + 0.433226i
\(483\) 0 0
\(484\) 9.42378 + 11.2308i 0.428353 + 0.510492i
\(485\) 5.93120 + 4.60017i 0.269322 + 0.208883i
\(486\) 0 0
\(487\) −15.7748 + 15.7748i −0.714827 + 0.714827i −0.967541 0.252714i \(-0.918677\pi\)
0.252714 + 0.967541i \(0.418677\pi\)
\(488\) −3.51296 + 40.1534i −0.159024 + 1.81766i
\(489\) 0 0
\(490\) −62.4719 + 56.6526i −2.82219 + 2.55931i
\(491\) −3.57036 9.80948i −0.161128 0.442696i 0.832687 0.553744i \(-0.186801\pi\)
−0.993815 + 0.111048i \(0.964579\pi\)
\(492\) 0 0
\(493\) 0.165848 0.236855i 0.00746942 0.0106674i
\(494\) −0.730398 1.26509i −0.0328622 0.0569190i
\(495\) 0 0
\(496\) −11.6879 + 20.2441i −0.524803 + 0.908985i
\(497\) 2.61809 + 5.61450i 0.117437 + 0.251845i
\(498\) 0 0
\(499\) −4.79129 + 5.71004i −0.214488 + 0.255617i −0.862551 0.505970i \(-0.831135\pi\)
0.648063 + 0.761586i \(0.275579\pi\)
\(500\) 42.6990 + 14.1959i 1.90956 + 0.634859i
\(501\) 0 0
\(502\) 58.5829 27.3177i 2.61468 1.21925i
\(503\) −5.79688 21.6342i −0.258470 0.964623i −0.966127 0.258067i \(-0.916914\pi\)
0.707657 0.706556i \(-0.249752\pi\)
\(504\) 0 0
\(505\) −9.61435 12.6649i −0.427833 0.563582i
\(506\) 8.57960 1.51281i 0.381410 0.0672528i
\(507\) 0 0
\(508\) 48.2303 + 22.4901i 2.13987 + 0.997838i
\(509\) −6.68306 + 37.9015i −0.296221 + 1.67996i 0.365975 + 0.930625i \(0.380736\pi\)
−0.662196 + 0.749331i \(0.730375\pi\)
\(510\) 0 0
\(511\) 7.93857 6.66126i 0.351182 0.294677i
\(512\) 28.4414 + 28.4414i 1.25694 + 1.25694i
\(513\) 0 0
\(514\) 39.9156i 1.76060i
\(515\) 1.25994 + 32.7482i 0.0555197 + 1.44306i
\(516\) 0 0
\(517\) −10.2408 14.6253i −0.450389 0.643222i
\(518\) 4.31713 9.25812i 0.189684 0.406778i
\(519\) 0 0
\(520\) −10.7849 + 3.33918i −0.472951 + 0.146433i
\(521\) 32.4577 18.7395i 1.42200 0.820992i 0.425529 0.904945i \(-0.360088\pi\)
0.996470 + 0.0839530i \(0.0267546\pi\)
\(522\) 0 0
\(523\) 20.3099 5.44201i 0.888088 0.237962i 0.214195 0.976791i \(-0.431287\pi\)
0.673893 + 0.738829i \(0.264621\pi\)
\(524\) 2.23387 + 0.813062i 0.0975871 + 0.0355188i
\(525\) 0 0
\(526\) 12.5864 + 10.5612i 0.548791 + 0.460491i
\(527\) 0.586341 + 6.70191i 0.0255414 + 0.291940i
\(528\) 0 0
\(529\) 7.28082 20.0039i 0.316557 0.869734i
\(530\) −48.2010 20.2586i −2.09372 0.879976i
\(531\) 0 0
\(532\) −10.7694 2.88566i −0.466914 0.125109i
\(533\) 3.62668 + 2.53943i 0.157089 + 0.109995i
\(534\) 0 0
\(535\) 6.10607 19.0219i 0.263988 0.822389i
\(536\) 38.1890 + 6.73375i 1.64951 + 0.290854i
\(537\) 0 0
\(538\) 7.83495 + 0.685470i 0.337789 + 0.0295527i
\(539\) −41.6784 −1.79521
\(540\) 0 0
\(541\) 4.57481 0.196686 0.0983432 0.995153i \(-0.468646\pi\)
0.0983432 + 0.995153i \(0.468646\pi\)
\(542\) 72.3509 + 6.32988i 3.10774 + 0.271892i
\(543\) 0 0
\(544\) −0.286324 0.0504866i −0.0122760 0.00216460i
\(545\) −17.7445 + 9.12070i −0.760089 + 0.390688i
\(546\) 0 0
\(547\) 8.96813 + 6.27955i 0.383449 + 0.268494i 0.749369 0.662152i \(-0.230357\pi\)
−0.365920 + 0.930646i \(0.619246\pi\)
\(548\) −66.8690 17.9175i −2.85650 0.765397i
\(549\) 0 0
\(550\) 16.3448 + 28.9995i 0.696943 + 1.23654i
\(551\) 0.0485199 0.133307i 0.00206702 0.00567908i
\(552\) 0 0
\(553\) −1.39649 15.9620i −0.0593849 0.678772i
\(554\) −17.7221 14.8706i −0.752939 0.631791i
\(555\) 0 0
\(556\) −45.3977 16.5234i −1.92529 0.700748i
\(557\) −0.862701 + 0.231160i −0.0365538 + 0.00979457i −0.277050 0.960856i \(-0.589357\pi\)
0.240496 + 0.970650i \(0.422690\pi\)
\(558\) 0 0
\(559\) −9.72313 + 5.61365i −0.411245 + 0.237432i
\(560\) −20.4582 + 38.8079i −0.864517 + 1.63993i
\(561\) 0 0
\(562\) 2.66107 5.70668i 0.112250 0.240722i
\(563\) −20.7218 29.5939i −0.873322 1.24723i −0.967804 0.251706i \(-0.919008\pi\)
0.0944822 0.995527i \(-0.469880\pi\)
\(564\) 0 0
\(565\) 7.29015 0.280479i 0.306699 0.0117998i
\(566\) 44.0558i 1.85180i
\(567\) 0 0
\(568\) 4.60305 + 4.60305i 0.193139 + 0.193139i
\(569\) 5.09704 4.27692i 0.213679 0.179298i −0.529666 0.848206i \(-0.677683\pi\)
0.743345 + 0.668908i \(0.233238\pi\)
\(570\) 0 0
\(571\) 1.91569 10.8644i 0.0801693 0.454663i −0.918126 0.396290i \(-0.870298\pi\)
0.998295 0.0583730i \(-0.0185913\pi\)
\(572\) −10.0521 4.68737i −0.420299 0.195989i
\(573\) 0 0
\(574\) 49.8148 8.78369i 2.07923 0.366624i
\(575\) −6.54242 0.0677626i −0.272838 0.00282590i
\(576\) 0 0
\(577\) −7.90648 29.5074i −0.329151 1.22841i −0.910073 0.414449i \(-0.863974\pi\)
0.580921 0.813960i \(-0.302692\pi\)
\(578\) 34.6463 16.1558i 1.44109 0.671993i
\(579\) 0 0
\(580\) −1.83206 1.18053i −0.0760723 0.0490190i
\(581\) −29.2731 + 34.8864i −1.21445 + 1.44733i
\(582\) 0 0
\(583\) −10.9203 23.4186i −0.452272 0.969901i
\(584\) 5.44482 9.43070i 0.225308 0.390245i
\(585\) 0 0
\(586\) −30.1281 52.1834i −1.24458 2.15568i
\(587\) 0.453527 0.647703i 0.0187191 0.0267336i −0.809683 0.586867i \(-0.800361\pi\)
0.828403 + 0.560133i \(0.189250\pi\)
\(588\) 0 0
\(589\) 1.12890 + 3.10162i 0.0465155 + 0.127800i
\(590\) −43.9058 48.4158i −1.80757 1.99325i
\(591\) 0 0
\(592\) 0.318184 3.63686i 0.0130773 0.149474i
\(593\) 27.9143 27.9143i 1.14630 1.14630i 0.159029 0.987274i \(-0.449164\pi\)
0.987274 0.159029i \(-0.0508363\pi\)
\(594\) 0 0
\(595\) 1.58314 + 12.5261i 0.0649025 + 0.513519i
\(596\) −25.3435 30.2032i −1.03811 1.23717i
\(597\) 0 0
\(598\) 2.67311 1.87173i 0.109312 0.0765408i
\(599\) 35.2332 12.8238i 1.43959 0.523967i 0.499925 0.866068i \(-0.333361\pi\)
0.939663 + 0.342101i \(0.111139\pi\)
\(600\) 0 0
\(601\) 0.988708 + 5.60724i 0.0403302 + 0.228724i 0.998310 0.0581113i \(-0.0185078\pi\)
−0.957980 + 0.286835i \(0.907397\pi\)
\(602\) −33.1997 + 123.903i −1.35312 + 5.04991i
\(603\) 0 0
\(604\) −53.7443 31.0293i −2.18683 1.26256i
\(605\) 1.80415 7.94312i 0.0733492 0.322934i
\(606\) 0 0
\(607\) 11.6898 1.02272i 0.474474 0.0415111i 0.152589 0.988290i \(-0.451239\pi\)
0.321885 + 0.946779i \(0.395683\pi\)
\(608\) −0.142102 + 0.0124323i −0.00576299 + 0.000504196i
\(609\) 0 0
\(610\) 37.6675 23.7235i 1.52511 0.960536i
\(611\) −5.79174 3.34386i −0.234309 0.135278i
\(612\) 0 0
\(613\) −4.37352 + 16.3222i −0.176645 + 0.659247i 0.819621 + 0.572906i \(0.194184\pi\)
−0.996266 + 0.0863408i \(0.972483\pi\)
\(614\) 8.28560 + 46.9900i 0.334380 + 1.89636i
\(615\) 0 0
\(616\) −59.9034 + 21.8030i −2.41358 + 0.878469i
\(617\) 24.1467 16.9077i 0.972111 0.680679i 0.0243643 0.999703i \(-0.492244\pi\)
0.947747 + 0.319024i \(0.103355\pi\)
\(618\) 0 0
\(619\) 26.5533 + 31.6450i 1.06727 + 1.27192i 0.960692 + 0.277615i \(0.0895439\pi\)
0.106575 + 0.994305i \(0.466012\pi\)
\(620\) 50.3091 6.35845i 2.02046 0.255362i
\(621\) 0 0
\(622\) −9.97910 + 9.97910i −0.400126 + 0.400126i
\(623\) 1.27044 14.5212i 0.0508991 0.581780i
\(624\) 0 0
\(625\) −8.06208 23.6644i −0.322483 0.946575i
\(626\) −9.89926 27.1980i −0.395654 1.08705i
\(627\) 0 0
\(628\) 39.0348 55.7475i 1.55766 2.22457i
\(629\) −0.525339 0.909914i −0.0209466 0.0362806i
\(630\) 0 0
\(631\) −9.08444 + 15.7347i −0.361646 + 0.626389i −0.988232 0.152963i \(-0.951118\pi\)
0.626586 + 0.779352i \(0.284452\pi\)
\(632\) −7.11566 15.2596i −0.283046 0.606994i
\(633\) 0 0
\(634\) −21.9246 + 26.1287i −0.870738 + 1.03770i
\(635\) −6.24981 28.8985i −0.248016 1.14680i
\(636\) 0 0
\(637\) −14.1489 + 6.59775i −0.560601 + 0.261412i
\(638\) −0.417310 1.55742i −0.0165215 0.0616589i
\(639\) 0 0
\(640\) 5.88032 42.9457i 0.232440 1.69758i
\(641\) −9.92814 + 1.75060i −0.392138 + 0.0691445i −0.366241 0.930520i \(-0.619355\pi\)
−0.0258971 + 0.999665i \(0.508244\pi\)
\(642\) 0 0
\(643\) 24.3420 + 11.3509i 0.959956 + 0.447635i 0.838464 0.544957i \(-0.183454\pi\)
0.121492 + 0.992592i \(0.461232\pi\)
\(644\) 4.32495 24.5280i 0.170427 0.966540i
\(645\) 0 0
\(646\) −1.31501 + 1.10342i −0.0517384 + 0.0434136i
\(647\) −21.7838 21.7838i −0.856411 0.856411i 0.134503 0.990913i \(-0.457056\pi\)
−0.990913 + 0.134503i \(0.957056\pi\)
\(648\) 0 0
\(649\) 32.3007i 1.26792i
\(650\) 10.1394 + 7.25731i 0.397699 + 0.284655i
\(651\) 0 0
\(652\) 24.9524 + 35.6357i 0.977210 + 1.39560i
\(653\) −10.1623 + 21.7931i −0.397681 + 0.852830i 0.600887 + 0.799334i \(0.294814\pi\)
−0.998568 + 0.0534961i \(0.982964\pi\)
\(654\) 0 0
\(655\) −0.390636 1.26169i −0.0152634 0.0492981i
\(656\) 15.6557 9.03883i 0.611253 0.352907i
\(657\) 0 0
\(658\) −73.8049 + 19.7760i −2.87721 + 0.770947i
\(659\) 7.76560 + 2.82645i 0.302505 + 0.110103i 0.488813 0.872389i \(-0.337430\pi\)
−0.186308 + 0.982491i \(0.559652\pi\)
\(660\) 0 0
\(661\) 16.2837 + 13.6636i 0.633361 + 0.531453i 0.901971 0.431796i \(-0.142120\pi\)
−0.268610 + 0.963249i \(0.586564\pi\)
\(662\) −6.75701 77.2329i −0.262618 3.00174i
\(663\) 0 0
\(664\) −16.3673 + 44.9689i −0.635176 + 1.74513i
\(665\) 2.34086 + 5.73516i 0.0907747 + 0.222400i
\(666\) 0 0
\(667\) 0.306108 + 0.0820213i 0.0118525 + 0.00317588i
\(668\) 3.46481 + 2.42608i 0.134057 + 0.0938680i
\(669\) 0 0
\(670\) −19.5785 38.0902i −0.756383 1.47155i
\(671\) 21.6656 + 3.82023i 0.836392 + 0.147478i
\(672\) 0 0
\(673\) −28.9385 2.53179i −1.11550 0.0975933i −0.485533 0.874218i \(-0.661374\pi\)
−0.629963 + 0.776625i \(0.716930\pi\)
\(674\) −8.33063 −0.320884
\(675\) 0 0
\(676\) 48.1660 1.85254
\(677\) 4.20773 + 0.368128i 0.161716 + 0.0141483i 0.167726 0.985834i \(-0.446358\pi\)
−0.00601017 + 0.999982i \(0.501913\pi\)
\(678\) 0 0
\(679\) 15.6340 + 2.75669i 0.599977 + 0.105792i
\(680\) 6.06511 + 11.7998i 0.232586 + 0.452500i
\(681\) 0 0
\(682\) 30.7300 + 21.5174i 1.17671 + 0.823943i
\(683\) −41.7463 11.1859i −1.59738 0.428017i −0.653130 0.757246i \(-0.726544\pi\)
−0.944250 + 0.329230i \(0.893211\pi\)
\(684\) 0 0
\(685\) 14.5348 + 35.6105i 0.555344 + 1.36061i
\(686\) −33.2133 + 91.2529i −1.26809 + 3.48405i
\(687\) 0 0
\(688\) 3.99548 + 45.6686i 0.152326 + 1.74110i
\(689\) −7.41441 6.22143i −0.282467 0.237018i
\(690\) 0 0
\(691\) 22.3741 + 8.14350i 0.851150 + 0.309793i 0.730509 0.682903i \(-0.239283\pi\)
0.120641 + 0.992696i \(0.461505\pi\)
\(692\) −71.2264 + 19.0850i −2.70762 + 0.725505i
\(693\) 0 0
\(694\) 74.3116 42.9038i 2.82083 1.62861i
\(695\) 7.93868 + 25.6405i 0.301131 + 0.972600i
\(696\) 0 0
\(697\) 2.19876 4.71526i 0.0832840 0.178603i
\(698\) 31.2301 + 44.6012i 1.18208 + 1.68818i
\(699\) 0 0
\(700\) 93.8880 15.5542i 3.54863 0.587892i
\(701\) 15.2816i 0.577177i −0.957453 0.288588i \(-0.906814\pi\)
0.957453 0.288588i \(-0.0931859\pi\)
\(702\) 0 0
\(703\) −0.364505 0.364505i −0.0137476 0.0137476i
\(704\) 15.9979 13.4239i 0.602945 0.505931i
\(705\) 0 0
\(706\) −11.6824 + 66.2543i −0.439674 + 2.49352i
\(707\) −30.4791 14.2126i −1.14628 0.534521i
\(708\) 0 0
\(709\) 28.5077 5.02667i 1.07063 0.188781i 0.389561 0.921001i \(-0.372627\pi\)
0.681068 + 0.732220i \(0.261516\pi\)
\(710\) 0.975310 7.12298i 0.0366027 0.267321i
\(711\) 0 0
\(712\) −3.96442 14.7954i −0.148573 0.554481i
\(713\) −6.68254 + 3.11612i −0.250263 + 0.116700i
\(714\) 0 0
\(715\) 1.30258 + 6.02298i 0.0487136 + 0.225247i
\(716\) −21.8760 + 26.0708i −0.817544 + 0.974311i
\(717\) 0 0
\(718\) −2.39754 5.14154i −0.0894755 0.191881i
\(719\) 5.81410 10.0703i 0.216829 0.375559i −0.737008 0.675884i \(-0.763762\pi\)
0.953837 + 0.300325i \(0.0970951\pi\)
\(720\) 0 0
\(721\) 34.6565 + 60.0268i 1.29068 + 2.23552i
\(722\) 26.2661 37.5119i 0.977524 1.39605i
\(723\) 0 0
\(724\) 1.40928 + 3.87196i 0.0523755 + 0.143900i
\(725\) 0.0930380 + 1.20732i 0.00345534 + 0.0448388i
\(726\) 0 0
\(727\) 3.61286 41.2951i 0.133993 1.53155i −0.570178 0.821521i \(-0.693126\pi\)
0.704171 0.710030i \(-0.251319\pi\)
\(728\) −16.8845 + 16.8845i −0.625780 + 0.625780i
\(729\) 0 0
\(730\) −11.9318 + 1.50804i −0.441617 + 0.0558149i
\(731\) 8.48063 + 10.1068i 0.313668 + 0.373814i
\(732\) 0 0
\(733\) 5.54883 3.88534i 0.204951 0.143508i −0.466595 0.884471i \(-0.654519\pi\)
0.671546 + 0.740963i \(0.265631\pi\)
\(734\) −71.9960 + 26.2044i −2.65742 + 0.967222i
\(735\) 0 0
\(736\) −0.0553335 0.313812i −0.00203962 0.0115673i
\(737\) 5.47803 20.4443i 0.201786 0.753075i
\(738\) 0 0
\(739\) −29.8815 17.2521i −1.09921 0.634629i −0.163197 0.986594i \(-0.552181\pi\)
−0.936014 + 0.351964i \(0.885514\pi\)
\(740\) −6.70126 + 4.22055i −0.246343 + 0.155150i
\(741\) 0 0
\(742\) −110.161 + 9.63788i −4.04415 + 0.353818i
\(743\) 41.3819 3.62044i 1.51815 0.132821i 0.702634 0.711551i \(-0.252007\pi\)
0.815519 + 0.578730i \(0.196452\pi\)
\(744\) 0 0
\(745\) −4.85193 + 21.3615i −0.177761 + 0.782625i
\(746\) 68.9031 + 39.7812i 2.52272 + 1.45649i
\(747\) 0 0
\(748\) −3.37336 + 12.5895i −0.123342 + 0.460319i
\(749\) −7.33715 41.6110i −0.268093 1.52043i
\(750\) 0 0
\(751\) 23.6063 8.59199i 0.861406 0.313526i 0.126724 0.991938i \(-0.459554\pi\)
0.734682 + 0.678412i \(0.237331\pi\)
\(752\) −22.3687 + 15.6627i −0.815703 + 0.571161i
\(753\) 0 0
\(754\) −0.388210 0.462651i −0.0141378 0.0168488i
\(755\) 4.32337 + 34.2072i 0.157344 + 1.24493i
\(756\) 0 0
\(757\) −27.9350 + 27.9350i −1.01531 + 1.01531i −0.0154328 + 0.999881i \(0.504913\pi\)
−0.999881 + 0.0154328i \(0.995087\pi\)
\(758\) 1.03689 11.8517i 0.0376615 0.430473i
\(759\) 0 0
\(760\) 4.37267 + 4.82182i 0.158613 + 0.174906i
\(761\) 16.3639 + 44.9594i 0.593191 + 1.62978i 0.764546 + 0.644569i \(0.222963\pi\)
−0.171355 + 0.985209i \(0.554814\pi\)
\(762\) 0 0
\(763\) −24.2029 + 34.5654i −0.876205 + 1.25135i
\(764\) −8.06045 13.9611i −0.291617 0.505095i
\(765\) 0 0
\(766\) 15.1312 26.2080i 0.546713 0.946935i
\(767\) −5.11326 10.9654i −0.184629 0.395938i
\(768\) 0 0
\(769\) 4.81494 5.73823i 0.173631 0.206926i −0.672210 0.740361i \(-0.734655\pi\)
0.845841 + 0.533435i \(0.179099\pi\)
\(770\) 59.1818 + 38.1353i 2.13277 + 1.37430i
\(771\) 0 0
\(772\) 0.890250 0.415130i 0.0320408 0.0149409i
\(773\) 9.18683 + 34.2857i 0.330427 + 1.23317i 0.908742 + 0.417358i \(0.137044\pi\)
−0.578315 + 0.815814i \(0.696290\pi\)
\(774\) 0 0
\(775\) −19.7144 20.1271i −0.708164 0.722987i
\(776\) 16.4283 2.89676i 0.589743 0.103988i
\(777\) 0 0
\(778\) −26.7413 12.4697i −0.958721 0.447059i
\(779\) 0.443250 2.51380i 0.0158811 0.0900661i
\(780\) 0 0
\(781\) 2.72180 2.28386i 0.0973936 0.0817229i
\(782\) −2.71158 2.71158i −0.0969659 0.0969659i
\(783\) 0 0
\(784\) 63.7449i 2.27660i
\(785\) −37.7830 + 1.45365i −1.34853 + 0.0518830i
\(786\) 0 0
\(787\) −15.3799 21.9648i