Properties

Label 405.2.r.a.197.1
Level $405$
Weight $2$
Character 405.197
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 197.1
Character \(\chi\) \(=\) 405.197
Dual form 405.2.r.a.368.1

$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{13}{18}\right)\)

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 −0.907809 0.419384i \(-0.862246\pi\)
−0.821192 + 0.570652i \(0.806690\pi\)
\(3\) 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 −0.474816 + 0.880085i \(0.657485\pi\)
−0.989406 + 0.145174i \(0.953626\pi\)
\(8\) −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 −0.997395 0.0721346i \(-0.977019\pi\)
0.717682 0.696371i \(-0.245203\pi\)
\(12\) 0 0
\(13\) 0.0885504 1.01214i 0.0245595 0.280716i −0.973978 0.226644i \(-0.927224\pi\)
0.998537 0.0540717i \(-0.0172200\pi\)
\(14\) 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 0.395944 0.918275i \(-0.370417\pi\)
−0.116240 + 0.993221i \(0.537084\pi\)
\(18\) 0 0
\(19\) 0.507294 + 0.292886i 0.116381 + 0.0671927i 0.557061 0.830472i \(-0.311929\pi\)
−0.440679 + 0.897665i \(0.645262\pi\)
\(20\) −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 −0.733242 0.679967i \(-0.761994\pi\)
0.889744 + 0.456460i \(0.150883\pi\)
\(24\) 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 0.659850 0.751397i \(-0.270620\pi\)
−0.625400 + 0.780304i \(0.715064\pi\)
\(30\) 0 0
\(31\) −0.978463 5.54914i −0.175737 0.996655i −0.937290 0.348552i \(-0.886674\pi\)
0.761552 0.648103i \(-0.224438\pi\)
\(32\) −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 −0.982117 0.188269i \(-0.939712\pi\)
0.944673 + 0.328013i \(0.106379\pi\)
\(38\) −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 0.939055 0.343766i \(-0.111703\pi\)
−0.501609 + 0.865095i \(0.667258\pi\)
\(42\) 0 0
\(43\) 4.67013 10.0151i 0.712188 1.52729i −0.132002 0.991249i \(-0.542141\pi\)
0.844191 0.536043i \(-0.180082\pi\)
\(44\) −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 0.443228 0.896409i \(-0.353833\pi\)
−0.993942 + 0.109908i \(0.964944\pi\)
\(48\) 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 0.0721125 0.997397i \(-0.477026\pi\)
−0.997397 + 0.0721125i \(0.977026\pi\)
\(54\) 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 −0.512354 0.858775i \(-0.671226\pi\)
−0.944495 + 0.328525i \(0.893449\pi\)
\(60\) 0 0
\(61\) −1.40842 + 7.98754i −0.180330 + 1.02270i 0.751481 + 0.659755i \(0.229340\pi\)
−0.931811 + 0.362945i \(0.881771\pi\)
\(62\) 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 −0.398222 0.917289i \(-0.630373\pi\)
−0.551458 + 0.834203i \(0.685928\pi\)
\(68\) 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 −0.565803 0.824541i \(-0.691434\pi\)
0.431172 + 0.902270i \(0.358100\pi\)
\(72\) 0 0
\(73\) −0.567144 2.11661i −0.0663792 0.247730i 0.924761 0.380547i \(-0.124264\pi\)
−0.991141 + 0.132817i \(0.957598\pi\)
\(74\) 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 −0.629491 0.777008i \(-0.716737\pi\)
0.874513 + 0.485002i \(0.161181\pi\)
\(80\) −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 0.891767 + 0.452495i \(0.149466\pi\)
−0.799644 + 0.600474i \(0.794979\pi\)
\(84\) 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 −0.772713 0.634756i \(-0.781101\pi\)
0.936071 + 0.351811i \(0.114434\pi\)
\(90\) 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 0.261987 0.965071i \(-0.415622\pi\)
−0.570886 + 0.821030i \(0.693400\pi\)
\(98\) −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 0.510831 0.859681i \(-0.329338\pi\)
0.185996 + 0.982550i \(0.440449\pi\)
\(102\) 0 0
\(103\) −13.2831 + 6.19401i −1.30882 + 0.610314i −0.946790 0.321852i \(-0.895695\pi\)
−0.362032 + 0.932166i \(0.617917\pi\)
\(104\) 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 −0.332397 0.943140i \(-0.607857\pi\)
0.943140 + 0.332397i \(0.107857\pi\)
\(108\) 0 0
\(109\) 8.92248i 0.854618i 0.904106 + 0.427309i \(0.140538\pi\)
−0.904106 + 0.427309i \(0.859462\pi\)
\(110\) −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 0.830716 0.556697i \(-0.187931\pi\)
−0.960428 + 0.278527i \(0.910154\pi\)
\(114\) 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 0.357065 0.934079i \(-0.383777\pi\)
0.776267 + 0.630404i \(0.217111\pi\)
\(128\) 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 −0.148179 0.988961i \(-0.547341\pi\)
0.199002 + 0.979999i \(0.436230\pi\)
\(132\) 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 −0.791110 0.611674i \(-0.790496\pi\)
−0.672875 + 0.739756i \(0.734941\pi\)
\(138\) 0 0
\(139\) −11.8215 + 2.08444i −1.00268 + 0.176800i −0.650804 0.759246i \(-0.725568\pi\)
−0.351878 + 0.936046i \(0.614457\pi\)
\(140\) −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 −0.896163 0.443725i \(-0.853657\pi\)
0.281367 + 0.959600i \(0.409212\pi\)
\(150\) 0 0
\(151\) −14.4897 + 5.27382i −1.17916 + 0.429178i −0.855904 0.517135i \(-0.826998\pi\)
−0.323252 + 0.946313i \(0.604776\pi\)
\(152\) −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 0.954052 + 0.299640i \(0.0968664\pi\)
−0.383716 + 0.923451i \(0.625356\pi\)
\(158\) −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 −0.341293 0.939957i \(-0.610865\pi\)
0.939957 + 0.341293i \(0.110865\pi\)
\(164\) 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 −0.385416 0.922743i \(-0.625942\pi\)
0.459122 + 0.888373i \(0.348164\pi\)
\(168\) 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 −0.327979 0.944685i \(-0.606368\pi\)
−0.934492 + 0.355985i \(0.884145\pi\)
\(174\) 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 0.663633 0.748058i \(-0.269014\pi\)
−0.979654 + 0.200694i \(0.935680\pi\)
\(180\) 0 0
\(181\) 0.511902 0.886641i 0.0380494 0.0659035i −0.846374 0.532590i \(-0.821219\pi\)
0.884423 + 0.466686i \(0.154552\pi\)
\(182\) −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 −0.851108 0.524991i \(-0.824069\pi\)
0.664808 + 0.747014i \(0.268513\pi\)
\(192\) 0 0
\(193\) 0.199928 + 0.139991i 0.0143911 + 0.0100768i 0.580750 0.814082i \(-0.302759\pi\)
−0.566359 + 0.824159i \(0.691648\pi\)
\(194\) 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 0.996491 + 0.0837043i \(0.0266751\pi\)
−0.821134 + 0.570735i \(0.806658\pi\)
\(198\) 0 0
\(199\) 4.26708 2.46360i 0.302486 0.174640i −0.341073 0.940037i \(-0.610790\pi\)
0.643559 + 0.765397i \(0.277457\pi\)
\(200\) 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 −0.709472 0.704734i \(-0.751066\pi\)
−0.996481 + 0.0838177i \(0.973289\pi\)
\(212\) −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 0.759470 0.650543i \(-0.225459\pi\)
−0.871064 + 0.491169i \(0.836570\pi\)
\(224\) 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 −0.619788 0.784769i \(-0.712782\pi\)
0.999560 0.0296545i \(-0.00944070\pi\)
\(228\) 0 0
\(229\) −6.17868 7.36346i −0.408298 0.486591i 0.522233 0.852803i \(-0.325099\pi\)
−0.930532 + 0.366212i \(0.880655\pi\)
\(230\) −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 −0.632829 0.774292i \(-0.718106\pi\)
0.935192 0.354142i \(-0.115227\pi\)
\(234\) 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 0.744688 + 0.667412i \(0.232598\pi\)
−0.471510 + 0.881861i \(0.656291\pi\)
\(240\) 0 0
\(241\) 5.17529 + 4.34259i 0.333370 + 0.279731i 0.794071 0.607825i \(-0.207958\pi\)
−0.460701 + 0.887555i \(0.652402\pi\)
\(242\) −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 −0.441721 0.897152i \(-0.645632\pi\)
−0.997817 + 0.0660346i \(0.978965\pi\)
\(252\) 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 0.814342 + 0.580385i \(0.197098\pi\)
−0.902753 + 0.430158i \(0.858458\pi\)
\(258\) 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 −0.730287 0.683141i \(-0.760613\pi\)
0.392170 + 0.919893i \(0.371725\pi\)
\(264\) 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 −0.318155 0.948039i \(-0.603063\pi\)
0.782050 + 0.623216i \(0.214174\pi\)
\(278\) 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 0.910767 0.412920i \(-0.135491\pi\)
−0.963108 + 0.269115i \(0.913269\pi\)
\(282\) 0 0
\(283\) 1.56435 17.8806i 0.0929908 1.06289i −0.796102 0.605163i \(-0.793108\pi\)
0.889093 0.457727i \(-0.151336\pi\)
\(284\) −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 −0.159631 0.987177i \(-0.551030\pi\)
0.982240 0.187630i \(-0.0600807\pi\)
\(294\) 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 0.660097 + 0.751180i \(0.270515\pi\)
−0.947251 + 0.320493i \(0.896151\pi\)
\(308\) 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 0.860582 0.509312i \(-0.170100\pi\)
−0.651013 + 0.759067i \(0.725656\pi\)
\(312\) 0 0
\(313\) 4.98349 10.6871i 0.281683 0.604072i −0.713657 0.700495i \(-0.752963\pi\)
0.995340 + 0.0964234i \(0.0307403\pi\)
\(314\) −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 0.978038 0.208427i \(-0.0668343\pi\)
−0.530366 + 0.847769i \(0.677945\pi\)
\(318\) 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 −0.338185 0.941080i \(-0.609813\pi\)
0.639658 0.768659i \(-0.279076\pi\)
\(332\) 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 0.178872 0.983872i \(-0.442755\pi\)
0.00530714 + 0.999986i \(0.498311\pi\)
\(338\) −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 −0.966928 0.255048i \(-0.917909\pi\)
−0.570376 0.821384i \(-0.693202\pi\)
\(348\) 0 0
\(349\) −14.2588 + 16.9930i −0.763258 + 0.909615i −0.998049 0.0624307i \(-0.980115\pi\)
0.234792 + 0.972046i \(0.424559\pi\)
\(350\) −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 0.745033 + 0.667028i \(0.232434\pi\)
−0.617886 + 0.786268i \(0.712011\pi\)
\(354\) 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 −0.833917 0.551890i \(-0.813907\pi\)
0.894909 + 0.446248i \(0.147240\pi\)
\(360\) 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 0.983435 0.181259i \(-0.0580172\pi\)
0.493288 + 0.869866i \(0.335795\pi\)
\(368\) 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 −0.990399 0.138237i \(-0.955857\pi\)
−0.530721 + 0.847547i \(0.678079\pi\)
\(374\) 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 \(-0.960272\pi\)
0.992221 0.124486i \(-0.0397282\pi\)
\(380\) −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 0.727046 0.686589i \(-0.240893\pi\)
−0.993294 + 0.115618i \(0.963115\pi\)
\(384\) 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 −0.0393859 0.999224i \(-0.512540\pi\)
0.612118 + 0.790767i \(0.290318\pi\)
\(390\) 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 −0.640327 0.768103i \(-0.721201\pi\)
−0.170488 + 0.985360i \(0.554534\pi\)
\(398\) −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 −0.548898 0.835889i \(-0.684953\pi\)
−0.229905 + 0.973213i \(0.573841\pi\)
\(402\) 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 −0.336257 0.941770i \(-0.609161\pi\)
0.00612663 + 0.999981i \(0.498050\pi\)
\(410\) 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 −0.00324717 0.999995i \(-0.501034\pi\)
0.984239 + 0.176845i \(0.0565892\pi\)
\(420\) 0 0
\(421\) −8.48131 + 3.08694i −0.413354 + 0.150448i −0.540322 0.841458i \(-0.681698\pi\)
0.126968 + 0.991907i \(0.459475\pi\)
\(422\) 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 \(-0.775365\pi\)
0.761151 0.648575i \(-0.224635\pi\)
\(432\) 0 0
\(433\) −0.461356 + 0.461356i −0.0221714 + 0.0221714i −0.718106 0.695934i \(-0.754991\pi\)
0.695934 + 0.718106i \(0.254991\pi\)
\(434\) −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 0.205251 0.978709i \(-0.434199\pi\)
−0.141866 + 0.989886i \(0.545310\pi\)
\(440\) −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 −0.387930 0.921689i \(-0.626810\pi\)
−0.955411 + 0.295278i \(0.904588\pi\)
\(444\) 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 0.999318 0.0369176i \(-0.0117539\pi\)
−0.531631 + 0.846976i \(0.678421\pi\)
\(450\) 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 −0.974446 0.224624i \(-0.927885\pi\)
0.920636 0.390422i \(-0.127671\pi\)
\(458\) 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 −0.672596 0.740010i \(-0.734821\pi\)
0.845563 + 0.533876i \(0.179265\pi\)
\(462\) 0 0
\(463\) −12.0734 8.45389i −0.561099 0.392885i 0.258339 0.966054i \(-0.416825\pi\)
−0.819437 + 0.573169i \(0.805714\pi\)
\(464\) 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 0.959720 + 0.280958i \(0.0906522\pi\)
−0.690663 + 0.723177i \(0.742681\pi\)
\(468\) 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 −0.756878 0.653556i \(-0.773276\pi\)
0.934762 0.355274i \(-0.115613\pi\)
\(480\) 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 0.252714 0.967541i \(-0.418677\pi\)
−0.967541 + 0.252714i \(0.918677\pi\)
\(488\) −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 −0.993815 0.111048i \(-0.964579\pi\)
0.832687 + 0.553744i \(0.186801\pi\)
\(492\) 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 0.648063 0.761586i \(-0.275579\pi\)
−0.862551 + 0.505970i \(0.831135\pi\)
\(500\) 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 0.707657 + 0.706556i \(0.249752\pi\)
−0.966127 + 0.258067i \(0.916914\pi\)
\(504\) 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 −0.662196 0.749331i \(-0.730375\pi\)
0.365975 0.930625i \(-0.380736\pi\)
\(510\) 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 0.996470 0.0839530i \(-0.0267546\pi\)
0.425529 + 0.904945i \(0.360088\pi\)
\(522\) 0 0
\(523\) 20.3099 + 5.44201i 0.888088 + 0.237962i 0.673893 0.738829i \(-0.264621\pi\)
0.214195 + 0.976791i \(0.431287\pi\)
\(524\) 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 −0.365920 0.930646i \(-0.619246\pi\)
0.749369 + 0.662152i \(0.230357\pi\)
\(548\) −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 0.240496 0.970650i \(-0.422690\pi\)
−0.277050 + 0.960856i \(0.589357\pi\)
\(558\) 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 0.0944822 + 0.995527i \(0.469880\pi\)
−0.967804 + 0.251706i \(0.919008\pi\)
\(564\) 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 0.743345 0.668908i \(-0.233238\pi\)
−0.529666 + 0.848206i \(0.677683\pi\)
\(570\) 0 0
\(571\) 1.91569 + 10.8644i 0.0801693 + 0.454663i 0.998295 + 0.0583730i \(0.0185913\pi\)
−0.918126 + 0.396290i \(0.870298\pi\)
\(572\) −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 0.580921 + 0.813960i \(0.302692\pi\)
−0.910073 + 0.414449i \(0.863974\pi\)
\(578\) 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 0.828403 0.560133i \(-0.189250\pi\)
−0.809683 + 0.586867i \(0.800361\pi\)
\(588\) 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 0.987274 + 0.159029i \(0.0508363\pi\)
0.159029 + 0.987274i \(0.449164\pi\)
\(594\) 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 0.939663 0.342101i \(-0.111139\pi\)
0.499925 + 0.866068i \(0.333361\pi\)
\(600\) 0 0
\(601\) 0.988708 5.60724i 0.0403302 0.228724i −0.957980 0.286835i \(-0.907397\pi\)
0.998310 + 0.0581113i \(0.0185078\pi\)
\(602\) −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 0.321885 0.946779i \(-0.395683\pi\)
0.152589 + 0.988290i \(0.451239\pi\)
\(608\) −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 −0.996266 0.0863408i \(-0.972483\pi\)
0.819621 0.572906i \(-0.194184\pi\)
\(614\) 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 0.947747 0.319024i \(-0.103355\pi\)
0.0243643 + 0.999703i \(0.492244\pi\)
\(618\) 0 0
\(619\) 26.5533 31.6450i 1.06727 1.27192i 0.106575 0.994305i \(-0.466012\pi\)
0.960692 0.277615i \(-0.0895439\pi\)
\(620\) 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 0.626586 0.779352i \(-0.284452\pi\)
−0.988232 + 0.152963i \(0.951118\pi\)
\(632\) −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 −0.0258971 0.999665i \(-0.508244\pi\)
−0.366241 + 0.930520i \(0.619355\pi\)
\(642\) 0 0
\(643\) 24.3420 11.3509i 0.959956 0.447635i 0.121492 0.992592i \(-0.461232\pi\)
0.838464 + 0.544957i \(0.183454\pi\)
\(644\) 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 −0.990913 0.134503i \(-0.957056\pi\)
0.134503 + 0.990913i \(0.457056\pi\)
\(648\) 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 −0.998568 0.0534961i \(-0.982964\pi\)
0.600887 0.799334i \(-0.294814\pi\)
\(654\) 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 −0.186308 0.982491i \(-0.559652\pi\)
0.488813 + 0.872389i \(0.337430\pi\)
\(660\) 0 0
\(661\) 16.2837 13.6636i 0.633361 0.531453i −0.268610 0.963249i \(-0.586564\pi\)
0.901971 + 0.431796i \(0.142120\pi\)
\(662\) −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 −0.629963 0.776625i \(-0.716930\pi\)
−0.485533 + 0.874218i \(0.661374\pi\)
\(674\) −8.33063 −0.320884
\(675\) 0 0
\(676\) 48.1660 1.85254
\(677\) 4.20773 0.368128i 0.161716 0.0141483i −0.00601017 0.999982i \(-0.501913\pi\)
0.167726 + 0.985834i \(0.446358\pi\)
\(678\) 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 −0.944250 0.329230i \(-0.893211\pi\)
−0.653130 + 0.757246i \(0.726544\pi\)
\(684\) 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 0.120641 0.992696i \(-0.461505\pi\)
0.730509 + 0.682903i \(0.239283\pi\)
\(692\) −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 \(0.0931859\pi\)
−0.957453 + 0.288588i \(0.906814\pi\)
\(702\) 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 0.681068 0.732220i \(-0.261516\pi\)
0.389561 + 0.921001i \(0.372627\pi\)
\(710\) 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 0.953837 0.300325i \(-0.0970951\pi\)
−0.737008 + 0.675884i \(0.763762\pi\)
\(720\) 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 0.704171 + 0.710030i \(0.251319\pi\)
−0.570178 + 0.821521i \(0.693126\pi\)
\(728\) −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 0.671546 0.740963i \(-0.265631\pi\)
−0.466595 + 0.884471i \(0.654519\pi\)
\(734\) −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 −0.936014 0.351964i \(-0.885514\pi\)
−0.163197 + 0.986594i \(0.552181\pi\)
\(740\) −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 0.815519 0.578730i \(-0.196452\pi\)
0.702634 + 0.711551i \(0.252007\pi\)
\(744\) 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 0.734682 0.678412i \(-0.237331\pi\)
0.126724 + 0.991938i \(0.459554\pi\)
\(752\) −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 −0.999881 0.0154328i \(-0.995087\pi\)
−0.0154328 0.999881i \(-0.504913\pi\)
\(758\) 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 −0.171355 0.985209i \(-0.554814\pi\)
0.764546 0.644569i \(-0.222963\pi\)
\(762\) 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 0.845841 0.533435i \(-0.179099\pi\)
−0.672210 + 0.740361i \(0.734655\pi\)
\(770\) 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 −0.578315 0.815814i \(-0.696290\pi\)
0.908742 0.417358i \(-0.137044\pi\)
\(774\) 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