Properties

Label 576.2.bd.a.109.1
Level $576$
Weight $2$
Character 576.109
Analytic conductor $4.599$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bd (of order \(16\), degree \(8\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(7\) over \(\Q(\zeta_{16})\)
Twist minimal: no (minimal twist has level 64)
Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label 109.1
Character \(\chi\) \(=\) 576.109
Dual form 576.2.bd.a.37.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.998819 - 1.00118i) q^{2} +(-0.00472188 + 1.99999i) q^{4} +(-0.0517508 - 0.260169i) q^{5} +(-0.515195 - 1.24379i) q^{7} +(2.00707 - 1.99290i) q^{8} +O(q^{10})\) \(q+(-0.998819 - 1.00118i) q^{2} +(-0.00472188 + 1.99999i) q^{4} +(-0.0517508 - 0.260169i) q^{5} +(-0.515195 - 1.24379i) q^{7} +(2.00707 - 1.99290i) q^{8} +(-0.208786 + 0.311673i) q^{10} +(4.11495 + 2.74952i) q^{11} +(-0.650168 + 3.26862i) q^{13} +(-0.730672 + 1.75812i) q^{14} +(-3.99996 - 0.0188875i) q^{16} +(-1.10212 - 1.10212i) q^{17} +(2.56547 + 0.510304i) q^{19} +(0.520580 - 0.102273i) q^{20} +(-1.35733 - 6.86609i) q^{22} +(-3.70792 - 1.53587i) q^{23} +(4.55439 - 1.88649i) q^{25} +(3.92187 - 2.61382i) q^{26} +(2.49001 - 1.02451i) q^{28} +(5.46390 - 3.65086i) q^{29} +8.22961i q^{31} +(3.97632 + 4.02354i) q^{32} +(-0.00260204 + 2.20424i) q^{34} +(-0.296934 + 0.198405i) q^{35} +(7.58710 - 1.50917i) q^{37} +(-2.05154 - 3.07820i) q^{38} +(-0.622359 - 0.419042i) q^{40} +(10.4659 + 4.33512i) q^{41} +(2.31618 - 3.46640i) q^{43} +(-5.51846 + 8.21690i) q^{44} +(2.16586 + 5.24635i) q^{46} +(-2.33317 - 2.33317i) q^{47} +(3.66816 - 3.66816i) q^{49} +(-6.43772 - 2.67550i) q^{50} +(-6.53414 - 1.31577i) q^{52} +(3.33837 + 2.23063i) q^{53} +(0.502388 - 1.21287i) q^{55} +(-3.51279 - 1.46964i) q^{56} +(-9.11262 - 1.82380i) q^{58} +(-1.16241 - 5.84382i) q^{59} +(-6.89488 - 10.3189i) q^{61} +(8.23932 - 8.21989i) q^{62} +(0.0566621 - 7.99980i) q^{64} +0.884038 q^{65} +(1.94793 + 2.91529i) q^{67} +(2.20944 - 2.19903i) q^{68} +(0.495222 + 0.0991136i) q^{70} +(5.39337 + 13.0208i) q^{71} +(-0.375531 + 0.906612i) q^{73} +(-9.08909 - 6.08867i) q^{74} +(-1.03272 + 5.12852i) q^{76} +(1.29983 - 6.53468i) q^{77} +(1.20158 - 1.20158i) q^{79} +(0.202087 + 1.04164i) q^{80} +(-6.11331 - 14.8083i) q^{82} +(-15.1088 - 3.00532i) q^{83} +(-0.229702 + 0.343773i) q^{85} +(-5.78393 + 1.14340i) q^{86} +(13.7385 - 2.68222i) q^{88} +(1.66533 - 0.689803i) q^{89} +(4.40044 - 0.875301i) q^{91} +(3.08924 - 7.40856i) q^{92} +(-0.00550847 + 4.66633i) q^{94} -0.693864i q^{95} +15.4207i q^{97} +(-7.33631 - 0.00866031i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 8q^{2} - 8q^{4} + 8q^{5} - 8q^{7} + 8q^{8} + O(q^{10}) \) \( 56q + 8q^{2} - 8q^{4} + 8q^{5} - 8q^{7} + 8q^{8} - 8q^{10} + 8q^{11} - 8q^{13} + 8q^{14} - 8q^{16} + 8q^{17} - 8q^{19} + 8q^{20} + 8q^{23} - 8q^{25} - 32q^{26} + 32q^{28} + 8q^{29} - 32q^{32} + 32q^{34} + 8q^{35} - 8q^{37} - 32q^{38} + 32q^{40} + 8q^{41} - 8q^{43} - 8q^{46} + 8q^{47} - 8q^{49} + 32q^{50} - 56q^{52} + 8q^{53} + 56q^{55} + 64q^{56} - 80q^{58} - 56q^{59} - 8q^{61} + 40q^{62} - 104q^{64} + 16q^{65} + 72q^{67} + 56q^{68} - 104q^{70} - 56q^{71} - 8q^{73} + 64q^{74} - 72q^{76} + 8q^{77} + 24q^{79} - 32q^{80} + 72q^{82} + 8q^{83} - 8q^{85} - 96q^{86} + 72q^{88} + 8q^{89} - 8q^{91} - 144q^{92} + 88q^{94} - 128q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{16}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.998819 1.00118i −0.706272 0.707941i
\(3\) 0 0
\(4\) −0.00472188 + 1.99999i −0.00236094 + 0.999997i
\(5\) −0.0517508 0.260169i −0.0231436 0.116351i 0.967487 0.252922i \(-0.0813917\pi\)
−0.990630 + 0.136571i \(0.956392\pi\)
\(6\) 0 0
\(7\) −0.515195 1.24379i −0.194725 0.470109i 0.796115 0.605145i \(-0.206885\pi\)
−0.990841 + 0.135036i \(0.956885\pi\)
\(8\) 2.00707 1.99290i 0.709606 0.704598i
\(9\) 0 0
\(10\) −0.208786 + 0.311673i −0.0660239 + 0.0985597i
\(11\) 4.11495 + 2.74952i 1.24071 + 0.829013i 0.990275 0.139122i \(-0.0444280\pi\)
0.250430 + 0.968135i \(0.419428\pi\)
\(12\) 0 0
\(13\) −0.650168 + 3.26862i −0.180324 + 0.906551i 0.779597 + 0.626281i \(0.215424\pi\)
−0.959921 + 0.280269i \(0.909576\pi\)
\(14\) −0.730672 + 1.75812i −0.195280 + 0.469879i
\(15\) 0 0
\(16\) −3.99996 0.0188875i −0.999989 0.00472187i
\(17\) −1.10212 1.10212i −0.267304 0.267304i 0.560709 0.828013i \(-0.310529\pi\)
−0.828013 + 0.560709i \(0.810529\pi\)
\(18\) 0 0
\(19\) 2.56547 + 0.510304i 0.588560 + 0.117072i 0.480381 0.877060i \(-0.340498\pi\)
0.108178 + 0.994132i \(0.465498\pi\)
\(20\) 0.520580 0.102273i 0.116405 0.0228689i
\(21\) 0 0
\(22\) −1.35733 6.86609i −0.289383 1.46385i
\(23\) −3.70792 1.53587i −0.773154 0.320251i −0.0390048 0.999239i \(-0.512419\pi\)
−0.734149 + 0.678988i \(0.762419\pi\)
\(24\) 0 0
\(25\) 4.55439 1.88649i 0.910878 0.377298i
\(26\) 3.92187 2.61382i 0.769142 0.512612i
\(27\) 0 0
\(28\) 2.49001 1.02451i 0.470567 0.193615i
\(29\) 5.46390 3.65086i 1.01462 0.677948i 0.0671349 0.997744i \(-0.478614\pi\)
0.947487 + 0.319795i \(0.103614\pi\)
\(30\) 0 0
\(31\) 8.22961i 1.47808i 0.673661 + 0.739041i \(0.264721\pi\)
−0.673661 + 0.739041i \(0.735279\pi\)
\(32\) 3.97632 + 4.02354i 0.702921 + 0.711268i
\(33\) 0 0
\(34\) −0.00260204 + 2.20424i −0.000446247 + 0.378024i
\(35\) −0.296934 + 0.198405i −0.0501909 + 0.0335365i
\(36\) 0 0
\(37\) 7.58710 1.50917i 1.24731 0.248106i 0.473087 0.881016i \(-0.343140\pi\)
0.774225 + 0.632910i \(0.218140\pi\)
\(38\) −2.05154 3.07820i −0.332803 0.499350i
\(39\) 0 0
\(40\) −0.622359 0.419042i −0.0984036 0.0662564i
\(41\) 10.4659 + 4.33512i 1.63450 + 0.677032i 0.995725 0.0923624i \(-0.0294418\pi\)
0.638774 + 0.769394i \(0.279442\pi\)
\(42\) 0 0
\(43\) 2.31618 3.46640i 0.353213 0.528621i −0.611734 0.791063i \(-0.709528\pi\)
0.964948 + 0.262442i \(0.0845278\pi\)
\(44\) −5.51846 + 8.21690i −0.831940 + 1.23874i
\(45\) 0 0
\(46\) 2.16586 + 5.24635i 0.319338 + 0.773532i
\(47\) −2.33317 2.33317i −0.340328 0.340328i 0.516163 0.856490i \(-0.327360\pi\)
−0.856490 + 0.516163i \(0.827360\pi\)
\(48\) 0 0
\(49\) 3.66816 3.66816i 0.524023 0.524023i
\(50\) −6.43772 2.67550i −0.910432 0.378373i
\(51\) 0 0
\(52\) −6.53414 1.31577i −0.906122 0.182464i
\(53\) 3.33837 + 2.23063i 0.458560 + 0.306400i 0.763310 0.646032i \(-0.223573\pi\)
−0.304750 + 0.952432i \(0.598573\pi\)
\(54\) 0 0
\(55\) 0.502388 1.21287i 0.0677420 0.163544i
\(56\) −3.51279 1.46964i −0.469416 0.196389i
\(57\) 0 0
\(58\) −9.11262 1.82380i −1.19655 0.239476i
\(59\) −1.16241 5.84382i −0.151333 0.760800i −0.979677 0.200581i \(-0.935717\pi\)
0.828345 0.560219i \(-0.189283\pi\)
\(60\) 0 0
\(61\) −6.89488 10.3189i −0.882799 1.32120i −0.946323 0.323222i \(-0.895234\pi\)
0.0635241 0.997980i \(-0.479766\pi\)
\(62\) 8.23932 8.21989i 1.04639 1.04393i
\(63\) 0 0
\(64\) 0.0566621 7.99980i 0.00708277 0.999975i
\(65\) 0.884038 0.109651
\(66\) 0 0
\(67\) 1.94793 + 2.91529i 0.237978 + 0.356159i 0.931165 0.364599i \(-0.118794\pi\)
−0.693187 + 0.720758i \(0.743794\pi\)
\(68\) 2.20944 2.19903i 0.267934 0.266672i
\(69\) 0 0
\(70\) 0.495222 + 0.0991136i 0.0591903 + 0.0118463i
\(71\) 5.39337 + 13.0208i 0.640076 + 1.54528i 0.826577 + 0.562824i \(0.190285\pi\)
−0.186501 + 0.982455i \(0.559715\pi\)
\(72\) 0 0
\(73\) −0.375531 + 0.906612i −0.0439526 + 0.106111i −0.944331 0.328996i \(-0.893290\pi\)
0.900379 + 0.435107i \(0.143290\pi\)
\(74\) −9.08909 6.08867i −1.05659 0.707793i
\(75\) 0 0
\(76\) −1.03272 + 5.12852i −0.118461 + 0.588282i
\(77\) 1.29983 6.53468i 0.148129 0.744696i
\(78\) 0 0
\(79\) 1.20158 1.20158i 0.135189 0.135189i −0.636274 0.771463i \(-0.719525\pi\)
0.771463 + 0.636274i \(0.219525\pi\)
\(80\) 0.202087 + 1.04164i 0.0225940 + 0.116459i
\(81\) 0 0
\(82\) −6.11331 14.8083i −0.675102 1.63530i
\(83\) −15.1088 3.00532i −1.65840 0.329877i −0.725012 0.688736i \(-0.758166\pi\)
−0.933392 + 0.358859i \(0.883166\pi\)
\(84\) 0 0
\(85\) −0.229702 + 0.343773i −0.0249147 + 0.0372874i
\(86\) −5.78393 + 1.14340i −0.623697 + 0.123296i
\(87\) 0 0
\(88\) 13.7385 2.68222i 1.46453 0.285926i
\(89\) 1.66533 0.689803i 0.176525 0.0731189i −0.292671 0.956213i \(-0.594544\pi\)
0.469195 + 0.883094i \(0.344544\pi\)
\(90\) 0 0
\(91\) 4.40044 0.875301i 0.461291 0.0917565i
\(92\) 3.08924 7.40856i 0.322075 0.772396i
\(93\) 0 0
\(94\) −0.00550847 + 4.66633i −0.000568156 + 0.481296i
\(95\) 0.693864i 0.0711889i
\(96\) 0 0
\(97\) 15.4207i 1.56574i 0.622188 + 0.782868i \(0.286244\pi\)
−0.622188 + 0.782868i \(0.713756\pi\)
\(98\) −7.33631 0.00866031i −0.741079 0.000874823i
\(99\) 0 0
\(100\) 3.75146 + 9.11766i 0.375146 + 0.911766i
\(101\) −8.24786 + 1.64060i −0.820692 + 0.163246i −0.587541 0.809195i \(-0.699904\pi\)
−0.233152 + 0.972440i \(0.574904\pi\)
\(102\) 0 0
\(103\) −9.41219 + 3.89866i −0.927410 + 0.384146i −0.794695 0.607008i \(-0.792369\pi\)
−0.132715 + 0.991154i \(0.542369\pi\)
\(104\) 5.20911 + 7.85606i 0.510795 + 0.770350i
\(105\) 0 0
\(106\) −1.10117 5.57030i −0.106955 0.541035i
\(107\) −1.05984 + 1.58616i −0.102459 + 0.153340i −0.879156 0.476533i \(-0.841893\pi\)
0.776698 + 0.629873i \(0.216893\pi\)
\(108\) 0 0
\(109\) 4.24989 + 0.845355i 0.407065 + 0.0809704i 0.394376 0.918949i \(-0.370961\pi\)
0.0126894 + 0.999919i \(0.495961\pi\)
\(110\) −1.71610 + 0.708459i −0.163623 + 0.0675489i
\(111\) 0 0
\(112\) 2.03727 + 4.98484i 0.192503 + 0.471023i
\(113\) −1.13449 + 1.13449i −0.106724 + 0.106724i −0.758453 0.651728i \(-0.774044\pi\)
0.651728 + 0.758453i \(0.274044\pi\)
\(114\) 0 0
\(115\) −0.207698 + 1.04417i −0.0193679 + 0.0973690i
\(116\) 7.27591 + 10.9450i 0.675551 + 1.01622i
\(117\) 0 0
\(118\) −4.68968 + 7.00069i −0.431720 + 0.644466i
\(119\) −0.803001 + 1.93862i −0.0736110 + 0.177713i
\(120\) 0 0
\(121\) 5.16345 + 12.4657i 0.469404 + 1.13324i
\(122\) −3.44436 + 17.2097i −0.311837 + 1.55810i
\(123\) 0 0
\(124\) −16.4592 0.0388592i −1.47808 0.00348966i
\(125\) −1.46337 2.19008i −0.130888 0.195887i
\(126\) 0 0
\(127\) −18.1894 −1.61405 −0.807025 0.590517i \(-0.798924\pi\)
−0.807025 + 0.590517i \(0.798924\pi\)
\(128\) −8.06583 + 7.93362i −0.712926 + 0.701240i
\(129\) 0 0
\(130\) −0.882994 0.885081i −0.0774437 0.0776267i
\(131\) 5.01304 + 7.50254i 0.437991 + 0.655500i 0.983143 0.182837i \(-0.0585281\pi\)
−0.545152 + 0.838337i \(0.683528\pi\)
\(132\) 0 0
\(133\) −0.687007 3.45382i −0.0595711 0.299484i
\(134\) 0.973095 4.86208i 0.0840626 0.420019i
\(135\) 0 0
\(136\) −4.40846 0.0156122i −0.378022 0.00133874i
\(137\) 2.99585 7.23263i 0.255953 0.617925i −0.742710 0.669613i \(-0.766460\pi\)
0.998663 + 0.0516877i \(0.0164600\pi\)
\(138\) 0 0
\(139\) 2.95817 + 1.97658i 0.250908 + 0.167652i 0.674664 0.738125i \(-0.264288\pi\)
−0.423756 + 0.905777i \(0.639288\pi\)
\(140\) −0.395406 0.594802i −0.0334179 0.0502700i
\(141\) 0 0
\(142\) 7.64911 18.4051i 0.641899 1.54452i
\(143\) −11.6625 + 11.6625i −0.975271 + 0.975271i
\(144\) 0 0
\(145\) −1.23260 1.23260i −0.102362 0.102362i
\(146\) 1.28277 0.529567i 0.106163 0.0438273i
\(147\) 0 0
\(148\) 2.98250 + 15.1813i 0.245160 + 1.24789i
\(149\) 4.93832 7.39072i 0.404563 0.605472i −0.572117 0.820172i \(-0.693878\pi\)
0.976680 + 0.214701i \(0.0688776\pi\)
\(150\) 0 0
\(151\) −3.73549 1.54729i −0.303990 0.125917i 0.225474 0.974249i \(-0.427607\pi\)
−0.529464 + 0.848332i \(0.677607\pi\)
\(152\) 6.16607 4.08853i 0.500134 0.331623i
\(153\) 0 0
\(154\) −7.84069 + 5.22560i −0.631821 + 0.421091i
\(155\) 2.14109 0.425888i 0.171976 0.0342082i
\(156\) 0 0
\(157\) 9.49118 6.34180i 0.757478 0.506131i −0.115848 0.993267i \(-0.536958\pi\)
0.873326 + 0.487136i \(0.161958\pi\)
\(158\) −2.40317 0.00283687i −0.191186 0.000225689i
\(159\) 0 0
\(160\) 0.841021 1.24274i 0.0664886 0.0982468i
\(161\) 5.40314i 0.425827i
\(162\) 0 0
\(163\) 0.00315871 0.00211058i 0.000247409 0.000165314i −0.555447 0.831552i \(-0.687453\pi\)
0.555694 + 0.831387i \(0.312453\pi\)
\(164\) −8.71963 + 20.9113i −0.680889 + 1.63290i
\(165\) 0 0
\(166\) 12.0821 + 18.1284i 0.937750 + 1.40704i
\(167\) 4.28839 1.77631i 0.331846 0.137455i −0.210538 0.977586i \(-0.567522\pi\)
0.542384 + 0.840131i \(0.317522\pi\)
\(168\) 0 0
\(169\) 1.74931 + 0.724587i 0.134562 + 0.0557374i
\(170\) 0.573609 0.113394i 0.0439938 0.00869694i
\(171\) 0 0
\(172\) 6.92185 + 4.64871i 0.527786 + 0.354461i
\(173\) −7.26821 1.44574i −0.552592 0.109917i −0.0891066 0.996022i \(-0.528401\pi\)
−0.463485 + 0.886105i \(0.653401\pi\)
\(174\) 0 0
\(175\) −4.69280 4.69280i −0.354742 0.354742i
\(176\) −16.4077 11.0757i −1.23678 0.834862i
\(177\) 0 0
\(178\) −2.35398 0.978308i −0.176438 0.0733273i
\(179\) −2.46773 + 12.4061i −0.184447 + 0.927277i 0.772056 + 0.635554i \(0.219228\pi\)
−0.956503 + 0.291722i \(0.905772\pi\)
\(180\) 0 0
\(181\) −13.4674 8.99863i −1.00102 0.668863i −0.0568753 0.998381i \(-0.518114\pi\)
−0.944149 + 0.329518i \(0.893114\pi\)
\(182\) −5.27157 3.53136i −0.390755 0.261762i
\(183\) 0 0
\(184\) −10.5029 + 4.30693i −0.774283 + 0.317511i
\(185\) −0.785277 1.89583i −0.0577347 0.139384i
\(186\) 0 0
\(187\) −1.50487 7.56549i −0.110047 0.553244i
\(188\) 4.67734 4.65531i 0.341130 0.339523i
\(189\) 0 0
\(190\) −0.694683 + 0.693044i −0.0503976 + 0.0502787i
\(191\) −17.2169 −1.24577 −0.622885 0.782313i \(-0.714040\pi\)
−0.622885 + 0.782313i \(0.714040\pi\)
\(192\) 0 0
\(193\) −12.7608 −0.918541 −0.459270 0.888296i \(-0.651889\pi\)
−0.459270 + 0.888296i \(0.651889\pi\)
\(194\) 15.4389 15.4025i 1.10845 1.10583i
\(195\) 0 0
\(196\) 7.31897 + 7.35362i 0.522784 + 0.525258i
\(197\) 0.972213 + 4.88764i 0.0692673 + 0.348230i 0.999840 0.0178765i \(-0.00569056\pi\)
−0.930573 + 0.366107i \(0.880691\pi\)
\(198\) 0 0
\(199\) 8.85562 + 21.3794i 0.627758 + 1.51554i 0.842402 + 0.538850i \(0.181141\pi\)
−0.214643 + 0.976692i \(0.568859\pi\)
\(200\) 5.38138 12.8628i 0.380521 0.909536i
\(201\) 0 0
\(202\) 9.88065 + 6.61892i 0.695200 + 0.465706i
\(203\) −7.35589 4.91505i −0.516282 0.344969i
\(204\) 0 0
\(205\) 0.586244 2.94725i 0.0409450 0.205845i
\(206\) 13.3043 + 5.52924i 0.926956 + 0.385240i
\(207\) 0 0
\(208\) 2.66238 13.0620i 0.184603 0.905689i
\(209\) 9.15371 + 9.15371i 0.633175 + 0.633175i
\(210\) 0 0
\(211\) −3.65496 0.727017i −0.251618 0.0500499i 0.0676697 0.997708i \(-0.478444\pi\)
−0.319288 + 0.947658i \(0.603444\pi\)
\(212\) −4.47700 + 6.66618i −0.307482 + 0.457835i
\(213\) 0 0
\(214\) 2.64662 0.523199i 0.180919 0.0357651i
\(215\) −1.02171 0.423207i −0.0696802 0.0288625i
\(216\) 0 0
\(217\) 10.2359 4.23985i 0.694859 0.287820i
\(218\) −3.39852 5.09926i −0.230177 0.345365i
\(219\) 0 0
\(220\) 2.42337 + 1.01050i 0.163383 + 0.0681279i
\(221\) 4.31898 2.88585i 0.290526 0.194123i
\(222\) 0 0
\(223\) 23.7016i 1.58718i −0.608456 0.793588i \(-0.708211\pi\)
0.608456 0.793588i \(-0.291789\pi\)
\(224\) 2.95586 7.01862i 0.197497 0.468951i
\(225\) 0 0
\(226\) 2.26899 + 0.00267847i 0.150931 + 0.000178169i
\(227\) 8.78436 5.86952i 0.583039 0.389574i −0.228785 0.973477i \(-0.573475\pi\)
0.811823 + 0.583903i \(0.198475\pi\)
\(228\) 0 0
\(229\) −14.0985 + 2.80436i −0.931653 + 0.185317i −0.637508 0.770444i \(-0.720035\pi\)
−0.294145 + 0.955761i \(0.595035\pi\)
\(230\) 1.25285 0.834990i 0.0826105 0.0550576i
\(231\) 0 0
\(232\) 3.69062 18.2166i 0.242301 1.19598i
\(233\) −5.04386 2.08924i −0.330435 0.136870i 0.211297 0.977422i \(-0.432231\pi\)
−0.541732 + 0.840551i \(0.682231\pi\)
\(234\) 0 0
\(235\) −0.486274 + 0.727761i −0.0317210 + 0.0474739i
\(236\) 11.6931 2.29721i 0.761155 0.149536i
\(237\) 0 0
\(238\) 2.74296 1.13238i 0.177799 0.0734012i
\(239\) −13.6816 13.6816i −0.884992 0.884992i 0.109045 0.994037i \(-0.465221\pi\)
−0.994037 + 0.109045i \(0.965221\pi\)
\(240\) 0 0
\(241\) 2.22031 2.22031i 0.143023 0.143023i −0.631970 0.774993i \(-0.717753\pi\)
0.774993 + 0.631970i \(0.217753\pi\)
\(242\) 7.32302 17.6205i 0.470742 1.13269i
\(243\) 0 0
\(244\) 20.6703 13.7410i 1.32328 0.879677i
\(245\) −1.14417 0.764510i −0.0730983 0.0488427i
\(246\) 0 0
\(247\) −3.33598 + 8.05376i −0.212263 + 0.512448i
\(248\) 16.4008 + 16.5174i 1.04145 + 1.04886i
\(249\) 0 0
\(250\) −0.731029 + 3.65259i −0.0462343 + 0.231010i
\(251\) −0.729724 3.66857i −0.0460598 0.231558i 0.950898 0.309505i \(-0.100163\pi\)
−0.996957 + 0.0779471i \(0.975163\pi\)
\(252\) 0 0
\(253\) −11.0350 16.5150i −0.693764 1.03829i
\(254\) 18.1679 + 18.2109i 1.13996 + 1.14265i
\(255\) 0 0
\(256\) 15.9993 + 0.151098i 0.999955 + 0.00944363i
\(257\) −17.3864 −1.08453 −0.542267 0.840206i \(-0.682434\pi\)
−0.542267 + 0.840206i \(0.682434\pi\)
\(258\) 0 0
\(259\) −5.78593 8.65925i −0.359520 0.538060i
\(260\) −0.00417432 + 1.76807i −0.000258880 + 0.109651i
\(261\) 0 0
\(262\) 2.50428 12.5126i 0.154715 0.773033i
\(263\) −0.656941 1.58600i −0.0405087 0.0977967i 0.902330 0.431045i \(-0.141855\pi\)
−0.942839 + 0.333249i \(0.891855\pi\)
\(264\) 0 0
\(265\) 0.407576 0.983975i 0.0250372 0.0604451i
\(266\) −2.77170 + 4.13755i −0.169944 + 0.253690i
\(267\) 0 0
\(268\) −5.83976 + 3.88209i −0.356720 + 0.237136i
\(269\) 1.25541 6.31135i 0.0765434 0.384810i −0.923456 0.383704i \(-0.874648\pi\)
0.999999 0.00110539i \(-0.000351857\pi\)
\(270\) 0 0
\(271\) −17.1048 + 17.1048i −1.03904 + 1.03904i −0.0398353 + 0.999206i \(0.512683\pi\)
−0.999206 + 0.0398353i \(0.987317\pi\)
\(272\) 4.38762 + 4.42925i 0.266039 + 0.268563i
\(273\) 0 0
\(274\) −10.2335 + 4.22470i −0.618227 + 0.255223i
\(275\) 23.9280 + 4.75958i 1.44292 + 0.287014i
\(276\) 0 0
\(277\) −4.08114 + 6.10786i −0.245212 + 0.366985i −0.933576 0.358380i \(-0.883329\pi\)
0.688364 + 0.725365i \(0.258329\pi\)
\(278\) −0.975757 4.93591i −0.0585220 0.296036i
\(279\) 0 0
\(280\) −0.200565 + 0.989973i −0.0119861 + 0.0591622i
\(281\) 16.8252 6.96925i 1.00371 0.415750i 0.180554 0.983565i \(-0.442211\pi\)
0.823156 + 0.567815i \(0.192211\pi\)
\(282\) 0 0
\(283\) 22.3174 4.43920i 1.32663 0.263883i 0.519608 0.854405i \(-0.326078\pi\)
0.807022 + 0.590522i \(0.201078\pi\)
\(284\) −26.0669 + 10.7252i −1.54679 + 0.636425i
\(285\) 0 0
\(286\) 23.3251 + 0.0275346i 1.37924 + 0.00162815i
\(287\) 15.2508i 0.900228i
\(288\) 0 0
\(289\) 14.5707i 0.857097i
\(290\) −0.00291010 + 2.46520i −0.000170887 + 0.144762i
\(291\) 0 0
\(292\) −1.81145 0.755341i −0.106007 0.0442030i
\(293\) 23.6486 4.70399i 1.38156 0.274810i 0.552290 0.833652i \(-0.313754\pi\)
0.829274 + 0.558842i \(0.188754\pi\)
\(294\) 0 0
\(295\) −1.46022 + 0.604844i −0.0850174 + 0.0352154i
\(296\) 12.2202 18.1494i 0.710286 1.05491i
\(297\) 0 0
\(298\) −12.3319 + 2.43784i −0.714370 + 0.141220i
\(299\) 7.43093 11.1212i 0.429742 0.643154i
\(300\) 0 0
\(301\) −5.50476 1.09497i −0.317289 0.0631127i
\(302\) 2.18196 + 5.28536i 0.125558 + 0.304139i
\(303\) 0 0
\(304\) −10.2521 2.08965i −0.588000 0.119850i
\(305\) −2.32784 + 2.32784i −0.133292 + 0.133292i
\(306\) 0 0
\(307\) 1.72081 8.65108i 0.0982116 0.493743i −0.900101 0.435681i \(-0.856508\pi\)
0.998313 0.0580626i \(-0.0184923\pi\)
\(308\) 13.0632 + 2.63051i 0.744345 + 0.149887i
\(309\) 0 0
\(310\) −2.56495 1.71823i −0.145679 0.0975887i
\(311\) −1.49356 + 3.60578i −0.0846923 + 0.204465i −0.960552 0.278101i \(-0.910295\pi\)
0.875860 + 0.482566i \(0.160295\pi\)
\(312\) 0 0
\(313\) 8.26474 + 19.9529i 0.467151 + 1.12780i 0.965401 + 0.260769i \(0.0839760\pi\)
−0.498250 + 0.867033i \(0.666024\pi\)
\(314\) −15.8292 3.16806i −0.893296 0.178784i
\(315\) 0 0
\(316\) 2.39749 + 2.40884i 0.134869 + 0.135508i
\(317\) −16.4821 24.6672i −0.925727 1.38545i −0.922728 0.385452i \(-0.874045\pi\)
−0.00299906 0.999996i \(-0.500955\pi\)
\(318\) 0 0
\(319\) 32.5219 1.82087
\(320\) −2.08423 + 0.399254i −0.116512 + 0.0223190i
\(321\) 0 0
\(322\) 5.40952 5.39676i 0.301461 0.300750i
\(323\) −2.26505 3.38988i −0.126030 0.188618i
\(324\) 0 0
\(325\) 3.20509 + 16.1131i 0.177786 + 0.893793i
\(326\) −0.00526805 0.00105435i −0.000291770 5.83949e-5i
\(327\) 0 0
\(328\) 29.6453 12.1567i 1.63689 0.671239i
\(329\) −1.69994 + 4.10401i −0.0937206 + 0.226261i
\(330\) 0 0
\(331\) −0.162367 0.108490i −0.00892448 0.00596315i 0.551100 0.834439i \(-0.314208\pi\)
−0.560024 + 0.828476i \(0.689208\pi\)
\(332\) 6.08197 30.2033i 0.333792 1.65762i
\(333\) 0 0
\(334\) −6.06174 2.51924i −0.331683 0.137847i
\(335\) 0.657660 0.657660i 0.0359318 0.0359318i
\(336\) 0 0
\(337\) 6.58517 + 6.58517i 0.358717 + 0.358717i 0.863340 0.504623i \(-0.168368\pi\)
−0.504623 + 0.863340i \(0.668368\pi\)
\(338\) −1.02180 2.47510i −0.0555786 0.134628i
\(339\) 0 0
\(340\) −0.686460 0.461026i −0.0372285 0.0250026i
\(341\) −22.6275 + 33.8645i −1.22535 + 1.83386i
\(342\) 0 0
\(343\) −15.1588 6.27897i −0.818497 0.339032i
\(344\) −2.25948 11.5732i −0.121823 0.623987i
\(345\) 0 0
\(346\) 5.81218 + 8.72081i 0.312465 + 0.468834i
\(347\) 24.8134 4.93570i 1.33206 0.264962i 0.522818 0.852444i \(-0.324881\pi\)
0.809237 + 0.587482i \(0.199881\pi\)
\(348\) 0 0
\(349\) −10.7430 + 7.17827i −0.575062 + 0.384244i −0.808825 0.588050i \(-0.799896\pi\)
0.233763 + 0.972294i \(0.424896\pi\)
\(350\) −0.0110794 + 9.38559i −0.000592220 + 0.501681i
\(351\) 0 0
\(352\) 5.29956 + 27.4897i 0.282467 + 1.46520i
\(353\) 15.3080i 0.814764i 0.913258 + 0.407382i \(0.133558\pi\)
−0.913258 + 0.407382i \(0.866442\pi\)
\(354\) 0 0
\(355\) 3.10848 2.07702i 0.164981 0.110237i
\(356\) 1.37174 + 3.33391i 0.0727020 + 0.176697i
\(357\) 0 0
\(358\) 14.8856 9.92082i 0.786727 0.524332i
\(359\) −7.28425 + 3.01723i −0.384448 + 0.159243i −0.566533 0.824039i \(-0.691715\pi\)
0.182085 + 0.983283i \(0.441715\pi\)
\(360\) 0 0
\(361\) −11.2325 4.65264i −0.591183 0.244876i
\(362\) 4.44225 + 22.4713i 0.233479 + 1.18107i
\(363\) 0 0
\(364\) 1.72982 + 8.80498i 0.0906672 + 0.461506i
\(365\) 0.255306 + 0.0507835i 0.0133633 + 0.00265813i
\(366\) 0 0
\(367\) −9.38201 9.38201i −0.489737 0.489737i 0.418486 0.908223i \(-0.362561\pi\)
−0.908223 + 0.418486i \(0.862561\pi\)
\(368\) 14.8025 + 6.21344i 0.771633 + 0.323898i
\(369\) 0 0
\(370\) −1.11371 + 2.67979i −0.0578992 + 0.139316i
\(371\) 1.05452 5.30144i 0.0547480 0.275237i
\(372\) 0 0
\(373\) 1.73641 + 1.16023i 0.0899078 + 0.0600745i 0.599712 0.800216i \(-0.295282\pi\)
−0.509804 + 0.860291i \(0.670282\pi\)
\(374\) −6.07132 + 9.06320i −0.313941 + 0.468647i
\(375\) 0 0
\(376\) −9.33262 0.0330508i −0.481293 0.00170446i
\(377\) 8.38081 + 20.2331i 0.431634 + 1.04206i
\(378\) 0 0
\(379\) −6.02722 30.3009i −0.309597 1.55645i −0.751711 0.659492i \(-0.770771\pi\)
0.442114 0.896959i \(-0.354229\pi\)
\(380\) 1.38772 + 0.00327634i 0.0711887 + 0.000168073i
\(381\) 0 0
\(382\) 17.1966 + 17.2372i 0.879852 + 0.881932i
\(383\) 28.6473 1.46381 0.731904 0.681408i \(-0.238632\pi\)
0.731904 + 0.681408i \(0.238632\pi\)
\(384\) 0 0
\(385\) −1.76739 −0.0900744
\(386\) 12.7457 + 12.7758i 0.648739 + 0.650273i
\(387\) 0 0
\(388\) −30.8413 0.0728147i −1.56573 0.00369661i
\(389\) 1.69036 + 8.49804i 0.0857049 + 0.430868i 0.999685 + 0.0251080i \(0.00799298\pi\)
−0.913980 + 0.405760i \(0.867007\pi\)
\(390\) 0 0
\(391\) 2.39386 + 5.77929i 0.121063 + 0.292271i
\(392\) 0.0519617 14.6725i 0.00262446 0.741075i
\(393\) 0 0
\(394\) 3.92234 5.85523i 0.197605 0.294982i
\(395\) −0.374798 0.250432i −0.0188581 0.0126006i
\(396\) 0 0
\(397\) 3.77514 18.9789i 0.189469 0.952525i −0.762653 0.646808i \(-0.776104\pi\)
0.952122 0.305718i \(-0.0988963\pi\)
\(398\) 12.5594 30.2202i 0.629547 1.51480i
\(399\) 0 0
\(400\) −18.2530 + 7.45985i −0.912649 + 0.372993i
\(401\) −22.1086 22.1086i −1.10405 1.10405i −0.993917 0.110133i \(-0.964872\pi\)
−0.110133 0.993917i \(-0.535128\pi\)
\(402\) 0 0
\(403\) −26.8994 5.35063i −1.33996 0.266534i
\(404\) −3.24225 16.5034i −0.161308 0.821076i
\(405\) 0 0
\(406\) 2.42635 + 12.2738i 0.120418 + 0.609139i
\(407\) 35.3701 + 14.6508i 1.75323 + 0.726212i
\(408\) 0 0
\(409\) −0.412610 + 0.170909i −0.0204023 + 0.00845089i −0.392861 0.919598i \(-0.628515\pi\)
0.372459 + 0.928049i \(0.378515\pi\)
\(410\) −3.53627 + 2.35683i −0.174644 + 0.116395i
\(411\) 0 0
\(412\) −7.75285 18.8427i −0.381955 0.928315i
\(413\) −6.66962 + 4.45650i −0.328191 + 0.219290i
\(414\) 0 0
\(415\) 4.08636i 0.200591i
\(416\) −15.7367 + 10.3811i −0.771554 + 0.508975i
\(417\) 0 0
\(418\) 0.0216114 18.3074i 0.00105705 0.895444i
\(419\) −24.9030 + 16.6397i −1.21659 + 0.812901i −0.987052 0.160398i \(-0.948722\pi\)
−0.229541 + 0.973299i \(0.573722\pi\)
\(420\) 0 0
\(421\) 27.6476 5.49946i 1.34746 0.268027i 0.531955 0.846772i \(-0.321457\pi\)
0.815508 + 0.578745i \(0.196457\pi\)
\(422\) 2.92277 + 4.38543i 0.142278 + 0.213479i
\(423\) 0 0
\(424\) 11.1458 2.17602i 0.541286 0.105677i
\(425\) −7.09863 2.94035i −0.344334 0.142628i
\(426\) 0 0
\(427\) −9.28237 + 13.8920i −0.449205 + 0.672283i
\(428\) −3.16731 2.12716i −0.153098 0.102820i
\(429\) 0 0
\(430\) 0.596799 + 1.44563i 0.0287802 + 0.0697143i
\(431\) −5.47861 5.47861i −0.263896 0.263896i 0.562739 0.826635i \(-0.309748\pi\)
−0.826635 + 0.562739i \(0.809748\pi\)
\(432\) 0 0
\(433\) −13.9653 + 13.9653i −0.671130 + 0.671130i −0.957977 0.286847i \(-0.907393\pi\)
0.286847 + 0.957977i \(0.407393\pi\)
\(434\) −14.4687 6.01314i −0.694519 0.288640i
\(435\) 0 0
\(436\) −1.71077 + 8.49576i −0.0819312 + 0.406873i
\(437\) −8.72880 5.83240i −0.417555 0.279001i
\(438\) 0 0
\(439\) 7.32429 17.6824i 0.349569 0.843935i −0.647102 0.762404i \(-0.724019\pi\)
0.996671 0.0815308i \(-0.0259809\pi\)
\(440\) −1.40881 3.43553i −0.0671624 0.163783i
\(441\) 0 0
\(442\) −7.20313 1.44163i −0.342618 0.0685715i
\(443\) −1.03061 5.18121i −0.0489656 0.246167i 0.948549 0.316631i \(-0.102552\pi\)
−0.997514 + 0.0704647i \(0.977552\pi\)
\(444\) 0 0
\(445\) −0.265647 0.397569i −0.0125929 0.0188466i
\(446\) −23.7295 + 23.6736i −1.12363 + 1.12098i
\(447\) 0 0
\(448\) −9.97927 + 4.05098i −0.471476 + 0.191391i
\(449\) −25.4195 −1.19962 −0.599809 0.800143i \(-0.704757\pi\)
−0.599809 + 0.800143i \(0.704757\pi\)
\(450\) 0 0
\(451\) 31.1472 + 46.6151i 1.46666 + 2.19502i
\(452\) −2.26362 2.27434i −0.106472 0.106976i
\(453\) 0 0
\(454\) −14.6504 2.93214i −0.687579 0.137612i
\(455\) −0.455452 1.09956i −0.0213519 0.0515481i
\(456\) 0 0
\(457\) 0.410387 0.990763i 0.0191971 0.0463459i −0.913990 0.405736i \(-0.867015\pi\)
0.933187 + 0.359390i \(0.117015\pi\)
\(458\) 16.8895 + 11.3140i 0.789193 + 0.528671i
\(459\) 0 0
\(460\) −2.08735 0.420324i −0.0973230 0.0195977i
\(461\) 0.499040 2.50885i 0.0232426 0.116849i −0.967422 0.253168i \(-0.918527\pi\)
0.990665 + 0.136320i \(0.0435274\pi\)
\(462\) 0 0
\(463\) −23.9046 + 23.9046i −1.11094 + 1.11094i −0.117915 + 0.993024i \(0.537621\pi\)
−0.993024 + 0.117915i \(0.962379\pi\)
\(464\) −21.9243 + 14.5001i −1.01781 + 0.673150i
\(465\) 0 0
\(466\) 2.94620 + 7.13658i 0.136480 + 0.330596i
\(467\) −32.9221 6.54862i −1.52345 0.303034i −0.638833 0.769345i \(-0.720583\pi\)
−0.884621 + 0.466311i \(0.845583\pi\)
\(468\) 0 0
\(469\) 2.62244 3.92476i 0.121093 0.181229i
\(470\) 1.21432 0.240053i 0.0560124 0.0110728i
\(471\) 0 0
\(472\) −13.9792 9.41238i −0.643445 0.433240i
\(473\) 19.0619 7.89570i 0.876468 0.363045i
\(474\) 0 0
\(475\) 12.6468 2.51561i 0.580277 0.115424i
\(476\) −3.87343 1.61515i −0.177538 0.0740304i
\(477\) 0 0
\(478\) −0.0323016 + 27.3633i −0.00147744 + 1.25157i
\(479\) 17.7201i 0.809654i 0.914393 + 0.404827i \(0.132668\pi\)
−0.914393 + 0.404827i \(0.867332\pi\)
\(480\) 0 0
\(481\) 25.7805i 1.17549i
\(482\) −4.44062 0.00524203i −0.202265 0.000238768i
\(483\) 0 0
\(484\) −24.9556 + 10.2680i −1.13435 + 0.466727i
\(485\) 4.01198 0.798033i 0.182175 0.0362368i
\(486\) 0 0
\(487\) 22.3630 9.26304i 1.01336 0.419749i 0.186682 0.982420i \(-0.440227\pi\)
0.826680 + 0.562672i \(0.190227\pi\)
\(488\) −34.4031 6.96995i −1.55736 0.315515i
\(489\) 0 0
\(490\) 0.377406 + 1.90913i 0.0170495 + 0.0862455i
\(491\) 16.5333 24.7438i 0.746136 1.11667i −0.243051 0.970013i \(-0.578148\pi\)
0.989187 0.146658i \(-0.0468517\pi\)
\(492\) 0 0
\(493\) −10.0456 1.99819i −0.452430 0.0899940i
\(494\) 11.3953 4.70433i 0.512699 0.211658i
\(495\) 0 0
\(496\) 0.155436 32.9181i 0.00697930 1.47806i
\(497\) 13.4165 13.4165i 0.601810 0.601810i
\(498\) 0 0
\(499\) −5.85555 + 29.4378i −0.262130 + 1.31782i 0.595419 + 0.803416i \(0.296986\pi\)
−0.857549 + 0.514402i \(0.828014\pi\)
\(500\) 4.38706 2.91638i 0.196195 0.130425i
\(501\) 0 0
\(502\) −2.94404 + 4.39482i −0.131399 + 0.196151i
\(503\) −2.73931 + 6.61328i −0.122140 + 0.294871i −0.973109 0.230343i \(-0.926015\pi\)
0.850970 + 0.525215i \(0.176015\pi\)
\(504\) 0 0
\(505\) 0.853666 + 2.06093i 0.0379876 + 0.0917102i
\(506\) −5.51256 + 27.5435i −0.245063 + 1.22446i
\(507\) 0 0
\(508\) 0.0858883 36.3788i 0.00381068 1.61405i
\(509\) −3.41939 5.11748i −0.151562 0.226829i 0.747917 0.663792i \(-0.231054\pi\)
−0.899479 + 0.436963i \(0.856054\pi\)
\(510\) 0 0
\(511\) 1.32111 0.0584423
\(512\) −15.8291 16.1691i −0.699555 0.714579i
\(513\) 0 0
\(514\) 17.3659 + 17.4069i 0.765976 + 0.767787i
\(515\) 1.50140 + 2.24700i 0.0661594 + 0.0990145i
\(516\) 0 0
\(517\) −3.18578 16.0160i −0.140110 0.704382i
\(518\) −2.89038 + 14.4418i −0.126996 + 0.634535i
\(519\) 0 0
\(520\) 1.77433 1.76180i 0.0778093 0.0772602i
\(521\) −5.10532 + 12.3253i −0.223668 + 0.539983i −0.995383 0.0959866i \(-0.969399\pi\)
0.771715 + 0.635969i \(0.219399\pi\)
\(522\) 0 0
\(523\) 22.7053 + 15.1712i 0.992835 + 0.663391i 0.942104 0.335321i \(-0.108845\pi\)
0.0507311 + 0.998712i \(0.483845\pi\)
\(524\) −15.0287 + 9.99062i −0.656532 + 0.436442i
\(525\) 0 0
\(526\) −0.931702 + 2.24184i −0.0406241 + 0.0977488i
\(527\) 9.07003 9.07003i 0.395097 0.395097i
\(528\) 0 0
\(529\) −4.87371 4.87371i −0.211900 0.211900i
\(530\) −1.39223 + 0.574756i −0.0604746 + 0.0249658i
\(531\) 0 0
\(532\) 6.91086 1.35770i 0.299624 0.0588638i
\(533\) −20.9744 + 31.3905i −0.908504 + 1.35967i
\(534\) 0 0
\(535\) 0.467517 + 0.193652i 0.0202125 + 0.00837231i
\(536\) 9.71953 + 1.96914i 0.419820 + 0.0850540i
\(537\) 0 0
\(538\) −7.57272 + 5.04701i −0.326483 + 0.217592i
\(539\) 25.1800 5.00861i 1.08458 0.215736i
\(540\) 0 0
\(541\) −1.36491 + 0.912006i −0.0586822 + 0.0392102i −0.584565 0.811347i \(-0.698735\pi\)
0.525883 + 0.850557i \(0.323735\pi\)
\(542\) 34.2095 + 0.0403834i 1.46943 + 0.00173462i
\(543\) 0 0
\(544\) 0.0520406 8.81682i 0.00223122 0.378018i
\(545\) 1.14944i 0.0492364i
\(546\) 0 0
\(547\) 35.6558 23.8244i 1.52453 1.01866i 0.540361 0.841434i \(-0.318288\pi\)
0.984170 0.177225i \(-0.0567122\pi\)
\(548\) 14.4511 + 6.02584i 0.617319 + 0.257411i
\(549\) 0 0
\(550\) −19.1346 28.7102i −0.815901 1.22421i
\(551\) 15.8805 6.57794i 0.676534 0.280230i
\(552\) 0 0
\(553\) −2.11357 0.875469i −0.0898782 0.0372287i
\(554\) 10.1914 2.01469i 0.432990 0.0855959i
\(555\) 0 0
\(556\) −3.96713 + 5.90699i −0.168244 + 0.250512i
\(557\) 2.38952 + 0.475305i 0.101247 + 0.0201393i 0.245454 0.969408i \(-0.421063\pi\)
−0.144207 + 0.989548i \(0.546063\pi\)
\(558\) 0 0
\(559\) 9.82443 + 9.82443i 0.415529 + 0.415529i
\(560\) 1.19147 0.788002i 0.0503487 0.0332991i
\(561\) 0 0
\(562\) −23.7828 9.88408i −1.00322 0.416935i
\(563\) −2.89115 + 14.5348i −0.121847 + 0.612567i 0.870811 + 0.491617i \(0.163594\pi\)
−0.992659 + 0.120950i \(0.961406\pi\)
\(564\) 0 0
\(565\) 0.353871 + 0.236449i 0.0148874 + 0.00994748i
\(566\) −26.7354 17.9097i −1.12377 0.752802i
\(567\) 0 0
\(568\) 36.7740 + 15.3851i 1.54300 + 0.645544i
\(569\) 13.6164 + 32.8729i 0.570829 + 1.37810i 0.900851 + 0.434129i \(0.142944\pi\)
−0.330022 + 0.943973i \(0.607056\pi\)
\(570\) 0 0
\(571\) −4.08279 20.5256i −0.170859 0.858968i −0.967180 0.254093i \(-0.918223\pi\)
0.796321 0.604875i \(-0.206777\pi\)
\(572\) −23.2700 23.3801i −0.972966 0.977571i
\(573\) 0 0
\(574\) −15.2688 + 15.2328i −0.637308 + 0.635805i
\(575\) −19.7847 −0.825079
\(576\) 0 0
\(577\) −13.2749 −0.552640 −0.276320 0.961066i \(-0.589115\pi\)
−0.276320 + 0.961066i \(0.589115\pi\)
\(578\) −14.5878 + 14.5534i −0.606774 + 0.605344i
\(579\) 0 0
\(580\) 2.47102 2.45938i 0.102603 0.102120i
\(581\) 4.04598 + 20.3405i 0.167855 + 0.843866i
\(582\) 0 0
\(583\) 7.60407 + 18.3578i 0.314928 + 0.760304i
\(584\) 1.05307 + 2.56803i 0.0435765 + 0.106266i
\(585\) 0 0
\(586\) −28.3302 18.9780i −1.17031 0.783975i
\(587\) 5.72679 + 3.82652i 0.236370 + 0.157937i 0.668114 0.744059i \(-0.267102\pi\)
−0.431744 + 0.901996i \(0.642102\pi\)
\(588\) 0 0
\(589\) −4.19960 + 21.1128i −0.173042 + 0.869939i
\(590\) 2.06406 + 0.857816i 0.0849758 + 0.0353157i
\(591\) 0 0
\(592\) −30.3766 + 5.89331i −1.24847 + 0.242213i
\(593\) −5.93109 5.93109i −0.243561 0.243561i 0.574761 0.818321i \(-0.305095\pi\)
−0.818321 + 0.574761i \(0.805095\pi\)
\(594\) 0 0
\(595\) 0.545923 + 0.108591i 0.0223807 + 0.00445179i
\(596\) 14.7581 + 9.91152i 0.604515 + 0.405991i
\(597\) 0 0
\(598\) −18.5565 + 3.66834i −0.758830 + 0.150010i
\(599\) −8.60956 3.56620i −0.351777 0.145711i 0.199796 0.979838i \(-0.435972\pi\)
−0.551573 + 0.834127i \(0.685972\pi\)
\(600\) 0 0
\(601\) −9.04530 + 3.74668i −0.368965 + 0.152830i −0.559459 0.828858i \(-0.688991\pi\)
0.190494 + 0.981688i \(0.438991\pi\)
\(602\) 4.40200 + 6.60493i 0.179412 + 0.269197i
\(603\) 0 0
\(604\) 3.11221 7.46366i 0.126634 0.303692i
\(605\) 2.97596 1.98847i 0.120990 0.0808430i
\(606\) 0 0
\(607\) 34.8085i 1.41283i −0.707796 0.706417i \(-0.750311\pi\)
0.707796 0.706417i \(-0.249689\pi\)
\(608\) 8.14791 + 12.3514i 0.330441 + 0.500916i
\(609\) 0 0
\(610\) 4.65568 + 0.00549590i 0.188503 + 0.000222523i
\(611\) 9.14318 6.10928i 0.369894 0.247155i
\(612\) 0 0
\(613\) 14.7093 2.92585i 0.594101 0.118174i 0.111123 0.993807i \(-0.464555\pi\)
0.482978 + 0.875632i \(0.339555\pi\)
\(614\) −10.3801 + 6.91802i −0.418905 + 0.279189i
\(615\) 0 0
\(616\) −10.4142 15.7060i −0.419598 0.632813i
\(617\) −7.99200 3.31040i −0.321746 0.133272i 0.215964 0.976401i \(-0.430711\pi\)
−0.537710 + 0.843130i \(0.680711\pi\)
\(618\) 0 0
\(619\) −4.66067 + 6.97519i −0.187328 + 0.280356i −0.913232 0.407440i \(-0.866422\pi\)
0.725904 + 0.687796i \(0.241422\pi\)
\(620\) 0.841665 + 4.28417i 0.0338021 + 0.172056i
\(621\) 0 0
\(622\) 5.10184 2.10620i 0.204565 0.0844509i
\(623\) −1.71594 1.71594i −0.0687477 0.0687477i
\(624\) 0 0
\(625\) 16.9348 16.9348i 0.677393 0.677393i
\(626\) 11.7214 28.2038i 0.468482 1.12725i
\(627\) 0 0
\(628\) 12.6387 + 19.0122i 0.504341 + 0.758671i
\(629\) −10.0252 6.69862i −0.399731 0.267092i
\(630\) 0 0
\(631\) 12.6693 30.5864i 0.504358 1.21763i −0.442731 0.896654i \(-0.645990\pi\)
0.947089 0.320972i \(-0.104010\pi\)
\(632\) 0.0170212 4.80631i 0.000677067 0.191185i
\(633\) 0 0
\(634\) −8.23367 + 41.1396i −0.327001 + 1.63386i
\(635\) 0.941317 + 4.73232i 0.0373550 + 0.187796i
\(636\) 0 0
\(637\) 9.60488 + 14.3747i 0.380559 + 0.569547i
\(638\) −32.4834 32.5602i −1.28603 1.28907i
\(639\) 0 0
\(640\) 2.48149 + 1.68791i 0.0980896 + 0.0667203i
\(641\) −10.2292 −0.404030 −0.202015 0.979382i \(-0.564749\pi\)
−0.202015 + 0.979382i \(0.564749\pi\)
\(642\) 0 0
\(643\) −4.22568 6.32418i −0.166645 0.249401i 0.738743 0.673987i \(-0.235420\pi\)
−0.905388 + 0.424586i \(0.860420\pi\)
\(644\) −10.8063 0.0255130i −0.425826 0.00100535i
\(645\) 0 0
\(646\) −1.13151 + 5.65359i −0.0445186 + 0.222438i
\(647\) 7.05188 + 17.0247i 0.277238 + 0.669311i 0.999757 0.0220394i \(-0.00701594\pi\)
−0.722519 + 0.691351i \(0.757016\pi\)
\(648\) 0 0
\(649\) 11.2845 27.2431i 0.442954 1.06939i
\(650\) 12.9308 19.3029i 0.507187 0.757123i
\(651\) 0 0
\(652\) 0.00420624 + 0.00632737i 0.000164729 + 0.000247799i
\(653\) −5.75170 + 28.9158i −0.225081 + 1.13156i 0.688604 + 0.725138i \(0.258224\pi\)
−0.913685 + 0.406423i \(0.866776\pi\)
\(654\) 0 0
\(655\) 1.69250 1.69250i 0.0661314 0.0661314i
\(656\) −41.7813 17.5380i −1.63128 0.684742i
\(657\) 0 0
\(658\) 5.80678 2.39722i 0.226372 0.0934534i
\(659\) 4.76397 + 0.947613i 0.185578 + 0.0369138i 0.287004 0.957929i \(-0.407341\pi\)
−0.101426 + 0.994843i \(0.532341\pi\)
\(660\) 0 0
\(661\) −14.3165 + 21.4261i −0.556846 + 0.833378i −0.997945 0.0640799i \(-0.979589\pi\)
0.441099 + 0.897458i \(0.354589\pi\)
\(662\) 0.0535570 + 0.270920i 0.00208155 + 0.0105296i
\(663\) 0 0
\(664\) −36.3137 + 24.0785i −1.40925 + 0.934426i
\(665\) −0.863022 + 0.357475i −0.0334665 + 0.0138623i
\(666\) 0 0
\(667\) −25.8670 + 5.14526i −1.00157 + 0.199225i
\(668\) 3.53236 + 8.58515i 0.136671 + 0.332169i
\(669\) 0 0
\(670\) −1.31532 0.00155270i −0.0508152 5.99859e-5i
\(671\) 61.4195i 2.37107i
\(672\) 0 0
\(673\) 7.18022i 0.276777i 0.990378 + 0.138389i \(0.0441923\pi\)
−0.990378 + 0.138389i \(0.955808\pi\)
\(674\) 0.0155472 13.1703i 0.000598856 0.507302i
\(675\) 0 0
\(676\) −1.45743 + 3.49518i −0.0560550 + 0.134430i
\(677\) −0.516673 + 0.102773i −0.0198574 + 0.00394987i −0.205009 0.978760i \(-0.565722\pi\)
0.185152 + 0.982710i \(0.440722\pi\)
\(678\) 0 0
\(679\) 19.1801 7.94467i 0.736066 0.304888i
\(680\) 0.224079 + 1.14775i 0.00859305 + 0.0440142i
\(681\) 0 0
\(682\) 56.5052 11.1703i 2.16370 0.427731i
\(683\) −10.6617 + 15.9564i −0.407960 + 0.610555i −0.977380 0.211492i \(-0.932168\pi\)
0.569420 + 0.822047i \(0.307168\pi\)
\(684\) 0 0
\(685\) −2.03674 0.405133i −0.0778199 0.0154793i
\(686\) 8.85449 + 21.4482i 0.338066 + 0.818896i
\(687\) 0 0
\(688\) −9.33007 + 13.8217i −0.355706 + 0.526948i
\(689\) −9.46156 + 9.46156i −0.360457 + 0.360457i
\(690\) 0 0
\(691\) 8.09941 40.7185i 0.308116 1.54901i −0.447677 0.894195i \(-0.647749\pi\)
0.755794 0.654810i \(-0.227251\pi\)
\(692\) 2.92578 14.5295i 0.111222 0.552331i
\(693\) 0 0
\(694\) −29.7257 19.9128i −1.12837 0.755881i
\(695\) 0.361158 0.871912i 0.0136995 0.0330735i
\(696\) 0 0
\(697\) −6.75687 16.3125i −0.255935 0.617881i
\(698\) 17.9171 + 3.58592i 0.678172 + 0.135729i
\(699\) 0 0
\(700\) 9.40773 9.36341i 0.355579 0.353904i
\(701\) −2.87333 4.30025i −0.108524 0.162418i 0.773232 0.634123i \(-0.218639\pi\)
−0.881756 + 0.471705i \(0.843639\pi\)
\(702\) 0 0
\(703\) 20.2346 0.763164
\(704\) 22.2288 32.7630i 0.837780 1.23480i
\(705\) 0 0
\(706\) 15.3261 15.2899i 0.576805 0.575445i
\(707\) 6.28982 + 9.41338i 0.236553 + 0.354027i
\(708\) 0 0
\(709\) 8.49385 + 42.7015i 0.318993 + 1.60369i 0.724286 + 0.689500i \(0.242170\pi\)
−0.405292 + 0.914187i \(0.632830\pi\)
\(710\) −5.18428 1.03758i −0.194563 0.0389397i
\(711\) 0 0
\(712\) 1.96773 4.70333i 0.0737436 0.176265i
\(713\) 12.6396 30.5147i 0.473357 1.14278i
\(714\) 0 0
\(715\) 3.63778 + 2.43068i 0.136045 + 0.0909024i
\(716\) −24.8005 4.99403i −0.926838 0.186635i
\(717\) 0 0
\(718\) 10.2964 + 4.27917i 0.384260 + 0.159697i
\(719\) −4.80412 + 4.80412i −0.179163 + 0.179163i −0.790991 0.611828i \(-0.790435\pi\)
0.611828 + 0.790991i \(0.290435\pi\)
\(720\) 0 0
\(721\) 9.69822 + 9.69822i 0.361181 + 0.361181i
\(722\) 6.56107 + 15.8929i 0.244178 + 0.591472i
\(723\) 0 0
\(724\) 18.0608 26.8923i 0.671225 0.999443i
\(725\) 17.9974 26.9350i 0.668408 1.00034i
\(726\) 0 0
\(727\) 3.79111 + 1.57033i 0.140604 + 0.0582402i 0.451876 0.892081i \(-0.350755\pi\)
−0.311272 + 0.950321i \(0.600755\pi\)
\(728\) 7.08759 10.5264i 0.262684 0.390136i
\(729\) 0 0
\(730\) −0.204161 0.306331i −0.00755634 0.0113378i
\(731\) −6.37310 + 1.26769i −0.235718 + 0.0468872i
\(732\) 0 0
\(733\) 37.2568 24.8942i 1.37611 0.919488i 0.376136 0.926564i \(-0.377253\pi\)
0.999975 + 0.00707651i \(0.00225254\pi\)
\(734\) −0.0221504 + 18.7640i −0.000817585 + 0.692592i
\(735\) 0 0
\(736\) −8.56424 21.0261i −0.315682 0.775031i
\(737\) 17.3522i 0.639175i
\(738\) 0 0
\(739\) −29.8791 + 19.9646i −1.09912 + 0.734409i −0.966477 0.256754i \(-0.917347\pi\)
−0.132645 + 0.991164i \(0.542347\pi\)
\(740\) 3.79535 1.56160i 0.139520 0.0574055i
\(741\) 0 0
\(742\) −6.36097 + 4.23941i −0.233518 + 0.155634i
\(743\) 18.9414 7.84578i 0.694892 0.287834i −0.00714476 0.999974i \(-0.502274\pi\)
0.702037 + 0.712141i \(0.252274\pi\)
\(744\) 0 0
\(745\) −2.17840 0.902321i −0.0798102 0.0330585i
\(746\) −0.572757 2.89732i −0.0209701 0.106078i
\(747\) 0 0
\(748\) 15.1380 2.97401i 0.553502 0.108740i
\(749\) 2.51888 + 0.501036i 0.0920379 + 0.0183075i
\(750\) 0 0
\(751\) −5.62839 5.62839i −0.205383 0.205383i 0.596919 0.802302i \(-0.296391\pi\)
−0.802302 + 0.596919i \(0.796391\pi\)
\(752\) 9.28850 + 9.37664i 0.338717 + 0.341931i
\(753\) 0 0
\(754\) 11.8860 28.5999i 0.432864 1.04155i
\(755\) −0.209242 + 1.05193i −0.00761510 + 0.0382837i
\(756\) 0 0
\(757\) −17.5865 11.7509i −0.639192 0.427095i 0.193293 0.981141i \(-0.438083\pi\)
−0.832486 + 0.554046i \(0.813083\pi\)
\(758\) −24.3165 + 36.2994i −0.883216 + 1.31845i
\(759\) 0 0
\(760\) −1.38280 1.39263i −0.0501596 0.0505161i
\(761\) −8.96561 21.6449i −0.325003 0.784627i −0.998949 0.0458456i \(-0.985402\pi\)
0.673946 0.738781i \(-0.264598\pi\)
\(762\) 0 0
\(763\) −1.13808 5.72150i −0.0412011 0.207132i
\(764\) 0.0812961 34.4337i 0.00294119 1.24577i
\(765\) 0 0
\(766\) −28.6135 28.6811i −1.03385 1.03629i
\(767\) 19.8570 0.716993
\(768\) 0 0
\(769\) 6.14218 0.221493 0.110746 0.993849i \(-0.464676\pi\)
0.110746 + 0.993849i \(0.464676\pi\)
\(770\) 1.76530 + 1.76947i 0.0636170 + 0.0637673i
\(771\) 0 0
\(772\) 0.0602549 25.5215i 0.00216862 0.918538i
\(773\) −3.65565 18.3782i −0.131485 0.661018i −0.989162 0.146830i \(-0.953093\pi\)
0.857677 0.514189i \(-0.171907\pi\)
\(774\) 0 0
\(775\) 15.5251 + 37.4808i 0.557677 + 1.34635i
\(776\) 30.7320 + 30.9504i 1.10321 + 1.11106i
\(777\) 0 0
\(778\) 6.81970 10.1804i 0.244498 0.364984i
\(779\) 24.6378 + 16.4624i 0.882739 + 0.589827i
\(780\) 0 0
\(781\) −13.6074 + 68.4090i −0.486911 + 2.44787i
\(782\) 3.39508 8.16915i 0.121408 0.292128i
\(783\) 0 0
\(784\) −14.7417 + 14.6032i −0.526491 + 0.521542i
\(785\) −2.14111 2.14111i −0.0764196 0.0764196i
\(786\) 0 0
\(787\) −43.2635 8.60564i −1.54218 0.306758i −0.650526 0.759484i \(-0.725452\pi\)
−0.891650 + 0.452726i \(0.850452\pi\)