Properties

Label 441.2.g.g.79.3
Level $441$
Weight $2$
Character 441.79
Analytic conductor $3.521$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 7 x^{10} + 37 x^{8} - 78 x^{6} + 123 x^{4} - 36 x^{2} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.3
Root \(1.29589 - 0.748185i\) of defining polynomial
Character \(\chi\) \(=\) 441.79
Dual form 441.2.g.g.67.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.119562 - 0.207087i) q^{2} +(-0.578751 + 1.63250i) q^{3} +(0.971410 - 1.68253i) q^{4} -2.59179 q^{5} +(0.407265 - 0.0753324i) q^{6} -0.942820 q^{8} +(-2.33009 - 1.88962i) q^{9} +O(q^{10})\) \(q+(-0.119562 - 0.207087i) q^{2} +(-0.578751 + 1.63250i) q^{3} +(0.971410 - 1.68253i) q^{4} -2.59179 q^{5} +(0.407265 - 0.0753324i) q^{6} -0.942820 q^{8} +(-2.33009 - 1.88962i) q^{9} +(0.309879 + 0.536725i) q^{10} +4.18194 q^{11} +(2.18452 + 2.55959i) q^{12} +(-1.84155 - 3.18966i) q^{13} +(1.50000 - 4.23109i) q^{15} +(-1.83009 - 3.16982i) q^{16} +(-0.855536 - 1.48183i) q^{17} +(-0.112725 + 0.708458i) q^{18} +(3.57780 - 6.19694i) q^{19} +(-2.51769 + 4.36077i) q^{20} +(-0.500000 - 0.866025i) q^{22} -5.12476 q^{23} +(0.545658 - 1.53915i) q^{24} +1.71737 q^{25} +(-0.440358 + 0.762722i) q^{26} +(4.43334 - 2.71026i) q^{27} +(1.06238 - 1.84010i) q^{29} +(-1.05555 + 0.195246i) q^{30} +(3.26793 - 5.66021i) q^{31} +(-1.38044 + 2.39099i) q^{32} +(-2.42030 + 6.82701i) q^{33} +(-0.204579 + 0.354341i) q^{34} +(-5.44282 + 2.08486i) q^{36} +(-0.830095 + 1.43777i) q^{37} -1.71107 q^{38} +(6.27292 - 1.16031i) q^{39} +2.44359 q^{40} +(5.10948 + 8.84988i) q^{41} +(0.830095 - 1.43777i) q^{43} +(4.06238 - 7.03625i) q^{44} +(6.03911 + 4.89749i) q^{45} +(0.612725 + 1.06127i) q^{46} +(-4.66912 - 8.08715i) q^{47} +(6.23389 - 1.15309i) q^{48} +(-0.205332 - 0.355645i) q^{50} +(2.91423 - 0.539049i) q^{51} -7.15561 q^{52} +(-5.32326 - 9.22015i) q^{53} +(-1.09132 - 0.594044i) q^{54} -10.8387 q^{55} +(8.04583 + 9.42724i) q^{57} -0.508080 q^{58} +(-3.03215 + 5.25183i) q^{59} +(-5.66182 - 6.63392i) q^{60} +(3.99298 + 6.91605i) q^{61} -1.56287 q^{62} -6.66019 q^{64} +(4.77292 + 8.26693i) q^{65} +(1.70316 - 0.315036i) q^{66} +(-4.13160 + 7.15614i) q^{67} -3.32431 q^{68} +(2.96596 - 8.36616i) q^{69} +6.23912 q^{71} +(2.19686 + 1.78157i) q^{72} +(-3.57780 - 6.19694i) q^{73} +0.396990 q^{74} +(-0.993929 + 2.80360i) q^{75} +(-6.95103 - 12.0395i) q^{76} +(-0.990285 - 1.16031i) q^{78} +(4.91423 + 8.51170i) q^{79} +(4.74322 + 8.21550i) q^{80} +(1.85868 + 8.80598i) q^{81} +(1.22180 - 2.11621i) q^{82} +(-3.44733 + 5.97094i) q^{83} +(2.21737 + 3.84060i) q^{85} -0.396990 q^{86} +(2.38910 + 2.79929i) q^{87} -3.94282 q^{88} +(2.51769 - 4.36077i) q^{89} +(0.292160 - 1.83617i) q^{90} +(-4.97825 + 8.62258i) q^{92} +(7.34897 + 8.61073i) q^{93} +(-1.11650 + 1.93383i) q^{94} +(-9.27292 + 16.0612i) q^{95} +(-3.10435 - 3.63735i) q^{96} +(-1.53167 + 2.65294i) q^{97} +(-9.74433 - 7.90228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 2q^{2} - 6q^{4} + 24q^{8} - 12q^{9} + O(q^{10}) \) \( 12q - 2q^{2} - 6q^{4} + 24q^{8} - 12q^{9} + 16q^{11} + 18q^{15} - 6q^{16} + 18q^{18} - 6q^{22} + 8q^{23} + 24q^{25} - 22q^{29} + 42q^{30} - 16q^{32} - 30q^{36} + 6q^{37} + 24q^{39} - 6q^{43} + 14q^{44} - 12q^{46} - 56q^{50} - 18q^{51} - 28q^{53} - 6q^{57} + 36q^{58} - 126q^{60} - 48q^{64} + 6q^{65} + 76q^{71} - 30q^{72} + 72q^{74} + 36q^{78} + 6q^{79} + 24q^{81} + 30q^{85} - 72q^{86} - 12q^{88} - 62q^{92} + 42q^{93} - 60q^{95} - 48q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.119562 0.207087i −0.0845428 0.146433i 0.820653 0.571426i \(-0.193610\pi\)
−0.905196 + 0.424994i \(0.860276\pi\)
\(3\) −0.578751 + 1.63250i −0.334142 + 0.942523i
\(4\) 0.971410 1.68253i 0.485705 0.841266i
\(5\) −2.59179 −1.15908 −0.579542 0.814943i \(-0.696768\pi\)
−0.579542 + 0.814943i \(0.696768\pi\)
\(6\) 0.407265 0.0753324i 0.166265 0.0307543i
\(7\) 0 0
\(8\) −0.942820 −0.333337
\(9\) −2.33009 1.88962i −0.776698 0.629873i
\(10\) 0.309879 + 0.536725i 0.0979922 + 0.169727i
\(11\) 4.18194 1.26090 0.630452 0.776228i \(-0.282870\pi\)
0.630452 + 0.776228i \(0.282870\pi\)
\(12\) 2.18452 + 2.55959i 0.630618 + 0.738890i
\(13\) −1.84155 3.18966i −0.510755 0.884653i −0.999922 0.0124633i \(-0.996033\pi\)
0.489168 0.872190i \(-0.337301\pi\)
\(14\) 0 0
\(15\) 1.50000 4.23109i 0.387298 1.09246i
\(16\) −1.83009 3.16982i −0.457524 0.792454i
\(17\) −0.855536 1.48183i −0.207498 0.359397i 0.743428 0.668816i \(-0.233199\pi\)
−0.950926 + 0.309419i \(0.899865\pi\)
\(18\) −0.112725 + 0.708458i −0.0265696 + 0.166985i
\(19\) 3.57780 6.19694i 0.820805 1.42168i −0.0842790 0.996442i \(-0.526859\pi\)
0.905084 0.425233i \(-0.139808\pi\)
\(20\) −2.51769 + 4.36077i −0.562973 + 0.975097i
\(21\) 0 0
\(22\) −0.500000 0.866025i −0.106600 0.184637i
\(23\) −5.12476 −1.06859 −0.534294 0.845299i \(-0.679422\pi\)
−0.534294 + 0.845299i \(0.679422\pi\)
\(24\) 0.545658 1.53915i 0.111382 0.314178i
\(25\) 1.71737 0.343474
\(26\) −0.440358 + 0.762722i −0.0863613 + 0.149582i
\(27\) 4.43334 2.71026i 0.853197 0.521589i
\(28\) 0 0
\(29\) 1.06238 1.84010i 0.197279 0.341698i −0.750366 0.661023i \(-0.770123\pi\)
0.947645 + 0.319325i \(0.103456\pi\)
\(30\) −1.05555 + 0.195246i −0.192715 + 0.0356468i
\(31\) 3.26793 5.66021i 0.586937 1.01660i −0.407694 0.913119i \(-0.633667\pi\)
0.994631 0.103486i \(-0.0329997\pi\)
\(32\) −1.38044 + 2.39099i −0.244029 + 0.422671i
\(33\) −2.42030 + 6.82701i −0.421321 + 1.18843i
\(34\) −0.204579 + 0.354341i −0.0350850 + 0.0607689i
\(35\) 0 0
\(36\) −5.44282 + 2.08486i −0.907137 + 0.347477i
\(37\) −0.830095 + 1.43777i −0.136467 + 0.236367i −0.926157 0.377139i \(-0.876908\pi\)
0.789690 + 0.613506i \(0.210241\pi\)
\(38\) −1.71107 −0.277573
\(39\) 6.27292 1.16031i 1.00447 0.185798i
\(40\) 2.44359 0.386366
\(41\) 5.10948 + 8.84988i 0.797967 + 1.38212i 0.920938 + 0.389708i \(0.127424\pi\)
−0.122972 + 0.992410i \(0.539242\pi\)
\(42\) 0 0
\(43\) 0.830095 1.43777i 0.126588 0.219257i −0.795764 0.605606i \(-0.792931\pi\)
0.922353 + 0.386349i \(0.126264\pi\)
\(44\) 4.06238 7.03625i 0.612427 1.06075i
\(45\) 6.03911 + 4.89749i 0.900258 + 0.730075i
\(46\) 0.612725 + 1.06127i 0.0903414 + 0.156476i
\(47\) −4.66912 8.08715i −0.681061 1.17963i −0.974657 0.223703i \(-0.928185\pi\)
0.293596 0.955930i \(-0.405148\pi\)
\(48\) 6.23389 1.15309i 0.899784 0.166434i
\(49\) 0 0
\(50\) −0.205332 0.355645i −0.0290383 0.0502958i
\(51\) 2.91423 0.539049i 0.408074 0.0754820i
\(52\) −7.15561 −0.992305
\(53\) −5.32326 9.22015i −0.731206 1.26649i −0.956368 0.292164i \(-0.905625\pi\)
0.225162 0.974321i \(-0.427709\pi\)
\(54\) −1.09132 0.594044i −0.148509 0.0808392i
\(55\) −10.8387 −1.46149
\(56\) 0 0
\(57\) 8.04583 + 9.42724i 1.06570 + 1.24867i
\(58\) −0.508080 −0.0667142
\(59\) −3.03215 + 5.25183i −0.394752 + 0.683730i −0.993069 0.117529i \(-0.962503\pi\)
0.598318 + 0.801259i \(0.295836\pi\)
\(60\) −5.66182 6.63392i −0.730938 0.856435i
\(61\) 3.99298 + 6.91605i 0.511249 + 0.885509i 0.999915 + 0.0130384i \(0.00415038\pi\)
−0.488666 + 0.872471i \(0.662516\pi\)
\(62\) −1.56287 −0.198485
\(63\) 0 0
\(64\) −6.66019 −0.832524
\(65\) 4.77292 + 8.26693i 0.592007 + 1.02539i
\(66\) 1.70316 0.315036i 0.209644 0.0387782i
\(67\) −4.13160 + 7.15614i −0.504755 + 0.874262i 0.495230 + 0.868762i \(0.335084\pi\)
−0.999985 + 0.00549964i \(0.998249\pi\)
\(68\) −3.32431 −0.403131
\(69\) 2.96596 8.36616i 0.357060 1.00717i
\(70\) 0 0
\(71\) 6.23912 0.740448 0.370224 0.928943i \(-0.379281\pi\)
0.370224 + 0.928943i \(0.379281\pi\)
\(72\) 2.19686 + 1.78157i 0.258902 + 0.209960i
\(73\) −3.57780 6.19694i −0.418750 0.725297i 0.577064 0.816699i \(-0.304198\pi\)
−0.995814 + 0.0914022i \(0.970865\pi\)
\(74\) 0.396990 0.0461492
\(75\) −0.993929 + 2.80360i −0.114769 + 0.323732i
\(76\) −6.95103 12.0395i −0.797338 1.38103i
\(77\) 0 0
\(78\) −0.990285 1.16031i −0.112128 0.131379i
\(79\) 4.91423 + 8.51170i 0.552894 + 0.957641i 0.998064 + 0.0621945i \(0.0198099\pi\)
−0.445170 + 0.895446i \(0.646857\pi\)
\(80\) 4.74322 + 8.21550i 0.530308 + 0.918521i
\(81\) 1.85868 + 8.80598i 0.206521 + 0.978442i
\(82\) 1.22180 2.11621i 0.134925 0.233696i
\(83\) −3.44733 + 5.97094i −0.378393 + 0.655396i −0.990829 0.135124i \(-0.956857\pi\)
0.612436 + 0.790521i \(0.290190\pi\)
\(84\) 0 0
\(85\) 2.21737 + 3.84060i 0.240508 + 0.416571i
\(86\) −0.396990 −0.0428085
\(87\) 2.38910 + 2.79929i 0.256139 + 0.300116i
\(88\) −3.94282 −0.420306
\(89\) 2.51769 4.36077i 0.266875 0.462240i −0.701178 0.712986i \(-0.747342\pi\)
0.968053 + 0.250745i \(0.0806757\pi\)
\(90\) 0.292160 1.83617i 0.0307963 0.193550i
\(91\) 0 0
\(92\) −4.97825 + 8.62258i −0.519018 + 0.898966i
\(93\) 7.34897 + 8.61073i 0.762053 + 0.892892i
\(94\) −1.11650 + 1.93383i −0.115158 + 0.199459i
\(95\) −9.27292 + 16.0612i −0.951381 + 1.64784i
\(96\) −3.10435 3.63735i −0.316837 0.371235i
\(97\) −1.53167 + 2.65294i −0.155518 + 0.269365i −0.933247 0.359234i \(-0.883038\pi\)
0.777730 + 0.628599i \(0.216371\pi\)
\(98\) 0 0
\(99\) −9.74433 7.90228i −0.979342 0.794209i
\(100\) 1.66827 2.88953i 0.166827 0.288953i
\(101\) −11.0997 −1.10446 −0.552229 0.833692i \(-0.686223\pi\)
−0.552229 + 0.833692i \(0.686223\pi\)
\(102\) −0.460060 0.539049i −0.0455527 0.0533738i
\(103\) 7.98597 0.786881 0.393440 0.919350i \(-0.371285\pi\)
0.393440 + 0.919350i \(0.371285\pi\)
\(104\) 1.73625 + 3.00728i 0.170254 + 0.294888i
\(105\) 0 0
\(106\) −1.27292 + 2.20475i −0.123636 + 0.214145i
\(107\) −1.97825 + 3.42642i −0.191244 + 0.331245i −0.945663 0.325149i \(-0.894586\pi\)
0.754419 + 0.656394i \(0.227919\pi\)
\(108\) −0.253498 10.0920i −0.0243929 0.971104i
\(109\) −3.63160 6.29012i −0.347844 0.602484i 0.638022 0.770018i \(-0.279753\pi\)
−0.985866 + 0.167534i \(0.946420\pi\)
\(110\) 1.29589 + 2.24456i 0.123559 + 0.214010i
\(111\) −1.86673 2.18724i −0.177182 0.207603i
\(112\) 0 0
\(113\) −3.46457 6.00082i −0.325920 0.564509i 0.655778 0.754953i \(-0.272341\pi\)
−0.981698 + 0.190444i \(0.939007\pi\)
\(114\) 0.990285 2.79332i 0.0927487 0.261619i
\(115\) 13.2823 1.23858
\(116\) −2.06402 3.57498i −0.191639 0.331929i
\(117\) −1.73625 + 10.9120i −0.160517 + 1.00882i
\(118\) 1.45011 0.133494
\(119\) 0 0
\(120\) −1.41423 + 3.98916i −0.129101 + 0.364158i
\(121\) 6.48865 0.589877
\(122\) 0.954815 1.65379i 0.0864449 0.149727i
\(123\) −17.4045 + 3.21934i −1.56931 + 0.290278i
\(124\) −6.34899 10.9968i −0.570156 0.987540i
\(125\) 8.50788 0.760968
\(126\) 0 0
\(127\) 9.11109 0.808479 0.404239 0.914653i \(-0.367536\pi\)
0.404239 + 0.914653i \(0.367536\pi\)
\(128\) 3.55718 + 6.16122i 0.314413 + 0.544580i
\(129\) 1.86673 + 2.18724i 0.164357 + 0.192575i
\(130\) 1.14132 1.97682i 0.100100 0.173378i
\(131\) −4.30286 −0.375943 −0.187971 0.982175i \(-0.560191\pi\)
−0.187971 + 0.982175i \(0.560191\pi\)
\(132\) 9.13555 + 10.7041i 0.795148 + 0.931669i
\(133\) 0 0
\(134\) 1.97592 0.170694
\(135\) −11.4903 + 7.02441i −0.988926 + 0.604565i
\(136\) 0.806617 + 1.39710i 0.0691668 + 0.119800i
\(137\) 20.5893 1.75907 0.879533 0.475838i \(-0.157855\pi\)
0.879533 + 0.475838i \(0.157855\pi\)
\(138\) −2.08714 + 0.386061i −0.177669 + 0.0328637i
\(139\) 7.88067 + 13.6497i 0.668429 + 1.15775i 0.978343 + 0.206989i \(0.0663665\pi\)
−0.309914 + 0.950765i \(0.600300\pi\)
\(140\) 0 0
\(141\) 15.9045 2.94188i 1.33940 0.247751i
\(142\) −0.745960 1.29204i −0.0625996 0.108426i
\(143\) −7.70127 13.3390i −0.644012 1.11546i
\(144\) −1.72545 + 10.8442i −0.143788 + 0.903680i
\(145\) −2.75347 + 4.76915i −0.228663 + 0.396056i
\(146\) −0.855536 + 1.48183i −0.0708047 + 0.122637i
\(147\) 0 0
\(148\) 1.61273 + 2.79332i 0.132565 + 0.229610i
\(149\) 6.06758 0.497076 0.248538 0.968622i \(-0.420050\pi\)
0.248538 + 0.968622i \(0.420050\pi\)
\(150\) 0.699425 0.129374i 0.0571078 0.0105633i
\(151\) 4.48865 0.365281 0.182641 0.983180i \(-0.441536\pi\)
0.182641 + 0.983180i \(0.441536\pi\)
\(152\) −3.37323 + 5.84260i −0.273605 + 0.473897i
\(153\) −0.806617 + 5.06945i −0.0652111 + 0.409841i
\(154\) 0 0
\(155\) −8.46978 + 14.6701i −0.680309 + 1.17833i
\(156\) 4.14132 11.6815i 0.331571 0.935270i
\(157\) −0.514457 + 0.891066i −0.0410582 + 0.0711148i −0.885824 0.464021i \(-0.846406\pi\)
0.844766 + 0.535136i \(0.179740\pi\)
\(158\) 1.17511 2.03534i 0.0934865 0.161923i
\(159\) 18.1327 3.35403i 1.43802 0.265992i
\(160\) 3.57780 6.19694i 0.282850 0.489911i
\(161\) 0 0
\(162\) 1.60138 1.43777i 0.125816 0.112962i
\(163\) −3.41423 + 5.91362i −0.267423 + 0.463190i −0.968196 0.250194i \(-0.919505\pi\)
0.700772 + 0.713385i \(0.252839\pi\)
\(164\) 19.8536 1.55031
\(165\) 6.27292 17.6942i 0.488346 1.37749i
\(166\) 1.64867 0.127962
\(167\) −8.99716 15.5835i −0.696221 1.20589i −0.969767 0.244032i \(-0.921530\pi\)
0.273546 0.961859i \(-0.411803\pi\)
\(168\) 0 0
\(169\) −0.282630 + 0.489530i −0.0217408 + 0.0376561i
\(170\) 0.530225 0.918376i 0.0406664 0.0704362i
\(171\) −20.0465 + 7.67877i −1.53299 + 0.587210i
\(172\) −1.61273 2.79332i −0.122969 0.212989i
\(173\) 0.415178 + 0.719110i 0.0315654 + 0.0546729i 0.881377 0.472414i \(-0.156617\pi\)
−0.849811 + 0.527087i \(0.823284\pi\)
\(174\) 0.294052 0.829440i 0.0222920 0.0628797i
\(175\) 0 0
\(176\) −7.65335 13.2560i −0.576893 0.999208i
\(177\) −6.81875 7.98947i −0.512528 0.600526i
\(178\) −1.20408 −0.0902493
\(179\) −3.78947 6.56355i −0.283238 0.490583i 0.688942 0.724816i \(-0.258075\pi\)
−0.972180 + 0.234233i \(0.924742\pi\)
\(180\) 14.1066 5.40353i 1.05145 0.402755i
\(181\) 0.409157 0.0304124 0.0152062 0.999884i \(-0.495160\pi\)
0.0152062 + 0.999884i \(0.495160\pi\)
\(182\) 0 0
\(183\) −13.6014 + 2.51586i −1.00544 + 0.185978i
\(184\) 4.83173 0.356200
\(185\) 2.15143 3.72639i 0.158176 0.273969i
\(186\) 0.904515 2.55139i 0.0663223 0.187077i
\(187\) −3.57780 6.19694i −0.261635 0.453165i
\(188\) −18.1425 −1.32318
\(189\) 0 0
\(190\) 4.43474 0.321730
\(191\) −8.01204 13.8773i −0.579731 1.00412i −0.995510 0.0946575i \(-0.969824\pi\)
0.415779 0.909466i \(-0.363509\pi\)
\(192\) 3.85459 10.8727i 0.278181 0.784673i
\(193\) 6.18715 10.7164i 0.445360 0.771387i −0.552717 0.833369i \(-0.686409\pi\)
0.998077 + 0.0619822i \(0.0197422\pi\)
\(194\) 0.732518 0.0525917
\(195\) −16.2581 + 3.00728i −1.16426 + 0.215356i
\(196\) 0 0
\(197\) 23.1021 1.64595 0.822977 0.568075i \(-0.192312\pi\)
0.822977 + 0.568075i \(0.192312\pi\)
\(198\) −0.471410 + 2.96273i −0.0335017 + 0.210552i
\(199\) 3.37323 + 5.84260i 0.239122 + 0.414171i 0.960463 0.278409i \(-0.0898072\pi\)
−0.721341 + 0.692580i \(0.756474\pi\)
\(200\) −1.61917 −0.114493
\(201\) −9.29121 10.8864i −0.655352 0.767871i
\(202\) 1.32710 + 2.29860i 0.0933741 + 0.161729i
\(203\) 0 0
\(204\) 1.92395 5.42692i 0.134703 0.379961i
\(205\) −13.2427 22.9370i −0.924910 1.60199i
\(206\) −0.954815 1.65379i −0.0665251 0.115225i
\(207\) 11.9412 + 9.68385i 0.829970 + 0.673074i
\(208\) −6.74043 + 11.6748i −0.467365 + 0.809500i
\(209\) 14.9622 25.9153i 1.03496 1.79260i
\(210\) 0 0
\(211\) −8.44282 14.6234i −0.581228 1.00672i −0.995334 0.0964875i \(-0.969239\pi\)
0.414106 0.910228i \(-0.364094\pi\)
\(212\) −20.6843 −1.42060
\(213\) −3.61090 + 10.1854i −0.247415 + 0.697889i
\(214\) 0.946090 0.0646734
\(215\) −2.15143 + 3.72639i −0.146726 + 0.254138i
\(216\) −4.17984 + 2.55528i −0.284402 + 0.173865i
\(217\) 0 0
\(218\) −0.868400 + 1.50411i −0.0588155 + 0.101871i
\(219\) 12.1871 2.25427i 0.823531 0.152330i
\(220\) −10.5288 + 18.2365i −0.709854 + 1.22950i
\(221\) −3.15103 + 5.45774i −0.211961 + 0.367128i
\(222\) −0.229758 + 0.648085i −0.0154204 + 0.0434966i
\(223\) 2.25071 3.89834i 0.150719 0.261052i −0.780773 0.624815i \(-0.785175\pi\)
0.931492 + 0.363762i \(0.118508\pi\)
\(224\) 0 0
\(225\) −4.00163 3.24517i −0.266776 0.216345i
\(226\) −0.828460 + 1.43494i −0.0551084 + 0.0954505i
\(227\) −6.06429 −0.402501 −0.201251 0.979540i \(-0.564501\pi\)
−0.201251 + 0.979540i \(0.564501\pi\)
\(228\) 23.6774 4.37965i 1.56808 0.290049i
\(229\) −11.0493 −0.730159 −0.365080 0.930976i \(-0.618958\pi\)
−0.365080 + 0.930976i \(0.618958\pi\)
\(230\) −1.58805 2.75059i −0.104713 0.181369i
\(231\) 0 0
\(232\) −1.00163 + 1.73488i −0.0657605 + 0.113901i
\(233\) 4.06922 7.04809i 0.266583 0.461736i −0.701394 0.712774i \(-0.747439\pi\)
0.967977 + 0.251038i \(0.0807719\pi\)
\(234\) 2.46733 0.945107i 0.161294 0.0617836i
\(235\) 12.1014 + 20.9602i 0.789407 + 1.36729i
\(236\) 5.89092 + 10.2034i 0.383466 + 0.664183i
\(237\) −16.7394 + 3.09632i −1.08734 + 0.201127i
\(238\) 0 0
\(239\) −10.5813 18.3273i −0.684445 1.18549i −0.973611 0.228214i \(-0.926711\pi\)
0.289166 0.957279i \(-0.406622\pi\)
\(240\) −16.1569 + 2.98857i −1.04292 + 0.192911i
\(241\) 13.6915 0.881945 0.440972 0.897521i \(-0.354634\pi\)
0.440972 + 0.897521i \(0.354634\pi\)
\(242\) −0.775794 1.34371i −0.0498699 0.0863772i
\(243\) −15.4515 2.06217i −0.991211 0.132288i
\(244\) 15.5153 0.993265
\(245\) 0 0
\(246\) 2.74759 + 3.21934i 0.175180 + 0.205257i
\(247\) −26.3549 −1.67692
\(248\) −3.08107 + 5.33656i −0.195648 + 0.338872i
\(249\) −7.75241 9.08344i −0.491289 0.575639i
\(250\) −1.01722 1.76187i −0.0643344 0.111430i
\(251\) 15.2040 0.959667 0.479833 0.877360i \(-0.340697\pi\)
0.479833 + 0.877360i \(0.340697\pi\)
\(252\) 0 0
\(253\) −21.4315 −1.34738
\(254\) −1.08934 1.88679i −0.0683511 0.118388i
\(255\) −7.55307 + 1.39710i −0.472992 + 0.0874899i
\(256\) −5.80959 + 10.0625i −0.363099 + 0.628906i
\(257\) 25.6215 1.59822 0.799112 0.601182i \(-0.205303\pi\)
0.799112 + 0.601182i \(0.205303\pi\)
\(258\) 0.229758 0.648085i 0.0143041 0.0403480i
\(259\) 0 0
\(260\) 18.5458 1.15016
\(261\) −5.95254 + 2.28011i −0.368453 + 0.141135i
\(262\) 0.514457 + 0.891066i 0.0317833 + 0.0550502i
\(263\) 7.10069 0.437847 0.218924 0.975742i \(-0.429745\pi\)
0.218924 + 0.975742i \(0.429745\pi\)
\(264\) 2.28191 6.43664i 0.140442 0.396148i
\(265\) 13.7968 + 23.8967i 0.847528 + 1.46796i
\(266\) 0 0
\(267\) 5.66182 + 6.63392i 0.346498 + 0.405989i
\(268\) 8.02696 + 13.9031i 0.490324 + 0.849267i
\(269\) 8.21572 + 14.2301i 0.500922 + 0.867622i 0.999999 + 0.00106448i \(0.000338834\pi\)
−0.499078 + 0.866557i \(0.666328\pi\)
\(270\) 2.82846 + 1.53964i 0.172135 + 0.0936993i
\(271\) −6.34899 + 10.9968i −0.385674 + 0.668007i −0.991862 0.127314i \(-0.959364\pi\)
0.606189 + 0.795321i \(0.292698\pi\)
\(272\) −3.13143 + 5.42379i −0.189871 + 0.328865i
\(273\) 0 0
\(274\) −2.46169 4.26378i −0.148716 0.257584i
\(275\) 7.18194 0.433087
\(276\) −11.1952 13.1173i −0.673870 0.789569i
\(277\) −0.828460 −0.0497773 −0.0248887 0.999690i \(-0.507923\pi\)
−0.0248887 + 0.999690i \(0.507923\pi\)
\(278\) 1.88445 3.26396i 0.113022 0.195760i
\(279\) −18.3102 + 7.01370i −1.09620 + 0.419899i
\(280\) 0 0
\(281\) −2.60985 + 4.52039i −0.155690 + 0.269664i −0.933310 0.359071i \(-0.883094\pi\)
0.777620 + 0.628735i \(0.216427\pi\)
\(282\) −2.51079 2.94188i −0.149516 0.175186i
\(283\) 3.67708 6.36890i 0.218580 0.378592i −0.735794 0.677205i \(-0.763191\pi\)
0.954374 + 0.298614i \(0.0965242\pi\)
\(284\) 6.06075 10.4975i 0.359639 0.622913i
\(285\) −20.8531 24.4334i −1.23523 1.44731i
\(286\) −1.84155 + 3.18966i −0.108893 + 0.188609i
\(287\) 0 0
\(288\) 7.73461 2.96273i 0.455766 0.174581i
\(289\) 7.03611 12.1869i 0.413889 0.716877i
\(290\) 1.31684 0.0773273
\(291\) −3.44445 4.03584i −0.201918 0.236585i
\(292\) −13.9021 −0.813557
\(293\) −3.91286 6.77728i −0.228592 0.395933i 0.728799 0.684728i \(-0.240079\pi\)
−0.957391 + 0.288795i \(0.906745\pi\)
\(294\) 0 0
\(295\) 7.85868 13.6116i 0.457550 0.792500i
\(296\) 0.782630 1.35556i 0.0454895 0.0787900i
\(297\) 18.5400 11.3341i 1.07580 0.657673i
\(298\) −0.725450 1.25652i −0.0420242 0.0727881i
\(299\) 9.43752 + 16.3463i 0.545786 + 0.945329i
\(300\) 3.75164 + 4.39576i 0.216601 + 0.253790i
\(301\) 0 0
\(302\) −0.536670 0.929540i −0.0308819 0.0534890i
\(303\) 6.42395 18.1202i 0.369046 1.04098i
\(304\) −26.1909 −1.50215
\(305\) −10.3490 17.9249i −0.592580 1.02638i
\(306\) 1.14626 0.439072i 0.0655271 0.0251001i
\(307\) 22.6709 1.29390 0.646948 0.762534i \(-0.276045\pi\)
0.646948 + 0.762534i \(0.276045\pi\)
\(308\) 0 0
\(309\) −4.62188 + 13.0371i −0.262930 + 0.741653i
\(310\) 4.05064 0.230061
\(311\) 16.1588 27.9879i 0.916281 1.58705i 0.111266 0.993791i \(-0.464509\pi\)
0.805015 0.593255i \(-0.202157\pi\)
\(312\) −5.91423 + 1.09396i −0.334827 + 0.0619335i
\(313\) 12.1598 + 21.0614i 0.687312 + 1.19046i 0.972704 + 0.232048i \(0.0745428\pi\)
−0.285392 + 0.958411i \(0.592124\pi\)
\(314\) 0.246037 0.0138847
\(315\) 0 0
\(316\) 19.0949 1.07417
\(317\) −2.56922 4.45002i −0.144302 0.249938i 0.784811 0.619736i \(-0.212760\pi\)
−0.929112 + 0.369798i \(0.879427\pi\)
\(318\) −2.86255 3.35403i −0.160524 0.188085i
\(319\) 4.44282 7.69519i 0.248750 0.430848i
\(320\) 17.2618 0.964964
\(321\) −4.44872 5.21253i −0.248303 0.290935i
\(322\) 0 0
\(323\) −12.2438 −0.681262
\(324\) 16.6219 + 5.42692i 0.923438 + 0.301496i
\(325\) −3.16263 5.47783i −0.175431 0.303855i
\(326\) 1.63284 0.0904349
\(327\) 12.3704 2.28817i 0.684084 0.126536i
\(328\) −4.81732 8.34384i −0.265992 0.460712i
\(329\) 0 0
\(330\) −4.41423 + 0.816506i −0.242995 + 0.0449472i
\(331\) 5.84897 + 10.1307i 0.321488 + 0.556834i 0.980795 0.195040i \(-0.0624835\pi\)
−0.659307 + 0.751874i \(0.729150\pi\)
\(332\) 6.69753 + 11.6005i 0.367575 + 0.636658i
\(333\) 4.65103 1.78157i 0.254875 0.0976294i
\(334\) −2.15143 + 3.72639i −0.117721 + 0.203899i
\(335\) 10.7082 18.5472i 0.585053 1.01334i
\(336\) 0 0
\(337\) 16.8473 + 29.1804i 0.917733 + 1.58956i 0.802850 + 0.596181i \(0.203316\pi\)
0.114883 + 0.993379i \(0.463351\pi\)
\(338\) 0.135167 0.00735211
\(339\) 11.8014 2.18293i 0.640966 0.118560i
\(340\) 8.61590 0.467263
\(341\) 13.6663 23.6707i 0.740071 1.28184i
\(342\) 3.98696 + 3.23327i 0.215590 + 0.174835i
\(343\) 0 0
\(344\) −0.782630 + 1.35556i −0.0421966 + 0.0730866i
\(345\) −7.68715 + 21.6833i −0.413862 + 1.16739i
\(346\) 0.0992788 0.171956i 0.00533726 0.00924441i
\(347\) −13.6557 + 23.6523i −0.733075 + 1.26972i 0.222488 + 0.974936i \(0.428582\pi\)
−0.955563 + 0.294788i \(0.904751\pi\)
\(348\) 7.03070 1.30048i 0.376885 0.0697129i
\(349\) −11.4585 + 19.8467i −0.613358 + 1.06237i 0.377312 + 0.926086i \(0.376848\pi\)
−0.990670 + 0.136281i \(0.956485\pi\)
\(350\) 0 0
\(351\) −16.8090 9.14978i −0.897200 0.488379i
\(352\) −5.77292 + 9.99898i −0.307697 + 0.532948i
\(353\) 10.2693 0.546581 0.273290 0.961932i \(-0.411888\pi\)
0.273290 + 0.961932i \(0.411888\pi\)
\(354\) −0.839255 + 2.36731i −0.0446059 + 0.125821i
\(355\) −16.1705 −0.858241
\(356\) −4.89142 8.47218i −0.259245 0.449025i
\(357\) 0 0
\(358\) −0.906150 + 1.56950i −0.0478915 + 0.0829505i
\(359\) −5.05034 + 8.74745i −0.266547 + 0.461673i −0.967968 0.251075i \(-0.919216\pi\)
0.701421 + 0.712747i \(0.252549\pi\)
\(360\) −5.69380 4.61745i −0.300090 0.243361i
\(361\) −16.1014 27.8884i −0.847441 1.46781i
\(362\) −0.0489195 0.0847311i −0.00257115 0.00445337i
\(363\) −3.75531 + 10.5927i −0.197103 + 0.555973i
\(364\) 0 0
\(365\) 9.27292 + 16.0612i 0.485367 + 0.840680i
\(366\) 2.14721 + 2.51586i 0.112236 + 0.131506i
\(367\) −7.77537 −0.405871 −0.202935 0.979192i \(-0.565048\pi\)
−0.202935 + 0.979192i \(0.565048\pi\)
\(368\) 9.37880 + 16.2446i 0.488904 + 0.846806i
\(369\) 4.81732 30.2760i 0.250780 1.57611i
\(370\) −1.02891 −0.0534907
\(371\) 0 0
\(372\) 21.6267 4.00032i 1.12129 0.207407i
\(373\) 24.1111 1.24842 0.624212 0.781255i \(-0.285420\pi\)
0.624212 + 0.781255i \(0.285420\pi\)
\(374\) −0.855536 + 1.48183i −0.0442387 + 0.0766237i
\(375\) −4.92395 + 13.8891i −0.254271 + 0.717230i
\(376\) 4.40214 + 7.62473i 0.227023 + 0.393215i
\(377\) −7.82573 −0.403045
\(378\) 0 0
\(379\) −13.3581 −0.686161 −0.343081 0.939306i \(-0.611470\pi\)
−0.343081 + 0.939306i \(0.611470\pi\)
\(380\) 18.0156 + 31.2039i 0.924181 + 1.60073i
\(381\) −5.27305 + 14.8738i −0.270147 + 0.762009i
\(382\) −1.91586 + 3.31838i −0.0980242 + 0.169783i
\(383\) −9.24040 −0.472162 −0.236081 0.971733i \(-0.575863\pi\)
−0.236081 + 0.971733i \(0.575863\pi\)
\(384\) −12.1169 + 2.24128i −0.618337 + 0.114375i
\(385\) 0 0
\(386\) −2.95898 −0.150608
\(387\) −4.65103 + 1.78157i −0.236425 + 0.0905623i
\(388\) 2.97577 + 5.15418i 0.151072 + 0.261664i
\(389\) 10.4484 0.529756 0.264878 0.964282i \(-0.414668\pi\)
0.264878 + 0.964282i \(0.414668\pi\)
\(390\) 2.56661 + 3.00728i 0.129965 + 0.152279i
\(391\) 4.38442 + 7.59404i 0.221730 + 0.384047i
\(392\) 0 0
\(393\) 2.49028 7.02441i 0.125618 0.354335i
\(394\) −2.76212 4.78413i −0.139154 0.241021i
\(395\) −12.7366 22.0605i −0.640850 1.10999i
\(396\) −22.7616 + 8.71878i −1.14381 + 0.438135i
\(397\) 0.204579 0.354341i 0.0102675 0.0177838i −0.860846 0.508866i \(-0.830065\pi\)
0.871114 + 0.491082i \(0.163398\pi\)
\(398\) 0.806617 1.39710i 0.0404321 0.0700304i
\(399\) 0 0
\(400\) −3.14295 5.44375i −0.157147 0.272187i
\(401\) 15.2528 0.761688 0.380844 0.924639i \(-0.375633\pi\)
0.380844 + 0.924639i \(0.375633\pi\)
\(402\) −1.14357 + 3.22569i −0.0570360 + 0.160883i
\(403\) −24.0722 −1.19912
\(404\) −10.7823 + 18.6756i −0.536441 + 0.929143i
\(405\) −4.81732 22.8232i −0.239375 1.13410i
\(406\) 0 0
\(407\) −3.47141 + 6.01266i −0.172071 + 0.298036i
\(408\) −2.74759 + 0.508226i −0.136026 + 0.0251610i
\(409\) 3.06335 5.30587i 0.151473 0.262359i −0.780296 0.625410i \(-0.784932\pi\)
0.931769 + 0.363051i \(0.118265\pi\)
\(410\) −3.16664 + 5.48477i −0.156389 + 0.270874i
\(411\) −11.9161 + 33.6120i −0.587778 + 1.65796i
\(412\) 7.75765 13.4366i 0.382192 0.661976i
\(413\) 0 0
\(414\) 0.577690 3.63068i 0.0283919 0.178438i
\(415\) 8.93474 15.4754i 0.438589 0.759659i
\(416\) 10.1686 0.498557
\(417\) −26.8441 + 4.96538i −1.31456 + 0.243156i
\(418\) −7.15561 −0.349992
\(419\) −0.781437 1.35349i −0.0381757 0.0661223i 0.846306 0.532697i \(-0.178821\pi\)
−0.884482 + 0.466574i \(0.845488\pi\)
\(420\) 0 0
\(421\) −11.6316 + 20.1465i −0.566889 + 0.981881i 0.429982 + 0.902838i \(0.358520\pi\)
−0.996871 + 0.0790438i \(0.974813\pi\)
\(422\) −2.01887 + 3.49679i −0.0982773 + 0.170221i
\(423\) −4.40214 + 27.6667i −0.214039 + 1.34520i
\(424\) 5.01887 + 8.69295i 0.243738 + 0.422167i
\(425\) −1.46927 2.54485i −0.0712702 0.123444i
\(426\) 2.54098 0.470008i 0.123111 0.0227720i
\(427\) 0 0
\(428\) 3.84338 + 6.65692i 0.185777 + 0.321775i
\(429\) 26.2330 4.85235i 1.26654 0.234274i
\(430\) 1.02891 0.0496187
\(431\) −0.502879 0.871011i −0.0242228 0.0419551i 0.853660 0.520831i \(-0.174378\pi\)
−0.877883 + 0.478876i \(0.841044\pi\)
\(432\) −16.7045 9.09286i −0.803693 0.437480i
\(433\) 13.1071 0.629889 0.314945 0.949110i \(-0.398014\pi\)
0.314945 + 0.949110i \(0.398014\pi\)
\(434\) 0 0
\(435\) −6.19205 7.25518i −0.296886 0.347859i
\(436\) −14.1111 −0.675799
\(437\) −18.3354 + 31.7579i −0.877101 + 1.51918i
\(438\) −1.92395 2.25427i −0.0919297 0.107713i
\(439\) −9.30704 16.1203i −0.444201 0.769378i 0.553795 0.832653i \(-0.313179\pi\)
−0.997996 + 0.0632744i \(0.979846\pi\)
\(440\) 10.2190 0.487170
\(441\) 0 0
\(442\) 1.50697 0.0716792
\(443\) 0.559503 + 0.969088i 0.0265828 + 0.0460427i 0.879011 0.476802i \(-0.158204\pi\)
−0.852428 + 0.522845i \(0.824871\pi\)
\(444\) −5.49346 + 1.01613i −0.260708 + 0.0482235i
\(445\) −6.52532 + 11.3022i −0.309330 + 0.535775i
\(446\) −1.07639 −0.0509687
\(447\) −3.51162 + 9.90531i −0.166094 + 0.468505i
\(448\) 0 0
\(449\) −39.4419 −1.86138 −0.930689 0.365813i \(-0.880791\pi\)
−0.930689 + 0.365813i \(0.880791\pi\)
\(450\) −0.193591 + 1.21668i −0.00912595 + 0.0573550i
\(451\) 21.3676 + 37.0097i 1.00616 + 1.74272i
\(452\) −13.4621 −0.633203
\(453\) −2.59781 + 7.32771i −0.122056 + 0.344286i
\(454\) 0.725057 + 1.25584i 0.0340286 + 0.0589393i
\(455\) 0 0
\(456\) −7.58577 8.88819i −0.355236 0.416228i
\(457\) 17.1202 + 29.6531i 0.800852 + 1.38712i 0.919056 + 0.394126i \(0.128953\pi\)
−0.118205 + 0.992989i \(0.537714\pi\)
\(458\) 1.32107 + 2.28817i 0.0617297 + 0.106919i
\(459\) −7.80903 4.25075i −0.364494 0.198408i
\(460\) 12.9026 22.3479i 0.601585 1.04198i
\(461\) −10.1938 + 17.6561i −0.474772 + 0.822328i −0.999583 0.0288903i \(-0.990803\pi\)
0.524811 + 0.851219i \(0.324136\pi\)
\(462\) 0 0
\(463\) −3.40451 5.89679i −0.158221 0.274047i 0.776006 0.630725i \(-0.217243\pi\)
−0.934227 + 0.356678i \(0.883909\pi\)
\(464\) −7.77704 −0.361040
\(465\) −19.0470 22.3172i −0.883282 1.03494i
\(466\) −1.94609 −0.0901509
\(467\) −12.3956 + 21.4698i −0.573598 + 0.993502i 0.422594 + 0.906319i \(0.361120\pi\)
−0.996192 + 0.0871825i \(0.972214\pi\)
\(468\) 16.6733 + 13.5214i 0.770721 + 0.625026i
\(469\) 0 0
\(470\) 2.89372 5.01207i 0.133477 0.231190i
\(471\) −1.15692 1.35556i −0.0533081 0.0624607i
\(472\) 2.85877 4.95153i 0.131586 0.227913i
\(473\) 3.47141 6.01266i 0.159616 0.276462i
\(474\) 2.64260 + 3.09632i 0.121379 + 0.142219i
\(475\) 6.14441 10.6424i 0.281925 0.488309i
\(476\) 0 0
\(477\) −5.01887 + 31.5428i −0.229798 + 1.44424i
\(478\) −2.53022 + 4.38248i −0.115730 + 0.200450i
\(479\) −11.0997 −0.507157 −0.253579 0.967315i \(-0.581608\pi\)
−0.253579 + 0.967315i \(0.581608\pi\)
\(480\) 8.04583 + 9.42724i 0.367240 + 0.430293i
\(481\) 6.11465 0.278804
\(482\) −1.63697 2.83532i −0.0745621 0.129145i
\(483\) 0 0
\(484\) 6.30314 10.9174i 0.286506 0.496244i
\(485\) 3.96978 6.87585i 0.180258 0.312216i
\(486\) 1.42035 + 3.44635i 0.0644285 + 0.156330i
\(487\) 5.01887 + 8.69295i 0.227427 + 0.393915i 0.957045 0.289940i \(-0.0936354\pi\)
−0.729618 + 0.683855i \(0.760302\pi\)
\(488\) −3.76466 6.52059i −0.170418 0.295173i
\(489\) −7.67798 8.99623i −0.347210 0.406824i
\(490\) 0 0
\(491\) 6.19398 + 10.7283i 0.279530 + 0.484161i 0.971268 0.237988i \(-0.0764879\pi\)
−0.691738 + 0.722149i \(0.743155\pi\)
\(492\) −11.4903 + 32.4109i −0.518022 + 1.46120i
\(493\) −3.63562 −0.163740
\(494\) 3.15103 + 5.45774i 0.141772 + 0.245556i
\(495\) 25.2552 + 20.4810i 1.13514 + 0.920554i
\(496\) −23.9225 −1.07415
\(497\) 0 0
\(498\) −0.954170 + 2.69145i −0.0427574 + 0.120607i
\(499\) 10.2222 0.457608 0.228804 0.973473i \(-0.426519\pi\)
0.228804 + 0.973473i \(0.426519\pi\)
\(500\) 8.26464 14.3148i 0.369606 0.640177i
\(501\) 30.6472 5.66886i 1.36922 0.253266i
\(502\) −1.81781 3.14854i −0.0811329 0.140526i
\(503\) −8.45753 −0.377102 −0.188551 0.982063i \(-0.560379\pi\)
−0.188551 + 0.982063i \(0.560379\pi\)
\(504\) 0 0
\(505\) 28.7680 1.28016
\(506\) 2.56238 + 4.43818i 0.113912 + 0.197301i
\(507\) −0.635584 0.744709i −0.0282273 0.0330737i
\(508\) 8.85060 15.3297i 0.392682 0.680145i
\(509\) −10.5657 −0.468317 −0.234159 0.972198i \(-0.575233\pi\)
−0.234159 + 0.972198i \(0.575233\pi\)
\(510\) 1.19238 + 1.39710i 0.0527994 + 0.0618647i
\(511\) 0 0
\(512\) 17.0071 0.751616
\(513\) −0.933660 37.1699i −0.0412221 1.64109i
\(514\) −3.06335 5.30587i −0.135118 0.234032i
\(515\) −20.6979 −0.912060
\(516\) 5.49346 1.01613i 0.241836 0.0447327i
\(517\) −19.5260 33.8200i −0.858752 1.48740i
\(518\) 0 0
\(519\) −1.41423 + 0.261592i −0.0620778 + 0.0114826i
\(520\) −4.50000 7.79423i −0.197338 0.341800i
\(521\) −9.87788 17.1090i −0.432758 0.749558i 0.564352 0.825534i \(-0.309126\pi\)
−0.997110 + 0.0759760i \(0.975793\pi\)
\(522\) 1.18388 + 0.960078i 0.0518168 + 0.0420215i
\(523\) 16.2641 28.1702i 0.711179 1.23180i −0.253236 0.967405i \(-0.581495\pi\)
0.964415 0.264394i \(-0.0851718\pi\)
\(524\) −4.17984 + 7.23970i −0.182597 + 0.316268i
\(525\) 0 0
\(526\) −0.848970 1.47046i −0.0370168 0.0641150i
\(527\) −11.1833 −0.487153
\(528\) 26.0698 4.82216i 1.13454 0.209858i
\(529\) 3.26320 0.141878
\(530\) 3.29913 5.71426i 0.143305 0.248211i
\(531\) 16.9891 6.50767i 0.737266 0.282409i
\(532\) 0 0
\(533\) 18.8187 32.5950i 0.815130 1.41185i
\(534\) 0.696860 1.96565i 0.0301561 0.0850621i
\(535\) 5.12720 8.88057i 0.221668 0.383940i
\(536\) 3.89536 6.74695i 0.168254 0.291424i
\(537\) 12.9081 2.38763i 0.557027 0.103034i
\(538\) 1.96457 3.40274i 0.0846987 0.146702i
\(539\) 0 0
\(540\) 0.657014 + 26.1563i 0.0282734 + 1.12559i
\(541\) −7.61109 + 13.1828i −0.327226 + 0.566773i −0.981960 0.189087i \(-0.939447\pi\)
0.654734 + 0.755859i \(0.272781\pi\)
\(542\) 3.03638 0.130424
\(543\) −0.236800 + 0.667948i −0.0101621 + 0.0286644i
\(544\) 4.72406 0.202542
\(545\) 9.41234 + 16.3027i 0.403180 + 0.698329i
\(546\) 0 0
\(547\) −11.6871 + 20.2427i −0.499706 + 0.865517i −1.00000 0.000339172i \(-0.999892\pi\)
0.500294 + 0.865856i \(0.333225\pi\)
\(548\) 20.0007 34.6422i 0.854387 1.47984i
\(549\) 3.76466 23.6603i 0.160672 1.00980i
\(550\) −0.858685 1.48729i −0.0366144 0.0634181i
\(551\) −7.60199 13.1670i −0.323856 0.560934i
\(552\) −2.79637 + 7.88779i −0.119021 + 0.335726i
\(553\) 0 0
\(554\) 0.0990521 + 0.171563i 0.00420832 + 0.00728902i
\(555\) 4.83818 + 5.66886i 0.205369 + 0.240629i
\(556\) 30.6214 1.29864
\(557\) −13.8337 23.9606i −0.586151 1.01524i −0.994731 0.102521i \(-0.967309\pi\)
0.408580 0.912723i \(-0.366024\pi\)
\(558\) 3.64165 + 2.95324i 0.154163 + 0.125020i
\(559\) −6.11465 −0.258622
\(560\) 0 0
\(561\) 12.1871 2.25427i 0.514542 0.0951755i
\(562\) 1.24815 0.0526500
\(563\) 4.27912 7.41166i 0.180343 0.312364i −0.761654 0.647984i \(-0.775612\pi\)
0.941998 + 0.335620i \(0.108946\pi\)
\(564\) 10.5000 29.6176i 0.442130 1.24713i
\(565\) 8.97944 + 15.5529i 0.377768 + 0.654313i
\(566\) −1.75855 −0.0739175
\(567\) 0 0
\(568\) −5.88237 −0.246819
\(569\) −6.86389 11.8886i −0.287749 0.498396i 0.685523 0.728051i \(-0.259574\pi\)
−0.973272 + 0.229655i \(0.926240\pi\)
\(570\) −2.56661 + 7.23970i −0.107503 + 0.303238i
\(571\) −5.35868 + 9.28151i −0.224254 + 0.388419i −0.956095 0.293056i \(-0.905328\pi\)
0.731841 + 0.681475i \(0.238661\pi\)
\(572\) −29.9244 −1.25120
\(573\) 27.2916 5.04816i 1.14012 0.210890i
\(574\) 0 0
\(575\) −8.80111 −0.367032
\(576\) 15.5189 + 12.5852i 0.646620 + 0.524384i
\(577\) −22.8177 39.5214i −0.949912 1.64530i −0.745605 0.666389i \(-0.767839\pi\)
−0.204307 0.978907i \(-0.565494\pi\)
\(578\) −3.36500 −0.139965
\(579\) 13.9138 + 16.3027i 0.578236 + 0.677515i
\(580\) 5.34950 + 9.26560i 0.222126 + 0.384733i
\(581\) 0 0
\(582\) −0.423945 + 1.19583i −0.0175731 + 0.0495689i
\(583\) −22.2616 38.5582i −0.921980 1.59692i
\(584\) 3.37323 + 5.84260i 0.139585 + 0.241768i
\(585\) 4.50000 28.2817i 0.186052 1.16931i
\(586\) −0.935657 + 1.62060i −0.0386516 + 0.0669466i
\(587\) −5.10948 + 8.84988i −0.210891 + 0.365274i −0.951994 0.306118i \(-0.900970\pi\)
0.741103 + 0.671392i \(0.234303\pi\)
\(588\) 0 0
\(589\) −23.3840 40.5023i −0.963521 1.66887i
\(590\) −3.75839 −0.154730
\(591\) −13.3703 + 37.7141i −0.549982 + 1.55135i
\(592\) 6.07661 0.249747
\(593\) 5.69804 9.86929i 0.233990 0.405283i −0.724988 0.688761i \(-0.758155\pi\)
0.958979 + 0.283478i \(0.0914883\pi\)
\(594\) −4.56382 2.48426i −0.187256 0.101930i
\(595\) 0 0
\(596\) 5.89411 10.2089i 0.241432 0.418173i
\(597\) −11.4903 + 2.12537i −0.470266 + 0.0869857i
\(598\) 2.25673 3.90877i 0.0922846 0.159842i
\(599\) 17.2873 29.9424i 0.706339 1.22341i −0.259867 0.965644i \(-0.583679\pi\)
0.966206 0.257771i \(-0.0829879\pi\)
\(600\) 0.937096 2.64329i 0.0382568 0.107912i
\(601\) −19.4207 + 33.6376i −0.792187 + 1.37211i 0.132423 + 0.991193i \(0.457724\pi\)
−0.924610 + 0.380915i \(0.875609\pi\)
\(602\) 0 0
\(603\) 23.1494 8.86734i 0.942716 0.361106i
\(604\) 4.36032 7.55230i 0.177419 0.307299i
\(605\) −16.8172 −0.683717
\(606\) −4.52051 + 0.836165i −0.183633 + 0.0339669i
\(607\) 41.3325 1.67763 0.838817 0.544414i \(-0.183248\pi\)
0.838817 + 0.544414i \(0.183248\pi\)
\(608\) 9.87788 + 17.1090i 0.400601 + 0.693861i
\(609\) 0 0
\(610\) −2.47468 + 4.28627i −0.100197 + 0.173546i
\(611\) −17.1969 + 29.7858i −0.695710 + 1.20501i
\(612\) 7.74595 + 6.28167i 0.313111 + 0.253921i
\(613\) 14.3285 + 24.8176i 0.578721 + 1.00237i 0.995626 + 0.0934244i \(0.0297813\pi\)
−0.416905 + 0.908950i \(0.636885\pi\)
\(614\) −2.71057 4.69485i −0.109390 0.189469i
\(615\) 45.1088 8.34384i 1.81896 0.336456i
\(616\) 0 0
\(617\) 16.8518 + 29.1883i 0.678430 + 1.17508i 0.975454 + 0.220205i \(0.0706726\pi\)
−0.297024 + 0.954870i \(0.595994\pi\)
\(618\) 3.25241 0.601602i 0.130831 0.0242000i
\(619\) −1.43807 −0.0578010 −0.0289005 0.999582i \(-0.509201\pi\)
−0.0289005 + 0.999582i \(0.509201\pi\)
\(620\) 16.4552 + 28.5013i 0.660859 + 1.14464i
\(621\) −22.7198 + 13.8894i −0.911715 + 0.557363i
\(622\) −7.72789 −0.309860
\(623\) 0 0
\(624\) −15.1580 17.7605i −0.606806 0.710990i
\(625\) −30.6375 −1.22550
\(626\) 2.90769 5.03626i 0.116215 0.201290i
\(627\) 33.6472 + 39.4242i 1.34374 + 1.57445i
\(628\) 0.999498 + 1.73118i 0.0398843 + 0.0690816i
\(629\) 2.84071 0.113266
\(630\) 0 0
\(631\) −30.7680 −1.22486 −0.612428 0.790527i \(-0.709807\pi\)
−0.612428 + 0.790527i \(0.709807\pi\)
\(632\) −4.63323 8.02500i −0.184300 0.319217i
\(633\) 28.7589 5.31958i 1.14307 0.211434i
\(634\) −0.614360 + 1.06410i −0.0243993 + 0.0422609i
\(635\) −23.6140 −0.937094
\(636\) 11.9710 33.7670i 0.474682 1.33895i
\(637\) 0 0
\(638\) −2.12476 −0.0841202
\(639\) −14.5377 11.7896i −0.575104 0.466388i
\(640\) −9.21946 15.9686i −0.364431 0.631213i
\(641\) 9.23912 0.364923 0.182462 0.983213i \(-0.441593\pi\)
0.182462 + 0.983213i \(0.441593\pi\)
\(642\) −0.547550 + 1.54449i −0.0216101 + 0.0609561i
\(643\) −12.7795 22.1348i −0.503976 0.872912i −0.999989 0.00459728i \(-0.998537\pi\)
0.496013 0.868315i \(-0.334797\pi\)
\(644\) 0 0
\(645\) −4.83818 5.66886i −0.190503 0.223211i
\(646\) 1.46389 + 2.53552i 0.0575958 + 0.0997588i
\(647\) 14.1556 + 24.5181i 0.556512 + 0.963908i 0.997784 + 0.0665343i \(0.0211942\pi\)
−0.441272 + 0.897374i \(0.645472\pi\)
\(648\) −1.75241 8.30245i −0.0688410 0.326151i
\(649\) −12.6803 + 21.9629i −0.497744 + 0.862118i
\(650\) −0.756258 + 1.30988i −0.0296629 + 0.0513776i
\(651\) 0 0
\(652\) 6.63323 + 11.4891i 0.259778 + 0.449948i
\(653\) −8.35021 −0.326769 −0.163385 0.986562i \(-0.552241\pi\)
−0.163385 + 0.986562i \(0.552241\pi\)
\(654\) −1.95287 2.28817i −0.0763634 0.0894744i
\(655\) 11.1521 0.435749
\(656\) 18.7017 32.3922i 0.730177 1.26470i
\(657\) −3.37323 + 21.2001i −0.131602 + 0.827096i
\(658\) 0 0
\(659\) 16.7862 29.0745i 0.653897 1.13258i −0.328272 0.944583i \(-0.606466\pi\)
0.982169 0.188000i \(-0.0602005\pi\)
\(660\) −23.6774 27.7427i −0.921643 1.07988i
\(661\) −8.47668 + 14.6820i −0.329705 + 0.571065i −0.982453 0.186509i \(-0.940283\pi\)
0.652748 + 0.757575i \(0.273616\pi\)
\(662\) 1.39862 2.42249i 0.0543591 0.0941527i
\(663\) −7.08609 8.30272i −0.275201 0.322451i
\(664\) 3.25021 5.62952i 0.126133 0.218468i
\(665\) 0 0
\(666\) −0.925025 0.750160i −0.0358440 0.0290681i
\(667\) −5.44445 + 9.43007i −0.210810 + 0.365134i
\(668\) −34.9597 −1.35263
\(669\) 5.06144 + 5.93045i 0.195686 + 0.229284i
\(670\) −5.12118 −0.197848
\(671\) 16.6984 + 28.9225i 0.644636 + 1.11654i
\(672\) 0 0
\(673\) 22.2157 38.4788i 0.856354 1.48325i −0.0190299 0.999819i \(-0.506058\pi\)
0.875384 0.483429i \(-0.160609\pi\)
\(674\) 4.02859 6.97772i 0.155175 0.268772i
\(675\) 7.61369 4.65451i 0.293051 0.179152i
\(676\) 0.549100 + 0.951068i 0.0211192 + 0.0365796i
\(677\) −7.18681 12.4479i −0.276212 0.478412i 0.694229 0.719755i \(-0.255746\pi\)
−0.970440 + 0.241342i \(0.922412\pi\)
\(678\) −1.86306 2.18293i −0.0715502 0.0838349i
\(679\) 0 0
\(680\) −2.09058 3.62099i −0.0801701 0.138859i
\(681\) 3.50972 9.89994i 0.134493 0.379367i
\(682\) −6.53585 −0.250271
\(683\) 16.1546 + 27.9806i 0.618138 + 1.07065i 0.989825 + 0.142289i \(0.0454462\pi\)
−0.371687 + 0.928358i \(0.621220\pi\)
\(684\) −6.55357 + 41.1881i −0.250582 + 1.57487i
\(685\) −53.3632 −2.03890
\(686\) 0 0
\(687\) 6.39480 18.0380i 0.243977 0.688192i
\(688\) −6.07661 −0.231669
\(689\) −19.6061 + 33.9588i −0.746934 + 1.29373i
\(690\) 5.40942 1.00059i 0.205933 0.0380917i
\(691\) −14.4981 25.1114i −0.551533 0.955283i −0.998164 0.0605650i \(-0.980710\pi\)
0.446631 0.894718i \(-0.352624\pi\)
\(692\) 1.61323 0.0613259
\(693\) 0 0
\(694\) 6.53078 0.247905
\(695\) −20.4250 35.3772i −0.774765 1.34193i
\(696\) −2.25249 2.63923i −0.0853806 0.100040i
\(697\) 8.74269 15.1428i 0.331153 0.573574i
\(698\) 5.47997 0.207420
\(699\) 9.15093 + 10.7221i 0.346120 + 0.405546i
\(700\) 0 0
\(701\) −26.3912 −0.996783 −0.498392 0.866952i \(-0.666076\pi\)
−0.498392 + 0.866952i \(0.666076\pi\)
\(702\) 0.114915 + 4.57489i 0.00433720 + 0.172668i
\(703\) 5.93984 + 10.2881i 0.224025 + 0.388023i
\(704\) −27.8525 −1.04973
\(705\) −41.2211 + 7.62473i −1.55248 + 0.287164i
\(706\) −1.22782 2.12664i −0.0462095 0.0800372i
\(707\) 0 0
\(708\) −20.0663 + 3.71170i −0.754139 + 0.139494i
\(709\) 3.94282 + 6.82916i 0.148076 + 0.256475i 0.930516 0.366251i \(-0.119359\pi\)
−0.782441 + 0.622725i \(0.786025\pi\)
\(710\) 1.93337 + 3.34870i 0.0725581 + 0.125674i
\(711\) 4.63323 29.1191i 0.173760 1.09205i
\(712\) −2.37373 + 4.11142i −0.0889592 + 0.154082i
\(713\) −16.7473 + 29.0073i −0.627193 + 1.08633i
\(714\) 0 0
\(715\) 19.9601 + 34.5718i 0.746464 + 1.29291i
\(716\) −14.7245 −0.550281
\(717\) 36.0431 6.66695i 1.34606 0.248982i
\(718\) 2.41531 0.0901385
\(719\) −16.5754 + 28.7095i −0.618159 + 1.07068i 0.371663 + 0.928368i \(0.378788\pi\)
−0.989822 + 0.142314i \(0.954546\pi\)
\(720\) 4.47200 28.1058i 0.166662 1.04744i
\(721\) 0 0
\(722\) −3.85021 + 6.66877i −0.143290 + 0.248186i
\(723\) −7.92395 + 22.3513i −0.294695 + 0.831253i
\(724\) 0.397460 0.688420i 0.0147715 0.0255849i
\(725\) 1.82450 3.16013i 0.0677603 0.117364i
\(726\) 2.64260 0.488805i 0.0980761 0.0181413i
\(727\) 16.5502 28.6658i 0.613814 1.06316i −0.376777 0.926304i \(-0.622968\pi\)
0.990591 0.136853i \(-0.0436989\pi\)
\(728\) 0 0
\(729\) 12.3090 24.0310i 0.455890 0.890036i
\(730\) 2.21737 3.84060i 0.0820685 0.142147i
\(731\) −2.84071 −0.105067
\(732\) −8.97949 + 25.3287i −0.331892 + 0.936175i
\(733\) 44.5589 1.64582 0.822911 0.568170i \(-0.192349\pi\)
0.822911 + 0.568170i \(0.192349\pi\)
\(734\) 0.929636 + 1.61018i 0.0343135 + 0.0594327i
\(735\) 0 0
\(736\) 7.07442 12.2533i 0.260767 0.451661i
\(737\) −17.2781 + 29.9266i −0.636448 + 1.10236i
\(738\) −6.84573 + 2.62225i −0.251995 + 0.0965262i
\(739\) −19.9045 34.4756i −0.732199 1.26821i −0.955941 0.293558i \(-0.905161\pi\)
0.223742 0.974648i \(-0.428173\pi\)
\(740\) −4.17984 7.23970i −0.153654 0.266137i
\(741\) 15.2529 43.0242i 0.560329 1.58053i
\(742\) 0 0
\(743\) −5.37072 9.30237i −0.197033 0.341271i 0.750532 0.660834i \(-0.229797\pi\)
−0.947565 + 0.319563i \(0.896464\pi\)
\(744\) −6.92876 8.11837i −0.254021 0.297634i
\(745\) −15.7259 −0.576152
\(746\) −2.88276 4.99309i −0.105545 0.182810i
\(747\) 19.3154 7.39873i 0.706713 0.270706i
\(748\) −13.9021 −0.508310
\(749\) 0 0
\(750\) 3.46496 0.640919i 0.126523 0.0234031i
\(751\) 19.7141 0.719378 0.359689 0.933072i \(-0.382883\pi\)
0.359689 + 0.933072i \(0.382883\pi\)
\(752\) −17.0899 + 29.6005i −0.623203 + 1.07942i
\(753\) −8.79931 + 24.8205i −0.320665 + 0.904508i
\(754\) 0.935657 + 1.62060i 0.0340746 + 0.0590189i
\(755\) −11.6336 −0.423391
\(756\) 0 0
\(757\) 35.3549 1.28499 0.642497 0.766288i \(-0.277898\pi\)
0.642497 + 0.766288i \(0.277898\pi\)
\(758\) 1.59712 + 2.76629i 0.0580100 + 0.100476i
\(759\) 12.4035 34.9868i 0.450218 1.26994i
\(760\) 8.74269 15.1428i 0.317131 0.549286i
\(761\) 39.1144 1.41790 0.708948 0.705261i \(-0.249170\pi\)
0.708948 + 0.705261i \(0.249170\pi\)
\(762\) 3.71063 0.686360i 0.134422 0.0248642i
\(763\) 0 0
\(764\) −31.1319 −1.12631
\(765\) 2.09058 13.1389i 0.0755851 0.475039i
\(766\) 1.10480 + 1.91357i 0.0399180 + 0.0691399i
\(767\) 22.3354 0.806486
\(768\) −13.0647 15.3078i −0.471432 0.552373i
\(769\) −18.9240 32.7773i −0.682415 1.18198i −0.974242 0.225507i \(-0.927596\pi\)
0.291826 0.956471i \(-0.405737\pi\)
\(770\) 0 0
\(771\) −14.8285 + 41.8270i −0.534034 + 1.50636i
\(772\) −12.0205 20.8201i −0.432628 0.749333i
\(773\) 14.9133 + 25.8305i 0.536393 + 0.929059i 0.999095 + 0.0425453i \(0.0135467\pi\)
−0.462702 + 0.886514i \(0.653120\pi\)
\(774\) 0.925025 + 0.750160i 0.0332493 + 0.0269639i
\(775\) 5.61224 9.72068i 0.201598 0.349177i
\(776\) 1.44409 2.50124i 0.0518399 0.0897894i
\(777\) 0 0
\(778\) −1.24923 2.16373i −0.0447870 0.0775734i
\(779\) 73.1229 2.61990
\(780\) −10.7334 + 30.2760i −0.384318 + 1.08406i