Properties

Label 441.2.g.g.79.4
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 79.4
Root \(-1.29589 + 0.748185i\) of defining polynomial
Character \(\chi\) \(=\) 441.79
Dual form 441.2.g.g.67.4

$q$-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 \(-0.303232\pi\)
0.579542 + 0.814943i \(0.303232\pi\)
\(6\) −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 \(0.00396730\pi\)
−0.489168 + 0.872190i \(0.662699\pi\)
\(14\) 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 0.950926 0.309419i \(-0.100135\pi\)
−0.743428 + 0.668816i \(0.766801\pi\)
\(18\) −0.112725 + 0.708458i −0.0265696 + 0.166985i
\(19\) −3.57780 + 6.19694i −0.820805 + 1.42168i 0.0842790 + 0.996442i \(0.473141\pi\)
−0.905084 + 0.425233i \(0.860192\pi\)
\(20\) 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 \(0.366333\pi\)
−0.994631 + 0.103486i \(0.967000\pi\)
\(32\) −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 \(-0.872576\pi\)
0.122972 0.992410i \(-0.460758\pi\)
\(42\) 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 \(0.0718146\pi\)
−0.293596 + 0.955930i \(0.594852\pi\)
\(48\) −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 −0.598318 0.801259i \(-0.704164\pi\)
0.993069 + 0.117529i \(0.0374972\pi\)
\(60\) −5.66182 6.63392i −0.730938 0.856435i
\(61\) −3.99298 6.91605i −0.511249 0.885509i −0.999915 0.0130384i \(-0.995850\pi\)
0.488666 0.872471i \(-0.337484\pi\)
\(62\) 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 0.995814 0.0914022i \(-0.0291349\pi\)
−0.577064 + 0.816699i \(0.695802\pi\)
\(74\) 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 −0.612436 0.790521i \(-0.709810\pi\)
0.990829 + 0.135124i \(0.0431434\pi\)
\(84\) 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 −0.968053 0.250745i \(-0.919324\pi\)
0.701178 + 0.712986i \(0.252658\pi\)
\(90\) −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 −0.777730 0.628599i \(-0.783629\pi\)
0.933247 + 0.359234i \(0.116962\pi\)
\(98\) 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 \(-0.313777\pi\)
0.552229 + 0.833692i \(0.313777\pi\)
\(102\) −0.460060 0.539049i −0.0455527 0.0533738i
\(103\) −7.98597 −0.786881 −0.393440 0.919350i \(-0.628715\pi\)
−0.393440 + 0.919350i \(0.628715\pi\)
\(104\) −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 \(-0.439809\pi\)
0.187971 + 0.982175i \(0.439809\pi\)
\(132\) −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 \(-0.933634\pi\)
0.309914 0.950765i \(-0.399700\pi\)
\(140\) 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 −0.844766 0.535136i \(-0.820260\pi\)
0.885824 + 0.464021i \(0.153594\pi\)
\(158\) 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 \(0.0784701\pi\)
−0.273546 + 0.961859i \(0.588197\pi\)
\(168\) 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 0.849811 0.527087i \(-0.176716\pi\)
−0.881377 + 0.472414i \(0.843383\pi\)
\(174\) −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 \(-0.504840\pi\)
−0.0152062 + 0.999884i \(0.504840\pi\)
\(182\) 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 0.721341 0.692580i \(-0.243526\pi\)
−0.960463 + 0.278409i \(0.910193\pi\)
\(200\) −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 −0.931492 0.363762i \(-0.881492\pi\)
0.780773 + 0.624815i \(0.214825\pi\)
\(224\) 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 \(-0.435499\pi\)
0.201251 + 0.979540i \(0.435499\pi\)
\(228\) 23.6774 4.37965i 1.56808 0.290049i
\(229\) 11.0493 0.730159 0.365080 0.930976i \(-0.381042\pi\)
0.365080 + 0.930976i \(0.381042\pi\)
\(230\) 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 \(-0.645366\pi\)
−0.440972 + 0.897521i \(0.645366\pi\)
\(242\) −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 \(-0.659303\pi\)
−0.479833 + 0.877360i \(0.659303\pi\)
\(252\) 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 \(-0.794697\pi\)
−0.799112 + 0.601182i \(0.794697\pi\)
\(258\) −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 \(-0.999661\pi\)
0.499078 0.866557i \(-0.333672\pi\)
\(270\) 2.82846 + 1.53964i 0.172135 + 0.0936993i
\(271\) 6.34899 10.9968i 0.385674 0.668007i −0.606189 0.795321i \(-0.707302\pi\)
0.991862 + 0.127314i \(0.0406357\pi\)
\(272\) 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 −0.954374 0.298614i \(-0.903476\pi\)
0.735794 + 0.677205i \(0.236809\pi\)
\(284\) 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 0.957391 0.288795i \(-0.0932545\pi\)
−0.728799 + 0.684728i \(0.759921\pi\)
\(294\) 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 \(-0.723955\pi\)
−0.646948 + 0.762534i \(0.723955\pi\)
\(308\) 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 \(0.535491\pi\)
−0.805015 + 0.593255i \(0.797843\pi\)
\(312\) −5.91423 + 1.09396i −0.334827 + 0.0619335i
\(313\) −12.1598 21.0614i −0.687312 1.19046i −0.972704 0.232048i \(-0.925457\pi\)
0.285392 0.958411i \(-0.407876\pi\)
\(314\) −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 \(-0.623152\pi\)
0.990670 0.136281i \(-0.0435150\pi\)
\(350\) 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 \(-0.588112\pi\)
−0.273290 + 0.961932i \(0.588112\pi\)
\(354\) −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 \(-0.434952\pi\)
0.202935 + 0.979192i \(0.434952\pi\)
\(368\) 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 \(-0.424137\pi\)
0.236081 + 0.971733i \(0.424137\pi\)
\(384\) 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 −0.871114 0.491082i \(-0.836602\pi\)
0.860846 + 0.508866i \(0.169935\pi\)
\(398\) −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 −0.931769 0.363051i \(-0.881735\pi\)
0.780296 + 0.625410i \(0.215068\pi\)
\(410\) −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 0.884482 0.466574i \(-0.154512\pi\)
−0.846306 + 0.532697i \(0.821179\pi\)
\(420\) 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 \(-0.601986\pi\)
−0.314945 + 0.949110i \(0.601986\pi\)
\(434\) 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 0.997996 0.0632744i \(-0.0201543\pi\)
−0.553795 + 0.832653i \(0.686821\pi\)
\(440\) −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 −0.524811 0.851219i \(-0.675864\pi\)
0.999583 + 0.0288903i \(0.00919735\pi\)
\(462\) 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 \(-0.638880\pi\)
0.996192 0.0871825i \(-0.0277863\pi\)
\(468\) −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 \(-0.418392\pi\)
0.253579 + 0.967315i \(0.418392\pi\)
\(480\) 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 \(-0.439621\pi\)
0.188551 + 0.982063i \(0.439621\pi\)
\(504\) 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 \(-0.424767\pi\)
0.234159 + 0.972198i \(0.424767\pi\)
\(510\) −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 0.997110 0.0759760i \(-0.0242072\pi\)
−0.564352 + 0.825534i \(0.690874\pi\)
\(522\) 1.18388 + 0.960078i 0.0518168 + 0.0420215i
\(523\) −16.2641 + 28.1702i −0.711179 + 1.23180i 0.253236 + 0.967405i \(0.418505\pi\)
−0.964415 + 0.264394i \(0.914828\pi\)
\(524\) 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 −0.941998 0.335620i \(-0.891054\pi\)
0.761654 + 0.647984i \(0.224388\pi\)
\(564\) 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 \(0.232161\pi\)
0.204307 + 0.978907i \(0.434506\pi\)
\(578\) −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 −0.741103 0.671392i \(-0.765697\pi\)
0.951994 + 0.306118i \(0.0990302\pi\)
\(588\) 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 −0.958979 0.283478i \(-0.908512\pi\)
0.724988 + 0.688761i \(0.241845\pi\)
\(594\) 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 \(-0.542276\pi\)
0.924610 0.380915i \(-0.124391\pi\)
\(602\) 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 \(-0.816752\pi\)
−0.838817 + 0.544414i \(0.816752\pi\)
\(608\) −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 \(-0.490799\pi\)
0.0289005 + 0.999582i \(0.490799\pi\)
\(620\) 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 \(0.00146337\pi\)
−0.496013 + 0.868315i \(0.665203\pi\)
\(644\) 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 \(-0.978806\pi\)
0.441272 0.897374i \(-0.354528\pi\)
\(648\) −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 −0.652748 0.757575i \(-0.726384\pi\)
0.982453 + 0.186509i \(0.0597175\pi\)
\(662\) 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 0.970440 0.241342i \(-0.0775876\pi\)
−0.694229 + 0.719755i \(0.744254\pi\)
\(678\) 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 \(0.0192902\pi\)
−0.446631 + 0.894718i \(0.647376\pi\)
\(692\) −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 \(-0.621212\pi\)
0.989822 0.142314i \(-0.0454544\pi\)
\(720\) −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 \(0.377032\pi\)
−0.990591 + 0.136853i \(0.956301\pi\)
\(728\) 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 \(-0.807651\pi\)
−0.822911 + 0.568170i \(0.807651\pi\)
\(734\) −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 \(-0.750830\pi\)
−0.708948 + 0.705261i \(0.750830\pi\)
\(762\) −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 \(0.0724038\pi\)
−0.291826 + 0.956471i \(0.594263\pi\)
\(770\) 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 \(-0.986453\pi\)
0.462702 0.886514i \(-0.346880\pi\)
\(774\) 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
\(781\) 26.