Properties

Label 441.2.g.f.67.3
Level $441$
Weight $2$
Character 441.67
Analytic conductor $3.521$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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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: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
Defining polynomial: \(x^{10} - 2 x^{9} + 9 x^{8} - 8 x^{7} + 40 x^{6} - 36 x^{5} + 90 x^{4} - 3 x^{3} + 36 x^{2} - 9 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.3
Root \(0.247934 - 0.429435i\) of defining polynomial
Character \(\chi\) \(=\) 441.67
Dual form 441.2.g.f.79.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.247934 - 0.429435i) q^{2} +(-1.59836 + 0.667278i) q^{3} +(0.877057 + 1.51911i) q^{4} +3.69258 q^{5} +(-0.109735 + 0.851830i) q^{6} +1.86155 q^{8} +(2.10948 - 2.13309i) q^{9} +O(q^{10})\) \(q+(0.247934 - 0.429435i) q^{2} +(-1.59836 + 0.667278i) q^{3} +(0.877057 + 1.51911i) q^{4} +3.69258 q^{5} +(-0.109735 + 0.851830i) q^{6} +1.86155 q^{8} +(2.10948 - 2.13309i) q^{9} +(0.915516 - 1.58572i) q^{10} -0.892568 q^{11} +(-2.41552 - 1.84283i) q^{12} +(-0.598355 + 1.03638i) q^{13} +(-5.90205 + 2.46398i) q^{15} +(-1.29257 + 2.23880i) q^{16} +(0.124991 - 0.216492i) q^{17} +(-0.393012 - 1.43475i) q^{18} +(-1.40414 - 2.43204i) q^{19} +(3.23860 + 5.60943i) q^{20} +(-0.221298 + 0.383300i) q^{22} +2.47772 q^{23} +(-2.97541 + 1.24217i) q^{24} +8.63514 q^{25} +(0.296705 + 0.513909i) q^{26} +(-1.94833 + 4.81705i) q^{27} +(2.07128 + 3.58755i) q^{29} +(-0.405204 + 3.14545i) q^{30} +(1.79257 + 3.10483i) q^{31} +(2.50249 + 4.33444i) q^{32} +(1.42664 - 0.595591i) q^{33} +(-0.0619793 - 0.107351i) q^{34} +(5.09054 + 1.33368i) q^{36} +(-2.36568 - 4.09747i) q^{37} -1.39253 q^{38} +(0.264830 - 2.05578i) q^{39} +6.87391 q^{40} +(2.39093 - 4.14121i) q^{41} +(-4.98928 - 8.64169i) q^{43} +(-0.782834 - 1.35591i) q^{44} +(7.78942 - 7.87662i) q^{45} +(0.614310 - 1.06402i) q^{46} +(-5.08653 + 8.81013i) q^{47} +(0.572088 - 4.44091i) q^{48} +(2.14095 - 3.70823i) q^{50} +(-0.0553208 + 0.429435i) q^{51} -2.09917 q^{52} +(-4.94465 + 8.56438i) q^{53} +(1.58555 + 2.03099i) q^{54} -3.29588 q^{55} +(3.86715 + 2.95031i) q^{57} +2.05416 q^{58} +(0.906186 + 1.56956i) q^{59} +(-8.91949 - 6.80481i) q^{60} +(5.40205 - 9.35663i) q^{61} +1.77776 q^{62} -2.68848 q^{64} +(-2.20948 + 3.82692i) q^{65} +(0.0979457 - 0.760316i) q^{66} +(-0.514685 - 0.891460i) q^{67} +0.438499 q^{68} +(-3.96027 + 1.65332i) q^{69} -4.94533 q^{71} +(3.92690 - 3.97085i) q^{72} +(0.915262 - 1.58528i) q^{73} -2.34613 q^{74} +(-13.8020 + 5.76204i) q^{75} +(2.46302 - 4.26607i) q^{76} +(-0.817161 - 0.623424i) q^{78} +(0.899562 - 1.55809i) q^{79} +(-4.77293 + 8.26696i) q^{80} +(-0.100184 - 8.99944i) q^{81} +(-1.18559 - 2.05350i) q^{82} +(-6.16156 - 10.6721i) q^{83} +(0.461541 - 0.799412i) q^{85} -4.94806 q^{86} +(-5.70453 - 4.35207i) q^{87} -1.66156 q^{88} +(1.20370 + 2.08488i) q^{89} +(-1.45123 - 5.29793i) q^{90} +(2.17310 + 3.76392i) q^{92} +(-4.93695 - 3.76648i) q^{93} +(2.52225 + 4.36867i) q^{94} +(-5.18489 - 8.98049i) q^{95} +(-6.89215 - 5.25813i) q^{96} +(-5.52210 - 9.56456i) q^{97} +(-1.88286 + 1.90393i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{2} - 2q^{3} - 4q^{4} + 8q^{5} + 2q^{6} - 6q^{8} - 4q^{9} + O(q^{10}) \) \( 10q + 2q^{2} - 2q^{3} - 4q^{4} + 8q^{5} + 2q^{6} - 6q^{8} - 4q^{9} + 7q^{10} - 8q^{11} - 22q^{12} + 8q^{13} - 19q^{15} + 2q^{16} - 12q^{17} - 2q^{18} - q^{19} - 5q^{20} - q^{22} - 6q^{23} - 3q^{24} + 2q^{25} - 11q^{26} + 7q^{27} + 7q^{29} - 26q^{30} + 3q^{31} - 2q^{32} + q^{33} - 3q^{34} + 34q^{36} + 40q^{38} + 20q^{39} - 6q^{40} - 5q^{41} - 7q^{43} - 10q^{44} + q^{45} + 3q^{46} - 27q^{47} + 5q^{48} + 19q^{50} + 24q^{51} - 20q^{52} - 21q^{53} + 53q^{54} - 4q^{55} - 4q^{57} + 20q^{58} - 30q^{59} - 41q^{60} + 14q^{61} + 12q^{62} - 50q^{64} - 11q^{65} + 41q^{66} - 2q^{67} + 54q^{68} - 15q^{69} - 6q^{71} + 48q^{72} - 15q^{73} + 72q^{74} - 31q^{75} - 5q^{76} - 20q^{78} - 4q^{79} - 20q^{80} + 8q^{81} + 5q^{82} - 9q^{83} - 6q^{85} + 16q^{86} - 32q^{87} + 36q^{88} - 28q^{89} - 28q^{90} + 27q^{92} - 12q^{93} + 3q^{94} - 14q^{95} + q^{96} + 12q^{97} + 35q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.247934 0.429435i 0.175316 0.303656i −0.764955 0.644084i \(-0.777239\pi\)
0.940271 + 0.340428i \(0.110572\pi\)
\(3\) −1.59836 + 0.667278i −0.922811 + 0.385253i
\(4\) 0.877057 + 1.51911i 0.438529 + 0.759554i
\(5\) 3.69258 1.65137 0.825686 0.564130i \(-0.190788\pi\)
0.825686 + 0.564130i \(0.190788\pi\)
\(6\) −0.109735 + 0.851830i −0.0447990 + 0.347758i
\(7\) 0 0
\(8\) 1.86155 0.658156
\(9\) 2.10948 2.13309i 0.703160 0.711031i
\(10\) 0.915516 1.58572i 0.289512 0.501449i
\(11\) −0.892568 −0.269119 −0.134560 0.990905i \(-0.542962\pi\)
−0.134560 + 0.990905i \(0.542962\pi\)
\(12\) −2.41552 1.84283i −0.697300 0.531980i
\(13\) −0.598355 + 1.03638i −0.165954 + 0.287441i −0.936994 0.349346i \(-0.886404\pi\)
0.771040 + 0.636787i \(0.219737\pi\)
\(14\) 0 0
\(15\) −5.90205 + 2.46398i −1.52390 + 0.636196i
\(16\) −1.29257 + 2.23880i −0.323143 + 0.559701i
\(17\) 0.124991 0.216492i 0.0303149 0.0525069i −0.850470 0.526024i \(-0.823682\pi\)
0.880785 + 0.473517i \(0.157016\pi\)
\(18\) −0.393012 1.43475i −0.0926339 0.338174i
\(19\) −1.40414 2.43204i −0.322131 0.557948i 0.658796 0.752321i \(-0.271066\pi\)
−0.980928 + 0.194374i \(0.937733\pi\)
\(20\) 3.23860 + 5.60943i 0.724174 + 1.25431i
\(21\) 0 0
\(22\) −0.221298 + 0.383300i −0.0471809 + 0.0817198i
\(23\) 2.47772 0.516639 0.258320 0.966059i \(-0.416831\pi\)
0.258320 + 0.966059i \(0.416831\pi\)
\(24\) −2.97541 + 1.24217i −0.607354 + 0.253557i
\(25\) 8.63514 1.72703
\(26\) 0.296705 + 0.513909i 0.0581887 + 0.100786i
\(27\) −1.94833 + 4.81705i −0.374957 + 0.927042i
\(28\) 0 0
\(29\) 2.07128 + 3.58755i 0.384626 + 0.666192i 0.991717 0.128440i \(-0.0409970\pi\)
−0.607091 + 0.794632i \(0.707664\pi\)
\(30\) −0.405204 + 3.14545i −0.0739798 + 0.574278i
\(31\) 1.79257 + 3.10483i 0.321956 + 0.557644i 0.980892 0.194555i \(-0.0623264\pi\)
−0.658936 + 0.752199i \(0.728993\pi\)
\(32\) 2.50249 + 4.33444i 0.442382 + 0.766229i
\(33\) 1.42664 0.595591i 0.248346 0.103679i
\(34\) −0.0619793 0.107351i −0.0106294 0.0184106i
\(35\) 0 0
\(36\) 5.09054 + 1.33368i 0.848423 + 0.222280i
\(37\) −2.36568 4.09747i −0.388915 0.673621i 0.603389 0.797447i \(-0.293817\pi\)
−0.992304 + 0.123826i \(0.960483\pi\)
\(38\) −1.39253 −0.225899
\(39\) 0.264830 2.05578i 0.0424067 0.329188i
\(40\) 6.87391 1.08686
\(41\) 2.39093 4.14121i 0.373400 0.646748i −0.616686 0.787209i \(-0.711525\pi\)
0.990086 + 0.140461i \(0.0448584\pi\)
\(42\) 0 0
\(43\) −4.98928 8.64169i −0.760859 1.31785i −0.942408 0.334464i \(-0.891445\pi\)
0.181550 0.983382i \(-0.441889\pi\)
\(44\) −0.782834 1.35591i −0.118017 0.204411i
\(45\) 7.78942 7.87662i 1.16118 1.17418i
\(46\) 0.614310 1.06402i 0.0905751 0.156881i
\(47\) −5.08653 + 8.81013i −0.741947 + 1.28509i 0.209661 + 0.977774i \(0.432764\pi\)
−0.951608 + 0.307316i \(0.900569\pi\)
\(48\) 0.572088 4.44091i 0.0825738 0.640990i
\(49\) 0 0
\(50\) 2.14095 3.70823i 0.302776 0.524423i
\(51\) −0.0553208 + 0.429435i −0.00774646 + 0.0601329i
\(52\) −2.09917 −0.291102
\(53\) −4.94465 + 8.56438i −0.679199 + 1.17641i 0.296023 + 0.955181i \(0.404339\pi\)
−0.975222 + 0.221227i \(0.928994\pi\)
\(54\) 1.58555 + 2.03099i 0.215766 + 0.276383i
\(55\) −3.29588 −0.444416
\(56\) 0 0
\(57\) 3.86715 + 2.95031i 0.512217 + 0.390778i
\(58\) 2.05416 0.269724
\(59\) 0.906186 + 1.56956i 0.117975 + 0.204339i 0.918965 0.394339i \(-0.129026\pi\)
−0.800990 + 0.598678i \(0.795693\pi\)
\(60\) −8.91949 6.80481i −1.15150 0.878497i
\(61\) 5.40205 9.35663i 0.691662 1.19799i −0.279631 0.960108i \(-0.590212\pi\)
0.971293 0.237886i \(-0.0764546\pi\)
\(62\) 1.77776 0.225776
\(63\) 0 0
\(64\) −2.68848 −0.336060
\(65\) −2.20948 + 3.82692i −0.274052 + 0.474671i
\(66\) 0.0979457 0.760316i 0.0120563 0.0935885i
\(67\) −0.514685 0.891460i −0.0628787 0.108909i 0.832872 0.553465i \(-0.186695\pi\)
−0.895751 + 0.444556i \(0.853361\pi\)
\(68\) 0.438499 0.0531758
\(69\) −3.96027 + 1.65332i −0.476761 + 0.199037i
\(70\) 0 0
\(71\) −4.94533 −0.586903 −0.293451 0.955974i \(-0.594804\pi\)
−0.293451 + 0.955974i \(0.594804\pi\)
\(72\) 3.92690 3.97085i 0.462789 0.467970i
\(73\) 0.915262 1.58528i 0.107123 0.185543i −0.807480 0.589894i \(-0.799169\pi\)
0.914604 + 0.404351i \(0.132503\pi\)
\(74\) −2.34613 −0.272732
\(75\) −13.8020 + 5.76204i −1.59372 + 0.665343i
\(76\) 2.46302 4.26607i 0.282527 0.489352i
\(77\) 0 0
\(78\) −0.817161 0.623424i −0.0925253 0.0705889i
\(79\) 0.899562 1.55809i 0.101209 0.175298i −0.810974 0.585082i \(-0.801062\pi\)
0.912183 + 0.409783i \(0.134396\pi\)
\(80\) −4.77293 + 8.26696i −0.533630 + 0.924274i
\(81\) −0.100184 8.99944i −0.0111316 0.999938i
\(82\) −1.18559 2.05350i −0.130926 0.226771i
\(83\) −6.16156 10.6721i −0.676319 1.17142i −0.976082 0.217405i \(-0.930241\pi\)
0.299763 0.954014i \(-0.403092\pi\)
\(84\) 0 0
\(85\) 0.461541 0.799412i 0.0500611 0.0867084i
\(86\) −4.94806 −0.533563
\(87\) −5.70453 4.35207i −0.611590 0.466591i
\(88\) −1.66156 −0.177123
\(89\) 1.20370 + 2.08488i 0.127592 + 0.220997i 0.922743 0.385415i \(-0.125942\pi\)
−0.795151 + 0.606412i \(0.792608\pi\)
\(90\) −1.45123 5.29793i −0.152973 0.558451i
\(91\) 0 0
\(92\) 2.17310 + 3.76392i 0.226561 + 0.392416i
\(93\) −4.93695 3.76648i −0.511938 0.390565i
\(94\) 2.52225 + 4.36867i 0.260150 + 0.450593i
\(95\) −5.18489 8.98049i −0.531958 0.921379i
\(96\) −6.89215 5.25813i −0.703427 0.536655i
\(97\) −5.52210 9.56456i −0.560684 0.971134i −0.997437 0.0715522i \(-0.977205\pi\)
0.436752 0.899582i \(-0.356129\pi\)
\(98\) 0 0
\(99\) −1.88286 + 1.90393i −0.189234 + 0.191352i
\(100\) 7.57351 + 13.1177i 0.757351 + 1.31177i
\(101\) 2.59964 0.258674 0.129337 0.991601i \(-0.458715\pi\)
0.129337 + 0.991601i \(0.458715\pi\)
\(102\) 0.170698 + 0.130228i 0.0169016 + 0.0128945i
\(103\) −9.71155 −0.956908 −0.478454 0.878113i \(-0.658803\pi\)
−0.478454 + 0.878113i \(0.658803\pi\)
\(104\) −1.11387 + 1.92927i −0.109224 + 0.189181i
\(105\) 0 0
\(106\) 2.45189 + 4.24680i 0.238149 + 0.412486i
\(107\) −5.45025 9.44012i −0.526896 0.912610i −0.999509 0.0313403i \(-0.990022\pi\)
0.472613 0.881270i \(-0.343311\pi\)
\(108\) −9.02642 + 1.26510i −0.868568 + 0.121735i
\(109\) −1.06096 + 1.83764i −0.101622 + 0.176014i −0.912353 0.409404i \(-0.865737\pi\)
0.810731 + 0.585419i \(0.199070\pi\)
\(110\) −0.817161 + 1.41536i −0.0779132 + 0.134950i
\(111\) 6.51535 + 4.97066i 0.618410 + 0.471794i
\(112\) 0 0
\(113\) 7.91318 13.7060i 0.744409 1.28935i −0.206061 0.978539i \(-0.566065\pi\)
0.950470 0.310816i \(-0.100602\pi\)
\(114\) 2.22576 0.929207i 0.208462 0.0870282i
\(115\) 9.14916 0.853164
\(116\) −3.63325 + 6.29298i −0.337339 + 0.584289i
\(117\) 0.948482 + 3.46258i 0.0876872 + 0.320115i
\(118\) 0.898698 0.0827318
\(119\) 0 0
\(120\) −10.9869 + 4.58681i −1.00297 + 0.418716i
\(121\) −10.2033 −0.927575
\(122\) −2.67871 4.63966i −0.242519 0.420055i
\(123\) −1.05822 + 8.21454i −0.0954162 + 0.740680i
\(124\) −3.14438 + 5.44623i −0.282374 + 0.489086i
\(125\) 13.4230 1.20059
\(126\) 0 0
\(127\) −1.26946 −0.112647 −0.0563233 0.998413i \(-0.517938\pi\)
−0.0563233 + 0.998413i \(0.517938\pi\)
\(128\) −5.67155 + 9.82342i −0.501299 + 0.868275i
\(129\) 13.7411 + 10.4833i 1.20983 + 0.923000i
\(130\) 1.09561 + 1.89765i 0.0960912 + 0.166435i
\(131\) 15.0289 1.31308 0.656540 0.754291i \(-0.272019\pi\)
0.656540 + 0.754291i \(0.272019\pi\)
\(132\) 2.15601 + 1.64485i 0.187657 + 0.143166i
\(133\) 0 0
\(134\) −0.510432 −0.0440946
\(135\) −7.19437 + 17.7873i −0.619193 + 1.53089i
\(136\) 0.232677 0.403009i 0.0199519 0.0345577i
\(137\) −0.488493 −0.0417347 −0.0208674 0.999782i \(-0.506643\pi\)
−0.0208674 + 0.999782i \(0.506643\pi\)
\(138\) −0.271891 + 2.11059i −0.0231449 + 0.179666i
\(139\) 4.93487 8.54745i 0.418570 0.724985i −0.577226 0.816585i \(-0.695865\pi\)
0.995796 + 0.0915997i \(0.0291980\pi\)
\(140\) 0 0
\(141\) 2.25128 17.4759i 0.189592 1.47173i
\(142\) −1.22612 + 2.12370i −0.102893 + 0.178217i
\(143\) 0.534073 0.925042i 0.0446614 0.0773559i
\(144\) 2.04892 + 7.47989i 0.170743 + 0.623325i
\(145\) 7.64835 + 13.2473i 0.635161 + 1.10013i
\(146\) −0.453849 0.786090i −0.0375609 0.0650573i
\(147\) 0 0
\(148\) 4.14967 7.18744i 0.341101 0.590804i
\(149\) 21.0240 1.72235 0.861175 0.508309i \(-0.169729\pi\)
0.861175 + 0.508309i \(0.169729\pi\)
\(150\) −0.947575 + 7.35567i −0.0773692 + 0.600588i
\(151\) 1.49838 0.121937 0.0609683 0.998140i \(-0.480581\pi\)
0.0609683 + 0.998140i \(0.480581\pi\)
\(152\) −2.61387 4.52735i −0.212013 0.367217i
\(153\) −0.198130 0.723303i −0.0160179 0.0584756i
\(154\) 0 0
\(155\) 6.61922 + 11.4648i 0.531669 + 0.920877i
\(156\) 3.35522 1.40073i 0.268632 0.112148i
\(157\) −8.33982 14.4450i −0.665590 1.15284i −0.979125 0.203259i \(-0.934847\pi\)
0.313535 0.949577i \(-0.398487\pi\)
\(158\) −0.446064 0.772606i −0.0354870 0.0614652i
\(159\) 2.18848 16.9884i 0.173558 1.34727i
\(160\) 9.24065 + 16.0053i 0.730538 + 1.26533i
\(161\) 0 0
\(162\) −3.88951 2.18825i −0.305589 0.171925i
\(163\) −3.34135 5.78738i −0.261714 0.453303i 0.704983 0.709224i \(-0.250954\pi\)
−0.966698 + 0.255921i \(0.917621\pi\)
\(164\) 8.38793 0.654987
\(165\) 5.26799 2.19927i 0.410112 0.171213i
\(166\) −6.11064 −0.474278
\(167\) −8.81549 + 15.2689i −0.682163 + 1.18154i 0.292156 + 0.956371i \(0.405627\pi\)
−0.974319 + 0.225170i \(0.927706\pi\)
\(168\) 0 0
\(169\) 5.78394 + 10.0181i 0.444919 + 0.770622i
\(170\) −0.228863 0.396403i −0.0175530 0.0304027i
\(171\) −8.14976 2.13518i −0.623228 0.163281i
\(172\) 8.75178 15.1585i 0.667317 1.15583i
\(173\) −1.94342 + 3.36611i −0.147756 + 0.255920i −0.930398 0.366552i \(-0.880538\pi\)
0.782642 + 0.622472i \(0.213872\pi\)
\(174\) −3.28328 + 1.37070i −0.248905 + 0.103912i
\(175\) 0 0
\(176\) 1.15371 1.99829i 0.0869642 0.150626i
\(177\) −2.49574 1.90404i −0.187591 0.143116i
\(178\) 1.19376 0.0894759
\(179\) 3.66758 6.35244i 0.274128 0.474804i −0.695787 0.718248i \(-0.744944\pi\)
0.969915 + 0.243445i \(0.0782775\pi\)
\(180\) 18.7972 + 4.92473i 1.40106 + 0.367067i
\(181\) −11.2566 −0.836693 −0.418346 0.908288i \(-0.637390\pi\)
−0.418346 + 0.908288i \(0.637390\pi\)
\(182\) 0 0
\(183\) −2.39093 + 18.5599i −0.176743 + 1.37199i
\(184\) 4.61238 0.340029
\(185\) −8.73545 15.1302i −0.642243 1.11240i
\(186\) −2.84149 + 1.18626i −0.208348 + 0.0869808i
\(187\) −0.111563 + 0.193234i −0.00815833 + 0.0141306i
\(188\) −17.8447 −1.30146
\(189\) 0 0
\(190\) −5.14204 −0.373043
\(191\) 11.9230 20.6512i 0.862715 1.49427i −0.00658302 0.999978i \(-0.502095\pi\)
0.869298 0.494288i \(-0.164571\pi\)
\(192\) 4.29715 1.79396i 0.310120 0.129468i
\(193\) −2.96728 5.13948i −0.213589 0.369948i 0.739246 0.673436i \(-0.235182\pi\)
−0.952835 + 0.303488i \(0.901849\pi\)
\(194\) −5.47647 −0.393188
\(195\) 0.977905 7.59112i 0.0700293 0.543611i
\(196\) 0 0
\(197\) −15.4682 −1.10206 −0.551032 0.834484i \(-0.685766\pi\)
−0.551032 + 0.834484i \(0.685766\pi\)
\(198\) 0.350790 + 1.28061i 0.0249296 + 0.0910092i
\(199\) −7.74818 + 13.4202i −0.549254 + 0.951336i 0.449072 + 0.893496i \(0.351755\pi\)
−0.998326 + 0.0578402i \(0.981579\pi\)
\(200\) 16.0747 1.13665
\(201\) 1.41750 + 1.08143i 0.0999828 + 0.0762784i
\(202\) 0.644540 1.11638i 0.0453497 0.0785480i
\(203\) 0 0
\(204\) −0.700877 + 0.292600i −0.0490712 + 0.0204861i
\(205\) 8.82870 15.2917i 0.616623 1.06802i
\(206\) −2.40783 + 4.17048i −0.167761 + 0.290571i
\(207\) 5.22669 5.28520i 0.363280 0.367347i
\(208\) −1.54684 2.67920i −0.107254 0.185769i
\(209\) 1.25329 + 2.17076i 0.0866918 + 0.150155i
\(210\) 0 0
\(211\) 0.771898 1.33697i 0.0531397 0.0920406i −0.838232 0.545314i \(-0.816410\pi\)
0.891372 + 0.453273i \(0.149744\pi\)
\(212\) −17.3469 −1.19139
\(213\) 7.90440 3.29991i 0.541600 0.226106i
\(214\) −5.40522 −0.369493
\(215\) −18.4233 31.9101i −1.25646 2.17625i
\(216\) −3.62691 + 8.96717i −0.246780 + 0.610138i
\(217\) 0 0
\(218\) 0.526098 + 0.911229i 0.0356319 + 0.0617162i
\(219\) −0.405092 + 3.14458i −0.0273736 + 0.212491i
\(220\) −2.89068 5.00680i −0.194889 0.337558i
\(221\) 0.149579 + 0.259078i 0.0100617 + 0.0174275i
\(222\) 3.74995 1.56552i 0.251680 0.105071i
\(223\) 2.72171 + 4.71414i 0.182259 + 0.315682i 0.942649 0.333784i \(-0.108326\pi\)
−0.760390 + 0.649466i \(0.774992\pi\)
\(224\) 0 0
\(225\) 18.2157 18.4196i 1.21438 1.22797i
\(226\) −3.92389 6.79638i −0.261014 0.452089i
\(227\) 16.0764 1.06703 0.533513 0.845792i \(-0.320872\pi\)
0.533513 + 0.845792i \(0.320872\pi\)
\(228\) −1.09012 + 8.46222i −0.0721951 + 0.560424i
\(229\) 9.96840 0.658730 0.329365 0.944203i \(-0.393165\pi\)
0.329365 + 0.944203i \(0.393165\pi\)
\(230\) 2.26839 3.92897i 0.149573 0.259068i
\(231\) 0 0
\(232\) 3.85578 + 6.67840i 0.253144 + 0.438458i
\(233\) 8.27045 + 14.3248i 0.541815 + 0.938451i 0.998800 + 0.0489765i \(0.0155959\pi\)
−0.456985 + 0.889474i \(0.651071\pi\)
\(234\) 1.72211 + 0.451180i 0.112578 + 0.0294946i
\(235\) −18.7824 + 32.5321i −1.22523 + 2.12216i
\(236\) −1.58955 + 2.75319i −0.103471 + 0.179217i
\(237\) −0.398143 + 3.09063i −0.0258621 + 0.200758i
\(238\) 0 0
\(239\) −11.0119 + 19.0732i −0.712303 + 1.23375i 0.251687 + 0.967809i \(0.419015\pi\)
−0.963990 + 0.265937i \(0.914319\pi\)
\(240\) 2.11248 16.3984i 0.136360 1.05851i
\(241\) −16.7201 −1.07703 −0.538517 0.842615i \(-0.681015\pi\)
−0.538517 + 0.842615i \(0.681015\pi\)
\(242\) −2.52975 + 4.38166i −0.162619 + 0.281664i
\(243\) 6.16526 + 14.3175i 0.395502 + 0.918465i
\(244\) 18.9516 1.21325
\(245\) 0 0
\(246\) 3.26524 + 2.49110i 0.208184 + 0.158827i
\(247\) 3.36069 0.213836
\(248\) 3.33696 + 5.77978i 0.211897 + 0.367017i
\(249\) 16.9696 + 12.9464i 1.07541 + 0.820444i
\(250\) 3.32803 5.76432i 0.210483 0.364568i
\(251\) 8.53099 0.538471 0.269236 0.963074i \(-0.413229\pi\)
0.269236 + 0.963074i \(0.413229\pi\)
\(252\) 0 0
\(253\) −2.21153 −0.139038
\(254\) −0.314743 + 0.545151i −0.0197488 + 0.0342058i
\(255\) −0.204276 + 1.58572i −0.0127923 + 0.0993017i
\(256\) 0.123861 + 0.214533i 0.00774131 + 0.0134083i
\(257\) 17.1197 1.06790 0.533950 0.845516i \(-0.320707\pi\)
0.533950 + 0.845516i \(0.320707\pi\)
\(258\) 7.90875 3.30173i 0.492377 0.205557i
\(259\) 0 0
\(260\) −7.75135 −0.480718
\(261\) 12.0219 + 3.14965i 0.744137 + 0.194958i
\(262\) 3.72617 6.45392i 0.230204 0.398725i
\(263\) 20.5527 1.26733 0.633666 0.773607i \(-0.281549\pi\)
0.633666 + 0.773607i \(0.281549\pi\)
\(264\) 2.65576 1.10872i 0.163451 0.0682370i
\(265\) −18.2585 + 31.6246i −1.12161 + 1.94269i
\(266\) 0 0
\(267\) −3.31514 2.52917i −0.202883 0.154783i
\(268\) 0.902816 1.56372i 0.0551483 0.0955196i
\(269\) −9.92267 + 17.1866i −0.604996 + 1.04788i 0.387057 + 0.922056i \(0.373492\pi\)
−0.992052 + 0.125827i \(0.959842\pi\)
\(270\) 5.85477 + 7.49960i 0.356310 + 0.456411i
\(271\) −5.32056 9.21548i −0.323201 0.559801i 0.657946 0.753065i \(-0.271426\pi\)
−0.981147 + 0.193265i \(0.938092\pi\)
\(272\) 0.323121 + 0.559663i 0.0195921 + 0.0339345i
\(273\) 0 0
\(274\) −0.121114 + 0.209776i −0.00731676 + 0.0126730i
\(275\) −7.70745 −0.464777
\(276\) −5.98496 4.56602i −0.360252 0.274842i
\(277\) −24.8813 −1.49497 −0.747487 0.664276i \(-0.768740\pi\)
−0.747487 + 0.664276i \(0.768740\pi\)
\(278\) −2.44705 4.23841i −0.146764 0.254203i
\(279\) 10.4043 + 2.72585i 0.622889 + 0.163192i
\(280\) 0 0
\(281\) −6.83733 11.8426i −0.407881 0.706470i 0.586771 0.809753i \(-0.300399\pi\)
−0.994652 + 0.103282i \(0.967065\pi\)
\(282\) −6.94657 5.29964i −0.413662 0.315589i
\(283\) 3.16089 + 5.47483i 0.187896 + 0.325445i 0.944548 0.328372i \(-0.106500\pi\)
−0.756653 + 0.653817i \(0.773167\pi\)
\(284\) −4.33734 7.51249i −0.257374 0.445784i
\(285\) 14.2798 + 10.8943i 0.845861 + 0.645320i
\(286\) −0.264830 0.458699i −0.0156597 0.0271234i
\(287\) 0 0
\(288\) 14.5247 + 3.80537i 0.855878 + 0.224234i
\(289\) 8.46875 + 14.6683i 0.498162 + 0.862842i
\(290\) 7.58515 0.445415
\(291\) 15.2085 + 11.6028i 0.891538 + 0.680168i
\(292\) 3.21095 0.187907
\(293\) 1.31508 2.27778i 0.0768277 0.133069i −0.825052 0.565057i \(-0.808854\pi\)
0.901880 + 0.431987i \(0.142188\pi\)
\(294\) 0 0
\(295\) 3.34616 + 5.79573i 0.194821 + 0.337440i
\(296\) −4.40382 7.62764i −0.255967 0.443348i
\(297\) 1.73902 4.29955i 0.100908 0.249485i
\(298\) 5.21256 9.02841i 0.301955 0.523002i
\(299\) −1.48255 + 2.56786i −0.0857384 + 0.148503i
\(300\) −20.8583 15.9131i −1.20426 0.918745i
\(301\) 0 0
\(302\) 0.371500 0.643457i 0.0213774 0.0370268i
\(303\) −4.15515 + 1.73468i −0.238707 + 0.0996550i
\(304\) 7.25980 0.416378
\(305\) 19.9475 34.5501i 1.14219 1.97833i
\(306\) −0.359735 0.0942478i −0.0205647 0.00538779i
\(307\) 2.79496 0.159517 0.0797583 0.996814i \(-0.474585\pi\)
0.0797583 + 0.996814i \(0.474585\pi\)
\(308\) 0 0
\(309\) 15.5225 6.48030i 0.883045 0.368652i
\(310\) 6.56452 0.372840
\(311\) −7.55013 13.0772i −0.428129 0.741541i 0.568578 0.822629i \(-0.307494\pi\)
−0.996707 + 0.0810885i \(0.974160\pi\)
\(312\) 0.492993 3.82692i 0.0279102 0.216657i
\(313\) −12.7392 + 22.0650i −0.720064 + 1.24719i 0.240910 + 0.970548i \(0.422554\pi\)
−0.960974 + 0.276640i \(0.910779\pi\)
\(314\) −8.27090 −0.466754
\(315\) 0 0
\(316\) 3.15587 0.177531
\(317\) −16.2605 + 28.1639i −0.913278 + 1.58184i −0.103875 + 0.994590i \(0.533124\pi\)
−0.809403 + 0.587253i \(0.800209\pi\)
\(318\) −6.75279 5.15181i −0.378678 0.288899i
\(319\) −1.84875 3.20214i −0.103510 0.179285i
\(320\) −9.92743 −0.554960
\(321\) 15.0106 + 11.4518i 0.837811 + 0.639179i
\(322\) 0 0
\(323\) −0.702021 −0.0390615
\(324\) 13.5833 8.04522i 0.754625 0.446957i
\(325\) −5.16688 + 8.94931i −0.286607 + 0.496418i
\(326\) −3.31373 −0.183531
\(327\) 0.469578 3.64516i 0.0259677 0.201578i
\(328\) 4.45083 7.70906i 0.245756 0.425661i
\(329\) 0 0
\(330\) 0.361672 2.80753i 0.0199094 0.154549i
\(331\) −9.04741 + 15.6706i −0.497291 + 0.861333i −0.999995 0.00312545i \(-0.999005\pi\)
0.502704 + 0.864458i \(0.332338\pi\)
\(332\) 10.8081 18.7201i 0.593170 1.02740i
\(333\) −13.7307 3.59733i −0.752435 0.197132i
\(334\) 4.37132 + 7.57135i 0.239188 + 0.414286i
\(335\) −1.90051 3.29179i −0.103836 0.179850i
\(336\) 0 0
\(337\) −12.5086 + 21.6656i −0.681389 + 1.18020i 0.293168 + 0.956061i \(0.405290\pi\)
−0.974557 + 0.224139i \(0.928043\pi\)
\(338\) 5.73615 0.312005
\(339\) −3.50234 + 27.1874i −0.190221 + 1.47662i
\(340\) 1.61919 0.0878130
\(341\) −1.59999 2.77127i −0.0866446 0.150073i
\(342\) −2.93752 + 2.97041i −0.158843 + 0.160621i
\(343\) 0 0
\(344\) −9.28778 16.0869i −0.500764 0.867348i
\(345\) −14.6236 + 6.10503i −0.787309 + 0.328684i
\(346\) 0.963682 + 1.66915i 0.0518078 + 0.0897338i
\(347\) −5.37444 9.30881i −0.288515 0.499723i 0.684940 0.728599i \(-0.259828\pi\)
−0.973456 + 0.228876i \(0.926495\pi\)
\(348\) 1.60807 12.4828i 0.0862013 0.669149i
\(349\) 1.64301 + 2.84577i 0.0879482 + 0.152331i 0.906644 0.421897i \(-0.138636\pi\)
−0.818695 + 0.574228i \(0.805302\pi\)
\(350\) 0 0
\(351\) −3.82651 4.90153i −0.204244 0.261624i
\(352\) −2.23365 3.86879i −0.119054 0.206207i
\(353\) −16.8192 −0.895195 −0.447598 0.894235i \(-0.647720\pi\)
−0.447598 + 0.894235i \(0.647720\pi\)
\(354\) −1.43644 + 0.599681i −0.0763458 + 0.0318727i
\(355\) −18.2610 −0.969195
\(356\) −2.11144 + 3.65711i −0.111906 + 0.193827i
\(357\) 0 0
\(358\) −1.81864 3.14997i −0.0961180 0.166481i
\(359\) 11.8921 + 20.5978i 0.627642 + 1.08711i 0.988024 + 0.154303i \(0.0493131\pi\)
−0.360382 + 0.932805i \(0.617354\pi\)
\(360\) 14.5004 14.6627i 0.764237 0.772792i
\(361\) 5.55680 9.62466i 0.292463 0.506561i
\(362\) −2.79088 + 4.83395i −0.146686 + 0.254067i
\(363\) 16.3085 6.80845i 0.855976 0.357351i
\(364\) 0 0
\(365\) 3.37968 5.85377i 0.176900 0.306401i
\(366\) 7.37747 + 5.62838i 0.385626 + 0.294200i
\(367\) 0.689984 0.0360169 0.0180084 0.999838i \(-0.494267\pi\)
0.0180084 + 0.999838i \(0.494267\pi\)
\(368\) −3.20263 + 5.54712i −0.166949 + 0.289164i
\(369\) −3.78998 13.8359i −0.197298 0.720267i
\(370\) −8.66327 −0.450382
\(371\) 0 0
\(372\) 1.39169 10.8032i 0.0721558 0.560119i
\(373\) −3.76012 −0.194691 −0.0973457 0.995251i \(-0.531035\pi\)
−0.0973457 + 0.995251i \(0.531035\pi\)
\(374\) 0.0553208 + 0.0958184i 0.00286057 + 0.00495465i
\(375\) −21.4548 + 8.95690i −1.10792 + 0.462532i
\(376\) −9.46882 + 16.4005i −0.488317 + 0.845790i
\(377\) −4.95744 −0.255321
\(378\) 0 0
\(379\) 32.8735 1.68860 0.844300 0.535872i \(-0.180017\pi\)
0.844300 + 0.535872i \(0.180017\pi\)
\(380\) 9.09489 15.7528i 0.466558 0.808102i
\(381\) 2.02905 0.847085i 0.103952 0.0433975i
\(382\) −5.91222 10.2403i −0.302495 0.523937i
\(383\) 1.07267 0.0548109 0.0274055 0.999624i \(-0.491275\pi\)
0.0274055 + 0.999624i \(0.491275\pi\)
\(384\) 2.51021 19.4858i 0.128099 0.994381i
\(385\) 0 0
\(386\) −2.94276 −0.149782
\(387\) −28.9583 7.58687i −1.47204 0.385662i
\(388\) 9.68640 16.7773i 0.491752 0.851740i
\(389\) −23.7436 −1.20385 −0.601925 0.798553i \(-0.705599\pi\)
−0.601925 + 0.798553i \(0.705599\pi\)
\(390\) −3.01743 2.30204i −0.152794 0.116569i
\(391\) 0.309693 0.536405i 0.0156619 0.0271271i
\(392\) 0 0
\(393\) −24.0215 + 10.0284i −1.21172 + 0.505868i
\(394\) −3.83510 + 6.64258i −0.193209 + 0.334648i
\(395\) 3.32170 5.75336i 0.167133 0.289483i
\(396\) −4.54365 1.19040i −0.228327 0.0598200i
\(397\) 0.0160489 + 0.0277975i 0.000805471 + 0.00139512i 0.866428 0.499302i \(-0.166410\pi\)
−0.865622 + 0.500697i \(0.833077\pi\)
\(398\) 3.84208 + 6.65467i 0.192586 + 0.333569i
\(399\) 0 0
\(400\) −11.1616 + 19.3324i −0.558078 + 0.966619i
\(401\) 24.5256 1.22475 0.612374 0.790568i \(-0.290215\pi\)
0.612374 + 0.790568i \(0.290215\pi\)
\(402\) 0.815851 0.340600i 0.0406910 0.0169876i
\(403\) −4.29039 −0.213719
\(404\) 2.28004 + 3.94914i 0.113436 + 0.196477i
\(405\) −0.369938 33.2312i −0.0183824 1.65127i
\(406\) 0 0
\(407\) 2.11153 + 3.65728i 0.104665 + 0.181284i
\(408\) −0.102982 + 0.799412i −0.00509838 + 0.0395768i
\(409\) 13.3948 + 23.2006i 0.662333 + 1.14719i 0.980001 + 0.198992i \(0.0637667\pi\)
−0.317669 + 0.948202i \(0.602900\pi\)
\(410\) −4.37787 7.58269i −0.216208 0.374483i
\(411\) 0.780785 0.325960i 0.0385133 0.0160784i
\(412\) −8.51759 14.7529i −0.419631 0.726823i
\(413\) 0 0
\(414\) −0.973773 3.55490i −0.0478583 0.174714i
\(415\) −22.7520 39.4077i −1.11685 1.93445i
\(416\) −5.98952 −0.293660
\(417\) −2.18416 + 16.9548i −0.106959 + 0.830280i
\(418\) 1.24293 0.0607938
\(419\) 10.5262 18.2320i 0.514240 0.890689i −0.485624 0.874168i \(-0.661407\pi\)
0.999864 0.0165215i \(-0.00525920\pi\)
\(420\) 0 0
\(421\) −7.44533 12.8957i −0.362863 0.628498i 0.625568 0.780170i \(-0.284867\pi\)
−0.988431 + 0.151672i \(0.951534\pi\)
\(422\) −0.382760 0.662959i −0.0186325 0.0322724i
\(423\) 8.06290 + 29.4349i 0.392032 + 1.43117i
\(424\) −9.20469 + 15.9430i −0.447019 + 0.774260i
\(425\) 1.07932 1.86944i 0.0523547 0.0906809i
\(426\) 0.542675 4.21258i 0.0262927 0.204100i
\(427\) 0 0
\(428\) 9.56037 16.5590i 0.462118 0.800412i
\(429\) −0.236379 + 1.83492i −0.0114125 + 0.0885908i
\(430\) −18.2711 −0.881110
\(431\) −7.95192 + 13.7731i −0.383031 + 0.663428i −0.991494 0.130154i \(-0.958453\pi\)
0.608463 + 0.793582i \(0.291786\pi\)
\(432\) −8.26607 10.5883i −0.397702 0.509431i
\(433\) 16.3658 0.786490 0.393245 0.919434i \(-0.371352\pi\)
0.393245 + 0.919434i \(0.371352\pi\)
\(434\) 0 0
\(435\) −21.0644 16.0704i −1.00996 0.770515i
\(436\) −3.72210 −0.178256
\(437\) −3.47905 6.02590i −0.166426 0.288258i
\(438\) 1.24995 + 0.953608i 0.0597251 + 0.0455652i
\(439\) −7.77236 + 13.4621i −0.370954 + 0.642512i −0.989713 0.143070i \(-0.954303\pi\)
0.618758 + 0.785582i \(0.287636\pi\)
\(440\) −6.13543 −0.292495
\(441\) 0 0
\(442\) 0.148343 0.00705594
\(443\) −0.895027 + 1.55023i −0.0425240 + 0.0736537i −0.886504 0.462721i \(-0.846873\pi\)
0.843980 + 0.536375i \(0.180207\pi\)
\(444\) −1.83663 + 14.2571i −0.0871625 + 0.676611i
\(445\) 4.44477 + 7.69857i 0.210702 + 0.364947i
\(446\) 2.69922 0.127812
\(447\) −33.6038 + 14.0288i −1.58940 + 0.663540i
\(448\) 0 0
\(449\) 13.5666 0.640250 0.320125 0.947375i \(-0.396275\pi\)
0.320125 + 0.947375i \(0.396275\pi\)
\(450\) −3.39372 12.3893i −0.159981 0.584036i
\(451\) −2.13407 + 3.69631i −0.100489 + 0.174053i
\(452\) 27.7612 1.30578
\(453\) −2.39495 + 0.999837i −0.112524 + 0.0469764i
\(454\) 3.98588 6.90375i 0.187067 0.324009i
\(455\) 0 0
\(456\) 7.19889 + 5.49214i 0.337119 + 0.257193i
\(457\) −1.28459 + 2.22497i −0.0600905 + 0.104080i −0.894506 0.447057i \(-0.852472\pi\)
0.834415 + 0.551136i \(0.185806\pi\)
\(458\) 2.47151 4.28078i 0.115486 0.200028i
\(459\) 0.799326 + 1.02389i 0.0373094 + 0.0477910i
\(460\) 8.02434 + 13.8986i 0.374137 + 0.648024i
\(461\) −18.0934 31.3388i −0.842695 1.45959i −0.887608 0.460600i \(-0.847634\pi\)
0.0449122 0.998991i \(-0.485699\pi\)
\(462\) 0 0
\(463\) 8.19224 14.1894i 0.380726 0.659436i −0.610440 0.792062i \(-0.709008\pi\)
0.991166 + 0.132626i \(0.0423409\pi\)
\(464\) −10.7091 −0.497158
\(465\) −18.2301 13.9080i −0.845400 0.644968i
\(466\) 8.20210 0.379955
\(467\) 4.35022 + 7.53480i 0.201304 + 0.348669i 0.948949 0.315430i \(-0.102149\pi\)
−0.747645 + 0.664099i \(0.768815\pi\)
\(468\) −4.42815 + 4.47772i −0.204692 + 0.206983i
\(469\) 0 0
\(470\) 9.31361 + 16.1316i 0.429605 + 0.744097i
\(471\) 22.9688 + 17.5233i 1.05835 + 0.807429i
\(472\) 1.68691 + 2.92181i 0.0776462 + 0.134487i
\(473\) 4.45328 + 7.71330i 0.204762 + 0.354658i
\(474\) 1.22851 + 0.937250i 0.0564274 + 0.0430493i
\(475\) −12.1249 21.0010i −0.556330 0.963591i
\(476\) 0 0
\(477\) 7.83799 + 28.6138i 0.358877 + 1.31014i
\(478\) 5.46047 + 9.45782i 0.249756 + 0.432591i
\(479\) 17.7674 0.811813 0.405907 0.913915i \(-0.366956\pi\)
0.405907 + 0.913915i \(0.366956\pi\)
\(480\) −25.4498 19.4160i −1.16162 0.886217i
\(481\) 5.66207 0.258168
\(482\) −4.14548 + 7.18018i −0.188821 + 0.327048i
\(483\) 0 0
\(484\) −8.94890 15.4999i −0.406768 0.704543i
\(485\) −20.3908 35.3179i −0.925898 1.60370i
\(486\) 7.67699 + 0.902212i 0.348235 + 0.0409251i
\(487\) 8.32763 14.4239i 0.377361 0.653608i −0.613316 0.789837i \(-0.710165\pi\)
0.990677 + 0.136229i \(0.0434983\pi\)
\(488\) 10.0562 17.4178i 0.455222 0.788467i
\(489\) 9.20245 + 7.02068i 0.416149 + 0.317486i
\(490\) 0 0
\(491\) −3.21021 + 5.56025i −0.144875 + 0.250930i −0.929326 0.369260i \(-0.879611\pi\)
0.784451 + 0.620190i \(0.212945\pi\)
\(492\) −13.4069 + 5.59708i −0.604429 + 0.252336i
\(493\) 1.03557 0.0466396
\(494\) 0.833230 1.44320i 0.0374888 0.0649325i
\(495\) −6.95259 + 7.03042i −0.312496 + 0.315994i
\(496\) −9.26814 −0.416152
\(497\) 0 0
\(498\) 9.76698 4.07750i 0.437669 0.182717i
\(499\) 11.1459 0.498960 0.249480 0.968380i \(-0.419740\pi\)
0.249480 + 0.968380i \(0.419740\pi\)
\(500\) 11.7728 + 20.3911i 0.526495 + 0.911916i
\(501\) 3.90170 30.2875i 0.174315 1.35314i
\(502\) 2.11512 3.66350i 0.0944026 0.163510i
\(503\) 17.7223 0.790200 0.395100 0.918638i \(-0.370710\pi\)
0.395100 + 0.918638i \(0.370710\pi\)
\(504\) 0 0
\(505\) 9.59939 0.427167
\(506\) −0.548314 + 0.949708i −0.0243755 + 0.0422197i
\(507\) −15.9296 12.1530i −0.707460 0.539732i
\(508\) −1.11339 1.92845i −0.0493988 0.0855612i
\(509\) −31.0823 −1.37770 −0.688848 0.724906i \(-0.741883\pi\)
−0.688848 + 0.724906i \(0.741883\pi\)
\(510\) 0.630316 + 0.480878i 0.0279109 + 0.0212936i
\(511\) 0 0
\(512\) −22.5634 −0.997169
\(513\) 14.4510 2.02539i 0.638026 0.0894230i
\(514\) 4.24456 7.35180i 0.187220 0.324274i
\(515\) −35.8607 −1.58021
\(516\) −3.87350 + 30.0686i −0.170522 + 1.32370i
\(517\) 4.54008 7.86365i 0.199672 0.345843i
\(518\) 0 0
\(519\) 0.860152 6.67704i 0.0377565 0.293089i
\(520\) −4.11304 + 7.12399i −0.180369 + 0.312408i
\(521\) 2.37986 4.12203i 0.104263 0.180590i −0.809174 0.587570i \(-0.800085\pi\)
0.913437 + 0.406980i \(0.133418\pi\)
\(522\) 4.33321 4.38172i 0.189659 0.191783i
\(523\) −20.1258 34.8588i −0.880038 1.52427i −0.851298 0.524683i \(-0.824184\pi\)
−0.0287402 0.999587i \(-0.509150\pi\)
\(524\) 13.1812 + 22.8305i 0.575823 + 0.997355i
\(525\) 0 0
\(526\) 5.09571 8.82602i 0.222183 0.384833i
\(527\) 0.896226 0.0390402
\(528\) −0.510628 + 3.96382i −0.0222222 + 0.172503i
\(529\) −16.8609 −0.733084
\(530\) 9.05381 + 15.6817i 0.393272 + 0.681168i
\(531\) 5.25960 + 1.37798i 0.228247 + 0.0597991i
\(532\) 0 0
\(533\) 2.86125 + 4.95583i 0.123935 + 0.214661i
\(534\) −1.90805 + 0.796568i −0.0825693 + 0.0344709i
\(535\) −20.1255 34.8584i −0.870101 1.50706i
\(536\) −0.958109 1.65949i −0.0413840 0.0716792i
\(537\) −1.62326 + 12.6008i −0.0700488 + 0.543763i
\(538\) 4.92033 + 8.52227i 0.212131 + 0.367421i
\(539\) 0 0
\(540\) −33.3308 + 4.67150i −1.43433 + 0.201029i
\(541\) 12.0547 + 20.8794i 0.518273 + 0.897675i 0.999775 + 0.0212301i \(0.00675826\pi\)
−0.481502 + 0.876445i \(0.659908\pi\)
\(542\) −5.27659 −0.226649
\(543\) 17.9920 7.51125i 0.772109 0.322339i
\(544\) 1.25116 0.0536431
\(545\) −3.91769 + 6.78564i −0.167815 + 0.290665i
\(546\) 0 0
\(547\) −6.17751 10.6998i −0.264131 0.457489i 0.703204 0.710988i \(-0.251752\pi\)
−0.967336 + 0.253499i \(0.918419\pi\)
\(548\) −0.428436 0.742073i −0.0183019 0.0316998i
\(549\) −8.56305 31.2607i −0.365462 1.33418i
\(550\) −1.91094 + 3.30985i −0.0814828 + 0.141132i
\(551\) 5.81671 10.0748i 0.247800 0.429203i
\(552\) −7.37223 + 3.07774i −0.313783 + 0.130997i
\(553\) 0 0
\(554\) −6.16893 + 10.6849i −0.262093 + 0.453958i
\(555\) 24.0584 + 18.3545i 1.02122 + 0.779107i
\(556\) 17.3127 0.734220
\(557\) 4.03845 6.99479i 0.171114 0.296379i −0.767695 0.640815i \(-0.778597\pi\)
0.938810 + 0.344436i \(0.111930\pi\)
\(558\) 3.75015 3.79213i 0.158757 0.160534i
\(559\) 11.9415 0.505070
\(560\) 0 0
\(561\) 0.0493776 0.383300i 0.00208472 0.0161829i
\(562\) −6.78083 −0.286032
\(563\) 22.6064 + 39.1554i 0.952744 + 1.65020i 0.739448 + 0.673214i \(0.235087\pi\)
0.213296 + 0.976988i \(0.431580\pi\)
\(564\) 28.5222 11.9074i 1.20100 0.501391i
\(565\) 29.2200 50.6106i 1.22930 2.12920i
\(566\) 3.13477 0.131764
\(567\) 0 0
\(568\) −9.20596 −0.386274
\(569\) −11.2149 + 19.4248i −0.470155 + 0.814332i −0.999418 0.0341263i \(-0.989135\pi\)
0.529263 + 0.848458i \(0.322468\pi\)
\(570\) 8.21881 3.43117i 0.344248 0.143716i
\(571\) 10.9134 + 18.9026i 0.456713 + 0.791050i 0.998785 0.0492820i \(-0.0156933\pi\)
−0.542072 + 0.840332i \(0.682360\pi\)
\(572\) 1.87365 0.0783413
\(573\) −5.27706 + 40.9638i −0.220452 + 1.71129i
\(574\) 0 0
\(575\) 21.3954 0.892251
\(576\) −5.67130 + 5.73479i −0.236304 + 0.238949i
\(577\) 16.1022 27.8898i 0.670342 1.16107i −0.307465 0.951559i \(-0.599481\pi\)
0.977807 0.209508i \(-0.0671861\pi\)
\(578\) 8.39877 0.349343
\(579\) 8.17222 + 6.23471i 0.339626 + 0.259106i
\(580\) −13.4161 + 23.2373i −0.557072 + 0.964878i
\(581\) 0 0
\(582\) 8.75335 3.65433i 0.362838 0.151477i
\(583\) 4.41343 7.64429i 0.182786 0.316594i
\(584\) 1.70380 2.95107i 0.0705039 0.122116i
\(585\) 3.50234 + 12.7858i 0.144804 + 0.528629i
\(586\) −0.652105 1.12948i −0.0269382 0.0466584i
\(587\) 9.72304 + 16.8408i 0.401313 + 0.695094i 0.993885 0.110424i \(-0.0352208\pi\)
−0.592572 + 0.805518i \(0.701887\pi\)
\(588\) 0 0
\(589\) 5.03404 8.71921i 0.207424 0.359269i
\(590\) 3.31851 0.136621
\(591\) 24.7237 10.3216i 1.01700 0.424574i
\(592\) 12.2313 0.502701
\(593\) 14.4202 + 24.9766i 0.592168 + 1.02566i 0.993940 + 0.109925i \(0.0350611\pi\)
−0.401772 + 0.915740i \(0.631606\pi\)
\(594\) −1.41521 1.81280i −0.0580669 0.0743801i
\(595\) 0 0
\(596\) 18.4392 + 31.9377i 0.755300 + 1.30822i
\(597\) 3.42932 26.6205i 0.140353 1.08950i
\(598\) 0.735152 + 1.27332i 0.0300626 + 0.0520699i
\(599\) 23.4994 + 40.7022i 0.960161 + 1.66305i 0.722089 + 0.691800i \(0.243182\pi\)
0.238072 + 0.971247i \(0.423484\pi\)
\(600\) −25.6931 + 10.7263i −1.04892 + 0.437899i
\(601\) 7.80843 + 13.5246i 0.318512 + 0.551680i 0.980178 0.198119i \(-0.0634834\pi\)
−0.661665 + 0.749799i \(0.730150\pi\)
\(602\) 0 0
\(603\) −2.98729 0.782646i −0.121652 0.0318718i
\(604\) 1.31417 + 2.27620i 0.0534727 + 0.0926174i
\(605\) −37.6766 −1.53177
\(606\) −0.285271 + 2.21445i −0.0115883 + 0.0899560i
\(607\) 28.6532 1.16300 0.581500 0.813547i \(-0.302466\pi\)
0.581500 + 0.813547i \(0.302466\pi\)
\(608\) 7.02769 12.1723i 0.285010 0.493652i
\(609\) 0 0
\(610\) −9.89134 17.1323i −0.400489 0.693667i
\(611\) −6.08711 10.5432i −0.246258 0.426531i
\(612\) 0.925004 0.935359i 0.0373911 0.0378097i
\(613\) 14.6734 25.4151i 0.592653 1.02651i −0.401220 0.915982i \(-0.631414\pi\)
0.993873 0.110524i \(-0.0352529\pi\)
\(614\) 0.692965 1.20025i 0.0279658 0.0484382i
\(615\) −3.90755 + 30.3328i −0.157568 + 1.22314i
\(616\) 0 0
\(617\) 2.06401 3.57497i 0.0830938 0.143923i −0.821484 0.570232i \(-0.806853\pi\)
0.904577 + 0.426310i \(0.140187\pi\)
\(618\) 1.06569 8.27259i 0.0428685 0.332772i
\(619\) −22.7130 −0.912912 −0.456456 0.889746i \(-0.650881\pi\)
−0.456456 + 0.889746i \(0.650881\pi\)
\(620\) −11.6109 + 20.1106i −0.466304 + 0.807662i
\(621\) −4.82742 + 11.9353i −0.193718 + 0.478947i
\(622\) −7.48774 −0.300231
\(623\) 0 0
\(624\) 4.26017 + 3.25014i 0.170543 + 0.130110i
\(625\) 6.38996 0.255598
\(626\) 6.31698 + 10.9413i 0.252477 + 0.437304i
\(627\) −3.45170 2.63335i −0.137848 0.105166i
\(628\) 14.6290 25.3382i 0.583761 1.01110i
\(629\) −1.18276 −0.0471597
\(630\) 0 0
\(631\) −38.6411 −1.53828 −0.769138 0.639082i \(-0.779314\pi\)
−0.769138 + 0.639082i \(0.779314\pi\)
\(632\) 1.67458 2.90045i 0.0666110 0.115374i
\(633\) −0.341639 + 2.65202i −0.0135789 + 0.105408i
\(634\) 8.06304 + 13.9656i 0.320224 + 0.554645i
\(635\) −4.68759 −0.186021
\(636\) 27.7266 11.5752i 1.09943 0.458988i
\(637\) 0 0
\(638\) −1.83348 −0.0725881
\(639\) −10.4321 + 10.5489i −0.412687 + 0.417306i
\(640\) −20.9427 + 36.2737i −0.827831 + 1.43385i
\(641\) −28.4726 −1.12460 −0.562301 0.826933i \(-0.690084\pi\)
−0.562301 + 0.826933i \(0.690084\pi\)
\(642\) 8.63946 3.60678i 0.340972 0.142348i
\(643\) 8.52125 14.7592i 0.336045 0.582048i −0.647640 0.761947i \(-0.724244\pi\)
0.983685 + 0.179899i \(0.0575771\pi\)
\(644\) 0 0
\(645\) 50.7400 + 38.7103i 1.99788 + 1.52422i
\(646\) −0.174055 + 0.301472i −0.00684810 + 0.0118613i
\(647\) −1.68809 + 2.92386i −0.0663657 + 0.114949i −0.897299 0.441423i \(-0.854474\pi\)
0.830933 + 0.556372i \(0.187807\pi\)
\(648\) −0.186497 16.7529i −0.00732631 0.658115i
\(649\) −0.808833 1.40094i −0.0317495 0.0549917i
\(650\) 2.56209 + 4.43768i 0.100494 + 0.174060i
\(651\) 0 0
\(652\) 5.86110 10.1517i 0.229538 0.397572i
\(653\) −18.3451 −0.717899 −0.358950 0.933357i \(-0.616865\pi\)
−0.358950 + 0.933357i \(0.616865\pi\)
\(654\) −1.44893 1.10541i −0.0566578 0.0432251i
\(655\) 55.4954 2.16838
\(656\) 6.18090 + 10.7056i 0.241324 + 0.417985i
\(657\) −1.45083 5.29646i −0.0566021 0.206635i
\(658\) 0 0
\(659\) −13.9248 24.1184i −0.542432 0.939519i −0.998764 0.0497098i \(-0.984170\pi\)
0.456332 0.889810i \(-0.349163\pi\)
\(660\) 7.96125 + 6.07376i 0.309891 + 0.236421i
\(661\) 19.5071 + 33.7872i 0.758737 + 1.31417i 0.943495 + 0.331387i \(0.107516\pi\)
−0.184758 + 0.982784i \(0.559150\pi\)
\(662\) 4.48633 + 7.77054i 0.174366 + 0.302011i
\(663\) −0.411957 0.314288i −0.0159991 0.0122059i
\(664\) −11.4700 19.8667i −0.445123 0.770976i
\(665\) 0 0
\(666\) −4.94911 + 5.00452i −0.191774 + 0.193921i
\(667\) 5.13203 + 8.88894i 0.198713 + 0.344181i
\(668\) −30.9268 −1.19659
\(669\) −7.49590 5.71873i −0.289808 0.221099i
\(670\) −1.88481 −0.0728165
\(671\) −4.82170 + 8.35143i −0.186140 + 0.322404i
\(672\) 0 0
\(673\) 24.6154 + 42.6352i 0.948856 + 1.64347i 0.747841 + 0.663878i \(0.231090\pi\)
0.201014 + 0.979588i \(0.435576\pi\)
\(674\) 6.20264 + 10.7433i 0.238917 + 0.413816i
\(675\) −16.8241 + 41.5959i −0.647561 + 1.60103i
\(676\) −10.1457 + 17.5729i −0.390219 + 0.675879i
\(677\) −11.6958 + 20.2577i −0.449505 + 0.778565i −0.998354 0.0573564i \(-0.981733\pi\)
0.548849 + 0.835922i \(0.315066\pi\)
\(678\) 10.8069 + 8.24471i 0.415035 + 0.316636i
\(679\) 0 0
\(680\) 0.859180 1.48814i 0.0329480 0.0570677i
\(681\) −25.6958 + 10.7274i −0.984663 + 0.411075i
\(682\) −1.58677 −0.0607607
\(683\) −15.1632 + 26.2634i −0.580204 + 1.00494i 0.415251 + 0.909707i \(0.363694\pi\)
−0.995455 + 0.0952356i \(0.969640\pi\)
\(684\) −3.90425 14.2530i −0.149283 0.544979i
\(685\) −1.80380 −0.0689196
\(686\) 0 0
\(687\) −15.9330 + 6.65169i −0.607884 + 0.253778i
\(688\) 25.7961 0.983466
\(689\) −5.91731 10.2491i −0.225432 0.390459i
\(690\) −1.00398 + 7.79353i −0.0382209 + 0.296695i
\(691\) −2.05665 + 3.56223i −0.0782387 + 0.135513i −0.902490 0.430711i \(-0.858263\pi\)
0.824251 + 0.566224i \(0.191596\pi\)
\(692\) −6.81797 −0.259180
\(693\) 0 0
\(694\) −5.33003 −0.202325
\(695\) 18.2224 31.5621i 0.691215 1.19722i
\(696\) −10.6192 8.10158i −0.402522 0.307090i
\(697\) −0.597691 1.03523i −0.0226392 0.0392122i
\(698\) 1.62943 0.0616749
\(699\) −22.7778 17.3775i −0.861534 0.657277i
\(700\) 0 0
\(701\) 29.1835 1.10225 0.551123 0.834424i \(-0.314200\pi\)
0.551123 + 0.834424i \(0.314200\pi\)
\(702\) −3.05361 + 0.427980i −0.115251 + 0.0161531i
\(703\) −6.64347 + 11.5068i −0.250563 + 0.433988i
\(704\) 2.39965 0.0904403
\(705\) 8.31303 64.5310i 0.313087 2.43038i
\(706\) −4.17005 + 7.22274i −0.156942 + 0.271831i
\(707\) 0 0
\(708\) 0.703531 5.46125i 0.0264403 0.205246i
\(709\) 21.2309 36.7729i 0.797342 1.38104i −0.123999 0.992282i \(-0.539572\pi\)
0.921341 0.388755i \(-0.127095\pi\)
\(710\) −4.52753 + 7.84192i −0.169915 + 0.294302i
\(711\) −1.42594 5.20560i −0.0534768 0.195225i
\(712\) 2.24075 + 3.88109i 0.0839757 + 0.145450i
\(713\) 4.44149 + 7.69288i 0.166335 + 0.288101i
\(714\) 0 0
\(715\) 1.97211 3.41579i 0.0737526 0.127743i
\(716\) 12.8667 0.480852
\(717\) 4.87385 37.8339i 0.182017 1.41293i
\(718\) 11.7938 0.440142
\(719\) 5.57126 + 9.64970i 0.207773 + 0.359873i 0.951013 0.309152i \(-0.100045\pi\)
−0.743240 + 0.669025i \(0.766712\pi\)
\(720\) 7.56580 + 27.6201i 0.281961 + 1.02934i
\(721\) 0 0
\(722\) −2.75544 4.77256i −0.102547 0.177616i
\(723\) 26.7246 11.1569i 0.993899 0.414931i
\(724\) −9.87264 17.0999i −0.366914 0.635513i
\(725\) 17.8858 + 30.9790i 0.664260 + 1.15053i
\(726\) 1.11966 8.69150i 0.0415544 0.322572i
\(727\) 14.3410 + 24.8393i 0.531878 + 0.921239i 0.999308 + 0.0372089i \(0.0118467\pi\)
−0.467430 + 0.884030i \(0.654820\pi\)
\(728\) 0 0
\(729\) −19.4080 18.7704i −0.718815 0.695202i
\(730\) −1.67588 2.90270i −0.0620269 0.107434i
\(731\) −2.49447 −0.0922614
\(732\) −30.2915 + 12.6460i −1.11960 + 0.467410i
\(733\) 25.0528 0.925348 0.462674 0.886529i \(-0.346890\pi\)
0.462674 + 0.886529i \(0.346890\pi\)
\(734\) 0.171071 0.296303i 0.00631433 0.0109367i
\(735\) 0 0
\(736\) 6.20047 + 10.7395i 0.228552 + 0.395864i
\(737\) 0.459391 + 0.795689i 0.0169219 + 0.0293096i
\(738\) −6.88127 1.80284i −0.253303 0.0663635i
\(739\) 13.7608 23.8344i 0.506198 0.876761i −0.493776 0.869589i \(-0.664384\pi\)
0.999974 0.00717223i \(-0.00228301\pi\)
\(740\) 15.3230 26.5402i 0.563284 0.975637i
\(741\) −5.37158 + 2.24252i −0.197330 + 0.0823809i
\(742\) 0 0
\(743\) −7.00608 + 12.1349i −0.257028 + 0.445186i −0.965444 0.260609i \(-0.916077\pi\)
0.708416 + 0.705795i \(0.249410\pi\)
\(744\) −9.19037 7.01147i −0.336935 0.257053i
\(745\) 77.6326 2.84424
\(746\) −0.932261 + 1.61472i −0.0341325 + 0.0591192i
\(747\) −35.7623 9.36947i −1.30848 0.342811i
\(748\) −0.391390 −0.0143106
\(749\) 0 0
\(750\) −1.47297 + 11.4342i −0.0537854 + 0.417516i
\(751\) −52.2594 −1.90697 −0.953486 0.301436i \(-0.902534\pi\)
−0.953486 + 0.301436i \(0.902534\pi\)
\(752\) −13.1494 22.7755i −0.479511 0.830537i
\(753\) −13.6356 + 5.69254i −0.496907 + 0.207448i
\(754\) −1.22912 + 2.12889i −0.0447618 + 0.0775298i
\(755\) 5.53289 0.201363
\(756\) 0 0
\(757\) −43.3447 −1.57539 −0.787694 0.616066i \(-0.788725\pi\)
−0.787694 + 0.616066i \(0.788725\pi\)
\(758\) 8.15047 14.1170i 0.296038 0.512753i
\(759\) 3.53481 1.47571i 0.128306 0.0535647i
\(760\) −9.65191 16.7176i −0.350112 0.606411i
\(761\) 17.2510 0.625348 0.312674 0.949860i \(-0.398775\pi\)
0.312674 + 0.949860i \(0.398775\pi\)
\(762\) 0.139304 1.08137i 0.00504646 0.0391738i
\(763\) 0 0
\(764\) 41.8285 1.51330
\(765\) −0.731610 2.67085i −0.0264514 0.0965650i
\(766\) 0.265952 0.460642i 0.00960922 0.0166437i
\(767\) −2.16889 −0.0783139
\(768\) −0.341127 0.260251i −0.0123094 0.00939100i
\(769\) 10.6727 18.4856i 0.384867 0.666609i −0.606884 0.794790i \(-0.707581\pi\)
0.991751 + 0.128182i \(0.0409141\pi\)
\(770\) 0 0
\(771\) −27.3634 + 11.4236i −0.985469 + 0.411411i
\(772\) 5.20495 9.01523i 0.187330 0.324465i
\(773\) 6.57357 11.3858i 0.236435 0.409517i −0.723254 0.690582i \(-0.757354\pi\)
0.959689 + 0.281065i \(0.0906877\pi\)
\(774\) −10.4378 + 10.5547i −0.375180 + 0.379380i
\(775\) 15.4791 + 26.8106i 0.556027 + 0.963066i
\(776\) −10.2796 17.8049i −0.369018 0.639158i
\(777\) 0 0
\(778\) −5.88685 + 10.1963i −0.211054 + 0.365556i
\(779\) −13.4288 −0.481136
\(780\) 12.3894 5.17230i 0.443612 0.185198i
\(781\) 4.41405