Properties

Label 441.2.f.f.295.3
Level $441$
Weight $2$
Character 441.295
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.f (of order \(3\), degree \(2\), 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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 295.3
Root \(0.247934 - 0.429435i\) of defining polynomial
Character \(\chi\) \(=\) 441.295
Dual form 441.2.f.f.148.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.247934 - 0.429435i) q^{2} +(1.37706 - 1.05058i) q^{3} +(0.877057 + 1.51911i) q^{4} +(-1.84629 - 3.19787i) q^{5} +(-0.109735 - 0.851830i) q^{6} +1.86155 q^{8} +(0.792574 - 2.89341i) q^{9} +O(q^{10})\) \(q+(0.247934 - 0.429435i) q^{2} +(1.37706 - 1.05058i) q^{3} +(0.877057 + 1.51911i) q^{4} +(-1.84629 - 3.19787i) q^{5} +(-0.109735 - 0.851830i) q^{6} +1.86155 q^{8} +(0.792574 - 2.89341i) q^{9} -1.83103 q^{10} +(0.446284 - 0.772987i) q^{11} +(2.80370 + 1.17048i) q^{12} +(-0.598355 - 1.03638i) q^{13} +(-5.90205 - 2.46398i) q^{15} +(-1.29257 + 2.23880i) q^{16} -0.249983 q^{17} +(-1.04602 - 1.05773i) q^{18} +2.80827 q^{19} +(3.23860 - 5.60943i) q^{20} +(-0.221298 - 0.383300i) q^{22} +(-1.23886 - 2.14576i) q^{23} +(2.56346 - 1.95570i) q^{24} +(-4.31757 + 7.47825i) q^{25} -0.593411 q^{26} +(-1.94833 - 4.81705i) q^{27} +(2.07128 - 3.58755i) q^{29} +(-2.52144 + 1.92364i) q^{30} +(1.79257 + 3.10483i) q^{31} +(2.50249 + 4.33444i) q^{32} +(-0.197524 - 1.53330i) q^{33} +(-0.0619793 + 0.107351i) q^{34} +(5.09054 - 1.33368i) q^{36} +4.73136 q^{37} +(0.696267 - 1.20597i) q^{38} +(-1.91277 - 0.798539i) q^{39} +(-3.43695 - 5.95298i) q^{40} +(2.39093 + 4.14121i) q^{41} +(-4.98928 + 8.64169i) q^{43} +1.56567 q^{44} +(-10.7161 + 2.80753i) q^{45} -1.22862 q^{46} +(-5.08653 + 8.81013i) q^{47} +(0.572088 + 4.44091i) q^{48} +(2.14095 + 3.70823i) q^{50} +(-0.344241 + 0.262626i) q^{51} +(1.04958 - 1.81793i) q^{52} +9.88929 q^{53} +(-2.55167 - 0.357630i) q^{54} -3.29588 q^{55} +(3.86715 - 2.95031i) q^{57} +(-1.02708 - 1.77895i) q^{58} +(0.906186 + 1.56956i) q^{59} +(-1.43339 - 11.1269i) q^{60} +(5.40205 - 9.35663i) q^{61} +1.77776 q^{62} -2.68848 q^{64} +(-2.20948 + 3.82692i) q^{65} +(-0.707426 - 0.295335i) q^{66} +(-0.514685 - 0.891460i) q^{67} +(-0.219249 - 0.379751i) q^{68} +(-3.96027 - 1.65332i) q^{69} -4.94533 q^{71} +(1.47541 - 5.38622i) q^{72} -1.83052 q^{73} +(1.17306 - 2.03181i) q^{74} +(1.91094 + 14.8339i) q^{75} +(2.46302 + 4.26607i) q^{76} +(-0.817161 + 0.623424i) q^{78} +(0.899562 - 1.55809i) q^{79} +9.54586 q^{80} +(-7.74365 - 4.58648i) q^{81} +2.37117 q^{82} +(-6.16156 + 10.6721i) q^{83} +(0.461541 + 0.799412i) q^{85} +(2.47403 + 4.28514i) q^{86} +(-0.916739 - 7.11630i) q^{87} +(0.830779 - 1.43895i) q^{88} -2.40741 q^{89} +(-1.45123 + 5.29793i) q^{90} +(2.17310 - 3.76392i) q^{92} +(5.73034 + 2.39229i) q^{93} +(2.52225 + 4.36867i) q^{94} +(-5.18489 - 8.98049i) q^{95} +(7.99975 + 3.33972i) q^{96} +(-5.52210 + 9.56456i) q^{97} +(-1.88286 - 1.90393i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{2} + q^{3} - 4q^{4} - 4q^{5} + 2q^{6} - 6q^{8} - 7q^{9} + O(q^{10}) \) \( 10q + 2q^{2} + q^{3} - 4q^{4} - 4q^{5} + 2q^{6} - 6q^{8} - 7q^{9} - 14q^{10} + 4q^{11} + 2q^{12} + 8q^{13} - 19q^{15} + 2q^{16} + 24q^{17} - 2q^{18} + 2q^{19} - 5q^{20} - q^{22} + 3q^{23} + 9q^{24} - q^{25} + 22q^{26} + 7q^{27} + 7q^{29} + 10q^{30} + 3q^{31} - 2q^{32} + 13q^{33} - 3q^{34} + 34q^{36} - 20q^{38} - 22q^{39} + 3q^{40} - 5q^{41} - 7q^{43} + 20q^{44} - 17q^{45} - 6q^{46} - 27q^{47} + 5q^{48} + 19q^{50} - 15q^{51} + 10q^{52} + 42q^{53} - 52q^{54} - 4q^{55} - 4q^{57} - 10q^{58} - 30q^{59} + 31q^{60} + 14q^{61} + 12q^{62} - 50q^{64} - 11q^{65} - 22q^{66} - 2q^{67} - 27q^{68} - 15q^{69} - 6q^{71} - 12q^{72} + 30q^{73} - 36q^{74} + 17q^{75} - 5q^{76} - 20q^{78} - 4q^{79} + 40q^{80} - 31q^{81} - 10q^{82} - 9q^{83} - 6q^{85} - 8q^{86} + 34q^{87} - 18q^{88} + 56q^{89} - 28q^{90} + 27q^{92} + 18q^{93} + 3q^{94} - 14q^{95} + 58q^{96} + 12q^{97} + 35q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.247934 0.429435i 0.175316 0.303656i −0.764955 0.644084i \(-0.777239\pi\)
0.940271 + 0.340428i \(0.110572\pi\)
\(3\) 1.37706 1.05058i 0.795044 0.606551i
\(4\) 0.877057 + 1.51911i 0.438529 + 0.759554i
\(5\) −1.84629 3.19787i −0.825686 1.43013i −0.901394 0.433000i \(-0.857455\pi\)
0.0757082 0.997130i \(-0.475878\pi\)
\(6\) −0.109735 0.851830i −0.0447990 0.347758i
\(7\) 0 0
\(8\) 1.86155 0.658156
\(9\) 0.792574 2.89341i 0.264191 0.964470i
\(10\) −1.83103 −0.579023
\(11\) 0.446284 0.772987i 0.134560 0.233064i −0.790869 0.611985i \(-0.790371\pi\)
0.925429 + 0.378921i \(0.123705\pi\)
\(12\) 2.80370 + 1.17048i 0.809358 + 0.337889i
\(13\) −0.598355 1.03638i −0.165954 0.287441i 0.771040 0.636787i \(-0.219737\pi\)
−0.936994 + 0.349346i \(0.886404\pi\)
\(14\) 0 0
\(15\) −5.90205 2.46398i −1.52390 0.636196i
\(16\) −1.29257 + 2.23880i −0.323143 + 0.559701i
\(17\) −0.249983 −0.0606298 −0.0303149 0.999540i \(-0.509651\pi\)
−0.0303149 + 0.999540i \(0.509651\pi\)
\(18\) −1.04602 1.05773i −0.246550 0.249310i
\(19\) 2.80827 0.644262 0.322131 0.946695i \(-0.395601\pi\)
0.322131 + 0.946695i \(0.395601\pi\)
\(20\) 3.23860 5.60943i 0.724174 1.25431i
\(21\) 0 0
\(22\) −0.221298 0.383300i −0.0471809 0.0817198i
\(23\) −1.23886 2.14576i −0.258320 0.447423i 0.707472 0.706741i \(-0.249835\pi\)
−0.965792 + 0.259318i \(0.916502\pi\)
\(24\) 2.56346 1.95570i 0.523263 0.399205i
\(25\) −4.31757 + 7.47825i −0.863514 + 1.49565i
\(26\) −0.593411 −0.116377
\(27\) −1.94833 4.81705i −0.374957 0.927042i
\(28\) 0 0
\(29\) 2.07128 3.58755i 0.384626 0.666192i −0.607091 0.794632i \(-0.707664\pi\)
0.991717 + 0.128440i \(0.0409970\pi\)
\(30\) −2.52144 + 1.92364i −0.460349 + 0.351207i
\(31\) 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
\(33\) −0.197524 1.53330i −0.0343845 0.266914i
\(34\) −0.0619793 + 0.107351i −0.0106294 + 0.0184106i
\(35\) 0 0
\(36\) 5.09054 1.33368i 0.848423 0.222280i
\(37\) 4.73136 0.777830 0.388915 0.921274i \(-0.372850\pi\)
0.388915 + 0.921274i \(0.372850\pi\)
\(38\) 0.696267 1.20597i 0.112949 0.195634i
\(39\) −1.91277 0.798539i −0.306288 0.127869i
\(40\) −3.43695 5.95298i −0.543430 0.941249i
\(41\) 2.39093 + 4.14121i 0.373400 + 0.646748i 0.990086 0.140461i \(-0.0448584\pi\)
−0.616686 + 0.787209i \(0.711525\pi\)
\(42\) 0 0
\(43\) −4.98928 + 8.64169i −0.760859 + 1.31785i 0.181550 + 0.983382i \(0.441889\pi\)
−0.942408 + 0.334464i \(0.891445\pi\)
\(44\) 1.56567 0.236033
\(45\) −10.7161 + 2.80753i −1.59746 + 0.418522i
\(46\) −1.22862 −0.181150
\(47\) −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
\(51\) −0.344241 + 0.262626i −0.0482034 + 0.0367751i
\(52\) 1.04958 1.81793i 0.145551 0.252102i
\(53\) 9.88929 1.35840 0.679199 0.733954i \(-0.262327\pi\)
0.679199 + 0.733954i \(0.262327\pi\)
\(54\) −2.55167 0.357630i −0.347238 0.0486673i
\(55\) −3.29588 −0.444416
\(56\) 0 0
\(57\) 3.86715 2.95031i 0.512217 0.390778i
\(58\) −1.02708 1.77895i −0.134862 0.233588i
\(59\) 0.906186 + 1.56956i 0.117975 + 0.204339i 0.918965 0.394339i \(-0.129026\pi\)
−0.800990 + 0.598678i \(0.795693\pi\)
\(60\) −1.43339 11.1269i −0.185050 1.43648i
\(61\) 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
\(66\) −0.707426 0.295335i −0.0870781 0.0363532i
\(67\) −0.514685 0.891460i −0.0628787 0.108909i 0.832872 0.553465i \(-0.186695\pi\)
−0.895751 + 0.444556i \(0.853361\pi\)
\(68\) −0.219249 0.379751i −0.0265879 0.0460516i
\(69\) −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 \(0.594804\pi\)
\(72\) 1.47541 5.38622i 0.173879 0.634772i
\(73\) −1.83052 −0.214247 −0.107123 0.994246i \(-0.534164\pi\)
−0.107123 + 0.994246i \(0.534164\pi\)
\(74\) 1.17306 2.03181i 0.136366 0.236193i
\(75\) 1.91094 + 14.8339i 0.220656 + 1.71287i
\(76\) 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 \(0.134396\pi\)
\(80\) 9.54586 1.06726
\(81\) −7.74365 4.58648i −0.860406 0.509609i
\(82\) 2.37117 0.261852
\(83\) −6.16156 + 10.6721i −0.676319 + 1.17142i 0.299763 + 0.954014i \(0.403092\pi\)
−0.976082 + 0.217405i \(0.930241\pi\)
\(84\) 0 0
\(85\) 0.461541 + 0.799412i 0.0500611 + 0.0867084i
\(86\) 2.47403 + 4.28514i 0.266781 + 0.462079i
\(87\) −0.916739 7.11630i −0.0982847 0.762948i
\(88\) 0.830779 1.43895i 0.0885613 0.153393i
\(89\) −2.40741 −0.255185 −0.127592 0.991827i \(-0.540725\pi\)
−0.127592 + 0.991827i \(0.540725\pi\)
\(90\) −1.45123 + 5.29793i −0.152973 + 0.558451i
\(91\) 0 0
\(92\) 2.17310 3.76392i 0.226561 0.392416i
\(93\) 5.73034 + 2.39229i 0.594209 + 0.248069i
\(94\) 2.52225 + 4.36867i 0.260150 + 0.450593i
\(95\) −5.18489 8.98049i −0.531958 0.921379i
\(96\) 7.99975 + 3.33972i 0.816471 + 0.340858i
\(97\) −5.52210 + 9.56456i −0.560684 + 0.971134i 0.436752 + 0.899582i \(0.356129\pi\)
−0.997437 + 0.0715522i \(0.977205\pi\)
\(98\) 0 0
\(99\) −1.88286 1.90393i −0.189234 0.191352i
\(100\) −15.1470 −1.51470
\(101\) −1.29982 + 2.25136i −0.129337 + 0.224018i −0.923420 0.383791i \(-0.874618\pi\)
0.794083 + 0.607810i \(0.207952\pi\)
\(102\) 0.0274318 + 0.212943i 0.00271615 + 0.0210845i
\(103\) 4.85578 + 8.41045i 0.478454 + 0.828706i 0.999695 0.0247032i \(-0.00786408\pi\)
−0.521241 + 0.853409i \(0.674531\pi\)
\(104\) −1.11387 1.92927i −0.109224 0.189181i
\(105\) 0 0
\(106\) 2.45189 4.24680i 0.238149 0.412486i
\(107\) 10.9005 1.05379 0.526896 0.849930i \(-0.323356\pi\)
0.526896 + 0.849930i \(0.323356\pi\)
\(108\) 5.60882 7.18456i 0.539709 0.691335i
\(109\) 2.12193 0.203244 0.101622 0.994823i \(-0.467597\pi\)
0.101622 + 0.994823i \(0.467597\pi\)
\(110\) −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 0.950470 + 0.310816i \(0.100602\pi\)
−0.206061 + 0.978539i \(0.566065\pi\)
\(114\) −0.308165 2.39217i −0.0288623 0.224047i
\(115\) −4.57458 + 7.92341i −0.426582 + 0.738861i
\(116\) 7.26651 0.674679
\(117\) −3.47292 + 0.909879i −0.321072 + 0.0841183i
\(118\) 0.898698 0.0827318
\(119\) 0 0
\(120\) −10.9869 4.58681i −1.00297 0.418716i
\(121\) 5.10166 + 8.83634i 0.463787 + 0.803303i
\(122\) −2.67871 4.63966i −0.242519 0.420055i
\(123\) 7.64311 + 3.19083i 0.689156 + 0.287707i
\(124\) −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
\(129\) 2.20824 + 17.1417i 0.194425 + 1.50925i
\(130\) 1.09561 + 1.89765i 0.0960912 + 0.166435i
\(131\) −7.51444 13.0154i −0.656540 1.13716i −0.981505 0.191435i \(-0.938686\pi\)
0.324965 0.945726i \(-0.394647\pi\)
\(132\) 2.15601 1.64485i 0.187657 0.143166i
\(133\) 0 0
\(134\) −0.510432 −0.0440946
\(135\) −11.8071 + 15.1242i −1.01619 + 1.30168i
\(136\) −0.465355 −0.0399038
\(137\) 0.244246 0.423047i 0.0208674 0.0361433i −0.855403 0.517963i \(-0.826691\pi\)
0.876271 + 0.481819i \(0.160024\pi\)
\(138\) −1.69188 + 1.29076i −0.144022 + 0.109877i
\(139\) 4.93487 + 8.54745i 0.418570 + 0.724985i 0.995796 0.0915997i \(-0.0291980\pi\)
−0.577226 + 0.816585i \(0.695865\pi\)
\(140\) 0 0
\(141\) 2.25128 + 17.4759i 0.189592 + 1.47173i
\(142\) −1.22612 + 2.12370i −0.102893 + 0.178217i
\(143\) −1.06815 −0.0893229
\(144\) 5.45332 + 5.51436i 0.454443 + 0.459530i
\(145\) −15.2967 −1.27032
\(146\) −0.453849 + 0.786090i −0.0375609 + 0.0650573i
\(147\) 0 0
\(148\) 4.14967 + 7.18744i 0.341101 + 0.590804i
\(149\) −10.5120 18.2073i −0.861175 1.49160i −0.870796 0.491645i \(-0.836396\pi\)
0.00962096 0.999954i \(-0.496938\pi\)
\(150\) 6.84399 + 2.85721i 0.558809 + 0.233290i
\(151\) −0.749191 + 1.29764i −0.0609683 + 0.105600i −0.894898 0.446270i \(-0.852752\pi\)
0.833930 + 0.551870i \(0.186086\pi\)
\(152\) 5.22773 0.424025
\(153\) −0.198130 + 0.723303i −0.0160179 + 0.0584756i
\(154\) 0 0
\(155\) 6.61922 11.4648i 0.531669 0.920877i
\(156\) −0.464542 3.60607i −0.0371931 0.288716i
\(157\) −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
\(159\) 13.6181 10.3895i 1.07999 0.823938i
\(160\) 9.24065 16.0053i 0.730538 1.26533i
\(161\) 0 0
\(162\) −3.88951 + 2.18825i −0.305589 + 0.171925i
\(163\) 6.68269 0.523429 0.261714 0.965145i \(-0.415712\pi\)
0.261714 + 0.965145i \(0.415712\pi\)
\(164\) −4.19396 + 7.26416i −0.327494 + 0.567236i
\(165\) −4.53861 + 3.46258i −0.353331 + 0.269561i
\(166\) 3.05532 + 5.29197i 0.237139 + 0.410737i
\(167\) −8.81549 15.2689i −0.682163 1.18154i −0.974319 0.225170i \(-0.927706\pi\)
0.292156 0.956371i \(-0.405627\pi\)
\(168\) 0 0
\(169\) 5.78394 10.0181i 0.444919 0.770622i
\(170\) 0.457727 0.0351061
\(171\) 2.22576 8.12549i 0.170208 0.621372i
\(172\) −17.5036 −1.33463
\(173\) −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
\(177\) 2.89681 + 1.20936i 0.217738 + 0.0909007i
\(178\) −0.596879 + 1.03382i −0.0447380 + 0.0774884i
\(179\) −7.33516 −0.548256 −0.274128 0.961693i \(-0.588389\pi\)
−0.274128 + 0.961693i \(0.588389\pi\)
\(180\) −13.6635 13.8165i −1.01842 1.02982i
\(181\) −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
\(184\) −2.30619 3.99444i −0.170015 0.294474i
\(185\) −8.73545 15.1302i −0.642243 1.11240i
\(186\) 2.44808 1.86768i 0.179502 0.136945i
\(187\) −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 \(-0.164571\pi\)
\(192\) −3.70219 + 2.82446i −0.267183 + 0.203838i
\(193\) −2.96728 5.13948i −0.213589 0.369948i 0.739246 0.673436i \(-0.235182\pi\)
−0.952835 + 0.303488i \(0.901849\pi\)
\(194\) 2.73823 + 4.74276i 0.196594 + 0.340510i
\(195\) 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 \(0.685766\pi\)
\(198\) −1.28444 + 0.336513i −0.0912811 + 0.0239150i
\(199\) 15.4964 1.09851 0.549254 0.835655i \(-0.314912\pi\)
0.549254 + 0.835655i \(0.314912\pi\)
\(200\) −8.03736 + 13.9211i −0.568327 + 0.984371i
\(201\) −1.64530 0.686875i −0.116050 0.0484485i
\(202\) 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
\(206\) 4.81565 0.335522
\(207\) −7.19047 + 1.88385i −0.499772 + 0.130936i
\(208\) 3.09367 0.214508
\(209\) 1.25329 2.17076i 0.0866918 0.150155i
\(210\) 0 0
\(211\) 0.771898 + 1.33697i 0.0531397 + 0.0920406i 0.891372 0.453273i \(-0.149744\pi\)
−0.838232 + 0.545314i \(0.816410\pi\)
\(212\) 8.67347 + 15.0229i 0.595697 + 1.03178i
\(213\) −6.81001 + 5.19545i −0.466614 + 0.355987i
\(214\) 2.70261 4.68105i 0.184746 0.319990i
\(215\) 36.8467 2.51292
\(216\) −3.62691 8.96717i −0.246780 0.610138i
\(217\) 0 0
\(218\) 0.526098 0.911229i 0.0356319 0.0617162i
\(219\) −2.52074 + 1.92311i −0.170336 + 0.129952i
\(220\) −2.89068 5.00680i −0.194889 0.337558i
\(221\) 0.149579 + 0.259078i 0.0100617 + 0.0174275i
\(222\) −0.519194 4.03031i −0.0348460 0.270497i
\(223\) 2.72171 4.71414i 0.182259 0.315682i −0.760390 0.649466i \(-0.774992\pi\)
0.942649 + 0.333784i \(0.108326\pi\)
\(224\) 0 0
\(225\) 18.2157 + 18.4196i 1.21438 + 1.22797i
\(226\) 7.84779 0.522027
\(227\) −8.03818 + 13.9225i −0.533513 + 0.924072i 0.465721 + 0.884932i \(0.345795\pi\)
−0.999234 + 0.0391399i \(0.987538\pi\)
\(228\) 7.87356 + 3.28703i 0.521439 + 0.217689i
\(229\) −4.98420 8.63289i −0.329365 0.570477i 0.653021 0.757340i \(-0.273501\pi\)
−0.982386 + 0.186863i \(0.940168\pi\)
\(230\) 2.26839 + 3.92897i 0.149573 + 0.259068i
\(231\) 0 0
\(232\) 3.85578 6.67840i 0.253144 0.438458i
\(233\) −16.5409 −1.08363 −0.541815 0.840498i \(-0.682263\pi\)
−0.541815 + 0.840498i \(0.682263\pi\)
\(234\) −0.470322 + 1.71698i −0.0307459 + 0.112243i
\(235\) 37.5648 2.45046
\(236\) −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 −0.963990 0.265937i \(-0.914319\pi\)
0.251687 0.967809i \(-0.419015\pi\)
\(240\) 13.1452 10.0287i 0.848519 0.647348i
\(241\) 8.36004 14.4800i 0.538517 0.932739i −0.460467 0.887677i \(-0.652318\pi\)
0.998984 0.0450623i \(-0.0143486\pi\)
\(242\) 5.05950 0.325237
\(243\) −15.4819 + 1.81946i −0.993165 + 0.116718i
\(244\) 18.9516 1.21325
\(245\) 0 0
\(246\) 3.26524 2.49110i 0.208184 0.158827i
\(247\) −1.68035 2.91045i −0.106918 0.185187i
\(248\) 3.33696 + 5.77978i 0.211897 + 0.367017i
\(249\) 2.72708 + 21.1693i 0.172822 + 1.34155i
\(250\) 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
\(255\) 1.47541 + 0.615952i 0.0923939 + 0.0385724i
\(256\) 0.123861 + 0.214533i 0.00774131 + 0.0134083i
\(257\) −8.55986 14.8261i −0.533950 0.924828i −0.999213 0.0396557i \(-0.987374\pi\)
0.465264 0.885172i \(-0.345959\pi\)
\(258\) 7.90875 + 3.30173i 0.492377 + 0.205557i
\(259\) 0 0
\(260\) −7.75135 −0.480718
\(261\) −8.73863 8.83645i −0.540908 0.546963i
\(262\) −7.45235 −0.460408
\(263\) −10.2763 + 17.7991i −0.633666 + 1.09754i 0.353130 + 0.935574i \(0.385117\pi\)
−0.986796 + 0.161967i \(0.948216\pi\)
\(264\) −0.367700 2.85432i −0.0226303 0.175671i
\(265\) −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
\(269\) 19.8453 1.20999 0.604996 0.796229i \(-0.293175\pi\)
0.604996 + 0.796229i \(0.293175\pi\)
\(270\) 3.56746 + 8.82018i 0.217109 + 0.536779i
\(271\) 10.6411 0.646402 0.323201 0.946330i \(-0.395241\pi\)
0.323201 + 0.946330i \(0.395241\pi\)
\(272\) 0.323121 0.559663i 0.0195921 0.0339345i
\(273\) 0 0
\(274\) −0.121114 0.209776i −0.00731676 0.0126730i
\(275\) 3.85373 + 6.67485i 0.232388 + 0.402509i
\(276\) −0.961806 7.46614i −0.0578939 0.449409i
\(277\) 12.4407 21.5479i 0.747487 1.29469i −0.201536 0.979481i \(-0.564593\pi\)
0.949024 0.315205i \(-0.102073\pi\)
\(278\) 4.89409 0.293528
\(279\) 10.4043 2.72585i 0.622889 0.163192i
\(280\) 0 0
\(281\) −6.83733 + 11.8426i −0.407881 + 0.706470i −0.994652 0.103282i \(-0.967065\pi\)
0.586771 + 0.809753i \(0.300399\pi\)
\(282\) 8.06290 + 3.36608i 0.480139 + 0.200447i
\(283\) 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
\(285\) −16.5746 6.91952i −0.981794 0.409877i
\(286\) −0.264830 + 0.458699i −0.0156597 + 0.0271234i
\(287\) 0 0
\(288\) 14.5247 3.80537i 0.855878 0.224234i
\(289\) −16.9375 −0.996324
\(290\) −3.79257 + 6.56893i −0.222708 + 0.385741i
\(291\) 2.44406 + 18.9723i 0.143273 + 1.11218i
\(292\) −1.60547 2.78076i −0.0939533 0.162732i
\(293\) 1.31508 + 2.27778i 0.0768277 + 0.133069i 0.901880 0.431987i \(-0.142188\pi\)
−0.825052 + 0.565057i \(0.808854\pi\)
\(294\) 0 0
\(295\) 3.34616 5.79573i 0.194821 0.337440i
\(296\) 8.80764 0.511934
\(297\) −4.59303 0.643739i −0.266515 0.0373535i
\(298\) −10.4251 −0.603911
\(299\) −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
\(303\) 0.575296 + 4.46581i 0.0330499 + 0.256554i
\(304\) −3.62990 + 6.28717i −0.208189 + 0.360594i
\(305\) −39.8950 −2.28438
\(306\) 0.261488 + 0.264415i 0.0149483 + 0.0151156i
\(307\) 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
\(310\) −3.28226 5.68504i −0.186420 0.322889i
\(311\) −7.55013 13.0772i −0.428129 0.741541i 0.568578 0.822629i \(-0.307494\pi\)
−0.996707 + 0.0810885i \(0.974160\pi\)
\(312\) −3.56071 1.48652i −0.201585 0.0841574i
\(313\) −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 \(0.800209\pi\)
\(318\) −1.08520 8.42399i −0.0608549 0.472394i
\(319\) −1.84875 3.20214i −0.103510 0.179285i
\(320\) 4.96372 + 8.59741i 0.277480 + 0.480610i
\(321\) 15.0106 11.4518i 0.837811 0.639179i
\(322\) 0 0
\(323\) −0.702021 −0.0390615
\(324\) 0.175735 15.7861i 0.00976303 0.877003i
\(325\) 10.3338 0.573214
\(326\) 1.65687 2.86978i 0.0917654 0.158942i
\(327\) 2.92201 2.22925i 0.161588 0.123278i
\(328\) 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 \(0.332338\pi\)
\(332\) −21.6162 −1.18634
\(333\) 3.74995 13.6898i 0.205496 0.750194i
\(334\) −8.74264 −0.478376
\(335\) −1.90051 + 3.29179i −0.103836 + 0.179850i
\(336\) 0 0
\(337\) −12.5086 21.6656i −0.681389 1.18020i −0.974557 0.224139i \(-0.928043\pi\)
0.293168 0.956061i \(-0.405290\pi\)
\(338\) −2.86807 4.96765i −0.156003 0.270204i
\(339\) 25.2961 + 10.5606i 1.37390 + 0.573572i
\(340\) −0.809596 + 1.40226i −0.0439065 + 0.0760483i
\(341\) 3.19999 0.173289
\(342\) −2.93752 2.97041i −0.158843 0.160621i
\(343\) 0 0
\(344\) −9.28778 + 16.0869i −0.500764 + 0.867348i
\(345\) 2.02469 + 15.7169i 0.109006 + 0.846171i
\(346\) 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 \(0.926495\pi\)
\(348\) 10.0064 7.63403i 0.536399 0.409227i
\(349\) 1.64301 2.84577i 0.0879482 0.152331i −0.818695 0.574228i \(-0.805302\pi\)
0.906644 + 0.421897i \(0.138636\pi\)
\(350\) 0 0
\(351\) −3.82651 + 4.90153i −0.204244 + 0.261624i
\(352\) 4.46729 0.238107
\(353\) 8.40960 14.5658i 0.447598 0.775262i −0.550631 0.834748i \(-0.685613\pi\)
0.998229 + 0.0594866i \(0.0189463\pi\)
\(354\) 1.23756 0.944152i 0.0657755 0.0501811i
\(355\) 9.13051 + 15.8145i 0.484597 + 0.839347i
\(356\) −2.11144 3.65711i −0.111906 0.193827i
\(357\) 0 0
\(358\) −1.81864 + 3.14997i −0.0961180 + 0.166481i
\(359\) −23.7842 −1.25528 −0.627642 0.778502i \(-0.715980\pi\)
−0.627642 + 0.778502i \(0.715980\pi\)
\(360\) −19.9485 + 5.22634i −1.05138 + 0.275453i
\(361\) −11.1136 −0.584926
\(362\) −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
\(366\) −8.56305 3.57488i −0.447598 0.186862i
\(367\) −0.344992 + 0.597544i −0.0180084 + 0.0311915i −0.874889 0.484323i \(-0.839066\pi\)
0.856881 + 0.515515i \(0.172399\pi\)
\(368\) 6.40526 0.333897
\(369\) 13.8772 3.63573i 0.722419 0.189268i
\(370\) −8.66327 −0.450382
\(371\) 0 0
\(372\) 1.39169 + 10.8032i 0.0721558 + 0.560119i
\(373\) 1.88006 + 3.25636i 0.0973457 + 0.168608i 0.910585 0.413321i \(-0.135631\pi\)
−0.813239 + 0.581929i \(0.802298\pi\)
\(374\) 0.0553208 + 0.0958184i 0.00286057 + 0.00495465i
\(375\) 18.4843 14.1020i 0.954525 0.728222i
\(376\) −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
\(381\) −1.74812 + 1.33367i −0.0895591 + 0.0683260i
\(382\) −5.91222 10.2403i −0.302495 0.523937i
\(383\) −0.536335 0.928960i −0.0274055 0.0474676i 0.851997 0.523546i \(-0.175391\pi\)
−0.879403 + 0.476078i \(0.842058\pi\)
\(384\) 2.51021 + 19.4858i 0.128099 + 0.994381i
\(385\) 0 0
\(386\) −2.94276 −0.149782
\(387\) 21.0496 + 21.2852i 1.07001 + 1.08199i
\(388\) −19.3728 −0.983505
\(389\) 11.8718 20.5626i 0.601925 1.04256i −0.390605 0.920559i \(-0.627734\pi\)
0.992529 0.122006i \(-0.0389326\pi\)
\(390\) 3.50234 + 1.46215i 0.177348 + 0.0740389i
\(391\) 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
\(395\) −6.64340 −0.334266
\(396\) 1.24091 4.53012i 0.0623579 0.227647i
\(397\) −0.0320978 −0.00161094 −0.000805471 1.00000i \(-0.500256\pi\)
−0.000805471 1.00000i \(0.500256\pi\)
\(398\) 3.84208 6.65467i 0.192586 0.333569i
\(399\) 0 0
\(400\) −11.1616 19.3324i −0.558078 0.966619i
\(401\) −12.2628 21.2398i −0.612374 1.06066i −0.990839 0.135048i \(-0.956881\pi\)
0.378465 0.925616i \(-0.376452\pi\)
\(402\) −0.702894 + 0.536248i −0.0350571 + 0.0267456i
\(403\) 2.14519 3.71558i 0.106860 0.185086i
\(404\) −4.56007 −0.226872
\(405\) −0.369938 + 33.2312i −0.0183824 + 1.65127i
\(406\) 0 0
\(407\) 2.11153 3.65728i 0.104665 0.181284i
\(408\) −0.640820 + 0.488891i −0.0317253 + 0.0242037i
\(409\) 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
\(411\) −0.108103 0.839160i −0.00533230 0.0413927i
\(412\) −8.51759 + 14.7529i −0.419631 + 0.726823i
\(413\) 0 0
\(414\) −0.973773 + 3.55490i −0.0478583 + 0.174714i
\(415\) 45.5041 2.23371
\(416\) 2.99476 5.18708i 0.146830 0.254317i
\(417\) 15.7754 + 6.58586i 0.772522 + 0.322511i
\(418\) −0.621466 1.07641i −0.0303969 0.0526490i
\(419\) 10.5262 + 18.2320i 0.514240 + 0.890689i 0.999864 + 0.0165215i \(0.00525920\pi\)
−0.485624 + 0.874168i \(0.661407\pi\)
\(420\) 0 0
\(421\) −7.44533 + 12.8957i −0.362863 + 0.628498i −0.988431 0.151672i \(-0.951534\pi\)
0.625568 + 0.780170i \(0.284867\pi\)
\(422\) 0.765520 0.0372649
\(423\) 21.4599 + 21.7001i 1.04342 + 1.05510i
\(424\) 18.4094 0.894038
\(425\) 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
\(429\) −1.47090 + 1.12217i −0.0710157 + 0.0541789i
\(430\) 9.13554 15.8232i 0.440555 0.763064i
\(431\) 15.9038 0.766061 0.383031 0.923736i \(-0.374880\pi\)
0.383031 + 0.923736i \(0.374880\pi\)
\(432\) 13.3028 + 1.86446i 0.640031 + 0.0897040i
\(433\) 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
\(436\) 1.86105 + 3.22344i 0.0891282 + 0.154375i
\(437\) −3.47905 6.02590i −0.166426 0.288258i
\(438\) 0.200872 + 1.55930i 0.00959804 + 0.0745060i
\(439\) −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 \(0.180207\pi\)
\(444\) 13.2653 + 5.53797i 0.629543 + 0.262820i
\(445\) 4.44477 + 7.69857i 0.210702 + 0.364947i
\(446\) −1.34961 2.33759i −0.0639058 0.110688i
\(447\) −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 \(0.396275\pi\)
\(450\) 12.4263 3.25559i 0.585781 0.153470i
\(451\) 4.26814 0.200979
\(452\) −13.8806 + 24.0419i −0.652890 + 1.13084i
\(453\) 0.331589 + 2.57400i 0.0155794 + 0.120937i
\(454\) 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 \(0.185806\pi\)
\(458\) −4.94301 −0.230972
\(459\) 0.487050 + 1.20418i 0.0227335 + 0.0562064i
\(460\) −16.0487 −0.748274
\(461\) −18.0934 + 31.3388i −0.842695 + 1.45959i 0.0449122 + 0.998991i \(0.485699\pi\)
−0.887608 + 0.460600i \(0.847634\pi\)
\(462\) 0 0
\(463\) 8.19224 + 14.1894i 0.380726 + 0.659436i 0.991166 0.132626i \(-0.0423409\pi\)
−0.610440 + 0.792062i \(0.709008\pi\)
\(464\) 5.35455 + 9.27436i 0.248579 + 0.430551i
\(465\) −2.92964 22.7417i −0.135859 1.05462i
\(466\) −4.10105 + 7.10323i −0.189978 + 0.329051i
\(467\) −8.70044 −0.402608 −0.201304 0.979529i \(-0.564518\pi\)
−0.201304 + 0.979529i \(0.564518\pi\)
\(468\) −4.42815 4.47772i −0.204692 0.206983i
\(469\) 0 0
\(470\) 9.31361 16.1316i 0.429605 0.744097i
\(471\) −26.6600 11.1300i −1.22843 0.512841i
\(472\) 1.68691 + 2.92181i 0.0776462 + 0.134487i
\(473\) 4.45328 + 7.71330i 0.204762 + 0.354658i
\(474\) −1.42594 0.595297i −0.0654955 0.0273429i
\(475\) −12.1249 + 21.0010i −0.556330 + 0.963591i
\(476\) 0 0
\(477\) 7.83799 28.6138i 0.358877 1.31014i
\(478\) −10.9209 −0.499513
\(479\) −8.88370 + 15.3870i −0.405907 + 0.703051i −0.994427 0.105432i \(-0.966378\pi\)
0.588520 + 0.808483i \(0.299711\pi\)
\(480\) −4.08988 31.7482i −0.186677 1.44910i
\(481\) −2.83103 4.90349i −0.129084 0.223580i
\(482\) −4.14548 7.18018i −0.188821 0.327048i
\(483\) 0 0
\(484\) −8.94890 + 15.4999i −0.406768 + 0.704543i
\(485\) 40.7816 1.85180
\(486\) −3.05716 + 7.09957i −0.138675 + 0.322043i
\(487\) −16.6553 −0.754722 −0.377361 0.926066i \(-0.623168\pi\)
−0.377361 + 0.926066i \(0.623168\pi\)
\(488\) 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 0.784451 0.620190i \(-0.212945\pi\)
−0.929326 + 0.369260i \(0.879611\pi\)
\(492\) 1.85623 + 14.4092i 0.0836854 + 0.649619i
\(493\) −0.517784 + 0.896827i −0.0233198 + 0.0403911i
\(494\) −1.66646 −0.0749776
\(495\) −2.61223 + 9.53633i −0.117411 + 0.428626i
\(496\) −9.26814 −0.416152
\(497\) 0 0
\(498\) 9.76698 + 4.07750i 0.437669 + 0.182717i
\(499\) −5.57296 9.65264i −0.249480 0.432112i 0.713902 0.700246i \(-0.246926\pi\)
−0.963382 + 0.268134i \(0.913593\pi\)
\(500\) 11.7728 + 20.3911i 0.526495 + 0.911916i
\(501\) −28.1806 11.7648i −1.25901 0.525611i
\(502\) 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
\(507\) −2.55995 19.8719i −0.113691 0.882544i
\(508\) −1.11339 1.92845i −0.0493988 0.0855612i
\(509\) 15.5411 + 26.9180i 0.688848 + 1.19312i 0.972211 + 0.234107i \(0.0752167\pi\)
−0.283362 + 0.959013i \(0.591450\pi\)
\(510\) 0.630316 0.480878i 0.0279109 0.0212936i
\(511\) 0 0
\(512\) −22.5634 −0.997169
\(513\) −5.47145 13.5276i −0.241571 0.597258i
\(514\) −8.48913 −0.374439
\(515\) 17.9303 31.0563i 0.790105 1.36850i
\(516\) −24.1034 + 18.3888i −1.06109 + 0.809524i
\(517\) 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
\(521\) −4.75971 −0.208527 −0.104263 0.994550i \(-0.533249\pi\)
−0.104263 + 0.994550i \(0.533249\pi\)
\(522\) −5.96128 + 1.56181i −0.260918 + 0.0683586i
\(523\) 40.2515 1.76008 0.880038 0.474904i \(-0.157517\pi\)
0.880038 + 0.474904i \(0.157517\pi\)
\(524\) 13.1812 22.8305i 0.575823 0.997355i
\(525\) 0 0
\(526\) 5.09571 + 8.82602i 0.222183 + 0.384833i
\(527\) −0.448113 0.776154i −0.0195201 0.0338098i
\(528\) 3.68808 + 1.53969i 0.160503 + 0.0670064i
\(529\) 8.43046 14.6020i 0.366542 0.634869i
\(530\) −18.1076 −0.786545
\(531\) 5.25960 1.37798i 0.228247 0.0597991i
\(532\) 0 0
\(533\) 2.86125 4.95583i 0.123935 0.214661i
\(534\) 0.264176 + 2.05070i 0.0114320 + 0.0887426i
\(535\) −20.1255 34.8584i −0.870101 1.50706i
\(536\) −0.958109 1.65949i −0.0413840 0.0716792i
\(537\) −10.1009 + 7.70616i −0.435888 + 0.332545i
\(538\) 4.92033 8.52227i 0.212131 0.367421i
\(539\) 0 0
\(540\) −33.3308 4.67150i −1.43433 0.201029i
\(541\) −24.1094 −1.03655 −0.518273 0.855215i \(-0.673425\pi\)
−0.518273 + 0.855215i \(0.673425\pi\)
\(542\) 2.63830 4.56966i 0.113325 0.196284i
\(543\) −15.5009 + 11.8259i −0.665208 + 0.507497i
\(544\) −0.625580 1.08354i −0.0268215 0.0464563i
\(545\) −3.91769 6.78564i −0.167815 0.290665i
\(546\) 0 0
\(547\) −6.17751 + 10.6998i −0.264131 + 0.457489i −0.967336 0.253499i \(-0.918419\pi\)
0.703204 + 0.710988i \(0.251752\pi\)
\(548\) 0.856872 0.0366038
\(549\) −22.7911 23.0462i −0.972699 0.983587i
\(550\) 3.82188 0.162966
\(551\) 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
\(555\) −27.9247 11.6579i −1.18534 0.494852i
\(556\) −8.65633 + 14.9932i −0.367110 + 0.635853i
\(557\) −8.07689 −0.342229 −0.171114 0.985251i \(-0.554737\pi\)
−0.171114 + 0.985251i \(0.554737\pi\)
\(558\) 1.40901 5.14379i 0.0596480 0.217754i
\(559\) 11.9415 0.505070
\(560\) 0 0
\(561\) 0.0493776 + 0.383300i 0.00208472 + 0.0161829i
\(562\) 3.39041 + 5.87237i 0.143016 + 0.247711i
\(563\) 22.6064 + 39.1554i 0.952744 + 1.65020i 0.739448 + 0.673214i \(0.235087\pi\)
0.213296 + 0.976988i \(0.431580\pi\)
\(564\) −24.5732 + 18.7473i −1.03472 + 0.789402i
\(565\) 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 \(0.322468\pi\)
\(570\) −7.08089 + 5.40211i −0.296586 + 0.226270i
\(571\) 10.9134 + 18.9026i 0.456713 + 0.791050i 0.998785 0.0492820i \(-0.0156933\pi\)
−0.542072 + 0.840332i \(0.682360\pi\)
\(572\) −0.936826 1.62263i −0.0391706 0.0678455i
\(573\) −5.27706 40.9638i −0.220452 1.71129i
\(574\) 0 0
\(575\) 21.3954 0.892251
\(576\) −2.13082 + 7.77888i −0.0887842 + 0.324120i
\(577\) −32.2044 −1.34068 −0.670342 0.742052i \(-0.733853\pi\)
−0.670342 + 0.742052i \(0.733853\pi\)
\(578\) −4.19939 + 7.27355i −0.174671 + 0.302540i
\(579\) −9.48553 3.96000i −0.394205 0.164572i
\(580\) −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
\(584\) −3.40761 −0.141008
\(585\) 9.32169 + 9.42604i 0.385404 + 0.389719i
\(586\) 1.30421 0.0538765
\(587\) 9.72304 16.8408i 0.401313 0.695094i −0.592572 0.805518i \(-0.701887\pi\)
0.993885 + 0.110424i \(0.0352208\pi\)
\(588\) 0 0
\(589\) 5.03404 + 8.71921i 0.207424 + 0.359269i
\(590\) −1.65926 2.87392i −0.0683105 0.118317i
\(591\) −21.3006 + 16.2505i −0.876190 + 0.668458i
\(592\) −6.11563 + 10.5926i −0.251351 + 0.435352i
\(593\) −28.8405 −1.18434 −0.592168 0.805815i \(-0.701728\pi\)
−0.592168 + 0.805815i \(0.701728\pi\)
\(594\) −1.41521 + 1.81280i −0.0580669 + 0.0743801i
\(595\) 0 0
\(596\) 18.4392 31.9377i 0.755300 1.30822i
\(597\) 21.3394 16.2801i 0.873363 0.666301i
\(598\) 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 \(0.423484\pi\)
\(600\) 3.55730 + 27.6140i 0.145226 + 1.12734i
\(601\) 7.80843 13.5246i 0.318512 0.551680i −0.661665 0.749799i \(-0.730150\pi\)
0.980178 + 0.198119i \(0.0634834\pi\)
\(602\) 0 0
\(603\) −2.98729 + 0.782646i −0.121652 + 0.0318718i
\(604\) −2.62833 −0.106945
\(605\) 18.8383 32.6289i 0.765885 1.32655i
\(606\) 2.06041 + 0.860175i 0.0836984 + 0.0349422i
\(607\) −14.3266 24.8144i −0.581500 1.00719i −0.995302 0.0968200i \(-0.969133\pi\)
0.413802 0.910367i \(-0.364200\pi\)
\(608\) 7.02769 + 12.1723i 0.285010 + 0.493652i
\(609\) 0 0
\(610\) −9.89134 + 17.1323i −0.400489 + 0.693667i
\(611\) 12.1742 0.492516
\(612\) −1.27255 + 0.333398i −0.0514397 + 0.0134768i
\(613\) −29.3468 −1.18531 −0.592653 0.805458i \(-0.701920\pi\)
−0.592653 + 0.805458i \(0.701920\pi\)
\(614\) 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 0.904577 0.426310i \(-0.140187\pi\)
−0.821484 + 0.570232i \(0.806853\pi\)
\(618\) 6.63143 5.05921i 0.266755 0.203511i
\(619\) 11.3565 19.6700i 0.456456 0.790605i −0.542315 0.840175i \(-0.682452\pi\)
0.998771 + 0.0495708i \(0.0157853\pi\)
\(620\) 23.2217 0.932608
\(621\) −7.92256 + 10.1483i −0.317921 + 0.407238i
\(622\) −7.48774 −0.300231
\(623\) 0 0
\(624\) 4.26017 3.25014i 0.170543 0.130110i
\(625\) −3.19498 5.53387i −0.127799 0.221355i
\(626\) 6.31698 + 10.9413i 0.252477 + 0.437304i
\(627\) −0.554701 4.30594i −0.0221526 0.171963i
\(628\) 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
\(633\) 2.46754 + 1.03014i 0.0980757 + 0.0409444i
\(634\) 8.06304 + 13.9656i 0.320224 + 0.554645i
\(635\) 2.34380 + 4.05958i 0.0930107 + 0.161099i
\(636\) 27.7266 + 11.5752i 1.09943 + 0.458988i
\(637\) 0 0
\(638\) −1.83348 −0.0725881
\(639\) −3.91954 + 14.3089i −0.155055 + 0.566050i
\(640\) 41.8853 1.65566
\(641\) 14.2363 24.6580i 0.562301 0.973933i −0.434995 0.900433i \(-0.643250\pi\)
0.997295 0.0735002i \(-0.0234169\pi\)
\(642\) −1.19616 9.28538i −0.0472088 0.366465i
\(643\) 8.52125 + 14.7592i 0.336045 + 0.582048i 0.983685 0.179899i \(-0.0575771\pi\)
−0.647640 + 0.761947i \(0.724244\pi\)
\(644\) 0 0
\(645\) 50.7400 38.7103i 1.99788 1.52422i
\(646\) −0.174055 + 0.301472i −0.00684810 + 0.0118613i
\(647\) 3.37618 0.132731 0.0663657 0.997795i \(-0.478860\pi\)
0.0663657 + 0.997795i \(0.478860\pi\)
\(648\) −14.4152 8.53795i −0.566281 0.335402i
\(649\) 1.61767 0.0634989
\(650\) 2.56209 4.43768i 0.100494 0.174060i
\(651\) 0 0
\(652\) 5.86110 + 10.1517i 0.229538 + 0.397572i
\(653\) 9.17255 + 15.8873i 0.358950 + 0.621719i 0.987786 0.155819i \(-0.0498017\pi\)
−0.628836 + 0.777538i \(0.716468\pi\)
\(654\) −0.232849 1.80752i −0.00910512 0.0706797i
\(655\) −27.7477 + 48.0604i −1.08419 + 1.87787i
\(656\) −12.3618 −0.482648
\(657\) −1.45083 + 5.29646i −0.0566021 + 0.206635i
\(658\) 0 0
\(659\) −13.9248 + 24.1184i −0.542432 + 0.939519i 0.456332 + 0.889810i \(0.349163\pi\)
−0.998764 + 0.0497098i \(0.984170\pi\)
\(660\) −9.24065 3.85777i −0.359692 0.150163i
\(661\) 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
\(663\) 0.478160 + 0.199621i 0.0185702 + 0.00775264i
\(664\) −11.4700 + 19.8667i −0.445123 + 0.770976i
\(665\) 0 0
\(666\) −4.94911 5.00452i −0.191774 0.193921i
\(667\) −10.2641 −0.397426
\(668\) 15.4634 26.7834i 0.598296 1.03628i
\(669\) −1.20462 9.35100i −0.0465732 0.361531i
\(670\) 0.942405 + 1.63229i 0.0364083 + 0.0630610i
\(671\) −4.82170 8.35143i −0.186140 0.322404i
\(672\) 0 0
\(673\) 24.6154 42.6352i 0.948856 1.64347i 0.201014 0.979588i \(-0.435576\pi\)
0.747841 0.663878i \(-0.231090\pi\)
\(674\) −12.4053 −0.477833
\(675\) 44.4352 + 6.22784i 1.71031 + 0.239710i
\(676\) 20.2914 0.780438
\(677\) −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
\(681\) 3.55767 + 27.6169i 0.136330 + 1.05828i
\(682\) 0.793387 1.37419i 0.0303803 0.0526203i
\(683\) 30.3264 1.16041 0.580204 0.814471i \(-0.302973\pi\)
0.580204 + 0.814471i \(0.302973\pi\)
\(684\) 14.2956 3.74535i 0.546607 0.143207i
\(685\) −1.80380 −0.0689196
\(686\) 0 0
\(687\) −15.9330 6.65169i −0.607884 0.253778i
\(688\) −12.8980 22.3401i −0.491733 0.851707i
\(689\) −5.91731 10.2491i −0.225432 0.390459i
\(690\) 7.25139 + 3.02729i 0.276056 + 0.115247i
\(691\) −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
\(696\) −1.70655 13.2473i −0.0646867 0.502139i
\(697\) −0.597691 1.03523i −0.0226392 0.0392122i
\(698\) −0.814716 1.41113i −0.0308375 0.0534120i
\(699\) −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 \(0.314200\pi\)
\(702\) 1.15616 + 2.85849i 0.0436365 + 0.107887i
\(703\) 13.2869 0.501127
\(704\) −1.19983 + 2.07816i −0.0452202 + 0.0783236i
\(705\) 51.7289 39.4648i 1.94822 1.48633i
\(706\) −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 \(-0.127095\pi\)
\(710\) 9.05507 0.339831
\(711\) −3.79522 3.83770i −0.142332 0.143925i
\(712\) −4.48150 −0.167951
\(713\) 4.44149 7.69288i 0.166335 0.288101i
\(714\) 0 0
\(715\) 1.97211 + 3.41579i 0.0737526 + 0.127743i
\(716\) −6.43336 11.1429i −0.240426 0.416430i
\(717\) −35.2020 14.6961i −1.31464 0.548834i
\(718\) −5.89692 + 10.2138i −0.220071 + 0.381175i
\(719\) −11.1425 −0.415546 −0.207773 0.978177i \(-0.566621\pi\)
−0.207773 + 0.978177i \(0.566621\pi\)
\(720\) 7.56580 27.6201i 0.281961 1.02934i
\(721\) 0 0
\(722\) −2.75544 + 4.77256i −0.102547 + 0.177616i
\(723\) −3.70012 28.7227i −0.137609 1.06821i
\(724\) −9.87264 17.0999i −0.366914 0.635513i
\(725\) 17.8858 + 30.9790i 0.664260 + 1.15053i
\(726\) 6.96723 5.31540i 0.258578 0.197273i
\(727\) 14.3410 24.8393i 0.531878 0.921239i −0.467430 0.884030i \(-0.654820\pi\)
0.999308 0.0372089i \(-0.0118467\pi\)
\(728\) 0 0
\(729\) −19.4080 + 18.7704i −0.718815 + 0.695202i
\(730\) 3.35175 0.124054
\(731\) 1.24724 2.16028i 0.0461307 0.0799007i
\(732\) 26.0975 19.9102i 0.964591 0.735901i
\(733\) −12.5264 21.6964i −0.462674 0.801375i 0.536419 0.843952i \(-0.319777\pi\)
−0.999093 + 0.0425768i \(0.986443\pi\)
\(734\) 0.171071 + 0.296303i 0.00631433 + 0.0109367i
\(735\) 0 0
\(736\) 6.20047 10.7395i 0.228552 0.395864i
\(737\) −0.918782 −0.0338438
\(738\) 1.87933 6.86077i 0.0691790 0.252549i
\(739\) −27.5216 −1.01240 −0.506198 0.862417i \(-0.668950\pi\)
−0.506198 + 0.862417i \(0.668950\pi\)
\(740\) 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 0.708416 0.705795i \(-0.249410\pi\)
−0.965444 + 0.260609i \(0.916077\pi\)
\(744\) 10.6673 + 4.45336i 0.391082 + 0.163268i
\(745\) −38.8163 + 67.2318i −1.42212 + 2.46318i
\(746\) 1.86452 0.0682650
\(747\) 25.9954 + 26.2864i 0.951121 + 0.961768i
\(748\) −0.391390 −0.0143106
\(749\) 0 0
\(750\) −1.47297 11.4342i −0.0537854 0.417516i
\(751\) 26.1297 + 45.2580i 0.953486 + 1.65149i 0.737795 + 0.675025i \(0.235867\pi\)
0.215692 + 0.976461i \(0.430799\pi\)
\(752\) −13.1494 22.7755i −0.479511 0.830537i
\(753\) 11.7477 8.96246i 0.428109 0.326610i
\(754\) −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
\(759\) −3.04540 + 2.32338i −0.110541 + 0.0843335i
\(760\) −9.65191 16.7176i −0.350112 0.606411i
\(761\) −8.62550 14.9398i −0.312674 0.541568i 0.666266 0.745714i \(-0.267891\pi\)
−0.978940 + 0.204146i \(0.934558\pi\)
\(762\) 0.139304 + 1.08137i 0.00504646 + 0.0391738i
\(763\) 0 0
\(764\) 41.8285 1.51330
\(765\) 2.67883 0.701834i 0.0968534 0.0253749i
\(766\) −0.531903 −0.0192184
\(767\) 1.08444 1.87831i 0.0391570 0.0678218i
\(768\) 0.395948 + 0.165299i 0.0142875 + 0.00596472i
\(769\) 10.6727 + 18.4856i 0.384867 + 0.666609i 0.991751 0.128182i \(-0.0409141\pi\)
−0.606884 + 0.794790i \(0.707581\pi\)
\(770\) 0 0
\(771\) −27.3634 11.4236i −0.985469 0.411411i
\(772\) 5.20495 9.01523i 0.187330 0.324465i
\(773\) −13.1471 −0.472870 −0.236435 0.971647i \(-0.575979\pi\)
−0.236435 + 0.971647i \(0.575979\pi\)
\(774\) 14.3595 3.76209i 0.516143 0.135225i
\(775\) −30.9583 −1.11205
\(776\) −10.2796 + 17.8049i −0.369018 + 0.639158i
\(777\) 0 0
\(778\) −5.88685 10.1963i −0.211054 0.365556i
\(779\) 6.71439 + 11.6297i 0.240568 + 0.416676i
\(780\) −10.6740 + 8.14339i −0.382192 + 0.291580i
\(781\) −2.20702 + 3.82268i