Properties

Label 441.2.f.e.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.e.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 \(0.142545\pi\)
−0.0757082 + 0.997130i \(0.524122\pi\)
\(6\) 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 0.936994 0.349346i \(-0.113596\pi\)
−0.771040 + 0.636787i \(0.780263\pi\)
\(14\) 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 \(-0.490349\pi\)
0.0303149 + 0.999540i \(0.490349\pi\)
\(18\) −1.04602 1.05773i −0.246550 0.249310i
\(19\) −2.80827 −0.644262 −0.322131 0.946695i \(-0.604399\pi\)
−0.322131 + 0.946695i \(0.604399\pi\)
\(20\) −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 0.658936 0.752199i \(-0.271007\pi\)
−0.980892 + 0.194555i \(0.937674\pi\)
\(32\) 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 0.616686 0.787209i \(-0.288475\pi\)
−0.990086 + 0.140461i \(0.955142\pi\)
\(42\) 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 \(-0.567236\pi\)
0.951608 0.307316i \(-0.0994308\pi\)
\(48\) −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 0.800990 0.598678i \(-0.204307\pi\)
−0.918965 + 0.394339i \(0.870974\pi\)
\(60\) −1.43339 11.1269i −0.185050 1.43648i
\(61\) −5.40205 + 9.35663i −0.691662 + 1.19799i 0.279631 + 0.960108i \(0.409788\pi\)
−0.971293 + 0.237886i \(0.923545\pi\)
\(62\) −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 \(-0.465836\pi\)
0.107123 + 0.994246i \(0.465836\pi\)
\(74\) 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 \(-0.596908\pi\)
0.976082 0.217405i \(-0.0697591\pi\)
\(84\) 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 \(-0.459275\pi\)
0.127592 + 0.991827i \(0.459275\pi\)
\(90\) 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 \(-0.643871\pi\)
0.997437 0.0715522i \(-0.0227952\pi\)
\(98\) 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 −0.794083 0.607810i \(-0.792048\pi\)
0.923420 + 0.383791i \(0.125382\pi\)
\(102\) 0.0274318 + 0.212943i 0.00271615 + 0.0210845i
\(103\) −4.85578 8.41045i −0.478454 0.828706i 0.521241 0.853409i \(-0.325469\pi\)
−0.999695 + 0.0247032i \(0.992136\pi\)
\(104\) 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 \(0.0613140\pi\)
−0.324965 + 0.945726i \(0.605353\pi\)
\(132\) −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 0.577226 0.816585i \(-0.304135\pi\)
−0.995796 + 0.0915997i \(0.970802\pi\)
\(140\) 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 \(0.0651534\pi\)
−0.313535 + 0.949577i \(0.601513\pi\)
\(158\) −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 \(0.0722939\pi\)
−0.292156 + 0.956371i \(0.594373\pi\)
\(168\) 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 −0.782642 0.622472i \(-0.786128\pi\)
0.930398 + 0.366552i \(0.119462\pi\)
\(174\) 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 \(-0.362610\pi\)
0.418346 + 0.908288i \(0.362610\pi\)
\(182\) 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 \(-0.685088\pi\)
−0.549254 + 0.835655i \(0.685088\pi\)
\(200\) −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 −0.942649 0.333784i \(-0.891674\pi\)
0.760390 + 0.649466i \(0.225008\pi\)
\(224\) 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 \(-0.654205\pi\)
0.999234 0.0391399i \(-0.0124618\pi\)
\(228\) 7.87356 + 3.28703i 0.521439 + 0.217689i
\(229\) 4.98420 + 8.63289i 0.329365 + 0.570477i 0.982386 0.186863i \(-0.0598319\pi\)
−0.653021 + 0.757340i \(0.726499\pi\)
\(230\) −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 \(0.347682\pi\)
−0.998984 + 0.0450623i \(0.985651\pi\)
\(242\) 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 \(-0.586771\pi\)
−0.269236 + 0.963074i \(0.586771\pi\)
\(252\) 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 \(0.0126261\pi\)
−0.465264 + 0.885172i \(0.654041\pi\)
\(258\) −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 \(-0.706825\pi\)
−0.604996 + 0.796229i \(0.706825\pi\)
\(270\) 3.56746 + 8.82018i 0.217109 + 0.536779i
\(271\) −10.6411 −0.646402 −0.323201 0.946330i \(-0.604759\pi\)
−0.323201 + 0.946330i \(0.604759\pi\)
\(272\) −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 0.756653 0.653817i \(-0.226833\pi\)
−0.944548 + 0.328372i \(0.893500\pi\)
\(284\) −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 0.825052 0.565057i \(-0.191146\pi\)
−0.901880 + 0.431987i \(0.857812\pi\)
\(294\) 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 \(-0.525415\pi\)
−0.0797583 + 0.996814i \(0.525415\pi\)
\(308\) 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 0.996707 0.0810885i \(-0.0258396\pi\)
−0.568578 + 0.822629i \(0.692506\pi\)
\(312\) −3.56071 1.48652i −0.201585 0.0841574i
\(313\) 12.7392 22.0650i 0.720064 1.24719i −0.240910 0.970548i \(-0.577446\pi\)
0.960974 0.276640i \(-0.0892209\pi\)
\(314\) 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 −0.906644 0.421897i \(-0.861364\pi\)
0.818695 + 0.574228i \(0.194698\pi\)
\(350\) 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 −0.998229 0.0594866i \(-0.981054\pi\)
0.550631 + 0.834748i \(0.314387\pi\)
\(354\) 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 −0.856881 0.515515i \(-0.827601\pi\)
0.874889 + 0.484323i \(0.160934\pi\)
\(368\) 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 0.879403 0.476078i \(-0.157942\pi\)
−0.851997 + 0.523546i \(0.824609\pi\)
\(384\) −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 \(-0.499744\pi\)
0.000805471 1.00000i \(0.499744\pi\)
\(398\) −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 \(-0.936233\pi\)
0.317669 0.948202i \(-0.397100\pi\)
\(410\) −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 \(-0.994741\pi\)
0.485624 0.874168i \(-0.338593\pi\)
\(420\) 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 \(-0.628648\pi\)
−0.393245 + 0.919434i \(0.628648\pi\)
\(434\) 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 −0.618758 0.785582i \(-0.712364\pi\)
0.989713 + 0.143070i \(0.0456973\pi\)
\(440\) 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 \(-0.514301\pi\)
0.887608 0.460600i \(-0.152366\pi\)
\(462\) 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 \(-0.435482\pi\)
0.201304 + 0.979529i \(0.435482\pi\)
\(468\) 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 −0.588520 0.808483i \(-0.700289\pi\)
0.994427 + 0.105432i \(0.0336224\pi\)
\(480\) −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 \(-0.629290\pi\)
−0.395100 + 0.918638i \(0.629290\pi\)
\(504\) 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 \(-0.924783\pi\)
0.283362 0.959013i \(-0.408550\pi\)
\(510\) −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 \(-0.466751\pi\)
0.104263 + 0.994550i \(0.466751\pi\)
\(522\) −5.96128 + 1.56181i −0.260918 + 0.0683586i
\(523\) −40.2515 −1.76008 −0.880038 0.474904i \(-0.842483\pi\)
−0.880038 + 0.474904i \(0.842483\pi\)
\(524\) −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 \(-0.764913\pi\)
−0.213296 0.976988i \(-0.568420\pi\)
\(564\) −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 \(-0.266147\pi\)
0.670342 + 0.742052i \(0.266147\pi\)
\(578\) −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 −0.993885 0.110424i \(-0.964779\pi\)
0.592572 + 0.805518i \(0.298113\pi\)
\(588\) 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 \(-0.298272\pi\)
0.592168 + 0.805815i \(0.298272\pi\)
\(594\) 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 −0.980178 0.198119i \(-0.936517\pi\)
0.661665 + 0.749799i \(0.269850\pi\)
\(602\) 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 \(0.0308671\pi\)
−0.413802 + 0.910367i \(0.635800\pi\)
\(608\) −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 −0.998771 0.0495708i \(-0.984215\pi\)
0.542315 + 0.840175i \(0.317548\pi\)
\(620\) 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 0.647640 0.761947i \(-0.275756\pi\)
−0.983685 + 0.179899i \(0.942423\pi\)
\(644\) 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 \(-0.521140\pi\)
−0.0663657 + 0.997795i \(0.521140\pi\)
\(648\) −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 \(-0.892484\pi\)
0.184758 0.982784i \(-0.440850\pi\)
\(662\) 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 −0.548849 0.835922i \(-0.684934\pi\)
0.998354 + 0.0573564i \(0.0182671\pi\)
\(678\) −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 −0.824251 0.566224i \(-0.808404\pi\)
0.902490 + 0.430711i \(0.141737\pi\)
\(692\) 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 \(-0.433379\pi\)
0.207773 + 0.978177i \(0.433379\pi\)
\(720\) −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 \(0.345180\pi\)
−0.999308 + 0.0372089i \(0.988153\pi\)
\(728\) 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 0.999093 0.0425768i \(-0.0135567\pi\)
−0.536419 + 0.843952i \(0.680223\pi\)
\(734\) −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 0.978940 0.204146i \(-0.0654419\pi\)
−0.666266 + 0.745714i \(0.732109\pi\)
\(762\) −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 0.606884 0.794790i \(-0.292419\pi\)
−0.991751 + 0.128182i \(0.959086\pi\)
\(770\) 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 \(-0.424021\pi\)
0.236435 + 0.971647i \(0.424021\pi\)
\(774\) 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