Properties

Label 637.2.f.j.295.6
Level $637$
Weight $2$
Character 637.295
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - x^{11} + 7 x^{10} - 2 x^{9} + 33 x^{8} - 11 x^{7} + 55 x^{6} + 17 x^{5} + 47 x^{4} + x^{3} + 8 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 295.6
Root \(-0.181721 - 0.314749i\) of defining polynomial
Character \(\chi\) \(=\) 637.295
Dual form 637.2.f.j.393.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.19402 - 2.06810i) q^{2} +(-1.37574 + 2.38285i) q^{3} +(-1.85136 - 3.20665i) q^{4} -0.982280 q^{5} +(3.28532 + 5.69033i) q^{6} -4.06616 q^{8} +(-2.28532 - 3.95828i) q^{9} +O(q^{10})\) \(q+(1.19402 - 2.06810i) q^{2} +(-1.37574 + 2.38285i) q^{3} +(-1.85136 - 3.20665i) q^{4} -0.982280 q^{5} +(3.28532 + 5.69033i) q^{6} -4.06616 q^{8} +(-2.28532 - 3.95828i) q^{9} +(-1.17286 + 2.03145i) q^{10} +(0.293901 - 0.509052i) q^{11} +10.1880 q^{12} +(-2.39227 - 2.69760i) q^{13} +(1.35136 - 2.34063i) q^{15} +(-1.15235 + 1.99593i) q^{16} +(-3.22710 - 5.58950i) q^{17} -10.9148 q^{18} +(-1.91345 - 3.31419i) q^{19} +(1.81855 + 3.14983i) q^{20} +(-0.701847 - 1.21563i) q^{22} +(-4.13001 + 7.15338i) q^{23} +(5.59398 - 9.68906i) q^{24} -4.03513 q^{25} +(-8.43532 + 1.72647i) q^{26} +4.32156 q^{27} +(1.98009 - 3.42962i) q^{29} +(-3.22710 - 5.58950i) q^{30} +2.98872 q^{31} +(-1.31430 - 2.27644i) q^{32} +(0.808663 + 1.40065i) q^{33} -15.4129 q^{34} +(-8.46189 + 14.6564i) q^{36} +(-0.877941 + 1.52064i) q^{37} -9.13877 q^{38} +(9.71911 - 1.98923i) q^{39} +3.99411 q^{40} +(1.83584 - 3.17977i) q^{41} +(-3.19042 - 5.52598i) q^{43} -2.17647 q^{44} +(2.24482 + 3.88814i) q^{45} +(9.86261 + 17.0825i) q^{46} +4.34059 q^{47} +(-3.17067 - 5.49176i) q^{48} +(-4.81802 + 8.34505i) q^{50} +17.7586 q^{51} +(-4.22130 + 12.6654i) q^{52} +0.425541 q^{53} +(5.16002 - 8.93742i) q^{54} +(-0.288693 + 0.500031i) q^{55} +10.5296 q^{57} +(-4.72853 - 8.19006i) q^{58} +(3.00431 + 5.20362i) q^{59} -10.0074 q^{60} +(1.10337 + 1.91109i) q^{61} +(3.56859 - 6.18097i) q^{62} -10.8866 q^{64} +(2.34988 + 2.64980i) q^{65} +3.86223 q^{66} +(-3.50651 + 6.07346i) q^{67} +(-11.9491 + 20.6964i) q^{68} +(-11.3636 - 19.6824i) q^{69} +(-1.80127 - 3.11988i) q^{71} +(9.29247 + 16.0950i) q^{72} -4.93427 q^{73} +(2.09656 + 3.63134i) q^{74} +(5.55128 - 9.61510i) q^{75} +(-7.08496 + 12.2715i) q^{76} +(7.49088 - 22.4753i) q^{78} +2.78541 q^{79} +(1.13193 - 1.96056i) q^{80} +(0.910609 - 1.57722i) q^{81} +(-4.38406 - 7.59342i) q^{82} +2.86819 q^{83} +(3.16992 + 5.49045i) q^{85} -15.2377 q^{86} +(5.44818 + 9.43652i) q^{87} +(-1.19505 + 2.06989i) q^{88} +(-1.04656 + 1.81269i) q^{89} +10.7214 q^{90} +30.5845 q^{92} +(-4.11170 + 7.12167i) q^{93} +(5.18275 - 8.97679i) q^{94} +(1.87954 + 3.25546i) q^{95} +7.23255 q^{96} +(3.84852 + 6.66584i) q^{97} -2.68663 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 2q^{2} - q^{3} - 4q^{4} + 2q^{5} + 9q^{6} - 6q^{8} + 3q^{9} + O(q^{10}) \) \( 12q + 2q^{2} - q^{3} - 4q^{4} + 2q^{5} + 9q^{6} - 6q^{8} + 3q^{9} - 4q^{10} + 4q^{11} + 10q^{12} + 2q^{13} - 2q^{15} + 8q^{16} - 5q^{17} - 6q^{18} + q^{19} + q^{20} - 5q^{22} - q^{23} + 11q^{24} - 14q^{25} - 11q^{26} + 8q^{27} + 3q^{29} - 5q^{30} + 32q^{31} + 8q^{32} - 16q^{33} - 32q^{34} - 21q^{36} - 13q^{37} - 34q^{38} + 43q^{39} - 10q^{40} + 8q^{41} - 11q^{43} - 42q^{44} + 7q^{45} + 16q^{46} - 2q^{47} - 21q^{48} + 6q^{50} + 40q^{51} + 16q^{52} + 4q^{53} + 18q^{54} - 9q^{55} + 42q^{57} - 8q^{58} - 13q^{59} - 40q^{60} + 5q^{61} - 5q^{62} - 30q^{64} - 14q^{65} + 36q^{66} - 11q^{67} - 29q^{68} - 23q^{69} + 6q^{71} + 25q^{72} - 60q^{73} - 3q^{74} + 3q^{75} + 9q^{76} + 16q^{78} - 14q^{79} + 7q^{80} - 6q^{81} - q^{82} + 54q^{83} - q^{85} + 14q^{86} - 16q^{87} - 4q^{89} + 16q^{90} + 54q^{92} - 7q^{93} - 45q^{94} - 6q^{95} + 38q^{96} + 35q^{97} - 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.19402 2.06810i 0.844299 1.46237i −0.0419302 0.999121i \(-0.513351\pi\)
0.886229 0.463248i \(-0.153316\pi\)
\(3\) −1.37574 + 2.38285i −0.794283 + 1.37574i 0.129010 + 0.991643i \(0.458820\pi\)
−0.923293 + 0.384096i \(0.874513\pi\)
\(4\) −1.85136 3.20665i −0.925680 1.60333i
\(5\) −0.982280 −0.439289 −0.219644 0.975580i \(-0.570490\pi\)
−0.219644 + 0.975580i \(0.570490\pi\)
\(6\) 3.28532 + 5.69033i 1.34122 + 2.32307i
\(7\) 0 0
\(8\) −4.06616 −1.43761
\(9\) −2.28532 3.95828i −0.761772 1.31943i
\(10\) −1.17286 + 2.03145i −0.370891 + 0.642402i
\(11\) 0.293901 0.509052i 0.0886146 0.153485i −0.818311 0.574775i \(-0.805089\pi\)
0.906926 + 0.421291i \(0.138423\pi\)
\(12\) 10.1880 2.94101
\(13\) −2.39227 2.69760i −0.663496 0.748179i
\(14\) 0 0
\(15\) 1.35136 2.34063i 0.348920 0.604347i
\(16\) −1.15235 + 1.99593i −0.288088 + 0.498983i
\(17\) −3.22710 5.58950i −0.782687 1.35565i −0.930371 0.366619i \(-0.880515\pi\)
0.147685 0.989035i \(-0.452818\pi\)
\(18\) −10.9148 −2.57265
\(19\) −1.91345 3.31419i −0.438975 0.760327i 0.558636 0.829413i \(-0.311325\pi\)
−0.997611 + 0.0690863i \(0.977992\pi\)
\(20\) 1.81855 + 3.14983i 0.406641 + 0.704323i
\(21\) 0 0
\(22\) −0.701847 1.21563i −0.149634 0.259174i
\(23\) −4.13001 + 7.15338i −0.861166 + 1.49158i 0.00963902 + 0.999954i \(0.496932\pi\)
−0.870805 + 0.491629i \(0.836402\pi\)
\(24\) 5.59398 9.68906i 1.14187 1.97777i
\(25\) −4.03513 −0.807025
\(26\) −8.43532 + 1.72647i −1.65430 + 0.338589i
\(27\) 4.32156 0.831685
\(28\) 0 0
\(29\) 1.98009 3.42962i 0.367694 0.636864i −0.621511 0.783406i \(-0.713481\pi\)
0.989205 + 0.146541i \(0.0468141\pi\)
\(30\) −3.22710 5.58950i −0.589185 1.02050i
\(31\) 2.98872 0.536790 0.268395 0.963309i \(-0.413507\pi\)
0.268395 + 0.963309i \(0.413507\pi\)
\(32\) −1.31430 2.27644i −0.232338 0.402421i
\(33\) 0.808663 + 1.40065i 0.140770 + 0.243821i
\(34\) −15.4129 −2.64329
\(35\) 0 0
\(36\) −8.46189 + 14.6564i −1.41031 + 2.44274i
\(37\) −0.877941 + 1.52064i −0.144333 + 0.249991i −0.929124 0.369769i \(-0.879437\pi\)
0.784791 + 0.619760i \(0.212770\pi\)
\(38\) −9.13877 −1.48250
\(39\) 9.71911 1.98923i 1.55630 0.318532i
\(40\) 3.99411 0.631524
\(41\) 1.83584 3.17977i 0.286710 0.496597i −0.686312 0.727307i \(-0.740772\pi\)
0.973023 + 0.230710i \(0.0741049\pi\)
\(42\) 0 0
\(43\) −3.19042 5.52598i −0.486535 0.842703i 0.513345 0.858182i \(-0.328406\pi\)
−0.999880 + 0.0154788i \(0.995073\pi\)
\(44\) −2.17647 −0.328115
\(45\) 2.24482 + 3.88814i 0.334638 + 0.579610i
\(46\) 9.86261 + 17.0825i 1.45416 + 2.51868i
\(47\) 4.34059 0.633141 0.316570 0.948569i \(-0.397469\pi\)
0.316570 + 0.948569i \(0.397469\pi\)
\(48\) −3.17067 5.49176i −0.457647 0.792668i
\(49\) 0 0
\(50\) −4.81802 + 8.34505i −0.681370 + 1.18017i
\(51\) 17.7586 2.48670
\(52\) −4.22130 + 12.6654i −0.585389 + 1.75638i
\(53\) 0.425541 0.0584525 0.0292263 0.999573i \(-0.490696\pi\)
0.0292263 + 0.999573i \(0.490696\pi\)
\(54\) 5.16002 8.93742i 0.702190 1.21623i
\(55\) −0.288693 + 0.500031i −0.0389274 + 0.0674242i
\(56\) 0 0
\(57\) 10.5296 1.39468
\(58\) −4.72853 8.19006i −0.620887 1.07541i
\(59\) 3.00431 + 5.20362i 0.391128 + 0.677454i 0.992599 0.121441i \(-0.0387516\pi\)
−0.601470 + 0.798895i \(0.705418\pi\)
\(60\) −10.0074 −1.29195
\(61\) 1.10337 + 1.91109i 0.141272 + 0.244691i 0.927976 0.372640i \(-0.121547\pi\)
−0.786704 + 0.617331i \(0.788214\pi\)
\(62\) 3.56859 6.18097i 0.453211 0.784985i
\(63\) 0 0
\(64\) −10.8866 −1.36083
\(65\) 2.34988 + 2.64980i 0.291467 + 0.328667i
\(66\) 3.86223 0.475408
\(67\) −3.50651 + 6.07346i −0.428389 + 0.741991i −0.996730 0.0808015i \(-0.974252\pi\)
0.568341 + 0.822793i \(0.307585\pi\)
\(68\) −11.9491 + 20.6964i −1.44904 + 2.50980i
\(69\) −11.3636 19.6824i −1.36802 2.36948i
\(70\) 0 0
\(71\) −1.80127 3.11988i −0.213771 0.370262i 0.739121 0.673573i \(-0.235241\pi\)
−0.952892 + 0.303311i \(0.901908\pi\)
\(72\) 9.29247 + 16.0950i 1.09513 + 1.89682i
\(73\) −4.93427 −0.577513 −0.288756 0.957403i \(-0.593242\pi\)
−0.288756 + 0.957403i \(0.593242\pi\)
\(74\) 2.09656 + 3.63134i 0.243720 + 0.422135i
\(75\) 5.55128 9.61510i 0.641007 1.11026i
\(76\) −7.08496 + 12.2715i −0.812701 + 1.40764i
\(77\) 0 0
\(78\) 7.49088 22.4753i 0.848175 2.54483i
\(79\) 2.78541 0.313383 0.156691 0.987648i \(-0.449917\pi\)
0.156691 + 0.987648i \(0.449917\pi\)
\(80\) 1.13193 1.96056i 0.126554 0.219198i
\(81\) 0.910609 1.57722i 0.101179 0.175247i
\(82\) −4.38406 7.59342i −0.484138 0.838552i
\(83\) 2.86819 0.314825 0.157412 0.987533i \(-0.449685\pi\)
0.157412 + 0.987533i \(0.449685\pi\)
\(84\) 0 0
\(85\) 3.16992 + 5.49045i 0.343826 + 0.595523i
\(86\) −15.2377 −1.64312
\(87\) 5.44818 + 9.43652i 0.584106 + 1.01170i
\(88\) −1.19505 + 2.06989i −0.127393 + 0.220651i
\(89\) −1.04656 + 1.81269i −0.110935 + 0.192145i −0.916147 0.400842i \(-0.868718\pi\)
0.805213 + 0.592986i \(0.202051\pi\)
\(90\) 10.7214 1.13014
\(91\) 0 0
\(92\) 30.5845 3.18866
\(93\) −4.11170 + 7.12167i −0.426363 + 0.738483i
\(94\) 5.18275 8.97679i 0.534560 0.925885i
\(95\) 1.87954 + 3.25546i 0.192837 + 0.334003i
\(96\) 7.23255 0.738169
\(97\) 3.84852 + 6.66584i 0.390758 + 0.676813i 0.992550 0.121840i \(-0.0388795\pi\)
−0.601791 + 0.798653i \(0.705546\pi\)
\(98\) 0 0
\(99\) −2.68663 −0.270016
\(100\) 7.47047 + 12.9392i 0.747047 + 1.29392i
\(101\) −1.31866 + 2.28399i −0.131212 + 0.227265i −0.924144 0.382045i \(-0.875220\pi\)
0.792932 + 0.609310i \(0.208553\pi\)
\(102\) 21.2041 36.7266i 2.09952 3.63647i
\(103\) 10.8619 1.07026 0.535128 0.844771i \(-0.320263\pi\)
0.535128 + 0.844771i \(0.320263\pi\)
\(104\) 9.72736 + 10.9689i 0.953846 + 1.07559i
\(105\) 0 0
\(106\) 0.508103 0.880061i 0.0493514 0.0854791i
\(107\) 7.99024 13.8395i 0.772446 1.33792i −0.163773 0.986498i \(-0.552366\pi\)
0.936219 0.351418i \(-0.114300\pi\)
\(108\) −8.00077 13.8577i −0.769874 1.33346i
\(109\) 9.23477 0.884530 0.442265 0.896884i \(-0.354175\pi\)
0.442265 + 0.896884i \(0.354175\pi\)
\(110\) 0.689410 + 1.19409i 0.0657327 + 0.113852i
\(111\) −2.41564 4.18400i −0.229282 0.397128i
\(112\) 0 0
\(113\) −5.09012 8.81635i −0.478838 0.829372i 0.520867 0.853638i \(-0.325609\pi\)
−0.999706 + 0.0242655i \(0.992275\pi\)
\(114\) 12.5726 21.7763i 1.17753 2.03954i
\(115\) 4.05682 7.02662i 0.378301 0.655236i
\(116\) −14.6635 −1.36147
\(117\) −5.21077 + 15.6342i −0.481736 + 1.44538i
\(118\) 14.3488 1.32092
\(119\) 0 0
\(120\) −5.49485 + 9.51736i −0.501609 + 0.868813i
\(121\) 5.32724 + 9.22706i 0.484295 + 0.838823i
\(122\) 5.26978 0.477104
\(123\) 5.05128 + 8.74908i 0.455459 + 0.788878i
\(124\) −5.53320 9.58378i −0.496896 0.860649i
\(125\) 8.87502 0.793806
\(126\) 0 0
\(127\) −2.12513 + 3.68083i −0.188575 + 0.326621i −0.944775 0.327719i \(-0.893720\pi\)
0.756201 + 0.654340i \(0.227053\pi\)
\(128\) −10.3702 + 17.9617i −0.916606 + 1.58761i
\(129\) 17.5568 1.54579
\(130\) 8.28585 1.69588i 0.726717 0.148739i
\(131\) 2.16957 0.189556 0.0947779 0.995498i \(-0.469786\pi\)
0.0947779 + 0.995498i \(0.469786\pi\)
\(132\) 2.99425 5.18620i 0.260616 0.451401i
\(133\) 0 0
\(134\) 8.37369 + 14.5037i 0.723376 + 1.25292i
\(135\) −4.24498 −0.365350
\(136\) 13.1219 + 22.7278i 1.12519 + 1.94889i
\(137\) −4.18158 7.24271i −0.357257 0.618787i 0.630245 0.776396i \(-0.282955\pi\)
−0.987501 + 0.157610i \(0.949621\pi\)
\(138\) −54.2735 −4.62007
\(139\) −0.288457 0.499622i −0.0244666 0.0423774i 0.853533 0.521039i \(-0.174455\pi\)
−0.877999 + 0.478662i \(0.841122\pi\)
\(140\) 0 0
\(141\) −5.97152 + 10.3430i −0.502893 + 0.871036i
\(142\) −8.60298 −0.721946
\(143\) −2.07631 + 0.424962i −0.173630 + 0.0355371i
\(144\) 10.5340 0.877830
\(145\) −1.94500 + 3.36885i −0.161524 + 0.279767i
\(146\) −5.89161 + 10.2046i −0.487593 + 0.844537i
\(147\) 0 0
\(148\) 6.50154 0.534423
\(149\) −1.40331 2.43061i −0.114964 0.199123i 0.802801 0.596246i \(-0.203342\pi\)
−0.917765 + 0.397123i \(0.870009\pi\)
\(150\) −13.2567 22.9612i −1.08240 1.87478i
\(151\) −23.0109 −1.87260 −0.936300 0.351202i \(-0.885773\pi\)
−0.936300 + 0.351202i \(0.885773\pi\)
\(152\) 7.78039 + 13.4760i 0.631073 + 1.09305i
\(153\) −14.7499 + 25.5476i −1.19246 + 2.06540i
\(154\) 0 0
\(155\) −2.93576 −0.235806
\(156\) −24.3724 27.4830i −1.95135 2.20040i
\(157\) −22.5760 −1.80176 −0.900879 0.434071i \(-0.857077\pi\)
−0.900879 + 0.434071i \(0.857077\pi\)
\(158\) 3.32583 5.76050i 0.264588 0.458281i
\(159\) −0.585433 + 1.01400i −0.0464278 + 0.0804154i
\(160\) 1.29101 + 2.23610i 0.102064 + 0.176779i
\(161\) 0 0
\(162\) −2.17457 3.76646i −0.170850 0.295921i
\(163\) −4.08857 7.08161i −0.320242 0.554675i 0.660296 0.751005i \(-0.270431\pi\)
−0.980538 + 0.196331i \(0.937097\pi\)
\(164\) −13.5952 −1.06161
\(165\) −0.794333 1.37583i −0.0618388 0.107108i
\(166\) 3.42467 5.93170i 0.265806 0.460389i
\(167\) −1.16386 + 2.01586i −0.0900619 + 0.155992i −0.907537 0.419972i \(-0.862040\pi\)
0.817475 + 0.575964i \(0.195373\pi\)
\(168\) 0 0
\(169\) −1.55408 + 12.9068i −0.119545 + 0.992829i
\(170\) 15.1398 1.16117
\(171\) −8.74566 + 15.1479i −0.668798 + 1.15839i
\(172\) −11.8133 + 20.4611i −0.900752 + 1.56015i
\(173\) −4.06686 7.04401i −0.309198 0.535546i 0.668989 0.743272i \(-0.266727\pi\)
−0.978187 + 0.207726i \(0.933394\pi\)
\(174\) 26.0209 1.97264
\(175\) 0 0
\(176\) 0.677355 + 1.17321i 0.0510576 + 0.0884343i
\(177\) −16.5326 −1.24267
\(178\) 2.49922 + 4.32877i 0.187324 + 0.324455i
\(179\) 10.4963 18.1801i 0.784528 1.35884i −0.144752 0.989468i \(-0.546239\pi\)
0.929281 0.369375i \(-0.120428\pi\)
\(180\) 8.31194 14.3967i 0.619536 1.07307i
\(181\) 1.60807 0.119527 0.0597635 0.998213i \(-0.480965\pi\)
0.0597635 + 0.998213i \(0.480965\pi\)
\(182\) 0 0
\(183\) −6.07180 −0.448841
\(184\) 16.7933 29.0868i 1.23802 2.14431i
\(185\) 0.862384 1.49369i 0.0634037 0.109818i
\(186\) 9.81889 + 17.0068i 0.719956 + 1.24700i
\(187\) −3.79379 −0.277430
\(188\) −8.03601 13.9188i −0.586086 1.01513i
\(189\) 0 0
\(190\) 8.97683 0.651247
\(191\) 5.78111 + 10.0132i 0.418307 + 0.724529i 0.995769 0.0918886i \(-0.0292904\pi\)
−0.577463 + 0.816417i \(0.695957\pi\)
\(192\) 14.9771 25.9412i 1.08088 1.87214i
\(193\) −11.7894 + 20.4199i −0.848621 + 1.46985i 0.0338178 + 0.999428i \(0.489233\pi\)
−0.882439 + 0.470427i \(0.844100\pi\)
\(194\) 18.3808 1.31967
\(195\) −9.54689 + 1.95398i −0.683667 + 0.139927i
\(196\) 0 0
\(197\) 0.735472 1.27387i 0.0524002 0.0907598i −0.838636 0.544693i \(-0.816646\pi\)
0.891036 + 0.453933i \(0.149980\pi\)
\(198\) −3.20788 + 5.55622i −0.227974 + 0.394863i
\(199\) 4.69700 + 8.13543i 0.332961 + 0.576706i 0.983091 0.183117i \(-0.0586189\pi\)
−0.650130 + 0.759823i \(0.725286\pi\)
\(200\) 16.4075 1.16018
\(201\) −9.64810 16.7110i −0.680524 1.17870i
\(202\) 3.14901 + 5.45425i 0.221564 + 0.383760i
\(203\) 0 0
\(204\) −32.8776 56.9456i −2.30189 3.98699i
\(205\) −1.80331 + 3.12343i −0.125949 + 0.218150i
\(206\) 12.9693 22.4635i 0.903615 1.56511i
\(207\) 37.7535 2.62405
\(208\) 8.14096 1.66623i 0.564474 0.115532i
\(209\) −2.24946 −0.155598
\(210\) 0 0
\(211\) 4.47109 7.74416i 0.307803 0.533130i −0.670079 0.742290i \(-0.733740\pi\)
0.977881 + 0.209160i \(0.0670730\pi\)
\(212\) −0.787829 1.36456i −0.0541083 0.0937184i
\(213\) 9.91229 0.679179
\(214\) −19.0810 33.0493i −1.30435 2.25920i
\(215\) 3.13389 + 5.42805i 0.213729 + 0.370190i
\(216\) −17.5722 −1.19563
\(217\) 0 0
\(218\) 11.0265 19.0984i 0.746808 1.29351i
\(219\) 6.78827 11.7576i 0.458709 0.794507i
\(220\) 2.13790 0.144137
\(221\) −7.35814 + 22.0770i −0.494962 + 1.48506i
\(222\) −11.5373 −0.774330
\(223\) 10.9098 18.8963i 0.730574 1.26539i −0.226064 0.974112i \(-0.572586\pi\)
0.956638 0.291279i \(-0.0940809\pi\)
\(224\) 0 0
\(225\) 9.22154 + 15.9722i 0.614769 + 1.06481i
\(226\) −24.3108 −1.61713
\(227\) −9.27627 16.0670i −0.615687 1.06640i −0.990263 0.139206i \(-0.955545\pi\)
0.374576 0.927196i \(-0.377788\pi\)
\(228\) −19.4941 33.7648i −1.29103 2.23613i
\(229\) −19.3505 −1.27872 −0.639359 0.768909i \(-0.720800\pi\)
−0.639359 + 0.768909i \(0.720800\pi\)
\(230\) −9.68784 16.7798i −0.638797 1.10643i
\(231\) 0 0
\(232\) −8.05137 + 13.9454i −0.528599 + 0.915560i
\(233\) 16.1634 1.05890 0.529450 0.848341i \(-0.322398\pi\)
0.529450 + 0.848341i \(0.322398\pi\)
\(234\) 26.1113 + 29.4439i 1.70695 + 1.92481i
\(235\) −4.26368 −0.278132
\(236\) 11.1241 19.2676i 0.724119 1.25421i
\(237\) −3.83199 + 6.63720i −0.248915 + 0.431133i
\(238\) 0 0
\(239\) 16.1037 1.04166 0.520831 0.853660i \(-0.325622\pi\)
0.520831 + 0.853660i \(0.325622\pi\)
\(240\) 3.11449 + 5.39445i 0.201039 + 0.348210i
\(241\) −2.00300 3.46930i −0.129025 0.223477i 0.794274 0.607559i \(-0.207851\pi\)
−0.923299 + 0.384082i \(0.874518\pi\)
\(242\) 25.4433 1.63556
\(243\) 8.98786 + 15.5674i 0.576572 + 0.998651i
\(244\) 4.08548 7.07625i 0.261546 0.453011i
\(245\) 0 0
\(246\) 24.1253 1.53817
\(247\) −4.36287 + 13.0901i −0.277603 + 0.832906i
\(248\) −12.1526 −0.771692
\(249\) −3.94588 + 6.83446i −0.250060 + 0.433116i
\(250\) 10.5969 18.3544i 0.670209 1.16084i
\(251\) 1.62344 + 2.81188i 0.102471 + 0.177484i 0.912702 0.408626i \(-0.133992\pi\)
−0.810231 + 0.586110i \(0.800659\pi\)
\(252\) 0 0
\(253\) 2.42763 + 4.20477i 0.152624 + 0.264352i
\(254\) 5.07489 + 8.78996i 0.318427 + 0.551531i
\(255\) −17.4439 −1.09238
\(256\) 13.8778 + 24.0371i 0.867365 + 1.50232i
\(257\) −13.4462 + 23.2895i −0.838751 + 1.45276i 0.0521891 + 0.998637i \(0.483380\pi\)
−0.890940 + 0.454122i \(0.849953\pi\)
\(258\) 20.9631 36.3092i 1.30511 2.26051i
\(259\) 0 0
\(260\) 4.14650 12.4410i 0.257155 0.771556i
\(261\) −18.1005 −1.12040
\(262\) 2.59050 4.48688i 0.160042 0.277200i
\(263\) 1.90353 3.29701i 0.117377 0.203302i −0.801351 0.598195i \(-0.795885\pi\)
0.918727 + 0.394893i \(0.129218\pi\)
\(264\) −3.28815 5.69525i −0.202372 0.350518i
\(265\) −0.418000 −0.0256775
\(266\) 0 0
\(267\) −2.87958 4.98757i −0.176227 0.305235i
\(268\) 25.9673 1.58620
\(269\) −11.9190 20.6444i −0.726716 1.25871i −0.958264 0.285886i \(-0.907712\pi\)
0.231548 0.972824i \(-0.425621\pi\)
\(270\) −5.06859 + 8.77905i −0.308464 + 0.534276i
\(271\) 4.95068 8.57482i 0.300732 0.520883i −0.675570 0.737296i \(-0.736102\pi\)
0.976302 + 0.216413i \(0.0694357\pi\)
\(272\) 14.8750 0.901931
\(273\) 0 0
\(274\) −19.9715 −1.20653
\(275\) −1.18593 + 2.05409i −0.0715142 + 0.123866i
\(276\) −42.0763 + 72.8783i −2.53270 + 4.38676i
\(277\) −5.89289 10.2068i −0.354069 0.613266i 0.632889 0.774243i \(-0.281869\pi\)
−0.986958 + 0.160977i \(0.948536\pi\)
\(278\) −1.37769 −0.0826285
\(279\) −6.83017 11.8302i −0.408912 0.708256i
\(280\) 0 0
\(281\) 12.9976 0.775372 0.387686 0.921791i \(-0.373274\pi\)
0.387686 + 0.921791i \(0.373274\pi\)
\(282\) 14.2602 + 24.6994i 0.849184 + 1.47083i
\(283\) −8.40249 + 14.5535i −0.499476 + 0.865118i −1.00000 0.000604910i \(-0.999807\pi\)
0.500524 + 0.865723i \(0.333141\pi\)
\(284\) −6.66959 + 11.5521i −0.395767 + 0.685489i
\(285\) −10.3430 −0.612668
\(286\) −1.60029 + 4.80143i −0.0946270 + 0.283914i
\(287\) 0 0
\(288\) −6.00719 + 10.4048i −0.353977 + 0.613107i
\(289\) −12.3283 + 21.3533i −0.725197 + 1.25608i
\(290\) 4.64474 + 8.04493i 0.272749 + 0.472414i
\(291\) −21.1783 −1.24149
\(292\) 9.13512 + 15.8225i 0.534592 + 0.925941i
\(293\) −7.04782 12.2072i −0.411738 0.713151i 0.583342 0.812227i \(-0.301745\pi\)
−0.995080 + 0.0990757i \(0.968411\pi\)
\(294\) 0 0
\(295\) −2.95108 5.11141i −0.171818 0.297598i
\(296\) 3.56985 6.18316i 0.207493 0.359389i
\(297\) 1.27011 2.19990i 0.0736994 0.127651i
\(298\) −6.70232 −0.388255
\(299\) 29.1770 5.97172i 1.68735 0.345353i
\(300\) −41.1097 −2.37347
\(301\) 0 0
\(302\) −27.4754 + 47.5888i −1.58103 + 2.73843i
\(303\) −3.62827 6.28434i −0.208439 0.361026i
\(304\) 8.81986 0.505854
\(305\) −1.08382 1.87723i −0.0620593 0.107490i
\(306\) 35.2233 + 61.0085i 2.01358 + 3.48762i
\(307\) −15.8786 −0.906240 −0.453120 0.891450i \(-0.649689\pi\)
−0.453120 + 0.891450i \(0.649689\pi\)
\(308\) 0 0
\(309\) −14.9431 + 25.8823i −0.850086 + 1.47239i
\(310\) −3.50535 + 6.07145i −0.199091 + 0.344835i
\(311\) 28.6034 1.62195 0.810975 0.585081i \(-0.198937\pi\)
0.810975 + 0.585081i \(0.198937\pi\)
\(312\) −39.5195 + 8.08853i −2.23735 + 0.457923i
\(313\) 18.5792 1.05016 0.525080 0.851053i \(-0.324035\pi\)
0.525080 + 0.851053i \(0.324035\pi\)
\(314\) −26.9561 + 46.6893i −1.52122 + 2.63483i
\(315\) 0 0
\(316\) −5.15679 8.93182i −0.290092 0.502454i
\(317\) 30.6445 1.72117 0.860584 0.509309i \(-0.170099\pi\)
0.860584 + 0.509309i \(0.170099\pi\)
\(318\) 1.39804 + 2.42147i 0.0783979 + 0.135789i
\(319\) −1.16390 2.01594i −0.0651660 0.112871i
\(320\) 10.6937 0.597796
\(321\) 21.9850 + 38.0791i 1.22708 + 2.12537i
\(322\) 0 0
\(323\) −12.3498 + 21.3904i −0.687160 + 1.19020i
\(324\) −6.74346 −0.374637
\(325\) 9.65311 + 10.8852i 0.535458 + 0.603800i
\(326\) −19.5273 −1.08152
\(327\) −12.7046 + 22.0051i −0.702568 + 1.21688i
\(328\) −7.46483 + 12.9295i −0.412177 + 0.713911i
\(329\) 0 0
\(330\) −3.79379 −0.208842
\(331\) −13.6138 23.5799i −0.748284 1.29607i −0.948644 0.316344i \(-0.897545\pi\)
0.200360 0.979722i \(-0.435789\pi\)
\(332\) −5.31005 9.19728i −0.291427 0.504766i
\(333\) 8.02549 0.439794
\(334\) 2.77933 + 4.81395i 0.152078 + 0.263407i
\(335\) 3.44438 5.96584i 0.188187 0.325949i
\(336\) 0 0
\(337\) −12.3160 −0.670898 −0.335449 0.942058i \(-0.608888\pi\)
−0.335449 + 0.942058i \(0.608888\pi\)
\(338\) 24.8369 + 18.6249i 1.35095 + 1.01306i
\(339\) 28.0107 1.52133
\(340\) 11.7373 20.3296i 0.636545 1.10253i
\(341\) 0.878389 1.52141i 0.0475674 0.0823892i
\(342\) 20.8850 + 36.1738i 1.12933 + 1.95606i
\(343\) 0 0
\(344\) 12.9728 + 22.4695i 0.699445 + 1.21148i
\(345\) 11.1623 + 19.3336i 0.600956 + 1.04089i
\(346\) −19.4236 −1.04422
\(347\) −3.07253 5.32177i −0.164942 0.285688i 0.771693 0.635996i \(-0.219410\pi\)
−0.936635 + 0.350308i \(0.886077\pi\)
\(348\) 20.1731 34.9408i 1.08139 1.87302i
\(349\) 6.51563 11.2854i 0.348774 0.604094i −0.637258 0.770650i \(-0.719932\pi\)
0.986032 + 0.166557i \(0.0532649\pi\)
\(350\) 0 0
\(351\) −10.3383 11.6578i −0.551820 0.622249i
\(352\) −1.54510 −0.0823541
\(353\) 15.8332 27.4240i 0.842718 1.45963i −0.0448710 0.998993i \(-0.514288\pi\)
0.887589 0.460637i \(-0.152379\pi\)
\(354\) −19.7402 + 34.1911i −1.04918 + 1.81724i
\(355\) 1.76935 + 3.06460i 0.0939072 + 0.162652i
\(356\) 7.75021 0.410761
\(357\) 0 0
\(358\) −25.0655 43.4147i −1.32475 2.29454i
\(359\) 19.9322 1.05198 0.525991 0.850490i \(-0.323695\pi\)
0.525991 + 0.850490i \(0.323695\pi\)
\(360\) −9.12780 15.8098i −0.481077 0.833251i
\(361\) 2.17744 3.77144i 0.114602 0.198497i
\(362\) 1.92007 3.32566i 0.100917 0.174793i
\(363\) −29.3156 −1.53867
\(364\) 0 0
\(365\) 4.84684 0.253695
\(366\) −7.24984 + 12.5571i −0.378955 + 0.656370i
\(367\) 9.85950 17.0772i 0.514662 0.891420i −0.485194 0.874407i \(-0.661251\pi\)
0.999855 0.0170133i \(-0.00541577\pi\)
\(368\) −9.51844 16.4864i −0.496183 0.859414i
\(369\) −16.7819 −0.873632
\(370\) −2.05940 3.56699i −0.107063 0.185439i
\(371\) 0 0
\(372\) 30.4490 1.57870
\(373\) −8.77345 15.1961i −0.454272 0.786823i 0.544374 0.838843i \(-0.316767\pi\)
−0.998646 + 0.0520202i \(0.983434\pi\)
\(374\) −4.52986 + 7.84595i −0.234234 + 0.405704i
\(375\) −12.2097 + 21.1478i −0.630507 + 1.09207i
\(376\) −17.6496 −0.910207
\(377\) −13.9887 + 2.86308i −0.720452 + 0.147456i
\(378\) 0 0
\(379\) 5.85068 10.1337i 0.300529 0.520532i −0.675727 0.737152i \(-0.736170\pi\)
0.976256 + 0.216620i \(0.0695034\pi\)
\(380\) 6.95942 12.0541i 0.357010 0.618360i
\(381\) −5.84725 10.1277i −0.299563 0.518859i
\(382\) 27.6110 1.41270
\(383\) −10.7644 18.6445i −0.550036 0.952690i −0.998271 0.0587748i \(-0.981281\pi\)
0.448235 0.893916i \(-0.352053\pi\)
\(384\) −28.5334 49.4213i −1.45609 2.52202i
\(385\) 0 0
\(386\) 28.1536 + 48.7634i 1.43298 + 2.48199i
\(387\) −14.5823 + 25.2572i −0.741258 + 1.28390i
\(388\) 14.2500 24.6817i 0.723435 1.25303i
\(389\) 26.4910 1.34315 0.671574 0.740938i \(-0.265619\pi\)
0.671574 + 0.740938i \(0.265619\pi\)
\(390\) −7.35814 + 22.0770i −0.372594 + 1.11791i
\(391\) 53.3118 2.69609
\(392\) 0 0
\(393\) −2.98476 + 5.16975i −0.150561 + 0.260779i
\(394\) −1.75633 3.04206i −0.0884828 0.153257i
\(395\) −2.73605 −0.137665
\(396\) 4.97392 + 8.61508i 0.249949 + 0.432924i
\(397\) −16.8995 29.2707i −0.848160 1.46906i −0.882849 0.469658i \(-0.844377\pi\)
0.0346887 0.999398i \(-0.488956\pi\)
\(398\) 22.4332 1.12447
\(399\) 0 0
\(400\) 4.64989 8.05384i 0.232494 0.402692i
\(401\) −10.8059 + 18.7164i −0.539623 + 0.934655i 0.459301 + 0.888281i \(0.348100\pi\)
−0.998924 + 0.0463741i \(0.985233\pi\)
\(402\) −46.0800 −2.29826
\(403\) −7.14983 8.06237i −0.356158 0.401615i
\(404\) 9.76527 0.485840
\(405\) −0.894473 + 1.54927i −0.0444467 + 0.0769839i
\(406\) 0 0
\(407\) 0.516056 + 0.893835i 0.0255799 + 0.0443058i
\(408\) −72.2093 −3.57489
\(409\) 3.87109 + 6.70492i 0.191413 + 0.331537i 0.945719 0.324986i \(-0.105360\pi\)
−0.754306 + 0.656523i \(0.772026\pi\)
\(410\) 4.30637 + 7.45886i 0.212677 + 0.368367i
\(411\) 23.0111 1.13505
\(412\) −20.1093 34.8303i −0.990714 1.71597i
\(413\) 0 0
\(414\) 45.0783 78.0780i 2.21548 3.83732i
\(415\) −2.81736 −0.138299
\(416\) −2.99675 + 8.99132i −0.146928 + 0.440836i
\(417\) 1.58737 0.0777337
\(418\) −2.68589 + 4.65211i −0.131371 + 0.227542i
\(419\) −4.05097 + 7.01649i −0.197903 + 0.342778i −0.947848 0.318722i \(-0.896746\pi\)
0.749945 + 0.661500i \(0.230080\pi\)
\(420\) 0 0
\(421\) −32.1124 −1.56506 −0.782530 0.622612i \(-0.786071\pi\)
−0.782530 + 0.622612i \(0.786071\pi\)
\(422\) −10.6771 18.4933i −0.519755 0.900242i
\(423\) −9.91963 17.1813i −0.482309 0.835384i
\(424\) −1.73032 −0.0840316
\(425\) 13.0218 + 22.5543i 0.631648 + 1.09405i
\(426\) 11.8355 20.4996i 0.573430 0.993210i
\(427\) 0 0
\(428\) −59.1713 −2.86015
\(429\) 1.84384 5.53217i 0.0890214 0.267096i
\(430\) 14.9677 0.721806
\(431\) 14.7640 25.5721i 0.711159 1.23176i −0.253263 0.967397i \(-0.581504\pi\)
0.964422 0.264366i \(-0.0851627\pi\)
\(432\) −4.97996 + 8.62554i −0.239598 + 0.414997i
\(433\) 11.0455 + 19.1314i 0.530813 + 0.919395i 0.999353 + 0.0359531i \(0.0114467\pi\)
−0.468540 + 0.883442i \(0.655220\pi\)
\(434\) 0 0
\(435\) −5.35164 9.26931i −0.256591 0.444429i
\(436\) −17.0969 29.6127i −0.818792 1.41819i
\(437\) 31.6102 1.51212
\(438\) −16.2106 28.0777i −0.774575 1.34160i
\(439\) −3.17790 + 5.50428i −0.151673 + 0.262705i −0.931843 0.362863i \(-0.881799\pi\)
0.780170 + 0.625568i \(0.215133\pi\)
\(440\) 1.17387 2.03321i 0.0559622 0.0969294i
\(441\) 0 0
\(442\) 36.8718 + 41.5777i 1.75381 + 1.97765i
\(443\) −13.5627 −0.644383 −0.322192 0.946675i \(-0.604420\pi\)
−0.322192 + 0.946675i \(0.604420\pi\)
\(444\) −8.94443 + 15.4922i −0.424484 + 0.735227i
\(445\) 1.02801 1.78057i 0.0487324 0.0844070i
\(446\) −26.0530 45.1251i −1.23365 2.13674i
\(447\) 7.72237 0.365255
\(448\) 0 0
\(449\) −10.9559 18.9762i −0.517041 0.895541i −0.999804 0.0197900i \(-0.993700\pi\)
0.482763 0.875751i \(-0.339633\pi\)
\(450\) 44.0428 2.07620
\(451\) −1.07911 1.86908i −0.0508134 0.0880115i
\(452\) −18.8473 + 32.6445i −0.886502 + 1.53547i
\(453\) 31.6570 54.8315i 1.48737 2.57621i
\(454\) −44.3041 −2.07930
\(455\) 0 0
\(456\) −42.8151 −2.00500
\(457\) −7.60732 + 13.1763i −0.355855 + 0.616359i −0.987264 0.159091i \(-0.949144\pi\)
0.631409 + 0.775450i \(0.282477\pi\)
\(458\) −23.1049 + 40.0188i −1.07962 + 1.86996i
\(459\) −13.9461 24.1554i −0.650949 1.12748i
\(460\) −30.0426 −1.40074
\(461\) −8.10813 14.0437i −0.377633 0.654080i 0.613084 0.790018i \(-0.289929\pi\)
−0.990717 + 0.135937i \(0.956595\pi\)
\(462\) 0 0
\(463\) −1.44769 −0.0672799 −0.0336400 0.999434i \(-0.510710\pi\)
−0.0336400 + 0.999434i \(0.510710\pi\)
\(464\) 4.56353 + 7.90426i 0.211856 + 0.366946i
\(465\) 4.03884 6.99547i 0.187297 0.324407i
\(466\) 19.2994 33.4275i 0.894027 1.54850i
\(467\) −14.0067 −0.648155 −0.324078 0.946031i \(-0.605054\pi\)
−0.324078 + 0.946031i \(0.605054\pi\)
\(468\) 59.7803 12.2353i 2.76334 0.565579i
\(469\) 0 0
\(470\) −5.09091 + 8.81772i −0.234826 + 0.406731i
\(471\) 31.0586 53.7951i 1.43111 2.47875i
\(472\) −12.2160 21.1588i −0.562288 0.973912i
\(473\) −3.75068 −0.172456
\(474\) 9.15094 + 15.8499i 0.420316 + 0.728009i
\(475\) 7.72100 + 13.3732i 0.354264 + 0.613603i
\(476\) 0 0
\(477\) −0.972495 1.68441i −0.0445275 0.0771239i
\(478\) 19.2281 33.3041i 0.879474 1.52329i
\(479\) −15.0122 + 26.0018i −0.685923 + 1.18805i 0.287223 + 0.957864i \(0.407268\pi\)
−0.973146 + 0.230189i \(0.926065\pi\)
\(480\) −7.10439 −0.324270
\(481\) 6.20235 1.26945i 0.282803 0.0578817i
\(482\) −9.56649 −0.435742
\(483\) 0 0
\(484\) 19.7253 34.1652i 0.896605 1.55296i
\(485\) −3.78033 6.54772i −0.171656 0.297317i
\(486\) 42.9267 1.94719
\(487\) 14.2452 + 24.6733i 0.645510 + 1.11806i 0.984184 + 0.177152i \(0.0566884\pi\)
−0.338674 + 0.940904i \(0.609978\pi\)
\(488\) −4.48649 7.77082i −0.203094 0.351769i
\(489\) 22.4992 1.01745
\(490\) 0 0
\(491\) 14.2339 24.6538i 0.642365 1.11261i −0.342539 0.939504i \(-0.611287\pi\)
0.984903 0.173105i \(-0.0553799\pi\)
\(492\) 18.7035 32.3954i 0.843218 1.46050i
\(493\) −25.5598 −1.15116
\(494\) 21.8624 + 24.6527i 0.983636 + 1.10918i
\(495\) 2.63902 0.118615
\(496\) −3.44406 + 5.96528i −0.154643 + 0.267849i
\(497\) 0 0
\(498\) 9.42290 + 16.3209i 0.422250 + 0.731359i
\(499\) −26.2329 −1.17434 −0.587172 0.809462i \(-0.699759\pi\)
−0.587172 + 0.809462i \(0.699759\pi\)
\(500\) −16.4309 28.4591i −0.734811 1.27273i
\(501\) −3.20233 5.54659i −0.143069 0.247803i
\(502\) 7.75367 0.346063
\(503\) 4.26588 + 7.38872i 0.190206 + 0.329447i 0.945318 0.326149i \(-0.105751\pi\)
−0.755112 + 0.655595i \(0.772418\pi\)
\(504\) 0 0
\(505\) 1.29529 2.24352i 0.0576398 0.0998351i
\(506\) 11.5945 0.515440
\(507\) −28.6169 21.4595i −1.27092 0.953050i
\(508\) 15.7375 0.698240
\(509\) −6.51298 + 11.2808i −0.288683 + 0.500014i −0.973496 0.228706i \(-0.926551\pi\)
0.684813 + 0.728719i \(0.259884\pi\)
\(510\) −20.8283 + 36.0758i −0.922295 + 1.59746i
\(511\) 0 0
\(512\) 24.8008 1.09605
\(513\) −8.26908 14.3225i −0.365089 0.632352i
\(514\) 32.1100 + 55.6162i 1.41631 + 2.45312i
\(515\) −10.6694 −0.470151
\(516\) −32.5039 56.2984i −1.43090 2.47840i
\(517\) 1.27571 2.20959i 0.0561055 0.0971775i
\(518\) 0 0
\(519\) 22.3798 0.982363
\(520\) −9.55499 10.7745i −0.419014 0.472493i
\(521\) −4.46570 −0.195646 −0.0978230 0.995204i \(-0.531188\pi\)
−0.0978230 + 0.995204i \(0.531188\pi\)
\(522\) −21.6124 + 37.4337i −0.945948 + 1.63843i
\(523\) −1.45406 + 2.51850i −0.0635815 + 0.110126i −0.896064 0.443925i \(-0.853586\pi\)
0.832482 + 0.554051i \(0.186919\pi\)
\(524\) −4.01665 6.95704i −0.175468 0.303920i
\(525\) 0 0
\(526\) −4.54570 7.87339i −0.198202 0.343296i
\(527\) −9.64490 16.7055i −0.420138 0.727701i
\(528\) −3.72746 −0.162217
\(529\) −22.6139 39.1684i −0.983213 1.70297i
\(530\) −0.499100 + 0.864466i −0.0216795 + 0.0375500i
\(531\) 13.7316 23.7838i 0.595901 1.03213i
\(532\) 0 0
\(533\) −12.9696 + 2.65451i −0.561775 + 0.114980i
\(534\) −13.7531 −0.595154
\(535\) −7.84866 + 13.5943i −0.339327 + 0.587732i
\(536\) 14.2581 24.6957i 0.615854 1.06669i
\(537\) 28.8803 + 50.0221i 1.24628 + 2.15861i
\(538\) −56.9262 −2.45426
\(539\) 0 0
\(540\) 7.85899 + 13.6122i 0.338197 + 0.585775i
\(541\) −18.4639 −0.793824 −0.396912 0.917857i \(-0.629918\pi\)
−0.396912 + 0.917857i \(0.629918\pi\)
\(542\) −11.8224 20.4770i −0.507815 0.879562i
\(543\) −2.21229 + 3.83180i −0.0949384 + 0.164438i
\(544\) −8.48277 + 14.6926i −0.363696 + 0.629940i
\(545\) −9.07112 −0.388564
\(546\) 0 0
\(547\) 34.9817 1.49571 0.747856 0.663861i \(-0.231083\pi\)
0.747856 + 0.663861i \(0.231083\pi\)
\(548\) −15.4832 + 26.8177i −0.661411 + 1.14560i
\(549\) 5.04310 8.73491i 0.215234 0.372797i
\(550\) 2.83204 + 4.90524i 0.120759 + 0.209160i
\(551\) −15.1552 −0.645633
\(552\) 46.2063 + 80.0317i 1.96667 + 3.40638i
\(553\) 0 0
\(554\) −28.1449 −1.19576
\(555\) 2.37283 + 4.10986i 0.100721 + 0.174454i
\(556\) −1.06808 + 1.84996i −0.0452965 + 0.0784559i
\(557\) −0.0265706 + 0.0460217i −0.00112583 + 0.00195000i −0.866588 0.499025i \(-0.833692\pi\)
0.865462 + 0.500975i \(0.167025\pi\)
\(558\) −32.6214 −1.38097
\(559\) −7.27451 + 21.8261i −0.307679 + 0.923146i
\(560\) 0 0
\(561\) 5.21927 9.04004i 0.220358 0.381671i
\(562\) 15.5194 26.8804i 0.654646 1.13388i
\(563\) 3.99253 + 6.91527i 0.168265 + 0.291444i 0.937810 0.347149i \(-0.112850\pi\)
−0.769545 + 0.638593i \(0.779517\pi\)
\(564\) 44.2218 1.86207
\(565\) 4.99992 + 8.66012i 0.210348 + 0.364334i
\(566\) 20.0655 + 34.7544i 0.843414 + 1.46084i
\(567\) 0 0
\(568\) 7.32424 + 12.6860i 0.307318 + 0.532291i
\(569\) 13.3621 23.1438i 0.560167 0.970237i −0.437315 0.899308i \(-0.644070\pi\)
0.997481 0.0709285i \(-0.0225962\pi\)
\(570\) −12.3498 + 21.3904i −0.517275 + 0.895946i
\(571\) 13.4929 0.564662 0.282331 0.959317i \(-0.408892\pi\)
0.282331 + 0.959317i \(0.408892\pi\)
\(572\) 5.20670 + 5.87124i 0.217703 + 0.245489i
\(573\) −31.8132 −1.32902
\(574\) 0 0
\(575\) 16.6651 28.8648i 0.694982 1.20374i
\(576\) 24.8794 + 43.0923i 1.03664 + 1.79551i
\(577\) −12.0132 −0.500118 −0.250059 0.968231i \(-0.580450\pi\)
−0.250059 + 0.968231i \(0.580450\pi\)
\(578\) 29.4406 + 50.9925i 1.22457 + 2.12101i
\(579\) −32.4383 56.1848i −1.34809 2.33496i
\(580\) 14.4036 0.598078
\(581\) 0 0
\(582\) −25.2872 + 43.7988i −1.04819 + 1.81552i
\(583\) 0.125067 0.216622i 0.00517974 0.00897158i
\(584\) 20.0636 0.830236
\(585\) 5.11843 15.3571i 0.211621 0.634939i
\(586\) −33.6609 −1.39052
\(587\) 5.21177 9.02705i 0.215113 0.372586i −0.738195 0.674588i \(-0.764321\pi\)
0.953307 + 0.302002i \(0.0976548\pi\)
\(588\) 0 0
\(589\) −5.71876 9.90518i −0.235637 0.408136i
\(590\) −14.0946 −0.580264
\(591\) 2.02364 + 3.50504i 0.0832412 + 0.144178i
\(592\) −2.02339 3.50462i −0.0831610 0.144039i
\(593\) 22.3501 0.917810 0.458905 0.888485i \(-0.348242\pi\)
0.458905 + 0.888485i \(0.348242\pi\)
\(594\) −3.03307 5.25344i −0.124449 0.215551i
\(595\) 0 0
\(596\) −5.19607 + 8.99986i −0.212839 + 0.368649i
\(597\) −25.8474 −1.05786
\(598\) 22.4878 67.4714i 0.919595 2.75911i
\(599\) 1.15893 0.0473524 0.0236762 0.999720i \(-0.492463\pi\)
0.0236762 + 0.999720i \(0.492463\pi\)
\(600\) −22.5724 + 39.0966i −0.921515 + 1.59611i
\(601\) 21.0907 36.5301i 0.860306 1.49009i −0.0113271 0.999936i \(-0.503606\pi\)
0.871633 0.490158i \(-0.163061\pi\)
\(602\) 0 0
\(603\) 32.0540 1.30534
\(604\) 42.6014 + 73.7879i 1.73343 + 3.00239i
\(605\) −5.23284 9.06355i −0.212745 0.368486i
\(606\) −17.3289 −0.703937
\(607\) −9.07844 15.7243i −0.368482 0.638230i 0.620846 0.783932i \(-0.286789\pi\)
−0.989328 + 0.145702i \(0.953456\pi\)
\(608\) −5.02970 + 8.71169i −0.203981 + 0.353306i
\(609\) 0 0
\(610\) −5.17640 −0.209586
\(611\) −10.3839 11.7092i −0.420087 0.473703i
\(612\) 109.229 4.41534
\(613\) 0.451323 0.781714i 0.0182288 0.0315731i −0.856767 0.515703i \(-0.827531\pi\)
0.874996 + 0.484130i \(0.160864\pi\)
\(614\) −18.9594 + 32.8386i −0.765137 + 1.32526i
\(615\) −4.96177 8.59404i −0.200078 0.346545i
\(616\) 0 0
\(617\) 13.0218 + 22.5544i 0.524238 + 0.908008i 0.999602 + 0.0282180i \(0.00898327\pi\)
−0.475363 + 0.879790i \(0.657683\pi\)
\(618\) 35.6848 + 61.8079i 1.43545 + 2.48628i
\(619\) −26.8341 −1.07855 −0.539277 0.842128i \(-0.681303\pi\)
−0.539277 + 0.842128i \(0.681303\pi\)
\(620\) 5.43515 + 9.41396i 0.218281 + 0.378074i
\(621\) −17.8481 + 30.9138i −0.716218 + 1.24053i
\(622\) 34.1530 59.1547i 1.36941 2.37189i
\(623\) 0 0
\(624\) −7.22948 + 21.6910i −0.289411 + 0.868335i
\(625\) 11.4579 0.458315
\(626\) 22.1839 38.4237i 0.886649 1.53572i
\(627\) 3.09467 5.36012i 0.123589 0.214063i
\(628\) 41.7962 + 72.3932i 1.66785 + 2.88880i
\(629\) 11.3328 0.451869
\(630\) 0 0
\(631\) 16.8061 + 29.1089i 0.669039 + 1.15881i 0.978173 + 0.207791i \(0.0666273\pi\)
−0.309135 + 0.951018i \(0.600039\pi\)
\(632\) −11.3259 −0.450521
\(633\) 12.3021 + 21.3079i 0.488965 + 0.846913i
\(634\) 36.5901 63.3760i 1.45318 2.51698i
\(635\) 2.08747 3.61561i 0.0828388 0.143481i
\(636\) 4.33539 0.171909
\(637\) 0 0
\(638\) −5.55889 −0.220078
\(639\) −8.23293 + 14.2598i −0.325690 + 0.564111i
\(640\) 10.1865 17.6435i 0.402655 0.697419i
\(641\) −10.5921 18.3460i −0.418361 0.724622i 0.577414 0.816452i \(-0.304062\pi\)
−0.995775 + 0.0918294i \(0.970729\pi\)
\(642\) 105.002 4.14410
\(643\) 0.330770 + 0.572910i 0.0130443 + 0.0225933i 0.872474 0.488661i \(-0.162514\pi\)
−0.859430 + 0.511254i \(0.829181\pi\)
\(644\) 0 0
\(645\) −17.2457 −0.679047
\(646\) 29.4917 + 51.0811i 1.16034 + 2.00976i
\(647\) −20.0162 + 34.6690i −0.786916 + 1.36298i 0.140931 + 0.990019i \(0.454990\pi\)
−0.927848 + 0.372960i \(0.878343\pi\)
\(648\) −3.70268 + 6.41323i −0.145455 + 0.251936i
\(649\) 3.53188 0.138639
\(650\) 34.0376 6.96654i 1.33506 0.273250i
\(651\) 0 0
\(652\) −15.1388 + 26.2212i −0.592883 + 1.02690i
\(653\) −6.35602 + 11.0089i −0.248730 + 0.430813i −0.963174 0.268880i \(-0.913347\pi\)
0.714444 + 0.699693i \(0.246680\pi\)
\(654\) 30.3391 + 52.5489i 1.18635 + 2.05482i
\(655\) −2.13112 −0.0832698
\(656\) 4.23107 + 7.32844i 0.165196 + 0.286127i
\(657\) 11.2764 + 19.5313i 0.439933 + 0.761987i
\(658\) 0 0
\(659\) 7.09522 + 12.2893i 0.276391 + 0.478723i 0.970485 0.241161i \(-0.0775283\pi\)
−0.694094 + 0.719884i \(0.744195\pi\)
\(660\) −2.94119 + 5.09430i −0.114486 + 0.198295i
\(661\) 25.0890 43.4554i 0.975848 1.69022i 0.298742 0.954334i \(-0.403433\pi\)
0.677106 0.735885i \(-0.263234\pi\)
\(662\) −65.0207 −2.52710
\(663\) −42.4834 47.9056i −1.64992 1.86050i
\(664\) −11.6625 −0.452594
\(665\) 0 0
\(666\) 9.58259 16.5975i 0.371318 0.643141i
\(667\) 16.3556 + 28.3287i 0.633290 + 1.09689i
\(668\) 8.61888 0.333474
\(669\) 30.0181 + 51.9928i 1.16057 + 2.01016i
\(670\) −8.22530 14.2466i −0.317771 0.550396i
\(671\) 1.29713 0.0500751
\(672\) 0 0
\(673\) 0.937137 1.62317i 0.0361240 0.0625685i −0.847398 0.530958i \(-0.821832\pi\)
0.883522 + 0.468389i \(0.155166\pi\)
\(674\) −14.7056 + 25.4708i −0.566438 + 0.981100i
\(675\) −17.4380 −0.671191
\(676\) 44.2647 18.9117i 1.70249 0.727373i
\(677\) 2.00879 0.0772041 0.0386020 0.999255i \(-0.487710\pi\)
0.0386020 + 0.999255i \(0.487710\pi\)
\(678\) 33.4453 57.9290i 1.28446 2.22475i
\(679\) 0 0
\(680\) −12.8894 22.3251i −0.494286 0.856128i
\(681\) 51.0469 1.95612
\(682\) −2.09762 3.63319i −0.0803222 0.139122i
\(683\) 7.05061 + 12.2120i 0.269784 + 0.467280i 0.968806 0.247820i \(-0.0797143\pi\)
−0.699022 + 0.715100i \(0.746381\pi\)
\(684\) 64.7655 2.47637
\(685\) 4.10748 + 7.11437i 0.156939 + 0.271826i
\(686\) 0 0
\(687\) 26.6212 46.1094i 1.01566 1.75918i
\(688\) 14.7060 0.560660
\(689\) −1.01801 1.14794i −0.0387830 0.0437330i
\(690\) 53.3118 2.02954
\(691\) −17.8460 + 30.9102i −0.678895 + 1.17588i 0.296419 + 0.955058i \(0.404207\pi\)
−0.975314 + 0.220822i \(0.929126\pi\)
\(692\) −15.0585 + 26.0820i −0.572437 + 0.991489i
\(693\) 0 0
\(694\) −14.6746 −0.557041
\(695\) 0.283346 + 0.490769i 0.0107479 + 0.0186159i
\(696\) −22.1532 38.3704i −0.839714 1.45443i
\(697\) −23.6978 −0.897618
\(698\) −15.5596 26.9500i −0.588938 1.02007i
\(699\) −22.2366 + 38.5150i −0.841066 + 1.45677i
\(700\) 0 0
\(701\) −6.15865 −0.232609 −0.116305 0.993214i \(-0.537105\pi\)
−0.116305 + 0.993214i \(0.537105\pi\)
\(702\) −36.4538 + 7.46106i −1.37586 + 0.281600i
\(703\) 6.71957 0.253434
\(704\) −3.19959 + 5.54185i −0.120589 + 0.208866i
\(705\) 5.86571 10.1597i 0.220915 0.382637i
\(706\) −37.8103 65.4894i −1.42301 2.46473i
\(707\) 0 0
\(708\) 30.6078 + 53.0143i 1.15031 + 1.99240i
\(709\) −17.0185 29.4770i −0.639144 1.10703i −0.985621 0.168972i \(-0.945955\pi\)
0.346477 0.938059i \(-0.387378\pi\)
\(710\) 8.45054 0.317143
\(711\) −6.36553 11.0254i −0.238726 0.413486i
\(712\) 4.25547 7.37069i 0.159480 0.276228i
\(713\) −12.3434 + 21.3794i −0.462265 + 0.800667i
\(714\) 0 0
\(715\) 2.03952 0.417432i 0.0762736 0.0156111i
\(716\) −77.7295 −2.90489
\(717\) −22.1545 + 38.3727i −0.827375 + 1.43306i
\(718\) 23.7994 41.2218i 0.888187 1.53838i
\(719\) −11.4824 19.8881i −0.428222 0.741702i 0.568493 0.822688i \(-0.307526\pi\)
−0.996715 + 0.0809859i \(0.974193\pi\)
\(720\) −10.3473 −0.385621
\(721\) 0 0
\(722\) −5.19981 9.00633i −0.193517 0.335181i
\(723\) 11.0224 0.409929
\(724\) −2.97712 5.15653i −0.110644 0.191641i
\(725\) −7.98992 + 13.8389i −0.296738 + 0.513966i
\(726\) −35.0034 + 60.6276i −1.29910 + 2.25010i
\(727\) −1.06558 −0.0395203 −0.0197601 0.999805i \(-0.506290\pi\)
−0.0197601 + 0.999805i \(0.506290\pi\)
\(728\) 0 0
\(729\) −43.9962 −1.62949
\(730\) 5.78721 10.0237i 0.214194 0.370996i
\(731\) −20.5916 + 35.6658i −0.761609 + 1.31915i
\(732\) 11.2411 + 19.4702i 0.415483 + 0.719637i
\(733\) 26.3378 0.972808 0.486404 0.873734i \(-0.338308\pi\)
0.486404 + 0.873734i \(0.338308\pi\)
\(734\) −23.5448 40.7809i −0.869056 1.50525i
\(735\) 0 0
\(736\) 21.7123 0.800326
\(737\) 2.06114 + 3.57000i 0.0759230 + 0.131502i
\(738\) −20.0379 + 34.7067i −0.737606 + 1.27757i
\(739\) −17.1075 + 29.6310i −0.629308 + 1.08999i 0.358383 + 0.933575i \(0.383328\pi\)
−0.987691 + 0.156419i \(0.950005\pi\)
\(740\) −6.38633 −0.234766
\(741\) −25.1897 28.4047i −0.925366 1.04347i
\(742\) 0 0
\(743\) −11.2391 + 19.4667i −0.412322 + 0.714163i −0.995143 0.0984379i \(-0.968615\pi\)
0.582821 + 0.812600i \(0.301949\pi\)
\(744\) 16.7188 28.9579i 0.612942 1.06165i
\(745\) 1.37845 + 2.38754i 0.0505023 + 0.0874726i
\(746\) −41.9027 −1.53417
\(747\) −6.55472 11.3531i −0.239825 0.415388i
\(748\) 7.02368 + 12.1654i 0.256811 + 0.444810i
\(749\) 0 0
\(750\) 29.1573 + 50.5018i 1.06467 + 1.84407i
\(751\) 21.2712 36.8428i 0.776197 1.34441i −0.157923 0.987451i \(-0.550480\pi\)
0.934119 0.356961i \(-0.116187\pi\)
\(752\) −5.00189 + 8.66353i −0.182400 + 0.315927i
\(753\) −8.93372 −0.325563
\(754\) −10.7816 + 32.3485i −0.392641 + 1.17806i
\(755\) 22.6031 0.822612
\(756\) 0 0
\(757\) 5.61902 9.73243i 0.204227 0.353731i −0.745659 0.666327i \(-0.767865\pi\)
0.949886 + 0.312596i \(0.101199\pi\)
\(758\) −13.9716 24.1996i −0.507473 0.878969i
\(759\) −13.3591 −0.484906
\(760\) −7.64252 13.2372i −0.277223 0.480165i
\(761\) 6.40422 + 11.0924i 0.232153 + 0.402101i 0.958441 0.285289i \(-0.0920897\pi\)
−0.726289 + 0.687390i \(0.758756\pi\)
\(762\) −27.9269 −1.01168
\(763\) 0 0
\(764\) 21.4059 37.0760i 0.774437 1.34136i
\(765\) 14.4885 25.0948i 0.523833 0.907306i
\(766\) −51.4117 −1.85758
\(767\) 6.85016 20.5529i 0.247345 0.742122i
\(768\) −76.3692 −2.75574
\(769\) −25.6759 + 44.4719i −0.925895 + 1.60370i −0.135780 + 0.990739i \(0.543354\pi\)
−0.790115 + 0.612958i \(0.789979\pi\)
\(770\) 0 0
\(771\) −36.9969 64.0805i −1.33241 2.30780i
\(772\) 87.3059 3.14221
\(773\) 10.0023 + 17.3245i 0.359759 + 0.623120i 0.987920 0.154963i \(-0.0495257\pi\)
−0.628162 + 0.778083i \(0.716192\pi\)
\(774\) 34.8230 + 60.3151i 1.25169 + 2.16798i
\(775\) −12.0599 −0.433203
\(776\) −15.6487 27.1044i −0.561756 0.972990i
\(777\) 0 0
\(778\) 31.6308 54.7861i 1.13402 1.96418i
\(779\) −14.0512 −0.503435
\(780\) 23.9405 + 26.9960i 0.857206 + 0.966613i
\(781\) −2.11758 −0.0757729
\(782\) 63.6552 110.254i 2.27631 3.94268i
\(783\) 8.55708 14.8213i 0.305805 0.529670i
\(784\) 0