Properties

Label 637.2.h.l.471.1
Level $637$
Weight $2$
Character 637.471
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.h (of order \(3\), degree \(2\), not 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 471.1
Root \(-0.181721 - 0.314749i\) of defining polynomial
Character \(\chi\) \(=\) 637.471
Dual form 637.2.h.l.165.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.38804 q^{2} +(-1.37574 + 2.38285i) q^{3} +3.70272 q^{4} +(0.491140 - 0.850679i) q^{5} +(3.28532 - 5.69033i) q^{6} -4.06616 q^{8} +(-2.28532 - 3.95828i) q^{9} +O(q^{10})\) \(q-2.38804 q^{2} +(-1.37574 + 2.38285i) q^{3} +3.70272 q^{4} +(0.491140 - 0.850679i) 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} +(-5.09398 + 8.82303i) q^{12} +(-2.39227 + 2.69760i) q^{13} +(1.35136 + 2.34063i) q^{15} +2.30470 q^{16} +6.45420 q^{17} +(5.45742 + 9.45253i) q^{18} +(-1.91345 - 3.31419i) q^{19} +(1.81855 - 3.14983i) q^{20} +(-0.701847 + 1.21563i) q^{22} +8.26001 q^{23} +(5.59398 - 9.68906i) q^{24} +(2.01756 + 3.49452i) q^{25} +(5.71283 - 6.44197i) q^{26} +4.32156 q^{27} +(1.98009 + 3.42962i) q^{29} +(-3.22710 - 5.58950i) q^{30} +(-1.49436 - 2.58831i) q^{31} +2.62861 q^{32} +(0.808663 + 1.40065i) q^{33} -15.4129 q^{34} +(-8.46189 - 14.6564i) q^{36} +1.75588 q^{37} +(4.56938 + 7.91440i) q^{38} +(-3.13683 - 9.41161i) q^{39} +(-1.99705 + 3.45900i) q^{40} +(1.83584 + 3.17977i) q^{41} +(-3.19042 + 5.52598i) q^{43} +(1.08823 - 1.88488i) q^{44} -4.48964 q^{45} -19.7252 q^{46} +(-2.17030 + 3.75906i) q^{47} +(-3.17067 + 5.49176i) q^{48} +(-4.81802 - 8.34505i) q^{50} +(-8.87930 + 15.3794i) q^{51} +(-8.85791 + 9.98846i) q^{52} +(-0.212770 - 0.368529i) q^{53} -10.3200 q^{54} +(-0.288693 - 0.500031i) q^{55} +10.5296 q^{57} +(-4.72853 - 8.19006i) q^{58} -6.00863 q^{59} +(5.00371 + 8.66669i) q^{60} +(1.10337 + 1.91109i) q^{61} +(3.56859 + 6.18097i) q^{62} -10.8866 q^{64} +(1.11985 + 3.35995i) q^{65} +(-1.93112 - 3.34479i) q^{66} +(-3.50651 + 6.07346i) q^{67} +23.8981 q^{68} +(-11.3636 + 19.6824i) q^{69} +(-1.80127 + 3.11988i) q^{71} +(9.29247 + 16.0950i) q^{72} +(2.46714 + 4.27321i) q^{73} -4.19311 q^{74} -11.1026 q^{75} +(-7.08496 - 12.2715i) q^{76} +(7.49088 + 22.4753i) q^{78} +(-1.39270 + 2.41223i) 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} +(7.61885 - 13.1962i) q^{86} -10.8964 q^{87} +(-1.19505 + 2.06989i) q^{88} +2.09311 q^{89} +10.7214 q^{90} +30.5845 q^{92} +8.22340 q^{93} +(5.18275 - 8.97679i) q^{94} -3.75908 q^{95} +(-3.61628 + 6.26357i) q^{96} +(3.84852 - 6.66584i) q^{97} -2.68663 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{2} - q^{3} + 8q^{4} - q^{5} + 9q^{6} - 6q^{8} + 3q^{9} + O(q^{10}) \) \( 12q - 4q^{2} - q^{3} + 8q^{4} - q^{5} + 9q^{6} - 6q^{8} + 3q^{9} - 4q^{10} + 4q^{11} - 5q^{12} + 2q^{13} - 2q^{15} - 16q^{16} + 10q^{17} + 3q^{18} + q^{19} + q^{20} - 5q^{22} + 2q^{23} + 11q^{24} + 7q^{25} + 16q^{26} + 8q^{27} + 3q^{29} - 5q^{30} - 16q^{31} - 16q^{32} - 16q^{33} - 32q^{34} - 21q^{36} + 26q^{37} + 17q^{38} - 20q^{39} + 5q^{40} + 8q^{41} - 11q^{43} + 21q^{44} - 14q^{45} - 32q^{46} + q^{47} - 21q^{48} + 6q^{50} - 20q^{51} - 41q^{52} - 2q^{53} - 36q^{54} - 9q^{55} + 42q^{57} - 8q^{58} + 26q^{59} + 20q^{60} + 5q^{61} - 5q^{62} - 30q^{64} - 5q^{65} - 18q^{66} - 11q^{67} + 58q^{68} - 23q^{69} + 6q^{71} + 25q^{72} + 30q^{73} + 6q^{74} - 6q^{75} + 9q^{76} + 16q^{78} + 7q^{79} + 7q^{80} - 6q^{81} - q^{82} + 54q^{83} - q^{85} - 7q^{86} + 32q^{87} + 8q^{89} + 16q^{90} + 54q^{92} + 14q^{93} - 45q^{94} + 12q^{95} - 19q^{96} + 35q^{97} - 20q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.38804 −1.68860 −0.844299 0.535873i \(-0.819983\pi\)
−0.844299 + 0.535873i \(0.819983\pi\)
\(3\) −1.37574 + 2.38285i −0.794283 + 1.37574i 0.129010 + 0.991643i \(0.458820\pi\)
−0.923293 + 0.384096i \(0.874513\pi\)
\(4\) 3.70272 1.85136
\(5\) 0.491140 0.850679i 0.219644 0.380435i −0.735055 0.678008i \(-0.762844\pi\)
0.954699 + 0.297572i \(0.0961769\pi\)
\(6\) 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 \(0.138423\pi\)
\(12\) −5.09398 + 8.82303i −1.47051 + 2.54699i
\(13\) −2.39227 + 2.69760i −0.663496 + 0.748179i
\(14\) 0 0
\(15\) 1.35136 + 2.34063i 0.348920 + 0.604347i
\(16\) 2.30470 0.576176
\(17\) 6.45420 1.56537 0.782687 0.622416i \(-0.213849\pi\)
0.782687 + 0.622416i \(0.213849\pi\)
\(18\) 5.45742 + 9.45253i 1.28633 + 2.22798i
\(19\) −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
\(23\) 8.26001 1.72233 0.861166 0.508324i \(-0.169735\pi\)
0.861166 + 0.508324i \(0.169735\pi\)
\(24\) 5.59398 9.68906i 1.14187 1.97777i
\(25\) 2.01756 + 3.49452i 0.403513 + 0.698904i
\(26\) 5.71283 6.44197i 1.12038 1.26337i
\(27\) 4.32156 0.831685
\(28\) 0 0
\(29\) 1.98009 + 3.42962i 0.367694 + 0.636864i 0.989205 0.146541i \(-0.0468141\pi\)
−0.621511 + 0.783406i \(0.713481\pi\)
\(30\) −3.22710 5.58950i −0.589185 1.02050i
\(31\) −1.49436 2.58831i −0.268395 0.464874i 0.700053 0.714091i \(-0.253160\pi\)
−0.968448 + 0.249218i \(0.919827\pi\)
\(32\) 2.62861 0.464676
\(33\) 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
\(37\) 1.75588 0.288665 0.144333 0.989529i \(-0.453896\pi\)
0.144333 + 0.989529i \(0.453896\pi\)
\(38\) 4.56938 + 7.91440i 0.741252 + 1.28389i
\(39\) −3.13683 9.41161i −0.502295 1.50706i
\(40\) −1.99705 + 3.45900i −0.315762 + 0.546916i
\(41\) 1.83584 + 3.17977i 0.286710 + 0.496597i 0.973023 0.230710i \(-0.0741049\pi\)
−0.686312 + 0.727307i \(0.740772\pi\)
\(42\) 0 0
\(43\) −3.19042 + 5.52598i −0.486535 + 0.842703i −0.999880 0.0154788i \(-0.995073\pi\)
0.513345 + 0.858182i \(0.328406\pi\)
\(44\) 1.08823 1.88488i 0.164058 0.284156i
\(45\) −4.48964 −0.669276
\(46\) −19.7252 −2.90832
\(47\) −2.17030 + 3.75906i −0.316570 + 0.548316i −0.979770 0.200127i \(-0.935865\pi\)
0.663200 + 0.748442i \(0.269198\pi\)
\(48\) −3.17067 + 5.49176i −0.457647 + 0.792668i
\(49\) 0 0
\(50\) −4.81802 8.34505i −0.681370 1.18017i
\(51\) −8.87930 + 15.3794i −1.24335 + 2.15355i
\(52\) −8.85791 + 9.98846i −1.22837 + 1.38515i
\(53\) −0.212770 0.368529i −0.0292263 0.0506214i 0.851042 0.525097i \(-0.175971\pi\)
−0.880269 + 0.474476i \(0.842638\pi\)
\(54\) −10.3200 −1.40438
\(55\) −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
\(59\) −6.00863 −0.782256 −0.391128 0.920336i \(-0.627915\pi\)
−0.391128 + 0.920336i \(0.627915\pi\)
\(60\) 5.00371 + 8.66669i 0.645977 + 1.11886i
\(61\) 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
\(65\) 1.11985 + 3.35995i 0.138901 + 0.416751i
\(66\) −1.93112 3.34479i −0.237704 0.411716i
\(67\) −3.50651 + 6.07346i −0.428389 + 0.741991i −0.996730 0.0808015i \(-0.974252\pi\)
0.568341 + 0.822793i \(0.307585\pi\)
\(68\) 23.8981 2.89807
\(69\) −11.3636 + 19.6824i −1.36802 + 2.36948i
\(70\) 0 0
\(71\) −1.80127 + 3.11988i −0.213771 + 0.370262i −0.952892 0.303311i \(-0.901908\pi\)
0.739121 + 0.673573i \(0.235241\pi\)
\(72\) 9.29247 + 16.0950i 1.09513 + 1.89682i
\(73\) 2.46714 + 4.27321i 0.288756 + 0.500141i 0.973513 0.228631i \(-0.0734249\pi\)
−0.684757 + 0.728772i \(0.740092\pi\)
\(74\) −4.19311 −0.487439
\(75\) −11.1026 −1.28201
\(76\) −7.08496 12.2715i −0.812701 1.40764i
\(77\) 0 0
\(78\) 7.49088 + 22.4753i 0.848175 + 2.54483i
\(79\) −1.39270 + 2.41223i −0.156691 + 0.271397i −0.933674 0.358125i \(-0.883416\pi\)
0.776982 + 0.629522i \(0.216749\pi\)
\(80\) 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
\(86\) 7.61885 13.1962i 0.821562 1.42299i
\(87\) −10.8964 −1.16821
\(88\) −1.19505 + 2.06989i −0.127393 + 0.220651i
\(89\) 2.09311 0.221870 0.110935 0.993828i \(-0.464616\pi\)
0.110935 + 0.993828i \(0.464616\pi\)
\(90\) 10.7214 1.13014
\(91\) 0 0
\(92\) 30.5845 3.18866
\(93\) 8.22340 0.852727
\(94\) 5.18275 8.97679i 0.534560 0.925885i
\(95\) −3.75908 −0.385674
\(96\) −3.61628 + 6.26357i −0.369085 + 0.639273i
\(97\) 3.84852 6.66584i 0.390758 0.676813i −0.601791 0.798653i \(-0.705546\pi\)
0.992550 + 0.121840i \(0.0388795\pi\)
\(98\) 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
\(103\) −5.43095 + 9.40669i −0.535128 + 0.926868i 0.464029 + 0.885820i \(0.346403\pi\)
−0.999157 + 0.0410486i \(0.986930\pi\)
\(104\) 9.72736 10.9689i 0.953846 1.07559i
\(105\) 0 0
\(106\) 0.508103 + 0.880061i 0.0493514 + 0.0854791i
\(107\) −15.9805 −1.54489 −0.772446 0.635080i \(-0.780967\pi\)
−0.772446 + 0.635080i \(0.780967\pi\)
\(108\) 16.0015 1.53975
\(109\) −4.61738 7.99754i −0.442265 0.766026i 0.555592 0.831455i \(-0.312492\pi\)
−0.997857 + 0.0654294i \(0.979158\pi\)
\(110\) 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 −0.999706 0.0242655i \(-0.992275\pi\)
0.520867 + 0.853638i \(0.325609\pi\)
\(114\) −25.1451 −2.35506
\(115\) 4.05682 7.02662i 0.378301 0.655236i
\(116\) 7.33173 + 12.6989i 0.680734 + 1.17907i
\(117\) 16.1450 + 3.30442i 1.49260 + 0.305494i
\(118\) 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
\(122\) −2.63489 4.56376i −0.238552 0.413184i
\(123\) −10.1026 −0.910917
\(124\) −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 0.756201 0.654340i \(-0.227053\pi\)
−0.944775 + 0.327719i \(0.893720\pi\)
\(128\) 20.7404 1.83321
\(129\) −8.77838 15.2046i −0.772893 1.33869i
\(130\) −2.67425 8.02369i −0.234547 0.703725i
\(131\) −1.08478 + 1.87890i −0.0947779 + 0.164160i −0.909516 0.415669i \(-0.863547\pi\)
0.814738 + 0.579829i \(0.196881\pi\)
\(132\) 2.99425 + 5.18620i 0.260616 + 0.451401i
\(133\) 0 0
\(134\) 8.37369 14.5037i 0.723376 1.25292i
\(135\) 2.12249 3.67626i 0.182675 0.316402i
\(136\) −26.2438 −2.25039
\(137\) 8.36316 0.714513 0.357257 0.934006i \(-0.383712\pi\)
0.357257 + 0.934006i \(0.383712\pi\)
\(138\) 27.1367 47.0022i 2.31003 4.00110i
\(139\) −0.288457 + 0.499622i −0.0244666 + 0.0423774i −0.877999 0.478662i \(-0.841122\pi\)
0.853533 + 0.521039i \(0.174455\pi\)
\(140\) 0 0
\(141\) −5.97152 10.3430i −0.502893 0.871036i
\(142\) 4.30149 7.45040i 0.360973 0.625224i
\(143\) 0.670127 + 2.01062i 0.0560388 + 0.168136i
\(144\) −5.26698 9.12267i −0.438915 0.760223i
\(145\) 3.89001 0.323048
\(146\) −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 \(0.870009\pi\)
\(150\) 26.5133 2.16480
\(151\) 11.5054 + 19.9280i 0.936300 + 1.62172i 0.772300 + 0.635258i \(0.219106\pi\)
0.164000 + 0.986460i \(0.447560\pi\)
\(152\) 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
\(156\) −11.6148 34.8486i −0.929930 2.79012i
\(157\) 11.2880 + 19.5513i 0.900879 + 1.56037i 0.826356 + 0.563148i \(0.190410\pi\)
0.0745227 + 0.997219i \(0.476257\pi\)
\(158\) 3.32583 5.76050i 0.264588 0.458281i
\(159\) 1.17087 0.0928557
\(160\) 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 \(0.937097\pi\)
\(164\) 6.79761 + 11.7738i 0.530804 + 0.919380i
\(165\) 1.58867 0.123678
\(166\) −6.84934 −0.531612
\(167\) −1.16386 2.01586i −0.0900619 0.155992i 0.817475 0.575964i \(-0.195373\pi\)
−0.907537 + 0.419972i \(0.862040\pi\)
\(168\) 0 0
\(169\) −1.55408 12.9068i −0.119545 0.992829i
\(170\) −7.56988 + 13.1114i −0.580583 + 1.00560i
\(171\) −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
\(177\) 8.26630 14.3177i 0.621333 1.07618i
\(178\) −4.99843 −0.374648
\(179\) 10.4963 18.1801i 0.784528 1.35884i −0.144752 0.989468i \(-0.546239\pi\)
0.929281 0.369375i \(-0.120428\pi\)
\(180\) −16.6239 −1.23907
\(181\) 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
\(184\) −33.5865 −2.47603
\(185\) 0.862384 1.49369i 0.0634037 0.109818i
\(186\) −19.6378 −1.43991
\(187\) 1.89690 3.28552i 0.138715 0.240261i
\(188\) −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 \(0.844100\pi\)
\(194\) −9.19041 + 15.9183i −0.659833 + 1.14286i
\(195\) −9.54689 1.95398i −0.683667 0.139927i
\(196\) 0 0
\(197\) 0.735472 + 1.27387i 0.0524002 + 0.0907598i 0.891036 0.453933i \(-0.149980\pi\)
−0.838636 + 0.544693i \(0.816646\pi\)
\(198\) 6.41577 0.455949
\(199\) −9.39399 −0.665922 −0.332961 0.942941i \(-0.608048\pi\)
−0.332961 + 0.942941i \(0.608048\pi\)
\(200\) −8.20374 14.2093i −0.580092 1.00475i
\(201\) −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
\(205\) 3.60662 0.251897
\(206\) 12.9693 22.4635i 0.903615 1.56511i
\(207\) −18.8767 32.6955i −1.31202 2.27249i
\(208\) −5.51348 + 6.21717i −0.382291 + 0.431083i
\(209\) −2.24946 −0.155598
\(210\) 0 0
\(211\) 4.47109 + 7.74416i 0.307803 + 0.533130i 0.977881 0.209160i \(-0.0670730\pi\)
−0.670079 + 0.742290i \(0.733740\pi\)
\(212\) −0.787829 1.36456i −0.0541083 0.0937184i
\(213\) −4.95615 8.58430i −0.339589 0.588186i
\(214\) 38.1620 2.60870
\(215\) 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
\(219\) −13.5765 −0.917418
\(220\) −1.06895 1.85148i −0.0720686 0.124827i
\(221\) −15.4402 + 17.4108i −1.03862 + 1.17118i
\(222\) 5.76863 9.99156i 0.387165 0.670589i
\(223\) 10.9098 + 18.8963i 0.730574 + 1.26539i 0.956638 + 0.291279i \(0.0940809\pi\)
−0.226064 + 0.974112i \(0.572586\pi\)
\(224\) 0 0
\(225\) 9.22154 15.9722i 0.614769 1.06481i
\(226\) 12.1554 21.0538i 0.808565 1.40048i
\(227\) 18.5525 1.23137 0.615687 0.787990i \(-0.288878\pi\)
0.615687 + 0.787990i \(0.288878\pi\)
\(228\) 38.9882 2.58206
\(229\) 9.67525 16.7580i 0.639359 1.10740i −0.346215 0.938155i \(-0.612533\pi\)
0.985574 0.169247i \(-0.0541334\pi\)
\(230\) −9.68784 + 16.7798i −0.638797 + 1.10643i
\(231\) 0 0
\(232\) −8.05137 13.9454i −0.528599 0.915560i
\(233\) −8.08170 + 13.9979i −0.529450 + 0.917034i 0.469960 + 0.882688i \(0.344268\pi\)
−0.999410 + 0.0343462i \(0.989065\pi\)
\(234\) −38.5548 7.89108i −2.52040 0.515856i
\(235\) 2.13184 + 3.69245i 0.139066 + 0.240869i
\(236\) −22.2483 −1.44824
\(237\) −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
\(241\) 4.00600 0.258049 0.129025 0.991641i \(-0.458815\pi\)
0.129025 + 0.991641i \(0.458815\pi\)
\(242\) −12.7217 22.0346i −0.817779 1.41643i
\(243\) 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
\(247\) 13.5178 + 2.76672i 0.860119 + 0.176042i
\(248\) 6.07631 + 10.5245i 0.385846 + 0.668305i
\(249\) −3.94588 + 6.83446i −0.250060 + 0.433116i
\(250\) −21.1939 −1.34042
\(251\) 1.62344 2.81188i 0.102471 0.177484i −0.810231 0.586110i \(-0.800659\pi\)
0.912702 + 0.408626i \(0.133992\pi\)
\(252\) 0 0
\(253\) 2.42763 4.20477i 0.152624 0.264352i
\(254\) 5.07489 + 8.78996i 0.318427 + 0.551531i
\(255\) 8.72195 + 15.1069i 0.546190 + 0.946029i
\(256\) −27.7557 −1.73473
\(257\) 26.8924 1.67750 0.838751 0.544516i \(-0.183287\pi\)
0.838751 + 0.544516i \(0.183287\pi\)
\(258\) 20.9631 + 36.3092i 1.30511 + 2.26051i
\(259\) 0 0
\(260\) 4.14650 + 12.4410i 0.257155 + 0.771556i
\(261\) 9.05027 15.6755i 0.560198 0.970291i
\(262\) 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
\(268\) −12.9836 + 22.4883i −0.793102 + 1.37369i
\(269\) 23.8381 1.45343 0.726716 0.686938i \(-0.241046\pi\)
0.726716 + 0.686938i \(0.241046\pi\)
\(270\) −5.06859 + 8.77905i −0.308464 + 0.534276i
\(271\) −9.90135 −0.601464 −0.300732 0.953709i \(-0.597231\pi\)
−0.300732 + 0.953709i \(0.597231\pi\)
\(272\) 14.8750 0.901931
\(273\) 0 0
\(274\) −19.9715 −1.20653
\(275\) 2.37186 0.143028
\(276\) −42.0763 + 72.8783i −2.53270 + 4.38676i
\(277\) 11.7858 0.708139 0.354069 0.935219i \(-0.384798\pi\)
0.354069 + 0.935219i \(0.384798\pi\)
\(278\) 0.688846 1.19312i 0.0413142 0.0715584i
\(279\) −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
\(285\) 5.17151 8.95733i 0.306334 0.530586i
\(286\) −1.60029 4.80143i −0.0946270 0.283914i
\(287\) 0 0
\(288\) −6.00719 10.4048i −0.353977 0.613107i
\(289\) 24.6567 1.45039
\(290\) −9.28948 −0.545497
\(291\) 10.5891 + 18.3409i 0.620746 + 1.07516i
\(292\) 9.13512 + 15.8225i 0.534592 + 0.925941i
\(293\) −7.04782 + 12.2072i −0.411738 + 0.713151i −0.995080 0.0990757i \(-0.968411\pi\)
0.583342 + 0.812227i \(0.301745\pi\)
\(294\) 0 0
\(295\) −2.95108 + 5.11141i −0.171818 + 0.297598i
\(296\) −7.13970 −0.414987
\(297\) 1.27011 2.19990i 0.0736994 0.127651i
\(298\) 3.35116 + 5.80438i 0.194128 + 0.336239i
\(299\) −19.7602 + 22.2822i −1.14276 + 1.28861i
\(300\) −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
\(304\) −4.40993 7.63822i −0.252927 0.438082i
\(305\) 2.16764 0.124119
\(306\) 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
\(310\) 7.01070 0.398181
\(311\) −14.3017 24.7713i −0.810975 1.40465i −0.912183 0.409784i \(-0.865604\pi\)
0.101208 0.994865i \(-0.467729\pi\)
\(312\) 12.7549 + 38.2692i 0.722103 + 2.16656i
\(313\) −9.28962 + 16.0901i −0.525080 + 0.909465i 0.474493 + 0.880259i \(0.342631\pi\)
−0.999573 + 0.0292063i \(0.990702\pi\)
\(314\) −26.9561 46.6893i −1.52122 2.63483i
\(315\) 0 0
\(316\) −5.15679 + 8.93182i −0.290092 + 0.502454i
\(317\) −15.3223 + 26.5389i −0.860584 + 1.49057i 0.0107826 + 0.999942i \(0.496568\pi\)
−0.871366 + 0.490633i \(0.836766\pi\)
\(318\) −2.79607 −0.156796
\(319\) 2.32781 0.130332
\(320\) −5.34685 + 9.26102i −0.298898 + 0.517707i
\(321\) 21.9850 38.0791i 1.22708 2.12537i
\(322\) 0 0
\(323\) −12.3498 21.3904i −0.687160 1.19020i
\(324\) 3.37173 5.84001i 0.187318 0.324445i
\(325\) −14.2534 2.91727i −0.790635 0.161821i
\(326\) 9.76366 + 16.9112i 0.540759 + 0.936622i
\(327\) 25.4093 1.40514
\(328\) −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 \(-0.435789\pi\)
\(332\) 10.6201 0.582854
\(333\) −4.01275 6.95028i −0.219897 0.380873i
\(334\) 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 \(0.608888\pi\)
\(338\) 3.71121 + 30.8219i 0.201863 + 1.67649i
\(339\) −14.0054 24.2580i −0.760666 1.31751i
\(340\) 11.7373 20.3296i 0.636545 1.10253i
\(341\) −1.75678 −0.0951348
\(342\) 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
\(346\) 9.71182 + 16.8214i 0.522111 + 0.904322i
\(347\) 6.14506 0.329884 0.164942 0.986303i \(-0.447256\pi\)
0.164942 + 0.986303i \(0.447256\pi\)
\(348\) −40.3462 −2.16278
\(349\) 6.51563 + 11.2854i 0.348774 + 0.604094i 0.986032 0.166557i \(-0.0532649\pi\)
−0.637258 + 0.770650i \(0.719932\pi\)
\(350\) 0 0
\(351\) −10.3383 + 11.6578i −0.551820 + 0.622249i
\(352\) 0.772550 1.33810i 0.0411771 0.0713208i
\(353\) 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
\(359\) −9.96610 + 17.2618i −0.525991 + 0.911043i 0.473551 + 0.880767i \(0.342972\pi\)
−0.999542 + 0.0302764i \(0.990361\pi\)
\(360\) 18.2556 0.962155
\(361\) 2.17744 3.77144i 0.114602 0.198497i
\(362\) −3.84014 −0.201833
\(363\) −29.3156 −1.53867
\(364\) 0 0
\(365\) 4.84684 0.253695
\(366\) 14.4997 0.757911
\(367\) 9.85950 17.0772i 0.514662 0.891420i −0.485194 0.874407i \(-0.661251\pi\)
0.999855 0.0170133i \(-0.00541577\pi\)
\(368\) 19.0369 0.992366
\(369\) 8.39096 14.5336i 0.436816 0.756588i
\(370\) −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
\(376\) 8.82478 15.2850i 0.455103 0.788262i
\(377\) −13.9887 2.86308i −0.720452 0.147456i
\(378\) 0 0
\(379\) 5.85068 + 10.1337i 0.300529 + 0.520532i 0.976256 0.216620i \(-0.0695034\pi\)
−0.675727 + 0.737152i \(0.736170\pi\)
\(380\) −13.9188 −0.714021
\(381\) 11.6945 0.599127
\(382\) −13.8055 23.9119i −0.706352 1.22344i
\(383\) −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
\(387\) 29.1645 1.48252
\(388\) 14.2500 24.6817i 0.723435 1.25303i
\(389\) −13.2455 22.9419i −0.671574 1.16320i −0.977458 0.211131i \(-0.932285\pi\)
0.305884 0.952069i \(-0.401048\pi\)
\(390\) 22.7983 + 4.66618i 1.15444 + 0.236281i
\(391\) 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
\(395\) 1.36802 + 2.36949i 0.0688327 + 0.119222i
\(396\) −9.94784 −0.499898
\(397\) −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
\(401\) 21.6119 1.07925 0.539623 0.841907i \(-0.318567\pi\)
0.539623 + 0.841907i \(0.318567\pi\)
\(402\) 23.0400 + 39.9065i 1.14913 + 1.99035i
\(403\) 10.5571 + 2.16075i 0.525888 + 0.107635i
\(404\) −4.88264 + 8.45697i −0.242920 + 0.420750i
\(405\) −0.894473 1.54927i −0.0444467 0.0769839i
\(406\) 0 0
\(407\) 0.516056 0.893835i 0.0255799 0.0443058i
\(408\) 36.1047 62.5351i 1.78745 3.09595i
\(409\) −7.74217 −0.382826 −0.191413 0.981510i \(-0.561307\pi\)
−0.191413 + 0.981510i \(0.561307\pi\)
\(410\) −8.61275 −0.425353
\(411\) −11.5055 + 19.9282i −0.567526 + 0.982984i
\(412\) −20.1093 + 34.8303i −0.990714 + 1.71597i
\(413\) 0 0
\(414\) 45.0783 + 78.0780i 2.21548 + 3.83732i
\(415\) 1.40868 2.43991i 0.0691495 0.119770i
\(416\) −6.28834 + 7.09092i −0.308311 + 0.347661i
\(417\) −0.793683 1.37470i −0.0388668 0.0673193i
\(418\) 5.37179 0.262743
\(419\) −4.05097 7.01649i −0.197903 0.342778i 0.749945 0.661500i \(-0.230080\pi\)
−0.947848 + 0.318722i \(0.896746\pi\)
\(420\) 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
\(423\) 19.8393 0.964618
\(424\) 0.865159 + 1.49850i 0.0420158 + 0.0727735i
\(425\) 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
\(429\) −5.71292 1.16927i −0.275822 0.0564531i
\(430\) −7.48384 12.9624i −0.360903 0.625102i
\(431\) 14.7640 25.5721i 0.711159 1.23176i −0.253263 0.967397i \(-0.581504\pi\)
0.964422 0.264366i \(-0.0851627\pi\)
\(432\) 9.95992 0.479197
\(433\) 11.0455 19.1314i 0.530813 0.919395i −0.468540 0.883442i \(-0.655220\pi\)
0.999353 0.0359531i \(-0.0114467\pi\)
\(434\) 0 0
\(435\) −5.35164 + 9.26931i −0.256591 + 0.444429i
\(436\) −17.0969 29.6127i −0.818792 1.41819i
\(437\) −15.8051 27.3752i −0.756060 1.30953i
\(438\) 32.4213 1.54915
\(439\) 6.35580 0.303346 0.151673 0.988431i \(-0.451534\pi\)
0.151673 + 0.988431i \(0.451534\pi\)
\(440\) 1.17387 + 2.03321i 0.0559622 + 0.0969294i
\(441\) 0 0
\(442\) 36.8718 41.5777i 1.75381 1.97765i
\(443\) 6.78135 11.7456i 0.322192 0.558052i −0.658748 0.752363i \(-0.728914\pi\)
0.980940 + 0.194311i \(0.0622472\pi\)
\(444\) −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 0.482763 + 0.875751i \(0.339633\pi\)
−0.999804 + 0.0197900i \(0.993700\pi\)
\(450\) −22.0214 + 38.1421i −1.03810 + 1.79804i
\(451\) 2.15823 0.101627
\(452\) −18.8473 + 32.6445i −0.886502 + 1.53547i
\(453\) −63.3139 −2.97475
\(454\) −44.3041 −2.07930
\(455\) 0 0
\(456\) −42.8151 −2.00500
\(457\) 15.2146 0.711710 0.355855 0.934541i \(-0.384190\pi\)
0.355855 + 0.934541i \(0.384190\pi\)
\(458\) −23.1049 + 40.0188i −1.07962 + 1.86996i
\(459\) 27.8922 1.30190
\(460\) 15.0213 26.0176i 0.700371 1.21308i
\(461\) −8.10813 + 14.0437i −0.377633 + 0.654080i −0.990717 0.135937i \(-0.956595\pi\)
0.613084 + 0.790018i \(0.289929\pi\)
\(462\) 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
\(467\) 7.00337 12.1302i 0.324078 0.561319i −0.657248 0.753675i \(-0.728279\pi\)
0.981325 + 0.192356i \(0.0616128\pi\)
\(468\) 59.7803 + 12.2353i 2.76334 + 0.565579i
\(469\) 0 0
\(470\) −5.09091 8.81772i −0.234826 0.406731i
\(471\) −62.1172 −2.86221
\(472\) 24.4320 1.12458
\(473\) 1.87534 + 3.24818i 0.0862282 + 0.149352i
\(474\) 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
\(478\) −38.4562 −1.75895
\(479\) −15.0122 + 26.0018i −0.685923 + 1.18805i 0.287223 + 0.957864i \(0.407268\pi\)
−0.973146 + 0.230189i \(0.926065\pi\)
\(480\) 3.55219 + 6.15258i 0.162135 + 0.280826i
\(481\) −4.20055 + 4.73667i −0.191528 + 0.215973i
\(482\) −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
\(486\) −21.4633 37.1756i −0.973597 1.68632i
\(487\) −28.4903 −1.29102 −0.645510 0.763752i \(-0.723355\pi\)
−0.645510 + 0.763752i \(0.723355\pi\)
\(488\) −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 0.984903 + 0.173105i \(0.0553799\pi\)
−0.342539 + 0.939504i \(0.611287\pi\)
\(492\) −37.4070 −1.68644
\(493\) 12.7799 + 22.1354i 0.575578 + 0.996930i
\(494\) −32.2811 6.60703i −1.45239 0.297264i
\(495\) −1.31951 + 2.28546i −0.0593076 + 0.102724i
\(496\) −3.44406 5.96528i −0.154643 0.267849i
\(497\) 0 0
\(498\) 9.42290 16.3209i 0.422250 0.731359i
\(499\) 13.1164 22.7183i 0.587172 1.01701i −0.407429 0.913237i \(-0.633575\pi\)
0.994601 0.103775i \(-0.0330921\pi\)
\(500\) 32.8617 1.46962
\(501\) 6.40465 0.286139
\(502\) −3.87684 + 6.71488i −0.173032 + 0.299700i
\(503\) 4.26588 7.38872i 0.190206 0.329447i −0.755112 0.655595i \(-0.772418\pi\)
0.945318 + 0.326149i \(0.105751\pi\)
\(504\) 0 0
\(505\) 1.29529 + 2.24352i 0.0576398 + 0.0998351i
\(506\) −5.79726 + 10.0412i −0.257720 + 0.446384i
\(507\) 32.8929 + 14.0532i 1.46083 + 0.624125i
\(508\) −7.86876 13.6291i −0.349120 0.604693i
\(509\) 13.0260 0.577366 0.288683 0.957425i \(-0.406783\pi\)
0.288683 + 0.957425i \(0.406783\pi\)
\(510\) −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
\(514\) −64.2200 −2.83262
\(515\) 5.33472 + 9.24000i 0.235076 + 0.407163i
\(516\) −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
\(520\) −4.55350 13.6621i −0.199684 0.599124i
\(521\) 2.23285 + 3.86741i 0.0978230 + 0.169434i 0.910783 0.412885i \(-0.135479\pi\)
−0.812960 + 0.582319i \(0.802145\pi\)
\(522\) −21.6124 + 37.4337i −0.945948 + 1.63843i
\(523\) 2.90811 0.127163 0.0635815 0.997977i \(-0.479748\pi\)
0.0635815 + 0.997977i \(0.479748\pi\)
\(524\) −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
\(528\) 1.86373 + 3.22807i 0.0811084 + 0.140484i
\(529\) 45.2278 1.96643
\(530\) 0.998200 0.0433590
\(531\) 13.7316 + 23.7838i 0.595901 + 1.03213i
\(532\) 0 0
\(533\) −12.9696 2.65451i −0.561775 0.114980i
\(534\) 6.87654 11.9105i 0.297577 0.515418i
\(535\) −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
\(541\) 9.23193 15.9902i 0.396912 0.687471i −0.596431 0.802664i \(-0.703415\pi\)
0.993343 + 0.115193i \(0.0367486\pi\)
\(542\) 23.6448 1.01563
\(543\) −2.21229 + 3.83180i −0.0949384 + 0.164438i
\(544\) 16.9655 0.727392
\(545\) −9.07112 −0.388564
\(546\) 0 0
\(547\) 34.9817 1.49571 0.747856 0.663861i \(-0.231083\pi\)
0.747856 + 0.663861i \(0.231083\pi\)
\(548\) 30.9665 1.32282
\(549\) 5.04310 8.73491i 0.215234 0.372797i
\(550\) −5.66408 −0.241517
\(551\) 7.57760 13.1248i 0.322817 0.559135i
\(552\) 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 \(0.167025\pi\)
\(558\) 16.3107 28.2510i 0.690487 1.19596i
\(559\) −7.27451 21.8261i −0.307679 0.923146i
\(560\) 0 0
\(561\) 5.21927 + 9.04004i 0.220358 + 0.381671i
\(562\) −31.0388 −1.30929
\(563\) −7.98506 −0.336530 −0.168265 0.985742i \(-0.553816\pi\)
−0.168265 + 0.985742i \(0.553816\pi\)
\(564\) −22.1109 38.2972i −0.931037 1.61260i
\(565\) 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
\(569\) −26.7241 −1.12033 −0.560167 0.828380i \(-0.689263\pi\)
−0.560167 + 0.828380i \(0.689263\pi\)
\(570\) −12.3498 + 21.3904i −0.517275 + 0.895946i
\(571\) −6.74647 11.6852i −0.282331 0.489012i 0.689627 0.724164i \(-0.257774\pi\)
−0.971958 + 0.235153i \(0.924441\pi\)
\(572\) 2.48129 + 7.44476i 0.103748 + 0.311281i
\(573\) −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
\(577\) 6.00662 + 10.4038i 0.250059 + 0.433115i 0.963542 0.267558i \(-0.0862167\pi\)
−0.713483 + 0.700673i \(0.752883\pi\)
\(578\) −58.8811 −2.44913
\(579\) −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
\(583\) −0.250134 −0.0103595
\(584\) −10.0318 17.3756i −0.415118 0.719005i
\(585\) 10.7404 12.1112i 0.444062 0.500739i
\(586\) 16.8305 29.1512i 0.695260 1.20422i
\(587\) 5.21177 + 9.02705i 0.215113 + 0.372586i 0.953307 0.302002i \(-0.0976548\pi\)
−0.738195 + 0.674588i \(0.764321\pi\)
\(588\) 0 0
\(589\) −5.71876 + 9.90518i −0.235637 + 0.408136i
\(590\) 7.04728 12.2062i 0.290132 0.502523i
\(591\) −4.04727 −0.166482
\(592\) 4.04679 0.166322
\(593\) −11.1751 + 19.3558i −0.458905 + 0.794847i −0.998903 0.0468194i \(-0.985091\pi\)
0.539998 + 0.841666i \(0.318425\pi\)
\(594\) −3.03307 + 5.25344i −0.124449 + 0.215551i
\(595\) 0 0
\(596\) −5.19607 8.99986i −0.212839 0.368649i
\(597\) 12.9237 22.3845i 0.528931 0.916135i
\(598\) 47.1880 53.2107i 1.92966 2.17595i
\(599\) −0.579463 1.00366i −0.0236762 0.0410084i 0.853945 0.520364i \(-0.174204\pi\)
−0.877621 + 0.479356i \(0.840870\pi\)
\(600\) 45.1448 1.84303
\(601\) 21.0907 + 36.5301i 0.860306 + 1.49009i 0.871633 + 0.490158i \(0.163061\pi\)
−0.0113271 + 0.999936i \(0.503606\pi\)
\(602\) 0 0
\(603\) 32.0540 1.30534
\(604\) 42.6014 + 73.7879i 1.73343 + 3.00239i
\(605\) 10.4657 0.425491
\(606\) 8.66444 + 15.0072i 0.351969 + 0.609628i
\(607\) −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
\(611\) −4.94851 14.8473i −0.200195 0.600657i
\(612\) −54.6147 94.5955i −2.20767 3.82380i
\(613\) 0.451323 0.781714i 0.0182288 0.0315731i −0.856767 0.515703i \(-0.827531\pi\)
0.874996 + 0.484130i \(0.160864\pi\)
\(614\) 37.9187 1.53027
\(615\) −4.96177 + 8.59404i −0.200078 + 0.346545i
\(616\) 0 0
\(617\) 13.0218 22.5544i 0.524238 0.908008i −0.475363 0.879790i \(-0.657683\pi\)
0.999602 0.0282180i \(-0.00898327\pi\)
\(618\) 35.6848 + 61.8079i 1.43545 + 2.48628i
\(619\) 13.4171 + 23.2390i 0.539277 + 0.934056i 0.998943 + 0.0459638i \(0.0146359\pi\)
−0.459666 + 0.888092i \(0.652031\pi\)
\(620\) −10.8703 −0.436562
\(621\) 35.6961 1.43244
\(622\) 34.1530 + 59.1547i 1.36941 + 2.37189i
\(623\) 0 0
\(624\) −7.22948 21.6910i −0.289411 0.868335i
\(625\) −5.72894 + 9.92281i −0.229158 + 0.396912i
\(626\) 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 −0.309135 0.951018i \(-0.600039\pi\)
0.978173 0.207791i \(-0.0666273\pi\)
\(632\) 5.66296 9.80853i 0.225260 0.390162i
\(633\) −24.6042 −0.977930
\(634\) 36.5901 63.3760i 1.45318 2.51698i
\(635\) −4.17494 −0.165678
\(636\) 4.33539 0.171909
\(637\) 0 0
\(638\) −5.55889 −0.220078
\(639\) 16.4659 0.651379
\(640\) 10.1865 17.6435i 0.402655 0.697419i
\(641\) 21.1841 0.836722 0.418361 0.908281i \(-0.362605\pi\)
0.418361 + 0.908281i \(0.362605\pi\)
\(642\) −52.5010 + 90.9343i −2.07205 + 3.58889i
\(643\) 0.330770 0.572910i 0.0130443 0.0225933i −0.859430 0.511254i \(-0.829181\pi\)
0.872474 + 0.488661i \(0.162514\pi\)
\(644\) 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
\(649\) −1.76594 + 3.05870i −0.0693193 + 0.120065i
\(650\) 34.0376 + 6.96654i 1.33506 + 0.273250i
\(651\) 0 0
\(652\) −15.1388 26.2212i −0.592883 1.02690i
\(653\) 12.7120 0.497460 0.248730 0.968573i \(-0.419987\pi\)
0.248730 + 0.968573i \(0.419987\pi\)
\(654\) −60.6782 −2.37271
\(655\) 1.06556 + 1.84560i 0.0416349 + 0.0721138i
\(656\) 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 −0.694094 0.719884i \(-0.744195\pi\)
0.970485 + 0.241161i \(0.0775283\pi\)
\(660\) 5.88239 0.228972
\(661\) 25.0890 43.4554i 0.975848 1.69022i 0.298742 0.954334i \(-0.403433\pi\)
0.677106 0.735885i \(-0.263234\pi\)
\(662\) 32.5104 + 56.3096i 1.26355 + 2.18853i
\(663\) −20.2458 60.7444i −0.786280 2.35912i
\(664\) −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
\(668\) −4.30944 7.46417i −0.166737 0.288797i
\(669\) −60.0362 −2.32113
\(670\) −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 0.883522 0.468389i \(-0.155166\pi\)
−0.847398 + 0.530958i \(0.821832\pi\)
\(674\) 29.4112 1.13288
\(675\) 8.71902 + 15.1018i 0.335595 + 0.581268i
\(676\) −5.75433 47.7902i −0.221321 1.83808i
\(677\) −1.00439 + 1.73966i −0.0386020 + 0.0668607i −0.884681 0.466197i \(-0.845624\pi\)
0.846079 + 0.533058i \(0.178957\pi\)
\(678\) 33.4453 + 57.9290i 1.28446 + 2.22475i
\(679\) 0 0
\(680\) −12.8894 + 22.3251i −0.494286 + 0.856128i
\(681\) −25.5234 + 44.2079i −0.978061 + 1.69405i
\(682\) 4.19525 0.160644
\(683\) −14.1012 −0.539568 −0.269784 0.962921i \(-0.586952\pi\)
−0.269784 + 0.962921i \(0.586952\pi\)
\(684\) −32.3828 + 56.0886i −1.23819 + 2.14460i
\(685\) 4.10748 7.11437i 0.156939 0.271826i
\(686\) 0 0
\(687\) 26.6212 + 46.1094i 1.01566 + 1.75918i
\(688\) −7.35298 + 12.7357i −0.280330 + 0.485546i
\(689\) 1.50315 + 0.307652i 0.0572654 + 0.0117206i
\(690\) −26.6559 46.1693i −1.01477 1.75764i
\(691\) 35.6920 1.35779 0.678895 0.734236i \(-0.262459\pi\)
0.678895 + 0.734236i \(0.262459\pi\)
\(692\) −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
\(696\) 44.3064 1.67943
\(697\) 11.8489 + 20.5229i 0.448809 + 0.777360i
\(698\) −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 \(0.537105\pi\)
\(702\) 24.6883 27.8394i 0.931802 1.05073i
\(703\) −3.35979 5.81932i −0.126717 0.219480i
\(704\) −3.19959 + 5.54185i −0.120589 + 0.208866i
\(705\) −11.7314 −0.441831
\(706\) −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 \(-0.387378\pi\)
\(710\) −4.22527 7.31838i −0.158571 0.274654i
\(711\) 12.7311 0.477452
\(712\) −8.51094 −0.318961
\(713\) −12.3434 21.3794i −0.462265 0.800667i
\(714\) 0 0
\(715\) 2.03952 + 0.417432i 0.0762736 + 0.0156111i
\(716\) 38.8648 67.3158i 1.45244 2.51571i
\(717\) −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
\(723\) −5.51122 + 9.54571i −0.204964 + 0.355009i
\(724\) 5.95424 0.221288
\(725\) −7.98992 + 13.8389i −0.296738 + 0.513966i
\(726\) 70.0067 2.59819
\(727\) −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
\(730\) −11.5744 −0.428389
\(731\) −20.5916 + 35.6658i −0.761609 + 1.31915i
\(732\) −22.4822 −0.830966
\(733\) −13.1689 + 22.8092i −0.486404 + 0.842476i −0.999878 0.0156289i \(-0.995025\pi\)
0.513474 + 0.858105i \(0.328358\pi\)
\(734\) −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 \(0.950005\pi\)
\(740\) 3.19317 5.53073i 0.117383 0.203314i
\(741\) −25.1897 + 28.4047i −0.925366 + 1.04347i
\(742\) 0 0
\(743\) −11.2391 19.4667i −0.412322 0.714163i 0.582821 0.812600i \(-0.301949\pi\)
−0.995143 + 0.0984379i \(0.968615\pi\)
\(744\) −33.4377 −1.22588
\(745\) −2.75689 −0.101005
\(746\) 20.9513 + 36.2888i 0.767083 + 1.32863i
\(747\) −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
\(751\) −42.5424 −1.55239 −0.776197 0.630491i \(-0.782854\pi\)
−0.776197 + 0.630491i \(0.782854\pi\)
\(752\) −5.00189 + 8.66353i −0.182400 + 0.315927i
\(753\) 4.46686 + 7.73683i 0.162781 + 0.281946i
\(754\) 33.4054 + 6.83715i 1.21655 + 0.248994i
\(755\) 22.6031 0.822612
\(756\) 0 0
\(757\) 5.61902 + 9.73243i 0.204227 + 0.353731i 0.949886 0.312596i \(-0.101199\pi\)
−0.745659 + 0.666327i \(0.767865\pi\)
\(758\) −13.9716 24.1996i −0.507473 0.878969i
\(759\) 6.67956 + 11.5693i 0.242453 + 0.419941i
\(760\) 15.2850 0.554447
\(761\) 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
\(765\) −28.9770 −1.04767
\(766\) 25.7058 + 44.5238i 0.928789 + 1.60871i
\(767\) 14.3743 16.2089i 0.519024 0.585268i
\(768\) 38.1846 66.1377i 1.37787 2.38654i
\(769\) −25.6759 44.4719i −0.925895 1.60370i −0.790115 0.612958i \(-0.789979\pi\)
−0.135780 0.990739i \(-0.543354\pi\)
\(770\) 0 0
\(771\) −36.9969 + 64.0805i −1.33241 + 2.30780i
\(772\) −43.6529 + 75.6091i −1.57110 + 2.72123i
\(773\) −20.0046 −0.719517 −0.359759 0.933045i \(-0.617141\pi\)
−0.359759 + 0.933045i \(0.617141\pi\)
\(774\) −69.6459 −2.50337
\(775\) 6.02993 10.4441i 0.216602 0.375165i
\(776\) −15.6487 + 27.1044i −0.561756 + 0.972990i
\(777\) 0 0
\(778\) 31.6308 + 54.7861i 1.13402 + 1.96418i
\(779\) 7.02558 12.1687i 0.251717 0.435987i
\(780\) −35.3495 7.23504i −1.26571 0.259056i
\(781\) 1.05879 + 1.83388i 0.0378864 + 0.0656212i
\(782\) −127.310 −4.55261
\(783\) 8.55708 + 14.8213i 0.305805 + 0.529670i