Properties

Label 637.2.e.n.508.3
Level $637$
Weight $2$
Character 637.508
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.e (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: \(x^{12} - 2 x^{11} + 9 x^{10} - 6 x^{9} + 34 x^{8} - 18 x^{7} + 85 x^{6} - 2 x^{5} + 92 x^{4} - 26 x^{3} + 43 x^{2} + 6 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 508.3
Root \(0.954516 + 1.65327i\) of defining polynomial
Character \(\chi\) \(=\) 637.508
Dual form 637.2.e.n.79.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.132313 - 0.229173i) q^{2} +(-1.45452 + 2.51930i) q^{3} +(0.964986 - 1.67141i) q^{4} +(0.717577 + 1.24288i) q^{5} +0.769807 q^{6} -1.03998 q^{8} +(-2.73124 - 4.73064i) q^{9} +O(q^{10})\) \(q+(-0.132313 - 0.229173i) q^{2} +(-1.45452 + 2.51930i) q^{3} +(0.964986 - 1.67141i) q^{4} +(0.717577 + 1.24288i) q^{5} +0.769807 q^{6} -1.03998 q^{8} +(-2.73124 - 4.73064i) q^{9} +(0.189890 - 0.328899i) q^{10} +(-2.75237 + 4.76725i) q^{11} +(2.80718 + 4.86217i) q^{12} +1.00000 q^{13} -4.17491 q^{15} +(-1.79237 - 3.10448i) q^{16} +(-2.41536 + 4.18353i) q^{17} +(-0.722758 + 1.25185i) q^{18} +(-1.41018 - 2.44250i) q^{19} +2.76981 q^{20} +1.45670 q^{22} +(2.99978 + 5.19577i) q^{23} +(1.51266 - 2.62001i) q^{24} +(1.47017 - 2.54640i) q^{25} +(-0.132313 - 0.229173i) q^{26} +7.16341 q^{27} +1.04188 q^{29} +(0.552396 + 0.956778i) q^{30} +(-4.60448 + 7.97519i) q^{31} +(-1.51428 + 2.62282i) q^{32} +(-8.00674 - 13.8681i) q^{33} +1.27834 q^{34} -10.5424 q^{36} +(-0.306249 - 0.530438i) q^{37} +(-0.373171 + 0.646351i) q^{38} +(-1.45452 + 2.51930i) q^{39} +(-0.746262 - 1.29256i) q^{40} -10.6196 q^{41} -8.43685 q^{43} +(5.31200 + 9.20066i) q^{44} +(3.91974 - 6.78919i) q^{45} +(0.793822 - 1.37494i) q^{46} +(-1.20461 - 2.08645i) q^{47} +10.4281 q^{48} -0.778091 q^{50} +(-7.02636 - 12.1700i) q^{51} +(0.964986 - 1.67141i) q^{52} +(0.914793 - 1.58447i) q^{53} +(-0.947814 - 1.64166i) q^{54} -7.90015 q^{55} +8.20452 q^{57} +(-0.137855 - 0.238771i) q^{58} +(0.435457 - 0.754234i) q^{59} +(-4.02873 + 6.97797i) q^{60} +(1.66626 + 2.88605i) q^{61} +2.43693 q^{62} -6.36804 q^{64} +(0.717577 + 1.24288i) q^{65} +(-2.11880 + 3.66986i) q^{66} +(3.31370 - 5.73951i) q^{67} +(4.66158 + 8.07410i) q^{68} -17.4529 q^{69} -6.85856 q^{71} +(2.84042 + 4.91975i) q^{72} +(-1.57074 + 2.72060i) q^{73} +(-0.0810415 + 0.140368i) q^{74} +(4.27676 + 7.40757i) q^{75} -5.44322 q^{76} +0.769807 q^{78} +(8.78614 + 15.2180i) q^{79} +(2.57233 - 4.45540i) q^{80} +(-2.22559 + 3.85484i) q^{81} +(1.40511 + 2.43372i) q^{82} +11.4525 q^{83} -6.93283 q^{85} +(1.11631 + 1.93350i) q^{86} +(-1.51543 + 2.62480i) q^{87} +(2.86240 - 4.95782i) q^{88} +(0.497659 + 0.861970i) q^{89} -2.07454 q^{90} +11.5790 q^{92} +(-13.3946 - 23.2001i) q^{93} +(-0.318772 + 0.552130i) q^{94} +(2.02383 - 3.50537i) q^{95} +(-4.40510 - 7.62986i) q^{96} +13.5090 q^{97} +30.0695 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 8q^{3} - 4q^{4} - 6q^{5} + 8q^{6} - 6q^{9} + O(q^{10}) \) \( 12q - 8q^{3} - 4q^{4} - 6q^{5} + 8q^{6} - 6q^{9} - 4q^{10} - 4q^{11} + 4q^{12} + 12q^{13} + 24q^{15} - 16q^{17} + 4q^{18} - 2q^{19} + 32q^{20} - 24q^{22} + 6q^{23} - 12q^{24} + 4q^{25} + 40q^{27} - 12q^{29} - 6q^{31} + 20q^{32} - 4q^{33} - 48q^{36} - 8q^{38} - 8q^{39} - 4q^{40} - 16q^{41} + 4q^{43} + 4q^{44} - 14q^{45} - 8q^{46} - 30q^{47} - 16q^{48} + 16q^{50} + 4q^{51} - 4q^{52} + 14q^{53} + 48q^{54} - 16q^{55} + 8q^{57} + 8q^{58} - 24q^{59} - 12q^{60} + 56q^{62} - 40q^{64} - 6q^{65} + 4q^{66} - 16q^{67} - 28q^{68} - 40q^{69} + 16q^{71} - 28q^{72} + 6q^{73} + 12q^{74} - 12q^{75} - 32q^{76} + 8q^{78} + 22q^{79} + 28q^{80} - 46q^{81} + 40q^{82} + 100q^{83} - 16q^{85} + 16q^{86} + 16q^{87} + 44q^{88} - 26q^{89} - 80q^{90} + 40q^{92} - 16q^{93} + 32q^{94} + 6q^{95} + 20q^{96} - 28q^{97} + 24q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.132313 0.229173i −0.0935596 0.162050i 0.815447 0.578832i \(-0.196491\pi\)
−0.909007 + 0.416782i \(0.863158\pi\)
\(3\) −1.45452 + 2.51930i −0.839765 + 1.45452i 0.0503252 + 0.998733i \(0.483974\pi\)
−0.890091 + 0.455784i \(0.849359\pi\)
\(4\) 0.964986 1.67141i 0.482493 0.835703i
\(5\) 0.717577 + 1.24288i 0.320910 + 0.555833i 0.980676 0.195639i \(-0.0626779\pi\)
−0.659766 + 0.751471i \(0.729345\pi\)
\(6\) 0.769807 0.314273
\(7\) 0 0
\(8\) −1.03998 −0.367687
\(9\) −2.73124 4.73064i −0.910412 1.57688i
\(10\) 0.189890 0.328899i 0.0600484 0.104007i
\(11\) −2.75237 + 4.76725i −0.829871 + 1.43738i 0.0682678 + 0.997667i \(0.478253\pi\)
−0.898139 + 0.439712i \(0.855081\pi\)
\(12\) 2.80718 + 4.86217i 0.810362 + 1.40359i
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) −4.17491 −1.07796
\(16\) −1.79237 3.10448i −0.448093 0.776119i
\(17\) −2.41536 + 4.18353i −0.585811 + 1.01465i 0.408963 + 0.912551i \(0.365891\pi\)
−0.994774 + 0.102104i \(0.967443\pi\)
\(18\) −0.722758 + 1.25185i −0.170356 + 0.295065i
\(19\) −1.41018 2.44250i −0.323518 0.560349i 0.657694 0.753286i \(-0.271532\pi\)
−0.981211 + 0.192937i \(0.938199\pi\)
\(20\) 2.76981 0.619348
\(21\) 0 0
\(22\) 1.45670 0.310570
\(23\) 2.99978 + 5.19577i 0.625498 + 1.08339i 0.988444 + 0.151584i \(0.0484373\pi\)
−0.362947 + 0.931810i \(0.618229\pi\)
\(24\) 1.51266 2.62001i 0.308771 0.534806i
\(25\) 1.47017 2.54640i 0.294033 0.509281i
\(26\) −0.132313 0.229173i −0.0259488 0.0449446i
\(27\) 7.16341 1.37860
\(28\) 0 0
\(29\) 1.04188 0.193472 0.0967361 0.995310i \(-0.469160\pi\)
0.0967361 + 0.995310i \(0.469160\pi\)
\(30\) 0.552396 + 0.956778i 0.100853 + 0.174683i
\(31\) −4.60448 + 7.97519i −0.826988 + 1.43239i 0.0734019 + 0.997302i \(0.476614\pi\)
−0.900390 + 0.435083i \(0.856719\pi\)
\(32\) −1.51428 + 2.62282i −0.267690 + 0.463653i
\(33\) −8.00674 13.8681i −1.39379 2.41412i
\(34\) 1.27834 0.219233
\(35\) 0 0
\(36\) −10.5424 −1.75707
\(37\) −0.306249 0.530438i −0.0503470 0.0872035i 0.839754 0.542968i \(-0.182699\pi\)
−0.890101 + 0.455764i \(0.849366\pi\)
\(38\) −0.373171 + 0.646351i −0.0605364 + 0.104852i
\(39\) −1.45452 + 2.51930i −0.232909 + 0.403410i
\(40\) −0.746262 1.29256i −0.117994 0.204372i
\(41\) −10.6196 −1.65850 −0.829249 0.558879i \(-0.811232\pi\)
−0.829249 + 0.558879i \(0.811232\pi\)
\(42\) 0 0
\(43\) −8.43685 −1.28661 −0.643304 0.765611i \(-0.722437\pi\)
−0.643304 + 0.765611i \(0.722437\pi\)
\(44\) 5.31200 + 9.20066i 0.800814 + 1.38705i
\(45\) 3.91974 6.78919i 0.584321 1.01207i
\(46\) 0.793822 1.37494i 0.117043 0.202724i
\(47\) −1.20461 2.08645i −0.175711 0.304340i 0.764696 0.644391i \(-0.222889\pi\)
−0.940407 + 0.340051i \(0.889556\pi\)
\(48\) 10.4281 1.50517
\(49\) 0 0
\(50\) −0.778091 −0.110039
\(51\) −7.02636 12.1700i −0.983888 1.70414i
\(52\) 0.964986 1.67141i 0.133820 0.231782i
\(53\) 0.914793 1.58447i 0.125657 0.217643i −0.796333 0.604859i \(-0.793230\pi\)
0.921989 + 0.387215i \(0.126563\pi\)
\(54\) −0.947814 1.64166i −0.128981 0.223402i
\(55\) −7.90015 −1.06526
\(56\) 0 0
\(57\) 8.20452 1.08672
\(58\) −0.137855 0.238771i −0.0181012 0.0313522i
\(59\) 0.435457 0.754234i 0.0566917 0.0981929i −0.836287 0.548292i \(-0.815278\pi\)
0.892978 + 0.450099i \(0.148611\pi\)
\(60\) −4.02873 + 6.97797i −0.520107 + 0.900851i
\(61\) 1.66626 + 2.88605i 0.213343 + 0.369521i 0.952759 0.303728i \(-0.0982314\pi\)
−0.739416 + 0.673249i \(0.764898\pi\)
\(62\) 2.43693 0.309491
\(63\) 0 0
\(64\) −6.36804 −0.796005
\(65\) 0.717577 + 1.24288i 0.0890044 + 0.154160i
\(66\) −2.11880 + 3.66986i −0.260806 + 0.451729i
\(67\) 3.31370 5.73951i 0.404833 0.701192i −0.589469 0.807791i \(-0.700663\pi\)
0.994302 + 0.106599i \(0.0339962\pi\)
\(68\) 4.66158 + 8.07410i 0.565300 + 0.979128i
\(69\) −17.4529 −2.10108
\(70\) 0 0
\(71\) −6.85856 −0.813961 −0.406980 0.913437i \(-0.633418\pi\)
−0.406980 + 0.913437i \(0.633418\pi\)
\(72\) 2.84042 + 4.91975i 0.334746 + 0.579798i
\(73\) −1.57074 + 2.72060i −0.183841 + 0.318422i −0.943185 0.332267i \(-0.892186\pi\)
0.759345 + 0.650689i \(0.225520\pi\)
\(74\) −0.0810415 + 0.140368i −0.00942089 + 0.0163175i
\(75\) 4.27676 + 7.40757i 0.493838 + 0.855353i
\(76\) −5.44322 −0.624380
\(77\) 0 0
\(78\) 0.769807 0.0871635
\(79\) 8.78614 + 15.2180i 0.988518 + 1.71216i 0.625116 + 0.780532i \(0.285052\pi\)
0.363402 + 0.931632i \(0.381615\pi\)
\(80\) 2.57233 4.45540i 0.287595 0.498129i
\(81\) −2.22559 + 3.85484i −0.247288 + 0.428315i
\(82\) 1.40511 + 2.43372i 0.155168 + 0.268760i
\(83\) 11.4525 1.25708 0.628538 0.777779i \(-0.283654\pi\)
0.628538 + 0.777779i \(0.283654\pi\)
\(84\) 0 0
\(85\) −6.93283 −0.751971
\(86\) 1.11631 + 1.93350i 0.120374 + 0.208495i
\(87\) −1.51543 + 2.62480i −0.162471 + 0.281409i
\(88\) 2.86240 4.95782i 0.305133 0.528505i
\(89\) 0.497659 + 0.861970i 0.0527517 + 0.0913687i 0.891195 0.453619i \(-0.149867\pi\)
−0.838444 + 0.544988i \(0.816534\pi\)
\(90\) −2.07454 −0.218675
\(91\) 0 0
\(92\) 11.5790 1.20719
\(93\) −13.3946 23.2001i −1.38895 2.40574i
\(94\) −0.318772 + 0.552130i −0.0328789 + 0.0569479i
\(95\) 2.02383 3.50537i 0.207640 0.359643i
\(96\) −4.40510 7.62986i −0.449594 0.778719i
\(97\) 13.5090 1.37163 0.685817 0.727774i \(-0.259445\pi\)
0.685817 + 0.727774i \(0.259445\pi\)
\(98\) 0 0
\(99\) 30.0695 3.02210
\(100\) −2.83738 4.91449i −0.283738 0.491449i
\(101\) 0.504033 0.873011i 0.0501532 0.0868678i −0.839859 0.542805i \(-0.817362\pi\)
0.890012 + 0.455937i \(0.150696\pi\)
\(102\) −1.85936 + 3.22051i −0.184104 + 0.318878i
\(103\) 6.38772 + 11.0639i 0.629401 + 1.09015i 0.987672 + 0.156537i \(0.0500331\pi\)
−0.358271 + 0.933618i \(0.616634\pi\)
\(104\) −1.03998 −0.101978
\(105\) 0 0
\(106\) −0.484157 −0.0470255
\(107\) 0.342748 + 0.593656i 0.0331347 + 0.0573909i 0.882117 0.471030i \(-0.156118\pi\)
−0.848983 + 0.528421i \(0.822784\pi\)
\(108\) 6.91259 11.9730i 0.665165 1.15210i
\(109\) 1.45172 2.51446i 0.139050 0.240841i −0.788087 0.615563i \(-0.788929\pi\)
0.927137 + 0.374722i \(0.122262\pi\)
\(110\) 1.04529 + 1.81050i 0.0996649 + 0.172625i
\(111\) 1.78177 0.169119
\(112\) 0 0
\(113\) 12.0315 1.13183 0.565915 0.824464i \(-0.308523\pi\)
0.565915 + 0.824464i \(0.308523\pi\)
\(114\) −1.08557 1.88026i −0.101673 0.176102i
\(115\) −4.30515 + 7.45673i −0.401457 + 0.695344i
\(116\) 1.00540 1.74140i 0.0933490 0.161685i
\(117\) −2.73124 4.73064i −0.252503 0.437348i
\(118\) −0.230467 −0.0212162
\(119\) 0 0
\(120\) 4.34180 0.396350
\(121\) −9.65109 16.7162i −0.877372 1.51965i
\(122\) 0.440938 0.763726i 0.0399206 0.0691445i
\(123\) 15.4463 26.7539i 1.39275 2.41231i
\(124\) 8.88651 + 15.3919i 0.798032 + 1.38223i
\(125\) 11.3956 1.01925
\(126\) 0 0
\(127\) 15.6659 1.39012 0.695062 0.718950i \(-0.255377\pi\)
0.695062 + 0.718950i \(0.255377\pi\)
\(128\) 3.87114 + 6.70502i 0.342164 + 0.592645i
\(129\) 12.2715 21.2549i 1.08045 1.87139i
\(130\) 0.189890 0.328899i 0.0166544 0.0288463i
\(131\) −6.06366 10.5026i −0.529784 0.917613i −0.999396 0.0347403i \(-0.988940\pi\)
0.469612 0.882873i \(-0.344394\pi\)
\(132\) −30.9056 −2.68998
\(133\) 0 0
\(134\) −1.75379 −0.151504
\(135\) 5.14030 + 8.90326i 0.442406 + 0.766270i
\(136\) 2.51192 4.35077i 0.215395 0.373075i
\(137\) −7.96873 + 13.8022i −0.680815 + 1.17921i 0.293918 + 0.955831i \(0.405041\pi\)
−0.974733 + 0.223375i \(0.928293\pi\)
\(138\) 2.30925 + 3.99974i 0.196577 + 0.340481i
\(139\) −6.64088 −0.563272 −0.281636 0.959521i \(-0.590877\pi\)
−0.281636 + 0.959521i \(0.590877\pi\)
\(140\) 0 0
\(141\) 7.00851 0.590223
\(142\) 0.907478 + 1.57180i 0.0761539 + 0.131902i
\(143\) −2.75237 + 4.76725i −0.230165 + 0.398657i
\(144\) −9.79077 + 16.9581i −0.815898 + 1.41318i
\(145\) 0.747629 + 1.29493i 0.0620872 + 0.107538i
\(146\) 0.831317 0.0688003
\(147\) 0 0
\(148\) −1.18210 −0.0971683
\(149\) 9.77512 + 16.9310i 0.800809 + 1.38704i 0.919084 + 0.394061i \(0.128930\pi\)
−0.118275 + 0.992981i \(0.537736\pi\)
\(150\) 1.13175 1.96024i 0.0924066 0.160053i
\(151\) −5.34401 + 9.25610i −0.434890 + 0.753251i −0.997287 0.0736163i \(-0.976546\pi\)
0.562397 + 0.826867i \(0.309879\pi\)
\(152\) 1.46655 + 2.54014i 0.118953 + 0.206033i
\(153\) 26.3877 2.13332
\(154\) 0 0
\(155\) −13.2163 −1.06156
\(156\) 2.80718 + 4.86217i 0.224754 + 0.389285i
\(157\) 7.53672 13.0540i 0.601496 1.04182i −0.391099 0.920349i \(-0.627905\pi\)
0.992595 0.121473i \(-0.0387617\pi\)
\(158\) 2.32505 4.02710i 0.184971 0.320379i
\(159\) 2.66116 + 4.60927i 0.211044 + 0.365539i
\(160\) −4.34646 −0.343618
\(161\) 0 0
\(162\) 1.17790 0.0925447
\(163\) 11.9067 + 20.6231i 0.932607 + 1.61532i 0.778847 + 0.627214i \(0.215805\pi\)
0.153760 + 0.988108i \(0.450862\pi\)
\(164\) −10.2477 + 17.7496i −0.800214 + 1.38601i
\(165\) 11.4909 19.9028i 0.894565 1.54943i
\(166\) −1.51532 2.62461i −0.117611 0.203709i
\(167\) −7.12371 −0.551249 −0.275625 0.961265i \(-0.588885\pi\)
−0.275625 + 0.961265i \(0.588885\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0.917305 + 1.58882i 0.0703541 + 0.121857i
\(171\) −7.70307 + 13.3421i −0.589069 + 1.02030i
\(172\) −8.14145 + 14.1014i −0.620779 + 1.07522i
\(173\) −5.61834 9.73125i −0.427155 0.739854i 0.569464 0.822016i \(-0.307151\pi\)
−0.996619 + 0.0821625i \(0.973817\pi\)
\(174\) 0.802047 0.0608030
\(175\) 0 0
\(176\) 19.7331 1.48744
\(177\) 1.26676 + 2.19409i 0.0952155 + 0.164918i
\(178\) 0.131694 0.228100i 0.00987086 0.0170968i
\(179\) 6.59725 11.4268i 0.493102 0.854078i −0.506867 0.862025i \(-0.669196\pi\)
0.999968 + 0.00794701i \(0.00252964\pi\)
\(180\) −7.56500 13.1030i −0.563862 0.976637i
\(181\) −13.7414 −1.02139 −0.510696 0.859761i \(-0.670612\pi\)
−0.510696 + 0.859761i \(0.670612\pi\)
\(182\) 0 0
\(183\) −9.69443 −0.716633
\(184\) −3.11970 5.40347i −0.229987 0.398349i
\(185\) 0.439514 0.761260i 0.0323137 0.0559690i
\(186\) −3.54456 + 6.13936i −0.259900 + 0.450159i
\(187\) −13.2959 23.0292i −0.972295 1.68407i
\(188\) −4.64974 −0.339117
\(189\) 0 0
\(190\) −1.07112 −0.0777069
\(191\) 8.16536 + 14.1428i 0.590824 + 1.02334i 0.994122 + 0.108269i \(0.0345308\pi\)
−0.403297 + 0.915069i \(0.632136\pi\)
\(192\) 9.26242 16.0430i 0.668458 1.15780i
\(193\) 7.02666 12.1705i 0.505790 0.876054i −0.494187 0.869355i \(-0.664534\pi\)
0.999978 0.00669897i \(-0.00213237\pi\)
\(194\) −1.78742 3.09591i −0.128330 0.222273i
\(195\) −4.17491 −0.298971
\(196\) 0 0
\(197\) −1.46898 −0.104660 −0.0523302 0.998630i \(-0.516665\pi\)
−0.0523302 + 0.998630i \(0.516665\pi\)
\(198\) −3.97859 6.89113i −0.282746 0.489731i
\(199\) 6.68860 11.5850i 0.474142 0.821239i −0.525419 0.850844i \(-0.676091\pi\)
0.999562 + 0.0296046i \(0.00942482\pi\)
\(200\) −1.52894 + 2.64820i −0.108112 + 0.187256i
\(201\) 9.63968 + 16.6964i 0.679930 + 1.17767i
\(202\) −0.266761 −0.0187692
\(203\) 0 0
\(204\) −27.1214 −1.89888
\(205\) −7.62036 13.1988i −0.532229 0.921848i
\(206\) 1.69036 2.92779i 0.117773 0.203989i
\(207\) 16.3862 28.3818i 1.13892 1.97267i
\(208\) −1.79237 3.10448i −0.124279 0.215257i
\(209\) 15.5254 1.07391
\(210\) 0 0
\(211\) 3.47044 0.238915 0.119457 0.992839i \(-0.461885\pi\)
0.119457 + 0.992839i \(0.461885\pi\)
\(212\) −1.76553 3.05798i −0.121257 0.210023i
\(213\) 9.97588 17.2787i 0.683536 1.18392i
\(214\) 0.0907001 0.157097i 0.00620013 0.0107389i
\(215\) −6.05409 10.4860i −0.412885 0.715138i
\(216\) −7.44977 −0.506893
\(217\) 0 0
\(218\) −0.768328 −0.0520378
\(219\) −4.56932 7.91430i −0.308766 0.534799i
\(220\) −7.62354 + 13.2044i −0.513979 + 0.890237i
\(221\) −2.41536 + 4.18353i −0.162475 + 0.281415i
\(222\) −0.235752 0.408335i −0.0158227 0.0274057i
\(223\) −9.91318 −0.663836 −0.331918 0.943308i \(-0.607696\pi\)
−0.331918 + 0.943308i \(0.607696\pi\)
\(224\) 0 0
\(225\) −16.0615 −1.07077
\(226\) −1.59193 2.75730i −0.105894 0.183413i
\(227\) −6.03634 + 10.4552i −0.400646 + 0.693939i −0.993804 0.111147i \(-0.964548\pi\)
0.593158 + 0.805086i \(0.297881\pi\)
\(228\) 7.91725 13.7131i 0.524333 0.908171i
\(229\) −2.02586 3.50888i −0.133872 0.231874i 0.791294 0.611436i \(-0.209408\pi\)
−0.925166 + 0.379563i \(0.876075\pi\)
\(230\) 2.27851 0.150241
\(231\) 0 0
\(232\) −1.08353 −0.0711372
\(233\) −6.27250 10.8643i −0.410925 0.711743i 0.584066 0.811706i \(-0.301461\pi\)
−0.994991 + 0.0999629i \(0.968128\pi\)
\(234\) −0.722758 + 1.25185i −0.0472481 + 0.0818362i
\(235\) 1.72880 2.99438i 0.112775 0.195332i
\(236\) −0.840421 1.45565i −0.0547067 0.0947548i
\(237\) −51.1184 −3.32049
\(238\) 0 0
\(239\) 13.3463 0.863299 0.431649 0.902042i \(-0.357932\pi\)
0.431649 + 0.902042i \(0.357932\pi\)
\(240\) 7.48298 + 12.9609i 0.483024 + 0.836623i
\(241\) −10.1927 + 17.6542i −0.656568 + 1.13721i 0.324930 + 0.945738i \(0.394659\pi\)
−0.981498 + 0.191471i \(0.938674\pi\)
\(242\) −2.55394 + 4.42355i −0.164173 + 0.284356i
\(243\) 4.27080 + 7.39724i 0.273972 + 0.474533i
\(244\) 6.43169 0.411747
\(245\) 0 0
\(246\) −8.17502 −0.521221
\(247\) −1.41018 2.44250i −0.0897276 0.155413i
\(248\) 4.78854 8.29400i 0.304073 0.526669i
\(249\) −16.6579 + 28.8522i −1.05565 + 1.82844i
\(250\) −1.50779 2.61157i −0.0953609 0.165170i
\(251\) 17.1921 1.08515 0.542577 0.840006i \(-0.317449\pi\)
0.542577 + 0.840006i \(0.317449\pi\)
\(252\) 0 0
\(253\) −33.0260 −2.07633
\(254\) −2.07281 3.59021i −0.130059 0.225270i
\(255\) 10.0839 17.4658i 0.631479 1.09375i
\(256\) −5.34363 + 9.25545i −0.333977 + 0.578465i
\(257\) 3.82348 + 6.62245i 0.238502 + 0.413097i 0.960285 0.279022i \(-0.0900104\pi\)
−0.721783 + 0.692120i \(0.756677\pi\)
\(258\) −6.49475 −0.404345
\(259\) 0 0
\(260\) 2.76981 0.171776
\(261\) −2.84562 4.92876i −0.176139 0.305082i
\(262\) −1.60460 + 2.77926i −0.0991328 + 0.171703i
\(263\) 0.0505186 0.0875008i 0.00311511 0.00539553i −0.864464 0.502695i \(-0.832342\pi\)
0.867579 + 0.497300i \(0.165675\pi\)
\(264\) 8.32681 + 14.4225i 0.512480 + 0.887641i
\(265\) 2.62574 0.161298
\(266\) 0 0
\(267\) −2.89541 −0.177196
\(268\) −6.39536 11.0771i −0.390659 0.676641i
\(269\) 3.78426 6.55453i 0.230730 0.399637i −0.727293 0.686327i \(-0.759222\pi\)
0.958023 + 0.286691i \(0.0925552\pi\)
\(270\) 1.36026 2.35604i 0.0827827 0.143384i
\(271\) 6.92768 + 11.9991i 0.420826 + 0.728893i 0.996021 0.0891242i \(-0.0284068\pi\)
−0.575194 + 0.818017i \(0.695073\pi\)
\(272\) 17.3169 1.04999
\(273\) 0 0
\(274\) 4.21748 0.254787
\(275\) 8.09289 + 14.0173i 0.488020 + 0.845275i
\(276\) −16.8418 + 29.1709i −1.01376 + 1.75588i
\(277\) −0.276468 + 0.478856i −0.0166113 + 0.0287717i −0.874212 0.485545i \(-0.838621\pi\)
0.857600 + 0.514317i \(0.171954\pi\)
\(278\) 0.878677 + 1.52191i 0.0526995 + 0.0912783i
\(279\) 50.3036 3.01160
\(280\) 0 0
\(281\) 1.14667 0.0684043 0.0342022 0.999415i \(-0.489111\pi\)
0.0342022 + 0.999415i \(0.489111\pi\)
\(282\) −0.927319 1.60616i −0.0552211 0.0956457i
\(283\) 2.02698 3.51083i 0.120491 0.208697i −0.799470 0.600706i \(-0.794886\pi\)
0.919962 + 0.392009i \(0.128220\pi\)
\(284\) −6.61841 + 11.4634i −0.392731 + 0.680229i
\(285\) 5.88737 + 10.1972i 0.348738 + 0.604032i
\(286\) 1.45670 0.0861365
\(287\) 0 0
\(288\) 16.5435 0.974833
\(289\) −3.16794 5.48703i −0.186349 0.322767i
\(290\) 0.197842 0.342673i 0.0116177 0.0201225i
\(291\) −19.6491 + 34.0332i −1.15185 + 1.99506i
\(292\) 3.03148 + 5.25067i 0.177404 + 0.307272i
\(293\) 15.0649 0.880102 0.440051 0.897973i \(-0.354960\pi\)
0.440051 + 0.897973i \(0.354960\pi\)
\(294\) 0 0
\(295\) 1.24990 0.0727718
\(296\) 0.318491 + 0.551643i 0.0185119 + 0.0320636i
\(297\) −19.7164 + 34.1497i −1.14406 + 1.98157i
\(298\) 2.58676 4.48039i 0.149847 0.259542i
\(299\) 2.99978 + 5.19577i 0.173482 + 0.300479i
\(300\) 16.5081 0.953094
\(301\) 0 0
\(302\) 2.82834 0.162752
\(303\) 1.46625 + 2.53962i 0.0842338 + 0.145897i
\(304\) −5.05513 + 8.75574i −0.289932 + 0.502176i
\(305\) −2.39134 + 4.14193i −0.136928 + 0.237166i
\(306\) −3.49144 6.04735i −0.199592 0.345704i
\(307\) −19.9408 −1.13808 −0.569040 0.822310i \(-0.692685\pi\)
−0.569040 + 0.822310i \(0.692685\pi\)
\(308\) 0 0
\(309\) −37.1642 −2.11420
\(310\) 1.74869 + 3.02881i 0.0993187 + 0.172025i
\(311\) 5.44780 9.43587i 0.308916 0.535059i −0.669209 0.743074i \(-0.733367\pi\)
0.978126 + 0.208015i \(0.0667003\pi\)
\(312\) 1.51266 2.62001i 0.0856376 0.148329i
\(313\) 0.0259595 + 0.0449632i 0.00146732 + 0.00254147i 0.866758 0.498729i \(-0.166200\pi\)
−0.865291 + 0.501270i \(0.832866\pi\)
\(314\) −3.98883 −0.225103
\(315\) 0 0
\(316\) 33.9140 1.90781
\(317\) −8.05049 13.9439i −0.452161 0.783165i 0.546359 0.837551i \(-0.316013\pi\)
−0.998520 + 0.0543857i \(0.982680\pi\)
\(318\) 0.704215 1.21974i 0.0394904 0.0683994i
\(319\) −2.86764 + 4.96690i −0.160557 + 0.278093i
\(320\) −4.56956 7.91471i −0.255446 0.442446i
\(321\) −1.99413 −0.111301
\(322\) 0 0
\(323\) 13.6244 0.758081
\(324\) 4.29533 + 7.43973i 0.238630 + 0.413318i
\(325\) 1.47017 2.54640i 0.0815502 0.141249i
\(326\) 3.15084 5.45741i 0.174509 0.302258i
\(327\) 4.22311 + 7.31463i 0.233538 + 0.404500i
\(328\) 11.0441 0.609808
\(329\) 0 0
\(330\) −6.08159 −0.334781
\(331\) −15.3931 26.6616i −0.846081 1.46546i −0.884679 0.466201i \(-0.845622\pi\)
0.0385973 0.999255i \(-0.487711\pi\)
\(332\) 11.0515 19.1418i 0.606530 1.05054i
\(333\) −1.67287 + 2.89750i −0.0916730 + 0.158782i
\(334\) 0.942561 + 1.63256i 0.0515746 + 0.0893299i
\(335\) 9.51135 0.519661
\(336\) 0 0
\(337\) −2.41842 −0.131740 −0.0658700 0.997828i \(-0.520982\pi\)
−0.0658700 + 0.997828i \(0.520982\pi\)
\(338\) −0.132313 0.229173i −0.00719689 0.0124654i
\(339\) −17.5000 + 30.3109i −0.950471 + 1.64626i
\(340\) −6.69009 + 11.5876i −0.362821 + 0.628424i
\(341\) −25.3465 43.9013i −1.37259 2.37739i
\(342\) 4.07687 0.220452
\(343\) 0 0
\(344\) 8.77411 0.473069
\(345\) −12.5238 21.6919i −0.674259 1.16785i
\(346\) −1.48676 + 2.57515i −0.0799289 + 0.138441i
\(347\) 0.246264 0.426541i 0.0132201 0.0228979i −0.859340 0.511405i \(-0.829125\pi\)
0.872560 + 0.488507i \(0.162458\pi\)
\(348\) 2.92474 + 5.06580i 0.156783 + 0.271555i
\(349\) −11.9442 −0.639356 −0.319678 0.947526i \(-0.603575\pi\)
−0.319678 + 0.947526i \(0.603575\pi\)
\(350\) 0 0
\(351\) 7.16341 0.382355
\(352\) −8.33574 14.4379i −0.444297 0.769544i
\(353\) −7.76497 + 13.4493i −0.413288 + 0.715835i −0.995247 0.0973828i \(-0.968953\pi\)
0.581959 + 0.813218i \(0.302286\pi\)
\(354\) 0.335218 0.580615i 0.0178166 0.0308593i
\(355\) −4.92154 8.52436i −0.261208 0.452426i
\(356\) 1.92094 0.101809
\(357\) 0 0
\(358\) −3.49162 −0.184538
\(359\) 4.25354 + 7.36735i 0.224493 + 0.388834i 0.956167 0.292821i \(-0.0945939\pi\)
−0.731674 + 0.681655i \(0.761261\pi\)
\(360\) −4.07644 + 7.06059i −0.214847 + 0.372126i
\(361\) 5.52278 9.56574i 0.290673 0.503460i
\(362\) 1.81817 + 3.14917i 0.0955611 + 0.165517i
\(363\) 56.1507 2.94715
\(364\) 0 0
\(365\) −4.50850 −0.235985
\(366\) 1.28270 + 2.22170i 0.0670479 + 0.116130i
\(367\) −2.59542 + 4.49540i −0.135480 + 0.234658i −0.925781 0.378061i \(-0.876591\pi\)
0.790301 + 0.612719i \(0.209924\pi\)
\(368\) 10.7534 18.6255i 0.560562 0.970921i
\(369\) 29.0046 + 50.2374i 1.50992 + 2.61525i
\(370\) −0.232614 −0.0120930
\(371\) 0 0
\(372\) −51.7023 −2.68064
\(373\) 5.07135 + 8.78384i 0.262585 + 0.454810i 0.966928 0.255049i \(-0.0820918\pi\)
−0.704343 + 0.709859i \(0.748758\pi\)
\(374\) −3.51846 + 6.09415i −0.181935 + 0.315121i
\(375\) −16.5751 + 28.7089i −0.855934 + 1.48252i
\(376\) 1.25277 + 2.16986i 0.0646065 + 0.111902i
\(377\) 1.04188 0.0536595
\(378\) 0 0
\(379\) −3.63670 −0.186805 −0.0934024 0.995628i \(-0.529774\pi\)
−0.0934024 + 0.995628i \(0.529774\pi\)
\(380\) −3.90593 6.76527i −0.200370 0.347051i
\(381\) −22.7863 + 39.4670i −1.16738 + 2.02196i
\(382\) 2.16077 3.74256i 0.110555 0.191486i
\(383\) −2.30140 3.98615i −0.117596 0.203683i 0.801218 0.598372i \(-0.204186\pi\)
−0.918815 + 0.394689i \(0.870852\pi\)
\(384\) −22.5226 −1.14935
\(385\) 0 0
\(386\) −3.71888 −0.189286
\(387\) 23.0430 + 39.9117i 1.17134 + 2.02883i
\(388\) 13.0360 22.5791i 0.661804 1.14628i
\(389\) −9.80519 + 16.9831i −0.497143 + 0.861077i −0.999995 0.00329604i \(-0.998951\pi\)
0.502852 + 0.864373i \(0.332284\pi\)
\(390\) 0.552396 + 0.956778i 0.0279717 + 0.0484483i
\(391\) −28.9822 −1.46569
\(392\) 0 0
\(393\) 35.2788 1.77958
\(394\) 0.194366 + 0.336651i 0.00979199 + 0.0169602i
\(395\) −12.6095 + 21.8402i −0.634451 + 1.09890i
\(396\) 29.0167 50.2583i 1.45814 2.52558i
\(397\) 9.93173 + 17.2023i 0.498459 + 0.863357i 0.999998 0.00177809i \(-0.000565985\pi\)
−0.501539 + 0.865135i \(0.667233\pi\)
\(398\) −3.53996 −0.177442
\(399\) 0 0
\(400\) −10.5403 −0.527017
\(401\) 7.55587 + 13.0872i 0.377322 + 0.653541i 0.990672 0.136270i \(-0.0435116\pi\)
−0.613350 + 0.789812i \(0.710178\pi\)
\(402\) 2.55091 4.41831i 0.127228 0.220365i
\(403\) −4.60448 + 7.97519i −0.229365 + 0.397272i
\(404\) −0.972770 1.68489i −0.0483971 0.0838263i
\(405\) −6.38813 −0.317429
\(406\) 0 0
\(407\) 3.37164 0.167126
\(408\) 7.30724 + 12.6565i 0.361763 + 0.626591i
\(409\) 17.6222 30.5225i 0.871360 1.50924i 0.0107701 0.999942i \(-0.496572\pi\)
0.860590 0.509298i \(-0.170095\pi\)
\(410\) −2.01655 + 3.49277i −0.0995903 + 0.172495i
\(411\) −23.1813 40.1512i −1.14345 1.98051i
\(412\) 24.6563 1.21473
\(413\) 0 0
\(414\) −8.67246 −0.426228
\(415\) 8.21805 + 14.2341i 0.403408 + 0.698723i
\(416\) −1.51428 + 2.62282i −0.0742439 + 0.128594i
\(417\) 9.65927 16.7304i 0.473017 0.819289i
\(418\) −2.05421 3.55800i −0.100475 0.174027i
\(419\) 1.50468 0.0735084 0.0367542 0.999324i \(-0.488298\pi\)
0.0367542 + 0.999324i \(0.488298\pi\)
\(420\) 0 0
\(421\) −24.5079 −1.19444 −0.597221 0.802077i \(-0.703728\pi\)
−0.597221 + 0.802077i \(0.703728\pi\)
\(422\) −0.459185 0.795332i −0.0223528 0.0387161i
\(423\) −6.58016 + 11.3972i −0.319938 + 0.554149i
\(424\) −0.951362 + 1.64781i −0.0462022 + 0.0800246i
\(425\) 7.10197 + 12.3010i 0.344496 + 0.596685i
\(426\) −5.27977 −0.255806
\(427\) 0 0
\(428\) 1.32299 0.0639490
\(429\) −8.00674 13.8681i −0.386569 0.669557i
\(430\) −1.60207 + 2.77487i −0.0772588 + 0.133816i
\(431\) −20.5327 + 35.5638i −0.989027 + 1.71305i −0.366574 + 0.930389i \(0.619469\pi\)
−0.622454 + 0.782657i \(0.713864\pi\)
\(432\) −12.8395 22.2386i −0.617740 1.06996i
\(433\) 6.65603 0.319869 0.159934 0.987128i \(-0.448872\pi\)
0.159934 + 0.987128i \(0.448872\pi\)
\(434\) 0 0
\(435\) −4.34975 −0.208555
\(436\) −2.80178 4.85283i −0.134181 0.232408i
\(437\) 8.46046 14.6540i 0.404719 0.700994i
\(438\) −1.20916 + 2.09433i −0.0577761 + 0.100071i
\(439\) −4.11495 7.12730i −0.196396 0.340168i 0.750961 0.660346i \(-0.229590\pi\)
−0.947357 + 0.320179i \(0.896257\pi\)
\(440\) 8.21596 0.391681
\(441\) 0 0
\(442\) 1.27834 0.0608043
\(443\) −8.84278 15.3161i −0.420133 0.727692i 0.575819 0.817577i \(-0.304683\pi\)
−0.995952 + 0.0898854i \(0.971350\pi\)
\(444\) 1.71939 2.97807i 0.0815986 0.141333i
\(445\) −0.714217 + 1.23706i −0.0338571 + 0.0586423i
\(446\) 1.31165 + 2.27184i 0.0621082 + 0.107575i
\(447\) −56.8723 −2.68997
\(448\) 0 0
\(449\) −14.5250 −0.685477 −0.342738 0.939431i \(-0.611354\pi\)
−0.342738 + 0.939431i \(0.611354\pi\)
\(450\) 2.12515 + 3.68087i 0.100180 + 0.173518i
\(451\) 29.2290 50.6261i 1.37634 2.38389i
\(452\) 11.6102 20.1095i 0.546100 0.945873i
\(453\) −15.5459 26.9263i −0.730411 1.26511i
\(454\) 3.19475 0.149937
\(455\) 0 0
\(456\) −8.53250 −0.399571
\(457\) −1.89460 3.28154i −0.0886255 0.153504i 0.818305 0.574784i \(-0.194914\pi\)
−0.906930 + 0.421281i \(0.861581\pi\)
\(458\) −0.536095 + 0.928544i −0.0250501 + 0.0433880i
\(459\) −17.3022 + 29.9683i −0.807599 + 1.39880i
\(460\) 8.30881 + 14.3913i 0.387400 + 0.670997i
\(461\) 13.1107 0.610627 0.305314 0.952252i \(-0.401239\pi\)
0.305314 + 0.952252i \(0.401239\pi\)
\(462\) 0 0
\(463\) 15.3027 0.711176 0.355588 0.934643i \(-0.384281\pi\)
0.355588 + 0.934643i \(0.384281\pi\)
\(464\) −1.86743 3.23449i −0.0866935 0.150158i
\(465\) 19.2233 33.2957i 0.891458 1.54405i
\(466\) −1.65987 + 2.87498i −0.0768920 + 0.133181i
\(467\) −15.3869 26.6509i −0.712022 1.23326i −0.964097 0.265550i \(-0.914446\pi\)
0.252075 0.967708i \(-0.418887\pi\)
\(468\) −10.5424 −0.487324
\(469\) 0 0
\(470\) −0.914975 −0.0422046
\(471\) 21.9246 + 37.9745i 1.01023 + 1.74977i
\(472\) −0.452865 + 0.784385i −0.0208448 + 0.0361042i
\(473\) 23.2213 40.2205i 1.06772 1.84934i
\(474\) 6.76364 + 11.7150i 0.310664 + 0.538086i
\(475\) −8.29280 −0.380500
\(476\) 0 0
\(477\) −9.99407 −0.457597
\(478\) −1.76589 3.05861i −0.0807699 0.139898i
\(479\) 0.858699 1.48731i 0.0392350 0.0679569i −0.845741 0.533593i \(-0.820841\pi\)
0.884976 + 0.465637i \(0.154175\pi\)
\(480\) 6.32200 10.9500i 0.288558 0.499798i
\(481\) −0.306249 0.530438i −0.0139637 0.0241859i
\(482\) 5.39451 0.245713
\(483\) 0 0
\(484\) −37.2527 −1.69330
\(485\) 9.69377 + 16.7901i 0.440171 + 0.762399i
\(486\) 1.13017 1.95751i 0.0512654 0.0887943i
\(487\) −11.3403 + 19.6419i −0.513877 + 0.890060i 0.485994 + 0.873962i \(0.338458\pi\)
−0.999870 + 0.0160982i \(0.994876\pi\)
\(488\) −1.73287 3.00142i −0.0784435 0.135868i
\(489\) −69.2741 −3.13268
\(490\) 0 0
\(491\) −13.1366 −0.592846 −0.296423 0.955057i \(-0.595794\pi\)
−0.296423 + 0.955057i \(0.595794\pi\)
\(492\) −29.8110 51.6342i −1.34398 2.32785i
\(493\) −2.51652 + 4.35873i −0.113338 + 0.196308i
\(494\) −0.373171 + 0.646351i −0.0167898 + 0.0290807i
\(495\) 21.5772 + 37.3728i 0.969822 + 1.67978i
\(496\) 33.0117 1.48227
\(497\) 0 0
\(498\) 8.81622 0.395064
\(499\) −7.01976 12.1586i −0.314248 0.544293i 0.665030 0.746817i \(-0.268419\pi\)
−0.979277 + 0.202524i \(0.935086\pi\)
\(500\) 10.9966 19.0467i 0.491783 0.851793i
\(501\) 10.3615 17.9467i 0.462920 0.801801i
\(502\) −2.27474 3.93996i −0.101527 0.175849i
\(503\) 0.367865 0.0164023 0.00820114 0.999966i \(-0.497389\pi\)
0.00820114 + 0.999966i \(0.497389\pi\)
\(504\) 0 0
\(505\) 1.44673 0.0643786
\(506\) 4.36978 + 7.56869i 0.194261 + 0.336469i
\(507\) −1.45452 + 2.51930i −0.0645973 + 0.111886i
\(508\) 15.1174 26.1841i 0.670725 1.16173i
\(509\) −20.6160 35.7079i −0.913787 1.58273i −0.808668 0.588266i \(-0.799811\pi\)
−0.105119 0.994460i \(-0.533522\pi\)
\(510\) −5.33694 −0.236324
\(511\) 0 0
\(512\) 18.3127 0.809315
\(513\) −10.1017 17.4967i −0.446001 0.772497i
\(514\) 1.01179 1.75248i 0.0446283 0.0772985i
\(515\) −9.16736 + 15.8783i −0.403962 + 0.699683i
\(516\) −23.6837 41.0214i −1.04262 1.80587i
\(517\) 13.2622 0.583269
\(518\) 0 0
\(519\) 32.6879 1.43484
\(520\) −0.746262 1.29256i −0.0327258 0.0566827i
\(521\) −0.520493 + 0.901521i −0.0228032 + 0.0394963i −0.877202 0.480122i \(-0.840592\pi\)
0.854399 + 0.519618i \(0.173926\pi\)
\(522\) −0.753027 + 1.30428i −0.0329591 + 0.0570868i
\(523\) 10.0104 + 17.3386i 0.437726 + 0.758163i 0.997514 0.0704727i \(-0.0224508\pi\)
−0.559788 + 0.828636i \(0.689117\pi\)
\(524\) −23.4054 −1.02247
\(525\) 0 0
\(526\) −0.0267371 −0.00116579
\(527\) −22.2429 38.5259i −0.968918 1.67822i
\(528\) −28.7021 + 49.7135i −1.24910 + 2.16350i
\(529\) −6.49737 + 11.2538i −0.282494 + 0.489295i
\(530\) −0.347420 0.601749i −0.0150910 0.0261383i
\(531\) −4.75735 −0.206451
\(532\) 0 0
\(533\) −10.6196 −0.459985
\(534\) 0.383101 + 0.663551i 0.0165784 + 0.0287147i
\(535\) −0.491895 + 0.851988i −0.0212665 + 0.0368346i
\(536\) −3.44617 + 5.96894i −0.148852 + 0.257819i
\(537\) 19.1916 + 33.2409i 0.828180 + 1.43445i
\(538\) −2.00283 −0.0863481
\(539\) 0 0
\(540\) 19.8413 0.853832
\(541\) 4.89375 + 8.47622i 0.210399 + 0.364421i 0.951839 0.306597i \(-0.0991905\pi\)
−0.741441 + 0.671018i \(0.765857\pi\)
\(542\) 1.83325 3.17528i 0.0787447 0.136390i
\(543\) 19.9871 34.6187i 0.857730 1.48563i
\(544\) −7.31508 12.6701i −0.313632 0.543226i
\(545\) 4.16689 0.178490
\(546\) 0 0
\(547\) −2.56174 −0.109532 −0.0547660 0.998499i \(-0.517441\pi\)
−0.0547660 + 0.998499i \(0.517441\pi\)
\(548\) 15.3794 + 26.6380i 0.656977 + 1.13792i
\(549\) 9.10192 15.7650i 0.388460 0.672833i
\(550\) 2.14159 3.70935i 0.0913179 0.158167i
\(551\) −1.46924 2.54480i −0.0625917 0.108412i
\(552\) 18.1506 0.772541
\(553\) 0 0
\(554\) 0.146321 0.00621660
\(555\) 1.27856 + 2.21453i 0.0542719 + 0.0940016i
\(556\) −6.40836 + 11.0996i −0.271775 + 0.470728i
\(557\) 13.7221 23.7674i 0.581424 1.00706i −0.413887 0.910328i \(-0.635829\pi\)
0.995311 0.0967277i \(-0.0308376\pi\)
\(558\) −6.65584 11.5283i −0.281764 0.488030i
\(559\) −8.43685 −0.356841
\(560\) 0 0
\(561\) 77.3567 3.26600
\(562\) −0.151719 0.262785i −0.00639988 0.0110849i
\(563\) −0.0813542 + 0.140910i −0.00342867 + 0.00593863i −0.867735 0.497028i \(-0.834425\pi\)
0.864306 + 0.502966i \(0.167758\pi\)
\(564\) 6.76312 11.7141i 0.284779 0.493251i
\(565\) 8.63353 + 14.9537i 0.363216 + 0.629108i
\(566\) −1.07278 −0.0450925
\(567\) 0 0
\(568\) 7.13273 0.299283
\(569\) 6.19503 + 10.7301i 0.259709 + 0.449830i 0.966164 0.257929i \(-0.0830399\pi\)
−0.706455 + 0.707758i \(0.749707\pi\)
\(570\) 1.55796 2.69846i 0.0652556 0.113026i
\(571\) 10.9061 18.8899i 0.456405 0.790517i −0.542363 0.840145i \(-0.682470\pi\)
0.998768 + 0.0496275i \(0.0158034\pi\)
\(572\) 5.31200 + 9.20066i 0.222106 + 0.384699i
\(573\) −47.5066 −1.98462
\(574\) 0 0
\(575\) 17.6407 0.735669
\(576\) 17.3926 + 30.1249i 0.724693 + 1.25520i
\(577\) −3.03292 + 5.25316i −0.126262 + 0.218692i −0.922226 0.386652i \(-0.873631\pi\)
0.795964 + 0.605345i \(0.206965\pi\)
\(578\) −0.838321 + 1.45201i −0.0348696 + 0.0603958i
\(579\) 20.4408 + 35.4045i 0.849490 + 1.47136i
\(580\) 2.88581 0.119827
\(581\) 0 0
\(582\) 10.3993 0.431067
\(583\) 5.03570 + 8.72209i 0.208557 + 0.361232i
\(584\) 1.63353 2.82935i 0.0675958 0.117079i
\(585\) 3.91974 6.78919i 0.162061 0.280699i
\(586\) −1.99329 3.45248i −0.0823420 0.142620i
\(587\) 20.5820 0.849510 0.424755 0.905308i \(-0.360360\pi\)
0.424755 + 0.905308i \(0.360360\pi\)
\(588\) 0 0
\(589\) 25.9726 1.07018
\(590\) −0.165378 0.286443i −0.00680850 0.0117927i
\(591\) 2.13666 3.70080i 0.0878903 0.152230i
\(592\) −1.09782 + 1.90148i −0.0451202 + 0.0781505i
\(593\) 12.0198 + 20.8189i 0.493595 + 0.854932i 0.999973 0.00738005i \(-0.00234917\pi\)
−0.506378 + 0.862312i \(0.669016\pi\)
\(594\) 10.4349 0.428151
\(595\) 0 0
\(596\) 37.7314 1.54554
\(597\) 19.4574 + 33.7011i 0.796337 + 1.37930i
\(598\) 0.793822 1.37494i 0.0324618 0.0562255i
\(599\) −16.1261 + 27.9313i −0.658896 + 1.14124i 0.322005 + 0.946738i \(0.395643\pi\)
−0.980902 + 0.194504i \(0.937690\pi\)
\(600\) −4.44773 7.70369i −0.181578 0.314502i
\(601\) 5.21454 0.212705 0.106353 0.994328i \(-0.466083\pi\)
0.106353 + 0.994328i \(0.466083\pi\)
\(602\) 0 0
\(603\) −36.2020 −1.47426
\(604\) 10.3138 + 17.8640i 0.419663 + 0.726877i
\(605\) 13.8508 23.9903i 0.563115 0.975344i
\(606\) 0.388008 0.672050i 0.0157618 0.0273002i
\(607\) −4.53524 7.85527i −0.184080 0.318836i 0.759186 0.650873i \(-0.225597\pi\)
−0.943266 + 0.332038i \(0.892264\pi\)
\(608\) 8.54165 0.346410
\(609\) 0 0
\(610\) 1.26563 0.0512437
\(611\) −1.20461 2.08645i −0.0487334 0.0844087i
\(612\) 25.4638 44.1045i 1.02931 1.78282i
\(613\) −10.0460 + 17.4002i −0.405754 + 0.702786i −0.994409 0.105598i \(-0.966324\pi\)
0.588655 + 0.808384i \(0.299658\pi\)
\(614\) 2.63843 + 4.56990i 0.106478 + 0.184426i
\(615\) 44.3357 1.78779
\(616\) 0 0
\(617\) −12.9556 −0.521572 −0.260786 0.965397i \(-0.583982\pi\)
−0.260786 + 0.965397i \(0.583982\pi\)
\(618\) 4.91732 + 8.51704i 0.197803 + 0.342606i
\(619\) 22.1822 38.4207i 0.891578 1.54426i 0.0535955 0.998563i \(-0.482932\pi\)
0.837983 0.545696i \(-0.183735\pi\)
\(620\) −12.7535 + 22.0897i −0.512193 + 0.887145i
\(621\) 21.4887 + 37.2195i 0.862310 + 1.49357i
\(622\) −2.88327 −0.115608
\(623\) 0 0
\(624\) 10.4281 0.417459
\(625\) 0.826381 + 1.43133i 0.0330553 + 0.0572534i
\(626\) 0.00686958 0.0118985i 0.000274563 0.000475558i
\(627\) −22.5819 + 39.1130i −0.901834 + 1.56202i
\(628\) −14.5457 25.1938i −0.580435 1.00534i
\(629\) 2.95880 0.117975
\(630\) 0 0
\(631\) 6.61717 0.263426 0.131713 0.991288i \(-0.457952\pi\)
0.131713 + 0.991288i \(0.457952\pi\)
\(632\) −9.13737 15.8264i −0.363465 0.629540i
\(633\) −5.04781 + 8.74306i −0.200632 + 0.347506i
\(634\) −2.13037 + 3.68991i −0.0846079 + 0.146545i
\(635\) 11.2415 + 19.4708i 0.446105 + 0.772676i
\(636\) 10.2719 0.407309
\(637\) 0 0
\(638\) 1.51771 0.0600866
\(639\) 18.7323 + 32.4454i 0.741040 + 1.28352i
\(640\) −5.55569 + 9.62273i −0.219608 + 0.380372i
\(641\) −9.47834 + 16.4170i −0.374372 + 0.648432i −0.990233 0.139424i \(-0.955475\pi\)
0.615861 + 0.787855i \(0.288808\pi\)
\(642\) 0.263850 + 0.457001i 0.0104133 + 0.0180364i
\(643\) 13.4019 0.528517 0.264259 0.964452i \(-0.414873\pi\)
0.264259 + 0.964452i \(0.414873\pi\)
\(644\) 0 0
\(645\) 35.2231 1.38691
\(646\) −1.80269 3.12234i −0.0709257 0.122847i
\(647\) −21.3794 + 37.0302i −0.840511 + 1.45581i 0.0489522 + 0.998801i \(0.484412\pi\)
−0.889463 + 0.457007i \(0.848922\pi\)
\(648\) 2.31456 4.00894i 0.0909245 0.157486i
\(649\) 2.39708 + 4.15186i 0.0940936 + 0.162975i
\(650\) −0.778091 −0.0305192
\(651\) 0 0
\(652\) 45.9593 1.79991
\(653\) −5.49260 9.51346i −0.214942 0.372290i 0.738313 0.674459i \(-0.235623\pi\)
−0.953255 + 0.302168i \(0.902290\pi\)
\(654\) 1.11755 1.93565i 0.0436995 0.0756898i
\(655\) 8.70228 15.0728i 0.340026 0.588943i
\(656\) 19.0342 + 32.9682i 0.743161 + 1.28719i
\(657\) 17.1602 0.669483
\(658\) 0 0
\(659\) −17.7614 −0.691884 −0.345942 0.938256i \(-0.612441\pi\)
−0.345942 + 0.938256i \(0.612441\pi\)
\(660\) −22.1771 38.4119i −0.863243 1.49518i
\(661\) −4.09127 + 7.08629i −0.159132 + 0.275625i −0.934556 0.355816i \(-0.884203\pi\)
0.775424 + 0.631441i \(0.217536\pi\)
\(662\) −4.07342 + 7.05538i −0.158318 + 0.274215i
\(663\) −7.02636 12.1700i −0.272881 0.472644i
\(664\) −11.9103 −0.462210
\(665\) 0 0
\(666\) 0.885374 0.0343076
\(667\) 3.12541 + 5.41337i 0.121016 + 0.209607i
\(668\) −6.87428 + 11.9066i −0.265974 + 0.460680i
\(669\) 14.4189 24.9742i 0.557466 0.965560i
\(670\) −1.25848 2.17975i −0.0486192 0.0842110i
\(671\) −18.3447 −0.708189
\(672\) 0 0
\(673\) 9.30129 0.358539 0.179269 0.983800i \(-0.442627\pi\)
0.179269 + 0.983800i \(0.442627\pi\)
\(674\) 0.319990 + 0.554238i 0.0123255 + 0.0213485i
\(675\) 10.5314 18.2409i 0.405354 0.702094i
\(676\) 0.964986 1.67141i 0.0371149 0.0642848i
\(677\) 20.5776 + 35.6415i 0.790862 + 1.36981i 0.925434 + 0.378909i \(0.123701\pi\)
−0.134572 + 0.990904i \(0.542966\pi\)
\(678\) 9.26195 0.355703
\(679\) 0 0
\(680\) 7.20997 0.276490
\(681\) −17.5599 30.4147i −0.672897 1.16549i
\(682\) −6.70734 + 11.6175i −0.256837 + 0.444856i
\(683\) −19.6421 + 34.0211i −0.751583 + 1.30178i 0.195472 + 0.980709i \(0.437376\pi\)
−0.947055 + 0.321071i \(0.895957\pi\)
\(684\) 14.8667 + 25.7499i 0.568443 + 0.984572i
\(685\) −22.8727 −0.873921
\(686\) 0 0
\(687\) 11.7866 0.449685
\(688\) 15.1220 + 26.1920i 0.576519 + 0.998561i
\(689\) 0.914793 1.58447i 0.0348509 0.0603634i
\(690\) −3.31413 + 5.74025i −0.126167 + 0.218527i
\(691\) 1.51678 + 2.62713i 0.0577009 + 0.0999409i 0.893433 0.449197i \(-0.148290\pi\)
−0.835732 + 0.549137i \(0.814956\pi\)
\(692\) −21.6865 −0.824397
\(693\) 0 0
\(694\) −0.130336 −0.00494748
\(695\) −4.76534 8.25382i −0.180760 0.313085i
\(696\) 1.57601 2.72973i 0.0597385 0.103470i
\(697\) 25.6501 44.4273i 0.971567 1.68280i
\(698\) 1.58037 + 2.73728i 0.0598179 + 0.103608i
\(699\) 36.4938 1.38032
\(700\) 0 0
\(701\) −26.2320 −0.990767 −0.495384 0.868674i \(-0.664972\pi\)
−0.495384 + 0.868674i \(0.664972\pi\)
\(702\) −0.947814 1.64166i −0.0357729 0.0619606i
\(703\) −0.863732 + 1.49603i −0.0325763 + 0.0564237i
\(704\) 17.5272 30.3580i 0.660582 1.14416i
\(705\) 5.02915 + 8.71074i 0.189409 + 0.328065i
\(706\) 4.10963 0.154668
\(707\) 0 0
\(708\) 4.88962 0.183763
\(709\) 3.93885 + 6.82229i 0.147927 + 0.256216i 0.930461 0.366391i \(-0.119407\pi\)
−0.782534 + 0.622607i \(0.786073\pi\)
\(710\) −1.30237 + 2.25577i −0.0488771 + 0.0846576i
\(711\) 47.9941 83.1282i 1.79992 3.11755i
\(712\) −0.517553 0.896428i −0.0193961 0.0335951i
\(713\) −55.2497 −2.06912
\(714\) 0 0
\(715\) −7.90015 −0.295449
\(716\) −12.7325 22.0534i −0.475837 0.824173i
\(717\) −19.4124 + 33.6232i −0.724968 + 1.25568i
\(718\) 1.12560 1.94960i 0.0420070 0.0727583i
\(719\) −22.8328 39.5476i −0.851519 1.47487i −0.879837 0.475276i \(-0.842348\pi\)
0.0283174 0.999599i \(-0.490985\pi\)
\(720\) −28.1025 −1.04732
\(721\) 0 0
\(722\) −2.92295 −0.108781
\(723\) −29.6508 51.3568i −1.10273 1.90998i
\(724\) −13.2603 + 22.9675i −0.492815 + 0.853580i
\(725\) 1.53174 2.65305i 0.0568873 0.0985317i
\(726\) −7.42948 12.8682i −0.275734 0.477585i
\(727\) 37.5947 1.39431 0.697155 0.716921i \(-0.254449\pi\)
0.697155 + 0.716921i \(0.254449\pi\)
\(728\) 0 0
\(729\) −38.2013 −1.41486
\(730\) 0.596534 + 1.03323i 0.0220787 + 0.0382414i
\(731\) 20.3780 35.2958i 0.753709 1.30546i
\(732\) −9.35499 + 16.2033i −0.345771 + 0.598892i
\(733\) −26.5905 46.0561i −0.982143 1.70112i −0.654003 0.756492i \(-0.726912\pi\)
−0.328139 0.944629i \(-0.606422\pi\)
\(734\) 1.37363 0.0507018
\(735\) 0 0
\(736\) −18.1701 −0.669758
\(737\) 18.2411 + 31.5945i 0.671919 + 1.16380i
\(738\) 7.67538 13.2941i 0.282535 0.489364i
\(739\) −20.9816 + 36.3412i −0.771822 + 1.33683i 0.164742 + 0.986337i \(0.447321\pi\)
−0.936564 + 0.350498i \(0.886012\pi\)
\(740\) −0.848250 1.46921i −0.0311823 0.0540093i
\(741\) 8.20452 0.301401
\(742\) 0 0
\(743\) −38.5424 −1.41398 −0.706991 0.707222i \(-0.749948\pi\)
−0.706991 + 0.707222i \(0.749948\pi\)
\(744\) 13.9300 + 24.1275i 0.510699 + 0.884557i
\(745\) −14.0288 + 24.2986i −0.513975 + 0.890232i
\(746\) 1.34201 2.32444i 0.0491346 0.0851037i
\(747\) −31.2795 54.1777i −1.14446 1.98226i
\(748\) −51.3216 −1.87650
\(749\) 0 0
\(750\) 8.77242 0.320323
\(751\) −18.1217 31.3877i −0.661270 1.14535i −0.980282 0.197602i \(-0.936685\pi\)
0.319013 0.947750i \(-0.396649\pi\)
\(752\) −4.31822 + 7.47938i −0.157469 + 0.272745i
\(753\) −25.0062 + 43.3119i −0.911275 + 1.57837i
\(754\) −0.137855 0.238771i −0.00502037 0.00869553i
\(755\) −15.3390 −0.558242
\(756\) 0 0
\(757\) 19.4752 0.707837 0.353919 0.935276i \(-0.384849\pi\)
0.353919 + 0.935276i \(0.384849\pi\)
\(758\) 0.481184 + 0.833435i 0.0174774 + 0.0302717i
\(759\) 48.0369 83.2024i 1.74363 3.02006i
\(760\) −2.10473 + 3.64550i −0.0763465 + 0.132236i
\(761\) 25.9529 + 44.9518i 0.940793 + 1.62950i 0.763963 + 0.645261i \(0.223251\pi\)
0.176831 + 0.984241i \(0.443415\pi\)
\(762\) 12.0597 0.436878
\(763\) 0 0
\(764\) 31.5178 1.14028
\(765\) 18.9352 + 32.7967i 0.684603 + 1.18577i
\(766\) −0.609013 + 1.05484i −0.0220045 + 0.0381129i
\(767\) 0.435457 0.754234i 0.0157234 0.0272338i
\(768\) −15.5448 26.9244i −0.560925 0.971550i
\(769\) −7.31376 −0.263741 −0.131870 0.991267i \(-0.542098\pi\)
−0.131870 + 0.991267i \(0.542098\pi\)
\(770\) 0 0
\(771\) −22.2452 −0.801142
\(772\) −13.5613 23.4888i −0.488081 0.845381i
\(773\) 7.09220 12.2841i 0.255089 0.441827i −0.709831 0.704372i \(-0.751229\pi\)
0.964920 + 0.262545i \(0.0845620\pi\)
\(774\) 6.09780 10.5617i 0.219181 0.379632i
\(775\) 13.5387 + 23.4497i 0.486324 + 0.842339i
\(776\) −14.0491 −0.504332
\(777\) 0 0
\(778\) 5.18943 0.186050
\(779\) 14.9755 + 25.9384i 0.536553 + 0.929338i
\(780\) −4.02873 + 6.97797i −0.144252 + 0.249851i
\(781\) 18.8773 32.6964i 0.675483 1.16997i
\(782\) 3.83473 + 6.64195i 0.137130 + 0.237516i
\(783\) 7.46341 0.266721
\(784\)