Properties

Label 637.2.e.n.508.2
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 508.2
Root \(-0.0731214 - 0.126650i\) of defining polynomial
Character \(\chi\) \(=\) 637.508
Dual form 637.2.e.n.79.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.916185 - 1.58688i) q^{2} +(-0.426879 + 0.739375i) q^{3} +(-0.678791 + 1.17570i) q^{4} +(-1.31278 - 2.27379i) q^{5} +1.56440 q^{6} -1.17715 q^{8} +(1.13555 + 1.96683i) q^{9} +O(q^{10})\) \(q+(-0.916185 - 1.58688i) q^{2} +(-0.426879 + 0.739375i) q^{3} +(-0.678791 + 1.17570i) q^{4} +(-1.31278 - 2.27379i) q^{5} +1.56440 q^{6} -1.17715 q^{8} +(1.13555 + 1.96683i) q^{9} +(-2.40549 + 4.16643i) q^{10} +(-1.63234 + 2.82730i) q^{11} +(-0.579522 - 1.00376i) q^{12} +1.00000 q^{13} +2.24158 q^{15} +(2.43607 + 4.21939i) q^{16} +(-2.26511 + 3.92328i) q^{17} +(2.08075 - 3.60396i) q^{18} +(-2.03308 - 3.52139i) q^{19} +3.56440 q^{20} +5.98212 q^{22} +(2.26633 + 3.92540i) q^{23} +(0.502500 - 0.870355i) q^{24} +(-0.946761 + 1.63984i) q^{25} +(-0.916185 - 1.58688i) q^{26} -4.50024 q^{27} -1.42268 q^{29} +(-2.05371 - 3.55712i) q^{30} +(1.40164 - 2.42771i) q^{31} +(3.28663 - 5.69261i) q^{32} +(-1.39363 - 2.41383i) q^{33} +8.30102 q^{34} -3.08320 q^{36} +(5.02517 + 8.70385i) q^{37} +(-3.72535 + 6.45249i) q^{38} +(-0.426879 + 0.739375i) q^{39} +(1.54533 + 2.67660i) q^{40} -2.84271 q^{41} +9.72632 q^{43} +(-2.21604 - 3.83829i) q^{44} +(2.98144 - 5.16401i) q^{45} +(4.15276 - 7.19278i) q^{46} +(4.72478 + 8.18356i) q^{47} -4.15962 q^{48} +3.46963 q^{50} +(-1.93385 - 3.34953i) q^{51} +(-0.678791 + 1.17570i) q^{52} +(-2.63219 + 4.55909i) q^{53} +(4.12305 + 7.14134i) q^{54} +8.57161 q^{55} +3.47151 q^{57} +(1.30344 + 2.25762i) q^{58} +(1.28395 - 2.22387i) q^{59} +(-1.52157 + 2.63543i) q^{60} +(5.59149 + 9.68475i) q^{61} -5.13664 q^{62} -2.30037 q^{64} +(-1.31278 - 2.27379i) q^{65} +(-2.55364 + 4.42303i) q^{66} +(0.990861 - 1.71622i) q^{67} +(-3.07506 - 5.32617i) q^{68} -3.86979 q^{69} -11.7544 q^{71} +(-1.33671 - 2.31525i) q^{72} +(-6.06956 + 10.5128i) q^{73} +(9.20797 - 15.9487i) q^{74} +(-0.808304 - 1.40002i) q^{75} +5.52013 q^{76} +1.56440 q^{78} +(-5.95445 - 10.3134i) q^{79} +(6.39602 - 11.0782i) q^{80} +(-1.48559 + 2.57312i) q^{81} +(2.60444 + 4.51103i) q^{82} +13.2233 q^{83} +11.8943 q^{85} +(-8.91111 - 15.4345i) q^{86} +(0.607310 - 1.05189i) q^{87} +(1.92151 - 3.32816i) q^{88} +(-5.33328 - 9.23751i) q^{89} -10.9262 q^{90} -6.15345 q^{92} +(1.19666 + 2.07268i) q^{93} +(8.65755 - 14.9953i) q^{94} +(-5.33795 + 9.24560i) q^{95} +(2.80598 + 4.86011i) q^{96} -13.7422 q^{97} -7.41443 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 8 q^{3} - 4 q^{4} - 6 q^{5} + 8 q^{6} - 6 q^{9} + O(q^{10}) \) \( 12 q - 8 q^{3} - 4 q^{4} - 6 q^{5} + 8 q^{6} - 6 q^{9} - 4 q^{10} - 4 q^{11} + 4 q^{12} + 12 q^{13} + 24 q^{15} - 16 q^{17} + 4 q^{18} - 2 q^{19} + 32 q^{20} - 24 q^{22} + 6 q^{23} - 12 q^{24} + 4 q^{25} + 40 q^{27} - 12 q^{29} - 6 q^{31} + 20 q^{32} - 4 q^{33} - 48 q^{36} - 8 q^{38} - 8 q^{39} - 4 q^{40} - 16 q^{41} + 4 q^{43} + 4 q^{44} - 14 q^{45} - 8 q^{46} - 30 q^{47} - 16 q^{48} + 16 q^{50} + 4 q^{51} - 4 q^{52} + 14 q^{53} + 48 q^{54} - 16 q^{55} + 8 q^{57} + 8 q^{58} - 24 q^{59} - 12 q^{60} + 56 q^{62} - 40 q^{64} - 6 q^{65} + 4 q^{66} - 16 q^{67} - 28 q^{68} - 40 q^{69} + 16 q^{71} - 28 q^{72} + 6 q^{73} + 12 q^{74} - 12 q^{75} - 32 q^{76} + 8 q^{78} + 22 q^{79} + 28 q^{80} - 46 q^{81} + 40 q^{82} + 100 q^{83} - 16 q^{85} + 16 q^{86} + 16 q^{87} + 44 q^{88} - 26 q^{89} - 80 q^{90} + 40 q^{92} - 16 q^{93} + 32 q^{94} + 6 q^{95} + 20 q^{96} - 28 q^{97} + 24 q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.916185 1.58688i −0.647841 1.12209i −0.983638 0.180159i \(-0.942339\pi\)
0.335797 0.941934i \(-0.390994\pi\)
\(3\) −0.426879 + 0.739375i −0.246458 + 0.426879i −0.962541 0.271137i \(-0.912600\pi\)
0.716082 + 0.698016i \(0.245934\pi\)
\(4\) −0.678791 + 1.17570i −0.339395 + 0.587850i
\(5\) −1.31278 2.27379i −0.587091 1.01687i −0.994611 0.103676i \(-0.966940\pi\)
0.407520 0.913196i \(-0.366394\pi\)
\(6\) 1.56440 0.638663
\(7\) 0 0
\(8\) −1.17715 −0.416185
\(9\) 1.13555 + 1.96683i 0.378516 + 0.655610i
\(10\) −2.40549 + 4.16643i −0.760683 + 1.31754i
\(11\) −1.63234 + 2.82730i −0.492170 + 0.852464i −0.999959 0.00901745i \(-0.997130\pi\)
0.507789 + 0.861481i \(0.330463\pi\)
\(12\) −0.579522 1.00376i −0.167294 0.289761i
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 2.24158 0.578775
\(16\) 2.43607 + 4.21939i 0.609017 + 1.05485i
\(17\) −2.26511 + 3.92328i −0.549369 + 0.951535i 0.448949 + 0.893557i \(0.351798\pi\)
−0.998318 + 0.0579773i \(0.981535\pi\)
\(18\) 2.08075 3.60396i 0.490437 0.849461i
\(19\) −2.03308 3.52139i −0.466420 0.807863i 0.532845 0.846213i \(-0.321123\pi\)
−0.999264 + 0.0383505i \(0.987790\pi\)
\(20\) 3.56440 0.797024
\(21\) 0 0
\(22\) 5.98212 1.27539
\(23\) 2.26633 + 3.92540i 0.472562 + 0.818502i 0.999507 0.0313975i \(-0.00999579\pi\)
−0.526945 + 0.849900i \(0.676662\pi\)
\(24\) 0.502500 0.870355i 0.102572 0.177661i
\(25\) −0.946761 + 1.63984i −0.189352 + 0.327968i
\(26\) −0.916185 1.58688i −0.179679 0.311213i
\(27\) −4.50024 −0.866071
\(28\) 0 0
\(29\) −1.42268 −0.264184 −0.132092 0.991237i \(-0.542169\pi\)
−0.132092 + 0.991237i \(0.542169\pi\)
\(30\) −2.05371 3.55712i −0.374954 0.649439i
\(31\) 1.40164 2.42771i 0.251742 0.436030i −0.712264 0.701912i \(-0.752330\pi\)
0.964005 + 0.265882i \(0.0856633\pi\)
\(32\) 3.28663 5.69261i 0.580999 1.00632i
\(33\) −1.39363 2.41383i −0.242599 0.420194i
\(34\) 8.30102 1.42361
\(35\) 0 0
\(36\) −3.08320 −0.513867
\(37\) 5.02517 + 8.70385i 0.826133 + 1.43090i 0.901050 + 0.433715i \(0.142797\pi\)
−0.0749173 + 0.997190i \(0.523869\pi\)
\(38\) −3.72535 + 6.45249i −0.604331 + 1.04673i
\(39\) −0.426879 + 0.739375i −0.0683553 + 0.118395i
\(40\) 1.54533 + 2.67660i 0.244339 + 0.423207i
\(41\) −2.84271 −0.443956 −0.221978 0.975052i \(-0.571251\pi\)
−0.221978 + 0.975052i \(0.571251\pi\)
\(42\) 0 0
\(43\) 9.72632 1.48325 0.741625 0.670815i \(-0.234056\pi\)
0.741625 + 0.670815i \(0.234056\pi\)
\(44\) −2.21604 3.83829i −0.334081 0.578644i
\(45\) 2.98144 5.16401i 0.444447 0.769805i
\(46\) 4.15276 7.19278i 0.612290 1.06052i
\(47\) 4.72478 + 8.18356i 0.689180 + 1.19369i 0.972103 + 0.234552i \(0.0753624\pi\)
−0.282923 + 0.959142i \(0.591304\pi\)
\(48\) −4.15962 −0.600390
\(49\) 0 0
\(50\) 3.46963 0.490680
\(51\) −1.93385 3.34953i −0.270793 0.469028i
\(52\) −0.678791 + 1.17570i −0.0941313 + 0.163040i
\(53\) −2.63219 + 4.55909i −0.361559 + 0.626239i −0.988218 0.153055i \(-0.951089\pi\)
0.626658 + 0.779294i \(0.284422\pi\)
\(54\) 4.12305 + 7.14134i 0.561076 + 0.971813i
\(55\) 8.57161 1.15580
\(56\) 0 0
\(57\) 3.47151 0.459812
\(58\) 1.30344 + 2.25762i 0.171149 + 0.296440i
\(59\) 1.28395 2.22387i 0.167156 0.289523i −0.770263 0.637727i \(-0.779875\pi\)
0.937419 + 0.348204i \(0.113208\pi\)
\(60\) −1.52157 + 2.63543i −0.196433 + 0.340233i
\(61\) 5.59149 + 9.68475i 0.715917 + 1.24000i 0.962605 + 0.270910i \(0.0873245\pi\)
−0.246688 + 0.969095i \(0.579342\pi\)
\(62\) −5.13664 −0.652354
\(63\) 0 0
\(64\) −2.30037 −0.287546
\(65\) −1.31278 2.27379i −0.162830 0.282030i
\(66\) −2.55364 + 4.42303i −0.314331 + 0.544438i
\(67\) 0.990861 1.71622i 0.121053 0.209670i −0.799130 0.601158i \(-0.794706\pi\)
0.920183 + 0.391488i \(0.128040\pi\)
\(68\) −3.07506 5.32617i −0.372906 0.645893i
\(69\) −3.86979 −0.465868
\(70\) 0 0
\(71\) −11.7544 −1.39499 −0.697495 0.716590i \(-0.745702\pi\)
−0.697495 + 0.716590i \(0.745702\pi\)
\(72\) −1.33671 2.31525i −0.157533 0.272855i
\(73\) −6.06956 + 10.5128i −0.710388 + 1.23043i 0.254323 + 0.967119i \(0.418147\pi\)
−0.964711 + 0.263309i \(0.915186\pi\)
\(74\) 9.20797 15.9487i 1.07041 1.85400i
\(75\) −0.808304 1.40002i −0.0933350 0.161661i
\(76\) 5.52013 0.633202
\(77\) 0 0
\(78\) 1.56440 0.177133
\(79\) −5.95445 10.3134i −0.669928 1.16035i −0.977924 0.208961i \(-0.932992\pi\)
0.307996 0.951388i \(-0.400342\pi\)
\(80\) 6.39602 11.0782i 0.715097 1.23858i
\(81\) −1.48559 + 2.57312i −0.165066 + 0.285902i
\(82\) 2.60444 + 4.51103i 0.287613 + 0.498160i
\(83\) 13.2233 1.45145 0.725723 0.687987i \(-0.241505\pi\)
0.725723 + 0.687987i \(0.241505\pi\)
\(84\) 0 0
\(85\) 11.8943 1.29012
\(86\) −8.91111 15.4345i −0.960909 1.66434i
\(87\) 0.607310 1.05189i 0.0651105 0.112775i
\(88\) 1.92151 3.32816i 0.204834 0.354783i
\(89\) −5.33328 9.23751i −0.565326 0.979174i −0.997019 0.0771532i \(-0.975417\pi\)
0.431693 0.902021i \(-0.357916\pi\)
\(90\) −10.9262 −1.15172
\(91\) 0 0
\(92\) −6.15345 −0.641542
\(93\) 1.19666 + 2.07268i 0.124088 + 0.214926i
\(94\) 8.65755 14.9953i 0.892958 1.54665i
\(95\) −5.33795 + 9.24560i −0.547662 + 0.948578i
\(96\) 2.80598 + 4.86011i 0.286384 + 0.496032i
\(97\) −13.7422 −1.39531 −0.697655 0.716433i \(-0.745773\pi\)
−0.697655 + 0.716433i \(0.745773\pi\)
\(98\) 0 0
\(99\) −7.41443 −0.745178
\(100\) −1.28531 2.22621i −0.128531 0.222621i
\(101\) −2.94729 + 5.10486i −0.293266 + 0.507952i −0.974580 0.224039i \(-0.928076\pi\)
0.681314 + 0.731991i \(0.261409\pi\)
\(102\) −3.54353 + 6.13757i −0.350862 + 0.607710i
\(103\) −1.39368 2.41393i −0.137324 0.237852i 0.789159 0.614189i \(-0.210517\pi\)
−0.926483 + 0.376337i \(0.877183\pi\)
\(104\) −1.17715 −0.115429
\(105\) 0 0
\(106\) 9.64630 0.936932
\(107\) 8.83236 + 15.2981i 0.853856 + 1.47892i 0.877702 + 0.479207i \(0.159076\pi\)
−0.0238454 + 0.999716i \(0.507591\pi\)
\(108\) 3.05472 5.29093i 0.293941 0.509120i
\(109\) 4.78225 8.28310i 0.458057 0.793377i −0.540802 0.841150i \(-0.681879\pi\)
0.998858 + 0.0477730i \(0.0152124\pi\)
\(110\) −7.85318 13.6021i −0.748771 1.29691i
\(111\) −8.58055 −0.814430
\(112\) 0 0
\(113\) −17.6017 −1.65583 −0.827916 0.560852i \(-0.810474\pi\)
−0.827916 + 0.560852i \(0.810474\pi\)
\(114\) −3.18054 5.50886i −0.297885 0.515952i
\(115\) 5.95037 10.3063i 0.554875 0.961071i
\(116\) 0.965699 1.67264i 0.0896629 0.155301i
\(117\) 1.13555 + 1.96683i 0.104982 + 0.181833i
\(118\) −4.70535 −0.433163
\(119\) 0 0
\(120\) −2.63868 −0.240877
\(121\) 0.170904 + 0.296015i 0.0155367 + 0.0269104i
\(122\) 10.2457 17.7460i 0.927600 1.60665i
\(123\) 1.21349 2.10183i 0.109417 0.189515i
\(124\) 1.90284 + 3.29581i 0.170880 + 0.295973i
\(125\) −8.15622 −0.729514
\(126\) 0 0
\(127\) −1.59482 −0.141517 −0.0707586 0.997493i \(-0.522542\pi\)
−0.0707586 + 0.997493i \(0.522542\pi\)
\(128\) −4.46569 7.73480i −0.394715 0.683667i
\(129\) −4.15196 + 7.19140i −0.365559 + 0.633167i
\(130\) −2.40549 + 4.16643i −0.210976 + 0.365420i
\(131\) −2.15140 3.72633i −0.187968 0.325571i 0.756604 0.653873i \(-0.226857\pi\)
−0.944573 + 0.328302i \(0.893524\pi\)
\(132\) 3.78392 0.329348
\(133\) 0 0
\(134\) −3.63125 −0.313692
\(135\) 5.90781 + 10.2326i 0.508463 + 0.880684i
\(136\) 2.66637 4.61828i 0.228639 0.396015i
\(137\) −4.91117 + 8.50640i −0.419590 + 0.726751i −0.995898 0.0904816i \(-0.971159\pi\)
0.576308 + 0.817232i \(0.304493\pi\)
\(138\) 3.54545 + 6.14089i 0.301808 + 0.522747i
\(139\) 10.0811 0.855070 0.427535 0.903999i \(-0.359382\pi\)
0.427535 + 0.903999i \(0.359382\pi\)
\(140\) 0 0
\(141\) −8.06763 −0.679417
\(142\) 10.7692 + 18.6528i 0.903731 + 1.56531i
\(143\) −1.63234 + 2.82730i −0.136503 + 0.236431i
\(144\) −5.53255 + 9.58266i −0.461046 + 0.798555i
\(145\) 1.86766 + 3.23487i 0.155100 + 0.268642i
\(146\) 22.2434 1.84087
\(147\) 0 0
\(148\) −13.6442 −1.12154
\(149\) 6.90619 + 11.9619i 0.565777 + 0.979955i 0.996977 + 0.0776983i \(0.0247571\pi\)
−0.431200 + 0.902256i \(0.641910\pi\)
\(150\) −1.48111 + 2.56536i −0.120932 + 0.209461i
\(151\) −10.6062 + 18.3704i −0.863117 + 1.49496i 0.00578805 + 0.999983i \(0.498158\pi\)
−0.868905 + 0.494979i \(0.835176\pi\)
\(152\) 2.39323 + 4.14520i 0.194117 + 0.336220i
\(153\) −10.2886 −0.831780
\(154\) 0 0
\(155\) −7.36015 −0.591182
\(156\) −0.579522 1.00376i −0.0463989 0.0803653i
\(157\) −11.7578 + 20.3650i −0.938372 + 1.62531i −0.169864 + 0.985468i \(0.554333\pi\)
−0.768508 + 0.639840i \(0.779000\pi\)
\(158\) −10.9108 + 18.8980i −0.868013 + 1.50344i
\(159\) −2.24725 3.89236i −0.178219 0.308684i
\(160\) −17.2584 −1.36440
\(161\) 0 0
\(162\) 5.44431 0.427745
\(163\) −3.91531 6.78151i −0.306671 0.531169i 0.670961 0.741492i \(-0.265882\pi\)
−0.977632 + 0.210323i \(0.932548\pi\)
\(164\) 1.92960 3.34217i 0.150677 0.260979i
\(165\) −3.65904 + 6.33764i −0.284856 + 0.493384i
\(166\) −12.1150 20.9838i −0.940306 1.62866i
\(167\) 12.7116 0.983654 0.491827 0.870693i \(-0.336329\pi\)
0.491827 + 0.870693i \(0.336329\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −10.8974 18.8748i −0.835791 1.44763i
\(171\) 4.61732 7.99743i 0.353095 0.611578i
\(172\) −6.60213 + 11.4352i −0.503408 + 0.871928i
\(173\) −2.62454 4.54583i −0.199540 0.345613i 0.748840 0.662751i \(-0.230611\pi\)
−0.948379 + 0.317138i \(0.897278\pi\)
\(174\) −2.22563 −0.168725
\(175\) 0 0
\(176\) −15.9060 −1.19896
\(177\) 1.09618 + 1.89865i 0.0823942 + 0.142711i
\(178\) −9.77254 + 16.9265i −0.732483 + 1.26870i
\(179\) 5.26275 9.11536i 0.393357 0.681314i −0.599533 0.800350i \(-0.704647\pi\)
0.992890 + 0.119036i \(0.0379804\pi\)
\(180\) 4.04755 + 7.01056i 0.301687 + 0.522537i
\(181\) −18.8177 −1.39871 −0.699356 0.714774i \(-0.746530\pi\)
−0.699356 + 0.714774i \(0.746530\pi\)
\(182\) 0 0
\(183\) −9.54755 −0.705775
\(184\) −2.66781 4.62078i −0.196673 0.340648i
\(185\) 13.1938 22.8524i 0.970031 1.68014i
\(186\) 2.19272 3.79791i 0.160778 0.278476i
\(187\) −7.39486 12.8083i −0.540766 0.936634i
\(188\) −12.8285 −0.935618
\(189\) 0 0
\(190\) 19.5622 1.41919
\(191\) −7.45722 12.9163i −0.539585 0.934589i −0.998926 0.0463292i \(-0.985248\pi\)
0.459341 0.888260i \(-0.348086\pi\)
\(192\) 0.981980 1.70084i 0.0708683 0.122747i
\(193\) 0.0265678 0.0460168i 0.00191239 0.00331236i −0.865068 0.501655i \(-0.832725\pi\)
0.866980 + 0.498343i \(0.166058\pi\)
\(194\) 12.5904 + 21.8072i 0.903939 + 1.56567i
\(195\) 2.24158 0.160523
\(196\) 0 0
\(197\) 10.0478 0.715875 0.357938 0.933745i \(-0.383480\pi\)
0.357938 + 0.933745i \(0.383480\pi\)
\(198\) 6.79299 + 11.7658i 0.482757 + 0.836159i
\(199\) −11.6457 + 20.1710i −0.825543 + 1.42988i 0.0759612 + 0.997111i \(0.475798\pi\)
−0.901504 + 0.432771i \(0.857536\pi\)
\(200\) 1.11448 1.93034i 0.0788056 0.136495i
\(201\) 0.845955 + 1.46524i 0.0596691 + 0.103350i
\(202\) 10.8011 0.759959
\(203\) 0 0
\(204\) 5.25072 0.367624
\(205\) 3.73184 + 6.46373i 0.260643 + 0.451446i
\(206\) −2.55374 + 4.42321i −0.177928 + 0.308180i
\(207\) −5.14706 + 8.91497i −0.357745 + 0.619633i
\(208\) 2.43607 + 4.21939i 0.168911 + 0.292562i
\(209\) 13.2747 0.918232
\(210\) 0 0
\(211\) −2.47457 −0.170356 −0.0851780 0.996366i \(-0.527146\pi\)
−0.0851780 + 0.996366i \(0.527146\pi\)
\(212\) −3.57342 6.18934i −0.245423 0.425085i
\(213\) 5.01770 8.69091i 0.343807 0.595491i
\(214\) 16.1842 28.0318i 1.10633 1.91621i
\(215\) −12.7685 22.1156i −0.870803 1.50827i
\(216\) 5.29745 0.360446
\(217\) 0 0
\(218\) −17.5257 −1.18699
\(219\) −5.18193 8.97537i −0.350162 0.606499i
\(220\) −5.81833 + 10.0776i −0.392272 + 0.679434i
\(221\) −2.26511 + 3.92328i −0.152367 + 0.263908i
\(222\) 7.86137 + 13.6163i 0.527621 + 0.913866i
\(223\) 6.17027 0.413192 0.206596 0.978426i \(-0.433761\pi\)
0.206596 + 0.978426i \(0.433761\pi\)
\(224\) 0 0
\(225\) −4.30038 −0.286692
\(226\) 16.1264 + 27.9318i 1.07272 + 1.85800i
\(227\) −5.79694 + 10.0406i −0.384757 + 0.666418i −0.991735 0.128300i \(-0.959048\pi\)
0.606979 + 0.794718i \(0.292381\pi\)
\(228\) −2.35643 + 4.08145i −0.156058 + 0.270301i
\(229\) 5.11909 + 8.86653i 0.338279 + 0.585917i 0.984109 0.177565i \(-0.0568219\pi\)
−0.645830 + 0.763481i \(0.723489\pi\)
\(230\) −21.8065 −1.43788
\(231\) 0 0
\(232\) 1.67470 0.109950
\(233\) −10.7411 18.6041i −0.703673 1.21880i −0.967168 0.254137i \(-0.918208\pi\)
0.263495 0.964661i \(-0.415125\pi\)
\(234\) 2.08075 3.60396i 0.136023 0.235598i
\(235\) 12.4052 21.4864i 0.809223 1.40162i
\(236\) 1.74307 + 3.01909i 0.113464 + 0.196526i
\(237\) 10.1673 0.660437
\(238\) 0 0
\(239\) 1.08591 0.0702414 0.0351207 0.999383i \(-0.488818\pi\)
0.0351207 + 0.999383i \(0.488818\pi\)
\(240\) 5.46065 + 9.45812i 0.352483 + 0.610519i
\(241\) 9.99149 17.3058i 0.643608 1.11476i −0.341013 0.940059i \(-0.610770\pi\)
0.984621 0.174704i \(-0.0558967\pi\)
\(242\) 0.313160 0.542408i 0.0201307 0.0348673i
\(243\) −8.01869 13.8888i −0.514399 0.890966i
\(244\) −15.1818 −0.971915
\(245\) 0 0
\(246\) −4.44713 −0.283538
\(247\) −2.03308 3.52139i −0.129362 0.224061i
\(248\) −1.64994 + 2.85778i −0.104771 + 0.181469i
\(249\) −5.64475 + 9.77699i −0.357721 + 0.619592i
\(250\) 7.47261 + 12.9429i 0.472609 + 0.818583i
\(251\) 20.1497 1.27184 0.635920 0.771755i \(-0.280621\pi\)
0.635920 + 0.771755i \(0.280621\pi\)
\(252\) 0 0
\(253\) −14.7977 −0.930325
\(254\) 1.46115 + 2.53078i 0.0916806 + 0.158795i
\(255\) −5.07742 + 8.79436i −0.317961 + 0.550724i
\(256\) −10.4832 + 18.1574i −0.655198 + 1.13484i
\(257\) 7.50869 + 13.0054i 0.468379 + 0.811257i 0.999347 0.0361353i \(-0.0115047\pi\)
−0.530968 + 0.847392i \(0.678171\pi\)
\(258\) 15.2158 0.947297
\(259\) 0 0
\(260\) 3.56440 0.221055
\(261\) −1.61552 2.79816i −0.0999981 0.173202i
\(262\) −3.94216 + 6.82801i −0.243547 + 0.421836i
\(263\) 10.5831 18.3305i 0.652582 1.13031i −0.329912 0.944012i \(-0.607019\pi\)
0.982494 0.186294i \(-0.0596477\pi\)
\(264\) 1.64051 + 2.84144i 0.100966 + 0.174879i
\(265\) 13.8219 0.849074
\(266\) 0 0
\(267\) 9.10665 0.557318
\(268\) 1.34517 + 2.32991i 0.0821696 + 0.142322i
\(269\) 2.05240 3.55486i 0.125137 0.216744i −0.796650 0.604442i \(-0.793396\pi\)
0.921786 + 0.387698i \(0.126730\pi\)
\(270\) 10.8253 18.7499i 0.658806 1.14109i
\(271\) −1.71622 2.97258i −0.104253 0.180571i 0.809180 0.587561i \(-0.199912\pi\)
−0.913433 + 0.406990i \(0.866578\pi\)
\(272\) −22.0718 −1.33830
\(273\) 0 0
\(274\) 17.9982 1.08731
\(275\) −3.09088 5.35356i −0.186387 0.322832i
\(276\) 2.62678 4.54971i 0.158113 0.273860i
\(277\) 0.180506 0.312645i 0.0108455 0.0187850i −0.860552 0.509363i \(-0.829881\pi\)
0.871397 + 0.490578i \(0.163214\pi\)
\(278\) −9.23618 15.9975i −0.553949 0.959468i
\(279\) 6.36652 0.381154
\(280\) 0 0
\(281\) 18.5213 1.10489 0.552445 0.833550i \(-0.313695\pi\)
0.552445 + 0.833550i \(0.313695\pi\)
\(282\) 7.39144 + 12.8024i 0.440154 + 0.762369i
\(283\) 0.805788 1.39567i 0.0478991 0.0829637i −0.841082 0.540908i \(-0.818081\pi\)
0.888981 + 0.457944i \(0.151414\pi\)
\(284\) 7.97877 13.8196i 0.473453 0.820045i
\(285\) −4.55731 7.89349i −0.269952 0.467570i
\(286\) 5.98212 0.353730
\(287\) 0 0
\(288\) 14.9285 0.879671
\(289\) −1.76140 3.05084i −0.103612 0.179461i
\(290\) 3.42224 5.92749i 0.200961 0.348074i
\(291\) 5.86626 10.1607i 0.343886 0.595628i
\(292\) −8.23992 14.2720i −0.482205 0.835203i
\(293\) −4.41671 −0.258027 −0.129013 0.991643i \(-0.541181\pi\)
−0.129013 + 0.991643i \(0.541181\pi\)
\(294\) 0 0
\(295\) −6.74217 −0.392544
\(296\) −5.91538 10.2457i −0.343824 0.595521i
\(297\) 7.34594 12.7235i 0.426255 0.738295i
\(298\) 12.6547 21.9186i 0.733067 1.26971i
\(299\) 2.26633 + 3.92540i 0.131065 + 0.227012i
\(300\) 2.19468 0.126710
\(301\) 0 0
\(302\) 38.8688 2.23665
\(303\) −2.51627 4.35831i −0.144556 0.250378i
\(304\) 9.90542 17.1567i 0.568115 0.984004i
\(305\) 14.6807 25.4278i 0.840617 1.45599i
\(306\) 9.42622 + 16.3267i 0.538861 + 0.933335i
\(307\) −5.78353 −0.330083 −0.165042 0.986287i \(-0.552776\pi\)
−0.165042 + 0.986287i \(0.552776\pi\)
\(308\) 0 0
\(309\) 2.37973 0.135378
\(310\) 6.74326 + 11.6797i 0.382992 + 0.663361i
\(311\) −7.14476 + 12.3751i −0.405142 + 0.701727i −0.994338 0.106264i \(-0.966111\pi\)
0.589196 + 0.807990i \(0.299445\pi\)
\(312\) 0.502500 0.870355i 0.0284485 0.0492742i
\(313\) −1.36862 2.37053i −0.0773592 0.133990i 0.824751 0.565497i \(-0.191315\pi\)
−0.902110 + 0.431507i \(0.857982\pi\)
\(314\) 43.0892 2.43166
\(315\) 0 0
\(316\) 16.1673 0.909481
\(317\) −5.32560 9.22422i −0.299116 0.518084i 0.676818 0.736150i \(-0.263358\pi\)
−0.975934 + 0.218067i \(0.930025\pi\)
\(318\) −4.11780 + 7.13224i −0.230915 + 0.399956i
\(319\) 2.32230 4.02234i 0.130024 0.225208i
\(320\) 3.01987 + 5.23057i 0.168816 + 0.292398i
\(321\) −15.0814 −0.841761
\(322\) 0 0
\(323\) 18.4205 1.02495
\(324\) −2.01681 3.49322i −0.112045 0.194068i
\(325\) −0.946761 + 1.63984i −0.0525169 + 0.0909619i
\(326\) −7.17430 + 12.4262i −0.397347 + 0.688226i
\(327\) 4.08288 + 7.07176i 0.225784 + 0.391069i
\(328\) 3.34629 0.184768
\(329\) 0 0
\(330\) 13.4094 0.738164
\(331\) 1.70813 + 2.95856i 0.0938872 + 0.162617i 0.909144 0.416483i \(-0.136737\pi\)
−0.815256 + 0.579100i \(0.803404\pi\)
\(332\) −8.97586 + 15.5466i −0.492614 + 0.853233i
\(333\) −11.4127 + 19.7673i −0.625410 + 1.08324i
\(334\) −11.6462 20.1718i −0.637251 1.10375i
\(335\) −5.20312 −0.284277
\(336\) 0 0
\(337\) 24.9606 1.35969 0.679844 0.733357i \(-0.262047\pi\)
0.679844 + 0.733357i \(0.262047\pi\)
\(338\) −0.916185 1.58688i −0.0498339 0.0863149i
\(339\) 7.51380 13.0143i 0.408094 0.706839i
\(340\) −8.07374 + 13.9841i −0.437860 + 0.758396i
\(341\) 4.57591 + 7.92572i 0.247800 + 0.429202i
\(342\) −16.9213 −0.914997
\(343\) 0 0
\(344\) −11.4493 −0.617306
\(345\) 5.08017 + 8.79911i 0.273507 + 0.473728i
\(346\) −4.80912 + 8.32964i −0.258540 + 0.447804i
\(347\) 9.59165 16.6132i 0.514907 0.891845i −0.484944 0.874545i \(-0.661160\pi\)
0.999850 0.0172992i \(-0.00550678\pi\)
\(348\) 0.824473 + 1.42803i 0.0441964 + 0.0765504i
\(349\) −3.94421 −0.211129 −0.105564 0.994412i \(-0.533665\pi\)
−0.105564 + 0.994412i \(0.533665\pi\)
\(350\) 0 0
\(351\) −4.50024 −0.240205
\(352\) 10.7298 + 18.5846i 0.571901 + 0.990562i
\(353\) −14.0116 + 24.2688i −0.745762 + 1.29170i 0.204076 + 0.978955i \(0.434581\pi\)
−0.949838 + 0.312743i \(0.898752\pi\)
\(354\) 2.00861 3.47902i 0.106757 0.184908i
\(355\) 15.4309 + 26.7271i 0.818986 + 1.41853i
\(356\) 14.4807 0.767476
\(357\) 0 0
\(358\) −19.2866 −1.01933
\(359\) −16.6116 28.7721i −0.876726 1.51853i −0.854912 0.518773i \(-0.826389\pi\)
−0.0218141 0.999762i \(-0.506944\pi\)
\(360\) −3.50960 + 6.07881i −0.184972 + 0.320382i
\(361\) 1.23320 2.13597i 0.0649054 0.112419i
\(362\) 17.2405 + 29.8615i 0.906142 + 1.56948i
\(363\) −0.291821 −0.0153166
\(364\) 0 0
\(365\) 31.8719 1.66825
\(366\) 8.74733 + 15.1508i 0.457230 + 0.791946i
\(367\) 14.1546 24.5164i 0.738862 1.27975i −0.214146 0.976802i \(-0.568697\pi\)
0.953008 0.302945i \(-0.0979699\pi\)
\(368\) −11.0419 + 19.1251i −0.575597 + 0.996963i
\(369\) −3.22803 5.59112i −0.168045 0.291062i
\(370\) −48.3520 −2.51370
\(371\) 0 0
\(372\) −3.24912 −0.168459
\(373\) 6.47573 + 11.2163i 0.335301 + 0.580758i 0.983543 0.180677i \(-0.0578287\pi\)
−0.648242 + 0.761435i \(0.724495\pi\)
\(374\) −13.5501 + 23.4695i −0.700660 + 1.21358i
\(375\) 3.48171 6.03051i 0.179795 0.311414i
\(376\) −5.56177 9.63327i −0.286827 0.496798i
\(377\) −1.42268 −0.0732716
\(378\) 0 0
\(379\) 0.168981 0.00867995 0.00433997 0.999991i \(-0.498619\pi\)
0.00433997 + 0.999991i \(0.498619\pi\)
\(380\) −7.24670 12.5516i −0.371748 0.643886i
\(381\) 0.680794 1.17917i 0.0348781 0.0604107i
\(382\) −13.6644 + 23.6674i −0.699131 + 1.21093i
\(383\) −5.09665 8.82766i −0.260427 0.451073i 0.705929 0.708283i \(-0.250530\pi\)
−0.966355 + 0.257210i \(0.917197\pi\)
\(384\) 7.62523 0.389124
\(385\) 0 0
\(386\) −0.0973641 −0.00495570
\(387\) 11.0447 + 19.1300i 0.561434 + 0.972432i
\(388\) 9.32809 16.1567i 0.473562 0.820233i
\(389\) 14.3332 24.8259i 0.726723 1.25872i −0.231537 0.972826i \(-0.574376\pi\)
0.958261 0.285896i \(-0.0922911\pi\)
\(390\) −2.05371 3.55712i −0.103993 0.180122i
\(391\) −20.5339 −1.03844
\(392\) 0 0
\(393\) 3.67354 0.185306
\(394\) −9.20564 15.9446i −0.463773 0.803279i
\(395\) −15.6337 + 27.0784i −0.786617 + 1.36246i
\(396\) 5.03284 8.71714i 0.252910 0.438053i
\(397\) 14.3206 + 24.8039i 0.718728 + 1.24487i 0.961504 + 0.274791i \(0.0886086\pi\)
−0.242776 + 0.970082i \(0.578058\pi\)
\(398\) 42.6785 2.13928
\(399\) 0 0
\(400\) −9.22550 −0.461275
\(401\) 7.14814 + 12.3809i 0.356961 + 0.618275i 0.987452 0.157922i \(-0.0504795\pi\)
−0.630490 + 0.776197i \(0.717146\pi\)
\(402\) 1.55010 2.68486i 0.0773121 0.133909i
\(403\) 1.40164 2.42771i 0.0698206 0.120933i
\(404\) −4.00118 6.93026i −0.199066 0.344793i
\(405\) 7.80100 0.387635
\(406\) 0 0
\(407\) −32.8112 −1.62639
\(408\) 2.27643 + 3.94289i 0.112700 + 0.195202i
\(409\) −12.8494 + 22.2558i −0.635362 + 1.10048i 0.351077 + 0.936347i \(0.385816\pi\)
−0.986438 + 0.164132i \(0.947518\pi\)
\(410\) 6.83810 11.8439i 0.337710 0.584931i
\(411\) −4.19295 7.26240i −0.206823 0.358228i
\(412\) 3.78408 0.186428
\(413\) 0 0
\(414\) 18.8626 0.927048
\(415\) −17.3592 30.0671i −0.852132 1.47594i
\(416\) 3.28663 5.69261i 0.161140 0.279103i
\(417\) −4.30342 + 7.45374i −0.210739 + 0.365011i
\(418\) −12.1621 21.0654i −0.594868 1.03034i
\(419\) 18.7999 0.918433 0.459216 0.888324i \(-0.348130\pi\)
0.459216 + 0.888324i \(0.348130\pi\)
\(420\) 0 0
\(421\) −18.0283 −0.878645 −0.439322 0.898329i \(-0.644781\pi\)
−0.439322 + 0.898329i \(0.644781\pi\)
\(422\) 2.26716 + 3.92684i 0.110364 + 0.191155i
\(423\) −10.7304 + 18.5857i −0.521732 + 0.903666i
\(424\) 3.09848 5.36673i 0.150476 0.260632i
\(425\) −4.28903 7.42882i −0.208048 0.360350i
\(426\) −18.3886 −0.890929
\(427\) 0 0
\(428\) −23.9813 −1.15918
\(429\) −1.39363 2.41383i −0.0672849 0.116541i
\(430\) −23.3966 + 40.5240i −1.12828 + 1.95424i
\(431\) −10.2791 + 17.8040i −0.495128 + 0.857587i −0.999984 0.00561653i \(-0.998212\pi\)
0.504856 + 0.863203i \(0.331546\pi\)
\(432\) −10.9629 18.9883i −0.527452 0.913574i
\(433\) 18.9235 0.909404 0.454702 0.890644i \(-0.349746\pi\)
0.454702 + 0.890644i \(0.349746\pi\)
\(434\) 0 0
\(435\) −3.18905 −0.152903
\(436\) 6.49229 + 11.2450i 0.310924 + 0.538537i
\(437\) 9.21524 15.9613i 0.440825 0.763531i
\(438\) −9.49522 + 16.4462i −0.453699 + 0.785830i
\(439\) 7.32750 + 12.6916i 0.349723 + 0.605737i 0.986200 0.165558i \(-0.0529425\pi\)
−0.636477 + 0.771295i \(0.719609\pi\)
\(440\) −10.0901 −0.481025
\(441\) 0 0
\(442\) 8.30102 0.394839
\(443\) 5.97962 + 10.3570i 0.284100 + 0.492076i 0.972391 0.233359i \(-0.0749718\pi\)
−0.688290 + 0.725435i \(0.741638\pi\)
\(444\) 5.82440 10.0882i 0.276414 0.478763i
\(445\) −14.0028 + 24.2536i −0.663796 + 1.14973i
\(446\) −5.65311 9.79148i −0.267683 0.463640i
\(447\) −11.7924 −0.557762
\(448\) 0 0
\(449\) −2.32245 −0.109603 −0.0548015 0.998497i \(-0.517453\pi\)
−0.0548015 + 0.998497i \(0.517453\pi\)
\(450\) 3.93994 + 6.82418i 0.185731 + 0.321695i
\(451\) 4.64027 8.03719i 0.218502 0.378457i
\(452\) 11.9479 20.6944i 0.561981 0.973380i
\(453\) −9.05508 15.6839i −0.425445 0.736892i
\(454\) 21.2443 0.997044
\(455\) 0 0
\(456\) −4.08648 −0.191367
\(457\) 9.29023 + 16.0912i 0.434579 + 0.752712i 0.997261 0.0739607i \(-0.0235639\pi\)
−0.562682 + 0.826673i \(0.690231\pi\)
\(458\) 9.38007 16.2468i 0.438302 0.759161i
\(459\) 10.1935 17.6557i 0.475793 0.824097i
\(460\) 8.07810 + 13.9917i 0.376644 + 0.652366i
\(461\) 27.8926 1.29909 0.649543 0.760325i \(-0.274960\pi\)
0.649543 + 0.760325i \(0.274960\pi\)
\(462\) 0 0
\(463\) −3.66462 −0.170309 −0.0851547 0.996368i \(-0.527138\pi\)
−0.0851547 + 0.996368i \(0.527138\pi\)
\(464\) −3.46574 6.00283i −0.160893 0.278674i
\(465\) 3.14189 5.44192i 0.145702 0.252363i
\(466\) −19.6817 + 34.0897i −0.911737 + 1.57917i
\(467\) −19.3766 33.5612i −0.896641 1.55303i −0.831760 0.555136i \(-0.812666\pi\)
−0.0648815 0.997893i \(-0.520667\pi\)
\(468\) −3.08320 −0.142521
\(469\) 0 0
\(470\) −45.4617 −2.09699
\(471\) −10.0383 17.3868i −0.462539 0.801142i
\(472\) −1.51140 + 2.61783i −0.0695680 + 0.120495i
\(473\) −15.8767 + 27.4992i −0.730011 + 1.26442i
\(474\) −9.31513 16.1343i −0.427858 0.741072i
\(475\) 7.69935 0.353270
\(476\) 0 0
\(477\) −11.9559 −0.547425
\(478\) −0.994891 1.72320i −0.0455052 0.0788174i
\(479\) 3.01715 5.22585i 0.137857 0.238775i −0.788828 0.614614i \(-0.789312\pi\)
0.926685 + 0.375838i \(0.122645\pi\)
\(480\) 7.36726 12.7605i 0.336268 0.582433i
\(481\) 5.02517 + 8.70385i 0.229128 + 0.396861i
\(482\) −36.6162 −1.66782
\(483\) 0 0
\(484\) −0.464032 −0.0210924
\(485\) 18.0405 + 31.2470i 0.819175 + 1.41885i
\(486\) −14.6932 + 25.4494i −0.666498 + 1.15441i
\(487\) 1.90125 3.29305i 0.0861537 0.149223i −0.819729 0.572752i \(-0.805876\pi\)
0.905882 + 0.423530i \(0.139209\pi\)
\(488\) −6.58202 11.4004i −0.297954 0.516072i
\(489\) 6.68545 0.302326
\(490\) 0 0
\(491\) −0.381464 −0.0172152 −0.00860761 0.999963i \(-0.502740\pi\)
−0.00860761 + 0.999963i \(0.502740\pi\)
\(492\) 1.64741 + 2.85340i 0.0742710 + 0.128641i
\(493\) 3.22251 5.58156i 0.145135 0.251381i
\(494\) −3.72535 + 6.45249i −0.167611 + 0.290311i
\(495\) 9.73348 + 16.8589i 0.437488 + 0.757751i
\(496\) 13.6580 0.613260
\(497\) 0 0
\(498\) 20.6865 0.926986
\(499\) −17.2870 29.9419i −0.773871 1.34038i −0.935427 0.353520i \(-0.884985\pi\)
0.161556 0.986864i \(-0.448349\pi\)
\(500\) 5.53636 9.58926i 0.247594 0.428845i
\(501\) −5.42632 + 9.39866i −0.242430 + 0.419901i
\(502\) −18.4609 31.9752i −0.823950 1.42712i
\(503\) −2.41090 −0.107497 −0.0537485 0.998555i \(-0.517117\pi\)
−0.0537485 + 0.998555i \(0.517117\pi\)
\(504\) 0 0
\(505\) 15.4765 0.688696
\(506\) 13.5575 + 23.4822i 0.602702 + 1.04391i
\(507\) −0.426879 + 0.739375i −0.0189583 + 0.0328368i
\(508\) 1.08255 1.87503i 0.0480303 0.0831908i
\(509\) 10.9577 + 18.9792i 0.485690 + 0.841239i 0.999865 0.0164459i \(-0.00523512\pi\)
−0.514175 + 0.857685i \(0.671902\pi\)
\(510\) 18.6074 0.823951
\(511\) 0 0
\(512\) 20.5553 0.908426
\(513\) 9.14933 + 15.8471i 0.403953 + 0.699667i
\(514\) 13.7587 23.8308i 0.606871 1.05113i
\(515\) −3.65919 + 6.33790i −0.161243 + 0.279281i
\(516\) −5.63662 9.76291i −0.248138 0.429788i
\(517\) −30.8499 −1.35678
\(518\) 0 0
\(519\) 4.48143 0.196713
\(520\) 1.54533 + 2.67660i 0.0677674 + 0.117377i
\(521\) 15.0725 26.1063i 0.660338 1.14374i −0.320188 0.947354i \(-0.603746\pi\)
0.980527 0.196386i \(-0.0629205\pi\)
\(522\) −2.96023 + 5.12727i −0.129566 + 0.224414i
\(523\) 9.04966 + 15.6745i 0.395714 + 0.685397i 0.993192 0.116489i \(-0.0371638\pi\)
−0.597478 + 0.801885i \(0.703830\pi\)
\(524\) 5.84139 0.255182
\(525\) 0 0
\(526\) −38.7843 −1.69108
\(527\) 6.34972 + 10.9980i 0.276598 + 0.479082i
\(528\) 6.78993 11.7605i 0.295494 0.511811i
\(529\) 1.22750 2.12609i 0.0533695 0.0924387i
\(530\) −12.6634 21.9337i −0.550065 0.952740i
\(531\) 5.83197 0.253086
\(532\) 0 0
\(533\) −2.84271 −0.123131
\(534\) −8.34338 14.4512i −0.361053 0.625363i
\(535\) 23.1898 40.1659i 1.00258 1.73653i
\(536\) −1.16639 + 2.02025i −0.0503805 + 0.0872615i
\(537\) 4.49312 + 7.78230i 0.193892 + 0.335831i
\(538\) −7.52151 −0.324275
\(539\) 0 0
\(540\) −16.0406 −0.690280
\(541\) −2.04445 3.54109i −0.0878977 0.152243i 0.818725 0.574186i \(-0.194682\pi\)
−0.906622 + 0.421943i \(0.861348\pi\)
\(542\) −3.14475 + 5.44686i −0.135079 + 0.233963i
\(543\) 8.03289 13.9134i 0.344724 0.597080i
\(544\) 14.8891 + 25.7887i 0.638366 + 1.10568i
\(545\) −25.1121 −1.07568
\(546\) 0 0
\(547\) −40.4264 −1.72851 −0.864255 0.503055i \(-0.832209\pi\)
−0.864255 + 0.503055i \(0.832209\pi\)
\(548\) −6.66731 11.5481i −0.284814 0.493311i
\(549\) −12.6988 + 21.9950i −0.541973 + 0.938724i
\(550\) −5.66364 + 9.80971i −0.241498 + 0.418287i
\(551\) 2.89241 + 5.00980i 0.123221 + 0.213425i
\(552\) 4.55532 0.193887
\(553\) 0 0
\(554\) −0.661507 −0.0281047
\(555\) 11.2643 + 19.5104i 0.478145 + 0.828171i
\(556\) −6.84297 + 11.8524i −0.290207 + 0.502653i
\(557\) −9.88450 + 17.1205i −0.418820 + 0.725417i −0.995821 0.0913260i \(-0.970889\pi\)
0.577001 + 0.816743i \(0.304223\pi\)
\(558\) −5.83291 10.1029i −0.246927 0.427690i
\(559\) 9.72632 0.411379
\(560\) 0 0
\(561\) 12.6268 0.533105
\(562\) −16.9690 29.3911i −0.715792 1.23979i
\(563\) −4.11196 + 7.12212i −0.173298 + 0.300162i −0.939571 0.342354i \(-0.888776\pi\)
0.766273 + 0.642515i \(0.222109\pi\)
\(564\) 5.47623 9.48511i 0.230591 0.399395i
\(565\) 23.1071 + 40.0227i 0.972124 + 1.68377i
\(566\) −2.95300 −0.124124
\(567\) 0 0
\(568\) 13.8367 0.580574
\(569\) −7.28849 12.6240i −0.305550 0.529227i 0.671834 0.740702i \(-0.265507\pi\)
−0.977384 + 0.211474i \(0.932174\pi\)
\(570\) −8.35068 + 14.4638i −0.349772 + 0.605822i
\(571\) 1.29411 2.24146i 0.0541568 0.0938023i −0.837676 0.546167i \(-0.816086\pi\)
0.891833 + 0.452365i \(0.149420\pi\)
\(572\) −2.21604 3.83829i −0.0926573 0.160487i
\(573\) 12.7333 0.531942
\(574\) 0 0
\(575\) −8.58269 −0.357923
\(576\) −2.61219 4.52444i −0.108841 0.188518i
\(577\) 11.9468 20.6925i 0.497353 0.861441i −0.502642 0.864495i \(-0.667639\pi\)
0.999995 + 0.00305340i \(0.000971930\pi\)
\(578\) −3.22754 + 5.59027i −0.134248 + 0.232525i
\(579\) 0.0226825 + 0.0392872i 0.000942651 + 0.00163272i
\(580\) −5.07099 −0.210561
\(581\) 0 0
\(582\) −21.4983 −0.891134
\(583\) −8.59329 14.8840i −0.355898 0.616433i
\(584\) 7.14478 12.3751i 0.295653 0.512086i
\(585\) 2.98144 5.16401i 0.123268 0.213506i
\(586\) 4.04652 + 7.00878i 0.167160 + 0.289530i
\(587\) 28.5759 1.17945 0.589726 0.807604i \(-0.299236\pi\)
0.589726 + 0.807604i \(0.299236\pi\)
\(588\) 0 0
\(589\) −11.3986 −0.469669
\(590\) 6.17707 + 10.6990i 0.254306 + 0.440471i
\(591\) −4.28919 + 7.42909i −0.176434 + 0.305592i
\(592\) −24.4833 + 42.4063i −1.00626 + 1.74289i
\(593\) 9.97874 + 17.2837i 0.409778 + 0.709756i 0.994865 0.101215i \(-0.0322729\pi\)
−0.585087 + 0.810971i \(0.698940\pi\)
\(594\) −26.9210 −1.10458
\(595\) 0 0
\(596\) −18.7514 −0.768088
\(597\) −9.94261 17.2211i −0.406924 0.704813i
\(598\) 4.15276 7.19278i 0.169819 0.294135i
\(599\) −0.588578 + 1.01945i −0.0240486 + 0.0416535i −0.877799 0.479029i \(-0.840989\pi\)
0.853751 + 0.520682i \(0.174322\pi\)
\(600\) 0.951495 + 1.64804i 0.0388446 + 0.0672809i
\(601\) −30.9250 −1.26146 −0.630729 0.776003i \(-0.717244\pi\)
−0.630729 + 0.776003i \(0.717244\pi\)
\(602\) 0 0
\(603\) 4.50069 0.183282
\(604\) −14.3987 24.9393i −0.585876 1.01477i
\(605\) 0.448718 0.777202i 0.0182430 0.0315977i
\(606\) −4.61074 + 7.98603i −0.187298 + 0.324410i
\(607\) −1.20354 2.08460i −0.0488503 0.0846111i 0.840566 0.541709i \(-0.182222\pi\)
−0.889417 + 0.457097i \(0.848889\pi\)
\(608\) −26.7279 −1.08396
\(609\) 0 0
\(610\) −53.8011 −2.17834
\(611\) 4.72478 + 8.18356i 0.191144 + 0.331071i
\(612\) 6.98377 12.0963i 0.282302 0.488962i
\(613\) 13.8871 24.0532i 0.560895 0.971499i −0.436524 0.899693i \(-0.643790\pi\)
0.997419 0.0718060i \(-0.0228762\pi\)
\(614\) 5.29878 + 9.17776i 0.213841 + 0.370384i
\(615\) −6.37216 −0.256950
\(616\) 0 0
\(617\) 26.2125 1.05527 0.527637 0.849470i \(-0.323078\pi\)
0.527637 + 0.849470i \(0.323078\pi\)
\(618\) −2.18028 3.77635i −0.0877036 0.151907i
\(619\) 8.61787 14.9266i 0.346381 0.599950i −0.639222 0.769022i \(-0.720744\pi\)
0.985604 + 0.169072i \(0.0540770\pi\)
\(620\) 4.99600 8.65333i 0.200644 0.347526i
\(621\) −10.1990 17.6652i −0.409273 0.708881i
\(622\) 26.1837 1.04987
\(623\) 0 0
\(624\) −4.15962 −0.166518
\(625\) 15.4411 + 26.7448i 0.617644 + 1.06979i
\(626\) −2.50783 + 4.34368i −0.100233 + 0.173608i
\(627\) −5.66669 + 9.81500i −0.226306 + 0.391973i
\(628\) −15.9621 27.6472i −0.636958 1.10324i
\(629\) −45.5302 −1.81541
\(630\) 0 0
\(631\) 39.2125 1.56103 0.780513 0.625140i \(-0.214958\pi\)
0.780513 + 0.625140i \(0.214958\pi\)
\(632\) 7.00927 + 12.1404i 0.278814 + 0.482920i
\(633\) 1.05634 1.82963i 0.0419857 0.0727214i
\(634\) −9.75848 + 16.9022i −0.387559 + 0.671271i
\(635\) 2.09364 + 3.62629i 0.0830835 + 0.143905i
\(636\) 6.10166 0.241946
\(637\) 0 0
\(638\) −8.51062 −0.336939
\(639\) −13.3477 23.1189i −0.528027 0.914569i
\(640\) −11.7249 + 20.3081i −0.463468 + 0.802749i
\(641\) 11.4368 19.8091i 0.451725 0.782411i −0.546768 0.837284i \(-0.684142\pi\)
0.998493 + 0.0548728i \(0.0174753\pi\)
\(642\) 13.8173 + 23.9323i 0.545327 + 0.944534i
\(643\) −46.7072 −1.84195 −0.920976 0.389620i \(-0.872606\pi\)
−0.920976 + 0.389620i \(0.872606\pi\)
\(644\) 0 0
\(645\) 21.8024 0.858467
\(646\) −16.8766 29.2312i −0.664001 1.15008i
\(647\) −2.96538 + 5.13618i −0.116581 + 0.201924i −0.918411 0.395629i \(-0.870527\pi\)
0.801830 + 0.597553i \(0.203860\pi\)
\(648\) 1.74876 3.02895i 0.0686979 0.118988i
\(649\) 4.19171 + 7.26025i 0.164539 + 0.284990i
\(650\) 3.46963 0.136090
\(651\) 0 0
\(652\) 10.6307 0.416330
\(653\) 9.40230 + 16.2853i 0.367940 + 0.637292i 0.989243 0.146279i \(-0.0467297\pi\)
−0.621303 + 0.783570i \(0.713396\pi\)
\(654\) 7.48135 12.9581i 0.292544 0.506701i
\(655\) −5.64860 + 9.78367i −0.220709 + 0.382280i
\(656\) −6.92502 11.9945i −0.270377 0.468306i
\(657\) −27.5691 −1.07557
\(658\) 0 0
\(659\) 23.1086 0.900184 0.450092 0.892982i \(-0.351391\pi\)
0.450092 + 0.892982i \(0.351391\pi\)
\(660\) −4.96744 8.60386i −0.193357 0.334905i
\(661\) 16.9543 29.3658i 0.659447 1.14220i −0.321312 0.946973i \(-0.604124\pi\)
0.980759 0.195222i \(-0.0625429\pi\)
\(662\) 3.12992 5.42119i 0.121648 0.210700i
\(663\) −1.93385 3.34953i −0.0751045 0.130085i
\(664\) −15.5658 −0.604071
\(665\) 0 0
\(666\) 41.8244 1.62066
\(667\) −3.22425 5.58457i −0.124844 0.216236i
\(668\) −8.62852 + 14.9450i −0.333848 + 0.578241i
\(669\) −2.63396 + 4.56215i −0.101835 + 0.176383i
\(670\) 4.76702 + 8.25672i 0.184166 + 0.318985i
\(671\) −36.5090 −1.40941
\(672\) 0 0
\(673\) 6.00430 0.231449 0.115724 0.993281i \(-0.463081\pi\)
0.115724 + 0.993281i \(0.463081\pi\)
\(674\) −22.8685 39.6094i −0.880862 1.52570i
\(675\) 4.26065 7.37967i 0.163993 0.284043i
\(676\) −0.678791 + 1.17570i −0.0261073 + 0.0452192i
\(677\) −10.1037 17.5002i −0.388318 0.672587i 0.603905 0.797056i \(-0.293611\pi\)
−0.992224 + 0.124469i \(0.960277\pi\)
\(678\) −27.5361 −1.05752
\(679\) 0 0
\(680\) −14.0014 −0.536928
\(681\) −4.94918 8.57224i −0.189653 0.328489i
\(682\) 8.38477 14.5228i 0.321069 0.556109i
\(683\) 15.8254 27.4104i 0.605541 1.04883i −0.386424 0.922321i \(-0.626290\pi\)
0.991966 0.126507i \(-0.0403767\pi\)
\(684\) 6.26838 + 10.8572i 0.239678 + 0.415134i
\(685\) 25.7891 0.985350
\(686\) 0 0
\(687\) −8.74092 −0.333487
\(688\) 23.6940 + 41.0391i 0.903324 + 1.56460i
\(689\) −2.63219 + 4.55909i −0.100279 + 0.173688i
\(690\) 9.30875 16.1232i 0.354378 0.613801i
\(691\) −4.84600 8.39351i −0.184350 0.319304i 0.759007 0.651082i \(-0.225685\pi\)
−0.943357 + 0.331778i \(0.892351\pi\)
\(692\) 7.12604 0.270891
\(693\) 0 0
\(694\) −35.1509 −1.33431
\(695\) −13.2343 22.9224i −0.502004 0.869497i
\(696\) −0.714895 + 1.23823i −0.0270980 + 0.0469352i
\(697\) 6.43903 11.1527i 0.243896 0.422440i
\(698\) 3.61363 + 6.25898i 0.136778 + 0.236906i
\(699\) 18.3406 0.693705
\(700\) 0 0
\(701\) −5.10365 −0.192762 −0.0963811 0.995345i \(-0.530727\pi\)
−0.0963811 + 0.995345i \(0.530727\pi\)
\(702\) 4.12305 + 7.14134i 0.155615 + 0.269532i
\(703\) 20.4331 35.3912i 0.770649 1.33480i
\(704\) 3.75500 6.50385i 0.141522 0.245123i
\(705\) 10.5910 + 18.3441i 0.398880 + 0.690880i
\(706\) 51.3489 1.93254
\(707\) 0 0
\(708\) −2.97632 −0.111857
\(709\) −13.0723 22.6418i −0.490939 0.850332i 0.509006 0.860763i \(-0.330013\pi\)
−0.999946 + 0.0104312i \(0.996680\pi\)
\(710\) 28.2751 48.9739i 1.06115 1.83796i
\(711\) 13.5231 23.4228i 0.507157 0.878422i
\(712\) 6.27806 + 10.8739i 0.235280 + 0.407518i
\(713\) 12.7063 0.475855
\(714\) 0 0
\(715\) 8.57161 0.320560
\(716\) 7.14462 + 12.3748i 0.267007 + 0.462469i
\(717\) −0.463550 + 0.802892i −0.0173116 + 0.0299846i
\(718\) −30.4386 + 52.7212i −1.13596 + 1.96754i
\(719\) 4.36442 + 7.55939i 0.162765 + 0.281918i 0.935859 0.352373i \(-0.114625\pi\)
−0.773094 + 0.634291i \(0.781292\pi\)
\(720\) 29.0520 1.08270
\(721\) 0 0
\(722\) −4.51937 −0.168193
\(723\) 8.53031 + 14.7749i 0.317245 + 0.549485i
\(724\) 12.7733 22.1240i 0.474716 0.822232i
\(725\) 1.34694 2.33296i 0.0500239 0.0866440i
\(726\) 0.267362 + 0.463085i 0.00992275 + 0.0171867i
\(727\) −21.8712 −0.811158 −0.405579 0.914060i \(-0.632930\pi\)
−0.405579 + 0.914060i \(0.632930\pi\)
\(728\) 0 0
\(729\) 4.77848 0.176981
\(730\) −29.2005 50.5768i −1.08076 1.87193i
\(731\) −22.0311 + 38.1590i −0.814851 + 1.41136i
\(732\) 6.48079 11.2251i 0.239537 0.414890i
\(733\) 17.7820 + 30.7993i 0.656793 + 1.13760i 0.981441 + 0.191764i \(0.0614209\pi\)
−0.324648 + 0.945835i \(0.605246\pi\)
\(734\) −51.8728 −1.91466
\(735\) 0 0
\(736\) 29.7943 1.09823
\(737\) 3.23485 + 5.60293i 0.119157 + 0.206387i
\(738\) −5.91495 + 10.2450i −0.217732 + 0.377123i
\(739\) 18.2447 31.6007i 0.671142 1.16245i −0.306439 0.951890i \(-0.599137\pi\)
0.977581 0.210561i \(-0.0675292\pi\)
\(740\) 17.9117 + 31.0240i 0.658448 + 1.14047i
\(741\) 3.47151 0.127529
\(742\) 0 0
\(743\) 12.4588 0.457071 0.228535 0.973536i \(-0.426606\pi\)
0.228535 + 0.973536i \(0.426606\pi\)
\(744\) −1.40865 2.43985i −0.0516435 0.0894492i
\(745\) 18.1326 31.4065i 0.664326 1.15065i
\(746\) 11.8659 20.5524i 0.434443 0.752477i
\(747\) 15.0157 + 26.0080i 0.549396 + 0.951582i
\(748\) 20.0783 0.734134
\(749\) 0 0
\(750\) −12.7596 −0.465914
\(751\) 9.47118 + 16.4046i 0.345608 + 0.598611i 0.985464 0.169884i \(-0.0543393\pi\)
−0.639856 + 0.768495i \(0.721006\pi\)
\(752\) −23.0198 + 39.8714i −0.839445 + 1.45396i
\(753\) −8.60150 + 14.8982i −0.313456 + 0.542922i
\(754\) 1.30344 + 2.25762i 0.0474683 + 0.0822175i
\(755\) 55.6940 2.02691
\(756\) 0 0
\(757\) −25.0956 −0.912114 −0.456057 0.889951i \(-0.650739\pi\)
−0.456057 + 0.889951i \(0.650739\pi\)
\(758\) −0.154817 0.268152i −0.00562322 0.00973971i
\(759\) 6.31683 10.9411i 0.229286 0.397136i
\(760\) 6.28356 10.8834i 0.227929 0.394784i
\(761\) −14.0308 24.3021i −0.508617 0.880951i −0.999950 0.00997886i \(-0.996824\pi\)
0.491333 0.870972i \(-0.336510\pi\)
\(762\) −2.49493 −0.0903818
\(763\) 0 0
\(764\) 20.2476 0.732531
\(765\) 13.5066 + 23.3941i 0.488331 + 0.845814i
\(766\) −9.33896 + 16.1756i −0.337430 + 0.584446i
\(767\) 1.28395 2.22387i 0.0463608 0.0802993i
\(768\) −8.95009 15.5020i −0.322958 0.559380i
\(769\) −23.2636 −0.838907 −0.419454 0.907777i \(-0.637778\pi\)
−0.419454 + 0.907777i \(0.637778\pi\)
\(770\) 0 0
\(771\) −12.8212 −0.461744
\(772\) 0.0360680 + 0.0624715i 0.00129811 + 0.00224840i
\(773\) −22.9059 + 39.6742i −0.823869 + 1.42698i 0.0789122 + 0.996882i \(0.474855\pi\)
−0.902781 + 0.430101i \(0.858478\pi\)
\(774\) 20.2380 35.0532i 0.727440 1.25996i
\(775\) 2.65404 + 4.59692i 0.0953358 + 0.165126i
\(776\) 16.1766 0.580708
\(777\) 0 0
\(778\) −52.5276 −1.88320
\(779\) 5.77944 + 10.0103i 0.207070 + 0.358655i
\(780\) −1.52157 + 2.63543i −0.0544808 + 0.0943635i
\(781\) 19.1872 33.2332i 0.686573 1.18918i
\(782\) 18.8129 + 32.5848i 0.672746 + 1.16523i
\(783\) 6.40238 0.228803