Properties

Label 637.2.e.o.79.2
Level $637$
Weight $2$
Character 637.79
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 79.2
Root \(-0.0731214 + 0.126650i\) of defining polynomial
Character \(\chi\) \(=\) 637.79
Dual form 637.2.e.o.508.2

$q$-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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 8q^{3} - 4q^{4} + 6q^{5} - 8q^{6} - 6q^{9} + O(q^{10}) \) \( 12q + 8q^{3} - 4q^{4} + 6q^{5} - 8q^{6} - 6q^{9} + 4q^{10} - 4q^{11} - 4q^{12} - 12q^{13} + 24q^{15} + 16q^{17} + 4q^{18} + 2q^{19} - 32q^{20} - 24q^{22} + 6q^{23} + 12q^{24} + 4q^{25} - 40q^{27} - 12q^{29} + 6q^{31} + 20q^{32} + 4q^{33} - 48q^{36} + 8q^{38} - 8q^{39} + 4q^{40} + 16q^{41} + 4q^{43} + 4q^{44} + 14q^{45} - 8q^{46} + 30q^{47} + 16q^{48} + 16q^{50} + 4q^{51} + 4q^{52} + 14q^{53} - 48q^{54} + 16q^{55} + 8q^{57} + 8q^{58} + 24q^{59} - 12q^{60} - 56q^{62} - 40q^{64} - 6q^{65} - 4q^{66} - 16q^{67} + 28q^{68} + 40q^{69} + 16q^{71} - 28q^{72} - 6q^{73} + 12q^{74} + 12q^{75} + 32q^{76} + 8q^{78} + 22q^{79} - 28q^{80} - 46q^{81} - 40q^{82} - 100q^{83} - 16q^{85} + 16q^{86} - 16q^{87} + 44q^{88} + 26q^{89} + 80q^{90} + 40q^{92} - 16q^{93} - 32q^{94} + 6q^{95} - 20q^{96} + 28q^{97} + 24q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.916185 + 1.58688i −0.647841 + 1.12209i 0.335797 + 0.941934i \(0.390994\pi\)
−0.983638 + 0.180159i \(0.942339\pi\)
\(3\) 0.426879 + 0.739375i 0.246458 + 0.426879i 0.962541 0.271137i \(-0.0873998\pi\)
−0.716082 + 0.698016i \(0.754066\pi\)
\(4\) −0.678791 1.17570i −0.339395 0.587850i
\(5\) 1.31278 2.27379i 0.587091 1.01687i −0.407520 0.913196i \(-0.633606\pi\)
0.994611 0.103676i \(-0.0330604\pi\)
\(6\) −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 0.507789 0.861481i \(-0.330463\pi\)
−0.999959 + 0.00901745i \(0.997130\pi\)
\(12\) 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 0.998318 + 0.0579773i \(0.0184651\pi\)
−0.448949 + 0.893557i \(0.648202\pi\)
\(18\) 2.08075 + 3.60396i 0.490437 + 0.849461i
\(19\) 2.03308 3.52139i 0.466420 0.807863i −0.532845 0.846213i \(-0.678877\pi\)
0.999264 + 0.0383505i \(0.0122103\pi\)
\(20\) −3.56440 −0.797024
\(21\) 0 0
\(22\) 5.98212 1.27539
\(23\) 2.26633 3.92540i 0.472562 0.818502i −0.526945 0.849900i \(-0.676662\pi\)
0.999507 + 0.0313975i \(0.00999579\pi\)
\(24\) −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 \(-0.247670\pi\)
−0.964005 + 0.265882i \(0.914337\pi\)
\(32\) 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 −0.0749173 0.997190i \(-0.523869\pi\)
0.901050 0.433715i \(-0.142797\pi\)
\(38\) 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 \(-0.428749\pi\)
0.221978 + 0.975052i \(0.428749\pi\)
\(42\) 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 0.282923 + 0.959142i \(0.408696\pi\)
−0.972103 + 0.234552i \(0.924638\pi\)
\(48\) 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 0.626658 0.779294i \(-0.284422\pi\)
−0.988218 + 0.153055i \(0.951089\pi\)
\(54\) −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 \(-0.220125\pi\)
−0.937419 + 0.348204i \(0.886792\pi\)
\(60\) −1.52157 2.63543i −0.196433 0.340233i
\(61\) −5.59149 + 9.68475i −0.715917 + 1.24000i 0.246688 + 0.969095i \(0.420658\pi\)
−0.962605 + 0.270910i \(0.912676\pi\)
\(62\) 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 0.920183 0.391488i \(-0.128040\pi\)
−0.799130 + 0.601158i \(0.794706\pi\)
\(68\) 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 0.964711 + 0.263309i \(0.0848139\pi\)
−0.254323 + 0.967119i \(0.581853\pi\)
\(74\) 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 0.307996 + 0.951388i \(0.400342\pi\)
−0.977924 + 0.208961i \(0.932992\pi\)
\(80\) −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 \(-0.758495\pi\)
−0.725723 + 0.687987i \(0.758495\pi\)
\(84\) 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 −0.431693 0.902021i \(-0.642084\pi\)
0.997019 0.0771532i \(-0.0245831\pi\)
\(90\) 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 \(-0.254227\pi\)
0.697655 + 0.716433i \(0.254227\pi\)
\(98\) 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 \(-0.0719244\pi\)
−0.681314 + 0.731991i \(0.738591\pi\)
\(102\) −3.54353 6.13757i −0.350862 0.607710i
\(103\) 1.39368 2.41393i 0.137324 0.237852i −0.789159 0.614189i \(-0.789483\pi\)
0.926483 + 0.376337i \(0.122817\pi\)
\(104\) 1.17715 0.115429
\(105\) 0 0
\(106\) 9.64630 0.936932
\(107\) 8.83236 15.2981i 0.853856 1.47892i −0.0238454 0.999716i \(-0.507591\pi\)
0.877702 0.479207i \(-0.159076\pi\)
\(108\) −3.05472 5.29093i −0.293941 0.509120i
\(109\) 4.78225 + 8.28310i 0.458057 + 0.793377i 0.998858 0.0477730i \(-0.0152124\pi\)
−0.540802 + 0.841150i \(0.681879\pi\)
\(110\) 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 \(-0.773143\pi\)
0.944573 + 0.328302i \(0.106476\pi\)
\(132\) −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 0.576308 0.817232i \(-0.304493\pi\)
−0.995898 + 0.0904816i \(0.971159\pi\)
\(138\) −3.54545 + 6.14089i −0.301808 + 0.522747i
\(139\) −10.0811 −0.855070 −0.427535 0.903999i \(-0.640618\pi\)
−0.427535 + 0.903999i \(0.640618\pi\)
\(140\) 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 −0.431200 0.902256i \(-0.641910\pi\)
0.996977 0.0776983i \(-0.0247571\pi\)
\(150\) 1.48111 + 2.56536i 0.120932 + 0.209461i
\(151\) −10.6062 18.3704i −0.863117 1.49496i −0.868905 0.494979i \(-0.835176\pi\)
0.00578805 0.999983i \(-0.498158\pi\)
\(152\) −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 0.768508 + 0.639840i \(0.221000\pi\)
0.169864 + 0.985468i \(0.445667\pi\)
\(158\) −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 −0.977632 0.210323i \(-0.932548\pi\)
0.670961 + 0.741492i \(0.265882\pi\)
\(164\) −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 \(-0.663671\pi\)
−0.491827 + 0.870693i \(0.663671\pi\)
\(168\) 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 \(-0.769389\pi\)
0.948379 + 0.317138i \(0.102722\pi\)
\(174\) 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 0.992890 0.119036i \(-0.0379804\pi\)
−0.599533 + 0.800350i \(0.704647\pi\)
\(180\) −4.04755 + 7.01056i −0.301687 + 0.522537i
\(181\) 18.8177 1.39871 0.699356 0.714774i \(-0.253470\pi\)
0.699356 + 0.714774i \(0.253470\pi\)
\(182\) 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 0.459341 + 0.888260i \(0.348086\pi\)
−0.998926 + 0.0463292i \(0.985248\pi\)
\(192\) −0.981980 1.70084i −0.0708683 0.122747i
\(193\) 0.0265678 + 0.0460168i 0.00191239 + 0.00331236i 0.866980 0.498343i \(-0.166058\pi\)
−0.865068 + 0.501655i \(0.832725\pi\)
\(194\) −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 0.901504 + 0.432771i \(0.142464\pi\)
−0.0759612 + 0.997111i \(0.524202\pi\)
\(200\) 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 \(-0.566239\pi\)
−0.206596 + 0.978426i \(0.566239\pi\)
\(224\) 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 \(-0.0409520\pi\)
−0.606979 + 0.794718i \(0.707619\pi\)
\(228\) −2.35643 4.08145i −0.156058 0.270301i
\(229\) −5.11909 + 8.86653i −0.338279 + 0.585917i −0.984109 0.177565i \(-0.943178\pi\)
0.645830 + 0.763481i \(0.276511\pi\)
\(230\) 21.8065 1.43788
\(231\) 0 0
\(232\) 1.67470 0.109950
\(233\) −10.7411 + 18.6041i −0.703673 + 1.21880i 0.263495 + 0.964661i \(0.415125\pi\)
−0.967168 + 0.254137i \(0.918208\pi\)
\(234\) −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 −0.984621 0.174704i \(-0.944103\pi\)
0.341013 0.940059i \(-0.389230\pi\)
\(242\) 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 \(-0.719379\pi\)
−0.635920 + 0.771755i \(0.719379\pi\)
\(252\) 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 \(-0.988495\pi\)
0.530968 + 0.847392i \(0.321829\pi\)
\(258\) −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 0.982494 + 0.186294i \(0.0596477\pi\)
−0.329912 + 0.944012i \(0.607019\pi\)
\(264\) −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 \(-0.206604\pi\)
−0.921786 + 0.387698i \(0.873270\pi\)
\(270\) 10.8253 + 18.7499i 0.658806 + 1.14109i
\(271\) 1.71622 2.97258i 0.104253 0.180571i −0.809180 0.587561i \(-0.800088\pi\)
0.913433 + 0.406990i \(0.133422\pi\)
\(272\) 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 0.871397 0.490578i \(-0.163214\pi\)
−0.860552 + 0.509363i \(0.829881\pi\)
\(278\) 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 \(-0.181919\pi\)
−0.888981 + 0.457944i \(0.848586\pi\)
\(284\) 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 \(-0.458819\pi\)
0.129013 + 0.991643i \(0.458819\pi\)
\(294\) 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 \(-0.447224\pi\)
0.165042 + 0.986287i \(0.447224\pi\)
\(308\) 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 \(-0.0338887\pi\)
−0.589196 + 0.807990i \(0.700555\pi\)
\(312\) 0.502500 + 0.870355i 0.0284485 + 0.0492742i
\(313\) 1.36862 2.37053i 0.0773592 0.133990i −0.824751 0.565497i \(-0.808685\pi\)
0.902110 + 0.431507i \(0.142018\pi\)
\(314\) −43.0892 −2.43166
\(315\) 0 0
\(316\) 16.1673 0.909481
\(317\) −5.32560 + 9.22422i −0.299116 + 0.518084i −0.975934 0.218067i \(-0.930025\pi\)
0.676818 + 0.736150i \(0.263358\pi\)
\(318\) 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 −0.815256 0.579100i \(-0.803404\pi\)
0.909144 + 0.416483i \(0.136737\pi\)
\(332\) 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 0.999850 + 0.0172992i \(0.00550678\pi\)
−0.484944 + 0.874545i \(0.661160\pi\)
\(348\) −0.824473 + 1.42803i −0.0441964 + 0.0765504i
\(349\) 3.94421 0.211129 0.105564 0.994412i \(-0.466335\pi\)
0.105564 + 0.994412i \(0.466335\pi\)
\(350\) 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 0.949838 + 0.312743i \(0.101248\pi\)
−0.204076 + 0.978955i \(0.565419\pi\)
\(354\) 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 −0.0218141 + 0.999762i \(0.506944\pi\)
−0.854912 + 0.518773i \(0.826389\pi\)
\(360\) 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 −0.953008 0.302945i \(-0.902030\pi\)
0.214146 0.976802i \(-0.431303\pi\)
\(368\) −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 −0.648242 0.761435i \(-0.724495\pi\)
0.983543 + 0.180677i \(0.0578287\pi\)
\(374\) 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 \(-0.749470\pi\)
0.966355 + 0.257210i \(0.0828034\pi\)
\(384\) −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 0.958261 + 0.285896i \(0.0922911\pi\)
−0.231537 + 0.972826i \(0.574376\pi\)
\(390\) 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 0.242776 + 0.970082i \(0.421942\pi\)
−0.961504 + 0.274791i \(0.911391\pi\)
\(398\) −42.6785 −2.13928
\(399\) 0 0
\(400\) −9.22550 −0.461275
\(401\) 7.14814 12.3809i 0.356961 0.618275i −0.630490 0.776197i \(-0.717146\pi\)
0.987452 + 0.157922i \(0.0504795\pi\)
\(402\) −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 0.986438 + 0.164132i \(0.0524824\pi\)
−0.351077 + 0.936347i \(0.614184\pi\)
\(410\) 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 \(-0.651870\pi\)
−0.459216 + 0.888324i \(0.651870\pi\)
\(420\) 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 0.504856 0.863203i \(-0.331546\pi\)
−0.999984 + 0.00561653i \(0.998212\pi\)
\(432\) 10.9629 18.9883i 0.527452 0.913574i
\(433\) −18.9235 −0.909404 −0.454702 0.890644i \(-0.650254\pi\)
−0.454702 + 0.890644i \(0.650254\pi\)
\(434\) 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 \(-0.947058\pi\)
0.636477 + 0.771295i \(0.280391\pi\)
\(440\) 10.0901 0.481025
\(441\) 0 0
\(442\) 8.30102 0.394839
\(443\) 5.97962 10.3570i 0.284100 0.492076i −0.688290 0.725435i \(-0.741638\pi\)
0.972391 + 0.233359i \(0.0749718\pi\)
\(444\) −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 −0.562682 0.826673i \(-0.690231\pi\)
0.997261 + 0.0739607i \(0.0235639\pi\)
\(458\) −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 \(-0.725040\pi\)
−0.649543 + 0.760325i \(0.725040\pi\)
\(462\) 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 0.0648815 0.997893i \(-0.479333\pi\)
0.831760 0.555136i \(-0.187334\pi\)
\(468\) 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 \(-0.210688\pi\)
−0.926685 + 0.375838i \(0.877355\pi\)
\(480\) 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 0.905882 0.423530i \(-0.139209\pi\)
−0.819729 + 0.572752i \(0.805876\pi\)
\(488\) 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 0.161556 + 0.986864i \(0.448349\pi\)
−0.935427 + 0.353520i \(0.884985\pi\)
\(500\) −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 \(-0.482883\pi\)
0.0537485 + 0.998555i \(0.482883\pi\)
\(504\) 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 \(-0.994765\pi\)
0.514175 + 0.857685i \(0.328098\pi\)
\(510\) −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 −0.980527 0.196386i \(-0.937079\pi\)
0.320188 0.947354i \(-0.396254\pi\)
\(522\) −2.96023 5.12727i −0.129566 0.224414i
\(523\) −9.04966 + 15.6745i −0.395714 + 0.685397i −0.993192 0.116489i \(-0.962836\pi\)
0.597478 + 0.801885i \(0.296170\pi\)
\(524\) −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 −0.906622 0.421943i \(-0.861348\pi\)
0.818725 + 0.574186i \(0.194682\pi\)
\(542\) 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 0.577001 0.816743i \(-0.304223\pi\)
−0.995821 + 0.0913260i \(0.970889\pi\)
\(558\) 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 \(-0.111224\pi\)
−0.766273 + 0.642515i \(0.777891\pi\)
\(564\) 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 −0.977384 0.211474i \(-0.932174\pi\)
0.671834 + 0.740702i \(0.265507\pi\)
\(570\) 8.35068 + 14.4638i 0.349772 + 0.605822i
\(571\) 1.29411 + 2.24146i 0.0541568 + 0.0938023i 0.891833 0.452365i \(-0.149420\pi\)
−0.837676 + 0.546167i \(0.816086\pi\)
\(572\) 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 \(-0.332361\pi\)
−0.999995 + 0.00305340i \(0.999028\pi\)
\(578\) −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 \(-0.700764\pi\)
−0.589726 + 0.807604i \(0.700764\pi\)
\(588\) 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 \(-0.967727\pi\)
0.585087 + 0.810971i \(0.301060\pi\)
\(594\) 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 0.853751 0.520682i \(-0.174322\pi\)
−0.877799 + 0.479029i \(0.840989\pi\)
\(600\) −0.951495 + 1.64804i −0.0388446 + 0.0672809i
\(601\) 30.9250 1.26146 0.630729 0.776003i \(-0.282756\pi\)
0.630729 + 0.776003i \(0.282756\pi\)
\(602\) 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 \(-0.817778\pi\)
0.889417 + 0.457097i \(0.151111\pi\)
\(608\) 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 0.997419 + 0.0718060i \(0.0228762\pi\)
−0.436524 + 0.899693i \(0.643790\pi\)
\(614\) −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 \(-0.279256\pi\)
−0.985604 + 0.169072i \(0.945923\pi\)
\(620\) 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 0.998493 0.0548728i \(-0.0174753\pi\)
−0.546768 + 0.837284i \(0.684142\pi\)
\(642\) −13.8173 + 23.9323i −0.545327 + 0.944534i
\(643\) 46.7072 1.84195 0.920976 0.389620i \(-0.127394\pi\)
0.920976 + 0.389620i \(0.127394\pi\)
\(644\) 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 \(-0.129473\pi\)
−0.801830 + 0.597553i \(0.796140\pi\)
\(648\) 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 −0.621303 0.783570i \(-0.713396\pi\)
0.989243 + 0.146279i \(0.0467297\pi\)
\(654\) −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 −0.980759 0.195222i \(-0.937457\pi\)
0.321312 0.946973i \(-0.395876\pi\)
\(662\) 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 \(-0.706389\pi\)
0.992224 + 0.124469i \(0.0397227\pi\)
\(678\) 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 0.991966 + 0.126507i \(0.0403767\pi\)
−0.386424 + 0.922321i \(0.626290\pi\)
\(684\) −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 \(-0.774315\pi\)
0.943357 + 0.331778i \(0.107649\pi\)
\(692\) −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 −0.999946 0.0104312i \(-0.996680\pi\)
0.509006 + 0.860763i \(0.330013\pi\)
\(710\) −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 \(-0.885375\pi\)
0.773094 + 0.634291i \(0.218708\pi\)
\(720\) −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 \(-0.367070\pi\)
0.405579 + 0.914060i \(0.367070\pi\)
\(728\) 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 0.324648 + 0.945835i \(0.394754\pi\)
−0.981441 + 0.191764i \(0.938579\pi\)
\(734\) 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 0.977581 + 0.210561i \(0.0675292\pi\)
−0.306439 + 0.951890i \(0.599137\pi\)
\(740\) −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 −0.639856 0.768495i \(-0.721006\pi\)
0.985464 + 0.169884i \(0.0543393\pi\)
\(752\) 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 −0.491333 0.870972i \(-0.663490\pi\)
0.999950 0.00997886i \(-0.00317642\pi\)
\(762\) 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 \(-0.362222\pi\)
0.419454 + 0.907777i \(0.362222\pi\)
\(770\) 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 0.902781 + 0.430101i \(0.141522\pi\)
−0.0789122 + 0.996882i \(0.525145\pi\)
\(774\) 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
\(784\) 0 0
\(785\) 61.7413 2.20364