Properties

Label 637.2.f.j.393.1
Level $637$
Weight $2$
Character 637.393
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 393.1
Root \(0.217953 - 0.377506i\) of defining polynomial
Character \(\chi\) \(=\) 637.393
Dual form 637.2.f.j.295.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.929081 - 1.60921i) q^{2} +(1.14703 + 1.98672i) q^{3} +(-0.726381 + 1.25813i) q^{4} +0.197362 q^{5} +(2.13137 - 3.69165i) q^{6} -1.01686 q^{8} +(-1.13137 + 1.95960i) q^{9} +O(q^{10})\) \(q+(-0.929081 - 1.60921i) q^{2} +(1.14703 + 1.98672i) q^{3} +(-0.726381 + 1.25813i) q^{4} +0.197362 q^{5} +(2.13137 - 3.69165i) q^{6} -1.01686 q^{8} +(-1.13137 + 1.95960i) q^{9} +(-0.183365 - 0.317598i) q^{10} +(2.09137 + 3.62236i) q^{11} -3.33274 q^{12} +(2.72221 - 2.36423i) q^{13} +(0.226381 + 0.392104i) q^{15} +(2.39750 + 4.15260i) q^{16} +(0.420653 - 0.728592i) q^{17} +4.20455 q^{18} +(0.675876 - 1.17065i) q^{19} +(-0.143360 + 0.248307i) q^{20} +(3.88610 - 6.73092i) q^{22} +(2.05760 + 3.56386i) q^{23} +(-1.16637 - 2.02021i) q^{24} -4.96105 q^{25} +(-6.33370 - 2.18406i) q^{26} +1.69131 q^{27} +(4.11931 + 7.13485i) q^{29} +(0.420653 - 0.728592i) q^{30} +1.28070 q^{31} +(3.43809 - 5.95495i) q^{32} +(-4.79774 + 8.30993i) q^{33} -1.56328 q^{34} +(-1.64362 - 2.84683i) q^{36} +(-1.52242 - 2.63692i) q^{37} -2.51177 q^{38} +(7.81953 + 2.69642i) q^{39} -0.200689 q^{40} +(2.69848 + 4.67390i) q^{41} +(-2.66389 + 4.61399i) q^{43} -6.07652 q^{44} +(-0.223290 + 0.386750i) q^{45} +(3.82334 - 6.62223i) q^{46} +11.6641 q^{47} +(-5.50003 + 9.52634i) q^{48} +(4.60921 + 7.98339i) q^{50} +1.93001 q^{51} +(0.997141 + 5.14222i) q^{52} +4.64796 q^{53} +(-1.57136 - 2.72168i) q^{54} +(0.412757 + 0.714916i) q^{55} +3.10101 q^{57} +(7.65434 - 13.2577i) q^{58} +(3.02905 - 5.24648i) q^{59} -0.657756 q^{60} +(-5.68285 + 9.84298i) q^{61} +(-1.18987 - 2.06092i) q^{62} -3.18704 q^{64} +(0.537262 - 0.466609i) q^{65} +17.8300 q^{66} +(-6.69851 - 11.6022i) q^{67} +(0.611109 + 1.05847i) q^{68} +(-4.72026 + 8.17574i) q^{69} +(2.98520 - 5.17051i) q^{71} +(1.15044 - 1.99263i) q^{72} -3.88547 q^{73} +(-2.82891 + 4.89982i) q^{74} +(-5.69049 - 9.85622i) q^{75} +(0.981887 + 1.70068i) q^{76} +(-2.92585 - 15.0885i) q^{78} -10.7334 q^{79} +(0.473177 + 0.819566i) q^{80} +(5.33411 + 9.23895i) q^{81} +(5.01421 - 8.68486i) q^{82} -3.07390 q^{83} +(0.0830210 - 0.143797i) q^{85} +9.89987 q^{86} +(-9.44997 + 16.3678i) q^{87} +(-2.12662 - 3.68341i) q^{88} +(-5.99207 - 10.3786i) q^{89} +0.829819 q^{90} -5.97840 q^{92} +(1.46901 + 2.54439i) q^{93} +(-10.8369 - 18.7700i) q^{94} +(0.133392 - 0.231042i) q^{95} +15.7744 q^{96} +(9.73637 - 16.8639i) q^{97} -9.46448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 2q^{2} - q^{3} - 4q^{4} + 2q^{5} + 9q^{6} - 6q^{8} + 3q^{9} + O(q^{10}) \) \( 12q + 2q^{2} - q^{3} - 4q^{4} + 2q^{5} + 9q^{6} - 6q^{8} + 3q^{9} - 4q^{10} + 4q^{11} + 10q^{12} + 2q^{13} - 2q^{15} + 8q^{16} - 5q^{17} - 6q^{18} + q^{19} + q^{20} - 5q^{22} - q^{23} + 11q^{24} - 14q^{25} - 11q^{26} + 8q^{27} + 3q^{29} - 5q^{30} + 32q^{31} + 8q^{32} - 16q^{33} - 32q^{34} - 21q^{36} - 13q^{37} - 34q^{38} + 43q^{39} - 10q^{40} + 8q^{41} - 11q^{43} - 42q^{44} + 7q^{45} + 16q^{46} - 2q^{47} - 21q^{48} + 6q^{50} + 40q^{51} + 16q^{52} + 4q^{53} + 18q^{54} - 9q^{55} + 42q^{57} - 8q^{58} - 13q^{59} - 40q^{60} + 5q^{61} - 5q^{62} - 30q^{64} - 14q^{65} + 36q^{66} - 11q^{67} - 29q^{68} - 23q^{69} + 6q^{71} + 25q^{72} - 60q^{73} - 3q^{74} + 3q^{75} + 9q^{76} + 16q^{78} - 14q^{79} + 7q^{80} - 6q^{81} - q^{82} + 54q^{83} - q^{85} + 14q^{86} - 16q^{87} - 4q^{89} + 16q^{90} + 54q^{92} - 7q^{93} - 45q^{94} - 6q^{95} + 38q^{96} + 35q^{97} - 20q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.929081 1.60921i −0.656959 1.13789i −0.981399 0.191980i \(-0.938509\pi\)
0.324440 0.945906i \(-0.394824\pi\)
\(3\) 1.14703 + 1.98672i 0.662240 + 1.14703i 0.980026 + 0.198871i \(0.0637276\pi\)
−0.317785 + 0.948163i \(0.602939\pi\)
\(4\) −0.726381 + 1.25813i −0.363191 + 0.629065i
\(5\) 0.197362 0.0882631 0.0441315 0.999026i \(-0.485948\pi\)
0.0441315 + 0.999026i \(0.485948\pi\)
\(6\) 2.13137 3.69165i 0.870130 1.50711i
\(7\) 0 0
\(8\) −1.01686 −0.359513
\(9\) −1.13137 + 1.95960i −0.377125 + 0.653199i
\(10\) −0.183365 0.317598i −0.0579852 0.100433i
\(11\) 2.09137 + 3.62236i 0.630571 + 1.09218i 0.987435 + 0.158025i \(0.0505127\pi\)
−0.356864 + 0.934156i \(0.616154\pi\)
\(12\) −3.33274 −0.962078
\(13\) 2.72221 2.36423i 0.755005 0.655719i
\(14\) 0 0
\(15\) 0.226381 + 0.392104i 0.0584514 + 0.101241i
\(16\) 2.39750 + 4.15260i 0.599376 + 1.03815i
\(17\) 0.420653 0.728592i 0.102023 0.176709i −0.810495 0.585746i \(-0.800802\pi\)
0.912518 + 0.409036i \(0.134135\pi\)
\(18\) 4.20455 0.991022
\(19\) 0.675876 1.17065i 0.155057 0.268566i −0.778023 0.628236i \(-0.783777\pi\)
0.933080 + 0.359670i \(0.117111\pi\)
\(20\) −0.143360 + 0.248307i −0.0320563 + 0.0555232i
\(21\) 0 0
\(22\) 3.88610 6.73092i 0.828519 1.43504i
\(23\) 2.05760 + 3.56386i 0.429038 + 0.743116i 0.996788 0.0800850i \(-0.0255192\pi\)
−0.567750 + 0.823201i \(0.692186\pi\)
\(24\) −1.16637 2.02021i −0.238084 0.412373i
\(25\) −4.96105 −0.992210
\(26\) −6.33370 2.18406i −1.24214 0.428330i
\(27\) 1.69131 0.325492
\(28\) 0 0
\(29\) 4.11931 + 7.13485i 0.764936 + 1.32491i 0.940280 + 0.340401i \(0.110563\pi\)
−0.175344 + 0.984507i \(0.556104\pi\)
\(30\) 0.420653 0.728592i 0.0768003 0.133022i
\(31\) 1.28070 0.230020 0.115010 0.993364i \(-0.463310\pi\)
0.115010 + 0.993364i \(0.463310\pi\)
\(32\) 3.43809 5.95495i 0.607774 1.05270i
\(33\) −4.79774 + 8.30993i −0.835180 + 1.44657i
\(34\) −1.56328 −0.268100
\(35\) 0 0
\(36\) −1.64362 2.84683i −0.273936 0.474471i
\(37\) −1.52242 2.63692i −0.250285 0.433506i 0.713319 0.700839i \(-0.247191\pi\)
−0.963604 + 0.267333i \(0.913858\pi\)
\(38\) −2.51177 −0.407463
\(39\) 7.81953 + 2.69642i 1.25213 + 0.431773i
\(40\) −0.200689 −0.0317317
\(41\) 2.69848 + 4.67390i 0.421431 + 0.729941i 0.996080 0.0884599i \(-0.0281945\pi\)
−0.574648 + 0.818400i \(0.694861\pi\)
\(42\) 0 0
\(43\) −2.66389 + 4.61399i −0.406239 + 0.703627i −0.994465 0.105070i \(-0.966493\pi\)
0.588226 + 0.808697i \(0.299827\pi\)
\(44\) −6.07652 −0.916070
\(45\) −0.223290 + 0.386750i −0.0332862 + 0.0576534i
\(46\) 3.82334 6.62223i 0.563721 0.976394i
\(47\) 11.6641 1.70138 0.850690 0.525668i \(-0.176185\pi\)
0.850690 + 0.525668i \(0.176185\pi\)
\(48\) −5.50003 + 9.52634i −0.793862 + 1.37501i
\(49\) 0 0
\(50\) 4.60921 + 7.98339i 0.651841 + 1.12902i
\(51\) 1.93001 0.270256
\(52\) 0.997141 + 5.14222i 0.138279 + 0.713098i
\(53\) 4.64796 0.638447 0.319223 0.947679i \(-0.396578\pi\)
0.319223 + 0.947679i \(0.396578\pi\)
\(54\) −1.57136 2.72168i −0.213835 0.370373i
\(55\) 0.412757 + 0.714916i 0.0556562 + 0.0963993i
\(56\) 0 0
\(57\) 3.10101 0.410739
\(58\) 7.65434 13.2577i 1.00506 1.74082i
\(59\) 3.02905 5.24648i 0.394349 0.683033i −0.598669 0.800997i \(-0.704303\pi\)
0.993018 + 0.117964i \(0.0376367\pi\)
\(60\) −0.657756 −0.0849160
\(61\) −5.68285 + 9.84298i −0.727614 + 1.26026i 0.230275 + 0.973126i \(0.426038\pi\)
−0.957889 + 0.287139i \(0.907296\pi\)
\(62\) −1.18987 2.06092i −0.151114 0.261737i
\(63\) 0 0
\(64\) −3.18704 −0.398380
\(65\) 0.537262 0.466609i 0.0666391 0.0578758i
\(66\) 17.8300 2.19472
\(67\) −6.69851 11.6022i −0.818354 1.41743i −0.906895 0.421357i \(-0.861554\pi\)
0.0885411 0.996073i \(-0.471780\pi\)
\(68\) 0.611109 + 1.05847i 0.0741078 + 0.128358i
\(69\) −4.72026 + 8.17574i −0.568253 + 0.984243i
\(70\) 0 0
\(71\) 2.98520 5.17051i 0.354278 0.613627i −0.632716 0.774384i \(-0.718060\pi\)
0.986994 + 0.160757i \(0.0513934\pi\)
\(72\) 1.15044 1.99263i 0.135581 0.234833i
\(73\) −3.88547 −0.454759 −0.227380 0.973806i \(-0.573016\pi\)
−0.227380 + 0.973806i \(0.573016\pi\)
\(74\) −2.82891 + 4.89982i −0.328854 + 0.569592i
\(75\) −5.69049 9.85622i −0.657081 1.13810i
\(76\) 0.981887 + 1.70068i 0.112630 + 0.195081i
\(77\) 0 0
\(78\) −2.92585 15.0885i −0.331287 1.70844i
\(79\) −10.7334 −1.20760 −0.603799 0.797136i \(-0.706347\pi\)
−0.603799 + 0.797136i \(0.706347\pi\)
\(80\) 0.473177 + 0.819566i 0.0529028 + 0.0916303i
\(81\) 5.33411 + 9.23895i 0.592679 + 1.02655i
\(82\) 5.01421 8.68486i 0.553726 0.959082i
\(83\) −3.07390 −0.337404 −0.168702 0.985667i \(-0.553958\pi\)
−0.168702 + 0.985667i \(0.553958\pi\)
\(84\) 0 0
\(85\) 0.0830210 0.143797i 0.00900489 0.0155969i
\(86\) 9.89987 1.06753
\(87\) −9.44997 + 16.3678i −1.01314 + 1.75482i
\(88\) −2.12662 3.68341i −0.226698 0.392653i
\(89\) −5.99207 10.3786i −0.635159 1.10013i −0.986482 0.163873i \(-0.947601\pi\)
0.351323 0.936254i \(-0.385732\pi\)
\(90\) 0.829819 0.0874706
\(91\) 0 0
\(92\) −5.97840 −0.623291
\(93\) 1.46901 + 2.54439i 0.152329 + 0.263841i
\(94\) −10.8369 18.7700i −1.11774 1.93598i
\(95\) 0.133392 0.231042i 0.0136858 0.0237045i
\(96\) 15.7744 1.60997
\(97\) 9.73637 16.8639i 0.988578 1.71227i 0.363771 0.931488i \(-0.381489\pi\)
0.624807 0.780779i \(-0.285178\pi\)
\(98\) 0 0
\(99\) −9.46448 −0.951216
\(100\) 3.60361 6.24164i 0.360361 0.624164i
\(101\) −8.46697 14.6652i −0.842495 1.45924i −0.887779 0.460270i \(-0.847753\pi\)
0.0452843 0.998974i \(-0.485581\pi\)
\(102\) −1.79314 3.10580i −0.177547 0.307520i
\(103\) 7.23425 0.712811 0.356406 0.934331i \(-0.384002\pi\)
0.356406 + 0.934331i \(0.384002\pi\)
\(104\) −2.76809 + 2.40408i −0.271434 + 0.235739i
\(105\) 0 0
\(106\) −4.31833 7.47957i −0.419434 0.726480i
\(107\) 4.92625 + 8.53251i 0.476238 + 0.824869i 0.999629 0.0272237i \(-0.00866664\pi\)
−0.523391 + 0.852093i \(0.675333\pi\)
\(108\) −1.22853 + 2.12788i −0.118216 + 0.204756i
\(109\) −13.8159 −1.32332 −0.661662 0.749802i \(-0.730149\pi\)
−0.661662 + 0.749802i \(0.730149\pi\)
\(110\) 0.766969 1.32843i 0.0731277 0.126661i
\(111\) 3.49255 6.04927i 0.331498 0.574171i
\(112\) 0 0
\(113\) 2.13432 3.69675i 0.200780 0.347761i −0.748000 0.663699i \(-0.768986\pi\)
0.948780 + 0.315938i \(0.102319\pi\)
\(114\) −2.88109 4.99019i −0.269839 0.467374i
\(115\) 0.406092 + 0.703371i 0.0378682 + 0.0655897i
\(116\) −11.9687 −1.11127
\(117\) 1.55310 + 8.00926i 0.143584 + 0.740456i
\(118\) −11.2569 −1.03629
\(119\) 0 0
\(120\) −0.230197 0.398713i −0.0210140 0.0363973i
\(121\) −3.24765 + 5.62509i −0.295240 + 0.511372i
\(122\) 21.1193 1.91205
\(123\) −6.19049 + 10.7222i −0.558178 + 0.966792i
\(124\) −0.930276 + 1.61129i −0.0835412 + 0.144698i
\(125\) −1.96593 −0.175839
\(126\) 0 0
\(127\) 1.09512 + 1.89680i 0.0971761 + 0.168314i 0.910515 0.413477i \(-0.135686\pi\)
−0.813339 + 0.581791i \(0.802352\pi\)
\(128\) −3.91516 6.78126i −0.346055 0.599385i
\(129\) −12.2223 −1.07611
\(130\) −1.25003 0.431052i −0.109635 0.0378057i
\(131\) −2.27612 −0.198865 −0.0994326 0.995044i \(-0.531703\pi\)
−0.0994326 + 0.995044i \(0.531703\pi\)
\(132\) −6.96998 12.0724i −0.606659 1.05076i
\(133\) 0 0
\(134\) −12.4469 + 21.5587i −1.07525 + 1.86239i
\(135\) 0.333800 0.0287289
\(136\) −0.427743 + 0.740873i −0.0366787 + 0.0635293i
\(137\) −6.72399 + 11.6463i −0.574469 + 0.995010i 0.421630 + 0.906768i \(0.361458\pi\)
−0.996099 + 0.0882417i \(0.971875\pi\)
\(138\) 17.5420 1.49328
\(139\) 2.02270 3.50342i 0.171563 0.297156i −0.767403 0.641165i \(-0.778452\pi\)
0.938966 + 0.344009i \(0.111785\pi\)
\(140\) 0 0
\(141\) 13.3791 + 23.1733i 1.12672 + 1.95154i
\(142\) −11.0940 −0.930984
\(143\) 14.2572 + 4.91634i 1.19225 + 0.411125i
\(144\) −10.8499 −0.904157
\(145\) 0.812996 + 1.40815i 0.0675156 + 0.116940i
\(146\) 3.60991 + 6.25255i 0.298758 + 0.517465i
\(147\) 0 0
\(148\) 4.42344 0.363605
\(149\) −7.67596 + 13.2952i −0.628840 + 1.08918i 0.358945 + 0.933359i \(0.383136\pi\)
−0.987785 + 0.155823i \(0.950197\pi\)
\(150\) −10.5738 + 18.3144i −0.863351 + 1.49537i
\(151\) 6.12108 0.498127 0.249063 0.968487i \(-0.419877\pi\)
0.249063 + 0.968487i \(0.419877\pi\)
\(152\) −0.687268 + 1.19038i −0.0557448 + 0.0965528i
\(153\) 0.951831 + 1.64862i 0.0769510 + 0.133283i
\(154\) 0 0
\(155\) 0.252762 0.0203023
\(156\) −9.07241 + 7.87935i −0.726374 + 0.630853i
\(157\) −4.53668 −0.362067 −0.181033 0.983477i \(-0.557944\pi\)
−0.181033 + 0.983477i \(0.557944\pi\)
\(158\) 9.97217 + 17.2723i 0.793343 + 1.37411i
\(159\) 5.33137 + 9.23421i 0.422805 + 0.732320i
\(160\) 0.678549 1.17528i 0.0536440 0.0929142i
\(161\) 0 0
\(162\) 9.91163 17.1674i 0.778731 1.34880i
\(163\) −0.911271 + 1.57837i −0.0713762 + 0.123627i −0.899505 0.436911i \(-0.856072\pi\)
0.828128 + 0.560538i \(0.189406\pi\)
\(164\) −7.84049 −0.612240
\(165\) −0.946893 + 1.64007i −0.0737155 + 0.127679i
\(166\) 2.85590 + 4.94656i 0.221661 + 0.383928i
\(167\) −5.35397 9.27336i −0.414303 0.717594i 0.581052 0.813866i \(-0.302641\pi\)
−0.995355 + 0.0962726i \(0.969308\pi\)
\(168\) 0 0
\(169\) 1.82086 12.8718i 0.140066 0.990142i
\(170\) −0.308533 −0.0236634
\(171\) 1.52934 + 2.64889i 0.116951 + 0.202566i
\(172\) −3.87000 6.70303i −0.295085 0.511102i
\(173\) −6.74634 + 11.6850i −0.512915 + 0.888395i 0.486973 + 0.873417i \(0.338101\pi\)
−0.999888 + 0.0149778i \(0.995232\pi\)
\(174\) 35.1191 2.66237
\(175\) 0 0
\(176\) −10.0281 + 17.3692i −0.755898 + 1.30925i
\(177\) 13.8977 1.04462
\(178\) −11.1342 + 19.2851i −0.834547 + 1.44548i
\(179\) −5.23458 9.06657i −0.391251 0.677667i 0.601364 0.798975i \(-0.294624\pi\)
−0.992615 + 0.121309i \(0.961291\pi\)
\(180\) −0.324388 0.561857i −0.0241785 0.0418783i
\(181\) −12.5209 −0.930674 −0.465337 0.885133i \(-0.654067\pi\)
−0.465337 + 0.885133i \(0.654067\pi\)
\(182\) 0 0
\(183\) −26.0737 −1.92742
\(184\) −2.09228 3.62393i −0.154245 0.267160i
\(185\) −0.300469 0.520428i −0.0220909 0.0382626i
\(186\) 2.72965 4.72789i 0.200148 0.346666i
\(187\) 3.51896 0.257332
\(188\) −8.47256 + 14.6749i −0.617925 + 1.07028i
\(189\) 0 0
\(190\) −0.495729 −0.0359640
\(191\) −6.55685 + 11.3568i −0.474437 + 0.821749i −0.999572 0.0292704i \(-0.990682\pi\)
0.525135 + 0.851019i \(0.324015\pi\)
\(192\) −3.65565 6.33176i −0.263823 0.456956i
\(193\) −0.520786 0.902028i −0.0374870 0.0649294i 0.846673 0.532113i \(-0.178602\pi\)
−0.884160 + 0.467184i \(0.845269\pi\)
\(194\) −36.1835 −2.59782
\(195\) 1.54328 + 0.532172i 0.110517 + 0.0381096i
\(196\) 0 0
\(197\) −0.739167 1.28027i −0.0526635 0.0912158i 0.838492 0.544914i \(-0.183438\pi\)
−0.891155 + 0.453698i \(0.850104\pi\)
\(198\) 8.79326 + 15.2304i 0.624910 + 1.08238i
\(199\) 7.04993 12.2108i 0.499756 0.865603i −0.500244 0.865885i \(-0.666756\pi\)
1.00000 0.000281618i \(8.96419e-5\pi\)
\(200\) 5.04467 0.356712
\(201\) 15.3668 26.6162i 1.08389 1.87736i
\(202\) −15.7330 + 27.2503i −1.10697 + 1.91733i
\(203\) 0 0
\(204\) −1.40192 + 2.42820i −0.0981543 + 0.170008i
\(205\) 0.532578 + 0.922451i 0.0371968 + 0.0644268i
\(206\) −6.72120 11.6415i −0.468288 0.811099i
\(207\) −9.31164 −0.647204
\(208\) 16.3442 + 5.63600i 1.13327 + 0.390786i
\(209\) 5.65402 0.391097
\(210\) 0 0
\(211\) −13.2346 22.9230i −0.911108 1.57809i −0.812501 0.582959i \(-0.801895\pi\)
−0.0986067 0.995126i \(-0.531439\pi\)
\(212\) −3.37619 + 5.84774i −0.231878 + 0.401624i
\(213\) 13.6965 0.938468
\(214\) 9.15376 15.8548i 0.625738 1.08381i
\(215\) −0.525751 + 0.910628i −0.0358559 + 0.0621043i
\(216\) −1.71981 −0.117019
\(217\) 0 0
\(218\) 12.8361 + 22.2328i 0.869370 + 1.50579i
\(219\) −4.45676 7.71934i −0.301160 0.521625i
\(220\) −1.19928 −0.0808552
\(221\) −0.577452 2.97790i −0.0388436 0.200315i
\(222\) −12.9794 −0.871122
\(223\) −0.364024 0.630508i −0.0243769 0.0422219i 0.853580 0.520962i \(-0.174427\pi\)
−0.877956 + 0.478740i \(0.841093\pi\)
\(224\) 0 0
\(225\) 5.61280 9.72165i 0.374187 0.648110i
\(226\) −7.93182 −0.527617
\(227\) −1.42598 + 2.46986i −0.0946454 + 0.163931i −0.909461 0.415790i \(-0.863505\pi\)
0.814815 + 0.579721i \(0.196838\pi\)
\(228\) −2.25252 + 3.90147i −0.149177 + 0.258381i
\(229\) −3.17352 −0.209712 −0.104856 0.994487i \(-0.533438\pi\)
−0.104856 + 0.994487i \(0.533438\pi\)
\(230\) 0.754584 1.30698i 0.0497558 0.0861795i
\(231\) 0 0
\(232\) −4.18874 7.25511i −0.275004 0.476321i
\(233\) 13.4071 0.878327 0.439163 0.898407i \(-0.355275\pi\)
0.439163 + 0.898407i \(0.355275\pi\)
\(234\) 11.4457 9.94051i 0.748227 0.649832i
\(235\) 2.30205 0.150169
\(236\) 4.40050 + 7.62188i 0.286448 + 0.496142i
\(237\) −12.3115 21.3242i −0.799721 1.38516i
\(238\) 0 0
\(239\) −15.5538 −1.00609 −0.503046 0.864259i \(-0.667788\pi\)
−0.503046 + 0.864259i \(0.667788\pi\)
\(240\) −1.08550 + 1.88014i −0.0700687 + 0.121363i
\(241\) −3.78787 + 6.56078i −0.243998 + 0.422617i −0.961849 0.273579i \(-0.911792\pi\)
0.717851 + 0.696196i \(0.245126\pi\)
\(242\) 12.0693 0.775844
\(243\) −9.69985 + 16.8006i −0.622245 + 1.07776i
\(244\) −8.25583 14.2995i −0.528525 0.915433i
\(245\) 0 0
\(246\) 23.0059 1.46680
\(247\) −0.927810 4.78468i −0.0590351 0.304442i
\(248\) −1.30229 −0.0826953
\(249\) −3.52587 6.10698i −0.223443 0.387014i
\(250\) 1.82651 + 3.16361i 0.115519 + 0.200084i
\(251\) 0.637382 1.10398i 0.0402312 0.0696825i −0.845209 0.534436i \(-0.820524\pi\)
0.885440 + 0.464754i \(0.153857\pi\)
\(252\) 0 0
\(253\) −8.60638 + 14.9067i −0.541079 + 0.937176i
\(254\) 2.03491 3.52456i 0.127682 0.221151i
\(255\) 0.380912 0.0238536
\(256\) −10.4620 + 18.1208i −0.653878 + 1.13255i
\(257\) −4.24010 7.34406i −0.264490 0.458110i 0.702940 0.711249i \(-0.251870\pi\)
−0.967430 + 0.253139i \(0.918537\pi\)
\(258\) 11.3555 + 19.6683i 0.706962 + 1.22449i
\(259\) 0 0
\(260\) 0.196798 + 1.01488i 0.0122049 + 0.0629402i
\(261\) −18.6419 −1.15390
\(262\) 2.11470 + 3.66276i 0.130646 + 0.226286i
\(263\) −6.39415 11.0750i −0.394280 0.682913i 0.598729 0.800952i \(-0.295673\pi\)
−0.993009 + 0.118038i \(0.962339\pi\)
\(264\) 4.87861 8.45000i 0.300258 0.520062i
\(265\) 0.917333 0.0563513
\(266\) 0 0
\(267\) 13.7462 23.8092i 0.841255 1.45710i
\(268\) 19.4627 1.18887
\(269\) −2.35586 + 4.08047i −0.143639 + 0.248790i −0.928864 0.370420i \(-0.879214\pi\)
0.785225 + 0.619210i \(0.212547\pi\)
\(270\) −0.310127 0.537156i −0.0188737 0.0326903i
\(271\) −9.00562 15.5982i −0.547052 0.947522i −0.998475 0.0552119i \(-0.982417\pi\)
0.451422 0.892310i \(-0.350917\pi\)
\(272\) 4.03407 0.244601
\(273\) 0 0
\(274\) 24.9885 1.50961
\(275\) −10.3754 17.9707i −0.625659 1.08367i
\(276\) −6.85742 11.8774i −0.412768 0.714936i
\(277\) 13.0604 22.6213i 0.784725 1.35918i −0.144438 0.989514i \(-0.546137\pi\)
0.929163 0.369670i \(-0.120529\pi\)
\(278\) −7.51700 −0.450840
\(279\) −1.44895 + 2.50965i −0.0867463 + 0.150249i
\(280\) 0 0
\(281\) −3.66197 −0.218455 −0.109227 0.994017i \(-0.534838\pi\)
−0.109227 + 0.994017i \(0.534838\pi\)
\(282\) 24.8605 43.0596i 1.48042 2.56416i
\(283\) 3.82263 + 6.62099i 0.227232 + 0.393577i 0.956987 0.290132i \(-0.0936991\pi\)
−0.729755 + 0.683709i \(0.760366\pi\)
\(284\) 4.33678 + 7.51153i 0.257341 + 0.445727i
\(285\) 0.612022 0.0362531
\(286\) −5.33465 27.5106i −0.315445 1.62674i
\(287\) 0 0
\(288\) 7.77953 + 13.4745i 0.458413 + 0.793995i
\(289\) 8.14610 + 14.1095i 0.479183 + 0.829968i
\(290\) 1.51068 2.61657i 0.0887100 0.153650i
\(291\) 44.6718 2.61871
\(292\) 2.82233 4.88842i 0.165164 0.286073i
\(293\) −8.57670 + 14.8553i −0.501056 + 0.867855i 0.498943 + 0.866635i \(0.333722\pi\)
−0.999999 + 0.00122001i \(0.999612\pi\)
\(294\) 0 0
\(295\) 0.597821 1.03546i 0.0348065 0.0602866i
\(296\) 1.54809 + 2.68136i 0.0899807 + 0.155851i
\(297\) 3.53715 + 6.12652i 0.205246 + 0.355497i
\(298\) 28.5264 1.65249
\(299\) 14.0270 + 4.83695i 0.811201 + 0.279728i
\(300\) 16.5339 0.954583
\(301\) 0 0
\(302\) −5.68698 9.85014i −0.327249 0.566812i
\(303\) 19.4238 33.6430i 1.11587 1.93274i
\(304\) 6.48166 0.371749
\(305\) −1.12158 + 1.94263i −0.0642215 + 0.111235i
\(306\) 1.76866 3.06340i 0.101107 0.175123i
\(307\) 28.0696 1.60201 0.801007 0.598655i \(-0.204298\pi\)
0.801007 + 0.598655i \(0.204298\pi\)
\(308\) 0 0
\(309\) 8.29793 + 14.3724i 0.472052 + 0.817619i
\(310\) −0.234836 0.406748i −0.0133378 0.0231017i
\(311\) 23.5341 1.33450 0.667248 0.744836i \(-0.267472\pi\)
0.667248 + 0.744836i \(0.267472\pi\)
\(312\) −7.95133 2.74187i −0.450155 0.155228i
\(313\) 3.34860 0.189274 0.0946370 0.995512i \(-0.469831\pi\)
0.0946370 + 0.995512i \(0.469831\pi\)
\(314\) 4.21494 + 7.30050i 0.237863 + 0.411991i
\(315\) 0 0
\(316\) 7.79652 13.5040i 0.438588 0.759658i
\(317\) −7.27834 −0.408793 −0.204396 0.978888i \(-0.565523\pi\)
−0.204396 + 0.978888i \(0.565523\pi\)
\(318\) 9.90655 17.1586i 0.555532 0.962209i
\(319\) −17.2300 + 29.8432i −0.964694 + 1.67090i
\(320\) −0.629002 −0.0351623
\(321\) −11.3011 + 19.5742i −0.630768 + 1.09252i
\(322\) 0 0
\(323\) −0.568618 0.984875i −0.0316388 0.0547999i
\(324\) −15.4984 −0.861021
\(325\) −13.5050 + 11.7290i −0.749123 + 0.650610i
\(326\) 3.38658 0.187565
\(327\) −15.8473 27.4484i −0.876359 1.51790i
\(328\) −2.74396 4.75268i −0.151510 0.262423i
\(329\) 0 0
\(330\) 3.51896 0.193712
\(331\) 7.16168 12.4044i 0.393642 0.681807i −0.599285 0.800536i \(-0.704548\pi\)
0.992927 + 0.118728i \(0.0378818\pi\)
\(332\) 2.23282 3.86736i 0.122542 0.212249i
\(333\) 6.88973 0.377555
\(334\) −9.94855 + 17.2314i −0.544360 + 0.942860i
\(335\) −1.32203 2.28983i −0.0722304 0.125107i
\(336\) 0 0
\(337\) 17.1802 0.935868 0.467934 0.883764i \(-0.344999\pi\)
0.467934 + 0.883764i \(0.344999\pi\)
\(338\) −22.4053 + 9.02883i −1.21869 + 0.491104i
\(339\) 9.79255 0.531858
\(340\) 0.120610 + 0.208902i 0.00654098 + 0.0113293i
\(341\) 2.67841 + 4.63915i 0.145044 + 0.251224i
\(342\) 2.84175 4.92206i 0.153664 0.266155i
\(343\) 0 0
\(344\) 2.70879 4.69176i 0.146048 0.252963i
\(345\) −0.931602 + 1.61358i −0.0501558 + 0.0868723i
\(346\) 25.0716 1.34786
\(347\) 3.85139 6.67080i 0.206753 0.358107i −0.743937 0.668250i \(-0.767044\pi\)
0.950690 + 0.310143i \(0.100377\pi\)
\(348\) −13.7286 23.7786i −0.735928 1.27466i
\(349\) 11.1850 + 19.3730i 0.598721 + 1.03702i 0.993010 + 0.118029i \(0.0376575\pi\)
−0.394289 + 0.918986i \(0.629009\pi\)
\(350\) 0 0
\(351\) 4.60409 3.99863i 0.245748 0.213431i
\(352\) 28.7613 1.53298
\(353\) −11.1311 19.2797i −0.592451 1.02616i −0.993901 0.110275i \(-0.964827\pi\)
0.401450 0.915881i \(-0.368506\pi\)
\(354\) −12.9121 22.3644i −0.686270 1.18865i
\(355\) 0.589165 1.02046i 0.0312697 0.0541606i
\(356\) 17.4101 0.922735
\(357\) 0 0
\(358\) −9.72670 + 16.8471i −0.514072 + 0.890399i
\(359\) −2.75842 −0.145584 −0.0727920 0.997347i \(-0.523191\pi\)
−0.0727920 + 0.997347i \(0.523191\pi\)
\(360\) 0.227054 0.393269i 0.0119668 0.0207271i
\(361\) 8.58638 + 14.8721i 0.451915 + 0.782740i
\(362\) 11.6330 + 20.1489i 0.611415 + 1.05900i
\(363\) −14.9006 −0.782081
\(364\) 0 0
\(365\) −0.766844 −0.0401385
\(366\) 24.2246 + 41.9582i 1.26624 + 2.19319i
\(367\) −7.07485 12.2540i −0.369304 0.639654i 0.620153 0.784481i \(-0.287071\pi\)
−0.989457 + 0.144827i \(0.953737\pi\)
\(368\) −9.86618 + 17.0887i −0.514310 + 0.890812i
\(369\) −12.2119 −0.635729
\(370\) −0.558320 + 0.967039i −0.0290257 + 0.0502740i
\(371\) 0 0
\(372\) −4.26823 −0.221298
\(373\) 2.52142 4.36723i 0.130554 0.226127i −0.793336 0.608784i \(-0.791658\pi\)
0.923890 + 0.382657i \(0.124991\pi\)
\(374\) −3.26940 5.66276i −0.169056 0.292814i
\(375\) −2.25499 3.90576i −0.116447 0.201693i
\(376\) −11.8607 −0.611668
\(377\) 28.0820 + 9.68358i 1.44630 + 0.498730i
\(378\) 0 0
\(379\) 3.02982 + 5.24780i 0.155631 + 0.269561i 0.933289 0.359127i \(-0.116925\pi\)
−0.777657 + 0.628688i \(0.783592\pi\)
\(380\) 0.193787 + 0.335650i 0.00994109 + 0.0172185i
\(381\) −2.51228 + 4.35139i −0.128708 + 0.222929i
\(382\) 24.3674 1.24674
\(383\) −2.27052 + 3.93266i −0.116018 + 0.200950i −0.918186 0.396149i \(-0.870346\pi\)
0.802168 + 0.597098i \(0.203680\pi\)
\(384\) 8.98165 15.5567i 0.458343 0.793873i
\(385\) 0 0
\(386\) −0.967705 + 1.67611i −0.0492549 + 0.0853120i
\(387\) −6.02771 10.4403i −0.306406 0.530710i
\(388\) 14.1446 + 24.4992i 0.718085 + 1.24376i
\(389\) 4.50765 0.228547 0.114273 0.993449i \(-0.463546\pi\)
0.114273 + 0.993449i \(0.463546\pi\)
\(390\) −0.577452 2.97790i −0.0292404 0.150792i
\(391\) 3.46213 0.175088
\(392\) 0 0
\(393\) −2.61078 4.52201i −0.131697 0.228105i
\(394\) −1.37349 + 2.37896i −0.0691955 + 0.119850i
\(395\) −2.11836 −0.106586
\(396\) 6.87482 11.9075i 0.345473 0.598376i
\(397\) 2.00174 3.46712i 0.100465 0.174010i −0.811412 0.584475i \(-0.801300\pi\)
0.911876 + 0.410465i \(0.134634\pi\)
\(398\) −26.1998 −1.31328
\(399\) 0 0
\(400\) −11.8941 20.6012i −0.594706 1.03006i
\(401\) −6.30674 10.9236i −0.314944 0.545498i 0.664482 0.747304i \(-0.268652\pi\)
−0.979426 + 0.201806i \(0.935319\pi\)
\(402\) −57.1081 −2.84829
\(403\) 3.48633 3.02786i 0.173667 0.150829i
\(404\) 24.6010 1.22394
\(405\) 1.05275 + 1.82342i 0.0523116 + 0.0906064i
\(406\) 0 0
\(407\) 6.36790 11.0295i 0.315645 0.546713i
\(408\) −1.96254 −0.0971604
\(409\) 10.3476 17.9226i 0.511657 0.886216i −0.488252 0.872703i \(-0.662365\pi\)
0.999909 0.0135128i \(-0.00430140\pi\)
\(410\) 0.989615 1.71406i 0.0488736 0.0846516i
\(411\) −30.8506 −1.52175
\(412\) −5.25482 + 9.10162i −0.258886 + 0.448404i
\(413\) 0 0
\(414\) 8.65126 + 14.9844i 0.425186 + 0.736444i
\(415\) −0.606672 −0.0297803
\(416\) −4.71965 24.3391i −0.231400 1.19332i
\(417\) 9.28042 0.454464
\(418\) −5.25304 9.09854i −0.256935 0.445024i
\(419\) −10.9088 18.8945i −0.532928 0.923058i −0.999261 0.0384484i \(-0.987758\pi\)
0.466333 0.884609i \(-0.345575\pi\)
\(420\) 0 0
\(421\) 9.42727 0.459457 0.229728 0.973255i \(-0.426216\pi\)
0.229728 + 0.973255i \(0.426216\pi\)
\(422\) −24.5920 + 42.5947i −1.19712 + 2.07348i
\(423\) −13.1964 + 22.8569i −0.641632 + 1.11134i
\(424\) −4.72631 −0.229530
\(425\) −2.08688 + 3.61458i −0.101228 + 0.175333i
\(426\) −12.7251 22.0406i −0.616535 1.06787i
\(427\) 0 0
\(428\) −14.3133 −0.691861
\(429\) 6.58611 + 33.9643i 0.317980 + 1.63981i
\(430\) 1.95386 0.0942235
\(431\) −10.2138 17.6908i −0.491980 0.852134i 0.507977 0.861370i \(-0.330393\pi\)
−0.999957 + 0.00923613i \(0.997060\pi\)
\(432\) 4.05491 + 7.02332i 0.195092 + 0.337909i
\(433\) 13.1743 22.8186i 0.633117 1.09659i −0.353794 0.935323i \(-0.615109\pi\)
0.986911 0.161267i \(-0.0515581\pi\)
\(434\) 0 0
\(435\) −1.86507 + 3.23039i −0.0894231 + 0.154885i
\(436\) 10.0356 17.3822i 0.480619 0.832457i
\(437\) 5.56272 0.266101
\(438\) −8.28138 + 14.3438i −0.395700 + 0.685372i
\(439\) 12.5655 + 21.7641i 0.599720 + 1.03875i 0.992862 + 0.119267i \(0.0380546\pi\)
−0.393142 + 0.919478i \(0.628612\pi\)
\(440\) −0.419714 0.726967i −0.0200091 0.0346568i
\(441\) 0 0
\(442\) −4.25558 + 3.69595i −0.202417 + 0.175799i
\(443\) 18.5199 0.879907 0.439953 0.898021i \(-0.354995\pi\)
0.439953 + 0.898021i \(0.354995\pi\)
\(444\) 5.07384 + 8.78815i 0.240794 + 0.417067i
\(445\) −1.18261 2.04834i −0.0560611 0.0971006i
\(446\) −0.676415 + 1.17159i −0.0320292 + 0.0554762i
\(447\) −35.2184 −1.66577
\(448\) 0 0
\(449\) −5.82155 + 10.0832i −0.274736 + 0.475856i −0.970068 0.242832i \(-0.921924\pi\)
0.695333 + 0.718688i \(0.255257\pi\)
\(450\) −20.8590 −0.983301
\(451\) −11.2870 + 19.5497i −0.531485 + 0.920559i
\(452\) 3.10066 + 5.37050i 0.145843 + 0.252607i
\(453\) 7.02109 + 12.1609i 0.329880 + 0.571368i
\(454\) 5.29939 0.248713
\(455\) 0 0
\(456\) −3.15328 −0.147666
\(457\) −10.2592 17.7695i −0.479906 0.831222i 0.519828 0.854271i \(-0.325996\pi\)
−0.999734 + 0.0230490i \(0.992663\pi\)
\(458\) 2.94845 + 5.10687i 0.137772 + 0.238629i
\(459\) 0.711453 1.23227i 0.0332078 0.0575176i
\(460\) −1.17991 −0.0550136
\(461\) 1.02038 1.76734i 0.0475236 0.0823134i −0.841285 0.540592i \(-0.818200\pi\)
0.888809 + 0.458278i \(0.151534\pi\)
\(462\) 0 0
\(463\) 3.03155 0.140888 0.0704441 0.997516i \(-0.477558\pi\)
0.0704441 + 0.997516i \(0.477558\pi\)
\(464\) −19.7521 + 34.2116i −0.916968 + 1.58824i
\(465\) 0.289926 + 0.502167i 0.0134450 + 0.0232874i
\(466\) −12.4563 21.5749i −0.577025 0.999436i
\(467\) 12.9274 0.598210 0.299105 0.954220i \(-0.403312\pi\)
0.299105 + 0.954220i \(0.403312\pi\)
\(468\) −11.2048 3.86378i −0.517943 0.178603i
\(469\) 0 0
\(470\) −2.13879 3.70449i −0.0986549 0.170875i
\(471\) −5.20373 9.01312i −0.239775 0.415303i
\(472\) −3.08011 + 5.33491i −0.141774 + 0.245559i
\(473\) −22.2847 −1.02465
\(474\) −22.8768 + 39.6238i −1.05077 + 1.81998i
\(475\) −3.35305 + 5.80766i −0.153849 + 0.266474i
\(476\) 0 0
\(477\) −5.25858 + 9.10814i −0.240774 + 0.417033i
\(478\) 14.4507 + 25.0294i 0.660962 + 1.14482i
\(479\) 18.2911 + 31.6810i 0.835740 + 1.44754i 0.893427 + 0.449209i \(0.148294\pi\)
−0.0576873 + 0.998335i \(0.518373\pi\)
\(480\) 3.11328 0.142101
\(481\) −10.3786 3.57888i −0.473225 0.163183i
\(482\) 14.0769 0.641187
\(483\) 0 0
\(484\) −4.71806 8.17191i −0.214457 0.371451i
\(485\) 1.92159 3.32829i 0.0872550 0.151130i
\(486\) 36.0478 1.63516
\(487\) −18.3748 + 31.8261i −0.832642 + 1.44218i 0.0632939 + 0.997995i \(0.479839\pi\)
−0.895936 + 0.444183i \(0.853494\pi\)
\(488\) 5.77864 10.0089i 0.261587 0.453081i
\(489\) −4.18103 −0.189073
\(490\) 0 0
\(491\) 4.09899 + 7.09965i 0.184985 + 0.320403i 0.943571 0.331169i \(-0.107443\pi\)
−0.758587 + 0.651572i \(0.774110\pi\)
\(492\) −8.99331 15.5769i −0.405450 0.702260i
\(493\) 6.93119 0.312165
\(494\) −6.83757 + 5.93840i −0.307637 + 0.267181i
\(495\) −1.86793 −0.0839572
\(496\) 3.07048 + 5.31823i 0.137869 + 0.238795i
\(497\) 0 0
\(498\) −6.55163 + 11.3478i −0.293585 + 0.508505i
\(499\) −43.2532 −1.93628 −0.968141 0.250407i \(-0.919436\pi\)
−0.968141 + 0.250407i \(0.919436\pi\)
\(500\) 1.42802 2.47340i 0.0638629 0.110614i
\(501\) 12.2824 21.2737i 0.548736 0.950439i
\(502\) −2.36872 −0.105721
\(503\) 0.00909609 0.0157549i 0.000405575 0.000702476i −0.865823 0.500351i \(-0.833204\pi\)
0.866228 + 0.499649i \(0.166538\pi\)
\(504\) 0 0
\(505\) −1.67106 2.89436i −0.0743612 0.128797i
\(506\) 31.9841 1.42187
\(507\) 27.6614 11.1469i 1.22848 0.495052i
\(508\) −3.18190 −0.141174
\(509\) 21.5503 + 37.3262i 0.955200 + 1.65446i 0.733909 + 0.679248i \(0.237694\pi\)
0.221292 + 0.975208i \(0.428973\pi\)
\(510\) −0.353897 0.612968i −0.0156708 0.0271427i
\(511\) 0 0
\(512\) 23.2197 1.02617
\(513\) 1.14311 1.97993i 0.0504697 0.0874161i
\(514\) −7.87878 + 13.6464i −0.347518 + 0.601919i
\(515\) 1.42777 0.0629149
\(516\) 8.87804 15.3772i 0.390834 0.676944i
\(517\) 24.3939 + 42.2514i 1.07284 + 1.85822i
\(518\) 0 0
\(519\) −30.9531 −1.35869
\(520\) −0.546317 + 0.474474i −0.0239576 + 0.0208071i
\(521\) −20.9540 −0.918012 −0.459006 0.888433i \(-0.651794\pi\)
−0.459006 + 0.888433i \(0.651794\pi\)
\(522\) 17.3198 + 29.9988i 0.758068 + 1.31301i
\(523\) −17.3701 30.0860i −0.759543 1.31557i −0.943084 0.332555i \(-0.892089\pi\)
0.183541 0.983012i \(-0.441244\pi\)
\(524\) 1.65333 2.86365i 0.0722260 0.125099i
\(525\) 0 0
\(526\) −11.8814 + 20.5791i −0.518052 + 0.897292i
\(527\) 0.538730 0.933107i 0.0234674 0.0406468i
\(528\) −46.0104 −2.00235
\(529\) 3.03260 5.25262i 0.131852 0.228375i
\(530\) −0.852276 1.47619i −0.0370205 0.0641214i
\(531\) 6.85398 + 11.8714i 0.297438 + 0.515177i
\(532\) 0 0
\(533\) 18.3960 + 6.34352i 0.796819 + 0.274769i
\(534\) −51.0854 −2.21068
\(535\) 0.972255 + 1.68400i 0.0420343 + 0.0728055i
\(536\) 6.81142 + 11.7977i 0.294209 + 0.509584i
\(537\) 12.0085 20.7993i 0.518205 0.897557i
\(538\) 8.75513 0.377460
\(539\) 0 0
\(540\) −0.242466 + 0.419964i −0.0104341 + 0.0180724i
\(541\) −3.29846 −0.141812 −0.0709059 0.997483i \(-0.522589\pi\)
−0.0709059 + 0.997483i \(0.522589\pi\)
\(542\) −16.7339 + 28.9839i −0.718782 + 1.24497i
\(543\) −14.3619 24.8756i −0.616330 1.06752i
\(544\) −2.89249 5.00993i −0.124014 0.214799i
\(545\) −2.72674 −0.116801
\(546\) 0 0
\(547\) 21.9417 0.938161 0.469080 0.883155i \(-0.344585\pi\)
0.469080 + 0.883155i \(0.344585\pi\)
\(548\) −9.76836 16.9193i −0.417284 0.722756i
\(549\) −12.8589 22.2722i −0.548803 0.950554i
\(550\) −19.2791 + 33.3924i −0.822065 + 1.42386i
\(551\) 11.1366 0.474434
\(552\) 4.79983 8.31354i 0.204294 0.353848i
\(553\) 0 0
\(554\) −48.5368 −2.06213
\(555\) 0.689297 1.19390i 0.0292590 0.0506781i
\(556\) 2.93850 + 5.08963i 0.124620 + 0.215848i
\(557\) 7.14329 + 12.3725i 0.302671 + 0.524241i 0.976740 0.214427i \(-0.0687884\pi\)
−0.674069 + 0.738668i \(0.735455\pi\)
\(558\) 5.38476 0.227955
\(559\) 3.65686 + 18.8583i 0.154669 + 0.797621i
\(560\) 0 0
\(561\) 4.03637 + 6.99119i 0.170416 + 0.295168i
\(562\) 3.40226 + 5.89289i 0.143516 + 0.248577i
\(563\) 3.39392 5.87844i 0.143037 0.247747i −0.785602 0.618732i \(-0.787647\pi\)
0.928639 + 0.370985i \(0.120980\pi\)
\(564\) −38.8733 −1.63686
\(565\) 0.421234 0.729599i 0.0177215 0.0306945i
\(566\) 7.10307 12.3029i 0.298564 0.517128i
\(567\) 0 0
\(568\) −3.03552 + 5.25767i −0.127367 + 0.220607i
\(569\) 8.66061 + 15.0006i 0.363072 + 0.628859i 0.988465 0.151451i \(-0.0483947\pi\)
−0.625393 + 0.780310i \(0.715061\pi\)
\(570\) −0.568618 0.984875i −0.0238168 0.0412519i
\(571\) −13.0116 −0.544520 −0.272260 0.962224i \(-0.587771\pi\)
−0.272260 + 0.962224i \(0.587771\pi\)
\(572\) −16.5416 + 14.3663i −0.691638 + 0.600685i
\(573\) −30.0837 −1.25676
\(574\) 0 0
\(575\) −10.2078 17.6805i −0.425696 0.737327i
\(576\) 3.60574 6.24532i 0.150239 0.260222i
\(577\) 0.731535 0.0304542 0.0152271 0.999884i \(-0.495153\pi\)
0.0152271 + 0.999884i \(0.495153\pi\)
\(578\) 15.1368 26.2177i 0.629607 1.09051i
\(579\) 1.19472 2.06931i 0.0496508 0.0859978i
\(580\) −2.36218 −0.0980842
\(581\) 0 0
\(582\) −41.5037 71.8865i −1.72038 2.97979i
\(583\) 9.72061 + 16.8366i 0.402586 + 0.697300i
\(584\) 3.95096 0.163492
\(585\) 0.306522 + 1.58073i 0.0126731 + 0.0653550i
\(586\) 31.8738 1.31669
\(587\) −4.26142 7.38099i −0.175888 0.304646i 0.764581 0.644528i \(-0.222946\pi\)
−0.940468 + 0.339882i \(0.889613\pi\)
\(588\) 0 0
\(589\) 0.865594 1.49925i 0.0356662 0.0617756i
\(590\) −2.22170 −0.0914657
\(591\) 1.69570 2.93704i 0.0697517 0.120814i
\(592\) 7.30004 12.6440i 0.300030 0.519667i
\(593\) 31.3093 1.28572 0.642860 0.765984i \(-0.277748\pi\)
0.642860 + 0.765984i \(0.277748\pi\)
\(594\) 6.57259 11.3841i 0.269677 0.467093i
\(595\) 0 0
\(596\) −11.1514 19.3147i −0.456777 0.791161i
\(597\) 32.3460 1.32383
\(598\) −5.24850 27.0663i −0.214627 1.10683i
\(599\) −0.750232 −0.0306537 −0.0153268 0.999883i \(-0.504879\pi\)
−0.0153268 + 0.999883i \(0.504879\pi\)
\(600\) 5.78641 + 10.0224i 0.236229 + 0.409161i
\(601\) −4.77652 8.27318i −0.194838 0.337470i 0.752009 0.659153i \(-0.229085\pi\)
−0.946848 + 0.321683i \(0.895752\pi\)
\(602\) 0 0
\(603\) 30.3141 1.23449
\(604\) −4.44624 + 7.70111i −0.180915 + 0.313354i
\(605\) −0.640963 + 1.11018i −0.0260588 + 0.0451352i
\(606\) −72.1851 −2.93232
\(607\) 11.1197 19.2599i 0.451336 0.781737i −0.547133 0.837045i \(-0.684281\pi\)
0.998469 + 0.0553087i \(0.0176143\pi\)
\(608\) −4.64745 8.04961i −0.188479 0.326455i
\(609\) 0 0
\(610\) 4.16815 0.168764
\(611\) 31.7521 27.5765i 1.28455 1.11563i
\(612\) −2.76557 −0.111791
\(613\) 4.13993 + 7.17057i 0.167210 + 0.289617i 0.937438 0.348152i \(-0.113191\pi\)
−0.770228 + 0.637769i \(0.779857\pi\)
\(614\) −26.0789 45.1699i −1.05246 1.82291i
\(615\) −1.22177 + 2.11617i −0.0492665 + 0.0853321i
\(616\) 0 0
\(617\) −10.1656 + 17.6073i −0.409252 + 0.708845i −0.994806 0.101789i \(-0.967543\pi\)
0.585554 + 0.810633i \(0.300877\pi\)
\(618\) 15.4189 26.7063i 0.620238 1.07428i
\(619\) −5.34097 −0.214672 −0.107336 0.994223i \(-0.534232\pi\)
−0.107336 + 0.994223i \(0.534232\pi\)
\(620\) −0.183601 + 0.318007i −0.00737361 + 0.0127715i
\(621\) 3.48003 + 6.02758i 0.139649 + 0.241879i
\(622\) −21.8651 37.8714i −0.876709 1.51850i
\(623\) 0 0
\(624\) 7.55018 + 38.9360i 0.302249 + 1.55869i
\(625\) 24.4172 0.976690
\(626\) −3.11112 5.38862i −0.124345 0.215372i
\(627\) 6.48536 + 11.2330i 0.259000 + 0.448601i
\(628\) 3.29536 5.70773i 0.131499 0.227763i
\(629\) −2.56165 −0.102140
\(630\) 0 0
\(631\) −3.23331 + 5.60026i −0.128716 + 0.222943i −0.923179 0.384369i \(-0.874419\pi\)
0.794463 + 0.607312i \(0.207752\pi\)
\(632\) 10.9143 0.434147
\(633\) 30.3611 52.5870i 1.20675 2.09014i
\(634\) 6.76217 + 11.7124i 0.268560 + 0.465160i
\(635\) 0.216135 + 0.374357i 0.00857707 + 0.0148559i
\(636\) −15.4904 −0.614236
\(637\) 0 0
\(638\) 64.0322 2.53506
\(639\) 6.75475 + 11.6996i 0.267214 + 0.462828i
\(640\) −0.772706 1.33837i −0.0305439 0.0529035i
\(641\) −11.6644 + 20.2034i −0.460717 + 0.797985i −0.998997 0.0447808i \(-0.985741\pi\)
0.538280 + 0.842766i \(0.319074\pi\)
\(642\) 41.9987 1.65756
\(643\) −1.79439 + 3.10797i −0.0707637 + 0.122566i −0.899236 0.437463i \(-0.855877\pi\)
0.828472 + 0.560030i \(0.189210\pi\)
\(644\) 0 0
\(645\) −2.41222 −0.0949810
\(646\) −1.05658 + 1.83006i −0.0415707 + 0.0720026i
\(647\) −19.8262 34.3400i −0.779448 1.35004i −0.932260 0.361788i \(-0.882166\pi\)
0.152812 0.988255i \(-0.451167\pi\)
\(648\) −5.42402 9.39467i −0.213076 0.369058i
\(649\) 25.3395 0.994661
\(650\) 31.4218 + 10.8352i 1.23246 + 0.424993i
\(651\) 0 0
\(652\) −1.32386 2.29299i −0.0518464 0.0898005i
\(653\) −9.06777 15.7058i −0.354849 0.614617i 0.632243 0.774770i \(-0.282135\pi\)
−0.987092 + 0.160153i \(0.948801\pi\)
\(654\) −29.4469 + 51.0035i −1.15146 + 1.99439i
\(655\) −0.449219 −0.0175525
\(656\) −12.9392 + 22.4114i −0.505192 + 0.875017i
\(657\) 4.39592 7.61395i 0.171501 0.297048i
\(658\) 0 0
\(659\) −6.74052 + 11.6749i −0.262573 + 0.454791i −0.966925 0.255061i \(-0.917905\pi\)
0.704352 + 0.709851i \(0.251238\pi\)
\(660\) −1.37561 2.38263i −0.0535456 0.0927437i
\(661\) 5.15611 + 8.93064i 0.200549 + 0.347362i 0.948706 0.316161i \(-0.102394\pi\)
−0.748156 + 0.663523i \(0.769061\pi\)
\(662\) −26.6151 −1.03443
\(663\) 5.25390 4.56299i 0.204044 0.177212i
\(664\) 3.12571 0.121301
\(665\) 0 0
\(666\) −6.40111 11.0870i −0.248038 0.429614i
\(667\) −16.9517 + 29.3613i −0.656374 + 1.13687i
\(668\) 15.5561 0.601884
\(669\) 0.835096 1.44643i 0.0322867 0.0559222i
\(670\) −2.45655 + 4.25487i −0.0949049 + 0.164380i
\(671\) −47.5397 −1.83525
\(672\) 0 0
\(673\) 4.61528 + 7.99390i 0.177906 + 0.308142i 0.941163 0.337953i \(-0.109734\pi\)
−0.763257 + 0.646095i \(0.776401\pi\)
\(674\) −15.9618 27.6467i −0.614827 1.06491i
\(675\) −8.39066 −0.322956
\(676\) 14.8718 + 11.6407i 0.571993 + 0.447721i
\(677\) 21.0934 0.810687 0.405343 0.914165i \(-0.367152\pi\)
0.405343 + 0.914165i \(0.367152\pi\)
\(678\) −9.09807 15.7583i −0.349409 0.605194i
\(679\) 0 0
\(680\) −0.0844203 + 0.146220i −0.00323737 + 0.00560729i
\(681\) −6.54258 −0.250712
\(682\) 4.97693 8.62029i 0.190576 0.330088i
\(683\) 19.1106 33.1005i 0.731246 1.26656i −0.225104 0.974335i \(-0.572272\pi\)
0.956351 0.292221i \(-0.0943944\pi\)
\(684\) −4.44353 −0.169902
\(685\) −1.32706 + 2.29854i −0.0507044 + 0.0878226i
\(686\) 0 0
\(687\) −3.64013 6.30490i −0.138880 0.240547i
\(688\) −25.5467 −0.973960
\(689\) 12.6527 10.9888i 0.482031 0.418642i
\(690\) 3.46213 0.131801
\(691\) −13.1161 22.7178i −0.498960 0.864224i 0.501039 0.865425i \(-0.332951\pi\)
−0.999999 + 0.00120019i \(0.999618\pi\)
\(692\) −9.80084 16.9755i −0.372572 0.645313i
\(693\) 0 0
\(694\) −14.3130 −0.543314
\(695\) 0.399204 0.691442i 0.0151427 0.0262279i
\(696\) 9.60925 16.6437i 0.364238 0.630878i
\(697\) 4.54049 0.171983
\(698\) 20.7836 35.9982i 0.786670 1.36255i
\(699\) 15.3784 + 26.6361i 0.581664 + 1.00747i
\(700\) 0 0
\(701\) −46.7346 −1.76514 −0.882570 0.470180i \(-0.844189\pi\)
−0.882570 + 0.470180i \(0.844189\pi\)
\(702\) −10.7122 3.69392i −0.404307 0.139418i
\(703\) −4.11588 −0.155233
\(704\) −6.66528 11.5446i −0.251207 0.435104i
\(705\) 2.64053 + 4.57353i 0.0994480 + 0.172249i
\(706\) −20.6835 + 35.8248i −0.778433 + 1.34828i
\(707\) 0 0
\(708\) −10.0950 + 17.4851i −0.379395 + 0.657131i
\(709\) 23.7232 41.0898i 0.890944 1.54316i 0.0521988 0.998637i \(-0.483377\pi\)
0.838745 0.544524i \(-0.183290\pi\)
\(710\) −2.18953 −0.0821715
\(711\) 12.1435 21.0331i 0.455415 0.788802i
\(712\) 6.09307 + 10.5535i 0.228348 + 0.395510i
\(713\) 2.63516 + 4.56423i 0.0986876 + 0.170932i
\(714\) 0 0
\(715\) 2.81384 + 0.970301i 0.105232 + 0.0362872i
\(716\) 15.2092 0.568395
\(717\) −17.8408 30.9011i −0.666275 1.15402i
\(718\) 2.56280 + 4.43890i 0.0956428 + 0.165658i
\(719\) −24.6190 + 42.6413i −0.918133 + 1.59025i −0.115884 + 0.993263i \(0.536970\pi\)
−0.802249 + 0.596990i \(0.796363\pi\)
\(720\) −2.14136 −0.0798037
\(721\) 0 0
\(722\) 15.9549 27.6347i 0.593779 1.02846i
\(723\) −17.3793 −0.646342
\(724\) 9.09498 15.7530i 0.338012 0.585454i
\(725\) −20.4361 35.3963i −0.758977 1.31459i
\(726\) 13.8439 + 23.9783i 0.513795 + 0.889919i
\(727\) 32.0495 1.18865 0.594325 0.804225i \(-0.297419\pi\)
0.594325 + 0.804225i \(0.297419\pi\)
\(728\) 0 0
\(729\) −12.4996 −0.462947
\(730\) 0.712460 + 1.23402i 0.0263693 + 0.0456730i
\(731\) 2.24114 + 3.88178i 0.0828917 + 0.143573i
\(732\) 18.9394 32.8041i 0.700022 1.21247i
\(733\) −28.2010 −1.04163 −0.520813 0.853670i \(-0.674371\pi\)
−0.520813 + 0.853670i \(0.674371\pi\)
\(734\) −13.1462 + 22.7699i −0.485236 + 0.840453i
\(735\) 0 0
\(736\) 28.2968 1.04303
\(737\) 28.0181 48.5288i 1.03206 1.78758i
\(738\) 11.3459 + 19.6516i 0.417648 + 0.723387i
\(739\) 21.2685 + 36.8381i 0.782375 + 1.35511i 0.930555 + 0.366153i \(0.119325\pi\)
−0.148180 + 0.988960i \(0.547342\pi\)
\(740\) 0.873021 0.0320929
\(741\) 8.44160 7.33149i 0.310110 0.269329i
\(742\) 0 0
\(743\) −7.95711 13.7821i −0.291918 0.505617i 0.682345 0.731030i \(-0.260960\pi\)
−0.974263 + 0.225413i \(0.927627\pi\)
\(744\) −1.49377 2.58728i −0.0547641 0.0948543i
\(745\) −1.51495 + 2.62396i −0.0555033 + 0.0961346i
\(746\) −9.37042 −0.343075
\(747\) 3.47773 6.02360i 0.127243 0.220392i
\(748\) −2.55611 + 4.42731i −0.0934605 + 0.161878i
\(749\) 0 0
\(750\) −4.19014 + 7.25754i −0.153002 + 0.265008i
\(751\) −9.09981 15.7613i −0.332057 0.575139i 0.650858 0.759199i \(-0.274409\pi\)
−0.982915 + 0.184060i \(0.941076\pi\)
\(752\) 27.9646 + 48.4362i 1.01977 + 1.76629i
\(753\) 2.92440 0.106571
\(754\) −10.5075 54.1868i −0.382661 1.97337i
\(755\) 1.20807 0.0439662
\(756\) 0 0
\(757\) 22.4502 + 38.8849i 0.815967 + 1.41330i 0.908632 + 0.417598i \(0.137128\pi\)
−0.0926649 + 0.995697i \(0.529539\pi\)
\(758\) 5.62989 9.75126i 0.204487 0.354182i
\(759\) −39.4872 −1.43330
\(760\) −0.135641 + 0.234937i −0.00492021 + 0.00852205i
\(761\) −13.2444 + 22.9399i −0.480108 + 0.831572i −0.999740 0.0228184i \(-0.992736\pi\)
0.519631 + 0.854391i \(0.326069\pi\)
\(762\) 9.33644 0.338223
\(763\) 0 0
\(764\) −9.52554 16.4987i −0.344622 0.596903i
\(765\) 0.187856 + 0.325375i 0.00679193 + 0.0117640i
\(766\) 8.43800 0.304877
\(767\) −4.15814 21.4434i −0.150142 0.774276i
\(768\) −48.0013 −1.73210
\(769\) 6.98127 + 12.0919i 0.251751 + 0.436045i 0.964008 0.265873i \(-0.0856603\pi\)
−0.712257 + 0.701919i \(0.752327\pi\)
\(770\) 0 0
\(771\) 9.72707 16.8478i 0.350312 0.606758i
\(772\) 1.51316 0.0544597
\(773\) 6.40564 11.0949i 0.230395 0.399056i −0.727529 0.686077i \(-0.759332\pi\)
0.957924 + 0.287021i \(0.0926648\pi\)
\(774\) −11.2005 + 19.3998i −0.402592 + 0.697310i
\(775\) −6.35361 −0.228228
\(776\) −9.90048 + 17.1481i −0.355406 + 0.615582i
\(777\) 0 0
\(778\) −4.18797 7.25378i −0.150146 0.260061i
\(779\) 7.29534 0.261383
\(780\) −1.79055 + 1.55509i −0.0641120 + 0.0556810i
\(781\) 24.9726 0.893590
\(782\) −3.21660 5.57132i −0.115025 0.199230i
\(783\) 6.96701 + 12.0672i 0.248981 + 0.431247i