Properties

Label 637.2.h.l.471.6
Level $637$
Weight $2$
Character 637.471
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

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

Embedding invariants

Embedding label 471.6
Root \(0.217953 + 0.377506i\) of defining polynomial
Character \(\chi\) \(=\) 637.471
Dual form 637.2.h.l.165.6

$q$-expansion

\(f(q)\) \(=\) \(q+1.85816 q^{2} +(1.14703 - 1.98672i) q^{3} +1.45276 q^{4} +(-0.0986811 + 0.170921i) q^{5} +(2.13137 - 3.69165i) q^{6} -1.01686 q^{8} +(-1.13137 - 1.95960i) q^{9} +O(q^{10})\) \(q+1.85816 q^{2} +(1.14703 - 1.98672i) q^{3} +1.45276 q^{4} +(-0.0986811 + 0.170921i) 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} +(1.66637 - 2.88623i) q^{12} +(2.72221 - 2.36423i) q^{13} +(0.226381 + 0.392104i) q^{15} -4.79501 q^{16} -0.841305 q^{17} +(-2.10227 - 3.64125i) q^{18} +(0.675876 + 1.17065i) q^{19} +(-0.143360 + 0.248307i) q^{20} +(3.88610 - 6.73092i) q^{22} -4.11519 q^{23} +(-1.16637 + 2.02021i) q^{24} +(2.48052 + 4.29639i) q^{25} +(5.05830 - 4.39312i) q^{26} +1.69131 q^{27} +(4.11931 + 7.13485i) q^{29} +(0.420653 + 0.728592i) q^{30} +(-0.640350 - 1.10912i) q^{31} -6.87618 q^{32} +(-4.79774 - 8.30993i) q^{33} -1.56328 q^{34} +(-1.64362 - 2.84683i) q^{36} +3.04485 q^{37} +(1.25589 + 2.17526i) q^{38} +(-1.57459 - 8.12012i) q^{39} +(0.100344 - 0.173802i) q^{40} +(2.69848 + 4.67390i) q^{41} +(-2.66389 + 4.61399i) q^{43} +(3.03826 - 5.26242i) q^{44} +0.446581 q^{45} -7.64669 q^{46} +(-5.83204 + 10.1014i) q^{47} +(-5.50003 + 9.52634i) q^{48} +(4.60921 + 7.98339i) q^{50} +(-0.965006 + 1.67144i) q^{51} +(3.95472 - 3.43466i) q^{52} +(-2.32398 - 4.02525i) q^{53} +3.14272 q^{54} +(0.412757 + 0.714916i) q^{55} +3.10101 q^{57} +(7.65434 + 13.2577i) q^{58} -6.05811 q^{59} +(0.328878 + 0.569634i) q^{60} +(-5.68285 - 9.84298i) q^{61} +(-1.18987 - 2.06092i) q^{62} -3.18704 q^{64} +(0.135465 + 0.698587i) q^{65} +(-8.91498 - 15.4412i) q^{66} +(-6.69851 + 11.6022i) q^{67} -1.22222 q^{68} +(-4.72026 + 8.17574i) q^{69} +(2.98520 - 5.17051i) q^{71} +(1.15044 + 1.99263i) q^{72} +(1.94273 + 3.36491i) q^{73} +5.65782 q^{74} +11.3810 q^{75} +(0.981887 + 1.70068i) q^{76} +(-2.92585 - 15.0885i) q^{78} +(5.36669 - 9.29537i) 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} +(-4.94994 + 8.57354i) q^{86} +18.8999 q^{87} +(-2.12662 + 3.68341i) q^{88} +11.9841 q^{89} +0.829819 q^{90} -5.97840 q^{92} -2.93801 q^{93} +(-10.8369 + 18.7700i) q^{94} -0.266785 q^{95} +(-7.88721 + 13.6611i) q^{96} +(9.73637 - 16.8639i) q^{97} -9.46448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{2} - q^{3} + 8q^{4} - q^{5} + 9q^{6} - 6q^{8} + 3q^{9} + O(q^{10}) \) \( 12q - 4q^{2} - q^{3} + 8q^{4} - q^{5} + 9q^{6} - 6q^{8} + 3q^{9} - 4q^{10} + 4q^{11} - 5q^{12} + 2q^{13} - 2q^{15} - 16q^{16} + 10q^{17} + 3q^{18} + q^{19} + q^{20} - 5q^{22} + 2q^{23} + 11q^{24} + 7q^{25} + 16q^{26} + 8q^{27} + 3q^{29} - 5q^{30} - 16q^{31} - 16q^{32} - 16q^{33} - 32q^{34} - 21q^{36} + 26q^{37} + 17q^{38} - 20q^{39} + 5q^{40} + 8q^{41} - 11q^{43} + 21q^{44} - 14q^{45} - 32q^{46} + q^{47} - 21q^{48} + 6q^{50} - 20q^{51} - 41q^{52} - 2q^{53} - 36q^{54} - 9q^{55} + 42q^{57} - 8q^{58} + 26q^{59} + 20q^{60} + 5q^{61} - 5q^{62} - 30q^{64} - 5q^{65} - 18q^{66} - 11q^{67} + 58q^{68} - 23q^{69} + 6q^{71} + 25q^{72} + 30q^{73} + 6q^{74} - 6q^{75} + 9q^{76} + 16q^{78} + 7q^{79} + 7q^{80} - 6q^{81} - q^{82} + 54q^{83} - q^{85} - 7q^{86} + 32q^{87} + 8q^{89} + 16q^{90} + 54q^{92} + 14q^{93} - 45q^{94} + 12q^{95} - 19q^{96} + 35q^{97} - 20q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.85816 1.31392 0.656959 0.753926i \(-0.271842\pi\)
0.656959 + 0.753926i \(0.271842\pi\)
\(3\) 1.14703 1.98672i 0.662240 1.14703i −0.317785 0.948163i \(-0.602939\pi\)
0.980026 0.198871i \(-0.0637276\pi\)
\(4\) 1.45276 0.726381
\(5\) −0.0986811 + 0.170921i −0.0441315 + 0.0764381i −0.887247 0.461294i \(-0.847385\pi\)
0.843116 + 0.537732i \(0.180719\pi\)
\(6\) 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 −0.356864 0.934156i \(-0.616154\pi\)
0.987435 0.158025i \(-0.0505127\pi\)
\(12\) 1.66637 2.88623i 0.481039 0.833184i
\(13\) 2.72221 2.36423i 0.755005 0.655719i
\(14\) 0 0
\(15\) 0.226381 + 0.392104i 0.0584514 + 0.101241i
\(16\) −4.79501 −1.19875
\(17\) −0.841305 −0.204047 −0.102023 0.994782i \(-0.532532\pi\)
−0.102023 + 0.994782i \(0.532532\pi\)
\(18\) −2.10227 3.64125i −0.495511 0.858250i
\(19\) 0.675876 + 1.17065i 0.155057 + 0.268566i 0.933080 0.359670i \(-0.117111\pi\)
−0.778023 + 0.628236i \(0.783777\pi\)
\(20\) −0.143360 + 0.248307i −0.0320563 + 0.0555232i
\(21\) 0 0
\(22\) 3.88610 6.73092i 0.828519 1.43504i
\(23\) −4.11519 −0.858077 −0.429038 0.903286i \(-0.641147\pi\)
−0.429038 + 0.903286i \(0.641147\pi\)
\(24\) −1.16637 + 2.02021i −0.238084 + 0.412373i
\(25\) 2.48052 + 4.29639i 0.496105 + 0.859279i
\(26\) 5.05830 4.39312i 0.992015 0.861561i
\(27\) 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
\(31\) −0.640350 1.10912i −0.115010 0.199203i 0.802774 0.596284i \(-0.203357\pi\)
−0.917784 + 0.397080i \(0.870023\pi\)
\(32\) −6.87618 −1.21555
\(33\) −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
\(37\) 3.04485 0.500570 0.250285 0.968172i \(-0.419476\pi\)
0.250285 + 0.968172i \(0.419476\pi\)
\(38\) 1.25589 + 2.17526i 0.203732 + 0.352874i
\(39\) −1.57459 8.12012i −0.252137 1.30026i
\(40\) 0.100344 0.173802i 0.0158659 0.0274805i
\(41\) 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 \(0.299827\pi\)
\(44\) 3.03826 5.26242i 0.458035 0.793340i
\(45\) 0.446581 0.0665724
\(46\) −7.64669 −1.12744
\(47\) −5.83204 + 10.1014i −0.850690 + 1.47344i 0.0298969 + 0.999553i \(0.490482\pi\)
−0.880587 + 0.473885i \(0.842851\pi\)
\(48\) −5.50003 + 9.52634i −0.793862 + 1.37501i
\(49\) 0 0
\(50\) 4.60921 + 7.98339i 0.651841 + 1.12902i
\(51\) −0.965006 + 1.67144i −0.135128 + 0.234048i
\(52\) 3.95472 3.43466i 0.548422 0.476302i
\(53\) −2.32398 4.02525i −0.319223 0.552911i 0.661103 0.750295i \(-0.270089\pi\)
−0.980326 + 0.197384i \(0.936755\pi\)
\(54\) 3.14272 0.427670
\(55\) 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
\(59\) −6.05811 −0.788698 −0.394349 0.918961i \(-0.629030\pi\)
−0.394349 + 0.918961i \(0.629030\pi\)
\(60\) 0.328878 + 0.569634i 0.0424580 + 0.0735394i
\(61\) −5.68285 9.84298i −0.727614 1.26026i −0.957889 0.287139i \(-0.907296\pi\)
0.230275 0.973126i \(-0.426038\pi\)
\(62\) −1.18987 2.06092i −0.151114 0.261737i
\(63\) 0 0
\(64\) −3.18704 −0.398380
\(65\) 0.135465 + 0.698587i 0.0168023 + 0.0866490i
\(66\) −8.91498 15.4412i −1.09736 1.90068i
\(67\) −6.69851 + 11.6022i −0.818354 + 1.41743i 0.0885411 + 0.996073i \(0.471780\pi\)
−0.906895 + 0.421357i \(0.861554\pi\)
\(68\) −1.22222 −0.148216
\(69\) −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
\(73\) 1.94273 + 3.36491i 0.227380 + 0.393833i 0.957031 0.289986i \(-0.0936508\pi\)
−0.729651 + 0.683820i \(0.760317\pi\)
\(74\) 5.65782 0.657708
\(75\) 11.3810 1.31416
\(76\) 0.981887 + 1.70068i 0.112630 + 0.195081i
\(77\) 0 0
\(78\) −2.92585 15.0885i −0.331287 1.70844i
\(79\) 5.36669 9.29537i 0.603799 1.04581i −0.388441 0.921474i \(-0.626986\pi\)
0.992240 0.124337i \(-0.0396805\pi\)
\(80\) 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
\(86\) −4.94994 + 8.57354i −0.533765 + 0.924509i
\(87\) 18.8999 2.02629
\(88\) −2.12662 + 3.68341i −0.226698 + 0.392653i
\(89\) 11.9841 1.27032 0.635159 0.772382i \(-0.280935\pi\)
0.635159 + 0.772382i \(0.280935\pi\)
\(90\) 0.829819 0.0874706
\(91\) 0 0
\(92\) −5.97840 −0.623291
\(93\) −2.93801 −0.304658
\(94\) −10.8369 + 18.7700i −1.11774 + 1.93598i
\(95\) −0.266785 −0.0273715
\(96\) −7.88721 + 13.6611i −0.804986 + 1.39428i
\(97\) 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 0.0452843 + 0.998974i \(0.485581\pi\)
−0.887779 + 0.460270i \(0.847753\pi\)
\(102\) −1.79314 + 3.10580i −0.177547 + 0.307520i
\(103\) −3.61712 + 6.26504i −0.356406 + 0.617313i −0.987357 0.158509i \(-0.949331\pi\)
0.630952 + 0.775822i \(0.282665\pi\)
\(104\) −2.76809 + 2.40408i −0.271434 + 0.235739i
\(105\) 0 0
\(106\) −4.31833 7.47957i −0.419434 0.726480i
\(107\) −9.85249 −0.952477 −0.476238 0.879316i \(-0.658000\pi\)
−0.476238 + 0.879316i \(0.658000\pi\)
\(108\) 2.45707 0.236431
\(109\) 6.90796 + 11.9649i 0.661662 + 1.14603i 0.980179 + 0.198115i \(0.0634821\pi\)
−0.318516 + 0.947917i \(0.603185\pi\)
\(110\) 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 \(0.102319\pi\)
\(114\) 5.76218 0.539677
\(115\) 0.406092 0.703371i 0.0378682 0.0655897i
\(116\) 5.98437 + 10.3652i 0.555635 + 0.962388i
\(117\) −7.71277 2.65961i −0.713046 0.245881i
\(118\) −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
\(122\) −10.5596 18.2898i −0.956026 1.65589i
\(123\) 12.3810 1.11636
\(124\) −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 \(0.802352\pi\)
\(128\) 7.83033 0.692110
\(129\) 6.11114 + 10.5848i 0.538056 + 0.931941i
\(130\) 0.251715 + 1.29809i 0.0220769 + 0.113850i
\(131\) 1.13806 1.97117i 0.0994326 0.172222i −0.812017 0.583633i \(-0.801631\pi\)
0.911450 + 0.411411i \(0.134964\pi\)
\(132\) −6.96998 12.0724i −0.606659 1.05076i
\(133\) 0 0
\(134\) −12.4469 + 21.5587i −1.07525 + 1.86239i
\(135\) −0.166900 + 0.289079i −0.0143645 + 0.0248800i
\(136\) 0.855486 0.0733573
\(137\) 13.4480 1.14894 0.574469 0.818526i \(-0.305209\pi\)
0.574469 + 0.818526i \(0.305209\pi\)
\(138\) −8.77101 + 15.1918i −0.746638 + 1.29321i
\(139\) 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
\(142\) 5.54698 9.60765i 0.465492 0.806256i
\(143\) −2.87093 14.8053i −0.240079 1.23808i
\(144\) 5.42494 + 9.39628i 0.452079 + 0.783023i
\(145\) −1.62599 −0.135031
\(146\) 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 −0.987785 0.155823i \(-0.950197\pi\)
0.358945 0.933359i \(-0.383136\pi\)
\(150\) 21.1477 1.72670
\(151\) −3.06054 5.30101i −0.249063 0.431390i 0.714203 0.699939i \(-0.246789\pi\)
−0.963266 + 0.268548i \(0.913456\pi\)
\(152\) −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
\(156\) −2.28751 11.7966i −0.183147 0.944484i
\(157\) 2.26834 + 3.92888i 0.181033 + 0.313559i 0.942233 0.334959i \(-0.108722\pi\)
−0.761199 + 0.648518i \(0.775389\pi\)
\(158\) 9.97217 17.2723i 0.793343 1.37411i
\(159\) −10.6627 −0.845611
\(160\) 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 0.828128 0.560538i \(-0.189406\pi\)
−0.899505 + 0.436911i \(0.856072\pi\)
\(164\) 3.92025 + 6.79007i 0.306120 + 0.530215i
\(165\) 1.89379 0.147431
\(166\) −5.71180 −0.443322
\(167\) −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
\(170\) 0.154266 0.267197i 0.0118317 0.0204931i
\(171\) 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 −0.999888 0.0149778i \(-0.995232\pi\)
0.486973 0.873417i \(-0.338101\pi\)
\(174\) 35.1191 2.66237
\(175\) 0 0
\(176\) −10.0281 + 17.3692i −0.755898 + 1.30925i
\(177\) −6.94886 + 12.0358i −0.522308 + 0.904664i
\(178\) 22.2685 1.66909
\(179\) −5.23458 + 9.06657i −0.391251 + 0.677667i −0.992615 0.121309i \(-0.961291\pi\)
0.601364 + 0.798975i \(0.294624\pi\)
\(180\) 0.648776 0.0483569
\(181\) −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
\(184\) 4.18455 0.308489
\(185\) −0.300469 + 0.520428i −0.0220909 + 0.0382626i
\(186\) −5.45930 −0.400295
\(187\) −1.75948 + 3.04751i −0.128666 + 0.222856i
\(188\) −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 0.525135 0.851019i \(-0.324015\pi\)
−0.999572 + 0.0292704i \(0.990682\pi\)
\(192\) −3.65565 + 6.33176i −0.263823 + 0.456956i
\(193\) −0.520786 + 0.902028i −0.0374870 + 0.0649294i −0.884160 0.467184i \(-0.845269\pi\)
0.846673 + 0.532113i \(0.178602\pi\)
\(194\) 18.0917 31.3358i 1.29891 2.24978i
\(195\) 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 \(0.850104\pi\)
\(198\) −17.5865 −1.24982
\(199\) −14.0999 −0.999512 −0.499756 0.866166i \(-0.666577\pi\)
−0.499756 + 0.866166i \(0.666577\pi\)
\(200\) −2.52233 4.36881i −0.178356 0.308922i
\(201\) 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
\(205\) −1.06516 −0.0743937
\(206\) −6.72120 + 11.6415i −0.468288 + 0.811099i
\(207\) 4.65582 + 8.06412i 0.323602 + 0.560495i
\(208\) −13.0530 + 11.3365i −0.905064 + 0.786044i
\(209\) 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
\(213\) −6.84825 11.8615i −0.469234 0.812737i
\(214\) −18.3075 −1.25148
\(215\) −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
\(219\) 8.91352 0.602320
\(220\) 0.599638 + 1.03860i 0.0404276 + 0.0700227i
\(221\) −2.29021 + 1.98904i −0.154056 + 0.133797i
\(222\) 6.48971 11.2405i 0.435561 0.754414i
\(223\) −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
\(226\) 3.96591 6.86916i 0.263808 0.456929i
\(227\) 2.85195 0.189291 0.0946454 0.995511i \(-0.469828\pi\)
0.0946454 + 0.995511i \(0.469828\pi\)
\(228\) 4.50503 0.298353
\(229\) 1.58676 2.74835i 0.104856 0.181616i −0.808823 0.588052i \(-0.799895\pi\)
0.913679 + 0.406436i \(0.133228\pi\)
\(230\) 0.754584 1.30698i 0.0497558 0.0861795i
\(231\) 0 0
\(232\) −4.18874 7.25511i −0.275004 0.476321i
\(233\) −6.70354 + 11.6109i −0.439163 + 0.760653i −0.997625 0.0688769i \(-0.978058\pi\)
0.558462 + 0.829530i \(0.311392\pi\)
\(234\) −14.3316 4.94198i −0.936884 0.323068i
\(235\) −1.15102 1.99363i −0.0750845 0.130050i
\(236\) −8.80099 −0.572896
\(237\) −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
\(241\) 7.57574 0.487996 0.243998 0.969776i \(-0.421541\pi\)
0.243998 + 0.969776i \(0.421541\pi\)
\(242\) −6.03465 10.4523i −0.387922 0.671900i
\(243\) −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
\(247\) 4.60756 + 1.58883i 0.293172 + 0.101095i
\(248\) 0.651143 + 1.12781i 0.0413476 + 0.0716162i
\(249\) −3.52587 + 6.10698i −0.223443 + 0.387014i
\(250\) −3.65302 −0.231038
\(251\) 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
\(255\) −0.190456 0.329879i −0.0119268 0.0206578i
\(256\) 20.9241 1.30776
\(257\) 8.48019 0.528980 0.264490 0.964388i \(-0.414796\pi\)
0.264490 + 0.964388i \(0.414796\pi\)
\(258\) 11.3555 + 19.6683i 0.706962 + 1.22449i
\(259\) 0 0
\(260\) 0.196798 + 1.01488i 0.0122049 + 0.0629402i
\(261\) 9.32095 16.1444i 0.576952 0.999311i
\(262\) 2.11470 3.66276i 0.130646 0.226286i
\(263\) −6.39415 + 11.0750i −0.394280 + 0.682913i −0.993009 0.118038i \(-0.962339\pi\)
0.598729 + 0.800952i \(0.295673\pi\)
\(264\) 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
\(268\) −9.73135 + 16.8552i −0.594437 + 1.02959i
\(269\) 4.71172 0.287278 0.143639 0.989630i \(-0.454120\pi\)
0.143639 + 0.989630i \(0.454120\pi\)
\(270\) −0.310127 + 0.537156i −0.0188737 + 0.0326903i
\(271\) 18.0112 1.09410 0.547052 0.837098i \(-0.315750\pi\)
0.547052 + 0.837098i \(0.315750\pi\)
\(272\) 4.03407 0.244601
\(273\) 0 0
\(274\) 24.9885 1.50961
\(275\) 20.7508 1.25132
\(276\) −6.85742 + 11.8774i −0.412768 + 0.714936i
\(277\) −26.1209 −1.56945 −0.784725 0.619844i \(-0.787196\pi\)
−0.784725 + 0.619844i \(0.787196\pi\)
\(278\) 3.75850 6.50991i 0.225420 0.390439i
\(279\) −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 −0.729755 0.683709i \(-0.760366\pi\)
0.956987 + 0.290132i \(0.0936991\pi\)
\(284\) 4.33678 7.51153i 0.257341 0.445727i
\(285\) −0.306011 + 0.530027i −0.0181265 + 0.0313961i
\(286\) −5.33465 27.5106i −0.315445 1.62674i
\(287\) 0 0
\(288\) 7.77953 + 13.4745i 0.458413 + 0.793995i
\(289\) −16.2922 −0.958365
\(290\) −3.02135 −0.177420
\(291\) −22.3359 38.6869i −1.30935 2.26787i
\(292\) 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
\(296\) −3.09617 −0.179961
\(297\) 3.53715 6.12652i 0.205246 0.355497i
\(298\) −14.2632 24.7045i −0.826244 1.43110i
\(299\) −11.2024 + 9.72925i −0.647852 + 0.562657i
\(300\) 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
\(304\) −3.24083 5.61328i −0.185874 0.321944i
\(305\) 2.24316 0.128443
\(306\) 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
\(310\) 0.469672 0.0266756
\(311\) −11.7670 20.3811i −0.667248 1.15571i −0.978671 0.205436i \(-0.934139\pi\)
0.311423 0.950271i \(-0.399194\pi\)
\(312\) 1.60113 + 8.25699i 0.0906464 + 0.467460i
\(313\) −1.67430 + 2.89997i −0.0946370 + 0.163916i −0.909457 0.415798i \(-0.863502\pi\)
0.814820 + 0.579714i \(0.196836\pi\)
\(314\) 4.21494 + 7.30050i 0.237863 + 0.411991i
\(315\) 0 0
\(316\) 7.79652 13.5040i 0.438588 0.759658i
\(317\) 3.63917 6.30323i 0.204396 0.354025i −0.745544 0.666456i \(-0.767810\pi\)
0.949940 + 0.312432i \(0.101144\pi\)
\(318\) −19.8131 −1.11106
\(319\) 34.4600 1.92939
\(320\) 0.314501 0.544732i 0.0175811 0.0304514i
\(321\) −11.3011 + 19.5742i −0.630768 + 1.09252i
\(322\) 0 0
\(323\) −0.568618 0.984875i −0.0316388 0.0547999i
\(324\) 7.74919 13.4220i 0.430511 0.745666i
\(325\) 16.9102 + 5.83116i 0.938007 + 0.323455i
\(326\) −1.69329 2.93286i −0.0937826 0.162436i
\(327\) 31.6946 1.75272
\(328\) −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 0.992927 0.118728i \(-0.0378818\pi\)
−0.599285 + 0.800536i \(0.704548\pi\)
\(332\) −4.46564 −0.245084
\(333\) −3.44486 5.96668i −0.188777 0.326972i
\(334\) −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 \(0.344999\pi\)
\(338\) 3.38344 23.9180i 0.184035 1.30097i
\(339\) −4.89627 8.48060i −0.265929 0.460603i
\(340\) 0.120610 0.208902i 0.00654098 0.0113293i
\(341\) −5.35683 −0.290089
\(342\) 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
\(346\) −12.5358 21.7126i −0.673928 1.16728i
\(347\) −7.70278 −0.413507 −0.206753 0.978393i \(-0.566290\pi\)
−0.206753 + 0.978393i \(0.566290\pi\)
\(348\) 27.4571 1.47186
\(349\) 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
\(352\) −14.3806 + 24.9080i −0.766490 + 1.32760i
\(353\) −11.1311 + 19.2797i −0.592451 + 1.02616i 0.401450 + 0.915881i \(0.368506\pi\)
−0.993901 + 0.110275i \(0.964827\pi\)
\(354\) −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
\(359\) 1.37921 2.38887i 0.0727920 0.126079i −0.827332 0.561713i \(-0.810142\pi\)
0.900124 + 0.435634i \(0.143476\pi\)
\(360\) −0.454108 −0.0239336
\(361\) 8.58638 14.8721i 0.451915 0.782740i
\(362\) −23.2659 −1.22283
\(363\) −14.9006 −0.782081
\(364\) 0 0
\(365\) −0.766844 −0.0401385
\(366\) −48.4491 −2.53248
\(367\) −7.07485 + 12.2540i −0.369304 + 0.639654i −0.989457 0.144827i \(-0.953737\pi\)
0.620153 + 0.784481i \(0.287071\pi\)
\(368\) 19.7324 1.02862
\(369\) 6.10597 10.5759i 0.317864 0.550557i
\(370\) −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 0.923890 0.382657i \(-0.124991\pi\)
−0.793336 + 0.608784i \(0.791658\pi\)
\(374\) −3.26940 + 5.66276i −0.169056 + 0.292814i
\(375\) −2.25499 + 3.90576i −0.116447 + 0.201693i
\(376\) 5.93034 10.2716i 0.305834 0.529720i
\(377\) 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 \(0.783592\pi\)
\(380\) −0.387575 −0.0198822
\(381\) 5.02456 0.257416
\(382\) −12.1837 21.1028i −0.623371 1.07971i
\(383\) −2.27052 3.93266i −0.116018 0.200950i 0.802168 0.597098i \(-0.203680\pi\)
−0.918186 + 0.396149i \(0.870346\pi\)
\(384\) 8.98165 15.5567i 0.458343 0.793873i
\(385\) 0 0
\(386\) −0.967705 + 1.67611i −0.0492549 + 0.0853120i
\(387\) 12.0554 0.612811
\(388\) 14.1446 24.4992i 0.718085 1.24376i
\(389\) −2.25383 3.90374i −0.114273 0.197927i 0.803216 0.595688i \(-0.203121\pi\)
−0.917489 + 0.397761i \(0.869787\pi\)
\(390\) 2.86766 + 0.988862i 0.145210 + 0.0500730i
\(391\) 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
\(395\) 1.05918 + 1.83456i 0.0532932 + 0.0923065i
\(396\) −13.7496 −0.690945
\(397\) 2.00174 + 3.46712i 0.100465 + 0.174010i 0.911876 0.410465i \(-0.134634\pi\)
−0.811412 + 0.584475i \(0.801300\pi\)
\(398\) −26.1998 −1.31328
\(399\) 0 0
\(400\) −11.8941 20.6012i −0.594706 1.03006i
\(401\) 12.6135 0.629887 0.314944 0.949110i \(-0.398014\pi\)
0.314944 + 0.949110i \(0.398014\pi\)
\(402\) 28.5541 + 49.4571i 1.42415 + 2.46670i
\(403\) −4.36537 1.50532i −0.217455 0.0749853i
\(404\) −12.3005 + 21.3051i −0.611972 + 1.05997i
\(405\) 1.05275 + 1.82342i 0.0523116 + 0.0906064i
\(406\) 0 0
\(407\) 6.36790 11.0295i 0.315645 0.546713i
\(408\) 0.981272 1.69961i 0.0485802 0.0841434i
\(409\) −20.6952 −1.02331 −0.511657 0.859190i \(-0.670968\pi\)
−0.511657 + 0.859190i \(0.670968\pi\)
\(410\) −1.97923 −0.0977472
\(411\) 15.4253 26.7174i 0.760873 1.31787i
\(412\) −5.25482 + 9.10162i −0.258886 + 0.448404i
\(413\) 0 0
\(414\) 8.65126 + 14.9844i 0.425186 + 0.736444i
\(415\) 0.303336 0.525393i 0.0148902 0.0257905i
\(416\) −18.7184 + 16.2569i −0.917746 + 0.797058i
\(417\) −4.64021 8.03708i −0.227232 0.393577i
\(418\) 10.5061 0.513869
\(419\) −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
\(423\) 26.3928 1.28326
\(424\) 2.36315 + 4.09310i 0.114765 + 0.198779i
\(425\) −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
\(429\) −32.7070 11.2784i −1.57911 0.544528i
\(430\) −0.976930 1.69209i −0.0471118 0.0816000i
\(431\) −10.2138 + 17.6908i −0.491980 + 0.852134i −0.999957 0.00923613i \(-0.997060\pi\)
0.507977 + 0.861370i \(0.330393\pi\)
\(432\) −8.10983 −0.390184
\(433\) 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
\(437\) −2.78136 4.81745i −0.133050 0.230450i
\(438\) 16.5628 0.791399
\(439\) −25.1310 −1.19944 −0.599720 0.800210i \(-0.704721\pi\)
−0.599720 + 0.800210i \(0.704721\pi\)
\(440\) −0.419714 0.726967i −0.0200091 0.0346568i
\(441\) 0 0
\(442\) −4.25558 + 3.69595i −0.202417 + 0.175799i
\(443\) −9.25995 + 16.0387i −0.439953 + 0.762022i −0.997685 0.0679994i \(-0.978338\pi\)
0.557732 + 0.830021i \(0.311672\pi\)
\(444\) 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 \(0.255257\pi\)
\(450\) 10.4295 18.0644i 0.491651 0.851564i
\(451\) 22.5740 1.06297
\(452\) 3.10066 5.37050i 0.145843 0.252607i
\(453\) −14.0422 −0.659759
\(454\) 5.29939 0.248713
\(455\) 0 0
\(456\) −3.15328 −0.147666
\(457\) 20.5184 0.959812 0.479906 0.877320i \(-0.340671\pi\)
0.479906 + 0.877320i \(0.340671\pi\)
\(458\) 2.94845 5.10687i 0.137772 0.238629i
\(459\) −1.42291 −0.0664156
\(460\) 0.589955 1.02183i 0.0275068 0.0476431i
\(461\) 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
\(467\) −6.46371 + 11.1955i −0.299105 + 0.518065i −0.975931 0.218078i \(-0.930021\pi\)
0.676827 + 0.736142i \(0.263355\pi\)
\(468\) −11.2048 3.86378i −0.517943 0.178603i
\(469\) 0 0
\(470\) −2.13879 3.70449i −0.0986549 0.170875i
\(471\) 10.4075 0.479550
\(472\) 6.16022 0.283547
\(473\) 11.1423 + 19.2991i 0.512326 + 0.887374i
\(474\) −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
\(478\) −28.9015 −1.32192
\(479\) 18.2911 31.6810i 0.835740 1.44754i −0.0576873 0.998335i \(-0.518373\pi\)
0.893427 0.449209i \(-0.148294\pi\)
\(480\) −1.55664 2.69618i −0.0710505 0.123063i
\(481\) 8.28872 7.19872i 0.377933 0.328233i
\(482\) 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
\(486\) −18.0239 31.2183i −0.817580 1.41609i
\(487\) 36.7496 1.66528 0.832642 0.553812i \(-0.186827\pi\)
0.832642 + 0.553812i \(0.186827\pi\)
\(488\) 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 \(0.774110\pi\)
\(492\) 17.9866 0.810900
\(493\) −3.46560 6.00259i −0.156083 0.270343i
\(494\) 8.56159 + 2.95231i 0.385204 + 0.132831i
\(495\) 0.933965 1.61768i 0.0419786 0.0727091i
\(496\) 3.07048 + 5.31823i 0.137869 + 0.238795i
\(497\) 0 0
\(498\) −6.55163 + 11.3478i −0.293585 + 0.508505i
\(499\) 21.6266 37.4584i 0.968141 1.67687i 0.267211 0.963638i \(-0.413898\pi\)
0.700929 0.713231i \(-0.252769\pi\)
\(500\) −2.85604 −0.127726
\(501\) −24.5648 −1.09747
\(502\) 1.18436 2.05137i 0.0528605 0.0915571i
\(503\) 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
\(506\) −15.9920 + 27.6990i −0.710933 + 1.23137i
\(507\) −23.4842 18.3820i −1.04297 0.816372i
\(508\) 1.59095 + 2.75560i 0.0705869 + 0.122260i
\(509\) −43.1006 −1.91040 −0.955200 0.295960i \(-0.904361\pi\)
−0.955200 + 0.295960i \(0.904361\pi\)
\(510\) −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
\(514\) 15.7576 0.695036
\(515\) −0.713884 1.23648i −0.0314575 0.0544859i
\(516\) 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
\(520\) −0.137748 0.710362i −0.00604065 0.0311514i
\(521\) 10.4770 + 18.1467i 0.459006 + 0.795022i 0.998909 0.0467056i \(-0.0148723\pi\)
−0.539903 + 0.841727i \(0.681539\pi\)
\(522\) 17.3198 29.9988i 0.758068 1.31301i
\(523\) 34.7403 1.51909 0.759543 0.650457i \(-0.225423\pi\)
0.759543 + 0.650457i \(0.225423\pi\)
\(524\) 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
\(528\) 23.0052 + 39.8462i 1.00117 + 1.73408i
\(529\) −6.06520 −0.263704
\(530\) 1.70455 0.0740410
\(531\) 6.85398 + 11.8714i 0.297438 + 0.515177i
\(532\) 0 0
\(533\) 18.3960 + 6.34352i 0.796819 + 0.274769i
\(534\) 25.5427 44.2413i 1.10534 1.91451i
\(535\) 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
\(541\) 1.64923 2.85655i 0.0709059 0.122813i −0.828393 0.560148i \(-0.810744\pi\)
0.899299 + 0.437335i \(0.144078\pi\)
\(542\) 33.4678 1.43756
\(543\) −14.3619 + 24.8756i −0.616330 + 1.06752i
\(544\) 5.78497 0.248029
\(545\) −2.72674 −0.116801
\(546\) 0 0
\(547\) 21.9417 0.938161 0.469080 0.883155i \(-0.344585\pi\)
0.469080 + 0.883155i \(0.344585\pi\)
\(548\) 19.5367 0.834567
\(549\) −12.8589 + 22.2722i −0.548803 + 0.950554i
\(550\) 38.5583 1.64413
\(551\) −5.56828 + 9.64455i −0.237217 + 0.410871i
\(552\) 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 −0.674069 0.738668i \(-0.735455\pi\)
0.976740 + 0.214427i \(0.0687884\pi\)
\(558\) −2.69238 + 4.66334i −0.113978 + 0.197415i
\(559\) 3.65686 + 18.8583i 0.154669 + 0.797621i
\(560\) 0 0
\(561\) 4.03637 + 6.99119i 0.170416 + 0.295168i
\(562\) −6.80453 −0.287032
\(563\) −6.78784 −0.286073 −0.143037 0.989717i \(-0.545687\pi\)
−0.143037 + 0.989717i \(0.545687\pi\)
\(564\) 19.4366 + 33.6652i 0.818430 + 1.41756i
\(565\) 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
\(569\) −17.3212 −0.726143 −0.363072 0.931761i \(-0.618272\pi\)
−0.363072 + 0.931761i \(0.618272\pi\)
\(570\) −0.568618 + 0.984875i −0.0238168 + 0.0412519i
\(571\) 6.50581 + 11.2684i 0.272260 + 0.471568i 0.969440 0.245328i \(-0.0788957\pi\)
−0.697180 + 0.716896i \(0.745562\pi\)
\(572\) −4.17078 21.5086i −0.174389 0.899318i
\(573\) −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
\(577\) −0.365767 0.633528i −0.0152271 0.0263741i 0.858311 0.513129i \(-0.171514\pi\)
−0.873539 + 0.486755i \(0.838180\pi\)
\(578\) −30.2735 −1.25921
\(579\) 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
\(583\) −19.4412 −0.805173
\(584\) −1.97548 3.42163i −0.0817459 0.141588i
\(585\) 1.21569 1.05582i 0.0502625 0.0436527i
\(586\) −15.9369 + 27.6035i −0.658347 + 1.14029i
\(587\) −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
\(590\) 1.11085 1.92404i 0.0457329 0.0792117i
\(591\) −3.39140 −0.139503
\(592\) −14.6001 −0.600059
\(593\) −15.6547 + 27.1147i −0.642860 + 1.11347i 0.341932 + 0.939725i \(0.388919\pi\)
−0.984791 + 0.173741i \(0.944415\pi\)
\(594\) 6.57259 11.3841i 0.269677 0.467093i
\(595\) 0 0
\(596\) −11.1514 19.3147i −0.456777 0.791161i
\(597\) −16.1730 + 28.0125i −0.661917 + 1.14647i
\(598\) −20.8159 + 18.0785i −0.851225 + 0.739285i
\(599\) 0.375116 + 0.649720i 0.0153268 + 0.0265468i 0.873587 0.486668i \(-0.161788\pi\)
−0.858260 + 0.513215i \(0.828454\pi\)
\(600\) −11.5728 −0.472458
\(601\) −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
\(605\) 1.28193 0.0521177
\(606\) 36.0925 + 62.5141i 1.46616 + 2.53946i
\(607\) 11.1197 + 19.2599i 0.451336 + 0.781737i 0.998469 0.0553087i \(-0.0176143\pi\)
−0.547133 + 0.837045i \(0.684281\pi\)
\(608\) −4.64745 8.04961i −0.188479 0.326455i
\(609\) 0 0
\(610\) 4.16815 0.168764
\(611\) 8.00594 + 41.2863i 0.323886 + 1.67027i
\(612\) 1.38278 + 2.39505i 0.0558957 + 0.0968143i
\(613\) 4.13993 7.17057i 0.167210 0.289617i −0.770228 0.637769i \(-0.779857\pi\)
0.937438 + 0.348152i \(0.113191\pi\)
\(614\) 52.1578 2.10492
\(615\) −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
\(619\) 2.67049 + 4.62542i 0.107336 + 0.185911i 0.914690 0.404156i \(-0.132435\pi\)
−0.807354 + 0.590067i \(0.799101\pi\)
\(620\) 0.367203 0.0147472
\(621\) −6.96005 −0.279297
\(622\) −21.8651 37.8714i −0.876709 1.51850i
\(623\) 0 0
\(624\) 7.55018 + 38.9360i 0.302249 + 1.55869i
\(625\) −12.2086 + 21.1459i −0.488345 + 0.845838i
\(626\) −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 \(0.207752\pi\)
\(632\) −5.45714 + 9.45205i −0.217074 + 0.375982i
\(633\) −60.7222 −2.41349
\(634\) 6.76217 11.7124i 0.268560 0.465160i
\(635\) −0.432271 −0.0171541
\(636\) −15.4904 −0.614236
\(637\) 0 0
\(638\) 64.0322 2.53506
\(639\) −13.5095 −0.534428
\(640\) −0.772706 + 1.33837i −0.0305439 + 0.0529035i
\(641\) 23.3289 0.921434 0.460717 0.887547i \(-0.347592\pi\)
0.460717 + 0.887547i \(0.347592\pi\)
\(642\) −20.9993 + 36.3719i −0.828778 + 1.43549i
\(643\) −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 0.152812 + 0.988255i \(0.451167\pi\)
−0.932260 + 0.361788i \(0.882166\pi\)
\(648\) −5.42402 + 9.39467i −0.213076 + 0.369058i
\(649\) −12.6697 + 21.9446i −0.497331 + 0.861402i
\(650\) 31.4218 + 10.8352i 1.23246 + 0.424993i
\(651\) 0 0
\(652\) −1.32386 2.29299i −0.0518464 0.0898005i
\(653\) 18.1355 0.709699 0.354849 0.934923i \(-0.384532\pi\)
0.354849 + 0.934923i \(0.384532\pi\)
\(654\) 58.8938 2.30293
\(655\) 0.224610 + 0.389035i 0.00877623 + 0.0152009i
\(656\) −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 \(0.251238\pi\)
\(660\) 2.75122 0.107091
\(661\) 5.15611 8.93064i 0.200549 0.347362i −0.748156 0.663523i \(-0.769061\pi\)
0.948706 + 0.316161i \(0.102394\pi\)
\(662\) 13.3076 + 23.0494i 0.517213 + 0.895839i
\(663\) 1.32471 + 6.83150i 0.0514476 + 0.265314i
\(664\) 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
\(668\) −7.77805 13.4720i −0.300942 0.521247i
\(669\) −1.67019 −0.0645733
\(670\) −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 \(0.776401\pi\)
\(674\) 31.9237 1.22965
\(675\) 4.19533 + 7.26652i 0.161478 + 0.279689i
\(676\) 2.64527 18.6997i 0.101741 0.719221i
\(677\) −10.5467 + 18.2674i −0.405343 + 0.702075i −0.994361 0.106045i \(-0.966181\pi\)
0.589018 + 0.808120i \(0.299515\pi\)
\(678\) −9.09807 15.7583i −0.349409 0.605194i
\(679\) 0 0
\(680\) −0.0844203 + 0.146220i −0.00323737 + 0.00560729i
\(681\) 3.27129 5.66604i 0.125356 0.217123i
\(682\) −9.95385 −0.381153
\(683\) −38.2212 −1.46249 −0.731246 0.682113i \(-0.761061\pi\)
−0.731246 + 0.682113i \(0.761061\pi\)
\(684\) 2.22176 3.84821i 0.0849512 0.147140i
\(685\) −1.32706 + 2.29854i −0.0507044 + 0.0878226i
\(686\) 0 0
\(687\) −3.64013 6.30490i −0.138880 0.240547i
\(688\) 12.7734 22.1241i 0.486980 0.843474i
\(689\) −15.8430 5.46317i −0.603570 0.208130i
\(690\) −1.73107 2.99830i −0.0659006 0.114143i
\(691\) 26.2322 0.997920 0.498960 0.866625i \(-0.333715\pi\)
0.498960 + 0.866625i \(0.333715\pi\)
\(692\) −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
\(696\) −19.2185 −0.728476
\(697\) −2.27024 3.93218i −0.0859916 0.148942i
\(698\) 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 \(0.844189\pi\)
\(702\) 8.55515 7.43011i 0.322893 0.280431i
\(703\) 2.05794 + 3.56446i 0.0776167 + 0.134436i
\(704\) −6.66528 + 11.5446i −0.251207 + 0.435104i
\(705\) −5.28105 −0.198896
\(706\) −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 0.838745 + 0.544524i \(0.183290\pi\)
0.0521988 + 0.998637i \(0.483377\pi\)
\(710\) 1.09476 + 1.89619i 0.0410858 + 0.0711626i
\(711\) −24.2869 −0.910830
\(712\) −12.1861 −0.456695
\(713\) 2.63516 + 4.56423i 0.0986876 + 0.170932i
\(714\) 0 0
\(715\) 2.81384 + 0.970301i 0.105232 + 0.0362872i
\(716\) −7.60461 + 13.1716i −0.284197 + 0.492244i
\(717\) −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 −0.802249 0.596990i \(-0.796363\pi\)
−0.115884 0.993263i \(-0.536970\pi\)
\(720\) −2.14136 −0.0798037
\(721\) 0 0
\(722\) 15.9549 27.6347i 0.593779 1.02846i
\(723\) 8.68963 15.0509i 0.323171 0.559748i
\(724\) −18.1900 −0.676024
\(725\) −20.4361 + 35.3963i −0.758977 + 1.31459i
\(726\) −27.6878 −1.02759
\(727\) 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
\(730\) −1.42492 −0.0527387
\(731\) 2.24114 3.88178i 0.0828917 0.143573i
\(732\) −37.8789 −1.40004
\(733\) 14.1005 24.4228i 0.520813 0.902075i −0.478894 0.877873i \(-0.658962\pi\)
0.999707 0.0242025i \(-0.00770464\pi\)
\(734\) −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 −0.148180 0.988960i \(-0.547342\pi\)
0.930555 0.366153i \(-0.119325\pi\)
\(740\) −0.436510 + 0.756058i −0.0160464 + 0.0277932i
\(741\) 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 \(0.927627\pi\)
\(744\) 2.98753 0.109528
\(745\) 3.02989 0.111007
\(746\) 4.68521 + 8.11502i 0.171538 + 0.297112i
\(747\) 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
\(751\) 18.1996 0.664114 0.332057 0.943259i \(-0.392257\pi\)
0.332057 + 0.943259i \(0.392257\pi\)
\(752\) 27.9646 48.4362i 1.01977 1.76629i
\(753\) −1.46220 2.53260i −0.0532855 0.0922931i
\(754\) 52.1809 + 17.9937i 1.90032 + 0.655290i
\(755\) 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
\(759\) 19.7436 + 34.1970i 0.716648 + 1.24127i
\(760\) 0.271282 0.00984042
\(761\) −13.2444 22.9399i −0.480108 0.831572i 0.519631 0.854391i \(-0.326069\pi\)
−0.999740 + 0.0228184i \(0.992736\pi\)
\(762\) 9.33644 0.338223
\(763\) 0 0
\(764\) −9.52554 16.4987i −0.344622 0.596903i
\(765\) −0.375711 −0.0135839
\(766\) −4.21900 7.30752i −0.152439 0.264031i
\(767\) −16.4914 + 14.3227i −0.595471 + 0.517164i
\(768\) 24.0006 41.5703i 0.866049 1.50004i
\(769\) 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
\(772\) −0.756579 + 1.31043i −0.0272299 + 0.0471635i
\(773\) −12.8113 −0.460790 −0.230395 0.973097i \(-0.574002\pi\)
−0.230395 + 0.973097i \(0.574002\pi\)
\(774\) 22.4009 0.805184
\(775\) 3.17681 5.50239i 0.114114 0.197652i
\(776\) −9.90048 + 17.1481i −0.355406 + 0.615582i
\(777\) 0 0
\(778\) −4.18797 7.25378i −0.150146 0.260061i
\(779\) −3.64767 + 6.31795i −0.130691 + 0.226364i
\(780\) 2.24202 + 0.773120i 0.0802772 + 0.0276821i
\(781\) −12.4863 21.6269i −0.446795 0.773871i
\(782\) 6.43320 0.230051
\(783\) 6.96701 + 12.0672i 0.248981