Properties

Label 1183.2.e.g.508.6
Level $1183$
Weight $2$
Character 1183.508
Analytic conductor $9.446$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.44630255912\)
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 508.6
Root \(0.217953 - 0.377506i\) of defining polynomial
Character \(\chi\) \(=\) 1183.508
Dual form 1183.2.e.g.170.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.929081 + 1.60921i) q^{2} +(-1.14703 + 1.98672i) q^{3} +(-0.726381 + 1.25813i) q^{4} +(-0.0986811 - 0.170921i) q^{5} -4.26275 q^{6} +(2.62662 + 0.317598i) q^{7} +1.01686 q^{8} +(-1.13137 - 1.95960i) q^{9} +O(q^{10})\) \(q+(0.929081 + 1.60921i) q^{2} +(-1.14703 + 1.98672i) q^{3} +(-0.726381 + 1.25813i) q^{4} +(-0.0986811 - 0.170921i) q^{5} -4.26275 q^{6} +(2.62662 + 0.317598i) q^{7} +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} +(1.92926 + 4.52187i) q^{14} +0.452762 q^{15} +(2.39750 + 4.15260i) q^{16} +(-0.420653 + 0.728592i) q^{17} +(2.10227 - 3.64125i) q^{18} +(0.675876 + 1.17065i) q^{19} +0.286720 q^{20} +(-3.64380 + 4.85406i) q^{21} -7.77220 q^{22} +(2.05760 + 3.56386i) q^{23} +(-1.16637 + 2.02021i) q^{24} +(2.48052 - 4.29639i) q^{25} -1.69131 q^{27} +(-2.30751 + 3.07393i) q^{28} -8.23861 q^{29} +(0.420653 + 0.728592i) q^{30} +(-0.640350 + 1.10912i) q^{31} +(-3.43809 + 5.95495i) q^{32} +(-4.79774 - 8.30993i) q^{33} -1.56328 q^{34} +(-0.204914 - 0.480285i) q^{35} +3.28723 q^{36} +(1.52242 + 2.63692i) q^{37} +(-1.25589 + 2.17526i) q^{38} +(-0.100344 - 0.173802i) q^{40} -5.39696 q^{41} +(-11.1966 - 1.35384i) q^{42} +5.32778 q^{43} +(-3.03826 - 5.26242i) q^{44} +(-0.223290 + 0.386750i) q^{45} +(-3.82334 + 6.62223i) q^{46} +(-5.83204 - 10.1014i) q^{47} -11.0001 q^{48} +(6.79826 + 1.66842i) q^{49} +9.21843 q^{50} +(-0.965006 - 1.67144i) q^{51} +(-2.32398 + 4.02525i) q^{53} +(-1.57136 - 2.72168i) q^{54} +0.825514 q^{55} +(2.67089 + 0.322952i) q^{56} -3.10101 q^{57} +(-7.65434 - 13.2577i) q^{58} +(3.02905 - 5.24648i) q^{59} +(-0.328878 + 0.569634i) q^{60} +(5.68285 + 9.84298i) q^{61} -2.37975 q^{62} +(-2.34932 - 5.50644i) q^{63} -3.18704 q^{64} +(8.91498 - 15.4412i) q^{66} +(6.69851 - 11.6022i) q^{67} +(-0.611109 - 1.05847i) q^{68} -9.44053 q^{69} +(0.582500 - 0.775973i) q^{70} +5.97040 q^{71} +(-1.15044 - 1.99263i) q^{72} +(1.94273 - 3.36491i) q^{73} +(-2.82891 + 4.89982i) q^{74} +(5.69049 + 9.85622i) q^{75} -1.96377 q^{76} +(-6.64368 + 8.85034i) q^{77} +(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} +(-3.46025 - 8.11027i) q^{84} +0.166042 q^{85} +(4.94994 + 8.57354i) 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} +(-7.88721 - 13.6611i) q^{96} -19.4727 q^{97} +(3.63129 + 12.4900i) q^{98} +9.46448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 2q^{2} + q^{3} - 4q^{4} - q^{5} - 18q^{6} + 6q^{7} + 6q^{8} + 3q^{9} + O(q^{10}) \) \( 12q - 2q^{2} + q^{3} - 4q^{4} - q^{5} - 18q^{6} + 6q^{7} + 6q^{8} + 3q^{9} + 4q^{10} - 4q^{11} + 5q^{12} - 2q^{14} - 4q^{15} + 8q^{16} + 5q^{17} - 3q^{18} + q^{19} - 2q^{20} + 9q^{21} + 10q^{22} - q^{23} + 11q^{24} + 7q^{25} - 8q^{27} - 8q^{28} - 6q^{29} - 5q^{30} - 16q^{31} - 8q^{32} - 16q^{33} - 32q^{34} - 28q^{35} + 42q^{36} + 13q^{37} - 17q^{38} - 5q^{40} - 16q^{41} - 52q^{42} + 22q^{43} - 21q^{44} + 7q^{45} - 16q^{46} + q^{47} - 42q^{48} + 6q^{49} + 12q^{50} - 20q^{51} - 2q^{53} + 18q^{54} - 18q^{55} + 9q^{56} - 42q^{57} + 8q^{58} - 13q^{59} - 20q^{60} - 5q^{61} - 10q^{62} - 8q^{63} - 30q^{64} + 18q^{66} + 11q^{67} + 29q^{68} - 46q^{69} + 39q^{70} + 12q^{71} - 25q^{72} + 30q^{73} - 3q^{74} - 3q^{75} - 18q^{76} + 11q^{77} + 7q^{79} + 7q^{80} - 6q^{81} + q^{82} + 54q^{83} - 41q^{84} - 2q^{85} + 7q^{86} + 16q^{87} - 4q^{89} - 16q^{90} + 54q^{92} + 7q^{93} + 45q^{94} - 6q^{95} - 19q^{96} - 70q^{97} + 82q^{98} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 \(0.0614909\pi\)
−0.324440 + 0.945906i \(0.605176\pi\)
\(3\) −1.14703 + 1.98672i −0.662240 + 1.14703i 0.317785 + 0.948163i \(0.397061\pi\)
−0.980026 + 0.198871i \(0.936272\pi\)
\(4\) −0.726381 + 1.25813i −0.363191 + 0.629065i
\(5\) −0.0986811 0.170921i −0.0441315 0.0764381i 0.843116 0.537732i \(-0.180719\pi\)
−0.887247 + 0.461294i \(0.847385\pi\)
\(6\) −4.26275 −1.74026
\(7\) 2.62662 + 0.317598i 0.992769 + 0.120041i
\(8\) 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 \(0.383846\pi\)
−0.987435 + 0.158025i \(0.949487\pi\)
\(12\) −1.66637 2.88623i −0.481039 0.833184i
\(13\) 0 0
\(14\) 1.92926 + 4.52187i 0.515616 + 1.20852i
\(15\) 0.452762 0.116903
\(16\) 2.39750 + 4.15260i 0.599376 + 1.03815i
\(17\) −0.420653 + 0.728592i −0.102023 + 0.176709i −0.912518 0.409036i \(-0.865865\pi\)
0.810495 + 0.585746i \(0.199198\pi\)
\(18\) 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 \(0.783777\pi\)
\(20\) 0.286720 0.0641126
\(21\) −3.64380 + 4.85406i −0.795143 + 1.05924i
\(22\) −7.77220 −1.65704
\(23\) 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
\(25\) 2.48052 4.29639i 0.496105 0.859279i
\(26\) 0 0
\(27\) −1.69131 −0.325492
\(28\) −2.30751 + 3.07393i −0.436078 + 0.580918i
\(29\) −8.23861 −1.52987 −0.764936 0.644106i \(-0.777230\pi\)
−0.764936 + 0.644106i \(0.777230\pi\)
\(30\) 0.420653 + 0.728592i 0.0768003 + 0.133022i
\(31\) −0.640350 + 1.10912i −0.115010 + 0.199203i −0.917784 0.397080i \(-0.870023\pi\)
0.802774 + 0.596284i \(0.203357\pi\)
\(32\) −3.43809 + 5.95495i −0.607774 + 1.05270i
\(33\) −4.79774 8.30993i −0.835180 1.44657i
\(34\) −1.56328 −0.268100
\(35\) −0.204914 0.480285i −0.0346367 0.0811829i
\(36\) 3.28723 0.547872
\(37\) 1.52242 + 2.63692i 0.250285 + 0.433506i 0.963604 0.267333i \(-0.0861423\pi\)
−0.713319 + 0.700839i \(0.752809\pi\)
\(38\) −1.25589 + 2.17526i −0.203732 + 0.352874i
\(39\) 0 0
\(40\) −0.100344 0.173802i −0.0158659 0.0274805i
\(41\) −5.39696 −0.842863 −0.421431 0.906860i \(-0.638472\pi\)
−0.421431 + 0.906860i \(0.638472\pi\)
\(42\) −11.1966 1.35384i −1.72768 0.208902i
\(43\) 5.32778 0.812479 0.406239 0.913767i \(-0.366840\pi\)
0.406239 + 0.913767i \(0.366840\pi\)
\(44\) −3.03826 5.26242i −0.458035 0.793340i
\(45\) −0.223290 + 0.386750i −0.0332862 + 0.0576534i
\(46\) −3.82334 + 6.62223i −0.563721 + 0.976394i
\(47\) −5.83204 10.1014i −0.850690 1.47344i −0.880587 0.473885i \(-0.842851\pi\)
0.0298969 0.999553i \(-0.490482\pi\)
\(48\) −11.0001 −1.58772
\(49\) 6.79826 + 1.66842i 0.971180 + 0.238346i
\(50\) 9.21843 1.30368
\(51\) −0.965006 1.67144i −0.135128 0.234048i
\(52\) 0 0
\(53\) −2.32398 + 4.02525i −0.319223 + 0.552911i −0.980326 0.197384i \(-0.936755\pi\)
0.661103 + 0.750295i \(0.270089\pi\)
\(54\) −1.57136 2.72168i −0.213835 0.370373i
\(55\) 0.825514 0.111312
\(56\) 2.67089 + 0.322952i 0.356913 + 0.0431562i
\(57\) −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 \(0.0376367\pi\)
\(60\) −0.328878 + 0.569634i −0.0424580 + 0.0735394i
\(61\) 5.68285 + 9.84298i 0.727614 + 1.26026i 0.957889 + 0.287139i \(0.0927042\pi\)
−0.230275 + 0.973126i \(0.573962\pi\)
\(62\) −2.37975 −0.302228
\(63\) −2.34932 5.50644i −0.295987 0.693746i
\(64\) −3.18704 −0.398380
\(65\) 0 0
\(66\) 8.91498 15.4412i 1.09736 1.90068i
\(67\) 6.69851 11.6022i 0.818354 1.41743i −0.0885411 0.996073i \(-0.528220\pi\)
0.906895 0.421357i \(-0.138446\pi\)
\(68\) −0.611109 1.05847i −0.0741078 0.128358i
\(69\) −9.44053 −1.13651
\(70\) 0.582500 0.775973i 0.0696221 0.0927465i
\(71\) 5.97040 0.708556 0.354278 0.935140i \(-0.384727\pi\)
0.354278 + 0.935140i \(0.384727\pi\)
\(72\) −1.15044 1.99263i −0.135581 0.234833i
\(73\) 1.94273 3.36491i 0.227380 0.393833i −0.729651 0.683820i \(-0.760317\pi\)
0.957031 + 0.289986i \(0.0936508\pi\)
\(74\) −2.82891 + 4.89982i −0.328854 + 0.569592i
\(75\) 5.69049 + 9.85622i 0.657081 + 1.13810i
\(76\) −1.96377 −0.225260
\(77\) −6.64368 + 8.85034i −0.757118 + 1.00859i
\(78\) 0 0
\(79\) 5.36669 + 9.29537i 0.603799 + 1.04581i 0.992240 + 0.124337i \(0.0396805\pi\)
−0.388441 + 0.921474i \(0.626986\pi\)
\(80\) 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 \(0.553958\pi\)
\(84\) −3.46025 8.11027i −0.377544 0.884903i
\(85\) 0.166042 0.0180098
\(86\) 4.94994 + 8.57354i 0.533765 + 0.924509i
\(87\) 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
\(96\) −7.88721 13.6611i −0.804986 1.39428i
\(97\) −19.4727 −1.97716 −0.988578 0.150709i \(-0.951844\pi\)
−0.988578 + 0.150709i \(0.951844\pi\)
\(98\) 3.63129 + 12.4900i 0.366815 + 1.26168i
\(99\) 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 \(-0.514419\pi\)
0.887779 0.460270i \(-0.152247\pi\)
\(102\) 1.79314 3.10580i 0.177547 0.307520i
\(103\) 3.61712 + 6.26504i 0.356406 + 0.617313i 0.987357 0.158509i \(-0.0506688\pi\)
−0.630952 + 0.775822i \(0.717335\pi\)
\(104\) 0 0
\(105\) 1.18923 + 0.143797i 0.116057 + 0.0140331i
\(106\) −8.63667 −0.838867
\(107\) 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
\(109\) −6.90796 + 11.9649i −0.661662 + 1.14603i 0.318516 + 0.947917i \(0.396815\pi\)
−0.980179 + 0.198115i \(0.936518\pi\)
\(110\) 0.766969 + 1.32843i 0.0731277 + 0.126661i
\(111\) −6.98509 −0.662995
\(112\) 4.97847 + 11.6687i 0.470421 + 1.10259i
\(113\) −4.26864 −0.401560 −0.200780 0.979636i \(-0.564348\pi\)
−0.200780 + 0.979636i \(0.564348\pi\)
\(114\) −2.88109 4.99019i −0.269839 0.467374i
\(115\) 0.406092 0.703371i 0.0378682 0.0655897i
\(116\) 5.98437 10.3652i 0.555635 0.962388i
\(117\) 0 0
\(118\) 11.2569 1.03629
\(119\) −1.33629 + 1.78014i −0.122498 + 0.163185i
\(120\) 0.460394 0.0420280
\(121\) −3.24765 5.62509i −0.295240 0.511372i
\(122\) −10.5596 + 18.2898i −0.956026 + 1.65589i
\(123\) 6.19049 10.7222i 0.558178 0.966792i
\(124\) −0.930276 1.61129i −0.0835412 0.144698i
\(125\) −1.96593 −0.175839
\(126\) 6.67833 8.89649i 0.594953 0.792562i
\(127\) −2.19024 −0.194352 −0.0971761 0.995267i \(-0.530981\pi\)
−0.0971761 + 0.995267i \(0.530981\pi\)
\(128\) 3.91516 + 6.78126i 0.346055 + 0.599385i
\(129\) −6.11114 + 10.5848i −0.538056 + 0.931941i
\(130\) 0 0
\(131\) −1.13806 1.97117i −0.0994326 0.172222i 0.812017 0.583633i \(-0.198369\pi\)
−0.911450 + 0.411411i \(0.865036\pi\)
\(132\) 13.9400 1.21332
\(133\) 1.40347 + 3.28951i 0.121696 + 0.285237i
\(134\) 24.8938 2.15050
\(135\) 0.166900 + 0.289079i 0.0143645 + 0.0248800i
\(136\) −0.427743 + 0.740873i −0.0366787 + 0.0635293i
\(137\) 6.72399 11.6463i 0.574469 0.995010i −0.421630 0.906768i \(-0.638542\pi\)
0.996099 0.0882417i \(-0.0281248\pi\)
\(138\) −8.77101 15.1918i −0.746638 1.29321i
\(139\) 4.04540 0.343126 0.171563 0.985173i \(-0.445118\pi\)
0.171563 + 0.985173i \(0.445118\pi\)
\(140\) 0.753106 + 0.0910619i 0.0636490 + 0.00769614i
\(141\) 26.7582 2.25344
\(142\) 5.54698 + 9.60765i 0.465492 + 0.806256i
\(143\) 0 0
\(144\) 5.42494 9.39628i 0.452079 0.783023i
\(145\) 0.812996 + 1.40815i 0.0675156 + 0.116940i
\(146\) 7.21982 0.597517
\(147\) −11.1125 + 11.5925i −0.916545 + 0.956135i
\(148\) −4.42344 −0.363605
\(149\) 7.67596 + 13.2952i 0.628840 + 1.08918i 0.987785 + 0.155823i \(0.0498031\pi\)
−0.358945 + 0.933359i \(0.616864\pi\)
\(150\) −10.5738 + 18.3144i −0.863351 + 1.49537i
\(151\) 3.06054 5.30101i 0.249063 0.431390i −0.714203 0.699939i \(-0.753211\pi\)
0.963266 + 0.268548i \(0.0865439\pi\)
\(152\) 0.687268 + 1.19038i 0.0557448 + 0.0965528i
\(153\) 1.90366 0.153902
\(154\) −20.4146 2.46844i −1.64506 0.198912i
\(155\) 0.252762 0.0203023
\(156\) 0 0
\(157\) −2.26834 + 3.92888i −0.181033 + 0.313559i −0.942233 0.334959i \(-0.891278\pi\)
0.761199 + 0.648518i \(0.224611\pi\)
\(158\) −9.97217 + 17.2723i −0.793343 + 1.37411i
\(159\) −5.33137 9.23421i −0.422805 0.732320i
\(160\) 1.35710 0.107288
\(161\) 4.27265 + 10.0144i 0.336732 + 0.789245i
\(162\) 19.8233 1.55746
\(163\) 0.911271 + 1.57837i 0.0713762 + 0.123627i 0.899505 0.436911i \(-0.143928\pi\)
−0.828128 + 0.560538i \(0.810594\pi\)
\(164\) 3.92025 6.79007i 0.306120 0.530215i
\(165\) −0.946893 + 1.64007i −0.0737155 + 0.127679i
\(166\) −2.85590 4.94656i −0.221661 0.383928i
\(167\) 10.7079 0.828606 0.414303 0.910139i \(-0.364025\pi\)
0.414303 + 0.910139i \(0.364025\pi\)
\(168\) −3.70522 + 4.93588i −0.285864 + 0.380812i
\(169\) 0 0
\(170\) 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 \(0.00476775\pi\)
−0.486973 + 0.873417i \(0.661899\pi\)
\(174\) 35.1191 2.66237
\(175\) 7.87992 10.4972i 0.595666 0.793512i
\(176\) −20.0563 −1.51180
\(177\) 6.94886 + 12.0358i 0.522308 + 0.904664i
\(178\) 11.1342 19.2851i 0.834547 1.44548i
\(179\) −5.23458 + 9.06657i −0.391251 + 0.677667i −0.992615 0.121309i \(-0.961291\pi\)
0.601364 + 0.798975i \(0.294624\pi\)
\(180\) −0.324388 0.561857i −0.0241785 0.0418783i
\(181\) 12.5209 0.930674 0.465337 0.885133i \(-0.345933\pi\)
0.465337 + 0.885133i \(0.345933\pi\)
\(182\) 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
\(187\) −1.75948 3.04751i −0.128666 0.222856i
\(188\) 16.9451 1.23585
\(189\) −4.44242 0.537156i −0.323139 0.0390724i
\(190\) 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 −0.846673 0.532113i \(-0.821398\pi\)
0.884160 + 0.467184i \(0.154731\pi\)
\(194\) −18.0917 31.3358i −1.29891 2.24978i
\(195\) 0 0
\(196\) −7.03722 + 7.34118i −0.502658 + 0.524370i
\(197\) −1.47833 −0.105327 −0.0526635 0.998612i \(-0.516771\pi\)
−0.0526635 + 0.998612i \(0.516771\pi\)
\(198\) 8.79326 + 15.2304i 0.624910 + 1.08238i
\(199\) −7.04993 + 12.2108i −0.499756 + 0.865603i −1.00000 0.000281618i \(-0.999910\pi\)
0.500244 + 0.865885i \(0.333244\pi\)
\(200\) 2.52233 4.36881i 0.178356 0.308922i
\(201\) 15.3668 + 26.6162i 1.08389 + 1.87736i
\(202\) 31.4660 2.21394
\(203\) −21.6397 2.61657i −1.51881 0.183647i
\(204\) 2.80385 0.196309
\(205\) 0.532578 + 0.922451i 0.0371968 + 0.0644268i
\(206\) −6.72120 + 11.6415i −0.468288 + 0.811099i
\(207\) 4.65582 8.06412i 0.323602 0.560495i
\(208\) 0 0
\(209\) −5.65402 −0.391097
\(210\) 0.873495 + 2.04733i 0.0602769 + 0.141279i
\(211\) 26.4692 1.82222 0.911108 0.412167i \(-0.135228\pi\)
0.911108 + 0.412167i \(0.135228\pi\)
\(212\) −3.37619 5.84774i −0.231878 0.401624i
\(213\) −6.84825 + 11.8615i −0.469234 + 0.812737i
\(214\) −9.15376 + 15.8548i −0.625738 + 1.08381i
\(215\) −0.525751 0.910628i −0.0358559 0.0621043i
\(216\) −1.71981 −0.117019
\(217\) −2.03421 + 2.70986i −0.138091 + 0.183957i
\(218\) −25.6722 −1.73874
\(219\) 4.45676 + 7.71934i 0.301160 + 0.521625i
\(220\) −0.599638 + 1.03860i −0.0404276 + 0.0700227i
\(221\) 0 0
\(222\) −6.48971 11.2405i −0.435561 0.754414i
\(223\) 0.728048 0.0487537 0.0243769 0.999703i \(-0.492240\pi\)
0.0243769 + 0.999703i \(0.492240\pi\)
\(224\) −10.9218 + 14.5495i −0.729746 + 0.972126i
\(225\) −11.2256 −0.748373
\(226\) −3.96591 6.86916i −0.263808 0.456929i
\(227\) −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
\(229\) 1.58676 + 2.74835i 0.104856 + 0.181616i 0.913679 0.406436i \(-0.133228\pi\)
−0.808823 + 0.588052i \(0.799895\pi\)
\(230\) 1.50917 0.0995116
\(231\) −9.96262 23.3508i −0.655492 1.53637i
\(232\) −8.37748 −0.550009
\(233\) −6.70354 11.6109i −0.439163 0.760653i 0.558462 0.829530i \(-0.311392\pi\)
−0.997625 + 0.0688769i \(0.978058\pi\)
\(234\) 0 0
\(235\) −1.15102 + 1.99363i −0.0750845 + 0.130050i
\(236\) 4.40050 + 7.62188i 0.286448 + 0.496142i
\(237\) −24.6231 −1.59944
\(238\) −4.10614 0.496495i −0.266162 0.0321830i
\(239\) 15.5538 1.00609 0.503046 0.864259i \(-0.332212\pi\)
0.503046 + 0.864259i \(0.332212\pi\)
\(240\) 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 \(0.245126\pi\)
\(242\) 6.03465 10.4523i 0.387922 0.671900i
\(243\) 9.69985 + 16.8006i 0.622245 + 1.07776i
\(244\) −16.5117 −1.05705
\(245\) −0.385693 1.32661i −0.0246410 0.0847537i
\(246\) 23.0059 1.46680
\(247\) 0 0
\(248\) −0.651143 + 1.12781i −0.0413476 + 0.0716162i
\(249\) 3.52587 6.10698i 0.223443 0.387014i
\(250\) −1.82651 3.16361i −0.115519 0.200084i
\(251\) 1.27476 0.0804624 0.0402312 0.999190i \(-0.487191\pi\)
0.0402312 + 0.999190i \(0.487191\pi\)
\(252\) 8.63432 + 1.04402i 0.543911 + 0.0657671i
\(253\) −17.2128 −1.08216
\(254\) −2.03491 3.52456i −0.127682 0.221151i
\(255\) −0.190456 + 0.329879i −0.0119268 + 0.0206578i
\(256\) −10.4620 + 18.1208i −0.653878 + 1.13255i
\(257\) 4.24010 + 7.34406i 0.264490 + 0.458110i 0.967430 0.253139i \(-0.0814631\pi\)
−0.702940 + 0.711249i \(0.748130\pi\)
\(258\) −22.7110 −1.41392
\(259\) 3.16135 + 7.40970i 0.196437 + 0.460416i
\(260\) 0 0
\(261\) 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
\(266\) −3.98959 + 5.31471i −0.244618 + 0.325866i
\(267\) 27.4925 1.68251
\(268\) 9.73135 + 16.8552i 0.594437 + 1.02959i
\(269\) 2.35586 4.08047i 0.143639 0.248790i −0.785225 0.619210i \(-0.787453\pi\)
0.928864 + 0.370420i \(0.120786\pi\)
\(270\) −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 \(-0.120529\pi\)
\(278\) 3.75850 + 6.50991i 0.225420 + 0.390439i
\(279\) 2.89790 0.173493
\(280\) −0.208368 0.488380i −0.0124523 0.0291863i
\(281\) 3.66197 0.218455 0.109227 0.994017i \(-0.465162\pi\)
0.109227 + 0.994017i \(0.465162\pi\)
\(282\) 24.8605 + 43.0596i 1.48042 + 2.56416i
\(283\) −3.82263 + 6.62099i −0.227232 + 0.393577i −0.956987 0.290132i \(-0.906301\pi\)
0.729755 + 0.683709i \(0.239634\pi\)
\(284\) −4.33678 + 7.51153i −0.257341 + 0.445727i
\(285\) 0.306011 + 0.530027i 0.0181265 + 0.0313961i
\(286\) 0 0
\(287\) −14.1757 1.71406i −0.836768 0.101178i
\(288\) 15.5591 0.916827
\(289\) 8.14610 + 14.1095i 0.479183 + 0.829968i
\(290\) −1.51068 + 2.61657i −0.0887100 + 0.153650i
\(291\) 22.3359 38.6869i 1.30935 2.26787i
\(292\) 2.82233 + 4.88842i 0.165164 + 0.286073i
\(293\) 17.1534 1.00211 0.501056 0.865415i \(-0.332945\pi\)
0.501056 + 0.865415i \(0.332945\pi\)
\(294\) −28.9793 7.11205i −1.69011 0.414783i
\(295\) −1.19564 −0.0696130
\(296\) 1.54809 + 2.68136i 0.0899807 + 0.155851i
\(297\) 3.53715 6.12652i 0.205246 0.355497i
\(298\) −14.2632 + 24.7045i −0.826244 + 1.43110i
\(299\) 0 0
\(300\) −16.5339 −0.954583
\(301\) 13.9940 + 1.69209i 0.806604 + 0.0975306i
\(302\) 11.3740 0.654498
\(303\) 19.4238 + 33.6430i 1.11587 + 1.93274i
\(304\) −3.24083 + 5.61328i −0.185874 + 0.321944i
\(305\) 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 \(0.204298\pi\)
\(308\) −6.30902 14.7873i −0.359490 0.842586i
\(309\) −16.5959 −0.944105
\(310\) 0.234836 + 0.406748i 0.0133378 + 0.0231017i
\(311\) 11.7670 20.3811i 0.667248 1.15571i −0.311423 0.950271i \(-0.600806\pi\)
0.978671 0.205436i \(-0.0658611\pi\)
\(312\) 0 0
\(313\) 1.67430 + 2.89997i 0.0946370 + 0.163916i 0.909457 0.415798i \(-0.136498\pi\)
−0.814820 + 0.579714i \(0.803164\pi\)
\(314\) −8.42989 −0.475726
\(315\) −0.709330 + 0.944930i −0.0399662 + 0.0532408i
\(316\) −15.5930 −0.877177
\(317\) −3.63917 6.30323i −0.204396 0.354025i 0.745544 0.666456i \(-0.232190\pi\)
−0.949940 + 0.312432i \(0.898856\pi\)
\(318\) 9.90655 17.1586i 0.555532 0.962209i
\(319\) 17.2300 29.8432i 0.964694 1.67090i
\(320\) 0.314501 + 0.544732i 0.0175811 + 0.0304514i
\(321\) −22.6023 −1.26154
\(322\) −12.1457 + 16.1798i −0.676852 + 0.901664i
\(323\) −1.13724 −0.0632775
\(324\) 7.74919 + 13.4220i 0.430511 + 0.745666i
\(325\) 0 0
\(326\) −1.69329 + 2.93286i −0.0937826 + 0.162436i
\(327\) −15.8473 27.4484i −0.876359 1.51790i
\(328\) −5.48792 −0.303020
\(329\) −12.1104 28.3847i −0.667666 1.56490i
\(330\) −3.51896 −0.193712
\(331\) −7.16168 12.4044i −0.393642 0.681807i 0.599285 0.800536i \(-0.295452\pi\)
−0.992927 + 0.118728i \(0.962118\pi\)
\(332\) 2.23282 3.86736i 0.122542 0.212249i
\(333\) 3.44486 5.96668i 0.188777 0.326972i
\(334\) 9.94855 + 17.2314i 0.544360 + 0.942860i
\(335\) −2.64407 −0.144461
\(336\) −28.8930 3.49360i −1.57624 0.190592i
\(337\) 17.1802 0.935868 0.467934 0.883764i \(-0.344999\pi\)
0.467934 + 0.883764i \(0.344999\pi\)
\(338\) 0 0
\(339\) 4.89627 8.48060i 0.265929 0.460603i
\(340\) −0.120610 + 0.208902i −0.00654098 + 0.0113293i
\(341\) −2.67841 4.63915i −0.145044 0.251224i
\(342\) 5.68351 0.307329
\(343\) 17.3266 + 6.54142i 0.935547 + 0.353203i
\(344\) 5.41758 0.292096
\(345\) 0.931602 + 1.61358i 0.0501558 + 0.0868723i
\(346\) −12.5358 + 21.7126i −0.673928 + 1.16728i
\(347\) 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
\(349\) −22.3701 −1.19744 −0.598721 0.800958i \(-0.704324\pi\)
−0.598721 + 0.800958i \(0.704324\pi\)
\(350\) 24.2133 + 2.92776i 1.29426 + 0.156495i
\(351\) 0 0
\(352\) −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
\(357\) −2.00386 4.69672i −0.106055 0.248577i
\(358\) −19.4534 −1.02814
\(359\) −1.37921 2.38887i −0.0727920 0.126079i 0.827332 0.561713i \(-0.189858\pi\)
−0.900124 + 0.435634i \(0.856524\pi\)
\(360\) −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 \(-0.712929\pi\)
0.989457 + 0.144827i \(0.0462626\pi\)
\(368\) −9.86618 + 17.0887i −0.514310 + 0.890812i
\(369\) 6.10597 + 10.5759i 0.317864 + 0.550557i
\(370\) 1.11664 0.0580514
\(371\) −7.38263 + 9.83472i −0.383287 + 0.510593i
\(372\) 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
\(377\) 0 0
\(378\) −3.26297 7.64787i −0.167829 0.393364i
\(379\) 6.05964 0.311263 0.155631 0.987815i \(-0.450259\pi\)
0.155631 + 0.987815i \(0.450259\pi\)
\(380\) 0.193787 + 0.335650i 0.00994109 + 0.0172185i
\(381\) 2.51228 4.35139i 0.128708 0.222929i
\(382\) 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 \(0.870346\pi\)
\(384\) −17.9633 −0.916686
\(385\) 2.16831 + 0.262182i 0.110507 + 0.0133620i
\(386\) 1.93541 0.0985098
\(387\) −6.02771 10.4403i −0.306406 0.530710i
\(388\) 14.1446 24.4992i 0.718085 1.24376i
\(389\) −2.25383 + 3.90374i −0.114273 + 0.197927i −0.917489 0.397761i \(-0.869787\pi\)
0.803216 + 0.595688i \(0.203121\pi\)
\(390\) 0 0
\(391\) −3.46213 −0.175088
\(392\) 6.91285 + 1.69654i 0.349152 + 0.0856883i
\(393\) 5.22157 0.263393
\(394\) −1.37349 2.37896i −0.0691955 0.119850i
\(395\) 1.05918 1.83456i 0.0532932 0.0923065i
\(396\) −6.87482 + 11.9075i −0.345473 + 0.598376i
\(397\) 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
\(399\) −8.14518 0.984875i −0.407769 0.0493054i
\(400\) 23.7883 1.18941
\(401\) 6.30674 + 10.9236i 0.314944 + 0.545498i 0.979426 0.201806i \(-0.0646810\pi\)
−0.664482 + 0.747304i \(0.731348\pi\)
\(402\) −28.5541 + 49.4571i −1.42415 + 2.46670i
\(403\) 0 0
\(404\) 12.3005 + 21.3051i 0.611972 + 1.05997i
\(405\) −2.10550 −0.104623
\(406\) −15.8944 37.2539i −0.788826 1.84888i
\(407\) −12.7358 −0.631290
\(408\) −0.981272 1.69961i −0.0485802 0.0841434i
\(409\) 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
\(411\) 15.4253 + 26.7174i 0.760873 + 1.31787i
\(412\) −10.5096 −0.517773
\(413\) 9.62244 12.8185i 0.473490 0.630756i
\(414\) 17.3025 0.850373
\(415\) 0.303336 + 0.525393i 0.0148902 + 0.0257905i
\(416\) 0 0
\(417\) −4.64021 + 8.03708i −0.227232 + 0.393577i
\(418\) −5.25304 9.09854i −0.256935 0.445024i
\(419\) −21.8175 −1.06586 −0.532928 0.846161i \(-0.678908\pi\)
−0.532928 + 0.846161i \(0.678908\pi\)
\(420\) −1.04475 + 1.39176i −0.0509787 + 0.0679109i
\(421\) −9.42727 −0.459457 −0.229728 0.973255i \(-0.573784\pi\)
−0.229728 + 0.973255i \(0.573784\pi\)
\(422\) 24.5920 + 42.5947i 1.19712 + 2.07348i
\(423\) −13.1964 + 22.8569i −0.641632 + 1.11134i
\(424\) −2.36315 + 4.09310i −0.114765 + 0.198779i
\(425\) 2.08688 + 3.61458i 0.101228 + 0.175333i
\(426\) −25.4503 −1.23307
\(427\) 11.8006 + 27.6586i 0.571070 + 1.33850i
\(428\) −14.3133 −0.691861
\(429\) 0 0
\(430\) 0.976930 1.69209i 0.0471118 0.0816000i
\(431\) 10.2138 17.6908i 0.491980 0.852134i −0.507977 0.861370i \(-0.669607\pi\)
0.999957 + 0.00923613i \(0.00293999\pi\)
\(432\) −4.05491 7.02332i −0.195092 0.337909i
\(433\) 26.3486 1.26623 0.633117 0.774056i \(-0.281775\pi\)
0.633117 + 0.774056i \(0.281775\pi\)
\(434\) −6.25069 0.755803i −0.300043 0.0362797i
\(435\) −3.73014 −0.178846
\(436\) −10.0356 17.3822i −0.480619 0.832457i
\(437\) −2.78136 + 4.81745i −0.133050 + 0.230450i
\(438\) −8.28138 + 14.3438i −0.395700 + 0.685372i
\(439\) −12.5655 21.7641i −0.599720 1.03875i −0.992862 0.119267i \(-0.961945\pi\)
0.393142 0.919478i \(-0.371388\pi\)
\(440\) 0.839429 0.0400182
\(441\) −4.42195 15.2095i −0.210569 0.724260i
\(442\) 0 0
\(443\) −9.25995 16.0387i −0.439953 0.762022i 0.557732 0.830021i \(-0.311672\pi\)
−0.997685 + 0.0679994i \(0.978338\pi\)
\(444\) 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
\(448\) −8.37115 1.01220i −0.395500 0.0478219i
\(449\) −11.6431 −0.549471 −0.274736 0.961520i \(-0.588590\pi\)
−0.274736 + 0.961520i \(0.588590\pi\)
\(450\) −10.4295 18.0644i −0.491651 0.851564i
\(451\) 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 0.999734 0.0230490i \(-0.00733739\pi\)
−0.519828 + 0.854271i \(0.674004\pi\)
\(458\) −2.94845 + 5.10687i −0.137772 + 0.238629i
\(459\) 0.711453 1.23227i 0.0332078 0.0575176i
\(460\) 0.589955 + 1.02183i 0.0275068 + 0.0476431i
\(461\) −2.04075 −0.0950473 −0.0475236 0.998870i \(-0.515133\pi\)
−0.0475236 + 0.998870i \(0.515133\pi\)
\(462\) 28.3203 37.7268i 1.31758 1.75521i
\(463\) −3.03155 −0.140888 −0.0704441 0.997516i \(-0.522442\pi\)
−0.0704441 + 0.997516i \(0.522442\pi\)
\(464\) −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 \(-0.0699787\pi\)
−0.676827 + 0.736142i \(0.736645\pi\)
\(468\) 0 0
\(469\) 21.2793 28.3470i 0.982585 1.30894i
\(470\) −4.27757 −0.197310
\(471\) −5.20373 9.01312i −0.239775 0.415303i
\(472\) 3.08011 5.33491i 0.141774 0.245559i
\(473\) −11.1423 + 19.2991i −0.512326 + 0.887374i
\(474\) −22.8768 39.6238i −1.05077 1.81998i
\(475\) 6.70611 0.307697
\(476\) −1.26898 2.97429i −0.0581637 0.136326i
\(477\) 10.5172 0.481548
\(478\) 14.4507 + 25.0294i 0.660962 + 1.14482i
\(479\) 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
\(481\) 0 0
\(482\) −14.0769 −0.641187
\(483\) −24.7967 2.99830i −1.12829 0.136427i
\(484\) 9.43611 0.428914
\(485\) 1.92159 + 3.32829i 0.0872550 + 0.151130i
\(486\) −18.0239 + 31.2183i −0.817580 + 1.41609i
\(487\) 18.3748 31.8261i 0.832642 1.44218i −0.0632939 0.997995i \(-0.520161\pi\)
0.895936 0.444183i \(-0.146506\pi\)
\(488\) 5.77864 + 10.0089i 0.261587 + 0.453081i
\(489\) −4.18103 −0.189073
\(490\) 1.77645 1.85319i 0.0802520 0.0837184i
\(491\) −8.19797 −0.369969 −0.184985 0.982741i \(-0.559224\pi\)
−0.184985 + 0.982741i \(0.559224\pi\)
\(492\) 8.99331 + 15.5769i 0.405450 + 0.702260i
\(493\) 3.46560 6.00259i 0.156083 0.270343i
\(494\) 0 0
\(495\) −0.933965 1.61768i −0.0419786 0.0727091i
\(496\) −6.14096 −0.275737
\(497\) 15.6820 + 1.89619i 0.703432 + 0.0850556i
\(498\) 13.1033 0.587171
\(499\) −21.6266 37.4584i −0.968141 1.67687i −0.700929 0.713231i \(-0.747231\pi\)
−0.267211 0.963638i \(-0.586102\pi\)
\(500\) 1.42802 2.47340i 0.0638629 0.110614i
\(501\) −12.2824 + 21.2737i −0.548736 + 0.950439i
\(502\) 1.18436 + 2.05137i 0.0528605 + 0.0915571i
\(503\) 0.0181922 0.000811149 0.000405575 1.00000i \(-0.499871\pi\)
0.000405575 1.00000i \(0.499871\pi\)
\(504\) −2.38892 5.59925i −0.106411 0.249411i
\(505\) −3.34212 −0.148722
\(506\) −15.9920 27.6990i −0.710933 1.23137i
\(507\) 0 0
\(508\) 1.59095 2.75560i 0.0705869 0.122260i
\(509\) 21.5503 + 37.3262i 0.955200 + 1.65446i 0.733909 + 0.679248i \(0.237694\pi\)
0.221292 + 0.975208i \(0.428973\pi\)
\(510\) −0.707795 −0.0313417
\(511\) 6.17151 8.22134i 0.273012 0.363691i
\(512\) −23.2197 −1.02617
\(513\) −1.14311 1.97993i −0.0504697 0.0874161i
\(514\) −7.87878 + 13.6464i −0.347518 + 0.601919i
\(515\) 0.713884 1.23648i 0.0314575 0.0544859i
\(516\) −8.87804 15.3772i −0.390834 0.676944i
\(517\) 48.7877 2.14568
\(518\) −8.98664 + 11.9715i −0.394850 + 0.525997i
\(519\) −30.9531 −1.35869
\(520\) 0 0
\(521\) −10.4770 + 18.1467i −0.459006 + 0.795022i −0.998909 0.0467056i \(-0.985128\pi\)
0.539903 + 0.841727i \(0.318461\pi\)
\(522\) −17.3198 + 29.9988i −0.758068 + 1.31301i
\(523\) 17.3701 + 30.0860i 0.759543 + 1.31557i 0.943084 + 0.332555i \(0.107911\pi\)
−0.183541 + 0.983012i \(0.558756\pi\)
\(524\) 3.30666 0.144452
\(525\) 11.8164 + 27.6958i 0.515712 + 1.20875i
\(526\) −23.7627 −1.03610
\(527\) −0.538730 0.933107i −0.0234674 0.0406468i
\(528\) 23.0052 39.8462i 1.00117 1.73408i
\(529\) 3.03260 5.25262i 0.131852 0.228375i
\(530\) 0.852276 + 1.47619i 0.0370205 + 0.0641214i
\(531\) −13.7080 −0.594875
\(532\) −5.15809 0.623691i −0.223631 0.0270404i
\(533\) 0 0
\(534\) 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
\(539\) −20.2613 + 21.1365i −0.872715 + 0.910411i
\(540\) −0.484932 −0.0208682
\(541\) −1.64923 2.85655i −0.0709059 0.122813i 0.828393 0.560148i \(-0.189256\pi\)
−0.899299 + 0.437335i \(0.855922\pi\)
\(542\) 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
\(551\) −5.56828 9.64455i −0.237217 0.410871i
\(552\) −9.59965 −0.408588
\(553\) 11.1440 + 26.1199i 0.473893 + 1.11073i
\(554\) 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 \(-0.931212\pi\)
0.674069 + 0.738668i \(0.264545\pi\)
\(558\) 2.69238 + 4.66334i 0.113978 + 0.197415i
\(559\) 0 0
\(560\) 1.50315 2.00241i 0.0635196 0.0846172i
\(561\) 8.07273 0.340831
\(562\) 3.40226 + 5.89289i 0.143516 + 0.248577i
\(563\) −3.39392 + 5.87844i −0.143037 + 0.247747i −0.928639 0.370985i \(-0.879020\pi\)
0.785602 + 0.618732i \(0.212353\pi\)
\(564\) −19.4366 + 33.6652i −0.818430 + 1.41756i
\(565\) 0.421234 + 0.729599i 0.0177215 + 0.0306945i
\(566\) −14.2061 −0.597128
\(567\) 16.9449 22.5731i 0.711621 0.947981i
\(568\) 6.07103 0.254735
\(569\) 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
\(571\) 6.50581 11.2684i 0.272260 0.471568i −0.697180 0.716896i \(-0.745562\pi\)
0.969440 + 0.245328i \(0.0788957\pi\)
\(572\) 0 0
\(573\) 30.0837 1.25676
\(574\) −10.4121 24.4043i −0.434593 1.01862i
\(575\) 20.4157 0.851392
\(576\) 3.60574 + 6.24532i 0.150239 + 0.260222i
\(577\) −0.365767 + 0.633528i −0.0152271 + 0.0263741i −0.873539 0.486755i \(-0.838180\pi\)
0.858311 + 0.513129i \(0.171514\pi\)
\(578\) −15.1368 + 26.2177i −0.629607 + 1.09051i
\(579\) 1.19472 + 2.06931i 0.0496508 + 0.0859978i
\(580\) −2.36218 −0.0980842
\(581\) −8.07396 0.976265i −0.334964 0.0405023i
\(582\) 83.0073 3.44076
\(583\) −9.72061 16.8366i −0.402586 0.697300i
\(584\) 1.97548 3.42163i 0.0817459 0.141588i
\(585\) 0 0
\(586\) 15.9369 + 27.6035i 0.658347 + 1.14029i
\(587\) 8.52284 0.351775 0.175888 0.984410i \(-0.443720\pi\)
0.175888 + 0.984410i \(0.443720\pi\)
\(588\) −6.51296 22.4016i −0.268590 0.923825i
\(589\) −1.73119 −0.0713323
\(590\) −1.11085 1.92404i −0.0457329 0.0792117i
\(591\) 1.69570 2.93704i 0.0697517 0.120814i
\(592\) −7.30004 + 12.6440i −0.300030 + 0.519667i
\(593\) −15.6547 27.1147i −0.642860 1.11347i −0.984791 0.173741i \(-0.944415\pi\)
0.341932 0.939725i \(-0.388919\pi\)
\(594\) 13.1452 0.539353
\(595\) 0.436129 + 0.0527346i 0.0178795 + 0.00216191i
\(596\) −22.3027 −0.913554
\(597\) −16.1730 28.0125i −0.661917 1.14647i
\(598\) 0 0
\(599\) 0.375116 0.649720i 0.0153268 0.0265468i −0.858260 0.513215i \(-0.828454\pi\)
0.873587 + 0.486668i \(0.161788\pi\)
\(600\) 5.78641 + 10.0224i 0.236229 + 0.409161i
\(601\) −9.55305 −0.389677 −0.194838 0.980835i \(-0.562418\pi\)
−0.194838 + 0.980835i \(0.562418\pi\)
\(602\) 10.2787 + 24.0915i 0.418927 + 0.981897i
\(603\) −30.3141 −1.23449
\(604\) 4.44624 + 7.70111i 0.180915 + 0.313354i
\(605\) −0.640963 + 1.11018i −0.0260588 + 0.0451352i
\(606\) −36.0925 + 62.5141i −1.46616 + 2.53946i
\(607\) −11.1197 19.2599i −0.451336 0.781737i 0.547133 0.837045i \(-0.315719\pi\)
−0.998469 + 0.0553087i \(0.982386\pi\)
\(608\) −9.29489 −0.376958
\(609\) 30.0199 39.9908i 1.21647 1.62051i
\(610\) 4.16815 0.168764
\(611\) 0 0
\(612\) −1.38278 + 2.39505i −0.0558957 + 0.0968143i
\(613\) −4.13993 + 7.17057i −0.167210 + 0.289617i −0.937438 0.348152i \(-0.886809\pi\)
0.770228 + 0.637769i \(0.220143\pi\)
\(614\) 26.0789 + 45.1699i 1.05246 + 1.82291i
\(615\) −2.44354 −0.0985330
\(616\) −6.75567 + 8.99952i −0.272194 + 0.362601i
\(617\) −20.3312 −0.818503 −0.409252 0.912422i \(-0.634210\pi\)
−0.409252 + 0.912422i \(0.634210\pi\)
\(618\) −15.4189 26.7063i −0.620238 1.07428i
\(619\) 2.67049 4.62542i 0.107336 0.185911i −0.807354 0.590067i \(-0.799101\pi\)
0.914690 + 0.404156i \(0.132435\pi\)
\(620\) −0.183601 + 0.318007i −0.00737361 + 0.0127715i
\(621\) −3.48003 6.02758i −0.139649 0.241879i
\(622\) 43.7301 1.75342
\(623\) −12.4427 29.1636i −0.498506 1.16842i
\(624\) 0 0
\(625\) −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
\(630\) −2.17962 0.263549i −0.0868381 0.0105001i
\(631\) −6.46662 −0.257432 −0.128716 0.991681i \(-0.541086\pi\)
−0.128716 + 0.991681i \(0.541086\pi\)
\(632\) 5.45714 + 9.45205i 0.217074 + 0.375982i
\(633\) −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 \(0.319074\pi\)
\(642\) −20.9993 36.3719i −0.828778 1.43549i
\(643\) 3.58878 0.141527 0.0707637 0.997493i \(-0.477456\pi\)
0.0707637 + 0.997493i \(0.477456\pi\)
\(644\) −15.7030 1.89873i −0.618784 0.0748204i
\(645\) 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 \(-0.548833\pi\)
0.932260 0.361788i \(-0.117834\pi\)
\(648\) 5.42402 9.39467i 0.213076 0.369058i
\(649\) 12.6697 + 21.9446i 0.497331 + 0.861402i
\(650\) 0 0
\(651\) −3.05042 7.14970i −0.119556 0.280219i
\(652\) −2.64772 −0.103693
\(653\) −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
\(655\) −0.224610 + 0.389035i −0.00877623 + 0.0152009i
\(656\) −12.9392 22.4114i −0.505192 0.875017i
\(657\) −8.79183 −0.343002
\(658\) 34.4256 45.8599i 1.34205 1.78780i
\(659\) 13.4810 0.525147 0.262573 0.964912i \(-0.415429\pi\)
0.262573 + 0.964912i \(0.415429\pi\)
\(660\) −1.37561 2.38263i −0.0535456 0.0927437i
\(661\) 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
\(663\) 0 0
\(664\) −3.12571 −0.121301
\(665\) 0.423750 0.564495i 0.0164323 0.0218902i
\(666\) 12.8022 0.496076
\(667\) −16.9517 29.3613i −0.656374 1.13687i
\(668\) −7.77805 + 13.4720i −0.300942 + 0.521247i
\(669\) −0.835096 + 1.44643i −0.0322867 + 0.0559222i
\(670\) −2.45655 4.25487i −0.0949049 0.164380i
\(671\) −47.5397 −1.83525
\(672\) −16.3780 38.3874i −0.631795 1.48082i
\(673\) −9.23056 −0.355812 −0.177906 0.984048i \(-0.556932\pi\)
−0.177906 + 0.984048i \(0.556932\pi\)
\(674\) 15.9618 + 27.6467i 0.614827 + 1.06491i
\(675\) −4.19533 + 7.26652i −0.161478 + 0.279689i
\(676\) 0 0
\(677\) 10.5467 + 18.2674i 0.405343 + 0.702075i 0.994361 0.106045i \(-0.0338187\pi\)
−0.589018 + 0.808120i \(0.700485\pi\)
\(678\) 18.1961 0.698818
\(679\) −51.1475 6.18450i −1.96286 0.237340i
\(680\) 0.168841 0.00647474
\(681\) −3.27129 5.66604i −0.125356 0.217123i
\(682\) 4.97693 8.62029i 0.190576 0.330088i
\(683\) −19.1106 + 33.1005i −0.731246 + 1.26656i 0.225104 + 0.974335i \(0.427728\pi\)
−0.956351 + 0.292221i \(0.905606\pi\)
\(684\) 2.22176 + 3.84821i 0.0849512 + 0.147140i
\(685\) −2.65412 −0.101409
\(686\) 5.57122 + 33.9597i 0.212710 + 1.29659i
\(687\) −7.28027 −0.277760
\(688\) 12.7734 + 22.1241i 0.486980 + 0.843474i
\(689\) 0 0
\(690\) −1.73107 + 2.99830i −0.0659006 + 0.114143i
\(691\) −13.1161 22.7178i −0.498960 0.864224i 0.501039 0.865425i \(-0.332951\pi\)
−0.999999 + 0.00120019i \(0.999618\pi\)
\(692\) −19.6017 −0.745144
\(693\) 24.8596 + 3.00590i 0.944338 + 0.114185i
\(694\) 14.3130 0.543314
\(695\) −0.399204 0.691442i −0.0151427 0.0262279i
\(696\) 9.60925 16.6437i 0.364238 0.630878i
\(697\) 2.27024 3.93218i 0.0859916 0.148942i
\(698\) −20.7836 35.9982i −0.786670 1.36255i
\(699\) 30.7567 1.16333
\(700\) 7.48299 + 17.5389i 0.282830 + 0.662909i
\(701\) −46.7346 −1.76514 −0.882570 0.470180i \(-0.844189\pi\)
−0.882570 + 0.470180i \(0.844189\pi\)
\(702\) 0 0
\(703\) −2.05794 + 3.56446i −0.0776167 + 0.134436i
\(704\) 6.66528 11.5446i 0.251207 0.435104i
\(705\) −2.64053 4.57353i −0.0994480 0.172249i
\(706\) −41.3669 −1.55687
\(707\) 26.8972 35.8309i 1.01157 1.34756i
\(708\) −20.1901 −0.758789
\(709\) −23.7232 41.0898i −0.890944 1.54316i −0.838745 0.544524i \(-0.816710\pi\)
−0.0521988 0.998637i \(-0.516623\pi\)
\(710\) 1.09476 1.89619i 0.0410858 0.0711626i
\(711\) 12.1435 21.0331i 0.455415 0.788802i
\(712\) −6.09307 10.5535i −0.228348 0.395510i
\(713\) −5.27032 −0.197375
\(714\) 5.69629 7.58827i 0.213178 0.283984i
\(715\) 0 0
\(716\) −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 \(0.203637\pi\)
0.115884 + 0.993263i \(0.463030\pi\)
\(720\) −2.14136 −0.0798037
\(721\) 7.51104 + 17.6047i 0.279726 + 0.655632i
\(722\) 31.9098 1.18756
\(723\) −8.68963 15.0509i −0.323171 0.559748i
\(724\) −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 \(-0.702581\pi\)
−0.594325 + 0.804225i \(0.702581\pi\)
\(728\) 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
\(733\) 14.1005 + 24.4228i 0.520813 + 0.902075i 0.999707 + 0.0242025i \(0.00770464\pi\)
−0.478894 + 0.877873i \(0.658962\pi\)
\(734\) 26.2924 0.970472
\(735\) 3.07800 + 0.755398i 0.113534 + 0.0278633i
\(736\) −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 \(0.452658\pi\)
−0.930555 + 0.366153i \(0.880675\pi\)
\(740\) 0.436510 + 0.756058i 0.0160464 + 0.0277932i
\(741\) 0 0
\(742\) −22.6852 2.74299i −0.832801 0.100698i
\(743\) −15.9142 −0.583836 −0.291918 0.956443i \(-0.594294\pi\)
−0.291918 + 0.956443i \(0.594294\pi\)
\(744\) −1.49377 2.58728i −0.0547641 0.0948543i
\(745\) 1.51495 2.62396i 0.0555033 0.0961346i
\(746\) −4.68521 + 8.11502i −0.171538 + 0.297112i
\(747\) 3.47773 + 6.02360i 0.127243 + 0.220392i
\(748\) 5.11221 0.186921
\(749\) 10.2295 + 23.9762i 0.373777 + 0.876072i
\(750\) 8.38028 0.306005
\(751\) −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
\(753\) −1.46220 + 2.53260i −0.0532855 + 0.0922931i
\(754\) 0 0
\(755\) −1.20807 −0.0439662
\(756\) 3.90270 5.19896i 0.141940 0.189084i
\(757\) −44.9004 −1.63193 −0.815967 0.578099i \(-0.803795\pi\)
−0.815967 + 0.578099i \(0.803795\pi\)
\(758\) 5.62989 + 9.75126i 0.204487 + 0.354182i
\(759\) 19.7436 34.1970i 0.716648 1.24127i
\(760\) 0.135641 0.234937i 0.00492021 0.00852205i
\(761\) −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
\(763\) −21.9446 + 29.2334i −0.794449 + 1.05832i
\(764\) 19.0511 0.689244
\(765\) −0.187856 0.325375i −0.00679193 0.0117640i
\(766\) 4.21900 7.30752i 0.152439 0.264031i
\(767\) 0 0
\(768\) −24.0006 41.5703i −0.866049 1.50004i
\(769\) −13.9625 −0.503502 −0.251751 0.967792i \(-0.581006\pi\)
−0.251751 + 0.967792i \(0.581006\pi\)
\(770\) 1.59263 + 3.73287i 0.0573944 + 0.134523i
\(771\) −19.4541 −0.700623
\(772\) 0.756579 + 1.31043i 0.0272299 + 0.0471635i
\(773\) 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
\(775\) 3.17681 + 5.50239i 0.114114 + 0.197652i
\(776\) −19.8010 −0.710813
\(777\) −18.3472 2.21845i −0.658201 0.0795865i
\(778\) −8.37594 −0.300292
\(779\) −3.64767 6.31795i −0.130691 0.226364i