Properties

Label 637.2.u.g.361.2
Level $637$
Weight $2$
Character 637.361
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.u (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.2346760387617129.1
Defining polynomial: \(x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.2
Root \(-1.38488 + 0.286553i\) of defining polynomial
Character \(\chi\) \(=\) 637.361
Dual form 637.2.u.g.30.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.19430 - 0.689527i) q^{2} -2.88120 q^{3} +(-0.0491037 - 0.0850501i) q^{4} +(-0.697972 + 0.402974i) q^{5} +(3.44101 + 1.98667i) q^{6} +2.89354i q^{8} +5.30133 q^{9} +O(q^{10})\) \(q+(-1.19430 - 0.689527i) q^{2} -2.88120 q^{3} +(-0.0491037 - 0.0850501i) q^{4} +(-0.697972 + 0.402974i) q^{5} +(3.44101 + 1.98667i) q^{6} +2.89354i q^{8} +5.30133 q^{9} +1.11145 q^{10} -5.27158i q^{11} +(0.141478 + 0.245047i) q^{12} +(2.36581 - 2.72084i) q^{13} +(2.01100 - 1.16105i) q^{15} +(1.89697 - 3.28565i) q^{16} +(0.280051 + 0.485062i) q^{17} +(-6.33136 - 3.65541i) q^{18} -5.84469i q^{19} +(0.0685460 + 0.0395750i) q^{20} +(-3.63490 + 6.29583i) q^{22} +(-0.802438 + 1.38986i) q^{23} -8.33689i q^{24} +(-2.17522 + 3.76760i) q^{25} +(-4.70157 + 1.61820i) q^{26} -6.63060 q^{27} +(-1.14008 - 1.97467i) q^{29} -3.20230 q^{30} +(3.01022 + 1.73795i) q^{31} +(0.480674 - 0.277517i) q^{32} +15.1885i q^{33} -0.772411i q^{34} +(-0.260315 - 0.450879i) q^{36} +(1.07557 + 0.620979i) q^{37} +(-4.03007 + 6.98029i) q^{38} +(-6.81636 + 7.83929i) q^{39} +(-1.16602 - 2.01961i) q^{40} +(-0.803413 + 0.463851i) q^{41} +(2.22356 - 3.85131i) q^{43} +(-0.448348 + 0.258854i) q^{44} +(-3.70018 + 2.13630i) q^{45} +(1.91670 - 1.10661i) q^{46} +(-3.32915 + 1.92209i) q^{47} +(-5.46556 + 9.46662i) q^{48} +(5.19572 - 2.99975i) q^{50} +(-0.806883 - 1.39756i) q^{51} +(-0.347577 - 0.0676087i) q^{52} +(-2.72727 + 4.72377i) q^{53} +(7.91890 + 4.57198i) q^{54} +(2.12431 + 3.67941i) q^{55} +16.8397i q^{57} +3.14446i q^{58} +(-9.52106 + 5.49698i) q^{59} +(-0.197495 - 0.114024i) q^{60} -7.30215 q^{61} +(-2.39673 - 4.15126i) q^{62} -8.35330 q^{64} +(-0.554837 + 2.85243i) q^{65} +(10.4729 - 18.1396i) q^{66} -7.34556i q^{67} +(0.0275031 - 0.0476367i) q^{68} +(2.31199 - 4.00448i) q^{69} +(-8.06668 - 4.65730i) q^{71} +15.3396i q^{72} +(4.33139 + 2.50073i) q^{73} +(-0.856364 - 1.48327i) q^{74} +(6.26726 - 10.8552i) q^{75} +(-0.497091 + 0.286996i) q^{76} +(13.5462 - 4.66237i) q^{78} +(-5.68437 - 9.84562i) q^{79} +3.05772i q^{80} +3.20012 q^{81} +1.27935 q^{82} +5.81962i q^{83} +(-0.390935 - 0.225707i) q^{85} +(-5.31117 + 3.06641i) q^{86} +(3.28479 + 5.68943i) q^{87} +15.2535 q^{88} +(-4.33832 - 2.50473i) q^{89} +5.89215 q^{90} +0.157611 q^{92} +(-8.67305 - 5.00739i) q^{93} +5.30133 q^{94} +(2.35526 + 4.07942i) q^{95} +(-1.38492 + 0.799583i) q^{96} +(-9.22171 - 5.32416i) q^{97} -27.9464i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 6q^{3} + 4q^{4} - 3q^{5} + 9q^{6} + 2q^{9} + O(q^{10}) \) \( 12q - 6q^{3} + 4q^{4} - 3q^{5} + 9q^{6} + 2q^{9} + 24q^{10} + q^{12} + 2q^{13} - 12q^{15} - 8q^{16} - 17q^{17} - 3q^{18} + 3q^{20} - 15q^{22} + 3q^{23} - 5q^{25} + 9q^{26} - 12q^{27} - q^{29} - 22q^{30} + 18q^{31} + 18q^{32} - 13q^{36} + 15q^{37} - 19q^{38} - q^{39} + q^{40} + 6q^{41} + 11q^{43} + 33q^{44} + 9q^{45} - 30q^{46} - 15q^{47} - 19q^{48} + 18q^{50} + 4q^{51} - 47q^{52} - 8q^{53} - 6q^{54} + 15q^{55} - 27q^{59} + 30q^{60} + 10q^{61} - 41q^{62} + 2q^{64} - 3q^{65} + 34q^{66} + 11q^{68} - 7q^{69} + 30q^{71} + 42q^{73} - 33q^{74} - q^{75} + 45q^{76} + 44q^{78} - 35q^{79} - 28q^{81} + 10q^{82} - 21q^{85} + 57q^{86} - 10q^{87} + 28q^{88} - 48q^{89} - 66q^{92} - 81q^{93} + 2q^{94} + 2q^{95} + 21q^{96} + 3q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.19430 0.689527i −0.844495 0.487570i 0.0142944 0.999898i \(-0.495450\pi\)
−0.858790 + 0.512328i \(0.828783\pi\)
\(3\) −2.88120 −1.66346 −0.831732 0.555178i \(-0.812650\pi\)
−0.831732 + 0.555178i \(0.812650\pi\)
\(4\) −0.0491037 0.0850501i −0.0245518 0.0425250i
\(5\) −0.697972 + 0.402974i −0.312142 + 0.180216i −0.647885 0.761738i \(-0.724346\pi\)
0.335742 + 0.941954i \(0.391013\pi\)
\(6\) 3.44101 + 1.98667i 1.40479 + 0.811054i
\(7\) 0 0
\(8\) 2.89354i 1.02302i
\(9\) 5.30133 1.76711
\(10\) 1.11145 0.351470
\(11\) 5.27158i 1.58944i −0.606976 0.794720i \(-0.707618\pi\)
0.606976 0.794720i \(-0.292382\pi\)
\(12\) 0.141478 + 0.245047i 0.0408411 + 0.0707389i
\(13\) 2.36581 2.72084i 0.656156 0.754625i
\(14\) 0 0
\(15\) 2.01100 1.16105i 0.519237 0.299782i
\(16\) 1.89697 3.28565i 0.474243 0.821412i
\(17\) 0.280051 + 0.485062i 0.0679223 + 0.117645i 0.897987 0.440023i \(-0.145030\pi\)
−0.830064 + 0.557668i \(0.811696\pi\)
\(18\) −6.33136 3.65541i −1.49232 0.861589i
\(19\) 5.84469i 1.34086i −0.741972 0.670431i \(-0.766109\pi\)
0.741972 0.670431i \(-0.233891\pi\)
\(20\) 0.0685460 + 0.0395750i 0.0153273 + 0.00884925i
\(21\) 0 0
\(22\) −3.63490 + 6.29583i −0.774963 + 1.34228i
\(23\) −0.802438 + 1.38986i −0.167320 + 0.289807i −0.937477 0.348048i \(-0.886845\pi\)
0.770157 + 0.637855i \(0.220178\pi\)
\(24\) 8.33689i 1.70176i
\(25\) −2.17522 + 3.76760i −0.435045 + 0.753520i
\(26\) −4.70157 + 1.61820i −0.922053 + 0.317355i
\(27\) −6.63060 −1.27606
\(28\) 0 0
\(29\) −1.14008 1.97467i −0.211707 0.366687i 0.740542 0.672010i \(-0.234569\pi\)
−0.952249 + 0.305323i \(0.901236\pi\)
\(30\) −3.20230 −0.584658
\(31\) 3.01022 + 1.73795i 0.540651 + 0.312145i 0.745343 0.666681i \(-0.232286\pi\)
−0.204692 + 0.978827i \(0.565619\pi\)
\(32\) 0.480674 0.277517i 0.0849719 0.0490585i
\(33\) 15.1885i 2.64398i
\(34\) 0.772411i 0.132467i
\(35\) 0 0
\(36\) −0.260315 0.450879i −0.0433858 0.0751464i
\(37\) 1.07557 + 0.620979i 0.176822 + 0.102088i 0.585799 0.810457i \(-0.300781\pi\)
−0.408977 + 0.912545i \(0.634114\pi\)
\(38\) −4.03007 + 6.98029i −0.653764 + 1.13235i
\(39\) −6.81636 + 7.83929i −1.09149 + 1.25529i
\(40\) −1.16602 2.01961i −0.184364 0.319329i
\(41\) −0.803413 + 0.463851i −0.125472 + 0.0724413i −0.561422 0.827529i \(-0.689746\pi\)
0.435950 + 0.899971i \(0.356412\pi\)
\(42\) 0 0
\(43\) 2.22356 3.85131i 0.339089 0.587320i −0.645172 0.764037i \(-0.723214\pi\)
0.984262 + 0.176717i \(0.0565478\pi\)
\(44\) −0.448348 + 0.258854i −0.0675910 + 0.0390237i
\(45\) −3.70018 + 2.13630i −0.551590 + 0.318461i
\(46\) 1.91670 1.10661i 0.282602 0.163160i
\(47\) −3.32915 + 1.92209i −0.485607 + 0.280365i −0.722750 0.691109i \(-0.757122\pi\)
0.237143 + 0.971475i \(0.423789\pi\)
\(48\) −5.46556 + 9.46662i −0.788885 + 1.36639i
\(49\) 0 0
\(50\) 5.19572 2.99975i 0.734786 0.424229i
\(51\) −0.806883 1.39756i −0.112986 0.195698i
\(52\) −0.347577 0.0676087i −0.0482003 0.00937564i
\(53\) −2.72727 + 4.72377i −0.374620 + 0.648860i −0.990270 0.139159i \(-0.955560\pi\)
0.615650 + 0.788019i \(0.288893\pi\)
\(54\) 7.91890 + 4.57198i 1.07763 + 0.622168i
\(55\) 2.12431 + 3.67941i 0.286442 + 0.496132i
\(56\) 0 0
\(57\) 16.8397i 2.23048i
\(58\) 3.14446i 0.412887i
\(59\) −9.52106 + 5.49698i −1.23954 + 0.715646i −0.968999 0.247063i \(-0.920534\pi\)
−0.270537 + 0.962710i \(0.587201\pi\)
\(60\) −0.197495 0.114024i −0.0254965 0.0147204i
\(61\) −7.30215 −0.934944 −0.467472 0.884008i \(-0.654835\pi\)
−0.467472 + 0.884008i \(0.654835\pi\)
\(62\) −2.39673 4.15126i −0.304385 0.527210i
\(63\) 0 0
\(64\) −8.35330 −1.04416
\(65\) −0.554837 + 2.85243i −0.0688191 + 0.353800i
\(66\) 10.4729 18.1396i 1.28912 2.23283i
\(67\) 7.34556i 0.897403i −0.893682 0.448701i \(-0.851887\pi\)
0.893682 0.448701i \(-0.148113\pi\)
\(68\) 0.0275031 0.0476367i 0.00333524 0.00577680i
\(69\) 2.31199 4.00448i 0.278330 0.482083i
\(70\) 0 0
\(71\) −8.06668 4.65730i −0.957339 0.552720i −0.0619857 0.998077i \(-0.519743\pi\)
−0.895353 + 0.445357i \(0.853077\pi\)
\(72\) 15.3396i 1.80779i
\(73\) 4.33139 + 2.50073i 0.506951 + 0.292688i 0.731579 0.681756i \(-0.238784\pi\)
−0.224629 + 0.974444i \(0.572117\pi\)
\(74\) −0.856364 1.48327i −0.0995503 0.172426i
\(75\) 6.26726 10.8552i 0.723681 1.25345i
\(76\) −0.497091 + 0.286996i −0.0570202 + 0.0329207i
\(77\) 0 0
\(78\) 13.5462 4.66237i 1.53380 0.527909i
\(79\) −5.68437 9.84562i −0.639542 1.10772i −0.985533 0.169481i \(-0.945791\pi\)
0.345992 0.938238i \(-0.387543\pi\)
\(80\) 3.05772i 0.341863i
\(81\) 3.20012 0.355568
\(82\) 1.27935 0.141281
\(83\) 5.81962i 0.638786i 0.947622 + 0.319393i \(0.103479\pi\)
−0.947622 + 0.319393i \(0.896521\pi\)
\(84\) 0 0
\(85\) −0.390935 0.225707i −0.0424029 0.0244813i
\(86\) −5.31117 + 3.06641i −0.572719 + 0.330659i
\(87\) 3.28479 + 5.68943i 0.352167 + 0.609971i
\(88\) 15.2535 1.62603
\(89\) −4.33832 2.50473i −0.459861 0.265501i 0.252125 0.967695i \(-0.418871\pi\)
−0.711986 + 0.702194i \(0.752204\pi\)
\(90\) 5.89215 0.621087
\(91\) 0 0
\(92\) 0.157611 0.0164320
\(93\) −8.67305 5.00739i −0.899354 0.519242i
\(94\) 5.30133 0.546791
\(95\) 2.35526 + 4.07942i 0.241644 + 0.418540i
\(96\) −1.38492 + 0.799583i −0.141348 + 0.0816071i
\(97\) −9.22171 5.32416i −0.936323 0.540586i −0.0475172 0.998870i \(-0.515131\pi\)
−0.888806 + 0.458284i \(0.848464\pi\)
\(98\) 0 0
\(99\) 27.9464i 2.80872i
\(100\) 0.427246 0.0427246
\(101\) 3.91554 0.389611 0.194805 0.980842i \(-0.437592\pi\)
0.194805 + 0.980842i \(0.437592\pi\)
\(102\) 2.22547i 0.220355i
\(103\) −4.22690 7.32120i −0.416488 0.721379i 0.579095 0.815260i \(-0.303406\pi\)
−0.995583 + 0.0938810i \(0.970073\pi\)
\(104\) 7.87287 + 6.84556i 0.771998 + 0.671262i
\(105\) 0 0
\(106\) 6.51434 3.76106i 0.632729 0.365306i
\(107\) 4.83761 8.37899i 0.467670 0.810028i −0.531648 0.846965i \(-0.678427\pi\)
0.999318 + 0.0369379i \(0.0117604\pi\)
\(108\) 0.325587 + 0.563933i 0.0313296 + 0.0542645i
\(109\) 12.6126 + 7.28189i 1.20807 + 0.697478i 0.962337 0.271860i \(-0.0876388\pi\)
0.245731 + 0.969338i \(0.420972\pi\)
\(110\) 5.85908i 0.558641i
\(111\) −3.09893 1.78917i −0.294137 0.169820i
\(112\) 0 0
\(113\) −9.75572 + 16.8974i −0.917741 + 1.58957i −0.114903 + 0.993377i \(0.536656\pi\)
−0.802838 + 0.596197i \(0.796678\pi\)
\(114\) 11.6115 20.1116i 1.08751 1.88363i
\(115\) 1.29345i 0.120615i
\(116\) −0.111964 + 0.193927i −0.0103956 + 0.0180057i
\(117\) 12.5419 14.4241i 1.15950 1.33351i
\(118\) 15.1613 1.39571
\(119\) 0 0
\(120\) 3.35955 + 5.81891i 0.306683 + 0.531191i
\(121\) −16.7895 −1.52632
\(122\) 8.72093 + 5.03503i 0.789556 + 0.455850i
\(123\) 2.31480 1.33645i 0.208718 0.120503i
\(124\) 0.341359i 0.0306550i
\(125\) 7.53598i 0.674038i
\(126\) 0 0
\(127\) −0.958656 1.66044i −0.0850670 0.147340i 0.820353 0.571858i \(-0.193777\pi\)
−0.905420 + 0.424517i \(0.860444\pi\)
\(128\) 9.01498 + 5.20480i 0.796819 + 0.460044i
\(129\) −6.40652 + 11.0964i −0.564063 + 0.976985i
\(130\) 2.62947 3.02407i 0.230619 0.265228i
\(131\) 7.79078 + 13.4940i 0.680684 + 1.17898i 0.974772 + 0.223201i \(0.0716506\pi\)
−0.294089 + 0.955778i \(0.595016\pi\)
\(132\) 1.29178 0.745811i 0.112435 0.0649145i
\(133\) 0 0
\(134\) −5.06496 + 8.77278i −0.437546 + 0.757852i
\(135\) 4.62797 2.67196i 0.398312 0.229966i
\(136\) −1.40355 + 0.810339i −0.120353 + 0.0694860i
\(137\) 6.79921 3.92553i 0.580896 0.335380i −0.180594 0.983558i \(-0.557802\pi\)
0.761489 + 0.648178i \(0.224469\pi\)
\(138\) −5.52240 + 3.18836i −0.470098 + 0.271411i
\(139\) 4.96241 8.59514i 0.420906 0.729030i −0.575122 0.818067i \(-0.695046\pi\)
0.996028 + 0.0890370i \(0.0283789\pi\)
\(140\) 0 0
\(141\) 9.59197 5.53793i 0.807790 0.466378i
\(142\) 6.42267 + 11.1244i 0.538979 + 0.933538i
\(143\) −14.3431 12.4715i −1.19943 1.04292i
\(144\) 10.0565 17.4183i 0.838039 1.45153i
\(145\) 1.59148 + 0.918843i 0.132165 + 0.0763058i
\(146\) −3.44864 5.97322i −0.285412 0.494347i
\(147\) 0 0
\(148\) 0.121969i 0.0100258i
\(149\) 7.91925i 0.648770i 0.945925 + 0.324385i \(0.105157\pi\)
−0.945925 + 0.324385i \(0.894843\pi\)
\(150\) −14.9699 + 8.64290i −1.22229 + 0.705690i
\(151\) −1.30005 0.750582i −0.105796 0.0610815i 0.446168 0.894949i \(-0.352788\pi\)
−0.551965 + 0.833868i \(0.686122\pi\)
\(152\) 16.9118 1.37173
\(153\) 1.48464 + 2.57148i 0.120026 + 0.207892i
\(154\) 0 0
\(155\) −2.80140 −0.225014
\(156\) 1.00144 + 0.194794i 0.0801794 + 0.0155960i
\(157\) 1.92846 3.34019i 0.153908 0.266576i −0.778753 0.627331i \(-0.784147\pi\)
0.932661 + 0.360754i \(0.117481\pi\)
\(158\) 15.6781i 1.24728i
\(159\) 7.85782 13.6102i 0.623166 1.07936i
\(160\) −0.223664 + 0.387398i −0.0176822 + 0.0306265i
\(161\) 0 0
\(162\) −3.82189 2.20657i −0.300276 0.173364i
\(163\) 14.3608i 1.12483i 0.826856 + 0.562414i \(0.190127\pi\)
−0.826856 + 0.562414i \(0.809873\pi\)
\(164\) 0.0789011 + 0.0455536i 0.00616114 + 0.00355714i
\(165\) −6.12057 10.6011i −0.476486 0.825297i
\(166\) 4.01279 6.95035i 0.311453 0.539452i
\(167\) 3.91563 2.26069i 0.303000 0.174937i −0.340790 0.940140i \(-0.610694\pi\)
0.643790 + 0.765202i \(0.277361\pi\)
\(168\) 0 0
\(169\) −1.80593 12.8740i −0.138918 0.990304i
\(170\) 0.311262 + 0.539121i 0.0238727 + 0.0413487i
\(171\) 30.9846i 2.36945i
\(172\) −0.436739 −0.0333011
\(173\) −19.5179 −1.48392 −0.741960 0.670444i \(-0.766104\pi\)
−0.741960 + 0.670444i \(0.766104\pi\)
\(174\) 9.05982i 0.686823i
\(175\) 0 0
\(176\) −17.3206 10.0000i −1.30559 0.753780i
\(177\) 27.4321 15.8379i 2.06192 1.19045i
\(178\) 3.45416 + 5.98278i 0.258900 + 0.448428i
\(179\) −20.8196 −1.55613 −0.778065 0.628183i \(-0.783799\pi\)
−0.778065 + 0.628183i \(0.783799\pi\)
\(180\) 0.363385 + 0.209800i 0.0270851 + 0.0156376i
\(181\) −16.5522 −1.23031 −0.615157 0.788405i \(-0.710907\pi\)
−0.615157 + 0.788405i \(0.710907\pi\)
\(182\) 0 0
\(183\) 21.0390 1.55525
\(184\) −4.02163 2.32189i −0.296478 0.171172i
\(185\) −1.00095 −0.0735916
\(186\) 6.90546 + 11.9606i 0.506333 + 0.876995i
\(187\) 2.55704 1.47631i 0.186990 0.107958i
\(188\) 0.326948 + 0.188763i 0.0238451 + 0.0137670i
\(189\) 0 0
\(190\) 6.49606i 0.471274i
\(191\) −4.25008 −0.307525 −0.153762 0.988108i \(-0.549139\pi\)
−0.153762 + 0.988108i \(0.549139\pi\)
\(192\) 24.0676 1.73693
\(193\) 11.5972i 0.834787i 0.908726 + 0.417393i \(0.137056\pi\)
−0.908726 + 0.417393i \(0.862944\pi\)
\(194\) 7.34231 + 12.7172i 0.527147 + 0.913045i
\(195\) 1.59860 8.21842i 0.114478 0.588533i
\(196\) 0 0
\(197\) −12.4892 + 7.21066i −0.889821 + 0.513738i −0.873884 0.486135i \(-0.838406\pi\)
−0.0159371 + 0.999873i \(0.505073\pi\)
\(198\) −19.2698 + 33.3763i −1.36944 + 2.37195i
\(199\) −3.52962 6.11348i −0.250208 0.433373i 0.713375 0.700783i \(-0.247166\pi\)
−0.963583 + 0.267409i \(0.913832\pi\)
\(200\) −10.9017 6.29410i −0.770867 0.445060i
\(201\) 21.1640i 1.49280i
\(202\) −4.67632 2.69987i −0.329024 0.189962i
\(203\) 0 0
\(204\) −0.0792419 + 0.137251i −0.00554804 + 0.00960949i
\(205\) 0.373840 0.647509i 0.0261101 0.0452240i
\(206\) 11.6582i 0.812268i
\(207\) −4.25399 + 7.36812i −0.295673 + 0.512120i
\(208\) −4.45186 12.9346i −0.308681 0.896850i
\(209\) −30.8107 −2.13122
\(210\) 0 0
\(211\) 13.2113 + 22.8827i 0.909505 + 1.57531i 0.814754 + 0.579807i \(0.196872\pi\)
0.0947513 + 0.995501i \(0.469794\pi\)
\(212\) 0.535677 0.0367904
\(213\) 23.2417 + 13.4186i 1.59250 + 0.919429i
\(214\) −11.5551 + 6.67133i −0.789890 + 0.456043i
\(215\) 3.58414i 0.244437i
\(216\) 19.1859i 1.30544i
\(217\) 0 0
\(218\) −10.0421 17.3935i −0.680138 1.17803i
\(219\) −12.4796 7.20511i −0.843294 0.486876i
\(220\) 0.208623 0.361345i 0.0140654 0.0243619i
\(221\) 1.98232 + 0.385590i 0.133345 + 0.0259376i
\(222\) 2.46736 + 4.27359i 0.165598 + 0.286825i
\(223\) −19.9191 + 11.5003i −1.33388 + 0.770115i −0.985892 0.167384i \(-0.946468\pi\)
−0.347987 + 0.937499i \(0.613135\pi\)
\(224\) 0 0
\(225\) −11.5316 + 19.9733i −0.768772 + 1.33155i
\(226\) 23.3024 13.4537i 1.55006 0.894925i
\(227\) 0.392628 0.226684i 0.0260596 0.0150455i −0.486914 0.873450i \(-0.661877\pi\)
0.512973 + 0.858405i \(0.328544\pi\)
\(228\) 1.43222 0.826893i 0.0948511 0.0547623i
\(229\) 15.0112 8.66674i 0.991970 0.572714i 0.0861077 0.996286i \(-0.472557\pi\)
0.905863 + 0.423571i \(0.139224\pi\)
\(230\) −0.891867 + 1.54476i −0.0588080 + 0.101858i
\(231\) 0 0
\(232\) 5.71380 3.29886i 0.375129 0.216581i
\(233\) 3.90756 + 6.76809i 0.255992 + 0.443392i 0.965165 0.261643i \(-0.0842644\pi\)
−0.709172 + 0.705035i \(0.750931\pi\)
\(234\) −24.9246 + 8.57862i −1.62937 + 0.560802i
\(235\) 1.54910 2.68313i 0.101052 0.175028i
\(236\) 0.935038 + 0.539844i 0.0608658 + 0.0351409i
\(237\) 16.3778 + 28.3672i 1.06385 + 1.84265i
\(238\) 0 0
\(239\) 13.5314i 0.875276i −0.899151 0.437638i \(-0.855815\pi\)
0.899151 0.437638i \(-0.144185\pi\)
\(240\) 8.80991i 0.568677i
\(241\) 19.5369 11.2796i 1.25848 0.726583i 0.285701 0.958319i \(-0.407774\pi\)
0.972779 + 0.231736i \(0.0744404\pi\)
\(242\) 20.0517 + 11.5768i 1.28897 + 0.744188i
\(243\) 10.6716 0.684585
\(244\) 0.358563 + 0.621049i 0.0229546 + 0.0397586i
\(245\) 0 0
\(246\) −3.68607 −0.235015
\(247\) −15.9024 13.8274i −1.01185 0.879815i
\(248\) −5.02884 + 8.71020i −0.319331 + 0.553098i
\(249\) 16.7675i 1.06260i
\(250\) −5.19626 + 9.00019i −0.328641 + 0.569222i
\(251\) 3.36618 5.83039i 0.212471 0.368011i −0.740016 0.672589i \(-0.765182\pi\)
0.952487 + 0.304578i \(0.0985154\pi\)
\(252\) 0 0
\(253\) 7.32677 + 4.23011i 0.460630 + 0.265945i
\(254\) 2.64408i 0.165904i
\(255\) 1.12636 + 0.650306i 0.0705356 + 0.0407238i
\(256\) 1.17560 + 2.03620i 0.0734750 + 0.127262i
\(257\) −8.26907 + 14.3225i −0.515811 + 0.893410i 0.484021 + 0.875056i \(0.339176\pi\)
−0.999832 + 0.0183536i \(0.994158\pi\)
\(258\) 15.3026 8.83494i 0.952696 0.550039i
\(259\) 0 0
\(260\) 0.269844 0.0928757i 0.0167350 0.00575991i
\(261\) −6.04392 10.4684i −0.374110 0.647977i
\(262\) 21.4878i 1.32752i
\(263\) −10.0227 −0.618028 −0.309014 0.951057i \(-0.599999\pi\)
−0.309014 + 0.951057i \(0.599999\pi\)
\(264\) −43.9485 −2.70485
\(265\) 4.39608i 0.270049i
\(266\) 0 0
\(267\) 12.4996 + 7.21663i 0.764962 + 0.441651i
\(268\) −0.624740 + 0.360694i −0.0381621 + 0.0220329i
\(269\) −7.86149 13.6165i −0.479323 0.830212i 0.520395 0.853925i \(-0.325785\pi\)
−0.999719 + 0.0237130i \(0.992451\pi\)
\(270\) −7.36956 −0.448497
\(271\) 4.51734 + 2.60809i 0.274409 + 0.158430i 0.630890 0.775873i \(-0.282690\pi\)
−0.356481 + 0.934303i \(0.616023\pi\)
\(272\) 2.12499 0.128847
\(273\) 0 0
\(274\) −10.8270 −0.654085
\(275\) 19.8612 + 11.4669i 1.19767 + 0.691478i
\(276\) −0.454108 −0.0273341
\(277\) −9.63619 16.6904i −0.578983 1.00283i −0.995596 0.0937439i \(-0.970117\pi\)
0.416614 0.909084i \(-0.363217\pi\)
\(278\) −11.8532 + 6.84343i −0.710906 + 0.410442i
\(279\) 15.9582 + 9.21345i 0.955390 + 0.551595i
\(280\) 0 0
\(281\) 2.14283i 0.127831i −0.997955 0.0639153i \(-0.979641\pi\)
0.997955 0.0639153i \(-0.0203588\pi\)
\(282\) −15.2742 −0.909566
\(283\) −15.7502 −0.936255 −0.468127 0.883661i \(-0.655071\pi\)
−0.468127 + 0.883661i \(0.655071\pi\)
\(284\) 0.914762i 0.0542812i
\(285\) −6.78597 11.7537i −0.401966 0.696226i
\(286\) 8.53048 + 24.7847i 0.504418 + 1.46555i
\(287\) 0 0
\(288\) 2.54821 1.47121i 0.150155 0.0866919i
\(289\) 8.34314 14.4507i 0.490773 0.850044i
\(290\) −1.26714 2.19474i −0.0744087 0.128880i
\(291\) 26.5696 + 15.3400i 1.55754 + 0.899246i
\(292\) 0.491180i 0.0287441i
\(293\) 20.0474 + 11.5744i 1.17118 + 0.676182i 0.953958 0.299940i \(-0.0969668\pi\)
0.217223 + 0.976122i \(0.430300\pi\)
\(294\) 0 0
\(295\) 4.43029 7.67348i 0.257941 0.446767i
\(296\) −1.79683 + 3.11220i −0.104439 + 0.180893i
\(297\) 34.9537i 2.02822i
\(298\) 5.46054 9.45793i 0.316320 0.547883i
\(299\) 1.88318 + 5.47145i 0.108907 + 0.316422i
\(300\) −1.23098 −0.0710708
\(301\) 0 0
\(302\) 1.03509 + 1.79283i 0.0595629 + 0.103166i
\(303\) −11.2815 −0.648103
\(304\) −19.2036 11.0872i −1.10140 0.635894i
\(305\) 5.09669 2.94258i 0.291836 0.168491i
\(306\) 4.09481i 0.234085i
\(307\) 4.23590i 0.241756i −0.992667 0.120878i \(-0.961429\pi\)
0.992667 0.120878i \(-0.0385709\pi\)
\(308\) 0 0
\(309\) 12.1785 + 21.0939i 0.692813 + 1.19999i
\(310\) 3.34570 + 1.93164i 0.190023 + 0.109710i
\(311\) −13.6251 + 23.5993i −0.772606 + 1.33819i 0.163524 + 0.986539i \(0.447714\pi\)
−0.936130 + 0.351654i \(0.885619\pi\)
\(312\) −22.6833 19.7234i −1.28419 1.11662i
\(313\) 1.34849 + 2.33565i 0.0762209 + 0.132018i 0.901617 0.432536i \(-0.142381\pi\)
−0.825396 + 0.564555i \(0.809048\pi\)
\(314\) −4.60631 + 2.65945i −0.259949 + 0.150082i
\(315\) 0 0
\(316\) −0.558247 + 0.966913i −0.0314039 + 0.0543931i
\(317\) −20.8456 + 12.0352i −1.17081 + 0.675966i −0.953870 0.300220i \(-0.902940\pi\)
−0.216937 + 0.976186i \(0.569607\pi\)
\(318\) −18.7691 + 10.8364i −1.05252 + 0.607674i
\(319\) −10.4096 + 6.01000i −0.582828 + 0.336496i
\(320\) 5.83037 3.36617i 0.325928 0.188174i
\(321\) −13.9381 + 24.1416i −0.777951 + 1.34745i
\(322\) 0 0
\(323\) 2.83504 1.63681i 0.157746 0.0910745i
\(324\) −0.157138 0.272170i −0.00872986 0.0151206i
\(325\) 5.10487 + 14.8318i 0.283167 + 0.822722i
\(326\) 9.90220 17.1511i 0.548432 0.949912i
\(327\) −36.3394 20.9806i −2.00958 1.16023i
\(328\) −1.34217 2.32471i −0.0741091 0.128361i
\(329\) 0 0
\(330\) 16.8812i 0.929279i
\(331\) 0.619723i 0.0340631i 0.999855 + 0.0170315i \(0.00542157\pi\)
−0.999855 + 0.0170315i \(0.994578\pi\)
\(332\) 0.494959 0.285765i 0.0271644 0.0156834i
\(333\) 5.70194 + 3.29201i 0.312464 + 0.180401i
\(334\) −6.23523 −0.341177
\(335\) 2.96007 + 5.12699i 0.161726 + 0.280117i
\(336\) 0 0
\(337\) −5.72118 −0.311652 −0.155826 0.987784i \(-0.549804\pi\)
−0.155826 + 0.987784i \(0.549804\pi\)
\(338\) −6.72012 + 16.6206i −0.365527 + 0.904039i
\(339\) 28.1082 48.6848i 1.52663 2.64420i
\(340\) 0.0443321i 0.00240425i
\(341\) 9.16174 15.8686i 0.496136 0.859333i
\(342\) −21.3647 + 37.0048i −1.15527 + 2.00099i
\(343\) 0 0
\(344\) 11.1439 + 6.43396i 0.600841 + 0.346896i
\(345\) 3.72668i 0.200638i
\(346\) 23.3102 + 13.4581i 1.25316 + 0.723514i
\(347\) 0.932429 + 1.61501i 0.0500554 + 0.0866985i 0.889968 0.456024i \(-0.150727\pi\)
−0.839912 + 0.542722i \(0.817394\pi\)
\(348\) 0.322591 0.558744i 0.0172927 0.0299518i
\(349\) 19.3273 11.1586i 1.03457 0.597307i 0.116277 0.993217i \(-0.462904\pi\)
0.918290 + 0.395909i \(0.129571\pi\)
\(350\) 0 0
\(351\) −15.6867 + 18.0408i −0.837295 + 0.962947i
\(352\) −1.46295 2.53391i −0.0779756 0.135058i
\(353\) 2.33199i 0.124119i 0.998072 + 0.0620597i \(0.0197669\pi\)
−0.998072 + 0.0620597i \(0.980233\pi\)
\(354\) −43.6827 −2.32171
\(355\) 7.50708 0.398435
\(356\) 0.491966i 0.0260741i
\(357\) 0 0
\(358\) 24.8648 + 14.3557i 1.31415 + 0.758722i
\(359\) 2.83281 1.63553i 0.149510 0.0863197i −0.423379 0.905953i \(-0.639156\pi\)
0.572889 + 0.819633i \(0.305823\pi\)
\(360\) −6.18147 10.7066i −0.325792 0.564289i
\(361\) −15.1603 −0.797913
\(362\) 19.7682 + 11.4132i 1.03899 + 0.599863i
\(363\) 48.3741 2.53898
\(364\) 0 0
\(365\) −4.03092 −0.210988
\(366\) −25.1268 14.5070i −1.31340 0.758291i
\(367\) −4.15290 −0.216780 −0.108390 0.994108i \(-0.534569\pi\)
−0.108390 + 0.994108i \(0.534569\pi\)
\(368\) 3.04440 + 5.27306i 0.158700 + 0.274877i
\(369\) −4.25916 + 2.45903i −0.221723 + 0.128012i
\(370\) 1.19544 + 0.690185i 0.0621477 + 0.0358810i
\(371\) 0 0
\(372\) 0.983525i 0.0509934i
\(373\) −11.1089 −0.575198 −0.287599 0.957751i \(-0.592857\pi\)
−0.287599 + 0.957751i \(0.592857\pi\)
\(374\) −4.07183 −0.210549
\(375\) 21.7127i 1.12124i
\(376\) −5.56165 9.63305i −0.286820 0.496787i
\(377\) −8.06996 1.56972i −0.415624 0.0808447i
\(378\) 0 0
\(379\) −4.01862 + 2.32015i −0.206422 + 0.119178i −0.599648 0.800264i \(-0.704693\pi\)
0.393225 + 0.919442i \(0.371359\pi\)
\(380\) 0.231304 0.400630i 0.0118656 0.0205519i
\(381\) 2.76208 + 4.78407i 0.141506 + 0.245095i
\(382\) 5.07586 + 2.93055i 0.259703 + 0.149940i
\(383\) 3.66933i 0.187494i 0.995596 + 0.0937469i \(0.0298845\pi\)
−0.995596 + 0.0937469i \(0.970116\pi\)
\(384\) −25.9740 14.9961i −1.32548 0.765266i
\(385\) 0 0
\(386\) 7.99661 13.8505i 0.407017 0.704973i
\(387\) 11.7878 20.4171i 0.599208 1.03786i
\(388\) 1.04574i 0.0530896i
\(389\) 8.44156 14.6212i 0.428004 0.741324i −0.568692 0.822551i \(-0.692550\pi\)
0.996696 + 0.0812262i \(0.0258836\pi\)
\(390\) −7.57603 + 8.71296i −0.383627 + 0.441198i
\(391\) −0.898894 −0.0454590
\(392\) 0 0
\(393\) −22.4468 38.8790i −1.13229 1.96119i
\(394\) 19.8878 1.00193
\(395\) 7.93506 + 4.58131i 0.399256 + 0.230511i
\(396\) −2.37684 + 1.37227i −0.119441 + 0.0689592i
\(397\) 16.7086i 0.838578i 0.907853 + 0.419289i \(0.137721\pi\)
−0.907853 + 0.419289i \(0.862279\pi\)
\(398\) 9.73508i 0.487976i
\(399\) 0 0
\(400\) 8.25267 + 14.2940i 0.412633 + 0.714702i
\(401\) 21.9221 + 12.6567i 1.09474 + 0.632046i 0.934833 0.355087i \(-0.115549\pi\)
0.159902 + 0.987133i \(0.448882\pi\)
\(402\) 14.5932 25.2761i 0.727842 1.26066i
\(403\) 11.8503 4.07867i 0.590304 0.203173i
\(404\) −0.192267 0.333017i −0.00956566 0.0165682i
\(405\) −2.23359 + 1.28956i −0.110988 + 0.0640789i
\(406\) 0 0
\(407\) 3.27354 5.66994i 0.162263 0.281048i
\(408\) 4.04391 2.33475i 0.200203 0.115587i
\(409\) −4.96529 + 2.86671i −0.245518 + 0.141750i −0.617710 0.786406i \(-0.711940\pi\)
0.372192 + 0.928156i \(0.378606\pi\)
\(410\) −0.892951 + 0.515546i −0.0440997 + 0.0254610i
\(411\) −19.5899 + 11.3102i −0.966299 + 0.557893i
\(412\) −0.415112 + 0.718996i −0.0204511 + 0.0354224i
\(413\) 0 0
\(414\) 10.1610 5.86648i 0.499388 0.288322i
\(415\) −2.34516 4.06193i −0.115119 0.199392i
\(416\) 0.382101 1.96439i 0.0187340 0.0963120i
\(417\) −14.2977 + 24.7643i −0.700161 + 1.21272i
\(418\) 36.7971 + 21.2448i 1.79981 + 1.03912i
\(419\) −17.1729 29.7443i −0.838950 1.45310i −0.890773 0.454448i \(-0.849836\pi\)
0.0518229 0.998656i \(-0.483497\pi\)
\(420\) 0 0
\(421\) 2.94167i 0.143368i −0.997427 0.0716842i \(-0.977163\pi\)
0.997427 0.0716842i \(-0.0228374\pi\)
\(422\) 36.4383i 1.77379i
\(423\) −17.6489 + 10.1896i −0.858121 + 0.495437i
\(424\) −13.6684 7.89148i −0.663798 0.383244i
\(425\) −2.43669 −0.118197
\(426\) −18.5050 32.0516i −0.896571 1.55291i
\(427\) 0 0
\(428\) −0.950178 −0.0459286
\(429\) 41.3254 + 35.9330i 1.99521 + 1.73486i
\(430\) 2.47137 4.28053i 0.119180 0.206426i
\(431\) 39.6955i 1.91207i −0.293258 0.956033i \(-0.594739\pi\)
0.293258 0.956033i \(-0.405261\pi\)
\(432\) −12.5781 + 21.7858i −0.605162 + 1.04817i
\(433\) 4.91827 8.51869i 0.236357 0.409382i −0.723309 0.690524i \(-0.757380\pi\)
0.959666 + 0.281142i \(0.0907133\pi\)
\(434\) 0 0
\(435\) −4.58538 2.64737i −0.219852 0.126932i
\(436\) 1.43027i 0.0684975i
\(437\) 8.12331 + 4.69000i 0.388591 + 0.224353i
\(438\) 9.93624 + 17.2101i 0.474772 + 0.822329i
\(439\) −14.2733 + 24.7220i −0.681226 + 1.17992i 0.293381 + 0.955996i \(0.405220\pi\)
−0.974607 + 0.223922i \(0.928114\pi\)
\(440\) −10.6465 + 6.14678i −0.507554 + 0.293036i
\(441\) 0 0
\(442\) −2.10161 1.82737i −0.0999632 0.0869193i
\(443\) −1.66951 2.89167i −0.0793207 0.137387i 0.823636 0.567118i \(-0.191942\pi\)
−0.902957 + 0.429731i \(0.858608\pi\)
\(444\) 0.351419i 0.0166776i
\(445\) 4.03736 0.191389
\(446\) 31.7190 1.50194
\(447\) 22.8170i 1.07921i
\(448\) 0 0
\(449\) 15.7487 + 9.09253i 0.743228 + 0.429103i 0.823242 0.567691i \(-0.192163\pi\)
−0.0800136 + 0.996794i \(0.525496\pi\)
\(450\) 27.5443 15.9027i 1.29845 0.749660i
\(451\) 2.44523 + 4.23526i 0.115141 + 0.199430i
\(452\) 1.91617 0.0901289
\(453\) 3.74570 + 2.16258i 0.175988 + 0.101607i
\(454\) −0.625219 −0.0293430
\(455\) 0 0
\(456\) −48.7265 −2.28183
\(457\) 7.55982 + 4.36466i 0.353633 + 0.204170i 0.666284 0.745698i \(-0.267884\pi\)
−0.312651 + 0.949868i \(0.601217\pi\)
\(458\) −23.9038 −1.11695
\(459\) −1.85691 3.21625i −0.0866729 0.150122i
\(460\) −0.110008 + 0.0635130i −0.00512914 + 0.00296131i
\(461\) 1.96695 + 1.13562i 0.0916099 + 0.0528910i 0.545105 0.838368i \(-0.316490\pi\)
−0.453495 + 0.891259i \(0.649823\pi\)
\(462\) 0 0
\(463\) 5.48326i 0.254829i −0.991850 0.127414i \(-0.959332\pi\)
0.991850 0.127414i \(-0.0406678\pi\)
\(464\) −8.65077 −0.401602
\(465\) 8.07139 0.374302
\(466\) 10.7775i 0.499257i
\(467\) −9.44095 16.3522i −0.436875 0.756690i 0.560572 0.828106i \(-0.310581\pi\)
−0.997447 + 0.0714164i \(0.977248\pi\)
\(468\) −1.84262 0.358416i −0.0851753 0.0165678i
\(469\) 0 0
\(470\) −3.70018 + 2.13630i −0.170677 + 0.0985401i
\(471\) −5.55629 + 9.62377i −0.256020 + 0.443440i
\(472\) −15.9058 27.5496i −0.732122 1.26807i
\(473\) −20.3025 11.7217i −0.933510 0.538962i
\(474\) 45.1718i 2.07481i
\(475\) 22.0204 + 12.7135i 1.01037 + 0.583335i
\(476\) 0 0
\(477\) −14.4582 + 25.0423i −0.661994 + 1.14661i
\(478\) −9.33030 + 16.1606i −0.426758 + 0.739166i
\(479\) 33.1354i 1.51399i −0.653418 0.756997i \(-0.726666\pi\)
0.653418 0.756997i \(-0.273334\pi\)
\(480\) 0.644422 1.11617i 0.0294137 0.0509461i
\(481\) 4.23417 1.45733i 0.193061 0.0664485i
\(482\) −31.1104 −1.41704
\(483\) 0 0
\(484\) 0.824428 + 1.42795i 0.0374740 + 0.0649069i
\(485\) 8.58199 0.389688
\(486\) −12.7451 7.35838i −0.578129 0.333783i
\(487\) −13.8185 + 7.97814i −0.626178 + 0.361524i −0.779270 0.626688i \(-0.784410\pi\)
0.153093 + 0.988212i \(0.451077\pi\)
\(488\) 21.1291i 0.956469i
\(489\) 41.3765i 1.87111i
\(490\) 0 0
\(491\) −15.8464 27.4468i −0.715138 1.23866i −0.962906 0.269836i \(-0.913031\pi\)
0.247769 0.968819i \(-0.420303\pi\)
\(492\) −0.227330 0.131249i −0.0102488 0.00591717i
\(493\) 0.638559 1.10602i 0.0287593 0.0498125i
\(494\) 9.45788 + 27.4792i 0.425530 + 1.23635i
\(495\) 11.2617 + 19.5058i 0.506174 + 0.876720i
\(496\) 11.4206 6.59368i 0.512800 0.296065i
\(497\) 0 0
\(498\) −11.5617 + 20.0254i −0.518090 + 0.897358i
\(499\) −20.9738 + 12.1092i −0.938916 + 0.542083i −0.889620 0.456701i \(-0.849031\pi\)
−0.0492955 + 0.998784i \(0.515698\pi\)
\(500\) −0.640935 + 0.370044i −0.0286635 + 0.0165489i
\(501\) −11.2817 + 6.51351i −0.504030 + 0.291002i
\(502\) −8.04043 + 4.64215i −0.358862 + 0.207189i
\(503\) 0.427249 0.740017i 0.0190501 0.0329957i −0.856343 0.516407i \(-0.827269\pi\)
0.875393 + 0.483411i \(0.160602\pi\)
\(504\) 0 0
\(505\) −2.73294 + 1.57786i −0.121614 + 0.0702139i
\(506\) −5.83356 10.1040i −0.259333 0.449179i
\(507\) 5.20326 + 37.0925i 0.231085 + 1.64733i
\(508\) −0.0941471 + 0.163068i −0.00417710 + 0.00723495i
\(509\) 1.12583 + 0.650000i 0.0499017 + 0.0288108i 0.524743 0.851261i \(-0.324161\pi\)
−0.474842 + 0.880071i \(0.657495\pi\)
\(510\) −0.896808 1.55332i −0.0397113 0.0687820i
\(511\) 0 0
\(512\) 24.0616i 1.06338i
\(513\) 38.7538i 1.71102i
\(514\) 19.7514 11.4035i 0.871199 0.502987i
\(515\) 5.90051 + 3.40666i 0.260007 + 0.150115i
\(516\) 1.25833 0.0553951
\(517\) 10.1324 + 17.5499i 0.445624 + 0.771844i
\(518\) 0 0
\(519\) 56.2351 2.46845
\(520\) −8.25362 1.60545i −0.361945 0.0704034i
\(521\) −12.5228 + 21.6901i −0.548632 + 0.950259i 0.449736 + 0.893161i \(0.351518\pi\)
−0.998369 + 0.0570974i \(0.981815\pi\)
\(522\) 16.6698i 0.729618i
\(523\) 6.41197 11.1059i 0.280376 0.485625i −0.691101 0.722758i \(-0.742874\pi\)
0.971477 + 0.237133i \(0.0762076\pi\)
\(524\) 0.765112 1.32521i 0.0334241 0.0578922i
\(525\) 0 0
\(526\) 11.9701 + 6.91095i 0.521922 + 0.301332i
\(527\) 1.94686i 0.0848065i
\(528\) 49.9040 + 28.8121i 2.17179 + 1.25389i
\(529\) 10.2122 + 17.6880i 0.444008 + 0.769045i
\(530\) −3.03122 + 5.25022i −0.131668 + 0.228055i
\(531\) −50.4743 + 29.1413i −2.19040 + 1.26463i
\(532\) 0 0
\(533\) −0.638656 + 3.28334i −0.0276632 + 0.142217i
\(534\) −9.95213 17.2376i −0.430671 0.745944i
\(535\) 7.79773i 0.337125i
\(536\) 21.2547 0.918063
\(537\) 59.9855 2.58857
\(538\) 21.6828i 0.934814i
\(539\) 0 0
\(540\) −0.454501 0.262406i −0.0195586 0.0112922i
\(541\) 24.8938 14.3725i 1.07027 0.617920i 0.142014 0.989865i \(-0.454642\pi\)
0.928255 + 0.371944i \(0.121309\pi\)
\(542\) −3.59670 6.22966i −0.154491 0.267587i
\(543\) 47.6902 2.04658
\(544\) 0.269226 + 0.155438i 0.0115430 + 0.00666434i
\(545\) −11.7376 −0.502785
\(546\) 0 0
\(547\) −8.88085 −0.379718 −0.189859 0.981811i \(-0.560803\pi\)
−0.189859 + 0.981811i \(0.560803\pi\)
\(548\) −0.667733 0.385516i −0.0285241 0.0164684i
\(549\) −38.7111 −1.65215
\(550\) −15.8134 27.3897i −0.674287 1.16790i
\(551\) −11.5413 + 6.66339i −0.491677 + 0.283870i
\(552\) 11.5871 + 6.68983i 0.493181 + 0.284738i
\(553\) 0 0
\(554\) 26.5777i 1.12918i
\(555\) 2.88395 0.122417
\(556\) −0.974690 −0.0413361
\(557\) 38.7273i 1.64093i −0.571696 0.820465i \(-0.693714\pi\)
0.571696 0.820465i \(-0.306286\pi\)
\(558\) −12.7059 22.0072i −0.537882 0.931639i
\(559\) −5.21830 15.1614i −0.220711 0.641259i
\(560\) 0 0
\(561\) −7.36736 + 4.25355i −0.311050 + 0.179585i
\(562\) −1.47754 + 2.55918i −0.0623263 + 0.107952i
\(563\) −3.45441 5.98321i −0.145586 0.252162i 0.784005 0.620754i \(-0.213173\pi\)
−0.929591 + 0.368592i \(0.879840\pi\)
\(564\) −0.942002 0.543865i −0.0396655 0.0229009i
\(565\) 15.7252i 0.661565i
\(566\) 18.8105 + 10.8602i 0.790663 + 0.456489i
\(567\) 0 0
\(568\) 13.4761 23.3413i 0.565444 0.979379i
\(569\) −1.41872 + 2.45730i −0.0594759 + 0.103015i −0.894230 0.447607i \(-0.852276\pi\)
0.834754 + 0.550623i \(0.185610\pi\)
\(570\) 18.7165i 0.783946i
\(571\) −23.3362 + 40.4195i −0.976589 + 1.69150i −0.302001 + 0.953307i \(0.597655\pi\)
−0.674588 + 0.738195i \(0.735679\pi\)
\(572\) −0.356404 + 1.83228i −0.0149020 + 0.0766115i
\(573\) 12.2453 0.511557
\(574\) 0 0
\(575\) −3.49096 6.04653i −0.145583 0.252158i
\(576\) −44.2836 −1.84515
\(577\) −9.88033 5.70441i −0.411323 0.237478i 0.280035 0.959990i \(-0.409654\pi\)
−0.691358 + 0.722512i \(0.742987\pi\)
\(578\) −19.9284 + 11.5057i −0.828911 + 0.478572i
\(579\) 33.4140i 1.38864i
\(580\) 0.180474i 0.00749379i
\(581\) 0 0
\(582\) −21.1547 36.6410i −0.876890 1.51882i
\(583\) 24.9017 + 14.3770i 1.03132 + 0.595436i
\(584\) −7.23597 + 12.5331i −0.299426 + 0.518622i
\(585\) −2.94138 + 15.1217i −0.121611 + 0.625204i
\(586\) −15.9617 27.6465i −0.659371 1.14206i
\(587\) 40.2191 23.2205i 1.66002 0.958413i 0.687318 0.726356i \(-0.258788\pi\)
0.972702 0.232057i \(-0.0745456\pi\)
\(588\) 0 0
\(589\) 10.1578 17.5938i 0.418544 0.724939i
\(590\) −10.5821 + 6.10961i −0.435660 + 0.251529i
\(591\) 35.9840 20.7754i 1.48018 0.854585i
\(592\) 4.08064 2.35596i 0.167713 0.0968292i
\(593\) 17.5462 10.1303i 0.720535 0.416001i −0.0944146 0.995533i \(-0.530098\pi\)
0.814950 + 0.579532i \(0.196765\pi\)
\(594\) 24.1016 41.7451i 0.988899 1.71282i
\(595\) 0 0
\(596\) 0.673533 0.388864i 0.0275890 0.0159285i
\(597\) 10.1696 + 17.6142i 0.416212 + 0.720901i
\(598\) 1.52364 7.83304i 0.0623061 0.320317i
\(599\) 19.4938 33.7642i 0.796494 1.37957i −0.125391 0.992107i \(-0.540019\pi\)
0.921886 0.387462i \(-0.126648\pi\)
\(600\) 31.4100 + 18.1346i 1.28231 + 0.740342i
\(601\) 9.56951 + 16.5749i 0.390348 + 0.676103i 0.992495 0.122282i \(-0.0390212\pi\)
−0.602147 + 0.798385i \(0.705688\pi\)
\(602\) 0 0
\(603\) 38.9412i 1.58581i
\(604\) 0.147425i 0.00599865i
\(605\) 11.7186 6.76575i 0.476430 0.275067i
\(606\) 13.4734 + 7.77888i 0.547320 + 0.315995i
\(607\) −43.3336 −1.75886 −0.879428 0.476033i \(-0.842074\pi\)
−0.879428 + 0.476033i \(0.842074\pi\)
\(608\) −1.62200 2.80939i −0.0657808 0.113936i
\(609\) 0 0
\(610\) −8.11595 −0.328605
\(611\) −2.64644 + 13.6054i −0.107063 + 0.550415i
\(612\) 0.145803 0.252538i 0.00589373 0.0102082i
\(613\) 10.3096i 0.416399i −0.978086 0.208200i \(-0.933240\pi\)
0.978086 0.208200i \(-0.0667604\pi\)
\(614\) −2.92077 + 5.05892i −0.117873 + 0.204161i
\(615\) −1.07711 + 1.86561i −0.0434332 + 0.0752285i
\(616\) 0 0
\(617\) −9.58684 5.53497i −0.385952 0.222829i 0.294453 0.955666i \(-0.404863\pi\)
−0.680405 + 0.732837i \(0.738196\pi\)
\(618\) 33.5898i 1.35118i
\(619\) 29.2384 + 16.8808i 1.17519 + 0.678498i 0.954897 0.296936i \(-0.0959647\pi\)
0.220295 + 0.975433i \(0.429298\pi\)
\(620\) 0.137559 + 0.238259i 0.00552450 + 0.00956871i
\(621\) 5.32065 9.21563i 0.213510 0.369810i
\(622\) 32.5447 18.7897i 1.30492 0.753399i
\(623\) 0 0
\(624\) 12.8267 + 37.2671i 0.513480 + 1.49188i
\(625\) −7.83931 13.5781i −0.313573 0.543124i
\(626\) 3.71927i 0.148652i
\(627\) 88.7719 3.54521
\(628\) −0.378778 −0.0151149
\(629\) 0.695623i 0.0277363i
\(630\) 0 0
\(631\) 33.4264 + 19.2987i 1.33068 + 0.768271i 0.985405 0.170229i \(-0.0544507\pi\)
0.345280 + 0.938500i \(0.387784\pi\)
\(632\) 28.4887 16.4480i 1.13322 0.654265i
\(633\) −38.0645 65.9296i −1.51293 2.62047i
\(634\) 33.1945 1.31832
\(635\) 1.33823 + 0.772627i 0.0531060 + 0.0306608i
\(636\) −1.54339 −0.0611995
\(637\) 0 0
\(638\) 16.5763 0.656260
\(639\) −42.7641 24.6899i −1.69172 0.976717i
\(640\) −8.38960 −0.331628
\(641\) 9.76141 + 16.9073i 0.385553 + 0.667797i 0.991846 0.127445i \(-0.0406775\pi\)
−0.606293 + 0.795241i \(0.707344\pi\)
\(642\) 33.2926 19.2215i 1.31395 0.758611i
\(643\) −10.8009 6.23589i −0.425945 0.245920i 0.271673 0.962390i \(-0.412423\pi\)
−0.697618 + 0.716470i \(0.745757\pi\)
\(644\) 0 0
\(645\) 10.3266i 0.406611i
\(646\) −4.51450 −0.177621
\(647\) 35.9391 1.41291 0.706455 0.707758i \(-0.250293\pi\)
0.706455 + 0.707758i \(0.250293\pi\)
\(648\) 9.25967i 0.363754i
\(649\) 28.9778 + 50.1910i 1.13748 + 1.97017i
\(650\) 4.13023 21.2336i 0.162001 0.832849i
\(651\) 0 0
\(652\) 1.22139 0.705171i 0.0478334 0.0276166i
\(653\) −2.42944 + 4.20791i −0.0950713 + 0.164668i −0.909638 0.415401i \(-0.863641\pi\)
0.814567 + 0.580069i \(0.196975\pi\)
\(654\) 28.9334 + 50.1141i 1.13138 + 1.95962i
\(655\) −10.8755 6.27897i −0.424941 0.245340i
\(656\) 3.51964i 0.137419i
\(657\) 22.9621 + 13.2572i 0.895838 + 0.517212i
\(658\) 0 0
\(659\) 11.8103 20.4560i 0.460063 0.796853i −0.538900 0.842370i \(-0.681160\pi\)
0.998964 + 0.0455166i \(0.0144934\pi\)
\(660\) −0.601085 + 1.04111i −0.0233972 + 0.0405251i
\(661\) 16.3932i 0.637623i 0.947818 + 0.318812i \(0.103284\pi\)
−0.947818 + 0.318812i \(0.896716\pi\)
\(662\) 0.427316 0.740134i 0.0166081 0.0287661i
\(663\) −5.71147 1.11096i −0.221815 0.0431462i
\(664\) −16.8393 −0.653492
\(665\) 0 0
\(666\) −4.53987 7.86328i −0.175916 0.304696i
\(667\) 3.65936 0.141691
\(668\) −0.384544 0.222016i −0.0148784 0.00859007i
\(669\) 57.3908 33.1346i 2.21886 1.28106i
\(670\) 8.16420i 0.315410i
\(671\) 38.4939i 1.48604i
\(672\) 0 0
\(673\) −7.12678 12.3439i −0.274717 0.475824i 0.695347 0.718675i \(-0.255251\pi\)
−0.970064 + 0.242851i \(0.921918\pi\)
\(674\) 6.83278 + 3.94491i 0.263189 + 0.151952i
\(675\) 14.4230 24.9814i 0.555143 0.961536i
\(676\) −1.00625 + 0.785753i −0.0387020 + 0.0302213i
\(677\) −5.13574 8.89537i −0.197383 0.341877i 0.750296 0.661102i \(-0.229911\pi\)
−0.947679 + 0.319225i \(0.896577\pi\)
\(678\) −67.1391 + 38.7628i −2.57846 + 1.48867i
\(679\) 0 0
\(680\) 0.653092 1.13119i 0.0250449 0.0433791i
\(681\) −1.13124 + 0.653122i −0.0433492 + 0.0250277i
\(682\) −21.8837 + 12.6345i −0.837969 + 0.483802i
\(683\) 1.92432 1.11101i 0.0736321 0.0425115i −0.462732 0.886498i \(-0.653131\pi\)
0.536364 + 0.843987i \(0.319797\pi\)
\(684\) −2.63524 + 1.52146i −0.100761 + 0.0581744i
\(685\) −3.16377 + 5.47981i −0.120881 + 0.209373i
\(686\) 0 0
\(687\) −43.2504 + 24.9706i −1.65011 + 0.952689i
\(688\) −8.43604 14.6117i −0.321621 0.557064i
\(689\) 6.40044 + 18.5960i 0.243837 + 0.708451i
\(690\) 2.56965 4.45076i 0.0978249 0.169438i
\(691\) −2.28643 1.32007i −0.0869800 0.0502179i 0.455879 0.890042i \(-0.349325\pi\)
−0.542859 + 0.839824i \(0.682658\pi\)
\(692\) 0.958402 + 1.66000i 0.0364330 + 0.0631038i
\(693\) 0 0
\(694\) 2.57174i 0.0976220i
\(695\) 7.99889i 0.303415i
\(696\) −16.4626 + 9.50469i −0.624014 + 0.360274i
\(697\) −0.449993 0.259804i −0.0170447 0.00984077i
\(698\) −30.7767 −1.16492
\(699\) −11.2585 19.5002i −0.425834 0.737566i
\(700\) 0 0
\(701\) −8.89991 −0.336145 −0.168072 0.985775i \(-0.553754\pi\)
−0.168072 + 0.985775i \(0.553754\pi\)
\(702\) 31.1742 10.7296i 1.17659 0.404965i
\(703\) 3.62943 6.28635i 0.136886 0.237094i
\(704\) 44.0351i 1.65964i
\(705\) −4.46328 + 7.73063i −0.168097 + 0.291152i
\(706\) 1.60797 2.78509i 0.0605168 0.104818i
\(707\) 0 0
\(708\) −2.69403 1.55540i −0.101248 0.0584556i
\(709\) 40.5944i 1.52456i −0.647250 0.762278i \(-0.724081\pi\)
0.647250 0.762278i \(-0.275919\pi\)
\(710\) −8.96569 5.17634i −0.336476 0.194265i
\(711\) −30.1347 52.1949i −1.13014 1.95746i
\(712\) 7.24754 12.5531i 0.271613 0.470448i
\(713\) −4.83103 + 2.78920i −0.180923 + 0.104456i
\(714\) 0 0
\(715\) 15.0368 + 2.92487i 0.562344 + 0.109384i
\(716\) 1.02232 + 1.77071i 0.0382059 + 0.0661745i
\(717\) 38.9868i 1.45599i
\(718\) −4.51096 −0.168348
\(719\) 14.5135 0.541262 0.270631 0.962683i \(-0.412768\pi\)
0.270631 + 0.962683i \(0.412768\pi\)
\(720\) 16.2100i 0.604110i
\(721\) 0 0
\(722\) 18.1059 + 10.4535i 0.673834 + 0.389038i
\(723\) −56.2896 + 32.4988i −2.09343 + 1.20864i
\(724\) 0.812773 + 1.40776i 0.0302065 + 0.0523191i
\(725\) 9.91969 0.368408
\(726\) −57.7730 33.3552i −2.14416 1.23793i
\(727\) −30.6942 −1.13839 −0.569193 0.822204i \(-0.692744\pi\)
−0.569193 + 0.822204i \(0.692744\pi\)
\(728\) 0 0
\(729\) −40.3475 −1.49435
\(730\) 4.81411 + 2.77943i 0.178178 + 0.102871i
\(731\) 2.49084 0.0921269
\(732\) −1.03309 1.78937i −0.0381842 0.0661369i
\(733\) −11.4873 + 6.63218i −0.424292 + 0.244965i −0.696912 0.717157i \(-0.745443\pi\)
0.272620 + 0.962122i \(0.412110\pi\)
\(734\) 4.95980 + 2.86354i 0.183069 + 0.105695i
\(735\) 0 0
\(736\) 0.890761i 0.0328339i
\(737\) −38.7227 −1.42637
\(738\) 6.78227 0.249659
\(739\) 7.25474i 0.266870i 0.991058 + 0.133435i \(0.0426008\pi\)
−0.991058 + 0.133435i \(0.957399\pi\)
\(740\) 0.0491505 + 0.0851312i 0.00180681 + 0.00312948i
\(741\) 45.8182 + 39.8395i 1.68317 + 1.46354i
\(742\) 0 0
\(743\) −40.0705 + 23.1347i −1.47004 + 0.848730i −0.999435 0.0336128i \(-0.989299\pi\)
−0.470608 + 0.882342i \(0.655965\pi\)
\(744\) 14.4891 25.0959i 0.531196 0.920059i
\(745\) −3.19125 5.52741i −0.116918 0.202509i
\(746\) 13.2673 + 7.65991i 0.485752 + 0.280449i
\(747\) 30.8517i 1.12881i
\(748\) −0.251121 0.144985i −0.00918188 0.00530116i
\(749\) 0 0
\(750\) 14.9715 25.9314i 0.546681 0.946880i
\(751\) −18.0130 + 31.1995i −0.657305 + 1.13848i 0.324006 + 0.946055i \(0.394970\pi\)
−0.981311 + 0.192430i \(0.938363\pi\)
\(752\) 14.5846i 0.531845i
\(753\) −9.69865 + 16.7985i −0.353438 + 0.612173i
\(754\) 8.55556 + 7.43917i 0.311575 + 0.270919i
\(755\) 1.20986 0.0440313
\(756\) 0 0
\(757\) 5.28132 + 9.14751i 0.191953 + 0.332472i 0.945897 0.324466i \(-0.105185\pi\)
−0.753945 + 0.656938i \(0.771851\pi\)
\(758\) 6.39923 0.232430
\(759\) −21.1099 12.1878i −0.766242 0.442390i
\(760\) −11.8040 + 6.81504i −0.428176 + 0.247207i
\(761\) 7.81202i 0.283185i −0.989925 0.141593i \(-0.954778\pi\)
0.989925 0.141593i \(-0.0452223\pi\)
\(762\) 7.61813i 0.275976i
\(763\) 0 0
\(764\) 0.208695 + 0.361470i 0.00755031 + 0.0130775i
\(765\) −2.07248 1.19654i −0.0749305 0.0432612i
\(766\) 2.53010 4.38226i 0.0914163 0.158338i
\(767\) −7.56855 + 38.9101i −0.273285 + 1.40496i
\(768\) −3.38714 5.86671i −0.122223 0.211696i
\(769\) −21.9030 + 12.6457i −0.789844 + 0.456017i −0.839908 0.542729i \(-0.817391\pi\)
0.0500637 + 0.998746i \(0.484058\pi\)
\(770\) 0 0
\(771\) 23.8249 41.2659i 0.858032 1.48615i
\(772\) 0.986345 0.569467i 0.0354993 0.0204956i
\(773\) 40.3572 23.3002i 1.45155 0.838051i 0.452977 0.891522i \(-0.350362\pi\)
0.998569 + 0.0534716i \(0.0170287\pi\)
\(774\) −28.1563 + 16.2560i −1.01206 + 0.584311i
\(775\) −13.0958 + 7.56086i −0.470415 + 0.271594i
\(776\) 15.4057 26.6834i 0.553032 0.957879i
\(777\) 0 0
\(778\) −20.1634 + 11.6414i −0.722895 + 0.417363i
\(779\) 2.71106 + 4.69570i 0.0971339 + 0.168241i
\(780\) −0.777475 + 0.267594i −0.0278381 + 0.00958140i
\(781\) −24.5513 +