Properties

Label 637.2.q.i.589.5
Level $637$
Weight $2$
Character 637.589
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.q (of order \(6\), degree \(2\), 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 589.5
Root \(-1.38488 + 0.286553i\) of defining polynomial
Character \(\chi\) \(=\) 637.589
Dual form 637.2.q.i.491.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.19430 + 0.689527i) q^{2} +(1.44060 - 2.49520i) q^{3} +(-0.0491037 - 0.0850501i) q^{4} +0.805948i q^{5} +(3.44101 - 1.98667i) q^{6} -2.89354i q^{8} +(-2.65067 - 4.59109i) q^{9} +O(q^{10})\) \(q+(1.19430 + 0.689527i) q^{2} +(1.44060 - 2.49520i) q^{3} +(-0.0491037 - 0.0850501i) q^{4} +0.805948i q^{5} +(3.44101 - 1.98667i) q^{6} -2.89354i q^{8} +(-2.65067 - 4.59109i) q^{9} +(-0.555723 + 0.962541i) q^{10} +(-4.56532 - 2.63579i) q^{11} -0.282955 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} -7.31083i q^{18} +(5.06165 - 2.92234i) q^{19} +(0.0685460 - 0.0395750i) q^{20} +(-3.63490 - 6.29583i) q^{22} +(-0.802438 + 1.38986i) q^{23} +(-7.21995 - 4.16844i) q^{24} +4.35045 q^{25} +(0.949380 + 4.88078i) q^{26} -6.63060 q^{27} +(-1.14008 + 1.97467i) q^{29} +(1.60115 + 2.77328i) q^{30} +3.47590i q^{31} +(-0.480674 + 0.277517i) q^{32} +(-13.1536 + 7.59424i) q^{33} +0.772411i q^{34} +(-0.260315 + 0.450879i) q^{36} +(-1.07557 - 0.620979i) q^{37} +8.06014 q^{38} +(10.1972 - 1.98350i) q^{39} +2.33205 q^{40} +(-0.803413 - 0.463851i) q^{41} +(2.22356 + 3.85131i) q^{43} +0.517708i q^{44} +(3.70018 - 2.13630i) q^{45} +(-1.91670 + 1.10661i) q^{46} +3.84418i q^{47} +(-5.46556 - 9.46662i) q^{48} +(5.19572 + 2.99975i) q^{50} +1.61377 q^{51} +(0.115238 - 0.334815i) q^{52} +5.45454 q^{53} +(-7.91890 - 4.57198i) q^{54} +(2.12431 - 3.67941i) q^{55} -16.8397i q^{57} +(-2.72318 + 1.57223i) q^{58} +(9.52106 - 5.49698i) q^{59} -0.228047i q^{60} +(3.65107 + 6.32385i) q^{61} +(-2.39673 + 4.15126i) q^{62} -8.35330 q^{64} +(-2.19286 + 1.90672i) q^{65} -20.9458 q^{66} +(-6.36144 - 3.67278i) q^{67} +(0.0275031 - 0.0476367i) q^{68} +(2.31199 + 4.00448i) q^{69} +(-8.06668 + 4.65730i) q^{71} +(-13.2845 + 7.66982i) q^{72} +5.00146i 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} +11.3687 q^{79} +(2.64806 + 1.52886i) q^{80} +(-1.60006 + 2.77138i) q^{81} +(-0.639676 - 1.10795i) q^{82} -5.81962i q^{83} +(-0.390935 + 0.225707i) q^{85} +6.13281i q^{86} +(3.28479 + 5.68943i) q^{87} +(-7.62677 + 13.2100i) q^{88} +(4.33832 + 2.50473i) q^{89} +5.89215 q^{90} +0.157611 q^{92} +(8.67305 + 5.00739i) q^{93} +(-2.65067 + 4.59109i) q^{94} +(2.35526 + 4.07942i) q^{95} +1.59917i q^{96} +(-9.22171 + 5.32416i) q^{97} +27.9464i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 3q^{3} + 4q^{4} + 9q^{6} - q^{9} + O(q^{10}) \) \( 12q + 3q^{3} + 4q^{4} + 9q^{6} - q^{9} - 12q^{10} - 12q^{11} - 2q^{12} + 2q^{13} - 12q^{15} - 8q^{16} - 17q^{17} + 9q^{19} + 3q^{20} - 15q^{22} + 3q^{23} + 15q^{24} + 10q^{25} - 15q^{26} - 12q^{27} - q^{29} + 11q^{30} - 18q^{32} - 6q^{33} - 13q^{36} - 15q^{37} + 38q^{38} + 5q^{39} - 2q^{40} + 6q^{41} + 11q^{43} - 9q^{45} + 30q^{46} - 19q^{48} + 18q^{50} - 8q^{51} + 40q^{52} + 16q^{53} + 6q^{54} + 15q^{55} + 24q^{58} + 27q^{59} - 5q^{61} - 41q^{62} + 2q^{64} - 18q^{65} - 68q^{66} - 15q^{67} + 11q^{68} - 7q^{69} + 30q^{71} - 57q^{72} - 33q^{74} - q^{75} + 45q^{76} + 44q^{78} + 70q^{79} - 63q^{80} + 14q^{81} - 5q^{82} - 21q^{85} - 10q^{87} - 14q^{88} + 48q^{89} - 66q^{92} + 81q^{93} - q^{94} + 2q^{95} + 3q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.19430 + 0.689527i 0.844495 + 0.487570i 0.858790 0.512328i \(-0.171217\pi\)
−0.0142944 + 0.999898i \(0.504550\pi\)
\(3\) 1.44060 2.49520i 0.831732 1.44060i −0.0649323 0.997890i \(-0.520683\pi\)
0.896664 0.442712i \(-0.145984\pi\)
\(4\) −0.0491037 0.0850501i −0.0245518 0.0425250i
\(5\) 0.805948i 0.360431i 0.983627 + 0.180216i \(0.0576795\pi\)
−0.983627 + 0.180216i \(0.942320\pi\)
\(6\) 3.44101 1.98667i 1.40479 0.811054i
\(7\) 0 0
\(8\) 2.89354i 1.02302i
\(9\) −2.65067 4.59109i −0.883555 1.53036i
\(10\) −0.555723 + 0.962541i −0.175735 + 0.304382i
\(11\) −4.56532 2.63579i −1.37650 0.794720i −0.384760 0.923017i \(-0.625716\pi\)
−0.991736 + 0.128296i \(0.959049\pi\)
\(12\) −0.282955 −0.0816822
\(13\) 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 \(0.811696\pi\)
\(18\) 7.31083i 1.72318i
\(19\) 5.06165 2.92234i 1.16122 0.670431i 0.209625 0.977782i \(-0.432776\pi\)
0.951596 + 0.307351i \(0.0994424\pi\)
\(20\) 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 \(0.220178\pi\)
\(24\) −7.21995 4.16844i −1.47377 0.850880i
\(25\) 4.35045 0.870089
\(26\) 0.949380 + 4.88078i 0.186189 + 0.957199i
\(27\) −6.63060 −1.27606
\(28\) 0 0
\(29\) −1.14008 + 1.97467i −0.211707 + 0.366687i −0.952249 0.305323i \(-0.901236\pi\)
0.740542 + 0.672010i \(0.234569\pi\)
\(30\) 1.60115 + 2.77328i 0.292329 + 0.506329i
\(31\) 3.47590i 0.624290i 0.950034 + 0.312145i \(0.101048\pi\)
−0.950034 + 0.312145i \(0.898952\pi\)
\(32\) −0.480674 + 0.277517i −0.0849719 + 0.0490585i
\(33\) −13.1536 + 7.59424i −2.28975 + 1.32199i
\(34\) 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 0.408977 0.912545i \(-0.365886\pi\)
−0.585799 + 0.810457i \(0.699219\pi\)
\(38\) 8.06014 1.30753
\(39\) 10.1972 1.98350i 1.63286 0.317614i
\(40\) 2.33205 0.368729
\(41\) −0.803413 0.463851i −0.125472 0.0724413i 0.435950 0.899971i \(-0.356412\pi\)
−0.561422 + 0.827529i \(0.689746\pi\)
\(42\) 0 0
\(43\) 2.22356 + 3.85131i 0.339089 + 0.587320i 0.984262 0.176717i \(-0.0565478\pi\)
−0.645172 + 0.764037i \(0.723214\pi\)
\(44\) 0.517708i 0.0780474i
\(45\) 3.70018 2.13630i 0.551590 0.318461i
\(46\) −1.91670 + 1.10661i −0.282602 + 0.163160i
\(47\) 3.84418i 0.560731i 0.959893 + 0.280365i \(0.0904556\pi\)
−0.959893 + 0.280365i \(0.909544\pi\)
\(48\) −5.46556 9.46662i −0.788885 1.36639i
\(49\) 0 0
\(50\) 5.19572 + 2.99975i 0.734786 + 0.424229i
\(51\) 1.61377 0.225973
\(52\) 0.115238 0.334815i 0.0159806 0.0464305i
\(53\) 5.45454 0.749239 0.374620 0.927179i \(-0.377773\pi\)
0.374620 + 0.927179i \(0.377773\pi\)
\(54\) −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
\(58\) −2.72318 + 1.57223i −0.357571 + 0.206444i
\(59\) 9.52106 5.49698i 1.23954 0.715646i 0.270537 0.962710i \(-0.412799\pi\)
0.968999 + 0.247063i \(0.0794655\pi\)
\(60\) 0.228047i 0.0294408i
\(61\) 3.65107 + 6.32385i 0.467472 + 0.809686i 0.999309 0.0371610i \(-0.0118314\pi\)
−0.531837 + 0.846847i \(0.678498\pi\)
\(62\) −2.39673 + 4.15126i −0.304385 + 0.527210i
\(63\) 0 0
\(64\) −8.35330 −1.04416
\(65\) −2.19286 + 1.90672i −0.271990 + 0.236499i
\(66\) −20.9458 −2.57824
\(67\) −6.36144 3.67278i −0.777174 0.448701i 0.0582541 0.998302i \(-0.481447\pi\)
−0.835428 + 0.549600i \(0.814780\pi\)
\(68\) 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 −0.895353 0.445357i \(-0.853077\pi\)
−0.0619857 + 0.998077i \(0.519743\pi\)
\(72\) −13.2845 + 7.66982i −1.56559 + 0.903896i
\(73\) 5.00146i 0.585376i 0.956208 + 0.292688i \(0.0945498\pi\)
−0.956208 + 0.292688i \(0.905450\pi\)
\(74\) −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
\(79\) 11.3687 1.27908 0.639542 0.768756i \(-0.279124\pi\)
0.639542 + 0.768756i \(0.279124\pi\)
\(80\) 2.64806 + 1.52886i 0.296062 + 0.170932i
\(81\) −1.60006 + 2.77138i −0.177784 + 0.307931i
\(82\) −0.639676 1.10795i −0.0706404 0.122353i
\(83\) 5.81962i 0.638786i −0.947622 0.319393i \(-0.896521\pi\)
0.947622 0.319393i \(-0.103479\pi\)
\(84\) 0 0
\(85\) −0.390935 + 0.225707i −0.0424029 + 0.0244813i
\(86\) 6.13281i 0.661318i
\(87\) 3.28479 + 5.68943i 0.352167 + 0.609971i
\(88\) −7.62677 + 13.2100i −0.813016 + 1.40819i
\(89\) 4.33832 + 2.50473i 0.459861 + 0.265501i 0.711986 0.702194i \(-0.247796\pi\)
−0.252125 + 0.967695i \(0.581129\pi\)
\(90\) 5.89215 0.621087
\(91\) 0 0
\(92\) 0.157611 0.0164320
\(93\) 8.67305 + 5.00739i 0.899354 + 0.519242i
\(94\) −2.65067 + 4.59109i −0.273395 + 0.473534i
\(95\) 2.35526 + 4.07942i 0.241644 + 0.418540i
\(96\) 1.59917i 0.163214i
\(97\) −9.22171 + 5.32416i −0.936323 + 0.540586i −0.888806 0.458284i \(-0.848464\pi\)
−0.0475172 + 0.998870i \(0.515131\pi\)
\(98\) 0 0
\(99\) 27.9464i 2.80872i
\(100\) −0.213623 0.370006i −0.0213623 0.0370006i
\(101\) −1.95777 + 3.39096i −0.194805 + 0.337413i −0.946837 0.321715i \(-0.895741\pi\)
0.752031 + 0.659127i \(0.229074\pi\)
\(102\) 1.92732 + 1.11274i 0.190833 + 0.110177i
\(103\) 8.45379 0.832977 0.416488 0.909141i \(-0.363261\pi\)
0.416488 + 0.909141i \(0.363261\pi\)
\(104\) 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
\(109\) 14.5638i 1.39496i 0.716606 + 0.697478i \(0.245695\pi\)
−0.716606 + 0.697478i \(0.754305\pi\)
\(110\) 5.07411 2.92954i 0.483798 0.279321i
\(111\) −3.09893 + 1.78917i −0.294137 + 0.169820i
\(112\) 0 0
\(113\) −9.75572 16.8974i −0.917741 1.58957i −0.802838 0.596197i \(-0.796678\pi\)
−0.114903 0.993377i \(-0.536656\pi\)
\(114\) 11.6115 20.1116i 1.08751 1.88363i
\(115\) −1.12016 0.646723i −0.104455 0.0603073i
\(116\) 0.223928 0.0207912
\(117\) 6.22065 18.0737i 0.575100 1.67091i
\(118\) 15.1613 1.39571
\(119\) 0 0
\(120\) 3.35955 5.81891i 0.306683 0.531191i
\(121\) 8.39477 + 14.5402i 0.763161 + 1.32183i
\(122\) 10.0701i 0.911701i
\(123\) −2.31480 + 1.33645i −0.208718 + 0.120503i
\(124\) 0.295626 0.170680i 0.0265480 0.0153275i
\(125\) 7.53598i 0.674038i
\(126\) 0 0
\(127\) −0.958656 + 1.66044i −0.0850670 + 0.147340i −0.905420 0.424517i \(-0.860444\pi\)
0.820353 + 0.571858i \(0.193777\pi\)
\(128\) −9.01498 5.20480i −0.796819 0.460044i
\(129\) 12.8130 1.12813
\(130\) −3.93365 + 0.765151i −0.345004 + 0.0671082i
\(131\) −15.5816 −1.36137 −0.680684 0.732577i \(-0.738317\pi\)
−0.680684 + 0.732577i \(0.738317\pi\)
\(132\) 1.29178 + 0.745811i 0.112435 + 0.0649145i
\(133\) 0 0
\(134\) −5.06496 8.77278i −0.437546 0.757852i
\(135\) 5.34392i 0.459932i
\(136\) 1.40355 0.810339i 0.120353 0.0694860i
\(137\) −6.79921 + 3.92553i −0.580896 + 0.335380i −0.761489 0.648178i \(-0.775531\pi\)
0.180594 + 0.983558i \(0.442198\pi\)
\(138\) 6.37671i 0.542822i
\(139\) 4.96241 + 8.59514i 0.420906 + 0.729030i 0.996028 0.0890370i \(-0.0283789\pi\)
−0.575122 + 0.818067i \(0.695046\pi\)
\(140\) 0 0
\(141\) 9.59197 + 5.53793i 0.807790 + 0.466378i
\(142\) −12.8453 −1.07796
\(143\) −3.62910 18.6573i −0.303481 1.56020i
\(144\) −20.1129 −1.67608
\(145\) −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
\(149\) −6.85827 + 3.95962i −0.561851 + 0.324385i −0.753888 0.657003i \(-0.771824\pi\)
0.192037 + 0.981388i \(0.438491\pi\)
\(150\) 14.9699 8.64290i 1.22229 0.705690i
\(151\) 1.50116i 0.122163i −0.998133 0.0610815i \(-0.980545\pi\)
0.998133 0.0610815i \(-0.0194550\pi\)
\(152\) −8.45592 14.6461i −0.685866 1.18795i
\(153\) 1.48464 2.57148i 0.120026 0.207892i
\(154\) 0 0
\(155\) −2.80140 −0.225014
\(156\) −0.669417 0.769876i −0.0535963 0.0616394i
\(157\) −3.85692 −0.307816 −0.153908 0.988085i \(-0.549186\pi\)
−0.153908 + 0.988085i \(0.549186\pi\)
\(158\) 13.5777 + 7.83906i 1.08018 + 0.623642i
\(159\) 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
\(163\) −12.4369 + 7.18042i −0.974130 + 0.562414i −0.900493 0.434871i \(-0.856794\pi\)
−0.0736372 + 0.997285i \(0.523461\pi\)
\(164\) 0.0911072i 0.00711427i
\(165\) −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 0.643790 0.765202i \(-0.277361\pi\)
−0.340790 + 0.940140i \(0.610694\pi\)
\(168\) 0 0
\(169\) −1.80593 + 12.8740i −0.138918 + 0.990304i
\(170\) −0.622523 −0.0477454
\(171\) −26.8335 15.4923i −2.05201 1.18473i
\(172\) 0.218370 0.378227i 0.0166505 0.0288396i
\(173\) 9.75896 + 16.9030i 0.741960 + 1.28511i 0.951602 + 0.307334i \(0.0994369\pi\)
−0.209642 + 0.977778i \(0.567230\pi\)
\(174\) 9.05982i 0.686823i
\(175\) 0 0
\(176\) −17.3206 + 10.0000i −1.30559 + 0.753780i
\(177\) 31.6759i 2.38090i
\(178\) 3.45416 + 5.98278i 0.258900 + 0.448428i
\(179\) 10.4098 18.0303i 0.778065 1.34765i −0.154990 0.987916i \(-0.549535\pi\)
0.933055 0.359733i \(-0.117132\pi\)
\(180\) −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
\(185\) 0.500477 0.866851i 0.0367958 0.0637322i
\(186\) 6.90546 + 11.9606i 0.506333 + 0.876995i
\(187\) 2.95262i 0.215917i
\(188\) 0.326948 0.188763i 0.0238451 0.0137670i
\(189\) 0 0
\(190\) 6.49606i 0.471274i
\(191\) 2.12504 + 3.68068i 0.153762 + 0.266324i 0.932608 0.360892i \(-0.117528\pi\)
−0.778845 + 0.627216i \(0.784194\pi\)
\(192\) −12.0338 + 20.8431i −0.868463 + 1.50422i
\(193\) 10.0435 + 5.79861i 0.722946 + 0.417393i 0.815836 0.578283i \(-0.196277\pi\)
−0.0928898 + 0.995676i \(0.529610\pi\)
\(194\) −14.6846 −1.05429
\(195\) 1.59860 + 8.21842i 0.114478 + 0.588533i
\(196\) 0 0
\(197\) −12.4892 7.21066i −0.889821 0.513738i −0.0159371 0.999873i \(-0.505073\pi\)
−0.873884 + 0.486135i \(0.838406\pi\)
\(198\) −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 \(0.913832\pi\)
\(200\) 12.5882i 0.890121i
\(201\) −18.3286 + 10.5820i −1.29280 + 0.746398i
\(202\) −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
\(206\) 10.0963 + 5.82912i 0.703445 + 0.406134i
\(207\) 8.50798 0.591345
\(208\) 13.4276 2.61185i 0.931035 0.181099i
\(209\) −30.8107 −2.13122
\(210\) 0 0
\(211\) 13.2113 22.8827i 0.909505 1.57531i 0.0947513 0.995501i \(-0.469794\pi\)
0.814754 0.579807i \(-0.196872\pi\)
\(212\) −0.267838 0.463909i −0.0183952 0.0318614i
\(213\) 26.8372i 1.83886i
\(214\) 11.5551 6.67133i 0.789890 0.456043i
\(215\) −3.10396 + 1.79207i −0.211688 + 0.122218i
\(216\) 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
\(220\) −0.417246 −0.0281307
\(221\) −0.657231 + 1.90954i −0.0442101 + 0.128449i
\(222\) −4.93472 −0.331197
\(223\) −19.9191 11.5003i −1.33388 0.770115i −0.347987 0.937499i \(-0.613135\pi\)
−0.985892 + 0.167384i \(0.946468\pi\)
\(224\) 0 0
\(225\) −11.5316 19.9733i −0.768772 1.33155i
\(226\) 26.9073i 1.78985i
\(227\) −0.392628 + 0.226684i −0.0260596 + 0.0150455i −0.512973 0.858405i \(-0.671456\pi\)
0.486914 + 0.873450i \(0.338123\pi\)
\(228\) −1.43222 + 0.826893i −0.0948511 + 0.0547623i
\(229\) 17.3335i 1.14543i −0.819755 0.572714i \(-0.805890\pi\)
0.819755 0.572714i \(-0.194110\pi\)
\(230\) −0.891867 1.54476i −0.0588080 0.101858i
\(231\) 0 0
\(232\) 5.71380 + 3.29886i 0.375129 + 0.216581i
\(233\) −7.81511 −0.511985 −0.255992 0.966679i \(-0.582402\pi\)
−0.255992 + 0.966679i \(0.582402\pi\)
\(234\) 19.8916 17.2960i 1.30035 1.13067i
\(235\) −3.09821 −0.202105
\(236\) −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 \(0.144185\pi\)
−0.899151 + 0.437638i \(0.855815\pi\)
\(240\) 7.62961 4.40496i 0.492489 0.284339i
\(241\) −19.5369 + 11.2796i −1.25848 + 0.726583i −0.972779 0.231736i \(-0.925560\pi\)
−0.285701 + 0.958319i \(0.592226\pi\)
\(242\) 23.1537i 1.48838i
\(243\) −5.33581 9.24189i −0.342292 0.592868i
\(244\) 0.358563 0.621049i 0.0229546 0.0397586i
\(245\) 0 0
\(246\) −3.68607 −0.235015
\(247\) 19.9261 + 6.85823i 1.26787 + 0.436379i
\(248\) 10.0577 0.638663
\(249\) −14.5211 8.38375i −0.920236 0.531299i
\(250\) −5.19626 + 9.00019i −0.328641 + 0.569222i
\(251\) 3.36618 + 5.83039i 0.212471 + 0.368011i 0.952487 0.304578i \(-0.0985154\pi\)
−0.740016 + 0.672589i \(0.765182\pi\)
\(252\) 0 0
\(253\) 7.32677 4.23011i 0.460630 0.265945i
\(254\) −2.28984 + 1.32204i −0.143677 + 0.0829521i
\(255\) 1.30061i 0.0814475i
\(256\) 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
\(261\) 12.0878 0.748219
\(262\) −18.6090 10.7439i −1.14967 0.663761i
\(263\) 5.01137 8.67994i 0.309014 0.535228i −0.669133 0.743143i \(-0.733334\pi\)
0.978147 + 0.207915i \(0.0666676\pi\)
\(264\) 21.9743 + 38.0606i 1.35242 + 2.34247i
\(265\) 4.39608i 0.270049i
\(266\) 0 0
\(267\) 12.4996 7.21663i 0.764962 0.441651i
\(268\) 0.721388i 0.0440658i
\(269\) −7.86149 13.6165i −0.479323 0.830212i 0.520395 0.853925i \(-0.325785\pi\)
−0.999719 + 0.0237130i \(0.992451\pi\)
\(270\) 3.68478 6.38223i 0.224249 0.388410i
\(271\) −4.51734 2.60809i −0.274409 0.158430i 0.356481 0.934303i \(-0.383977\pi\)
−0.630890 + 0.775873i \(0.717310\pi\)
\(272\) 2.12499 0.128847
\(273\) 0 0
\(274\) −10.8270 −0.654085
\(275\) −19.8612 11.4669i −1.19767 0.691478i
\(276\) 0.227054 0.393269i 0.0136671 0.0236720i
\(277\) −9.63619 16.6904i −0.578983 1.00283i −0.995596 0.0937439i \(-0.970117\pi\)
0.416614 0.909084i \(-0.363217\pi\)
\(278\) 13.6869i 0.820884i
\(279\) 15.9582 9.21345i 0.955390 0.551595i
\(280\) 0 0
\(281\) 2.14283i 0.127831i 0.997955 + 0.0639153i \(0.0203588\pi\)
−0.997955 + 0.0639153i \(0.979641\pi\)
\(282\) 7.63711 + 13.2279i 0.454783 + 0.787707i
\(283\) 7.87512 13.6401i 0.468127 0.810820i −0.531209 0.847241i \(-0.678262\pi\)
0.999337 + 0.0364203i \(0.0115955\pi\)
\(284\) 0.792207 + 0.457381i 0.0470089 + 0.0271406i
\(285\) 13.5719 0.803933
\(286\) 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
\(291\) 30.6800i 1.79849i
\(292\) 0.425374 0.245590i 0.0248932 0.0143721i
\(293\) 20.0474 11.5744i 1.17118 0.676182i 0.217223 0.976122i \(-0.430300\pi\)
0.953958 + 0.299940i \(0.0969668\pi\)
\(294\) 0 0
\(295\) 4.43029 + 7.67348i 0.257941 + 0.446767i
\(296\) −1.79683 + 3.11220i −0.104439 + 0.180893i
\(297\) 30.2708 + 17.4769i 1.75649 + 1.01411i
\(298\) −10.9211 −0.632641
\(299\) −5.68001 + 1.10484i −0.328483 + 0.0638946i
\(300\) −1.23098 −0.0710708
\(301\) 0 0
\(302\) 1.03509 1.79283i 0.0595629 0.103166i
\(303\) 5.64073 + 9.77003i 0.324052 + 0.561274i
\(304\) 22.1744i 1.27179i
\(305\) −5.09669 + 2.94258i −0.291836 + 0.168491i
\(306\) 3.54621 2.04740i 0.202723 0.117042i
\(307\) 4.23590i 0.241756i 0.992667 + 0.120878i \(0.0385709\pi\)
−0.992667 + 0.120878i \(0.961429\pi\)
\(308\) 0 0
\(309\) 12.1785 21.0939i 0.692813 1.19999i
\(310\) −3.34570 1.93164i −0.190023 0.109710i
\(311\) 27.2501 1.54521 0.772606 0.634885i \(-0.218953\pi\)
0.772606 + 0.634885i \(0.218953\pi\)
\(312\) −5.73934 29.5061i −0.324926 1.67045i
\(313\) −2.69697 −0.152442 −0.0762209 0.997091i \(-0.524285\pi\)
−0.0762209 + 0.997091i \(0.524285\pi\)
\(314\) −4.60631 2.65945i −0.259949 0.150082i
\(315\) 0 0
\(316\) −0.558247 0.966913i −0.0314039 0.0543931i
\(317\) 24.0705i 1.35193i 0.736933 + 0.675966i \(0.236273\pi\)
−0.736933 + 0.675966i \(0.763727\pi\)
\(318\) 18.7691 10.8364i 1.05252 0.607674i
\(319\) 10.4096 6.01000i 0.582828 0.336496i
\(320\) 6.73233i 0.376349i
\(321\) −13.9381 24.1416i −0.777951 1.34745i
\(322\) 0 0
\(323\) 2.83504 + 1.63681i 0.157746 + 0.0910745i
\(324\) 0.314275 0.0174597
\(325\) 10.2923 + 11.8369i 0.570915 + 0.656591i
\(326\) −19.8044 −1.09686
\(327\) 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
\(331\) −0.536696 + 0.309862i −0.0294995 + 0.0170315i −0.514677 0.857384i \(-0.672088\pi\)
0.485178 + 0.874416i \(0.338755\pi\)
\(332\) −0.494959 + 0.285765i −0.0271644 + 0.0156834i
\(333\) 6.58403i 0.360803i
\(334\) 3.11762 + 5.39987i 0.170588 + 0.295468i
\(335\) 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 \(0.549804\pi\)
\(338\) −11.0338 + 14.1301i −0.600158 + 0.768575i
\(339\) −56.2164 −3.05326
\(340\) 0.0383927 + 0.0221660i 0.00208214 + 0.00120212i
\(341\) 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
\(345\) −3.22740 + 1.86334i −0.173757 + 0.100319i
\(346\) 26.9163i 1.44703i
\(347\) 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 0.918290 0.395909i \(-0.129571\pi\)
0.116277 + 0.993217i \(0.462904\pi\)
\(350\) 0 0
\(351\) −15.6867 18.0408i −0.837295 0.962947i
\(352\) 2.92591 0.155951
\(353\) 2.01956 + 1.16600i 0.107491 + 0.0620597i 0.552781 0.833326i \(-0.313566\pi\)
−0.445291 + 0.895386i \(0.646900\pi\)
\(354\) 21.8414 37.8304i 1.16086 2.01066i
\(355\) −3.75354 6.50133i −0.199217 0.345055i
\(356\) 0.491966i 0.0260741i
\(357\) 0 0
\(358\) 24.8648 14.3557i 1.31415 0.758722i
\(359\) 3.27105i 0.172639i −0.996267 0.0863197i \(-0.972489\pi\)
0.996267 0.0863197i \(-0.0275107\pi\)
\(360\) −6.18147 10.7066i −0.325792 0.564289i
\(361\) 7.58017 13.1292i 0.398956 0.691013i
\(362\) −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
\(367\) 2.07645 3.59652i 0.108390 0.187737i −0.806728 0.590923i \(-0.798764\pi\)
0.915118 + 0.403186i \(0.132097\pi\)
\(368\) 3.04440 + 5.27306i 0.158700 + 0.274877i
\(369\) 4.91805i 0.256024i
\(370\) 1.19544 0.690185i 0.0621477 0.0358810i
\(371\) 0 0
\(372\) 0.983525i 0.0509934i
\(373\) 5.55446 + 9.62061i 0.287599 + 0.498136i 0.973236 0.229807i \(-0.0738096\pi\)
−0.685637 + 0.727944i \(0.740476\pi\)
\(374\) 2.03591 3.52630i 0.105275 0.182341i
\(375\) 18.8037 + 10.8563i 0.971021 + 0.560619i
\(376\) 11.1233 0.573640
\(377\) −8.06996 + 1.56972i −0.415624 + 0.0808447i
\(378\) 0 0
\(379\) −4.01862 2.32015i −0.206422 0.119178i 0.393225 0.919442i \(-0.371359\pi\)
−0.599648 + 0.800264i \(0.704693\pi\)
\(380\) 0.231304 0.400630i 0.0118656 0.0205519i
\(381\) 2.76208 + 4.78407i 0.141506 + 0.245095i
\(382\) 5.86109i 0.299880i
\(383\) −3.17773 + 1.83466i −0.162374 + 0.0937469i −0.578985 0.815338i \(-0.696551\pi\)
0.416611 + 0.909085i \(0.363218\pi\)
\(384\) −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
\(388\) 0.905640 + 0.522872i 0.0459769 + 0.0265448i
\(389\) −16.8831 −0.856008 −0.428004 0.903777i \(-0.640783\pi\)
−0.428004 + 0.903777i \(0.640783\pi\)
\(390\) −3.75763 + 10.9175i −0.190275 + 0.552830i
\(391\) −0.898894 −0.0454590
\(392\) 0 0
\(393\) −22.4468 + 38.8790i −1.13229 + 1.96119i
\(394\) −9.94390 17.2233i −0.500966 0.867699i
\(395\) 9.16262i 0.461021i
\(396\) 2.37684 1.37227i 0.119441 0.0689592i
\(397\) −14.4700 + 8.35428i −0.726230 + 0.419289i −0.817041 0.576579i \(-0.804387\pi\)
0.0908114 + 0.995868i \(0.471054\pi\)
\(398\) 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 −0.159902 0.987133i \(-0.551118\pi\)
−0.934833 + 0.355087i \(0.884451\pi\)
\(402\) −29.1864 −1.45568
\(403\) −9.45737 + 8.22331i −0.471105 + 0.409632i
\(404\) 0.384535 0.0191313
\(405\) −2.23359 1.28956i −0.110988 0.0640789i
\(406\) 0 0
\(407\) 3.27354 + 5.66994i 0.162263 + 0.281048i
\(408\) 4.66950i 0.231175i
\(409\) 4.96529 2.86671i 0.245518 0.141750i −0.372192 0.928156i \(-0.621394\pi\)
0.617710 + 0.786406i \(0.288060\pi\)
\(410\) 0.892951 0.515546i 0.0440997 0.0254610i
\(411\) 22.6205i 1.11579i
\(412\) −0.415112 0.718996i −0.0204511 0.0354224i
\(413\) 0 0
\(414\) 10.1610 + 5.86648i 0.499388 + 0.288322i
\(415\) 4.69031 0.230238
\(416\) −1.89226 0.651284i −0.0927756 0.0319318i
\(417\) 28.5954 1.40032
\(418\) −36.7971 21.2448i −1.79981 1.03912i
\(419\) −17.1729 + 29.7443i −0.838950 + 1.45310i 0.0518229 + 0.998656i \(0.483497\pi\)
−0.890773 + 0.454448i \(0.849836\pi\)
\(420\) 0 0
\(421\) 2.94167i 0.143368i 0.997427 + 0.0716842i \(0.0228374\pi\)
−0.997427 + 0.0716842i \(0.977163\pi\)
\(422\) 31.5565 18.2191i 1.53614 0.886894i
\(423\) 17.6489 10.1896i 0.858121 0.495437i
\(424\) 15.7830i 0.766488i
\(425\) 1.21835 + 2.11024i 0.0590985 + 0.102362i
\(426\) −18.5050 + 32.0516i −0.896571 + 1.55291i
\(427\) 0 0
\(428\) −0.950178 −0.0459286
\(429\) −51.7816 17.8224i −2.50004 0.860472i
\(430\) −4.94273 −0.238360
\(431\) −34.3773 19.8478i −1.65590 0.956033i −0.974578 0.224048i \(-0.928073\pi\)
−0.681321 0.731985i \(-0.738594\pi\)
\(432\) −12.5781 + 21.7858i −0.605162 + 1.04817i
\(433\) 4.91827 + 8.51869i 0.236357 + 0.409382i 0.959666 0.281142i \(-0.0907133\pi\)
−0.723309 + 0.690524i \(0.757380\pi\)
\(434\) 0 0
\(435\) −4.58538 + 2.64737i −0.219852 + 0.126932i
\(436\) 1.23865 0.715135i 0.0593206 0.0342488i
\(437\) 9.37999i 0.448706i
\(438\) 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
\(443\) 3.33901 0.158641 0.0793207 0.996849i \(-0.474725\pi\)
0.0793207 + 0.996849i \(0.474725\pi\)
\(444\) 0.304337 + 0.175709i 0.0144432 + 0.00833880i
\(445\) −2.01868 + 3.49646i −0.0956947 + 0.165748i
\(446\) −15.8595 27.4695i −0.750969 1.30072i
\(447\) 22.8170i 1.07921i
\(448\) 0 0
\(449\) 15.7487 9.09253i 0.743228 0.429103i −0.0800136 0.996794i \(-0.525496\pi\)
0.823242 + 0.567691i \(0.192163\pi\)
\(450\) 31.8054i 1.49932i
\(451\) 2.44523 + 4.23526i 0.115141 + 0.199430i
\(452\) −0.958084 + 1.65945i −0.0450645 + 0.0780539i
\(453\) −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 0.312651 0.949868i \(-0.398783\pi\)
−0.666284 + 0.745698i \(0.732116\pi\)
\(458\) 11.9519 20.7013i 0.558476 0.967309i
\(459\) −1.85691 3.21625i −0.0866729 0.150122i
\(460\) 0.127026i 0.00592262i
\(461\) 1.96695 1.13562i 0.0916099 0.0528910i −0.453495 0.891259i \(-0.649823\pi\)
0.545105 + 0.838368i \(0.316490\pi\)
\(462\) 0 0
\(463\) 5.48326i 0.254829i 0.991850 + 0.127414i \(0.0406678\pi\)
−0.991850 + 0.127414i \(0.959332\pi\)
\(464\) 4.32538 + 7.49178i 0.200801 + 0.347797i
\(465\) −4.03570 + 6.99003i −0.187151 + 0.324155i
\(466\) −9.33356 5.38873i −0.432369 0.249628i
\(467\) 18.8819 0.873750 0.436875 0.899522i \(-0.356085\pi\)
0.436875 + 0.899522i \(0.356085\pi\)
\(468\) −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
\(473\) 23.4433i 1.07792i
\(474\) 39.1200 22.5859i 1.79684 1.03741i
\(475\) 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
\(479\) −28.6961 16.5677i −1.31116 0.756997i −0.328869 0.944375i \(-0.606668\pi\)
−0.982288 + 0.187378i \(0.940001\pi\)
\(480\) −1.28884 −0.0588275
\(481\) −0.854998 4.39556i −0.0389846 0.200420i
\(482\) −31.1104 −1.41704
\(483\) 0 0
\(484\) 0.824428 1.42795i 0.0374740 0.0649069i
\(485\) −4.29100 7.43222i −0.194844 0.337480i
\(486\) 14.7168i 0.667565i
\(487\) 13.8185 7.97814i 0.626178 0.361524i −0.153093 0.988212i \(-0.548923\pi\)
0.779270 + 0.626688i \(0.215590\pi\)
\(488\) 18.2983 10.5645i 0.828326 0.478234i
\(489\) 41.3765i 1.87111i
\(490\) 0 0
\(491\) −15.8464 + 27.4468i −0.715138 + 1.23866i 0.247769 + 0.968819i \(0.420303\pi\)
−0.962906 + 0.269836i \(0.913031\pi\)
\(492\) 0.227330 + 0.131249i 0.0102488 + 0.00591717i
\(493\) −1.27712 −0.0575185
\(494\) 19.0687 + 21.9304i 0.857942 + 0.986693i
\(495\) −22.5233 −1.01235
\(496\) 11.4206 + 6.59368i 0.512800 + 0.296065i
\(497\) 0 0
\(498\) −11.5617 20.0254i −0.518090 0.897358i
\(499\) 24.2184i 1.08417i 0.840325 + 0.542083i \(0.182364\pi\)
−0.840325 + 0.542083i \(0.817636\pi\)
\(500\) 0.640935 0.370044i 0.0286635 0.0165489i
\(501\) 11.2817 6.51351i 0.504030 0.291002i
\(502\) 9.28429i 0.414378i
\(503\) 0.427249 + 0.740017i 0.0190501 + 0.0329957i 0.875393 0.483411i \(-0.160602\pi\)
−0.856343 + 0.516407i \(0.827269\pi\)
\(504\) 0 0
\(505\) −2.73294 1.57786i −0.121614 0.0702139i
\(506\) 11.6671 0.518667
\(507\) 29.5214 + 23.0524i 1.31109 + 1.02379i
\(508\) 0.188294 0.00835420
\(509\) −1.12583 0.650000i −0.0499017 0.0288108i 0.474842 0.880071i \(-0.342505\pi\)
−0.524743 + 0.851261i \(0.675839\pi\)
\(510\) −0.896808 + 1.55332i −0.0397113 + 0.0687820i
\(511\) 0 0
\(512\) 24.0616i 1.06338i
\(513\) −33.5618 + 19.3769i −1.48179 + 0.855511i
\(514\) −19.7514 + 11.4035i −0.871199 + 0.502987i
\(515\) 6.81332i 0.300231i
\(516\) −0.629167 1.08975i −0.0276976 0.0479736i
\(517\) 10.1324 17.5499i 0.445624 0.771844i
\(518\) 0 0
\(519\) 56.2351 2.46845
\(520\) 5.51717 + 6.34512i 0.241944 + 0.278252i
\(521\) 25.0455 1.09726 0.548632 0.836064i \(-0.315149\pi\)
0.548632 + 0.836064i \(0.315149\pi\)
\(522\) 14.4365 + 8.33490i 0.631867 + 0.364809i
\(523\) 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
\(527\) −1.68603 + 0.973429i −0.0734446 + 0.0424032i
\(528\) 57.6242i 2.50777i
\(529\) 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
\(534\) 19.9043 0.861342
\(535\) 6.75303 + 3.89886i 0.291959 + 0.168563i
\(536\) −10.6273 + 18.4071i −0.459031 + 0.795066i
\(537\) −29.9928 51.9490i −1.29428 2.24176i
\(538\) 21.6828i 0.934814i
\(539\) 0 0
\(540\) −0.454501 + 0.262406i −0.0195586 + 0.0112922i
\(541\) 28.7449i 1.23584i −0.786241 0.617920i \(-0.787975\pi\)
0.786241 0.617920i \(-0.212025\pi\)
\(542\) −3.59670 6.22966i −0.154491 0.267587i
\(543\) −23.8451 + 41.3009i −1.02329 + 1.77239i
\(544\) −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
\(549\) 19.3556 33.5248i 0.826075 1.43080i
\(550\) −15.8134 27.3897i −0.674287 1.16790i
\(551\) 13.3268i 0.567740i
\(552\) 11.5871 6.68983i 0.493181 0.284738i
\(553\) 0 0
\(554\) 26.5777i 1.12918i
\(555\) −1.44198 2.49757i −0.0612084 0.106016i
\(556\) 0.487345 0.844106i 0.0206680 0.0357981i
\(557\) −33.5389 19.3637i −1.42109 0.820465i −0.424695 0.905336i \(-0.639619\pi\)
−0.996392 + 0.0848711i \(0.972952\pi\)
\(558\) 25.4117 1.07576
\(559\) −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 \(0.879840\pi\)
\(564\) 1.08773i 0.0458017i
\(565\) 13.6184 7.86260i 0.572932 0.330782i
\(566\) 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 \(0.185610\pi\)
\(570\) 16.2089 + 9.35823i 0.678917 + 0.391973i
\(571\) 46.6724 1.95318 0.976589 0.215113i \(-0.0690119\pi\)
0.976589 + 0.215113i \(0.0690119\pi\)
\(572\) −1.40860 + 1.22480i −0.0588965 + 0.0512113i
\(573\) 12.2453 0.511557
\(574\) 0 0
\(575\) −3.49096 + 6.04653i −0.145583 + 0.252158i
\(576\) 22.1418 + 38.3507i 0.922576 + 1.59795i
\(577\) 11.4088i 0.474955i −0.971393 0.237478i \(-0.923679\pi\)
0.971393 0.237478i \(-0.0763207\pi\)
\(578\) 19.9284 11.5057i 0.828911 0.478572i
\(579\) 28.9373 16.7070i 1.20259 0.694318i
\(580\) 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
\(584\) 14.4719 0.598853
\(585\) 14.5664 + 5.01352i 0.602248 + 0.207284i
\(586\) 31.9234 1.31874
\(587\) 40.2191 + 23.2205i 1.66002 + 0.958413i 0.972702 + 0.232057i \(0.0745456\pi\)
0.687318 + 0.726356i \(0.258788\pi\)
\(588\) 0 0
\(589\) 10.1578 + 17.5938i 0.418544 + 0.724939i
\(590\) 12.2192i 0.503057i
\(591\) −35.9840 + 20.7754i −1.48018 + 0.854585i
\(592\) −4.08064 + 2.35596i −0.167713 + 0.0968292i
\(593\) 20.2606i 0.832002i −0.909364 0.416001i \(-0.863431\pi\)
0.909364 0.416001i \(-0.136569\pi\)
\(594\) 24.1016 + 41.7451i 0.988899 + 1.71282i
\(595\) 0 0
\(596\) 0.673533 + 0.388864i 0.0275890 + 0.0159285i
\(597\) −20.3391 −0.832424
\(598\) −7.54543 2.59701i −0.308556 0.106200i
\(599\) −38.9876 −1.59299 −0.796494 0.604646i \(-0.793315\pi\)
−0.796494 + 0.604646i \(0.793315\pi\)
\(600\) −31.4100 18.1346i −1.28231 0.740342i
\(601\) 9.56951 16.5749i 0.390348 0.676103i −0.602147 0.798385i \(-0.705688\pi\)
0.992495 + 0.122282i \(0.0390212\pi\)
\(602\) 0 0
\(603\) 38.9412i 1.58581i
\(604\) −0.127674 + 0.0737127i −0.00519499 + 0.00299933i
\(605\) −11.7186 + 6.76575i −0.476430 + 0.275067i
\(606\) 15.5578i 0.631991i
\(607\) 21.6668 + 37.5280i 0.879428 + 1.52321i 0.851970 + 0.523590i \(0.175408\pi\)
0.0274572 + 0.999623i \(0.491259\pi\)
\(608\) −1.62200 + 2.80939i −0.0657808 + 0.113936i
\(609\) 0 0
\(610\) −8.11595 −0.328605
\(611\) −10.4594 + 9.09457i −0.423141 + 0.367927i
\(612\) −0.291606 −0.0117875
\(613\) −8.92834 5.15478i −0.360612 0.208200i 0.308737 0.951147i \(-0.400094\pi\)
−0.669349 + 0.742948i \(0.733427\pi\)
\(614\) −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 −0.680405 0.732837i \(-0.738196\pi\)
0.294453 + 0.955666i \(0.404863\pi\)
\(618\) 29.0896 16.7949i 1.17015 0.675589i
\(619\) 33.7616i 1.35700i 0.734603 + 0.678498i \(0.237369\pi\)
−0.734603 + 0.678498i \(0.762631\pi\)
\(620\) 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
\(625\) 15.6786 0.627145
\(626\) −3.22098 1.85964i −0.128736 0.0743260i
\(627\) −44.3860 + 76.8787i −1.77260 + 3.07024i
\(628\) 0.189389 + 0.328031i 0.00755745 + 0.0130899i
\(629\) 0.695623i 0.0277363i
\(630\) 0 0
\(631\) 33.4264 19.2987i 1.33068 0.768271i 0.345280 0.938500i \(-0.387784\pi\)
0.985405 + 0.170229i \(0.0544507\pi\)
\(632\) 32.8959i 1.30853i
\(633\) −38.0645 65.9296i −1.51293 2.62047i
\(634\) −16.5972 + 28.7473i −0.659161 + 1.14170i
\(635\) −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
\(640\) 4.19480 7.26560i 0.165814 0.287198i
\(641\) 9.76141 + 16.9073i 0.385553 + 0.667797i 0.991846 0.127445i \(-0.0406775\pi\)
−0.606293 + 0.795241i \(0.707344\pi\)
\(642\) 38.4429i 1.51722i
\(643\) −10.8009 + 6.23589i −0.425945 + 0.245920i −0.697618 0.716470i \(-0.745757\pi\)
0.271673 + 0.962390i \(0.412423\pi\)
\(644\) 0 0
\(645\) 10.3266i 0.406611i
\(646\) 2.25725 + 3.90967i 0.0888103 + 0.153824i
\(647\) −17.9695 + 31.1241i −0.706455 + 1.22362i 0.259709 + 0.965687i \(0.416373\pi\)
−0.966164 + 0.257929i \(0.916960\pi\)
\(648\) 8.01911 + 4.62984i 0.315021 + 0.181877i
\(649\) −57.9556 −2.27496
\(650\) 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
\(655\) 12.5579i 0.490679i
\(656\) −3.04810 + 1.75982i −0.119008 + 0.0687095i
\(657\) 22.9621 13.2572i 0.895838 0.517212i
\(658\) 0 0
\(659\) 11.8103 + 20.4560i 0.460063 + 0.796853i 0.998964 0.0455166i \(-0.0144934\pi\)
−0.538900 + 0.842370i \(0.681160\pi\)
\(660\) −0.601085 + 1.04111i −0.0233972 + 0.0405251i
\(661\) 14.1970 + 8.19662i 0.552198 + 0.318812i 0.750008 0.661429i \(-0.230050\pi\)
−0.197810 + 0.980240i \(0.563383\pi\)
\(662\) −0.854633 −0.0332162
\(663\) 3.81786 + 4.39080i 0.148273 + 0.170525i
\(664\) −16.8393 −0.653492
\(665\) 0 0
\(666\) −4.53987 + 7.86328i −0.175916 + 0.304696i
\(667\) −1.82968 3.16910i −0.0708456 0.122708i
\(668\) 0.444033i 0.0171801i
\(669\) −57.3908 + 33.1346i −2.21886 + 1.28106i
\(670\) 7.07040 4.08210i 0.273154 0.157705i
\(671\) 38.4939i 1.48604i
\(672\) 0 0
\(673\) −7.12678 + 12.3439i −0.274717 + 0.475824i −0.970064 0.242851i \(-0.921918\pi\)
0.695347 + 0.718675i \(0.255251\pi\)
\(674\) −6.83278 3.94491i −0.263189 0.151952i
\(675\) −28.8461 −1.11029
\(676\) 1.18361 0.478564i 0.0455234 0.0184063i
\(677\) 10.2715 0.394765 0.197383 0.980327i \(-0.436756\pi\)
0.197383 + 0.980327i \(0.436756\pi\)
\(678\) −67.1391 38.7628i −2.57846 1.48867i
\(679\) 0 0
\(680\) 0.653092 + 1.13119i 0.0250449 + 0.0433791i
\(681\) 1.30624i 0.0500554i
\(682\) 21.8837 12.6345i 0.837969 0.483802i
\(683\) −1.92432 + 1.11101i −0.0736321 + 0.0425115i −0.536364 0.843987i \(-0.680203\pi\)
0.462732 + 0.886498i \(0.346869\pi\)
\(684\) 3.04292i 0.116349i
\(685\) −3.16377 5.47981i −0.120881 0.209373i
\(686\) 0 0
\(687\) −43.2504 24.9706i −1.65011 0.952689i
\(688\) 16.8721 0.643242
\(689\) 12.9044 + 14.8409i 0.491618 + 0.565395i
\(690\) −5.13930 −0.195650
\(691\) 2.28643 + 1.32007i 0.0869800 + 0.0502179i 0.542859 0.839824i \(-0.317342\pi\)
−0.455879 + 0.890042i \(0.650675\pi\)
\(692\) 0.958402 1.66000i 0.0364330 0.0631038i
\(693\) 0 0
\(694\) 2.57174i 0.0976220i
\(695\) −6.92724 + 3.99944i −0.262765 + 0.151708i
\(696\) 16.4626 9.50469i 0.624014 0.360274i
\(697\) 0.519607i 0.0196815i
\(698\) 15.3884 + 26.6534i 0.582458 + 1.00885i
\(699\) −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 \(0.553754\pi\)
\(702\) −6.29496 32.3625i −0.237588 1.22144i
\(703\) −7.25885 −0.273773
\(704\) 38.1355 + 22.0175i 1.43729 + 0.829818i
\(705\) −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
\(709\) 35.1558 20.2972i 1.32030 0.762278i 0.336527 0.941674i \(-0.390748\pi\)
0.983777 + 0.179396i \(0.0574143\pi\)
\(710\) 10.3527i 0.388529i
\(711\) −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
\(716\) −2.04464 −0.0764118
\(717\) 33.7636 + 19.4934i 1.26092 + 0.727995i
\(718\) 2.25548 3.90661i 0.0841738 0.145793i
\(719\) −7.25674 12.5690i −0.270631 0.468746i 0.698393 0.715715i \(-0.253899\pi\)
−0.969024 + 0.246968i \(0.920566\pi\)
\(720\) 16.2100i 0.604110i
\(721\) 0 0
\(722\) 18.1059 10.4535i 0.673834 0.389038i
\(723\) 64.9977i 2.41729i
\(724\) 0.812773 + 1.40776i 0.0302065 + 0.0523191i
\(725\) −4.95984 + 8.59070i −0.184204 + 0.319051i
\(726\) 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
\(731\) −1.24542 + 2.15713i −0.0460635 + 0.0797842i
\(732\) −1.03309 1.78937i −0.0381842 0.0661369i
\(733\) 13.2644i 0.489930i 0.969532 + 0.244965i \(0.0787765\pi\)
−0.969532 + 0.244965i \(0.921223\pi\)
\(734\) 4.95980 2.86354i 0.183069 0.105695i
\(735\) 0 0
\(736\) 0.890761i 0.0328339i
\(737\) 19.3613 + 33.5348i 0.713184 + 1.23527i
\(738\) −3.39113 + 5.87361i −0.124829 + 0.216211i
\(739\) 6.28279 + 3.62737i 0.231116 + 0.133435i 0.611087 0.791564i \(-0.290733\pi\)
−0.379971 + 0.924999i \(0.624066\pi\)
\(740\) −0.0983010 −0.00361362
\(741\) 45.8182 39.8395i 1.68317 1.46354i
\(742\) 0 0
\(743\) −40.0705 23.1347i −1.47004 0.848730i −0.470608 0.882342i \(-0.655965\pi\)
−0.999435 + 0.0336128i \(0.989299\pi\)
\(744\) 14.4891 25.0959i 0.531196 0.920059i
\(745\) −3.19125 5.52741i −0.116918 0.202509i
\(746\) 15.3198i 0.560898i
\(747\) −26.7184 + 15.4259i −0.977574 + 0.564403i
\(748\) −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 \(0.938363\pi\)
\(752\) 12.6306 + 7.29229i 0.460591 + 0.265922i
\(753\) 19.3973 0.706877
\(754\) −10.7203 3.68975i −0.390410 0.134373i
\(755\) 1.20986 0.0440313
\(756\) 0 0
\(757\) 5.28132 9.14751i 0.191953 0.332472i −0.753945 0.656938i \(-0.771851\pi\)
0.945897 + 0.324466i \(0.105185\pi\)
\(758\) −3.19961 5.54189i −0.116215 0.201291i
\(759\) 24.3756i 0.884780i
\(760\) 11.8040 6.81504i 0.428176 0.247207i
\(761\) 6.76541 3.90601i 0.245246 0.141593i −0.372340 0.928097i \(-0.621444\pi\)
0.617585 + 0.786504i \(0.288111\pi\)
\(762\) 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
\(766\) −5.06020 −0.182833
\(767\) 37.4814 + 12.9005i 1.35337 + 0.465809i
\(768\) 6.77429 0.244446
\(769\) −21.9030 12.6457i −0.789844 0.456017i 0.0500637 0.998746i \(-0.484058\pi\)
−0.839908 + 0.542729i \(0.817391\pi\)
\(770\) 0 0
\(771\) 23.8249 + 41.2659i 0.858032 + 1.48615i
\(772\) 1.13893i 0.0409911i
\(773\) −40.3572 + 23.3002i −1.45155 + 0.838051i −0.998569 0.0534716i \(-0.982971\pi\)
−0.452977 + 0.891522i \(0.649638\pi\)
\(774\) 28.1563 16.2560i 1.01206 0.584311i
\(775\) 15.1217i 0.543188i
\(776\) 15.4057 + 26.6834i 0.553032 + 0.957879i
\(777\) 0 0
\(778\) −20.1634 11.6414i −0.722895 0.417363i
\(779\) −5.42212 −0.194268
\(780\) 0.620480 0.539516i 0.0222168 0.0193178i
\(781\) 49.1026 1.75703
\(782\) −1.07355 − <