Properties

Label 637.2.q.g.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.g.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 \(0.479317\pi\)
−0.896664 + 0.442712i \(0.854016\pi\)
\(4\) −0.0491037 0.0850501i −0.0245518 0.0425250i
\(5\) 0.805948i 0.360431i −0.983627 0.180216i \(-0.942320\pi\)
0.983627 0.180216i \(-0.0576795\pi\)
\(6\) −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 0.830064 0.557668i \(-0.188304\pi\)
−0.897987 + 0.440023i \(0.854970\pi\)
\(18\) 7.31083i 1.72318i
\(19\) −5.06165 + 2.92234i −1.16122 + 0.670431i −0.951596 0.307351i \(-0.900558\pi\)
−0.209625 + 0.977782i \(0.567224\pi\)
\(20\) −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 \(-0.898952\pi\)
0.950034 0.312145i \(-0.101048\pi\)
\(32\) −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 0.561422 0.827529i \(-0.310254\pi\)
−0.435950 + 0.899971i \(0.643588\pi\)
\(42\) 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 \(-0.909544\pi\)
0.959893 0.280365i \(-0.0904556\pi\)
\(48\) 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 −0.968999 0.247063i \(-0.920534\pi\)
−0.270537 + 0.962710i \(0.587201\pi\)
\(60\) 0.228047i 0.0294408i
\(61\) −3.65107 6.32385i −0.467472 0.809686i 0.531837 0.846847i \(-0.321502\pi\)
−0.999309 + 0.0371610i \(0.988169\pi\)
\(62\) 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 \(-0.905450\pi\)
0.956208 0.292688i \(-0.0945498\pi\)
\(74\) −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 \(0.103479\pi\)
−0.947622 + 0.319393i \(0.896521\pi\)
\(84\) 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 0.252125 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
\(94\) 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 0.0475172 0.998870i \(-0.484869\pi\)
0.888806 + 0.458284i \(0.151536\pi\)
\(98\) 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 −0.752031 0.659127i \(-0.770926\pi\)
0.946837 + 0.321715i \(0.104259\pi\)
\(102\) 1.92732 + 1.11274i 0.190833 + 0.110177i
\(103\) −8.45379 −0.832977 −0.416488 0.909141i \(-0.636739\pi\)
−0.416488 + 0.909141i \(0.636739\pi\)
\(104\) −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 \(-0.261683\pi\)
0.680684 + 0.732577i \(0.261683\pi\)
\(132\) −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 0.575122 0.818067i \(-0.304954\pi\)
−0.996028 + 0.0890370i \(0.971621\pi\)
\(140\) 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 \(-0.450814\pi\)
0.153908 + 0.988085i \(0.450814\pi\)
\(158\) 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 0.340790 0.940140i \(-0.389306\pi\)
−0.643790 + 0.765202i \(0.722639\pi\)
\(168\) 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 \(-0.900563\pi\)
0.209642 0.977778i \(-0.432770\pi\)
\(174\) 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 \(-0.289093\pi\)
0.615157 + 0.788405i \(0.289093\pi\)
\(182\) 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 0.963583 0.267409i \(-0.0861676\pi\)
−0.713375 + 0.700783i \(0.752834\pi\)
\(200\) 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 0.985892 0.167384i \(-0.0535321\pi\)
0.347987 + 0.937499i \(0.386865\pi\)
\(224\) 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 −0.486914 0.873450i \(-0.661877\pi\)
0.512973 + 0.858405i \(0.328544\pi\)
\(228\) −1.43222 + 0.826893i −0.0948511 + 0.0547623i
\(229\) 17.3335i 1.14543i 0.819755 + 0.572714i \(0.194110\pi\)
−0.819755 + 0.572714i \(0.805890\pi\)
\(230\) 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 0.285701 0.958319i \(-0.407774\pi\)
0.972779 + 0.231736i \(0.0744404\pi\)
\(242\) 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 0.740016 0.672589i \(-0.234818\pi\)
−0.952487 + 0.304578i \(0.901485\pi\)
\(252\) 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 \(-0.660824\pi\)
0.999832 0.0183536i \(-0.00584248\pi\)
\(258\) −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 0.999719 0.0237130i \(-0.00754880\pi\)
−0.520395 + 0.853925i \(0.674215\pi\)
\(270\) 3.68478 6.38223i 0.224249 0.388410i
\(271\) 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
\(276\) −0.227054 + 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 −0.999337 0.0364203i \(-0.988405\pi\)
0.531209 + 0.847241i \(0.321738\pi\)
\(284\) 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 −0.953958 0.299940i \(-0.903033\pi\)
−0.217223 + 0.976122i \(0.569700\pi\)
\(294\) 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 \(-0.961429\pi\)
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
\(311\) −27.2501 −1.54521 −0.772606 0.634885i \(-0.781047\pi\)
−0.772606 + 0.634885i \(0.781047\pi\)
\(312\) −5.73934 29.5061i −0.324926 1.67045i
\(313\) 2.69697 0.152442 0.0762209 0.997091i \(-0.475715\pi\)
0.0762209 + 0.997091i \(0.475715\pi\)
\(314\) 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 −0.116277 0.993217i \(-0.537096\pi\)
−0.918290 + 0.395909i \(0.870429\pi\)
\(350\) 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 0.445291 0.895386i \(-0.353100\pi\)
−0.552781 + 0.833326i \(0.686434\pi\)
\(354\) 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 −0.915118 0.403186i \(-0.867903\pi\)
0.806728 + 0.590923i \(0.201236\pi\)
\(368\) 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 −0.416611 0.909085i \(-0.636782\pi\)
0.578985 + 0.815338i \(0.303449\pi\)
\(384\) 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 −0.0908114 0.995868i \(-0.528946\pi\)
0.817041 + 0.576579i \(0.195613\pi\)
\(398\) 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 −0.617710 0.786406i \(-0.711940\pi\)
0.372192 + 0.928156i \(0.378606\pi\)
\(410\) 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 \(-0.516503\pi\)
0.890773 0.454448i \(-0.150164\pi\)
\(420\) 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 0.723309 0.690524i \(-0.242620\pi\)
−0.959666 + 0.281142i \(0.909287\pi\)
\(434\) 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 \(-0.594780\pi\)
0.974607 0.223922i \(-0.0718863\pi\)
\(440\) 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 −0.545105 0.838368i \(-0.683510\pi\)
0.453495 + 0.891259i \(0.350177\pi\)
\(462\) 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 \(-0.643915\pi\)
−0.436875 + 0.899522i \(0.643915\pi\)
\(468\) 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 0.982288 0.187378i \(-0.0599991\pi\)
0.328869 + 0.944375i \(0.393332\pi\)
\(480\) −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 0.856343 0.516407i \(-0.172731\pi\)
−0.875393 + 0.483411i \(0.839398\pi\)
\(504\) 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 0.524743 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
\(513\) −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 \(-0.684851\pi\)
−0.548632 + 0.836064i \(0.684851\pi\)
\(522\) 14.4365 + 8.33490i 0.631867 + 0.364809i
\(523\) −6.41197 + 11.1059i −0.280376 + 0.485625i −0.971477 0.237133i \(-0.923792\pi\)
0.691101 + 0.722758i \(0.257126\pi\)
\(524\) −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 0.929591 0.368592i \(-0.120160\pi\)
−0.784005 + 0.620754i \(0.786827\pi\)
\(564\) 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 \(0.0763207\pi\)
−0.971393 + 0.237478i \(0.923679\pi\)
\(578\) 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 \(-0.925454\pi\)
−0.687318 0.726356i \(-0.741212\pi\)
\(588\) 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 \(0.136569\pi\)
−0.909364 + 0.416001i \(0.863431\pi\)
\(594\) −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 −0.992495 0.122282i \(-0.960979\pi\)
0.602147 + 0.798385i \(0.294312\pi\)
\(602\) 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 \(-0.824592\pi\)
−0.0274572 0.999623i \(-0.508741\pi\)
\(608\) 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 \(-0.762631\pi\)
0.734603 0.678498i \(-0.237369\pi\)
\(620\) 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 −0.271673 0.962390i \(-0.587577\pi\)
0.697618 + 0.716470i \(0.254243\pi\)
\(644\) 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 \(-0.583627\pi\)
0.966164 0.257929i \(-0.0830401\pi\)
\(648\) 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 0.197810 0.980240i \(-0.436617\pi\)
−0.750008 + 0.661429i \(0.769950\pi\)
\(662\) −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 \(-0.563244\pi\)
−0.197383 + 0.980327i \(0.563244\pi\)
\(678\) 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 0.455879 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
\(695\) −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 0.969024 0.246968i \(-0.0794344\pi\)
−0.698393 + 0.715715i \(0.746101\pi\)
\(720\) 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 \(-0.307256\pi\)
0.569193 + 0.822204i \(0.307256\pi\)
\(728\) 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 \(-0.921223\pi\)
0.969532 0.244965i \(-0.0787765\pi\)
\(734\) −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 −0.617585 0.786504i \(-0.711889\pi\)
0.372340 + 0.928097i \(0.378556\pi\)
\(762\) 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 0.839908 0.542729i \(-0.182609\pi\)
−0.0500637 + 0.998746i \(0.515942\pi\)
\(770\) 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 0.452977 0.891522i \(-0.350362\pi\)
0.998569 + 0.0534716i \(0.0170287\pi\)
\(774\) 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