Properties

Label 637.2.q.i.491.5
Level $637$
Weight $2$
Character 637.491
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 491.5
Root \(-1.38488 - 0.286553i\) of defining polynomial
Character \(\chi\) \(=\) 637.491
Dual form 637.2.q.i.589.5

$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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 −0.0142944 0.999898i \(-0.504550\pi\)
0.858790 + 0.512328i \(0.171217\pi\)
\(3\) 1.44060 + 2.49520i 0.831732 + 1.44060i 0.896664 + 0.442712i \(0.145984\pi\)
−0.0649323 + 0.997890i \(0.520683\pi\)
\(4\) −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 −0.991736 0.128296i \(-0.959049\pi\)
−0.384760 + 0.923017i \(0.625716\pi\)
\(12\) −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 \(-0.811696\pi\)
0.897987 + 0.440023i \(0.145030\pi\)
\(18\) 7.31083i 1.72318i
\(19\) 5.06165 + 2.92234i 1.16122 + 0.670431i 0.951596 0.307351i \(-0.0994424\pi\)
0.209625 + 0.977782i \(0.432776\pi\)
\(20\) 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 0.770157 0.637855i \(-0.220178\pi\)
−0.937477 + 0.348048i \(0.886845\pi\)
\(24\) −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 0.740542 0.672010i \(-0.234569\pi\)
−0.952249 + 0.305323i \(0.901236\pi\)
\(30\) 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 −0.585799 0.810457i \(-0.699219\pi\)
0.408977 + 0.912545i \(0.365886\pi\)
\(38\) 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 \(-0.689746\pi\)
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 \(0.0565478\pi\)
\(44\) 0.517708i 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 \(-0.0794655\pi\)
0.270537 + 0.962710i \(0.412799\pi\)
\(60\) 0.228047i 0.0294408i
\(61\) 3.65107 6.32385i 0.467472 0.809686i −0.531837 0.846847i \(-0.678498\pi\)
0.999309 + 0.0371610i \(0.0118314\pi\)
\(62\) −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 −0.835428 0.549600i \(-0.814780\pi\)
0.0582541 + 0.998302i \(0.481447\pi\)
\(68\) 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 \(0.853077\pi\)
\(72\) −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 \(-0.581129\pi\)
0.711986 + 0.702194i \(0.247796\pi\)
\(90\) 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 \(-0.515131\pi\)
−0.888806 + 0.458284i \(0.848464\pi\)
\(98\) 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 \(-0.229074\pi\)
−0.946837 + 0.321715i \(0.895741\pi\)
\(102\) 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 0.999318 0.0369379i \(-0.0117604\pi\)
−0.531648 + 0.846965i \(0.678427\pi\)
\(108\) 0.325587 0.563933i 0.0313296 0.0542645i
\(109\) 14.5638i 1.39496i −0.716606 0.697478i \(-0.754305\pi\)
0.716606 0.697478i \(-0.245695\pi\)
\(110\) 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 −0.114903 + 0.993377i \(0.536656\pi\)
−0.802838 + 0.596197i \(0.796678\pi\)
\(114\) 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 0.820353 0.571858i \(-0.193777\pi\)
−0.905420 + 0.424517i \(0.860444\pi\)
\(128\) −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 0.180594 0.983558i \(-0.442198\pi\)
−0.761489 + 0.648178i \(0.775531\pi\)
\(138\) 6.37671i 0.542822i
\(139\) 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
\(142\) −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 0.192037 0.981388i \(-0.438491\pi\)
−0.753888 + 0.657003i \(0.771824\pi\)
\(150\) 14.9699 + 8.64290i 1.22229 + 0.705690i
\(151\) 1.50116i 0.122163i 0.998133 + 0.0610815i \(0.0194550\pi\)
−0.998133 + 0.0610815i \(0.980545\pi\)
\(152\) −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 −0.0736372 0.997285i \(-0.523461\pi\)
−0.900493 + 0.434871i \(0.856794\pi\)
\(164\) 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 \(-0.610694\pi\)
0.643790 + 0.765202i \(0.277361\pi\)
\(168\) 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 −0.209642 0.977778i \(-0.567230\pi\)
0.951602 0.307334i \(-0.0994369\pi\)
\(174\) 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 0.933055 + 0.359733i \(0.117132\pi\)
−0.154990 + 0.987916i \(0.549535\pi\)
\(180\) −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 −0.778845 0.627216i \(-0.784194\pi\)
0.932608 + 0.360892i \(0.117528\pi\)
\(192\) −12.0338 20.8431i −0.868463 1.50422i
\(193\) 10.0435 5.79861i 0.722946 0.417393i −0.0928898 0.995676i \(-0.529610\pi\)
0.815836 + 0.578283i \(0.196277\pi\)
\(194\) −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 −0.873884 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 −0.963583 0.267409i \(-0.913832\pi\)
0.713375 + 0.700783i \(0.247166\pi\)
\(200\) 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 0.814754 + 0.579807i \(0.196872\pi\)
0.0947513 + 0.995501i \(0.469794\pi\)
\(212\) −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 \(-0.946468\pi\)
−0.347987 + 0.937499i \(0.613135\pi\)
\(224\) 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 \(-0.338123\pi\)
−0.512973 + 0.858405i \(0.671456\pi\)
\(228\) −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 \(-0.855815\pi\)
0.899151 0.437638i \(-0.144185\pi\)
\(240\) 7.62961 + 4.40496i 0.492489 + 0.284339i
\(241\) −19.5369 11.2796i −1.25848 0.726583i −0.285701 0.958319i \(-0.592226\pi\)
−0.972779 + 0.231736i \(0.925560\pi\)
\(242\) 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 \(-0.765182\pi\)
0.952487 + 0.304578i \(0.0985154\pi\)
\(252\) 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 −0.999832 0.0183536i \(-0.994158\pi\)
0.484021 0.875056i \(-0.339176\pi\)
\(258\) 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 0.978147 0.207915i \(-0.0666676\pi\)
−0.669133 + 0.743143i \(0.733334\pi\)
\(264\) 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 \(-0.992451\pi\)
0.520395 + 0.853925i \(0.325785\pi\)
\(270\) 3.68478 + 6.38223i 0.224249 + 0.388410i
\(271\) −4.51734 + 2.60809i −0.274409 + 0.158430i −0.630890 0.775873i \(-0.717310\pi\)
0.356481 + 0.934303i \(0.383977\pi\)
\(272\) 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 0.416614 + 0.909084i \(0.363217\pi\)
−0.995596 + 0.0937439i \(0.970117\pi\)
\(278\) 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 \(-0.979641\pi\)
0.997955 0.0639153i \(-0.0203588\pi\)
\(282\) 7.63711 13.2279i 0.454783 0.787707i
\(283\) 7.87512 + 13.6401i 0.468127 + 0.810820i 0.999337 0.0364203i \(-0.0115955\pi\)
−0.531209 + 0.847241i \(0.678262\pi\)
\(284\) 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 \(-0.0969668\pi\)
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
\(297\) 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 \(-0.218953\pi\)
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 \(-0.763727\pi\)
0.736933 0.675966i \(-0.236273\pi\)
\(318\) 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 0.485178 0.874416i \(-0.338755\pi\)
−0.514677 + 0.857384i \(0.672088\pi\)
\(332\) −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 −0.839912 0.542722i \(-0.817394\pi\)
0.889968 + 0.456024i \(0.150727\pi\)
\(348\) 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
\(352\) 2.92591 0.155951
\(353\) 2.01956 1.16600i 0.107491 0.0620597i −0.445291 0.895386i \(-0.646900\pi\)
0.552781 + 0.833326i \(0.313566\pi\)
\(354\) 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 \(0.0275107\pi\)
−0.996267 + 0.0863197i \(0.972489\pi\)
\(360\) −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 \(-0.132097\pi\)
−0.806728 + 0.590923i \(0.798764\pi\)
\(368\) 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 −0.685637 0.727944i \(-0.740476\pi\)
0.973236 + 0.229807i \(0.0738096\pi\)
\(374\) 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 −0.599648 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
\(382\) 5.86109i 0.299880i
\(383\) −3.17773 1.83466i −0.162374 0.0937469i 0.416611 0.909085i \(-0.363218\pi\)
−0.578985 + 0.815338i \(0.696551\pi\)
\(384\) −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 \(-0.471054\pi\)
−0.817041 + 0.576579i \(0.804387\pi\)
\(398\) 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 \(-0.884451\pi\)
−0.159902 + 0.987133i \(0.551118\pi\)
\(402\) −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 \(-0.288060\pi\)
−0.372192 + 0.928156i \(0.621394\pi\)
\(410\) 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 −0.890773 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 \(-0.0228374\pi\)
\(422\) 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 −0.681321 + 0.731985i \(0.738594\pi\)
−0.974578 + 0.224048i \(0.928073\pi\)
\(432\) −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
\(436\) 1.23865 + 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 −0.974607 0.223922i \(-0.928114\pi\)
0.293381 0.955996i \(-0.405220\pi\)
\(440\) −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 0.823242 0.567691i \(-0.192163\pi\)
−0.0800136 + 0.996794i \(0.525496\pi\)
\(450\) 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 −0.666284 0.745698i \(-0.732116\pi\)
0.312651 + 0.949868i \(0.398783\pi\)
\(458\) 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 \(-0.316490\pi\)
−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 \(-0.0406678\pi\)
\(464\) 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 −0.982288 0.187378i \(-0.940001\pi\)
−0.328869 + 0.944375i \(0.606668\pi\)
\(480\) −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 0.779270 0.626688i \(-0.215590\pi\)
−0.153093 + 0.988212i \(0.548923\pi\)
\(488\) 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 −0.962906 0.269836i \(-0.913031\pi\)
0.247769 0.968819i \(-0.420303\pi\)
\(492\) 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 \(-0.817636\pi\)
0.840325 0.542083i \(-0.182364\pi\)
\(500\) 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 \(-0.827269\pi\)
0.875393 + 0.483411i \(0.160602\pi\)
\(504\) 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 \(-0.675839\pi\)
0.474842 + 0.880071i \(0.342505\pi\)
\(510\) −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 0.971477 0.237133i \(-0.0762076\pi\)
−0.691101 + 0.722758i \(0.742874\pi\)
\(524\) 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 \(0.212025\pi\)
−0.786241 + 0.617920i \(0.787975\pi\)
\(542\) −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 −0.996392 0.0848711i \(-0.972952\pi\)
−0.424695 + 0.905336i \(0.639619\pi\)
\(558\) 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 \(-0.879840\pi\)
0.784005 + 0.620754i \(0.213173\pi\)
\(564\) 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 0.834754 0.550623i \(-0.185610\pi\)
−0.894230 + 0.447607i \(0.852276\pi\)
\(570\) 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 0.687318 0.726356i \(-0.258788\pi\)
0.972702 0.232057i \(-0.0745456\pi\)
\(588\) 0 0
\(589\) 10.1578 17.5938i 0.418544 0.724939i
\(590\) 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 \(-0.0390212\pi\)
−0.602147 + 0.798385i \(0.705688\pi\)
\(602\) 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 0.0274572 0.999623i \(-0.491259\pi\)
0.851970 0.523590i \(-0.175408\pi\)
\(608\) −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 −0.669349 0.742948i \(-0.733427\pi\)
0.308737 + 0.951147i \(0.400094\pi\)
\(614\) −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 \(0.738196\pi\)
\(618\) 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 0.985405 0.170229i \(-0.0544507\pi\)
0.345280 + 0.938500i \(0.387784\pi\)
\(632\) 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 −0.606293 0.795241i \(-0.707344\pi\)
0.991846 + 0.127445i \(0.0406775\pi\)
\(642\) 38.4429i 1.51722i
\(643\) −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
\(646\) 2.25725 3.90967i 0.0888103 0.153824i
\(647\) −17.9695 31.1241i −0.706455 1.22362i −0.966164 0.257929i \(-0.916960\pi\)
0.259709 0.965687i \(-0.416373\pi\)
\(648\) 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 0.814567 0.580069i \(-0.196975\pi\)
−0.909638 + 0.415401i \(0.863641\pi\)
\(654\) 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 −0.538900 0.842370i \(-0.681160\pi\)
0.998964 + 0.0455166i \(0.0144934\pi\)
\(660\) −0.601085 1.04111i −0.0233972 0.0405251i
\(661\) 14.1970 8.19662i 0.552198 0.318812i −0.197810 0.980240i \(-0.563383\pi\)
0.750008 + 0.661429i \(0.230050\pi\)
\(662\) −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 0.695347 0.718675i \(-0.255251\pi\)
−0.970064 + 0.242851i \(0.921918\pi\)
\(674\) −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 0.462732 0.886498i \(-0.346869\pi\)
−0.536364 + 0.843987i \(0.680203\pi\)
\(684\) 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 \(-0.650675\pi\)
0.542859 + 0.839824i \(0.317342\pi\)
\(692\) 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 0.983777 0.179396i \(-0.0574143\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(710\) 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 \(-0.920566\pi\)
0.698393 + 0.715715i \(0.253899\pi\)
\(720\) 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 \(-0.921223\pi\)
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 −0.379971 0.924999i \(-0.624066\pi\)
0.611087 + 0.791564i \(0.290733\pi\)
\(740\) −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 −0.999435 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
\(746\) 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 −0.981311 0.192430i \(-0.938363\pi\)
0.324006 0.946055i \(-0.394970\pi\)
\(752\) 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 0.945897 0.324466i \(-0.105185\pi\)
−0.753945 + 0.656938i \(0.771851\pi\)
\(758\) −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 \(-0.288111\pi\)
−0.372340 + 0.928097i \(0.621444\pi\)
\(762\) 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 \(-0.817391\pi\)
0.0500637 + 0.998746i \(0.484058\pi\)
\(770\) 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 \(-0.649638\pi\)
−0.998569 + 0.0534716i \(0.982971\pi\)
\(774\) 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