Properties

Label 637.2.h.m.165.6
Level $637$
Weight $2$
Character 637.165
Analytic conductor $5.086$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 8 x^{14} + 45 x^{12} + 124 x^{10} + 248 x^{8} + 250 x^{6} + 177 x^{4} + 14 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 165.6
Root \(-1.04641 - 1.81243i\) of defining polynomial
Character \(\chi\) \(=\) 637.165
Dual form 637.2.h.m.471.6

$q$-expansion

\(f(q)\) \(=\) \(q-0.579810 q^{2} +(0.946019 + 1.63855i) q^{3} -1.66382 q^{4} +(-0.736809 - 1.27619i) q^{5} +(-0.548512 - 0.950050i) q^{6} +2.12432 q^{8} +(-0.289905 + 0.502131i) q^{9} +O(q^{10})\) \(q-0.579810 q^{2} +(0.946019 + 1.63855i) q^{3} -1.66382 q^{4} +(-0.736809 - 1.27619i) q^{5} +(-0.548512 - 0.950050i) q^{6} +2.12432 q^{8} +(-0.289905 + 0.502131i) q^{9} +(0.427209 + 0.739948i) q^{10} +(-0.289905 - 0.502131i) q^{11} +(-1.57401 - 2.72626i) q^{12} +(-0.128893 - 3.60325i) q^{13} +(1.39407 - 2.41460i) q^{15} +2.09594 q^{16} -1.19657 q^{17} +(0.168090 - 0.291141i) q^{18} +(0.230479 - 0.399201i) q^{19} +(1.22592 + 2.12335i) q^{20} +(0.168090 + 0.291141i) q^{22} +2.36795 q^{23} +(2.00965 + 3.48081i) q^{24} +(1.41423 - 2.44951i) q^{25} +(0.0747335 + 2.08920i) q^{26} +4.57909 q^{27} +(3.44550 - 5.96777i) q^{29} +(-0.808297 + 1.40001i) q^{30} +(-2.22171 + 3.84811i) q^{31} -5.46389 q^{32} +(0.548512 - 0.950050i) q^{33} +0.693783 q^{34} +(0.482350 - 0.835455i) q^{36} +9.16301 q^{37} +(-0.133634 + 0.231461i) q^{38} +(5.78218 - 3.61994i) q^{39} +(-1.56522 - 2.71104i) q^{40} +(2.00845 - 3.47874i) q^{41} +(-4.02951 - 6.97931i) q^{43} +(0.482350 + 0.835455i) q^{44} +0.854419 q^{45} -1.37296 q^{46} +(5.75964 + 9.97598i) q^{47} +(1.98280 + 3.43430i) q^{48} +(-0.819983 + 1.42025i) q^{50} +(-1.13198 - 1.96064i) q^{51} +(0.214455 + 5.99515i) q^{52} +(4.69760 - 8.13647i) q^{53} -2.65501 q^{54} +(-0.427209 + 0.739948i) q^{55} +0.872150 q^{57} +(-1.99773 + 3.46018i) q^{58} +0.240919 q^{59} +(-2.31948 + 4.01746i) q^{60} +(-3.86355 + 6.69187i) q^{61} +(1.28817 - 2.23118i) q^{62} -1.02385 q^{64} +(-4.50346 + 2.81940i) q^{65} +(-0.318033 + 0.550849i) q^{66} +(0.724287 + 1.25450i) q^{67} +1.99088 q^{68} +(2.24013 + 3.88001i) q^{69} +(6.25725 + 10.8379i) q^{71} +(-0.615852 + 1.06669i) q^{72} +(1.84701 - 3.19911i) q^{73} -5.31281 q^{74} +5.35154 q^{75} +(-0.383476 + 0.664199i) q^{76} +(-3.35257 + 2.09888i) q^{78} +(-8.03967 - 13.9251i) q^{79} +(-1.54430 - 2.67481i) q^{80} +(5.20163 + 9.00948i) q^{81} +(-1.16452 + 2.01701i) q^{82} -15.4005 q^{83} +(0.881643 + 1.52705i) q^{85} +(2.33635 + 4.04668i) q^{86} +13.0380 q^{87} +(-0.615852 - 1.06669i) q^{88} +2.49107 q^{89} -0.495401 q^{90} -3.93984 q^{92} -8.40712 q^{93} +(-3.33950 - 5.78418i) q^{94} -0.679276 q^{95} +(-5.16894 - 8.95287i) q^{96} +(-7.82275 - 13.5494i) q^{97} +0.336180 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 8q^{2} + 24q^{4} + 24q^{8} - 4q^{9} + O(q^{10}) \) \( 16q - 8q^{2} + 24q^{4} + 24q^{8} - 4q^{9} - 4q^{11} - 8q^{15} + 8q^{16} + 28q^{18} + 28q^{22} - 24q^{23} + 12q^{25} + 8q^{29} + 28q^{30} + 4q^{36} + 16q^{37} + 20q^{39} + 32q^{43} + 4q^{44} + 8q^{46} + 36q^{50} + 44q^{51} + 4q^{53} - 96q^{57} - 48q^{58} - 64q^{60} - 64q^{64} - 68q^{65} + 20q^{67} + 8q^{71} + 28q^{72} - 152q^{74} + 28q^{78} + 4q^{79} + 56q^{81} + 36q^{85} - 4q^{86} + 28q^{88} - 160q^{92} - 16q^{93} - 104q^{95} + 56q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.579810 −0.409988 −0.204994 0.978763i \(-0.565717\pi\)
−0.204994 + 0.978763i \(0.565717\pi\)
\(3\) 0.946019 + 1.63855i 0.546185 + 0.946019i 0.998531 + 0.0541772i \(0.0172536\pi\)
−0.452347 + 0.891842i \(0.649413\pi\)
\(4\) −1.66382 −0.831910
\(5\) −0.736809 1.27619i −0.329511 0.570729i 0.652904 0.757441i \(-0.273550\pi\)
−0.982415 + 0.186711i \(0.940217\pi\)
\(6\) −0.548512 0.950050i −0.223929 0.387856i
\(7\) 0 0
\(8\) 2.12432 0.751061
\(9\) −0.289905 + 0.502131i −0.0966351 + 0.167377i
\(10\) 0.427209 + 0.739948i 0.135095 + 0.233992i
\(11\) −0.289905 0.502131i −0.0874097 0.151398i 0.819006 0.573785i \(-0.194526\pi\)
−0.906415 + 0.422387i \(0.861192\pi\)
\(12\) −1.57401 2.72626i −0.454376 0.787003i
\(13\) −0.128893 3.60325i −0.0357485 0.999361i
\(14\) 0 0
\(15\) 1.39407 2.41460i 0.359947 0.623447i
\(16\) 2.09594 0.523984
\(17\) −1.19657 −0.290211 −0.145105 0.989416i \(-0.546352\pi\)
−0.145105 + 0.989416i \(0.546352\pi\)
\(18\) 0.168090 0.291141i 0.0396192 0.0686225i
\(19\) 0.230479 0.399201i 0.0528755 0.0915831i −0.838376 0.545092i \(-0.816495\pi\)
0.891252 + 0.453509i \(0.149828\pi\)
\(20\) 1.22592 + 2.12335i 0.274123 + 0.474796i
\(21\) 0 0
\(22\) 0.168090 + 0.291141i 0.0358369 + 0.0620714i
\(23\) 2.36795 0.493752 0.246876 0.969047i \(-0.420596\pi\)
0.246876 + 0.969047i \(0.420596\pi\)
\(24\) 2.00965 + 3.48081i 0.410218 + 0.710518i
\(25\) 1.41423 2.44951i 0.282845 0.489902i
\(26\) 0.0747335 + 2.08920i 0.0146565 + 0.409726i
\(27\) 4.57909 0.881247
\(28\) 0 0
\(29\) 3.44550 5.96777i 0.639813 1.10819i −0.345661 0.938359i \(-0.612345\pi\)
0.985474 0.169828i \(-0.0543214\pi\)
\(30\) −0.808297 + 1.40001i −0.147574 + 0.255606i
\(31\) −2.22171 + 3.84811i −0.399031 + 0.691141i −0.993607 0.112898i \(-0.963987\pi\)
0.594576 + 0.804040i \(0.297320\pi\)
\(32\) −5.46389 −0.965888
\(33\) 0.548512 0.950050i 0.0954837 0.165383i
\(34\) 0.693783 0.118983
\(35\) 0 0
\(36\) 0.482350 0.835455i 0.0803917 0.139242i
\(37\) 9.16301 1.50639 0.753195 0.657798i \(-0.228512\pi\)
0.753195 + 0.657798i \(0.228512\pi\)
\(38\) −0.133634 + 0.231461i −0.0216783 + 0.0375479i
\(39\) 5.78218 3.61994i 0.925889 0.579654i
\(40\) −1.56522 2.71104i −0.247483 0.428653i
\(41\) 2.00845 3.47874i 0.313667 0.543288i −0.665486 0.746410i \(-0.731776\pi\)
0.979153 + 0.203123i \(0.0651090\pi\)
\(42\) 0 0
\(43\) −4.02951 6.97931i −0.614494 1.06433i −0.990473 0.137706i \(-0.956027\pi\)
0.375979 0.926628i \(-0.377306\pi\)
\(44\) 0.482350 + 0.835455i 0.0727170 + 0.125950i
\(45\) 0.854419 0.127369
\(46\) −1.37296 −0.202432
\(47\) 5.75964 + 9.97598i 0.840129 + 1.45515i 0.889785 + 0.456381i \(0.150854\pi\)
−0.0496552 + 0.998766i \(0.515812\pi\)
\(48\) 1.98280 + 3.43430i 0.286192 + 0.495699i
\(49\) 0 0
\(50\) −0.819983 + 1.42025i −0.115963 + 0.200854i
\(51\) −1.13198 1.96064i −0.158509 0.274545i
\(52\) 0.214455 + 5.99515i 0.0297395 + 0.831378i
\(53\) 4.69760 8.13647i 0.645264 1.11763i −0.338976 0.940795i \(-0.610081\pi\)
0.984240 0.176836i \(-0.0565861\pi\)
\(54\) −2.65501 −0.361300
\(55\) −0.427209 + 0.739948i −0.0576049 + 0.0997746i
\(56\) 0 0
\(57\) 0.872150 0.115519
\(58\) −1.99773 + 3.46018i −0.262315 + 0.454344i
\(59\) 0.240919 0.0313650 0.0156825 0.999877i \(-0.495008\pi\)
0.0156825 + 0.999877i \(0.495008\pi\)
\(60\) −2.31948 + 4.01746i −0.299444 + 0.518652i
\(61\) −3.86355 + 6.69187i −0.494677 + 0.856806i −0.999981 0.00613544i \(-0.998047\pi\)
0.505304 + 0.862941i \(0.331380\pi\)
\(62\) 1.28817 2.23118i 0.163598 0.283360i
\(63\) 0 0
\(64\) −1.02385 −0.127982
\(65\) −4.50346 + 2.81940i −0.558585 + 0.349703i
\(66\) −0.318033 + 0.550849i −0.0391471 + 0.0678048i
\(67\) 0.724287 + 1.25450i 0.0884857 + 0.153262i 0.906871 0.421408i \(-0.138464\pi\)
−0.818385 + 0.574670i \(0.805131\pi\)
\(68\) 1.99088 0.241429
\(69\) 2.24013 + 3.88001i 0.269680 + 0.467099i
\(70\) 0 0
\(71\) 6.25725 + 10.8379i 0.742599 + 1.28622i 0.951308 + 0.308241i \(0.0997405\pi\)
−0.208709 + 0.977978i \(0.566926\pi\)
\(72\) −0.615852 + 1.06669i −0.0725788 + 0.125710i
\(73\) 1.84701 3.19911i 0.216176 0.374427i −0.737460 0.675391i \(-0.763975\pi\)
0.953636 + 0.300963i \(0.0973082\pi\)
\(74\) −5.31281 −0.617601
\(75\) 5.35154 0.617943
\(76\) −0.383476 + 0.664199i −0.0439877 + 0.0761889i
\(77\) 0 0
\(78\) −3.35257 + 2.09888i −0.379603 + 0.237651i
\(79\) −8.03967 13.9251i −0.904533 1.56670i −0.821542 0.570147i \(-0.806886\pi\)
−0.0829909 0.996550i \(-0.526447\pi\)
\(80\) −1.54430 2.67481i −0.172658 0.299053i
\(81\) 5.20163 + 9.00948i 0.577958 + 1.00105i
\(82\) −1.16452 + 2.01701i −0.128600 + 0.222741i
\(83\) −15.4005 −1.69042 −0.845212 0.534431i \(-0.820526\pi\)
−0.845212 + 0.534431i \(0.820526\pi\)
\(84\) 0 0
\(85\) 0.881643 + 1.52705i 0.0956276 + 0.165632i
\(86\) 2.33635 + 4.04668i 0.251935 + 0.436364i
\(87\) 13.0380 1.39782
\(88\) −0.615852 1.06669i −0.0656500 0.113709i
\(89\) 2.49107 0.264052 0.132026 0.991246i \(-0.457852\pi\)
0.132026 + 0.991246i \(0.457852\pi\)
\(90\) −0.495401 −0.0522198
\(91\) 0 0
\(92\) −3.93984 −0.410757
\(93\) −8.40712 −0.871778
\(94\) −3.33950 5.78418i −0.344443 0.596593i
\(95\) −0.679276 −0.0696922
\(96\) −5.16894 8.95287i −0.527553 0.913749i
\(97\) −7.82275 13.5494i −0.794280 1.37573i −0.923295 0.384091i \(-0.874515\pi\)
0.129015 0.991643i \(-0.458818\pi\)
\(98\) 0 0
\(99\) 0.336180 0.0337874
\(100\) −2.35302 + 4.07555i −0.235302 + 0.407555i
\(101\) −7.00682 12.1362i −0.697205 1.20759i −0.969432 0.245361i \(-0.921093\pi\)
0.272227 0.962233i \(-0.412240\pi\)
\(102\) 0.656332 + 1.13680i 0.0649866 + 0.112560i
\(103\) −5.37461 9.30910i −0.529576 0.917253i −0.999405 0.0344951i \(-0.989018\pi\)
0.469829 0.882758i \(-0.344316\pi\)
\(104\) −0.273810 7.65445i −0.0268493 0.750581i
\(105\) 0 0
\(106\) −2.72371 + 4.71761i −0.264551 + 0.458215i
\(107\) 3.75523 0.363031 0.181516 0.983388i \(-0.441900\pi\)
0.181516 + 0.983388i \(0.441900\pi\)
\(108\) −7.61878 −0.733118
\(109\) 4.10417 7.10862i 0.393108 0.680883i −0.599750 0.800187i \(-0.704733\pi\)
0.992858 + 0.119305i \(0.0380666\pi\)
\(110\) 0.247700 0.429030i 0.0236173 0.0409064i
\(111\) 8.66838 + 15.0141i 0.822766 + 1.42507i
\(112\) 0 0
\(113\) 3.90423 + 6.76233i 0.367279 + 0.636146i 0.989139 0.146982i \(-0.0469560\pi\)
−0.621860 + 0.783129i \(0.713623\pi\)
\(114\) −0.505682 −0.0473614
\(115\) −1.74473 3.02196i −0.162697 0.281799i
\(116\) −5.73269 + 9.92930i −0.532266 + 0.921913i
\(117\) 1.84667 + 0.979879i 0.170724 + 0.0905898i
\(118\) −0.139687 −0.0128593
\(119\) 0 0
\(120\) 2.96145 5.12939i 0.270342 0.468247i
\(121\) 5.33191 9.23514i 0.484719 0.839558i
\(122\) 2.24013 3.88001i 0.202812 0.351280i
\(123\) 7.60014 0.685281
\(124\) 3.69652 6.40257i 0.331958 0.574967i
\(125\) −11.5361 −1.03182
\(126\) 0 0
\(127\) 0.469682 0.813513i 0.0416775 0.0721876i −0.844434 0.535659i \(-0.820063\pi\)
0.886112 + 0.463472i \(0.153396\pi\)
\(128\) 11.5214 1.01836
\(129\) 7.62398 13.2051i 0.671254 1.16265i
\(130\) 2.61115 1.63471i 0.229013 0.143374i
\(131\) 0.568583 + 0.984814i 0.0496773 + 0.0860436i 0.889795 0.456361i \(-0.150847\pi\)
−0.840117 + 0.542404i \(0.817514\pi\)
\(132\) −0.912625 + 1.58071i −0.0794338 + 0.137583i
\(133\) 0 0
\(134\) −0.419949 0.727373i −0.0362781 0.0628355i
\(135\) −3.37391 5.84379i −0.290380 0.502954i
\(136\) −2.54190 −0.217966
\(137\) −8.63997 −0.738162 −0.369081 0.929397i \(-0.620328\pi\)
−0.369081 + 0.929397i \(0.620328\pi\)
\(138\) −1.29885 2.24967i −0.110565 0.191505i
\(139\) 7.27709 + 12.6043i 0.617235 + 1.06908i 0.989988 + 0.141151i \(0.0450804\pi\)
−0.372753 + 0.927930i \(0.621586\pi\)
\(140\) 0 0
\(141\) −10.8975 + 18.8749i −0.917731 + 1.58956i
\(142\) −3.62802 6.28391i −0.304457 0.527334i
\(143\) −1.77193 + 1.10932i −0.148177 + 0.0927661i
\(144\) −0.607623 + 1.05243i −0.0506352 + 0.0877028i
\(145\) −10.1547 −0.843301
\(146\) −1.07091 + 1.85488i −0.0886295 + 0.153511i
\(147\) 0 0
\(148\) −15.2456 −1.25318
\(149\) −6.69011 + 11.5876i −0.548075 + 0.949294i 0.450331 + 0.892861i \(0.351306\pi\)
−0.998406 + 0.0564323i \(0.982027\pi\)
\(150\) −3.10288 −0.253349
\(151\) −8.06958 + 13.9769i −0.656693 + 1.13743i 0.324774 + 0.945792i \(0.394712\pi\)
−0.981467 + 0.191634i \(0.938621\pi\)
\(152\) 0.489611 0.848032i 0.0397127 0.0687845i
\(153\) 0.346892 0.600834i 0.0280445 0.0485745i
\(154\) 0 0
\(155\) 6.54790 0.525940
\(156\) −9.62050 + 6.02293i −0.770257 + 0.482220i
\(157\) 0.314340 0.544453i 0.0250871 0.0434521i −0.853209 0.521569i \(-0.825347\pi\)
0.878296 + 0.478117i \(0.158680\pi\)
\(158\) 4.66148 + 8.07393i 0.370848 + 0.642327i
\(159\) 17.7761 1.40973
\(160\) 4.02584 + 6.97296i 0.318271 + 0.551261i
\(161\) 0 0
\(162\) −3.01596 5.22379i −0.236956 0.410420i
\(163\) 5.84207 10.1188i 0.457586 0.792563i −0.541246 0.840864i \(-0.682047\pi\)
0.998833 + 0.0483011i \(0.0153807\pi\)
\(164\) −3.34170 + 5.78800i −0.260943 + 0.451967i
\(165\) −1.61659 −0.125852
\(166\) 8.92937 0.693054
\(167\) −11.0293 + 19.1033i −0.853474 + 1.47826i 0.0245803 + 0.999698i \(0.492175\pi\)
−0.878054 + 0.478562i \(0.841158\pi\)
\(168\) 0 0
\(169\) −12.9668 + 0.928867i −0.997444 + 0.0714513i
\(170\) −0.511186 0.885399i −0.0392061 0.0679070i
\(171\) 0.133634 + 0.231461i 0.0102193 + 0.0177003i
\(172\) 6.70437 + 11.6123i 0.511204 + 0.885431i
\(173\) −5.69534 + 9.86463i −0.433009 + 0.749994i −0.997131 0.0756980i \(-0.975881\pi\)
0.564122 + 0.825692i \(0.309215\pi\)
\(174\) −7.55958 −0.573090
\(175\) 0 0
\(176\) −0.607623 1.05243i −0.0458013 0.0793302i
\(177\) 0.227914 + 0.394759i 0.0171311 + 0.0296719i
\(178\) −1.44435 −0.108258
\(179\) 1.73621 + 3.00721i 0.129771 + 0.224769i 0.923588 0.383387i \(-0.125243\pi\)
−0.793817 + 0.608157i \(0.791909\pi\)
\(180\) −1.42160 −0.105960
\(181\) 21.0992 1.56829 0.784145 0.620578i \(-0.213102\pi\)
0.784145 + 0.620578i \(0.213102\pi\)
\(182\) 0 0
\(183\) −14.6200 −1.08074
\(184\) 5.03029 0.370838
\(185\) −6.75138 11.6937i −0.496372 0.859741i
\(186\) 4.87453 0.357418
\(187\) 0.346892 + 0.600834i 0.0253672 + 0.0439373i
\(188\) −9.58300 16.5982i −0.698912 1.21055i
\(189\) 0 0
\(190\) 0.393851 0.0285730
\(191\) −5.95945 + 10.3221i −0.431211 + 0.746879i −0.996978 0.0776864i \(-0.975247\pi\)
0.565767 + 0.824565i \(0.308580\pi\)
\(192\) −0.968585 1.67764i −0.0699016 0.121073i
\(193\) −7.18970 12.4529i −0.517526 0.896381i −0.999793 0.0203567i \(-0.993520\pi\)
0.482267 0.876024i \(-0.339814\pi\)
\(194\) 4.53571 + 7.85608i 0.325645 + 0.564034i
\(195\) −8.88009 4.71195i −0.635916 0.337430i
\(196\) 0 0
\(197\) −3.48462 + 6.03553i −0.248269 + 0.430014i −0.963046 0.269339i \(-0.913195\pi\)
0.714777 + 0.699353i \(0.246528\pi\)
\(198\) −0.194921 −0.0138524
\(199\) 3.57352 0.253320 0.126660 0.991946i \(-0.459574\pi\)
0.126660 + 0.991946i \(0.459574\pi\)
\(200\) 3.00427 5.20355i 0.212434 0.367946i
\(201\) −1.37038 + 2.37357i −0.0966591 + 0.167418i
\(202\) 4.06263 + 7.03668i 0.285846 + 0.495099i
\(203\) 0 0
\(204\) 1.88341 + 3.26216i 0.131865 + 0.228397i
\(205\) −5.91938 −0.413427
\(206\) 3.11626 + 5.39751i 0.217120 + 0.376062i
\(207\) −0.686481 + 1.18902i −0.0477138 + 0.0826426i
\(208\) −0.270152 7.55218i −0.0187316 0.523649i
\(209\) −0.267268 −0.0184873
\(210\) 0 0
\(211\) 7.05694 12.2230i 0.485820 0.841464i −0.514048 0.857762i \(-0.671855\pi\)
0.999867 + 0.0162974i \(0.00518784\pi\)
\(212\) −7.81595 + 13.5376i −0.536802 + 0.929768i
\(213\) −11.8390 + 20.5057i −0.811192 + 1.40503i
\(214\) −2.17732 −0.148838
\(215\) −5.93795 + 10.2848i −0.404965 + 0.701420i
\(216\) 9.72746 0.661870
\(217\) 0 0
\(218\) −2.37964 + 4.12165i −0.161169 + 0.279154i
\(219\) 6.98922 0.472288
\(220\) 0.710799 1.23114i 0.0479221 0.0830035i
\(221\) 0.154229 + 4.31153i 0.0103746 + 0.290025i
\(222\) −5.02602 8.70532i −0.337324 0.584263i
\(223\) 0.454565 0.787329i 0.0304399 0.0527235i −0.850404 0.526130i \(-0.823643\pi\)
0.880844 + 0.473407i \(0.156976\pi\)
\(224\) 0 0
\(225\) 0.819983 + 1.42025i 0.0546655 + 0.0946835i
\(226\) −2.26371 3.92087i −0.150580 0.260812i
\(227\) −2.33512 −0.154988 −0.0774938 0.996993i \(-0.524692\pi\)
−0.0774938 + 0.996993i \(0.524692\pi\)
\(228\) −1.45110 −0.0961015
\(229\) 8.34036 + 14.4459i 0.551147 + 0.954614i 0.998192 + 0.0601030i \(0.0191429\pi\)
−0.447045 + 0.894511i \(0.647524\pi\)
\(230\) 1.01161 + 1.75216i 0.0667036 + 0.115534i
\(231\) 0 0
\(232\) 7.31934 12.6775i 0.480538 0.832317i
\(233\) 8.26321 + 14.3123i 0.541341 + 0.937630i 0.998827 + 0.0484137i \(0.0154166\pi\)
−0.457486 + 0.889217i \(0.651250\pi\)
\(234\) −1.07072 0.568144i −0.0699949 0.0371407i
\(235\) 8.48750 14.7008i 0.553664 0.958973i
\(236\) −0.400846 −0.0260928
\(237\) 15.2114 26.3469i 0.988084 1.71141i
\(238\) 0 0
\(239\) 3.18043 0.205725 0.102862 0.994696i \(-0.467200\pi\)
0.102862 + 0.994696i \(0.467200\pi\)
\(240\) 2.92188 5.06085i 0.188607 0.326676i
\(241\) 15.8598 1.02162 0.510811 0.859693i \(-0.329345\pi\)
0.510811 + 0.859693i \(0.329345\pi\)
\(242\) −3.09150 + 5.35463i −0.198729 + 0.344209i
\(243\) −2.97304 + 5.14945i −0.190720 + 0.330338i
\(244\) 6.42825 11.1341i 0.411527 0.712785i
\(245\) 0 0
\(246\) −4.40664 −0.280957
\(247\) −1.46813 0.779018i −0.0934147 0.0495677i
\(248\) −4.71962 + 8.17463i −0.299696 + 0.519089i
\(249\) −14.5692 25.2345i −0.923284 1.59917i
\(250\) 6.68878 0.423035
\(251\) 1.24788 + 2.16139i 0.0787654 + 0.136426i 0.902718 0.430234i \(-0.141569\pi\)
−0.823952 + 0.566659i \(0.808236\pi\)
\(252\) 0 0
\(253\) −0.686481 1.18902i −0.0431587 0.0747531i
\(254\) −0.272326 + 0.471683i −0.0170873 + 0.0295960i
\(255\) −1.66810 + 2.88924i −0.104461 + 0.180931i
\(256\) −4.63253 −0.289533
\(257\) −10.5204 −0.656245 −0.328123 0.944635i \(-0.606416\pi\)
−0.328123 + 0.944635i \(0.606416\pi\)
\(258\) −4.42046 + 7.65647i −0.275206 + 0.476671i
\(259\) 0 0
\(260\) 7.49294 4.69097i 0.464693 0.290921i
\(261\) 1.99773 + 3.46018i 0.123657 + 0.214180i
\(262\) −0.329670 0.571006i −0.0203671 0.0352768i
\(263\) 15.6749 + 27.1498i 0.966558 + 1.67413i 0.705370 + 0.708839i \(0.250781\pi\)
0.261188 + 0.965288i \(0.415886\pi\)
\(264\) 1.16522 2.01821i 0.0717140 0.124212i
\(265\) −13.8449 −0.850486
\(266\) 0 0
\(267\) 2.35660 + 4.08174i 0.144221 + 0.249799i
\(268\) −1.20508 2.08727i −0.0736122 0.127500i
\(269\) 21.1265 1.28811 0.644054 0.764980i \(-0.277251\pi\)
0.644054 + 0.764980i \(0.277251\pi\)
\(270\) 1.95623 + 3.38829i 0.119052 + 0.206205i
\(271\) −6.52007 −0.396066 −0.198033 0.980195i \(-0.563455\pi\)
−0.198033 + 0.980195i \(0.563455\pi\)
\(272\) −2.50793 −0.152066
\(273\) 0 0
\(274\) 5.00954 0.302638
\(275\) −1.63997 −0.0988937
\(276\) −3.72717 6.45565i −0.224349 0.388584i
\(277\) −14.5310 −0.873081 −0.436540 0.899685i \(-0.643796\pi\)
−0.436540 + 0.899685i \(0.643796\pi\)
\(278\) −4.21933 7.30810i −0.253059 0.438311i
\(279\) −1.28817 2.23118i −0.0771207 0.133577i
\(280\) 0 0
\(281\) 27.1832 1.62161 0.810807 0.585314i \(-0.199029\pi\)
0.810807 + 0.585314i \(0.199029\pi\)
\(282\) 6.31846 10.9439i 0.376259 0.651699i
\(283\) 4.28791 + 7.42688i 0.254890 + 0.441482i 0.964866 0.262744i \(-0.0846274\pi\)
−0.709976 + 0.704226i \(0.751294\pi\)
\(284\) −10.4109 18.0323i −0.617775 1.07002i
\(285\) −0.642608 1.11303i −0.0380648 0.0659302i
\(286\) 1.02739 0.643196i 0.0607506 0.0380330i
\(287\) 0 0
\(288\) 1.58401 2.74358i 0.0933387 0.161667i
\(289\) −15.5682 −0.915778
\(290\) 5.88779 0.345743
\(291\) 14.8009 25.6360i 0.867647 1.50281i
\(292\) −3.07309 + 5.32274i −0.179839 + 0.311490i
\(293\) −5.24356 9.08212i −0.306332 0.530583i 0.671225 0.741254i \(-0.265768\pi\)
−0.977557 + 0.210671i \(0.932435\pi\)
\(294\) 0 0
\(295\) −0.177511 0.307458i −0.0103351 0.0179009i
\(296\) 19.4652 1.13139
\(297\) −1.32750 2.29930i −0.0770295 0.133419i
\(298\) 3.87899 6.71862i 0.224704 0.389199i
\(299\) −0.305213 8.53231i −0.0176509 0.493436i
\(300\) −8.90400 −0.514073
\(301\) 0 0
\(302\) 4.67882 8.10396i 0.269236 0.466331i
\(303\) 13.2572 22.9621i 0.761605 1.31914i
\(304\) 0.483069 0.836701i 0.0277059 0.0479881i
\(305\) 11.3868 0.652006
\(306\) −0.201131 + 0.348370i −0.0114979 + 0.0199150i
\(307\) 19.1751 1.09438 0.547190 0.837008i \(-0.315697\pi\)
0.547190 + 0.837008i \(0.315697\pi\)
\(308\) 0 0
\(309\) 10.1690 17.6132i 0.578493 1.00198i
\(310\) −3.79654 −0.215629
\(311\) −1.74427 + 3.02117i −0.0989086 + 0.171315i −0.911233 0.411891i \(-0.864868\pi\)
0.812325 + 0.583206i \(0.198202\pi\)
\(312\) 12.2832 7.68991i 0.695399 0.435356i
\(313\) −10.1607 17.5989i −0.574318 0.994748i −0.996115 0.0880579i \(-0.971934\pi\)
0.421797 0.906690i \(-0.361399\pi\)
\(314\) −0.182258 + 0.315680i −0.0102854 + 0.0178148i
\(315\) 0 0
\(316\) 13.3766 + 23.1689i 0.752490 + 1.30335i
\(317\) 13.9110 + 24.0946i 0.781320 + 1.35329i 0.931173 + 0.364578i \(0.118787\pi\)
−0.149853 + 0.988708i \(0.547880\pi\)
\(318\) −10.3067 −0.577974
\(319\) −3.99547 −0.223703
\(320\) 0.754384 + 1.30663i 0.0421714 + 0.0730429i
\(321\) 3.55252 + 6.15314i 0.198282 + 0.343435i
\(322\) 0 0
\(323\) −0.275784 + 0.477672i −0.0153450 + 0.0265784i
\(324\) −8.65457 14.9902i −0.480809 0.832786i
\(325\) −9.00848 4.78008i −0.499700 0.265151i
\(326\) −3.38729 + 5.86697i −0.187605 + 0.324941i
\(327\) 15.5305 0.858837
\(328\) 4.26660 7.38996i 0.235583 0.408042i
\(329\) 0 0
\(330\) 0.937318 0.0515976
\(331\) 4.67148 8.09123i 0.256768 0.444734i −0.708607 0.705604i \(-0.750676\pi\)
0.965374 + 0.260869i \(0.0840092\pi\)
\(332\) 25.6237 1.40628
\(333\) −2.65640 + 4.60103i −0.145570 + 0.252135i
\(334\) 6.39491 11.0763i 0.349914 0.606069i
\(335\) 1.06732 1.84866i 0.0583140 0.101003i
\(336\) 0 0
\(337\) 22.9182 1.24844 0.624218 0.781250i \(-0.285418\pi\)
0.624218 + 0.781250i \(0.285418\pi\)
\(338\) 7.51827 0.538567i 0.408940 0.0292942i
\(339\) −7.38696 + 12.7946i −0.401205 + 0.694907i
\(340\) −1.46689 2.54074i −0.0795535 0.137791i
\(341\) 2.57634 0.139517
\(342\) −0.0774824 0.134204i −0.00418977 0.00725690i
\(343\) 0 0
\(344\) −8.55996 14.8263i −0.461522 0.799380i
\(345\) 3.30109 5.71766i 0.177725 0.307828i
\(346\) 3.30222 5.71961i 0.177528 0.307488i
\(347\) −26.6711 −1.43178 −0.715889 0.698214i \(-0.753978\pi\)
−0.715889 + 0.698214i \(0.753978\pi\)
\(348\) −21.6929 −1.16286
\(349\) −7.61723 + 13.1934i −0.407741 + 0.706228i −0.994636 0.103435i \(-0.967017\pi\)
0.586895 + 0.809663i \(0.300350\pi\)
\(350\) 0 0
\(351\) −0.590213 16.4996i −0.0315033 0.880683i
\(352\) 1.58401 + 2.74358i 0.0844280 + 0.146234i
\(353\) 11.2044 + 19.4066i 0.596352 + 1.03291i 0.993355 + 0.115094i \(0.0367170\pi\)
−0.397003 + 0.917817i \(0.629950\pi\)
\(354\) −0.132147 0.228885i −0.00702353 0.0121651i
\(355\) 9.22079 15.9709i 0.489389 0.847646i
\(356\) −4.14468 −0.219668
\(357\) 0 0
\(358\) −1.00667 1.74361i −0.0532044 0.0921528i
\(359\) −8.01927 13.8898i −0.423241 0.733075i 0.573013 0.819546i \(-0.305774\pi\)
−0.996254 + 0.0864711i \(0.972441\pi\)
\(360\) 1.81506 0.0956620
\(361\) 9.39376 + 16.2705i 0.494408 + 0.856340i
\(362\) −12.2335 −0.642980
\(363\) 20.1764 1.05898
\(364\) 0 0
\(365\) −5.44356 −0.284929
\(366\) 8.47682 0.443090
\(367\) 3.45002 + 5.97561i 0.180090 + 0.311924i 0.941911 0.335863i \(-0.109028\pi\)
−0.761821 + 0.647787i \(0.775695\pi\)
\(368\) 4.96308 0.258718
\(369\) 1.16452 + 2.01701i 0.0606225 + 0.105001i
\(370\) 3.91452 + 6.78015i 0.203506 + 0.352483i
\(371\) 0 0
\(372\) 13.9879 0.725240
\(373\) −3.84264 + 6.65566i −0.198965 + 0.344617i −0.948193 0.317695i \(-0.897091\pi\)
0.749228 + 0.662312i \(0.230425\pi\)
\(374\) −0.201131 0.348370i −0.0104003 0.0180138i
\(375\) −10.9134 18.9026i −0.563566 0.976125i
\(376\) 12.2353 + 21.1922i 0.630988 + 1.09290i
\(377\) −21.9475 11.6458i −1.13035 0.599788i
\(378\) 0 0
\(379\) 12.5817 21.7922i 0.646281 1.11939i −0.337723 0.941245i \(-0.609657\pi\)
0.984004 0.178146i \(-0.0570098\pi\)
\(380\) 1.13019 0.0579776
\(381\) 1.77731 0.0910545
\(382\) 3.45535 5.98484i 0.176791 0.306211i
\(383\) 11.0218 19.0904i 0.563189 0.975473i −0.434026 0.900900i \(-0.642907\pi\)
0.997216 0.0745724i \(-0.0237592\pi\)
\(384\) 10.8995 + 18.8785i 0.556212 + 0.963387i
\(385\) 0 0
\(386\) 4.16866 + 7.22033i 0.212179 + 0.367505i
\(387\) 4.67270 0.237527
\(388\) 13.0156 + 22.5438i 0.660769 + 1.14449i
\(389\) 5.49058 9.50996i 0.278383 0.482174i −0.692600 0.721322i \(-0.743535\pi\)
0.970983 + 0.239148i \(0.0768681\pi\)
\(390\) 5.14877 + 2.73204i 0.260718 + 0.138342i
\(391\) −2.83342 −0.143292
\(392\) 0 0
\(393\) −1.07578 + 1.86331i −0.0542660 + 0.0939914i
\(394\) 2.02042 3.49946i 0.101787 0.176300i
\(395\) −11.8474 + 20.5203i −0.596107 + 1.03249i
\(396\) −0.559343 −0.0281081
\(397\) −12.5382 + 21.7168i −0.629275 + 1.08994i 0.358423 + 0.933559i \(0.383315\pi\)
−0.987698 + 0.156377i \(0.950019\pi\)
\(398\) −2.07196 −0.103858
\(399\) 0 0
\(400\) 2.96413 5.13402i 0.148206 0.256701i
\(401\) −22.6601 −1.13159 −0.565797 0.824545i \(-0.691431\pi\)
−0.565797 + 0.824545i \(0.691431\pi\)
\(402\) 0.794560 1.37622i 0.0396291 0.0686395i
\(403\) 14.1521 + 7.50937i 0.704964 + 0.374068i
\(404\) 11.6581 + 20.1924i 0.580012 + 1.00461i
\(405\) 7.66521 13.2765i 0.380887 0.659716i
\(406\) 0 0
\(407\) −2.65640 4.60103i −0.131673 0.228064i
\(408\) −2.40468 4.16503i −0.119050 0.206200i
\(409\) −17.1465 −0.847839 −0.423919 0.905700i \(-0.639346\pi\)
−0.423919 + 0.905700i \(0.639346\pi\)
\(410\) 3.43212 0.169500
\(411\) −8.17358 14.1570i −0.403173 0.698316i
\(412\) 8.94238 + 15.4887i 0.440560 + 0.763072i
\(413\) 0 0
\(414\) 0.398029 0.689407i 0.0195621 0.0338825i
\(415\) 11.3472 + 19.6540i 0.557013 + 0.964775i
\(416\) 0.704257 + 19.6877i 0.0345291 + 0.965271i
\(417\) −13.7685 + 23.8478i −0.674248 + 1.16783i
\(418\) 0.154965 0.00757958
\(419\) 16.9902 29.4279i 0.830027 1.43765i −0.0679891 0.997686i \(-0.521658\pi\)
0.898016 0.439963i \(-0.145008\pi\)
\(420\) 0 0
\(421\) −32.3623 −1.57724 −0.788621 0.614879i \(-0.789205\pi\)
−0.788621 + 0.614879i \(0.789205\pi\)
\(422\) −4.09169 + 7.08701i −0.199180 + 0.344990i
\(423\) −6.67900 −0.324744
\(424\) 9.97920 17.2845i 0.484633 0.839409i
\(425\) −1.69222 + 2.93101i −0.0820847 + 0.142175i
\(426\) 6.86435 11.8894i 0.332579 0.576044i
\(427\) 0 0
\(428\) −6.24802 −0.302009
\(429\) −3.49397 1.85397i −0.168690 0.0895104i
\(430\) 3.44288 5.96325i 0.166031 0.287574i
\(431\) 9.45640 + 16.3790i 0.455499 + 0.788947i 0.998717 0.0506447i \(-0.0161276\pi\)
−0.543218 + 0.839592i \(0.682794\pi\)
\(432\) 9.59749 0.461759
\(433\) −9.57006 16.5758i −0.459908 0.796584i 0.539048 0.842275i \(-0.318784\pi\)
−0.998956 + 0.0456914i \(0.985451\pi\)
\(434\) 0 0
\(435\) −9.60653 16.6390i −0.460598 0.797779i
\(436\) −6.82859 + 11.8275i −0.327030 + 0.566433i
\(437\) 0.545763 0.945289i 0.0261074 0.0452193i
\(438\) −4.05242 −0.193632
\(439\) 9.60289 0.458321 0.229160 0.973389i \(-0.426402\pi\)
0.229160 + 0.973389i \(0.426402\pi\)
\(440\) −0.907530 + 1.57189i −0.0432648 + 0.0749368i
\(441\) 0 0
\(442\) −0.0894239 2.49987i −0.00425346 0.118907i
\(443\) 20.1998 + 34.9871i 0.959721 + 1.66229i 0.723175 + 0.690665i \(0.242682\pi\)
0.236546 + 0.971620i \(0.423984\pi\)
\(444\) −14.4226 24.9807i −0.684468 1.18553i
\(445\) −1.83544 3.17907i −0.0870081 0.150703i
\(446\) −0.263561 + 0.456502i −0.0124800 + 0.0216160i
\(447\) −25.3159 −1.19740
\(448\) 0 0
\(449\) 13.3112 + 23.0556i 0.628194 + 1.08806i 0.987914 + 0.155003i \(0.0495387\pi\)
−0.359720 + 0.933060i \(0.617128\pi\)
\(450\) −0.475435 0.823477i −0.0224122 0.0388191i
\(451\) −2.32904 −0.109670
\(452\) −6.49594 11.2513i −0.305543 0.529217i
\(453\) −30.5359 −1.43470
\(454\) 1.35393 0.0635430
\(455\) 0 0
\(456\) 1.85273 0.0867619
\(457\) −1.61287 −0.0754468 −0.0377234 0.999288i \(-0.512011\pi\)
−0.0377234 + 0.999288i \(0.512011\pi\)
\(458\) −4.83583 8.37590i −0.225963 0.391380i
\(459\) −5.47920 −0.255747
\(460\) 2.90291 + 5.02799i 0.135349 + 0.234431i
\(461\) 7.96032 + 13.7877i 0.370749 + 0.642156i 0.989681 0.143289i \(-0.0457677\pi\)
−0.618932 + 0.785445i \(0.712434\pi\)
\(462\) 0 0
\(463\) −28.8475 −1.34066 −0.670328 0.742065i \(-0.733847\pi\)
−0.670328 + 0.742065i \(0.733847\pi\)
\(464\) 7.22154 12.5081i 0.335252 0.580673i
\(465\) 6.19444 + 10.7291i 0.287260 + 0.497549i
\(466\) −4.79110 8.29842i −0.221943 0.384417i
\(467\) 3.72268 + 6.44787i 0.172265 + 0.298372i 0.939211 0.343339i \(-0.111558\pi\)
−0.766946 + 0.641711i \(0.778225\pi\)
\(468\) −3.07252 1.63034i −0.142027 0.0753626i
\(469\) 0 0
\(470\) −4.92114 + 8.52367i −0.226995 + 0.393167i
\(471\) 1.18949 0.0548087
\(472\) 0.511789 0.0235570
\(473\) −2.33635 + 4.04668i −0.107425 + 0.186066i
\(474\) −8.81971 + 15.2762i −0.405103 + 0.701658i
\(475\) −0.651899 1.12912i −0.0299112 0.0518077i
\(476\) 0 0
\(477\) 2.72371 + 4.71761i 0.124710 + 0.216005i
\(478\) −1.84404 −0.0843446
\(479\) −18.6263 32.2617i −0.851058 1.47408i −0.880254 0.474503i \(-0.842628\pi\)
0.0291956 0.999574i \(-0.490705\pi\)
\(480\) −7.61704 + 13.1931i −0.347669 + 0.602180i
\(481\) −1.18105 33.0166i −0.0538512 1.50543i
\(482\) −9.19570 −0.418853
\(483\) 0 0
\(484\) −8.87134 + 15.3656i −0.403243 + 0.698437i
\(485\) −11.5277 + 19.9666i −0.523448 + 0.906638i
\(486\) 1.72380 2.98571i 0.0781931 0.135434i
\(487\) 24.1726 1.09537 0.547684 0.836686i \(-0.315510\pi\)
0.547684 + 0.836686i \(0.315510\pi\)
\(488\) −8.20742 + 14.2157i −0.371533 + 0.643513i
\(489\) 22.1069 0.999707
\(490\) 0 0
\(491\) −3.03571 + 5.25800i −0.137000 + 0.237290i −0.926360 0.376640i \(-0.877079\pi\)
0.789360 + 0.613931i \(0.210413\pi\)
\(492\) −12.6453 −0.570092
\(493\) −4.12277 + 7.14086i −0.185680 + 0.321608i
\(494\) 0.851236 + 0.451683i 0.0382989 + 0.0203222i
\(495\) −0.247700 0.429030i −0.0111333 0.0192835i
\(496\) −4.65656 + 8.06540i −0.209086 + 0.362147i
\(497\) 0 0
\(498\) 8.44736 + 14.6313i 0.378535 + 0.655642i
\(499\) 1.25782 + 2.17861i 0.0563079 + 0.0975281i 0.892805 0.450443i \(-0.148734\pi\)
−0.836497 + 0.547971i \(0.815400\pi\)
\(500\) 19.1941 0.858385
\(501\) −41.7358 −1.86462
\(502\) −0.723533 1.25320i −0.0322929 0.0559329i
\(503\) 17.0026 + 29.4493i 0.758107 + 1.31308i 0.943815 + 0.330474i \(0.107209\pi\)
−0.185708 + 0.982605i \(0.559458\pi\)
\(504\) 0 0
\(505\) −10.3254 + 17.8841i −0.459473 + 0.795831i
\(506\) 0.398029 + 0.689407i 0.0176946 + 0.0306479i
\(507\) −13.7888 20.3680i −0.612383 0.904576i
\(508\) −0.781466 + 1.35354i −0.0346719 + 0.0600536i
\(509\) 29.3048 1.29891 0.649457 0.760399i \(-0.274996\pi\)
0.649457 + 0.760399i \(0.274996\pi\)
\(510\) 0.967183 1.67521i 0.0428276 0.0741795i
\(511\) 0 0
\(512\) −20.3568 −0.899654
\(513\) 1.05538 1.82798i 0.0465964 0.0807073i
\(514\) 6.09984 0.269053
\(515\) −7.92012 + 13.7180i −0.349002 + 0.604489i
\(516\) −12.6849 + 21.9709i −0.558423 + 0.967217i
\(517\) 3.33950 5.78418i 0.146871 0.254388i
\(518\) 0 0
\(519\) −21.5516 −0.946011
\(520\) −9.56679 + 5.98930i −0.419531 + 0.262648i
\(521\) 4.57386 7.92216i 0.200385 0.347076i −0.748268 0.663397i \(-0.769114\pi\)
0.948652 + 0.316321i \(0.102448\pi\)
\(522\) −1.15831 2.00625i −0.0506977 0.0878111i
\(523\) −14.1075 −0.616876 −0.308438 0.951244i \(-0.599806\pi\)
−0.308438 + 0.951244i \(0.599806\pi\)
\(524\) −0.946019 1.63855i −0.0413270 0.0715805i
\(525\) 0 0
\(526\) −9.08849 15.7417i −0.396277 0.686372i
\(527\) 2.65843 4.60453i 0.115803 0.200577i
\(528\) 1.14965 1.99125i 0.0500319 0.0866578i
\(529\) −17.3928 −0.756209
\(530\) 8.02743 0.348689
\(531\) −0.0698437 + 0.120973i −0.00303096 + 0.00524977i
\(532\) 0 0
\(533\) −12.7936 6.78856i −0.554154 0.294045i
\(534\) −1.36638 2.36664i −0.0591290 0.102414i
\(535\) −2.76688 4.79238i −0.119623 0.207193i
\(536\) 1.53862 + 2.66496i 0.0664582 + 0.115109i
\(537\) −3.28498 + 5.68976i −0.141758 + 0.245531i
\(538\) −12.2494 −0.528109
\(539\) 0 0
\(540\) 5.61359 + 9.72302i 0.241570 + 0.418412i
\(541\) −3.90147 6.75754i −0.167737 0.290529i 0.769887 0.638181i \(-0.220313\pi\)
−0.937624 + 0.347651i \(0.886979\pi\)
\(542\) 3.78041 0.162382
\(543\) 19.9602 + 34.5721i 0.856576 + 1.48363i
\(544\) 6.53792 0.280311
\(545\) −12.0959 −0.518133
\(546\) 0 0
\(547\) 6.99390 0.299038 0.149519 0.988759i \(-0.452228\pi\)
0.149519 + 0.988759i \(0.452228\pi\)
\(548\) 14.3753 0.614084
\(549\) −2.24013 3.88001i −0.0956063 0.165595i
\(550\) 0.950869 0.0405452
\(551\) −1.58823 2.75089i −0.0676608 0.117192i
\(552\) 4.75875 + 8.24240i 0.202546 + 0.350820i
\(553\) 0 0
\(554\) 8.42520 0.357952
\(555\) 12.7739 22.1250i 0.542221 0.939154i
\(556\) −12.1078 20.9713i −0.513484 0.889380i
\(557\) 3.62124 + 6.27218i 0.153437 + 0.265761i 0.932489 0.361199i \(-0.117632\pi\)
−0.779052 + 0.626960i \(0.784299\pi\)
\(558\) 0.746894 + 1.29366i 0.0316186 + 0.0547650i
\(559\) −24.6288 + 15.4189i −1.04169 + 0.652149i
\(560\) 0 0
\(561\) −0.656332 + 1.13680i −0.0277104 + 0.0479958i
\(562\) −15.7611 −0.664842
\(563\) 15.9321 0.671459 0.335730 0.941958i \(-0.391017\pi\)
0.335730 + 0.941958i \(0.391017\pi\)
\(564\) 18.1314 31.4045i 0.763470 1.32237i
\(565\) 5.75334 9.96509i 0.242045 0.419234i
\(566\) −2.48618 4.30618i −0.104502 0.181002i
\(567\) 0 0
\(568\) 13.2924 + 23.0231i 0.557737 + 0.966029i
\(569\) −42.2759 −1.77230 −0.886149 0.463401i \(-0.846629\pi\)
−0.886149 + 0.463401i \(0.846629\pi\)
\(570\) 0.372591 + 0.645346i 0.0156061 + 0.0270306i
\(571\) −6.81247 + 11.7995i −0.285093 + 0.493795i −0.972632 0.232352i \(-0.925358\pi\)
0.687539 + 0.726148i \(0.258691\pi\)
\(572\) 2.94818 1.84571i 0.123270 0.0771730i
\(573\) −22.5510 −0.942082
\(574\) 0 0
\(575\) 3.34882 5.80032i 0.139655 0.241890i
\(576\) 0.296821 0.514108i 0.0123675 0.0214212i
\(577\) −13.1925 + 22.8500i −0.549209 + 0.951258i 0.449120 + 0.893472i \(0.351738\pi\)
−0.998329 + 0.0577867i \(0.981596\pi\)
\(578\) 9.02662 0.375458
\(579\) 13.6032 23.5614i 0.565329 0.979179i
\(580\) 16.8956 0.701550
\(581\) 0 0
\(582\) −8.58174 + 14.8640i −0.355725 + 0.616133i
\(583\) −5.44743 −0.225609
\(584\) 3.92364 6.79594i 0.162361 0.281218i
\(585\) −0.110129 3.07868i −0.00455326 0.127288i
\(586\) 3.04027 + 5.26591i 0.125592 + 0.217533i
\(587\) −11.0720 + 19.1773i −0.456990 + 0.791530i −0.998800 0.0489708i \(-0.984406\pi\)
0.541810 + 0.840501i \(0.317739\pi\)
\(588\) 0 0
\(589\) 1.02411 + 1.77382i 0.0421979 + 0.0730889i
\(590\) 0.102923 + 0.178268i 0.00423727 + 0.00733916i
\(591\) −13.1861 −0.542402
\(592\) 19.2051 0.789324
\(593\) −13.0419 22.5893i −0.535568 0.927630i −0.999136 0.0415689i \(-0.986764\pi\)
0.463568 0.886061i \(-0.346569\pi\)
\(594\) 0.769700 + 1.33316i 0.0315812 + 0.0547002i
\(595\) 0 0
\(596\) 11.1311 19.2797i 0.455949 0.789727i
\(597\) 3.38062 + 5.85540i 0.138360 + 0.239646i
\(598\) 0.176965 + 4.94712i 0.00723665 + 0.202303i
\(599\) 8.42202 14.5874i 0.344114 0.596024i −0.641078 0.767476i \(-0.721512\pi\)
0.985192 + 0.171452i \(0.0548458\pi\)
\(600\) 11.3684 0.464113
\(601\) 4.31691 7.47710i 0.176090 0.304997i −0.764448 0.644686i \(-0.776988\pi\)
0.940538 + 0.339688i \(0.110322\pi\)
\(602\) 0 0
\(603\) −0.839898 −0.0342033
\(604\) 13.4263 23.2551i 0.546309 0.946235i
\(605\) −15.7144 −0.638881
\(606\) −7.68665 + 13.3137i −0.312249 + 0.540831i
\(607\) 10.9181 18.9107i 0.443153 0.767564i −0.554768 0.832005i \(-0.687193\pi\)
0.997922 + 0.0644411i \(0.0205265\pi\)
\(608\) −1.25931 + 2.18119i −0.0510718 + 0.0884590i
\(609\) 0 0
\(610\) −6.60218 −0.267315
\(611\) 35.2036 22.0392i 1.42418 0.891612i
\(612\) −0.577165 + 0.999680i −0.0233305 + 0.0404096i
\(613\) 24.0244 + 41.6114i 0.970334 + 1.68067i 0.694543 + 0.719451i \(0.255607\pi\)
0.275791 + 0.961218i \(0.411060\pi\)
\(614\) −11.1179 −0.448683
\(615\) −5.59985 9.69922i −0.225808 0.391110i
\(616\) 0 0
\(617\) 8.23709 + 14.2671i 0.331613 + 0.574370i 0.982828 0.184523i \(-0.0590739\pi\)
−0.651215 + 0.758893i \(0.725741\pi\)
\(618\) −5.89608 + 10.2123i −0.237175 + 0.410799i
\(619\) 21.0267 36.4192i 0.845133 1.46381i −0.0403733 0.999185i \(-0.512855\pi\)
0.885506 0.464628i \(-0.153812\pi\)
\(620\) −10.8945 −0.437535
\(621\) 10.8431 0.435117
\(622\) 1.01135 1.75170i 0.0405513 0.0702370i
\(623\) 0 0
\(624\) 12.1191 7.58716i 0.485151 0.303730i
\(625\) 1.42880 + 2.47475i 0.0571519 + 0.0989900i
\(626\) 5.89129 + 10.2040i 0.235463 + 0.407835i
\(627\) −0.252841 0.437933i −0.0100975 0.0174894i
\(628\) −0.523006 + 0.905872i −0.0208702 + 0.0361482i
\(629\) −10.9642 −0.437170
\(630\) 0 0
\(631\) 6.06667 + 10.5078i 0.241510 + 0.418308i 0.961145 0.276045i \(-0.0890239\pi\)
−0.719634 + 0.694353i \(0.755691\pi\)
\(632\) −17.0788 29.5814i −0.679360 1.17669i
\(633\) 26.7040 1.06139
\(634\) −8.06575 13.9703i −0.320332 0.554831i
\(635\) −1.38426 −0.0549328
\(636\) −29.5762 −1.17277
\(637\) 0 0
\(638\) 2.31661 0.0917157
\(639\) −7.25604 −0.287044
\(640\) −8.48908 14.7035i −0.335560 0.581207i
\(641\) −0.404355 −0.0159711 −0.00798553 0.999968i \(-0.502542\pi\)
−0.00798553 + 0.999968i \(0.502542\pi\)
\(642\) −2.05979 3.56765i −0.0812933 0.140804i
\(643\) 14.1741 + 24.5503i 0.558973 + 0.968169i 0.997583 + 0.0694914i \(0.0221377\pi\)
−0.438610 + 0.898678i \(0.644529\pi\)
\(644\) 0 0
\(645\) −22.4697 −0.884742
\(646\) 0.159902 0.276959i 0.00629128 0.0108968i
\(647\) −17.4045 30.1455i −0.684242 1.18514i −0.973675 0.227943i \(-0.926800\pi\)
0.289433 0.957198i \(-0.406533\pi\)
\(648\) 11.0499 + 19.1390i 0.434082 + 0.751852i
\(649\) −0.0698437 0.120973i −0.00274160 0.00474860i
\(650\) 5.22321 + 2.77154i 0.204871 + 0.108709i
\(651\) 0 0
\(652\) −9.72016 + 16.8358i −0.380671 + 0.659341i
\(653\) −25.1500 −0.984195 −0.492098 0.870540i \(-0.663770\pi\)
−0.492098 + 0.870540i \(0.663770\pi\)
\(654\) −9.00473 −0.352113
\(655\) 0.837873 1.45124i 0.0327384 0.0567046i
\(656\) 4.20959 7.29122i 0.164357 0.284674i
\(657\) 1.07091 + 1.85488i 0.0417803 + 0.0723657i
\(658\) 0 0
\(659\) −4.33723 7.51230i −0.168954 0.292638i 0.769098 0.639131i \(-0.220706\pi\)
−0.938053 + 0.346493i \(0.887372\pi\)
\(660\) 2.68972 0.104697
\(661\) 9.50000 + 16.4545i 0.369507 + 0.640005i 0.989489 0.144612i \(-0.0461932\pi\)
−0.619982 + 0.784616i \(0.712860\pi\)
\(662\) −2.70857 + 4.69138i −0.105272 + 0.182336i
\(663\) −6.91878 + 4.33151i −0.268703 + 0.168222i
\(664\) −32.7156 −1.26961
\(665\) 0 0
\(666\) 1.54021 2.66772i 0.0596819 0.103372i
\(667\) 8.15877 14.1314i 0.315909 0.547170i
\(668\) 18.3508 31.7845i 0.710013 1.22978i
\(669\) 1.72011 0.0665032
\(670\) −0.618844 + 1.07187i −0.0239080 + 0.0414099i
\(671\) 4.48026 0.172958
\(672\) 0 0
\(673\) 0.284273 0.492376i 0.0109579 0.0189797i −0.860494 0.509460i \(-0.829845\pi\)
0.871452 + 0.490480i \(0.163179\pi\)
\(674\) −13.2882 −0.511843
\(675\) 6.47587 11.2165i 0.249256 0.431725i
\(676\) 21.5744 1.54547i 0.829784 0.0594411i
\(677\) 13.8398 + 23.9713i 0.531908 + 0.921292i 0.999306 + 0.0372449i \(0.0118581\pi\)
−0.467398 + 0.884047i \(0.654809\pi\)
\(678\) 4.28304 7.41844i 0.164489 0.284903i
\(679\) 0 0
\(680\) 1.87289 + 3.24394i 0.0718221 + 0.124400i
\(681\) −2.20907 3.82622i −0.0846518 0.146621i
\(682\) −1.49379 −0.0572001
\(683\) −23.7917 −0.910363 −0.455181 0.890399i \(-0.650426\pi\)
−0.455181 + 0.890399i \(0.650426\pi\)
\(684\) −0.222343 0.385110i −0.00850150 0.0147250i
\(685\) 6.36600 + 11.0262i 0.243232 + 0.421291i
\(686\) 0 0
\(687\) −15.7803 + 27.3323i −0.602056 + 1.04279i
\(688\) −8.44559 14.6282i −0.321985 0.557694i
\(689\) −29.9232 15.8779i −1.13998 0.604898i
\(690\) −1.91401 + 3.31516i −0.0728650 + 0.126206i
\(691\) −36.8433 −1.40159 −0.700793 0.713365i \(-0.747170\pi\)
−0.700793 + 0.713365i \(0.747170\pi\)
\(692\) 9.47603 16.4130i 0.360224 0.623927i
\(693\) 0 0
\(694\) 15.4642 0.587012
\(695\) 10.7236 18.5739i 0.406771 0.704548i
\(696\) 27.6969 1.04985
\(697\) −2.40325 + 4.16255i −0.0910296 + 0.157668i
\(698\) 4.41655 7.64969i 0.167169 0.289545i
\(699\) −15.6343 + 27.0794i −0.591344 + 1.02424i
\(700\) 0 0
\(701\) 2.34987 0.0887533 0.0443767 0.999015i \(-0.485870\pi\)
0.0443767 + 0.999015i \(0.485870\pi\)
\(702\) 0.342212 + 9.56664i 0.0129160 + 0.361070i
\(703\) 2.11188 3.65788i 0.0796511 0.137960i
\(704\) 0.296821 + 0.514108i 0.0111868 + 0.0193762i
\(705\) 32.1174 1.20961
\(706\) −6.49645 11.2522i −0.244497 0.423481i
\(707\) 0 0
\(708\) −0.379208 0.656807i −0.0142515 0.0246843i
\(709\) −5.04160 + 8.73231i −0.189341 + 0.327949i −0.945031 0.326981i \(-0.893969\pi\)
0.755689 + 0.654930i \(0.227302\pi\)
\(710\) −5.34631 + 9.26008i −0.200643 + 0.347525i
\(711\) 9.32297 0.349639
\(712\) 5.29182 0.198319
\(713\) −5.26090 + 9.11214i −0.197022 + 0.341252i
\(714\) 0 0
\(715\) 2.72128 + 1.44397i 0.101770 + 0.0540013i
\(716\) −2.88875 5.00346i −0.107958 0.186988i
\(717\) 3.00875 + 5.21130i 0.112364 + 0.194620i
\(718\) 4.64966 + 8.05344i 0.173524 + 0.300552i
\(719\) 3.25113 5.63113i 0.121247 0.210006i −0.799013 0.601314i \(-0.794644\pi\)
0.920260 + 0.391308i \(0.127977\pi\)
\(720\) 1.79081 0.0667394
\(721\) 0 0
\(722\) −5.44660 9.43379i −0.202701 0.351089i
\(723\) 15.0037 + 25.9872i 0.557994 + 0.966474i
\(724\) −35.1052 −1.30468
\(725\) −9.74542 16.8796i −0.361936 0.626891i
\(726\) −11.6985 −0.434171
\(727\) 3.12636 0.115950 0.0579750 0.998318i \(-0.481536\pi\)
0.0579750 + 0.998318i \(0.481536\pi\)
\(728\) 0 0
\(729\) 19.9595 0.739242
\(730\) 3.15623 0.116817
\(731\) 4.82158 + 8.35123i 0.178333 + 0.308881i
\(732\) 24.3250 0.899078
\(733\) −3.83220 6.63756i −0.141545 0.245164i 0.786533 0.617548i \(-0.211874\pi\)
−0.928079 + 0.372384i \(0.878540\pi\)
\(734\) −2.00036 3.46472i −0.0738346 0.127885i
\(735\) 0 0
\(736\) −12.9382 −0.476909
\(737\) 0.419949 0.727373i 0.0154690 0.0267931i
\(738\) −0.675201 1.16948i −0.0248545 0.0430493i
\(739\) −10.2162 17.6950i −0.375810 0.650922i 0.614638 0.788809i \(-0.289302\pi\)
−0.990448 + 0.137887i \(0.955969\pi\)
\(740\) 11.2331 + 19.4563i 0.412936 + 0.715227i
\(741\) −0.112414 3.14257i −0.00412964 0.115445i
\(742\) 0 0
\(743\) −5.07080 + 8.78288i −0.186030 + 0.322213i −0.943923 0.330166i \(-0.892895\pi\)
0.757893 + 0.652378i \(0.226229\pi\)
\(744\) −17.8594 −0.654758
\(745\) 19.7173 0.722387
\(746\) 2.22801 3.85902i 0.0815731 0.141289i
\(747\) 4.46469 7.73306i 0.163354 0.282938i
\(748\) −0.577165 0.999680i −0.0211033 0.0365519i
\(749\) 0 0
\(750\) 6.32771 + 10.9599i 0.231055 + 0.400200i
\(751\) −22.2961 −0.813598 −0.406799 0.913518i \(-0.633355\pi\)
−0.406799 + 0.913518i \(0.633355\pi\)
\(752\) 12.0718 + 20.9090i 0.440214 + 0.762474i
\(753\) −2.36104 + 4.08943i −0.0860409 + 0.149027i
\(754\) 12.7254 + 6.75234i 0.463431 + 0.245906i
\(755\) 23.7829 0.865550
\(756\) 0 0
\(757\) −12.2909 + 21.2884i −0.446720 + 0.773741i −0.998170 0.0604666i \(-0.980741\pi\)
0.551451 + 0.834207i \(0.314074\pi\)
\(758\) −7.29503 + 12.6354i −0.264967 + 0.458937i
\(759\) 1.29885 2.24967i 0.0471452 0.0816580i
\(760\) −1.44300 −0.0523431
\(761\) −17.6167 + 30.5130i −0.638603 + 1.10609i 0.347136 + 0.937815i \(0.387154\pi\)
−0.985739 + 0.168279i \(0.946179\pi\)
\(762\) −1.03050 −0.0373312
\(763\) 0 0
\(764\) 9.91545 17.1741i 0.358728 0.621336i
\(765\) −1.02237 −0.0369639
\(766\) −6.39057 + 11.0688i −0.230901 + 0.399932i
\(767\) −0.0310528 0.868091i −0.00112125 0.0313449i
\(768\) −4.38246 7.59065i −0.158138 0.273904i
\(769\) 4.62257 8.00653i 0.166694 0.288723i −0.770561 0.637366i \(-0.780024\pi\)
0.937256 + 0.348643i \(0.113357\pi\)
\(770\) 0 0
\(771\) −9.95251 17.2383i −0.358431 0.620821i
\(772\) 11.9624 + 20.7194i 0.430535 + 0.745708i
\(773\) 6.32671 0.227556 0.113778 0.993506i \(-0.463705\pi\)
0.113778 + 0.993506i \(0.463705\pi\)
\(774\) −2.70928 −0.0973830
\(775\) 6.28400 + 10.8842i 0.225728 + 0.390972i
\(776\) −16.6180 28.7833i −0.596553 1.03326i
\(777\) 0 0
\(778\) −3.18349 + 5.51397i −0.114134 + 0.197686i
\(779\) −0.925812 1.60355i −0.0331706 0.0574532i
\(780\) 14.7749 + 7.83984i 0.529025 + 0.280711i
\(781\) 3.62802 6.28391i 0.129821 0.224856i
\(782\) 1.64285 0.0587480