Properties

Label 349.2.e.a.123.18
Level 349
Weight 2
Character 349.123
Analytic conductor 2.787
Analytic rank 0
Dimension 58
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 349.e (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.78677903054\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 123.18
Character \(\chi\) = 349.123
Dual form 349.2.e.a.227.18

$q$-expansion

\(f(q)\) \(=\) \(q+(0.531309 - 0.306751i) q^{2} +(0.869046 - 1.50523i) q^{3} +(-0.811807 + 1.40609i) q^{4} +(-1.66390 + 2.88196i) q^{5} -1.06632i q^{6} +(-1.62203 + 0.936479i) q^{7} +2.22310i q^{8} +(-0.0104823 - 0.0181558i) q^{9} +O(q^{10})\) \(q+(0.531309 - 0.306751i) q^{2} +(0.869046 - 1.50523i) q^{3} +(-0.811807 + 1.40609i) q^{4} +(-1.66390 + 2.88196i) q^{5} -1.06632i q^{6} +(-1.62203 + 0.936479i) q^{7} +2.22310i q^{8} +(-0.0104823 - 0.0181558i) q^{9} +2.04162i q^{10} +1.41258i q^{11} +(1.41100 + 2.44392i) q^{12} +(-0.199242 + 0.115033i) q^{13} +(-0.574532 + 0.995119i) q^{14} +(2.89202 + 5.00912i) q^{15} +(-0.941677 - 1.63103i) q^{16} +2.97207 q^{17} +(-0.0111386 - 0.00643089i) q^{18} +(-0.723681 + 1.25345i) q^{19} +(-2.70154 - 4.67920i) q^{20} +3.25538i q^{21} +(0.433310 + 0.750515i) q^{22} +(-0.563129 - 0.975369i) q^{23} +(3.34628 + 1.93197i) q^{24} +(-3.03714 - 5.26049i) q^{25} +(-0.0705728 + 0.122236i) q^{26} +5.17784 q^{27} -3.04096i q^{28} +(0.522000 - 0.904130i) q^{29} +(3.07311 + 1.77426i) q^{30} -5.04008 q^{31} +(-4.85116 - 2.80082i) q^{32} +(2.12626 + 1.22759i) q^{33} +(1.57909 - 0.911686i) q^{34} -6.23284i q^{35} +0.0340383 q^{36} +8.62141 q^{37} +0.887960i q^{38} +0.399875i q^{39} +(-6.40688 - 3.69902i) q^{40} +9.91019 q^{41} +(0.998590 + 1.72961i) q^{42} +(-0.0676083 - 0.0390337i) q^{43} +(-1.98621 - 1.14674i) q^{44} +0.0697659 q^{45} +(-0.598391 - 0.345481i) q^{46} -1.68060i q^{47} -3.27344 q^{48} +(-1.74601 + 3.02418i) q^{49} +(-3.22732 - 1.86329i) q^{50} +(2.58287 - 4.47366i) q^{51} -0.373537i q^{52} +0.199686i q^{53} +(2.75103 - 1.58831i) q^{54} +(-4.07100 - 2.35039i) q^{55} +(-2.08188 - 3.60593i) q^{56} +(1.25782 + 2.17861i) q^{57} -0.640496i q^{58} +(-0.146886 - 0.0848048i) q^{59} -9.39104 q^{60} +10.8056i q^{61} +(-2.67784 + 1.54605i) q^{62} +(0.0340051 + 0.0196328i) q^{63} +0.330093 q^{64} -0.765612i q^{65} +1.50626 q^{66} +3.43607 q^{67} +(-2.41275 + 4.17901i) q^{68} -1.95754 q^{69} +(-1.91193 - 3.31156i) q^{70} +(-3.54124 + 2.04454i) q^{71} +(0.0403621 - 0.0233031i) q^{72} +(-4.82755 + 8.36157i) q^{73} +(4.58063 - 2.64463i) q^{74} -10.5577 q^{75} +(-1.17498 - 2.03512i) q^{76} +(-1.32285 - 2.29124i) q^{77} +(0.122662 + 0.212457i) q^{78} -1.92126i q^{79} +6.26744 q^{80} +(4.53123 - 7.84832i) q^{81} +(5.26537 - 3.03996i) q^{82} +(-7.78968 - 13.4921i) q^{83} +(-4.57736 - 2.64274i) q^{84} +(-4.94524 + 8.56540i) q^{85} -0.0478945 q^{86} +(-0.907284 - 1.57146i) q^{87} -3.14030 q^{88} +(6.55579 + 3.78499i) q^{89} +(0.0370672 - 0.0214008i) q^{90} +(0.215451 - 0.373173i) q^{91} +1.82861 q^{92} +(-4.38006 + 7.58649i) q^{93} +(-0.515525 - 0.892916i) q^{94} +(-2.40827 - 4.17124i) q^{95} +(-8.43176 + 4.86808i) q^{96} +(10.6607 - 6.15496i) q^{97} +2.14237i q^{98} +(0.0256465 - 0.0148070i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} + O(q^{10}) \) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} - q^{12} - 3q^{13} - 10q^{14} + q^{15} - 29q^{16} - 10q^{17} + 15q^{18} - 9q^{19} - 3q^{22} - 17q^{23} - 48q^{24} - 29q^{25} - 4q^{26} + 18q^{27} - 2q^{29} + 9q^{30} + 32q^{31} + 9q^{32} - 12q^{33} - 63q^{34} + 24q^{36} - 16q^{37} + 54q^{40} - 10q^{41} - 15q^{42} - 45q^{43} + 18q^{44} - 2q^{45} + 27q^{46} + 6q^{48} + 35q^{49} + 6q^{50} - 14q^{51} + 27q^{54} + 24q^{55} + 11q^{56} - 29q^{57} - 18q^{59} + 116q^{60} - 9q^{62} - 21q^{63} - 132q^{64} + 130q^{66} + 58q^{67} + 42q^{69} + 40q^{70} - 24q^{71} + 72q^{72} - 6q^{73} + 30q^{74} - 58q^{75} + 37q^{76} - 4q^{77} - 33q^{78} - 40q^{80} - 81q^{81} + 21q^{82} + 12q^{83} + 18q^{84} - 11q^{85} - 126q^{86} - 42q^{87} - 50q^{88} + 3q^{89} - 12q^{90} - 28q^{91} - 120q^{92} + 31q^{93} + 29q^{94} + 60q^{95} - 120q^{96} - 15q^{97} + 39q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/349\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.531309 0.306751i 0.375692 0.216906i −0.300250 0.953860i \(-0.597070\pi\)
0.675942 + 0.736955i \(0.263737\pi\)
\(3\) 0.869046 1.50523i 0.501744 0.869046i −0.498254 0.867031i \(-0.666025\pi\)
0.999998 0.00201497i \(-0.000641386\pi\)
\(4\) −0.811807 + 1.40609i −0.405904 + 0.703046i
\(5\) −1.66390 + 2.88196i −0.744120 + 1.28885i 0.206485 + 0.978450i \(0.433798\pi\)
−0.950605 + 0.310404i \(0.899536\pi\)
\(6\) 1.06632i 0.435325i
\(7\) −1.62203 + 0.936479i −0.613070 + 0.353956i −0.774166 0.632983i \(-0.781830\pi\)
0.161096 + 0.986939i \(0.448497\pi\)
\(8\) 2.22310i 0.785983i
\(9\) −0.0104823 0.0181558i −0.00349409 0.00605194i
\(10\) 2.04162i 0.645616i
\(11\) 1.41258i 0.425908i 0.977062 + 0.212954i \(0.0683085\pi\)
−0.977062 + 0.212954i \(0.931692\pi\)
\(12\) 1.41100 + 2.44392i 0.407320 + 0.705498i
\(13\) −0.199242 + 0.115033i −0.0552599 + 0.0319043i −0.527375 0.849632i \(-0.676824\pi\)
0.472116 + 0.881537i \(0.343491\pi\)
\(14\) −0.574532 + 0.995119i −0.153550 + 0.265957i
\(15\) 2.89202 + 5.00912i 0.746715 + 1.29335i
\(16\) −0.941677 1.63103i −0.235419 0.407758i
\(17\) 2.97207 0.720833 0.360417 0.932791i \(-0.382635\pi\)
0.360417 + 0.932791i \(0.382635\pi\)
\(18\) −0.0111386 0.00643089i −0.00262540 0.00151578i
\(19\) −0.723681 + 1.25345i −0.166024 + 0.287562i −0.937018 0.349280i \(-0.886426\pi\)
0.770995 + 0.636842i \(0.219760\pi\)
\(20\) −2.70154 4.67920i −0.604082 1.04630i
\(21\) 3.25538i 0.710381i
\(22\) 0.433310 + 0.750515i 0.0923820 + 0.160010i
\(23\) −0.563129 0.975369i −0.117421 0.203378i 0.801324 0.598230i \(-0.204129\pi\)
−0.918745 + 0.394852i \(0.870796\pi\)
\(24\) 3.34628 + 1.93197i 0.683056 + 0.394362i
\(25\) −3.03714 5.26049i −0.607429 1.05210i
\(26\) −0.0705728 + 0.122236i −0.0138405 + 0.0239724i
\(27\) 5.17784 0.996475
\(28\) 3.04096i 0.574688i
\(29\) 0.522000 0.904130i 0.0969329 0.167893i −0.813481 0.581592i \(-0.802430\pi\)
0.910414 + 0.413699i \(0.135763\pi\)
\(30\) 3.07311 + 1.77426i 0.561070 + 0.323934i
\(31\) −5.04008 −0.905225 −0.452612 0.891707i \(-0.649508\pi\)
−0.452612 + 0.891707i \(0.649508\pi\)
\(32\) −4.85116 2.80082i −0.857572 0.495119i
\(33\) 2.12626 + 1.22759i 0.370134 + 0.213697i
\(34\) 1.57909 0.911686i 0.270811 0.156353i
\(35\) 6.23284i 1.05354i
\(36\) 0.0340383 0.00567305
\(37\) 8.62141 1.41735 0.708676 0.705534i \(-0.249293\pi\)
0.708676 + 0.705534i \(0.249293\pi\)
\(38\) 0.887960i 0.144046i
\(39\) 0.399875i 0.0640312i
\(40\) −6.40688 3.69902i −1.01302 0.584866i
\(41\) 9.91019 1.54771 0.773856 0.633362i \(-0.218326\pi\)
0.773856 + 0.633362i \(0.218326\pi\)
\(42\) 0.998590 + 1.72961i 0.154086 + 0.266884i
\(43\) −0.0676083 0.0390337i −0.0103102 0.00595258i 0.494836 0.868986i \(-0.335228\pi\)
−0.505146 + 0.863034i \(0.668561\pi\)
\(44\) −1.98621 1.14674i −0.299433 0.172878i
\(45\) 0.0697659 0.0104001
\(46\) −0.598391 0.345481i −0.0882280 0.0509384i
\(47\) 1.68060i 0.245140i −0.992460 0.122570i \(-0.960886\pi\)
0.992460 0.122570i \(-0.0391137\pi\)
\(48\) −3.27344 −0.472481
\(49\) −1.74601 + 3.02418i −0.249430 + 0.432026i
\(50\) −3.22732 1.86329i −0.456412 0.263510i
\(51\) 2.58287 4.47366i 0.361674 0.626437i
\(52\) 0.373537i 0.0518003i
\(53\) 0.199686i 0.0274289i 0.999906 + 0.0137145i \(0.00436559\pi\)
−0.999906 + 0.0137145i \(0.995634\pi\)
\(54\) 2.75103 1.58831i 0.374368 0.216141i
\(55\) −4.07100 2.35039i −0.548933 0.316927i
\(56\) −2.08188 3.60593i −0.278203 0.481862i
\(57\) 1.25782 + 2.17861i 0.166603 + 0.288565i
\(58\) 0.640496i 0.0841013i
\(59\) −0.146886 0.0848048i −0.0191230 0.0110407i 0.490408 0.871493i \(-0.336848\pi\)
−0.509531 + 0.860452i \(0.670181\pi\)
\(60\) −9.39104 −1.21238
\(61\) 10.8056i 1.38351i 0.722130 + 0.691757i \(0.243163\pi\)
−0.722130 + 0.691757i \(0.756837\pi\)
\(62\) −2.67784 + 1.54605i −0.340086 + 0.196349i
\(63\) 0.0340051 + 0.0196328i 0.00428424 + 0.00247351i
\(64\) 0.330093 0.0412617
\(65\) 0.765612i 0.0949625i
\(66\) 1.50626 0.185408
\(67\) 3.43607 0.419783 0.209891 0.977725i \(-0.432689\pi\)
0.209891 + 0.977725i \(0.432689\pi\)
\(68\) −2.41275 + 4.17901i −0.292589 + 0.506779i
\(69\) −1.95754 −0.235660
\(70\) −1.91193 3.31156i −0.228520 0.395807i
\(71\) −3.54124 + 2.04454i −0.420268 + 0.242642i −0.695192 0.718824i \(-0.744681\pi\)
0.274924 + 0.961466i \(0.411347\pi\)
\(72\) 0.0403621 0.0233031i 0.00475672 0.00274629i
\(73\) −4.82755 + 8.36157i −0.565022 + 0.978648i 0.432025 + 0.901862i \(0.357799\pi\)
−0.997048 + 0.0767860i \(0.975534\pi\)
\(74\) 4.58063 2.64463i 0.532488 0.307432i
\(75\) −10.5577 −1.21909
\(76\) −1.17498 2.03512i −0.134779 0.233445i
\(77\) −1.32285 2.29124i −0.150753 0.261111i
\(78\) 0.122662 + 0.212457i 0.0138887 + 0.0240560i
\(79\) 1.92126i 0.216158i −0.994142 0.108079i \(-0.965530\pi\)
0.994142 0.108079i \(-0.0344700\pi\)
\(80\) 6.26744 0.700721
\(81\) 4.53123 7.84832i 0.503470 0.872035i
\(82\) 5.26537 3.03996i 0.581463 0.335708i
\(83\) −7.78968 13.4921i −0.855029 1.48095i −0.876619 0.481186i \(-0.840206\pi\)
0.0215900 0.999767i \(-0.493127\pi\)
\(84\) −4.57736 2.64274i −0.499430 0.288346i
\(85\) −4.94524 + 8.56540i −0.536386 + 0.929048i
\(86\) −0.0478945 −0.00516460
\(87\) −0.907284 1.57146i −0.0972710 0.168478i
\(88\) −3.14030 −0.334757
\(89\) 6.55579 + 3.78499i 0.694912 + 0.401208i 0.805450 0.592664i \(-0.201924\pi\)
−0.110537 + 0.993872i \(0.535257\pi\)
\(90\) 0.0370672 0.0214008i 0.00390723 0.00225584i
\(91\) 0.215451 0.373173i 0.0225854 0.0391191i
\(92\) 1.82861 0.190646
\(93\) −4.38006 + 7.58649i −0.454191 + 0.786682i
\(94\) −0.515525 0.892916i −0.0531724 0.0920973i
\(95\) −2.40827 4.17124i −0.247083 0.427961i
\(96\) −8.43176 + 4.86808i −0.860563 + 0.496846i
\(97\) 10.6607 6.15496i 1.08243 0.624942i 0.150880 0.988552i \(-0.451789\pi\)
0.931551 + 0.363610i \(0.118456\pi\)
\(98\) 2.14237i 0.216412i
\(99\) 0.0256465 0.0148070i 0.00257757 0.00148816i
\(100\) 9.86230 0.986230
\(101\) 3.34782i 0.333120i −0.986031 0.166560i \(-0.946734\pi\)
0.986031 0.166560i \(-0.0532660\pi\)
\(102\) 3.16919i 0.313797i
\(103\) 9.50600i 0.936654i 0.883555 + 0.468327i \(0.155143\pi\)
−0.883555 + 0.468327i \(0.844857\pi\)
\(104\) −0.255729 0.442935i −0.0250763 0.0434333i
\(105\) −9.38187 5.41663i −0.915577 0.528609i
\(106\) 0.0612538 + 0.106095i 0.00594950 + 0.0103048i
\(107\) 15.8476 9.14961i 1.53204 0.884526i 0.532776 0.846256i \(-0.321149\pi\)
0.999267 0.0382700i \(-0.0121847\pi\)
\(108\) −4.20341 + 7.28052i −0.404473 + 0.700568i
\(109\) 5.20785 9.02025i 0.498821 0.863984i −0.501178 0.865344i \(-0.667100\pi\)
0.999999 + 0.00136073i \(0.000433134\pi\)
\(110\) −2.88394 −0.274973
\(111\) 7.49240 12.9772i 0.711148 1.23174i
\(112\) 3.05486 + 1.76372i 0.288657 + 0.166656i
\(113\) 3.40247 1.96442i 0.320078 0.184797i −0.331350 0.943508i \(-0.607504\pi\)
0.651427 + 0.758711i \(0.274171\pi\)
\(114\) 1.33659 + 0.771678i 0.125183 + 0.0722743i
\(115\) 3.74797 0.349500
\(116\) 0.847527 + 1.46796i 0.0786909 + 0.136297i
\(117\) 0.00417702 + 0.00241160i 0.000386166 + 0.000222953i
\(118\) −0.104056 −0.00957913
\(119\) −4.82079 + 2.78328i −0.441921 + 0.255143i
\(120\) −11.1358 + 6.42923i −1.01655 + 0.586906i
\(121\) 9.00463 0.818602
\(122\) 3.31463 + 5.74111i 0.300092 + 0.519775i
\(123\) 8.61241 14.9171i 0.776555 1.34503i
\(124\) 4.09157 7.08681i 0.367434 0.636415i
\(125\) 3.57502 0.319759
\(126\) 0.0240896 0.00214607
\(127\) 3.28949i 0.291895i 0.989292 + 0.145947i \(0.0466231\pi\)
−0.989292 + 0.145947i \(0.953377\pi\)
\(128\) 9.87770 5.70289i 0.873073 0.504069i
\(129\) −0.117509 + 0.0678441i −0.0103461 + 0.00597334i
\(130\) −0.234852 0.406776i −0.0205979 0.0356767i
\(131\) 11.0415i 0.964705i −0.875977 0.482352i \(-0.839783\pi\)
0.875977 0.482352i \(-0.160217\pi\)
\(132\) −3.45222 + 1.99314i −0.300477 + 0.173481i
\(133\) 2.71085i 0.235060i
\(134\) 1.82561 1.05402i 0.157709 0.0910534i
\(135\) −8.61542 + 14.9223i −0.741497 + 1.28431i
\(136\) 6.60720i 0.566563i
\(137\) −0.816731 0.471540i −0.0697781 0.0402864i 0.464705 0.885466i \(-0.346160\pi\)
−0.534483 + 0.845179i \(0.679494\pi\)
\(138\) −1.04006 + 0.600478i −0.0885357 + 0.0511161i
\(139\) −17.3068 −1.46794 −0.733971 0.679180i \(-0.762335\pi\)
−0.733971 + 0.679180i \(0.762335\pi\)
\(140\) 8.76395 + 5.05987i 0.740689 + 0.427637i
\(141\) −2.52969 1.46052i −0.213038 0.122998i
\(142\) −1.25433 + 2.17256i −0.105261 + 0.182317i
\(143\) −0.162492 0.281445i −0.0135883 0.0235356i
\(144\) −0.0197418 + 0.0341938i −0.00164515 + 0.00284949i
\(145\) 1.73711 + 3.00877i 0.144259 + 0.249865i
\(146\) 5.92343i 0.490227i
\(147\) 3.03473 + 5.25631i 0.250300 + 0.433533i
\(148\) −6.99893 + 12.1225i −0.575308 + 0.996463i
\(149\) 2.47107 1.42667i 0.202438 0.116878i −0.395354 0.918529i \(-0.629378\pi\)
0.597792 + 0.801651i \(0.296045\pi\)
\(150\) −5.60938 + 3.23858i −0.458004 + 0.264429i
\(151\) −3.15012 + 5.45617i −0.256353 + 0.444017i −0.965262 0.261283i \(-0.915854\pi\)
0.708909 + 0.705300i \(0.249188\pi\)
\(152\) −2.78654 1.60881i −0.226019 0.130492i
\(153\) −0.0311540 0.0539604i −0.00251865 0.00436244i
\(154\) −1.40568 0.811571i −0.113273 0.0653983i
\(155\) 8.38620 14.5253i 0.673596 1.16670i
\(156\) −0.562260 0.324621i −0.0450169 0.0259905i
\(157\) 2.48806 4.30944i 0.198569 0.343931i −0.749496 0.662009i \(-0.769704\pi\)
0.948065 + 0.318078i \(0.103037\pi\)
\(158\) −0.589348 1.02078i −0.0468860 0.0812089i
\(159\) 0.300573 + 0.173536i 0.0238370 + 0.0137623i
\(160\) 16.1437 9.32058i 1.27627 0.736856i
\(161\) 1.82683 + 1.05472i 0.143974 + 0.0831234i
\(162\) 5.55984i 0.436822i
\(163\) 23.7195i 1.85786i 0.370261 + 0.928928i \(0.379268\pi\)
−0.370261 + 0.928928i \(0.620732\pi\)
\(164\) −8.04516 + 13.9346i −0.628222 + 1.08811i
\(165\) −7.07577 + 4.08520i −0.550848 + 0.318032i
\(166\) −8.27745 4.77899i −0.642455 0.370921i
\(167\) 21.8368i 1.68978i 0.534936 + 0.844892i \(0.320336\pi\)
−0.534936 + 0.844892i \(0.679664\pi\)
\(168\) −7.23701 −0.558348
\(169\) −6.47353 + 11.2125i −0.497964 + 0.862499i
\(170\) 6.06783i 0.465381i
\(171\) 0.0303433 0.00232041
\(172\) 0.109770 0.0633756i 0.00836987 0.00483235i
\(173\) 2.04175 1.17881i 0.155232 0.0896231i −0.420372 0.907352i \(-0.638100\pi\)
0.575604 + 0.817729i \(0.304767\pi\)
\(174\) −0.964095 0.556621i −0.0730879 0.0421973i
\(175\) 9.85267 + 5.68844i 0.744792 + 0.430006i
\(176\) 2.30396 1.33019i 0.173668 0.100267i
\(177\) −0.255302 + 0.147399i −0.0191897 + 0.0110792i
\(178\) 4.64420 0.348097
\(179\) 13.2228i 0.988317i −0.869372 0.494158i \(-0.835476\pi\)
0.869372 0.494158i \(-0.164524\pi\)
\(180\) −0.0566364 + 0.0980972i −0.00422143 + 0.00731173i
\(181\) −19.0033 −1.41250 −0.706251 0.707962i \(-0.749615\pi\)
−0.706251 + 0.707962i \(0.749615\pi\)
\(182\) 0.264360i 0.0195957i
\(183\) 16.2649 + 9.39056i 1.20234 + 0.694170i
\(184\) 2.16834 1.25189i 0.159852 0.0922906i
\(185\) −14.3452 + 24.8466i −1.05468 + 1.82676i
\(186\) 5.37436i 0.394067i
\(187\) 4.19828i 0.307009i
\(188\) 2.36307 + 1.36432i 0.172345 + 0.0995034i
\(189\) −8.39861 + 4.84894i −0.610909 + 0.352708i
\(190\) −2.55907 1.47748i −0.185654 0.107188i
\(191\) −12.8844 22.3164i −0.932279 1.61475i −0.779416 0.626507i \(-0.784484\pi\)
−0.152863 0.988247i \(-0.548849\pi\)
\(192\) 0.286866 0.496867i 0.0207028 0.0358583i
\(193\) −13.2079 7.62557i −0.950723 0.548900i −0.0574177 0.998350i \(-0.518287\pi\)
−0.893306 + 0.449450i \(0.851620\pi\)
\(194\) 3.77609 6.54037i 0.271107 0.469571i
\(195\) −1.15242 0.665352i −0.0825268 0.0476469i
\(196\) −2.83485 4.91011i −0.202489 0.350722i
\(197\) 20.3521 + 11.7503i 1.45003 + 0.837175i 0.998482 0.0550715i \(-0.0175387\pi\)
0.451548 + 0.892247i \(0.350872\pi\)
\(198\) 0.00908413 0.0157342i 0.000645581 0.00111818i
\(199\) 9.72255 5.61331i 0.689213 0.397917i −0.114104 0.993469i \(-0.536400\pi\)
0.803317 + 0.595552i \(0.203066\pi\)
\(200\) 11.6946 6.75186i 0.826931 0.477429i
\(201\) 2.98610 5.17208i 0.210624 0.364811i
\(202\) −1.02695 1.77872i −0.0722557 0.125151i
\(203\) 1.95537i 0.137240i
\(204\) 4.19358 + 7.26350i 0.293609 + 0.508546i
\(205\) −16.4896 + 28.5608i −1.15168 + 1.99477i
\(206\) 2.91598 + 5.05062i 0.203166 + 0.351893i
\(207\) −0.0118057 + 0.0204481i −0.000820556 + 0.00142124i
\(208\) 0.375244 + 0.216647i 0.0260185 + 0.0150218i
\(209\) −1.77060 1.02226i −0.122475 0.0707109i
\(210\) −6.64623 −0.458633
\(211\) 15.4516 8.92101i 1.06373 0.614148i 0.137272 0.990533i \(-0.456167\pi\)
0.926463 + 0.376386i \(0.122833\pi\)
\(212\) −0.280776 0.162106i −0.0192838 0.0111335i
\(213\) 7.10719i 0.486976i
\(214\) 5.61331 9.72253i 0.383718 0.664619i
\(215\) 0.224987 0.129896i 0.0153440 0.00885886i
\(216\) 11.5108i 0.783213i
\(217\) 8.17516 4.71993i 0.554966 0.320410i
\(218\) 6.39005i 0.432789i
\(219\) 8.39073 + 14.5332i 0.566993 + 0.982061i
\(220\) 6.60973 3.81613i 0.445628 0.257283i
\(221\) −0.592163 + 0.341885i −0.0398332 + 0.0229977i
\(222\) 9.19322i 0.617008i
\(223\) 14.0792 0.942814 0.471407 0.881916i \(-0.343746\pi\)
0.471407 + 0.881916i \(0.343746\pi\)
\(224\) 10.4916 0.701002
\(225\) −0.0636723 + 0.110284i −0.00424482 + 0.00735224i
\(226\) 1.20517 2.08742i 0.0801670 0.138853i
\(227\) −1.92421 3.33283i −0.127714 0.221207i 0.795076 0.606509i \(-0.207431\pi\)
−0.922791 + 0.385302i \(0.874097\pi\)
\(228\) −4.08444 −0.270499
\(229\) −7.24349 + 4.18203i −0.478664 + 0.276357i −0.719859 0.694120i \(-0.755794\pi\)
0.241196 + 0.970476i \(0.422460\pi\)
\(230\) 1.99133 1.14969i 0.131304 0.0758086i
\(231\) −4.59847 −0.302557
\(232\) 2.00997 + 1.16046i 0.131961 + 0.0761877i
\(233\) −0.830685 1.43879i −0.0544200 0.0942582i 0.837532 0.546388i \(-0.183998\pi\)
−0.891952 + 0.452130i \(0.850664\pi\)
\(234\) 0.00295905 0.000193439
\(235\) 4.84342 + 2.79635i 0.315950 + 0.182414i
\(236\) 0.238487 0.137690i 0.0155242 0.00896288i
\(237\) −2.89194 1.66966i −0.187852 0.108456i
\(238\) −1.70755 + 2.95757i −0.110684 + 0.191710i
\(239\) 21.4273 1.38602 0.693010 0.720928i \(-0.256284\pi\)
0.693010 + 0.720928i \(0.256284\pi\)
\(240\) 5.44669 9.43395i 0.351582 0.608959i
\(241\) 6.71725 11.6346i 0.432696 0.749452i −0.564408 0.825496i \(-0.690896\pi\)
0.997104 + 0.0760440i \(0.0242290\pi\)
\(242\) 4.78424 2.76218i 0.307542 0.177560i
\(243\) −0.108933 0.188677i −0.00698805 0.0121037i
\(244\) −15.1937 8.77206i −0.972674 0.561574i
\(245\) −5.81039 10.0639i −0.371212 0.642958i
\(246\) 10.5675i 0.673757i
\(247\) 0.332988i 0.0211875i
\(248\) 11.2046i 0.711492i
\(249\) −27.0784 −1.71602
\(250\) 1.89944 1.09664i 0.120131 0.0693576i
\(251\) 10.1744i 0.642205i −0.947044 0.321103i \(-0.895947\pi\)
0.947044 0.321103i \(-0.104053\pi\)
\(252\) −0.0552112 + 0.0318762i −0.00347798 + 0.00200801i
\(253\) 1.37778 0.795464i 0.0866205 0.0500104i
\(254\) 1.00905 + 1.74773i 0.0633137 + 0.109663i
\(255\) 8.59528 + 14.8875i 0.538257 + 0.932289i
\(256\) 3.16864 5.48825i 0.198040 0.343016i
\(257\) 23.2200 1.44843 0.724213 0.689577i \(-0.242203\pi\)
0.724213 + 0.689577i \(0.242203\pi\)
\(258\) −0.0416225 + 0.0720923i −0.00259130 + 0.00448827i
\(259\) −13.9842 + 8.07377i −0.868935 + 0.501680i
\(260\) 1.07652 + 0.621530i 0.0667630 + 0.0385456i
\(261\) −0.0218870 −0.00135477
\(262\) −3.38701 5.86647i −0.209250 0.362432i
\(263\) −1.47541 −0.0909775 −0.0454888 0.998965i \(-0.514485\pi\)
−0.0454888 + 0.998965i \(0.514485\pi\)
\(264\) −2.72906 + 4.72687i −0.167962 + 0.290919i
\(265\) −0.575487 0.332258i −0.0353519 0.0204104i
\(266\) −0.831556 1.44030i −0.0509860 0.0883103i
\(267\) 11.3946 6.57866i 0.697336 0.402607i
\(268\) −2.78943 + 4.83143i −0.170391 + 0.295127i
\(269\) −28.1811 −1.71823 −0.859117 0.511780i \(-0.828986\pi\)
−0.859117 + 0.511780i \(0.828986\pi\)
\(270\) 10.5712i 0.643340i
\(271\) 10.2245 + 17.7093i 0.621093 + 1.07577i 0.989282 + 0.146014i \(0.0466446\pi\)
−0.368189 + 0.929751i \(0.620022\pi\)
\(272\) −2.79873 4.84755i −0.169698 0.293926i
\(273\) −0.374474 0.648609i −0.0226642 0.0392556i
\(274\) −0.578582 −0.0349534
\(275\) 7.43084 4.29020i 0.448097 0.258709i
\(276\) 1.58915 2.75248i 0.0956554 0.165680i
\(277\) −18.5938 + 10.7351i −1.11719 + 0.645013i −0.940683 0.339286i \(-0.889815\pi\)
−0.176511 + 0.984299i \(0.556481\pi\)
\(278\) −9.19525 + 5.30888i −0.551494 + 0.318405i
\(279\) 0.0528314 + 0.0915067i 0.00316294 + 0.00547836i
\(280\) 13.8562 0.828067
\(281\) 5.28970 9.16204i 0.315557 0.546561i −0.663998 0.747734i \(-0.731142\pi\)
0.979556 + 0.201173i \(0.0644752\pi\)
\(282\) −1.79206 −0.106716
\(283\) −18.5789 −1.10440 −0.552201 0.833711i \(-0.686212\pi\)
−0.552201 + 0.833711i \(0.686212\pi\)
\(284\) 6.63908i 0.393957i
\(285\) −8.37159 −0.495890
\(286\) −0.172667 0.0996895i −0.0102100 0.00589476i
\(287\) −16.0746 + 9.28069i −0.948855 + 0.547822i
\(288\) 0.117436i 0.00691996i
\(289\) −8.16679 −0.480399
\(290\) 1.84589 + 1.06572i 0.108394 + 0.0625814i
\(291\) 21.3958i 1.25424i
\(292\) −7.83809 13.5760i −0.458689 0.794473i
\(293\) 13.0255 + 22.5608i 0.760958 + 1.31802i 0.942357 + 0.334608i \(0.108604\pi\)
−0.181400 + 0.983409i \(0.558063\pi\)
\(294\) 3.22476 + 1.86181i 0.188072 + 0.108583i
\(295\) 0.488809 0.282214i 0.0284596 0.0164311i
\(296\) 19.1662i 1.11401i
\(297\) 7.31410i 0.424407i
\(298\) 0.875268 1.51601i 0.0507029 0.0878200i
\(299\) 0.224398 + 0.129557i 0.0129773 + 0.00749245i
\(300\) 8.57080 14.8451i 0.494835 0.857080i
\(301\) 0.146217 0.00842780
\(302\) 3.86521i 0.222418i
\(303\) −5.03924 2.90941i −0.289497 0.167141i
\(304\) 2.72590 0.156341
\(305\) −31.1413 17.9795i −1.78315 1.02950i
\(306\) −0.0331048 0.0191131i −0.00189248 0.00109262i
\(307\) 2.95447 + 5.11729i 0.168621 + 0.292059i 0.937935 0.346811i \(-0.112735\pi\)
−0.769315 + 0.638870i \(0.779402\pi\)
\(308\) 4.29560 0.244764
\(309\) 14.3087 + 8.26115i 0.813995 + 0.469961i
\(310\) 10.2899i 0.584427i
\(311\) 17.7597i 1.00706i −0.863978 0.503530i \(-0.832034\pi\)
0.863978 0.503530i \(-0.167966\pi\)
\(312\) −0.888960 −0.0503274
\(313\) −23.4479 −1.32535 −0.662676 0.748906i \(-0.730580\pi\)
−0.662676 + 0.748906i \(0.730580\pi\)
\(314\) 3.05286i 0.172283i
\(315\) −0.113162 + 0.0653343i −0.00637597 + 0.00368117i
\(316\) 2.70146 + 1.55969i 0.151969 + 0.0877395i
\(317\) 5.49568 + 3.17293i 0.308668 + 0.178210i 0.646330 0.763058i \(-0.276303\pi\)
−0.337662 + 0.941267i \(0.609636\pi\)
\(318\) 0.212930 0.0119405
\(319\) 1.27715 + 0.737365i 0.0715069 + 0.0412845i
\(320\) −0.549243 + 0.951317i −0.0307036 + 0.0531803i
\(321\) 31.8057i 1.77522i
\(322\) 1.29414 0.0721198
\(323\) −2.15083 + 3.72535i −0.119675 + 0.207284i
\(324\) 7.35697 + 12.7426i 0.408720 + 0.707925i
\(325\) 1.21026 + 0.698741i 0.0671329 + 0.0387592i
\(326\) 7.27599 + 12.6024i 0.402980 + 0.697981i
\(327\) −9.05172 15.6780i −0.500561 0.866997i
\(328\) 22.0313i 1.21647i
\(329\) 1.57385 + 2.72598i 0.0867689 + 0.150288i
\(330\) −2.50628 + 4.34100i −0.137966 + 0.238964i
\(331\) −8.26094 4.76945i −0.454062 0.262153i 0.255482 0.966814i \(-0.417766\pi\)
−0.709544 + 0.704661i \(0.751099\pi\)
\(332\) 25.2949 1.38824
\(333\) −0.0903719 0.156529i −0.00495235 0.00857772i
\(334\) 6.69847 + 11.6021i 0.366524 + 0.634839i
\(335\) −5.71729 + 9.90263i −0.312369 + 0.541039i
\(336\) 5.30962 3.06551i 0.289664 0.167237i
\(337\) −10.8759 18.8376i −0.592449 1.02615i −0.993902 0.110272i \(-0.964828\pi\)
0.401453 0.915880i \(-0.368505\pi\)
\(338\) 7.94306i 0.432045i
\(339\) 6.82868i 0.370883i
\(340\) −8.02916 13.9069i −0.435442 0.754208i
\(341\) 7.11950i 0.385543i
\(342\) 0.0161216 0.00930783i 0.000871758 0.000503310i
\(343\) 19.6511i 1.06106i
\(344\) 0.0867756 0.150300i 0.00467863 0.00810362i
\(345\) 3.25716 5.64156i 0.175360 0.303732i
\(346\) 0.723201 1.25262i 0.0388795 0.0673413i
\(347\) 26.8484 15.5009i 1.44130 0.832132i 0.443359 0.896344i \(-0.353787\pi\)
0.997936 + 0.0642118i \(0.0204533\pi\)
\(348\) 2.94616 0.157931
\(349\) −13.5793 12.8297i −0.726884 0.686761i
\(350\) 6.97975 0.373083
\(351\) −1.03164 + 0.595620i −0.0550651 + 0.0317919i
\(352\) 3.95637 6.85264i 0.210875 0.365247i
\(353\) −1.04883 + 1.81663i −0.0558237 + 0.0966895i −0.892587 0.450876i \(-0.851112\pi\)
0.836763 + 0.547565i \(0.184445\pi\)
\(354\) −0.0904294 + 0.156628i −0.00480627 + 0.00832470i
\(355\) 13.6076i 0.722219i
\(356\) −10.6441 + 6.14536i −0.564135 + 0.325704i
\(357\) 9.67521i 0.512066i
\(358\) −4.05610 7.02538i −0.214372 0.371303i
\(359\) 25.6085i 1.35156i 0.737101 + 0.675782i \(0.236194\pi\)
−0.737101 + 0.675782i \(0.763806\pi\)
\(360\) 0.155096i 0.00817429i
\(361\) 8.45257 + 14.6403i 0.444872 + 0.770541i
\(362\) −10.0966 + 5.82927i −0.530665 + 0.306380i
\(363\) 7.82543 13.5541i 0.410729 0.711403i
\(364\) 0.349810 + 0.605889i 0.0183350 + 0.0317572i
\(365\) −16.0652 27.8257i −0.840889 1.45646i
\(366\) 11.5223 0.602278
\(367\) −20.4888 11.8292i −1.06951 0.617481i −0.141461 0.989944i \(-0.545180\pi\)
−0.928047 + 0.372463i \(0.878513\pi\)
\(368\) −1.06057 + 1.83697i −0.0552862 + 0.0957585i
\(369\) −0.103881 0.179927i −0.00540784 0.00936665i
\(370\) 17.6016i 0.915064i
\(371\) −0.187002 0.323896i −0.00970864 0.0168159i
\(372\) −7.11153 12.3175i −0.368716 0.638634i
\(373\) −7.28703 4.20717i −0.377308 0.217839i 0.299338 0.954147i \(-0.403234\pi\)
−0.676646 + 0.736308i \(0.736567\pi\)
\(374\) 1.28783 + 2.23058i 0.0665920 + 0.115341i
\(375\) 3.10685 5.38123i 0.160437 0.277885i
\(376\) 3.73613 0.192676
\(377\) 0.240188i 0.0123703i
\(378\) −2.97484 + 5.15257i −0.153009 + 0.265019i
\(379\) 5.22242 + 3.01517i 0.268258 + 0.154879i 0.628096 0.778136i \(-0.283835\pi\)
−0.359838 + 0.933015i \(0.617168\pi\)
\(380\) 7.82020 0.401168
\(381\) 4.95144 + 2.85872i 0.253670 + 0.146457i
\(382\) −13.6911 7.90458i −0.700499 0.404434i
\(383\) −0.167612 + 0.0967709i −0.00856458 + 0.00494476i −0.504276 0.863542i \(-0.668241\pi\)
0.495712 + 0.868487i \(0.334907\pi\)
\(384\) 19.8243i 1.01165i
\(385\) 8.80437 0.448712
\(386\) −9.35661 −0.476239
\(387\) 0.00163664i 8.31953e-5i
\(388\) 19.9866i 1.01467i
\(389\) −19.7186 11.3845i −0.999770 0.577218i −0.0915901 0.995797i \(-0.529195\pi\)
−0.908180 + 0.418579i \(0.862528\pi\)
\(390\) −0.816390 −0.0413395
\(391\) −1.67366 2.89887i −0.0846407 0.146602i
\(392\) −6.72305 3.88155i −0.339565 0.196048i
\(393\) −16.6201 9.59562i −0.838373 0.484035i
\(394\) 14.4177 0.726353
\(395\) 5.53699 + 3.19678i 0.278596 + 0.160848i
\(396\) 0.0480818i 0.00241620i
\(397\) −27.8060 −1.39554 −0.697772 0.716320i \(-0.745825\pi\)
−0.697772 + 0.716320i \(0.745825\pi\)
\(398\) 3.44378 5.96480i 0.172621 0.298989i
\(399\) −4.08046 2.35585i −0.204278 0.117940i
\(400\) −5.72002 + 9.90736i −0.286001 + 0.495368i
\(401\) 3.81576i 0.190550i −0.995451 0.0952749i \(-0.969627\pi\)
0.995451 0.0952749i \(-0.0303730\pi\)
\(402\) 3.66396i 0.182742i
\(403\) 1.00420 0.579773i 0.0500226 0.0288806i
\(404\) 4.70734 + 2.71778i 0.234199 + 0.135215i
\(405\) 15.0790 + 26.1177i 0.749284 + 1.29780i
\(406\) 0.599812 + 1.03890i 0.0297681 + 0.0515599i
\(407\) 12.1784i 0.603661i
\(408\) 9.94537 + 5.74196i 0.492369 + 0.284270i
\(409\) 3.25947 0.161171 0.0805853 0.996748i \(-0.474321\pi\)
0.0805853 + 0.996748i \(0.474321\pi\)
\(410\) 20.2328i 0.999227i
\(411\) −1.41955 + 0.819580i −0.0700215 + 0.0404269i
\(412\) −13.3663 7.71704i −0.658511 0.380191i
\(413\) 0.317672 0.0156316
\(414\) 0.0144857i 0.000711933i
\(415\) 51.8451 2.54497
\(416\) 1.28874 0.0631858
\(417\) −15.0404 + 26.0507i −0.736531 + 1.27571i
\(418\) −1.25431 −0.0613504
\(419\) −15.1268 26.2003i −0.738991 1.27997i −0.952950 0.303128i \(-0.901969\pi\)
0.213959 0.976843i \(-0.431364\pi\)
\(420\) 15.2325 8.79452i 0.743272 0.429128i
\(421\) 8.95658 5.17108i 0.436517 0.252023i −0.265602 0.964083i \(-0.585571\pi\)
0.702119 + 0.712060i \(0.252237\pi\)
\(422\) 5.47306 9.47962i 0.266424 0.461461i
\(423\) −0.0305126 + 0.0176165i −0.00148357 + 0.000856542i
\(424\) −0.443921 −0.0215587
\(425\) −9.02661 15.6345i −0.437855 0.758387i
\(426\) 2.18014 + 3.77611i 0.105628 + 0.182953i
\(427\) −10.1192 17.5270i −0.489703 0.848191i
\(428\) 29.7109i 1.43613i
\(429\) −0.564854 −0.0272714
\(430\) 0.0796918 0.138030i 0.00384308 0.00665641i
\(431\) 8.44729 4.87705i 0.406892 0.234919i −0.282562 0.959249i \(-0.591184\pi\)
0.689453 + 0.724330i \(0.257851\pi\)
\(432\) −4.87585 8.44523i −0.234590 0.406321i
\(433\) 33.4358 + 19.3042i 1.60682 + 0.927699i 0.990075 + 0.140537i \(0.0448830\pi\)
0.616747 + 0.787162i \(0.288450\pi\)
\(434\) 2.89569 5.01548i 0.138997 0.240751i
\(435\) 6.03853 0.289525
\(436\) 8.45554 + 14.6454i 0.404947 + 0.701388i
\(437\) 1.63010 0.0779784
\(438\) 8.91614 + 5.14773i 0.426030 + 0.245968i
\(439\) −6.00345 + 3.46609i −0.286529 + 0.165428i −0.636376 0.771379i \(-0.719567\pi\)
0.349846 + 0.936807i \(0.386234\pi\)
\(440\) 5.22515 9.05022i 0.249099 0.431452i
\(441\) 0.0732087 0.00348613
\(442\) −0.209747 + 0.363293i −0.00997666 + 0.0172801i
\(443\) −17.2172 29.8211i −0.818014 1.41684i −0.907144 0.420821i \(-0.861742\pi\)
0.0891298 0.996020i \(-0.471591\pi\)
\(444\) 12.1648 + 21.0700i 0.577315 + 0.999939i
\(445\) −21.8164 + 12.5957i −1.03420 + 0.597093i
\(446\) 7.48041 4.31882i 0.354208 0.204502i
\(447\) 4.95938i 0.234571i
\(448\) −0.535421 + 0.309126i −0.0252963 + 0.0146048i
\(449\) 1.55122 0.0732066 0.0366033 0.999330i \(-0.488346\pi\)
0.0366033 + 0.999330i \(0.488346\pi\)
\(450\) 0.0781262i 0.00368290i
\(451\) 13.9989i 0.659183i
\(452\) 6.37891i 0.300039i
\(453\) 5.47520 + 9.48333i 0.257247 + 0.445566i
\(454\) −2.04470 1.18051i −0.0959624 0.0554039i
\(455\) 0.716980 + 1.24185i 0.0336125 + 0.0582186i
\(456\) −4.84327 + 2.79626i −0.226807 + 0.130947i
\(457\) −8.27396 + 14.3309i −0.387040 + 0.670372i −0.992050 0.125845i \(-0.959836\pi\)
0.605010 + 0.796218i \(0.293169\pi\)
\(458\) −2.56569 + 4.44390i −0.119887 + 0.207650i
\(459\) 15.3889 0.718293
\(460\) −3.04263 + 5.26999i −0.141863 + 0.245715i
\(461\) −5.81772 3.35886i −0.270958 0.156438i 0.358365 0.933582i \(-0.383334\pi\)
−0.629323 + 0.777144i \(0.716668\pi\)
\(462\) −2.44321 + 1.41059i −0.113668 + 0.0656264i
\(463\) 9.41200 + 5.43402i 0.437413 + 0.252540i 0.702499 0.711684i \(-0.252067\pi\)
−0.265087 + 0.964225i \(0.585401\pi\)
\(464\) −1.96622 −0.0912796
\(465\) −14.5760 25.2464i −0.675945 1.17077i
\(466\) −0.882700 0.509627i −0.0408903 0.0236080i
\(467\) −2.58142 −0.119454 −0.0597269 0.998215i \(-0.519023\pi\)
−0.0597269 + 0.998215i \(0.519023\pi\)
\(468\) −0.00678187 + 0.00391552i −0.000313492 + 0.000180995i
\(469\) −5.57341 + 3.21781i −0.257356 + 0.148585i
\(470\) 3.43114 0.158266
\(471\) −4.32447 7.49021i −0.199261 0.345131i
\(472\) 0.188529 0.326542i 0.00867777 0.0150303i
\(473\) 0.0551381 0.0955019i 0.00253525 0.00439118i
\(474\) −2.04868 −0.0940991
\(475\) 8.79169 0.403390
\(476\) 9.03796i 0.414254i
\(477\) 0.00362546 0.00209316i 0.000165998 9.58391e-5i
\(478\) 11.3845 6.57286i 0.520716 0.300636i
\(479\) −0.128922 0.223300i −0.00589061 0.0102028i 0.863065 0.505093i \(-0.168542\pi\)
−0.868956 + 0.494890i \(0.835208\pi\)
\(480\) 32.4000i 1.47885i
\(481\) −1.71775 + 0.991744i −0.0783227 + 0.0452196i
\(482\) 8.24210i 0.375417i
\(483\) 3.17519 1.83320i 0.144476 0.0834134i
\(484\) −7.31002 + 12.6613i −0.332274 + 0.575515i
\(485\) 40.9650i 1.86013i
\(486\) −0.115754 0.0668306i −0.00525071 0.00303150i
\(487\) 3.74062 2.15965i 0.169504 0.0978629i −0.412848 0.910800i \(-0.635466\pi\)
0.582352 + 0.812937i \(0.302133\pi\)
\(488\) −24.0219 −1.08742
\(489\) 35.7034 + 20.6133i 1.61456 + 0.932168i
\(490\) −6.17422 3.56469i −0.278923 0.161036i
\(491\) 2.01333 3.48719i 0.0908603 0.157375i −0.817013 0.576619i \(-0.804372\pi\)
0.907873 + 0.419244i \(0.137705\pi\)
\(492\) 13.9832 + 24.2197i 0.630413 + 1.09191i
\(493\) 1.55142 2.68714i 0.0698725 0.121023i
\(494\) −0.102144 0.176919i −0.00459569 0.00795997i
\(495\) 0.0985497i 0.00442948i
\(496\) 4.74613 + 8.22054i 0.213107 + 0.369113i
\(497\) 3.82933 6.63260i 0.171769 0.297513i
\(498\) −14.3870 + 8.30632i −0.644696 + 0.372215i
\(499\) 27.1828 15.6940i 1.21687 0.702559i 0.252621 0.967565i \(-0.418707\pi\)
0.964247 + 0.265006i \(0.0853740\pi\)
\(500\) −2.90222 + 5.02680i −0.129791 + 0.224805i
\(501\) 32.8695 + 18.9772i 1.46850 + 0.847839i
\(502\) −3.12102 5.40577i −0.139298 0.241271i
\(503\) −23.7100 13.6890i −1.05717 0.610360i −0.132525 0.991180i \(-0.542309\pi\)
−0.924649 + 0.380819i \(0.875642\pi\)
\(504\) −0.0436457 + 0.0755966i −0.00194413 + 0.00336734i
\(505\) 9.64828 + 5.57044i 0.429343 + 0.247881i
\(506\) 0.488019 0.845274i 0.0216951 0.0375770i
\(507\) 11.2516 + 19.4883i 0.499701 + 0.865508i
\(508\) −4.62532 2.67043i −0.205216 0.118481i
\(509\) 7.16921 4.13915i 0.317770 0.183464i −0.332628 0.943058i \(-0.607935\pi\)
0.650398 + 0.759594i \(0.274602\pi\)
\(510\) 9.13349 + 5.27322i 0.404438 + 0.233502i
\(511\) 18.0836i 0.799972i
\(512\) 18.9236i 0.836314i
\(513\) −3.74710 + 6.49017i −0.165439 + 0.286548i
\(514\) 12.3370 7.12277i 0.544162 0.314172i
\(515\) −27.3959 15.8171i −1.20721 0.696983i
\(516\) 0.220305i 0.00969840i
\(517\) 2.37397 0.104407
\(518\) −4.95328 + 8.57933i −0.217635 + 0.376954i
\(519\) 4.09775i 0.179871i
\(520\) 1.70203 0.0746389
\(521\) −25.5662 + 14.7606i −1.12007 + 0.646675i −0.941420 0.337237i \(-0.890508\pi\)
−0.178655 + 0.983912i \(0.557174\pi\)
\(522\) −0.0116287 + 0.00671385i −0.000508976 + 0.000293857i
\(523\) 28.6615 + 16.5477i 1.25328 + 0.723582i 0.971760 0.235972i \(-0.0758275\pi\)
0.281522 + 0.959555i \(0.409161\pi\)
\(524\) 15.5254 + 8.96361i 0.678232 + 0.391577i
\(525\) 17.1249 9.88704i 0.747390 0.431506i
\(526\) −0.783897 + 0.452583i −0.0341795 + 0.0197336i
\(527\) −14.9795 −0.652516
\(528\) 4.62399i 0.201233i
\(529\) 10.8658 18.8201i 0.472425 0.818264i
\(530\) −0.407682 −0.0177086
\(531\) 0.00355579i 0.000154308i
\(532\) 3.81170 + 2.20069i 0.165258 + 0.0954119i
\(533\) −1.97453 + 1.13999i −0.0855263 + 0.0493787i
\(534\) 4.03602 6.99059i 0.174656 0.302513i
\(535\) 60.8962i 2.63277i
\(536\) 7.63872i 0.329942i
\(537\) −19.9033 11.4912i −0.858893 0.495882i
\(538\) −14.9729 + 8.64459i −0.645526 + 0.372695i
\(539\) −4.27189 2.46638i −0.184003 0.106234i
\(540\) −13.9881 24.2281i −0.601953 1.04261i
\(541\) 14.0233 24.2891i 0.602909 1.04427i −0.389469 0.921040i \(-0.627341\pi\)
0.992378 0.123230i \(-0.0393252\pi\)
\(542\) 10.8647 + 6.27275i 0.466680 + 0.269438i
\(543\) −16.5147 + 28.6043i −0.708714 + 1.22753i
\(544\) −14.4180 8.32423i −0.618166 0.356898i
\(545\) 17.3307 + 30.0176i 0.742365 + 1.28581i
\(546\) −0.397923 0.229741i −0.0170295 0.00983200i
\(547\) 7.28566 12.6191i 0.311512 0.539555i −0.667178 0.744898i \(-0.732498\pi\)
0.978690 + 0.205344i \(0.0658312\pi\)
\(548\) 1.32606 0.765600i 0.0566464 0.0327048i
\(549\) 0.196184 0.113267i 0.00837295 0.00483412i
\(550\) 2.63205 4.55884i 0.112231 0.194390i
\(551\) 0.755522 + 1.30860i 0.0321863 + 0.0557484i
\(552\) 4.35180i 0.185225i
\(553\) 1.79922 + 3.11634i 0.0765105 + 0.132520i
\(554\) −6.58604 + 11.4074i −0.279814 + 0.484652i
\(555\) 24.9333 + 43.1857i 1.05836 + 1.83313i
\(556\) 14.0498 24.3349i 0.595843 1.03203i
\(557\) −4.68419 2.70442i −0.198476 0.114590i 0.397469 0.917616i \(-0.369889\pi\)
−0.595944 + 0.803026i \(0.703222\pi\)
\(558\) 0.0561396 + 0.0324122i 0.00237658 + 0.00137212i
\(559\) 0.0179606 0.000759652
\(560\) −10.1660 + 5.86933i −0.429591 + 0.248024i
\(561\) 6.31939 + 3.64850i 0.266805 + 0.154040i
\(562\) 6.49049i 0.273785i
\(563\) −20.6412 + 35.7516i −0.869923 + 1.50675i −0.00784914 + 0.999969i \(0.502498\pi\)
−0.862074 + 0.506782i \(0.830835\pi\)
\(564\) 4.10724 2.37132i 0.172946 0.0998505i
\(565\) 13.0744i 0.550044i
\(566\) −9.87114 + 5.69910i −0.414915 + 0.239551i
\(567\) 16.9736i 0.712824i
\(568\) −4.54520 7.87252i −0.190712 0.330324i
\(569\) 0.643856 0.371730i 0.0269918 0.0155837i −0.486443 0.873712i \(-0.661706\pi\)
0.513435 + 0.858128i \(0.328373\pi\)
\(570\) −4.44790 + 2.56799i −0.186302 + 0.107561i
\(571\) 7.66294i 0.320684i 0.987062 + 0.160342i \(0.0512597\pi\)
−0.987062 + 0.160342i \(0.948740\pi\)
\(572\) 0.527650 0.0220622
\(573\) −44.7884 −1.87106
\(574\) −5.69372 + 9.86182i −0.237651 + 0.411624i
\(575\) −3.42061 + 5.92467i −0.142649 + 0.247076i
\(576\) −0.00346013 0.00599312i −0.000144172 0.000249713i
\(577\) −45.5001 −1.89419 −0.947097 0.320947i \(-0.895999\pi\)
−0.947097 + 0.320947i \(0.895999\pi\)
\(578\) −4.33909 + 2.50517i −0.180482 + 0.104201i
\(579\) −22.9565 + 13.2539i −0.954039 + 0.550815i
\(580\) −5.64081 −0.234222
\(581\) 25.2702 + 14.5898i 1.04838 + 0.605285i
\(582\) −6.56318 11.3678i −0.272053 0.471209i
\(583\) −0.282071 −0.0116822
\(584\) −18.5886 10.7321i −0.769201 0.444098i
\(585\) −0.0139003 + 0.00802535i −0.000574707 + 0.000331807i
\(586\) 13.8411 + 7.99117i 0.571771 + 0.330112i
\(587\) −20.7141 + 35.8779i −0.854964 + 1.48084i 0.0217140 + 0.999764i \(0.493088\pi\)
−0.876678 + 0.481077i \(0.840246\pi\)
\(588\) −9.85447 −0.406391
\(589\) 3.64741 6.31750i 0.150289 0.260308i
\(590\) 0.173139 0.299885i 0.00712802 0.0123461i
\(591\) 35.3739 20.4231i 1.45509 0.840095i
\(592\) −8.11859 14.0618i −0.333672 0.577937i
\(593\) 16.7709 + 9.68267i 0.688697 + 0.397620i 0.803124 0.595812i \(-0.203170\pi\)
−0.114426 + 0.993432i \(0.536503\pi\)
\(594\) 2.24361 + 3.88604i 0.0920563 + 0.159446i
\(595\) 18.5245i 0.759428i
\(596\) 4.63274i 0.189764i
\(597\) 19.5129i 0.798610i
\(598\) 0.158966 0.00650062
\(599\) −30.9837 + 17.8885i −1.26596 + 0.730903i −0.974221 0.225595i \(-0.927567\pi\)
−0.291740 + 0.956498i \(0.594234\pi\)
\(600\) 23.4707i 0.958188i
\(601\) 24.9309 14.3939i 1.01695 0.587139i 0.103734 0.994605i \(-0.466921\pi\)
0.913220 + 0.407467i \(0.133588\pi\)
\(602\) 0.0776863 0.0448522i 0.00316626 0.00182804i
\(603\) −0.0360178 0.0623847i −0.00146676 0.00254050i
\(604\) −5.11459 8.85872i −0.208110 0.360456i
\(605\) −14.9828 + 25.9510i −0.609138 + 1.05506i
\(606\) −3.56986 −0.145015
\(607\) 1.15276 1.99664i 0.0467891 0.0810411i −0.841682 0.539973i \(-0.818434\pi\)
0.888471 + 0.458932i \(0.151768\pi\)
\(608\) 7.02138 4.05380i 0.284755 0.164403i
\(609\) 2.94328 + 1.69931i 0.119268 + 0.0688593i
\(610\) −22.0609 −0.893219
\(611\) 0.193324 + 0.334846i 0.00782103 + 0.0135464i
\(612\) 0.101164 0.00408933
\(613\) −1.82628 + 3.16321i −0.0737629 + 0.127761i −0.900548 0.434757i \(-0.856834\pi\)
0.826785 + 0.562518i \(0.190167\pi\)
\(614\) 3.13947 + 1.81257i 0.126699 + 0.0731496i
\(615\) 28.6604 + 49.6413i 1.15570 + 2.00173i
\(616\) 5.09365 2.94082i 0.205229 0.118489i
\(617\) 10.5166 18.2152i 0.423381 0.733318i −0.572886 0.819635i \(-0.694176\pi\)
0.996268 + 0.0863168i \(0.0275097\pi\)
\(618\) 10.1365 0.407749
\(619\) 15.1100i 0.607322i −0.952780 0.303661i \(-0.901791\pi\)
0.952780 0.303661i \(-0.0982090\pi\)
\(620\) 13.6160 + 23.5835i 0.546830 + 0.947138i
\(621\) −2.91579 5.05030i −0.117007 0.202662i
\(622\) −5.44781 9.43588i −0.218437 0.378344i
\(623\) −14.1783 −0.568040
\(624\) 0.652209 0.376553i 0.0261092 0.0150742i
\(625\) 9.23724 15.9994i 0.369490 0.639975i
\(626\) −12.4581 + 7.19267i −0.497924 + 0.287477i
\(627\) −3.07746 + 1.77677i −0.122902 + 0.0709575i
\(628\) 4.03965 + 6.99688i 0.161200 + 0.279206i
\(629\) 25.6235 1.02167
\(630\) −0.0400827 + 0.0694253i −0.00159693 + 0.00276597i
\(631\) 24.6149 0.979904 0.489952 0.871749i \(-0.337014\pi\)
0.489952 + 0.871749i \(0.337014\pi\)
\(632\) 4.27114 0.169897
\(633\) 31.0111i 1.23258i
\(634\) 3.89320 0.154619
\(635\) −9.48019 5.47339i −0.376210 0.217205i
\(636\) −0.488015 + 0.281756i −0.0193511 + 0.0111723i
\(637\) 0.803394i 0.0318316i
\(638\) 0.904750 0.0358194
\(639\) 0.0742405 + 0.0428628i 0.00293691 + 0.00169562i
\(640\) 37.9562i 1.50035i
\(641\) 23.4479 + 40.6130i 0.926137 + 1.60412i 0.789723 + 0.613464i \(0.210224\pi\)
0.136414 + 0.990652i \(0.456442\pi\)
\(642\) −9.75644 16.8987i −0.385056 0.666937i
\(643\) −22.1319 12.7779i −0.872796 0.503909i −0.00451991 0.999990i \(-0.501439\pi\)
−0.868277 + 0.496081i \(0.834772\pi\)
\(644\) −2.96606 + 1.71246i −0.116879 + 0.0674802i
\(645\) 0.451544i 0.0177795i
\(646\) 2.63908i 0.103833i
\(647\) 1.91741 3.32105i 0.0753810 0.130564i −0.825871 0.563859i \(-0.809316\pi\)
0.901252 + 0.433295i \(0.142649\pi\)
\(648\) 17.4476 + 10.0734i 0.685405 + 0.395719i
\(649\) 0.119793 0.207488i 0.00470230 0.00814463i
\(650\) 0.857359 0.0336284
\(651\) 16.4073i 0.643055i
\(652\) −33.3518 19.2557i −1.30616 0.754110i
\(653\) 34.2862 1.34172 0.670861 0.741583i \(-0.265925\pi\)
0.670861 + 0.741583i \(0.265925\pi\)
\(654\) −9.61851 5.55325i −0.376113 0.217149i
\(655\) 31.8213 + 18.3721i 1.24336 + 0.717856i
\(656\) −9.33220 16.1638i −0.364361 0.631092i
\(657\) 0.202415 0.00789695
\(658\) 1.67239 + 0.965558i 0.0651967 + 0.0376414i
\(659\) 18.9914i 0.739800i −0.929071 0.369900i \(-0.879392\pi\)
0.929071 0.369900i \(-0.120608\pi\)
\(660\) 13.2656i 0.516362i
\(661\) 8.93945 0.347704 0.173852 0.984772i \(-0.444378\pi\)
0.173852 + 0.984772i \(0.444378\pi\)
\(662\) −5.85214 −0.227450
\(663\) 1.18846i 0.0461558i
\(664\) 29.9943 17.3172i 1.16400 0.672038i
\(665\) 7.81257 + 4.51059i 0.302958 + 0.174913i
\(666\) −0.0960308 0.0554434i −0.00372112 0.00214839i
\(667\) −1.17581 −0.0455277
\(668\) −30.7046 17.7273i −1.18800 0.685890i
\(669\) 12.2355 21.1925i 0.473051 0.819349i
\(670\) 7.01514i 0.271018i
\(671\) −15.2637 −0.589250
\(672\) 9.11771 15.7923i 0.351723 0.609203i
\(673\) 10.0331 + 17.3778i 0.386747 + 0.669865i 0.992010 0.126160i \(-0.0402654\pi\)
−0.605263 + 0.796026i \(0.706932\pi\)
\(674\) −11.5569 6.67240i −0.445156 0.257011i
\(675\) −15.7258 27.2379i −0.605288 1.04839i
\(676\) −10.5105 18.2048i −0.404251 0.700183i
\(677\) 45.4038i 1.74501i −0.488607 0.872504i \(-0.662495\pi\)
0.488607 0.872504i \(-0.337505\pi\)
\(678\) −2.09470 3.62814i −0.0804467 0.139338i
\(679\) −11.5280 + 19.9671i −0.442404 + 0.766266i
\(680\) −19.0417 10.9937i −0.730216 0.421591i
\(681\) −6.68890 −0.256319
\(682\) −2.18392 3.78265i −0.0836264 0.144845i
\(683\) −2.05789 3.56437i −0.0787430 0.136387i 0.823965 0.566641i \(-0.191757\pi\)
−0.902708 + 0.430254i \(0.858424\pi\)
\(684\) −0.0246329 + 0.0426654i −0.000941862 + 0.00163135i
\(685\) 2.71792 1.56919i 0.103846 0.0599558i
\(686\) −6.02801 10.4408i −0.230150 0.398632i
\(687\) 14.5375i 0.554641i
\(688\) 0.147028i 0.00560541i
\(689\) −0.0229704 0.0397858i −0.000875101 0.00151572i
\(690\) 3.99655i 0.152146i
\(691\) −2.28162 + 1.31730i −0.0867970 + 0.0501123i −0.542770 0.839881i \(-0.682625\pi\)
0.455973 + 0.889993i \(0.349291\pi\)
\(692\) 3.82786i 0.145513i
\(693\) −0.0277329 + 0.0480348i −0.00105349 + 0.00182469i
\(694\) 9.50984 16.4715i 0.360989 0.625251i
\(695\) 28.7968 49.8775i 1.09233 1.89196i
\(696\) 3.49351 2.01698i 0.132421 0.0764534i
\(697\) 29.4538 1.11564
\(698\) −11.1503 2.65109i −0.422047 0.100345i
\(699\) −2.88761 −0.109220
\(700\) −15.9969 + 9.23584i −0.604628 + 0.349082i
\(701\) −0.443390 + 0.767973i −0.0167466 + 0.0290060i −0.874277 0.485427i \(-0.838664\pi\)
0.857531 + 0.514433i \(0.171998\pi\)
\(702\) −0.365414 + 0.632916i −0.0137917 + 0.0238879i
\(703\) −6.23915 + 10.8065i −0.235314 + 0.407576i
\(704\) 0.466283i 0.0175737i
\(705\) 8.41831 4.86032i 0.317052 0.183050i
\(706\) 1.28692i 0.0484340i
\(707\) 3.13516 + 5.43026i 0.117910 + 0.204226i
\(708\) 0.478637i 0.0179883i
\(709\) 26.1593i 0.982432i −0.871038 0.491216i \(-0.836553\pi\)
0.871038 0.491216i \(-0.163447\pi\)
\(710\) −4.17416 7.22986i −0.156653 0.271332i
\(711\) −0.0348820 + 0.0201391i −0.00130818 + 0.000755276i
\(712\) −8.41439 + 14.5742i −0.315343 + 0.546189i
\(713\) 2.83822 + 4.91594i 0.106292 + 0.184103i
\(714\) 2.96788 + 5.14052i 0.111070 + 0.192379i
\(715\) 1.08149 0.0404453
\(716\) 18.5924 + 10.7343i 0.694832 + 0.401161i
\(717\) 18.6213 32.2531i 0.695427 1.20451i
\(718\) 7.85543 + 13.6060i 0.293162 + 0.507772i
\(719\) 13.0545i 0.486850i −0.969920 0.243425i \(-0.921729\pi\)
0.969920 0.243425i \(-0.0782709\pi\)
\(720\) −0.0656969 0.113790i −0.00244838 0.00424072i
\(721\) −8.90217 15.4190i −0.331534 0.574234i
\(722\) 8.98185 + 5.18567i 0.334270 + 0.192991i
\(723\) −11.6752 20.2220i −0.434205 0.752066i
\(724\) 15.4270 26.7203i 0.573339 0.993053i
\(725\) −6.34155 −0.235519
\(726\) 9.60185i 0.356358i
\(727\) 17.3905 30.1213i 0.644979 1.11714i −0.339327 0.940669i \(-0.610199\pi\)
0.984306 0.176469i \(-0.0564674\pi\)
\(728\) 0.829599 + 0.478969i 0.0307470 + 0.0177518i
\(729\) 26.8087 0.992914
\(730\) −17.0711 9.85601i −0.631830 0.364787i
\(731\) −0.200937 0.116011i −0.00743191 0.00429082i
\(732\) −26.4080 + 15.2467i −0.976067 + 0.563533i
\(733\) 39.7094i 1.46670i −0.679851 0.733350i \(-0.737956\pi\)
0.679851 0.733350i \(-0.262044\pi\)
\(734\) −14.5145 −0.535741
\(735\) −20.1980 −0.745014
\(736\) 6.30889i 0.232549i
\(737\) 4.85372i 0.178789i
\(738\) −0.110386 0.0637314i −0.00406336 0.00234598i
\(739\) 4.77294 0.175575 0.0877877 0.996139i \(-0.472020\pi\)
0.0877877 + 0.996139i \(0.472020\pi\)
\(740\) −23.2911 40.3413i −0.856197 1.48298i
\(741\) −0.501224 0.289382i −0.0184129 0.0106307i
\(742\) −0.198711 0.114726i −0.00729491 0.00421172i
\(743\) 27.1790 0.997100 0.498550 0.866861i \(-0.333866\pi\)
0.498550 + 0.866861i \(0.333866\pi\)
\(744\) −16.8655 9.73730i −0.618319 0.356987i
\(745\) 9.49539i 0.347884i
\(746\) −5.16221 −0.189002
\(747\) −0.163307 + 0.282856i −0.00597509 + 0.0103492i
\(748\) −5.90317 3.40820i −0.215841 0.124616i
\(749\) −17.1368 + 29.6819i −0.626166 + 1.08455i
\(750\) 3.81212i 0.139199i
\(751\) 0.119762i 0.00437016i 0.999998 + 0.00218508i \(0.000695533\pi\)
−0.999998 + 0.00218508i \(0.999304\pi\)
\(752\) −2.74111 + 1.58258i −0.0999580 + 0.0577108i
\(753\) −15.3149 8.84206i −0.558106 0.322223i
\(754\) 0.0736780 + 0.127614i 0.00268319 + 0.00464743i
\(755\) −10.4830 18.1571i −0.381515 0.660804i
\(756\) 15.7456i 0.572663i
\(757\) 31.5162 + 18.1959i 1.14548 + 0.661342i 0.947781 0.318922i \(-0.103321\pi\)
0.197696 + 0.980263i \(0.436654\pi\)
\(758\) 3.69962 0.134376
\(759\) 2.76518i 0.100370i
\(760\) 9.27308 5.35381i 0.336370 0.194203i
\(761\) 29.8156 + 17.2140i 1.08081 + 0.624008i 0.931116 0.364724i \(-0.118837\pi\)
0.149698 + 0.988732i \(0.452170\pi\)
\(762\) 3.50766 0.127069
\(763\) 19.5082i 0.706243i
\(764\) 41.8384 1.51366
\(765\) 0.207349 0.00749672