Properties

Label 441.2.g.g.79.5
Level $441$
Weight $2$
Character 441.79
Analytic conductor $3.521$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 7 x^{10} + 37 x^{8} - 78 x^{6} + 123 x^{4} - 36 x^{2} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.5
Root \(0.474636 - 0.274031i\) of defining polynomial
Character \(\chi\) \(=\) 441.79
Dual form 441.2.g.g.67.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.849814 + 1.47192i) q^{2} +(-1.58016 - 0.709292i) q^{3} +(-0.444368 + 0.769668i) q^{4} -0.949271 q^{5} +(-0.298820 - 2.92864i) q^{6} +1.88874 q^{8} +(1.99381 + 2.24159i) q^{9} +O(q^{10})\) \(q+(0.849814 + 1.47192i) q^{2} +(-1.58016 - 0.709292i) q^{3} +(-0.444368 + 0.769668i) q^{4} -0.949271 q^{5} +(-0.298820 - 2.92864i) q^{6} +1.88874 q^{8} +(1.99381 + 2.24159i) q^{9} +(-0.806704 - 1.39725i) q^{10} -0.588364 q^{11} +(1.24809 - 0.901012i) q^{12} +(2.50987 + 4.34722i) q^{13} +(1.50000 + 0.673310i) q^{15} +(2.49381 + 4.31941i) q^{16} +(3.79121 + 6.56657i) q^{17} +(-1.60507 + 4.83967i) q^{18} +(2.23061 - 3.86353i) q^{19} +(0.421826 - 0.730623i) q^{20} +(-0.500000 - 0.866025i) q^{22} +2.47710 q^{23} +(-2.98450 - 1.33966i) q^{24} -4.09888 q^{25} +(-4.26584 + 7.38866i) q^{26} +(-1.56060 - 4.95626i) q^{27} +(-2.73855 + 4.74331i) q^{29} +(0.283662 + 2.78007i) q^{30} +(3.03731 - 5.26078i) q^{31} +(-2.34981 + 4.07000i) q^{32} +(0.929709 + 0.417322i) q^{33} +(-6.44364 + 11.1607i) q^{34} +(-2.61126 + 0.538481i) q^{36} +(3.49381 - 6.05146i) q^{37} +7.58242 q^{38} +(-0.882546 - 8.64953i) q^{39} -1.79292 q^{40} +(0.527445 + 0.913562i) q^{41} +(-3.49381 + 6.05146i) q^{43} +(0.261450 - 0.452845i) q^{44} +(-1.89267 - 2.12788i) q^{45} +(2.10507 + 3.64610i) q^{46} +(3.73840 + 6.47510i) q^{47} +(-0.876899 - 8.59419i) q^{48} +(-3.48329 - 6.03323i) q^{50} +(-1.33310 - 13.0653i) q^{51} -4.46122 q^{52} +(-3.46108 - 5.99476i) q^{53} +(5.96901 - 6.50898i) q^{54} +0.558517 q^{55} +(-6.26509 + 4.52284i) q^{57} -9.30903 q^{58} +(-5.21512 + 9.03284i) q^{59} +(-1.18478 + 0.855304i) q^{60} +(-5.82644 - 10.0917i) q^{61} +10.3246 q^{62} +1.98762 q^{64} +(-2.38255 - 4.12669i) q^{65} +(0.175815 + 1.72310i) q^{66} +(5.93199 - 10.2745i) q^{67} -6.73877 q^{68} +(-3.91421 - 1.75699i) q^{69} +4.30037 q^{71} +(3.76578 + 4.23377i) q^{72} +(-2.23061 - 3.86353i) q^{73} +11.8764 q^{74} +(6.47689 + 2.90731i) q^{75} +(1.98242 + 3.43366i) q^{76} +(11.9814 - 8.64953i) q^{78} +(0.666896 + 1.15510i) q^{79} +(-2.36730 - 4.10029i) q^{80} +(-1.04944 + 8.93861i) q^{81} +(-0.896461 + 1.55272i) q^{82} +(2.84194 - 4.92238i) q^{83} +(-3.59888 - 6.23345i) q^{85} -11.8764 q^{86} +(7.69174 - 5.55275i) q^{87} -1.11126 q^{88} +(-0.421826 + 0.730623i) q^{89} +(1.52365 - 4.59415i) q^{90} +(-1.10074 + 1.90654i) q^{92} +(-8.53087 + 6.15854i) q^{93} +(-6.35389 + 11.0053i) q^{94} +(-2.11745 + 3.66754i) q^{95} +(6.59990 - 4.76454i) q^{96} +(1.70317 - 2.94997i) q^{97} +(-1.17309 - 1.31887i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 2q^{2} - 6q^{4} + 24q^{8} - 12q^{9} + O(q^{10}) \) \( 12q - 2q^{2} - 6q^{4} + 24q^{8} - 12q^{9} + 16q^{11} + 18q^{15} - 6q^{16} + 18q^{18} - 6q^{22} + 8q^{23} + 24q^{25} - 22q^{29} + 42q^{30} - 16q^{32} - 30q^{36} + 6q^{37} + 24q^{39} - 6q^{43} + 14q^{44} - 12q^{46} - 56q^{50} - 18q^{51} - 28q^{53} - 6q^{57} + 36q^{58} - 126q^{60} - 48q^{64} + 6q^{65} + 76q^{71} - 30q^{72} + 72q^{74} + 36q^{78} + 6q^{79} + 24q^{81} + 30q^{85} - 72q^{86} - 12q^{88} - 62q^{92} + 42q^{93} - 60q^{95} - 48q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.849814 + 1.47192i 0.600909 + 1.04081i 0.992684 + 0.120744i \(0.0385280\pi\)
−0.391774 + 0.920061i \(0.628139\pi\)
\(3\) −1.58016 0.709292i −0.912306 0.409510i
\(4\) −0.444368 + 0.769668i −0.222184 + 0.384834i
\(5\) −0.949271 −0.424527 −0.212263 0.977212i \(-0.568084\pi\)
−0.212263 + 0.977212i \(0.568084\pi\)
\(6\) −0.298820 2.92864i −0.121993 1.19561i
\(7\) 0 0
\(8\) 1.88874 0.667769
\(9\) 1.99381 + 2.24159i 0.664603 + 0.747196i
\(10\) −0.806704 1.39725i −0.255102 0.441850i
\(11\) −0.588364 −0.177398 −0.0886992 0.996058i \(-0.528271\pi\)
−0.0886992 + 0.996058i \(0.528271\pi\)
\(12\) 1.24809 0.901012i 0.360293 0.260100i
\(13\) 2.50987 + 4.34722i 0.696112 + 1.20570i 0.969804 + 0.243885i \(0.0784218\pi\)
−0.273692 + 0.961817i \(0.588245\pi\)
\(14\) 0 0
\(15\) 1.50000 + 0.673310i 0.387298 + 0.173848i
\(16\) 2.49381 + 4.31941i 0.623453 + 1.07985i
\(17\) 3.79121 + 6.56657i 0.919503 + 1.59263i 0.800171 + 0.599772i \(0.204742\pi\)
0.119332 + 0.992854i \(0.461925\pi\)
\(18\) −1.60507 + 4.83967i −0.378320 + 1.14072i
\(19\) 2.23061 3.86353i 0.511737 0.886355i −0.488170 0.872748i \(-0.662336\pi\)
0.999907 0.0136063i \(-0.00433116\pi\)
\(20\) 0.421826 0.730623i 0.0943231 0.163372i
\(21\) 0 0
\(22\) −0.500000 0.866025i −0.106600 0.184637i
\(23\) 2.47710 0.516511 0.258256 0.966077i \(-0.416852\pi\)
0.258256 + 0.966077i \(0.416852\pi\)
\(24\) −2.98450 1.33966i −0.609209 0.273458i
\(25\) −4.09888 −0.819777
\(26\) −4.26584 + 7.38866i −0.836601 + 1.44904i
\(27\) −1.56060 4.95626i −0.300337 0.953833i
\(28\) 0 0
\(29\) −2.73855 + 4.74331i −0.508536 + 0.880810i 0.491415 + 0.870925i \(0.336480\pi\)
−0.999951 + 0.00988468i \(0.996854\pi\)
\(30\) 0.283662 + 2.78007i 0.0517893 + 0.507569i
\(31\) 3.03731 5.26078i 0.545518 0.944865i −0.453056 0.891482i \(-0.649666\pi\)
0.998574 0.0533826i \(-0.0170003\pi\)
\(32\) −2.34981 + 4.07000i −0.415392 + 0.719481i
\(33\) 0.929709 + 0.417322i 0.161842 + 0.0726464i
\(34\) −6.44364 + 11.1607i −1.10508 + 1.91405i
\(35\) 0 0
\(36\) −2.61126 + 0.538481i −0.435211 + 0.0897469i
\(37\) 3.49381 6.05146i 0.574379 0.994853i −0.421730 0.906721i \(-0.638577\pi\)
0.996109 0.0881319i \(-0.0280897\pi\)
\(38\) 7.58242 1.23003
\(39\) −0.882546 8.64953i −0.141320 1.38503i
\(40\) −1.79292 −0.283486
\(41\) 0.527445 + 0.913562i 0.0823731 + 0.142674i 0.904269 0.426964i \(-0.140417\pi\)
−0.821896 + 0.569638i \(0.807083\pi\)
\(42\) 0 0
\(43\) −3.49381 + 6.05146i −0.532801 + 0.922838i 0.466465 + 0.884540i \(0.345527\pi\)
−0.999266 + 0.0382990i \(0.987806\pi\)
\(44\) 0.261450 0.452845i 0.0394151 0.0682689i
\(45\) −1.89267 2.12788i −0.282142 0.317205i
\(46\) 2.10507 + 3.64610i 0.310376 + 0.537587i
\(47\) 3.73840 + 6.47510i 0.545301 + 0.944490i 0.998588 + 0.0531249i \(0.0169181\pi\)
−0.453286 + 0.891365i \(0.649749\pi\)
\(48\) −0.876899 8.59419i −0.126569 1.24046i
\(49\) 0 0
\(50\) −3.48329 6.03323i −0.492612 0.853228i
\(51\) −1.33310 13.0653i −0.186672 1.82951i
\(52\) −4.46122 −0.618660
\(53\) −3.46108 5.99476i −0.475416 0.823444i 0.524188 0.851603i \(-0.324369\pi\)
−0.999603 + 0.0281586i \(0.991036\pi\)
\(54\) 5.96901 6.50898i 0.812279 0.885760i
\(55\) 0.558517 0.0753104
\(56\) 0 0
\(57\) −6.26509 + 4.52284i −0.829832 + 0.599065i
\(58\) −9.30903 −1.22234
\(59\) −5.21512 + 9.03284i −0.678950 + 1.17598i 0.296347 + 0.955080i \(0.404231\pi\)
−0.975297 + 0.220896i \(0.929102\pi\)
\(60\) −1.18478 + 0.855304i −0.152954 + 0.110419i
\(61\) −5.82644 10.0917i −0.745999 1.29211i −0.949726 0.313081i \(-0.898639\pi\)
0.203727 0.979028i \(-0.434695\pi\)
\(62\) 10.3246 1.31123
\(63\) 0 0
\(64\) 1.98762 0.248453
\(65\) −2.38255 4.12669i −0.295518 0.511853i
\(66\) 0.175815 + 1.72310i 0.0216413 + 0.212099i
\(67\) 5.93199 10.2745i 0.724708 1.25523i −0.234387 0.972143i \(-0.575308\pi\)
0.959094 0.283087i \(-0.0913585\pi\)
\(68\) −6.73877 −0.817195
\(69\) −3.91421 1.75699i −0.471216 0.211516i
\(70\) 0 0
\(71\) 4.30037 0.510360 0.255180 0.966894i \(-0.417865\pi\)
0.255180 + 0.966894i \(0.417865\pi\)
\(72\) 3.76578 + 4.23377i 0.443802 + 0.498955i
\(73\) −2.23061 3.86353i −0.261073 0.452192i 0.705454 0.708756i \(-0.250743\pi\)
−0.966527 + 0.256563i \(0.917410\pi\)
\(74\) 11.8764 1.38060
\(75\) 6.47689 + 2.90731i 0.747887 + 0.335707i
\(76\) 1.98242 + 3.43366i 0.227400 + 0.393868i
\(77\) 0 0
\(78\) 11.9814 8.64953i 1.35663 0.979367i
\(79\) 0.666896 + 1.15510i 0.0750317 + 0.129959i 0.901100 0.433611i \(-0.142761\pi\)
−0.826068 + 0.563570i \(0.809428\pi\)
\(80\) −2.36730 4.10029i −0.264672 0.458426i
\(81\) −1.04944 + 8.93861i −0.116605 + 0.993178i
\(82\) −0.896461 + 1.55272i −0.0989976 + 0.171469i
\(83\) 2.84194 4.92238i 0.311943 0.540301i −0.666840 0.745201i \(-0.732353\pi\)
0.978783 + 0.204900i \(0.0656868\pi\)
\(84\) 0 0
\(85\) −3.59888 6.23345i −0.390354 0.676113i
\(86\) −11.8764 −1.28066
\(87\) 7.69174 5.55275i 0.824641 0.595318i
\(88\) −1.11126 −0.118461
\(89\) −0.421826 + 0.730623i −0.0447134 + 0.0774459i −0.887516 0.460777i \(-0.847571\pi\)
0.842803 + 0.538223i \(0.180904\pi\)
\(90\) 1.52365 4.59415i 0.160607 0.484266i
\(91\) 0 0
\(92\) −1.10074 + 1.90654i −0.114760 + 0.198771i
\(93\) −8.53087 + 6.15854i −0.884610 + 0.638610i
\(94\) −6.35389 + 11.0053i −0.655353 + 1.13511i
\(95\) −2.11745 + 3.66754i −0.217246 + 0.376281i
\(96\) 6.59990 4.76454i 0.673599 0.486279i
\(97\) 1.70317 2.94997i 0.172930 0.299524i −0.766513 0.642229i \(-0.778010\pi\)
0.939443 + 0.342705i \(0.111343\pi\)
\(98\) 0 0
\(99\) −1.17309 1.31887i −0.117900 0.132551i
\(100\) 1.82141 3.15478i 0.182141 0.315478i
\(101\) −9.58658 −0.953900 −0.476950 0.878930i \(-0.658258\pi\)
−0.476950 + 0.878930i \(0.658258\pi\)
\(102\) 18.0982 13.0653i 1.79199 1.29366i
\(103\) −11.6529 −1.14819 −0.574096 0.818788i \(-0.694647\pi\)
−0.574096 + 0.818788i \(0.694647\pi\)
\(104\) 4.74048 + 8.21075i 0.464842 + 0.805130i
\(105\) 0 0
\(106\) 5.88255 10.1889i 0.571363 0.989630i
\(107\) 1.89926 3.28961i 0.183608 0.318018i −0.759499 0.650509i \(-0.774556\pi\)
0.943107 + 0.332491i \(0.107889\pi\)
\(108\) 4.50816 + 1.00126i 0.433797 + 0.0963465i
\(109\) 6.43199 + 11.1405i 0.616073 + 1.06707i 0.990195 + 0.139690i \(0.0446106\pi\)
−0.374123 + 0.927379i \(0.622056\pi\)
\(110\) 0.474636 + 0.822093i 0.0452547 + 0.0783835i
\(111\) −9.81303 + 7.08414i −0.931411 + 0.672397i
\(112\) 0 0
\(113\) −4.51052 7.81245i −0.424314 0.734934i 0.572042 0.820224i \(-0.306151\pi\)
−0.996356 + 0.0852908i \(0.972818\pi\)
\(114\) −11.9814 5.37815i −1.12216 0.503710i
\(115\) −2.35144 −0.219273
\(116\) −2.43385 4.21555i −0.225977 0.391404i
\(117\) −4.74048 + 14.2936i −0.438257 + 1.32145i
\(118\) −17.7275 −1.63195
\(119\) 0 0
\(120\) 2.83310 + 1.27171i 0.258626 + 0.116090i
\(121\) −10.6538 −0.968530
\(122\) 9.90278 17.1521i 0.896556 1.55288i
\(123\) −0.185466 1.81769i −0.0167229 0.163895i
\(124\) 2.69937 + 4.67545i 0.242411 + 0.419867i
\(125\) 8.63731 0.772544
\(126\) 0 0
\(127\) 6.43268 0.570808 0.285404 0.958407i \(-0.407872\pi\)
0.285404 + 0.958407i \(0.407872\pi\)
\(128\) 6.38874 + 11.0656i 0.564690 + 0.978071i
\(129\) 9.81303 7.08414i 0.863989 0.623724i
\(130\) 4.04944 7.01384i 0.355160 0.615154i
\(131\) 6.63315 0.579541 0.289770 0.957096i \(-0.406421\pi\)
0.289770 + 0.957096i \(0.406421\pi\)
\(132\) −0.734332 + 0.530123i −0.0639154 + 0.0461413i
\(133\) 0 0
\(134\) 20.1643 1.74193
\(135\) 1.48143 + 4.70484i 0.127501 + 0.404928i
\(136\) 7.16059 + 12.4025i 0.614016 + 1.06351i
\(137\) 14.0334 1.19896 0.599478 0.800391i \(-0.295375\pi\)
0.599478 + 0.800391i \(0.295375\pi\)
\(138\) −0.740208 7.25453i −0.0630107 0.617546i
\(139\) −4.40254 7.62541i −0.373418 0.646779i 0.616671 0.787221i \(-0.288481\pi\)
−0.990089 + 0.140442i \(0.955148\pi\)
\(140\) 0 0
\(141\) −1.31453 12.8833i −0.110704 1.08497i
\(142\) 3.65452 + 6.32981i 0.306680 + 0.531186i
\(143\) −1.47672 2.55775i −0.123489 0.213890i
\(144\) −4.71015 + 14.2022i −0.392512 + 1.18351i
\(145\) 2.59963 4.50268i 0.215887 0.373928i
\(146\) 3.79121 6.56657i 0.313763 0.543453i
\(147\) 0 0
\(148\) 3.10507 + 5.37815i 0.255236 + 0.442081i
\(149\) −4.36584 −0.357663 −0.178832 0.983880i \(-0.557232\pi\)
−0.178832 + 0.983880i \(0.557232\pi\)
\(150\) 1.22483 + 12.0041i 0.100007 + 0.980134i
\(151\) −12.6538 −1.02975 −0.514877 0.857264i \(-0.672162\pi\)
−0.514877 + 0.857264i \(0.672162\pi\)
\(152\) 4.21303 7.29719i 0.341722 0.591880i
\(153\) −7.16059 + 21.5908i −0.578899 + 1.74551i
\(154\) 0 0
\(155\) −2.88323 + 4.99391i −0.231587 + 0.401120i
\(156\) 7.04944 + 3.16431i 0.564407 + 0.253347i
\(157\) −5.63694 + 9.76347i −0.449877 + 0.779210i −0.998378 0.0569405i \(-0.981865\pi\)
0.548501 + 0.836150i \(0.315199\pi\)
\(158\) −1.13348 + 1.96324i −0.0901745 + 0.156187i
\(159\) 1.21702 + 11.9276i 0.0965160 + 0.945920i
\(160\) 2.23061 3.86353i 0.176345 0.305439i
\(161\) 0 0
\(162\) −14.0488 + 6.05146i −1.10377 + 0.475447i
\(163\) 0.833104 1.44298i 0.0652537 0.113023i −0.831553 0.555446i \(-0.812548\pi\)
0.896807 + 0.442423i \(0.145881\pi\)
\(164\) −0.937519 −0.0732080
\(165\) −0.882546 0.396151i −0.0687061 0.0308404i
\(166\) 9.66047 0.749798
\(167\) −1.95135 3.37984i −0.151000 0.261540i 0.780595 0.625037i \(-0.214916\pi\)
−0.931595 + 0.363497i \(0.881583\pi\)
\(168\) 0 0
\(169\) −6.09888 + 10.5636i −0.469145 + 0.812583i
\(170\) 6.11677 10.5945i 0.469134 0.812565i
\(171\) 13.1079 2.70303i 1.00238 0.206706i
\(172\) −3.10507 5.37815i −0.236760 0.410080i
\(173\) −8.05705 13.9552i −0.612566 1.06100i −0.990806 0.135288i \(-0.956804\pi\)
0.378240 0.925708i \(-0.376529\pi\)
\(174\) 14.7098 + 6.60282i 1.11514 + 0.500559i
\(175\) 0 0
\(176\) −1.46727 2.54138i −0.110599 0.191564i
\(177\) 14.6476 10.5743i 1.10098 0.794813i
\(178\) −1.43389 −0.107475
\(179\) −7.14400 12.3738i −0.533967 0.924859i −0.999213 0.0396767i \(-0.987367\pi\)
0.465245 0.885182i \(-0.345966\pi\)
\(180\) 2.47880 0.511165i 0.184759 0.0381000i
\(181\) 12.8873 0.957905 0.478952 0.877841i \(-0.341017\pi\)
0.478952 + 0.877841i \(0.341017\pi\)
\(182\) 0 0
\(183\) 2.04875 + 20.0791i 0.151448 + 1.48429i
\(184\) 4.67859 0.344910
\(185\) −3.31657 + 5.74447i −0.243839 + 0.422342i
\(186\) −16.3145 7.32316i −1.19624 0.536960i
\(187\) −2.23061 3.86353i −0.163118 0.282529i
\(188\) −6.64490 −0.484629
\(189\) 0 0
\(190\) −7.19777 −0.522181
\(191\) 1.08217 + 1.87438i 0.0783034 + 0.135625i 0.902518 0.430652i \(-0.141716\pi\)
−0.824215 + 0.566277i \(0.808383\pi\)
\(192\) −3.14076 1.40980i −0.226665 0.101744i
\(193\) −5.21565 + 9.03377i −0.375431 + 0.650265i −0.990391 0.138293i \(-0.955839\pi\)
0.614961 + 0.788558i \(0.289172\pi\)
\(194\) 5.78949 0.415661
\(195\) 0.837775 + 8.21075i 0.0599943 + 0.587984i
\(196\) 0 0
\(197\) −18.7848 −1.33836 −0.669179 0.743101i \(-0.733354\pi\)
−0.669179 + 0.743101i \(0.733354\pi\)
\(198\) 0.944368 2.84748i 0.0671133 0.202362i
\(199\) −4.21303 7.29719i −0.298654 0.517284i 0.677174 0.735823i \(-0.263204\pi\)
−0.975828 + 0.218539i \(0.929871\pi\)
\(200\) −7.74171 −0.547422
\(201\) −16.6611 + 12.0278i −1.17518 + 0.848379i
\(202\) −8.14681 14.1107i −0.573208 0.992825i
\(203\) 0 0
\(204\) 10.6483 + 4.77975i 0.745532 + 0.334650i
\(205\) −0.500689 0.867218i −0.0349696 0.0605692i
\(206\) −9.90278 17.1521i −0.689960 1.19505i
\(207\) 4.93887 + 5.55264i 0.343275 + 0.385935i
\(208\) −12.5183 + 21.6823i −0.867986 + 1.50340i
\(209\) −1.31241 + 2.27316i −0.0907814 + 0.157238i
\(210\) 0 0
\(211\) −5.61126 9.71899i −0.386295 0.669083i 0.605653 0.795729i \(-0.292912\pi\)
−0.991948 + 0.126646i \(0.959579\pi\)
\(212\) 6.15197 0.422519
\(213\) −6.79527 3.05022i −0.465605 0.208998i
\(214\) 6.45606 0.441327
\(215\) 3.31657 5.74447i 0.226188 0.391770i
\(216\) −2.94756 9.36107i −0.200556 0.636940i
\(217\) 0 0
\(218\) −10.9320 + 18.9348i −0.740408 + 1.28242i
\(219\) 0.784350 + 7.68715i 0.0530015 + 0.519449i
\(220\) −0.248187 + 0.429872i −0.0167328 + 0.0289820i
\(221\) −19.0309 + 32.9624i −1.28016 + 2.21729i
\(222\) −18.7665 8.42380i −1.25953 0.565369i
\(223\) 10.3774 17.9742i 0.694923 1.20364i −0.275283 0.961363i \(-0.588772\pi\)
0.970206 0.242279i \(-0.0778951\pi\)
\(224\) 0 0
\(225\) −8.17240 9.18801i −0.544826 0.612534i
\(226\) 7.66621 13.2783i 0.509949 0.883257i
\(227\) −10.4302 −0.692279 −0.346139 0.938183i \(-0.612508\pi\)
−0.346139 + 0.938183i \(0.612508\pi\)
\(228\) −0.697080 6.83185i −0.0461653 0.452450i
\(229\) 15.0592 0.995141 0.497570 0.867424i \(-0.334226\pi\)
0.497570 + 0.867424i \(0.334226\pi\)
\(230\) −1.99829 3.46113i −0.131763 0.228220i
\(231\) 0 0
\(232\) −5.17240 + 8.95886i −0.339585 + 0.588178i
\(233\) −2.19344 + 3.79915i −0.143697 + 0.248890i −0.928886 0.370366i \(-0.879232\pi\)
0.785189 + 0.619256i \(0.212566\pi\)
\(234\) −25.0676 + 5.16931i −1.63872 + 0.337929i
\(235\) −3.54875 6.14662i −0.231495 0.400961i
\(236\) −4.63486 8.02781i −0.301704 0.522566i
\(237\) −0.234501 2.29826i −0.0152325 0.149288i
\(238\) 0 0
\(239\) 4.77561 + 8.27160i 0.308909 + 0.535046i 0.978124 0.208023i \(-0.0667029\pi\)
−0.669215 + 0.743069i \(0.733370\pi\)
\(240\) 0.832415 + 8.15822i 0.0537322 + 0.526611i
\(241\) 10.5358 0.678674 0.339337 0.940665i \(-0.389797\pi\)
0.339337 + 0.940665i \(0.389797\pi\)
\(242\) −9.05377 15.6816i −0.581999 1.00805i
\(243\) 7.99837 13.3801i 0.513095 0.858332i
\(244\) 10.3563 0.662996
\(245\) 0 0
\(246\) 2.51788 1.81769i 0.160534 0.115892i
\(247\) 22.3942 1.42491
\(248\) 5.73668 9.93623i 0.364280 0.630951i
\(249\) −7.98212 + 5.76238i −0.505846 + 0.365176i
\(250\) 7.34011 + 12.7134i 0.464229 + 0.804068i
\(251\) −24.4346 −1.54230 −0.771148 0.636656i \(-0.780317\pi\)
−0.771148 + 0.636656i \(0.780317\pi\)
\(252\) 0 0
\(253\) −1.45744 −0.0916282
\(254\) 5.46658 + 9.46839i 0.343004 + 0.594100i
\(255\) 1.26548 + 12.4025i 0.0792472 + 0.776675i
\(256\) −8.87085 + 15.3648i −0.554428 + 0.960298i
\(257\) 4.00832 0.250032 0.125016 0.992155i \(-0.460102\pi\)
0.125016 + 0.992155i \(0.460102\pi\)
\(258\) 18.7665 + 8.42380i 1.16835 + 0.524443i
\(259\) 0 0
\(260\) 4.23491 0.262638
\(261\) −16.0927 + 3.31855i −0.996113 + 0.205413i
\(262\) 5.63694 + 9.76347i 0.348251 + 0.603189i
\(263\) 17.6872 1.09064 0.545321 0.838227i \(-0.316408\pi\)
0.545321 + 0.838227i \(0.316408\pi\)
\(264\) 1.75597 + 0.788211i 0.108073 + 0.0485110i
\(265\) 3.28550 + 5.69066i 0.201827 + 0.349574i
\(266\) 0 0
\(267\) 1.18478 0.855304i 0.0725072 0.0523438i
\(268\) 5.27197 + 9.13132i 0.322037 + 0.557784i
\(269\) 7.11366 + 12.3212i 0.433727 + 0.751238i 0.997191 0.0749032i \(-0.0238648\pi\)
−0.563463 + 0.826141i \(0.690531\pi\)
\(270\) −5.66621 + 6.17878i −0.344834 + 0.376029i
\(271\) 2.69937 4.67545i 0.163975 0.284013i −0.772316 0.635239i \(-0.780902\pi\)
0.936291 + 0.351226i \(0.114235\pi\)
\(272\) −18.9091 + 32.7515i −1.14653 + 1.98585i
\(273\) 0 0
\(274\) 11.9258 + 20.6561i 0.720464 + 1.24788i
\(275\) 2.41164 0.145427
\(276\) 3.09165 2.23190i 0.186095 0.134344i
\(277\) 7.66621 0.460618 0.230309 0.973118i \(-0.426026\pi\)
0.230309 + 0.973118i \(0.426026\pi\)
\(278\) 7.48267 12.9604i 0.448781 0.777311i
\(279\) 17.8483 3.68059i 1.06855 0.220351i
\(280\) 0 0
\(281\) 11.3312 19.6263i 0.675965 1.17081i −0.300220 0.953870i \(-0.597060\pi\)
0.976186 0.216936i \(-0.0696065\pi\)
\(282\) 17.8461 12.8833i 1.06272 0.767189i
\(283\) 15.9246 27.5822i 0.946619 1.63959i 0.194144 0.980973i \(-0.437807\pi\)
0.752476 0.658620i \(-0.228859\pi\)
\(284\) −1.91095 + 3.30986i −0.113394 + 0.196404i
\(285\) 5.94727 4.29340i 0.352286 0.254319i
\(286\) 2.50987 4.34722i 0.148412 0.257057i
\(287\) 0 0
\(288\) −13.8083 + 2.84748i −0.813664 + 0.167790i
\(289\) −20.2465 + 35.0680i −1.19097 + 2.06282i
\(290\) 8.83680 0.518915
\(291\) −4.78366 + 3.45338i −0.280423 + 0.202441i
\(292\) 3.96485 0.232025
\(293\) −13.7468 23.8102i −0.803097 1.39100i −0.917568 0.397578i \(-0.869851\pi\)
0.114472 0.993427i \(-0.463483\pi\)
\(294\) 0 0
\(295\) 4.95056 8.57462i 0.288233 0.499234i
\(296\) 6.59888 11.4296i 0.383552 0.664332i
\(297\) 0.918200 + 2.91609i 0.0532793 + 0.169208i
\(298\) −3.71015 6.42617i −0.214923 0.372258i
\(299\) 6.21720 + 10.7685i 0.359550 + 0.622758i
\(300\) −5.11578 + 3.69314i −0.295360 + 0.213224i
\(301\) 0 0
\(302\) −10.7534 18.6254i −0.618789 1.07177i
\(303\) 15.1483 + 6.79968i 0.870249 + 0.390632i
\(304\) 22.2509 1.27618
\(305\) 5.53087 + 9.57975i 0.316697 + 0.548535i
\(306\) −37.8652 + 7.80835i −2.16461 + 0.446374i
\(307\) 14.8176 0.845683 0.422841 0.906204i \(-0.361033\pi\)
0.422841 + 0.906204i \(0.361033\pi\)
\(308\) 0 0
\(309\) 18.4134 + 8.26530i 1.04750 + 0.470196i
\(310\) −9.80085 −0.556651
\(311\) −14.5318 + 25.1698i −0.824021 + 1.42725i 0.0786442 + 0.996903i \(0.474941\pi\)
−0.902665 + 0.430343i \(0.858392\pi\)
\(312\) −1.66690 16.3367i −0.0943694 0.924883i
\(313\) 12.2390 + 21.1986i 0.691790 + 1.19822i 0.971251 + 0.238058i \(0.0765110\pi\)
−0.279461 + 0.960157i \(0.590156\pi\)
\(314\) −19.1614 −1.08134
\(315\) 0 0
\(316\) −1.18539 −0.0666834
\(317\) 3.69344 + 6.39722i 0.207444 + 0.359304i 0.950909 0.309472i \(-0.100152\pi\)
−0.743465 + 0.668775i \(0.766819\pi\)
\(318\) −16.5222 + 11.9276i −0.926521 + 0.668867i
\(319\) 1.61126 2.79079i 0.0902135 0.156254i
\(320\) −1.88679 −0.105475
\(321\) −5.33442 + 3.85098i −0.297738 + 0.214941i
\(322\) 0 0
\(323\) 33.8268 1.88218
\(324\) −6.41342 4.77975i −0.356301 0.265542i
\(325\) −10.2877 17.8188i −0.570657 0.988407i
\(326\) 2.83193 0.156846
\(327\) −2.26168 22.1660i −0.125071 1.22578i
\(328\) 0.996205 + 1.72548i 0.0550062 + 0.0952736i
\(329\) 0 0
\(330\) −0.166896 1.63569i −0.00918734 0.0900419i
\(331\) −10.0309 17.3740i −0.551347 0.954960i −0.998178 0.0603420i \(-0.980781\pi\)
0.446831 0.894618i \(-0.352552\pi\)
\(332\) 2.52573 + 4.37470i 0.138618 + 0.240093i
\(333\) 20.5309 4.23377i 1.12508 0.232009i
\(334\) 3.31657 5.74447i 0.181475 0.314324i
\(335\) −5.63106 + 9.75329i −0.307658 + 0.532879i
\(336\) 0 0
\(337\) −3.20327 5.54823i −0.174493 0.302231i 0.765493 0.643445i \(-0.222495\pi\)
−0.939986 + 0.341214i \(0.889162\pi\)
\(338\) −20.7317 −1.12765
\(339\) 1.58604 + 15.5442i 0.0861416 + 0.844245i
\(340\) 6.39692 0.346921
\(341\) −1.78705 + 3.09526i −0.0967740 + 0.167617i
\(342\) 15.1179 + 16.9967i 0.817482 + 0.919074i
\(343\) 0 0
\(344\) −6.59888 + 11.4296i −0.355788 + 0.616243i
\(345\) 3.71565 + 1.66786i 0.200044 + 0.0897944i
\(346\) 13.6940 23.7187i 0.736194 1.27512i
\(347\) 14.5963 25.2816i 0.783572 1.35719i −0.146276 0.989244i \(-0.546729\pi\)
0.929848 0.367943i \(-0.119938\pi\)
\(348\) 0.855815 + 8.38755i 0.0458765 + 0.449620i
\(349\) 2.17192 3.76188i 0.116260 0.201369i −0.802022 0.597294i \(-0.796243\pi\)
0.918283 + 0.395925i \(0.129576\pi\)
\(350\) 0 0
\(351\) 17.6291 19.2238i 0.940970 1.02609i
\(352\) 1.38255 2.39464i 0.0736899 0.127635i
\(353\) 25.7007 1.36791 0.683955 0.729525i \(-0.260259\pi\)
0.683955 + 0.729525i \(0.260259\pi\)
\(354\) 28.0123 + 12.5740i 1.48884 + 0.668300i
\(355\) −4.08222 −0.216662
\(356\) −0.374892 0.649331i −0.0198692 0.0344145i
\(357\) 0 0
\(358\) 12.1421 21.0308i 0.641732 1.11151i
\(359\) −10.3436 + 17.9157i −0.545916 + 0.945554i 0.452633 + 0.891697i \(0.350485\pi\)
−0.998549 + 0.0538567i \(0.982849\pi\)
\(360\) −3.57475 4.01899i −0.188406 0.211820i
\(361\) −0.451246 0.781582i −0.0237498 0.0411359i
\(362\) 10.9518 + 18.9691i 0.575614 + 0.996992i
\(363\) 16.8348 + 7.55667i 0.883595 + 0.396622i
\(364\) 0 0
\(365\) 2.11745 + 3.66754i 0.110833 + 0.191968i
\(366\) −27.8138 + 20.0791i −1.45385 + 1.04955i
\(367\) −2.84781 −0.148655 −0.0743273 0.997234i \(-0.523681\pi\)
−0.0743273 + 0.997234i \(0.523681\pi\)
\(368\) 6.17742 + 10.6996i 0.322020 + 0.557755i
\(369\) −0.996205 + 3.00379i −0.0518604 + 0.156371i
\(370\) −11.2739 −0.586101
\(371\) 0 0
\(372\) −0.949180 9.30259i −0.0492127 0.482317i
\(373\) 21.4327 1.10974 0.554871 0.831936i \(-0.312768\pi\)
0.554871 + 0.831936i \(0.312768\pi\)
\(374\) 3.79121 6.56657i 0.196039 0.339549i
\(375\) −13.6483 6.12637i −0.704797 0.316364i
\(376\) 7.06085 + 12.2297i 0.364135 + 0.630701i
\(377\) −27.4936 −1.41599
\(378\) 0 0
\(379\) 27.0494 1.38943 0.694716 0.719284i \(-0.255530\pi\)
0.694716 + 0.719284i \(0.255530\pi\)
\(380\) −1.88186 3.25947i −0.0965372 0.167207i
\(381\) −10.1647 4.56265i −0.520751 0.233751i
\(382\) −1.83929 + 3.18575i −0.0941064 + 0.162997i
\(383\) −14.4268 −0.737175 −0.368588 0.929593i \(-0.620159\pi\)
−0.368588 + 0.929593i \(0.620159\pi\)
\(384\) −2.24647 22.0169i −0.114640 1.12355i
\(385\) 0 0
\(386\) −17.7293 −0.902399
\(387\) −20.5309 + 4.23377i −1.04364 + 0.215215i
\(388\) 1.51366 + 2.62174i 0.0768446 + 0.133099i
\(389\) −6.10755 −0.309665 −0.154832 0.987941i \(-0.549484\pi\)
−0.154832 + 0.987941i \(0.549484\pi\)
\(390\) −11.3736 + 8.21075i −0.575926 + 0.415768i
\(391\) 9.39120 + 16.2660i 0.474933 + 0.822609i
\(392\) 0 0
\(393\) −10.4814 4.70484i −0.528718 0.237328i
\(394\) −15.9635 27.6497i −0.804232 1.39297i
\(395\) −0.633065 1.09650i −0.0318530 0.0551710i
\(396\) 1.53637 0.316823i 0.0772057 0.0159210i
\(397\) 6.44364 11.1607i 0.323397 0.560140i −0.657789 0.753202i \(-0.728508\pi\)
0.981187 + 0.193061i \(0.0618417\pi\)
\(398\) 7.16059 12.4025i 0.358928 0.621682i
\(399\) 0 0
\(400\) −10.2218 17.7047i −0.511092 0.885237i
\(401\) 8.39060 0.419006 0.209503 0.977808i \(-0.432815\pi\)
0.209503 + 0.977808i \(0.432815\pi\)
\(402\) −31.8629 14.3024i −1.58918 0.713339i
\(403\) 30.4930 1.51897
\(404\) 4.25997 7.37848i 0.211941 0.367093i
\(405\) 0.996205 8.48516i 0.0495018 0.421631i
\(406\) 0 0
\(407\) −2.05563 + 3.56046i −0.101894 + 0.176485i
\(408\) −2.51788 24.6769i −0.124654 1.22169i
\(409\) −3.40633 + 5.89994i −0.168432 + 0.291733i −0.937869 0.346990i \(-0.887204\pi\)
0.769437 + 0.638723i \(0.220537\pi\)
\(410\) 0.850985 1.47395i 0.0420271 0.0727931i
\(411\) −22.1750 9.95379i −1.09381 0.490984i
\(412\) 5.17817 8.96885i 0.255110 0.441864i
\(413\) 0 0
\(414\) −3.97593 + 11.9883i −0.195406 + 0.589194i
\(415\) −2.69777 + 4.67267i −0.132428 + 0.229372i
\(416\) −23.5909 −1.15664
\(417\) 1.54806 + 15.1721i 0.0758091 + 0.742979i
\(418\) −4.46122 −0.218205
\(419\) 5.16231 + 8.94137i 0.252195 + 0.436815i 0.964130 0.265431i \(-0.0855142\pi\)
−0.711935 + 0.702246i \(0.752181\pi\)
\(420\) 0 0
\(421\) −1.56801 + 2.71588i −0.0764202 + 0.132364i −0.901703 0.432356i \(-0.857682\pi\)
0.825283 + 0.564720i \(0.191016\pi\)
\(422\) 9.53706 16.5187i 0.464257 0.804117i
\(423\) −7.06085 + 21.2901i −0.343310 + 1.03516i
\(424\) −6.53706 11.3225i −0.317468 0.549870i
\(425\) −15.5397 26.9156i −0.753787 1.30560i
\(426\) −1.28504 12.5942i −0.0622603 0.610192i
\(427\) 0 0
\(428\) 1.68794 + 2.92359i 0.0815895 + 0.141317i
\(429\) 0.519258 + 5.08907i 0.0250700 + 0.245703i
\(430\) 11.2739 0.543675
\(431\) −15.9363 27.6025i −0.767625 1.32957i −0.938847 0.344334i \(-0.888105\pi\)
0.171222 0.985233i \(-0.445229\pi\)
\(432\) 17.5163 19.1008i 0.842752 0.918989i
\(433\) 7.48855 0.359877 0.179938 0.983678i \(-0.442410\pi\)
0.179938 + 0.983678i \(0.442410\pi\)
\(434\) 0 0
\(435\) −7.30154 + 5.27107i −0.350082 + 0.252728i
\(436\) −11.4327 −0.547526
\(437\) 5.52544 9.57035i 0.264318 0.457812i
\(438\) −10.6483 + 7.68715i −0.508797 + 0.367306i
\(439\) −1.14465 1.98259i −0.0546311 0.0946238i 0.837417 0.546565i \(-0.184065\pi\)
−0.892048 + 0.451941i \(0.850732\pi\)
\(440\) 1.05489 0.0502900
\(441\) 0 0
\(442\) −64.6908 −3.07703
\(443\) −18.6749 32.3458i −0.887270 1.53680i −0.843090 0.537773i \(-0.819266\pi\)
−0.0441800 0.999024i \(-0.514067\pi\)
\(444\) −1.09184 10.7007i −0.0518163 0.507834i
\(445\) 0.400427 0.693560i 0.0189821 0.0328779i
\(446\) 35.2755 1.67034
\(447\) 6.89872 + 3.09665i 0.326298 + 0.146467i
\(448\) 0 0
\(449\) −6.20286 −0.292731 −0.146366 0.989231i \(-0.546758\pi\)
−0.146366 + 0.989231i \(0.546758\pi\)
\(450\) 6.57901 19.8372i 0.310138 0.935136i
\(451\) −0.310330 0.537507i −0.0146129 0.0253102i
\(452\) 8.01732 0.377103
\(453\) 19.9951 + 8.97526i 0.939450 + 0.421694i
\(454\) −8.86376 15.3525i −0.415997 0.720527i
\(455\) 0 0
\(456\) −11.8331 + 8.54245i −0.554136 + 0.400037i
\(457\) −10.0858 17.4691i −0.471795 0.817172i 0.527685 0.849440i \(-0.323060\pi\)
−0.999479 + 0.0322682i \(0.989727\pi\)
\(458\) 12.7975 + 22.1660i 0.597989 + 1.03575i
\(459\) 26.6291 29.0380i 1.24294 1.35538i
\(460\) 1.04490 1.80983i 0.0487189 0.0843836i
\(461\) 11.2680 19.5168i 0.524803 0.908986i −0.474780 0.880105i \(-0.657472\pi\)
0.999583 0.0288813i \(-0.00919447\pi\)
\(462\) 0 0
\(463\) 13.8145 + 23.9275i 0.642016 + 1.11200i 0.984982 + 0.172656i \(0.0552350\pi\)
−0.342966 + 0.939348i \(0.611432\pi\)
\(464\) −27.3177 −1.26819
\(465\) 8.09811 5.84612i 0.375541 0.271107i
\(466\) −7.45606 −0.345395
\(467\) −10.0612 + 17.4265i −0.465577 + 0.806404i −0.999227 0.0393016i \(-0.987487\pi\)
0.533650 + 0.845705i \(0.320820\pi\)
\(468\) −8.89483 10.0002i −0.411164 0.462261i
\(469\) 0 0
\(470\) 6.03156 10.4470i 0.278215 0.481883i
\(471\) 15.8324 11.4296i 0.729519 0.526648i
\(472\) −9.84997 + 17.0607i −0.453382 + 0.785280i
\(473\) 2.05563 3.56046i 0.0945181 0.163710i
\(474\) 3.18358 2.29826i 0.146227 0.105563i
\(475\) −9.14301 + 15.8362i −0.419510 + 0.726613i
\(476\) 0 0
\(477\) 6.53706 19.7107i 0.299312 0.902493i
\(478\) −8.11677 + 14.0586i −0.371252 + 0.643028i
\(479\) −9.58658 −0.438022 −0.219011 0.975722i \(-0.570283\pi\)
−0.219011 + 0.975722i \(0.570283\pi\)
\(480\) −6.26509 + 4.52284i −0.285961 + 0.206439i
\(481\) 35.0760 1.59933
\(482\) 8.95351 + 15.5079i 0.407821 + 0.706367i
\(483\) 0 0
\(484\) 4.73422 8.19991i 0.215192 0.372723i
\(485\) −1.61677 + 2.80032i −0.0734135 + 0.127156i
\(486\) 26.4915 + 0.402398i 1.20168 + 0.0182531i
\(487\) −6.53706 11.3225i −0.296223 0.513073i 0.679046 0.734096i \(-0.262394\pi\)
−0.975269 + 0.221023i \(0.929060\pi\)
\(488\) −11.0046 19.0605i −0.498155 0.862830i
\(489\) −2.33993 + 1.68922i −0.105815 + 0.0763893i
\(490\) 0 0
\(491\) −7.67054 13.2858i −0.346167 0.599578i 0.639398 0.768876i \(-0.279183\pi\)
−0.985565 + 0.169298i \(0.945850\pi\)
\(492\) 1.48143 + 0.664975i 0.0667880 + 0.0299794i
\(493\) −41.5297 −1.87040
\(494\) 19.0309 + 32.9624i 0.856239 + 1.48305i
\(495\) 1.11358 + 1.25197i 0.0500515 + 0.0562717i
\(496\) 30.2979 1.36042
\(497\) 0 0
\(498\) −15.2651 6.85210i −0.684045 0.307050i
\(499\) 4.86535 0.217803 0.108902 0.994053i \(-0.465267\pi\)
0.108902 + 0.994053i \(0.465267\pi\)
\(500\) −3.83814 + 6.64786i −0.171647 + 0.297301i
\(501\) 0.686155 + 6.72477i 0.0306551 + 0.300440i
\(502\) −20.7648 35.9657i −0.926780 1.60523i
\(503\) 16.0085 0.713783 0.356892 0.934146i \(-0.383837\pi\)
0.356892 + 0.934146i \(0.383837\pi\)
\(504\) 0 0
\(505\) 9.10026 0.404956
\(506\) −1.23855 2.14523i −0.0550603 0.0953672i
\(507\) 17.1299 12.3663i 0.760764 0.549205i
\(508\) −2.85848 + 4.95102i −0.126824 + 0.219666i
\(509\) −31.1851 −1.38225 −0.691127 0.722733i \(-0.742885\pi\)
−0.691127 + 0.722733i \(0.742885\pi\)
\(510\) −17.1801 + 12.4025i −0.760747 + 0.549192i
\(511\) 0 0
\(512\) −4.59937 −0.203265
\(513\) −22.6298 5.02607i −0.999128 0.221907i
\(514\) 3.40633 + 5.89994i 0.150247 + 0.260235i
\(515\) 11.0617 0.487439
\(516\) 1.09184 + 10.7007i 0.0480655 + 0.471074i
\(517\) −2.19954 3.80971i −0.0967356 0.167551i
\(518\) 0 0
\(519\) 2.83310 + 27.7663i 0.124359 + 1.21880i
\(520\) −4.50000 7.79423i −0.197338 0.341800i
\(521\) −10.4830 18.1572i −0.459270 0.795480i 0.539652 0.841888i \(-0.318556\pi\)
−0.998923 + 0.0464085i \(0.985222\pi\)
\(522\) −18.5604 20.8670i −0.812369 0.913325i
\(523\) −21.7821 + 37.7277i −0.952465 + 1.64972i −0.212401 + 0.977183i \(0.568128\pi\)
−0.740064 + 0.672536i \(0.765205\pi\)
\(524\) −2.94756 + 5.10532i −0.128765 + 0.223027i
\(525\) 0 0
\(526\) 15.0309 + 26.0342i 0.655377 + 1.13515i
\(527\) 46.0604 2.00642
\(528\) 0.515936 + 5.05651i 0.0224532 + 0.220056i
\(529\) −16.8640 −0.733216
\(530\) −5.58413 + 9.67200i −0.242559 + 0.420125i
\(531\) −30.6459 + 6.31963i −1.32992 + 0.274249i
\(532\) 0 0
\(533\) −2.64764 + 4.58584i −0.114682 + 0.198635i
\(534\) 2.26578 + 1.01705i 0.0980499 + 0.0440120i
\(535\) −1.80291 + 3.12273i −0.0779466 + 0.135007i
\(536\) 11.2040 19.4058i 0.483937 0.838204i
\(537\) 2.51205 + 24.6197i 0.108403 + 1.06242i
\(538\) −12.0906 + 20.9415i −0.521262 + 0.902852i
\(539\) 0 0
\(540\) −4.27946 0.950469i −0.184159 0.0409017i
\(541\) −4.93268 + 8.54365i −0.212072 + 0.367320i −0.952363 0.304967i \(-0.901355\pi\)
0.740291 + 0.672287i \(0.234688\pi\)
\(542\) 9.17585 0.394137
\(543\) −20.3640 9.14085i −0.873902 0.392271i
\(544\) −35.6345 −1.52782
\(545\) −6.10570 10.5754i −0.261539 0.453000i
\(546\) 0 0
\(547\) −0.284350 + 0.492509i −0.0121579 + 0.0210582i −0.872040 0.489434i \(-0.837203\pi\)
0.859882 + 0.510492i \(0.170537\pi\)
\(548\) −6.23600 + 10.8011i −0.266389 + 0.461399i
\(549\) 11.0046 33.1814i 0.469665 1.41615i
\(550\) 2.04944 + 3.54974i 0.0873885 + 0.151361i
\(551\) 12.2173 + 21.1609i 0.520473 + 0.901487i
\(552\) −7.39292 3.31848i −0.314663 0.141244i
\(553\) 0 0
\(554\) 6.51485 + 11.2841i 0.276789 + 0.479413i
\(555\) 9.31522 6.72477i 0.395409 0.285450i
\(556\) 7.82538 0.331870
\(557\) 1.29349 + 2.24040i 0.0548071 + 0.0949286i 0.892127 0.451784i \(-0.149212\pi\)
−0.837320 + 0.546713i \(0.815879\pi\)
\(558\) 20.5853 + 23.1435i 0.871446 + 0.979744i
\(559\) −35.0760 −1.48356
\(560\) 0 0
\(561\) 0.784350 + 7.68715i 0.0331153 + 0.324552i
\(562\) 38.5178 1.62478
\(563\) 16.6416 28.8240i 0.701358 1.21479i −0.266632 0.963798i \(-0.585911\pi\)
0.967990 0.250989i \(-0.0807558\pi\)
\(564\) 10.5000 + 4.71317i 0.442130 + 0.198460i
\(565\) 4.28171 + 7.41613i 0.180133 + 0.311999i
\(566\) 54.1318 2.27533
\(567\) 0 0
\(568\) 8.12227 0.340803
\(569\) 2.67673 + 4.63623i 0.112214 + 0.194361i 0.916663 0.399662i \(-0.130872\pi\)
−0.804448 + 0.594022i \(0.797539\pi\)
\(570\) 11.3736 + 5.10532i 0.476389 + 0.213838i
\(571\) −2.45056 + 4.24449i −0.102553 + 0.177626i −0.912736 0.408551i \(-0.866034\pi\)
0.810183 + 0.586177i \(0.199368\pi\)
\(572\) 2.62482 0.109749
\(573\) −0.380525 3.72940i −0.0158967 0.155798i
\(574\) 0 0
\(575\) −10.1533 −0.423424
\(576\) 3.96294 + 4.45543i 0.165122 + 0.185643i
\(577\) 18.0378 + 31.2425i 0.750925 + 1.30064i 0.947375 + 0.320127i \(0.103725\pi\)
−0.196450 + 0.980514i \(0.562941\pi\)
\(578\) −68.8231 −2.86266
\(579\) 14.6491 10.5754i 0.608797 0.439498i
\(580\) 2.31038 + 4.00170i 0.0959333 + 0.166161i
\(581\) 0 0
\(582\) −9.14833 4.10644i −0.379210 0.170217i
\(583\) 2.03637 + 3.52710i 0.0843380 + 0.146078i
\(584\) −4.21303 7.29719i −0.174337 0.301960i
\(585\) 4.50000 13.5685i 0.186052 0.560990i
\(586\) 23.3645 40.4684i 0.965177 1.67174i
\(587\) −0.527445 + 0.913562i −0.0217700 + 0.0377068i −0.876705 0.481028i \(-0.840263\pi\)
0.854935 + 0.518735i \(0.173597\pi\)
\(588\) 0 0
\(589\) −13.5501 23.4695i −0.558323 0.967045i
\(590\) 16.8282 0.692807
\(591\) 29.6829 + 13.3239i 1.22099 + 0.548071i
\(592\) 34.8516 1.43239
\(593\) 7.53548 13.0518i 0.309445 0.535975i −0.668796 0.743446i \(-0.733190\pi\)
0.978241 + 0.207471i \(0.0665233\pi\)
\(594\) −3.51195 + 3.82965i −0.144097 + 0.157132i
\(595\) 0 0
\(596\) 1.94004 3.36024i 0.0794670 0.137641i
\(597\) 1.48143 + 14.5190i 0.0606309 + 0.594223i
\(598\) −10.5669 + 18.3024i −0.432114 + 0.748443i
\(599\) −21.0283 + 36.4221i −0.859194 + 1.48817i 0.0135047 + 0.999909i \(0.495701\pi\)
−0.872699 + 0.488259i \(0.837632\pi\)
\(600\) 12.2331 + 5.49113i 0.499416 + 0.224175i
\(601\) −9.44989 + 16.3677i −0.385469 + 0.667652i −0.991834 0.127534i \(-0.959294\pi\)
0.606365 + 0.795186i \(0.292627\pi\)
\(602\) 0 0
\(603\) 34.8585 7.18833i 1.41955 0.292732i
\(604\) 5.62296 9.73924i 0.228795 0.396284i
\(605\) 10.1134 0.411167
\(606\) 2.86467 + 28.0756i 0.116369 + 1.14049i
\(607\) −29.4425 −1.19504 −0.597518 0.801856i \(-0.703846\pi\)
−0.597518 + 0.801856i \(0.703846\pi\)
\(608\) 10.4830 + 18.1572i 0.425143 + 0.736370i
\(609\) 0 0
\(610\) −9.40043 + 16.2820i −0.380612 + 0.659240i
\(611\) −18.7658 + 32.5033i −0.759182 + 1.31494i
\(612\) −13.4358 15.1055i −0.543111 0.610605i
\(613\) 5.83379 + 10.1044i 0.235625 + 0.408114i 0.959454 0.281865i \(-0.0909531\pi\)
−0.723829 + 0.689979i \(0.757620\pi\)
\(614\) 12.5922 + 21.8103i 0.508179 + 0.880191i
\(615\) 0.176057 + 1.72548i 0.00709932 + 0.0695780i
\(616\) 0 0
\(617\) 16.4054 + 28.4151i 0.660458 + 1.14395i 0.980495 + 0.196542i \(0.0629713\pi\)
−0.320037 + 0.947405i \(0.603695\pi\)
\(618\) 3.48212 + 34.1271i 0.140071 + 1.37279i
\(619\) −24.1612 −0.971119 −0.485560 0.874204i \(-0.661384\pi\)
−0.485560 + 0.874204i \(0.661384\pi\)
\(620\) −2.56243 4.43827i −0.102910 0.178245i
\(621\) −3.86576 12.2772i −0.155127 0.492665i
\(622\) −49.3972 −1.98065
\(623\) 0 0
\(624\) 35.1599 25.3824i 1.40752 1.01611i
\(625\) 12.2953 0.491811
\(626\) −20.8018 + 36.0297i −0.831406 + 1.44004i
\(627\) 3.68615 2.66108i 0.147211 0.106273i
\(628\) −5.00975 8.67714i −0.199911 0.346256i
\(629\) 52.9830 2.11257
\(630\) 0 0
\(631\) −11.1003 −0.441894 −0.220947 0.975286i \(-0.570915\pi\)
−0.220947 + 0.975286i \(0.570915\pi\)
\(632\) 1.25959 + 2.18168i 0.0501038 + 0.0867824i
\(633\) 1.97309 + 19.3376i 0.0784233 + 0.768600i
\(634\) −6.27747 + 10.8729i −0.249310 + 0.431818i
\(635\) −6.10635 −0.242323
\(636\) −9.72109 4.36354i −0.385466 0.173026i
\(637\) 0 0
\(638\) 5.47710 0.216840
\(639\) 8.57413 + 9.63967i 0.339187 + 0.381339i
\(640\) −6.06464 10.5043i −0.239726 0.415218i
\(641\) 7.30037 0.288347 0.144174 0.989552i \(-0.453948\pi\)
0.144174 + 0.989552i \(0.453948\pi\)
\(642\) −10.2016 4.57923i −0.402625 0.180728i
\(643\) −10.6256 18.4041i −0.419033 0.725787i 0.576809 0.816879i \(-0.304298\pi\)
−0.995842 + 0.0910922i \(0.970964\pi\)
\(644\) 0 0
\(645\) −9.31522 + 6.72477i −0.366787 + 0.264787i
\(646\) 28.7465 + 49.7904i 1.13102 + 1.95898i
\(647\) −8.47300 14.6757i −0.333108 0.576960i 0.650011 0.759924i \(-0.274764\pi\)
−0.983120 + 0.182964i \(0.941431\pi\)
\(648\) −1.98212 + 16.8827i −0.0778650 + 0.663214i
\(649\) 3.06839 5.31460i 0.120445 0.208616i
\(650\) 17.4852 30.2853i 0.685826 1.18789i
\(651\) 0 0
\(652\) 0.740409 + 1.28243i 0.0289967 + 0.0502237i
\(653\) −3.73305 −0.146085 −0.0730427 0.997329i \(-0.523271\pi\)
−0.0730427 + 0.997329i \(0.523271\pi\)
\(654\) 30.7046 22.1660i 1.20064 0.866758i
\(655\) −6.29665 −0.246031
\(656\) −2.63070 + 4.55650i −0.102711 + 0.177902i
\(657\) 4.21303 12.7033i 0.164366 0.495601i
\(658\) 0 0
\(659\) 11.7992 20.4368i 0.459632 0.796105i −0.539310 0.842107i \(-0.681315\pi\)
0.998941 + 0.0460022i \(0.0146481\pi\)
\(660\) 0.697080 0.503230i 0.0271338 0.0195882i
\(661\) −17.2588 + 29.8930i −0.671288 + 1.16270i 0.306252 + 0.951951i \(0.400925\pi\)
−0.977539 + 0.210754i \(0.932408\pi\)
\(662\) 17.0488 29.5293i 0.662619 1.14769i
\(663\) 53.4518 38.5875i 2.07590 1.49861i
\(664\) 5.36767 9.29708i 0.208306 0.360796i
\(665\) 0 0
\(666\) 23.6792 + 26.6219i 0.917550 + 1.03158i
\(667\) −6.78366 + 11.7496i −0.262664 + 0.454948i
\(668\) 3.46847 0.134199
\(669\) −29.1469 + 21.0415i −1.12689 + 0.813512i
\(670\) −19.1414 −0.739498
\(671\) 3.42807 + 5.93759i 0.132339 + 0.229218i
\(672\) 0 0
\(673\) 12.2287 21.1808i 0.471382 0.816458i −0.528082 0.849194i \(-0.677088\pi\)
0.999464 + 0.0327353i \(0.0104218\pi\)
\(674\) 5.44437 9.42992i 0.209709 0.363227i
\(675\) 6.39671 + 20.3151i 0.246210 + 0.781930i
\(676\) −5.42030 9.38823i −0.208473 0.361086i
\(677\) 4.16022 + 7.20572i 0.159890 + 0.276938i 0.934829 0.355098i \(-0.115553\pi\)
−0.774939 + 0.632037i \(0.782219\pi\)
\(678\) −21.5320 + 15.5442i −0.826931 + 0.596971i
\(679\) 0 0
\(680\) −6.79734 11.7733i −0.260666 0.451487i
\(681\) 16.4814 + 7.39808i 0.631570 + 0.283495i
\(682\) −6.07463 −0.232610
\(683\) 21.2312 + 36.7735i 0.812389 + 1.40710i 0.911188 + 0.411991i \(0.135167\pi\)
−0.0987988 + 0.995107i \(0.531500\pi\)
\(684\) −3.74427 + 11.2898i −0.143166 + 0.431678i
\(685\) −13.3215 −0.508989
\(686\) 0 0
\(687\) −23.7960 10.6814i −0.907873 0.407520i
\(688\) −34.8516 −1.32870
\(689\) 17.3737 30.0921i 0.661885 1.14642i
\(690\) 0.702658 + 6.88651i 0.0267497 + 0.262165i
\(691\) −17.6964 30.6511i −0.673204 1.16602i −0.976990 0.213284i \(-0.931584\pi\)
0.303786 0.952740i \(-0.401749\pi\)
\(692\) 14.3212 0.544410
\(693\) 0 0
\(694\) 49.6167 1.88342
\(695\) 4.17920 + 7.23859i 0.158526 + 0.274575i
\(696\) 14.5277 10.4877i 0.550669 0.397535i
\(697\) −3.99931 + 6.92701i −0.151485 + 0.262379i
\(698\) 7.38293 0.279448
\(699\) 6.16069 4.44747i 0.233019 0.168219i
\(700\) 0 0
\(701\) −7.00372 −0.264527 −0.132263 0.991215i \(-0.542224\pi\)
−0.132263 + 0.991215i \(0.542224\pi\)
\(702\) 43.2774 + 9.61192i 1.63340 + 0.362778i
\(703\) −15.5867 26.9969i −0.587862 1.01821i
\(704\) −1.16944 −0.0440751
\(705\) 1.24785 + 12.2297i 0.0469967 + 0.460599i
\(706\) 21.8408 + 37.8294i 0.821989 + 1.42373i
\(707\) 0 0
\(708\) 1.62976 + 15.9727i 0.0612500 + 0.600291i
\(709\) 1.11126 + 1.92477i 0.0417344 + 0.0722861i 0.886138 0.463421i \(-0.153378\pi\)
−0.844404 + 0.535707i \(0.820045\pi\)
\(710\) −3.46913 6.00870i −0.130194 0.225503i
\(711\) −1.25959 + 3.79795i −0.0472383 + 0.142434i
\(712\) −0.796717 + 1.37995i −0.0298582 + 0.0517160i
\(713\) 7.52373 13.0315i 0.281766 0.488033i
\(714\) 0 0
\(715\) 1.40180 + 2.42800i 0.0524245 + 0.0908019i
\(716\) 12.6983 0.474556
\(717\) −1.67925 16.4578i −0.0627127 0.614626i
\(718\) −35.1606 −1.31218
\(719\) −13.0088 + 22.5319i −0.485145 + 0.840296i −0.999854 0.0170686i \(-0.994567\pi\)
0.514709 + 0.857365i \(0.327900\pi\)
\(720\) 4.47121 13.4817i 0.166632 0.502434i
\(721\) 0 0
\(722\) 0.766951 1.32840i 0.0285430 0.0494379i
\(723\) −16.6483 7.47299i −0.619158 0.277924i
\(724\) −5.72670 + 9.91893i −0.212831 + 0.368634i
\(725\) 11.2250 19.4423i 0.416886 0.722068i
\(726\) 3.18358 + 31.2012i 0.118154 + 1.15798i
\(727\) 0.685875 1.18797i 0.0254377 0.0440594i −0.853026 0.521868i \(-0.825235\pi\)
0.878464 + 0.477809i \(0.158569\pi\)
\(728\) 0 0
\(729\) −22.1291 + 15.4695i −0.819595 + 0.572943i
\(730\) −3.59888 + 6.23345i −0.133201 + 0.230710i
\(731\) −52.9830 −1.95965
\(732\) −16.3647 7.34566i −0.604855 0.271504i
\(733\) −0.800174 −0.0295551 −0.0147776 0.999891i \(-0.504704\pi\)
−0.0147776 + 0.999891i \(0.504704\pi\)
\(734\) −2.42011 4.19176i −0.0893280 0.154721i
\(735\) 0 0
\(736\) −5.82072 + 10.0818i −0.214555 + 0.371620i
\(737\) −3.49017 + 6.04515i −0.128562 + 0.222676i
\(738\) −5.26792 + 1.08632i −0.193915 + 0.0399881i
\(739\) −2.68547 4.65136i −0.0987865 0.171103i 0.812396 0.583106i \(-0.198163\pi\)
−0.911183 + 0.412003i \(0.864829\pi\)
\(740\) −2.94756 5.10532i −0.108354 0.187675i
\(741\) −35.3864 15.8840i −1.29995 0.583513i
\(742\) 0 0
\(743\) 6.63162 + 11.4863i 0.243290 + 0.421391i 0.961650 0.274281i \(-0.0884399\pi\)
−0.718359 + 0.695672i \(0.755107\pi\)
\(744\) −16.1126 + 11.6318i −0.590715 + 0.426444i
\(745\) 4.14436 0.151838
\(746\) 18.2138 + 31.5472i 0.666854 + 1.15503i
\(747\) 16.7002 3.44384i 0.611030 0.126003i
\(748\) 3.96485 0.144969
\(749\) 0 0
\(750\) −2.58100 25.2955i −0.0942449 0.923662i
\(751\) 5.55632 0.202753 0.101377 0.994848i \(-0.467675\pi\)
0.101377 + 0.994848i \(0.467675\pi\)
\(752\) −18.6457 + 32.2953i −0.679939 + 1.17769i
\(753\) 38.6105 + 17.3312i 1.40704 + 0.631585i
\(754\) −23.3645 40.4684i −0.850883 1.47377i
\(755\) 12.0119 0.437158
\(756\) 0 0
\(757\) −13.3942 −0.486819 −0.243410 0.969924i \(-0.578266\pi\)
−0.243410 + 0.969924i \(0.578266\pi\)
\(758\) 22.9869 + 39.8145i 0.834923 + 1.44613i
\(759\) 2.30298 + 1.03375i 0.0835930 + 0.0375227i
\(760\) −3.99931 + 6.92701i −0.145070 + 0.251269i
\(761\) −12.8438 −0.465588 −0.232794 0.972526i \(-0.574787\pi\)
−0.232794 + 0.972526i \(0.574787\pi\)
\(762\) −1.92221 18.8390i −0.0696345 0.682464i
\(763\) 0 0
\(764\) −1.92353 −0.0695910
\(765\) 6.79734 20.4955i 0.245758 0.741018i
\(766\) −12.2601 21.2351i −0.442975 0.767256i
\(767\) −52.3570 −1.89050
\(768\) 24.9155 17.9868i 0.899060 0.649042i
\(769\) −1.48259 2.56793i −0.0534636 0.0926018i 0.838055 0.545586i \(-0.183693\pi\)
−0.891519 + 0.452984i \(0.850359\pi\)
\(770\) 0 0
\(771\) −6.33379 2.84307i −0.228106 0.102391i
\(772\) −4.63533 8.02864i −0.166829 0.288957i
\(773\) 9.63939 + 16.6959i 0.346705 + 0.600510i 0.985662 0.168732i \(-0.0539673\pi\)
−0.638957 + 0.769242i \(0.720634\pi\)
\(774\) −23.6792 26.6219i −0.851131 0.956905i
\(775\) −12.4496 + 21.5633i −0.447203 + 0.774578i
\(776\) 3.21683 5.57171i 0.115477 0.200013i
\(777\) 0 0
\(778\) −5.19028 8.98983i −0.186080 0.322301i
\(779\) 4.70610 0.168614
\(780\) −6.69183 3.00379i −0.239606 0.107553i
\(781\) −2.53018