Properties

Label 441.2.g.g.79.6
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 79.6
Root \(-0.474636 + 0.274031i\) of defining polynomial
Character \(\chi\) \(=\) 441.79
Dual form 441.2.g.g.67.6

$q$-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 \(-0.431916\pi\)
0.212263 + 0.977212i \(0.431916\pi\)
\(6\) 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 \(-0.921578\pi\)
0.273692 0.961817i \(-0.411755\pi\)
\(14\) 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 \(-0.795258\pi\)
−0.119332 0.992854i \(-0.538075\pi\)
\(18\) −1.60507 + 4.83967i −0.378320 + 1.14072i
\(19\) −2.23061 + 3.86353i −0.511737 + 0.886355i 0.488170 + 0.872748i \(0.337664\pi\)
−0.999907 + 0.0136063i \(0.995669\pi\)
\(20\) −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 \(0.350334\pi\)
−0.998574 + 0.0533826i \(0.983000\pi\)
\(32\) −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 0.821896 0.569638i \(-0.192917\pi\)
−0.904269 + 0.426964i \(0.859583\pi\)
\(42\) 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 \(-0.983082\pi\)
0.453286 0.891365i \(-0.350251\pi\)
\(48\) 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 \(-0.595769\pi\)
0.975297 0.220896i \(-0.0708981\pi\)
\(60\) −1.18478 + 0.855304i −0.152954 + 0.110419i
\(61\) 5.82644 + 10.0917i 0.745999 + 1.29211i 0.949726 + 0.313081i \(0.101361\pi\)
−0.203727 + 0.979028i \(0.565305\pi\)
\(62\) −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 0.966527 0.256563i \(-0.0825903\pi\)
−0.705454 + 0.708756i \(0.749257\pi\)
\(74\) 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 −0.978783 0.204900i \(-0.934313\pi\)
0.666840 + 0.745201i \(0.267647\pi\)
\(84\) 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 −0.842803 0.538223i \(-0.819096\pi\)
0.887516 + 0.460777i \(0.152429\pi\)
\(90\) −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 −0.939443 0.342705i \(-0.888657\pi\)
0.766513 + 0.642229i \(0.221990\pi\)
\(98\) 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 \(-0.341742\pi\)
0.476950 + 0.878930i \(0.341742\pi\)
\(102\) 18.0982 13.0653i 1.79199 1.29366i
\(103\) 11.6529 1.14819 0.574096 0.818788i \(-0.305353\pi\)
0.574096 + 0.818788i \(0.305353\pi\)
\(104\) −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 \(-0.593579\pi\)
−0.289770 + 0.957096i \(0.593579\pi\)
\(132\) 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 0.990089 0.140442i \(-0.0448523\pi\)
−0.616671 + 0.787221i \(0.711519\pi\)
\(140\) 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 −0.548501 0.836150i \(-0.684801\pi\)
0.998378 + 0.0569405i \(0.0181345\pi\)
\(158\) −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 0.931595 0.363497i \(-0.118417\pi\)
−0.780595 + 0.625037i \(0.785084\pi\)
\(168\) 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 \(0.0431961\pi\)
−0.378240 + 0.925708i \(0.623471\pi\)
\(174\) −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 \(-0.658983\pi\)
−0.478952 + 0.877841i \(0.658983\pi\)
\(182\) 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 0.975828 0.218539i \(-0.0701290\pi\)
−0.677174 + 0.735823i \(0.736796\pi\)
\(200\) −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 \(0.411228\pi\)
−0.970206 + 0.242279i \(0.922105\pi\)
\(224\) 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 \(-0.387492\pi\)
0.346139 + 0.938183i \(0.387492\pi\)
\(228\) −0.697080 6.83185i −0.0461653 0.452450i
\(229\) −15.0592 −0.995141 −0.497570 0.867424i \(-0.665774\pi\)
−0.497570 + 0.867424i \(0.665774\pi\)
\(230\) 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 \(-0.610203\pi\)
−0.339337 + 0.940665i \(0.610203\pi\)
\(242\) −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 \(-0.219683\pi\)
0.771148 + 0.636656i \(0.219683\pi\)
\(252\) 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 \(-0.539898\pi\)
−0.125016 + 0.992155i \(0.539898\pi\)
\(258\) −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 0.563463 0.826141i \(-0.309469\pi\)
−0.997191 + 0.0749032i \(0.976135\pi\)
\(270\) −5.66621 + 6.17878i −0.344834 + 0.376029i
\(271\) −2.69937 + 4.67545i −0.163975 + 0.284013i −0.936291 0.351226i \(-0.885765\pi\)
0.772316 + 0.635239i \(0.219098\pi\)
\(272\) 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 \(0.562193\pi\)
−0.752476 + 0.658620i \(0.771141\pi\)
\(284\) −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 \(0.130149\pi\)
−0.114472 + 0.993427i \(0.536517\pi\)
\(294\) 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 \(-0.638967\pi\)
−0.422841 + 0.906204i \(0.638967\pi\)
\(308\) 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 \(-0.525059\pi\)
0.902665 0.430343i \(-0.141608\pi\)
\(312\) −1.66690 16.3367i −0.0943694 0.924883i
\(313\) −12.2390 21.1986i −0.691790 1.19822i −0.971251 0.238058i \(-0.923489\pi\)
0.279461 0.960157i \(-0.409844\pi\)
\(314\) 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 −0.918283 0.395925i \(-0.870424\pi\)
0.802022 + 0.597294i \(0.203757\pi\)
\(350\) 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 \(-0.739741\pi\)
−0.683955 + 0.729525i \(0.739741\pi\)
\(354\) 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 \(-0.476319\pi\)
0.0743273 + 0.997234i \(0.476319\pi\)
\(368\) 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 \(-0.379841\pi\)
0.368588 + 0.929593i \(0.379841\pi\)
\(384\) 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 −0.981187 0.193061i \(-0.938158\pi\)
0.657789 + 0.753202i \(0.271492\pi\)
\(398\) −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 −0.769437 0.638723i \(-0.779463\pi\)
0.937869 + 0.346990i \(0.112796\pi\)
\(410\) 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 0.711935 0.702246i \(-0.247819\pi\)
−0.964130 + 0.265431i \(0.914486\pi\)
\(420\) 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 \(-0.557590\pi\)
−0.179938 + 0.983678i \(0.557590\pi\)
\(434\) 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 0.892048 0.451941i \(-0.149268\pi\)
−0.837417 + 0.546565i \(0.815935\pi\)
\(440\) −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 \(0.342528\pi\)
−0.999583 + 0.0288813i \(0.990806\pi\)
\(462\) 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 −0.533650 0.845705i \(-0.679180\pi\)
0.999227 + 0.0393016i \(0.0125133\pi\)
\(468\) 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 \(-0.429717\pi\)
0.219011 + 0.975722i \(0.429717\pi\)
\(480\) −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 \(-0.616163\pi\)
−0.356892 + 0.934146i \(0.616163\pi\)
\(504\) 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 \(-0.257115\pi\)
0.691127 + 0.722733i \(0.257115\pi\)
\(510\) 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 0.998923 0.0464085i \(-0.0147776\pi\)
−0.539652 + 0.841888i \(0.681444\pi\)
\(522\) −18.5604 20.8670i −0.812369 0.913325i
\(523\) 21.7821 37.7277i 0.952465 1.64972i 0.212401 0.977183i \(-0.431872\pi\)
0.740064 0.672536i \(-0.234795\pi\)
\(524\) 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 \(0.414089\pi\)
−0.967990 + 0.250989i \(0.919244\pi\)
\(564\) 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 \(-0.896275\pi\)
0.196450 0.980514i \(-0.437059\pi\)
\(578\) −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 −0.854935 0.518735i \(-0.826403\pi\)
0.876705 + 0.481028i \(0.159737\pi\)
\(588\) 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 −0.978241 0.207471i \(-0.933477\pi\)
0.668796 + 0.743446i \(0.266810\pi\)
\(594\) 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 −0.606365 0.795186i \(-0.707373\pi\)
0.991834 + 0.127534i \(0.0407064\pi\)
\(602\) 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 \(-0.296154\pi\)
0.597518 + 0.801856i \(0.296154\pi\)
\(608\) −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 \(-0.338616\pi\)
0.485560 + 0.874204i \(0.338616\pi\)
\(620\) −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 0.995842 0.0910922i \(-0.0290358\pi\)
−0.576809 + 0.816879i \(0.695702\pi\)
\(644\) 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 0.983120 0.182964i \(-0.0585693\pi\)
−0.650011 + 0.759924i \(0.725236\pi\)
\(648\) −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 \(-0.599075\pi\)
0.977539 0.210754i \(-0.0675918\pi\)
\(662\) 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 0.774939 0.632037i \(-0.217781\pi\)
−0.934829 + 0.355098i \(0.884447\pi\)
\(678\) 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 \(0.0684159\pi\)
−0.303786 + 0.952740i \(0.598251\pi\)
\(692\) −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 −0.514709 0.857365i \(-0.672100\pi\)
0.999854 + 0.0170686i \(0.00543337\pi\)
\(720\) −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 −0.878464 0.477809i \(-0.841431\pi\)
0.853026 + 0.521868i \(0.174765\pi\)
\(728\) 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 \(-0.495296\pi\)
0.0147776 + 0.999891i \(0.495296\pi\)
\(734\) 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 \(-0.425213\pi\)
0.232794 + 0.972526i \(0.425213\pi\)
\(762\) 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 0.891519 0.452984i \(-0.149641\pi\)
−0.838055 + 0.545586i \(0.816307\pi\)
\(770\) 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 0.638957 0.769242i \(-0.279366\pi\)
−0.985662 + 0.168732i \(0.946033\pi\)
\(774\) −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 −0.0905371