Properties

Label 668.2.e.a.21.4
Level $668$
Weight $2$
Character 668.21
Analytic conductor $5.334$
Analytic rank $0$
Dimension $1148$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 668 = 2^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 668.e (of order \(83\), degree \(82\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.33400685502\)
Analytic rank: \(0\)
Dimension: \(1148\)
Relative dimension: \(14\) over \(\Q(\zeta_{83})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{83}]$

Embedding invariants

Embedding label 21.4
Character \(\chi\) \(=\) 668.21
Dual form 668.2.e.a.509.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.77371 - 0.270614i) q^{3} +(-1.21708 - 1.44428i) q^{5} +(-0.212405 + 0.294689i) q^{7} +(0.209294 + 0.0653857i) q^{9} +O(q^{10})\) \(q+(-1.77371 - 0.270614i) q^{3} +(-1.21708 - 1.44428i) q^{5} +(-0.212405 + 0.294689i) q^{7} +(0.209294 + 0.0653857i) q^{9} +(-2.42906 + 2.29492i) q^{11} +(-0.424686 + 3.18696i) q^{13} +(1.76790 + 2.89109i) q^{15} +(2.82992 - 4.25704i) q^{17} +(5.24079 + 1.21109i) q^{19} +(0.456490 - 0.465212i) q^{21} +(0.693178 + 3.28150i) q^{23} +(0.242860 - 1.41202i) q^{25} +(4.48341 + 2.18904i) q^{27} +(-0.511898 + 2.42332i) q^{29} +(0.832857 - 0.159530i) q^{31} +(4.92948 - 3.41318i) q^{33} +(0.684128 - 0.0518884i) q^{35} +(-0.474860 + 0.148352i) q^{37} +(1.61570 - 5.53781i) q^{39} +(-0.439269 + 0.174689i) q^{41} +(11.5486 + 4.09369i) q^{43} +(-0.160292 - 0.381859i) q^{45} +(-2.37229 + 9.44702i) q^{47} +(2.17173 + 6.51564i) q^{49} +(-6.17147 + 6.78493i) q^{51} +(1.38084 + 1.03554i) q^{53} +(6.27088 + 0.715144i) q^{55} +(-8.96789 - 3.56636i) q^{57} +(2.10406 + 3.16513i) q^{59} +(4.62066 + 5.92443i) q^{61} +(-0.0637234 + 0.0477883i) q^{63} +(5.11975 - 3.26542i) q^{65} +(-8.41804 + 9.98949i) q^{67} +(-0.341476 - 6.00800i) q^{69} +(-1.33750 - 14.0923i) q^{71} +(3.57533 - 6.37713i) q^{73} +(-0.812875 + 2.43880i) q^{75} +(-0.160344 - 1.20327i) q^{77} +(7.02518 + 0.266034i) q^{79} +(-7.90070 - 5.47046i) q^{81} +(-7.61971 + 2.06748i) q^{83} +(-9.59262 + 1.09396i) q^{85} +(1.56374 - 4.15974i) q^{87} +(2.52173 - 4.12384i) q^{89} +(-0.848957 - 0.802075i) q^{91} +(-1.52042 + 0.0575760i) q^{93} +(-4.62931 - 9.04319i) q^{95} +(-17.4069 - 3.33420i) q^{97} +(-0.658442 + 0.321486i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1148q - 2q^{5} - 14q^{9} + O(q^{10}) \) \( 1148q - 2q^{5} - 14q^{9} + 2q^{11} + 4q^{13} + 14q^{15} + 2q^{17} + 2q^{19} + 14q^{23} - 6q^{25} + 2q^{29} - 2q^{31} + 16q^{33} - 2q^{35} + 10q^{37} + 6q^{39} + 4q^{41} + 4q^{43} - 2q^{45} + 2q^{47} - 30q^{49} - 2q^{51} - 6q^{55} - 4q^{57} + 6q^{59} + 2q^{61} + 14q^{63} + 22q^{65} + 12q^{67} - 14q^{69} - 8q^{71} - 18q^{73} - 26q^{75} - 2q^{79} - 6q^{81} - 22q^{83} + 34q^{85} + 2q^{87} + 14q^{89} - 6q^{91} + 32q^{93} - 8q^{95} + 44q^{97} + 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/668\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(335\)
\(\chi(n)\) \(e\left(\frac{23}{83}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.77371 0.270614i −1.02405 0.156239i −0.383008 0.923745i \(-0.625112\pi\)
−0.641042 + 0.767506i \(0.721498\pi\)
\(4\) 0 0
\(5\) −1.21708 1.44428i −0.544296 0.645903i 0.421001 0.907060i \(-0.361679\pi\)
−0.965296 + 0.261157i \(0.915896\pi\)
\(6\) 0 0
\(7\) −0.212405 + 0.294689i −0.0802814 + 0.111382i −0.849463 0.527648i \(-0.823074\pi\)
0.769181 + 0.639030i \(0.220664\pi\)
\(8\) 0 0
\(9\) 0.209294 + 0.0653857i 0.0697645 + 0.0217952i
\(10\) 0 0
\(11\) −2.42906 + 2.29492i −0.732389 + 0.691944i −0.959432 0.281940i \(-0.909022\pi\)
0.227043 + 0.973885i \(0.427094\pi\)
\(12\) 0 0
\(13\) −0.424686 + 3.18696i −0.117787 + 0.883904i 0.828367 + 0.560186i \(0.189270\pi\)
−0.946154 + 0.323718i \(0.895067\pi\)
\(14\) 0 0
\(15\) 1.76790 + 2.89109i 0.456471 + 0.746477i
\(16\) 0 0
\(17\) 2.82992 4.25704i 0.686357 1.03248i −0.310288 0.950642i \(-0.600426\pi\)
0.996645 0.0818423i \(-0.0260804\pi\)
\(18\) 0 0
\(19\) 5.24079 + 1.21109i 1.20232 + 0.277844i 0.778349 0.627832i \(-0.216057\pi\)
0.423971 + 0.905676i \(0.360636\pi\)
\(20\) 0 0
\(21\) 0.456490 0.465212i 0.0996144 0.101518i
\(22\) 0 0
\(23\) 0.693178 + 3.28150i 0.144538 + 0.684240i 0.988914 + 0.148489i \(0.0474411\pi\)
−0.844376 + 0.535750i \(0.820029\pi\)
\(24\) 0 0
\(25\) 0.242860 1.41202i 0.0485719 0.282405i
\(26\) 0 0
\(27\) 4.48341 + 2.18904i 0.862833 + 0.421281i
\(28\) 0 0
\(29\) −0.511898 + 2.42332i −0.0950571 + 0.450000i 0.904658 + 0.426138i \(0.140126\pi\)
−0.999715 + 0.0238616i \(0.992404\pi\)
\(30\) 0 0
\(31\) 0.832857 0.159530i 0.149586 0.0286523i −0.112786 0.993619i \(-0.535977\pi\)
0.262371 + 0.964967i \(0.415495\pi\)
\(32\) 0 0
\(33\) 4.92948 3.41318i 0.858112 0.594158i
\(34\) 0 0
\(35\) 0.684128 0.0518884i 0.115639 0.00877073i
\(36\) 0 0
\(37\) −0.474860 + 0.148352i −0.0780665 + 0.0243889i −0.336982 0.941511i \(-0.609406\pi\)
0.258915 + 0.965900i \(0.416635\pi\)
\(38\) 0 0
\(39\) 1.61570 5.53781i 0.258720 0.886759i
\(40\) 0 0
\(41\) −0.439269 + 0.174689i −0.0686022 + 0.0272818i −0.403581 0.914944i \(-0.632235\pi\)
0.334979 + 0.942226i \(0.391271\pi\)
\(42\) 0 0
\(43\) 11.5486 + 4.09369i 1.76115 + 0.624282i 0.999713 0.0239549i \(-0.00762581\pi\)
0.761439 + 0.648237i \(0.224493\pi\)
\(44\) 0 0
\(45\) −0.160292 0.381859i −0.0238949 0.0569242i
\(46\) 0 0
\(47\) −2.37229 + 9.44702i −0.346035 + 1.37799i 0.509601 + 0.860411i \(0.329793\pi\)
−0.855635 + 0.517579i \(0.826833\pi\)
\(48\) 0 0
\(49\) 2.17173 + 6.51564i 0.310247 + 0.930806i
\(50\) 0 0
\(51\) −6.17147 + 6.78493i −0.864178 + 0.950081i
\(52\) 0 0
\(53\) 1.38084 + 1.03554i 0.189672 + 0.142242i 0.690572 0.723264i \(-0.257359\pi\)
−0.500900 + 0.865505i \(0.666997\pi\)
\(54\) 0 0
\(55\) 6.27088 + 0.715144i 0.845565 + 0.0964300i
\(56\) 0 0
\(57\) −8.96789 3.56636i −1.18783 0.472375i
\(58\) 0 0
\(59\) 2.10406 + 3.16513i 0.273925 + 0.412065i 0.943855 0.330359i \(-0.107170\pi\)
−0.669930 + 0.742424i \(0.733676\pi\)
\(60\) 0 0
\(61\) 4.62066 + 5.92443i 0.591614 + 0.758546i 0.987131 0.159913i \(-0.0511213\pi\)
−0.395517 + 0.918459i \(0.629435\pi\)
\(62\) 0 0
\(63\) −0.0637234 + 0.0477883i −0.00802839 + 0.00602076i
\(64\) 0 0
\(65\) 5.11975 3.26542i 0.635027 0.405026i
\(66\) 0 0
\(67\) −8.41804 + 9.98949i −1.02843 + 1.22041i −0.0533424 + 0.998576i \(0.516987\pi\)
−0.975084 + 0.221834i \(0.928796\pi\)
\(68\) 0 0
\(69\) −0.341476 6.00800i −0.0411089 0.723278i
\(70\) 0 0
\(71\) −1.33750 14.0923i −0.158732 1.67245i −0.619552 0.784956i \(-0.712686\pi\)
0.460820 0.887494i \(-0.347555\pi\)
\(72\) 0 0
\(73\) 3.57533 6.37713i 0.418461 0.746387i −0.579168 0.815208i \(-0.696623\pi\)
0.997629 + 0.0688213i \(0.0219238\pi\)
\(74\) 0 0
\(75\) −0.812875 + 2.43880i −0.0938627 + 0.281608i
\(76\) 0 0
\(77\) −0.160344 1.20327i −0.0182729 0.137125i
\(78\) 0 0
\(79\) 7.02518 + 0.266034i 0.790395 + 0.0299312i 0.429954 0.902851i \(-0.358530\pi\)
0.360441 + 0.932782i \(0.382626\pi\)
\(80\) 0 0
\(81\) −7.90070 5.47046i −0.877855 0.607828i
\(82\) 0 0
\(83\) −7.61971 + 2.06748i −0.836372 + 0.226935i −0.654190 0.756330i \(-0.726990\pi\)
−0.182181 + 0.983265i \(0.558316\pi\)
\(84\) 0 0
\(85\) −9.59262 + 1.09396i −1.04047 + 0.118657i
\(86\) 0 0
\(87\) 1.56374 4.15974i 0.167651 0.445971i
\(88\) 0 0
\(89\) 2.52173 4.12384i 0.267302 0.437126i −0.691011 0.722844i \(-0.742835\pi\)
0.958314 + 0.285718i \(0.0922321\pi\)
\(90\) 0 0
\(91\) −0.848957 0.802075i −0.0889948 0.0840803i
\(92\) 0 0
\(93\) −1.52042 + 0.0575760i −0.157660 + 0.00597035i
\(94\) 0 0
\(95\) −4.62931 9.04319i −0.474958 0.927812i
\(96\) 0 0
\(97\) −17.4069 3.33420i −1.76740 0.338537i −0.801608 0.597850i \(-0.796022\pi\)
−0.965793 + 0.259314i \(0.916504\pi\)
\(98\) 0 0
\(99\) −0.658442 + 0.321486i −0.0661759 + 0.0323106i
\(100\) 0 0
\(101\) 4.53855 1.60880i 0.451603 0.160081i −0.0985735 0.995130i \(-0.531428\pi\)
0.550176 + 0.835048i \(0.314560\pi\)
\(102\) 0 0
\(103\) −0.144821 + 7.65135i −0.0142696 + 0.753910i 0.918903 + 0.394482i \(0.129076\pi\)
−0.933173 + 0.359427i \(0.882972\pi\)
\(104\) 0 0
\(105\) −1.22748 0.0930998i −0.119790 0.00908561i
\(106\) 0 0
\(107\) 0.146050 + 7.71627i 0.0141192 + 0.745960i 0.934706 + 0.355422i \(0.115663\pi\)
−0.920587 + 0.390538i \(0.872289\pi\)
\(108\) 0 0
\(109\) 4.29164 8.38356i 0.411065 0.803000i −0.588922 0.808190i \(-0.700447\pi\)
0.999987 + 0.00519038i \(0.00165216\pi\)
\(110\) 0 0
\(111\) 0.882409 0.134629i 0.0837546 0.0127784i
\(112\) 0 0
\(113\) −5.23597 4.58452i −0.492558 0.431275i 0.376180 0.926547i \(-0.377237\pi\)
−0.868738 + 0.495271i \(0.835069\pi\)
\(114\) 0 0
\(115\) 3.89576 4.99500i 0.363281 0.465786i
\(116\) 0 0
\(117\) −0.297266 + 0.639242i −0.0274822 + 0.0590979i
\(118\) 0 0
\(119\) 0.653416 + 1.73816i 0.0598985 + 0.159337i
\(120\) 0 0
\(121\) 0.00947595 0.166722i 0.000861450 0.0151565i
\(122\) 0 0
\(123\) 0.826407 0.190974i 0.0745146 0.0172196i
\(124\) 0 0
\(125\) −10.4834 + 6.14108i −0.937661 + 0.549275i
\(126\) 0 0
\(127\) −1.21146 + 12.7643i −0.107500 + 1.13265i 0.764998 + 0.644033i \(0.222740\pi\)
−0.872498 + 0.488619i \(0.837501\pi\)
\(128\) 0 0
\(129\) −19.3761 10.3862i −1.70597 0.914457i
\(130\) 0 0
\(131\) 6.08128 + 6.68578i 0.531324 + 0.584139i 0.945322 0.326138i \(-0.105748\pi\)
−0.413998 + 0.910278i \(0.635868\pi\)
\(132\) 0 0
\(133\) −1.47006 + 1.28716i −0.127471 + 0.111611i
\(134\) 0 0
\(135\) −2.29509 9.13956i −0.197529 0.786608i
\(136\) 0 0
\(137\) −3.55524 12.1855i −0.303744 1.04108i −0.958465 0.285210i \(-0.907937\pi\)
0.654721 0.755871i \(-0.272786\pi\)
\(138\) 0 0
\(139\) 4.66463 2.06274i 0.395649 0.174959i −0.197031 0.980397i \(-0.563130\pi\)
0.592680 + 0.805438i \(0.298070\pi\)
\(140\) 0 0
\(141\) 6.76425 16.1143i 0.569653 1.35707i
\(142\) 0 0
\(143\) −6.28223 8.71594i −0.525347 0.728863i
\(144\) 0 0
\(145\) 4.12299 2.21006i 0.342395 0.183535i
\(146\) 0 0
\(147\) −2.08879 12.1445i −0.172280 1.00167i
\(148\) 0 0
\(149\) 2.53370 + 1.61602i 0.207568 + 0.132389i 0.637437 0.770502i \(-0.279994\pi\)
−0.429869 + 0.902891i \(0.641440\pi\)
\(150\) 0 0
\(151\) −1.22242 2.18036i −0.0994789 0.177435i 0.818002 0.575216i \(-0.195082\pi\)
−0.917481 + 0.397780i \(0.869781\pi\)
\(152\) 0 0
\(153\) 0.870634 0.705936i 0.0703866 0.0570715i
\(154\) 0 0
\(155\) −1.24406 1.00872i −0.0999254 0.0810224i
\(156\) 0 0
\(157\) 7.76214 + 16.6918i 0.619486 + 1.33215i 0.925003 + 0.379960i \(0.124062\pi\)
−0.305517 + 0.952187i \(0.598829\pi\)
\(158\) 0 0
\(159\) −2.16897 2.21041i −0.172010 0.175297i
\(160\) 0 0
\(161\) −1.11426 0.492733i −0.0878156 0.0388328i
\(162\) 0 0
\(163\) −11.2663 6.59973i −0.882447 0.516931i −0.00685176 0.999977i \(-0.502181\pi\)
−0.875595 + 0.483046i \(0.839530\pi\)
\(164\) 0 0
\(165\) −10.9292 2.96544i −0.850835 0.230859i
\(166\) 0 0
\(167\) 5.09867 + 11.8745i 0.394547 + 0.918876i
\(168\) 0 0
\(169\) 2.57001 + 0.697327i 0.197693 + 0.0536405i
\(170\) 0 0
\(171\) 1.01768 + 0.596147i 0.0778237 + 0.0455885i
\(172\) 0 0
\(173\) −1.94957 0.862118i −0.148223 0.0655457i 0.328988 0.944334i \(-0.393292\pi\)
−0.477212 + 0.878788i \(0.658353\pi\)
\(174\) 0 0
\(175\) 0.364524 + 0.371488i 0.0275554 + 0.0280819i
\(176\) 0 0
\(177\) −2.87546 6.18340i −0.216133 0.464773i
\(178\) 0 0
\(179\) −3.97866 3.22601i −0.297379 0.241123i 0.469474 0.882946i \(-0.344444\pi\)
−0.766853 + 0.641823i \(0.778178\pi\)
\(180\) 0 0
\(181\) 0.435438 0.353066i 0.0323658 0.0262432i −0.613491 0.789702i \(-0.710235\pi\)
0.645857 + 0.763459i \(0.276500\pi\)
\(182\) 0 0
\(183\) −6.59246 11.7586i −0.487328 0.869223i
\(184\) 0 0
\(185\) 0.792206 + 0.505276i 0.0582441 + 0.0371487i
\(186\) 0 0
\(187\) 2.89553 + 16.8351i 0.211742 + 1.23110i
\(188\) 0 0
\(189\) −1.59738 + 0.856250i −0.116193 + 0.0622830i
\(190\) 0 0
\(191\) −5.46467 7.58166i −0.395410 0.548589i 0.565752 0.824575i \(-0.308586\pi\)
−0.961162 + 0.275986i \(0.910996\pi\)
\(192\) 0 0
\(193\) 0.604207 1.43939i 0.0434918 0.103609i −0.898856 0.438244i \(-0.855601\pi\)
0.942348 + 0.334634i \(0.108613\pi\)
\(194\) 0 0
\(195\) −9.96461 + 4.40643i −0.713580 + 0.315551i
\(196\) 0 0
\(197\) 3.99468 + 13.6917i 0.284609 + 0.975495i 0.969140 + 0.246511i \(0.0792842\pi\)
−0.684531 + 0.728984i \(0.739993\pi\)
\(198\) 0 0
\(199\) 4.95979 + 19.7510i 0.351590 + 1.40011i 0.847064 + 0.531491i \(0.178368\pi\)
−0.495474 + 0.868623i \(0.665006\pi\)
\(200\) 0 0
\(201\) 17.6344 15.4404i 1.24384 1.08908i
\(202\) 0 0
\(203\) −0.605397 0.665575i −0.0424905 0.0467142i
\(204\) 0 0
\(205\) 0.786926 + 0.421818i 0.0549613 + 0.0294611i
\(206\) 0 0
\(207\) −0.0694854 + 0.732121i −0.00482957 + 0.0508859i
\(208\) 0 0
\(209\) −15.5096 + 9.08538i −1.07282 + 0.628449i
\(210\) 0 0
\(211\) 6.27799 1.45078i 0.432195 0.0998758i −0.00345072 0.999994i \(-0.501098\pi\)
0.435646 + 0.900118i \(0.356520\pi\)
\(212\) 0 0
\(213\) −1.44124 + 25.3576i −0.0987525 + 1.73747i
\(214\) 0 0
\(215\) −8.14320 21.6619i −0.555362 1.47733i
\(216\) 0 0
\(217\) −0.129891 + 0.279319i −0.00881758 + 0.0189614i
\(218\) 0 0
\(219\) −8.06733 + 10.3436i −0.545139 + 0.698958i
\(220\) 0 0
\(221\) 12.3652 + 10.8268i 0.831773 + 0.728286i
\(222\) 0 0
\(223\) 7.72708 1.17892i 0.517444 0.0789462i 0.113155 0.993577i \(-0.463904\pi\)
0.404289 + 0.914631i \(0.367519\pi\)
\(224\) 0 0
\(225\) 0.143155 0.279648i 0.00954368 0.0186432i
\(226\) 0 0
\(227\) −0.253262 13.3806i −0.0168096 0.888104i −0.904206 0.427097i \(-0.859536\pi\)
0.887396 0.461007i \(-0.152512\pi\)
\(228\) 0 0
\(229\) −3.63069 0.275373i −0.239923 0.0181972i −0.0448819 0.998992i \(-0.514291\pi\)
−0.195041 + 0.980795i \(0.562484\pi\)
\(230\) 0 0
\(231\) −0.0412173 + 2.17764i −0.00271190 + 0.143278i
\(232\) 0 0
\(233\) 8.57804 3.04069i 0.561966 0.199202i −0.0379297 0.999280i \(-0.512076\pi\)
0.599895 + 0.800078i \(0.295209\pi\)
\(234\) 0 0
\(235\) 16.5315 8.07154i 1.07839 0.526529i
\(236\) 0 0
\(237\) −12.3886 2.37298i −0.804728 0.154142i
\(238\) 0 0
\(239\) 0.125755 + 0.245657i 0.00813441 + 0.0158903i 0.894177 0.447713i \(-0.147761\pi\)
−0.886043 + 0.463603i \(0.846556\pi\)
\(240\) 0 0
\(241\) 21.9426 0.830935i 1.41345 0.0535253i 0.679970 0.733240i \(-0.261993\pi\)
0.733477 + 0.679715i \(0.237896\pi\)
\(242\) 0 0
\(243\) 1.65314 + 1.56185i 0.106049 + 0.100193i
\(244\) 0 0
\(245\) 6.76726 11.0667i 0.432345 0.707023i
\(246\) 0 0
\(247\) −6.08539 + 16.1879i −0.387204 + 1.03001i
\(248\) 0 0
\(249\) 14.0746 1.60510i 0.891943 0.101719i
\(250\) 0 0
\(251\) −5.87699 + 1.59462i −0.370952 + 0.100651i −0.442459 0.896789i \(-0.645894\pi\)
0.0715071 + 0.997440i \(0.477219\pi\)
\(252\) 0 0
\(253\) −9.21455 6.38017i −0.579314 0.401118i
\(254\) 0 0
\(255\) 17.3105 + 0.655526i 1.08403 + 0.0410506i
\(256\) 0 0
\(257\) 2.58702 + 19.4137i 0.161374 + 1.21100i 0.865496 + 0.500916i \(0.167004\pi\)
−0.704122 + 0.710079i \(0.748659\pi\)
\(258\) 0 0
\(259\) 0.0571449 0.171447i 0.00355081 0.0106532i
\(260\) 0 0
\(261\) −0.265588 + 0.473715i −0.0164395 + 0.0293222i
\(262\) 0 0
\(263\) −1.36244 14.3551i −0.0840117 0.885174i −0.933740 0.357953i \(-0.883475\pi\)
0.849728 0.527221i \(-0.176766\pi\)
\(264\) 0 0
\(265\) −0.184984 3.25465i −0.0113635 0.199931i
\(266\) 0 0
\(267\) −5.58877 + 6.63206i −0.342027 + 0.405876i
\(268\) 0 0
\(269\) 5.78769 3.69145i 0.352882 0.225071i −0.349395 0.936976i \(-0.613613\pi\)
0.702277 + 0.711904i \(0.252167\pi\)
\(270\) 0 0
\(271\) −14.7388 + 11.0532i −0.895321 + 0.671431i −0.944907 0.327339i \(-0.893848\pi\)
0.0495864 + 0.998770i \(0.484210\pi\)
\(272\) 0 0
\(273\) 1.28875 + 1.65239i 0.0779986 + 0.100007i
\(274\) 0 0
\(275\) 2.65056 + 3.98724i 0.159835 + 0.240439i
\(276\) 0 0
\(277\) 8.16754 + 3.24807i 0.490740 + 0.195158i 0.601786 0.798658i \(-0.294456\pi\)
−0.111046 + 0.993815i \(0.535420\pi\)
\(278\) 0 0
\(279\) 0.184743 + 0.0210684i 0.0110603 + 0.00126133i
\(280\) 0 0
\(281\) 10.2142 + 7.66000i 0.609330 + 0.456957i 0.859423 0.511265i \(-0.170823\pi\)
−0.250093 + 0.968222i \(0.580461\pi\)
\(282\) 0 0
\(283\) 3.31636 3.64602i 0.197137 0.216734i −0.633209 0.773981i \(-0.718263\pi\)
0.830347 + 0.557247i \(0.188142\pi\)
\(284\) 0 0
\(285\) 5.76384 + 17.2927i 0.341420 + 1.02433i
\(286\) 0 0
\(287\) 0.0418239 0.166552i 0.00246879 0.00983127i
\(288\) 0 0
\(289\) −3.53411 8.41920i −0.207889 0.495247i
\(290\) 0 0
\(291\) 29.9724 + 10.6244i 1.75702 + 0.622815i
\(292\) 0 0
\(293\) 8.74361 3.47716i 0.510807 0.203138i −0.0998956 0.994998i \(-0.531851\pi\)
0.610703 + 0.791860i \(0.290887\pi\)
\(294\) 0 0
\(295\) 2.01053 6.89108i 0.117058 0.401214i
\(296\) 0 0
\(297\) −15.9141 + 4.97176i −0.923433 + 0.288491i
\(298\) 0 0
\(299\) −10.7524 + 0.815525i −0.621826 + 0.0471630i
\(300\) 0 0
\(301\) −3.65935 + 2.53374i −0.210921 + 0.146042i
\(302\) 0 0
\(303\) −8.48543 + 1.62534i −0.487475 + 0.0933733i
\(304\) 0 0
\(305\) 2.93284 13.8841i 0.167934 0.794999i
\(306\) 0 0
\(307\) −17.0366 8.31819i −0.972332 0.474744i −0.117174 0.993111i \(-0.537383\pi\)
−0.855158 + 0.518367i \(0.826540\pi\)
\(308\) 0 0
\(309\) 2.32743 13.5321i 0.132403 0.769812i
\(310\) 0 0
\(311\) −3.54265 16.7709i −0.200885 0.950989i −0.955539 0.294866i \(-0.904725\pi\)
0.754654 0.656124i \(-0.227805\pi\)
\(312\) 0 0
\(313\) −11.3538 + 11.5708i −0.641756 + 0.654018i −0.955328 0.295547i \(-0.904498\pi\)
0.313572 + 0.949564i \(0.398474\pi\)
\(314\) 0 0
\(315\) 0.146576 + 0.0338723i 0.00825864 + 0.00190849i
\(316\) 0 0
\(317\) −15.7050 + 23.6249i −0.882078 + 1.32691i 0.0623037 + 0.998057i \(0.480155\pi\)
−0.944382 + 0.328851i \(0.893339\pi\)
\(318\) 0 0
\(319\) −4.31790 7.06116i −0.241756 0.395349i
\(320\) 0 0
\(321\) 1.82908 13.7259i 0.102089 0.766107i
\(322\) 0 0
\(323\) 19.9867 18.8830i 1.11209 1.05068i
\(324\) 0 0
\(325\) 4.39693 + 1.37365i 0.243898 + 0.0761964i
\(326\) 0 0
\(327\) −9.88083 + 13.7086i −0.546411 + 0.758088i
\(328\) 0 0
\(329\) −2.28005 2.70568i −0.125703 0.149169i
\(330\) 0 0
\(331\) 18.7316 + 2.85787i 1.02958 + 0.157083i 0.643551 0.765403i \(-0.277460\pi\)
0.386030 + 0.922486i \(0.373846\pi\)
\(332\) 0 0
\(333\) −0.109085 −0.00597784
\(334\) 0 0
\(335\) 24.6731 1.34803
\(336\) 0 0
\(337\) 18.6505 + 2.84550i 1.01596 + 0.155004i 0.637368 0.770560i \(-0.280023\pi\)
0.378591 + 0.925564i \(0.376409\pi\)
\(338\) 0 0
\(339\) 8.04644 + 9.54852i 0.437023 + 0.518605i
\(340\) 0 0
\(341\) −1.65695 + 2.29885i −0.0897290 + 0.124490i
\(342\) 0 0
\(343\) −4.80850 1.50223i −0.259635 0.0811128i
\(344\) 0 0
\(345\) −8.26165 + 7.80542i −0.444792 + 0.420230i
\(346\) 0 0
\(347\) 1.56815 11.7679i 0.0841829 0.631732i −0.897473 0.441070i \(-0.854599\pi\)
0.981656 0.190662i \(-0.0610636\pi\)
\(348\) 0 0
\(349\) 11.6605 + 19.0687i 0.624171 + 1.02072i 0.995730 + 0.0923124i \(0.0294258\pi\)
−0.371559 + 0.928409i \(0.621177\pi\)
\(350\) 0 0
\(351\) −8.88042 + 13.3588i −0.474002 + 0.713040i
\(352\) 0 0
\(353\) 22.1801 + 5.12559i 1.18053 + 0.272807i 0.769398 0.638770i \(-0.220556\pi\)
0.411129 + 0.911577i \(0.365135\pi\)
\(354\) 0 0
\(355\) −18.7254 + 19.0832i −0.993843 + 1.01283i
\(356\) 0 0
\(357\) −0.688597 3.25981i −0.0364444 0.172528i
\(358\) 0 0
\(359\) 5.67172 32.9763i 0.299342 1.74042i −0.312929 0.949776i \(-0.601310\pi\)
0.612271 0.790648i \(-0.290256\pi\)
\(360\) 0 0
\(361\) 8.92558 + 4.35795i 0.469768 + 0.229366i
\(362\) 0 0
\(363\) −0.0619248 + 0.293152i −0.00325021 + 0.0153865i
\(364\) 0 0
\(365\) −13.5618 + 2.59770i −0.709860 + 0.135970i
\(366\) 0 0
\(367\) −28.8923 + 20.0051i −1.50817 + 1.04426i −0.527275 + 0.849695i \(0.676786\pi\)
−0.980890 + 0.194562i \(0.937672\pi\)
\(368\) 0 0
\(369\) −0.103358 + 0.00783931i −0.00538062 + 0.000408098i
\(370\) 0 0
\(371\) −0.598457 + 0.186965i −0.0310703 + 0.00970672i
\(372\) 0 0
\(373\) −2.38330 + 8.16874i −0.123403 + 0.422961i −0.998094 0.0617200i \(-0.980341\pi\)
0.874691 + 0.484681i \(0.161064\pi\)
\(374\) 0 0
\(375\) 20.2563 8.05553i 1.04603 0.415986i
\(376\) 0 0
\(377\) −7.50563 2.66055i −0.386560 0.137025i
\(378\) 0 0
\(379\) 3.81816 + 9.09589i 0.196126 + 0.467225i 0.990037 0.140809i \(-0.0449705\pi\)
−0.793911 + 0.608034i \(0.791958\pi\)
\(380\) 0 0
\(381\) 5.60298 22.3124i 0.287049 1.14310i
\(382\) 0 0
\(383\) 11.9320 + 35.7986i 0.609697 + 1.82922i 0.556841 + 0.830619i \(0.312013\pi\)
0.0528566 + 0.998602i \(0.483167\pi\)
\(384\) 0 0
\(385\) −1.54271 + 1.69606i −0.0786237 + 0.0864392i
\(386\) 0 0
\(387\) 2.14939 + 1.61190i 0.109260 + 0.0819375i
\(388\) 0 0
\(389\) −31.6500 3.60943i −1.60472 0.183006i −0.735532 0.677490i \(-0.763068\pi\)
−0.869187 + 0.494484i \(0.835357\pi\)
\(390\) 0 0
\(391\) 15.9311 + 6.33549i 0.805671 + 0.320400i
\(392\) 0 0
\(393\) −8.97714 13.5043i −0.452837 0.681202i
\(394\) 0 0
\(395\) −8.16600 10.4701i −0.410876 0.526810i
\(396\) 0 0
\(397\) −22.8412 + 17.1294i −1.14637 + 0.859701i −0.991739 0.128271i \(-0.959057\pi\)
−0.154630 + 0.987972i \(0.549419\pi\)
\(398\) 0 0
\(399\) 2.95579 1.88523i 0.147974 0.0943795i
\(400\) 0 0
\(401\) 23.1470 27.4681i 1.15591 1.37169i 0.239769 0.970830i \(-0.422928\pi\)
0.916139 0.400860i \(-0.131288\pi\)
\(402\) 0 0
\(403\) 0.154712 + 2.72203i 0.00770674 + 0.135594i
\(404\) 0 0
\(405\) 1.71491 + 18.0688i 0.0852145 + 0.897848i
\(406\) 0 0
\(407\) 0.813009 1.45012i 0.0402993 0.0718799i
\(408\) 0 0
\(409\) −2.45338 + 7.36066i −0.121312 + 0.363961i −0.991728 0.128355i \(-0.959030\pi\)
0.870416 + 0.492316i \(0.163850\pi\)
\(410\) 0 0
\(411\) 3.00837 + 22.5757i 0.148392 + 1.11358i
\(412\) 0 0
\(413\) −1.37964 0.0522451i −0.0678877 0.00257081i
\(414\) 0 0
\(415\) 12.2598 + 8.48873i 0.601811 + 0.416695i
\(416\) 0 0
\(417\) −8.83190 + 2.39638i −0.432500 + 0.117351i
\(418\) 0 0
\(419\) −23.4255 + 2.67149i −1.14441 + 0.130511i −0.664835 0.746990i \(-0.731498\pi\)
−0.479574 + 0.877501i \(0.659209\pi\)
\(420\) 0 0
\(421\) 13.1687 35.0303i 0.641804 1.70727i −0.0631354 0.998005i \(-0.520110\pi\)
0.704939 0.709268i \(-0.250974\pi\)
\(422\) 0 0
\(423\) −1.11421 + 1.82209i −0.0541746 + 0.0885929i
\(424\) 0 0
\(425\) −5.32378 5.02978i −0.258241 0.243980i
\(426\) 0 0
\(427\) −2.72731 + 0.103280i −0.131984 + 0.00499805i
\(428\) 0 0
\(429\) 8.78419 + 17.1596i 0.424105 + 0.828472i
\(430\) 0 0
\(431\) 2.47624 + 0.474310i 0.119276 + 0.0228467i 0.247416 0.968909i \(-0.420419\pi\)
−0.128140 + 0.991756i \(0.540901\pi\)
\(432\) 0 0
\(433\) 29.6356 14.4697i 1.42419 0.695368i 0.444485 0.895787i \(-0.353387\pi\)
0.979710 + 0.200419i \(0.0642302\pi\)
\(434\) 0 0
\(435\) −7.91104 + 2.80426i −0.379305 + 0.134454i
\(436\) 0 0
\(437\) −0.341399 + 18.0372i −0.0163313 + 0.862834i
\(438\) 0 0
\(439\) 2.90456 + 0.220299i 0.138627 + 0.0105143i 0.144759 0.989467i \(-0.453759\pi\)
−0.00613238 + 0.999981i \(0.501952\pi\)
\(440\) 0 0
\(441\) 0.0284988 + 1.50568i 0.00135709 + 0.0716992i
\(442\) 0 0
\(443\) 2.50637 4.89610i 0.119081 0.232621i −0.822974 0.568080i \(-0.807687\pi\)
0.942055 + 0.335459i \(0.108891\pi\)
\(444\) 0 0
\(445\) −9.02513 + 1.37696i −0.427832 + 0.0652742i
\(446\) 0 0
\(447\) −4.05672 3.55199i −0.191876 0.168003i
\(448\) 0 0
\(449\) 12.1221 15.5425i 0.572078 0.733497i −0.412010 0.911179i \(-0.635173\pi\)
0.984088 + 0.177682i \(0.0568599\pi\)
\(450\) 0 0
\(451\) 0.666114 1.43242i 0.0313661 0.0674498i
\(452\) 0 0
\(453\) 1.57817 + 4.19813i 0.0741491 + 0.197245i
\(454\) 0 0
\(455\) −0.125173 + 2.20232i −0.00586821 + 0.103247i
\(456\) 0 0
\(457\) 28.7425 6.64211i 1.34452 0.310705i 0.509285 0.860598i \(-0.329910\pi\)
0.835235 + 0.549893i \(0.185332\pi\)
\(458\) 0 0
\(459\) 22.0065 12.8913i 1.02718 0.601713i
\(460\) 0 0
\(461\) −3.31885 + 34.9684i −0.154574 + 1.62864i 0.495385 + 0.868673i \(0.335027\pi\)
−0.649959 + 0.759969i \(0.725214\pi\)
\(462\) 0 0
\(463\) −10.5369 5.64811i −0.489690 0.262490i 0.208998 0.977916i \(-0.432980\pi\)
−0.698689 + 0.715426i \(0.746233\pi\)
\(464\) 0 0
\(465\) 1.93363 + 2.12584i 0.0896698 + 0.0985833i
\(466\) 0 0
\(467\) −19.5938 + 17.1560i −0.906692 + 0.793884i −0.979076 0.203493i \(-0.934771\pi\)
0.0723843 + 0.997377i \(0.476939\pi\)
\(468\) 0 0
\(469\) −1.15576 4.60252i −0.0533682 0.212524i
\(470\) 0 0
\(471\) −9.25074 31.7068i −0.426252 1.46097i
\(472\) 0 0
\(473\) −37.4470 + 16.5594i −1.72182 + 0.761402i
\(474\) 0 0
\(475\) 2.98287 7.10600i 0.136863 0.326046i
\(476\) 0 0
\(477\) 0.221291 + 0.307018i 0.0101322 + 0.0140574i
\(478\) 0 0
\(479\) 28.9066 15.4949i 1.32078 0.707981i 0.347515 0.937674i \(-0.387025\pi\)
0.973263 + 0.229694i \(0.0737724\pi\)
\(480\) 0 0
\(481\) −0.271125 1.57636i −0.0123622 0.0718760i
\(482\) 0 0
\(483\) 1.84302 + 1.17550i 0.0838604 + 0.0534870i
\(484\) 0 0
\(485\) 16.3701 + 29.1985i 0.743327 + 1.32583i
\(486\) 0 0
\(487\) 7.81750 6.33865i 0.354245 0.287232i −0.436095 0.899901i \(-0.643639\pi\)
0.790340 + 0.612669i \(0.209904\pi\)
\(488\) 0 0
\(489\) 18.1972 + 14.7548i 0.822905 + 0.667236i
\(490\) 0 0
\(491\) −9.12141 19.6148i −0.411644 0.885201i −0.997215 0.0745805i \(-0.976238\pi\)
0.585571 0.810621i \(-0.300870\pi\)
\(492\) 0 0
\(493\) 8.86756 + 9.03698i 0.399375 + 0.407005i
\(494\) 0 0
\(495\) 1.26569 + 0.559701i 0.0568888 + 0.0251567i
\(496\) 0 0
\(497\) 4.43694 + 2.59912i 0.199024 + 0.116587i
\(498\) 0 0
\(499\) 23.0324 + 6.24944i 1.03107 + 0.279763i 0.736909 0.675992i \(-0.236285\pi\)
0.294162 + 0.955756i \(0.404959\pi\)
\(500\) 0 0
\(501\) −5.83015 22.4416i −0.260472 1.00262i
\(502\) 0 0
\(503\) 19.8118 + 5.37558i 0.883362 + 0.239685i 0.674513 0.738263i \(-0.264354\pi\)
0.208849 + 0.977948i \(0.433028\pi\)
\(504\) 0 0
\(505\) −7.84735 4.59692i −0.349202 0.204560i
\(506\) 0 0
\(507\) −4.36973 1.93233i −0.194067 0.0858179i
\(508\) 0 0
\(509\) −19.5449 19.9183i −0.866312 0.882864i 0.127736 0.991808i \(-0.459229\pi\)
−0.994048 + 0.108944i \(0.965253\pi\)
\(510\) 0 0
\(511\) 1.11985 + 2.40814i 0.0495394 + 0.106530i
\(512\) 0 0
\(513\) 20.8455 + 16.9021i 0.920351 + 0.746248i
\(514\) 0 0
\(515\) 11.2270 9.10316i 0.494720 0.401133i
\(516\) 0 0
\(517\) −15.9177 28.3916i −0.700061 1.24866i
\(518\) 0 0
\(519\) 3.22467 + 2.05673i 0.141547 + 0.0902803i
\(520\) 0 0
\(521\) 1.40825 + 8.18781i 0.0616966 + 0.358714i 0.999920 + 0.0126829i \(0.00403720\pi\)
−0.938223 + 0.346031i \(0.887529\pi\)
\(522\) 0 0
\(523\) −12.1289 + 6.50148i −0.530359 + 0.284290i −0.715728 0.698379i \(-0.753905\pi\)
0.185369 + 0.982669i \(0.440652\pi\)
\(524\) 0 0
\(525\) −0.546028 0.757557i −0.0238306 0.0330625i
\(526\) 0 0
\(527\) 1.67780 3.99697i 0.0730860 0.174111i
\(528\) 0 0
\(529\) 10.7474 4.75257i 0.467276 0.206633i
\(530\) 0 0
\(531\) 0.233412 + 0.800017i 0.0101292 + 0.0347178i
\(532\) 0 0
\(533\) −0.370174 1.47412i −0.0160340 0.0638512i
\(534\) 0 0
\(535\) 10.9667 9.60227i 0.474133 0.415143i
\(536\) 0 0
\(537\) 6.18397 + 6.79868i 0.266858 + 0.293385i
\(538\) 0 0
\(539\) −20.2281 10.8429i −0.871288 0.467039i
\(540\) 0 0
\(541\) 0.580942 6.12100i 0.0249767 0.263162i −0.974304 0.225237i \(-0.927684\pi\)
0.999281 0.0379250i \(-0.0120748\pi\)
\(542\) 0 0
\(543\) −0.867884 + 0.508400i −0.0372445 + 0.0218175i
\(544\) 0 0
\(545\) −17.3315 + 4.00514i −0.742401 + 0.171561i
\(546\) 0 0
\(547\) −1.15124 + 20.2553i −0.0492237 + 0.866052i 0.874982 + 0.484156i \(0.160873\pi\)
−0.924205 + 0.381896i \(0.875271\pi\)
\(548\) 0 0
\(549\) 0.579700 + 1.54207i 0.0247410 + 0.0658140i
\(550\) 0 0
\(551\) −5.61762 + 12.0802i −0.239319 + 0.514633i
\(552\) 0 0
\(553\) −1.57058 + 2.01374i −0.0667878 + 0.0856328i
\(554\) 0 0
\(555\) −1.26841 1.11059i −0.0538409 0.0471421i
\(556\) 0 0
\(557\) −16.5742 + 2.52872i −0.702271 + 0.107145i −0.492125 0.870525i \(-0.663780\pi\)
−0.210146 + 0.977670i \(0.567394\pi\)
\(558\) 0 0
\(559\) −17.9510 + 35.0665i −0.759245 + 1.48316i
\(560\) 0 0
\(561\) −0.580015 30.6440i −0.0244883 1.29379i
\(562\) 0 0
\(563\) 5.18952 + 0.393604i 0.218712 + 0.0165885i 0.184529 0.982827i \(-0.440924\pi\)
0.0341836 + 0.999416i \(0.489117\pi\)
\(564\) 0 0
\(565\) −0.248745 + 13.1420i −0.0104648 + 0.552886i
\(566\) 0 0
\(567\) 3.29023 1.16630i 0.138177 0.0489799i
\(568\) 0 0
\(569\) −31.0648 + 15.1675i −1.30231 + 0.635855i −0.953515 0.301345i \(-0.902564\pi\)
−0.348791 + 0.937201i \(0.613408\pi\)
\(570\) 0 0
\(571\) 9.93218 + 1.90246i 0.415649 + 0.0796154i 0.391689 0.920098i \(-0.371891\pi\)
0.0239595 + 0.999713i \(0.492373\pi\)
\(572\) 0 0
\(573\) 7.64102 + 14.9265i 0.319208 + 0.623562i
\(574\) 0 0
\(575\) 4.80190 0.181841i 0.200253 0.00758331i
\(576\) 0 0
\(577\) −19.0323 17.9813i −0.792325 0.748571i 0.179631 0.983734i \(-0.442510\pi\)
−0.971956 + 0.235164i \(0.924437\pi\)
\(578\) 0 0
\(579\) −1.46120 + 2.38954i −0.0607256 + 0.0993059i
\(580\) 0 0
\(581\) 1.00920 2.68459i 0.0418686 0.111375i
\(582\) 0 0
\(583\) −5.73060 + 0.653530i −0.237337 + 0.0270664i
\(584\) 0 0
\(585\) 1.28504 0.348674i 0.0531300 0.0144159i
\(586\) 0 0
\(587\) −24.3593 16.8664i −1.00542 0.696152i −0.0522608 0.998633i \(-0.516643\pi\)
−0.953155 + 0.302482i \(0.902185\pi\)
\(588\) 0 0
\(589\) 4.55804 + 0.172606i 0.187811 + 0.00711213i
\(590\) 0 0
\(591\) −3.38022 25.3661i −0.139044 1.04342i
\(592\) 0 0
\(593\) 2.79622 8.38925i 0.114827 0.344505i −0.875508 0.483204i \(-0.839473\pi\)
0.990335 + 0.138699i \(0.0442921\pi\)
\(594\) 0 0
\(595\) 1.71514 3.05920i 0.0703138 0.125415i
\(596\) 0 0
\(597\) −3.45232 36.3747i −0.141294 1.48872i
\(598\) 0 0
\(599\) −0.385358 6.78008i −0.0157453 0.277027i −0.996606 0.0823168i \(-0.973768\pi\)
0.980861 0.194710i \(-0.0623765\pi\)
\(600\) 0 0
\(601\) 7.75934 9.20783i 0.316510 0.375595i −0.583017 0.812460i \(-0.698128\pi\)
0.899527 + 0.436865i \(0.143911\pi\)
\(602\) 0 0
\(603\) −2.41501 + 1.54032i −0.0983469 + 0.0627266i
\(604\) 0 0
\(605\) −0.252327 + 0.189228i −0.0102585 + 0.00769323i
\(606\) 0 0
\(607\) −28.7825 36.9039i −1.16825 1.49788i −0.830830 0.556526i \(-0.812134\pi\)
−0.337416 0.941356i \(-0.609553\pi\)
\(608\) 0 0
\(609\) 0.893683 + 1.34436i 0.0362139 + 0.0544764i
\(610\) 0 0
\(611\) −29.0998 11.5724i −1.17725 0.468170i
\(612\) 0 0
\(613\) −19.1411 2.18289i −0.773102 0.0881662i −0.282170 0.959364i \(-0.591054\pi\)
−0.490932 + 0.871198i \(0.663344\pi\)
\(614\) 0 0
\(615\) −1.28163 0.961135i −0.0516802 0.0387567i
\(616\) 0 0
\(617\) −8.25093 + 9.07110i −0.332170 + 0.365189i −0.882954 0.469459i \(-0.844449\pi\)
0.550784 + 0.834648i \(0.314329\pi\)
\(618\) 0 0
\(619\) −5.98977 17.9706i −0.240749 0.722299i −0.997634 0.0687503i \(-0.978099\pi\)
0.756885 0.653549i \(-0.226720\pi\)
\(620\) 0 0
\(621\) −4.07553 + 16.2297i −0.163545 + 0.651275i
\(622\) 0 0
\(623\) 0.679623 + 1.61905i 0.0272285 + 0.0648657i
\(624\) 0 0
\(625\) 14.8764 + 5.27331i 0.595058 + 0.210932i
\(626\) 0 0
\(627\) 29.9681 11.9177i 1.19681 0.475947i
\(628\) 0 0
\(629\) −0.712277 + 2.44132i −0.0284004 + 0.0973420i
\(630\) 0 0
\(631\) −3.95326 + 1.23504i −0.157377 + 0.0491663i −0.375871 0.926672i \(-0.622657\pi\)
0.218494 + 0.975838i \(0.429885\pi\)
\(632\) 0 0
\(633\) −11.5279 + 0.874347i −0.458194 + 0.0347522i
\(634\) 0 0
\(635\) 19.9098 13.7855i 0.790095 0.547063i
\(636\) 0 0
\(637\) −21.6874 + 4.15411i −0.859286 + 0.164592i
\(638\) 0 0
\(639\) 0.641506 3.03688i 0.0253776 0.120137i
\(640\) 0 0
\(641\) −23.5892 11.5175i −0.931719 0.454915i −0.0906744 0.995881i \(-0.528902\pi\)
−0.841045 + 0.540966i \(0.818059\pi\)
\(642\) 0 0
\(643\) 6.88750 40.0450i 0.271616 1.57922i −0.453923 0.891041i \(-0.649976\pi\)
0.725539 0.688181i \(-0.241590\pi\)
\(644\) 0 0
\(645\) 8.58165 + 40.6255i 0.337902 + 1.59963i
\(646\) 0 0
\(647\) −23.4348 + 23.8825i −0.921316 + 0.938919i −0.998310 0.0581127i \(-0.981492\pi\)
0.0769944 + 0.997032i \(0.475468\pi\)
\(648\) 0 0
\(649\) −12.3746 2.85964i −0.485746 0.112251i
\(650\) 0 0
\(651\) 0.305976 0.460279i 0.0119922 0.0180398i
\(652\) 0 0
\(653\) −3.95714 6.47120i −0.154855 0.253237i 0.766258 0.642533i \(-0.222116\pi\)
−0.921113 + 0.389295i \(0.872719\pi\)
\(654\) 0 0
\(655\) 2.25474 16.9202i 0.0881001 0.661128i
\(656\) 0 0
\(657\) 1.16527 1.10092i 0.0454614 0.0429509i
\(658\) 0 0
\(659\) −26.1528 8.17044i −1.01877 0.318275i −0.257200 0.966358i \(-0.582800\pi\)
−0.761570 + 0.648083i \(0.775571\pi\)
\(660\) 0 0
\(661\) 4.50953 6.25650i 0.175401 0.243350i −0.714359 0.699779i \(-0.753282\pi\)
0.889760 + 0.456430i \(0.150872\pi\)
\(662\) 0 0
\(663\) −19.0024 22.5497i −0.737991 0.875757i
\(664\) 0 0
\(665\) 3.64822 + 0.556607i 0.141472 + 0.0215843i
\(666\) 0 0
\(667\) −8.30696 −0.321647
\(668\) 0 0
\(669\) −14.0246 −0.542223
\(670\) 0 0
\(671\) −24.8200 3.78677i −0.958164 0.146187i
\(672\) 0 0
\(673\) −24.4536 29.0186i −0.942619 1.11858i −0.992793 0.119843i \(-0.961761\pi\)
0.0501741 0.998740i \(-0.484022\pi\)
\(674\) 0 0
\(675\) 4.17982 5.79906i 0.160881 0.223206i
\(676\) 0 0
\(677\) 43.0794 + 13.4585i 1.65567 + 0.517251i 0.976278 0.216520i \(-0.0694708\pi\)
0.679396 + 0.733772i \(0.262242\pi\)
\(678\) 0 0
\(679\) 4.67985 4.42142i 0.179596 0.169678i
\(680\) 0 0
\(681\) −3.17177 + 23.8019i −0.121543 + 0.912090i
\(682\) 0 0
\(683\) −17.7807 29.0772i −0.680360 1.11261i −0.986990 0.160780i \(-0.948599\pi\)
0.306631 0.951829i \(-0.400798\pi\)
\(684\) 0 0
\(685\) −13.2724 + 19.9656i −0.507111 + 0.762845i
\(686\) 0 0
\(687\) 6.36526 + 1.47095i 0.242850 + 0.0561201i
\(688\) 0 0
\(689\) −3.88663 + 3.96089i −0.148069 + 0.150898i
\(690\) 0 0
\(691\) 0.472048 + 2.23467i 0.0179576 + 0.0850110i 0.986464 0.163977i \(-0.0524322\pi\)
−0.968507 + 0.248988i \(0.919902\pi\)
\(692\) 0 0
\(693\) 0.0451175 0.262321i 0.00171387 0.00996474i
\(694\) 0 0
\(695\) −8.65642 4.22652i −0.328357 0.160321i
\(696\) 0 0
\(697\) −0.499439 + 2.36434i −0.0189176 + 0.0895558i
\(698\) 0 0
\(699\) −16.0378 + 3.07195i −0.606604 + 0.116192i
\(700\) 0 0
\(701\) −2.50911 + 1.73731i −0.0947679 + 0.0656174i −0.615700 0.787981i \(-0.711127\pi\)
0.520932 + 0.853598i \(0.325584\pi\)
\(702\) 0 0
\(703\) −2.66831 + 0.202381i −0.100637 + 0.00763293i
\(704\) 0 0
\(705\) −31.5062 + 9.84291i −1.18659 + 0.370705i
\(706\) 0 0
\(707\) −0.489914 + 1.67918i −0.0184251 + 0.0631520i
\(708\) 0 0
\(709\) 7.98345 3.17486i 0.299825 0.119234i −0.214779 0.976663i \(-0.568903\pi\)
0.514603 + 0.857428i \(0.327939\pi\)
\(710\) 0 0
\(711\) 1.45293 + 0.515026i 0.0544892 + 0.0193150i
\(712\) 0 0
\(713\) 1.10081 + 2.62244i 0.0412258 + 0.0982110i
\(714\) 0 0
\(715\) −4.94229 + 19.6813i −0.184831 + 0.736040i
\(716\) 0 0
\(717\) −0.156574 0.469755i −0.00584737 0.0175433i
\(718\) 0 0
\(719\) −27.9022 + 30.6758i −1.04058 + 1.14402i −0.0511945 + 0.998689i \(0.516303\pi\)
−0.989384 + 0.145327i \(0.953577\pi\)
\(720\) 0 0
\(721\) −2.22401 1.66786i −0.0828264 0.0621143i
\(722\) 0 0
\(723\) −39.1446 4.46413i −1.45580 0.166023i
\(724\) 0 0
\(725\) 3.29747 + 1.31134i 0.122465 + 0.0487019i
\(726\) 0 0
\(727\) 8.84419 + 13.3043i 0.328013 + 0.493429i 0.959404 0.282036i \(-0.0910097\pi\)
−0.631391 + 0.775465i \(0.717516\pi\)
\(728\) 0 0
\(729\) 15.2204 + 19.5150i 0.563718 + 0.722778i
\(730\) 0 0
\(731\) 50.1088 37.5783i 1.85334 1.38988i
\(732\) 0 0
\(733\) 0.0347219 0.0221460i 0.00128248 0.000817980i −0.537102 0.843518i \(-0.680481\pi\)
0.538384 + 0.842700i \(0.319035\pi\)
\(734\) 0 0
\(735\) −14.9979 + 17.7977i −0.553207 + 0.656478i
\(736\) 0 0
\(737\) −2.47717 43.5838i −0.0912476 1.60543i
\(738\) 0 0
\(739\) −2.21432 23.3308i −0.0814549 0.858236i −0.939021 0.343861i \(-0.888265\pi\)
0.857566 0.514375i \(-0.171976\pi\)
\(740\) 0 0
\(741\) 15.1744 27.0657i 0.557444 0.994285i
\(742\) 0 0
\(743\) 0.682358 2.04722i 0.0250333 0.0751052i −0.935430 0.353512i \(-0.884987\pi\)
0.960463 + 0.278407i \(0.0898065\pi\)
\(744\) 0 0
\(745\) −0.749732 5.62620i −0.0274680 0.206128i
\(746\) 0 0
\(747\) −1.72994 0.0655104i −0.0632952 0.00239690i
\(748\) 0 0
\(749\) −2.30492 1.59593i −0.0842200 0.0583141i
\(750\) 0 0
\(751\) 11.7698 3.19354i 0.429488 0.116534i −0.0405558 0.999177i \(-0.512913\pi\)
0.470044 + 0.882643i \(0.344238\pi\)
\(752\) 0 0
\(753\) 10.8556 1.23799i 0.395599 0.0451150i
\(754\) 0 0
\(755\) −1.66128 + 4.41919i −0.0604601 + 0.160831i
\(756\) 0 0
\(757\) −13.2136 + 21.6085i −0.480257 + 0.785375i −0.997515 0.0704546i \(-0.977555\pi\)
0.517258 + 0.855829i \(0.326953\pi\)
\(758\) 0 0
\(759\) 14.6173 + 13.8101i 0.530576 + 0.501276i
\(760\) 0 0
\(761\) 6.68636 0.253203i 0.242380 0.00917861i 0.0836280 0.996497i \(-0.473349\pi\)
0.158752 + 0.987318i \(0.449253\pi\)
\(762\) 0 0
\(763\) 1.55898 + 3.04541i 0.0564388 + 0.110251i
\(764\) 0 0
\(765\) −2.07920 0.398261i −0.0751738 0.0143992i
\(766\) 0 0
\(767\) −10.9807 + 5.36137i −0.396490 + 0.193588i
\(768\) 0 0
\(769\) −7.87642 + 2.79198i −0.284031 + 0.100682i −0.472305 0.881435i \(-0.656578\pi\)
0.188274 + 0.982116i \(0.439711\pi\)
\(770\) 0 0
\(771\) 0.665007 35.1344i 0.0239496 1.26533i
\(772\) 0 0
\(773\) 46.3099 + 3.51242i 1.66565 + 0.126333i 0.874416 0.485178i \(-0.161245\pi\)
0.791236 + 0.611511i \(0.209438\pi\)
\(774\) 0 0
\(775\) −0.0229924 1.21476i −0.000825910 0.0436354i
\(776\) 0 0
\(777\) −0.147754 + 0.288632i −0.00530065 + 0.0103546i
\(778\) 0 0
\(779\) −2.51368 + 0.383511i −0.0900620 + 0.0137407i
\(780\) 0 0
\(781\) 35.5896 + 31.1616i 1.27350 + 1.11505i
\(782\) 0 0
\(783\) −7.59980 + 9.74418i −0.271595 + 0.348229i
\(784\) 0 0
\(785\) 14.6605 31.5260i 0.523254 1.12521i
\(786\) 0 0
\(787\) −11.2536 29.9360i −0.401149 1.06710i −0.969666 0.244432i \(-0.921399\pi\)
0.568518 0.822671i \(-0.307517\pi\)
\(788\) 0 0
\(789\) −1.46812 + 25.8305i −0.0522666 + 0.919589i
\(790\) 0 0
\(791\) 2.46315 0.569209i 0.0875796 0.0202387i
\(792\) 0 0
\(793\) −20.8433 + 12.2098i −0.740166 + 0.433583i
\(794\) 0 0
\(795\) −0.552645 + 5.82285i −0.0196003 + 0.206515i
\(796\) 0 0