Properties

Label 819.2.fm.e.622.2
Level $819$
Weight $2$
Character 819.622
Analytic conductor $6.540$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.fm (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 622.2
Character \(\chi\) \(=\) 819.622
Dual form 819.2.fm.e.370.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.385482 + 1.43864i) q^{2} +(-0.189037 - 0.109141i) q^{4} +(1.07205 - 1.07205i) q^{5} +(1.81743 + 1.92274i) q^{7} +(-1.87643 + 1.87643i) q^{8} +O(q^{10})\) \(q+(-0.385482 + 1.43864i) q^{2} +(-0.189037 - 0.109141i) q^{4} +(1.07205 - 1.07205i) q^{5} +(1.81743 + 1.92274i) q^{7} +(-1.87643 + 1.87643i) q^{8} +(1.12904 + 1.95556i) q^{10} +(-1.68564 - 0.451666i) q^{11} +(3.51131 + 0.818944i) q^{13} +(-3.46672 + 1.87345i) q^{14} +(-2.19446 - 3.80091i) q^{16} +(-1.43508 + 2.48563i) q^{17} +(0.389597 + 1.45400i) q^{19} +(-0.319663 + 0.0856533i) q^{20} +(1.29957 - 2.25092i) q^{22} +(3.21155 - 1.85419i) q^{23} +2.70140i q^{25} +(-2.53172 + 4.73583i) q^{26} +(-0.133713 - 0.561826i) q^{28} +(1.65473 + 2.86608i) q^{29} +(1.32380 - 1.32380i) q^{31} +(1.18757 - 0.318208i) q^{32} +(-3.02273 - 3.02273i) q^{34} +(4.00967 + 0.112899i) q^{35} +(-5.83082 - 1.56236i) q^{37} -2.24196 q^{38} +4.02327i q^{40} +(3.10007 + 0.830662i) q^{41} +(3.29020 + 1.89960i) q^{43} +(0.269354 + 0.269354i) q^{44} +(1.42951 + 5.33502i) q^{46} +(5.86346 + 5.86346i) q^{47} +(-0.393883 + 6.98891i) q^{49} +(-3.88635 - 1.04134i) q^{50} +(-0.574389 - 0.538038i) q^{52} +1.37219 q^{53} +(-2.29131 + 1.32289i) q^{55} +(-7.01818 - 0.197610i) q^{56} +(-4.76112 + 1.27574i) q^{58} +(-0.967827 + 0.259328i) q^{59} +(-0.0305081 - 0.0176138i) q^{61} +(1.39417 + 2.41477i) q^{62} -6.94669i q^{64} +(4.64227 - 2.88636i) q^{65} +(-1.26183 + 4.70921i) q^{67} +(0.542567 - 0.313251i) q^{68} +(-1.70808 + 5.72495i) q^{70} +(-11.4087 + 3.05695i) q^{71} +(-11.3351 - 11.3351i) q^{73} +(4.49535 - 7.78618i) q^{74} +(0.0850419 - 0.317381i) q^{76} +(-2.19510 - 4.06193i) q^{77} -3.53025 q^{79} +(-6.42736 - 1.72221i) q^{80} +(-2.39005 + 4.13968i) q^{82} +(10.8414 - 10.8414i) q^{83} +(1.12625 + 4.20321i) q^{85} +(-4.00116 + 4.00116i) q^{86} +(4.01051 - 2.31547i) q^{88} +(-2.02252 + 7.54814i) q^{89} +(4.80695 + 8.23973i) q^{91} -0.809469 q^{92} +(-10.6957 + 6.17514i) q^{94} +(1.97643 + 1.14109i) q^{95} +(-2.46851 - 9.21262i) q^{97} +(-9.90269 - 3.26076i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + O(q^{10}) \) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + 2q^{10} + 4q^{11} + 6q^{13} - 34q^{14} + 14q^{16} + 8q^{17} + 2q^{19} - 44q^{20} - 4q^{22} + 18q^{23} + 28q^{26} - 32q^{28} + 18q^{29} - 14q^{31} + 8q^{32} - 66q^{34} - 22q^{35} - 24q^{37} - 24q^{38} - 6q^{43} + 20q^{44} - 58q^{46} + 28q^{47} + 8q^{49} - 70q^{50} + 28q^{52} + 80q^{53} + 60q^{55} + 54q^{56} - 4q^{58} + 42q^{59} + 36q^{61} - 52q^{62} - 14q^{65} + 26q^{67} + 72q^{68} - 116q^{70} + 4q^{71} + 12q^{73} + 18q^{74} - 48q^{76} - 28q^{77} - 4q^{79} + 98q^{80} + 20q^{82} + 36q^{83} - 10q^{85} + 40q^{86} + 96q^{88} + 54q^{89} + 148q^{91} + 4q^{92} - 60q^{95} - 40q^{97} - 36q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{12}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.385482 + 1.43864i −0.272577 + 1.01727i 0.684870 + 0.728665i \(0.259859\pi\)
−0.957448 + 0.288607i \(0.906808\pi\)
\(3\) 0 0
\(4\) −0.189037 0.109141i −0.0945186 0.0545703i
\(5\) 1.07205 1.07205i 0.479437 0.479437i −0.425515 0.904952i \(-0.639907\pi\)
0.904952 + 0.425515i \(0.139907\pi\)
\(6\) 0 0
\(7\) 1.81743 + 1.92274i 0.686925 + 0.726729i
\(8\) −1.87643 + 1.87643i −0.663418 + 0.663418i
\(9\) 0 0
\(10\) 1.12904 + 1.95556i 0.357034 + 0.618401i
\(11\) −1.68564 0.451666i −0.508240 0.136182i −0.00441837 0.999990i \(-0.501406\pi\)
−0.503822 + 0.863808i \(0.668073\pi\)
\(12\) 0 0
\(13\) 3.51131 + 0.818944i 0.973863 + 0.227134i
\(14\) −3.46672 + 1.87345i −0.926521 + 0.500700i
\(15\) 0 0
\(16\) −2.19446 3.80091i −0.548614 0.950228i
\(17\) −1.43508 + 2.48563i −0.348058 + 0.602854i −0.985904 0.167310i \(-0.946492\pi\)
0.637847 + 0.770164i \(0.279825\pi\)
\(18\) 0 0
\(19\) 0.389597 + 1.45400i 0.0893798 + 0.333570i 0.996108 0.0881466i \(-0.0280944\pi\)
−0.906728 + 0.421717i \(0.861428\pi\)
\(20\) −0.319663 + 0.0856533i −0.0714787 + 0.0191527i
\(21\) 0 0
\(22\) 1.29957 2.25092i 0.277069 0.479898i
\(23\) 3.21155 1.85419i 0.669654 0.386625i −0.126292 0.991993i \(-0.540307\pi\)
0.795946 + 0.605368i \(0.206974\pi\)
\(24\) 0 0
\(25\) 2.70140i 0.540281i
\(26\) −2.53172 + 4.73583i −0.496510 + 0.928772i
\(27\) 0 0
\(28\) −0.133713 0.561826i −0.0252693 0.106175i
\(29\) 1.65473 + 2.86608i 0.307276 + 0.532217i 0.977765 0.209702i \(-0.0672493\pi\)
−0.670490 + 0.741919i \(0.733916\pi\)
\(30\) 0 0
\(31\) 1.32380 1.32380i 0.237761 0.237761i −0.578161 0.815922i \(-0.696230\pi\)
0.815922 + 0.578161i \(0.196230\pi\)
\(32\) 1.18757 0.318208i 0.209934 0.0562517i
\(33\) 0 0
\(34\) −3.02273 3.02273i −0.518394 0.518394i
\(35\) 4.00967 + 0.112899i 0.677757 + 0.0190835i
\(36\) 0 0
\(37\) −5.83082 1.56236i −0.958580 0.256851i −0.254581 0.967051i \(-0.581938\pi\)
−0.703999 + 0.710201i \(0.748604\pi\)
\(38\) −2.24196 −0.363694
\(39\) 0 0
\(40\) 4.02327i 0.636134i
\(41\) 3.10007 + 0.830662i 0.484150 + 0.129728i 0.492634 0.870236i \(-0.336034\pi\)
−0.00848433 + 0.999964i \(0.502701\pi\)
\(42\) 0 0
\(43\) 3.29020 + 1.89960i 0.501751 + 0.289686i 0.729436 0.684049i \(-0.239782\pi\)
−0.227685 + 0.973735i \(0.573116\pi\)
\(44\) 0.269354 + 0.269354i 0.0406066 + 0.0406066i
\(45\) 0 0
\(46\) 1.42951 + 5.33502i 0.210770 + 0.786605i
\(47\) 5.86346 + 5.86346i 0.855273 + 0.855273i 0.990777 0.135504i \(-0.0432652\pi\)
−0.135504 + 0.990777i \(0.543265\pi\)
\(48\) 0 0
\(49\) −0.393883 + 6.98891i −0.0562690 + 0.998416i
\(50\) −3.88635 1.04134i −0.549612 0.147268i
\(51\) 0 0
\(52\) −0.574389 0.538038i −0.0796534 0.0746125i
\(53\) 1.37219 0.188484 0.0942422 0.995549i \(-0.469957\pi\)
0.0942422 + 0.995549i \(0.469957\pi\)
\(54\) 0 0
\(55\) −2.29131 + 1.32289i −0.308960 + 0.178378i
\(56\) −7.01818 0.197610i −0.937843 0.0264067i
\(57\) 0 0
\(58\) −4.76112 + 1.27574i −0.625166 + 0.167513i
\(59\) −0.967827 + 0.259328i −0.126000 + 0.0337617i −0.321268 0.946988i \(-0.604109\pi\)
0.195268 + 0.980750i \(0.437442\pi\)
\(60\) 0 0
\(61\) −0.0305081 0.0176138i −0.00390616 0.00225522i 0.498046 0.867151i \(-0.334051\pi\)
−0.501952 + 0.864896i \(0.667385\pi\)
\(62\) 1.39417 + 2.41477i 0.177059 + 0.306676i
\(63\) 0 0
\(64\) 6.94669i 0.868336i
\(65\) 4.64227 2.88636i 0.575803 0.358009i
\(66\) 0 0
\(67\) −1.26183 + 4.70921i −0.154157 + 0.575322i 0.845019 + 0.534736i \(0.179589\pi\)
−0.999176 + 0.0405858i \(0.987078\pi\)
\(68\) 0.542567 0.313251i 0.0657959 0.0379873i
\(69\) 0 0
\(70\) −1.70808 + 5.72495i −0.204154 + 0.684262i
\(71\) −11.4087 + 3.05695i −1.35396 + 0.362793i −0.861595 0.507596i \(-0.830534\pi\)
−0.492366 + 0.870388i \(0.663868\pi\)
\(72\) 0 0
\(73\) −11.3351 11.3351i −1.32667 1.32667i −0.908258 0.418410i \(-0.862587\pi\)
−0.418410 0.908258i \(-0.637413\pi\)
\(74\) 4.49535 7.78618i 0.522574 0.905125i
\(75\) 0 0
\(76\) 0.0850419 0.317381i 0.00975497 0.0364061i
\(77\) −2.19510 4.06193i −0.250155 0.462900i
\(78\) 0 0
\(79\) −3.53025 −0.397184 −0.198592 0.980082i \(-0.563637\pi\)
−0.198592 + 0.980082i \(0.563637\pi\)
\(80\) −6.42736 1.72221i −0.718600 0.192548i
\(81\) 0 0
\(82\) −2.39005 + 4.13968i −0.263937 + 0.457151i
\(83\) 10.8414 10.8414i 1.19000 1.19000i 0.212936 0.977066i \(-0.431698\pi\)
0.977066 0.212936i \(-0.0683025\pi\)
\(84\) 0 0
\(85\) 1.12625 + 4.20321i 0.122159 + 0.455902i
\(86\) −4.00116 + 4.00116i −0.431456 + 0.431456i
\(87\) 0 0
\(88\) 4.01051 2.31547i 0.427522 0.246830i
\(89\) −2.02252 + 7.54814i −0.214386 + 0.800101i 0.771995 + 0.635628i \(0.219259\pi\)
−0.986382 + 0.164473i \(0.947408\pi\)
\(90\) 0 0
\(91\) 4.80695 + 8.23973i 0.503906 + 0.863759i
\(92\) −0.809469 −0.0843930
\(93\) 0 0
\(94\) −10.6957 + 6.17514i −1.10317 + 0.636918i
\(95\) 1.97643 + 1.14109i 0.202778 + 0.117074i
\(96\) 0 0
\(97\) −2.46851 9.21262i −0.250640 0.935400i −0.970465 0.241244i \(-0.922445\pi\)
0.719825 0.694156i \(-0.244222\pi\)
\(98\) −9.90269 3.26076i −1.00032 0.329386i
\(99\) 0 0
\(100\) 0.294833 0.510666i 0.0294833 0.0510666i
\(101\) −6.74473 11.6822i −0.671125 1.16242i −0.977585 0.210540i \(-0.932478\pi\)
0.306460 0.951883i \(-0.400855\pi\)
\(102\) 0 0
\(103\) 8.93370 0.880264 0.440132 0.897933i \(-0.354932\pi\)
0.440132 + 0.897933i \(0.354932\pi\)
\(104\) −8.12543 + 5.05205i −0.796764 + 0.495394i
\(105\) 0 0
\(106\) −0.528954 + 1.97408i −0.0513766 + 0.191740i
\(107\) 6.52366 + 11.2993i 0.630666 + 1.09235i 0.987416 + 0.158146i \(0.0505516\pi\)
−0.356750 + 0.934200i \(0.616115\pi\)
\(108\) 0 0
\(109\) −14.0320 14.0320i −1.34402 1.34402i −0.892015 0.452007i \(-0.850708\pi\)
−0.452007 0.892015i \(-0.649292\pi\)
\(110\) −1.01990 3.80632i −0.0972436 0.362918i
\(111\) 0 0
\(112\) 3.31990 11.1273i 0.313701 1.05143i
\(113\) 5.60312 9.70489i 0.527097 0.912959i −0.472404 0.881382i \(-0.656614\pi\)
0.999501 0.0315769i \(-0.0100529\pi\)
\(114\) 0 0
\(115\) 1.45516 5.43074i 0.135695 0.506419i
\(116\) 0.722393i 0.0670725i
\(117\) 0 0
\(118\) 1.49232i 0.137379i
\(119\) −7.38739 + 1.75817i −0.677201 + 0.161172i
\(120\) 0 0
\(121\) −6.88890 3.97731i −0.626263 0.361573i
\(122\) 0.0371003 0.0371003i 0.00335890 0.00335890i
\(123\) 0 0
\(124\) −0.394727 + 0.105767i −0.0354475 + 0.00949814i
\(125\) 8.25632 + 8.25632i 0.738467 + 0.738467i
\(126\) 0 0
\(127\) 3.67035 2.11908i 0.325691 0.188038i −0.328235 0.944596i \(-0.606454\pi\)
0.653926 + 0.756558i \(0.273121\pi\)
\(128\) 12.3689 + 3.31424i 1.09327 + 0.292940i
\(129\) 0 0
\(130\) 2.36293 + 7.79120i 0.207242 + 0.683333i
\(131\) 7.27464i 0.635589i −0.948160 0.317794i \(-0.897058\pi\)
0.948160 0.317794i \(-0.102942\pi\)
\(132\) 0 0
\(133\) −2.08760 + 3.39164i −0.181018 + 0.294092i
\(134\) −6.28845 3.63064i −0.543239 0.313639i
\(135\) 0 0
\(136\) −1.97129 7.35694i −0.169036 0.630852i
\(137\) 5.38885 + 20.1115i 0.460400 + 1.71824i 0.671706 + 0.740818i \(0.265562\pi\)
−0.211306 + 0.977420i \(0.567772\pi\)
\(138\) 0 0
\(139\) 16.2490 + 9.38137i 1.37822 + 0.795718i 0.991946 0.126665i \(-0.0404272\pi\)
0.386278 + 0.922382i \(0.373761\pi\)
\(140\) −0.745654 0.458960i −0.0630193 0.0387892i
\(141\) 0 0
\(142\) 17.5914i 1.47624i
\(143\) −5.54893 2.96639i −0.464025 0.248062i
\(144\) 0 0
\(145\) 4.84654 + 1.29863i 0.402484 + 0.107845i
\(146\) 20.6765 11.9376i 1.71120 0.987963i
\(147\) 0 0
\(148\) 0.931724 + 0.931724i 0.0765872 + 0.0765872i
\(149\) 1.73434 0.464716i 0.142083 0.0380710i −0.187077 0.982345i \(-0.559901\pi\)
0.329160 + 0.944274i \(0.393235\pi\)
\(150\) 0 0
\(151\) 14.9709 14.9709i 1.21832 1.21832i 0.250095 0.968221i \(-0.419538\pi\)
0.968221 0.250095i \(-0.0804619\pi\)
\(152\) −3.45938 1.99727i −0.280593 0.162000i
\(153\) 0 0
\(154\) 6.68982 1.59216i 0.539081 0.128300i
\(155\) 2.83836i 0.227983i
\(156\) 0 0
\(157\) 19.5001i 1.55628i −0.628093 0.778138i \(-0.716164\pi\)
0.628093 0.778138i \(-0.283836\pi\)
\(158\) 1.36085 5.07876i 0.108263 0.404044i
\(159\) 0 0
\(160\) 0.931999 1.61427i 0.0736810 0.127619i
\(161\) 9.40190 + 2.80512i 0.740973 + 0.221075i
\(162\) 0 0
\(163\) 3.90415 + 14.5705i 0.305797 + 1.14125i 0.932257 + 0.361796i \(0.117836\pi\)
−0.626460 + 0.779453i \(0.715497\pi\)
\(164\) −0.495370 0.495370i −0.0386819 0.0386819i
\(165\) 0 0
\(166\) 11.4177 + 19.7761i 0.886188 + 1.53492i
\(167\) 2.08221 7.77093i 0.161127 0.601333i −0.837376 0.546627i \(-0.815911\pi\)
0.998503 0.0547052i \(-0.0174219\pi\)
\(168\) 0 0
\(169\) 11.6587 + 5.75114i 0.896820 + 0.442396i
\(170\) −6.48105 −0.497074
\(171\) 0 0
\(172\) −0.414647 0.718190i −0.0316166 0.0547615i
\(173\) 10.9025 18.8837i 0.828903 1.43570i −0.0699960 0.997547i \(-0.522299\pi\)
0.898899 0.438155i \(-0.144368\pi\)
\(174\) 0 0
\(175\) −5.19410 + 4.90962i −0.392637 + 0.371132i
\(176\) 1.98232 + 7.39814i 0.149423 + 0.557656i
\(177\) 0 0
\(178\) −10.0794 5.81935i −0.755484 0.436179i
\(179\) −8.41680 + 4.85944i −0.629101 + 0.363212i −0.780404 0.625276i \(-0.784986\pi\)
0.151303 + 0.988487i \(0.451653\pi\)
\(180\) 0 0
\(181\) 13.6038 1.01116 0.505580 0.862779i \(-0.331278\pi\)
0.505580 + 0.862779i \(0.331278\pi\)
\(182\) −13.7070 + 3.73921i −1.01603 + 0.277168i
\(183\) 0 0
\(184\) −2.54699 + 9.50550i −0.187767 + 0.700755i
\(185\) −7.92588 + 4.57601i −0.582722 + 0.336435i
\(186\) 0 0
\(187\) 3.54170 3.54170i 0.258995 0.258995i
\(188\) −0.468470 1.74835i −0.0341667 0.127512i
\(189\) 0 0
\(190\) −2.40350 + 2.40350i −0.174368 + 0.174368i
\(191\) −0.423116 + 0.732859i −0.0306156 + 0.0530278i −0.880927 0.473252i \(-0.843080\pi\)
0.850312 + 0.526280i \(0.176413\pi\)
\(192\) 0 0
\(193\) −1.53179 0.410441i −0.110260 0.0295442i 0.203267 0.979123i \(-0.434844\pi\)
−0.313527 + 0.949579i \(0.601511\pi\)
\(194\) 14.2052 1.01987
\(195\) 0 0
\(196\) 0.837233 1.27818i 0.0598024 0.0912982i
\(197\) 1.35016 5.03888i 0.0961951 0.359005i −0.901003 0.433813i \(-0.857168\pi\)
0.997198 + 0.0748081i \(0.0238344\pi\)
\(198\) 0 0
\(199\) −0.678170 + 1.17462i −0.0480742 + 0.0832670i −0.889061 0.457788i \(-0.848642\pi\)
0.840987 + 0.541055i \(0.181975\pi\)
\(200\) −5.06899 5.06899i −0.358432 0.358432i
\(201\) 0 0
\(202\) 19.4065 5.19995i 1.36543 0.365867i
\(203\) −2.50337 + 8.39052i −0.175702 + 0.588899i
\(204\) 0 0
\(205\) 4.21396 2.43293i 0.294316 0.169923i
\(206\) −3.44379 + 12.8524i −0.239940 + 0.895468i
\(207\) 0 0
\(208\) −4.59270 15.1433i −0.318446 1.05000i
\(209\) 2.62689i 0.181706i
\(210\) 0 0
\(211\) 12.4140 + 21.5017i 0.854616 + 1.48024i 0.877001 + 0.480488i \(0.159541\pi\)
−0.0223853 + 0.999749i \(0.507126\pi\)
\(212\) −0.259394 0.149761i −0.0178153 0.0102857i
\(213\) 0 0
\(214\) −18.7704 + 5.02951i −1.28312 + 0.343810i
\(215\) 5.56375 1.49080i 0.379444 0.101672i
\(216\) 0 0
\(217\) 4.95123 + 0.139411i 0.336112 + 0.00946384i
\(218\) 25.5961 14.7779i 1.73358 1.00089i
\(219\) 0 0
\(220\) 0.577523 0.0389366
\(221\) −7.07461 + 7.55258i −0.475890 + 0.508042i
\(222\) 0 0
\(223\) −13.6453 3.65626i −0.913760 0.244841i −0.228844 0.973463i \(-0.573494\pi\)
−0.684916 + 0.728622i \(0.740161\pi\)
\(224\) 2.77015 + 1.70507i 0.185089 + 0.113924i
\(225\) 0 0
\(226\) 11.8019 + 11.8019i 0.785053 + 0.785053i
\(227\) −5.76681 21.5220i −0.382757 1.42847i −0.841673 0.539988i \(-0.818429\pi\)
0.458916 0.888480i \(-0.348238\pi\)
\(228\) 0 0
\(229\) 8.69387 + 8.69387i 0.574507 + 0.574507i 0.933385 0.358877i \(-0.116840\pi\)
−0.358877 + 0.933385i \(0.616840\pi\)
\(230\) 7.25194 + 4.18691i 0.478179 + 0.276077i
\(231\) 0 0
\(232\) −8.48298 2.27301i −0.556935 0.149230i
\(233\) 26.8466i 1.75878i −0.476104 0.879389i \(-0.657952\pi\)
0.476104 0.879389i \(-0.342048\pi\)
\(234\) 0 0
\(235\) 12.5719 0.820099
\(236\) 0.211259 + 0.0566065i 0.0137518 + 0.00368477i
\(237\) 0 0
\(238\) 0.318328 11.3055i 0.0206341 0.732829i
\(239\) −6.42765 6.42765i −0.415770 0.415770i 0.467973 0.883743i \(-0.344984\pi\)
−0.883743 + 0.467973i \(0.844984\pi\)
\(240\) 0 0
\(241\) −21.5089 + 5.76329i −1.38551 + 0.371246i −0.873120 0.487506i \(-0.837907\pi\)
−0.512391 + 0.858752i \(0.671240\pi\)
\(242\) 8.37746 8.37746i 0.538523 0.538523i
\(243\) 0 0
\(244\) 0.00384478 + 0.00665935i 0.000246137 + 0.000426321i
\(245\) 7.07022 + 7.91475i 0.451700 + 0.505655i
\(246\) 0 0
\(247\) 0.177256 + 5.42450i 0.0112785 + 0.345153i
\(248\) 4.96803i 0.315470i
\(249\) 0 0
\(250\) −15.0605 + 8.69520i −0.952511 + 0.549933i
\(251\) 15.2735 26.4545i 0.964055 1.66979i 0.251921 0.967748i \(-0.418938\pi\)
0.712134 0.702044i \(-0.247729\pi\)
\(252\) 0 0
\(253\) −6.25099 + 1.67495i −0.392996 + 0.105303i
\(254\) 1.63374 + 6.09718i 0.102510 + 0.382571i
\(255\) 0 0
\(256\) −2.58931 + 4.48482i −0.161832 + 0.280301i
\(257\) 6.53903 + 11.3259i 0.407894 + 0.706493i 0.994654 0.103268i \(-0.0329300\pi\)
−0.586760 + 0.809761i \(0.699597\pi\)
\(258\) 0 0
\(259\) −7.59309 14.0506i −0.471812 0.873065i
\(260\) −1.19258 + 0.0389699i −0.0739608 + 0.00241681i
\(261\) 0 0
\(262\) 10.4656 + 2.80425i 0.646566 + 0.173247i
\(263\) 4.59748 + 7.96308i 0.283493 + 0.491024i 0.972243 0.233975i \(-0.0751734\pi\)
−0.688750 + 0.724999i \(0.741840\pi\)
\(264\) 0 0
\(265\) 1.47106 1.47106i 0.0903664 0.0903664i
\(266\) −4.07461 4.31072i −0.249831 0.264307i
\(267\) 0 0
\(268\) 0.752500 0.752500i 0.0459662 0.0459662i
\(269\) −10.0654 5.81128i −0.613700 0.354320i 0.160712 0.987001i \(-0.448621\pi\)
−0.774412 + 0.632681i \(0.781954\pi\)
\(270\) 0 0
\(271\) 5.43020 20.2658i 0.329861 1.23106i −0.579473 0.814991i \(-0.696742\pi\)
0.909334 0.416067i \(-0.136592\pi\)
\(272\) 12.5969 0.763798
\(273\) 0 0
\(274\) −31.0104 −1.87341
\(275\) 1.22013 4.55360i 0.0735768 0.274592i
\(276\) 0 0
\(277\) −13.6743 7.89485i −0.821608 0.474356i 0.0293625 0.999569i \(-0.490652\pi\)
−0.850971 + 0.525213i \(0.823986\pi\)
\(278\) −19.7601 + 19.7601i −1.18513 + 1.18513i
\(279\) 0 0
\(280\) −7.73571 + 7.31201i −0.462297 + 0.436976i
\(281\) 6.16446 6.16446i 0.367741 0.367741i −0.498912 0.866653i \(-0.666267\pi\)
0.866653 + 0.498912i \(0.166267\pi\)
\(282\) 0 0
\(283\) −2.66486 4.61567i −0.158410 0.274373i 0.775886 0.630873i \(-0.217303\pi\)
−0.934295 + 0.356500i \(0.883970\pi\)
\(284\) 2.49030 + 0.667274i 0.147772 + 0.0395954i
\(285\) 0 0
\(286\) 6.40658 6.83942i 0.378829 0.404423i
\(287\) 4.03702 + 7.47032i 0.238298 + 0.440959i
\(288\) 0 0
\(289\) 4.38109 + 7.58828i 0.257711 + 0.446369i
\(290\) −3.73652 + 6.47183i −0.219416 + 0.380039i
\(291\) 0 0
\(292\) 0.905632 + 3.37986i 0.0529981 + 0.197792i
\(293\) −20.8745 + 5.59331i −1.21950 + 0.326764i −0.810483 0.585762i \(-0.800795\pi\)
−0.409018 + 0.912526i \(0.634129\pi\)
\(294\) 0 0
\(295\) −0.759548 + 1.31558i −0.0442226 + 0.0765958i
\(296\) 13.8728 8.00945i 0.806339 0.465540i
\(297\) 0 0
\(298\) 2.67424i 0.154914i
\(299\) 12.7952 3.88056i 0.739967 0.224418i
\(300\) 0 0
\(301\) 2.32728 + 9.77861i 0.134142 + 0.563630i
\(302\) 15.7667 + 27.3088i 0.907274 + 1.57144i
\(303\) 0 0
\(304\) 4.67156 4.67156i 0.267933 0.267933i
\(305\) −0.0515893 + 0.0138233i −0.00295399 + 0.000791520i
\(306\) 0 0
\(307\) −3.48509 3.48509i −0.198904 0.198904i 0.600626 0.799530i \(-0.294918\pi\)
−0.799530 + 0.600626i \(0.794918\pi\)
\(308\) −0.0283660 + 1.00743i −0.00161630 + 0.0574037i
\(309\) 0 0
\(310\) 4.08338 + 1.09414i 0.231920 + 0.0621429i
\(311\) 16.5536 0.938671 0.469335 0.883020i \(-0.344494\pi\)
0.469335 + 0.883020i \(0.344494\pi\)
\(312\) 0 0
\(313\) 21.0200i 1.18812i −0.804421 0.594060i \(-0.797524\pi\)
0.804421 0.594060i \(-0.202476\pi\)
\(314\) 28.0536 + 7.51694i 1.58316 + 0.424205i
\(315\) 0 0
\(316\) 0.667349 + 0.385294i 0.0375413 + 0.0216745i
\(317\) −10.3124 10.3124i −0.579204 0.579204i 0.355480 0.934684i \(-0.384317\pi\)
−0.934684 + 0.355480i \(0.884317\pi\)
\(318\) 0 0
\(319\) −1.49477 5.57856i −0.0836911 0.312339i
\(320\) −7.44722 7.44722i −0.416312 0.416312i
\(321\) 0 0
\(322\) −7.65982 + 12.4446i −0.426865 + 0.693511i
\(323\) −4.17320 1.11821i −0.232203 0.0622187i
\(324\) 0 0
\(325\) −2.21230 + 9.48548i −0.122716 + 0.526160i
\(326\) −22.4667 −1.24431
\(327\) 0 0
\(328\) −7.37575 + 4.25839i −0.407258 + 0.235130i
\(329\) −0.617489 + 21.9304i −0.0340433 + 1.20906i
\(330\) 0 0
\(331\) 22.7352 6.09189i 1.24964 0.334840i 0.427444 0.904042i \(-0.359414\pi\)
0.822198 + 0.569202i \(0.192748\pi\)
\(332\) −3.23268 + 0.866193i −0.177416 + 0.0475385i
\(333\) 0 0
\(334\) 10.3769 + 5.99111i 0.567799 + 0.327819i
\(335\) 3.69578 + 6.40128i 0.201922 + 0.349739i
\(336\) 0 0
\(337\) 14.6004i 0.795337i −0.917529 0.397668i \(-0.869819\pi\)
0.917529 0.397668i \(-0.130181\pi\)
\(338\) −12.7680 + 14.5556i −0.694489 + 0.791723i
\(339\) 0 0
\(340\) 0.245839 0.917483i 0.0133325 0.0497575i
\(341\) −2.82936 + 1.63353i −0.153219 + 0.0884607i
\(342\) 0 0
\(343\) −14.1537 + 11.9445i −0.764230 + 0.644944i
\(344\) −9.73830 + 2.60937i −0.525054 + 0.140688i
\(345\) 0 0
\(346\) 22.9641 + 22.9641i 1.23456 + 1.23456i
\(347\) 8.48574 14.6977i 0.455538 0.789016i −0.543181 0.839616i \(-0.682780\pi\)
0.998719 + 0.0506002i \(0.0161134\pi\)
\(348\) 0 0
\(349\) −0.728645 + 2.71934i −0.0390035 + 0.145563i −0.982682 0.185302i \(-0.940674\pi\)
0.943678 + 0.330865i \(0.107340\pi\)
\(350\) −5.06093 9.36502i −0.270518 0.500581i
\(351\) 0 0
\(352\) −2.14553 −0.114357
\(353\) −30.6157 8.20345i −1.62951 0.436625i −0.675733 0.737146i \(-0.736173\pi\)
−0.953775 + 0.300521i \(0.902839\pi\)
\(354\) 0 0
\(355\) −8.95350 + 15.5079i −0.475203 + 0.823075i
\(356\) 1.20614 1.20614i 0.0639253 0.0639253i
\(357\) 0 0
\(358\) −3.74646 13.9820i −0.198006 0.738970i
\(359\) −12.8172 + 12.8172i −0.676466 + 0.676466i −0.959199 0.282733i \(-0.908759\pi\)
0.282733 + 0.959199i \(0.408759\pi\)
\(360\) 0 0
\(361\) 14.4922 8.36705i 0.762745 0.440371i
\(362\) −5.24402 + 19.5709i −0.275619 + 1.02863i
\(363\) 0 0
\(364\) −0.00940337 2.08225i −0.000492870 0.109140i
\(365\) −24.3036 −1.27211
\(366\) 0 0
\(367\) −3.51454 + 2.02912i −0.183457 + 0.105919i −0.588916 0.808194i \(-0.700445\pi\)
0.405459 + 0.914113i \(0.367112\pi\)
\(368\) −14.0952 8.13787i −0.734764 0.424216i
\(369\) 0 0
\(370\) −3.52794 13.1665i −0.183409 0.684492i
\(371\) 2.49386 + 2.63836i 0.129475 + 0.136977i
\(372\) 0 0
\(373\) 5.07453 8.78935i 0.262749 0.455095i −0.704222 0.709980i \(-0.748704\pi\)
0.966972 + 0.254884i \(0.0820374\pi\)
\(374\) 3.72997 + 6.46050i 0.192872 + 0.334065i
\(375\) 0 0
\(376\) −22.0047 −1.13481
\(377\) 3.46312 + 11.4188i 0.178360 + 0.588099i
\(378\) 0 0
\(379\) 1.04136 3.88639i 0.0534908 0.199630i −0.934009 0.357249i \(-0.883715\pi\)
0.987500 + 0.157618i \(0.0503815\pi\)
\(380\) −0.249080 0.431418i −0.0127775 0.0221313i
\(381\) 0 0
\(382\) −0.891216 0.891216i −0.0455986 0.0455986i
\(383\) −0.289889 1.08188i −0.0148126 0.0552815i 0.958124 0.286354i \(-0.0924433\pi\)
−0.972937 + 0.231072i \(0.925777\pi\)
\(384\) 0 0
\(385\) −6.70787 2.00134i −0.341865 0.101998i
\(386\) 1.18095 2.04547i 0.0601090 0.104112i
\(387\) 0 0
\(388\) −0.538830 + 2.01094i −0.0273550 + 0.102090i
\(389\) 2.46580i 0.125021i −0.998044 0.0625106i \(-0.980089\pi\)
0.998044 0.0625106i \(-0.0199107\pi\)
\(390\) 0 0
\(391\) 10.6436i 0.538271i
\(392\) −12.3751 13.8533i −0.625037 0.699697i
\(393\) 0 0
\(394\) 6.72867 + 3.88480i 0.338985 + 0.195713i
\(395\) −3.78462 + 3.78462i −0.190425 + 0.190425i
\(396\) 0 0
\(397\) −13.8529 + 3.71187i −0.695257 + 0.186294i −0.589105 0.808056i \(-0.700520\pi\)
−0.106152 + 0.994350i \(0.533853\pi\)
\(398\) −1.42844 1.42844i −0.0716012 0.0716012i
\(399\) 0 0
\(400\) 10.2678 5.92812i 0.513390 0.296406i
\(401\) −9.59670 2.57143i −0.479236 0.128411i 0.0111107 0.999938i \(-0.496463\pi\)
−0.490347 + 0.871527i \(0.663130\pi\)
\(402\) 0 0
\(403\) 5.73238 3.56415i 0.285550 0.177543i
\(404\) 2.94450i 0.146494i
\(405\) 0 0
\(406\) −11.1059 6.83584i −0.551178 0.339257i
\(407\) 9.12300 + 5.26716i 0.452210 + 0.261084i
\(408\) 0 0
\(409\) 9.20429 + 34.3509i 0.455123 + 1.69854i 0.687726 + 0.725970i \(0.258609\pi\)
−0.232603 + 0.972572i \(0.574724\pi\)
\(410\) 1.87570 + 7.00022i 0.0926344 + 0.345716i
\(411\) 0 0
\(412\) −1.68880 0.975031i −0.0832013 0.0480363i
\(413\) −2.25758 1.38957i −0.111088 0.0683763i
\(414\) 0 0
\(415\) 23.2452i 1.14106i
\(416\) 4.43051 0.144776i 0.217224 0.00709821i
\(417\) 0 0
\(418\) 3.77914 + 1.01262i 0.184844 + 0.0495288i
\(419\) −22.2160 + 12.8264i −1.08532 + 0.626611i −0.932327 0.361616i \(-0.882225\pi\)
−0.152995 + 0.988227i \(0.548892\pi\)
\(420\) 0 0
\(421\) −9.66177 9.66177i −0.470886 0.470886i 0.431315 0.902201i \(-0.358050\pi\)
−0.902201 + 0.431315i \(0.858050\pi\)
\(422\) −35.7186 + 9.57077i −1.73875 + 0.465898i
\(423\) 0 0
\(424\) −2.57481 + 2.57481i −0.125044 + 0.125044i
\(425\) −6.71469 3.87673i −0.325710 0.188049i
\(426\) 0 0
\(427\) −0.0215794 0.0906712i −0.00104430 0.00438789i
\(428\) 2.84799i 0.137663i
\(429\) 0 0
\(430\) 8.57890i 0.413712i
\(431\) 1.68005 6.27002i 0.0809250 0.302016i −0.913586 0.406645i \(-0.866699\pi\)
0.994511 + 0.104629i \(0.0333654\pi\)
\(432\) 0 0
\(433\) −16.7283 + 28.9743i −0.803912 + 1.39242i 0.113111 + 0.993582i \(0.463918\pi\)
−0.917023 + 0.398834i \(0.869415\pi\)
\(434\) −2.10918 + 7.06930i −0.101244 + 0.339337i
\(435\) 0 0
\(436\) 1.12111 + 4.18403i 0.0536913 + 0.200379i
\(437\) 3.94720 + 3.94720i 0.188820 + 0.188820i
\(438\) 0 0
\(439\) −9.81984 17.0085i −0.468675 0.811769i 0.530684 0.847570i \(-0.321935\pi\)
−0.999359 + 0.0358007i \(0.988602\pi\)
\(440\) 1.81717 6.78178i 0.0866303 0.323309i
\(441\) 0 0
\(442\) −8.13831 13.0892i −0.387100 0.622590i
\(443\) −16.3344 −0.776072 −0.388036 0.921644i \(-0.626846\pi\)
−0.388036 + 0.921644i \(0.626846\pi\)
\(444\) 0 0
\(445\) 5.92376 + 10.2603i 0.280813 + 0.486383i
\(446\) 10.5201 18.2213i 0.498140 0.862804i
\(447\) 0 0
\(448\) 13.3567 12.6251i 0.631045 0.596481i
\(449\) 5.76005 + 21.4968i 0.271834 + 1.01450i 0.957934 + 0.286990i \(0.0926546\pi\)
−0.686100 + 0.727507i \(0.740679\pi\)
\(450\) 0 0
\(451\) −4.85043 2.80040i −0.228398 0.131865i
\(452\) −2.11840 + 1.22306i −0.0996410 + 0.0575277i
\(453\) 0 0
\(454\) 33.1855 1.55747
\(455\) 13.9867 + 3.68012i 0.655709 + 0.172527i
\(456\) 0 0
\(457\) −2.56831 + 9.58507i −0.120141 + 0.448371i −0.999620 0.0275663i \(-0.991224\pi\)
0.879479 + 0.475937i \(0.157891\pi\)
\(458\) −15.8587 + 9.15602i −0.741028 + 0.427833i
\(459\) 0 0
\(460\) −0.867794 + 0.867794i −0.0404611 + 0.0404611i
\(461\) 9.43198 + 35.2006i 0.439291 + 1.63946i 0.730584 + 0.682823i \(0.239248\pi\)
−0.291293 + 0.956634i \(0.594085\pi\)
\(462\) 0 0
\(463\) −5.57925 + 5.57925i −0.259290 + 0.259290i −0.824765 0.565476i \(-0.808693\pi\)
0.565476 + 0.824765i \(0.308693\pi\)
\(464\) 7.26247 12.5790i 0.337152 0.583964i
\(465\) 0 0
\(466\) 38.6226 + 10.3489i 1.78916 + 0.479403i
\(467\) 23.2676 1.07670 0.538349 0.842722i \(-0.319048\pi\)
0.538349 + 0.842722i \(0.319048\pi\)
\(468\) 0 0
\(469\) −11.3479 + 6.13250i −0.523997 + 0.283173i
\(470\) −4.84624 + 18.0864i −0.223540 + 0.834264i
\(471\) 0 0
\(472\) 1.32945 2.30267i 0.0611928 0.105989i
\(473\) −4.68812 4.68812i −0.215560 0.215560i
\(474\) 0 0
\(475\) −3.92783 + 1.05246i −0.180221 + 0.0482902i
\(476\) 1.58838 + 0.473904i 0.0728033 + 0.0217214i
\(477\) 0 0
\(478\) 11.7248 6.76932i 0.536280 0.309622i
\(479\) −9.64340 + 35.9897i −0.440618 + 1.64441i 0.286634 + 0.958040i \(0.407464\pi\)
−0.727252 + 0.686370i \(0.759203\pi\)
\(480\) 0 0
\(481\) −19.1943 10.2611i −0.875187 0.467864i
\(482\) 33.1652i 1.51063i
\(483\) 0 0
\(484\) 0.868172 + 1.50372i 0.0394624 + 0.0683508i
\(485\) −12.5228 7.23004i −0.568631 0.328299i
\(486\) 0 0
\(487\) −40.0906 + 10.7422i −1.81668 + 0.486777i −0.996369 0.0851447i \(-0.972865\pi\)
−0.820308 + 0.571922i \(0.806198\pi\)
\(488\) 0.0902975 0.0241951i 0.00408757 0.00109526i
\(489\) 0 0
\(490\) −14.1119 + 7.12050i −0.637511 + 0.321672i
\(491\) −7.22040 + 4.16870i −0.325852 + 0.188131i −0.653998 0.756496i \(-0.726910\pi\)
0.328146 + 0.944627i \(0.393576\pi\)
\(492\) 0 0
\(493\) −9.49867 −0.427799
\(494\) −7.87223 1.83604i −0.354189 0.0826074i
\(495\) 0 0
\(496\) −7.93666 2.12662i −0.356366 0.0954881i
\(497\) −26.6122 16.3802i −1.19372 0.734751i
\(498\) 0 0
\(499\) −6.61818 6.61818i −0.296270 0.296270i 0.543281 0.839551i \(-0.317182\pi\)
−0.839551 + 0.543281i \(0.817182\pi\)
\(500\) −0.659651 2.46185i −0.0295005 0.110097i
\(501\) 0 0
\(502\) 32.1708 + 32.1708i 1.43585 + 1.43585i
\(503\) 6.07077 + 3.50496i 0.270682 + 0.156278i 0.629198 0.777245i \(-0.283384\pi\)
−0.358515 + 0.933524i \(0.616717\pi\)
\(504\) 0 0
\(505\) −19.7547 5.29324i −0.879071 0.235546i
\(506\) 9.63859i 0.428487i
\(507\) 0 0
\(508\) −0.925111 −0.0410452
\(509\) −6.23491 1.67064i −0.276357 0.0740498i 0.117978 0.993016i \(-0.462359\pi\)
−0.394336 + 0.918966i \(0.629025\pi\)
\(510\) 0 0
\(511\) 1.19371 42.3951i 0.0528067 1.87545i
\(512\) 12.6554 + 12.6554i 0.559297 + 0.559297i
\(513\) 0 0
\(514\) −18.8146 + 5.04136i −0.829878 + 0.222365i
\(515\) 9.57741 9.57741i 0.422031 0.422031i
\(516\) 0 0
\(517\) −7.23536 12.5320i −0.318211 0.551157i
\(518\) 23.1408 5.50744i 1.01675 0.241983i
\(519\) 0 0
\(520\) −3.29483 + 14.1270i −0.144488 + 0.619508i
\(521\) 13.2340i 0.579793i 0.957058 + 0.289896i \(0.0936208\pi\)
−0.957058 + 0.289896i \(0.906379\pi\)
\(522\) 0 0
\(523\) 35.3268 20.3959i 1.54473 0.891852i 0.546203 0.837653i \(-0.316073\pi\)
0.998530 0.0541990i \(-0.0172605\pi\)
\(524\) −0.793960 + 1.37518i −0.0346843 + 0.0600749i
\(525\) 0 0
\(526\) −13.2282 + 3.54450i −0.576779 + 0.154547i
\(527\) 1.39072 + 5.19023i 0.0605806 + 0.226090i
\(528\) 0 0
\(529\) −4.62397 + 8.00896i −0.201042 + 0.348216i
\(530\) 1.54926 + 2.68339i 0.0672954 + 0.116559i
\(531\) 0 0
\(532\) 0.764799 0.413304i 0.0331583 0.0179190i
\(533\) 10.2051 + 5.45550i 0.442030 + 0.236304i
\(534\) 0 0
\(535\) 19.1072 + 5.11975i 0.826075 + 0.221346i
\(536\) −6.46878 11.2042i −0.279409 0.483950i
\(537\) 0 0
\(538\) 12.2404 12.2404i 0.527721 0.527721i
\(539\) 3.82060 11.6029i 0.164565 0.499772i
\(540\) 0 0
\(541\) −14.4412 + 14.4412i −0.620878 + 0.620878i −0.945756 0.324878i \(-0.894677\pi\)
0.324878 + 0.945756i \(0.394677\pi\)
\(542\) 27.0619 + 15.6242i 1.16241 + 0.671117i
\(543\) 0 0
\(544\) −0.913306 + 3.40851i −0.0391577 + 0.146138i
\(545\) −30.0861 −1.28875
\(546\) 0 0
\(547\) 3.47188 0.148447 0.0742234 0.997242i \(-0.476352\pi\)
0.0742234 + 0.997242i \(0.476352\pi\)
\(548\) 1.17629 4.38996i 0.0502484 0.187530i
\(549\) 0 0
\(550\) 6.08065 + 3.51066i 0.259280 + 0.149695i
\(551\) −3.52259 + 3.52259i −0.150067 + 0.150067i
\(552\) 0 0
\(553\) −6.41599 6.78777i −0.272836 0.288645i
\(554\) 16.6290 16.6290i 0.706500 0.706500i
\(555\) 0 0
\(556\) −2.04778 3.54686i −0.0868452 0.150420i
\(557\) 42.2673 + 11.3255i 1.79092 + 0.479876i 0.992503 0.122224i \(-0.0390027\pi\)
0.798420 + 0.602100i \(0.205669\pi\)
\(558\) 0 0
\(559\) 9.99727 + 9.36459i 0.422840 + 0.396080i
\(560\) −8.36993 15.4881i −0.353694 0.654494i
\(561\) 0 0
\(562\) 6.49215 + 11.2447i 0.273855 + 0.474330i
\(563\) −2.66750 + 4.62024i −0.112422 + 0.194720i −0.916746 0.399470i \(-0.869194\pi\)
0.804325 + 0.594190i \(0.202527\pi\)
\(564\) 0 0
\(565\) −4.39731 16.4110i −0.184996 0.690416i
\(566\) 7.66755 2.05451i 0.322291 0.0863577i
\(567\) 0 0
\(568\) 15.6714 27.1437i 0.657559 1.13893i
\(569\) −15.8463 + 9.14887i −0.664312 + 0.383541i −0.793918 0.608025i \(-0.791962\pi\)
0.129606 + 0.991566i \(0.458629\pi\)
\(570\) 0 0
\(571\) 33.5009i 1.40197i 0.713176 + 0.700985i \(0.247256\pi\)
−0.713176 + 0.700985i \(0.752744\pi\)
\(572\) 0.725200 + 1.16637i 0.0303221 + 0.0487684i
\(573\) 0 0
\(574\) −12.3033 + 2.92814i −0.513530 + 0.122218i
\(575\) 5.00891 + 8.67568i 0.208886 + 0.361801i
\(576\) 0 0
\(577\) 8.55149 8.55149i 0.356003 0.356003i −0.506334 0.862337i \(-0.669000\pi\)
0.862337 + 0.506334i \(0.169000\pi\)
\(578\) −12.6056 + 3.37767i −0.524325 + 0.140493i
\(579\) 0 0
\(580\) −0.774444 0.774444i −0.0321570 0.0321570i
\(581\) 40.5489 + 1.14173i 1.68225 + 0.0473668i
\(582\) 0 0
\(583\) −2.31302 0.619771i −0.0957953 0.0256683i
\(584\) 42.5389 1.76027
\(585\) 0 0
\(586\) 32.1870i 1.32963i
\(587\) 42.3546 + 11.3489i 1.74816 + 0.468419i 0.984232 0.176881i \(-0.0566009\pi\)
0.763929 + 0.645300i \(0.223268\pi\)
\(588\) 0 0
\(589\) 2.44055 + 1.40905i 0.100561 + 0.0580589i
\(590\) −1.59985 1.59985i −0.0658647 0.0658647i
\(591\) 0 0
\(592\) 6.85708 + 25.5910i 0.281824 + 1.05178i
\(593\) −29.3548 29.3548i −1.20546 1.20546i −0.972483 0.232973i \(-0.925155\pi\)
−0.232973 0.972483i \(-0.574845\pi\)
\(594\) 0 0
\(595\) −6.03482 + 9.80453i −0.247403 + 0.401947i
\(596\) −0.378575 0.101439i −0.0155070 0.00415510i
\(597\) 0 0
\(598\) 0.650389 + 19.9036i 0.0265964 + 0.813919i
\(599\) 17.3994 0.710920 0.355460 0.934691i \(-0.384324\pi\)
0.355460 + 0.934691i \(0.384324\pi\)
\(600\) 0 0
\(601\) 3.87707 2.23843i 0.158149 0.0913074i −0.418837 0.908062i \(-0.637562\pi\)
0.576986 + 0.816754i \(0.304229\pi\)
\(602\) −14.9650 0.421368i −0.609929 0.0171737i
\(603\) 0 0
\(604\) −4.46400 + 1.19612i −0.181638 + 0.0486696i
\(605\) −11.6491 + 3.12138i −0.473605 + 0.126902i
\(606\) 0 0
\(607\) 12.0061 + 6.93170i 0.487311 + 0.281349i 0.723458 0.690368i \(-0.242551\pi\)
−0.236147 + 0.971717i \(0.575885\pi\)
\(608\) 0.925346 + 1.60275i 0.0375277 + 0.0649999i
\(609\) 0 0
\(610\) 0.0795470i 0.00322077i
\(611\) 15.7866 + 25.3903i 0.638657 + 1.02718i
\(612\) 0 0
\(613\) 3.20626 11.9659i 0.129500 0.483299i −0.870461 0.492238i \(-0.836179\pi\)
0.999960 + 0.00893943i \(0.00284555\pi\)
\(614\) 6.35722 3.67034i 0.256557 0.148123i
\(615\) 0 0
\(616\) 11.7409 + 3.50297i 0.473053 + 0.141139i
\(617\) −4.24013 + 1.13614i −0.170701 + 0.0457392i −0.343157 0.939278i \(-0.611496\pi\)
0.172456 + 0.985017i \(0.444830\pi\)
\(618\) 0 0
\(619\) −3.42700 3.42700i −0.137743 0.137743i 0.634873 0.772616i \(-0.281052\pi\)
−0.772616 + 0.634873i \(0.781052\pi\)
\(620\) −0.309781 + 0.536556i −0.0124411 + 0.0215486i
\(621\) 0 0
\(622\) −6.38114 + 23.8147i −0.255860 + 0.954883i
\(623\) −18.1889 + 9.82944i −0.728724 + 0.393808i
\(624\) 0 0
\(625\) 4.19541 0.167816
\(626\) 30.2402 + 8.10283i 1.20864 + 0.323854i
\(627\) 0 0
\(628\) −2.12825 + 3.68624i −0.0849265 + 0.147097i
\(629\) 12.2511 12.2511i 0.488485 0.488485i
\(630\) 0 0
\(631\) 7.50951 + 28.0259i 0.298949 + 1.11569i 0.938030 + 0.346554i \(0.112648\pi\)
−0.639081 + 0.769139i \(0.720685\pi\)
\(632\) 6.62427 6.62427i 0.263499 0.263499i
\(633\) 0 0
\(634\) 18.8111 10.8606i 0.747086 0.431330i
\(635\) 1.66305 6.20658i 0.0659961 0.246301i
\(636\) 0 0
\(637\) −7.10658 + 24.2177i −0.281573 + 0.959540i
\(638\) 8.60175 0.340546
\(639\) 0 0
\(640\) 16.8132 9.70709i 0.664599 0.383707i
\(641\) −30.8187 17.7932i −1.21726 0.702788i −0.252932 0.967484i \(-0.581395\pi\)
−0.964332 + 0.264696i \(0.914728\pi\)
\(642\) 0 0
\(643\) −1.54772 5.77618i −0.0610362 0.227790i 0.928669 0.370909i \(-0.120954\pi\)
−0.989706 + 0.143118i \(0.954287\pi\)
\(644\) −1.47116 1.55640i −0.0579716 0.0613308i
\(645\) 0 0
\(646\) 3.21739 5.57269i 0.126587 0.219255i
\(647\) −8.50730 14.7351i −0.334456 0.579296i 0.648924 0.760853i \(-0.275219\pi\)
−0.983380 + 0.181558i \(0.941886\pi\)
\(648\) 0 0
\(649\) 1.74854 0.0686361
\(650\) −12.7934 6.83919i −0.501798 0.268255i
\(651\) 0 0
\(652\) 0.852204 3.18047i 0.0333749 0.124557i
\(653\) −4.76337 8.25040i −0.186405 0.322863i 0.757644 0.652668i \(-0.226350\pi\)
−0.944049 + 0.329805i \(0.893017\pi\)
\(654\) 0 0
\(655\) −7.79881 7.79881i −0.304725 0.304725i
\(656\) −3.64571 13.6060i −0.142341 0.531223i
\(657\) 0 0
\(658\) −31.3119 9.34211i −1.22066 0.364193i
\(659\) 14.3837 24.9132i 0.560308 0.970482i −0.437161 0.899383i \(-0.644016\pi\)
0.997469 0.0710991i \(-0.0226507\pi\)
\(660\) 0 0
\(661\) −5.58403 + 20.8399i −0.217193 + 0.810577i 0.768189 + 0.640223i \(0.221158\pi\)
−0.985383 + 0.170354i \(0.945509\pi\)
\(662\) 35.0561i 1.36250i
\(663\) 0 0
\(664\) 40.6864i 1.57894i
\(665\) 1.39800 + 5.87403i 0.0542121 + 0.227785i
\(666\) 0 0
\(667\) 10.6285 + 6.13636i 0.411537 + 0.237601i
\(668\) −1.24174 + 1.24174i −0.0480444 + 0.0480444i
\(669\) 0 0
\(670\) −10.6338 + 2.84932i −0.410819 + 0.110079i
\(671\) 0.0434701 + 0.0434701i 0.00167814 + 0.00167814i
\(672\) 0 0
\(673\) 24.5175 14.1552i 0.945082 0.545643i 0.0535322 0.998566i \(-0.482952\pi\)
0.891550 + 0.452923i \(0.149619\pi\)
\(674\) 21.0048 + 5.62821i 0.809074 + 0.216791i
\(675\) 0 0
\(676\) −1.57624 2.35961i −0.0606245 0.0907544i
\(677\) 19.7036i 0.757270i 0.925546 + 0.378635i \(0.123606\pi\)
−0.925546 + 0.378635i \(0.876394\pi\)
\(678\) 0 0
\(679\) 13.2271 21.4896i 0.507611 0.824696i
\(680\) −10.0004 5.77371i −0.383496 0.221412i
\(681\) 0 0
\(682\) −1.25940 4.70013i −0.0482248 0.179977i
\(683\) −6.28752 23.4653i −0.240585 0.897876i −0.975551 0.219772i \(-0.929469\pi\)
0.734966 0.678104i \(-0.237198\pi\)
\(684\) 0 0
\(685\) 27.3377 + 15.7834i 1.04452 + 0.603053i
\(686\) −11.7279 24.9665i −0.447772 0.953227i
\(687\) 0 0
\(688\) 16.6744i 0.635704i
\(689\) 4.81818 + 1.12374i 0.183558 + 0.0428113i
\(690\) 0 0
\(691\) −20.9371 5.61007i −0.796483 0.213417i −0.162444 0.986718i \(-0.551938\pi\)
−0.634039 + 0.773301i \(0.718604\pi\)
\(692\) −4.12196 + 2.37982i −0.156694 + 0.0904671i
\(693\) 0 0
\(694\) 17.8736 + 17.8736i 0.678474 + 0.678474i
\(695\) 27.4771 7.36248i 1.04227 0.279275i
\(696\) 0 0
\(697\) −6.51357 + 6.51357i −0.246719 + 0.246719i
\(698\) −3.63127 2.09652i −0.137446 0.0793543i
\(699\) 0 0
\(700\) 1.51772 0.361212i 0.0573643 0.0136525i
\(701\) 33.2903i 1.25736i −0.777665 0.628678i \(-0.783596\pi\)
0.777665 0.628678i \(-0.216404\pi\)
\(702\) 0 0
\(703\) 9.08668i 0.342711i
\(704\) −3.13758 + 11.7096i −0.118252 + 0.441323i
\(705\) 0 0
\(706\) 23.6036 40.8827i 0.888334 1.53864i
\(707\) 10.2038 34.2000i 0.383754 1.28622i
\(708\) 0 0
\(709\) 0.389951 + 1.45532i 0.0146449 + 0.0546556i 0.972862 0.231388i \(-0.0743266\pi\)
−0.958217 + 0.286043i \(0.907660\pi\)
\(710\) −18.8589 18.8589i −0.707762 0.707762i
\(711\) 0 0
\(712\) −10.3684 17.9587i −0.388574 0.673030i
\(713\) 1.79687 6.70601i 0.0672933 0.251142i
\(714\) 0 0
\(715\) −9.12887 + 2.76862i −0.341400 + 0.103540i
\(716\) 2.12145 0.0792823
\(717\) 0 0
\(718\) −13.4985 23.3801i −0.503761 0.872539i
\(719\) 16.0502 27.7997i 0.598570 1.03675i −0.394463 0.918912i \(-0.629069\pi\)
0.993032 0.117841i \(-0.0375974\pi\)
\(720\) 0 0
\(721\) 16.2364 + 17.1772i 0.604675 + 0.639713i
\(722\) 6.45070 + 24.0744i 0.240070 + 0.895955i
\(723\) 0 0
\(724\) −2.57162 1.48473i −0.0955735 0.0551794i
\(725\) −7.74243 + 4.47009i −0.287546 + 0.166015i
\(726\) 0 0
\(727\) 33.7702 1.25247 0.626233 0.779636i \(-0.284596\pi\)
0.626233 + 0.779636i \(0.284596\pi\)
\(728\) −24.4812 6.44137i −0.907334 0.238733i
\(729\) 0 0
\(730\) 9.36860 34.9641i 0.346748 1.29408i
\(731\) −9.44341 + 5.45215i −0.349277 + 0.201655i
\(732\) 0 0
\(733\) 5.09323 5.09323i 0.188123 0.188123i −0.606761 0.794884i \(-0.707532\pi\)
0.794884 + 0.606761i \(0.207532\pi\)
\(734\) −1.56438 5.83834i −0.0577423 0.215497i
\(735\) 0 0
\(736\) 3.22391 3.22391i 0.118835 0.118835i
\(737\) 4.25399 7.36812i 0.156698 0.271408i
\(738\) 0 0
\(739\) 22.0821 + 5.91687i 0.812302 + 0.217656i 0.640978 0.767559i \(-0.278529\pi\)
0.171324 + 0.985215i \(0.445196\pi\)
\(740\) 1.99772 0.0734375
\(741\) 0 0
\(742\) −4.75699 + 2.57072i −0.174635 + 0.0943741i
\(743\) 2.69085 10.0424i 0.0987179 0.368420i −0.898839 0.438279i \(-0.855588\pi\)
0.997557 + 0.0698588i \(0.0222549\pi\)
\(744\) 0 0
\(745\) 1.36111 2.35751i 0.0498672 0.0863725i
\(746\) 10.6886 + 10.6886i 0.391336 + 0.391336i
\(747\) 0 0
\(748\) −1.05606 + 0.282970i −0.0386133 + 0.0103464i
\(749\) −9.86937 + 33.0791i −0.360619 + 1.20868i
\(750\) 0 0
\(751\) −35.7335 + 20.6307i −1.30393 + 0.752827i −0.981076 0.193621i \(-0.937977\pi\)
−0.322858 + 0.946448i \(0.604643\pi\)
\(752\) 9.41938 35.1536i 0.343489 1.28192i
\(753\) 0 0
\(754\) −17.7625 + 0.580426i −0.646874 + 0.0211379i
\(755\) 32.0993i 1.16821i
\(756\) 0 0
\(757\) 9.58077 + 16.5944i 0.348219 + 0.603133i 0.985933 0.167140i \(-0.0534532\pi\)
−0.637714 + 0.770273i \(0.720120\pi\)
\(758\) 5.18969 + 2.99627i 0.188498 + 0.108829i
\(759\) 0 0
\(760\) −5.84982 + 1.56745i −0.212195 + 0.0568576i
\(761\) −16.3307 + 4.37578i −0.591986 + 0.158622i −0.542361 0.840146i \(-0.682469\pi\)
−0.0496251 + 0.998768i \(0.515803\pi\)
\(762\) 0 0
\(763\) 1.47773 52.4821i 0.0534974 1.89998i
\(764\) 0.159969 0.0923584i 0.00578749 0.00334141i
\(765\) 0 0
\(766\) 1.66818 0.0602739
\(767\) −3.61072 + 0.117987i −0.130376 + 0.00426027i
\(768\) 0 0
\(769\) −47.1631 12.6373i −1.70074 0.455713i −0.727617 0.685984i \(-0.759372\pi\)
−0.973127 + 0.230271i \(0.926039\pi\)
\(770\) 5.46497 8.87872i 0.196944 0.319967i
\(771\) 0 0
\(772\) 0.244769 + 0.244769i 0.00880943 + 0.00880943i
\(773\) −2.27204 8.47936i −0.0817195 0.304981i 0.912953 0.408064i \(-0.133796\pi\)
−0.994673 + 0.103083i \(0.967129\pi\)
\(774\) 0 0
\(775\) 3.57611 + 3.57611i 0.128458 + 0.128458i
\(776\) 21.9188 + 12.6548i 0.786840 + 0.454282i
\(777\) 0 0
\(778\) 3.54740 + 0.950523i 0.127180 + 0.0340779i
\(779\) 4.83112i 0.173093i
\(780\) 0 0
\(781\) 20.6117 0.737543
\(782\) −15.3123 4.10293i −0.547568 0.146721i
\(783\) 0 0
\(784\) 27.4286 13.8398i 0.979593 0.494277i
\(785\) −20.9051 20.9051i −0.746136 0.746136i
\(786\) 0 0
\(787\) 21.5745 5.78087i 0.769047 0.206066i 0.147097 0.989122i \(-0.453007\pi\)
0.621951 + 0.783056i \(0.286340\pi\)
\(788\) −0.805178 +