Properties

Label 804.2.s.b.5.12
Level 804
Weight 2
Character 804.5
Analytic conductor 6.420
Analytic rank 0
Dimension 200
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.s (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(200\)
Relative dimension: \(20\) over \(\Q(\zeta_{22})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 5.12
Character \(\chi\) = 804.5
Dual form 804.2.s.b.161.12

$q$-expansion

\(f(q)\) \(=\) \(q+(0.185769 + 1.72206i) q^{3} +(-2.83063 + 0.831147i) q^{5} +(-2.86249 - 2.48036i) q^{7} +(-2.93098 + 0.639810i) q^{9} +O(q^{10})\) \(q+(0.185769 + 1.72206i) q^{3} +(-2.83063 + 0.831147i) q^{5} +(-2.86249 - 2.48036i) q^{7} +(-2.93098 + 0.639810i) q^{9} +(3.88931 - 1.14200i) q^{11} +(-0.777890 - 1.21042i) q^{13} +(-1.95713 - 4.72011i) q^{15} +(5.27916 + 0.759028i) q^{17} +(-0.130434 - 0.150529i) q^{19} +(3.73957 - 5.39016i) q^{21} +(-0.694228 + 0.317043i) q^{23} +(3.11537 - 2.00213i) q^{25} +(-1.64628 - 4.92847i) q^{27} -8.71464i q^{29} +(3.86518 - 6.01434i) q^{31} +(2.68911 + 6.48548i) q^{33} +(10.1642 + 4.64183i) q^{35} -2.50144 q^{37} +(1.93991 - 1.56443i) q^{39} +(0.0416445 - 0.289644i) q^{41} +(-6.85998 - 0.986316i) q^{43} +(7.76473 - 4.24714i) q^{45} +(6.89272 - 3.14780i) q^{47} +(1.04545 + 7.27129i) q^{49} +(-0.326389 + 9.23202i) q^{51} +(0.173569 + 1.20720i) q^{53} +(-10.0600 + 6.46518i) q^{55} +(0.234989 - 0.252578i) q^{57} +(-0.206913 + 0.321963i) q^{59} +(3.48314 - 11.8625i) q^{61} +(9.97687 + 5.43844i) q^{63} +(3.20795 + 2.77971i) q^{65} +(-8.15987 + 0.645356i) q^{67} +(-0.674933 - 1.13660i) q^{69} +(0.756392 - 0.108753i) q^{71} +(-11.2432 - 3.30131i) q^{73} +(4.02652 + 4.99292i) q^{75} +(-13.9657 - 6.37792i) q^{77} +(8.00157 + 12.4507i) q^{79} +(8.18129 - 3.75054i) q^{81} +(3.51473 + 11.9701i) q^{83} +(-15.5742 + 2.23923i) q^{85} +(15.0071 - 1.61891i) q^{87} +(0.0142974 + 0.00652940i) q^{89} +(-0.775578 + 5.39427i) q^{91} +(11.0751 + 5.53880i) q^{93} +(0.494321 + 0.317681i) q^{95} -15.9958i q^{97} +(-10.6688 + 5.83561i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 200q - 10q^{9} + O(q^{10}) \) \( 200q - 10q^{9} + 2q^{15} + 6q^{19} - 10q^{21} - 20q^{25} - 44q^{31} - 5q^{33} + 78q^{39} - 22q^{43} - 22q^{45} - 16q^{49} + 36q^{55} + 66q^{57} + 176q^{61} + 132q^{63} + 46q^{67} - 26q^{73} - 165q^{75} - 44q^{79} + 42q^{81} - 66q^{87} - 20q^{91} + 84q^{93} - 55q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{22}\right)\) \(1\)

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
\(3\) 0.185769 + 1.72206i 0.107254 + 0.994232i
\(4\) 0 0
\(5\) −2.83063 + 0.831147i −1.26589 + 0.371700i −0.844685 0.535263i \(-0.820212\pi\)
−0.421209 + 0.906964i \(0.638394\pi\)
\(6\) 0 0
\(7\) −2.86249 2.48036i −1.08192 0.937489i −0.0836625 0.996494i \(-0.526662\pi\)
−0.998258 + 0.0590050i \(0.981207\pi\)
\(8\) 0 0
\(9\) −2.93098 + 0.639810i −0.976993 + 0.213270i
\(10\) 0 0
\(11\) 3.88931 1.14200i 1.17267 0.344327i 0.363327 0.931662i \(-0.381641\pi\)
0.809344 + 0.587334i \(0.199823\pi\)
\(12\) 0 0
\(13\) −0.777890 1.21042i −0.215748 0.335710i 0.716464 0.697625i \(-0.245760\pi\)
−0.932211 + 0.361914i \(0.882123\pi\)
\(14\) 0 0
\(15\) −1.95713 4.72011i −0.505328 1.21873i
\(16\) 0 0
\(17\) 5.27916 + 0.759028i 1.28038 + 0.184091i 0.748732 0.662872i \(-0.230663\pi\)
0.531651 + 0.846964i \(0.321572\pi\)
\(18\) 0 0
\(19\) −0.130434 0.150529i −0.0299236 0.0345336i 0.740591 0.671957i \(-0.234546\pi\)
−0.770514 + 0.637423i \(0.780000\pi\)
\(20\) 0 0
\(21\) 3.73957 5.39016i 0.816042 1.17623i
\(22\) 0 0
\(23\) −0.694228 + 0.317043i −0.144756 + 0.0661081i −0.486476 0.873694i \(-0.661718\pi\)
0.341720 + 0.939802i \(0.388991\pi\)
\(24\) 0 0
\(25\) 3.11537 2.00213i 0.623074 0.400425i
\(26\) 0 0
\(27\) −1.64628 4.92847i −0.316826 0.948484i
\(28\) 0 0
\(29\) 8.71464i 1.61827i −0.587624 0.809134i \(-0.699937\pi\)
0.587624 0.809134i \(-0.300063\pi\)
\(30\) 0 0
\(31\) 3.86518 6.01434i 0.694207 1.08021i −0.297873 0.954605i \(-0.596277\pi\)
0.992081 0.125602i \(-0.0400864\pi\)
\(32\) 0 0
\(33\) 2.68911 + 6.48548i 0.468114 + 1.12898i
\(34\) 0 0
\(35\) 10.1642 + 4.64183i 1.71806 + 0.784612i
\(36\) 0 0
\(37\) −2.50144 −0.411234 −0.205617 0.978633i \(-0.565920\pi\)
−0.205617 + 0.978633i \(0.565920\pi\)
\(38\) 0 0
\(39\) 1.93991 1.56443i 0.310634 0.250509i
\(40\) 0 0
\(41\) 0.0416445 0.289644i 0.00650378 0.0452348i −0.986311 0.164895i \(-0.947271\pi\)
0.992815 + 0.119660i \(0.0381805\pi\)
\(42\) 0 0
\(43\) −6.85998 0.986316i −1.04614 0.150412i −0.402248 0.915531i \(-0.631771\pi\)
−0.643889 + 0.765119i \(0.722680\pi\)
\(44\) 0 0
\(45\) 7.76473 4.24714i 1.15750 0.633126i
\(46\) 0 0
\(47\) 6.89272 3.14780i 1.00541 0.459154i 0.156489 0.987680i \(-0.449982\pi\)
0.848917 + 0.528526i \(0.177255\pi\)
\(48\) 0 0
\(49\) 1.04545 + 7.27129i 0.149351 + 1.03876i
\(50\) 0 0
\(51\) −0.326389 + 9.23202i −0.0457036 + 1.29274i
\(52\) 0 0
\(53\) 0.173569 + 1.20720i 0.0238415 + 0.165821i 0.998264 0.0589041i \(-0.0187606\pi\)
−0.974422 + 0.224725i \(0.927852\pi\)
\(54\) 0 0
\(55\) −10.0600 + 6.46518i −1.35649 + 0.871764i
\(56\) 0 0
\(57\) 0.234989 0.252578i 0.0311250 0.0334548i
\(58\) 0 0
\(59\) −0.206913 + 0.321963i −0.0269378 + 0.0419160i −0.854461 0.519515i \(-0.826113\pi\)
0.827524 + 0.561431i \(0.189749\pi\)
\(60\) 0 0
\(61\) 3.48314 11.8625i 0.445970 1.51883i −0.363456 0.931612i \(-0.618403\pi\)
0.809425 0.587223i \(-0.199779\pi\)
\(62\) 0 0
\(63\) 9.97687 + 5.43844i 1.25697 + 0.685180i
\(64\) 0 0
\(65\) 3.20795 + 2.77971i 0.397897 + 0.344780i
\(66\) 0 0
\(67\) −8.15987 + 0.645356i −0.996887 + 0.0788428i
\(68\) 0 0
\(69\) −0.674933 1.13660i −0.0812524 0.136831i
\(70\) 0 0
\(71\) 0.756392 0.108753i 0.0897672 0.0129066i −0.0972849 0.995257i \(-0.531016\pi\)
0.187052 + 0.982350i \(0.440107\pi\)
\(72\) 0 0
\(73\) −11.2432 3.30131i −1.31592 0.386390i −0.452903 0.891560i \(-0.649612\pi\)
−0.863020 + 0.505170i \(0.831430\pi\)
\(74\) 0 0
\(75\) 4.02652 + 4.99292i 0.464943 + 0.576533i
\(76\) 0 0
\(77\) −13.9657 6.37792i −1.59154 0.726832i
\(78\) 0 0
\(79\) 8.00157 + 12.4507i 0.900247 + 1.40081i 0.916105 + 0.400938i \(0.131316\pi\)
−0.0158579 + 0.999874i \(0.505048\pi\)
\(80\) 0 0
\(81\) 8.18129 3.75054i 0.909032 0.416727i
\(82\) 0 0
\(83\) 3.51473 + 11.9701i 0.385792 + 1.31389i 0.892219 + 0.451603i \(0.149148\pi\)
−0.506428 + 0.862282i \(0.669034\pi\)
\(84\) 0 0
\(85\) −15.5742 + 2.23923i −1.68926 + 0.242878i
\(86\) 0 0
\(87\) 15.0071 1.61891i 1.60893 0.173565i
\(88\) 0 0
\(89\) 0.0142974 + 0.00652940i 0.00151552 + 0.000692115i 0.416173 0.909286i \(-0.363371\pi\)
−0.414657 + 0.909978i \(0.636098\pi\)
\(90\) 0 0
\(91\) −0.775578 + 5.39427i −0.0813027 + 0.565473i
\(92\) 0 0
\(93\) 11.0751 + 5.53880i 1.14843 + 0.574347i
\(94\) 0 0
\(95\) 0.494321 + 0.317681i 0.0507162 + 0.0325933i
\(96\) 0 0
\(97\) 15.9958i 1.62413i −0.583566 0.812066i \(-0.698343\pi\)
0.583566 0.812066i \(-0.301657\pi\)
\(98\) 0 0
\(99\) −10.6688 + 5.83561i −1.07226 + 0.586501i
\(100\) 0 0
\(101\) −9.07482 10.4729i −0.902979 1.04209i −0.998909 0.0467048i \(-0.985128\pi\)
0.0959301 0.995388i \(-0.469417\pi\)
\(102\) 0 0
\(103\) 0.156435 + 0.100534i 0.0154140 + 0.00990596i 0.548325 0.836265i \(-0.315266\pi\)
−0.532911 + 0.846171i \(0.678902\pi\)
\(104\) 0 0
\(105\) −6.10532 + 18.3656i −0.595818 + 1.79230i
\(106\) 0 0
\(107\) 3.20448 10.9135i 0.309789 1.05504i −0.646571 0.762854i \(-0.723798\pi\)
0.956360 0.292191i \(-0.0943842\pi\)
\(108\) 0 0
\(109\) −7.91640 12.3182i −0.758254 1.17987i −0.978866 0.204504i \(-0.934442\pi\)
0.220612 0.975362i \(-0.429195\pi\)
\(110\) 0 0
\(111\) −0.464689 4.30763i −0.0441064 0.408862i
\(112\) 0 0
\(113\) −13.2015 3.87631i −1.24189 0.364653i −0.406166 0.913799i \(-0.633135\pi\)
−0.835726 + 0.549147i \(0.814953\pi\)
\(114\) 0 0
\(115\) 1.70159 1.47444i 0.158674 0.137492i
\(116\) 0 0
\(117\) 3.05442 + 3.05002i 0.282381 + 0.281974i
\(118\) 0 0
\(119\) −13.2289 15.2669i −1.21269 1.39952i
\(120\) 0 0
\(121\) 4.56877 2.93617i 0.415343 0.266925i
\(122\) 0 0
\(123\) 0.506521 + 0.0179076i 0.0456714 + 0.00161467i
\(124\) 0 0
\(125\) 2.50523 2.89118i 0.224074 0.258595i
\(126\) 0 0
\(127\) 2.59056 2.98967i 0.229875 0.265290i −0.629080 0.777340i \(-0.716568\pi\)
0.858956 + 0.512050i \(0.171114\pi\)
\(128\) 0 0
\(129\) 0.424125 11.9965i 0.0373422 1.05623i
\(130\) 0 0
\(131\) −3.04712 + 1.39157i −0.266228 + 0.121582i −0.544057 0.839048i \(-0.683112\pi\)
0.277829 + 0.960631i \(0.410385\pi\)
\(132\) 0 0
\(133\) 0.754410i 0.0654157i
\(134\) 0 0
\(135\) 8.75627 + 12.5823i 0.753620 + 1.08292i
\(136\) 0 0
\(137\) 6.27585 + 13.7422i 0.536182 + 1.17407i 0.962942 + 0.269710i \(0.0869277\pi\)
−0.426760 + 0.904365i \(0.640345\pi\)
\(138\) 0 0
\(139\) −4.37634 14.9044i −0.371196 1.26418i −0.907464 0.420130i \(-0.861985\pi\)
0.536268 0.844048i \(-0.319834\pi\)
\(140\) 0 0
\(141\) 6.70115 + 11.2849i 0.564339 + 0.950361i
\(142\) 0 0
\(143\) −4.40776 3.81935i −0.368595 0.319390i
\(144\) 0 0
\(145\) 7.24315 + 24.6679i 0.601510 + 2.04856i
\(146\) 0 0
\(147\) −12.3274 + 3.15111i −1.01675 + 0.259899i
\(148\) 0 0
\(149\) −13.7776 + 11.9383i −1.12870 + 0.978026i −0.999907 0.0136454i \(-0.995656\pi\)
−0.128795 + 0.991671i \(0.541111\pi\)
\(150\) 0 0
\(151\) −0.470875 + 3.27501i −0.0383192 + 0.266516i −0.999970 0.00776115i \(-0.997530\pi\)
0.961651 + 0.274277i \(0.0884386\pi\)
\(152\) 0 0
\(153\) −15.9587 + 1.15296i −1.29019 + 0.0932113i
\(154\) 0 0
\(155\) −5.94209 + 20.2369i −0.477280 + 1.62547i
\(156\) 0 0
\(157\) −4.94188 10.8212i −0.394405 0.863626i −0.997807 0.0661893i \(-0.978916\pi\)
0.603402 0.797437i \(-0.293811\pi\)
\(158\) 0 0
\(159\) −2.04662 + 0.523155i −0.162308 + 0.0414889i
\(160\) 0 0
\(161\) 2.77360 + 0.814403i 0.218591 + 0.0641840i
\(162\) 0 0
\(163\) 17.8684 1.39956 0.699781 0.714357i \(-0.253281\pi\)
0.699781 + 0.714357i \(0.253281\pi\)
\(164\) 0 0
\(165\) −13.0023 16.1229i −1.01222 1.25517i
\(166\) 0 0
\(167\) −0.518218 + 0.449039i −0.0401009 + 0.0347477i −0.674681 0.738110i \(-0.735719\pi\)
0.634580 + 0.772857i \(0.281173\pi\)
\(168\) 0 0
\(169\) 4.54039 9.94207i 0.349261 0.764775i
\(170\) 0 0
\(171\) 0.478609 + 0.357744i 0.0366001 + 0.0273573i
\(172\) 0 0
\(173\) −11.6014 + 18.0521i −0.882037 + 1.37248i 0.0455864 + 0.998960i \(0.485484\pi\)
−0.927624 + 0.373516i \(0.878152\pi\)
\(174\) 0 0
\(175\) −13.8837 1.99618i −1.04951 0.150897i
\(176\) 0 0
\(177\) −0.592878 0.296506i −0.0445634 0.0222868i
\(178\) 0 0
\(179\) 1.38815 3.03963i 0.103755 0.227192i −0.850633 0.525759i \(-0.823781\pi\)
0.954389 + 0.298567i \(0.0965086\pi\)
\(180\) 0 0
\(181\) −1.03125 2.25813i −0.0766526 0.167846i 0.867426 0.497566i \(-0.165773\pi\)
−0.944079 + 0.329720i \(0.893046\pi\)
\(182\) 0 0
\(183\) 21.0749 + 3.79449i 1.55790 + 0.280497i
\(184\) 0 0
\(185\) 7.08064 2.07906i 0.520579 0.152856i
\(186\) 0 0
\(187\) 21.3991 3.07672i 1.56486 0.224992i
\(188\) 0 0
\(189\) −7.51194 + 18.1911i −0.546413 + 1.32320i
\(190\) 0 0
\(191\) −2.31794 + 5.07558i −0.167720 + 0.367256i −0.974765 0.223235i \(-0.928338\pi\)
0.807045 + 0.590491i \(0.201066\pi\)
\(192\) 0 0
\(193\) 17.2923 + 11.1131i 1.24473 + 0.799938i 0.986118 0.166044i \(-0.0530994\pi\)
0.258609 + 0.965982i \(0.416736\pi\)
\(194\) 0 0
\(195\) −4.19088 + 6.04067i −0.300115 + 0.432581i
\(196\) 0 0
\(197\) 0.352396 + 2.45097i 0.0251072 + 0.174624i 0.998517 0.0544480i \(-0.0173399\pi\)
−0.973409 + 0.229072i \(0.926431\pi\)
\(198\) 0 0
\(199\) −3.29690 + 3.80483i −0.233711 + 0.269717i −0.860476 0.509492i \(-0.829833\pi\)
0.626764 + 0.779209i \(0.284379\pi\)
\(200\) 0 0
\(201\) −2.62719 13.9319i −0.185308 0.982681i
\(202\) 0 0
\(203\) −21.6155 + 24.9456i −1.51711 + 1.75084i
\(204\) 0 0
\(205\) 0.122857 + 0.854487i 0.00858068 + 0.0596800i
\(206\) 0 0
\(207\) 1.83192 1.37342i 0.127327 0.0954593i
\(208\) 0 0
\(209\) −0.679202 0.436497i −0.0469814 0.0301931i
\(210\) 0 0
\(211\) −9.04523 + 19.8063i −0.622699 + 1.36352i 0.290840 + 0.956772i \(0.406065\pi\)
−0.913540 + 0.406750i \(0.866662\pi\)
\(212\) 0 0
\(213\) 0.327793 + 1.28235i 0.0224600 + 0.0878651i
\(214\) 0 0
\(215\) 20.2378 2.90976i 1.38021 0.198444i
\(216\) 0 0
\(217\) −25.9818 + 7.62895i −1.76376 + 0.517887i
\(218\) 0 0
\(219\) 3.59642 19.9748i 0.243023 1.34977i
\(220\) 0 0
\(221\) −3.18786 6.98043i −0.214439 0.469555i
\(222\) 0 0
\(223\) 9.31921 20.4062i 0.624060 1.36650i −0.288469 0.957489i \(-0.593146\pi\)
0.912529 0.409012i \(-0.134127\pi\)
\(224\) 0 0
\(225\) −7.85011 + 7.86144i −0.523340 + 0.524096i
\(226\) 0 0
\(227\) 4.40653 + 0.633564i 0.292472 + 0.0420511i 0.286989 0.957934i \(-0.407346\pi\)
0.00548275 + 0.999985i \(0.498255\pi\)
\(228\) 0 0
\(229\) 8.29963 12.9145i 0.548455 0.853413i −0.450775 0.892638i \(-0.648852\pi\)
0.999230 + 0.0392245i \(0.0124888\pi\)
\(230\) 0 0
\(231\) 8.38877 25.2346i 0.551941 1.66031i
\(232\) 0 0
\(233\) 5.70613 12.4947i 0.373821 0.818553i −0.625446 0.780267i \(-0.715083\pi\)
0.999267 0.0382859i \(-0.0121898\pi\)
\(234\) 0 0
\(235\) −16.8944 + 14.6391i −1.10207 + 0.954950i
\(236\) 0 0
\(237\) −19.9544 + 16.0921i −1.29618 + 1.04530i
\(238\) 0 0
\(239\) 23.3595 1.51100 0.755500 0.655148i \(-0.227394\pi\)
0.755500 + 0.655148i \(0.227394\pi\)
\(240\) 0 0
\(241\) 2.15759 + 0.633526i 0.138983 + 0.0408090i 0.350484 0.936569i \(-0.386017\pi\)
−0.211501 + 0.977378i \(0.567835\pi\)
\(242\) 0 0
\(243\) 7.97848 + 13.3919i 0.511820 + 0.859093i
\(244\) 0 0
\(245\) −9.00280 19.7134i −0.575168 1.25944i
\(246\) 0 0
\(247\) −0.0807398 + 0.274974i −0.00513735 + 0.0174962i
\(248\) 0 0
\(249\) −19.9602 + 8.27624i −1.26493 + 0.524485i
\(250\) 0 0
\(251\) −2.12352 + 14.7694i −0.134035 + 0.932237i 0.806183 + 0.591666i \(0.201530\pi\)
−0.940219 + 0.340571i \(0.889380\pi\)
\(252\) 0 0
\(253\) −2.33800 + 2.02589i −0.146989 + 0.127367i
\(254\) 0 0
\(255\) −6.74928 26.4037i −0.422656 1.65346i
\(256\) 0 0
\(257\) −3.22142 10.9711i −0.200947 0.684361i −0.996877 0.0789730i \(-0.974836\pi\)
0.795930 0.605389i \(-0.206982\pi\)
\(258\) 0 0
\(259\) 7.16035 + 6.20448i 0.444923 + 0.385528i
\(260\) 0 0
\(261\) 5.57571 + 25.5424i 0.345128 + 1.58104i
\(262\) 0 0
\(263\) 4.21240 + 14.3461i 0.259747 + 0.884619i 0.981337 + 0.192297i \(0.0615938\pi\)
−0.721589 + 0.692321i \(0.756588\pi\)
\(264\) 0 0
\(265\) −1.49466 3.27286i −0.0918165 0.201050i
\(266\) 0 0
\(267\) −0.00858801 + 0.0258339i −0.000525578 + 0.00158101i
\(268\) 0 0
\(269\) 20.8104i 1.26884i 0.772990 + 0.634418i \(0.218760\pi\)
−0.772990 + 0.634418i \(0.781240\pi\)
\(270\) 0 0
\(271\) −26.4716 + 12.0892i −1.60804 + 0.734366i −0.998303 0.0582400i \(-0.981451\pi\)
−0.609734 + 0.792606i \(0.708724\pi\)
\(272\) 0 0
\(273\) −9.43333 0.333506i −0.570931 0.0201847i
\(274\) 0 0
\(275\) 9.83020 11.3447i 0.592784 0.684109i
\(276\) 0 0
\(277\) −16.1014 + 18.5820i −0.967440 + 1.11648i 0.0257141 + 0.999669i \(0.491814\pi\)
−0.993154 + 0.116815i \(0.962731\pi\)
\(278\) 0 0
\(279\) −7.48074 + 20.1009i −0.447860 + 1.20341i
\(280\) 0 0
\(281\) 27.7394 17.8271i 1.65480 1.06347i 0.729681 0.683788i \(-0.239669\pi\)
0.925116 0.379685i \(-0.123968\pi\)
\(282\) 0 0
\(283\) 3.38795 + 3.90990i 0.201393 + 0.232420i 0.847458 0.530863i \(-0.178132\pi\)
−0.646065 + 0.763282i \(0.723587\pi\)
\(284\) 0 0
\(285\) −0.455236 + 0.910265i −0.0269658 + 0.0539194i
\(286\) 0 0
\(287\) −0.837630 + 0.725810i −0.0494437 + 0.0428432i
\(288\) 0 0
\(289\) 10.9820 + 3.22460i 0.645999 + 0.189682i
\(290\) 0 0
\(291\) 27.5458 2.97153i 1.61476 0.174194i
\(292\) 0 0
\(293\) 1.03101 + 1.60428i 0.0602322 + 0.0937231i 0.870063 0.492940i \(-0.164078\pi\)
−0.809831 + 0.586663i \(0.800441\pi\)
\(294\) 0 0
\(295\) 0.318095 1.08333i 0.0185202 0.0630741i
\(296\) 0 0
\(297\) −12.0312 17.2883i −0.698121 1.00317i
\(298\) 0 0
\(299\) 0.923788 + 0.593682i 0.0534240 + 0.0343335i
\(300\) 0 0
\(301\) 17.1902 + 19.8386i 0.990827 + 1.14348i
\(302\) 0 0
\(303\) 16.3491 17.5729i 0.939234 1.00954i
\(304\) 0 0
\(305\) 36.4732i 2.08845i
\(306\) 0 0
\(307\) 2.28977 + 1.47155i 0.130684 + 0.0839857i 0.604350 0.796719i \(-0.293433\pi\)
−0.473665 + 0.880705i \(0.657069\pi\)
\(308\) 0 0
\(309\) −0.144066 + 0.288066i −0.00819561 + 0.0163875i
\(310\) 0 0
\(311\) 0.224559 1.56184i 0.0127336 0.0885639i −0.982464 0.186454i \(-0.940300\pi\)
0.995197 + 0.0978904i \(0.0312095\pi\)
\(312\) 0 0
\(313\) 2.15289 + 0.983191i 0.121688 + 0.0555732i 0.475329 0.879808i \(-0.342329\pi\)
−0.353640 + 0.935381i \(0.615056\pi\)
\(314\) 0 0
\(315\) −32.7609 7.10196i −1.84587 0.400150i
\(316\) 0 0
\(317\) −1.60985 + 0.231462i −0.0904183 + 0.0130002i −0.187375 0.982288i \(-0.559998\pi\)
0.0969572 + 0.995289i \(0.469089\pi\)
\(318\) 0 0
\(319\) −9.95216 33.8939i −0.557214 1.89770i
\(320\) 0 0
\(321\) 19.3889 + 3.49093i 1.08218 + 0.194845i
\(322\) 0 0
\(323\) −0.574325 0.893667i −0.0319563 0.0497250i
\(324\) 0 0
\(325\) −4.84683 2.21347i −0.268854 0.122781i
\(326\) 0 0
\(327\) 19.7420 15.9208i 1.09173 0.880425i
\(328\) 0 0
\(329\) −27.5380 8.08590i −1.51822 0.445790i
\(330\) 0 0
\(331\) 28.3260 4.07266i 1.55694 0.223853i 0.690570 0.723265i \(-0.257360\pi\)
0.866365 + 0.499412i \(0.166450\pi\)
\(332\) 0 0
\(333\) 7.33167 1.60045i 0.401773 0.0877039i
\(334\) 0 0
\(335\) 22.5612 8.60881i 1.23265 0.470350i
\(336\) 0 0
\(337\) −15.2316 13.1983i −0.829719 0.718956i 0.132514 0.991181i \(-0.457695\pi\)
−0.962234 + 0.272225i \(0.912240\pi\)
\(338\) 0 0
\(339\) 4.22281 23.4539i 0.229352 1.27384i
\(340\) 0 0
\(341\) 8.16449 27.8057i 0.442132 1.50576i
\(342\) 0 0
\(343\) 0.708644 1.10267i 0.0382632 0.0595387i
\(344\) 0 0
\(345\) 2.85517 + 2.65633i 0.153717 + 0.143012i
\(346\) 0 0
\(347\) −24.7044 + 15.8765i −1.32620 + 0.852297i −0.995801 0.0915445i \(-0.970820\pi\)
−0.330399 + 0.943841i \(0.607183\pi\)
\(348\) 0 0
\(349\) −2.66838 18.5590i −0.142835 0.993439i −0.927581 0.373622i \(-0.878116\pi\)
0.784746 0.619817i \(-0.212793\pi\)
\(350\) 0 0
\(351\) −4.68489 + 5.82649i −0.250061 + 0.310995i
\(352\) 0 0
\(353\) −1.25495 8.72836i −0.0667942 0.464564i −0.995578 0.0939411i \(-0.970053\pi\)
0.928784 0.370623i \(-0.120856\pi\)
\(354\) 0 0
\(355\) −2.05067 + 0.936511i −0.108838 + 0.0497048i
\(356\) 0 0
\(357\) 23.8331 25.6170i 1.26138 1.35580i
\(358\) 0 0
\(359\) −4.63866 0.666939i −0.244819 0.0351997i 0.0188128 0.999823i \(-0.494011\pi\)
−0.263632 + 0.964623i \(0.584920\pi\)
\(360\) 0 0
\(361\) 2.69834 18.7673i 0.142018 0.987755i
\(362\) 0 0
\(363\) 5.90500 + 7.32225i 0.309932 + 0.384318i
\(364\) 0 0
\(365\) 34.5693 1.80944
\(366\) 0 0
\(367\) 10.3001 + 4.70390i 0.537661 + 0.245541i 0.665689 0.746229i \(-0.268138\pi\)
−0.128029 + 0.991770i \(0.540865\pi\)
\(368\) 0 0
\(369\) 0.0632579 + 0.875586i 0.00329307 + 0.0455812i
\(370\) 0 0
\(371\) 2.49745 3.88610i 0.129661 0.201756i
\(372\) 0 0
\(373\) 27.8273i 1.44084i 0.693538 + 0.720420i \(0.256051\pi\)
−0.693538 + 0.720420i \(0.743949\pi\)
\(374\) 0 0
\(375\) 5.44418 + 3.77706i 0.281136 + 0.195046i
\(376\) 0 0
\(377\) −10.5484 + 6.77903i −0.543269 + 0.349138i
\(378\) 0 0
\(379\) 33.4407 15.2718i 1.71773 0.784461i 0.722027 0.691865i \(-0.243210\pi\)
0.995704 0.0925970i \(-0.0295168\pi\)
\(380\) 0 0
\(381\) 5.62963 + 3.90572i 0.288415 + 0.200096i
\(382\) 0 0
\(383\) −12.5766 14.5142i −0.642634 0.741639i 0.337205 0.941431i \(-0.390519\pi\)
−0.979838 + 0.199793i \(0.935973\pi\)
\(384\) 0 0
\(385\) 44.8327 + 6.44597i 2.28488 + 0.328517i
\(386\) 0 0
\(387\) 20.7375 1.49821i 1.05415 0.0761583i
\(388\) 0 0
\(389\) −10.8893 16.9441i −0.552109 0.859098i 0.447268 0.894400i \(-0.352397\pi\)
−0.999377 + 0.0353022i \(0.988761\pi\)
\(390\) 0 0
\(391\) −3.90558 + 1.14678i −0.197514 + 0.0579952i
\(392\) 0 0
\(393\) −2.96243 4.98881i −0.149435 0.251652i
\(394\) 0 0
\(395\) −32.9978 28.5928i −1.66030 1.43866i
\(396\) 0 0
\(397\) −12.5930 + 3.69765i −0.632026 + 0.185580i −0.582027 0.813170i \(-0.697740\pi\)
−0.0499993 + 0.998749i \(0.515922\pi\)
\(398\) 0 0
\(399\) −1.29914 + 0.140146i −0.0650383 + 0.00701607i
\(400\) 0 0
\(401\) 30.6091 1.52854 0.764272 0.644894i \(-0.223099\pi\)
0.764272 + 0.644894i \(0.223099\pi\)
\(402\) 0 0
\(403\) −10.2866 −0.512410
\(404\) 0 0
\(405\) −20.0409 + 17.4162i −0.995841 + 0.865419i
\(406\) 0 0
\(407\) −9.72888 + 2.85666i −0.482243 + 0.141599i
\(408\) 0 0
\(409\) 6.14065 + 5.32091i 0.303636 + 0.263102i 0.793329 0.608793i \(-0.208346\pi\)
−0.489694 + 0.871895i \(0.662891\pi\)
\(410\) 0 0
\(411\) −22.4990 + 13.3603i −1.10979 + 0.659013i
\(412\) 0 0
\(413\) 1.39087 0.408397i 0.0684404 0.0200959i
\(414\) 0 0
\(415\) −19.8978 30.9615i −0.976743 1.51984i
\(416\) 0 0
\(417\) 24.8533 10.3051i 1.21707 0.504642i
\(418\) 0 0
\(419\) 19.7307 + 2.83685i 0.963908 + 0.138589i 0.606259 0.795267i \(-0.292669\pi\)
0.357649 + 0.933856i \(0.383579\pi\)
\(420\) 0 0
\(421\) −4.74306 5.47379i −0.231163 0.266776i 0.628304 0.777968i \(-0.283750\pi\)
−0.859467 + 0.511192i \(0.829204\pi\)
\(422\) 0 0
\(423\) −18.1884 + 13.6362i −0.884352 + 0.663013i
\(424\) 0 0
\(425\) 17.9662 8.20488i 0.871488 0.397995i
\(426\) 0 0
\(427\) −39.3937 + 25.3168i −1.90639 + 1.22517i
\(428\) 0 0
\(429\) 5.75832 8.29994i 0.278014 0.400725i
\(430\) 0 0
\(431\) 10.6012i 0.510640i −0.966857 0.255320i \(-0.917819\pi\)
0.966857 0.255320i \(-0.0821809\pi\)
\(432\) 0 0
\(433\) 12.1735 18.9423i 0.585021 0.910310i −0.414979 0.909831i \(-0.636211\pi\)
1.00000 0.000479079i \(-0.000152496\pi\)
\(434\) 0 0
\(435\) −41.1340 + 17.0557i −1.97223 + 0.817756i
\(436\) 0 0
\(437\) 0.138275 + 0.0631480i 0.00661458 + 0.00302078i
\(438\) 0 0
\(439\) −13.7539 −0.656438 −0.328219 0.944602i \(-0.606448\pi\)
−0.328219 + 0.944602i \(0.606448\pi\)
\(440\) 0 0
\(441\) −7.71645 20.6431i −0.367450 0.983005i
\(442\) 0 0
\(443\) −2.76881 + 19.2575i −0.131550 + 0.914950i 0.811985 + 0.583678i \(0.198387\pi\)
−0.943535 + 0.331272i \(0.892522\pi\)
\(444\) 0 0
\(445\) −0.0458975 0.00659906i −0.00217575 0.000312825i
\(446\) 0 0
\(447\) −23.1180 21.5080i −1.09344 1.01729i
\(448\) 0 0
\(449\) 38.1025 17.4008i 1.79817 0.821196i 0.836005 0.548722i \(-0.184886\pi\)
0.962163 0.272473i \(-0.0878417\pi\)
\(450\) 0 0
\(451\) −0.168806 1.17407i −0.00794878 0.0552850i
\(452\) 0 0
\(453\) −5.72723 0.202481i −0.269089 0.00951337i
\(454\) 0 0
\(455\) −2.28805 15.9138i −0.107266 0.746049i
\(456\) 0 0
\(457\) −11.0054 + 7.07271i −0.514809 + 0.330848i −0.772115 0.635482i \(-0.780801\pi\)
0.257307 + 0.966330i \(0.417165\pi\)
\(458\) 0 0
\(459\) −4.95010 27.2677i −0.231051 1.27275i
\(460\) 0 0
\(461\) 11.9303 18.5639i 0.555649 0.864607i −0.443855 0.896099i \(-0.646389\pi\)
0.999504 + 0.0314915i \(0.0100257\pi\)
\(462\) 0 0
\(463\) −11.2952 + 38.4680i −0.524934 + 1.78776i 0.0862514 + 0.996273i \(0.472511\pi\)
−0.611185 + 0.791488i \(0.709307\pi\)
\(464\) 0 0
\(465\) −35.9530 6.47325i −1.66728 0.300190i
\(466\) 0 0
\(467\) −17.4693 15.1372i −0.808382 0.700467i 0.149144 0.988816i \(-0.452348\pi\)
−0.957525 + 0.288349i \(0.906894\pi\)
\(468\) 0 0
\(469\) 24.9583 + 18.3921i 1.15247 + 0.849269i
\(470\) 0 0
\(471\) 17.7167 10.5205i 0.816343 0.484757i
\(472\) 0 0
\(473\) −27.8070 + 3.99804i −1.27857 + 0.183830i
\(474\) 0 0
\(475\) −0.707727 0.207807i −0.0324727 0.00953486i
\(476\) 0 0
\(477\) −1.28110 3.42722i −0.0586576 0.156921i
\(478\) 0 0
\(479\) 23.8724 + 10.9021i 1.09076 + 0.498132i 0.877848 0.478940i \(-0.158979\pi\)
0.212909 + 0.977072i \(0.431706\pi\)
\(480\) 0 0
\(481\) 1.94584 + 3.02779i 0.0887229 + 0.138055i
\(482\) 0 0
\(483\) −0.887202 + 4.92760i −0.0403691 + 0.224214i
\(484\) 0 0
\(485\) 13.2949 + 45.2782i 0.603690 + 2.05598i
\(486\) 0 0
\(487\) −1.33732 + 0.192278i −0.0605997 + 0.00871293i −0.172548 0.985001i \(-0.555200\pi\)
0.111948 + 0.993714i \(0.464291\pi\)
\(488\) 0 0
\(489\) 3.31939 + 30.7705i 0.150108 + 1.39149i
\(490\) 0 0
\(491\) −29.2186 13.3437i −1.31862 0.602193i −0.373109 0.927788i \(-0.621708\pi\)
−0.945509 + 0.325595i \(0.894435\pi\)
\(492\) 0 0
\(493\) 6.61466 46.0059i 0.297909 2.07200i
\(494\) 0 0
\(495\) 25.3492 25.3858i 1.13936 1.14101i
\(496\) 0 0
\(497\) −2.43491 1.56482i −0.109221 0.0701919i
\(498\) 0 0
\(499\) 12.9260i 0.578646i −0.957231 0.289323i \(-0.906570\pi\)
0.957231 0.289323i \(-0.0934302\pi\)
\(500\) 0 0
\(501\) −0.869541 0.808986i −0.0388482 0.0361428i
\(502\) 0 0
\(503\) −12.5972 14.5380i −0.561682 0.648215i 0.401883 0.915691i \(-0.368356\pi\)
−0.963565 + 0.267476i \(0.913810\pi\)
\(504\) 0 0
\(505\) 34.3919 + 22.1024i 1.53042 + 0.983542i
\(506\) 0 0
\(507\) 17.9643 + 5.97190i 0.797823 + 0.265221i
\(508\) 0 0
\(509\) −5.63479 + 19.1903i −0.249758 + 0.850597i 0.735207 + 0.677842i \(0.237085\pi\)
−0.984965 + 0.172754i \(0.944733\pi\)
\(510\) 0 0
\(511\) 23.9952 + 37.3373i 1.06149 + 1.65171i
\(512\) 0 0
\(513\) −0.527145 + 0.890650i −0.0232740 + 0.0393232i
\(514\) 0 0
\(515\) −0.526367 0.154555i −0.0231945 0.00681052i
\(516\) 0 0
\(517\) 23.2131 20.1143i 1.02091 0.884625i
\(518\) 0 0
\(519\) −33.2420 16.6248i −1.45916 0.729746i
\(520\) 0 0
\(521\) −14.3488 16.5594i −0.628632 0.725480i 0.348690 0.937238i \(-0.386627\pi\)
−0.977322 + 0.211758i \(0.932081\pi\)
\(522\) 0 0
\(523\) −1.74778 + 1.12323i −0.0764251 + 0.0491154i −0.578295 0.815828i \(-0.696282\pi\)
0.501870 + 0.864943i \(0.332645\pi\)
\(524\) 0 0
\(525\) 0.858376 24.2794i 0.0374626 1.05964i
\(526\) 0 0
\(527\) 24.9700 28.8169i 1.08771 1.25528i
\(528\) 0 0
\(529\) −14.6804 + 16.9420i −0.638277 + 0.736610i
\(530\) 0 0
\(531\) 0.400463 1.07605i 0.0173786 0.0466967i
\(532\) 0 0
\(533\) −0.382986 + 0.174904i −0.0165890 + 0.00757592i
\(534\) 0 0
\(535\) 33.5553i 1.45072i
\(536\) 0 0
\(537\) 5.49229 + 1.82581i 0.237010 + 0.0787895i
\(538\) 0 0
\(539\) 12.3699 + 27.0864i 0.532811 + 1.16669i
\(540\) 0 0
\(541\) −10.1591 34.5988i −0.436775 1.48752i −0.824563 0.565770i \(-0.808579\pi\)
0.387788 0.921748i \(-0.373239\pi\)
\(542\) 0 0
\(543\) 3.69707 2.19537i 0.158656 0.0942125i
\(544\) 0 0
\(545\) 32.6466 + 28.2884i 1.39843 + 1.21174i
\(546\) 0 0
\(547\) 7.92881 + 27.0031i 0.339012 + 1.15457i 0.935907 + 0.352248i \(0.114583\pi\)
−0.596895 + 0.802319i \(0.703599\pi\)
\(548\) 0 0
\(549\) −2.61928 + 36.9972i −0.111788 + 1.57900i
\(550\) 0 0
\(551\) −1.31180 + 1.13668i −0.0558847 + 0.0484244i
\(552\) 0 0
\(553\) 7.97780 55.4868i 0.339251 2.35954i
\(554\) 0 0
\(555\) 4.89563 + 11.8071i 0.207808 + 0.501182i
\(556\) 0 0
\(557\) −6.49987 + 22.1365i −0.275409 + 0.937955i 0.699366 + 0.714764i \(0.253466\pi\)
−0.974775 + 0.223192i \(0.928352\pi\)
\(558\) 0 0
\(559\) 4.14245 + 9.07070i 0.175207 + 0.383650i
\(560\) 0 0
\(561\) 9.27359 + 36.2789i 0.391531 + 1.53170i
\(562\) 0 0
\(563\) 23.5092 + 6.90294i 0.990797 + 0.290924i 0.736674 0.676248i \(-0.236395\pi\)
0.254123 + 0.967172i \(0.418213\pi\)
\(564\) 0 0
\(565\) 40.5903 1.70765
\(566\) 0 0
\(567\) −32.7216 9.55667i −1.37418 0.401343i
\(568\) 0 0
\(569\) −4.98397 + 4.31864i −0.208939 + 0.181047i −0.753043 0.657971i \(-0.771415\pi\)
0.544104 + 0.839018i \(0.316870\pi\)
\(570\) 0 0
\(571\) 8.65212 18.9455i 0.362080 0.792844i −0.637666 0.770313i \(-0.720100\pi\)
0.999746 0.0225316i \(-0.00717263\pi\)
\(572\) 0 0
\(573\) −9.17105 3.04875i −0.383126 0.127363i
\(574\) 0 0
\(575\) −1.52802 + 2.37764i −0.0637226 + 0.0991544i
\(576\) 0 0
\(577\) 20.2236 + 2.90771i 0.841918 + 0.121049i 0.549762 0.835321i \(-0.314718\pi\)
0.292156 + 0.956371i \(0.405627\pi\)
\(578\) 0 0
\(579\) −15.9250 + 31.8429i −0.661822 + 1.32334i
\(580\) 0 0
\(581\) 19.6292 42.9820i 0.814358 1.78319i
\(582\) 0 0
\(583\) 2.05369 + 4.49694i 0.0850550 + 0.186244i
\(584\) 0 0
\(585\) −11.1809 6.09478i −0.462274 0.251988i
\(586\) 0 0
\(587\) 13.5582 3.98104i 0.559606 0.164315i 0.0103159 0.999947i \(-0.496716\pi\)
0.549290 + 0.835632i \(0.314898\pi\)
\(588\) 0 0
\(589\) −1.40948 + 0.202653i −0.0580767 + 0.00835017i
\(590\) 0 0
\(591\) −4.15525 + 1.06216i −0.170924 + 0.0436914i
\(592\) 0 0
\(593\) −8.23739 + 18.0374i −0.338269 + 0.740706i −0.999959 0.00907163i \(-0.997112\pi\)
0.661690 + 0.749778i \(0.269840\pi\)
\(594\) 0 0
\(595\) 50.1351 + 32.2198i 2.05534 + 1.32088i
\(596\) 0 0
\(597\) −7.16460 4.97064i −0.293228 0.203435i
\(598\) 0 0
\(599\) 3.41470 + 23.7497i 0.139521 + 0.970388i 0.932508 + 0.361150i \(0.117616\pi\)
−0.792987 + 0.609239i \(0.791475\pi\)
\(600\) 0 0
\(601\) −13.9003 + 16.0418i −0.567004 + 0.654358i −0.964759 0.263134i \(-0.915244\pi\)
0.397755 + 0.917492i \(0.369789\pi\)
\(602\) 0 0
\(603\) 23.5035 7.11229i 0.957137 0.289635i
\(604\) 0 0
\(605\) −10.4921 + 12.1085i −0.426564 + 0.492281i
\(606\) 0 0
\(607\) 2.80749 + 19.5266i 0.113953 + 0.792558i 0.964010 + 0.265867i \(0.0856583\pi\)
−0.850057 + 0.526691i \(0.823433\pi\)
\(608\) 0 0
\(609\) −46.9733 32.5890i −1.90345 1.32057i
\(610\) 0 0
\(611\) −9.17194 5.89445i −0.371057 0.238464i
\(612\) 0 0
\(613\) −3.16626 + 6.93315i −0.127884 + 0.280027i −0.962734 0.270451i \(-0.912827\pi\)
0.834850 + 0.550478i \(0.185555\pi\)
\(614\) 0 0
\(615\) −1.44865 + 0.370304i −0.0584154 + 0.0149321i
\(616\) 0 0
\(617\) −3.30061 + 0.474556i −0.132877 + 0.0191049i −0.208433 0.978037i \(-0.566836\pi\)
0.0755552 + 0.997142i \(0.475927\pi\)
\(618\) 0 0
\(619\) 45.2582 13.2890i 1.81908 0.534130i 0.819822 0.572619i \(-0.194072\pi\)
0.999259 + 0.0384883i \(0.0122542\pi\)
\(620\) 0 0
\(621\) 2.70543 + 2.89954i 0.108565 + 0.116354i
\(622\) 0 0
\(623\) −0.0247309 0.0541531i −0.000990822 0.00216960i
\(624\) 0 0
\(625\) −12.3803 + 27.1090i −0.495211 + 1.08436i
\(626\) 0 0
\(627\) 0.625499 1.25071i 0.0249800 0.0499487i
\(628\) 0 0
\(629\) −13.2055 1.89866i −0.526537 0.0757046i
\(630\) 0 0
\(631\) −19.5180 + 30.3706i −0.776999 + 1.20903i 0.196537 + 0.980496i \(0.437031\pi\)
−0.973535 + 0.228537i \(0.926606\pi\)
\(632\) 0 0
\(633\) −35.7879 11.8970i −1.42244 0.472865i
\(634\) 0 0
\(635\) −4.84806 + 10.6158i −0.192389 + 0.421274i
\(636\) 0 0
\(637\) 7.98807 6.92170i 0.316499 0.274248i
\(638\) 0 0
\(639\) −2.14739 + 0.802699i −0.0849493 + 0.0317543i
\(640\) 0 0
\(641\) −19.0369 −0.751914 −0.375957 0.926637i \(-0.622686\pi\)
−0.375957 + 0.926637i \(0.622686\pi\)
\(642\) 0 0
\(643\) −26.1566 7.68027i −1.03152 0.302880i −0.278189 0.960526i \(-0.589734\pi\)
−0.753327 + 0.657646i \(0.771552\pi\)
\(644\) 0 0
\(645\) 8.77033 + 34.3102i 0.345331 + 1.35096i
\(646\) 0 0
\(647\) −19.9666 43.7207i −0.784968 1.71884i −0.690524 0.723310i \(-0.742620\pi\)
−0.0944441 0.995530i \(-0.530107\pi\)
\(648\) 0 0
\(649\) −0.437066 + 1.48851i −0.0171564 + 0.0584292i
\(650\) 0 0
\(651\) −17.9641 43.3250i −0.704069 1.69804i
\(652\) 0 0
\(653\) −1.49965 + 10.4303i −0.0586860 + 0.408170i 0.939210 + 0.343342i \(0.111559\pi\)
−0.997896 + 0.0648281i \(0.979350\pi\)
\(654\) 0 0
\(655\) 7.46865 6.47162i 0.291824 0.252867i
\(656\) 0 0
\(657\) 35.0659 + 2.48255i 1.36805 + 0.0968534i
\(658\) 0 0
\(659\) −3.84876 13.1077i −0.149926 0.510602i 0.849941 0.526878i \(-0.176637\pi\)
−0.999868 + 0.0162753i \(0.994819\pi\)
\(660\) 0 0
\(661\) −6.20052 5.37278i −0.241172 0.208977i 0.525885 0.850556i \(-0.323734\pi\)
−0.767057 + 0.641579i \(0.778280\pi\)
\(662\) 0 0
\(663\) 11.4285 6.78643i 0.443847 0.263563i
\(664\) 0 0
\(665\) −0.627026 2.13545i −0.0243150 0.0828093i
\(666\) 0 0
\(667\) 2.76292 + 6.04994i 0.106981 + 0.234255i
\(668\) 0 0
\(669\) 36.8719 + 12.2574i 1.42555 + 0.473898i
\(670\) 0 0
\(671\) 50.1146i 1.93465i
\(672\) 0 0
\(673\) 12.7092 5.80409i 0.489903 0.223731i −0.155118 0.987896i \(-0.549576\pi\)
0.645021 + 0.764165i \(0.276849\pi\)
\(674\) 0 0
\(675\) −14.9962 12.0579i −0.577203 0.464110i
\(676\) 0 0
\(677\) −1.10341 + 1.27340i −0.0424073 + 0.0489407i −0.776557 0.630047i \(-0.783036\pi\)
0.734150 + 0.678988i \(0.237581\pi\)
\(678\) 0 0
\(679\) −39.6755 + 45.7880i −1.52261 + 1.75718i
\(680\) 0 0
\(681\) −0.272438 + 7.70601i −0.0104399 + 0.295295i
\(682\) 0 0
\(683\) −12.0221 + 7.72614i −0.460013 + 0.295633i −0.750048 0.661384i \(-0.769970\pi\)
0.290035 + 0.957016i \(0.406333\pi\)
\(684\) 0 0
\(685\) −29.1864 33.6828i −1.11515 1.28696i
\(686\) 0 0
\(687\) 23.7813 + 11.8934i 0.907314 + 0.453760i
\(688\) 0 0
\(689\) 1.32620 1.14916i 0.0505241 0.0437794i
\(690\) 0 0
\(691\) −16.0896 4.72433i −0.612077 0.179722i −0.0390213 0.999238i \(-0.512424\pi\)
−0.573056 + 0.819516i \(0.694242\pi\)
\(692\) 0 0
\(693\) 45.0139 + 9.75817i 1.70994 + 0.370682i
\(694\) 0 0
\(695\) 24.7755 + 38.5515i 0.939790 + 1.46234i
\(696\) 0 0
\(697\) 0.439696 1.49747i 0.0166547 0.0567206i
\(698\) 0 0
\(699\) 22.5766 + 7.50517i 0.853925 + 0.283872i
\(700\) 0 0
\(701\) −14.5696 9.36331i −0.550286 0.353647i 0.235764 0.971810i \(-0.424241\pi\)
−0.786050 + 0.618163i \(0.787877\pi\)
\(702\) 0 0
\(703\) 0.326272 + 0.376538i 0.0123056 + 0.0142014i
\(704\) 0 0
\(705\) −28.3479 26.3737i −1.06764 0.993292i
\(706\) 0 0
\(707\) 52.4875i 1.97399i
\(708\) 0 0
\(709\) 20.9318 + 13.4520i 0.786110 + 0.505202i 0.871056 0.491183i \(-0.163436\pi\)
−0.0849464 + 0.996386i \(0.527072\pi\)
\(710\) 0 0
\(711\) −31.4185 31.3732i −1.17829 1.17659i
\(712\) 0 0
\(713\) −0.776511 + 5.40075i −0.0290806 + 0.202260i
\(714\) 0 0
\(715\) 15.6512 + 7.14764i 0.585320 + 0.267307i
\(716\) 0 0
\(717\) 4.33947 + 40.2265i 0.162060 + 1.50228i
\(718\) 0 0
\(719\) 6.05908 0.871164i 0.225966 0.0324889i −0.0284019 0.999597i \(-0.509042\pi\)
0.254367 + 0.967108i \(0.418133\pi\)
\(720\) 0 0
\(721\) −0.198431 0.675794i −0.00738996 0.0251679i
\(722\) 0 0
\(723\) −0.690157 + 3.83319i −0.0256672 + 0.142558i
\(724\) 0 0
\(725\) −17.4478 27.1493i −0.647996 1.00830i
\(726\) 0 0
\(727\) −14.1305 6.45316i −0.524070 0.239335i 0.135771 0.990740i \(-0.456649\pi\)
−0.659840 + 0.751406i \(0.729376\pi\)
\(728\) 0 0
\(729\) −21.5796 + 16.2272i −0.799243 + 0.601008i
\(730\) 0 0
\(731\) −35.4663 10.4138i −1.31177 0.385169i
\(732\) 0 0
\(733\) −25.2314 + 3.62773i −0.931944 + 0.133993i −0.591531 0.806282i \(-0.701476\pi\)
−0.340414 + 0.940276i \(0.610567\pi\)
\(734\) 0 0
\(735\) 32.2752 19.1655i 1.19049 0.706929i
\(736\) 0 0
\(737\) −30.9993 + 11.8286i −1.14187 + 0.435712i
\(738\) 0 0
\(739\) −14.2599 12.3563i −0.524558 0.454532i 0.351881 0.936045i \(-0.385542\pi\)
−0.876439 + 0.481512i \(0.840088\pi\)
\(740\) 0 0
\(741\) −0.488521 0.0879570i −0.0179463 0.00323118i
\(742\) 0 0
\(743\) −11.9043 + 40.5424i −0.436728 + 1.48736i 0.387910 + 0.921697i \(0.373197\pi\)
−0.824638 + 0.565661i \(0.808621\pi\)
\(744\) 0 0
\(745\) 29.0766 45.2441i 1.06529 1.65762i
\(746\) 0 0
\(747\) −17.9602 32.8353i −0.657128 1.20138i
\(748\) 0 0
\(749\) −36.2422 + 23.2914i −1.32426 + 0.851050i
\(750\) 0 0
\(751\) 0.861200 + 5.98978i 0.0314256 + 0.218570i 0.999483 0.0321598i \(-0.0102385\pi\)
−0.968057 + 0.250730i \(0.919329\pi\)
\(752\) 0 0
\(753\) −25.8283 0.913135i −0.941236 0.0332765i
\(754\) 0 0
\(755\) −1.38914 9.66168i −0.0505560 0.351625i
\(756\) 0 0
\(757\) 0.504090 0.230210i 0.0183215 0.00836714i −0.406233 0.913769i \(-0.633158\pi\)
0.424555 + 0.905402i \(0.360431\pi\)
\(758\) 0 0
\(759\) −3.92303 3.64983i −0.142397 0.132481i
\(760\) 0 0
\(761\) −1.51723 0.218144i −0.0549995 0.00790773i 0.114760 0.993393i \(-0.463390\pi\)
−0.169760 + 0.985485i \(0.554299\pi\)
\(762\) 0 0
\(763\) −7.89288 + 54.8962i −0.285741 + 1.98738i
\(764\) 0 0
\(765\) 44.2149 16.5276i 1.59859 0.597558i
\(766\) 0 0
\(767\) 0.550666 0.0198834
\(768\) 0 0
\(769\) 5.52872 + 2.52488i 0.199371 + 0.0910496i 0.512598 0.858629i \(-0.328683\pi\)
−0.313228 + 0.949678i \(0.601410\pi\)
\(770\) 0 0
\(771\) 18.2945 7.58558i 0.658862 0.273188i
\(772\) 0 0
\(773\) 16.8998 26.2967i 0.607845 0.945825i −0.391823 0.920041i \(-0.628155\pi\)
0.999668 0.0257841i \(-0.00820825\pi\)
\(774\) 0 0
\(775\) 26.4755i 0.951028i
\(776\) 0 0