Properties

Label 1148.2.ba.a.113.3
Level $1148$
Weight $2$
Character 1148.113
Analytic conductor $9.167$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.ba (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 113.3
Character \(\chi\) \(=\) 1148.113
Dual form 1148.2.ba.a.701.18

$q$-expansion

\(f(q)\) \(=\) \(q-2.47691i q^{3} +(0.848862 + 2.61253i) q^{5} +(-0.587785 - 0.809017i) q^{7} -3.13508 q^{9} +O(q^{10})\) \(q-2.47691i q^{3} +(0.848862 + 2.61253i) q^{5} +(-0.587785 - 0.809017i) q^{7} -3.13508 q^{9} +(0.155866 + 0.0506441i) q^{11} +(0.900389 - 1.23928i) q^{13} +(6.47099 - 2.10255i) q^{15} +(4.74636 + 1.54219i) q^{17} +(-1.52565 - 2.09988i) q^{19} +(-2.00386 + 1.45589i) q^{21} +(-3.99142 - 2.89994i) q^{23} +(-2.05965 + 1.49642i) q^{25} +0.334588i q^{27} +(7.83715 - 2.54645i) q^{29} +(2.93261 - 9.02563i) q^{31} +(0.125441 - 0.386067i) q^{33} +(1.61463 - 2.22235i) q^{35} +(-0.271365 - 0.835175i) q^{37} +(-3.06958 - 2.23018i) q^{39} +(6.38925 - 0.421255i) q^{41} +(2.34171 + 1.70135i) q^{43} +(-2.66125 - 8.19049i) q^{45} +(0.824651 - 1.13504i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(3.81986 - 11.7563i) q^{51} +(0.299152 - 0.0972005i) q^{53} +0.450195i q^{55} +(-5.20122 + 3.77891i) q^{57} +(2.07298 + 1.50611i) q^{59} +(-6.09102 + 4.42538i) q^{61} +(1.84276 + 2.53634i) q^{63} +(4.00196 + 1.30031i) q^{65} +(3.85065 - 1.25115i) q^{67} +(-7.18288 + 9.88639i) q^{69} +(-2.81283 - 0.913945i) q^{71} -9.41632 q^{73} +(3.70650 + 5.10156i) q^{75} +(-0.0506441 - 0.155866i) q^{77} +0.527193i q^{79} -8.57650 q^{81} -7.32300 q^{83} +13.7091i q^{85} +(-6.30732 - 19.4119i) q^{87} +(4.01496 + 5.52611i) q^{89} -1.53183 q^{91} +(-22.3557 - 7.26380i) q^{93} +(4.19093 - 5.76832i) q^{95} +(11.1577 - 3.62537i) q^{97} +(-0.488654 - 0.158773i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{5} - 60q^{9} + O(q^{10}) \) \( 80q - 4q^{5} - 60q^{9} + 10q^{11} + 20q^{15} - 10q^{17} - 30q^{19} - 4q^{21} - 20q^{25} + 2q^{31} + 10q^{33} + 10q^{37} + 36q^{39} - 14q^{41} + 30q^{43} + 44q^{45} - 60q^{47} + 20q^{49} - 32q^{51} + 16q^{57} - 60q^{59} + 44q^{61} - 10q^{65} - 10q^{67} - 40q^{71} - 88q^{73} - 70q^{75} - 8q^{77} - 40q^{81} + 28q^{83} - 24q^{87} + 24q^{91} - 100q^{93} + 120q^{97} - 100q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.47691i 1.43004i −0.699102 0.715022i \(-0.746417\pi\)
0.699102 0.715022i \(-0.253583\pi\)
\(4\) 0 0
\(5\) 0.848862 + 2.61253i 0.379622 + 1.16836i 0.940307 + 0.340328i \(0.110538\pi\)
−0.560684 + 0.828030i \(0.689462\pi\)
\(6\) 0 0
\(7\) −0.587785 0.809017i −0.222162 0.305780i
\(8\) 0 0
\(9\) −3.13508 −1.04503
\(10\) 0 0
\(11\) 0.155866 + 0.0506441i 0.0469955 + 0.0152698i 0.332420 0.943131i \(-0.392135\pi\)
−0.285425 + 0.958401i \(0.592135\pi\)
\(12\) 0 0
\(13\) 0.900389 1.23928i 0.249723 0.343714i −0.665691 0.746227i \(-0.731863\pi\)
0.915414 + 0.402513i \(0.131863\pi\)
\(14\) 0 0
\(15\) 6.47099 2.10255i 1.67080 0.542877i
\(16\) 0 0
\(17\) 4.74636 + 1.54219i 1.15116 + 0.374035i 0.821581 0.570092i \(-0.193092\pi\)
0.329581 + 0.944127i \(0.393092\pi\)
\(18\) 0 0
\(19\) −1.52565 2.09988i −0.350009 0.481746i 0.597322 0.802001i \(-0.296231\pi\)
−0.947331 + 0.320255i \(0.896231\pi\)
\(20\) 0 0
\(21\) −2.00386 + 1.45589i −0.437279 + 0.317701i
\(22\) 0 0
\(23\) −3.99142 2.89994i −0.832269 0.604678i 0.0879317 0.996127i \(-0.471974\pi\)
−0.920200 + 0.391448i \(0.871974\pi\)
\(24\) 0 0
\(25\) −2.05965 + 1.49642i −0.411929 + 0.299284i
\(26\) 0 0
\(27\) 0.334588i 0.0643916i
\(28\) 0 0
\(29\) 7.83715 2.54645i 1.45532 0.472863i 0.528685 0.848818i \(-0.322685\pi\)
0.926638 + 0.375955i \(0.122685\pi\)
\(30\) 0 0
\(31\) 2.93261 9.02563i 0.526712 1.62105i −0.234195 0.972190i \(-0.575245\pi\)
0.760906 0.648862i \(-0.224755\pi\)
\(32\) 0 0
\(33\) 0.125441 0.386067i 0.0218364 0.0672057i
\(34\) 0 0
\(35\) 1.61463 2.22235i 0.272922 0.375645i
\(36\) 0 0
\(37\) −0.271365 0.835175i −0.0446121 0.137302i 0.926269 0.376862i \(-0.122997\pi\)
−0.970882 + 0.239560i \(0.922997\pi\)
\(38\) 0 0
\(39\) −3.06958 2.23018i −0.491527 0.357115i
\(40\) 0 0
\(41\) 6.38925 0.421255i 0.997834 0.0657889i
\(42\) 0 0
\(43\) 2.34171 + 1.70135i 0.357108 + 0.259454i 0.751845 0.659340i \(-0.229164\pi\)
−0.394737 + 0.918794i \(0.629164\pi\)
\(44\) 0 0
\(45\) −2.66125 8.19049i −0.396716 1.22097i
\(46\) 0 0
\(47\) 0.824651 1.13504i 0.120288 0.165562i −0.744627 0.667481i \(-0.767373\pi\)
0.864915 + 0.501919i \(0.167373\pi\)
\(48\) 0 0
\(49\) −0.309017 + 0.951057i −0.0441453 + 0.135865i
\(50\) 0 0
\(51\) 3.81986 11.7563i 0.534887 1.64621i
\(52\) 0 0
\(53\) 0.299152 0.0972005i 0.0410917 0.0133515i −0.288399 0.957510i \(-0.593123\pi\)
0.329491 + 0.944159i \(0.393123\pi\)
\(54\) 0 0
\(55\) 0.450195i 0.0607043i
\(56\) 0 0
\(57\) −5.20122 + 3.77891i −0.688918 + 0.500528i
\(58\) 0 0
\(59\) 2.07298 + 1.50611i 0.269878 + 0.196078i 0.714491 0.699645i \(-0.246658\pi\)
−0.444612 + 0.895723i \(0.646658\pi\)
\(60\) 0 0
\(61\) −6.09102 + 4.42538i −0.779875 + 0.566612i −0.904942 0.425536i \(-0.860086\pi\)
0.125066 + 0.992148i \(0.460086\pi\)
\(62\) 0 0
\(63\) 1.84276 + 2.53634i 0.232165 + 0.319548i
\(64\) 0 0
\(65\) 4.00196 + 1.30031i 0.496382 + 0.161284i
\(66\) 0 0
\(67\) 3.85065 1.25115i 0.470432 0.152853i −0.0642008 0.997937i \(-0.520450\pi\)
0.534633 + 0.845084i \(0.320450\pi\)
\(68\) 0 0
\(69\) −7.18288 + 9.88639i −0.864717 + 1.19018i
\(70\) 0 0
\(71\) −2.81283 0.913945i −0.333822 0.108465i 0.137310 0.990528i \(-0.456154\pi\)
−0.471132 + 0.882063i \(0.656154\pi\)
\(72\) 0 0
\(73\) −9.41632 −1.10210 −0.551048 0.834473i \(-0.685772\pi\)
−0.551048 + 0.834473i \(0.685772\pi\)
\(74\) 0 0
\(75\) 3.70650 + 5.10156i 0.427990 + 0.589077i
\(76\) 0 0
\(77\) −0.0506441 0.155866i −0.00577143 0.0177626i
\(78\) 0 0
\(79\) 0.527193i 0.0593138i 0.999560 + 0.0296569i \(0.00944147\pi\)
−0.999560 + 0.0296569i \(0.990559\pi\)
\(80\) 0 0
\(81\) −8.57650 −0.952945
\(82\) 0 0
\(83\) −7.32300 −0.803804 −0.401902 0.915683i \(-0.631651\pi\)
−0.401902 + 0.915683i \(0.631651\pi\)
\(84\) 0 0
\(85\) 13.7091i 1.48696i
\(86\) 0 0
\(87\) −6.30732 19.4119i −0.676215 2.08118i
\(88\) 0 0
\(89\) 4.01496 + 5.52611i 0.425584 + 0.585767i 0.966933 0.255032i \(-0.0820859\pi\)
−0.541348 + 0.840799i \(0.682086\pi\)
\(90\) 0 0
\(91\) −1.53183 −0.160580
\(92\) 0 0
\(93\) −22.3557 7.26380i −2.31818 0.753221i
\(94\) 0 0
\(95\) 4.19093 5.76832i 0.429980 0.591817i
\(96\) 0 0
\(97\) 11.1577 3.62537i 1.13290 0.368101i 0.318221 0.948017i \(-0.396915\pi\)
0.814676 + 0.579916i \(0.196915\pi\)
\(98\) 0 0
\(99\) −0.488654 0.158773i −0.0491116 0.0159573i
\(100\) 0 0
\(101\) −1.98319 2.72962i −0.197335 0.271608i 0.698870 0.715249i \(-0.253687\pi\)
−0.896205 + 0.443641i \(0.853687\pi\)
\(102\) 0 0
\(103\) −1.36426 + 0.991196i −0.134425 + 0.0976655i −0.652966 0.757387i \(-0.726475\pi\)
0.518541 + 0.855053i \(0.326475\pi\)
\(104\) 0 0
\(105\) −5.50456 3.99929i −0.537190 0.390291i
\(106\) 0 0
\(107\) 14.1729 10.2972i 1.37014 0.995468i 0.372418 0.928065i \(-0.378529\pi\)
0.997726 0.0674026i \(-0.0214712\pi\)
\(108\) 0 0
\(109\) 8.48403i 0.812623i −0.913735 0.406312i \(-0.866815\pi\)
0.913735 0.406312i \(-0.133185\pi\)
\(110\) 0 0
\(111\) −2.06865 + 0.672146i −0.196348 + 0.0637973i
\(112\) 0 0
\(113\) 1.81543 5.58731i 0.170781 0.525610i −0.828635 0.559790i \(-0.810882\pi\)
0.999416 + 0.0341796i \(0.0108818\pi\)
\(114\) 0 0
\(115\) 4.18800 12.8893i 0.390533 1.20194i
\(116\) 0 0
\(117\) −2.82280 + 3.88524i −0.260968 + 0.359191i
\(118\) 0 0
\(119\) −1.54219 4.74636i −0.141372 0.435098i
\(120\) 0 0
\(121\) −8.87746 6.44985i −0.807042 0.586350i
\(122\) 0 0
\(123\) −1.04341 15.8256i −0.0940811 1.42695i
\(124\) 0 0
\(125\) 5.45395 + 3.96252i 0.487816 + 0.354419i
\(126\) 0 0
\(127\) 1.72960 + 5.32315i 0.153477 + 0.472353i 0.998003 0.0631604i \(-0.0201180\pi\)
−0.844526 + 0.535514i \(0.820118\pi\)
\(128\) 0 0
\(129\) 4.21410 5.80022i 0.371031 0.510680i
\(130\) 0 0
\(131\) −4.76665 + 14.6702i −0.416464 + 1.28174i 0.494471 + 0.869194i \(0.335362\pi\)
−0.910935 + 0.412550i \(0.864638\pi\)
\(132\) 0 0
\(133\) −0.802084 + 2.46856i −0.0695495 + 0.214051i
\(134\) 0 0
\(135\) −0.874121 + 0.284019i −0.0752324 + 0.0244445i
\(136\) 0 0
\(137\) 6.49271i 0.554709i −0.960768 0.277355i \(-0.910542\pi\)
0.960768 0.277355i \(-0.0894577\pi\)
\(138\) 0 0
\(139\) −13.3649 + 9.71018i −1.13360 + 0.823607i −0.986214 0.165473i \(-0.947085\pi\)
−0.147383 + 0.989079i \(0.547085\pi\)
\(140\) 0 0
\(141\) −2.81138 2.04259i −0.236761 0.172017i
\(142\) 0 0
\(143\) 0.203103 0.147563i 0.0169843 0.0123398i
\(144\) 0 0
\(145\) 13.3053 + 18.3132i 1.10495 + 1.52083i
\(146\) 0 0
\(147\) 2.35568 + 0.765407i 0.194293 + 0.0631297i
\(148\) 0 0
\(149\) −20.1266 + 6.53952i −1.64883 + 0.535738i −0.978487 0.206311i \(-0.933854\pi\)
−0.670346 + 0.742049i \(0.733854\pi\)
\(150\) 0 0
\(151\) −12.5667 + 17.2965i −1.02266 + 1.40757i −0.112341 + 0.993670i \(0.535835\pi\)
−0.910321 + 0.413903i \(0.864165\pi\)
\(152\) 0 0
\(153\) −14.8802 4.83488i −1.20300 0.390877i
\(154\) 0 0
\(155\) 26.0691 2.09392
\(156\) 0 0
\(157\) 4.35909 + 5.99977i 0.347893 + 0.478834i 0.946726 0.322040i \(-0.104369\pi\)
−0.598833 + 0.800874i \(0.704369\pi\)
\(158\) 0 0
\(159\) −0.240757 0.740973i −0.0190933 0.0587630i
\(160\) 0 0
\(161\) 4.93367i 0.388827i
\(162\) 0 0
\(163\) 14.8114 1.16011 0.580057 0.814576i \(-0.303030\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(164\) 0 0
\(165\) 1.11509 0.0868098
\(166\) 0 0
\(167\) 22.7365i 1.75940i 0.475528 + 0.879701i \(0.342257\pi\)
−0.475528 + 0.879701i \(0.657743\pi\)
\(168\) 0 0
\(169\) 3.29211 + 10.1321i 0.253239 + 0.779390i
\(170\) 0 0
\(171\) 4.78305 + 6.58330i 0.365769 + 0.503438i
\(172\) 0 0
\(173\) 5.02308 0.381897 0.190949 0.981600i \(-0.438844\pi\)
0.190949 + 0.981600i \(0.438844\pi\)
\(174\) 0 0
\(175\) 2.42126 + 0.786715i 0.183030 + 0.0594701i
\(176\) 0 0
\(177\) 3.73049 5.13457i 0.280401 0.385938i
\(178\) 0 0
\(179\) 5.27510 1.71398i 0.394279 0.128109i −0.105166 0.994455i \(-0.533537\pi\)
0.499445 + 0.866346i \(0.333537\pi\)
\(180\) 0 0
\(181\) −2.75954 0.896629i −0.205115 0.0666459i 0.204658 0.978834i \(-0.434392\pi\)
−0.409772 + 0.912188i \(0.634392\pi\)
\(182\) 0 0
\(183\) 10.9613 + 15.0869i 0.810281 + 1.11526i
\(184\) 0 0
\(185\) 1.95157 1.41790i 0.143482 0.104246i
\(186\) 0 0
\(187\) 0.661696 + 0.480750i 0.0483880 + 0.0351559i
\(188\) 0 0
\(189\) 0.270688 0.196666i 0.0196896 0.0143054i
\(190\) 0 0
\(191\) 3.55967i 0.257569i 0.991673 + 0.128784i \(0.0411075\pi\)
−0.991673 + 0.128784i \(0.958892\pi\)
\(192\) 0 0
\(193\) 17.1027 5.55699i 1.23108 0.400001i 0.379972 0.924998i \(-0.375934\pi\)
0.851104 + 0.524997i \(0.175934\pi\)
\(194\) 0 0
\(195\) 3.22076 9.91249i 0.230644 0.709848i
\(196\) 0 0
\(197\) 5.25992 16.1884i 0.374754 1.15337i −0.568891 0.822413i \(-0.692627\pi\)
0.943645 0.330961i \(-0.107373\pi\)
\(198\) 0 0
\(199\) −14.4383 + 19.8727i −1.02351 + 1.40874i −0.113790 + 0.993505i \(0.536299\pi\)
−0.909716 + 0.415231i \(0.863701\pi\)
\(200\) 0 0
\(201\) −3.09899 9.53772i −0.218586 0.672739i
\(202\) 0 0
\(203\) −6.66668 4.84363i −0.467909 0.339956i
\(204\) 0 0
\(205\) 6.52413 + 16.3345i 0.455665 + 1.14085i
\(206\) 0 0
\(207\) 12.5134 + 9.09154i 0.869744 + 0.631906i
\(208\) 0 0
\(209\) −0.131452 0.404566i −0.00909270 0.0279844i
\(210\) 0 0
\(211\) 11.8499 16.3100i 0.815783 1.12283i −0.174622 0.984636i \(-0.555870\pi\)
0.990405 0.138194i \(-0.0441297\pi\)
\(212\) 0 0
\(213\) −2.26376 + 6.96713i −0.155110 + 0.477380i
\(214\) 0 0
\(215\) −2.45704 + 7.56201i −0.167569 + 0.515725i
\(216\) 0 0
\(217\) −9.02563 + 2.93261i −0.612700 + 0.199078i
\(218\) 0 0
\(219\) 23.3234i 1.57605i
\(220\) 0 0
\(221\) 6.18478 4.49350i 0.416033 0.302266i
\(222\) 0 0
\(223\) −0.687250 0.499316i −0.0460216 0.0334367i 0.564537 0.825408i \(-0.309055\pi\)
−0.610558 + 0.791971i \(0.709055\pi\)
\(224\) 0 0
\(225\) 6.45716 4.69140i 0.430478 0.312760i
\(226\) 0 0
\(227\) 6.61213 + 9.10082i 0.438863 + 0.604043i 0.969959 0.243269i \(-0.0782197\pi\)
−0.531096 + 0.847312i \(0.678220\pi\)
\(228\) 0 0
\(229\) 16.8320 + 5.46903i 1.11229 + 0.361404i 0.806819 0.590799i \(-0.201187\pi\)
0.305468 + 0.952202i \(0.401187\pi\)
\(230\) 0 0
\(231\) −0.386067 + 0.125441i −0.0254013 + 0.00825340i
\(232\) 0 0
\(233\) 3.39424 4.67177i 0.222364 0.306058i −0.683230 0.730203i \(-0.739425\pi\)
0.905594 + 0.424145i \(0.139425\pi\)
\(234\) 0 0
\(235\) 3.66533 + 1.19094i 0.239099 + 0.0776881i
\(236\) 0 0
\(237\) 1.30581 0.0848214
\(238\) 0 0
\(239\) −3.38345 4.65692i −0.218857 0.301231i 0.685445 0.728125i \(-0.259608\pi\)
−0.904302 + 0.426894i \(0.859608\pi\)
\(240\) 0 0
\(241\) −0.200267 0.616359i −0.0129003 0.0397032i 0.944399 0.328801i \(-0.106645\pi\)
−0.957299 + 0.289098i \(0.906645\pi\)
\(242\) 0 0
\(243\) 22.2470i 1.42715i
\(244\) 0 0
\(245\) −2.74697 −0.175498
\(246\) 0 0
\(247\) −3.97602 −0.252988
\(248\) 0 0
\(249\) 18.1384i 1.14948i
\(250\) 0 0
\(251\) 0.724737 + 2.23051i 0.0457450 + 0.140789i 0.971320 0.237775i \(-0.0764181\pi\)
−0.925575 + 0.378564i \(0.876418\pi\)
\(252\) 0 0
\(253\) −0.475264 0.654144i −0.0298796 0.0411257i
\(254\) 0 0
\(255\) 33.9562 2.12642
\(256\) 0 0
\(257\) −7.91677 2.57231i −0.493835 0.160457i 0.0515034 0.998673i \(-0.483599\pi\)
−0.545338 + 0.838216i \(0.683599\pi\)
\(258\) 0 0
\(259\) −0.516166 + 0.710442i −0.0320730 + 0.0441447i
\(260\) 0 0
\(261\) −24.5701 + 7.98332i −1.52085 + 0.494155i
\(262\) 0 0
\(263\) 7.36148 + 2.39189i 0.453928 + 0.147490i 0.527053 0.849833i \(-0.323297\pi\)
−0.0731245 + 0.997323i \(0.523297\pi\)
\(264\) 0 0
\(265\) 0.507878 + 0.699034i 0.0311987 + 0.0429413i
\(266\) 0 0
\(267\) 13.6877 9.94468i 0.837673 0.608605i
\(268\) 0 0
\(269\) 3.98183 + 2.89297i 0.242776 + 0.176387i 0.702519 0.711665i \(-0.252058\pi\)
−0.459743 + 0.888052i \(0.652058\pi\)
\(270\) 0 0
\(271\) −10.1834 + 7.39865i −0.618596 + 0.449436i −0.852431 0.522840i \(-0.824872\pi\)
0.233835 + 0.972276i \(0.424872\pi\)
\(272\) 0 0
\(273\) 3.79421i 0.229636i
\(274\) 0 0
\(275\) −0.396815 + 0.128933i −0.0239288 + 0.00777495i
\(276\) 0 0
\(277\) 1.00393 3.08977i 0.0603201 0.185646i −0.916356 0.400365i \(-0.868883\pi\)
0.976676 + 0.214719i \(0.0688834\pi\)
\(278\) 0 0
\(279\) −9.19396 + 28.2961i −0.550428 + 1.69404i
\(280\) 0 0
\(281\) 8.44508 11.6237i 0.503791 0.693409i −0.479066 0.877779i \(-0.659024\pi\)
0.982857 + 0.184370i \(0.0590245\pi\)
\(282\) 0 0
\(283\) 2.11438 + 6.50738i 0.125687 + 0.386823i 0.994026 0.109148i \(-0.0348121\pi\)
−0.868339 + 0.495971i \(0.834812\pi\)
\(284\) 0 0
\(285\) −14.2876 10.3806i −0.846325 0.614891i
\(286\) 0 0
\(287\) −4.09631 4.92141i −0.241798 0.290501i
\(288\) 0 0
\(289\) 6.39634 + 4.64721i 0.376255 + 0.273366i
\(290\) 0 0
\(291\) −8.97972 27.6367i −0.526400 1.62009i
\(292\) 0 0
\(293\) −6.24497 + 8.59546i −0.364835 + 0.502152i −0.951488 0.307686i \(-0.900445\pi\)
0.586653 + 0.809838i \(0.300445\pi\)
\(294\) 0 0
\(295\) −2.17507 + 6.69418i −0.126638 + 0.389750i
\(296\) 0 0
\(297\) −0.0169449 + 0.0521511i −0.000983244 + 0.00302611i
\(298\) 0 0
\(299\) −7.18766 + 2.33541i −0.415673 + 0.135060i
\(300\) 0 0
\(301\) 2.89452i 0.166837i
\(302\) 0 0
\(303\) −6.76103 + 4.91218i −0.388411 + 0.282197i
\(304\) 0 0
\(305\) −16.7319 12.1564i −0.958064 0.696074i
\(306\) 0 0
\(307\) 0.847494 0.615740i 0.0483690 0.0351422i −0.563338 0.826227i \(-0.690483\pi\)
0.611707 + 0.791084i \(0.290483\pi\)
\(308\) 0 0
\(309\) 2.45510 + 3.37916i 0.139666 + 0.192234i
\(310\) 0 0
\(311\) 1.73717 + 0.564442i 0.0985061 + 0.0320066i 0.357855 0.933777i \(-0.383508\pi\)
−0.259349 + 0.965784i \(0.583508\pi\)
\(312\) 0 0
\(313\) −13.5739 + 4.41044i −0.767244 + 0.249293i −0.666385 0.745608i \(-0.732159\pi\)
−0.100859 + 0.994901i \(0.532159\pi\)
\(314\) 0 0
\(315\) −5.06200 + 6.96725i −0.285211 + 0.392560i
\(316\) 0 0
\(317\) −4.74945 1.54319i −0.266756 0.0866742i 0.172585 0.984995i \(-0.444788\pi\)
−0.439341 + 0.898320i \(0.644788\pi\)
\(318\) 0 0
\(319\) 1.35051 0.0756141
\(320\) 0 0
\(321\) −25.5052 35.1049i −1.42356 1.95937i
\(322\) 0 0
\(323\) −4.00290 12.3196i −0.222727 0.685484i
\(324\) 0 0
\(325\) 3.89984i 0.216324i
\(326\) 0 0
\(327\) −21.0142 −1.16209
\(328\) 0 0
\(329\) −1.40298 −0.0773488
\(330\) 0 0
\(331\) 26.0992i 1.43454i 0.696794 + 0.717271i \(0.254609\pi\)
−0.696794 + 0.717271i \(0.745391\pi\)
\(332\) 0 0
\(333\) 0.850751 + 2.61834i 0.0466209 + 0.143484i
\(334\) 0 0
\(335\) 6.53735 + 8.99788i 0.357173 + 0.491607i
\(336\) 0 0
\(337\) 12.2879 0.669364 0.334682 0.942331i \(-0.391371\pi\)
0.334682 + 0.942331i \(0.391371\pi\)
\(338\) 0 0
\(339\) −13.8393 4.49665i −0.751646 0.244225i
\(340\) 0 0
\(341\) 0.914190 1.25827i 0.0495061 0.0681394i
\(342\) 0 0
\(343\) 0.951057 0.309017i 0.0513522 0.0166853i
\(344\) 0 0
\(345\) −31.9257 10.3733i −1.71882 0.558480i
\(346\) 0 0
\(347\) −0.408068 0.561658i −0.0219063 0.0301514i 0.797923 0.602759i \(-0.205932\pi\)
−0.819830 + 0.572608i \(0.805932\pi\)
\(348\) 0 0
\(349\) −17.1142 + 12.4342i −0.916102 + 0.665587i −0.942551 0.334063i \(-0.891580\pi\)
0.0264488 + 0.999650i \(0.491580\pi\)
\(350\) 0 0
\(351\) 0.414649 + 0.301260i 0.0221323 + 0.0160801i
\(352\) 0 0
\(353\) −24.5437 + 17.8320i −1.30633 + 0.949103i −0.999996 0.00282206i \(-0.999102\pi\)
−0.306332 + 0.951925i \(0.599102\pi\)
\(354\) 0 0
\(355\) 8.12442i 0.431199i
\(356\) 0 0
\(357\) −11.7563 + 3.81986i −0.622210 + 0.202168i
\(358\) 0 0
\(359\) 5.14939 15.8482i 0.271774 0.836436i −0.718280 0.695754i \(-0.755070\pi\)
0.990055 0.140682i \(-0.0449295\pi\)
\(360\) 0 0
\(361\) 3.78944 11.6627i 0.199444 0.613826i
\(362\) 0 0
\(363\) −15.9757 + 21.9887i −0.838507 + 1.15411i
\(364\) 0 0
\(365\) −7.99315 24.6004i −0.418381 1.28764i
\(366\) 0 0
\(367\) 21.0582 + 15.2997i 1.09923 + 0.798637i 0.980934 0.194341i \(-0.0622569\pi\)
0.118296 + 0.992978i \(0.462257\pi\)
\(368\) 0 0
\(369\) −20.0308 + 1.32067i −1.04276 + 0.0687513i
\(370\) 0 0
\(371\) −0.254474 0.184886i −0.0132116 0.00959882i
\(372\) 0 0
\(373\) 10.3720 + 31.9217i 0.537041 + 1.65284i 0.739197 + 0.673489i \(0.235205\pi\)
−0.202156 + 0.979353i \(0.564795\pi\)
\(374\) 0 0
\(375\) 9.81481 13.5089i 0.506835 0.697598i
\(376\) 0 0
\(377\) 3.90073 12.0052i 0.200898 0.618300i
\(378\) 0 0
\(379\) 1.74548 5.37205i 0.0896595 0.275944i −0.896166 0.443720i \(-0.853659\pi\)
0.985825 + 0.167776i \(0.0536586\pi\)
\(380\) 0 0
\(381\) 13.1850 4.28406i 0.675486 0.219479i
\(382\) 0 0
\(383\) 32.9177i 1.68202i −0.541022 0.841008i \(-0.681962\pi\)
0.541022 0.841008i \(-0.318038\pi\)
\(384\) 0 0
\(385\) 0.364215 0.264618i 0.0185621 0.0134862i
\(386\) 0 0
\(387\) −7.34147 5.33389i −0.373188 0.271137i
\(388\) 0 0
\(389\) −19.2319 + 13.9728i −0.975098 + 0.708450i −0.956608 0.291379i \(-0.905886\pi\)
−0.0184904 + 0.999829i \(0.505886\pi\)
\(390\) 0 0
\(391\) −14.4725 19.9197i −0.731905 1.00738i
\(392\) 0 0
\(393\) 36.3369 + 11.8066i 1.83295 + 0.595562i
\(394\) 0 0
\(395\) −1.37731 + 0.447514i −0.0692998 + 0.0225169i
\(396\) 0 0
\(397\) −10.7349 + 14.7753i −0.538770 + 0.741553i −0.988435 0.151644i \(-0.951543\pi\)
0.449665 + 0.893197i \(0.351543\pi\)
\(398\) 0 0
\(399\) 6.11440 + 1.98669i 0.306103 + 0.0994588i
\(400\) 0 0
\(401\) 6.65854 0.332512 0.166256 0.986083i \(-0.446832\pi\)
0.166256 + 0.986083i \(0.446832\pi\)
\(402\) 0 0
\(403\) −8.54480 11.7609i −0.425647 0.585852i
\(404\) 0 0
\(405\) −7.28026 22.4063i −0.361759 1.11338i
\(406\) 0 0
\(407\) 0.143919i 0.00713378i
\(408\) 0 0
\(409\) 23.0934 1.14189 0.570947 0.820987i \(-0.306576\pi\)
0.570947 + 0.820987i \(0.306576\pi\)
\(410\) 0 0
\(411\) −16.0818 −0.793259
\(412\) 0 0
\(413\) 2.56234i 0.126084i
\(414\) 0 0
\(415\) −6.21621 19.1315i −0.305142 0.939130i
\(416\) 0 0
\(417\) 24.0512 + 33.1037i 1.17779 + 1.62110i
\(418\) 0 0
\(419\) 32.3711 1.58143 0.790716 0.612183i \(-0.209708\pi\)
0.790716 + 0.612183i \(0.209708\pi\)
\(420\) 0 0
\(421\) −18.3641 5.96684i −0.895009 0.290806i −0.174834 0.984598i \(-0.555939\pi\)
−0.720176 + 0.693792i \(0.755939\pi\)
\(422\) 0 0
\(423\) −2.58535 + 3.55843i −0.125704 + 0.173017i
\(424\) 0 0
\(425\) −12.0836 + 3.92620i −0.586140 + 0.190449i
\(426\) 0 0
\(427\) 7.16042 + 2.32656i 0.346517 + 0.112590i
\(428\) 0 0
\(429\) −0.365499 0.503067i −0.0176465 0.0242883i
\(430\) 0 0
\(431\) −19.6933 + 14.3080i −0.948591 + 0.689192i −0.950473 0.310807i \(-0.899401\pi\)
0.00188235 + 0.999998i \(0.499401\pi\)
\(432\) 0 0
\(433\) −5.37243 3.90330i −0.258183 0.187581i 0.451163 0.892442i \(-0.351009\pi\)
−0.709346 + 0.704861i \(0.751009\pi\)
\(434\) 0 0
\(435\) 45.3601 32.9561i 2.17485 1.58012i
\(436\) 0 0
\(437\) 12.8058i 0.612585i
\(438\) 0 0
\(439\) −33.2402 + 10.8004i −1.58647 + 0.515474i −0.963712 0.266944i \(-0.913986\pi\)
−0.622754 + 0.782418i \(0.713986\pi\)
\(440\) 0 0
\(441\) 0.968794 2.98164i 0.0461330 0.141983i
\(442\) 0 0
\(443\) −0.410449 + 1.26323i −0.0195010 + 0.0600179i −0.960333 0.278854i \(-0.910045\pi\)
0.940832 + 0.338872i \(0.110045\pi\)
\(444\) 0 0
\(445\) −11.0290 + 15.1801i −0.522824 + 0.719605i
\(446\) 0 0
\(447\) 16.1978 + 49.8517i 0.766129 + 2.35790i
\(448\) 0 0
\(449\) −32.9213 23.9187i −1.55365 1.12880i −0.940981 0.338459i \(-0.890094\pi\)
−0.612673 0.790337i \(-0.709906\pi\)
\(450\) 0 0
\(451\) 1.01720 + 0.257918i 0.0478983 + 0.0121449i
\(452\) 0 0
\(453\) 42.8420 + 31.1265i 2.01289 + 1.46245i
\(454\) 0 0
\(455\) −1.30031 4.00196i −0.0609597 0.187615i
\(456\) 0 0
\(457\) −12.5892 + 17.3275i −0.588897 + 0.810548i −0.994636 0.103442i \(-0.967015\pi\)
0.405738 + 0.913989i \(0.367015\pi\)
\(458\) 0 0
\(459\) −0.515998 + 1.58808i −0.0240847 + 0.0741251i
\(460\) 0 0
\(461\) 5.30162 16.3167i 0.246921 0.759945i −0.748393 0.663255i \(-0.769174\pi\)
0.995315 0.0966901i \(-0.0308256\pi\)
\(462\) 0 0
\(463\) −28.2718 + 9.18607i −1.31390 + 0.426913i −0.880397 0.474238i \(-0.842724\pi\)
−0.433506 + 0.901151i \(0.642724\pi\)
\(464\) 0 0
\(465\) 64.5708i 2.99440i
\(466\) 0 0
\(467\) 20.3039 14.7516i 0.939551 0.682624i −0.00876181 0.999962i \(-0.502789\pi\)
0.948312 + 0.317338i \(0.102789\pi\)
\(468\) 0 0
\(469\) −3.27556 2.37984i −0.151251 0.109891i
\(470\) 0 0
\(471\) 14.8609 10.7971i 0.684754 0.497503i
\(472\) 0 0
\(473\) 0.278831 + 0.383778i 0.0128207 + 0.0176461i
\(474\) 0 0
\(475\) 6.28462 + 2.04200i 0.288358 + 0.0936932i
\(476\) 0 0
\(477\) −0.937867 + 0.304732i −0.0429420 + 0.0139527i
\(478\) 0 0
\(479\) −4.57051 + 6.29077i −0.208832 + 0.287433i −0.900566 0.434720i \(-0.856847\pi\)
0.691734 + 0.722153i \(0.256847\pi\)
\(480\) 0 0
\(481\) −1.27935 0.415686i −0.0583333 0.0189536i
\(482\) 0 0
\(483\) 12.2202 0.556040
\(484\) 0 0
\(485\) 18.9428 + 26.0725i 0.860146 + 1.18389i
\(486\) 0 0
\(487\) −5.43355 16.7227i −0.246218 0.757780i −0.995434 0.0954544i \(-0.969570\pi\)
0.749216 0.662326i \(-0.230430\pi\)
\(488\) 0 0
\(489\) 36.6864i 1.65902i
\(490\) 0 0
\(491\) 20.0345 0.904144 0.452072 0.891982i \(-0.350685\pi\)
0.452072 + 0.891982i \(0.350685\pi\)
\(492\) 0 0
\(493\) 41.1251 1.85218
\(494\) 0 0
\(495\) 1.41140i 0.0634377i
\(496\) 0 0
\(497\) 0.913945 + 2.81283i 0.0409960 + 0.126173i
\(498\) 0 0
\(499\) 15.2086 + 20.9328i 0.680830 + 0.937082i 0.999943 0.0106342i \(-0.00338503\pi\)
−0.319113 + 0.947717i \(0.603385\pi\)
\(500\) 0 0
\(501\) 56.3162 2.51602
\(502\) 0 0
\(503\) −35.5368 11.5466i −1.58451 0.514838i −0.621295 0.783577i \(-0.713393\pi\)
−0.963213 + 0.268739i \(0.913393\pi\)
\(504\) 0 0
\(505\) 5.44777 7.49821i 0.242422 0.333666i
\(506\) 0 0
\(507\) 25.0962 8.15426i 1.11456 0.362143i
\(508\) 0 0
\(509\) −21.6203 7.02485i −0.958301 0.311371i −0.212217 0.977223i \(-0.568068\pi\)
−0.746084 + 0.665852i \(0.768068\pi\)
\(510\) 0 0
\(511\) 5.53477 + 7.61796i 0.244844 + 0.336999i
\(512\) 0 0
\(513\) 0.702596 0.510466i 0.0310204 0.0225376i
\(514\) 0 0
\(515\) −3.74760 2.72279i −0.165139 0.119980i
\(516\) 0 0
\(517\) 0.186018 0.135150i 0.00818107 0.00594390i
\(518\) 0 0
\(519\) 12.4417i 0.546130i
\(520\) 0 0
\(521\) −42.3511 + 13.7607i −1.85544 + 0.602868i −0.859681 + 0.510831i \(0.829338\pi\)
−0.995756 + 0.0920373i \(0.970662\pi\)
\(522\) 0 0
\(523\) 4.49661 13.8391i 0.196623 0.605143i −0.803331 0.595533i \(-0.796941\pi\)
0.999954 0.00961007i \(-0.00305903\pi\)
\(524\) 0 0
\(525\) 1.94862 5.99724i 0.0850449 0.261741i
\(526\) 0 0
\(527\) 27.8384 38.3163i 1.21266 1.66908i
\(528\) 0 0
\(529\) 0.414410 + 1.27542i 0.0180178 + 0.0554532i
\(530\) 0 0
\(531\) −6.49895 4.72176i −0.282030 0.204907i
\(532\) 0 0
\(533\) 5.23076 8.29736i 0.226569 0.359399i
\(534\) 0 0
\(535\) 38.9325 + 28.2861i 1.68320 + 1.22292i
\(536\) 0 0
\(537\) −4.24538 13.0659i −0.183202 0.563837i
\(538\) 0 0
\(539\) −0.0963307 + 0.132588i −0.00414926 + 0.00571096i
\(540\) 0 0
\(541\) −8.17414 + 25.1574i −0.351434 + 1.08160i 0.606615 + 0.794996i \(0.292527\pi\)
−0.958049 + 0.286606i \(0.907473\pi\)
\(542\) 0 0
\(543\) −2.22087 + 6.83513i −0.0953066 + 0.293323i
\(544\) 0 0
\(545\) 22.1648 7.20177i 0.949434 0.308490i
\(546\) 0 0
\(547\) 15.3456i 0.656129i −0.944655 0.328064i \(-0.893604\pi\)
0.944655 0.328064i \(-0.106396\pi\)
\(548\) 0 0
\(549\) 19.0959 13.8739i 0.814991 0.592126i
\(550\) 0 0
\(551\) −17.3040 12.5721i −0.737176 0.535590i
\(552\) 0 0
\(553\) 0.426508 0.309876i 0.0181370 0.0131773i
\(554\) 0 0
\(555\) −3.51200 4.83385i −0.149076 0.205186i
\(556\) 0 0
\(557\) 25.6337 + 8.32889i 1.08613 + 0.352906i 0.796751 0.604307i \(-0.206550\pi\)
0.289382 + 0.957214i \(0.406550\pi\)
\(558\) 0 0
\(559\) 4.21691 1.37016i 0.178356 0.0579515i
\(560\) 0 0
\(561\) 1.19078 1.63896i 0.0502746 0.0691970i
\(562\) 0 0
\(563\) 22.1374 + 7.19289i 0.932981 + 0.303144i 0.735781 0.677219i \(-0.236815\pi\)
0.197200 + 0.980363i \(0.436815\pi\)
\(564\) 0 0
\(565\) 16.1381 0.678933
\(566\) 0 0
\(567\) 5.04114 + 6.93854i 0.211708 + 0.291391i
\(568\) 0 0
\(569\) −9.46306 29.1243i −0.396712 1.22095i −0.927620 0.373525i \(-0.878149\pi\)
0.530908 0.847430i \(-0.321851\pi\)
\(570\) 0 0
\(571\) 6.87036i 0.287516i 0.989613 + 0.143758i \(0.0459186\pi\)
−0.989613 + 0.143758i \(0.954081\pi\)
\(572\) 0 0
\(573\) 8.81699 0.368335
\(574\) 0 0
\(575\) 12.5604 0.523807
\(576\) 0 0
\(577\) 11.6288i 0.484115i 0.970262 + 0.242058i \(0.0778223\pi\)
−0.970262 + 0.242058i \(0.922178\pi\)
\(578\) 0 0
\(579\) −13.7642 42.3617i −0.572019 1.76049i
\(580\) 0 0
\(581\) 4.30435 + 5.92443i 0.178575 + 0.245787i
\(582\) 0 0
\(583\) 0.0515504 0.00213500
\(584\) 0 0
\(585\) −12.5465 4.07659i −0.518733 0.168546i
\(586\) 0 0
\(587\) −9.24716 + 12.7276i −0.381671 + 0.525325i −0.956026 0.293281i \(-0.905253\pi\)
0.574355 + 0.818606i \(0.305253\pi\)
\(588\) 0 0
\(589\) −23.4269 + 7.61186i −0.965289 + 0.313641i
\(590\) 0 0
\(591\) −40.0971 13.0284i −1.64938 0.535915i
\(592\) 0 0
\(593\) −14.7060 20.2410i −0.603901 0.831199i 0.392157 0.919898i \(-0.371729\pi\)
−0.996058 + 0.0886993i \(0.971729\pi\)
\(594\) 0 0
\(595\) 11.0909 8.05801i 0.454683 0.330346i
\(596\) 0 0
\(597\) 49.2228 + 35.7625i 2.01456 + 1.46366i
\(598\) 0 0
\(599\) −10.5101 + 7.63607i −0.429433 + 0.312001i −0.781422 0.624003i \(-0.785505\pi\)
0.351989 + 0.936004i \(0.385505\pi\)
\(600\) 0 0
\(601\) 41.5825i 1.69618i −0.529849 0.848092i \(-0.677751\pi\)
0.529849 0.848092i \(-0.322249\pi\)
\(602\) 0 0
\(603\) −12.0721 + 3.92247i −0.491615 + 0.159735i
\(604\) 0 0
\(605\) 9.31468 28.6676i 0.378695 1.16550i
\(606\) 0 0
\(607\) 4.59912 14.1546i 0.186672 0.574519i −0.813301 0.581844i \(-0.802332\pi\)
0.999973 + 0.00732491i \(0.00233161\pi\)
\(608\) 0 0
\(609\) −11.9972 + 16.5128i −0.486152 + 0.669131i
\(610\) 0 0
\(611\) −0.664119 2.04395i −0.0268674 0.0826892i
\(612\) 0 0
\(613\) 19.1568 + 13.9182i 0.773735 + 0.562151i 0.903092 0.429447i \(-0.141291\pi\)
−0.129358 + 0.991598i \(0.541291\pi\)
\(614\) 0 0
\(615\) 40.4591 16.1597i 1.63147 0.651621i
\(616\) 0 0
\(617\) −11.5918 8.42190i −0.466666 0.339053i 0.329474 0.944165i \(-0.393128\pi\)
−0.796141 + 0.605112i \(0.793128\pi\)
\(618\) 0 0
\(619\) 10.0788 + 31.0193i 0.405101 + 1.24677i 0.920811 + 0.390009i \(0.127528\pi\)
−0.515710 + 0.856763i \(0.672472\pi\)
\(620\) 0 0
\(621\) 0.970285 1.33548i 0.0389362 0.0535911i
\(622\) 0 0
\(623\) 2.11079 6.49634i 0.0845669 0.260270i
\(624\) 0 0
\(625\) −9.65613 + 29.7185i −0.386245 + 1.18874i
\(626\) 0 0
\(627\) −1.00207 + 0.325594i −0.0400190 + 0.0130030i
\(628\) 0 0
\(629\) 4.38254i 0.174743i
\(630\) 0 0
\(631\) 14.3712 10.4413i 0.572109 0.415661i −0.263762 0.964588i \(-0.584963\pi\)
0.835871 + 0.548926i \(0.184963\pi\)
\(632\) 0 0
\(633\) −40.3985 29.3512i −1.60570 1.16661i
\(634\) 0 0
\(635\) −12.4387 + 9.03724i −0.493614 + 0.358632i
\(636\) 0 0
\(637\) 0.900389 + 1.23928i 0.0356747 + 0.0491020i
\(638\) 0 0
\(639\) 8.81847 + 2.86529i 0.348853 + 0.113349i
\(640\) 0 0
\(641\) 6.55926 2.13123i 0.259075 0.0841786i −0.176600 0.984283i \(-0.556510\pi\)
0.435675 + 0.900104i \(0.356510\pi\)
\(642\) 0 0
\(643\) −27.1918 + 37.4263i −1.07234 + 1.47595i −0.204657 + 0.978834i \(0.565608\pi\)
−0.867684 + 0.497116i \(0.834392\pi\)
\(644\) 0 0
\(645\) 18.7304 + 6.08588i 0.737509 + 0.239631i
\(646\) 0 0
\(647\) −1.87973 −0.0738996 −0.0369498 0.999317i \(-0.511764\pi\)
−0.0369498 + 0.999317i \(0.511764\pi\)
\(648\) 0 0
\(649\) 0.246832 + 0.339735i 0.00968900 + 0.0133358i
\(650\) 0 0
\(651\) 7.26380 + 22.3557i 0.284691 + 0.876188i
\(652\) 0 0
\(653\) 33.9076i 1.32691i 0.748217 + 0.663454i \(0.230910\pi\)
−0.748217 + 0.663454i \(0.769090\pi\)
\(654\) 0 0
\(655\) −42.3726 −1.65563
\(656\) 0 0
\(657\) 29.5209 1.15172
\(658\) 0 0
\(659\) 6.71100i 0.261424i −0.991420 0.130712i \(-0.958274\pi\)
0.991420 0.130712i \(-0.0417263\pi\)
\(660\) 0 0
\(661\) 1.55752 + 4.79356i 0.0605806 + 0.186448i 0.976767 0.214305i \(-0.0687486\pi\)
−0.916186 + 0.400753i \(0.868749\pi\)
\(662\) 0 0
\(663\) −11.1300 15.3191i −0.432253 0.594946i
\(664\) 0 0
\(665\) −7.13004 −0.276491
\(666\) 0 0
\(667\) −38.6659 12.5633i −1.49715 0.486453i
\(668\) 0 0
\(669\) −1.23676 + 1.70226i −0.0478159 + 0.0658130i
\(670\) 0 0
\(671\) −1.17350 + 0.381295i −0.0453027 + 0.0147197i
\(672\) 0 0
\(673\) −1.03487 0.336250i −0.0398914 0.0129615i 0.289003 0.957328i \(-0.406676\pi\)
−0.328895 + 0.944367i \(0.606676\pi\)
\(674\) 0 0
\(675\) −0.500685 0.689134i −0.0192714 0.0265248i
\(676\) 0 0
\(677\) 15.1924 11.0379i 0.583892 0.424222i −0.256233 0.966615i \(-0.582482\pi\)
0.840125 + 0.542393i \(0.182482\pi\)
\(678\) 0 0
\(679\) −9.49134 6.89587i −0.364244 0.264639i
\(680\) 0 0
\(681\) 22.5419 16.3777i 0.863808 0.627593i
\(682\) 0 0
\(683\) 19.8963i 0.761309i −0.924717 0.380655i \(-0.875699\pi\)
0.924717 0.380655i \(-0.124301\pi\)
\(684\) 0 0
\(685\) 16.9624 5.51141i 0.648099 0.210580i
\(686\) 0 0
\(687\) 13.5463 41.6912i 0.516824 1.59062i
\(688\) 0 0
\(689\) 0.148895 0.458252i 0.00567245 0.0174580i
\(690\) 0 0
\(691\) 14.0448 19.3310i 0.534288 0.735385i −0.453488 0.891262i \(-0.649821\pi\)
0.987776 + 0.155878i \(0.0498206\pi\)
\(692\) 0 0
\(693\) 0.158773 + 0.488654i 0.00603130 + 0.0185624i
\(694\) 0 0
\(695\) −36.7131 26.6736i −1.39261 1.01179i
\(696\) 0 0
\(697\) 30.9754 + 7.85399i 1.17328 + 0.297491i
\(698\) 0 0
\(699\) −11.5716 8.40723i −0.437676 0.317990i
\(700\) 0 0
\(701\) 3.76115 + 11.5756i 0.142057 + 0.437206i 0.996621 0.0821402i \(-0.0261755\pi\)
−0.854564 + 0.519346i \(0.826176\pi\)
\(702\) 0 0
\(703\) −1.33976 + 1.84402i −0.0505300 + 0.0695486i
\(704\) 0 0
\(705\) 2.94984 9.07868i 0.111097 0.341923i
\(706\) 0 0
\(707\) −1.04262 + 3.20887i −0.0392119 + 0.120682i
\(708\) 0 0
\(709\) −19.8955 + 6.46443i −0.747190 + 0.242777i −0.657772 0.753217i \(-0.728501\pi\)
−0.0894185 + 0.995994i \(0.528501\pi\)
\(710\) 0 0
\(711\) 1.65279i 0.0619846i
\(712\) 0 0
\(713\) −37.8790 + 27.5207i −1.41858 + 1.03066i
\(714\) 0 0
\(715\) 0.557918 + 0.405351i 0.0208649 + 0.0151593i
\(716\) 0 0
\(717\) −11.5348 + 8.38050i −0.430774 + 0.312975i
\(718\) 0 0
\(719\) −17.7061 24.3703i −0.660325 0.908859i 0.339167 0.940726i \(-0.389855\pi\)
−0.999492 + 0.0318667i \(0.989855\pi\)
\(720\) 0 0
\(721\) 1.60379 + 0.521103i 0.0597282 + 0.0194069i
\(722\) 0 0
\(723\) −1.52667 + 0.496044i −0.0567773 + 0.0184481i
\(724\) 0 0
\(725\) −12.3312 + 16.9725i −0.457970 + 0.630341i
\(726\) 0 0
\(727\) −24.3722 7.91900i −0.903914 0.293700i −0.180063 0.983655i \(-0.557630\pi\)
−0.723852 + 0.689956i \(0.757630\pi\)
\(728\) 0 0
\(729\) 29.3743 1.08794
\(730\) 0 0
\(731\) 8.49082 + 11.6866i 0.314044 + 0.432245i
\(732\) 0 0
\(733\) −1.19680 3.68338i −0.0442049 0.136049i 0.926518 0.376250i \(-0.122787\pi\)
−0.970723 + 0.240201i \(0.922787\pi\)
\(734\) 0 0
\(735\) 6.80401i 0.250970i
\(736\) 0 0
\(737\) 0.663551 0.0244422
\(738\) 0 0
\(739\) 18.6299 0.685313 0.342657 0.939461i \(-0.388673\pi\)
0.342657 + 0.939461i \(0.388673\pi\)
\(740\) 0 0
\(741\) 9.84825i 0.361785i
\(742\) 0 0
\(743\) −4.46240 13.7339i −0.163710 0.503846i 0.835229 0.549902i \(-0.185335\pi\)
−0.998939 + 0.0460556i \(0.985335\pi\)
\(744\) 0 0
\(745\) −34.1693 47.0301i −1.25187 1.72305i
\(746\) 0 0
\(747\) 22.9582 0.839997
\(748\) 0 0
\(749\) −16.6612 5.41356i −0.608788 0.197807i
\(750\) 0 0
\(751\) 3.81761 5.25449i 0.139307 0.191739i −0.733663 0.679513i \(-0.762191\pi\)
0.872970 + 0.487774i \(0.162191\pi\)
\(752\) 0 0
\(753\) 5.52478 1.79511i 0.201334 0.0654174i
\(754\) 0 0
\(755\) −55.8551 18.1484i −2.03277 0.660488i
\(756\) 0 0
\(757\) −14.2623 19.6304i −0.518372 0.713478i 0.466931 0.884294i \(-0.345360\pi\)
−0.985303 + 0.170816i \(0.945360\pi\)
\(758\) 0 0
\(759\) −1.62026 + 1.17719i −0.0588116 + 0.0427291i
\(760\) 0 0
\(761\) −25.4652 18.5015i −0.923112 0.670680i 0.0211847 0.999776i \(-0.493256\pi\)
−0.944297 + 0.329096i \(0.893256\pi\)
\(762\) 0 0
\(763\) −6.86373 + 4.98679i −0.248484 + 0.180534i
\(764\) 0 0
\(765\) 42.9792i 1.55392i
\(766\) 0 0
\(767\) 3.73297 1.21292i 0.134790 0.0437958i
\(768\) 0 0
\(769\) −12.8712 + 39.6134i −0.464147 + 1.42850i 0.395905 + 0.918291i \(0.370431\pi\)
−0.860052 + 0.510206i \(0.829569\pi\)
\(770\) 0 0
\(771\) −6.37139 + 19.6091i −0.229460 + 0.706205i
\(772\) 0 0
\(773\) 25.8514 35.5814i 0.929811 1.27977i −0.0301226 0.999546i \(-0.509590\pi\)
0.959933 0.280228i \(-0.0904102\pi\)
\(774\) 0 0
\(775\) 7.46601 + 22.9780i 0.268187 + 0.825395i
\(776\) 0 0
\(777\) 1.75970 + 1.27850i 0.0631289 + 0.0458658i
\(778\) 0 0
\(779\) −10.6324 12.7740i −0.380944 0.457676i
\(780\) 0 0
\(781\) −0.392140 0.284907i −0.0140319 0.0101948i
\(782\) 0 0
\(783\) 0.852011 + 2.62222i 0.0304484 + 0.0937105i
\(784\) 0 0
\(785\) −11.9743 + 16.4812i −0.427381 + 0.588240i
\(786\) 0 0
\(787\) −0.650560 + 2.00222i −0.0231899 + 0.0713713i −0.961982 0.273114i \(-0.911946\pi\)
0.938792 + 0.344485i \(0.111946\pi\)
\(788\) 0 0
\(789\) 5.92449 18.2337i 0.210918 0.649137i
\(790\) 0 0
\(791\) −5.58731 + 1.81543i −0.198662 + 0.0645492i
\(792\) 0 0
\(793\) 11.5330i 0.409550i
\(794\) 0 0
\(795\) 1.73144 1.25797i 0.0614080 0.0446155i
\(796\) 0 0
\(797\) −4.38745 3.18767i −0.155411