Properties

Label 1520.2.q.j.881.1
Level $1520$
Weight $2$
Character 1520.881
Analytic conductor $12.137$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1520.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.1372611072\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.3518667.1
Defining polynomial: \( x^{6} - x^{5} + 7x^{4} - 8x^{3} + 43x^{2} - 42x + 49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 881.1
Root \(-1.25351 - 2.17114i\) of defining polynomial
Character \(\chi\) \(=\) 1520.881
Dual form 1520.2.q.j.961.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.25351 - 2.17114i) q^{3} +(0.500000 + 0.866025i) q^{5} -3.50702 q^{7} +(-1.64257 + 2.84502i) q^{9} +O(q^{10})\) \(q+(-1.25351 - 2.17114i) q^{3} +(0.500000 + 0.866025i) q^{5} -3.50702 q^{7} +(-1.64257 + 2.84502i) q^{9} +4.50702 q^{11} +(2.50000 - 4.33013i) q^{13} +(1.25351 - 2.17114i) q^{15} +(-0.0793049 - 0.137360i) q^{17} +(4.26053 + 0.920816i) q^{19} +(4.39608 + 7.61423i) q^{21} +(0.579305 - 1.00339i) q^{23} +(-0.500000 + 0.866025i) q^{25} +0.714858 q^{27} +(1.75351 - 3.03717i) q^{29} +2.28514 q^{31} +(-5.64959 - 9.78538i) q^{33} +(-1.75351 - 3.03717i) q^{35} -10.9648 q^{37} -12.5351 q^{39} +(-3.03865 - 5.26310i) q^{41} +(-1.67420 - 2.89981i) q^{43} -3.28514 q^{45} +(1.53163 - 2.65287i) q^{47} +5.29918 q^{49} +(-0.198819 + 0.344364i) q^{51} +(2.87147 - 4.97353i) q^{53} +(2.25351 + 3.90319i) q^{55} +(-3.34139 - 10.4045i) q^{57} +(1.53163 + 2.65287i) q^{59} +(0.436734 - 0.756445i) q^{61} +(5.76053 - 9.97753i) q^{63} +5.00000 q^{65} +(-4.22188 + 7.31250i) q^{67} -2.90466 q^{69} +(-8.11796 - 14.0607i) q^{71} +(3.57930 + 6.19954i) q^{73} +2.50702 q^{75} -15.8062 q^{77} +(-5.06327 - 8.76983i) q^{79} +(4.03163 + 6.98299i) q^{81} -4.85543 q^{83} +(0.0793049 - 0.137360i) q^{85} -8.79216 q^{87} +(0.556248 - 0.963449i) q^{89} +(-8.76755 + 15.1858i) q^{91} +(-2.86445 - 4.96137i) q^{93} +(1.33281 + 4.15013i) q^{95} +(-0.809757 - 1.40254i) q^{97} +(-7.40310 + 12.8225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{3} + 3 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + q^{3} + 3 q^{5} - 4 q^{7} - 4 q^{9} + 10 q^{11} + 15 q^{13} - q^{15} - q^{17} + 12 q^{21} + 4 q^{23} - 3 q^{25} + 16 q^{27} + 2 q^{29} + 2 q^{31} - 11 q^{33} - 2 q^{35} - 4 q^{37} + 10 q^{39} + 2 q^{41} - q^{43} - 8 q^{45} + 6 q^{47} - 14 q^{49} - 6 q^{51} - 11 q^{53} + 5 q^{55} - 19 q^{57} + 6 q^{59} + 9 q^{61} + 9 q^{63} + 30 q^{65} - 20 q^{67} - 10 q^{69} - 29 q^{71} + 22 q^{73} - 2 q^{75} - 32 q^{77} - 24 q^{79} + 21 q^{81} + 6 q^{83} + q^{85} - 24 q^{87} + 14 q^{89} - 10 q^{91} - 6 q^{93} - 7 q^{97} - 13 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(401\) \(1141\) \(1217\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.25351 2.17114i −0.723714 1.25351i −0.959501 0.281705i \(-0.909100\pi\)
0.235787 0.971805i \(-0.424233\pi\)
\(4\) 0 0
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) −3.50702 −1.32553 −0.662764 0.748828i \(-0.730617\pi\)
−0.662764 + 0.748828i \(0.730617\pi\)
\(8\) 0 0
\(9\) −1.64257 + 2.84502i −0.547524 + 0.948339i
\(10\) 0 0
\(11\) 4.50702 1.35892 0.679459 0.733714i \(-0.262215\pi\)
0.679459 + 0.733714i \(0.262215\pi\)
\(12\) 0 0
\(13\) 2.50000 4.33013i 0.693375 1.20096i −0.277350 0.960769i \(-0.589456\pi\)
0.970725 0.240192i \(-0.0772105\pi\)
\(14\) 0 0
\(15\) 1.25351 2.17114i 0.323655 0.560586i
\(16\) 0 0
\(17\) −0.0793049 0.137360i −0.0192343 0.0333147i 0.856248 0.516565i \(-0.172790\pi\)
−0.875482 + 0.483250i \(0.839456\pi\)
\(18\) 0 0
\(19\) 4.26053 + 0.920816i 0.977432 + 0.211250i
\(20\) 0 0
\(21\) 4.39608 + 7.61423i 0.959303 + 1.66156i
\(22\) 0 0
\(23\) 0.579305 1.00339i 0.120793 0.209220i −0.799287 0.600949i \(-0.794789\pi\)
0.920081 + 0.391729i \(0.128123\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 0.714858 0.137574
\(28\) 0 0
\(29\) 1.75351 3.03717i 0.325619 0.563988i −0.656019 0.754745i \(-0.727761\pi\)
0.981637 + 0.190757i \(0.0610942\pi\)
\(30\) 0 0
\(31\) 2.28514 0.410424 0.205212 0.978718i \(-0.434212\pi\)
0.205212 + 0.978718i \(0.434212\pi\)
\(32\) 0 0
\(33\) −5.64959 9.78538i −0.983467 1.70342i
\(34\) 0 0
\(35\) −1.75351 3.03717i −0.296397 0.513375i
\(36\) 0 0
\(37\) −10.9648 −1.80260 −0.901302 0.433192i \(-0.857387\pi\)
−0.901302 + 0.433192i \(0.857387\pi\)
\(38\) 0 0
\(39\) −12.5351 −2.00722
\(40\) 0 0
\(41\) −3.03865 5.26310i −0.474558 0.821958i 0.525018 0.851091i \(-0.324059\pi\)
−0.999576 + 0.0291332i \(0.990725\pi\)
\(42\) 0 0
\(43\) −1.67420 2.89981i −0.255314 0.442216i 0.709667 0.704537i \(-0.248845\pi\)
−0.964981 + 0.262321i \(0.915512\pi\)
\(44\) 0 0
\(45\) −3.28514 −0.489720
\(46\) 0 0
\(47\) 1.53163 2.65287i 0.223412 0.386960i −0.732430 0.680842i \(-0.761614\pi\)
0.955842 + 0.293882i \(0.0949472\pi\)
\(48\) 0 0
\(49\) 5.29918 0.757026
\(50\) 0 0
\(51\) −0.198819 + 0.344364i −0.0278402 + 0.0482207i
\(52\) 0 0
\(53\) 2.87147 4.97353i 0.394426 0.683166i −0.598602 0.801047i \(-0.704277\pi\)
0.993028 + 0.117881i \(0.0376100\pi\)
\(54\) 0 0
\(55\) 2.25351 + 3.90319i 0.303863 + 0.526306i
\(56\) 0 0
\(57\) −3.34139 10.4045i −0.442578 1.37810i
\(58\) 0 0
\(59\) 1.53163 + 2.65287i 0.199402 + 0.345374i 0.948335 0.317272i \(-0.102767\pi\)
−0.748933 + 0.662646i \(0.769433\pi\)
\(60\) 0 0
\(61\) 0.436734 0.756445i 0.0559180 0.0968528i −0.836711 0.547644i \(-0.815525\pi\)
0.892629 + 0.450791i \(0.148858\pi\)
\(62\) 0 0
\(63\) 5.76053 9.97753i 0.725758 1.25705i
\(64\) 0 0
\(65\) 5.00000 0.620174
\(66\) 0 0
\(67\) −4.22188 + 7.31250i −0.515784 + 0.893365i 0.484048 + 0.875042i \(0.339166\pi\)
−0.999832 + 0.0183230i \(0.994167\pi\)
\(68\) 0 0
\(69\) −2.90466 −0.349680
\(70\) 0 0
\(71\) −8.11796 14.0607i −0.963424 1.66870i −0.713790 0.700359i \(-0.753023\pi\)
−0.249634 0.968340i \(-0.580310\pi\)
\(72\) 0 0
\(73\) 3.57930 + 6.19954i 0.418926 + 0.725601i 0.995832 0.0912097i \(-0.0290733\pi\)
−0.576906 + 0.816811i \(0.695740\pi\)
\(74\) 0 0
\(75\) 2.50702 0.289486
\(76\) 0 0
\(77\) −15.8062 −1.80128
\(78\) 0 0
\(79\) −5.06327 8.76983i −0.569662 0.986683i −0.996599 0.0824022i \(-0.973741\pi\)
0.426937 0.904281i \(-0.359593\pi\)
\(80\) 0 0
\(81\) 4.03163 + 6.98299i 0.447959 + 0.775888i
\(82\) 0 0
\(83\) −4.85543 −0.532952 −0.266476 0.963841i \(-0.585859\pi\)
−0.266476 + 0.963841i \(0.585859\pi\)
\(84\) 0 0
\(85\) 0.0793049 0.137360i 0.00860183 0.0148988i
\(86\) 0 0
\(87\) −8.79216 −0.942619
\(88\) 0 0
\(89\) 0.556248 0.963449i 0.0589621 0.102125i −0.835038 0.550193i \(-0.814554\pi\)
0.894000 + 0.448067i \(0.147888\pi\)
\(90\) 0 0
\(91\) −8.76755 + 15.1858i −0.919089 + 1.59191i
\(92\) 0 0
\(93\) −2.86445 4.96137i −0.297029 0.514470i
\(94\) 0 0
\(95\) 1.33281 + 4.15013i 0.136744 + 0.425795i
\(96\) 0 0
\(97\) −0.809757 1.40254i −0.0822184 0.142406i 0.821984 0.569510i \(-0.192867\pi\)
−0.904203 + 0.427104i \(0.859534\pi\)
\(98\) 0 0
\(99\) −7.40310 + 12.8225i −0.744039 + 1.28871i
\(100\) 0 0
\(101\) −6.15661 + 10.6636i −0.612605 + 1.06106i 0.378194 + 0.925726i \(0.376545\pi\)
−0.990800 + 0.135337i \(0.956788\pi\)
\(102\) 0 0
\(103\) −10.6164 −1.04606 −0.523032 0.852313i \(-0.675199\pi\)
−0.523032 + 0.852313i \(0.675199\pi\)
\(104\) 0 0
\(105\) −4.39608 + 7.61423i −0.429014 + 0.743073i
\(106\) 0 0
\(107\) 2.17265 0.210038 0.105019 0.994470i \(-0.466510\pi\)
0.105019 + 0.994470i \(0.466510\pi\)
\(108\) 0 0
\(109\) −7.91012 13.7007i −0.757652 1.31229i −0.944045 0.329816i \(-0.893013\pi\)
0.186393 0.982475i \(-0.440320\pi\)
\(110\) 0 0
\(111\) 13.7445 + 23.8062i 1.30457 + 2.25958i
\(112\) 0 0
\(113\) 9.83828 0.925507 0.462754 0.886487i \(-0.346861\pi\)
0.462754 + 0.886487i \(0.346861\pi\)
\(114\) 0 0
\(115\) 1.15861 0.108041
\(116\) 0 0
\(117\) 8.21286 + 14.2251i 0.759279 + 1.31511i
\(118\) 0 0
\(119\) 0.278124 + 0.481725i 0.0254956 + 0.0441596i
\(120\) 0 0
\(121\) 9.31322 0.846656
\(122\) 0 0
\(123\) −7.61796 + 13.1947i −0.686888 + 1.18972i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 7.85543 13.6060i 0.697056 1.20734i −0.272426 0.962177i \(-0.587826\pi\)
0.969483 0.245160i \(-0.0788407\pi\)
\(128\) 0 0
\(129\) −4.19726 + 7.26987i −0.369548 + 0.640076i
\(130\) 0 0
\(131\) −5.76755 9.98968i −0.503913 0.872803i −0.999990 0.00452412i \(-0.998560\pi\)
0.496077 0.868279i \(-0.334773\pi\)
\(132\) 0 0
\(133\) −14.9418 3.22932i −1.29561 0.280017i
\(134\) 0 0
\(135\) 0.357429 + 0.619085i 0.0307626 + 0.0532823i
\(136\) 0 0
\(137\) −0.0546904 + 0.0947266i −0.00467252 + 0.00809304i −0.868352 0.495948i \(-0.834821\pi\)
0.863680 + 0.504041i \(0.168154\pi\)
\(138\) 0 0
\(139\) 0.721876 1.25033i 0.0612287 0.106051i −0.833786 0.552088i \(-0.813831\pi\)
0.895015 + 0.446036i \(0.147165\pi\)
\(140\) 0 0
\(141\) −7.67967 −0.646745
\(142\) 0 0
\(143\) 11.2675 19.5160i 0.942240 1.63201i
\(144\) 0 0
\(145\) 3.50702 0.291242
\(146\) 0 0
\(147\) −6.64257 11.5053i −0.547870 0.948939i
\(148\) 0 0
\(149\) −0.864447 1.49727i −0.0708183 0.122661i 0.828442 0.560075i \(-0.189228\pi\)
−0.899260 + 0.437414i \(0.855894\pi\)
\(150\) 0 0
\(151\) 20.1406 1.63902 0.819508 0.573068i \(-0.194247\pi\)
0.819508 + 0.573068i \(0.194247\pi\)
\(152\) 0 0
\(153\) 0.521056 0.0421249
\(154\) 0 0
\(155\) 1.14257 + 1.97899i 0.0917735 + 0.158956i
\(156\) 0 0
\(157\) −1.88906 3.27195i −0.150764 0.261130i 0.780745 0.624850i \(-0.214840\pi\)
−0.931508 + 0.363720i \(0.881507\pi\)
\(158\) 0 0
\(159\) −14.3976 −1.14181
\(160\) 0 0
\(161\) −2.03163 + 3.51889i −0.160115 + 0.277328i
\(162\) 0 0
\(163\) 1.61640 0.126606 0.0633031 0.997994i \(-0.479837\pi\)
0.0633031 + 0.997994i \(0.479837\pi\)
\(164\) 0 0
\(165\) 5.64959 9.78538i 0.439820 0.761791i
\(166\) 0 0
\(167\) 3.24649 5.62309i 0.251221 0.435128i −0.712641 0.701529i \(-0.752501\pi\)
0.963862 + 0.266401i \(0.0858346\pi\)
\(168\) 0 0
\(169\) −6.00000 10.3923i −0.461538 0.799408i
\(170\) 0 0
\(171\) −9.61796 + 10.6088i −0.735504 + 0.811273i
\(172\) 0 0
\(173\) −4.26053 7.37945i −0.323922 0.561049i 0.657372 0.753567i \(-0.271668\pi\)
−0.981294 + 0.192517i \(0.938335\pi\)
\(174\) 0 0
\(175\) 1.75351 3.03717i 0.132553 0.229588i
\(176\) 0 0
\(177\) 3.83983 6.65079i 0.288620 0.499904i
\(178\) 0 0
\(179\) 10.2711 0.767698 0.383849 0.923396i \(-0.374598\pi\)
0.383849 + 0.923396i \(0.374598\pi\)
\(180\) 0 0
\(181\) −6.13355 + 10.6236i −0.455903 + 0.789648i −0.998740 0.0501908i \(-0.984017\pi\)
0.542836 + 0.839838i \(0.317350\pi\)
\(182\) 0 0
\(183\) −2.18980 −0.161875
\(184\) 0 0
\(185\) −5.48240 9.49580i −0.403074 0.698145i
\(186\) 0 0
\(187\) −0.357429 0.619085i −0.0261378 0.0452720i
\(188\) 0 0
\(189\) −2.50702 −0.182359
\(190\) 0 0
\(191\) −5.71085 −0.413223 −0.206611 0.978423i \(-0.566244\pi\)
−0.206611 + 0.978423i \(0.566244\pi\)
\(192\) 0 0
\(193\) 5.07930 + 8.79761i 0.365616 + 0.633266i 0.988875 0.148750i \(-0.0475249\pi\)
−0.623259 + 0.782016i \(0.714192\pi\)
\(194\) 0 0
\(195\) −6.26755 10.8557i −0.448828 0.777393i
\(196\) 0 0
\(197\) 16.2038 1.15448 0.577238 0.816576i \(-0.304131\pi\)
0.577238 + 0.816576i \(0.304131\pi\)
\(198\) 0 0
\(199\) 0.167186 0.289574i 0.0118515 0.0205274i −0.860039 0.510229i \(-0.829561\pi\)
0.871890 + 0.489701i \(0.162894\pi\)
\(200\) 0 0
\(201\) 21.1686 1.49312
\(202\) 0 0
\(203\) −6.14959 + 10.6514i −0.431617 + 0.747582i
\(204\) 0 0
\(205\) 3.03865 5.26310i 0.212229 0.367591i
\(206\) 0 0
\(207\) 1.90310 + 3.29626i 0.132275 + 0.229106i
\(208\) 0 0
\(209\) 19.2023 + 4.15013i 1.32825 + 0.287071i
\(210\) 0 0
\(211\) 1.01404 + 1.75636i 0.0698092 + 0.120913i 0.898817 0.438324i \(-0.144428\pi\)
−0.829008 + 0.559237i \(0.811094\pi\)
\(212\) 0 0
\(213\) −20.3519 + 35.2505i −1.39449 + 2.41532i
\(214\) 0 0
\(215\) 1.67420 2.89981i 0.114180 0.197765i
\(216\) 0 0
\(217\) −8.01404 −0.544028
\(218\) 0 0
\(219\) 8.97338 15.5424i 0.606365 1.05026i
\(220\) 0 0
\(221\) −0.793049 −0.0533463
\(222\) 0 0
\(223\) −9.61596 16.6553i −0.643932 1.11532i −0.984547 0.175120i \(-0.943969\pi\)
0.340615 0.940203i \(-0.389365\pi\)
\(224\) 0 0
\(225\) −1.64257 2.84502i −0.109505 0.189668i
\(226\) 0 0
\(227\) −4.00000 −0.265489 −0.132745 0.991150i \(-0.542379\pi\)
−0.132745 + 0.991150i \(0.542379\pi\)
\(228\) 0 0
\(229\) −12.9788 −0.857666 −0.428833 0.903384i \(-0.641075\pi\)
−0.428833 + 0.903384i \(0.641075\pi\)
\(230\) 0 0
\(231\) 19.8132 + 34.3175i 1.30361 + 2.25793i
\(232\) 0 0
\(233\) −13.5367 23.4462i −0.886815 1.53601i −0.843619 0.536943i \(-0.819579\pi\)
−0.0431968 0.999067i \(-0.513754\pi\)
\(234\) 0 0
\(235\) 3.06327 0.199825
\(236\) 0 0
\(237\) −12.6937 + 21.9861i −0.824545 + 1.42815i
\(238\) 0 0
\(239\) −20.0602 −1.29758 −0.648792 0.760966i \(-0.724725\pi\)
−0.648792 + 0.760966i \(0.724725\pi\)
\(240\) 0 0
\(241\) 10.7922 18.6926i 0.695184 1.20409i −0.274934 0.961463i \(-0.588656\pi\)
0.970119 0.242631i \(-0.0780105\pi\)
\(242\) 0 0
\(243\) 11.1797 19.3637i 0.717176 1.24219i
\(244\) 0 0
\(245\) 2.64959 + 4.58922i 0.169276 + 0.293195i
\(246\) 0 0
\(247\) 14.6386 16.1466i 0.931430 1.02738i
\(248\) 0 0
\(249\) 6.08632 + 10.5418i 0.385705 + 0.668061i
\(250\) 0 0
\(251\) −3.63400 + 6.29426i −0.229376 + 0.397290i −0.957623 0.288024i \(-0.907002\pi\)
0.728248 + 0.685314i \(0.240335\pi\)
\(252\) 0 0
\(253\) 2.61094 4.52228i 0.164148 0.284313i
\(254\) 0 0
\(255\) −0.397638 −0.0249010
\(256\) 0 0
\(257\) −7.53865 + 13.0573i −0.470248 + 0.814494i −0.999421 0.0340202i \(-0.989169\pi\)
0.529173 + 0.848514i \(0.322502\pi\)
\(258\) 0 0
\(259\) 38.4538 2.38940
\(260\) 0 0
\(261\) 5.76053 + 9.97753i 0.356568 + 0.617593i
\(262\) 0 0
\(263\) 10.0773 + 17.4544i 0.621393 + 1.07628i 0.989227 + 0.146393i \(0.0467663\pi\)
−0.367833 + 0.929892i \(0.619900\pi\)
\(264\) 0 0
\(265\) 5.74293 0.352786
\(266\) 0 0
\(267\) −2.78905 −0.170687
\(268\) 0 0
\(269\) 3.86245 + 6.68995i 0.235497 + 0.407894i 0.959417 0.281991i \(-0.0909947\pi\)
−0.723920 + 0.689884i \(0.757661\pi\)
\(270\) 0 0
\(271\) −2.64257 4.57707i −0.160525 0.278037i 0.774532 0.632534i \(-0.217985\pi\)
−0.935057 + 0.354497i \(0.884652\pi\)
\(272\) 0 0
\(273\) 43.9608 2.66063
\(274\) 0 0
\(275\) −2.25351 + 3.90319i −0.135892 + 0.235371i
\(276\) 0 0
\(277\) 30.6264 1.84016 0.920082 0.391726i \(-0.128122\pi\)
0.920082 + 0.391726i \(0.128122\pi\)
\(278\) 0 0
\(279\) −3.75351 + 6.50127i −0.224717 + 0.389221i
\(280\) 0 0
\(281\) −6.68122 + 11.5722i −0.398568 + 0.690341i −0.993550 0.113399i \(-0.963826\pi\)
0.594981 + 0.803740i \(0.297159\pi\)
\(282\) 0 0
\(283\) 2.04767 + 3.54667i 0.121721 + 0.210828i 0.920447 0.390868i \(-0.127825\pi\)
−0.798725 + 0.601696i \(0.794492\pi\)
\(284\) 0 0
\(285\) 7.33983 8.09596i 0.434774 0.479563i
\(286\) 0 0
\(287\) 10.6566 + 18.4578i 0.629040 + 1.08953i
\(288\) 0 0
\(289\) 8.48742 14.7006i 0.499260 0.864744i
\(290\) 0 0
\(291\) −2.03008 + 3.51619i −0.119005 + 0.206123i
\(292\) 0 0
\(293\) 12.1726 0.711134 0.355567 0.934651i \(-0.384288\pi\)
0.355567 + 0.934651i \(0.384288\pi\)
\(294\) 0 0
\(295\) −1.53163 + 2.65287i −0.0891751 + 0.154456i
\(296\) 0 0
\(297\) 3.22188 0.186952
\(298\) 0 0
\(299\) −2.89652 5.01693i −0.167510 0.290136i
\(300\) 0 0
\(301\) 5.87147 + 10.1697i 0.338426 + 0.586170i
\(302\) 0 0
\(303\) 30.8695 1.77340
\(304\) 0 0
\(305\) 0.873467 0.0500146
\(306\) 0 0
\(307\) 12.2675 + 21.2480i 0.700146 + 1.21269i 0.968415 + 0.249344i \(0.0802150\pi\)
−0.268269 + 0.963344i \(0.586452\pi\)
\(308\) 0 0
\(309\) 13.3078 + 23.0497i 0.757052 + 1.31125i
\(310\) 0 0
\(311\) 10.2038 0.578606 0.289303 0.957238i \(-0.406576\pi\)
0.289303 + 0.957238i \(0.406576\pi\)
\(312\) 0 0
\(313\) 15.9910 27.6972i 0.903864 1.56554i 0.0814282 0.996679i \(-0.474052\pi\)
0.822435 0.568859i \(-0.192615\pi\)
\(314\) 0 0
\(315\) 11.5211 0.649138
\(316\) 0 0
\(317\) −1.11796 + 1.93636i −0.0627907 + 0.108757i −0.895712 0.444635i \(-0.853333\pi\)
0.832921 + 0.553392i \(0.186667\pi\)
\(318\) 0 0
\(319\) 7.90310 13.6886i 0.442489 0.766413i
\(320\) 0 0
\(321\) −2.72343 4.71713i −0.152007 0.263284i
\(322\) 0 0
\(323\) −0.211397 0.658252i −0.0117625 0.0366261i
\(324\) 0 0
\(325\) 2.50000 + 4.33013i 0.138675 + 0.240192i
\(326\) 0 0
\(327\) −19.8308 + 34.3480i −1.09665 + 1.89945i
\(328\) 0 0
\(329\) −5.37147 + 9.30365i −0.296139 + 0.512927i
\(330\) 0 0
\(331\) 10.0913 0.554670 0.277335 0.960773i \(-0.410549\pi\)
0.277335 + 0.960773i \(0.410549\pi\)
\(332\) 0 0
\(333\) 18.0105 31.1951i 0.986968 1.70948i
\(334\) 0 0
\(335\) −8.44375 −0.461331
\(336\) 0 0
\(337\) −2.80620 4.86048i −0.152863 0.264767i 0.779416 0.626507i \(-0.215516\pi\)
−0.932279 + 0.361740i \(0.882183\pi\)
\(338\) 0 0
\(339\) −12.3324 21.3603i −0.669802 1.16013i
\(340\) 0 0
\(341\) 10.2992 0.557732
\(342\) 0 0
\(343\) 5.96481 0.322069
\(344\) 0 0
\(345\) −1.45233 2.51551i −0.0781907 0.135430i
\(346\) 0 0
\(347\) 2.73747 + 4.74144i 0.146955 + 0.254534i 0.930101 0.367305i \(-0.119719\pi\)
−0.783146 + 0.621838i \(0.786386\pi\)
\(348\) 0 0
\(349\) −18.8202 −1.00742 −0.503712 0.863872i \(-0.668033\pi\)
−0.503712 + 0.863872i \(0.668033\pi\)
\(350\) 0 0
\(351\) 1.78714 3.09542i 0.0953907 0.165222i
\(352\) 0 0
\(353\) −12.7008 −0.675996 −0.337998 0.941147i \(-0.609750\pi\)
−0.337998 + 0.941147i \(0.609750\pi\)
\(354\) 0 0
\(355\) 8.11796 14.0607i 0.430856 0.746265i
\(356\) 0 0
\(357\) 0.697262 1.20769i 0.0369030 0.0639179i
\(358\) 0 0
\(359\) −5.54021 9.59592i −0.292401 0.506453i 0.681976 0.731375i \(-0.261121\pi\)
−0.974377 + 0.224921i \(0.927788\pi\)
\(360\) 0 0
\(361\) 17.3042 + 7.84632i 0.910747 + 0.412964i
\(362\) 0 0
\(363\) −11.6742 20.2203i −0.612737 1.06129i
\(364\) 0 0
\(365\) −3.57930 + 6.19954i −0.187349 + 0.324499i
\(366\) 0 0
\(367\) −10.3202 + 17.8752i −0.538712 + 0.933076i 0.460262 + 0.887783i \(0.347756\pi\)
−0.998974 + 0.0452932i \(0.985578\pi\)
\(368\) 0 0
\(369\) 19.9648 1.03933
\(370\) 0 0
\(371\) −10.0703 + 17.4422i −0.522823 + 0.905556i
\(372\) 0 0
\(373\) 4.55313 0.235752 0.117876 0.993028i \(-0.462391\pi\)
0.117876 + 0.993028i \(0.462391\pi\)
\(374\) 0 0
\(375\) 1.25351 + 2.17114i 0.0647309 + 0.112117i
\(376\) 0 0
\(377\) −8.76755 15.1858i −0.451552 0.782110i
\(378\) 0 0
\(379\) 19.9187 1.02315 0.511577 0.859237i \(-0.329061\pi\)
0.511577 + 0.859237i \(0.329061\pi\)
\(380\) 0 0
\(381\) −39.3874 −2.01788
\(382\) 0 0
\(383\) −9.98742 17.2987i −0.510333 0.883923i −0.999928 0.0119734i \(-0.996189\pi\)
0.489595 0.871950i \(-0.337145\pi\)
\(384\) 0 0
\(385\) −7.90310 13.6886i −0.402779 0.697634i
\(386\) 0 0
\(387\) 11.0000 0.559161
\(388\) 0 0
\(389\) −6.90110 + 11.9531i −0.349900 + 0.606044i −0.986231 0.165372i \(-0.947118\pi\)
0.636332 + 0.771416i \(0.280451\pi\)
\(390\) 0 0
\(391\) −0.183767 −0.00929349
\(392\) 0 0
\(393\) −14.4593 + 25.0443i −0.729378 + 1.26332i
\(394\) 0 0
\(395\) 5.06327 8.76983i 0.254761 0.441258i
\(396\) 0 0
\(397\) 8.27457 + 14.3320i 0.415289 + 0.719301i 0.995459 0.0951945i \(-0.0303473\pi\)
−0.580170 + 0.814495i \(0.697014\pi\)
\(398\) 0 0
\(399\) 11.7183 + 36.4886i 0.586650 + 1.82672i
\(400\) 0 0
\(401\) −4.26253 7.38292i −0.212861 0.368685i 0.739748 0.672884i \(-0.234945\pi\)
−0.952609 + 0.304199i \(0.901611\pi\)
\(402\) 0 0
\(403\) 5.71286 9.89496i 0.284578 0.492903i
\(404\) 0 0
\(405\) −4.03163 + 6.98299i −0.200333 + 0.346988i
\(406\) 0 0
\(407\) −49.4186 −2.44959
\(408\) 0 0
\(409\) 5.78314 10.0167i 0.285958 0.495294i −0.686883 0.726768i \(-0.741022\pi\)
0.972841 + 0.231474i \(0.0743549\pi\)
\(410\) 0 0
\(411\) 0.274220 0.0135263
\(412\) 0 0
\(413\) −5.37147 9.30365i −0.264313 0.457803i
\(414\) 0 0
\(415\) −2.42771 4.20492i −0.119172 0.206412i
\(416\) 0 0
\(417\) −3.61951 −0.177248
\(418\) 0 0
\(419\) 21.7149 1.06084 0.530420 0.847735i \(-0.322034\pi\)
0.530420 + 0.847735i \(0.322034\pi\)
\(420\) 0 0
\(421\) 3.46135 + 5.99523i 0.168696 + 0.292190i 0.937962 0.346739i \(-0.112711\pi\)
−0.769266 + 0.638929i \(0.779378\pi\)
\(422\) 0 0
\(423\) 5.03163 + 8.71504i 0.244646 + 0.423740i
\(424\) 0 0
\(425\) 0.158610 0.00769371
\(426\) 0 0
\(427\) −1.53163 + 2.65287i −0.0741209 + 0.128381i
\(428\) 0 0
\(429\) −56.4959 −2.72765
\(430\) 0 0
\(431\) −13.9894 + 24.2304i −0.673847 + 1.16714i 0.302958 + 0.953004i \(0.402026\pi\)
−0.976805 + 0.214133i \(0.931307\pi\)
\(432\) 0 0
\(433\) −3.12698 + 5.41608i −0.150273 + 0.260280i −0.931328 0.364182i \(-0.881349\pi\)
0.781055 + 0.624462i \(0.214682\pi\)
\(434\) 0 0
\(435\) −4.39608 7.61423i −0.210776 0.365075i
\(436\) 0 0
\(437\) 3.39208 3.74152i 0.162265 0.178981i
\(438\) 0 0
\(439\) 15.5988 + 27.0179i 0.744490 + 1.28949i 0.950433 + 0.310931i \(0.100641\pi\)
−0.205942 + 0.978564i \(0.566026\pi\)
\(440\) 0 0
\(441\) −8.70428 + 15.0763i −0.414490 + 0.717917i
\(442\) 0 0
\(443\) −16.3519 + 28.3223i −0.776901 + 1.34563i 0.156819 + 0.987627i \(0.449876\pi\)
−0.933720 + 0.358004i \(0.883457\pi\)
\(444\) 0 0
\(445\) 1.11250 0.0527373
\(446\) 0 0
\(447\) −2.16719 + 3.75368i −0.102504 + 0.177543i
\(448\) 0 0
\(449\) 25.6304 1.20958 0.604788 0.796387i \(-0.293258\pi\)
0.604788 + 0.796387i \(0.293258\pi\)
\(450\) 0 0
\(451\) −13.6953 23.7209i −0.644885 1.11697i
\(452\) 0 0
\(453\) −25.2464 43.7280i −1.18618 2.05452i
\(454\) 0 0
\(455\) −17.5351 −0.822058
\(456\) 0 0
\(457\) 33.1646 1.55138 0.775688 0.631116i \(-0.217403\pi\)
0.775688 + 0.631116i \(0.217403\pi\)
\(458\) 0 0
\(459\) −0.0566917 0.0981929i −0.00264614 0.00458325i
\(460\) 0 0
\(461\) −1.08788 1.88426i −0.0506677 0.0877590i 0.839579 0.543237i \(-0.182802\pi\)
−0.890247 + 0.455478i \(0.849468\pi\)
\(462\) 0 0
\(463\) 6.20072 0.288172 0.144086 0.989565i \(-0.453976\pi\)
0.144086 + 0.989565i \(0.453976\pi\)
\(464\) 0 0
\(465\) 2.86445 4.96137i 0.132836 0.230078i
\(466\) 0 0
\(467\) 17.1546 0.793821 0.396910 0.917857i \(-0.370082\pi\)
0.396910 + 0.917857i \(0.370082\pi\)
\(468\) 0 0
\(469\) 14.8062 25.6451i 0.683687 1.18418i
\(470\) 0 0
\(471\) −4.73591 + 8.20284i −0.218219 + 0.377967i
\(472\) 0 0
\(473\) −7.54567 13.0695i −0.346950 0.600936i
\(474\) 0 0
\(475\) −2.92771 + 3.22932i −0.134333 + 0.148171i
\(476\) 0 0
\(477\) 9.43318 + 16.3387i 0.431915 + 0.748099i
\(478\) 0 0
\(479\) −17.8891 + 30.9848i −0.817372 + 1.41573i 0.0902399 + 0.995920i \(0.471237\pi\)
−0.907612 + 0.419810i \(0.862097\pi\)
\(480\) 0 0
\(481\) −27.4120 + 47.4790i −1.24988 + 2.16486i
\(482\) 0 0
\(483\) 10.1867 0.463510
\(484\) 0 0
\(485\) 0.809757 1.40254i 0.0367692 0.0636861i
\(486\) 0 0
\(487\) 23.7149 1.07462 0.537311 0.843384i \(-0.319440\pi\)
0.537311 + 0.843384i \(0.319440\pi\)
\(488\) 0 0
\(489\) −2.02617 3.50943i −0.0916267 0.158702i
\(490\) 0 0
\(491\) −19.5933 33.9367i −0.884235 1.53154i −0.846588 0.532249i \(-0.821347\pi\)
−0.0376474 0.999291i \(-0.511986\pi\)
\(492\) 0 0
\(493\) −0.556248 −0.0250521
\(494\) 0 0
\(495\) −14.8062 −0.665489
\(496\) 0 0
\(497\) 28.4698 + 49.3112i 1.27705 + 2.21191i
\(498\) 0 0
\(499\) −4.68824 8.12027i −0.209875 0.363513i 0.741800 0.670621i \(-0.233972\pi\)
−0.951675 + 0.307107i \(0.900639\pi\)
\(500\) 0 0
\(501\) −16.2780 −0.727249
\(502\) 0 0
\(503\) 6.74649 11.6853i 0.300811 0.521020i −0.675509 0.737352i \(-0.736076\pi\)
0.976320 + 0.216332i \(0.0694093\pi\)
\(504\) 0 0
\(505\) −12.3132 −0.547931
\(506\) 0 0
\(507\) −15.0421 + 26.0537i −0.668044 + 1.15709i
\(508\) 0 0
\(509\) −12.8534 + 22.2628i −0.569718 + 0.986781i 0.426875 + 0.904310i \(0.359614\pi\)
−0.996594 + 0.0824703i \(0.973719\pi\)
\(510\) 0 0
\(511\) −12.5527 21.7419i −0.555298 0.961805i
\(512\) 0 0
\(513\) 3.04567 + 0.658252i 0.134470 + 0.0290625i
\(514\) 0 0
\(515\) −5.30820 9.19407i −0.233907 0.405139i
\(516\) 0 0
\(517\) 6.90310 11.9565i 0.303598 0.525847i
\(518\) 0 0
\(519\) −10.6812 + 18.5004i −0.468854 + 0.812078i
\(520\) 0 0
\(521\) −37.7358 −1.65324 −0.826618 0.562763i \(-0.809738\pi\)
−0.826618 + 0.562763i \(0.809738\pi\)
\(522\) 0 0
\(523\) 19.2003 33.2559i 0.839570 1.45418i −0.0506855 0.998715i \(-0.516141\pi\)
0.890255 0.455462i \(-0.150526\pi\)
\(524\) 0 0
\(525\) −8.79216 −0.383721
\(526\) 0 0
\(527\) −0.181223 0.313888i −0.00789420 0.0136732i
\(528\) 0 0
\(529\) 10.8288 + 18.7561i 0.470818 + 0.815481i
\(530\) 0 0
\(531\) −10.0633 −0.436709
\(532\) 0 0
\(533\) −30.3865 −1.31619
\(534\) 0 0
\(535\) 1.08632 + 1.88157i 0.0469659 + 0.0813473i
\(536\) 0 0
\(537\) −12.8749 22.3000i −0.555594 0.962317i
\(538\) 0 0
\(539\) 23.8835 1.02874
\(540\) 0 0
\(541\) 6.40310 11.0905i 0.275291 0.476818i −0.694918 0.719089i \(-0.744559\pi\)
0.970208 + 0.242272i \(0.0778926\pi\)
\(542\) 0 0
\(543\) 30.7539 1.31977
\(544\) 0 0
\(545\) 7.91012 13.7007i 0.338832 0.586875i
\(546\) 0 0
\(547\) −9.12853 + 15.8111i −0.390308 + 0.676033i −0.992490 0.122326i \(-0.960965\pi\)
0.602182 + 0.798359i \(0.294298\pi\)
\(548\) 0 0
\(549\) 1.43473 + 2.48503i 0.0612329 + 0.106058i
\(550\) 0 0
\(551\) 10.2675 11.3253i 0.437412 0.482473i
\(552\) 0 0
\(553\) 17.7570 + 30.7560i 0.755103 + 1.30788i
\(554\) 0 0
\(555\) −13.7445 + 23.8062i −0.583421 + 1.01051i
\(556\) 0 0
\(557\) −7.45233 + 12.9078i −0.315765 + 0.546922i −0.979600 0.200958i \(-0.935595\pi\)
0.663835 + 0.747879i \(0.268928\pi\)
\(558\) 0 0
\(559\) −16.7420 −0.708113
\(560\) 0 0
\(561\) −0.896081 + 1.55206i −0.0378326 + 0.0655279i
\(562\) 0 0
\(563\) −45.7810 −1.92944 −0.964720 0.263276i \(-0.915197\pi\)
−0.964720 + 0.263276i \(0.915197\pi\)
\(564\) 0 0
\(565\) 4.91914 + 8.52020i 0.206950 + 0.358447i
\(566\) 0 0
\(567\) −14.1390 24.4895i −0.593783 1.02846i
\(568\) 0 0
\(569\) 0.379598 0.0159136 0.00795679 0.999968i \(-0.497467\pi\)
0.00795679 + 0.999968i \(0.497467\pi\)
\(570\) 0 0
\(571\) 15.8514 0.663361 0.331681 0.943392i \(-0.392384\pi\)
0.331681 + 0.943392i \(0.392384\pi\)
\(572\) 0 0
\(573\) 7.15861 + 12.3991i 0.299055 + 0.517979i
\(574\) 0 0
\(575\) 0.579305 + 1.00339i 0.0241587 + 0.0418441i
\(576\) 0 0
\(577\) −19.2350 −0.800765 −0.400382 0.916348i \(-0.631123\pi\)
−0.400382 + 0.916348i \(0.631123\pi\)
\(578\) 0 0
\(579\) 12.7339 22.0558i 0.529203 0.916607i
\(580\) 0 0
\(581\) 17.0281 0.706444
\(582\) 0 0
\(583\) 12.9418 22.4158i 0.535993 0.928366i
\(584\) 0 0
\(585\) −8.21286 + 14.2251i −0.339560 + 0.588135i
\(586\) 0 0
\(587\) 20.4242 + 35.3757i 0.842995 + 1.46011i 0.887351 + 0.461095i \(0.152543\pi\)
−0.0443559 + 0.999016i \(0.514124\pi\)
\(588\) 0 0
\(589\) 9.73591 + 2.10419i 0.401161 + 0.0867018i
\(590\) 0 0
\(591\) −20.3117 35.1808i −0.835510 1.44715i
\(592\) 0 0
\(593\) 7.12342 12.3381i 0.292524 0.506666i −0.681882 0.731462i \(-0.738838\pi\)
0.974406 + 0.224796i \(0.0721716\pi\)
\(594\) 0 0
\(595\) −0.278124 + 0.481725i −0.0114020 + 0.0197488i
\(596\) 0 0
\(597\) −0.838276 −0.0343083
\(598\) 0 0
\(599\) −7.92571 + 13.7277i −0.323836 + 0.560900i −0.981276 0.192607i \(-0.938306\pi\)
0.657440 + 0.753507i \(0.271639\pi\)
\(600\) 0 0
\(601\) 16.4718 0.671900 0.335950 0.941880i \(-0.390943\pi\)
0.335950 + 0.941880i \(0.390943\pi\)
\(602\) 0 0
\(603\) −13.8695 24.0226i −0.564808 0.978277i
\(604\) 0 0
\(605\) 4.65661 + 8.06548i 0.189318 + 0.327908i
\(606\) 0 0
\(607\) 10.3914 0.421774 0.210887 0.977510i \(-0.432365\pi\)
0.210887 + 0.977510i \(0.432365\pi\)
\(608\) 0 0
\(609\) 30.8343 1.24947
\(610\) 0 0
\(611\) −7.65817 13.2643i −0.309816 0.536617i
\(612\) 0 0
\(613\) 10.8925 + 18.8664i 0.439945 + 0.762007i 0.997685 0.0680090i \(-0.0216647\pi\)
−0.557740 + 0.830016i \(0.688331\pi\)
\(614\) 0 0
\(615\) −15.2359 −0.614371
\(616\) 0 0
\(617\) 21.3855 37.0408i 0.860948 1.49121i −0.0100671 0.999949i \(-0.503205\pi\)
0.871015 0.491256i \(-0.163462\pi\)
\(618\) 0 0
\(619\) −28.7882 −1.15709 −0.578547 0.815649i \(-0.696380\pi\)
−0.578547 + 0.815649i \(0.696380\pi\)
\(620\) 0 0
\(621\) 0.414120 0.717278i 0.0166181 0.0287834i
\(622\) 0 0
\(623\) −1.95077 + 3.37883i −0.0781560 + 0.135370i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) −15.0597 46.8931i −0.601427 1.87273i
\(628\) 0 0
\(629\) 0.869563 + 1.50613i 0.0346718 + 0.0600532i
\(630\) 0 0
\(631\) −9.69370 + 16.7900i −0.385900 + 0.668399i −0.991894 0.127071i \(-0.959442\pi\)
0.605993 + 0.795470i \(0.292776\pi\)
\(632\) 0 0
\(633\) 2.54221 4.40324i 0.101044 0.175013i
\(634\) 0 0
\(635\) 15.7109 0.623466
\(636\) 0 0
\(637\) 13.2479 22.9461i 0.524903 0.909158i
\(638\) 0 0
\(639\) 53.3373 2.10999
\(640\) 0 0
\(641\) −20.3433 35.2356i −0.803512 1.39172i −0.917291 0.398217i \(-0.869629\pi\)
0.113779 0.993506i \(-0.463704\pi\)
\(642\) 0 0
\(643\) −17.0527 29.5361i −0.672492 1.16479i −0.977195 0.212344i \(-0.931890\pi\)
0.304703 0.952448i \(-0.401443\pi\)
\(644\) 0 0
\(645\) −8.39452 −0.330534
\(646\) 0 0
\(647\) 48.0029 1.88719 0.943595 0.331103i \(-0.107421\pi\)
0.943595 + 0.331103i \(0.107421\pi\)
\(648\) 0 0
\(649\) 6.90310 + 11.9565i 0.270970 + 0.469334i
\(650\) 0 0
\(651\) 10.0457 + 17.3996i 0.393721 + 0.681945i
\(652\) 0 0
\(653\) 3.90866 0.152958 0.0764788 0.997071i \(-0.475632\pi\)
0.0764788 + 0.997071i \(0.475632\pi\)
\(654\) 0 0
\(655\) 5.76755 9.98968i 0.225357 0.390329i
\(656\) 0 0
\(657\) −23.5171 −0.917488
\(658\) 0 0
\(659\) 6.54411 11.3347i 0.254922 0.441539i −0.709952 0.704250i \(-0.751283\pi\)
0.964874 + 0.262711i \(0.0846167\pi\)
\(660\) 0 0
\(661\) 11.9714 20.7350i 0.465633 0.806500i −0.533597 0.845739i \(-0.679160\pi\)
0.999230 + 0.0392391i \(0.0124934\pi\)
\(662\) 0 0
\(663\) 0.994095 + 1.72182i 0.0386074 + 0.0668700i
\(664\) 0 0
\(665\) −4.67420 14.5546i −0.181258 0.564403i
\(666\) 0 0
\(667\) −2.03163 3.51889i −0.0786652 0.136252i
\(668\) 0 0
\(669\) −24.1074 + 41.7552i −0.932045 + 1.61435i
\(670\) 0 0
\(671\) 1.96837 3.40931i 0.0759880 0.131615i
\(672\) 0 0
\(673\) −11.3304 −0.436754 −0.218377 0.975865i \(-0.570076\pi\)
−0.218377 + 0.975865i \(0.570076\pi\)
\(674\) 0 0
\(675\) −0.357429 + 0.619085i −0.0137574 + 0.0238286i
\(676\) 0 0
\(677\) 8.90466 0.342234 0.171117 0.985251i \(-0.445262\pi\)
0.171117 + 0.985251i \(0.445262\pi\)
\(678\) 0 0
\(679\) 2.83983 + 4.91873i 0.108983 + 0.188764i
\(680\) 0 0
\(681\) 5.01404 + 8.68457i 0.192138 + 0.332793i
\(682\) 0 0
\(683\) 26.6977 1.02156 0.510780 0.859712i \(-0.329357\pi\)
0.510780 + 0.859712i \(0.329357\pi\)
\(684\) 0 0
\(685\) −0.109381 −0.00417923
\(686\) 0 0
\(687\) 16.2691 + 28.1789i 0.620705 + 1.07509i
\(688\) 0 0
\(689\) −14.3573 24.8676i −0.546971 0.947381i
\(690\) 0 0
\(691\) −35.9708 −1.36840 −0.684198 0.729297i \(-0.739847\pi\)
−0.684198 + 0.729297i \(0.739847\pi\)
\(692\) 0 0
\(693\) 25.9628 44.9689i 0.986245 1.70823i
\(694\) 0 0
\(695\) 1.44375 0.0547646
\(696\) 0 0
\(697\) −0.481960 + 0.834779i −0.0182555 + 0.0316195i
\(698\) 0 0
\(699\) −33.9366 + 58.7800i −1.28360 + 2.22326i
\(700\) 0 0
\(701\) −1.22543 2.12252i −0.0462840 0.0801663i 0.841955 0.539547i \(-0.181405\pi\)
−0.888239 + 0.459381i \(0.848071\pi\)
\(702\) 0 0
\(703\) −46.7159 10.0966i −1.76192 0.380799i
\(704\) 0 0
\(705\) −3.83983 6.65079i −0.144616 0.250483i
\(706\) 0 0
\(707\) 21.5913 37.3973i 0.812026 1.40647i
\(708\) 0 0
\(709\) 25.1440 43.5507i 0.944304 1.63558i 0.187165 0.982329i \(-0.440070\pi\)
0.757139 0.653254i \(-0.226597\pi\)
\(710\) 0 0
\(711\) 33.2671 1.24761
\(712\) 0 0
\(713\) 1.32379 2.29288i 0.0495765 0.0858690i
\(714\) 0 0
\(715\) 22.5351 0.842765
\(716\) 0 0
\(717\) 25.1456 + 43.5534i 0.939079 + 1.62653i
\(718\) 0 0
\(719\) −24.0491 41.6543i −0.896881 1.55344i −0.831459 0.555586i \(-0.812494\pi\)
−0.0654223 0.997858i \(-0.520839\pi\)
\(720\) 0 0
\(721\) 37.2319 1.38659
\(722\) 0 0
\(723\) −54.1123 −2.01246
\(724\) 0 0
\(725\) 1.75351 + 3.03717i 0.0651237 + 0.112798i
\(726\) 0 0
\(727\) −8.33983 14.4450i −0.309307 0.535736i 0.668904 0.743349i \(-0.266764\pi\)
−0.978211 + 0.207613i \(0.933430\pi\)
\(728\) 0 0
\(729\) −31.8655 −1.18020
\(730\) 0 0
\(731\) −0.265545 + 0.459938i −0.00982155 + 0.0170114i
\(732\) 0 0
\(733\) −4.13365 −0.152680 −0.0763399 0.997082i \(-0.524323\pi\)
−0.0763399 + 0.997082i \(0.524323\pi\)
\(734\) 0 0
\(735\) 6.64257 11.5053i 0.245015 0.424378i
\(736\) 0 0
\(737\) −19.0281 + 32.9576i −0.700908 + 1.21401i
\(738\) 0 0
\(739\) 23.4870 + 40.6806i 0.863982 + 1.49646i 0.868054 + 0.496470i \(0.165371\pi\)
−0.00407159 + 0.999992i \(0.501296\pi\)
\(740\) 0 0
\(741\) −53.4061 11.5425i −1.96192 0.424025i
\(742\) 0 0
\(743\) 20.6069 + 35.6923i 0.755995 + 1.30942i 0.944878 + 0.327422i \(0.106180\pi\)
−0.188883 + 0.982000i \(0.560487\pi\)
\(744\) 0 0
\(745\) 0.864447 1.49727i 0.0316709 0.0548556i
\(746\) 0 0
\(747\) 7.97539 13.8138i 0.291804 0.505420i
\(748\) 0 0
\(749\) −7.61951 −0.278411
\(750\) 0 0
\(751\) 2.98942 5.17783i 0.109086 0.188942i −0.806314 0.591487i \(-0.798541\pi\)
0.915400 + 0.402545i \(0.131874\pi\)
\(752\) 0 0
\(753\) 18.2210 0.664010
\(754\) 0 0
\(755\) 10.0703 + 17.4422i 0.366495 + 0.634788i
\(756\) 0 0
\(757\) −18.1968 31.5178i −0.661375 1.14553i −0.980255 0.197739i \(-0.936640\pi\)
0.318880 0.947795i \(-0.396693\pi\)
\(758\) 0 0
\(759\) −13.0913 −0.475186
\(760\) 0 0
\(761\) −2.71397 −0.0983813 −0.0491907 0.998789i \(-0.515664\pi\)
−0.0491907 + 0.998789i \(0.515664\pi\)
\(762\) 0 0
\(763\) 27.7409 + 48.0487i 1.00429 + 1.73948i
\(764\) 0 0
\(765\) 0.260528 + 0.451248i 0.00941941 + 0.0163149i
\(766\) 0 0
\(767\) 15.3163 0.553041
\(768\) 0 0
\(769\) −19.8995 + 34.4670i −0.717596 + 1.24291i 0.244354 + 0.969686i \(0.421424\pi\)
−0.961950 + 0.273226i \(0.911909\pi\)
\(770\) 0 0
\(771\) 37.7991 1.36130
\(772\) 0 0
\(773\) −22.4874 + 38.9494i −0.808816 + 1.40091i 0.104868 + 0.994486i \(0.466558\pi\)
−0.913684 + 0.406425i \(0.866775\pi\)
\(774\) 0 0
\(775\) −1.14257 + 1.97899i −0.0410424 + 0.0710875i
\(776\) 0 0
\(777\) −48.2022 83.4886i −1.72924 2.99514i
\(778\) 0 0
\(779\) −8.09992 25.2216i −0.290210 0.903658i
\(780\) 0 0
\(781\) −36.5878 63.3719i −1.30921 2.26762i
\(782\) 0 0
\(783\) 1.25351 2.17114i 0.0447968 0.0775903i
\(784\) 0 0
\(785\) 1.88906 3.27195i 0.0674235 0.116781i
\(786\) 0 0
\(787\) 17.7149 0.631466 0.315733 0.948848i \(-0.397750\pi\)
0.315733 + 0.948848i \(0.397750\pi\)
\(788\) 0 0
\(789\) 25.2640 43.7585i 0.899422 1.55784i
\(790\) 0 0
\(791\) −34.5030 −1.22679
\(792\) 0 0
\(793\) −2.18367 3.78222i −0.0775443 0.134311i
\(794\) 0 0
\(795\) −7.19882 12.4687i −0.255316