Properties

Label 1008.2.r.j.673.1
Level 1008
Weight 2
Character 1008.673
Analytic conductor 8.049
Analytic rank 0
Dimension 6
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Defining polynomial: \(x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 673.1
Root \(0.500000 - 0.224437i\) of defining polynomial
Character \(\chi\) \(=\) 1008.673
Dual form 1008.2.r.j.337.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.64400 + 0.545231i) q^{3} +(0.849814 + 1.47192i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(2.40545 - 1.79272i) q^{9} +O(q^{10})\) \(q+(-1.64400 + 0.545231i) q^{3} +(0.849814 + 1.47192i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(2.40545 - 1.79272i) q^{9} +(1.23855 - 2.14523i) q^{11} +(-0.388736 - 0.673310i) q^{13} +(-2.19963 - 1.95649i) q^{15} +2.81089 q^{17} +4.98762 q^{19} +(0.349814 - 1.69636i) q^{21} +(0.356004 + 0.616617i) q^{23} +(1.05563 - 1.82841i) q^{25} +(-2.97710 + 4.25874i) q^{27} +(-2.25526 + 3.90623i) q^{29} +(2.54944 + 4.41576i) q^{31} +(-0.866524 + 4.20205i) q^{33} -1.69963 q^{35} -6.87636 q^{37} +(1.00619 + 0.894969i) q^{39} +(2.93818 + 5.08907i) q^{41} +(-2.32691 + 4.03033i) q^{43} +(4.68292 + 2.01715i) q^{45} +(6.49381 - 11.2476i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-4.62110 + 1.53259i) q^{51} +1.88874 q^{53} +4.21015 q^{55} +(-8.19963 + 2.71941i) q^{57} +(7.14400 + 12.3738i) q^{59} +(-7.15452 + 12.3920i) q^{61} +(0.349814 + 2.97954i) q^{63} +(0.660706 - 1.14438i) q^{65} +(3.99381 + 6.91748i) q^{67} +(-0.921468 - 0.819611i) q^{69} +10.2632 q^{71} +4.98762 q^{73} +(-0.738550 + 3.58146i) q^{75} +(1.23855 + 2.14523i) q^{77} +(-4.60507 + 7.97622i) q^{79} +(2.57234 - 8.62456i) q^{81} +(4.40545 - 7.63046i) q^{83} +(2.38874 + 4.13741i) q^{85} +(1.57784 - 7.65146i) q^{87} +9.65383 q^{89} +0.777472 q^{91} +(-6.59888 - 5.86946i) q^{93} +(4.23855 + 7.34138i) q^{95} +(-4.32072 + 7.48371i) q^{97} +(-0.866524 - 7.38061i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 2q^{3} - q^{5} - 3q^{7} + 8q^{9} + O(q^{10}) \) \( 6q + 2q^{3} - q^{5} - 3q^{7} + 8q^{9} + 2q^{11} - 3q^{13} - q^{15} + 4q^{17} - 6q^{19} - 4q^{21} + 14q^{23} + 6q^{25} - 7q^{27} - q^{29} - 3q^{31} + 8q^{33} + 2q^{35} - 6q^{37} + 24q^{39} + 3q^{43} + 23q^{45} + 21q^{47} - 3q^{49} - 5q^{51} + 12q^{53} - 12q^{55} - 37q^{57} + 31q^{59} - 6q^{61} - 4q^{63} - 15q^{65} + 6q^{67} + 5q^{69} - 34q^{71} - 6q^{73} + q^{75} + 2q^{77} - 9q^{79} + 8q^{81} + 20q^{83} + 15q^{85} + 23q^{87} + 24q^{89} + 6q^{91} - 3q^{93} + 20q^{95} + 9q^{97} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) −1.64400 + 0.545231i −0.949162 + 0.314789i
\(4\) 0 0
\(5\) 0.849814 + 1.47192i 0.380048 + 0.658263i 0.991069 0.133352i \(-0.0425740\pi\)
−0.611020 + 0.791615i \(0.709241\pi\)
\(6\) 0 0
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) 0 0
\(9\) 2.40545 1.79272i 0.801815 0.597572i
\(10\) 0 0
\(11\) 1.23855 2.14523i 0.373437 0.646812i −0.616655 0.787234i \(-0.711513\pi\)
0.990092 + 0.140422i \(0.0448459\pi\)
\(12\) 0 0
\(13\) −0.388736 0.673310i −0.107816 0.186743i 0.807069 0.590457i \(-0.201052\pi\)
−0.914885 + 0.403714i \(0.867719\pi\)
\(14\) 0 0
\(15\) −2.19963 1.95649i −0.567942 0.505163i
\(16\) 0 0
\(17\) 2.81089 0.681742 0.340871 0.940110i \(-0.389278\pi\)
0.340871 + 0.940110i \(0.389278\pi\)
\(18\) 0 0
\(19\) 4.98762 1.14424 0.572119 0.820170i \(-0.306121\pi\)
0.572119 + 0.820170i \(0.306121\pi\)
\(20\) 0 0
\(21\) 0.349814 1.69636i 0.0763357 0.370176i
\(22\) 0 0
\(23\) 0.356004 + 0.616617i 0.0742320 + 0.128574i 0.900752 0.434334i \(-0.143016\pi\)
−0.826520 + 0.562907i \(0.809683\pi\)
\(24\) 0 0
\(25\) 1.05563 1.82841i 0.211126 0.365682i
\(26\) 0 0
\(27\) −2.97710 + 4.25874i −0.572943 + 0.819595i
\(28\) 0 0
\(29\) −2.25526 + 3.90623i −0.418791 + 0.725368i −0.995818 0.0913573i \(-0.970879\pi\)
0.577027 + 0.816725i \(0.304213\pi\)
\(30\) 0 0
\(31\) 2.54944 + 4.41576i 0.457893 + 0.793095i 0.998849 0.0479563i \(-0.0152708\pi\)
−0.540956 + 0.841051i \(0.681937\pi\)
\(32\) 0 0
\(33\) −0.866524 + 4.20205i −0.150843 + 0.731483i
\(34\) 0 0
\(35\) −1.69963 −0.287290
\(36\) 0 0
\(37\) −6.87636 −1.13047 −0.565233 0.824931i \(-0.691214\pi\)
−0.565233 + 0.824931i \(0.691214\pi\)
\(38\) 0 0
\(39\) 1.00619 + 0.894969i 0.161119 + 0.143310i
\(40\) 0 0
\(41\) 2.93818 + 5.08907i 0.458866 + 0.794780i 0.998901 0.0468628i \(-0.0149223\pi\)
−0.540035 + 0.841643i \(0.681589\pi\)
\(42\) 0 0
\(43\) −2.32691 + 4.03033i −0.354851 + 0.614620i −0.987092 0.160151i \(-0.948802\pi\)
0.632241 + 0.774771i \(0.282135\pi\)
\(44\) 0 0
\(45\) 4.68292 + 2.01715i 0.698088 + 0.300699i
\(46\) 0 0
\(47\) 6.49381 11.2476i 0.947220 1.64063i 0.195975 0.980609i \(-0.437213\pi\)
0.751245 0.660023i \(-0.229454\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 0 0
\(51\) −4.62110 + 1.53259i −0.647083 + 0.214605i
\(52\) 0 0
\(53\) 1.88874 0.259438 0.129719 0.991551i \(-0.458593\pi\)
0.129719 + 0.991551i \(0.458593\pi\)
\(54\) 0 0
\(55\) 4.21015 0.567696
\(56\) 0 0
\(57\) −8.19963 + 2.71941i −1.08607 + 0.360194i
\(58\) 0 0
\(59\) 7.14400 + 12.3738i 0.930069 + 1.61093i 0.783199 + 0.621771i \(0.213587\pi\)
0.146870 + 0.989156i \(0.453080\pi\)
\(60\) 0 0
\(61\) −7.15452 + 12.3920i −0.916042 + 1.58663i −0.110673 + 0.993857i \(0.535301\pi\)
−0.805369 + 0.592774i \(0.798033\pi\)
\(62\) 0 0
\(63\) 0.349814 + 2.97954i 0.0440724 + 0.375386i
\(64\) 0 0
\(65\) 0.660706 1.14438i 0.0819505 0.141942i
\(66\) 0 0
\(67\) 3.99381 + 6.91748i 0.487922 + 0.845105i 0.999904 0.0138913i \(-0.00442187\pi\)
−0.511982 + 0.858996i \(0.671089\pi\)
\(68\) 0 0
\(69\) −0.921468 0.819611i −0.110932 0.0986696i
\(70\) 0 0
\(71\) 10.2632 1.21802 0.609011 0.793162i \(-0.291567\pi\)
0.609011 + 0.793162i \(0.291567\pi\)
\(72\) 0 0
\(73\) 4.98762 0.583757 0.291878 0.956455i \(-0.405720\pi\)
0.291878 + 0.956455i \(0.405720\pi\)
\(74\) 0 0
\(75\) −0.738550 + 3.58146i −0.0852804 + 0.413551i
\(76\) 0 0
\(77\) 1.23855 + 2.14523i 0.141146 + 0.244472i
\(78\) 0 0
\(79\) −4.60507 + 7.97622i −0.518111 + 0.897395i 0.481667 + 0.876354i \(0.340031\pi\)
−0.999779 + 0.0210410i \(0.993302\pi\)
\(80\) 0 0
\(81\) 2.57234 8.62456i 0.285816 0.958285i
\(82\) 0 0
\(83\) 4.40545 7.63046i 0.483561 0.837551i −0.516261 0.856431i \(-0.672677\pi\)
0.999822 + 0.0188798i \(0.00600997\pi\)
\(84\) 0 0
\(85\) 2.38874 + 4.13741i 0.259095 + 0.448765i
\(86\) 0 0
\(87\) 1.57784 7.65146i 0.169163 0.820322i
\(88\) 0 0
\(89\) 9.65383 1.02330 0.511652 0.859193i \(-0.329034\pi\)
0.511652 + 0.859193i \(0.329034\pi\)
\(90\) 0 0
\(91\) 0.777472 0.0815012
\(92\) 0 0
\(93\) −6.59888 5.86946i −0.684272 0.608635i
\(94\) 0 0
\(95\) 4.23855 + 7.34138i 0.434866 + 0.753210i
\(96\) 0 0
\(97\) −4.32072 + 7.48371i −0.438703 + 0.759856i −0.997590 0.0693880i \(-0.977895\pi\)
0.558887 + 0.829244i \(0.311229\pi\)
\(98\) 0 0
\(99\) −0.866524 7.38061i −0.0870890 0.741779i
\(100\) 0 0
\(101\) −1.20582 + 2.08854i −0.119983 + 0.207817i −0.919761 0.392479i \(-0.871617\pi\)
0.799777 + 0.600297i \(0.204951\pi\)
\(102\) 0 0
\(103\) −2.16690 3.75317i −0.213511 0.369811i 0.739300 0.673376i \(-0.235156\pi\)
−0.952811 + 0.303565i \(0.901823\pi\)
\(104\) 0 0
\(105\) 2.79418 0.926690i 0.272684 0.0904357i
\(106\) 0 0
\(107\) −19.1978 −1.85592 −0.927959 0.372682i \(-0.878438\pi\)
−0.927959 + 0.372682i \(0.878438\pi\)
\(108\) 0 0
\(109\) 18.9629 1.81631 0.908156 0.418631i \(-0.137490\pi\)
0.908156 + 0.418631i \(0.137490\pi\)
\(110\) 0 0
\(111\) 11.3047 3.74920i 1.07299 0.355859i
\(112\) 0 0
\(113\) −6.46472 11.1972i −0.608150 1.05335i −0.991545 0.129762i \(-0.958579\pi\)
0.383395 0.923584i \(-0.374755\pi\)
\(114\) 0 0
\(115\) −0.605074 + 1.04802i −0.0564235 + 0.0977283i
\(116\) 0 0
\(117\) −2.14214 0.922719i −0.198041 0.0853054i
\(118\) 0 0
\(119\) −1.40545 + 2.43430i −0.128837 + 0.223152i
\(120\) 0 0
\(121\) 2.43199 + 4.21233i 0.221090 + 0.382939i
\(122\) 0 0
\(123\) −7.60507 6.76443i −0.685726 0.609928i
\(124\) 0 0
\(125\) 12.0865 1.08105
\(126\) 0 0
\(127\) −17.6291 −1.56433 −0.782163 0.623073i \(-0.785884\pi\)
−0.782163 + 0.623073i \(0.785884\pi\)
\(128\) 0 0
\(129\) 1.62797 7.89456i 0.143335 0.695077i
\(130\) 0 0
\(131\) −2.84362 4.92530i −0.248449 0.430326i 0.714647 0.699485i \(-0.246587\pi\)
−0.963096 + 0.269160i \(0.913254\pi\)
\(132\) 0 0
\(133\) −2.49381 + 4.31941i −0.216241 + 0.374540i
\(134\) 0 0
\(135\) −8.79851 0.762918i −0.757255 0.0656615i
\(136\) 0 0
\(137\) 9.72617 16.8462i 0.830963 1.43927i −0.0663128 0.997799i \(-0.521124\pi\)
0.897276 0.441471i \(-0.145543\pi\)
\(138\) 0 0
\(139\) −1.49381 2.58736i −0.126703 0.219457i 0.795694 0.605699i \(-0.207106\pi\)
−0.922397 + 0.386242i \(0.873773\pi\)
\(140\) 0 0
\(141\) −4.54325 + 22.0317i −0.382611 + 1.85540i
\(142\) 0 0
\(143\) −1.92587 −0.161050
\(144\) 0 0
\(145\) −7.66621 −0.636644
\(146\) 0 0
\(147\) 1.29418 + 1.15113i 0.106742 + 0.0949433i
\(148\) 0 0
\(149\) −4.04944 7.01384i −0.331743 0.574596i 0.651111 0.758983i \(-0.274303\pi\)
−0.982854 + 0.184387i \(0.940970\pi\)
\(150\) 0 0
\(151\) −4.43199 + 7.67643i −0.360670 + 0.624699i −0.988071 0.153997i \(-0.950785\pi\)
0.627401 + 0.778696i \(0.284119\pi\)
\(152\) 0 0
\(153\) 6.76145 5.03913i 0.546631 0.407390i
\(154\) 0 0
\(155\) −4.33310 + 7.50516i −0.348043 + 0.602829i
\(156\) 0 0
\(157\) 4.38255 + 7.59079i 0.349765 + 0.605811i 0.986208 0.165513i \(-0.0529280\pi\)
−0.636442 + 0.771324i \(0.719595\pi\)
\(158\) 0 0
\(159\) −3.10507 + 1.02980i −0.246248 + 0.0816683i
\(160\) 0 0
\(161\) −0.712008 −0.0561141
\(162\) 0 0
\(163\) 1.98762 0.155682 0.0778412 0.996966i \(-0.475197\pi\)
0.0778412 + 0.996966i \(0.475197\pi\)
\(164\) 0 0
\(165\) −6.92147 + 2.29550i −0.538836 + 0.178705i
\(166\) 0 0
\(167\) 1.31089 + 2.27053i 0.101440 + 0.175699i 0.912278 0.409571i \(-0.134322\pi\)
−0.810838 + 0.585270i \(0.800988\pi\)
\(168\) 0 0
\(169\) 6.19777 10.7349i 0.476751 0.825758i
\(170\) 0 0
\(171\) 11.9975 8.94138i 0.917468 0.683765i
\(172\) 0 0
\(173\) 2.61491 4.52915i 0.198808 0.344345i −0.749334 0.662192i \(-0.769626\pi\)
0.948142 + 0.317847i \(0.102960\pi\)
\(174\) 0 0
\(175\) 1.05563 + 1.82841i 0.0797983 + 0.138215i
\(176\) 0 0
\(177\) −18.4913 16.4473i −1.38989 1.23625i
\(178\) 0 0
\(179\) 4.76509 0.356160 0.178080 0.984016i \(-0.443011\pi\)
0.178080 + 0.984016i \(0.443011\pi\)
\(180\) 0 0
\(181\) −10.4313 −0.775352 −0.387676 0.921796i \(-0.626722\pi\)
−0.387676 + 0.921796i \(0.626722\pi\)
\(182\) 0 0
\(183\) 5.00550 24.2732i 0.370017 1.79433i
\(184\) 0 0
\(185\) −5.84362 10.1215i −0.429632 0.744144i
\(186\) 0 0
\(187\) 3.48143 6.03001i 0.254587 0.440958i
\(188\) 0 0
\(189\) −2.19963 4.70761i −0.159999 0.342429i
\(190\) 0 0
\(191\) 6.66071 11.5367i 0.481952 0.834765i −0.517834 0.855481i \(-0.673261\pi\)
0.999785 + 0.0207164i \(0.00659470\pi\)
\(192\) 0 0
\(193\) 7.32072 + 12.6799i 0.526957 + 0.912717i 0.999507 + 0.0314125i \(0.0100005\pi\)
−0.472549 + 0.881304i \(0.656666\pi\)
\(194\) 0 0
\(195\) −0.462249 + 2.24159i −0.0331023 + 0.160524i
\(196\) 0 0
\(197\) −18.4858 −1.31706 −0.658528 0.752556i \(-0.728821\pi\)
−0.658528 + 0.752556i \(0.728821\pi\)
\(198\) 0 0
\(199\) −23.6167 −1.67414 −0.837071 0.547094i \(-0.815734\pi\)
−0.837071 + 0.547094i \(0.815734\pi\)
\(200\) 0 0
\(201\) −10.3374 9.19476i −0.729146 0.648549i
\(202\) 0 0
\(203\) −2.25526 3.90623i −0.158288 0.274163i
\(204\) 0 0
\(205\) −4.99381 + 8.64953i −0.348783 + 0.604110i
\(206\) 0 0
\(207\) 1.96177 + 0.845025i 0.136352 + 0.0587333i
\(208\) 0 0
\(209\) 6.17742 10.6996i 0.427301 0.740107i
\(210\) 0 0
\(211\) −7.27747 12.6050i −0.501002 0.867761i −0.999999 0.00115718i \(-0.999632\pi\)
0.498998 0.866603i \(-0.333702\pi\)
\(212\) 0 0
\(213\) −16.8727 + 5.59583i −1.15610 + 0.383420i
\(214\) 0 0
\(215\) −7.90978 −0.539442
\(216\) 0 0
\(217\) −5.09888 −0.346135
\(218\) 0 0
\(219\) −8.19963 + 2.71941i −0.554080 + 0.183760i
\(220\) 0 0
\(221\) −1.09269 1.89260i −0.0735026 0.127310i
\(222\) 0 0
\(223\) 4.72253 8.17966i 0.316244 0.547750i −0.663457 0.748214i \(-0.730912\pi\)
0.979701 + 0.200464i \(0.0642449\pi\)
\(224\) 0 0
\(225\) −0.738550 6.29059i −0.0492367 0.419372i
\(226\) 0 0
\(227\) 9.55563 16.5508i 0.634230 1.09852i −0.352448 0.935831i \(-0.614651\pi\)
0.986678 0.162687i \(-0.0520159\pi\)
\(228\) 0 0
\(229\) −5.72253 9.91171i −0.378155 0.654984i 0.612639 0.790363i \(-0.290108\pi\)
−0.990794 + 0.135379i \(0.956775\pi\)
\(230\) 0 0
\(231\) −3.20582 2.85146i −0.210927 0.187612i
\(232\) 0 0
\(233\) −1.19049 −0.0779913 −0.0389956 0.999239i \(-0.512416\pi\)
−0.0389956 + 0.999239i \(0.512416\pi\)
\(234\) 0 0
\(235\) 22.0741 1.43996
\(236\) 0 0
\(237\) 3.22184 15.6237i 0.209281 1.01487i
\(238\) 0 0
\(239\) 12.1414 + 21.0296i 0.785365 + 1.36029i 0.928781 + 0.370630i \(0.120858\pi\)
−0.143416 + 0.989663i \(0.545809\pi\)
\(240\) 0 0
\(241\) 10.7095 18.5493i 0.689857 1.19487i −0.282027 0.959406i \(-0.591007\pi\)
0.971884 0.235461i \(-0.0756599\pi\)
\(242\) 0 0
\(243\) 0.473458 + 15.5813i 0.0303723 + 0.999539i
\(244\) 0 0
\(245\) 0.849814 1.47192i 0.0542926 0.0940376i
\(246\) 0 0
\(247\) −1.93887 3.35822i −0.123367 0.213678i
\(248\) 0 0
\(249\) −3.08217 + 14.9464i −0.195325 + 0.947191i
\(250\) 0 0
\(251\) 2.67996 0.169158 0.0845789 0.996417i \(-0.473045\pi\)
0.0845789 + 0.996417i \(0.473045\pi\)
\(252\) 0 0
\(253\) 1.76371 0.110884
\(254\) 0 0
\(255\) −6.18292 5.49948i −0.387189 0.344391i
\(256\) 0 0
\(257\) 5.54256 + 9.60000i 0.345736 + 0.598832i 0.985487 0.169750i \(-0.0542961\pi\)
−0.639752 + 0.768582i \(0.720963\pi\)
\(258\) 0 0
\(259\) 3.43818 5.95510i 0.213638 0.370032i
\(260\) 0 0
\(261\) 1.57784 + 13.4393i 0.0976661 + 0.831869i
\(262\) 0 0
\(263\) 6.70396 11.6116i 0.413384 0.716002i −0.581873 0.813279i \(-0.697680\pi\)
0.995257 + 0.0972776i \(0.0310135\pi\)
\(264\) 0 0
\(265\) 1.60507 + 2.78007i 0.0985989 + 0.170778i
\(266\) 0 0
\(267\) −15.8709 + 5.26357i −0.971281 + 0.322125i
\(268\) 0 0
\(269\) 4.09022 0.249385 0.124693 0.992195i \(-0.460206\pi\)
0.124693 + 0.992195i \(0.460206\pi\)
\(270\) 0 0
\(271\) −6.12364 −0.371985 −0.185992 0.982551i \(-0.559550\pi\)
−0.185992 + 0.982551i \(0.559550\pi\)
\(272\) 0 0
\(273\) −1.27816 + 0.423902i −0.0773578 + 0.0256557i
\(274\) 0 0
\(275\) −2.61491 4.52915i −0.157685 0.273118i
\(276\) 0 0
\(277\) −7.88255 + 13.6530i −0.473616 + 0.820327i −0.999544 0.0302019i \(-0.990385\pi\)
0.525928 + 0.850529i \(0.323718\pi\)
\(278\) 0 0
\(279\) 14.0488 + 6.05146i 0.841077 + 0.362291i
\(280\) 0 0
\(281\) 10.5946 18.3503i 0.632018 1.09469i −0.355120 0.934821i \(-0.615560\pi\)
0.987139 0.159867i \(-0.0511065\pi\)
\(282\) 0 0
\(283\) 3.43818 + 5.95510i 0.204378 + 0.353994i 0.949935 0.312449i \(-0.101149\pi\)
−0.745556 + 0.666443i \(0.767816\pi\)
\(284\) 0 0
\(285\) −10.9709 9.75822i −0.649861 0.578027i
\(286\) 0 0
\(287\) −5.87636 −0.346870
\(288\) 0 0
\(289\) −9.09888 −0.535228
\(290\) 0 0
\(291\) 3.02290 14.6590i 0.177206 0.859325i
\(292\) 0 0
\(293\) 13.7534 + 23.8216i 0.803482 + 1.39167i 0.917311 + 0.398172i \(0.130355\pi\)
−0.113829 + 0.993500i \(0.536311\pi\)
\(294\) 0 0
\(295\) −12.1421 + 21.0308i −0.706943 + 1.22446i
\(296\) 0 0
\(297\) 5.44870 + 11.6612i 0.316166 + 0.676653i
\(298\) 0 0
\(299\) 0.276783 0.479402i 0.0160068 0.0277245i
\(300\) 0 0
\(301\) −2.32691 4.03033i −0.134121 0.232305i
\(302\) 0 0
\(303\) 0.843624 4.09100i 0.0484649 0.235022i
\(304\) 0 0
\(305\) −24.3200 −1.39256
\(306\) 0 0
\(307\) 21.5178 1.22809 0.614043 0.789273i \(-0.289542\pi\)
0.614043 + 0.789273i \(0.289542\pi\)
\(308\) 0 0
\(309\) 5.60872 + 4.98874i 0.319069 + 0.283800i
\(310\) 0 0
\(311\) 9.19275 + 15.9223i 0.521273 + 0.902871i 0.999694 + 0.0247407i \(0.00787601\pi\)
−0.478421 + 0.878131i \(0.658791\pi\)
\(312\) 0 0
\(313\) 0.000688709 0.00119288i 3.89281e−5 6.74255e-5i −0.866006 0.500034i \(-0.833321\pi\)
0.866045 + 0.499966i \(0.166654\pi\)
\(314\) 0 0
\(315\) −4.08836 + 3.04695i −0.230353 + 0.171676i
\(316\) 0 0
\(317\) −7.04944 + 12.2100i −0.395936 + 0.685781i −0.993220 0.116248i \(-0.962913\pi\)
0.597284 + 0.802030i \(0.296247\pi\)
\(318\) 0 0
\(319\) 5.58650 + 9.67611i 0.312784 + 0.541758i
\(320\) 0 0
\(321\) 31.5611 10.4672i 1.76157 0.584223i
\(322\) 0 0
\(323\) 14.0197 0.780075
\(324\) 0 0
\(325\) −1.64145 −0.0910512
\(326\) 0 0
\(327\) −31.1749 + 10.3391i −1.72397 + 0.571756i
\(328\) 0 0
\(329\) 6.49381 + 11.2476i 0.358015 + 0.620101i
\(330\) 0 0
\(331\) 6.98143 12.0922i 0.383734 0.664647i −0.607859 0.794045i \(-0.707971\pi\)
0.991593 + 0.129398i \(0.0413046\pi\)
\(332\) 0 0
\(333\) −16.5407 + 12.3274i −0.906425 + 0.675535i
\(334\) 0 0
\(335\) −6.78799 + 11.7571i −0.370868 + 0.642362i
\(336\) 0 0
\(337\) −12.0982 20.9547i −0.659031 1.14147i −0.980867 0.194679i \(-0.937633\pi\)
0.321836 0.946795i \(-0.395700\pi\)
\(338\) 0 0
\(339\) 16.7330 + 14.8834i 0.908814 + 0.808357i
\(340\) 0 0
\(341\) 12.6304 0.683977
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 0.423327 2.05285i 0.0227912 0.110521i
\(346\) 0 0
\(347\) −16.3578 28.3325i −0.878132 1.52097i −0.853389 0.521275i \(-0.825456\pi\)
−0.0247435 0.999694i \(-0.507877\pi\)
\(348\) 0 0
\(349\) 11.8887 20.5919i 0.636389 1.10226i −0.349830 0.936813i \(-0.613760\pi\)
0.986219 0.165445i \(-0.0529062\pi\)
\(350\) 0 0
\(351\) 4.02476 + 0.348986i 0.214826 + 0.0186275i
\(352\) 0 0
\(353\) −10.0309 + 17.3740i −0.533889 + 0.924724i 0.465327 + 0.885139i \(0.345937\pi\)
−0.999216 + 0.0395847i \(0.987396\pi\)
\(354\) 0 0
\(355\) 8.72184 + 15.1067i 0.462907 + 0.801779i
\(356\) 0 0
\(357\) 0.983290 4.76828i 0.0520412 0.252364i
\(358\) 0 0
\(359\) −8.30175 −0.438150 −0.219075 0.975708i \(-0.570304\pi\)
−0.219075 + 0.975708i \(0.570304\pi\)
\(360\) 0 0
\(361\) 5.87636 0.309282
\(362\) 0 0
\(363\) −6.29487 5.59905i −0.330395 0.293874i
\(364\) 0 0
\(365\) 4.23855 + 7.34138i 0.221856 + 0.384266i
\(366\) 0 0
\(367\) 5.77197 9.99735i 0.301294 0.521857i −0.675135 0.737694i \(-0.735915\pi\)
0.976429 + 0.215837i \(0.0692480\pi\)
\(368\) 0 0
\(369\) 16.1909 + 6.97418i 0.842864 + 0.363061i
\(370\) 0 0
\(371\) −0.944368 + 1.63569i −0.0490291 + 0.0849210i
\(372\) 0 0
\(373\) −1.42580 2.46956i −0.0738250 0.127869i 0.826750 0.562570i \(-0.190187\pi\)
−0.900575 + 0.434701i \(0.856854\pi\)
\(374\) 0 0
\(375\) −19.8702 + 6.58994i −1.02609 + 0.340303i
\(376\) 0 0
\(377\) 3.50680 0.180609
\(378\) 0 0
\(379\) −35.9519 −1.84672 −0.923361 0.383932i \(-0.874570\pi\)
−0.923361 + 0.383932i \(0.874570\pi\)
\(380\) 0 0
\(381\) 28.9821 9.61192i 1.48480 0.492433i
\(382\) 0 0
\(383\) −0.915278 1.58531i −0.0467685 0.0810054i 0.841694 0.539956i \(-0.181559\pi\)
−0.888462 + 0.458950i \(0.848226\pi\)
\(384\) 0 0
\(385\) −2.10507 + 3.64610i −0.107285 + 0.185822i
\(386\) 0 0
\(387\) 1.62797 + 13.8662i 0.0827546 + 0.704861i
\(388\) 0 0
\(389\) 5.69530 9.86454i 0.288763 0.500152i −0.684752 0.728776i \(-0.740089\pi\)
0.973515 + 0.228624i \(0.0734227\pi\)
\(390\) 0 0
\(391\) 1.00069 + 1.73324i 0.0506070 + 0.0876539i
\(392\) 0 0
\(393\) 7.36033 + 6.54674i 0.371280 + 0.330240i
\(394\) 0 0
\(395\) −15.6538 −0.787630
\(396\) 0 0
\(397\) −10.4313 −0.523532 −0.261766 0.965131i \(-0.584305\pi\)
−0.261766 + 0.965131i \(0.584305\pi\)
\(398\) 0 0
\(399\) 1.74474 8.46079i 0.0873462 0.423569i
\(400\) 0 0
\(401\) 17.0371 + 29.5091i 0.850790 + 1.47361i 0.880496 + 0.474053i \(0.157210\pi\)
−0.0297058 + 0.999559i \(0.509457\pi\)
\(402\) 0 0
\(403\) 1.98212 3.43313i 0.0987364 0.171016i
\(404\) 0 0
\(405\) 14.8807 3.54299i 0.739427 0.176053i
\(406\) 0 0
\(407\) −8.51671 + 14.7514i −0.422158 + 0.731199i
\(408\) 0 0
\(409\) −1.98762 3.44266i −0.0982815 0.170229i 0.812692 0.582694i \(-0.198001\pi\)
−0.910973 + 0.412465i \(0.864668\pi\)
\(410\) 0 0
\(411\) −6.80470 + 32.9981i −0.335651 + 1.62768i
\(412\) 0 0
\(413\) −14.2880 −0.703066
\(414\) 0 0
\(415\) 14.9752 0.735106
\(416\) 0 0
\(417\) 3.86652 + 3.43913i 0.189345 + 0.168415i
\(418\) 0 0
\(419\) −4.72184 8.17847i −0.230677 0.399544i 0.727331 0.686287i \(-0.240761\pi\)
−0.958008 + 0.286743i \(0.907427\pi\)
\(420\) 0 0
\(421\) 3.16002 5.47331i 0.154010 0.266753i −0.778688 0.627411i \(-0.784115\pi\)
0.932698 + 0.360658i \(0.117448\pi\)
\(422\) 0 0
\(423\) −4.54325 38.6971i −0.220900 1.88152i
\(424\) 0 0
\(425\) 2.96727 5.13946i 0.143934 0.249300i
\(426\) 0 0
\(427\) −7.15452 12.3920i −0.346231 0.599690i
\(428\) 0 0
\(429\) 3.16613 1.05005i 0.152862 0.0506967i
\(430\) 0 0
\(431\) 27.7541 1.33687 0.668434 0.743772i \(-0.266965\pi\)
0.668434 + 0.743772i \(0.266965\pi\)
\(432\) 0 0
\(433\) 11.2473 0.540510 0.270255 0.962789i \(-0.412892\pi\)
0.270255 + 0.962789i \(0.412892\pi\)
\(434\) 0 0
\(435\) 12.6032 4.17985i 0.604278 0.200409i
\(436\) 0 0
\(437\) 1.77561 + 3.07545i 0.0849391 + 0.147119i
\(438\) 0 0
\(439\) −7.54325 + 13.0653i −0.360020 + 0.623573i −0.987964 0.154686i \(-0.950563\pi\)
0.627944 + 0.778259i \(0.283897\pi\)
\(440\) 0 0
\(441\) −2.75526 1.18682i −0.131203 0.0565152i
\(442\) 0 0
\(443\) 3.96658 6.87032i 0.188458 0.326419i −0.756278 0.654250i \(-0.772984\pi\)
0.944736 + 0.327831i \(0.106318\pi\)
\(444\) 0 0
\(445\) 8.20396 + 14.2097i 0.388905 + 0.673603i
\(446\) 0 0
\(447\) 10.4814 + 9.32284i 0.495755 + 0.440955i
\(448\) 0 0
\(449\) −32.5636 −1.53677 −0.768386 0.639987i \(-0.778940\pi\)
−0.768386 + 0.639987i \(0.778940\pi\)
\(450\) 0 0
\(451\) 14.5563 0.685430
\(452\) 0 0
\(453\) 3.10074 15.0365i 0.145686 0.706475i
\(454\) 0 0
\(455\) 0.660706 + 1.14438i 0.0309744 + 0.0536492i
\(456\) 0 0
\(457\) −5.70396 + 9.87955i −0.266820 + 0.462146i −0.968039 0.250800i \(-0.919306\pi\)
0.701219 + 0.712946i \(0.252640\pi\)
\(458\) 0 0
\(459\) −8.36831 + 11.9709i −0.390599 + 0.558752i
\(460\) 0 0
\(461\) −2.45853 + 4.25830i −0.114505 + 0.198329i −0.917582 0.397547i \(-0.869862\pi\)
0.803077 + 0.595876i \(0.203195\pi\)
\(462\) 0 0
\(463\) 7.59957 + 13.1628i 0.353182 + 0.611729i 0.986805 0.161913i \(-0.0517663\pi\)
−0.633623 + 0.773642i \(0.718433\pi\)
\(464\) 0 0
\(465\) 3.03156 14.7010i 0.140585 0.681742i
\(466\) 0 0
\(467\) −23.7810 −1.10046 −0.550228 0.835015i \(-0.685459\pi\)
−0.550228 + 0.835015i \(0.685459\pi\)
\(468\) 0 0
\(469\) −7.98762 −0.368834
\(470\) 0 0
\(471\) −11.3436 10.0897i −0.522687 0.464910i
\(472\) 0 0
\(473\) 5.76400 + 9.98354i 0.265029 + 0.459044i
\(474\) 0 0
\(475\) 5.26509 9.11941i 0.241579 0.418427i
\(476\) 0 0
\(477\) 4.54325 3.38597i 0.208021 0.155033i
\(478\) 0 0
\(479\) 3.02909 5.24654i 0.138403 0.239720i −0.788489 0.615048i \(-0.789137\pi\)
0.926892 + 0.375328i \(0.122470\pi\)
\(480\) 0 0
\(481\) 2.67309 + 4.62992i 0.121882 + 0.211106i
\(482\) 0 0
\(483\) 1.17054 0.388209i 0.0532613 0.0176641i
\(484\) 0 0
\(485\) −14.6872 −0.666914
\(486\) 0 0
\(487\) −1.13602 −0.0514781 −0.0257391 0.999669i \(-0.508194\pi\)
−0.0257391 + 0.999669i \(0.508194\pi\)
\(488\) 0 0
\(489\) −3.26764 + 1.08371i −0.147768 + 0.0490072i
\(490\) 0 0
\(491\) −16.4382 28.4718i −0.741845 1.28491i −0.951655 0.307170i \(-0.900618\pi\)
0.209810 0.977742i \(-0.432715\pi\)
\(492\) 0 0
\(493\) −6.33929 + 10.9800i −0.285507 + 0.494513i
\(494\) 0 0
\(495\) 10.1273 7.54760i 0.455188 0.339239i
\(496\) 0 0
\(497\) −5.13162 + 8.88822i −0.230184 + 0.398691i
\(498\) 0 0
\(499\) 13.0989 + 22.6879i 0.586387 + 1.01565i 0.994701 + 0.102810i \(0.0327834\pi\)
−0.408314 + 0.912841i \(0.633883\pi\)
\(500\) 0 0
\(501\) −3.39307 3.01801i −0.151591 0.134835i
\(502\) 0 0
\(503\) 25.8516 1.15267 0.576333 0.817215i \(-0.304483\pi\)
0.576333 + 0.817215i \(0.304483\pi\)
\(504\) 0 0
\(505\) −4.09888 −0.182398
\(506\) 0 0
\(507\) −4.33613 + 21.0273i −0.192574 + 0.933854i
\(508\) 0 0
\(509\) −17.5858 30.4595i −0.779478 1.35009i −0.932243 0.361832i \(-0.882151\pi\)
0.152766 0.988262i \(-0.451182\pi\)
\(510\) 0 0
\(511\) −2.49381 + 4.31941i −0.110320 + 0.191079i
\(512\) 0 0
\(513\) −14.8486 + 21.2410i −0.655584 + 0.937812i
\(514\) 0 0
\(515\) 3.68292 6.37900i 0.162289 0.281092i
\(516\) 0 0
\(517\) −16.0858 27.8615i −0.707453 1.22535i
\(518\) 0 0
\(519\) −1.82946 + 8.87163i −0.0803045 + 0.389421i
\(520\) 0 0
\(521\) −17.8626 −0.782575 −0.391287 0.920269i \(-0.627970\pi\)
−0.391287 + 0.920269i \(0.627970\pi\)
\(522\) 0 0
\(523\) 22.8640 0.999772 0.499886 0.866091i \(-0.333375\pi\)
0.499886 + 0.866091i \(0.333375\pi\)
\(524\) 0 0
\(525\) −2.73236 2.43033i −0.119250 0.106068i
\(526\) 0 0
\(527\) 7.16621 + 12.4122i 0.312165 + 0.540685i
\(528\) 0 0
\(529\) 11.2465 19.4795i 0.488979 0.846937i
\(530\) 0 0
\(531\) 39.3671 + 16.9573i 1.70839 + 0.735883i
\(532\) 0 0
\(533\) 2.28435 3.95661i 0.0989462 0.171380i
\(534\) 0 0
\(535\) −16.3145 28.2576i −0.705339 1.22168i
\(536\) 0 0
\(537\) −7.83379 + 2.59808i −0.338053 + 0.112115i
\(538\) 0 0
\(539\) −2.47710 −0.106696
\(540\) 0 0
\(541\) 22.3077 0.959081 0.479541 0.877520i \(-0.340803\pi\)
0.479541 + 0.877520i \(0.340803\pi\)
\(542\) 0 0
\(543\) 17.1490 5.68747i 0.735935 0.244073i
\(544\) 0 0
\(545\) 16.1149 + 27.9118i 0.690287 + 1.19561i
\(546\) 0 0
\(547\) 10.8083 18.7206i 0.462131 0.800435i −0.536936 0.843623i \(-0.680418\pi\)
0.999067 + 0.0431882i \(0.0137515\pi\)
\(548\) 0 0
\(549\) 5.00550 + 42.6343i 0.213630 + 1.81959i
\(550\) 0 0
\(551\) −11.2484 + 19.4828i −0.479197 + 0.829994i
\(552\) 0 0
\(553\) −4.60507 7.97622i −0.195828 0.339183i
\(554\) 0 0
\(555\) 15.1254 + 13.4535i 0.642039 + 0.571069i
\(556\) 0 0
\(557\) 3.17535 0.134544 0.0672720 0.997735i \(-0.478570\pi\)
0.0672720 + 0.997735i \(0.478570\pi\)
\(558\) 0 0
\(559\) 3.61822 0.153034
\(560\) 0 0
\(561\) −2.43571 + 11.8115i −0.102836 + 0.498682i
\(562\) 0 0
\(563\) 21.8814 + 37.8997i 0.922190 + 1.59728i 0.796019 + 0.605271i \(0.206935\pi\)
0.126171 + 0.992009i \(0.459731\pi\)
\(564\) 0 0
\(565\) 10.9876 19.0311i 0.462253 0.800645i
\(566\) 0 0
\(567\) 6.18292 + 6.53999i 0.259658 + 0.274654i
\(568\) 0 0
\(569\) 11.9313 20.6656i 0.500186 0.866348i −0.499814 0.866133i \(-0.666598\pi\)
1.00000 0.000214897i \(-6.84039e-5\pi\)
\(570\) 0 0
\(571\) 5.11058 + 8.85178i 0.213871 + 0.370435i 0.952923 0.303213i \(-0.0980595\pi\)
−0.739052 + 0.673649i \(0.764726\pi\)
\(572\) 0 0
\(573\) −4.66002 + 22.5979i −0.194675 + 0.944040i
\(574\) 0 0
\(575\) 1.50324 0.0626893
\(576\) 0 0
\(577\) −36.0370 −1.50024 −0.750120 0.661302i \(-0.770004\pi\)
−0.750120 + 0.661302i \(0.770004\pi\)
\(578\) 0 0
\(579\) −18.9487 16.8542i −0.787481 0.700435i
\(580\) 0 0
\(581\) 4.40545 + 7.63046i 0.182769 + 0.316565i
\(582\) 0 0
\(583\) 2.33929 4.05178i 0.0968836 0.167807i
\(584\) 0 0
\(585\) −0.462249 3.93720i −0.0191116 0.162783i
\(586\) 0 0
\(587\) −10.5142 + 18.2111i −0.433966 + 0.751651i −0.997211 0.0746391i \(-0.976220\pi\)
0.563245 + 0.826290i \(0.309553\pi\)
\(588\) 0 0
\(589\) 12.7156 + 22.0242i 0.523939 + 0.907489i
\(590\) 0 0
\(591\) 30.3905 10.0790i 1.25010 0.414595i
\(592\) 0 0
\(593\) −25.1606 −1.03322 −0.516612 0.856220i \(-0.672807\pi\)
−0.516612 + 0.856220i \(0.672807\pi\)
\(594\) 0 0
\(595\) −4.77747 −0.195857
\(596\) 0 0
\(597\) 38.8257 12.8766i 1.58903 0.527002i
\(598\) 0 0
\(599\) −1.11126 1.92477i −0.0454050 0.0786438i 0.842430 0.538806i \(-0.181125\pi\)
−0.887835 + 0.460162i \(0.847791\pi\)
\(600\) 0 0
\(601\) −14.0494 + 24.3343i −0.573089 + 0.992619i 0.423158 + 0.906056i \(0.360922\pi\)
−0.996246 + 0.0865627i \(0.972412\pi\)
\(602\) 0 0
\(603\) 22.0080 + 9.47987i 0.896234 + 0.386050i
\(604\) 0 0
\(605\) −4.13348 + 7.15939i −0.168050 + 0.291071i
\(606\) 0 0
\(607\) −3.26509 5.65531i −0.132526 0.229542i 0.792124 0.610361i \(-0.208975\pi\)
−0.924650 + 0.380819i \(0.875642\pi\)
\(608\) 0 0
\(609\) 5.83743 + 5.19218i 0.236545 + 0.210398i
\(610\) 0 0
\(611\) −10.0975 −0.408501
\(612\) 0 0
\(613\) 10.7280 0.433298 0.216649 0.976250i \(-0.430487\pi\)
0.216649 + 0.976250i \(0.430487\pi\)
\(614\) 0 0
\(615\) 3.49381 16.9426i 0.140884 0.683191i
\(616\) 0 0
\(617\) 15.5265 + 26.8928i 0.625075 + 1.08266i 0.988526 + 0.151049i \(0.0482650\pi\)
−0.363451 + 0.931613i \(0.618402\pi\)
\(618\) 0 0
\(619\) −0.723217 + 1.25265i −0.0290685 + 0.0503482i −0.880194 0.474615i \(-0.842587\pi\)
0.851125 + 0.524963i \(0.175921\pi\)
\(620\) 0 0
\(621\) −3.68587 0.319601i −0.147909 0.0128252i
\(622\) 0 0
\(623\) −4.82691 + 8.36046i −0.193386 + 0.334955i
\(624\) 0 0
\(625\) 4.99312 + 8.64834i 0.199725 + 0.345934i
\(626\) 0 0
\(627\) −4.32189 + 20.9582i −0.172600 + 0.836991i
\(628\) 0 0
\(629\) −19.3287 −0.770686
\(630\) 0 0
\(631\) −0.0741250 −0.00295087 −0.00147544 0.999999i \(-0.500470\pi\)
−0.00147544 + 0.999999i \(0.500470\pi\)
\(632\) 0 0
\(633\) 18.8367 + 16.7546i 0.748693 + 0.665935i
\(634\) 0 0
\(635\) −14.9814 25.9486i −0.594520 1.02974i
\(636\) 0 0
\(637\) −0.388736 + 0.673310i −0.0154023 + 0.0266775i
\(638\) 0 0
\(639\) 24.6877 18.3991i 0.976628 0.727855i
\(640\) 0 0
\(641\) 23.5204 40.7384i 0.928998 1.60907i 0.143996 0.989578i \(-0.454005\pi\)
0.785002 0.619494i \(-0.212662\pi\)
\(642\) 0 0
\(643\) −16.8647 29.2105i −0.665077 1.15195i −0.979264 0.202587i \(-0.935065\pi\)
0.314187 0.949361i \(-0.398268\pi\)
\(644\) 0 0
\(645\) 13.0036 4.31266i 0.512018 0.169811i
\(646\) 0 0
\(647\) −44.9629 −1.76767 −0.883836 0.467796i \(-0.845048\pi\)
−0.883836 + 0.467796i \(0.845048\pi\)
\(648\) 0 0
\(649\) 35.3928 1.38929
\(650\) 0 0
\(651\) 8.38255 2.78007i 0.328538 0.108960i
\(652\) 0 0
\(653\) −20.8578 36.1267i −0.816228 1.41375i −0.908443 0.418010i \(-0.862728\pi\)
0.0922143 0.995739i \(-0.470606\pi\)
\(654\) 0 0
\(655\) 4.83310 8.37118i 0.188845 0.327089i
\(656\) 0 0
\(657\) 11.9975 8.94138i 0.468065 0.348837i
\(658\) 0 0
\(659\) −10.5259 + 18.2313i −0.410029 + 0.710191i −0.994892 0.100941i \(-0.967815\pi\)
0.584863 + 0.811132i \(0.301148\pi\)
\(660\) 0 0
\(661\) −11.2218 19.4368i −0.436479 0.756004i 0.560936 0.827859i \(-0.310441\pi\)
−0.997415 + 0.0718553i \(0.977108\pi\)
\(662\) 0 0
\(663\) 2.82829 + 2.51566i 0.109842 + 0.0977001i
\(664\) 0 0
\(665\) −8.47710 −0.328728
\(666\) 0 0
\(667\) −3.21153 −0.124351
\(668\) 0 0
\(669\) −3.30401 + 16.0222i −0.127741 + 0.619454i
\(670\) 0 0
\(671\) 17.7225 + 30.6962i 0.684168 + 1.18501i
\(672\) 0 0
\(673\) 5.83929 10.1140i 0.225088 0.389864i −0.731258 0.682101i \(-0.761066\pi\)
0.956346 + 0.292237i \(0.0943996\pi\)
\(674\) 0 0
\(675\) 4.64400 + 9.93902i 0.178747 + 0.382553i
\(676\) 0 0
\(677\) −5.23422 + 9.06593i −0.201167 + 0.348432i −0.948905 0.315562i \(-0.897807\pi\)
0.747737 + 0.663995i \(0.231140\pi\)
\(678\) 0 0
\(679\) −4.32072 7.48371i −0.165814 0.287199i
\(680\) 0 0
\(681\) −6.68539 + 32.4195i −0.256185 + 1.24232i
\(682\) 0 0
\(683\) −32.8158 −1.25566 −0.627832 0.778349i \(-0.716057\pi\)
−0.627832 + 0.778349i \(0.716057\pi\)
\(684\) 0 0
\(685\) 33.0617 1.26322
\(686\) 0 0
\(687\) 14.8120 + 13.1747i 0.565113 + 0.502647i
\(688\) 0 0
\(689\) −0.734219 1.27171i −0.0279715 0.0484481i
\(690\) 0 0
\(691\) 2.95056 5.11052i 0.112245 0.194413i −0.804430 0.594047i \(-0.797529\pi\)
0.916675 + 0.399634i \(0.130863\pi\)
\(692\) 0 0
\(693\) 6.82505 + 2.93987i 0.259262 + 0.111676i
\(694\) 0 0
\(695\) 2.53892 4.39754i 0.0963068 0.166808i
\(696\) 0 0
\(697\) 8.25890 + 14.3048i 0.312828 + 0.541834i
\(698\) 0 0
\(699\) 1.95715 0.649089i 0.0740263 0.0245508i
\(700\) 0 0
\(701\) −12.3782 −0.467519 −0.233759 0.972294i \(-0.575103\pi\)
−0.233759 + 0.972294i \(0.575103\pi\)
\(702\) 0 0
\(703\) −34.2967 −1.29352
\(704\) 0 0
\(705\) −36.2898 + 12.0355i −1.36675 + 0.453283i
\(706\) 0 0
\(707\) −1.20582 2.08854i −0.0453495 0.0785476i
\(708\) 0 0
\(709\) 6.64145 11.5033i 0.249425 0.432016i −0.713942 0.700205i \(-0.753092\pi\)
0.963366 + 0.268189i \(0.0864251\pi\)
\(710\) 0 0
\(711\) 3.22184 + 27.4420i 0.120828 + 1.02915i
\(712\) 0 0
\(713\) −1.81522 + 3.14406i −0.0679806 + 0.117746i
\(714\) 0 0
\(715\) −1.63664 2.83474i −0.0612067 0.106013i
\(716\) 0 0
\(717\) −31.4265 27.9527i −1.17364 1.04391i
\(718\) 0 0
\(719\) 24.3694 0.908825 0.454413 0.890791i \(-0.349849\pi\)
0.454413 + 0.890791i \(0.349849\pi\)
\(720\) 0 0
\(721\) 4.33379 0.161399
\(722\) 0 0
\(723\) −7.49264 + 36.3342i −0.278654 + 1.35128i
\(724\) 0 0
\(725\) 4.76145 + 8.24707i 0.176836 + 0.306289i
\(726\) 0 0
\(727\) −7.99450 + 13.8469i −0.296500 + 0.513552i −0.975333 0.220740i \(-0.929153\pi\)
0.678833 + 0.734293i \(0.262486\pi\)
\(728\) 0 0
\(729\) −9.27375 25.3574i −0.343472 0.939163i
\(730\) 0 0
\(731\) −6.54070 + 11.3288i −0.241917 + 0.419012i
\(732\) 0 0
\(733\) 21.1414 + 36.6181i 0.780877 + 1.35252i 0.931431 + 0.363917i \(0.118561\pi\)
−0.150554 + 0.988602i \(0.548106\pi\)
\(734\) 0 0
\(735\) −0.594554 + 2.88318i −0.0219304 + 0.106348i
\(736\) 0 0
\(737\) 19.7861 0.728832
\(738\) 0 0
\(739\) 3.08650 0.113539 0.0567695 0.998387i \(-0.481920\pi\)
0.0567695 + 0.998387i \(0.481920\pi\)
\(740\) 0 0
\(741\) 5.01849 + 4.46376i 0.184359 + 0.163980i
\(742\) 0 0
\(743\) 3.31522 + 5.74213i 0.121624 + 0.210658i 0.920408 0.390959i \(-0.127857\pi\)
−0.798784 + 0.601617i \(0.794523\pi\)
\(744\) 0 0
\(745\) 6.88255 11.9209i 0.252157 0.436749i
\(746\) 0 0
\(747\) −3.08217 26.2524i −0.112771 0.960524i
\(748\) 0 0
\(749\) 9.59888 16.6258i 0.350736 0.607492i
\(750\) 0 0
\(751\) −21.3702 37.0142i −0.779808 1.35067i −0.932052 0.362325i \(-0.881983\pi\)
0.152243 0.988343i \(-0.451350\pi\)
\(752\) 0 0
\(753\) −4.40585 + 1.46120i −0.160558 + 0.0532491i
\(754\) 0 0
\(755\) −15.0655 −0.548288
\(756\) 0 0
\(757\) −31.0232 −1.12756 −0.563779 0.825926i \(-0.690653\pi\)
−0.563779 + 0.825926i \(0.690653\pi\)
\(758\) 0 0
\(759\) −2.89954 + 0.961632i −0.105247 + 0.0349050i
\(760\) 0 0
\(761\) −11.8182 20.4697i −0.428409 0.742025i 0.568323 0.822805i \(-0.307592\pi\)
−0.996732 + 0.0807799i \(0.974259\pi\)
\(762\) 0 0
\(763\) −9.48143 + 16.4223i −0.343251 + 0.594528i
\(764\) 0 0
\(765\) 13.1632 + 5.67000i 0.475916 + 0.204999i
\(766\) 0 0
\(767\) 5.55425 9.62025i 0.200553 0.347367i
\(768\) 0 0
\(769\) 1.73422 + 3.00376i 0.0625375 + 0.108318i 0.895599 0.444862i \(-0.146747\pi\)
−0.833061 + 0.553180i \(0.813414\pi\)
\(770\) 0 0
\(771\) −14.3462 12.7604i −0.516665 0.459554i
\(772\) 0 0
\(773\) 34.5970 1.24437 0.622184 0.782871i \(-0.286245\pi\)
0.622184 + 0.782871i \(0.286245\pi\)
\(774\) 0 0
\(775\) 10.7651 0.386694
\(776\) 0 0
\(777\) −2.40545 + 11.6648i −0.0862949 + 0.418471i
\(778\) 0 0
\(779\) 14.6545 + 25.3824i 0.525053 + 0.909418i
\(780\) 0 0
\(781\) 12.7115 22.0170i 0.454854 0.787831i
\(782\) 0 0
\(783\) −9.92147 21.2338i −0.354564 0.758834i
\(784\) 0 0
\(785\) −7.44870 + 12.9015i −0.265855 + 0.460475i
\(786\) 0 0
\(787\) −6.07963 10.5302i −0.216715 0.375362i 0.737087 0.675798i \(-0.236201\pi\)
−0.953802 + 0.300437i \(0.902868\pi\)
\(788\) 0 0
\(789\) −4.69028 + 22.7446i −0.166978 + 0.809730i
\(790\) 0 0
\(791\) 12.9294 0.459718
\(792\) 0 0
\(793\) 11.1249 0.395056
\(794\) 0 0
\(795\) −4.15452 3.69529i −0.147346 0.131058i
\(796\) 0 0
\(797\) −2.89493 5.01416i −0.102544 0.177611i 0.810188 0.586170i \(-0.199365\pi\)
−0.912732 + 0.408559i \(0.866031\pi\)
\(798\) 0 0
\(799\) 18.2534 31.6158i 0.645759 1.11849i
\(800\) 0 0