Properties

Label 280.2.q.d.81.1
Level $280$
Weight $2$
Character 280.81
Analytic conductor $2.236$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 81.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 280.81
Dual form 280.2.q.d.121.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.207107 + 0.358719i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(1.62132 + 2.09077i) q^{7} +(1.41421 + 2.44949i) q^{9} +O(q^{10})\) \(q+(-0.207107 + 0.358719i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(1.62132 + 2.09077i) q^{7} +(1.41421 + 2.44949i) q^{9} +(-0.414214 + 0.717439i) q^{11} +2.00000 q^{13} +0.414214 q^{15} +(3.82843 - 6.63103i) q^{17} +(2.82843 + 4.89898i) q^{19} +(-1.08579 + 0.148586i) q^{21} +(2.79289 + 4.83743i) q^{23} +(-0.500000 + 0.866025i) q^{25} -2.41421 q^{27} -7.82843 q^{29} +(-0.414214 + 0.717439i) q^{31} +(-0.171573 - 0.297173i) q^{33} +(1.00000 - 2.44949i) q^{35} +(-2.82843 - 4.89898i) q^{37} +(-0.414214 + 0.717439i) q^{39} +5.82843 q^{41} -6.89949 q^{43} +(1.41421 - 2.44949i) q^{45} +(-5.82843 - 10.0951i) q^{47} +(-1.74264 + 6.77962i) q^{49} +(1.58579 + 2.74666i) q^{51} +(2.82843 - 4.89898i) q^{53} +0.828427 q^{55} -2.34315 q^{57} +(2.00000 - 3.46410i) q^{59} +(-3.32843 - 5.76500i) q^{61} +(-2.82843 + 6.92820i) q^{63} +(-1.00000 - 1.73205i) q^{65} +(6.44975 - 11.1713i) q^{67} -2.31371 q^{69} -12.0000 q^{71} +(-1.82843 + 3.16693i) q^{73} +(-0.207107 - 0.358719i) q^{75} +(-2.17157 + 0.297173i) q^{77} +(2.00000 + 3.46410i) q^{79} +(-3.74264 + 6.48244i) q^{81} -4.75736 q^{83} -7.65685 q^{85} +(1.62132 - 2.80821i) q^{87} +(2.67157 + 4.62730i) q^{89} +(3.24264 + 4.18154i) q^{91} +(-0.171573 - 0.297173i) q^{93} +(2.82843 - 4.89898i) q^{95} +6.00000 q^{97} -2.34315 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{3} - 2q^{5} - 2q^{7} + O(q^{10}) \) \( 4q + 2q^{3} - 2q^{5} - 2q^{7} + 4q^{11} + 8q^{13} - 4q^{15} + 4q^{17} - 10q^{21} + 14q^{23} - 2q^{25} - 4q^{27} - 20q^{29} + 4q^{31} - 12q^{33} + 4q^{35} + 4q^{39} + 12q^{41} + 12q^{43} - 12q^{47} + 10q^{49} + 12q^{51} - 8q^{55} - 32q^{57} + 8q^{59} - 2q^{61} - 4q^{65} + 6q^{67} + 36q^{69} - 48q^{71} + 4q^{73} + 2q^{75} - 20q^{77} + 8q^{79} + 2q^{81} - 36q^{83} - 8q^{85} - 2q^{87} + 22q^{89} - 4q^{91} - 12q^{93} + 24q^{97} - 32q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) −0.207107 + 0.358719i −0.119573 + 0.207107i −0.919599 0.392859i \(-0.871486\pi\)
0.800025 + 0.599966i \(0.204819\pi\)
\(4\) 0 0
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0 0
\(7\) 1.62132 + 2.09077i 0.612801 + 0.790237i
\(8\) 0 0
\(9\) 1.41421 + 2.44949i 0.471405 + 0.816497i
\(10\) 0 0
\(11\) −0.414214 + 0.717439i −0.124890 + 0.216316i −0.921690 0.387927i \(-0.873191\pi\)
0.796800 + 0.604243i \(0.206524\pi\)
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 0.414214 0.106949
\(16\) 0 0
\(17\) 3.82843 6.63103i 0.928530 1.60826i 0.142747 0.989759i \(-0.454407\pi\)
0.785783 0.618502i \(-0.212260\pi\)
\(18\) 0 0
\(19\) 2.82843 + 4.89898i 0.648886 + 1.12390i 0.983389 + 0.181509i \(0.0580980\pi\)
−0.334504 + 0.942394i \(0.608569\pi\)
\(20\) 0 0
\(21\) −1.08579 + 0.148586i −0.236938 + 0.0324242i
\(22\) 0 0
\(23\) 2.79289 + 4.83743i 0.582358 + 1.00867i 0.995199 + 0.0978712i \(0.0312033\pi\)
−0.412841 + 0.910803i \(0.635463\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) −2.41421 −0.464616
\(28\) 0 0
\(29\) −7.82843 −1.45370 −0.726851 0.686795i \(-0.759017\pi\)
−0.726851 + 0.686795i \(0.759017\pi\)
\(30\) 0 0
\(31\) −0.414214 + 0.717439i −0.0743950 + 0.128856i −0.900823 0.434187i \(-0.857036\pi\)
0.826428 + 0.563042i \(0.190369\pi\)
\(32\) 0 0
\(33\) −0.171573 0.297173i −0.0298670 0.0517312i
\(34\) 0 0
\(35\) 1.00000 2.44949i 0.169031 0.414039i
\(36\) 0 0
\(37\) −2.82843 4.89898i −0.464991 0.805387i 0.534211 0.845351i \(-0.320609\pi\)
−0.999201 + 0.0399642i \(0.987276\pi\)
\(38\) 0 0
\(39\) −0.414214 + 0.717439i −0.0663273 + 0.114882i
\(40\) 0 0
\(41\) 5.82843 0.910247 0.455124 0.890428i \(-0.349595\pi\)
0.455124 + 0.890428i \(0.349595\pi\)
\(42\) 0 0
\(43\) −6.89949 −1.05216 −0.526082 0.850434i \(-0.676339\pi\)
−0.526082 + 0.850434i \(0.676339\pi\)
\(44\) 0 0
\(45\) 1.41421 2.44949i 0.210819 0.365148i
\(46\) 0 0
\(47\) −5.82843 10.0951i −0.850163 1.47253i −0.881060 0.473004i \(-0.843170\pi\)
0.0308969 0.999523i \(-0.490164\pi\)
\(48\) 0 0
\(49\) −1.74264 + 6.77962i −0.248949 + 0.968517i
\(50\) 0 0
\(51\) 1.58579 + 2.74666i 0.222055 + 0.384610i
\(52\) 0 0
\(53\) 2.82843 4.89898i 0.388514 0.672927i −0.603736 0.797185i \(-0.706322\pi\)
0.992250 + 0.124258i \(0.0396551\pi\)
\(54\) 0 0
\(55\) 0.828427 0.111705
\(56\) 0 0
\(57\) −2.34315 −0.310357
\(58\) 0 0
\(59\) 2.00000 3.46410i 0.260378 0.450988i −0.705965 0.708247i \(-0.749486\pi\)
0.966342 + 0.257260i \(0.0828195\pi\)
\(60\) 0 0
\(61\) −3.32843 5.76500i −0.426161 0.738133i 0.570367 0.821390i \(-0.306801\pi\)
−0.996528 + 0.0832569i \(0.973468\pi\)
\(62\) 0 0
\(63\) −2.82843 + 6.92820i −0.356348 + 0.872872i
\(64\) 0 0
\(65\) −1.00000 1.73205i −0.124035 0.214834i
\(66\) 0 0
\(67\) 6.44975 11.1713i 0.787962 1.36479i −0.139251 0.990257i \(-0.544470\pi\)
0.927213 0.374533i \(-0.122197\pi\)
\(68\) 0 0
\(69\) −2.31371 −0.278538
\(70\) 0 0
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) −1.82843 + 3.16693i −0.214001 + 0.370661i −0.952963 0.303086i \(-0.901983\pi\)
0.738962 + 0.673747i \(0.235316\pi\)
\(74\) 0 0
\(75\) −0.207107 0.358719i −0.0239146 0.0414214i
\(76\) 0 0
\(77\) −2.17157 + 0.297173i −0.247474 + 0.0338660i
\(78\) 0 0
\(79\) 2.00000 + 3.46410i 0.225018 + 0.389742i 0.956325 0.292306i \(-0.0944227\pi\)
−0.731307 + 0.682048i \(0.761089\pi\)
\(80\) 0 0
\(81\) −3.74264 + 6.48244i −0.415849 + 0.720272i
\(82\) 0 0
\(83\) −4.75736 −0.522188 −0.261094 0.965313i \(-0.584083\pi\)
−0.261094 + 0.965313i \(0.584083\pi\)
\(84\) 0 0
\(85\) −7.65685 −0.830502
\(86\) 0 0
\(87\) 1.62132 2.80821i 0.173824 0.301072i
\(88\) 0 0
\(89\) 2.67157 + 4.62730i 0.283186 + 0.490493i 0.972168 0.234286i \(-0.0752752\pi\)
−0.688982 + 0.724779i \(0.741942\pi\)
\(90\) 0 0
\(91\) 3.24264 + 4.18154i 0.339921 + 0.438345i
\(92\) 0 0
\(93\) −0.171573 0.297173i −0.0177913 0.0308154i
\(94\) 0 0
\(95\) 2.82843 4.89898i 0.290191 0.502625i
\(96\) 0 0
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 0 0
\(99\) −2.34315 −0.235495
\(100\) 0 0
\(101\) 5.74264 9.94655i 0.571414 0.989718i −0.425007 0.905190i \(-0.639728\pi\)
0.996421 0.0845282i \(-0.0269383\pi\)
\(102\) 0 0
\(103\) −3.79289 6.56948i −0.373725 0.647310i 0.616410 0.787425i \(-0.288586\pi\)
−0.990135 + 0.140115i \(0.955253\pi\)
\(104\) 0 0
\(105\) 0.671573 + 0.866025i 0.0655388 + 0.0845154i
\(106\) 0 0
\(107\) 2.79289 + 4.83743i 0.269999 + 0.467652i 0.968861 0.247604i \(-0.0796432\pi\)
−0.698862 + 0.715256i \(0.746310\pi\)
\(108\) 0 0
\(109\) −9.15685 + 15.8601i −0.877068 + 1.51913i −0.0225237 + 0.999746i \(0.507170\pi\)
−0.854544 + 0.519379i \(0.826163\pi\)
\(110\) 0 0
\(111\) 2.34315 0.222402
\(112\) 0 0
\(113\) 11.3137 1.06430 0.532152 0.846649i \(-0.321383\pi\)
0.532152 + 0.846649i \(0.321383\pi\)
\(114\) 0 0
\(115\) 2.79289 4.83743i 0.260439 0.451093i
\(116\) 0 0
\(117\) 2.82843 + 4.89898i 0.261488 + 0.452911i
\(118\) 0 0
\(119\) 20.0711 2.74666i 1.83991 0.251786i
\(120\) 0 0
\(121\) 5.15685 + 8.93193i 0.468805 + 0.811994i
\(122\) 0 0
\(123\) −1.20711 + 2.09077i −0.108841 + 0.188518i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −4.34315 −0.385392 −0.192696 0.981259i \(-0.561723\pi\)
−0.192696 + 0.981259i \(0.561723\pi\)
\(128\) 0 0
\(129\) 1.42893 2.47498i 0.125810 0.217910i
\(130\) 0 0
\(131\) −6.82843 11.8272i −0.596602 1.03335i −0.993319 0.115404i \(-0.963184\pi\)
0.396716 0.917941i \(-0.370150\pi\)
\(132\) 0 0
\(133\) −5.65685 + 13.8564i −0.490511 + 1.20150i
\(134\) 0 0
\(135\) 1.20711 + 2.09077i 0.103891 + 0.179945i
\(136\) 0 0
\(137\) 2.00000 3.46410i 0.170872 0.295958i −0.767853 0.640626i \(-0.778675\pi\)
0.938725 + 0.344668i \(0.112008\pi\)
\(138\) 0 0
\(139\) 2.48528 0.210799 0.105399 0.994430i \(-0.466388\pi\)
0.105399 + 0.994430i \(0.466388\pi\)
\(140\) 0 0
\(141\) 4.82843 0.406627
\(142\) 0 0
\(143\) −0.828427 + 1.43488i −0.0692766 + 0.119991i
\(144\) 0 0
\(145\) 3.91421 + 6.77962i 0.325058 + 0.563017i
\(146\) 0 0
\(147\) −2.07107 2.02922i −0.170819 0.167368i
\(148\) 0 0
\(149\) −2.32843 4.03295i −0.190752 0.330392i 0.754748 0.656015i \(-0.227759\pi\)
−0.945500 + 0.325623i \(0.894426\pi\)
\(150\) 0 0
\(151\) 5.58579 9.67487i 0.454565 0.787329i −0.544098 0.839022i \(-0.683128\pi\)
0.998663 + 0.0516921i \(0.0164614\pi\)
\(152\) 0 0
\(153\) 21.6569 1.75085
\(154\) 0 0
\(155\) 0.828427 0.0665409
\(156\) 0 0
\(157\) −0.656854 + 1.13770i −0.0524227 + 0.0907987i −0.891046 0.453913i \(-0.850028\pi\)
0.838623 + 0.544712i \(0.183361\pi\)
\(158\) 0 0
\(159\) 1.17157 + 2.02922i 0.0929118 + 0.160928i
\(160\) 0 0
\(161\) −5.58579 + 13.6823i −0.440222 + 1.07832i
\(162\) 0 0
\(163\) 7.82843 + 13.5592i 0.613170 + 1.06204i 0.990703 + 0.136045i \(0.0434392\pi\)
−0.377533 + 0.925996i \(0.623227\pi\)
\(164\) 0 0
\(165\) −0.171573 + 0.297173i −0.0133569 + 0.0231349i
\(166\) 0 0
\(167\) 2.07107 0.160264 0.0801320 0.996784i \(-0.474466\pi\)
0.0801320 + 0.996784i \(0.474466\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) −8.00000 + 13.8564i −0.611775 + 1.05963i
\(172\) 0 0
\(173\) −5.17157 8.95743i −0.393187 0.681021i 0.599681 0.800239i \(-0.295294\pi\)
−0.992868 + 0.119219i \(0.961961\pi\)
\(174\) 0 0
\(175\) −2.62132 + 0.358719i −0.198153 + 0.0271166i
\(176\) 0 0
\(177\) 0.828427 + 1.43488i 0.0622684 + 0.107852i
\(178\) 0 0
\(179\) 3.24264 5.61642i 0.242366 0.419791i −0.719022 0.694988i \(-0.755410\pi\)
0.961388 + 0.275197i \(0.0887431\pi\)
\(180\) 0 0
\(181\) −4.17157 −0.310071 −0.155035 0.987909i \(-0.549549\pi\)
−0.155035 + 0.987909i \(0.549549\pi\)
\(182\) 0 0
\(183\) 2.75736 0.203830
\(184\) 0 0
\(185\) −2.82843 + 4.89898i −0.207950 + 0.360180i
\(186\) 0 0
\(187\) 3.17157 + 5.49333i 0.231928 + 0.401712i
\(188\) 0 0
\(189\) −3.91421 5.04757i −0.284717 0.367156i
\(190\) 0 0
\(191\) 2.75736 + 4.77589i 0.199516 + 0.345571i 0.948371 0.317162i \(-0.102730\pi\)
−0.748856 + 0.662733i \(0.769397\pi\)
\(192\) 0 0
\(193\) 2.65685 4.60181i 0.191245 0.331245i −0.754418 0.656394i \(-0.772081\pi\)
0.945663 + 0.325149i \(0.105414\pi\)
\(194\) 0 0
\(195\) 0.828427 0.0593249
\(196\) 0 0
\(197\) 0.343146 0.0244481 0.0122241 0.999925i \(-0.496109\pi\)
0.0122241 + 0.999925i \(0.496109\pi\)
\(198\) 0 0
\(199\) 11.6569 20.1903i 0.826332 1.43125i −0.0745642 0.997216i \(-0.523757\pi\)
0.900897 0.434034i \(-0.142910\pi\)
\(200\) 0 0
\(201\) 2.67157 + 4.62730i 0.188438 + 0.326385i
\(202\) 0 0
\(203\) −12.6924 16.3674i −0.890831 1.14877i
\(204\) 0 0
\(205\) −2.91421 5.04757i −0.203538 0.352537i
\(206\) 0 0
\(207\) −7.89949 + 13.6823i −0.549053 + 0.950987i
\(208\) 0 0
\(209\) −4.68629 −0.324158
\(210\) 0 0
\(211\) 26.6274 1.83311 0.916553 0.399912i \(-0.130959\pi\)
0.916553 + 0.399912i \(0.130959\pi\)
\(212\) 0 0
\(213\) 2.48528 4.30463i 0.170289 0.294949i
\(214\) 0 0
\(215\) 3.44975 + 5.97514i 0.235271 + 0.407501i
\(216\) 0 0
\(217\) −2.17157 + 0.297173i −0.147416 + 0.0201734i
\(218\) 0 0
\(219\) −0.757359 1.31178i −0.0511776 0.0886422i
\(220\) 0 0
\(221\) 7.65685 13.2621i 0.515056 0.892103i
\(222\) 0 0
\(223\) −14.9706 −1.00250 −0.501252 0.865302i \(-0.667127\pi\)
−0.501252 + 0.865302i \(0.667127\pi\)
\(224\) 0 0
\(225\) −2.82843 −0.188562
\(226\) 0 0
\(227\) −7.00000 + 12.1244i −0.464606 + 0.804722i −0.999184 0.0403978i \(-0.987137\pi\)
0.534577 + 0.845120i \(0.320471\pi\)
\(228\) 0 0
\(229\) 7.00000 + 12.1244i 0.462573 + 0.801200i 0.999088 0.0426906i \(-0.0135930\pi\)
−0.536515 + 0.843891i \(0.680260\pi\)
\(230\) 0 0
\(231\) 0.343146 0.840532i 0.0225773 0.0553029i
\(232\) 0 0
\(233\) −5.82843 10.0951i −0.381833 0.661354i 0.609491 0.792793i \(-0.291374\pi\)
−0.991324 + 0.131439i \(0.958040\pi\)
\(234\) 0 0
\(235\) −5.82843 + 10.0951i −0.380205 + 0.658534i
\(236\) 0 0
\(237\) −1.65685 −0.107624
\(238\) 0 0
\(239\) −30.4853 −1.97193 −0.985964 0.166955i \(-0.946606\pi\)
−0.985964 + 0.166955i \(0.946606\pi\)
\(240\) 0 0
\(241\) 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i \(-0.728952\pi\)
0.980917 + 0.194429i \(0.0622852\pi\)
\(242\) 0 0
\(243\) −5.17157 8.95743i −0.331757 0.574619i
\(244\) 0 0
\(245\) 6.74264 1.88064i 0.430772 0.120150i
\(246\) 0 0
\(247\) 5.65685 + 9.79796i 0.359937 + 0.623429i
\(248\) 0 0
\(249\) 0.985281 1.70656i 0.0624397 0.108149i
\(250\) 0 0
\(251\) −27.4558 −1.73300 −0.866499 0.499179i \(-0.833635\pi\)
−0.866499 + 0.499179i \(0.833635\pi\)
\(252\) 0 0
\(253\) −4.62742 −0.290923
\(254\) 0 0
\(255\) 1.58579 2.74666i 0.0993058 0.172003i
\(256\) 0 0
\(257\) −7.65685 13.2621i −0.477621 0.827265i 0.522050 0.852915i \(-0.325168\pi\)
−0.999671 + 0.0256506i \(0.991834\pi\)
\(258\) 0 0
\(259\) 5.65685 13.8564i 0.351500 0.860995i
\(260\) 0 0
\(261\) −11.0711 19.1757i −0.685282 1.18694i
\(262\) 0 0
\(263\) 7.86396 13.6208i 0.484913 0.839893i −0.514937 0.857228i \(-0.672185\pi\)
0.999850 + 0.0173347i \(0.00551807\pi\)
\(264\) 0 0
\(265\) −5.65685 −0.347498
\(266\) 0 0
\(267\) −2.21320 −0.135446
\(268\) 0 0
\(269\) 3.32843 5.76500i 0.202938 0.351499i −0.746536 0.665345i \(-0.768284\pi\)
0.949474 + 0.313847i \(0.101618\pi\)
\(270\) 0 0
\(271\) 1.65685 + 2.86976i 0.100647 + 0.174325i 0.911951 0.410298i \(-0.134575\pi\)
−0.811305 + 0.584624i \(0.801242\pi\)
\(272\) 0 0
\(273\) −2.17157 + 0.297173i −0.131430 + 0.0179857i
\(274\) 0 0
\(275\) −0.414214 0.717439i −0.0249780 0.0432632i
\(276\) 0 0
\(277\) −14.3137 + 24.7921i −0.860027 + 1.48961i 0.0118739 + 0.999930i \(0.496220\pi\)
−0.871901 + 0.489682i \(0.837113\pi\)
\(278\) 0 0
\(279\) −2.34315 −0.140280
\(280\) 0 0
\(281\) 2.68629 0.160251 0.0801254 0.996785i \(-0.474468\pi\)
0.0801254 + 0.996785i \(0.474468\pi\)
\(282\) 0 0
\(283\) −9.00000 + 15.5885i −0.534994 + 0.926638i 0.464169 + 0.885747i \(0.346353\pi\)
−0.999164 + 0.0408910i \(0.986980\pi\)
\(284\) 0 0
\(285\) 1.17157 + 2.02922i 0.0693980 + 0.120201i
\(286\) 0 0
\(287\) 9.44975 + 12.1859i 0.557801 + 0.719311i
\(288\) 0 0
\(289\) −20.8137 36.0504i −1.22434 2.12061i
\(290\) 0 0
\(291\) −1.24264 + 2.15232i −0.0728449 + 0.126171i
\(292\) 0 0
\(293\) 16.9706 0.991431 0.495715 0.868485i \(-0.334906\pi\)
0.495715 + 0.868485i \(0.334906\pi\)
\(294\) 0 0
\(295\) −4.00000 −0.232889
\(296\) 0 0
\(297\) 1.00000 1.73205i 0.0580259 0.100504i
\(298\) 0 0
\(299\) 5.58579 + 9.67487i 0.323034 + 0.559512i
\(300\) 0 0
\(301\) −11.1863 14.4253i −0.644767 0.831458i
\(302\) 0 0
\(303\) 2.37868 + 4.11999i 0.136652 + 0.236687i
\(304\) 0 0
\(305\) −3.32843 + 5.76500i −0.190585 + 0.330103i
\(306\) 0 0
\(307\) 4.75736 0.271517 0.135758 0.990742i \(-0.456653\pi\)
0.135758 + 0.990742i \(0.456653\pi\)
\(308\) 0 0
\(309\) 3.14214 0.178750
\(310\) 0 0
\(311\) −10.8284 + 18.7554i −0.614024 + 1.06352i 0.376531 + 0.926404i \(0.377117\pi\)
−0.990555 + 0.137116i \(0.956217\pi\)
\(312\) 0 0
\(313\) −10.4853 18.1610i −0.592663 1.02652i −0.993872 0.110536i \(-0.964743\pi\)
0.401209 0.915987i \(-0.368590\pi\)
\(314\) 0 0
\(315\) 7.41421 1.01461i 0.417744 0.0571669i
\(316\) 0 0
\(317\) 11.0000 + 19.0526i 0.617822 + 1.07010i 0.989882 + 0.141890i \(0.0453179\pi\)
−0.372061 + 0.928208i \(0.621349\pi\)
\(318\) 0 0
\(319\) 3.24264 5.61642i 0.181553 0.314459i
\(320\) 0 0
\(321\) −2.31371 −0.129139
\(322\) 0 0
\(323\) 43.3137 2.41004
\(324\) 0 0
\(325\) −1.00000 + 1.73205i −0.0554700 + 0.0960769i
\(326\) 0 0
\(327\) −3.79289 6.56948i −0.209747 0.363293i
\(328\) 0 0
\(329\) 11.6569 28.5533i 0.642663 1.57420i
\(330\) 0 0
\(331\) −13.2426 22.9369i −0.727881 1.26073i −0.957777 0.287512i \(-0.907172\pi\)
0.229896 0.973215i \(-0.426162\pi\)
\(332\) 0 0
\(333\) 8.00000 13.8564i 0.438397 0.759326i
\(334\) 0 0
\(335\) −12.8995 −0.704775
\(336\) 0 0
\(337\) 24.9706 1.36023 0.680117 0.733104i \(-0.261929\pi\)
0.680117 + 0.733104i \(0.261929\pi\)
\(338\) 0 0
\(339\) −2.34315 + 4.05845i −0.127262 + 0.220425i
\(340\) 0 0
\(341\) −0.343146 0.594346i −0.0185824 0.0321856i
\(342\) 0 0
\(343\) −17.0000 + 7.34847i −0.917914 + 0.396780i
\(344\) 0 0
\(345\) 1.15685 + 2.00373i 0.0622829 + 0.107877i
\(346\) 0 0
\(347\) −5.69239 + 9.85951i −0.305583 + 0.529286i −0.977391 0.211440i \(-0.932185\pi\)
0.671808 + 0.740726i \(0.265518\pi\)
\(348\) 0 0
\(349\) 9.82843 0.526104 0.263052 0.964782i \(-0.415271\pi\)
0.263052 + 0.964782i \(0.415271\pi\)
\(350\) 0 0
\(351\) −4.82843 −0.257722
\(352\) 0 0
\(353\) −16.8284 + 29.1477i −0.895687 + 1.55138i −0.0627345 + 0.998030i \(0.519982\pi\)
−0.832952 + 0.553345i \(0.813351\pi\)
\(354\) 0 0
\(355\) 6.00000 + 10.3923i 0.318447 + 0.551566i
\(356\) 0 0
\(357\) −3.17157 + 7.76874i −0.167857 + 0.411165i
\(358\) 0 0
\(359\) 3.24264 + 5.61642i 0.171140 + 0.296423i 0.938819 0.344412i \(-0.111922\pi\)
−0.767679 + 0.640835i \(0.778588\pi\)
\(360\) 0 0
\(361\) −6.50000 + 11.2583i −0.342105 + 0.592544i
\(362\) 0 0
\(363\) −4.27208 −0.224226
\(364\) 0 0
\(365\) 3.65685 0.191408
\(366\) 0 0
\(367\) −10.7929 + 18.6938i −0.563384 + 0.975810i 0.433814 + 0.901003i \(0.357168\pi\)
−0.997198 + 0.0748078i \(0.976166\pi\)
\(368\) 0 0
\(369\) 8.24264 + 14.2767i 0.429095 + 0.743214i
\(370\) 0 0
\(371\) 14.8284 2.02922i 0.769854 0.105352i
\(372\) 0 0
\(373\) −6.00000 10.3923i −0.310668 0.538093i 0.667839 0.744306i \(-0.267219\pi\)
−0.978507 + 0.206213i \(0.933886\pi\)
\(374\) 0 0
\(375\) −0.207107 + 0.358719i −0.0106949 + 0.0185242i
\(376\) 0 0
\(377\) −15.6569 −0.806369
\(378\) 0 0
\(379\) 4.68629 0.240719 0.120359 0.992730i \(-0.461595\pi\)
0.120359 + 0.992730i \(0.461595\pi\)
\(380\) 0 0
\(381\) 0.899495 1.55797i 0.0460825 0.0798173i
\(382\) 0 0
\(383\) 0.449747 + 0.778985i 0.0229810 + 0.0398043i 0.877287 0.479966i \(-0.159351\pi\)
−0.854306 + 0.519770i \(0.826018\pi\)
\(384\) 0 0
\(385\) 1.34315 + 1.73205i 0.0684530 + 0.0882735i
\(386\) 0 0
\(387\) −9.75736 16.9002i −0.495994 0.859088i
\(388\) 0 0
\(389\) −2.65685 + 4.60181i −0.134708 + 0.233321i −0.925486 0.378782i \(-0.876343\pi\)
0.790778 + 0.612103i \(0.209676\pi\)
\(390\) 0 0
\(391\) 42.7696 2.16295
\(392\) 0 0
\(393\) 5.65685 0.285351
\(394\) 0 0
\(395\) 2.00000 3.46410i 0.100631 0.174298i
\(396\) 0 0
\(397\) 12.3137 + 21.3280i 0.618007 + 1.07042i 0.989849 + 0.142124i \(0.0453931\pi\)
−0.371842 + 0.928296i \(0.621274\pi\)
\(398\) 0 0
\(399\) −3.79899 4.89898i −0.190187 0.245256i
\(400\) 0 0
\(401\) 16.1569 + 27.9845i 0.806835 + 1.39748i 0.915045 + 0.403351i \(0.132155\pi\)
−0.108211 + 0.994128i \(0.534512\pi\)
\(402\) 0 0
\(403\) −0.828427 + 1.43488i −0.0412669 + 0.0714764i
\(404\) 0 0
\(405\) 7.48528 0.371947
\(406\) 0 0
\(407\) 4.68629 0.232291
\(408\) 0 0
\(409\) 12.5711 21.7737i 0.621599 1.07664i −0.367589 0.929988i \(-0.619817\pi\)
0.989188 0.146653i \(-0.0468501\pi\)
\(410\) 0 0
\(411\) 0.828427 + 1.43488i 0.0408633 + 0.0707773i
\(412\) 0 0
\(413\) 10.4853 1.43488i 0.515947 0.0706057i
\(414\) 0 0
\(415\) 2.37868 + 4.11999i 0.116765 + 0.202243i
\(416\) 0 0
\(417\) −0.514719 + 0.891519i −0.0252059 + 0.0436579i
\(418\) 0 0
\(419\) −15.3137 −0.748124 −0.374062 0.927404i \(-0.622035\pi\)
−0.374062 + 0.927404i \(0.622035\pi\)
\(420\) 0 0
\(421\) 27.3431 1.33262 0.666312 0.745673i \(-0.267872\pi\)
0.666312 + 0.745673i \(0.267872\pi\)
\(422\) 0 0
\(423\) 16.4853 28.5533i 0.801542 1.38831i
\(424\) 0 0
\(425\) 3.82843 + 6.63103i 0.185706 + 0.321652i
\(426\) 0 0
\(427\) 6.65685 16.3059i 0.322148 0.789098i
\(428\) 0 0
\(429\) −0.343146 0.594346i −0.0165672 0.0286953i
\(430\) 0 0
\(431\) 0.414214 0.717439i 0.0199520 0.0345578i −0.855877 0.517179i \(-0.826982\pi\)
0.875829 + 0.482622i \(0.160315\pi\)
\(432\) 0 0
\(433\) −19.3137 −0.928158 −0.464079 0.885794i \(-0.653615\pi\)
−0.464079 + 0.885794i \(0.653615\pi\)
\(434\) 0 0
\(435\) −3.24264 −0.155473
\(436\) 0 0
\(437\) −15.7990 + 27.3647i −0.755768 + 1.30903i
\(438\) 0 0
\(439\) 9.17157 + 15.8856i 0.437735 + 0.758180i 0.997514 0.0704621i \(-0.0224474\pi\)
−0.559779 + 0.828642i \(0.689114\pi\)
\(440\) 0 0
\(441\) −19.0711 + 5.31925i −0.908146 + 0.253297i
\(442\) 0 0
\(443\) 7.79289 + 13.4977i 0.370252 + 0.641294i 0.989604 0.143819i \(-0.0459382\pi\)
−0.619353 + 0.785113i \(0.712605\pi\)
\(444\) 0 0
\(445\) 2.67157 4.62730i 0.126645 0.219355i
\(446\) 0 0
\(447\) 1.92893 0.0912354
\(448\) 0 0
\(449\) −7.48528 −0.353252 −0.176626 0.984278i \(-0.556518\pi\)
−0.176626 + 0.984278i \(0.556518\pi\)
\(450\) 0 0
\(451\) −2.41421 + 4.18154i −0.113681 + 0.196901i
\(452\) 0 0
\(453\) 2.31371 + 4.00746i 0.108708 + 0.188287i
\(454\) 0 0
\(455\) 2.00000 4.89898i 0.0937614 0.229668i
\(456\) 0 0
\(457\) −14.4853 25.0892i −0.677593 1.17363i −0.975704 0.219094i \(-0.929690\pi\)
0.298111 0.954531i \(-0.403643\pi\)
\(458\) 0 0
\(459\) −9.24264 + 16.0087i −0.431410 + 0.747223i
\(460\) 0 0
\(461\) 1.31371 0.0611855 0.0305928 0.999532i \(-0.490261\pi\)
0.0305928 + 0.999532i \(0.490261\pi\)
\(462\) 0 0
\(463\) 14.8995 0.692438 0.346219 0.938154i \(-0.387465\pi\)
0.346219 + 0.938154i \(0.387465\pi\)
\(464\) 0 0
\(465\) −0.171573 + 0.297173i −0.00795650 + 0.0137811i
\(466\) 0 0
\(467\) 18.9350 + 32.7964i 0.876209 + 1.51764i 0.855470 + 0.517853i \(0.173269\pi\)
0.0207390 + 0.999785i \(0.493398\pi\)
\(468\) 0 0
\(469\) 33.8137 4.62730i 1.56137 0.213669i
\(470\) 0 0
\(471\) −0.272078 0.471253i −0.0125367 0.0217142i
\(472\) 0 0
\(473\) 2.85786 4.94997i 0.131405 0.227600i
\(474\) 0 0
\(475\) −5.65685 −0.259554
\(476\) 0 0
\(477\) 16.0000 0.732590
\(478\) 0 0
\(479\) 0.757359 1.31178i 0.0346046 0.0599370i −0.848204 0.529669i \(-0.822316\pi\)
0.882809 + 0.469732i \(0.155649\pi\)
\(480\) 0 0
\(481\) −5.65685 9.79796i −0.257930 0.446748i
\(482\) 0 0
\(483\) −3.75126 4.83743i −0.170688 0.220111i
\(484\) 0 0
\(485\) −3.00000 5.19615i −0.136223 0.235945i
\(486\) 0 0
\(487\) 19.1421 33.1552i 0.867413 1.50240i 0.00278182 0.999996i \(-0.499115\pi\)
0.864631 0.502407i \(-0.167552\pi\)
\(488\) 0 0
\(489\) −6.48528 −0.293275
\(490\) 0 0
\(491\) 1.51472 0.0683583 0.0341791 0.999416i \(-0.489118\pi\)
0.0341791 + 0.999416i \(0.489118\pi\)
\(492\) 0 0
\(493\) −29.9706 + 51.9105i −1.34981 + 2.33793i
\(494\) 0 0
\(495\) 1.17157 + 2.02922i 0.0526583 + 0.0912068i
\(496\) 0 0
\(497\) −19.4558 25.0892i −0.872714 1.12541i
\(498\) 0 0
\(499\) −22.0711 38.2282i −0.988037 1.71133i −0.627576 0.778555i \(-0.715953\pi\)
−0.360461 0.932774i \(-0.617381\pi\)
\(500\) 0 0
\(501\) −0.428932 + 0.742932i −0.0191633 + 0.0331918i
\(502\) 0 0
\(503\) −3.92893 −0.175182 −0.0875912 0.996157i \(-0.527917\pi\)
−0.0875912 + 0.996157i \(0.527917\pi\)
\(504\) 0 0
\(505\) −11.4853 −0.511088
\(506\) 0 0
\(507\) 1.86396 3.22848i 0.0827814 0.143382i
\(508\) 0 0
\(509\) 16.7426 + 28.9991i 0.742105 + 1.28536i 0.951535 + 0.307539i \(0.0995055\pi\)
−0.209431 + 0.977823i \(0.567161\pi\)
\(510\) 0 0
\(511\) −9.58579 + 1.31178i −0.424050 + 0.0580299i
\(512\) 0 0
\(513\) −6.82843 11.8272i −0.301482 0.522183i
\(514\) 0 0
\(515\) −3.79289 + 6.56948i −0.167135 + 0.289486i
\(516\) 0 0
\(517\) 9.65685 0.424708
\(518\) 0 0
\(519\) 4.28427 0.188059
\(520\) 0 0
\(521\) −18.3137 + 31.7203i −0.802338 + 1.38969i 0.115735 + 0.993280i \(0.463078\pi\)
−0.918073 + 0.396410i \(0.870256\pi\)
\(522\) 0 0
\(523\) −13.9706 24.1977i −0.610890 1.05809i −0.991091 0.133189i \(-0.957478\pi\)
0.380201 0.924904i \(-0.375855\pi\)
\(524\) 0 0
\(525\) 0.414214 1.01461i 0.0180778 0.0442813i
\(526\) 0 0
\(527\) 3.17157 + 5.49333i 0.138156 + 0.239293i
\(528\) 0 0
\(529\) −4.10051 + 7.10228i −0.178283 + 0.308795i
\(530\) 0 0
\(531\) 11.3137 0.490973
\(532\) 0 0
\(533\) 11.6569 0.504914
\(534\) 0 0
\(535\) 2.79289 4.83743i 0.120747 0.209140i
\(536\) 0 0
\(537\) 1.34315 + 2.32640i 0.0579610 + 0.100391i
\(538\) 0 0
\(539\) −4.14214 4.05845i −0.178414 0.174810i
\(540\) 0 0
\(541\) 11.7426 + 20.3389i 0.504856 + 0.874435i 0.999984 + 0.00561582i \(0.00178758\pi\)
−0.495129 + 0.868820i \(0.664879\pi\)
\(542\) 0 0
\(543\) 0.863961 1.49642i 0.0370761 0.0642177i
\(544\) 0 0
\(545\) 18.3137 0.784473
\(546\) 0 0
\(547\) −2.27208 −0.0971470 −0.0485735 0.998820i \(-0.515468\pi\)
−0.0485735 + 0.998820i \(0.515468\pi\)
\(548\) 0 0
\(549\) 9.41421 16.3059i 0.401789 0.695919i
\(550\) 0 0
\(551\) −22.1421 38.3513i −0.943287 1.63382i
\(552\) 0 0
\(553\) −4.00000 + 9.79796i −0.170097 + 0.416652i
\(554\) 0 0
\(555\) −1.17157 2.02922i −0.0497305 0.0861358i
\(556\) 0 0
\(557\) 8.65685 14.9941i 0.366803 0.635321i −0.622261 0.782810i \(-0.713786\pi\)
0.989064 + 0.147489i \(0.0471191\pi\)
\(558\) 0 0
\(559\) −13.7990 −0.583635
\(560\) 0 0
\(561\) −2.62742 −0.110930
\(562\) 0 0
\(563\) 2.03553 3.52565i 0.0857875 0.148588i −0.819939 0.572451i \(-0.805993\pi\)
0.905727 + 0.423863i \(0.139326\pi\)
\(564\) 0 0
\(565\) −5.65685 9.79796i −0.237986 0.412203i
\(566\) 0 0
\(567\) −19.6213 + 2.68512i −0.824018 + 0.112764i
\(568\) 0 0
\(569\) 18.3137 + 31.7203i 0.767751 + 1.32978i 0.938780 + 0.344517i \(0.111957\pi\)
−0.171029 + 0.985266i \(0.554709\pi\)
\(570\) 0 0
\(571\) 10.4853 18.1610i 0.438795 0.760016i −0.558801 0.829301i \(-0.688739\pi\)
0.997597 + 0.0692856i \(0.0220720\pi\)
\(572\) 0 0
\(573\) −2.28427 −0.0954268
\(574\) 0 0
\(575\) −5.58579 −0.232943
\(576\) 0 0
\(577\) 11.1421 19.2987i 0.463853 0.803417i −0.535296 0.844665i \(-0.679800\pi\)
0.999149 + 0.0412474i \(0.0131332\pi\)
\(578\) 0 0
\(579\) 1.10051 + 1.90613i 0.0457354 + 0.0792161i
\(580\) 0 0
\(581\) −7.71320 9.94655i −0.319998 0.412652i
\(582\) 0 0
\(583\) 2.34315 + 4.05845i 0.0970432 + 0.168084i
\(584\) 0 0
\(585\) 2.82843 4.89898i 0.116941 0.202548i
\(586\) 0 0
\(587\) −22.6863 −0.936363 −0.468182 0.883632i \(-0.655091\pi\)
−0.468182 + 0.883632i \(0.655091\pi\)
\(588\) 0 0
\(589\) −4.68629 −0.193095
\(590\) 0 0
\(591\) −0.0710678 + 0.123093i −0.00292334 + 0.00506337i
\(592\) 0 0
\(593\) −14.9706 25.9298i −0.614767 1.06481i −0.990425 0.138050i \(-0.955917\pi\)
0.375658 0.926758i \(-0.377417\pi\)
\(594\) 0 0
\(595\) −12.4142 16.0087i −0.508933 0.656294i
\(596\) 0 0
\(597\) 4.82843 + 8.36308i 0.197614 + 0.342278i
\(598\) 0 0
\(599\) −21.3137 + 36.9164i −0.870855 + 1.50836i −0.00974040 + 0.999953i \(0.503101\pi\)
−0.861114 + 0.508412i \(0.830233\pi\)
\(600\) 0 0
\(601\) −34.0000 −1.38689 −0.693444 0.720510i \(-0.743908\pi\)
−0.693444 + 0.720510i \(0.743908\pi\)
\(602\) 0 0
\(603\) 36.4853 1.48580
\(604\) 0 0
\(605\) 5.15685 8.93193i 0.209656 0.363135i
\(606\) 0 0
\(607\) −13.6213 23.5928i −0.552872 0.957603i −0.998066 0.0621685i \(-0.980198\pi\)
0.445193 0.895434i \(-0.353135\pi\)
\(608\) 0 0
\(609\) 8.50000 1.16320i 0.344437 0.0471352i
\(610\) 0 0
\(611\) −11.6569 20.1903i −0.471586 0.816811i
\(612\) 0 0
\(613\) −19.4853 + 33.7495i −0.787003 + 1.36313i 0.140792 + 0.990039i \(0.455035\pi\)
−0.927795 + 0.373090i \(0.878298\pi\)
\(614\) 0 0
\(615\) 2.41421 0.0973505
\(616\) 0 0
\(617\) −12.6863 −0.510731 −0.255365 0.966845i \(-0.582196\pi\)
−0.255365 + 0.966845i \(0.582196\pi\)
\(618\) 0 0
\(619\) −19.7279 + 34.1698i −0.792932 + 1.37340i 0.131212 + 0.991354i \(0.458113\pi\)
−0.924144 + 0.382044i \(0.875220\pi\)
\(620\) 0 0
\(621\) −6.74264 11.6786i −0.270573 0.468646i
\(622\) 0 0
\(623\) −5.34315 + 13.0880i −0.214069 + 0.524359i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 0.970563 1.68106i 0.0387605 0.0671352i
\(628\) 0 0
\(629\) −43.3137 −1.72703
\(630\) 0 0
\(631\) −1.51472 −0.0603000 −0.0301500 0.999545i \(-0.509598\pi\)
−0.0301500 + 0.999545i \(0.509598\pi\)
\(632\) 0 0
\(633\) −5.51472 + 9.55177i −0.219190 + 0.379649i
\(634\) 0 0
\(635\) 2.17157 + 3.76127i 0.0861762 + 0.149262i
\(636\) 0 0
\(637\) −3.48528 + 13.5592i −0.138092 + 0.537236i
\(638\) 0 0
\(639\) −16.9706 29.3939i −0.671345 1.16280i
\(640\) 0 0
\(641\) −7.05635 + 12.2220i −0.278709 + 0.482738i −0.971064 0.238819i \(-0.923240\pi\)
0.692355 + 0.721557i \(0.256573\pi\)
\(642\) 0 0
\(643\) 26.0000 1.02534 0.512670 0.858586i \(-0.328656\pi\)
0.512670 + 0.858586i \(0.328656\pi\)
\(644\) 0 0
\(645\) −2.85786 −0.112528
\(646\) 0 0
\(647\) 10.3787 17.9764i 0.408028 0.706725i −0.586641 0.809847i \(-0.699550\pi\)
0.994669 + 0.103122i \(0.0328832\pi\)
\(648\) 0 0
\(649\) 1.65685 + 2.86976i 0.0650372 + 0.112648i
\(650\) 0 0
\(651\) 0.343146 0.840532i 0.0134489 0.0329430i
\(652\) 0 0
\(653\) 7.82843 + 13.5592i 0.306350 + 0.530614i 0.977561 0.210653i \(-0.0675589\pi\)
−0.671211 + 0.741266i \(0.734226\pi\)
\(654\) 0 0
\(655\) −6.82843 + 11.8272i −0.266809 + 0.462126i
\(656\) 0 0
\(657\) −10.3431 −0.403525
\(658\) 0 0
\(659\) 12.6863 0.494188 0.247094 0.968992i \(-0.420524\pi\)
0.247094 + 0.968992i \(0.420524\pi\)
\(660\) 0 0
\(661\) 25.1569 43.5729i 0.978488 1.69479i 0.310581 0.950547i \(-0.399476\pi\)
0.667907 0.744244i \(-0.267190\pi\)
\(662\) 0 0
\(663\) 3.17157 + 5.49333i 0.123174 + 0.213343i
\(664\) 0 0
\(665\) 14.8284 2.02922i 0.575022 0.0786899i
\(666\) 0 0
\(667\) −21.8640 37.8695i −0.846576 1.46631i
\(668\) 0 0
\(669\) 3.10051 5.37023i 0.119872 0.207625i
\(670\) 0 0
\(671\) 5.51472 0.212893
\(672\) 0 0
\(673\) −5.65685 −0.218056 −0.109028 0.994039i \(-0.534774\pi\)
−0.109028 + 0.994039i \(0.534774\pi\)
\(674\) 0 0
\(675\) 1.20711 2.09077i 0.0464616 0.0804738i
\(676\) 0 0
\(677\) −11.4853 19.8931i −0.441415 0.764554i 0.556380 0.830928i \(-0.312190\pi\)
−0.997795 + 0.0663747i \(0.978857\pi\)
\(678\) 0 0
\(679\) 9.72792 + 12.5446i 0.373323 + 0.481418i
\(680\) 0 0
\(681\) −2.89949 5.02207i −0.111109 0.192446i
\(682\) 0 0
\(683\) 0.964466 1.67050i 0.0369043 0.0639201i −0.846983 0.531619i \(-0.821584\pi\)
0.883888 + 0.467699i \(0.154917\pi\)
\(684\) 0 0
\(685\) −4.00000 −0.152832
\(686\) 0 0
\(687\) −5.79899 −0.221245
\(688\) 0 0
\(689\) 5.65685 9.79796i 0.215509 0.373273i
\(690\) 0 0
\(691\) 21.3848 + 37.0395i 0.813515 + 1.40905i 0.910389 + 0.413753i \(0.135782\pi\)
−0.0968739 + 0.995297i \(0.530884\pi\)
\(692\) 0 0
\(693\) −3.79899 4.89898i −0.144312 0.186097i
\(694\) 0 0
\(695\) −1.24264 2.15232i −0.0471360 0.0816420i
\(696\) 0 0
\(697\) 22.3137 38.6485i 0.845192 1.46392i
\(698\) 0 0
\(699\) 4.82843 0.182628
\(700\) 0 0
\(701\) −11.0000 −0.415464 −0.207732 0.978186i \(-0.566608\pi\)
−0.207732 + 0.978186i \(0.566608\pi\)
\(702\) 0 0
\(703\) 16.0000 27.7128i 0.603451 1.04521i
\(704\) 0 0
\(705\) −2.41421 4.18154i −0.0909245 0.157486i
\(706\) 0 0
\(707\) 30.1066 4.11999i 1.13228 0.154948i
\(708\) 0 0
\(709\) 17.7132 + 30.6802i 0.665233 + 1.15222i 0.979222 + 0.202791i \(0.0650013\pi\)
−0.313989 + 0.949427i \(0.601665\pi\)
\(710\) 0 0
\(711\) −5.65685 + 9.79796i −0.212149 + 0.367452i
\(712\) 0 0
\(713\) −4.62742 −0.173298
\(714\) 0 0
\(715\) 1.65685 0.0619628
\(716\) 0 0
\(717\) 6.31371 10.9357i 0.235790 0.408400i
\(718\) 0 0
\(719\) 12.8995 + 22.3426i 0.481070 + 0.833238i 0.999764 0.0217223i \(-0.00691496\pi\)
−0.518694 + 0.854960i \(0.673582\pi\)
\(720\) 0 0
\(721\) 7.58579 18.5813i 0.282509 0.692004i
\(722\) 0 0
\(723\) 2.07107 + 3.58719i 0.0770238 + 0.133409i
\(724\) 0 0
\(725\) 3.91421 6.77962i 0.145370 0.251789i
\(726\) 0 0
\(727\) 38.0711 1.41198 0.705989 0.708223i \(-0.250503\pi\)
0.705989 + 0.708223i \(0.250503\pi\)
\(728\) 0 0
\(729\) −18.1716 −0.673021
\(730\) 0 0
\(731\) −26.4142 + 45.7508i −0.976965 + 1.69215i
\(732\) 0 0
\(733\) −3.82843 6.63103i −0.141406 0.244923i 0.786620 0.617437i \(-0.211829\pi\)
−0.928026 + 0.372514i \(0.878496\pi\)
\(734\) 0 0
\(735\) −0.721825 + 2.80821i −0.0266249 + 0.103582i
\(736\) 0 0
\(737\) 5.34315 + 9.25460i 0.196817 + 0.340898i
\(738\) 0 0
\(739\) −8.41421 + 14.5738i −0.309522 + 0.536108i −0.978258 0.207392i \(-0.933502\pi\)
0.668736 + 0.743500i \(0.266836\pi\)
\(740\) 0 0
\(741\) −4.68629 −0.172155
\(742\) 0 0
\(743\) −10.7574 −0.394649 −0.197325 0.980338i \(-0.563225\pi\)
−0.197325 + 0.980338i \(0.563225\pi\)
\(744\) 0 0
\(745\) −2.32843 + 4.03295i −0.0853070 + 0.147756i
\(746\) 0 0
\(747\) −6.72792 11.6531i −0.246162 0.426365i
\(748\) 0 0
\(749\) −5.58579 + 13.6823i −0.204100 + 0.499941i
\(750\) 0 0
\(751\) 6.00000 + 10.3923i 0.218943 + 0.379221i 0.954485 0.298259i \(-0.0964058\pi\)
−0.735542 + 0.677479i \(0.763072\pi\)
\(752\) 0 0
\(753\) 5.68629 9.84895i 0.207220 0.358916i
\(754\) 0 0
\(755\) −11.1716 −0.406575
\(756\) 0 0
\(757\) 6.00000 0.218074 0.109037 0.994038i \(-0.465223\pi\)
0.109037 + 0.994038i \(0.465223\pi\)
\(758\) 0 0
\(759\) 0.958369 1.65994i 0.0347866 0.0602522i
\(760\) 0 0
\(761\) 21.9706 + 38.0541i 0.796432 + 1.37946i 0.921926 + 0.387367i \(0.126615\pi\)
−0.125493 + 0.992094i \(0.540051\pi\)
\(762\) 0 0
\(763\) −48.0061 + 6.56948i −1.73794 + 0.237831i
\(764\) 0 0
\(765\) −10.8284 18.7554i −0.391503 0.678102i
\(766\) 0 0
\(767\) 4.00000 6.92820i 0.144432 0.250163i
\(768\) 0 0
\(769\) 43.2548 1.55981 0.779905 0.625898i \(-0.215268\pi\)
0.779905 + 0.625898i \(0.215268\pi\)
\(770\) 0 0
\(771\) 6.34315 0.228443
\(772\) 0 0
\(773\) −12.1716 + 21.0818i −0.437781 + 0.758259i −0.997518 0.0704113i \(-0.977569\pi\)
0.559737 + 0.828670i \(0.310902\pi\)
\(774\) 0 0
\(775\) −0.414214 0.717439i −0.0148790 0.0257712i
\(776\) 0 0
\(777\) 3.79899 + 4.89898i 0.136288 + 0.175750i
\(778\) 0 0
\(779\) 16.4853 + 28.5533i 0.590647 + 1.02303i
\(780\) 0 0
\(781\) 4.97056 8.60927i 0.177861 0.308064i
\(782\) 0 0
\(783\) 18.8995 0.675413
\(784\) 0 0
\(785\) 1.31371 0.0468883
\(786\) 0 0
\(787\) 0.792893 1.37333i 0.0282636 0.0489540i −0.851548 0.524277i \(-0.824336\pi\)
0.879811 + 0.475323i \(0.157669\pi\)
\(788\) 0 0
\(789\) 3.25736 + 5.64191i 0.115965 + 0.200857i
\(790\) 0 0
\(791\) 18.3431 + 23.6544i 0.652207 + 0.841052i
\(792\) 0 0
\(793\) −6.65685 11.5300i −0.236392 0.409443i
\(794\) 0 0
\(795\) 1.17157 2.02922i 0.0415514 0.0719691i
\(796\) 0 0
\(797\) −35.3137 −1.25088