Properties

Label 300.2.m.a.181.2
Level $300$
Weight $2$
Character 300.181
Analytic conductor $2.396$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.m (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\Q(\zeta_{15})\)
Defining polynomial: \(x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 181.2
Root \(-0.978148 - 0.207912i\) of defining polynomial
Character \(\chi\) \(=\) 300.181
Dual form 300.2.m.a.121.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.809017 + 0.587785i) q^{3} +(2.04275 + 0.909491i) q^{5} +0.747238 q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.809017 + 0.587785i) q^{3} +(2.04275 + 0.909491i) q^{5} +0.747238 q^{7} +(0.309017 - 0.951057i) q^{9} +(0.0646021 + 0.198825i) q^{11} +(-0.773659 + 2.38108i) q^{13} +(-2.18720 + 0.464905i) q^{15} +(5.51712 + 4.00842i) q^{17} +(-1.00739 - 0.731913i) q^{19} +(-0.604528 + 0.439216i) q^{21} +(1.00457 + 3.09174i) q^{23} +(3.34565 + 3.71572i) q^{25} +(0.309017 + 0.951057i) q^{27} +(4.19332 - 3.04662i) q^{29} +(-3.02547 - 2.19813i) q^{31} +(-0.169131 - 0.122881i) q^{33} +(1.52642 + 0.679606i) q^{35} +(0.607352 - 1.86924i) q^{37} +(-0.773659 - 2.38108i) q^{39} +(0.993096 - 3.05644i) q^{41} -12.7127 q^{43} +(1.49622 - 1.66172i) q^{45} +(5.24425 - 3.81017i) q^{47} -6.44163 q^{49} -6.81953 q^{51} +(-3.35177 + 2.43520i) q^{53} +(-0.0488635 + 0.464905i) q^{55} +1.24520 q^{57} +(3.61882 - 11.1376i) q^{59} +(-3.85634 - 11.8686i) q^{61} +(0.230909 - 0.710666i) q^{63} +(-3.74596 + 4.16031i) q^{65} +(-2.35995 - 1.71460i) q^{67} +(-2.62999 - 1.91080i) q^{69} +(-5.29912 + 3.85004i) q^{71} +(-0.778516 - 2.39603i) q^{73} +(-4.89074 - 1.03956i) q^{75} +(0.0482732 + 0.148570i) q^{77} +(8.28621 - 6.02028i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(4.59240 + 3.33658i) q^{83} +(7.62447 + 13.2060i) q^{85} +(-1.60171 + 4.92954i) q^{87} +(-0.284829 - 0.876615i) q^{89} +(-0.578108 + 1.77923i) q^{91} +3.73968 q^{93} +(-1.39218 - 2.41133i) q^{95} +(12.5757 - 9.13679i) q^{97} +0.209057 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{3} + 5q^{5} - 8q^{7} - 2q^{9} + O(q^{10}) \) \( 8q - 2q^{3} + 5q^{5} - 8q^{7} - 2q^{9} - 2q^{11} - 5q^{15} + 7q^{17} + 5q^{19} - 3q^{21} + 7q^{23} + 5q^{25} - 2q^{27} + 27q^{29} - 3q^{31} + 3q^{33} + 20q^{35} - 9q^{37} + 20q^{41} - 68q^{43} - 5q^{45} - 7q^{47} - 8q^{49} - 8q^{51} - 11q^{53} + 5q^{55} - 10q^{57} + 2q^{59} - 14q^{61} + 7q^{63} - 35q^{65} + 28q^{67} + 2q^{69} - 15q^{71} + 6q^{73} + 5q^{75} + 17q^{77} + 24q^{79} - 2q^{81} + 2q^{83} + 10q^{85} - 23q^{87} + 5q^{91} - 18q^{93} + 5q^{95} + 34q^{97} - 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{5}\right)\)

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
\(3\) −0.809017 + 0.587785i −0.467086 + 0.339358i
\(4\) 0 0
\(5\) 2.04275 + 0.909491i 0.913545 + 0.406737i
\(6\) 0 0
\(7\) 0.747238 0.282430 0.141215 0.989979i \(-0.454899\pi\)
0.141215 + 0.989979i \(0.454899\pi\)
\(8\) 0 0
\(9\) 0.309017 0.951057i 0.103006 0.317019i
\(10\) 0 0
\(11\) 0.0646021 + 0.198825i 0.0194783 + 0.0599480i 0.960323 0.278889i \(-0.0899663\pi\)
−0.940845 + 0.338837i \(0.889966\pi\)
\(12\) 0 0
\(13\) −0.773659 + 2.38108i −0.214574 + 0.660392i 0.784609 + 0.619991i \(0.212864\pi\)
−0.999184 + 0.0404014i \(0.987136\pi\)
\(14\) 0 0
\(15\) −2.18720 + 0.464905i −0.564734 + 0.120038i
\(16\) 0 0
\(17\) 5.51712 + 4.00842i 1.33810 + 0.972185i 0.999512 + 0.0312497i \(0.00994869\pi\)
0.338586 + 0.940935i \(0.390051\pi\)
\(18\) 0 0
\(19\) −1.00739 0.731913i −0.231112 0.167912i 0.466203 0.884678i \(-0.345622\pi\)
−0.697314 + 0.716766i \(0.745622\pi\)
\(20\) 0 0
\(21\) −0.604528 + 0.439216i −0.131919 + 0.0958447i
\(22\) 0 0
\(23\) 1.00457 + 3.09174i 0.209467 + 0.644673i 0.999500 + 0.0316092i \(0.0100632\pi\)
−0.790033 + 0.613064i \(0.789937\pi\)
\(24\) 0 0
\(25\) 3.34565 + 3.71572i 0.669131 + 0.743145i
\(26\) 0 0
\(27\) 0.309017 + 0.951057i 0.0594703 + 0.183031i
\(28\) 0 0
\(29\) 4.19332 3.04662i 0.778680 0.565744i −0.125903 0.992043i \(-0.540183\pi\)
0.904582 + 0.426299i \(0.140183\pi\)
\(30\) 0 0
\(31\) −3.02547 2.19813i −0.543390 0.394796i 0.281953 0.959428i \(-0.409018\pi\)
−0.825342 + 0.564633i \(0.809018\pi\)
\(32\) 0 0
\(33\) −0.169131 0.122881i −0.0294419 0.0213908i
\(34\) 0 0
\(35\) 1.52642 + 0.679606i 0.258012 + 0.114874i
\(36\) 0 0
\(37\) 0.607352 1.86924i 0.0998480 0.307301i −0.888639 0.458608i \(-0.848348\pi\)
0.988487 + 0.151307i \(0.0483483\pi\)
\(38\) 0 0
\(39\) −0.773659 2.38108i −0.123885 0.381278i
\(40\) 0 0
\(41\) 0.993096 3.05644i 0.155096 0.477335i −0.843075 0.537796i \(-0.819257\pi\)
0.998171 + 0.0604609i \(0.0192570\pi\)
\(42\) 0 0
\(43\) −12.7127 −1.93866 −0.969332 0.245755i \(-0.920964\pi\)
−0.969332 + 0.245755i \(0.920964\pi\)
\(44\) 0 0
\(45\) 1.49622 1.66172i 0.223044 0.247715i
\(46\) 0 0
\(47\) 5.24425 3.81017i 0.764952 0.555770i −0.135473 0.990781i \(-0.543255\pi\)
0.900425 + 0.435011i \(0.143255\pi\)
\(48\) 0 0
\(49\) −6.44163 −0.920234
\(50\) 0 0
\(51\) −6.81953 −0.954926
\(52\) 0 0
\(53\) −3.35177 + 2.43520i −0.460401 + 0.334501i −0.793688 0.608325i \(-0.791842\pi\)
0.333288 + 0.942825i \(0.391842\pi\)
\(54\) 0 0
\(55\) −0.0488635 + 0.464905i −0.00658875 + 0.0626877i
\(56\) 0 0
\(57\) 1.24520 0.164931
\(58\) 0 0
\(59\) 3.61882 11.1376i 0.471131 1.44999i −0.379975 0.924997i \(-0.624067\pi\)
0.851106 0.524995i \(-0.175933\pi\)
\(60\) 0 0
\(61\) −3.85634 11.8686i −0.493753 1.51962i −0.818891 0.573949i \(-0.805411\pi\)
0.325138 0.945667i \(-0.394589\pi\)
\(62\) 0 0
\(63\) 0.230909 0.710666i 0.0290918 0.0895355i
\(64\) 0 0
\(65\) −3.74596 + 4.16031i −0.464629 + 0.516023i
\(66\) 0 0
\(67\) −2.35995 1.71460i −0.288314 0.209472i 0.434222 0.900806i \(-0.357023\pi\)
−0.722535 + 0.691334i \(0.757023\pi\)
\(68\) 0 0
\(69\) −2.62999 1.91080i −0.316614 0.230034i
\(70\) 0 0
\(71\) −5.29912 + 3.85004i −0.628890 + 0.456916i −0.856016 0.516950i \(-0.827067\pi\)
0.227125 + 0.973866i \(0.427067\pi\)
\(72\) 0 0
\(73\) −0.778516 2.39603i −0.0911184 0.280434i 0.895104 0.445857i \(-0.147101\pi\)
−0.986223 + 0.165423i \(0.947101\pi\)
\(74\) 0 0
\(75\) −4.89074 1.03956i −0.564734 0.120038i
\(76\) 0 0
\(77\) 0.0482732 + 0.148570i 0.00550124 + 0.0169311i
\(78\) 0 0
\(79\) 8.28621 6.02028i 0.932271 0.677335i −0.0142765 0.999898i \(-0.504545\pi\)
0.946548 + 0.322563i \(0.104545\pi\)
\(80\) 0 0
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) 0 0
\(83\) 4.59240 + 3.33658i 0.504082 + 0.366237i 0.810574 0.585636i \(-0.199155\pi\)
−0.306492 + 0.951873i \(0.599155\pi\)
\(84\) 0 0
\(85\) 7.62447 + 13.2060i 0.826990 + 1.43239i
\(86\) 0 0
\(87\) −1.60171 + 4.92954i −0.171721 + 0.528502i
\(88\) 0 0
\(89\) −0.284829 0.876615i −0.0301919 0.0929210i 0.934825 0.355109i \(-0.115556\pi\)
−0.965017 + 0.262188i \(0.915556\pi\)
\(90\) 0 0
\(91\) −0.578108 + 1.77923i −0.0606022 + 0.186514i
\(92\) 0 0
\(93\) 3.73968 0.387787
\(94\) 0 0
\(95\) −1.39218 2.41133i −0.142835 0.247397i
\(96\) 0 0
\(97\) 12.5757 9.13679i 1.27687 0.927700i 0.277416 0.960750i \(-0.410522\pi\)
0.999454 + 0.0330496i \(0.0105219\pi\)
\(98\) 0 0
\(99\) 0.209057 0.0210110
\(100\) 0 0
\(101\) −11.0405 −1.09857 −0.549285 0.835635i \(-0.685100\pi\)
−0.549285 + 0.835635i \(0.685100\pi\)
\(102\) 0 0
\(103\) −11.2326 + 8.16097i −1.10678 + 0.804124i −0.982154 0.188079i \(-0.939774\pi\)
−0.124628 + 0.992203i \(0.539774\pi\)
\(104\) 0 0
\(105\) −1.63436 + 0.347395i −0.159497 + 0.0339022i
\(106\) 0 0
\(107\) 1.02510 0.0991002 0.0495501 0.998772i \(-0.484221\pi\)
0.0495501 + 0.998772i \(0.484221\pi\)
\(108\) 0 0
\(109\) −2.07199 + 6.37694i −0.198461 + 0.610800i 0.801458 + 0.598051i \(0.204058\pi\)
−0.999919 + 0.0127488i \(0.995942\pi\)
\(110\) 0 0
\(111\) 0.607352 + 1.86924i 0.0576473 + 0.177420i
\(112\) 0 0
\(113\) 2.57151 7.91428i 0.241907 0.744513i −0.754223 0.656618i \(-0.771986\pi\)
0.996130 0.0878944i \(-0.0280138\pi\)
\(114\) 0 0
\(115\) −0.759830 + 7.22930i −0.0708546 + 0.674136i
\(116\) 0 0
\(117\) 2.02547 + 1.47159i 0.187254 + 0.136048i
\(118\) 0 0
\(119\) 4.12260 + 2.99525i 0.377918 + 0.274574i
\(120\) 0 0
\(121\) 8.86383 6.43995i 0.805803 0.585450i
\(122\) 0 0
\(123\) 0.993096 + 3.05644i 0.0895445 + 0.275590i
\(124\) 0 0
\(125\) 3.45492 + 10.6331i 0.309017 + 0.951057i
\(126\) 0 0
\(127\) −4.49195 13.8248i −0.398597 1.22675i −0.926125 0.377217i \(-0.876881\pi\)
0.527529 0.849537i \(-0.323119\pi\)
\(128\) 0 0
\(129\) 10.2848 7.47232i 0.905523 0.657901i
\(130\) 0 0
\(131\) −6.00611 4.36370i −0.524757 0.381258i 0.293636 0.955917i \(-0.405135\pi\)
−0.818393 + 0.574659i \(0.805135\pi\)
\(132\) 0 0
\(133\) −0.752762 0.546913i −0.0652727 0.0474234i
\(134\) 0 0
\(135\) −0.233733 + 2.22382i −0.0201165 + 0.191396i
\(136\) 0 0
\(137\) −2.26676 + 6.97636i −0.193662 + 0.596030i 0.806328 + 0.591469i \(0.201452\pi\)
−0.999990 + 0.00456114i \(0.998548\pi\)
\(138\) 0 0
\(139\) 6.10219 + 18.7806i 0.517581 + 1.59295i 0.778536 + 0.627600i \(0.215963\pi\)
−0.260954 + 0.965351i \(0.584037\pi\)
\(140\) 0 0
\(141\) −2.00313 + 6.16499i −0.168694 + 0.519185i
\(142\) 0 0
\(143\) −0.523398 −0.0437687
\(144\) 0 0
\(145\) 11.3368 2.40971i 0.941468 0.200115i
\(146\) 0 0
\(147\) 5.21139 3.78630i 0.429828 0.312289i
\(148\) 0 0
\(149\) −21.7551 −1.78224 −0.891122 0.453763i \(-0.850081\pi\)
−0.891122 + 0.453763i \(0.850081\pi\)
\(150\) 0 0
\(151\) 10.1308 0.824432 0.412216 0.911086i \(-0.364755\pi\)
0.412216 + 0.911086i \(0.364755\pi\)
\(152\) 0 0
\(153\) 5.51712 4.00842i 0.446033 0.324062i
\(154\) 0 0
\(155\) −4.18109 7.24186i −0.335833 0.581680i
\(156\) 0 0
\(157\) −9.99520 −0.797704 −0.398852 0.917015i \(-0.630591\pi\)
−0.398852 + 0.917015i \(0.630591\pi\)
\(158\) 0 0
\(159\) 1.28026 3.94024i 0.101531 0.312481i
\(160\) 0 0
\(161\) 0.750652 + 2.31027i 0.0591597 + 0.182075i
\(162\) 0 0
\(163\) −0.792035 + 2.43763i −0.0620369 + 0.190930i −0.977272 0.211991i \(-0.932005\pi\)
0.915235 + 0.402921i \(0.132005\pi\)
\(164\) 0 0
\(165\) −0.233733 0.404837i −0.0181961 0.0315165i
\(166\) 0 0
\(167\) 16.8690 + 12.2560i 1.30536 + 0.948401i 0.999993 0.00383355i \(-0.00122026\pi\)
0.305369 + 0.952234i \(0.401220\pi\)
\(168\) 0 0
\(169\) 5.44624 + 3.95692i 0.418941 + 0.304379i
\(170\) 0 0
\(171\) −1.00739 + 0.731913i −0.0770372 + 0.0559708i
\(172\) 0 0
\(173\) 0.635016 + 1.95438i 0.0482794 + 0.148589i 0.972290 0.233778i \(-0.0751090\pi\)
−0.924011 + 0.382367i \(0.875109\pi\)
\(174\) 0 0
\(175\) 2.50000 + 2.77653i 0.188982 + 0.209886i
\(176\) 0 0
\(177\) 3.61882 + 11.1376i 0.272007 + 0.837153i
\(178\) 0 0
\(179\) 15.8247 11.4973i 1.18279 0.859349i 0.190309 0.981724i \(-0.439051\pi\)
0.992484 + 0.122375i \(0.0390510\pi\)
\(180\) 0 0
\(181\) 5.96251 + 4.33202i 0.443190 + 0.321996i 0.786901 0.617079i \(-0.211684\pi\)
−0.343711 + 0.939075i \(0.611684\pi\)
\(182\) 0 0
\(183\) 10.0960 + 7.33519i 0.746319 + 0.542233i
\(184\) 0 0
\(185\) 2.94072 3.26600i 0.216206 0.240121i
\(186\) 0 0
\(187\) −0.440557 + 1.35589i −0.0322167 + 0.0991528i
\(188\) 0 0
\(189\) 0.230909 + 0.710666i 0.0167962 + 0.0516933i
\(190\) 0 0
\(191\) −0.693806 + 2.13532i −0.0502021 + 0.154506i −0.973015 0.230743i \(-0.925884\pi\)
0.922813 + 0.385249i \(0.125884\pi\)
\(192\) 0 0
\(193\) 1.10589 0.0796035 0.0398018 0.999208i \(-0.487327\pi\)
0.0398018 + 0.999208i \(0.487327\pi\)
\(194\) 0 0
\(195\) 0.585176 5.56758i 0.0419054 0.398703i
\(196\) 0 0
\(197\) −16.6953 + 12.1299i −1.18949 + 0.864217i −0.993211 0.116331i \(-0.962887\pi\)
−0.196282 + 0.980547i \(0.562887\pi\)
\(198\) 0 0
\(199\) −12.3822 −0.877749 −0.438874 0.898548i \(-0.644623\pi\)
−0.438874 + 0.898548i \(0.644623\pi\)
\(200\) 0 0
\(201\) 2.91706 0.205753
\(202\) 0 0
\(203\) 3.13341 2.27655i 0.219922 0.159783i
\(204\) 0 0
\(205\) 4.80845 5.34032i 0.335837 0.372984i
\(206\) 0 0
\(207\) 3.25085 0.225950
\(208\) 0 0
\(209\) 0.0804429 0.247578i 0.00556435 0.0171253i
\(210\) 0 0
\(211\) 6.37422 + 19.6178i 0.438820 + 1.35055i 0.889121 + 0.457671i \(0.151316\pi\)
−0.450302 + 0.892876i \(0.648684\pi\)
\(212\) 0 0
\(213\) 2.02409 6.22949i 0.138688 0.426838i
\(214\) 0 0
\(215\) −25.9688 11.5621i −1.77106 0.788526i
\(216\) 0 0
\(217\) −2.26074 1.64253i −0.153469 0.111502i
\(218\) 0 0
\(219\) 2.03818 + 1.48083i 0.137728 + 0.100065i
\(220\) 0 0
\(221\) −13.8127 + 10.0355i −0.929145 + 0.675063i
\(222\) 0 0
\(223\) −1.28385 3.95129i −0.0859732 0.264598i 0.898823 0.438312i \(-0.144423\pi\)
−0.984796 + 0.173713i \(0.944423\pi\)
\(224\) 0 0
\(225\) 4.56773 2.03368i 0.304515 0.135579i
\(226\) 0 0
\(227\) −7.30175 22.4725i −0.484634 1.49155i −0.832510 0.554010i \(-0.813097\pi\)
0.347876 0.937541i \(-0.386903\pi\)
\(228\) 0 0
\(229\) −14.7565 + 10.7212i −0.975139 + 0.708480i −0.956617 0.291348i \(-0.905896\pi\)
−0.0185221 + 0.999828i \(0.505896\pi\)
\(230\) 0 0
\(231\) −0.126381 0.0918211i −0.00831525 0.00604138i
\(232\) 0 0
\(233\) −1.83438 1.33276i −0.120174 0.0873117i 0.526075 0.850438i \(-0.323663\pi\)
−0.646249 + 0.763127i \(0.723663\pi\)
\(234\) 0 0
\(235\) 14.1780 3.01363i 0.924871 0.196587i
\(236\) 0 0
\(237\) −3.16505 + 9.74102i −0.205592 + 0.632747i
\(238\) 0 0
\(239\) 5.28631 + 16.2696i 0.341943 + 1.05239i 0.963200 + 0.268786i \(0.0866223\pi\)
−0.621257 + 0.783607i \(0.713378\pi\)
\(240\) 0 0
\(241\) 8.71435 26.8200i 0.561341 1.72763i −0.117240 0.993104i \(-0.537405\pi\)
0.678581 0.734526i \(-0.262595\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −13.1586 5.85861i −0.840675 0.374293i
\(246\) 0 0
\(247\) 2.52212 1.83243i 0.160479 0.116595i
\(248\) 0 0
\(249\) −5.67652 −0.359735
\(250\) 0 0
\(251\) 23.9575 1.51219 0.756093 0.654464i \(-0.227106\pi\)
0.756093 + 0.654464i \(0.227106\pi\)
\(252\) 0 0
\(253\) −0.549819 + 0.399467i −0.0345668 + 0.0251142i
\(254\) 0 0
\(255\) −13.9306 6.20230i −0.872368 0.388403i
\(256\) 0 0
\(257\) −28.5421 −1.78041 −0.890204 0.455561i \(-0.849439\pi\)
−0.890204 + 0.455561i \(0.849439\pi\)
\(258\) 0 0
\(259\) 0.453837 1.39677i 0.0282000 0.0867908i
\(260\) 0 0
\(261\) −1.60171 4.92954i −0.0991431 0.305131i
\(262\) 0 0
\(263\) −1.09911 + 3.38270i −0.0677738 + 0.208586i −0.979208 0.202860i \(-0.934976\pi\)
0.911434 + 0.411447i \(0.134976\pi\)
\(264\) 0 0
\(265\) −9.06161 + 1.92611i −0.556650 + 0.118320i
\(266\) 0 0
\(267\) 0.745693 + 0.541778i 0.0456357 + 0.0331563i
\(268\) 0 0
\(269\) −23.6733 17.1997i −1.44339 1.04868i −0.987321 0.158736i \(-0.949258\pi\)
−0.456066 0.889946i \(-0.650742\pi\)
\(270\) 0 0
\(271\) 20.0784 14.5878i 1.21968 0.886147i 0.223603 0.974680i \(-0.428218\pi\)
0.996073 + 0.0885338i \(0.0282181\pi\)
\(272\) 0 0
\(273\) −0.578108 1.77923i −0.0349887 0.107684i
\(274\) 0 0
\(275\) −0.522642 + 0.905243i −0.0315165 + 0.0545882i
\(276\) 0 0
\(277\) −5.38539 16.5745i −0.323577 0.995867i −0.972079 0.234654i \(-0.924604\pi\)
0.648502 0.761213i \(-0.275396\pi\)
\(278\) 0 0
\(279\) −3.02547 + 2.19813i −0.181130 + 0.131599i
\(280\) 0 0
\(281\) −3.03664 2.20625i −0.181151 0.131614i 0.493515 0.869738i \(-0.335712\pi\)
−0.674665 + 0.738124i \(0.735712\pi\)
\(282\) 0 0
\(283\) −13.2464 9.62409i −0.787418 0.572093i 0.119778 0.992801i \(-0.461782\pi\)
−0.907196 + 0.420708i \(0.861782\pi\)
\(284\) 0 0
\(285\) 2.54364 + 1.13250i 0.150672 + 0.0670836i
\(286\) 0 0
\(287\) 0.742080 2.28389i 0.0438036 0.134814i
\(288\) 0 0
\(289\) 9.11787 + 28.0619i 0.536345 + 1.65070i
\(290\) 0 0
\(291\) −4.80349 + 14.7836i −0.281586 + 0.866632i
\(292\) 0 0
\(293\) 8.70991 0.508838 0.254419 0.967094i \(-0.418116\pi\)
0.254419 + 0.967094i \(0.418116\pi\)
\(294\) 0 0
\(295\) 17.5219 19.4600i 1.02016 1.13301i
\(296\) 0 0
\(297\) −0.169131 + 0.122881i −0.00981395 + 0.00713025i
\(298\) 0 0
\(299\) −8.13888 −0.470683
\(300\) 0 0
\(301\) −9.49939 −0.547536
\(302\) 0 0
\(303\) 8.93194 6.48944i 0.513127 0.372808i
\(304\) 0 0
\(305\) 2.91684 27.7518i 0.167018 1.58907i
\(306\) 0 0
\(307\) −17.7123 −1.01090 −0.505448 0.862857i \(-0.668673\pi\)
−0.505448 + 0.862857i \(0.668673\pi\)
\(308\) 0 0
\(309\) 4.29048 13.2047i 0.244077 0.751191i
\(310\) 0 0
\(311\) 6.26921 + 19.2946i 0.355494 + 1.09410i 0.955722 + 0.294270i \(0.0950763\pi\)
−0.600228 + 0.799829i \(0.704924\pi\)
\(312\) 0 0
\(313\) 6.41831 19.7535i 0.362785 1.11654i −0.588572 0.808445i \(-0.700310\pi\)
0.951357 0.308091i \(-0.0996902\pi\)
\(314\) 0 0
\(315\) 1.11803 1.24170i 0.0629941 0.0699620i
\(316\) 0 0
\(317\) 13.5633 + 9.85429i 0.761789 + 0.553472i 0.899458 0.437006i \(-0.143961\pi\)
−0.137670 + 0.990478i \(0.543961\pi\)
\(318\) 0 0
\(319\) 0.876642 + 0.636918i 0.0490825 + 0.0356606i
\(320\) 0 0
\(321\) −0.829324 + 0.602539i −0.0462884 + 0.0336305i
\(322\) 0 0
\(323\) −2.62408 8.07610i −0.146008 0.449366i
\(324\) 0 0
\(325\) −11.4358 + 5.09156i −0.634345 + 0.282429i
\(326\) 0 0
\(327\) −2.07199 6.37694i −0.114582 0.352646i
\(328\) 0 0
\(329\) 3.91870 2.84711i 0.216045 0.156966i
\(330\) 0 0
\(331\) 21.2090 + 15.4092i 1.16575 + 0.846968i 0.990494 0.137555i \(-0.0439243\pi\)
0.175257 + 0.984523i \(0.443924\pi\)
\(332\) 0 0
\(333\) −1.59007 1.15525i −0.0871352 0.0633074i
\(334\) 0 0
\(335\) −3.26137 5.64886i −0.178188 0.308630i
\(336\) 0 0
\(337\) −8.03519 + 24.7298i −0.437705 + 1.34712i 0.452584 + 0.891722i \(0.350502\pi\)
−0.890289 + 0.455395i \(0.849498\pi\)
\(338\) 0 0
\(339\) 2.57151 + 7.91428i 0.139665 + 0.429845i
\(340\) 0 0
\(341\) 0.241591 0.743542i 0.0130829 0.0402651i
\(342\) 0 0
\(343\) −10.0441 −0.542331
\(344\) 0 0
\(345\) −3.63456 6.29525i −0.195678 0.338925i
\(346\) 0 0
\(347\) −3.72256 + 2.70460i −0.199838 + 0.145191i −0.683204 0.730228i \(-0.739414\pi\)
0.483366 + 0.875418i \(0.339414\pi\)
\(348\) 0 0
\(349\) −29.2108 −1.56362 −0.781810 0.623516i \(-0.785703\pi\)
−0.781810 + 0.623516i \(0.785703\pi\)
\(350\) 0 0
\(351\) −2.50361 −0.133633
\(352\) 0 0
\(353\) 22.7505 16.5292i 1.21088 0.879759i 0.215574 0.976488i \(-0.430838\pi\)
0.995311 + 0.0967283i \(0.0308378\pi\)
\(354\) 0 0
\(355\) −14.3264 + 3.04516i −0.760364 + 0.161620i
\(356\) 0 0
\(357\) −5.09582 −0.269699
\(358\) 0 0
\(359\) −2.90570 + 8.94282i −0.153357 + 0.471984i −0.997991 0.0633604i \(-0.979818\pi\)
0.844634 + 0.535345i \(0.179818\pi\)
\(360\) 0 0
\(361\) −5.39218 16.5954i −0.283799 0.873444i
\(362\) 0 0
\(363\) −3.38568 + 10.4201i −0.177702 + 0.546911i
\(364\) 0 0
\(365\) 0.588850 5.60253i 0.0308218 0.293250i
\(366\) 0 0
\(367\) −17.8033 12.9349i −0.929326 0.675195i 0.0165016 0.999864i \(-0.494747\pi\)
−0.945828 + 0.324669i \(0.894747\pi\)
\(368\) 0 0
\(369\) −2.59996 1.88898i −0.135349 0.0983365i
\(370\) 0 0
\(371\) −2.50457 + 1.81968i −0.130031 + 0.0944728i
\(372\) 0 0
\(373\) 5.75384 + 17.7085i 0.297923 + 0.916911i 0.982224 + 0.187712i \(0.0601072\pi\)
−0.684302 + 0.729199i \(0.739893\pi\)
\(374\) 0 0
\(375\) −9.04508 6.57164i −0.467086 0.339358i
\(376\) 0 0
\(377\) 4.01005 + 12.3417i 0.206528 + 0.635628i
\(378\) 0 0
\(379\) 13.6515 9.91838i 0.701230 0.509473i −0.179103 0.983830i \(-0.557320\pi\)
0.880332 + 0.474357i \(0.157320\pi\)
\(380\) 0 0
\(381\) 11.7601 + 8.54421i 0.602488 + 0.437733i
\(382\) 0 0
\(383\) 7.32847 + 5.32445i 0.374467 + 0.272066i 0.759061 0.651020i \(-0.225658\pi\)
−0.384594 + 0.923086i \(0.625658\pi\)
\(384\) 0 0
\(385\) −0.0365126 + 0.347395i −0.00186086 + 0.0177049i
\(386\) 0 0
\(387\) −3.92843 + 12.0905i −0.199693 + 0.614593i
\(388\) 0 0
\(389\) 10.2225 + 31.4616i 0.518301 + 1.59517i 0.777194 + 0.629261i \(0.216642\pi\)
−0.258893 + 0.965906i \(0.583358\pi\)
\(390\) 0 0
\(391\) −6.85069 + 21.0843i −0.346454 + 1.06628i
\(392\) 0 0
\(393\) 7.42396 0.374489
\(394\) 0 0
\(395\) 22.4020 4.76170i 1.12717 0.239587i
\(396\) 0 0
\(397\) 17.5773 12.7706i 0.882177 0.640939i −0.0516494 0.998665i \(-0.516448\pi\)
0.933827 + 0.357726i \(0.116448\pi\)
\(398\) 0 0
\(399\) 0.930465 0.0465815
\(400\) 0 0
\(401\) 20.1663 1.00706 0.503529 0.863978i \(-0.332035\pi\)
0.503529 + 0.863978i \(0.332035\pi\)
\(402\) 0 0
\(403\) 7.57460 5.50327i 0.377318 0.274137i
\(404\) 0 0
\(405\) −1.11803 1.93649i −0.0555556 0.0962250i
\(406\) 0 0
\(407\) 0.410887 0.0203669
\(408\) 0 0
\(409\) −4.34139 + 13.3614i −0.214668 + 0.660679i 0.784509 + 0.620117i \(0.212915\pi\)
−0.999177 + 0.0405623i \(0.987085\pi\)
\(410\) 0 0
\(411\) −2.26676 6.97636i −0.111811 0.344118i
\(412\) 0 0
\(413\) 2.70412 8.32244i 0.133061 0.409520i
\(414\) 0 0
\(415\) 6.34655 + 10.9925i 0.311540 + 0.539602i
\(416\) 0 0
\(417\) −15.9757 11.6071i −0.782336 0.568400i
\(418\) 0 0
\(419\) 16.3919 + 11.9094i 0.800794 + 0.581811i 0.911147 0.412081i \(-0.135198\pi\)
−0.110353 + 0.993892i \(0.535198\pi\)
\(420\) 0 0
\(421\) −3.54258 + 2.57384i −0.172655 + 0.125441i −0.670757 0.741677i \(-0.734031\pi\)
0.498102 + 0.867119i \(0.334031\pi\)
\(422\) 0 0
\(423\) −2.00313 6.16499i −0.0973953 0.299752i
\(424\) 0 0
\(425\) 3.56418 + 33.9109i 0.172888 + 1.64492i
\(426\) 0 0
\(427\) −2.88160 8.86866i −0.139450 0.429184i
\(428\) 0 0
\(429\) 0.423438 0.307645i 0.0204438 0.0148533i
\(430\) 0 0
\(431\) −0.944967 0.686559i −0.0455175 0.0330704i 0.564794 0.825232i \(-0.308956\pi\)
−0.610311 + 0.792162i \(0.708956\pi\)
\(432\) 0 0
\(433\) −1.81940 1.32187i −0.0874347 0.0635250i 0.543209 0.839597i \(-0.317209\pi\)
−0.630644 + 0.776072i \(0.717209\pi\)
\(434\) 0 0
\(435\) −7.75525 + 8.61308i −0.371836 + 0.412966i
\(436\) 0 0
\(437\) 1.25089 3.84985i 0.0598383 0.184163i
\(438\) 0 0
\(439\) 6.83477 + 21.0353i 0.326206 + 1.00396i 0.970893 + 0.239512i \(0.0769875\pi\)
−0.644688 + 0.764446i \(0.723013\pi\)
\(440\) 0 0
\(441\) −1.99057 + 6.12636i −0.0947893 + 0.291731i
\(442\) 0 0
\(443\) 28.1534 1.33761 0.668804 0.743439i \(-0.266807\pi\)
0.668804 + 0.743439i \(0.266807\pi\)
\(444\) 0 0
\(445\) 0.215438 2.04975i 0.0102127 0.0971677i
\(446\) 0 0
\(447\) 17.6002 12.7873i 0.832462 0.604819i
\(448\) 0 0
\(449\) 16.5924 0.783044 0.391522 0.920169i \(-0.371949\pi\)
0.391522 + 0.920169i \(0.371949\pi\)
\(450\) 0 0
\(451\) 0.671852 0.0316363
\(452\) 0 0
\(453\) −8.19598 + 5.95473i −0.385081 + 0.279777i
\(454\) 0 0
\(455\) −2.79912 + 3.10874i −0.131225 + 0.145740i
\(456\) 0 0
\(457\) −11.1599 −0.522039 −0.261019 0.965334i \(-0.584059\pi\)
−0.261019 + 0.965334i \(0.584059\pi\)
\(458\) 0 0
\(459\) −2.10735 + 6.48576i −0.0983628 + 0.302729i
\(460\) 0 0
\(461\) 1.93631 + 5.95935i 0.0901830 + 0.277555i 0.985968 0.166932i \(-0.0533861\pi\)
−0.895785 + 0.444487i \(0.853386\pi\)
\(462\) 0 0
\(463\) −5.26243 + 16.1961i −0.244566 + 0.752696i 0.751142 + 0.660141i \(0.229503\pi\)
−0.995708 + 0.0925550i \(0.970497\pi\)
\(464\) 0 0
\(465\) 7.63923 + 3.40121i 0.354261 + 0.157727i
\(466\) 0 0
\(467\) 15.1159 + 10.9823i 0.699481 + 0.508202i 0.879763 0.475413i \(-0.157701\pi\)
−0.180282 + 0.983615i \(0.557701\pi\)
\(468\) 0 0
\(469\) −1.76344 1.28122i −0.0814283 0.0591611i
\(470\) 0 0
\(471\) 8.08629 5.87503i 0.372597 0.270707i
\(472\) 0 0
\(473\) −0.821266 2.52760i −0.0377618 0.116219i
\(474\) 0 0
\(475\) −0.650797 6.19192i −0.0298606 0.284105i
\(476\) 0 0
\(477\) 1.28026 + 3.94024i 0.0586191 + 0.180411i
\(478\) 0 0
\(479\) −2.38111 + 1.72998i −0.108796 + 0.0790448i −0.640853 0.767664i \(-0.721419\pi\)
0.532057 + 0.846708i \(0.321419\pi\)
\(480\) 0 0
\(481\) 3.98092 + 2.89230i 0.181514 + 0.131878i
\(482\) 0 0
\(483\) −1.96523 1.42782i −0.0894212 0.0649683i
\(484\) 0 0
\(485\) 33.9989 7.22668i 1.54381 0.328147i
\(486\) 0 0
\(487\) −4.33109 + 13.3297i −0.196261 + 0.604028i 0.803699 + 0.595036i \(0.202862\pi\)
−0.999960 + 0.00899199i \(0.997138\pi\)
\(488\) 0 0
\(489\) −0.792035 2.43763i −0.0358170 0.110234i
\(490\) 0 0
\(491\) 2.76416 8.50720i 0.124745 0.383925i −0.869110 0.494619i \(-0.835308\pi\)
0.993854 + 0.110695i \(0.0353075\pi\)
\(492\) 0 0
\(493\) 35.3472 1.59196
\(494\) 0 0
\(495\) 0.427051 + 0.190135i 0.0191945 + 0.00854595i
\(496\) 0 0
\(497\) −3.95971 + 2.87690i −0.177617 + 0.129046i
\(498\) 0 0
\(499\) −2.39366 −0.107155 −0.0535774 0.998564i \(-0.517062\pi\)
−0.0535774 + 0.998564i \(0.517062\pi\)
\(500\) 0 0
\(501\) −20.8512 −0.931564
\(502\) 0 0
\(503\) −6.81519 + 4.95152i −0.303874 + 0.220777i −0.729264 0.684233i \(-0.760137\pi\)
0.425389 + 0.905010i \(0.360137\pi\)
\(504\) 0 0
\(505\) −22.5530 10.0412i −1.00359 0.446829i
\(506\) 0 0
\(507\) −6.73192 −0.298975
\(508\) 0 0
\(509\) 9.98528 30.7315i 0.442590 1.36215i −0.442516 0.896761i \(-0.645914\pi\)
0.885106 0.465390i \(-0.154086\pi\)
\(510\) 0 0
\(511\) −0.581737 1.79040i −0.0257345 0.0792027i
\(512\) 0 0
\(513\) 0.384789 1.18426i 0.0169889 0.0522864i
\(514\) 0 0
\(515\) −30.3677 + 6.45486i −1.33816 + 0.284435i
\(516\) 0 0
\(517\) 1.09635 + 0.796543i 0.0482173 + 0.0350319i
\(518\) 0 0
\(519\) −1.66249 1.20787i −0.0729754 0.0530197i
\(520\) 0 0
\(521\) −2.88427 + 2.09554i −0.126362 + 0.0918074i −0.649171 0.760642i \(-0.724884\pi\)
0.522809 + 0.852450i \(0.324884\pi\)
\(522\) 0 0
\(523\) −10.0241 30.8511i −0.438325 1.34903i −0.889640 0.456662i \(-0.849045\pi\)
0.451315 0.892365i \(-0.350955\pi\)
\(524\) 0 0
\(525\) −3.65455 0.776798i −0.159497 0.0339022i
\(526\) 0 0
\(527\) −7.88082 24.2547i −0.343294 1.05655i
\(528\) 0 0
\(529\) 10.0577 7.30732i 0.437290 0.317710i
\(530\) 0 0
\(531\) −9.47420 6.88341i −0.411145 0.298715i
\(532\) 0 0
\(533\) 6.50929 + 4.72928i 0.281949 + 0.204848i
\(534\) 0 0
\(535\) 2.09402 + 0.932320i 0.0905326 + 0.0403077i
\(536\) 0 0
\(537\) −6.04449 + 18.6030i −0.260839 + 0.802781i
\(538\) 0 0
\(539\) −0.416143 1.28076i −0.0179246 0.0551661i
\(540\) 0 0
\(541\) −3.40378 + 10.4757i −0.146340 + 0.450388i −0.997181 0.0750356i \(-0.976093\pi\)
0.850841 + 0.525423i \(0.176093\pi\)
\(542\) 0 0
\(543\) −7.37007 −0.316280
\(544\) 0 0
\(545\) −10.0323 + 11.1420i −0.429738 + 0.477272i
\(546\) 0 0
\(547\) 4.31795 3.13718i 0.184622 0.134136i −0.491635 0.870801i \(-0.663601\pi\)
0.676258 + 0.736665i \(0.263601\pi\)
\(548\) 0 0
\(549\) −12.4794 −0.532606
\(550\) 0 0
\(551\) −6.45418 −0.274957
\(552\) 0 0
\(553\) 6.19177 4.49859i 0.263301 0.191299i
\(554\) 0 0
\(555\) −0.459386 + 4.37076i −0.0194998 + 0.185529i
\(556\) 0 0
\(557\) −0.0652731 −0.00276571 −0.00138286 0.999999i \(-0.500440\pi\)
−0.00138286 + 0.999999i \(0.500440\pi\)
\(558\) 0 0
\(559\) 9.83527 30.2699i 0.415988 1.28028i
\(560\) 0 0
\(561\) −0.440557 1.35589i −0.0186003 0.0572459i
\(562\) 0 0
\(563\) −8.88197 + 27.3359i −0.374330 + 1.15207i 0.569599 + 0.821923i \(0.307098\pi\)
−0.943929 + 0.330147i \(0.892902\pi\)
\(564\) 0 0
\(565\) 12.4509 13.8281i 0.523814 0.581754i
\(566\) 0 0
\(567\) −0.604528 0.439216i −0.0253878 0.0184453i
\(568\) 0 0
\(569\) 6.68501 + 4.85694i 0.280250 + 0.203614i 0.719026 0.694983i \(-0.244588\pi\)
−0.438776 + 0.898596i \(0.644588\pi\)
\(570\) 0 0
\(571\) −9.49451 + 6.89817i −0.397333 + 0.288679i −0.768454 0.639905i \(-0.778974\pi\)
0.371121 + 0.928585i \(0.378974\pi\)
\(572\) 0 0
\(573\) −0.693806 2.13532i −0.0289842 0.0892041i
\(574\) 0 0
\(575\) −8.12713 + 14.0766i −0.338925 + 0.587035i
\(576\) 0 0
\(577\) 6.60944 + 20.3418i 0.275154 + 0.846838i 0.989178 + 0.146717i \(0.0468707\pi\)
−0.714024 + 0.700121i \(0.753129\pi\)
\(578\) 0 0
\(579\) −0.894682 + 0.650024i −0.0371817 + 0.0270141i
\(580\) 0 0
\(581\) 3.43162 + 2.49322i 0.142368 + 0.103436i
\(582\) 0 0
\(583\) −0.700710 0.509096i −0.0290204 0.0210846i
\(584\) 0 0
\(585\) 2.79912 + 4.84823i 0.115730 + 0.200449i
\(586\) 0 0
\(587\) 12.7412 39.2133i 0.525885 1.61851i −0.236674 0.971589i \(-0.576057\pi\)
0.762559 0.646918i \(-0.223943\pi\)
\(588\) 0 0
\(589\) 1.43899 + 4.42876i 0.0592925 + 0.182484i
\(590\) 0 0
\(591\) 6.37705 19.6265i 0.262317 0.807328i
\(592\) 0 0
\(593\) −23.2238 −0.953685 −0.476843 0.878989i \(-0.658219\pi\)
−0.476843 + 0.878989i \(0.658219\pi\)
\(594\) 0 0
\(595\) 5.69730 + 9.86801i 0.233566 + 0.404549i
\(596\) 0 0
\(597\) 10.0174 7.27806i 0.409984 0.297871i
\(598\) 0 0
\(599\) −22.6226 −0.924335 −0.462168 0.886793i \(-0.652928\pi\)
−0.462168 + 0.886793i \(0.652928\pi\)
\(600\) 0 0
\(601\) −12.9540 −0.528405 −0.264203 0.964467i \(-0.585109\pi\)
−0.264203 + 0.964467i \(0.585109\pi\)
\(602\) 0 0
\(603\) −2.35995 + 1.71460i −0.0961045 + 0.0698240i
\(604\) 0 0
\(605\) 23.9637 5.09363i 0.974261 0.207086i
\(606\) 0 0
\(607\) 4.54036 0.184288 0.0921439 0.995746i \(-0.470628\pi\)
0.0921439 + 0.995746i \(0.470628\pi\)
\(608\) 0 0
\(609\) −1.19686 + 3.68354i −0.0484990 + 0.149265i
\(610\) 0 0
\(611\) 5.01505 + 15.4347i 0.202887 + 0.624423i
\(612\) 0 0
\(613\) −7.83471 + 24.1128i −0.316441 + 0.973905i 0.658716 + 0.752391i \(0.271100\pi\)
−0.975157 + 0.221514i \(0.928900\pi\)
\(614\) 0 0
\(615\) −0.751153 + 7.14675i −0.0302894 + 0.288185i
\(616\) 0 0
\(617\) 36.5829 + 26.5790i 1.47277 + 1.07003i 0.979799 + 0.199986i \(0.0640896\pi\)
0.492972 + 0.870045i \(0.335910\pi\)
\(618\) 0 0
\(619\) −25.3666 18.4299i −1.01957 0.740762i −0.0533766 0.998574i \(-0.516998\pi\)
−0.966195 + 0.257812i \(0.916998\pi\)
\(620\) 0 0
\(621\) −2.62999 + 1.91080i −0.105538 + 0.0766779i
\(622\) 0 0
\(623\) −0.212835 0.655040i −0.00852707 0.0262436i
\(624\) 0 0
\(625\) −2.61321 + 24.8630i −0.104528 + 0.994522i
\(626\) 0 0
\(627\) 0.0804429 + 0.247578i 0.00321258 + 0.00988730i
\(628\) 0 0
\(629\) 10.8435 7.87828i 0.432360 0.314128i
\(630\) 0 0
\(631\) −25.8455 18.7779i −1.02889 0.747535i −0.0608071 0.998150i \(-0.519367\pi\)
−0.968087 + 0.250614i \(0.919367\pi\)
\(632\) 0 0
\(633\) −16.6879 12.1245i −0.663286 0.481905i
\(634\) 0 0
\(635\) 3.39760 32.3260i 0.134830 1.28282i
\(636\) 0 0
\(637\) 4.98363 15.3380i 0.197459 0.607715i
\(638\) 0 0
\(639\) 2.02409 + 6.22949i 0.0800716 + 0.246435i
\(640\) 0 0
\(641\) 12.7727 39.3103i 0.504491 1.55267i −0.297132 0.954836i \(-0.596030\pi\)
0.801624 0.597829i \(-0.203970\pi\)
\(642\) 0 0
\(643\) −33.2313 −1.31052 −0.655258 0.755406i \(-0.727440\pi\)
−0.655258 + 0.755406i \(0.727440\pi\)
\(644\) 0 0
\(645\) 27.8052 5.91018i 1.09483 0.232713i
\(646\) 0 0
\(647\) −27.2571 + 19.8034i −1.07159 + 0.778553i −0.976197 0.216887i \(-0.930410\pi\)
−0.0953892 + 0.995440i \(0.530410\pi\)
\(648\) 0 0
\(649\) 2.44822 0.0961009
\(650\) 0 0
\(651\) 2.79443 0.109522
\(652\) 0 0
\(653\) −17.6754 + 12.8419i −0.691692 + 0.502544i −0.877216 0.480096i \(-0.840602\pi\)
0.185524 + 0.982640i \(0.440602\pi\)
\(654\) 0 0
\(655\) −8.30025 14.3764i −0.324317 0.561734i
\(656\) 0 0
\(657\) −2.51933 −0.0982885
\(658\) 0 0
\(659\) −3.48829 + 10.7359i −0.135884 + 0.418209i −0.995727 0.0923507i \(-0.970562\pi\)
0.859842 + 0.510560i \(0.170562\pi\)
\(660\) 0 0
\(661\) −11.3014 34.7821i −0.439573 1.35287i −0.888327 0.459211i \(-0.848132\pi\)
0.448754 0.893655i \(-0.351868\pi\)
\(662\) 0 0
\(663\) 5.27599 16.2378i 0.204903 0.630625i
\(664\) 0 0
\(665\) −1.04029 1.80184i −0.0403408 0.0698722i
\(666\) 0 0
\(667\) 13.6319 + 9.90412i 0.527828 + 0.383489i
\(668\) 0 0
\(669\) 3.36117 + 2.44203i 0.129950 + 0.0944145i
\(670\) 0 0
\(671\) 2.11064 1.53347i 0.0814804 0.0591990i
\(672\) 0 0
\(673\) 2.37563 + 7.31143i 0.0915737 + 0.281835i 0.986346 0.164689i \(-0.0526619\pi\)
−0.894772 + 0.446523i \(0.852662\pi\)
\(674\) 0 0
\(675\) −2.50000 + 4.33013i −0.0962250 + 0.166667i
\(676\) 0 0
\(677\) −11.5253 35.4711i −0.442952 1.36327i −0.884714 0.466133i \(-0.845647\pi\)
0.441763 0.897132i \(-0.354353\pi\)
\(678\) 0 0
\(679\) 9.39705 6.82736i 0.360626 0.262010i
\(680\) 0 0
\(681\) 19.1162 + 13.8888i 0.732535 + 0.532218i
\(682\) 0 0
\(683\) −29.5125 21.4421i −1.12926 0.820458i −0.143676 0.989625i \(-0.545892\pi\)
−0.985587 + 0.169166i \(0.945892\pi\)
\(684\) 0 0
\(685\) −10.9753 + 12.1894i −0.419346 + 0.465731i
\(686\) 0 0
\(687\) 5.63649 17.3473i 0.215046 0.661842i
\(688\) 0 0
\(689\) −3.20528 9.86483i −0.122111 0.375820i
\(690\) 0 0
\(691\) −9.99734 + 30.7686i −0.380317 + 1.17049i 0.559504 + 0.828827i \(0.310992\pi\)
−0.939821 + 0.341667i \(0.889008\pi\)
\(692\) 0 0
\(693\) 0.156215 0.00593413
\(694\) 0 0
\(695\) −4.61555 + 43.9140i −0.175078 + 1.66575i
\(696\) 0 0
\(697\) 17.7305 12.8820i 0.671591 0.487940i
\(698\) 0 0
\(699\) 2.26742 0.0857617
\(700\) 0 0
\(701\) 5.27498 0.199233 0.0996166 0.995026i \(-0.468238\pi\)
0.0996166 + 0.995026i \(0.468238\pi\)
\(702\) 0 0
\(703\) −1.97996 + 1.43853i −0.0746756 + 0.0542550i
\(704\) 0 0
\(705\) −9.69888 + 10.7717i −0.365281 + 0.405686i
\(706\) 0 0
\(707\) −8.24988 −0.310268
\(708\) 0 0
\(709\) 9.03055 27.7932i 0.339149 1.04379i −0.625493 0.780230i \(-0.715102\pi\)
0.964642 0.263564i \(-0.0848981\pi\)
\(710\) 0 0
\(711\) −3.16505 9.74102i −0.118699 0.365317i
\(712\) 0 0
\(713\) 3.75677 11.5621i 0.140692 0.433005i
\(714\) 0 0
\(715\) −1.06917 0.476025i −0.0399847 0.0178023i
\(716\) 0 0
\(717\) −13.8397 10.0552i −0.516855 0.375517i
\(718\) 0 0
\(719\) −35.5675 25.8413i −1.32644 0.963718i −0.999828 0.0185605i \(-0.994092\pi\)
−0.326616 0.945157i \(-0.605908\pi\)
\(720\) 0 0
\(721\) −8.39344 + 6.09819i −0.312588 + 0.227108i
\(722\) 0 0
\(723\) 8.71435 + 26.8200i 0.324090 + 0.997447i
\(724\) 0 0
\(725\) 25.3498 + 5.38827i 0.941468 + 0.200115i
\(726\) 0 0
\(727\) 9.24768 + 28.4614i 0.342977 + 1.05558i 0.962658 + 0.270721i \(0.0872622\pi\)
−0.619680 + 0.784854i \(0.712738\pi\)
\(728\) 0 0
\(729\) −0.809017 + 0.587785i −0.0299636 + 0.0217698i
\(730\) 0 0
\(731\) −70.1373 50.9577i −2.59412 1.88474i
\(732\) 0 0
\(733\) 13.3702 + 9.71402i 0.493840 + 0.358795i 0.806659 0.591017i \(-0.201273\pi\)
−0.312819 + 0.949813i \(0.601273\pi\)
\(734\) 0 0
\(735\) 14.0892 2.99475i 0.519687 0.110463i
\(736\) 0 0
\(737\) 0.188448 0.579984i 0.00694158 0.0213640i
\(738\) 0 0
\(739\) −15.7285 48.4073i −0.578581 1.78069i −0.623648 0.781706i \(-0.714350\pi\)
0.0450666 0.998984i \(-0.485650\pi\)
\(740\) 0 0
\(741\) −0.963364 + 2.96493i −0.0353901 + 0.108919i
\(742\) 0 0
\(743\) −28.6937 −1.05267 −0.526336 0.850277i \(-0.676434\pi\)
−0.526336 + 0.850277i \(0.676434\pi\)
\(744\) 0 0
\(745\) −44.4402 19.7860i −1.62816 0.724904i
\(746\) 0 0
\(747\) 4.59240 3.33658i 0.168027 0.122079i
\(748\) 0 0
\(749\) 0.765995 0.0279888
\(750\) 0 0
\(751\) −0.927935 −0.0338608 −0.0169304 0.999857i \(-0.505389\pi\)
−0.0169304 + 0.999857i \(0.505389\pi\)
\(752\) 0 0
\(753\) −19.3821 + 14.0819i −0.706322 + 0.513173i
\(754\) 0 0
\(755\) 20.6947 + 9.21385i 0.753156 + 0.335327i
\(756\) 0 0
\(757\) 41.4243 1.50559 0.752796 0.658254i \(-0.228705\pi\)
0.752796 + 0.658254i \(0.228705\pi\)
\(758\) 0 0
\(759\) 0.210012 0.646350i 0.00762295 0.0234610i
\(760\) 0 0
\(761\) 1.17031 + 3.60185i 0.0424237 + 0.130567i 0.970025 0.243005i \(-0.0781330\pi\)
−0.927601 + 0.373572i \(0.878133\pi\)
\(762\) 0 0
\(763\) −1.54827 + 4.76509i −0.0560513 + 0.172508i
\(764\) 0 0
\(765\) 14.9157 3.17043i 0.539279 0.114627i
\(766\) 0 0
\(767\) 23.7197 + 17.2334i 0.856470 + 0.622262i
\(768\) 0 0
\(769\) 1.06014 + 0.770234i 0.0382295 + 0.0277753i 0.606736 0.794903i \(-0.292479\pi\)
−0.568506 + 0.822679i \(0.692479\pi\)
\(770\) 0 0
\(771\) 23.0911 16.7766i 0.831604 0.604196i
\(772\) 0 0
\(773\) 9.00241 + 27.7066i 0.323794 + 0.996536i 0.971982 + 0.235055i \(0.0755272\pi\)
−0.648188 + 0.761480i \(0.724473\pi\)
\(774\) 0 0
\(775\) −1.95452 18.5960i −0.0702083 0.667987i
\(776\) 0 0
\(777\) 0.453837 + 1.39677i 0.0162813 + 0.0501087i
\(778\) 0 0
\(779\) −3.23748 + 2.35217i −0.115995 + 0.0842752i
\(780\) 0 0
\(781\) −1.10782 0.804877i −0.0396409 0.0288008i
\(782\) 0 0
\(783\) 4.19332 + 3.04662i 0.149857 + 0.108877i
\(784\) 0 0
\(785\) −20.4177 9.09055i −0.728739 0.324455i
\(786\) 0 0
\(787\) −14.4050 + 44.3341i −0.513484 + 1.58034i 0.272540 + 0.962145i \(0.412136\pi\)
−0.786023 + 0.618197i \(0.787864\pi\)
\(788\) 0 0
\(789\) −1.09911 3.38270i −0.0391292 0.120427i
\(790\) 0 0
\(791\) 1.92153 5.91385i 0.0683217 0.210272i
\(792\) 0 0
\(793\) 31.2435 1.10949
\(794\) 0 0
\(795\)