Properties

Label 300.2.m.a.121.2
Level $300$
Weight $2$
Character 300.121
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 121.2
Root \(-0.978148 + 0.207912i\) of defining polynomial
Character \(\chi\) \(=\) 300.121
Dual form 300.2.m.a.181.2

$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\)

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 −0.940845 0.338837i \(-0.889966\pi\)
0.960323 + 0.278889i \(0.0899663\pi\)
\(12\) 0 0
\(13\) −0.773659 2.38108i −0.214574 0.660392i −0.999184 0.0404014i \(-0.987136\pi\)
0.784609 0.619991i \(-0.212864\pi\)
\(14\) 0 0
\(15\) −2.18720 0.464905i −0.564734 0.120038i
\(16\) 0 0
\(17\) 5.51712 4.00842i 1.33810 0.972185i 0.338586 0.940935i \(-0.390051\pi\)
0.999512 0.0312497i \(-0.00994869\pi\)
\(18\) 0 0
\(19\) −1.00739 + 0.731913i −0.231112 + 0.167912i −0.697314 0.716766i \(-0.745622\pi\)
0.466203 + 0.884678i \(0.345622\pi\)
\(20\) 0 0
\(21\) −0.604528 0.439216i −0.131919 0.0958447i
\(22\) 0 0
\(23\) 1.00457 3.09174i 0.209467 0.644673i −0.790033 0.613064i \(-0.789937\pi\)
0.999500 0.0316092i \(-0.0100632\pi\)
\(24\) 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 0.904582 0.426299i \(-0.140183\pi\)
−0.125903 + 0.992043i \(0.540183\pi\)
\(30\) 0 0
\(31\) −3.02547 + 2.19813i −0.543390 + 0.394796i −0.825342 0.564633i \(-0.809018\pi\)
0.281953 + 0.959428i \(0.409018\pi\)
\(32\) 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 0.988487 0.151307i \(-0.0483483\pi\)
−0.888639 + 0.458608i \(0.848348\pi\)
\(38\) 0 0
\(39\) −0.773659 + 2.38108i −0.123885 + 0.381278i
\(40\) 0 0
\(41\) 0.993096 + 3.05644i 0.155096 + 0.477335i 0.998171 0.0604609i \(-0.0192570\pi\)
−0.843075 + 0.537796i \(0.819257\pi\)
\(42\) 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 0.900425 0.435011i \(-0.143255\pi\)
−0.135473 + 0.990781i \(0.543255\pi\)
\(48\) 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 0.333288 0.942825i \(-0.391842\pi\)
−0.793688 + 0.608325i \(0.791842\pi\)
\(54\) 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 0.851106 + 0.524995i \(0.175933\pi\)
−0.379975 + 0.924997i \(0.624067\pi\)
\(60\) 0 0
\(61\) −3.85634 + 11.8686i −0.493753 + 1.51962i 0.325138 + 0.945667i \(0.394589\pi\)
−0.818891 + 0.573949i \(0.805411\pi\)
\(62\) 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 −0.722535 0.691334i \(-0.757023\pi\)
0.434222 + 0.900806i \(0.357023\pi\)
\(68\) 0 0
\(69\) −2.62999 + 1.91080i −0.316614 + 0.230034i
\(70\) 0 0
\(71\) −5.29912 3.85004i −0.628890 0.456916i 0.227125 0.973866i \(-0.427067\pi\)
−0.856016 + 0.516950i \(0.827067\pi\)
\(72\) 0 0
\(73\) −0.778516 + 2.39603i −0.0911184 + 0.280434i −0.986223 0.165423i \(-0.947101\pi\)
0.895104 + 0.445857i \(0.147101\pi\)
\(74\) 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 0.946548 0.322563i \(-0.104545\pi\)
−0.0142765 + 0.999898i \(0.504545\pi\)
\(80\) 0 0
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) 0 0
\(83\) 4.59240 3.33658i 0.504082 0.366237i −0.306492 0.951873i \(-0.599155\pi\)
0.810574 + 0.585636i \(0.199155\pi\)
\(84\) 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 −0.965017 0.262188i \(-0.915556\pi\)
0.934825 + 0.355109i \(0.115556\pi\)
\(90\) 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 0.999454 0.0330496i \(-0.0105219\pi\)
0.277416 + 0.960750i \(0.410522\pi\)
\(98\) 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 −0.124628 0.992203i \(-0.539774\pi\)
−0.982154 + 0.188079i \(0.939774\pi\)
\(104\) 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 −0.999919 0.0127488i \(-0.995942\pi\)
0.801458 0.598051i \(-0.204058\pi\)
\(110\) 0 0
\(111\) 0.607352 1.86924i 0.0576473 0.177420i
\(112\) 0 0
\(113\) 2.57151 + 7.91428i 0.241907 + 0.744513i 0.996130 + 0.0878944i \(0.0280138\pi\)
−0.754223 + 0.656618i \(0.771986\pi\)
\(114\) 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 0.527529 + 0.849537i \(0.323119\pi\)
−0.926125 + 0.377217i \(0.876881\pi\)
\(128\) 0 0
\(129\) 10.2848 + 7.47232i 0.905523 + 0.657901i
\(130\) 0 0
\(131\) −6.00611 + 4.36370i −0.524757 + 0.381258i −0.818393 0.574659i \(-0.805135\pi\)
0.293636 + 0.955917i \(0.405135\pi\)
\(132\) 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 −0.999990 0.00456114i \(-0.998548\pi\)
0.806328 0.591469i \(-0.201452\pi\)
\(138\) 0 0
\(139\) 6.10219 18.7806i 0.517581 1.59295i −0.260954 0.965351i \(-0.584037\pi\)
0.778536 0.627600i \(-0.215963\pi\)
\(140\) 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 0.915235 0.402921i \(-0.132005\pi\)
−0.977272 + 0.211991i \(0.932005\pi\)
\(164\) 0 0
\(165\) −0.233733 + 0.404837i −0.0181961 + 0.0315165i
\(166\) 0 0
\(167\) 16.8690 12.2560i 1.30536 0.948401i 0.305369 0.952234i \(-0.401220\pi\)
0.999993 + 0.00383355i \(0.00122026\pi\)
\(168\) 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 −0.924011 0.382367i \(-0.875109\pi\)
0.972290 + 0.233778i \(0.0751090\pi\)
\(174\) 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 0.992484 0.122375i \(-0.0390510\pi\)
0.190309 + 0.981724i \(0.439051\pi\)
\(180\) 0 0
\(181\) 5.96251 4.33202i 0.443190 0.321996i −0.343711 0.939075i \(-0.611684\pi\)
0.786901 + 0.617079i \(0.211684\pi\)
\(182\) 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 0.922813 0.385249i \(-0.125884\pi\)
−0.973015 + 0.230743i \(0.925884\pi\)
\(192\) 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 −0.196282 0.980547i \(-0.562887\pi\)
−0.993211 + 0.116331i \(0.962887\pi\)
\(198\) 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 −0.450302 0.892876i \(-0.648684\pi\)
0.889121 0.457671i \(-0.151316\pi\)
\(212\) 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 −0.984796 0.173713i \(-0.944423\pi\)
0.898823 + 0.438312i \(0.144423\pi\)
\(224\) 0 0
\(225\) 4.56773 + 2.03368i 0.304515 + 0.135579i
\(226\) 0 0
\(227\) −7.30175 + 22.4725i −0.484634 + 1.49155i 0.347876 + 0.937541i \(0.386903\pi\)
−0.832510 + 0.554010i \(0.813097\pi\)
\(228\) 0 0
\(229\) −14.7565 10.7212i −0.975139 0.708480i −0.0185221 0.999828i \(-0.505896\pi\)
−0.956617 + 0.291348i \(0.905896\pi\)
\(230\) 0 0
\(231\) −0.126381 + 0.0918211i −0.00831525 + 0.00604138i
\(232\) 0 0
\(233\) −1.83438 + 1.33276i −0.120174 + 0.0873117i −0.646249 0.763127i \(-0.723663\pi\)
0.526075 + 0.850438i \(0.323663\pi\)
\(234\) 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 −0.621257 0.783607i \(-0.713378\pi\)
0.963200 0.268786i \(-0.0866223\pi\)
\(240\) 0 0
\(241\) 8.71435 + 26.8200i 0.561341 + 1.72763i 0.678581 + 0.734526i \(0.262595\pi\)
−0.117240 + 0.993104i \(0.537405\pi\)
\(242\) 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 0.911434 0.411447i \(-0.134976\pi\)
−0.979208 + 0.202860i \(0.934976\pi\)
\(264\) 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 −0.456066 + 0.889946i \(0.650742\pi\)
−0.987321 + 0.158736i \(0.949258\pi\)
\(270\) 0 0
\(271\) 20.0784 + 14.5878i 1.21968 + 0.886147i 0.996073 0.0885338i \(-0.0282181\pi\)
0.223603 + 0.974680i \(0.428218\pi\)
\(272\) 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 0.648502 + 0.761213i \(0.275396\pi\)
−0.972079 + 0.234654i \(0.924604\pi\)
\(278\) 0 0
\(279\) −3.02547 2.19813i −0.181130 0.131599i
\(280\) 0 0
\(281\) −3.03664 + 2.20625i −0.181151 + 0.131614i −0.674665 0.738124i \(-0.735712\pi\)
0.493515 + 0.869738i \(0.335712\pi\)
\(282\) 0 0
\(283\) −13.2464 + 9.62409i −0.787418 + 0.572093i −0.907196 0.420708i \(-0.861782\pi\)
0.119778 + 0.992801i \(0.461782\pi\)
\(284\) 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 −0.600228 0.799829i \(-0.704924\pi\)
0.955722 0.294270i \(-0.0950763\pi\)
\(312\) 0 0
\(313\) 6.41831 + 19.7535i 0.362785 + 1.11654i 0.951357 + 0.308091i \(0.0996902\pi\)
−0.588572 + 0.808445i \(0.700310\pi\)
\(314\) 0 0
\(315\) 1.11803 + 1.24170i 0.0629941 + 0.0699620i
\(316\) 0 0
\(317\) 13.5633 9.85429i 0.761789 0.553472i −0.137670 0.990478i \(-0.543961\pi\)
0.899458 + 0.437006i \(0.143961\pi\)
\(318\) 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 0.175257 0.984523i \(-0.443924\pi\)
0.990494 + 0.137555i \(0.0439243\pi\)
\(332\) 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 −0.890289 0.455395i \(-0.849498\pi\)
0.452584 0.891722i \(-0.350502\pi\)
\(338\) 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 0.483366 0.875418i \(-0.339414\pi\)
−0.683204 + 0.730228i \(0.739414\pi\)
\(348\) 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 0.995311 0.0967283i \(-0.0308378\pi\)
0.215574 + 0.976488i \(0.430838\pi\)
\(354\) 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 0.844634 0.535345i \(-0.179818\pi\)
−0.997991 + 0.0633604i \(0.979818\pi\)
\(360\) 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 −0.945828 0.324669i \(-0.894747\pi\)
0.0165016 + 0.999864i \(0.494747\pi\)
\(368\) 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 −0.684302 0.729199i \(-0.739893\pi\)
0.982224 0.187712i \(-0.0601072\pi\)
\(374\) 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 0.880332 0.474357i \(-0.157320\pi\)
−0.179103 + 0.983830i \(0.557320\pi\)
\(380\) 0 0
\(381\) 11.7601 8.54421i 0.602488 0.437733i
\(382\) 0 0
\(383\) 7.32847 5.32445i 0.374467 0.272066i −0.384594 0.923086i \(-0.625658\pi\)
0.759061 + 0.651020i \(0.225658\pi\)
\(384\) 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 −0.258893 0.965906i \(-0.583358\pi\)
0.777194 0.629261i \(-0.216642\pi\)
\(390\) 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 0.933827 0.357726i \(-0.116448\pi\)
−0.0516494 + 0.998665i \(0.516448\pi\)
\(398\) 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 −0.999177 0.0405623i \(-0.987085\pi\)
0.784509 0.620117i \(-0.212915\pi\)
\(410\) 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 −0.110353 0.993892i \(-0.535198\pi\)
0.911147 + 0.412081i \(0.135198\pi\)
\(420\) 0 0
\(421\) −3.54258 2.57384i −0.172655 0.125441i 0.498102 0.867119i \(-0.334031\pi\)
−0.670757 + 0.741677i \(0.734031\pi\)
\(422\) 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 −0.610311 0.792162i \(-0.708956\pi\)
0.564794 + 0.825232i \(0.308956\pi\)
\(432\) 0 0
\(433\) −1.81940 + 1.32187i −0.0874347 + 0.0635250i −0.630644 0.776072i \(-0.717209\pi\)
0.543209 + 0.839597i \(0.317209\pi\)
\(434\) 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 −0.644688 0.764446i \(-0.723013\pi\)
0.970893 0.239512i \(-0.0769875\pi\)
\(440\) 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 −0.895785 0.444487i \(-0.853386\pi\)
0.985968 + 0.166932i \(0.0533861\pi\)
\(462\) 0 0
\(463\) −5.26243 16.1961i −0.244566 0.752696i −0.995708 0.0925550i \(-0.970497\pi\)
0.751142 0.660141i \(-0.229503\pi\)
\(464\) 0 0
\(465\) 7.63923 3.40121i 0.354261 0.157727i
\(466\) 0 0
\(467\) 15.1159 10.9823i 0.699481 0.508202i −0.180282 0.983615i \(-0.557701\pi\)
0.879763 + 0.475413i \(0.157701\pi\)
\(468\) 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 0.532057 0.846708i \(-0.321419\pi\)
−0.640853 + 0.767664i \(0.721419\pi\)
\(480\) 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 −0.999960 0.00899199i \(-0.997138\pi\)
0.803699 0.595036i \(-0.202862\pi\)
\(488\) 0 0
\(489\) −0.792035 + 2.43763i −0.0358170 + 0.110234i
\(490\) 0 0
\(491\) 2.76416 + 8.50720i 0.124745 + 0.383925i 0.993854 0.110695i \(-0.0353075\pi\)
−0.869110 + 0.494619i \(0.835308\pi\)
\(492\) 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 0.425389 0.905010i \(-0.360137\pi\)
−0.729264 + 0.684233i \(0.760137\pi\)
\(504\) 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 0.885106 + 0.465390i \(0.154086\pi\)
−0.442516 + 0.896761i \(0.645914\pi\)
\(510\) 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 0.522809 0.852450i \(-0.324884\pi\)
−0.649171 + 0.760642i \(0.724884\pi\)
\(522\) 0 0
\(523\) −10.0241 + 30.8511i −0.438325 + 1.34903i 0.451315 + 0.892365i \(0.350955\pi\)
−0.889640 + 0.456662i \(0.849045\pi\)
\(524\) 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 0.850841 0.525423i \(-0.176093\pi\)
−0.997181 + 0.0750356i \(0.976093\pi\)
\(542\) 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 0.676258 0.736665i \(-0.263601\pi\)
−0.491635 + 0.870801i \(0.663601\pi\)
\(548\) 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 −0.943929 0.330147i \(-0.892902\pi\)
0.569599 0.821923i \(-0.307098\pi\)
\(564\) 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 −0.438776 0.898596i \(-0.644588\pi\)
0.719026 + 0.694983i \(0.244588\pi\)
\(570\) 0 0
\(571\) −9.49451 6.89817i −0.397333 0.288679i 0.371121 0.928585i \(-0.378974\pi\)
−0.768454 + 0.639905i \(0.778974\pi\)
\(572\) 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 −0.714024 0.700121i \(-0.753129\pi\)
0.989178 0.146717i \(-0.0468707\pi\)
\(578\) 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 0.762559 + 0.646918i \(0.223943\pi\)
−0.236674 + 0.971589i \(0.576057\pi\)
\(588\) 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 −0.975157 0.221514i \(-0.928900\pi\)
0.658716 0.752391i \(-0.271100\pi\)
\(614\) 0 0
\(615\) −0.751153 7.14675i −0.0302894 0.288185i
\(616\) 0 0
\(617\) 36.5829 26.5790i 1.47277 1.07003i 0.492972 0.870045i \(-0.335910\pi\)
0.979799 0.199986i \(-0.0640896\pi\)
\(618\) 0 0
\(619\) −25.3666 + 18.4299i −1.01957 + 0.740762i −0.966195 0.257812i \(-0.916998\pi\)
−0.0533766 + 0.998574i \(0.516998\pi\)
\(620\) 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 −0.968087 0.250614i \(-0.919367\pi\)
−0.0608071 + 0.998150i \(0.519367\pi\)
\(632\) 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 0.801624 + 0.597829i \(0.203970\pi\)
−0.297132 + 0.954836i \(0.596030\pi\)
\(642\) 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 −0.0953892 0.995440i \(-0.530410\pi\)
−0.976197 + 0.216887i \(0.930410\pi\)
\(648\) 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 0.185524 0.982640i \(-0.440602\pi\)
−0.877216 + 0.480096i \(0.840602\pi\)
\(654\) 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 0.859842 0.510560i \(-0.170562\pi\)
−0.995727 + 0.0923507i \(0.970562\pi\)
\(660\) 0 0
\(661\) −11.3014 + 34.7821i −0.439573 + 1.35287i 0.448754 + 0.893655i \(0.351868\pi\)
−0.888327 + 0.459211i \(0.848132\pi\)
\(662\) 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 −0.894772 0.446523i \(-0.852662\pi\)
0.986346 + 0.164689i \(0.0526619\pi\)
\(674\) 0 0
\(675\) −2.50000 4.33013i −0.0962250 0.166667i
\(676\) 0 0
\(677\) −11.5253 + 35.4711i −0.442952 + 1.36327i 0.441763 + 0.897132i \(0.354353\pi\)
−0.884714 + 0.466133i \(0.845647\pi\)
\(678\) 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 −0.985587 0.169166i \(-0.945892\pi\)
−0.143676 + 0.989625i \(0.545892\pi\)
\(684\) 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 −0.939821 0.341667i \(-0.889008\pi\)
0.559504 0.828827i \(-0.310992\pi\)
\(692\) 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 0.964642 + 0.263564i \(0.0848981\pi\)
−0.625493 + 0.780230i \(0.715102\pi\)
\(710\) 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 −0.326616 + 0.945157i \(0.605908\pi\)
−0.999828 + 0.0185605i \(0.994092\pi\)
\(720\) 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 −0.619680 0.784854i \(-0.712738\pi\)
0.962658 0.270721i \(-0.0872622\pi\)
\(728\) 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 −0.312819 0.949813i \(-0.601273\pi\)
0.806659 + 0.591017i \(0.201273\pi\)
\(734\) 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 0.0450666 + 0.998984i \(0.485650\pi\)
−0.623648 + 0.781706i \(0.714350\pi\)
\(740\) 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 −0.927601 0.373572i \(-0.878133\pi\)
0.970025 + 0.243005i \(0.0781330\pi\)
\(762\) 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 −0.568506 0.822679i \(-0.692479\pi\)
0.606736 + 0.794903i \(0.292479\pi\)
\(770\) 0 0
\(771\) 23.0911 + 16.7766i 0.831604 + 0.604196i
\(772\) 0 0
\(773\) 9.00241 27.7066i 0.323794 0.996536i −0.648188 0.761480i \(-0.724473\pi\)
0.971982 0.235055i \(-0.0755272\pi\)
\(774\) 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 −0.786023 0.618197i \(-0.787864\pi\)
0.272540 0.962145i \(-0.412136\pi\)
\(788\) 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
\(795\) 6.19886 + 6.88453i 0.219851 + 0.244169i