Properties

Label 128.3.h.a.47.4
Level $128$
Weight $3$
Character 128.47
Analytic conductor $3.488$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 128.h (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.48774738381\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 47.4
Character \(\chi\) \(=\) 128.47
Dual form 128.3.h.a.79.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.299792 + 0.723762i) q^{3} +(1.34740 + 3.25291i) q^{5} +(-0.583225 - 0.583225i) q^{7} +(5.93000 + 5.93000i) q^{9} +O(q^{10})\) \(q+(-0.299792 + 0.723762i) q^{3} +(1.34740 + 3.25291i) q^{5} +(-0.583225 - 0.583225i) q^{7} +(5.93000 + 5.93000i) q^{9} +(3.03620 + 7.33003i) q^{11} +(-6.38385 + 15.4120i) q^{13} -2.75827 q^{15} -19.0889i q^{17} +(29.6679 + 12.2888i) q^{19} +(0.596962 - 0.247270i) q^{21} +(-15.2998 + 15.2998i) q^{23} +(8.91173 - 8.91173i) q^{25} +(-12.5835 + 5.21227i) q^{27} +(-20.5148 - 8.49749i) q^{29} -53.6582i q^{31} -6.21542 q^{33} +(1.11134 - 2.68301i) q^{35} +(-3.80237 - 9.17973i) q^{37} +(-9.24078 - 9.24078i) q^{39} +(14.5108 + 14.5108i) q^{41} +(-20.3685 - 49.1739i) q^{43} +(-11.2997 + 27.2799i) q^{45} -4.73351 q^{47} -48.3197i q^{49} +(13.8158 + 5.72269i) q^{51} +(61.4006 - 25.4330i) q^{53} +(-19.7530 + 19.7530i) q^{55} +(-17.7884 + 17.7884i) q^{57} +(-42.4656 + 17.5898i) q^{59} +(-27.7452 - 11.4924i) q^{61} -6.91705i q^{63} -58.7354 q^{65} +(9.42323 - 22.7497i) q^{67} +(-6.48665 - 15.6602i) q^{69} +(95.1299 + 95.1299i) q^{71} +(37.1241 + 37.1241i) q^{73} +(3.77831 + 9.12164i) q^{75} +(2.50427 - 6.04584i) q^{77} +70.3394 q^{79} +64.8066i q^{81} +(-14.5221 - 6.01526i) q^{83} +(62.0944 - 25.7203i) q^{85} +(12.3003 - 12.3003i) q^{87} +(-60.8411 + 60.8411i) q^{89} +(12.7119 - 5.26543i) q^{91} +(38.8357 + 16.0863i) q^{93} +113.065i q^{95} +31.8287 q^{97} +(-25.4624 + 61.4718i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 28q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 8q^{15} + 4q^{19} - 4q^{21} + 68q^{23} - 4q^{25} + 100q^{27} - 4q^{29} - 8q^{33} - 92q^{35} - 4q^{37} - 188q^{39} - 4q^{41} - 92q^{43} - 40q^{45} + 8q^{47} - 224q^{51} - 164q^{53} - 252q^{55} - 4q^{57} - 124q^{59} - 68q^{61} - 8q^{65} + 164q^{67} + 188q^{69} + 260q^{71} - 4q^{73} + 488q^{75} + 220q^{77} + 520q^{79} + 484q^{83} + 96q^{85} + 452q^{87} - 4q^{89} + 196q^{91} + 32q^{93} - 8q^{97} - 216q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.299792 + 0.723762i −0.0999307 + 0.241254i −0.965936 0.258781i \(-0.916679\pi\)
0.866005 + 0.500035i \(0.166679\pi\)
\(4\) 0 0
\(5\) 1.34740 + 3.25291i 0.269480 + 0.650582i 0.999459 0.0328874i \(-0.0104703\pi\)
−0.729979 + 0.683469i \(0.760470\pi\)
\(6\) 0 0
\(7\) −0.583225 0.583225i −0.0833178 0.0833178i 0.664220 0.747537i \(-0.268764\pi\)
−0.747537 + 0.664220i \(0.768764\pi\)
\(8\) 0 0
\(9\) 5.93000 + 5.93000i 0.658889 + 0.658889i
\(10\) 0 0
\(11\) 3.03620 + 7.33003i 0.276018 + 0.666366i 0.999718 0.0237484i \(-0.00756007\pi\)
−0.723700 + 0.690115i \(0.757560\pi\)
\(12\) 0 0
\(13\) −6.38385 + 15.4120i −0.491065 + 1.18554i 0.463113 + 0.886299i \(0.346732\pi\)
−0.954179 + 0.299238i \(0.903268\pi\)
\(14\) 0 0
\(15\) −2.75827 −0.183885
\(16\) 0 0
\(17\) 19.0889i 1.12287i −0.827519 0.561437i \(-0.810249\pi\)
0.827519 0.561437i \(-0.189751\pi\)
\(18\) 0 0
\(19\) 29.6679 + 12.2888i 1.56147 + 0.646781i 0.985343 0.170582i \(-0.0545648\pi\)
0.576123 + 0.817363i \(0.304565\pi\)
\(20\) 0 0
\(21\) 0.596962 0.247270i 0.0284268 0.0117748i
\(22\) 0 0
\(23\) −15.2998 + 15.2998i −0.665208 + 0.665208i −0.956603 0.291395i \(-0.905881\pi\)
0.291395 + 0.956603i \(0.405881\pi\)
\(24\) 0 0
\(25\) 8.91173 8.91173i 0.356469 0.356469i
\(26\) 0 0
\(27\) −12.5835 + 5.21227i −0.466057 + 0.193047i
\(28\) 0 0
\(29\) −20.5148 8.49749i −0.707405 0.293017i −0.000174983 1.00000i \(-0.500056\pi\)
−0.707231 + 0.706983i \(0.750056\pi\)
\(30\) 0 0
\(31\) 53.6582i 1.73091i −0.500988 0.865454i \(-0.667030\pi\)
0.500988 0.865454i \(-0.332970\pi\)
\(32\) 0 0
\(33\) −6.21542 −0.188346
\(34\) 0 0
\(35\) 1.11134 2.68301i 0.0317526 0.0766575i
\(36\) 0 0
\(37\) −3.80237 9.17973i −0.102767 0.248101i 0.864130 0.503268i \(-0.167869\pi\)
−0.966897 + 0.255168i \(0.917869\pi\)
\(38\) 0 0
\(39\) −9.24078 9.24078i −0.236943 0.236943i
\(40\) 0 0
\(41\) 14.5108 + 14.5108i 0.353922 + 0.353922i 0.861567 0.507644i \(-0.169484\pi\)
−0.507644 + 0.861567i \(0.669484\pi\)
\(42\) 0 0
\(43\) −20.3685 49.1739i −0.473686 1.14358i −0.962522 0.271203i \(-0.912579\pi\)
0.488837 0.872375i \(-0.337421\pi\)
\(44\) 0 0
\(45\) −11.2997 + 27.2799i −0.251104 + 0.606219i
\(46\) 0 0
\(47\) −4.73351 −0.100713 −0.0503565 0.998731i \(-0.516036\pi\)
−0.0503565 + 0.998731i \(0.516036\pi\)
\(48\) 0 0
\(49\) 48.3197i 0.986116i
\(50\) 0 0
\(51\) 13.8158 + 5.72269i 0.270898 + 0.112210i
\(52\) 0 0
\(53\) 61.4006 25.4330i 1.15850 0.479867i 0.281126 0.959671i \(-0.409292\pi\)
0.877376 + 0.479803i \(0.159292\pi\)
\(54\) 0 0
\(55\) −19.7530 + 19.7530i −0.359145 + 0.359145i
\(56\) 0 0
\(57\) −17.7884 + 17.7884i −0.312077 + 0.312077i
\(58\) 0 0
\(59\) −42.4656 + 17.5898i −0.719757 + 0.298133i −0.712335 0.701840i \(-0.752362\pi\)
−0.00742152 + 0.999972i \(0.502362\pi\)
\(60\) 0 0
\(61\) −27.7452 11.4924i −0.454839 0.188400i 0.143489 0.989652i \(-0.454168\pi\)
−0.598328 + 0.801251i \(0.704168\pi\)
\(62\) 0 0
\(63\) 6.91705i 0.109794i
\(64\) 0 0
\(65\) −58.7354 −0.903621
\(66\) 0 0
\(67\) 9.42323 22.7497i 0.140645 0.339548i −0.837824 0.545940i \(-0.816172\pi\)
0.978469 + 0.206393i \(0.0661725\pi\)
\(68\) 0 0
\(69\) −6.48665 15.6602i −0.0940094 0.226959i
\(70\) 0 0
\(71\) 95.1299 + 95.1299i 1.33986 + 1.33986i 0.896193 + 0.443664i \(0.146322\pi\)
0.443664 + 0.896193i \(0.353678\pi\)
\(72\) 0 0
\(73\) 37.1241 + 37.1241i 0.508550 + 0.508550i 0.914081 0.405531i \(-0.132913\pi\)
−0.405531 + 0.914081i \(0.632913\pi\)
\(74\) 0 0
\(75\) 3.77831 + 9.12164i 0.0503774 + 0.121622i
\(76\) 0 0
\(77\) 2.50427 6.04584i 0.0325230 0.0785174i
\(78\) 0 0
\(79\) 70.3394 0.890372 0.445186 0.895438i \(-0.353138\pi\)
0.445186 + 0.895438i \(0.353138\pi\)
\(80\) 0 0
\(81\) 64.8066i 0.800081i
\(82\) 0 0
\(83\) −14.5221 6.01526i −0.174965 0.0724730i 0.293481 0.955965i \(-0.405186\pi\)
−0.468447 + 0.883492i \(0.655186\pi\)
\(84\) 0 0
\(85\) 62.0944 25.7203i 0.730522 0.302592i
\(86\) 0 0
\(87\) 12.3003 12.3003i 0.141383 0.141383i
\(88\) 0 0
\(89\) −60.8411 + 60.8411i −0.683608 + 0.683608i −0.960811 0.277204i \(-0.910592\pi\)
0.277204 + 0.960811i \(0.410592\pi\)
\(90\) 0 0
\(91\) 12.7119 5.26543i 0.139691 0.0578618i
\(92\) 0 0
\(93\) 38.8357 + 16.0863i 0.417589 + 0.172971i
\(94\) 0 0
\(95\) 113.065i 1.19016i
\(96\) 0 0
\(97\) 31.8287 0.328131 0.164066 0.986449i \(-0.447539\pi\)
0.164066 + 0.986449i \(0.447539\pi\)
\(98\) 0 0
\(99\) −25.4624 + 61.4718i −0.257196 + 0.620927i
\(100\) 0 0
\(101\) 11.0397 + 26.6521i 0.109304 + 0.263883i 0.969061 0.246820i \(-0.0793855\pi\)
−0.859758 + 0.510702i \(0.829385\pi\)
\(102\) 0 0
\(103\) −56.0862 56.0862i −0.544526 0.544526i 0.380326 0.924852i \(-0.375812\pi\)
−0.924852 + 0.380326i \(0.875812\pi\)
\(104\) 0 0
\(105\) 1.60869 + 1.60869i 0.0153209 + 0.0153209i
\(106\) 0 0
\(107\) −5.85623 14.1382i −0.0547311 0.132133i 0.894149 0.447770i \(-0.147782\pi\)
−0.948880 + 0.315637i \(0.897782\pi\)
\(108\) 0 0
\(109\) 37.6258 90.8367i 0.345191 0.833364i −0.651983 0.758233i \(-0.726063\pi\)
0.997174 0.0751304i \(-0.0239373\pi\)
\(110\) 0 0
\(111\) 7.78386 0.0701248
\(112\) 0 0
\(113\) 82.4104i 0.729295i 0.931146 + 0.364648i \(0.118811\pi\)
−0.931146 + 0.364648i \(0.881189\pi\)
\(114\) 0 0
\(115\) −70.3837 29.1539i −0.612032 0.253512i
\(116\) 0 0
\(117\) −129.249 + 53.5368i −1.10470 + 0.457580i
\(118\) 0 0
\(119\) −11.1331 + 11.1331i −0.0935555 + 0.0935555i
\(120\) 0 0
\(121\) 41.0491 41.0491i 0.339249 0.339249i
\(122\) 0 0
\(123\) −14.8526 + 6.15215i −0.120753 + 0.0500175i
\(124\) 0 0
\(125\) 122.319 + 50.6664i 0.978556 + 0.405331i
\(126\) 0 0
\(127\) 60.4972i 0.476356i −0.971221 0.238178i \(-0.923450\pi\)
0.971221 0.238178i \(-0.0765502\pi\)
\(128\) 0 0
\(129\) 41.6965 0.323229
\(130\) 0 0
\(131\) 56.4124 136.192i 0.430629 1.03963i −0.548456 0.836179i \(-0.684784\pi\)
0.979085 0.203451i \(-0.0652157\pi\)
\(132\) 0 0
\(133\) −10.1359 24.4702i −0.0762096 0.183986i
\(134\) 0 0
\(135\) −33.9101 33.9101i −0.251186 0.251186i
\(136\) 0 0
\(137\) −139.949 139.949i −1.02152 1.02152i −0.999763 0.0217604i \(-0.993073\pi\)
−0.0217604 0.999763i \(-0.506927\pi\)
\(138\) 0 0
\(139\) 2.63118 + 6.35223i 0.0189293 + 0.0456995i 0.933062 0.359717i \(-0.117127\pi\)
−0.914132 + 0.405416i \(0.867127\pi\)
\(140\) 0 0
\(141\) 1.41907 3.42593i 0.0100643 0.0242974i
\(142\) 0 0
\(143\) −132.353 −0.925545
\(144\) 0 0
\(145\) 78.1822i 0.539187i
\(146\) 0 0
\(147\) 34.9720 + 14.4859i 0.237905 + 0.0985433i
\(148\) 0 0
\(149\) −134.849 + 55.8563i −0.905027 + 0.374874i −0.786151 0.618035i \(-0.787929\pi\)
−0.118876 + 0.992909i \(0.537929\pi\)
\(150\) 0 0
\(151\) 131.423 131.423i 0.870353 0.870353i −0.122158 0.992511i \(-0.538981\pi\)
0.992511 + 0.122158i \(0.0389814\pi\)
\(152\) 0 0
\(153\) 113.197 113.197i 0.739850 0.739850i
\(154\) 0 0
\(155\) 174.545 72.2990i 1.12610 0.466445i
\(156\) 0 0
\(157\) −151.775 62.8673i −0.966720 0.400429i −0.157230 0.987562i \(-0.550256\pi\)
−0.809490 + 0.587133i \(0.800256\pi\)
\(158\) 0 0
\(159\) 52.0640i 0.327447i
\(160\) 0 0
\(161\) 17.8464 0.110847
\(162\) 0 0
\(163\) −75.6492 + 182.633i −0.464106 + 1.12045i 0.502591 + 0.864524i \(0.332380\pi\)
−0.966696 + 0.255926i \(0.917620\pi\)
\(164\) 0 0
\(165\) −8.37466 20.2182i −0.0507555 0.122535i
\(166\) 0 0
\(167\) −148.515 148.515i −0.889310 0.889310i 0.105147 0.994457i \(-0.466469\pi\)
−0.994457 + 0.105147i \(0.966469\pi\)
\(168\) 0 0
\(169\) −77.2745 77.2745i −0.457246 0.457246i
\(170\) 0 0
\(171\) 103.058 + 248.803i 0.602677 + 1.45499i
\(172\) 0 0
\(173\) 14.9093 35.9942i 0.0861808 0.208059i −0.874914 0.484279i \(-0.839082\pi\)
0.961094 + 0.276220i \(0.0890819\pi\)
\(174\) 0 0
\(175\) −10.3951 −0.0594005
\(176\) 0 0
\(177\) 36.0083i 0.203437i
\(178\) 0 0
\(179\) −276.876 114.686i −1.54679 0.640703i −0.564062 0.825733i \(-0.690762\pi\)
−0.982733 + 0.185029i \(0.940762\pi\)
\(180\) 0 0
\(181\) −82.1686 + 34.0354i −0.453970 + 0.188041i −0.597939 0.801542i \(-0.704014\pi\)
0.143969 + 0.989582i \(0.454014\pi\)
\(182\) 0 0
\(183\) 16.6356 16.6356i 0.0909047 0.0909047i
\(184\) 0 0
\(185\) 24.7375 24.7375i 0.133716 0.133716i
\(186\) 0 0
\(187\) 139.922 57.9576i 0.748246 0.309933i
\(188\) 0 0
\(189\) 10.3790 + 4.29911i 0.0549151 + 0.0227466i
\(190\) 0 0
\(191\) 178.857i 0.936426i 0.883616 + 0.468213i \(0.155102\pi\)
−0.883616 + 0.468213i \(0.844898\pi\)
\(192\) 0 0
\(193\) 197.034 1.02090 0.510450 0.859908i \(-0.329479\pi\)
0.510450 + 0.859908i \(0.329479\pi\)
\(194\) 0 0
\(195\) 17.6084 42.5104i 0.0902995 0.218002i
\(196\) 0 0
\(197\) 62.3398 + 150.502i 0.316446 + 0.763968i 0.999437 + 0.0335413i \(0.0106785\pi\)
−0.682992 + 0.730426i \(0.739321\pi\)
\(198\) 0 0
\(199\) −22.3835 22.3835i −0.112480 0.112480i 0.648627 0.761107i \(-0.275344\pi\)
−0.761107 + 0.648627i \(0.775344\pi\)
\(200\) 0 0
\(201\) 13.6404 + 13.6404i 0.0678625 + 0.0678625i
\(202\) 0 0
\(203\) 7.00877 + 16.9207i 0.0345260 + 0.0833530i
\(204\) 0 0
\(205\) −27.6505 + 66.7542i −0.134881 + 0.325630i
\(206\) 0 0
\(207\) −181.456 −0.876597
\(208\) 0 0
\(209\) 254.778i 1.21903i
\(210\) 0 0
\(211\) 315.926 + 130.861i 1.49728 + 0.620194i 0.972887 0.231282i \(-0.0742919\pi\)
0.524394 + 0.851476i \(0.324292\pi\)
\(212\) 0 0
\(213\) −97.3706 + 40.3322i −0.457139 + 0.189353i
\(214\) 0 0
\(215\) 132.514 132.514i 0.616343 0.616343i
\(216\) 0 0
\(217\) −31.2948 + 31.2948i −0.144216 + 0.144216i
\(218\) 0 0
\(219\) −37.9986 + 15.7395i −0.173509 + 0.0718699i
\(220\) 0 0
\(221\) 294.197 + 121.860i 1.33121 + 0.551405i
\(222\) 0 0
\(223\) 103.995i 0.466346i −0.972435 0.233173i \(-0.925089\pi\)
0.972435 0.233173i \(-0.0749109\pi\)
\(224\) 0 0
\(225\) 105.693 0.469748
\(226\) 0 0
\(227\) −19.9655 + 48.2010i −0.0879538 + 0.212339i −0.961736 0.273979i \(-0.911660\pi\)
0.873782 + 0.486318i \(0.161660\pi\)
\(228\) 0 0
\(229\) 52.0405 + 125.637i 0.227251 + 0.548633i 0.995841 0.0911090i \(-0.0290412\pi\)
−0.768590 + 0.639742i \(0.779041\pi\)
\(230\) 0 0
\(231\) 3.62499 + 3.62499i 0.0156926 + 0.0156926i
\(232\) 0 0
\(233\) −0.497550 0.497550i −0.00213541 0.00213541i 0.706038 0.708174i \(-0.250481\pi\)
−0.708174 + 0.706038i \(0.750481\pi\)
\(234\) 0 0
\(235\) −6.37793 15.3977i −0.0271401 0.0655220i
\(236\) 0 0
\(237\) −21.0872 + 50.9090i −0.0889755 + 0.214806i
\(238\) 0 0
\(239\) 80.2602 0.335817 0.167908 0.985803i \(-0.446299\pi\)
0.167908 + 0.985803i \(0.446299\pi\)
\(240\) 0 0
\(241\) 9.94799i 0.0412780i −0.999787 0.0206390i \(-0.993430\pi\)
0.999787 0.0206390i \(-0.00657006\pi\)
\(242\) 0 0
\(243\) −160.156 66.3389i −0.659080 0.273000i
\(244\) 0 0
\(245\) 157.180 65.1059i 0.641549 0.265738i
\(246\) 0 0
\(247\) −378.790 + 378.790i −1.53356 + 1.53356i
\(248\) 0 0
\(249\) 8.70723 8.70723i 0.0349688 0.0349688i
\(250\) 0 0
\(251\) 37.4569 15.5152i 0.149231 0.0618134i −0.306818 0.951768i \(-0.599264\pi\)
0.456049 + 0.889955i \(0.349264\pi\)
\(252\) 0 0
\(253\) −158.601 65.6947i −0.626881 0.259663i
\(254\) 0 0
\(255\) 52.6523i 0.206480i
\(256\) 0 0
\(257\) −351.412 −1.36736 −0.683680 0.729782i \(-0.739622\pi\)
−0.683680 + 0.729782i \(0.739622\pi\)
\(258\) 0 0
\(259\) −3.13621 + 7.57148i −0.0121089 + 0.0292335i
\(260\) 0 0
\(261\) −71.2625 172.043i −0.273036 0.659168i
\(262\) 0 0
\(263\) 347.609 + 347.609i 1.32171 + 1.32171i 0.912393 + 0.409316i \(0.134233\pi\)
0.409316 + 0.912393i \(0.365767\pi\)
\(264\) 0 0
\(265\) 165.462 + 165.462i 0.624386 + 0.624386i
\(266\) 0 0
\(267\) −25.7948 62.2741i −0.0966097 0.233236i
\(268\) 0 0
\(269\) 77.8419 187.927i 0.289375 0.698613i −0.710613 0.703584i \(-0.751582\pi\)
0.999988 + 0.00497024i \(0.00158208\pi\)
\(270\) 0 0
\(271\) 380.417 1.40375 0.701876 0.712299i \(-0.252346\pi\)
0.701876 + 0.712299i \(0.252346\pi\)
\(272\) 0 0
\(273\) 10.7789i 0.0394832i
\(274\) 0 0
\(275\) 92.3810 + 38.2655i 0.335931 + 0.139147i
\(276\) 0 0
\(277\) 130.082 53.8819i 0.469612 0.194519i −0.135312 0.990803i \(-0.543204\pi\)
0.604924 + 0.796284i \(0.293204\pi\)
\(278\) 0 0
\(279\) 318.193 318.193i 1.14048 1.14048i
\(280\) 0 0
\(281\) −40.5881 + 40.5881i −0.144442 + 0.144442i −0.775630 0.631188i \(-0.782568\pi\)
0.631188 + 0.775630i \(0.282568\pi\)
\(282\) 0 0
\(283\) −442.450 + 183.269i −1.56343 + 0.647593i −0.985681 0.168622i \(-0.946068\pi\)
−0.577748 + 0.816215i \(0.696068\pi\)
\(284\) 0 0
\(285\) −81.8320 33.8959i −0.287130 0.118933i
\(286\) 0 0
\(287\) 16.9261i 0.0589761i
\(288\) 0 0
\(289\) −75.3848 −0.260847
\(290\) 0 0
\(291\) −9.54200 + 23.0364i −0.0327904 + 0.0791629i
\(292\) 0 0
\(293\) −141.261 341.035i −0.482120 1.16394i −0.958600 0.284756i \(-0.908087\pi\)
0.476479 0.879186i \(-0.341913\pi\)
\(294\) 0 0
\(295\) −114.436 114.436i −0.387920 0.387920i
\(296\) 0 0
\(297\) −76.4122 76.4122i −0.257280 0.257280i
\(298\) 0 0
\(299\) −138.128 333.471i −0.461968 1.11529i
\(300\) 0 0
\(301\) −16.8000 + 40.5588i −0.0558140 + 0.134747i
\(302\) 0 0
\(303\) −22.5994 −0.0745856
\(304\) 0 0
\(305\) 105.737i 0.346680i
\(306\) 0 0
\(307\) −27.5569 11.4145i −0.0897620 0.0371807i 0.337351 0.941379i \(-0.390469\pi\)
−0.427113 + 0.904198i \(0.640469\pi\)
\(308\) 0 0
\(309\) 57.4073 23.7789i 0.185784 0.0769543i
\(310\) 0 0
\(311\) −262.516 + 262.516i −0.844102 + 0.844102i −0.989389 0.145288i \(-0.953589\pi\)
0.145288 + 0.989389i \(0.453589\pi\)
\(312\) 0 0
\(313\) −346.338 + 346.338i −1.10651 + 1.10651i −0.112907 + 0.993606i \(0.536016\pi\)
−0.993606 + 0.112907i \(0.963984\pi\)
\(314\) 0 0
\(315\) 22.5005 9.32003i 0.0714303 0.0295874i
\(316\) 0 0
\(317\) 37.8371 + 15.6726i 0.119360 + 0.0494405i 0.441564 0.897230i \(-0.354424\pi\)
−0.322204 + 0.946670i \(0.604424\pi\)
\(318\) 0 0
\(319\) 176.174i 0.552269i
\(320\) 0 0
\(321\) 11.9883 0.0373469
\(322\) 0 0
\(323\) 234.580 566.326i 0.726253 1.75333i
\(324\) 0 0
\(325\) 80.4563 + 194.239i 0.247558 + 0.597657i
\(326\) 0 0
\(327\) 54.4642 + 54.4642i 0.166557 + 0.166557i
\(328\) 0 0
\(329\) 2.76070 + 2.76070i 0.00839118 + 0.00839118i
\(330\) 0 0
\(331\) −123.850 298.999i −0.374168 0.903321i −0.993034 0.117825i \(-0.962408\pi\)
0.618867 0.785496i \(-0.287592\pi\)
\(332\) 0 0
\(333\) 31.8878 76.9839i 0.0957591 0.231183i
\(334\) 0 0
\(335\) 86.6995 0.258805
\(336\) 0 0
\(337\) 553.901i 1.64362i −0.569759 0.821812i \(-0.692963\pi\)
0.569759 0.821812i \(-0.307037\pi\)
\(338\) 0 0
\(339\) −59.6455 24.7060i −0.175945 0.0728790i
\(340\) 0 0
\(341\) 393.316 162.917i 1.15342 0.477762i
\(342\) 0 0
\(343\) −56.7593 + 56.7593i −0.165479 + 0.165479i
\(344\) 0 0
\(345\) 42.2010 42.2010i 0.122322 0.122322i
\(346\) 0 0
\(347\) −149.596 + 61.9645i −0.431111 + 0.178572i −0.587677 0.809095i \(-0.699958\pi\)
0.156566 + 0.987667i \(0.449958\pi\)
\(348\) 0 0
\(349\) −354.488 146.834i −1.01572 0.420727i −0.188184 0.982134i \(-0.560260\pi\)
−0.827540 + 0.561407i \(0.810260\pi\)
\(350\) 0 0
\(351\) 227.212i 0.647327i
\(352\) 0 0
\(353\) −360.254 −1.02055 −0.510275 0.860011i \(-0.670456\pi\)
−0.510275 + 0.860011i \(0.670456\pi\)
\(354\) 0 0
\(355\) −181.271 + 437.627i −0.510622 + 1.23275i
\(356\) 0 0
\(357\) −4.72010 11.3953i −0.0132216 0.0319197i
\(358\) 0 0
\(359\) −92.0047 92.0047i −0.256280 0.256280i 0.567259 0.823539i \(-0.308004\pi\)
−0.823539 + 0.567259i \(0.808004\pi\)
\(360\) 0 0
\(361\) 473.901 + 473.901i 1.31275 + 1.31275i
\(362\) 0 0
\(363\) 17.4036 + 42.0160i 0.0479438 + 0.115746i
\(364\) 0 0
\(365\) −70.7404 + 170.782i −0.193809 + 0.467897i
\(366\) 0 0
\(367\) −254.513 −0.693496 −0.346748 0.937958i \(-0.612714\pi\)
−0.346748 + 0.937958i \(0.612714\pi\)
\(368\) 0 0
\(369\) 172.098i 0.466391i
\(370\) 0 0
\(371\) −50.6435 20.9772i −0.136505 0.0565424i
\(372\) 0 0
\(373\) 440.477 182.452i 1.18090 0.489147i 0.296122 0.955150i \(-0.404307\pi\)
0.884783 + 0.466004i \(0.154307\pi\)
\(374\) 0 0
\(375\) −73.3408 + 73.3408i −0.195575 + 0.195575i
\(376\) 0 0
\(377\) 261.926 261.926i 0.694765 0.694765i
\(378\) 0 0
\(379\) −124.964 + 51.7618i −0.329720 + 0.136575i −0.541402 0.840764i \(-0.682106\pi\)
0.211681 + 0.977339i \(0.432106\pi\)
\(380\) 0 0
\(381\) 43.7856 + 18.1366i 0.114923 + 0.0476026i
\(382\) 0 0
\(383\) 182.483i 0.476458i −0.971209 0.238229i \(-0.923433\pi\)
0.971209 0.238229i \(-0.0765669\pi\)
\(384\) 0 0
\(385\) 23.0408 0.0598463
\(386\) 0 0
\(387\) 170.816 412.386i 0.441385 1.06560i
\(388\) 0 0
\(389\) −134.979 325.868i −0.346990 0.837708i −0.996972 0.0777583i \(-0.975224\pi\)
0.649982 0.759949i \(-0.274776\pi\)
\(390\) 0 0
\(391\) 292.055 + 292.055i 0.746945 + 0.746945i
\(392\) 0 0
\(393\) 81.6583 + 81.6583i 0.207782 + 0.207782i
\(394\) 0 0
\(395\) 94.7752 + 228.808i 0.239937 + 0.579260i
\(396\) 0 0
\(397\) −272.283 + 657.350i −0.685852 + 1.65579i 0.0671236 + 0.997745i \(0.478618\pi\)
−0.752976 + 0.658048i \(0.771382\pi\)
\(398\) 0 0
\(399\) 20.7492 0.0520031
\(400\) 0 0
\(401\) 74.4996i 0.185785i −0.995676 0.0928923i \(-0.970389\pi\)
0.995676 0.0928923i \(-0.0296112\pi\)
\(402\) 0 0
\(403\) 826.978 + 342.546i 2.05206 + 0.849989i
\(404\) 0 0
\(405\) −210.810 + 87.3203i −0.520518 + 0.215606i
\(406\) 0 0
\(407\) 55.7429 55.7429i 0.136961 0.136961i
\(408\) 0 0
\(409\) −289.633 + 289.633i −0.708149 + 0.708149i −0.966146 0.257997i \(-0.916938\pi\)
0.257997 + 0.966146i \(0.416938\pi\)
\(410\) 0 0
\(411\) 143.245 59.3341i 0.348528 0.144365i
\(412\) 0 0
\(413\) 35.0258 + 14.5082i 0.0848083 + 0.0351288i
\(414\) 0 0
\(415\) 55.3441i 0.133359i
\(416\) 0 0
\(417\) −5.38631 −0.0129168
\(418\) 0 0
\(419\) −234.290 + 565.626i −0.559165 + 1.34994i 0.351264 + 0.936277i \(0.385752\pi\)
−0.910428 + 0.413667i \(0.864248\pi\)
\(420\) 0 0
\(421\) 205.463 + 496.031i 0.488035 + 1.17822i 0.955707 + 0.294319i \(0.0950929\pi\)
−0.467672 + 0.883902i \(0.654907\pi\)
\(422\) 0 0
\(423\) −28.0697 28.0697i −0.0663587 0.0663587i
\(424\) 0 0
\(425\) −170.115 170.115i −0.400270 0.400270i
\(426\) 0 0
\(427\) 9.47901 + 22.8843i 0.0221991 + 0.0535933i
\(428\) 0 0
\(429\) 39.6783 95.7920i 0.0924903 0.223291i
\(430\) 0 0
\(431\) 94.1706 0.218493 0.109247 0.994015i \(-0.465156\pi\)
0.109247 + 0.994015i \(0.465156\pi\)
\(432\) 0 0
\(433\) 66.2703i 0.153049i −0.997068 0.0765246i \(-0.975618\pi\)
0.997068 0.0765246i \(-0.0243824\pi\)
\(434\) 0 0
\(435\) 56.5853 + 23.4384i 0.130081 + 0.0538814i
\(436\) 0 0
\(437\) −641.928 + 265.895i −1.46894 + 0.608456i
\(438\) 0 0
\(439\) −393.404 + 393.404i −0.896137 + 0.896137i −0.995092 0.0989551i \(-0.968450\pi\)
0.0989551 + 0.995092i \(0.468450\pi\)
\(440\) 0 0
\(441\) 286.536 286.536i 0.649742 0.649742i
\(442\) 0 0
\(443\) −124.298 + 51.4859i −0.280583 + 0.116221i −0.518537 0.855055i \(-0.673523\pi\)
0.237954 + 0.971276i \(0.423523\pi\)
\(444\) 0 0
\(445\) −279.888 115.933i −0.628961 0.260524i
\(446\) 0 0
\(447\) 114.344i 0.255803i
\(448\) 0 0
\(449\) 621.505 1.38420 0.692099 0.721802i \(-0.256686\pi\)
0.692099 + 0.721802i \(0.256686\pi\)
\(450\) 0 0
\(451\) −62.3070 + 150.422i −0.138153 + 0.333531i
\(452\) 0 0
\(453\) 55.7195 + 134.519i 0.123001 + 0.296951i
\(454\) 0 0
\(455\) 34.2559 + 34.2559i 0.0752877 + 0.0752877i
\(456\) 0 0
\(457\) −121.890 121.890i −0.266718 0.266718i 0.561058 0.827776i \(-0.310394\pi\)
−0.827776 + 0.561058i \(0.810394\pi\)
\(458\) 0 0
\(459\) 99.4964 + 240.205i 0.216768 + 0.523323i
\(460\) 0 0
\(461\) 92.0148 222.143i 0.199598 0.481873i −0.792111 0.610378i \(-0.791018\pi\)
0.991709 + 0.128505i \(0.0410177\pi\)
\(462\) 0 0
\(463\) 133.158 0.287598 0.143799 0.989607i \(-0.454068\pi\)
0.143799 + 0.989607i \(0.454068\pi\)
\(464\) 0 0
\(465\) 148.004i 0.318288i
\(466\) 0 0
\(467\) 414.267 + 171.595i 0.887082 + 0.367441i 0.779239 0.626727i \(-0.215606\pi\)
0.107843 + 0.994168i \(0.465606\pi\)
\(468\) 0 0
\(469\) −18.7640 + 7.77232i −0.0400086 + 0.0165721i
\(470\) 0 0
\(471\) 91.0019 91.0019i 0.193210 0.193210i
\(472\) 0 0
\(473\) 298.603 298.603i 0.631296 0.631296i
\(474\) 0 0
\(475\) 373.907 154.877i 0.787172 0.326058i
\(476\) 0 0
\(477\) 514.924 + 213.288i 1.07950 + 0.447145i
\(478\) 0 0
\(479\) 293.655i 0.613059i 0.951861 + 0.306530i \(0.0991679\pi\)
−0.951861 + 0.306530i \(0.900832\pi\)
\(480\) 0 0
\(481\) 165.752 0.344598
\(482\) 0 0
\(483\) −5.35022 + 12.9166i −0.0110771 + 0.0267424i
\(484\) 0 0
\(485\) 42.8860 + 103.536i 0.0884247 + 0.213476i
\(486\) 0 0
\(487\) −468.368 468.368i −0.961741 0.961741i 0.0375532 0.999295i \(-0.488044\pi\)
−0.999295 + 0.0375532i \(0.988044\pi\)
\(488\) 0 0
\(489\) −109.504 109.504i −0.223935 0.223935i
\(490\) 0 0
\(491\) 120.443 + 290.775i 0.245301 + 0.592210i 0.997794 0.0663911i \(-0.0211485\pi\)
−0.752492 + 0.658601i \(0.771149\pi\)
\(492\) 0 0
\(493\) −162.207 + 391.603i −0.329021 + 0.794328i
\(494\) 0 0
\(495\) −234.270 −0.473273
\(496\) 0 0
\(497\) 110.964i 0.223268i
\(498\) 0 0
\(499\) −572.626 237.190i −1.14755 0.475330i −0.273837 0.961776i \(-0.588293\pi\)
−0.873711 + 0.486446i \(0.838293\pi\)
\(500\) 0 0
\(501\) 152.013 62.9658i 0.303419 0.125680i
\(502\) 0 0
\(503\) 397.129 397.129i 0.789520 0.789520i −0.191895 0.981415i \(-0.561463\pi\)
0.981415 + 0.191895i \(0.0614634\pi\)
\(504\) 0 0
\(505\) −71.8222 + 71.8222i −0.142222 + 0.142222i
\(506\) 0 0
\(507\) 79.0946 32.7621i 0.156005 0.0646195i
\(508\) 0 0
\(509\) −16.5014 6.83509i −0.0324192 0.0134285i 0.366415 0.930452i \(-0.380585\pi\)
−0.398834 + 0.917023i \(0.630585\pi\)
\(510\) 0 0
\(511\) 43.3034i 0.0847425i
\(512\) 0 0
\(513\) −437.380 −0.852592
\(514\) 0 0
\(515\) 106.873 258.014i 0.207520 0.500998i
\(516\) 0 0
\(517\) −14.3719 34.6968i −0.0277986 0.0671117i
\(518\) 0 0
\(519\) 21.5815 + 21.5815i 0.0415829 + 0.0415829i
\(520\) 0 0
\(521\) −11.8175 11.8175i −0.0226824 0.0226824i 0.695675 0.718357i \(-0.255106\pi\)
−0.718357 + 0.695675i \(0.755106\pi\)
\(522\) 0 0
\(523\) −141.420 341.417i −0.270401 0.652806i 0.729100 0.684408i \(-0.239939\pi\)
−0.999501 + 0.0316019i \(0.989939\pi\)
\(524\) 0 0
\(525\) 3.11636 7.52357i 0.00593593 0.0143306i
\(526\) 0 0
\(527\) −1024.27 −1.94359
\(528\) 0 0
\(529\) 60.8334i 0.114997i
\(530\) 0 0
\(531\) −356.129 147.514i −0.670677 0.277803i
\(532\) 0 0
\(533\) −316.275 + 131.006i −0.593387 + 0.245789i
\(534\) 0 0
\(535\) 38.0996 38.0996i 0.0712142 0.0712142i
\(536\) 0 0
\(537\) 166.011 166.011i 0.309145 0.309145i
\(538\) 0 0
\(539\) 354.185 146.708i 0.657115 0.272186i
\(540\) 0 0
\(541\) −117.048 48.4829i −0.216355 0.0896172i 0.271874 0.962333i \(-0.412357\pi\)
−0.488229 + 0.872716i \(0.662357\pi\)
\(542\) 0 0
\(543\) 69.6741i 0.128313i
\(544\) 0 0
\(545\) 346.180 0.635193
\(546\) 0 0
\(547\) 113.911 275.005i 0.208247 0.502752i −0.784901 0.619622i \(-0.787286\pi\)
0.993147 + 0.116870i \(0.0372860\pi\)
\(548\) 0 0
\(549\) −96.3789 232.679i −0.175553 0.423824i
\(550\) 0 0
\(551\) −504.205 504.205i −0.915072 0.915072i
\(552\) 0 0
\(553\) −41.0237 41.0237i −0.0741838 0.0741838i
\(554\) 0 0
\(555\) 10.4880 + 25.3202i 0.0188972 + 0.0456220i
\(556\) 0 0
\(557\) 87.2197 210.567i 0.156588 0.378037i −0.826043 0.563607i \(-0.809413\pi\)
0.982631 + 0.185570i \(0.0594131\pi\)
\(558\) 0 0
\(559\) 887.896 1.58836
\(560\) 0 0
\(561\) 118.645i 0.211489i
\(562\) 0 0
\(563\) −697.221 288.798i −1.23840 0.512963i −0.335188 0.942151i \(-0.608800\pi\)
−0.903215 + 0.429188i \(0.858800\pi\)
\(564\) 0 0
\(565\) −268.074 + 111.040i −0.474466 + 0.196530i
\(566\) 0 0
\(567\) 37.7968 37.7968i 0.0666610 0.0666610i
\(568\) 0 0
\(569\) −252.850 + 252.850i −0.444376 + 0.444376i −0.893480 0.449104i \(-0.851743\pi\)
0.449104 + 0.893480i \(0.351743\pi\)
\(570\) 0 0
\(571\) −352.993 + 146.215i −0.618202 + 0.256068i −0.669731 0.742604i \(-0.733591\pi\)
0.0515290 + 0.998672i \(0.483591\pi\)
\(572\) 0 0
\(573\) −129.450 53.6200i −0.225917 0.0935777i
\(574\) 0 0
\(575\) 272.695i 0.474252i
\(576\) 0 0
\(577\) −197.099 −0.341593 −0.170797 0.985306i \(-0.554634\pi\)
−0.170797 + 0.985306i \(0.554634\pi\)
\(578\) 0 0
\(579\) −59.0691 + 142.605i −0.102019 + 0.246296i
\(580\) 0 0
\(581\) 4.96141 + 11.9779i 0.00853944 + 0.0206160i
\(582\) 0 0
\(583\) 372.849 + 372.849i 0.639535 + 0.639535i
\(584\) 0 0
\(585\) −348.301 348.301i −0.595386 0.595386i
\(586\) 0 0
\(587\) 238.745 + 576.382i 0.406721 + 0.981912i 0.985994 + 0.166778i \(0.0533365\pi\)
−0.579273 + 0.815134i \(0.696664\pi\)
\(588\) 0 0
\(589\) 659.396 1591.92i 1.11952 2.70276i
\(590\) 0 0
\(591\) −127.616 −0.215933
\(592\) 0 0
\(593\) 276.598i 0.466438i 0.972424 + 0.233219i \(0.0749260\pi\)
−0.972424 + 0.233219i \(0.925074\pi\)
\(594\) 0 0
\(595\) −51.2157 21.2142i −0.0860768 0.0356542i
\(596\) 0 0
\(597\) 22.9108 9.48995i 0.0383765 0.0158961i
\(598\) 0 0
\(599\) 710.727 710.727i 1.18652 1.18652i 0.208501 0.978022i \(-0.433141\pi\)
0.978022 0.208501i \(-0.0668585\pi\)
\(600\) 0 0
\(601\) −215.219 + 215.219i −0.358102 + 0.358102i −0.863113 0.505011i \(-0.831488\pi\)
0.505011 + 0.863113i \(0.331488\pi\)
\(602\) 0 0
\(603\) 190.786 79.0260i 0.316394 0.131055i
\(604\) 0 0
\(605\) 188.839 + 78.2195i 0.312130 + 0.129288i
\(606\) 0 0
\(607\) 683.779i 1.12649i 0.826290 + 0.563245i \(0.190447\pi\)
−0.826290 + 0.563245i \(0.809553\pi\)
\(608\) 0 0
\(609\) −14.3477 −0.0235595
\(610\) 0 0
\(611\) 30.2180 72.9527i 0.0494566 0.119399i
\(612\) 0 0
\(613\) −296.111 714.875i −0.483052 1.16619i −0.958152 0.286259i \(-0.907588\pi\)
0.475100 0.879932i \(-0.342412\pi\)
\(614\) 0 0
\(615\) −40.0248 40.0248i −0.0650809 0.0650809i
\(616\) 0 0
\(617\) −275.822 275.822i −0.447037 0.447037i 0.447331 0.894368i \(-0.352374\pi\)
−0.894368 + 0.447331i \(0.852374\pi\)
\(618\) 0 0
\(619\) −201.130 485.570i −0.324927 0.784443i −0.998954 0.0457357i \(-0.985437\pi\)
0.674027 0.738707i \(-0.264563\pi\)
\(620\) 0 0
\(621\) 112.779 272.272i 0.181608 0.438441i
\(622\) 0 0
\(623\) 70.9681 0.113913
\(624\) 0 0
\(625\) 151.085i 0.241735i
\(626\) 0 0
\(627\) −184.398 76.3803i −0.294096 0.121819i
\(628\) 0 0
\(629\) −175.231 + 72.5829i −0.278586 + 0.115394i
\(630\) 0 0
\(631\) −48.9545 + 48.9545i −0.0775823 + 0.0775823i −0.744833 0.667251i \(-0.767471\pi\)
0.667251 + 0.744833i \(0.267471\pi\)
\(632\) 0 0
\(633\) −189.424 + 189.424i −0.299249 + 0.299249i
\(634\) 0 0
\(635\) 196.792 81.5139i 0.309909 0.128368i
\(636\) 0 0
\(637\) 744.702 + 308.466i 1.16908 + 0.484248i
\(638\) 0 0
\(639\) 1128.24i 1.76564i
\(640\) 0 0
\(641\) 320.295 0.499680 0.249840 0.968287i \(-0.419622\pi\)
0.249840 + 0.968287i \(0.419622\pi\)
\(642\) 0 0
\(643\) −39.8184 + 96.1302i −0.0619260 + 0.149503i −0.951813 0.306677i \(-0.900783\pi\)
0.889887 + 0.456180i \(0.150783\pi\)
\(644\) 0 0
\(645\) 56.1818 + 135.635i 0.0871036 + 0.210287i
\(646\) 0 0
\(647\) 134.372 + 134.372i 0.207684 + 0.207684i 0.803282 0.595598i \(-0.203085\pi\)
−0.595598 + 0.803282i \(0.703085\pi\)
\(648\) 0 0
\(649\) −257.868 257.868i −0.397331 0.397331i
\(650\) 0 0
\(651\) −13.2680 32.0319i −0.0203810 0.0492041i
\(652\) 0 0
\(653\) −358.760 + 866.123i −0.549403 + 1.32638i 0.368521 + 0.929619i \(0.379864\pi\)
−0.917924 + 0.396756i \(0.870136\pi\)
\(654\) 0 0
\(655\) 519.029 0.792410
\(656\) 0 0
\(657\) 440.293i 0.670156i
\(658\) 0 0
\(659\) −596.224 246.964i −0.904741 0.374756i −0.118700 0.992930i \(-0.537873\pi\)
−0.786041 + 0.618174i \(0.787873\pi\)
\(660\) 0 0
\(661\) 16.3196 6.75978i 0.0246892 0.0102266i −0.370305 0.928910i \(-0.620747\pi\)
0.394994 + 0.918684i \(0.370747\pi\)
\(662\) 0 0
\(663\) −176.396 + 176.396i −0.266057 + 0.266057i
\(664\) 0 0
\(665\) 65.9422 65.9422i 0.0991612 0.0991612i
\(666\) 0 0
\(667\) 443.881 183.862i 0.665489 0.275655i
\(668\) 0 0
\(669\) 75.2678 + 31.1769i 0.112508 + 0.0466023i
\(670\) 0 0
\(671\) 238.266i 0.355091i
\(672\) 0 0
\(673\) −334.752 −0.497403 −0.248701 0.968580i \(-0.580004\pi\)
−0.248701 + 0.968580i \(0.580004\pi\)
\(674\) 0 0
\(675\) −65.6908 + 158.592i −0.0973197 + 0.234950i
\(676\) 0 0
\(677\) 294.364 + 710.658i 0.434807 + 1.04972i 0.977717 + 0.209926i \(0.0673222\pi\)
−0.542911 + 0.839790i \(0.682678\pi\)
\(678\) 0 0
\(679\) −18.5633 18.5633i −0.0273392 0.0273392i
\(680\) 0 0
\(681\) −28.9006 28.9006i −0.0424384 0.0424384i
\(682\) 0 0
\(683\) 118.311 + 285.628i 0.173223 + 0.418196i 0.986518 0.163655i \(-0.0523285\pi\)
−0.813295 + 0.581851i \(0.802328\pi\)
\(684\) 0 0
\(685\) 266.674 643.807i 0.389305 0.939865i
\(686\) 0 0
\(687\) −106.533 −0.155069
\(688\) 0 0
\(689\) 1108.67i 1.60909i
\(690\) 0 0
\(691\) 13.1275 + 5.43758i 0.0189978 + 0.00786914i 0.392162 0.919896i \(-0.371727\pi\)
−0.373164 + 0.927765i \(0.621727\pi\)
\(692\) 0 0
\(693\) 50.7022 21.0015i 0.0731633 0.0303052i
\(694\) 0 0
\(695\) −17.1180 + 17.1180i −0.0246302 + 0.0246302i
\(696\) 0 0
\(697\) 276.995 276.995i 0.397410 0.397410i
\(698\) 0 0
\(699\) 0.509270 0.210946i 0.000728569 0.000301783i
\(700\) 0 0
\(701\) −100.100 41.4627i −0.142796 0.0591480i 0.310141 0.950691i \(-0.399624\pi\)
−0.452937 + 0.891543i \(0.649624\pi\)
\(702\) 0 0
\(703\) 319.070i 0.453869i
\(704\) 0 0
\(705\) 13.0563 0.0185196
\(706\) 0 0
\(707\) 9.10558 21.9828i 0.0128792 0.0310931i
\(708\) 0 0
\(709\) 273.663 + 660.681i 0.385985 + 0.931849i 0.990781 + 0.135470i \(0.0432543\pi\)
−0.604797 + 0.796380i \(0.706746\pi\)
\(710\) 0 0
\(711\) 417.113 + 417.113i 0.586657 + 0.586657i
\(712\) 0 0
\(713\) 820.958 + 820.958i 1.15141 + 1.15141i
\(714\) 0 0
\(715\) −178.332 430.532i −0.249416 0.602143i
\(716\) 0 0
\(717\) −24.0614 + 58.0893i −0.0335584 + 0.0810171i
\(718\) 0 0
\(719\) 532.079 0.740026 0.370013 0.929026i \(-0.379353\pi\)
0.370013 + 0.929026i \(0.379353\pi\)
\(720\) 0 0
\(721\) 65.4218i 0.0907375i
\(722\) 0 0
\(723\) 7.19998 + 2.98233i 0.00995848 + 0.00412494i
\(724\) 0 0
\(725\) −258.549 + 107.095i −0.356620 + 0.147717i
\(726\) 0 0
\(727\) −305.054 + 305.054i −0.419606 + 0.419606i −0.885068 0.465462i \(-0.845888\pi\)
0.465462 + 0.885068i \(0.345888\pi\)
\(728\) 0 0
\(729\) −316.399 + 316.399i −0.434018 + 0.434018i
\(730\) 0 0
\(731\) −938.673 + 388.811i −1.28409 + 0.531889i
\(732\) 0 0
\(733\) 344.710 + 142.783i 0.470272 + 0.194793i 0.605218 0.796060i \(-0.293086\pi\)
−0.134946 + 0.990853i \(0.543086\pi\)
\(734\) 0 0
\(735\) 133.279i 0.181332i
\(736\) 0 0
\(737\) 195.367 0.265084
\(738\) 0 0
\(739\) −107.676 + 259.954i −0.145706 + 0.351765i −0.979836 0.199803i \(-0.935970\pi\)
0.834131 + 0.551567i \(0.185970\pi\)
\(740\) 0 0
\(741\) −160.596 387.713i −0.216728 0.523229i
\(742\) 0 0
\(743\) 470.112 + 470.112i 0.632721 + 0.632721i 0.948750 0.316029i \(-0.102350\pi\)
−0.316029 + 0.948750i \(0.602350\pi\)
\(744\) 0 0
\(745\) −363.391 363.391i −0.487773 0.487773i
\(746\) 0 0
\(747\) −50.4457 121.787i −0.0675311 0.163034i
\(748\) 0 0
\(749\) −4.83025 + 11.6612i −0.00644893 + 0.0155691i
\(750\) 0 0
\(751\) −844.801 −1.12490 −0.562451 0.826831i \(-0.690141\pi\)
−0.562451 + 0.826831i \(0.690141\pi\)
\(752\) 0 0
\(753\) 31.7612i 0.0421796i
\(754\) 0 0
\(755\) 604.588 + 250.428i 0.800778 + 0.331693i
\(756\) 0 0
\(757\) 1050.78 435.247i 1.38808 0.574962i 0.441452 0.897285i \(-0.354464\pi\)
0.946630 + 0.322322i \(0.104464\pi\)
\(758\) 0 0
\(759\) 95.0946 95.0946i 0.125289 0.125289i
\(760\) 0 0
\(761\) −44.1359 + 44.1359i −0.0579972 + 0.0579972i −0.735511 0.677513i \(-0.763058\pi\)
0.677513 + 0.735511i \(0.263058\pi\)
\(762\) 0 0
\(763\) −74.9225 + 31.0339i −0.0981946 + 0.0406735i
\(764\) 0 0
\(765\) 520.741 + 215.698i 0.680708 + 0.281958i
\(766\) 0 0
\(767\) 766.771i 0.999701i
\(768\) 0 0
\(769\) 794.025 1.03254 0.516271 0.856425i \(-0.327320\pi\)
0.516271 + 0.856425i \(0.327320\pi\)
\(770\) 0 0
\(771\) 105.350 254.338i 0.136641 0.329881i
\(772\) 0 0
\(773\) −395.664 955.218i −0.511856 1.23573i −0.942803 0.333351i \(-0.891820\pi\)
0.430947 0.902377i \(-0.358180\pi\)
\(774\) 0 0
\(775\) −478.187 478.187i −0.617016 0.617016i
\(776\) 0 0
\(777\) −4.53974 4.53974i −0.00584265 0.00584265i
\(778\) 0 0
\(779\) 252.184 + 608.826i 0.323728 + 0.781548i
\(780\) 0 0
\(781\) −408.472 + 986.138i −0.523011 + 1.26266i
\(782\) 0 0
\(783\) 302.440 0.386257
\(784\) 0 0
\(785\) 578.418i 0.736838i
\(786\) 0 0
\(787\) 445.085 + 184.360i 0.565547 + 0.234257i 0.647091 0.762413i \(-0.275985\pi\)
−0.0815444 + 0.996670i \(0.525985\pi\)
\(788\) 0 0
\(789\) −355.797 + 147.376i −0.450947 + 0.186788i
\(790\) 0 0
\(791\) 48.0638 48.0638i 0.0607633 0.0607633i
\(792\) 0 0
\(793\) 354.242 354.242i 0.446711 0.446711i
\(794\) 0 0
\(795\) −169.360 + 70.1511i −0.213031 + 0.0882403i
\(796\) 0 0
\(797\) −1384.22 573.363i −1.73679 0.719402i −0.999016 0.0443527i \(-0.985877\pi\)