Properties

Label 128.3.h.a.79.4
Level $128$
Weight $3$
Character 128.79
Analytic conductor $3.488$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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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 79.4
Character \(\chi\) \(=\) 128.79
Dual form 128.3.h.a.47.4

$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

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

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 0.866005 0.500035i \(-0.166679\pi\)
−0.965936 + 0.258781i \(0.916679\pi\)
\(4\) 0 0
\(5\) 1.34740 3.25291i 0.269480 0.650582i −0.729979 0.683469i \(-0.760470\pi\)
0.999459 + 0.0328874i \(0.0104703\pi\)
\(6\) 0 0
\(7\) −0.583225 + 0.583225i −0.0833178 + 0.0833178i −0.747537 0.664220i \(-0.768764\pi\)
0.664220 + 0.747537i \(0.268764\pi\)
\(8\) 0 0
\(9\) 5.93000 5.93000i 0.658889 0.658889i
\(10\) 0 0
\(11\) 3.03620 7.33003i 0.276018 0.666366i −0.723700 0.690115i \(-0.757560\pi\)
0.999718 + 0.0237484i \(0.00756007\pi\)
\(12\) 0 0
\(13\) −6.38385 15.4120i −0.491065 1.18554i −0.954179 0.299238i \(-0.903268\pi\)
0.463113 0.886299i \(-0.346732\pi\)
\(14\) 0 0
\(15\) −2.75827 −0.183885
\(16\) 0 0
\(17\) 19.0889i 1.12287i 0.827519 + 0.561437i \(0.189751\pi\)
−0.827519 + 0.561437i \(0.810249\pi\)
\(18\) 0 0
\(19\) 29.6679 12.2888i 1.56147 0.646781i 0.576123 0.817363i \(-0.304565\pi\)
0.985343 + 0.170582i \(0.0545648\pi\)
\(20\) 0 0
\(21\) 0.596962 + 0.247270i 0.0284268 + 0.0117748i
\(22\) 0 0
\(23\) −15.2998 15.2998i −0.665208 0.665208i 0.291395 0.956603i \(-0.405881\pi\)
−0.956603 + 0.291395i \(0.905881\pi\)
\(24\) 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 −0.707231 0.706983i \(-0.750056\pi\)
−0.000174983 1.00000i \(0.500056\pi\)
\(30\) 0 0
\(31\) 53.6582i 1.73091i 0.500988 + 0.865454i \(0.332970\pi\)
−0.500988 + 0.865454i \(0.667030\pi\)
\(32\) 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 −0.966897 0.255168i \(-0.917869\pi\)
0.864130 + 0.503268i \(0.167869\pi\)
\(38\) 0 0
\(39\) −9.24078 + 9.24078i −0.236943 + 0.236943i
\(40\) 0 0
\(41\) 14.5108 14.5108i 0.353922 0.353922i −0.507644 0.861567i \(-0.669484\pi\)
0.861567 + 0.507644i \(0.169484\pi\)
\(42\) 0 0
\(43\) −20.3685 + 49.1739i −0.473686 + 1.14358i 0.488837 + 0.872375i \(0.337421\pi\)
−0.962522 + 0.271203i \(0.912579\pi\)
\(44\) 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 0.877376 0.479803i \(-0.159292\pi\)
0.281126 + 0.959671i \(0.409292\pi\)
\(54\) 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 −0.00742152 0.999972i \(-0.502362\pi\)
−0.712335 + 0.701840i \(0.752362\pi\)
\(60\) 0 0
\(61\) −27.7452 + 11.4924i −0.454839 + 0.188400i −0.598328 0.801251i \(-0.704168\pi\)
0.143489 + 0.989652i \(0.454168\pi\)
\(62\) 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 0.978469 0.206393i \(-0.0661725\pi\)
−0.837824 + 0.545940i \(0.816172\pi\)
\(68\) 0 0
\(69\) −6.48665 + 15.6602i −0.0940094 + 0.226959i
\(70\) 0 0
\(71\) 95.1299 95.1299i 1.33986 1.33986i 0.443664 0.896193i \(-0.353678\pi\)
0.896193 0.443664i \(-0.146322\pi\)
\(72\) 0 0
\(73\) 37.1241 37.1241i 0.508550 0.508550i −0.405531 0.914081i \(-0.632913\pi\)
0.914081 + 0.405531i \(0.132913\pi\)
\(74\) 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 −0.468447 0.883492i \(-0.655186\pi\)
0.293481 + 0.955965i \(0.405186\pi\)
\(84\) 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 0.277204 0.960811i \(-0.410592\pi\)
−0.960811 + 0.277204i \(0.910592\pi\)
\(90\) 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 −0.859758 0.510702i \(-0.829385\pi\)
0.969061 + 0.246820i \(0.0793855\pi\)
\(102\) 0 0
\(103\) −56.0862 + 56.0862i −0.544526 + 0.544526i −0.924852 0.380326i \(-0.875812\pi\)
0.380326 + 0.924852i \(0.375812\pi\)
\(104\) 0 0
\(105\) 1.60869 1.60869i 0.0153209 0.0153209i
\(106\) 0 0
\(107\) −5.85623 + 14.1382i −0.0547311 + 0.132133i −0.948880 0.315637i \(-0.897782\pi\)
0.894149 + 0.447770i \(0.147782\pi\)
\(108\) 0 0
\(109\) 37.6258 + 90.8367i 0.345191 + 0.833364i 0.997174 + 0.0751304i \(0.0239373\pi\)
−0.651983 + 0.758233i \(0.726063\pi\)
\(110\) 0 0
\(111\) 7.78386 0.0701248
\(112\) 0 0
\(113\) 82.4104i 0.729295i −0.931146 0.364648i \(-0.881189\pi\)
0.931146 0.364648i \(-0.118811\pi\)
\(114\) 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 \(0.0765502\pi\)
−0.971221 + 0.238178i \(0.923450\pi\)
\(128\) 0 0
\(129\) 41.6965 0.323229
\(130\) 0 0
\(131\) 56.4124 + 136.192i 0.430629 + 1.03963i 0.979085 + 0.203451i \(0.0652157\pi\)
−0.548456 + 0.836179i \(0.684784\pi\)
\(132\) 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 −0.0217604 + 0.999763i \(0.506927\pi\)
−0.999763 + 0.0217604i \(0.993073\pi\)
\(138\) 0 0
\(139\) 2.63118 6.35223i 0.0189293 0.0456995i −0.914132 0.405416i \(-0.867127\pi\)
0.933062 + 0.359717i \(0.117127\pi\)
\(140\) 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 −0.118876 0.992909i \(-0.537929\pi\)
−0.786151 + 0.618035i \(0.787929\pi\)
\(150\) 0 0
\(151\) 131.423 + 131.423i 0.870353 + 0.870353i 0.992511 0.122158i \(-0.0389814\pi\)
−0.122158 + 0.992511i \(0.538981\pi\)
\(152\) 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 −0.809490 0.587133i \(-0.800256\pi\)
−0.157230 + 0.987562i \(0.550256\pi\)
\(158\) 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 −0.966696 0.255926i \(-0.917620\pi\)
0.502591 0.864524i \(-0.332380\pi\)
\(164\) 0 0
\(165\) −8.37466 + 20.2182i −0.0507555 + 0.122535i
\(166\) 0 0
\(167\) −148.515 + 148.515i −0.889310 + 0.889310i −0.994457 0.105147i \(-0.966469\pi\)
0.105147 + 0.994457i \(0.466469\pi\)
\(168\) 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 0.961094 0.276220i \(-0.0890819\pi\)
−0.874914 + 0.484279i \(0.839082\pi\)
\(174\) 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 −0.982733 0.185029i \(-0.940762\pi\)
−0.564062 + 0.825733i \(0.690762\pi\)
\(180\) 0 0
\(181\) −82.1686 34.0354i −0.453970 0.188041i 0.143969 0.989582i \(-0.454014\pi\)
−0.597939 + 0.801542i \(0.704014\pi\)
\(182\) 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 \(-0.844898\pi\)
0.883616 0.468213i \(-0.155102\pi\)
\(192\) 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 −0.682992 0.730426i \(-0.739321\pi\)
0.999437 0.0335413i \(-0.0106785\pi\)
\(198\) 0 0
\(199\) −22.3835 + 22.3835i −0.112480 + 0.112480i −0.761107 0.648627i \(-0.775344\pi\)
0.648627 + 0.761107i \(0.275344\pi\)
\(200\) 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 0.524394 0.851476i \(-0.324292\pi\)
0.972887 + 0.231282i \(0.0742919\pi\)
\(212\) 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 \(0.0749109\pi\)
−0.972435 + 0.233173i \(0.925089\pi\)
\(224\) 0 0
\(225\) 105.693 0.469748
\(226\) 0 0
\(227\) −19.9655 48.2010i −0.0879538 0.212339i 0.873782 0.486318i \(-0.161660\pi\)
−0.961736 + 0.273979i \(0.911660\pi\)
\(228\) 0 0
\(229\) 52.0405 125.637i 0.227251 0.548633i −0.768590 0.639742i \(-0.779041\pi\)
0.995841 + 0.0911090i \(0.0290412\pi\)
\(230\) 0 0
\(231\) 3.62499 3.62499i 0.0156926 0.0156926i
\(232\) 0 0
\(233\) −0.497550 + 0.497550i −0.00213541 + 0.00213541i −0.708174 0.706038i \(-0.750481\pi\)
0.706038 + 0.708174i \(0.250481\pi\)
\(234\) 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 \(0.00657006\pi\)
−0.999787 + 0.0206390i \(0.993430\pi\)
\(242\) 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 0.456049 0.889955i \(-0.349264\pi\)
−0.306818 + 0.951768i \(0.599264\pi\)
\(252\) 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 0.409316 0.912393i \(-0.365767\pi\)
0.912393 0.409316i \(-0.134233\pi\)
\(264\) 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 0.999988 0.00497024i \(-0.00158208\pi\)
−0.710613 + 0.703584i \(0.751582\pi\)
\(270\) 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 0.604924 0.796284i \(-0.293204\pi\)
−0.135312 + 0.990803i \(0.543204\pi\)
\(278\) 0 0
\(279\) 318.193 + 318.193i 1.14048 + 1.14048i
\(280\) 0 0
\(281\) −40.5881 40.5881i −0.144442 0.144442i 0.631188 0.775630i \(-0.282568\pi\)
−0.775630 + 0.631188i \(0.782568\pi\)
\(282\) 0 0
\(283\) −442.450 183.269i −1.56343 0.647593i −0.577748 0.816215i \(-0.696068\pi\)
−0.985681 + 0.168622i \(0.946068\pi\)
\(284\) 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 0.476479 + 0.879186i \(0.341913\pi\)
−0.958600 + 0.284756i \(0.908087\pi\)
\(294\) 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 −0.427113 0.904198i \(-0.640469\pi\)
0.337351 + 0.941379i \(0.390469\pi\)
\(308\) 0 0
\(309\) 57.4073 + 23.7789i 0.185784 + 0.0769543i
\(310\) 0 0
\(311\) −262.516 262.516i −0.844102 0.844102i 0.145288 0.989389i \(-0.453589\pi\)
−0.989389 + 0.145288i \(0.953589\pi\)
\(312\) 0 0
\(313\) −346.338 346.338i −1.10651 1.10651i −0.993606 0.112907i \(-0.963984\pi\)
−0.112907 0.993606i \(-0.536016\pi\)
\(314\) 0 0
\(315\) 22.5005 + 9.32003i 0.0714303 + 0.0295874i
\(316\) 0 0
\(317\) 37.8371 15.6726i 0.119360 0.0494405i −0.322204 0.946670i \(-0.604424\pi\)
0.441564 + 0.897230i \(0.354424\pi\)
\(318\) 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 0.618867 + 0.785496i \(0.287592\pi\)
−0.993034 + 0.117825i \(0.962408\pi\)
\(332\) 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 \(0.307037\pi\)
−0.569759 + 0.821812i \(0.692963\pi\)
\(338\) 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 0.156566 0.987667i \(-0.449958\pi\)
−0.587677 + 0.809095i \(0.699958\pi\)
\(348\) 0 0
\(349\) −354.488 + 146.834i −1.01572 + 0.420727i −0.827540 0.561407i \(-0.810260\pi\)
−0.188184 + 0.982134i \(0.560260\pi\)
\(350\) 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 −0.823539 0.567259i \(-0.808004\pi\)
0.567259 + 0.823539i \(0.308004\pi\)
\(360\) 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 0.884783 0.466004i \(-0.154307\pi\)
0.296122 + 0.955150i \(0.404307\pi\)
\(374\) 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 0.211681 0.977339i \(-0.432106\pi\)
−0.541402 + 0.840764i \(0.682106\pi\)
\(380\) 0 0
\(381\) 43.7856 18.1366i 0.114923 0.0476026i
\(382\) 0 0
\(383\) 182.483i 0.476458i 0.971209 + 0.238229i \(0.0765669\pi\)
−0.971209 + 0.238229i \(0.923433\pi\)
\(384\) 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 0.649982 + 0.759949i \(0.274776\pi\)
−0.996972 + 0.0777583i \(0.975224\pi\)
\(390\) 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 −0.752976 0.658048i \(-0.771382\pi\)
0.0671236 0.997745i \(-0.478618\pi\)
\(398\) 0 0
\(399\) 20.7492 0.0520031
\(400\) 0 0
\(401\) 74.4996i 0.185785i 0.995676 + 0.0928923i \(0.0296112\pi\)
−0.995676 + 0.0928923i \(0.970389\pi\)
\(402\) 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 0.257997 0.966146i \(-0.416938\pi\)
−0.966146 + 0.257997i \(0.916938\pi\)
\(410\) 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 −0.910428 0.413667i \(-0.864248\pi\)
0.351264 0.936277i \(-0.385752\pi\)
\(420\) 0 0
\(421\) 205.463 496.031i 0.488035 1.17822i −0.467672 0.883902i \(-0.654907\pi\)
0.955707 0.294319i \(-0.0950929\pi\)
\(422\) 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 \(0.0243824\pi\)
−0.997068 + 0.0765246i \(0.975618\pi\)
\(434\) 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 0.0989551 0.995092i \(-0.468450\pi\)
−0.995092 + 0.0989551i \(0.968450\pi\)
\(440\) 0 0
\(441\) 286.536 + 286.536i 0.649742 + 0.649742i
\(442\) 0 0
\(443\) −124.298 51.4859i −0.280583 0.116221i 0.237954 0.971276i \(-0.423523\pi\)
−0.518537 + 0.855055i \(0.673523\pi\)
\(444\) 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 −0.827776 0.561058i \(-0.810394\pi\)
0.561058 + 0.827776i \(0.310394\pi\)
\(458\) 0 0
\(459\) 99.4964 240.205i 0.216768 0.523323i
\(460\) 0 0
\(461\) 92.0148 + 222.143i 0.199598 + 0.481873i 0.991709 0.128505i \(-0.0410177\pi\)
−0.792111 + 0.610378i \(0.791018\pi\)
\(462\) 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 0.107843 0.994168i \(-0.465606\pi\)
0.779239 + 0.626727i \(0.215606\pi\)
\(468\) 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 \(-0.900832\pi\)
0.951861 0.306530i \(-0.0991679\pi\)
\(480\) 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 −0.999295 0.0375532i \(-0.988044\pi\)
0.0375532 + 0.999295i \(0.488044\pi\)
\(488\) 0 0
\(489\) −109.504 + 109.504i −0.223935 + 0.223935i
\(490\) 0 0
\(491\) 120.443 290.775i 0.245301 0.592210i −0.752492 0.658601i \(-0.771149\pi\)
0.997794 + 0.0663911i \(0.0211485\pi\)
\(492\) 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 −0.873711 0.486446i \(-0.838293\pi\)
−0.273837 + 0.961776i \(0.588293\pi\)
\(500\) 0 0
\(501\) 152.013 + 62.9658i 0.303419 + 0.125680i
\(502\) 0 0
\(503\) 397.129 + 397.129i 0.789520 + 0.789520i 0.981415 0.191895i \(-0.0614634\pi\)
−0.191895 + 0.981415i \(0.561463\pi\)
\(504\) 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 −0.398834 0.917023i \(-0.630585\pi\)
0.366415 + 0.930452i \(0.380585\pi\)
\(510\) 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 −0.718357 0.695675i \(-0.755106\pi\)
0.695675 + 0.718357i \(0.255106\pi\)
\(522\) 0 0
\(523\) −141.420 + 341.417i −0.270401 + 0.652806i −0.999501 0.0316019i \(-0.989939\pi\)
0.729100 + 0.684408i \(0.239939\pi\)
\(524\) 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 −0.488229 0.872716i \(-0.662357\pi\)
0.271874 + 0.962333i \(0.412357\pi\)
\(542\) 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 0.993147 0.116870i \(-0.0372860\pi\)
−0.784901 + 0.619622i \(0.787286\pi\)
\(548\) 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 0.982631 0.185570i \(-0.0594131\pi\)
−0.826043 + 0.563607i \(0.809413\pi\)
\(558\) 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 −0.903215 0.429188i \(-0.858800\pi\)
−0.335188 + 0.942151i \(0.608800\pi\)
\(564\) 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 0.449104 0.893480i \(-0.351743\pi\)
−0.893480 + 0.449104i \(0.851743\pi\)
\(570\) 0 0
\(571\) −352.993 146.215i −0.618202 0.256068i 0.0515290 0.998672i \(-0.483591\pi\)
−0.669731 + 0.742604i \(0.733591\pi\)
\(572\) 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 −0.579273 0.815134i \(-0.696664\pi\)
0.985994 0.166778i \(-0.0533365\pi\)
\(588\) 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 \(-0.925074\pi\)
0.972424 0.233219i \(-0.0749260\pi\)
\(594\) 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 0.978022 + 0.208501i \(0.0668585\pi\)
0.208501 + 0.978022i \(0.433141\pi\)
\(600\) 0 0
\(601\) −215.219 215.219i −0.358102 0.358102i 0.505011 0.863113i \(-0.331488\pi\)
−0.863113 + 0.505011i \(0.831488\pi\)
\(602\) 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 \(-0.809553\pi\)
0.826290 0.563245i \(-0.190447\pi\)
\(608\) 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 0.475100 + 0.879932i \(0.342412\pi\)
−0.958152 + 0.286259i \(0.907588\pi\)
\(614\) 0 0
\(615\) −40.0248 + 40.0248i −0.0650809 + 0.0650809i
\(616\) 0 0
\(617\) −275.822 + 275.822i −0.447037 + 0.447037i −0.894368 0.447331i \(-0.852374\pi\)
0.447331 + 0.894368i \(0.352374\pi\)
\(618\) 0 0
\(619\) −201.130 + 485.570i −0.324927 + 0.784443i 0.674027 + 0.738707i \(0.264563\pi\)
−0.998954 + 0.0457357i \(0.985437\pi\)
\(620\) 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 0.667251 0.744833i \(-0.267471\pi\)
−0.744833 + 0.667251i \(0.767471\pi\)
\(632\) 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 0.889887 0.456180i \(-0.150783\pi\)
−0.951813 + 0.306677i \(0.900783\pi\)
\(644\) 0 0
\(645\) 56.1818 135.635i 0.0871036 0.210287i
\(646\) 0 0
\(647\) 134.372 134.372i 0.207684 0.207684i −0.595598 0.803282i \(-0.703085\pi\)
0.803282 + 0.595598i \(0.203085\pi\)
\(648\) 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 −0.917924 0.396756i \(-0.870136\pi\)
0.368521 0.929619i \(-0.379864\pi\)
\(654\) 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 −0.786041 0.618174i \(-0.787873\pi\)
−0.118700 + 0.992930i \(0.537873\pi\)
\(660\) 0 0
\(661\) 16.3196 + 6.75978i 0.0246892 + 0.0102266i 0.394994 0.918684i \(-0.370747\pi\)
−0.370305 + 0.928910i \(0.620747\pi\)
\(662\) 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 −0.542911 0.839790i \(-0.682678\pi\)
0.977717 0.209926i \(-0.0673222\pi\)
\(678\) 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 −0.813295 0.581851i \(-0.802328\pi\)
0.986518 + 0.163655i \(0.0523285\pi\)
\(684\) 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 −0.373164 0.927765i \(-0.621727\pi\)
0.392162 + 0.919896i \(0.371727\pi\)
\(692\) 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 −0.452937 0.891543i \(-0.649624\pi\)
0.310141 + 0.950691i \(0.399624\pi\)
\(702\) 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 −0.604797 0.796380i \(-0.706746\pi\)
0.990781 0.135470i \(-0.0432543\pi\)
\(710\) 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 0.465462 0.885068i \(-0.345888\pi\)
−0.885068 + 0.465462i \(0.845888\pi\)
\(728\) 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 −0.134946 0.990853i \(-0.543086\pi\)
0.605218 + 0.796060i \(0.293086\pi\)
\(734\) 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 0.834131 0.551567i \(-0.185970\pi\)
−0.979836 + 0.199803i \(0.935970\pi\)
\(740\) 0 0
\(741\) −160.596 + 387.713i −0.216728 + 0.523229i
\(742\) 0 0
\(743\) 470.112 470.112i 0.632721 0.632721i −0.316029 0.948750i \(-0.602350\pi\)
0.948750 + 0.316029i \(0.102350\pi\)
\(744\) 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 0.946630 0.322322i \(-0.104464\pi\)
0.441452 + 0.897285i \(0.354464\pi\)
\(758\) 0 0
\(759\) 95.0946 + 95.0946i 0.125289 + 0.125289i
\(760\) 0 0
\(761\) −44.1359 44.1359i −0.0579972 0.0579972i 0.677513 0.735511i \(-0.263058\pi\)
−0.735511 + 0.677513i \(0.763058\pi\)
\(762\) 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 0.430947 + 0.902377i \(0.358180\pi\)
−0.942803 + 0.333351i \(0.891820\pi\)
\(774\) 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 −0.0815444 0.996670i \(-0.525985\pi\)
0.647091 + 0.762413i \(0.275985\pi\)
\(788\) 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 −0.737773 + 0.675049i \(0.764123\pi\)
−0