Properties

Label 804.2.ba.b.41.8
Level 804
Weight 2
Character 804.41
Analytic conductor 6.420
Analytic rank 0
Dimension 440
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.ba (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(440\)
Relative dimension: \(22\) over \(\Q(\zeta_{66})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label 41.8
Character \(\chi\) = 804.41
Dual form 804.2.ba.b.353.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.05930 + 1.37036i) q^{3} +(-0.533599 + 3.71127i) q^{5} +(0.465124 + 4.87100i) q^{7} +(-0.755762 - 2.90324i) q^{9} +O(q^{10})\) \(q+(-1.05930 + 1.37036i) q^{3} +(-0.533599 + 3.71127i) q^{5} +(0.465124 + 4.87100i) q^{7} +(-0.755762 - 2.90324i) q^{9} +(-4.53378 + 1.81505i) q^{11} +(3.30733 + 3.46863i) q^{13} +(-4.52052 - 4.66257i) q^{15} +(5.33974 - 1.84810i) q^{17} +(-0.797858 - 0.0761862i) q^{19} +(-7.16773 - 4.52247i) q^{21} +(2.77501 - 0.132190i) q^{23} +(-8.69130 - 2.55200i) q^{25} +(4.77906 + 2.03974i) q^{27} +(0.708402 - 0.408996i) q^{29} +(5.31235 - 5.57143i) q^{31} +(2.31537 - 8.13559i) q^{33} +(-18.3258 - 0.872965i) q^{35} +(2.23579 - 3.87250i) q^{37} +(-8.25673 + 0.857906i) q^{39} +(7.67348 + 1.47894i) q^{41} +(0.934610 + 0.809844i) q^{43} +(11.1780 - 1.25566i) q^{45} +(0.757376 - 1.46910i) q^{47} +(-16.6368 + 3.20649i) q^{49} +(-3.12383 + 9.27505i) q^{51} +(-1.96721 - 2.27028i) q^{53} +(-4.31692 - 17.7946i) q^{55} +(0.949574 - 1.01265i) q^{57} +(2.87219 + 9.78178i) q^{59} +(-1.09942 + 2.74622i) q^{61} +(13.7902 - 5.03169i) q^{63} +(-14.6378 + 10.4235i) q^{65} +(-8.18444 - 0.122098i) q^{67} +(-2.75843 + 3.94279i) q^{69} +(-0.732584 - 0.253550i) q^{71} +(7.12244 + 2.85140i) q^{73} +(12.7039 - 9.20686i) q^{75} +(-10.9499 - 21.2398i) q^{77} +(-8.83315 + 2.14290i) q^{79} +(-7.85765 + 4.38832i) q^{81} +(-1.89921 + 2.41505i) q^{83} +(4.00952 + 20.8033i) q^{85} +(-0.189940 + 1.40401i) q^{87} +(2.68891 - 4.18402i) q^{89} +(-15.3574 + 17.7234i) q^{91} +(2.00748 + 13.1816i) q^{93} +(0.708484 - 2.92041i) q^{95} +(-3.01975 - 1.74345i) q^{97} +(8.69600 + 11.7909i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 440q - 12q^{7} + 4q^{9} + O(q^{10}) \) \( 440q - 12q^{7} + 4q^{9} - 2q^{15} - 10q^{19} + 22q^{21} - 68q^{25} + 50q^{31} + 11q^{33} - 22q^{37} - 45q^{39} + 22q^{43} + 22q^{45} - 18q^{49} - 6q^{51} + 126q^{55} - 183q^{57} - 56q^{61} - 141q^{63} - 12q^{67} + 33q^{69} + 356q^{73} + 165q^{75} + 228q^{79} + 24q^{81} - 6q^{85} + 75q^{87} - 4q^{91} - 75q^{93} + 12q^{97} + 88q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{53}{66}\right)\) \(1\)

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
\(3\) −1.05930 + 1.37036i −0.611588 + 0.791177i
\(4\) 0 0
\(5\) −0.533599 + 3.71127i −0.238633 + 1.65973i 0.420194 + 0.907434i \(0.361962\pi\)
−0.658827 + 0.752294i \(0.728947\pi\)
\(6\) 0 0
\(7\) 0.465124 + 4.87100i 0.175801 + 1.84107i 0.466824 + 0.884350i \(0.345398\pi\)
−0.291023 + 0.956716i \(0.593996\pi\)
\(8\) 0 0
\(9\) −0.755762 2.90324i −0.251921 0.967748i
\(10\) 0 0
\(11\) −4.53378 + 1.81505i −1.36699 + 0.547259i −0.935009 0.354625i \(-0.884608\pi\)
−0.431978 + 0.901884i \(0.642184\pi\)
\(12\) 0 0
\(13\) 3.30733 + 3.46863i 0.917289 + 0.962026i 0.999401 0.0345976i \(-0.0110150\pi\)
−0.0821118 + 0.996623i \(0.526166\pi\)
\(14\) 0 0
\(15\) −4.52052 4.66257i −1.16719 1.20387i
\(16\) 0 0
\(17\) 5.33974 1.84810i 1.29508 0.448231i 0.409325 0.912389i \(-0.365764\pi\)
0.885752 + 0.464158i \(0.153643\pi\)
\(18\) 0 0
\(19\) −0.797858 0.0761862i −0.183041 0.0174783i 0.00313289 0.999995i \(-0.499003\pi\)
−0.186174 + 0.982517i \(0.559609\pi\)
\(20\) 0 0
\(21\) −7.16773 4.52247i −1.56413 0.986885i
\(22\) 0 0
\(23\) 2.77501 0.132190i 0.578630 0.0275635i 0.243773 0.969832i \(-0.421615\pi\)
0.334857 + 0.942269i \(0.391312\pi\)
\(24\) 0 0
\(25\) −8.69130 2.55200i −1.73826 0.510399i
\(26\) 0 0
\(27\) 4.77906 + 2.03974i 0.919731 + 0.392549i
\(28\) 0 0
\(29\) 0.708402 0.408996i 0.131547 0.0759486i −0.432782 0.901498i \(-0.642468\pi\)
0.564329 + 0.825550i \(0.309135\pi\)
\(30\) 0 0
\(31\) 5.31235 5.57143i 0.954126 1.00066i −0.0458722 0.998947i \(-0.514607\pi\)
0.999999 0.00171155i \(-0.000544804\pi\)
\(32\) 0 0
\(33\) 2.31537 8.13559i 0.403054 1.41622i
\(34\) 0 0
\(35\) −18.3258 0.872965i −3.09762 0.147558i
\(36\) 0 0
\(37\) 2.23579 3.87250i 0.367561 0.636635i −0.621622 0.783317i \(-0.713526\pi\)
0.989184 + 0.146682i \(0.0468594\pi\)
\(38\) 0 0
\(39\) −8.25673 + 0.857906i −1.32214 + 0.137375i
\(40\) 0 0
\(41\) 7.67348 + 1.47894i 1.19840 + 0.230972i 0.749128 0.662425i \(-0.230473\pi\)
0.449268 + 0.893397i \(0.351685\pi\)
\(42\) 0 0
\(43\) 0.934610 + 0.809844i 0.142527 + 0.123500i 0.723206 0.690632i \(-0.242668\pi\)
−0.580680 + 0.814132i \(0.697213\pi\)
\(44\) 0 0
\(45\) 11.1780 1.25566i 1.66632 0.187183i
\(46\) 0 0
\(47\) 0.757376 1.46910i 0.110475 0.214291i −0.827117 0.562030i \(-0.810020\pi\)
0.937591 + 0.347740i \(0.113051\pi\)
\(48\) 0 0
\(49\) −16.6368 + 3.20649i −2.37669 + 0.458070i
\(50\) 0 0
\(51\) −3.12383 + 9.27505i −0.437424 + 1.29877i
\(52\) 0 0
\(53\) −1.96721 2.27028i −0.270217 0.311846i 0.604382 0.796695i \(-0.293420\pi\)
−0.874598 + 0.484848i \(0.838875\pi\)
\(54\) 0 0
\(55\) −4.31692 17.7946i −0.582093 2.39942i
\(56\) 0 0
\(57\) 0.949574 1.01265i 0.125774 0.134128i
\(58\) 0 0
\(59\) 2.87219 + 9.78178i 0.373927 + 1.27348i 0.904731 + 0.425984i \(0.140072\pi\)
−0.530804 + 0.847495i \(0.678110\pi\)
\(60\) 0 0
\(61\) −1.09942 + 2.74622i −0.140766 + 0.351617i −0.981952 0.189129i \(-0.939434\pi\)
0.841186 + 0.540746i \(0.181858\pi\)
\(62\) 0 0
\(63\) 13.7902 5.03169i 1.73740 0.633933i
\(64\) 0 0
\(65\) −14.6378 + 10.4235i −1.81560 + 1.29288i
\(66\) 0 0
\(67\) −8.18444 0.122098i −0.999889 0.0149167i
\(68\) 0 0
\(69\) −2.75843 + 3.94279i −0.332075 + 0.474656i
\(70\) 0 0
\(71\) −0.732584 0.253550i −0.0869417 0.0300908i 0.283251 0.959046i \(-0.408587\pi\)
−0.370193 + 0.928955i \(0.620708\pi\)
\(72\) 0 0
\(73\) 7.12244 + 2.85140i 0.833619 + 0.333731i 0.748907 0.662675i \(-0.230579\pi\)
0.0847116 + 0.996406i \(0.473003\pi\)
\(74\) 0 0
\(75\) 12.7039 9.20686i 1.46691 1.06312i
\(76\) 0 0
\(77\) −10.9499 21.2398i −1.24786 2.42050i
\(78\) 0 0
\(79\) −8.83315 + 2.14290i −0.993807 + 0.241095i −0.699513 0.714620i \(-0.746600\pi\)
−0.294294 + 0.955715i \(0.595085\pi\)
\(80\) 0 0
\(81\) −7.85765 + 4.38832i −0.873072 + 0.487591i
\(82\) 0 0
\(83\) −1.89921 + 2.41505i −0.208466 + 0.265086i −0.879031 0.476765i \(-0.841809\pi\)
0.670565 + 0.741851i \(0.266052\pi\)
\(84\) 0 0
\(85\) 4.00952 + 20.8033i 0.434893 + 2.25644i
\(86\) 0 0
\(87\) −0.189940 + 1.40401i −0.0203637 + 0.150526i
\(88\) 0 0
\(89\) 2.68891 4.18402i 0.285024 0.443506i −0.668989 0.743273i \(-0.733273\pi\)
0.954012 + 0.299767i \(0.0969089\pi\)
\(90\) 0 0
\(91\) −15.3574 + 17.7234i −1.60989 + 1.85792i
\(92\) 0 0
\(93\) 2.00748 + 13.1816i 0.208166 + 1.36687i
\(94\) 0 0
\(95\) 0.708484 2.92041i 0.0726889 0.299628i
\(96\) 0 0
\(97\) −3.01975 1.74345i −0.306609 0.177021i 0.338799 0.940859i \(-0.389979\pi\)
−0.645408 + 0.763838i \(0.723313\pi\)
\(98\) 0 0
\(99\) 8.69600 + 11.7909i 0.873981 + 1.18503i
\(100\) 0 0
\(101\) 3.43000 4.81676i 0.341298 0.479286i −0.607879 0.794030i \(-0.707979\pi\)
0.949177 + 0.314744i \(0.101919\pi\)
\(102\) 0 0
\(103\) 8.46000 + 8.06659i 0.833589 + 0.794825i 0.980951 0.194257i \(-0.0622297\pi\)
−0.147362 + 0.989083i \(0.547078\pi\)
\(104\) 0 0
\(105\) 20.6088 24.1881i 2.01121 2.36052i
\(106\) 0 0
\(107\) 6.07296 0.873160i 0.587095 0.0844115i 0.157635 0.987497i \(-0.449613\pi\)
0.429460 + 0.903086i \(0.358704\pi\)
\(108\) 0 0
\(109\) 3.94134 13.4230i 0.377512 1.28569i −0.523549 0.851995i \(-0.675392\pi\)
0.901061 0.433692i \(-0.142789\pi\)
\(110\) 0 0
\(111\) 2.93834 + 7.16597i 0.278895 + 0.680164i
\(112\) 0 0
\(113\) 11.7712 9.25700i 1.10734 0.870825i 0.114882 0.993379i \(-0.463351\pi\)
0.992462 + 0.122554i \(0.0391084\pi\)
\(114\) 0 0
\(115\) −0.990152 + 10.3693i −0.0923322 + 0.966946i
\(116\) 0 0
\(117\) 7.57073 12.2235i 0.699914 1.13006i
\(118\) 0 0
\(119\) 11.4858 + 25.1503i 1.05290 + 2.30552i
\(120\) 0 0
\(121\) 9.29969 8.86723i 0.845426 0.806112i
\(122\) 0 0
\(123\) −10.1552 + 8.94877i −0.915664 + 0.806883i
\(124\) 0 0
\(125\) 6.32096 13.8410i 0.565364 1.23798i
\(126\) 0 0
\(127\) 7.86576 0.751089i 0.697974 0.0666484i 0.259963 0.965618i \(-0.416289\pi\)
0.438010 + 0.898970i \(0.355683\pi\)
\(128\) 0 0
\(129\) −2.09981 + 0.422881i −0.184878 + 0.0372326i
\(130\) 0 0
\(131\) −10.9782 17.0825i −0.959173 1.49250i −0.867938 0.496673i \(-0.834555\pi\)
−0.0912354 0.995829i \(-0.529082\pi\)
\(132\) 0 0
\(133\) 3.92180i 0.340064i
\(134\) 0 0
\(135\) −10.1201 + 16.6480i −0.871003 + 1.43283i
\(136\) 0 0
\(137\) 0.698213 0.448714i 0.0596523 0.0383362i −0.510475 0.859893i \(-0.670530\pi\)
0.570127 + 0.821557i \(0.306894\pi\)
\(138\) 0 0
\(139\) −14.4038 2.07095i −1.22171 0.175656i −0.498874 0.866674i \(-0.666253\pi\)
−0.722837 + 0.691019i \(0.757162\pi\)
\(140\) 0 0
\(141\) 1.21091 + 2.59410i 0.101977 + 0.218463i
\(142\) 0 0
\(143\) −21.2905 9.72304i −1.78040 0.813081i
\(144\) 0 0
\(145\) 1.13989 + 2.84731i 0.0946627 + 0.236456i
\(146\) 0 0
\(147\) 13.2294 26.1951i 1.09114 2.16053i
\(148\) 0 0
\(149\) 15.8294 7.22903i 1.29679 0.592225i 0.357042 0.934088i \(-0.383785\pi\)
0.939750 + 0.341863i \(0.111058\pi\)
\(150\) 0 0
\(151\) −1.33081 3.84513i −0.108300 0.312912i 0.877809 0.479010i \(-0.159004\pi\)
−0.986109 + 0.166098i \(0.946883\pi\)
\(152\) 0 0
\(153\) −9.40106 14.1058i −0.760031 1.14039i
\(154\) 0 0
\(155\) 17.8424 + 22.6885i 1.43314 + 1.82238i
\(156\) 0 0
\(157\) 0.486177 + 10.2061i 0.0388012 + 0.814536i 0.931469 + 0.363821i \(0.118528\pi\)
−0.892668 + 0.450715i \(0.851169\pi\)
\(158\) 0 0
\(159\) 5.19496 0.290870i 0.411987 0.0230675i
\(160\) 0 0
\(161\) 1.93462 + 13.4556i 0.152470 + 1.06045i
\(162\) 0 0
\(163\) 9.53176 + 16.5095i 0.746585 + 1.29312i 0.949451 + 0.313916i \(0.101641\pi\)
−0.202866 + 0.979207i \(0.565026\pi\)
\(164\) 0 0
\(165\) 28.9579 + 12.9341i 2.25437 + 1.00692i
\(166\) 0 0
\(167\) 13.0007 + 9.25777i 1.00603 + 0.716387i 0.959262 0.282519i \(-0.0911699\pi\)
0.0467636 + 0.998906i \(0.485109\pi\)
\(168\) 0 0
\(169\) −0.474386 + 9.95858i −0.0364912 + 0.766045i
\(170\) 0 0
\(171\) 0.381804 + 2.37395i 0.0291973 + 0.181541i
\(172\) 0 0
\(173\) −13.9426 3.38243i −1.06003 0.257161i −0.332408 0.943136i \(-0.607861\pi\)
−0.727626 + 0.685974i \(0.759376\pi\)
\(174\) 0 0
\(175\) 8.38825 43.5224i 0.634092 3.28998i
\(176\) 0 0
\(177\) −16.4470 6.42592i −1.23624 0.483002i
\(178\) 0 0
\(179\) 4.92153 + 3.16288i 0.367853 + 0.236404i 0.711487 0.702699i \(-0.248022\pi\)
−0.343635 + 0.939103i \(0.611658\pi\)
\(180\) 0 0
\(181\) 18.2823 + 9.42518i 1.35891 + 0.700568i 0.974876 0.222750i \(-0.0715034\pi\)
0.384036 + 0.923318i \(0.374534\pi\)
\(182\) 0 0
\(183\) −2.59868 4.41567i −0.192100 0.326416i
\(184\) 0 0
\(185\) 13.1789 + 10.3640i 0.968929 + 0.761974i
\(186\) 0 0
\(187\) −20.8548 + 18.0708i −1.52505 + 1.32147i
\(188\) 0 0
\(189\) −7.71275 + 24.2276i −0.561020 + 1.76230i
\(190\) 0 0
\(191\) −5.09319 + 2.62572i −0.368530 + 0.189991i −0.632537 0.774530i \(-0.717986\pi\)
0.264006 + 0.964521i \(0.414956\pi\)
\(192\) 0 0
\(193\) −22.9411 + 6.73612i −1.65134 + 0.484877i −0.969185 0.246333i \(-0.920774\pi\)
−0.682153 + 0.731210i \(0.738956\pi\)
\(194\) 0 0
\(195\) 1.22187 31.1007i 0.0875000 2.22717i
\(196\) 0 0
\(197\) −3.54775 + 10.2505i −0.252767 + 0.730321i 0.745215 + 0.666824i \(0.232347\pi\)
−0.997982 + 0.0634974i \(0.979775\pi\)
\(198\) 0 0
\(199\) −8.11414 11.3947i −0.575196 0.807750i 0.419805 0.907614i \(-0.362098\pi\)
−0.995001 + 0.0998647i \(0.968159\pi\)
\(200\) 0 0
\(201\) 8.83711 11.0863i 0.623321 0.781966i
\(202\) 0 0
\(203\) 2.32172 + 3.26039i 0.162952 + 0.228835i
\(204\) 0 0
\(205\) −9.58331 + 27.6892i −0.669328 + 1.93390i
\(206\) 0 0
\(207\) −2.48103 7.95663i −0.172443 0.553024i
\(208\) 0 0
\(209\) 3.75560 1.10274i 0.259780 0.0762783i
\(210\) 0 0
\(211\) 5.45382 2.81164i 0.375456 0.193561i −0.260161 0.965565i \(-0.583776\pi\)
0.635618 + 0.772004i \(0.280745\pi\)
\(212\) 0 0
\(213\) 1.12348 0.735317i 0.0769796 0.0503831i
\(214\) 0 0
\(215\) −3.50425 + 3.03645i −0.238988 + 0.207084i
\(216\) 0 0
\(217\) 29.6094 + 23.2851i 2.01002 + 1.58069i
\(218\) 0 0
\(219\) −11.4522 + 6.73981i −0.773871 + 0.455434i
\(220\) 0 0
\(221\) 24.0707 + 12.4093i 1.61917 + 0.834740i
\(222\) 0 0
\(223\) −2.10672 1.35391i −0.141077 0.0906645i 0.468199 0.883623i \(-0.344903\pi\)
−0.609275 + 0.792959i \(0.708540\pi\)
\(224\) 0 0
\(225\) −0.840511 + 27.1617i −0.0560341 + 1.81078i
\(226\) 0 0
\(227\) 0.199328 1.03421i 0.0132298 0.0686430i −0.974714 0.223457i \(-0.928266\pi\)
0.987944 + 0.154814i \(0.0494779\pi\)
\(228\) 0 0
\(229\) −15.4322 3.74380i −1.01979 0.247397i −0.309192 0.951000i \(-0.600059\pi\)
−0.710594 + 0.703602i \(0.751574\pi\)
\(230\) 0 0
\(231\) 40.7054 + 7.49411i 2.67822 + 0.493076i
\(232\) 0 0
\(233\) 0.834864 17.5260i 0.0546938 1.14816i −0.790067 0.613020i \(-0.789954\pi\)
0.844761 0.535144i \(-0.179743\pi\)
\(234\) 0 0
\(235\) 5.04810 + 3.59474i 0.329302 + 0.234495i
\(236\) 0 0
\(237\) 6.42043 14.3746i 0.417052 0.933728i
\(238\) 0 0
\(239\) −9.54110 16.5257i −0.617162 1.06896i −0.990001 0.141060i \(-0.954949\pi\)
0.372839 0.927896i \(-0.378385\pi\)
\(240\) 0 0
\(241\) 0.0434228 + 0.302012i 0.00279711 + 0.0194543i 0.991172 0.132581i \(-0.0423264\pi\)
−0.988375 + 0.152035i \(0.951417\pi\)
\(242\) 0 0
\(243\) 2.31004 15.4163i 0.148189 0.988959i
\(244\) 0 0
\(245\) −3.02272 63.4547i −0.193115 4.05397i
\(246\) 0 0
\(247\) −2.37452 3.01945i −0.151087 0.192123i
\(248\) 0 0
\(249\) −1.29764 5.16086i −0.0822345 0.327056i
\(250\) 0 0
\(251\) 4.47101 + 12.9181i 0.282207 + 0.815385i 0.993637 + 0.112628i \(0.0359267\pi\)
−0.711430 + 0.702757i \(0.751952\pi\)
\(252\) 0 0
\(253\) −12.3414 + 5.63611i −0.775895 + 0.354339i
\(254\) 0 0
\(255\) −32.7553 16.5425i −2.05122 1.03593i
\(256\) 0 0
\(257\) −0.845843 2.11281i −0.0527622 0.131794i 0.899645 0.436622i \(-0.143825\pi\)
−0.952407 + 0.304828i \(0.901401\pi\)
\(258\) 0 0
\(259\) 19.9029 + 9.08934i 1.23670 + 0.564784i
\(260\) 0 0
\(261\) −1.72280 1.74756i −0.106638 0.108171i
\(262\) 0 0
\(263\) −19.7695 2.84242i −1.21904 0.175271i −0.497388 0.867528i \(-0.665707\pi\)
−0.721651 + 0.692257i \(0.756617\pi\)
\(264\) 0 0
\(265\) 9.47530 6.08941i 0.582063 0.374069i
\(266\) 0 0
\(267\) 2.88525 + 8.11691i 0.176574 + 0.496747i
\(268\) 0 0
\(269\) 9.12100i 0.556117i 0.960564 + 0.278059i \(0.0896910\pi\)
−0.960564 + 0.278059i \(0.910309\pi\)
\(270\) 0 0
\(271\) 10.8934 + 16.9505i 0.661728 + 1.02967i 0.996186 + 0.0872580i \(0.0278105\pi\)
−0.334458 + 0.942411i \(0.608553\pi\)
\(272\) 0 0
\(273\) −8.01927 39.8195i −0.485348 2.40999i
\(274\) 0 0
\(275\) 44.0365 4.20497i 2.65550 0.253569i
\(276\) 0 0
\(277\) 9.75628 21.3633i 0.586198 1.28359i −0.351515 0.936182i \(-0.614333\pi\)
0.937713 0.347412i \(-0.112939\pi\)
\(278\) 0 0
\(279\) −20.1901 11.2124i −1.20875 0.671267i
\(280\) 0 0
\(281\) −0.823515 + 0.785220i −0.0491268 + 0.0468423i −0.714245 0.699896i \(-0.753230\pi\)
0.665118 + 0.746738i \(0.268381\pi\)
\(282\) 0 0
\(283\) −13.7602 30.1306i −0.817957 1.79108i −0.568486 0.822693i \(-0.692471\pi\)
−0.249471 0.968382i \(-0.580257\pi\)
\(284\) 0 0
\(285\) 3.25151 + 4.06447i 0.192603 + 0.240758i
\(286\) 0 0
\(287\) −3.63481 + 38.0654i −0.214556 + 2.24693i
\(288\) 0 0
\(289\) 11.7344 9.22806i 0.690261 0.542827i
\(290\) 0 0
\(291\) 5.58797 2.29129i 0.327573 0.134318i
\(292\) 0 0
\(293\) −9.21663 + 31.3890i −0.538441 + 1.83376i 0.0135425 + 0.999908i \(0.495689\pi\)
−0.551984 + 0.833855i \(0.686129\pi\)
\(294\) 0 0
\(295\) −37.8354 + 5.43990i −2.20286 + 0.316724i
\(296\) 0 0
\(297\) −25.3695 0.573508i −1.47209 0.0332783i
\(298\) 0 0
\(299\) 9.63641 + 9.18830i 0.557288 + 0.531373i
\(300\) 0 0
\(301\) −3.51004 + 4.92916i −0.202315 + 0.284112i
\(302\) 0 0
\(303\) 2.96729 + 9.80273i 0.170466 + 0.563152i
\(304\) 0 0
\(305\) −9.60529 5.54562i −0.549997 0.317541i
\(306\) 0 0
\(307\) 4.87404 20.0911i 0.278176 1.14666i −0.645585 0.763688i \(-0.723386\pi\)
0.923761 0.382969i \(-0.125098\pi\)
\(308\) 0 0
\(309\) −20.0158 + 3.04828i −1.13866 + 0.173410i
\(310\) 0 0
\(311\) 8.21488 9.48048i 0.465823 0.537589i −0.473422 0.880836i \(-0.656981\pi\)
0.939245 + 0.343247i \(0.111527\pi\)
\(312\) 0 0
\(313\) −3.46146 + 5.38613i −0.195653 + 0.304442i −0.925194 0.379495i \(-0.876098\pi\)
0.729540 + 0.683938i \(0.239734\pi\)
\(314\) 0 0
\(315\) 11.3155 + 53.8640i 0.637556 + 3.03489i
\(316\) 0 0
\(317\) −2.26860 11.7706i −0.127417 0.661102i −0.988327 0.152345i \(-0.951317\pi\)
0.860910 0.508757i \(-0.169895\pi\)
\(318\) 0 0
\(319\) −2.46939 + 3.14008i −0.138259 + 0.175811i
\(320\) 0 0
\(321\) −5.23655 + 9.24707i −0.292276 + 0.516121i
\(322\) 0 0
\(323\) −4.40115 + 1.06771i −0.244887 + 0.0594089i
\(324\) 0 0
\(325\) −19.8931 38.5872i −1.10347 2.14043i
\(326\) 0 0
\(327\) 14.2192 + 19.6200i 0.786324 + 1.08499i
\(328\) 0 0
\(329\) 7.50828 + 3.00586i 0.413945 + 0.165719i
\(330\) 0 0
\(331\) 10.7107 + 3.70701i 0.588714 + 0.203756i 0.605153 0.796109i \(-0.293112\pi\)
−0.0164396 + 0.999865i \(0.505233\pi\)
\(332\) 0 0
\(333\) −12.9325 3.56435i −0.708699 0.195325i
\(334\) 0 0
\(335\) 4.82035 30.3095i 0.263364 1.65598i
\(336\) 0 0
\(337\) −8.64439 + 6.15564i −0.470890 + 0.335319i −0.790743 0.612148i \(-0.790306\pi\)
0.319854 + 0.947467i \(0.396366\pi\)
\(338\) 0 0
\(339\) 0.216123 + 25.9368i 0.0117382 + 1.40869i
\(340\) 0 0
\(341\) −13.9726 + 34.9019i −0.756658 + 1.89004i
\(342\) 0 0
\(343\) −13.7071 46.6820i −0.740112 2.52059i
\(344\) 0 0
\(345\) −13.1608 12.3411i −0.708556 0.664424i
\(346\) 0 0
\(347\) −1.36470 5.62536i −0.0732608 0.301985i 0.923379 0.383889i \(-0.125415\pi\)
−0.996640 + 0.0819032i \(0.973900\pi\)
\(348\) 0 0
\(349\) 5.43189 + 6.26874i 0.290762 + 0.335558i 0.882272 0.470740i \(-0.156013\pi\)
−0.591509 + 0.806298i \(0.701468\pi\)
\(350\) 0 0
\(351\) 8.73083 + 23.3229i 0.466017 + 1.24489i
\(352\) 0 0
\(353\) 6.86685 1.32348i 0.365485 0.0704415i −0.00320227 0.999995i \(-0.501019\pi\)
0.368688 + 0.929553i \(0.379807\pi\)
\(354\) 0 0
\(355\) 1.33190 2.58352i 0.0706897 0.137119i
\(356\) 0 0
\(357\) −46.6318 10.9021i −2.46802 0.577002i
\(358\) 0 0
\(359\) 12.2268 + 10.5946i 0.645305 + 0.559160i 0.914833 0.403832i \(-0.132322\pi\)
−0.269528 + 0.962993i \(0.586868\pi\)
\(360\) 0 0
\(361\) −18.0259 3.47420i −0.948730 0.182853i
\(362\) 0 0
\(363\) 2.30012 + 22.1370i 0.120725 + 1.16189i
\(364\) 0 0
\(365\) −14.3828 + 24.9118i −0.752831 + 1.30394i
\(366\) 0 0
\(367\) −9.72493 0.463255i −0.507637 0.0241817i −0.207798 0.978172i \(-0.566630\pi\)
−0.299839 + 0.953990i \(0.596933\pi\)
\(368\) 0 0
\(369\) −1.50560 23.3957i −0.0783782 1.21793i
\(370\) 0 0
\(371\) 10.1435 10.6382i 0.526626 0.552309i
\(372\) 0 0
\(373\) −25.0267 + 14.4491i −1.29583 + 0.748148i −0.979681 0.200561i \(-0.935724\pi\)
−0.316150 + 0.948709i \(0.602390\pi\)
\(374\) 0 0
\(375\) 12.2713 + 23.3238i 0.633687 + 1.20443i
\(376\) 0 0
\(377\) 3.76158 + 1.10450i 0.193731 + 0.0568846i
\(378\) 0 0
\(379\) 18.3552 0.874365i 0.942843 0.0449131i 0.429472 0.903080i \(-0.358700\pi\)
0.513371 + 0.858167i \(0.328397\pi\)
\(380\) 0 0
\(381\) −7.30295 + 11.5745i −0.374141 + 0.592982i
\(382\) 0 0
\(383\) −22.0786 2.10825i −1.12816 0.107727i −0.485760 0.874092i \(-0.661457\pi\)
−0.642405 + 0.766366i \(0.722063\pi\)
\(384\) 0 0
\(385\) 84.6696 29.3044i 4.31516 1.49349i
\(386\) 0 0
\(387\) 1.64483 3.32545i 0.0836115 0.169042i
\(388\) 0 0
\(389\) −15.4709 16.2254i −0.784404 0.822660i 0.203280 0.979121i \(-0.434840\pi\)
−0.987684 + 0.156461i \(0.949991\pi\)
\(390\) 0 0
\(391\) 14.5735 5.83436i 0.737015 0.295056i
\(392\) 0 0
\(393\) 35.0384 + 3.05137i 1.76745 + 0.153921i
\(394\) 0 0
\(395\) −3.23950 33.9256i −0.162997 1.70698i
\(396\) 0 0
\(397\) −1.76566 + 12.2804i −0.0886159 + 0.616337i 0.896319 + 0.443410i \(0.146232\pi\)
−0.984935 + 0.172927i \(0.944678\pi\)
\(398\) 0 0
\(399\) 5.37428 + 4.15437i 0.269050 + 0.207979i
\(400\) 0 0
\(401\) −2.10669 −0.105203 −0.0526014 0.998616i \(-0.516751\pi\)
−0.0526014 + 0.998616i \(0.516751\pi\)
\(402\) 0 0
\(403\) 36.8950 1.83787
\(404\) 0 0
\(405\) −12.0934 31.5034i −0.600926 1.56542i
\(406\) 0 0
\(407\) −3.10779 + 21.6151i −0.154047 + 1.07142i
\(408\) 0 0
\(409\) −1.28849 13.4937i −0.0637118 0.667220i −0.969762 0.244051i \(-0.921524\pi\)
0.906051 0.423169i \(-0.139082\pi\)
\(410\) 0 0
\(411\) −0.124719 + 1.43212i −0.00615192 + 0.0706415i
\(412\) 0 0
\(413\) −46.3111 + 18.5402i −2.27882 + 0.912303i
\(414\) 0 0
\(415\) −7.94946 8.33715i −0.390224 0.409255i
\(416\) 0 0
\(417\) 18.0959 17.5446i 0.886158 0.859160i
\(418\) 0 0
\(419\) −17.8513 + 6.17839i −0.872092 + 0.301834i −0.726214 0.687468i \(-0.758722\pi\)
−0.145878 + 0.989303i \(0.546601\pi\)
\(420\) 0 0
\(421\) 23.2635 + 2.22139i 1.13379 + 0.108264i 0.645033 0.764154i \(-0.276843\pi\)
0.488760 + 0.872419i \(0.337450\pi\)
\(422\) 0 0
\(423\) −4.83756 1.08855i −0.235210 0.0529273i
\(424\) 0 0
\(425\) −51.1256 + 2.43541i −2.47996 + 0.118135i
\(426\) 0 0
\(427\) −13.8882 4.07794i −0.672097 0.197345i
\(428\) 0 0
\(429\) 35.8771 18.8760i 1.73216 0.911340i
\(430\) 0 0
\(431\) 6.01884 3.47498i 0.289918 0.167384i −0.347987 0.937499i \(-0.613135\pi\)
0.637905 + 0.770115i \(0.279801\pi\)
\(432\) 0 0
\(433\) −0.695343 + 0.729255i −0.0334161 + 0.0350458i −0.740230 0.672354i \(-0.765283\pi\)
0.706814 + 0.707400i \(0.250132\pi\)
\(434\) 0 0
\(435\) −5.10932 1.45410i −0.244973 0.0697187i
\(436\) 0 0
\(437\) −2.22414 0.105949i −0.106395 0.00506821i
\(438\) 0 0
\(439\) −5.84219 + 10.1190i −0.278832 + 0.482952i −0.971095 0.238694i \(-0.923281\pi\)
0.692262 + 0.721646i \(0.256614\pi\)
\(440\) 0 0
\(441\) 21.8827 + 45.8774i 1.04203 + 2.18464i
\(442\) 0 0
\(443\) 9.84616 + 1.89769i 0.467805 + 0.0901620i 0.417706 0.908582i \(-0.362834\pi\)
0.0500990 + 0.998744i \(0.484046\pi\)
\(444\) 0 0
\(445\) 14.0932 + 12.2119i 0.668083 + 0.578897i
\(446\) 0 0
\(447\) −6.86171 + 29.3496i −0.324548 + 1.38819i
\(448\) 0 0
\(449\) −9.45743 + 18.3448i −0.446323 + 0.865747i 0.553143 + 0.833086i \(0.313428\pi\)
−0.999467 + 0.0326605i \(0.989602\pi\)
\(450\) 0 0
\(451\) −37.4742 + 7.22257i −1.76459 + 0.340097i
\(452\) 0 0
\(453\) 6.67893 + 2.24946i 0.313804 + 0.105689i
\(454\) 0 0
\(455\) −57.5815 66.4526i −2.69946 3.11535i
\(456\) 0 0
\(457\) 9.84714 + 40.5905i 0.460630 + 1.89874i 0.437949 + 0.899000i \(0.355705\pi\)
0.0226813 + 0.999743i \(0.492780\pi\)
\(458\) 0 0
\(459\) 29.2886 + 2.05951i 1.36708 + 0.0961298i
\(460\) 0 0
\(461\) −2.29028 7.79999i −0.106669 0.363282i 0.888808 0.458279i \(-0.151534\pi\)
−0.995478 + 0.0949973i \(0.969716\pi\)
\(462\) 0 0
\(463\) 15.3993 38.4657i 0.715668 1.78765i 0.106953 0.994264i \(-0.465890\pi\)
0.608715 0.793389i \(-0.291685\pi\)
\(464\) 0 0
\(465\) −49.9918 + 0.416566i −2.31831 + 0.0193178i
\(466\) 0 0
\(467\) −9.76188 + 6.95140i −0.451726 + 0.321673i −0.783176 0.621800i \(-0.786402\pi\)
0.331450 + 0.943473i \(0.392462\pi\)
\(468\) 0 0
\(469\) −3.21204 39.9232i −0.148318 1.84348i
\(470\) 0 0
\(471\) −14.5010 10.1451i −0.668172 0.467462i
\(472\) 0 0
\(473\) −5.70722 1.97529i −0.262418 0.0908239i
\(474\) 0 0
\(475\) 6.74000 + 2.69829i 0.309252 + 0.123806i
\(476\) 0 0
\(477\) −5.10443 + 7.42707i −0.233716 + 0.340062i
\(478\) 0 0
\(479\) −4.33542 8.40954i −0.198090 0.384242i 0.768779 0.639515i \(-0.220865\pi\)
−0.966869 + 0.255273i \(0.917835\pi\)
\(480\) 0 0
\(481\) 20.8268 5.05252i 0.949619 0.230375i
\(482\) 0 0
\(483\) −20.4883 11.6024i −0.932252 0.527928i
\(484\) 0 0
\(485\) 8.08175 10.2768i 0.366973 0.466645i
\(486\) 0 0
\(487\) 2.76782 + 14.3608i 0.125422 + 0.650750i 0.989164 + 0.146816i \(0.0469024\pi\)
−0.863742 + 0.503934i \(0.831885\pi\)
\(488\) 0 0
\(489\) −32.7209 4.42660i −1.47969 0.200178i
\(490\) 0 0
\(491\) −15.2253 + 23.6910i −0.687107 + 1.06916i 0.306010 + 0.952028i \(0.401006\pi\)
−0.993116 + 0.117131i \(0.962630\pi\)
\(492\) 0 0
\(493\) 3.02681 3.49313i 0.136321 0.157323i
\(494\) 0 0
\(495\) −48.3994 + 25.9815i −2.17539 + 1.16778i
\(496\) 0 0
\(497\) 0.894299 3.68635i 0.0401148 0.165355i
\(498\) 0 0
\(499\) 11.0192 + 6.36192i 0.493285 + 0.284798i 0.725936 0.687762i \(-0.241407\pi\)
−0.232651 + 0.972560i \(0.574740\pi\)
\(500\) 0 0
\(501\) −26.4581 + 8.00887i −1.18206 + 0.357810i
\(502\) 0 0
\(503\) 5.49284 7.71361i 0.244914 0.343933i −0.673760 0.738950i \(-0.735322\pi\)
0.918674 + 0.395017i \(0.129261\pi\)
\(504\) 0 0
\(505\) 16.0460 + 15.2999i 0.714039 + 0.680835i
\(506\) 0 0
\(507\) −13.1443 11.1992i −0.583759 0.497374i
\(508\) 0 0
\(509\) −8.35315 + 1.20100i −0.370247 + 0.0532335i −0.324927 0.945739i \(-0.605340\pi\)
−0.0453199 + 0.998973i \(0.514431\pi\)
\(510\) 0 0
\(511\) −10.5763 + 36.0197i −0.467870 + 1.59342i
\(512\) 0 0
\(513\) −3.65761 1.99152i −0.161488 0.0879280i
\(514\) 0 0
\(515\) −34.4515 + 27.0930i −1.51812 + 1.19386i
\(516\) 0 0
\(517\) −0.767276 + 8.03527i −0.0337447 + 0.353391i
\(518\) 0 0
\(519\) 19.4045 15.5233i 0.851764 0.681397i
\(520\) 0 0
\(521\) 8.77518 + 19.2150i 0.384447 + 0.841822i 0.998613 + 0.0526454i \(0.0167653\pi\)
−0.614166 + 0.789177i \(0.710507\pi\)
\(522\) 0 0
\(523\) 27.3032 26.0335i 1.19388 1.13837i 0.206763 0.978391i \(-0.433707\pi\)
0.987121 0.159975i \(-0.0511414\pi\)
\(524\) 0 0
\(525\) 50.7555 + 57.5982i 2.21515 + 2.51379i
\(526\) 0 0
\(527\) 18.0700 39.5678i 0.787141 1.72360i
\(528\) 0 0
\(529\) −15.2126 + 1.45263i −0.661419 + 0.0631579i
\(530\) 0 0
\(531\) 26.2282 15.7314i 1.13821 0.682683i
\(532\) 0 0
\(533\) 20.2489 + 31.5078i 0.877075 + 1.36476i
\(534\) 0 0
\(535\) 23.0043i 0.994562i
\(536\) 0 0
\(537\) −9.54766 + 3.39382i −0.412012 + 0.146454i
\(538\) 0 0
\(539\) 69.6078 44.7342i 2.99822 1.92684i
\(540\) 0 0
\(541\) 23.0816 + 3.31863i 0.992356 + 0.142679i 0.619321 0.785138i \(-0.287408\pi\)
0.373035 + 0.927817i \(0.378317\pi\)
\(542\) 0 0
\(543\) −32.2823 + 15.0692i −1.38537 + 0.646681i
\(544\) 0 0
\(545\) 47.7131 + 21.7899i 2.04381 + 0.933375i
\(546\) 0 0
\(547\) 6.94641 + 17.3513i 0.297007 + 0.741888i 0.999543 + 0.0302394i \(0.00962697\pi\)
−0.702535 + 0.711649i \(0.747949\pi\)
\(548\) 0 0
\(549\) 8.80383 + 1.11640i 0.375738 + 0.0476466i
\(550\) 0 0
\(551\) −0.596364 + 0.272350i −0.0254059 + 0.0116025i
\(552\) 0 0
\(553\) −14.5466 42.0296i −0.618584 1.78728i
\(554\) 0 0
\(555\) −28.1627 + 7.08119i −1.19544 + 0.300580i
\(556\) 0 0
\(557\) −17.6149 22.3992i −0.746367 0.949083i 0.253466 0.967344i \(-0.418429\pi\)
−0.999833 + 0.0182614i \(0.994187\pi\)
\(558\) 0 0
\(559\) 0.282016 + 5.92024i 0.0119280 + 0.250400i
\(560\) 0 0
\(561\) −2.67194 47.7210i −0.112809 2.01478i
\(562\) 0 0
\(563\) 0.0111183 + 0.0773297i 0.000468582 + 0.00325906i 0.990054 0.140685i \(-0.0449305\pi\)
−0.989586 + 0.143944i \(0.954021\pi\)
\(564\) 0 0
\(565\) 28.0741 + 48.6257i 1.18108 + 2.04570i
\(566\) 0 0
\(567\) −25.0303 36.2335i −1.05117 1.52166i
\(568\) 0 0
\(569\) −9.88026 7.03570i −0.414202 0.294952i 0.353895 0.935285i \(-0.384857\pi\)
−0.768097 + 0.640333i \(0.778796\pi\)
\(570\) 0 0
\(571\) 1.63747 34.3747i 0.0685258 1.43853i −0.658839 0.752284i \(-0.728952\pi\)
0.727365 0.686251i \(-0.240745\pi\)
\(572\) 0 0
\(573\) 1.79704 9.76093i 0.0750726 0.407769i
\(574\) 0 0
\(575\) −24.4558 5.93292i −1.01988 0.247420i
\(576\) 0 0
\(577\) 3.04334 15.7903i 0.126696 0.657361i −0.861937 0.507015i \(-0.830749\pi\)
0.988633 0.150346i \(-0.0480389\pi\)
\(578\) 0 0
\(579\) 15.0707 38.5731i 0.626315 1.60304i
\(580\) 0 0
\(581\) −12.6471 8.12778i −0.524689 0.337197i
\(582\) 0 0
\(583\) 13.0396 + 6.72236i 0.540043 + 0.278412i
\(584\) 0 0
\(585\) 41.3248 + 34.6194i 1.70857 + 1.43134i
\(586\) 0 0
\(587\) 35.7420 + 28.1078i 1.47523 + 1.16013i 0.951257 + 0.308401i \(0.0997938\pi\)
0.523975 + 0.851734i \(0.324449\pi\)
\(588\) 0 0
\(589\) −4.66297 + 4.04048i −0.192134 + 0.166485i
\(590\) 0 0
\(591\) −10.2888 15.7201i −0.423224 0.646639i
\(592\) 0 0
\(593\) −33.7065 + 17.3769i −1.38416 + 0.713583i −0.979605 0.200931i \(-0.935603\pi\)
−0.404553 + 0.914515i \(0.632573\pi\)
\(594\) 0 0
\(595\) −99.4682 + 29.2065i −4.07780 + 1.19735i
\(596\) 0 0
\(597\) 24.2101 + 0.951158i 0.990855 + 0.0389283i
\(598\) 0 0
\(599\) 3.15041 9.10251i 0.128722 0.371919i −0.862162 0.506632i \(-0.830890\pi\)
0.990885 + 0.134714i \(0.0430114\pi\)
\(600\) 0 0
\(601\) −10.8131 15.1848i −0.441075 0.619403i 0.532868 0.846199i \(-0.321114\pi\)
−0.973942 + 0.226796i \(0.927175\pi\)
\(602\) 0 0
\(603\) 5.83101 + 23.8537i 0.237457 + 0.971398i
\(604\) 0 0
\(605\) 27.9464 + 39.2452i 1.13618 + 1.59554i
\(606\) 0 0
\(607\) 3.93230 11.3616i 0.159607 0.461154i −0.836636 0.547760i \(-0.815481\pi\)
0.996243 + 0.0866057i \(0.0276020\pi\)
\(608\) 0 0
\(609\) −6.92730 0.272157i −0.280708 0.0110284i
\(610\) 0 0
\(611\) 7.60068 2.23176i 0.307490 0.0902873i
\(612\) 0 0
\(613\) −17.1672 + 8.85032i −0.693378 + 0.357461i −0.768621 0.639704i \(-0.779057\pi\)
0.0752434 + 0.997165i \(0.476027\pi\)
\(614\) 0 0
\(615\) −27.7925 42.4637i −1.12070 1.71230i
\(616\) 0 0
\(617\) 24.4072 21.1489i 0.982596 0.851424i −0.00630820 0.999980i \(-0.502008\pi\)
0.988904 + 0.148556i \(0.0474625\pi\)
\(618\) 0 0
\(619\) −26.6396 20.9496i −1.07074 0.842037i −0.0827500 0.996570i \(-0.526370\pi\)
−0.987988 + 0.154533i \(0.950613\pi\)
\(620\) 0 0
\(621\) 13.5316 + 5.02857i 0.543004 + 0.201790i
\(622\) 0 0
\(623\) 21.6311 + 11.1516i 0.866631 + 0.446779i
\(624\) 0 0
\(625\) 9.89339 + 6.35810i 0.395736 + 0.254324i
\(626\) 0 0
\(627\) −2.46715 + 6.31465i −0.0985287 + 0.252183i
\(628\) 0 0
\(629\) 4.78176 24.8101i 0.190661 0.989244i
\(630\) 0 0
\(631\) 38.0721 + 9.23620i 1.51563 + 0.367687i 0.905407 0.424544i \(-0.139566\pi\)
0.610221 + 0.792232i \(0.291081\pi\)
\(632\) 0 0
\(633\) −1.92428 + 10.4521i −0.0764835 + 0.415432i
\(634\) 0 0
\(635\) −1.40967 + 29.5927i −0.0559412 + 1.17435i
\(636\) 0 0
\(637\) −66.1457 47.1021i −2.62079 1.86625i
\(638\) 0 0
\(639\) −0.182458 + 2.31849i −0.00721791 + 0.0917182i
\(640\) 0 0
\(641\) 16.4876 + 28.5574i 0.651223 + 1.12795i 0.982826 + 0.184532i \(0.0590770\pi\)
−0.331604 + 0.943419i \(0.607590\pi\)
\(642\) 0 0
\(643\) −3.51556 24.4512i −0.138640 0.964263i −0.933783 0.357841i \(-0.883513\pi\)
0.795143 0.606422i \(-0.207396\pi\)
\(644\) 0 0
\(645\) −0.448968 8.01860i −0.0176781 0.315732i
\(646\) 0 0
\(647\) 0.690949 + 14.5048i 0.0271640 + 0.570243i 0.970892 + 0.239519i \(0.0769898\pi\)
−0.943728 + 0.330724i \(0.892707\pi\)
\(648\) 0 0
\(649\) −30.7763 39.1353i −1.20808 1.53619i
\(650\) 0 0
\(651\) −63.2741 + 15.9095i −2.47991 + 0.623544i
\(652\) 0 0
\(653\) −2.80684 8.10983i −0.109840 0.317362i 0.876663 0.481105i \(-0.159764\pi\)
−0.986503 + 0.163743i \(0.947643\pi\)
\(654\) 0 0
\(655\) 69.2556 31.6280i 2.70604 1.23581i
\(656\) 0 0
\(657\) 2.89543 22.8332i 0.112961 0.890807i
\(658\) 0 0
\(659\) −16.5295 41.2886i −0.643896 1.60837i −0.785790 0.618493i \(-0.787744\pi\)
0.141894 0.989882i \(-0.454681\pi\)
\(660\) 0 0
\(661\) 4.92817 + 2.25062i 0.191684 + 0.0875390i 0.508945 0.860799i \(-0.330036\pi\)
−0.317261 + 0.948338i \(0.602763\pi\)
\(662\) 0 0
\(663\) −42.5033 + 19.8403i −1.65069 + 0.770532i
\(664\) 0 0
\(665\) 14.5549 + 2.09267i 0.564413 + 0.0811504i
\(666\) 0 0
\(667\) 1.91176 1.22861i 0.0740235 0.0475720i
\(668\) 0 0
\(669\) 4.08700 1.45277i 0.158012 0.0561673i
\(670\) 0 0
\(671\) 14.4462i 0.557691i
\(672\) 0 0
\(673\) −0.328051 0.510457i −0.0126454 0.0196767i 0.834873 0.550442i \(-0.185541\pi\)
−0.847519 + 0.530766i \(0.821904\pi\)
\(674\) 0 0
\(675\) −36.3309 29.9242i −1.39838 1.15178i
\(676\) 0 0
\(677\) 39.1751 3.74077i 1.50562 0.143769i 0.690616 0.723222i \(-0.257340\pi\)
0.815006 + 0.579452i \(0.196733\pi\)
\(678\) 0 0
\(679\) 7.08780 15.5201i 0.272005 0.595608i
\(680\) 0 0
\(681\) 1.20609 + 1.36869i 0.0462175 + 0.0524483i
\(682\) 0 0
\(683\) 3.94309 3.75973i 0.150878 0.143862i −0.610881 0.791723i \(-0.709185\pi\)
0.761759 + 0.647861i \(0.224336\pi\)
\(684\) 0 0
\(685\) 1.29273 + 2.83069i 0.0493927 + 0.108155i
\(686\) 0 0
\(687\) 21.4777 17.1818i 0.819424 0.655525i
\(688\) 0 0
\(689\) 1.36855 14.3321i 0.0521375 0.546009i
\(690\) 0 0
\(691\) 24.3141 19.1208i 0.924950 0.727389i −0.0373717 0.999301i \(-0.511899\pi\)
0.962322 + 0.271913i \(0.0876561\pi\)
\(692\) 0 0
\(693\) −53.3889 + 47.8425i −2.02808 + 1.81739i
\(694\) 0 0
\(695\) 15.3717 52.3511i 0.583081 1.98579i
\(696\) 0 0
\(697\) 43.7076 6.28421i 1.65554 0.238031i
\(698\) 0 0
\(699\) 23.1325 + 19.7093i 0.874950 + 0.745476i
\(700\) 0 0
\(701\) 22.5112 + 21.4644i 0.850236 + 0.810698i 0.983599 0.180369i \(-0.0577292\pi\)
−0.133363 + 0.991067i \(0.542578\pi\)
\(702\) 0 0
\(703\) −2.07887 + 2.91937i −0.0784062 + 0.110106i
\(704\) 0 0
\(705\) −10.2735 + 3.10980i −0.386924 + 0.117122i
\(706\) 0 0
\(707\) 25.0578 + 14.4672i 0.942397 + 0.544093i
\(708\) 0 0
\(709\) −3.87992 + 15.9933i −0.145714 + 0.600640i 0.851387 + 0.524539i \(0.175762\pi\)
−0.997100 + 0.0761008i \(0.975753\pi\)
\(710\) 0 0
\(711\) 12.8971 + 24.0253i 0.483680 + 0.901018i
\(712\) 0 0
\(713\) 14.0053 16.1630i 0.524504 0.605310i
\(714\) 0 0
\(715\) 47.4454 73.8264i 1.77436 2.76095i
\(716\) 0 0
\(717\) 32.7530 + 4.43094i 1.22318 + 0.165476i
\(718\) 0 0
\(719\) −6.50917 33.7728i −0.242751 1.25951i −0.874762 0.484552i \(-0.838983\pi\)
0.632011 0.774959i \(-0.282230\pi\)
\(720\) 0 0
\(721\) −35.3575 + 44.9607i −1.31678 + 1.67442i
\(722\) 0 0
\(723\) −0.459862 0.260417i −0.0171025 0.00968501i
\(724\) 0 0
\(725\) −7.20069 + 1.74687i −0.267427 + 0.0648770i
\(726\) 0 0
\(727\) 6.11610 + 11.8636i 0.226834 + 0.439996i 0.974596 0.223971i \(-0.0719020\pi\)
−0.747762 + 0.663967i \(0.768872\pi\)
\(728\) 0 0
\(729\) 18.6789 + 19.4961i 0.691810 + 0.722079i
\(730\) 0 0
\(731\) 6.48725 + 2.59710i 0.239939 + 0.0960573i
\(732\) 0 0
\(733\) 16.9333 + 5.86068i 0.625446 + 0.216469i 0.621363 0.783523i \(-0.286579\pi\)
0.00408290 + 0.999992i \(0.498700\pi\)
\(734\) 0 0
\(735\) 90.1576 + 63.0754i 3.32551 + 2.32657i
\(736\) 0 0
\(737\) 37.3281 14.3016i 1.37500 0.526807i
\(738\) 0 0
\(739\) −5.44897 + 3.88019i −0.200443 + 0.142735i −0.675872 0.737019i \(-0.736233\pi\)
0.475428 + 0.879755i \(0.342293\pi\)
\(740\) 0 0
\(741\) 6.65306 0.0554379i 0.244406 0.00203656i
\(742\) 0 0
\(743\) −4.78178 + 11.9443i −0.175427 + 0.438194i −0.989857 0.142067i \(-0.954625\pi\)
0.814430 + 0.580261i \(0.197050\pi\)
\(744\) 0 0
\(745\) 18.3823 + 62.6044i 0.673476 + 2.29365i
\(746\) 0 0
\(747\) 8.44682 + 3.68868i 0.309053 + 0.134962i
\(748\) 0 0
\(749\) 7.07785 + 29.1753i 0.258619 + 1.06604i
\(750\) 0 0
\(751\) 2.13402 + 2.46280i 0.0778716 + 0.0898687i 0.793348 0.608768i \(-0.208336\pi\)
−0.715477 + 0.698637i \(0.753790\pi\)
\(752\) 0 0
\(753\) −22.4386 7.55730i −0.817708 0.275403i
\(754\) 0 0
\(755\) 14.9804 2.88724i 0.545193 0.105077i
\(756\) 0 0
\(757\) −3.03669 + 5.89035i −0.110370 + 0.214088i −0.937551 0.347847i \(-0.886913\pi\)
0.827181 + 0.561936i \(0.189943\pi\)
\(758\) 0 0
\(759\) 5.34973 22.8824i 0.194183 0.830579i
\(760\) 0 0
\(761\) 1.35085 + 1.17052i 0.0489682 + 0.0424312i 0.679001 0.734137i \(-0.262413\pi\)
−0.630033 + 0.776568i \(0.716959\pi\)
\(762\) 0 0
\(763\) 67.2166 + 12.9549i 2.43340 + 0.469000i
\(764\) 0 0
\(765\) 57.3669 27.3630i 2.07411 0.989310i
\(766\) 0 0
\(767\) −24.4301 + 42.3142i −0.882120 + 1.52788i
\(768\) 0 0
\(769\) 40.5918 + 1.93363i 1.46378 + 0.0697283i 0.764270 0.644897i \(-0.223100\pi\)
0.699508 + 0.714625i \(0.253403\pi\)
\(770\) 0 0
\(771\) 3.79131 + 1.07900i 0.136541 + 0.0388592i
\(772\) 0 0
\(773\) 20.8125 21.8276i 0.748575 0.785083i −0.233744 0.972298i \(-0.575098\pi\)
0.982319 + 0.187215i \(0.0599462\pi\)
\(774\) 0