Properties

Label 224.3.s.a.33.1
Level 224
Weight 3
Character 224.33
Analytic conductor 6.104
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 224.s (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.10355792167\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{20} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 33.1
Root \(-0.707107 + 3.42121i\) of \(x^{16} + 36 x^{14} + 522 x^{12} + 3644 x^{10} + 12219 x^{8} + 15156 x^{6} + 15478 x^{4} - 10992 x^{2} + 11025\)
Character \(\chi\) \(=\) 224.33
Dual form 224.3.s.a.129.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.19011 + 2.41916i) q^{3} +(-0.0446470 - 0.0257769i) q^{5} +(-6.12357 - 3.39144i) q^{7} +(7.20469 - 12.4789i) q^{9} +O(q^{10})\) \(q+(-4.19011 + 2.41916i) q^{3} +(-0.0446470 - 0.0257769i) q^{5} +(-6.12357 - 3.39144i) q^{7} +(7.20469 - 12.4789i) q^{9} +(-0.894964 - 1.55012i) q^{11} +5.87602i q^{13} +0.249434 q^{15} +(23.0248 - 13.2934i) q^{17} +(22.8134 + 13.1713i) q^{19} +(33.8629 - 0.603422i) q^{21} +(12.8386 - 22.2371i) q^{23} +(-12.4987 - 21.6483i) q^{25} +26.1723i q^{27} -27.1749 q^{29} +(25.7249 - 14.8523i) q^{31} +(7.50000 + 4.33013i) q^{33} +(0.185978 + 0.309264i) q^{35} +(30.8629 - 53.4561i) q^{37} +(-14.2150 - 24.6212i) q^{39} +65.7376i q^{41} -9.52546 q^{43} +(-0.643335 + 0.371430i) q^{45} +(-61.2978 - 35.3903i) q^{47} +(25.9963 + 41.5354i) q^{49} +(-64.3176 + 111.401i) q^{51} +(-4.86555 - 8.42738i) q^{53} +0.0922778i q^{55} -127.454 q^{57} +(54.3535 - 31.3810i) q^{59} +(-66.1830 - 38.2108i) q^{61} +(-86.4398 + 51.9811i) q^{63} +(0.151466 - 0.262346i) q^{65} +(-51.5236 - 89.2415i) q^{67} +124.234i q^{69} +90.1681 q^{71} +(-28.8184 + 16.6383i) q^{73} +(104.742 + 60.4726i) q^{75} +(0.223235 + 12.5275i) q^{77} +(32.4323 - 56.1743i) q^{79} +(1.52712 + 2.64505i) q^{81} +29.1364i q^{83} -1.37065 q^{85} +(113.866 - 65.7405i) q^{87} +(18.7689 + 10.8362i) q^{89} +(19.9281 - 35.9822i) q^{91} +(-71.8602 + 124.466i) q^{93} +(-0.679033 - 1.17612i) q^{95} -123.061i q^{97} -25.7918 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 8q^{9} + O(q^{10}) \) \( 16q + 8q^{9} + 48q^{17} + 56q^{21} + 16q^{25} + 112q^{29} + 120q^{33} + 8q^{37} - 72q^{45} - 128q^{49} - 24q^{53} - 528q^{57} - 360q^{61} - 8q^{65} + 72q^{73} + 32q^{81} + 720q^{85} + 408q^{89} - 232q^{93} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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
\(3\) −4.19011 + 2.41916i −1.39670 + 0.806387i −0.994046 0.108963i \(-0.965247\pi\)
−0.402658 + 0.915351i \(0.631914\pi\)
\(4\) 0 0
\(5\) −0.0446470 0.0257769i −0.00892939 0.00515539i 0.495529 0.868592i \(-0.334974\pi\)
−0.504458 + 0.863436i \(0.668308\pi\)
\(6\) 0 0
\(7\) −6.12357 3.39144i −0.874796 0.484491i
\(8\) 0 0
\(9\) 7.20469 12.4789i 0.800521 1.38654i
\(10\) 0 0
\(11\) −0.894964 1.55012i −0.0813604 0.140920i 0.822474 0.568803i \(-0.192593\pi\)
−0.903835 + 0.427882i \(0.859260\pi\)
\(12\) 0 0
\(13\) 5.87602i 0.452002i 0.974127 + 0.226001i \(0.0725652\pi\)
−0.974127 + 0.226001i \(0.927435\pi\)
\(14\) 0 0
\(15\) 0.249434 0.0166290
\(16\) 0 0
\(17\) 23.0248 13.2934i 1.35440 0.781962i 0.365536 0.930797i \(-0.380886\pi\)
0.988862 + 0.148835i \(0.0475523\pi\)
\(18\) 0 0
\(19\) 22.8134 + 13.1713i 1.20071 + 0.693227i 0.960712 0.277547i \(-0.0895215\pi\)
0.239993 + 0.970775i \(0.422855\pi\)
\(20\) 0 0
\(21\) 33.8629 0.603422i 1.61252 0.0287344i
\(22\) 0 0
\(23\) 12.8386 22.2371i 0.558199 0.966830i −0.439448 0.898268i \(-0.644826\pi\)
0.997647 0.0685614i \(-0.0218409\pi\)
\(24\) 0 0
\(25\) −12.4987 21.6483i −0.499947 0.865933i
\(26\) 0 0
\(27\) 26.1723i 0.969345i
\(28\) 0 0
\(29\) −27.1749 −0.937066 −0.468533 0.883446i \(-0.655217\pi\)
−0.468533 + 0.883446i \(0.655217\pi\)
\(30\) 0 0
\(31\) 25.7249 14.8523i 0.829837 0.479106i −0.0239601 0.999713i \(-0.507627\pi\)
0.853797 + 0.520606i \(0.174294\pi\)
\(32\) 0 0
\(33\) 7.50000 + 4.33013i 0.227273 + 0.131216i
\(34\) 0 0
\(35\) 0.185978 + 0.309264i 0.00531366 + 0.00883612i
\(36\) 0 0
\(37\) 30.8629 53.4561i 0.834132 1.44476i −0.0606029 0.998162i \(-0.519302\pi\)
0.894735 0.446597i \(-0.147364\pi\)
\(38\) 0 0
\(39\) −14.2150 24.6212i −0.364488 0.631312i
\(40\) 0 0
\(41\) 65.7376i 1.60336i 0.597755 + 0.801679i \(0.296059\pi\)
−0.597755 + 0.801679i \(0.703941\pi\)
\(42\) 0 0
\(43\) −9.52546 −0.221522 −0.110761 0.993847i \(-0.535329\pi\)
−0.110761 + 0.993847i \(0.535329\pi\)
\(44\) 0 0
\(45\) −0.643335 + 0.371430i −0.0142963 + 0.00825399i
\(46\) 0 0
\(47\) −61.2978 35.3903i −1.30421 0.752986i −0.323086 0.946370i \(-0.604720\pi\)
−0.981123 + 0.193384i \(0.938054\pi\)
\(48\) 0 0
\(49\) 25.9963 + 41.5354i 0.530537 + 0.847662i
\(50\) 0 0
\(51\) −64.3176 + 111.401i −1.26113 + 2.18434i
\(52\) 0 0
\(53\) −4.86555 8.42738i −0.0918028 0.159007i 0.816467 0.577392i \(-0.195930\pi\)
−0.908270 + 0.418385i \(0.862596\pi\)
\(54\) 0 0
\(55\) 0.0922778i 0.00167778i
\(56\) 0 0
\(57\) −127.454 −2.23604
\(58\) 0 0
\(59\) 54.3535 31.3810i 0.921246 0.531881i 0.0372134 0.999307i \(-0.488152\pi\)
0.884032 + 0.467426i \(0.154819\pi\)
\(60\) 0 0
\(61\) −66.1830 38.2108i −1.08497 0.626406i −0.152735 0.988267i \(-0.548808\pi\)
−0.932232 + 0.361861i \(0.882141\pi\)
\(62\) 0 0
\(63\) −86.4398 + 51.9811i −1.37206 + 0.825098i
\(64\) 0 0
\(65\) 0.151466 0.262346i 0.00233024 0.00403610i
\(66\) 0 0
\(67\) −51.5236 89.2415i −0.769009 1.33196i −0.938101 0.346363i \(-0.887417\pi\)
0.169091 0.985600i \(-0.445917\pi\)
\(68\) 0 0
\(69\) 124.234i 1.80050i
\(70\) 0 0
\(71\) 90.1681 1.26997 0.634986 0.772523i \(-0.281006\pi\)
0.634986 + 0.772523i \(0.281006\pi\)
\(72\) 0 0
\(73\) −28.8184 + 16.6383i −0.394773 + 0.227922i −0.684226 0.729270i \(-0.739860\pi\)
0.289453 + 0.957192i \(0.406527\pi\)
\(74\) 0 0
\(75\) 104.742 + 60.4726i 1.39656 + 0.806302i
\(76\) 0 0
\(77\) 0.223235 + 12.5275i 0.00289915 + 0.162695i
\(78\) 0 0
\(79\) 32.4323 56.1743i 0.410535 0.711068i −0.584413 0.811456i \(-0.698675\pi\)
0.994948 + 0.100389i \(0.0320086\pi\)
\(80\) 0 0
\(81\) 1.52712 + 2.64505i 0.0188534 + 0.0326550i
\(82\) 0 0
\(83\) 29.1364i 0.351041i 0.984476 + 0.175520i \(0.0561608\pi\)
−0.984476 + 0.175520i \(0.943839\pi\)
\(84\) 0 0
\(85\) −1.37065 −0.0161253
\(86\) 0 0
\(87\) 113.866 65.7405i 1.30880 0.755638i
\(88\) 0 0
\(89\) 18.7689 + 10.8362i 0.210887 + 0.121755i 0.601723 0.798705i \(-0.294481\pi\)
−0.390837 + 0.920460i \(0.627814\pi\)
\(90\) 0 0
\(91\) 19.9281 35.9822i 0.218991 0.395409i
\(92\) 0 0
\(93\) −71.8602 + 124.466i −0.772691 + 1.33834i
\(94\) 0 0
\(95\) −0.679033 1.17612i −0.00714771 0.0123802i
\(96\) 0 0
\(97\) 123.061i 1.26867i −0.773056 0.634337i \(-0.781273\pi\)
0.773056 0.634337i \(-0.218727\pi\)
\(98\) 0 0
\(99\) −25.7918 −0.260523
\(100\) 0 0
\(101\) −48.9543 + 28.2638i −0.484696 + 0.279840i −0.722372 0.691505i \(-0.756948\pi\)
0.237675 + 0.971345i \(0.423615\pi\)
\(102\) 0 0
\(103\) 25.6062 + 14.7838i 0.248604 + 0.143532i 0.619125 0.785293i \(-0.287487\pi\)
−0.370521 + 0.928824i \(0.620821\pi\)
\(104\) 0 0
\(105\) −1.52743 0.845941i −0.0145469 0.00805658i
\(106\) 0 0
\(107\) 14.9054 25.8169i 0.139303 0.241279i −0.787930 0.615765i \(-0.788847\pi\)
0.927233 + 0.374485i \(0.122181\pi\)
\(108\) 0 0
\(109\) −40.7751 70.6246i −0.374084 0.647932i 0.616106 0.787663i \(-0.288709\pi\)
−0.990189 + 0.139731i \(0.955376\pi\)
\(110\) 0 0
\(111\) 298.649i 2.69053i
\(112\) 0 0
\(113\) 43.3994 0.384065 0.192033 0.981389i \(-0.438492\pi\)
0.192033 + 0.981389i \(0.438492\pi\)
\(114\) 0 0
\(115\) −1.14641 + 0.661879i −0.00996876 + 0.00575547i
\(116\) 0 0
\(117\) 73.3262 + 42.3349i 0.626720 + 0.361837i
\(118\) 0 0
\(119\) −186.077 + 3.31582i −1.56368 + 0.0278640i
\(120\) 0 0
\(121\) 58.8981 102.014i 0.486761 0.843095i
\(122\) 0 0
\(123\) −159.030 275.448i −1.29293 2.23942i
\(124\) 0 0
\(125\) 2.57756i 0.0206205i
\(126\) 0 0
\(127\) −94.0304 −0.740397 −0.370199 0.928953i \(-0.620710\pi\)
−0.370199 + 0.928953i \(0.620710\pi\)
\(128\) 0 0
\(129\) 39.9127 23.0436i 0.309401 0.178633i
\(130\) 0 0
\(131\) 108.932 + 62.8918i 0.831540 + 0.480090i 0.854380 0.519649i \(-0.173937\pi\)
−0.0228396 + 0.999739i \(0.507271\pi\)
\(132\) 0 0
\(133\) −95.0298 158.026i −0.714510 1.18816i
\(134\) 0 0
\(135\) 0.674642 1.16851i 0.00499735 0.00865566i
\(136\) 0 0
\(137\) 124.928 + 216.382i 0.911884 + 1.57943i 0.811400 + 0.584491i \(0.198706\pi\)
0.100484 + 0.994939i \(0.467961\pi\)
\(138\) 0 0
\(139\) 2.08301i 0.0149857i 0.999972 + 0.00749284i \(0.00238507\pi\)
−0.999972 + 0.00749284i \(0.997615\pi\)
\(140\) 0 0
\(141\) 342.460 2.42879
\(142\) 0 0
\(143\) 9.10856 5.25883i 0.0636962 0.0367750i
\(144\) 0 0
\(145\) 1.21328 + 0.700486i 0.00836743 + 0.00483094i
\(146\) 0 0
\(147\) −209.408 111.149i −1.42455 0.756114i
\(148\) 0 0
\(149\) 10.8122 18.7273i 0.0725652 0.125687i −0.827460 0.561525i \(-0.810215\pi\)
0.900025 + 0.435838i \(0.143548\pi\)
\(150\) 0 0
\(151\) 44.0090 + 76.2258i 0.291450 + 0.504807i 0.974153 0.225890i \(-0.0725289\pi\)
−0.682703 + 0.730696i \(0.739196\pi\)
\(152\) 0 0
\(153\) 383.098i 2.50391i
\(154\) 0 0
\(155\) −1.53139 −0.00987992
\(156\) 0 0
\(157\) 142.568 82.3115i 0.908075 0.524277i 0.0282634 0.999601i \(-0.491002\pi\)
0.879811 + 0.475323i \(0.157669\pi\)
\(158\) 0 0
\(159\) 40.7744 + 23.5411i 0.256443 + 0.148057i
\(160\) 0 0
\(161\) −154.034 + 92.6292i −0.956731 + 0.575337i
\(162\) 0 0
\(163\) −82.4420 + 142.794i −0.505779 + 0.876035i 0.494199 + 0.869349i \(0.335462\pi\)
−0.999978 + 0.00668599i \(0.997872\pi\)
\(164\) 0 0
\(165\) −0.223235 0.386654i −0.00135294 0.00234336i
\(166\) 0 0
\(167\) 18.8929i 0.113131i −0.998399 0.0565655i \(-0.981985\pi\)
0.998399 0.0565655i \(-0.0180150\pi\)
\(168\) 0 0
\(169\) 134.472 0.795695
\(170\) 0 0
\(171\) 328.727 189.791i 1.92238 1.10989i
\(172\) 0 0
\(173\) −85.2911 49.2428i −0.493012 0.284641i 0.232811 0.972522i \(-0.425208\pi\)
−0.725823 + 0.687881i \(0.758541\pi\)
\(174\) 0 0
\(175\) 3.11760 + 174.954i 0.0178148 + 0.999735i
\(176\) 0 0
\(177\) −151.831 + 262.980i −0.857805 + 1.48576i
\(178\) 0 0
\(179\) −35.1481 60.8784i −0.196358 0.340103i 0.750987 0.660317i \(-0.229578\pi\)
−0.947345 + 0.320215i \(0.896245\pi\)
\(180\) 0 0
\(181\) 204.167i 1.12800i −0.825776 0.563999i \(-0.809262\pi\)
0.825776 0.563999i \(-0.190738\pi\)
\(182\) 0 0
\(183\) 369.752 2.02050
\(184\) 0 0
\(185\) −2.75587 + 1.59110i −0.0148966 + 0.00860055i
\(186\) 0 0
\(187\) −41.2127 23.7942i −0.220389 0.127242i
\(188\) 0 0
\(189\) 88.7617 160.268i 0.469639 0.847980i
\(190\) 0 0
\(191\) −95.3517 + 165.154i −0.499224 + 0.864681i −1.00000 0.000896163i \(-0.999715\pi\)
0.500776 + 0.865577i \(0.333048\pi\)
\(192\) 0 0
\(193\) −42.7740 74.0868i −0.221627 0.383869i 0.733675 0.679500i \(-0.237803\pi\)
−0.955302 + 0.295631i \(0.904470\pi\)
\(194\) 0 0
\(195\) 1.46568i 0.00751631i
\(196\) 0 0
\(197\) 275.164 1.39677 0.698386 0.715721i \(-0.253902\pi\)
0.698386 + 0.715721i \(0.253902\pi\)
\(198\) 0 0
\(199\) 179.161 103.439i 0.900308 0.519793i 0.0230082 0.999735i \(-0.492676\pi\)
0.877300 + 0.479942i \(0.159342\pi\)
\(200\) 0 0
\(201\) 431.779 + 249.288i 2.14816 + 1.24024i
\(202\) 0 0
\(203\) 166.408 + 92.1620i 0.819742 + 0.454000i
\(204\) 0 0
\(205\) 1.69452 2.93499i 0.00826593 0.0143170i
\(206\) 0 0
\(207\) −184.996 320.423i −0.893701 1.54793i
\(208\) 0 0
\(209\) 47.1514i 0.225605i
\(210\) 0 0
\(211\) 78.7325 0.373140 0.186570 0.982442i \(-0.440263\pi\)
0.186570 + 0.982442i \(0.440263\pi\)
\(212\) 0 0
\(213\) −377.814 + 218.131i −1.77378 + 1.02409i
\(214\) 0 0
\(215\) 0.425283 + 0.245537i 0.00197806 + 0.00114203i
\(216\) 0 0
\(217\) −207.899 + 3.70467i −0.958061 + 0.0170722i
\(218\) 0 0
\(219\) 80.5017 139.433i 0.367588 0.636680i
\(220\) 0 0
\(221\) 78.1120 + 135.294i 0.353448 + 0.612190i
\(222\) 0 0
\(223\) 155.408i 0.696896i 0.937328 + 0.348448i \(0.113291\pi\)
−0.937328 + 0.348448i \(0.886709\pi\)
\(224\) 0 0
\(225\) −360.196 −1.60087
\(226\) 0 0
\(227\) −70.8987 + 40.9334i −0.312329 + 0.180323i −0.647968 0.761667i \(-0.724381\pi\)
0.335639 + 0.941991i \(0.391048\pi\)
\(228\) 0 0
\(229\) −355.669 205.346i −1.55314 0.896707i −0.997883 0.0650290i \(-0.979286\pi\)
−0.555258 0.831678i \(-0.687381\pi\)
\(230\) 0 0
\(231\) −31.2415 51.9516i −0.135244 0.224899i
\(232\) 0 0
\(233\) −18.9359 + 32.7979i −0.0812699 + 0.140764i −0.903796 0.427964i \(-0.859231\pi\)
0.822526 + 0.568728i \(0.192564\pi\)
\(234\) 0 0
\(235\) 1.82451 + 3.16014i 0.00776387 + 0.0134474i
\(236\) 0 0
\(237\) 313.836i 1.32420i
\(238\) 0 0
\(239\) −428.133 −1.79135 −0.895676 0.444707i \(-0.853308\pi\)
−0.895676 + 0.444707i \(0.853308\pi\)
\(240\) 0 0
\(241\) 180.155 104.012i 0.747530 0.431587i −0.0772706 0.997010i \(-0.524621\pi\)
0.824801 + 0.565423i \(0.191287\pi\)
\(242\) 0 0
\(243\) −216.791 125.164i −0.892143 0.515079i
\(244\) 0 0
\(245\) −0.0900009 2.52454i −0.000367350 0.0103042i
\(246\) 0 0
\(247\) −77.3949 + 134.052i −0.313340 + 0.542721i
\(248\) 0 0
\(249\) −70.4856 122.085i −0.283075 0.490300i
\(250\) 0 0
\(251\) 375.625i 1.49652i 0.663408 + 0.748258i \(0.269109\pi\)
−0.663408 + 0.748258i \(0.730891\pi\)
\(252\) 0 0
\(253\) −45.9603 −0.181661
\(254\) 0 0
\(255\) 5.74317 3.31582i 0.0225222 0.0130032i
\(256\) 0 0
\(257\) −62.4373 36.0482i −0.242947 0.140265i 0.373584 0.927597i \(-0.378129\pi\)
−0.616530 + 0.787331i \(0.711462\pi\)
\(258\) 0 0
\(259\) −370.284 + 222.673i −1.42967 + 0.859741i
\(260\) 0 0
\(261\) −195.787 + 339.113i −0.750141 + 1.29928i
\(262\) 0 0
\(263\) −104.550 181.086i −0.397529 0.688541i 0.595891 0.803065i \(-0.296799\pi\)
−0.993420 + 0.114524i \(0.963466\pi\)
\(264\) 0 0
\(265\) 0.501676i 0.00189312i
\(266\) 0 0
\(267\) −104.858 −0.392728
\(268\) 0 0
\(269\) −244.956 + 141.425i −0.910616 + 0.525744i −0.880629 0.473806i \(-0.842880\pi\)
−0.0299865 + 0.999550i \(0.509546\pi\)
\(270\) 0 0
\(271\) 171.410 + 98.9636i 0.632509 + 0.365179i 0.781723 0.623625i \(-0.214341\pi\)
−0.149214 + 0.988805i \(0.547674\pi\)
\(272\) 0 0
\(273\) 3.54572 + 198.979i 0.0129880 + 0.728861i
\(274\) 0 0
\(275\) −22.3717 + 38.7490i −0.0813517 + 0.140905i
\(276\) 0 0
\(277\) 118.659 + 205.524i 0.428372 + 0.741963i 0.996729 0.0808197i \(-0.0257538\pi\)
−0.568356 + 0.822783i \(0.692420\pi\)
\(278\) 0 0
\(279\) 428.025i 1.53414i
\(280\) 0 0
\(281\) −239.870 −0.853628 −0.426814 0.904339i \(-0.640364\pi\)
−0.426814 + 0.904339i \(0.640364\pi\)
\(282\) 0 0
\(283\) −119.663 + 69.0872i −0.422836 + 0.244124i −0.696290 0.717761i \(-0.745167\pi\)
0.273454 + 0.961885i \(0.411834\pi\)
\(284\) 0 0
\(285\) 5.69044 + 3.28538i 0.0199665 + 0.0115276i
\(286\) 0 0
\(287\) 222.945 402.549i 0.776812 1.40261i
\(288\) 0 0
\(289\) 208.927 361.872i 0.722930 1.25215i
\(290\) 0 0
\(291\) 297.705 + 515.641i 1.02304 + 1.77196i
\(292\) 0 0
\(293\) 385.332i 1.31513i 0.753400 + 0.657563i \(0.228413\pi\)
−0.753400 + 0.657563i \(0.771587\pi\)
\(294\) 0 0
\(295\) −3.23562 −0.0109682
\(296\) 0 0
\(297\) 40.5703 23.4233i 0.136600 0.0788663i
\(298\) 0 0
\(299\) 130.666 + 75.4398i 0.437009 + 0.252307i
\(300\) 0 0
\(301\) 58.3299 + 32.3050i 0.193787 + 0.107326i
\(302\) 0 0
\(303\) 136.749 236.857i 0.451318 0.781706i
\(304\) 0 0
\(305\) 1.96991 + 3.41199i 0.00645873 + 0.0111868i
\(306\) 0 0
\(307\) 222.533i 0.724864i −0.932010 0.362432i \(-0.881946\pi\)
0.932010 0.362432i \(-0.118054\pi\)
\(308\) 0 0
\(309\) −143.057 −0.462968
\(310\) 0 0
\(311\) −171.841 + 99.2124i −0.552543 + 0.319011i −0.750147 0.661271i \(-0.770017\pi\)
0.197604 + 0.980282i \(0.436684\pi\)
\(312\) 0 0
\(313\) −328.619 189.729i −1.04990 0.606161i −0.127280 0.991867i \(-0.540625\pi\)
−0.922622 + 0.385705i \(0.873958\pi\)
\(314\) 0 0
\(315\) 5.19919 0.0926473i 0.0165054 0.000294118i
\(316\) 0 0
\(317\) 129.813 224.843i 0.409505 0.709284i −0.585329 0.810796i \(-0.699035\pi\)
0.994834 + 0.101512i \(0.0323680\pi\)
\(318\) 0 0
\(319\) 24.3206 + 42.1245i 0.0762400 + 0.132052i
\(320\) 0 0
\(321\) 144.234i 0.449327i
\(322\) 0 0
\(323\) 700.364 2.16831
\(324\) 0 0
\(325\) 127.206 73.4425i 0.391403 0.225977i
\(326\) 0 0
\(327\) 341.705 + 197.283i 1.04497 + 0.603313i
\(328\) 0 0
\(329\) 255.338 + 424.603i 0.776103 + 1.29059i
\(330\) 0 0
\(331\) 273.589 473.869i 0.826552 1.43163i −0.0741761 0.997245i \(-0.523633\pi\)
0.900728 0.434384i \(-0.143034\pi\)
\(332\) 0 0
\(333\) −444.715 770.269i −1.33548 2.31312i
\(334\) 0 0
\(335\) 5.31248i 0.0158582i
\(336\) 0 0
\(337\) −408.705 −1.21277 −0.606387 0.795170i \(-0.707382\pi\)
−0.606387 + 0.795170i \(0.707382\pi\)
\(338\) 0 0
\(339\) −181.848 + 104.990i −0.536425 + 0.309705i
\(340\) 0 0
\(341\) −46.0458 26.5846i −0.135032 0.0779606i
\(342\) 0 0
\(343\) −18.3257 342.510i −0.0534276 0.998572i
\(344\) 0 0
\(345\) 3.20238 5.54669i 0.00928227 0.0160774i
\(346\) 0 0
\(347\) 133.575 + 231.358i 0.384941 + 0.666738i 0.991761 0.128102i \(-0.0408884\pi\)
−0.606820 + 0.794839i \(0.707555\pi\)
\(348\) 0 0
\(349\) 466.080i 1.33547i 0.744398 + 0.667736i \(0.232737\pi\)
−0.744398 + 0.667736i \(0.767263\pi\)
\(350\) 0 0
\(351\) −153.789 −0.438146
\(352\) 0 0
\(353\) 230.205 132.909i 0.652139 0.376513i −0.137136 0.990552i \(-0.543790\pi\)
0.789275 + 0.614039i \(0.210456\pi\)
\(354\) 0 0
\(355\) −4.02573 2.32426i −0.0113401 0.00654720i
\(356\) 0 0
\(357\) 771.664 464.045i 2.16152 1.29985i
\(358\) 0 0
\(359\) −144.903 + 250.979i −0.403628 + 0.699105i −0.994161 0.107909i \(-0.965584\pi\)
0.590532 + 0.807014i \(0.298918\pi\)
\(360\) 0 0
\(361\) 166.467 + 288.330i 0.461128 + 0.798698i
\(362\) 0 0
\(363\) 569.936i 1.57007i
\(364\) 0 0
\(365\) 1.71554 0.00470011
\(366\) 0 0
\(367\) 6.07460 3.50717i 0.0165520 0.00955632i −0.491701 0.870764i \(-0.663625\pi\)
0.508253 + 0.861208i \(0.330291\pi\)
\(368\) 0 0
\(369\) 820.333 + 473.619i 2.22312 + 1.28352i
\(370\) 0 0
\(371\) 1.21363 + 68.1069i 0.00327125 + 0.183576i
\(372\) 0 0
\(373\) 286.998 497.096i 0.769433 1.33270i −0.168438 0.985712i \(-0.553872\pi\)
0.937871 0.346984i \(-0.112794\pi\)
\(374\) 0 0
\(375\) −6.23553 10.8002i −0.0166281 0.0288007i
\(376\) 0 0
\(377\) 159.680i 0.423555i
\(378\) 0 0
\(379\) −678.807 −1.79105 −0.895524 0.445014i \(-0.853199\pi\)
−0.895524 + 0.445014i \(0.853199\pi\)
\(380\) 0 0
\(381\) 393.998 227.475i 1.03412 0.597047i
\(382\) 0 0
\(383\) −358.444 206.948i −0.935886 0.540334i −0.0472179 0.998885i \(-0.515036\pi\)
−0.888668 + 0.458550i \(0.848369\pi\)
\(384\) 0 0
\(385\) 0.312954 0.565070i 0.000812868 0.00146771i
\(386\) 0 0
\(387\) −68.6280 + 118.867i −0.177333 + 0.307150i
\(388\) 0 0
\(389\) −69.2438 119.934i −0.178005 0.308313i 0.763192 0.646171i \(-0.223631\pi\)
−0.941197 + 0.337858i \(0.890298\pi\)
\(390\) 0 0
\(391\) 682.672i 1.74596i
\(392\) 0 0
\(393\) −608.582 −1.54855
\(394\) 0 0
\(395\) −2.89600 + 1.67201i −0.00733166 + 0.00423293i
\(396\) 0 0
\(397\) 3.62003 + 2.09002i 0.00911846 + 0.00526455i 0.504552 0.863381i \(-0.331658\pi\)
−0.495434 + 0.868646i \(0.664991\pi\)
\(398\) 0 0
\(399\) 780.475 + 432.253i 1.95608 + 1.08334i
\(400\) 0 0
\(401\) 301.027 521.394i 0.750690 1.30023i −0.196798 0.980444i \(-0.563054\pi\)
0.947489 0.319790i \(-0.103612\pi\)
\(402\) 0 0
\(403\) 87.2724 + 151.160i 0.216557 + 0.375088i
\(404\) 0 0
\(405\) 0.157458i 0.000388785i
\(406\) 0 0
\(407\) −110.485 −0.271461
\(408\) 0 0
\(409\) −155.272 + 89.6463i −0.379638 + 0.219184i −0.677661 0.735375i \(-0.737006\pi\)
0.298023 + 0.954559i \(0.403673\pi\)
\(410\) 0 0
\(411\) −1046.93 604.443i −2.54726 1.47066i
\(412\) 0 0
\(413\) −439.264 + 7.82750i −1.06359 + 0.0189528i
\(414\) 0 0
\(415\) 0.751046 1.30085i 0.00180975 0.00313458i
\(416\) 0 0
\(417\) −5.03914 8.72804i −0.0120843 0.0209305i
\(418\) 0 0
\(419\) 605.541i 1.44521i −0.691263 0.722603i \(-0.742946\pi\)
0.691263 0.722603i \(-0.257054\pi\)
\(420\) 0 0
\(421\) 582.852 1.38445 0.692224 0.721683i \(-0.256631\pi\)
0.692224 + 0.721683i \(0.256631\pi\)
\(422\) 0 0
\(423\) −883.264 + 509.953i −2.08809 + 1.20556i
\(424\) 0 0
\(425\) −575.558 332.299i −1.35425 0.781879i
\(426\) 0 0
\(427\) 275.687 + 458.442i 0.645637 + 1.07363i
\(428\) 0 0
\(429\) −25.4439 + 44.0702i −0.0593098 + 0.102728i
\(430\) 0 0
\(431\) −137.702 238.507i −0.319495 0.553382i 0.660888 0.750485i \(-0.270180\pi\)
−0.980383 + 0.197103i \(0.936847\pi\)
\(432\) 0 0
\(433\) 27.7972i 0.0641967i −0.999485 0.0320984i \(-0.989781\pi\)
0.999485 0.0320984i \(-0.0102190\pi\)
\(434\) 0 0
\(435\) −6.77836 −0.0155824
\(436\) 0 0
\(437\) 585.783 338.202i 1.34047 0.773918i
\(438\) 0 0
\(439\) 254.750 + 147.080i 0.580295 + 0.335034i 0.761251 0.648458i \(-0.224586\pi\)
−0.180955 + 0.983491i \(0.557919\pi\)
\(440\) 0 0
\(441\) 705.611 25.1554i 1.60003 0.0570416i
\(442\) 0 0
\(443\) 145.445 251.918i 0.328319 0.568665i −0.653860 0.756616i \(-0.726851\pi\)
0.982178 + 0.187951i \(0.0601847\pi\)
\(444\) 0 0
\(445\) −0.558650 0.967610i −0.00125539 0.00217440i
\(446\) 0 0
\(447\) 104.626i 0.234063i
\(448\) 0 0
\(449\) 433.407 0.965271 0.482635 0.875821i \(-0.339680\pi\)
0.482635 + 0.875821i \(0.339680\pi\)
\(450\) 0 0
\(451\) 101.901 58.8328i 0.225946 0.130450i
\(452\) 0 0
\(453\) −368.805 212.930i −0.814139 0.470043i
\(454\) 0 0
\(455\) −1.81724 + 1.09281i −0.00399394 + 0.00240178i
\(456\) 0 0
\(457\) 28.6828 49.6801i 0.0627632 0.108709i −0.832936 0.553369i \(-0.813342\pi\)
0.895700 + 0.444660i \(0.146675\pi\)
\(458\) 0 0
\(459\) 347.918 + 602.612i 0.757991 + 1.31288i
\(460\) 0 0
\(461\) 567.060i 1.23007i 0.788501 + 0.615033i \(0.210857\pi\)
−0.788501 + 0.615033i \(0.789143\pi\)
\(462\) 0 0
\(463\) −0.548177 −0.00118397 −0.000591984 1.00000i \(-0.500188\pi\)
−0.000591984 1.00000i \(0.500188\pi\)
\(464\) 0 0
\(465\) 6.41668 3.70467i 0.0137993 0.00796704i
\(466\) 0 0
\(467\) −88.5154 51.1044i −0.189540 0.109431i 0.402227 0.915540i \(-0.368236\pi\)
−0.591767 + 0.806109i \(0.701570\pi\)
\(468\) 0 0
\(469\) 12.8518 + 721.216i 0.0274025 + 1.53777i
\(470\) 0 0
\(471\) −398.250 + 689.789i −0.845541 + 1.46452i
\(472\) 0 0
\(473\) 8.52495 + 14.7656i 0.0180231 + 0.0312170i
\(474\) 0 0
\(475\) 658.496i 1.38631i
\(476\) 0 0
\(477\) −140.219 −0.293960
\(478\) 0 0
\(479\) 389.828 225.067i 0.813837 0.469869i −0.0344496 0.999406i \(-0.510968\pi\)
0.848287 + 0.529537i \(0.177635\pi\)
\(480\) 0 0
\(481\) 314.109 + 181.351i 0.653034 + 0.377029i
\(482\) 0 0
\(483\) 421.333 760.759i 0.872326 1.57507i
\(484\) 0 0
\(485\) −3.17215 + 5.49432i −0.00654051 + 0.0113285i
\(486\) 0 0
\(487\) 470.386 + 814.732i 0.965885 + 1.67296i 0.707219 + 0.706995i \(0.249950\pi\)
0.258666 + 0.965967i \(0.416717\pi\)
\(488\) 0 0
\(489\) 797.762i 1.63142i
\(490\) 0 0
\(491\) 514.670 1.04821 0.524103 0.851655i \(-0.324401\pi\)
0.524103 + 0.851655i \(0.324401\pi\)
\(492\) 0 0
\(493\) −625.696 + 361.246i −1.26916 + 0.732750i
\(494\) 0 0
\(495\) 1.15152 + 0.664832i 0.00232631 + 0.00134310i
\(496\) 0 0
\(497\) −552.151 305.799i −1.11097 0.615290i
\(498\) 0 0
\(499\) 124.004 214.780i 0.248504 0.430422i −0.714607 0.699526i \(-0.753394\pi\)
0.963111 + 0.269105i \(0.0867277\pi\)
\(500\) 0 0
\(501\) 45.7049 + 79.1633i 0.0912274 + 0.158011i
\(502\) 0 0
\(503\) 164.798i 0.327630i 0.986491 + 0.163815i \(0.0523800\pi\)
−0.986491 + 0.163815i \(0.947620\pi\)
\(504\) 0 0
\(505\) 2.91422 0.00577073
\(506\) 0 0
\(507\) −563.454 + 325.310i −1.11135 + 0.641638i
\(508\) 0 0
\(509\) 109.542 + 63.2438i 0.215209 + 0.124251i 0.603730 0.797189i \(-0.293680\pi\)
−0.388521 + 0.921440i \(0.627014\pi\)
\(510\) 0 0
\(511\) 232.900 4.15017i 0.455773 0.00812167i
\(512\) 0 0
\(513\) −344.724 + 597.079i −0.671977 + 1.16390i
\(514\) 0 0
\(515\) −0.762160 1.32010i −0.00147992 0.00256330i
\(516\) 0 0
\(517\) 126.692i 0.245053i
\(518\) 0 0
\(519\) 476.505 0.918122
\(520\) 0 0
\(521\) −44.7559 + 25.8398i −0.0859039 + 0.0495966i −0.542337 0.840161i \(-0.682460\pi\)
0.456433 + 0.889758i \(0.349127\pi\)
\(522\) 0 0
\(523\) 297.579 + 171.808i 0.568986 + 0.328504i 0.756744 0.653711i \(-0.226789\pi\)
−0.187758 + 0.982215i \(0.560122\pi\)
\(524\) 0 0
\(525\) −436.304 725.533i −0.831056 1.38197i
\(526\) 0 0
\(527\) 394.874 683.942i 0.749286 1.29780i
\(528\) 0 0
\(529\) −65.1585 112.858i −0.123173 0.213342i
\(530\) 0 0
\(531\) 904.361i 1.70313i
\(532\) 0 0
\(533\) −386.276 −0.724720
\(534\) 0 0
\(535\) −1.33096 + 0.768430i −0.00248778 + 0.00143632i
\(536\) 0 0
\(537\) 294.549 + 170.058i 0.548509 + 0.316682i
\(538\) 0 0
\(539\) 41.1193 77.4702i 0.0762881 0.143730i
\(540\) 0 0
\(541\) −382.006 + 661.654i −0.706111 + 1.22302i 0.260177 + 0.965561i \(0.416219\pi\)
−0.966289 + 0.257460i \(0.917114\pi\)
\(542\) 0 0
\(543\) 493.914 + 855.485i 0.909603 + 1.57548i
\(544\) 0 0
\(545\) 4.20423i 0.00771419i
\(546\) 0 0
\(547\) −59.3354 −0.108474 −0.0542371 0.998528i \(-0.517273\pi\)
−0.0542371 + 0.998528i \(0.517273\pi\)
\(548\) 0 0
\(549\) −953.655 + 550.593i −1.73708 + 1.00290i
\(550\) 0 0
\(551\) −619.952 357.929i −1.12514 0.649600i
\(552\) 0 0
\(553\) −389.113 + 233.996i −0.703640 + 0.423139i
\(554\) 0 0
\(555\) 7.69826 13.3338i 0.0138707 0.0240248i
\(556\) 0 0
\(557\) 365.048 + 632.281i 0.655382 + 1.13515i 0.981798 + 0.189929i \(0.0608257\pi\)
−0.326416 + 0.945226i \(0.605841\pi\)
\(558\) 0 0
\(559\) 55.9718i 0.100128i
\(560\) 0 0
\(561\) 230.248 0.410424
\(562\) 0 0
\(563\) −412.415 + 238.108i −0.732531 + 0.422927i −0.819347 0.573298i \(-0.805664\pi\)
0.0868167 + 0.996224i \(0.472331\pi\)
\(564\) 0 0
\(565\) −1.93765 1.11870i −0.00342947 0.00198000i
\(566\) 0 0
\(567\) −0.380917 21.3763i −0.000671811 0.0377007i
\(568\) 0 0
\(569\) −208.701 + 361.480i −0.366785 + 0.635291i −0.989061 0.147508i \(-0.952875\pi\)
0.622276 + 0.782798i \(0.286208\pi\)
\(570\) 0 0
\(571\) −492.001 852.171i −0.861648 1.49242i −0.870337 0.492456i \(-0.836099\pi\)
0.00868931 0.999962i \(-0.497234\pi\)
\(572\) 0 0
\(573\) 922.685i 1.61027i
\(574\) 0 0
\(575\) −641.861 −1.11628
\(576\) 0 0
\(577\) 80.3564 46.3938i 0.139266 0.0804052i −0.428748 0.903424i \(-0.641045\pi\)
0.568014 + 0.823019i \(0.307712\pi\)
\(578\) 0 0
\(579\) 358.456 + 206.955i 0.619095 + 0.357435i
\(580\) 0 0
\(581\) 98.8141 178.419i 0.170076 0.307089i
\(582\) 0 0
\(583\) −8.70898 + 15.0844i −0.0149382 + 0.0258738i
\(584\) 0 0
\(585\) −2.18253 3.78025i −0.00373082 0.00646196i
\(586\) 0 0
\(587\) 648.667i 1.10506i 0.833495 + 0.552528i \(0.186337\pi\)
−0.833495 + 0.552528i \(0.813663\pi\)
\(588\) 0 0
\(589\) 782.498 1.32852
\(590\) 0 0
\(591\) −1152.97 + 665.667i −1.95088 + 1.12634i
\(592\) 0 0
\(593\) −453.392 261.766i −0.764574 0.441427i 0.0663617 0.997796i \(-0.478861\pi\)
−0.830936 + 0.556369i \(0.812194\pi\)
\(594\) 0 0
\(595\) 8.39327 + 4.64847i 0.0141063 + 0.00781255i
\(596\) 0 0
\(597\) −500.471 + 866.841i −0.838309 + 1.45199i
\(598\) 0 0
\(599\) 445.522 + 771.668i 0.743777 + 1.28826i 0.950764 + 0.309916i \(0.100301\pi\)
−0.206987 + 0.978344i \(0.566366\pi\)
\(600\) 0 0
\(601\) 502.034i 0.835331i 0.908601 + 0.417666i \(0.137152\pi\)
−0.908601 + 0.417666i \(0.862848\pi\)
\(602\) 0 0
\(603\) −1484.85 −2.46243
\(604\) 0 0
\(605\) −5.25924 + 3.03642i −0.00869296 + 0.00501888i
\(606\) 0 0
\(607\) 263.638 + 152.212i 0.434330 + 0.250760i 0.701189 0.712975i \(-0.252653\pi\)
−0.266860 + 0.963735i \(0.585986\pi\)
\(608\) 0 0
\(609\) −920.221 + 16.3979i −1.51104 + 0.0269260i
\(610\) 0 0
\(611\) 207.954 360.187i 0.340351 0.589505i
\(612\) 0 0
\(613\) 249.053 + 431.373i 0.406286 + 0.703708i 0.994470 0.105019i \(-0.0334904\pi\)
−0.588184 + 0.808727i \(0.700157\pi\)
\(614\) 0 0
\(615\) 16.3972i 0.0266622i
\(616\) 0 0
\(617\) 242.250 0.392626 0.196313 0.980541i \(-0.437103\pi\)
0.196313 + 0.980541i \(0.437103\pi\)
\(618\) 0 0
\(619\) −468.171 + 270.298i −0.756334 + 0.436669i −0.827978 0.560761i \(-0.810509\pi\)
0.0716442 + 0.997430i \(0.477175\pi\)
\(620\) 0 0
\(621\) 581.996 + 336.016i 0.937192 + 0.541088i
\(622\) 0 0
\(623\) −78.1824 130.010i −0.125493 0.208684i
\(624\) 0 0
\(625\) −312.400 + 541.093i −0.499841 + 0.865749i
\(626\) 0 0
\(627\) 114.067 + 197.570i 0.181925 + 0.315103i
\(628\) 0 0
\(629\) 1641.09i 2.60904i
\(630\) 0 0
\(631\) −808.138 −1.28073 −0.640363 0.768073i \(-0.721216\pi\)
−0.640363 + 0.768073i \(0.721216\pi\)
\(632\) 0 0
\(633\) −329.898 + 190.467i −0.521166 + 0.300895i
\(634\) 0 0
\(635\) 4.19817 + 2.42382i 0.00661130 + 0.00381703i
\(636\) 0 0
\(637\) −244.063 + 152.755i −0.383144 + 0.239804i
\(638\) 0 0
\(639\) 649.633 1125.20i 1.01664 1.76087i
\(640\) 0 0
\(641\) −155.277 268.947i −0.242241 0.419574i 0.719111 0.694895i \(-0.244549\pi\)
−0.961352 + 0.275321i \(0.911216\pi\)
\(642\) 0 0
\(643\) 342.761i 0.533065i −0.963826 0.266533i \(-0.914122\pi\)
0.963826 0.266533i \(-0.0858780\pi\)
\(644\) 0 0
\(645\) −2.37598 −0.00368369
\(646\) 0 0
\(647\) −447.656 + 258.454i −0.691895 + 0.399466i −0.804321 0.594195i \(-0.797471\pi\)
0.112427 + 0.993660i \(0.464138\pi\)
\(648\) 0 0
\(649\) −97.2889 56.1698i −0.149906 0.0865482i
\(650\) 0 0
\(651\) 862.159 518.465i 1.32436 0.796413i
\(652\) 0 0
\(653\) 381.777 661.256i 0.584650 1.01264i −0.410269 0.911965i \(-0.634565\pi\)
0.994919 0.100679i \(-0.0321016\pi\)
\(654\) 0 0
\(655\) −3.24231 5.61585i −0.00495010 0.00857382i
\(656\) 0 0
\(657\) 479.496i 0.729827i
\(658\) 0 0
\(659\) 593.617 0.900785 0.450392 0.892831i \(-0.351284\pi\)
0.450392 + 0.892831i \(0.351284\pi\)
\(660\) 0 0
\(661\) −275.162 + 158.865i −0.416282 + 0.240340i −0.693485 0.720471i \(-0.743926\pi\)
0.277204 + 0.960811i \(0.410592\pi\)
\(662\) 0 0
\(663\) −654.596 377.931i −0.987325 0.570032i
\(664\) 0 0
\(665\) 0.169374 + 9.50495i 0.000254698 + 0.0142932i
\(666\) 0 0
\(667\) −348.887 + 604.291i −0.523070 + 0.905983i
\(668\) 0 0
\(669\) −375.957 651.176i −0.561968 0.973358i
\(670\) 0 0
\(671\) 136.789i 0.203859i
\(672\) 0 0
\(673\) 567.441 0.843152 0.421576 0.906793i \(-0.361477\pi\)
0.421576 + 0.906793i \(0.361477\pi\)
\(674\) 0 0
\(675\) 566.587 327.119i 0.839388 0.484621i
\(676\) 0 0
\(677\) −541.094 312.401i −0.799253 0.461449i 0.0439568 0.999033i \(-0.486004\pi\)
−0.843210 + 0.537584i \(0.819337\pi\)
\(678\) 0 0
\(679\) −417.355 + 753.576i −0.614661 + 1.10983i
\(680\) 0 0
\(681\) 198.049 343.031i 0.290821 0.503717i
\(682\) 0 0
\(683\) 46.4425 + 80.4407i 0.0679977 + 0.117776i 0.898020 0.439955i \(-0.145006\pi\)
−0.830022 + 0.557731i \(0.811672\pi\)
\(684\) 0 0
\(685\) 12.8811i 0.0188045i
\(686\) 0 0
\(687\) 1987.06 2.89237
\(688\) 0 0
\(689\) 49.5194 28.5901i 0.0718715 0.0414950i
\(690\) 0 0
\(691\) 422.387 + 243.865i 0.611269 + 0.352916i 0.773462 0.633843i \(-0.218523\pi\)
−0.162193 + 0.986759i \(0.551857\pi\)
\(692\) 0 0
\(693\) 157.938 + 87.4711i 0.227904 + 0.126221i
\(694\) 0 0
\(695\) 0.0536936 0.0930000i 7.72570e−5 0.000133813i
\(696\) 0 0
\(697\) 873.874 + 1513.59i 1.25376 + 2.17158i
\(698\) 0 0
\(699\) 183.236i 0.262140i
\(700\) 0 0
\(701\) 548.723 0.782772 0.391386 0.920227i \(-0.371996\pi\)
0.391386 + 0.920227i \(0.371996\pi\)
\(702\) 0 0
\(703\) 1408.17 813.010i 2.00309 1.15649i
\(704\) 0 0
\(705\) −15.2898 8.82756i −0.0216876 0.0125214i
\(706\) 0 0
\(707\) 395.630 7.04996i 0.559590 0.00997166i
\(708\) 0 0
\(709\) 125.886 218.041i 0.177555 0.307533i −0.763488 0.645822i \(-0.776515\pi\)
0.941042 + 0.338289i \(0.109848\pi\)
\(710\) 0 0
\(711\) −467.329 809.437i −0.657284 1.13845i
\(712\) 0 0
\(713\) 762.730i 1.06975i
\(714\) 0 0
\(715\) −0.542226 −0.000758358
\(716\) 0 0
\(717\) 1793.93 1035.72i 2.50199 1.44452i
\(718\) 0 0
\(719\) −348.643 201.289i −0.484900 0.279957i 0.237556 0.971374i \(-0.423654\pi\)
−0.722456 + 0.691417i \(0.756987\pi\)
\(720\) 0 0
\(721\) −106.663 177.371i −0.147938 0.246007i
\(722\) 0 0
\(723\) −503.246 + 871.647i −0.696052 + 1.20560i
\(724\) 0 0
\(725\) 339.650 + 588.291i 0.468483 + 0.811437i
\(726\) 0 0
\(727\) 419.973i 0.577680i −0.957377 0.288840i \(-0.906730\pi\)
0.957377 0.288840i \(-0.0932695\pi\)
\(728\) 0 0
\(729\) 1183.68 1.62371
\(730\) 0 0
\(731\) −219.322 + 126.625i −0.300030 + 0.173222i
\(732\) 0 0
\(733\) 382.547 + 220.863i 0.521892 + 0.301314i 0.737708 0.675120i \(-0.235908\pi\)
−0.215817 + 0.976434i \(0.569241\pi\)
\(734\) 0 0
\(735\) 6.48437 + 10.3604i 0.00882228 + 0.0140957i
\(736\) 0 0
\(737\) −92.2236 + 159.736i −0.125134 + 0.216738i
\(738\) 0 0
\(739\) 219.526 + 380.231i 0.297059 + 0.514521i 0.975462 0.220169i \(-0.0706610\pi\)
−0.678403 + 0.734690i \(0.737328\pi\)
\(740\) 0 0
\(741\) 748.924i 1.01069i
\(742\) 0 0
\(743\) 882.165 1.18730 0.593651 0.804723i \(-0.297686\pi\)
0.593651 + 0.804723i \(0.297686\pi\)
\(744\) 0 0
\(745\) −0.965466 + 0.557412i −0.00129593 + 0.000748204i
\(746\) 0 0
\(747\) 363.589 + 209.918i 0.486733 + 0.281015i
\(748\) 0 0
\(749\) −178.830 + 107.541i −0.238759 + 0.143579i
\(750\) 0 0
\(751\) −57.8178 + 100.143i −0.0769877 + 0.133347i −0.901949 0.431843i \(-0.857864\pi\)
0.824961 + 0.565189i \(0.191197\pi\)
\(752\) 0 0
\(753\) −908.699 1573.91i −1.20677 2.09019i
\(754\) 0 0
\(755\) 4.53767i 0.00601015i
\(756\) 0 0
\(757\) −885.222 −1.16938 −0.584691 0.811256i \(-0.698784\pi\)
−0.584691 + 0.811256i \(0.698784\pi\)
\(758\) 0 0
\(759\) 192.579 111.185i 0.253727 0.146489i
\(760\) 0 0
\(761\) 479.807 + 277.017i 0.630495 + 0.364017i 0.780944 0.624601i \(-0.214738\pi\)
−0.150448 + 0.988618i \(0.548072\pi\)
\(762\) 0 0
\(763\) 10.1707 + 570.761i 0.0133299 + 0.748049i
\(764\) 0 0
\(765\) −9.87509 + 17.1042i −0.0129086 + 0.0223584i
\(766\) 0 0
\(767\) 184.395 + 319.382i 0.240411 + 0.416405i
\(768\) 0 0
\(769\) 502.045i 0.652854i 0.945222 + 0.326427i \(0.105845\pi\)
−0.945222 + 0.326427i \(0.894155\pi\)
\(770\) 0 0
\(771\) 348.826 0.452433
\(772\) 0 0
\(773\) −1029.64 + 594.462i −1.33200 + 0.769032i −0.985606 0.169057i \(-0.945928\pi\)
−0.346396 + 0.938088i \(0.612595\pi\)
\(774\) 0 0
\(775\) −643.055 371.268i −0.829748 0.479055i
\(776\) 0 0
\(777\) 1012.85 1828.80i 1.30354 2.35367i
\(778\) 0 0
\(779\) −865.852 + 1499.70i −1.11149 + 1.92516i
\(780\) 0 0
\(781\) −80.6972 139.772i −0.103325 0.178965i
\(782\) 0 0
\(783\) 711.230i 0.908340i
\(784\) 0 0
\(785\) −8.48695 −0.0108114
\(786\) 0 0
\(787\) −245.089 + 141.502i −0.311421 + 0.179799i −0.647562 0.762013i \(-0.724211\pi\)
0.336141 + 0.941812i \(0.390878\pi\)
\(788\) 0 0
\(789\) 876.154 + 505.848i 1.11046 + 0.641125i
\(790\) 0 0
\(791\) −265.759 147.186i