Properties

Label 224.3.n.a.17.12
Level 224
Weight 3
Character 224.17
Analytic conductor 6.104
Analytic rank 0
Dimension 28
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.n (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.10355792167\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.12
Character \(\chi\) \(=\) 224.17
Dual form 224.3.n.a.145.12

$q$-expansion

\(f(q)\) \(=\) \(q+(1.93494 - 3.35141i) q^{3} +(-2.33882 - 4.05096i) q^{5} +(-6.95505 + 0.792023i) q^{7} +(-2.98798 - 5.17534i) q^{9} +O(q^{10})\) \(q+(1.93494 - 3.35141i) q^{3} +(-2.33882 - 4.05096i) q^{5} +(-6.95505 + 0.792023i) q^{7} +(-2.98798 - 5.17534i) q^{9} +(-12.6383 - 7.29671i) q^{11} +12.7102 q^{13} -18.1019 q^{15} +(-16.9068 - 9.76116i) q^{17} +(8.86233 + 15.3500i) q^{19} +(-10.8032 + 24.8418i) q^{21} +(4.43038 + 7.67364i) q^{23} +(1.55984 - 2.70172i) q^{25} +11.7027 q^{27} -35.4981i q^{29} +(-25.1331 - 14.5106i) q^{31} +(-48.9086 + 28.2374i) q^{33} +(19.4751 + 26.3222i) q^{35} +(10.5802 - 6.10847i) q^{37} +(24.5934 - 42.5970i) q^{39} +22.0903i q^{41} -79.8001i q^{43} +(-13.9767 + 24.2084i) q^{45} +(36.5041 - 21.0756i) q^{47} +(47.7454 - 11.0171i) q^{49} +(-65.4273 + 37.7745i) q^{51} +(-31.3096 - 18.0766i) q^{53} +68.2627i q^{55} +68.5923 q^{57} +(-1.20348 + 2.08449i) q^{59} +(-14.6224 - 25.3268i) q^{61} +(24.8805 + 33.6282i) q^{63} +(-29.7268 - 51.4883i) q^{65} +(35.2303 + 20.3402i) q^{67} +34.2900 q^{69} +22.6174 q^{71} +(66.1587 + 38.1967i) q^{73} +(-6.03639 - 10.4553i) q^{75} +(93.6789 + 40.7391i) q^{77} +(68.4014 + 118.475i) q^{79} +(49.5358 - 85.7985i) q^{81} +49.9942 q^{83} +91.3184i q^{85} +(-118.969 - 68.6866i) q^{87} +(0.970023 - 0.560043i) q^{89} +(-88.3998 + 10.0667i) q^{91} +(-97.2622 + 56.1544i) q^{93} +(41.4548 - 71.8018i) q^{95} +158.827i q^{97} +87.2097i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{7} - 32q^{9} + O(q^{10}) \) \( 28q + 4q^{7} - 32q^{9} - 28q^{15} - 6q^{17} - 30q^{23} - 32q^{25} + 6q^{31} - 6q^{33} + 20q^{39} + 294q^{47} - 20q^{49} + 124q^{57} - 432q^{63} - 52q^{65} + 136q^{71} + 234q^{73} + 162q^{79} - 18q^{81} - 48q^{87} - 150q^{89} - 290q^{95} + O(q^{100}) \)

Character values

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

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

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
\(3\) 1.93494 3.35141i 0.644980 1.11714i −0.339326 0.940669i \(-0.610199\pi\)
0.984306 0.176469i \(-0.0564676\pi\)
\(4\) 0 0
\(5\) −2.33882 4.05096i −0.467764 0.810191i 0.531557 0.847022i \(-0.321607\pi\)
−0.999322 + 0.0368311i \(0.988274\pi\)
\(6\) 0 0
\(7\) −6.95505 + 0.792023i −0.993578 + 0.113146i
\(8\) 0 0
\(9\) −2.98798 5.17534i −0.331998 0.575037i
\(10\) 0 0
\(11\) −12.6383 7.29671i −1.14893 0.663337i −0.200306 0.979733i \(-0.564194\pi\)
−0.948627 + 0.316396i \(0.897527\pi\)
\(12\) 0 0
\(13\) 12.7102 0.977705 0.488853 0.872366i \(-0.337416\pi\)
0.488853 + 0.872366i \(0.337416\pi\)
\(14\) 0 0
\(15\) −18.1019 −1.20679
\(16\) 0 0
\(17\) −16.9068 9.76116i −0.994519 0.574186i −0.0878969 0.996130i \(-0.528015\pi\)
−0.906622 + 0.421944i \(0.861348\pi\)
\(18\) 0 0
\(19\) 8.86233 + 15.3500i 0.466439 + 0.807895i 0.999265 0.0383291i \(-0.0122035\pi\)
−0.532827 + 0.846224i \(0.678870\pi\)
\(20\) 0 0
\(21\) −10.8032 + 24.8418i −0.514438 + 1.18294i
\(22\) 0 0
\(23\) 4.43038 + 7.67364i 0.192625 + 0.333636i 0.946119 0.323818i \(-0.104967\pi\)
−0.753494 + 0.657454i \(0.771633\pi\)
\(24\) 0 0
\(25\) 1.55984 2.70172i 0.0623936 0.108069i
\(26\) 0 0
\(27\) 11.7027 0.433432
\(28\) 0 0
\(29\) 35.4981i 1.22407i −0.790830 0.612036i \(-0.790351\pi\)
0.790830 0.612036i \(-0.209649\pi\)
\(30\) 0 0
\(31\) −25.1331 14.5106i −0.810747 0.468085i 0.0364685 0.999335i \(-0.488389\pi\)
−0.847215 + 0.531250i \(0.821722\pi\)
\(32\) 0 0
\(33\) −48.9086 + 28.2374i −1.48208 + 0.855678i
\(34\) 0 0
\(35\) 19.4751 + 26.3222i 0.556430 + 0.752063i
\(36\) 0 0
\(37\) 10.5802 6.10847i 0.285951 0.165094i −0.350163 0.936689i \(-0.613874\pi\)
0.636114 + 0.771595i \(0.280541\pi\)
\(38\) 0 0
\(39\) 24.5934 42.5970i 0.630600 1.09223i
\(40\) 0 0
\(41\) 22.0903i 0.538788i 0.963030 + 0.269394i \(0.0868233\pi\)
−0.963030 + 0.269394i \(0.913177\pi\)
\(42\) 0 0
\(43\) 79.8001i 1.85582i −0.372809 0.927908i \(-0.621605\pi\)
0.372809 0.927908i \(-0.378395\pi\)
\(44\) 0 0
\(45\) −13.9767 + 24.2084i −0.310593 + 0.537964i
\(46\) 0 0
\(47\) 36.5041 21.0756i 0.776682 0.448418i −0.0585708 0.998283i \(-0.518654\pi\)
0.835253 + 0.549865i \(0.185321\pi\)
\(48\) 0 0
\(49\) 47.7454 11.0171i 0.974396 0.224839i
\(50\) 0 0
\(51\) −65.4273 + 37.7745i −1.28289 + 0.740676i
\(52\) 0 0
\(53\) −31.3096 18.0766i −0.590748 0.341068i 0.174645 0.984631i \(-0.444122\pi\)
−0.765393 + 0.643563i \(0.777455\pi\)
\(54\) 0 0
\(55\) 68.2627i 1.24114i
\(56\) 0 0
\(57\) 68.5923 1.20337
\(58\) 0 0
\(59\) −1.20348 + 2.08449i −0.0203979 + 0.0353303i −0.876044 0.482231i \(-0.839827\pi\)
0.855646 + 0.517561i \(0.173160\pi\)
\(60\) 0 0
\(61\) −14.6224 25.3268i −0.239712 0.415194i 0.720919 0.693019i \(-0.243720\pi\)
−0.960632 + 0.277825i \(0.910386\pi\)
\(62\) 0 0
\(63\) 24.8805 + 33.6282i 0.394929 + 0.533780i
\(64\) 0 0
\(65\) −29.7268 51.4883i −0.457335 0.792128i
\(66\) 0 0
\(67\) 35.2303 + 20.3402i 0.525825 + 0.303585i 0.739315 0.673360i \(-0.235150\pi\)
−0.213490 + 0.976945i \(0.568483\pi\)
\(68\) 0 0
\(69\) 34.2900 0.496957
\(70\) 0 0
\(71\) 22.6174 0.318554 0.159277 0.987234i \(-0.449084\pi\)
0.159277 + 0.987234i \(0.449084\pi\)
\(72\) 0 0
\(73\) 66.1587 + 38.1967i 0.906283 + 0.523243i 0.879233 0.476391i \(-0.158055\pi\)
0.0270498 + 0.999634i \(0.491389\pi\)
\(74\) 0 0
\(75\) −6.03639 10.4553i −0.0804852 0.139404i
\(76\) 0 0
\(77\) 93.6789 + 40.7391i 1.21661 + 0.529080i
\(78\) 0 0
\(79\) 68.4014 + 118.475i 0.865840 + 1.49968i 0.866211 + 0.499679i \(0.166549\pi\)
−0.000370612 1.00000i \(0.500118\pi\)
\(80\) 0 0
\(81\) 49.5358 85.7985i 0.611553 1.05924i
\(82\) 0 0
\(83\) 49.9942 0.602340 0.301170 0.953571i \(-0.402623\pi\)
0.301170 + 0.953571i \(0.402623\pi\)
\(84\) 0 0
\(85\) 91.3184i 1.07433i
\(86\) 0 0
\(87\) −118.969 68.6866i −1.36746 0.789502i
\(88\) 0 0
\(89\) 0.970023 0.560043i 0.0108991 0.00629262i −0.494541 0.869155i \(-0.664664\pi\)
0.505440 + 0.862862i \(0.331330\pi\)
\(90\) 0 0
\(91\) −88.3998 + 10.0667i −0.971427 + 0.110624i
\(92\) 0 0
\(93\) −97.2622 + 56.1544i −1.04583 + 0.603810i
\(94\) 0 0
\(95\) 41.4548 71.8018i 0.436366 0.755809i
\(96\) 0 0
\(97\) 158.827i 1.63740i 0.574225 + 0.818698i \(0.305304\pi\)
−0.574225 + 0.818698i \(0.694696\pi\)
\(98\) 0 0
\(99\) 87.2097i 0.880906i
\(100\) 0 0
\(101\) 34.8122 60.2965i 0.344675 0.596995i −0.640620 0.767858i \(-0.721322\pi\)
0.985295 + 0.170864i \(0.0546557\pi\)
\(102\) 0 0
\(103\) −16.9911 + 9.80983i −0.164962 + 0.0952411i −0.580208 0.814468i \(-0.697029\pi\)
0.415246 + 0.909709i \(0.363696\pi\)
\(104\) 0 0
\(105\) 125.900 14.3371i 1.19904 0.136544i
\(106\) 0 0
\(107\) 38.7540 22.3747i 0.362187 0.209109i −0.307852 0.951434i \(-0.599610\pi\)
0.670040 + 0.742325i \(0.266277\pi\)
\(108\) 0 0
\(109\) 49.0210 + 28.3023i 0.449734 + 0.259654i 0.707718 0.706495i \(-0.249725\pi\)
−0.257984 + 0.966149i \(0.583058\pi\)
\(110\) 0 0
\(111\) 47.2781i 0.425929i
\(112\) 0 0
\(113\) −188.632 −1.66931 −0.834657 0.550770i \(-0.814334\pi\)
−0.834657 + 0.550770i \(0.814334\pi\)
\(114\) 0 0
\(115\) 20.7237 35.8945i 0.180206 0.312126i
\(116\) 0 0
\(117\) −37.9777 65.7794i −0.324596 0.562217i
\(118\) 0 0
\(119\) 125.319 + 54.4987i 1.05310 + 0.457972i
\(120\) 0 0
\(121\) 45.9838 + 79.6463i 0.380032 + 0.658234i
\(122\) 0 0
\(123\) 74.0337 + 42.7434i 0.601900 + 0.347507i
\(124\) 0 0
\(125\) −131.534 −1.05227
\(126\) 0 0
\(127\) −45.8547 −0.361060 −0.180530 0.983569i \(-0.557781\pi\)
−0.180530 + 0.983569i \(0.557781\pi\)
\(128\) 0 0
\(129\) −267.443 154.408i −2.07320 1.19696i
\(130\) 0 0
\(131\) −60.4982 104.786i −0.461818 0.799893i 0.537233 0.843434i \(-0.319469\pi\)
−0.999052 + 0.0435409i \(0.986136\pi\)
\(132\) 0 0
\(133\) −73.7955 99.7409i −0.554854 0.749932i
\(134\) 0 0
\(135\) −27.3704 47.4069i −0.202744 0.351163i
\(136\) 0 0
\(137\) 72.6207 125.783i 0.530078 0.918122i −0.469306 0.883036i \(-0.655496\pi\)
0.999384 0.0350869i \(-0.0111708\pi\)
\(138\) 0 0
\(139\) −86.3503 −0.621225 −0.310613 0.950537i \(-0.600534\pi\)
−0.310613 + 0.950537i \(0.600534\pi\)
\(140\) 0 0
\(141\) 163.120i 1.15688i
\(142\) 0 0
\(143\) −160.634 92.7424i −1.12332 0.648548i
\(144\) 0 0
\(145\) −143.801 + 83.0236i −0.991732 + 0.572577i
\(146\) 0 0
\(147\) 55.4615 181.332i 0.377289 1.23355i
\(148\) 0 0
\(149\) 189.536 109.429i 1.27205 0.734421i 0.296680 0.954977i \(-0.404121\pi\)
0.975374 + 0.220556i \(0.0707873\pi\)
\(150\) 0 0
\(151\) 41.6552 72.1490i 0.275862 0.477808i −0.694490 0.719502i \(-0.744370\pi\)
0.970352 + 0.241695i \(0.0777033\pi\)
\(152\) 0 0
\(153\) 116.665i 0.762514i
\(154\) 0 0
\(155\) 135.751i 0.875813i
\(156\) 0 0
\(157\) −17.7207 + 30.6932i −0.112871 + 0.195498i −0.916927 0.399056i \(-0.869338\pi\)
0.804056 + 0.594554i \(0.202671\pi\)
\(158\) 0 0
\(159\) −121.164 + 69.9543i −0.762041 + 0.439964i
\(160\) 0 0
\(161\) −36.8912 49.8616i −0.229138 0.309699i
\(162\) 0 0
\(163\) 9.05412 5.22740i 0.0555468 0.0320699i −0.471969 0.881615i \(-0.656457\pi\)
0.527516 + 0.849545i \(0.323123\pi\)
\(164\) 0 0
\(165\) 228.777 + 132.084i 1.38653 + 0.800511i
\(166\) 0 0
\(167\) 78.8843i 0.472361i 0.971709 + 0.236181i \(0.0758957\pi\)
−0.971709 + 0.236181i \(0.924104\pi\)
\(168\) 0 0
\(169\) −7.45163 −0.0440925
\(170\) 0 0
\(171\) 52.9610 91.7311i 0.309713 0.536439i
\(172\) 0 0
\(173\) 95.9208 + 166.140i 0.554456 + 0.960345i 0.997946 + 0.0640660i \(0.0204068\pi\)
−0.443490 + 0.896279i \(0.646260\pi\)
\(174\) 0 0
\(175\) −8.70893 + 20.0260i −0.0497653 + 0.114434i
\(176\) 0 0
\(177\) 4.65732 + 8.06671i 0.0263125 + 0.0455746i
\(178\) 0 0
\(179\) −60.5426 34.9543i −0.338227 0.195275i 0.321261 0.946991i \(-0.395893\pi\)
−0.659488 + 0.751715i \(0.729227\pi\)
\(180\) 0 0
\(181\) −343.635 −1.89853 −0.949267 0.314472i \(-0.898173\pi\)
−0.949267 + 0.314472i \(0.898173\pi\)
\(182\) 0 0
\(183\) −113.174 −0.618438
\(184\) 0 0
\(185\) −49.4903 28.5732i −0.267515 0.154450i
\(186\) 0 0
\(187\) 142.449 + 246.728i 0.761757 + 1.31940i
\(188\) 0 0
\(189\) −81.3925 + 9.26878i −0.430648 + 0.0490411i
\(190\) 0 0
\(191\) −69.8895 121.052i −0.365913 0.633781i 0.623009 0.782215i \(-0.285910\pi\)
−0.988922 + 0.148434i \(0.952577\pi\)
\(192\) 0 0
\(193\) −11.4616 + 19.8521i −0.0593867 + 0.102861i −0.894190 0.447687i \(-0.852248\pi\)
0.834804 + 0.550548i \(0.185581\pi\)
\(194\) 0 0
\(195\) −230.078 −1.17989
\(196\) 0 0
\(197\) 287.788i 1.46085i 0.682992 + 0.730426i \(0.260678\pi\)
−0.682992 + 0.730426i \(0.739322\pi\)
\(198\) 0 0
\(199\) 56.7091 + 32.7410i 0.284970 + 0.164528i 0.635671 0.771960i \(-0.280723\pi\)
−0.350701 + 0.936487i \(0.614057\pi\)
\(200\) 0 0
\(201\) 136.337 78.7141i 0.678293 0.391613i
\(202\) 0 0
\(203\) 28.1153 + 246.891i 0.138499 + 1.21621i
\(204\) 0 0
\(205\) 89.4868 51.6652i 0.436521 0.252026i
\(206\) 0 0
\(207\) 26.4758 45.8574i 0.127902 0.221533i
\(208\) 0 0
\(209\) 258.663i 1.23762i
\(210\) 0 0
\(211\) 17.8985i 0.0848270i −0.999100 0.0424135i \(-0.986495\pi\)
0.999100 0.0424135i \(-0.0135047\pi\)
\(212\) 0 0
\(213\) 43.7632 75.8001i 0.205461 0.355869i
\(214\) 0 0
\(215\) −323.267 + 186.638i −1.50357 + 0.868084i
\(216\) 0 0
\(217\) 186.295 + 81.0161i 0.858502 + 0.373346i
\(218\) 0 0
\(219\) 256.026 147.817i 1.16907 0.674962i
\(220\) 0 0
\(221\) −214.889 124.066i −0.972346 0.561384i
\(222\) 0 0
\(223\) 258.973i 1.16132i 0.814148 + 0.580658i \(0.197205\pi\)
−0.814148 + 0.580658i \(0.802795\pi\)
\(224\) 0 0
\(225\) −18.6431 −0.0828581
\(226\) 0 0
\(227\) 58.6721 101.623i 0.258468 0.447679i −0.707364 0.706849i \(-0.750116\pi\)
0.965832 + 0.259171i \(0.0834492\pi\)
\(228\) 0 0
\(229\) 43.5475 + 75.4264i 0.190164 + 0.329373i 0.945304 0.326190i \(-0.105765\pi\)
−0.755141 + 0.655563i \(0.772431\pi\)
\(230\) 0 0
\(231\) 317.797 235.129i 1.37574 1.01787i
\(232\) 0 0
\(233\) 155.825 + 269.897i 0.668778 + 1.15836i 0.978246 + 0.207448i \(0.0665159\pi\)
−0.309468 + 0.950910i \(0.600151\pi\)
\(234\) 0 0
\(235\) −170.753 98.5843i −0.726608 0.419507i
\(236\) 0 0
\(237\) 529.410 2.23380
\(238\) 0 0
\(239\) 140.823 0.589218 0.294609 0.955618i \(-0.404811\pi\)
0.294609 + 0.955618i \(0.404811\pi\)
\(240\) 0 0
\(241\) −41.6447 24.0436i −0.172799 0.0997658i 0.411106 0.911588i \(-0.365143\pi\)
−0.583905 + 0.811822i \(0.698476\pi\)
\(242\) 0 0
\(243\) −139.035 240.816i −0.572162 0.991014i
\(244\) 0 0
\(245\) −156.298 167.647i −0.637950 0.684275i
\(246\) 0 0
\(247\) 112.642 + 195.101i 0.456039 + 0.789883i
\(248\) 0 0
\(249\) 96.7357 167.551i 0.388497 0.672896i
\(250\) 0 0
\(251\) −152.080 −0.605895 −0.302947 0.953007i \(-0.597971\pi\)
−0.302947 + 0.953007i \(0.597971\pi\)
\(252\) 0 0
\(253\) 129.309i 0.511101i
\(254\) 0 0
\(255\) 306.046 + 176.696i 1.20018 + 0.692924i
\(256\) 0 0
\(257\) 126.153 72.8347i 0.490869 0.283403i −0.234066 0.972221i \(-0.575203\pi\)
0.724935 + 0.688817i \(0.241870\pi\)
\(258\) 0 0
\(259\) −68.7477 + 50.8645i −0.265435 + 0.196388i
\(260\) 0 0
\(261\) −183.714 + 106.068i −0.703887 + 0.406389i
\(262\) 0 0
\(263\) 176.696 306.047i 0.671850 1.16368i −0.305529 0.952183i \(-0.598833\pi\)
0.977379 0.211495i \(-0.0678333\pi\)
\(264\) 0 0
\(265\) 169.112i 0.638158i
\(266\) 0 0
\(267\) 4.33460i 0.0162345i
\(268\) 0 0
\(269\) 66.6490 115.439i 0.247766 0.429143i −0.715140 0.698981i \(-0.753637\pi\)
0.962906 + 0.269838i \(0.0869703\pi\)
\(270\) 0 0
\(271\) 326.342 188.414i 1.20421 0.695253i 0.242725 0.970095i \(-0.421959\pi\)
0.961489 + 0.274842i \(0.0886255\pi\)
\(272\) 0 0
\(273\) −137.310 + 315.743i −0.502969 + 1.15657i
\(274\) 0 0
\(275\) −39.4273 + 22.7634i −0.143372 + 0.0827759i
\(276\) 0 0
\(277\) −67.4788 38.9589i −0.243606 0.140646i 0.373227 0.927740i \(-0.378251\pi\)
−0.616833 + 0.787094i \(0.711585\pi\)
\(278\) 0 0
\(279\) 173.430i 0.621613i
\(280\) 0 0
\(281\) 324.564 1.15503 0.577516 0.816380i \(-0.304022\pi\)
0.577516 + 0.816380i \(0.304022\pi\)
\(282\) 0 0
\(283\) −149.741 + 259.359i −0.529119 + 0.916462i 0.470304 + 0.882505i \(0.344144\pi\)
−0.999423 + 0.0339572i \(0.989189\pi\)
\(284\) 0 0
\(285\) −160.425 277.864i −0.562895 0.974963i
\(286\) 0 0
\(287\) −17.4960 153.639i −0.0609618 0.535328i
\(288\) 0 0
\(289\) 46.0604 + 79.7789i 0.159378 + 0.276052i
\(290\) 0 0
\(291\) 532.296 + 307.321i 1.82920 + 1.05609i
\(292\) 0 0
\(293\) −81.7250 −0.278925 −0.139463 0.990227i \(-0.544537\pi\)
−0.139463 + 0.990227i \(0.544537\pi\)
\(294\) 0 0
\(295\) 11.2589 0.0381657
\(296\) 0 0
\(297\) −147.901 85.3908i −0.497984 0.287511i
\(298\) 0 0
\(299\) 56.3108 + 97.5332i 0.188331 + 0.326198i
\(300\) 0 0
\(301\) 63.2035 + 555.013i 0.209979 + 1.84390i
\(302\) 0 0
\(303\) −134.719 233.340i −0.444617 0.770099i
\(304\) 0 0
\(305\) −68.3986 + 118.470i −0.224258 + 0.388425i
\(306\) 0 0
\(307\) 361.930 1.17892 0.589462 0.807796i \(-0.299340\pi\)
0.589462 + 0.807796i \(0.299340\pi\)
\(308\) 0 0
\(309\) 75.9257i 0.245714i
\(310\) 0 0
\(311\) −163.508 94.4017i −0.525751 0.303542i 0.213534 0.976936i \(-0.431503\pi\)
−0.739284 + 0.673393i \(0.764836\pi\)
\(312\) 0 0
\(313\) −22.2463 + 12.8439i −0.0710745 + 0.0410349i −0.535116 0.844779i \(-0.679732\pi\)
0.464042 + 0.885813i \(0.346399\pi\)
\(314\) 0 0
\(315\) 78.0351 179.440i 0.247730 0.569651i
\(316\) 0 0
\(317\) −432.257 + 249.564i −1.36359 + 0.787268i −0.990100 0.140367i \(-0.955172\pi\)
−0.373489 + 0.927635i \(0.621838\pi\)
\(318\) 0 0
\(319\) −259.019 + 448.634i −0.811972 + 1.40638i
\(320\) 0 0
\(321\) 173.174i 0.539484i
\(322\) 0 0
\(323\) 346.027i 1.07129i
\(324\) 0 0
\(325\) 19.8258 34.3393i 0.0610025 0.105659i
\(326\) 0 0
\(327\) 189.705 109.526i 0.580138 0.334943i
\(328\) 0 0
\(329\) −237.195 + 175.494i −0.720958 + 0.533417i
\(330\) 0 0
\(331\) −216.384 + 124.930i −0.653729 + 0.377431i −0.789883 0.613257i \(-0.789859\pi\)
0.136154 + 0.990688i \(0.456526\pi\)
\(332\) 0 0
\(333\) −63.2268 36.5040i −0.189870 0.109622i
\(334\) 0 0
\(335\) 190.288i 0.568025i
\(336\) 0 0
\(337\) −84.4039 −0.250457 −0.125228 0.992128i \(-0.539966\pi\)
−0.125228 + 0.992128i \(0.539966\pi\)
\(338\) 0 0
\(339\) −364.992 + 632.185i −1.07667 + 1.86485i
\(340\) 0 0
\(341\) 211.760 + 366.778i 0.620996 + 1.07560i
\(342\) 0 0
\(343\) −323.346 + 114.440i −0.942699 + 0.333645i
\(344\) 0 0
\(345\) −80.1982 138.907i −0.232459 0.402630i
\(346\) 0 0
\(347\) −326.707 188.624i −0.941518 0.543586i −0.0510824 0.998694i \(-0.516267\pi\)
−0.890436 + 0.455109i \(0.849600\pi\)
\(348\) 0 0
\(349\) 400.193 1.14668 0.573342 0.819316i \(-0.305647\pi\)
0.573342 + 0.819316i \(0.305647\pi\)
\(350\) 0 0
\(351\) 148.743 0.423768
\(352\) 0 0
\(353\) 256.293 + 147.971i 0.726043 + 0.419181i 0.816973 0.576676i \(-0.195650\pi\)
−0.0909296 + 0.995857i \(0.528984\pi\)
\(354\) 0 0
\(355\) −52.8980 91.6220i −0.149008 0.258090i
\(356\) 0 0
\(357\) 425.132 314.543i 1.19085 0.881074i
\(358\) 0 0
\(359\) −102.587 177.686i −0.285757 0.494946i 0.687035 0.726624i \(-0.258912\pi\)
−0.972793 + 0.231678i \(0.925578\pi\)
\(360\) 0 0
\(361\) 23.4181 40.5613i 0.0648701 0.112358i
\(362\) 0 0
\(363\) 355.904 0.980451
\(364\) 0 0
\(365\) 357.341i 0.979017i
\(366\) 0 0
\(367\) 306.216 + 176.794i 0.834377 + 0.481728i 0.855349 0.518052i \(-0.173343\pi\)
−0.0209719 + 0.999780i \(0.506676\pi\)
\(368\) 0 0
\(369\) 114.325 66.0054i 0.309823 0.178876i
\(370\) 0 0
\(371\) 232.077 + 100.926i 0.625545 + 0.272037i
\(372\) 0 0
\(373\) 310.062 179.014i 0.831264 0.479931i −0.0230210 0.999735i \(-0.507328\pi\)
0.854285 + 0.519804i \(0.173995\pi\)
\(374\) 0 0
\(375\) −254.510 + 440.824i −0.678693 + 1.17553i
\(376\) 0 0
\(377\) 451.187i 1.19678i
\(378\) 0 0
\(379\) 514.679i 1.35799i −0.734142 0.678996i \(-0.762415\pi\)
0.734142 0.678996i \(-0.237585\pi\)
\(380\) 0 0
\(381\) −88.7260 + 153.678i −0.232877 + 0.403354i
\(382\) 0 0
\(383\) −450.193 + 259.919i −1.17544 + 0.678639i −0.954955 0.296752i \(-0.904097\pi\)
−0.220483 + 0.975391i \(0.570763\pi\)
\(384\) 0 0
\(385\) −54.0657 474.771i −0.140430 1.23317i
\(386\) 0 0
\(387\) −412.992 + 238.441i −1.06716 + 0.616127i
\(388\) 0 0
\(389\) 91.3278 + 52.7281i 0.234776 + 0.135548i 0.612773 0.790259i \(-0.290054\pi\)
−0.377997 + 0.925807i \(0.623387\pi\)
\(390\) 0 0
\(391\) 172.982i 0.442410i
\(392\) 0 0
\(393\) −468.241 −1.19145
\(394\) 0 0
\(395\) 319.957 554.182i 0.810018 1.40299i
\(396\) 0 0
\(397\) −185.762 321.749i −0.467914 0.810450i 0.531414 0.847112i \(-0.321661\pi\)
−0.999328 + 0.0366619i \(0.988328\pi\)
\(398\) 0 0
\(399\) −477.063 + 54.3267i −1.19565 + 0.136157i
\(400\) 0 0
\(401\) −149.636 259.177i −0.373157 0.646327i 0.616893 0.787047i \(-0.288391\pi\)
−0.990049 + 0.140721i \(0.955058\pi\)
\(402\) 0 0
\(403\) −319.446 184.433i −0.792671 0.457649i
\(404\) 0 0
\(405\) −463.421 −1.14425
\(406\) 0 0
\(407\) −178.287 −0.438052
\(408\) 0 0
\(409\) −17.6410 10.1850i −0.0431320 0.0249023i 0.478279 0.878208i \(-0.341261\pi\)
−0.521411 + 0.853306i \(0.674594\pi\)
\(410\) 0 0
\(411\) −281.033 486.764i −0.683780 1.18434i
\(412\) 0 0
\(413\) 6.71929 15.4509i 0.0162695 0.0374113i
\(414\) 0 0
\(415\) −116.927 202.524i −0.281753 0.488010i
\(416\) 0 0
\(417\) −167.083 + 289.396i −0.400678 + 0.693994i
\(418\) 0 0
\(419\) 183.085 0.436956 0.218478 0.975842i \(-0.429891\pi\)
0.218478 + 0.975842i \(0.429891\pi\)
\(420\) 0 0
\(421\) 293.022i 0.696014i −0.937492 0.348007i \(-0.886859\pi\)
0.937492 0.348007i \(-0.113141\pi\)
\(422\) 0 0
\(423\) −218.147 125.947i −0.515714 0.297748i
\(424\) 0 0
\(425\) −52.7438 + 30.4517i −0.124103 + 0.0716510i
\(426\) 0 0
\(427\) 121.759 + 164.568i 0.285150 + 0.385405i
\(428\) 0 0
\(429\) −621.636 + 358.902i −1.44903 + 0.836601i
\(430\) 0 0
\(431\) −37.6108 + 65.1439i −0.0872641 + 0.151146i −0.906354 0.422520i \(-0.861146\pi\)
0.819090 + 0.573666i \(0.194479\pi\)
\(432\) 0 0
\(433\) 506.209i 1.16907i 0.811367 + 0.584536i \(0.198724\pi\)
−0.811367 + 0.584536i \(0.801276\pi\)
\(434\) 0 0
\(435\) 642.583i 1.47720i
\(436\) 0 0
\(437\) −78.5269 + 136.013i −0.179696 + 0.311242i
\(438\) 0 0
\(439\) 141.358 81.6130i 0.322000 0.185907i −0.330284 0.943882i \(-0.607144\pi\)
0.652284 + 0.757975i \(0.273811\pi\)
\(440\) 0 0
\(441\) −199.680 214.180i −0.452788 0.485668i
\(442\) 0 0
\(443\) 98.4732 56.8535i 0.222287 0.128338i −0.384722 0.923033i \(-0.625703\pi\)
0.607009 + 0.794695i \(0.292369\pi\)
\(444\) 0 0
\(445\) −4.53742 2.61968i −0.0101964 0.00588692i
\(446\) 0 0
\(447\) 846.952i 1.89475i
\(448\) 0 0
\(449\) 391.120 0.871091 0.435546 0.900167i \(-0.356555\pi\)
0.435546 + 0.900167i \(0.356555\pi\)
\(450\) 0 0
\(451\) 161.186 279.183i 0.357398 0.619031i
\(452\) 0 0
\(453\) −161.201 279.208i −0.355851 0.616353i
\(454\) 0 0
\(455\) 247.531 + 334.559i 0.544025 + 0.735296i
\(456\) 0 0
\(457\) −286.893 496.913i −0.627774 1.08734i −0.987997 0.154471i \(-0.950633\pi\)
0.360223 0.932866i \(-0.382701\pi\)
\(458\) 0 0
\(459\) −197.855 114.231i −0.431056 0.248870i
\(460\) 0 0
\(461\) 847.131 1.83759 0.918797 0.394729i \(-0.129162\pi\)
0.918797 + 0.394729i \(0.129162\pi\)
\(462\) 0 0
\(463\) −109.055 −0.235539 −0.117770 0.993041i \(-0.537574\pi\)
−0.117770 + 0.993041i \(0.537574\pi\)
\(464\) 0 0
\(465\) 454.958 + 262.670i 0.978404 + 0.564882i
\(466\) 0 0
\(467\) 321.205 + 556.343i 0.687805 + 1.19131i 0.972546 + 0.232709i \(0.0747590\pi\)
−0.284741 + 0.958604i \(0.591908\pi\)
\(468\) 0 0
\(469\) −261.138 113.564i −0.556798 0.242141i
\(470\) 0 0
\(471\) 68.5771 + 118.779i 0.145599 + 0.252185i
\(472\) 0 0
\(473\) −582.278 + 1008.53i −1.23103 + 2.13221i
\(474\) 0 0
\(475\) 55.2952 0.116411
\(476\) 0 0
\(477\) 216.050i 0.452936i
\(478\) 0 0
\(479\) 367.909 + 212.412i 0.768077 + 0.443449i 0.832188 0.554493i \(-0.187088\pi\)
−0.0641112 + 0.997943i \(0.520421\pi\)
\(480\) 0 0
\(481\) 134.476 77.6397i 0.279576 0.161413i
\(482\) 0 0
\(483\) −238.489 + 27.1585i −0.493766 + 0.0562288i
\(484\) 0 0
\(485\) 643.403 371.469i 1.32660 0.765915i
\(486\) 0 0
\(487\) 388.616 673.103i 0.797980 1.38214i −0.122949 0.992413i \(-0.539235\pi\)
0.920929 0.389729i \(-0.127431\pi\)
\(488\) 0 0
\(489\) 40.4588i 0.0827379i
\(490\) 0 0
\(491\) 476.370i 0.970203i 0.874458 + 0.485102i \(0.161217\pi\)
−0.874458 + 0.485102i \(0.838783\pi\)
\(492\) 0 0
\(493\) −346.502 + 600.160i −0.702845 + 1.21736i
\(494\) 0 0
\(495\) 353.283 203.968i 0.713702 0.412056i
\(496\) 0 0
\(497\) −157.305 + 17.9135i −0.316509 + 0.0360432i
\(498\) 0 0
\(499\) 377.065 217.698i 0.755641 0.436269i −0.0720876 0.997398i \(-0.522966\pi\)
0.827728 + 0.561129i \(0.189633\pi\)
\(500\) 0 0
\(501\) 264.374 + 152.636i 0.527693 + 0.304663i
\(502\) 0 0
\(503\) 375.404i 0.746329i 0.927765 + 0.373165i \(0.121727\pi\)
−0.927765 + 0.373165i \(0.878273\pi\)
\(504\) 0 0
\(505\) −325.678 −0.644907
\(506\) 0 0
\(507\) −14.4185 + 24.9735i −0.0284388 + 0.0492574i
\(508\) 0 0
\(509\) 73.9117 + 128.019i 0.145210 + 0.251510i 0.929451 0.368945i \(-0.120281\pi\)
−0.784242 + 0.620456i \(0.786948\pi\)
\(510\) 0 0
\(511\) −490.389 213.261i −0.959666 0.417340i
\(512\) 0 0
\(513\) 103.713 + 179.636i 0.202169 + 0.350167i
\(514\) 0 0
\(515\) 79.4784 + 45.8869i 0.154327 + 0.0891007i
\(516\) 0 0
\(517\) −615.131 −1.18981
\(518\) 0 0
\(519\) 742.404 1.43045
\(520\) 0 0
\(521\) 755.302 + 436.074i 1.44972 + 0.836994i 0.998464 0.0554019i \(-0.0176440\pi\)
0.451253 + 0.892396i \(0.350977\pi\)
\(522\) 0 0
\(523\) 178.600 + 309.344i 0.341491 + 0.591480i 0.984710 0.174202i \(-0.0557347\pi\)
−0.643219 + 0.765683i \(0.722401\pi\)
\(524\) 0 0
\(525\) 50.2642 + 67.9364i 0.0957414 + 0.129403i
\(526\) 0 0
\(527\) 283.281 + 490.657i 0.537535 + 0.931038i
\(528\) 0 0
\(529\) 225.244 390.133i 0.425791 0.737492i
\(530\) 0 0
\(531\) 14.3839 0.0270883
\(532\) 0 0
\(533\) 280.771i 0.526776i
\(534\) 0 0
\(535\) −181.278 104.661i −0.338836 0.195627i
\(536\) 0 0
\(537\) −234.293 + 135.269i −0.436299 + 0.251897i
\(538\) 0 0
\(539\) −683.808 209.147i −1.26866 0.388028i
\(540\) 0 0
\(541\) 807.198 466.036i 1.49205 0.861434i 0.492089 0.870545i \(-0.336233\pi\)
0.999958 + 0.00911085i \(0.00290011\pi\)
\(542\) 0 0
\(543\) −664.912 + 1151.66i −1.22452 + 2.12092i
\(544\) 0 0
\(545\) 264.776i 0.485827i
\(546\) 0 0
\(547\) 151.397i 0.276778i 0.990378 + 0.138389i \(0.0441924\pi\)
−0.990378 + 0.138389i \(0.955808\pi\)
\(548\) 0 0
\(549\) −87.3832 + 151.352i −0.159168 + 0.275687i
\(550\) 0 0
\(551\) 544.896 314.596i 0.988922 0.570954i
\(552\) 0 0
\(553\) −569.569 769.821i −1.02996 1.39208i
\(554\) 0 0
\(555\) −191.522 + 110.575i −0.345084 + 0.199234i
\(556\) 0 0
\(557\) −775.593 447.789i −1.39245 0.803929i −0.398861 0.917011i \(-0.630594\pi\)
−0.993586 + 0.113082i \(0.963928\pi\)
\(558\) 0 0
\(559\) 1014.27i 1.81444i
\(560\) 0 0
\(561\) 1102.52 1.96527
\(562\) 0 0
\(563\) 139.958 242.414i 0.248592 0.430575i −0.714543 0.699591i \(-0.753365\pi\)
0.963136 + 0.269017i \(0.0866987\pi\)
\(564\) 0 0
\(565\) 441.177 + 764.142i 0.780845 + 1.35246i
\(566\) 0 0
\(567\) −276.569 + 635.966i −0.487776 + 1.12163i
\(568\) 0 0
\(569\) −160.963 278.796i −0.282887 0.489975i 0.689207 0.724564i \(-0.257959\pi\)
−0.972095 + 0.234589i \(0.924626\pi\)
\(570\) 0 0
\(571\) 712.583 + 411.410i 1.24796 + 0.720508i 0.970702 0.240288i \(-0.0772419\pi\)
0.277255 + 0.960796i \(0.410575\pi\)
\(572\) 0 0
\(573\) −540.928 −0.944027
\(574\) 0 0
\(575\) 27.6427 0.0480742
\(576\) 0 0
\(577\) 833.162 + 481.027i 1.44396 + 0.833668i 0.998111 0.0614420i \(-0.0195699\pi\)
0.445845 + 0.895110i \(0.352903\pi\)
\(578\) 0 0
\(579\) 44.3551 + 76.8253i 0.0766064 + 0.132686i
\(580\) 0 0
\(581\) −347.712 + 39.5966i −0.598472 + 0.0681524i
\(582\) 0 0
\(583\) 263.800 + 456.914i 0.452486 + 0.783729i
\(584\) 0 0
\(585\) −177.646 + 307.692i −0.303669 + 0.525970i
\(586\) 0 0
\(587\) −885.638 −1.50875 −0.754377 0.656442i \(-0.772061\pi\)
−0.754377 + 0.656442i \(0.772061\pi\)
\(588\) 0 0
\(589\) 514.392i 0.873331i
\(590\) 0 0
\(591\) 964.496 + 556.852i 1.63197 + 0.942220i
\(592\) 0 0
\(593\) 290.818 167.904i 0.490418 0.283143i −0.234330 0.972157i \(-0.575290\pi\)
0.724748 + 0.689014i \(0.241956\pi\)
\(594\) 0 0
\(595\) −72.3263 635.124i −0.121557 1.06743i
\(596\) 0 0
\(597\) 219.457 126.704i 0.367600 0.212234i
\(598\) 0 0
\(599\) −30.1532 + 52.2269i −0.0503393 + 0.0871902i −0.890097 0.455771i \(-0.849364\pi\)
0.839758 + 0.542961i \(0.182697\pi\)
\(600\) 0 0
\(601\) 509.153i 0.847176i −0.905855 0.423588i \(-0.860770\pi\)
0.905855 0.423588i \(-0.139230\pi\)
\(602\) 0 0
\(603\) 243.105i 0.403159i
\(604\) 0 0
\(605\) 215.096 372.557i 0.355530 0.615797i
\(606\) 0 0
\(607\) 900.363 519.825i 1.48330 0.856384i 0.483480 0.875355i \(-0.339373\pi\)
0.999820 + 0.0189717i \(0.00603923\pi\)
\(608\) 0 0
\(609\) 881.835 + 383.493i 1.44800 + 0.629709i
\(610\) 0 0
\(611\) 463.973 267.875i 0.759366 0.438420i
\(612\) 0 0
\(613\) −172.277 99.4641i −0.281039 0.162258i 0.352855 0.935678i \(-0.385211\pi\)
−0.633894 + 0.773420i \(0.718544\pi\)
\(614\) 0 0
\(615\) 399.876i 0.650206i
\(616\) 0 0
\(617\) 136.689 0.221538 0.110769 0.993846i \(-0.464669\pi\)
0.110769 + 0.993846i \(0.464669\pi\)
\(618\) 0 0
\(619\) −230.938 + 399.997i −0.373083 + 0.646199i −0.990038 0.140799i \(-0.955033\pi\)
0.616955 + 0.786998i \(0.288366\pi\)
\(620\) 0 0
\(621\) 51.8472 + 89.8019i 0.0834898 + 0.144609i
\(622\) 0 0
\(623\) −6.30299 + 4.66341i −0.0101172 + 0.00748541i
\(624\) 0 0
\(625\) 268.638 + 465.294i 0.429821 + 0.744471i
\(626\) 0 0
\(627\) −866.888 500.498i −1.38260 0.798242i
\(628\) 0 0
\(629\) −238.503 −0.379178
\(630\) 0 0
\(631\) −1042.33 −1.65187 −0.825933 0.563768i \(-0.809351\pi\)
−0.825933 + 0.563768i \(0.809351\pi\)
\(632\) 0 0
\(633\) −59.9853 34.6325i −0.0947635 0.0547117i
\(634\) 0 0
\(635\) 107.246 + 185.755i 0.168891 + 0.292528i
\(636\) 0 0
\(637\) 606.852 140.029i 0.952672 0.219826i
\(638\) 0 0
\(639\) −67.5803 117.052i −0.105759 0.183181i
\(640\) 0 0
\(641\) −61.3334 + 106.233i −0.0956840 + 0.165730i −0.909894 0.414841i \(-0.863837\pi\)
0.814210 + 0.580571i \(0.197170\pi\)
\(642\) 0 0
\(643\) −720.813 −1.12102 −0.560508 0.828149i \(-0.689394\pi\)
−0.560508 + 0.828149i \(0.689394\pi\)
\(644\) 0 0
\(645\) 1444.53i 2.23959i
\(646\) 0 0
\(647\) −510.825 294.925i −0.789528 0.455834i 0.0502683 0.998736i \(-0.483992\pi\)
−0.839796 + 0.542901i \(0.817326\pi\)
\(648\) 0 0
\(649\) 30.4198 17.5629i 0.0468717 0.0270614i
\(650\) 0 0
\(651\) 631.988 467.590i 0.970796 0.718265i
\(652\) 0 0
\(653\) −215.294 + 124.300i −0.329700 + 0.190352i −0.655708 0.755015i \(-0.727630\pi\)
0.326008 + 0.945367i \(0.394296\pi\)
\(654\) 0 0
\(655\) −282.989 + 490.151i −0.432044 + 0.748322i
\(656\) 0 0
\(657\) 456.524i 0.694862i
\(658\) 0 0
\(659\) 640.918i 0.972562i −0.873802 0.486281i \(-0.838353\pi\)
0.873802 0.486281i \(-0.161647\pi\)
\(660\) 0 0
\(661\) 483.321 837.137i 0.731197 1.26647i −0.225175 0.974318i \(-0.572295\pi\)
0.956372 0.292152i \(-0.0943712\pi\)
\(662\) 0 0
\(663\) −831.593 + 480.120i −1.25429 + 0.724163i
\(664\) 0 0
\(665\) −231.451 + 532.218i −0.348047 + 0.800328i
\(666\) 0 0
\(667\) 272.399 157.270i 0.408395 0.235787i
\(668\) 0 0
\(669\) 867.927 + 501.098i 1.29735 + 0.749025i
\(670\) 0 0
\(671\) 426.783i 0.636040i
\(672\) 0 0
\(673\) −754.537 −1.12115 −0.560577 0.828102i \(-0.689421\pi\)
−0.560577 + 0.828102i \(0.689421\pi\)
\(674\) 0 0
\(675\) 18.2543 31.6173i 0.0270433 0.0468404i
\(676\) 0 0
\(677\) −380.978 659.874i −0.562745 0.974703i −0.997256 0.0740362i \(-0.976412\pi\)
0.434511 0.900667i \(1.64308\pi\)
\(678\) 0 0
\(679\) −125.795 1104.65i −0.185265 1.62688i
\(680\) 0 0
\(681\) −227.054 393.269i −0.333413 0.577488i
\(682\) 0 0
\(683\) 657.604 + 379.668i 0.962817 + 0.555883i 0.897039 0.441952i \(-0.145714\pi\)
0.0657781 + 0.997834i \(0.479047\pi\)
\(684\) 0 0
\(685\) −679.387 −0.991806
\(686\) 0 0
\(687\) 337.047 0.490607
\(688\) 0 0
\(689\) −397.951 229.757i −0.577577 0.333464i
\(690\) 0 0
\(691\) 245.076 + 424.484i 0.354669 + 0.614304i 0.987061 0.160344i \(-0.0512604\pi\)
−0.632393 + 0.774648i \(0.717927\pi\)
\(692\) 0 0
\(693\) −69.0721 606.548i −0.0996711 0.875249i
\(694\) 0 0
\(695\) 201.958 + 349.801i 0.290587 + 0.503311i
\(696\) 0 0
\(697\) 215.627 373.477i 0.309364 0.535835i
\(698\) 0 0
\(699\) 1206.05 1.72539
\(700\) 0 0
\(701\) 577.533i 0.823870i 0.911213 + 0.411935i \(0.135147\pi\)
−0.911213 + 0.411935i \(0.864853\pi\)
\(702\) 0 0
\(703\) 187.530 + 108.271i 0.266757 + 0.154012i
\(704\) 0 0
\(705\) −660.793 + 381.509i −0.937295 + 0.541148i
\(706\) 0 0
\(707\) −194.364 + 446.937i −0.274914 + 0.632160i
\(708\) 0 0
\(709\) −615.814 + 355.540i −0.868567 + 0.501467i −0.866872 0.498531i \(-0.833873\pi\)
−0.00169497 + 0.999999i \(0.500540\pi\)
\(710\) 0 0
\(711\) 408.764 708.000i 0.574914 0.995781i
\(712\) 0 0
\(713\) 257.150i 0.360659i
\(714\) 0 0
\(715\) 867.631i 1.21347i
\(716\) 0 0
\(717\) 272.484 471.957i 0.380034 0.658238i
\(718\) 0 0
\(719\) 150.440 86.8564i 0.209235 0.120802i −0.391721 0.920084i \(-0.628120\pi\)
0.600956 + 0.799282i \(0.294787\pi\)
\(720\) 0 0
\(721\) 110.404 81.6852i 0.153127 0.113294i
\(722\) 0 0
\(723\) −161.160 + 93.0457i −0.222904 + 0.128694i
\(724\) 0 0
\(725\) −95.9059 55.3713i −0.132284 0.0763742i
\(726\) 0 0
\(727\) 1056.57i 1.45333i 0.686993 + 0.726664i \(0.258930\pi\)
−0.686993 + 0.726664i \(0.741070\pi\)
\(728\) 0 0
\(729\) −184.457 −0.253028
\(730\) 0 0
\(731\) −778.941 + 1349.17i −1.06558 + 1.84564i
\(732\) 0 0
\(733\) 115.299 + 199.703i 0.157297 + 0.272446i 0.933893 0.357553i \(-0.116389\pi\)
−0.776596 + 0.629999i \(0.783055\pi\)
\(734\) 0 0
\(735\) −864.283 + 199.431i −1.17589 + 0.271334i
\(736\) 0 0
\(737\) −296.833 514.130i −0.402758 0.697598i
\(738\) 0 0
\(739\) −77.4971 44.7430i −0.104868 0.0605453i 0.446649 0.894709i \(-0.352617\pi\)
−0.551517 + 0.834164i \(0.685951\pi\)
\(740\) 0 0
\(741\) 871.820 1.17654
\(742\) 0 0
\(743\) 236.120 0.317793 0.158897 0.987295i \(-0.449206\pi\)
0.158897 + 0.987295i \(0.449206\pi\)
\(744\) 0 0
\(745\) −886.581 511.868i −1.19004 0.687071i
\(746\) 0 0
\(747\) −149.382 258.737i −0.199976 0.346368i
\(748\) 0 0
\(749\) −251.815 + 186.311i −0.336202 + 0.248746i
\(750\) 0 0
\(751\) −717.692 1243.08i −0.955649 1.65523i −0.732877 0.680361i \(-0.761823\pi\)
−0.222772 0.974871i \(-0.571510\pi\)
\(752\) 0 0
\(753\) −294.265 + 509.682i −0.390790 + 0.676868i
\(754\) 0 0
\(755\) −389.696 −0.516154
\(756\) 0 0
\(757\) 692.645i 0.914987i 0.889213 + 0.457494i \(0.151253\pi\)
−0.889213 + 0.457494i \(0.848747\pi\)
\(758\) 0 0
\(759\) −433.367 250.204i −0.570971 0.329650i
\(760\) 0 0
\(761\) −999.810 + 577.241i −1.31381 + 0.758529i −0.982725 0.185071i \(-0.940748\pi\)
−0.331086 + 0.943601i \(0.607415\pi\)
\(762\) 0 0
\(763\) −363.359 158.018i −0.476224 0.207101i
\(764\) 0 0
\(765\) 472.603 272.858i 0.617782 0.356677i
\(766\) 0 0
\(767\) −15.2964 + 26.4942i −0.0199432 + 0.0345426i
\(768\) 0 0
\(769\) 894.095i 1.16267i 0.813663 + 0.581336i \(0.197470\pi\)
−0.813663 + 0.581336i \(0.802530\pi\)
\(770\) 0 0
\(771\) 563.723i 0.731158i
\(772\) 0 0
\(773\) −464.538 + 804.603i −0.600954 + 1.04088i 0.391722 + 0.920083i \(0.371879\pi\)
−0.992677 + 0.120800i \(0.961454\pi\)
\(774\) 0 0
\(775\) −78.4073 + 45.2685i −0.101171 + 0.0584109i
\(776\) 0 0
\(777\) 37.4454 + 328.822i 0.0481922 + 0.423194i
\(778\) 0 0
\(779\) −339.086 + 195.772i −0.435284 + 0.251311i
\(780\) 0 0
\(781\) −285.844 165.032i −0.365998 0.211309i
\(782\) 0 0
\(783\) 415.422i 0.530552i
\(784\) 0 0
\(785\) 165.782 0.211188
\(786\) 0 0
\(787\) 693.013 1200.33i 0.880576 1.52520i 0.0298746 0.999554i \(-0.490489\pi\)
0.850702