Properties

Label 224.3.n.a.17.3
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 17.3
Character \(\chi\) \(=\) 224.17
Dual form 224.3.n.a.145.3

$q$-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 \(0.389801\pi\)
−0.984306 + 0.176469i \(0.943532\pi\)
\(4\) 0 0
\(5\) 2.33882 + 4.05096i 0.467764 + 0.810191i 0.999322 0.0368311i \(-0.0117264\pi\)
−0.531557 + 0.847022i \(0.678393\pi\)
\(6\) 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 0.948627 0.316396i \(-0.102473\pi\)
0.200306 + 0.979733i \(0.435806\pi\)
\(12\) 0 0
\(13\) −12.7102 −0.977705 −0.488853 0.872366i \(-0.662584\pi\)
−0.488853 + 0.872366i \(0.662584\pi\)
\(14\) 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 0.532827 0.846224i \(-0.321130\pi\)
−0.999265 + 0.0383291i \(0.987796\pi\)
\(20\) 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 \(0.209649\pi\)
−0.790830 + 0.612036i \(0.790351\pi\)
\(30\) 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 −0.636114 0.771595i \(-0.719459\pi\)
0.350163 + 0.936689i \(0.386126\pi\)
\(38\) 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 \(0.378395\pi\)
−0.372809 + 0.927908i \(0.621605\pi\)
\(44\) 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 0.765393 0.643563i \(-0.222545\pi\)
−0.174645 + 0.984631i \(0.555878\pi\)
\(54\) 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 −0.855646 0.517561i \(-0.826840\pi\)
0.876044 + 0.482231i \(0.160173\pi\)
\(60\) 0 0
\(61\) 14.6224 + 25.3268i 0.239712 + 0.415194i 0.960632 0.277825i \(-0.0896136\pi\)
−0.720919 + 0.693019i \(0.756280\pi\)
\(62\) 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 0.213490 0.976945i \(-0.431517\pi\)
−0.739315 + 0.673360i \(0.764850\pi\)
\(68\) 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 \(-0.597377\pi\)
−0.301170 + 0.953571i \(0.597377\pi\)
\(84\) 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 −0.985295 0.170864i \(-0.945344\pi\)
0.640620 + 0.767858i \(0.278678\pi\)
\(102\) 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 −0.670040 0.742325i \(-0.733723\pi\)
0.307852 + 0.951434i \(0.400390\pi\)
\(108\) 0 0
\(109\) −49.0210 28.3023i −0.449734 0.259654i 0.257984 0.966149i \(-0.416942\pi\)
−0.707718 + 0.706495i \(0.750275\pi\)
\(110\) 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 0.999052 0.0435409i \(-0.0138639\pi\)
−0.537233 + 0.843434i \(0.680531\pi\)
\(132\) 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 \(-0.399466\pi\)
0.310613 + 0.950537i \(0.399466\pi\)
\(140\) 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 −0.975374 0.220556i \(-0.929213\pi\)
−0.296680 + 0.954977i \(0.595879\pi\)
\(150\) 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 −0.804056 0.594554i \(-0.797329\pi\)
0.916927 + 0.399056i \(0.130662\pi\)
\(158\) 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 −0.527516 0.849545i \(-0.676877\pi\)
0.471969 + 0.881615i \(0.343543\pi\)
\(164\) 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 \(-0.979593\pi\)
0.443490 0.896279i \(1.64626\pi\)
\(174\) 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 0.659488 0.751715i \(-0.270773\pi\)
−0.321261 + 0.946991i \(0.604107\pi\)
\(180\) 0 0
\(181\) 343.635 1.89853 0.949267 0.314472i \(-0.101827\pi\)
0.949267 + 0.314472i \(0.101827\pi\)
\(182\) 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 \(-0.739322\pi\)
0.682992 0.730426i \(-0.260678\pi\)
\(198\) 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 \(0.0135047\pi\)
−0.999100 + 0.0424135i \(0.986495\pi\)
\(212\) 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 −0.965832 0.259171i \(-0.916551\pi\)
0.707364 + 0.706849i \(0.249884\pi\)
\(228\) 0 0
\(229\) −43.5475 75.4264i −0.190164 0.329373i 0.755141 0.655563i \(-0.227569\pi\)
−0.945304 + 0.326190i \(0.894235\pi\)
\(230\) 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 \(-0.402029\pi\)
0.302947 + 0.953007i \(0.402029\pi\)
\(252\) 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 −0.962906 0.269838i \(-0.913030\pi\)
0.715140 + 0.698981i \(0.246363\pi\)
\(270\) 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 0.616833 0.787094i \(-0.288415\pi\)
−0.373227 + 0.927740i \(0.621749\pi\)
\(278\) 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 \(-0.655856\pi\)
0.999423 0.0339572i \(-0.0108110\pi\)
\(284\) 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 \(-0.455463\pi\)
0.139463 + 0.990227i \(0.455463\pi\)
\(294\) 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 \(-0.700660\pi\)
−0.589462 + 0.807796i \(0.700660\pi\)
\(308\) 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 0.373489 0.927635i \(-0.378162\pi\)
0.990100 + 0.140367i \(0.0448282\pi\)
\(318\) 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 −0.136154 0.990688i \(-0.543474\pi\)
0.789883 + 0.613257i \(0.210141\pi\)
\(332\) 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 0.890436 0.455109i \(-0.150400\pi\)
0.0510824 + 0.998694i \(0.483733\pi\)
\(348\) 0 0
\(349\) −400.193 −1.14668 −0.573342 0.819316i \(-0.694353\pi\)
−0.573342 + 0.819316i \(0.694353\pi\)
\(350\) 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 −0.854285 0.519804i \(-0.826005\pi\)
0.0230210 + 0.999735i \(0.492672\pi\)
\(374\) 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 \(0.237585\pi\)
−0.734142 + 0.678996i \(0.762415\pi\)
\(380\) 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 0.377997 0.925807i \(-0.376613\pi\)
−0.612773 + 0.790259i \(0.709946\pi\)
\(390\) 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 0.999328 0.0366619i \(-0.0116725\pi\)
−0.531414 + 0.847112i \(0.678339\pi\)
\(398\) 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 \(-0.570109\pi\)
−0.218478 + 0.975842i \(0.570109\pi\)
\(420\) 0 0
\(421\) 293.022i 0.696014i 0.937492 + 0.348007i \(0.113141\pi\)
−0.937492 + 0.348007i \(0.886859\pi\)
\(422\) 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 −0.607009 0.794695i \(-0.707631\pi\)
0.384722 + 0.923033i \(0.374297\pi\)
\(444\) 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 \(-0.870838\pi\)
−0.918797 + 0.394729i \(0.870838\pi\)
\(462\) 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 \(-0.925241\pi\)
0.284741 0.958604i \(1.59191\pi\)
\(468\) 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 \(-0.838783\pi\)
0.874458 0.485102i \(-0.161217\pi\)
\(492\) 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 −0.827728 0.561129i \(-0.810367\pi\)
0.0720876 + 0.997398i \(0.477034\pi\)
\(500\) 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 0.784242 0.620456i \(-0.213052\pi\)
−0.929451 + 0.368945i \(0.879719\pi\)
\(510\) 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 0.643219 0.765683i \(-0.277599\pi\)
−0.984710 + 0.174202i \(0.944265\pi\)
\(524\) 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 −0.999958 0.00911085i \(-0.997100\pi\)
−0.492089 + 0.870545i \(0.663767\pi\)
\(542\) 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 \(-0.955808\pi\)
0.990378 0.138389i \(-0.0441924\pi\)
\(548\) 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 0.993586 0.113082i \(-0.0360722\pi\)
0.398861 + 0.917011i \(0.369406\pi\)
\(558\) 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 −0.963136 0.269017i \(-0.913301\pi\)
0.714543 + 0.699591i \(0.246635\pi\)
\(564\) 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 −0.277255 0.960796i \(-0.589425\pi\)
−0.970702 + 0.240288i \(0.922758\pi\)
\(572\) 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 \(-0.227939\pi\)
0.754377 + 0.656442i \(0.227939\pi\)
\(588\) 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 0.633894 0.773420i \(-0.281456\pi\)
−0.352855 + 0.935678i \(0.614789\pi\)
\(614\) 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 −0.616955 0.786998i \(-0.711634\pi\)
0.990038 + 0.140799i \(0.0449673\pi\)
\(620\) 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 \(-0.310606\pi\)
0.560508 + 0.828149i \(0.310606\pi\)
\(644\) 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 −0.326008 0.945367i \(-0.605704\pi\)
0.655708 + 0.755015i \(0.272370\pi\)
\(654\) 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 \(0.161647\pi\)
−0.873802 + 0.486281i \(0.838353\pi\)
\(660\) 0 0
\(661\) −483.321 + 837.137i −0.731197 + 1.26647i 0.225175 + 0.974318i \(0.427705\pi\)
−0.956372 + 0.292152i \(0.905629\pi\)
\(662\) 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 \(0.0235880\pi\)
−0.434511 + 0.900667i \(0.643079\pi\)
\(678\) 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 −0.0657781 0.997834i \(-0.520953\pi\)
−0.897039 + 0.441952i \(0.854286\pi\)
\(684\) 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 0.632393 0.774648i \(-0.282073\pi\)
−0.987061 + 0.160344i \(0.948740\pi\)
\(692\) 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 \(-0.864853\pi\)
0.911213 0.411935i \(-0.135147\pi\)
\(702\) 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 0.00169497 0.999999i \(-0.499460\pi\)
0.866872 + 0.498531i \(0.166127\pi\)
\(710\) 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 0.776596 0.629999i \(-0.216945\pi\)
−0.933893 + 0.357553i \(0.883611\pi\)
\(734\) 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 0.551517 0.834164i \(-0.314049\pi\)
−0.446649 + 0.894709i \(0.647383\pi\)
\(740\) 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 \(-0.848747\pi\)
0.889213 0.457494i \(-0.151253\pi\)
\(758\) 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 \(-0.628121\pi\)
0.992677 0.120800i \(-0.0385460\pi\)
\(774\) 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 \(0.509511\pi\)
−0.850702 + 0.525649i