Properties

Label 224.3.s.b.129.4
Level 224
Weight 3
Character 224.129
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: \( 2^{20}\cdot 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 129.4
Root \(-0.162551 + 0.910345i\) of \(x^{16} - 26 x^{14} - 16 x^{13} + 469 x^{12} + 144 x^{11} - 4526 x^{10} + 4440 x^{9} + 32608 x^{8} - 33728 x^{7} - 49760 x^{6} + 203528 x^{5} + 27401 x^{4} - 156928 x^{3} + 114964 x^{2} - 248608 x + 208849\)
Character \(\chi\) \(=\) 224.129
Dual form 224.3.s.b.33.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.729881 - 0.421397i) q^{3} +(-1.21685 + 0.702550i) q^{5} +(1.56553 + 6.82269i) q^{7} +(-4.14485 - 7.17909i) q^{9} +O(q^{10})\) \(q+(-0.729881 - 0.421397i) q^{3} +(-1.21685 + 0.702550i) q^{5} +(1.56553 + 6.82269i) q^{7} +(-4.14485 - 7.17909i) q^{9} +(-7.44562 + 12.8962i) q^{11} +2.67477i q^{13} +1.18421 q^{15} +(11.7354 + 6.77544i) q^{17} +(-25.2564 + 14.5818i) q^{19} +(1.73241 - 5.63947i) q^{21} +(11.4367 + 19.8089i) q^{23} +(-11.5128 + 19.9408i) q^{25} +14.5717i q^{27} -3.76543 q^{29} +(11.4937 + 6.63592i) q^{31} +(10.8688 - 6.27513i) q^{33} +(-6.69830 - 7.20235i) q^{35} +(-1.32272 - 2.29102i) q^{37} +(1.12714 - 1.95227i) q^{39} -45.2712i q^{41} -51.5858 q^{43} +(10.0873 + 5.82393i) q^{45} +(58.1281 - 33.5603i) q^{47} +(-44.0982 + 21.3623i) q^{49} +(-5.71030 - 9.89054i) q^{51} +(-19.9616 + 34.5744i) q^{53} -20.9237i q^{55} +24.5789 q^{57} +(-11.0804 - 6.39728i) q^{59} +(67.4084 - 38.9182i) q^{61} +(42.4918 - 39.5181i) q^{63} +(-1.87916 - 3.25480i) q^{65} +(22.9199 - 39.6985i) q^{67} -19.2775i q^{69} +40.6812 q^{71} +(55.6834 + 32.1488i) q^{73} +(16.8060 - 9.70296i) q^{75} +(-99.6431 - 30.6098i) q^{77} +(-40.2603 - 69.7329i) q^{79} +(-31.1632 + 53.9762i) q^{81} -121.864i q^{83} -19.0403 q^{85} +(2.74832 + 1.58674i) q^{87} +(-39.7614 + 22.9562i) q^{89} +(-18.2492 + 4.18744i) q^{91} +(-5.59271 - 9.68687i) q^{93} +(20.4889 - 35.4878i) q^{95} -134.268i q^{97} +123.444 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 40q^{9} + O(q^{10}) \) \( 16q + 40q^{9} - 48q^{17} - 136q^{21} + 80q^{25} - 16q^{29} - 264q^{33} + 72q^{37} + 312q^{45} + 128q^{49} + 40q^{53} + 368q^{57} + 216q^{61} - 168q^{65} - 312q^{73} + 64q^{77} - 384q^{81} - 1072q^{85} + 24q^{89} - 168q^{93} + O(q^{100}) \)

Character values

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

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

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
\(3\) −0.729881 0.421397i −0.243294 0.140466i 0.373396 0.927672i \(-0.378193\pi\)
−0.616690 + 0.787206i \(0.711527\pi\)
\(4\) 0 0
\(5\) −1.21685 + 0.702550i −0.243371 + 0.140510i −0.616725 0.787179i \(-0.711541\pi\)
0.373354 + 0.927689i \(0.378208\pi\)
\(6\) 0 0
\(7\) 1.56553 + 6.82269i 0.223647 + 0.974670i
\(8\) 0 0
\(9\) −4.14485 7.17909i −0.460539 0.797677i
\(10\) 0 0
\(11\) −7.44562 + 12.8962i −0.676874 + 1.17238i 0.299043 + 0.954240i \(0.403333\pi\)
−0.975917 + 0.218141i \(0.930001\pi\)
\(12\) 0 0
\(13\) 2.67477i 0.205752i 0.994694 + 0.102876i \(0.0328045\pi\)
−0.994694 + 0.102876i \(0.967196\pi\)
\(14\) 0 0
\(15\) 1.18421 0.0789474
\(16\) 0 0
\(17\) 11.7354 + 6.77544i 0.690318 + 0.398555i 0.803731 0.594993i \(-0.202845\pi\)
−0.113413 + 0.993548i \(0.536178\pi\)
\(18\) 0 0
\(19\) −25.2564 + 14.5818i −1.32928 + 0.767462i −0.985189 0.171473i \(-0.945147\pi\)
−0.344095 + 0.938935i \(0.611814\pi\)
\(20\) 0 0
\(21\) 1.73241 5.63947i 0.0824958 0.268546i
\(22\) 0 0
\(23\) 11.4367 + 19.8089i 0.497247 + 0.861257i 0.999995 0.00317621i \(-0.00101102\pi\)
−0.502748 + 0.864433i \(0.667678\pi\)
\(24\) 0 0
\(25\) −11.5128 + 19.9408i −0.460514 + 0.797633i
\(26\) 0 0
\(27\) 14.5717i 0.539691i
\(28\) 0 0
\(29\) −3.76543 −0.129843 −0.0649213 0.997890i \(-0.520680\pi\)
−0.0649213 + 0.997890i \(0.520680\pi\)
\(30\) 0 0
\(31\) 11.4937 + 6.63592i 0.370766 + 0.214062i 0.673793 0.738920i \(-0.264664\pi\)
−0.303027 + 0.952982i \(0.597997\pi\)
\(32\) 0 0
\(33\) 10.8688 6.27513i 0.329359 0.190155i
\(34\) 0 0
\(35\) −6.69830 7.20235i −0.191380 0.205781i
\(36\) 0 0
\(37\) −1.32272 2.29102i −0.0357491 0.0619193i 0.847597 0.530640i \(-0.178048\pi\)
−0.883346 + 0.468721i \(0.844715\pi\)
\(38\) 0 0
\(39\) 1.12714 1.95227i 0.0289011 0.0500581i
\(40\) 0 0
\(41\) 45.2712i 1.10417i −0.833786 0.552087i \(-0.813832\pi\)
0.833786 0.552087i \(-0.186168\pi\)
\(42\) 0 0
\(43\) −51.5858 −1.19967 −0.599834 0.800124i \(-0.704767\pi\)
−0.599834 + 0.800124i \(0.704767\pi\)
\(44\) 0 0
\(45\) 10.0873 + 5.82393i 0.224163 + 0.129421i
\(46\) 0 0
\(47\) 58.1281 33.5603i 1.23677 0.714049i 0.268336 0.963325i \(-0.413526\pi\)
0.968432 + 0.249276i \(0.0801928\pi\)
\(48\) 0 0
\(49\) −44.0982 + 21.3623i −0.899964 + 0.435964i
\(50\) 0 0
\(51\) −5.71030 9.89054i −0.111967 0.193932i
\(52\) 0 0
\(53\) −19.9616 + 34.5744i −0.376633 + 0.652348i −0.990570 0.137007i \(-0.956252\pi\)
0.613937 + 0.789355i \(0.289585\pi\)
\(54\) 0 0
\(55\) 20.9237i 0.380431i
\(56\) 0 0
\(57\) 24.5789 0.431209
\(58\) 0 0
\(59\) −11.0804 6.39728i −0.187804 0.108429i 0.403150 0.915134i \(-0.367915\pi\)
−0.590954 + 0.806705i \(0.701249\pi\)
\(60\) 0 0
\(61\) 67.4084 38.9182i 1.10506 0.638004i 0.167511 0.985870i \(-0.446427\pi\)
0.937544 + 0.347866i \(0.113094\pi\)
\(62\) 0 0
\(63\) 42.4918 39.5181i 0.674473 0.627271i
\(64\) 0 0
\(65\) −1.87916 3.25480i −0.0289102 0.0500739i
\(66\) 0 0
\(67\) 22.9199 39.6985i 0.342089 0.592515i −0.642732 0.766091i \(-0.722199\pi\)
0.984820 + 0.173576i \(0.0555324\pi\)
\(68\) 0 0
\(69\) 19.2775i 0.279385i
\(70\) 0 0
\(71\) 40.6812 0.572975 0.286487 0.958084i \(-0.407512\pi\)
0.286487 + 0.958084i \(0.407512\pi\)
\(72\) 0 0
\(73\) 55.6834 + 32.1488i 0.762786 + 0.440395i 0.830295 0.557324i \(-0.188172\pi\)
−0.0675092 + 0.997719i \(0.521505\pi\)
\(74\) 0 0
\(75\) 16.8060 9.70296i 0.224080 0.129373i
\(76\) 0 0
\(77\) −99.6431 30.6098i −1.29407 0.397530i
\(78\) 0 0
\(79\) −40.2603 69.7329i −0.509624 0.882695i −0.999938 0.0111488i \(-0.996451\pi\)
0.490314 0.871546i \(-0.336882\pi\)
\(80\) 0 0
\(81\) −31.1632 + 53.9762i −0.384731 + 0.666373i
\(82\) 0 0
\(83\) 121.864i 1.46824i −0.679021 0.734118i \(-0.737596\pi\)
0.679021 0.734118i \(-0.262404\pi\)
\(84\) 0 0
\(85\) −19.0403 −0.224004
\(86\) 0 0
\(87\) 2.74832 + 1.58674i 0.0315899 + 0.0182384i
\(88\) 0 0
\(89\) −39.7614 + 22.9562i −0.446757 + 0.257935i −0.706460 0.707753i \(-0.749709\pi\)
0.259703 + 0.965689i \(0.416375\pi\)
\(90\) 0 0
\(91\) −18.2492 + 4.18744i −0.200540 + 0.0460158i
\(92\) 0 0
\(93\) −5.59271 9.68687i −0.0601367 0.104160i
\(94\) 0 0
\(95\) 20.4889 35.4878i 0.215672 0.373555i
\(96\) 0 0
\(97\) 134.268i 1.38421i −0.721798 0.692104i \(-0.756684\pi\)
0.721798 0.692104i \(-0.243316\pi\)
\(98\) 0 0
\(99\) 123.444 1.24691
\(100\) 0 0
\(101\) 170.810 + 98.6169i 1.69118 + 0.976405i 0.953565 + 0.301188i \(0.0973831\pi\)
0.737619 + 0.675218i \(0.235950\pi\)
\(102\) 0 0
\(103\) −121.371 + 70.0736i −1.17836 + 0.680326i −0.955635 0.294555i \(-0.904829\pi\)
−0.222725 + 0.974881i \(0.571495\pi\)
\(104\) 0 0
\(105\) 1.85392 + 8.07950i 0.0176564 + 0.0769477i
\(106\) 0 0
\(107\) 53.0099 + 91.8159i 0.495420 + 0.858093i 0.999986 0.00528051i \(-0.00168085\pi\)
−0.504566 + 0.863373i \(0.668348\pi\)
\(108\) 0 0
\(109\) −71.3762 + 123.627i −0.654828 + 1.13419i 0.327109 + 0.944986i \(0.393925\pi\)
−0.981937 + 0.189208i \(0.939408\pi\)
\(110\) 0 0
\(111\) 2.22956i 0.0200861i
\(112\) 0 0
\(113\) 108.519 0.960344 0.480172 0.877174i \(-0.340574\pi\)
0.480172 + 0.877174i \(0.340574\pi\)
\(114\) 0 0
\(115\) −27.8335 16.0697i −0.242030 0.139736i
\(116\) 0 0
\(117\) 19.2024 11.0865i 0.164123 0.0947567i
\(118\) 0 0
\(119\) −27.8546 + 90.6742i −0.234072 + 0.761968i
\(120\) 0 0
\(121\) −50.3745 87.2512i −0.416318 0.721084i
\(122\) 0 0
\(123\) −19.0771 + 33.0426i −0.155099 + 0.268639i
\(124\) 0 0
\(125\) 67.4809i 0.539847i
\(126\) 0 0
\(127\) −139.789 −1.10070 −0.550351 0.834934i \(-0.685506\pi\)
−0.550351 + 0.834934i \(0.685506\pi\)
\(128\) 0 0
\(129\) 37.6515 + 21.7381i 0.291872 + 0.168512i
\(130\) 0 0
\(131\) 82.2943 47.5126i 0.628200 0.362692i −0.151854 0.988403i \(-0.548524\pi\)
0.780055 + 0.625711i \(0.215191\pi\)
\(132\) 0 0
\(133\) −139.027 149.488i −1.04531 1.12397i
\(134\) 0 0
\(135\) −10.2373 17.7316i −0.0758320 0.131345i
\(136\) 0 0
\(137\) −76.7845 + 132.995i −0.560471 + 0.970764i 0.436984 + 0.899469i \(0.356046\pi\)
−0.997455 + 0.0712949i \(0.977287\pi\)
\(138\) 0 0
\(139\) 217.529i 1.56496i 0.622676 + 0.782480i \(0.286046\pi\)
−0.622676 + 0.782480i \(0.713954\pi\)
\(140\) 0 0
\(141\) −56.5689 −0.401198
\(142\) 0 0
\(143\) −34.4944 19.9153i −0.241219 0.139268i
\(144\) 0 0
\(145\) 4.58198 2.64541i 0.0315998 0.0182442i
\(146\) 0 0
\(147\) 41.1885 + 2.99096i 0.280194 + 0.0203467i
\(148\) 0 0
\(149\) −32.0451 55.5037i −0.215068 0.372508i 0.738226 0.674554i \(-0.235664\pi\)
−0.953294 + 0.302045i \(0.902331\pi\)
\(150\) 0 0
\(151\) −136.023 + 235.598i −0.900813 + 1.56025i −0.0743729 + 0.997230i \(0.523696\pi\)
−0.826440 + 0.563024i \(0.809638\pi\)
\(152\) 0 0
\(153\) 112.333i 0.734201i
\(154\) 0 0
\(155\) −18.6483 −0.120311
\(156\) 0 0
\(157\) 187.295 + 108.135i 1.19296 + 0.688757i 0.958977 0.283484i \(-0.0914902\pi\)
0.233984 + 0.972240i \(0.424824\pi\)
\(158\) 0 0
\(159\) 29.1391 16.8235i 0.183265 0.105808i
\(160\) 0 0
\(161\) −117.246 + 109.040i −0.728233 + 0.677269i
\(162\) 0 0
\(163\) −27.3465 47.3655i −0.167770 0.290586i 0.769866 0.638206i \(-0.220323\pi\)
−0.937635 + 0.347620i \(0.886990\pi\)
\(164\) 0 0
\(165\) −8.81718 + 15.2718i −0.0534375 + 0.0925564i
\(166\) 0 0
\(167\) 248.098i 1.48562i 0.669504 + 0.742809i \(0.266507\pi\)
−0.669504 + 0.742809i \(0.733493\pi\)
\(168\) 0 0
\(169\) 161.846 0.957666
\(170\) 0 0
\(171\) 209.368 + 120.879i 1.22437 + 0.706892i
\(172\) 0 0
\(173\) 224.883 129.836i 1.29990 0.750499i 0.319515 0.947581i \(-0.396480\pi\)
0.980387 + 0.197082i \(0.0631467\pi\)
\(174\) 0 0
\(175\) −154.074 47.3306i −0.880422 0.270461i
\(176\) 0 0
\(177\) 5.39159 + 9.33851i 0.0304610 + 0.0527600i
\(178\) 0 0
\(179\) 69.0883 119.664i 0.385968 0.668516i −0.605935 0.795514i \(-0.707201\pi\)
0.991903 + 0.126998i \(0.0405341\pi\)
\(180\) 0 0
\(181\) 114.497i 0.632579i 0.948663 + 0.316290i \(0.102437\pi\)
−0.948663 + 0.316290i \(0.897563\pi\)
\(182\) 0 0
\(183\) −65.6001 −0.358471
\(184\) 0 0
\(185\) 3.21911 + 1.85855i 0.0174006 + 0.0100462i
\(186\) 0 0
\(187\) −174.755 + 100.895i −0.934517 + 0.539544i
\(188\) 0 0
\(189\) −99.4180 + 22.8124i −0.526021 + 0.120700i
\(190\) 0 0
\(191\) 76.2145 + 132.007i 0.399029 + 0.691138i 0.993606 0.112900i \(-0.0360141\pi\)
−0.594578 + 0.804038i \(0.702681\pi\)
\(192\) 0 0
\(193\) −121.156 + 209.848i −0.627749 + 1.08729i 0.360253 + 0.932855i \(0.382690\pi\)
−0.988002 + 0.154439i \(0.950643\pi\)
\(194\) 0 0
\(195\) 3.16750i 0.0162436i
\(196\) 0 0
\(197\) −197.518 −1.00263 −0.501314 0.865265i \(-0.667150\pi\)
−0.501314 + 0.865265i \(0.667150\pi\)
\(198\) 0 0
\(199\) −142.172 82.0833i −0.714435 0.412479i 0.0982663 0.995160i \(-0.468670\pi\)
−0.812701 + 0.582681i \(0.802004\pi\)
\(200\) 0 0
\(201\) −33.4577 + 19.3168i −0.166456 + 0.0961035i
\(202\) 0 0
\(203\) −5.89490 25.6904i −0.0290389 0.126554i
\(204\) 0 0
\(205\) 31.8053 + 55.0883i 0.155148 + 0.268724i
\(206\) 0 0
\(207\) 94.8066 164.210i 0.458003 0.793284i
\(208\) 0 0
\(209\) 434.282i 2.07790i
\(210\) 0 0
\(211\) 53.1445 0.251870 0.125935 0.992039i \(-0.459807\pi\)
0.125935 + 0.992039i \(0.459807\pi\)
\(212\) 0 0
\(213\) −29.6925 17.1429i −0.139401 0.0804833i
\(214\) 0 0
\(215\) 62.7723 36.2416i 0.291964 0.168565i
\(216\) 0 0
\(217\) −27.2810 + 88.8070i −0.125719 + 0.409249i
\(218\) 0 0
\(219\) −27.0948 46.9296i −0.123721 0.214291i
\(220\) 0 0
\(221\) −18.1228 + 31.3896i −0.0820035 + 0.142034i
\(222\) 0 0
\(223\) 310.755i 1.39352i −0.717303 0.696761i \(-0.754624\pi\)
0.717303 0.696761i \(-0.245376\pi\)
\(224\) 0 0
\(225\) 190.876 0.848338
\(226\) 0 0
\(227\) −43.2131 24.9491i −0.190366 0.109908i 0.401788 0.915733i \(-0.368389\pi\)
−0.592154 + 0.805825i \(0.701722\pi\)
\(228\) 0 0
\(229\) 182.833 105.559i 0.798398 0.460955i −0.0445127 0.999009i \(-0.514174\pi\)
0.842911 + 0.538054i \(0.180840\pi\)
\(230\) 0 0
\(231\) 59.8287 + 64.3308i 0.258999 + 0.278488i
\(232\) 0 0
\(233\) −37.7274 65.3457i −0.161920 0.280454i 0.773637 0.633629i \(-0.218435\pi\)
−0.935557 + 0.353175i \(0.885102\pi\)
\(234\) 0 0
\(235\) −47.1556 + 81.6759i −0.200662 + 0.347557i
\(236\) 0 0
\(237\) 67.8623i 0.286339i
\(238\) 0 0
\(239\) 310.396 1.29873 0.649365 0.760477i \(-0.275035\pi\)
0.649365 + 0.760477i \(0.275035\pi\)
\(240\) 0 0
\(241\) 93.7200 + 54.1093i 0.388880 + 0.224520i 0.681675 0.731656i \(-0.261252\pi\)
−0.292795 + 0.956175i \(0.594585\pi\)
\(242\) 0 0
\(243\) 159.066 91.8366i 0.654591 0.377929i
\(244\) 0 0
\(245\) 38.6530 56.9759i 0.157767 0.232555i
\(246\) 0 0
\(247\) −39.0030 67.5551i −0.157907 0.273502i
\(248\) 0 0
\(249\) −51.3530 + 88.9460i −0.206237 + 0.357213i
\(250\) 0 0
\(251\) 302.023i 1.20328i −0.798768 0.601639i \(-0.794515\pi\)
0.798768 0.601639i \(-0.205485\pi\)
\(252\) 0 0
\(253\) −340.613 −1.34629
\(254\) 0 0
\(255\) 13.8972 + 8.02355i 0.0544988 + 0.0314649i
\(256\) 0 0
\(257\) −89.8068 + 51.8500i −0.349443 + 0.201751i −0.664440 0.747342i \(-0.731330\pi\)
0.314997 + 0.949093i \(0.397996\pi\)
\(258\) 0 0
\(259\) 13.5601 12.6112i 0.0523557 0.0486917i
\(260\) 0 0
\(261\) 15.6072 + 27.0324i 0.0597975 + 0.103572i
\(262\) 0 0
\(263\) 128.972 223.386i 0.490387 0.849375i −0.509552 0.860440i \(-0.670189\pi\)
0.999939 + 0.0110651i \(0.00352220\pi\)
\(264\) 0 0
\(265\) 56.0960i 0.211683i
\(266\) 0 0
\(267\) 38.6948 0.144924
\(268\) 0 0
\(269\) 140.523 + 81.1310i 0.522390 + 0.301602i 0.737912 0.674897i \(-0.235812\pi\)
−0.215522 + 0.976499i \(0.569145\pi\)
\(270\) 0 0
\(271\) 54.3429 31.3749i 0.200527 0.115775i −0.396374 0.918089i \(-0.629732\pi\)
0.596901 + 0.802315i \(0.296398\pi\)
\(272\) 0 0
\(273\) 15.0843 + 4.63381i 0.0552538 + 0.0169737i
\(274\) 0 0
\(275\) −171.441 296.944i −0.623420 1.07980i
\(276\) 0 0
\(277\) 128.576 222.701i 0.464175 0.803974i −0.534989 0.844859i \(-0.679684\pi\)
0.999164 + 0.0408848i \(0.0130177\pi\)
\(278\) 0 0
\(279\) 110.019i 0.394335i
\(280\) 0 0
\(281\) 230.243 0.819369 0.409685 0.912227i \(-0.365639\pi\)
0.409685 + 0.912227i \(0.365639\pi\)
\(282\) 0 0
\(283\) −354.637 204.750i −1.25313 0.723497i −0.281402 0.959590i \(-0.590800\pi\)
−0.971730 + 0.236093i \(0.924133\pi\)
\(284\) 0 0
\(285\) −29.9089 + 17.2679i −0.104943 + 0.0605891i
\(286\) 0 0
\(287\) 308.871 70.8733i 1.07621 0.246945i
\(288\) 0 0
\(289\) −52.6868 91.2562i −0.182307 0.315765i
\(290\) 0 0
\(291\) −56.5803 + 97.9999i −0.194434 + 0.336769i
\(292\) 0 0
\(293\) 438.106i 1.49524i 0.664126 + 0.747621i \(0.268804\pi\)
−0.664126 + 0.747621i \(0.731196\pi\)
\(294\) 0 0
\(295\) 17.9776 0.0609412
\(296\) 0 0
\(297\) −187.919 108.495i −0.632724 0.365303i
\(298\) 0 0
\(299\) −52.9843 + 30.5905i −0.177205 + 0.102309i
\(300\) 0 0
\(301\) −80.7590 351.954i −0.268302 1.16928i
\(302\) 0 0
\(303\) −83.1138 143.957i −0.274303 0.475107i
\(304\) 0 0
\(305\) −54.6840 + 94.7155i −0.179292 + 0.310543i
\(306\) 0 0
\(307\) 136.514i 0.444672i 0.974970 + 0.222336i \(0.0713682\pi\)
−0.974970 + 0.222336i \(0.928632\pi\)
\(308\) 0 0
\(309\) 118.115 0.382250
\(310\) 0 0
\(311\) 503.092 + 290.461i 1.61766 + 0.933957i 0.987523 + 0.157473i \(0.0503348\pi\)
0.630138 + 0.776484i \(0.282999\pi\)
\(312\) 0 0
\(313\) −162.118 + 93.5987i −0.517948 + 0.299037i −0.736095 0.676879i \(-0.763332\pi\)
0.218147 + 0.975916i \(0.429999\pi\)
\(314\) 0 0
\(315\) −23.9428 + 77.9403i −0.0760090 + 0.247430i
\(316\) 0 0
\(317\) −82.9440 143.663i −0.261653 0.453196i 0.705028 0.709179i \(-0.250934\pi\)
−0.966681 + 0.255983i \(0.917601\pi\)
\(318\) 0 0
\(319\) 28.0360 48.5597i 0.0878871 0.152225i
\(320\) 0 0
\(321\) 89.3530i 0.278358i
\(322\) 0 0
\(323\) −395.192 −1.22350
\(324\) 0 0
\(325\) −53.3372 30.7943i −0.164115 0.0947516i
\(326\) 0 0
\(327\) 104.192 60.1555i 0.318631 0.183962i
\(328\) 0 0
\(329\) 319.973 + 344.051i 0.972562 + 1.04575i
\(330\) 0 0
\(331\) 209.099 + 362.170i 0.631719 + 1.09417i 0.987200 + 0.159486i \(0.0509836\pi\)
−0.355481 + 0.934683i \(0.615683\pi\)
\(332\) 0 0
\(333\) −10.9649 + 18.9918i −0.0329277 + 0.0570325i
\(334\) 0 0
\(335\) 64.4096i 0.192268i
\(336\) 0 0
\(337\) 104.000 0.308607 0.154303 0.988024i \(-0.450687\pi\)
0.154303 + 0.988024i \(0.450687\pi\)
\(338\) 0 0
\(339\) −79.2059 45.7295i −0.233646 0.134895i
\(340\) 0 0
\(341\) −171.156 + 98.8170i −0.501924 + 0.289786i
\(342\) 0 0
\(343\) −214.785 267.425i −0.626196 0.779666i
\(344\) 0 0
\(345\) 13.5434 + 23.4579i 0.0392563 + 0.0679940i
\(346\) 0 0
\(347\) −48.9796 + 84.8352i −0.141152 + 0.244482i −0.927931 0.372753i \(-0.878414\pi\)
0.786779 + 0.617235i \(0.211747\pi\)
\(348\) 0 0
\(349\) 248.606i 0.712339i 0.934421 + 0.356169i \(0.115917\pi\)
−0.934421 + 0.356169i \(0.884083\pi\)
\(350\) 0 0
\(351\) −38.9759 −0.111042
\(352\) 0 0
\(353\) −113.804 65.7047i −0.322390 0.186132i 0.330067 0.943957i \(-0.392929\pi\)
−0.652458 + 0.757825i \(0.726262\pi\)
\(354\) 0 0
\(355\) −49.5030 + 28.5806i −0.139445 + 0.0805087i
\(356\) 0 0
\(357\) 58.5404 54.4436i 0.163979 0.152503i
\(358\) 0 0
\(359\) 176.634 + 305.939i 0.492016 + 0.852196i 0.999958 0.00919491i \(-0.00292687\pi\)
−0.507942 + 0.861391i \(0.669594\pi\)
\(360\) 0 0
\(361\) 244.757 423.931i 0.677996 1.17432i
\(362\) 0 0
\(363\) 84.9107i 0.233914i
\(364\) 0 0
\(365\) −90.3446 −0.247519
\(366\) 0 0
\(367\) 105.306 + 60.7983i 0.286937 + 0.165663i 0.636560 0.771228i \(-0.280357\pi\)
−0.349623 + 0.936891i \(0.613690\pi\)
\(368\) 0 0
\(369\) −325.006 + 187.642i −0.880774 + 0.508515i
\(370\) 0 0
\(371\) −267.141 82.0642i −0.720057 0.221197i
\(372\) 0 0
\(373\) 245.458 + 425.145i 0.658063 + 1.13980i 0.981116 + 0.193418i \(0.0619573\pi\)
−0.323053 + 0.946381i \(0.604709\pi\)
\(374\) 0 0
\(375\) −28.4363 + 49.2531i −0.0758301 + 0.131342i
\(376\) 0 0
\(377\) 10.0717i 0.0267153i
\(378\) 0 0
\(379\) −325.094 −0.857768 −0.428884 0.903360i \(-0.641093\pi\)
−0.428884 + 0.903360i \(0.641093\pi\)
\(380\) 0 0
\(381\) 102.029 + 58.9067i 0.267794 + 0.154611i
\(382\) 0 0
\(383\) −385.028 + 222.296i −1.00529 + 0.580407i −0.909810 0.415024i \(-0.863773\pi\)
−0.0954837 + 0.995431i \(0.530440\pi\)
\(384\) 0 0
\(385\) 142.756 32.7567i 0.370794 0.0850822i
\(386\) 0 0
\(387\) 213.815 + 370.339i 0.552494 + 0.956948i
\(388\) 0 0
\(389\) 209.219 362.379i 0.537839 0.931565i −0.461181 0.887306i \(-0.652574\pi\)
0.999020 0.0442585i \(-0.0140925\pi\)
\(390\) 0 0
\(391\) 309.954i 0.792721i
\(392\) 0 0
\(393\) −80.0867 −0.203783
\(394\) 0 0
\(395\) 97.9817 + 56.5698i 0.248055 + 0.143215i
\(396\) 0 0
\(397\) 378.814 218.708i 0.954192 0.550903i 0.0598112 0.998210i \(-0.480950\pi\)
0.894381 + 0.447307i \(0.147617\pi\)
\(398\) 0 0
\(399\) 38.4790 + 167.694i 0.0964385 + 0.420286i
\(400\) 0 0
\(401\) 45.2362 + 78.3513i 0.112808 + 0.195390i 0.916902 0.399113i \(-0.130682\pi\)
−0.804093 + 0.594503i \(0.797349\pi\)
\(402\) 0 0
\(403\) −17.7496 + 30.7432i −0.0440436 + 0.0762858i
\(404\) 0 0
\(405\) 87.5748i 0.216234i
\(406\) 0 0
\(407\) 39.3938 0.0967907
\(408\) 0 0
\(409\) −607.126 350.524i −1.48442 0.857028i −0.484573 0.874751i \(-0.661025\pi\)
−0.999843 + 0.0177233i \(0.994358\pi\)
\(410\) 0 0
\(411\) 112.087 64.7136i 0.272718 0.157454i
\(412\) 0 0
\(413\) 26.3000 85.6134i 0.0636803 0.207296i
\(414\) 0 0
\(415\) 85.6153 + 148.290i 0.206302 + 0.357326i
\(416\) 0 0
\(417\) 91.6663 158.771i 0.219823 0.380745i
\(418\) 0 0
\(419\) 374.252i 0.893202i 0.894733 + 0.446601i \(0.147366\pi\)
−0.894733 + 0.446601i \(0.852634\pi\)
\(420\) 0 0
\(421\) −733.801 −1.74299 −0.871497 0.490400i \(-0.836851\pi\)
−0.871497 + 0.490400i \(0.836851\pi\)
\(422\) 0 0
\(423\) −481.865 278.205i −1.13916 0.657694i
\(424\) 0 0
\(425\) −270.216 + 156.009i −0.635802 + 0.367081i
\(426\) 0 0
\(427\) 371.057 + 398.979i 0.868986 + 0.934376i
\(428\) 0 0
\(429\) 16.7845 + 29.0717i 0.0391248 + 0.0677662i
\(430\) 0 0
\(431\) −416.503 + 721.405i −0.966365 + 1.67379i −0.260462 + 0.965484i \(0.583875\pi\)
−0.705903 + 0.708308i \(0.749459\pi\)
\(432\) 0 0
\(433\) 414.085i 0.956316i 0.878274 + 0.478158i \(0.158695\pi\)
−0.878274 + 0.478158i \(0.841305\pi\)
\(434\) 0 0
\(435\) −4.45907 −0.0102507
\(436\) 0 0
\(437\) −577.698 333.534i −1.32196 0.763236i
\(438\) 0 0
\(439\) 61.9802 35.7843i 0.141185 0.0815132i −0.427744 0.903900i \(-0.640691\pi\)
0.568929 + 0.822387i \(0.307358\pi\)
\(440\) 0 0
\(441\) 336.142 + 228.042i 0.762227 + 0.517102i
\(442\) 0 0
\(443\) −414.628 718.157i −0.935956 1.62112i −0.772921 0.634503i \(-0.781205\pi\)
−0.163035 0.986620i \(-0.552128\pi\)
\(444\) 0 0
\(445\) 32.2558 55.8687i 0.0724850 0.125548i
\(446\) 0 0
\(447\) 54.0149i 0.120839i
\(448\) 0 0
\(449\) 247.153 0.550452 0.275226 0.961380i \(-0.411247\pi\)
0.275226 + 0.961380i \(0.411247\pi\)
\(450\) 0 0
\(451\) 583.825 + 337.072i 1.29451 + 0.747388i
\(452\) 0 0
\(453\) 198.561 114.639i 0.438325 0.253067i
\(454\) 0 0
\(455\) 19.2646 17.9164i 0.0423399 0.0393768i
\(456\) 0 0
\(457\) 240.746 + 416.984i 0.526796 + 0.912437i 0.999512 + 0.0312226i \(0.00994009\pi\)
−0.472717 + 0.881214i \(0.656727\pi\)
\(458\) 0 0
\(459\) −98.7294 + 171.004i −0.215097 + 0.372559i
\(460\) 0 0
\(461\) 256.190i 0.555727i 0.960621 + 0.277863i \(0.0896263\pi\)
−0.960621 + 0.277863i \(0.910374\pi\)
\(462\) 0 0
\(463\) −142.004 −0.306705 −0.153353 0.988172i \(-0.549007\pi\)
−0.153353 + 0.988172i \(0.549007\pi\)
\(464\) 0 0
\(465\) 13.6110 + 7.85832i 0.0292710 + 0.0168996i
\(466\) 0 0
\(467\) −375.153 + 216.594i −0.803324 + 0.463800i −0.844632 0.535347i \(-0.820181\pi\)
0.0413078 + 0.999146i \(0.486848\pi\)
\(468\) 0 0
\(469\) 306.732 + 94.2265i 0.654014 + 0.200909i
\(470\) 0 0
\(471\) −91.1354 157.851i −0.193493 0.335140i
\(472\) 0 0
\(473\) 384.088 665.260i 0.812025 1.40647i
\(474\) 0 0
\(475\) 671.511i 1.41371i
\(476\) 0 0
\(477\) 330.950 0.693816
\(478\) 0 0
\(479\) −227.894 131.575i −0.475770 0.274686i 0.242882 0.970056i \(-0.421907\pi\)
−0.718652 + 0.695370i \(0.755241\pi\)
\(480\) 0 0
\(481\) 6.12795 3.53797i 0.0127400 0.00735545i
\(482\) 0 0
\(483\) 131.525 30.1796i 0.272308 0.0624836i
\(484\) 0 0
\(485\) 94.3302 + 163.385i 0.194495 + 0.336876i
\(486\) 0 0
\(487\) 338.504 586.307i 0.695081 1.20392i −0.275072 0.961424i \(-0.588702\pi\)
0.970153 0.242492i \(-0.0779649\pi\)
\(488\) 0 0
\(489\) 46.0950i 0.0942637i
\(490\) 0 0
\(491\) 807.748 1.64511 0.822554 0.568686i \(-0.192548\pi\)
0.822554 + 0.568686i \(0.192548\pi\)
\(492\) 0 0
\(493\) −44.1889 25.5125i −0.0896326 0.0517494i
\(494\) 0 0
\(495\) −150.213 + 86.7255i −0.303461 + 0.175203i
\(496\) 0 0
\(497\) 63.6876 + 277.555i 0.128144 + 0.558461i
\(498\) 0 0
\(499\) 78.2519 + 135.536i 0.156817 + 0.271616i 0.933719 0.358006i \(-0.116543\pi\)
−0.776902 + 0.629622i \(0.783210\pi\)
\(500\) 0 0
\(501\) 104.548 181.082i 0.208678 0.361441i
\(502\) 0 0
\(503\) 499.753i 0.993545i −0.867881 0.496773i \(-0.834518\pi\)
0.867881 0.496773i \(-0.165482\pi\)
\(504\) 0 0
\(505\) −277.133 −0.548779
\(506\) 0 0
\(507\) −118.128 68.2013i −0.232994 0.134519i
\(508\) 0 0
\(509\) −462.478 + 267.012i −0.908602 + 0.524582i −0.879981 0.475009i \(-0.842445\pi\)
−0.0286209 + 0.999590i \(0.509112\pi\)
\(510\) 0 0
\(511\) −132.167 + 430.240i −0.258645 + 0.841958i
\(512\) 0 0
\(513\) −212.481 368.027i −0.414193 0.717403i
\(514\) 0 0
\(515\) 98.4604 170.538i 0.191185 0.331143i
\(516\) 0 0
\(517\) 999.509i 1.93329i
\(518\) 0 0
\(519\) −218.851 −0.421677
\(520\) 0 0
\(521\) −623.856 360.184i −1.19742 0.691331i −0.237442 0.971402i \(-0.576309\pi\)
−0.959979 + 0.280070i \(0.909642\pi\)
\(522\) 0 0
\(523\) 523.499 302.243i 1.00095 0.577902i 0.0924242 0.995720i \(-0.470538\pi\)
0.908531 + 0.417818i \(0.137205\pi\)
\(524\) 0 0
\(525\) 92.5107 + 99.4721i 0.176211 + 0.189471i
\(526\) 0 0
\(527\) 89.9225 + 155.750i 0.170631 + 0.295542i
\(528\) 0 0
\(529\) 2.90487 5.03138i 0.00549125 0.00951112i
\(530\) 0 0
\(531\) 106.063i 0.199742i
\(532\) 0 0
\(533\) 121.090 0.227186
\(534\) 0 0
\(535\) −129.011 74.4843i −0.241141 0.139223i
\(536\) 0 0
\(537\) −100.853 + 58.2272i −0.187807 + 0.108431i
\(538\) 0 0
\(539\) 52.8470 727.754i 0.0980463 1.35019i
\(540\) 0 0
\(541\) −177.344 307.168i −0.327807 0.567779i 0.654269 0.756262i \(-0.272976\pi\)
−0.982077 + 0.188483i \(0.939643\pi\)
\(542\) 0 0
\(543\) 48.2487 83.5692i 0.0888557 0.153903i
\(544\) 0 0
\(545\) 200.581i 0.368039i
\(546\) 0 0
\(547\) 867.407 1.58575 0.792877 0.609382i \(-0.208583\pi\)
0.792877 + 0.609382i \(0.208583\pi\)
\(548\) 0 0
\(549\) −558.795 322.620i −1.01784 0.587651i
\(550\) 0 0
\(551\) 95.1012 54.9067i 0.172597 0.0996492i
\(552\) 0 0
\(553\) 412.737 383.853i 0.746360 0.694128i
\(554\) 0 0
\(555\) −1.56638 2.71304i −0.00282230 0.00488837i
\(556\) 0 0
\(557\) 67.3674 116.684i 0.120947 0.209486i −0.799194 0.601073i \(-0.794740\pi\)
0.920141 + 0.391586i \(0.128074\pi\)
\(558\) 0 0
\(559\) 137.980i 0.246834i
\(560\) 0 0
\(561\) 170.067 0.303150
\(562\) 0 0
\(563\) −413.611 238.798i −0.734655 0.424153i 0.0854680 0.996341i \(-0.472761\pi\)
−0.820123 + 0.572188i \(0.806095\pi\)
\(564\) 0 0
\(565\) −132.051 + 76.2399i −0.233719 + 0.134938i
\(566\) 0 0
\(567\) −417.050 128.115i −0.735538 0.225953i
\(568\) 0 0
\(569\) 166.341 + 288.110i 0.292338 + 0.506345i 0.974362 0.224985i \(-0.0722333\pi\)
−0.682024 + 0.731330i \(0.738900\pi\)
\(570\) 0 0
\(571\) 525.564 910.304i 0.920427 1.59423i 0.121672 0.992570i \(-0.461174\pi\)
0.798755 0.601657i \(-0.205492\pi\)
\(572\) 0 0
\(573\) 128.466i 0.224199i
\(574\) 0 0
\(575\) −526.675 −0.915956
\(576\) 0 0
\(577\) 350.366 + 202.284i 0.607221 + 0.350579i 0.771877 0.635772i \(-0.219318\pi\)
−0.164656 + 0.986351i \(0.552651\pi\)
\(578\) 0 0
\(579\) 176.858 102.109i 0.305455 0.176355i
\(580\) 0 0
\(581\) 831.438 190.781i 1.43105 0.328367i
\(582\) 0 0
\(583\) −297.252 514.856i −0.509867 0.883115i
\(584\) 0 0
\(585\) −15.5777 + 26.9813i −0.0266285 + 0.0461220i
\(586\) 0 0
\(587\) 64.6639i 0.110160i 0.998482 + 0.0550800i \(0.0175414\pi\)
−0.998482 + 0.0550800i \(0.982459\pi\)
\(588\) 0 0
\(589\) −387.054 −0.657137
\(590\) 0 0
\(591\) 144.165 + 83.2335i 0.243933 + 0.140835i
\(592\) 0 0
\(593\) 36.0843 20.8333i 0.0608504 0.0351320i −0.469266 0.883057i \(-0.655482\pi\)
0.530117 + 0.847925i \(0.322148\pi\)
\(594\) 0 0
\(595\) −29.8082 129.906i −0.0500979 0.218330i
\(596\) 0 0
\(597\) 69.1794 + 119.822i 0.115878 + 0.200707i
\(598\) 0 0
\(599\) 60.0025 103.927i 0.100171 0.173502i −0.811584 0.584236i \(-0.801394\pi\)
0.911755 + 0.410734i \(0.134728\pi\)
\(600\) 0 0
\(601\) 1120.08i 1.86369i 0.362858 + 0.931844i \(0.381801\pi\)
−0.362858 + 0.931844i \(0.618199\pi\)
\(602\) 0 0
\(603\) −379.999 −0.630180
\(604\) 0 0
\(605\) 122.597 + 70.7812i 0.202639 + 0.116994i
\(606\) 0 0
\(607\) 383.831 221.605i 0.632342 0.365083i −0.149317 0.988789i \(-0.547707\pi\)
0.781658 + 0.623707i \(0.214374\pi\)
\(608\) 0 0
\(609\) −6.52328 + 21.2350i −0.0107115 + 0.0348687i
\(610\) 0 0
\(611\) 89.7662 + 155.480i 0.146917 + 0.254467i
\(612\) 0 0
\(613\) 568.642 984.916i 0.927637 1.60672i 0.140374 0.990099i \(-0.455170\pi\)
0.787264 0.616617i \(-0.211497\pi\)
\(614\) 0 0
\(615\) 53.6106i 0.0871717i
\(616\) 0 0
\(617\) −357.454 −0.579343 −0.289671 0.957126i \(-0.593546\pi\)
−0.289671 + 0.957126i \(0.593546\pi\)
\(618\) 0 0
\(619\) 686.616 + 396.418i 1.10923 + 0.640416i 0.938631 0.344923i \(-0.112095\pi\)
0.170603 + 0.985340i \(0.445428\pi\)
\(620\) 0 0
\(621\) −288.649 + 166.651i −0.464813 + 0.268360i
\(622\) 0 0
\(623\) −218.871 235.341i −0.351318 0.377754i
\(624\) 0 0
\(625\) −240.412 416.407i −0.384660 0.666250i
\(626\) 0 0
\(627\) −183.005 + 316.974i −0.291874 + 0.505541i
\(628\) 0 0
\(629\) 35.8480i 0.0569920i
\(630\) 0 0
\(631\) 587.326 0.930786 0.465393 0.885104i \(-0.345913\pi\)
0.465393 + 0.885104i \(0.345913\pi\)
\(632\) 0 0
\(633\) −38.7892 22.3950i −0.0612783 0.0353791i
\(634\) 0 0
\(635\) 170.103 98.2088i 0.267878 0.154660i
\(636\) 0 0
\(637\) −57.1392 117.953i −0.0897004 0.185169i
\(638\) 0 0
\(639\) −168.617 292.054i −0.263877 0.457048i
\(640\) 0 0
\(641\) −229.349 + 397.244i −0.357798 + 0.619725i −0.987593 0.157037i \(-0.949806\pi\)
0.629794 + 0.776762i \(0.283139\pi\)
\(642\) 0 0
\(643\) 242.009i 0.376374i 0.982133 + 0.188187i \(0.0602611\pi\)
−0.982133 + 0.188187i \(0.939739\pi\)
\(644\) 0 0
\(645\) −61.0884 −0.0947107
\(646\) 0 0
\(647\) 68.6970 + 39.6622i 0.106178 + 0.0613017i 0.552148 0.833746i \(-0.313808\pi\)
−0.445971 + 0.895048i \(0.647141\pi\)
\(648\) 0 0
\(649\) 165.001 95.2634i 0.254239 0.146785i
\(650\) 0 0
\(651\) 57.3349 53.3224i 0.0880721 0.0819085i
\(652\) 0 0
\(653\) 56.1079 + 97.1817i 0.0859232 + 0.148823i 0.905784 0.423739i \(-0.139283\pi\)
−0.819861 + 0.572563i \(0.805949\pi\)
\(654\) 0 0
\(655\) −66.7600 + 115.632i −0.101924 + 0.176537i
\(656\) 0 0
\(657\) 533.008i 0.811275i
\(658\) 0 0
\(659\) −811.930 −1.23206 −0.616032 0.787721i \(-0.711261\pi\)
−0.616032 + 0.787721i \(0.711261\pi\)
\(660\) 0 0
\(661\) −317.842 183.506i −0.480850 0.277619i 0.239921 0.970792i \(-0.422879\pi\)
−0.720771 + 0.693174i \(0.756212\pi\)
\(662\) 0 0
\(663\) 26.4549 15.2738i 0.0399019 0.0230374i
\(664\) 0 0
\(665\) 274.198 + 84.2321i 0.412328 + 0.126665i
\(666\) 0 0
\(667\) −43.0640 74.5891i −0.0645638 0.111828i
\(668\) 0 0
\(669\) −130.952 + 226.815i −0.195742 + 0.339035i
\(670\) 0 0
\(671\) 1159.08i 1.72739i
\(672\) 0 0
\(673\) −504.526 −0.749668 −0.374834 0.927092i \(-0.622300\pi\)
−0.374834 + 0.927092i \(0.622300\pi\)
\(674\) 0 0
\(675\) −290.571 167.761i −0.430476 0.248535i
\(676\) 0 0
\(677\) −519.740 + 300.072i −0.767710 + 0.443238i −0.832057 0.554690i \(-0.812837\pi\)
0.0643468 + 0.997928i \(0.479504\pi\)
\(678\) 0 0
\(679\) 916.071 210.201i 1.34915 0.309574i
\(680\) 0 0
\(681\) 21.0270 + 36.4198i 0.0308766 + 0.0534798i
\(682\) 0 0
\(683\) 105.717 183.107i 0.154783 0.268093i −0.778197 0.628020i \(-0.783865\pi\)
0.932980 + 0.359928i \(0.117199\pi\)
\(684\) 0 0
\(685\) 215.780i 0.315007i
\(686\) 0 0
\(687\) −177.929 −0.258994
\(688\) 0 0
\(689\) −92.4787 53.3926i −0.134222 0.0774929i
\(690\) 0 0
\(691\) 16.6678 9.62318i 0.0241213 0.0139265i −0.487891 0.872905i \(-0.662234\pi\)
0.512012 + 0.858978i \(0.328900\pi\)
\(692\) 0 0
\(693\) 193.255 + 842.219i 0.278867 + 1.21532i
\(694\) 0 0
\(695\) −152.825 264.701i −0.219893 0.380865i
\(696\) 0 0
\(697\) 306.732 531.275i 0.440075 0.762232i
\(698\) 0 0
\(699\) 63.5928i 0.0909768i
\(700\) 0 0
\(701\) 1073.36 1.53119 0.765595 0.643323i \(-0.222445\pi\)
0.765595 + 0.643323i \(0.222445\pi\)
\(702\) 0 0
\(703\) 66.8142 + 38.5752i 0.0950415 + 0.0548722i
\(704\) 0 0
\(705\) 68.8360 39.7425i 0.0976397 0.0563723i
\(706\) 0 0
\(707\) −405.425 + 1319.77i −0.573445 + 1.86672i
\(708\) 0 0
\(709\) 128.799 + 223.086i 0.181663 + 0.314649i 0.942447 0.334356i \(-0.108519\pi\)
−0.760784 + 0.649005i \(0.775185\pi\)
\(710\) 0 0
\(711\) −333.746 + 578.065i −0.469403 + 0.813030i
\(712\) 0 0
\(713\) 303.571i 0.425766i
\(714\) 0 0
\(715\) 55.9661 0.0782743
\(716\) 0 0
\(717\) −226.553 130.800i −0.315973 0.182427i
\(718\) 0 0
\(719\) −278.533 + 160.811i −0.387389 + 0.223659i −0.681028 0.732257i \(-0.738467\pi\)
0.293639 + 0.955916i \(0.405134\pi\)
\(720\) 0 0
\(721\) −668.101 718.375i −0.926630 0.996359i
\(722\) 0 0
\(723\) −45.6030 78.9867i −0.0630747 0.109249i
\(724\) 0 0
\(725\) 43.3509 75.0859i 0.0597943 0.103567i
\(726\) 0 0
\(727\) 19.9115i 0.0273886i −0.999906 0.0136943i \(-0.995641\pi\)
0.999906 0.0136943i \(-0.00435917\pi\)
\(728\) 0 0
\(729\) 406.138 0.557117
\(730\) 0 0
\(731\) −605.380 349.516i −0.828153 0.478134i
\(732\) 0 0
\(733\) 514.080 296.804i 0.701337 0.404917i −0.106508 0.994312i \(-0.533967\pi\)
0.807845 + 0.589395i \(0.200634\pi\)
\(734\) 0 0
\(735\) −52.2216 + 25.2974i −0.0710498 + 0.0344182i
\(736\) 0 0
\(737\) 341.306 + 591.160i 0.463102 + 0.802116i
\(738\) 0 0
\(739\) −505.499 + 875.550i −0.684031 + 1.18478i 0.289709 + 0.957115i \(0.406441\pi\)
−0.973740 + 0.227662i \(0.926892\pi\)
\(740\) 0 0
\(741\) 65.7430i 0.0887219i
\(742\) 0 0
\(743\) 581.910 0.783189 0.391595 0.920138i \(-0.371924\pi\)
0.391595 + 0.920138i \(0.371924\pi\)
\(744\) 0 0
\(745\) 77.9883 + 45.0266i 0.104682 + 0.0604383i
\(746\) 0 0
\(747\) −874.870 + 505.106i −1.17118 + 0.676180i
\(748\) 0 0
\(749\) −543.443 + 505.411i −0.725558 + 0.674781i
\(750\) 0 0
\(751\) 605.277 + 1048.37i 0.805962 + 1.39597i 0.915640 + 0.402000i \(0.131685\pi\)
−0.109678 + 0.993967i \(0.534982\pi\)
\(752\) 0 0
\(753\) −127.272 + 220.441i −0.169019 + 0.292750i
\(754\) 0 0
\(755\) 382.251i 0.506293i
\(756\) 0 0
\(757\) −245.833 −0.324746 −0.162373 0.986729i \(-0.551915\pi\)
−0.162373 + 0.986729i \(0.551915\pi\)
\(758\) 0 0
\(759\) 248.607 + 143.533i 0.327545 + 0.189108i
\(760\) 0 0
\(761\) 59.4109 34.3009i 0.0780694 0.0450734i −0.460457 0.887682i \(-0.652314\pi\)
0.538527 + 0.842609i \(0.318981\pi\)
\(762\) 0 0
\(763\) −955.212 293.436i −1.25192 0.384582i
\(764\) 0 0
\(765\) 78.9194 + 136.692i 0.103163 + 0.178683i
\(766\) 0 0
\(767\) 17.1113 29.6376i 0.0223094 0.0386409i
\(768\) 0 0
\(769\) 540.953i 0.703450i 0.936103 + 0.351725i \(0.114405\pi\)
−0.936103 + 0.351725i \(0.885595\pi\)
\(770\) 0 0
\(771\) 87.3977 0.113356
\(772\) 0 0
\(773\) −223.462 129.016i −0.289085 0.166903i 0.348444 0.937329i \(-0.386710\pi\)
−0.637529 + 0.770426i \(0.720043\pi\)
\(774\) 0 0
\(775\) −264.651 + 152.797i −0.341486 + 0.197157i
\(776\) 0 0
\(777\) −15.2116 + 3.49044i −0.0195773 + 0.00449220i
\(778\) 0 0
\(779\) 660.134 + 1143.39i 0.847412 + 1.46776i
\(780\) 0 0
\(781\) −302.897 + 524.633i −0.387832 + 0.671745i
\(782\) 0 0
\(783\) 54.8686i 0.0700749i
\(784\) 0 0
\(785\) −303.880 −0.387109
\(786\) 0 0
\(787\) 156.307 + 90.2438i 0.198611 + 0.114668i 0.596007 0.802979i \(-0.296753\pi\)
−0.397396 + 0.917647i \(0.630086\pi\)
\(788\) 0 0
\(789\) −188.268 + 108.697i −0.238616 + 0.137765i
\(790\) 0 0