Properties

Label 230.3.d.a.91.6
Level $230$
Weight $3$
Character 230.91
Analytic conductor $6.267$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 230.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.26704608029\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \( x^{16} + 78x^{14} + 2165x^{12} + 28310x^{10} + 184804x^{8} + 569634x^{6} + 696037x^{4} + 285578x^{2} + 529 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 91.6
Root \(1.01877i\) of defining polynomial
Character \(\chi\) \(=\) 230.91
Dual form 230.3.d.a.91.5

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} +2.34854 q^{3} +2.00000 q^{4} +2.23607i q^{5} -3.32134 q^{6} +7.61815i q^{7} -2.82843 q^{8} -3.48436 q^{9} +O(q^{10})\) \(q-1.41421 q^{2} +2.34854 q^{3} +2.00000 q^{4} +2.23607i q^{5} -3.32134 q^{6} +7.61815i q^{7} -2.82843 q^{8} -3.48436 q^{9} -3.16228i q^{10} +12.3764i q^{11} +4.69708 q^{12} -13.0302 q^{13} -10.7737i q^{14} +5.25149i q^{15} +4.00000 q^{16} -9.13040i q^{17} +4.92764 q^{18} +14.4549i q^{19} +4.47214i q^{20} +17.8915i q^{21} -17.5029i q^{22} +(22.5529 - 4.51289i) q^{23} -6.64267 q^{24} -5.00000 q^{25} +18.4275 q^{26} -29.3200 q^{27} +15.2363i q^{28} -21.2813 q^{29} -7.42673i q^{30} +36.8428 q^{31} -5.65685 q^{32} +29.0666i q^{33} +12.9123i q^{34} -17.0347 q^{35} -6.96873 q^{36} +56.9603i q^{37} -20.4424i q^{38} -30.6019 q^{39} -6.32456i q^{40} +70.7680 q^{41} -25.3024i q^{42} +70.0086i q^{43} +24.7529i q^{44} -7.79128i q^{45} +(-31.8946 + 6.38219i) q^{46} -66.2614 q^{47} +9.39416 q^{48} -9.03623 q^{49} +7.07107 q^{50} -21.4431i q^{51} -26.0604 q^{52} -77.4364i q^{53} +41.4648 q^{54} -27.6746 q^{55} -21.5474i q^{56} +33.9480i q^{57} +30.0963 q^{58} +82.7923 q^{59} +10.5030i q^{60} +23.9941i q^{61} -52.1036 q^{62} -26.5444i q^{63} +8.00000 q^{64} -29.1364i q^{65} -41.1063i q^{66} -118.512i q^{67} -18.2608i q^{68} +(52.9664 - 10.5987i) q^{69} +24.0907 q^{70} +69.0263 q^{71} +9.85527 q^{72} +25.9840 q^{73} -80.5540i q^{74} -11.7427 q^{75} +28.9099i q^{76} -94.2857 q^{77} +43.2777 q^{78} -28.8543i q^{79} +8.94427i q^{80} -37.4999 q^{81} -100.081 q^{82} -69.3871i q^{83} +35.7831i q^{84} +20.4162 q^{85} -99.0071i q^{86} -49.9800 q^{87} -35.0059i q^{88} -45.4428i q^{89} +11.0185i q^{90} -99.2661i q^{91} +(45.1058 - 9.02579i) q^{92} +86.5269 q^{93} +93.7077 q^{94} -32.3222 q^{95} -13.2853 q^{96} -74.4458i q^{97} +12.7792 q^{98} -43.1241i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9} + 24 q^{13} + 64 q^{16} - 32 q^{18} + 4 q^{23} - 16 q^{24} - 80 q^{25} + 96 q^{26} - 96 q^{27} - 108 q^{29} - 116 q^{31} + 60 q^{35} + 128 q^{36} + 248 q^{39} - 156 q^{41} - 124 q^{46} - 128 q^{47} - 28 q^{49} + 48 q^{52} + 224 q^{54} + 160 q^{58} + 204 q^{59} + 64 q^{62} + 128 q^{64} - 268 q^{69} - 120 q^{70} + 236 q^{71} - 64 q^{72} - 112 q^{73} - 936 q^{77} - 432 q^{78} - 136 q^{81} - 64 q^{82} + 60 q^{85} - 152 q^{87} + 8 q^{92} + 856 q^{93} - 216 q^{94} - 160 q^{95} - 32 q^{96} + 256 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 −0.707107
\(3\) 2.34854 0.782846 0.391423 0.920211i \(-0.371983\pi\)
0.391423 + 0.920211i \(0.371983\pi\)
\(4\) 2.00000 0.500000
\(5\) 2.23607i 0.447214i
\(6\) −3.32134 −0.553556
\(7\) 7.61815i 1.08831i 0.838986 + 0.544154i \(0.183149\pi\)
−0.838986 + 0.544154i \(0.816851\pi\)
\(8\) −2.82843 −0.353553
\(9\) −3.48436 −0.387152
\(10\) 3.16228i 0.316228i
\(11\) 12.3764i 1.12513i 0.826752 + 0.562566i \(0.190186\pi\)
−0.826752 + 0.562566i \(0.809814\pi\)
\(12\) 4.69708 0.391423
\(13\) −13.0302 −1.00232 −0.501162 0.865354i \(-0.667094\pi\)
−0.501162 + 0.865354i \(0.667094\pi\)
\(14\) 10.7737i 0.769549i
\(15\) 5.25149i 0.350100i
\(16\) 4.00000 0.250000
\(17\) 9.13040i 0.537083i −0.963268 0.268541i \(-0.913458\pi\)
0.963268 0.268541i \(-0.0865416\pi\)
\(18\) 4.92764 0.273758
\(19\) 14.4549i 0.760787i 0.924825 + 0.380393i \(0.124211\pi\)
−0.924825 + 0.380393i \(0.875789\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 17.8915i 0.851977i
\(22\) 17.5029i 0.795588i
\(23\) 22.5529 4.51289i 0.980561 0.196213i
\(24\) −6.64267 −0.276778
\(25\) −5.00000 −0.200000
\(26\) 18.4275 0.708750
\(27\) −29.3200 −1.08593
\(28\) 15.2363i 0.544154i
\(29\) −21.2813 −0.733839 −0.366919 0.930253i \(-0.619588\pi\)
−0.366919 + 0.930253i \(0.619588\pi\)
\(30\) 7.42673i 0.247558i
\(31\) 36.8428 1.18848 0.594239 0.804288i \(-0.297453\pi\)
0.594239 + 0.804288i \(0.297453\pi\)
\(32\) −5.65685 −0.176777
\(33\) 29.0666i 0.880805i
\(34\) 12.9123i 0.379775i
\(35\) −17.0347 −0.486706
\(36\) −6.96873 −0.193576
\(37\) 56.9603i 1.53947i 0.638365 + 0.769734i \(0.279611\pi\)
−0.638365 + 0.769734i \(0.720389\pi\)
\(38\) 20.4424i 0.537957i
\(39\) −30.6019 −0.784665
\(40\) 6.32456i 0.158114i
\(41\) 70.7680 1.72605 0.863024 0.505163i \(-0.168567\pi\)
0.863024 + 0.505163i \(0.168567\pi\)
\(42\) 25.3024i 0.602439i
\(43\) 70.0086i 1.62811i 0.580790 + 0.814053i \(0.302744\pi\)
−0.580790 + 0.814053i \(0.697256\pi\)
\(44\) 24.7529i 0.562566i
\(45\) 7.79128i 0.173139i
\(46\) −31.8946 + 6.38219i −0.693362 + 0.138743i
\(47\) −66.2614 −1.40982 −0.704908 0.709299i \(-0.749012\pi\)
−0.704908 + 0.709299i \(0.749012\pi\)
\(48\) 9.39416 0.195712
\(49\) −9.03623 −0.184413
\(50\) 7.07107 0.141421
\(51\) 21.4431i 0.420453i
\(52\) −26.0604 −0.501162
\(53\) 77.4364i 1.46106i −0.682879 0.730532i \(-0.739272\pi\)
0.682879 0.730532i \(-0.260728\pi\)
\(54\) 41.4648 0.767866
\(55\) −27.6746 −0.503174
\(56\) 21.5474i 0.384775i
\(57\) 33.9480i 0.595579i
\(58\) 30.0963 0.518902
\(59\) 82.7923 1.40326 0.701630 0.712541i \(-0.252456\pi\)
0.701630 + 0.712541i \(0.252456\pi\)
\(60\) 10.5030i 0.175050i
\(61\) 23.9941i 0.393346i 0.980469 + 0.196673i \(0.0630137\pi\)
−0.980469 + 0.196673i \(0.936986\pi\)
\(62\) −52.1036 −0.840381
\(63\) 26.5444i 0.421340i
\(64\) 8.00000 0.125000
\(65\) 29.1364i 0.448253i
\(66\) 41.1063i 0.622823i
\(67\) 118.512i 1.76884i −0.466695 0.884418i \(-0.654555\pi\)
0.466695 0.884418i \(-0.345445\pi\)
\(68\) 18.2608i 0.268541i
\(69\) 52.9664 10.5987i 0.767629 0.153604i
\(70\) 24.0907 0.344153
\(71\) 69.0263 0.972202 0.486101 0.873903i \(-0.338419\pi\)
0.486101 + 0.873903i \(0.338419\pi\)
\(72\) 9.85527 0.136879
\(73\) 25.9840 0.355945 0.177973 0.984035i \(-0.443046\pi\)
0.177973 + 0.984035i \(0.443046\pi\)
\(74\) 80.5540i 1.08857i
\(75\) −11.7427 −0.156569
\(76\) 28.9099i 0.380393i
\(77\) −94.2857 −1.22449
\(78\) 43.2777 0.554842
\(79\) 28.8543i 0.365244i −0.983183 0.182622i \(-0.941541\pi\)
0.983183 0.182622i \(-0.0584585\pi\)
\(80\) 8.94427i 0.111803i
\(81\) −37.4999 −0.462962
\(82\) −100.081 −1.22050
\(83\) 69.3871i 0.835989i −0.908449 0.417995i \(-0.862733\pi\)
0.908449 0.417995i \(-0.137267\pi\)
\(84\) 35.7831i 0.425989i
\(85\) 20.4162 0.240191
\(86\) 99.0071i 1.15125i
\(87\) −49.9800 −0.574483
\(88\) 35.0059i 0.397794i
\(89\) 45.4428i 0.510594i −0.966863 0.255297i \(-0.917827\pi\)
0.966863 0.255297i \(-0.0821732\pi\)
\(90\) 11.0185i 0.122428i
\(91\) 99.2661i 1.09084i
\(92\) 45.1058 9.02579i 0.490281 0.0981064i
\(93\) 86.5269 0.930396
\(94\) 93.7077 0.996891
\(95\) −32.3222 −0.340234
\(96\) −13.2853 −0.138389
\(97\) 74.4458i 0.767482i −0.923441 0.383741i \(-0.874636\pi\)
0.923441 0.383741i \(-0.125364\pi\)
\(98\) 12.7792 0.130400
\(99\) 43.1241i 0.435597i
\(100\) −10.0000 −0.100000
\(101\) −17.0563 −0.168874 −0.0844372 0.996429i \(-0.526909\pi\)
−0.0844372 + 0.996429i \(0.526909\pi\)
\(102\) 30.3251i 0.297305i
\(103\) 153.952i 1.49468i 0.664442 + 0.747340i \(0.268669\pi\)
−0.664442 + 0.747340i \(0.731331\pi\)
\(104\) 36.8550 0.354375
\(105\) −40.0067 −0.381016
\(106\) 109.512i 1.03313i
\(107\) 112.821i 1.05441i −0.849740 0.527203i \(-0.823241\pi\)
0.849740 0.527203i \(-0.176759\pi\)
\(108\) −58.6400 −0.542963
\(109\) 97.6061i 0.895468i 0.894167 + 0.447734i \(0.147769\pi\)
−0.894167 + 0.447734i \(0.852231\pi\)
\(110\) 39.1378 0.355798
\(111\) 133.773i 1.20517i
\(112\) 30.4726i 0.272077i
\(113\) 57.0620i 0.504974i 0.967600 + 0.252487i \(0.0812485\pi\)
−0.967600 + 0.252487i \(0.918752\pi\)
\(114\) 48.0097i 0.421138i
\(115\) 10.0911 + 50.4298i 0.0877490 + 0.438520i
\(116\) −42.5627 −0.366919
\(117\) 45.4020 0.388051
\(118\) −117.086 −0.992255
\(119\) 69.5568 0.584511
\(120\) 14.8535i 0.123779i
\(121\) −32.1765 −0.265921
\(122\) 33.9328i 0.278137i
\(123\) 166.201 1.35123
\(124\) 73.6857 0.594239
\(125\) 11.1803i 0.0894427i
\(126\) 37.5395i 0.297932i
\(127\) −151.376 −1.19194 −0.595969 0.803007i \(-0.703232\pi\)
−0.595969 + 0.803007i \(0.703232\pi\)
\(128\) −11.3137 −0.0883883
\(129\) 164.418i 1.27456i
\(130\) 41.2051i 0.316962i
\(131\) 46.7334 0.356743 0.178372 0.983963i \(-0.442917\pi\)
0.178372 + 0.983963i \(0.442917\pi\)
\(132\) 58.1331i 0.440403i
\(133\) −110.120 −0.827970
\(134\) 167.601i 1.25076i
\(135\) 65.5616i 0.485641i
\(136\) 25.8247i 0.189887i
\(137\) 31.1949i 0.227700i −0.993498 0.113850i \(-0.963682\pi\)
0.993498 0.113850i \(-0.0363183\pi\)
\(138\) −74.9058 + 14.9888i −0.542796 + 0.108615i
\(139\) 36.5517 0.262962 0.131481 0.991319i \(-0.458027\pi\)
0.131481 + 0.991319i \(0.458027\pi\)
\(140\) −34.0694 −0.243353
\(141\) −155.617 −1.10367
\(142\) −97.6180 −0.687451
\(143\) 161.268i 1.12775i
\(144\) −13.9375 −0.0967879
\(145\) 47.5865i 0.328183i
\(146\) −36.7470 −0.251691
\(147\) −21.2219 −0.144367
\(148\) 113.921i 0.769734i
\(149\) 182.281i 1.22336i 0.791104 + 0.611681i \(0.209506\pi\)
−0.791104 + 0.611681i \(0.790494\pi\)
\(150\) 16.6067 0.110711
\(151\) 40.9462 0.271167 0.135584 0.990766i \(-0.456709\pi\)
0.135584 + 0.990766i \(0.456709\pi\)
\(152\) 40.8848i 0.268979i
\(153\) 31.8136i 0.207932i
\(154\) 133.340 0.865845
\(155\) 82.3831i 0.531504i
\(156\) −61.2039 −0.392333
\(157\) 252.396i 1.60762i 0.594887 + 0.803810i \(0.297197\pi\)
−0.594887 + 0.803810i \(0.702803\pi\)
\(158\) 40.8062i 0.258267i
\(159\) 181.862i 1.14379i
\(160\) 12.6491i 0.0790569i
\(161\) 34.3799 + 171.811i 0.213540 + 1.06715i
\(162\) 53.0329 0.327364
\(163\) −46.9686 −0.288151 −0.144076 0.989567i \(-0.546021\pi\)
−0.144076 + 0.989567i \(0.546021\pi\)
\(164\) 141.536 0.863024
\(165\) −64.9948 −0.393908
\(166\) 98.1282i 0.591134i
\(167\) 78.4530 0.469778 0.234889 0.972022i \(-0.424527\pi\)
0.234889 + 0.972022i \(0.424527\pi\)
\(168\) 50.6049i 0.301220i
\(169\) 0.786229 0.00465224
\(170\) −28.8729 −0.169840
\(171\) 50.3663i 0.294540i
\(172\) 140.017i 0.814053i
\(173\) 137.080 0.792369 0.396184 0.918171i \(-0.370334\pi\)
0.396184 + 0.918171i \(0.370334\pi\)
\(174\) 70.6824 0.406221
\(175\) 38.0908i 0.217661i
\(176\) 49.5058i 0.281283i
\(177\) 194.441 1.09854
\(178\) 64.2659i 0.361044i
\(179\) −55.6699 −0.311005 −0.155503 0.987835i \(-0.549700\pi\)
−0.155503 + 0.987835i \(0.549700\pi\)
\(180\) 15.5826i 0.0865697i
\(181\) 23.7317i 0.131114i −0.997849 0.0655572i \(-0.979118\pi\)
0.997849 0.0655572i \(-0.0208825\pi\)
\(182\) 140.383i 0.771337i
\(183\) 56.3511i 0.307929i
\(184\) −63.7893 + 12.7644i −0.346681 + 0.0693717i
\(185\) −127.367 −0.688471
\(186\) −122.367 −0.657890
\(187\) 113.002 0.604289
\(188\) −132.523 −0.704908
\(189\) 223.364i 1.18182i
\(190\) 45.7105 0.240582
\(191\) 351.658i 1.84114i −0.390576 0.920571i \(-0.627724\pi\)
0.390576 0.920571i \(-0.372276\pi\)
\(192\) 18.7883 0.0978558
\(193\) −39.4808 −0.204564 −0.102282 0.994755i \(-0.532614\pi\)
−0.102282 + 0.994755i \(0.532614\pi\)
\(194\) 105.282i 0.542692i
\(195\) 68.4280i 0.350913i
\(196\) −18.0725 −0.0922064
\(197\) −225.017 −1.14222 −0.571108 0.820875i \(-0.693486\pi\)
−0.571108 + 0.820875i \(0.693486\pi\)
\(198\) 60.9866i 0.308013i
\(199\) 37.0872i 0.186368i −0.995649 0.0931840i \(-0.970296\pi\)
0.995649 0.0931840i \(-0.0297045\pi\)
\(200\) 14.1421 0.0707107
\(201\) 278.330i 1.38473i
\(202\) 24.1213 0.119412
\(203\) 162.124i 0.798642i
\(204\) 42.8862i 0.210227i
\(205\) 158.242i 0.771912i
\(206\) 217.721i 1.05690i
\(207\) −78.5826 + 15.7246i −0.379626 + 0.0759641i
\(208\) −52.1208 −0.250581
\(209\) −178.901 −0.855985
\(210\) 56.5780 0.269419
\(211\) 217.064 1.02874 0.514369 0.857569i \(-0.328026\pi\)
0.514369 + 0.857569i \(0.328026\pi\)
\(212\) 154.873i 0.730532i
\(213\) 162.111 0.761085
\(214\) 159.554i 0.745577i
\(215\) −156.544 −0.728111
\(216\) 82.9295 0.383933
\(217\) 280.674i 1.29343i
\(218\) 138.036i 0.633192i
\(219\) 61.0245 0.278651
\(220\) −55.3492 −0.251587
\(221\) 118.971i 0.538330i
\(222\) 189.184i 0.852181i
\(223\) 269.398 1.20806 0.604030 0.796961i \(-0.293561\pi\)
0.604030 + 0.796961i \(0.293561\pi\)
\(224\) 43.0948i 0.192387i
\(225\) 17.4218 0.0774303
\(226\) 80.6979i 0.357070i
\(227\) 175.997i 0.775319i −0.921803 0.387659i \(-0.873284\pi\)
0.921803 0.387659i \(-0.126716\pi\)
\(228\) 67.8960i 0.297789i
\(229\) 63.0669i 0.275401i −0.990474 0.137701i \(-0.956029\pi\)
0.990474 0.137701i \(-0.0439712\pi\)
\(230\) −14.2710 71.3186i −0.0620479 0.310081i
\(231\) −221.434 −0.958587
\(232\) 60.1927 0.259451
\(233\) 4.48041 0.0192292 0.00961461 0.999954i \(-0.496940\pi\)
0.00961461 + 0.999954i \(0.496940\pi\)
\(234\) −64.2081 −0.274394
\(235\) 148.165i 0.630489i
\(236\) 165.585 0.701630
\(237\) 67.7655i 0.285930i
\(238\) −98.3682 −0.413312
\(239\) 85.5205 0.357826 0.178913 0.983865i \(-0.442742\pi\)
0.178913 + 0.983865i \(0.442742\pi\)
\(240\) 21.0060i 0.0875249i
\(241\) 257.515i 1.06853i 0.845318 + 0.534263i \(0.179411\pi\)
−0.845318 + 0.534263i \(0.820589\pi\)
\(242\) 45.5044 0.188035
\(243\) 175.810 0.723498
\(244\) 47.9882i 0.196673i
\(245\) 20.2056i 0.0824719i
\(246\) −235.044 −0.955464
\(247\) 188.351i 0.762554i
\(248\) −104.207 −0.420191
\(249\) 162.958i 0.654451i
\(250\) 15.8114i 0.0632456i
\(251\) 121.438i 0.483816i 0.970299 + 0.241908i \(0.0777733\pi\)
−0.970299 + 0.241908i \(0.922227\pi\)
\(252\) 53.0888i 0.210670i
\(253\) 55.8536 + 279.125i 0.220765 + 1.10326i
\(254\) 214.078 0.842827
\(255\) 47.9482 0.188032
\(256\) 16.0000 0.0625000
\(257\) 192.295 0.748230 0.374115 0.927382i \(-0.377947\pi\)
0.374115 + 0.927382i \(0.377947\pi\)
\(258\) 232.522i 0.901248i
\(259\) −433.932 −1.67541
\(260\) 58.2728i 0.224126i
\(261\) 74.1519 0.284107
\(262\) −66.0910 −0.252256
\(263\) 417.798i 1.58858i 0.607536 + 0.794292i \(0.292158\pi\)
−0.607536 + 0.794292i \(0.707842\pi\)
\(264\) 82.2127i 0.311412i
\(265\) 173.153 0.653407
\(266\) 155.733 0.585463
\(267\) 106.724i 0.399716i
\(268\) 237.024i 0.884418i
\(269\) −474.878 −1.76534 −0.882672 0.469989i \(-0.844258\pi\)
−0.882672 + 0.469989i \(0.844258\pi\)
\(270\) 92.7180i 0.343400i
\(271\) −32.0762 −0.118362 −0.0591812 0.998247i \(-0.518849\pi\)
−0.0591812 + 0.998247i \(0.518849\pi\)
\(272\) 36.5216i 0.134271i
\(273\) 233.130i 0.853957i
\(274\) 44.1162i 0.161008i
\(275\) 61.8822i 0.225026i
\(276\) 105.933 21.1974i 0.383814 0.0768022i
\(277\) 459.038 1.65718 0.828589 0.559858i \(-0.189144\pi\)
0.828589 + 0.559858i \(0.189144\pi\)
\(278\) −51.6919 −0.185942
\(279\) −128.374 −0.460121
\(280\) 48.1814 0.172076
\(281\) 321.543i 1.14428i 0.820156 + 0.572140i \(0.193887\pi\)
−0.820156 + 0.572140i \(0.806113\pi\)
\(282\) 220.076 0.780412
\(283\) 428.712i 1.51488i −0.652904 0.757441i \(-0.726449\pi\)
0.652904 0.757441i \(-0.273551\pi\)
\(284\) 138.053 0.486101
\(285\) −75.9100 −0.266351
\(286\) 228.067i 0.797437i
\(287\) 539.121i 1.87847i
\(288\) 19.7105 0.0684394
\(289\) 205.636 0.711542
\(290\) 67.2975i 0.232060i
\(291\) 174.839i 0.600821i
\(292\) 51.9680 0.177973
\(293\) 359.840i 1.22812i 0.789258 + 0.614062i \(0.210466\pi\)
−0.789258 + 0.614062i \(0.789534\pi\)
\(294\) 30.0123 0.102083
\(295\) 185.129i 0.627557i
\(296\) 161.108i 0.544284i
\(297\) 362.878i 1.22181i
\(298\) 257.784i 0.865048i
\(299\) −293.869 + 58.8039i −0.982840 + 0.196669i
\(300\) −23.4854 −0.0782846
\(301\) −533.336 −1.77188
\(302\) −57.9067 −0.191744
\(303\) −40.0574 −0.132203
\(304\) 57.8198i 0.190197i
\(305\) −53.6524 −0.175910
\(306\) 44.9913i 0.147030i
\(307\) −448.843 −1.46203 −0.731014 0.682362i \(-0.760953\pi\)
−0.731014 + 0.682362i \(0.760953\pi\)
\(308\) −188.571 −0.612245
\(309\) 361.562i 1.17010i
\(310\) 116.507i 0.375830i
\(311\) 187.562 0.603094 0.301547 0.953451i \(-0.402497\pi\)
0.301547 + 0.953451i \(0.402497\pi\)
\(312\) 86.5554 0.277421
\(313\) 93.4265i 0.298487i −0.988800 0.149244i \(-0.952316\pi\)
0.988800 0.149244i \(-0.0476839\pi\)
\(314\) 356.942i 1.13676i
\(315\) 59.3551 0.188429
\(316\) 57.7086i 0.182622i
\(317\) 453.069 1.42924 0.714620 0.699513i \(-0.246600\pi\)
0.714620 + 0.699513i \(0.246600\pi\)
\(318\) 257.192i 0.808780i
\(319\) 263.387i 0.825665i
\(320\) 17.8885i 0.0559017i
\(321\) 264.965i 0.825437i
\(322\) −48.6205 242.978i −0.150995 0.754590i
\(323\) 131.979 0.408605
\(324\) −74.9999 −0.231481
\(325\) 65.1510 0.200465
\(326\) 66.4237 0.203754
\(327\) 229.232i 0.701014i
\(328\) −200.162 −0.610250
\(329\) 504.789i 1.53431i
\(330\) 91.9166 0.278535
\(331\) −178.326 −0.538749 −0.269374 0.963036i \(-0.586817\pi\)
−0.269374 + 0.963036i \(0.586817\pi\)
\(332\) 138.774i 0.417995i
\(333\) 198.470i 0.596007i
\(334\) −110.949 −0.332183
\(335\) 265.001 0.791048
\(336\) 71.5661i 0.212994i
\(337\) 85.7271i 0.254383i 0.991878 + 0.127192i \(0.0405963\pi\)
−0.991878 + 0.127192i \(0.959404\pi\)
\(338\) −1.11190 −0.00328963
\(339\) 134.012i 0.395317i
\(340\) 40.8324 0.120095
\(341\) 455.984i 1.33720i
\(342\) 71.2287i 0.208271i
\(343\) 304.450i 0.887610i
\(344\) 198.014i 0.575623i
\(345\) 23.6994 + 118.436i 0.0686940 + 0.343294i
\(346\) −193.860 −0.560289
\(347\) 216.730 0.624582 0.312291 0.949986i \(-0.398904\pi\)
0.312291 + 0.949986i \(0.398904\pi\)
\(348\) −99.9601 −0.287242
\(349\) −528.822 −1.51525 −0.757624 0.652691i \(-0.773640\pi\)
−0.757624 + 0.652691i \(0.773640\pi\)
\(350\) 53.8685i 0.153910i
\(351\) 382.046 1.08845
\(352\) 70.0118i 0.198897i
\(353\) −28.7915 −0.0815623 −0.0407811 0.999168i \(-0.512985\pi\)
−0.0407811 + 0.999168i \(0.512985\pi\)
\(354\) −274.981 −0.776783
\(355\) 154.348i 0.434782i
\(356\) 90.8857i 0.255297i
\(357\) 163.357 0.457582
\(358\) 78.7292 0.219914
\(359\) 55.5671i 0.154783i −0.997001 0.0773914i \(-0.975341\pi\)
0.997001 0.0773914i \(-0.0246591\pi\)
\(360\) 22.0371i 0.0612140i
\(361\) 152.055 0.421204
\(362\) 33.5617i 0.0927119i
\(363\) −75.5677 −0.208176
\(364\) 198.532i 0.545418i
\(365\) 58.1020i 0.159184i
\(366\) 79.6924i 0.217739i
\(367\) 164.288i 0.447652i 0.974629 + 0.223826i \(0.0718547\pi\)
−0.974629 + 0.223826i \(0.928145\pi\)
\(368\) 90.2116 18.0516i 0.245140 0.0490532i
\(369\) −246.581 −0.668242
\(370\) 180.124 0.486822
\(371\) 589.922 1.59009
\(372\) 173.054 0.465198
\(373\) 25.1481i 0.0674212i 0.999432 + 0.0337106i \(0.0107325\pi\)
−0.999432 + 0.0337106i \(0.989268\pi\)
\(374\) −159.809 −0.427297
\(375\) 26.2575i 0.0700199i
\(376\) 187.415 0.498445
\(377\) 277.300 0.735544
\(378\) 315.885i 0.835674i
\(379\) 456.740i 1.20512i 0.798074 + 0.602560i \(0.205852\pi\)
−0.798074 + 0.602560i \(0.794148\pi\)
\(380\) −64.6445 −0.170117
\(381\) −355.513 −0.933104
\(382\) 497.319i 1.30188i
\(383\) 371.017i 0.968712i −0.874871 0.484356i \(-0.839054\pi\)
0.874871 0.484356i \(-0.160946\pi\)
\(384\) −26.5707 −0.0691945
\(385\) 210.829i 0.547608i
\(386\) 55.8343 0.144648
\(387\) 243.935i 0.630324i
\(388\) 148.892i 0.383741i
\(389\) 400.013i 1.02831i 0.857697 + 0.514155i \(0.171895\pi\)
−0.857697 + 0.514155i \(0.828105\pi\)
\(390\) 96.7718i 0.248133i
\(391\) −41.2045 205.917i −0.105382 0.526642i
\(392\) 25.5583 0.0651998
\(393\) 109.755 0.279275
\(394\) 318.222 0.807669
\(395\) 64.5202 0.163342
\(396\) 86.2481i 0.217798i
\(397\) 264.267 0.665659 0.332830 0.942987i \(-0.391997\pi\)
0.332830 + 0.942987i \(0.391997\pi\)
\(398\) 52.4493i 0.131782i
\(399\) −258.621 −0.648173
\(400\) −20.0000 −0.0500000
\(401\) 425.319i 1.06065i −0.847796 0.530323i \(-0.822071\pi\)
0.847796 0.530323i \(-0.177929\pi\)
\(402\) 393.618i 0.979150i
\(403\) −480.070 −1.19124
\(404\) −34.1126 −0.0844372
\(405\) 83.8524i 0.207043i
\(406\) 229.278i 0.564725i
\(407\) −704.966 −1.73210
\(408\) 60.6503i 0.148653i
\(409\) −241.558 −0.590607 −0.295304 0.955403i \(-0.595421\pi\)
−0.295304 + 0.955403i \(0.595421\pi\)
\(410\) 223.788i 0.545824i
\(411\) 73.2624i 0.178254i
\(412\) 307.904i 0.747340i
\(413\) 630.725i 1.52718i
\(414\) 111.133 22.2379i 0.268436 0.0537147i
\(415\) 155.154 0.373866
\(416\) 73.7100 0.177187
\(417\) 85.8431 0.205859
\(418\) 253.004 0.605273
\(419\) 358.352i 0.855256i 0.903955 + 0.427628i \(0.140651\pi\)
−0.903955 + 0.427628i \(0.859349\pi\)
\(420\) −80.0133 −0.190508
\(421\) 672.051i 1.59632i −0.602446 0.798160i \(-0.705807\pi\)
0.602446 0.798160i \(-0.294193\pi\)
\(422\) −306.975 −0.727428
\(423\) 230.879 0.545813
\(424\) 219.023i 0.516564i
\(425\) 45.6520i 0.107417i
\(426\) −229.260 −0.538168
\(427\) −182.791 −0.428081
\(428\) 225.643i 0.527203i
\(429\) 378.743i 0.882852i
\(430\) 221.387 0.514852
\(431\) 819.926i 1.90238i 0.308604 + 0.951191i \(0.400138\pi\)
−0.308604 + 0.951191i \(0.599862\pi\)
\(432\) −117.280 −0.271482
\(433\) 316.231i 0.730326i −0.930944 0.365163i \(-0.881013\pi\)
0.930944 0.365163i \(-0.118987\pi\)
\(434\) 396.933i 0.914593i
\(435\) 111.759i 0.256917i
\(436\) 195.212i 0.447734i
\(437\) 65.2336 + 326.001i 0.149276 + 0.745998i
\(438\) −86.3017 −0.197036
\(439\) 208.878 0.475805 0.237903 0.971289i \(-0.423540\pi\)
0.237903 + 0.971289i \(0.423540\pi\)
\(440\) 78.2755 0.177899
\(441\) 31.4855 0.0713957
\(442\) 168.250i 0.380657i
\(443\) −706.981 −1.59589 −0.797947 0.602728i \(-0.794081\pi\)
−0.797947 + 0.602728i \(0.794081\pi\)
\(444\) 267.547i 0.602583i
\(445\) 101.613 0.228344
\(446\) −380.986 −0.854228
\(447\) 428.094i 0.957705i
\(448\) 60.9452i 0.136038i
\(449\) −524.552 −1.16827 −0.584134 0.811658i \(-0.698566\pi\)
−0.584134 + 0.811658i \(0.698566\pi\)
\(450\) −24.6382 −0.0547515
\(451\) 875.856i 1.94203i
\(452\) 114.124i 0.252487i
\(453\) 96.1639 0.212282
\(454\) 248.898i 0.548233i
\(455\) 221.966 0.487837
\(456\) 96.0194i 0.210569i
\(457\) 786.926i 1.72194i −0.508657 0.860969i \(-0.669858\pi\)
0.508657 0.860969i \(-0.330142\pi\)
\(458\) 89.1901i 0.194738i
\(459\) 267.704i 0.583232i
\(460\) 20.1823 + 100.860i 0.0438745 + 0.219260i
\(461\) −38.2459 −0.0829629 −0.0414814 0.999139i \(-0.513208\pi\)
−0.0414814 + 0.999139i \(0.513208\pi\)
\(462\) 313.154 0.677823
\(463\) −525.945 −1.13595 −0.567976 0.823045i \(-0.692273\pi\)
−0.567976 + 0.823045i \(0.692273\pi\)
\(464\) −85.1253 −0.183460
\(465\) 193.480i 0.416086i
\(466\) −6.33625 −0.0135971
\(467\) 166.631i 0.356812i −0.983957 0.178406i \(-0.942906\pi\)
0.983957 0.178406i \(-0.0570941\pi\)
\(468\) 90.8040 0.194026
\(469\) 902.843 1.92504
\(470\) 209.537i 0.445823i
\(471\) 592.762i 1.25852i
\(472\) −234.172 −0.496127
\(473\) −866.458 −1.83183
\(474\) 95.8349i 0.202183i
\(475\) 72.2747i 0.152157i
\(476\) 139.114 0.292255
\(477\) 269.817i 0.565653i
\(478\) −120.944 −0.253021
\(479\) 32.0653i 0.0669422i −0.999440 0.0334711i \(-0.989344\pi\)
0.999440 0.0334711i \(-0.0106562\pi\)
\(480\) 29.7069i 0.0618894i
\(481\) 742.204i 1.54304i
\(482\) 364.181i 0.755562i
\(483\) 80.7425 + 403.506i 0.167169 + 0.835416i
\(484\) −64.3530 −0.132961
\(485\) 166.466 0.343228
\(486\) −248.633 −0.511591
\(487\) 685.808 1.40823 0.704115 0.710085i \(-0.251344\pi\)
0.704115 + 0.710085i \(0.251344\pi\)
\(488\) 67.8655i 0.139069i
\(489\) −110.308 −0.225578
\(490\) 28.5751i 0.0583165i
\(491\) 775.805 1.58005 0.790026 0.613074i \(-0.210067\pi\)
0.790026 + 0.613074i \(0.210067\pi\)
\(492\) 332.403 0.675615
\(493\) 194.307i 0.394132i
\(494\) 266.368i 0.539207i
\(495\) 96.4283 0.194805
\(496\) 147.371 0.297120
\(497\) 525.853i 1.05805i
\(498\) 230.458i 0.462767i
\(499\) 392.467 0.786507 0.393253 0.919430i \(-0.371350\pi\)
0.393253 + 0.919430i \(0.371350\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) 184.250 0.367764
\(502\) 171.739i 0.342110i
\(503\) 633.449i 1.25934i −0.776862 0.629671i \(-0.783190\pi\)
0.776862 0.629671i \(-0.216810\pi\)
\(504\) 75.0789i 0.148966i
\(505\) 38.1391i 0.0755229i
\(506\) −78.9889 394.742i −0.156105 0.780123i
\(507\) 1.84649 0.00364199
\(508\) −302.752 −0.595969
\(509\) 540.009 1.06092 0.530460 0.847710i \(-0.322019\pi\)
0.530460 + 0.847710i \(0.322019\pi\)
\(510\) −67.8091 −0.132959
\(511\) 197.950i 0.387378i
\(512\) −22.6274 −0.0441942
\(513\) 423.819i 0.826158i
\(514\) −271.946 −0.529078
\(515\) −344.247 −0.668441
\(516\) 328.836i 0.637279i
\(517\) 820.080i 1.58623i
\(518\) 613.673 1.18470
\(519\) 321.937 0.620303
\(520\) 82.4102i 0.158481i
\(521\) 396.259i 0.760574i −0.924869 0.380287i \(-0.875825\pi\)
0.924869 0.380287i \(-0.124175\pi\)
\(522\) −104.867 −0.200894
\(523\) 27.4737i 0.0525309i 0.999655 + 0.0262655i \(0.00836152\pi\)
−0.999655 + 0.0262655i \(0.991638\pi\)
\(524\) 93.4668 0.178372
\(525\) 89.4576i 0.170395i
\(526\) 590.855i 1.12330i
\(527\) 336.390i 0.638311i
\(528\) 116.266i 0.220201i
\(529\) 488.268 203.558i 0.923001 0.384797i
\(530\) −244.875 −0.462029
\(531\) −288.479 −0.543274
\(532\) −220.240 −0.413985
\(533\) −922.121 −1.73006
\(534\) 150.931i 0.282642i
\(535\) 252.276 0.471544
\(536\) 335.203i 0.625378i
\(537\) −130.743 −0.243469
\(538\) 671.578 1.24829
\(539\) 111.836i 0.207489i
\(540\) 131.123i 0.242821i
\(541\) −802.725 −1.48378 −0.741890 0.670522i \(-0.766070\pi\)
−0.741890 + 0.670522i \(0.766070\pi\)
\(542\) 45.3626 0.0836948
\(543\) 55.7349i 0.102643i
\(544\) 51.6494i 0.0949437i
\(545\) −218.254 −0.400466
\(546\) 329.696i 0.603839i
\(547\) −439.126 −0.802790 −0.401395 0.915905i \(-0.631475\pi\)
−0.401395 + 0.915905i \(0.631475\pi\)
\(548\) 62.3897i 0.113850i
\(549\) 83.6042i 0.152284i
\(550\) 87.5147i 0.159118i
\(551\) 307.620i 0.558295i
\(552\) −149.812 + 29.9777i −0.271398 + 0.0543074i
\(553\) 219.817 0.397498
\(554\) −649.178 −1.17180
\(555\) −299.127 −0.538967
\(556\) 73.1034 0.131481
\(557\) 795.405i 1.42802i 0.700137 + 0.714008i \(0.253122\pi\)
−0.700137 + 0.714008i \(0.746878\pi\)
\(558\) 181.548 0.325355
\(559\) 912.226i 1.63189i
\(560\) −68.1388 −0.121676
\(561\) 265.390 0.473065
\(562\) 454.730i 0.809128i
\(563\) 214.573i 0.381124i 0.981675 + 0.190562i \(0.0610309\pi\)
−0.981675 + 0.190562i \(0.938969\pi\)
\(564\) −311.235 −0.551835
\(565\) −127.595 −0.225831
\(566\) 606.290i 1.07118i
\(567\) 285.680i 0.503845i
\(568\) −195.236 −0.343725
\(569\) 1101.54i 1.93592i −0.251114 0.967958i \(-0.580797\pi\)
0.251114 0.967958i \(-0.419203\pi\)
\(570\) 107.353 0.188339
\(571\) 560.543i 0.981686i −0.871248 0.490843i \(-0.836689\pi\)
0.871248 0.490843i \(-0.163311\pi\)
\(572\) 322.535i 0.563873i
\(573\) 825.882i 1.44133i
\(574\) 762.433i 1.32828i
\(575\) −112.765 + 22.5645i −0.196112 + 0.0392425i
\(576\) −27.8749 −0.0483939
\(577\) 795.419 1.37854 0.689271 0.724504i \(-0.257931\pi\)
0.689271 + 0.724504i \(0.257931\pi\)
\(578\) −290.813 −0.503136
\(579\) −92.7222 −0.160142
\(580\) 95.1730i 0.164091i
\(581\) 528.602 0.909813
\(582\) 247.259i 0.424844i
\(583\) 958.387 1.64389
\(584\) −73.4939 −0.125846
\(585\) 101.522i 0.173542i
\(586\) 508.891i 0.868415i
\(587\) 579.454 0.987144 0.493572 0.869705i \(-0.335691\pi\)
0.493572 + 0.869705i \(0.335691\pi\)
\(588\) −42.4439 −0.0721834
\(589\) 532.561i 0.904179i
\(590\) 261.812i 0.443750i
\(591\) −528.460 −0.894180
\(592\) 227.841i 0.384867i
\(593\) −175.139 −0.295344 −0.147672 0.989036i \(-0.547178\pi\)
−0.147672 + 0.989036i \(0.547178\pi\)
\(594\) 513.187i 0.863950i
\(595\) 155.534i 0.261401i
\(596\) 364.562i 0.611681i
\(597\) 87.1009i 0.145898i
\(598\) 415.594 83.1613i 0.694973 0.139066i
\(599\) −512.672 −0.855879 −0.427940 0.903807i \(-0.640760\pi\)
−0.427940 + 0.903807i \(0.640760\pi\)
\(600\) 33.2134 0.0553556
\(601\) −175.570 −0.292130 −0.146065 0.989275i \(-0.546661\pi\)
−0.146065 + 0.989275i \(0.546661\pi\)
\(602\) 754.251 1.25291
\(603\) 412.939i 0.684808i
\(604\) 81.8925 0.135584
\(605\) 71.9488i 0.118924i
\(606\) 56.6497 0.0934814
\(607\) −173.873 −0.286447 −0.143223 0.989690i \(-0.545747\pi\)
−0.143223 + 0.989690i \(0.545747\pi\)
\(608\) 81.7695i 0.134489i
\(609\) 380.755i 0.625214i
\(610\) 75.8760 0.124387
\(611\) 863.399 1.41309
\(612\) 63.6273i 0.103966i
\(613\) 560.182i 0.913837i −0.889509 0.456919i \(-0.848953\pi\)
0.889509 0.456919i \(-0.151047\pi\)
\(614\) 634.760 1.03381
\(615\) 371.638i 0.604289i
\(616\) 266.680 0.432922
\(617\) 308.240i 0.499578i −0.968300 0.249789i \(-0.919639\pi\)
0.968300 0.249789i \(-0.0803613\pi\)
\(618\) 511.326i 0.827389i
\(619\) 424.114i 0.685161i −0.939489 0.342580i \(-0.888699\pi\)
0.939489 0.342580i \(-0.111301\pi\)
\(620\) 164.766i 0.265752i
\(621\) −661.252 + 132.318i −1.06482 + 0.213073i
\(622\) −265.253 −0.426452
\(623\) 346.190 0.555683
\(624\) −122.408 −0.196166
\(625\) 25.0000 0.0400000
\(626\) 132.125i 0.211062i
\(627\) −420.156 −0.670105
\(628\) 504.792i 0.803810i
\(629\) 520.070 0.826821
\(630\) −83.9408 −0.133239
\(631\) 172.251i 0.272981i 0.990641 + 0.136491i \(0.0435823\pi\)
−0.990641 + 0.136491i \(0.956418\pi\)
\(632\) 81.6123i 0.129133i
\(633\) 509.783 0.805344
\(634\) −640.737 −1.01063
\(635\) 338.487i 0.533051i
\(636\) 363.725i 0.571894i
\(637\) 117.744 0.184841
\(638\) 372.486i 0.583834i
\(639\) −240.513 −0.376390
\(640\) 25.2982i 0.0395285i
\(641\) 365.954i 0.570912i −0.958392 0.285456i \(-0.907855\pi\)
0.958392 0.285456i \(-0.0921450\pi\)
\(642\) 374.718i 0.583672i
\(643\) 823.317i 1.28043i −0.768195 0.640215i \(-0.778845\pi\)
0.768195 0.640215i \(-0.221155\pi\)
\(644\) 68.7598 + 343.623i 0.106770 + 0.533576i
\(645\) −367.650 −0.569999
\(646\) −186.647 −0.288927
\(647\) −828.654 −1.28076 −0.640381 0.768057i \(-0.721224\pi\)
−0.640381 + 0.768057i \(0.721224\pi\)
\(648\) 106.066 0.163682
\(649\) 1024.68i 1.57885i
\(650\) −92.1375 −0.141750
\(651\) 659.175i 1.01256i
\(652\) −93.9372 −0.144076
\(653\) −912.811 −1.39787 −0.698937 0.715183i \(-0.746343\pi\)
−0.698937 + 0.715183i \(0.746343\pi\)
\(654\) 324.182i 0.495692i
\(655\) 104.499i 0.159541i
\(656\) 283.072 0.431512
\(657\) −90.5378 −0.137805
\(658\) 713.880i 1.08492i
\(659\) 247.106i 0.374971i 0.982267 + 0.187486i \(0.0600338\pi\)
−0.982267 + 0.187486i \(0.939966\pi\)
\(660\) −129.990 −0.196954
\(661\) 937.016i 1.41757i −0.705423 0.708787i \(-0.749243\pi\)
0.705423 0.708787i \(-0.250757\pi\)
\(662\) 252.191 0.380953
\(663\) 279.408i 0.421430i
\(664\) 196.256i 0.295567i
\(665\) 246.236i 0.370279i
\(666\) 280.680i 0.421441i
\(667\) −479.956 + 96.0404i −0.719574 + 0.143989i
\(668\) 156.906 0.234889
\(669\) 632.691 0.945726
\(670\) −374.768 −0.559355
\(671\) −296.962 −0.442566
\(672\) 101.210i 0.150610i
\(673\) 1174.75 1.74554 0.872769 0.488134i \(-0.162322\pi\)
0.872769 + 0.488134i \(0.162322\pi\)
\(674\) 121.236i 0.179876i
\(675\) 146.600 0.217185
\(676\) 1.57246 0.00232612
\(677\) 266.022i 0.392943i 0.980510 + 0.196471i \(0.0629483\pi\)
−0.980510 + 0.196471i \(0.937052\pi\)
\(678\) 189.522i 0.279531i
\(679\) 567.139 0.835256
\(680\) −57.7457 −0.0849202
\(681\) 413.337i 0.606955i
\(682\) 644.858i 0.945540i
\(683\) −214.808 −0.314507 −0.157254 0.987558i \(-0.550264\pi\)
−0.157254 + 0.987558i \(0.550264\pi\)
\(684\) 100.733i 0.147270i
\(685\) 69.7539 0.101830
\(686\) 430.557i 0.627635i
\(687\) 148.115i 0.215597i
\(688\) 280.034i 0.407027i
\(689\) 1009.01i 1.46446i
\(690\) −33.5161 167.494i −0.0485740 0.242746i
\(691\) −998.531 −1.44505 −0.722526 0.691344i \(-0.757019\pi\)
−0.722526 + 0.691344i \(0.757019\pi\)
\(692\) 274.160 0.396184
\(693\) 328.526 0.474063
\(694\) −306.502 −0.441646
\(695\) 81.7321i 0.117600i
\(696\) 141.365 0.203110
\(697\) 646.140i 0.927030i
\(698\) 747.867 1.07144
\(699\) 10.5224 0.0150535
\(700\) 76.1815i 0.108831i
\(701\) 1089.04i 1.55356i 0.629773 + 0.776779i \(0.283148\pi\)
−0.629773 + 0.776779i \(0.716852\pi\)
\(702\) −540.294 −0.769650
\(703\) −823.358 −1.17121
\(704\) 99.0116i 0.140641i
\(705\) 347.971i 0.493576i
\(706\) 40.7173 0.0576732
\(707\) 129.938i 0.183787i
\(708\) 388.882 0.549268
\(709\) 779.102i 1.09887i −0.835535 0.549437i \(-0.814842\pi\)
0.835535 0.549437i \(-0.185158\pi\)
\(710\) 218.280i 0.307437i
\(711\) 100.539i 0.141405i
\(712\) 128.532i 0.180522i
\(713\) 830.913 166.268i 1.16538 0.233195i
\(714\) −231.021 −0.323559
\(715\) 360.605 0.504343
\(716\) −111.340 −0.155503
\(717\) 200.848 0.280123
\(718\) 78.5837i 0.109448i
\(719\) −802.454 −1.11607 −0.558035 0.829817i \(-0.688445\pi\)
−0.558035 + 0.829817i \(0.688445\pi\)
\(720\) 31.1651i 0.0432849i
\(721\) −1172.83 −1.62667
\(722\) −215.038 −0.297836
\(723\) 604.784i 0.836492i
\(724\) 47.4634i 0.0655572i
\(725\) 106.407 0.146768
\(726\) 106.869 0.147202
\(727\) 19.7852i 0.0272149i 0.999907 + 0.0136075i \(0.00433152\pi\)
−0.999907 + 0.0136075i \(0.995668\pi\)
\(728\) 280.767i 0.385669i
\(729\) 750.396 1.02935
\(730\) 82.1687i 0.112560i
\(731\) 639.207 0.874428
\(732\) 112.702i 0.153965i
\(733\) 609.029i 0.830871i 0.909623 + 0.415436i \(0.136371\pi\)
−0.909623 + 0.415436i \(0.863629\pi\)
\(734\) 232.339i 0.316538i
\(735\) 47.4537i 0.0645628i
\(736\) −127.579 + 25.5288i −0.173340 + 0.0346858i
\(737\) 1466.76 1.99017
\(738\) 348.719 0.472519
\(739\) 780.692 1.05642 0.528209 0.849115i \(-0.322864\pi\)
0.528209 + 0.849115i \(0.322864\pi\)
\(740\) −254.734 −0.344235
\(741\) 442.349i 0.596963i
\(742\) −834.276 −1.12436
\(743\) 46.4819i 0.0625598i 0.999511 + 0.0312799i \(0.00995832\pi\)
−0.999511 + 0.0312799i \(0.990042\pi\)
\(744\) −244.735 −0.328945
\(745\) −407.593 −0.547104
\(746\) 35.5648i 0.0476740i
\(747\) 241.770i 0.323655i
\(748\) 226.004 0.302144
\(749\) 859.490 1.14752
\(750\) 37.1337i 0.0495116i
\(751\) 1258.62i 1.67592i −0.545728 0.837962i \(-0.683747\pi\)
0.545728 0.837962i \(-0.316253\pi\)
\(752\) −265.045 −0.352454
\(753\) 285.202i 0.378754i
\(754\) −392.161 −0.520108
\(755\) 91.5586i 0.121270i
\(756\) 446.729i 0.590911i
\(757\) 615.435i 0.812992i 0.913653 + 0.406496i \(0.133249\pi\)
−0.913653 + 0.406496i \(0.866751\pi\)
\(758\) 645.928i 0.852148i
\(759\) 131.174 + 655.536i 0.172825 + 0.863684i
\(760\) 91.4211 0.120291
\(761\) −795.461 −1.04528 −0.522642 0.852552i \(-0.675053\pi\)
−0.522642 + 0.852552i \(0.675053\pi\)
\(762\) 502.771 0.659804
\(763\) −743.578 −0.974545
\(764\) 703.316i 0.920571i
\(765\) −71.1375 −0.0929902
\(766\) 524.697i 0.684983i
\(767\) −1078.80 −1.40652
\(768\) 37.5766 0.0489279
\(769\) 1031.00i 1.34070i 0.742046 + 0.670349i \(0.233855\pi\)
−0.742046 + 0.670349i \(0.766145\pi\)
\(770\) 298.157i 0.387217i
\(771\) 451.613 0.585749
\(772\) −78.9616 −0.102282
\(773\) 1281.23i 1.65747i 0.559638 + 0.828737i \(0.310940\pi\)
−0.559638 + 0.828737i \(0.689060\pi\)
\(774\) 344.977i 0.445706i
\(775\) −184.214 −0.237696
\(776\) 210.564i 0.271346i
\(777\) −1019.11 −1.31159
\(778\) 565.704i 0.727126i
\(779\) 1022.95i 1.31315i
\(780\) 136.856i 0.175456i
\(781\) 854.301i 1.09386i
\(782\) 58.2720 + 291.211i 0.0745166 + 0.372392i
\(783\) 623.969 0.796895
\(784\) −36.1449 −0.0461032
\(785\) −564.375 −0.718949
\(786\) −155.217 −0.197477
\(787\) 1496.92i 1.90206i 0.309096 + 0.951031i \(0.399973\pi\)
−0.309096 +