Properties

Label 483.3.f.a.22.2
Level $483$
Weight $3$
Character 483.22
Analytic conductor $13.161$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 483.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.1607967686\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 22.2
Character \(\chi\) \(=\) 483.22
Dual form 483.3.f.a.22.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.89548 q^{2} -1.73205 q^{3} +11.1748 q^{4} -5.58204i q^{5} +6.74717 q^{6} -2.64575i q^{7} -27.9492 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-3.89548 q^{2} -1.73205 q^{3} +11.1748 q^{4} -5.58204i q^{5} +6.74717 q^{6} -2.64575i q^{7} -27.9492 q^{8} +3.00000 q^{9} +21.7447i q^{10} +2.39573i q^{11} -19.3553 q^{12} +3.11386 q^{13} +10.3065i q^{14} +9.66838i q^{15} +64.1766 q^{16} +21.5972i q^{17} -11.6864 q^{18} +28.1601i q^{19} -62.3781i q^{20} +4.58258i q^{21} -9.33253i q^{22} +(-12.2020 - 19.4964i) q^{23} +48.4095 q^{24} -6.15917 q^{25} -12.1300 q^{26} -5.19615 q^{27} -29.5657i q^{28} -26.5764 q^{29} -37.6630i q^{30} -10.2295 q^{31} -138.202 q^{32} -4.14953i q^{33} -84.1314i q^{34} -14.7687 q^{35} +33.5243 q^{36} +23.1532i q^{37} -109.697i q^{38} -5.39336 q^{39} +156.014i q^{40} +43.5431 q^{41} -17.8513i q^{42} -37.6961i q^{43} +26.7718i q^{44} -16.7461i q^{45} +(47.5326 + 75.9481i) q^{46} -31.7454 q^{47} -111.157 q^{48} -7.00000 q^{49} +23.9929 q^{50} -37.4074i q^{51} +34.7967 q^{52} +76.1649i q^{53} +20.2415 q^{54} +13.3731 q^{55} +73.9467i q^{56} -48.7747i q^{57} +103.528 q^{58} +80.8498 q^{59} +108.042i q^{60} +58.9379i q^{61} +39.8488 q^{62} -7.93725i q^{63} +281.657 q^{64} -17.3817i q^{65} +16.1644i q^{66} -11.9484i q^{67} +241.344i q^{68} +(21.1345 + 33.7688i) q^{69} +57.5312 q^{70} +105.964 q^{71} -83.8477 q^{72} -15.6066 q^{73} -90.1930i q^{74} +10.6680 q^{75} +314.683i q^{76} +6.33851 q^{77} +21.0097 q^{78} +118.357i q^{79} -358.236i q^{80} +9.00000 q^{81} -169.621 q^{82} -52.9699i q^{83} +51.2093i q^{84} +120.556 q^{85} +146.844i q^{86} +46.0317 q^{87} -66.9588i q^{88} +6.05127i q^{89} +65.2342i q^{90} -8.23850i q^{91} +(-136.355 - 217.869i) q^{92} +17.7180 q^{93} +123.664 q^{94} +157.191 q^{95} +239.373 q^{96} -46.7582i q^{97} +27.2684 q^{98} +7.18719i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 4q^{2} + 116q^{4} - 24q^{6} - 4q^{8} + 144q^{9} + O(q^{10}) \) \( 48q + 4q^{2} + 116q^{4} - 24q^{6} - 4q^{8} + 144q^{9} + 16q^{13} + 324q^{16} + 12q^{18} - 4q^{23} - 24q^{24} - 176q^{25} + 136q^{26} - 128q^{29} - 8q^{31} - 252q^{32} - 56q^{35} + 348q^{36} + 96q^{39} - 24q^{41} - 148q^{46} - 408q^{47} - 96q^{48} - 336q^{49} + 236q^{50} - 32q^{52} - 72q^{54} - 24q^{55} - 56q^{58} + 136q^{59} + 184q^{62} + 716q^{64} - 48q^{69} - 112q^{70} + 48q^{71} - 12q^{72} - 224q^{73} - 48q^{75} + 224q^{77} - 96q^{78} + 432q^{81} + 640q^{82} - 424q^{85} + 312q^{87} + 1060q^{92} + 192q^{93} + 216q^{94} + 624q^{95} + 48q^{96} - 28q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(346\) \(442\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.89548 −1.94774 −0.973871 0.227104i \(-0.927074\pi\)
−0.973871 + 0.227104i \(0.927074\pi\)
\(3\) −1.73205 −0.577350
\(4\) 11.1748 2.79370
\(5\) 5.58204i 1.11641i −0.829704 0.558204i \(-0.811491\pi\)
0.829704 0.558204i \(-0.188509\pi\)
\(6\) 6.74717 1.12453
\(7\) 2.64575i 0.377964i
\(8\) −27.9492 −3.49365
\(9\) 3.00000 0.333333
\(10\) 21.7447i 2.17447i
\(11\) 2.39573i 0.217794i 0.994053 + 0.108897i \(0.0347318\pi\)
−0.994053 + 0.108897i \(0.965268\pi\)
\(12\) −19.3553 −1.61294
\(13\) 3.11386 0.239528 0.119764 0.992802i \(-0.461786\pi\)
0.119764 + 0.992802i \(0.461786\pi\)
\(14\) 10.3065i 0.736177i
\(15\) 9.66838i 0.644558i
\(16\) 64.1766 4.01104
\(17\) 21.5972i 1.27042i 0.772339 + 0.635211i \(0.219087\pi\)
−0.772339 + 0.635211i \(0.780913\pi\)
\(18\) −11.6864 −0.649247
\(19\) 28.1601i 1.48211i 0.671444 + 0.741055i \(0.265674\pi\)
−0.671444 + 0.741055i \(0.734326\pi\)
\(20\) 62.3781i 3.11890i
\(21\) 4.58258i 0.218218i
\(22\) 9.33253i 0.424206i
\(23\) −12.2020 19.4964i −0.530521 0.847672i
\(24\) 48.4095 2.01706
\(25\) −6.15917 −0.246367
\(26\) −12.1300 −0.466538
\(27\) −5.19615 −0.192450
\(28\) 29.5657i 1.05592i
\(29\) −26.5764 −0.916427 −0.458214 0.888842i \(-0.651511\pi\)
−0.458214 + 0.888842i \(0.651511\pi\)
\(30\) 37.6630i 1.25543i
\(31\) −10.2295 −0.329983 −0.164992 0.986295i \(-0.552760\pi\)
−0.164992 + 0.986295i \(0.552760\pi\)
\(32\) −138.202 −4.31881
\(33\) 4.14953i 0.125743i
\(34\) 84.1314i 2.47445i
\(35\) −14.7687 −0.421963
\(36\) 33.5243 0.931232
\(37\) 23.1532i 0.625763i 0.949792 + 0.312881i \(0.101294\pi\)
−0.949792 + 0.312881i \(0.898706\pi\)
\(38\) 109.697i 2.88677i
\(39\) −5.39336 −0.138291
\(40\) 156.014i 3.90034i
\(41\) 43.5431 1.06203 0.531013 0.847363i \(-0.321811\pi\)
0.531013 + 0.847363i \(0.321811\pi\)
\(42\) 17.8513i 0.425032i
\(43\) 37.6961i 0.876653i −0.898816 0.438326i \(-0.855571\pi\)
0.898816 0.438326i \(-0.144429\pi\)
\(44\) 26.7718i 0.608449i
\(45\) 16.7461i 0.372136i
\(46\) 47.5326 + 75.9481i 1.03332 + 1.65104i
\(47\) −31.7454 −0.675435 −0.337717 0.941248i \(-0.609655\pi\)
−0.337717 + 0.941248i \(0.609655\pi\)
\(48\) −111.157 −2.31577
\(49\) −7.00000 −0.142857
\(50\) 23.9929 0.479858
\(51\) 37.4074i 0.733478i
\(52\) 34.7967 0.669167
\(53\) 76.1649i 1.43707i 0.695489 + 0.718537i \(0.255188\pi\)
−0.695489 + 0.718537i \(0.744812\pi\)
\(54\) 20.2415 0.374843
\(55\) 13.3731 0.243147
\(56\) 73.9467i 1.32048i
\(57\) 48.7747i 0.855696i
\(58\) 103.528 1.78496
\(59\) 80.8498 1.37034 0.685168 0.728385i \(-0.259729\pi\)
0.685168 + 0.728385i \(0.259729\pi\)
\(60\) 108.042i 1.80070i
\(61\) 58.9379i 0.966196i 0.875566 + 0.483098i \(0.160489\pi\)
−0.875566 + 0.483098i \(0.839511\pi\)
\(62\) 39.8488 0.642722
\(63\) 7.93725i 0.125988i
\(64\) 281.657 4.40089
\(65\) 17.3817i 0.267411i
\(66\) 16.1644i 0.244915i
\(67\) 11.9484i 0.178334i −0.996017 0.0891669i \(-0.971580\pi\)
0.996017 0.0891669i \(-0.0284204\pi\)
\(68\) 241.344i 3.54917i
\(69\) 21.1345 + 33.7688i 0.306297 + 0.489403i
\(70\) 57.5312 0.821874
\(71\) 105.964 1.49246 0.746229 0.665690i \(-0.231863\pi\)
0.746229 + 0.665690i \(0.231863\pi\)
\(72\) −83.8477 −1.16455
\(73\) −15.6066 −0.213788 −0.106894 0.994270i \(-0.534091\pi\)
−0.106894 + 0.994270i \(0.534091\pi\)
\(74\) 90.1930i 1.21882i
\(75\) 10.6680 0.142240
\(76\) 314.683i 4.14056i
\(77\) 6.33851 0.0823183
\(78\) 21.0097 0.269356
\(79\) 118.357i 1.49819i 0.662461 + 0.749096i \(0.269512\pi\)
−0.662461 + 0.749096i \(0.730488\pi\)
\(80\) 358.236i 4.47795i
\(81\) 9.00000 0.111111
\(82\) −169.621 −2.06855
\(83\) 52.9699i 0.638192i −0.947722 0.319096i \(-0.896621\pi\)
0.947722 0.319096i \(-0.103379\pi\)
\(84\) 51.2093i 0.609634i
\(85\) 120.556 1.41831
\(86\) 146.844i 1.70749i
\(87\) 46.0317 0.529099
\(88\) 66.9588i 0.760896i
\(89\) 6.05127i 0.0679918i 0.999422 + 0.0339959i \(0.0108233\pi\)
−0.999422 + 0.0339959i \(0.989177\pi\)
\(90\) 65.2342i 0.724825i
\(91\) 8.23850i 0.0905329i
\(92\) −136.355 217.869i −1.48212 2.36814i
\(93\) 17.7180 0.190516
\(94\) 123.664 1.31557
\(95\) 157.191 1.65464
\(96\) 239.373 2.49347
\(97\) 46.7582i 0.482044i −0.970520 0.241022i \(-0.922517\pi\)
0.970520 0.241022i \(-0.0774825\pi\)
\(98\) 27.2684 0.278249
\(99\) 7.18719i 0.0725979i
\(100\) −68.8273 −0.688273
\(101\) 131.523 1.30221 0.651105 0.758987i \(-0.274306\pi\)
0.651105 + 0.758987i \(0.274306\pi\)
\(102\) 145.720i 1.42863i
\(103\) 141.443i 1.37323i −0.727019 0.686617i \(-0.759095\pi\)
0.727019 0.686617i \(-0.240905\pi\)
\(104\) −87.0300 −0.836827
\(105\) 25.5801 0.243620
\(106\) 296.699i 2.79905i
\(107\) 140.823i 1.31610i 0.752973 + 0.658052i \(0.228619\pi\)
−0.752973 + 0.658052i \(0.771381\pi\)
\(108\) −58.0659 −0.537647
\(109\) 61.9580i 0.568422i 0.958762 + 0.284211i \(0.0917317\pi\)
−0.958762 + 0.284211i \(0.908268\pi\)
\(110\) −52.0945 −0.473587
\(111\) 40.1026i 0.361284i
\(112\) 169.795i 1.51603i
\(113\) 195.137i 1.72688i 0.504452 + 0.863440i \(0.331695\pi\)
−0.504452 + 0.863440i \(0.668305\pi\)
\(114\) 190.001i 1.66668i
\(115\) −108.830 + 68.1120i −0.946347 + 0.592278i
\(116\) −296.985 −2.56022
\(117\) 9.34158 0.0798425
\(118\) −314.949 −2.66906
\(119\) 57.1408 0.480174
\(120\) 270.224i 2.25186i
\(121\) 115.260 0.952566
\(122\) 229.592i 1.88190i
\(123\) −75.4189 −0.613161
\(124\) −114.312 −0.921873
\(125\) 105.170i 0.841362i
\(126\) 30.9194i 0.245392i
\(127\) −124.857 −0.983130 −0.491565 0.870841i \(-0.663575\pi\)
−0.491565 + 0.870841i \(0.663575\pi\)
\(128\) −544.381 −4.25298
\(129\) 65.2915i 0.506136i
\(130\) 67.7100i 0.520846i
\(131\) −243.837 −1.86135 −0.930674 0.365849i \(-0.880779\pi\)
−0.930674 + 0.365849i \(0.880779\pi\)
\(132\) 46.3701i 0.351288i
\(133\) 74.5046 0.560185
\(134\) 46.5446i 0.347348i
\(135\) 29.0051i 0.214853i
\(136\) 603.624i 4.43841i
\(137\) 207.001i 1.51095i 0.655175 + 0.755477i \(0.272595\pi\)
−0.655175 + 0.755477i \(0.727405\pi\)
\(138\) −82.3290 131.546i −0.596587 0.953231i
\(139\) 182.843 1.31542 0.657708 0.753273i \(-0.271526\pi\)
0.657708 + 0.753273i \(0.271526\pi\)
\(140\) −165.037 −1.17883
\(141\) 54.9847 0.389962
\(142\) −412.783 −2.90692
\(143\) 7.45997i 0.0521676i
\(144\) 192.530 1.33701
\(145\) 148.350i 1.02311i
\(146\) 60.7951 0.416405
\(147\) 12.1244 0.0824786
\(148\) 258.732i 1.74819i
\(149\) 155.134i 1.04117i 0.853811 + 0.520583i \(0.174285\pi\)
−0.853811 + 0.520583i \(0.825715\pi\)
\(150\) −41.5570 −0.277046
\(151\) 84.9068 0.562296 0.281148 0.959664i \(-0.409285\pi\)
0.281148 + 0.959664i \(0.409285\pi\)
\(152\) 787.053i 5.17798i
\(153\) 64.7915i 0.423474i
\(154\) −24.6915 −0.160335
\(155\) 57.1014i 0.368396i
\(156\) −60.2696 −0.386344
\(157\) 237.995i 1.51589i −0.652316 0.757947i \(-0.726202\pi\)
0.652316 0.757947i \(-0.273798\pi\)
\(158\) 461.058i 2.91809i
\(159\) 131.921i 0.829695i
\(160\) 771.449i 4.82155i
\(161\) −51.5827 + 32.2834i −0.320390 + 0.200518i
\(162\) −35.0593 −0.216416
\(163\) 252.259 1.54760 0.773800 0.633430i \(-0.218354\pi\)
0.773800 + 0.633430i \(0.218354\pi\)
\(164\) 486.585 2.96698
\(165\) −23.1628 −0.140381
\(166\) 206.343i 1.24303i
\(167\) 130.396 0.780812 0.390406 0.920643i \(-0.372335\pi\)
0.390406 + 0.920643i \(0.372335\pi\)
\(168\) 128.079i 0.762378i
\(169\) −159.304 −0.942627
\(170\) −469.625 −2.76250
\(171\) 84.4803i 0.494037i
\(172\) 421.245i 2.44910i
\(173\) 310.218 1.79317 0.896584 0.442874i \(-0.146041\pi\)
0.896584 + 0.442874i \(0.146041\pi\)
\(174\) −179.315 −1.03055
\(175\) 16.2956i 0.0931178i
\(176\) 153.750i 0.873579i
\(177\) −140.036 −0.791164
\(178\) 23.5726i 0.132430i
\(179\) 34.5495 0.193014 0.0965069 0.995332i \(-0.469233\pi\)
0.0965069 + 0.995332i \(0.469233\pi\)
\(180\) 187.134i 1.03963i
\(181\) 83.8097i 0.463037i −0.972831 0.231518i \(-0.925631\pi\)
0.972831 0.231518i \(-0.0743694\pi\)
\(182\) 32.0929i 0.176335i
\(183\) 102.084i 0.557833i
\(184\) 341.036 + 544.911i 1.85346 + 2.96147i
\(185\) 129.242 0.698607
\(186\) −69.0201 −0.371076
\(187\) −51.7410 −0.276690
\(188\) −354.748 −1.88696
\(189\) 13.7477i 0.0727393i
\(190\) −612.334 −3.22281
\(191\) 157.259i 0.823347i −0.911331 0.411673i \(-0.864944\pi\)
0.911331 0.411673i \(-0.135056\pi\)
\(192\) −487.844 −2.54085
\(193\) 20.9082 0.108333 0.0541663 0.998532i \(-0.482750\pi\)
0.0541663 + 0.998532i \(0.482750\pi\)
\(194\) 182.146i 0.938896i
\(195\) 30.1060i 0.154390i
\(196\) −78.2235 −0.399099
\(197\) 333.061 1.69066 0.845332 0.534242i \(-0.179403\pi\)
0.845332 + 0.534242i \(0.179403\pi\)
\(198\) 27.9976i 0.141402i
\(199\) 276.096i 1.38742i −0.720256 0.693708i \(-0.755976\pi\)
0.720256 0.693708i \(-0.244024\pi\)
\(200\) 172.144 0.860720
\(201\) 20.6952i 0.102961i
\(202\) −512.347 −2.53637
\(203\) 70.3145i 0.346377i
\(204\) 418.020i 2.04912i
\(205\) 243.059i 1.18566i
\(206\) 550.989i 2.67471i
\(207\) −36.6060 58.4893i −0.176840 0.282557i
\(208\) 199.837 0.960754
\(209\) −67.4640 −0.322794
\(210\) −99.6469 −0.474509
\(211\) −128.933 −0.611059 −0.305529 0.952183i \(-0.598833\pi\)
−0.305529 + 0.952183i \(0.598833\pi\)
\(212\) 851.126i 4.01475i
\(213\) −183.536 −0.861671
\(214\) 548.574i 2.56343i
\(215\) −210.421 −0.978702
\(216\) 145.228 0.672354
\(217\) 27.0647i 0.124722i
\(218\) 241.356i 1.10714i
\(219\) 27.0313 0.123431
\(220\) 149.441 0.679278
\(221\) 67.2506i 0.304301i
\(222\) 156.219i 0.703688i
\(223\) −38.4977 −0.172635 −0.0863176 0.996268i \(-0.527510\pi\)
−0.0863176 + 0.996268i \(0.527510\pi\)
\(224\) 365.648i 1.63236i
\(225\) −18.4775 −0.0821222
\(226\) 760.154i 3.36351i
\(227\) 33.7442i 0.148653i 0.997234 + 0.0743265i \(0.0236807\pi\)
−0.997234 + 0.0743265i \(0.976319\pi\)
\(228\) 545.047i 2.39056i
\(229\) 251.499i 1.09825i 0.835741 + 0.549124i \(0.185038\pi\)
−0.835741 + 0.549124i \(0.814962\pi\)
\(230\) 423.945 265.329i 1.84324 1.15360i
\(231\) −10.9786 −0.0475265
\(232\) 742.790 3.20168
\(233\) −263.749 −1.13197 −0.565986 0.824415i \(-0.691504\pi\)
−0.565986 + 0.824415i \(0.691504\pi\)
\(234\) −36.3899 −0.155513
\(235\) 177.204i 0.754060i
\(236\) 903.479 3.82830
\(237\) 205.001i 0.864982i
\(238\) −222.591 −0.935255
\(239\) 224.446 0.939105 0.469553 0.882905i \(-0.344415\pi\)
0.469553 + 0.882905i \(0.344415\pi\)
\(240\) 620.484i 2.58535i
\(241\) 233.230i 0.967760i 0.875134 + 0.483880i \(0.160773\pi\)
−0.875134 + 0.483880i \(0.839227\pi\)
\(242\) −448.995 −1.85535
\(243\) −15.5885 −0.0641500
\(244\) 658.619i 2.69926i
\(245\) 39.0743i 0.159487i
\(246\) 293.793 1.19428
\(247\) 87.6865i 0.355006i
\(248\) 285.906 1.15285
\(249\) 91.7466i 0.368460i
\(250\) 409.689i 1.63876i
\(251\) 41.8187i 0.166608i −0.996524 0.0833042i \(-0.973453\pi\)
0.996524 0.0833042i \(-0.0265473\pi\)
\(252\) 88.6971i 0.351973i
\(253\) 46.7082 29.2327i 0.184618 0.115544i
\(254\) 486.380 1.91488
\(255\) −208.810 −0.818861
\(256\) 993.999 3.88281
\(257\) 272.834 1.06161 0.530806 0.847493i \(-0.321889\pi\)
0.530806 + 0.847493i \(0.321889\pi\)
\(258\) 254.342i 0.985821i
\(259\) 61.2577 0.236516
\(260\) 194.237i 0.747064i
\(261\) −79.7292 −0.305476
\(262\) 949.861 3.62543
\(263\) 390.161i 1.48350i 0.670676 + 0.741751i \(0.266004\pi\)
−0.670676 + 0.741751i \(0.733996\pi\)
\(264\) 115.976i 0.439303i
\(265\) 425.155 1.60436
\(266\) −290.231 −1.09110
\(267\) 10.4811i 0.0392551i
\(268\) 133.520i 0.498210i
\(269\) −202.017 −0.750992 −0.375496 0.926824i \(-0.622528\pi\)
−0.375496 + 0.926824i \(0.622528\pi\)
\(270\) 112.989i 0.418478i
\(271\) −210.812 −0.777906 −0.388953 0.921258i \(-0.627163\pi\)
−0.388953 + 0.921258i \(0.627163\pi\)
\(272\) 1386.03i 5.09571i
\(273\) 14.2695i 0.0522692i
\(274\) 806.367i 2.94295i
\(275\) 14.7557i 0.0536571i
\(276\) 236.173 + 377.359i 0.855700 + 1.36724i
\(277\) −228.883 −0.826294 −0.413147 0.910664i \(-0.635570\pi\)
−0.413147 + 0.910664i \(0.635570\pi\)
\(278\) −712.261 −2.56209
\(279\) −30.6884 −0.109994
\(280\) 412.774 1.47419
\(281\) 185.090i 0.658685i −0.944211 0.329342i \(-0.893173\pi\)
0.944211 0.329342i \(-0.106827\pi\)
\(282\) −214.192 −0.759546
\(283\) 186.339i 0.658442i −0.944253 0.329221i \(-0.893214\pi\)
0.944253 0.329221i \(-0.106786\pi\)
\(284\) 1184.13 4.16947
\(285\) −272.262 −0.955306
\(286\) 29.0602i 0.101609i
\(287\) 115.204i 0.401408i
\(288\) −414.606 −1.43960
\(289\) −177.438 −0.613972
\(290\) 577.897i 1.99275i
\(291\) 80.9876i 0.278308i
\(292\) −174.400 −0.597260
\(293\) 287.630i 0.981671i −0.871252 0.490836i \(-0.836692\pi\)
0.871252 0.490836i \(-0.163308\pi\)
\(294\) −47.2302 −0.160647
\(295\) 451.307i 1.52985i
\(296\) 647.115i 2.18620i
\(297\) 12.4486i 0.0419144i
\(298\) 604.320i 2.02792i
\(299\) −37.9953 60.7092i −0.127075 0.203041i
\(300\) 119.212 0.397375
\(301\) −99.7344 −0.331344
\(302\) −330.753 −1.09521
\(303\) −227.805 −0.751832
\(304\) 1807.22i 5.94480i
\(305\) 328.994 1.07867
\(306\) 252.394i 0.824818i
\(307\) 106.999 0.348530 0.174265 0.984699i \(-0.444245\pi\)
0.174265 + 0.984699i \(0.444245\pi\)
\(308\) 70.8314 0.229972
\(309\) 244.987i 0.792837i
\(310\) 222.437i 0.717540i
\(311\) −439.744 −1.41397 −0.706985 0.707229i \(-0.749945\pi\)
−0.706985 + 0.707229i \(0.749945\pi\)
\(312\) 150.740 0.483142
\(313\) 396.790i 1.26770i 0.773456 + 0.633850i \(0.218526\pi\)
−0.773456 + 0.633850i \(0.781474\pi\)
\(314\) 927.107i 2.95257i
\(315\) −44.3061 −0.140654
\(316\) 1322.62i 4.18549i
\(317\) 495.819 1.56410 0.782050 0.623216i \(-0.214174\pi\)
0.782050 + 0.623216i \(0.214174\pi\)
\(318\) 513.898i 1.61603i
\(319\) 63.6699i 0.199592i
\(320\) 1572.22i 4.91318i
\(321\) 243.913i 0.759853i
\(322\) 200.940 125.760i 0.624036 0.390558i
\(323\) −608.178 −1.88290
\(324\) 100.573 0.310411
\(325\) −19.1788 −0.0590116
\(326\) −982.669 −3.01432
\(327\) 107.314i 0.328179i
\(328\) −1217.00 −3.71035
\(329\) 83.9905i 0.255290i
\(330\) 90.2304 0.273425
\(331\) −136.372 −0.412001 −0.206001 0.978552i \(-0.566045\pi\)
−0.206001 + 0.978552i \(0.566045\pi\)
\(332\) 591.927i 1.78291i
\(333\) 69.4597i 0.208588i
\(334\) −507.954 −1.52082
\(335\) −66.6962 −0.199093
\(336\) 294.094i 0.875280i
\(337\) 414.570i 1.23018i 0.788458 + 0.615089i \(0.210880\pi\)
−0.788458 + 0.615089i \(0.789120\pi\)
\(338\) 620.565 1.83599
\(339\) 337.988i 0.997014i
\(340\) 1347.19 3.96232
\(341\) 24.5071i 0.0718683i
\(342\) 329.091i 0.962255i
\(343\) 18.5203i 0.0539949i
\(344\) 1053.58i 3.06272i
\(345\) 188.499 117.973i 0.546374 0.341952i
\(346\) −1208.45 −3.49263
\(347\) −311.459 −0.897577 −0.448788 0.893638i \(-0.648144\pi\)
−0.448788 + 0.893638i \(0.648144\pi\)
\(348\) 514.394 1.47814
\(349\) 154.371 0.442323 0.221161 0.975237i \(-0.429015\pi\)
0.221161 + 0.975237i \(0.429015\pi\)
\(350\) 63.4793i 0.181369i
\(351\) −16.1801 −0.0460971
\(352\) 331.095i 0.940610i
\(353\) −263.060 −0.745212 −0.372606 0.927990i \(-0.621536\pi\)
−0.372606 + 0.927990i \(0.621536\pi\)
\(354\) 545.508 1.54098
\(355\) 591.498i 1.66619i
\(356\) 67.6216i 0.189948i
\(357\) −98.9707 −0.277229
\(358\) −134.587 −0.375941
\(359\) 313.582i 0.873487i −0.899586 0.436743i \(-0.856132\pi\)
0.899586 0.436743i \(-0.143868\pi\)
\(360\) 468.041i 1.30011i
\(361\) −431.990 −1.19665
\(362\) 326.479i 0.901876i
\(363\) −199.637 −0.549964
\(364\) 92.0634i 0.252921i
\(365\) 87.1164i 0.238675i
\(366\) 397.665i 1.08652i
\(367\) 518.592i 1.41306i 0.707685 + 0.706528i \(0.249740\pi\)
−0.707685 + 0.706528i \(0.750260\pi\)
\(368\) −783.083 1251.22i −2.12794 3.40004i
\(369\) 130.629 0.354009
\(370\) −503.461 −1.36070
\(371\) 201.513 0.543163
\(372\) 197.995 0.532243
\(373\) 271.102i 0.726814i 0.931630 + 0.363407i \(0.118387\pi\)
−0.931630 + 0.363407i \(0.881613\pi\)
\(374\) 201.556 0.538920
\(375\) 182.160i 0.485761i
\(376\) 887.260 2.35973
\(377\) −82.7551 −0.219510
\(378\) 53.5540i 0.141677i
\(379\) 91.5954i 0.241676i −0.992672 0.120838i \(-0.961442\pi\)
0.992672 0.120838i \(-0.0385582\pi\)
\(380\) 1756.57 4.62256
\(381\) 216.260 0.567610
\(382\) 612.601i 1.60367i
\(383\) 444.007i 1.15929i 0.814870 + 0.579644i \(0.196808\pi\)
−0.814870 + 0.579644i \(0.803192\pi\)
\(384\) 942.895 2.45546
\(385\) 35.3818i 0.0919008i
\(386\) −81.4474 −0.211004
\(387\) 113.088i 0.292218i
\(388\) 522.513i 1.34668i
\(389\) 293.326i 0.754051i −0.926203 0.377026i \(-0.876947\pi\)
0.926203 0.377026i \(-0.123053\pi\)
\(390\) 117.277i 0.300711i
\(391\) 421.068 263.529i 1.07690 0.673986i
\(392\) 195.645 0.499093
\(393\) 422.337 1.07465
\(394\) −1297.43 −3.29297
\(395\) 660.675 1.67259
\(396\) 80.3153i 0.202816i
\(397\) 389.331 0.980683 0.490342 0.871530i \(-0.336872\pi\)
0.490342 + 0.871530i \(0.336872\pi\)
\(398\) 1075.53i 2.70233i
\(399\) −129.046 −0.323423
\(400\) −395.274 −0.988186
\(401\) 660.220i 1.64644i −0.567726 0.823218i \(-0.692177\pi\)
0.567726 0.823218i \(-0.307823\pi\)
\(402\) 80.6177i 0.200541i
\(403\) −31.8532 −0.0790401
\(404\) 1469.74 3.63798
\(405\) 50.2384i 0.124045i
\(406\) 273.909i 0.674653i
\(407\) −55.4689 −0.136287
\(408\) 1045.51i 2.56252i
\(409\) −705.366 −1.72461 −0.862306 0.506388i \(-0.830980\pi\)
−0.862306 + 0.506388i \(0.830980\pi\)
\(410\) 946.833i 2.30935i
\(411\) 358.536i 0.872349i
\(412\) 1580.60i 3.83640i
\(413\) 213.909i 0.517938i
\(414\) 142.598 + 227.844i 0.344439 + 0.550348i
\(415\) −295.680 −0.712482
\(416\) −430.341 −1.03447
\(417\) −316.693 −0.759456
\(418\) 262.805 0.628720
\(419\) 391.119i 0.933458i 0.884400 + 0.466729i \(0.154568\pi\)
−0.884400 + 0.466729i \(0.845432\pi\)
\(420\) 285.852 0.680601
\(421\) 624.843i 1.48419i 0.670296 + 0.742094i \(0.266167\pi\)
−0.670296 + 0.742094i \(0.733833\pi\)
\(422\) 502.258 1.19018
\(423\) −95.2363 −0.225145
\(424\) 2128.75i 5.02064i
\(425\) 133.021i 0.312990i
\(426\) 714.961 1.67831
\(427\) 155.935 0.365188
\(428\) 1573.67i 3.67679i
\(429\) 12.9210i 0.0301190i
\(430\) 819.691 1.90626
\(431\) 319.684i 0.741726i 0.928688 + 0.370863i \(0.120938\pi\)
−0.928688 + 0.370863i \(0.879062\pi\)
\(432\) −333.471 −0.771925
\(433\) 250.183i 0.577789i −0.957361 0.288895i \(-0.906712\pi\)
0.957361 0.288895i \(-0.0932877\pi\)
\(434\) 105.430i 0.242926i
\(435\) 256.951i 0.590691i
\(436\) 692.367i 1.58800i
\(437\) 549.022 343.609i 1.25634 0.786291i
\(438\) −105.300 −0.240411
\(439\) −244.377 −0.556668 −0.278334 0.960484i \(-0.589782\pi\)
−0.278334 + 0.960484i \(0.589782\pi\)
\(440\) −373.767 −0.849470
\(441\) −21.0000 −0.0476190
\(442\) 261.973i 0.592700i
\(443\) −718.170 −1.62115 −0.810576 0.585634i \(-0.800846\pi\)
−0.810576 + 0.585634i \(0.800846\pi\)
\(444\) 448.137i 1.00932i
\(445\) 33.7784 0.0759066
\(446\) 149.967 0.336249
\(447\) 268.699i 0.601117i
\(448\) 745.193i 1.66338i
\(449\) 263.218 0.586233 0.293116 0.956077i \(-0.405308\pi\)
0.293116 + 0.956077i \(0.405308\pi\)
\(450\) 71.9788 0.159953
\(451\) 104.318i 0.231303i
\(452\) 2180.62i 4.82438i
\(453\) −147.063 −0.324642
\(454\) 131.450i 0.289538i
\(455\) −45.9876 −0.101072
\(456\) 1363.22i 2.98951i
\(457\) 661.998i 1.44857i 0.689499 + 0.724286i \(0.257831\pi\)
−0.689499 + 0.724286i \(0.742169\pi\)
\(458\) 979.708i 2.13910i
\(459\) 112.222i 0.244493i
\(460\) −1216.15 + 761.137i −2.64381 + 1.65465i
\(461\) 299.234 0.649098 0.324549 0.945869i \(-0.394788\pi\)
0.324549 + 0.945869i \(0.394788\pi\)
\(462\) 42.7670 0.0925693
\(463\) −131.514 −0.284047 −0.142024 0.989863i \(-0.545361\pi\)
−0.142024 + 0.989863i \(0.545361\pi\)
\(464\) −1705.58 −3.67582
\(465\) 98.9025i 0.212694i
\(466\) 1027.43 2.20479
\(467\) 397.109i 0.850341i 0.905113 + 0.425170i \(0.139786\pi\)
−0.905113 + 0.425170i \(0.860214\pi\)
\(468\) 104.390 0.223056
\(469\) −31.6124 −0.0674038
\(470\) 690.296i 1.46871i
\(471\) 412.220i 0.875202i
\(472\) −2259.69 −4.78748
\(473\) 90.3096 0.190929
\(474\) 798.577i 1.68476i
\(475\) 173.443i 0.365142i
\(476\) 638.535 1.34146
\(477\) 228.495i 0.479024i
\(478\) −874.326 −1.82913
\(479\) 631.433i 1.31823i −0.752041 0.659116i \(-0.770930\pi\)
0.752041 0.659116i \(-0.229070\pi\)
\(480\) 1336.19i 2.78373i
\(481\) 72.0959i 0.149887i
\(482\) 908.544i 1.88495i
\(483\) 89.3439 55.9166i 0.184977 0.115769i
\(484\) 1288.01 2.66118
\(485\) −261.006 −0.538157
\(486\) 60.7246 0.124948
\(487\) −656.345 −1.34773 −0.673865 0.738854i \(-0.735367\pi\)
−0.673865 + 0.738854i \(0.735367\pi\)
\(488\) 1647.27i 3.37555i
\(489\) −436.925 −0.893507
\(490\) 152.213i 0.310639i
\(491\) −126.007 −0.256633 −0.128317 0.991733i \(-0.540957\pi\)
−0.128317 + 0.991733i \(0.540957\pi\)
\(492\) −842.789 −1.71299
\(493\) 573.975i 1.16425i
\(494\) 341.581i 0.691460i
\(495\) 40.1192 0.0810489
\(496\) −656.494 −1.32358
\(497\) 280.356i 0.564096i
\(498\) 357.397i 0.717665i
\(499\) 241.457 0.483882 0.241941 0.970291i \(-0.422216\pi\)
0.241941 + 0.970291i \(0.422216\pi\)
\(500\) 1175.25i 2.35051i
\(501\) −225.852 −0.450802
\(502\) 162.904i 0.324510i
\(503\) 571.589i 1.13636i −0.822905 0.568180i \(-0.807648\pi\)
0.822905 0.568180i \(-0.192352\pi\)
\(504\) 221.840i 0.440159i
\(505\) 734.168i 1.45380i
\(506\) −181.951 + 113.875i −0.359587 + 0.225050i
\(507\) 275.922 0.544226
\(508\) −1395.26 −2.74657
\(509\) 173.270 0.340413 0.170206 0.985408i \(-0.445557\pi\)
0.170206 + 0.985408i \(0.445557\pi\)
\(510\) 813.414 1.59493
\(511\) 41.2911i 0.0808044i
\(512\) −1694.58 −3.30973
\(513\) 146.324i 0.285232i
\(514\) −1062.82 −2.06775
\(515\) −789.541 −1.53309
\(516\) 729.618i 1.41399i
\(517\) 76.0535i 0.147105i
\(518\) −238.628 −0.460672
\(519\) −537.313 −1.03529
\(520\) 485.805i 0.934240i
\(521\) 580.938i 1.11504i 0.830162 + 0.557522i \(0.188248\pi\)
−0.830162 + 0.557522i \(0.811752\pi\)
\(522\) 310.584 0.594988
\(523\) 298.842i 0.571399i 0.958319 + 0.285699i \(0.0922259\pi\)
−0.958319 + 0.285699i \(0.907774\pi\)
\(524\) −2724.82 −5.20004
\(525\) 28.2248i 0.0537616i
\(526\) 1519.86i 2.88948i
\(527\) 220.928i 0.419218i
\(528\) 266.303i 0.504361i
\(529\) −231.223 + 475.791i −0.437094 + 0.899416i
\(530\) −1656.19 −3.12488
\(531\) 242.549 0.456779
\(532\) 832.572 1.56499
\(533\) 135.587 0.254385
\(534\) 40.8290i 0.0764588i
\(535\) 786.080 1.46931
\(536\) 333.948i 0.623036i
\(537\) −59.8414 −0.111437
\(538\) 786.953 1.46274
\(539\) 16.7701i 0.0311134i
\(540\) 324.126i 0.600233i
\(541\) 696.281 1.28703 0.643513 0.765435i \(-0.277476\pi\)
0.643513 + 0.765435i \(0.277476\pi\)
\(542\) 821.216 1.51516
\(543\) 145.163i 0.267334i
\(544\) 2984.77i 5.48671i
\(545\) 345.852 0.634591
\(546\) 55.5866i 0.101807i
\(547\) 525.802 0.961247 0.480623 0.876927i \(-0.340410\pi\)
0.480623 + 0.876927i \(0.340410\pi\)
\(548\) 2313.19i 4.22114i
\(549\) 176.814i 0.322065i
\(550\) 57.4806i 0.104510i
\(551\) 748.393i 1.35825i
\(552\) −590.692 943.813i −1.07009 1.70981i
\(553\) 313.144 0.566264
\(554\) 891.611 1.60941
\(555\) −223.854 −0.403341
\(556\) 2043.23 3.67487
\(557\) 79.5046i 0.142737i 0.997450 + 0.0713686i \(0.0227367\pi\)
−0.997450 + 0.0713686i \(0.977263\pi\)
\(558\) 119.546 0.214241
\(559\) 117.380i 0.209983i
\(560\) −947.804 −1.69251
\(561\) 89.6181 0.159747
\(562\) 721.017i 1.28295i
\(563\) 577.470i 1.02570i 0.858478 + 0.512851i \(0.171411\pi\)
−0.858478 + 0.512851i \(0.828589\pi\)
\(564\) 614.442 1.08944
\(565\) 1089.26 1.92790
\(566\) 725.880i 1.28247i
\(567\) 23.8118i 0.0419961i
\(568\) −2961.63 −5.21413
\(569\) 532.318i 0.935533i −0.883852 0.467767i \(-0.845059\pi\)
0.883852 0.467767i \(-0.154941\pi\)
\(570\) 1060.59 1.86069
\(571\) 300.680i 0.526585i 0.964716 + 0.263293i \(0.0848085\pi\)
−0.964716 + 0.263293i \(0.915192\pi\)
\(572\) 83.3635i 0.145740i
\(573\) 272.381i 0.475360i
\(574\) 448.776i 0.781840i
\(575\) 75.1541 + 120.082i 0.130703 + 0.208838i
\(576\) 844.970 1.46696
\(577\) −7.55944 −0.0131013 −0.00655064 0.999979i \(-0.502085\pi\)
−0.00655064 + 0.999979i \(0.502085\pi\)
\(578\) 691.206 1.19586
\(579\) −36.2140 −0.0625458
\(580\) 1657.78i 2.85825i
\(581\) −140.145 −0.241214
\(582\) 315.486i 0.542072i
\(583\) −182.471 −0.312986
\(584\) 436.191 0.746903
\(585\) 52.1451i 0.0891368i
\(586\) 1120.46i 1.91204i
\(587\) −363.672 −0.619543 −0.309772 0.950811i \(-0.600253\pi\)
−0.309772 + 0.950811i \(0.600253\pi\)
\(588\) 135.487 0.230420
\(589\) 288.063i 0.489071i
\(590\) 1758.06i 2.97976i
\(591\) −576.878 −0.976105
\(592\) 1485.90i 2.50996i
\(593\) 455.135 0.767512 0.383756 0.923435i \(-0.374630\pi\)
0.383756 + 0.923435i \(0.374630\pi\)
\(594\) 48.4932i 0.0816384i
\(595\) 318.962i 0.536070i
\(596\) 1733.58i 2.90870i
\(597\) 478.212i 0.801025i
\(598\) 148.010 + 236.492i 0.247508 + 0.395471i
\(599\) −893.265 −1.49126 −0.745630 0.666360i \(-0.767851\pi\)
−0.745630 + 0.666360i \(0.767851\pi\)
\(600\) −298.162 −0.496937
\(601\) 476.950 0.793594 0.396797 0.917906i \(-0.370122\pi\)
0.396797 + 0.917906i \(0.370122\pi\)
\(602\) 388.514 0.645371
\(603\) 35.8451i 0.0594446i
\(604\) 948.815 1.57089
\(605\) 643.389i 1.06345i
\(606\) 887.410 1.46437
\(607\) 375.828 0.619157 0.309579 0.950874i \(-0.399812\pi\)
0.309579 + 0.950874i \(0.399812\pi\)
\(608\) 3891.78i 6.40095i
\(609\) 121.788i 0.199981i
\(610\) −1281.59 −2.10097
\(611\) −98.8508 −0.161785
\(612\) 724.031i 1.18306i
\(613\) 176.512i 0.287947i −0.989582 0.143974i \(-0.954012\pi\)
0.989582 0.143974i \(-0.0459881\pi\)
\(614\) −416.811 −0.678845
\(615\) 420.991i 0.684538i
\(616\) −177.156 −0.287592
\(617\) 97.9061i 0.158681i −0.996848 0.0793404i \(-0.974719\pi\)
0.996848 0.0793404i \(-0.0252814\pi\)
\(618\) 954.342i 1.54424i
\(619\) 199.557i 0.322387i −0.986923 0.161193i \(-0.948466\pi\)
0.986923 0.161193i \(-0.0515343\pi\)
\(620\) 638.095i 1.02919i
\(621\) 63.4034 + 101.307i 0.102099 + 0.163134i
\(622\) 1713.02 2.75405
\(623\) 16.0102 0.0256985
\(624\) −346.128 −0.554692
\(625\) −741.044 −1.18567
\(626\) 1545.69i 2.46915i
\(627\) 116.851 0.186365
\(628\) 2659.55i 4.23495i
\(629\) −500.044 −0.794983
\(630\) 172.593 0.273958
\(631\) 846.206i 1.34106i 0.741884 + 0.670528i \(0.233932\pi\)
−0.741884 + 0.670528i \(0.766068\pi\)
\(632\) 3307.99i 5.23417i
\(633\) 223.319 0.352795
\(634\) −1931.46 −3.04646
\(635\) 696.959i 1.09757i
\(636\) 1474.19i 2.31791i
\(637\) −21.7970 −0.0342182
\(638\) 248.025i 0.388754i
\(639\) 317.893 0.497486
\(640\) 3038.76i 4.74806i
\(641\) 1184.11i 1.84728i 0.383255 + 0.923642i \(0.374803\pi\)
−0.383255 + 0.923642i \(0.625197\pi\)
\(642\) 950.158i 1.48000i
\(643\) 668.278i 1.03931i −0.854375 0.519656i \(-0.826060\pi\)
0.854375 0.519656i \(-0.173940\pi\)
\(644\) −576.426 + 360.760i −0.895071 + 0.560187i
\(645\) 364.460 0.565054
\(646\) 2369.15 3.66741
\(647\) −299.560 −0.462998 −0.231499 0.972835i \(-0.574363\pi\)
−0.231499 + 0.972835i \(0.574363\pi\)
\(648\) −251.543 −0.388184
\(649\) 193.694i 0.298451i
\(650\) 74.7106 0.114939
\(651\) 46.8774i 0.0720083i
\(652\) 2818.94 4.32352
\(653\) 132.906 0.203531 0.101766 0.994808i \(-0.467551\pi\)
0.101766 + 0.994808i \(0.467551\pi\)
\(654\) 418.042i 0.639207i
\(655\) 1361.11i 2.07802i
\(656\) 2794.45 4.25983
\(657\) −46.8197 −0.0712628
\(658\) 327.183i 0.497239i
\(659\) 29.8198i 0.0452500i −0.999744 0.0226250i \(-0.992798\pi\)
0.999744 0.0226250i \(-0.00720238\pi\)
\(660\) −258.840 −0.392181
\(661\) 536.340i 0.811406i 0.914005 + 0.405703i \(0.132973\pi\)
−0.914005 + 0.405703i \(0.867027\pi\)
\(662\) 531.236 0.802472
\(663\) 116.481i 0.175688i
\(664\) 1480.47i 2.22962i
\(665\) 415.888i 0.625395i
\(666\) 270.579i 0.406275i
\(667\) 324.285 + 518.145i 0.486184 + 0.776829i
\(668\) 1457.14 2.18135
\(669\) 66.6799 0.0996710
\(670\) 259.814 0.387782
\(671\) −141.199 −0.210431
\(672\) 633.321i 0.942442i
\(673\) −153.495 −0.228076 −0.114038 0.993476i \(-0.536379\pi\)
−0.114038 + 0.993476i \(0.536379\pi\)
\(674\) 1614.95i 2.39607i
\(675\) 32.0040 0.0474133
\(676\) −1780.19 −2.63341
\(677\) 899.450i 1.32858i 0.747474 + 0.664291i \(0.231266\pi\)
−0.747474 + 0.664291i \(0.768734\pi\)
\(678\) 1316.63i 1.94193i
\(679\) −123.711 −0.182195
\(680\) −3369.46 −4.95508
\(681\) 58.4467i 0.0858248i
\(682\) 95.4669i 0.139981i
\(683\) −731.776 −1.07141 −0.535707 0.844404i \(-0.679955\pi\)
−0.535707 + 0.844404i \(0.679955\pi\)
\(684\) 944.048i 1.38019i
\(685\) 1155.49 1.68684
\(686\) 72.1453i 0.105168i
\(687\) 435.608i 0.634073i
\(688\) 2419.21i 3.51629i
\(689\) 237.167i 0.344219i
\(690\) −734.294 + 459.563i −1.06419 + 0.666034i
\(691\) 87.6166 0.126797 0.0633984 0.997988i \(-0.479806\pi\)
0.0633984 + 0.997988i \(0.479806\pi\)
\(692\) 3466.62 5.00956
\(693\) 19.0155 0.0274394
\(694\) 1213.28 1.74825
\(695\) 1020.64i 1.46854i
\(696\) −1286.55 −1.84849
\(697\) 940.408i 1.34922i
\(698\) −601.348 −0.861530
\(699\) 456.827 0.653544
\(700\) 182.100i 0.260143i
\(701\) 397.477i 0.567014i 0.958970 + 0.283507i \(0.0914980\pi\)
−0.958970 + 0.283507i \(0.908502\pi\)
\(702\) 63.0292 0.0897852
\(703\) −651.997 −0.927449
\(704\) 674.774i 0.958485i
\(705\) 306.927i 0.435357i
\(706\) 1024.74 1.45148
\(707\) 347.978i 0.492189i
\(708\) −1564.87 −2.21027
\(709\) 61.1930i 0.0863089i −0.999068 0.0431545i \(-0.986259\pi\)
0.999068 0.0431545i \(-0.0137408\pi\)
\(710\) 2304.17i 3.24531i
\(711\) 355.072i 0.499398i
\(712\) 169.128i 0.237540i
\(713\) 124.820 + 199.439i 0.175063 + 0.279717i
\(714\) 385.539 0.539970
\(715\) 41.6418 0.0582403
\(716\) 386.083 0.539222
\(717\) −388.752 −0.542193
\(718\) 1221.55i 1.70133i
\(719\) −1328.79 −1.84810 −0.924051 0.382269i \(-0.875143\pi\)
−0.924051 + 0.382269i \(0.875143\pi\)
\(720\) 1074.71i 1.49265i
\(721\) −374.223 −0.519034
\(722\) 1682.81 2.33076
\(723\) 403.967i 0.558737i
\(724\) 936.555i 1.29358i
\(725\) 163.688 0.225777
\(726\) 777.682 1.07119
\(727\) 158.956i 0.218647i −0.994006 0.109323i \(-0.965132\pi\)
0.994006 0.109323i \(-0.0348684\pi\)
\(728\) 230.260i 0.316291i
\(729\) 27.0000 0.0370370
\(730\) 339.360i 0.464877i
\(731\) 814.128 1.11372
\(732\) 1140.76i 1.55842i
\(733\) 981.315i 1.33877i −0.742918 0.669383i \(-0.766559\pi\)
0.742918 0.669383i \(-0.233441\pi\)
\(734\) 2020.16i 2.75227i
\(735\) 67.6786i 0.0920798i
\(736\) 1686.34 + 2694.45i 2.29122 + 3.66093i
\(737\) 28.6251 0.0388400
\(738\) −508.864 −0.689518
\(739\) 1204.10 1.62936 0.814681 0.579909i \(-0.196912\pi\)
0.814681 + 0.579909i \(0.196912\pi\)
\(740\) 1444.25 1.95169
\(741\) 151.878i 0.204963i
\(742\) −784.992 −1.05794
\(743\) 871.920i 1.17351i 0.809764 + 0.586756i \(0.199595\pi\)
−0.809764 + 0.586756i \(0.800405\pi\)
\(744\) −495.204 −0.665597
\(745\) 865.962 1.16237
\(746\) 1056.07i 1.41565i
\(747\) 158.910i 0.212731i
\(748\) −578.195 −0.772987
\(749\) 372.583 0.497440
\(750\) 709.602i 0.946136i
\(751\) 251.990i 0.335539i 0.985826 + 0.167770i \(0.0536565\pi\)
−0.985826 + 0.167770i \(0.946344\pi\)
\(752\) −2037.31 −2.70919
\(753\) 72.4322i 0.0961914i
\(754\) 322.371 0.427548
\(755\) 473.953i 0.627752i
\(756\) 153.628i 0.203211i
\(757\) 638.815i 0.843877i −0.906625 0.421938i \(-0.861350\pi\)
0.906625 0.421938i \(-0.138650\pi\)
\(758\) 356.808i 0.470723i
\(759\) −80.9010 + 50.6325i −0.106589 + 0.0667095i
\(760\) −4393.36 −5.78074
\(761\) −558.838 −0.734347 −0.367174 0.930152i \(-0.619675\pi\)
−0.367174 + 0.930152i \(0.619675\pi\)
\(762\) −842.435 −1.10556
\(763\) 163.926 0.214843
\(764\) 1757.34i 2.30018i
\(765\) 361.669 0.472770
\(766\) 1729.62i 2.25799i
\(767\) 251.755 0.328233
\(768\) −1721.66 −2.24174
\(769\) 334.303i 0.434724i −0.976091 0.217362i \(-0.930255\pi\)
0.976091 0.217362i \(-0.0697452\pi\)
\(770\) 137.829i 0.178999i
\(771\) −472.563 −0.612922
\(772\) 233.644 0.302648
\(773\) 272.063i 0.351957i 0.984394 + 0.175978i \(0.0563089\pi\)
−0.984394 + 0.175978i \(0.943691\pi\)
\(774\) 440.533i 0.569164i
\(775\) 63.0051 0.0812969
\(776\) 1306.86i 1.68409i
\(777\) −106.101 −0.136553
\(778\) 1142.65i 1.46870i
\(779\) 1226.18i 1.57404i
\(780\) 336.428i 0.431317i
\(781\) 253.862i 0.325048i
\(782\) −1640.26 + 1026.57i −2.09752 + 1.31275i
\(783\) 138.095 0.176366
\(784\) −449.236 −0.573005
\(785\) −1328.50 −1.69236
\(786\) −1645.21 −2.09314
\(787\) 874.132i 1.11071i 0.831612 + 0.555357i \(0.187418\pi\)
−0.831612 + 0.555357i \(0.812582\pi\)
\(788\) 3721.88 4.72320
\(789\) 675.778i 0.856500i
\(790\) −2573.65 −3.25778
\(791\) 516.285 0.652699