Properties

Label 8003.2.a.c.1.11
Level 8003
Weight 2
Character 8003.1
Self dual Yes
Analytic conductor 63.904
Analytic rank 0
Dimension 172
CM No

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Newspace parameters

Level: \( N \) = \( 8003 = 53 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9042767376\)
Analytic rank: \(0\)
Dimension: \(172\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.55384 q^{2}\) \(+0.729856 q^{3}\) \(+4.52207 q^{4}\) \(+2.13397 q^{5}\) \(-1.86393 q^{6}\) \(-2.81962 q^{7}\) \(-6.44096 q^{8}\) \(-2.46731 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.55384 q^{2}\) \(+0.729856 q^{3}\) \(+4.52207 q^{4}\) \(+2.13397 q^{5}\) \(-1.86393 q^{6}\) \(-2.81962 q^{7}\) \(-6.44096 q^{8}\) \(-2.46731 q^{9}\) \(-5.44980 q^{10}\) \(+1.09285 q^{11}\) \(+3.30046 q^{12}\) \(-4.42859 q^{13}\) \(+7.20085 q^{14}\) \(+1.55749 q^{15}\) \(+7.40501 q^{16}\) \(-5.59961 q^{17}\) \(+6.30110 q^{18}\) \(-3.27913 q^{19}\) \(+9.64995 q^{20}\) \(-2.05792 q^{21}\) \(-2.79097 q^{22}\) \(-0.823175 q^{23}\) \(-4.70098 q^{24}\) \(-0.446190 q^{25}\) \(+11.3099 q^{26}\) \(-3.99035 q^{27}\) \(-12.7505 q^{28}\) \(-8.28436 q^{29}\) \(-3.97757 q^{30}\) \(-1.53338 q^{31}\) \(-6.02925 q^{32}\) \(+0.797626 q^{33}\) \(+14.3005 q^{34}\) \(-6.01698 q^{35}\) \(-11.1574 q^{36}\) \(-8.71974 q^{37}\) \(+8.37437 q^{38}\) \(-3.23224 q^{39}\) \(-13.7448 q^{40}\) \(+0.597035 q^{41}\) \(+5.25559 q^{42}\) \(+8.37632 q^{43}\) \(+4.94197 q^{44}\) \(-5.26515 q^{45}\) \(+2.10225 q^{46}\) \(+7.48019 q^{47}\) \(+5.40459 q^{48}\) \(+0.950276 q^{49}\) \(+1.13950 q^{50}\) \(-4.08691 q^{51}\) \(-20.0264 q^{52}\) \(-1.00000 q^{53}\) \(+10.1907 q^{54}\) \(+2.33211 q^{55}\) \(+18.1611 q^{56}\) \(-2.39330 q^{57}\) \(+21.1569 q^{58}\) \(-4.64532 q^{59}\) \(+7.04308 q^{60}\) \(-2.21778 q^{61}\) \(+3.91599 q^{62}\) \(+6.95688 q^{63}\) \(+0.587685 q^{64}\) \(-9.45046 q^{65}\) \(-2.03701 q^{66}\) \(+11.9902 q^{67}\) \(-25.3219 q^{68}\) \(-0.600800 q^{69}\) \(+15.3664 q^{70}\) \(+8.81328 q^{71}\) \(+15.8919 q^{72}\) \(+3.30737 q^{73}\) \(+22.2688 q^{74}\) \(-0.325655 q^{75}\) \(-14.8285 q^{76}\) \(-3.08144 q^{77}\) \(+8.25460 q^{78}\) \(-1.24481 q^{79}\) \(+15.8020 q^{80}\) \(+4.48955 q^{81}\) \(-1.52473 q^{82}\) \(-7.45671 q^{83}\) \(-9.30607 q^{84}\) \(-11.9494 q^{85}\) \(-21.3917 q^{86}\) \(-6.04639 q^{87}\) \(-7.03903 q^{88}\) \(-6.00577 q^{89}\) \(+13.4463 q^{90}\) \(+12.4870 q^{91}\) \(-3.72246 q^{92}\) \(-1.11914 q^{93}\) \(-19.1032 q^{94}\) \(-6.99756 q^{95}\) \(-4.40048 q^{96}\) \(-9.70815 q^{97}\) \(-2.42685 q^{98}\) \(-2.69641 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 66q^{12} \) \(\mathstrut +\mathstrut 121q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 212q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 40q^{18} \) \(\mathstrut +\mathstrut 41q^{19} \) \(\mathstrut +\mathstrut 64q^{20} \) \(\mathstrut +\mathstrut 56q^{21} \) \(\mathstrut +\mathstrut 50q^{22} \) \(\mathstrut +\mathstrut 28q^{23} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 231q^{25} \) \(\mathstrut +\mathstrut 38q^{26} \) \(\mathstrut +\mathstrut 100q^{27} \) \(\mathstrut +\mathstrut 80q^{28} \) \(\mathstrut +\mathstrut 26q^{29} \) \(\mathstrut +\mathstrut 55q^{30} \) \(\mathstrut +\mathstrut 66q^{31} \) \(\mathstrut +\mathstrut 65q^{32} \) \(\mathstrut +\mathstrut 99q^{33} \) \(\mathstrut +\mathstrut 81q^{34} \) \(\mathstrut +\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 212q^{36} \) \(\mathstrut +\mathstrut 153q^{37} \) \(\mathstrut +\mathstrut q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 59q^{40} \) \(\mathstrut +\mathstrut 40q^{41} \) \(\mathstrut +\mathstrut 50q^{42} \) \(\mathstrut +\mathstrut 39q^{43} \) \(\mathstrut -\mathstrut 51q^{44} \) \(\mathstrut +\mathstrut 123q^{45} \) \(\mathstrut +\mathstrut 59q^{46} \) \(\mathstrut +\mathstrut 29q^{47} \) \(\mathstrut +\mathstrut 128q^{48} \) \(\mathstrut +\mathstrut 245q^{49} \) \(\mathstrut +\mathstrut 19q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 215q^{52} \) \(\mathstrut -\mathstrut 172q^{53} \) \(\mathstrut +\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut 40q^{55} \) \(\mathstrut +\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 54q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 54q^{60} \) \(\mathstrut +\mathstrut 100q^{61} \) \(\mathstrut -\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 92q^{63} \) \(\mathstrut +\mathstrut 253q^{64} \) \(\mathstrut +\mathstrut 77q^{65} \) \(\mathstrut +\mathstrut 14q^{66} \) \(\mathstrut +\mathstrut 126q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut +\mathstrut 47q^{69} \) \(\mathstrut +\mathstrut 72q^{70} \) \(\mathstrut +\mathstrut 38q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 185q^{73} \) \(\mathstrut +\mathstrut 48q^{74} \) \(\mathstrut +\mathstrut 75q^{75} \) \(\mathstrut +\mathstrut 38q^{76} \) \(\mathstrut +\mathstrut 120q^{77} \) \(\mathstrut +\mathstrut 75q^{78} \) \(\mathstrut +\mathstrut 79q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 232q^{81} \) \(\mathstrut +\mathstrut 110q^{82} \) \(\mathstrut +\mathstrut 90q^{83} \) \(\mathstrut +\mathstrut 158q^{84} \) \(\mathstrut +\mathstrut 115q^{85} \) \(\mathstrut +\mathstrut 68q^{86} \) \(\mathstrut +\mathstrut 61q^{87} \) \(\mathstrut +\mathstrut 15q^{88} \) \(\mathstrut -\mathstrut 36q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 33q^{91} \) \(\mathstrut +\mathstrut 139q^{92} \) \(\mathstrut +\mathstrut 103q^{93} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 45q^{95} \) \(\mathstrut +\mathstrut 34q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut -\mathstrut 36q^{98} \) \(\mathstrut +\mathstrut 27q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.55384 −1.80583 −0.902917 0.429815i \(-0.858579\pi\)
−0.902917 + 0.429815i \(0.858579\pi\)
\(3\) 0.729856 0.421383 0.210691 0.977553i \(-0.432428\pi\)
0.210691 + 0.977553i \(0.432428\pi\)
\(4\) 4.52207 2.26104
\(5\) 2.13397 0.954338 0.477169 0.878811i \(-0.341663\pi\)
0.477169 + 0.878811i \(0.341663\pi\)
\(6\) −1.86393 −0.760947
\(7\) −2.81962 −1.06572 −0.532859 0.846204i \(-0.678882\pi\)
−0.532859 + 0.846204i \(0.678882\pi\)
\(8\) −6.44096 −2.27722
\(9\) −2.46731 −0.822437
\(10\) −5.44980 −1.72338
\(11\) 1.09285 0.329508 0.164754 0.986335i \(-0.447317\pi\)
0.164754 + 0.986335i \(0.447317\pi\)
\(12\) 3.30046 0.952762
\(13\) −4.42859 −1.22827 −0.614135 0.789201i \(-0.710495\pi\)
−0.614135 + 0.789201i \(0.710495\pi\)
\(14\) 7.20085 1.92451
\(15\) 1.55749 0.402142
\(16\) 7.40501 1.85125
\(17\) −5.59961 −1.35811 −0.679053 0.734090i \(-0.737609\pi\)
−0.679053 + 0.734090i \(0.737609\pi\)
\(18\) 6.30110 1.48518
\(19\) −3.27913 −0.752285 −0.376143 0.926562i \(-0.622750\pi\)
−0.376143 + 0.926562i \(0.622750\pi\)
\(20\) 9.64995 2.15779
\(21\) −2.05792 −0.449075
\(22\) −2.79097 −0.595037
\(23\) −0.823175 −0.171644 −0.0858220 0.996310i \(-0.527352\pi\)
−0.0858220 + 0.996310i \(0.527352\pi\)
\(24\) −4.70098 −0.959583
\(25\) −0.446190 −0.0892381
\(26\) 11.3099 2.21805
\(27\) −3.99035 −0.767943
\(28\) −12.7505 −2.40963
\(29\) −8.28436 −1.53837 −0.769184 0.639028i \(-0.779337\pi\)
−0.769184 + 0.639028i \(0.779337\pi\)
\(30\) −3.97757 −0.726201
\(31\) −1.53338 −0.275402 −0.137701 0.990474i \(-0.543971\pi\)
−0.137701 + 0.990474i \(0.543971\pi\)
\(32\) −6.02925 −1.06583
\(33\) 0.797626 0.138849
\(34\) 14.3005 2.45251
\(35\) −6.01698 −1.01706
\(36\) −11.1574 −1.85956
\(37\) −8.71974 −1.43352 −0.716758 0.697322i \(-0.754375\pi\)
−0.716758 + 0.697322i \(0.754375\pi\)
\(38\) 8.37437 1.35850
\(39\) −3.23224 −0.517572
\(40\) −13.7448 −2.17324
\(41\) 0.597035 0.0932412 0.0466206 0.998913i \(-0.485155\pi\)
0.0466206 + 0.998913i \(0.485155\pi\)
\(42\) 5.25559 0.810955
\(43\) 8.37632 1.27738 0.638688 0.769466i \(-0.279477\pi\)
0.638688 + 0.769466i \(0.279477\pi\)
\(44\) 4.94197 0.745030
\(45\) −5.26515 −0.784883
\(46\) 2.10225 0.309960
\(47\) 7.48019 1.09110 0.545549 0.838079i \(-0.316321\pi\)
0.545549 + 0.838079i \(0.316321\pi\)
\(48\) 5.40459 0.780086
\(49\) 0.950276 0.135754
\(50\) 1.13950 0.161149
\(51\) −4.08691 −0.572282
\(52\) −20.0264 −2.77716
\(53\) −1.00000 −0.137361
\(54\) 10.1907 1.38678
\(55\) 2.33211 0.314462
\(56\) 18.1611 2.42688
\(57\) −2.39330 −0.317000
\(58\) 21.1569 2.77804
\(59\) −4.64532 −0.604769 −0.302384 0.953186i \(-0.597783\pi\)
−0.302384 + 0.953186i \(0.597783\pi\)
\(60\) 7.04308 0.909257
\(61\) −2.21778 −0.283958 −0.141979 0.989870i \(-0.545347\pi\)
−0.141979 + 0.989870i \(0.545347\pi\)
\(62\) 3.91599 0.497331
\(63\) 6.95688 0.876485
\(64\) 0.587685 0.0734606
\(65\) −9.45046 −1.17219
\(66\) −2.03701 −0.250738
\(67\) 11.9902 1.46483 0.732415 0.680858i \(-0.238393\pi\)
0.732415 + 0.680858i \(0.238393\pi\)
\(68\) −25.3219 −3.07073
\(69\) −0.600800 −0.0723278
\(70\) 15.3664 1.83663
\(71\) 8.81328 1.04594 0.522972 0.852350i \(-0.324823\pi\)
0.522972 + 0.852350i \(0.324823\pi\)
\(72\) 15.8919 1.87287
\(73\) 3.30737 0.387099 0.193549 0.981091i \(-0.438000\pi\)
0.193549 + 0.981091i \(0.438000\pi\)
\(74\) 22.2688 2.58869
\(75\) −0.325655 −0.0376034
\(76\) −14.8285 −1.70094
\(77\) −3.08144 −0.351162
\(78\) 8.25460 0.934649
\(79\) −1.24481 −0.140052 −0.0700258 0.997545i \(-0.522308\pi\)
−0.0700258 + 0.997545i \(0.522308\pi\)
\(80\) 15.8020 1.76672
\(81\) 4.48955 0.498839
\(82\) −1.52473 −0.168378
\(83\) −7.45671 −0.818480 −0.409240 0.912427i \(-0.634206\pi\)
−0.409240 + 0.912427i \(0.634206\pi\)
\(84\) −9.30607 −1.01538
\(85\) −11.9494 −1.29609
\(86\) −21.3917 −2.30673
\(87\) −6.04639 −0.648241
\(88\) −7.03903 −0.750363
\(89\) −6.00577 −0.636610 −0.318305 0.947988i \(-0.603114\pi\)
−0.318305 + 0.947988i \(0.603114\pi\)
\(90\) 13.4463 1.41737
\(91\) 12.4870 1.30899
\(92\) −3.72246 −0.388093
\(93\) −1.11914 −0.116050
\(94\) −19.1032 −1.97034
\(95\) −6.99756 −0.717935
\(96\) −4.40048 −0.449122
\(97\) −9.70815 −0.985713 −0.492856 0.870111i \(-0.664047\pi\)
−0.492856 + 0.870111i \(0.664047\pi\)
\(98\) −2.42685 −0.245149
\(99\) −2.69641 −0.270999
\(100\) −2.01771 −0.201771
\(101\) −9.28873 −0.924264 −0.462132 0.886811i \(-0.652915\pi\)
−0.462132 + 0.886811i \(0.652915\pi\)
\(102\) 10.4373 1.03345
\(103\) −2.82231 −0.278091 −0.139045 0.990286i \(-0.544403\pi\)
−0.139045 + 0.990286i \(0.544403\pi\)
\(104\) 28.5244 2.79705
\(105\) −4.39153 −0.428569
\(106\) 2.55384 0.248050
\(107\) 17.0750 1.65070 0.825350 0.564621i \(-0.190978\pi\)
0.825350 + 0.564621i \(0.190978\pi\)
\(108\) −18.0447 −1.73635
\(109\) −19.3215 −1.85066 −0.925331 0.379160i \(-0.876213\pi\)
−0.925331 + 0.379160i \(0.876213\pi\)
\(110\) −5.95583 −0.567866
\(111\) −6.36416 −0.604059
\(112\) −20.8793 −1.97291
\(113\) 19.3590 1.82114 0.910569 0.413357i \(-0.135644\pi\)
0.910569 + 0.413357i \(0.135644\pi\)
\(114\) 6.11209 0.572449
\(115\) −1.75663 −0.163806
\(116\) −37.4625 −3.47831
\(117\) 10.9267 1.01017
\(118\) 11.8634 1.09211
\(119\) 15.7888 1.44736
\(120\) −10.0317 −0.915767
\(121\) −9.80567 −0.891425
\(122\) 5.66385 0.512781
\(123\) 0.435750 0.0392902
\(124\) −6.93404 −0.622695
\(125\) −11.6220 −1.03950
\(126\) −17.7667 −1.58279
\(127\) 12.8436 1.13969 0.569843 0.821754i \(-0.307004\pi\)
0.569843 + 0.821754i \(0.307004\pi\)
\(128\) 10.5576 0.933173
\(129\) 6.11351 0.538264
\(130\) 24.1349 2.11677
\(131\) 20.8926 1.82539 0.912697 0.408637i \(-0.133996\pi\)
0.912697 + 0.408637i \(0.133996\pi\)
\(132\) 3.60693 0.313943
\(133\) 9.24593 0.801723
\(134\) −30.6209 −2.64524
\(135\) −8.51527 −0.732878
\(136\) 36.0669 3.09271
\(137\) 12.4552 1.06412 0.532059 0.846707i \(-0.321418\pi\)
0.532059 + 0.846707i \(0.321418\pi\)
\(138\) 1.53434 0.130612
\(139\) −8.59927 −0.729380 −0.364690 0.931129i \(-0.618825\pi\)
−0.364690 + 0.931129i \(0.618825\pi\)
\(140\) −27.2092 −2.29960
\(141\) 5.45946 0.459770
\(142\) −22.5077 −1.88880
\(143\) −4.83980 −0.404725
\(144\) −18.2705 −1.52254
\(145\) −17.6785 −1.46812
\(146\) −8.44648 −0.699036
\(147\) 0.693565 0.0572043
\(148\) −39.4313 −3.24123
\(149\) −4.75411 −0.389472 −0.194736 0.980856i \(-0.562385\pi\)
−0.194736 + 0.980856i \(0.562385\pi\)
\(150\) 0.831669 0.0679055
\(151\) 1.00000 0.0813788
\(152\) 21.1208 1.71312
\(153\) 13.8160 1.11696
\(154\) 7.86948 0.634141
\(155\) −3.27217 −0.262827
\(156\) −14.6164 −1.17025
\(157\) 17.3100 1.38149 0.690745 0.723098i \(-0.257283\pi\)
0.690745 + 0.723098i \(0.257283\pi\)
\(158\) 3.17903 0.252910
\(159\) −0.729856 −0.0578814
\(160\) −12.8662 −1.01716
\(161\) 2.32104 0.182924
\(162\) −11.4656 −0.900820
\(163\) −5.71813 −0.447878 −0.223939 0.974603i \(-0.571892\pi\)
−0.223939 + 0.974603i \(0.571892\pi\)
\(164\) 2.69984 0.210822
\(165\) 1.70211 0.132509
\(166\) 19.0432 1.47804
\(167\) −3.56364 −0.275763 −0.137881 0.990449i \(-0.544029\pi\)
−0.137881 + 0.990449i \(0.544029\pi\)
\(168\) 13.2550 1.02264
\(169\) 6.61242 0.508648
\(170\) 30.5167 2.34053
\(171\) 8.09064 0.618707
\(172\) 37.8783 2.88820
\(173\) 12.0800 0.918429 0.459215 0.888325i \(-0.348131\pi\)
0.459215 + 0.888325i \(0.348131\pi\)
\(174\) 15.4415 1.17062
\(175\) 1.25809 0.0951026
\(176\) 8.09259 0.610002
\(177\) −3.39041 −0.254839
\(178\) 15.3377 1.14961
\(179\) −15.2596 −1.14056 −0.570280 0.821450i \(-0.693165\pi\)
−0.570280 + 0.821450i \(0.693165\pi\)
\(180\) −23.8094 −1.77465
\(181\) 2.66986 0.198449 0.0992244 0.995065i \(-0.468364\pi\)
0.0992244 + 0.995065i \(0.468364\pi\)
\(182\) −31.8896 −2.36382
\(183\) −1.61866 −0.119655
\(184\) 5.30204 0.390872
\(185\) −18.6076 −1.36806
\(186\) 2.85811 0.209567
\(187\) −6.11956 −0.447506
\(188\) 33.8260 2.46701
\(189\) 11.2513 0.818411
\(190\) 17.8706 1.29647
\(191\) 18.9374 1.37026 0.685131 0.728420i \(-0.259745\pi\)
0.685131 + 0.728420i \(0.259745\pi\)
\(192\) 0.428926 0.0309550
\(193\) 25.9853 1.87046 0.935232 0.354035i \(-0.115191\pi\)
0.935232 + 0.354035i \(0.115191\pi\)
\(194\) 24.7930 1.78003
\(195\) −6.89748 −0.493939
\(196\) 4.29722 0.306944
\(197\) −7.16000 −0.510129 −0.255064 0.966924i \(-0.582097\pi\)
−0.255064 + 0.966924i \(0.582097\pi\)
\(198\) 6.88619 0.489380
\(199\) 10.8023 0.765752 0.382876 0.923800i \(-0.374934\pi\)
0.382876 + 0.923800i \(0.374934\pi\)
\(200\) 2.87390 0.203215
\(201\) 8.75109 0.617254
\(202\) 23.7219 1.66907
\(203\) 23.3588 1.63946
\(204\) −18.4813 −1.29395
\(205\) 1.27405 0.0889837
\(206\) 7.20772 0.502186
\(207\) 2.03103 0.141166
\(208\) −32.7938 −2.27384
\(209\) −3.58362 −0.247884
\(210\) 11.2152 0.773925
\(211\) 8.33284 0.573657 0.286828 0.957982i \(-0.407399\pi\)
0.286828 + 0.957982i \(0.407399\pi\)
\(212\) −4.52207 −0.310577
\(213\) 6.43243 0.440743
\(214\) −43.6067 −2.98089
\(215\) 17.8748 1.21905
\(216\) 25.7017 1.74878
\(217\) 4.32354 0.293501
\(218\) 49.3439 3.34199
\(219\) 2.41391 0.163117
\(220\) 10.5460 0.711010
\(221\) 24.7984 1.66812
\(222\) 16.2530 1.09083
\(223\) 24.0462 1.61026 0.805128 0.593101i \(-0.202097\pi\)
0.805128 + 0.593101i \(0.202097\pi\)
\(224\) 17.0002 1.13587
\(225\) 1.10089 0.0733927
\(226\) −49.4396 −3.28867
\(227\) 10.8952 0.723138 0.361569 0.932345i \(-0.382241\pi\)
0.361569 + 0.932345i \(0.382241\pi\)
\(228\) −10.8227 −0.716749
\(229\) 29.6467 1.95911 0.979554 0.201181i \(-0.0644778\pi\)
0.979554 + 0.201181i \(0.0644778\pi\)
\(230\) 4.48614 0.295807
\(231\) −2.24901 −0.147974
\(232\) 53.3593 3.50321
\(233\) −22.6440 −1.48345 −0.741727 0.670701i \(-0.765993\pi\)
−0.741727 + 0.670701i \(0.765993\pi\)
\(234\) −27.9050 −1.82421
\(235\) 15.9625 1.04128
\(236\) −21.0065 −1.36740
\(237\) −0.908529 −0.0590153
\(238\) −40.3220 −2.61369
\(239\) −16.9562 −1.09681 −0.548403 0.836214i \(-0.684764\pi\)
−0.548403 + 0.836214i \(0.684764\pi\)
\(240\) 11.5332 0.744466
\(241\) −21.1323 −1.36125 −0.680624 0.732633i \(-0.738291\pi\)
−0.680624 + 0.732633i \(0.738291\pi\)
\(242\) 25.0421 1.60976
\(243\) 15.2478 0.978145
\(244\) −10.0290 −0.642040
\(245\) 2.02786 0.129555
\(246\) −1.11283 −0.0709517
\(247\) 14.5219 0.924009
\(248\) 9.87641 0.627153
\(249\) −5.44233 −0.344893
\(250\) 29.6806 1.87717
\(251\) −20.7156 −1.30756 −0.653779 0.756685i \(-0.726818\pi\)
−0.653779 + 0.756685i \(0.726818\pi\)
\(252\) 31.4595 1.98177
\(253\) −0.899610 −0.0565580
\(254\) −32.8004 −2.05808
\(255\) −8.72133 −0.546151
\(256\) −28.1378 −1.75862
\(257\) −23.9538 −1.49420 −0.747099 0.664713i \(-0.768554\pi\)
−0.747099 + 0.664713i \(0.768554\pi\)
\(258\) −15.6129 −0.972016
\(259\) 24.5864 1.52772
\(260\) −42.7357 −2.65036
\(261\) 20.4401 1.26521
\(262\) −53.3562 −3.29636
\(263\) 26.9296 1.66055 0.830274 0.557356i \(-0.188184\pi\)
0.830274 + 0.557356i \(0.188184\pi\)
\(264\) −5.13748 −0.316190
\(265\) −2.13397 −0.131088
\(266\) −23.6126 −1.44778
\(267\) −4.38335 −0.268257
\(268\) 54.2204 3.31204
\(269\) 20.9728 1.27874 0.639368 0.768901i \(-0.279196\pi\)
0.639368 + 0.768901i \(0.279196\pi\)
\(270\) 21.7466 1.32346
\(271\) 10.9587 0.665694 0.332847 0.942981i \(-0.391991\pi\)
0.332847 + 0.942981i \(0.391991\pi\)
\(272\) −41.4652 −2.51420
\(273\) 9.11369 0.551585
\(274\) −31.8085 −1.92162
\(275\) −0.487621 −0.0294047
\(276\) −2.71686 −0.163536
\(277\) 1.90354 0.114373 0.0571864 0.998364i \(-0.481787\pi\)
0.0571864 + 0.998364i \(0.481787\pi\)
\(278\) 21.9611 1.31714
\(279\) 3.78331 0.226501
\(280\) 38.7551 2.31606
\(281\) −20.3148 −1.21188 −0.605938 0.795512i \(-0.707202\pi\)
−0.605938 + 0.795512i \(0.707202\pi\)
\(282\) −13.9426 −0.830268
\(283\) −21.9415 −1.30428 −0.652142 0.758097i \(-0.726129\pi\)
−0.652142 + 0.758097i \(0.726129\pi\)
\(284\) 39.8543 2.36492
\(285\) −5.10721 −0.302525
\(286\) 12.3601 0.730866
\(287\) −1.68341 −0.0993688
\(288\) 14.8760 0.876578
\(289\) 14.3557 0.844450
\(290\) 45.1481 2.65119
\(291\) −7.08555 −0.415362
\(292\) 14.9562 0.875245
\(293\) 10.4996 0.613393 0.306697 0.951807i \(-0.400776\pi\)
0.306697 + 0.951807i \(0.400776\pi\)
\(294\) −1.77125 −0.103301
\(295\) −9.91294 −0.577154
\(296\) 56.1635 3.26444
\(297\) −4.36087 −0.253043
\(298\) 12.1412 0.703322
\(299\) 3.64551 0.210825
\(300\) −1.47264 −0.0850227
\(301\) −23.6181 −1.36132
\(302\) −2.55384 −0.146957
\(303\) −6.77944 −0.389469
\(304\) −24.2820 −1.39267
\(305\) −4.73267 −0.270992
\(306\) −35.2837 −2.01704
\(307\) −18.3866 −1.04938 −0.524690 0.851293i \(-0.675819\pi\)
−0.524690 + 0.851293i \(0.675819\pi\)
\(308\) −13.9345 −0.793991
\(309\) −2.05988 −0.117183
\(310\) 8.35659 0.474622
\(311\) −18.3769 −1.04206 −0.521028 0.853539i \(-0.674451\pi\)
−0.521028 + 0.853539i \(0.674451\pi\)
\(312\) 20.8187 1.17863
\(313\) 6.66064 0.376482 0.188241 0.982123i \(-0.439721\pi\)
0.188241 + 0.982123i \(0.439721\pi\)
\(314\) −44.2070 −2.49474
\(315\) 14.8458 0.836463
\(316\) −5.62910 −0.316662
\(317\) 3.83014 0.215122 0.107561 0.994198i \(-0.465696\pi\)
0.107561 + 0.994198i \(0.465696\pi\)
\(318\) 1.86393 0.104524
\(319\) −9.05360 −0.506904
\(320\) 1.25410 0.0701063
\(321\) 12.4623 0.695576
\(322\) −5.92756 −0.330330
\(323\) 18.3619 1.02168
\(324\) 20.3021 1.12789
\(325\) 1.97600 0.109608
\(326\) 14.6032 0.808794
\(327\) −14.1019 −0.779837
\(328\) −3.84548 −0.212331
\(329\) −21.0913 −1.16280
\(330\) −4.34690 −0.239289
\(331\) 19.4957 1.07158 0.535791 0.844350i \(-0.320013\pi\)
0.535791 + 0.844350i \(0.320013\pi\)
\(332\) −33.7198 −1.85061
\(333\) 21.5143 1.17898
\(334\) 9.10095 0.497982
\(335\) 25.5866 1.39794
\(336\) −15.2389 −0.831351
\(337\) 22.3863 1.21946 0.609729 0.792610i \(-0.291278\pi\)
0.609729 + 0.792610i \(0.291278\pi\)
\(338\) −16.8870 −0.918533
\(339\) 14.1293 0.767396
\(340\) −54.0360 −2.93051
\(341\) −1.67576 −0.0907473
\(342\) −20.6622 −1.11728
\(343\) 17.0579 0.921042
\(344\) −53.9515 −2.90887
\(345\) −1.28209 −0.0690252
\(346\) −30.8505 −1.65853
\(347\) 7.23197 0.388233 0.194116 0.980979i \(-0.437816\pi\)
0.194116 + 0.980979i \(0.437816\pi\)
\(348\) −27.3422 −1.46570
\(349\) 29.8632 1.59854 0.799271 0.600971i \(-0.205219\pi\)
0.799271 + 0.600971i \(0.205219\pi\)
\(350\) −3.21295 −0.171740
\(351\) 17.6716 0.943242
\(352\) −6.58909 −0.351199
\(353\) −10.7817 −0.573850 −0.286925 0.957953i \(-0.592633\pi\)
−0.286925 + 0.957953i \(0.592633\pi\)
\(354\) 8.65856 0.460197
\(355\) 18.8072 0.998185
\(356\) −27.1585 −1.43940
\(357\) 11.5236 0.609891
\(358\) 38.9706 2.05966
\(359\) −35.7863 −1.88873 −0.944365 0.328900i \(-0.893322\pi\)
−0.944365 + 0.328900i \(0.893322\pi\)
\(360\) 33.9127 1.78735
\(361\) −8.24727 −0.434067
\(362\) −6.81837 −0.358366
\(363\) −7.15673 −0.375631
\(364\) 56.4670 2.95967
\(365\) 7.05782 0.369423
\(366\) 4.13380 0.216077
\(367\) 0.419435 0.0218943 0.0109472 0.999940i \(-0.496515\pi\)
0.0109472 + 0.999940i \(0.496515\pi\)
\(368\) −6.09562 −0.317756
\(369\) −1.47307 −0.0766850
\(370\) 47.5208 2.47049
\(371\) 2.81962 0.146388
\(372\) −5.06085 −0.262393
\(373\) −17.7337 −0.918214 −0.459107 0.888381i \(-0.651830\pi\)
−0.459107 + 0.888381i \(0.651830\pi\)
\(374\) 15.6283 0.808122
\(375\) −8.48238 −0.438028
\(376\) −48.1796 −2.48467
\(377\) 36.6880 1.88953
\(378\) −28.7339 −1.47791
\(379\) −23.7837 −1.22169 −0.610843 0.791752i \(-0.709169\pi\)
−0.610843 + 0.791752i \(0.709169\pi\)
\(380\) −31.6435 −1.62328
\(381\) 9.37398 0.480244
\(382\) −48.3630 −2.47446
\(383\) −18.4771 −0.944136 −0.472068 0.881562i \(-0.656492\pi\)
−0.472068 + 0.881562i \(0.656492\pi\)
\(384\) 7.70556 0.393223
\(385\) −6.57568 −0.335128
\(386\) −66.3622 −3.37775
\(387\) −20.6670 −1.05056
\(388\) −43.9010 −2.22873
\(389\) −1.01483 −0.0514537 −0.0257268 0.999669i \(-0.508190\pi\)
−0.0257268 + 0.999669i \(0.508190\pi\)
\(390\) 17.6150 0.891971
\(391\) 4.60946 0.233111
\(392\) −6.12069 −0.309142
\(393\) 15.2486 0.769190
\(394\) 18.2855 0.921208
\(395\) −2.65637 −0.133657
\(396\) −12.1934 −0.612740
\(397\) 35.1697 1.76512 0.882560 0.470201i \(-0.155818\pi\)
0.882560 + 0.470201i \(0.155818\pi\)
\(398\) −27.5872 −1.38282
\(399\) 6.74820 0.337832
\(400\) −3.30404 −0.165202
\(401\) −1.01543 −0.0507083 −0.0253541 0.999679i \(-0.508071\pi\)
−0.0253541 + 0.999679i \(0.508071\pi\)
\(402\) −22.3488 −1.11466
\(403\) 6.79069 0.338269
\(404\) −42.0043 −2.08979
\(405\) 9.58054 0.476061
\(406\) −59.6545 −2.96060
\(407\) −9.52940 −0.472355
\(408\) 26.3236 1.30321
\(409\) −13.2334 −0.654348 −0.327174 0.944964i \(-0.606096\pi\)
−0.327174 + 0.944964i \(0.606096\pi\)
\(410\) −3.25372 −0.160690
\(411\) 9.09050 0.448401
\(412\) −12.7627 −0.628773
\(413\) 13.0980 0.644512
\(414\) −5.18691 −0.254923
\(415\) −15.9124 −0.781107
\(416\) 26.7011 1.30913
\(417\) −6.27623 −0.307348
\(418\) 9.15196 0.447637
\(419\) 20.3812 0.995684 0.497842 0.867268i \(-0.334126\pi\)
0.497842 + 0.867268i \(0.334126\pi\)
\(420\) −19.8588 −0.969012
\(421\) 27.7561 1.35275 0.676374 0.736558i \(-0.263550\pi\)
0.676374 + 0.736558i \(0.263550\pi\)
\(422\) −21.2807 −1.03593
\(423\) −18.4559 −0.897359
\(424\) 6.44096 0.312801
\(425\) 2.49849 0.121195
\(426\) −16.4274 −0.795909
\(427\) 6.25331 0.302619
\(428\) 77.2143 3.73229
\(429\) −3.53236 −0.170544
\(430\) −45.6492 −2.20140
\(431\) −23.8871 −1.15060 −0.575300 0.817943i \(-0.695115\pi\)
−0.575300 + 0.817943i \(0.695115\pi\)
\(432\) −29.5486 −1.42166
\(433\) 2.60680 0.125275 0.0626375 0.998036i \(-0.480049\pi\)
0.0626375 + 0.998036i \(0.480049\pi\)
\(434\) −11.0416 −0.530014
\(435\) −12.9028 −0.618642
\(436\) −87.3732 −4.18442
\(437\) 2.69930 0.129125
\(438\) −6.16472 −0.294562
\(439\) −5.80839 −0.277219 −0.138610 0.990347i \(-0.544263\pi\)
−0.138610 + 0.990347i \(0.544263\pi\)
\(440\) −15.0211 −0.716101
\(441\) −2.34463 −0.111649
\(442\) −63.3310 −3.01235
\(443\) −20.4494 −0.971580 −0.485790 0.874076i \(-0.661468\pi\)
−0.485790 + 0.874076i \(0.661468\pi\)
\(444\) −28.7792 −1.36580
\(445\) −12.8161 −0.607542
\(446\) −61.4102 −2.90785
\(447\) −3.46982 −0.164117
\(448\) −1.65705 −0.0782883
\(449\) 12.6569 0.597316 0.298658 0.954360i \(-0.403461\pi\)
0.298658 + 0.954360i \(0.403461\pi\)
\(450\) −2.81149 −0.132535
\(451\) 0.652472 0.0307237
\(452\) 87.5427 4.11766
\(453\) 0.729856 0.0342916
\(454\) −27.8245 −1.30587
\(455\) 26.6467 1.24922
\(456\) 15.4151 0.721880
\(457\) −8.77412 −0.410436 −0.205218 0.978716i \(-0.565790\pi\)
−0.205218 + 0.978716i \(0.565790\pi\)
\(458\) −75.7128 −3.53782
\(459\) 22.3444 1.04295
\(460\) −7.94360 −0.370372
\(461\) 1.06999 0.0498345 0.0249172 0.999690i \(-0.492068\pi\)
0.0249172 + 0.999690i \(0.492068\pi\)
\(462\) 5.74359 0.267216
\(463\) −31.2019 −1.45007 −0.725037 0.688710i \(-0.758177\pi\)
−0.725037 + 0.688710i \(0.758177\pi\)
\(464\) −61.3458 −2.84791
\(465\) −2.38821 −0.110751
\(466\) 57.8289 2.67887
\(467\) 6.90823 0.319675 0.159837 0.987143i \(-0.448903\pi\)
0.159837 + 0.987143i \(0.448903\pi\)
\(468\) 49.4114 2.28404
\(469\) −33.8077 −1.56110
\(470\) −40.7655 −1.88037
\(471\) 12.6338 0.582136
\(472\) 29.9203 1.37719
\(473\) 9.15409 0.420906
\(474\) 2.32023 0.106572
\(475\) 1.46312 0.0671325
\(476\) 71.3981 3.27253
\(477\) 2.46731 0.112970
\(478\) 43.3033 1.98065
\(479\) −22.3765 −1.02241 −0.511204 0.859460i \(-0.670800\pi\)
−0.511204 + 0.859460i \(0.670800\pi\)
\(480\) −9.39048 −0.428615
\(481\) 38.6162 1.76075
\(482\) 53.9683 2.45819
\(483\) 1.69403 0.0770810
\(484\) −44.3420 −2.01554
\(485\) −20.7169 −0.940704
\(486\) −38.9403 −1.76637
\(487\) 9.68816 0.439012 0.219506 0.975611i \(-0.429555\pi\)
0.219506 + 0.975611i \(0.429555\pi\)
\(488\) 14.2847 0.646636
\(489\) −4.17341 −0.188728
\(490\) −5.17881 −0.233955
\(491\) −43.0213 −1.94152 −0.970762 0.240043i \(-0.922838\pi\)
−0.970762 + 0.240043i \(0.922838\pi\)
\(492\) 1.97049 0.0888367
\(493\) 46.3892 2.08926
\(494\) −37.0867 −1.66861
\(495\) −5.75405 −0.258625
\(496\) −11.3547 −0.509839
\(497\) −24.8501 −1.11468
\(498\) 13.8988 0.622820
\(499\) 13.4548 0.602319 0.301160 0.953574i \(-0.402626\pi\)
0.301160 + 0.953574i \(0.402626\pi\)
\(500\) −52.5555 −2.35035
\(501\) −2.60095 −0.116202
\(502\) 52.9043 2.36123
\(503\) −29.8700 −1.33184 −0.665918 0.746025i \(-0.731960\pi\)
−0.665918 + 0.746025i \(0.731960\pi\)
\(504\) −44.8090 −1.99595
\(505\) −19.8218 −0.882060
\(506\) 2.29746 0.102134
\(507\) 4.82612 0.214335
\(508\) 58.0797 2.57687
\(509\) −29.4385 −1.30484 −0.652419 0.757859i \(-0.726246\pi\)
−0.652419 + 0.757859i \(0.726246\pi\)
\(510\) 22.2728 0.986258
\(511\) −9.32555 −0.412538
\(512\) 50.7441 2.24260
\(513\) 13.0849 0.577712
\(514\) 61.1741 2.69827
\(515\) −6.02272 −0.265393
\(516\) 27.6457 1.21704
\(517\) 8.17476 0.359525
\(518\) −62.7896 −2.75882
\(519\) 8.81670 0.387010
\(520\) 60.8701 2.66933
\(521\) −5.49431 −0.240710 −0.120355 0.992731i \(-0.538403\pi\)
−0.120355 + 0.992731i \(0.538403\pi\)
\(522\) −52.2006 −2.28476
\(523\) 9.05912 0.396127 0.198064 0.980189i \(-0.436535\pi\)
0.198064 + 0.980189i \(0.436535\pi\)
\(524\) 94.4779 4.12728
\(525\) 0.918224 0.0400746
\(526\) −68.7737 −2.99867
\(527\) 8.58631 0.374025
\(528\) 5.90643 0.257044
\(529\) −22.3224 −0.970538
\(530\) 5.44980 0.236724
\(531\) 11.4614 0.497384
\(532\) 41.8108 1.81273
\(533\) −2.64402 −0.114525
\(534\) 11.1943 0.484427
\(535\) 36.4374 1.57533
\(536\) −77.2281 −3.33575
\(537\) −11.1373 −0.480612
\(538\) −53.5611 −2.30918
\(539\) 1.03851 0.0447319
\(540\) −38.5067 −1.65706
\(541\) 7.67049 0.329780 0.164890 0.986312i \(-0.447273\pi\)
0.164890 + 0.986312i \(0.447273\pi\)
\(542\) −27.9867 −1.20213
\(543\) 1.94861 0.0836229
\(544\) 33.7614 1.44751
\(545\) −41.2314 −1.76616
\(546\) −23.2749 −0.996072
\(547\) −31.9952 −1.36802 −0.684008 0.729475i \(-0.739764\pi\)
−0.684008 + 0.729475i \(0.739764\pi\)
\(548\) 56.3233 2.40601
\(549\) 5.47196 0.233538
\(550\) 1.24530 0.0530999
\(551\) 27.1655 1.15729
\(552\) 3.86973 0.164707
\(553\) 3.50988 0.149255
\(554\) −4.86134 −0.206538
\(555\) −13.5809 −0.576477
\(556\) −38.8865 −1.64916
\(557\) −26.5681 −1.12573 −0.562863 0.826550i \(-0.690300\pi\)
−0.562863 + 0.826550i \(0.690300\pi\)
\(558\) −9.66196 −0.409023
\(559\) −37.0953 −1.56896
\(560\) −44.5558 −1.88283
\(561\) −4.46640 −0.188571
\(562\) 51.8805 2.18845
\(563\) −23.1168 −0.974256 −0.487128 0.873331i \(-0.661955\pi\)
−0.487128 + 0.873331i \(0.661955\pi\)
\(564\) 24.6881 1.03956
\(565\) 41.3114 1.73798
\(566\) 56.0349 2.35532
\(567\) −12.6588 −0.531621
\(568\) −56.7660 −2.38185
\(569\) −1.69936 −0.0712409 −0.0356204 0.999365i \(-0.511341\pi\)
−0.0356204 + 0.999365i \(0.511341\pi\)
\(570\) 13.0430 0.546310
\(571\) −15.2525 −0.638296 −0.319148 0.947705i \(-0.603397\pi\)
−0.319148 + 0.947705i \(0.603397\pi\)
\(572\) −21.8860 −0.915098
\(573\) 13.8216 0.577404
\(574\) 4.29916 0.179444
\(575\) 0.367293 0.0153172
\(576\) −1.45000 −0.0604167
\(577\) −9.06043 −0.377191 −0.188595 0.982055i \(-0.560393\pi\)
−0.188595 + 0.982055i \(0.560393\pi\)
\(578\) −36.6620 −1.52494
\(579\) 18.9656 0.788181
\(580\) −79.9437 −3.31948
\(581\) 21.0251 0.872269
\(582\) 18.0953 0.750076
\(583\) −1.09285 −0.0452614
\(584\) −21.3027 −0.881511
\(585\) 23.3172 0.964048
\(586\) −26.8143 −1.10769
\(587\) −21.7927 −0.899482 −0.449741 0.893159i \(-0.648484\pi\)
−0.449741 + 0.893159i \(0.648484\pi\)
\(588\) 3.13635 0.129341
\(589\) 5.02815 0.207181
\(590\) 25.3160 1.04224
\(591\) −5.22577 −0.214959
\(592\) −64.5698 −2.65380
\(593\) −44.8556 −1.84200 −0.921000 0.389562i \(-0.872626\pi\)
−0.921000 + 0.389562i \(0.872626\pi\)
\(594\) 11.1369 0.456954
\(595\) 33.6927 1.38127
\(596\) −21.4984 −0.880610
\(597\) 7.88410 0.322675
\(598\) −9.31002 −0.380715
\(599\) −7.71732 −0.315321 −0.157660 0.987493i \(-0.550395\pi\)
−0.157660 + 0.987493i \(0.550395\pi\)
\(600\) 2.09753 0.0856313
\(601\) 44.4377 1.81265 0.906325 0.422581i \(-0.138876\pi\)
0.906325 + 0.422581i \(0.138876\pi\)
\(602\) 60.3166 2.45832
\(603\) −29.5834 −1.20473
\(604\) 4.52207 0.184001
\(605\) −20.9250 −0.850721
\(606\) 17.3136 0.703316
\(607\) 22.9546 0.931699 0.465849 0.884864i \(-0.345749\pi\)
0.465849 + 0.884864i \(0.345749\pi\)
\(608\) 19.7707 0.801808
\(609\) 17.0486 0.690842
\(610\) 12.0865 0.489367
\(611\) −33.1267 −1.34016
\(612\) 62.4769 2.52548
\(613\) 33.0754 1.33590 0.667951 0.744205i \(-0.267171\pi\)
0.667951 + 0.744205i \(0.267171\pi\)
\(614\) 46.9564 1.89501
\(615\) 0.929875 0.0374962
\(616\) 19.8474 0.799675
\(617\) 1.87003 0.0752847 0.0376423 0.999291i \(-0.488015\pi\)
0.0376423 + 0.999291i \(0.488015\pi\)
\(618\) 5.26060 0.211612
\(619\) 15.7357 0.632472 0.316236 0.948680i \(-0.397581\pi\)
0.316236 + 0.948680i \(0.397581\pi\)
\(620\) −14.7970 −0.594262
\(621\) 3.28476 0.131813
\(622\) 46.9315 1.88178
\(623\) 16.9340 0.678447
\(624\) −23.9347 −0.958156
\(625\) −22.5700 −0.902798
\(626\) −17.0102 −0.679863
\(627\) −2.61552 −0.104454
\(628\) 78.2772 3.12360
\(629\) 48.8272 1.94687
\(630\) −37.9136 −1.51051
\(631\) 31.3859 1.24945 0.624727 0.780844i \(-0.285210\pi\)
0.624727 + 0.780844i \(0.285210\pi\)
\(632\) 8.01775 0.318929
\(633\) 6.08178 0.241729
\(634\) −9.78154 −0.388475
\(635\) 27.4078 1.08765
\(636\) −3.30046 −0.130872
\(637\) −4.20838 −0.166742
\(638\) 23.1214 0.915385
\(639\) −21.7451 −0.860223
\(640\) 22.5296 0.890562
\(641\) −1.10668 −0.0437113 −0.0218556 0.999761i \(-0.506957\pi\)
−0.0218556 + 0.999761i \(0.506957\pi\)
\(642\) −31.8266 −1.25610
\(643\) 13.4690 0.531166 0.265583 0.964088i \(-0.414436\pi\)
0.265583 + 0.964088i \(0.414436\pi\)
\(644\) 10.4959 0.413598
\(645\) 13.0460 0.513686
\(646\) −46.8932 −1.84499
\(647\) −9.06661 −0.356445 −0.178223 0.983990i \(-0.557035\pi\)
−0.178223 + 0.983990i \(0.557035\pi\)
\(648\) −28.9170 −1.13597
\(649\) −5.07665 −0.199276
\(650\) −5.04637 −0.197935
\(651\) 3.15556 0.123676
\(652\) −25.8578 −1.01267
\(653\) −29.7557 −1.16443 −0.582216 0.813034i \(-0.697814\pi\)
−0.582216 + 0.813034i \(0.697814\pi\)
\(654\) 36.0139 1.40826
\(655\) 44.5841 1.74204
\(656\) 4.42105 0.172613
\(657\) −8.16031 −0.318364
\(658\) 53.8637 2.09983
\(659\) 2.36426 0.0920983 0.0460492 0.998939i \(-0.485337\pi\)
0.0460492 + 0.998939i \(0.485337\pi\)
\(660\) 7.69706 0.299608
\(661\) −32.7273 −1.27294 −0.636472 0.771300i \(-0.719607\pi\)
−0.636472 + 0.771300i \(0.719607\pi\)
\(662\) −49.7889 −1.93510
\(663\) 18.0993 0.702917
\(664\) 48.0284 1.86386
\(665\) 19.7305 0.765115
\(666\) −54.9440 −2.12904
\(667\) 6.81948 0.264051
\(668\) −16.1150 −0.623510
\(669\) 17.5503 0.678534
\(670\) −65.3439 −2.52446
\(671\) −2.42371 −0.0935664
\(672\) 12.4077 0.478638
\(673\) −17.5284 −0.675671 −0.337835 0.941205i \(-0.609695\pi\)
−0.337835 + 0.941205i \(0.609695\pi\)
\(674\) −57.1708 −2.20214
\(675\) 1.78046 0.0685298
\(676\) 29.9019 1.15007
\(677\) −21.9636 −0.844130 −0.422065 0.906566i \(-0.638695\pi\)
−0.422065 + 0.906566i \(0.638695\pi\)
\(678\) −36.0838 −1.38579
\(679\) 27.3733 1.05049
\(680\) 76.9655 2.95149
\(681\) 7.95191 0.304718
\(682\) 4.27960 0.163875
\(683\) 16.0766 0.615154 0.307577 0.951523i \(-0.400482\pi\)
0.307577 + 0.951523i \(0.400482\pi\)
\(684\) 36.5865 1.39892
\(685\) 26.5789 1.01553
\(686\) −43.5632 −1.66325
\(687\) 21.6378 0.825534
\(688\) 62.0267 2.36475
\(689\) 4.42859 0.168716
\(690\) 3.27424 0.124648
\(691\) 46.0777 1.75288 0.876439 0.481513i \(-0.159913\pi\)
0.876439 + 0.481513i \(0.159913\pi\)
\(692\) 54.6269 2.07660
\(693\) 7.60286 0.288809
\(694\) −18.4693 −0.701084
\(695\) −18.3505 −0.696076
\(696\) 38.9446 1.47619
\(697\) −3.34317 −0.126631
\(698\) −76.2657 −2.88670
\(699\) −16.5268 −0.625102
\(700\) 5.68917 0.215031
\(701\) 9.81293 0.370629 0.185315 0.982679i \(-0.440670\pi\)
0.185315 + 0.982679i \(0.440670\pi\)
\(702\) −45.1304 −1.70334
\(703\) 28.5932 1.07841
\(704\) 0.642254 0.0242059
\(705\) 11.6503 0.438776
\(706\) 27.5346 1.03628
\(707\) 26.1907 0.985004
\(708\) −15.3317 −0.576200
\(709\) −2.26986 −0.0852465 −0.0426232 0.999091i \(-0.513572\pi\)
−0.0426232 + 0.999091i \(0.513572\pi\)
\(710\) −48.0306 −1.80256
\(711\) 3.07132 0.115184
\(712\) 38.6829 1.44970
\(713\) 1.26224 0.0472711
\(714\) −29.4293 −1.10136
\(715\) −10.3280 −0.386244
\(716\) −69.0053 −2.57885
\(717\) −12.3756 −0.462175
\(718\) 91.3923 3.41073
\(719\) −1.74326 −0.0650128 −0.0325064 0.999472i \(-0.510349\pi\)
−0.0325064 + 0.999472i \(0.510349\pi\)
\(720\) −38.9885 −1.45302
\(721\) 7.95786 0.296366
\(722\) 21.0622 0.783853
\(723\) −15.4235 −0.573606
\(724\) 12.0733 0.448700
\(725\) 3.69640 0.137281
\(726\) 18.2771 0.678327
\(727\) 43.4349 1.61091 0.805456 0.592655i \(-0.201920\pi\)
0.805456 + 0.592655i \(0.201920\pi\)
\(728\) −80.4280 −2.98086
\(729\) −2.33996 −0.0866651
\(730\) −18.0245 −0.667117
\(731\) −46.9041 −1.73481
\(732\) −7.31972 −0.270544
\(733\) −32.8810 −1.21449 −0.607244 0.794515i \(-0.707725\pi\)
−0.607244 + 0.794515i \(0.707725\pi\)
\(734\) −1.07117 −0.0395375
\(735\) 1.48004 0.0545922
\(736\) 4.96313 0.182943
\(737\) 13.1035 0.482673
\(738\) 3.76198 0.138480
\(739\) −48.7941 −1.79492 −0.897460 0.441095i \(-0.854590\pi\)
−0.897460 + 0.441095i \(0.854590\pi\)
\(740\) −84.1451 −3.09323
\(741\) 10.5989 0.389362
\(742\) −7.20085 −0.264352
\(743\) 21.7432 0.797679 0.398840 0.917021i \(-0.369413\pi\)
0.398840 + 0.917021i \(0.369413\pi\)
\(744\) 7.20836 0.264271
\(745\) −10.1451 −0.371688
\(746\) 45.2888 1.65814
\(747\) 18.3980 0.673148
\(748\) −27.6731 −1.01183
\(749\) −48.1450 −1.75918
\(750\) 21.6626 0.791006
\(751\) 42.1164 1.53685 0.768425 0.639940i \(-0.221041\pi\)
0.768425 + 0.639940i \(0.221041\pi\)
\(752\) 55.3909 2.01990
\(753\) −15.1194 −0.550983
\(754\) −93.6952 −3.41218
\(755\) 2.13397 0.0776630
\(756\) 50.8791 1.85046
\(757\) −10.7465 −0.390588 −0.195294 0.980745i \(-0.562566\pi\)
−0.195294 + 0.980745i \(0.562566\pi\)
\(758\) 60.7396 2.20616
\(759\) −0.656586 −0.0238326
\(760\) 45.0710 1.63490
\(761\) 36.2695 1.31477 0.657384 0.753556i \(-0.271663\pi\)
0.657384 + 0.753556i \(0.271663\pi\)
\(762\) −23.9396 −0.867240
\(763\) 54.4793 1.97228
\(764\) 85.6363 3.09821
\(765\) 29.4828 1.06595
\(766\) 47.1875 1.70495
\(767\) 20.5722 0.742819
\(768\) −20.5366 −0.741050
\(769\) −22.1488 −0.798705 −0.399353 0.916797i \(-0.630765\pi\)
−0.399353 + 0.916797i \(0.630765\pi\)
\(770\) 16.7932 0.605185
\(771\) −17.4828 −0.629629
\(772\) 117.508 4.22919
\(773\) −14.5901 −0.524769 −0.262384 0.964963i \(-0.584509\pi\)
−0.262384 + 0.964963i \(0.584509\pi\)
\(774\) 52.7800 1.89714
\(775\) 0.684178 0.0245764
\(776\) 62.5298 2.24469
\(777\) 17.9445 0.643756
\(778\) 2.59170 0.0929168
\(779\) −1.95776 −0.0701440
\(780\) −31.1909 −1.11681
\(781\) 9.63163 0.344647
\(782\) −11.7718 −0.420959
\(783\) 33.0575 1.18138
\(784\) 7.03680 0.251314
\(785\) 36.9390 1.31841
\(786\) −38.9424 −1.38903
\(787\) 39.3555 1.40287 0.701437 0.712732i \(-0.252542\pi\)
0.701437 + 0.712732i \(0.252542\pi\)
\(788\) −32.3781 −1.15342
\(789\) 19.6547 0.699726
\(790\) 6.78394 0.241362
\(791\) −54.5850 −1.94082
\(792\) 17.3675 0.617126
\(793\) 9.82166 0.348777
\(794\) −89.8177 −3.18751
\(795\) −1.55749 −0.0552384
\(796\) 48.8486 1.73139
\(797\) −33.9897 −1.20398 −0.601988 0.798505i \(-0.705624\pi\)
−0.601988 + 0.798505i \(0.705624\pi\)
\(798\) −17.2338 −0.610069
\(799\) −41.8862 −1.48183
\(800\) 2.69019 0.0951127
\(801\) 14.8181 0.523572
\(802\) 2.59325 0.0915707
\(803\) 3.61448 0.127552
\(804\) 39.5731 1.39563
\(805\) 4.95303 0.174571
\(806\) −17.3423 −0.610857
\(807\) 15.3071 0.538837
\(808\) 59.8284 2.10476
\(809\) −20.1773 −0.709396 −0.354698 0.934981i \(-0.615416\pi\)
−0.354698 + 0.934981i \(0.615416\pi\)
\(810\) −24.4671 −0.859687
\(811\) 9.21731 0.323663 0.161832 0.986818i \(-0.448260\pi\)
0.161832 + 0.986818i \(0.448260\pi\)
\(812\) 105.630 3.70689
\(813\) 7.99828 0.280512
\(814\) 24.3365 0.852995
\(815\) −12.2023 −0.427427
\(816\) −30.2636 −1.05944
\(817\) −27.4671 −0.960951
\(818\) 33.7958 1.18164
\(819\) −30.8092 −1.07656
\(820\) 5.76136 0.201195
\(821\) 5.70135 0.198978 0.0994892 0.995039i \(-0.468279\pi\)
0.0994892 + 0.995039i \(0.468279\pi\)
\(822\) −23.2156 −0.809738
\(823\) 24.6078 0.857774 0.428887 0.903358i \(-0.358906\pi\)
0.428887 + 0.903358i \(0.358906\pi\)
\(824\) 18.1784 0.633275
\(825\) −0.355893 −0.0123906
\(826\) −33.4502 −1.16388
\(827\) 8.66963 0.301472 0.150736 0.988574i \(-0.451836\pi\)
0.150736 + 0.988574i \(0.451836\pi\)
\(828\) 9.18446 0.319182
\(829\) 25.7103 0.892956 0.446478 0.894795i \(-0.352678\pi\)
0.446478 + 0.894795i \(0.352678\pi\)
\(830\) 40.6375 1.41055
\(831\) 1.38931 0.0481948
\(832\) −2.60262 −0.0902295
\(833\) −5.32118 −0.184368
\(834\) 16.0285 0.555020
\(835\) −7.60469 −0.263171
\(836\) −16.2054 −0.560475
\(837\) 6.11871 0.211493
\(838\) −52.0501 −1.79804
\(839\) 7.72525 0.266705 0.133353 0.991069i \(-0.457426\pi\)
0.133353 + 0.991069i \(0.457426\pi\)
\(840\) 28.2857 0.975949
\(841\) 39.6306 1.36657
\(842\) −70.8844 −2.44284
\(843\) −14.8269 −0.510664
\(844\) 37.6817 1.29706
\(845\) 14.1107 0.485422
\(846\) 47.1334 1.62048
\(847\) 27.6483 0.950007
\(848\) −7.40501 −0.254289
\(849\) −16.0141 −0.549603
\(850\) −6.38074 −0.218858
\(851\) 7.17787 0.246054
\(852\) 29.0879 0.996536
\(853\) −44.5631 −1.52581 −0.762906 0.646509i \(-0.776228\pi\)
−0.762906 + 0.646509i \(0.776228\pi\)
\(854\) −15.9699 −0.546480
\(855\) 17.2652 0.590456
\(856\) −109.979 −3.75901
\(857\) 41.5158 1.41815 0.709077 0.705131i \(-0.249112\pi\)
0.709077 + 0.705131i \(0.249112\pi\)
\(858\) 9.02107 0.307974
\(859\) 19.1047 0.651845 0.325923 0.945396i \(-0.394325\pi\)
0.325923 + 0.945396i \(0.394325\pi\)
\(860\) 80.8310 2.75632
\(861\) −1.22865 −0.0418723
\(862\) 61.0036 2.07779
\(863\) 39.1858 1.33390 0.666950 0.745102i \(-0.267599\pi\)
0.666950 + 0.745102i \(0.267599\pi\)
\(864\) 24.0588 0.818497
\(865\) 25.7784 0.876492
\(866\) −6.65734 −0.226226
\(867\) 10.4776 0.355837
\(868\) 19.5514 0.663617
\(869\) −1.36039 −0.0461481
\(870\) 32.9516 1.11716
\(871\) −53.0995 −1.79921
\(872\) 124.449 4.21437
\(873\) 23.9530 0.810686
\(874\) −6.89357 −0.233179
\(875\) 32.7696 1.10782
\(876\) 10.9159 0.368813
\(877\) −39.9717 −1.34975 −0.674875 0.737932i \(-0.735802\pi\)
−0.674875 + 0.737932i \(0.735802\pi\)
\(878\) 14.8337 0.500612
\(879\) 7.66320 0.258473
\(880\) 17.2693 0.582149
\(881\) 29.7652 1.00281 0.501407 0.865211i \(-0.332816\pi\)
0.501407 + 0.865211i \(0.332816\pi\)
\(882\) 5.98779 0.201619
\(883\) −4.26862 −0.143650 −0.0718252 0.997417i \(-0.522882\pi\)
−0.0718252 + 0.997417i \(0.522882\pi\)
\(884\) 112.140 3.77168
\(885\) −7.23502 −0.243203
\(886\) 52.2244 1.75451
\(887\) −10.1905 −0.342162 −0.171081 0.985257i \(-0.554726\pi\)
−0.171081 + 0.985257i \(0.554726\pi\)
\(888\) 40.9913 1.37558
\(889\) −36.2141 −1.21458
\(890\) 32.7302 1.09712
\(891\) 4.90642 0.164371
\(892\) 108.739 3.64085
\(893\) −24.5286 −0.820817
\(894\) 8.86134 0.296368
\(895\) −32.5636 −1.08848
\(896\) −29.7686 −0.994498
\(897\) 2.66070 0.0888381
\(898\) −32.3237 −1.07865
\(899\) 12.7030 0.423670
\(900\) 4.97831 0.165944
\(901\) 5.59961 0.186550
\(902\) −1.66631 −0.0554820
\(903\) −17.2378 −0.573638
\(904\) −124.690 −4.14714
\(905\) 5.69738 0.189387
\(906\) −1.86393 −0.0619250
\(907\) −2.14239 −0.0711368 −0.0355684 0.999367i \(-0.511324\pi\)
−0.0355684 + 0.999367i \(0.511324\pi\)
\(908\) 49.2688 1.63504
\(909\) 22.9182 0.760148
\(910\) −68.0514 −2.25588
\(911\) −12.5564 −0.416012 −0.208006 0.978128i \(-0.566697\pi\)
−0.208006 + 0.978128i \(0.566697\pi\)
\(912\) −17.7224 −0.586847
\(913\) −8.14909 −0.269696
\(914\) 22.4076 0.741179
\(915\) −3.45417 −0.114191
\(916\) 134.065 4.42962
\(917\) −58.9092 −1.94535
\(918\) −57.0639 −1.88339
\(919\) 2.62984 0.0867504 0.0433752 0.999059i \(-0.486189\pi\)
0.0433752 + 0.999059i \(0.486189\pi\)
\(920\) 11.3144 0.373024
\(921\) −13.4196 −0.442191
\(922\) −2.73258 −0.0899928
\(923\) −39.0304 −1.28470
\(924\) −10.1702 −0.334574
\(925\) 3.89066 0.127924
\(926\) 79.6844 2.61859
\(927\) 6.96352 0.228712
\(928\) 49.9485 1.63964
\(929\) −41.7999 −1.37141 −0.685705 0.727880i \(-0.740506\pi\)
−0.685705 + 0.727880i \(0.740506\pi\)
\(930\) 6.09911 0.199998
\(931\) −3.11608 −0.102125
\(932\) −102.398 −3.35415
\(933\) −13.4125 −0.439105
\(934\) −17.6425 −0.577280
\(935\) −13.0589 −0.427073
\(936\) −70.3785 −2.30039
\(937\) 10.2185 0.333823 0.166911 0.985972i \(-0.446621\pi\)
0.166911 + 0.985972i \(0.446621\pi\)
\(938\) 86.3394 2.81908
\(939\) 4.86131 0.158643
\(940\) 72.1835 2.35437
\(941\) 24.0777 0.784912 0.392456 0.919771i \(-0.371626\pi\)
0.392456 + 0.919771i \(0.371626\pi\)
\(942\) −32.2647 −1.05124
\(943\) −0.491465 −0.0160043
\(944\) −34.3986 −1.11958
\(945\) 24.0099 0.781041
\(946\) −23.3780 −0.760086
\(947\) 16.1112 0.523543 0.261771 0.965130i \(-0.415693\pi\)
0.261771 + 0.965130i \(0.415693\pi\)
\(948\) −4.10844 −0.133436
\(949\) −14.6470 −0.475462
\(950\) −3.73656 −0.121230
\(951\) 2.79545 0.0906487
\(952\) −101.695 −3.29596
\(953\) 51.8519 1.67965 0.839824 0.542858i \(-0.182658\pi\)
0.839824 + 0.542858i \(0.182658\pi\)
\(954\) −6.30110 −0.204006
\(955\) 40.4117 1.30769
\(956\) −76.6772 −2.47992
\(957\) −6.60783 −0.213601
\(958\) 57.1458 1.84630
\(959\) −35.1189 −1.13405
\(960\) 0.915313 0.0295416
\(961\) −28.6488 −0.924154
\(962\) −98.6193 −3.17961
\(963\) −42.1292 −1.35760
\(964\) −95.5616 −3.07783
\(965\) 55.4518 1.78506
\(966\) −4.32627 −0.139195
\(967\) −59.9603 −1.92819 −0.964096 0.265553i \(-0.914446\pi\)
−0.964096 + 0.265553i \(0.914446\pi\)
\(968\) 63.1580 2.02997
\(969\) 13.4015 0.430519
\(970\) 52.9074 1.69876
\(971\) 41.8943 1.34445 0.672227 0.740345i \(-0.265338\pi\)
0.672227 + 0.740345i \(0.265338\pi\)
\(972\) 68.9516 2.21162
\(973\) 24.2467 0.777313
\(974\) −24.7420 −0.792783
\(975\) 1.44219 0.0461871
\(976\) −16.4227 −0.525678
\(977\) −42.7352 −1.36722 −0.683609 0.729848i \(-0.739591\pi\)
−0.683609 + 0.729848i \(0.739591\pi\)
\(978\) 10.6582 0.340812
\(979\) −6.56343 −0.209768
\(980\) 9.17012 0.292929
\(981\) 47.6721 1.52205
\(982\) 109.869 3.50607
\(983\) −24.5491 −0.782993 −0.391497 0.920179i \(-0.628043\pi\)
−0.391497 + 0.920179i \(0.628043\pi\)
\(984\) −2.80665 −0.0894727
\(985\) −15.2792 −0.486836
\(986\) −118.470 −3.77287
\(987\) −15.3936 −0.489985
\(988\) 65.6693 2.08922
\(989\) −6.89518 −0.219254
\(990\) 14.6949 0.467034
\(991\) −27.0581 −0.859529 −0.429765 0.902941i \(-0.641403\pi\)
−0.429765 + 0.902941i \(0.641403\pi\)
\(992\) 9.24510 0.293532
\(993\) 14.2291 0.451547
\(994\) 63.4632 2.01293
\(995\) 23.0517 0.730787
\(996\) −24.6106 −0.779817
\(997\) 0.763959 0.0241948 0.0120974 0.999927i \(-0.496149\pi\)
0.0120974 + 0.999927i \(0.496149\pi\)
\(998\) −34.3613 −1.08769
\(999\) 34.7948 1.10086
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 \(a_p\))