Properties

Label 8041.2.a.j.1.1
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 82
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(0\)
Dimension: \(82\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.77655 q^{2}\) \(-0.377305 q^{3}\) \(+5.70922 q^{4}\) \(-1.07900 q^{5}\) \(+1.04760 q^{6}\) \(-3.82470 q^{7}\) \(-10.2988 q^{8}\) \(-2.85764 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.77655 q^{2}\) \(-0.377305 q^{3}\) \(+5.70922 q^{4}\) \(-1.07900 q^{5}\) \(+1.04760 q^{6}\) \(-3.82470 q^{7}\) \(-10.2988 q^{8}\) \(-2.85764 q^{9}\) \(+2.99589 q^{10}\) \(+1.00000 q^{11}\) \(-2.15412 q^{12}\) \(+6.34070 q^{13}\) \(+10.6195 q^{14}\) \(+0.407111 q^{15}\) \(+17.1768 q^{16}\) \(+1.00000 q^{17}\) \(+7.93438 q^{18}\) \(+2.71507 q^{19}\) \(-6.16025 q^{20}\) \(+1.44308 q^{21}\) \(-2.77655 q^{22}\) \(+3.31642 q^{23}\) \(+3.88580 q^{24}\) \(-3.83576 q^{25}\) \(-17.6053 q^{26}\) \(+2.21011 q^{27}\) \(-21.8360 q^{28}\) \(+8.14728 q^{29}\) \(-1.13036 q^{30}\) \(-0.300360 q^{31}\) \(-27.0945 q^{32}\) \(-0.377305 q^{33}\) \(-2.77655 q^{34}\) \(+4.12685 q^{35}\) \(-16.3149 q^{36}\) \(-5.07135 q^{37}\) \(-7.53852 q^{38}\) \(-2.39238 q^{39}\) \(+11.1124 q^{40}\) \(+1.83975 q^{41}\) \(-4.00677 q^{42}\) \(+1.00000 q^{43}\) \(+5.70922 q^{44}\) \(+3.08339 q^{45}\) \(-9.20821 q^{46}\) \(+8.66756 q^{47}\) \(-6.48087 q^{48}\) \(+7.62830 q^{49}\) \(+10.6502 q^{50}\) \(-0.377305 q^{51}\) \(+36.2005 q^{52}\) \(+6.74749 q^{53}\) \(-6.13649 q^{54}\) \(-1.07900 q^{55}\) \(+39.3899 q^{56}\) \(-1.02441 q^{57}\) \(-22.6213 q^{58}\) \(+11.7431 q^{59}\) \(+2.32429 q^{60}\) \(-9.86038 q^{61}\) \(+0.833964 q^{62}\) \(+10.9296 q^{63}\) \(+40.8755 q^{64}\) \(-6.84162 q^{65}\) \(+1.04760 q^{66}\) \(-2.48384 q^{67}\) \(+5.70922 q^{68}\) \(-1.25130 q^{69}\) \(-11.4584 q^{70}\) \(+11.9966 q^{71}\) \(+29.4304 q^{72}\) \(-0.972938 q^{73}\) \(+14.0809 q^{74}\) \(+1.44725 q^{75}\) \(+15.5009 q^{76}\) \(-3.82470 q^{77}\) \(+6.64255 q^{78}\) \(-8.47241 q^{79}\) \(-18.5337 q^{80}\) \(+7.73904 q^{81}\) \(-5.10816 q^{82}\) \(-8.08161 q^{83}\) \(+8.23884 q^{84}\) \(-1.07900 q^{85}\) \(-2.77655 q^{86}\) \(-3.07401 q^{87}\) \(-10.2988 q^{88}\) \(+1.74033 q^{89}\) \(-8.56119 q^{90}\) \(-24.2513 q^{91}\) \(+18.9342 q^{92}\) \(+0.113327 q^{93}\) \(-24.0659 q^{94}\) \(-2.92956 q^{95}\) \(+10.2229 q^{96}\) \(-5.49821 q^{97}\) \(-21.1803 q^{98}\) \(-2.85764 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 82q^{11} \) \(\mathstrut +\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 26q^{13} \) \(\mathstrut +\mathstrut 17q^{14} \) \(\mathstrut +\mathstrut 66q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut +\mathstrut 82q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 9q^{20} \) \(\mathstrut +\mathstrut 22q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 117q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 30q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 26q^{30} \) \(\mathstrut +\mathstrut 40q^{31} \) \(\mathstrut +\mathstrut 58q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 160q^{36} \) \(\mathstrut +\mathstrut 31q^{37} \) \(\mathstrut +\mathstrut 18q^{38} \) \(\mathstrut +\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 29q^{40} \) \(\mathstrut +\mathstrut 42q^{41} \) \(\mathstrut -\mathstrut 51q^{42} \) \(\mathstrut +\mathstrut 82q^{43} \) \(\mathstrut +\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 84q^{47} \) \(\mathstrut -\mathstrut 46q^{48} \) \(\mathstrut +\mathstrut 136q^{49} \) \(\mathstrut +\mathstrut 59q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut +\mathstrut 83q^{53} \) \(\mathstrut +\mathstrut 24q^{54} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 23q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 96q^{59} \) \(\mathstrut +\mathstrut 184q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 148q^{64} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut +\mathstrut 10q^{66} \) \(\mathstrut +\mathstrut 78q^{67} \) \(\mathstrut +\mathstrut 98q^{68} \) \(\mathstrut +\mathstrut 61q^{69} \) \(\mathstrut -\mathstrut 3q^{70} \) \(\mathstrut +\mathstrut 155q^{71} \) \(\mathstrut +\mathstrut 50q^{72} \) \(\mathstrut -\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 10q^{74} \) \(\mathstrut -\mathstrut 19q^{75} \) \(\mathstrut +\mathstrut 44q^{76} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 27q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 19q^{80} \) \(\mathstrut +\mathstrut 150q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 54q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 11q^{85} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 81q^{90} \) \(\mathstrut -\mathstrut 14q^{91} \) \(\mathstrut +\mathstrut 60q^{92} \) \(\mathstrut +\mathstrut 36q^{93} \) \(\mathstrut +\mathstrut 19q^{94} \) \(\mathstrut +\mathstrut 111q^{95} \) \(\mathstrut -\mathstrut 6q^{96} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 5q^{98} \) \(\mathstrut +\mathstrut 108q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.77655 −1.96332 −0.981658 0.190650i \(-0.938941\pi\)
−0.981658 + 0.190650i \(0.938941\pi\)
\(3\) −0.377305 −0.217837 −0.108918 0.994051i \(-0.534739\pi\)
−0.108918 + 0.994051i \(0.534739\pi\)
\(4\) 5.70922 2.85461
\(5\) −1.07900 −0.482543 −0.241272 0.970458i \(-0.577564\pi\)
−0.241272 + 0.970458i \(0.577564\pi\)
\(6\) 1.04760 0.427683
\(7\) −3.82470 −1.44560 −0.722800 0.691058i \(-0.757145\pi\)
−0.722800 + 0.691058i \(0.757145\pi\)
\(8\) −10.2988 −3.64119
\(9\) −2.85764 −0.952547
\(10\) 2.99589 0.947385
\(11\) 1.00000 0.301511
\(12\) −2.15412 −0.621839
\(13\) 6.34070 1.75859 0.879297 0.476273i \(-0.158013\pi\)
0.879297 + 0.476273i \(0.158013\pi\)
\(14\) 10.6195 2.83817
\(15\) 0.407111 0.105116
\(16\) 17.1768 4.29419
\(17\) 1.00000 0.242536
\(18\) 7.93438 1.87015
\(19\) 2.71507 0.622880 0.311440 0.950266i \(-0.399189\pi\)
0.311440 + 0.950266i \(0.399189\pi\)
\(20\) −6.16025 −1.37747
\(21\) 1.44308 0.314905
\(22\) −2.77655 −0.591962
\(23\) 3.31642 0.691522 0.345761 0.938323i \(-0.387621\pi\)
0.345761 + 0.938323i \(0.387621\pi\)
\(24\) 3.88580 0.793185
\(25\) −3.83576 −0.767152
\(26\) −17.6053 −3.45268
\(27\) 2.21011 0.425337
\(28\) −21.8360 −4.12662
\(29\) 8.14728 1.51291 0.756456 0.654045i \(-0.226929\pi\)
0.756456 + 0.654045i \(0.226929\pi\)
\(30\) −1.13036 −0.206375
\(31\) −0.300360 −0.0539462 −0.0269731 0.999636i \(-0.508587\pi\)
−0.0269731 + 0.999636i \(0.508587\pi\)
\(32\) −27.0945 −4.78967
\(33\) −0.377305 −0.0656803
\(34\) −2.77655 −0.476174
\(35\) 4.12685 0.697564
\(36\) −16.3149 −2.71915
\(37\) −5.07135 −0.833726 −0.416863 0.908969i \(-0.636870\pi\)
−0.416863 + 0.908969i \(0.636870\pi\)
\(38\) −7.53852 −1.22291
\(39\) −2.39238 −0.383087
\(40\) 11.1124 1.75703
\(41\) 1.83975 0.287321 0.143661 0.989627i \(-0.454113\pi\)
0.143661 + 0.989627i \(0.454113\pi\)
\(42\) −4.00677 −0.618258
\(43\) 1.00000 0.152499
\(44\) 5.70922 0.860697
\(45\) 3.08339 0.459645
\(46\) −9.20821 −1.35768
\(47\) 8.66756 1.26429 0.632147 0.774848i \(-0.282174\pi\)
0.632147 + 0.774848i \(0.282174\pi\)
\(48\) −6.48087 −0.935433
\(49\) 7.62830 1.08976
\(50\) 10.6502 1.50616
\(51\) −0.377305 −0.0528332
\(52\) 36.2005 5.02010
\(53\) 6.74749 0.926840 0.463420 0.886139i \(-0.346622\pi\)
0.463420 + 0.886139i \(0.346622\pi\)
\(54\) −6.13649 −0.835071
\(55\) −1.07900 −0.145492
\(56\) 39.3899 5.26370
\(57\) −1.02441 −0.135686
\(58\) −22.6213 −2.97032
\(59\) 11.7431 1.52882 0.764411 0.644730i \(-0.223030\pi\)
0.764411 + 0.644730i \(0.223030\pi\)
\(60\) 2.32429 0.300064
\(61\) −9.86038 −1.26249 −0.631246 0.775582i \(-0.717456\pi\)
−0.631246 + 0.775582i \(0.717456\pi\)
\(62\) 0.833964 0.105913
\(63\) 10.9296 1.37700
\(64\) 40.8755 5.10944
\(65\) −6.84162 −0.848598
\(66\) 1.04760 0.128951
\(67\) −2.48384 −0.303449 −0.151725 0.988423i \(-0.548483\pi\)
−0.151725 + 0.988423i \(0.548483\pi\)
\(68\) 5.70922 0.692345
\(69\) −1.25130 −0.150639
\(70\) −11.4584 −1.36954
\(71\) 11.9966 1.42374 0.711870 0.702312i \(-0.247849\pi\)
0.711870 + 0.702312i \(0.247849\pi\)
\(72\) 29.4304 3.46840
\(73\) −0.972938 −0.113874 −0.0569369 0.998378i \(-0.518133\pi\)
−0.0569369 + 0.998378i \(0.518133\pi\)
\(74\) 14.0809 1.63687
\(75\) 1.44725 0.167114
\(76\) 15.5009 1.77808
\(77\) −3.82470 −0.435865
\(78\) 6.64255 0.752120
\(79\) −8.47241 −0.953220 −0.476610 0.879115i \(-0.658135\pi\)
−0.476610 + 0.879115i \(0.658135\pi\)
\(80\) −18.5337 −2.07213
\(81\) 7.73904 0.859893
\(82\) −5.10816 −0.564102
\(83\) −8.08161 −0.887072 −0.443536 0.896257i \(-0.646276\pi\)
−0.443536 + 0.896257i \(0.646276\pi\)
\(84\) 8.23884 0.898931
\(85\) −1.07900 −0.117034
\(86\) −2.77655 −0.299403
\(87\) −3.07401 −0.329568
\(88\) −10.2988 −1.09786
\(89\) 1.74033 0.184475 0.0922374 0.995737i \(-0.470598\pi\)
0.0922374 + 0.995737i \(0.470598\pi\)
\(90\) −8.56119 −0.902429
\(91\) −24.2513 −2.54222
\(92\) 18.9342 1.97403
\(93\) 0.113327 0.0117515
\(94\) −24.0659 −2.48221
\(95\) −2.92956 −0.300566
\(96\) 10.2229 1.04337
\(97\) −5.49821 −0.558259 −0.279129 0.960253i \(-0.590046\pi\)
−0.279129 + 0.960253i \(0.590046\pi\)
\(98\) −21.1803 −2.13954
\(99\) −2.85764 −0.287204
\(100\) −21.8992 −2.18992
\(101\) −15.7110 −1.56330 −0.781652 0.623715i \(-0.785623\pi\)
−0.781652 + 0.623715i \(0.785623\pi\)
\(102\) 1.04760 0.103728
\(103\) −12.2569 −1.20771 −0.603855 0.797094i \(-0.706369\pi\)
−0.603855 + 0.797094i \(0.706369\pi\)
\(104\) −65.3018 −6.40337
\(105\) −1.55708 −0.151955
\(106\) −18.7347 −1.81968
\(107\) −8.84137 −0.854727 −0.427364 0.904080i \(-0.640558\pi\)
−0.427364 + 0.904080i \(0.640558\pi\)
\(108\) 12.6180 1.21417
\(109\) 7.82520 0.749519 0.374759 0.927122i \(-0.377725\pi\)
0.374759 + 0.927122i \(0.377725\pi\)
\(110\) 2.99589 0.285647
\(111\) 1.91345 0.181616
\(112\) −65.6959 −6.20768
\(113\) 0.302064 0.0284158 0.0142079 0.999899i \(-0.495477\pi\)
0.0142079 + 0.999899i \(0.495477\pi\)
\(114\) 2.84432 0.266395
\(115\) −3.57842 −0.333689
\(116\) 46.5146 4.31877
\(117\) −18.1195 −1.67514
\(118\) −32.6053 −3.00156
\(119\) −3.82470 −0.350609
\(120\) −4.19277 −0.382746
\(121\) 1.00000 0.0909091
\(122\) 27.3778 2.47867
\(123\) −0.694147 −0.0625891
\(124\) −1.71482 −0.153995
\(125\) 9.53378 0.852727
\(126\) −30.3466 −2.70349
\(127\) −6.34337 −0.562883 −0.281442 0.959578i \(-0.590813\pi\)
−0.281442 + 0.959578i \(0.590813\pi\)
\(128\) −59.3040 −5.24178
\(129\) −0.377305 −0.0332198
\(130\) 18.9961 1.66607
\(131\) −3.12080 −0.272665 −0.136333 0.990663i \(-0.543532\pi\)
−0.136333 + 0.990663i \(0.543532\pi\)
\(132\) −2.15412 −0.187492
\(133\) −10.3843 −0.900434
\(134\) 6.89650 0.595767
\(135\) −2.38471 −0.205243
\(136\) −10.2988 −0.883118
\(137\) 14.3215 1.22357 0.611786 0.791023i \(-0.290451\pi\)
0.611786 + 0.791023i \(0.290451\pi\)
\(138\) 3.47430 0.295752
\(139\) 15.5651 1.32022 0.660108 0.751171i \(-0.270511\pi\)
0.660108 + 0.751171i \(0.270511\pi\)
\(140\) 23.5611 1.99127
\(141\) −3.27031 −0.275410
\(142\) −33.3093 −2.79525
\(143\) 6.34070 0.530236
\(144\) −49.0850 −4.09042
\(145\) −8.79091 −0.730045
\(146\) 2.70141 0.223570
\(147\) −2.87819 −0.237389
\(148\) −28.9535 −2.37996
\(149\) 19.0463 1.56033 0.780167 0.625571i \(-0.215134\pi\)
0.780167 + 0.625571i \(0.215134\pi\)
\(150\) −4.01836 −0.328098
\(151\) −4.78383 −0.389302 −0.194651 0.980873i \(-0.562357\pi\)
−0.194651 + 0.980873i \(0.562357\pi\)
\(152\) −27.9620 −2.26802
\(153\) −2.85764 −0.231027
\(154\) 10.6195 0.855740
\(155\) 0.324088 0.0260314
\(156\) −13.6586 −1.09356
\(157\) −1.98360 −0.158308 −0.0791542 0.996862i \(-0.525222\pi\)
−0.0791542 + 0.996862i \(0.525222\pi\)
\(158\) 23.5240 1.87147
\(159\) −2.54586 −0.201900
\(160\) 29.2349 2.31122
\(161\) −12.6843 −0.999664
\(162\) −21.4878 −1.68824
\(163\) −0.246816 −0.0193321 −0.00966607 0.999953i \(-0.503077\pi\)
−0.00966607 + 0.999953i \(0.503077\pi\)
\(164\) 10.5036 0.820190
\(165\) 0.407111 0.0316936
\(166\) 22.4390 1.74160
\(167\) 19.6127 1.51768 0.758839 0.651278i \(-0.225767\pi\)
0.758839 + 0.651278i \(0.225767\pi\)
\(168\) −14.8620 −1.14663
\(169\) 27.2045 2.09266
\(170\) 2.99589 0.229775
\(171\) −7.75869 −0.593322
\(172\) 5.70922 0.435324
\(173\) −2.29051 −0.174144 −0.0870720 0.996202i \(-0.527751\pi\)
−0.0870720 + 0.996202i \(0.527751\pi\)
\(174\) 8.53512 0.647046
\(175\) 14.6706 1.10899
\(176\) 17.1768 1.29475
\(177\) −4.43072 −0.333034
\(178\) −4.83211 −0.362182
\(179\) −15.3327 −1.14602 −0.573008 0.819549i \(-0.694224\pi\)
−0.573008 + 0.819549i \(0.694224\pi\)
\(180\) 17.6038 1.31211
\(181\) 4.90643 0.364692 0.182346 0.983234i \(-0.441631\pi\)
0.182346 + 0.983234i \(0.441631\pi\)
\(182\) 67.3348 4.99119
\(183\) 3.72037 0.275017
\(184\) −34.1553 −2.51796
\(185\) 5.47199 0.402309
\(186\) −0.314658 −0.0230719
\(187\) 1.00000 0.0731272
\(188\) 49.4850 3.60907
\(189\) −8.45302 −0.614867
\(190\) 8.13406 0.590107
\(191\) −16.4020 −1.18681 −0.593404 0.804904i \(-0.702216\pi\)
−0.593404 + 0.804904i \(0.702216\pi\)
\(192\) −15.4225 −1.11302
\(193\) −10.4332 −0.751000 −0.375500 0.926822i \(-0.622529\pi\)
−0.375500 + 0.926822i \(0.622529\pi\)
\(194\) 15.2661 1.09604
\(195\) 2.58137 0.184856
\(196\) 43.5517 3.11083
\(197\) −10.0979 −0.719446 −0.359723 0.933059i \(-0.617129\pi\)
−0.359723 + 0.933059i \(0.617129\pi\)
\(198\) 7.93438 0.563872
\(199\) −19.0556 −1.35082 −0.675409 0.737444i \(-0.736033\pi\)
−0.675409 + 0.737444i \(0.736033\pi\)
\(200\) 39.5038 2.79334
\(201\) 0.937163 0.0661024
\(202\) 43.6224 3.06926
\(203\) −31.1609 −2.18706
\(204\) −2.15412 −0.150818
\(205\) −1.98509 −0.138645
\(206\) 34.0319 2.37112
\(207\) −9.47715 −0.658707
\(208\) 108.913 7.55174
\(209\) 2.71507 0.187805
\(210\) 4.32330 0.298336
\(211\) 9.27076 0.638225 0.319113 0.947717i \(-0.396615\pi\)
0.319113 + 0.947717i \(0.396615\pi\)
\(212\) 38.5229 2.64577
\(213\) −4.52639 −0.310143
\(214\) 24.5485 1.67810
\(215\) −1.07900 −0.0735872
\(216\) −22.7616 −1.54873
\(217\) 1.14878 0.0779846
\(218\) −21.7271 −1.47154
\(219\) 0.367094 0.0248059
\(220\) −6.16025 −0.415324
\(221\) 6.34070 0.426522
\(222\) −5.31277 −0.356570
\(223\) −14.0343 −0.939809 −0.469904 0.882717i \(-0.655712\pi\)
−0.469904 + 0.882717i \(0.655712\pi\)
\(224\) 103.628 6.92394
\(225\) 10.9612 0.730748
\(226\) −0.838696 −0.0557892
\(227\) −18.6858 −1.24022 −0.620110 0.784515i \(-0.712912\pi\)
−0.620110 + 0.784515i \(0.712912\pi\)
\(228\) −5.84857 −0.387331
\(229\) −6.49404 −0.429139 −0.214569 0.976709i \(-0.568835\pi\)
−0.214569 + 0.976709i \(0.568835\pi\)
\(230\) 9.93565 0.655138
\(231\) 1.44308 0.0949474
\(232\) −83.9075 −5.50879
\(233\) −24.7451 −1.62111 −0.810553 0.585665i \(-0.800833\pi\)
−0.810553 + 0.585665i \(0.800833\pi\)
\(234\) 50.3095 3.28884
\(235\) −9.35230 −0.610077
\(236\) 67.0439 4.36419
\(237\) 3.19668 0.207647
\(238\) 10.6195 0.688357
\(239\) −6.01216 −0.388894 −0.194447 0.980913i \(-0.562291\pi\)
−0.194447 + 0.980913i \(0.562291\pi\)
\(240\) 6.99286 0.451387
\(241\) −13.1084 −0.844388 −0.422194 0.906506i \(-0.638740\pi\)
−0.422194 + 0.906506i \(0.638740\pi\)
\(242\) −2.77655 −0.178483
\(243\) −9.55032 −0.612653
\(244\) −56.2951 −3.60393
\(245\) −8.23093 −0.525855
\(246\) 1.92733 0.122882
\(247\) 17.2155 1.09539
\(248\) 3.09336 0.196428
\(249\) 3.04923 0.193237
\(250\) −26.4710 −1.67417
\(251\) 26.0697 1.64550 0.822751 0.568402i \(-0.192438\pi\)
0.822751 + 0.568402i \(0.192438\pi\)
\(252\) 62.3996 3.93080
\(253\) 3.31642 0.208502
\(254\) 17.6127 1.10512
\(255\) 0.407111 0.0254943
\(256\) 82.9093 5.18183
\(257\) 14.4621 0.902121 0.451061 0.892493i \(-0.351046\pi\)
0.451061 + 0.892493i \(0.351046\pi\)
\(258\) 1.04760 0.0652210
\(259\) 19.3964 1.20523
\(260\) −39.0603 −2.42242
\(261\) −23.2820 −1.44112
\(262\) 8.66504 0.535328
\(263\) −11.1975 −0.690467 −0.345233 0.938517i \(-0.612200\pi\)
−0.345233 + 0.938517i \(0.612200\pi\)
\(264\) 3.88580 0.239154
\(265\) −7.28054 −0.447240
\(266\) 28.8326 1.76784
\(267\) −0.656635 −0.0401854
\(268\) −14.1808 −0.866229
\(269\) 18.3467 1.11862 0.559308 0.828960i \(-0.311067\pi\)
0.559308 + 0.828960i \(0.311067\pi\)
\(270\) 6.62127 0.402958
\(271\) 22.1695 1.34670 0.673349 0.739324i \(-0.264855\pi\)
0.673349 + 0.739324i \(0.264855\pi\)
\(272\) 17.1768 1.04149
\(273\) 9.15011 0.553790
\(274\) −39.7644 −2.40226
\(275\) −3.83576 −0.231305
\(276\) −7.14396 −0.430016
\(277\) −11.2740 −0.677392 −0.338696 0.940896i \(-0.609986\pi\)
−0.338696 + 0.940896i \(0.609986\pi\)
\(278\) −43.2173 −2.59200
\(279\) 0.858321 0.0513863
\(280\) −42.5017 −2.53996
\(281\) 7.26596 0.433451 0.216725 0.976233i \(-0.430462\pi\)
0.216725 + 0.976233i \(0.430462\pi\)
\(282\) 9.08018 0.540717
\(283\) −13.2482 −0.787527 −0.393763 0.919212i \(-0.628827\pi\)
−0.393763 + 0.919212i \(0.628827\pi\)
\(284\) 68.4915 4.06422
\(285\) 1.10534 0.0654744
\(286\) −17.6053 −1.04102
\(287\) −7.03650 −0.415351
\(288\) 77.4262 4.56238
\(289\) 1.00000 0.0588235
\(290\) 24.4084 1.43331
\(291\) 2.07450 0.121609
\(292\) −5.55472 −0.325065
\(293\) −22.5600 −1.31797 −0.658984 0.752157i \(-0.729013\pi\)
−0.658984 + 0.752157i \(0.729013\pi\)
\(294\) 7.99144 0.466070
\(295\) −12.6708 −0.737722
\(296\) 52.2290 3.03575
\(297\) 2.21011 0.128244
\(298\) −52.8830 −3.06343
\(299\) 21.0285 1.21611
\(300\) 8.26267 0.477045
\(301\) −3.82470 −0.220452
\(302\) 13.2825 0.764324
\(303\) 5.92783 0.340545
\(304\) 46.6361 2.67476
\(305\) 10.6393 0.609207
\(306\) 7.93438 0.453578
\(307\) 29.4190 1.67903 0.839515 0.543337i \(-0.182839\pi\)
0.839515 + 0.543337i \(0.182839\pi\)
\(308\) −21.8360 −1.24422
\(309\) 4.62459 0.263084
\(310\) −0.899846 −0.0511078
\(311\) 16.0107 0.907881 0.453940 0.891032i \(-0.350018\pi\)
0.453940 + 0.891032i \(0.350018\pi\)
\(312\) 24.6387 1.39489
\(313\) 24.5730 1.38895 0.694473 0.719519i \(-0.255637\pi\)
0.694473 + 0.719519i \(0.255637\pi\)
\(314\) 5.50756 0.310810
\(315\) −11.7930 −0.664463
\(316\) −48.3708 −2.72107
\(317\) 22.8723 1.28464 0.642319 0.766437i \(-0.277972\pi\)
0.642319 + 0.766437i \(0.277972\pi\)
\(318\) 7.06870 0.396393
\(319\) 8.14728 0.456160
\(320\) −44.1047 −2.46553
\(321\) 3.33589 0.186191
\(322\) 35.2186 1.96266
\(323\) 2.71507 0.151071
\(324\) 44.1839 2.45466
\(325\) −24.3214 −1.34911
\(326\) 0.685297 0.0379551
\(327\) −2.95248 −0.163273
\(328\) −18.9473 −1.04619
\(329\) −33.1508 −1.82766
\(330\) −1.13036 −0.0622245
\(331\) 25.0669 1.37780 0.688901 0.724856i \(-0.258094\pi\)
0.688901 + 0.724856i \(0.258094\pi\)
\(332\) −46.1397 −2.53225
\(333\) 14.4921 0.794163
\(334\) −54.4557 −2.97968
\(335\) 2.68006 0.146427
\(336\) 24.7874 1.35226
\(337\) 0.0132308 0.000720728 0 0.000360364 1.00000i \(-0.499885\pi\)
0.000360364 1.00000i \(0.499885\pi\)
\(338\) −75.5347 −4.10854
\(339\) −0.113970 −0.00619001
\(340\) −6.16025 −0.334086
\(341\) −0.300360 −0.0162654
\(342\) 21.5424 1.16488
\(343\) −2.40306 −0.129753
\(344\) −10.2988 −0.555276
\(345\) 1.35015 0.0726898
\(346\) 6.35970 0.341900
\(347\) 5.44151 0.292116 0.146058 0.989276i \(-0.453341\pi\)
0.146058 + 0.989276i \(0.453341\pi\)
\(348\) −17.5502 −0.940788
\(349\) 22.4302 1.20066 0.600329 0.799753i \(-0.295036\pi\)
0.600329 + 0.799753i \(0.295036\pi\)
\(350\) −40.7337 −2.17731
\(351\) 14.0137 0.747995
\(352\) −27.0945 −1.44414
\(353\) −3.94113 −0.209765 −0.104883 0.994485i \(-0.533447\pi\)
−0.104883 + 0.994485i \(0.533447\pi\)
\(354\) 12.3021 0.653850
\(355\) −12.9444 −0.687016
\(356\) 9.93594 0.526604
\(357\) 1.44308 0.0763756
\(358\) 42.5719 2.24999
\(359\) 3.72413 0.196552 0.0982761 0.995159i \(-0.468667\pi\)
0.0982761 + 0.995159i \(0.468667\pi\)
\(360\) −31.7554 −1.67365
\(361\) −11.6284 −0.612021
\(362\) −13.6229 −0.716006
\(363\) −0.377305 −0.0198034
\(364\) −138.456 −7.25706
\(365\) 1.04980 0.0549490
\(366\) −10.3298 −0.539946
\(367\) 11.2058 0.584938 0.292469 0.956275i \(-0.405523\pi\)
0.292469 + 0.956275i \(0.405523\pi\)
\(368\) 56.9654 2.96953
\(369\) −5.25735 −0.273687
\(370\) −15.1932 −0.789859
\(371\) −25.8071 −1.33984
\(372\) 0.647010 0.0335459
\(373\) −11.5166 −0.596309 −0.298154 0.954518i \(-0.596371\pi\)
−0.298154 + 0.954518i \(0.596371\pi\)
\(374\) −2.77655 −0.143572
\(375\) −3.59714 −0.185755
\(376\) −89.2658 −4.60353
\(377\) 51.6595 2.66060
\(378\) 23.4702 1.20718
\(379\) 24.0052 1.23307 0.616533 0.787329i \(-0.288537\pi\)
0.616533 + 0.787329i \(0.288537\pi\)
\(380\) −16.7255 −0.858000
\(381\) 2.39338 0.122617
\(382\) 45.5410 2.33008
\(383\) −2.74070 −0.140043 −0.0700215 0.997545i \(-0.522307\pi\)
−0.0700215 + 0.997545i \(0.522307\pi\)
\(384\) 22.3757 1.14185
\(385\) 4.12685 0.210324
\(386\) 28.9684 1.47445
\(387\) −2.85764 −0.145262
\(388\) −31.3905 −1.59361
\(389\) −22.2080 −1.12599 −0.562996 0.826460i \(-0.690351\pi\)
−0.562996 + 0.826460i \(0.690351\pi\)
\(390\) −7.16731 −0.362931
\(391\) 3.31642 0.167719
\(392\) −78.5626 −3.96801
\(393\) 1.17749 0.0593966
\(394\) 28.0373 1.41250
\(395\) 9.14172 0.459970
\(396\) −16.3149 −0.819855
\(397\) −15.3192 −0.768850 −0.384425 0.923156i \(-0.625600\pi\)
−0.384425 + 0.923156i \(0.625600\pi\)
\(398\) 52.9089 2.65208
\(399\) 3.91805 0.196148
\(400\) −65.8859 −3.29430
\(401\) 12.8519 0.641792 0.320896 0.947114i \(-0.396016\pi\)
0.320896 + 0.947114i \(0.396016\pi\)
\(402\) −2.60208 −0.129780
\(403\) −1.90449 −0.0948695
\(404\) −89.6976 −4.46262
\(405\) −8.35042 −0.414936
\(406\) 86.5197 4.29390
\(407\) −5.07135 −0.251378
\(408\) 3.88580 0.192376
\(409\) −20.5660 −1.01693 −0.508463 0.861084i \(-0.669786\pi\)
−0.508463 + 0.861084i \(0.669786\pi\)
\(410\) 5.51170 0.272204
\(411\) −5.40358 −0.266539
\(412\) −69.9774 −3.44754
\(413\) −44.9138 −2.21006
\(414\) 26.3138 1.29325
\(415\) 8.72006 0.428051
\(416\) −171.798 −8.42308
\(417\) −5.87279 −0.287592
\(418\) −7.53852 −0.368721
\(419\) 2.77441 0.135539 0.0677693 0.997701i \(-0.478412\pi\)
0.0677693 + 0.997701i \(0.478412\pi\)
\(420\) −8.88970 −0.433773
\(421\) 28.6953 1.39852 0.699262 0.714865i \(-0.253512\pi\)
0.699262 + 0.714865i \(0.253512\pi\)
\(422\) −25.7407 −1.25304
\(423\) −24.7688 −1.20430
\(424\) −69.4913 −3.37480
\(425\) −3.83576 −0.186062
\(426\) 12.5677 0.608909
\(427\) 37.7130 1.82506
\(428\) −50.4773 −2.43991
\(429\) −2.39238 −0.115505
\(430\) 2.99589 0.144475
\(431\) −37.2012 −1.79192 −0.895960 0.444134i \(-0.853511\pi\)
−0.895960 + 0.444134i \(0.853511\pi\)
\(432\) 37.9626 1.82648
\(433\) 0.674910 0.0324341 0.0162171 0.999868i \(-0.494838\pi\)
0.0162171 + 0.999868i \(0.494838\pi\)
\(434\) −3.18966 −0.153108
\(435\) 3.31685 0.159031
\(436\) 44.6758 2.13958
\(437\) 9.00432 0.430735
\(438\) −1.01925 −0.0487019
\(439\) −30.1215 −1.43762 −0.718810 0.695207i \(-0.755313\pi\)
−0.718810 + 0.695207i \(0.755313\pi\)
\(440\) 11.1124 0.529765
\(441\) −21.7990 −1.03805
\(442\) −17.6053 −0.837397
\(443\) 4.46539 0.212157 0.106079 0.994358i \(-0.466170\pi\)
0.106079 + 0.994358i \(0.466170\pi\)
\(444\) 10.9243 0.518443
\(445\) −1.87782 −0.0890170
\(446\) 38.9670 1.84514
\(447\) −7.18626 −0.339898
\(448\) −156.337 −7.38621
\(449\) −31.0984 −1.46762 −0.733812 0.679352i \(-0.762261\pi\)
−0.733812 + 0.679352i \(0.762261\pi\)
\(450\) −30.4344 −1.43469
\(451\) 1.83975 0.0866306
\(452\) 1.72455 0.0811161
\(453\) 1.80496 0.0848044
\(454\) 51.8821 2.43495
\(455\) 26.1671 1.22673
\(456\) 10.5502 0.494059
\(457\) 22.7678 1.06503 0.532517 0.846419i \(-0.321246\pi\)
0.532517 + 0.846419i \(0.321246\pi\)
\(458\) 18.0310 0.842535
\(459\) 2.21011 0.103159
\(460\) −20.4300 −0.952553
\(461\) 33.5055 1.56051 0.780253 0.625464i \(-0.215090\pi\)
0.780253 + 0.625464i \(0.215090\pi\)
\(462\) −4.00677 −0.186412
\(463\) 17.7999 0.827229 0.413615 0.910452i \(-0.364266\pi\)
0.413615 + 0.910452i \(0.364266\pi\)
\(464\) 139.944 6.49673
\(465\) −0.122280 −0.00567059
\(466\) 68.7060 3.18274
\(467\) 1.32975 0.0615337 0.0307669 0.999527i \(-0.490205\pi\)
0.0307669 + 0.999527i \(0.490205\pi\)
\(468\) −103.448 −4.78188
\(469\) 9.49993 0.438666
\(470\) 25.9671 1.19777
\(471\) 0.748421 0.0344854
\(472\) −120.940 −5.56672
\(473\) 1.00000 0.0459800
\(474\) −8.87573 −0.407676
\(475\) −10.4144 −0.477843
\(476\) −21.8360 −1.00085
\(477\) −19.2819 −0.882858
\(478\) 16.6931 0.763523
\(479\) 5.93727 0.271281 0.135640 0.990758i \(-0.456691\pi\)
0.135640 + 0.990758i \(0.456691\pi\)
\(480\) −11.0305 −0.503469
\(481\) −32.1560 −1.46619
\(482\) 36.3962 1.65780
\(483\) 4.78585 0.217764
\(484\) 5.70922 0.259510
\(485\) 5.93257 0.269384
\(486\) 26.5169 1.20283
\(487\) 15.4558 0.700371 0.350186 0.936680i \(-0.386119\pi\)
0.350186 + 0.936680i \(0.386119\pi\)
\(488\) 101.550 4.59697
\(489\) 0.0931248 0.00421125
\(490\) 22.8536 1.03242
\(491\) 35.9178 1.62095 0.810473 0.585776i \(-0.199210\pi\)
0.810473 + 0.585776i \(0.199210\pi\)
\(492\) −3.96304 −0.178668
\(493\) 8.14728 0.366935
\(494\) −47.7995 −2.15060
\(495\) 3.08339 0.138588
\(496\) −5.15921 −0.231655
\(497\) −45.8835 −2.05816
\(498\) −8.46633 −0.379385
\(499\) 36.5852 1.63778 0.818889 0.573952i \(-0.194590\pi\)
0.818889 + 0.573952i \(0.194590\pi\)
\(500\) 54.4305 2.43420
\(501\) −7.39997 −0.330606
\(502\) −72.3837 −3.23064
\(503\) −16.4617 −0.733992 −0.366996 0.930222i \(-0.619614\pi\)
−0.366996 + 0.930222i \(0.619614\pi\)
\(504\) −112.562 −5.01392
\(505\) 16.9522 0.754362
\(506\) −9.20821 −0.409355
\(507\) −10.2644 −0.455857
\(508\) −36.2157 −1.60681
\(509\) 28.4605 1.26149 0.630746 0.775990i \(-0.282749\pi\)
0.630746 + 0.775990i \(0.282749\pi\)
\(510\) −1.13036 −0.0500534
\(511\) 3.72119 0.164616
\(512\) −111.594 −4.93180
\(513\) 6.00061 0.264934
\(514\) −40.1547 −1.77115
\(515\) 13.2252 0.582772
\(516\) −2.15412 −0.0948296
\(517\) 8.66756 0.381199
\(518\) −53.8550 −2.36625
\(519\) 0.864218 0.0379350
\(520\) 70.4607 3.08990
\(521\) −38.7264 −1.69664 −0.848318 0.529487i \(-0.822384\pi\)
−0.848318 + 0.529487i \(0.822384\pi\)
\(522\) 64.6436 2.82937
\(523\) 7.89941 0.345417 0.172709 0.984973i \(-0.444748\pi\)
0.172709 + 0.984973i \(0.444748\pi\)
\(524\) −17.8173 −0.778353
\(525\) −5.53529 −0.241580
\(526\) 31.0904 1.35561
\(527\) −0.300360 −0.0130839
\(528\) −6.48087 −0.282044
\(529\) −12.0013 −0.521797
\(530\) 20.2148 0.878074
\(531\) −33.5576 −1.45627
\(532\) −59.2864 −2.57039
\(533\) 11.6653 0.505281
\(534\) 1.82318 0.0788966
\(535\) 9.53983 0.412443
\(536\) 25.5806 1.10492
\(537\) 5.78508 0.249645
\(538\) −50.9404 −2.19620
\(539\) 7.62830 0.328574
\(540\) −13.6149 −0.585890
\(541\) 21.7778 0.936300 0.468150 0.883649i \(-0.344921\pi\)
0.468150 + 0.883649i \(0.344921\pi\)
\(542\) −61.5546 −2.64400
\(543\) −1.85122 −0.0794434
\(544\) −27.0945 −1.16167
\(545\) −8.44339 −0.361675
\(546\) −25.4057 −1.08726
\(547\) −33.8642 −1.44793 −0.723965 0.689836i \(-0.757682\pi\)
−0.723965 + 0.689836i \(0.757682\pi\)
\(548\) 81.7648 3.49282
\(549\) 28.1774 1.20258
\(550\) 10.6502 0.454125
\(551\) 22.1204 0.942362
\(552\) 12.8869 0.548505
\(553\) 32.4044 1.37797
\(554\) 31.3029 1.32993
\(555\) −2.06461 −0.0876377
\(556\) 88.8647 3.76870
\(557\) −37.5570 −1.59134 −0.795671 0.605729i \(-0.792882\pi\)
−0.795671 + 0.605729i \(0.792882\pi\)
\(558\) −2.38317 −0.100888
\(559\) 6.34070 0.268183
\(560\) 70.8859 2.99547
\(561\) −0.377305 −0.0159298
\(562\) −20.1743 −0.851001
\(563\) 28.4408 1.19864 0.599319 0.800510i \(-0.295438\pi\)
0.599319 + 0.800510i \(0.295438\pi\)
\(564\) −18.6709 −0.786188
\(565\) −0.325927 −0.0137119
\(566\) 36.7844 1.54616
\(567\) −29.5995 −1.24306
\(568\) −123.551 −5.18410
\(569\) −1.61319 −0.0676286 −0.0338143 0.999428i \(-0.510765\pi\)
−0.0338143 + 0.999428i \(0.510765\pi\)
\(570\) −3.06902 −0.128547
\(571\) −2.37582 −0.0994249 −0.0497125 0.998764i \(-0.515830\pi\)
−0.0497125 + 0.998764i \(0.515830\pi\)
\(572\) 36.2005 1.51362
\(573\) 6.18856 0.258531
\(574\) 19.5372 0.815466
\(575\) −12.7210 −0.530502
\(576\) −116.808 −4.86698
\(577\) −30.1521 −1.25525 −0.627625 0.778516i \(-0.715973\pi\)
−0.627625 + 0.778516i \(0.715973\pi\)
\(578\) −2.77655 −0.115489
\(579\) 3.93650 0.163596
\(580\) −50.1892 −2.08400
\(581\) 30.9097 1.28235
\(582\) −5.75995 −0.238758
\(583\) 6.74749 0.279453
\(584\) 10.0201 0.414636
\(585\) 19.5509 0.808330
\(586\) 62.6388 2.58759
\(587\) 39.7574 1.64096 0.820482 0.571673i \(-0.193705\pi\)
0.820482 + 0.571673i \(0.193705\pi\)
\(588\) −16.4322 −0.677654
\(589\) −0.815498 −0.0336020
\(590\) 35.1811 1.44838
\(591\) 3.80999 0.156722
\(592\) −87.1095 −3.58018
\(593\) −34.9683 −1.43598 −0.717988 0.696055i \(-0.754937\pi\)
−0.717988 + 0.696055i \(0.754937\pi\)
\(594\) −6.13649 −0.251783
\(595\) 4.12685 0.169184
\(596\) 108.740 4.45415
\(597\) 7.18977 0.294258
\(598\) −58.3865 −2.38760
\(599\) 45.1951 1.84662 0.923310 0.384055i \(-0.125473\pi\)
0.923310 + 0.384055i \(0.125473\pi\)
\(600\) −14.9050 −0.608493
\(601\) 20.0870 0.819365 0.409683 0.912228i \(-0.365639\pi\)
0.409683 + 0.912228i \(0.365639\pi\)
\(602\) 10.6195 0.432817
\(603\) 7.09792 0.289050
\(604\) −27.3119 −1.11131
\(605\) −1.07900 −0.0438676
\(606\) −16.4589 −0.668598
\(607\) −18.5524 −0.753020 −0.376510 0.926412i \(-0.622876\pi\)
−0.376510 + 0.926412i \(0.622876\pi\)
\(608\) −73.5633 −2.98339
\(609\) 11.7571 0.476423
\(610\) −29.5407 −1.19607
\(611\) 54.9585 2.22338
\(612\) −16.3149 −0.659491
\(613\) −39.8737 −1.61049 −0.805243 0.592946i \(-0.797965\pi\)
−0.805243 + 0.592946i \(0.797965\pi\)
\(614\) −81.6832 −3.29647
\(615\) 0.748984 0.0302020
\(616\) 39.3899 1.58706
\(617\) −29.0402 −1.16911 −0.584557 0.811353i \(-0.698732\pi\)
−0.584557 + 0.811353i \(0.698732\pi\)
\(618\) −12.8404 −0.516517
\(619\) 19.3293 0.776909 0.388455 0.921468i \(-0.373009\pi\)
0.388455 + 0.921468i \(0.373009\pi\)
\(620\) 1.85029 0.0743095
\(621\) 7.32968 0.294130
\(622\) −44.4543 −1.78246
\(623\) −6.65624 −0.266677
\(624\) −41.0933 −1.64505
\(625\) 8.89185 0.355674
\(626\) −68.2280 −2.72694
\(627\) −1.02441 −0.0409109
\(628\) −11.3248 −0.451909
\(629\) −5.07135 −0.202208
\(630\) 32.7440 1.30455
\(631\) 25.2507 1.00521 0.502607 0.864515i \(-0.332374\pi\)
0.502607 + 0.864515i \(0.332374\pi\)
\(632\) 87.2559 3.47085
\(633\) −3.49790 −0.139029
\(634\) −63.5062 −2.52215
\(635\) 6.84450 0.271616
\(636\) −14.5349 −0.576345
\(637\) 48.3688 1.91644
\(638\) −22.6213 −0.895586
\(639\) −34.2821 −1.35618
\(640\) 63.9890 2.52939
\(641\) −13.0410 −0.515089 −0.257545 0.966266i \(-0.582913\pi\)
−0.257545 + 0.966266i \(0.582913\pi\)
\(642\) −9.26226 −0.365552
\(643\) 37.4430 1.47661 0.738303 0.674469i \(-0.235627\pi\)
0.738303 + 0.674469i \(0.235627\pi\)
\(644\) −72.4175 −2.85365
\(645\) 0.407111 0.0160300
\(646\) −7.53852 −0.296599
\(647\) −6.87204 −0.270168 −0.135084 0.990834i \(-0.543130\pi\)
−0.135084 + 0.990834i \(0.543130\pi\)
\(648\) −79.7031 −3.13103
\(649\) 11.7431 0.460957
\(650\) 67.5296 2.64873
\(651\) −0.433442 −0.0169879
\(652\) −1.40913 −0.0551857
\(653\) 48.5171 1.89862 0.949310 0.314340i \(-0.101783\pi\)
0.949310 + 0.314340i \(0.101783\pi\)
\(654\) 8.19772 0.320556
\(655\) 3.36734 0.131573
\(656\) 31.6010 1.23381
\(657\) 2.78031 0.108470
\(658\) 92.0448 3.58828
\(659\) 35.6802 1.38990 0.694952 0.719056i \(-0.255426\pi\)
0.694952 + 0.719056i \(0.255426\pi\)
\(660\) 2.32429 0.0904728
\(661\) 6.17494 0.240177 0.120089 0.992763i \(-0.461682\pi\)
0.120089 + 0.992763i \(0.461682\pi\)
\(662\) −69.5995 −2.70506
\(663\) −2.39238 −0.0929122
\(664\) 83.2312 3.23000
\(665\) 11.2047 0.434499
\(666\) −40.2381 −1.55919
\(667\) 27.0198 1.04621
\(668\) 111.973 4.33238
\(669\) 5.29522 0.204725
\(670\) −7.44132 −0.287483
\(671\) −9.86038 −0.380656
\(672\) −39.0993 −1.50829
\(673\) 10.2145 0.393741 0.196870 0.980430i \(-0.436922\pi\)
0.196870 + 0.980430i \(0.436922\pi\)
\(674\) −0.0367360 −0.00141502
\(675\) −8.47747 −0.326298
\(676\) 155.317 5.97372
\(677\) 2.92324 0.112349 0.0561747 0.998421i \(-0.482110\pi\)
0.0561747 + 0.998421i \(0.482110\pi\)
\(678\) 0.316444 0.0121529
\(679\) 21.0290 0.807019
\(680\) 11.1124 0.426142
\(681\) 7.05024 0.270166
\(682\) 0.833964 0.0319341
\(683\) −11.5384 −0.441503 −0.220751 0.975330i \(-0.570851\pi\)
−0.220751 + 0.975330i \(0.570851\pi\)
\(684\) −44.2961 −1.69370
\(685\) −15.4529 −0.590426
\(686\) 6.67222 0.254747
\(687\) 2.45023 0.0934822
\(688\) 17.1768 0.654858
\(689\) 42.7839 1.62994
\(690\) −3.74877 −0.142713
\(691\) −19.1189 −0.727316 −0.363658 0.931533i \(-0.618472\pi\)
−0.363658 + 0.931533i \(0.618472\pi\)
\(692\) −13.0770 −0.497113
\(693\) 10.9296 0.415182
\(694\) −15.1086 −0.573515
\(695\) −16.7948 −0.637061
\(696\) 31.6587 1.20002
\(697\) 1.83975 0.0696856
\(698\) −62.2784 −2.35727
\(699\) 9.33645 0.353137
\(700\) 83.7578 3.16575
\(701\) −22.8964 −0.864786 −0.432393 0.901685i \(-0.642331\pi\)
−0.432393 + 0.901685i \(0.642331\pi\)
\(702\) −38.9097 −1.46855
\(703\) −13.7691 −0.519311
\(704\) 40.8755 1.54055
\(705\) 3.52866 0.132897
\(706\) 10.9427 0.411835
\(707\) 60.0898 2.25991
\(708\) −25.2960 −0.950681
\(709\) 8.51075 0.319628 0.159814 0.987147i \(-0.448911\pi\)
0.159814 + 0.987147i \(0.448911\pi\)
\(710\) 35.9407 1.34883
\(711\) 24.2111 0.907987
\(712\) −17.9234 −0.671707
\(713\) −0.996120 −0.0373050
\(714\) −4.00677 −0.149950
\(715\) −6.84162 −0.255862
\(716\) −87.5376 −3.27143
\(717\) 2.26842 0.0847156
\(718\) −10.3402 −0.385894
\(719\) −21.1661 −0.789363 −0.394682 0.918818i \(-0.629145\pi\)
−0.394682 + 0.918818i \(0.629145\pi\)
\(720\) 52.9627 1.97380
\(721\) 46.8790 1.74586
\(722\) 32.2868 1.20159
\(723\) 4.94587 0.183939
\(724\) 28.0119 1.04105
\(725\) −31.2510 −1.16063
\(726\) 1.04760 0.0388802
\(727\) −5.60901 −0.208027 −0.104013 0.994576i \(-0.533168\pi\)
−0.104013 + 0.994576i \(0.533168\pi\)
\(728\) 249.760 9.25671
\(729\) −19.6137 −0.726435
\(730\) −2.91482 −0.107882
\(731\) 1.00000 0.0369863
\(732\) 21.2404 0.785068
\(733\) 35.0686 1.29529 0.647644 0.761943i \(-0.275755\pi\)
0.647644 + 0.761943i \(0.275755\pi\)
\(734\) −31.1135 −1.14842
\(735\) 3.10557 0.114551
\(736\) −89.8567 −3.31216
\(737\) −2.48384 −0.0914934
\(738\) 14.5973 0.537334
\(739\) −40.0410 −1.47293 −0.736466 0.676475i \(-0.763507\pi\)
−0.736466 + 0.676475i \(0.763507\pi\)
\(740\) 31.2408 1.14843
\(741\) −6.49547 −0.238617
\(742\) 71.6547 2.63053
\(743\) 30.1558 1.10631 0.553154 0.833079i \(-0.313424\pi\)
0.553154 + 0.833079i \(0.313424\pi\)
\(744\) −1.16714 −0.0427893
\(745\) −20.5510 −0.752929
\(746\) 31.9765 1.17074
\(747\) 23.0943 0.844978
\(748\) 5.70922 0.208750
\(749\) 33.8155 1.23559
\(750\) 9.98763 0.364697
\(751\) −50.0634 −1.82684 −0.913419 0.407021i \(-0.866568\pi\)
−0.913419 + 0.407021i \(0.866568\pi\)
\(752\) 148.881 5.42912
\(753\) −9.83620 −0.358451
\(754\) −143.435 −5.22360
\(755\) 5.16175 0.187855
\(756\) −48.2601 −1.75520
\(757\) 23.5262 0.855074 0.427537 0.903998i \(-0.359381\pi\)
0.427537 + 0.903998i \(0.359381\pi\)
\(758\) −66.6517 −2.42090
\(759\) −1.25130 −0.0454194
\(760\) 30.1710 1.09442
\(761\) −21.0535 −0.763190 −0.381595 0.924330i \(-0.624625\pi\)
−0.381595 + 0.924330i \(0.624625\pi\)
\(762\) −6.64535 −0.240735
\(763\) −29.9290 −1.08350
\(764\) −93.6428 −3.38788
\(765\) 3.08339 0.111480
\(766\) 7.60968 0.274949
\(767\) 74.4595 2.68858
\(768\) −31.2821 −1.12879
\(769\) 11.7780 0.424725 0.212363 0.977191i \(-0.431884\pi\)
0.212363 + 0.977191i \(0.431884\pi\)
\(770\) −11.4584 −0.412932
\(771\) −5.45662 −0.196515
\(772\) −59.5656 −2.14381
\(773\) −8.02273 −0.288558 −0.144279 0.989537i \(-0.546086\pi\)
−0.144279 + 0.989537i \(0.546086\pi\)
\(774\) 7.93438 0.285195
\(775\) 1.15211 0.0413849
\(776\) 56.6252 2.03272
\(777\) −7.31835 −0.262544
\(778\) 61.6617 2.21068
\(779\) 4.99506 0.178966
\(780\) 14.7376 0.527692
\(781\) 11.9966 0.429274
\(782\) −9.20821 −0.329285
\(783\) 18.0064 0.643497
\(784\) 131.030 4.67963
\(785\) 2.14030 0.0763907
\(786\) −3.26936 −0.116614
\(787\) −12.6242 −0.450005 −0.225002 0.974358i \(-0.572239\pi\)
−0.225002 + 0.974358i \(0.572239\pi\)
\(788\) −57.6512 −2.05374
\(789\) 4.22486 0.150409
\(790\) −25.3824 −0.903067
\(791\) −1.15530 −0.0410779
\(792\) 29.4304 1.04576
\(793\) −62.5218 −2.22021
\(794\) 42.5346 1.50950
\(795\) 2.74698 0.0974254
\(796\) −108.793 −3.85606
\(797\) −36.9899 −1.31025 −0.655124 0.755521i \(-0.727384\pi\)
−0.655124 + 0.755521i \(0.727384\pi\)
\(798\) −10.8787 −0.385100
\(799\) 8.66756 0.306636
\(800\) 103.928 3.67440
\(801\) −4.97324 −0.175721
\(802\) −35.6838 −1.26004
\(803\) −0.972938 −0.0343342
\(804\) 5.35047 0.188697
\(805\) 13.6864 0.482381
\(806\) 5.28792 0.186259
\(807\) −6.92229 −0.243676
\(808\) 161.805 5.69228
\(809\) 40.2673 1.41572 0.707862 0.706351i \(-0.249660\pi\)
0.707862 + 0.706351i \(0.249660\pi\)
\(810\) 23.1853 0.814650
\(811\) 33.3352 1.17056 0.585279 0.810832i \(-0.300985\pi\)
0.585279 + 0.810832i \(0.300985\pi\)
\(812\) −177.904 −6.24322
\(813\) −8.36464 −0.293361
\(814\) 14.0809 0.493534
\(815\) 0.266314 0.00932859
\(816\) −6.48087 −0.226876
\(817\) 2.71507 0.0949883
\(818\) 57.1026 1.99655
\(819\) 69.3014 2.42159
\(820\) −11.3333 −0.395777
\(821\) −34.6699 −1.20999 −0.604994 0.796230i \(-0.706824\pi\)
−0.604994 + 0.796230i \(0.706824\pi\)
\(822\) 15.0033 0.523300
\(823\) −17.0426 −0.594066 −0.297033 0.954867i \(-0.595997\pi\)
−0.297033 + 0.954867i \(0.595997\pi\)
\(824\) 126.232 4.39750
\(825\) 1.44725 0.0503868
\(826\) 124.705 4.33905
\(827\) −46.4347 −1.61469 −0.807346 0.590078i \(-0.799097\pi\)
−0.807346 + 0.590078i \(0.799097\pi\)
\(828\) −54.1071 −1.88035
\(829\) −42.4748 −1.47521 −0.737605 0.675233i \(-0.764043\pi\)
−0.737605 + 0.675233i \(0.764043\pi\)
\(830\) −24.2117 −0.840399
\(831\) 4.25375 0.147561
\(832\) 259.180 8.98544
\(833\) 7.62830 0.264305
\(834\) 16.3061 0.564633
\(835\) −21.1621 −0.732346
\(836\) 15.5009 0.536111
\(837\) −0.663830 −0.0229453
\(838\) −7.70328 −0.266105
\(839\) −6.27558 −0.216657 −0.108329 0.994115i \(-0.534550\pi\)
−0.108329 + 0.994115i \(0.534550\pi\)
\(840\) 16.0361 0.553297
\(841\) 37.3781 1.28890
\(842\) −79.6739 −2.74575
\(843\) −2.74148 −0.0944215
\(844\) 52.9288 1.82188
\(845\) −29.3537 −1.00980
\(846\) 68.7717 2.36442
\(847\) −3.82470 −0.131418
\(848\) 115.900 3.98003
\(849\) 4.99862 0.171552
\(850\) 10.6502 0.365298
\(851\) −16.8188 −0.576540
\(852\) −25.8421 −0.885337
\(853\) 8.19762 0.280681 0.140341 0.990103i \(-0.455180\pi\)
0.140341 + 0.990103i \(0.455180\pi\)
\(854\) −104.712 −3.58317
\(855\) 8.37163 0.286304
\(856\) 91.0558 3.11222
\(857\) 30.0186 1.02542 0.512708 0.858563i \(-0.328642\pi\)
0.512708 + 0.858563i \(0.328642\pi\)
\(858\) 6.64255 0.226773
\(859\) −12.2797 −0.418979 −0.209489 0.977811i \(-0.567180\pi\)
−0.209489 + 0.977811i \(0.567180\pi\)
\(860\) −6.16025 −0.210063
\(861\) 2.65490 0.0904788
\(862\) 103.291 3.51811
\(863\) 47.5951 1.62016 0.810078 0.586322i \(-0.199425\pi\)
0.810078 + 0.586322i \(0.199425\pi\)
\(864\) −59.8818 −2.03722
\(865\) 2.47145 0.0840320
\(866\) −1.87392 −0.0636784
\(867\) −0.377305 −0.0128139
\(868\) 6.55867 0.222616
\(869\) −8.47241 −0.287407
\(870\) −9.20939 −0.312228
\(871\) −15.7493 −0.533644
\(872\) −80.5905 −2.72914
\(873\) 15.7119 0.531768
\(874\) −25.0009 −0.845669
\(875\) −36.4638 −1.23270
\(876\) 2.09582 0.0708112
\(877\) 12.7459 0.430400 0.215200 0.976570i \(-0.430960\pi\)
0.215200 + 0.976570i \(0.430960\pi\)
\(878\) 83.6338 2.82250
\(879\) 8.51198 0.287102
\(880\) −18.5337 −0.624772
\(881\) −29.9871 −1.01029 −0.505145 0.863034i \(-0.668561\pi\)
−0.505145 + 0.863034i \(0.668561\pi\)
\(882\) 60.5258 2.03801
\(883\) 2.27882 0.0766884 0.0383442 0.999265i \(-0.487792\pi\)
0.0383442 + 0.999265i \(0.487792\pi\)
\(884\) 36.2005 1.21755
\(885\) 4.78075 0.160703
\(886\) −12.3984 −0.416532
\(887\) 37.1401 1.24704 0.623521 0.781806i \(-0.285701\pi\)
0.623521 + 0.781806i \(0.285701\pi\)
\(888\) −19.7063 −0.661299
\(889\) 24.2615 0.813704
\(890\) 5.21385 0.174769
\(891\) 7.73904 0.259268
\(892\) −80.1252 −2.68279
\(893\) 23.5330 0.787503
\(894\) 19.9530 0.667328
\(895\) 16.5439 0.553003
\(896\) 226.820 7.57752
\(897\) −7.93413 −0.264913
\(898\) 86.3462 2.88141
\(899\) −2.44711 −0.0816158
\(900\) 62.5801 2.08600
\(901\) 6.74749 0.224792
\(902\) −5.10816 −0.170083
\(903\) 1.44308 0.0480225
\(904\) −3.11091 −0.103467
\(905\) −5.29404 −0.175980
\(906\) −5.01156 −0.166498
\(907\) 6.18018 0.205209 0.102605 0.994722i \(-0.467282\pi\)
0.102605 + 0.994722i \(0.467282\pi\)
\(908\) −106.681 −3.54035
\(909\) 44.8964 1.48912
\(910\) −72.6542 −2.40846
\(911\) 58.8512 1.94983 0.974914 0.222581i \(-0.0714483\pi\)
0.974914 + 0.222581i \(0.0714483\pi\)
\(912\) −17.5960 −0.582662
\(913\) −8.08161 −0.267462
\(914\) −63.2160 −2.09100
\(915\) −4.01427 −0.132708
\(916\) −37.0759 −1.22502
\(917\) 11.9361 0.394165
\(918\) −6.13649 −0.202534
\(919\) 19.9257 0.657289 0.328645 0.944454i \(-0.393408\pi\)
0.328645 + 0.944454i \(0.393408\pi\)
\(920\) 36.8535 1.21503
\(921\) −11.0999 −0.365754
\(922\) −93.0296 −3.06377
\(923\) 76.0671 2.50378
\(924\) 8.23884 0.271038
\(925\) 19.4525 0.639594
\(926\) −49.4221 −1.62411
\(927\) 35.0259 1.15040
\(928\) −220.746 −7.24634
\(929\) 42.6711 1.39999 0.699996 0.714147i \(-0.253185\pi\)
0.699996 + 0.714147i \(0.253185\pi\)
\(930\) 0.339516 0.0111332
\(931\) 20.7114 0.678788
\(932\) −141.275 −4.62763
\(933\) −6.04089 −0.197770
\(934\) −3.69213 −0.120810
\(935\) −1.07900 −0.0352871
\(936\) 186.609 6.09951
\(937\) 25.9637 0.848198 0.424099 0.905616i \(-0.360591\pi\)
0.424099 + 0.905616i \(0.360591\pi\)
\(938\) −26.3770 −0.861240
\(939\) −9.27149 −0.302564
\(940\) −53.3943 −1.74153
\(941\) −12.4935 −0.407276 −0.203638 0.979046i \(-0.565277\pi\)
−0.203638 + 0.979046i \(0.565277\pi\)
\(942\) −2.07803 −0.0677058
\(943\) 6.10140 0.198689
\(944\) 201.708 6.56505
\(945\) 9.12080 0.296700
\(946\) −2.77655 −0.0902734
\(947\) 43.2910 1.40677 0.703385 0.710809i \(-0.251671\pi\)
0.703385 + 0.710809i \(0.251671\pi\)
\(948\) 18.2505 0.592750
\(949\) −6.16911 −0.200258
\(950\) 28.9160 0.938158
\(951\) −8.62984 −0.279842
\(952\) 39.3899 1.27663
\(953\) −22.6473 −0.733617 −0.366809 0.930296i \(-0.619550\pi\)
−0.366809 + 0.930296i \(0.619550\pi\)
\(954\) 53.5372 1.73333
\(955\) 17.6978 0.572687
\(956\) −34.3248 −1.11014
\(957\) −3.07401 −0.0993685
\(958\) −16.4851 −0.532610
\(959\) −54.7755 −1.76879
\(960\) 16.6409 0.537083
\(961\) −30.9098 −0.997090
\(962\) 89.2826 2.87859
\(963\) 25.2655 0.814168
\(964\) −74.8389 −2.41040
\(965\) 11.2574 0.362390
\(966\) −13.2881 −0.427539
\(967\) 20.0352 0.644289 0.322145 0.946690i \(-0.395596\pi\)
0.322145 + 0.946690i \(0.395596\pi\)
\(968\) −10.2988 −0.331017
\(969\) −1.02441 −0.0329087
\(970\) −16.4721 −0.528886
\(971\) 22.8856 0.734433 0.367216 0.930136i \(-0.380311\pi\)
0.367216 + 0.930136i \(0.380311\pi\)
\(972\) −54.5249 −1.74889
\(973\) −59.5318 −1.90850
\(974\) −42.9139 −1.37505
\(975\) 9.17658 0.293886
\(976\) −169.369 −5.42139
\(977\) −7.33985 −0.234823 −0.117411 0.993083i \(-0.537460\pi\)
−0.117411 + 0.993083i \(0.537460\pi\)
\(978\) −0.258566 −0.00826802
\(979\) 1.74033 0.0556212
\(980\) −46.9922 −1.50111
\(981\) −22.3616 −0.713952
\(982\) −99.7274 −3.18243
\(983\) −10.7895 −0.344131 −0.172065 0.985086i \(-0.555044\pi\)
−0.172065 + 0.985086i \(0.555044\pi\)
\(984\) 7.14890 0.227899
\(985\) 10.8956 0.347164
\(986\) −22.6213 −0.720409
\(987\) 12.5079 0.398132
\(988\) 98.2868 3.12692
\(989\) 3.31642 0.105456
\(990\) −8.56119 −0.272093
\(991\) −43.3699 −1.37769 −0.688846 0.724908i \(-0.741882\pi\)
−0.688846 + 0.724908i \(0.741882\pi\)
\(992\) 8.13808 0.258384
\(993\) −9.45786 −0.300136
\(994\) 127.398 4.04081
\(995\) 20.5610 0.651828
\(996\) 17.4087 0.551616
\(997\) 19.0086 0.602009 0.301005 0.953623i \(-0.402678\pi\)
0.301005 + 0.953623i \(0.402678\pi\)
\(998\) −101.581 −3.21548
\(999\) −11.2083 −0.354614
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 \(a_p\))