Properties

Label 8011.2.a.b.1.3
Level 8011
Weight 2
Character 8011.1
Self dual Yes
Analytic conductor 63.968
Analytic rank 0
Dimension 358
CM No

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Newspace parameters

Level: \( N \) = \( 8011 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8011.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9681570592\)
Analytic rank: \(0\)
Dimension: \(358\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 8011.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.79545 q^{2}\) \(-2.80135 q^{3}\) \(+5.81452 q^{4}\) \(+0.0114194 q^{5}\) \(+7.83103 q^{6}\) \(+2.04645 q^{7}\) \(-10.6633 q^{8}\) \(+4.84758 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.79545 q^{2}\) \(-2.80135 q^{3}\) \(+5.81452 q^{4}\) \(+0.0114194 q^{5}\) \(+7.83103 q^{6}\) \(+2.04645 q^{7}\) \(-10.6633 q^{8}\) \(+4.84758 q^{9}\) \(-0.0319223 q^{10}\) \(+2.83233 q^{11}\) \(-16.2885 q^{12}\) \(-4.48788 q^{13}\) \(-5.72075 q^{14}\) \(-0.0319897 q^{15}\) \(+18.1796 q^{16}\) \(+0.296507 q^{17}\) \(-13.5511 q^{18}\) \(-3.81702 q^{19}\) \(+0.0663982 q^{20}\) \(-5.73284 q^{21}\) \(-7.91763 q^{22}\) \(+2.26186 q^{23}\) \(+29.8716 q^{24}\) \(-4.99987 q^{25}\) \(+12.5456 q^{26}\) \(-5.17573 q^{27}\) \(+11.8991 q^{28}\) \(-8.53845 q^{29}\) \(+0.0894256 q^{30}\) \(-5.07961 q^{31}\) \(-29.4935 q^{32}\) \(-7.93436 q^{33}\) \(-0.828870 q^{34}\) \(+0.0233692 q^{35}\) \(+28.1863 q^{36}\) \(-4.77154 q^{37}\) \(+10.6703 q^{38}\) \(+12.5721 q^{39}\) \(-0.121768 q^{40}\) \(-4.60380 q^{41}\) \(+16.0258 q^{42}\) \(-8.56991 q^{43}\) \(+16.4686 q^{44}\) \(+0.0553564 q^{45}\) \(-6.32290 q^{46}\) \(-8.81606 q^{47}\) \(-50.9275 q^{48}\) \(-2.81203 q^{49}\) \(+13.9769 q^{50}\) \(-0.830622 q^{51}\) \(-26.0949 q^{52}\) \(+2.70133 q^{53}\) \(+14.4685 q^{54}\) \(+0.0323435 q^{55}\) \(-21.8219 q^{56}\) \(+10.6928 q^{57}\) \(+23.8688 q^{58}\) \(+4.17702 q^{59}\) \(-0.186005 q^{60}\) \(-9.11193 q^{61}\) \(+14.1998 q^{62}\) \(+9.92034 q^{63}\) \(+46.0883 q^{64}\) \(-0.0512489 q^{65}\) \(+22.1801 q^{66}\) \(-10.3243 q^{67}\) \(+1.72405 q^{68}\) \(-6.33626 q^{69}\) \(-0.0653274 q^{70}\) \(-7.07339 q^{71}\) \(-51.6911 q^{72}\) \(-16.4255 q^{73}\) \(+13.3386 q^{74}\) \(+14.0064 q^{75}\) \(-22.1941 q^{76}\) \(+5.79623 q^{77}\) \(-35.1448 q^{78}\) \(+10.4480 q^{79}\) \(+0.207600 q^{80}\) \(-0.0437062 q^{81}\) \(+12.8697 q^{82}\) \(-11.1628 q^{83}\) \(-33.3337 q^{84}\) \(+0.00338593 q^{85}\) \(+23.9567 q^{86}\) \(+23.9192 q^{87}\) \(-30.2019 q^{88}\) \(-10.5469 q^{89}\) \(-0.154746 q^{90}\) \(-9.18424 q^{91}\) \(+13.1516 q^{92}\) \(+14.2298 q^{93}\) \(+24.6448 q^{94}\) \(-0.0435880 q^{95}\) \(+82.6217 q^{96}\) \(-7.21992 q^{97}\) \(+7.86088 q^{98}\) \(+13.7300 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut 21q^{10} \) \(\mathstrut +\mathstrut 70q^{11} \) \(\mathstrut +\mathstrut 20q^{12} \) \(\mathstrut +\mathstrut 53q^{13} \) \(\mathstrut +\mathstrut 69q^{14} \) \(\mathstrut +\mathstrut 28q^{15} \) \(\mathstrut +\mathstrut 449q^{16} \) \(\mathstrut +\mathstrut 88q^{17} \) \(\mathstrut +\mathstrut 86q^{18} \) \(\mathstrut +\mathstrut 44q^{19} \) \(\mathstrut +\mathstrut 136q^{20} \) \(\mathstrut +\mathstrut 125q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 104q^{23} \) \(\mathstrut +\mathstrut 84q^{24} \) \(\mathstrut +\mathstrut 444q^{25} \) \(\mathstrut +\mathstrut 100q^{26} \) \(\mathstrut +\mathstrut 32q^{27} \) \(\mathstrut +\mathstrut 46q^{28} \) \(\mathstrut +\mathstrut 373q^{29} \) \(\mathstrut +\mathstrut 99q^{30} \) \(\mathstrut +\mathstrut 30q^{31} \) \(\mathstrut +\mathstrut 221q^{32} \) \(\mathstrut +\mathstrut 56q^{33} \) \(\mathstrut +\mathstrut 26q^{34} \) \(\mathstrut +\mathstrut 164q^{35} \) \(\mathstrut +\mathstrut 599q^{36} \) \(\mathstrut +\mathstrut 81q^{37} \) \(\mathstrut +\mathstrut 66q^{38} \) \(\mathstrut +\mathstrut 143q^{39} \) \(\mathstrut +\mathstrut 42q^{40} \) \(\mathstrut +\mathstrut 182q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut +\mathstrut 40q^{43} \) \(\mathstrut +\mathstrut 184q^{44} \) \(\mathstrut +\mathstrut 198q^{45} \) \(\mathstrut +\mathstrut 54q^{46} \) \(\mathstrut +\mathstrut 66q^{47} \) \(\mathstrut +\mathstrut 5q^{48} \) \(\mathstrut +\mathstrut 479q^{49} \) \(\mathstrut +\mathstrut 184q^{50} \) \(\mathstrut +\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 64q^{52} \) \(\mathstrut +\mathstrut 221q^{53} \) \(\mathstrut +\mathstrut 67q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 174q^{56} \) \(\mathstrut +\mathstrut 84q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut +\mathstrut 127q^{59} \) \(\mathstrut +\mathstrut 29q^{60} \) \(\mathstrut +\mathstrut 174q^{61} \) \(\mathstrut +\mathstrut 86q^{62} \) \(\mathstrut +\mathstrut 48q^{63} \) \(\mathstrut +\mathstrut 549q^{64} \) \(\mathstrut +\mathstrut 202q^{65} \) \(\mathstrut +\mathstrut 32q^{66} \) \(\mathstrut +\mathstrut 29q^{67} \) \(\mathstrut +\mathstrut 172q^{68} \) \(\mathstrut +\mathstrut 249q^{69} \) \(\mathstrut +\mathstrut 12q^{70} \) \(\mathstrut +\mathstrut 185q^{71} \) \(\mathstrut +\mathstrut 218q^{72} \) \(\mathstrut +\mathstrut 57q^{73} \) \(\mathstrut +\mathstrut 272q^{74} \) \(\mathstrut +\mathstrut 24q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 384q^{77} \) \(\mathstrut +\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 93q^{79} \) \(\mathstrut +\mathstrut 215q^{80} \) \(\mathstrut +\mathstrut 702q^{81} \) \(\mathstrut +\mathstrut 48q^{82} \) \(\mathstrut +\mathstrut 121q^{83} \) \(\mathstrut +\mathstrut 179q^{84} \) \(\mathstrut +\mathstrut 177q^{85} \) \(\mathstrut +\mathstrut 209q^{86} \) \(\mathstrut +\mathstrut 91q^{87} \) \(\mathstrut +\mathstrut 36q^{88} \) \(\mathstrut +\mathstrut 186q^{89} \) \(\mathstrut +\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut +\mathstrut 272q^{92} \) \(\mathstrut +\mathstrut 220q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 170q^{95} \) \(\mathstrut +\mathstrut 162q^{96} \) \(\mathstrut +\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 196q^{98} \) \(\mathstrut +\mathstrut 152q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.79545 −1.97668 −0.988339 0.152267i \(-0.951343\pi\)
−0.988339 + 0.152267i \(0.951343\pi\)
\(3\) −2.80135 −1.61736 −0.808681 0.588247i \(-0.799818\pi\)
−0.808681 + 0.588247i \(0.799818\pi\)
\(4\) 5.81452 2.90726
\(5\) 0.0114194 0.00510690 0.00255345 0.999997i \(-0.499187\pi\)
0.00255345 + 0.999997i \(0.499187\pi\)
\(6\) 7.83103 3.19701
\(7\) 2.04645 0.773486 0.386743 0.922187i \(-0.373600\pi\)
0.386743 + 0.922187i \(0.373600\pi\)
\(8\) −10.6633 −3.77004
\(9\) 4.84758 1.61586
\(10\) −0.0319223 −0.0100947
\(11\) 2.83233 0.853980 0.426990 0.904256i \(-0.359574\pi\)
0.426990 + 0.904256i \(0.359574\pi\)
\(12\) −16.2885 −4.70209
\(13\) −4.48788 −1.24471 −0.622357 0.782733i \(-0.713825\pi\)
−0.622357 + 0.782733i \(0.713825\pi\)
\(14\) −5.72075 −1.52893
\(15\) −0.0319897 −0.00825971
\(16\) 18.1796 4.54490
\(17\) 0.296507 0.0719136 0.0359568 0.999353i \(-0.488552\pi\)
0.0359568 + 0.999353i \(0.488552\pi\)
\(18\) −13.5511 −3.19404
\(19\) −3.81702 −0.875684 −0.437842 0.899052i \(-0.644257\pi\)
−0.437842 + 0.899052i \(0.644257\pi\)
\(20\) 0.0663982 0.0148471
\(21\) −5.73284 −1.25101
\(22\) −7.91763 −1.68804
\(23\) 2.26186 0.471630 0.235815 0.971798i \(-0.424224\pi\)
0.235815 + 0.971798i \(0.424224\pi\)
\(24\) 29.8716 6.09752
\(25\) −4.99987 −0.999974
\(26\) 12.5456 2.46040
\(27\) −5.17573 −0.996069
\(28\) 11.8991 2.24873
\(29\) −8.53845 −1.58555 −0.792775 0.609514i \(-0.791364\pi\)
−0.792775 + 0.609514i \(0.791364\pi\)
\(30\) 0.0894256 0.0163268
\(31\) −5.07961 −0.912325 −0.456162 0.889897i \(-0.650776\pi\)
−0.456162 + 0.889897i \(0.650776\pi\)
\(32\) −29.4935 −5.21376
\(33\) −7.93436 −1.38119
\(34\) −0.828870 −0.142150
\(35\) 0.0233692 0.00395012
\(36\) 28.1863 4.69772
\(37\) −4.77154 −0.784436 −0.392218 0.919872i \(-0.628292\pi\)
−0.392218 + 0.919872i \(0.628292\pi\)
\(38\) 10.6703 1.73095
\(39\) 12.5721 2.01315
\(40\) −0.121768 −0.0192532
\(41\) −4.60380 −0.718993 −0.359497 0.933146i \(-0.617052\pi\)
−0.359497 + 0.933146i \(0.617052\pi\)
\(42\) 16.0258 2.47284
\(43\) −8.56991 −1.30690 −0.653450 0.756970i \(-0.726679\pi\)
−0.653450 + 0.756970i \(0.726679\pi\)
\(44\) 16.4686 2.48274
\(45\) 0.0553564 0.00825204
\(46\) −6.32290 −0.932261
\(47\) −8.81606 −1.28595 −0.642977 0.765886i \(-0.722301\pi\)
−0.642977 + 0.765886i \(0.722301\pi\)
\(48\) −50.9275 −7.35075
\(49\) −2.81203 −0.401719
\(50\) 13.9769 1.97663
\(51\) −0.830622 −0.116310
\(52\) −26.0949 −3.61871
\(53\) 2.70133 0.371056 0.185528 0.982639i \(-0.440600\pi\)
0.185528 + 0.982639i \(0.440600\pi\)
\(54\) 14.4685 1.96891
\(55\) 0.0323435 0.00436119
\(56\) −21.8219 −2.91607
\(57\) 10.6928 1.41630
\(58\) 23.8688 3.13412
\(59\) 4.17702 0.543802 0.271901 0.962325i \(-0.412348\pi\)
0.271901 + 0.962325i \(0.412348\pi\)
\(60\) −0.186005 −0.0240131
\(61\) −9.11193 −1.16666 −0.583331 0.812234i \(-0.698251\pi\)
−0.583331 + 0.812234i \(0.698251\pi\)
\(62\) 14.1998 1.80337
\(63\) 9.92034 1.24985
\(64\) 46.0883 5.76104
\(65\) −0.0512489 −0.00635664
\(66\) 22.1801 2.73018
\(67\) −10.3243 −1.26132 −0.630659 0.776060i \(-0.717215\pi\)
−0.630659 + 0.776060i \(0.717215\pi\)
\(68\) 1.72405 0.209071
\(69\) −6.33626 −0.762797
\(70\) −0.0653274 −0.00780812
\(71\) −7.07339 −0.839457 −0.419729 0.907650i \(-0.637875\pi\)
−0.419729 + 0.907650i \(0.637875\pi\)
\(72\) −51.6911 −6.09186
\(73\) −16.4255 −1.92246 −0.961232 0.275742i \(-0.911076\pi\)
−0.961232 + 0.275742i \(0.911076\pi\)
\(74\) 13.3386 1.55058
\(75\) 14.0064 1.61732
\(76\) −22.1941 −2.54584
\(77\) 5.79623 0.660542
\(78\) −35.1448 −3.97936
\(79\) 10.4480 1.17549 0.587746 0.809045i \(-0.300015\pi\)
0.587746 + 0.809045i \(0.300015\pi\)
\(80\) 0.207600 0.0232104
\(81\) −0.0437062 −0.00485624
\(82\) 12.8697 1.42122
\(83\) −11.1628 −1.22527 −0.612636 0.790365i \(-0.709891\pi\)
−0.612636 + 0.790365i \(0.709891\pi\)
\(84\) −33.3337 −3.63700
\(85\) 0.00338593 0.000367256 0
\(86\) 23.9567 2.58332
\(87\) 23.9192 2.56441
\(88\) −30.2019 −3.21954
\(89\) −10.5469 −1.11797 −0.558983 0.829179i \(-0.688808\pi\)
−0.558983 + 0.829179i \(0.688808\pi\)
\(90\) −0.154746 −0.0163116
\(91\) −9.18424 −0.962770
\(92\) 13.1516 1.37115
\(93\) 14.2298 1.47556
\(94\) 24.6448 2.54192
\(95\) −0.0435880 −0.00447203
\(96\) 82.6217 8.43254
\(97\) −7.21992 −0.733072 −0.366536 0.930404i \(-0.619456\pi\)
−0.366536 + 0.930404i \(0.619456\pi\)
\(98\) 7.86088 0.794069
\(99\) 13.7300 1.37991
\(100\) −29.0718 −2.90718
\(101\) 15.5294 1.54523 0.772617 0.634873i \(-0.218947\pi\)
0.772617 + 0.634873i \(0.218947\pi\)
\(102\) 2.32196 0.229908
\(103\) 0.195042 0.0192181 0.00960905 0.999954i \(-0.496941\pi\)
0.00960905 + 0.999954i \(0.496941\pi\)
\(104\) 47.8556 4.69262
\(105\) −0.0654655 −0.00638877
\(106\) −7.55142 −0.733459
\(107\) 7.14254 0.690495 0.345248 0.938512i \(-0.387795\pi\)
0.345248 + 0.938512i \(0.387795\pi\)
\(108\) −30.0944 −2.89583
\(109\) 14.1909 1.35924 0.679622 0.733563i \(-0.262144\pi\)
0.679622 + 0.733563i \(0.262144\pi\)
\(110\) −0.0904144 −0.00862068
\(111\) 13.3668 1.26872
\(112\) 37.2037 3.51542
\(113\) 6.39714 0.601792 0.300896 0.953657i \(-0.402714\pi\)
0.300896 + 0.953657i \(0.402714\pi\)
\(114\) −29.8912 −2.79957
\(115\) 0.0258290 0.00240857
\(116\) −49.6470 −4.60960
\(117\) −21.7554 −2.01129
\(118\) −11.6766 −1.07492
\(119\) 0.606788 0.0556242
\(120\) 0.341115 0.0311394
\(121\) −2.97790 −0.270718
\(122\) 25.4719 2.30612
\(123\) 12.8969 1.16287
\(124\) −29.5355 −2.65236
\(125\) −0.114192 −0.0102137
\(126\) −27.7318 −2.47054
\(127\) −2.13941 −0.189842 −0.0949210 0.995485i \(-0.530260\pi\)
−0.0949210 + 0.995485i \(0.530260\pi\)
\(128\) −69.8504 −6.17396
\(129\) 24.0074 2.11373
\(130\) 0.143263 0.0125650
\(131\) 5.86256 0.512214 0.256107 0.966648i \(-0.417560\pi\)
0.256107 + 0.966648i \(0.417560\pi\)
\(132\) −46.1345 −4.01549
\(133\) −7.81135 −0.677330
\(134\) 28.8611 2.49322
\(135\) −0.0591036 −0.00508683
\(136\) −3.16174 −0.271117
\(137\) 0.439957 0.0375880 0.0187940 0.999823i \(-0.494017\pi\)
0.0187940 + 0.999823i \(0.494017\pi\)
\(138\) 17.7127 1.50780
\(139\) 15.0205 1.27402 0.637010 0.770855i \(-0.280171\pi\)
0.637010 + 0.770855i \(0.280171\pi\)
\(140\) 0.135881 0.0114840
\(141\) 24.6969 2.07985
\(142\) 19.7733 1.65934
\(143\) −12.7112 −1.06296
\(144\) 88.1270 7.34392
\(145\) −0.0975038 −0.00809725
\(146\) 45.9167 3.80009
\(147\) 7.87750 0.649725
\(148\) −27.7442 −2.28056
\(149\) 16.3800 1.34190 0.670951 0.741502i \(-0.265886\pi\)
0.670951 + 0.741502i \(0.265886\pi\)
\(150\) −39.1541 −3.19692
\(151\) −4.54505 −0.369871 −0.184935 0.982751i \(-0.559208\pi\)
−0.184935 + 0.982751i \(0.559208\pi\)
\(152\) 40.7019 3.30136
\(153\) 1.43734 0.116202
\(154\) −16.2031 −1.30568
\(155\) −0.0580060 −0.00465915
\(156\) 73.1010 5.85276
\(157\) 17.0652 1.36195 0.680975 0.732306i \(-0.261556\pi\)
0.680975 + 0.732306i \(0.261556\pi\)
\(158\) −29.2068 −2.32357
\(159\) −7.56738 −0.600132
\(160\) −0.336798 −0.0266262
\(161\) 4.62879 0.364799
\(162\) 0.122178 0.00959923
\(163\) −0.317234 −0.0248477 −0.0124238 0.999923i \(-0.503955\pi\)
−0.0124238 + 0.999923i \(0.503955\pi\)
\(164\) −26.7689 −2.09030
\(165\) −0.0906055 −0.00705363
\(166\) 31.2049 2.42197
\(167\) −17.2292 −1.33323 −0.666616 0.745401i \(-0.732258\pi\)
−0.666616 + 0.745401i \(0.732258\pi\)
\(168\) 61.1308 4.71635
\(169\) 7.14109 0.549315
\(170\) −0.00946519 −0.000725947 0
\(171\) −18.5033 −1.41498
\(172\) −49.8299 −3.79950
\(173\) 8.01130 0.609088 0.304544 0.952498i \(-0.401496\pi\)
0.304544 + 0.952498i \(0.401496\pi\)
\(174\) −66.8649 −5.06901
\(175\) −10.2320 −0.773466
\(176\) 51.4906 3.88125
\(177\) −11.7013 −0.879524
\(178\) 29.4832 2.20986
\(179\) 23.2943 1.74110 0.870548 0.492083i \(-0.163764\pi\)
0.870548 + 0.492083i \(0.163764\pi\)
\(180\) 0.321871 0.0239908
\(181\) −5.16127 −0.383634 −0.191817 0.981431i \(-0.561438\pi\)
−0.191817 + 0.981431i \(0.561438\pi\)
\(182\) 25.6740 1.90309
\(183\) 25.5257 1.88692
\(184\) −24.1188 −1.77806
\(185\) −0.0544880 −0.00400604
\(186\) −39.7786 −2.91671
\(187\) 0.839807 0.0614128
\(188\) −51.2611 −3.73860
\(189\) −10.5919 −0.770446
\(190\) 0.121848 0.00883978
\(191\) 12.9250 0.935220 0.467610 0.883935i \(-0.345115\pi\)
0.467610 + 0.883935i \(0.345115\pi\)
\(192\) −129.110 −9.31769
\(193\) 3.16917 0.228122 0.114061 0.993474i \(-0.463614\pi\)
0.114061 + 0.993474i \(0.463614\pi\)
\(194\) 20.1829 1.44905
\(195\) 0.143566 0.0102810
\(196\) −16.3506 −1.16790
\(197\) 5.10470 0.363695 0.181848 0.983327i \(-0.441792\pi\)
0.181848 + 0.983327i \(0.441792\pi\)
\(198\) −38.3813 −2.72764
\(199\) 22.3335 1.58318 0.791589 0.611053i \(-0.209254\pi\)
0.791589 + 0.611053i \(0.209254\pi\)
\(200\) 53.3150 3.76994
\(201\) 28.9221 2.04001
\(202\) −43.4116 −3.05443
\(203\) −17.4735 −1.22640
\(204\) −4.82967 −0.338144
\(205\) −0.0525726 −0.00367183
\(206\) −0.545230 −0.0379880
\(207\) 10.9645 0.762088
\(208\) −81.5879 −5.65710
\(209\) −10.8111 −0.747817
\(210\) 0.183005 0.0126286
\(211\) −2.93558 −0.202094 −0.101047 0.994882i \(-0.532219\pi\)
−0.101047 + 0.994882i \(0.532219\pi\)
\(212\) 15.7069 1.07876
\(213\) 19.8151 1.35771
\(214\) −19.9666 −1.36489
\(215\) −0.0978631 −0.00667421
\(216\) 55.1902 3.75522
\(217\) −10.3952 −0.705671
\(218\) −39.6699 −2.68679
\(219\) 46.0137 3.10932
\(220\) 0.188062 0.0126791
\(221\) −1.33069 −0.0895119
\(222\) −37.3661 −2.50785
\(223\) −19.9098 −1.33326 −0.666629 0.745390i \(-0.732263\pi\)
−0.666629 + 0.745390i \(0.732263\pi\)
\(224\) −60.3570 −4.03277
\(225\) −24.2373 −1.61582
\(226\) −17.8829 −1.18955
\(227\) 25.5590 1.69641 0.848205 0.529668i \(-0.177683\pi\)
0.848205 + 0.529668i \(0.177683\pi\)
\(228\) 62.1736 4.11755
\(229\) −29.2406 −1.93227 −0.966137 0.258031i \(-0.916926\pi\)
−0.966137 + 0.258031i \(0.916926\pi\)
\(230\) −0.0722037 −0.00476097
\(231\) −16.2373 −1.06834
\(232\) 91.0479 5.97759
\(233\) 15.9418 1.04438 0.522192 0.852828i \(-0.325115\pi\)
0.522192 + 0.852828i \(0.325115\pi\)
\(234\) 60.8160 3.97566
\(235\) −0.100674 −0.00656724
\(236\) 24.2874 1.58097
\(237\) −29.2685 −1.90120
\(238\) −1.69624 −0.109951
\(239\) 7.60391 0.491856 0.245928 0.969288i \(-0.420907\pi\)
0.245928 + 0.969288i \(0.420907\pi\)
\(240\) −0.581560 −0.0375395
\(241\) 19.3748 1.24804 0.624021 0.781407i \(-0.285498\pi\)
0.624021 + 0.781407i \(0.285498\pi\)
\(242\) 8.32456 0.535123
\(243\) 15.6496 1.00392
\(244\) −52.9815 −3.39179
\(245\) −0.0321117 −0.00205154
\(246\) −36.0525 −2.29863
\(247\) 17.1303 1.08998
\(248\) 54.1653 3.43950
\(249\) 31.2708 1.98171
\(250\) 0.319219 0.0201892
\(251\) −9.34290 −0.589719 −0.294859 0.955541i \(-0.595273\pi\)
−0.294859 + 0.955541i \(0.595273\pi\)
\(252\) 57.6820 3.63363
\(253\) 6.40633 0.402763
\(254\) 5.98060 0.375256
\(255\) −0.00948519 −0.000593985 0
\(256\) 103.086 6.44290
\(257\) −23.3233 −1.45487 −0.727435 0.686176i \(-0.759288\pi\)
−0.727435 + 0.686176i \(0.759288\pi\)
\(258\) −67.1113 −4.17817
\(259\) −9.76473 −0.606751
\(260\) −0.297987 −0.0184804
\(261\) −41.3908 −2.56203
\(262\) −16.3885 −1.01248
\(263\) 10.1041 0.623048 0.311524 0.950238i \(-0.399161\pi\)
0.311524 + 0.950238i \(0.399161\pi\)
\(264\) 84.6063 5.20716
\(265\) 0.0308475 0.00189495
\(266\) 21.8362 1.33886
\(267\) 29.5455 1.80816
\(268\) −60.0310 −3.66698
\(269\) −20.9829 −1.27935 −0.639676 0.768645i \(-0.720931\pi\)
−0.639676 + 0.768645i \(0.720931\pi\)
\(270\) 0.165221 0.0100550
\(271\) −8.31265 −0.504958 −0.252479 0.967602i \(-0.581246\pi\)
−0.252479 + 0.967602i \(0.581246\pi\)
\(272\) 5.39038 0.326840
\(273\) 25.7283 1.55715
\(274\) −1.22988 −0.0742995
\(275\) −14.1613 −0.853958
\(276\) −36.8423 −2.21765
\(277\) −14.6574 −0.880680 −0.440340 0.897831i \(-0.645142\pi\)
−0.440340 + 0.897831i \(0.645142\pi\)
\(278\) −41.9890 −2.51833
\(279\) −24.6238 −1.47419
\(280\) −0.249193 −0.0148921
\(281\) −7.22490 −0.431001 −0.215501 0.976504i \(-0.569138\pi\)
−0.215501 + 0.976504i \(0.569138\pi\)
\(282\) −69.0388 −4.11120
\(283\) 8.03331 0.477531 0.238765 0.971077i \(-0.423257\pi\)
0.238765 + 0.971077i \(0.423257\pi\)
\(284\) −41.1284 −2.44052
\(285\) 0.122105 0.00723290
\(286\) 35.5334 2.10113
\(287\) −9.42146 −0.556131
\(288\) −142.972 −8.42471
\(289\) −16.9121 −0.994828
\(290\) 0.272567 0.0160057
\(291\) 20.2256 1.18564
\(292\) −95.5066 −5.58910
\(293\) −10.0692 −0.588249 −0.294124 0.955767i \(-0.595028\pi\)
−0.294124 + 0.955767i \(0.595028\pi\)
\(294\) −22.0211 −1.28430
\(295\) 0.0476990 0.00277714
\(296\) 50.8803 2.95736
\(297\) −14.6594 −0.850623
\(298\) −45.7894 −2.65251
\(299\) −10.1510 −0.587045
\(300\) 81.4405 4.70197
\(301\) −17.5379 −1.01087
\(302\) 12.7054 0.731116
\(303\) −43.5034 −2.49920
\(304\) −69.3918 −3.97989
\(305\) −0.104053 −0.00595803
\(306\) −4.01801 −0.229695
\(307\) −33.3082 −1.90100 −0.950498 0.310729i \(-0.899427\pi\)
−0.950498 + 0.310729i \(0.899427\pi\)
\(308\) 33.7023 1.92037
\(309\) −0.546383 −0.0310826
\(310\) 0.162153 0.00920965
\(311\) 23.5089 1.33307 0.666533 0.745475i \(-0.267777\pi\)
0.666533 + 0.745475i \(0.267777\pi\)
\(312\) −134.060 −7.58967
\(313\) 8.74768 0.494448 0.247224 0.968958i \(-0.420482\pi\)
0.247224 + 0.968958i \(0.420482\pi\)
\(314\) −47.7048 −2.69214
\(315\) 0.113284 0.00638284
\(316\) 60.7501 3.41746
\(317\) 20.1567 1.13211 0.566056 0.824367i \(-0.308469\pi\)
0.566056 + 0.824367i \(0.308469\pi\)
\(318\) 21.1542 1.18627
\(319\) −24.1837 −1.35403
\(320\) 0.526300 0.0294211
\(321\) −20.0088 −1.11678
\(322\) −12.9395 −0.721091
\(323\) −1.13177 −0.0629736
\(324\) −0.254130 −0.0141184
\(325\) 22.4388 1.24468
\(326\) 0.886810 0.0491159
\(327\) −39.7538 −2.19839
\(328\) 49.0916 2.71063
\(329\) −18.0416 −0.994668
\(330\) 0.253283 0.0139428
\(331\) 22.3708 1.22961 0.614805 0.788679i \(-0.289235\pi\)
0.614805 + 0.788679i \(0.289235\pi\)
\(332\) −64.9061 −3.56218
\(333\) −23.1304 −1.26754
\(334\) 48.1632 2.63537
\(335\) −0.117897 −0.00644143
\(336\) −104.221 −5.68570
\(337\) −16.8980 −0.920495 −0.460247 0.887791i \(-0.652239\pi\)
−0.460247 + 0.887791i \(0.652239\pi\)
\(338\) −19.9625 −1.08582
\(339\) −17.9206 −0.973316
\(340\) 0.0196876 0.00106771
\(341\) −14.3871 −0.779107
\(342\) 51.7250 2.79697
\(343\) −20.0799 −1.08421
\(344\) 91.3834 4.92706
\(345\) −0.0723562 −0.00389553
\(346\) −22.3952 −1.20397
\(347\) 28.0395 1.50524 0.752620 0.658455i \(-0.228790\pi\)
0.752620 + 0.658455i \(0.228790\pi\)
\(348\) 139.079 7.45540
\(349\) 8.43495 0.451513 0.225756 0.974184i \(-0.427515\pi\)
0.225756 + 0.974184i \(0.427515\pi\)
\(350\) 28.6030 1.52889
\(351\) 23.2280 1.23982
\(352\) −83.5354 −4.45245
\(353\) −14.2815 −0.760128 −0.380064 0.924960i \(-0.624098\pi\)
−0.380064 + 0.924960i \(0.624098\pi\)
\(354\) 32.7104 1.73854
\(355\) −0.0807738 −0.00428703
\(356\) −61.3250 −3.25022
\(357\) −1.69983 −0.0899644
\(358\) −65.1179 −3.44159
\(359\) 3.99165 0.210671 0.105336 0.994437i \(-0.466408\pi\)
0.105336 + 0.994437i \(0.466408\pi\)
\(360\) −0.590281 −0.0311105
\(361\) −4.43037 −0.233177
\(362\) 14.4280 0.758321
\(363\) 8.34215 0.437849
\(364\) −53.4019 −2.79902
\(365\) −0.187569 −0.00981783
\(366\) −71.3558 −3.72983
\(367\) −26.2953 −1.37261 −0.686303 0.727316i \(-0.740767\pi\)
−0.686303 + 0.727316i \(0.740767\pi\)
\(368\) 41.1197 2.14351
\(369\) −22.3173 −1.16179
\(370\) 0.152318 0.00791866
\(371\) 5.52814 0.287007
\(372\) 82.7393 4.28983
\(373\) 33.1377 1.71581 0.857903 0.513812i \(-0.171767\pi\)
0.857903 + 0.513812i \(0.171767\pi\)
\(374\) −2.34763 −0.121393
\(375\) 0.319893 0.0165192
\(376\) 94.0081 4.84810
\(377\) 38.3196 1.97356
\(378\) 29.6090 1.52292
\(379\) −0.235235 −0.0120832 −0.00604160 0.999982i \(-0.501923\pi\)
−0.00604160 + 0.999982i \(0.501923\pi\)
\(380\) −0.253443 −0.0130014
\(381\) 5.99324 0.307043
\(382\) −36.1311 −1.84863
\(383\) −10.5833 −0.540779 −0.270390 0.962751i \(-0.587153\pi\)
−0.270390 + 0.962751i \(0.587153\pi\)
\(384\) 195.676 9.98553
\(385\) 0.0661894 0.00337332
\(386\) −8.85924 −0.450924
\(387\) −41.5433 −2.11177
\(388\) −41.9804 −2.13123
\(389\) 0.890161 0.0451329 0.0225665 0.999745i \(-0.492816\pi\)
0.0225665 + 0.999745i \(0.492816\pi\)
\(390\) −0.401331 −0.0203222
\(391\) 0.670657 0.0339166
\(392\) 29.9855 1.51450
\(393\) −16.4231 −0.828435
\(394\) −14.2699 −0.718908
\(395\) 0.119310 0.00600313
\(396\) 79.8331 4.01176
\(397\) 14.2263 0.713997 0.356999 0.934105i \(-0.383800\pi\)
0.356999 + 0.934105i \(0.383800\pi\)
\(398\) −62.4321 −3.12944
\(399\) 21.8823 1.09549
\(400\) −90.8956 −4.54478
\(401\) 16.7337 0.835643 0.417822 0.908529i \(-0.362794\pi\)
0.417822 + 0.908529i \(0.362794\pi\)
\(402\) −80.8501 −4.03244
\(403\) 22.7967 1.13558
\(404\) 90.2960 4.49240
\(405\) −0.000499098 0 −2.48004e−5 0
\(406\) 48.8463 2.42420
\(407\) −13.5146 −0.669893
\(408\) 8.85715 0.438494
\(409\) 4.10538 0.202998 0.101499 0.994836i \(-0.467636\pi\)
0.101499 + 0.994836i \(0.467636\pi\)
\(410\) 0.146964 0.00725803
\(411\) −1.23247 −0.0607935
\(412\) 1.13408 0.0558720
\(413\) 8.54807 0.420623
\(414\) −30.6508 −1.50640
\(415\) −0.127472 −0.00625735
\(416\) 132.363 6.48965
\(417\) −42.0777 −2.06055
\(418\) 30.2217 1.47819
\(419\) 28.0980 1.37268 0.686338 0.727283i \(-0.259217\pi\)
0.686338 + 0.727283i \(0.259217\pi\)
\(420\) −0.380650 −0.0185738
\(421\) 17.2177 0.839139 0.419569 0.907723i \(-0.362181\pi\)
0.419569 + 0.907723i \(0.362181\pi\)
\(422\) 8.20627 0.399475
\(423\) −42.7365 −2.07792
\(424\) −28.8050 −1.39890
\(425\) −1.48250 −0.0719117
\(426\) −55.3920 −2.68375
\(427\) −18.6471 −0.902398
\(428\) 41.5304 2.00745
\(429\) 35.6085 1.71919
\(430\) 0.273571 0.0131928
\(431\) −37.4389 −1.80337 −0.901685 0.432393i \(-0.857669\pi\)
−0.901685 + 0.432393i \(0.857669\pi\)
\(432\) −94.0926 −4.52703
\(433\) 30.5454 1.46792 0.733958 0.679195i \(-0.237671\pi\)
0.733958 + 0.679195i \(0.237671\pi\)
\(434\) 29.0592 1.39488
\(435\) 0.273143 0.0130962
\(436\) 82.5133 3.95167
\(437\) −8.63355 −0.412999
\(438\) −128.629 −6.14613
\(439\) 3.44668 0.164501 0.0822505 0.996612i \(-0.473789\pi\)
0.0822505 + 0.996612i \(0.473789\pi\)
\(440\) −0.344888 −0.0164419
\(441\) −13.6316 −0.649122
\(442\) 3.71987 0.176936
\(443\) −10.1765 −0.483501 −0.241750 0.970338i \(-0.577721\pi\)
−0.241750 + 0.970338i \(0.577721\pi\)
\(444\) 77.7213 3.68849
\(445\) −0.120439 −0.00570934
\(446\) 55.6567 2.63542
\(447\) −45.8862 −2.17034
\(448\) 94.3175 4.45608
\(449\) 18.5161 0.873828 0.436914 0.899503i \(-0.356071\pi\)
0.436914 + 0.899503i \(0.356071\pi\)
\(450\) 67.7540 3.19395
\(451\) −13.0395 −0.614006
\(452\) 37.1963 1.74957
\(453\) 12.7323 0.598215
\(454\) −71.4488 −3.35326
\(455\) −0.104878 −0.00491677
\(456\) −114.021 −5.33950
\(457\) 39.9782 1.87010 0.935050 0.354516i \(-0.115354\pi\)
0.935050 + 0.354516i \(0.115354\pi\)
\(458\) 81.7405 3.81948
\(459\) −1.53464 −0.0716309
\(460\) 0.150183 0.00700234
\(461\) 2.48689 0.115826 0.0579130 0.998322i \(-0.481555\pi\)
0.0579130 + 0.998322i \(0.481555\pi\)
\(462\) 45.3905 2.11176
\(463\) −39.9679 −1.85746 −0.928732 0.370751i \(-0.879100\pi\)
−0.928732 + 0.370751i \(0.879100\pi\)
\(464\) −155.225 −7.20616
\(465\) 0.162495 0.00753554
\(466\) −44.5645 −2.06441
\(467\) −15.8949 −0.735527 −0.367763 0.929919i \(-0.619876\pi\)
−0.367763 + 0.929919i \(0.619876\pi\)
\(468\) −126.497 −5.84733
\(469\) −21.1282 −0.975612
\(470\) 0.281429 0.0129813
\(471\) −47.8056 −2.20277
\(472\) −44.5407 −2.05015
\(473\) −24.2728 −1.11607
\(474\) 81.8186 3.75806
\(475\) 19.0846 0.875661
\(476\) 3.52818 0.161714
\(477\) 13.0949 0.599575
\(478\) −21.2563 −0.972241
\(479\) −9.25773 −0.422997 −0.211498 0.977378i \(-0.567834\pi\)
−0.211498 + 0.977378i \(0.567834\pi\)
\(480\) 0.943489 0.0430642
\(481\) 21.4141 0.976399
\(482\) −54.1613 −2.46698
\(483\) −12.9669 −0.590013
\(484\) −17.3151 −0.787048
\(485\) −0.0824471 −0.00374373
\(486\) −43.7476 −1.98443
\(487\) −6.90361 −0.312833 −0.156416 0.987691i \(-0.549994\pi\)
−0.156416 + 0.987691i \(0.549994\pi\)
\(488\) 97.1630 4.39836
\(489\) 0.888684 0.0401877
\(490\) 0.0897665 0.00405524
\(491\) −29.3402 −1.32411 −0.662053 0.749457i \(-0.730315\pi\)
−0.662053 + 0.749457i \(0.730315\pi\)
\(492\) 74.9891 3.38077
\(493\) −2.53171 −0.114023
\(494\) −47.8869 −2.15453
\(495\) 0.156788 0.00704708
\(496\) −92.3452 −4.14642
\(497\) −14.4754 −0.649309
\(498\) −87.4159 −3.91720
\(499\) −18.0955 −0.810068 −0.405034 0.914302i \(-0.632740\pi\)
−0.405034 + 0.914302i \(0.632740\pi\)
\(500\) −0.663974 −0.0296938
\(501\) 48.2650 2.15632
\(502\) 26.1176 1.16568
\(503\) 27.4886 1.22566 0.612828 0.790217i \(-0.290032\pi\)
0.612828 + 0.790217i \(0.290032\pi\)
\(504\) −105.783 −4.71197
\(505\) 0.177336 0.00789136
\(506\) −17.9086 −0.796132
\(507\) −20.0047 −0.888441
\(508\) −12.4396 −0.551920
\(509\) −21.8882 −0.970178 −0.485089 0.874465i \(-0.661213\pi\)
−0.485089 + 0.874465i \(0.661213\pi\)
\(510\) 0.0265153 0.00117412
\(511\) −33.6141 −1.48700
\(512\) −148.472 −6.56158
\(513\) 19.7558 0.872242
\(514\) 65.1992 2.87581
\(515\) 0.00222726 9.81450e−5 0
\(516\) 139.591 6.14516
\(517\) −24.9700 −1.09818
\(518\) 27.2968 1.19935
\(519\) −22.4425 −0.985116
\(520\) 0.546481 0.0239648
\(521\) −19.6099 −0.859126 −0.429563 0.903037i \(-0.641332\pi\)
−0.429563 + 0.903037i \(0.641332\pi\)
\(522\) 115.706 5.06430
\(523\) 28.6317 1.25198 0.625989 0.779832i \(-0.284695\pi\)
0.625989 + 0.779832i \(0.284695\pi\)
\(524\) 34.0879 1.48914
\(525\) 28.6634 1.25097
\(526\) −28.2456 −1.23157
\(527\) −1.50614 −0.0656085
\(528\) −144.243 −6.27739
\(529\) −17.8840 −0.777565
\(530\) −0.0862326 −0.00374570
\(531\) 20.2484 0.878707
\(532\) −45.4192 −1.96917
\(533\) 20.6613 0.894941
\(534\) −82.5929 −3.57414
\(535\) 0.0815634 0.00352629
\(536\) 110.091 4.75522
\(537\) −65.2555 −2.81598
\(538\) 58.6567 2.52887
\(539\) −7.96461 −0.343060
\(540\) −0.343659 −0.0147887
\(541\) 15.6578 0.673180 0.336590 0.941651i \(-0.390726\pi\)
0.336590 + 0.941651i \(0.390726\pi\)
\(542\) 23.2376 0.998139
\(543\) 14.4585 0.620475
\(544\) −8.74504 −0.374940
\(545\) 0.162051 0.00694152
\(546\) −71.9221 −3.07798
\(547\) 15.5171 0.663461 0.331731 0.943374i \(-0.392367\pi\)
0.331731 + 0.943374i \(0.392367\pi\)
\(548\) 2.55814 0.109278
\(549\) −44.1708 −1.88516
\(550\) 39.5871 1.68800
\(551\) 32.5914 1.38844
\(552\) 67.5654 2.87577
\(553\) 21.3813 0.909227
\(554\) 40.9741 1.74082
\(555\) 0.152640 0.00647922
\(556\) 87.3369 3.70391
\(557\) −4.22462 −0.179003 −0.0895014 0.995987i \(-0.528527\pi\)
−0.0895014 + 0.995987i \(0.528527\pi\)
\(558\) 68.8345 2.91400
\(559\) 38.4608 1.62672
\(560\) 0.424843 0.0179529
\(561\) −2.35260 −0.0993267
\(562\) 20.1968 0.851951
\(563\) 17.1645 0.723396 0.361698 0.932295i \(-0.382197\pi\)
0.361698 + 0.932295i \(0.382197\pi\)
\(564\) 143.601 6.04667
\(565\) 0.0730514 0.00307329
\(566\) −22.4567 −0.943925
\(567\) −0.0894426 −0.00375624
\(568\) 75.4256 3.16479
\(569\) −3.76276 −0.157743 −0.0788716 0.996885i \(-0.525132\pi\)
−0.0788716 + 0.996885i \(0.525132\pi\)
\(570\) −0.341339 −0.0142971
\(571\) 29.9350 1.25274 0.626370 0.779526i \(-0.284540\pi\)
0.626370 + 0.779526i \(0.284540\pi\)
\(572\) −73.9093 −3.09030
\(573\) −36.2075 −1.51259
\(574\) 26.3372 1.09929
\(575\) −11.3090 −0.471618
\(576\) 223.417 9.30903
\(577\) 19.8565 0.826636 0.413318 0.910587i \(-0.364370\pi\)
0.413318 + 0.910587i \(0.364370\pi\)
\(578\) 47.2768 1.96646
\(579\) −8.87796 −0.368956
\(580\) −0.566938 −0.0235408
\(581\) −22.8441 −0.947731
\(582\) −56.5395 −2.34364
\(583\) 7.65106 0.316875
\(584\) 175.150 7.24776
\(585\) −0.248433 −0.0102714
\(586\) 28.1479 1.16278
\(587\) −8.15324 −0.336520 −0.168260 0.985743i \(-0.553815\pi\)
−0.168260 + 0.985743i \(0.553815\pi\)
\(588\) 45.8038 1.88892
\(589\) 19.3890 0.798908
\(590\) −0.133340 −0.00548952
\(591\) −14.3001 −0.588227
\(592\) −86.7446 −3.56518
\(593\) 47.0412 1.93175 0.965876 0.259004i \(-0.0833944\pi\)
0.965876 + 0.259004i \(0.0833944\pi\)
\(594\) 40.9795 1.68141
\(595\) 0.00692915 0.000284067 0
\(596\) 95.2418 3.90126
\(597\) −62.5640 −2.56057
\(598\) 28.3764 1.16040
\(599\) 2.63317 0.107589 0.0537943 0.998552i \(-0.482868\pi\)
0.0537943 + 0.998552i \(0.482868\pi\)
\(600\) −149.354 −6.09736
\(601\) −28.5421 −1.16426 −0.582128 0.813097i \(-0.697780\pi\)
−0.582128 + 0.813097i \(0.697780\pi\)
\(602\) 49.0263 1.99816
\(603\) −50.0480 −2.03811
\(604\) −26.4273 −1.07531
\(605\) −0.0340058 −0.00138253
\(606\) 121.611 4.94012
\(607\) 43.3050 1.75770 0.878848 0.477101i \(-0.158312\pi\)
0.878848 + 0.477101i \(0.158312\pi\)
\(608\) 112.577 4.56561
\(609\) 48.9495 1.98353
\(610\) 0.290873 0.0117771
\(611\) 39.5654 1.60065
\(612\) 8.35746 0.337830
\(613\) −2.75874 −0.111425 −0.0557123 0.998447i \(-0.517743\pi\)
−0.0557123 + 0.998447i \(0.517743\pi\)
\(614\) 93.1112 3.75766
\(615\) 0.147274 0.00593868
\(616\) −61.8068 −2.49027
\(617\) 15.5746 0.627010 0.313505 0.949587i \(-0.398497\pi\)
0.313505 + 0.949587i \(0.398497\pi\)
\(618\) 1.52738 0.0614404
\(619\) −7.12769 −0.286486 −0.143243 0.989688i \(-0.545753\pi\)
−0.143243 + 0.989688i \(0.545753\pi\)
\(620\) −0.337277 −0.0135454
\(621\) −11.7068 −0.469776
\(622\) −65.7178 −2.63505
\(623\) −21.5837 −0.864731
\(624\) 228.556 9.14958
\(625\) 24.9980 0.999922
\(626\) −24.4537 −0.977365
\(627\) 30.2856 1.20949
\(628\) 99.2259 3.95954
\(629\) −1.41480 −0.0564116
\(630\) −0.316680 −0.0126168
\(631\) −36.5200 −1.45384 −0.726918 0.686724i \(-0.759048\pi\)
−0.726918 + 0.686724i \(0.759048\pi\)
\(632\) −111.410 −4.43165
\(633\) 8.22361 0.326859
\(634\) −56.3469 −2.23782
\(635\) −0.0244307 −0.000969504 0
\(636\) −44.0007 −1.74474
\(637\) 12.6201 0.500025
\(638\) 67.6043 2.67648
\(639\) −34.2888 −1.35645
\(640\) −0.797648 −0.0315298
\(641\) 8.97926 0.354660 0.177330 0.984151i \(-0.443254\pi\)
0.177330 + 0.984151i \(0.443254\pi\)
\(642\) 55.9335 2.20752
\(643\) 6.43155 0.253636 0.126818 0.991926i \(-0.459524\pi\)
0.126818 + 0.991926i \(0.459524\pi\)
\(644\) 26.9142 1.06057
\(645\) 0.274149 0.0107946
\(646\) 3.16381 0.124479
\(647\) −30.9828 −1.21806 −0.609029 0.793148i \(-0.708441\pi\)
−0.609029 + 0.793148i \(0.708441\pi\)
\(648\) 0.466051 0.0183082
\(649\) 11.8307 0.464396
\(650\) −62.7265 −2.46034
\(651\) 29.1206 1.14132
\(652\) −1.84456 −0.0722386
\(653\) 26.9923 1.05629 0.528144 0.849155i \(-0.322888\pi\)
0.528144 + 0.849155i \(0.322888\pi\)
\(654\) 111.130 4.34551
\(655\) 0.0669468 0.00261583
\(656\) −83.6952 −3.26775
\(657\) −79.6241 −3.10643
\(658\) 50.4344 1.96614
\(659\) −16.3289 −0.636082 −0.318041 0.948077i \(-0.603025\pi\)
−0.318041 + 0.948077i \(0.603025\pi\)
\(660\) −0.526827 −0.0205067
\(661\) 7.11354 0.276685 0.138342 0.990384i \(-0.455823\pi\)
0.138342 + 0.990384i \(0.455823\pi\)
\(662\) −62.5364 −2.43054
\(663\) 3.72773 0.144773
\(664\) 119.032 4.61932
\(665\) −0.0892008 −0.00345906
\(666\) 64.6598 2.50552
\(667\) −19.3128 −0.747793
\(668\) −100.179 −3.87605
\(669\) 55.7743 2.15636
\(670\) 0.329576 0.0127326
\(671\) −25.8080 −0.996307
\(672\) 169.081 6.52246
\(673\) 11.8750 0.457747 0.228873 0.973456i \(-0.426496\pi\)
0.228873 + 0.973456i \(0.426496\pi\)
\(674\) 47.2375 1.81952
\(675\) 25.8780 0.996043
\(676\) 41.5220 1.59700
\(677\) 5.95851 0.229004 0.114502 0.993423i \(-0.463473\pi\)
0.114502 + 0.993423i \(0.463473\pi\)
\(678\) 50.0962 1.92393
\(679\) −14.7752 −0.567021
\(680\) −0.0361051 −0.00138457
\(681\) −71.5998 −2.74371
\(682\) 40.2185 1.54004
\(683\) 3.46453 0.132567 0.0662833 0.997801i \(-0.478886\pi\)
0.0662833 + 0.997801i \(0.478886\pi\)
\(684\) −107.588 −4.11372
\(685\) 0.00502404 0.000191959 0
\(686\) 56.1322 2.14314
\(687\) 81.9132 3.12519
\(688\) −155.798 −5.93973
\(689\) −12.1233 −0.461859
\(690\) 0.202268 0.00770021
\(691\) −29.8821 −1.13677 −0.568384 0.822763i \(-0.692431\pi\)
−0.568384 + 0.822763i \(0.692431\pi\)
\(692\) 46.5819 1.77078
\(693\) 28.0977 1.06734
\(694\) −78.3830 −2.97538
\(695\) 0.171525 0.00650630
\(696\) −255.057 −9.66792
\(697\) −1.36506 −0.0517054
\(698\) −23.5794 −0.892495
\(699\) −44.6587 −1.68915
\(700\) −59.4941 −2.24867
\(701\) 19.8498 0.749718 0.374859 0.927082i \(-0.377691\pi\)
0.374859 + 0.927082i \(0.377691\pi\)
\(702\) −64.9328 −2.45073
\(703\) 18.2131 0.686918
\(704\) 130.537 4.91981
\(705\) 0.282023 0.0106216
\(706\) 39.9232 1.50253
\(707\) 31.7802 1.19522
\(708\) −68.0375 −2.55700
\(709\) −41.3929 −1.55454 −0.777271 0.629166i \(-0.783397\pi\)
−0.777271 + 0.629166i \(0.783397\pi\)
\(710\) 0.225799 0.00847408
\(711\) 50.6475 1.89943
\(712\) 112.464 4.21478
\(713\) −11.4894 −0.430280
\(714\) 4.75178 0.177831
\(715\) −0.145154 −0.00542844
\(716\) 135.445 5.06182
\(717\) −21.3012 −0.795509
\(718\) −11.1584 −0.416429
\(719\) 26.9170 1.00383 0.501917 0.864916i \(-0.332628\pi\)
0.501917 + 0.864916i \(0.332628\pi\)
\(720\) 1.00636 0.0375047
\(721\) 0.399145 0.0148649
\(722\) 12.3849 0.460917
\(723\) −54.2758 −2.01854
\(724\) −30.0103 −1.11532
\(725\) 42.6911 1.58551
\(726\) −23.3200 −0.865487
\(727\) −17.1819 −0.637241 −0.318620 0.947882i \(-0.603219\pi\)
−0.318620 + 0.947882i \(0.603219\pi\)
\(728\) 97.9341 3.62968
\(729\) −43.7090 −1.61885
\(730\) 0.524340 0.0194067
\(731\) −2.54104 −0.0939838
\(732\) 148.420 5.48575
\(733\) −23.9574 −0.884889 −0.442444 0.896796i \(-0.645889\pi\)
−0.442444 + 0.896796i \(0.645889\pi\)
\(734\) 73.5072 2.71320
\(735\) 0.0899561 0.00331808
\(736\) −66.7101 −2.45897
\(737\) −29.2419 −1.07714
\(738\) 62.3868 2.29649
\(739\) 33.6922 1.23939 0.619694 0.784843i \(-0.287257\pi\)
0.619694 + 0.784843i \(0.287257\pi\)
\(740\) −0.316822 −0.0116466
\(741\) −47.9881 −1.76289
\(742\) −15.4536 −0.567320
\(743\) −27.6938 −1.01599 −0.507994 0.861361i \(-0.669613\pi\)
−0.507994 + 0.861361i \(0.669613\pi\)
\(744\) −151.736 −5.56292
\(745\) 0.187049 0.00685296
\(746\) −92.6347 −3.39160
\(747\) −54.1124 −1.97987
\(748\) 4.88307 0.178543
\(749\) 14.6169 0.534089
\(750\) −0.894244 −0.0326532
\(751\) −25.6372 −0.935516 −0.467758 0.883857i \(-0.654938\pi\)
−0.467758 + 0.883857i \(0.654938\pi\)
\(752\) −160.272 −5.84453
\(753\) 26.1728 0.953788
\(754\) −107.120 −3.90109
\(755\) −0.0519016 −0.00188889
\(756\) −61.5867 −2.23989
\(757\) −4.76737 −0.173273 −0.0866366 0.996240i \(-0.527612\pi\)
−0.0866366 + 0.996240i \(0.527612\pi\)
\(758\) 0.657587 0.0238846
\(759\) −17.9464 −0.651413
\(760\) 0.464791 0.0168597
\(761\) 30.0482 1.08925 0.544623 0.838681i \(-0.316673\pi\)
0.544623 + 0.838681i \(0.316673\pi\)
\(762\) −16.7538 −0.606926
\(763\) 29.0410 1.05136
\(764\) 75.1527 2.71893
\(765\) 0.0164136 0.000593434 0
\(766\) 29.5849 1.06895
\(767\) −18.7460 −0.676878
\(768\) −288.781 −10.4205
\(769\) 32.0385 1.15534 0.577668 0.816272i \(-0.303963\pi\)
0.577668 + 0.816272i \(0.303963\pi\)
\(770\) −0.185029 −0.00666798
\(771\) 65.3369 2.35305
\(772\) 18.4272 0.663209
\(773\) −6.70720 −0.241241 −0.120621 0.992699i \(-0.538488\pi\)
−0.120621 + 0.992699i \(0.538488\pi\)
\(774\) 116.132 4.17429
\(775\) 25.3974 0.912301
\(776\) 76.9881 2.76371
\(777\) 27.3545 0.981336
\(778\) −2.48840 −0.0892133
\(779\) 17.5728 0.629611
\(780\) 0.834768 0.0298895
\(781\) −20.0342 −0.716880
\(782\) −1.87479 −0.0670422
\(783\) 44.1927 1.57932
\(784\) −51.1216 −1.82577
\(785\) 0.194874 0.00695535
\(786\) 45.9099 1.63755
\(787\) −41.6414 −1.48435 −0.742177 0.670204i \(-0.766207\pi\)
−0.742177 + 0.670204i \(0.766207\pi\)
\(788\) 29.6814 1.05736
\(789\) −28.3053 −1.00769
\(790\) −0.333524 −0.0118663
\(791\) 13.0914 0.465478
\(792\) −146.406 −5.20232
\(793\) 40.8933 1.45216
\(794\) −39.7688 −1.41134
\(795\) −0.0864148 −0.00306482
\(796\) 129.858 4.60271
\(797\) 11.4007 0.403833 0.201917 0.979403i \(-0.435283\pi\)
0.201917 + 0.979403i \(0.435283\pi\)
\(798\) −61.1709 −2.16543
\(799\) −2.61402 −0.0924775
\(800\) 147.464 5.21363
\(801\) −51.1268 −1.80648
\(802\) −46.7783 −1.65180
\(803\) −46.5225 −1.64175
\(804\) 168.168 5.93083
\(805\) 0.0528579 0.00186300
\(806\) −63.7269 −2.24468
\(807\) 58.7806 2.06918
\(808\) −165.594 −5.82559
\(809\) −8.79100 −0.309075 −0.154538 0.987987i \(-0.549389\pi\)
−0.154538 + 0.987987i \(0.549389\pi\)
\(810\) 0.00139520 4.90224e−5 0
\(811\) 41.3019 1.45031 0.725153 0.688587i \(-0.241769\pi\)
0.725153 + 0.688587i \(0.241769\pi\)
\(812\) −101.600 −3.56547
\(813\) 23.2867 0.816700
\(814\) 37.7793 1.32416
\(815\) −0.00362261 −0.000126895 0
\(816\) −15.1004 −0.528618
\(817\) 32.7115 1.14443
\(818\) −11.4764 −0.401262
\(819\) −44.5213 −1.55570
\(820\) −0.305684 −0.0106750
\(821\) 14.0404 0.490013 0.245006 0.969521i \(-0.421210\pi\)
0.245006 + 0.969521i \(0.421210\pi\)
\(822\) 3.44532 0.120169
\(823\) −17.2200 −0.600250 −0.300125 0.953900i \(-0.597028\pi\)
−0.300125 + 0.953900i \(0.597028\pi\)
\(824\) −2.07979 −0.0724530
\(825\) 39.6708 1.38116
\(826\) −23.8957 −0.831437
\(827\) 54.9549 1.91097 0.955485 0.295041i \(-0.0953334\pi\)
0.955485 + 0.295041i \(0.0953334\pi\)
\(828\) 63.7535 2.21559
\(829\) 5.78512 0.200925 0.100463 0.994941i \(-0.467968\pi\)
0.100463 + 0.994941i \(0.467968\pi\)
\(830\) 0.356341 0.0123688
\(831\) 41.0606 1.42438
\(832\) −206.839 −7.17085
\(833\) −0.833788 −0.0288890
\(834\) 117.626 4.07305
\(835\) −0.196746 −0.00680869
\(836\) −62.8611 −2.17410
\(837\) 26.2907 0.908738
\(838\) −78.5464 −2.71334
\(839\) 41.4352 1.43050 0.715251 0.698868i \(-0.246313\pi\)
0.715251 + 0.698868i \(0.246313\pi\)
\(840\) 0.698077 0.0240859
\(841\) 43.9051 1.51397
\(842\) −48.1311 −1.65871
\(843\) 20.2395 0.697085
\(844\) −17.0690 −0.587540
\(845\) 0.0815469 0.00280530
\(846\) 119.468 4.10738
\(847\) −6.09413 −0.209397
\(848\) 49.1091 1.68641
\(849\) −22.5041 −0.772340
\(850\) 4.14424 0.142146
\(851\) −10.7925 −0.369964
\(852\) 115.215 3.94720
\(853\) 48.4532 1.65901 0.829503 0.558502i \(-0.188624\pi\)
0.829503 + 0.558502i \(0.188624\pi\)
\(854\) 52.1270 1.78375
\(855\) −0.211296 −0.00722618
\(856\) −76.1629 −2.60319
\(857\) −14.4670 −0.494184 −0.247092 0.968992i \(-0.579475\pi\)
−0.247092 + 0.968992i \(0.579475\pi\)
\(858\) −99.5416 −3.39829
\(859\) 16.8019 0.573272 0.286636 0.958040i \(-0.407463\pi\)
0.286636 + 0.958040i \(0.407463\pi\)
\(860\) −0.569027 −0.0194037
\(861\) 26.3928 0.899466
\(862\) 104.659 3.56468
\(863\) −34.2698 −1.16656 −0.583278 0.812272i \(-0.698230\pi\)
−0.583278 + 0.812272i \(0.698230\pi\)
\(864\) 152.650 5.19327
\(865\) 0.0914841 0.00311055
\(866\) −85.3879 −2.90160
\(867\) 47.3767 1.60900
\(868\) −60.4429 −2.05157
\(869\) 29.5922 1.00385
\(870\) −0.763555 −0.0258870
\(871\) 46.3344 1.56998
\(872\) −151.322 −5.12440
\(873\) −34.9992 −1.18454
\(874\) 24.1346 0.816366
\(875\) −0.233689 −0.00790014
\(876\) 267.548 9.03960
\(877\) 6.39451 0.215927 0.107964 0.994155i \(-0.465567\pi\)
0.107964 + 0.994155i \(0.465567\pi\)
\(878\) −9.63500 −0.325166
\(879\) 28.2074 0.951411
\(880\) 0.587991 0.0198212
\(881\) −14.6581 −0.493844 −0.246922 0.969035i \(-0.579419\pi\)
−0.246922 + 0.969035i \(0.579419\pi\)
\(882\) 38.1063 1.28310
\(883\) −21.1515 −0.711805 −0.355903 0.934523i \(-0.615827\pi\)
−0.355903 + 0.934523i \(0.615827\pi\)
\(884\) −7.73732 −0.260234
\(885\) −0.133622 −0.00449164
\(886\) 28.4479 0.955726
\(887\) −36.3024 −1.21891 −0.609457 0.792819i \(-0.708613\pi\)
−0.609457 + 0.792819i \(0.708613\pi\)
\(888\) −142.534 −4.78311
\(889\) −4.37820 −0.146840
\(890\) 0.336680 0.0112855
\(891\) −0.123790 −0.00414713
\(892\) −115.766 −3.87613
\(893\) 33.6510 1.12609
\(894\) 128.272 4.29007
\(895\) 0.266006 0.00889161
\(896\) −142.946 −4.77547
\(897\) 28.4364 0.949464
\(898\) −51.7607 −1.72728
\(899\) 43.3720 1.44654
\(900\) −140.928 −4.69760
\(901\) 0.800964 0.0266840
\(902\) 36.4512 1.21369
\(903\) 49.1299 1.63494
\(904\) −68.2145 −2.26878
\(905\) −0.0589385 −0.00195918
\(906\) −35.5924 −1.18248
\(907\) −35.7582 −1.18733 −0.593665 0.804712i \(-0.702320\pi\)
−0.593665 + 0.804712i \(0.702320\pi\)
\(908\) 148.613 4.93191
\(909\) 75.2800 2.49688
\(910\) 0.293182 0.00971888
\(911\) −36.5844 −1.21210 −0.606048 0.795428i \(-0.707246\pi\)
−0.606048 + 0.795428i \(0.707246\pi\)
\(912\) 194.391 6.43693
\(913\) −31.6166 −1.04636
\(914\) −111.757 −3.69659
\(915\) 0.291488 0.00963630
\(916\) −170.020 −5.61762
\(917\) 11.9974 0.396190
\(918\) 4.29000 0.141591
\(919\) −41.9150 −1.38265 −0.691324 0.722545i \(-0.742972\pi\)
−0.691324 + 0.722545i \(0.742972\pi\)
\(920\) −0.275422 −0.00908040
\(921\) 93.3079 3.07460
\(922\) −6.95196 −0.228951
\(923\) 31.7446 1.04488
\(924\) −94.4120 −3.10593
\(925\) 23.8571 0.784416
\(926\) 111.728 3.67161
\(927\) 0.945484 0.0310538
\(928\) 251.829 8.26668
\(929\) 9.59368 0.314759 0.157379 0.987538i \(-0.449695\pi\)
0.157379 + 0.987538i \(0.449695\pi\)
\(930\) −0.454247 −0.0148953
\(931\) 10.7336 0.351779
\(932\) 92.6940 3.03629
\(933\) −65.8567 −2.15605
\(934\) 44.4332 1.45390
\(935\) 0.00959008 0.000313629 0
\(936\) 231.984 7.58262
\(937\) −0.277619 −0.00906940 −0.00453470 0.999990i \(-0.501443\pi\)
−0.00453470 + 0.999990i \(0.501443\pi\)
\(938\) 59.0629 1.92847
\(939\) −24.5053 −0.799701
\(940\) −0.585370 −0.0190927
\(941\) −20.6316 −0.672571 −0.336285 0.941760i \(-0.609171\pi\)
−0.336285 + 0.941760i \(0.609171\pi\)
\(942\) 133.638 4.35416
\(943\) −10.4131 −0.339099
\(944\) 75.9365 2.47152
\(945\) −0.120953 −0.00393459
\(946\) 67.8534 2.20610
\(947\) 13.2042 0.429078 0.214539 0.976715i \(-0.431175\pi\)
0.214539 + 0.976715i \(0.431175\pi\)
\(948\) −170.183 −5.52727
\(949\) 73.7159 2.39292
\(950\) −53.3500 −1.73090
\(951\) −56.4660 −1.83103
\(952\) −6.47035 −0.209705
\(953\) 11.9856 0.388251 0.194126 0.980977i \(-0.437813\pi\)
0.194126 + 0.980977i \(0.437813\pi\)
\(954\) −36.6061 −1.18517
\(955\) 0.147596 0.00477608
\(956\) 44.2131 1.42995
\(957\) 67.7471 2.18995
\(958\) 25.8795 0.836129
\(959\) 0.900351 0.0290738
\(960\) −1.47435 −0.0475845
\(961\) −5.19758 −0.167664
\(962\) −59.8620 −1.93003
\(963\) 34.6240 1.11574
\(964\) 112.655 3.62838
\(965\) 0.0361900 0.00116500
\(966\) 36.2482 1.16627
\(967\) −1.11335 −0.0358029 −0.0179014 0.999840i \(-0.505699\pi\)
−0.0179014 + 0.999840i \(0.505699\pi\)
\(968\) 31.7542 1.02062
\(969\) 3.17050 0.101851
\(970\) 0.230476 0.00740015
\(971\) 18.7273 0.600989 0.300494 0.953784i \(-0.402848\pi\)
0.300494 + 0.953784i \(0.402848\pi\)
\(972\) 90.9950 2.91866
\(973\) 30.7387 0.985438
\(974\) 19.2987 0.618370
\(975\) −62.8591 −2.01310
\(976\) −165.651 −5.30236
\(977\) −24.4749 −0.783023 −0.391511 0.920173i \(-0.628048\pi\)
−0.391511 + 0.920173i \(0.628048\pi\)
\(978\) −2.48427 −0.0794381
\(979\) −29.8722 −0.954721
\(980\) −0.186714 −0.00596436
\(981\) 68.7916 2.19635
\(982\) 82.0191 2.61733
\(983\) −26.4161 −0.842544 −0.421272 0.906934i \(-0.638416\pi\)
−0.421272 + 0.906934i \(0.638416\pi\)
\(984\) −137.523 −4.38407
\(985\) 0.0582926 0.00185736
\(986\) 7.07726 0.225386
\(987\) 50.5410 1.60874
\(988\) 99.6046 3.16885
\(989\) −19.3839 −0.616373
\(990\) −0.438291 −0.0139298
\(991\) −23.4603 −0.745240 −0.372620 0.927984i \(-0.621540\pi\)
−0.372620 + 0.927984i \(0.621540\pi\)
\(992\) 149.815 4.75664
\(993\) −62.6685 −1.98872
\(994\) 40.4651 1.28347
\(995\) 0.255035 0.00808514
\(996\) 181.825 5.76134
\(997\) 21.5343 0.681999 0.340999 0.940064i \(-0.389235\pi\)
0.340999 + 0.940064i \(0.389235\pi\)
\(998\) 50.5851 1.60124
\(999\) 24.6962 0.781352
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 \(a_p\))