Properties

Label 8041.2.a.j.1.10
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 1.10
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.30649 q^{2}\) \(-1.79768 q^{3}\) \(+3.31992 q^{4}\) \(+3.97246 q^{5}\) \(+4.14634 q^{6}\) \(+2.36407 q^{7}\) \(-3.04439 q^{8}\) \(+0.231661 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.30649 q^{2}\) \(-1.79768 q^{3}\) \(+3.31992 q^{4}\) \(+3.97246 q^{5}\) \(+4.14634 q^{6}\) \(+2.36407 q^{7}\) \(-3.04439 q^{8}\) \(+0.231661 q^{9}\) \(-9.16247 q^{10}\) \(+1.00000 q^{11}\) \(-5.96816 q^{12}\) \(+5.03650 q^{13}\) \(-5.45271 q^{14}\) \(-7.14123 q^{15}\) \(+0.382023 q^{16}\) \(+1.00000 q^{17}\) \(-0.534324 q^{18}\) \(+4.61118 q^{19}\) \(+13.1883 q^{20}\) \(-4.24984 q^{21}\) \(-2.30649 q^{22}\) \(+2.01155 q^{23}\) \(+5.47284 q^{24}\) \(+10.7805 q^{25}\) \(-11.6167 q^{26}\) \(+4.97659 q^{27}\) \(+7.84851 q^{28}\) \(+4.72977 q^{29}\) \(+16.4712 q^{30}\) \(+2.96757 q^{31}\) \(+5.20764 q^{32}\) \(-1.79768 q^{33}\) \(-2.30649 q^{34}\) \(+9.39117 q^{35}\) \(+0.769095 q^{36}\) \(-2.93712 q^{37}\) \(-10.6357 q^{38}\) \(-9.05402 q^{39}\) \(-12.0937 q^{40}\) \(+2.94886 q^{41}\) \(+9.80223 q^{42}\) \(+1.00000 q^{43}\) \(+3.31992 q^{44}\) \(+0.920264 q^{45}\) \(-4.63962 q^{46}\) \(+0.804974 q^{47}\) \(-0.686755 q^{48}\) \(-1.41119 q^{49}\) \(-24.8651 q^{50}\) \(-1.79768 q^{51}\) \(+16.7208 q^{52}\) \(+2.26444 q^{53}\) \(-11.4785 q^{54}\) \(+3.97246 q^{55}\) \(-7.19713 q^{56}\) \(-8.28943 q^{57}\) \(-10.9092 q^{58}\) \(-5.18744 q^{59}\) \(-23.7083 q^{60}\) \(-3.03068 q^{61}\) \(-6.84467 q^{62}\) \(+0.547661 q^{63}\) \(-12.7754 q^{64}\) \(+20.0073 q^{65}\) \(+4.14634 q^{66}\) \(+9.82283 q^{67}\) \(+3.31992 q^{68}\) \(-3.61612 q^{69}\) \(-21.6607 q^{70}\) \(+3.86568 q^{71}\) \(-0.705265 q^{72}\) \(+4.61176 q^{73}\) \(+6.77445 q^{74}\) \(-19.3799 q^{75}\) \(+15.3087 q^{76}\) \(+2.36407 q^{77}\) \(+20.8831 q^{78}\) \(-12.2298 q^{79}\) \(+1.51757 q^{80}\) \(-9.64132 q^{81}\) \(-6.80154 q^{82}\) \(+0.879944 q^{83}\) \(-14.1091 q^{84}\) \(+3.97246 q^{85}\) \(-2.30649 q^{86}\) \(-8.50262 q^{87}\) \(-3.04439 q^{88}\) \(+5.21525 q^{89}\) \(-2.12258 q^{90}\) \(+11.9066 q^{91}\) \(+6.67817 q^{92}\) \(-5.33474 q^{93}\) \(-1.85667 q^{94}\) \(+18.3177 q^{95}\) \(-9.36168 q^{96}\) \(-5.31064 q^{97}\) \(+3.25490 q^{98}\) \(+0.231661 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(82q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 82q^{11} \) \(\mathstrut +\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 26q^{13} \) \(\mathstrut +\mathstrut 17q^{14} \) \(\mathstrut +\mathstrut 66q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut +\mathstrut 82q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 9q^{20} \) \(\mathstrut +\mathstrut 22q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 117q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 30q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 26q^{30} \) \(\mathstrut +\mathstrut 40q^{31} \) \(\mathstrut +\mathstrut 58q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 160q^{36} \) \(\mathstrut +\mathstrut 31q^{37} \) \(\mathstrut +\mathstrut 18q^{38} \) \(\mathstrut +\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 29q^{40} \) \(\mathstrut +\mathstrut 42q^{41} \) \(\mathstrut -\mathstrut 51q^{42} \) \(\mathstrut +\mathstrut 82q^{43} \) \(\mathstrut +\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 84q^{47} \) \(\mathstrut -\mathstrut 46q^{48} \) \(\mathstrut +\mathstrut 136q^{49} \) \(\mathstrut +\mathstrut 59q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut +\mathstrut 83q^{53} \) \(\mathstrut +\mathstrut 24q^{54} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 23q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 96q^{59} \) \(\mathstrut +\mathstrut 184q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 148q^{64} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut +\mathstrut 10q^{66} \) \(\mathstrut +\mathstrut 78q^{67} \) \(\mathstrut +\mathstrut 98q^{68} \) \(\mathstrut +\mathstrut 61q^{69} \) \(\mathstrut -\mathstrut 3q^{70} \) \(\mathstrut +\mathstrut 155q^{71} \) \(\mathstrut +\mathstrut 50q^{72} \) \(\mathstrut -\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 10q^{74} \) \(\mathstrut -\mathstrut 19q^{75} \) \(\mathstrut +\mathstrut 44q^{76} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 27q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 19q^{80} \) \(\mathstrut +\mathstrut 150q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 54q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 11q^{85} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut +\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 81q^{90} \) \(\mathstrut -\mathstrut 14q^{91} \) \(\mathstrut +\mathstrut 60q^{92} \) \(\mathstrut +\mathstrut 36q^{93} \) \(\mathstrut +\mathstrut 19q^{94} \) \(\mathstrut +\mathstrut 111q^{95} \) \(\mathstrut -\mathstrut 6q^{96} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 5q^{98} \) \(\mathstrut +\mathstrut 108q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.30649 −1.63094 −0.815469 0.578801i \(-0.803521\pi\)
−0.815469 + 0.578801i \(0.803521\pi\)
\(3\) −1.79768 −1.03789 −0.518946 0.854807i \(-0.673675\pi\)
−0.518946 + 0.854807i \(0.673675\pi\)
\(4\) 3.31992 1.65996
\(5\) 3.97246 1.77654 0.888270 0.459322i \(-0.151907\pi\)
0.888270 + 0.459322i \(0.151907\pi\)
\(6\) 4.14634 1.69274
\(7\) 2.36407 0.893533 0.446767 0.894651i \(-0.352575\pi\)
0.446767 + 0.894651i \(0.352575\pi\)
\(8\) −3.04439 −1.07635
\(9\) 0.231661 0.0772202
\(10\) −9.16247 −2.89743
\(11\) 1.00000 0.301511
\(12\) −5.96816 −1.72286
\(13\) 5.03650 1.39687 0.698437 0.715672i \(-0.253879\pi\)
0.698437 + 0.715672i \(0.253879\pi\)
\(14\) −5.45271 −1.45730
\(15\) −7.14123 −1.84386
\(16\) 0.382023 0.0955057
\(17\) 1.00000 0.242536
\(18\) −0.534324 −0.125941
\(19\) 4.61118 1.05788 0.528938 0.848660i \(-0.322590\pi\)
0.528938 + 0.848660i \(0.322590\pi\)
\(20\) 13.1883 2.94898
\(21\) −4.24984 −0.927391
\(22\) −2.30649 −0.491746
\(23\) 2.01155 0.419437 0.209718 0.977762i \(-0.432745\pi\)
0.209718 + 0.977762i \(0.432745\pi\)
\(24\) 5.47284 1.11714
\(25\) 10.7805 2.15609
\(26\) −11.6167 −2.27821
\(27\) 4.97659 0.957746
\(28\) 7.84851 1.48323
\(29\) 4.72977 0.878296 0.439148 0.898415i \(-0.355280\pi\)
0.439148 + 0.898415i \(0.355280\pi\)
\(30\) 16.4712 3.00722
\(31\) 2.96757 0.532991 0.266495 0.963836i \(-0.414134\pi\)
0.266495 + 0.963836i \(0.414134\pi\)
\(32\) 5.20764 0.920589
\(33\) −1.79768 −0.312936
\(34\) −2.30649 −0.395561
\(35\) 9.39117 1.58740
\(36\) 0.769095 0.128182
\(37\) −2.93712 −0.482859 −0.241430 0.970418i \(-0.577616\pi\)
−0.241430 + 0.970418i \(0.577616\pi\)
\(38\) −10.6357 −1.72533
\(39\) −9.05402 −1.44980
\(40\) −12.0937 −1.91218
\(41\) 2.94886 0.460535 0.230268 0.973127i \(-0.426040\pi\)
0.230268 + 0.973127i \(0.426040\pi\)
\(42\) 9.80223 1.51252
\(43\) 1.00000 0.152499
\(44\) 3.31992 0.500497
\(45\) 0.920264 0.137185
\(46\) −4.63962 −0.684075
\(47\) 0.804974 0.117418 0.0587088 0.998275i \(-0.481302\pi\)
0.0587088 + 0.998275i \(0.481302\pi\)
\(48\) −0.686755 −0.0991246
\(49\) −1.41119 −0.201599
\(50\) −24.8651 −3.51646
\(51\) −1.79768 −0.251726
\(52\) 16.7208 2.31875
\(53\) 2.26444 0.311045 0.155522 0.987832i \(-0.450294\pi\)
0.155522 + 0.987832i \(0.450294\pi\)
\(54\) −11.4785 −1.56202
\(55\) 3.97246 0.535647
\(56\) −7.19713 −0.961757
\(57\) −8.28943 −1.09796
\(58\) −10.9092 −1.43245
\(59\) −5.18744 −0.675348 −0.337674 0.941263i \(-0.609640\pi\)
−0.337674 + 0.941263i \(0.609640\pi\)
\(60\) −23.7083 −3.06073
\(61\) −3.03068 −0.388039 −0.194020 0.980998i \(-0.562153\pi\)
−0.194020 + 0.980998i \(0.562153\pi\)
\(62\) −6.84467 −0.869275
\(63\) 0.547661 0.0689988
\(64\) −12.7754 −1.59693
\(65\) 20.0073 2.48160
\(66\) 4.14634 0.510380
\(67\) 9.82283 1.20005 0.600025 0.799981i \(-0.295157\pi\)
0.600025 + 0.799981i \(0.295157\pi\)
\(68\) 3.31992 0.402599
\(69\) −3.61612 −0.435330
\(70\) −21.6607 −2.58895
\(71\) 3.86568 0.458772 0.229386 0.973336i \(-0.426328\pi\)
0.229386 + 0.973336i \(0.426328\pi\)
\(72\) −0.705265 −0.0831162
\(73\) 4.61176 0.539766 0.269883 0.962893i \(-0.413015\pi\)
0.269883 + 0.962893i \(0.413015\pi\)
\(74\) 6.77445 0.787514
\(75\) −19.3799 −2.23779
\(76\) 15.3087 1.75603
\(77\) 2.36407 0.269410
\(78\) 20.8831 2.36454
\(79\) −12.2298 −1.37596 −0.687978 0.725732i \(-0.741501\pi\)
−0.687978 + 0.725732i \(0.741501\pi\)
\(80\) 1.51757 0.169670
\(81\) −9.64132 −1.07126
\(82\) −6.80154 −0.751105
\(83\) 0.879944 0.0965864 0.0482932 0.998833i \(-0.484622\pi\)
0.0482932 + 0.998833i \(0.484622\pi\)
\(84\) −14.1091 −1.53943
\(85\) 3.97246 0.430874
\(86\) −2.30649 −0.248716
\(87\) −8.50262 −0.911577
\(88\) −3.04439 −0.324533
\(89\) 5.21525 0.552815 0.276408 0.961040i \(-0.410856\pi\)
0.276408 + 0.961040i \(0.410856\pi\)
\(90\) −2.12258 −0.223740
\(91\) 11.9066 1.24815
\(92\) 6.67817 0.696248
\(93\) −5.33474 −0.553187
\(94\) −1.85667 −0.191501
\(95\) 18.3177 1.87936
\(96\) −9.36168 −0.955472
\(97\) −5.31064 −0.539214 −0.269607 0.962970i \(-0.586894\pi\)
−0.269607 + 0.962970i \(0.586894\pi\)
\(98\) 3.25490 0.328795
\(99\) 0.231661 0.0232828
\(100\) 35.7903 3.57903
\(101\) 10.9985 1.09439 0.547194 0.837006i \(-0.315696\pi\)
0.547194 + 0.837006i \(0.315696\pi\)
\(102\) 4.14634 0.410549
\(103\) 5.30396 0.522614 0.261307 0.965256i \(-0.415846\pi\)
0.261307 + 0.965256i \(0.415846\pi\)
\(104\) −15.3330 −1.50353
\(105\) −16.8823 −1.64755
\(106\) −5.22292 −0.507295
\(107\) 3.18411 0.307819 0.153910 0.988085i \(-0.450814\pi\)
0.153910 + 0.988085i \(0.450814\pi\)
\(108\) 16.5219 1.58982
\(109\) −6.03357 −0.577912 −0.288956 0.957342i \(-0.593308\pi\)
−0.288956 + 0.957342i \(0.593308\pi\)
\(110\) −9.16247 −0.873607
\(111\) 5.28001 0.501156
\(112\) 0.903127 0.0853375
\(113\) −2.87695 −0.270641 −0.135321 0.990802i \(-0.543206\pi\)
−0.135321 + 0.990802i \(0.543206\pi\)
\(114\) 19.1195 1.79071
\(115\) 7.99080 0.745146
\(116\) 15.7025 1.45794
\(117\) 1.16676 0.107867
\(118\) 11.9648 1.10145
\(119\) 2.36407 0.216714
\(120\) 21.7407 1.98464
\(121\) 1.00000 0.0909091
\(122\) 6.99026 0.632868
\(123\) −5.30112 −0.477986
\(124\) 9.85208 0.884743
\(125\) 22.9627 2.05385
\(126\) −1.26318 −0.112533
\(127\) −0.497074 −0.0441082 −0.0220541 0.999757i \(-0.507021\pi\)
−0.0220541 + 0.999757i \(0.507021\pi\)
\(128\) 19.0512 1.68390
\(129\) −1.79768 −0.158277
\(130\) −46.1468 −4.04734
\(131\) 15.8516 1.38496 0.692482 0.721435i \(-0.256517\pi\)
0.692482 + 0.721435i \(0.256517\pi\)
\(132\) −5.96816 −0.519461
\(133\) 10.9011 0.945247
\(134\) −22.6563 −1.95721
\(135\) 19.7693 1.70147
\(136\) −3.04439 −0.261054
\(137\) −3.74813 −0.320224 −0.160112 0.987099i \(-0.551186\pi\)
−0.160112 + 0.987099i \(0.551186\pi\)
\(138\) 8.34057 0.709996
\(139\) 9.20379 0.780655 0.390328 0.920676i \(-0.372362\pi\)
0.390328 + 0.920676i \(0.372362\pi\)
\(140\) 31.1779 2.63502
\(141\) −1.44709 −0.121867
\(142\) −8.91618 −0.748229
\(143\) 5.03650 0.421173
\(144\) 0.0884997 0.00737497
\(145\) 18.7888 1.56033
\(146\) −10.6370 −0.880324
\(147\) 2.53687 0.209238
\(148\) −9.75100 −0.801527
\(149\) −6.52470 −0.534525 −0.267262 0.963624i \(-0.586119\pi\)
−0.267262 + 0.963624i \(0.586119\pi\)
\(150\) 44.6996 3.64970
\(151\) 6.42473 0.522837 0.261419 0.965226i \(-0.415810\pi\)
0.261419 + 0.965226i \(0.415810\pi\)
\(152\) −14.0382 −1.13865
\(153\) 0.231661 0.0187287
\(154\) −5.45271 −0.439392
\(155\) 11.7885 0.946879
\(156\) −30.0586 −2.40662
\(157\) −14.1635 −1.13037 −0.565184 0.824965i \(-0.691195\pi\)
−0.565184 + 0.824965i \(0.691195\pi\)
\(158\) 28.2079 2.24410
\(159\) −4.07075 −0.322831
\(160\) 20.6872 1.63546
\(161\) 4.75543 0.374781
\(162\) 22.2376 1.74715
\(163\) 4.34203 0.340094 0.170047 0.985436i \(-0.445608\pi\)
0.170047 + 0.985436i \(0.445608\pi\)
\(164\) 9.78999 0.764470
\(165\) −7.14123 −0.555944
\(166\) −2.02959 −0.157526
\(167\) 7.71459 0.596973 0.298486 0.954414i \(-0.403518\pi\)
0.298486 + 0.954414i \(0.403518\pi\)
\(168\) 12.9382 0.998200
\(169\) 12.3663 0.951256
\(170\) −9.16247 −0.702729
\(171\) 1.06823 0.0816894
\(172\) 3.31992 0.253141
\(173\) −21.3548 −1.62358 −0.811789 0.583952i \(-0.801506\pi\)
−0.811789 + 0.583952i \(0.801506\pi\)
\(174\) 19.6113 1.48673
\(175\) 25.4858 1.92654
\(176\) 0.382023 0.0287960
\(177\) 9.32537 0.700938
\(178\) −12.0289 −0.901608
\(179\) 13.5048 1.00940 0.504698 0.863296i \(-0.331604\pi\)
0.504698 + 0.863296i \(0.331604\pi\)
\(180\) 3.05520 0.227721
\(181\) −13.6974 −1.01812 −0.509060 0.860731i \(-0.670007\pi\)
−0.509060 + 0.860731i \(0.670007\pi\)
\(182\) −27.4626 −2.03566
\(183\) 5.44821 0.402743
\(184\) −6.12393 −0.451462
\(185\) −11.6676 −0.857819
\(186\) 12.3045 0.902213
\(187\) 1.00000 0.0731272
\(188\) 2.67245 0.194908
\(189\) 11.7650 0.855778
\(190\) −42.2497 −3.06512
\(191\) 3.65345 0.264354 0.132177 0.991226i \(-0.457803\pi\)
0.132177 + 0.991226i \(0.457803\pi\)
\(192\) 22.9662 1.65744
\(193\) 14.9246 1.07430 0.537148 0.843488i \(-0.319502\pi\)
0.537148 + 0.843488i \(0.319502\pi\)
\(194\) 12.2490 0.879424
\(195\) −35.9668 −2.57564
\(196\) −4.68504 −0.334646
\(197\) −23.6293 −1.68352 −0.841760 0.539851i \(-0.818481\pi\)
−0.841760 + 0.539851i \(0.818481\pi\)
\(198\) −0.534324 −0.0379728
\(199\) 19.9392 1.41345 0.706727 0.707486i \(-0.250171\pi\)
0.706727 + 0.707486i \(0.250171\pi\)
\(200\) −32.8199 −2.32072
\(201\) −17.6583 −1.24552
\(202\) −25.3679 −1.78488
\(203\) 11.1815 0.784787
\(204\) −5.96816 −0.417855
\(205\) 11.7143 0.818159
\(206\) −12.2335 −0.852351
\(207\) 0.465997 0.0323890
\(208\) 1.92406 0.133409
\(209\) 4.61118 0.318962
\(210\) 38.9390 2.68705
\(211\) −10.3178 −0.710304 −0.355152 0.934809i \(-0.615571\pi\)
−0.355152 + 0.934809i \(0.615571\pi\)
\(212\) 7.51776 0.516322
\(213\) −6.94927 −0.476156
\(214\) −7.34413 −0.502034
\(215\) 3.97246 0.270920
\(216\) −15.1507 −1.03087
\(217\) 7.01552 0.476245
\(218\) 13.9164 0.942538
\(219\) −8.29048 −0.560219
\(220\) 13.1883 0.889152
\(221\) 5.03650 0.338792
\(222\) −12.1783 −0.817355
\(223\) −24.3295 −1.62922 −0.814610 0.580009i \(-0.803049\pi\)
−0.814610 + 0.580009i \(0.803049\pi\)
\(224\) 12.3112 0.822577
\(225\) 2.49741 0.166494
\(226\) 6.63568 0.441399
\(227\) 3.67046 0.243617 0.121809 0.992554i \(-0.461131\pi\)
0.121809 + 0.992554i \(0.461131\pi\)
\(228\) −27.5202 −1.82257
\(229\) −3.79206 −0.250586 −0.125293 0.992120i \(-0.539987\pi\)
−0.125293 + 0.992120i \(0.539987\pi\)
\(230\) −18.4307 −1.21529
\(231\) −4.24984 −0.279619
\(232\) −14.3992 −0.945357
\(233\) −14.4413 −0.946080 −0.473040 0.881041i \(-0.656843\pi\)
−0.473040 + 0.881041i \(0.656843\pi\)
\(234\) −2.69112 −0.175924
\(235\) 3.19773 0.208597
\(236\) −17.2219 −1.12105
\(237\) 21.9852 1.42809
\(238\) −5.45271 −0.353446
\(239\) 6.58703 0.426080 0.213040 0.977043i \(-0.431664\pi\)
0.213040 + 0.977043i \(0.431664\pi\)
\(240\) −2.72811 −0.176099
\(241\) −15.4574 −0.995699 −0.497850 0.867263i \(-0.665877\pi\)
−0.497850 + 0.867263i \(0.665877\pi\)
\(242\) −2.30649 −0.148267
\(243\) 2.40224 0.154104
\(244\) −10.0616 −0.644130
\(245\) −5.60590 −0.358148
\(246\) 12.2270 0.779566
\(247\) 23.2242 1.47772
\(248\) −9.03441 −0.573686
\(249\) −1.58186 −0.100246
\(250\) −52.9634 −3.34970
\(251\) 1.77896 0.112287 0.0561433 0.998423i \(-0.482120\pi\)
0.0561433 + 0.998423i \(0.482120\pi\)
\(252\) 1.81819 0.114535
\(253\) 2.01155 0.126465
\(254\) 1.14650 0.0719377
\(255\) −7.14123 −0.447201
\(256\) −18.3906 −1.14941
\(257\) −28.2634 −1.76302 −0.881510 0.472165i \(-0.843473\pi\)
−0.881510 + 0.472165i \(0.843473\pi\)
\(258\) 4.14634 0.258140
\(259\) −6.94354 −0.431451
\(260\) 66.4227 4.11936
\(261\) 1.09570 0.0678223
\(262\) −36.5617 −2.25879
\(263\) −3.86383 −0.238254 −0.119127 0.992879i \(-0.538010\pi\)
−0.119127 + 0.992879i \(0.538010\pi\)
\(264\) 5.47284 0.336830
\(265\) 8.99541 0.552584
\(266\) −25.1434 −1.54164
\(267\) −9.37536 −0.573763
\(268\) 32.6110 1.99203
\(269\) 18.7882 1.14554 0.572768 0.819717i \(-0.305870\pi\)
0.572768 + 0.819717i \(0.305870\pi\)
\(270\) −45.5979 −2.77500
\(271\) −21.7851 −1.32335 −0.661674 0.749791i \(-0.730154\pi\)
−0.661674 + 0.749791i \(0.730154\pi\)
\(272\) 0.382023 0.0231635
\(273\) −21.4043 −1.29545
\(274\) 8.64504 0.522266
\(275\) 10.7805 0.650087
\(276\) −12.0052 −0.722630
\(277\) 4.44164 0.266872 0.133436 0.991057i \(-0.457399\pi\)
0.133436 + 0.991057i \(0.457399\pi\)
\(278\) −21.2285 −1.27320
\(279\) 0.687468 0.0411577
\(280\) −28.5903 −1.70860
\(281\) −24.5731 −1.46591 −0.732956 0.680276i \(-0.761860\pi\)
−0.732956 + 0.680276i \(0.761860\pi\)
\(282\) 3.33770 0.198757
\(283\) −11.0069 −0.654294 −0.327147 0.944973i \(-0.606087\pi\)
−0.327147 + 0.944973i \(0.606087\pi\)
\(284\) 12.8338 0.761543
\(285\) −32.9295 −1.95057
\(286\) −11.6167 −0.686908
\(287\) 6.97131 0.411503
\(288\) 1.20641 0.0710881
\(289\) 1.00000 0.0588235
\(290\) −43.3364 −2.54480
\(291\) 9.54684 0.559646
\(292\) 15.3107 0.895989
\(293\) 13.3828 0.781834 0.390917 0.920426i \(-0.372158\pi\)
0.390917 + 0.920426i \(0.372158\pi\)
\(294\) −5.85128 −0.341254
\(295\) −20.6069 −1.19978
\(296\) 8.94172 0.519727
\(297\) 4.97659 0.288771
\(298\) 15.0492 0.871776
\(299\) 10.1312 0.585900
\(300\) −64.3396 −3.71465
\(301\) 2.36407 0.136263
\(302\) −14.8186 −0.852715
\(303\) −19.7717 −1.13586
\(304\) 1.76157 0.101033
\(305\) −12.0393 −0.689368
\(306\) −0.534324 −0.0305453
\(307\) 7.62337 0.435089 0.217544 0.976050i \(-0.430195\pi\)
0.217544 + 0.976050i \(0.430195\pi\)
\(308\) 7.84851 0.447210
\(309\) −9.53482 −0.542417
\(310\) −27.1902 −1.54430
\(311\) −1.07712 −0.0610777 −0.0305388 0.999534i \(-0.509722\pi\)
−0.0305388 + 0.999534i \(0.509722\pi\)
\(312\) 27.5639 1.56050
\(313\) −6.48880 −0.366769 −0.183384 0.983041i \(-0.558705\pi\)
−0.183384 + 0.983041i \(0.558705\pi\)
\(314\) 32.6680 1.84356
\(315\) 2.17556 0.122579
\(316\) −40.6018 −2.28403
\(317\) 8.97582 0.504132 0.252066 0.967710i \(-0.418890\pi\)
0.252066 + 0.967710i \(0.418890\pi\)
\(318\) 9.38916 0.526518
\(319\) 4.72977 0.264816
\(320\) −50.7500 −2.83701
\(321\) −5.72402 −0.319483
\(322\) −10.9684 −0.611244
\(323\) 4.61118 0.256573
\(324\) −32.0084 −1.77824
\(325\) 54.2958 3.01179
\(326\) −10.0149 −0.554673
\(327\) 10.8464 0.599810
\(328\) −8.97748 −0.495698
\(329\) 1.90301 0.104916
\(330\) 16.4712 0.906710
\(331\) 20.5957 1.13204 0.566022 0.824390i \(-0.308482\pi\)
0.566022 + 0.824390i \(0.308482\pi\)
\(332\) 2.92134 0.160330
\(333\) −0.680415 −0.0372865
\(334\) −17.7937 −0.973626
\(335\) 39.0209 2.13194
\(336\) −1.62354 −0.0885711
\(337\) −30.2896 −1.64998 −0.824991 0.565146i \(-0.808820\pi\)
−0.824991 + 0.565146i \(0.808820\pi\)
\(338\) −28.5229 −1.55144
\(339\) 5.17185 0.280896
\(340\) 13.1883 0.715234
\(341\) 2.96757 0.160703
\(342\) −2.46386 −0.133230
\(343\) −19.8846 −1.07367
\(344\) −3.04439 −0.164142
\(345\) −14.3649 −0.773381
\(346\) 49.2548 2.64795
\(347\) −16.3565 −0.878062 −0.439031 0.898472i \(-0.644678\pi\)
−0.439031 + 0.898472i \(0.644678\pi\)
\(348\) −28.2280 −1.51318
\(349\) −35.5578 −1.90336 −0.951682 0.307086i \(-0.900646\pi\)
−0.951682 + 0.307086i \(0.900646\pi\)
\(350\) −58.7828 −3.14207
\(351\) 25.0646 1.33785
\(352\) 5.20764 0.277568
\(353\) 12.5560 0.668291 0.334145 0.942522i \(-0.391552\pi\)
0.334145 + 0.942522i \(0.391552\pi\)
\(354\) −21.5089 −1.14319
\(355\) 15.3563 0.815027
\(356\) 17.3142 0.917651
\(357\) −4.24984 −0.224925
\(358\) −31.1487 −1.64626
\(359\) −4.29395 −0.226626 −0.113313 0.993559i \(-0.536146\pi\)
−0.113313 + 0.993559i \(0.536146\pi\)
\(360\) −2.80164 −0.147659
\(361\) 2.26294 0.119102
\(362\) 31.5930 1.66049
\(363\) −1.79768 −0.0943538
\(364\) 39.5290 2.07188
\(365\) 18.3200 0.958915
\(366\) −12.5663 −0.656849
\(367\) 1.24864 0.0651785 0.0325892 0.999469i \(-0.489625\pi\)
0.0325892 + 0.999469i \(0.489625\pi\)
\(368\) 0.768457 0.0400586
\(369\) 0.683136 0.0355626
\(370\) 26.9113 1.39905
\(371\) 5.35329 0.277929
\(372\) −17.7109 −0.918267
\(373\) 30.4820 1.57830 0.789149 0.614202i \(-0.210522\pi\)
0.789149 + 0.614202i \(0.210522\pi\)
\(374\) −2.30649 −0.119266
\(375\) −41.2797 −2.13167
\(376\) −2.45065 −0.126383
\(377\) 23.8215 1.22687
\(378\) −27.1359 −1.39572
\(379\) −21.4909 −1.10391 −0.551957 0.833873i \(-0.686119\pi\)
−0.551957 + 0.833873i \(0.686119\pi\)
\(380\) 60.8134 3.11966
\(381\) 0.893581 0.0457795
\(382\) −8.42666 −0.431146
\(383\) −12.9004 −0.659179 −0.329590 0.944124i \(-0.606910\pi\)
−0.329590 + 0.944124i \(0.606910\pi\)
\(384\) −34.2480 −1.74771
\(385\) 9.39117 0.478618
\(386\) −34.4235 −1.75211
\(387\) 0.231661 0.0117760
\(388\) −17.6309 −0.895073
\(389\) −34.4946 −1.74895 −0.874473 0.485074i \(-0.838793\pi\)
−0.874473 + 0.485074i \(0.838793\pi\)
\(390\) 82.9572 4.20070
\(391\) 2.01155 0.101728
\(392\) 4.29621 0.216991
\(393\) −28.4962 −1.43744
\(394\) 54.5010 2.74572
\(395\) −48.5823 −2.44444
\(396\) 0.769095 0.0386485
\(397\) −19.8626 −0.996875 −0.498437 0.866926i \(-0.666093\pi\)
−0.498437 + 0.866926i \(0.666093\pi\)
\(398\) −45.9897 −2.30526
\(399\) −19.5968 −0.981065
\(400\) 4.11839 0.205919
\(401\) 5.32106 0.265721 0.132860 0.991135i \(-0.457584\pi\)
0.132860 + 0.991135i \(0.457584\pi\)
\(402\) 40.7289 2.03137
\(403\) 14.9461 0.744520
\(404\) 36.5140 1.81664
\(405\) −38.2998 −1.90313
\(406\) −25.7901 −1.27994
\(407\) −2.93712 −0.145588
\(408\) 5.47284 0.270946
\(409\) 25.3552 1.25373 0.626867 0.779126i \(-0.284337\pi\)
0.626867 + 0.779126i \(0.284337\pi\)
\(410\) −27.0189 −1.33437
\(411\) 6.73794 0.332358
\(412\) 17.6087 0.867518
\(413\) −12.2635 −0.603445
\(414\) −1.07482 −0.0528245
\(415\) 3.49555 0.171590
\(416\) 26.2283 1.28595
\(417\) −16.5455 −0.810236
\(418\) −10.6357 −0.520207
\(419\) −16.0949 −0.786289 −0.393144 0.919477i \(-0.628613\pi\)
−0.393144 + 0.919477i \(0.628613\pi\)
\(420\) −56.0480 −2.73486
\(421\) 25.1303 1.22477 0.612387 0.790558i \(-0.290209\pi\)
0.612387 + 0.790558i \(0.290209\pi\)
\(422\) 23.7979 1.15846
\(423\) 0.186481 0.00906701
\(424\) −6.89383 −0.334794
\(425\) 10.7805 0.522930
\(426\) 16.0285 0.776581
\(427\) −7.16474 −0.346726
\(428\) 10.5710 0.510968
\(429\) −9.05402 −0.437132
\(430\) −9.16247 −0.441853
\(431\) −27.7556 −1.33694 −0.668469 0.743740i \(-0.733050\pi\)
−0.668469 + 0.743740i \(0.733050\pi\)
\(432\) 1.90117 0.0914702
\(433\) −23.4623 −1.12753 −0.563763 0.825937i \(-0.690647\pi\)
−0.563763 + 0.825937i \(0.690647\pi\)
\(434\) −16.1813 −0.776726
\(435\) −33.7764 −1.61945
\(436\) −20.0310 −0.959310
\(437\) 9.27560 0.443712
\(438\) 19.1219 0.913682
\(439\) −14.9357 −0.712842 −0.356421 0.934326i \(-0.616003\pi\)
−0.356421 + 0.934326i \(0.616003\pi\)
\(440\) −12.0937 −0.576545
\(441\) −0.326917 −0.0155675
\(442\) −11.6167 −0.552548
\(443\) −26.4690 −1.25758 −0.628789 0.777576i \(-0.716449\pi\)
−0.628789 + 0.777576i \(0.716449\pi\)
\(444\) 17.5292 0.831899
\(445\) 20.7174 0.982099
\(446\) 56.1158 2.65716
\(447\) 11.7293 0.554779
\(448\) −30.2020 −1.42691
\(449\) −12.1365 −0.572756 −0.286378 0.958117i \(-0.592451\pi\)
−0.286378 + 0.958117i \(0.592451\pi\)
\(450\) −5.76027 −0.271542
\(451\) 2.94886 0.138857
\(452\) −9.55125 −0.449253
\(453\) −11.5496 −0.542649
\(454\) −8.46591 −0.397325
\(455\) 47.2986 2.21739
\(456\) 25.2362 1.18179
\(457\) −24.0835 −1.12658 −0.563290 0.826259i \(-0.690465\pi\)
−0.563290 + 0.826259i \(0.690465\pi\)
\(458\) 8.74636 0.408691
\(459\) 4.97659 0.232288
\(460\) 26.5288 1.23691
\(461\) 38.0126 1.77042 0.885211 0.465189i \(-0.154014\pi\)
0.885211 + 0.465189i \(0.154014\pi\)
\(462\) 9.80223 0.456041
\(463\) −8.42811 −0.391688 −0.195844 0.980635i \(-0.562745\pi\)
−0.195844 + 0.980635i \(0.562745\pi\)
\(464\) 1.80688 0.0838823
\(465\) −21.1921 −0.982758
\(466\) 33.3088 1.54300
\(467\) 7.65618 0.354286 0.177143 0.984185i \(-0.443315\pi\)
0.177143 + 0.984185i \(0.443315\pi\)
\(468\) 3.87355 0.179055
\(469\) 23.2218 1.07228
\(470\) −7.37555 −0.340209
\(471\) 25.4614 1.17320
\(472\) 15.7926 0.726912
\(473\) 1.00000 0.0459800
\(474\) −50.7088 −2.32913
\(475\) 49.7106 2.28088
\(476\) 7.84851 0.359736
\(477\) 0.524582 0.0240190
\(478\) −15.1930 −0.694910
\(479\) −15.8805 −0.725600 −0.362800 0.931867i \(-0.618179\pi\)
−0.362800 + 0.931867i \(0.618179\pi\)
\(480\) −37.1889 −1.69743
\(481\) −14.7928 −0.674494
\(482\) 35.6524 1.62392
\(483\) −8.54875 −0.388982
\(484\) 3.31992 0.150905
\(485\) −21.0963 −0.957935
\(486\) −5.54075 −0.251334
\(487\) 9.58877 0.434509 0.217254 0.976115i \(-0.430290\pi\)
0.217254 + 0.976115i \(0.430290\pi\)
\(488\) 9.22657 0.417667
\(489\) −7.80559 −0.352981
\(490\) 12.9300 0.584117
\(491\) 10.5643 0.476762 0.238381 0.971172i \(-0.423383\pi\)
0.238381 + 0.971172i \(0.423383\pi\)
\(492\) −17.5993 −0.793437
\(493\) 4.72977 0.213018
\(494\) −53.5665 −2.41007
\(495\) 0.920264 0.0413628
\(496\) 1.13368 0.0509036
\(497\) 9.13873 0.409928
\(498\) 3.64855 0.163495
\(499\) −3.31503 −0.148401 −0.0742006 0.997243i \(-0.523641\pi\)
−0.0742006 + 0.997243i \(0.523641\pi\)
\(500\) 76.2344 3.40930
\(501\) −13.8684 −0.619593
\(502\) −4.10315 −0.183133
\(503\) 5.41307 0.241357 0.120678 0.992692i \(-0.461493\pi\)
0.120678 + 0.992692i \(0.461493\pi\)
\(504\) −1.66729 −0.0742671
\(505\) 43.6910 1.94422
\(506\) −4.63962 −0.206256
\(507\) −22.2307 −0.987301
\(508\) −1.65025 −0.0732178
\(509\) 22.4941 0.997034 0.498517 0.866880i \(-0.333878\pi\)
0.498517 + 0.866880i \(0.333878\pi\)
\(510\) 16.4712 0.729357
\(511\) 10.9025 0.482298
\(512\) 4.31549 0.190719
\(513\) 22.9479 1.01318
\(514\) 65.1893 2.87538
\(515\) 21.0698 0.928445
\(516\) −5.96816 −0.262734
\(517\) 0.804974 0.0354027
\(518\) 16.0153 0.703670
\(519\) 38.3892 1.68510
\(520\) −60.9100 −2.67108
\(521\) 25.4152 1.11346 0.556729 0.830694i \(-0.312056\pi\)
0.556729 + 0.830694i \(0.312056\pi\)
\(522\) −2.52723 −0.110614
\(523\) 5.89531 0.257784 0.128892 0.991659i \(-0.458858\pi\)
0.128892 + 0.991659i \(0.458858\pi\)
\(524\) 52.6261 2.29898
\(525\) −45.8153 −1.99954
\(526\) 8.91190 0.388577
\(527\) 2.96757 0.129269
\(528\) −0.686755 −0.0298872
\(529\) −18.9537 −0.824073
\(530\) −20.7479 −0.901230
\(531\) −1.20173 −0.0521505
\(532\) 36.1908 1.56907
\(533\) 14.8520 0.643310
\(534\) 21.6242 0.935772
\(535\) 12.6488 0.546854
\(536\) −29.9045 −1.29168
\(537\) −24.2773 −1.04764
\(538\) −43.3349 −1.86830
\(539\) −1.41119 −0.0607843
\(540\) 65.6326 2.82438
\(541\) −29.8660 −1.28404 −0.642020 0.766688i \(-0.721904\pi\)
−0.642020 + 0.766688i \(0.721904\pi\)
\(542\) 50.2471 2.15830
\(543\) 24.6236 1.05670
\(544\) 5.20764 0.223276
\(545\) −23.9682 −1.02668
\(546\) 49.3689 2.11280
\(547\) −36.5808 −1.56408 −0.782041 0.623227i \(-0.785821\pi\)
−0.782041 + 0.623227i \(0.785821\pi\)
\(548\) −12.4435 −0.531559
\(549\) −0.702091 −0.0299645
\(550\) −24.8651 −1.06025
\(551\) 21.8098 0.929129
\(552\) 11.0089 0.468569
\(553\) −28.9120 −1.22946
\(554\) −10.2446 −0.435252
\(555\) 20.9746 0.890324
\(556\) 30.5558 1.29586
\(557\) 4.75495 0.201474 0.100737 0.994913i \(-0.467880\pi\)
0.100737 + 0.994913i \(0.467880\pi\)
\(558\) −1.58564 −0.0671256
\(559\) 5.03650 0.213021
\(560\) 3.58764 0.151605
\(561\) −1.79768 −0.0758982
\(562\) 56.6778 2.39081
\(563\) −28.1317 −1.18561 −0.592805 0.805346i \(-0.701980\pi\)
−0.592805 + 0.805346i \(0.701980\pi\)
\(564\) −4.80421 −0.202294
\(565\) −11.4286 −0.480805
\(566\) 25.3874 1.06711
\(567\) −22.7927 −0.957204
\(568\) −11.7686 −0.493801
\(569\) 3.73881 0.156739 0.0783696 0.996924i \(-0.475029\pi\)
0.0783696 + 0.996924i \(0.475029\pi\)
\(570\) 75.9516 3.18126
\(571\) −21.4103 −0.895994 −0.447997 0.894035i \(-0.647863\pi\)
−0.447997 + 0.894035i \(0.647863\pi\)
\(572\) 16.7208 0.699130
\(573\) −6.56774 −0.274371
\(574\) −16.0793 −0.671137
\(575\) 21.6854 0.904345
\(576\) −2.95957 −0.123315
\(577\) 16.2220 0.675330 0.337665 0.941266i \(-0.390363\pi\)
0.337665 + 0.941266i \(0.390363\pi\)
\(578\) −2.30649 −0.0959375
\(579\) −26.8297 −1.11500
\(580\) 62.3774 2.59008
\(581\) 2.08025 0.0863032
\(582\) −22.0197 −0.912748
\(583\) 2.26444 0.0937836
\(584\) −14.0400 −0.580978
\(585\) 4.63491 0.191630
\(586\) −30.8675 −1.27512
\(587\) 5.49789 0.226922 0.113461 0.993542i \(-0.463806\pi\)
0.113461 + 0.993542i \(0.463806\pi\)
\(588\) 8.42221 0.347326
\(589\) 13.6840 0.563838
\(590\) 47.5298 1.95677
\(591\) 42.4780 1.74731
\(592\) −1.12205 −0.0461158
\(593\) −38.6582 −1.58750 −0.793751 0.608243i \(-0.791875\pi\)
−0.793751 + 0.608243i \(0.791875\pi\)
\(594\) −11.4785 −0.470968
\(595\) 9.39117 0.385000
\(596\) −21.6615 −0.887289
\(597\) −35.8444 −1.46701
\(598\) −23.3675 −0.955567
\(599\) −22.5254 −0.920362 −0.460181 0.887825i \(-0.652215\pi\)
−0.460181 + 0.887825i \(0.652215\pi\)
\(600\) 58.9998 2.40866
\(601\) −33.6816 −1.37390 −0.686951 0.726704i \(-0.741051\pi\)
−0.686951 + 0.726704i \(0.741051\pi\)
\(602\) −5.45271 −0.222236
\(603\) 2.27556 0.0926682
\(604\) 21.3296 0.867888
\(605\) 3.97246 0.161504
\(606\) 45.6034 1.85251
\(607\) −17.1069 −0.694348 −0.347174 0.937801i \(-0.612859\pi\)
−0.347174 + 0.937801i \(0.612859\pi\)
\(608\) 24.0133 0.973869
\(609\) −20.1008 −0.814524
\(610\) 27.7686 1.12432
\(611\) 4.05425 0.164018
\(612\) 0.769095 0.0310888
\(613\) −37.3777 −1.50967 −0.754836 0.655914i \(-0.772283\pi\)
−0.754836 + 0.655914i \(0.772283\pi\)
\(614\) −17.5833 −0.709603
\(615\) −21.0585 −0.849161
\(616\) −7.19713 −0.289981
\(617\) 20.4256 0.822305 0.411153 0.911567i \(-0.365126\pi\)
0.411153 + 0.911567i \(0.365126\pi\)
\(618\) 21.9920 0.884649
\(619\) −9.59815 −0.385782 −0.192891 0.981220i \(-0.561786\pi\)
−0.192891 + 0.981220i \(0.561786\pi\)
\(620\) 39.1370 1.57178
\(621\) 10.0107 0.401714
\(622\) 2.48436 0.0996139
\(623\) 12.3292 0.493959
\(624\) −3.45884 −0.138465
\(625\) 37.3162 1.49265
\(626\) 14.9664 0.598177
\(627\) −8.28943 −0.331048
\(628\) −47.0216 −1.87637
\(629\) −2.93712 −0.117111
\(630\) −5.01793 −0.199919
\(631\) −2.81773 −0.112172 −0.0560861 0.998426i \(-0.517862\pi\)
−0.0560861 + 0.998426i \(0.517862\pi\)
\(632\) 37.2321 1.48101
\(633\) 18.5481 0.737219
\(634\) −20.7027 −0.822208
\(635\) −1.97461 −0.0783600
\(636\) −13.5145 −0.535887
\(637\) −7.10746 −0.281608
\(638\) −10.9092 −0.431899
\(639\) 0.895527 0.0354265
\(640\) 75.6802 2.99152
\(641\) 26.4632 1.04523 0.522616 0.852568i \(-0.324956\pi\)
0.522616 + 0.852568i \(0.324956\pi\)
\(642\) 13.2024 0.521058
\(643\) −10.6832 −0.421305 −0.210652 0.977561i \(-0.567559\pi\)
−0.210652 + 0.977561i \(0.567559\pi\)
\(644\) 15.7876 0.622120
\(645\) −7.14123 −0.281186
\(646\) −10.6357 −0.418454
\(647\) −27.2263 −1.07038 −0.535188 0.844733i \(-0.679759\pi\)
−0.535188 + 0.844733i \(0.679759\pi\)
\(648\) 29.3519 1.15305
\(649\) −5.18744 −0.203625
\(650\) −125.233 −4.91205
\(651\) −12.6117 −0.494291
\(652\) 14.4152 0.564542
\(653\) 43.2871 1.69396 0.846978 0.531628i \(-0.178420\pi\)
0.846978 + 0.531628i \(0.178420\pi\)
\(654\) −25.0173 −0.978253
\(655\) 62.9701 2.46044
\(656\) 1.12653 0.0439837
\(657\) 1.06836 0.0416808
\(658\) −4.38929 −0.171112
\(659\) 39.2963 1.53076 0.765382 0.643576i \(-0.222550\pi\)
0.765382 + 0.643576i \(0.222550\pi\)
\(660\) −23.7083 −0.922844
\(661\) 36.7242 1.42840 0.714202 0.699940i \(-0.246790\pi\)
0.714202 + 0.699940i \(0.246790\pi\)
\(662\) −47.5040 −1.84630
\(663\) −9.05402 −0.351629
\(664\) −2.67889 −0.103961
\(665\) 43.3043 1.67927
\(666\) 1.56937 0.0608120
\(667\) 9.51416 0.368390
\(668\) 25.6118 0.990951
\(669\) 43.7366 1.69096
\(670\) −90.0014 −3.47706
\(671\) −3.03068 −0.116998
\(672\) −22.1316 −0.853746
\(673\) −21.6886 −0.836036 −0.418018 0.908439i \(-0.637275\pi\)
−0.418018 + 0.908439i \(0.637275\pi\)
\(674\) 69.8629 2.69102
\(675\) 53.6500 2.06499
\(676\) 41.0552 1.57905
\(677\) 7.81484 0.300349 0.150174 0.988660i \(-0.452016\pi\)
0.150174 + 0.988660i \(0.452016\pi\)
\(678\) −11.9288 −0.458124
\(679\) −12.5547 −0.481805
\(680\) −12.0937 −0.463773
\(681\) −6.59833 −0.252848
\(682\) −6.84467 −0.262096
\(683\) −6.99262 −0.267565 −0.133783 0.991011i \(-0.542712\pi\)
−0.133783 + 0.991011i \(0.542712\pi\)
\(684\) 3.54643 0.135601
\(685\) −14.8893 −0.568891
\(686\) 45.8638 1.75109
\(687\) 6.81692 0.260082
\(688\) 0.382023 0.0145645
\(689\) 11.4049 0.434491
\(690\) 33.1326 1.26134
\(691\) 40.5559 1.54282 0.771409 0.636340i \(-0.219552\pi\)
0.771409 + 0.636340i \(0.219552\pi\)
\(692\) −70.8963 −2.69507
\(693\) 0.547661 0.0208039
\(694\) 37.7261 1.43206
\(695\) 36.5617 1.38687
\(696\) 25.8853 0.981178
\(697\) 2.94886 0.111696
\(698\) 82.0138 3.10427
\(699\) 25.9608 0.981930
\(700\) 84.6106 3.19798
\(701\) −38.9586 −1.47144 −0.735722 0.677283i \(-0.763157\pi\)
−0.735722 + 0.677283i \(0.763157\pi\)
\(702\) −57.8114 −2.18195
\(703\) −13.5436 −0.510805
\(704\) −12.7754 −0.481492
\(705\) −5.74850 −0.216501
\(706\) −28.9604 −1.08994
\(707\) 26.0011 0.977871
\(708\) 30.9595 1.16353
\(709\) 51.8099 1.94576 0.972881 0.231307i \(-0.0743000\pi\)
0.972881 + 0.231307i \(0.0743000\pi\)
\(710\) −35.4192 −1.32926
\(711\) −2.83315 −0.106252
\(712\) −15.8772 −0.595024
\(713\) 5.96940 0.223556
\(714\) 9.80223 0.366839
\(715\) 20.0073 0.748231
\(716\) 44.8348 1.67556
\(717\) −11.8414 −0.442225
\(718\) 9.90397 0.369613
\(719\) −1.97125 −0.0735151 −0.0367575 0.999324i \(-0.511703\pi\)
−0.0367575 + 0.999324i \(0.511703\pi\)
\(720\) 0.351562 0.0131019
\(721\) 12.5389 0.466973
\(722\) −5.21945 −0.194248
\(723\) 27.7875 1.03343
\(724\) −45.4743 −1.69004
\(725\) 50.9892 1.89369
\(726\) 4.14634 0.153885
\(727\) −19.0114 −0.705095 −0.352548 0.935794i \(-0.614685\pi\)
−0.352548 + 0.935794i \(0.614685\pi\)
\(728\) −36.2483 −1.34345
\(729\) 24.6055 0.911314
\(730\) −42.2551 −1.56393
\(731\) 1.00000 0.0369863
\(732\) 18.0876 0.668537
\(733\) −32.4912 −1.20009 −0.600046 0.799966i \(-0.704851\pi\)
−0.600046 + 0.799966i \(0.704851\pi\)
\(734\) −2.87998 −0.106302
\(735\) 10.0776 0.371719
\(736\) 10.4754 0.386129
\(737\) 9.82283 0.361829
\(738\) −1.57565 −0.0580005
\(739\) −6.70734 −0.246733 −0.123367 0.992361i \(-0.539369\pi\)
−0.123367 + 0.992361i \(0.539369\pi\)
\(740\) −38.7355 −1.42394
\(741\) −41.7497 −1.53371
\(742\) −12.3473 −0.453285
\(743\) −11.4142 −0.418745 −0.209372 0.977836i \(-0.567142\pi\)
−0.209372 + 0.977836i \(0.567142\pi\)
\(744\) 16.2410 0.595424
\(745\) −25.9192 −0.949604
\(746\) −70.3066 −2.57411
\(747\) 0.203848 0.00745843
\(748\) 3.31992 0.121388
\(749\) 7.52744 0.275047
\(750\) 95.2114 3.47663
\(751\) 3.03628 0.110796 0.0553978 0.998464i \(-0.482357\pi\)
0.0553978 + 0.998464i \(0.482357\pi\)
\(752\) 0.307518 0.0112140
\(753\) −3.19800 −0.116541
\(754\) −54.9441 −2.00095
\(755\) 25.5220 0.928841
\(756\) 39.0588 1.42056
\(757\) −20.5266 −0.746050 −0.373025 0.927821i \(-0.621680\pi\)
−0.373025 + 0.927821i \(0.621680\pi\)
\(758\) 49.5686 1.80041
\(759\) −3.61612 −0.131257
\(760\) −55.7662 −2.02285
\(761\) 39.0941 1.41716 0.708579 0.705631i \(-0.249337\pi\)
0.708579 + 0.705631i \(0.249337\pi\)
\(762\) −2.06104 −0.0746636
\(763\) −14.2638 −0.516383
\(764\) 12.1292 0.438817
\(765\) 0.920264 0.0332722
\(766\) 29.7547 1.07508
\(767\) −26.1266 −0.943375
\(768\) 33.0605 1.19297
\(769\) −10.5632 −0.380919 −0.190460 0.981695i \(-0.560998\pi\)
−0.190460 + 0.981695i \(0.560998\pi\)
\(770\) −21.6607 −0.780597
\(771\) 50.8085 1.82982
\(772\) 49.5484 1.78329
\(773\) 2.62092 0.0942681 0.0471340 0.998889i \(-0.484991\pi\)
0.0471340 + 0.998889i \(0.484991\pi\)
\(774\) −0.534324 −0.0192059
\(775\) 31.9918 1.14918
\(776\) 16.1676 0.580384
\(777\) 12.4823 0.447799
\(778\) 79.5616 2.85242
\(779\) 13.5977 0.487189
\(780\) −119.407 −4.27545
\(781\) 3.86568 0.138325
\(782\) −4.63962 −0.165913
\(783\) 23.5381 0.841185
\(784\) −0.539107 −0.0192538
\(785\) −56.2639 −2.00815
\(786\) 65.7263 2.34438
\(787\) 42.1682 1.50314 0.751568 0.659656i \(-0.229298\pi\)
0.751568 + 0.659656i \(0.229298\pi\)
\(788\) −78.4475 −2.79458
\(789\) 6.94593 0.247282
\(790\) 112.055 3.98673
\(791\) −6.80131 −0.241827
\(792\) −0.705265 −0.0250605
\(793\) −15.2640 −0.542042
\(794\) 45.8130 1.62584
\(795\) −16.1709 −0.573523
\(796\) 66.1966 2.34628
\(797\) 31.4080 1.11253 0.556263 0.831006i \(-0.312235\pi\)
0.556263 + 0.831006i \(0.312235\pi\)
\(798\) 45.1998 1.60006
\(799\) 0.804974 0.0284779
\(800\) 56.1408 1.98488
\(801\) 1.20817 0.0426885
\(802\) −12.2730 −0.433374
\(803\) 4.61176 0.162745
\(804\) −58.6242 −2.06752
\(805\) 18.8908 0.665813
\(806\) −34.4732 −1.21427
\(807\) −33.7752 −1.18894
\(808\) −33.4835 −1.17795
\(809\) 20.0924 0.706412 0.353206 0.935546i \(-0.385091\pi\)
0.353206 + 0.935546i \(0.385091\pi\)
\(810\) 88.3383 3.10389
\(811\) −1.68860 −0.0592948 −0.0296474 0.999560i \(-0.509438\pi\)
−0.0296474 + 0.999560i \(0.509438\pi\)
\(812\) 37.1216 1.30271
\(813\) 39.1626 1.37349
\(814\) 6.77445 0.237444
\(815\) 17.2486 0.604191
\(816\) −0.686755 −0.0240412
\(817\) 4.61118 0.161325
\(818\) −58.4817 −2.04476
\(819\) 2.75830 0.0963827
\(820\) 38.8904 1.35811
\(821\) 8.08410 0.282137 0.141068 0.990000i \(-0.454946\pi\)
0.141068 + 0.990000i \(0.454946\pi\)
\(822\) −15.5410 −0.542056
\(823\) −48.9410 −1.70597 −0.852987 0.521931i \(-0.825212\pi\)
−0.852987 + 0.521931i \(0.825212\pi\)
\(824\) −16.1473 −0.562517
\(825\) −19.3799 −0.674720
\(826\) 28.2856 0.984182
\(827\) 36.6010 1.27274 0.636371 0.771384i \(-0.280435\pi\)
0.636371 + 0.771384i \(0.280435\pi\)
\(828\) 1.54707 0.0537644
\(829\) 40.4011 1.40319 0.701594 0.712577i \(-0.252472\pi\)
0.701594 + 0.712577i \(0.252472\pi\)
\(830\) −8.06246 −0.279852
\(831\) −7.98465 −0.276985
\(832\) −64.3435 −2.23071
\(833\) −1.41119 −0.0488949
\(834\) 38.1621 1.32144
\(835\) 30.6459 1.06055
\(836\) 15.3087 0.529463
\(837\) 14.7684 0.510470
\(838\) 37.1229 1.28239
\(839\) 49.1878 1.69815 0.849076 0.528270i \(-0.177159\pi\)
0.849076 + 0.528270i \(0.177159\pi\)
\(840\) 51.3963 1.77334
\(841\) −6.62927 −0.228596
\(842\) −57.9629 −1.99753
\(843\) 44.1747 1.52146
\(844\) −34.2541 −1.17908
\(845\) 49.1248 1.68994
\(846\) −0.430117 −0.0147877
\(847\) 2.36407 0.0812303
\(848\) 0.865068 0.0297066
\(849\) 19.7870 0.679087
\(850\) −24.8651 −0.852866
\(851\) −5.90816 −0.202529
\(852\) −23.0710 −0.790400
\(853\) −8.59589 −0.294318 −0.147159 0.989113i \(-0.547013\pi\)
−0.147159 + 0.989113i \(0.547013\pi\)
\(854\) 16.5254 0.565489
\(855\) 4.24350 0.145125
\(856\) −9.69366 −0.331322
\(857\) −6.09109 −0.208068 −0.104034 0.994574i \(-0.533175\pi\)
−0.104034 + 0.994574i \(0.533175\pi\)
\(858\) 20.8831 0.712936
\(859\) 21.3565 0.728676 0.364338 0.931267i \(-0.381295\pi\)
0.364338 + 0.931267i \(0.381295\pi\)
\(860\) 13.1883 0.449716
\(861\) −12.5322 −0.427096
\(862\) 64.0181 2.18046
\(863\) 37.7200 1.28400 0.642002 0.766703i \(-0.278104\pi\)
0.642002 + 0.766703i \(0.278104\pi\)
\(864\) 25.9163 0.881690
\(865\) −84.8313 −2.88435
\(866\) 54.1157 1.83893
\(867\) −1.79768 −0.0610525
\(868\) 23.2910 0.790547
\(869\) −12.2298 −0.414866
\(870\) 77.9050 2.64123
\(871\) 49.4727 1.67632
\(872\) 18.3685 0.622037
\(873\) −1.23027 −0.0416382
\(874\) −21.3941 −0.723667
\(875\) 54.2854 1.83518
\(876\) −27.5237 −0.929940
\(877\) −22.9518 −0.775029 −0.387514 0.921864i \(-0.626666\pi\)
−0.387514 + 0.921864i \(0.626666\pi\)
\(878\) 34.4491 1.16260
\(879\) −24.0581 −0.811459
\(880\) 1.51757 0.0511573
\(881\) −40.4541 −1.36293 −0.681467 0.731849i \(-0.738658\pi\)
−0.681467 + 0.731849i \(0.738658\pi\)
\(882\) 0.754033 0.0253896
\(883\) −31.5257 −1.06092 −0.530462 0.847708i \(-0.677982\pi\)
−0.530462 + 0.847708i \(0.677982\pi\)
\(884\) 16.7208 0.562380
\(885\) 37.0447 1.24524
\(886\) 61.0505 2.05103
\(887\) 53.9270 1.81069 0.905346 0.424676i \(-0.139612\pi\)
0.905346 + 0.424676i \(0.139612\pi\)
\(888\) −16.0744 −0.539421
\(889\) −1.17512 −0.0394121
\(890\) −47.7846 −1.60174
\(891\) −9.64132 −0.322996
\(892\) −80.7718 −2.70444
\(893\) 3.71188 0.124213
\(894\) −27.0537 −0.904810
\(895\) 53.6473 1.79323
\(896\) 45.0383 1.50462
\(897\) −18.2126 −0.608101
\(898\) 27.9927 0.934129
\(899\) 14.0359 0.468124
\(900\) 8.29120 0.276373
\(901\) 2.26444 0.0754395
\(902\) −6.80154 −0.226467
\(903\) −4.24984 −0.141426
\(904\) 8.75856 0.291305
\(905\) −54.4124 −1.80873
\(906\) 26.6391 0.885026
\(907\) 37.3036 1.23865 0.619323 0.785136i \(-0.287407\pi\)
0.619323 + 0.785136i \(0.287407\pi\)
\(908\) 12.1856 0.404395
\(909\) 2.54791 0.0845088
\(910\) −109.094 −3.61643
\(911\) −19.4609 −0.644769 −0.322384 0.946609i \(-0.604484\pi\)
−0.322384 + 0.946609i \(0.604484\pi\)
\(912\) −3.16675 −0.104862
\(913\) 0.879944 0.0291219
\(914\) 55.5485 1.83738
\(915\) 21.6428 0.715489
\(916\) −12.5893 −0.415963
\(917\) 37.4743 1.23751
\(918\) −11.4785 −0.378847
\(919\) −0.333493 −0.0110009 −0.00550046 0.999985i \(-0.501751\pi\)
−0.00550046 + 0.999985i \(0.501751\pi\)
\(920\) −24.3271 −0.802040
\(921\) −13.7044 −0.451575
\(922\) −87.6758 −2.88745
\(923\) 19.4695 0.640847
\(924\) −14.1091 −0.464156
\(925\) −31.6635 −1.04109
\(926\) 19.4394 0.638818
\(927\) 1.22872 0.0403564
\(928\) 24.6309 0.808550
\(929\) −48.7790 −1.60039 −0.800194 0.599742i \(-0.795270\pi\)
−0.800194 + 0.599742i \(0.795270\pi\)
\(930\) 48.8794 1.60282
\(931\) −6.50725 −0.213266
\(932\) −47.9439 −1.57046
\(933\) 1.93631 0.0633921
\(934\) −17.6589 −0.577818
\(935\) 3.97246 0.129913
\(936\) −3.55206 −0.116103
\(937\) −13.6133 −0.444726 −0.222363 0.974964i \(-0.571377\pi\)
−0.222363 + 0.974964i \(0.571377\pi\)
\(938\) −53.5610 −1.74883
\(939\) 11.6648 0.380666
\(940\) 10.6162 0.346263
\(941\) 1.09381 0.0356572 0.0178286 0.999841i \(-0.494325\pi\)
0.0178286 + 0.999841i \(0.494325\pi\)
\(942\) −58.7267 −1.91342
\(943\) 5.93178 0.193165
\(944\) −1.98172 −0.0644995
\(945\) 46.7360 1.52032
\(946\) −2.30649 −0.0749906
\(947\) 17.8443 0.579863 0.289931 0.957047i \(-0.406368\pi\)
0.289931 + 0.957047i \(0.406368\pi\)
\(948\) 72.9891 2.37058
\(949\) 23.2271 0.753984
\(950\) −114.657 −3.71998
\(951\) −16.1357 −0.523235
\(952\) −7.19713 −0.233260
\(953\) −28.7536 −0.931420 −0.465710 0.884937i \(-0.654201\pi\)
−0.465710 + 0.884937i \(0.654201\pi\)
\(954\) −1.20995 −0.0391735
\(955\) 14.5132 0.469636
\(956\) 21.8684 0.707275
\(957\) −8.50262 −0.274851
\(958\) 36.6284 1.18341
\(959\) −8.86082 −0.286131
\(960\) 91.2323 2.94451
\(961\) −22.1936 −0.715921
\(962\) 34.1195 1.10006
\(963\) 0.737633 0.0237699
\(964\) −51.3173 −1.65282
\(965\) 59.2874 1.90853
\(966\) 19.7177 0.634405
\(967\) −34.8048 −1.11925 −0.559624 0.828747i \(-0.689054\pi\)
−0.559624 + 0.828747i \(0.689054\pi\)
\(968\) −3.04439 −0.0978503
\(969\) −8.28943 −0.266295
\(970\) 48.6586 1.56233
\(971\) −46.7985 −1.50184 −0.750918 0.660395i \(-0.770389\pi\)
−0.750918 + 0.660395i \(0.770389\pi\)
\(972\) 7.97524 0.255806
\(973\) 21.7584 0.697541
\(974\) −22.1164 −0.708657
\(975\) −97.6067 −3.12592
\(976\) −1.15779 −0.0370600
\(977\) −3.80196 −0.121635 −0.0608177 0.998149i \(-0.519371\pi\)
−0.0608177 + 0.998149i \(0.519371\pi\)
\(978\) 18.0036 0.575690
\(979\) 5.21525 0.166680
\(980\) −18.6111 −0.594511
\(981\) −1.39774 −0.0446265
\(982\) −24.3666 −0.777570
\(983\) −23.6880 −0.755531 −0.377765 0.925901i \(-0.623307\pi\)
−0.377765 + 0.925901i \(0.623307\pi\)
\(984\) 16.1387 0.514482
\(985\) −93.8667 −2.99084
\(986\) −10.9092 −0.347419
\(987\) −3.42101 −0.108892
\(988\) 77.1024 2.45295
\(989\) 2.01155 0.0639635
\(990\) −2.12258 −0.0674601
\(991\) 14.2183 0.451659 0.225830 0.974167i \(-0.427491\pi\)
0.225830 + 0.974167i \(0.427491\pi\)
\(992\) 15.4540 0.490665
\(993\) −37.0246 −1.17494
\(994\) −21.0784 −0.668568
\(995\) 79.2078 2.51106
\(996\) −5.25165 −0.166405
\(997\) −53.4245 −1.69197 −0.845986 0.533206i \(-0.820987\pi\)
−0.845986 + 0.533206i \(0.820987\pi\)
\(998\) 7.64611 0.242033
\(999\) −14.6168 −0.462457
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 \(a_p\))