Properties

Label 8042.2.a.c.1.3
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 0
Dimension 86
CM No

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Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(0\)
Dimension: \(86\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-3.00414 q^{3}\) \(+1.00000 q^{4}\) \(-0.143261 q^{5}\) \(+3.00414 q^{6}\) \(-0.146700 q^{7}\) \(-1.00000 q^{8}\) \(+6.02484 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-3.00414 q^{3}\) \(+1.00000 q^{4}\) \(-0.143261 q^{5}\) \(+3.00414 q^{6}\) \(-0.146700 q^{7}\) \(-1.00000 q^{8}\) \(+6.02484 q^{9}\) \(+0.143261 q^{10}\) \(+0.117687 q^{11}\) \(-3.00414 q^{12}\) \(-6.33848 q^{13}\) \(+0.146700 q^{14}\) \(+0.430375 q^{15}\) \(+1.00000 q^{16}\) \(+4.19606 q^{17}\) \(-6.02484 q^{18}\) \(+2.12556 q^{19}\) \(-0.143261 q^{20}\) \(+0.440707 q^{21}\) \(-0.117687 q^{22}\) \(+6.31069 q^{23}\) \(+3.00414 q^{24}\) \(-4.97948 q^{25}\) \(+6.33848 q^{26}\) \(-9.08704 q^{27}\) \(-0.146700 q^{28}\) \(+1.74846 q^{29}\) \(-0.430375 q^{30}\) \(-5.62193 q^{31}\) \(-1.00000 q^{32}\) \(-0.353548 q^{33}\) \(-4.19606 q^{34}\) \(+0.0210164 q^{35}\) \(+6.02484 q^{36}\) \(+4.37146 q^{37}\) \(-2.12556 q^{38}\) \(+19.0417 q^{39}\) \(+0.143261 q^{40}\) \(-4.63468 q^{41}\) \(-0.440707 q^{42}\) \(+1.74631 q^{43}\) \(+0.117687 q^{44}\) \(-0.863123 q^{45}\) \(-6.31069 q^{46}\) \(-3.49996 q^{47}\) \(-3.00414 q^{48}\) \(-6.97848 q^{49}\) \(+4.97948 q^{50}\) \(-12.6055 q^{51}\) \(-6.33848 q^{52}\) \(+11.4668 q^{53}\) \(+9.08704 q^{54}\) \(-0.0168599 q^{55}\) \(+0.146700 q^{56}\) \(-6.38546 q^{57}\) \(-1.74846 q^{58}\) \(+6.01860 q^{59}\) \(+0.430375 q^{60}\) \(+1.18916 q^{61}\) \(+5.62193 q^{62}\) \(-0.883845 q^{63}\) \(+1.00000 q^{64}\) \(+0.908056 q^{65}\) \(+0.353548 q^{66}\) \(+14.6051 q^{67}\) \(+4.19606 q^{68}\) \(-18.9582 q^{69}\) \(-0.0210164 q^{70}\) \(-7.58579 q^{71}\) \(-6.02484 q^{72}\) \(+4.40295 q^{73}\) \(-4.37146 q^{74}\) \(+14.9590 q^{75}\) \(+2.12556 q^{76}\) \(-0.0172647 q^{77}\) \(-19.0417 q^{78}\) \(-9.92100 q^{79}\) \(-0.143261 q^{80}\) \(+9.22419 q^{81}\) \(+4.63468 q^{82}\) \(-15.2838 q^{83}\) \(+0.440707 q^{84}\) \(-0.601130 q^{85}\) \(-1.74631 q^{86}\) \(-5.25263 q^{87}\) \(-0.117687 q^{88}\) \(+8.97895 q^{89}\) \(+0.863123 q^{90}\) \(+0.929857 q^{91}\) \(+6.31069 q^{92}\) \(+16.8891 q^{93}\) \(+3.49996 q^{94}\) \(-0.304509 q^{95}\) \(+3.00414 q^{96}\) \(-6.41299 q^{97}\) \(+6.97848 q^{98}\) \(+0.709045 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 45q^{13} \) \(\mathstrut -\mathstrut 35q^{14} \) \(\mathstrut +\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 86q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 72q^{18} \) \(\mathstrut +\mathstrut 47q^{19} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 12q^{24} \) \(\mathstrut +\mathstrut 112q^{25} \) \(\mathstrut -\mathstrut 45q^{26} \) \(\mathstrut +\mathstrut 51q^{27} \) \(\mathstrut +\mathstrut 35q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut -\mathstrut 17q^{30} \) \(\mathstrut +\mathstrut 24q^{31} \) \(\mathstrut -\mathstrut 86q^{32} \) \(\mathstrut +\mathstrut 43q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 42q^{35} \) \(\mathstrut +\mathstrut 72q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut -\mathstrut 15q^{42} \) \(\mathstrut +\mathstrut 72q^{43} \) \(\mathstrut +\mathstrut 13q^{44} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut +\mathstrut 12q^{48} \) \(\mathstrut +\mathstrut 89q^{49} \) \(\mathstrut -\mathstrut 112q^{50} \) \(\mathstrut +\mathstrut 56q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut -\mathstrut 7q^{53} \) \(\mathstrut -\mathstrut 51q^{54} \) \(\mathstrut +\mathstrut 48q^{55} \) \(\mathstrut -\mathstrut 35q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 31q^{61} \) \(\mathstrut -\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 98q^{63} \) \(\mathstrut +\mathstrut 86q^{64} \) \(\mathstrut -\mathstrut 9q^{65} \) \(\mathstrut -\mathstrut 43q^{66} \) \(\mathstrut +\mathstrut 157q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 42q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 72q^{72} \) \(\mathstrut +\mathstrut 74q^{73} \) \(\mathstrut -\mathstrut 61q^{74} \) \(\mathstrut +\mathstrut 76q^{75} \) \(\mathstrut +\mathstrut 47q^{76} \) \(\mathstrut -\mathstrut 13q^{77} \) \(\mathstrut -\mathstrut 20q^{78} \) \(\mathstrut +\mathstrut 57q^{79} \) \(\mathstrut -\mathstrut 4q^{80} \) \(\mathstrut +\mathstrut 34q^{81} \) \(\mathstrut +\mathstrut 16q^{82} \) \(\mathstrut +\mathstrut 65q^{83} \) \(\mathstrut +\mathstrut 15q^{84} \) \(\mathstrut +\mathstrut 102q^{85} \) \(\mathstrut -\mathstrut 72q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 91q^{91} \) \(\mathstrut +\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 57q^{93} \) \(\mathstrut -\mathstrut 11q^{94} \) \(\mathstrut -\mathstrut 13q^{95} \) \(\mathstrut -\mathstrut 12q^{96} \) \(\mathstrut +\mathstrut 64q^{97} \) \(\mathstrut -\mathstrut 89q^{98} \) \(\mathstrut +\mathstrut 56q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −3.00414 −1.73444 −0.867220 0.497926i \(-0.834095\pi\)
−0.867220 + 0.497926i \(0.834095\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.143261 −0.0640682 −0.0320341 0.999487i \(-0.510199\pi\)
−0.0320341 + 0.999487i \(0.510199\pi\)
\(6\) 3.00414 1.22643
\(7\) −0.146700 −0.0554474 −0.0277237 0.999616i \(-0.508826\pi\)
−0.0277237 + 0.999616i \(0.508826\pi\)
\(8\) −1.00000 −0.353553
\(9\) 6.02484 2.00828
\(10\) 0.143261 0.0453030
\(11\) 0.117687 0.0354839 0.0177420 0.999843i \(-0.494352\pi\)
0.0177420 + 0.999843i \(0.494352\pi\)
\(12\) −3.00414 −0.867220
\(13\) −6.33848 −1.75798 −0.878990 0.476841i \(-0.841782\pi\)
−0.878990 + 0.476841i \(0.841782\pi\)
\(14\) 0.146700 0.0392073
\(15\) 0.430375 0.111122
\(16\) 1.00000 0.250000
\(17\) 4.19606 1.01769 0.508847 0.860857i \(-0.330072\pi\)
0.508847 + 0.860857i \(0.330072\pi\)
\(18\) −6.02484 −1.42007
\(19\) 2.12556 0.487636 0.243818 0.969821i \(-0.421600\pi\)
0.243818 + 0.969821i \(0.421600\pi\)
\(20\) −0.143261 −0.0320341
\(21\) 0.440707 0.0961702
\(22\) −0.117687 −0.0250909
\(23\) 6.31069 1.31587 0.657935 0.753074i \(-0.271430\pi\)
0.657935 + 0.753074i \(0.271430\pi\)
\(24\) 3.00414 0.613217
\(25\) −4.97948 −0.995895
\(26\) 6.33848 1.24308
\(27\) −9.08704 −1.74880
\(28\) −0.146700 −0.0277237
\(29\) 1.74846 0.324682 0.162341 0.986735i \(-0.448096\pi\)
0.162341 + 0.986735i \(0.448096\pi\)
\(30\) −0.430375 −0.0785754
\(31\) −5.62193 −1.00973 −0.504864 0.863199i \(-0.668457\pi\)
−0.504864 + 0.863199i \(0.668457\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.353548 −0.0615447
\(34\) −4.19606 −0.719618
\(35\) 0.0210164 0.00355242
\(36\) 6.02484 1.00414
\(37\) 4.37146 0.718663 0.359332 0.933210i \(-0.383005\pi\)
0.359332 + 0.933210i \(0.383005\pi\)
\(38\) −2.12556 −0.344811
\(39\) 19.0417 3.04911
\(40\) 0.143261 0.0226515
\(41\) −4.63468 −0.723816 −0.361908 0.932214i \(-0.617875\pi\)
−0.361908 + 0.932214i \(0.617875\pi\)
\(42\) −0.440707 −0.0680026
\(43\) 1.74631 0.266310 0.133155 0.991095i \(-0.457489\pi\)
0.133155 + 0.991095i \(0.457489\pi\)
\(44\) 0.117687 0.0177420
\(45\) −0.863123 −0.128667
\(46\) −6.31069 −0.930461
\(47\) −3.49996 −0.510522 −0.255261 0.966872i \(-0.582161\pi\)
−0.255261 + 0.966872i \(0.582161\pi\)
\(48\) −3.00414 −0.433610
\(49\) −6.97848 −0.996926
\(50\) 4.97948 0.704204
\(51\) −12.6055 −1.76513
\(52\) −6.33848 −0.878990
\(53\) 11.4668 1.57509 0.787546 0.616256i \(-0.211351\pi\)
0.787546 + 0.616256i \(0.211351\pi\)
\(54\) 9.08704 1.23659
\(55\) −0.0168599 −0.00227339
\(56\) 0.146700 0.0196036
\(57\) −6.38546 −0.845775
\(58\) −1.74846 −0.229585
\(59\) 6.01860 0.783555 0.391778 0.920060i \(-0.371860\pi\)
0.391778 + 0.920060i \(0.371860\pi\)
\(60\) 0.430375 0.0555612
\(61\) 1.18916 0.152256 0.0761281 0.997098i \(-0.475744\pi\)
0.0761281 + 0.997098i \(0.475744\pi\)
\(62\) 5.62193 0.713986
\(63\) −0.883845 −0.111354
\(64\) 1.00000 0.125000
\(65\) 0.908056 0.112631
\(66\) 0.353548 0.0435187
\(67\) 14.6051 1.78430 0.892151 0.451737i \(-0.149196\pi\)
0.892151 + 0.451737i \(0.149196\pi\)
\(68\) 4.19606 0.508847
\(69\) −18.9582 −2.28230
\(70\) −0.0210164 −0.00251194
\(71\) −7.58579 −0.900268 −0.450134 0.892961i \(-0.648624\pi\)
−0.450134 + 0.892961i \(0.648624\pi\)
\(72\) −6.02484 −0.710034
\(73\) 4.40295 0.515327 0.257663 0.966235i \(-0.417047\pi\)
0.257663 + 0.966235i \(0.417047\pi\)
\(74\) −4.37146 −0.508172
\(75\) 14.9590 1.72732
\(76\) 2.12556 0.243818
\(77\) −0.0172647 −0.00196749
\(78\) −19.0417 −2.15605
\(79\) −9.92100 −1.11620 −0.558100 0.829774i \(-0.688469\pi\)
−0.558100 + 0.829774i \(0.688469\pi\)
\(80\) −0.143261 −0.0160170
\(81\) 9.22419 1.02491
\(82\) 4.63468 0.511815
\(83\) −15.2838 −1.67761 −0.838805 0.544432i \(-0.816745\pi\)
−0.838805 + 0.544432i \(0.816745\pi\)
\(84\) 0.440707 0.0480851
\(85\) −0.601130 −0.0652017
\(86\) −1.74631 −0.188310
\(87\) −5.25263 −0.563141
\(88\) −0.117687 −0.0125455
\(89\) 8.97895 0.951767 0.475883 0.879508i \(-0.342128\pi\)
0.475883 + 0.879508i \(0.342128\pi\)
\(90\) 0.863123 0.0909812
\(91\) 0.929857 0.0974755
\(92\) 6.31069 0.657935
\(93\) 16.8891 1.75131
\(94\) 3.49996 0.360994
\(95\) −0.304509 −0.0312419
\(96\) 3.00414 0.306608
\(97\) −6.41299 −0.651140 −0.325570 0.945518i \(-0.605556\pi\)
−0.325570 + 0.945518i \(0.605556\pi\)
\(98\) 6.97848 0.704933
\(99\) 0.709045 0.0712617
\(100\) −4.97948 −0.497948
\(101\) −4.75450 −0.473090 −0.236545 0.971620i \(-0.576015\pi\)
−0.236545 + 0.971620i \(0.576015\pi\)
\(102\) 12.6055 1.24813
\(103\) 2.09799 0.206721 0.103360 0.994644i \(-0.467040\pi\)
0.103360 + 0.994644i \(0.467040\pi\)
\(104\) 6.33848 0.621540
\(105\) −0.0631361 −0.00616145
\(106\) −11.4668 −1.11376
\(107\) 13.9416 1.34778 0.673891 0.738831i \(-0.264622\pi\)
0.673891 + 0.738831i \(0.264622\pi\)
\(108\) −9.08704 −0.874401
\(109\) 15.3448 1.46976 0.734881 0.678196i \(-0.237238\pi\)
0.734881 + 0.678196i \(0.237238\pi\)
\(110\) 0.0168599 0.00160753
\(111\) −13.1325 −1.24648
\(112\) −0.146700 −0.0138619
\(113\) −4.43684 −0.417382 −0.208691 0.977982i \(-0.566920\pi\)
−0.208691 + 0.977982i \(0.566920\pi\)
\(114\) 6.38546 0.598053
\(115\) −0.904075 −0.0843054
\(116\) 1.74846 0.162341
\(117\) −38.1884 −3.53052
\(118\) −6.01860 −0.554057
\(119\) −0.615562 −0.0564285
\(120\) −0.430375 −0.0392877
\(121\) −10.9861 −0.998741
\(122\) −1.18916 −0.107661
\(123\) 13.9232 1.25542
\(124\) −5.62193 −0.504864
\(125\) 1.42967 0.127873
\(126\) 0.883845 0.0787392
\(127\) 17.6214 1.56365 0.781825 0.623498i \(-0.214289\pi\)
0.781825 + 0.623498i \(0.214289\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −5.24616 −0.461899
\(130\) −0.908056 −0.0796418
\(131\) −8.25962 −0.721646 −0.360823 0.932634i \(-0.617504\pi\)
−0.360823 + 0.932634i \(0.617504\pi\)
\(132\) −0.353548 −0.0307724
\(133\) −0.311819 −0.0270382
\(134\) −14.6051 −1.26169
\(135\) 1.30182 0.112043
\(136\) −4.19606 −0.359809
\(137\) 17.7800 1.51905 0.759524 0.650479i \(-0.225432\pi\)
0.759524 + 0.650479i \(0.225432\pi\)
\(138\) 18.9582 1.61383
\(139\) −18.3371 −1.55534 −0.777668 0.628676i \(-0.783597\pi\)
−0.777668 + 0.628676i \(0.783597\pi\)
\(140\) 0.0210164 0.00177621
\(141\) 10.5144 0.885470
\(142\) 7.58579 0.636586
\(143\) −0.745956 −0.0623800
\(144\) 6.02484 0.502070
\(145\) −0.250486 −0.0208018
\(146\) −4.40295 −0.364391
\(147\) 20.9643 1.72911
\(148\) 4.37146 0.359332
\(149\) −7.59093 −0.621873 −0.310936 0.950431i \(-0.600643\pi\)
−0.310936 + 0.950431i \(0.600643\pi\)
\(150\) −14.9590 −1.22140
\(151\) −12.6027 −1.02560 −0.512798 0.858509i \(-0.671391\pi\)
−0.512798 + 0.858509i \(0.671391\pi\)
\(152\) −2.12556 −0.172405
\(153\) 25.2806 2.04381
\(154\) 0.0172647 0.00139123
\(155\) 0.805402 0.0646914
\(156\) 19.0417 1.52455
\(157\) −23.0055 −1.83604 −0.918020 0.396535i \(-0.870213\pi\)
−0.918020 + 0.396535i \(0.870213\pi\)
\(158\) 9.92100 0.789272
\(159\) −34.4480 −2.73190
\(160\) 0.143261 0.0113258
\(161\) −0.925780 −0.0729617
\(162\) −9.22419 −0.724721
\(163\) −7.96081 −0.623539 −0.311769 0.950158i \(-0.600922\pi\)
−0.311769 + 0.950158i \(0.600922\pi\)
\(164\) −4.63468 −0.361908
\(165\) 0.0506495 0.00394306
\(166\) 15.2838 1.18625
\(167\) 22.0414 1.70561 0.852806 0.522228i \(-0.174899\pi\)
0.852806 + 0.522228i \(0.174899\pi\)
\(168\) −0.440707 −0.0340013
\(169\) 27.1764 2.09049
\(170\) 0.601130 0.0461046
\(171\) 12.8061 0.979310
\(172\) 1.74631 0.133155
\(173\) −3.46386 −0.263352 −0.131676 0.991293i \(-0.542036\pi\)
−0.131676 + 0.991293i \(0.542036\pi\)
\(174\) 5.25263 0.398200
\(175\) 0.730490 0.0552199
\(176\) 0.117687 0.00887098
\(177\) −18.0807 −1.35903
\(178\) −8.97895 −0.673001
\(179\) 3.47610 0.259816 0.129908 0.991526i \(-0.458532\pi\)
0.129908 + 0.991526i \(0.458532\pi\)
\(180\) −0.863123 −0.0643334
\(181\) 1.99572 0.148341 0.0741705 0.997246i \(-0.476369\pi\)
0.0741705 + 0.997246i \(0.476369\pi\)
\(182\) −0.929857 −0.0689256
\(183\) −3.57240 −0.264079
\(184\) −6.31069 −0.465231
\(185\) −0.626258 −0.0460434
\(186\) −16.8891 −1.23837
\(187\) 0.493821 0.0361118
\(188\) −3.49996 −0.255261
\(189\) 1.33307 0.0969666
\(190\) 0.304509 0.0220914
\(191\) −15.1161 −1.09376 −0.546881 0.837211i \(-0.684185\pi\)
−0.546881 + 0.837211i \(0.684185\pi\)
\(192\) −3.00414 −0.216805
\(193\) −19.1486 −1.37835 −0.689173 0.724596i \(-0.742026\pi\)
−0.689173 + 0.724596i \(0.742026\pi\)
\(194\) 6.41299 0.460426
\(195\) −2.72793 −0.195351
\(196\) −6.97848 −0.498463
\(197\) −14.4147 −1.02701 −0.513503 0.858088i \(-0.671653\pi\)
−0.513503 + 0.858088i \(0.671653\pi\)
\(198\) −0.709045 −0.0503896
\(199\) 0.101937 0.00722611 0.00361306 0.999993i \(-0.498850\pi\)
0.00361306 + 0.999993i \(0.498850\pi\)
\(200\) 4.97948 0.352102
\(201\) −43.8759 −3.09476
\(202\) 4.75450 0.334525
\(203\) −0.256500 −0.0180028
\(204\) −12.6055 −0.882564
\(205\) 0.663968 0.0463736
\(206\) −2.09799 −0.146174
\(207\) 38.0209 2.64264
\(208\) −6.33848 −0.439495
\(209\) 0.250150 0.0173032
\(210\) 0.0631361 0.00435680
\(211\) −9.12493 −0.628186 −0.314093 0.949392i \(-0.601700\pi\)
−0.314093 + 0.949392i \(0.601700\pi\)
\(212\) 11.4668 0.787546
\(213\) 22.7888 1.56146
\(214\) −13.9416 −0.953025
\(215\) −0.250178 −0.0170620
\(216\) 9.08704 0.618295
\(217\) 0.824738 0.0559869
\(218\) −15.3448 −1.03928
\(219\) −13.2271 −0.893803
\(220\) −0.0168599 −0.00113670
\(221\) −26.5966 −1.78908
\(222\) 13.1325 0.881393
\(223\) 7.75136 0.519070 0.259535 0.965734i \(-0.416431\pi\)
0.259535 + 0.965734i \(0.416431\pi\)
\(224\) 0.146700 0.00980182
\(225\) −30.0006 −2.00004
\(226\) 4.43684 0.295134
\(227\) 16.3899 1.08783 0.543917 0.839139i \(-0.316941\pi\)
0.543917 + 0.839139i \(0.316941\pi\)
\(228\) −6.38546 −0.422888
\(229\) −2.65714 −0.175589 −0.0877943 0.996139i \(-0.527982\pi\)
−0.0877943 + 0.996139i \(0.527982\pi\)
\(230\) 0.904075 0.0596129
\(231\) 0.0518655 0.00341250
\(232\) −1.74846 −0.114792
\(233\) 2.56307 0.167912 0.0839562 0.996469i \(-0.473244\pi\)
0.0839562 + 0.996469i \(0.473244\pi\)
\(234\) 38.1884 2.49645
\(235\) 0.501407 0.0327082
\(236\) 6.01860 0.391778
\(237\) 29.8040 1.93598
\(238\) 0.615562 0.0399010
\(239\) −0.605731 −0.0391815 −0.0195908 0.999808i \(-0.506236\pi\)
−0.0195908 + 0.999808i \(0.506236\pi\)
\(240\) 0.430375 0.0277806
\(241\) −28.9977 −1.86790 −0.933952 0.357397i \(-0.883664\pi\)
−0.933952 + 0.357397i \(0.883664\pi\)
\(242\) 10.9861 0.706216
\(243\) −0.449626 −0.0288435
\(244\) 1.18916 0.0761281
\(245\) 0.999742 0.0638712
\(246\) −13.9232 −0.887713
\(247\) −13.4728 −0.857254
\(248\) 5.62193 0.356993
\(249\) 45.9145 2.90971
\(250\) −1.42967 −0.0904201
\(251\) 10.1312 0.639479 0.319739 0.947506i \(-0.396405\pi\)
0.319739 + 0.947506i \(0.396405\pi\)
\(252\) −0.883845 −0.0556770
\(253\) 0.742686 0.0466923
\(254\) −17.6214 −1.10567
\(255\) 1.80588 0.113088
\(256\) 1.00000 0.0625000
\(257\) −1.29014 −0.0804765 −0.0402382 0.999190i \(-0.512812\pi\)
−0.0402382 + 0.999190i \(0.512812\pi\)
\(258\) 5.24616 0.326612
\(259\) −0.641293 −0.0398480
\(260\) 0.908056 0.0563153
\(261\) 10.5342 0.652052
\(262\) 8.25962 0.510281
\(263\) 3.29653 0.203273 0.101636 0.994822i \(-0.467592\pi\)
0.101636 + 0.994822i \(0.467592\pi\)
\(264\) 0.353548 0.0217593
\(265\) −1.64275 −0.100913
\(266\) 0.311819 0.0191189
\(267\) −26.9740 −1.65078
\(268\) 14.6051 0.892151
\(269\) −2.96748 −0.180931 −0.0904653 0.995900i \(-0.528835\pi\)
−0.0904653 + 0.995900i \(0.528835\pi\)
\(270\) −1.30182 −0.0792260
\(271\) 6.81422 0.413935 0.206967 0.978348i \(-0.433641\pi\)
0.206967 + 0.978348i \(0.433641\pi\)
\(272\) 4.19606 0.254423
\(273\) −2.79342 −0.169065
\(274\) −17.7800 −1.07413
\(275\) −0.586019 −0.0353383
\(276\) −18.9582 −1.14115
\(277\) 19.2518 1.15673 0.578364 0.815779i \(-0.303691\pi\)
0.578364 + 0.815779i \(0.303691\pi\)
\(278\) 18.3371 1.09979
\(279\) −33.8712 −2.02782
\(280\) −0.0210164 −0.00125597
\(281\) −20.5585 −1.22642 −0.613209 0.789920i \(-0.710122\pi\)
−0.613209 + 0.789920i \(0.710122\pi\)
\(282\) −10.5144 −0.626122
\(283\) 10.3320 0.614171 0.307086 0.951682i \(-0.400646\pi\)
0.307086 + 0.951682i \(0.400646\pi\)
\(284\) −7.58579 −0.450134
\(285\) 0.914786 0.0541873
\(286\) 0.745956 0.0441093
\(287\) 0.679909 0.0401337
\(288\) −6.02484 −0.355017
\(289\) 0.606890 0.0356994
\(290\) 0.250486 0.0147091
\(291\) 19.2655 1.12936
\(292\) 4.40295 0.257663
\(293\) −19.2625 −1.12533 −0.562665 0.826685i \(-0.690224\pi\)
−0.562665 + 0.826685i \(0.690224\pi\)
\(294\) −20.9643 −1.22266
\(295\) −0.862229 −0.0502009
\(296\) −4.37146 −0.254086
\(297\) −1.06943 −0.0620544
\(298\) 7.59093 0.439731
\(299\) −40.0002 −2.31327
\(300\) 14.9590 0.863660
\(301\) −0.256184 −0.0147662
\(302\) 12.6027 0.725206
\(303\) 14.2832 0.820547
\(304\) 2.12556 0.121909
\(305\) −0.170360 −0.00975477
\(306\) −25.2806 −1.44519
\(307\) 24.0421 1.37216 0.686078 0.727528i \(-0.259331\pi\)
0.686078 + 0.727528i \(0.259331\pi\)
\(308\) −0.0172647 −0.000983747 0
\(309\) −6.30264 −0.358545
\(310\) −0.805402 −0.0457438
\(311\) −1.21572 −0.0689370 −0.0344685 0.999406i \(-0.510974\pi\)
−0.0344685 + 0.999406i \(0.510974\pi\)
\(312\) −19.0417 −1.07802
\(313\) −22.7088 −1.28358 −0.641789 0.766881i \(-0.721808\pi\)
−0.641789 + 0.766881i \(0.721808\pi\)
\(314\) 23.0055 1.29828
\(315\) 0.126620 0.00713425
\(316\) −9.92100 −0.558100
\(317\) −11.0177 −0.618815 −0.309407 0.950930i \(-0.600131\pi\)
−0.309407 + 0.950930i \(0.600131\pi\)
\(318\) 34.4480 1.93175
\(319\) 0.205771 0.0115210
\(320\) −0.143261 −0.00800852
\(321\) −41.8823 −2.33764
\(322\) 0.925780 0.0515917
\(323\) 8.91895 0.496264
\(324\) 9.22419 0.512455
\(325\) 31.5623 1.75076
\(326\) 7.96081 0.440909
\(327\) −46.0978 −2.54921
\(328\) 4.63468 0.255908
\(329\) 0.513445 0.0283072
\(330\) −0.0506495 −0.00278816
\(331\) 10.9201 0.600224 0.300112 0.953904i \(-0.402976\pi\)
0.300112 + 0.953904i \(0.402976\pi\)
\(332\) −15.2838 −0.838805
\(333\) 26.3373 1.44328
\(334\) −22.0414 −1.20605
\(335\) −2.09234 −0.114317
\(336\) 0.440707 0.0240426
\(337\) −8.71803 −0.474901 −0.237451 0.971400i \(-0.576312\pi\)
−0.237451 + 0.971400i \(0.576312\pi\)
\(338\) −27.1764 −1.47820
\(339\) 13.3289 0.723925
\(340\) −0.601130 −0.0326009
\(341\) −0.661627 −0.0358291
\(342\) −12.8061 −0.692477
\(343\) 2.05065 0.110724
\(344\) −1.74631 −0.0941548
\(345\) 2.71597 0.146223
\(346\) 3.46386 0.186218
\(347\) 2.70409 0.145163 0.0725816 0.997362i \(-0.476876\pi\)
0.0725816 + 0.997362i \(0.476876\pi\)
\(348\) −5.25263 −0.281570
\(349\) −11.6485 −0.623530 −0.311765 0.950159i \(-0.600920\pi\)
−0.311765 + 0.950159i \(0.600920\pi\)
\(350\) −0.730490 −0.0390463
\(351\) 57.5981 3.07436
\(352\) −0.117687 −0.00627273
\(353\) −13.2598 −0.705749 −0.352875 0.935671i \(-0.614796\pi\)
−0.352875 + 0.935671i \(0.614796\pi\)
\(354\) 18.0807 0.960979
\(355\) 1.08675 0.0576785
\(356\) 8.97895 0.475883
\(357\) 1.84923 0.0978718
\(358\) −3.47610 −0.183718
\(359\) 10.4909 0.553686 0.276843 0.960915i \(-0.410712\pi\)
0.276843 + 0.960915i \(0.410712\pi\)
\(360\) 0.863123 0.0454906
\(361\) −14.4820 −0.762211
\(362\) −1.99572 −0.104893
\(363\) 33.0039 1.73226
\(364\) 0.929857 0.0487377
\(365\) −0.630771 −0.0330160
\(366\) 3.57240 0.186732
\(367\) 7.05660 0.368351 0.184176 0.982893i \(-0.441038\pi\)
0.184176 + 0.982893i \(0.441038\pi\)
\(368\) 6.31069 0.328968
\(369\) −27.9232 −1.45363
\(370\) 0.626258 0.0325576
\(371\) −1.68219 −0.0873348
\(372\) 16.8891 0.875656
\(373\) 3.96851 0.205481 0.102741 0.994708i \(-0.467239\pi\)
0.102741 + 0.994708i \(0.467239\pi\)
\(374\) −0.493821 −0.0255349
\(375\) −4.29492 −0.221789
\(376\) 3.49996 0.180497
\(377\) −11.0826 −0.570783
\(378\) −1.33307 −0.0685657
\(379\) 32.0302 1.64528 0.822640 0.568562i \(-0.192500\pi\)
0.822640 + 0.568562i \(0.192500\pi\)
\(380\) −0.304509 −0.0156210
\(381\) −52.9372 −2.71206
\(382\) 15.1161 0.773406
\(383\) −1.91383 −0.0977920 −0.0488960 0.998804i \(-0.515570\pi\)
−0.0488960 + 0.998804i \(0.515570\pi\)
\(384\) 3.00414 0.153304
\(385\) 0.00247335 0.000126054 0
\(386\) 19.1486 0.974638
\(387\) 10.5213 0.534825
\(388\) −6.41299 −0.325570
\(389\) 13.9441 0.706995 0.353498 0.935435i \(-0.384992\pi\)
0.353498 + 0.935435i \(0.384992\pi\)
\(390\) 2.72793 0.138134
\(391\) 26.4800 1.33915
\(392\) 6.97848 0.352466
\(393\) 24.8130 1.25165
\(394\) 14.4147 0.726204
\(395\) 1.42129 0.0715128
\(396\) 0.709045 0.0356308
\(397\) −14.6579 −0.735657 −0.367828 0.929894i \(-0.619899\pi\)
−0.367828 + 0.929894i \(0.619899\pi\)
\(398\) −0.101937 −0.00510963
\(399\) 0.936749 0.0468961
\(400\) −4.97948 −0.248974
\(401\) −35.0260 −1.74912 −0.874558 0.484920i \(-0.838849\pi\)
−0.874558 + 0.484920i \(0.838849\pi\)
\(402\) 43.8759 2.18833
\(403\) 35.6345 1.77508
\(404\) −4.75450 −0.236545
\(405\) −1.32147 −0.0656641
\(406\) 0.256500 0.0127299
\(407\) 0.514463 0.0255010
\(408\) 12.6055 0.624067
\(409\) 18.8063 0.929911 0.464956 0.885334i \(-0.346070\pi\)
0.464956 + 0.885334i \(0.346070\pi\)
\(410\) −0.663968 −0.0327911
\(411\) −53.4136 −2.63470
\(412\) 2.09799 0.103360
\(413\) −0.882930 −0.0434461
\(414\) −38.0209 −1.86863
\(415\) 2.18956 0.107481
\(416\) 6.33848 0.310770
\(417\) 55.0873 2.69763
\(418\) −0.250150 −0.0122352
\(419\) −8.86558 −0.433112 −0.216556 0.976270i \(-0.569482\pi\)
−0.216556 + 0.976270i \(0.569482\pi\)
\(420\) −0.0631361 −0.00308073
\(421\) −7.60121 −0.370460 −0.185230 0.982695i \(-0.559303\pi\)
−0.185230 + 0.982695i \(0.559303\pi\)
\(422\) 9.12493 0.444194
\(423\) −21.0867 −1.02527
\(424\) −11.4668 −0.556879
\(425\) −20.8942 −1.01352
\(426\) −22.7888 −1.10412
\(427\) −0.174450 −0.00844222
\(428\) 13.9416 0.673891
\(429\) 2.24096 0.108194
\(430\) 0.250178 0.0120647
\(431\) 15.4499 0.744193 0.372097 0.928194i \(-0.378639\pi\)
0.372097 + 0.928194i \(0.378639\pi\)
\(432\) −9.08704 −0.437200
\(433\) 12.4640 0.598983 0.299491 0.954099i \(-0.403183\pi\)
0.299491 + 0.954099i \(0.403183\pi\)
\(434\) −0.824738 −0.0395887
\(435\) 0.752495 0.0360794
\(436\) 15.3448 0.734881
\(437\) 13.4137 0.641666
\(438\) 13.2271 0.632014
\(439\) 27.3398 1.30486 0.652429 0.757849i \(-0.273750\pi\)
0.652429 + 0.757849i \(0.273750\pi\)
\(440\) 0.0168599 0.000803765 0
\(441\) −42.0442 −2.00211
\(442\) 26.5966 1.26507
\(443\) −20.7905 −0.987787 −0.493894 0.869522i \(-0.664427\pi\)
−0.493894 + 0.869522i \(0.664427\pi\)
\(444\) −13.1325 −0.623239
\(445\) −1.28633 −0.0609779
\(446\) −7.75136 −0.367038
\(447\) 22.8042 1.07860
\(448\) −0.146700 −0.00693093
\(449\) 6.33018 0.298740 0.149370 0.988781i \(-0.452276\pi\)
0.149370 + 0.988781i \(0.452276\pi\)
\(450\) 30.0006 1.41424
\(451\) −0.545441 −0.0256838
\(452\) −4.43684 −0.208691
\(453\) 37.8604 1.77883
\(454\) −16.3899 −0.769215
\(455\) −0.133212 −0.00624507
\(456\) 6.38546 0.299027
\(457\) 9.74286 0.455752 0.227876 0.973690i \(-0.426822\pi\)
0.227876 + 0.973690i \(0.426822\pi\)
\(458\) 2.65714 0.124160
\(459\) −38.1297 −1.77974
\(460\) −0.904075 −0.0421527
\(461\) 20.5671 0.957904 0.478952 0.877841i \(-0.341017\pi\)
0.478952 + 0.877841i \(0.341017\pi\)
\(462\) −0.0518655 −0.00241300
\(463\) −12.2838 −0.570875 −0.285437 0.958397i \(-0.592139\pi\)
−0.285437 + 0.958397i \(0.592139\pi\)
\(464\) 1.74846 0.0811704
\(465\) −2.41954 −0.112203
\(466\) −2.56307 −0.118732
\(467\) −18.8945 −0.874333 −0.437167 0.899381i \(-0.644018\pi\)
−0.437167 + 0.899381i \(0.644018\pi\)
\(468\) −38.1884 −1.76526
\(469\) −2.14258 −0.0989350
\(470\) −0.501407 −0.0231282
\(471\) 69.1117 3.18450
\(472\) −6.01860 −0.277029
\(473\) 0.205518 0.00944973
\(474\) −29.8040 −1.36894
\(475\) −10.5842 −0.485634
\(476\) −0.615562 −0.0282142
\(477\) 69.0859 3.16323
\(478\) 0.605731 0.0277055
\(479\) 15.8799 0.725571 0.362785 0.931873i \(-0.381826\pi\)
0.362785 + 0.931873i \(0.381826\pi\)
\(480\) −0.430375 −0.0196438
\(481\) −27.7084 −1.26339
\(482\) 28.9977 1.32081
\(483\) 2.78117 0.126548
\(484\) −10.9861 −0.499370
\(485\) 0.918730 0.0417174
\(486\) 0.449626 0.0203954
\(487\) 41.5460 1.88263 0.941313 0.337534i \(-0.109593\pi\)
0.941313 + 0.337534i \(0.109593\pi\)
\(488\) −1.18916 −0.0538307
\(489\) 23.9154 1.08149
\(490\) −0.999742 −0.0451638
\(491\) 22.1488 0.999559 0.499780 0.866153i \(-0.333414\pi\)
0.499780 + 0.866153i \(0.333414\pi\)
\(492\) 13.9232 0.627708
\(493\) 7.33665 0.330426
\(494\) 13.4728 0.606170
\(495\) −0.101578 −0.00456561
\(496\) −5.62193 −0.252432
\(497\) 1.11284 0.0499176
\(498\) −45.9145 −2.05748
\(499\) 42.4407 1.89991 0.949953 0.312393i \(-0.101131\pi\)
0.949953 + 0.312393i \(0.101131\pi\)
\(500\) 1.42967 0.0639367
\(501\) −66.2153 −2.95828
\(502\) −10.1312 −0.452180
\(503\) −27.8906 −1.24358 −0.621791 0.783183i \(-0.713595\pi\)
−0.621791 + 0.783183i \(0.713595\pi\)
\(504\) 0.883845 0.0393696
\(505\) 0.681133 0.0303100
\(506\) −0.742686 −0.0330164
\(507\) −81.6416 −3.62583
\(508\) 17.6214 0.781825
\(509\) −7.03088 −0.311638 −0.155819 0.987786i \(-0.549802\pi\)
−0.155819 + 0.987786i \(0.549802\pi\)
\(510\) −1.80588 −0.0799656
\(511\) −0.645914 −0.0285736
\(512\) −1.00000 −0.0441942
\(513\) −19.3150 −0.852779
\(514\) 1.29014 0.0569055
\(515\) −0.300559 −0.0132442
\(516\) −5.24616 −0.230949
\(517\) −0.411900 −0.0181153
\(518\) 0.641293 0.0281768
\(519\) 10.4059 0.456769
\(520\) −0.908056 −0.0398209
\(521\) 14.6755 0.642947 0.321474 0.946919i \(-0.395822\pi\)
0.321474 + 0.946919i \(0.395822\pi\)
\(522\) −10.5342 −0.461070
\(523\) 28.2656 1.23597 0.617984 0.786191i \(-0.287950\pi\)
0.617984 + 0.786191i \(0.287950\pi\)
\(524\) −8.25962 −0.360823
\(525\) −2.19449 −0.0957755
\(526\) −3.29653 −0.143736
\(527\) −23.5899 −1.02759
\(528\) −0.353548 −0.0153862
\(529\) 16.8249 0.731516
\(530\) 1.64275 0.0713564
\(531\) 36.2611 1.57360
\(532\) −0.311819 −0.0135191
\(533\) 29.3769 1.27245
\(534\) 26.9740 1.16728
\(535\) −1.99728 −0.0863499
\(536\) −14.6051 −0.630846
\(537\) −10.4427 −0.450635
\(538\) 2.96748 0.127937
\(539\) −0.821275 −0.0353748
\(540\) 1.30182 0.0560213
\(541\) 25.6007 1.10066 0.550330 0.834947i \(-0.314502\pi\)
0.550330 + 0.834947i \(0.314502\pi\)
\(542\) −6.81422 −0.292696
\(543\) −5.99543 −0.257288
\(544\) −4.19606 −0.179904
\(545\) −2.19830 −0.0941650
\(546\) 2.79342 0.119547
\(547\) 39.3113 1.68083 0.840415 0.541944i \(-0.182311\pi\)
0.840415 + 0.541944i \(0.182311\pi\)
\(548\) 17.7800 0.759524
\(549\) 7.16449 0.305773
\(550\) 0.586019 0.0249879
\(551\) 3.71646 0.158326
\(552\) 18.9582 0.806914
\(553\) 1.45541 0.0618904
\(554\) −19.2518 −0.817930
\(555\) 1.88137 0.0798595
\(556\) −18.3371 −0.777668
\(557\) 17.3929 0.736962 0.368481 0.929635i \(-0.379878\pi\)
0.368481 + 0.929635i \(0.379878\pi\)
\(558\) 33.8712 1.43388
\(559\) −11.0690 −0.468168
\(560\) 0.0210164 0.000888104 0
\(561\) −1.48351 −0.0626337
\(562\) 20.5585 0.867209
\(563\) 3.86127 0.162733 0.0813665 0.996684i \(-0.474072\pi\)
0.0813665 + 0.996684i \(0.474072\pi\)
\(564\) 10.5144 0.442735
\(565\) 0.635624 0.0267409
\(566\) −10.3320 −0.434285
\(567\) −1.35319 −0.0568287
\(568\) 7.58579 0.318293
\(569\) 5.94360 0.249169 0.124584 0.992209i \(-0.460240\pi\)
0.124584 + 0.992209i \(0.460240\pi\)
\(570\) −0.914786 −0.0383162
\(571\) 28.0852 1.17533 0.587664 0.809105i \(-0.300048\pi\)
0.587664 + 0.809105i \(0.300048\pi\)
\(572\) −0.745956 −0.0311900
\(573\) 45.4108 1.89706
\(574\) −0.679909 −0.0283788
\(575\) −31.4240 −1.31047
\(576\) 6.02484 0.251035
\(577\) −7.17816 −0.298831 −0.149415 0.988775i \(-0.547739\pi\)
−0.149415 + 0.988775i \(0.547739\pi\)
\(578\) −0.606890 −0.0252433
\(579\) 57.5250 2.39066
\(580\) −0.250486 −0.0104009
\(581\) 2.24213 0.0930192
\(582\) −19.2655 −0.798581
\(583\) 1.34950 0.0558904
\(584\) −4.40295 −0.182196
\(585\) 5.47089 0.226194
\(586\) 19.2625 0.795729
\(587\) −17.7193 −0.731352 −0.365676 0.930742i \(-0.619162\pi\)
−0.365676 + 0.930742i \(0.619162\pi\)
\(588\) 20.9643 0.864554
\(589\) −11.9497 −0.492380
\(590\) 0.862229 0.0354974
\(591\) 43.3038 1.78128
\(592\) 4.37146 0.179666
\(593\) 40.0397 1.64424 0.822118 0.569318i \(-0.192793\pi\)
0.822118 + 0.569318i \(0.192793\pi\)
\(594\) 1.06943 0.0438791
\(595\) 0.0881859 0.00361527
\(596\) −7.59093 −0.310936
\(597\) −0.306232 −0.0125333
\(598\) 40.0002 1.63573
\(599\) 28.0194 1.14484 0.572421 0.819960i \(-0.306004\pi\)
0.572421 + 0.819960i \(0.306004\pi\)
\(600\) −14.9590 −0.610700
\(601\) 10.7073 0.436759 0.218379 0.975864i \(-0.429923\pi\)
0.218379 + 0.975864i \(0.429923\pi\)
\(602\) 0.256184 0.0104413
\(603\) 87.9937 3.58338
\(604\) −12.6027 −0.512798
\(605\) 1.57388 0.0639875
\(606\) −14.2832 −0.580214
\(607\) 20.9526 0.850441 0.425221 0.905090i \(-0.360196\pi\)
0.425221 + 0.905090i \(0.360196\pi\)
\(608\) −2.12556 −0.0862027
\(609\) 0.770561 0.0312247
\(610\) 0.170360 0.00689767
\(611\) 22.1845 0.897487
\(612\) 25.2806 1.02191
\(613\) 47.7736 1.92956 0.964779 0.263061i \(-0.0847320\pi\)
0.964779 + 0.263061i \(0.0847320\pi\)
\(614\) −24.0421 −0.970261
\(615\) −1.99465 −0.0804321
\(616\) 0.0172647 0.000695614 0
\(617\) −24.1784 −0.973386 −0.486693 0.873573i \(-0.661797\pi\)
−0.486693 + 0.873573i \(0.661797\pi\)
\(618\) 6.30264 0.253530
\(619\) 13.4611 0.541046 0.270523 0.962713i \(-0.412803\pi\)
0.270523 + 0.962713i \(0.412803\pi\)
\(620\) 0.805402 0.0323457
\(621\) −57.3455 −2.30120
\(622\) 1.21572 0.0487458
\(623\) −1.31721 −0.0527730
\(624\) 19.0417 0.762277
\(625\) 24.6926 0.987703
\(626\) 22.7088 0.907627
\(627\) −0.751485 −0.0300114
\(628\) −23.0055 −0.918020
\(629\) 18.3429 0.731379
\(630\) −0.126620 −0.00504468
\(631\) 26.8916 1.07054 0.535269 0.844682i \(-0.320210\pi\)
0.535269 + 0.844682i \(0.320210\pi\)
\(632\) 9.92100 0.394636
\(633\) 27.4125 1.08955
\(634\) 11.0177 0.437568
\(635\) −2.52446 −0.100180
\(636\) −34.4480 −1.36595
\(637\) 44.2330 1.75257
\(638\) −0.205771 −0.00814656
\(639\) −45.7032 −1.80799
\(640\) 0.143261 0.00566288
\(641\) −2.72993 −0.107826 −0.0539128 0.998546i \(-0.517169\pi\)
−0.0539128 + 0.998546i \(0.517169\pi\)
\(642\) 41.8823 1.65296
\(643\) 31.9989 1.26191 0.630956 0.775818i \(-0.282663\pi\)
0.630956 + 0.775818i \(0.282663\pi\)
\(644\) −0.925780 −0.0364808
\(645\) 0.751569 0.0295930
\(646\) −8.91895 −0.350912
\(647\) 11.6185 0.456770 0.228385 0.973571i \(-0.426656\pi\)
0.228385 + 0.973571i \(0.426656\pi\)
\(648\) −9.22419 −0.362361
\(649\) 0.708310 0.0278036
\(650\) −31.5623 −1.23798
\(651\) −2.47763 −0.0971058
\(652\) −7.96081 −0.311769
\(653\) 42.3683 1.65800 0.829000 0.559249i \(-0.188910\pi\)
0.829000 + 0.559249i \(0.188910\pi\)
\(654\) 46.0978 1.80257
\(655\) 1.18328 0.0462346
\(656\) −4.63468 −0.180954
\(657\) 26.5271 1.03492
\(658\) −0.513445 −0.0200162
\(659\) 40.4560 1.57594 0.787972 0.615711i \(-0.211131\pi\)
0.787972 + 0.615711i \(0.211131\pi\)
\(660\) 0.0506495 0.00197153
\(661\) 3.39615 0.132095 0.0660475 0.997816i \(-0.478961\pi\)
0.0660475 + 0.997816i \(0.478961\pi\)
\(662\) −10.9201 −0.424423
\(663\) 79.9000 3.10306
\(664\) 15.2838 0.593125
\(665\) 0.0446715 0.00173229
\(666\) −26.3373 −1.02055
\(667\) 11.0340 0.427239
\(668\) 22.0414 0.852806
\(669\) −23.2862 −0.900295
\(670\) 2.09234 0.0808343
\(671\) 0.139948 0.00540265
\(672\) −0.440707 −0.0170007
\(673\) 5.56443 0.214493 0.107246 0.994232i \(-0.465797\pi\)
0.107246 + 0.994232i \(0.465797\pi\)
\(674\) 8.71803 0.335806
\(675\) 45.2487 1.74162
\(676\) 27.1764 1.04525
\(677\) 25.3145 0.972914 0.486457 0.873704i \(-0.338289\pi\)
0.486457 + 0.873704i \(0.338289\pi\)
\(678\) −13.3289 −0.511892
\(679\) 0.940787 0.0361041
\(680\) 0.601130 0.0230523
\(681\) −49.2374 −1.88678
\(682\) 0.661627 0.0253350
\(683\) −32.8936 −1.25864 −0.629320 0.777147i \(-0.716666\pi\)
−0.629320 + 0.777147i \(0.716666\pi\)
\(684\) 12.8061 0.489655
\(685\) −2.54718 −0.0973226
\(686\) −2.05065 −0.0782940
\(687\) 7.98241 0.304548
\(688\) 1.74631 0.0665775
\(689\) −72.6824 −2.76898
\(690\) −2.71597 −0.103395
\(691\) 26.8369 1.02092 0.510461 0.859901i \(-0.329475\pi\)
0.510461 + 0.859901i \(0.329475\pi\)
\(692\) −3.46386 −0.131676
\(693\) −0.104017 −0.00395128
\(694\) −2.70409 −0.102646
\(695\) 2.62699 0.0996475
\(696\) 5.25263 0.199100
\(697\) −19.4474 −0.736623
\(698\) 11.6485 0.440903
\(699\) −7.69982 −0.291234
\(700\) 0.730490 0.0276099
\(701\) −8.25374 −0.311740 −0.155870 0.987778i \(-0.549818\pi\)
−0.155870 + 0.987778i \(0.549818\pi\)
\(702\) −57.5981 −2.17390
\(703\) 9.29178 0.350446
\(704\) 0.117687 0.00443549
\(705\) −1.50630 −0.0567304
\(706\) 13.2598 0.499040
\(707\) 0.697486 0.0262317
\(708\) −18.0807 −0.679515
\(709\) 4.80417 0.180424 0.0902121 0.995923i \(-0.471245\pi\)
0.0902121 + 0.995923i \(0.471245\pi\)
\(710\) −1.08675 −0.0407849
\(711\) −59.7724 −2.24164
\(712\) −8.97895 −0.336500
\(713\) −35.4783 −1.32867
\(714\) −1.84923 −0.0692058
\(715\) 0.106866 0.00399657
\(716\) 3.47610 0.129908
\(717\) 1.81970 0.0679580
\(718\) −10.4909 −0.391515
\(719\) 42.3968 1.58113 0.790567 0.612376i \(-0.209786\pi\)
0.790567 + 0.612376i \(0.209786\pi\)
\(720\) −0.863123 −0.0321667
\(721\) −0.307775 −0.0114621
\(722\) 14.4820 0.538965
\(723\) 87.1130 3.23977
\(724\) 1.99572 0.0741705
\(725\) −8.70643 −0.323349
\(726\) −33.0039 −1.22489
\(727\) −14.1494 −0.524773 −0.262387 0.964963i \(-0.584510\pi\)
−0.262387 + 0.964963i \(0.584510\pi\)
\(728\) −0.929857 −0.0344628
\(729\) −26.3218 −0.974883
\(730\) 0.630771 0.0233459
\(731\) 7.32762 0.271022
\(732\) −3.57240 −0.132040
\(733\) −20.2727 −0.748790 −0.374395 0.927269i \(-0.622150\pi\)
−0.374395 + 0.927269i \(0.622150\pi\)
\(734\) −7.05660 −0.260464
\(735\) −3.00336 −0.110781
\(736\) −6.31069 −0.232615
\(737\) 1.71883 0.0633140
\(738\) 27.9232 1.02787
\(739\) −5.82019 −0.214099 −0.107050 0.994254i \(-0.534140\pi\)
−0.107050 + 0.994254i \(0.534140\pi\)
\(740\) −0.626258 −0.0230217
\(741\) 40.4742 1.48686
\(742\) 1.68219 0.0617550
\(743\) 16.1719 0.593291 0.296645 0.954988i \(-0.404132\pi\)
0.296645 + 0.954988i \(0.404132\pi\)
\(744\) −16.8891 −0.619183
\(745\) 1.08748 0.0398423
\(746\) −3.96851 −0.145297
\(747\) −92.0822 −3.36911
\(748\) 0.493821 0.0180559
\(749\) −2.04523 −0.0747310
\(750\) 4.29492 0.156828
\(751\) −11.3104 −0.412723 −0.206361 0.978476i \(-0.566162\pi\)
−0.206361 + 0.978476i \(0.566162\pi\)
\(752\) −3.49996 −0.127631
\(753\) −30.4357 −1.10914
\(754\) 11.0826 0.403605
\(755\) 1.80548 0.0657081
\(756\) 1.33307 0.0484833
\(757\) −18.8954 −0.686763 −0.343382 0.939196i \(-0.611572\pi\)
−0.343382 + 0.939196i \(0.611572\pi\)
\(758\) −32.0302 −1.16339
\(759\) −2.23113 −0.0809849
\(760\) 0.304509 0.0110457
\(761\) 24.6449 0.893378 0.446689 0.894689i \(-0.352603\pi\)
0.446689 + 0.894689i \(0.352603\pi\)
\(762\) 52.9372 1.91771
\(763\) −2.25108 −0.0814946
\(764\) −15.1161 −0.546881
\(765\) −3.62171 −0.130943
\(766\) 1.91383 0.0691494
\(767\) −38.1488 −1.37747
\(768\) −3.00414 −0.108402
\(769\) −27.6468 −0.996968 −0.498484 0.866899i \(-0.666110\pi\)
−0.498484 + 0.866899i \(0.666110\pi\)
\(770\) −0.00247335 −8.91334e−5 0
\(771\) 3.87575 0.139582
\(772\) −19.1486 −0.689173
\(773\) 0.540811 0.0194516 0.00972582 0.999953i \(-0.496904\pi\)
0.00972582 + 0.999953i \(0.496904\pi\)
\(774\) −10.5213 −0.378179
\(775\) 27.9943 1.00558
\(776\) 6.41299 0.230213
\(777\) 1.92653 0.0691140
\(778\) −13.9441 −0.499921
\(779\) −9.85128 −0.352959
\(780\) −2.72793 −0.0976754
\(781\) −0.892748 −0.0319450
\(782\) −26.4800 −0.946924
\(783\) −15.8884 −0.567804
\(784\) −6.97848 −0.249231
\(785\) 3.29579 0.117632
\(786\) −24.8130 −0.885052
\(787\) −32.7652 −1.16795 −0.583977 0.811770i \(-0.698504\pi\)
−0.583977 + 0.811770i \(0.698504\pi\)
\(788\) −14.4147 −0.513503
\(789\) −9.90324 −0.352565
\(790\) −1.42129 −0.0505672
\(791\) 0.650884 0.0231428
\(792\) −0.709045 −0.0251948
\(793\) −7.53746 −0.267663
\(794\) 14.6579 0.520188
\(795\) 4.93504 0.175028
\(796\) 0.101937 0.00361306
\(797\) −4.04701 −0.143352 −0.0716762 0.997428i \(-0.522835\pi\)
−0.0716762 + 0.997428i \(0.522835\pi\)
\(798\) −0.936749 −0.0331605
\(799\) −14.6860 −0.519555
\(800\) 4.97948 0.176051
\(801\) 54.0967 1.91141
\(802\) 35.0260 1.23681
\(803\) 0.518170 0.0182858
\(804\) −43.8759 −1.54738
\(805\) 0.132628 0.00467452
\(806\) −35.6345 −1.25517
\(807\) 8.91472 0.313813
\(808\) 4.75450 0.167263
\(809\) −19.8640 −0.698380 −0.349190 0.937052i \(-0.613543\pi\)
−0.349190 + 0.937052i \(0.613543\pi\)
\(810\) 1.32147 0.0464316
\(811\) 38.7045 1.35910 0.679550 0.733629i \(-0.262175\pi\)
0.679550 + 0.733629i \(0.262175\pi\)
\(812\) −0.256500 −0.00900138
\(813\) −20.4709 −0.717945
\(814\) −0.514463 −0.0180319
\(815\) 1.14047 0.0399490
\(816\) −12.6055 −0.441282
\(817\) 3.71188 0.129862
\(818\) −18.8063 −0.657547
\(819\) 5.60224 0.195758
\(820\) 0.663968 0.0231868
\(821\) 46.1297 1.60994 0.804969 0.593317i \(-0.202182\pi\)
0.804969 + 0.593317i \(0.202182\pi\)
\(822\) 53.4136 1.86301
\(823\) 9.16276 0.319394 0.159697 0.987166i \(-0.448948\pi\)
0.159697 + 0.987166i \(0.448948\pi\)
\(824\) −2.09799 −0.0730869
\(825\) 1.76048 0.0612921
\(826\) 0.882930 0.0307211
\(827\) −46.9732 −1.63342 −0.816709 0.577050i \(-0.804204\pi\)
−0.816709 + 0.577050i \(0.804204\pi\)
\(828\) 38.0209 1.32132
\(829\) 4.56661 0.158605 0.0793025 0.996851i \(-0.474731\pi\)
0.0793025 + 0.996851i \(0.474731\pi\)
\(830\) −2.18956 −0.0760008
\(831\) −57.8350 −2.00627
\(832\) −6.33848 −0.219747
\(833\) −29.2821 −1.01456
\(834\) −55.0873 −1.90752
\(835\) −3.15766 −0.109275
\(836\) 0.250150 0.00865162
\(837\) 51.0867 1.76582
\(838\) 8.86558 0.306256
\(839\) −22.8508 −0.788897 −0.394449 0.918918i \(-0.629064\pi\)
−0.394449 + 0.918918i \(0.629064\pi\)
\(840\) 0.0631361 0.00217840
\(841\) −25.9429 −0.894582
\(842\) 7.60121 0.261955
\(843\) 61.7606 2.12715
\(844\) −9.12493 −0.314093
\(845\) −3.89331 −0.133934
\(846\) 21.0867 0.724977
\(847\) 1.61167 0.0553776
\(848\) 11.4668 0.393773
\(849\) −31.0386 −1.06524
\(850\) 20.8942 0.716664
\(851\) 27.5869 0.945668
\(852\) 22.7888 0.780730
\(853\) −33.1947 −1.13657 −0.568283 0.822833i \(-0.692392\pi\)
−0.568283 + 0.822833i \(0.692392\pi\)
\(854\) 0.174450 0.00596955
\(855\) −1.83462 −0.0627426
\(856\) −13.9416 −0.476513
\(857\) 49.9132 1.70500 0.852501 0.522726i \(-0.175085\pi\)
0.852501 + 0.522726i \(0.175085\pi\)
\(858\) −2.24096 −0.0765050
\(859\) 42.3128 1.44370 0.721848 0.692052i \(-0.243293\pi\)
0.721848 + 0.692052i \(0.243293\pi\)
\(860\) −0.250178 −0.00853100
\(861\) −2.04254 −0.0696096
\(862\) −15.4499 −0.526224
\(863\) −54.1283 −1.84255 −0.921275 0.388911i \(-0.872851\pi\)
−0.921275 + 0.388911i \(0.872851\pi\)
\(864\) 9.08704 0.309147
\(865\) 0.496235 0.0168725
\(866\) −12.4640 −0.423545
\(867\) −1.82318 −0.0619184
\(868\) 0.824738 0.0279934
\(869\) −1.16757 −0.0396071
\(870\) −0.752495 −0.0255120
\(871\) −92.5745 −3.13677
\(872\) −15.3448 −0.519639
\(873\) −38.6372 −1.30767
\(874\) −13.4137 −0.453726
\(875\) −0.209732 −0.00709025
\(876\) −13.2271 −0.446902
\(877\) 3.55012 0.119879 0.0599395 0.998202i \(-0.480909\pi\)
0.0599395 + 0.998202i \(0.480909\pi\)
\(878\) −27.3398 −0.922675
\(879\) 57.8673 1.95182
\(880\) −0.0168599 −0.000568348 0
\(881\) −1.70024 −0.0572825 −0.0286413 0.999590i \(-0.509118\pi\)
−0.0286413 + 0.999590i \(0.509118\pi\)
\(882\) 42.0442 1.41570
\(883\) 37.5465 1.26354 0.631770 0.775156i \(-0.282329\pi\)
0.631770 + 0.775156i \(0.282329\pi\)
\(884\) −26.5966 −0.894542
\(885\) 2.59026 0.0870705
\(886\) 20.7905 0.698471
\(887\) −45.2411 −1.51905 −0.759524 0.650479i \(-0.774568\pi\)
−0.759524 + 0.650479i \(0.774568\pi\)
\(888\) 13.1325 0.440696
\(889\) −2.58507 −0.0867004
\(890\) 1.28633 0.0431179
\(891\) 1.08557 0.0363679
\(892\) 7.75136 0.259535
\(893\) −7.43937 −0.248949
\(894\) −22.8042 −0.762686
\(895\) −0.497989 −0.0166459
\(896\) 0.146700 0.00490091
\(897\) 120.166 4.01223
\(898\) −6.33018 −0.211241
\(899\) −9.82974 −0.327840
\(900\) −30.0006 −1.00002
\(901\) 48.1155 1.60296
\(902\) 0.545441 0.0181612
\(903\) 0.769613 0.0256111
\(904\) 4.43684 0.147567
\(905\) −0.285909 −0.00950393
\(906\) −37.8604 −1.25783
\(907\) −7.19189 −0.238803 −0.119401 0.992846i \(-0.538098\pi\)
−0.119401 + 0.992846i \(0.538098\pi\)
\(908\) 16.3899 0.543917
\(909\) −28.6451 −0.950098
\(910\) 0.133212 0.00441593
\(911\) −14.4244 −0.477900 −0.238950 0.971032i \(-0.576803\pi\)
−0.238950 + 0.971032i \(0.576803\pi\)
\(912\) −6.38546 −0.211444
\(913\) −1.79870 −0.0595282
\(914\) −9.74286 −0.322265
\(915\) 0.511784 0.0169191
\(916\) −2.65714 −0.0877943
\(917\) 1.21169 0.0400135
\(918\) 38.1297 1.25847
\(919\) −18.5273 −0.611158 −0.305579 0.952167i \(-0.598850\pi\)
−0.305579 + 0.952167i \(0.598850\pi\)
\(920\) 0.904075 0.0298065
\(921\) −72.2258 −2.37992
\(922\) −20.5671 −0.677340
\(923\) 48.0824 1.58265
\(924\) 0.0518655 0.00170625
\(925\) −21.7676 −0.715713
\(926\) 12.2838 0.403670
\(927\) 12.6400 0.415154
\(928\) −1.74846 −0.0573961
\(929\) −38.0357 −1.24791 −0.623956 0.781460i \(-0.714475\pi\)
−0.623956 + 0.781460i \(0.714475\pi\)
\(930\) 2.41954 0.0793398
\(931\) −14.8332 −0.486137
\(932\) 2.56307 0.0839562
\(933\) 3.65218 0.119567
\(934\) 18.8945 0.618247
\(935\) −0.0707451 −0.00231361
\(936\) 38.1884 1.24823
\(937\) 19.1756 0.626440 0.313220 0.949681i \(-0.398592\pi\)
0.313220 + 0.949681i \(0.398592\pi\)
\(938\) 2.14258 0.0699576
\(939\) 68.2204 2.22629
\(940\) 0.501407 0.0163541
\(941\) −51.1645 −1.66792 −0.833958 0.551828i \(-0.813930\pi\)
−0.833958 + 0.551828i \(0.813930\pi\)
\(942\) −69.1117 −2.25178
\(943\) −29.2481 −0.952448
\(944\) 6.01860 0.195889
\(945\) −0.190977 −0.00621247
\(946\) −0.205518 −0.00668197
\(947\) −44.9508 −1.46071 −0.730353 0.683070i \(-0.760644\pi\)
−0.730353 + 0.683070i \(0.760644\pi\)
\(948\) 29.8040 0.967990
\(949\) −27.9081 −0.905934
\(950\) 10.5842 0.343395
\(951\) 33.0986 1.07330
\(952\) 0.615562 0.0199505
\(953\) 6.97623 0.225982 0.112991 0.993596i \(-0.463957\pi\)
0.112991 + 0.993596i \(0.463957\pi\)
\(954\) −69.0859 −2.23674
\(955\) 2.16554 0.0700753
\(956\) −0.605731 −0.0195908
\(957\) −0.618165 −0.0199824
\(958\) −15.8799 −0.513056
\(959\) −2.60833 −0.0842273
\(960\) 0.430375 0.0138903
\(961\) 0.606098 0.0195516
\(962\) 27.7084 0.893355
\(963\) 83.9957 2.70672
\(964\) −28.9977 −0.933952
\(965\) 2.74324 0.0883082
\(966\) −2.78117 −0.0894827
\(967\) −31.2281 −1.00423 −0.502115 0.864801i \(-0.667444\pi\)
−0.502115 + 0.864801i \(0.667444\pi\)
\(968\) 10.9861 0.353108
\(969\) −26.7938 −0.860740
\(970\) −0.918730 −0.0294986
\(971\) −11.1372 −0.357410 −0.178705 0.983903i \(-0.557191\pi\)
−0.178705 + 0.983903i \(0.557191\pi\)
\(972\) −0.449626 −0.0144218
\(973\) 2.69006 0.0862394
\(974\) −41.5460 −1.33122
\(975\) −94.8176 −3.03659
\(976\) 1.18916 0.0380640
\(977\) 16.9926 0.543642 0.271821 0.962348i \(-0.412374\pi\)
0.271821 + 0.962348i \(0.412374\pi\)
\(978\) −23.9154 −0.764729
\(979\) 1.05670 0.0337724
\(980\) 0.999742 0.0319356
\(981\) 92.4498 2.95170
\(982\) −22.1488 −0.706795
\(983\) 31.8893 1.01711 0.508556 0.861029i \(-0.330179\pi\)
0.508556 + 0.861029i \(0.330179\pi\)
\(984\) −13.9232 −0.443856
\(985\) 2.06507 0.0657985
\(986\) −7.33665 −0.233647
\(987\) −1.54246 −0.0490970
\(988\) −13.4728 −0.428627
\(989\) 11.0204 0.350430
\(990\) 0.101578 0.00322837
\(991\) −50.8613 −1.61566 −0.807831 0.589414i \(-0.799359\pi\)
−0.807831 + 0.589414i \(0.799359\pi\)
\(992\) 5.62193 0.178496
\(993\) −32.8056 −1.04105
\(994\) −1.11284 −0.0352970
\(995\) −0.0146036 −0.000462964 0
\(996\) 45.9145 1.45486
\(997\) 54.0886 1.71300 0.856502 0.516144i \(-0.172633\pi\)
0.856502 + 0.516144i \(0.172633\pi\)
\(998\) −42.4407 −1.34344
\(999\) −39.7236 −1.25680
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 \(a_p\))