Properties

Label 8042.2.a.c.1.4
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 1.4
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-2.84562 q^{3}\) \(+1.00000 q^{4}\) \(+0.429228 q^{5}\) \(+2.84562 q^{6}\) \(+3.51713 q^{7}\) \(-1.00000 q^{8}\) \(+5.09754 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-2.84562 q^{3}\) \(+1.00000 q^{4}\) \(+0.429228 q^{5}\) \(+2.84562 q^{6}\) \(+3.51713 q^{7}\) \(-1.00000 q^{8}\) \(+5.09754 q^{9}\) \(-0.429228 q^{10}\) \(+0.633387 q^{11}\) \(-2.84562 q^{12}\) \(-1.35895 q^{13}\) \(-3.51713 q^{14}\) \(-1.22142 q^{15}\) \(+1.00000 q^{16}\) \(+4.77007 q^{17}\) \(-5.09754 q^{18}\) \(+5.60070 q^{19}\) \(+0.429228 q^{20}\) \(-10.0084 q^{21}\) \(-0.633387 q^{22}\) \(-8.50962 q^{23}\) \(+2.84562 q^{24}\) \(-4.81576 q^{25}\) \(+1.35895 q^{26}\) \(-5.96881 q^{27}\) \(+3.51713 q^{28}\) \(-4.80339 q^{29}\) \(+1.22142 q^{30}\) \(+2.72438 q^{31}\) \(-1.00000 q^{32}\) \(-1.80238 q^{33}\) \(-4.77007 q^{34}\) \(+1.50965 q^{35}\) \(+5.09754 q^{36}\) \(+9.73464 q^{37}\) \(-5.60070 q^{38}\) \(+3.86706 q^{39}\) \(-0.429228 q^{40}\) \(+3.50901 q^{41}\) \(+10.0084 q^{42}\) \(-4.31818 q^{43}\) \(+0.633387 q^{44}\) \(+2.18801 q^{45}\) \(+8.50962 q^{46}\) \(+4.58579 q^{47}\) \(-2.84562 q^{48}\) \(+5.37023 q^{49}\) \(+4.81576 q^{50}\) \(-13.5738 q^{51}\) \(-1.35895 q^{52}\) \(-5.76851 q^{53}\) \(+5.96881 q^{54}\) \(+0.271867 q^{55}\) \(-3.51713 q^{56}\) \(-15.9374 q^{57}\) \(+4.80339 q^{58}\) \(+9.76681 q^{59}\) \(-1.22142 q^{60}\) \(+0.329878 q^{61}\) \(-2.72438 q^{62}\) \(+17.9287 q^{63}\) \(+1.00000 q^{64}\) \(-0.583300 q^{65}\) \(+1.80238 q^{66}\) \(+4.35355 q^{67}\) \(+4.77007 q^{68}\) \(+24.2151 q^{69}\) \(-1.50965 q^{70}\) \(-14.2205 q^{71}\) \(-5.09754 q^{72}\) \(+16.6078 q^{73}\) \(-9.73464 q^{74}\) \(+13.7038 q^{75}\) \(+5.60070 q^{76}\) \(+2.22771 q^{77}\) \(-3.86706 q^{78}\) \(-4.92710 q^{79}\) \(+0.429228 q^{80}\) \(+1.69232 q^{81}\) \(-3.50901 q^{82}\) \(+15.1441 q^{83}\) \(-10.0084 q^{84}\) \(+2.04745 q^{85}\) \(+4.31818 q^{86}\) \(+13.6686 q^{87}\) \(-0.633387 q^{88}\) \(-1.70946 q^{89}\) \(-2.18801 q^{90}\) \(-4.77962 q^{91}\) \(-8.50962 q^{92}\) \(-7.75254 q^{93}\) \(-4.58579 q^{94}\) \(+2.40397 q^{95}\) \(+2.84562 q^{96}\) \(+7.40527 q^{97}\) \(-5.37023 q^{98}\) \(+3.22872 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 45q^{13} \) \(\mathstrut -\mathstrut 35q^{14} \) \(\mathstrut +\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 86q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 72q^{18} \) \(\mathstrut +\mathstrut 47q^{19} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 12q^{24} \) \(\mathstrut +\mathstrut 112q^{25} \) \(\mathstrut -\mathstrut 45q^{26} \) \(\mathstrut +\mathstrut 51q^{27} \) \(\mathstrut +\mathstrut 35q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut -\mathstrut 17q^{30} \) \(\mathstrut +\mathstrut 24q^{31} \) \(\mathstrut -\mathstrut 86q^{32} \) \(\mathstrut +\mathstrut 43q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 42q^{35} \) \(\mathstrut +\mathstrut 72q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut -\mathstrut 15q^{42} \) \(\mathstrut +\mathstrut 72q^{43} \) \(\mathstrut +\mathstrut 13q^{44} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut +\mathstrut 12q^{48} \) \(\mathstrut +\mathstrut 89q^{49} \) \(\mathstrut -\mathstrut 112q^{50} \) \(\mathstrut +\mathstrut 56q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut -\mathstrut 7q^{53} \) \(\mathstrut -\mathstrut 51q^{54} \) \(\mathstrut +\mathstrut 48q^{55} \) \(\mathstrut -\mathstrut 35q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 31q^{61} \) \(\mathstrut -\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 98q^{63} \) \(\mathstrut +\mathstrut 86q^{64} \) \(\mathstrut -\mathstrut 9q^{65} \) \(\mathstrut -\mathstrut 43q^{66} \) \(\mathstrut +\mathstrut 157q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 42q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 72q^{72} \) \(\mathstrut +\mathstrut 74q^{73} \) \(\mathstrut -\mathstrut 61q^{74} \) \(\mathstrut +\mathstrut 76q^{75} \) \(\mathstrut +\mathstrut 47q^{76} \) \(\mathstrut -\mathstrut 13q^{77} \) \(\mathstrut -\mathstrut 20q^{78} \) \(\mathstrut +\mathstrut 57q^{79} \) \(\mathstrut -\mathstrut 4q^{80} \) \(\mathstrut +\mathstrut 34q^{81} \) \(\mathstrut +\mathstrut 16q^{82} \) \(\mathstrut +\mathstrut 65q^{83} \) \(\mathstrut +\mathstrut 15q^{84} \) \(\mathstrut +\mathstrut 102q^{85} \) \(\mathstrut -\mathstrut 72q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 91q^{91} \) \(\mathstrut +\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 57q^{93} \) \(\mathstrut -\mathstrut 11q^{94} \) \(\mathstrut -\mathstrut 13q^{95} \) \(\mathstrut -\mathstrut 12q^{96} \) \(\mathstrut +\mathstrut 64q^{97} \) \(\mathstrut -\mathstrut 89q^{98} \) \(\mathstrut +\mathstrut 56q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.84562 −1.64292 −0.821459 0.570267i \(-0.806840\pi\)
−0.821459 + 0.570267i \(0.806840\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.429228 0.191956 0.0959782 0.995383i \(-0.469402\pi\)
0.0959782 + 0.995383i \(0.469402\pi\)
\(6\) 2.84562 1.16172
\(7\) 3.51713 1.32935 0.664676 0.747132i \(-0.268570\pi\)
0.664676 + 0.747132i \(0.268570\pi\)
\(8\) −1.00000 −0.353553
\(9\) 5.09754 1.69918
\(10\) −0.429228 −0.135734
\(11\) 0.633387 0.190973 0.0954867 0.995431i \(-0.469559\pi\)
0.0954867 + 0.995431i \(0.469559\pi\)
\(12\) −2.84562 −0.821459
\(13\) −1.35895 −0.376906 −0.188453 0.982082i \(-0.560347\pi\)
−0.188453 + 0.982082i \(0.560347\pi\)
\(14\) −3.51713 −0.939993
\(15\) −1.22142 −0.315369
\(16\) 1.00000 0.250000
\(17\) 4.77007 1.15691 0.578457 0.815713i \(-0.303655\pi\)
0.578457 + 0.815713i \(0.303655\pi\)
\(18\) −5.09754 −1.20150
\(19\) 5.60070 1.28489 0.642444 0.766333i \(-0.277921\pi\)
0.642444 + 0.766333i \(0.277921\pi\)
\(20\) 0.429228 0.0959782
\(21\) −10.0084 −2.18402
\(22\) −0.633387 −0.135039
\(23\) −8.50962 −1.77438 −0.887189 0.461406i \(-0.847345\pi\)
−0.887189 + 0.461406i \(0.847345\pi\)
\(24\) 2.84562 0.580859
\(25\) −4.81576 −0.963153
\(26\) 1.35895 0.266513
\(27\) −5.96881 −1.14870
\(28\) 3.51713 0.664676
\(29\) −4.80339 −0.891967 −0.445983 0.895041i \(-0.647146\pi\)
−0.445983 + 0.895041i \(0.647146\pi\)
\(30\) 1.22142 0.222999
\(31\) 2.72438 0.489313 0.244656 0.969610i \(-0.421325\pi\)
0.244656 + 0.969610i \(0.421325\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.80238 −0.313754
\(34\) −4.77007 −0.818061
\(35\) 1.50965 0.255178
\(36\) 5.09754 0.849591
\(37\) 9.73464 1.60037 0.800183 0.599756i \(-0.204736\pi\)
0.800183 + 0.599756i \(0.204736\pi\)
\(38\) −5.60070 −0.908553
\(39\) 3.86706 0.619225
\(40\) −0.429228 −0.0678669
\(41\) 3.50901 0.548016 0.274008 0.961727i \(-0.411651\pi\)
0.274008 + 0.961727i \(0.411651\pi\)
\(42\) 10.0084 1.54433
\(43\) −4.31818 −0.658516 −0.329258 0.944240i \(-0.606799\pi\)
−0.329258 + 0.944240i \(0.606799\pi\)
\(44\) 0.633387 0.0954867
\(45\) 2.18801 0.326169
\(46\) 8.50962 1.25467
\(47\) 4.58579 0.668907 0.334453 0.942412i \(-0.391448\pi\)
0.334453 + 0.942412i \(0.391448\pi\)
\(48\) −2.84562 −0.410730
\(49\) 5.37023 0.767175
\(50\) 4.81576 0.681052
\(51\) −13.5738 −1.90071
\(52\) −1.35895 −0.188453
\(53\) −5.76851 −0.792366 −0.396183 0.918172i \(-0.629665\pi\)
−0.396183 + 0.918172i \(0.629665\pi\)
\(54\) 5.96881 0.812252
\(55\) 0.271867 0.0366586
\(56\) −3.51713 −0.469997
\(57\) −15.9374 −2.11097
\(58\) 4.80339 0.630716
\(59\) 9.76681 1.27153 0.635765 0.771882i \(-0.280685\pi\)
0.635765 + 0.771882i \(0.280685\pi\)
\(60\) −1.22142 −0.157684
\(61\) 0.329878 0.0422366 0.0211183 0.999777i \(-0.493277\pi\)
0.0211183 + 0.999777i \(0.493277\pi\)
\(62\) −2.72438 −0.345996
\(63\) 17.9287 2.25881
\(64\) 1.00000 0.125000
\(65\) −0.583300 −0.0723495
\(66\) 1.80238 0.221857
\(67\) 4.35355 0.531871 0.265935 0.963991i \(-0.414319\pi\)
0.265935 + 0.963991i \(0.414319\pi\)
\(68\) 4.77007 0.578457
\(69\) 24.2151 2.91516
\(70\) −1.50965 −0.180438
\(71\) −14.2205 −1.68766 −0.843830 0.536610i \(-0.819705\pi\)
−0.843830 + 0.536610i \(0.819705\pi\)
\(72\) −5.09754 −0.600751
\(73\) 16.6078 1.94380 0.971898 0.235404i \(-0.0756413\pi\)
0.971898 + 0.235404i \(0.0756413\pi\)
\(74\) −9.73464 −1.13163
\(75\) 13.7038 1.58238
\(76\) 5.60070 0.642444
\(77\) 2.22771 0.253871
\(78\) −3.86706 −0.437858
\(79\) −4.92710 −0.554343 −0.277171 0.960821i \(-0.589397\pi\)
−0.277171 + 0.960821i \(0.589397\pi\)
\(80\) 0.429228 0.0479891
\(81\) 1.69232 0.188036
\(82\) −3.50901 −0.387506
\(83\) 15.1441 1.66228 0.831141 0.556062i \(-0.187688\pi\)
0.831141 + 0.556062i \(0.187688\pi\)
\(84\) −10.0084 −1.09201
\(85\) 2.04745 0.222077
\(86\) 4.31818 0.465641
\(87\) 13.6686 1.46543
\(88\) −0.633387 −0.0675193
\(89\) −1.70946 −0.181203 −0.0906013 0.995887i \(-0.528879\pi\)
−0.0906013 + 0.995887i \(0.528879\pi\)
\(90\) −2.18801 −0.230636
\(91\) −4.77962 −0.501040
\(92\) −8.50962 −0.887189
\(93\) −7.75254 −0.803901
\(94\) −4.58579 −0.472989
\(95\) 2.40397 0.246643
\(96\) 2.84562 0.290430
\(97\) 7.40527 0.751892 0.375946 0.926642i \(-0.377318\pi\)
0.375946 + 0.926642i \(0.377318\pi\)
\(98\) −5.37023 −0.542475
\(99\) 3.22872 0.324498
\(100\) −4.81576 −0.481576
\(101\) −1.38538 −0.137850 −0.0689252 0.997622i \(-0.521957\pi\)
−0.0689252 + 0.997622i \(0.521957\pi\)
\(102\) 13.5738 1.34401
\(103\) 4.39754 0.433302 0.216651 0.976249i \(-0.430487\pi\)
0.216651 + 0.976249i \(0.430487\pi\)
\(104\) 1.35895 0.133256
\(105\) −4.29589 −0.419236
\(106\) 5.76851 0.560288
\(107\) 8.06980 0.780137 0.390069 0.920786i \(-0.372451\pi\)
0.390069 + 0.920786i \(0.372451\pi\)
\(108\) −5.96881 −0.574349
\(109\) 1.92364 0.184252 0.0921259 0.995747i \(-0.470634\pi\)
0.0921259 + 0.995747i \(0.470634\pi\)
\(110\) −0.271867 −0.0259215
\(111\) −27.7011 −2.62927
\(112\) 3.51713 0.332338
\(113\) 5.69299 0.535552 0.267776 0.963481i \(-0.413711\pi\)
0.267776 + 0.963481i \(0.413711\pi\)
\(114\) 15.9374 1.49268
\(115\) −3.65256 −0.340603
\(116\) −4.80339 −0.445983
\(117\) −6.92732 −0.640431
\(118\) −9.76681 −0.899108
\(119\) 16.7770 1.53794
\(120\) 1.22142 0.111500
\(121\) −10.5988 −0.963529
\(122\) −0.329878 −0.0298658
\(123\) −9.98532 −0.900346
\(124\) 2.72438 0.244656
\(125\) −4.21320 −0.376840
\(126\) −17.9287 −1.59722
\(127\) 8.12828 0.721268 0.360634 0.932707i \(-0.382560\pi\)
0.360634 + 0.932707i \(0.382560\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 12.2879 1.08189
\(130\) 0.583300 0.0511588
\(131\) 13.9418 1.21810 0.609052 0.793131i \(-0.291550\pi\)
0.609052 + 0.793131i \(0.291550\pi\)
\(132\) −1.80238 −0.156877
\(133\) 19.6984 1.70807
\(134\) −4.35355 −0.376089
\(135\) −2.56198 −0.220500
\(136\) −4.77007 −0.409031
\(137\) −17.4737 −1.49288 −0.746440 0.665453i \(-0.768238\pi\)
−0.746440 + 0.665453i \(0.768238\pi\)
\(138\) −24.2151 −2.06133
\(139\) −9.01758 −0.764861 −0.382430 0.923984i \(-0.624913\pi\)
−0.382430 + 0.923984i \(0.624913\pi\)
\(140\) 1.50965 0.127589
\(141\) −13.0494 −1.09896
\(142\) 14.2205 1.19336
\(143\) −0.860743 −0.0719789
\(144\) 5.09754 0.424795
\(145\) −2.06175 −0.171219
\(146\) −16.6078 −1.37447
\(147\) −15.2816 −1.26041
\(148\) 9.73464 0.800183
\(149\) 5.61480 0.459983 0.229991 0.973193i \(-0.426130\pi\)
0.229991 + 0.973193i \(0.426130\pi\)
\(150\) −13.7038 −1.11891
\(151\) 19.0649 1.55148 0.775739 0.631054i \(-0.217377\pi\)
0.775739 + 0.631054i \(0.217377\pi\)
\(152\) −5.60070 −0.454277
\(153\) 24.3157 1.96581
\(154\) −2.22771 −0.179514
\(155\) 1.16938 0.0939267
\(156\) 3.86706 0.309613
\(157\) 17.0634 1.36181 0.680904 0.732373i \(-0.261587\pi\)
0.680904 + 0.732373i \(0.261587\pi\)
\(158\) 4.92710 0.391979
\(159\) 16.4150 1.30179
\(160\) −0.429228 −0.0339334
\(161\) −29.9295 −2.35877
\(162\) −1.69232 −0.132962
\(163\) −5.64536 −0.442179 −0.221090 0.975254i \(-0.570961\pi\)
−0.221090 + 0.975254i \(0.570961\pi\)
\(164\) 3.50901 0.274008
\(165\) −0.773630 −0.0602270
\(166\) −15.1441 −1.17541
\(167\) −12.9756 −1.00408 −0.502040 0.864844i \(-0.667417\pi\)
−0.502040 + 0.864844i \(0.667417\pi\)
\(168\) 10.0084 0.772166
\(169\) −11.1532 −0.857942
\(170\) −2.04745 −0.157032
\(171\) 28.5498 2.18326
\(172\) −4.31818 −0.329258
\(173\) −16.4284 −1.24903 −0.624514 0.781014i \(-0.714703\pi\)
−0.624514 + 0.781014i \(0.714703\pi\)
\(174\) −13.6686 −1.03621
\(175\) −16.9377 −1.28037
\(176\) 0.633387 0.0477433
\(177\) −27.7926 −2.08902
\(178\) 1.70946 0.128130
\(179\) 11.4895 0.858766 0.429383 0.903122i \(-0.358731\pi\)
0.429383 + 0.903122i \(0.358731\pi\)
\(180\) 2.18801 0.163084
\(181\) −21.2078 −1.57636 −0.788182 0.615442i \(-0.788977\pi\)
−0.788182 + 0.615442i \(0.788977\pi\)
\(182\) 4.77962 0.354289
\(183\) −0.938707 −0.0693913
\(184\) 8.50962 0.627337
\(185\) 4.17838 0.307200
\(186\) 7.75254 0.568444
\(187\) 3.02130 0.220940
\(188\) 4.58579 0.334453
\(189\) −20.9931 −1.52702
\(190\) −2.40397 −0.174403
\(191\) −7.73973 −0.560027 −0.280014 0.959996i \(-0.590339\pi\)
−0.280014 + 0.959996i \(0.590339\pi\)
\(192\) −2.84562 −0.205365
\(193\) 27.0912 1.95007 0.975034 0.222056i \(-0.0712768\pi\)
0.975034 + 0.222056i \(0.0712768\pi\)
\(194\) −7.40527 −0.531668
\(195\) 1.65985 0.118864
\(196\) 5.37023 0.383588
\(197\) −11.5701 −0.824338 −0.412169 0.911107i \(-0.635229\pi\)
−0.412169 + 0.911107i \(0.635229\pi\)
\(198\) −3.22872 −0.229455
\(199\) −12.1766 −0.863179 −0.431589 0.902070i \(-0.642047\pi\)
−0.431589 + 0.902070i \(0.642047\pi\)
\(200\) 4.81576 0.340526
\(201\) −12.3885 −0.873820
\(202\) 1.38538 0.0974749
\(203\) −16.8942 −1.18574
\(204\) −13.5738 −0.950357
\(205\) 1.50617 0.105195
\(206\) −4.39754 −0.306391
\(207\) −43.3781 −3.01499
\(208\) −1.35895 −0.0942264
\(209\) 3.54741 0.245379
\(210\) 4.29589 0.296445
\(211\) −16.5120 −1.13673 −0.568366 0.822776i \(-0.692424\pi\)
−0.568366 + 0.822776i \(0.692424\pi\)
\(212\) −5.76851 −0.396183
\(213\) 40.4661 2.77269
\(214\) −8.06980 −0.551640
\(215\) −1.85348 −0.126406
\(216\) 5.96881 0.406126
\(217\) 9.58200 0.650469
\(218\) −1.92364 −0.130286
\(219\) −47.2594 −3.19350
\(220\) 0.271867 0.0183293
\(221\) −6.48231 −0.436047
\(222\) 27.7011 1.85917
\(223\) 15.4303 1.03329 0.516646 0.856199i \(-0.327180\pi\)
0.516646 + 0.856199i \(0.327180\pi\)
\(224\) −3.51713 −0.234998
\(225\) −24.5486 −1.63657
\(226\) −5.69299 −0.378692
\(227\) 11.6490 0.773171 0.386585 0.922254i \(-0.373654\pi\)
0.386585 + 0.922254i \(0.373654\pi\)
\(228\) −15.9374 −1.05548
\(229\) 1.98296 0.131038 0.0655188 0.997851i \(-0.479130\pi\)
0.0655188 + 0.997851i \(0.479130\pi\)
\(230\) 3.65256 0.240843
\(231\) −6.33920 −0.417089
\(232\) 4.80339 0.315358
\(233\) 0.00288630 0.000189088 0 9.45439e−5 1.00000i \(-0.499970\pi\)
9.45439e−5 1.00000i \(0.499970\pi\)
\(234\) 6.92732 0.452853
\(235\) 1.96835 0.128401
\(236\) 9.76681 0.635765
\(237\) 14.0207 0.910740
\(238\) −16.7770 −1.08749
\(239\) −23.0845 −1.49321 −0.746606 0.665266i \(-0.768318\pi\)
−0.746606 + 0.665266i \(0.768318\pi\)
\(240\) −1.22142 −0.0788422
\(241\) 7.29859 0.470144 0.235072 0.971978i \(-0.424467\pi\)
0.235072 + 0.971978i \(0.424467\pi\)
\(242\) 10.5988 0.681318
\(243\) 13.0907 0.839770
\(244\) 0.329878 0.0211183
\(245\) 2.30505 0.147264
\(246\) 9.98532 0.636641
\(247\) −7.61108 −0.484282
\(248\) −2.72438 −0.172998
\(249\) −43.0944 −2.73099
\(250\) 4.21320 0.266466
\(251\) 11.7886 0.744090 0.372045 0.928215i \(-0.378657\pi\)
0.372045 + 0.928215i \(0.378657\pi\)
\(252\) 17.9287 1.12940
\(253\) −5.38988 −0.338859
\(254\) −8.12828 −0.510014
\(255\) −5.82626 −0.364854
\(256\) 1.00000 0.0625000
\(257\) −19.0902 −1.19081 −0.595406 0.803425i \(-0.703009\pi\)
−0.595406 + 0.803425i \(0.703009\pi\)
\(258\) −12.2879 −0.765010
\(259\) 34.2380 2.12745
\(260\) −0.583300 −0.0361747
\(261\) −24.4855 −1.51561
\(262\) −13.9418 −0.861329
\(263\) 8.58402 0.529313 0.264657 0.964343i \(-0.414741\pi\)
0.264657 + 0.964343i \(0.414741\pi\)
\(264\) 1.80238 0.110929
\(265\) −2.47601 −0.152100
\(266\) −19.6984 −1.20779
\(267\) 4.86448 0.297701
\(268\) 4.35355 0.265935
\(269\) −0.0773441 −0.00471575 −0.00235788 0.999997i \(-0.500751\pi\)
−0.00235788 + 0.999997i \(0.500751\pi\)
\(270\) 2.56198 0.155917
\(271\) 10.6466 0.646736 0.323368 0.946273i \(-0.395185\pi\)
0.323368 + 0.946273i \(0.395185\pi\)
\(272\) 4.77007 0.289228
\(273\) 13.6010 0.823168
\(274\) 17.4737 1.05563
\(275\) −3.05024 −0.183937
\(276\) 24.2151 1.45758
\(277\) −18.1652 −1.09144 −0.545719 0.837968i \(-0.683743\pi\)
−0.545719 + 0.837968i \(0.683743\pi\)
\(278\) 9.01758 0.540838
\(279\) 13.8876 0.831431
\(280\) −1.50965 −0.0902189
\(281\) 2.45064 0.146193 0.0730965 0.997325i \(-0.476712\pi\)
0.0730965 + 0.997325i \(0.476712\pi\)
\(282\) 13.0494 0.777082
\(283\) −11.7531 −0.698648 −0.349324 0.937002i \(-0.613589\pi\)
−0.349324 + 0.937002i \(0.613589\pi\)
\(284\) −14.2205 −0.843830
\(285\) −6.84079 −0.405214
\(286\) 0.860743 0.0508968
\(287\) 12.3417 0.728506
\(288\) −5.09754 −0.300376
\(289\) 5.75362 0.338448
\(290\) 2.06175 0.121070
\(291\) −21.0726 −1.23530
\(292\) 16.6078 0.971898
\(293\) 17.2185 1.00592 0.502958 0.864311i \(-0.332245\pi\)
0.502958 + 0.864311i \(0.332245\pi\)
\(294\) 15.2816 0.891242
\(295\) 4.19219 0.244078
\(296\) −9.73464 −0.565815
\(297\) −3.78057 −0.219371
\(298\) −5.61480 −0.325257
\(299\) 11.5642 0.668773
\(300\) 13.7038 0.791191
\(301\) −15.1876 −0.875399
\(302\) −19.0649 −1.09706
\(303\) 3.94226 0.226477
\(304\) 5.60070 0.321222
\(305\) 0.141593 0.00810758
\(306\) −24.3157 −1.39003
\(307\) −3.19733 −0.182481 −0.0912406 0.995829i \(-0.529083\pi\)
−0.0912406 + 0.995829i \(0.529083\pi\)
\(308\) 2.22771 0.126935
\(309\) −12.5137 −0.711880
\(310\) −1.16938 −0.0664162
\(311\) 4.24105 0.240488 0.120244 0.992744i \(-0.461632\pi\)
0.120244 + 0.992744i \(0.461632\pi\)
\(312\) −3.86706 −0.218929
\(313\) −14.0391 −0.793538 −0.396769 0.917919i \(-0.629869\pi\)
−0.396769 + 0.917919i \(0.629869\pi\)
\(314\) −17.0634 −0.962943
\(315\) 7.69551 0.433593
\(316\) −4.92710 −0.277171
\(317\) 16.6810 0.936898 0.468449 0.883491i \(-0.344813\pi\)
0.468449 + 0.883491i \(0.344813\pi\)
\(318\) −16.4150 −0.920507
\(319\) −3.04240 −0.170342
\(320\) 0.429228 0.0239946
\(321\) −22.9636 −1.28170
\(322\) 29.9295 1.66790
\(323\) 26.7157 1.48650
\(324\) 1.69232 0.0940180
\(325\) 6.54440 0.363018
\(326\) 5.64536 0.312668
\(327\) −5.47396 −0.302711
\(328\) −3.50901 −0.193753
\(329\) 16.1288 0.889212
\(330\) 0.773630 0.0425869
\(331\) 21.8671 1.20193 0.600964 0.799276i \(-0.294784\pi\)
0.600964 + 0.799276i \(0.294784\pi\)
\(332\) 15.1441 0.831141
\(333\) 49.6228 2.71931
\(334\) 12.9756 0.709992
\(335\) 1.86866 0.102096
\(336\) −10.0084 −0.546004
\(337\) 18.7613 1.02199 0.510997 0.859582i \(-0.329276\pi\)
0.510997 + 0.859582i \(0.329276\pi\)
\(338\) 11.1532 0.606657
\(339\) −16.2001 −0.879868
\(340\) 2.04745 0.111038
\(341\) 1.72559 0.0934457
\(342\) −28.5498 −1.54380
\(343\) −5.73213 −0.309506
\(344\) 4.31818 0.232820
\(345\) 10.3938 0.559583
\(346\) 16.4284 0.883196
\(347\) −21.9322 −1.17738 −0.588692 0.808357i \(-0.700357\pi\)
−0.588692 + 0.808357i \(0.700357\pi\)
\(348\) 13.6686 0.732714
\(349\) 26.5199 1.41958 0.709789 0.704414i \(-0.248790\pi\)
0.709789 + 0.704414i \(0.248790\pi\)
\(350\) 16.9377 0.905357
\(351\) 8.11133 0.432951
\(352\) −0.633387 −0.0337596
\(353\) −2.48535 −0.132282 −0.0661409 0.997810i \(-0.521069\pi\)
−0.0661409 + 0.997810i \(0.521069\pi\)
\(354\) 27.7926 1.47716
\(355\) −6.10382 −0.323957
\(356\) −1.70946 −0.0906013
\(357\) −47.7409 −2.52672
\(358\) −11.4895 −0.607240
\(359\) 13.5278 0.713972 0.356986 0.934110i \(-0.383804\pi\)
0.356986 + 0.934110i \(0.383804\pi\)
\(360\) −2.18801 −0.115318
\(361\) 12.3678 0.650937
\(362\) 21.2078 1.11466
\(363\) 30.1602 1.58300
\(364\) −4.77962 −0.250520
\(365\) 7.12852 0.373124
\(366\) 0.938707 0.0490670
\(367\) −12.8053 −0.668431 −0.334216 0.942497i \(-0.608471\pi\)
−0.334216 + 0.942497i \(0.608471\pi\)
\(368\) −8.50962 −0.443594
\(369\) 17.8874 0.931179
\(370\) −4.17838 −0.217224
\(371\) −20.2886 −1.05333
\(372\) −7.75254 −0.401951
\(373\) −17.2802 −0.894736 −0.447368 0.894350i \(-0.647639\pi\)
−0.447368 + 0.894350i \(0.647639\pi\)
\(374\) −3.02130 −0.156228
\(375\) 11.9892 0.619117
\(376\) −4.58579 −0.236494
\(377\) 6.52758 0.336187
\(378\) 20.9931 1.07977
\(379\) 20.8109 1.06898 0.534491 0.845174i \(-0.320503\pi\)
0.534491 + 0.845174i \(0.320503\pi\)
\(380\) 2.40397 0.123321
\(381\) −23.1300 −1.18498
\(382\) 7.73973 0.395999
\(383\) 2.71888 0.138928 0.0694640 0.997584i \(-0.477871\pi\)
0.0694640 + 0.997584i \(0.477871\pi\)
\(384\) 2.84562 0.145215
\(385\) 0.956193 0.0487321
\(386\) −27.0912 −1.37891
\(387\) −22.0121 −1.11894
\(388\) 7.40527 0.375946
\(389\) −24.8561 −1.26026 −0.630128 0.776491i \(-0.716998\pi\)
−0.630128 + 0.776491i \(0.716998\pi\)
\(390\) −1.65985 −0.0840497
\(391\) −40.5915 −2.05280
\(392\) −5.37023 −0.271237
\(393\) −39.6731 −2.00124
\(394\) 11.5701 0.582895
\(395\) −2.11485 −0.106410
\(396\) 3.22872 0.162249
\(397\) −1.60167 −0.0803855 −0.0401927 0.999192i \(-0.512797\pi\)
−0.0401927 + 0.999192i \(0.512797\pi\)
\(398\) 12.1766 0.610360
\(399\) −56.0541 −2.80622
\(400\) −4.81576 −0.240788
\(401\) 23.8655 1.19179 0.595894 0.803063i \(-0.296798\pi\)
0.595894 + 0.803063i \(0.296798\pi\)
\(402\) 12.3885 0.617884
\(403\) −3.70230 −0.184425
\(404\) −1.38538 −0.0689252
\(405\) 0.726392 0.0360947
\(406\) 16.8942 0.838443
\(407\) 6.16580 0.305627
\(408\) 13.5738 0.672004
\(409\) −33.7230 −1.66750 −0.833749 0.552144i \(-0.813810\pi\)
−0.833749 + 0.552144i \(0.813810\pi\)
\(410\) −1.50617 −0.0743842
\(411\) 49.7235 2.45268
\(412\) 4.39754 0.216651
\(413\) 34.3512 1.69031
\(414\) 43.3781 2.13192
\(415\) 6.50027 0.319086
\(416\) 1.35895 0.0666281
\(417\) 25.6606 1.25660
\(418\) −3.54741 −0.173509
\(419\) 2.13433 0.104269 0.0521344 0.998640i \(-0.483398\pi\)
0.0521344 + 0.998640i \(0.483398\pi\)
\(420\) −4.29589 −0.209618
\(421\) 21.9042 1.06754 0.533772 0.845628i \(-0.320774\pi\)
0.533772 + 0.845628i \(0.320774\pi\)
\(422\) 16.5120 0.803790
\(423\) 23.3763 1.13659
\(424\) 5.76851 0.280144
\(425\) −22.9716 −1.11428
\(426\) −40.4661 −1.96059
\(427\) 1.16023 0.0561473
\(428\) 8.06980 0.390069
\(429\) 2.44935 0.118256
\(430\) 1.85348 0.0893828
\(431\) −24.5546 −1.18275 −0.591376 0.806396i \(-0.701415\pi\)
−0.591376 + 0.806396i \(0.701415\pi\)
\(432\) −5.96881 −0.287175
\(433\) 20.4556 0.983033 0.491516 0.870868i \(-0.336443\pi\)
0.491516 + 0.870868i \(0.336443\pi\)
\(434\) −9.58200 −0.459951
\(435\) 5.86694 0.281298
\(436\) 1.92364 0.0921259
\(437\) −47.6598 −2.27988
\(438\) 47.2594 2.25814
\(439\) −17.9590 −0.857135 −0.428568 0.903510i \(-0.640982\pi\)
−0.428568 + 0.903510i \(0.640982\pi\)
\(440\) −0.271867 −0.0129608
\(441\) 27.3750 1.30357
\(442\) 6.48231 0.308332
\(443\) 21.7385 1.03283 0.516415 0.856339i \(-0.327266\pi\)
0.516415 + 0.856339i \(0.327266\pi\)
\(444\) −27.7011 −1.31464
\(445\) −0.733749 −0.0347830
\(446\) −15.4303 −0.730648
\(447\) −15.9776 −0.755714
\(448\) 3.51713 0.166169
\(449\) −32.2658 −1.52272 −0.761358 0.648332i \(-0.775467\pi\)
−0.761358 + 0.648332i \(0.775467\pi\)
\(450\) 24.5486 1.15723
\(451\) 2.22256 0.104656
\(452\) 5.69299 0.267776
\(453\) −54.2514 −2.54895
\(454\) −11.6490 −0.546714
\(455\) −2.05154 −0.0961779
\(456\) 15.9374 0.746339
\(457\) −33.8914 −1.58537 −0.792686 0.609630i \(-0.791318\pi\)
−0.792686 + 0.609630i \(0.791318\pi\)
\(458\) −1.98296 −0.0926576
\(459\) −28.4717 −1.32894
\(460\) −3.65256 −0.170302
\(461\) −1.54068 −0.0717566 −0.0358783 0.999356i \(-0.511423\pi\)
−0.0358783 + 0.999356i \(0.511423\pi\)
\(462\) 6.33920 0.294926
\(463\) 15.6630 0.727923 0.363962 0.931414i \(-0.381424\pi\)
0.363962 + 0.931414i \(0.381424\pi\)
\(464\) −4.80339 −0.222992
\(465\) −3.32761 −0.154314
\(466\) −0.00288630 −0.000133705 0
\(467\) 31.7694 1.47011 0.735057 0.678005i \(-0.237155\pi\)
0.735057 + 0.678005i \(0.237155\pi\)
\(468\) −6.92732 −0.320216
\(469\) 15.3120 0.707043
\(470\) −1.96835 −0.0907932
\(471\) −48.5559 −2.23734
\(472\) −9.76681 −0.449554
\(473\) −2.73508 −0.125759
\(474\) −14.0207 −0.643990
\(475\) −26.9716 −1.23754
\(476\) 16.7770 0.768972
\(477\) −29.4053 −1.34637
\(478\) 23.0845 1.05586
\(479\) −11.8342 −0.540716 −0.270358 0.962760i \(-0.587142\pi\)
−0.270358 + 0.962760i \(0.587142\pi\)
\(480\) 1.22142 0.0557499
\(481\) −13.2289 −0.603187
\(482\) −7.29859 −0.332442
\(483\) 85.1678 3.87527
\(484\) −10.5988 −0.481765
\(485\) 3.17855 0.144330
\(486\) −13.0907 −0.593807
\(487\) −2.58528 −0.117150 −0.0585751 0.998283i \(-0.518656\pi\)
−0.0585751 + 0.998283i \(0.518656\pi\)
\(488\) −0.329878 −0.0149329
\(489\) 16.0646 0.726464
\(490\) −2.30505 −0.104132
\(491\) −19.4643 −0.878409 −0.439205 0.898387i \(-0.644740\pi\)
−0.439205 + 0.898387i \(0.644740\pi\)
\(492\) −9.98532 −0.450173
\(493\) −22.9125 −1.03193
\(494\) 7.61108 0.342439
\(495\) 1.38586 0.0622896
\(496\) 2.72438 0.122328
\(497\) −50.0153 −2.24349
\(498\) 43.0944 1.93110
\(499\) 12.6107 0.564534 0.282267 0.959336i \(-0.408914\pi\)
0.282267 + 0.959336i \(0.408914\pi\)
\(500\) −4.21320 −0.188420
\(501\) 36.9236 1.64962
\(502\) −11.7886 −0.526151
\(503\) 30.0351 1.33920 0.669599 0.742723i \(-0.266466\pi\)
0.669599 + 0.742723i \(0.266466\pi\)
\(504\) −17.9287 −0.798610
\(505\) −0.594643 −0.0264613
\(506\) 5.38988 0.239609
\(507\) 31.7379 1.40953
\(508\) 8.12828 0.360634
\(509\) 39.3093 1.74235 0.871177 0.490969i \(-0.163357\pi\)
0.871177 + 0.490969i \(0.163357\pi\)
\(510\) 5.82626 0.257991
\(511\) 58.4118 2.58399
\(512\) −1.00000 −0.0441942
\(513\) −33.4295 −1.47595
\(514\) 19.0902 0.842032
\(515\) 1.88754 0.0831752
\(516\) 12.2879 0.540944
\(517\) 2.90458 0.127743
\(518\) −34.2380 −1.50433
\(519\) 46.7489 2.05205
\(520\) 0.583300 0.0255794
\(521\) 32.4056 1.41971 0.709857 0.704346i \(-0.248760\pi\)
0.709857 + 0.704346i \(0.248760\pi\)
\(522\) 24.4855 1.07170
\(523\) 27.5459 1.20450 0.602250 0.798308i \(-0.294271\pi\)
0.602250 + 0.798308i \(0.294271\pi\)
\(524\) 13.9418 0.609052
\(525\) 48.1982 2.10354
\(526\) −8.58402 −0.374281
\(527\) 12.9955 0.566092
\(528\) −1.80238 −0.0784384
\(529\) 49.4136 2.14842
\(530\) 2.47601 0.107551
\(531\) 49.7868 2.16056
\(532\) 19.6984 0.854034
\(533\) −4.76859 −0.206550
\(534\) −4.86448 −0.210507
\(535\) 3.46378 0.149752
\(536\) −4.35355 −0.188045
\(537\) −32.6948 −1.41088
\(538\) 0.0773441 0.00333454
\(539\) 3.40143 0.146510
\(540\) −2.56198 −0.110250
\(541\) −37.7326 −1.62225 −0.811126 0.584871i \(-0.801145\pi\)
−0.811126 + 0.584871i \(0.801145\pi\)
\(542\) −10.6466 −0.457311
\(543\) 60.3493 2.58984
\(544\) −4.77007 −0.204515
\(545\) 0.825681 0.0353683
\(546\) −13.6010 −0.582068
\(547\) 17.0789 0.730241 0.365121 0.930960i \(-0.381028\pi\)
0.365121 + 0.930960i \(0.381028\pi\)
\(548\) −17.4737 −0.746440
\(549\) 1.68157 0.0717676
\(550\) 3.05024 0.130063
\(551\) −26.9023 −1.14608
\(552\) −24.2151 −1.03066
\(553\) −17.3293 −0.736916
\(554\) 18.1652 0.771763
\(555\) −11.8901 −0.504705
\(556\) −9.01758 −0.382430
\(557\) 11.1709 0.473324 0.236662 0.971592i \(-0.423947\pi\)
0.236662 + 0.971592i \(0.423947\pi\)
\(558\) −13.8876 −0.587911
\(559\) 5.86820 0.248198
\(560\) 1.50965 0.0637944
\(561\) −8.59748 −0.362986
\(562\) −2.45064 −0.103374
\(563\) 33.8736 1.42760 0.713801 0.700348i \(-0.246972\pi\)
0.713801 + 0.700348i \(0.246972\pi\)
\(564\) −13.0494 −0.549480
\(565\) 2.44359 0.102803
\(566\) 11.7531 0.494019
\(567\) 5.95213 0.249966
\(568\) 14.2205 0.596678
\(569\) −26.2691 −1.10126 −0.550629 0.834750i \(-0.685612\pi\)
−0.550629 + 0.834750i \(0.685612\pi\)
\(570\) 6.84079 0.286529
\(571\) 40.9950 1.71559 0.857794 0.513994i \(-0.171835\pi\)
0.857794 + 0.513994i \(0.171835\pi\)
\(572\) −0.860743 −0.0359895
\(573\) 22.0243 0.920079
\(574\) −12.3417 −0.515131
\(575\) 40.9803 1.70900
\(576\) 5.09754 0.212398
\(577\) 11.8808 0.494604 0.247302 0.968938i \(-0.420456\pi\)
0.247302 + 0.968938i \(0.420456\pi\)
\(578\) −5.75362 −0.239319
\(579\) −77.0912 −3.20380
\(580\) −2.06175 −0.0856094
\(581\) 53.2638 2.20976
\(582\) 21.0726 0.873487
\(583\) −3.65370 −0.151321
\(584\) −16.6078 −0.687235
\(585\) −2.97340 −0.122935
\(586\) −17.2185 −0.711290
\(587\) −24.2425 −1.00060 −0.500298 0.865853i \(-0.666776\pi\)
−0.500298 + 0.865853i \(0.666776\pi\)
\(588\) −15.2816 −0.630203
\(589\) 15.2584 0.628712
\(590\) −4.19219 −0.172590
\(591\) 32.9242 1.35432
\(592\) 9.73464 0.400091
\(593\) 17.4280 0.715683 0.357841 0.933782i \(-0.383513\pi\)
0.357841 + 0.933782i \(0.383513\pi\)
\(594\) 3.78057 0.155119
\(595\) 7.20115 0.295218
\(596\) 5.61480 0.229991
\(597\) 34.6501 1.41813
\(598\) −11.5642 −0.472894
\(599\) −12.4903 −0.510339 −0.255169 0.966896i \(-0.582131\pi\)
−0.255169 + 0.966896i \(0.582131\pi\)
\(600\) −13.7038 −0.559456
\(601\) 33.4430 1.36417 0.682085 0.731273i \(-0.261073\pi\)
0.682085 + 0.731273i \(0.261073\pi\)
\(602\) 15.1876 0.619000
\(603\) 22.1924 0.903745
\(604\) 19.0649 0.775739
\(605\) −4.54931 −0.184956
\(606\) −3.94226 −0.160143
\(607\) 15.1189 0.613657 0.306829 0.951765i \(-0.400732\pi\)
0.306829 + 0.951765i \(0.400732\pi\)
\(608\) −5.60070 −0.227138
\(609\) 48.0743 1.94807
\(610\) −0.141593 −0.00573293
\(611\) −6.23188 −0.252115
\(612\) 24.3157 0.982903
\(613\) 32.1700 1.29934 0.649668 0.760218i \(-0.274908\pi\)
0.649668 + 0.760218i \(0.274908\pi\)
\(614\) 3.19733 0.129034
\(615\) −4.28597 −0.172827
\(616\) −2.22771 −0.0897568
\(617\) 21.1811 0.852717 0.426359 0.904554i \(-0.359796\pi\)
0.426359 + 0.904554i \(0.359796\pi\)
\(618\) 12.5137 0.503375
\(619\) 28.8993 1.16156 0.580780 0.814060i \(-0.302748\pi\)
0.580780 + 0.814060i \(0.302748\pi\)
\(620\) 1.16938 0.0469634
\(621\) 50.7923 2.03822
\(622\) −4.24105 −0.170051
\(623\) −6.01241 −0.240882
\(624\) 3.86706 0.154806
\(625\) 22.2704 0.890816
\(626\) 14.0391 0.561116
\(627\) −10.0946 −0.403138
\(628\) 17.0634 0.680904
\(629\) 46.4350 1.85148
\(630\) −7.69551 −0.306597
\(631\) 0.213575 0.00850227 0.00425114 0.999991i \(-0.498647\pi\)
0.00425114 + 0.999991i \(0.498647\pi\)
\(632\) 4.92710 0.195990
\(633\) 46.9868 1.86756
\(634\) −16.6810 −0.662487
\(635\) 3.48888 0.138452
\(636\) 16.4150 0.650897
\(637\) −7.29788 −0.289153
\(638\) 3.04240 0.120450
\(639\) −72.4895 −2.86764
\(640\) −0.429228 −0.0169667
\(641\) −45.5558 −1.79935 −0.899673 0.436564i \(-0.856195\pi\)
−0.899673 + 0.436564i \(0.856195\pi\)
\(642\) 22.9636 0.906300
\(643\) 3.61783 0.142673 0.0713367 0.997452i \(-0.477274\pi\)
0.0713367 + 0.997452i \(0.477274\pi\)
\(644\) −29.9295 −1.17939
\(645\) 5.27430 0.207675
\(646\) −26.7157 −1.05112
\(647\) 39.4449 1.55074 0.775369 0.631508i \(-0.217564\pi\)
0.775369 + 0.631508i \(0.217564\pi\)
\(648\) −1.69232 −0.0664808
\(649\) 6.18617 0.242828
\(650\) −6.54440 −0.256692
\(651\) −27.2667 −1.06867
\(652\) −5.64536 −0.221090
\(653\) −11.2106 −0.438705 −0.219352 0.975646i \(-0.570394\pi\)
−0.219352 + 0.975646i \(0.570394\pi\)
\(654\) 5.47396 0.214049
\(655\) 5.98422 0.233823
\(656\) 3.50901 0.137004
\(657\) 84.6590 3.30286
\(658\) −16.1288 −0.628768
\(659\) 2.64933 0.103203 0.0516015 0.998668i \(-0.483567\pi\)
0.0516015 + 0.998668i \(0.483567\pi\)
\(660\) −0.773630 −0.0301135
\(661\) −45.3415 −1.76358 −0.881789 0.471643i \(-0.843661\pi\)
−0.881789 + 0.471643i \(0.843661\pi\)
\(662\) −21.8671 −0.849891
\(663\) 18.4462 0.716390
\(664\) −15.1441 −0.587705
\(665\) 8.45510 0.327875
\(666\) −49.6228 −1.92284
\(667\) 40.8750 1.58269
\(668\) −12.9756 −0.502040
\(669\) −43.9089 −1.69762
\(670\) −1.86866 −0.0721928
\(671\) 0.208941 0.00806606
\(672\) 10.0084 0.386083
\(673\) 30.6763 1.18248 0.591241 0.806495i \(-0.298638\pi\)
0.591241 + 0.806495i \(0.298638\pi\)
\(674\) −18.7613 −0.722659
\(675\) 28.7444 1.10637
\(676\) −11.1532 −0.428971
\(677\) −7.07706 −0.271993 −0.135997 0.990709i \(-0.543424\pi\)
−0.135997 + 0.990709i \(0.543424\pi\)
\(678\) 16.2001 0.622160
\(679\) 26.0453 0.999528
\(680\) −2.04745 −0.0785160
\(681\) −33.1486 −1.27026
\(682\) −1.72559 −0.0660761
\(683\) 15.6469 0.598713 0.299357 0.954141i \(-0.403228\pi\)
0.299357 + 0.954141i \(0.403228\pi\)
\(684\) 28.5498 1.09163
\(685\) −7.50020 −0.286568
\(686\) 5.73213 0.218854
\(687\) −5.64275 −0.215284
\(688\) −4.31818 −0.164629
\(689\) 7.83914 0.298647
\(690\) −10.3938 −0.395685
\(691\) 42.2042 1.60552 0.802762 0.596299i \(-0.203363\pi\)
0.802762 + 0.596299i \(0.203363\pi\)
\(692\) −16.4284 −0.624514
\(693\) 11.3558 0.431372
\(694\) 21.9322 0.832537
\(695\) −3.87059 −0.146820
\(696\) −13.6686 −0.518107
\(697\) 16.7383 0.634007
\(698\) −26.5199 −1.00379
\(699\) −0.00821331 −0.000310656 0
\(700\) −16.9377 −0.640184
\(701\) 22.6128 0.854074 0.427037 0.904234i \(-0.359557\pi\)
0.427037 + 0.904234i \(0.359557\pi\)
\(702\) −8.11133 −0.306142
\(703\) 54.5208 2.05629
\(704\) 0.633387 0.0238717
\(705\) −5.60117 −0.210952
\(706\) 2.48535 0.0935374
\(707\) −4.87256 −0.183252
\(708\) −27.7926 −1.04451
\(709\) −5.22135 −0.196092 −0.0980460 0.995182i \(-0.531259\pi\)
−0.0980460 + 0.995182i \(0.531259\pi\)
\(710\) 6.10382 0.229072
\(711\) −25.1161 −0.941929
\(712\) 1.70946 0.0640648
\(713\) −23.1834 −0.868226
\(714\) 47.7409 1.78666
\(715\) −0.369455 −0.0138168
\(716\) 11.4895 0.429383
\(717\) 65.6897 2.45323
\(718\) −13.5278 −0.504855
\(719\) −23.6107 −0.880532 −0.440266 0.897867i \(-0.645116\pi\)
−0.440266 + 0.897867i \(0.645116\pi\)
\(720\) 2.18801 0.0815422
\(721\) 15.4667 0.576011
\(722\) −12.3678 −0.460282
\(723\) −20.7690 −0.772408
\(724\) −21.2078 −0.788182
\(725\) 23.1320 0.859100
\(726\) −30.1602 −1.11935
\(727\) −28.5271 −1.05801 −0.529007 0.848618i \(-0.677435\pi\)
−0.529007 + 0.848618i \(0.677435\pi\)
\(728\) 4.77962 0.177144
\(729\) −42.3282 −1.56771
\(730\) −7.12852 −0.263839
\(731\) −20.5980 −0.761845
\(732\) −0.938707 −0.0346956
\(733\) −12.8966 −0.476347 −0.238174 0.971223i \(-0.576549\pi\)
−0.238174 + 0.971223i \(0.576549\pi\)
\(734\) 12.8053 0.472652
\(735\) −6.55929 −0.241943
\(736\) 8.50962 0.313669
\(737\) 2.75748 0.101573
\(738\) −17.8874 −0.658443
\(739\) 30.7871 1.13252 0.566261 0.824226i \(-0.308390\pi\)
0.566261 + 0.824226i \(0.308390\pi\)
\(740\) 4.17838 0.153600
\(741\) 21.6582 0.795635
\(742\) 20.2886 0.744819
\(743\) −8.14805 −0.298923 −0.149461 0.988768i \(-0.547754\pi\)
−0.149461 + 0.988768i \(0.547754\pi\)
\(744\) 7.75254 0.284222
\(745\) 2.41003 0.0882966
\(746\) 17.2802 0.632674
\(747\) 77.1978 2.82452
\(748\) 3.02130 0.110470
\(749\) 28.3826 1.03708
\(750\) −11.9892 −0.437782
\(751\) 6.28735 0.229429 0.114714 0.993399i \(-0.463405\pi\)
0.114714 + 0.993399i \(0.463405\pi\)
\(752\) 4.58579 0.167227
\(753\) −33.5459 −1.22248
\(754\) −6.52758 −0.237720
\(755\) 8.18317 0.297816
\(756\) −20.9931 −0.763512
\(757\) −49.9553 −1.81566 −0.907828 0.419342i \(-0.862261\pi\)
−0.907828 + 0.419342i \(0.862261\pi\)
\(758\) −20.8109 −0.755884
\(759\) 15.3375 0.556718
\(760\) −2.40397 −0.0872013
\(761\) −32.4178 −1.17514 −0.587572 0.809172i \(-0.699916\pi\)
−0.587572 + 0.809172i \(0.699916\pi\)
\(762\) 23.1300 0.837911
\(763\) 6.76571 0.244935
\(764\) −7.73973 −0.280014
\(765\) 10.4370 0.377349
\(766\) −2.71888 −0.0982370
\(767\) −13.2726 −0.479247
\(768\) −2.84562 −0.102682
\(769\) 51.0330 1.84030 0.920149 0.391569i \(-0.128068\pi\)
0.920149 + 0.391569i \(0.128068\pi\)
\(770\) −0.956193 −0.0344588
\(771\) 54.3234 1.95641
\(772\) 27.0912 0.975034
\(773\) −22.7259 −0.817392 −0.408696 0.912670i \(-0.634016\pi\)
−0.408696 + 0.912670i \(0.634016\pi\)
\(774\) 22.0121 0.791208
\(775\) −13.1200 −0.471283
\(776\) −7.40527 −0.265834
\(777\) −97.4284 −3.49522
\(778\) 24.8561 0.891135
\(779\) 19.6529 0.704139
\(780\) 1.65985 0.0594321
\(781\) −9.00707 −0.322298
\(782\) 40.5915 1.45155
\(783\) 28.6705 1.02460
\(784\) 5.37023 0.191794
\(785\) 7.32408 0.261408
\(786\) 39.6731 1.41509
\(787\) 48.1159 1.71515 0.857573 0.514362i \(-0.171971\pi\)
0.857573 + 0.514362i \(0.171971\pi\)
\(788\) −11.5701 −0.412169
\(789\) −24.4268 −0.869618
\(790\) 2.11485 0.0752430
\(791\) 20.0230 0.711936
\(792\) −3.22872 −0.114727
\(793\) −0.448289 −0.0159192
\(794\) 1.60167 0.0568411
\(795\) 7.04577 0.249888
\(796\) −12.1766 −0.431589
\(797\) −27.9294 −0.989311 −0.494655 0.869089i \(-0.664706\pi\)
−0.494655 + 0.869089i \(0.664706\pi\)
\(798\) 56.0541 1.98429
\(799\) 21.8746 0.773867
\(800\) 4.81576 0.170263
\(801\) −8.71406 −0.307896
\(802\) −23.8655 −0.842722
\(803\) 10.5192 0.371213
\(804\) −12.3885 −0.436910
\(805\) −12.8466 −0.452781
\(806\) 3.70230 0.130408
\(807\) 0.220092 0.00774760
\(808\) 1.38538 0.0487375
\(809\) 0.917026 0.0322409 0.0161205 0.999870i \(-0.494868\pi\)
0.0161205 + 0.999870i \(0.494868\pi\)
\(810\) −0.726392 −0.0255228
\(811\) 5.54988 0.194883 0.0974414 0.995241i \(-0.468934\pi\)
0.0974414 + 0.995241i \(0.468934\pi\)
\(812\) −16.8942 −0.592869
\(813\) −30.2962 −1.06253
\(814\) −6.16580 −0.216111
\(815\) −2.42315 −0.0848791
\(816\) −13.5738 −0.475179
\(817\) −24.1848 −0.846119
\(818\) 33.7230 1.17910
\(819\) −24.3643 −0.851358
\(820\) 1.50617 0.0525976
\(821\) −35.6576 −1.24446 −0.622230 0.782834i \(-0.713773\pi\)
−0.622230 + 0.782834i \(0.713773\pi\)
\(822\) −49.7235 −1.73431
\(823\) −42.1602 −1.46961 −0.734806 0.678278i \(-0.762727\pi\)
−0.734806 + 0.678278i \(0.762727\pi\)
\(824\) −4.39754 −0.153195
\(825\) 8.67982 0.302193
\(826\) −34.3512 −1.19523
\(827\) 33.9213 1.17956 0.589779 0.807565i \(-0.299215\pi\)
0.589779 + 0.807565i \(0.299215\pi\)
\(828\) −43.3781 −1.50749
\(829\) 30.5091 1.05962 0.529812 0.848115i \(-0.322262\pi\)
0.529812 + 0.848115i \(0.322262\pi\)
\(830\) −6.50027 −0.225628
\(831\) 51.6911 1.79314
\(832\) −1.35895 −0.0471132
\(833\) 25.6164 0.887555
\(834\) −25.6606 −0.888553
\(835\) −5.56948 −0.192740
\(836\) 3.54741 0.122690
\(837\) −16.2613 −0.562073
\(838\) −2.13433 −0.0737292
\(839\) 16.5873 0.572659 0.286329 0.958131i \(-0.407565\pi\)
0.286329 + 0.958131i \(0.407565\pi\)
\(840\) 4.29589 0.148222
\(841\) −5.92747 −0.204395
\(842\) −21.9042 −0.754868
\(843\) −6.97359 −0.240183
\(844\) −16.5120 −0.568366
\(845\) −4.78728 −0.164688
\(846\) −23.3763 −0.803693
\(847\) −37.2775 −1.28087
\(848\) −5.76851 −0.198092
\(849\) 33.4448 1.14782
\(850\) 22.9716 0.787918
\(851\) −82.8381 −2.83965
\(852\) 40.4661 1.38634
\(853\) 44.0155 1.50706 0.753531 0.657412i \(-0.228349\pi\)
0.753531 + 0.657412i \(0.228349\pi\)
\(854\) −1.16023 −0.0397021
\(855\) 12.2544 0.419090
\(856\) −8.06980 −0.275820
\(857\) 8.26829 0.282439 0.141220 0.989978i \(-0.454898\pi\)
0.141220 + 0.989978i \(0.454898\pi\)
\(858\) −2.44935 −0.0836193
\(859\) 42.0065 1.43324 0.716622 0.697461i \(-0.245687\pi\)
0.716622 + 0.697461i \(0.245687\pi\)
\(860\) −1.85348 −0.0632032
\(861\) −35.1197 −1.19688
\(862\) 24.5546 0.836332
\(863\) 47.8403 1.62850 0.814251 0.580513i \(-0.197148\pi\)
0.814251 + 0.580513i \(0.197148\pi\)
\(864\) 5.96881 0.203063
\(865\) −7.05152 −0.239759
\(866\) −20.4556 −0.695109
\(867\) −16.3726 −0.556042
\(868\) 9.58200 0.325234
\(869\) −3.12076 −0.105865
\(870\) −5.86694 −0.198908
\(871\) −5.91627 −0.200465
\(872\) −1.92364 −0.0651428
\(873\) 37.7487 1.27760
\(874\) 47.6598 1.61212
\(875\) −14.8184 −0.500953
\(876\) −47.2594 −1.59675
\(877\) −18.6809 −0.630808 −0.315404 0.948958i \(-0.602140\pi\)
−0.315404 + 0.948958i \(0.602140\pi\)
\(878\) 17.9590 0.606086
\(879\) −48.9973 −1.65264
\(880\) 0.271867 0.00916464
\(881\) −26.1604 −0.881365 −0.440683 0.897663i \(-0.645264\pi\)
−0.440683 + 0.897663i \(0.645264\pi\)
\(882\) −27.3750 −0.921763
\(883\) 15.1819 0.510912 0.255456 0.966821i \(-0.417774\pi\)
0.255456 + 0.966821i \(0.417774\pi\)
\(884\) −6.48231 −0.218024
\(885\) −11.9294 −0.401001
\(886\) −21.7385 −0.730321
\(887\) −2.57938 −0.0866073 −0.0433036 0.999062i \(-0.513788\pi\)
−0.0433036 + 0.999062i \(0.513788\pi\)
\(888\) 27.7011 0.929587
\(889\) 28.5882 0.958819
\(890\) 0.733749 0.0245953
\(891\) 1.07190 0.0359099
\(892\) 15.4303 0.516646
\(893\) 25.6836 0.859470
\(894\) 15.9776 0.534370
\(895\) 4.93162 0.164846
\(896\) −3.51713 −0.117499
\(897\) −32.9072 −1.09874
\(898\) 32.2658 1.07672
\(899\) −13.0862 −0.436451
\(900\) −24.5486 −0.818286
\(901\) −27.5162 −0.916699
\(902\) −2.22256 −0.0740033
\(903\) 43.2181 1.43821
\(904\) −5.69299 −0.189346
\(905\) −9.10298 −0.302593
\(906\) 54.2514 1.80238
\(907\) 7.04633 0.233970 0.116985 0.993134i \(-0.462677\pi\)
0.116985 + 0.993134i \(0.462677\pi\)
\(908\) 11.6490 0.386585
\(909\) −7.06203 −0.234233
\(910\) 2.05154 0.0680080
\(911\) −48.4958 −1.60674 −0.803368 0.595482i \(-0.796961\pi\)
−0.803368 + 0.595482i \(0.796961\pi\)
\(912\) −15.9374 −0.527742
\(913\) 9.59208 0.317452
\(914\) 33.8914 1.12103
\(915\) −0.402919 −0.0133201
\(916\) 1.98296 0.0655188
\(917\) 49.0353 1.61929
\(918\) 28.4717 0.939705
\(919\) 50.8741 1.67818 0.839091 0.543990i \(-0.183087\pi\)
0.839091 + 0.543990i \(0.183087\pi\)
\(920\) 3.65256 0.120421
\(921\) 9.09838 0.299802
\(922\) 1.54068 0.0507396
\(923\) 19.3250 0.636089
\(924\) −6.33920 −0.208544
\(925\) −46.8797 −1.54140
\(926\) −15.6630 −0.514719
\(927\) 22.4166 0.736259
\(928\) 4.80339 0.157679
\(929\) −18.0499 −0.592197 −0.296098 0.955157i \(-0.595686\pi\)
−0.296098 + 0.955157i \(0.595686\pi\)
\(930\) 3.32761 0.109116
\(931\) 30.0770 0.985734
\(932\) 0.00288630 9.45439e−5 0
\(933\) −12.0684 −0.395102
\(934\) −31.7694 −1.03953
\(935\) 1.29683 0.0424108
\(936\) 6.92732 0.226427
\(937\) −46.6570 −1.52422 −0.762109 0.647449i \(-0.775836\pi\)
−0.762109 + 0.647449i \(0.775836\pi\)
\(938\) −15.3120 −0.499955
\(939\) 39.9500 1.30372
\(940\) 1.96835 0.0642005
\(941\) −25.6653 −0.836666 −0.418333 0.908294i \(-0.637386\pi\)
−0.418333 + 0.908294i \(0.637386\pi\)
\(942\) 48.5559 1.58204
\(943\) −29.8604 −0.972388
\(944\) 9.76681 0.317883
\(945\) −9.01082 −0.293122
\(946\) 2.73508 0.0889250
\(947\) 7.56033 0.245678 0.122839 0.992427i \(-0.460800\pi\)
0.122839 + 0.992427i \(0.460800\pi\)
\(948\) 14.0207 0.455370
\(949\) −22.5692 −0.732627
\(950\) 26.9716 0.875075
\(951\) −47.4677 −1.53925
\(952\) −16.7770 −0.543745
\(953\) −1.58447 −0.0513261 −0.0256630 0.999671i \(-0.508170\pi\)
−0.0256630 + 0.999671i \(0.508170\pi\)
\(954\) 29.4053 0.952030
\(955\) −3.32211 −0.107501
\(956\) −23.0845 −0.746606
\(957\) 8.65752 0.279858
\(958\) 11.8342 0.382344
\(959\) −61.4573 −1.98456
\(960\) −1.22142 −0.0394211
\(961\) −23.5778 −0.760573
\(962\) 13.2289 0.426518
\(963\) 41.1362 1.32559
\(964\) 7.29859 0.235072
\(965\) 11.6283 0.374328
\(966\) −85.1678 −2.74023
\(967\) 8.52213 0.274053 0.137027 0.990567i \(-0.456245\pi\)
0.137027 + 0.990567i \(0.456245\pi\)
\(968\) 10.5988 0.340659
\(969\) −76.0228 −2.44220
\(970\) −3.17855 −0.102057
\(971\) 33.3728 1.07099 0.535493 0.844540i \(-0.320126\pi\)
0.535493 + 0.844540i \(0.320126\pi\)
\(972\) 13.0907 0.419885
\(973\) −31.7160 −1.01677
\(974\) 2.58528 0.0828377
\(975\) −18.6229 −0.596409
\(976\) 0.329878 0.0105591
\(977\) 13.7304 0.439274 0.219637 0.975582i \(-0.429513\pi\)
0.219637 + 0.975582i \(0.429513\pi\)
\(978\) −16.0646 −0.513688
\(979\) −1.08275 −0.0346049
\(980\) 2.30505 0.0736321
\(981\) 9.80586 0.313077
\(982\) 19.4643 0.621129
\(983\) 52.6277 1.67856 0.839282 0.543696i \(-0.182976\pi\)
0.839282 + 0.543696i \(0.182976\pi\)
\(984\) 9.98532 0.318320
\(985\) −4.96622 −0.158237
\(986\) 22.9125 0.729683
\(987\) −45.8965 −1.46090
\(988\) −7.61108 −0.242141
\(989\) 36.7460 1.16846
\(990\) −1.38586 −0.0440454
\(991\) 33.6380 1.06855 0.534273 0.845312i \(-0.320585\pi\)
0.534273 + 0.845312i \(0.320585\pi\)
\(992\) −2.72438 −0.0864991
\(993\) −62.2256 −1.97467
\(994\) 50.0153 1.58639
\(995\) −5.22655 −0.165693
\(996\) −43.0944 −1.36550
\(997\) 35.1386 1.11285 0.556425 0.830898i \(-0.312173\pi\)
0.556425 + 0.830898i \(0.312173\pi\)
\(998\) −12.6107 −0.399186
\(999\) −58.1042 −1.83834
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 \(a_p\))