Properties

Label 8003.2.a.c.1.17
Level 8003
Weight 2
Character 8003.1
Self dual Yes
Analytic conductor 63.904
Analytic rank 0
Dimension 172
CM No

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Newspace parameters

Level: \( N \) = \( 8003 = 53 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9042767376\)
Analytic rank: \(0\)
Dimension: \(172\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.35311 q^{2}\) \(-1.80440 q^{3}\) \(+3.53712 q^{4}\) \(-3.84522 q^{5}\) \(+4.24595 q^{6}\) \(+1.90458 q^{7}\) \(-3.61701 q^{8}\) \(+0.255862 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.35311 q^{2}\) \(-1.80440 q^{3}\) \(+3.53712 q^{4}\) \(-3.84522 q^{5}\) \(+4.24595 q^{6}\) \(+1.90458 q^{7}\) \(-3.61701 q^{8}\) \(+0.255862 q^{9}\) \(+9.04823 q^{10}\) \(-2.80030 q^{11}\) \(-6.38238 q^{12}\) \(+3.55060 q^{13}\) \(-4.48168 q^{14}\) \(+6.93832 q^{15}\) \(+1.43698 q^{16}\) \(-4.12706 q^{17}\) \(-0.602070 q^{18}\) \(-1.33253 q^{19}\) \(-13.6010 q^{20}\) \(-3.43662 q^{21}\) \(+6.58941 q^{22}\) \(-0.584909 q^{23}\) \(+6.52654 q^{24}\) \(+9.78575 q^{25}\) \(-8.35495 q^{26}\) \(+4.95152 q^{27}\) \(+6.73672 q^{28}\) \(+1.42701 q^{29}\) \(-16.3266 q^{30}\) \(+6.82428 q^{31}\) \(+3.85265 q^{32}\) \(+5.05286 q^{33}\) \(+9.71143 q^{34}\) \(-7.32352 q^{35}\) \(+0.905013 q^{36}\) \(+6.39256 q^{37}\) \(+3.13558 q^{38}\) \(-6.40671 q^{39}\) \(+13.9082 q^{40}\) \(+4.82712 q^{41}\) \(+8.08674 q^{42}\) \(-5.73628 q^{43}\) \(-9.90500 q^{44}\) \(-0.983845 q^{45}\) \(+1.37636 q^{46}\) \(-12.3330 q^{47}\) \(-2.59289 q^{48}\) \(-3.37259 q^{49}\) \(-23.0269 q^{50}\) \(+7.44687 q^{51}\) \(+12.5589 q^{52}\) \(-1.00000 q^{53}\) \(-11.6515 q^{54}\) \(+10.7678 q^{55}\) \(-6.88888 q^{56}\) \(+2.40441 q^{57}\) \(-3.35790 q^{58}\) \(-0.538284 q^{59}\) \(+24.5417 q^{60}\) \(+0.689413 q^{61}\) \(-16.0583 q^{62}\) \(+0.487308 q^{63}\) \(-11.9397 q^{64}\) \(-13.6529 q^{65}\) \(-11.8899 q^{66}\) \(-11.9097 q^{67}\) \(-14.5979 q^{68}\) \(+1.05541 q^{69}\) \(+17.2330 q^{70}\) \(+9.00501 q^{71}\) \(-0.925454 q^{72}\) \(+12.8350 q^{73}\) \(-15.0424 q^{74}\) \(-17.6574 q^{75}\) \(-4.71331 q^{76}\) \(-5.33339 q^{77}\) \(+15.0757 q^{78}\) \(+4.71078 q^{79}\) \(-5.52551 q^{80}\) \(-9.70212 q^{81}\) \(-11.3587 q^{82}\) \(+1.64652 q^{83}\) \(-12.1557 q^{84}\) \(+15.8695 q^{85}\) \(+13.4981 q^{86}\) \(-2.57489 q^{87}\) \(+10.1287 q^{88}\) \(-4.30222 q^{89}\) \(+2.31510 q^{90}\) \(+6.76239 q^{91}\) \(-2.06889 q^{92}\) \(-12.3137 q^{93}\) \(+29.0209 q^{94}\) \(+5.12387 q^{95}\) \(-6.95173 q^{96}\) \(-8.95518 q^{97}\) \(+7.93607 q^{98}\) \(-0.716489 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 66q^{12} \) \(\mathstrut +\mathstrut 121q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 212q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 40q^{18} \) \(\mathstrut +\mathstrut 41q^{19} \) \(\mathstrut +\mathstrut 64q^{20} \) \(\mathstrut +\mathstrut 56q^{21} \) \(\mathstrut +\mathstrut 50q^{22} \) \(\mathstrut +\mathstrut 28q^{23} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 231q^{25} \) \(\mathstrut +\mathstrut 38q^{26} \) \(\mathstrut +\mathstrut 100q^{27} \) \(\mathstrut +\mathstrut 80q^{28} \) \(\mathstrut +\mathstrut 26q^{29} \) \(\mathstrut +\mathstrut 55q^{30} \) \(\mathstrut +\mathstrut 66q^{31} \) \(\mathstrut +\mathstrut 65q^{32} \) \(\mathstrut +\mathstrut 99q^{33} \) \(\mathstrut +\mathstrut 81q^{34} \) \(\mathstrut +\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 212q^{36} \) \(\mathstrut +\mathstrut 153q^{37} \) \(\mathstrut +\mathstrut q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 59q^{40} \) \(\mathstrut +\mathstrut 40q^{41} \) \(\mathstrut +\mathstrut 50q^{42} \) \(\mathstrut +\mathstrut 39q^{43} \) \(\mathstrut -\mathstrut 51q^{44} \) \(\mathstrut +\mathstrut 123q^{45} \) \(\mathstrut +\mathstrut 59q^{46} \) \(\mathstrut +\mathstrut 29q^{47} \) \(\mathstrut +\mathstrut 128q^{48} \) \(\mathstrut +\mathstrut 245q^{49} \) \(\mathstrut +\mathstrut 19q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 215q^{52} \) \(\mathstrut -\mathstrut 172q^{53} \) \(\mathstrut +\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut 40q^{55} \) \(\mathstrut +\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 54q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 54q^{60} \) \(\mathstrut +\mathstrut 100q^{61} \) \(\mathstrut -\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 92q^{63} \) \(\mathstrut +\mathstrut 253q^{64} \) \(\mathstrut +\mathstrut 77q^{65} \) \(\mathstrut +\mathstrut 14q^{66} \) \(\mathstrut +\mathstrut 126q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut +\mathstrut 47q^{69} \) \(\mathstrut +\mathstrut 72q^{70} \) \(\mathstrut +\mathstrut 38q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 185q^{73} \) \(\mathstrut +\mathstrut 48q^{74} \) \(\mathstrut +\mathstrut 75q^{75} \) \(\mathstrut +\mathstrut 38q^{76} \) \(\mathstrut +\mathstrut 120q^{77} \) \(\mathstrut +\mathstrut 75q^{78} \) \(\mathstrut +\mathstrut 79q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 232q^{81} \) \(\mathstrut +\mathstrut 110q^{82} \) \(\mathstrut +\mathstrut 90q^{83} \) \(\mathstrut +\mathstrut 158q^{84} \) \(\mathstrut +\mathstrut 115q^{85} \) \(\mathstrut +\mathstrut 68q^{86} \) \(\mathstrut +\mathstrut 61q^{87} \) \(\mathstrut +\mathstrut 15q^{88} \) \(\mathstrut -\mathstrut 36q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 33q^{91} \) \(\mathstrut +\mathstrut 139q^{92} \) \(\mathstrut +\mathstrut 103q^{93} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 45q^{95} \) \(\mathstrut +\mathstrut 34q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut -\mathstrut 36q^{98} \) \(\mathstrut +\mathstrut 27q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.35311 −1.66390 −0.831950 0.554851i \(-0.812775\pi\)
−0.831950 + 0.554851i \(0.812775\pi\)
\(3\) −1.80440 −1.04177 −0.520886 0.853626i \(-0.674398\pi\)
−0.520886 + 0.853626i \(0.674398\pi\)
\(4\) 3.53712 1.76856
\(5\) −3.84522 −1.71964 −0.859818 0.510600i \(-0.829423\pi\)
−0.859818 + 0.510600i \(0.829423\pi\)
\(6\) 4.24595 1.73340
\(7\) 1.90458 0.719862 0.359931 0.932979i \(-0.382800\pi\)
0.359931 + 0.932979i \(0.382800\pi\)
\(8\) −3.61701 −1.27881
\(9\) 0.255862 0.0852872
\(10\) 9.04823 2.86130
\(11\) −2.80030 −0.844322 −0.422161 0.906521i \(-0.638728\pi\)
−0.422161 + 0.906521i \(0.638728\pi\)
\(12\) −6.38238 −1.84244
\(13\) 3.55060 0.984759 0.492380 0.870381i \(-0.336127\pi\)
0.492380 + 0.870381i \(0.336127\pi\)
\(14\) −4.48168 −1.19778
\(15\) 6.93832 1.79147
\(16\) 1.43698 0.359245
\(17\) −4.12706 −1.00096 −0.500480 0.865748i \(-0.666843\pi\)
−0.500480 + 0.865748i \(0.666843\pi\)
\(18\) −0.602070 −0.141909
\(19\) −1.33253 −0.305703 −0.152851 0.988249i \(-0.548846\pi\)
−0.152851 + 0.988249i \(0.548846\pi\)
\(20\) −13.6010 −3.04128
\(21\) −3.43662 −0.749932
\(22\) 6.58941 1.40487
\(23\) −0.584909 −0.121962 −0.0609810 0.998139i \(-0.519423\pi\)
−0.0609810 + 0.998139i \(0.519423\pi\)
\(24\) 6.52654 1.33222
\(25\) 9.78575 1.95715
\(26\) −8.35495 −1.63854
\(27\) 4.95152 0.952921
\(28\) 6.73672 1.27312
\(29\) 1.42701 0.264988 0.132494 0.991184i \(-0.457701\pi\)
0.132494 + 0.991184i \(0.457701\pi\)
\(30\) −16.3266 −2.98082
\(31\) 6.82428 1.22568 0.612838 0.790208i \(-0.290028\pi\)
0.612838 + 0.790208i \(0.290028\pi\)
\(32\) 3.85265 0.681059
\(33\) 5.05286 0.879591
\(34\) 9.71143 1.66550
\(35\) −7.32352 −1.23790
\(36\) 0.905013 0.150836
\(37\) 6.39256 1.05093 0.525465 0.850815i \(-0.323891\pi\)
0.525465 + 0.850815i \(0.323891\pi\)
\(38\) 3.13558 0.508659
\(39\) −6.40671 −1.02589
\(40\) 13.9082 2.19908
\(41\) 4.82712 0.753870 0.376935 0.926240i \(-0.376978\pi\)
0.376935 + 0.926240i \(0.376978\pi\)
\(42\) 8.08674 1.24781
\(43\) −5.73628 −0.874774 −0.437387 0.899273i \(-0.644096\pi\)
−0.437387 + 0.899273i \(0.644096\pi\)
\(44\) −9.90500 −1.49323
\(45\) −0.983845 −0.146663
\(46\) 1.37636 0.202933
\(47\) −12.3330 −1.79896 −0.899478 0.436966i \(-0.856053\pi\)
−0.899478 + 0.436966i \(0.856053\pi\)
\(48\) −2.59289 −0.374251
\(49\) −3.37259 −0.481798
\(50\) −23.0269 −3.25650
\(51\) 7.44687 1.04277
\(52\) 12.5589 1.74161
\(53\) −1.00000 −0.137361
\(54\) −11.6515 −1.58557
\(55\) 10.7678 1.45193
\(56\) −6.88888 −0.920565
\(57\) 2.40441 0.318472
\(58\) −3.35790 −0.440914
\(59\) −0.538284 −0.0700786 −0.0350393 0.999386i \(-0.511156\pi\)
−0.0350393 + 0.999386i \(0.511156\pi\)
\(60\) 24.5417 3.16832
\(61\) 0.689413 0.0882702 0.0441351 0.999026i \(-0.485947\pi\)
0.0441351 + 0.999026i \(0.485947\pi\)
\(62\) −16.0583 −2.03940
\(63\) 0.487308 0.0613951
\(64\) −11.9397 −1.49246
\(65\) −13.6529 −1.69343
\(66\) −11.8899 −1.46355
\(67\) −11.9097 −1.45500 −0.727499 0.686109i \(-0.759317\pi\)
−0.727499 + 0.686109i \(0.759317\pi\)
\(68\) −14.5979 −1.77026
\(69\) 1.05541 0.127057
\(70\) 17.2330 2.05974
\(71\) 9.00501 1.06870 0.534349 0.845264i \(-0.320557\pi\)
0.534349 + 0.845264i \(0.320557\pi\)
\(72\) −0.925454 −0.109066
\(73\) 12.8350 1.50222 0.751109 0.660178i \(-0.229519\pi\)
0.751109 + 0.660178i \(0.229519\pi\)
\(74\) −15.0424 −1.74864
\(75\) −17.6574 −2.03890
\(76\) −4.71331 −0.540654
\(77\) −5.33339 −0.607796
\(78\) 15.0757 1.70698
\(79\) 4.71078 0.530004 0.265002 0.964248i \(-0.414627\pi\)
0.265002 + 0.964248i \(0.414627\pi\)
\(80\) −5.52551 −0.617771
\(81\) −9.70212 −1.07801
\(82\) −11.3587 −1.25436
\(83\) 1.64652 0.180729 0.0903644 0.995909i \(-0.471197\pi\)
0.0903644 + 0.995909i \(0.471197\pi\)
\(84\) −12.1557 −1.32630
\(85\) 15.8695 1.72129
\(86\) 13.4981 1.45554
\(87\) −2.57489 −0.276057
\(88\) 10.1287 1.07972
\(89\) −4.30222 −0.456035 −0.228017 0.973657i \(-0.573224\pi\)
−0.228017 + 0.973657i \(0.573224\pi\)
\(90\) 2.31510 0.244032
\(91\) 6.76239 0.708891
\(92\) −2.06889 −0.215697
\(93\) −12.3137 −1.27687
\(94\) 29.0209 2.99328
\(95\) 5.12387 0.525698
\(96\) −6.95173 −0.709508
\(97\) −8.95518 −0.909261 −0.454630 0.890680i \(-0.650229\pi\)
−0.454630 + 0.890680i \(0.650229\pi\)
\(98\) 7.93607 0.801664
\(99\) −0.716489 −0.0720099
\(100\) 34.6134 3.46134
\(101\) 16.4544 1.63727 0.818636 0.574312i \(-0.194731\pi\)
0.818636 + 0.574312i \(0.194731\pi\)
\(102\) −17.5233 −1.73507
\(103\) 3.10359 0.305806 0.152903 0.988241i \(-0.451138\pi\)
0.152903 + 0.988241i \(0.451138\pi\)
\(104\) −12.8426 −1.25932
\(105\) 13.2146 1.28961
\(106\) 2.35311 0.228554
\(107\) 15.2027 1.46970 0.734848 0.678232i \(-0.237253\pi\)
0.734848 + 0.678232i \(0.237253\pi\)
\(108\) 17.5141 1.68530
\(109\) 10.1527 0.972455 0.486227 0.873832i \(-0.338373\pi\)
0.486227 + 0.873832i \(0.338373\pi\)
\(110\) −25.3378 −2.41586
\(111\) −11.5347 −1.09483
\(112\) 2.73684 0.258607
\(113\) 18.3745 1.72853 0.864265 0.503038i \(-0.167784\pi\)
0.864265 + 0.503038i \(0.167784\pi\)
\(114\) −5.65785 −0.529906
\(115\) 2.24911 0.209730
\(116\) 5.04749 0.468648
\(117\) 0.908462 0.0839874
\(118\) 1.26664 0.116604
\(119\) −7.86031 −0.720553
\(120\) −25.0960 −2.29094
\(121\) −3.15832 −0.287120
\(122\) −1.62226 −0.146873
\(123\) −8.71006 −0.785360
\(124\) 24.1383 2.16768
\(125\) −18.4023 −1.64595
\(126\) −1.14669 −0.102155
\(127\) −15.8265 −1.40438 −0.702188 0.711991i \(-0.747793\pi\)
−0.702188 + 0.711991i \(0.747793\pi\)
\(128\) 20.3900 1.80224
\(129\) 10.3505 0.911315
\(130\) 32.1266 2.81769
\(131\) −15.6303 −1.36562 −0.682811 0.730595i \(-0.739243\pi\)
−0.682811 + 0.730595i \(0.739243\pi\)
\(132\) 17.8726 1.55561
\(133\) −2.53790 −0.220064
\(134\) 28.0247 2.42097
\(135\) −19.0397 −1.63868
\(136\) 14.9276 1.28003
\(137\) −15.1757 −1.29655 −0.648273 0.761408i \(-0.724508\pi\)
−0.648273 + 0.761408i \(0.724508\pi\)
\(138\) −2.48350 −0.211409
\(139\) 10.4954 0.890209 0.445105 0.895479i \(-0.353166\pi\)
0.445105 + 0.895479i \(0.353166\pi\)
\(140\) −25.9042 −2.18930
\(141\) 22.2537 1.87410
\(142\) −21.1898 −1.77821
\(143\) −9.94275 −0.831454
\(144\) 0.367668 0.0306390
\(145\) −5.48716 −0.455684
\(146\) −30.2020 −2.49954
\(147\) 6.08550 0.501924
\(148\) 22.6113 1.85863
\(149\) 7.04647 0.577269 0.288635 0.957439i \(-0.406799\pi\)
0.288635 + 0.957439i \(0.406799\pi\)
\(150\) 41.5498 3.39253
\(151\) 1.00000 0.0813788
\(152\) 4.81977 0.390935
\(153\) −1.05596 −0.0853691
\(154\) 12.5500 1.01131
\(155\) −26.2409 −2.10772
\(156\) −22.6613 −1.81436
\(157\) 4.70891 0.375812 0.187906 0.982187i \(-0.439830\pi\)
0.187906 + 0.982187i \(0.439830\pi\)
\(158\) −11.0850 −0.881873
\(159\) 1.80440 0.143098
\(160\) −14.8143 −1.17117
\(161\) −1.11400 −0.0877959
\(162\) 22.8301 1.79371
\(163\) 5.02629 0.393690 0.196845 0.980435i \(-0.436930\pi\)
0.196845 + 0.980435i \(0.436930\pi\)
\(164\) 17.0741 1.33326
\(165\) −19.4294 −1.51258
\(166\) −3.87444 −0.300715
\(167\) −7.00578 −0.542124 −0.271062 0.962562i \(-0.587375\pi\)
−0.271062 + 0.962562i \(0.587375\pi\)
\(168\) 12.4303 0.959018
\(169\) −0.393238 −0.0302491
\(170\) −37.3426 −2.86405
\(171\) −0.340943 −0.0260725
\(172\) −20.2899 −1.54709
\(173\) −17.8212 −1.35492 −0.677462 0.735558i \(-0.736920\pi\)
−0.677462 + 0.735558i \(0.736920\pi\)
\(174\) 6.05900 0.459331
\(175\) 18.6377 1.40888
\(176\) −4.02398 −0.303319
\(177\) 0.971280 0.0730058
\(178\) 10.1236 0.758796
\(179\) −9.72363 −0.726778 −0.363389 0.931637i \(-0.618380\pi\)
−0.363389 + 0.931637i \(0.618380\pi\)
\(180\) −3.47998 −0.259382
\(181\) −5.81566 −0.432274 −0.216137 0.976363i \(-0.569346\pi\)
−0.216137 + 0.976363i \(0.569346\pi\)
\(182\) −15.9126 −1.17952
\(183\) −1.24398 −0.0919574
\(184\) 2.11562 0.155966
\(185\) −24.5808 −1.80722
\(186\) 28.9756 2.12459
\(187\) 11.5570 0.845132
\(188\) −43.6234 −3.18156
\(189\) 9.43056 0.685972
\(190\) −12.0570 −0.874708
\(191\) −25.8370 −1.86950 −0.934752 0.355302i \(-0.884378\pi\)
−0.934752 + 0.355302i \(0.884378\pi\)
\(192\) 21.5439 1.55480
\(193\) −8.83345 −0.635845 −0.317923 0.948117i \(-0.602985\pi\)
−0.317923 + 0.948117i \(0.602985\pi\)
\(194\) 21.0725 1.51292
\(195\) 24.6352 1.76416
\(196\) −11.9292 −0.852089
\(197\) 15.4238 1.09890 0.549452 0.835526i \(-0.314837\pi\)
0.549452 + 0.835526i \(0.314837\pi\)
\(198\) 1.68598 0.119817
\(199\) −14.7189 −1.04340 −0.521698 0.853130i \(-0.674701\pi\)
−0.521698 + 0.853130i \(0.674701\pi\)
\(200\) −35.3952 −2.50282
\(201\) 21.4898 1.51577
\(202\) −38.7190 −2.72426
\(203\) 2.71784 0.190755
\(204\) 26.3405 1.84420
\(205\) −18.5614 −1.29638
\(206\) −7.30309 −0.508830
\(207\) −0.149656 −0.0104018
\(208\) 5.10214 0.353770
\(209\) 3.73148 0.258112
\(210\) −31.0953 −2.14578
\(211\) −15.9379 −1.09721 −0.548604 0.836083i \(-0.684840\pi\)
−0.548604 + 0.836083i \(0.684840\pi\)
\(212\) −3.53712 −0.242930
\(213\) −16.2486 −1.11334
\(214\) −35.7735 −2.44543
\(215\) 22.0573 1.50429
\(216\) −17.9097 −1.21860
\(217\) 12.9974 0.882318
\(218\) −23.8905 −1.61807
\(219\) −23.1594 −1.56497
\(220\) 38.0869 2.56782
\(221\) −14.6535 −0.985704
\(222\) 27.1425 1.82168
\(223\) −8.83776 −0.591820 −0.295910 0.955216i \(-0.595623\pi\)
−0.295910 + 0.955216i \(0.595623\pi\)
\(224\) 7.33767 0.490269
\(225\) 2.50380 0.166920
\(226\) −43.2372 −2.87610
\(227\) 6.91640 0.459058 0.229529 0.973302i \(-0.426281\pi\)
0.229529 + 0.973302i \(0.426281\pi\)
\(228\) 8.50470 0.563238
\(229\) −28.3674 −1.87457 −0.937287 0.348559i \(-0.886671\pi\)
−0.937287 + 0.348559i \(0.886671\pi\)
\(230\) −5.29239 −0.348970
\(231\) 9.62356 0.633184
\(232\) −5.16150 −0.338869
\(233\) 18.5452 1.21494 0.607468 0.794344i \(-0.292185\pi\)
0.607468 + 0.794344i \(0.292185\pi\)
\(234\) −2.13771 −0.139747
\(235\) 47.4232 3.09355
\(236\) −1.90397 −0.123938
\(237\) −8.50013 −0.552143
\(238\) 18.4962 1.19893
\(239\) 16.4167 1.06191 0.530955 0.847400i \(-0.321833\pi\)
0.530955 + 0.847400i \(0.321833\pi\)
\(240\) 9.97024 0.643576
\(241\) −25.0950 −1.61651 −0.808256 0.588832i \(-0.799588\pi\)
−0.808256 + 0.588832i \(0.799588\pi\)
\(242\) 7.43187 0.477739
\(243\) 2.65194 0.170122
\(244\) 2.43854 0.156111
\(245\) 12.9684 0.828518
\(246\) 20.4957 1.30676
\(247\) −4.73127 −0.301044
\(248\) −24.6835 −1.56740
\(249\) −2.97098 −0.188278
\(250\) 43.3026 2.73869
\(251\) 15.1638 0.957131 0.478565 0.878052i \(-0.341157\pi\)
0.478565 + 0.878052i \(0.341157\pi\)
\(252\) 1.72367 0.108581
\(253\) 1.63792 0.102975
\(254\) 37.2415 2.33674
\(255\) −28.6349 −1.79319
\(256\) −24.1006 −1.50629
\(257\) −29.0134 −1.80980 −0.904902 0.425620i \(-0.860056\pi\)
−0.904902 + 0.425620i \(0.860056\pi\)
\(258\) −24.3560 −1.51634
\(259\) 12.1751 0.756525
\(260\) −48.2918 −2.99493
\(261\) 0.365116 0.0226001
\(262\) 36.7797 2.27226
\(263\) 2.55500 0.157548 0.0787740 0.996892i \(-0.474899\pi\)
0.0787740 + 0.996892i \(0.474899\pi\)
\(264\) −18.2763 −1.12483
\(265\) 3.84522 0.236210
\(266\) 5.97196 0.366164
\(267\) 7.76294 0.475084
\(268\) −42.1259 −2.57325
\(269\) 19.0170 1.15949 0.579743 0.814800i \(-0.303153\pi\)
0.579743 + 0.814800i \(0.303153\pi\)
\(270\) 44.8025 2.72660
\(271\) −12.6717 −0.769750 −0.384875 0.922969i \(-0.625755\pi\)
−0.384875 + 0.922969i \(0.625755\pi\)
\(272\) −5.93051 −0.359590
\(273\) −12.2021 −0.738502
\(274\) 35.7100 2.15732
\(275\) −27.4030 −1.65246
\(276\) 3.73311 0.224707
\(277\) 6.45196 0.387661 0.193830 0.981035i \(-0.437909\pi\)
0.193830 + 0.981035i \(0.437909\pi\)
\(278\) −24.6968 −1.48122
\(279\) 1.74607 0.104535
\(280\) 26.4893 1.58304
\(281\) −31.0699 −1.85347 −0.926736 0.375713i \(-0.877398\pi\)
−0.926736 + 0.375713i \(0.877398\pi\)
\(282\) −52.3654 −3.11831
\(283\) 9.12172 0.542230 0.271115 0.962547i \(-0.412608\pi\)
0.271115 + 0.962547i \(0.412608\pi\)
\(284\) 31.8518 1.89006
\(285\) −9.24551 −0.547657
\(286\) 23.3964 1.38346
\(287\) 9.19362 0.542682
\(288\) 0.985746 0.0580856
\(289\) 0.0326444 0.00192026
\(290\) 12.9119 0.758212
\(291\) 16.1587 0.947242
\(292\) 45.3988 2.65676
\(293\) −19.8562 −1.16001 −0.580006 0.814612i \(-0.696950\pi\)
−0.580006 + 0.814612i \(0.696950\pi\)
\(294\) −14.3198 −0.835150
\(295\) 2.06982 0.120510
\(296\) −23.1220 −1.34394
\(297\) −13.8658 −0.804573
\(298\) −16.5811 −0.960518
\(299\) −2.07678 −0.120103
\(300\) −62.4564 −3.60592
\(301\) −10.9252 −0.629717
\(302\) −2.35311 −0.135406
\(303\) −29.6903 −1.70566
\(304\) −1.91482 −0.109822
\(305\) −2.65095 −0.151793
\(306\) 2.48478 0.142046
\(307\) −9.39714 −0.536323 −0.268162 0.963374i \(-0.586416\pi\)
−0.268162 + 0.963374i \(0.586416\pi\)
\(308\) −18.8648 −1.07492
\(309\) −5.60012 −0.318580
\(310\) 61.7476 3.50703
\(311\) 5.40836 0.306680 0.153340 0.988174i \(-0.450997\pi\)
0.153340 + 0.988174i \(0.450997\pi\)
\(312\) 23.1731 1.31192
\(313\) 14.1408 0.799286 0.399643 0.916671i \(-0.369134\pi\)
0.399643 + 0.916671i \(0.369134\pi\)
\(314\) −11.0806 −0.625313
\(315\) −1.87381 −0.105577
\(316\) 16.6626 0.937343
\(317\) −12.1072 −0.680008 −0.340004 0.940424i \(-0.610428\pi\)
−0.340004 + 0.940424i \(0.610428\pi\)
\(318\) −4.24595 −0.238101
\(319\) −3.99604 −0.223736
\(320\) 45.9107 2.56649
\(321\) −27.4317 −1.53109
\(322\) 2.62137 0.146083
\(323\) 5.49942 0.305996
\(324\) −34.3176 −1.90653
\(325\) 34.7453 1.92732
\(326\) −11.8274 −0.655060
\(327\) −18.3196 −1.01308
\(328\) −17.4598 −0.964054
\(329\) −23.4892 −1.29500
\(330\) 45.7195 2.51677
\(331\) 10.6090 0.583126 0.291563 0.956552i \(-0.405825\pi\)
0.291563 + 0.956552i \(0.405825\pi\)
\(332\) 5.82393 0.319630
\(333\) 1.63561 0.0896309
\(334\) 16.4854 0.902039
\(335\) 45.7953 2.50207
\(336\) −4.93835 −0.269409
\(337\) 6.83443 0.372295 0.186148 0.982522i \(-0.440400\pi\)
0.186148 + 0.982522i \(0.440400\pi\)
\(338\) 0.925332 0.0503314
\(339\) −33.1550 −1.80073
\(340\) 56.1323 3.04420
\(341\) −19.1100 −1.03487
\(342\) 0.802275 0.0433821
\(343\) −19.7554 −1.06669
\(344\) 20.7482 1.11867
\(345\) −4.05829 −0.218491
\(346\) 41.9353 2.25446
\(347\) 23.2338 1.24725 0.623627 0.781722i \(-0.285659\pi\)
0.623627 + 0.781722i \(0.285659\pi\)
\(348\) −9.10770 −0.488224
\(349\) 8.32539 0.445648 0.222824 0.974859i \(-0.428473\pi\)
0.222824 + 0.974859i \(0.428473\pi\)
\(350\) −43.8566 −2.34423
\(351\) 17.5809 0.938398
\(352\) −10.7886 −0.575033
\(353\) 17.1503 0.912819 0.456409 0.889770i \(-0.349135\pi\)
0.456409 + 0.889770i \(0.349135\pi\)
\(354\) −2.28553 −0.121474
\(355\) −34.6263 −1.83777
\(356\) −15.2175 −0.806525
\(357\) 14.1831 0.750651
\(358\) 22.8808 1.20929
\(359\) −30.5554 −1.61265 −0.806326 0.591471i \(-0.798547\pi\)
−0.806326 + 0.591471i \(0.798547\pi\)
\(360\) 3.55858 0.187554
\(361\) −17.2244 −0.906546
\(362\) 13.6849 0.719261
\(363\) 5.69888 0.299113
\(364\) 23.9194 1.25372
\(365\) −49.3533 −2.58327
\(366\) 2.92721 0.153008
\(367\) −1.31055 −0.0684099 −0.0342050 0.999415i \(-0.510890\pi\)
−0.0342050 + 0.999415i \(0.510890\pi\)
\(368\) −0.840503 −0.0438143
\(369\) 1.23508 0.0642954
\(370\) 57.8413 3.00703
\(371\) −1.90458 −0.0988807
\(372\) −43.5552 −2.25823
\(373\) 9.53902 0.493912 0.246956 0.969027i \(-0.420570\pi\)
0.246956 + 0.969027i \(0.420570\pi\)
\(374\) −27.1949 −1.40622
\(375\) 33.2051 1.71470
\(376\) 44.6087 2.30052
\(377\) 5.06673 0.260950
\(378\) −22.1911 −1.14139
\(379\) −19.5084 −1.00208 −0.501039 0.865425i \(-0.667049\pi\)
−0.501039 + 0.865425i \(0.667049\pi\)
\(380\) 18.1237 0.929728
\(381\) 28.5574 1.46304
\(382\) 60.7974 3.11066
\(383\) 9.17255 0.468696 0.234348 0.972153i \(-0.424705\pi\)
0.234348 + 0.972153i \(0.424705\pi\)
\(384\) −36.7918 −1.87752
\(385\) 20.5081 1.04519
\(386\) 20.7861 1.05798
\(387\) −1.46769 −0.0746071
\(388\) −31.6755 −1.60808
\(389\) −21.2039 −1.07508 −0.537539 0.843239i \(-0.680646\pi\)
−0.537539 + 0.843239i \(0.680646\pi\)
\(390\) −57.9693 −2.93539
\(391\) 2.41396 0.122079
\(392\) 12.1987 0.616127
\(393\) 28.2033 1.42267
\(394\) −36.2940 −1.82846
\(395\) −18.1140 −0.911414
\(396\) −2.53431 −0.127354
\(397\) −22.4239 −1.12542 −0.562711 0.826654i \(-0.690242\pi\)
−0.562711 + 0.826654i \(0.690242\pi\)
\(398\) 34.6352 1.73611
\(399\) 4.57939 0.229256
\(400\) 14.0619 0.703096
\(401\) 1.91817 0.0957888 0.0478944 0.998852i \(-0.484749\pi\)
0.0478944 + 0.998852i \(0.484749\pi\)
\(402\) −50.5679 −2.52210
\(403\) 24.2303 1.20700
\(404\) 58.2011 2.89561
\(405\) 37.3068 1.85379
\(406\) −6.39538 −0.317397
\(407\) −17.9011 −0.887324
\(408\) −26.9354 −1.33350
\(409\) −9.61261 −0.475313 −0.237657 0.971349i \(-0.576379\pi\)
−0.237657 + 0.971349i \(0.576379\pi\)
\(410\) 43.6769 2.15705
\(411\) 27.3830 1.35070
\(412\) 10.9778 0.540836
\(413\) −1.02520 −0.0504469
\(414\) 0.352156 0.0173075
\(415\) −6.33123 −0.310788
\(416\) 13.6792 0.670679
\(417\) −18.9379 −0.927394
\(418\) −8.78057 −0.429472
\(419\) 36.2877 1.77277 0.886386 0.462946i \(-0.153208\pi\)
0.886386 + 0.462946i \(0.153208\pi\)
\(420\) 46.7415 2.28075
\(421\) 10.2013 0.497183 0.248592 0.968608i \(-0.420032\pi\)
0.248592 + 0.968608i \(0.420032\pi\)
\(422\) 37.5035 1.82564
\(423\) −3.15555 −0.153428
\(424\) 3.61701 0.175658
\(425\) −40.3864 −1.95903
\(426\) 38.2348 1.85248
\(427\) 1.31304 0.0635424
\(428\) 53.7736 2.59925
\(429\) 17.9407 0.866185
\(430\) −51.9032 −2.50299
\(431\) −40.8801 −1.96912 −0.984562 0.175038i \(-0.943995\pi\)
−0.984562 + 0.175038i \(0.943995\pi\)
\(432\) 7.11524 0.342332
\(433\) 35.3484 1.69874 0.849368 0.527801i \(-0.176983\pi\)
0.849368 + 0.527801i \(0.176983\pi\)
\(434\) −30.5842 −1.46809
\(435\) 9.90103 0.474718
\(436\) 35.9114 1.71984
\(437\) 0.779408 0.0372841
\(438\) 54.4966 2.60395
\(439\) −22.0036 −1.05017 −0.525087 0.851049i \(-0.675967\pi\)
−0.525087 + 0.851049i \(0.675967\pi\)
\(440\) −38.9472 −1.85673
\(441\) −0.862916 −0.0410912
\(442\) 34.4814 1.64011
\(443\) 25.8762 1.22942 0.614708 0.788755i \(-0.289274\pi\)
0.614708 + 0.788755i \(0.289274\pi\)
\(444\) −40.7998 −1.93627
\(445\) 16.5430 0.784214
\(446\) 20.7962 0.984729
\(447\) −12.7147 −0.601382
\(448\) −22.7400 −1.07436
\(449\) 0.645734 0.0304741 0.0152370 0.999884i \(-0.495150\pi\)
0.0152370 + 0.999884i \(0.495150\pi\)
\(450\) −5.89171 −0.277738
\(451\) −13.5174 −0.636509
\(452\) 64.9929 3.05701
\(453\) −1.80440 −0.0847781
\(454\) −16.2750 −0.763826
\(455\) −26.0029 −1.21904
\(456\) −8.69679 −0.407265
\(457\) 24.9280 1.16608 0.583042 0.812442i \(-0.301862\pi\)
0.583042 + 0.812442i \(0.301862\pi\)
\(458\) 66.7517 3.11910
\(459\) −20.4353 −0.953836
\(460\) 7.95536 0.370921
\(461\) 28.2474 1.31561 0.657806 0.753187i \(-0.271485\pi\)
0.657806 + 0.753187i \(0.271485\pi\)
\(462\) −22.6453 −1.05355
\(463\) −34.5296 −1.60473 −0.802363 0.596836i \(-0.796424\pi\)
−0.802363 + 0.596836i \(0.796424\pi\)
\(464\) 2.05058 0.0951958
\(465\) 47.3491 2.19576
\(466\) −43.6389 −2.02153
\(467\) 8.17572 0.378327 0.189164 0.981946i \(-0.439422\pi\)
0.189164 + 0.981946i \(0.439422\pi\)
\(468\) 3.21334 0.148537
\(469\) −22.6829 −1.04740
\(470\) −111.592 −5.14736
\(471\) −8.49675 −0.391510
\(472\) 1.94698 0.0896169
\(473\) 16.0633 0.738591
\(474\) 20.0017 0.918709
\(475\) −13.0398 −0.598306
\(476\) −27.8029 −1.27434
\(477\) −0.255862 −0.0117151
\(478\) −38.6304 −1.76691
\(479\) 34.4184 1.57262 0.786309 0.617833i \(-0.211989\pi\)
0.786309 + 0.617833i \(0.211989\pi\)
\(480\) 26.7310 1.22010
\(481\) 22.6974 1.03491
\(482\) 59.0513 2.68971
\(483\) 2.01011 0.0914632
\(484\) −11.1714 −0.507789
\(485\) 34.4347 1.56360
\(486\) −6.24029 −0.283065
\(487\) 26.7313 1.21131 0.605657 0.795726i \(-0.292911\pi\)
0.605657 + 0.795726i \(0.292911\pi\)
\(488\) −2.49361 −0.112881
\(489\) −9.06944 −0.410134
\(490\) −30.5160 −1.37857
\(491\) −33.9627 −1.53271 −0.766357 0.642415i \(-0.777932\pi\)
−0.766357 + 0.642415i \(0.777932\pi\)
\(492\) −30.8085 −1.38896
\(493\) −5.88934 −0.265243
\(494\) 11.1332 0.500906
\(495\) 2.75506 0.123831
\(496\) 9.80635 0.440318
\(497\) 17.1507 0.769315
\(498\) 6.99103 0.313276
\(499\) −25.0656 −1.12209 −0.561045 0.827786i \(-0.689600\pi\)
−0.561045 + 0.827786i \(0.689600\pi\)
\(500\) −65.0911 −2.91096
\(501\) 12.6412 0.564769
\(502\) −35.6821 −1.59257
\(503\) −10.6357 −0.474224 −0.237112 0.971482i \(-0.576201\pi\)
−0.237112 + 0.971482i \(0.576201\pi\)
\(504\) −1.76260 −0.0785124
\(505\) −63.2708 −2.81551
\(506\) −3.85421 −0.171340
\(507\) 0.709559 0.0315126
\(508\) −55.9803 −2.48372
\(509\) −10.6109 −0.470320 −0.235160 0.971957i \(-0.575561\pi\)
−0.235160 + 0.971957i \(0.575561\pi\)
\(510\) 67.3810 2.98368
\(511\) 24.4452 1.08139
\(512\) 15.9313 0.704072
\(513\) −6.59804 −0.291311
\(514\) 68.2716 3.01133
\(515\) −11.9340 −0.525875
\(516\) 36.6111 1.61171
\(517\) 34.5362 1.51890
\(518\) −28.6494 −1.25878
\(519\) 32.1566 1.41152
\(520\) 49.3825 2.16557
\(521\) 33.7033 1.47657 0.738285 0.674489i \(-0.235636\pi\)
0.738285 + 0.674489i \(0.235636\pi\)
\(522\) −0.859158 −0.0376043
\(523\) 36.0316 1.57555 0.787777 0.615961i \(-0.211232\pi\)
0.787777 + 0.615961i \(0.211232\pi\)
\(524\) −55.2861 −2.41519
\(525\) −33.6299 −1.46773
\(526\) −6.01219 −0.262144
\(527\) −28.1642 −1.22685
\(528\) 7.26086 0.315989
\(529\) −22.6579 −0.985125
\(530\) −9.04823 −0.393030
\(531\) −0.137726 −0.00597681
\(532\) −8.97686 −0.389196
\(533\) 17.1392 0.742380
\(534\) −18.2670 −0.790492
\(535\) −58.4576 −2.52734
\(536\) 43.0774 1.86066
\(537\) 17.5453 0.757137
\(538\) −44.7490 −1.92927
\(539\) 9.44426 0.406793
\(540\) −67.3458 −2.89810
\(541\) −3.40648 −0.146456 −0.0732281 0.997315i \(-0.523330\pi\)
−0.0732281 + 0.997315i \(0.523330\pi\)
\(542\) 29.8179 1.28079
\(543\) 10.4938 0.450331
\(544\) −15.9001 −0.681713
\(545\) −39.0395 −1.67227
\(546\) 28.7128 1.22879
\(547\) 38.3083 1.63795 0.818973 0.573832i \(-0.194544\pi\)
0.818973 + 0.573832i \(0.194544\pi\)
\(548\) −53.6782 −2.29302
\(549\) 0.176394 0.00752832
\(550\) 64.4823 2.74953
\(551\) −1.90152 −0.0810077
\(552\) −3.81743 −0.162481
\(553\) 8.97203 0.381530
\(554\) −15.1822 −0.645029
\(555\) 44.3537 1.88271
\(556\) 37.1235 1.57439
\(557\) −20.4224 −0.865326 −0.432663 0.901556i \(-0.642426\pi\)
−0.432663 + 0.901556i \(0.642426\pi\)
\(558\) −4.10870 −0.173935
\(559\) −20.3672 −0.861442
\(560\) −10.5238 −0.444710
\(561\) −20.8535 −0.880435
\(562\) 73.1108 3.08399
\(563\) 4.23181 0.178349 0.0891747 0.996016i \(-0.471577\pi\)
0.0891747 + 0.996016i \(0.471577\pi\)
\(564\) 78.7141 3.31446
\(565\) −70.6541 −2.97244
\(566\) −21.4644 −0.902216
\(567\) −18.4784 −0.776021
\(568\) −32.5712 −1.36666
\(569\) −4.17826 −0.175162 −0.0875808 0.996157i \(-0.527914\pi\)
−0.0875808 + 0.996157i \(0.527914\pi\)
\(570\) 21.7557 0.911245
\(571\) 20.1383 0.842763 0.421382 0.906883i \(-0.361545\pi\)
0.421382 + 0.906883i \(0.361545\pi\)
\(572\) −35.1687 −1.47048
\(573\) 46.6204 1.94759
\(574\) −21.6336 −0.902969
\(575\) −5.72378 −0.238698
\(576\) −3.05490 −0.127288
\(577\) −4.89918 −0.203956 −0.101978 0.994787i \(-0.532517\pi\)
−0.101978 + 0.994787i \(0.532517\pi\)
\(578\) −0.0768159 −0.00319512
\(579\) 15.9391 0.662405
\(580\) −19.4087 −0.805904
\(581\) 3.13592 0.130100
\(582\) −38.0232 −1.57611
\(583\) 2.80030 0.115977
\(584\) −46.4242 −1.92105
\(585\) −3.49324 −0.144428
\(586\) 46.7238 1.93014
\(587\) 23.2312 0.958854 0.479427 0.877582i \(-0.340845\pi\)
0.479427 + 0.877582i \(0.340845\pi\)
\(588\) 21.5251 0.887682
\(589\) −9.09354 −0.374693
\(590\) −4.87052 −0.200516
\(591\) −27.8308 −1.14481
\(592\) 9.18598 0.377541
\(593\) 43.7425 1.79629 0.898145 0.439700i \(-0.144915\pi\)
0.898145 + 0.439700i \(0.144915\pi\)
\(594\) 32.6276 1.33873
\(595\) 30.2246 1.23909
\(596\) 24.9242 1.02094
\(597\) 26.5588 1.08698
\(598\) 4.88689 0.199840
\(599\) −29.6513 −1.21152 −0.605759 0.795648i \(-0.707131\pi\)
−0.605759 + 0.795648i \(0.707131\pi\)
\(600\) 63.8671 2.60736
\(601\) −13.2691 −0.541257 −0.270629 0.962684i \(-0.587232\pi\)
−0.270629 + 0.962684i \(0.587232\pi\)
\(602\) 25.7081 1.04779
\(603\) −3.04723 −0.124093
\(604\) 3.53712 0.143923
\(605\) 12.1444 0.493742
\(606\) 69.8645 2.83805
\(607\) 31.0067 1.25852 0.629261 0.777194i \(-0.283358\pi\)
0.629261 + 0.777194i \(0.283358\pi\)
\(608\) −5.13377 −0.208202
\(609\) −4.90408 −0.198723
\(610\) 6.23796 0.252568
\(611\) −43.7896 −1.77154
\(612\) −3.73505 −0.150980
\(613\) −16.9202 −0.683402 −0.341701 0.939809i \(-0.611003\pi\)
−0.341701 + 0.939809i \(0.611003\pi\)
\(614\) 22.1125 0.892388
\(615\) 33.4921 1.35053
\(616\) 19.2909 0.777253
\(617\) −9.24958 −0.372374 −0.186187 0.982514i \(-0.559613\pi\)
−0.186187 + 0.982514i \(0.559613\pi\)
\(618\) 13.1777 0.530085
\(619\) 28.1957 1.13328 0.566640 0.823965i \(-0.308243\pi\)
0.566640 + 0.823965i \(0.308243\pi\)
\(620\) −92.8172 −3.72763
\(621\) −2.89619 −0.116220
\(622\) −12.7265 −0.510284
\(623\) −8.19392 −0.328282
\(624\) −9.20631 −0.368547
\(625\) 21.8321 0.873285
\(626\) −33.2749 −1.32993
\(627\) −6.73308 −0.268893
\(628\) 16.6560 0.664645
\(629\) −26.3825 −1.05194
\(630\) 4.40928 0.175670
\(631\) 38.4034 1.52881 0.764407 0.644734i \(-0.223032\pi\)
0.764407 + 0.644734i \(0.223032\pi\)
\(632\) −17.0389 −0.677772
\(633\) 28.7583 1.14304
\(634\) 28.4895 1.13146
\(635\) 60.8565 2.41502
\(636\) 6.38238 0.253078
\(637\) −11.9747 −0.474455
\(638\) 9.40313 0.372273
\(639\) 2.30404 0.0911463
\(640\) −78.4043 −3.09920
\(641\) −3.75700 −0.148393 −0.0741963 0.997244i \(-0.523639\pi\)
−0.0741963 + 0.997244i \(0.523639\pi\)
\(642\) 64.5497 2.54757
\(643\) −45.5802 −1.79751 −0.898754 0.438454i \(-0.855526\pi\)
−0.898754 + 0.438454i \(0.855526\pi\)
\(644\) −3.94037 −0.155272
\(645\) −39.8002 −1.56713
\(646\) −12.9407 −0.509147
\(647\) 20.1977 0.794053 0.397026 0.917807i \(-0.370042\pi\)
0.397026 + 0.917807i \(0.370042\pi\)
\(648\) 35.0927 1.37857
\(649\) 1.50736 0.0591689
\(650\) −81.7594 −3.20687
\(651\) −23.4524 −0.919174
\(652\) 17.7786 0.696264
\(653\) −4.27647 −0.167351 −0.0836756 0.996493i \(-0.526666\pi\)
−0.0836756 + 0.996493i \(0.526666\pi\)
\(654\) 43.1080 1.68565
\(655\) 60.1019 2.34838
\(656\) 6.93648 0.270824
\(657\) 3.28397 0.128120
\(658\) 55.2726 2.15475
\(659\) −19.5038 −0.759759 −0.379879 0.925036i \(-0.624034\pi\)
−0.379879 + 0.925036i \(0.624034\pi\)
\(660\) −68.7241 −2.67508
\(661\) 42.1724 1.64032 0.820159 0.572136i \(-0.193885\pi\)
0.820159 + 0.572136i \(0.193885\pi\)
\(662\) −24.9642 −0.970262
\(663\) 26.4409 1.02688
\(664\) −5.95547 −0.231117
\(665\) 9.75880 0.378430
\(666\) −3.84877 −0.149137
\(667\) −0.834669 −0.0323185
\(668\) −24.7803 −0.958779
\(669\) 15.9469 0.616541
\(670\) −107.761 −4.16319
\(671\) −1.93056 −0.0745285
\(672\) −13.2401 −0.510748
\(673\) 13.3046 0.512855 0.256428 0.966563i \(-0.417455\pi\)
0.256428 + 0.966563i \(0.417455\pi\)
\(674\) −16.0822 −0.619462
\(675\) 48.4544 1.86501
\(676\) −1.39093 −0.0534973
\(677\) −12.1419 −0.466651 −0.233325 0.972399i \(-0.574961\pi\)
−0.233325 + 0.972399i \(0.574961\pi\)
\(678\) 78.0173 2.99624
\(679\) −17.0558 −0.654542
\(680\) −57.4001 −2.20119
\(681\) −12.4800 −0.478233
\(682\) 44.9680 1.72191
\(683\) 37.7651 1.44504 0.722520 0.691350i \(-0.242984\pi\)
0.722520 + 0.691350i \(0.242984\pi\)
\(684\) −1.20596 −0.0461109
\(685\) 58.3539 2.22959
\(686\) 46.4866 1.77487
\(687\) 51.1862 1.95288
\(688\) −8.24292 −0.314258
\(689\) −3.55060 −0.135267
\(690\) 9.54960 0.363547
\(691\) −3.69727 −0.140651 −0.0703254 0.997524i \(-0.522404\pi\)
−0.0703254 + 0.997524i \(0.522404\pi\)
\(692\) −63.0359 −2.39626
\(693\) −1.36461 −0.0518372
\(694\) −54.6715 −2.07530
\(695\) −40.3572 −1.53084
\(696\) 9.31341 0.353024
\(697\) −19.9218 −0.754593
\(698\) −19.5905 −0.741513
\(699\) −33.4630 −1.26569
\(700\) 65.9238 2.49169
\(701\) 16.8630 0.636905 0.318453 0.947939i \(-0.396837\pi\)
0.318453 + 0.947939i \(0.396837\pi\)
\(702\) −41.3697 −1.56140
\(703\) −8.51826 −0.321272
\(704\) 33.4347 1.26012
\(705\) −85.5705 −3.22277
\(706\) −40.3565 −1.51884
\(707\) 31.3386 1.17861
\(708\) 3.43553 0.129115
\(709\) −12.9245 −0.485389 −0.242695 0.970103i \(-0.578031\pi\)
−0.242695 + 0.970103i \(0.578031\pi\)
\(710\) 81.4794 3.05787
\(711\) 1.20531 0.0452025
\(712\) 15.5612 0.583180
\(713\) −3.99158 −0.149486
\(714\) −33.3745 −1.24901
\(715\) 38.2321 1.42980
\(716\) −34.3937 −1.28535
\(717\) −29.6224 −1.10627
\(718\) 71.9002 2.68329
\(719\) −14.9450 −0.557355 −0.278678 0.960385i \(-0.589896\pi\)
−0.278678 + 0.960385i \(0.589896\pi\)
\(720\) −1.41377 −0.0526880
\(721\) 5.91103 0.220138
\(722\) 40.5308 1.50840
\(723\) 45.2814 1.68403
\(724\) −20.5707 −0.764503
\(725\) 13.9643 0.518622
\(726\) −13.4101 −0.497694
\(727\) −49.0836 −1.82041 −0.910204 0.414160i \(-0.864075\pi\)
−0.910204 + 0.414160i \(0.864075\pi\)
\(728\) −24.4596 −0.906535
\(729\) 24.3212 0.900785
\(730\) 116.134 4.29830
\(731\) 23.6740 0.875614
\(732\) −4.40009 −0.162632
\(733\) 27.3340 1.00960 0.504801 0.863236i \(-0.331566\pi\)
0.504801 + 0.863236i \(0.331566\pi\)
\(734\) 3.08386 0.113827
\(735\) −23.4001 −0.863126
\(736\) −2.25345 −0.0830634
\(737\) 33.3506 1.22849
\(738\) −2.90627 −0.106981
\(739\) 20.3891 0.750025 0.375012 0.927020i \(-0.377638\pi\)
0.375012 + 0.927020i \(0.377638\pi\)
\(740\) −86.9453 −3.19617
\(741\) 8.53711 0.313619
\(742\) 4.48168 0.164527
\(743\) −13.6273 −0.499937 −0.249968 0.968254i \(-0.580420\pi\)
−0.249968 + 0.968254i \(0.580420\pi\)
\(744\) 44.5389 1.63288
\(745\) −27.0953 −0.992693
\(746\) −22.4464 −0.821820
\(747\) 0.421281 0.0154139
\(748\) 40.8785 1.49467
\(749\) 28.9546 1.05798
\(750\) −78.1352 −2.85309
\(751\) 20.3610 0.742985 0.371492 0.928436i \(-0.378846\pi\)
0.371492 + 0.928436i \(0.378846\pi\)
\(752\) −17.7223 −0.646266
\(753\) −27.3616 −0.997111
\(754\) −11.9226 −0.434194
\(755\) −3.84522 −0.139942
\(756\) 33.3570 1.21318
\(757\) −10.0112 −0.363863 −0.181932 0.983311i \(-0.558235\pi\)
−0.181932 + 0.983311i \(0.558235\pi\)
\(758\) 45.9053 1.66736
\(759\) −2.95547 −0.107277
\(760\) −18.5331 −0.672266
\(761\) 26.7578 0.969971 0.484986 0.874522i \(-0.338825\pi\)
0.484986 + 0.874522i \(0.338825\pi\)
\(762\) −67.1986 −2.43435
\(763\) 19.3366 0.700033
\(764\) −91.3888 −3.30633
\(765\) 4.06039 0.146804
\(766\) −21.5840 −0.779862
\(767\) −1.91123 −0.0690105
\(768\) 43.4872 1.56921
\(769\) 49.4422 1.78293 0.891465 0.453090i \(-0.149678\pi\)
0.891465 + 0.453090i \(0.149678\pi\)
\(770\) −48.2577 −1.73909
\(771\) 52.3517 1.88540
\(772\) −31.2450 −1.12453
\(773\) 2.36338 0.0850050 0.0425025 0.999096i \(-0.486467\pi\)
0.0425025 + 0.999096i \(0.486467\pi\)
\(774\) 3.45364 0.124139
\(775\) 66.7807 2.39883
\(776\) 32.3910 1.16277
\(777\) −21.9688 −0.788126
\(778\) 49.8950 1.78882
\(779\) −6.43227 −0.230460
\(780\) 87.1377 3.12003
\(781\) −25.2167 −0.902325
\(782\) −5.68030 −0.203127
\(783\) 7.06586 0.252513
\(784\) −4.84634 −0.173084
\(785\) −18.1068 −0.646259
\(786\) −66.3654 −2.36717
\(787\) −30.2935 −1.07985 −0.539923 0.841714i \(-0.681547\pi\)
−0.539923 + 0.841714i \(0.681547\pi\)
\(788\) 54.5560 1.94348
\(789\) −4.61024 −0.164129
\(790\) 42.6242 1.51650
\(791\) 34.9957 1.24430
\(792\) 2.59155 0.0920867
\(793\) 2.44783 0.0869249
\(794\) 52.7658 1.87259
\(795\) −6.93832 −0.246077
\(796\) −52.0625 −1.84531
\(797\) 15.1434 0.536406 0.268203 0.963362i \(-0.413570\pi\)
0.268203 + 0.963362i \(0.413570\pi\)
\(798\) −10.7758 −0.381459
\(799\) 50.8992 1.80068
\(800\) 37.7011 1.33293
\(801\) −1.10077 −0.0388939
\(802\) −4.51366 −0.159383
\(803\) −35.9417 −1.26836
\(804\) 76.0120 2.68074
\(805\) 4.28360 0.150977
\(806\) −57.0165 −2.00832
\(807\) −34.3142 −1.20792
\(808\) −59.5157 −2.09375
\(809\) −14.4502 −0.508043 −0.254021 0.967199i \(-0.581753\pi\)
−0.254021 + 0.967199i \(0.581753\pi\)
\(810\) −87.7870 −3.08452
\(811\) −38.7108 −1.35932 −0.679660 0.733528i \(-0.737872\pi\)
−0.679660 + 0.733528i \(0.737872\pi\)
\(812\) 9.61334 0.337362
\(813\) 22.8648 0.801904
\(814\) 42.1232 1.47642
\(815\) −19.3272 −0.677003
\(816\) 10.7010 0.374610
\(817\) 7.64375 0.267421
\(818\) 22.6195 0.790873
\(819\) 1.73024 0.0604593
\(820\) −65.6538 −2.29273
\(821\) 31.8600 1.11192 0.555961 0.831208i \(-0.312350\pi\)
0.555961 + 0.831208i \(0.312350\pi\)
\(822\) −64.4352 −2.24744
\(823\) 13.7169 0.478140 0.239070 0.971002i \(-0.423157\pi\)
0.239070 + 0.971002i \(0.423157\pi\)
\(824\) −11.2257 −0.391067
\(825\) 49.4460 1.72149
\(826\) 2.41241 0.0839386
\(827\) 41.9407 1.45842 0.729210 0.684290i \(-0.239888\pi\)
0.729210 + 0.684290i \(0.239888\pi\)
\(828\) −0.529351 −0.0183962
\(829\) −16.7671 −0.582346 −0.291173 0.956670i \(-0.594045\pi\)
−0.291173 + 0.956670i \(0.594045\pi\)
\(830\) 14.8981 0.517120
\(831\) −11.6419 −0.403854
\(832\) −42.3930 −1.46971
\(833\) 13.9189 0.482261
\(834\) 44.5630 1.54309
\(835\) 26.9388 0.932256
\(836\) 13.1987 0.456486
\(837\) 33.7906 1.16797
\(838\) −85.3890 −2.94971
\(839\) −7.65569 −0.264304 −0.132152 0.991229i \(-0.542189\pi\)
−0.132152 + 0.991229i \(0.542189\pi\)
\(840\) −47.7973 −1.64916
\(841\) −26.9637 −0.929781
\(842\) −24.0049 −0.827263
\(843\) 56.0625 1.93089
\(844\) −56.3741 −1.94048
\(845\) 1.51209 0.0520174
\(846\) 7.42535 0.255289
\(847\) −6.01526 −0.206687
\(848\) −1.43698 −0.0493461
\(849\) −16.4592 −0.564880
\(850\) 95.0336 3.25962
\(851\) −3.73907 −0.128174
\(852\) −57.4734 −1.96901
\(853\) 2.64851 0.0906833 0.0453417 0.998972i \(-0.485562\pi\)
0.0453417 + 0.998972i \(0.485562\pi\)
\(854\) −3.08972 −0.105728
\(855\) 1.31100 0.0448353
\(856\) −54.9882 −1.87946
\(857\) 53.5765 1.83014 0.915069 0.403297i \(-0.132136\pi\)
0.915069 + 0.403297i \(0.132136\pi\)
\(858\) −42.2164 −1.44124
\(859\) 18.2029 0.621073 0.310537 0.950561i \(-0.399491\pi\)
0.310537 + 0.950561i \(0.399491\pi\)
\(860\) 78.0192 2.66043
\(861\) −16.5890 −0.565351
\(862\) 96.1952 3.27642
\(863\) −18.9773 −0.645994 −0.322997 0.946400i \(-0.604690\pi\)
−0.322997 + 0.946400i \(0.604690\pi\)
\(864\) 19.0765 0.648996
\(865\) 68.5266 2.32998
\(866\) −83.1786 −2.82653
\(867\) −0.0589036 −0.00200047
\(868\) 45.9732 1.56043
\(869\) −13.1916 −0.447494
\(870\) −23.2982 −0.789883
\(871\) −42.2865 −1.43282
\(872\) −36.7225 −1.24358
\(873\) −2.29129 −0.0775483
\(874\) −1.83403 −0.0620370
\(875\) −35.0485 −1.18486
\(876\) −81.9176 −2.76774
\(877\) 26.3519 0.889842 0.444921 0.895570i \(-0.353232\pi\)
0.444921 + 0.895570i \(0.353232\pi\)
\(878\) 51.7768 1.74738
\(879\) 35.8285 1.20847
\(880\) 15.4731 0.521598
\(881\) −0.349839 −0.0117864 −0.00589318 0.999983i \(-0.501876\pi\)
−0.00589318 + 0.999983i \(0.501876\pi\)
\(882\) 2.03053 0.0683717
\(883\) −16.6834 −0.561443 −0.280721 0.959789i \(-0.590574\pi\)
−0.280721 + 0.959789i \(0.590574\pi\)
\(884\) −51.8314 −1.74328
\(885\) −3.73479 −0.125544
\(886\) −60.8895 −2.04562
\(887\) 5.21847 0.175219 0.0876096 0.996155i \(-0.472077\pi\)
0.0876096 + 0.996155i \(0.472077\pi\)
\(888\) 41.7213 1.40007
\(889\) −30.1428 −1.01096
\(890\) −38.9275 −1.30485
\(891\) 27.1688 0.910191
\(892\) −31.2602 −1.04667
\(893\) 16.4341 0.549946
\(894\) 29.9190 1.00064
\(895\) 37.3895 1.24979
\(896\) 38.8344 1.29737
\(897\) 3.74734 0.125120
\(898\) −1.51948 −0.0507058
\(899\) 9.73829 0.324790
\(900\) 8.85623 0.295208
\(901\) 4.12706 0.137492
\(902\) 31.8079 1.05909
\(903\) 19.7134 0.656021
\(904\) −66.4608 −2.21045
\(905\) 22.3625 0.743355
\(906\) 4.24595 0.141062
\(907\) 53.1472 1.76472 0.882362 0.470571i \(-0.155952\pi\)
0.882362 + 0.470571i \(0.155952\pi\)
\(908\) 24.4641 0.811871
\(909\) 4.21005 0.139638
\(910\) 61.1877 2.02835
\(911\) 40.8536 1.35354 0.676770 0.736195i \(-0.263379\pi\)
0.676770 + 0.736195i \(0.263379\pi\)
\(912\) 3.45509 0.114410
\(913\) −4.61074 −0.152593
\(914\) −58.6583 −1.94025
\(915\) 4.78337 0.158133
\(916\) −100.339 −3.31530
\(917\) −29.7690 −0.983060
\(918\) 48.0864 1.58709
\(919\) 50.7667 1.67464 0.837319 0.546715i \(-0.184122\pi\)
0.837319 + 0.546715i \(0.184122\pi\)
\(920\) −8.13505 −0.268205
\(921\) 16.9562 0.558726
\(922\) −66.4692 −2.18905
\(923\) 31.9732 1.05241
\(924\) 34.0397 1.11982
\(925\) 62.5560 2.05683
\(926\) 81.2519 2.67010
\(927\) 0.794090 0.0260813
\(928\) 5.49776 0.180473
\(929\) −50.2826 −1.64972 −0.824860 0.565337i \(-0.808746\pi\)
−0.824860 + 0.565337i \(0.808746\pi\)
\(930\) −111.417 −3.65352
\(931\) 4.49407 0.147287
\(932\) 65.5966 2.14869
\(933\) −9.75884 −0.319490
\(934\) −19.2384 −0.629498
\(935\) −44.4393 −1.45332
\(936\) −3.28592 −0.107404
\(937\) 34.4182 1.12439 0.562196 0.827004i \(-0.309957\pi\)
0.562196 + 0.827004i \(0.309957\pi\)
\(938\) 53.3753 1.74276
\(939\) −25.5157 −0.832673
\(940\) 167.742 5.47113
\(941\) −17.5056 −0.570667 −0.285333 0.958428i \(-0.592104\pi\)
−0.285333 + 0.958428i \(0.592104\pi\)
\(942\) 19.9938 0.651433
\(943\) −2.82343 −0.0919435
\(944\) −0.773503 −0.0251754
\(945\) −36.2626 −1.17962
\(946\) −37.7987 −1.22894
\(947\) 52.2435 1.69769 0.848843 0.528645i \(-0.177300\pi\)
0.848843 + 0.528645i \(0.177300\pi\)
\(948\) −30.0660 −0.976497
\(949\) 45.5718 1.47932
\(950\) 30.6840 0.995521
\(951\) 21.8462 0.708413
\(952\) 28.4308 0.921448
\(953\) −14.7214 −0.476871 −0.238436 0.971158i \(-0.576635\pi\)
−0.238436 + 0.971158i \(0.576635\pi\)
\(954\) 0.602070 0.0194927
\(955\) 99.3492 3.21487
\(956\) 58.0680 1.87805
\(957\) 7.21047 0.233081
\(958\) −80.9903 −2.61668
\(959\) −28.9033 −0.933335
\(960\) −82.8413 −2.67369
\(961\) 15.5708 0.502283
\(962\) −53.4095 −1.72199
\(963\) 3.88978 0.125346
\(964\) −88.7641 −2.85890
\(965\) 33.9666 1.09342
\(966\) −4.73001 −0.152186
\(967\) 27.5561 0.886144 0.443072 0.896486i \(-0.353889\pi\)
0.443072 + 0.896486i \(0.353889\pi\)
\(968\) 11.4237 0.367171
\(969\) −9.92316 −0.318778
\(970\) −81.0285 −2.60167
\(971\) −39.5353 −1.26875 −0.634374 0.773026i \(-0.718742\pi\)
−0.634374 + 0.773026i \(0.718742\pi\)
\(972\) 9.38022 0.300871
\(973\) 19.9893 0.640828
\(974\) −62.9018 −2.01550
\(975\) −62.6944 −2.00783
\(976\) 0.990672 0.0317106
\(977\) −37.9776 −1.21501 −0.607506 0.794315i \(-0.707830\pi\)
−0.607506 + 0.794315i \(0.707830\pi\)
\(978\) 21.3414 0.682422
\(979\) 12.0475 0.385040
\(980\) 45.8706 1.46528
\(981\) 2.59769 0.0829379
\(982\) 79.9178 2.55028
\(983\) 9.06913 0.289260 0.144630 0.989486i \(-0.453801\pi\)
0.144630 + 0.989486i \(0.453801\pi\)
\(984\) 31.5044 1.00432
\(985\) −59.3081 −1.88971
\(986\) 13.8583 0.441337
\(987\) 42.3839 1.34909
\(988\) −16.7351 −0.532414
\(989\) 3.35520 0.106689
\(990\) −6.48296 −0.206042
\(991\) −44.7024 −1.42002 −0.710009 0.704192i \(-0.751309\pi\)
−0.710009 + 0.704192i \(0.751309\pi\)
\(992\) 26.2916 0.834758
\(993\) −19.1430 −0.607484
\(994\) −40.3575 −1.28006
\(995\) 56.5975 1.79426
\(996\) −10.5087 −0.332981
\(997\) −25.7328 −0.814967 −0.407484 0.913212i \(-0.633594\pi\)
−0.407484 + 0.913212i \(0.633594\pi\)
\(998\) 58.9820 1.86704
\(999\) 31.6529 1.00145
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 \(a_p\))