Properties

Label 6001.2.a.b.1.14
Level 6001
Weight 2
Character 6001.1
Self dual Yes
Analytic conductor 47.918
Analytic rank 1
Dimension 114
CM No

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Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.918226253\)
Analytic rank: \(1\)
Dimension: \(114\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.31236 q^{2}\) \(+3.26187 q^{3}\) \(+3.34699 q^{4}\) \(-1.15202 q^{5}\) \(-7.54261 q^{6}\) \(-3.58394 q^{7}\) \(-3.11471 q^{8}\) \(+7.63982 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.31236 q^{2}\) \(+3.26187 q^{3}\) \(+3.34699 q^{4}\) \(-1.15202 q^{5}\) \(-7.54261 q^{6}\) \(-3.58394 q^{7}\) \(-3.11471 q^{8}\) \(+7.63982 q^{9}\) \(+2.66388 q^{10}\) \(+3.98929 q^{11}\) \(+10.9175 q^{12}\) \(-4.27275 q^{13}\) \(+8.28735 q^{14}\) \(-3.75774 q^{15}\) \(+0.508350 q^{16}\) \(+1.00000 q^{17}\) \(-17.6660 q^{18}\) \(+5.24357 q^{19}\) \(-3.85579 q^{20}\) \(-11.6904 q^{21}\) \(-9.22464 q^{22}\) \(-1.89550 q^{23}\) \(-10.1598 q^{24}\) \(-3.67285 q^{25}\) \(+9.88011 q^{26}\) \(+15.1345 q^{27}\) \(-11.9954 q^{28}\) \(-0.888851 q^{29}\) \(+8.68923 q^{30}\) \(-9.53721 q^{31}\) \(+5.05394 q^{32}\) \(+13.0125 q^{33}\) \(-2.31236 q^{34}\) \(+4.12877 q^{35}\) \(+25.5704 q^{36}\) \(-5.09602 q^{37}\) \(-12.1250 q^{38}\) \(-13.9372 q^{39}\) \(+3.58821 q^{40}\) \(-8.77913 q^{41}\) \(+27.0323 q^{42}\) \(+7.99375 q^{43}\) \(+13.3521 q^{44}\) \(-8.80122 q^{45}\) \(+4.38308 q^{46}\) \(+10.3254 q^{47}\) \(+1.65817 q^{48}\) \(+5.84464 q^{49}\) \(+8.49294 q^{50}\) \(+3.26187 q^{51}\) \(-14.3008 q^{52}\) \(-4.06792 q^{53}\) \(-34.9964 q^{54}\) \(-4.59573 q^{55}\) \(+11.1630 q^{56}\) \(+17.1039 q^{57}\) \(+2.05534 q^{58}\) \(-11.4318 q^{59}\) \(-12.5771 q^{60}\) \(-2.07854 q^{61}\) \(+22.0534 q^{62}\) \(-27.3807 q^{63}\) \(-12.7032 q^{64}\) \(+4.92228 q^{65}\) \(-30.0896 q^{66}\) \(-11.4960 q^{67}\) \(+3.34699 q^{68}\) \(-6.18289 q^{69}\) \(-9.54718 q^{70}\) \(-5.73616 q^{71}\) \(-23.7959 q^{72}\) \(-3.58856 q^{73}\) \(+11.7838 q^{74}\) \(-11.9804 q^{75}\) \(+17.5502 q^{76}\) \(-14.2974 q^{77}\) \(+32.2277 q^{78}\) \(-5.05647 q^{79}\) \(-0.585629 q^{80}\) \(+26.4474 q^{81}\) \(+20.3005 q^{82}\) \(+0.365274 q^{83}\) \(-39.1275 q^{84}\) \(-1.15202 q^{85}\) \(-18.4844 q^{86}\) \(-2.89932 q^{87}\) \(-12.4255 q^{88}\) \(-10.1520 q^{89}\) \(+20.3516 q^{90}\) \(+15.3133 q^{91}\) \(-6.34422 q^{92}\) \(-31.1092 q^{93}\) \(-23.8761 q^{94}\) \(-6.04069 q^{95}\) \(+16.4853 q^{96}\) \(+2.81422 q^{97}\) \(-13.5149 q^{98}\) \(+30.4774 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut -\mathstrut 19q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 49q^{12} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 110q^{16} \) \(\mathstrut +\mathstrut 114q^{17} \) \(\mathstrut -\mathstrut 21q^{18} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 88q^{20} \) \(\mathstrut -\mathstrut 30q^{21} \) \(\mathstrut -\mathstrut 36q^{22} \) \(\mathstrut -\mathstrut 77q^{23} \) \(\mathstrut -\mathstrut 72q^{24} \) \(\mathstrut +\mathstrut 119q^{25} \) \(\mathstrut -\mathstrut 79q^{26} \) \(\mathstrut -\mathstrut 77q^{27} \) \(\mathstrut -\mathstrut 92q^{28} \) \(\mathstrut -\mathstrut 65q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 131q^{31} \) \(\mathstrut -\mathstrut 30q^{32} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 33q^{35} \) \(\mathstrut +\mathstrut 109q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 14q^{38} \) \(\mathstrut -\mathstrut 83q^{39} \) \(\mathstrut -\mathstrut 42q^{40} \) \(\mathstrut -\mathstrut 99q^{41} \) \(\mathstrut +\mathstrut 29q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 73q^{45} \) \(\mathstrut -\mathstrut 35q^{46} \) \(\mathstrut -\mathstrut 113q^{47} \) \(\mathstrut -\mathstrut 86q^{48} \) \(\mathstrut +\mathstrut 101q^{49} \) \(\mathstrut -\mathstrut 44q^{50} \) \(\mathstrut -\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut 3q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 78q^{54} \) \(\mathstrut -\mathstrut 63q^{55} \) \(\mathstrut -\mathstrut 117q^{56} \) \(\mathstrut -\mathstrut 64q^{57} \) \(\mathstrut -\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 134q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 30q^{61} \) \(\mathstrut -\mathstrut 30q^{62} \) \(\mathstrut -\mathstrut 154q^{63} \) \(\mathstrut +\mathstrut 117q^{64} \) \(\mathstrut -\mathstrut 66q^{65} \) \(\mathstrut -\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 110q^{68} \) \(\mathstrut -\mathstrut 35q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 233q^{71} \) \(\mathstrut +\mathstrut 16q^{72} \) \(\mathstrut -\mathstrut 56q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 100q^{75} \) \(\mathstrut -\mathstrut 64q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 50q^{78} \) \(\mathstrut -\mathstrut 154q^{79} \) \(\mathstrut -\mathstrut 128q^{80} \) \(\mathstrut +\mathstrut 118q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 53q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut -\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 52q^{88} \) \(\mathstrut -\mathstrut 118q^{89} \) \(\mathstrut -\mathstrut 5q^{90} \) \(\mathstrut -\mathstrut 95q^{91} \) \(\mathstrut -\mathstrut 102q^{92} \) \(\mathstrut +\mathstrut 47q^{93} \) \(\mathstrut -\mathstrut 3q^{94} \) \(\mathstrut -\mathstrut 158q^{95} \) \(\mathstrut -\mathstrut 144q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut -\mathstrut 131q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.31236 −1.63508 −0.817541 0.575870i \(-0.804663\pi\)
−0.817541 + 0.575870i \(0.804663\pi\)
\(3\) 3.26187 1.88324 0.941622 0.336672i \(-0.109301\pi\)
0.941622 + 0.336672i \(0.109301\pi\)
\(4\) 3.34699 1.67349
\(5\) −1.15202 −0.515199 −0.257599 0.966252i \(-0.582931\pi\)
−0.257599 + 0.966252i \(0.582931\pi\)
\(6\) −7.54261 −3.07926
\(7\) −3.58394 −1.35460 −0.677301 0.735706i \(-0.736851\pi\)
−0.677301 + 0.735706i \(0.736851\pi\)
\(8\) −3.11471 −1.10122
\(9\) 7.63982 2.54661
\(10\) 2.66388 0.842392
\(11\) 3.98929 1.20281 0.601407 0.798943i \(-0.294607\pi\)
0.601407 + 0.798943i \(0.294607\pi\)
\(12\) 10.9175 3.15160
\(13\) −4.27275 −1.18505 −0.592523 0.805553i \(-0.701868\pi\)
−0.592523 + 0.805553i \(0.701868\pi\)
\(14\) 8.28735 2.21489
\(15\) −3.75774 −0.970245
\(16\) 0.508350 0.127087
\(17\) 1.00000 0.242536
\(18\) −17.6660 −4.16391
\(19\) 5.24357 1.20296 0.601479 0.798889i \(-0.294578\pi\)
0.601479 + 0.798889i \(0.294578\pi\)
\(20\) −3.85579 −0.862182
\(21\) −11.6904 −2.55105
\(22\) −9.22464 −1.96670
\(23\) −1.89550 −0.395240 −0.197620 0.980279i \(-0.563321\pi\)
−0.197620 + 0.980279i \(0.563321\pi\)
\(24\) −10.1598 −2.07386
\(25\) −3.67285 −0.734570
\(26\) 9.88011 1.93765
\(27\) 15.1345 2.91264
\(28\) −11.9954 −2.26692
\(29\) −0.888851 −0.165055 −0.0825277 0.996589i \(-0.526299\pi\)
−0.0825277 + 0.996589i \(0.526299\pi\)
\(30\) 8.68923 1.58643
\(31\) −9.53721 −1.71293 −0.856467 0.516202i \(-0.827345\pi\)
−0.856467 + 0.516202i \(0.827345\pi\)
\(32\) 5.05394 0.893419
\(33\) 13.0125 2.26519
\(34\) −2.31236 −0.396566
\(35\) 4.12877 0.697889
\(36\) 25.5704 4.26173
\(37\) −5.09602 −0.837780 −0.418890 0.908037i \(-0.637581\pi\)
−0.418890 + 0.908037i \(0.637581\pi\)
\(38\) −12.1250 −1.96693
\(39\) −13.9372 −2.23173
\(40\) 3.58821 0.567346
\(41\) −8.77913 −1.37107 −0.685535 0.728039i \(-0.740432\pi\)
−0.685535 + 0.728039i \(0.740432\pi\)
\(42\) 27.0323 4.17117
\(43\) 7.99375 1.21903 0.609517 0.792773i \(-0.291363\pi\)
0.609517 + 0.792773i \(0.291363\pi\)
\(44\) 13.3521 2.01290
\(45\) −8.80122 −1.31201
\(46\) 4.38308 0.646249
\(47\) 10.3254 1.50612 0.753060 0.657952i \(-0.228577\pi\)
0.753060 + 0.657952i \(0.228577\pi\)
\(48\) 1.65817 0.239337
\(49\) 5.84464 0.834948
\(50\) 8.49294 1.20108
\(51\) 3.26187 0.456754
\(52\) −14.3008 −1.98317
\(53\) −4.06792 −0.558772 −0.279386 0.960179i \(-0.590131\pi\)
−0.279386 + 0.960179i \(0.590131\pi\)
\(54\) −34.9964 −4.76240
\(55\) −4.59573 −0.619688
\(56\) 11.1630 1.49171
\(57\) 17.1039 2.26546
\(58\) 2.05534 0.269879
\(59\) −11.4318 −1.48829 −0.744147 0.668016i \(-0.767144\pi\)
−0.744147 + 0.668016i \(0.767144\pi\)
\(60\) −12.5771 −1.62370
\(61\) −2.07854 −0.266130 −0.133065 0.991107i \(-0.542482\pi\)
−0.133065 + 0.991107i \(0.542482\pi\)
\(62\) 22.0534 2.80079
\(63\) −27.3807 −3.44964
\(64\) −12.7032 −1.58790
\(65\) 4.92228 0.610534
\(66\) −30.0896 −3.70378
\(67\) −11.4960 −1.40446 −0.702229 0.711952i \(-0.747812\pi\)
−0.702229 + 0.711952i \(0.747812\pi\)
\(68\) 3.34699 0.405882
\(69\) −6.18289 −0.744333
\(70\) −9.54718 −1.14111
\(71\) −5.73616 −0.680756 −0.340378 0.940289i \(-0.610555\pi\)
−0.340378 + 0.940289i \(0.610555\pi\)
\(72\) −23.7959 −2.80437
\(73\) −3.58856 −0.420009 −0.210004 0.977700i \(-0.567348\pi\)
−0.210004 + 0.977700i \(0.567348\pi\)
\(74\) 11.7838 1.36984
\(75\) −11.9804 −1.38338
\(76\) 17.5502 2.01314
\(77\) −14.2974 −1.62934
\(78\) 32.2277 3.64906
\(79\) −5.05647 −0.568898 −0.284449 0.958691i \(-0.591811\pi\)
−0.284449 + 0.958691i \(0.591811\pi\)
\(80\) −0.585629 −0.0654753
\(81\) 26.4474 2.93860
\(82\) 20.3005 2.24181
\(83\) 0.365274 0.0400940 0.0200470 0.999799i \(-0.493618\pi\)
0.0200470 + 0.999799i \(0.493618\pi\)
\(84\) −39.1275 −4.26916
\(85\) −1.15202 −0.124954
\(86\) −18.4844 −1.99322
\(87\) −2.89932 −0.310840
\(88\) −12.4255 −1.32456
\(89\) −10.1520 −1.07611 −0.538057 0.842908i \(-0.680842\pi\)
−0.538057 + 0.842908i \(0.680842\pi\)
\(90\) 20.3516 2.14524
\(91\) 15.3133 1.60527
\(92\) −6.34422 −0.661431
\(93\) −31.1092 −3.22587
\(94\) −23.8761 −2.46263
\(95\) −6.04069 −0.619762
\(96\) 16.4853 1.68253
\(97\) 2.81422 0.285740 0.142870 0.989741i \(-0.454367\pi\)
0.142870 + 0.989741i \(0.454367\pi\)
\(98\) −13.5149 −1.36521
\(99\) 30.4774 3.06310
\(100\) −12.2930 −1.22930
\(101\) 14.0450 1.39753 0.698763 0.715353i \(-0.253734\pi\)
0.698763 + 0.715353i \(0.253734\pi\)
\(102\) −7.54261 −0.746830
\(103\) 13.4353 1.32382 0.661910 0.749583i \(-0.269746\pi\)
0.661910 + 0.749583i \(0.269746\pi\)
\(104\) 13.3084 1.30499
\(105\) 13.4675 1.31430
\(106\) 9.40647 0.913638
\(107\) 3.58337 0.346418 0.173209 0.984885i \(-0.444586\pi\)
0.173209 + 0.984885i \(0.444586\pi\)
\(108\) 50.6550 4.87428
\(109\) 1.42208 0.136211 0.0681054 0.997678i \(-0.478305\pi\)
0.0681054 + 0.997678i \(0.478305\pi\)
\(110\) 10.6270 1.01324
\(111\) −16.6226 −1.57774
\(112\) −1.82190 −0.172153
\(113\) 1.26745 0.119232 0.0596160 0.998221i \(-0.481012\pi\)
0.0596160 + 0.998221i \(0.481012\pi\)
\(114\) −39.5502 −3.70422
\(115\) 2.18366 0.203627
\(116\) −2.97497 −0.276219
\(117\) −32.6430 −3.01785
\(118\) 26.4344 2.43348
\(119\) −3.58394 −0.328539
\(120\) 11.7043 1.06845
\(121\) 4.91440 0.446763
\(122\) 4.80633 0.435144
\(123\) −28.6364 −2.58206
\(124\) −31.9209 −2.86658
\(125\) 9.99129 0.893648
\(126\) 63.3139 5.64045
\(127\) −4.84100 −0.429569 −0.214785 0.976661i \(-0.568905\pi\)
−0.214785 + 0.976661i \(0.568905\pi\)
\(128\) 19.2664 1.70293
\(129\) 26.0746 2.29574
\(130\) −11.3821 −0.998274
\(131\) 14.6260 1.27788 0.638939 0.769258i \(-0.279374\pi\)
0.638939 + 0.769258i \(0.279374\pi\)
\(132\) 43.5528 3.79079
\(133\) −18.7927 −1.62953
\(134\) 26.5828 2.29640
\(135\) −17.4353 −1.50059
\(136\) −3.11471 −0.267084
\(137\) −11.1706 −0.954368 −0.477184 0.878803i \(-0.658343\pi\)
−0.477184 + 0.878803i \(0.658343\pi\)
\(138\) 14.2970 1.21705
\(139\) −9.26502 −0.785849 −0.392925 0.919571i \(-0.628537\pi\)
−0.392925 + 0.919571i \(0.628537\pi\)
\(140\) 13.8189 1.16791
\(141\) 33.6803 2.83639
\(142\) 13.2640 1.11309
\(143\) −17.0452 −1.42539
\(144\) 3.88370 0.323642
\(145\) 1.02397 0.0850363
\(146\) 8.29802 0.686749
\(147\) 19.0645 1.57241
\(148\) −17.0563 −1.40202
\(149\) −14.9608 −1.22564 −0.612820 0.790223i \(-0.709965\pi\)
−0.612820 + 0.790223i \(0.709965\pi\)
\(150\) 27.7029 2.26193
\(151\) 13.5969 1.10650 0.553250 0.833015i \(-0.313387\pi\)
0.553250 + 0.833015i \(0.313387\pi\)
\(152\) −16.3322 −1.32472
\(153\) 7.63982 0.617643
\(154\) 33.0606 2.66410
\(155\) 10.9870 0.882501
\(156\) −46.6475 −3.73479
\(157\) 23.0423 1.83898 0.919488 0.393118i \(-0.128604\pi\)
0.919488 + 0.393118i \(0.128604\pi\)
\(158\) 11.6924 0.930194
\(159\) −13.2690 −1.05230
\(160\) −5.82224 −0.460288
\(161\) 6.79337 0.535393
\(162\) −61.1558 −4.80486
\(163\) 7.60787 0.595895 0.297947 0.954582i \(-0.403698\pi\)
0.297947 + 0.954582i \(0.403698\pi\)
\(164\) −29.3837 −2.29448
\(165\) −14.9907 −1.16702
\(166\) −0.844643 −0.0655570
\(167\) 7.71734 0.597185 0.298593 0.954381i \(-0.403483\pi\)
0.298593 + 0.954381i \(0.403483\pi\)
\(168\) 36.4121 2.80926
\(169\) 5.25636 0.404335
\(170\) 2.66388 0.204310
\(171\) 40.0599 3.06346
\(172\) 26.7550 2.04005
\(173\) −13.1814 −1.00216 −0.501080 0.865401i \(-0.667064\pi\)
−0.501080 + 0.865401i \(0.667064\pi\)
\(174\) 6.70426 0.508248
\(175\) 13.1633 0.995051
\(176\) 2.02795 0.152863
\(177\) −37.2891 −2.80282
\(178\) 23.4751 1.75953
\(179\) −1.00906 −0.0754205 −0.0377103 0.999289i \(-0.512006\pi\)
−0.0377103 + 0.999289i \(0.512006\pi\)
\(180\) −29.4576 −2.19564
\(181\) −9.93127 −0.738185 −0.369093 0.929393i \(-0.620331\pi\)
−0.369093 + 0.929393i \(0.620331\pi\)
\(182\) −35.4097 −2.62474
\(183\) −6.77994 −0.501187
\(184\) 5.90395 0.435245
\(185\) 5.87071 0.431623
\(186\) 71.9355 5.27457
\(187\) 3.98929 0.291725
\(188\) 34.5591 2.52048
\(189\) −54.2412 −3.94547
\(190\) 13.9682 1.01336
\(191\) −22.4867 −1.62708 −0.813540 0.581509i \(-0.802462\pi\)
−0.813540 + 0.581509i \(0.802462\pi\)
\(192\) −41.4363 −2.99040
\(193\) −22.4804 −1.61818 −0.809088 0.587688i \(-0.800038\pi\)
−0.809088 + 0.587688i \(0.800038\pi\)
\(194\) −6.50747 −0.467209
\(195\) 16.0559 1.14978
\(196\) 19.5619 1.39728
\(197\) −5.91158 −0.421182 −0.210591 0.977574i \(-0.567539\pi\)
−0.210591 + 0.977574i \(0.567539\pi\)
\(198\) −70.4746 −5.00842
\(199\) 3.97628 0.281871 0.140936 0.990019i \(-0.454989\pi\)
0.140936 + 0.990019i \(0.454989\pi\)
\(200\) 11.4399 0.808922
\(201\) −37.4984 −2.64494
\(202\) −32.4769 −2.28507
\(203\) 3.18559 0.223585
\(204\) 10.9175 0.764374
\(205\) 10.1137 0.706374
\(206\) −31.0672 −2.16455
\(207\) −14.4813 −1.00652
\(208\) −2.17205 −0.150605
\(209\) 20.9181 1.44694
\(210\) −31.1417 −2.14898
\(211\) −4.31634 −0.297149 −0.148574 0.988901i \(-0.547468\pi\)
−0.148574 + 0.988901i \(0.547468\pi\)
\(212\) −13.6153 −0.935101
\(213\) −18.7106 −1.28203
\(214\) −8.28603 −0.566422
\(215\) −9.20895 −0.628045
\(216\) −47.1397 −3.20745
\(217\) 34.1808 2.32034
\(218\) −3.28836 −0.222716
\(219\) −11.7054 −0.790979
\(220\) −15.3819 −1.03704
\(221\) −4.27275 −0.287416
\(222\) 38.4373 2.57974
\(223\) 7.42527 0.497233 0.248617 0.968602i \(-0.420024\pi\)
0.248617 + 0.968602i \(0.420024\pi\)
\(224\) −18.1130 −1.21023
\(225\) −28.0599 −1.87066
\(226\) −2.93080 −0.194954
\(227\) 13.0694 0.867445 0.433722 0.901047i \(-0.357200\pi\)
0.433722 + 0.901047i \(0.357200\pi\)
\(228\) 57.2464 3.79124
\(229\) −27.1475 −1.79395 −0.896977 0.442076i \(-0.854242\pi\)
−0.896977 + 0.442076i \(0.854242\pi\)
\(230\) −5.04939 −0.332947
\(231\) −46.6362 −3.06844
\(232\) 2.76852 0.181762
\(233\) −17.0330 −1.11587 −0.557934 0.829885i \(-0.688406\pi\)
−0.557934 + 0.829885i \(0.688406\pi\)
\(234\) 75.4823 4.93443
\(235\) −11.8951 −0.775951
\(236\) −38.2621 −2.49065
\(237\) −16.4936 −1.07137
\(238\) 8.28735 0.537189
\(239\) −8.43692 −0.545739 −0.272869 0.962051i \(-0.587973\pi\)
−0.272869 + 0.962051i \(0.587973\pi\)
\(240\) −1.91025 −0.123306
\(241\) 1.83825 0.118412 0.0592061 0.998246i \(-0.481143\pi\)
0.0592061 + 0.998246i \(0.481143\pi\)
\(242\) −11.3638 −0.730495
\(243\) 40.8646 2.62147
\(244\) −6.95685 −0.445367
\(245\) −6.73314 −0.430164
\(246\) 66.2176 4.22188
\(247\) −22.4044 −1.42556
\(248\) 29.7057 1.88631
\(249\) 1.19148 0.0755068
\(250\) −23.1034 −1.46119
\(251\) −28.0184 −1.76850 −0.884252 0.467010i \(-0.845331\pi\)
−0.884252 + 0.467010i \(0.845331\pi\)
\(252\) −91.6428 −5.77295
\(253\) −7.56170 −0.475400
\(254\) 11.1941 0.702381
\(255\) −3.75774 −0.235319
\(256\) −19.1445 −1.19653
\(257\) −2.98989 −0.186504 −0.0932520 0.995643i \(-0.529726\pi\)
−0.0932520 + 0.995643i \(0.529726\pi\)
\(258\) −60.2937 −3.75372
\(259\) 18.2638 1.13486
\(260\) 16.4748 1.02173
\(261\) −6.79066 −0.420332
\(262\) −33.8205 −2.08943
\(263\) −8.27783 −0.510433 −0.255217 0.966884i \(-0.582147\pi\)
−0.255217 + 0.966884i \(0.582147\pi\)
\(264\) −40.5304 −2.49447
\(265\) 4.68632 0.287878
\(266\) 43.4553 2.66441
\(267\) −33.1147 −2.02659
\(268\) −38.4769 −2.35035
\(269\) −32.1027 −1.95733 −0.978667 0.205453i \(-0.934133\pi\)
−0.978667 + 0.205453i \(0.934133\pi\)
\(270\) 40.3165 2.45358
\(271\) 27.2641 1.65617 0.828087 0.560599i \(-0.189429\pi\)
0.828087 + 0.560599i \(0.189429\pi\)
\(272\) 0.508350 0.0308232
\(273\) 49.9500 3.02311
\(274\) 25.8304 1.56047
\(275\) −14.6521 −0.883552
\(276\) −20.6941 −1.24564
\(277\) 0.978675 0.0588029 0.0294014 0.999568i \(-0.490640\pi\)
0.0294014 + 0.999568i \(0.490640\pi\)
\(278\) 21.4240 1.28493
\(279\) −72.8626 −4.36217
\(280\) −12.8599 −0.768528
\(281\) −17.5299 −1.04575 −0.522873 0.852411i \(-0.675140\pi\)
−0.522873 + 0.852411i \(0.675140\pi\)
\(282\) −77.8808 −4.63773
\(283\) 1.29771 0.0771409 0.0385704 0.999256i \(-0.487720\pi\)
0.0385704 + 0.999256i \(0.487720\pi\)
\(284\) −19.1988 −1.13924
\(285\) −19.7040 −1.16716
\(286\) 39.4146 2.33063
\(287\) 31.4639 1.85726
\(288\) 38.6112 2.27519
\(289\) 1.00000 0.0588235
\(290\) −2.36779 −0.139041
\(291\) 9.17962 0.538119
\(292\) −12.0109 −0.702882
\(293\) 33.2107 1.94019 0.970094 0.242730i \(-0.0780429\pi\)
0.970094 + 0.242730i \(0.0780429\pi\)
\(294\) −44.0838 −2.57102
\(295\) 13.1697 0.766767
\(296\) 15.8726 0.922579
\(297\) 60.3759 3.50336
\(298\) 34.5948 2.00402
\(299\) 8.09900 0.468377
\(300\) −40.0982 −2.31507
\(301\) −28.6491 −1.65131
\(302\) −31.4409 −1.80922
\(303\) 45.8129 2.63188
\(304\) 2.66557 0.152881
\(305\) 2.39452 0.137110
\(306\) −17.6660 −1.00990
\(307\) 15.2836 0.872283 0.436142 0.899878i \(-0.356345\pi\)
0.436142 + 0.899878i \(0.356345\pi\)
\(308\) −47.8531 −2.72668
\(309\) 43.8243 2.49308
\(310\) −25.4060 −1.44296
\(311\) −2.08720 −0.118354 −0.0591772 0.998247i \(-0.518848\pi\)
−0.0591772 + 0.998247i \(0.518848\pi\)
\(312\) 43.4103 2.45762
\(313\) −11.0153 −0.622621 −0.311311 0.950308i \(-0.600768\pi\)
−0.311311 + 0.950308i \(0.600768\pi\)
\(314\) −53.2820 −3.00688
\(315\) 31.5431 1.77725
\(316\) −16.9240 −0.952047
\(317\) 2.43821 0.136944 0.0684719 0.997653i \(-0.478188\pi\)
0.0684719 + 0.997653i \(0.478188\pi\)
\(318\) 30.6827 1.72060
\(319\) −3.54588 −0.198531
\(320\) 14.6343 0.818084
\(321\) 11.6885 0.652389
\(322\) −15.7087 −0.875411
\(323\) 5.24357 0.291760
\(324\) 88.5192 4.91773
\(325\) 15.6932 0.870500
\(326\) −17.5921 −0.974337
\(327\) 4.63866 0.256518
\(328\) 27.3445 1.50985
\(329\) −37.0058 −2.04019
\(330\) 34.6638 1.90818
\(331\) −21.2898 −1.17020 −0.585098 0.810963i \(-0.698944\pi\)
−0.585098 + 0.810963i \(0.698944\pi\)
\(332\) 1.22257 0.0670971
\(333\) −38.9327 −2.13350
\(334\) −17.8452 −0.976447
\(335\) 13.2436 0.723574
\(336\) −5.94279 −0.324206
\(337\) −12.8010 −0.697312 −0.348656 0.937251i \(-0.613362\pi\)
−0.348656 + 0.937251i \(0.613362\pi\)
\(338\) −12.1546 −0.661121
\(339\) 4.13427 0.224543
\(340\) −3.85579 −0.209110
\(341\) −38.0467 −2.06034
\(342\) −92.6328 −5.00901
\(343\) 4.14075 0.223579
\(344\) −24.8982 −1.34242
\(345\) 7.12281 0.383479
\(346\) 30.4800 1.63861
\(347\) 12.5153 0.671855 0.335928 0.941888i \(-0.390950\pi\)
0.335928 + 0.941888i \(0.390950\pi\)
\(348\) −9.70399 −0.520188
\(349\) −10.1359 −0.542562 −0.271281 0.962500i \(-0.587447\pi\)
−0.271281 + 0.962500i \(0.587447\pi\)
\(350\) −30.4382 −1.62699
\(351\) −64.6659 −3.45161
\(352\) 20.1616 1.07462
\(353\) 1.00000 0.0532246
\(354\) 86.2257 4.58284
\(355\) 6.60816 0.350725
\(356\) −33.9788 −1.80087
\(357\) −11.6904 −0.618720
\(358\) 2.33330 0.123319
\(359\) −6.07354 −0.320549 −0.160275 0.987072i \(-0.551238\pi\)
−0.160275 + 0.987072i \(0.551238\pi\)
\(360\) 27.4133 1.44481
\(361\) 8.49503 0.447107
\(362\) 22.9646 1.20699
\(363\) 16.0301 0.841364
\(364\) 51.2533 2.68640
\(365\) 4.13409 0.216388
\(366\) 15.6776 0.819483
\(367\) −1.73911 −0.0907807 −0.0453904 0.998969i \(-0.514453\pi\)
−0.0453904 + 0.998969i \(0.514453\pi\)
\(368\) −0.963578 −0.0502300
\(369\) −67.0710 −3.49158
\(370\) −13.5752 −0.705740
\(371\) 14.5792 0.756914
\(372\) −104.122 −5.39848
\(373\) −32.9244 −1.70476 −0.852381 0.522921i \(-0.824842\pi\)
−0.852381 + 0.522921i \(0.824842\pi\)
\(374\) −9.22464 −0.476995
\(375\) 32.5903 1.68296
\(376\) −32.1608 −1.65857
\(377\) 3.79783 0.195598
\(378\) 125.425 6.45117
\(379\) −8.44074 −0.433572 −0.216786 0.976219i \(-0.569557\pi\)
−0.216786 + 0.976219i \(0.569557\pi\)
\(380\) −20.2181 −1.03717
\(381\) −15.7907 −0.808984
\(382\) 51.9972 2.66041
\(383\) −6.37503 −0.325749 −0.162874 0.986647i \(-0.552077\pi\)
−0.162874 + 0.986647i \(0.552077\pi\)
\(384\) 62.8447 3.20703
\(385\) 16.4708 0.839432
\(386\) 51.9827 2.64585
\(387\) 61.0708 3.10440
\(388\) 9.41915 0.478185
\(389\) 8.22512 0.417030 0.208515 0.978019i \(-0.433137\pi\)
0.208515 + 0.978019i \(0.433137\pi\)
\(390\) −37.1269 −1.87999
\(391\) −1.89550 −0.0958597
\(392\) −18.2044 −0.919460
\(393\) 47.7081 2.40656
\(394\) 13.6697 0.688668
\(395\) 5.82515 0.293095
\(396\) 102.008 5.12607
\(397\) −24.0508 −1.20708 −0.603538 0.797335i \(-0.706243\pi\)
−0.603538 + 0.797335i \(0.706243\pi\)
\(398\) −9.19457 −0.460882
\(399\) −61.2993 −3.06880
\(400\) −1.86709 −0.0933547
\(401\) −38.0085 −1.89805 −0.949026 0.315197i \(-0.897929\pi\)
−0.949026 + 0.315197i \(0.897929\pi\)
\(402\) 86.7097 4.32469
\(403\) 40.7501 2.02991
\(404\) 47.0083 2.33875
\(405\) −30.4679 −1.51396
\(406\) −7.36622 −0.365579
\(407\) −20.3295 −1.00769
\(408\) −10.1598 −0.502985
\(409\) 33.9260 1.67753 0.838767 0.544491i \(-0.183277\pi\)
0.838767 + 0.544491i \(0.183277\pi\)
\(410\) −23.3865 −1.15498
\(411\) −36.4371 −1.79731
\(412\) 44.9678 2.21540
\(413\) 40.9709 2.01605
\(414\) 33.4859 1.64574
\(415\) −0.420802 −0.0206564
\(416\) −21.5942 −1.05874
\(417\) −30.2213 −1.47995
\(418\) −48.3701 −2.36586
\(419\) −35.0056 −1.71014 −0.855068 0.518516i \(-0.826485\pi\)
−0.855068 + 0.518516i \(0.826485\pi\)
\(420\) 45.0756 2.19947
\(421\) 20.2970 0.989217 0.494608 0.869116i \(-0.335311\pi\)
0.494608 + 0.869116i \(0.335311\pi\)
\(422\) 9.98090 0.485863
\(423\) 78.8845 3.83550
\(424\) 12.6704 0.615329
\(425\) −3.67285 −0.178159
\(426\) 43.2656 2.09622
\(427\) 7.44937 0.360500
\(428\) 11.9935 0.579728
\(429\) −55.5993 −2.68436
\(430\) 21.2944 1.02691
\(431\) −35.8336 −1.72605 −0.863023 0.505165i \(-0.831432\pi\)
−0.863023 + 0.505165i \(0.831432\pi\)
\(432\) 7.69363 0.370160
\(433\) 25.3031 1.21599 0.607994 0.793942i \(-0.291974\pi\)
0.607994 + 0.793942i \(0.291974\pi\)
\(434\) −79.0382 −3.79395
\(435\) 3.34007 0.160144
\(436\) 4.75969 0.227948
\(437\) −9.93920 −0.475457
\(438\) 27.0671 1.29332
\(439\) 32.0332 1.52886 0.764430 0.644706i \(-0.223020\pi\)
0.764430 + 0.644706i \(0.223020\pi\)
\(440\) 14.3144 0.682412
\(441\) 44.6520 2.12629
\(442\) 9.88011 0.469949
\(443\) 22.9457 1.09018 0.545091 0.838377i \(-0.316495\pi\)
0.545091 + 0.838377i \(0.316495\pi\)
\(444\) −55.6355 −2.64035
\(445\) 11.6953 0.554412
\(446\) −17.1699 −0.813017
\(447\) −48.8004 −2.30818
\(448\) 45.5276 2.15098
\(449\) −31.2108 −1.47293 −0.736465 0.676475i \(-0.763507\pi\)
−0.736465 + 0.676475i \(0.763507\pi\)
\(450\) 64.8845 3.05869
\(451\) −35.0225 −1.64914
\(452\) 4.24215 0.199534
\(453\) 44.3514 2.08381
\(454\) −30.2210 −1.41834
\(455\) −17.6412 −0.827031
\(456\) −53.2736 −2.49477
\(457\) −18.1571 −0.849351 −0.424675 0.905346i \(-0.639612\pi\)
−0.424675 + 0.905346i \(0.639612\pi\)
\(458\) 62.7746 2.93326
\(459\) 15.1345 0.706419
\(460\) 7.30867 0.340768
\(461\) −4.07140 −0.189624 −0.0948120 0.995495i \(-0.530225\pi\)
−0.0948120 + 0.995495i \(0.530225\pi\)
\(462\) 107.839 5.01715
\(463\) 0.541809 0.0251800 0.0125900 0.999921i \(-0.495992\pi\)
0.0125900 + 0.999921i \(0.495992\pi\)
\(464\) −0.451847 −0.0209765
\(465\) 35.8384 1.66196
\(466\) 39.3863 1.82454
\(467\) 28.8533 1.33517 0.667585 0.744534i \(-0.267328\pi\)
0.667585 + 0.744534i \(0.267328\pi\)
\(468\) −109.256 −5.05035
\(469\) 41.2009 1.90248
\(470\) 27.5057 1.26874
\(471\) 75.1611 3.46324
\(472\) 35.6068 1.63894
\(473\) 31.8893 1.46627
\(474\) 38.1390 1.75178
\(475\) −19.2589 −0.883657
\(476\) −11.9954 −0.549809
\(477\) −31.0782 −1.42297
\(478\) 19.5092 0.892328
\(479\) −16.4647 −0.752293 −0.376146 0.926560i \(-0.622751\pi\)
−0.376146 + 0.926560i \(0.622751\pi\)
\(480\) −18.9914 −0.866835
\(481\) 21.7740 0.992809
\(482\) −4.25069 −0.193614
\(483\) 22.1591 1.00828
\(484\) 16.4484 0.747655
\(485\) −3.24203 −0.147213
\(486\) −94.4935 −4.28631
\(487\) 6.67110 0.302296 0.151148 0.988511i \(-0.451703\pi\)
0.151148 + 0.988511i \(0.451703\pi\)
\(488\) 6.47406 0.293067
\(489\) 24.8159 1.12221
\(490\) 15.5694 0.703354
\(491\) 29.8188 1.34570 0.672852 0.739777i \(-0.265069\pi\)
0.672852 + 0.739777i \(0.265069\pi\)
\(492\) −95.8458 −4.32106
\(493\) −0.888851 −0.0400318
\(494\) 51.8070 2.33091
\(495\) −35.1106 −1.57810
\(496\) −4.84824 −0.217692
\(497\) 20.5580 0.922154
\(498\) −2.75512 −0.123460
\(499\) 36.5895 1.63797 0.818986 0.573813i \(-0.194536\pi\)
0.818986 + 0.573813i \(0.194536\pi\)
\(500\) 33.4407 1.49551
\(501\) 25.1730 1.12465
\(502\) 64.7884 2.89165
\(503\) 1.09744 0.0489326 0.0244663 0.999701i \(-0.492211\pi\)
0.0244663 + 0.999701i \(0.492211\pi\)
\(504\) 85.2830 3.79881
\(505\) −16.1801 −0.720003
\(506\) 17.4853 0.777318
\(507\) 17.1456 0.761462
\(508\) −16.2028 −0.718882
\(509\) −12.4961 −0.553880 −0.276940 0.960887i \(-0.589320\pi\)
−0.276940 + 0.960887i \(0.589320\pi\)
\(510\) 8.68923 0.384766
\(511\) 12.8612 0.568945
\(512\) 5.73590 0.253493
\(513\) 79.3589 3.50378
\(514\) 6.91368 0.304949
\(515\) −15.4777 −0.682030
\(516\) 87.2713 3.84191
\(517\) 41.1911 1.81158
\(518\) −42.2325 −1.85559
\(519\) −42.9959 −1.88731
\(520\) −15.3315 −0.672331
\(521\) −12.6025 −0.552125 −0.276062 0.961140i \(-0.589030\pi\)
−0.276062 + 0.961140i \(0.589030\pi\)
\(522\) 15.7024 0.687277
\(523\) −6.36361 −0.278261 −0.139131 0.990274i \(-0.544431\pi\)
−0.139131 + 0.990274i \(0.544431\pi\)
\(524\) 48.9530 2.13852
\(525\) 42.9370 1.87392
\(526\) 19.1413 0.834600
\(527\) −9.53721 −0.415447
\(528\) 6.61492 0.287878
\(529\) −19.4071 −0.843786
\(530\) −10.8364 −0.470705
\(531\) −87.3369 −3.79010
\(532\) −62.8988 −2.72701
\(533\) 37.5110 1.62478
\(534\) 76.5729 3.31363
\(535\) −4.12811 −0.178474
\(536\) 35.8067 1.54661
\(537\) −3.29142 −0.142035
\(538\) 74.2328 3.20040
\(539\) 23.3159 1.00429
\(540\) −58.3556 −2.51122
\(541\) 3.05462 0.131328 0.0656641 0.997842i \(-0.479083\pi\)
0.0656641 + 0.997842i \(0.479083\pi\)
\(542\) −63.0442 −2.70798
\(543\) −32.3945 −1.39018
\(544\) 5.05394 0.216686
\(545\) −1.63827 −0.0701756
\(546\) −115.502 −4.94303
\(547\) 12.5049 0.534670 0.267335 0.963604i \(-0.413857\pi\)
0.267335 + 0.963604i \(0.413857\pi\)
\(548\) −37.3878 −1.59713
\(549\) −15.8797 −0.677728
\(550\) 33.8808 1.44468
\(551\) −4.66075 −0.198555
\(552\) 19.2579 0.819672
\(553\) 18.1221 0.770630
\(554\) −2.26304 −0.0961475
\(555\) 19.1495 0.812852
\(556\) −31.0099 −1.31511
\(557\) 22.6211 0.958485 0.479242 0.877683i \(-0.340911\pi\)
0.479242 + 0.877683i \(0.340911\pi\)
\(558\) 168.484 7.13251
\(559\) −34.1552 −1.44461
\(560\) 2.09886 0.0886930
\(561\) 13.0125 0.549390
\(562\) 40.5354 1.70988
\(563\) −3.97719 −0.167619 −0.0838093 0.996482i \(-0.526709\pi\)
−0.0838093 + 0.996482i \(0.526709\pi\)
\(564\) 112.727 4.74668
\(565\) −1.46013 −0.0614281
\(566\) −3.00077 −0.126132
\(567\) −94.7860 −3.98064
\(568\) 17.8665 0.749661
\(569\) −35.4068 −1.48433 −0.742164 0.670218i \(-0.766201\pi\)
−0.742164 + 0.670218i \(0.766201\pi\)
\(570\) 45.5626 1.90841
\(571\) 14.9937 0.627467 0.313733 0.949511i \(-0.398420\pi\)
0.313733 + 0.949511i \(0.398420\pi\)
\(572\) −57.0501 −2.38538
\(573\) −73.3487 −3.06419
\(574\) −72.7557 −3.03677
\(575\) 6.96190 0.290331
\(576\) −97.0503 −4.04376
\(577\) −38.7499 −1.61318 −0.806589 0.591112i \(-0.798689\pi\)
−0.806589 + 0.591112i \(0.798689\pi\)
\(578\) −2.31236 −0.0961813
\(579\) −73.3283 −3.04742
\(580\) 3.42723 0.142308
\(581\) −1.30912 −0.0543115
\(582\) −21.2265 −0.879868
\(583\) −16.2281 −0.672099
\(584\) 11.1773 0.462521
\(585\) 37.6054 1.55479
\(586\) −76.7949 −3.17237
\(587\) −10.8143 −0.446356 −0.223178 0.974778i \(-0.571643\pi\)
−0.223178 + 0.974778i \(0.571643\pi\)
\(588\) 63.8086 2.63142
\(589\) −50.0090 −2.06059
\(590\) −30.4529 −1.25373
\(591\) −19.2828 −0.793189
\(592\) −2.59056 −0.106471
\(593\) 16.5566 0.679898 0.339949 0.940444i \(-0.389590\pi\)
0.339949 + 0.940444i \(0.389590\pi\)
\(594\) −139.611 −5.72829
\(595\) 4.12877 0.169263
\(596\) −50.0737 −2.05110
\(597\) 12.9701 0.530832
\(598\) −18.7278 −0.765836
\(599\) 26.6085 1.08719 0.543597 0.839347i \(-0.317062\pi\)
0.543597 + 0.839347i \(0.317062\pi\)
\(600\) 37.3155 1.52340
\(601\) 21.9492 0.895325 0.447662 0.894203i \(-0.352257\pi\)
0.447662 + 0.894203i \(0.352257\pi\)
\(602\) 66.2469 2.70002
\(603\) −87.8272 −3.57660
\(604\) 45.5087 1.85172
\(605\) −5.66148 −0.230172
\(606\) −105.936 −4.30334
\(607\) −6.57319 −0.266798 −0.133399 0.991062i \(-0.542589\pi\)
−0.133399 + 0.991062i \(0.542589\pi\)
\(608\) 26.5007 1.07475
\(609\) 10.3910 0.421064
\(610\) −5.53698 −0.224186
\(611\) −44.1180 −1.78482
\(612\) 25.5704 1.03362
\(613\) −37.6993 −1.52266 −0.761330 0.648365i \(-0.775453\pi\)
−0.761330 + 0.648365i \(0.775453\pi\)
\(614\) −35.3412 −1.42625
\(615\) 32.9897 1.33027
\(616\) 44.5322 1.79425
\(617\) −25.7889 −1.03822 −0.519112 0.854706i \(-0.673737\pi\)
−0.519112 + 0.854706i \(0.673737\pi\)
\(618\) −101.337 −4.07638
\(619\) −41.2309 −1.65721 −0.828604 0.559835i \(-0.810865\pi\)
−0.828604 + 0.559835i \(0.810865\pi\)
\(620\) 36.7735 1.47686
\(621\) −28.6875 −1.15119
\(622\) 4.82635 0.193519
\(623\) 36.3843 1.45771
\(624\) −7.08495 −0.283625
\(625\) 6.85410 0.274164
\(626\) 25.4713 1.01804
\(627\) 68.2322 2.72493
\(628\) 77.1223 3.07751
\(629\) −5.09602 −0.203192
\(630\) −72.9388 −2.90595
\(631\) 12.1105 0.482112 0.241056 0.970511i \(-0.422506\pi\)
0.241056 + 0.970511i \(0.422506\pi\)
\(632\) 15.7495 0.626480
\(633\) −14.0793 −0.559604
\(634\) −5.63802 −0.223914
\(635\) 5.57692 0.221314
\(636\) −44.4113 −1.76102
\(637\) −24.9727 −0.989453
\(638\) 8.19933 0.324615
\(639\) −43.8232 −1.73362
\(640\) −22.1953 −0.877347
\(641\) 38.1557 1.50706 0.753530 0.657413i \(-0.228349\pi\)
0.753530 + 0.657413i \(0.228349\pi\)
\(642\) −27.0280 −1.06671
\(643\) 10.3160 0.406821 0.203411 0.979093i \(-0.434797\pi\)
0.203411 + 0.979093i \(0.434797\pi\)
\(644\) 22.7373 0.895976
\(645\) −30.0384 −1.18276
\(646\) −12.1250 −0.477052
\(647\) −11.9820 −0.471061 −0.235531 0.971867i \(-0.575683\pi\)
−0.235531 + 0.971867i \(0.575683\pi\)
\(648\) −82.3761 −3.23604
\(649\) −45.6047 −1.79014
\(650\) −36.2882 −1.42334
\(651\) 111.493 4.36977
\(652\) 25.4635 0.997226
\(653\) −1.76915 −0.0692323 −0.0346161 0.999401i \(-0.511021\pi\)
−0.0346161 + 0.999401i \(0.511021\pi\)
\(654\) −10.7262 −0.419428
\(655\) −16.8494 −0.658361
\(656\) −4.46287 −0.174246
\(657\) −27.4159 −1.06960
\(658\) 85.5705 3.33588
\(659\) −2.03827 −0.0793997 −0.0396999 0.999212i \(-0.512640\pi\)
−0.0396999 + 0.999212i \(0.512640\pi\)
\(660\) −50.1737 −1.95301
\(661\) 14.7410 0.573357 0.286679 0.958027i \(-0.407449\pi\)
0.286679 + 0.958027i \(0.407449\pi\)
\(662\) 49.2297 1.91337
\(663\) −13.9372 −0.541274
\(664\) −1.13772 −0.0441522
\(665\) 21.6495 0.839531
\(666\) 90.0262 3.48844
\(667\) 1.68482 0.0652365
\(668\) 25.8298 0.999386
\(669\) 24.2203 0.936411
\(670\) −30.6239 −1.18310
\(671\) −8.29189 −0.320105
\(672\) −59.0824 −2.27915
\(673\) 22.5140 0.867852 0.433926 0.900948i \(-0.357128\pi\)
0.433926 + 0.900948i \(0.357128\pi\)
\(674\) 29.6003 1.14016
\(675\) −55.5868 −2.13954
\(676\) 17.5930 0.676652
\(677\) −38.3223 −1.47285 −0.736423 0.676521i \(-0.763487\pi\)
−0.736423 + 0.676521i \(0.763487\pi\)
\(678\) −9.55991 −0.367146
\(679\) −10.0860 −0.387065
\(680\) 3.58821 0.137602
\(681\) 42.6307 1.63361
\(682\) 87.9774 3.36883
\(683\) 45.1175 1.72637 0.863187 0.504885i \(-0.168465\pi\)
0.863187 + 0.504885i \(0.168465\pi\)
\(684\) 134.080 5.12668
\(685\) 12.8687 0.491689
\(686\) −9.57488 −0.365570
\(687\) −88.5516 −3.37845
\(688\) 4.06362 0.154924
\(689\) 17.3812 0.662170
\(690\) −16.4705 −0.627020
\(691\) 8.83381 0.336054 0.168027 0.985782i \(-0.446260\pi\)
0.168027 + 0.985782i \(0.446260\pi\)
\(692\) −44.1178 −1.67711
\(693\) −109.229 −4.14928
\(694\) −28.9398 −1.09854
\(695\) 10.6735 0.404868
\(696\) 9.03055 0.342302
\(697\) −8.77913 −0.332533
\(698\) 23.4378 0.887134
\(699\) −55.5595 −2.10145
\(700\) 44.0574 1.66521
\(701\) −16.1642 −0.610512 −0.305256 0.952270i \(-0.598742\pi\)
−0.305256 + 0.952270i \(0.598742\pi\)
\(702\) 149.531 5.64367
\(703\) −26.7213 −1.00781
\(704\) −50.6767 −1.90995
\(705\) −38.8003 −1.46130
\(706\) −2.31236 −0.0870266
\(707\) −50.3363 −1.89309
\(708\) −124.806 −4.69050
\(709\) 33.3612 1.25290 0.626452 0.779460i \(-0.284506\pi\)
0.626452 + 0.779460i \(0.284506\pi\)
\(710\) −15.2804 −0.573464
\(711\) −38.6306 −1.44876
\(712\) 31.6207 1.18504
\(713\) 18.0778 0.677019
\(714\) 27.0323 1.01166
\(715\) 19.6364 0.734360
\(716\) −3.37730 −0.126216
\(717\) −27.5202 −1.02776
\(718\) 14.0442 0.524124
\(719\) 1.82738 0.0681499 0.0340750 0.999419i \(-0.489152\pi\)
0.0340750 + 0.999419i \(0.489152\pi\)
\(720\) −4.47410 −0.166740
\(721\) −48.1514 −1.79325
\(722\) −19.6435 −0.731057
\(723\) 5.99614 0.222999
\(724\) −33.2398 −1.23535
\(725\) 3.26462 0.121245
\(726\) −37.0674 −1.37570
\(727\) 42.9680 1.59359 0.796797 0.604247i \(-0.206526\pi\)
0.796797 + 0.604247i \(0.206526\pi\)
\(728\) −47.6965 −1.76775
\(729\) 53.9529 1.99826
\(730\) −9.55948 −0.353812
\(731\) 7.99375 0.295659
\(732\) −22.6924 −0.838734
\(733\) −9.21150 −0.340235 −0.170117 0.985424i \(-0.554415\pi\)
−0.170117 + 0.985424i \(0.554415\pi\)
\(734\) 4.02144 0.148434
\(735\) −21.9626 −0.810104
\(736\) −9.57976 −0.353115
\(737\) −45.8607 −1.68930
\(738\) 155.092 5.70902
\(739\) −9.85307 −0.362451 −0.181226 0.983442i \(-0.558006\pi\)
−0.181226 + 0.983442i \(0.558006\pi\)
\(740\) 19.6492 0.722319
\(741\) −73.0805 −2.68468
\(742\) −33.7123 −1.23762
\(743\) 24.5063 0.899048 0.449524 0.893268i \(-0.351594\pi\)
0.449524 + 0.893268i \(0.351594\pi\)
\(744\) 96.8962 3.55239
\(745\) 17.2352 0.631448
\(746\) 76.1330 2.78743
\(747\) 2.79063 0.102104
\(748\) 13.3521 0.488201
\(749\) −12.8426 −0.469258
\(750\) −75.3604 −2.75177
\(751\) 7.70312 0.281091 0.140545 0.990074i \(-0.455114\pi\)
0.140545 + 0.990074i \(0.455114\pi\)
\(752\) 5.24893 0.191409
\(753\) −91.3924 −3.33053
\(754\) −8.78194 −0.319819
\(755\) −15.6639 −0.570067
\(756\) −181.545 −6.60272
\(757\) 41.6208 1.51274 0.756368 0.654147i \(-0.226972\pi\)
0.756368 + 0.654147i \(0.226972\pi\)
\(758\) 19.5180 0.708925
\(759\) −24.6653 −0.895294
\(760\) 18.8150 0.682493
\(761\) 39.6205 1.43624 0.718121 0.695918i \(-0.245002\pi\)
0.718121 + 0.695918i \(0.245002\pi\)
\(762\) 36.5138 1.32276
\(763\) −5.09666 −0.184512
\(764\) −75.2627 −2.72291
\(765\) −8.80122 −0.318209
\(766\) 14.7413 0.532626
\(767\) 48.8452 1.76370
\(768\) −62.4468 −2.25336
\(769\) 4.09206 0.147564 0.0737818 0.997274i \(-0.476493\pi\)
0.0737818 + 0.997274i \(0.476493\pi\)
\(770\) −38.0864 −1.37254
\(771\) −9.75263 −0.351233
\(772\) −75.2417 −2.70801
\(773\) −2.54936 −0.0916942 −0.0458471 0.998948i \(-0.514599\pi\)
−0.0458471 + 0.998948i \(0.514599\pi\)
\(774\) −141.217 −5.07595
\(775\) 35.0288 1.25827
\(776\) −8.76548 −0.314662
\(777\) 59.5743 2.13722
\(778\) −19.0194 −0.681879
\(779\) −46.0340 −1.64934
\(780\) 53.7388 1.92416
\(781\) −22.8832 −0.818824
\(782\) 4.38308 0.156738
\(783\) −13.4523 −0.480747
\(784\) 2.97112 0.106111
\(785\) −26.5452 −0.947438
\(786\) −110.318 −3.93492
\(787\) −0.169565 −0.00604436 −0.00302218 0.999995i \(-0.500962\pi\)
−0.00302218 + 0.999995i \(0.500962\pi\)
\(788\) −19.7860 −0.704846
\(789\) −27.0013 −0.961270
\(790\) −13.4698 −0.479235
\(791\) −4.54248 −0.161512
\(792\) −94.9285 −3.37314
\(793\) 8.88108 0.315376
\(794\) 55.6140 1.97367
\(795\) 15.2862 0.542145
\(796\) 13.3086 0.471709
\(797\) 19.5849 0.693732 0.346866 0.937915i \(-0.387246\pi\)
0.346866 + 0.937915i \(0.387246\pi\)
\(798\) 141.746 5.01774
\(799\) 10.3254 0.365288
\(800\) −18.5624 −0.656279
\(801\) −77.5598 −2.74044
\(802\) 87.8891 3.10347
\(803\) −14.3158 −0.505193
\(804\) −125.507 −4.42628
\(805\) −7.82609 −0.275834
\(806\) −94.2287 −3.31906
\(807\) −104.715 −3.68614
\(808\) −43.7460 −1.53898
\(809\) 26.8590 0.944312 0.472156 0.881515i \(-0.343476\pi\)
0.472156 + 0.881515i \(0.343476\pi\)
\(810\) 70.4527 2.47545
\(811\) −26.7078 −0.937838 −0.468919 0.883241i \(-0.655356\pi\)
−0.468919 + 0.883241i \(0.655356\pi\)
\(812\) 10.6621 0.374167
\(813\) 88.9320 3.11898
\(814\) 47.0090 1.64766
\(815\) −8.76441 −0.307004
\(816\) 1.65817 0.0580477
\(817\) 41.9158 1.46645
\(818\) −78.4490 −2.74290
\(819\) 116.991 4.08799
\(820\) 33.8505 1.18211
\(821\) −45.2479 −1.57916 −0.789581 0.613647i \(-0.789702\pi\)
−0.789581 + 0.613647i \(0.789702\pi\)
\(822\) 84.2555 2.93875
\(823\) −23.8418 −0.831073 −0.415537 0.909576i \(-0.636406\pi\)
−0.415537 + 0.909576i \(0.636406\pi\)
\(824\) −41.8471 −1.45781
\(825\) −47.7932 −1.66394
\(826\) −94.7393 −3.29640
\(827\) −14.2975 −0.497172 −0.248586 0.968610i \(-0.579966\pi\)
−0.248586 + 0.968610i \(0.579966\pi\)
\(828\) −48.4687 −1.68441
\(829\) 1.97498 0.0685937 0.0342969 0.999412i \(-0.489081\pi\)
0.0342969 + 0.999412i \(0.489081\pi\)
\(830\) 0.973045 0.0337749
\(831\) 3.19231 0.110740
\(832\) 54.2776 1.88174
\(833\) 5.84464 0.202505
\(834\) 69.8825 2.41983
\(835\) −8.89052 −0.307669
\(836\) 70.0126 2.42144
\(837\) −144.341 −4.98916
\(838\) 80.9454 2.79621
\(839\) −9.24858 −0.319296 −0.159648 0.987174i \(-0.551036\pi\)
−0.159648 + 0.987174i \(0.551036\pi\)
\(840\) −41.9475 −1.44733
\(841\) −28.2099 −0.972757
\(842\) −46.9340 −1.61745
\(843\) −57.1803 −1.96940
\(844\) −14.4467 −0.497277
\(845\) −6.05542 −0.208313
\(846\) −182.409 −6.27135
\(847\) −17.6129 −0.605187
\(848\) −2.06793 −0.0710129
\(849\) 4.23297 0.145275
\(850\) 8.49294 0.291305
\(851\) 9.65952 0.331124
\(852\) −62.6242 −2.14547
\(853\) −37.3539 −1.27897 −0.639486 0.768803i \(-0.720853\pi\)
−0.639486 + 0.768803i \(0.720853\pi\)
\(854\) −17.2256 −0.589448
\(855\) −46.1498 −1.57829
\(856\) −11.1612 −0.381481
\(857\) 0.403087 0.0137692 0.00688459 0.999976i \(-0.497809\pi\)
0.00688459 + 0.999976i \(0.497809\pi\)
\(858\) 128.565 4.38915
\(859\) 9.88573 0.337297 0.168648 0.985676i \(-0.446060\pi\)
0.168648 + 0.985676i \(0.446060\pi\)
\(860\) −30.8222 −1.05103
\(861\) 102.631 3.49767
\(862\) 82.8601 2.82223
\(863\) −29.8666 −1.01667 −0.508335 0.861159i \(-0.669739\pi\)
−0.508335 + 0.861159i \(0.669739\pi\)
\(864\) 76.4890 2.60221
\(865\) 15.1852 0.516312
\(866\) −58.5097 −1.98824
\(867\) 3.26187 0.110779
\(868\) 114.403 3.88308
\(869\) −20.1717 −0.684279
\(870\) −7.72343 −0.261849
\(871\) 49.1194 1.66435
\(872\) −4.42938 −0.149998
\(873\) 21.5001 0.727669
\(874\) 22.9830 0.777411
\(875\) −35.8082 −1.21054
\(876\) −39.1779 −1.32370
\(877\) −12.5636 −0.424243 −0.212122 0.977243i \(-0.568037\pi\)
−0.212122 + 0.977243i \(0.568037\pi\)
\(878\) −74.0721 −2.49981
\(879\) 108.329 3.65385
\(880\) −2.33624 −0.0787546
\(881\) 39.5541 1.33261 0.666306 0.745678i \(-0.267874\pi\)
0.666306 + 0.745678i \(0.267874\pi\)
\(882\) −103.251 −3.47665
\(883\) 37.9863 1.27834 0.639171 0.769065i \(-0.279278\pi\)
0.639171 + 0.769065i \(0.279278\pi\)
\(884\) −14.3008 −0.480989
\(885\) 42.9578 1.44401
\(886\) −53.0586 −1.78254
\(887\) −59.2432 −1.98919 −0.994595 0.103827i \(-0.966891\pi\)
−0.994595 + 0.103827i \(0.966891\pi\)
\(888\) 51.7746 1.73744
\(889\) 17.3499 0.581896
\(890\) −27.0438 −0.906510
\(891\) 105.506 3.53459
\(892\) 24.8523 0.832116
\(893\) 54.1422 1.81180
\(894\) 112.844 3.77406
\(895\) 1.16245 0.0388566
\(896\) −69.0498 −2.30679
\(897\) 26.4179 0.882069
\(898\) 72.1706 2.40836
\(899\) 8.47716 0.282729
\(900\) −93.9163 −3.13054
\(901\) −4.06792 −0.135522
\(902\) 80.9844 2.69649
\(903\) −93.4498 −3.10982
\(904\) −3.94775 −0.131300
\(905\) 11.4410 0.380312
\(906\) −102.556 −3.40720
\(907\) −16.4680 −0.546810 −0.273405 0.961899i \(-0.588150\pi\)
−0.273405 + 0.961899i \(0.588150\pi\)
\(908\) 43.7430 1.45166
\(909\) 107.301 3.55895
\(910\) 40.7927 1.35226
\(911\) −29.3614 −0.972787 −0.486393 0.873740i \(-0.661688\pi\)
−0.486393 + 0.873740i \(0.661688\pi\)
\(912\) 8.69475 0.287912
\(913\) 1.45718 0.0482257
\(914\) 41.9856 1.38876
\(915\) 7.81062 0.258211
\(916\) −90.8622 −3.00217
\(917\) −52.4187 −1.73102
\(918\) −34.9964 −1.15505
\(919\) 27.9161 0.920867 0.460433 0.887694i \(-0.347694\pi\)
0.460433 + 0.887694i \(0.347694\pi\)
\(920\) −6.80146 −0.224238
\(921\) 49.8533 1.64272
\(922\) 9.41452 0.310051
\(923\) 24.5091 0.806728
\(924\) −156.091 −5.13501
\(925\) 18.7169 0.615409
\(926\) −1.25286 −0.0411714
\(927\) 102.643 3.37125
\(928\) −4.49220 −0.147464
\(929\) 27.1665 0.891304 0.445652 0.895206i \(-0.352972\pi\)
0.445652 + 0.895206i \(0.352972\pi\)
\(930\) −82.8710 −2.71745
\(931\) 30.6468 1.00441
\(932\) −57.0092 −1.86740
\(933\) −6.80819 −0.222890
\(934\) −66.7190 −2.18311
\(935\) −4.59573 −0.150297
\(936\) 101.674 3.32331
\(937\) 51.5572 1.68430 0.842150 0.539244i \(-0.181290\pi\)
0.842150 + 0.539244i \(0.181290\pi\)
\(938\) −95.2712 −3.11071
\(939\) −35.9305 −1.17255
\(940\) −39.8127 −1.29855
\(941\) 54.6798 1.78251 0.891255 0.453502i \(-0.149826\pi\)
0.891255 + 0.453502i \(0.149826\pi\)
\(942\) −173.799 −5.66268
\(943\) 16.6409 0.541901
\(944\) −5.81135 −0.189143
\(945\) 62.4869 2.03270
\(946\) −73.7395 −2.39748
\(947\) 31.7075 1.03036 0.515178 0.857083i \(-0.327726\pi\)
0.515178 + 0.857083i \(0.327726\pi\)
\(948\) −55.2038 −1.79294
\(949\) 15.3330 0.497730
\(950\) 44.5333 1.44485
\(951\) 7.95315 0.257898
\(952\) 11.1630 0.361793
\(953\) 42.4695 1.37572 0.687861 0.725842i \(-0.258550\pi\)
0.687861 + 0.725842i \(0.258550\pi\)
\(954\) 71.8638 2.32668
\(955\) 25.9051 0.838269
\(956\) −28.2383 −0.913291
\(957\) −11.5662 −0.373883
\(958\) 38.0723 1.23006
\(959\) 40.0348 1.29279
\(960\) 47.7354 1.54065
\(961\) 59.9584 1.93414
\(962\) −50.3492 −1.62332
\(963\) 27.3763 0.882190
\(964\) 6.15260 0.198162
\(965\) 25.8979 0.833682
\(966\) −51.2398 −1.64861
\(967\) −16.5359 −0.531757 −0.265879 0.964006i \(-0.585662\pi\)
−0.265879 + 0.964006i \(0.585662\pi\)
\(968\) −15.3069 −0.491984
\(969\) 17.1039 0.549455
\(970\) 7.49673 0.240705
\(971\) −38.5556 −1.23731 −0.618654 0.785663i \(-0.712322\pi\)
−0.618654 + 0.785663i \(0.712322\pi\)
\(972\) 136.773 4.38701
\(973\) 33.2053 1.06451
\(974\) −15.4260 −0.494280
\(975\) 51.1891 1.63936
\(976\) −1.05663 −0.0338218
\(977\) −36.7138 −1.17458 −0.587289 0.809377i \(-0.699805\pi\)
−0.587289 + 0.809377i \(0.699805\pi\)
\(978\) −57.3832 −1.83491
\(979\) −40.4994 −1.29437
\(980\) −22.5357 −0.719877
\(981\) 10.8645 0.346876
\(982\) −68.9517 −2.20034
\(983\) −42.7103 −1.36225 −0.681123 0.732169i \(-0.738508\pi\)
−0.681123 + 0.732169i \(0.738508\pi\)
\(984\) 89.1943 2.84341
\(985\) 6.81025 0.216993
\(986\) 2.05534 0.0654553
\(987\) −120.708 −3.84218
\(988\) −74.9874 −2.38567
\(989\) −15.1522 −0.481811
\(990\) 81.1881 2.58033
\(991\) 10.9158 0.346751 0.173375 0.984856i \(-0.444533\pi\)
0.173375 + 0.984856i \(0.444533\pi\)
\(992\) −48.2005 −1.53037
\(993\) −69.4448 −2.20376
\(994\) −47.5375 −1.50780
\(995\) −4.58075 −0.145220
\(996\) 3.98786 0.126360
\(997\) 0.555837 0.0176035 0.00880177 0.999961i \(-0.497198\pi\)
0.00880177 + 0.999961i \(0.497198\pi\)
\(998\) −84.6080 −2.67822
\(999\) −77.1258 −2.44015
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 \(a_p\))