Properties

Label 8018.2.a.f.1.19
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 34
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(34\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-0.350444 q^{3}\) \(+1.00000 q^{4}\) \(-0.178230 q^{5}\) \(+0.350444 q^{6}\) \(-3.90849 q^{7}\) \(-1.00000 q^{8}\) \(-2.87719 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-0.350444 q^{3}\) \(+1.00000 q^{4}\) \(-0.178230 q^{5}\) \(+0.350444 q^{6}\) \(-3.90849 q^{7}\) \(-1.00000 q^{8}\) \(-2.87719 q^{9}\) \(+0.178230 q^{10}\) \(-1.52727 q^{11}\) \(-0.350444 q^{12}\) \(-0.315173 q^{13}\) \(+3.90849 q^{14}\) \(+0.0624595 q^{15}\) \(+1.00000 q^{16}\) \(+6.70888 q^{17}\) \(+2.87719 q^{18}\) \(-1.00000 q^{19}\) \(-0.178230 q^{20}\) \(+1.36971 q^{21}\) \(+1.52727 q^{22}\) \(-3.64189 q^{23}\) \(+0.350444 q^{24}\) \(-4.96823 q^{25}\) \(+0.315173 q^{26}\) \(+2.05962 q^{27}\) \(-3.90849 q^{28}\) \(+7.13883 q^{29}\) \(-0.0624595 q^{30}\) \(+7.92567 q^{31}\) \(-1.00000 q^{32}\) \(+0.535221 q^{33}\) \(-6.70888 q^{34}\) \(+0.696609 q^{35}\) \(-2.87719 q^{36}\) \(+7.58524 q^{37}\) \(+1.00000 q^{38}\) \(+0.110451 q^{39}\) \(+0.178230 q^{40}\) \(-5.82883 q^{41}\) \(-1.36971 q^{42}\) \(-4.70286 q^{43}\) \(-1.52727 q^{44}\) \(+0.512800 q^{45}\) \(+3.64189 q^{46}\) \(-1.67658 q^{47}\) \(-0.350444 q^{48}\) \(+8.27632 q^{49}\) \(+4.96823 q^{50}\) \(-2.35108 q^{51}\) \(-0.315173 q^{52}\) \(+3.11276 q^{53}\) \(-2.05962 q^{54}\) \(+0.272204 q^{55}\) \(+3.90849 q^{56}\) \(+0.350444 q^{57}\) \(-7.13883 q^{58}\) \(-13.1462 q^{59}\) \(+0.0624595 q^{60}\) \(+3.19516 q^{61}\) \(-7.92567 q^{62}\) \(+11.2455 q^{63}\) \(+1.00000 q^{64}\) \(+0.0561732 q^{65}\) \(-0.535221 q^{66}\) \(+2.05631 q^{67}\) \(+6.70888 q^{68}\) \(+1.27628 q^{69}\) \(-0.696609 q^{70}\) \(+5.71954 q^{71}\) \(+2.87719 q^{72}\) \(+5.78654 q^{73}\) \(-7.58524 q^{74}\) \(+1.74109 q^{75}\) \(-1.00000 q^{76}\) \(+5.96931 q^{77}\) \(-0.110451 q^{78}\) \(-5.62658 q^{79}\) \(-0.178230 q^{80}\) \(+7.90979 q^{81}\) \(+5.82883 q^{82}\) \(+5.96257 q^{83}\) \(+1.36971 q^{84}\) \(-1.19572 q^{85}\) \(+4.70286 q^{86}\) \(-2.50176 q^{87}\) \(+1.52727 q^{88}\) \(+6.61534 q^{89}\) \(-0.512800 q^{90}\) \(+1.23185 q^{91}\) \(-3.64189 q^{92}\) \(-2.77750 q^{93}\) \(+1.67658 q^{94}\) \(+0.178230 q^{95}\) \(+0.350444 q^{96}\) \(+5.63552 q^{97}\) \(-8.27632 q^{98}\) \(+4.39423 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut -\mathstrut 7q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut -\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 34q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 38q^{18} \) \(\mathstrut -\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 7q^{20} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 31q^{27} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 17q^{30} \) \(\mathstrut -\mathstrut 28q^{31} \) \(\mathstrut -\mathstrut 34q^{32} \) \(\mathstrut -\mathstrut 16q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 36q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 7q^{40} \) \(\mathstrut +\mathstrut 9q^{41} \) \(\mathstrut -\mathstrut 24q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 22q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut -\mathstrut 29q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 22q^{49} \) \(\mathstrut -\mathstrut 5q^{50} \) \(\mathstrut -\mathstrut 21q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut -\mathstrut 9q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut -\mathstrut 28q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 24q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 23q^{61} \) \(\mathstrut +\mathstrut 28q^{62} \) \(\mathstrut -\mathstrut 27q^{63} \) \(\mathstrut +\mathstrut 34q^{64} \) \(\mathstrut -\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 16q^{66} \) \(\mathstrut -\mathstrut 51q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 17q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut -\mathstrut 38q^{72} \) \(\mathstrut -\mathstrut 26q^{73} \) \(\mathstrut +\mathstrut 36q^{74} \) \(\mathstrut -\mathstrut 109q^{75} \) \(\mathstrut -\mathstrut 34q^{76} \) \(\mathstrut -\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 9q^{78} \) \(\mathstrut -\mathstrut 36q^{79} \) \(\mathstrut +\mathstrut 7q^{80} \) \(\mathstrut +\mathstrut 6q^{81} \) \(\mathstrut -\mathstrut 9q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 22q^{90} \) \(\mathstrut -\mathstrut 41q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut -\mathstrut 33q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut -\mathstrut 56q^{97} \) \(\mathstrut -\mathstrut 22q^{98} \) \(\mathstrut -\mathstrut 28q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −0.350444 −0.202329 −0.101164 0.994870i \(-0.532257\pi\)
−0.101164 + 0.994870i \(0.532257\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.178230 −0.0797067 −0.0398534 0.999206i \(-0.512689\pi\)
−0.0398534 + 0.999206i \(0.512689\pi\)
\(6\) 0.350444 0.143068
\(7\) −3.90849 −1.47727 −0.738636 0.674105i \(-0.764530\pi\)
−0.738636 + 0.674105i \(0.764530\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.87719 −0.959063
\(10\) 0.178230 0.0563612
\(11\) −1.52727 −0.460488 −0.230244 0.973133i \(-0.573952\pi\)
−0.230244 + 0.973133i \(0.573952\pi\)
\(12\) −0.350444 −0.101164
\(13\) −0.315173 −0.0874134 −0.0437067 0.999044i \(-0.513917\pi\)
−0.0437067 + 0.999044i \(0.513917\pi\)
\(14\) 3.90849 1.04459
\(15\) 0.0624595 0.0161270
\(16\) 1.00000 0.250000
\(17\) 6.70888 1.62714 0.813571 0.581466i \(-0.197520\pi\)
0.813571 + 0.581466i \(0.197520\pi\)
\(18\) 2.87719 0.678160
\(19\) −1.00000 −0.229416
\(20\) −0.178230 −0.0398534
\(21\) 1.36971 0.298895
\(22\) 1.52727 0.325614
\(23\) −3.64189 −0.759387 −0.379693 0.925112i \(-0.623971\pi\)
−0.379693 + 0.925112i \(0.623971\pi\)
\(24\) 0.350444 0.0715340
\(25\) −4.96823 −0.993647
\(26\) 0.315173 0.0618106
\(27\) 2.05962 0.396375
\(28\) −3.90849 −0.738636
\(29\) 7.13883 1.32565 0.662824 0.748775i \(-0.269358\pi\)
0.662824 + 0.748775i \(0.269358\pi\)
\(30\) −0.0624595 −0.0114035
\(31\) 7.92567 1.42349 0.711746 0.702436i \(-0.247905\pi\)
0.711746 + 0.702436i \(0.247905\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.535221 0.0931700
\(34\) −6.70888 −1.15056
\(35\) 0.696609 0.117748
\(36\) −2.87719 −0.479532
\(37\) 7.58524 1.24701 0.623503 0.781821i \(-0.285709\pi\)
0.623503 + 0.781821i \(0.285709\pi\)
\(38\) 1.00000 0.162221
\(39\) 0.110451 0.0176862
\(40\) 0.178230 0.0281806
\(41\) −5.82883 −0.910310 −0.455155 0.890412i \(-0.650416\pi\)
−0.455155 + 0.890412i \(0.650416\pi\)
\(42\) −1.36971 −0.211350
\(43\) −4.70286 −0.717180 −0.358590 0.933495i \(-0.616742\pi\)
−0.358590 + 0.933495i \(0.616742\pi\)
\(44\) −1.52727 −0.230244
\(45\) 0.512800 0.0764438
\(46\) 3.64189 0.536968
\(47\) −1.67658 −0.244555 −0.122277 0.992496i \(-0.539020\pi\)
−0.122277 + 0.992496i \(0.539020\pi\)
\(48\) −0.350444 −0.0505822
\(49\) 8.27632 1.18233
\(50\) 4.96823 0.702614
\(51\) −2.35108 −0.329218
\(52\) −0.315173 −0.0437067
\(53\) 3.11276 0.427570 0.213785 0.976881i \(-0.431421\pi\)
0.213785 + 0.976881i \(0.431421\pi\)
\(54\) −2.05962 −0.280279
\(55\) 0.272204 0.0367040
\(56\) 3.90849 0.522294
\(57\) 0.350444 0.0464174
\(58\) −7.13883 −0.937375
\(59\) −13.1462 −1.71149 −0.855746 0.517397i \(-0.826901\pi\)
−0.855746 + 0.517397i \(0.826901\pi\)
\(60\) 0.0624595 0.00806348
\(61\) 3.19516 0.409098 0.204549 0.978856i \(-0.434427\pi\)
0.204549 + 0.978856i \(0.434427\pi\)
\(62\) −7.92567 −1.00656
\(63\) 11.2455 1.41680
\(64\) 1.00000 0.125000
\(65\) 0.0561732 0.00696743
\(66\) −0.535221 −0.0658811
\(67\) 2.05631 0.251218 0.125609 0.992080i \(-0.459912\pi\)
0.125609 + 0.992080i \(0.459912\pi\)
\(68\) 6.70888 0.813571
\(69\) 1.27628 0.153646
\(70\) −0.696609 −0.0832607
\(71\) 5.71954 0.678785 0.339393 0.940645i \(-0.389779\pi\)
0.339393 + 0.940645i \(0.389779\pi\)
\(72\) 2.87719 0.339080
\(73\) 5.78654 0.677263 0.338631 0.940919i \(-0.390036\pi\)
0.338631 + 0.940919i \(0.390036\pi\)
\(74\) −7.58524 −0.881766
\(75\) 1.74109 0.201043
\(76\) −1.00000 −0.114708
\(77\) 5.96931 0.680266
\(78\) −0.110451 −0.0125061
\(79\) −5.62658 −0.633040 −0.316520 0.948586i \(-0.602514\pi\)
−0.316520 + 0.948586i \(0.602514\pi\)
\(80\) −0.178230 −0.0199267
\(81\) 7.90979 0.878865
\(82\) 5.82883 0.643686
\(83\) 5.96257 0.654478 0.327239 0.944942i \(-0.393882\pi\)
0.327239 + 0.944942i \(0.393882\pi\)
\(84\) 1.36971 0.149447
\(85\) −1.19572 −0.129694
\(86\) 4.70286 0.507123
\(87\) −2.50176 −0.268217
\(88\) 1.52727 0.162807
\(89\) 6.61534 0.701225 0.350613 0.936521i \(-0.385973\pi\)
0.350613 + 0.936521i \(0.385973\pi\)
\(90\) −0.512800 −0.0540539
\(91\) 1.23185 0.129133
\(92\) −3.64189 −0.379693
\(93\) −2.77750 −0.288014
\(94\) 1.67658 0.172926
\(95\) 0.178230 0.0182860
\(96\) 0.350444 0.0357670
\(97\) 5.63552 0.572201 0.286100 0.958200i \(-0.407641\pi\)
0.286100 + 0.958200i \(0.407641\pi\)
\(98\) −8.27632 −0.836034
\(99\) 4.39423 0.441637
\(100\) −4.96823 −0.496823
\(101\) 3.83173 0.381272 0.190636 0.981661i \(-0.438945\pi\)
0.190636 + 0.981661i \(0.438945\pi\)
\(102\) 2.35108 0.232792
\(103\) −1.12275 −0.110628 −0.0553138 0.998469i \(-0.517616\pi\)
−0.0553138 + 0.998469i \(0.517616\pi\)
\(104\) 0.315173 0.0309053
\(105\) −0.244122 −0.0238239
\(106\) −3.11276 −0.302338
\(107\) −0.421369 −0.0407353 −0.0203677 0.999793i \(-0.506484\pi\)
−0.0203677 + 0.999793i \(0.506484\pi\)
\(108\) 2.05962 0.198187
\(109\) 19.8217 1.89857 0.949287 0.314411i \(-0.101807\pi\)
0.949287 + 0.314411i \(0.101807\pi\)
\(110\) −0.272204 −0.0259536
\(111\) −2.65820 −0.252305
\(112\) −3.90849 −0.369318
\(113\) 3.23659 0.304472 0.152236 0.988344i \(-0.451353\pi\)
0.152236 + 0.988344i \(0.451353\pi\)
\(114\) −0.350444 −0.0328221
\(115\) 0.649093 0.0605282
\(116\) 7.13883 0.662824
\(117\) 0.906814 0.0838350
\(118\) 13.1462 1.21021
\(119\) −26.2216 −2.40373
\(120\) −0.0624595 −0.00570174
\(121\) −8.66746 −0.787951
\(122\) −3.19516 −0.289276
\(123\) 2.04268 0.184182
\(124\) 7.92567 0.711746
\(125\) 1.77663 0.158907
\(126\) −11.2455 −1.00183
\(127\) −2.71343 −0.240778 −0.120389 0.992727i \(-0.538414\pi\)
−0.120389 + 0.992727i \(0.538414\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.64809 0.145106
\(130\) −0.0561732 −0.00492672
\(131\) −5.20115 −0.454427 −0.227213 0.973845i \(-0.572961\pi\)
−0.227213 + 0.973845i \(0.572961\pi\)
\(132\) 0.535221 0.0465850
\(133\) 3.90849 0.338909
\(134\) −2.05631 −0.177638
\(135\) −0.367086 −0.0315937
\(136\) −6.70888 −0.575282
\(137\) −10.8685 −0.928556 −0.464278 0.885690i \(-0.653686\pi\)
−0.464278 + 0.885690i \(0.653686\pi\)
\(138\) −1.27628 −0.108644
\(139\) 0.716808 0.0607989 0.0303994 0.999538i \(-0.490322\pi\)
0.0303994 + 0.999538i \(0.490322\pi\)
\(140\) 0.696609 0.0588742
\(141\) 0.587547 0.0494804
\(142\) −5.71954 −0.479973
\(143\) 0.481354 0.0402528
\(144\) −2.87719 −0.239766
\(145\) −1.27235 −0.105663
\(146\) −5.78654 −0.478897
\(147\) −2.90038 −0.239220
\(148\) 7.58524 0.623503
\(149\) −12.5612 −1.02905 −0.514527 0.857474i \(-0.672032\pi\)
−0.514527 + 0.857474i \(0.672032\pi\)
\(150\) −1.74109 −0.142159
\(151\) 10.0366 0.816768 0.408384 0.912810i \(-0.366092\pi\)
0.408384 + 0.912810i \(0.366092\pi\)
\(152\) 1.00000 0.0811107
\(153\) −19.3027 −1.56053
\(154\) −5.96931 −0.481021
\(155\) −1.41259 −0.113462
\(156\) 0.110451 0.00884312
\(157\) −10.5317 −0.840524 −0.420262 0.907403i \(-0.638062\pi\)
−0.420262 + 0.907403i \(0.638062\pi\)
\(158\) 5.62658 0.447627
\(159\) −1.09085 −0.0865098
\(160\) 0.178230 0.0140903
\(161\) 14.2343 1.12182
\(162\) −7.90979 −0.621451
\(163\) −2.70092 −0.211552 −0.105776 0.994390i \(-0.533733\pi\)
−0.105776 + 0.994390i \(0.533733\pi\)
\(164\) −5.82883 −0.455155
\(165\) −0.0953922 −0.00742627
\(166\) −5.96257 −0.462786
\(167\) 13.5906 1.05167 0.525836 0.850586i \(-0.323752\pi\)
0.525836 + 0.850586i \(0.323752\pi\)
\(168\) −1.36971 −0.105675
\(169\) −12.9007 −0.992359
\(170\) 1.19572 0.0917076
\(171\) 2.87719 0.220024
\(172\) −4.70286 −0.358590
\(173\) 18.5724 1.41204 0.706018 0.708194i \(-0.250490\pi\)
0.706018 + 0.708194i \(0.250490\pi\)
\(174\) 2.50176 0.189658
\(175\) 19.4183 1.46789
\(176\) −1.52727 −0.115122
\(177\) 4.60701 0.346284
\(178\) −6.61534 −0.495841
\(179\) 12.9704 0.969452 0.484726 0.874666i \(-0.338919\pi\)
0.484726 + 0.874666i \(0.338919\pi\)
\(180\) 0.512800 0.0382219
\(181\) −9.98409 −0.742112 −0.371056 0.928611i \(-0.621004\pi\)
−0.371056 + 0.928611i \(0.621004\pi\)
\(182\) −1.23185 −0.0913110
\(183\) −1.11972 −0.0827723
\(184\) 3.64189 0.268484
\(185\) −1.35191 −0.0993947
\(186\) 2.77750 0.203656
\(187\) −10.2462 −0.749279
\(188\) −1.67658 −0.122277
\(189\) −8.05003 −0.585553
\(190\) −0.178230 −0.0129301
\(191\) −0.371920 −0.0269112 −0.0134556 0.999909i \(-0.504283\pi\)
−0.0134556 + 0.999909i \(0.504283\pi\)
\(192\) −0.350444 −0.0252911
\(193\) 3.37266 0.242770 0.121385 0.992606i \(-0.461267\pi\)
0.121385 + 0.992606i \(0.461267\pi\)
\(194\) −5.63552 −0.404607
\(195\) −0.0196856 −0.00140971
\(196\) 8.27632 0.591166
\(197\) −26.2737 −1.87193 −0.935963 0.352099i \(-0.885468\pi\)
−0.935963 + 0.352099i \(0.885468\pi\)
\(198\) −4.39423 −0.312285
\(199\) −6.26480 −0.444100 −0.222050 0.975035i \(-0.571275\pi\)
−0.222050 + 0.975035i \(0.571275\pi\)
\(200\) 4.96823 0.351307
\(201\) −0.720620 −0.0508286
\(202\) −3.83173 −0.269600
\(203\) −27.9021 −1.95834
\(204\) −2.35108 −0.164609
\(205\) 1.03887 0.0725578
\(206\) 1.12275 0.0782255
\(207\) 10.4784 0.728300
\(208\) −0.315173 −0.0218533
\(209\) 1.52727 0.105643
\(210\) 0.244122 0.0168460
\(211\) −1.00000 −0.0688428
\(212\) 3.11276 0.213785
\(213\) −2.00438 −0.137338
\(214\) 0.421369 0.0288042
\(215\) 0.838189 0.0571640
\(216\) −2.05962 −0.140140
\(217\) −30.9774 −2.10289
\(218\) −19.8217 −1.34249
\(219\) −2.02786 −0.137030
\(220\) 0.272204 0.0183520
\(221\) −2.11446 −0.142234
\(222\) 2.65820 0.178407
\(223\) 6.21424 0.416136 0.208068 0.978114i \(-0.433282\pi\)
0.208068 + 0.978114i \(0.433282\pi\)
\(224\) 3.90849 0.261147
\(225\) 14.2945 0.952970
\(226\) −3.23659 −0.215294
\(227\) −17.2456 −1.14463 −0.572314 0.820034i \(-0.693954\pi\)
−0.572314 + 0.820034i \(0.693954\pi\)
\(228\) 0.350444 0.0232087
\(229\) −0.785104 −0.0518811 −0.0259406 0.999663i \(-0.508258\pi\)
−0.0259406 + 0.999663i \(0.508258\pi\)
\(230\) −0.649093 −0.0427999
\(231\) −2.09191 −0.137637
\(232\) −7.13883 −0.468687
\(233\) −11.8271 −0.774821 −0.387411 0.921907i \(-0.626630\pi\)
−0.387411 + 0.921907i \(0.626630\pi\)
\(234\) −0.906814 −0.0592803
\(235\) 0.298817 0.0194926
\(236\) −13.1462 −0.855746
\(237\) 1.97180 0.128082
\(238\) 26.2216 1.69969
\(239\) −5.54195 −0.358479 −0.179239 0.983805i \(-0.557364\pi\)
−0.179239 + 0.983805i \(0.557364\pi\)
\(240\) 0.0624595 0.00403174
\(241\) 16.5329 1.06498 0.532489 0.846437i \(-0.321257\pi\)
0.532489 + 0.846437i \(0.321257\pi\)
\(242\) 8.66746 0.557165
\(243\) −8.95081 −0.574195
\(244\) 3.19516 0.204549
\(245\) −1.47509 −0.0942397
\(246\) −2.04268 −0.130236
\(247\) 0.315173 0.0200540
\(248\) −7.92567 −0.503281
\(249\) −2.08955 −0.132420
\(250\) −1.77663 −0.112364
\(251\) −3.08097 −0.194469 −0.0972344 0.995262i \(-0.531000\pi\)
−0.0972344 + 0.995262i \(0.531000\pi\)
\(252\) 11.2455 0.708398
\(253\) 5.56214 0.349688
\(254\) 2.71343 0.170256
\(255\) 0.419033 0.0262409
\(256\) 1.00000 0.0625000
\(257\) 0.207315 0.0129320 0.00646598 0.999979i \(-0.497942\pi\)
0.00646598 + 0.999979i \(0.497942\pi\)
\(258\) −1.64809 −0.102605
\(259\) −29.6468 −1.84217
\(260\) 0.0561732 0.00348372
\(261\) −20.5398 −1.27138
\(262\) 5.20115 0.321328
\(263\) −13.4049 −0.826583 −0.413291 0.910599i \(-0.635621\pi\)
−0.413291 + 0.910599i \(0.635621\pi\)
\(264\) −0.535221 −0.0329406
\(265\) −0.554786 −0.0340802
\(266\) −3.90849 −0.239645
\(267\) −2.31831 −0.141878
\(268\) 2.05631 0.125609
\(269\) −11.2749 −0.687441 −0.343721 0.939072i \(-0.611687\pi\)
−0.343721 + 0.939072i \(0.611687\pi\)
\(270\) 0.367086 0.0223401
\(271\) −23.7771 −1.44435 −0.722177 0.691708i \(-0.756859\pi\)
−0.722177 + 0.691708i \(0.756859\pi\)
\(272\) 6.70888 0.406786
\(273\) −0.431695 −0.0261274
\(274\) 10.8685 0.656588
\(275\) 7.58781 0.457562
\(276\) 1.27628 0.0768229
\(277\) −3.22032 −0.193490 −0.0967451 0.995309i \(-0.530843\pi\)
−0.0967451 + 0.995309i \(0.530843\pi\)
\(278\) −0.716808 −0.0429913
\(279\) −22.8037 −1.36522
\(280\) −0.696609 −0.0416304
\(281\) −24.0598 −1.43529 −0.717643 0.696411i \(-0.754779\pi\)
−0.717643 + 0.696411i \(0.754779\pi\)
\(282\) −0.587547 −0.0349879
\(283\) −17.9884 −1.06930 −0.534649 0.845074i \(-0.679556\pi\)
−0.534649 + 0.845074i \(0.679556\pi\)
\(284\) 5.71954 0.339393
\(285\) −0.0624595 −0.00369978
\(286\) −0.481354 −0.0284630
\(287\) 22.7819 1.34478
\(288\) 2.87719 0.169540
\(289\) 28.0090 1.64759
\(290\) 1.27235 0.0747151
\(291\) −1.97493 −0.115773
\(292\) 5.78654 0.338631
\(293\) −6.08806 −0.355668 −0.177834 0.984060i \(-0.556909\pi\)
−0.177834 + 0.984060i \(0.556909\pi\)
\(294\) 2.90038 0.169154
\(295\) 2.34304 0.136417
\(296\) −7.58524 −0.440883
\(297\) −3.14559 −0.182526
\(298\) 12.5612 0.727651
\(299\) 1.14783 0.0663806
\(300\) 1.74109 0.100522
\(301\) 18.3811 1.05947
\(302\) −10.0366 −0.577542
\(303\) −1.34281 −0.0771422
\(304\) −1.00000 −0.0573539
\(305\) −0.569471 −0.0326078
\(306\) 19.3027 1.10346
\(307\) −22.8889 −1.30634 −0.653169 0.757213i \(-0.726561\pi\)
−0.653169 + 0.757213i \(0.726561\pi\)
\(308\) 5.96931 0.340133
\(309\) 0.393460 0.0223831
\(310\) 1.41259 0.0802297
\(311\) 6.32785 0.358819 0.179410 0.983774i \(-0.442581\pi\)
0.179410 + 0.983774i \(0.442581\pi\)
\(312\) −0.110451 −0.00625303
\(313\) 8.71500 0.492601 0.246301 0.969194i \(-0.420785\pi\)
0.246301 + 0.969194i \(0.420785\pi\)
\(314\) 10.5317 0.594340
\(315\) −2.00428 −0.112928
\(316\) −5.62658 −0.316520
\(317\) −18.9379 −1.06366 −0.531830 0.846851i \(-0.678496\pi\)
−0.531830 + 0.846851i \(0.678496\pi\)
\(318\) 1.09085 0.0611717
\(319\) −10.9029 −0.610445
\(320\) −0.178230 −0.00996334
\(321\) 0.147666 0.00824192
\(322\) −14.2343 −0.793247
\(323\) −6.70888 −0.373292
\(324\) 7.90979 0.439433
\(325\) 1.56586 0.0868580
\(326\) 2.70092 0.149590
\(327\) −6.94639 −0.384136
\(328\) 5.82883 0.321843
\(329\) 6.55291 0.361273
\(330\) 0.0953922 0.00525117
\(331\) −15.3285 −0.842530 −0.421265 0.906938i \(-0.638414\pi\)
−0.421265 + 0.906938i \(0.638414\pi\)
\(332\) 5.96257 0.327239
\(333\) −21.8242 −1.19596
\(334\) −13.5906 −0.743645
\(335\) −0.366495 −0.0200237
\(336\) 1.36971 0.0747236
\(337\) 3.20160 0.174402 0.0872010 0.996191i \(-0.472208\pi\)
0.0872010 + 0.996191i \(0.472208\pi\)
\(338\) 12.9007 0.701704
\(339\) −1.13424 −0.0616035
\(340\) −1.19572 −0.0648471
\(341\) −12.1046 −0.655501
\(342\) −2.87719 −0.155581
\(343\) −4.98848 −0.269353
\(344\) 4.70286 0.253561
\(345\) −0.227471 −0.0122466
\(346\) −18.5724 −0.998460
\(347\) −7.73645 −0.415315 −0.207657 0.978202i \(-0.566584\pi\)
−0.207657 + 0.978202i \(0.566584\pi\)
\(348\) −2.50176 −0.134108
\(349\) 18.1960 0.974009 0.487004 0.873400i \(-0.338090\pi\)
0.487004 + 0.873400i \(0.338090\pi\)
\(350\) −19.4183 −1.03795
\(351\) −0.649139 −0.0346485
\(352\) 1.52727 0.0814035
\(353\) −11.8165 −0.628927 −0.314463 0.949270i \(-0.601825\pi\)
−0.314463 + 0.949270i \(0.601825\pi\)
\(354\) −4.60701 −0.244860
\(355\) −1.01939 −0.0541037
\(356\) 6.61534 0.350613
\(357\) 9.18920 0.486344
\(358\) −12.9704 −0.685506
\(359\) −4.87578 −0.257334 −0.128667 0.991688i \(-0.541070\pi\)
−0.128667 + 0.991688i \(0.541070\pi\)
\(360\) −0.512800 −0.0270270
\(361\) 1.00000 0.0526316
\(362\) 9.98409 0.524752
\(363\) 3.03746 0.159425
\(364\) 1.23185 0.0645667
\(365\) −1.03133 −0.0539824
\(366\) 1.11972 0.0585288
\(367\) −20.7486 −1.08307 −0.541534 0.840679i \(-0.682156\pi\)
−0.541534 + 0.840679i \(0.682156\pi\)
\(368\) −3.64189 −0.189847
\(369\) 16.7706 0.873045
\(370\) 1.35191 0.0702827
\(371\) −12.1662 −0.631638
\(372\) −2.77750 −0.144007
\(373\) 3.88759 0.201292 0.100646 0.994922i \(-0.467909\pi\)
0.100646 + 0.994922i \(0.467909\pi\)
\(374\) 10.2462 0.529820
\(375\) −0.622610 −0.0321515
\(376\) 1.67658 0.0864631
\(377\) −2.24997 −0.115879
\(378\) 8.05003 0.414049
\(379\) 2.86778 0.147308 0.0736540 0.997284i \(-0.476534\pi\)
0.0736540 + 0.997284i \(0.476534\pi\)
\(380\) 0.178230 0.00914299
\(381\) 0.950905 0.0487163
\(382\) 0.371920 0.0190291
\(383\) 10.3522 0.528975 0.264487 0.964389i \(-0.414797\pi\)
0.264487 + 0.964389i \(0.414797\pi\)
\(384\) 0.350444 0.0178835
\(385\) −1.06391 −0.0542217
\(386\) −3.37266 −0.171664
\(387\) 13.5310 0.687821
\(388\) 5.63552 0.286100
\(389\) 16.1807 0.820394 0.410197 0.911997i \(-0.365460\pi\)
0.410197 + 0.911997i \(0.365460\pi\)
\(390\) 0.0196856 0.000996817 0
\(391\) −24.4330 −1.23563
\(392\) −8.27632 −0.418017
\(393\) 1.82271 0.0919436
\(394\) 26.2737 1.32365
\(395\) 1.00282 0.0504575
\(396\) 4.39423 0.220819
\(397\) 7.66033 0.384461 0.192230 0.981350i \(-0.438428\pi\)
0.192230 + 0.981350i \(0.438428\pi\)
\(398\) 6.26480 0.314026
\(399\) −1.36971 −0.0685711
\(400\) −4.96823 −0.248412
\(401\) 36.2291 1.80920 0.904598 0.426266i \(-0.140171\pi\)
0.904598 + 0.426266i \(0.140171\pi\)
\(402\) 0.720620 0.0359412
\(403\) −2.49796 −0.124432
\(404\) 3.83173 0.190636
\(405\) −1.40976 −0.0700514
\(406\) 27.9021 1.38476
\(407\) −11.5847 −0.574231
\(408\) 2.35108 0.116396
\(409\) −6.16561 −0.304870 −0.152435 0.988314i \(-0.548711\pi\)
−0.152435 + 0.988314i \(0.548711\pi\)
\(410\) −1.03887 −0.0513061
\(411\) 3.80879 0.187874
\(412\) −1.12275 −0.0553138
\(413\) 51.3819 2.52834
\(414\) −10.4784 −0.514986
\(415\) −1.06271 −0.0521663
\(416\) 0.315173 0.0154527
\(417\) −0.251201 −0.0123014
\(418\) −1.52727 −0.0747010
\(419\) 22.0812 1.07874 0.539369 0.842070i \(-0.318663\pi\)
0.539369 + 0.842070i \(0.318663\pi\)
\(420\) −0.244122 −0.0119120
\(421\) −5.97402 −0.291156 −0.145578 0.989347i \(-0.546504\pi\)
−0.145578 + 0.989347i \(0.546504\pi\)
\(422\) 1.00000 0.0486792
\(423\) 4.82384 0.234543
\(424\) −3.11276 −0.151169
\(425\) −33.3313 −1.61680
\(426\) 2.00438 0.0971124
\(427\) −12.4882 −0.604349
\(428\) −0.421369 −0.0203677
\(429\) −0.168687 −0.00814430
\(430\) −0.838189 −0.0404211
\(431\) 30.4508 1.46676 0.733382 0.679817i \(-0.237941\pi\)
0.733382 + 0.679817i \(0.237941\pi\)
\(432\) 2.05962 0.0990937
\(433\) −13.8536 −0.665759 −0.332880 0.942969i \(-0.608020\pi\)
−0.332880 + 0.942969i \(0.608020\pi\)
\(434\) 30.9774 1.48696
\(435\) 0.445888 0.0213787
\(436\) 19.8217 0.949287
\(437\) 3.64189 0.174215
\(438\) 2.02786 0.0968947
\(439\) 2.92118 0.139420 0.0697102 0.997567i \(-0.477793\pi\)
0.0697102 + 0.997567i \(0.477793\pi\)
\(440\) −0.272204 −0.0129768
\(441\) −23.8125 −1.13393
\(442\) 2.11446 0.100575
\(443\) 26.4299 1.25572 0.627861 0.778325i \(-0.283930\pi\)
0.627861 + 0.778325i \(0.283930\pi\)
\(444\) −2.65820 −0.126153
\(445\) −1.17905 −0.0558924
\(446\) −6.21424 −0.294253
\(447\) 4.40199 0.208207
\(448\) −3.90849 −0.184659
\(449\) 14.6511 0.691429 0.345715 0.938340i \(-0.387637\pi\)
0.345715 + 0.938340i \(0.387637\pi\)
\(450\) −14.2945 −0.673852
\(451\) 8.90217 0.419187
\(452\) 3.23659 0.152236
\(453\) −3.51727 −0.165256
\(454\) 17.2456 0.809375
\(455\) −0.219553 −0.0102928
\(456\) −0.350444 −0.0164110
\(457\) −38.6663 −1.80873 −0.904367 0.426755i \(-0.859657\pi\)
−0.904367 + 0.426755i \(0.859657\pi\)
\(458\) 0.785104 0.0366855
\(459\) 13.8178 0.644958
\(460\) 0.649093 0.0302641
\(461\) 15.1128 0.703875 0.351937 0.936024i \(-0.385523\pi\)
0.351937 + 0.936024i \(0.385523\pi\)
\(462\) 2.09191 0.0973243
\(463\) −15.5067 −0.720658 −0.360329 0.932825i \(-0.617336\pi\)
−0.360329 + 0.932825i \(0.617336\pi\)
\(464\) 7.13883 0.331412
\(465\) 0.495033 0.0229566
\(466\) 11.8271 0.547881
\(467\) −32.0065 −1.48108 −0.740542 0.672010i \(-0.765431\pi\)
−0.740542 + 0.672010i \(0.765431\pi\)
\(468\) 0.906814 0.0419175
\(469\) −8.03706 −0.371117
\(470\) −0.298817 −0.0137834
\(471\) 3.69078 0.170062
\(472\) 13.1462 0.605103
\(473\) 7.18252 0.330253
\(474\) −1.97180 −0.0905677
\(475\) 4.96823 0.227958
\(476\) −26.2216 −1.20187
\(477\) −8.95600 −0.410067
\(478\) 5.54195 0.253483
\(479\) 4.50579 0.205875 0.102937 0.994688i \(-0.467176\pi\)
0.102937 + 0.994688i \(0.467176\pi\)
\(480\) −0.0624595 −0.00285087
\(481\) −2.39067 −0.109005
\(482\) −16.5329 −0.753053
\(483\) −4.98832 −0.226977
\(484\) −8.66746 −0.393975
\(485\) −1.00442 −0.0456082
\(486\) 8.95081 0.406017
\(487\) −3.49804 −0.158511 −0.0792557 0.996854i \(-0.525254\pi\)
−0.0792557 + 0.996854i \(0.525254\pi\)
\(488\) −3.19516 −0.144638
\(489\) 0.946519 0.0428031
\(490\) 1.47509 0.0666376
\(491\) −19.9387 −0.899821 −0.449910 0.893074i \(-0.648544\pi\)
−0.449910 + 0.893074i \(0.648544\pi\)
\(492\) 2.04268 0.0920910
\(493\) 47.8936 2.15702
\(494\) −0.315173 −0.0141803
\(495\) −0.783182 −0.0352014
\(496\) 7.92567 0.355873
\(497\) −22.3548 −1.00275
\(498\) 2.08955 0.0936348
\(499\) −3.53741 −0.158356 −0.0791782 0.996860i \(-0.525230\pi\)
−0.0791782 + 0.996860i \(0.525230\pi\)
\(500\) 1.77663 0.0794535
\(501\) −4.76274 −0.212784
\(502\) 3.08097 0.137510
\(503\) −14.5430 −0.648442 −0.324221 0.945981i \(-0.605102\pi\)
−0.324221 + 0.945981i \(0.605102\pi\)
\(504\) −11.2455 −0.500913
\(505\) −0.682928 −0.0303899
\(506\) −5.56214 −0.247267
\(507\) 4.52096 0.200783
\(508\) −2.71343 −0.120389
\(509\) −16.2845 −0.721796 −0.360898 0.932605i \(-0.617530\pi\)
−0.360898 + 0.932605i \(0.617530\pi\)
\(510\) −0.419033 −0.0185551
\(511\) −22.6166 −1.00050
\(512\) −1.00000 −0.0441942
\(513\) −2.05962 −0.0909346
\(514\) −0.207315 −0.00914427
\(515\) 0.200107 0.00881776
\(516\) 1.64809 0.0725530
\(517\) 2.56059 0.112614
\(518\) 29.6468 1.30261
\(519\) −6.50859 −0.285695
\(520\) −0.0561732 −0.00246336
\(521\) 39.4238 1.72719 0.863593 0.504189i \(-0.168209\pi\)
0.863593 + 0.504189i \(0.168209\pi\)
\(522\) 20.5398 0.899002
\(523\) 1.49680 0.0654503 0.0327251 0.999464i \(-0.489581\pi\)
0.0327251 + 0.999464i \(0.489581\pi\)
\(524\) −5.20115 −0.227213
\(525\) −6.80502 −0.296996
\(526\) 13.4049 0.584482
\(527\) 53.1724 2.31623
\(528\) 0.535221 0.0232925
\(529\) −9.73663 −0.423332
\(530\) 0.554786 0.0240984
\(531\) 37.8241 1.64143
\(532\) 3.90849 0.169455
\(533\) 1.83709 0.0795733
\(534\) 2.31831 0.100323
\(535\) 0.0751005 0.00324688
\(536\) −2.05631 −0.0888189
\(537\) −4.54539 −0.196148
\(538\) 11.2749 0.486094
\(539\) −12.6401 −0.544449
\(540\) −0.367086 −0.0157969
\(541\) −0.0467454 −0.00200974 −0.00100487 0.999999i \(-0.500320\pi\)
−0.00100487 + 0.999999i \(0.500320\pi\)
\(542\) 23.7771 1.02131
\(543\) 3.49886 0.150151
\(544\) −6.70888 −0.287641
\(545\) −3.53281 −0.151329
\(546\) 0.431695 0.0184749
\(547\) 19.6108 0.838498 0.419249 0.907871i \(-0.362294\pi\)
0.419249 + 0.907871i \(0.362294\pi\)
\(548\) −10.8685 −0.464278
\(549\) −9.19307 −0.392351
\(550\) −7.58781 −0.323545
\(551\) −7.13883 −0.304125
\(552\) −1.27628 −0.0543220
\(553\) 21.9914 0.935171
\(554\) 3.22032 0.136818
\(555\) 0.473770 0.0201104
\(556\) 0.716808 0.0303994
\(557\) 21.6090 0.915602 0.457801 0.889055i \(-0.348637\pi\)
0.457801 + 0.889055i \(0.348637\pi\)
\(558\) 22.8037 0.965356
\(559\) 1.48222 0.0626911
\(560\) 0.696609 0.0294371
\(561\) 3.59073 0.151601
\(562\) 24.0598 1.01490
\(563\) −33.0227 −1.39174 −0.695870 0.718168i \(-0.744981\pi\)
−0.695870 + 0.718168i \(0.744981\pi\)
\(564\) 0.587547 0.0247402
\(565\) −0.576855 −0.0242685
\(566\) 17.9884 0.756108
\(567\) −30.9153 −1.29832
\(568\) −5.71954 −0.239987
\(569\) −28.6710 −1.20195 −0.600975 0.799268i \(-0.705221\pi\)
−0.600975 + 0.799268i \(0.705221\pi\)
\(570\) 0.0624595 0.00261614
\(571\) 16.0721 0.672595 0.336298 0.941756i \(-0.390825\pi\)
0.336298 + 0.941756i \(0.390825\pi\)
\(572\) 0.481354 0.0201264
\(573\) 0.130337 0.00544490
\(574\) −22.7819 −0.950900
\(575\) 18.0938 0.754562
\(576\) −2.87719 −0.119883
\(577\) −24.4920 −1.01962 −0.509808 0.860288i \(-0.670284\pi\)
−0.509808 + 0.860288i \(0.670284\pi\)
\(578\) −28.0090 −1.16502
\(579\) −1.18193 −0.0491193
\(580\) −1.27235 −0.0528315
\(581\) −23.3047 −0.966841
\(582\) 1.97493 0.0818636
\(583\) −4.75401 −0.196891
\(584\) −5.78654 −0.239449
\(585\) −0.161621 −0.00668221
\(586\) 6.08806 0.251496
\(587\) 1.70612 0.0704190 0.0352095 0.999380i \(-0.488790\pi\)
0.0352095 + 0.999380i \(0.488790\pi\)
\(588\) −2.90038 −0.119610
\(589\) −7.92567 −0.326572
\(590\) −2.34304 −0.0964616
\(591\) 9.20746 0.378744
\(592\) 7.58524 0.311751
\(593\) −18.4026 −0.755705 −0.377852 0.925866i \(-0.623337\pi\)
−0.377852 + 0.925866i \(0.623337\pi\)
\(594\) 3.14559 0.129065
\(595\) 4.67347 0.191593
\(596\) −12.5612 −0.514527
\(597\) 2.19546 0.0898542
\(598\) −1.14783 −0.0469382
\(599\) 36.7569 1.50185 0.750923 0.660390i \(-0.229609\pi\)
0.750923 + 0.660390i \(0.229609\pi\)
\(600\) −1.74109 −0.0710796
\(601\) 14.5290 0.592649 0.296324 0.955087i \(-0.404239\pi\)
0.296324 + 0.955087i \(0.404239\pi\)
\(602\) −18.3811 −0.749158
\(603\) −5.91638 −0.240934
\(604\) 10.0366 0.408384
\(605\) 1.54480 0.0628050
\(606\) 1.34281 0.0545478
\(607\) −17.9592 −0.728942 −0.364471 0.931215i \(-0.618750\pi\)
−0.364471 + 0.931215i \(0.618750\pi\)
\(608\) 1.00000 0.0405554
\(609\) 9.77811 0.396229
\(610\) 0.569471 0.0230572
\(611\) 0.528414 0.0213773
\(612\) −19.3027 −0.780266
\(613\) −14.1782 −0.572652 −0.286326 0.958132i \(-0.592434\pi\)
−0.286326 + 0.958132i \(0.592434\pi\)
\(614\) 22.8889 0.923720
\(615\) −0.364065 −0.0146805
\(616\) −5.96931 −0.240510
\(617\) 31.1767 1.25513 0.627563 0.778565i \(-0.284052\pi\)
0.627563 + 0.778565i \(0.284052\pi\)
\(618\) −0.393460 −0.0158273
\(619\) −4.33432 −0.174211 −0.0871056 0.996199i \(-0.527762\pi\)
−0.0871056 + 0.996199i \(0.527762\pi\)
\(620\) −1.41259 −0.0567310
\(621\) −7.50093 −0.301002
\(622\) −6.32785 −0.253724
\(623\) −25.8560 −1.03590
\(624\) 0.110451 0.00442156
\(625\) 24.5245 0.980981
\(626\) −8.71500 −0.348322
\(627\) −0.535221 −0.0213747
\(628\) −10.5317 −0.420262
\(629\) 50.8884 2.02905
\(630\) 2.00428 0.0798523
\(631\) −35.6623 −1.41969 −0.709847 0.704356i \(-0.751236\pi\)
−0.709847 + 0.704356i \(0.751236\pi\)
\(632\) 5.62658 0.223813
\(633\) 0.350444 0.0139289
\(634\) 18.9379 0.752122
\(635\) 0.483614 0.0191916
\(636\) −1.09085 −0.0432549
\(637\) −2.60848 −0.103352
\(638\) 10.9029 0.431650
\(639\) −16.4562 −0.650998
\(640\) 0.178230 0.00704514
\(641\) −22.6249 −0.893628 −0.446814 0.894627i \(-0.647442\pi\)
−0.446814 + 0.894627i \(0.647442\pi\)
\(642\) −0.147666 −0.00582792
\(643\) 9.33857 0.368277 0.184139 0.982900i \(-0.441050\pi\)
0.184139 + 0.982900i \(0.441050\pi\)
\(644\) 14.2343 0.560910
\(645\) −0.293738 −0.0115659
\(646\) 6.70888 0.263957
\(647\) 15.8243 0.622118 0.311059 0.950391i \(-0.399316\pi\)
0.311059 + 0.950391i \(0.399316\pi\)
\(648\) −7.90979 −0.310726
\(649\) 20.0778 0.788121
\(650\) −1.56586 −0.0614179
\(651\) 10.8558 0.425474
\(652\) −2.70092 −0.105776
\(653\) −5.01270 −0.196162 −0.0980811 0.995178i \(-0.531270\pi\)
−0.0980811 + 0.995178i \(0.531270\pi\)
\(654\) 6.94639 0.271625
\(655\) 0.926999 0.0362209
\(656\) −5.82883 −0.227578
\(657\) −16.6490 −0.649538
\(658\) −6.55291 −0.255459
\(659\) −20.6192 −0.803211 −0.401606 0.915813i \(-0.631548\pi\)
−0.401606 + 0.915813i \(0.631548\pi\)
\(660\) −0.0953922 −0.00371314
\(661\) −23.0752 −0.897521 −0.448761 0.893652i \(-0.648134\pi\)
−0.448761 + 0.893652i \(0.648134\pi\)
\(662\) 15.3285 0.595759
\(663\) 0.740999 0.0287780
\(664\) −5.96257 −0.231393
\(665\) −0.696609 −0.0270133
\(666\) 21.8242 0.845669
\(667\) −25.9989 −1.00668
\(668\) 13.5906 0.525836
\(669\) −2.17774 −0.0841963
\(670\) 0.366495 0.0141589
\(671\) −4.87985 −0.188385
\(672\) −1.36971 −0.0528376
\(673\) −32.8708 −1.26708 −0.633538 0.773712i \(-0.718398\pi\)
−0.633538 + 0.773712i \(0.718398\pi\)
\(674\) −3.20160 −0.123321
\(675\) −10.2327 −0.393857
\(676\) −12.9007 −0.496179
\(677\) −27.6238 −1.06167 −0.530835 0.847475i \(-0.678121\pi\)
−0.530835 + 0.847475i \(0.678121\pi\)
\(678\) 1.13424 0.0435603
\(679\) −22.0264 −0.845296
\(680\) 1.19572 0.0458538
\(681\) 6.04360 0.231591
\(682\) 12.1046 0.463509
\(683\) 28.4349 1.08803 0.544016 0.839075i \(-0.316903\pi\)
0.544016 + 0.839075i \(0.316903\pi\)
\(684\) 2.87719 0.110012
\(685\) 1.93708 0.0740121
\(686\) 4.98848 0.190461
\(687\) 0.275135 0.0104970
\(688\) −4.70286 −0.179295
\(689\) −0.981059 −0.0373754
\(690\) 0.227471 0.00865966
\(691\) 8.57183 0.326088 0.163044 0.986619i \(-0.447869\pi\)
0.163044 + 0.986619i \(0.447869\pi\)
\(692\) 18.5724 0.706018
\(693\) −17.1748 −0.652418
\(694\) 7.73645 0.293672
\(695\) −0.127756 −0.00484608
\(696\) 2.50176 0.0948290
\(697\) −39.1049 −1.48120
\(698\) −18.1960 −0.688728
\(699\) 4.14475 0.156769
\(700\) 19.4183 0.733943
\(701\) 23.0686 0.871288 0.435644 0.900119i \(-0.356521\pi\)
0.435644 + 0.900119i \(0.356521\pi\)
\(702\) 0.649139 0.0245002
\(703\) −7.58524 −0.286083
\(704\) −1.52727 −0.0575610
\(705\) −0.104718 −0.00394392
\(706\) 11.8165 0.444718
\(707\) −14.9763 −0.563242
\(708\) 4.60701 0.173142
\(709\) −17.6685 −0.663554 −0.331777 0.943358i \(-0.607648\pi\)
−0.331777 + 0.943358i \(0.607648\pi\)
\(710\) 1.01939 0.0382571
\(711\) 16.1887 0.607125
\(712\) −6.61534 −0.247921
\(713\) −28.8644 −1.08098
\(714\) −9.18920 −0.343897
\(715\) −0.0857915 −0.00320842
\(716\) 12.9704 0.484726
\(717\) 1.94214 0.0725306
\(718\) 4.87578 0.181963
\(719\) −39.2821 −1.46498 −0.732488 0.680779i \(-0.761641\pi\)
−0.732488 + 0.680779i \(0.761641\pi\)
\(720\) 0.512800 0.0191109
\(721\) 4.38825 0.163427
\(722\) −1.00000 −0.0372161
\(723\) −5.79385 −0.215476
\(724\) −9.98409 −0.371056
\(725\) −35.4674 −1.31723
\(726\) −3.03746 −0.112731
\(727\) 26.8301 0.995072 0.497536 0.867443i \(-0.334238\pi\)
0.497536 + 0.867443i \(0.334238\pi\)
\(728\) −1.23185 −0.0456555
\(729\) −20.5926 −0.762689
\(730\) 1.03133 0.0381713
\(731\) −31.5509 −1.16695
\(732\) −1.11972 −0.0413861
\(733\) −19.3579 −0.715002 −0.357501 0.933913i \(-0.616371\pi\)
−0.357501 + 0.933913i \(0.616371\pi\)
\(734\) 20.7486 0.765844
\(735\) 0.516934 0.0190674
\(736\) 3.64189 0.134242
\(737\) −3.14053 −0.115683
\(738\) −16.7706 −0.617336
\(739\) 5.60953 0.206350 0.103175 0.994663i \(-0.467100\pi\)
0.103175 + 0.994663i \(0.467100\pi\)
\(740\) −1.35191 −0.0496973
\(741\) −0.110451 −0.00405750
\(742\) 12.1662 0.446635
\(743\) −31.1987 −1.14457 −0.572285 0.820055i \(-0.693943\pi\)
−0.572285 + 0.820055i \(0.693943\pi\)
\(744\) 2.77750 0.101828
\(745\) 2.23878 0.0820225
\(746\) −3.88759 −0.142335
\(747\) −17.1555 −0.627685
\(748\) −10.2462 −0.374640
\(749\) 1.64692 0.0601771
\(750\) 0.622610 0.0227345
\(751\) 1.29229 0.0471564 0.0235782 0.999722i \(-0.492494\pi\)
0.0235782 + 0.999722i \(0.492494\pi\)
\(752\) −1.67658 −0.0611386
\(753\) 1.07970 0.0393466
\(754\) 2.24997 0.0819391
\(755\) −1.78882 −0.0651019
\(756\) −8.05003 −0.292777
\(757\) −28.4963 −1.03572 −0.517858 0.855467i \(-0.673270\pi\)
−0.517858 + 0.855467i \(0.673270\pi\)
\(758\) −2.86778 −0.104163
\(759\) −1.94922 −0.0707520
\(760\) −0.178230 −0.00646507
\(761\) 34.8944 1.26492 0.632460 0.774593i \(-0.282045\pi\)
0.632460 + 0.774593i \(0.282045\pi\)
\(762\) −0.950905 −0.0344477
\(763\) −77.4729 −2.80471
\(764\) −0.371920 −0.0134556
\(765\) 3.44032 0.124385
\(766\) −10.3522 −0.374042
\(767\) 4.14334 0.149607
\(768\) −0.350444 −0.0126455
\(769\) −23.3590 −0.842346 −0.421173 0.906980i \(-0.638382\pi\)
−0.421173 + 0.906980i \(0.638382\pi\)
\(770\) 1.06391 0.0383406
\(771\) −0.0726522 −0.00261651
\(772\) 3.37266 0.121385
\(773\) 29.8991 1.07540 0.537698 0.843137i \(-0.319294\pi\)
0.537698 + 0.843137i \(0.319294\pi\)
\(774\) −13.5310 −0.486363
\(775\) −39.3766 −1.41445
\(776\) −5.63552 −0.202303
\(777\) 10.3896 0.372723
\(778\) −16.1807 −0.580106
\(779\) 5.82883 0.208839
\(780\) −0.0196856 −0.000704856 0
\(781\) −8.73526 −0.312572
\(782\) 24.4330 0.873722
\(783\) 14.7033 0.525454
\(784\) 8.27632 0.295583
\(785\) 1.87707 0.0669954
\(786\) −1.82271 −0.0650140
\(787\) −41.2586 −1.47071 −0.735356 0.677681i \(-0.762985\pi\)
−0.735356 + 0.677681i \(0.762985\pi\)
\(788\) −26.2737 −0.935963
\(789\) 4.69767 0.167242
\(790\) −1.00282 −0.0356788
\(791\) −12.6502 −0.449788
\(792\) −4.39423 −0.156142
\(793\) −1.00703 −0.0357606
\(794\) −7.66033 −0.271855
\(795\) 0.194421 0.00689541
\(796\) −6.26480 −0.222050
\(797\) −25.2412 −0.894088 −0.447044 0.894512i \(-0.647523\pi\)
−0.447044 + 0.894512i \(0.647523\pi\)
\(798\) 1.36971 0.0484871
\(799\) −11.2480 −0.397925
\(800\) 4.96823 0.175654
\(801\) −19.0336 −0.672519
\(802\) −36.2291 −1.27929
\(803\) −8.83758 −0.311871
\(804\) −0.720620 −0.0254143
\(805\) −2.53698 −0.0894166
\(806\) 2.49796 0.0879870
\(807\) 3.95121 0.139089
\(808\) −3.83173 −0.134800
\(809\) 1.69656 0.0596478 0.0298239 0.999555i \(-0.490505\pi\)
0.0298239 + 0.999555i \(0.490505\pi\)
\(810\) 1.40976 0.0495339
\(811\) −23.1413 −0.812600 −0.406300 0.913740i \(-0.633181\pi\)
−0.406300 + 0.913740i \(0.633181\pi\)
\(812\) −27.9021 −0.979171
\(813\) 8.33253 0.292235
\(814\) 11.5847 0.406043
\(815\) 0.481383 0.0168621
\(816\) −2.35108 −0.0823044
\(817\) 4.70286 0.164532
\(818\) 6.16561 0.215575
\(819\) −3.54428 −0.123847
\(820\) 1.03887 0.0362789
\(821\) 37.2451 1.29986 0.649931 0.759993i \(-0.274798\pi\)
0.649931 + 0.759993i \(0.274798\pi\)
\(822\) −3.80879 −0.132847
\(823\) −18.5852 −0.647839 −0.323919 0.946085i \(-0.605001\pi\)
−0.323919 + 0.946085i \(0.605001\pi\)
\(824\) 1.12275 0.0391127
\(825\) −2.65910 −0.0925780
\(826\) −51.3819 −1.78780
\(827\) 11.8046 0.410486 0.205243 0.978711i \(-0.434201\pi\)
0.205243 + 0.978711i \(0.434201\pi\)
\(828\) 10.4784 0.364150
\(829\) −14.2287 −0.494182 −0.247091 0.968992i \(-0.579475\pi\)
−0.247091 + 0.968992i \(0.579475\pi\)
\(830\) 1.06271 0.0368871
\(831\) 1.12854 0.0391486
\(832\) −0.315173 −0.0109267
\(833\) 55.5248 1.92382
\(834\) 0.251201 0.00869838
\(835\) −2.42225 −0.0838254
\(836\) 1.52727 0.0528216
\(837\) 16.3239 0.564237
\(838\) −22.0812 −0.762783
\(839\) −33.7128 −1.16390 −0.581948 0.813226i \(-0.697709\pi\)
−0.581948 + 0.813226i \(0.697709\pi\)
\(840\) 0.244122 0.00842302
\(841\) 21.9630 0.757343
\(842\) 5.97402 0.205878
\(843\) 8.43160 0.290400
\(844\) −1.00000 −0.0344214
\(845\) 2.29928 0.0790977
\(846\) −4.82384 −0.165847
\(847\) 33.8767 1.16402
\(848\) 3.11276 0.106893
\(849\) 6.30391 0.216350
\(850\) 33.3313 1.14325
\(851\) −27.6246 −0.946959
\(852\) −2.00438 −0.0686689
\(853\) 5.09969 0.174610 0.0873050 0.996182i \(-0.472175\pi\)
0.0873050 + 0.996182i \(0.472175\pi\)
\(854\) 12.4882 0.427339
\(855\) −0.512800 −0.0175374
\(856\) 0.421369 0.0144021
\(857\) 12.5681 0.429318 0.214659 0.976689i \(-0.431136\pi\)
0.214659 + 0.976689i \(0.431136\pi\)
\(858\) 0.168687 0.00575889
\(859\) −36.7667 −1.25447 −0.627233 0.778832i \(-0.715812\pi\)
−0.627233 + 0.778832i \(0.715812\pi\)
\(860\) 0.838189 0.0285820
\(861\) −7.98379 −0.272087
\(862\) −30.4508 −1.03716
\(863\) −3.51129 −0.119526 −0.0597629 0.998213i \(-0.519034\pi\)
−0.0597629 + 0.998213i \(0.519034\pi\)
\(864\) −2.05962 −0.0700698
\(865\) −3.31016 −0.112549
\(866\) 13.8536 0.470763
\(867\) −9.81560 −0.333355
\(868\) −30.9774 −1.05144
\(869\) 8.59328 0.291507
\(870\) −0.445888 −0.0151170
\(871\) −0.648093 −0.0219598
\(872\) −19.8217 −0.671247
\(873\) −16.2145 −0.548776
\(874\) −3.64189 −0.123189
\(875\) −6.94396 −0.234749
\(876\) −2.02786 −0.0685149
\(877\) −26.0693 −0.880297 −0.440149 0.897925i \(-0.645074\pi\)
−0.440149 + 0.897925i \(0.645074\pi\)
\(878\) −2.92118 −0.0985852
\(879\) 2.13352 0.0719620
\(880\) 0.272204 0.00917600
\(881\) −3.66429 −0.123453 −0.0617266 0.998093i \(-0.519661\pi\)
−0.0617266 + 0.998093i \(0.519661\pi\)
\(882\) 23.8125 0.801810
\(883\) −50.1886 −1.68898 −0.844490 0.535571i \(-0.820096\pi\)
−0.844490 + 0.535571i \(0.820096\pi\)
\(884\) −2.11446 −0.0711170
\(885\) −0.821105 −0.0276012
\(886\) −26.4299 −0.887930
\(887\) 2.58173 0.0866861 0.0433431 0.999060i \(-0.486199\pi\)
0.0433431 + 0.999060i \(0.486199\pi\)
\(888\) 2.65820 0.0892033
\(889\) 10.6054 0.355695
\(890\) 1.17905 0.0395219
\(891\) −12.0803 −0.404707
\(892\) 6.21424 0.208068
\(893\) 1.67658 0.0561047
\(894\) −4.40199 −0.147225
\(895\) −2.31171 −0.0772718
\(896\) 3.90849 0.130574
\(897\) −0.402249 −0.0134307
\(898\) −14.6511 −0.488914
\(899\) 56.5801 1.88705
\(900\) 14.2945 0.476485
\(901\) 20.8831 0.695718
\(902\) −8.90217 −0.296410
\(903\) −6.44154 −0.214361
\(904\) −3.23659 −0.107647
\(905\) 1.77946 0.0591513
\(906\) 3.51727 0.116853
\(907\) 57.4999 1.90925 0.954626 0.297808i \(-0.0962555\pi\)
0.954626 + 0.297808i \(0.0962555\pi\)
\(908\) −17.2456 −0.572314
\(909\) −11.0246 −0.365664
\(910\) 0.219553 0.00727810
\(911\) 0.499116 0.0165365 0.00826823 0.999966i \(-0.497368\pi\)
0.00826823 + 0.999966i \(0.497368\pi\)
\(912\) 0.350444 0.0116044
\(913\) −9.10644 −0.301379
\(914\) 38.6663 1.27897
\(915\) 0.199568 0.00659750
\(916\) −0.785104 −0.0259406
\(917\) 20.3287 0.671312
\(918\) −13.8178 −0.456054
\(919\) 4.17123 0.137596 0.0687981 0.997631i \(-0.478084\pi\)
0.0687981 + 0.997631i \(0.478084\pi\)
\(920\) −0.649093 −0.0214000
\(921\) 8.02126 0.264310
\(922\) −15.1128 −0.497714
\(923\) −1.80265 −0.0593349
\(924\) −2.09191 −0.0688187
\(925\) −37.6852 −1.23908
\(926\) 15.5067 0.509582
\(927\) 3.23036 0.106099
\(928\) −7.13883 −0.234344
\(929\) −11.3410 −0.372085 −0.186042 0.982542i \(-0.559566\pi\)
−0.186042 + 0.982542i \(0.559566\pi\)
\(930\) −0.495033 −0.0162328
\(931\) −8.27632 −0.271245
\(932\) −11.8271 −0.387411
\(933\) −2.21756 −0.0725995
\(934\) 32.0065 1.04728
\(935\) 1.82618 0.0597226
\(936\) −0.906814 −0.0296401
\(937\) 31.2345 1.02039 0.510194 0.860059i \(-0.329574\pi\)
0.510194 + 0.860059i \(0.329574\pi\)
\(938\) 8.03706 0.262419
\(939\) −3.05412 −0.0996674
\(940\) 0.298817 0.00974632
\(941\) −8.50659 −0.277307 −0.138653 0.990341i \(-0.544277\pi\)
−0.138653 + 0.990341i \(0.544277\pi\)
\(942\) −3.69078 −0.120252
\(943\) 21.2280 0.691277
\(944\) −13.1462 −0.427873
\(945\) 1.43475 0.0466725
\(946\) −7.18252 −0.233524
\(947\) 21.4703 0.697691 0.348846 0.937180i \(-0.386574\pi\)
0.348846 + 0.937180i \(0.386574\pi\)
\(948\) 1.97180 0.0640411
\(949\) −1.82376 −0.0592019
\(950\) −4.96823 −0.161191
\(951\) 6.63668 0.215209
\(952\) 26.2216 0.849847
\(953\) −25.9185 −0.839582 −0.419791 0.907621i \(-0.637897\pi\)
−0.419791 + 0.907621i \(0.637897\pi\)
\(954\) 8.95600 0.289961
\(955\) 0.0662871 0.00214500
\(956\) −5.54195 −0.179239
\(957\) 3.82085 0.123511
\(958\) −4.50579 −0.145575
\(959\) 42.4793 1.37173
\(960\) 0.0624595 0.00201587
\(961\) 31.8163 1.02633
\(962\) 2.39067 0.0770782
\(963\) 1.21236 0.0390677
\(964\) 16.5329 0.532489
\(965\) −0.601108 −0.0193504
\(966\) 4.98832 0.160497
\(967\) 31.6303 1.01716 0.508580 0.861015i \(-0.330171\pi\)
0.508580 + 0.861015i \(0.330171\pi\)
\(968\) 8.66746 0.278583
\(969\) 2.35108 0.0755277
\(970\) 1.00442 0.0322499
\(971\) 47.7418 1.53211 0.766053 0.642777i \(-0.222218\pi\)
0.766053 + 0.642777i \(0.222218\pi\)
\(972\) −8.95081 −0.287097
\(973\) −2.80164 −0.0898165
\(974\) 3.49804 0.112085
\(975\) −0.548744 −0.0175739
\(976\) 3.19516 0.102274
\(977\) 43.2744 1.38447 0.692236 0.721671i \(-0.256626\pi\)
0.692236 + 0.721671i \(0.256626\pi\)
\(978\) −0.946519 −0.0302663
\(979\) −10.1034 −0.322906
\(980\) −1.47509 −0.0471199
\(981\) −57.0308 −1.82085
\(982\) 19.9387 0.636269
\(983\) 12.5169 0.399228 0.199614 0.979875i \(-0.436031\pi\)
0.199614 + 0.979875i \(0.436031\pi\)
\(984\) −2.04268 −0.0651181
\(985\) 4.68276 0.149205
\(986\) −47.8936 −1.52524
\(987\) −2.29643 −0.0730960
\(988\) 0.315173 0.0100270
\(989\) 17.1273 0.544617
\(990\) 0.783182 0.0248912
\(991\) −3.47662 −0.110439 −0.0552193 0.998474i \(-0.517586\pi\)
−0.0552193 + 0.998474i \(0.517586\pi\)
\(992\) −7.92567 −0.251640
\(993\) 5.37177 0.170468
\(994\) 22.3548 0.709051
\(995\) 1.11657 0.0353977
\(996\) −2.08955 −0.0662098
\(997\) −34.8244 −1.10290 −0.551450 0.834208i \(-0.685925\pi\)
−0.551450 + 0.834208i \(0.685925\pi\)
\(998\) 3.53741 0.111975
\(999\) 15.6227 0.494282
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 \(a_p\))