Properties

Label 6017.2.a.c.1.1
Level 6017
Weight 2
Character 6017.1
Self dual Yes
Analytic conductor 48.046
Analytic rank 1
Dimension 106
CM No

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Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(1\)
Dimension: \(106\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.78235 q^{2}\) \(-0.369906 q^{3}\) \(+5.74149 q^{4}\) \(-3.02150 q^{5}\) \(+1.02921 q^{6}\) \(-3.23246 q^{7}\) \(-10.4101 q^{8}\) \(-2.86317 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.78235 q^{2}\) \(-0.369906 q^{3}\) \(+5.74149 q^{4}\) \(-3.02150 q^{5}\) \(+1.02921 q^{6}\) \(-3.23246 q^{7}\) \(-10.4101 q^{8}\) \(-2.86317 q^{9}\) \(+8.40687 q^{10}\) \(+1.00000 q^{11}\) \(-2.12381 q^{12}\) \(-1.60091 q^{13}\) \(+8.99385 q^{14}\) \(+1.11767 q^{15}\) \(+17.4817 q^{16}\) \(-5.40853 q^{17}\) \(+7.96635 q^{18}\) \(-8.12643 q^{19}\) \(-17.3479 q^{20}\) \(+1.19571 q^{21}\) \(-2.78235 q^{22}\) \(+7.83182 q^{23}\) \(+3.85077 q^{24}\) \(+4.12945 q^{25}\) \(+4.45431 q^{26}\) \(+2.16882 q^{27}\) \(-18.5591 q^{28}\) \(+8.88985 q^{29}\) \(-3.10975 q^{30}\) \(-4.53381 q^{31}\) \(-27.8200 q^{32}\) \(-0.369906 q^{33}\) \(+15.0484 q^{34}\) \(+9.76687 q^{35}\) \(-16.4389 q^{36}\) \(+4.86447 q^{37}\) \(+22.6106 q^{38}\) \(+0.592188 q^{39}\) \(+31.4542 q^{40}\) \(-4.18181 q^{41}\) \(-3.32688 q^{42}\) \(-10.7011 q^{43}\) \(+5.74149 q^{44}\) \(+8.65106 q^{45}\) \(-21.7909 q^{46}\) \(+3.41901 q^{47}\) \(-6.46659 q^{48}\) \(+3.44880 q^{49}\) \(-11.4896 q^{50}\) \(+2.00065 q^{51}\) \(-9.19164 q^{52}\) \(-1.59181 q^{53}\) \(-6.03443 q^{54}\) \(-3.02150 q^{55}\) \(+33.6504 q^{56}\) \(+3.00602 q^{57}\) \(-24.7347 q^{58}\) \(+3.95433 q^{59}\) \(+6.41709 q^{60}\) \(+8.90823 q^{61}\) \(+12.6147 q^{62}\) \(+9.25508 q^{63}\) \(+42.4417 q^{64}\) \(+4.83716 q^{65}\) \(+1.02921 q^{66}\) \(-6.11719 q^{67}\) \(-31.0530 q^{68}\) \(-2.89703 q^{69}\) \(-27.1749 q^{70}\) \(+10.6733 q^{71}\) \(+29.8060 q^{72}\) \(-9.38126 q^{73}\) \(-13.5347 q^{74}\) \(-1.52751 q^{75}\) \(-46.6578 q^{76}\) \(-3.23246 q^{77}\) \(-1.64768 q^{78}\) \(+14.4939 q^{79}\) \(-52.8210 q^{80}\) \(+7.78725 q^{81}\) \(+11.6353 q^{82}\) \(+12.8185 q^{83}\) \(+6.86513 q^{84}\) \(+16.3419 q^{85}\) \(+29.7743 q^{86}\) \(-3.28841 q^{87}\) \(-10.4101 q^{88}\) \(+1.63937 q^{89}\) \(-24.0703 q^{90}\) \(+5.17489 q^{91}\) \(+44.9663 q^{92}\) \(+1.67708 q^{93}\) \(-9.51290 q^{94}\) \(+24.5540 q^{95}\) \(+10.2908 q^{96}\) \(-10.9231 q^{97}\) \(-9.59577 q^{98}\) \(-2.86317 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut -\mathstrut 30q^{10} \) \(\mathstrut +\mathstrut 106q^{11} \) \(\mathstrut -\mathstrut 26q^{12} \) \(\mathstrut -\mathstrut 72q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut -\mathstrut 46q^{15} \) \(\mathstrut +\mathstrut 75q^{16} \) \(\mathstrut -\mathstrut 65q^{17} \) \(\mathstrut -\mathstrut 37q^{18} \) \(\mathstrut -\mathstrut 63q^{19} \) \(\mathstrut -\mathstrut 25q^{20} \) \(\mathstrut -\mathstrut 27q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut -\mathstrut 56q^{24} \) \(\mathstrut +\mathstrut 74q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 54q^{27} \) \(\mathstrut -\mathstrut 115q^{28} \) \(\mathstrut -\mathstrut 45q^{29} \) \(\mathstrut -\mathstrut 14q^{30} \) \(\mathstrut -\mathstrut 89q^{31} \) \(\mathstrut -\mathstrut 96q^{32} \) \(\mathstrut -\mathstrut 15q^{33} \) \(\mathstrut -\mathstrut 26q^{34} \) \(\mathstrut -\mathstrut 52q^{35} \) \(\mathstrut +\mathstrut 91q^{36} \) \(\mathstrut -\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 7q^{38} \) \(\mathstrut -\mathstrut 34q^{39} \) \(\mathstrut -\mathstrut 74q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 94q^{43} \) \(\mathstrut +\mathstrut 93q^{44} \) \(\mathstrut -\mathstrut 46q^{45} \) \(\mathstrut -\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 105q^{47} \) \(\mathstrut -\mathstrut 57q^{48} \) \(\mathstrut +\mathstrut 80q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 36q^{51} \) \(\mathstrut -\mathstrut 137q^{52} \) \(\mathstrut -\mathstrut 61q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 32q^{56} \) \(\mathstrut -\mathstrut 71q^{57} \) \(\mathstrut -\mathstrut 28q^{58} \) \(\mathstrut -\mathstrut 15q^{59} \) \(\mathstrut -\mathstrut 21q^{60} \) \(\mathstrut -\mathstrut 80q^{61} \) \(\mathstrut -\mathstrut 84q^{62} \) \(\mathstrut -\mathstrut 182q^{63} \) \(\mathstrut +\mathstrut 55q^{64} \) \(\mathstrut -\mathstrut 73q^{65} \) \(\mathstrut -\mathstrut 22q^{66} \) \(\mathstrut -\mathstrut 58q^{67} \) \(\mathstrut -\mathstrut 145q^{68} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 39q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 100q^{72} \) \(\mathstrut -\mathstrut 155q^{73} \) \(\mathstrut -\mathstrut 15q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 132q^{76} \) \(\mathstrut -\mathstrut 66q^{77} \) \(\mathstrut -\mathstrut 45q^{78} \) \(\mathstrut -\mathstrut 50q^{79} \) \(\mathstrut -\mathstrut 28q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut -\mathstrut 57q^{82} \) \(\mathstrut -\mathstrut 96q^{83} \) \(\mathstrut -\mathstrut 27q^{84} \) \(\mathstrut -\mathstrut 74q^{85} \) \(\mathstrut +\mathstrut 54q^{86} \) \(\mathstrut -\mathstrut 182q^{87} \) \(\mathstrut -\mathstrut 39q^{88} \) \(\mathstrut +\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 53q^{90} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 49q^{95} \) \(\mathstrut -\mathstrut 56q^{96} \) \(\mathstrut -\mathstrut 102q^{97} \) \(\mathstrut -\mathstrut 76q^{98} \) \(\mathstrut +\mathstrut 97q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.78235 −1.96742 −0.983710 0.179760i \(-0.942468\pi\)
−0.983710 + 0.179760i \(0.942468\pi\)
\(3\) −0.369906 −0.213565 −0.106783 0.994282i \(-0.534055\pi\)
−0.106783 + 0.994282i \(0.534055\pi\)
\(4\) 5.74149 2.87074
\(5\) −3.02150 −1.35125 −0.675627 0.737243i \(-0.736127\pi\)
−0.675627 + 0.737243i \(0.736127\pi\)
\(6\) 1.02921 0.420173
\(7\) −3.23246 −1.22176 −0.610878 0.791725i \(-0.709183\pi\)
−0.610878 + 0.791725i \(0.709183\pi\)
\(8\) −10.4101 −3.68054
\(9\) −2.86317 −0.954390
\(10\) 8.40687 2.65849
\(11\) 1.00000 0.301511
\(12\) −2.12381 −0.613091
\(13\) −1.60091 −0.444014 −0.222007 0.975045i \(-0.571261\pi\)
−0.222007 + 0.975045i \(0.571261\pi\)
\(14\) 8.99385 2.40371
\(15\) 1.11767 0.288581
\(16\) 17.4817 4.37043
\(17\) −5.40853 −1.31176 −0.655881 0.754865i \(-0.727703\pi\)
−0.655881 + 0.754865i \(0.727703\pi\)
\(18\) 7.96635 1.87769
\(19\) −8.12643 −1.86433 −0.932166 0.362031i \(-0.882083\pi\)
−0.932166 + 0.362031i \(0.882083\pi\)
\(20\) −17.3479 −3.87911
\(21\) 1.19571 0.260924
\(22\) −2.78235 −0.593200
\(23\) 7.83182 1.63305 0.816523 0.577313i \(-0.195899\pi\)
0.816523 + 0.577313i \(0.195899\pi\)
\(24\) 3.85077 0.786036
\(25\) 4.12945 0.825889
\(26\) 4.45431 0.873562
\(27\) 2.16882 0.417390
\(28\) −18.5591 −3.50735
\(29\) 8.88985 1.65080 0.825402 0.564545i \(-0.190948\pi\)
0.825402 + 0.564545i \(0.190948\pi\)
\(30\) −3.10975 −0.567760
\(31\) −4.53381 −0.814297 −0.407148 0.913362i \(-0.633477\pi\)
−0.407148 + 0.913362i \(0.633477\pi\)
\(32\) −27.8200 −4.91794
\(33\) −0.369906 −0.0643923
\(34\) 15.0484 2.58079
\(35\) 9.76687 1.65090
\(36\) −16.4389 −2.73981
\(37\) 4.86447 0.799715 0.399857 0.916577i \(-0.369060\pi\)
0.399857 + 0.916577i \(0.369060\pi\)
\(38\) 22.6106 3.66793
\(39\) 0.592188 0.0948259
\(40\) 31.4542 4.97335
\(41\) −4.18181 −0.653089 −0.326545 0.945182i \(-0.605884\pi\)
−0.326545 + 0.945182i \(0.605884\pi\)
\(42\) −3.32688 −0.513348
\(43\) −10.7011 −1.63190 −0.815952 0.578120i \(-0.803787\pi\)
−0.815952 + 0.578120i \(0.803787\pi\)
\(44\) 5.74149 0.865562
\(45\) 8.65106 1.28962
\(46\) −21.7909 −3.21289
\(47\) 3.41901 0.498714 0.249357 0.968412i \(-0.419781\pi\)
0.249357 + 0.968412i \(0.419781\pi\)
\(48\) −6.46659 −0.933372
\(49\) 3.44880 0.492685
\(50\) −11.4896 −1.62487
\(51\) 2.00065 0.280147
\(52\) −9.19164 −1.27465
\(53\) −1.59181 −0.218652 −0.109326 0.994006i \(-0.534869\pi\)
−0.109326 + 0.994006i \(0.534869\pi\)
\(54\) −6.03443 −0.821181
\(55\) −3.02150 −0.407419
\(56\) 33.6504 4.49672
\(57\) 3.00602 0.398156
\(58\) −24.7347 −3.24783
\(59\) 3.95433 0.514811 0.257405 0.966304i \(-0.417132\pi\)
0.257405 + 0.966304i \(0.417132\pi\)
\(60\) 6.41709 0.828443
\(61\) 8.90823 1.14058 0.570291 0.821443i \(-0.306830\pi\)
0.570291 + 0.821443i \(0.306830\pi\)
\(62\) 12.6147 1.60206
\(63\) 9.25508 1.16603
\(64\) 42.4417 5.30522
\(65\) 4.83716 0.599976
\(66\) 1.02921 0.126687
\(67\) −6.11719 −0.747333 −0.373667 0.927563i \(-0.621900\pi\)
−0.373667 + 0.927563i \(0.621900\pi\)
\(68\) −31.0530 −3.76573
\(69\) −2.89703 −0.348762
\(70\) −27.1749 −3.24802
\(71\) 10.6733 1.26669 0.633343 0.773872i \(-0.281682\pi\)
0.633343 + 0.773872i \(0.281682\pi\)
\(72\) 29.8060 3.51267
\(73\) −9.38126 −1.09799 −0.548997 0.835824i \(-0.684990\pi\)
−0.548997 + 0.835824i \(0.684990\pi\)
\(74\) −13.5347 −1.57338
\(75\) −1.52751 −0.176381
\(76\) −46.6578 −5.35202
\(77\) −3.23246 −0.368373
\(78\) −1.64768 −0.186563
\(79\) 14.4939 1.63069 0.815347 0.578972i \(-0.196546\pi\)
0.815347 + 0.578972i \(0.196546\pi\)
\(80\) −52.8210 −5.90557
\(81\) 7.78725 0.865250
\(82\) 11.6353 1.28490
\(83\) 12.8185 1.40701 0.703507 0.710688i \(-0.251616\pi\)
0.703507 + 0.710688i \(0.251616\pi\)
\(84\) 6.86513 0.749047
\(85\) 16.3419 1.77252
\(86\) 29.7743 3.21064
\(87\) −3.28841 −0.352554
\(88\) −10.4101 −1.10973
\(89\) 1.63937 0.173773 0.0868865 0.996218i \(-0.472308\pi\)
0.0868865 + 0.996218i \(0.472308\pi\)
\(90\) −24.0703 −2.53723
\(91\) 5.17489 0.542476
\(92\) 44.9663 4.68806
\(93\) 1.67708 0.173905
\(94\) −9.51290 −0.981181
\(95\) 24.5540 2.51919
\(96\) 10.2908 1.05030
\(97\) −10.9231 −1.10907 −0.554536 0.832159i \(-0.687104\pi\)
−0.554536 + 0.832159i \(0.687104\pi\)
\(98\) −9.59577 −0.969320
\(99\) −2.86317 −0.287759
\(100\) 23.7092 2.37092
\(101\) 14.8175 1.47440 0.737201 0.675674i \(-0.236147\pi\)
0.737201 + 0.675674i \(0.236147\pi\)
\(102\) −5.56651 −0.551166
\(103\) −0.149015 −0.0146828 −0.00734142 0.999973i \(-0.502337\pi\)
−0.00734142 + 0.999973i \(0.502337\pi\)
\(104\) 16.6658 1.63421
\(105\) −3.61282 −0.352575
\(106\) 4.42898 0.430180
\(107\) 0.761562 0.0736230 0.0368115 0.999322i \(-0.488280\pi\)
0.0368115 + 0.999322i \(0.488280\pi\)
\(108\) 12.4523 1.19822
\(109\) −7.34630 −0.703648 −0.351824 0.936066i \(-0.614438\pi\)
−0.351824 + 0.936066i \(0.614438\pi\)
\(110\) 8.40687 0.801564
\(111\) −1.79940 −0.170791
\(112\) −56.5090 −5.33960
\(113\) 12.5236 1.17812 0.589060 0.808089i \(-0.299498\pi\)
0.589060 + 0.808089i \(0.299498\pi\)
\(114\) −8.36380 −0.783341
\(115\) −23.6638 −2.20666
\(116\) 51.0410 4.73904
\(117\) 4.58369 0.423762
\(118\) −11.0024 −1.01285
\(119\) 17.4829 1.60265
\(120\) −11.6351 −1.06213
\(121\) 1.00000 0.0909091
\(122\) −24.7859 −2.24401
\(123\) 1.54688 0.139477
\(124\) −26.0308 −2.33764
\(125\) 2.63037 0.235268
\(126\) −25.7509 −2.29407
\(127\) −8.02483 −0.712088 −0.356044 0.934469i \(-0.615875\pi\)
−0.356044 + 0.934469i \(0.615875\pi\)
\(128\) −62.4478 −5.51966
\(129\) 3.95840 0.348518
\(130\) −13.4587 −1.18041
\(131\) −3.50424 −0.306167 −0.153083 0.988213i \(-0.548920\pi\)
−0.153083 + 0.988213i \(0.548920\pi\)
\(132\) −2.12381 −0.184854
\(133\) 26.2684 2.27776
\(134\) 17.0202 1.47032
\(135\) −6.55309 −0.564000
\(136\) 56.3036 4.82799
\(137\) 5.60118 0.478541 0.239271 0.970953i \(-0.423092\pi\)
0.239271 + 0.970953i \(0.423092\pi\)
\(138\) 8.06057 0.686162
\(139\) 1.03733 0.0879850 0.0439925 0.999032i \(-0.485992\pi\)
0.0439925 + 0.999032i \(0.485992\pi\)
\(140\) 56.0764 4.73932
\(141\) −1.26471 −0.106508
\(142\) −29.6968 −2.49210
\(143\) −1.60091 −0.133875
\(144\) −50.0531 −4.17110
\(145\) −26.8607 −2.23066
\(146\) 26.1020 2.16022
\(147\) −1.27573 −0.105220
\(148\) 27.9293 2.29578
\(149\) −16.2552 −1.33168 −0.665840 0.746095i \(-0.731927\pi\)
−0.665840 + 0.746095i \(0.731927\pi\)
\(150\) 4.25006 0.347016
\(151\) 13.3041 1.08267 0.541337 0.840805i \(-0.317918\pi\)
0.541337 + 0.840805i \(0.317918\pi\)
\(152\) 84.5974 6.86175
\(153\) 15.4855 1.25193
\(154\) 8.99385 0.724745
\(155\) 13.6989 1.10032
\(156\) 3.40004 0.272221
\(157\) 19.3566 1.54482 0.772412 0.635122i \(-0.219050\pi\)
0.772412 + 0.635122i \(0.219050\pi\)
\(158\) −40.3272 −3.20826
\(159\) 0.588820 0.0466964
\(160\) 84.0582 6.64538
\(161\) −25.3160 −1.99518
\(162\) −21.6669 −1.70231
\(163\) −10.1512 −0.795106 −0.397553 0.917579i \(-0.630140\pi\)
−0.397553 + 0.917579i \(0.630140\pi\)
\(164\) −24.0098 −1.87485
\(165\) 1.11767 0.0870105
\(166\) −35.6656 −2.76819
\(167\) −6.56475 −0.507996 −0.253998 0.967205i \(-0.581746\pi\)
−0.253998 + 0.967205i \(0.581746\pi\)
\(168\) −12.4475 −0.960343
\(169\) −10.4371 −0.802852
\(170\) −45.4688 −3.48730
\(171\) 23.2674 1.77930
\(172\) −61.4403 −4.68478
\(173\) −7.38958 −0.561819 −0.280910 0.959734i \(-0.590636\pi\)
−0.280910 + 0.959734i \(0.590636\pi\)
\(174\) 9.14952 0.693623
\(175\) −13.3483 −1.00903
\(176\) 17.4817 1.31773
\(177\) −1.46273 −0.109946
\(178\) −4.56131 −0.341884
\(179\) −24.4864 −1.83020 −0.915098 0.403230i \(-0.867887\pi\)
−0.915098 + 0.403230i \(0.867887\pi\)
\(180\) 49.6700 3.70218
\(181\) 8.74888 0.650299 0.325149 0.945663i \(-0.394585\pi\)
0.325149 + 0.945663i \(0.394585\pi\)
\(182\) −14.3984 −1.06728
\(183\) −3.29521 −0.243589
\(184\) −81.5304 −6.01050
\(185\) −14.6980 −1.08062
\(186\) −4.66624 −0.342145
\(187\) −5.40853 −0.395511
\(188\) 19.6302 1.43168
\(189\) −7.01063 −0.509948
\(190\) −68.3179 −4.95630
\(191\) −9.71590 −0.703018 −0.351509 0.936185i \(-0.614331\pi\)
−0.351509 + 0.936185i \(0.614331\pi\)
\(192\) −15.6994 −1.13301
\(193\) 2.94363 0.211887 0.105944 0.994372i \(-0.466214\pi\)
0.105944 + 0.994372i \(0.466214\pi\)
\(194\) 30.3919 2.18201
\(195\) −1.78929 −0.128134
\(196\) 19.8012 1.41437
\(197\) 3.85864 0.274917 0.137458 0.990508i \(-0.456107\pi\)
0.137458 + 0.990508i \(0.456107\pi\)
\(198\) 7.96635 0.566144
\(199\) 11.0852 0.785809 0.392904 0.919579i \(-0.371470\pi\)
0.392904 + 0.919579i \(0.371470\pi\)
\(200\) −42.9882 −3.03972
\(201\) 2.26278 0.159604
\(202\) −41.2277 −2.90077
\(203\) −28.7361 −2.01688
\(204\) 11.4867 0.804229
\(205\) 12.6353 0.882490
\(206\) 0.414611 0.0288873
\(207\) −22.4238 −1.55856
\(208\) −27.9868 −1.94053
\(209\) −8.12643 −0.562117
\(210\) 10.0521 0.693664
\(211\) 18.7079 1.28790 0.643951 0.765067i \(-0.277294\pi\)
0.643951 + 0.765067i \(0.277294\pi\)
\(212\) −9.13936 −0.627694
\(213\) −3.94811 −0.270520
\(214\) −2.11894 −0.144847
\(215\) 32.3334 2.20512
\(216\) −22.5777 −1.53622
\(217\) 14.6554 0.994871
\(218\) 20.4400 1.38437
\(219\) 3.47018 0.234493
\(220\) −17.3479 −1.16960
\(221\) 8.65859 0.582440
\(222\) 5.00656 0.336018
\(223\) 0.533409 0.0357197 0.0178598 0.999841i \(-0.494315\pi\)
0.0178598 + 0.999841i \(0.494315\pi\)
\(224\) 89.9272 6.00851
\(225\) −11.8233 −0.788221
\(226\) −34.8451 −2.31786
\(227\) −6.99185 −0.464065 −0.232033 0.972708i \(-0.574538\pi\)
−0.232033 + 0.972708i \(0.574538\pi\)
\(228\) 17.2590 1.14301
\(229\) 2.12478 0.140410 0.0702048 0.997533i \(-0.477635\pi\)
0.0702048 + 0.997533i \(0.477635\pi\)
\(230\) 65.8411 4.34143
\(231\) 1.19571 0.0786717
\(232\) −92.5447 −6.07586
\(233\) −19.0126 −1.24556 −0.622778 0.782399i \(-0.713996\pi\)
−0.622778 + 0.782399i \(0.713996\pi\)
\(234\) −12.7534 −0.833719
\(235\) −10.3305 −0.673890
\(236\) 22.7038 1.47789
\(237\) −5.36139 −0.348260
\(238\) −48.6435 −3.15309
\(239\) 3.58014 0.231580 0.115790 0.993274i \(-0.463060\pi\)
0.115790 + 0.993274i \(0.463060\pi\)
\(240\) 19.5388 1.26122
\(241\) 15.0887 0.971950 0.485975 0.873973i \(-0.338465\pi\)
0.485975 + 0.873973i \(0.338465\pi\)
\(242\) −2.78235 −0.178856
\(243\) −9.38701 −0.602177
\(244\) 51.1465 3.27432
\(245\) −10.4205 −0.665743
\(246\) −4.30396 −0.274410
\(247\) 13.0097 0.827789
\(248\) 47.1976 2.99705
\(249\) −4.74164 −0.300489
\(250\) −7.31863 −0.462871
\(251\) −9.64924 −0.609055 −0.304527 0.952504i \(-0.598498\pi\)
−0.304527 + 0.952504i \(0.598498\pi\)
\(252\) 53.1380 3.34738
\(253\) 7.83182 0.492382
\(254\) 22.3279 1.40098
\(255\) −6.04495 −0.378549
\(256\) 88.8685 5.55428
\(257\) −15.1105 −0.942568 −0.471284 0.881982i \(-0.656209\pi\)
−0.471284 + 0.881982i \(0.656209\pi\)
\(258\) −11.0137 −0.685681
\(259\) −15.7242 −0.977055
\(260\) 27.7725 1.72238
\(261\) −25.4532 −1.57551
\(262\) 9.75003 0.602359
\(263\) 28.1168 1.73376 0.866879 0.498519i \(-0.166123\pi\)
0.866879 + 0.498519i \(0.166123\pi\)
\(264\) 3.85077 0.236999
\(265\) 4.80965 0.295454
\(266\) −73.0879 −4.48131
\(267\) −0.606413 −0.0371119
\(268\) −35.1218 −2.14540
\(269\) −14.6323 −0.892148 −0.446074 0.894996i \(-0.647178\pi\)
−0.446074 + 0.894996i \(0.647178\pi\)
\(270\) 18.2330 1.10963
\(271\) 14.2099 0.863190 0.431595 0.902068i \(-0.357951\pi\)
0.431595 + 0.902068i \(0.357951\pi\)
\(272\) −94.5504 −5.73296
\(273\) −1.91422 −0.115854
\(274\) −15.5845 −0.941492
\(275\) 4.12945 0.249015
\(276\) −16.6333 −1.00121
\(277\) −10.3365 −0.621063 −0.310531 0.950563i \(-0.600507\pi\)
−0.310531 + 0.950563i \(0.600507\pi\)
\(278\) −2.88621 −0.173103
\(279\) 12.9811 0.777156
\(280\) −101.675 −6.07622
\(281\) 29.9564 1.78705 0.893526 0.449012i \(-0.148224\pi\)
0.893526 + 0.449012i \(0.148224\pi\)
\(282\) 3.51888 0.209546
\(283\) −19.4708 −1.15742 −0.578711 0.815533i \(-0.696444\pi\)
−0.578711 + 0.815533i \(0.696444\pi\)
\(284\) 61.2805 3.63633
\(285\) −9.08267 −0.538011
\(286\) 4.45431 0.263389
\(287\) 13.5175 0.797915
\(288\) 79.6535 4.69363
\(289\) 12.2522 0.720717
\(290\) 74.7359 4.38864
\(291\) 4.04052 0.236859
\(292\) −53.8624 −3.15206
\(293\) −0.306046 −0.0178794 −0.00893969 0.999960i \(-0.502846\pi\)
−0.00893969 + 0.999960i \(0.502846\pi\)
\(294\) 3.54953 0.207013
\(295\) −11.9480 −0.695640
\(296\) −50.6399 −2.94338
\(297\) 2.16882 0.125848
\(298\) 45.2278 2.61997
\(299\) −12.5381 −0.725095
\(300\) −8.77016 −0.506346
\(301\) 34.5909 1.99379
\(302\) −37.0168 −2.13008
\(303\) −5.48110 −0.314881
\(304\) −142.064 −8.14793
\(305\) −26.9162 −1.54122
\(306\) −43.0862 −2.46308
\(307\) 33.1585 1.89245 0.946226 0.323505i \(-0.104861\pi\)
0.946226 + 0.323505i \(0.104861\pi\)
\(308\) −18.5591 −1.05750
\(309\) 0.0551214 0.00313574
\(310\) −38.1152 −2.16480
\(311\) −10.5200 −0.596533 −0.298267 0.954483i \(-0.596408\pi\)
−0.298267 + 0.954483i \(0.596408\pi\)
\(312\) −6.16476 −0.349011
\(313\) −16.6291 −0.939932 −0.469966 0.882685i \(-0.655734\pi\)
−0.469966 + 0.882685i \(0.655734\pi\)
\(314\) −53.8569 −3.03932
\(315\) −27.9642 −1.57560
\(316\) 83.2168 4.68131
\(317\) 10.6028 0.595515 0.297758 0.954641i \(-0.403761\pi\)
0.297758 + 0.954641i \(0.403761\pi\)
\(318\) −1.63830 −0.0918715
\(319\) 8.88985 0.497736
\(320\) −128.238 −7.16870
\(321\) −0.281706 −0.0157233
\(322\) 70.4381 3.92536
\(323\) 43.9521 2.44556
\(324\) 44.7104 2.48391
\(325\) −6.61089 −0.366706
\(326\) 28.2443 1.56431
\(327\) 2.71744 0.150275
\(328\) 43.5333 2.40372
\(329\) −11.0518 −0.609307
\(330\) −3.10975 −0.171186
\(331\) −16.7418 −0.920214 −0.460107 0.887863i \(-0.652189\pi\)
−0.460107 + 0.887863i \(0.652189\pi\)
\(332\) 73.5973 4.03918
\(333\) −13.9278 −0.763240
\(334\) 18.2655 0.999442
\(335\) 18.4831 1.00984
\(336\) 20.9030 1.14035
\(337\) −0.917724 −0.0499916 −0.0249958 0.999688i \(-0.507957\pi\)
−0.0249958 + 0.999688i \(0.507957\pi\)
\(338\) 29.0396 1.57955
\(339\) −4.63255 −0.251606
\(340\) 93.8266 5.08846
\(341\) −4.53381 −0.245520
\(342\) −64.7380 −3.50063
\(343\) 11.4791 0.619814
\(344\) 111.400 6.00629
\(345\) 8.75338 0.471266
\(346\) 20.5604 1.10533
\(347\) 2.27193 0.121963 0.0609817 0.998139i \(-0.480577\pi\)
0.0609817 + 0.998139i \(0.480577\pi\)
\(348\) −18.8804 −1.01209
\(349\) −4.03550 −0.216015 −0.108008 0.994150i \(-0.534447\pi\)
−0.108008 + 0.994150i \(0.534447\pi\)
\(350\) 37.1396 1.98520
\(351\) −3.47210 −0.185327
\(352\) −27.8200 −1.48281
\(353\) 26.8131 1.42712 0.713559 0.700596i \(-0.247082\pi\)
0.713559 + 0.700596i \(0.247082\pi\)
\(354\) 4.06984 0.216309
\(355\) −32.2493 −1.71161
\(356\) 9.41243 0.498858
\(357\) −6.46701 −0.342270
\(358\) 68.1297 3.60077
\(359\) −27.5883 −1.45606 −0.728029 0.685547i \(-0.759563\pi\)
−0.728029 + 0.685547i \(0.759563\pi\)
\(360\) −90.0588 −4.74652
\(361\) 47.0389 2.47573
\(362\) −24.3425 −1.27941
\(363\) −0.369906 −0.0194150
\(364\) 29.7116 1.55731
\(365\) 28.3455 1.48367
\(366\) 9.16843 0.479242
\(367\) 4.42264 0.230860 0.115430 0.993316i \(-0.463175\pi\)
0.115430 + 0.993316i \(0.463175\pi\)
\(368\) 136.914 7.13712
\(369\) 11.9732 0.623302
\(370\) 40.8950 2.12603
\(371\) 5.14546 0.267139
\(372\) 9.62896 0.499238
\(373\) 18.8035 0.973611 0.486805 0.873510i \(-0.338162\pi\)
0.486805 + 0.873510i \(0.338162\pi\)
\(374\) 15.0484 0.778136
\(375\) −0.972990 −0.0502450
\(376\) −35.5924 −1.83554
\(377\) −14.2319 −0.732980
\(378\) 19.5060 1.00328
\(379\) 15.1435 0.777869 0.388935 0.921265i \(-0.372843\pi\)
0.388935 + 0.921265i \(0.372843\pi\)
\(380\) 140.977 7.23194
\(381\) 2.96843 0.152077
\(382\) 27.0331 1.38313
\(383\) −23.6585 −1.20889 −0.604445 0.796647i \(-0.706605\pi\)
−0.604445 + 0.796647i \(0.706605\pi\)
\(384\) 23.0998 1.17881
\(385\) 9.76687 0.497766
\(386\) −8.19022 −0.416871
\(387\) 30.6391 1.55747
\(388\) −62.7149 −3.18386
\(389\) −5.21352 −0.264336 −0.132168 0.991227i \(-0.542194\pi\)
−0.132168 + 0.991227i \(0.542194\pi\)
\(390\) 4.97845 0.252093
\(391\) −42.3586 −2.14217
\(392\) −35.9025 −1.81335
\(393\) 1.29624 0.0653866
\(394\) −10.7361 −0.540877
\(395\) −43.7934 −2.20348
\(396\) −16.4389 −0.826084
\(397\) 5.59129 0.280619 0.140310 0.990108i \(-0.455190\pi\)
0.140310 + 0.990108i \(0.455190\pi\)
\(398\) −30.8429 −1.54602
\(399\) −9.71682 −0.486450
\(400\) 72.1899 3.60949
\(401\) 9.67610 0.483201 0.241601 0.970376i \(-0.422328\pi\)
0.241601 + 0.970376i \(0.422328\pi\)
\(402\) −6.29586 −0.314009
\(403\) 7.25825 0.361559
\(404\) 85.0748 4.23263
\(405\) −23.5292 −1.16917
\(406\) 79.9540 3.96805
\(407\) 4.86447 0.241123
\(408\) −20.8270 −1.03109
\(409\) −13.6318 −0.674050 −0.337025 0.941496i \(-0.609421\pi\)
−0.337025 + 0.941496i \(0.609421\pi\)
\(410\) −35.1560 −1.73623
\(411\) −2.07191 −0.102200
\(412\) −0.855566 −0.0421507
\(413\) −12.7822 −0.628972
\(414\) 62.3910 3.06635
\(415\) −38.7311 −1.90123
\(416\) 44.5375 2.18363
\(417\) −0.383714 −0.0187905
\(418\) 22.6106 1.10592
\(419\) 24.0912 1.17693 0.588465 0.808523i \(-0.299732\pi\)
0.588465 + 0.808523i \(0.299732\pi\)
\(420\) −20.7430 −1.01215
\(421\) −15.2927 −0.745322 −0.372661 0.927967i \(-0.621555\pi\)
−0.372661 + 0.927967i \(0.621555\pi\)
\(422\) −52.0519 −2.53385
\(423\) −9.78922 −0.475968
\(424\) 16.5710 0.804757
\(425\) −22.3342 −1.08337
\(426\) 10.9850 0.532226
\(427\) −28.7955 −1.39351
\(428\) 4.37250 0.211353
\(429\) 0.592188 0.0285911
\(430\) −89.9629 −4.33839
\(431\) 27.7104 1.33476 0.667382 0.744716i \(-0.267415\pi\)
0.667382 + 0.744716i \(0.267415\pi\)
\(432\) 37.9147 1.82417
\(433\) 1.25243 0.0601879 0.0300939 0.999547i \(-0.490419\pi\)
0.0300939 + 0.999547i \(0.490419\pi\)
\(434\) −40.7764 −1.95733
\(435\) 9.93592 0.476391
\(436\) −42.1787 −2.01999
\(437\) −63.6447 −3.04454
\(438\) −9.65528 −0.461347
\(439\) 29.1559 1.39154 0.695768 0.718266i \(-0.255064\pi\)
0.695768 + 0.718266i \(0.255064\pi\)
\(440\) 31.4542 1.49952
\(441\) −9.87449 −0.470214
\(442\) −24.0913 −1.14590
\(443\) 6.65121 0.316009 0.158004 0.987438i \(-0.449494\pi\)
0.158004 + 0.987438i \(0.449494\pi\)
\(444\) −10.3312 −0.490298
\(445\) −4.95335 −0.234811
\(446\) −1.48413 −0.0702757
\(447\) 6.01290 0.284401
\(448\) −137.191 −6.48168
\(449\) −31.4116 −1.48240 −0.741202 0.671282i \(-0.765744\pi\)
−0.741202 + 0.671282i \(0.765744\pi\)
\(450\) 32.8966 1.55076
\(451\) −4.18181 −0.196914
\(452\) 71.9041 3.38208
\(453\) −4.92128 −0.231222
\(454\) 19.4538 0.913012
\(455\) −15.6359 −0.733024
\(456\) −31.2931 −1.46543
\(457\) −13.1643 −0.615799 −0.307900 0.951419i \(-0.599626\pi\)
−0.307900 + 0.951419i \(0.599626\pi\)
\(458\) −5.91190 −0.276245
\(459\) −11.7301 −0.547516
\(460\) −135.866 −6.33476
\(461\) −17.5224 −0.816098 −0.408049 0.912960i \(-0.633791\pi\)
−0.408049 + 0.912960i \(0.633791\pi\)
\(462\) −3.32688 −0.154780
\(463\) −26.2381 −1.21939 −0.609694 0.792637i \(-0.708708\pi\)
−0.609694 + 0.792637i \(0.708708\pi\)
\(464\) 155.410 7.21473
\(465\) −5.06730 −0.234991
\(466\) 52.8997 2.45053
\(467\) 40.8247 1.88914 0.944571 0.328307i \(-0.106478\pi\)
0.944571 + 0.328307i \(0.106478\pi\)
\(468\) 26.3172 1.21651
\(469\) 19.7736 0.913058
\(470\) 28.7432 1.32583
\(471\) −7.16012 −0.329921
\(472\) −41.1652 −1.89478
\(473\) −10.7011 −0.492037
\(474\) 14.9173 0.685173
\(475\) −33.5577 −1.53973
\(476\) 100.378 4.60080
\(477\) 4.55762 0.208679
\(478\) −9.96121 −0.455615
\(479\) 42.5468 1.94401 0.972007 0.234951i \(-0.0754929\pi\)
0.972007 + 0.234951i \(0.0754929\pi\)
\(480\) −31.0936 −1.41922
\(481\) −7.78761 −0.355084
\(482\) −41.9821 −1.91223
\(483\) 9.36455 0.426102
\(484\) 5.74149 0.260977
\(485\) 33.0041 1.49864
\(486\) 26.1180 1.18474
\(487\) −19.8231 −0.898272 −0.449136 0.893463i \(-0.648268\pi\)
−0.449136 + 0.893463i \(0.648268\pi\)
\(488\) −92.7360 −4.19796
\(489\) 3.75500 0.169807
\(490\) 28.9936 1.30980
\(491\) −13.1086 −0.591581 −0.295790 0.955253i \(-0.595583\pi\)
−0.295790 + 0.955253i \(0.595583\pi\)
\(492\) 8.88138 0.400403
\(493\) −48.0810 −2.16546
\(494\) −36.1977 −1.62861
\(495\) 8.65106 0.388836
\(496\) −79.2589 −3.55883
\(497\) −34.5009 −1.54758
\(498\) 13.1929 0.591189
\(499\) −8.04610 −0.360193 −0.180097 0.983649i \(-0.557641\pi\)
−0.180097 + 0.983649i \(0.557641\pi\)
\(500\) 15.1023 0.675394
\(501\) 2.42834 0.108490
\(502\) 26.8476 1.19827
\(503\) −12.6910 −0.565862 −0.282931 0.959140i \(-0.591307\pi\)
−0.282931 + 0.959140i \(0.591307\pi\)
\(504\) −96.3468 −4.29163
\(505\) −44.7712 −1.99229
\(506\) −21.7909 −0.968723
\(507\) 3.86073 0.171461
\(508\) −46.0745 −2.04422
\(509\) 21.8502 0.968492 0.484246 0.874932i \(-0.339094\pi\)
0.484246 + 0.874932i \(0.339094\pi\)
\(510\) 16.8192 0.744766
\(511\) 30.3245 1.34148
\(512\) −122.368 −5.40794
\(513\) −17.6248 −0.778153
\(514\) 42.0428 1.85443
\(515\) 0.450247 0.0198403
\(516\) 22.7271 1.00051
\(517\) 3.41901 0.150368
\(518\) 43.7503 1.92228
\(519\) 2.73345 0.119985
\(520\) −50.3555 −2.20824
\(521\) −4.52379 −0.198191 −0.0990955 0.995078i \(-0.531595\pi\)
−0.0990955 + 0.995078i \(0.531595\pi\)
\(522\) 70.8197 3.09969
\(523\) −21.0835 −0.921918 −0.460959 0.887422i \(-0.652494\pi\)
−0.460959 + 0.887422i \(0.652494\pi\)
\(524\) −20.1196 −0.878927
\(525\) 4.93760 0.215495
\(526\) −78.2309 −3.41103
\(527\) 24.5213 1.06816
\(528\) −6.46659 −0.281422
\(529\) 38.3373 1.66684
\(530\) −13.3821 −0.581283
\(531\) −11.3219 −0.491330
\(532\) 150.820 6.53886
\(533\) 6.69473 0.289981
\(534\) 1.68725 0.0730146
\(535\) −2.30106 −0.0994835
\(536\) 63.6808 2.75059
\(537\) 9.05765 0.390866
\(538\) 40.7123 1.75523
\(539\) 3.44880 0.148550
\(540\) −37.6245 −1.61910
\(541\) 2.02550 0.0870831 0.0435416 0.999052i \(-0.486136\pi\)
0.0435416 + 0.999052i \(0.486136\pi\)
\(542\) −39.5369 −1.69826
\(543\) −3.23626 −0.138881
\(544\) 150.466 6.45116
\(545\) 22.1968 0.950807
\(546\) 5.32605 0.227934
\(547\) 1.00000 0.0427569
\(548\) 32.1591 1.37377
\(549\) −25.5058 −1.08856
\(550\) −11.4896 −0.489917
\(551\) −72.2428 −3.07765
\(552\) 30.1586 1.28363
\(553\) −46.8511 −1.99231
\(554\) 28.7599 1.22189
\(555\) 5.43688 0.230783
\(556\) 5.95581 0.252582
\(557\) −32.1446 −1.36201 −0.681005 0.732278i \(-0.738457\pi\)
−0.681005 + 0.732278i \(0.738457\pi\)
\(558\) −36.1179 −1.52899
\(559\) 17.1316 0.724588
\(560\) 170.742 7.21516
\(561\) 2.00065 0.0844674
\(562\) −83.3494 −3.51588
\(563\) 17.2461 0.726838 0.363419 0.931626i \(-0.381609\pi\)
0.363419 + 0.931626i \(0.381609\pi\)
\(564\) −7.26134 −0.305757
\(565\) −37.8400 −1.59194
\(566\) 54.1748 2.27713
\(567\) −25.1720 −1.05712
\(568\) −111.110 −4.66209
\(569\) 33.9742 1.42427 0.712137 0.702040i \(-0.247727\pi\)
0.712137 + 0.702040i \(0.247727\pi\)
\(570\) 25.2712 1.05849
\(571\) 6.72731 0.281529 0.140765 0.990043i \(-0.455044\pi\)
0.140765 + 0.990043i \(0.455044\pi\)
\(572\) −9.19164 −0.384322
\(573\) 3.59397 0.150140
\(574\) −37.6106 −1.56984
\(575\) 32.3411 1.34872
\(576\) −121.518 −5.06325
\(577\) −29.0145 −1.20789 −0.603944 0.797027i \(-0.706405\pi\)
−0.603944 + 0.797027i \(0.706405\pi\)
\(578\) −34.0899 −1.41795
\(579\) −1.08887 −0.0452518
\(580\) −154.220 −6.40365
\(581\) −41.4353 −1.71903
\(582\) −11.2421 −0.466002
\(583\) −1.59181 −0.0659260
\(584\) 97.6603 4.04121
\(585\) −13.8496 −0.572611
\(586\) 0.851527 0.0351763
\(587\) 8.41581 0.347358 0.173679 0.984802i \(-0.444435\pi\)
0.173679 + 0.984802i \(0.444435\pi\)
\(588\) −7.32459 −0.302061
\(589\) 36.8437 1.51812
\(590\) 33.2436 1.36862
\(591\) −1.42733 −0.0587126
\(592\) 85.0394 3.49510
\(593\) −8.04906 −0.330535 −0.165268 0.986249i \(-0.552849\pi\)
−0.165268 + 0.986249i \(0.552849\pi\)
\(594\) −6.03443 −0.247595
\(595\) −52.8244 −2.16559
\(596\) −93.3292 −3.82291
\(597\) −4.10048 −0.167821
\(598\) 34.8853 1.42657
\(599\) −31.2227 −1.27572 −0.637862 0.770151i \(-0.720181\pi\)
−0.637862 + 0.770151i \(0.720181\pi\)
\(600\) 15.9016 0.649179
\(601\) −29.4266 −1.20033 −0.600167 0.799874i \(-0.704899\pi\)
−0.600167 + 0.799874i \(0.704899\pi\)
\(602\) −96.2441 −3.92262
\(603\) 17.5145 0.713247
\(604\) 76.3855 3.10808
\(605\) −3.02150 −0.122841
\(606\) 15.2503 0.619503
\(607\) −40.6510 −1.64997 −0.824987 0.565151i \(-0.808818\pi\)
−0.824987 + 0.565151i \(0.808818\pi\)
\(608\) 226.078 9.16866
\(609\) 10.6297 0.430735
\(610\) 74.8904 3.03222
\(611\) −5.47355 −0.221436
\(612\) 88.9101 3.59398
\(613\) 26.1867 1.05767 0.528836 0.848724i \(-0.322629\pi\)
0.528836 + 0.848724i \(0.322629\pi\)
\(614\) −92.2585 −3.72325
\(615\) −4.67389 −0.188469
\(616\) 33.6504 1.35581
\(617\) 11.0233 0.443781 0.221890 0.975072i \(-0.428777\pi\)
0.221890 + 0.975072i \(0.428777\pi\)
\(618\) −0.153367 −0.00616933
\(619\) 22.1315 0.889542 0.444771 0.895644i \(-0.353285\pi\)
0.444771 + 0.895644i \(0.353285\pi\)
\(620\) 78.6521 3.15874
\(621\) 16.9858 0.681617
\(622\) 29.2703 1.17363
\(623\) −5.29920 −0.212308
\(624\) 10.3525 0.414430
\(625\) −28.5949 −1.14380
\(626\) 46.2680 1.84924
\(627\) 3.00602 0.120049
\(628\) 111.136 4.43480
\(629\) −26.3097 −1.04903
\(630\) 77.8063 3.09988
\(631\) 42.4264 1.68897 0.844484 0.535581i \(-0.179907\pi\)
0.844484 + 0.535581i \(0.179907\pi\)
\(632\) −150.884 −6.00184
\(633\) −6.92015 −0.275051
\(634\) −29.5009 −1.17163
\(635\) 24.2470 0.962212
\(636\) 3.38070 0.134054
\(637\) −5.52123 −0.218759
\(638\) −24.7347 −0.979257
\(639\) −30.5594 −1.20891
\(640\) 188.686 7.45847
\(641\) −0.856853 −0.0338437 −0.0169218 0.999857i \(-0.505387\pi\)
−0.0169218 + 0.999857i \(0.505387\pi\)
\(642\) 0.783807 0.0309344
\(643\) −42.6715 −1.68280 −0.841400 0.540413i \(-0.818268\pi\)
−0.841400 + 0.540413i \(0.818268\pi\)
\(644\) −145.352 −5.72766
\(645\) −11.9603 −0.470936
\(646\) −122.290 −4.81144
\(647\) −2.60122 −0.102265 −0.0511323 0.998692i \(-0.516283\pi\)
−0.0511323 + 0.998692i \(0.516283\pi\)
\(648\) −81.0664 −3.18459
\(649\) 3.95433 0.155221
\(650\) 18.3938 0.721466
\(651\) −5.42110 −0.212470
\(652\) −58.2832 −2.28255
\(653\) −19.9689 −0.781443 −0.390721 0.920509i \(-0.627774\pi\)
−0.390721 + 0.920509i \(0.627774\pi\)
\(654\) −7.56087 −0.295654
\(655\) 10.5881 0.413709
\(656\) −73.1053 −2.85428
\(657\) 26.8601 1.04791
\(658\) 30.7501 1.19876
\(659\) −42.1816 −1.64316 −0.821581 0.570091i \(-0.806908\pi\)
−0.821581 + 0.570091i \(0.806908\pi\)
\(660\) 6.41709 0.249785
\(661\) −33.4395 −1.30065 −0.650324 0.759657i \(-0.725367\pi\)
−0.650324 + 0.759657i \(0.725367\pi\)
\(662\) 46.5817 1.81045
\(663\) −3.20286 −0.124389
\(664\) −133.443 −5.17857
\(665\) −79.3698 −3.07783
\(666\) 38.7521 1.50161
\(667\) 69.6237 2.69584
\(668\) −37.6915 −1.45833
\(669\) −0.197311 −0.00762848
\(670\) −51.4264 −1.98678
\(671\) 8.90823 0.343899
\(672\) −33.2646 −1.28321
\(673\) −31.6600 −1.22040 −0.610201 0.792246i \(-0.708912\pi\)
−0.610201 + 0.792246i \(0.708912\pi\)
\(674\) 2.55343 0.0983546
\(675\) 8.95603 0.344718
\(676\) −59.9243 −2.30478
\(677\) −16.5866 −0.637474 −0.318737 0.947843i \(-0.603259\pi\)
−0.318737 + 0.947843i \(0.603259\pi\)
\(678\) 12.8894 0.495014
\(679\) 35.3085 1.35502
\(680\) −170.121 −6.52385
\(681\) 2.58633 0.0991082
\(682\) 12.6147 0.483041
\(683\) 20.4749 0.783449 0.391724 0.920083i \(-0.371879\pi\)
0.391724 + 0.920083i \(0.371879\pi\)
\(684\) 133.589 5.10791
\(685\) −16.9240 −0.646631
\(686\) −31.9390 −1.21944
\(687\) −0.785969 −0.0299866
\(688\) −187.074 −7.13212
\(689\) 2.54835 0.0970844
\(690\) −24.3550 −0.927179
\(691\) 15.1715 0.577151 0.288576 0.957457i \(-0.406818\pi\)
0.288576 + 0.957457i \(0.406818\pi\)
\(692\) −42.4272 −1.61284
\(693\) 9.25508 0.351571
\(694\) −6.32130 −0.239953
\(695\) −3.13428 −0.118890
\(696\) 34.2328 1.29759
\(697\) 22.6175 0.856697
\(698\) 11.2282 0.424993
\(699\) 7.03287 0.266008
\(700\) −76.6390 −2.89668
\(701\) −13.4535 −0.508133 −0.254067 0.967187i \(-0.581768\pi\)
−0.254067 + 0.967187i \(0.581768\pi\)
\(702\) 9.66060 0.364616
\(703\) −39.5308 −1.49093
\(704\) 42.4417 1.59958
\(705\) 3.82133 0.143920
\(706\) −74.6035 −2.80774
\(707\) −47.8971 −1.80136
\(708\) −8.39826 −0.315626
\(709\) −37.6205 −1.41287 −0.706433 0.707780i \(-0.749697\pi\)
−0.706433 + 0.707780i \(0.749697\pi\)
\(710\) 89.7289 3.36747
\(711\) −41.4986 −1.55632
\(712\) −17.0661 −0.639579
\(713\) −35.5080 −1.32978
\(714\) 17.9935 0.673390
\(715\) 4.83716 0.180900
\(716\) −140.588 −5.25403
\(717\) −1.32431 −0.0494574
\(718\) 76.7605 2.86468
\(719\) 16.9198 0.631000 0.315500 0.948926i \(-0.397828\pi\)
0.315500 + 0.948926i \(0.397828\pi\)
\(720\) 151.235 5.63621
\(721\) 0.481684 0.0179388
\(722\) −130.879 −4.87081
\(723\) −5.58140 −0.207575
\(724\) 50.2316 1.86684
\(725\) 36.7102 1.36338
\(726\) 1.02921 0.0381975
\(727\) 11.4690 0.425362 0.212681 0.977122i \(-0.431781\pi\)
0.212681 + 0.977122i \(0.431781\pi\)
\(728\) −53.8714 −1.99661
\(729\) −19.8894 −0.736646
\(730\) −78.8671 −2.91900
\(731\) 57.8773 2.14067
\(732\) −18.9194 −0.699281
\(733\) −17.4214 −0.643473 −0.321736 0.946829i \(-0.604266\pi\)
−0.321736 + 0.946829i \(0.604266\pi\)
\(734\) −12.3053 −0.454198
\(735\) 3.85462 0.142180
\(736\) −217.881 −8.03122
\(737\) −6.11719 −0.225329
\(738\) −33.3138 −1.22630
\(739\) −12.3820 −0.455479 −0.227740 0.973722i \(-0.573134\pi\)
−0.227740 + 0.973722i \(0.573134\pi\)
\(740\) −84.3884 −3.10218
\(741\) −4.81237 −0.176787
\(742\) −14.3165 −0.525575
\(743\) −7.06478 −0.259182 −0.129591 0.991568i \(-0.541366\pi\)
−0.129591 + 0.991568i \(0.541366\pi\)
\(744\) −17.4587 −0.640066
\(745\) 49.1151 1.79944
\(746\) −52.3181 −1.91550
\(747\) −36.7016 −1.34284
\(748\) −31.0530 −1.13541
\(749\) −2.46172 −0.0899493
\(750\) 2.70720 0.0988531
\(751\) −23.6430 −0.862746 −0.431373 0.902174i \(-0.641971\pi\)
−0.431373 + 0.902174i \(0.641971\pi\)
\(752\) 59.7703 2.17960
\(753\) 3.56931 0.130073
\(754\) 39.5982 1.44208
\(755\) −40.1984 −1.46297
\(756\) −40.2514 −1.46393
\(757\) 38.9078 1.41413 0.707064 0.707150i \(-0.250019\pi\)
0.707064 + 0.707150i \(0.250019\pi\)
\(758\) −42.1346 −1.53040
\(759\) −2.89703 −0.105156
\(760\) −255.611 −9.27198
\(761\) −8.90114 −0.322666 −0.161333 0.986900i \(-0.551579\pi\)
−0.161333 + 0.986900i \(0.551579\pi\)
\(762\) −8.25922 −0.299200
\(763\) 23.7466 0.859685
\(764\) −55.7837 −2.01818
\(765\) −46.7895 −1.69168
\(766\) 65.8262 2.37840
\(767\) −6.33055 −0.228583
\(768\) −32.8730 −1.18620
\(769\) 28.1138 1.01381 0.506905 0.862002i \(-0.330789\pi\)
0.506905 + 0.862002i \(0.330789\pi\)
\(770\) −27.1749 −0.979315
\(771\) 5.58947 0.201300
\(772\) 16.9008 0.608274
\(773\) 30.9353 1.11267 0.556333 0.830959i \(-0.312208\pi\)
0.556333 + 0.830959i \(0.312208\pi\)
\(774\) −85.2488 −3.06420
\(775\) −18.7221 −0.672519
\(776\) 113.711 4.08199
\(777\) 5.81648 0.208665
\(778\) 14.5059 0.520060
\(779\) 33.9832 1.21758
\(780\) −10.2732 −0.367840
\(781\) 10.6733 0.381920
\(782\) 117.857 4.21454
\(783\) 19.2805 0.689029
\(784\) 60.2909 2.15325
\(785\) −58.4859 −2.08745
\(786\) −3.60659 −0.128643
\(787\) −28.3099 −1.00914 −0.504570 0.863371i \(-0.668349\pi\)
−0.504570 + 0.863371i \(0.668349\pi\)
\(788\) 22.1543 0.789215
\(789\) −10.4006 −0.370270
\(790\) 121.849 4.33518
\(791\) −40.4820 −1.43937
\(792\) 29.8060 1.05911
\(793\) −14.2613 −0.506434
\(794\) −15.5570 −0.552096
\(795\) −1.77912 −0.0630988
\(796\) 63.6456 2.25586
\(797\) −4.89838 −0.173509 −0.0867547 0.996230i \(-0.527650\pi\)
−0.0867547 + 0.996230i \(0.527650\pi\)
\(798\) 27.0356 0.957051
\(799\) −18.4918 −0.654194
\(800\) −114.881 −4.06167
\(801\) −4.69380 −0.165847
\(802\) −26.9223 −0.950660
\(803\) −9.38126 −0.331057
\(804\) 12.9917 0.458183
\(805\) 76.4923 2.69600
\(806\) −20.1950 −0.711339
\(807\) 5.41258 0.190532
\(808\) −154.253 −5.42660
\(809\) −36.9797 −1.30014 −0.650068 0.759876i \(-0.725260\pi\)
−0.650068 + 0.759876i \(0.725260\pi\)
\(810\) 65.4664 2.30026
\(811\) −20.5398 −0.721250 −0.360625 0.932711i \(-0.617437\pi\)
−0.360625 + 0.932711i \(0.617437\pi\)
\(812\) −164.988 −5.78994
\(813\) −5.25632 −0.184347
\(814\) −13.5347 −0.474391
\(815\) 30.6719 1.07439
\(816\) 34.9748 1.22436
\(817\) 86.9618 3.04241
\(818\) 37.9285 1.32614
\(819\) −14.8166 −0.517734
\(820\) 72.5457 2.53340
\(821\) 38.5094 1.34399 0.671993 0.740557i \(-0.265438\pi\)
0.671993 + 0.740557i \(0.265438\pi\)
\(822\) 5.76479 0.201070
\(823\) 54.4941 1.89955 0.949773 0.312939i \(-0.101314\pi\)
0.949773 + 0.312939i \(0.101314\pi\)
\(824\) 1.55126 0.0540408
\(825\) −1.52751 −0.0531810
\(826\) 35.5647 1.23745
\(827\) −0.725418 −0.0252253 −0.0126126 0.999920i \(-0.504015\pi\)
−0.0126126 + 0.999920i \(0.504015\pi\)
\(828\) −128.746 −4.47424
\(829\) 27.6414 0.960026 0.480013 0.877261i \(-0.340632\pi\)
0.480013 + 0.877261i \(0.340632\pi\)
\(830\) 107.764 3.74053
\(831\) 3.82355 0.132637
\(832\) −67.9456 −2.35559
\(833\) −18.6529 −0.646286
\(834\) 1.06763 0.0369689
\(835\) 19.8354 0.686432
\(836\) −46.6578 −1.61370
\(837\) −9.83302 −0.339879
\(838\) −67.0301 −2.31552
\(839\) −40.7885 −1.40818 −0.704088 0.710112i \(-0.748644\pi\)
−0.704088 + 0.710112i \(0.748644\pi\)
\(840\) 37.6100 1.29767
\(841\) 50.0295 1.72516
\(842\) 42.5498 1.46636
\(843\) −11.0811 −0.381652
\(844\) 107.411 3.69724
\(845\) 31.5356 1.08486
\(846\) 27.2371 0.936429
\(847\) −3.23246 −0.111069
\(848\) −27.8276 −0.955603
\(849\) 7.20238 0.247185
\(850\) 62.1417 2.13144
\(851\) 38.0977 1.30597
\(852\) −22.6680 −0.776594
\(853\) −4.53519 −0.155282 −0.0776409 0.996981i \(-0.524739\pi\)
−0.0776409 + 0.996981i \(0.524739\pi\)
\(854\) 80.1193 2.74163
\(855\) −70.3023 −2.40429
\(856\) −7.92798 −0.270973
\(857\) −16.1709 −0.552386 −0.276193 0.961102i \(-0.589073\pi\)
−0.276193 + 0.961102i \(0.589073\pi\)
\(858\) −1.64768 −0.0562507
\(859\) −29.1048 −0.993043 −0.496521 0.868024i \(-0.665390\pi\)
−0.496521 + 0.868024i \(0.665390\pi\)
\(860\) 185.642 6.33033
\(861\) −5.00022 −0.170407
\(862\) −77.1002 −2.62604
\(863\) 40.5085 1.37892 0.689462 0.724322i \(-0.257847\pi\)
0.689462 + 0.724322i \(0.257847\pi\)
\(864\) −60.3367 −2.05270
\(865\) 22.3276 0.759161
\(866\) −3.48470 −0.118415
\(867\) −4.53216 −0.153920
\(868\) 84.1436 2.85602
\(869\) 14.4939 0.491673
\(870\) −27.6452 −0.937261
\(871\) 9.79309 0.331826
\(872\) 76.4760 2.58981
\(873\) 31.2747 1.05849
\(874\) 177.082 5.98989
\(875\) −8.50258 −0.287440
\(876\) 19.9240 0.673170
\(877\) −50.0943 −1.69156 −0.845782 0.533528i \(-0.820866\pi\)
−0.845782 + 0.533528i \(0.820866\pi\)
\(878\) −81.1221 −2.73774
\(879\) 0.113208 0.00381842
\(880\) −52.8210 −1.78060
\(881\) 24.5202 0.826106 0.413053 0.910707i \(-0.364462\pi\)
0.413053 + 0.910707i \(0.364462\pi\)
\(882\) 27.4743 0.925109
\(883\) 8.22067 0.276648 0.138324 0.990387i \(-0.455829\pi\)
0.138324 + 0.990387i \(0.455829\pi\)
\(884\) 49.7132 1.67204
\(885\) 4.41964 0.148565
\(886\) −18.5060 −0.621722
\(887\) −26.9097 −0.903539 −0.451769 0.892135i \(-0.649207\pi\)
−0.451769 + 0.892135i \(0.649207\pi\)
\(888\) 18.7320 0.628605
\(889\) 25.9399 0.869997
\(890\) 13.7820 0.461973
\(891\) 7.78725 0.260883
\(892\) 3.06256 0.102542
\(893\) −27.7844 −0.929769
\(894\) −16.7300 −0.559536
\(895\) 73.9855 2.47306
\(896\) 201.860 6.74367
\(897\) 4.63791 0.154855
\(898\) 87.3981 2.91651
\(899\) −40.3049 −1.34424
\(900\) −67.8834 −2.26278
\(901\) 8.60935 0.286819
\(902\) 11.6353 0.387412
\(903\) −12.7954 −0.425804
\(904\) −130.372 −4.33612
\(905\) −26.4347 −0.878720
\(906\) 13.6927 0.454910
\(907\) −0.368288 −0.0122288 −0.00611441 0.999981i \(-0.501946\pi\)
−0.00611441 + 0.999981i \(0.501946\pi\)
\(908\) −40.1436 −1.33221
\(909\) −42.4252 −1.40715
\(910\) 43.5047 1.44217
\(911\) 50.0968 1.65978 0.829890 0.557927i \(-0.188403\pi\)
0.829890 + 0.557927i \(0.188403\pi\)
\(912\) 52.5503 1.74012
\(913\) 12.8185 0.424231
\(914\) 36.6277 1.21154
\(915\) 9.95646 0.329150
\(916\) 12.1994 0.403080
\(917\) 11.3273 0.374061
\(918\) 32.6374 1.07719
\(919\) −3.32382 −0.109643 −0.0548213 0.998496i \(-0.517459\pi\)
−0.0548213 + 0.998496i \(0.517459\pi\)
\(920\) 246.344 8.12171
\(921\) −12.2655 −0.404162
\(922\) 48.7534 1.60561
\(923\) −17.0870 −0.562426
\(924\) 6.86513 0.225846
\(925\) 20.0876 0.660476
\(926\) 73.0037 2.39905
\(927\) 0.426654 0.0140132
\(928\) −247.316 −8.11855
\(929\) −22.0958 −0.724941 −0.362471 0.931995i \(-0.618067\pi\)
−0.362471 + 0.931995i \(0.618067\pi\)
\(930\) 14.0990 0.462325
\(931\) −28.0264 −0.918529
\(932\) −109.161 −3.57567
\(933\) 3.89140 0.127399
\(934\) −113.589 −3.71674
\(935\) 16.3419 0.534436
\(936\) −47.7169 −1.55968
\(937\) 12.1518 0.396983 0.198492 0.980103i \(-0.436396\pi\)
0.198492 + 0.980103i \(0.436396\pi\)
\(938\) −55.0170 −1.79637
\(939\) 6.15120 0.200737
\(940\) −59.3127 −1.93457
\(941\) 30.7389 1.00206 0.501030 0.865430i \(-0.332955\pi\)
0.501030 + 0.865430i \(0.332955\pi\)
\(942\) 19.9220 0.649093
\(943\) −32.7512 −1.06653
\(944\) 69.1286 2.24994
\(945\) 21.1826 0.689070
\(946\) 29.7743 0.968045
\(947\) 32.9084 1.06938 0.534690 0.845049i \(-0.320429\pi\)
0.534690 + 0.845049i \(0.320429\pi\)
\(948\) −30.7824 −0.999765
\(949\) 15.0186 0.487524
\(950\) 93.3693 3.02930
\(951\) −3.92206 −0.127181
\(952\) −181.999 −5.89862
\(953\) −8.92071 −0.288970 −0.144485 0.989507i \(-0.546153\pi\)
−0.144485 + 0.989507i \(0.546153\pi\)
\(954\) −12.6809 −0.410560
\(955\) 29.3566 0.949956
\(956\) 20.5553 0.664807
\(957\) −3.28841 −0.106299
\(958\) −118.380 −3.82469
\(959\) −18.1056 −0.584660
\(960\) 47.4358 1.53099
\(961\) −10.4446 −0.336921
\(962\) 21.6679 0.698600
\(963\) −2.18048 −0.0702651
\(964\) 86.6317 2.79022
\(965\) −8.89418 −0.286314
\(966\) −26.0555 −0.838321
\(967\) 43.8786 1.41104 0.705520 0.708690i \(-0.250714\pi\)
0.705520 + 0.708690i \(0.250714\pi\)
\(968\) −10.4101 −0.334595
\(969\) −16.2581 −0.522286
\(970\) −91.8291 −2.94846
\(971\) −2.58510 −0.0829597 −0.0414798 0.999139i \(-0.513207\pi\)
−0.0414798 + 0.999139i \(0.513207\pi\)
\(972\) −53.8954 −1.72870
\(973\) −3.35312 −0.107496
\(974\) 55.1550 1.76728
\(975\) 2.44541 0.0783157
\(976\) 155.731 4.98484
\(977\) 40.0582 1.28158 0.640788 0.767718i \(-0.278608\pi\)
0.640788 + 0.767718i \(0.278608\pi\)
\(978\) −10.4477 −0.334082
\(979\) 1.63937 0.0523945
\(980\) −59.8294 −1.91118
\(981\) 21.0337 0.671554
\(982\) 36.4726 1.16389
\(983\) −46.8066 −1.49290 −0.746449 0.665443i \(-0.768243\pi\)
−0.746449 + 0.665443i \(0.768243\pi\)
\(984\) −16.1032 −0.513352
\(985\) −11.6589 −0.371482
\(986\) 133.778 4.26037
\(987\) 4.08813 0.130127
\(988\) 74.6952 2.37637
\(989\) −83.8091 −2.66497
\(990\) −24.0703 −0.765005
\(991\) 8.10580 0.257489 0.128745 0.991678i \(-0.458905\pi\)
0.128745 + 0.991678i \(0.458905\pi\)
\(992\) 126.131 4.00466
\(993\) 6.19290 0.196526
\(994\) 95.9938 3.04474
\(995\) −33.4939 −1.06183
\(996\) −27.2241 −0.862628
\(997\) −45.1827 −1.43095 −0.715475 0.698638i \(-0.753790\pi\)
−0.715475 + 0.698638i \(0.753790\pi\)
\(998\) 22.3871 0.708651
\(999\) 10.5502 0.333793
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 \(a_p\))