Properties

Label 8013.2.a.d.1.8
Level 8013
Weight 2
Character 8013.1
Self dual Yes
Analytic conductor 63.984
Analytic rank 0
Dimension 129
CM No

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Newspace parameters

Level: \( N \) = \( 8013 = 3 \cdot 2671 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9841271397\)
Analytic rank: \(0\)
Dimension: \(129\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 8013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.58900 q^{2}\) \(+1.00000 q^{3}\) \(+4.70290 q^{4}\) \(-3.13677 q^{5}\) \(-2.58900 q^{6}\) \(+5.18243 q^{7}\) \(-6.99780 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.58900 q^{2}\) \(+1.00000 q^{3}\) \(+4.70290 q^{4}\) \(-3.13677 q^{5}\) \(-2.58900 q^{6}\) \(+5.18243 q^{7}\) \(-6.99780 q^{8}\) \(+1.00000 q^{9}\) \(+8.12109 q^{10}\) \(+3.07795 q^{11}\) \(+4.70290 q^{12}\) \(+1.01286 q^{13}\) \(-13.4173 q^{14}\) \(-3.13677 q^{15}\) \(+8.71148 q^{16}\) \(+7.25364 q^{17}\) \(-2.58900 q^{18}\) \(+5.96116 q^{19}\) \(-14.7519 q^{20}\) \(+5.18243 q^{21}\) \(-7.96880 q^{22}\) \(-7.91632 q^{23}\) \(-6.99780 q^{24}\) \(+4.83934 q^{25}\) \(-2.62228 q^{26}\) \(+1.00000 q^{27}\) \(+24.3725 q^{28}\) \(-8.81122 q^{29}\) \(+8.12109 q^{30}\) \(-6.72996 q^{31}\) \(-8.55838 q^{32}\) \(+3.07795 q^{33}\) \(-18.7796 q^{34}\) \(-16.2561 q^{35}\) \(+4.70290 q^{36}\) \(-2.27457 q^{37}\) \(-15.4334 q^{38}\) \(+1.01286 q^{39}\) \(+21.9505 q^{40}\) \(-2.30062 q^{41}\) \(-13.4173 q^{42}\) \(+1.33463 q^{43}\) \(+14.4753 q^{44}\) \(-3.13677 q^{45}\) \(+20.4953 q^{46}\) \(+5.80601 q^{47}\) \(+8.71148 q^{48}\) \(+19.8576 q^{49}\) \(-12.5290 q^{50}\) \(+7.25364 q^{51}\) \(+4.76337 q^{52}\) \(+2.49814 q^{53}\) \(-2.58900 q^{54}\) \(-9.65482 q^{55}\) \(-36.2656 q^{56}\) \(+5.96116 q^{57}\) \(+22.8122 q^{58}\) \(+6.15954 q^{59}\) \(-14.7519 q^{60}\) \(+11.0981 q^{61}\) \(+17.4238 q^{62}\) \(+5.18243 q^{63}\) \(+4.73466 q^{64}\) \(-3.17710 q^{65}\) \(-7.96880 q^{66}\) \(-7.41039 q^{67}\) \(+34.1131 q^{68}\) \(-7.91632 q^{69}\) \(+42.0870 q^{70}\) \(+10.6743 q^{71}\) \(-6.99780 q^{72}\) \(-0.487453 q^{73}\) \(+5.88884 q^{74}\) \(+4.83934 q^{75}\) \(+28.0348 q^{76}\) \(+15.9513 q^{77}\) \(-2.62228 q^{78}\) \(+2.07524 q^{79}\) \(-27.3259 q^{80}\) \(+1.00000 q^{81}\) \(+5.95630 q^{82}\) \(+11.9859 q^{83}\) \(+24.3725 q^{84}\) \(-22.7530 q^{85}\) \(-3.45534 q^{86}\) \(-8.81122 q^{87}\) \(-21.5389 q^{88}\) \(+2.15121 q^{89}\) \(+8.12109 q^{90}\) \(+5.24906 q^{91}\) \(-37.2297 q^{92}\) \(-6.72996 q^{93}\) \(-15.0317 q^{94}\) \(-18.6988 q^{95}\) \(-8.55838 q^{96}\) \(+1.02023 q^{97}\) \(-51.4113 q^{98}\) \(+3.07795 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut 41q^{10} \) \(\mathstrut +\mathstrut 51q^{11} \) \(\mathstrut +\mathstrut 151q^{12} \) \(\mathstrut +\mathstrut 56q^{13} \) \(\mathstrut +\mathstrut 5q^{14} \) \(\mathstrut +\mathstrut 16q^{15} \) \(\mathstrut +\mathstrut 195q^{16} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 15q^{18} \) \(\mathstrut +\mathstrut 93q^{19} \) \(\mathstrut +\mathstrut 44q^{20} \) \(\mathstrut +\mathstrut 61q^{21} \) \(\mathstrut +\mathstrut 46q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 42q^{24} \) \(\mathstrut +\mathstrut 193q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut +\mathstrut 129q^{27} \) \(\mathstrut +\mathstrut 145q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 41q^{30} \) \(\mathstrut +\mathstrut 67q^{31} \) \(\mathstrut +\mathstrut 89q^{32} \) \(\mathstrut +\mathstrut 51q^{33} \) \(\mathstrut +\mathstrut 73q^{34} \) \(\mathstrut +\mathstrut 56q^{35} \) \(\mathstrut +\mathstrut 151q^{36} \) \(\mathstrut +\mathstrut 95q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 103q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 5q^{42} \) \(\mathstrut +\mathstrut 150q^{43} \) \(\mathstrut +\mathstrut 69q^{44} \) \(\mathstrut +\mathstrut 16q^{45} \) \(\mathstrut +\mathstrut 72q^{46} \) \(\mathstrut +\mathstrut 53q^{47} \) \(\mathstrut +\mathstrut 195q^{48} \) \(\mathstrut +\mathstrut 240q^{49} \) \(\mathstrut +\mathstrut 17q^{50} \) \(\mathstrut +\mathstrut 18q^{51} \) \(\mathstrut +\mathstrut 124q^{52} \) \(\mathstrut +\mathstrut 34q^{53} \) \(\mathstrut +\mathstrut 15q^{54} \) \(\mathstrut +\mathstrut 66q^{55} \) \(\mathstrut -\mathstrut 17q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 57q^{58} \) \(\mathstrut +\mathstrut 49q^{59} \) \(\mathstrut +\mathstrut 44q^{60} \) \(\mathstrut +\mathstrut 113q^{61} \) \(\mathstrut +\mathstrut 27q^{62} \) \(\mathstrut +\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 262q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 46q^{66} \) \(\mathstrut +\mathstrut 185q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut +\mathstrut 50q^{69} \) \(\mathstrut +\mathstrut 25q^{70} \) \(\mathstrut +\mathstrut 41q^{71} \) \(\mathstrut +\mathstrut 42q^{72} \) \(\mathstrut +\mathstrut 153q^{73} \) \(\mathstrut -\mathstrut q^{74} \) \(\mathstrut +\mathstrut 193q^{75} \) \(\mathstrut +\mathstrut 190q^{76} \) \(\mathstrut +\mathstrut 39q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 101q^{79} \) \(\mathstrut +\mathstrut 48q^{80} \) \(\mathstrut +\mathstrut 129q^{81} \) \(\mathstrut +\mathstrut 15q^{82} \) \(\mathstrut +\mathstrut 162q^{83} \) \(\mathstrut +\mathstrut 145q^{84} \) \(\mathstrut +\mathstrut 99q^{85} \) \(\mathstrut +\mathstrut 13q^{86} \) \(\mathstrut +\mathstrut 24q^{87} \) \(\mathstrut +\mathstrut 86q^{88} \) \(\mathstrut -\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 117q^{91} \) \(\mathstrut +\mathstrut 56q^{92} \) \(\mathstrut +\mathstrut 67q^{93} \) \(\mathstrut +\mathstrut 49q^{94} \) \(\mathstrut +\mathstrut 71q^{95} \) \(\mathstrut +\mathstrut 89q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut +\mathstrut 40q^{98} \) \(\mathstrut +\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.58900 −1.83070 −0.915348 0.402663i \(-0.868085\pi\)
−0.915348 + 0.402663i \(0.868085\pi\)
\(3\) 1.00000 0.577350
\(4\) 4.70290 2.35145
\(5\) −3.13677 −1.40281 −0.701404 0.712764i \(-0.747443\pi\)
−0.701404 + 0.712764i \(0.747443\pi\)
\(6\) −2.58900 −1.05695
\(7\) 5.18243 1.95878 0.979388 0.201990i \(-0.0647407\pi\)
0.979388 + 0.201990i \(0.0647407\pi\)
\(8\) −6.99780 −2.47410
\(9\) 1.00000 0.333333
\(10\) 8.12109 2.56811
\(11\) 3.07795 0.928036 0.464018 0.885826i \(-0.346407\pi\)
0.464018 + 0.885826i \(0.346407\pi\)
\(12\) 4.70290 1.35761
\(13\) 1.01286 0.280916 0.140458 0.990087i \(-0.455142\pi\)
0.140458 + 0.990087i \(0.455142\pi\)
\(14\) −13.4173 −3.58592
\(15\) −3.13677 −0.809911
\(16\) 8.71148 2.17787
\(17\) 7.25364 1.75927 0.879633 0.475654i \(-0.157788\pi\)
0.879633 + 0.475654i \(0.157788\pi\)
\(18\) −2.58900 −0.610232
\(19\) 5.96116 1.36758 0.683792 0.729677i \(-0.260329\pi\)
0.683792 + 0.729677i \(0.260329\pi\)
\(20\) −14.7519 −3.29863
\(21\) 5.18243 1.13090
\(22\) −7.96880 −1.69895
\(23\) −7.91632 −1.65067 −0.825333 0.564646i \(-0.809013\pi\)
−0.825333 + 0.564646i \(0.809013\pi\)
\(24\) −6.99780 −1.42842
\(25\) 4.83934 0.967869
\(26\) −2.62228 −0.514272
\(27\) 1.00000 0.192450
\(28\) 24.3725 4.60596
\(29\) −8.81122 −1.63620 −0.818101 0.575074i \(-0.804973\pi\)
−0.818101 + 0.575074i \(0.804973\pi\)
\(30\) 8.12109 1.48270
\(31\) −6.72996 −1.20874 −0.604368 0.796705i \(-0.706575\pi\)
−0.604368 + 0.796705i \(0.706575\pi\)
\(32\) −8.55838 −1.51292
\(33\) 3.07795 0.535802
\(34\) −18.7796 −3.22068
\(35\) −16.2561 −2.74778
\(36\) 4.70290 0.783817
\(37\) −2.27457 −0.373936 −0.186968 0.982366i \(-0.559866\pi\)
−0.186968 + 0.982366i \(0.559866\pi\)
\(38\) −15.4334 −2.50363
\(39\) 1.01286 0.162187
\(40\) 21.9505 3.47068
\(41\) −2.30062 −0.359297 −0.179648 0.983731i \(-0.557496\pi\)
−0.179648 + 0.983731i \(0.557496\pi\)
\(42\) −13.4173 −2.07033
\(43\) 1.33463 0.203529 0.101764 0.994809i \(-0.467551\pi\)
0.101764 + 0.994809i \(0.467551\pi\)
\(44\) 14.4753 2.18223
\(45\) −3.13677 −0.467602
\(46\) 20.4953 3.02187
\(47\) 5.80601 0.846894 0.423447 0.905921i \(-0.360820\pi\)
0.423447 + 0.905921i \(0.360820\pi\)
\(48\) 8.71148 1.25739
\(49\) 19.8576 2.83680
\(50\) −12.5290 −1.77187
\(51\) 7.25364 1.01571
\(52\) 4.76337 0.660560
\(53\) 2.49814 0.343146 0.171573 0.985171i \(-0.445115\pi\)
0.171573 + 0.985171i \(0.445115\pi\)
\(54\) −2.58900 −0.352318
\(55\) −9.65482 −1.30186
\(56\) −36.2656 −4.84620
\(57\) 5.96116 0.789575
\(58\) 22.8122 2.99539
\(59\) 6.15954 0.801904 0.400952 0.916099i \(-0.368679\pi\)
0.400952 + 0.916099i \(0.368679\pi\)
\(60\) −14.7519 −1.90447
\(61\) 11.0981 1.42096 0.710481 0.703717i \(-0.248478\pi\)
0.710481 + 0.703717i \(0.248478\pi\)
\(62\) 17.4238 2.21283
\(63\) 5.18243 0.652925
\(64\) 4.73466 0.591833
\(65\) −3.17710 −0.394071
\(66\) −7.96880 −0.980891
\(67\) −7.41039 −0.905323 −0.452662 0.891682i \(-0.649525\pi\)
−0.452662 + 0.891682i \(0.649525\pi\)
\(68\) 34.1131 4.13683
\(69\) −7.91632 −0.953013
\(70\) 42.0870 5.03036
\(71\) 10.6743 1.26681 0.633405 0.773820i \(-0.281657\pi\)
0.633405 + 0.773820i \(0.281657\pi\)
\(72\) −6.99780 −0.824699
\(73\) −0.487453 −0.0570520 −0.0285260 0.999593i \(-0.509081\pi\)
−0.0285260 + 0.999593i \(0.509081\pi\)
\(74\) 5.88884 0.684564
\(75\) 4.83934 0.558799
\(76\) 28.0348 3.21581
\(77\) 15.9513 1.81781
\(78\) −2.62228 −0.296915
\(79\) 2.07524 0.233483 0.116742 0.993162i \(-0.462755\pi\)
0.116742 + 0.993162i \(0.462755\pi\)
\(80\) −27.3259 −3.05513
\(81\) 1.00000 0.111111
\(82\) 5.95630 0.657763
\(83\) 11.9859 1.31562 0.657809 0.753184i \(-0.271483\pi\)
0.657809 + 0.753184i \(0.271483\pi\)
\(84\) 24.3725 2.65925
\(85\) −22.7530 −2.46791
\(86\) −3.45534 −0.372599
\(87\) −8.81122 −0.944662
\(88\) −21.5389 −2.29605
\(89\) 2.15121 0.228028 0.114014 0.993479i \(-0.463629\pi\)
0.114014 + 0.993479i \(0.463629\pi\)
\(90\) 8.12109 0.856038
\(91\) 5.24906 0.550251
\(92\) −37.2297 −3.88146
\(93\) −6.72996 −0.697865
\(94\) −15.0317 −1.55041
\(95\) −18.6988 −1.91846
\(96\) −8.55838 −0.873486
\(97\) 1.02023 0.103589 0.0517945 0.998658i \(-0.483506\pi\)
0.0517945 + 0.998658i \(0.483506\pi\)
\(98\) −51.4113 −5.19332
\(99\) 3.07795 0.309345
\(100\) 22.7590 2.27590
\(101\) 8.44534 0.840342 0.420171 0.907445i \(-0.361970\pi\)
0.420171 + 0.907445i \(0.361970\pi\)
\(102\) −18.7796 −1.85946
\(103\) −7.02341 −0.692037 −0.346019 0.938228i \(-0.612467\pi\)
−0.346019 + 0.938228i \(0.612467\pi\)
\(104\) −7.08777 −0.695013
\(105\) −16.2561 −1.58643
\(106\) −6.46768 −0.628197
\(107\) 17.6121 1.70263 0.851315 0.524655i \(-0.175806\pi\)
0.851315 + 0.524655i \(0.175806\pi\)
\(108\) 4.70290 0.452537
\(109\) 1.14771 0.109931 0.0549653 0.998488i \(-0.482495\pi\)
0.0549653 + 0.998488i \(0.482495\pi\)
\(110\) 24.9963 2.38330
\(111\) −2.27457 −0.215892
\(112\) 45.1466 4.26596
\(113\) 5.52424 0.519677 0.259838 0.965652i \(-0.416331\pi\)
0.259838 + 0.965652i \(0.416331\pi\)
\(114\) −15.4334 −1.44547
\(115\) 24.8317 2.31557
\(116\) −41.4383 −3.84745
\(117\) 1.01286 0.0936387
\(118\) −15.9470 −1.46804
\(119\) 37.5915 3.44601
\(120\) 21.9505 2.00380
\(121\) −1.52623 −0.138749
\(122\) −28.7328 −2.60135
\(123\) −2.30062 −0.207440
\(124\) −31.6503 −2.84229
\(125\) 0.503945 0.0450742
\(126\) −13.4173 −1.19531
\(127\) 5.47321 0.485669 0.242834 0.970068i \(-0.421923\pi\)
0.242834 + 0.970068i \(0.421923\pi\)
\(128\) 4.85874 0.429456
\(129\) 1.33463 0.117507
\(130\) 8.22551 0.721425
\(131\) 11.4817 1.00316 0.501582 0.865110i \(-0.332752\pi\)
0.501582 + 0.865110i \(0.332752\pi\)
\(132\) 14.4753 1.25991
\(133\) 30.8933 2.67879
\(134\) 19.1855 1.65737
\(135\) −3.13677 −0.269970
\(136\) −50.7595 −4.35259
\(137\) −11.4893 −0.981594 −0.490797 0.871274i \(-0.663294\pi\)
−0.490797 + 0.871274i \(0.663294\pi\)
\(138\) 20.4953 1.74468
\(139\) −6.86691 −0.582444 −0.291222 0.956655i \(-0.594062\pi\)
−0.291222 + 0.956655i \(0.594062\pi\)
\(140\) −76.4509 −6.46128
\(141\) 5.80601 0.488954
\(142\) −27.6358 −2.31915
\(143\) 3.11752 0.260700
\(144\) 8.71148 0.725957
\(145\) 27.6388 2.29528
\(146\) 1.26201 0.104445
\(147\) 19.8576 1.63783
\(148\) −10.6971 −0.879293
\(149\) −10.5530 −0.864539 −0.432269 0.901745i \(-0.642287\pi\)
−0.432269 + 0.901745i \(0.642287\pi\)
\(150\) −12.5290 −1.02299
\(151\) −12.2609 −0.997775 −0.498888 0.866667i \(-0.666258\pi\)
−0.498888 + 0.866667i \(0.666258\pi\)
\(152\) −41.7150 −3.38354
\(153\) 7.25364 0.586422
\(154\) −41.2977 −3.32787
\(155\) 21.1104 1.69563
\(156\) 4.76337 0.381375
\(157\) −4.99350 −0.398525 −0.199263 0.979946i \(-0.563855\pi\)
−0.199263 + 0.979946i \(0.563855\pi\)
\(158\) −5.37280 −0.427437
\(159\) 2.49814 0.198116
\(160\) 26.8457 2.12234
\(161\) −41.0258 −3.23329
\(162\) −2.58900 −0.203411
\(163\) −1.57054 −0.123014 −0.0615071 0.998107i \(-0.519591\pi\)
−0.0615071 + 0.998107i \(0.519591\pi\)
\(164\) −10.8196 −0.844868
\(165\) −9.65482 −0.751627
\(166\) −31.0313 −2.40850
\(167\) −18.3862 −1.42277 −0.711383 0.702804i \(-0.751931\pi\)
−0.711383 + 0.702804i \(0.751931\pi\)
\(168\) −36.2656 −2.79795
\(169\) −11.9741 −0.921086
\(170\) 58.9075 4.51800
\(171\) 5.96116 0.455862
\(172\) 6.27661 0.478587
\(173\) −18.4161 −1.40015 −0.700077 0.714068i \(-0.746851\pi\)
−0.700077 + 0.714068i \(0.746851\pi\)
\(174\) 22.8122 1.72939
\(175\) 25.0796 1.89584
\(176\) 26.8135 2.02114
\(177\) 6.15954 0.462980
\(178\) −5.56947 −0.417449
\(179\) 2.59883 0.194245 0.0971227 0.995272i \(-0.469036\pi\)
0.0971227 + 0.995272i \(0.469036\pi\)
\(180\) −14.7519 −1.09954
\(181\) −25.7664 −1.91520 −0.957602 0.288094i \(-0.906978\pi\)
−0.957602 + 0.288094i \(0.906978\pi\)
\(182\) −13.5898 −1.00734
\(183\) 11.0981 0.820392
\(184\) 55.3968 4.08391
\(185\) 7.13480 0.524561
\(186\) 17.4238 1.27758
\(187\) 22.3263 1.63266
\(188\) 27.3051 1.99143
\(189\) 5.18243 0.376966
\(190\) 48.4112 3.51211
\(191\) 13.0262 0.942540 0.471270 0.881989i \(-0.343796\pi\)
0.471270 + 0.881989i \(0.343796\pi\)
\(192\) 4.73466 0.341695
\(193\) −12.0347 −0.866277 −0.433138 0.901327i \(-0.642594\pi\)
−0.433138 + 0.901327i \(0.642594\pi\)
\(194\) −2.64138 −0.189640
\(195\) −3.17710 −0.227517
\(196\) 93.3884 6.67060
\(197\) 7.54398 0.537486 0.268743 0.963212i \(-0.413392\pi\)
0.268743 + 0.963212i \(0.413392\pi\)
\(198\) −7.96880 −0.566318
\(199\) 19.0235 1.34854 0.674272 0.738483i \(-0.264458\pi\)
0.674272 + 0.738483i \(0.264458\pi\)
\(200\) −33.8648 −2.39460
\(201\) −7.41039 −0.522689
\(202\) −21.8649 −1.53841
\(203\) −45.6636 −3.20495
\(204\) 34.1131 2.38840
\(205\) 7.21652 0.504024
\(206\) 18.1836 1.26691
\(207\) −7.91632 −0.550222
\(208\) 8.82348 0.611799
\(209\) 18.3482 1.26917
\(210\) 42.0870 2.90428
\(211\) 0.338456 0.0233003 0.0116501 0.999932i \(-0.496292\pi\)
0.0116501 + 0.999932i \(0.496292\pi\)
\(212\) 11.7485 0.806891
\(213\) 10.6743 0.731394
\(214\) −45.5978 −3.11700
\(215\) −4.18642 −0.285511
\(216\) −6.99780 −0.476140
\(217\) −34.8776 −2.36764
\(218\) −2.97142 −0.201250
\(219\) −0.487453 −0.0329390
\(220\) −45.4057 −3.06125
\(221\) 7.34690 0.494206
\(222\) 5.88884 0.395233
\(223\) 9.83348 0.658498 0.329249 0.944243i \(-0.393204\pi\)
0.329249 + 0.944243i \(0.393204\pi\)
\(224\) −44.3532 −2.96348
\(225\) 4.83934 0.322623
\(226\) −14.3022 −0.951370
\(227\) −14.4122 −0.956570 −0.478285 0.878205i \(-0.658741\pi\)
−0.478285 + 0.878205i \(0.658741\pi\)
\(228\) 28.0348 1.85665
\(229\) 25.5377 1.68758 0.843788 0.536676i \(-0.180320\pi\)
0.843788 + 0.536676i \(0.180320\pi\)
\(230\) −64.2892 −4.23910
\(231\) 15.9513 1.04952
\(232\) 61.6592 4.04812
\(233\) 25.4905 1.66994 0.834968 0.550299i \(-0.185486\pi\)
0.834968 + 0.550299i \(0.185486\pi\)
\(234\) −2.62228 −0.171424
\(235\) −18.2121 −1.18803
\(236\) 28.9677 1.88564
\(237\) 2.07524 0.134802
\(238\) −97.3242 −6.30859
\(239\) −8.14532 −0.526877 −0.263439 0.964676i \(-0.584857\pi\)
−0.263439 + 0.964676i \(0.584857\pi\)
\(240\) −27.3259 −1.76388
\(241\) −9.03631 −0.582080 −0.291040 0.956711i \(-0.594001\pi\)
−0.291040 + 0.956711i \(0.594001\pi\)
\(242\) 3.95141 0.254007
\(243\) 1.00000 0.0641500
\(244\) 52.1931 3.34132
\(245\) −62.2888 −3.97949
\(246\) 5.95630 0.379760
\(247\) 6.03781 0.384176
\(248\) 47.0949 2.99053
\(249\) 11.9859 0.759573
\(250\) −1.30471 −0.0825172
\(251\) 6.27854 0.396298 0.198149 0.980172i \(-0.436507\pi\)
0.198149 + 0.980172i \(0.436507\pi\)
\(252\) 24.3725 1.53532
\(253\) −24.3660 −1.53188
\(254\) −14.1701 −0.889113
\(255\) −22.7530 −1.42485
\(256\) −22.0486 −1.37804
\(257\) −17.3431 −1.08184 −0.540918 0.841075i \(-0.681923\pi\)
−0.540918 + 0.841075i \(0.681923\pi\)
\(258\) −3.45534 −0.215120
\(259\) −11.7878 −0.732457
\(260\) −14.9416 −0.926639
\(261\) −8.81122 −0.545401
\(262\) −29.7262 −1.83649
\(263\) −1.50004 −0.0924963 −0.0462481 0.998930i \(-0.514726\pi\)
−0.0462481 + 0.998930i \(0.514726\pi\)
\(264\) −21.5389 −1.32563
\(265\) −7.83610 −0.481368
\(266\) −79.9827 −4.90405
\(267\) 2.15121 0.131652
\(268\) −34.8503 −2.12882
\(269\) 15.7426 0.959844 0.479922 0.877311i \(-0.340665\pi\)
0.479922 + 0.877311i \(0.340665\pi\)
\(270\) 8.12109 0.494234
\(271\) 9.29233 0.564469 0.282234 0.959345i \(-0.408924\pi\)
0.282234 + 0.959345i \(0.408924\pi\)
\(272\) 63.1899 3.83145
\(273\) 5.24906 0.317688
\(274\) 29.7457 1.79700
\(275\) 14.8952 0.898217
\(276\) −37.2297 −2.24096
\(277\) 7.05145 0.423681 0.211840 0.977304i \(-0.432054\pi\)
0.211840 + 0.977304i \(0.432054\pi\)
\(278\) 17.7784 1.06628
\(279\) −6.72996 −0.402912
\(280\) 113.757 6.79828
\(281\) −25.5843 −1.52623 −0.763117 0.646261i \(-0.776332\pi\)
−0.763117 + 0.646261i \(0.776332\pi\)
\(282\) −15.0317 −0.895127
\(283\) 0.286131 0.0170087 0.00850435 0.999964i \(-0.497293\pi\)
0.00850435 + 0.999964i \(0.497293\pi\)
\(284\) 50.2004 2.97884
\(285\) −18.6988 −1.10762
\(286\) −8.07125 −0.477263
\(287\) −11.9228 −0.703781
\(288\) −8.55838 −0.504307
\(289\) 35.6153 2.09501
\(290\) −71.5568 −4.20196
\(291\) 1.02023 0.0598072
\(292\) −2.29244 −0.134155
\(293\) −7.58655 −0.443211 −0.221605 0.975136i \(-0.571130\pi\)
−0.221605 + 0.975136i \(0.571130\pi\)
\(294\) −51.4113 −2.99837
\(295\) −19.3211 −1.12492
\(296\) 15.9170 0.925154
\(297\) 3.07795 0.178601
\(298\) 27.3218 1.58271
\(299\) −8.01810 −0.463699
\(300\) 22.7590 1.31399
\(301\) 6.91661 0.398667
\(302\) 31.7433 1.82662
\(303\) 8.44534 0.485172
\(304\) 51.9305 2.97842
\(305\) −34.8121 −1.99334
\(306\) −18.7796 −1.07356
\(307\) 12.8976 0.736105 0.368052 0.929805i \(-0.380025\pi\)
0.368052 + 0.929805i \(0.380025\pi\)
\(308\) 75.0172 4.27450
\(309\) −7.02341 −0.399548
\(310\) −54.6546 −3.10418
\(311\) −15.8834 −0.900667 −0.450334 0.892860i \(-0.648695\pi\)
−0.450334 + 0.892860i \(0.648695\pi\)
\(312\) −7.08777 −0.401266
\(313\) 27.7054 1.56600 0.783002 0.622020i \(-0.213688\pi\)
0.783002 + 0.622020i \(0.213688\pi\)
\(314\) 12.9282 0.729579
\(315\) −16.2561 −0.915928
\(316\) 9.75967 0.549024
\(317\) −14.6549 −0.823101 −0.411551 0.911387i \(-0.635013\pi\)
−0.411551 + 0.911387i \(0.635013\pi\)
\(318\) −6.46768 −0.362689
\(319\) −27.1205 −1.51846
\(320\) −14.8516 −0.830227
\(321\) 17.6121 0.983014
\(322\) 106.216 5.91916
\(323\) 43.2401 2.40594
\(324\) 4.70290 0.261272
\(325\) 4.90156 0.271890
\(326\) 4.06612 0.225202
\(327\) 1.14771 0.0634685
\(328\) 16.0993 0.888934
\(329\) 30.0893 1.65888
\(330\) 24.9963 1.37600
\(331\) 0.242102 0.0133071 0.00665355 0.999978i \(-0.497882\pi\)
0.00665355 + 0.999978i \(0.497882\pi\)
\(332\) 56.3683 3.09361
\(333\) −2.27457 −0.124645
\(334\) 47.6018 2.60465
\(335\) 23.2447 1.26999
\(336\) 45.1466 2.46295
\(337\) 34.0579 1.85525 0.927626 0.373511i \(-0.121846\pi\)
0.927626 + 0.373511i \(0.121846\pi\)
\(338\) 31.0010 1.68623
\(339\) 5.52424 0.300035
\(340\) −107.005 −5.80317
\(341\) −20.7145 −1.12175
\(342\) −15.4334 −0.834544
\(343\) 66.6337 3.59788
\(344\) −9.33945 −0.503549
\(345\) 24.8317 1.33689
\(346\) 47.6793 2.56326
\(347\) −27.1169 −1.45571 −0.727855 0.685731i \(-0.759483\pi\)
−0.727855 + 0.685731i \(0.759483\pi\)
\(348\) −41.4383 −2.22133
\(349\) −10.5112 −0.562654 −0.281327 0.959612i \(-0.590775\pi\)
−0.281327 + 0.959612i \(0.590775\pi\)
\(350\) −64.9309 −3.47070
\(351\) 1.01286 0.0540623
\(352\) −26.3423 −1.40405
\(353\) 28.3923 1.51117 0.755586 0.655049i \(-0.227352\pi\)
0.755586 + 0.655049i \(0.227352\pi\)
\(354\) −15.9470 −0.847575
\(355\) −33.4830 −1.77709
\(356\) 10.1169 0.536195
\(357\) 37.5915 1.98955
\(358\) −6.72835 −0.355605
\(359\) 16.4215 0.866691 0.433346 0.901228i \(-0.357333\pi\)
0.433346 + 0.901228i \(0.357333\pi\)
\(360\) 21.9505 1.15689
\(361\) 16.5355 0.870288
\(362\) 66.7092 3.50616
\(363\) −1.52623 −0.0801065
\(364\) 24.6858 1.29389
\(365\) 1.52903 0.0800330
\(366\) −28.7328 −1.50189
\(367\) 28.1337 1.46857 0.734283 0.678843i \(-0.237518\pi\)
0.734283 + 0.678843i \(0.237518\pi\)
\(368\) −68.9628 −3.59494
\(369\) −2.30062 −0.119766
\(370\) −18.4720 −0.960311
\(371\) 12.9465 0.672146
\(372\) −31.6503 −1.64099
\(373\) −31.0784 −1.60918 −0.804590 0.593831i \(-0.797615\pi\)
−0.804590 + 0.593831i \(0.797615\pi\)
\(374\) −57.8028 −2.98891
\(375\) 0.503945 0.0260236
\(376\) −40.6293 −2.09530
\(377\) −8.92451 −0.459636
\(378\) −13.4173 −0.690111
\(379\) 15.3729 0.789653 0.394827 0.918756i \(-0.370805\pi\)
0.394827 + 0.918756i \(0.370805\pi\)
\(380\) −87.9387 −4.51116
\(381\) 5.47321 0.280401
\(382\) −33.7247 −1.72550
\(383\) 13.8558 0.708001 0.354000 0.935245i \(-0.384821\pi\)
0.354000 + 0.935245i \(0.384821\pi\)
\(384\) 4.85874 0.247947
\(385\) −50.0355 −2.55004
\(386\) 31.1578 1.58589
\(387\) 1.33463 0.0678428
\(388\) 4.79806 0.243585
\(389\) −20.1130 −1.01977 −0.509884 0.860243i \(-0.670312\pi\)
−0.509884 + 0.860243i \(0.670312\pi\)
\(390\) 8.22551 0.416515
\(391\) −57.4221 −2.90396
\(392\) −138.960 −7.01852
\(393\) 11.4817 0.579177
\(394\) −19.5313 −0.983974
\(395\) −6.50957 −0.327532
\(396\) 14.4753 0.727411
\(397\) 31.6025 1.58608 0.793042 0.609168i \(-0.208496\pi\)
0.793042 + 0.609168i \(0.208496\pi\)
\(398\) −49.2519 −2.46877
\(399\) 30.8933 1.54660
\(400\) 42.1578 2.10789
\(401\) −4.71867 −0.235639 −0.117820 0.993035i \(-0.537590\pi\)
−0.117820 + 0.993035i \(0.537590\pi\)
\(402\) 19.1855 0.956884
\(403\) −6.81649 −0.339554
\(404\) 39.7176 1.97602
\(405\) −3.13677 −0.155867
\(406\) 118.223 5.86730
\(407\) −7.00100 −0.347026
\(408\) −50.7595 −2.51297
\(409\) 15.6575 0.774214 0.387107 0.922035i \(-0.373474\pi\)
0.387107 + 0.922035i \(0.373474\pi\)
\(410\) −18.6836 −0.922715
\(411\) −11.4893 −0.566724
\(412\) −33.0304 −1.62729
\(413\) 31.9214 1.57075
\(414\) 20.4953 1.00729
\(415\) −37.5969 −1.84556
\(416\) −8.66842 −0.425004
\(417\) −6.86691 −0.336274
\(418\) −47.5033 −2.32346
\(419\) 31.2654 1.52741 0.763707 0.645563i \(-0.223377\pi\)
0.763707 + 0.645563i \(0.223377\pi\)
\(420\) −76.4509 −3.73042
\(421\) 17.8954 0.872168 0.436084 0.899906i \(-0.356365\pi\)
0.436084 + 0.899906i \(0.356365\pi\)
\(422\) −0.876261 −0.0426557
\(423\) 5.80601 0.282298
\(424\) −17.4815 −0.848977
\(425\) 35.1028 1.70274
\(426\) −27.6358 −1.33896
\(427\) 57.5150 2.78334
\(428\) 82.8281 4.00365
\(429\) 3.11752 0.150515
\(430\) 10.8386 0.522685
\(431\) −25.7198 −1.23888 −0.619440 0.785044i \(-0.712640\pi\)
−0.619440 + 0.785044i \(0.712640\pi\)
\(432\) 8.71148 0.419131
\(433\) 2.43206 0.116877 0.0584387 0.998291i \(-0.481388\pi\)
0.0584387 + 0.998291i \(0.481388\pi\)
\(434\) 90.2979 4.33444
\(435\) 27.6388 1.32518
\(436\) 5.39756 0.258496
\(437\) −47.1905 −2.25743
\(438\) 1.26201 0.0603013
\(439\) −15.5075 −0.740133 −0.370066 0.929005i \(-0.620665\pi\)
−0.370066 + 0.929005i \(0.620665\pi\)
\(440\) 67.5625 3.22092
\(441\) 19.8576 0.945600
\(442\) −19.0211 −0.904741
\(443\) −25.3601 −1.20489 −0.602447 0.798159i \(-0.705808\pi\)
−0.602447 + 0.798159i \(0.705808\pi\)
\(444\) −10.6971 −0.507660
\(445\) −6.74785 −0.319879
\(446\) −25.4588 −1.20551
\(447\) −10.5530 −0.499142
\(448\) 24.5371 1.15927
\(449\) −3.64164 −0.171860 −0.0859298 0.996301i \(-0.527386\pi\)
−0.0859298 + 0.996301i \(0.527386\pi\)
\(450\) −12.5290 −0.590625
\(451\) −7.08119 −0.333440
\(452\) 25.9799 1.22199
\(453\) −12.2609 −0.576066
\(454\) 37.3131 1.75119
\(455\) −16.4651 −0.771897
\(456\) −41.7150 −1.95349
\(457\) −7.26109 −0.339659 −0.169830 0.985473i \(-0.554322\pi\)
−0.169830 + 0.985473i \(0.554322\pi\)
\(458\) −66.1169 −3.08944
\(459\) 7.25364 0.338571
\(460\) 116.781 5.44494
\(461\) 18.5499 0.863956 0.431978 0.901884i \(-0.357816\pi\)
0.431978 + 0.901884i \(0.357816\pi\)
\(462\) −41.2977 −1.92135
\(463\) −24.8013 −1.15261 −0.576306 0.817234i \(-0.695506\pi\)
−0.576306 + 0.817234i \(0.695506\pi\)
\(464\) −76.7588 −3.56344
\(465\) 21.1104 0.978970
\(466\) −65.9947 −3.05715
\(467\) −21.8676 −1.01191 −0.505957 0.862559i \(-0.668861\pi\)
−0.505957 + 0.862559i \(0.668861\pi\)
\(468\) 4.76337 0.220187
\(469\) −38.4038 −1.77332
\(470\) 47.1512 2.17492
\(471\) −4.99350 −0.230089
\(472\) −43.1033 −1.98399
\(473\) 4.10791 0.188882
\(474\) −5.37280 −0.246781
\(475\) 28.8481 1.32364
\(476\) 176.789 8.10311
\(477\) 2.49814 0.114382
\(478\) 21.0882 0.964552
\(479\) 15.0290 0.686695 0.343347 0.939209i \(-0.388439\pi\)
0.343347 + 0.939209i \(0.388439\pi\)
\(480\) 26.8457 1.22533
\(481\) −2.30381 −0.105045
\(482\) 23.3950 1.06561
\(483\) −41.0258 −1.86674
\(484\) −7.17773 −0.326260
\(485\) −3.20024 −0.145315
\(486\) −2.58900 −0.117439
\(487\) −31.3745 −1.42172 −0.710858 0.703336i \(-0.751693\pi\)
−0.710858 + 0.703336i \(0.751693\pi\)
\(488\) −77.6620 −3.51560
\(489\) −1.57054 −0.0710222
\(490\) 161.265 7.28523
\(491\) −33.6092 −1.51676 −0.758380 0.651812i \(-0.774009\pi\)
−0.758380 + 0.651812i \(0.774009\pi\)
\(492\) −10.8196 −0.487785
\(493\) −63.9134 −2.87852
\(494\) −15.6319 −0.703311
\(495\) −9.65482 −0.433952
\(496\) −58.6279 −2.63247
\(497\) 55.3190 2.48140
\(498\) −31.0313 −1.39055
\(499\) −5.69371 −0.254886 −0.127443 0.991846i \(-0.540677\pi\)
−0.127443 + 0.991846i \(0.540677\pi\)
\(500\) 2.37000 0.105990
\(501\) −18.3862 −0.821435
\(502\) −16.2551 −0.725501
\(503\) 43.3295 1.93197 0.965983 0.258605i \(-0.0832628\pi\)
0.965983 + 0.258605i \(0.0832628\pi\)
\(504\) −36.2656 −1.61540
\(505\) −26.4911 −1.17884
\(506\) 63.0835 2.80441
\(507\) −11.9741 −0.531789
\(508\) 25.7400 1.14203
\(509\) 22.3110 0.988918 0.494459 0.869201i \(-0.335366\pi\)
0.494459 + 0.869201i \(0.335366\pi\)
\(510\) 58.9075 2.60847
\(511\) −2.52619 −0.111752
\(512\) 47.3662 2.09331
\(513\) 5.96116 0.263192
\(514\) 44.9013 1.98051
\(515\) 22.0308 0.970795
\(516\) 6.27661 0.276313
\(517\) 17.8706 0.785948
\(518\) 30.5185 1.34091
\(519\) −18.4161 −0.808379
\(520\) 22.2327 0.974970
\(521\) 26.9276 1.17972 0.589860 0.807506i \(-0.299183\pi\)
0.589860 + 0.807506i \(0.299183\pi\)
\(522\) 22.8122 0.998464
\(523\) 12.2573 0.535975 0.267987 0.963422i \(-0.413641\pi\)
0.267987 + 0.963422i \(0.413641\pi\)
\(524\) 53.9975 2.35889
\(525\) 25.0796 1.09456
\(526\) 3.88359 0.169333
\(527\) −48.8167 −2.12649
\(528\) 26.8135 1.16691
\(529\) 39.6681 1.72470
\(530\) 20.2876 0.881239
\(531\) 6.15954 0.267301
\(532\) 145.288 6.29904
\(533\) −2.33020 −0.100932
\(534\) −5.56947 −0.241014
\(535\) −55.2453 −2.38846
\(536\) 51.8564 2.23986
\(537\) 2.59883 0.112148
\(538\) −40.7575 −1.75718
\(539\) 61.1207 2.63265
\(540\) −14.7519 −0.634822
\(541\) −41.5884 −1.78803 −0.894013 0.448042i \(-0.852122\pi\)
−0.894013 + 0.448042i \(0.852122\pi\)
\(542\) −24.0578 −1.03337
\(543\) −25.7664 −1.10574
\(544\) −62.0794 −2.66163
\(545\) −3.60010 −0.154211
\(546\) −13.5898 −0.581590
\(547\) −15.5817 −0.666227 −0.333114 0.942887i \(-0.608099\pi\)
−0.333114 + 0.942887i \(0.608099\pi\)
\(548\) −54.0329 −2.30817
\(549\) 11.0981 0.473654
\(550\) −38.5637 −1.64436
\(551\) −52.5251 −2.23765
\(552\) 55.3968 2.35785
\(553\) 10.7548 0.457341
\(554\) −18.2562 −0.775631
\(555\) 7.13480 0.302855
\(556\) −32.2944 −1.36959
\(557\) 39.4222 1.67037 0.835185 0.549968i \(-0.185360\pi\)
0.835185 + 0.549968i \(0.185360\pi\)
\(558\) 17.4238 0.737610
\(559\) 1.35179 0.0571744
\(560\) −141.615 −5.98432
\(561\) 22.3263 0.942618
\(562\) 66.2377 2.79407
\(563\) −1.50615 −0.0634766 −0.0317383 0.999496i \(-0.510104\pi\)
−0.0317383 + 0.999496i \(0.510104\pi\)
\(564\) 27.3051 1.14975
\(565\) −17.3283 −0.729006
\(566\) −0.740792 −0.0311378
\(567\) 5.18243 0.217642
\(568\) −74.6969 −3.13421
\(569\) −1.10393 −0.0462790 −0.0231395 0.999732i \(-0.507366\pi\)
−0.0231395 + 0.999732i \(0.507366\pi\)
\(570\) 48.4112 2.02772
\(571\) −20.8711 −0.873428 −0.436714 0.899601i \(-0.643858\pi\)
−0.436714 + 0.899601i \(0.643858\pi\)
\(572\) 14.6614 0.613024
\(573\) 13.0262 0.544176
\(574\) 30.8681 1.28841
\(575\) −38.3098 −1.59763
\(576\) 4.73466 0.197278
\(577\) 0.893001 0.0371761 0.0185880 0.999827i \(-0.494083\pi\)
0.0185880 + 0.999827i \(0.494083\pi\)
\(578\) −92.2078 −3.83534
\(579\) −12.0347 −0.500145
\(580\) 129.983 5.39723
\(581\) 62.1159 2.57700
\(582\) −2.64138 −0.109489
\(583\) 7.68915 0.318452
\(584\) 3.41110 0.141152
\(585\) −3.17710 −0.131357
\(586\) 19.6415 0.811385
\(587\) −11.6045 −0.478971 −0.239485 0.970900i \(-0.576979\pi\)
−0.239485 + 0.970900i \(0.576979\pi\)
\(588\) 93.3884 3.85127
\(589\) −40.1184 −1.65305
\(590\) 50.0222 2.05938
\(591\) 7.54398 0.310318
\(592\) −19.8148 −0.814384
\(593\) −15.2866 −0.627745 −0.313872 0.949465i \(-0.601626\pi\)
−0.313872 + 0.949465i \(0.601626\pi\)
\(594\) −7.96880 −0.326964
\(595\) −117.916 −4.83408
\(596\) −49.6299 −2.03292
\(597\) 19.0235 0.778582
\(598\) 20.7588 0.848892
\(599\) −24.2869 −0.992338 −0.496169 0.868226i \(-0.665260\pi\)
−0.496169 + 0.868226i \(0.665260\pi\)
\(600\) −33.8648 −1.38252
\(601\) 2.18062 0.0889495 0.0444748 0.999011i \(-0.485839\pi\)
0.0444748 + 0.999011i \(0.485839\pi\)
\(602\) −17.9071 −0.729838
\(603\) −7.41039 −0.301774
\(604\) −57.6617 −2.34622
\(605\) 4.78745 0.194638
\(606\) −21.8649 −0.888203
\(607\) 25.1637 1.02136 0.510682 0.859769i \(-0.329393\pi\)
0.510682 + 0.859769i \(0.329393\pi\)
\(608\) −51.0179 −2.06905
\(609\) −45.6636 −1.85038
\(610\) 90.1284 3.64919
\(611\) 5.88066 0.237906
\(612\) 34.1131 1.37894
\(613\) 33.2060 1.34118 0.670590 0.741828i \(-0.266041\pi\)
0.670590 + 0.741828i \(0.266041\pi\)
\(614\) −33.3918 −1.34758
\(615\) 7.21652 0.290998
\(616\) −111.624 −4.49745
\(617\) 40.0478 1.61226 0.806132 0.591735i \(-0.201557\pi\)
0.806132 + 0.591735i \(0.201557\pi\)
\(618\) 18.1836 0.731451
\(619\) 32.3170 1.29893 0.649465 0.760392i \(-0.274993\pi\)
0.649465 + 0.760392i \(0.274993\pi\)
\(620\) 99.2799 3.98718
\(621\) −7.91632 −0.317671
\(622\) 41.1222 1.64885
\(623\) 11.1485 0.446655
\(624\) 8.82348 0.353222
\(625\) −25.7775 −1.03110
\(626\) −71.7292 −2.86688
\(627\) 18.3482 0.732755
\(628\) −23.4840 −0.937112
\(629\) −16.4989 −0.657853
\(630\) 42.0870 1.67679
\(631\) −46.2885 −1.84272 −0.921358 0.388714i \(-0.872919\pi\)
−0.921358 + 0.388714i \(0.872919\pi\)
\(632\) −14.5221 −0.577660
\(633\) 0.338456 0.0134524
\(634\) 37.9415 1.50685
\(635\) −17.1682 −0.681300
\(636\) 11.7485 0.465859
\(637\) 20.1129 0.796903
\(638\) 70.2148 2.77983
\(639\) 10.6743 0.422270
\(640\) −15.2408 −0.602444
\(641\) −5.52413 −0.218190 −0.109095 0.994031i \(-0.534795\pi\)
−0.109095 + 0.994031i \(0.534795\pi\)
\(642\) −45.5978 −1.79960
\(643\) 26.0076 1.02564 0.512820 0.858496i \(-0.328601\pi\)
0.512820 + 0.858496i \(0.328601\pi\)
\(644\) −192.940 −7.60291
\(645\) −4.18642 −0.164840
\(646\) −111.948 −4.40455
\(647\) −43.8682 −1.72464 −0.862319 0.506365i \(-0.830989\pi\)
−0.862319 + 0.506365i \(0.830989\pi\)
\(648\) −6.99780 −0.274900
\(649\) 18.9588 0.744196
\(650\) −12.6901 −0.497748
\(651\) −34.8776 −1.36696
\(652\) −7.38609 −0.289262
\(653\) 1.79159 0.0701103 0.0350552 0.999385i \(-0.488839\pi\)
0.0350552 + 0.999385i \(0.488839\pi\)
\(654\) −2.97142 −0.116192
\(655\) −36.0156 −1.40725
\(656\) −20.0418 −0.782501
\(657\) −0.487453 −0.0190173
\(658\) −77.9010 −3.03690
\(659\) 6.06276 0.236171 0.118086 0.993003i \(-0.462324\pi\)
0.118086 + 0.993003i \(0.462324\pi\)
\(660\) −45.4057 −1.76741
\(661\) 19.8947 0.773814 0.386907 0.922119i \(-0.373543\pi\)
0.386907 + 0.922119i \(0.373543\pi\)
\(662\) −0.626800 −0.0243613
\(663\) 7.34690 0.285330
\(664\) −83.8747 −3.25497
\(665\) −96.9053 −3.75783
\(666\) 5.88884 0.228188
\(667\) 69.7525 2.70083
\(668\) −86.4685 −3.34556
\(669\) 9.83348 0.380184
\(670\) −60.1805 −2.32497
\(671\) 34.1593 1.31870
\(672\) −44.3532 −1.71096
\(673\) −7.73906 −0.298319 −0.149159 0.988813i \(-0.547657\pi\)
−0.149159 + 0.988813i \(0.547657\pi\)
\(674\) −88.1757 −3.39640
\(675\) 4.83934 0.186266
\(676\) −56.3131 −2.16589
\(677\) −29.4605 −1.13226 −0.566130 0.824316i \(-0.691560\pi\)
−0.566130 + 0.824316i \(0.691560\pi\)
\(678\) −14.3022 −0.549274
\(679\) 5.28729 0.202908
\(680\) 159.221 6.10585
\(681\) −14.4122 −0.552276
\(682\) 53.6297 2.05359
\(683\) 34.1778 1.30778 0.653889 0.756591i \(-0.273136\pi\)
0.653889 + 0.756591i \(0.273136\pi\)
\(684\) 28.0348 1.07194
\(685\) 36.0392 1.37699
\(686\) −172.514 −6.58663
\(687\) 25.5377 0.974323
\(688\) 11.6266 0.443259
\(689\) 2.53026 0.0963953
\(690\) −64.2892 −2.44745
\(691\) 43.2751 1.64626 0.823132 0.567850i \(-0.192225\pi\)
0.823132 + 0.567850i \(0.192225\pi\)
\(692\) −86.6093 −3.29239
\(693\) 15.9513 0.605938
\(694\) 70.2055 2.66497
\(695\) 21.5400 0.817057
\(696\) 61.6592 2.33719
\(697\) −16.6879 −0.632098
\(698\) 27.2136 1.03005
\(699\) 25.4905 0.964138
\(700\) 117.947 4.45797
\(701\) 9.92122 0.374719 0.187360 0.982291i \(-0.440007\pi\)
0.187360 + 0.982291i \(0.440007\pi\)
\(702\) −2.62228 −0.0989717
\(703\) −13.5591 −0.511389
\(704\) 14.5730 0.549242
\(705\) −18.2121 −0.685909
\(706\) −73.5077 −2.76650
\(707\) 43.7674 1.64604
\(708\) 28.9677 1.08867
\(709\) −17.9596 −0.674488 −0.337244 0.941417i \(-0.609495\pi\)
−0.337244 + 0.941417i \(0.609495\pi\)
\(710\) 86.6873 3.25332
\(711\) 2.07524 0.0778278
\(712\) −15.0537 −0.564162
\(713\) 53.2765 1.99522
\(714\) −97.3242 −3.64227
\(715\) −9.77896 −0.365712
\(716\) 12.2220 0.456759
\(717\) −8.14532 −0.304193
\(718\) −42.5151 −1.58665
\(719\) −31.0657 −1.15855 −0.579277 0.815130i \(-0.696665\pi\)
−0.579277 + 0.815130i \(0.696665\pi\)
\(720\) −27.3259 −1.01838
\(721\) −36.3983 −1.35555
\(722\) −42.8103 −1.59323
\(723\) −9.03631 −0.336064
\(724\) −121.177 −4.50351
\(725\) −42.6405 −1.58363
\(726\) 3.95141 0.146651
\(727\) −35.3498 −1.31105 −0.655525 0.755174i \(-0.727553\pi\)
−0.655525 + 0.755174i \(0.727553\pi\)
\(728\) −36.7319 −1.36138
\(729\) 1.00000 0.0370370
\(730\) −3.95865 −0.146516
\(731\) 9.68089 0.358061
\(732\) 52.1931 1.92911
\(733\) −45.7739 −1.69070 −0.845349 0.534215i \(-0.820607\pi\)
−0.845349 + 0.534215i \(0.820607\pi\)
\(734\) −72.8380 −2.68850
\(735\) −62.2888 −2.29756
\(736\) 67.7509 2.49733
\(737\) −22.8088 −0.840173
\(738\) 5.95630 0.219254
\(739\) −17.0292 −0.626430 −0.313215 0.949682i \(-0.601406\pi\)
−0.313215 + 0.949682i \(0.601406\pi\)
\(740\) 33.5542 1.23348
\(741\) 6.03781 0.221804
\(742\) −33.5183 −1.23050
\(743\) 39.2325 1.43930 0.719650 0.694337i \(-0.244302\pi\)
0.719650 + 0.694337i \(0.244302\pi\)
\(744\) 47.0949 1.72658
\(745\) 33.1025 1.21278
\(746\) 80.4619 2.94592
\(747\) 11.9859 0.438540
\(748\) 104.998 3.83912
\(749\) 91.2737 3.33507
\(750\) −1.30471 −0.0476413
\(751\) 27.7034 1.01091 0.505456 0.862852i \(-0.331324\pi\)
0.505456 + 0.862852i \(0.331324\pi\)
\(752\) 50.5790 1.84442
\(753\) 6.27854 0.228803
\(754\) 23.1055 0.841454
\(755\) 38.4596 1.39969
\(756\) 24.3725 0.886418
\(757\) −27.0986 −0.984916 −0.492458 0.870336i \(-0.663902\pi\)
−0.492458 + 0.870336i \(0.663902\pi\)
\(758\) −39.8004 −1.44562
\(759\) −24.3660 −0.884431
\(760\) 130.851 4.74645
\(761\) −6.54814 −0.237370 −0.118685 0.992932i \(-0.537868\pi\)
−0.118685 + 0.992932i \(0.537868\pi\)
\(762\) −14.1701 −0.513329
\(763\) 5.94793 0.215329
\(764\) 61.2607 2.21634
\(765\) −22.7530 −0.822637
\(766\) −35.8727 −1.29613
\(767\) 6.23874 0.225268
\(768\) −22.0486 −0.795610
\(769\) 8.93807 0.322315 0.161157 0.986929i \(-0.448477\pi\)
0.161157 + 0.986929i \(0.448477\pi\)
\(770\) 129.542 4.66836
\(771\) −17.3431 −0.624598
\(772\) −56.5980 −2.03701
\(773\) 39.5917 1.42401 0.712006 0.702173i \(-0.247787\pi\)
0.712006 + 0.702173i \(0.247787\pi\)
\(774\) −3.45534 −0.124200
\(775\) −32.5686 −1.16990
\(776\) −7.13939 −0.256289
\(777\) −11.7878 −0.422884
\(778\) 52.0724 1.86688
\(779\) −13.7144 −0.491368
\(780\) −14.9416 −0.534995
\(781\) 32.8551 1.17565
\(782\) 148.666 5.31627
\(783\) −8.81122 −0.314887
\(784\) 172.989 6.17818
\(785\) 15.6635 0.559054
\(786\) −29.7262 −1.06030
\(787\) −27.9948 −0.997909 −0.498954 0.866628i \(-0.666282\pi\)
−0.498954 + 0.866628i \(0.666282\pi\)
\(788\) 35.4786 1.26387
\(789\) −1.50004 −0.0534027
\(790\) 16.8533 0.599612
\(791\) 28.6290 1.01793
\(792\) −21.5389 −0.765350
\(793\) 11.2408 0.399171
\(794\) −81.8187 −2.90364
\(795\) −7.83610 −0.277918
\(796\) 89.4659 3.17103
\(797\) 6.10535 0.216263 0.108131 0.994137i \(-0.465513\pi\)
0.108131 + 0.994137i \(0.465513\pi\)
\(798\) −79.9827 −2.83136
\(799\) 42.1147 1.48991
\(800\) −41.4169 −1.46431
\(801\) 2.15121 0.0760092
\(802\) 12.2166 0.431384
\(803\) −1.50035 −0.0529464
\(804\) −34.8503 −1.22908
\(805\) 128.689 4.53568
\(806\) 17.6479 0.621620
\(807\) 15.7426 0.554166
\(808\) −59.0988 −2.07909
\(809\) −28.8585 −1.01461 −0.507306 0.861766i \(-0.669359\pi\)
−0.507306 + 0.861766i \(0.669359\pi\)
\(810\) 8.12109 0.285346
\(811\) 34.8022 1.22207 0.611036 0.791603i \(-0.290753\pi\)
0.611036 + 0.791603i \(0.290753\pi\)
\(812\) −214.751 −7.53629
\(813\) 9.29233 0.325896
\(814\) 18.1256 0.635300
\(815\) 4.92642 0.172565
\(816\) 63.1899 2.21209
\(817\) 7.95592 0.278342
\(818\) −40.5372 −1.41735
\(819\) 5.24906 0.183417
\(820\) 33.9386 1.18519
\(821\) −54.0615 −1.88676 −0.943380 0.331713i \(-0.892373\pi\)
−0.943380 + 0.331713i \(0.892373\pi\)
\(822\) 29.7457 1.03750
\(823\) −44.7392 −1.55951 −0.779756 0.626084i \(-0.784657\pi\)
−0.779756 + 0.626084i \(0.784657\pi\)
\(824\) 49.1484 1.71217
\(825\) 14.8952 0.518586
\(826\) −82.6444 −2.87557
\(827\) 17.1697 0.597050 0.298525 0.954402i \(-0.403505\pi\)
0.298525 + 0.954402i \(0.403505\pi\)
\(828\) −37.2297 −1.29382
\(829\) 21.9088 0.760924 0.380462 0.924796i \(-0.375765\pi\)
0.380462 + 0.924796i \(0.375765\pi\)
\(830\) 97.3383 3.37866
\(831\) 7.05145 0.244612
\(832\) 4.79554 0.166255
\(833\) 144.040 4.99069
\(834\) 17.7784 0.615616
\(835\) 57.6733 1.99587
\(836\) 86.2895 2.98439
\(837\) −6.72996 −0.232622
\(838\) −80.9460 −2.79623
\(839\) −12.5103 −0.431905 −0.215953 0.976404i \(-0.569286\pi\)
−0.215953 + 0.976404i \(0.569286\pi\)
\(840\) 113.757 3.92499
\(841\) 48.6376 1.67716
\(842\) −46.3311 −1.59668
\(843\) −25.5843 −0.881171
\(844\) 1.59172 0.0547894
\(845\) 37.5601 1.29211
\(846\) −15.0317 −0.516802
\(847\) −7.90961 −0.271777
\(848\) 21.7625 0.747328
\(849\) 0.286131 0.00981998
\(850\) −90.8811 −3.11720
\(851\) 18.0062 0.617244
\(852\) 50.2004 1.71984
\(853\) −30.2828 −1.03686 −0.518432 0.855119i \(-0.673484\pi\)
−0.518432 + 0.855119i \(0.673484\pi\)
\(854\) −148.906 −5.09546
\(855\) −18.6988 −0.639486
\(856\) −123.246 −4.21247
\(857\) 9.23836 0.315576 0.157788 0.987473i \(-0.449564\pi\)
0.157788 + 0.987473i \(0.449564\pi\)
\(858\) −8.07125 −0.275548
\(859\) 20.4742 0.698571 0.349286 0.937016i \(-0.386424\pi\)
0.349286 + 0.937016i \(0.386424\pi\)
\(860\) −19.6883 −0.671366
\(861\) −11.9228 −0.406328
\(862\) 66.5885 2.26801
\(863\) 35.8291 1.21964 0.609819 0.792541i \(-0.291242\pi\)
0.609819 + 0.792541i \(0.291242\pi\)
\(864\) −8.55838 −0.291162
\(865\) 57.7673 1.96415
\(866\) −6.29660 −0.213967
\(867\) 35.6153 1.20956
\(868\) −164.026 −5.56740
\(869\) 6.38750 0.216681
\(870\) −71.5568 −2.42600
\(871\) −7.50567 −0.254320
\(872\) −8.03144 −0.271979
\(873\) 1.02023 0.0345297
\(874\) 122.176 4.13266
\(875\) 2.61166 0.0882903
\(876\) −2.29244 −0.0774544
\(877\) 44.3110 1.49628 0.748138 0.663543i \(-0.230948\pi\)
0.748138 + 0.663543i \(0.230948\pi\)
\(878\) 40.1489 1.35496
\(879\) −7.58655 −0.255888
\(880\) −84.1078 −2.83527
\(881\) −52.2531 −1.76045 −0.880227 0.474554i \(-0.842609\pi\)
−0.880227 + 0.474554i \(0.842609\pi\)
\(882\) −51.4113 −1.73111
\(883\) −48.0257 −1.61619 −0.808097 0.589050i \(-0.799502\pi\)
−0.808097 + 0.589050i \(0.799502\pi\)
\(884\) 34.5517 1.16210
\(885\) −19.3211 −0.649471
\(886\) 65.6572 2.20580
\(887\) 1.77558 0.0596181 0.0298091 0.999556i \(-0.490510\pi\)
0.0298091 + 0.999556i \(0.490510\pi\)
\(888\) 15.9170 0.534138
\(889\) 28.3645 0.951316
\(890\) 17.4702 0.585601
\(891\) 3.07795 0.103115
\(892\) 46.2459 1.54843
\(893\) 34.6106 1.15820
\(894\) 27.3218 0.913777
\(895\) −8.15193 −0.272489
\(896\) 25.1801 0.841208
\(897\) −8.01810 −0.267717
\(898\) 9.42819 0.314623
\(899\) 59.2992 1.97774
\(900\) 22.7590 0.758632
\(901\) 18.1206 0.603685
\(902\) 18.3332 0.610428
\(903\) 6.91661 0.230170
\(904\) −38.6575 −1.28573
\(905\) 80.8235 2.68666
\(906\) 31.7433 1.05460
\(907\) 14.9102 0.495086 0.247543 0.968877i \(-0.420377\pi\)
0.247543 + 0.968877i \(0.420377\pi\)
\(908\) −67.7791 −2.24933
\(909\) 8.44534 0.280114
\(910\) 42.6281 1.41311
\(911\) −20.3190 −0.673199 −0.336600 0.941648i \(-0.609277\pi\)
−0.336600 + 0.941648i \(0.609277\pi\)
\(912\) 51.9305 1.71959
\(913\) 36.8919 1.22094
\(914\) 18.7989 0.621813
\(915\) −34.8121 −1.15085
\(916\) 120.101 3.96825
\(917\) 59.5033 1.96497
\(918\) −18.7796 −0.619820
\(919\) −49.4532 −1.63131 −0.815655 0.578538i \(-0.803623\pi\)
−0.815655 + 0.578538i \(0.803623\pi\)
\(920\) −173.767 −5.72894
\(921\) 12.8976 0.424990
\(922\) −48.0257 −1.58164
\(923\) 10.8116 0.355868
\(924\) 75.0172 2.46788
\(925\) −11.0074 −0.361921
\(926\) 64.2104 2.11008
\(927\) −7.02341 −0.230679
\(928\) 75.4098 2.47545
\(929\) −30.3994 −0.997371 −0.498686 0.866783i \(-0.666184\pi\)
−0.498686 + 0.866783i \(0.666184\pi\)
\(930\) −54.6546 −1.79220
\(931\) 118.374 3.87956
\(932\) 119.879 3.92677
\(933\) −15.8834 −0.520000
\(934\) 56.6152 1.85251
\(935\) −70.0326 −2.29031
\(936\) −7.08777 −0.231671
\(937\) 16.3985 0.535716 0.267858 0.963458i \(-0.413684\pi\)
0.267858 + 0.963458i \(0.413684\pi\)
\(938\) 99.4274 3.24642
\(939\) 27.7054 0.904132
\(940\) −85.6499 −2.79359
\(941\) −7.36842 −0.240204 −0.120102 0.992762i \(-0.538322\pi\)
−0.120102 + 0.992762i \(0.538322\pi\)
\(942\) 12.9282 0.421222
\(943\) 18.2124 0.593079
\(944\) 53.6587 1.74644
\(945\) −16.2561 −0.528811
\(946\) −10.6354 −0.345785
\(947\) 30.6708 0.996668 0.498334 0.866985i \(-0.333945\pi\)
0.498334 + 0.866985i \(0.333945\pi\)
\(948\) 9.75967 0.316979
\(949\) −0.493720 −0.0160268
\(950\) −74.6876 −2.42319
\(951\) −14.6549 −0.475218
\(952\) −263.058 −8.52575
\(953\) 14.4813 0.469097 0.234548 0.972104i \(-0.424639\pi\)
0.234548 + 0.972104i \(0.424639\pi\)
\(954\) −6.46768 −0.209399
\(955\) −40.8601 −1.32220
\(956\) −38.3067 −1.23893
\(957\) −27.1205 −0.876681
\(958\) −38.9101 −1.25713
\(959\) −59.5423 −1.92272
\(960\) −14.8516 −0.479332
\(961\) 14.2924 0.461045
\(962\) 5.96456 0.192305
\(963\) 17.6121 0.567543
\(964\) −42.4969 −1.36873
\(965\) 37.7501 1.21522
\(966\) 106.216 3.41743
\(967\) 13.4446 0.432349 0.216174 0.976355i \(-0.430642\pi\)
0.216174 + 0.976355i \(0.430642\pi\)
\(968\) 10.6803 0.343277
\(969\) 43.2401 1.38907
\(970\) 8.28541 0.266029
\(971\) −20.3832 −0.654127 −0.327064 0.945002i \(-0.606059\pi\)
−0.327064 + 0.945002i \(0.606059\pi\)
\(972\) 4.70290 0.150846
\(973\) −35.5873 −1.14088
\(974\) 81.2285 2.60273
\(975\) 4.90156 0.156976
\(976\) 96.6805 3.09467
\(977\) 48.3690 1.54746 0.773731 0.633514i \(-0.218388\pi\)
0.773731 + 0.633514i \(0.218388\pi\)
\(978\) 4.06612 0.130020
\(979\) 6.62131 0.211618
\(980\) −292.938 −9.35756
\(981\) 1.14771 0.0366435
\(982\) 87.0140 2.77673
\(983\) −38.7186 −1.23493 −0.617466 0.786597i \(-0.711841\pi\)
−0.617466 + 0.786597i \(0.711841\pi\)
\(984\) 16.0993 0.513227
\(985\) −23.6637 −0.753990
\(986\) 165.472 5.26969
\(987\) 30.0893 0.957752
\(988\) 28.3952 0.903372
\(989\) −10.5653 −0.335958
\(990\) 24.9963 0.794435
\(991\) −35.0461 −1.11327 −0.556637 0.830756i \(-0.687909\pi\)
−0.556637 + 0.830756i \(0.687909\pi\)
\(992\) 57.5976 1.82873
\(993\) 0.242102 0.00768286
\(994\) −143.221 −4.54269
\(995\) −59.6725 −1.89175
\(996\) 56.3683 1.78610
\(997\) 49.7947 1.57701 0.788507 0.615026i \(-0.210855\pi\)
0.788507 + 0.615026i \(0.210855\pi\)
\(998\) 14.7410 0.466618
\(999\) −2.27457 −0.0719641
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 \(a_p\))