Properties

Label 8007.2.a.e.1.5
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 46
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(46\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.45922 q^{2}\) \(+1.00000 q^{3}\) \(+4.04774 q^{4}\) \(+2.82362 q^{5}\) \(-2.45922 q^{6}\) \(+4.27749 q^{7}\) \(-5.03584 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.45922 q^{2}\) \(+1.00000 q^{3}\) \(+4.04774 q^{4}\) \(+2.82362 q^{5}\) \(-2.45922 q^{6}\) \(+4.27749 q^{7}\) \(-5.03584 q^{8}\) \(+1.00000 q^{9}\) \(-6.94390 q^{10}\) \(-3.19677 q^{11}\) \(+4.04774 q^{12}\) \(+0.537035 q^{13}\) \(-10.5193 q^{14}\) \(+2.82362 q^{15}\) \(+4.28873 q^{16}\) \(-1.00000 q^{17}\) \(-2.45922 q^{18}\) \(-4.65843 q^{19}\) \(+11.4293 q^{20}\) \(+4.27749 q^{21}\) \(+7.86155 q^{22}\) \(-1.04489 q^{23}\) \(-5.03584 q^{24}\) \(+2.97284 q^{25}\) \(-1.32068 q^{26}\) \(+1.00000 q^{27}\) \(+17.3142 q^{28}\) \(-9.34609 q^{29}\) \(-6.94390 q^{30}\) \(-8.67933 q^{31}\) \(-0.475238 q^{32}\) \(-3.19677 q^{33}\) \(+2.45922 q^{34}\) \(+12.0780 q^{35}\) \(+4.04774 q^{36}\) \(-5.77798 q^{37}\) \(+11.4561 q^{38}\) \(+0.537035 q^{39}\) \(-14.2193 q^{40}\) \(-7.18874 q^{41}\) \(-10.5193 q^{42}\) \(-1.84695 q^{43}\) \(-12.9397 q^{44}\) \(+2.82362 q^{45}\) \(+2.56962 q^{46}\) \(-9.23665 q^{47}\) \(+4.28873 q^{48}\) \(+11.2969 q^{49}\) \(-7.31086 q^{50}\) \(-1.00000 q^{51}\) \(+2.17378 q^{52}\) \(+1.01554 q^{53}\) \(-2.45922 q^{54}\) \(-9.02647 q^{55}\) \(-21.5408 q^{56}\) \(-4.65843 q^{57}\) \(+22.9840 q^{58}\) \(-13.4723 q^{59}\) \(+11.4293 q^{60}\) \(+2.60984 q^{61}\) \(+21.3443 q^{62}\) \(+4.27749 q^{63}\) \(-7.40875 q^{64}\) \(+1.51638 q^{65}\) \(+7.86155 q^{66}\) \(+2.87750 q^{67}\) \(-4.04774 q^{68}\) \(-1.04489 q^{69}\) \(-29.7025 q^{70}\) \(+15.8287 q^{71}\) \(-5.03584 q^{72}\) \(+9.34396 q^{73}\) \(+14.2093 q^{74}\) \(+2.97284 q^{75}\) \(-18.8561 q^{76}\) \(-13.6742 q^{77}\) \(-1.32068 q^{78}\) \(+3.82203 q^{79}\) \(+12.1098 q^{80}\) \(+1.00000 q^{81}\) \(+17.6787 q^{82}\) \(-6.64544 q^{83}\) \(+17.3142 q^{84}\) \(-2.82362 q^{85}\) \(+4.54204 q^{86}\) \(-9.34609 q^{87}\) \(+16.0984 q^{88}\) \(-8.76855 q^{89}\) \(-6.94390 q^{90}\) \(+2.29716 q^{91}\) \(-4.22946 q^{92}\) \(-8.67933 q^{93}\) \(+22.7149 q^{94}\) \(-13.1536 q^{95}\) \(-0.475238 q^{96}\) \(+14.0107 q^{97}\) \(-27.7816 q^{98}\) \(-3.19677 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 43q^{12} \) \(\mathstrut -\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 19q^{15} \) \(\mathstrut +\mathstrut 33q^{16} \) \(\mathstrut -\mathstrut 46q^{17} \) \(\mathstrut -\mathstrut 5q^{18} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 56q^{20} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 64q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 11q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut +\mathstrut 46q^{27} \) \(\mathstrut -\mathstrut 38q^{28} \) \(\mathstrut -\mathstrut 51q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 19q^{31} \) \(\mathstrut -\mathstrut 61q^{32} \) \(\mathstrut -\mathstrut 25q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 39q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut -\mathstrut 48q^{38} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 53q^{41} \) \(\mathstrut -\mathstrut 28q^{42} \) \(\mathstrut -\mathstrut 33q^{43} \) \(\mathstrut -\mathstrut 62q^{44} \) \(\mathstrut -\mathstrut 19q^{45} \) \(\mathstrut +\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 45q^{47} \) \(\mathstrut +\mathstrut 33q^{48} \) \(\mathstrut +\mathstrut 21q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 63q^{52} \) \(\mathstrut -\mathstrut 47q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 82q^{56} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut -\mathstrut 21q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 74q^{64} \) \(\mathstrut -\mathstrut 85q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut -\mathstrut 52q^{67} \) \(\mathstrut -\mathstrut 43q^{68} \) \(\mathstrut -\mathstrut 64q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 48q^{71} \) \(\mathstrut -\mathstrut 18q^{72} \) \(\mathstrut -\mathstrut 39q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 42q^{76} \) \(\mathstrut -\mathstrut 78q^{77} \) \(\mathstrut -\mathstrut 13q^{78} \) \(\mathstrut -\mathstrut 26q^{79} \) \(\mathstrut -\mathstrut 78q^{80} \) \(\mathstrut +\mathstrut 46q^{81} \) \(\mathstrut +\mathstrut 3q^{82} \) \(\mathstrut -\mathstrut 47q^{83} \) \(\mathstrut -\mathstrut 38q^{84} \) \(\mathstrut +\mathstrut 19q^{85} \) \(\mathstrut -\mathstrut 6q^{86} \) \(\mathstrut -\mathstrut 51q^{87} \) \(\mathstrut -\mathstrut 58q^{88} \) \(\mathstrut -\mathstrut 58q^{89} \) \(\mathstrut -\mathstrut 10q^{90} \) \(\mathstrut -\mathstrut 43q^{91} \) \(\mathstrut -\mathstrut 68q^{92} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 78q^{95} \) \(\mathstrut -\mathstrut 61q^{96} \) \(\mathstrut -\mathstrut 44q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut -\mathstrut 25q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.45922 −1.73893 −0.869464 0.493996i \(-0.835536\pi\)
−0.869464 + 0.493996i \(0.835536\pi\)
\(3\) 1.00000 0.577350
\(4\) 4.04774 2.02387
\(5\) 2.82362 1.26276 0.631381 0.775473i \(-0.282488\pi\)
0.631381 + 0.775473i \(0.282488\pi\)
\(6\) −2.45922 −1.00397
\(7\) 4.27749 1.61674 0.808370 0.588675i \(-0.200350\pi\)
0.808370 + 0.588675i \(0.200350\pi\)
\(8\) −5.03584 −1.78044
\(9\) 1.00000 0.333333
\(10\) −6.94390 −2.19585
\(11\) −3.19677 −0.963862 −0.481931 0.876209i \(-0.660064\pi\)
−0.481931 + 0.876209i \(0.660064\pi\)
\(12\) 4.04774 1.16848
\(13\) 0.537035 0.148947 0.0744734 0.997223i \(-0.476272\pi\)
0.0744734 + 0.997223i \(0.476272\pi\)
\(14\) −10.5193 −2.81139
\(15\) 2.82362 0.729056
\(16\) 4.28873 1.07218
\(17\) −1.00000 −0.242536
\(18\) −2.45922 −0.579643
\(19\) −4.65843 −1.06872 −0.534358 0.845258i \(-0.679447\pi\)
−0.534358 + 0.845258i \(0.679447\pi\)
\(20\) 11.4293 2.55567
\(21\) 4.27749 0.933425
\(22\) 7.86155 1.67609
\(23\) −1.04489 −0.217875 −0.108938 0.994049i \(-0.534745\pi\)
−0.108938 + 0.994049i \(0.534745\pi\)
\(24\) −5.03584 −1.02794
\(25\) 2.97284 0.594568
\(26\) −1.32068 −0.259008
\(27\) 1.00000 0.192450
\(28\) 17.3142 3.27207
\(29\) −9.34609 −1.73553 −0.867763 0.496979i \(-0.834443\pi\)
−0.867763 + 0.496979i \(0.834443\pi\)
\(30\) −6.94390 −1.26778
\(31\) −8.67933 −1.55885 −0.779427 0.626493i \(-0.784490\pi\)
−0.779427 + 0.626493i \(0.784490\pi\)
\(32\) −0.475238 −0.0840110
\(33\) −3.19677 −0.556486
\(34\) 2.45922 0.421752
\(35\) 12.0780 2.04156
\(36\) 4.04774 0.674624
\(37\) −5.77798 −0.949893 −0.474947 0.880015i \(-0.657533\pi\)
−0.474947 + 0.880015i \(0.657533\pi\)
\(38\) 11.4561 1.85842
\(39\) 0.537035 0.0859944
\(40\) −14.2193 −2.24827
\(41\) −7.18874 −1.12269 −0.561347 0.827581i \(-0.689717\pi\)
−0.561347 + 0.827581i \(0.689717\pi\)
\(42\) −10.5193 −1.62316
\(43\) −1.84695 −0.281657 −0.140828 0.990034i \(-0.544977\pi\)
−0.140828 + 0.990034i \(0.544977\pi\)
\(44\) −12.9397 −1.95073
\(45\) 2.82362 0.420921
\(46\) 2.56962 0.378869
\(47\) −9.23665 −1.34730 −0.673652 0.739048i \(-0.735275\pi\)
−0.673652 + 0.739048i \(0.735275\pi\)
\(48\) 4.28873 0.619025
\(49\) 11.2969 1.61385
\(50\) −7.31086 −1.03391
\(51\) −1.00000 −0.140028
\(52\) 2.17378 0.301449
\(53\) 1.01554 0.139496 0.0697478 0.997565i \(-0.477781\pi\)
0.0697478 + 0.997565i \(0.477781\pi\)
\(54\) −2.45922 −0.334657
\(55\) −9.02647 −1.21713
\(56\) −21.5408 −2.87850
\(57\) −4.65843 −0.617023
\(58\) 22.9840 3.01795
\(59\) −13.4723 −1.75394 −0.876969 0.480547i \(-0.840438\pi\)
−0.876969 + 0.480547i \(0.840438\pi\)
\(60\) 11.4293 1.47552
\(61\) 2.60984 0.334156 0.167078 0.985944i \(-0.446567\pi\)
0.167078 + 0.985944i \(0.446567\pi\)
\(62\) 21.3443 2.71073
\(63\) 4.27749 0.538913
\(64\) −7.40875 −0.926094
\(65\) 1.51638 0.188084
\(66\) 7.86155 0.967689
\(67\) 2.87750 0.351543 0.175771 0.984431i \(-0.443758\pi\)
0.175771 + 0.984431i \(0.443758\pi\)
\(68\) −4.04774 −0.490861
\(69\) −1.04489 −0.125790
\(70\) −29.7025 −3.55012
\(71\) 15.8287 1.87852 0.939262 0.343200i \(-0.111511\pi\)
0.939262 + 0.343200i \(0.111511\pi\)
\(72\) −5.03584 −0.593479
\(73\) 9.34396 1.09363 0.546814 0.837254i \(-0.315840\pi\)
0.546814 + 0.837254i \(0.315840\pi\)
\(74\) 14.2093 1.65180
\(75\) 2.97284 0.343274
\(76\) −18.8561 −2.16294
\(77\) −13.6742 −1.55831
\(78\) −1.32068 −0.149538
\(79\) 3.82203 0.430012 0.215006 0.976613i \(-0.431023\pi\)
0.215006 + 0.976613i \(0.431023\pi\)
\(80\) 12.1098 1.35391
\(81\) 1.00000 0.111111
\(82\) 17.6787 1.95228
\(83\) −6.64544 −0.729432 −0.364716 0.931119i \(-0.618834\pi\)
−0.364716 + 0.931119i \(0.618834\pi\)
\(84\) 17.3142 1.88913
\(85\) −2.82362 −0.306265
\(86\) 4.54204 0.489781
\(87\) −9.34609 −1.00201
\(88\) 16.0984 1.71610
\(89\) −8.76855 −0.929464 −0.464732 0.885451i \(-0.653849\pi\)
−0.464732 + 0.885451i \(0.653849\pi\)
\(90\) −6.94390 −0.731951
\(91\) 2.29716 0.240808
\(92\) −4.22946 −0.440951
\(93\) −8.67933 −0.900005
\(94\) 22.7149 2.34287
\(95\) −13.1536 −1.34953
\(96\) −0.475238 −0.0485038
\(97\) 14.0107 1.42257 0.711285 0.702904i \(-0.248114\pi\)
0.711285 + 0.702904i \(0.248114\pi\)
\(98\) −27.7816 −2.80636
\(99\) −3.19677 −0.321287
\(100\) 12.0333 1.20333
\(101\) −6.64364 −0.661067 −0.330534 0.943794i \(-0.607229\pi\)
−0.330534 + 0.943794i \(0.607229\pi\)
\(102\) 2.45922 0.243499
\(103\) 13.7755 1.35734 0.678669 0.734444i \(-0.262557\pi\)
0.678669 + 0.734444i \(0.262557\pi\)
\(104\) −2.70442 −0.265190
\(105\) 12.0780 1.17869
\(106\) −2.49744 −0.242573
\(107\) 4.18323 0.404408 0.202204 0.979343i \(-0.435190\pi\)
0.202204 + 0.979343i \(0.435190\pi\)
\(108\) 4.04774 0.389494
\(109\) −6.51227 −0.623763 −0.311881 0.950121i \(-0.600959\pi\)
−0.311881 + 0.950121i \(0.600959\pi\)
\(110\) 22.1980 2.11650
\(111\) −5.77798 −0.548421
\(112\) 18.3450 1.73344
\(113\) 2.08121 0.195783 0.0978917 0.995197i \(-0.468790\pi\)
0.0978917 + 0.995197i \(0.468790\pi\)
\(114\) 11.4561 1.07296
\(115\) −2.95038 −0.275125
\(116\) −37.8306 −3.51248
\(117\) 0.537035 0.0496489
\(118\) 33.1312 3.04997
\(119\) −4.27749 −0.392117
\(120\) −14.2193 −1.29804
\(121\) −0.780666 −0.0709696
\(122\) −6.41816 −0.581073
\(123\) −7.18874 −0.648187
\(124\) −35.1317 −3.15492
\(125\) −5.72393 −0.511964
\(126\) −10.5193 −0.937131
\(127\) −21.3532 −1.89479 −0.947395 0.320066i \(-0.896295\pi\)
−0.947395 + 0.320066i \(0.896295\pi\)
\(128\) 19.1702 1.69442
\(129\) −1.84695 −0.162615
\(130\) −3.72912 −0.327065
\(131\) −10.0499 −0.878062 −0.439031 0.898472i \(-0.644678\pi\)
−0.439031 + 0.898472i \(0.644678\pi\)
\(132\) −12.9397 −1.12626
\(133\) −19.9264 −1.72784
\(134\) −7.07640 −0.611308
\(135\) 2.82362 0.243019
\(136\) 5.03584 0.431820
\(137\) −17.8050 −1.52118 −0.760592 0.649230i \(-0.775091\pi\)
−0.760592 + 0.649230i \(0.775091\pi\)
\(138\) 2.56962 0.218740
\(139\) −3.67569 −0.311768 −0.155884 0.987775i \(-0.549823\pi\)
−0.155884 + 0.987775i \(0.549823\pi\)
\(140\) 48.8887 4.13185
\(141\) −9.23665 −0.777867
\(142\) −38.9263 −3.26662
\(143\) −1.71678 −0.143564
\(144\) 4.28873 0.357394
\(145\) −26.3898 −2.19156
\(146\) −22.9788 −1.90174
\(147\) 11.2969 0.931755
\(148\) −23.3878 −1.92246
\(149\) −10.0174 −0.820653 −0.410327 0.911939i \(-0.634585\pi\)
−0.410327 + 0.911939i \(0.634585\pi\)
\(150\) −7.31086 −0.596929
\(151\) 6.73957 0.548458 0.274229 0.961664i \(-0.411577\pi\)
0.274229 + 0.961664i \(0.411577\pi\)
\(152\) 23.4591 1.90278
\(153\) −1.00000 −0.0808452
\(154\) 33.6277 2.70980
\(155\) −24.5072 −1.96846
\(156\) 2.17378 0.174042
\(157\) 1.00000 0.0798087
\(158\) −9.39920 −0.747760
\(159\) 1.01554 0.0805378
\(160\) −1.34189 −0.106086
\(161\) −4.46952 −0.352247
\(162\) −2.45922 −0.193214
\(163\) 19.2725 1.50954 0.754768 0.655991i \(-0.227749\pi\)
0.754768 + 0.655991i \(0.227749\pi\)
\(164\) −29.0982 −2.27219
\(165\) −9.02647 −0.702710
\(166\) 16.3426 1.26843
\(167\) 12.3806 0.958042 0.479021 0.877804i \(-0.340992\pi\)
0.479021 + 0.877804i \(0.340992\pi\)
\(168\) −21.5408 −1.66191
\(169\) −12.7116 −0.977815
\(170\) 6.94390 0.532572
\(171\) −4.65843 −0.356239
\(172\) −7.47596 −0.570037
\(173\) 7.04944 0.535959 0.267979 0.963425i \(-0.413644\pi\)
0.267979 + 0.963425i \(0.413644\pi\)
\(174\) 22.9840 1.74242
\(175\) 12.7163 0.961262
\(176\) −13.7101 −1.03344
\(177\) −13.4723 −1.01264
\(178\) 21.5637 1.61627
\(179\) −5.87911 −0.439425 −0.219713 0.975565i \(-0.570512\pi\)
−0.219713 + 0.975565i \(0.570512\pi\)
\(180\) 11.4293 0.851889
\(181\) −7.34617 −0.546036 −0.273018 0.962009i \(-0.588022\pi\)
−0.273018 + 0.962009i \(0.588022\pi\)
\(182\) −5.64922 −0.418748
\(183\) 2.60984 0.192925
\(184\) 5.26191 0.387913
\(185\) −16.3148 −1.19949
\(186\) 21.3443 1.56504
\(187\) 3.19677 0.233771
\(188\) −37.3876 −2.72677
\(189\) 4.27749 0.311142
\(190\) 32.3476 2.34674
\(191\) 4.92504 0.356363 0.178182 0.983998i \(-0.442979\pi\)
0.178182 + 0.983998i \(0.442979\pi\)
\(192\) −7.40875 −0.534681
\(193\) 17.1994 1.23804 0.619019 0.785376i \(-0.287530\pi\)
0.619019 + 0.785376i \(0.287530\pi\)
\(194\) −34.4553 −2.47375
\(195\) 1.51638 0.108591
\(196\) 45.7270 3.26622
\(197\) 21.1151 1.50439 0.752194 0.658942i \(-0.228996\pi\)
0.752194 + 0.658942i \(0.228996\pi\)
\(198\) 7.86155 0.558696
\(199\) −23.9759 −1.69961 −0.849804 0.527098i \(-0.823280\pi\)
−0.849804 + 0.527098i \(0.823280\pi\)
\(200\) −14.9708 −1.05859
\(201\) 2.87750 0.202963
\(202\) 16.3382 1.14955
\(203\) −39.9778 −2.80589
\(204\) −4.04774 −0.283399
\(205\) −20.2983 −1.41769
\(206\) −33.8769 −2.36031
\(207\) −1.04489 −0.0726251
\(208\) 2.30320 0.159698
\(209\) 14.8919 1.03009
\(210\) −29.7025 −2.04966
\(211\) 12.1321 0.835209 0.417605 0.908629i \(-0.362870\pi\)
0.417605 + 0.908629i \(0.362870\pi\)
\(212\) 4.11066 0.282321
\(213\) 15.8287 1.08457
\(214\) −10.2875 −0.703236
\(215\) −5.21508 −0.355665
\(216\) −5.03584 −0.342645
\(217\) −37.1258 −2.52026
\(218\) 16.0151 1.08468
\(219\) 9.34396 0.631407
\(220\) −36.5368 −2.46331
\(221\) −0.537035 −0.0361249
\(222\) 14.2093 0.953665
\(223\) −1.74290 −0.116713 −0.0583566 0.998296i \(-0.518586\pi\)
−0.0583566 + 0.998296i \(0.518586\pi\)
\(224\) −2.03283 −0.135824
\(225\) 2.97284 0.198189
\(226\) −5.11813 −0.340453
\(227\) 19.2034 1.27458 0.637288 0.770625i \(-0.280056\pi\)
0.637288 + 0.770625i \(0.280056\pi\)
\(228\) −18.8561 −1.24878
\(229\) −26.5978 −1.75763 −0.878816 0.477161i \(-0.841666\pi\)
−0.878816 + 0.477161i \(0.841666\pi\)
\(230\) 7.25563 0.478422
\(231\) −13.6742 −0.899693
\(232\) 47.0654 3.09000
\(233\) −21.9668 −1.43909 −0.719546 0.694445i \(-0.755650\pi\)
−0.719546 + 0.694445i \(0.755650\pi\)
\(234\) −1.32068 −0.0863359
\(235\) −26.0808 −1.70133
\(236\) −54.5322 −3.54974
\(237\) 3.82203 0.248268
\(238\) 10.5193 0.681863
\(239\) 6.77243 0.438072 0.219036 0.975717i \(-0.429709\pi\)
0.219036 + 0.975717i \(0.429709\pi\)
\(240\) 12.1098 0.781682
\(241\) −30.3120 −1.95257 −0.976285 0.216491i \(-0.930539\pi\)
−0.976285 + 0.216491i \(0.930539\pi\)
\(242\) 1.91983 0.123411
\(243\) 1.00000 0.0641500
\(244\) 10.5640 0.676289
\(245\) 31.8983 2.03790
\(246\) 17.6787 1.12715
\(247\) −2.50174 −0.159182
\(248\) 43.7077 2.77544
\(249\) −6.64544 −0.421138
\(250\) 14.0764 0.890268
\(251\) −15.2650 −0.963516 −0.481758 0.876304i \(-0.660002\pi\)
−0.481758 + 0.876304i \(0.660002\pi\)
\(252\) 17.3142 1.09069
\(253\) 3.34028 0.210002
\(254\) 52.5121 3.29490
\(255\) −2.82362 −0.176822
\(256\) −32.3261 −2.02038
\(257\) −16.7718 −1.04620 −0.523098 0.852273i \(-0.675224\pi\)
−0.523098 + 0.852273i \(0.675224\pi\)
\(258\) 4.54204 0.282775
\(259\) −24.7152 −1.53573
\(260\) 6.13793 0.380658
\(261\) −9.34609 −0.578508
\(262\) 24.7148 1.52689
\(263\) 0.183039 0.0112867 0.00564335 0.999984i \(-0.498204\pi\)
0.00564335 + 0.999984i \(0.498204\pi\)
\(264\) 16.0984 0.990789
\(265\) 2.86751 0.176150
\(266\) 49.0032 3.00458
\(267\) −8.76855 −0.536626
\(268\) 11.6474 0.711478
\(269\) 24.3485 1.48455 0.742277 0.670093i \(-0.233746\pi\)
0.742277 + 0.670093i \(0.233746\pi\)
\(270\) −6.94390 −0.422592
\(271\) 9.97250 0.605786 0.302893 0.953025i \(-0.402047\pi\)
0.302893 + 0.953025i \(0.402047\pi\)
\(272\) −4.28873 −0.260043
\(273\) 2.29716 0.139031
\(274\) 43.7863 2.64523
\(275\) −9.50349 −0.573082
\(276\) −4.22946 −0.254583
\(277\) 21.7960 1.30959 0.654797 0.755805i \(-0.272754\pi\)
0.654797 + 0.755805i \(0.272754\pi\)
\(278\) 9.03930 0.542141
\(279\) −8.67933 −0.519618
\(280\) −60.8230 −3.63487
\(281\) −21.6113 −1.28922 −0.644610 0.764511i \(-0.722980\pi\)
−0.644610 + 0.764511i \(0.722980\pi\)
\(282\) 22.7149 1.35265
\(283\) 17.0175 1.01159 0.505794 0.862655i \(-0.331200\pi\)
0.505794 + 0.862655i \(0.331200\pi\)
\(284\) 64.0706 3.80189
\(285\) −13.1536 −0.779154
\(286\) 4.22193 0.249648
\(287\) −30.7498 −1.81510
\(288\) −0.475238 −0.0280037
\(289\) 1.00000 0.0588235
\(290\) 64.8983 3.81096
\(291\) 14.0107 0.821321
\(292\) 37.8220 2.21336
\(293\) 28.3764 1.65776 0.828882 0.559423i \(-0.188977\pi\)
0.828882 + 0.559423i \(0.188977\pi\)
\(294\) −27.7816 −1.62025
\(295\) −38.0405 −2.21481
\(296\) 29.0970 1.69123
\(297\) −3.19677 −0.185495
\(298\) 24.6348 1.42706
\(299\) −0.561144 −0.0324518
\(300\) 12.0333 0.694743
\(301\) −7.90029 −0.455365
\(302\) −16.5741 −0.953730
\(303\) −6.64364 −0.381667
\(304\) −19.9787 −1.14586
\(305\) 7.36921 0.421960
\(306\) 2.45922 0.140584
\(307\) 24.9877 1.42612 0.713061 0.701102i \(-0.247308\pi\)
0.713061 + 0.701102i \(0.247308\pi\)
\(308\) −55.3494 −3.15383
\(309\) 13.7755 0.783660
\(310\) 60.2684 3.42301
\(311\) −17.7126 −1.00439 −0.502195 0.864754i \(-0.667474\pi\)
−0.502195 + 0.864754i \(0.667474\pi\)
\(312\) −2.70442 −0.153108
\(313\) −11.4673 −0.648170 −0.324085 0.946028i \(-0.605056\pi\)
−0.324085 + 0.946028i \(0.605056\pi\)
\(314\) −2.45922 −0.138782
\(315\) 12.0780 0.680519
\(316\) 15.4706 0.870289
\(317\) −12.4978 −0.701945 −0.350972 0.936386i \(-0.614149\pi\)
−0.350972 + 0.936386i \(0.614149\pi\)
\(318\) −2.49744 −0.140049
\(319\) 29.8773 1.67281
\(320\) −20.9195 −1.16944
\(321\) 4.18323 0.233485
\(322\) 10.9915 0.612533
\(323\) 4.65843 0.259202
\(324\) 4.04774 0.224875
\(325\) 1.59652 0.0885590
\(326\) −47.3952 −2.62498
\(327\) −6.51227 −0.360129
\(328\) 36.2014 1.99889
\(329\) −39.5097 −2.17824
\(330\) 22.1980 1.22196
\(331\) −13.3860 −0.735761 −0.367880 0.929873i \(-0.619916\pi\)
−0.367880 + 0.929873i \(0.619916\pi\)
\(332\) −26.8990 −1.47628
\(333\) −5.77798 −0.316631
\(334\) −30.4466 −1.66597
\(335\) 8.12498 0.443915
\(336\) 18.3450 1.00080
\(337\) 4.76598 0.259620 0.129810 0.991539i \(-0.458563\pi\)
0.129810 + 0.991539i \(0.458563\pi\)
\(338\) 31.2606 1.70035
\(339\) 2.08121 0.113036
\(340\) −11.4293 −0.619840
\(341\) 27.7458 1.50252
\(342\) 11.4561 0.619473
\(343\) 18.3801 0.992430
\(344\) 9.30092 0.501472
\(345\) −2.95038 −0.158843
\(346\) −17.3361 −0.931994
\(347\) 16.1440 0.866655 0.433328 0.901236i \(-0.357339\pi\)
0.433328 + 0.901236i \(0.357339\pi\)
\(348\) −37.8306 −2.02793
\(349\) 21.8287 1.16847 0.584233 0.811586i \(-0.301395\pi\)
0.584233 + 0.811586i \(0.301395\pi\)
\(350\) −31.2721 −1.67157
\(351\) 0.537035 0.0286648
\(352\) 1.51923 0.0809750
\(353\) 14.9000 0.793048 0.396524 0.918024i \(-0.370216\pi\)
0.396524 + 0.918024i \(0.370216\pi\)
\(354\) 33.1312 1.76090
\(355\) 44.6944 2.37213
\(356\) −35.4928 −1.88112
\(357\) −4.27749 −0.226389
\(358\) 14.4580 0.764129
\(359\) 2.36781 0.124968 0.0624840 0.998046i \(-0.480098\pi\)
0.0624840 + 0.998046i \(0.480098\pi\)
\(360\) −14.2193 −0.749423
\(361\) 2.70092 0.142154
\(362\) 18.0658 0.949518
\(363\) −0.780666 −0.0409743
\(364\) 9.29832 0.487364
\(365\) 26.3838 1.38099
\(366\) −6.41816 −0.335483
\(367\) 25.2616 1.31865 0.659323 0.751859i \(-0.270843\pi\)
0.659323 + 0.751859i \(0.270843\pi\)
\(368\) −4.48126 −0.233602
\(369\) −7.18874 −0.374231
\(370\) 40.1217 2.08583
\(371\) 4.34398 0.225528
\(372\) −35.1317 −1.82149
\(373\) 13.1367 0.680192 0.340096 0.940391i \(-0.389540\pi\)
0.340096 + 0.940391i \(0.389540\pi\)
\(374\) −7.86155 −0.406511
\(375\) −5.72393 −0.295582
\(376\) 46.5143 2.39879
\(377\) −5.01918 −0.258501
\(378\) −10.5193 −0.541053
\(379\) 25.3983 1.30462 0.652312 0.757950i \(-0.273799\pi\)
0.652312 + 0.757950i \(0.273799\pi\)
\(380\) −53.2425 −2.73128
\(381\) −21.3532 −1.09396
\(382\) −12.1117 −0.619690
\(383\) 1.68455 0.0860763 0.0430381 0.999073i \(-0.486296\pi\)
0.0430381 + 0.999073i \(0.486296\pi\)
\(384\) 19.1702 0.978275
\(385\) −38.6106 −1.96778
\(386\) −42.2970 −2.15286
\(387\) −1.84695 −0.0938855
\(388\) 56.7116 2.87910
\(389\) 19.6316 0.995362 0.497681 0.867360i \(-0.334185\pi\)
0.497681 + 0.867360i \(0.334185\pi\)
\(390\) −3.72912 −0.188831
\(391\) 1.04489 0.0528425
\(392\) −56.8895 −2.87335
\(393\) −10.0499 −0.506949
\(394\) −51.9266 −2.61602
\(395\) 10.7920 0.543003
\(396\) −12.9397 −0.650244
\(397\) 1.42929 0.0717343 0.0358671 0.999357i \(-0.488581\pi\)
0.0358671 + 0.999357i \(0.488581\pi\)
\(398\) 58.9620 2.95550
\(399\) −19.9264 −0.997566
\(400\) 12.7497 0.637486
\(401\) 23.8472 1.19087 0.595436 0.803403i \(-0.296979\pi\)
0.595436 + 0.803403i \(0.296979\pi\)
\(402\) −7.07640 −0.352939
\(403\) −4.66110 −0.232186
\(404\) −26.8918 −1.33792
\(405\) 2.82362 0.140307
\(406\) 98.3141 4.87924
\(407\) 18.4709 0.915566
\(408\) 5.03584 0.249311
\(409\) −5.93584 −0.293509 −0.146754 0.989173i \(-0.546883\pi\)
−0.146754 + 0.989173i \(0.546883\pi\)
\(410\) 49.9179 2.46527
\(411\) −17.8050 −0.878256
\(412\) 55.7596 2.74708
\(413\) −57.6274 −2.83566
\(414\) 2.56962 0.126290
\(415\) −18.7642 −0.921099
\(416\) −0.255219 −0.0125132
\(417\) −3.67569 −0.179999
\(418\) −36.6224 −1.79126
\(419\) −30.5487 −1.49240 −0.746201 0.665721i \(-0.768124\pi\)
−0.746201 + 0.665721i \(0.768124\pi\)
\(420\) 48.8887 2.38552
\(421\) 35.7120 1.74049 0.870247 0.492615i \(-0.163959\pi\)
0.870247 + 0.492615i \(0.163959\pi\)
\(422\) −29.8355 −1.45237
\(423\) −9.23665 −0.449102
\(424\) −5.11411 −0.248363
\(425\) −2.97284 −0.144204
\(426\) −38.9263 −1.88598
\(427\) 11.1636 0.540243
\(428\) 16.9326 0.818469
\(429\) −1.71678 −0.0828868
\(430\) 12.8250 0.618476
\(431\) 10.4534 0.503521 0.251761 0.967790i \(-0.418990\pi\)
0.251761 + 0.967790i \(0.418990\pi\)
\(432\) 4.28873 0.206342
\(433\) −27.6875 −1.33057 −0.665287 0.746587i \(-0.731691\pi\)
−0.665287 + 0.746587i \(0.731691\pi\)
\(434\) 91.3003 4.38255
\(435\) −26.3898 −1.26530
\(436\) −26.3600 −1.26241
\(437\) 4.86755 0.232847
\(438\) −22.9788 −1.09797
\(439\) 1.74863 0.0834576 0.0417288 0.999129i \(-0.486713\pi\)
0.0417288 + 0.999129i \(0.486713\pi\)
\(440\) 45.4558 2.16702
\(441\) 11.2969 0.537949
\(442\) 1.32068 0.0628186
\(443\) 27.4503 1.30421 0.652103 0.758131i \(-0.273887\pi\)
0.652103 + 0.758131i \(0.273887\pi\)
\(444\) −23.3878 −1.10993
\(445\) −24.7591 −1.17369
\(446\) 4.28617 0.202956
\(447\) −10.0174 −0.473804
\(448\) −31.6909 −1.49725
\(449\) 20.4193 0.963648 0.481824 0.876268i \(-0.339975\pi\)
0.481824 + 0.876268i \(0.339975\pi\)
\(450\) −7.31086 −0.344637
\(451\) 22.9808 1.08212
\(452\) 8.42418 0.396240
\(453\) 6.73957 0.316653
\(454\) −47.2254 −2.21640
\(455\) 6.48632 0.304083
\(456\) 23.4591 1.09857
\(457\) 7.15108 0.334514 0.167257 0.985913i \(-0.446509\pi\)
0.167257 + 0.985913i \(0.446509\pi\)
\(458\) 65.4097 3.05639
\(459\) −1.00000 −0.0466760
\(460\) −11.9424 −0.556817
\(461\) −14.6639 −0.682968 −0.341484 0.939888i \(-0.610929\pi\)
−0.341484 + 0.939888i \(0.610929\pi\)
\(462\) 33.6277 1.56450
\(463\) −5.56437 −0.258598 −0.129299 0.991606i \(-0.541273\pi\)
−0.129299 + 0.991606i \(0.541273\pi\)
\(464\) −40.0829 −1.86080
\(465\) −24.5072 −1.13649
\(466\) 54.0210 2.50248
\(467\) −31.6309 −1.46370 −0.731852 0.681464i \(-0.761344\pi\)
−0.731852 + 0.681464i \(0.761344\pi\)
\(468\) 2.17378 0.100483
\(469\) 12.3085 0.568353
\(470\) 64.1384 2.95848
\(471\) 1.00000 0.0460776
\(472\) 67.8441 3.12278
\(473\) 5.90426 0.271478
\(474\) −9.39920 −0.431720
\(475\) −13.8488 −0.635425
\(476\) −17.3142 −0.793594
\(477\) 1.01554 0.0464985
\(478\) −16.6549 −0.761776
\(479\) −41.2334 −1.88400 −0.942000 0.335613i \(-0.891057\pi\)
−0.942000 + 0.335613i \(0.891057\pi\)
\(480\) −1.34189 −0.0612487
\(481\) −3.10298 −0.141484
\(482\) 74.5438 3.39538
\(483\) −4.46952 −0.203370
\(484\) −3.15993 −0.143633
\(485\) 39.5609 1.79637
\(486\) −2.45922 −0.111552
\(487\) −23.0766 −1.04570 −0.522850 0.852425i \(-0.675131\pi\)
−0.522850 + 0.852425i \(0.675131\pi\)
\(488\) −13.1427 −0.594944
\(489\) 19.2725 0.871531
\(490\) −78.4447 −3.54377
\(491\) −42.4561 −1.91602 −0.958008 0.286743i \(-0.907428\pi\)
−0.958008 + 0.286743i \(0.907428\pi\)
\(492\) −29.0982 −1.31185
\(493\) 9.34609 0.420927
\(494\) 6.15231 0.276806
\(495\) −9.02647 −0.405710
\(496\) −37.2233 −1.67138
\(497\) 67.7073 3.03709
\(498\) 16.3426 0.732328
\(499\) −0.302886 −0.0135590 −0.00677952 0.999977i \(-0.502158\pi\)
−0.00677952 + 0.999977i \(0.502158\pi\)
\(500\) −23.1690 −1.03615
\(501\) 12.3806 0.553126
\(502\) 37.5398 1.67548
\(503\) −35.0804 −1.56416 −0.782078 0.623181i \(-0.785840\pi\)
−0.782078 + 0.623181i \(0.785840\pi\)
\(504\) −21.5408 −0.959502
\(505\) −18.7591 −0.834771
\(506\) −8.21447 −0.365178
\(507\) −12.7116 −0.564542
\(508\) −86.4323 −3.83481
\(509\) 26.1299 1.15819 0.579093 0.815262i \(-0.303407\pi\)
0.579093 + 0.815262i \(0.303407\pi\)
\(510\) 6.94390 0.307481
\(511\) 39.9687 1.76811
\(512\) 41.1566 1.81888
\(513\) −4.65843 −0.205674
\(514\) 41.2454 1.81926
\(515\) 38.8968 1.71400
\(516\) −7.47596 −0.329111
\(517\) 29.5275 1.29862
\(518\) 60.7801 2.67052
\(519\) 7.04944 0.309436
\(520\) −7.63627 −0.334872
\(521\) 12.5119 0.548156 0.274078 0.961707i \(-0.411627\pi\)
0.274078 + 0.961707i \(0.411627\pi\)
\(522\) 22.9840 1.00598
\(523\) 1.35910 0.0594294 0.0297147 0.999558i \(-0.490540\pi\)
0.0297147 + 0.999558i \(0.490540\pi\)
\(524\) −40.6793 −1.77708
\(525\) 12.7163 0.554985
\(526\) −0.450133 −0.0196267
\(527\) 8.67933 0.378078
\(528\) −13.7101 −0.596655
\(529\) −21.9082 −0.952530
\(530\) −7.05183 −0.306312
\(531\) −13.4723 −0.584646
\(532\) −80.6568 −3.49692
\(533\) −3.86061 −0.167221
\(534\) 21.5637 0.933155
\(535\) 11.8118 0.510671
\(536\) −14.4906 −0.625900
\(537\) −5.87911 −0.253702
\(538\) −59.8782 −2.58153
\(539\) −36.1137 −1.55553
\(540\) 11.4293 0.491838
\(541\) 3.94295 0.169520 0.0847602 0.996401i \(-0.472988\pi\)
0.0847602 + 0.996401i \(0.472988\pi\)
\(542\) −24.5245 −1.05342
\(543\) −7.34617 −0.315254
\(544\) 0.475238 0.0203757
\(545\) −18.3882 −0.787664
\(546\) −5.64922 −0.241764
\(547\) 26.5602 1.13563 0.567816 0.823155i \(-0.307788\pi\)
0.567816 + 0.823155i \(0.307788\pi\)
\(548\) −72.0701 −3.07868
\(549\) 2.60984 0.111385
\(550\) 23.3711 0.996548
\(551\) 43.5381 1.85478
\(552\) 5.26191 0.223962
\(553\) 16.3487 0.695218
\(554\) −53.6010 −2.27729
\(555\) −16.3148 −0.692526
\(556\) −14.8782 −0.630977
\(557\) −19.3734 −0.820878 −0.410439 0.911888i \(-0.634625\pi\)
−0.410439 + 0.911888i \(0.634625\pi\)
\(558\) 21.3443 0.903578
\(559\) −0.991875 −0.0419518
\(560\) 51.7994 2.18892
\(561\) 3.19677 0.134968
\(562\) 53.1468 2.24186
\(563\) 38.3610 1.61672 0.808361 0.588687i \(-0.200355\pi\)
0.808361 + 0.588687i \(0.200355\pi\)
\(564\) −37.3876 −1.57430
\(565\) 5.87654 0.247228
\(566\) −41.8498 −1.75908
\(567\) 4.27749 0.179638
\(568\) −79.7110 −3.34460
\(569\) 23.8214 0.998644 0.499322 0.866417i \(-0.333583\pi\)
0.499322 + 0.866417i \(0.333583\pi\)
\(570\) 32.3476 1.35489
\(571\) −8.73348 −0.365485 −0.182742 0.983161i \(-0.558497\pi\)
−0.182742 + 0.983161i \(0.558497\pi\)
\(572\) −6.94907 −0.290555
\(573\) 4.92504 0.205746
\(574\) 75.6204 3.15633
\(575\) −3.10630 −0.129542
\(576\) −7.40875 −0.308698
\(577\) 3.02177 0.125798 0.0628989 0.998020i \(-0.479965\pi\)
0.0628989 + 0.998020i \(0.479965\pi\)
\(578\) −2.45922 −0.102290
\(579\) 17.1994 0.714782
\(580\) −106.819 −4.43543
\(581\) −28.4258 −1.17930
\(582\) −34.4553 −1.42822
\(583\) −3.24646 −0.134455
\(584\) −47.0547 −1.94714
\(585\) 1.51638 0.0626948
\(586\) −69.7836 −2.88273
\(587\) 10.9557 0.452191 0.226096 0.974105i \(-0.427404\pi\)
0.226096 + 0.974105i \(0.427404\pi\)
\(588\) 45.7270 1.88575
\(589\) 40.4320 1.66597
\(590\) 93.5499 3.85139
\(591\) 21.1151 0.868559
\(592\) −24.7802 −1.01846
\(593\) −14.0083 −0.575252 −0.287626 0.957743i \(-0.592866\pi\)
−0.287626 + 0.957743i \(0.592866\pi\)
\(594\) 7.86155 0.322563
\(595\) −12.0780 −0.495150
\(596\) −40.5477 −1.66090
\(597\) −23.9759 −0.981269
\(598\) 1.37997 0.0564313
\(599\) 40.0636 1.63696 0.818478 0.574538i \(-0.194818\pi\)
0.818478 + 0.574538i \(0.194818\pi\)
\(600\) −14.9708 −0.611178
\(601\) 38.9751 1.58983 0.794914 0.606722i \(-0.207516\pi\)
0.794914 + 0.606722i \(0.207516\pi\)
\(602\) 19.4285 0.791848
\(603\) 2.87750 0.117181
\(604\) 27.2800 1.11001
\(605\) −2.20430 −0.0896177
\(606\) 16.3382 0.663692
\(607\) 15.6268 0.634274 0.317137 0.948380i \(-0.397279\pi\)
0.317137 + 0.948380i \(0.397279\pi\)
\(608\) 2.21386 0.0897839
\(609\) −39.9778 −1.61998
\(610\) −18.1225 −0.733757
\(611\) −4.96041 −0.200677
\(612\) −4.04774 −0.163620
\(613\) −25.0999 −1.01378 −0.506889 0.862012i \(-0.669204\pi\)
−0.506889 + 0.862012i \(0.669204\pi\)
\(614\) −61.4501 −2.47992
\(615\) −20.2983 −0.818506
\(616\) 68.8608 2.77448
\(617\) −40.7679 −1.64125 −0.820626 0.571465i \(-0.806375\pi\)
−0.820626 + 0.571465i \(0.806375\pi\)
\(618\) −33.8769 −1.36273
\(619\) 28.8748 1.16058 0.580288 0.814411i \(-0.302940\pi\)
0.580288 + 0.814411i \(0.302940\pi\)
\(620\) −99.1986 −3.98391
\(621\) −1.04489 −0.0419301
\(622\) 43.5592 1.74656
\(623\) −37.5074 −1.50270
\(624\) 2.30320 0.0922018
\(625\) −31.0264 −1.24106
\(626\) 28.2005 1.12712
\(627\) 14.8919 0.594726
\(628\) 4.04774 0.161522
\(629\) 5.77798 0.230383
\(630\) −29.7025 −1.18337
\(631\) −42.3304 −1.68515 −0.842573 0.538582i \(-0.818960\pi\)
−0.842573 + 0.538582i \(0.818960\pi\)
\(632\) −19.2471 −0.765610
\(633\) 12.1321 0.482208
\(634\) 30.7347 1.22063
\(635\) −60.2934 −2.39267
\(636\) 4.11066 0.162998
\(637\) 6.06685 0.240377
\(638\) −73.4747 −2.90889
\(639\) 15.8287 0.626175
\(640\) 54.1294 2.13965
\(641\) −32.0473 −1.26579 −0.632896 0.774237i \(-0.718134\pi\)
−0.632896 + 0.774237i \(0.718134\pi\)
\(642\) −10.2875 −0.406013
\(643\) 23.8842 0.941900 0.470950 0.882160i \(-0.343911\pi\)
0.470950 + 0.882160i \(0.343911\pi\)
\(644\) −18.0915 −0.712903
\(645\) −5.21508 −0.205343
\(646\) −11.4561 −0.450733
\(647\) 47.7991 1.87918 0.939588 0.342307i \(-0.111208\pi\)
0.939588 + 0.342307i \(0.111208\pi\)
\(648\) −5.03584 −0.197826
\(649\) 43.0677 1.69055
\(650\) −3.92619 −0.153998
\(651\) −37.1258 −1.45507
\(652\) 78.0100 3.05511
\(653\) −26.5989 −1.04090 −0.520448 0.853893i \(-0.674235\pi\)
−0.520448 + 0.853893i \(0.674235\pi\)
\(654\) 16.0151 0.626239
\(655\) −28.3771 −1.10878
\(656\) −30.8306 −1.20373
\(657\) 9.34396 0.364543
\(658\) 97.1629 3.78780
\(659\) 6.41364 0.249840 0.124920 0.992167i \(-0.460133\pi\)
0.124920 + 0.992167i \(0.460133\pi\)
\(660\) −36.5368 −1.42219
\(661\) 28.3451 1.10250 0.551249 0.834341i \(-0.314152\pi\)
0.551249 + 0.834341i \(0.314152\pi\)
\(662\) 32.9190 1.27943
\(663\) −0.537035 −0.0208567
\(664\) 33.4654 1.29871
\(665\) −56.2645 −2.18185
\(666\) 14.2093 0.550599
\(667\) 9.76566 0.378128
\(668\) 50.1136 1.93895
\(669\) −1.74290 −0.0673844
\(670\) −19.9811 −0.771936
\(671\) −8.34306 −0.322080
\(672\) −2.03283 −0.0784180
\(673\) 38.9978 1.50326 0.751628 0.659587i \(-0.229269\pi\)
0.751628 + 0.659587i \(0.229269\pi\)
\(674\) −11.7206 −0.451460
\(675\) 2.97284 0.114425
\(676\) −51.4533 −1.97897
\(677\) −18.1078 −0.695939 −0.347970 0.937506i \(-0.613129\pi\)
−0.347970 + 0.937506i \(0.613129\pi\)
\(678\) −5.11813 −0.196561
\(679\) 59.9306 2.29992
\(680\) 14.2193 0.545286
\(681\) 19.2034 0.735877
\(682\) −68.2330 −2.61278
\(683\) 16.1734 0.618858 0.309429 0.950923i \(-0.399862\pi\)
0.309429 + 0.950923i \(0.399862\pi\)
\(684\) −18.8561 −0.720981
\(685\) −50.2746 −1.92089
\(686\) −45.2006 −1.72577
\(687\) −26.5978 −1.01477
\(688\) −7.92106 −0.301987
\(689\) 0.545382 0.0207774
\(690\) 7.25563 0.276217
\(691\) 7.42506 0.282462 0.141231 0.989977i \(-0.454894\pi\)
0.141231 + 0.989977i \(0.454894\pi\)
\(692\) 28.5343 1.08471
\(693\) −13.6742 −0.519438
\(694\) −39.7016 −1.50705
\(695\) −10.3787 −0.393688
\(696\) 47.0654 1.78401
\(697\) 7.18874 0.272293
\(698\) −53.6816 −2.03188
\(699\) −21.9668 −0.830860
\(700\) 51.4723 1.94547
\(701\) 22.5837 0.852973 0.426486 0.904494i \(-0.359751\pi\)
0.426486 + 0.904494i \(0.359751\pi\)
\(702\) −1.32068 −0.0498460
\(703\) 26.9163 1.01517
\(704\) 23.6841 0.892627
\(705\) −26.0808 −0.982261
\(706\) −36.6424 −1.37905
\(707\) −28.4181 −1.06877
\(708\) −54.5322 −2.04945
\(709\) −37.6548 −1.41416 −0.707078 0.707136i \(-0.749987\pi\)
−0.707078 + 0.707136i \(0.749987\pi\)
\(710\) −109.913 −4.12496
\(711\) 3.82203 0.143337
\(712\) 44.1570 1.65485
\(713\) 9.06897 0.339636
\(714\) 10.5193 0.393674
\(715\) −4.84753 −0.181287
\(716\) −23.7971 −0.889340
\(717\) 6.77243 0.252921
\(718\) −5.82294 −0.217310
\(719\) 20.4295 0.761893 0.380947 0.924597i \(-0.375598\pi\)
0.380947 + 0.924597i \(0.375598\pi\)
\(720\) 12.1098 0.451304
\(721\) 58.9245 2.19446
\(722\) −6.64216 −0.247195
\(723\) −30.3120 −1.12732
\(724\) −29.7354 −1.10511
\(725\) −27.7844 −1.03189
\(726\) 1.91983 0.0712514
\(727\) 30.0043 1.11280 0.556399 0.830915i \(-0.312183\pi\)
0.556399 + 0.830915i \(0.312183\pi\)
\(728\) −11.5681 −0.428744
\(729\) 1.00000 0.0370370
\(730\) −64.8835 −2.40145
\(731\) 1.84695 0.0683118
\(732\) 10.5640 0.390455
\(733\) −30.3144 −1.11969 −0.559844 0.828598i \(-0.689139\pi\)
−0.559844 + 0.828598i \(0.689139\pi\)
\(734\) −62.1238 −2.29303
\(735\) 31.8983 1.17658
\(736\) 0.496573 0.0183039
\(737\) −9.19871 −0.338839
\(738\) 17.6787 0.650761
\(739\) −11.8085 −0.434383 −0.217192 0.976129i \(-0.569690\pi\)
−0.217192 + 0.976129i \(0.569690\pi\)
\(740\) −66.0382 −2.42761
\(741\) −2.50174 −0.0919036
\(742\) −10.6828 −0.392177
\(743\) −33.4717 −1.22796 −0.613978 0.789323i \(-0.710432\pi\)
−0.613978 + 0.789323i \(0.710432\pi\)
\(744\) 43.7077 1.60240
\(745\) −28.2852 −1.03629
\(746\) −32.3060 −1.18281
\(747\) −6.64544 −0.243144
\(748\) 12.9397 0.473122
\(749\) 17.8937 0.653822
\(750\) 14.0764 0.513997
\(751\) 3.84339 0.140247 0.0701237 0.997538i \(-0.477661\pi\)
0.0701237 + 0.997538i \(0.477661\pi\)
\(752\) −39.6135 −1.44456
\(753\) −15.2650 −0.556286
\(754\) 12.3432 0.449514
\(755\) 19.0300 0.692573
\(756\) 17.3142 0.629711
\(757\) −43.3583 −1.57588 −0.787942 0.615749i \(-0.788853\pi\)
−0.787942 + 0.615749i \(0.788853\pi\)
\(758\) −62.4600 −2.26865
\(759\) 3.34028 0.121245
\(760\) 66.2396 2.40276
\(761\) 22.0285 0.798532 0.399266 0.916835i \(-0.369265\pi\)
0.399266 + 0.916835i \(0.369265\pi\)
\(762\) 52.5121 1.90231
\(763\) −27.8562 −1.00846
\(764\) 19.9353 0.721233
\(765\) −2.82362 −0.102088
\(766\) −4.14266 −0.149680
\(767\) −7.23507 −0.261243
\(768\) −32.3261 −1.16647
\(769\) −22.4708 −0.810318 −0.405159 0.914246i \(-0.632784\pi\)
−0.405159 + 0.914246i \(0.632784\pi\)
\(770\) 94.9519 3.42183
\(771\) −16.7718 −0.604021
\(772\) 69.6186 2.50563
\(773\) −3.44582 −0.123938 −0.0619688 0.998078i \(-0.519738\pi\)
−0.0619688 + 0.998078i \(0.519738\pi\)
\(774\) 4.54204 0.163260
\(775\) −25.8023 −0.926845
\(776\) −70.5556 −2.53280
\(777\) −24.7152 −0.886654
\(778\) −48.2784 −1.73086
\(779\) 33.4882 1.19984
\(780\) 6.13793 0.219773
\(781\) −50.6008 −1.81064
\(782\) −2.56962 −0.0918893
\(783\) −9.34609 −0.334002
\(784\) 48.4495 1.73034
\(785\) 2.82362 0.100779
\(786\) 24.7148 0.881548
\(787\) −1.35257 −0.0482140 −0.0241070 0.999709i \(-0.507674\pi\)
−0.0241070 + 0.999709i \(0.507674\pi\)
\(788\) 85.4685 3.04469
\(789\) 0.183039 0.00651637
\(790\) −26.5398 −0.944243
\(791\) 8.90234 0.316531
\(792\) 16.0984 0.572032
\(793\) 1.40158 0.0497714
\(794\) −3.51494 −0.124741
\(795\) 2.86751 0.101700
\(796\) −97.0484 −3.43979
\(797\) 4.65406 0.164855 0.0824277 0.996597i \(-0.473733\pi\)
0.0824277 + 0.996597i \(0.473733\pi\)
\(798\) 49.0032 1.73470
\(799\) 9.23665 0.326769
\(800\) −1.41281 −0.0499503
\(801\) −8.76855 −0.309821
\(802\) −58.6454 −2.07084
\(803\) −29.8705 −1.05411
\(804\) 11.6474 0.410772
\(805\) −12.6202 −0.444805
\(806\) 11.4627 0.403755
\(807\) 24.3485 0.857108
\(808\) 33.4563 1.17699
\(809\) −15.3152 −0.538453 −0.269226 0.963077i \(-0.586768\pi\)
−0.269226 + 0.963077i \(0.586768\pi\)
\(810\) −6.94390 −0.243984
\(811\) 44.6870 1.56917 0.784587 0.620019i \(-0.212875\pi\)
0.784587 + 0.620019i \(0.212875\pi\)
\(812\) −161.820 −5.67876
\(813\) 9.97250 0.349751
\(814\) −45.4238 −1.59210
\(815\) 54.4182 1.90619
\(816\) −4.28873 −0.150136
\(817\) 8.60386 0.301011
\(818\) 14.5975 0.510390
\(819\) 2.29716 0.0802693
\(820\) −82.1623 −2.86923
\(821\) 41.2781 1.44062 0.720308 0.693654i \(-0.244000\pi\)
0.720308 + 0.693654i \(0.244000\pi\)
\(822\) 43.7863 1.52722
\(823\) −10.1629 −0.354256 −0.177128 0.984188i \(-0.556681\pi\)
−0.177128 + 0.984188i \(0.556681\pi\)
\(824\) −69.3711 −2.41666
\(825\) −9.50349 −0.330869
\(826\) 141.718 4.93101
\(827\) 3.91567 0.136161 0.0680807 0.997680i \(-0.478312\pi\)
0.0680807 + 0.997680i \(0.478312\pi\)
\(828\) −4.22946 −0.146984
\(829\) −27.7387 −0.963406 −0.481703 0.876334i \(-0.659982\pi\)
−0.481703 + 0.876334i \(0.659982\pi\)
\(830\) 46.1452 1.60172
\(831\) 21.7960 0.756094
\(832\) −3.97876 −0.137939
\(833\) −11.2969 −0.391415
\(834\) 9.03930 0.313005
\(835\) 34.9582 1.20978
\(836\) 60.2786 2.08478
\(837\) −8.67933 −0.300002
\(838\) 75.1259 2.59518
\(839\) 15.5886 0.538177 0.269089 0.963115i \(-0.413278\pi\)
0.269089 + 0.963115i \(0.413278\pi\)
\(840\) −60.8230 −2.09859
\(841\) 58.3494 2.01205
\(842\) −87.8234 −3.02659
\(843\) −21.6113 −0.744332
\(844\) 49.1077 1.69036
\(845\) −35.8927 −1.23475
\(846\) 22.7149 0.780955
\(847\) −3.33929 −0.114739
\(848\) 4.35539 0.149565
\(849\) 17.0175 0.584040
\(850\) 7.31086 0.250760
\(851\) 6.03737 0.206958
\(852\) 64.0706 2.19502
\(853\) 21.3620 0.731422 0.365711 0.930728i \(-0.380826\pi\)
0.365711 + 0.930728i \(0.380826\pi\)
\(854\) −27.4536 −0.939444
\(855\) −13.1536 −0.449845
\(856\) −21.0661 −0.720023
\(857\) 25.8274 0.882249 0.441124 0.897446i \(-0.354580\pi\)
0.441124 + 0.897446i \(0.354580\pi\)
\(858\) 4.22193 0.144134
\(859\) 27.5648 0.940498 0.470249 0.882534i \(-0.344164\pi\)
0.470249 + 0.882534i \(0.344164\pi\)
\(860\) −21.1093 −0.719821
\(861\) −30.7498 −1.04795
\(862\) −25.7071 −0.875587
\(863\) −16.4001 −0.558267 −0.279134 0.960252i \(-0.590047\pi\)
−0.279134 + 0.960252i \(0.590047\pi\)
\(864\) −0.475238 −0.0161679
\(865\) 19.9049 0.676789
\(866\) 68.0895 2.31377
\(867\) 1.00000 0.0339618
\(868\) −150.276 −5.10068
\(869\) −12.2182 −0.414472
\(870\) 64.8983 2.20026
\(871\) 1.54532 0.0523612
\(872\) 32.7948 1.11057
\(873\) 14.0107 0.474190
\(874\) −11.9704 −0.404904
\(875\) −24.4841 −0.827712
\(876\) 37.8220 1.27789
\(877\) −7.63702 −0.257884 −0.128942 0.991652i \(-0.541158\pi\)
−0.128942 + 0.991652i \(0.541158\pi\)
\(878\) −4.30026 −0.145127
\(879\) 28.3764 0.957111
\(880\) −38.7121 −1.30498
\(881\) 10.2482 0.345272 0.172636 0.984986i \(-0.444772\pi\)
0.172636 + 0.984986i \(0.444772\pi\)
\(882\) −27.7816 −0.935455
\(883\) −35.9183 −1.20875 −0.604373 0.796702i \(-0.706576\pi\)
−0.604373 + 0.796702i \(0.706576\pi\)
\(884\) −2.17378 −0.0731121
\(885\) −38.0405 −1.27872
\(886\) −67.5063 −2.26792
\(887\) 12.9928 0.436255 0.218128 0.975920i \(-0.430005\pi\)
0.218128 + 0.975920i \(0.430005\pi\)
\(888\) 29.0970 0.976430
\(889\) −91.3381 −3.06338
\(890\) 60.8879 2.04097
\(891\) −3.19677 −0.107096
\(892\) −7.05481 −0.236213
\(893\) 43.0283 1.43989
\(894\) 24.6348 0.823912
\(895\) −16.6004 −0.554889
\(896\) 82.0003 2.73944
\(897\) −0.561144 −0.0187361
\(898\) −50.2155 −1.67571
\(899\) 81.1178 2.70543
\(900\) 12.0333 0.401110
\(901\) −1.01554 −0.0338326
\(902\) −56.5146 −1.88173
\(903\) −7.90029 −0.262905
\(904\) −10.4806 −0.348580
\(905\) −20.7428 −0.689514
\(906\) −16.5741 −0.550636
\(907\) 37.2800 1.23786 0.618931 0.785445i \(-0.287566\pi\)
0.618931 + 0.785445i \(0.287566\pi\)
\(908\) 77.7306 2.57958
\(909\) −6.64364 −0.220356
\(910\) −15.9513 −0.528779
\(911\) 52.0471 1.72440 0.862199 0.506570i \(-0.169087\pi\)
0.862199 + 0.506570i \(0.169087\pi\)
\(912\) −19.9787 −0.661562
\(913\) 21.2439 0.703072
\(914\) −17.5861 −0.581695
\(915\) 7.36921 0.243618
\(916\) −107.661 −3.55722
\(917\) −42.9883 −1.41960
\(918\) 2.45922 0.0811662
\(919\) −23.8943 −0.788199 −0.394099 0.919068i \(-0.628943\pi\)
−0.394099 + 0.919068i \(0.628943\pi\)
\(920\) 14.8577 0.489842
\(921\) 24.9877 0.823372
\(922\) 36.0618 1.18763
\(923\) 8.50058 0.279800
\(924\) −55.3494 −1.82086
\(925\) −17.1770 −0.564777
\(926\) 13.6840 0.449684
\(927\) 13.7755 0.452446
\(928\) 4.44162 0.145803
\(929\) −6.87302 −0.225497 −0.112748 0.993624i \(-0.535965\pi\)
−0.112748 + 0.993624i \(0.535965\pi\)
\(930\) 60.2684 1.97628
\(931\) −52.6259 −1.72474
\(932\) −88.9158 −2.91254
\(933\) −17.7126 −0.579885
\(934\) 77.7872 2.54527
\(935\) 9.02647 0.295197
\(936\) −2.70442 −0.0883968
\(937\) −25.3647 −0.828627 −0.414314 0.910134i \(-0.635978\pi\)
−0.414314 + 0.910134i \(0.635978\pi\)
\(938\) −30.2692 −0.988326
\(939\) −11.4673 −0.374221
\(940\) −105.568 −3.44326
\(941\) −13.6757 −0.445816 −0.222908 0.974839i \(-0.571555\pi\)
−0.222908 + 0.974839i \(0.571555\pi\)
\(942\) −2.45922 −0.0801256
\(943\) 7.51147 0.244607
\(944\) −57.7789 −1.88054
\(945\) 12.0780 0.392898
\(946\) −14.5198 −0.472081
\(947\) 31.5260 1.02446 0.512229 0.858849i \(-0.328820\pi\)
0.512229 + 0.858849i \(0.328820\pi\)
\(948\) 15.4706 0.502462
\(949\) 5.01804 0.162892
\(950\) 34.0571 1.10496
\(951\) −12.4978 −0.405268
\(952\) 21.5408 0.698140
\(953\) −38.7891 −1.25650 −0.628251 0.778010i \(-0.716229\pi\)
−0.628251 + 0.778010i \(0.716229\pi\)
\(954\) −2.49744 −0.0808576
\(955\) 13.9064 0.450002
\(956\) 27.4131 0.886602
\(957\) 29.8773 0.965796
\(958\) 101.402 3.27614
\(959\) −76.1607 −2.45936
\(960\) −20.9195 −0.675174
\(961\) 44.3308 1.43003
\(962\) 7.63089 0.246030
\(963\) 4.18323 0.134803
\(964\) −122.695 −3.95175
\(965\) 48.5645 1.56335
\(966\) 10.9915 0.353646
\(967\) −40.2174 −1.29330 −0.646652 0.762785i \(-0.723831\pi\)
−0.646652 + 0.762785i \(0.723831\pi\)
\(968\) 3.93131 0.126357
\(969\) 4.65843 0.149650
\(970\) −97.2887 −3.12375
\(971\) −22.2842 −0.715135 −0.357567 0.933887i \(-0.616394\pi\)
−0.357567 + 0.933887i \(0.616394\pi\)
\(972\) 4.04774 0.129831
\(973\) −15.7227 −0.504047
\(974\) 56.7503 1.81840
\(975\) 1.59652 0.0511296
\(976\) 11.1929 0.358276
\(977\) −16.9512 −0.542317 −0.271159 0.962535i \(-0.587407\pi\)
−0.271159 + 0.962535i \(0.587407\pi\)
\(978\) −47.3952 −1.51553
\(979\) 28.0310 0.895875
\(980\) 129.116 4.12446
\(981\) −6.51227 −0.207921
\(982\) 104.409 3.33181
\(983\) −14.5140 −0.462926 −0.231463 0.972844i \(-0.574351\pi\)
−0.231463 + 0.972844i \(0.574351\pi\)
\(984\) 36.2014 1.15406
\(985\) 59.6210 1.89968
\(986\) −22.9840 −0.731961
\(987\) −39.5097 −1.25761
\(988\) −10.1264 −0.322163
\(989\) 1.92986 0.0613660
\(990\) 22.1980 0.705500
\(991\) −37.5055 −1.19140 −0.595701 0.803206i \(-0.703126\pi\)
−0.595701 + 0.803206i \(0.703126\pi\)
\(992\) 4.12475 0.130961
\(993\) −13.3860 −0.424792
\(994\) −166.507 −5.28127
\(995\) −67.6990 −2.14620
\(996\) −26.8990 −0.852328
\(997\) −7.72403 −0.244623 −0.122311 0.992492i \(-0.539031\pi\)
−0.122311 + 0.992492i \(0.539031\pi\)
\(998\) 0.744862 0.0235782
\(999\) −5.77798 −0.182807
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 \(a_p\))