Properties

Label 6026.2.a.h.1.15
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(24\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+0.977360 q^{3}\) \(+1.00000 q^{4}\) \(+1.34259 q^{5}\) \(-0.977360 q^{6}\) \(-1.08765 q^{7}\) \(-1.00000 q^{8}\) \(-2.04477 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+0.977360 q^{3}\) \(+1.00000 q^{4}\) \(+1.34259 q^{5}\) \(-0.977360 q^{6}\) \(-1.08765 q^{7}\) \(-1.00000 q^{8}\) \(-2.04477 q^{9}\) \(-1.34259 q^{10}\) \(+3.05583 q^{11}\) \(+0.977360 q^{12}\) \(+1.13909 q^{13}\) \(+1.08765 q^{14}\) \(+1.31220 q^{15}\) \(+1.00000 q^{16}\) \(-3.38956 q^{17}\) \(+2.04477 q^{18}\) \(+2.02326 q^{19}\) \(+1.34259 q^{20}\) \(-1.06303 q^{21}\) \(-3.05583 q^{22}\) \(-1.00000 q^{23}\) \(-0.977360 q^{24}\) \(-3.19745 q^{25}\) \(-1.13909 q^{26}\) \(-4.93056 q^{27}\) \(-1.08765 q^{28}\) \(+1.84426 q^{29}\) \(-1.31220 q^{30}\) \(+1.02560 q^{31}\) \(-1.00000 q^{32}\) \(+2.98665 q^{33}\) \(+3.38956 q^{34}\) \(-1.46027 q^{35}\) \(-2.04477 q^{36}\) \(-2.61798 q^{37}\) \(-2.02326 q^{38}\) \(+1.11331 q^{39}\) \(-1.34259 q^{40}\) \(-7.20544 q^{41}\) \(+1.06303 q^{42}\) \(-5.50653 q^{43}\) \(+3.05583 q^{44}\) \(-2.74529 q^{45}\) \(+1.00000 q^{46}\) \(+5.56770 q^{47}\) \(+0.977360 q^{48}\) \(-5.81701 q^{49}\) \(+3.19745 q^{50}\) \(-3.31282 q^{51}\) \(+1.13909 q^{52}\) \(-13.2665 q^{53}\) \(+4.93056 q^{54}\) \(+4.10273 q^{55}\) \(+1.08765 q^{56}\) \(+1.97745 q^{57}\) \(-1.84426 q^{58}\) \(+5.29844 q^{59}\) \(+1.31220 q^{60}\) \(+4.01137 q^{61}\) \(-1.02560 q^{62}\) \(+2.22400 q^{63}\) \(+1.00000 q^{64}\) \(+1.52934 q^{65}\) \(-2.98665 q^{66}\) \(-9.80250 q^{67}\) \(-3.38956 q^{68}\) \(-0.977360 q^{69}\) \(+1.46027 q^{70}\) \(-7.93317 q^{71}\) \(+2.04477 q^{72}\) \(+3.80586 q^{73}\) \(+2.61798 q^{74}\) \(-3.12506 q^{75}\) \(+2.02326 q^{76}\) \(-3.32369 q^{77}\) \(-1.11331 q^{78}\) \(+2.61951 q^{79}\) \(+1.34259 q^{80}\) \(+1.31537 q^{81}\) \(+7.20544 q^{82}\) \(+9.13497 q^{83}\) \(-1.06303 q^{84}\) \(-4.55079 q^{85}\) \(+5.50653 q^{86}\) \(+1.80251 q^{87}\) \(-3.05583 q^{88}\) \(-8.47498 q^{89}\) \(+2.74529 q^{90}\) \(-1.23894 q^{91}\) \(-1.00000 q^{92}\) \(+1.00239 q^{93}\) \(-5.56770 q^{94}\) \(+2.71641 q^{95}\) \(-0.977360 q^{96}\) \(+1.60299 q^{97}\) \(+5.81701 q^{98}\) \(-6.24846 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 27q^{18} \) \(\mathstrut -\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut q^{20} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut -\mathstrut 7q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 23q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 27q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 20q^{38} \) \(\mathstrut -\mathstrut 39q^{39} \) \(\mathstrut +\mathstrut q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut -\mathstrut 44q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 13q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 32q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut -\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut +\mathstrut 21q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut -\mathstrut 13q^{55} \) \(\mathstrut +\mathstrut 7q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 6q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 40q^{61} \) \(\mathstrut +\mathstrut 23q^{62} \) \(\mathstrut -\mathstrut 54q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 29q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 17q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 5q^{70} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 27q^{72} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut +\mathstrut 6q^{74} \) \(\mathstrut -\mathstrut 36q^{75} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 39q^{78} \) \(\mathstrut -\mathstrut 53q^{79} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut +\mathstrut 24q^{81} \) \(\mathstrut +\mathstrut q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 37q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 7q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut +\mathstrut 13q^{90} \) \(\mathstrut -\mathstrut 44q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 23q^{93} \) \(\mathstrut -\mathstrut 32q^{94} \) \(\mathstrut +\mathstrut 28q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut -\mathstrut 20q^{97} \) \(\mathstrut +\mathstrut 13q^{98} \) \(\mathstrut -\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.977360 0.564279 0.282140 0.959373i \(-0.408956\pi\)
0.282140 + 0.959373i \(0.408956\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.34259 0.600425 0.300213 0.953872i \(-0.402942\pi\)
0.300213 + 0.953872i \(0.402942\pi\)
\(6\) −0.977360 −0.399006
\(7\) −1.08765 −0.411094 −0.205547 0.978647i \(-0.565897\pi\)
−0.205547 + 0.978647i \(0.565897\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.04477 −0.681589
\(10\) −1.34259 −0.424565
\(11\) 3.05583 0.921368 0.460684 0.887564i \(-0.347604\pi\)
0.460684 + 0.887564i \(0.347604\pi\)
\(12\) 0.977360 0.282140
\(13\) 1.13909 0.315928 0.157964 0.987445i \(-0.449507\pi\)
0.157964 + 0.987445i \(0.449507\pi\)
\(14\) 1.08765 0.290688
\(15\) 1.31220 0.338807
\(16\) 1.00000 0.250000
\(17\) −3.38956 −0.822089 −0.411044 0.911615i \(-0.634836\pi\)
−0.411044 + 0.911615i \(0.634836\pi\)
\(18\) 2.04477 0.481956
\(19\) 2.02326 0.464167 0.232083 0.972696i \(-0.425446\pi\)
0.232083 + 0.972696i \(0.425446\pi\)
\(20\) 1.34259 0.300213
\(21\) −1.06303 −0.231972
\(22\) −3.05583 −0.651506
\(23\) −1.00000 −0.208514
\(24\) −0.977360 −0.199503
\(25\) −3.19745 −0.639490
\(26\) −1.13909 −0.223395
\(27\) −4.93056 −0.948886
\(28\) −1.08765 −0.205547
\(29\) 1.84426 0.342470 0.171235 0.985230i \(-0.445224\pi\)
0.171235 + 0.985230i \(0.445224\pi\)
\(30\) −1.31220 −0.239573
\(31\) 1.02560 0.184204 0.0921020 0.995750i \(-0.470641\pi\)
0.0921020 + 0.995750i \(0.470641\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.98665 0.519909
\(34\) 3.38956 0.581305
\(35\) −1.46027 −0.246831
\(36\) −2.04477 −0.340794
\(37\) −2.61798 −0.430393 −0.215196 0.976571i \(-0.569039\pi\)
−0.215196 + 0.976571i \(0.569039\pi\)
\(38\) −2.02326 −0.328215
\(39\) 1.11331 0.178272
\(40\) −1.34259 −0.212282
\(41\) −7.20544 −1.12530 −0.562650 0.826695i \(-0.690218\pi\)
−0.562650 + 0.826695i \(0.690218\pi\)
\(42\) 1.06303 0.164029
\(43\) −5.50653 −0.839737 −0.419869 0.907585i \(-0.637924\pi\)
−0.419869 + 0.907585i \(0.637924\pi\)
\(44\) 3.05583 0.460684
\(45\) −2.74529 −0.409243
\(46\) 1.00000 0.147442
\(47\) 5.56770 0.812133 0.406066 0.913844i \(-0.366900\pi\)
0.406066 + 0.913844i \(0.366900\pi\)
\(48\) 0.977360 0.141070
\(49\) −5.81701 −0.831001
\(50\) 3.19745 0.452187
\(51\) −3.31282 −0.463888
\(52\) 1.13909 0.157964
\(53\) −13.2665 −1.82229 −0.911144 0.412089i \(-0.864799\pi\)
−0.911144 + 0.412089i \(0.864799\pi\)
\(54\) 4.93056 0.670964
\(55\) 4.10273 0.553213
\(56\) 1.08765 0.145344
\(57\) 1.97745 0.261920
\(58\) −1.84426 −0.242163
\(59\) 5.29844 0.689799 0.344899 0.938640i \(-0.387913\pi\)
0.344899 + 0.938640i \(0.387913\pi\)
\(60\) 1.31220 0.169404
\(61\) 4.01137 0.513604 0.256802 0.966464i \(-0.417331\pi\)
0.256802 + 0.966464i \(0.417331\pi\)
\(62\) −1.02560 −0.130252
\(63\) 2.22400 0.280197
\(64\) 1.00000 0.125000
\(65\) 1.52934 0.189691
\(66\) −2.98665 −0.367631
\(67\) −9.80250 −1.19757 −0.598783 0.800911i \(-0.704349\pi\)
−0.598783 + 0.800911i \(0.704349\pi\)
\(68\) −3.38956 −0.411044
\(69\) −0.977360 −0.117660
\(70\) 1.46027 0.174536
\(71\) −7.93317 −0.941494 −0.470747 0.882268i \(-0.656015\pi\)
−0.470747 + 0.882268i \(0.656015\pi\)
\(72\) 2.04477 0.240978
\(73\) 3.80586 0.445442 0.222721 0.974882i \(-0.428506\pi\)
0.222721 + 0.974882i \(0.428506\pi\)
\(74\) 2.61798 0.304333
\(75\) −3.12506 −0.360851
\(76\) 2.02326 0.232083
\(77\) −3.32369 −0.378769
\(78\) −1.11331 −0.126057
\(79\) 2.61951 0.294718 0.147359 0.989083i \(-0.452923\pi\)
0.147359 + 0.989083i \(0.452923\pi\)
\(80\) 1.34259 0.150106
\(81\) 1.31537 0.146152
\(82\) 7.20544 0.795707
\(83\) 9.13497 1.00269 0.501346 0.865247i \(-0.332838\pi\)
0.501346 + 0.865247i \(0.332838\pi\)
\(84\) −1.06303 −0.115986
\(85\) −4.55079 −0.493603
\(86\) 5.50653 0.593784
\(87\) 1.80251 0.193249
\(88\) −3.05583 −0.325753
\(89\) −8.47498 −0.898346 −0.449173 0.893445i \(-0.648281\pi\)
−0.449173 + 0.893445i \(0.648281\pi\)
\(90\) 2.74529 0.289379
\(91\) −1.23894 −0.129876
\(92\) −1.00000 −0.104257
\(93\) 1.00239 0.103942
\(94\) −5.56770 −0.574265
\(95\) 2.71641 0.278697
\(96\) −0.977360 −0.0997514
\(97\) 1.60299 0.162759 0.0813793 0.996683i \(-0.474067\pi\)
0.0813793 + 0.996683i \(0.474067\pi\)
\(98\) 5.81701 0.587607
\(99\) −6.24846 −0.627994
\(100\) −3.19745 −0.319745
\(101\) −12.4278 −1.23662 −0.618308 0.785936i \(-0.712182\pi\)
−0.618308 + 0.785936i \(0.712182\pi\)
\(102\) 3.31282 0.328018
\(103\) 6.16490 0.607446 0.303723 0.952760i \(-0.401770\pi\)
0.303723 + 0.952760i \(0.401770\pi\)
\(104\) −1.13909 −0.111697
\(105\) −1.42721 −0.139282
\(106\) 13.2665 1.28855
\(107\) 11.9928 1.15939 0.579695 0.814833i \(-0.303172\pi\)
0.579695 + 0.814833i \(0.303172\pi\)
\(108\) −4.93056 −0.474443
\(109\) 2.28864 0.219212 0.109606 0.993975i \(-0.465041\pi\)
0.109606 + 0.993975i \(0.465041\pi\)
\(110\) −4.10273 −0.391180
\(111\) −2.55871 −0.242862
\(112\) −1.08765 −0.102774
\(113\) 4.66948 0.439268 0.219634 0.975582i \(-0.429514\pi\)
0.219634 + 0.975582i \(0.429514\pi\)
\(114\) −1.97745 −0.185205
\(115\) −1.34259 −0.125197
\(116\) 1.84426 0.171235
\(117\) −2.32918 −0.215333
\(118\) −5.29844 −0.487761
\(119\) 3.68667 0.337956
\(120\) −1.31220 −0.119787
\(121\) −1.66189 −0.151081
\(122\) −4.01137 −0.363173
\(123\) −7.04231 −0.634984
\(124\) 1.02560 0.0921020
\(125\) −11.0058 −0.984391
\(126\) −2.22400 −0.198130
\(127\) −4.36870 −0.387659 −0.193830 0.981035i \(-0.562091\pi\)
−0.193830 + 0.981035i \(0.562091\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −5.38186 −0.473846
\(130\) −1.52934 −0.134132
\(131\) −1.00000 −0.0873704
\(132\) 2.98665 0.259954
\(133\) −2.20060 −0.190816
\(134\) 9.80250 0.846807
\(135\) −6.61972 −0.569735
\(136\) 3.38956 0.290652
\(137\) 13.1951 1.12733 0.563667 0.826002i \(-0.309390\pi\)
0.563667 + 0.826002i \(0.309390\pi\)
\(138\) 0.977360 0.0831984
\(139\) −12.7683 −1.08299 −0.541497 0.840703i \(-0.682142\pi\)
−0.541497 + 0.840703i \(0.682142\pi\)
\(140\) −1.46027 −0.123416
\(141\) 5.44165 0.458270
\(142\) 7.93317 0.665737
\(143\) 3.48088 0.291086
\(144\) −2.04477 −0.170397
\(145\) 2.47609 0.205628
\(146\) −3.80586 −0.314975
\(147\) −5.68531 −0.468917
\(148\) −2.61798 −0.215196
\(149\) −0.816955 −0.0669276 −0.0334638 0.999440i \(-0.510654\pi\)
−0.0334638 + 0.999440i \(0.510654\pi\)
\(150\) 3.12506 0.255160
\(151\) −9.22880 −0.751029 −0.375514 0.926817i \(-0.622534\pi\)
−0.375514 + 0.926817i \(0.622534\pi\)
\(152\) −2.02326 −0.164108
\(153\) 6.93086 0.560327
\(154\) 3.32369 0.267830
\(155\) 1.37697 0.110601
\(156\) 1.11331 0.0891358
\(157\) 5.69698 0.454669 0.227334 0.973817i \(-0.426999\pi\)
0.227334 + 0.973817i \(0.426999\pi\)
\(158\) −2.61951 −0.208397
\(159\) −12.9661 −1.02828
\(160\) −1.34259 −0.106141
\(161\) 1.08765 0.0857191
\(162\) −1.31537 −0.103345
\(163\) 17.8122 1.39516 0.697581 0.716505i \(-0.254260\pi\)
0.697581 + 0.716505i \(0.254260\pi\)
\(164\) −7.20544 −0.562650
\(165\) 4.00985 0.312166
\(166\) −9.13497 −0.709011
\(167\) −21.9424 −1.69796 −0.848979 0.528427i \(-0.822782\pi\)
−0.848979 + 0.528427i \(0.822782\pi\)
\(168\) 1.06303 0.0820145
\(169\) −11.7025 −0.900189
\(170\) 4.55079 0.349030
\(171\) −4.13709 −0.316371
\(172\) −5.50653 −0.419869
\(173\) 10.8450 0.824533 0.412266 0.911063i \(-0.364737\pi\)
0.412266 + 0.911063i \(0.364737\pi\)
\(174\) −1.80251 −0.136648
\(175\) 3.47772 0.262891
\(176\) 3.05583 0.230342
\(177\) 5.17849 0.389239
\(178\) 8.47498 0.635227
\(179\) −12.3874 −0.925881 −0.462941 0.886389i \(-0.653206\pi\)
−0.462941 + 0.886389i \(0.653206\pi\)
\(180\) −2.74529 −0.204622
\(181\) −18.3079 −1.36082 −0.680409 0.732833i \(-0.738198\pi\)
−0.680409 + 0.732833i \(0.738198\pi\)
\(182\) 1.23894 0.0918364
\(183\) 3.92056 0.289816
\(184\) 1.00000 0.0737210
\(185\) −3.51487 −0.258419
\(186\) −1.00239 −0.0734984
\(187\) −10.3579 −0.757446
\(188\) 5.56770 0.406066
\(189\) 5.36274 0.390082
\(190\) −2.71641 −0.197069
\(191\) −20.2664 −1.46643 −0.733214 0.679998i \(-0.761981\pi\)
−0.733214 + 0.679998i \(0.761981\pi\)
\(192\) 0.977360 0.0705349
\(193\) 5.17560 0.372548 0.186274 0.982498i \(-0.440359\pi\)
0.186274 + 0.982498i \(0.440359\pi\)
\(194\) −1.60299 −0.115088
\(195\) 1.49472 0.107039
\(196\) −5.81701 −0.415501
\(197\) −13.4412 −0.957648 −0.478824 0.877911i \(-0.658937\pi\)
−0.478824 + 0.877911i \(0.658937\pi\)
\(198\) 6.24846 0.444059
\(199\) 8.30474 0.588707 0.294354 0.955697i \(-0.404896\pi\)
0.294354 + 0.955697i \(0.404896\pi\)
\(200\) 3.19745 0.226094
\(201\) −9.58057 −0.675762
\(202\) 12.4278 0.874420
\(203\) −2.00592 −0.140788
\(204\) −3.31282 −0.231944
\(205\) −9.67396 −0.675659
\(206\) −6.16490 −0.429529
\(207\) 2.04477 0.142121
\(208\) 1.13909 0.0789820
\(209\) 6.18273 0.427668
\(210\) 1.42721 0.0984872
\(211\) 0.899204 0.0619038 0.0309519 0.999521i \(-0.490146\pi\)
0.0309519 + 0.999521i \(0.490146\pi\)
\(212\) −13.2665 −0.911144
\(213\) −7.75356 −0.531265
\(214\) −11.9928 −0.819813
\(215\) −7.39302 −0.504200
\(216\) 4.93056 0.335482
\(217\) −1.11550 −0.0757252
\(218\) −2.28864 −0.155006
\(219\) 3.71970 0.251354
\(220\) 4.10273 0.276606
\(221\) −3.86103 −0.259721
\(222\) 2.55871 0.171729
\(223\) −0.869638 −0.0582353 −0.0291176 0.999576i \(-0.509270\pi\)
−0.0291176 + 0.999576i \(0.509270\pi\)
\(224\) 1.08765 0.0726719
\(225\) 6.53804 0.435869
\(226\) −4.66948 −0.310609
\(227\) 17.7853 1.18045 0.590227 0.807237i \(-0.299038\pi\)
0.590227 + 0.807237i \(0.299038\pi\)
\(228\) 1.97745 0.130960
\(229\) −22.8703 −1.51131 −0.755657 0.654968i \(-0.772682\pi\)
−0.755657 + 0.654968i \(0.772682\pi\)
\(230\) 1.34259 0.0885279
\(231\) −3.24844 −0.213732
\(232\) −1.84426 −0.121082
\(233\) 13.2246 0.866375 0.433187 0.901304i \(-0.357389\pi\)
0.433187 + 0.901304i \(0.357389\pi\)
\(234\) 2.32918 0.152263
\(235\) 7.47515 0.487625
\(236\) 5.29844 0.344899
\(237\) 2.56021 0.166303
\(238\) −3.68667 −0.238971
\(239\) −11.0212 −0.712902 −0.356451 0.934314i \(-0.616013\pi\)
−0.356451 + 0.934314i \(0.616013\pi\)
\(240\) 1.31220 0.0847019
\(241\) −23.1444 −1.49086 −0.745431 0.666582i \(-0.767756\pi\)
−0.745431 + 0.666582i \(0.767756\pi\)
\(242\) 1.66189 0.106830
\(243\) 16.0773 1.03136
\(244\) 4.01137 0.256802
\(245\) −7.80987 −0.498954
\(246\) 7.04231 0.449001
\(247\) 2.30468 0.146643
\(248\) −1.02560 −0.0651259
\(249\) 8.92815 0.565799
\(250\) 11.0058 0.696069
\(251\) −17.8805 −1.12861 −0.564303 0.825568i \(-0.690855\pi\)
−0.564303 + 0.825568i \(0.690855\pi\)
\(252\) 2.22400 0.140099
\(253\) −3.05583 −0.192119
\(254\) 4.36870 0.274116
\(255\) −4.44776 −0.278530
\(256\) 1.00000 0.0625000
\(257\) 10.8135 0.674530 0.337265 0.941410i \(-0.390498\pi\)
0.337265 + 0.941410i \(0.390498\pi\)
\(258\) 5.38186 0.335060
\(259\) 2.84745 0.176932
\(260\) 1.52934 0.0948456
\(261\) −3.77108 −0.233424
\(262\) 1.00000 0.0617802
\(263\) −24.8936 −1.53500 −0.767502 0.641046i \(-0.778501\pi\)
−0.767502 + 0.641046i \(0.778501\pi\)
\(264\) −2.98665 −0.183816
\(265\) −17.8114 −1.09415
\(266\) 2.20060 0.134928
\(267\) −8.28311 −0.506918
\(268\) −9.80250 −0.598783
\(269\) 17.4400 1.06334 0.531668 0.846953i \(-0.321566\pi\)
0.531668 + 0.846953i \(0.321566\pi\)
\(270\) 6.61972 0.402863
\(271\) 9.07271 0.551128 0.275564 0.961283i \(-0.411135\pi\)
0.275564 + 0.961283i \(0.411135\pi\)
\(272\) −3.38956 −0.205522
\(273\) −1.21089 −0.0732865
\(274\) −13.1951 −0.797146
\(275\) −9.77086 −0.589205
\(276\) −0.977360 −0.0588302
\(277\) −1.94904 −0.117106 −0.0585532 0.998284i \(-0.518649\pi\)
−0.0585532 + 0.998284i \(0.518649\pi\)
\(278\) 12.7683 0.765793
\(279\) −2.09712 −0.125551
\(280\) 1.46027 0.0872681
\(281\) 4.47670 0.267058 0.133529 0.991045i \(-0.457369\pi\)
0.133529 + 0.991045i \(0.457369\pi\)
\(282\) −5.44165 −0.324046
\(283\) 27.1025 1.61108 0.805538 0.592545i \(-0.201877\pi\)
0.805538 + 0.592545i \(0.201877\pi\)
\(284\) −7.93317 −0.470747
\(285\) 2.65491 0.157263
\(286\) −3.48088 −0.205829
\(287\) 7.83702 0.462605
\(288\) 2.04477 0.120489
\(289\) −5.51089 −0.324170
\(290\) −2.47609 −0.145401
\(291\) 1.56669 0.0918413
\(292\) 3.80586 0.222721
\(293\) −33.4634 −1.95495 −0.977477 0.211041i \(-0.932315\pi\)
−0.977477 + 0.211041i \(0.932315\pi\)
\(294\) 5.68531 0.331574
\(295\) 7.11364 0.414172
\(296\) 2.61798 0.152167
\(297\) −15.0669 −0.874273
\(298\) 0.816955 0.0473250
\(299\) −1.13909 −0.0658756
\(300\) −3.12506 −0.180425
\(301\) 5.98919 0.345211
\(302\) 9.22880 0.531058
\(303\) −12.1465 −0.697797
\(304\) 2.02326 0.116042
\(305\) 5.38564 0.308381
\(306\) −6.93086 −0.396211
\(307\) 13.4270 0.766317 0.383158 0.923683i \(-0.374836\pi\)
0.383158 + 0.923683i \(0.374836\pi\)
\(308\) −3.32369 −0.189385
\(309\) 6.02533 0.342769
\(310\) −1.37697 −0.0782065
\(311\) 7.13048 0.404333 0.202166 0.979351i \(-0.435202\pi\)
0.202166 + 0.979351i \(0.435202\pi\)
\(312\) −1.11331 −0.0630286
\(313\) −28.0091 −1.58317 −0.791585 0.611059i \(-0.790744\pi\)
−0.791585 + 0.611059i \(0.790744\pi\)
\(314\) −5.69698 −0.321499
\(315\) 2.98592 0.168238
\(316\) 2.61951 0.147359
\(317\) 28.0041 1.57287 0.786433 0.617675i \(-0.211925\pi\)
0.786433 + 0.617675i \(0.211925\pi\)
\(318\) 12.9661 0.727103
\(319\) 5.63575 0.315541
\(320\) 1.34259 0.0750531
\(321\) 11.7213 0.654220
\(322\) −1.08765 −0.0606126
\(323\) −6.85794 −0.381586
\(324\) 1.31537 0.0730762
\(325\) −3.64220 −0.202033
\(326\) −17.8122 −0.986529
\(327\) 2.23683 0.123697
\(328\) 7.20544 0.397854
\(329\) −6.05573 −0.333863
\(330\) −4.00985 −0.220735
\(331\) −10.3894 −0.571056 −0.285528 0.958370i \(-0.592169\pi\)
−0.285528 + 0.958370i \(0.592169\pi\)
\(332\) 9.13497 0.501346
\(333\) 5.35315 0.293351
\(334\) 21.9424 1.20064
\(335\) −13.1608 −0.719049
\(336\) −1.06303 −0.0579930
\(337\) −7.84056 −0.427103 −0.213551 0.976932i \(-0.568503\pi\)
−0.213551 + 0.976932i \(0.568503\pi\)
\(338\) 11.7025 0.636530
\(339\) 4.56376 0.247870
\(340\) −4.55079 −0.246801
\(341\) 3.13407 0.169720
\(342\) 4.13709 0.223708
\(343\) 13.9405 0.752715
\(344\) 5.50653 0.296892
\(345\) −1.31220 −0.0706462
\(346\) −10.8450 −0.583033
\(347\) −9.70702 −0.521100 −0.260550 0.965460i \(-0.583904\pi\)
−0.260550 + 0.965460i \(0.583904\pi\)
\(348\) 1.80251 0.0966245
\(349\) 0.644751 0.0345128 0.0172564 0.999851i \(-0.494507\pi\)
0.0172564 + 0.999851i \(0.494507\pi\)
\(350\) −3.47772 −0.185892
\(351\) −5.61637 −0.299780
\(352\) −3.05583 −0.162876
\(353\) 21.2459 1.13081 0.565403 0.824815i \(-0.308721\pi\)
0.565403 + 0.824815i \(0.308721\pi\)
\(354\) −5.17849 −0.275234
\(355\) −10.6510 −0.565296
\(356\) −8.47498 −0.449173
\(357\) 3.60320 0.190702
\(358\) 12.3874 0.654697
\(359\) 28.1546 1.48594 0.742970 0.669324i \(-0.233416\pi\)
0.742970 + 0.669324i \(0.233416\pi\)
\(360\) 2.74529 0.144689
\(361\) −14.9064 −0.784549
\(362\) 18.3079 0.962243
\(363\) −1.62427 −0.0852519
\(364\) −1.23894 −0.0649381
\(365\) 5.10972 0.267455
\(366\) −3.92056 −0.204931
\(367\) −30.4735 −1.59071 −0.795353 0.606147i \(-0.792715\pi\)
−0.795353 + 0.606147i \(0.792715\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 14.7334 0.766992
\(370\) 3.51487 0.182729
\(371\) 14.4293 0.749132
\(372\) 1.00239 0.0519712
\(373\) 11.0261 0.570908 0.285454 0.958392i \(-0.407856\pi\)
0.285454 + 0.958392i \(0.407856\pi\)
\(374\) 10.3579 0.535595
\(375\) −10.7567 −0.555471
\(376\) −5.56770 −0.287132
\(377\) 2.10079 0.108196
\(378\) −5.36274 −0.275829
\(379\) 33.8550 1.73902 0.869508 0.493918i \(-0.164436\pi\)
0.869508 + 0.493918i \(0.164436\pi\)
\(380\) 2.71641 0.139349
\(381\) −4.26979 −0.218748
\(382\) 20.2664 1.03692
\(383\) −11.8256 −0.604260 −0.302130 0.953267i \(-0.597698\pi\)
−0.302130 + 0.953267i \(0.597698\pi\)
\(384\) −0.977360 −0.0498757
\(385\) −4.46235 −0.227423
\(386\) −5.17560 −0.263431
\(387\) 11.2596 0.572356
\(388\) 1.60299 0.0813793
\(389\) 24.4588 1.24011 0.620055 0.784558i \(-0.287110\pi\)
0.620055 + 0.784558i \(0.287110\pi\)
\(390\) −1.49472 −0.0756879
\(391\) 3.38956 0.171417
\(392\) 5.81701 0.293803
\(393\) −0.977360 −0.0493013
\(394\) 13.4412 0.677159
\(395\) 3.51694 0.176956
\(396\) −6.24846 −0.313997
\(397\) −15.7383 −0.789883 −0.394941 0.918706i \(-0.629235\pi\)
−0.394941 + 0.918706i \(0.629235\pi\)
\(398\) −8.30474 −0.416279
\(399\) −2.15078 −0.107674
\(400\) −3.19745 −0.159872
\(401\) 14.1335 0.705792 0.352896 0.935663i \(-0.385197\pi\)
0.352896 + 0.935663i \(0.385197\pi\)
\(402\) 9.58057 0.477836
\(403\) 1.16826 0.0581952
\(404\) −12.4278 −0.618308
\(405\) 1.76601 0.0877535
\(406\) 2.00592 0.0995519
\(407\) −8.00009 −0.396550
\(408\) 3.31282 0.164009
\(409\) 9.11375 0.450646 0.225323 0.974284i \(-0.427656\pi\)
0.225323 + 0.974284i \(0.427656\pi\)
\(410\) 9.67396 0.477763
\(411\) 12.8964 0.636131
\(412\) 6.16490 0.303723
\(413\) −5.76287 −0.283572
\(414\) −2.04477 −0.100495
\(415\) 12.2645 0.602042
\(416\) −1.13909 −0.0558487
\(417\) −12.4792 −0.611111
\(418\) −6.18273 −0.302407
\(419\) −16.6027 −0.811093 −0.405547 0.914074i \(-0.632919\pi\)
−0.405547 + 0.914074i \(0.632919\pi\)
\(420\) −1.42721 −0.0696409
\(421\) 26.7918 1.30575 0.652877 0.757464i \(-0.273562\pi\)
0.652877 + 0.757464i \(0.273562\pi\)
\(422\) −0.899204 −0.0437726
\(423\) −11.3847 −0.553541
\(424\) 13.2665 0.644276
\(425\) 10.8379 0.525717
\(426\) 7.75356 0.375661
\(427\) −4.36299 −0.211140
\(428\) 11.9928 0.579695
\(429\) 3.40208 0.164254
\(430\) 7.39302 0.356523
\(431\) −2.77242 −0.133543 −0.0667713 0.997768i \(-0.521270\pi\)
−0.0667713 + 0.997768i \(0.521270\pi\)
\(432\) −4.93056 −0.237221
\(433\) −25.1108 −1.20675 −0.603375 0.797458i \(-0.706178\pi\)
−0.603375 + 0.797458i \(0.706178\pi\)
\(434\) 1.11550 0.0535458
\(435\) 2.42003 0.116032
\(436\) 2.28864 0.109606
\(437\) −2.02326 −0.0967855
\(438\) −3.71970 −0.177734
\(439\) −24.2836 −1.15899 −0.579495 0.814975i \(-0.696750\pi\)
−0.579495 + 0.814975i \(0.696750\pi\)
\(440\) −4.10273 −0.195590
\(441\) 11.8944 0.566401
\(442\) 3.86103 0.183650
\(443\) −5.83354 −0.277160 −0.138580 0.990351i \(-0.544254\pi\)
−0.138580 + 0.990351i \(0.544254\pi\)
\(444\) −2.55871 −0.121431
\(445\) −11.3784 −0.539390
\(446\) 0.869638 0.0411786
\(447\) −0.798460 −0.0377658
\(448\) −1.08765 −0.0513868
\(449\) 8.73062 0.412024 0.206012 0.978550i \(-0.433951\pi\)
0.206012 + 0.978550i \(0.433951\pi\)
\(450\) −6.53804 −0.308206
\(451\) −22.0186 −1.03682
\(452\) 4.66948 0.219634
\(453\) −9.01986 −0.423790
\(454\) −17.7853 −0.834707
\(455\) −1.66339 −0.0779810
\(456\) −1.97745 −0.0926026
\(457\) 6.33039 0.296123 0.148062 0.988978i \(-0.452697\pi\)
0.148062 + 0.988978i \(0.452697\pi\)
\(458\) 22.8703 1.06866
\(459\) 16.7124 0.780068
\(460\) −1.34259 −0.0625987
\(461\) 25.3714 1.18166 0.590831 0.806795i \(-0.298800\pi\)
0.590831 + 0.806795i \(0.298800\pi\)
\(462\) 3.24844 0.151131
\(463\) 16.1769 0.751805 0.375903 0.926659i \(-0.377333\pi\)
0.375903 + 0.926659i \(0.377333\pi\)
\(464\) 1.84426 0.0856176
\(465\) 1.34579 0.0624097
\(466\) −13.2246 −0.612620
\(467\) 17.8833 0.827541 0.413771 0.910381i \(-0.364212\pi\)
0.413771 + 0.910381i \(0.364212\pi\)
\(468\) −2.32918 −0.107667
\(469\) 10.6617 0.492313
\(470\) −7.47515 −0.344803
\(471\) 5.56801 0.256560
\(472\) −5.29844 −0.243881
\(473\) −16.8270 −0.773707
\(474\) −2.56021 −0.117594
\(475\) −6.46926 −0.296830
\(476\) 3.68667 0.168978
\(477\) 27.1268 1.24205
\(478\) 11.0212 0.504098
\(479\) −4.95166 −0.226247 −0.113124 0.993581i \(-0.536086\pi\)
−0.113124 + 0.993581i \(0.536086\pi\)
\(480\) −1.31220 −0.0598933
\(481\) −2.98212 −0.135973
\(482\) 23.1444 1.05420
\(483\) 1.06303 0.0483695
\(484\) −1.66189 −0.0755405
\(485\) 2.15215 0.0977243
\(486\) −16.0773 −0.729279
\(487\) 11.5578 0.523734 0.261867 0.965104i \(-0.415662\pi\)
0.261867 + 0.965104i \(0.415662\pi\)
\(488\) −4.01137 −0.181586
\(489\) 17.4090 0.787262
\(490\) 7.80987 0.352814
\(491\) −28.3671 −1.28019 −0.640096 0.768295i \(-0.721105\pi\)
−0.640096 + 0.768295i \(0.721105\pi\)
\(492\) −7.04231 −0.317492
\(493\) −6.25122 −0.281541
\(494\) −2.30468 −0.103692
\(495\) −8.38913 −0.377064
\(496\) 1.02560 0.0460510
\(497\) 8.62854 0.387043
\(498\) −8.92815 −0.400080
\(499\) −4.72561 −0.211547 −0.105774 0.994390i \(-0.533732\pi\)
−0.105774 + 0.994390i \(0.533732\pi\)
\(500\) −11.0058 −0.492195
\(501\) −21.4457 −0.958122
\(502\) 17.8805 0.798045
\(503\) −39.8092 −1.77501 −0.887503 0.460802i \(-0.847562\pi\)
−0.887503 + 0.460802i \(0.847562\pi\)
\(504\) −2.22400 −0.0990648
\(505\) −16.6855 −0.742496
\(506\) 3.05583 0.135848
\(507\) −11.4375 −0.507958
\(508\) −4.36870 −0.193830
\(509\) 5.86870 0.260126 0.130063 0.991506i \(-0.458482\pi\)
0.130063 + 0.991506i \(0.458482\pi\)
\(510\) 4.44776 0.196950
\(511\) −4.13946 −0.183119
\(512\) −1.00000 −0.0441942
\(513\) −9.97577 −0.440441
\(514\) −10.8135 −0.476965
\(515\) 8.27694 0.364726
\(516\) −5.38186 −0.236923
\(517\) 17.0140 0.748273
\(518\) −2.84745 −0.125110
\(519\) 10.5995 0.465267
\(520\) −1.52934 −0.0670660
\(521\) −2.89066 −0.126642 −0.0633211 0.997993i \(-0.520169\pi\)
−0.0633211 + 0.997993i \(0.520169\pi\)
\(522\) 3.77108 0.165056
\(523\) −17.9706 −0.785800 −0.392900 0.919581i \(-0.628528\pi\)
−0.392900 + 0.919581i \(0.628528\pi\)
\(524\) −1.00000 −0.0436852
\(525\) 3.39898 0.148344
\(526\) 24.8936 1.08541
\(527\) −3.47635 −0.151432
\(528\) 2.98665 0.129977
\(529\) 1.00000 0.0434783
\(530\) 17.8114 0.773679
\(531\) −10.8341 −0.470159
\(532\) −2.20060 −0.0954082
\(533\) −8.20768 −0.355514
\(534\) 8.28311 0.358445
\(535\) 16.1015 0.696127
\(536\) 9.80250 0.423403
\(537\) −12.1070 −0.522456
\(538\) −17.4400 −0.751892
\(539\) −17.7758 −0.765658
\(540\) −6.61972 −0.284867
\(541\) −29.9398 −1.28721 −0.643606 0.765357i \(-0.722563\pi\)
−0.643606 + 0.765357i \(0.722563\pi\)
\(542\) −9.07271 −0.389706
\(543\) −17.8934 −0.767881
\(544\) 3.38956 0.145326
\(545\) 3.07271 0.131620
\(546\) 1.21089 0.0518214
\(547\) −16.4989 −0.705440 −0.352720 0.935729i \(-0.614743\pi\)
−0.352720 + 0.935729i \(0.614743\pi\)
\(548\) 13.1951 0.563667
\(549\) −8.20232 −0.350067
\(550\) 9.77086 0.416631
\(551\) 3.73141 0.158963
\(552\) 0.977360 0.0415992
\(553\) −2.84912 −0.121157
\(554\) 1.94904 0.0828068
\(555\) −3.43530 −0.145820
\(556\) −12.7683 −0.541497
\(557\) 17.3769 0.736284 0.368142 0.929770i \(-0.379994\pi\)
0.368142 + 0.929770i \(0.379994\pi\)
\(558\) 2.09712 0.0887782
\(559\) −6.27246 −0.265297
\(560\) −1.46027 −0.0617079
\(561\) −10.1234 −0.427411
\(562\) −4.47670 −0.188838
\(563\) 9.87953 0.416372 0.208186 0.978089i \(-0.433244\pi\)
0.208186 + 0.978089i \(0.433244\pi\)
\(564\) 5.44165 0.229135
\(565\) 6.26920 0.263747
\(566\) −27.1025 −1.13920
\(567\) −1.43067 −0.0600824
\(568\) 7.93317 0.332868
\(569\) −31.8109 −1.33358 −0.666790 0.745245i \(-0.732332\pi\)
−0.666790 + 0.745245i \(0.732332\pi\)
\(570\) −2.65491 −0.111202
\(571\) −37.0210 −1.54928 −0.774639 0.632403i \(-0.782069\pi\)
−0.774639 + 0.632403i \(0.782069\pi\)
\(572\) 3.48088 0.145543
\(573\) −19.8076 −0.827475
\(574\) −7.83702 −0.327111
\(575\) 3.19745 0.133343
\(576\) −2.04477 −0.0851986
\(577\) −40.0244 −1.66624 −0.833118 0.553095i \(-0.813447\pi\)
−0.833118 + 0.553095i \(0.813447\pi\)
\(578\) 5.51089 0.229223
\(579\) 5.05843 0.210221
\(580\) 2.47609 0.102814
\(581\) −9.93568 −0.412201
\(582\) −1.56669 −0.0649416
\(583\) −40.5400 −1.67900
\(584\) −3.80586 −0.157488
\(585\) −3.12714 −0.129291
\(586\) 33.4634 1.38236
\(587\) 14.2726 0.589093 0.294546 0.955637i \(-0.404831\pi\)
0.294546 + 0.955637i \(0.404831\pi\)
\(588\) −5.68531 −0.234458
\(589\) 2.07506 0.0855014
\(590\) −7.11364 −0.292864
\(591\) −13.1369 −0.540381
\(592\) −2.61798 −0.107598
\(593\) −23.4674 −0.963691 −0.481846 0.876256i \(-0.660033\pi\)
−0.481846 + 0.876256i \(0.660033\pi\)
\(594\) 15.0669 0.618204
\(595\) 4.94969 0.202917
\(596\) −0.816955 −0.0334638
\(597\) 8.11672 0.332195
\(598\) 1.13909 0.0465811
\(599\) −34.7621 −1.42034 −0.710170 0.704030i \(-0.751382\pi\)
−0.710170 + 0.704030i \(0.751382\pi\)
\(600\) 3.12506 0.127580
\(601\) −30.2985 −1.23590 −0.617952 0.786216i \(-0.712037\pi\)
−0.617952 + 0.786216i \(0.712037\pi\)
\(602\) −5.98919 −0.244101
\(603\) 20.0438 0.816248
\(604\) −9.22880 −0.375514
\(605\) −2.23124 −0.0907129
\(606\) 12.1465 0.493417
\(607\) −29.5440 −1.19915 −0.599576 0.800318i \(-0.704664\pi\)
−0.599576 + 0.800318i \(0.704664\pi\)
\(608\) −2.02326 −0.0820539
\(609\) −1.96050 −0.0794436
\(610\) −5.38564 −0.218058
\(611\) 6.34214 0.256576
\(612\) 6.93086 0.280163
\(613\) 46.0877 1.86146 0.930732 0.365701i \(-0.119171\pi\)
0.930732 + 0.365701i \(0.119171\pi\)
\(614\) −13.4270 −0.541868
\(615\) −9.45494 −0.381260
\(616\) 3.32369 0.133915
\(617\) 27.7635 1.11772 0.558859 0.829263i \(-0.311239\pi\)
0.558859 + 0.829263i \(0.311239\pi\)
\(618\) −6.02533 −0.242374
\(619\) 19.0086 0.764019 0.382009 0.924158i \(-0.375232\pi\)
0.382009 + 0.924158i \(0.375232\pi\)
\(620\) 1.37697 0.0553004
\(621\) 4.93056 0.197856
\(622\) −7.13048 −0.285906
\(623\) 9.21785 0.369305
\(624\) 1.11331 0.0445679
\(625\) 1.21091 0.0484365
\(626\) 28.0091 1.11947
\(627\) 6.04276 0.241324
\(628\) 5.69698 0.227334
\(629\) 8.87378 0.353821
\(630\) −2.98592 −0.118962
\(631\) 23.3994 0.931517 0.465759 0.884912i \(-0.345782\pi\)
0.465759 + 0.884912i \(0.345782\pi\)
\(632\) −2.61951 −0.104199
\(633\) 0.878847 0.0349310
\(634\) −28.0041 −1.11218
\(635\) −5.86538 −0.232760
\(636\) −12.9661 −0.514139
\(637\) −6.62613 −0.262537
\(638\) −5.63575 −0.223121
\(639\) 16.2215 0.641712
\(640\) −1.34259 −0.0530706
\(641\) −21.0647 −0.832007 −0.416003 0.909363i \(-0.636570\pi\)
−0.416003 + 0.909363i \(0.636570\pi\)
\(642\) −11.7213 −0.462603
\(643\) 2.19744 0.0866585 0.0433293 0.999061i \(-0.486204\pi\)
0.0433293 + 0.999061i \(0.486204\pi\)
\(644\) 1.08765 0.0428596
\(645\) −7.22564 −0.284509
\(646\) 6.85794 0.269822
\(647\) 43.5428 1.71185 0.855923 0.517104i \(-0.172990\pi\)
0.855923 + 0.517104i \(0.172990\pi\)
\(648\) −1.31537 −0.0516727
\(649\) 16.1912 0.635558
\(650\) 3.64220 0.142859
\(651\) −1.09025 −0.0427302
\(652\) 17.8122 0.697581
\(653\) −29.4533 −1.15260 −0.576299 0.817239i \(-0.695504\pi\)
−0.576299 + 0.817239i \(0.695504\pi\)
\(654\) −2.23683 −0.0874668
\(655\) −1.34259 −0.0524594
\(656\) −7.20544 −0.281325
\(657\) −7.78210 −0.303608
\(658\) 6.05573 0.236077
\(659\) −6.60498 −0.257294 −0.128647 0.991690i \(-0.541063\pi\)
−0.128647 + 0.991690i \(0.541063\pi\)
\(660\) 4.00985 0.156083
\(661\) −13.4755 −0.524135 −0.262068 0.965050i \(-0.584404\pi\)
−0.262068 + 0.965050i \(0.584404\pi\)
\(662\) 10.3894 0.403797
\(663\) −3.77362 −0.146555
\(664\) −9.13497 −0.354505
\(665\) −2.95451 −0.114571
\(666\) −5.35315 −0.207430
\(667\) −1.84426 −0.0714100
\(668\) −21.9424 −0.848979
\(669\) −0.849950 −0.0328610
\(670\) 13.1608 0.508444
\(671\) 12.2581 0.473218
\(672\) 1.06303 0.0410073
\(673\) 17.3540 0.668947 0.334473 0.942405i \(-0.391442\pi\)
0.334473 + 0.942405i \(0.391442\pi\)
\(674\) 7.84056 0.302007
\(675\) 15.7652 0.606803
\(676\) −11.7025 −0.450095
\(677\) −23.7168 −0.911512 −0.455756 0.890105i \(-0.650631\pi\)
−0.455756 + 0.890105i \(0.650631\pi\)
\(678\) −4.56376 −0.175270
\(679\) −1.74349 −0.0669091
\(680\) 4.55079 0.174515
\(681\) 17.3827 0.666106
\(682\) −3.13407 −0.120010
\(683\) 29.4933 1.12853 0.564265 0.825594i \(-0.309160\pi\)
0.564265 + 0.825594i \(0.309160\pi\)
\(684\) −4.13709 −0.158185
\(685\) 17.7156 0.676880
\(686\) −13.9405 −0.532250
\(687\) −22.3525 −0.852803
\(688\) −5.50653 −0.209934
\(689\) −15.1117 −0.575712
\(690\) 1.31220 0.0499544
\(691\) −28.8651 −1.09808 −0.549040 0.835796i \(-0.685007\pi\)
−0.549040 + 0.835796i \(0.685007\pi\)
\(692\) 10.8450 0.412266
\(693\) 6.79616 0.258165
\(694\) 9.70702 0.368474
\(695\) −17.1426 −0.650257
\(696\) −1.80251 −0.0683238
\(697\) 24.4233 0.925097
\(698\) −0.644751 −0.0244042
\(699\) 12.9252 0.488877
\(700\) 3.47772 0.131445
\(701\) 31.4782 1.18891 0.594457 0.804128i \(-0.297367\pi\)
0.594457 + 0.804128i \(0.297367\pi\)
\(702\) 5.61637 0.211976
\(703\) −5.29683 −0.199774
\(704\) 3.05583 0.115171
\(705\) 7.30591 0.275157
\(706\) −21.2459 −0.799600
\(707\) 13.5172 0.508366
\(708\) 5.17849 0.194620
\(709\) 36.2435 1.36115 0.680577 0.732676i \(-0.261729\pi\)
0.680577 + 0.732676i \(0.261729\pi\)
\(710\) 10.6510 0.399725
\(711\) −5.35629 −0.200877
\(712\) 8.47498 0.317613
\(713\) −1.02560 −0.0384092
\(714\) −3.60320 −0.134846
\(715\) 4.67340 0.174775
\(716\) −12.3874 −0.462941
\(717\) −10.7717 −0.402276
\(718\) −28.1546 −1.05072
\(719\) −44.1278 −1.64569 −0.822845 0.568266i \(-0.807615\pi\)
−0.822845 + 0.568266i \(0.807615\pi\)
\(720\) −2.74529 −0.102311
\(721\) −6.70528 −0.249717
\(722\) 14.9064 0.554760
\(723\) −22.6204 −0.841263
\(724\) −18.3079 −0.680409
\(725\) −5.89692 −0.219006
\(726\) 1.62427 0.0602822
\(727\) 3.23433 0.119954 0.0599772 0.998200i \(-0.480897\pi\)
0.0599772 + 0.998200i \(0.480897\pi\)
\(728\) 1.23894 0.0459182
\(729\) 11.7672 0.435821
\(730\) −5.10972 −0.189119
\(731\) 18.6647 0.690339
\(732\) 3.92056 0.144908
\(733\) −27.7708 −1.02574 −0.512869 0.858467i \(-0.671417\pi\)
−0.512869 + 0.858467i \(0.671417\pi\)
\(734\) 30.4735 1.12480
\(735\) −7.63305 −0.281549
\(736\) 1.00000 0.0368605
\(737\) −29.9548 −1.10340
\(738\) −14.7334 −0.542345
\(739\) 0.113971 0.00419249 0.00209625 0.999998i \(-0.499333\pi\)
0.00209625 + 0.999998i \(0.499333\pi\)
\(740\) −3.51487 −0.129209
\(741\) 2.25250 0.0827478
\(742\) −14.4293 −0.529717
\(743\) 10.6334 0.390100 0.195050 0.980793i \(-0.437513\pi\)
0.195050 + 0.980793i \(0.437513\pi\)
\(744\) −1.00239 −0.0367492
\(745\) −1.09684 −0.0401850
\(746\) −11.0261 −0.403693
\(747\) −18.6789 −0.683424
\(748\) −10.3579 −0.378723
\(749\) −13.0440 −0.476619
\(750\) 10.7567 0.392778
\(751\) 4.01884 0.146650 0.0733248 0.997308i \(-0.476639\pi\)
0.0733248 + 0.997308i \(0.476639\pi\)
\(752\) 5.56770 0.203033
\(753\) −17.4757 −0.636849
\(754\) −2.10079 −0.0765061
\(755\) −12.3905 −0.450937
\(756\) 5.36274 0.195041
\(757\) 33.1181 1.20370 0.601849 0.798610i \(-0.294431\pi\)
0.601849 + 0.798610i \(0.294431\pi\)
\(758\) −33.8550 −1.22967
\(759\) −2.98665 −0.108408
\(760\) −2.71641 −0.0985344
\(761\) −5.72492 −0.207528 −0.103764 0.994602i \(-0.533089\pi\)
−0.103764 + 0.994602i \(0.533089\pi\)
\(762\) 4.26979 0.154678
\(763\) −2.48925 −0.0901168
\(764\) −20.2664 −0.733214
\(765\) 9.30531 0.336434
\(766\) 11.8256 0.427276
\(767\) 6.03543 0.217927
\(768\) 0.977360 0.0352675
\(769\) −22.9595 −0.827940 −0.413970 0.910291i \(-0.635858\pi\)
−0.413970 + 0.910291i \(0.635858\pi\)
\(770\) 4.46235 0.160812
\(771\) 10.5687 0.380624
\(772\) 5.17560 0.186274
\(773\) 16.9375 0.609201 0.304600 0.952480i \(-0.401477\pi\)
0.304600 + 0.952480i \(0.401477\pi\)
\(774\) −11.2596 −0.404717
\(775\) −3.27932 −0.117797
\(776\) −1.60299 −0.0575438
\(777\) 2.78299 0.0998391
\(778\) −24.4588 −0.876890
\(779\) −14.5784 −0.522327
\(780\) 1.49472 0.0535194
\(781\) −24.2424 −0.867462
\(782\) −3.38956 −0.121210
\(783\) −9.09322 −0.324965
\(784\) −5.81701 −0.207750
\(785\) 7.64872 0.272995
\(786\) 0.977360 0.0348613
\(787\) 11.3264 0.403744 0.201872 0.979412i \(-0.435298\pi\)
0.201872 + 0.979412i \(0.435298\pi\)
\(788\) −13.4412 −0.478824
\(789\) −24.3300 −0.866171
\(790\) −3.51694 −0.125127
\(791\) −5.07877 −0.180580
\(792\) 6.24846 0.222029
\(793\) 4.56934 0.162262
\(794\) 15.7383 0.558532
\(795\) −17.4082 −0.617405
\(796\) 8.30474 0.294354
\(797\) 17.3872 0.615887 0.307944 0.951405i \(-0.400359\pi\)
0.307944 + 0.951405i \(0.400359\pi\)
\(798\) 2.15078 0.0761368
\(799\) −18.8721 −0.667645
\(800\) 3.19745 0.113047
\(801\) 17.3294 0.612303
\(802\) −14.1335 −0.499070
\(803\) 11.6301 0.410416
\(804\) −9.58057 −0.337881
\(805\) 1.46027 0.0514679
\(806\) −1.16826 −0.0411502
\(807\) 17.0452 0.600018
\(808\) 12.4278 0.437210
\(809\) −26.4030 −0.928279 −0.464140 0.885762i \(-0.653636\pi\)
−0.464140 + 0.885762i \(0.653636\pi\)
\(810\) −1.76601 −0.0620511
\(811\) −9.18322 −0.322467 −0.161233 0.986916i \(-0.551547\pi\)
−0.161233 + 0.986916i \(0.551547\pi\)
\(812\) −2.00592 −0.0703938
\(813\) 8.86731 0.310990
\(814\) 8.00009 0.280403
\(815\) 23.9146 0.837691
\(816\) −3.31282 −0.115972
\(817\) −11.1411 −0.389778
\(818\) −9.11375 −0.318655
\(819\) 2.53335 0.0885222
\(820\) −9.67396 −0.337829
\(821\) 56.1117 1.95831 0.979157 0.203106i \(-0.0651036\pi\)
0.979157 + 0.203106i \(0.0651036\pi\)
\(822\) −12.8964 −0.449813
\(823\) −37.7029 −1.31424 −0.657121 0.753785i \(-0.728226\pi\)
−0.657121 + 0.753785i \(0.728226\pi\)
\(824\) −6.16490 −0.214764
\(825\) −9.54965 −0.332476
\(826\) 5.76287 0.200516
\(827\) −4.73970 −0.164815 −0.0824077 0.996599i \(-0.526261\pi\)
−0.0824077 + 0.996599i \(0.526261\pi\)
\(828\) 2.04477 0.0710606
\(829\) 14.1949 0.493009 0.246505 0.969142i \(-0.420718\pi\)
0.246505 + 0.969142i \(0.420718\pi\)
\(830\) −12.2645 −0.425708
\(831\) −1.90491 −0.0660808
\(832\) 1.13909 0.0394910
\(833\) 19.7171 0.683157
\(834\) 12.4792 0.432121
\(835\) −29.4597 −1.01950
\(836\) 6.18273 0.213834
\(837\) −5.05680 −0.174789
\(838\) 16.6027 0.573529
\(839\) 28.7673 0.993158 0.496579 0.867991i \(-0.334589\pi\)
0.496579 + 0.867991i \(0.334589\pi\)
\(840\) 1.42721 0.0492436
\(841\) −25.5987 −0.882714
\(842\) −26.7918 −0.923308
\(843\) 4.37535 0.150695
\(844\) 0.899204 0.0309519
\(845\) −15.7116 −0.540496
\(846\) 11.3847 0.391412
\(847\) 1.80756 0.0621086
\(848\) −13.2665 −0.455572
\(849\) 26.4889 0.909096
\(850\) −10.8379 −0.371738
\(851\) 2.61798 0.0897430
\(852\) −7.75356 −0.265633
\(853\) −19.0966 −0.653855 −0.326927 0.945049i \(-0.606013\pi\)
−0.326927 + 0.945049i \(0.606013\pi\)
\(854\) 4.36299 0.149298
\(855\) −5.55442 −0.189957
\(856\) −11.9928 −0.409906
\(857\) 12.3672 0.422456 0.211228 0.977437i \(-0.432254\pi\)
0.211228 + 0.977437i \(0.432254\pi\)
\(858\) −3.40208 −0.116145
\(859\) −1.71691 −0.0585801 −0.0292900 0.999571i \(-0.509325\pi\)
−0.0292900 + 0.999571i \(0.509325\pi\)
\(860\) −7.39302 −0.252100
\(861\) 7.65959 0.261038
\(862\) 2.77242 0.0944289
\(863\) −11.7362 −0.399503 −0.199752 0.979847i \(-0.564014\pi\)
−0.199752 + 0.979847i \(0.564014\pi\)
\(864\) 4.93056 0.167741
\(865\) 14.5605 0.495070
\(866\) 25.1108 0.853301
\(867\) −5.38613 −0.182922
\(868\) −1.11550 −0.0378626
\(869\) 8.00479 0.271544
\(870\) −2.42003 −0.0820467
\(871\) −11.1660 −0.378345
\(872\) −2.28864 −0.0775031
\(873\) −3.27773 −0.110934
\(874\) 2.02326 0.0684377
\(875\) 11.9705 0.404678
\(876\) 3.71970 0.125677
\(877\) 30.4781 1.02917 0.514586 0.857439i \(-0.327946\pi\)
0.514586 + 0.857439i \(0.327946\pi\)
\(878\) 24.2836 0.819530
\(879\) −32.7058 −1.10314
\(880\) 4.10273 0.138303
\(881\) −11.7812 −0.396919 −0.198460 0.980109i \(-0.563594\pi\)
−0.198460 + 0.980109i \(0.563594\pi\)
\(882\) −11.8944 −0.400506
\(883\) 10.2471 0.344841 0.172421 0.985023i \(-0.444841\pi\)
0.172421 + 0.985023i \(0.444841\pi\)
\(884\) −3.86103 −0.129860
\(885\) 6.95259 0.233709
\(886\) 5.83354 0.195982
\(887\) 22.6551 0.760683 0.380342 0.924846i \(-0.375806\pi\)
0.380342 + 0.924846i \(0.375806\pi\)
\(888\) 2.55871 0.0858645
\(889\) 4.75163 0.159365
\(890\) 11.3784 0.381406
\(891\) 4.01955 0.134660
\(892\) −0.869638 −0.0291176
\(893\) 11.2649 0.376965
\(894\) 0.798460 0.0267045
\(895\) −16.6313 −0.555922
\(896\) 1.08765 0.0363360
\(897\) −1.11331 −0.0371722
\(898\) −8.73062 −0.291345
\(899\) 1.89148 0.0630844
\(900\) 6.53804 0.217935
\(901\) 44.9674 1.49808
\(902\) 22.0186 0.733139
\(903\) 5.85360 0.194796
\(904\) −4.66948 −0.155305
\(905\) −24.5801 −0.817069
\(906\) 9.01986 0.299665
\(907\) 12.5588 0.417007 0.208503 0.978022i \(-0.433141\pi\)
0.208503 + 0.978022i \(0.433141\pi\)
\(908\) 17.7853 0.590227
\(909\) 25.4120 0.842864
\(910\) 1.66339 0.0551409
\(911\) −16.1396 −0.534729 −0.267365 0.963595i \(-0.586153\pi\)
−0.267365 + 0.963595i \(0.586153\pi\)
\(912\) 1.97745 0.0654799
\(913\) 27.9149 0.923849
\(914\) −6.33039 −0.209391
\(915\) 5.26371 0.174013
\(916\) −22.8703 −0.755657
\(917\) 1.08765 0.0359175
\(918\) −16.7124 −0.551592
\(919\) −22.2275 −0.733218 −0.366609 0.930375i \(-0.619481\pi\)
−0.366609 + 0.930375i \(0.619481\pi\)
\(920\) 1.34259 0.0442639
\(921\) 13.1230 0.432417
\(922\) −25.3714 −0.835562
\(923\) −9.03663 −0.297444
\(924\) −3.24844 −0.106866
\(925\) 8.37084 0.275232
\(926\) −16.1769 −0.531607
\(927\) −12.6058 −0.414028
\(928\) −1.84426 −0.0605408
\(929\) 47.1627 1.54736 0.773680 0.633577i \(-0.218414\pi\)
0.773680 + 0.633577i \(0.218414\pi\)
\(930\) −1.34579 −0.0441303
\(931\) −11.7693 −0.385723
\(932\) 13.2246 0.433187
\(933\) 6.96905 0.228156
\(934\) −17.8833 −0.585160
\(935\) −13.9065 −0.454790
\(936\) 2.32918 0.0761317
\(937\) −14.2267 −0.464767 −0.232384 0.972624i \(-0.574652\pi\)
−0.232384 + 0.972624i \(0.574652\pi\)
\(938\) −10.6617 −0.348118
\(939\) −27.3750 −0.893350
\(940\) 7.47515 0.243812
\(941\) 21.7894 0.710315 0.355157 0.934807i \(-0.384427\pi\)
0.355157 + 0.934807i \(0.384427\pi\)
\(942\) −5.56801 −0.181415
\(943\) 7.20544 0.234641
\(944\) 5.29844 0.172450
\(945\) 7.19996 0.234215
\(946\) 16.8270 0.547094
\(947\) 18.1897 0.591084 0.295542 0.955330i \(-0.404500\pi\)
0.295542 + 0.955330i \(0.404500\pi\)
\(948\) 2.56021 0.0831517
\(949\) 4.33524 0.140728
\(950\) 6.46926 0.209890
\(951\) 27.3701 0.887536
\(952\) −3.68667 −0.119486
\(953\) 25.6055 0.829444 0.414722 0.909948i \(-0.363879\pi\)
0.414722 + 0.909948i \(0.363879\pi\)
\(954\) −27.1268 −0.878263
\(955\) −27.2095 −0.880480
\(956\) −11.0212 −0.356451
\(957\) 5.50815 0.178053
\(958\) 4.95166 0.159981
\(959\) −14.3517 −0.463441
\(960\) 1.31220 0.0423509
\(961\) −29.9481 −0.966069
\(962\) 2.98212 0.0961475
\(963\) −24.5225 −0.790228
\(964\) −23.1444 −0.745431
\(965\) 6.94872 0.223687
\(966\) −1.06303 −0.0342024
\(967\) −15.9968 −0.514423 −0.257211 0.966355i \(-0.582804\pi\)
−0.257211 + 0.966355i \(0.582804\pi\)
\(968\) 1.66189 0.0534152
\(969\) −6.70268 −0.215321
\(970\) −2.15215 −0.0691015
\(971\) −3.87290 −0.124287 −0.0621436 0.998067i \(-0.519794\pi\)
−0.0621436 + 0.998067i \(0.519794\pi\)
\(972\) 16.0773 0.515678
\(973\) 13.8875 0.445213
\(974\) −11.5578 −0.370336
\(975\) −3.55974 −0.114003
\(976\) 4.01137 0.128401
\(977\) 37.6902 1.20582 0.602908 0.797811i \(-0.294009\pi\)
0.602908 + 0.797811i \(0.294009\pi\)
\(978\) −17.4090 −0.556678
\(979\) −25.8981 −0.827707
\(980\) −7.80987 −0.249477
\(981\) −4.67973 −0.149412
\(982\) 28.3671 0.905232
\(983\) −19.8076 −0.631764 −0.315882 0.948798i \(-0.602300\pi\)
−0.315882 + 0.948798i \(0.602300\pi\)
\(984\) 7.04231 0.224501
\(985\) −18.0461 −0.574996
\(986\) 6.25122 0.199080
\(987\) −5.91863 −0.188392
\(988\) 2.30468 0.0733217
\(989\) 5.50653 0.175097
\(990\) 8.38913 0.266624
\(991\) −59.4399 −1.88817 −0.944086 0.329700i \(-0.893052\pi\)
−0.944086 + 0.329700i \(0.893052\pi\)
\(992\) −1.02560 −0.0325630
\(993\) −10.1542 −0.322235
\(994\) −8.62854 −0.273681
\(995\) 11.1499 0.353475
\(996\) 8.92815 0.282899
\(997\) −6.06009 −0.191925 −0.0959625 0.995385i \(-0.530593\pi\)
−0.0959625 + 0.995385i \(0.530593\pi\)
\(998\) 4.72561 0.149587
\(999\) 12.9081 0.408393
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 \(a_p\))