Properties

Label 8013.2.a.d.1.1
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 1.1
Character \(\chi\) = 8013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.80990 q^{2}\) \(+1.00000 q^{3}\) \(+5.89553 q^{4}\) \(+3.04419 q^{5}\) \(-2.80990 q^{6}\) \(+3.35815 q^{7}\) \(-10.9460 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.80990 q^{2}\) \(+1.00000 q^{3}\) \(+5.89553 q^{4}\) \(+3.04419 q^{5}\) \(-2.80990 q^{6}\) \(+3.35815 q^{7}\) \(-10.9460 q^{8}\) \(+1.00000 q^{9}\) \(-8.55386 q^{10}\) \(+3.20260 q^{11}\) \(+5.89553 q^{12}\) \(+6.42536 q^{13}\) \(-9.43606 q^{14}\) \(+3.04419 q^{15}\) \(+18.9662 q^{16}\) \(-6.70387 q^{17}\) \(-2.80990 q^{18}\) \(+5.19441 q^{19}\) \(+17.9471 q^{20}\) \(+3.35815 q^{21}\) \(-8.99897 q^{22}\) \(-1.38780 q^{23}\) \(-10.9460 q^{24}\) \(+4.26709 q^{25}\) \(-18.0546 q^{26}\) \(+1.00000 q^{27}\) \(+19.7981 q^{28}\) \(+5.04354 q^{29}\) \(-8.55386 q^{30}\) \(-9.32809 q^{31}\) \(-31.4010 q^{32}\) \(+3.20260 q^{33}\) \(+18.8372 q^{34}\) \(+10.2228 q^{35}\) \(+5.89553 q^{36}\) \(+1.94322 q^{37}\) \(-14.5958 q^{38}\) \(+6.42536 q^{39}\) \(-33.3218 q^{40}\) \(-8.32135 q^{41}\) \(-9.43606 q^{42}\) \(+7.92471 q^{43}\) \(+18.8810 q^{44}\) \(+3.04419 q^{45}\) \(+3.89957 q^{46}\) \(+3.46968 q^{47}\) \(+18.9662 q^{48}\) \(+4.27717 q^{49}\) \(-11.9901 q^{50}\) \(-6.70387 q^{51}\) \(+37.8809 q^{52}\) \(+0.587042 q^{53}\) \(-2.80990 q^{54}\) \(+9.74931 q^{55}\) \(-36.7584 q^{56}\) \(+5.19441 q^{57}\) \(-14.1718 q^{58}\) \(+1.13952 q^{59}\) \(+17.9471 q^{60}\) \(+0.747596 q^{61}\) \(+26.2110 q^{62}\) \(+3.35815 q^{63}\) \(+50.3013 q^{64}\) \(+19.5600 q^{65}\) \(-8.99897 q^{66}\) \(+6.42956 q^{67}\) \(-39.5228 q^{68}\) \(-1.38780 q^{69}\) \(-28.7252 q^{70}\) \(-7.60177 q^{71}\) \(-10.9460 q^{72}\) \(-11.8116 q^{73}\) \(-5.46025 q^{74}\) \(+4.26709 q^{75}\) \(+30.6238 q^{76}\) \(+10.7548 q^{77}\) \(-18.0546 q^{78}\) \(-16.7142 q^{79}\) \(+57.7367 q^{80}\) \(+1.00000 q^{81}\) \(+23.3821 q^{82}\) \(+8.13069 q^{83}\) \(+19.7981 q^{84}\) \(-20.4078 q^{85}\) \(-22.2676 q^{86}\) \(+5.04354 q^{87}\) \(-35.0558 q^{88}\) \(+8.78685 q^{89}\) \(-8.55386 q^{90}\) \(+21.5773 q^{91}\) \(-8.18180 q^{92}\) \(-9.32809 q^{93}\) \(-9.74945 q^{94}\) \(+15.8128 q^{95}\) \(-31.4010 q^{96}\) \(-5.64165 q^{97}\) \(-12.0184 q^{98}\) \(+3.20260 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut 41q^{10} \) \(\mathstrut +\mathstrut 51q^{11} \) \(\mathstrut +\mathstrut 151q^{12} \) \(\mathstrut +\mathstrut 56q^{13} \) \(\mathstrut +\mathstrut 5q^{14} \) \(\mathstrut +\mathstrut 16q^{15} \) \(\mathstrut +\mathstrut 195q^{16} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 15q^{18} \) \(\mathstrut +\mathstrut 93q^{19} \) \(\mathstrut +\mathstrut 44q^{20} \) \(\mathstrut +\mathstrut 61q^{21} \) \(\mathstrut +\mathstrut 46q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 42q^{24} \) \(\mathstrut +\mathstrut 193q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut +\mathstrut 129q^{27} \) \(\mathstrut +\mathstrut 145q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 41q^{30} \) \(\mathstrut +\mathstrut 67q^{31} \) \(\mathstrut +\mathstrut 89q^{32} \) \(\mathstrut +\mathstrut 51q^{33} \) \(\mathstrut +\mathstrut 73q^{34} \) \(\mathstrut +\mathstrut 56q^{35} \) \(\mathstrut +\mathstrut 151q^{36} \) \(\mathstrut +\mathstrut 95q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 103q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 5q^{42} \) \(\mathstrut +\mathstrut 150q^{43} \) \(\mathstrut +\mathstrut 69q^{44} \) \(\mathstrut +\mathstrut 16q^{45} \) \(\mathstrut +\mathstrut 72q^{46} \) \(\mathstrut +\mathstrut 53q^{47} \) \(\mathstrut +\mathstrut 195q^{48} \) \(\mathstrut +\mathstrut 240q^{49} \) \(\mathstrut +\mathstrut 17q^{50} \) \(\mathstrut +\mathstrut 18q^{51} \) \(\mathstrut +\mathstrut 124q^{52} \) \(\mathstrut +\mathstrut 34q^{53} \) \(\mathstrut +\mathstrut 15q^{54} \) \(\mathstrut +\mathstrut 66q^{55} \) \(\mathstrut -\mathstrut 17q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 57q^{58} \) \(\mathstrut +\mathstrut 49q^{59} \) \(\mathstrut +\mathstrut 44q^{60} \) \(\mathstrut +\mathstrut 113q^{61} \) \(\mathstrut +\mathstrut 27q^{62} \) \(\mathstrut +\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 262q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 46q^{66} \) \(\mathstrut +\mathstrut 185q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut +\mathstrut 50q^{69} \) \(\mathstrut +\mathstrut 25q^{70} \) \(\mathstrut +\mathstrut 41q^{71} \) \(\mathstrut +\mathstrut 42q^{72} \) \(\mathstrut +\mathstrut 153q^{73} \) \(\mathstrut -\mathstrut q^{74} \) \(\mathstrut +\mathstrut 193q^{75} \) \(\mathstrut +\mathstrut 190q^{76} \) \(\mathstrut +\mathstrut 39q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 101q^{79} \) \(\mathstrut +\mathstrut 48q^{80} \) \(\mathstrut +\mathstrut 129q^{81} \) \(\mathstrut +\mathstrut 15q^{82} \) \(\mathstrut +\mathstrut 162q^{83} \) \(\mathstrut +\mathstrut 145q^{84} \) \(\mathstrut +\mathstrut 99q^{85} \) \(\mathstrut +\mathstrut 13q^{86} \) \(\mathstrut +\mathstrut 24q^{87} \) \(\mathstrut +\mathstrut 86q^{88} \) \(\mathstrut -\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 117q^{91} \) \(\mathstrut +\mathstrut 56q^{92} \) \(\mathstrut +\mathstrut 67q^{93} \) \(\mathstrut +\mathstrut 49q^{94} \) \(\mathstrut +\mathstrut 71q^{95} \) \(\mathstrut +\mathstrut 89q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut +\mathstrut 40q^{98} \) \(\mathstrut +\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.80990 −1.98690 −0.993449 0.114275i \(-0.963545\pi\)
−0.993449 + 0.114275i \(0.963545\pi\)
\(3\) 1.00000 0.577350
\(4\) 5.89553 2.94776
\(5\) 3.04419 1.36140 0.680701 0.732561i \(-0.261675\pi\)
0.680701 + 0.732561i \(0.261675\pi\)
\(6\) −2.80990 −1.14714
\(7\) 3.35815 1.26926 0.634631 0.772816i \(-0.281152\pi\)
0.634631 + 0.772816i \(0.281152\pi\)
\(8\) −10.9460 −3.87001
\(9\) 1.00000 0.333333
\(10\) −8.55386 −2.70497
\(11\) 3.20260 0.965620 0.482810 0.875725i \(-0.339616\pi\)
0.482810 + 0.875725i \(0.339616\pi\)
\(12\) 5.89553 1.70189
\(13\) 6.42536 1.78207 0.891037 0.453931i \(-0.149979\pi\)
0.891037 + 0.453931i \(0.149979\pi\)
\(14\) −9.43606 −2.52189
\(15\) 3.04419 0.786006
\(16\) 18.9662 4.74155
\(17\) −6.70387 −1.62593 −0.812963 0.582315i \(-0.802147\pi\)
−0.812963 + 0.582315i \(0.802147\pi\)
\(18\) −2.80990 −0.662299
\(19\) 5.19441 1.19168 0.595840 0.803103i \(-0.296819\pi\)
0.595840 + 0.803103i \(0.296819\pi\)
\(20\) 17.9471 4.01310
\(21\) 3.35815 0.732808
\(22\) −8.99897 −1.91859
\(23\) −1.38780 −0.289376 −0.144688 0.989477i \(-0.546218\pi\)
−0.144688 + 0.989477i \(0.546218\pi\)
\(24\) −10.9460 −2.23435
\(25\) 4.26709 0.853418
\(26\) −18.0546 −3.54080
\(27\) 1.00000 0.192450
\(28\) 19.7981 3.74148
\(29\) 5.04354 0.936562 0.468281 0.883580i \(-0.344874\pi\)
0.468281 + 0.883580i \(0.344874\pi\)
\(30\) −8.55386 −1.56171
\(31\) −9.32809 −1.67537 −0.837687 0.546151i \(-0.816093\pi\)
−0.837687 + 0.546151i \(0.816093\pi\)
\(32\) −31.4010 −5.55097
\(33\) 3.20260 0.557501
\(34\) 18.8372 3.23055
\(35\) 10.2228 1.72798
\(36\) 5.89553 0.982588
\(37\) 1.94322 0.319464 0.159732 0.987160i \(-0.448937\pi\)
0.159732 + 0.987160i \(0.448937\pi\)
\(38\) −14.5958 −2.36775
\(39\) 6.42536 1.02888
\(40\) −33.3218 −5.26864
\(41\) −8.32135 −1.29958 −0.649788 0.760116i \(-0.725142\pi\)
−0.649788 + 0.760116i \(0.725142\pi\)
\(42\) −9.43606 −1.45602
\(43\) 7.92471 1.20851 0.604253 0.796792i \(-0.293471\pi\)
0.604253 + 0.796792i \(0.293471\pi\)
\(44\) 18.8810 2.84642
\(45\) 3.04419 0.453801
\(46\) 3.89957 0.574960
\(47\) 3.46968 0.506105 0.253053 0.967453i \(-0.418565\pi\)
0.253053 + 0.967453i \(0.418565\pi\)
\(48\) 18.9662 2.73754
\(49\) 4.27717 0.611024
\(50\) −11.9901 −1.69565
\(51\) −6.70387 −0.938729
\(52\) 37.8809 5.25313
\(53\) 0.587042 0.0806364 0.0403182 0.999187i \(-0.487163\pi\)
0.0403182 + 0.999187i \(0.487163\pi\)
\(54\) −2.80990 −0.382379
\(55\) 9.74931 1.31460
\(56\) −36.7584 −4.91205
\(57\) 5.19441 0.688017
\(58\) −14.1718 −1.86085
\(59\) 1.13952 0.148353 0.0741764 0.997245i \(-0.476367\pi\)
0.0741764 + 0.997245i \(0.476367\pi\)
\(60\) 17.9471 2.31696
\(61\) 0.747596 0.0957198 0.0478599 0.998854i \(-0.484760\pi\)
0.0478599 + 0.998854i \(0.484760\pi\)
\(62\) 26.2110 3.32880
\(63\) 3.35815 0.423087
\(64\) 50.3013 6.28766
\(65\) 19.5600 2.42612
\(66\) −8.99897 −1.10770
\(67\) 6.42956 0.785496 0.392748 0.919646i \(-0.371524\pi\)
0.392748 + 0.919646i \(0.371524\pi\)
\(68\) −39.5228 −4.79285
\(69\) −1.38780 −0.167071
\(70\) −28.7252 −3.43331
\(71\) −7.60177 −0.902164 −0.451082 0.892483i \(-0.648962\pi\)
−0.451082 + 0.892483i \(0.648962\pi\)
\(72\) −10.9460 −1.29000
\(73\) −11.8116 −1.38244 −0.691221 0.722643i \(-0.742927\pi\)
−0.691221 + 0.722643i \(0.742927\pi\)
\(74\) −5.46025 −0.634742
\(75\) 4.26709 0.492721
\(76\) 30.6238 3.51279
\(77\) 10.7548 1.22562
\(78\) −18.0546 −2.04428
\(79\) −16.7142 −1.88049 −0.940247 0.340494i \(-0.889406\pi\)
−0.940247 + 0.340494i \(0.889406\pi\)
\(80\) 57.7367 6.45516
\(81\) 1.00000 0.111111
\(82\) 23.3821 2.58213
\(83\) 8.13069 0.892459 0.446229 0.894919i \(-0.352767\pi\)
0.446229 + 0.894919i \(0.352767\pi\)
\(84\) 19.7981 2.16015
\(85\) −20.4078 −2.21354
\(86\) −22.2676 −2.40118
\(87\) 5.04354 0.540724
\(88\) −35.0558 −3.73696
\(89\) 8.78685 0.931404 0.465702 0.884942i \(-0.345802\pi\)
0.465702 + 0.884942i \(0.345802\pi\)
\(90\) −8.55386 −0.901656
\(91\) 21.5773 2.26192
\(92\) −8.18180 −0.853012
\(93\) −9.32809 −0.967278
\(94\) −9.74945 −1.00558
\(95\) 15.8128 1.62236
\(96\) −31.4010 −3.20485
\(97\) −5.64165 −0.572822 −0.286411 0.958107i \(-0.592462\pi\)
−0.286411 + 0.958107i \(0.592462\pi\)
\(98\) −12.0184 −1.21404
\(99\) 3.20260 0.321873
\(100\) 25.1567 2.51567
\(101\) 9.71049 0.966229 0.483115 0.875557i \(-0.339505\pi\)
0.483115 + 0.875557i \(0.339505\pi\)
\(102\) 18.8372 1.86516
\(103\) −12.4125 −1.22304 −0.611519 0.791229i \(-0.709441\pi\)
−0.611519 + 0.791229i \(0.709441\pi\)
\(104\) −70.3322 −6.89664
\(105\) 10.2228 0.997647
\(106\) −1.64953 −0.160216
\(107\) 13.5602 1.31092 0.655459 0.755231i \(-0.272475\pi\)
0.655459 + 0.755231i \(0.272475\pi\)
\(108\) 5.89553 0.567298
\(109\) −1.33687 −0.128049 −0.0640244 0.997948i \(-0.520394\pi\)
−0.0640244 + 0.997948i \(0.520394\pi\)
\(110\) −27.3946 −2.61197
\(111\) 1.94322 0.184442
\(112\) 63.6914 6.01827
\(113\) −2.02195 −0.190209 −0.0951044 0.995467i \(-0.530319\pi\)
−0.0951044 + 0.995467i \(0.530319\pi\)
\(114\) −14.5958 −1.36702
\(115\) −4.22472 −0.393957
\(116\) 29.7343 2.76076
\(117\) 6.42536 0.594024
\(118\) −3.20193 −0.294762
\(119\) −22.5126 −2.06373
\(120\) −33.3218 −3.04185
\(121\) −0.743368 −0.0675789
\(122\) −2.10067 −0.190186
\(123\) −8.32135 −0.750310
\(124\) −54.9940 −4.93861
\(125\) −2.23112 −0.199557
\(126\) −9.43606 −0.840631
\(127\) −11.3783 −1.00966 −0.504830 0.863219i \(-0.668445\pi\)
−0.504830 + 0.863219i \(0.668445\pi\)
\(128\) −78.5394 −6.94197
\(129\) 7.92471 0.697732
\(130\) −54.9616 −4.82045
\(131\) −19.9280 −1.74112 −0.870560 0.492063i \(-0.836243\pi\)
−0.870560 + 0.492063i \(0.836243\pi\)
\(132\) 18.8810 1.64338
\(133\) 17.4436 1.51255
\(134\) −18.0664 −1.56070
\(135\) 3.04419 0.262002
\(136\) 73.3808 6.29235
\(137\) 15.6869 1.34022 0.670110 0.742262i \(-0.266247\pi\)
0.670110 + 0.742262i \(0.266247\pi\)
\(138\) 3.89957 0.331953
\(139\) 9.20531 0.780785 0.390392 0.920649i \(-0.372339\pi\)
0.390392 + 0.920649i \(0.372339\pi\)
\(140\) 60.2691 5.09367
\(141\) 3.46968 0.292200
\(142\) 21.3602 1.79251
\(143\) 20.5778 1.72080
\(144\) 18.9662 1.58052
\(145\) 15.3535 1.27504
\(146\) 33.1894 2.74677
\(147\) 4.27717 0.352775
\(148\) 11.4563 0.941704
\(149\) 0.979608 0.0802527 0.0401263 0.999195i \(-0.487224\pi\)
0.0401263 + 0.999195i \(0.487224\pi\)
\(150\) −11.9901 −0.978987
\(151\) 7.47753 0.608512 0.304256 0.952590i \(-0.401592\pi\)
0.304256 + 0.952590i \(0.401592\pi\)
\(152\) −56.8582 −4.61181
\(153\) −6.70387 −0.541976
\(154\) −30.2199 −2.43519
\(155\) −28.3965 −2.28086
\(156\) 37.8809 3.03290
\(157\) 5.68385 0.453620 0.226810 0.973939i \(-0.427170\pi\)
0.226810 + 0.973939i \(0.427170\pi\)
\(158\) 46.9652 3.73635
\(159\) 0.587042 0.0465554
\(160\) −95.5907 −7.55711
\(161\) −4.66043 −0.367294
\(162\) −2.80990 −0.220766
\(163\) 16.2555 1.27323 0.636613 0.771183i \(-0.280335\pi\)
0.636613 + 0.771183i \(0.280335\pi\)
\(164\) −49.0587 −3.83084
\(165\) 9.74931 0.758983
\(166\) −22.8464 −1.77323
\(167\) 14.5432 1.12538 0.562691 0.826667i \(-0.309766\pi\)
0.562691 + 0.826667i \(0.309766\pi\)
\(168\) −36.7584 −2.83598
\(169\) 28.2852 2.17579
\(170\) 57.3440 4.39808
\(171\) 5.19441 0.397227
\(172\) 46.7204 3.56239
\(173\) 6.95597 0.528853 0.264426 0.964406i \(-0.414817\pi\)
0.264426 + 0.964406i \(0.414817\pi\)
\(174\) −14.1718 −1.07436
\(175\) 14.3295 1.08321
\(176\) 60.7411 4.57853
\(177\) 1.13952 0.0856515
\(178\) −24.6901 −1.85060
\(179\) −12.2263 −0.913836 −0.456918 0.889509i \(-0.651047\pi\)
−0.456918 + 0.889509i \(0.651047\pi\)
\(180\) 17.9471 1.33770
\(181\) 20.6717 1.53651 0.768256 0.640142i \(-0.221125\pi\)
0.768256 + 0.640142i \(0.221125\pi\)
\(182\) −60.6301 −4.49420
\(183\) 0.747596 0.0552639
\(184\) 15.1909 1.11989
\(185\) 5.91553 0.434919
\(186\) 26.2110 1.92188
\(187\) −21.4698 −1.57003
\(188\) 20.4556 1.49188
\(189\) 3.35815 0.244269
\(190\) −44.4323 −3.22346
\(191\) −14.1794 −1.02598 −0.512992 0.858393i \(-0.671463\pi\)
−0.512992 + 0.858393i \(0.671463\pi\)
\(192\) 50.3013 3.63018
\(193\) −0.765741 −0.0551192 −0.0275596 0.999620i \(-0.508774\pi\)
−0.0275596 + 0.999620i \(0.508774\pi\)
\(194\) 15.8525 1.13814
\(195\) 19.5600 1.40072
\(196\) 25.2162 1.80116
\(197\) 18.5619 1.32248 0.661240 0.750174i \(-0.270030\pi\)
0.661240 + 0.750174i \(0.270030\pi\)
\(198\) −8.99897 −0.639529
\(199\) −8.00176 −0.567229 −0.283615 0.958938i \(-0.591534\pi\)
−0.283615 + 0.958938i \(0.591534\pi\)
\(200\) −46.7077 −3.30274
\(201\) 6.42956 0.453506
\(202\) −27.2855 −1.91980
\(203\) 16.9370 1.18874
\(204\) −39.5228 −2.76715
\(205\) −25.3318 −1.76925
\(206\) 34.8778 2.43005
\(207\) −1.38780 −0.0964586
\(208\) 121.865 8.44979
\(209\) 16.6356 1.15071
\(210\) −28.7252 −1.98222
\(211\) 0.888070 0.0611373 0.0305686 0.999533i \(-0.490268\pi\)
0.0305686 + 0.999533i \(0.490268\pi\)
\(212\) 3.46092 0.237697
\(213\) −7.60177 −0.520864
\(214\) −38.1029 −2.60466
\(215\) 24.1243 1.64526
\(216\) −10.9460 −0.744784
\(217\) −31.3251 −2.12649
\(218\) 3.75647 0.254420
\(219\) −11.8116 −0.798154
\(220\) 57.4774 3.87512
\(221\) −43.0747 −2.89752
\(222\) −5.46025 −0.366468
\(223\) 3.86891 0.259081 0.129541 0.991574i \(-0.458650\pi\)
0.129541 + 0.991574i \(0.458650\pi\)
\(224\) −105.449 −7.04563
\(225\) 4.26709 0.284473
\(226\) 5.68147 0.377926
\(227\) 22.1461 1.46989 0.734944 0.678128i \(-0.237209\pi\)
0.734944 + 0.678128i \(0.237209\pi\)
\(228\) 30.6238 2.02811
\(229\) −23.0646 −1.52415 −0.762075 0.647489i \(-0.775819\pi\)
−0.762075 + 0.647489i \(0.775819\pi\)
\(230\) 11.8710 0.782753
\(231\) 10.7548 0.707614
\(232\) −55.2068 −3.62450
\(233\) 10.4477 0.684449 0.342224 0.939618i \(-0.388820\pi\)
0.342224 + 0.939618i \(0.388820\pi\)
\(234\) −18.0546 −1.18027
\(235\) 10.5624 0.689013
\(236\) 6.71807 0.437309
\(237\) −16.7142 −1.08570
\(238\) 63.2581 4.10041
\(239\) −7.95972 −0.514871 −0.257436 0.966295i \(-0.582878\pi\)
−0.257436 + 0.966295i \(0.582878\pi\)
\(240\) 57.7367 3.72689
\(241\) 14.2075 0.915187 0.457593 0.889162i \(-0.348712\pi\)
0.457593 + 0.889162i \(0.348712\pi\)
\(242\) 2.08879 0.134272
\(243\) 1.00000 0.0641500
\(244\) 4.40747 0.282159
\(245\) 13.0205 0.831850
\(246\) 23.3821 1.49079
\(247\) 33.3759 2.12366
\(248\) 102.106 6.48371
\(249\) 8.13069 0.515261
\(250\) 6.26922 0.396500
\(251\) −18.6693 −1.17840 −0.589198 0.807989i \(-0.700556\pi\)
−0.589198 + 0.807989i \(0.700556\pi\)
\(252\) 19.7981 1.24716
\(253\) −4.44456 −0.279427
\(254\) 31.9718 2.00609
\(255\) −20.4078 −1.27799
\(256\) 120.085 7.50533
\(257\) −10.4419 −0.651345 −0.325673 0.945483i \(-0.605591\pi\)
−0.325673 + 0.945483i \(0.605591\pi\)
\(258\) −22.2676 −1.38632
\(259\) 6.52563 0.405483
\(260\) 115.317 7.15163
\(261\) 5.04354 0.312187
\(262\) 55.9957 3.45943
\(263\) −5.53127 −0.341073 −0.170537 0.985351i \(-0.554550\pi\)
−0.170537 + 0.985351i \(0.554550\pi\)
\(264\) −35.0558 −2.15753
\(265\) 1.78707 0.109779
\(266\) −49.0148 −3.00529
\(267\) 8.78685 0.537746
\(268\) 37.9057 2.31546
\(269\) 11.5422 0.703737 0.351869 0.936049i \(-0.385546\pi\)
0.351869 + 0.936049i \(0.385546\pi\)
\(270\) −8.55386 −0.520572
\(271\) 22.0844 1.34153 0.670765 0.741670i \(-0.265966\pi\)
0.670765 + 0.741670i \(0.265966\pi\)
\(272\) −127.147 −7.70942
\(273\) 21.5773 1.30592
\(274\) −44.0785 −2.66288
\(275\) 13.6658 0.824077
\(276\) −8.18180 −0.492487
\(277\) 3.78938 0.227682 0.113841 0.993499i \(-0.463685\pi\)
0.113841 + 0.993499i \(0.463685\pi\)
\(278\) −25.8660 −1.55134
\(279\) −9.32809 −0.558458
\(280\) −111.900 −6.68728
\(281\) 1.91327 0.114136 0.0570682 0.998370i \(-0.481825\pi\)
0.0570682 + 0.998370i \(0.481825\pi\)
\(282\) −9.74945 −0.580572
\(283\) 18.7545 1.11484 0.557420 0.830231i \(-0.311791\pi\)
0.557420 + 0.830231i \(0.311791\pi\)
\(284\) −44.8164 −2.65937
\(285\) 15.8128 0.936668
\(286\) −57.8216 −3.41906
\(287\) −27.9443 −1.64950
\(288\) −31.4010 −1.85032
\(289\) 27.9418 1.64364
\(290\) −43.1417 −2.53337
\(291\) −5.64165 −0.330719
\(292\) −69.6356 −4.07512
\(293\) −30.8106 −1.79997 −0.899986 0.435919i \(-0.856423\pi\)
−0.899986 + 0.435919i \(0.856423\pi\)
\(294\) −12.0184 −0.700928
\(295\) 3.46891 0.201968
\(296\) −21.2706 −1.23633
\(297\) 3.20260 0.185834
\(298\) −2.75260 −0.159454
\(299\) −8.91709 −0.515689
\(300\) 25.1567 1.45243
\(301\) 26.6124 1.53391
\(302\) −21.0111 −1.20905
\(303\) 9.71049 0.557853
\(304\) 98.5183 5.65041
\(305\) 2.27582 0.130313
\(306\) 18.8372 1.07685
\(307\) −14.0122 −0.799718 −0.399859 0.916577i \(-0.630941\pi\)
−0.399859 + 0.916577i \(0.630941\pi\)
\(308\) 63.4053 3.61285
\(309\) −12.4125 −0.706122
\(310\) 79.7912 4.53183
\(311\) −10.0144 −0.567864 −0.283932 0.958844i \(-0.591639\pi\)
−0.283932 + 0.958844i \(0.591639\pi\)
\(312\) −70.3322 −3.98178
\(313\) 16.3140 0.922124 0.461062 0.887368i \(-0.347469\pi\)
0.461062 + 0.887368i \(0.347469\pi\)
\(314\) −15.9710 −0.901297
\(315\) 10.2228 0.575992
\(316\) −98.5390 −5.54325
\(317\) 10.8648 0.610226 0.305113 0.952316i \(-0.401306\pi\)
0.305113 + 0.952316i \(0.401306\pi\)
\(318\) −1.64953 −0.0925009
\(319\) 16.1524 0.904362
\(320\) 153.127 8.56004
\(321\) 13.5602 0.756858
\(322\) 13.0953 0.729775
\(323\) −34.8227 −1.93758
\(324\) 5.89553 0.327529
\(325\) 27.4176 1.52085
\(326\) −45.6762 −2.52977
\(327\) −1.33687 −0.0739290
\(328\) 91.0858 5.02937
\(329\) 11.6517 0.642380
\(330\) −27.3946 −1.50802
\(331\) 10.3965 0.571441 0.285721 0.958313i \(-0.407767\pi\)
0.285721 + 0.958313i \(0.407767\pi\)
\(332\) 47.9347 2.63076
\(333\) 1.94322 0.106488
\(334\) −40.8648 −2.23602
\(335\) 19.5728 1.06938
\(336\) 63.6914 3.47465
\(337\) 20.5785 1.12098 0.560490 0.828161i \(-0.310613\pi\)
0.560490 + 0.828161i \(0.310613\pi\)
\(338\) −79.4786 −4.32306
\(339\) −2.02195 −0.109817
\(340\) −120.315 −6.52500
\(341\) −29.8741 −1.61777
\(342\) −14.5958 −0.789249
\(343\) −9.14367 −0.493712
\(344\) −86.7442 −4.67693
\(345\) −4.22472 −0.227451
\(346\) −19.5456 −1.05078
\(347\) 32.1402 1.72537 0.862687 0.505737i \(-0.168780\pi\)
0.862687 + 0.505737i \(0.168780\pi\)
\(348\) 29.7343 1.59393
\(349\) −16.9573 −0.907705 −0.453852 0.891077i \(-0.649951\pi\)
−0.453852 + 0.891077i \(0.649951\pi\)
\(350\) −40.2645 −2.15223
\(351\) 6.42536 0.342960
\(352\) −100.565 −5.36012
\(353\) −8.54370 −0.454735 −0.227368 0.973809i \(-0.573012\pi\)
−0.227368 + 0.973809i \(0.573012\pi\)
\(354\) −3.20193 −0.170181
\(355\) −23.1412 −1.22821
\(356\) 51.8031 2.74556
\(357\) −22.5126 −1.19149
\(358\) 34.3546 1.81570
\(359\) −6.18853 −0.326618 −0.163309 0.986575i \(-0.552217\pi\)
−0.163309 + 0.986575i \(0.552217\pi\)
\(360\) −33.3218 −1.75621
\(361\) 7.98191 0.420101
\(362\) −58.0853 −3.05289
\(363\) −0.743368 −0.0390167
\(364\) 127.210 6.66760
\(365\) −35.9567 −1.88206
\(366\) −2.10067 −0.109804
\(367\) 2.79062 0.145669 0.0728346 0.997344i \(-0.476795\pi\)
0.0728346 + 0.997344i \(0.476795\pi\)
\(368\) −26.3213 −1.37209
\(369\) −8.32135 −0.433192
\(370\) −16.6221 −0.864139
\(371\) 1.97137 0.102349
\(372\) −54.9940 −2.85131
\(373\) −18.6934 −0.967906 −0.483953 0.875094i \(-0.660799\pi\)
−0.483953 + 0.875094i \(0.660799\pi\)
\(374\) 60.3279 3.11948
\(375\) −2.23112 −0.115214
\(376\) −37.9793 −1.95863
\(377\) 32.4065 1.66902
\(378\) −9.43606 −0.485339
\(379\) −37.8175 −1.94255 −0.971276 0.237954i \(-0.923523\pi\)
−0.971276 + 0.237954i \(0.923523\pi\)
\(380\) 93.2247 4.78232
\(381\) −11.3783 −0.582928
\(382\) 39.8426 2.03853
\(383\) −24.5986 −1.25693 −0.628465 0.777838i \(-0.716316\pi\)
−0.628465 + 0.777838i \(0.716316\pi\)
\(384\) −78.5394 −4.00795
\(385\) 32.7397 1.66857
\(386\) 2.15165 0.109516
\(387\) 7.92471 0.402836
\(388\) −33.2605 −1.68855
\(389\) 5.32796 0.270138 0.135069 0.990836i \(-0.456874\pi\)
0.135069 + 0.990836i \(0.456874\pi\)
\(390\) −54.9616 −2.78309
\(391\) 9.30361 0.470504
\(392\) −46.8181 −2.36467
\(393\) −19.9280 −1.00524
\(394\) −52.1571 −2.62763
\(395\) −50.8812 −2.56011
\(396\) 18.8810 0.948806
\(397\) −24.8955 −1.24947 −0.624736 0.780836i \(-0.714793\pi\)
−0.624736 + 0.780836i \(0.714793\pi\)
\(398\) 22.4841 1.12703
\(399\) 17.4436 0.873273
\(400\) 80.9305 4.04652
\(401\) −32.7752 −1.63671 −0.818357 0.574710i \(-0.805115\pi\)
−0.818357 + 0.574710i \(0.805115\pi\)
\(402\) −18.0664 −0.901071
\(403\) −59.9363 −2.98564
\(404\) 57.2484 2.84822
\(405\) 3.04419 0.151267
\(406\) −47.5911 −2.36191
\(407\) 6.22336 0.308480
\(408\) 73.3808 3.63289
\(409\) 11.1653 0.552086 0.276043 0.961145i \(-0.410977\pi\)
0.276043 + 0.961145i \(0.410977\pi\)
\(410\) 71.1797 3.51531
\(411\) 15.6869 0.773777
\(412\) −73.1782 −3.60523
\(413\) 3.82668 0.188298
\(414\) 3.89957 0.191653
\(415\) 24.7514 1.21500
\(416\) −201.763 −9.89223
\(417\) 9.20531 0.450786
\(418\) −46.7444 −2.28634
\(419\) −27.6146 −1.34906 −0.674531 0.738247i \(-0.735654\pi\)
−0.674531 + 0.738247i \(0.735654\pi\)
\(420\) 60.2691 2.94083
\(421\) −23.0100 −1.12144 −0.560720 0.828005i \(-0.689476\pi\)
−0.560720 + 0.828005i \(0.689476\pi\)
\(422\) −2.49539 −0.121474
\(423\) 3.46968 0.168702
\(424\) −6.42578 −0.312064
\(425\) −28.6060 −1.38760
\(426\) 21.3602 1.03490
\(427\) 2.51054 0.121493
\(428\) 79.9447 3.86428
\(429\) 20.5778 0.993507
\(430\) −67.7869 −3.26897
\(431\) −16.5516 −0.797263 −0.398632 0.917111i \(-0.630515\pi\)
−0.398632 + 0.917111i \(0.630515\pi\)
\(432\) 18.9662 0.912512
\(433\) −24.0720 −1.15683 −0.578414 0.815743i \(-0.696328\pi\)
−0.578414 + 0.815743i \(0.696328\pi\)
\(434\) 88.0204 4.22511
\(435\) 15.3535 0.736143
\(436\) −7.88155 −0.377458
\(437\) −7.20879 −0.344843
\(438\) 33.1894 1.58585
\(439\) 1.33516 0.0637236 0.0318618 0.999492i \(-0.489856\pi\)
0.0318618 + 0.999492i \(0.489856\pi\)
\(440\) −106.716 −5.08750
\(441\) 4.27717 0.203675
\(442\) 121.036 5.75708
\(443\) 39.9217 1.89674 0.948369 0.317169i \(-0.102732\pi\)
0.948369 + 0.317169i \(0.102732\pi\)
\(444\) 11.4563 0.543693
\(445\) 26.7488 1.26802
\(446\) −10.8712 −0.514768
\(447\) 0.979608 0.0463339
\(448\) 168.919 7.98068
\(449\) −7.11287 −0.335677 −0.167838 0.985815i \(-0.553679\pi\)
−0.167838 + 0.985815i \(0.553679\pi\)
\(450\) −11.9901 −0.565218
\(451\) −26.6499 −1.25490
\(452\) −11.9205 −0.560691
\(453\) 7.47753 0.351325
\(454\) −62.2283 −2.92052
\(455\) 65.6854 3.07938
\(456\) −56.8582 −2.66263
\(457\) −20.5783 −0.962610 −0.481305 0.876553i \(-0.659837\pi\)
−0.481305 + 0.876553i \(0.659837\pi\)
\(458\) 64.8091 3.02833
\(459\) −6.70387 −0.312910
\(460\) −24.9070 −1.16129
\(461\) −1.67068 −0.0778113 −0.0389056 0.999243i \(-0.512387\pi\)
−0.0389056 + 0.999243i \(0.512387\pi\)
\(462\) −30.2199 −1.40596
\(463\) −9.34083 −0.434105 −0.217053 0.976160i \(-0.569644\pi\)
−0.217053 + 0.976160i \(0.569644\pi\)
\(464\) 95.6568 4.44076
\(465\) −28.3965 −1.31685
\(466\) −29.3568 −1.35993
\(467\) 17.1994 0.795895 0.397947 0.917408i \(-0.369723\pi\)
0.397947 + 0.917408i \(0.369723\pi\)
\(468\) 37.8809 1.75104
\(469\) 21.5914 0.997000
\(470\) −29.6792 −1.36900
\(471\) 5.68385 0.261898
\(472\) −12.4732 −0.574127
\(473\) 25.3797 1.16696
\(474\) 46.9652 2.15718
\(475\) 22.1650 1.01700
\(476\) −132.724 −6.08338
\(477\) 0.587042 0.0268788
\(478\) 22.3660 1.02300
\(479\) 19.4740 0.889788 0.444894 0.895583i \(-0.353241\pi\)
0.444894 + 0.895583i \(0.353241\pi\)
\(480\) −95.5907 −4.36310
\(481\) 12.4859 0.569308
\(482\) −39.9217 −1.81838
\(483\) −4.66043 −0.212057
\(484\) −4.38255 −0.199207
\(485\) −17.1742 −0.779842
\(486\) −2.80990 −0.127460
\(487\) −30.3286 −1.37432 −0.687159 0.726507i \(-0.741143\pi\)
−0.687159 + 0.726507i \(0.741143\pi\)
\(488\) −8.18321 −0.370437
\(489\) 16.2555 0.735098
\(490\) −36.5863 −1.65280
\(491\) 18.2150 0.822031 0.411016 0.911628i \(-0.365174\pi\)
0.411016 + 0.911628i \(0.365174\pi\)
\(492\) −49.0587 −2.21174
\(493\) −33.8112 −1.52278
\(494\) −93.7830 −4.21950
\(495\) 9.74931 0.438199
\(496\) −176.918 −7.94387
\(497\) −25.5279 −1.14508
\(498\) −22.8464 −1.02377
\(499\) −28.3566 −1.26942 −0.634708 0.772752i \(-0.718880\pi\)
−0.634708 + 0.772752i \(0.718880\pi\)
\(500\) −13.1536 −0.588248
\(501\) 14.5432 0.649740
\(502\) 52.4588 2.34135
\(503\) 19.1039 0.851799 0.425900 0.904770i \(-0.359958\pi\)
0.425900 + 0.904770i \(0.359958\pi\)
\(504\) −36.7584 −1.63735
\(505\) 29.5606 1.31543
\(506\) 12.4888 0.555193
\(507\) 28.2852 1.25619
\(508\) −67.0810 −2.97624
\(509\) 29.0448 1.28739 0.643693 0.765284i \(-0.277401\pi\)
0.643693 + 0.765284i \(0.277401\pi\)
\(510\) 57.3440 2.53923
\(511\) −39.6651 −1.75468
\(512\) −180.349 −7.97036
\(513\) 5.19441 0.229339
\(514\) 29.3406 1.29416
\(515\) −37.7860 −1.66505
\(516\) 46.7204 2.05675
\(517\) 11.1120 0.488705
\(518\) −18.3364 −0.805653
\(519\) 6.95597 0.305333
\(520\) −214.105 −9.38911
\(521\) −4.67184 −0.204677 −0.102339 0.994750i \(-0.532632\pi\)
−0.102339 + 0.994750i \(0.532632\pi\)
\(522\) −14.1718 −0.620284
\(523\) −3.51047 −0.153502 −0.0767510 0.997050i \(-0.524455\pi\)
−0.0767510 + 0.997050i \(0.524455\pi\)
\(524\) −117.486 −5.13241
\(525\) 14.3295 0.625392
\(526\) 15.5423 0.677677
\(527\) 62.5343 2.72404
\(528\) 60.7411 2.64342
\(529\) −21.0740 −0.916262
\(530\) −5.02147 −0.218119
\(531\) 1.13952 0.0494509
\(532\) 102.839 4.45865
\(533\) −53.4676 −2.31594
\(534\) −24.6901 −1.06845
\(535\) 41.2799 1.78469
\(536\) −70.3783 −3.03988
\(537\) −12.2263 −0.527603
\(538\) −32.4323 −1.39825
\(539\) 13.6981 0.590017
\(540\) 17.9471 0.772321
\(541\) −11.5446 −0.496340 −0.248170 0.968716i \(-0.579829\pi\)
−0.248170 + 0.968716i \(0.579829\pi\)
\(542\) −62.0549 −2.66548
\(543\) 20.6717 0.887106
\(544\) 210.508 9.02547
\(545\) −4.06968 −0.174326
\(546\) −60.6301 −2.59473
\(547\) −18.5907 −0.794883 −0.397442 0.917628i \(-0.630102\pi\)
−0.397442 + 0.917628i \(0.630102\pi\)
\(548\) 92.4825 3.95065
\(549\) 0.747596 0.0319066
\(550\) −38.3994 −1.63736
\(551\) 26.1982 1.11608
\(552\) 15.1909 0.646567
\(553\) −56.1288 −2.38684
\(554\) −10.6478 −0.452380
\(555\) 5.91553 0.251100
\(556\) 54.2702 2.30157
\(557\) −23.1557 −0.981139 −0.490569 0.871402i \(-0.663211\pi\)
−0.490569 + 0.871402i \(0.663211\pi\)
\(558\) 26.2110 1.10960
\(559\) 50.9191 2.15365
\(560\) 193.889 8.19329
\(561\) −21.4698 −0.906455
\(562\) −5.37611 −0.226777
\(563\) 29.8727 1.25899 0.629493 0.777006i \(-0.283263\pi\)
0.629493 + 0.777006i \(0.283263\pi\)
\(564\) 20.4556 0.861337
\(565\) −6.15519 −0.258951
\(566\) −52.6982 −2.21507
\(567\) 3.35815 0.141029
\(568\) 83.2093 3.49138
\(569\) 19.2278 0.806073 0.403037 0.915184i \(-0.367955\pi\)
0.403037 + 0.915184i \(0.367955\pi\)
\(570\) −44.4323 −1.86106
\(571\) 15.3237 0.641278 0.320639 0.947201i \(-0.396102\pi\)
0.320639 + 0.947201i \(0.396102\pi\)
\(572\) 121.317 5.07253
\(573\) −14.1794 −0.592352
\(574\) 78.5207 3.27739
\(575\) −5.92186 −0.246958
\(576\) 50.3013 2.09589
\(577\) 4.30161 0.179078 0.0895391 0.995983i \(-0.471461\pi\)
0.0895391 + 0.995983i \(0.471461\pi\)
\(578\) −78.5138 −3.26574
\(579\) −0.765741 −0.0318231
\(580\) 90.5169 3.75851
\(581\) 27.3041 1.13276
\(582\) 15.8525 0.657105
\(583\) 1.88006 0.0778640
\(584\) 129.290 5.35007
\(585\) 19.5600 0.808707
\(586\) 86.5745 3.57636
\(587\) −26.0410 −1.07483 −0.537413 0.843319i \(-0.680598\pi\)
−0.537413 + 0.843319i \(0.680598\pi\)
\(588\) 25.2162 1.03990
\(589\) −48.4539 −1.99651
\(590\) −9.74729 −0.401290
\(591\) 18.5619 0.763535
\(592\) 36.8555 1.51475
\(593\) −38.1855 −1.56809 −0.784044 0.620705i \(-0.786847\pi\)
−0.784044 + 0.620705i \(0.786847\pi\)
\(594\) −8.99897 −0.369232
\(595\) −68.5326 −2.80956
\(596\) 5.77531 0.236566
\(597\) −8.00176 −0.327490
\(598\) 25.0561 1.02462
\(599\) −28.8538 −1.17893 −0.589467 0.807793i \(-0.700662\pi\)
−0.589467 + 0.807793i \(0.700662\pi\)
\(600\) −46.7077 −1.90684
\(601\) 31.6629 1.29156 0.645778 0.763525i \(-0.276533\pi\)
0.645778 + 0.763525i \(0.276533\pi\)
\(602\) −74.7780 −3.04773
\(603\) 6.42956 0.261832
\(604\) 44.0840 1.79375
\(605\) −2.26295 −0.0920022
\(606\) −27.2855 −1.10840
\(607\) −41.0335 −1.66550 −0.832750 0.553649i \(-0.813235\pi\)
−0.832750 + 0.553649i \(0.813235\pi\)
\(608\) −163.110 −6.61498
\(609\) 16.9370 0.686320
\(610\) −6.39483 −0.258919
\(611\) 22.2939 0.901916
\(612\) −39.5228 −1.59762
\(613\) 41.0538 1.65815 0.829073 0.559140i \(-0.188868\pi\)
0.829073 + 0.559140i \(0.188868\pi\)
\(614\) 39.3728 1.58896
\(615\) −25.3318 −1.02147
\(616\) −117.723 −4.74318
\(617\) −36.6857 −1.47691 −0.738456 0.674302i \(-0.764445\pi\)
−0.738456 + 0.674302i \(0.764445\pi\)
\(618\) 34.8778 1.40299
\(619\) 26.0404 1.04665 0.523325 0.852133i \(-0.324691\pi\)
0.523325 + 0.852133i \(0.324691\pi\)
\(620\) −167.412 −6.72343
\(621\) −1.38780 −0.0556904
\(622\) 28.1394 1.12829
\(623\) 29.5075 1.18219
\(624\) 121.865 4.87849
\(625\) −28.1274 −1.12510
\(626\) −45.8408 −1.83217
\(627\) 16.6356 0.664362
\(628\) 33.5093 1.33717
\(629\) −13.0271 −0.519425
\(630\) −28.7252 −1.14444
\(631\) 22.6266 0.900750 0.450375 0.892839i \(-0.351290\pi\)
0.450375 + 0.892839i \(0.351290\pi\)
\(632\) 182.954 7.27753
\(633\) 0.888070 0.0352976
\(634\) −30.5289 −1.21246
\(635\) −34.6377 −1.37455
\(636\) 3.46092 0.137234
\(637\) 27.4823 1.08889
\(638\) −45.3867 −1.79688
\(639\) −7.60177 −0.300721
\(640\) −239.089 −9.45082
\(641\) −11.9147 −0.470603 −0.235301 0.971922i \(-0.575608\pi\)
−0.235301 + 0.971922i \(0.575608\pi\)
\(642\) −38.1029 −1.50380
\(643\) 18.9926 0.748994 0.374497 0.927228i \(-0.377815\pi\)
0.374497 + 0.927228i \(0.377815\pi\)
\(644\) −27.4757 −1.08269
\(645\) 24.1243 0.949894
\(646\) 97.8481 3.84978
\(647\) 6.29853 0.247621 0.123810 0.992306i \(-0.460489\pi\)
0.123810 + 0.992306i \(0.460489\pi\)
\(648\) −10.9460 −0.430001
\(649\) 3.64942 0.143252
\(650\) −77.0406 −3.02178
\(651\) −31.3251 −1.22773
\(652\) 95.8346 3.75317
\(653\) −28.7468 −1.12495 −0.562476 0.826814i \(-0.690151\pi\)
−0.562476 + 0.826814i \(0.690151\pi\)
\(654\) 3.75647 0.146889
\(655\) −60.6647 −2.37036
\(656\) −157.824 −6.16201
\(657\) −11.8116 −0.460814
\(658\) −32.7401 −1.27634
\(659\) −34.5340 −1.34525 −0.672627 0.739982i \(-0.734834\pi\)
−0.672627 + 0.739982i \(0.734834\pi\)
\(660\) 57.4774 2.23730
\(661\) −33.1508 −1.28942 −0.644709 0.764428i \(-0.723021\pi\)
−0.644709 + 0.764428i \(0.723021\pi\)
\(662\) −29.2130 −1.13540
\(663\) −43.0747 −1.67288
\(664\) −88.9988 −3.45382
\(665\) 53.1017 2.05919
\(666\) −5.46025 −0.211581
\(667\) −6.99941 −0.271018
\(668\) 85.7396 3.31736
\(669\) 3.86891 0.149581
\(670\) −54.9976 −2.12474
\(671\) 2.39425 0.0924289
\(672\) −105.449 −4.06780
\(673\) −25.6144 −0.987362 −0.493681 0.869643i \(-0.664349\pi\)
−0.493681 + 0.869643i \(0.664349\pi\)
\(674\) −57.8234 −2.22727
\(675\) 4.26709 0.164240
\(676\) 166.756 6.41370
\(677\) 14.9934 0.576242 0.288121 0.957594i \(-0.406969\pi\)
0.288121 + 0.957594i \(0.406969\pi\)
\(678\) 5.68147 0.218195
\(679\) −18.9455 −0.727061
\(680\) 223.385 8.56643
\(681\) 22.1461 0.848640
\(682\) 83.9432 3.21435
\(683\) −30.1693 −1.15440 −0.577199 0.816604i \(-0.695854\pi\)
−0.577199 + 0.816604i \(0.695854\pi\)
\(684\) 30.6238 1.17093
\(685\) 47.7538 1.82458
\(686\) 25.6928 0.980955
\(687\) −23.0646 −0.879969
\(688\) 150.302 5.73020
\(689\) 3.77195 0.143700
\(690\) 11.8710 0.451922
\(691\) −13.9364 −0.530166 −0.265083 0.964226i \(-0.585399\pi\)
−0.265083 + 0.964226i \(0.585399\pi\)
\(692\) 41.0092 1.55893
\(693\) 10.7548 0.408541
\(694\) −90.3106 −3.42814
\(695\) 28.0227 1.06296
\(696\) −55.2068 −2.09261
\(697\) 55.7852 2.11302
\(698\) 47.6484 1.80352
\(699\) 10.4477 0.395167
\(700\) 84.4801 3.19305
\(701\) 14.7241 0.556120 0.278060 0.960564i \(-0.410309\pi\)
0.278060 + 0.960564i \(0.410309\pi\)
\(702\) −18.0546 −0.681427
\(703\) 10.0939 0.380698
\(704\) 161.095 6.07149
\(705\) 10.5624 0.397802
\(706\) 24.0069 0.903513
\(707\) 32.6093 1.22640
\(708\) 6.71807 0.252481
\(709\) −29.7409 −1.11694 −0.558471 0.829524i \(-0.688612\pi\)
−0.558471 + 0.829524i \(0.688612\pi\)
\(710\) 65.0245 2.44033
\(711\) −16.7142 −0.626831
\(712\) −96.1812 −3.60454
\(713\) 12.9455 0.484813
\(714\) 63.2581 2.36737
\(715\) 62.6428 2.34271
\(716\) −72.0804 −2.69377
\(717\) −7.95972 −0.297261
\(718\) 17.3891 0.648957
\(719\) −31.7025 −1.18230 −0.591152 0.806560i \(-0.701327\pi\)
−0.591152 + 0.806560i \(0.701327\pi\)
\(720\) 57.7367 2.15172
\(721\) −41.6830 −1.55236
\(722\) −22.4284 −0.834697
\(723\) 14.2075 0.528383
\(724\) 121.870 4.52928
\(725\) 21.5212 0.799279
\(726\) 2.08879 0.0775223
\(727\) 20.0741 0.744509 0.372254 0.928131i \(-0.378585\pi\)
0.372254 + 0.928131i \(0.378585\pi\)
\(728\) −236.186 −8.75364
\(729\) 1.00000 0.0370370
\(730\) 101.035 3.73946
\(731\) −53.1262 −1.96494
\(732\) 4.40747 0.162905
\(733\) −43.9540 −1.62348 −0.811739 0.584021i \(-0.801479\pi\)
−0.811739 + 0.584021i \(0.801479\pi\)
\(734\) −7.84136 −0.289430
\(735\) 13.0205 0.480269
\(736\) 43.5783 1.60632
\(737\) 20.5913 0.758490
\(738\) 23.3821 0.860708
\(739\) 37.9757 1.39696 0.698479 0.715631i \(-0.253861\pi\)
0.698479 + 0.715631i \(0.253861\pi\)
\(740\) 34.8752 1.28204
\(741\) 33.3759 1.22610
\(742\) −5.53936 −0.203356
\(743\) 4.43263 0.162618 0.0813088 0.996689i \(-0.474090\pi\)
0.0813088 + 0.996689i \(0.474090\pi\)
\(744\) 102.106 3.74337
\(745\) 2.98211 0.109256
\(746\) 52.5265 1.92313
\(747\) 8.13069 0.297486
\(748\) −126.576 −4.62807
\(749\) 45.5373 1.66390
\(750\) 6.26922 0.228919
\(751\) 23.4537 0.855839 0.427919 0.903817i \(-0.359247\pi\)
0.427919 + 0.903817i \(0.359247\pi\)
\(752\) 65.8067 2.39972
\(753\) −18.6693 −0.680347
\(754\) −91.0591 −3.31618
\(755\) 22.7630 0.828431
\(756\) 19.7981 0.720049
\(757\) 35.9715 1.30741 0.653703 0.756751i \(-0.273215\pi\)
0.653703 + 0.756751i \(0.273215\pi\)
\(758\) 106.263 3.85965
\(759\) −4.44456 −0.161327
\(760\) −173.087 −6.27853
\(761\) −20.6344 −0.747998 −0.373999 0.927429i \(-0.622014\pi\)
−0.373999 + 0.927429i \(0.622014\pi\)
\(762\) 31.9718 1.15822
\(763\) −4.48941 −0.162527
\(764\) −83.5950 −3.02436
\(765\) −20.4078 −0.737847
\(766\) 69.1195 2.49739
\(767\) 7.32182 0.264376
\(768\) 120.085 4.33320
\(769\) 47.5189 1.71358 0.856788 0.515669i \(-0.172457\pi\)
0.856788 + 0.515669i \(0.172457\pi\)
\(770\) −91.9951 −3.31527
\(771\) −10.4419 −0.376054
\(772\) −4.51445 −0.162478
\(773\) 8.41211 0.302562 0.151281 0.988491i \(-0.451660\pi\)
0.151281 + 0.988491i \(0.451660\pi\)
\(774\) −22.2676 −0.800393
\(775\) −39.8038 −1.42979
\(776\) 61.7537 2.21683
\(777\) 6.52563 0.234106
\(778\) −14.9710 −0.536737
\(779\) −43.2245 −1.54868
\(780\) 115.317 4.12900
\(781\) −24.3454 −0.871147
\(782\) −26.1422 −0.934843
\(783\) 5.04354 0.180241
\(784\) 81.1217 2.89720
\(785\) 17.3027 0.617560
\(786\) 55.9957 1.99730
\(787\) −0.188091 −0.00670471 −0.00335236 0.999994i \(-0.501067\pi\)
−0.00335236 + 0.999994i \(0.501067\pi\)
\(788\) 109.432 3.89836
\(789\) −5.53127 −0.196919
\(790\) 142.971 5.08668
\(791\) −6.79000 −0.241425
\(792\) −35.0558 −1.24565
\(793\) 4.80357 0.170580
\(794\) 69.9540 2.48257
\(795\) 1.78707 0.0633807
\(796\) −47.1746 −1.67206
\(797\) 27.4696 0.973024 0.486512 0.873674i \(-0.338269\pi\)
0.486512 + 0.873674i \(0.338269\pi\)
\(798\) −49.0148 −1.73510
\(799\) −23.2603 −0.822890
\(800\) −133.991 −4.73730
\(801\) 8.78685 0.310468
\(802\) 92.0950 3.25199
\(803\) −37.8278 −1.33491
\(804\) 37.9057 1.33683
\(805\) −14.1872 −0.500034
\(806\) 168.415 5.93216
\(807\) 11.5422 0.406303
\(808\) −106.291 −3.73932
\(809\) 21.4368 0.753678 0.376839 0.926279i \(-0.377011\pi\)
0.376839 + 0.926279i \(0.377011\pi\)
\(810\) −8.55386 −0.300552
\(811\) −49.4912 −1.73787 −0.868936 0.494925i \(-0.835196\pi\)
−0.868936 + 0.494925i \(0.835196\pi\)
\(812\) 99.8523 3.50413
\(813\) 22.0844 0.774533
\(814\) −17.4870 −0.612919
\(815\) 49.4847 1.73337
\(816\) −127.147 −4.45103
\(817\) 41.1642 1.44015
\(818\) −31.3732 −1.09694
\(819\) 21.5773 0.753972
\(820\) −149.344 −5.21532
\(821\) −9.86523 −0.344299 −0.172149 0.985071i \(-0.555071\pi\)
−0.172149 + 0.985071i \(0.555071\pi\)
\(822\) −44.0785 −1.53742
\(823\) −34.0689 −1.18757 −0.593783 0.804625i \(-0.702366\pi\)
−0.593783 + 0.804625i \(0.702366\pi\)
\(824\) 135.868 4.73317
\(825\) 13.6658 0.475781
\(826\) −10.7526 −0.374130
\(827\) 15.3046 0.532192 0.266096 0.963947i \(-0.414266\pi\)
0.266096 + 0.963947i \(0.414266\pi\)
\(828\) −8.18180 −0.284337
\(829\) 45.1962 1.56973 0.784864 0.619668i \(-0.212733\pi\)
0.784864 + 0.619668i \(0.212733\pi\)
\(830\) −69.5488 −2.41407
\(831\) 3.78938 0.131452
\(832\) 323.204 11.2051
\(833\) −28.6736 −0.993481
\(834\) −25.8660 −0.895666
\(835\) 44.2721 1.53210
\(836\) 98.0757 3.39202
\(837\) −9.32809 −0.322426
\(838\) 77.5942 2.68045
\(839\) −22.4717 −0.775808 −0.387904 0.921700i \(-0.626801\pi\)
−0.387904 + 0.921700i \(0.626801\pi\)
\(840\) −111.900 −3.86091
\(841\) −3.56271 −0.122852
\(842\) 64.6559 2.22819
\(843\) 1.91327 0.0658967
\(844\) 5.23564 0.180218
\(845\) 86.1055 2.96212
\(846\) −9.74945 −0.335193
\(847\) −2.49634 −0.0857753
\(848\) 11.1340 0.382341
\(849\) 18.7545 0.643653
\(850\) 80.3800 2.75701
\(851\) −2.69680 −0.0924451
\(852\) −44.8164 −1.53539
\(853\) 12.2200 0.418406 0.209203 0.977872i \(-0.432913\pi\)
0.209203 + 0.977872i \(0.432913\pi\)
\(854\) −7.05436 −0.241395
\(855\) 15.8128 0.540785
\(856\) −148.431 −5.07326
\(857\) 21.7194 0.741921 0.370961 0.928649i \(-0.379028\pi\)
0.370961 + 0.928649i \(0.379028\pi\)
\(858\) −57.8216 −1.97400
\(859\) −25.3645 −0.865425 −0.432712 0.901532i \(-0.642443\pi\)
−0.432712 + 0.901532i \(0.642443\pi\)
\(860\) 142.226 4.84985
\(861\) −27.9443 −0.952340
\(862\) 46.5084 1.58408
\(863\) 51.8460 1.76486 0.882430 0.470445i \(-0.155906\pi\)
0.882430 + 0.470445i \(0.155906\pi\)
\(864\) −31.4010 −1.06828
\(865\) 21.1753 0.719982
\(866\) 67.6400 2.29850
\(867\) 27.9418 0.948955
\(868\) −184.678 −6.26838
\(869\) −53.5288 −1.81584
\(870\) −43.1417 −1.46264
\(871\) 41.3122 1.39981
\(872\) 14.6334 0.495550
\(873\) −5.64165 −0.190941
\(874\) 20.2560 0.685169
\(875\) −7.49243 −0.253290
\(876\) −69.6356 −2.35277
\(877\) 10.2240 0.345241 0.172621 0.984988i \(-0.444777\pi\)
0.172621 + 0.984988i \(0.444777\pi\)
\(878\) −3.75166 −0.126612
\(879\) −30.8106 −1.03921
\(880\) 184.907 6.23323
\(881\) 18.0377 0.607704 0.303852 0.952719i \(-0.401727\pi\)
0.303852 + 0.952719i \(0.401727\pi\)
\(882\) −12.0184 −0.404681
\(883\) 40.5288 1.36390 0.681951 0.731398i \(-0.261132\pi\)
0.681951 + 0.731398i \(0.261132\pi\)
\(884\) −253.948 −8.54121
\(885\) 3.46891 0.116606
\(886\) −112.176 −3.76863
\(887\) −22.0297 −0.739685 −0.369843 0.929094i \(-0.620588\pi\)
−0.369843 + 0.929094i \(0.620588\pi\)
\(888\) −21.2706 −0.713794
\(889\) −38.2100 −1.28152
\(890\) −75.1615 −2.51942
\(891\) 3.20260 0.107291
\(892\) 22.8093 0.763711
\(893\) 18.0230 0.603115
\(894\) −2.75260 −0.0920607
\(895\) −37.2191 −1.24410
\(896\) −263.747 −8.81118
\(897\) −8.91709 −0.297733
\(898\) 19.9864 0.666956
\(899\) −47.0466 −1.56909
\(900\) 25.1567 0.838558
\(901\) −3.93545 −0.131109
\(902\) 74.8836 2.49335
\(903\) 26.6124 0.885604
\(904\) 22.1323 0.736110
\(905\) 62.9285 2.09181
\(906\) −21.0111 −0.698047
\(907\) 0.533840 0.0177259 0.00886293 0.999961i \(-0.497179\pi\)
0.00886293 + 0.999961i \(0.497179\pi\)
\(908\) 130.563 4.33288
\(909\) 9.71049 0.322076
\(910\) −184.569 −6.11841
\(911\) 19.1447 0.634293 0.317146 0.948377i \(-0.397275\pi\)
0.317146 + 0.948377i \(0.397275\pi\)
\(912\) 98.5183 3.26227
\(913\) 26.0393 0.861776
\(914\) 57.8228 1.91261
\(915\) 2.27582 0.0752364
\(916\) −135.978 −4.49284
\(917\) −66.9213 −2.20994
\(918\) 18.8372 0.621720
\(919\) −35.0232 −1.15531 −0.577654 0.816282i \(-0.696032\pi\)
−0.577654 + 0.816282i \(0.696032\pi\)
\(920\) 46.2439 1.52462
\(921\) −14.0122 −0.461717
\(922\) 4.69444 0.154603
\(923\) −48.8441 −1.60772
\(924\) 63.4053 2.08588
\(925\) 8.29190 0.272636
\(926\) 26.2468 0.862523
\(927\) −12.4125 −0.407680
\(928\) −158.372 −5.19883
\(929\) −58.4514 −1.91773 −0.958864 0.283864i \(-0.908383\pi\)
−0.958864 + 0.283864i \(0.908383\pi\)
\(930\) 79.7912 2.61646
\(931\) 22.2174 0.728145
\(932\) 61.5944 2.01759
\(933\) −10.0144 −0.327857
\(934\) −48.3287 −1.58136
\(935\) −65.3581 −2.13744
\(936\) −70.3322 −2.29888
\(937\) 0.192396 0.00628532 0.00314266 0.999995i \(-0.499000\pi\)
0.00314266 + 0.999995i \(0.499000\pi\)
\(938\) −60.6697 −1.98094
\(939\) 16.3140 0.532389
\(940\) 62.2708 2.03105
\(941\) −37.0622 −1.20819 −0.604097 0.796911i \(-0.706466\pi\)
−0.604097 + 0.796911i \(0.706466\pi\)
\(942\) −15.9710 −0.520364
\(943\) 11.5483 0.376066
\(944\) 21.6124 0.703422
\(945\) 10.2228 0.332549
\(946\) −71.3143 −2.31863
\(947\) 48.2761 1.56876 0.784381 0.620279i \(-0.212981\pi\)
0.784381 + 0.620279i \(0.212981\pi\)
\(948\) −98.5390 −3.20040
\(949\) −75.8937 −2.46361
\(950\) −62.2815 −2.02068
\(951\) 10.8648 0.352314
\(952\) 246.424 7.98664
\(953\) −30.4525 −0.986452 −0.493226 0.869901i \(-0.664182\pi\)
−0.493226 + 0.869901i \(0.664182\pi\)
\(954\) −1.64953 −0.0534054
\(955\) −43.1647 −1.39678
\(956\) −46.9267 −1.51772
\(957\) 16.1524 0.522134
\(958\) −54.7198 −1.76792
\(959\) 52.6789 1.70109
\(960\) 153.127 4.94214
\(961\) 56.0132 1.80688
\(962\) −35.0841 −1.13116
\(963\) 13.5602 0.436972
\(964\) 83.7608 2.69776
\(965\) −2.33106 −0.0750395
\(966\) 13.0953 0.421336
\(967\) −45.3354 −1.45789 −0.728944 0.684573i \(-0.759988\pi\)
−0.728944 + 0.684573i \(0.759988\pi\)
\(968\) 8.13694 0.261531
\(969\) −34.8227 −1.11866
\(970\) 48.2579 1.54947
\(971\) −1.99811 −0.0641225 −0.0320613 0.999486i \(-0.510207\pi\)
−0.0320613 + 0.999486i \(0.510207\pi\)
\(972\) 5.89553 0.189099
\(973\) 30.9128 0.991020
\(974\) 85.2202 2.73063
\(975\) 27.4176 0.878065
\(976\) 14.1791 0.453860
\(977\) 28.9072 0.924824 0.462412 0.886665i \(-0.346984\pi\)
0.462412 + 0.886665i \(0.346984\pi\)
\(978\) −45.6762 −1.46056
\(979\) 28.1407 0.899382
\(980\) 76.7628 2.45210
\(981\) −1.33687 −0.0426830
\(982\) −51.1823 −1.63329
\(983\) 40.6034 1.29505 0.647523 0.762046i \(-0.275805\pi\)
0.647523 + 0.762046i \(0.275805\pi\)
\(984\) 91.0858 2.90371
\(985\) 56.5059 1.80043
\(986\) 95.0061 3.02561
\(987\) 11.6517 0.370878
\(988\) 196.769 6.26005
\(989\) −10.9979 −0.349713
\(990\) −27.3946 −0.870657
\(991\) −6.03170 −0.191603 −0.0958017 0.995400i \(-0.530541\pi\)
−0.0958017 + 0.995400i \(0.530541\pi\)
\(992\) 292.911 9.29995
\(993\) 10.3965 0.329922
\(994\) 71.7307 2.27516
\(995\) −24.3589 −0.772228
\(996\) 47.9347 1.51887
\(997\) −8.20945 −0.259996 −0.129998 0.991514i \(-0.541497\pi\)
−0.129998 + 0.991514i \(0.541497\pi\)
\(998\) 79.6792 2.52220
\(999\) 1.94322 0.0614808
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 \(a_p\))