Properties

Label 8021.2.a.a.1.4
Level 8021
Weight 2
Character 8021.1
Self dual Yes
Analytic conductor 64.048
Analytic rank 1
Dimension 134
CM No

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Newspace parameters

Level: \( N \) = \( 8021 = 13 \cdot 617 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8021.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0480074613\)
Analytic rank: \(1\)
Dimension: \(134\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 8021.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.56606 q^{2}\) \(+0.368471 q^{3}\) \(+4.58465 q^{4}\) \(+3.51803 q^{5}\) \(-0.945517 q^{6}\) \(+1.16169 q^{7}\) \(-6.63237 q^{8}\) \(-2.86423 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.56606 q^{2}\) \(+0.368471 q^{3}\) \(+4.58465 q^{4}\) \(+3.51803 q^{5}\) \(-0.945517 q^{6}\) \(+1.16169 q^{7}\) \(-6.63237 q^{8}\) \(-2.86423 q^{9}\) \(-9.02747 q^{10}\) \(-0.924806 q^{11}\) \(+1.68931 q^{12}\) \(+1.00000 q^{13}\) \(-2.98096 q^{14}\) \(+1.29629 q^{15}\) \(+7.84974 q^{16}\) \(+5.92274 q^{17}\) \(+7.34978 q^{18}\) \(+0.924101 q^{19}\) \(+16.1290 q^{20}\) \(+0.428048 q^{21}\) \(+2.37310 q^{22}\) \(+2.41802 q^{23}\) \(-2.44383 q^{24}\) \(+7.37655 q^{25}\) \(-2.56606 q^{26}\) \(-2.16080 q^{27}\) \(+5.32593 q^{28}\) \(-4.74162 q^{29}\) \(-3.32636 q^{30}\) \(-0.769674 q^{31}\) \(-6.87814 q^{32}\) \(-0.340764 q^{33}\) \(-15.1981 q^{34}\) \(+4.08685 q^{35}\) \(-13.1315 q^{36}\) \(-6.08456 q^{37}\) \(-2.37130 q^{38}\) \(+0.368471 q^{39}\) \(-23.3329 q^{40}\) \(-4.97559 q^{41}\) \(-1.09840 q^{42}\) \(-11.3315 q^{43}\) \(-4.23991 q^{44}\) \(-10.0765 q^{45}\) \(-6.20478 q^{46}\) \(-11.6750 q^{47}\) \(+2.89240 q^{48}\) \(-5.65048 q^{49}\) \(-18.9287 q^{50}\) \(+2.18236 q^{51}\) \(+4.58465 q^{52}\) \(-11.0098 q^{53}\) \(+5.54473 q^{54}\) \(-3.25350 q^{55}\) \(-7.70474 q^{56}\) \(+0.340504 q^{57}\) \(+12.1673 q^{58}\) \(-4.56413 q^{59}\) \(+5.94305 q^{60}\) \(+0.707416 q^{61}\) \(+1.97503 q^{62}\) \(-3.32734 q^{63}\) \(+1.95023 q^{64}\) \(+3.51803 q^{65}\) \(+0.874420 q^{66}\) \(+14.6843 q^{67}\) \(+27.1537 q^{68}\) \(+0.890969 q^{69}\) \(-10.4871 q^{70}\) \(+3.66391 q^{71}\) \(+18.9966 q^{72}\) \(-11.8834 q^{73}\) \(+15.6133 q^{74}\) \(+2.71804 q^{75}\) \(+4.23668 q^{76}\) \(-1.07434 q^{77}\) \(-0.945517 q^{78}\) \(-1.72189 q^{79}\) \(+27.6156 q^{80}\) \(+7.79650 q^{81}\) \(+12.7677 q^{82}\) \(-13.0038 q^{83}\) \(+1.96245 q^{84}\) \(+20.8364 q^{85}\) \(+29.0774 q^{86}\) \(-1.74715 q^{87}\) \(+6.13365 q^{88}\) \(+5.41057 q^{89}\) \(+25.8568 q^{90}\) \(+1.16169 q^{91}\) \(+11.0858 q^{92}\) \(-0.283602 q^{93}\) \(+29.9588 q^{94}\) \(+3.25102 q^{95}\) \(-2.53439 q^{96}\) \(-13.2766 q^{97}\) \(+14.4995 q^{98}\) \(+2.64886 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 47q^{11} \) \(\mathstrut -\mathstrut 53q^{12} \) \(\mathstrut +\mathstrut 134q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 87q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 52q^{22} \) \(\mathstrut -\mathstrut 44q^{23} \) \(\mathstrut -\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 58q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 117q^{27} \) \(\mathstrut -\mathstrut 71q^{28} \) \(\mathstrut -\mathstrut 42q^{29} \) \(\mathstrut -\mathstrut 21q^{30} \) \(\mathstrut -\mathstrut 82q^{31} \) \(\mathstrut -\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 30q^{34} \) \(\mathstrut -\mathstrut 54q^{35} \) \(\mathstrut +\mathstrut 32q^{36} \) \(\mathstrut -\mathstrut 55q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut 33q^{39} \) \(\mathstrut -\mathstrut 86q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut +\mathstrut 6q^{42} \) \(\mathstrut -\mathstrut 148q^{43} \) \(\mathstrut -\mathstrut 54q^{44} \) \(\mathstrut -\mathstrut 24q^{45} \) \(\mathstrut -\mathstrut 57q^{46} \) \(\mathstrut -\mathstrut 21q^{47} \) \(\mathstrut -\mathstrut 82q^{48} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 17q^{50} \) \(\mathstrut -\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 98q^{52} \) \(\mathstrut -\mathstrut 17q^{53} \) \(\mathstrut -\mathstrut 10q^{54} \) \(\mathstrut -\mathstrut 148q^{55} \) \(\mathstrut -\mathstrut 47q^{56} \) \(\mathstrut -\mathstrut q^{57} \) \(\mathstrut -\mathstrut 58q^{58} \) \(\mathstrut -\mathstrut 64q^{59} \) \(\mathstrut -\mathstrut 16q^{60} \) \(\mathstrut -\mathstrut 112q^{61} \) \(\mathstrut -\mathstrut 15q^{62} \) \(\mathstrut -\mathstrut 58q^{63} \) \(\mathstrut -\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 20q^{66} \) \(\mathstrut -\mathstrut 110q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 40q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 28q^{72} \) \(\mathstrut -\mathstrut 43q^{73} \) \(\mathstrut -\mathstrut 52q^{74} \) \(\mathstrut -\mathstrut 150q^{75} \) \(\mathstrut -\mathstrut 96q^{76} \) \(\mathstrut -\mathstrut 24q^{77} \) \(\mathstrut -\mathstrut 16q^{78} \) \(\mathstrut -\mathstrut 228q^{79} \) \(\mathstrut +\mathstrut 20q^{80} \) \(\mathstrut +\mathstrut 54q^{81} \) \(\mathstrut -\mathstrut 89q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 77q^{87} \) \(\mathstrut -\mathstrut 95q^{88} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 46q^{90} \) \(\mathstrut -\mathstrut 32q^{91} \) \(\mathstrut -\mathstrut 62q^{92} \) \(\mathstrut -\mathstrut 9q^{93} \) \(\mathstrut -\mathstrut 87q^{94} \) \(\mathstrut -\mathstrut 61q^{95} \) \(\mathstrut -\mathstrut 54q^{96} \) \(\mathstrut -\mathstrut 38q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut -\mathstrut 193q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.56606 −1.81448 −0.907238 0.420617i \(-0.861814\pi\)
−0.907238 + 0.420617i \(0.861814\pi\)
\(3\) 0.368471 0.212737 0.106368 0.994327i \(-0.466078\pi\)
0.106368 + 0.994327i \(0.466078\pi\)
\(4\) 4.58465 2.29233
\(5\) 3.51803 1.57331 0.786656 0.617392i \(-0.211811\pi\)
0.786656 + 0.617392i \(0.211811\pi\)
\(6\) −0.945517 −0.386006
\(7\) 1.16169 0.439077 0.219538 0.975604i \(-0.429545\pi\)
0.219538 + 0.975604i \(0.429545\pi\)
\(8\) −6.63237 −2.34490
\(9\) −2.86423 −0.954743
\(10\) −9.02747 −2.85474
\(11\) −0.924806 −0.278839 −0.139420 0.990233i \(-0.544524\pi\)
−0.139420 + 0.990233i \(0.544524\pi\)
\(12\) 1.68931 0.487662
\(13\) 1.00000 0.277350
\(14\) −2.98096 −0.796694
\(15\) 1.29629 0.334701
\(16\) 7.84974 1.96243
\(17\) 5.92274 1.43647 0.718237 0.695798i \(-0.244949\pi\)
0.718237 + 0.695798i \(0.244949\pi\)
\(18\) 7.34978 1.73236
\(19\) 0.924101 0.212003 0.106002 0.994366i \(-0.466195\pi\)
0.106002 + 0.994366i \(0.466195\pi\)
\(20\) 16.1290 3.60654
\(21\) 0.428048 0.0934077
\(22\) 2.37310 0.505948
\(23\) 2.41802 0.504192 0.252096 0.967702i \(-0.418880\pi\)
0.252096 + 0.967702i \(0.418880\pi\)
\(24\) −2.44383 −0.498846
\(25\) 7.37655 1.47531
\(26\) −2.56606 −0.503245
\(27\) −2.16080 −0.415846
\(28\) 5.32593 1.00651
\(29\) −4.74162 −0.880497 −0.440248 0.897876i \(-0.645110\pi\)
−0.440248 + 0.897876i \(0.645110\pi\)
\(30\) −3.32636 −0.607308
\(31\) −0.769674 −0.138238 −0.0691188 0.997608i \(-0.522019\pi\)
−0.0691188 + 0.997608i \(0.522019\pi\)
\(32\) −6.87814 −1.21589
\(33\) −0.340764 −0.0593194
\(34\) −15.1981 −2.60645
\(35\) 4.08685 0.690804
\(36\) −13.1315 −2.18858
\(37\) −6.08456 −1.00029 −0.500147 0.865940i \(-0.666721\pi\)
−0.500147 + 0.865940i \(0.666721\pi\)
\(38\) −2.37130 −0.384675
\(39\) 0.368471 0.0590026
\(40\) −23.3329 −3.68925
\(41\) −4.97559 −0.777057 −0.388529 0.921437i \(-0.627017\pi\)
−0.388529 + 0.921437i \(0.627017\pi\)
\(42\) −1.09840 −0.169486
\(43\) −11.3315 −1.72804 −0.864021 0.503456i \(-0.832062\pi\)
−0.864021 + 0.503456i \(0.832062\pi\)
\(44\) −4.23991 −0.639191
\(45\) −10.0765 −1.50211
\(46\) −6.20478 −0.914844
\(47\) −11.6750 −1.70298 −0.851489 0.524373i \(-0.824300\pi\)
−0.851489 + 0.524373i \(0.824300\pi\)
\(48\) 2.89240 0.417482
\(49\) −5.65048 −0.807212
\(50\) −18.9287 −2.67692
\(51\) 2.18236 0.305591
\(52\) 4.58465 0.635777
\(53\) −11.0098 −1.51231 −0.756154 0.654394i \(-0.772924\pi\)
−0.756154 + 0.654394i \(0.772924\pi\)
\(54\) 5.54473 0.754542
\(55\) −3.25350 −0.438701
\(56\) −7.70474 −1.02959
\(57\) 0.340504 0.0451009
\(58\) 12.1673 1.59764
\(59\) −4.56413 −0.594199 −0.297100 0.954846i \(-0.596019\pi\)
−0.297100 + 0.954846i \(0.596019\pi\)
\(60\) 5.94305 0.767244
\(61\) 0.707416 0.0905754 0.0452877 0.998974i \(-0.485580\pi\)
0.0452877 + 0.998974i \(0.485580\pi\)
\(62\) 1.97503 0.250829
\(63\) −3.32734 −0.419205
\(64\) 1.95023 0.243779
\(65\) 3.51803 0.436358
\(66\) 0.874420 0.107634
\(67\) 14.6843 1.79397 0.896987 0.442057i \(-0.145751\pi\)
0.896987 + 0.442057i \(0.145751\pi\)
\(68\) 27.1537 3.29287
\(69\) 0.890969 0.107260
\(70\) −10.4871 −1.25345
\(71\) 3.66391 0.434826 0.217413 0.976080i \(-0.430238\pi\)
0.217413 + 0.976080i \(0.430238\pi\)
\(72\) 18.9966 2.23877
\(73\) −11.8834 −1.39085 −0.695423 0.718600i \(-0.744783\pi\)
−0.695423 + 0.718600i \(0.744783\pi\)
\(74\) 15.6133 1.81501
\(75\) 2.71804 0.313853
\(76\) 4.23668 0.485981
\(77\) −1.07434 −0.122432
\(78\) −0.945517 −0.107059
\(79\) −1.72189 −0.193728 −0.0968640 0.995298i \(-0.530881\pi\)
−0.0968640 + 0.995298i \(0.530881\pi\)
\(80\) 27.6156 3.08752
\(81\) 7.79650 0.866277
\(82\) 12.7677 1.40995
\(83\) −13.0038 −1.42735 −0.713677 0.700475i \(-0.752972\pi\)
−0.713677 + 0.700475i \(0.752972\pi\)
\(84\) 1.96245 0.214121
\(85\) 20.8364 2.26002
\(86\) 29.0774 3.13549
\(87\) −1.74715 −0.187314
\(88\) 6.13365 0.653849
\(89\) 5.41057 0.573519 0.286760 0.958003i \(-0.407422\pi\)
0.286760 + 0.958003i \(0.407422\pi\)
\(90\) 25.8568 2.72554
\(91\) 1.16169 0.121778
\(92\) 11.0858 1.15577
\(93\) −0.283602 −0.0294082
\(94\) 29.9588 3.09001
\(95\) 3.25102 0.333547
\(96\) −2.53439 −0.258665
\(97\) −13.2766 −1.34804 −0.674019 0.738714i \(-0.735433\pi\)
−0.674019 + 0.738714i \(0.735433\pi\)
\(98\) 14.4995 1.46467
\(99\) 2.64886 0.266220
\(100\) 33.8189 3.38189
\(101\) −10.4935 −1.04414 −0.522069 0.852903i \(-0.674840\pi\)
−0.522069 + 0.852903i \(0.674840\pi\)
\(102\) −5.60005 −0.554488
\(103\) −14.7421 −1.45259 −0.726293 0.687385i \(-0.758758\pi\)
−0.726293 + 0.687385i \(0.758758\pi\)
\(104\) −6.63237 −0.650357
\(105\) 1.50589 0.146959
\(106\) 28.2517 2.74405
\(107\) 0.579234 0.0559966 0.0279983 0.999608i \(-0.491087\pi\)
0.0279983 + 0.999608i \(0.491087\pi\)
\(108\) −9.90651 −0.953254
\(109\) 1.95040 0.186814 0.0934072 0.995628i \(-0.470224\pi\)
0.0934072 + 0.995628i \(0.470224\pi\)
\(110\) 8.34866 0.796013
\(111\) −2.24198 −0.212799
\(112\) 9.11894 0.861659
\(113\) −9.29825 −0.874706 −0.437353 0.899290i \(-0.644084\pi\)
−0.437353 + 0.899290i \(0.644084\pi\)
\(114\) −0.873753 −0.0818345
\(115\) 8.50667 0.793251
\(116\) −21.7387 −2.01839
\(117\) −2.86423 −0.264798
\(118\) 11.7118 1.07816
\(119\) 6.88037 0.630722
\(120\) −8.59749 −0.784840
\(121\) −10.1447 −0.922249
\(122\) −1.81527 −0.164347
\(123\) −1.83336 −0.165309
\(124\) −3.52869 −0.316886
\(125\) 8.36078 0.747811
\(126\) 8.53815 0.760639
\(127\) −17.1288 −1.51993 −0.759966 0.649963i \(-0.774784\pi\)
−0.759966 + 0.649963i \(0.774784\pi\)
\(128\) 8.75188 0.773564
\(129\) −4.17534 −0.367618
\(130\) −9.02747 −0.791762
\(131\) −2.54135 −0.222039 −0.111019 0.993818i \(-0.535412\pi\)
−0.111019 + 0.993818i \(0.535412\pi\)
\(132\) −1.56228 −0.135979
\(133\) 1.07352 0.0930857
\(134\) −37.6808 −3.25513
\(135\) −7.60175 −0.654255
\(136\) −39.2818 −3.36838
\(137\) 2.45405 0.209664 0.104832 0.994490i \(-0.466570\pi\)
0.104832 + 0.994490i \(0.466570\pi\)
\(138\) −2.28628 −0.194621
\(139\) 14.5829 1.23690 0.618452 0.785823i \(-0.287760\pi\)
0.618452 + 0.785823i \(0.287760\pi\)
\(140\) 18.7368 1.58355
\(141\) −4.30191 −0.362286
\(142\) −9.40180 −0.788982
\(143\) −0.924806 −0.0773361
\(144\) −22.4834 −1.87362
\(145\) −16.6812 −1.38530
\(146\) 30.4935 2.52366
\(147\) −2.08204 −0.171724
\(148\) −27.8956 −2.29300
\(149\) −6.49244 −0.531881 −0.265941 0.963989i \(-0.585682\pi\)
−0.265941 + 0.963989i \(0.585682\pi\)
\(150\) −6.97466 −0.569478
\(151\) −18.0753 −1.47095 −0.735474 0.677553i \(-0.763041\pi\)
−0.735474 + 0.677553i \(0.763041\pi\)
\(152\) −6.12898 −0.497126
\(153\) −16.9641 −1.37146
\(154\) 2.75681 0.222150
\(155\) −2.70774 −0.217491
\(156\) 1.68931 0.135253
\(157\) 13.1171 1.04686 0.523431 0.852068i \(-0.324652\pi\)
0.523431 + 0.852068i \(0.324652\pi\)
\(158\) 4.41848 0.351515
\(159\) −4.05678 −0.321723
\(160\) −24.1975 −1.91298
\(161\) 2.80898 0.221379
\(162\) −20.0063 −1.57184
\(163\) −3.11486 −0.243975 −0.121987 0.992532i \(-0.538927\pi\)
−0.121987 + 0.992532i \(0.538927\pi\)
\(164\) −22.8114 −1.78127
\(165\) −1.19882 −0.0933279
\(166\) 33.3686 2.58990
\(167\) −4.65879 −0.360508 −0.180254 0.983620i \(-0.557692\pi\)
−0.180254 + 0.983620i \(0.557692\pi\)
\(168\) −2.83897 −0.219031
\(169\) 1.00000 0.0769231
\(170\) −53.4673 −4.10076
\(171\) −2.64684 −0.202409
\(172\) −51.9511 −3.96124
\(173\) 23.4676 1.78421 0.892103 0.451832i \(-0.149230\pi\)
0.892103 + 0.451832i \(0.149230\pi\)
\(174\) 4.48328 0.339877
\(175\) 8.56925 0.647774
\(176\) −7.25948 −0.547204
\(177\) −1.68175 −0.126408
\(178\) −13.8838 −1.04064
\(179\) 17.4583 1.30489 0.652446 0.757835i \(-0.273743\pi\)
0.652446 + 0.757835i \(0.273743\pi\)
\(180\) −46.1970 −3.44332
\(181\) 14.3167 1.06415 0.532076 0.846697i \(-0.321412\pi\)
0.532076 + 0.846697i \(0.321412\pi\)
\(182\) −2.98096 −0.220963
\(183\) 0.260662 0.0192687
\(184\) −16.0372 −1.18228
\(185\) −21.4057 −1.57378
\(186\) 0.727740 0.0533605
\(187\) −5.47738 −0.400546
\(188\) −53.5259 −3.90378
\(189\) −2.51017 −0.182588
\(190\) −8.34230 −0.605214
\(191\) 13.9878 1.01212 0.506060 0.862498i \(-0.331101\pi\)
0.506060 + 0.862498i \(0.331101\pi\)
\(192\) 0.718603 0.0518607
\(193\) −5.71643 −0.411477 −0.205739 0.978607i \(-0.565960\pi\)
−0.205739 + 0.978607i \(0.565960\pi\)
\(194\) 34.0686 2.44598
\(195\) 1.29629 0.0928294
\(196\) −25.9055 −1.85039
\(197\) 13.5512 0.965484 0.482742 0.875763i \(-0.339641\pi\)
0.482742 + 0.875763i \(0.339641\pi\)
\(198\) −6.79712 −0.483050
\(199\) −6.28467 −0.445508 −0.222754 0.974875i \(-0.571505\pi\)
−0.222754 + 0.974875i \(0.571505\pi\)
\(200\) −48.9240 −3.45945
\(201\) 5.41074 0.381644
\(202\) 26.9268 1.89457
\(203\) −5.50828 −0.386606
\(204\) 10.0053 0.700514
\(205\) −17.5043 −1.22255
\(206\) 37.8292 2.63568
\(207\) −6.92576 −0.481374
\(208\) 7.84974 0.544281
\(209\) −0.854614 −0.0591149
\(210\) −3.86419 −0.266655
\(211\) 15.6436 1.07695 0.538474 0.842642i \(-0.319001\pi\)
0.538474 + 0.842642i \(0.319001\pi\)
\(212\) −50.4760 −3.46670
\(213\) 1.35004 0.0925035
\(214\) −1.48635 −0.101605
\(215\) −39.8647 −2.71875
\(216\) 14.3312 0.975115
\(217\) −0.894121 −0.0606969
\(218\) −5.00484 −0.338970
\(219\) −4.37869 −0.295884
\(220\) −14.9161 −1.00565
\(221\) 5.92274 0.398406
\(222\) 5.75305 0.386120
\(223\) 15.1192 1.01245 0.506227 0.862400i \(-0.331040\pi\)
0.506227 + 0.862400i \(0.331040\pi\)
\(224\) −7.99025 −0.533871
\(225\) −21.1281 −1.40854
\(226\) 23.8598 1.58713
\(227\) 12.0949 0.802764 0.401382 0.915911i \(-0.368530\pi\)
0.401382 + 0.915911i \(0.368530\pi\)
\(228\) 1.56109 0.103386
\(229\) −0.960080 −0.0634439 −0.0317219 0.999497i \(-0.510099\pi\)
−0.0317219 + 0.999497i \(0.510099\pi\)
\(230\) −21.8286 −1.43934
\(231\) −0.395861 −0.0260458
\(232\) 31.4482 2.06467
\(233\) 21.5227 1.41000 0.705000 0.709207i \(-0.250947\pi\)
0.705000 + 0.709207i \(0.250947\pi\)
\(234\) 7.34978 0.480470
\(235\) −41.0731 −2.67931
\(236\) −20.9250 −1.36210
\(237\) −0.634467 −0.0412131
\(238\) −17.6554 −1.14443
\(239\) −3.38739 −0.219112 −0.109556 0.993981i \(-0.534943\pi\)
−0.109556 + 0.993981i \(0.534943\pi\)
\(240\) 10.1756 0.656829
\(241\) −26.0082 −1.67534 −0.837668 0.546180i \(-0.816081\pi\)
−0.837668 + 0.546180i \(0.816081\pi\)
\(242\) 26.0320 1.67340
\(243\) 9.35517 0.600135
\(244\) 3.24326 0.207628
\(245\) −19.8786 −1.27000
\(246\) 4.70451 0.299949
\(247\) 0.924101 0.0587991
\(248\) 5.10476 0.324153
\(249\) −4.79153 −0.303651
\(250\) −21.4542 −1.35689
\(251\) −26.2838 −1.65902 −0.829508 0.558495i \(-0.811379\pi\)
−0.829508 + 0.558495i \(0.811379\pi\)
\(252\) −15.2547 −0.960956
\(253\) −2.23620 −0.140589
\(254\) 43.9534 2.75788
\(255\) 7.67760 0.480790
\(256\) −26.3583 −1.64739
\(257\) 12.6595 0.789675 0.394838 0.918751i \(-0.370801\pi\)
0.394838 + 0.918751i \(0.370801\pi\)
\(258\) 10.7142 0.667034
\(259\) −7.06835 −0.439206
\(260\) 16.1290 1.00028
\(261\) 13.5811 0.840648
\(262\) 6.52125 0.402884
\(263\) −27.6983 −1.70795 −0.853976 0.520312i \(-0.825815\pi\)
−0.853976 + 0.520312i \(0.825815\pi\)
\(264\) 2.26007 0.139098
\(265\) −38.7327 −2.37933
\(266\) −2.75471 −0.168902
\(267\) 1.99364 0.122009
\(268\) 67.3225 4.11237
\(269\) 23.0036 1.40255 0.701277 0.712889i \(-0.252614\pi\)
0.701277 + 0.712889i \(0.252614\pi\)
\(270\) 19.5065 1.18713
\(271\) 8.11604 0.493014 0.246507 0.969141i \(-0.420717\pi\)
0.246507 + 0.969141i \(0.420717\pi\)
\(272\) 46.4919 2.81899
\(273\) 0.428048 0.0259066
\(274\) −6.29724 −0.380430
\(275\) −6.82187 −0.411374
\(276\) 4.08479 0.245875
\(277\) −24.9784 −1.50080 −0.750402 0.660981i \(-0.770140\pi\)
−0.750402 + 0.660981i \(0.770140\pi\)
\(278\) −37.4205 −2.24433
\(279\) 2.20452 0.131981
\(280\) −27.1055 −1.61986
\(281\) 4.93511 0.294404 0.147202 0.989106i \(-0.452973\pi\)
0.147202 + 0.989106i \(0.452973\pi\)
\(282\) 11.0389 0.657359
\(283\) −8.99268 −0.534559 −0.267280 0.963619i \(-0.586125\pi\)
−0.267280 + 0.963619i \(0.586125\pi\)
\(284\) 16.7978 0.996763
\(285\) 1.19790 0.0709578
\(286\) 2.37310 0.140325
\(287\) −5.78009 −0.341188
\(288\) 19.7006 1.16087
\(289\) 18.0788 1.06346
\(290\) 42.8048 2.51359
\(291\) −4.89205 −0.286777
\(292\) −54.4813 −3.18827
\(293\) −4.30272 −0.251367 −0.125684 0.992070i \(-0.540112\pi\)
−0.125684 + 0.992070i \(0.540112\pi\)
\(294\) 5.34263 0.311588
\(295\) −16.0568 −0.934861
\(296\) 40.3550 2.34559
\(297\) 1.99832 0.115954
\(298\) 16.6600 0.965086
\(299\) 2.41802 0.139838
\(300\) 12.4613 0.719453
\(301\) −13.1637 −0.758743
\(302\) 46.3823 2.66900
\(303\) −3.86653 −0.222127
\(304\) 7.25395 0.416042
\(305\) 2.48871 0.142503
\(306\) 43.5308 2.48849
\(307\) 31.8890 1.82000 0.910000 0.414609i \(-0.136082\pi\)
0.910000 + 0.414609i \(0.136082\pi\)
\(308\) −4.92545 −0.280654
\(309\) −5.43205 −0.309018
\(310\) 6.94821 0.394632
\(311\) −29.3223 −1.66271 −0.831357 0.555738i \(-0.812436\pi\)
−0.831357 + 0.555738i \(0.812436\pi\)
\(312\) −2.44383 −0.138355
\(313\) −16.8683 −0.953454 −0.476727 0.879051i \(-0.658177\pi\)
−0.476727 + 0.879051i \(0.658177\pi\)
\(314\) −33.6593 −1.89951
\(315\) −11.7057 −0.659541
\(316\) −7.89428 −0.444088
\(317\) 25.9600 1.45806 0.729028 0.684484i \(-0.239972\pi\)
0.729028 + 0.684484i \(0.239972\pi\)
\(318\) 10.4099 0.583760
\(319\) 4.38508 0.245517
\(320\) 6.86097 0.383540
\(321\) 0.213431 0.0119125
\(322\) −7.20801 −0.401687
\(323\) 5.47321 0.304537
\(324\) 35.7442 1.98579
\(325\) 7.37655 0.409177
\(326\) 7.99291 0.442686
\(327\) 0.718665 0.0397423
\(328\) 33.0000 1.82212
\(329\) −13.5627 −0.747738
\(330\) 3.07624 0.169341
\(331\) −8.37774 −0.460482 −0.230241 0.973134i \(-0.573952\pi\)
−0.230241 + 0.973134i \(0.573952\pi\)
\(332\) −59.6180 −3.27196
\(333\) 17.4276 0.955024
\(334\) 11.9547 0.654134
\(335\) 51.6599 2.82248
\(336\) 3.36006 0.183307
\(337\) 33.8307 1.84287 0.921437 0.388528i \(-0.127016\pi\)
0.921437 + 0.388528i \(0.127016\pi\)
\(338\) −2.56606 −0.139575
\(339\) −3.42613 −0.186082
\(340\) 95.5275 5.18071
\(341\) 0.711799 0.0385461
\(342\) 6.79194 0.367266
\(343\) −14.6959 −0.793504
\(344\) 75.1549 4.05208
\(345\) 3.13446 0.168754
\(346\) −60.2191 −3.23740
\(347\) −3.87470 −0.208005 −0.104003 0.994577i \(-0.533165\pi\)
−0.104003 + 0.994577i \(0.533165\pi\)
\(348\) −8.01007 −0.429385
\(349\) 29.5675 1.58271 0.791356 0.611356i \(-0.209376\pi\)
0.791356 + 0.611356i \(0.209376\pi\)
\(350\) −21.9892 −1.17537
\(351\) −2.16080 −0.115335
\(352\) 6.36094 0.339039
\(353\) 10.9908 0.584981 0.292490 0.956268i \(-0.405516\pi\)
0.292490 + 0.956268i \(0.405516\pi\)
\(354\) 4.31547 0.229364
\(355\) 12.8897 0.684117
\(356\) 24.8056 1.31469
\(357\) 2.53522 0.134178
\(358\) −44.7989 −2.36770
\(359\) 19.7969 1.04484 0.522421 0.852687i \(-0.325029\pi\)
0.522421 + 0.852687i \(0.325029\pi\)
\(360\) 66.8307 3.52229
\(361\) −18.1460 −0.955055
\(362\) −36.7375 −1.93088
\(363\) −3.73804 −0.196196
\(364\) 5.32593 0.279155
\(365\) −41.8062 −2.18824
\(366\) −0.668874 −0.0349626
\(367\) 5.21710 0.272330 0.136165 0.990686i \(-0.456522\pi\)
0.136165 + 0.990686i \(0.456522\pi\)
\(368\) 18.9808 0.989443
\(369\) 14.2512 0.741890
\(370\) 54.9282 2.85558
\(371\) −12.7899 −0.664019
\(372\) −1.30022 −0.0674132
\(373\) 34.1448 1.76795 0.883975 0.467534i \(-0.154858\pi\)
0.883975 + 0.467534i \(0.154858\pi\)
\(374\) 14.0553 0.726781
\(375\) 3.08070 0.159087
\(376\) 77.4331 3.99331
\(377\) −4.74162 −0.244206
\(378\) 6.44125 0.331302
\(379\) −37.1216 −1.90681 −0.953404 0.301698i \(-0.902447\pi\)
−0.953404 + 0.301698i \(0.902447\pi\)
\(380\) 14.9048 0.764599
\(381\) −6.31145 −0.323345
\(382\) −35.8935 −1.83647
\(383\) 27.4182 1.40100 0.700502 0.713650i \(-0.252959\pi\)
0.700502 + 0.713650i \(0.252959\pi\)
\(384\) 3.22481 0.164565
\(385\) −3.77955 −0.192623
\(386\) 14.6687 0.746616
\(387\) 32.4561 1.64984
\(388\) −60.8688 −3.09014
\(389\) −33.2309 −1.68488 −0.842438 0.538794i \(-0.818880\pi\)
−0.842438 + 0.538794i \(0.818880\pi\)
\(390\) −3.32636 −0.168437
\(391\) 14.3213 0.724259
\(392\) 37.4761 1.89283
\(393\) −0.936413 −0.0472358
\(394\) −34.7732 −1.75185
\(395\) −6.05767 −0.304795
\(396\) 12.1441 0.610263
\(397\) −17.5305 −0.879829 −0.439915 0.898040i \(-0.644991\pi\)
−0.439915 + 0.898040i \(0.644991\pi\)
\(398\) 16.1268 0.808364
\(399\) 0.395560 0.0198027
\(400\) 57.9040 2.89520
\(401\) 2.88368 0.144004 0.0720020 0.997404i \(-0.477061\pi\)
0.0720020 + 0.997404i \(0.477061\pi\)
\(402\) −13.8843 −0.692485
\(403\) −0.769674 −0.0383402
\(404\) −48.1089 −2.39351
\(405\) 27.4283 1.36292
\(406\) 14.1346 0.701487
\(407\) 5.62703 0.278922
\(408\) −14.4742 −0.716579
\(409\) −2.82408 −0.139642 −0.0698209 0.997560i \(-0.522243\pi\)
−0.0698209 + 0.997560i \(0.522243\pi\)
\(410\) 44.9171 2.21830
\(411\) 0.904246 0.0446032
\(412\) −67.5876 −3.32980
\(413\) −5.30210 −0.260899
\(414\) 17.7719 0.873441
\(415\) −45.7479 −2.24567
\(416\) −6.87814 −0.337228
\(417\) 5.37336 0.263135
\(418\) 2.19299 0.107263
\(419\) 14.9784 0.731742 0.365871 0.930666i \(-0.380771\pi\)
0.365871 + 0.930666i \(0.380771\pi\)
\(420\) 6.90397 0.336879
\(421\) −23.5829 −1.14936 −0.574680 0.818378i \(-0.694874\pi\)
−0.574680 + 0.818378i \(0.694874\pi\)
\(422\) −40.1423 −1.95410
\(423\) 33.4399 1.62591
\(424\) 73.0208 3.54620
\(425\) 43.6894 2.11925
\(426\) −3.46429 −0.167845
\(427\) 0.821797 0.0397695
\(428\) 2.65558 0.128363
\(429\) −0.340764 −0.0164522
\(430\) 102.295 4.93311
\(431\) 36.6722 1.76644 0.883220 0.468959i \(-0.155371\pi\)
0.883220 + 0.468959i \(0.155371\pi\)
\(432\) −16.9617 −0.816070
\(433\) −13.2868 −0.638522 −0.319261 0.947667i \(-0.603435\pi\)
−0.319261 + 0.947667i \(0.603435\pi\)
\(434\) 2.29437 0.110133
\(435\) −6.14652 −0.294703
\(436\) 8.94190 0.428239
\(437\) 2.23449 0.106890
\(438\) 11.2360 0.536875
\(439\) −24.0992 −1.15019 −0.575096 0.818086i \(-0.695035\pi\)
−0.575096 + 0.818086i \(0.695035\pi\)
\(440\) 21.5784 1.02871
\(441\) 16.1843 0.770680
\(442\) −15.1981 −0.722899
\(443\) −18.8930 −0.897634 −0.448817 0.893624i \(-0.648155\pi\)
−0.448817 + 0.893624i \(0.648155\pi\)
\(444\) −10.2787 −0.487806
\(445\) 19.0346 0.902325
\(446\) −38.7966 −1.83707
\(447\) −2.39227 −0.113151
\(448\) 2.26556 0.107038
\(449\) 11.9037 0.561769 0.280885 0.959742i \(-0.409372\pi\)
0.280885 + 0.959742i \(0.409372\pi\)
\(450\) 54.2160 2.55577
\(451\) 4.60146 0.216674
\(452\) −42.6292 −2.00511
\(453\) −6.66023 −0.312925
\(454\) −31.0361 −1.45660
\(455\) 4.08685 0.191595
\(456\) −2.25835 −0.105757
\(457\) 24.9730 1.16819 0.584095 0.811686i \(-0.301450\pi\)
0.584095 + 0.811686i \(0.301450\pi\)
\(458\) 2.46362 0.115117
\(459\) −12.7978 −0.597352
\(460\) 39.0001 1.81839
\(461\) 13.0471 0.607663 0.303831 0.952726i \(-0.401734\pi\)
0.303831 + 0.952726i \(0.401734\pi\)
\(462\) 1.01580 0.0472594
\(463\) −25.8594 −1.20179 −0.600894 0.799329i \(-0.705189\pi\)
−0.600894 + 0.799329i \(0.705189\pi\)
\(464\) −37.2205 −1.72792
\(465\) −0.997722 −0.0462683
\(466\) −55.2285 −2.55841
\(467\) −18.4343 −0.853038 −0.426519 0.904478i \(-0.640260\pi\)
−0.426519 + 0.904478i \(0.640260\pi\)
\(468\) −13.1315 −0.607004
\(469\) 17.0586 0.787692
\(470\) 105.396 4.86155
\(471\) 4.83328 0.222706
\(472\) 30.2710 1.39334
\(473\) 10.4795 0.481846
\(474\) 1.62808 0.0747802
\(475\) 6.81668 0.312771
\(476\) 31.5441 1.44582
\(477\) 31.5345 1.44387
\(478\) 8.69225 0.397574
\(479\) 18.9057 0.863826 0.431913 0.901915i \(-0.357839\pi\)
0.431913 + 0.901915i \(0.357839\pi\)
\(480\) −8.91608 −0.406961
\(481\) −6.08456 −0.277432
\(482\) 66.7386 3.03986
\(483\) 1.03503 0.0470954
\(484\) −46.5101 −2.11409
\(485\) −46.7076 −2.12088
\(486\) −24.0059 −1.08893
\(487\) 25.6016 1.16012 0.580059 0.814575i \(-0.303030\pi\)
0.580059 + 0.814575i \(0.303030\pi\)
\(488\) −4.69184 −0.212390
\(489\) −1.14774 −0.0519024
\(490\) 51.0096 2.30438
\(491\) −27.3066 −1.23233 −0.616164 0.787618i \(-0.711314\pi\)
−0.616164 + 0.787618i \(0.711314\pi\)
\(492\) −8.40533 −0.378941
\(493\) −28.0834 −1.26481
\(494\) −2.37130 −0.106690
\(495\) 9.31876 0.418847
\(496\) −6.04174 −0.271282
\(497\) 4.25632 0.190922
\(498\) 12.2953 0.550967
\(499\) −10.1010 −0.452183 −0.226092 0.974106i \(-0.572595\pi\)
−0.226092 + 0.974106i \(0.572595\pi\)
\(500\) 38.3313 1.71423
\(501\) −1.71663 −0.0766933
\(502\) 67.4457 3.01025
\(503\) 17.2934 0.771074 0.385537 0.922692i \(-0.374016\pi\)
0.385537 + 0.922692i \(0.374016\pi\)
\(504\) 22.0681 0.982993
\(505\) −36.9163 −1.64276
\(506\) 5.73821 0.255095
\(507\) 0.368471 0.0163644
\(508\) −78.5294 −3.48418
\(509\) 13.5896 0.602350 0.301175 0.953569i \(-0.402621\pi\)
0.301175 + 0.953569i \(0.402621\pi\)
\(510\) −19.7012 −0.872382
\(511\) −13.8048 −0.610688
\(512\) 50.1331 2.21559
\(513\) −1.99679 −0.0881606
\(514\) −32.4849 −1.43285
\(515\) −51.8633 −2.28537
\(516\) −19.1425 −0.842700
\(517\) 10.7971 0.474857
\(518\) 18.1378 0.796929
\(519\) 8.64711 0.379566
\(520\) −23.3329 −1.02321
\(521\) 36.4538 1.59707 0.798536 0.601947i \(-0.205608\pi\)
0.798536 + 0.601947i \(0.205608\pi\)
\(522\) −34.8499 −1.52534
\(523\) 2.82906 0.123706 0.0618531 0.998085i \(-0.480299\pi\)
0.0618531 + 0.998085i \(0.480299\pi\)
\(524\) −11.6512 −0.508985
\(525\) 3.15752 0.137805
\(526\) 71.0755 3.09904
\(527\) −4.55858 −0.198575
\(528\) −2.67491 −0.116410
\(529\) −17.1532 −0.745791
\(530\) 99.3904 4.31724
\(531\) 13.0727 0.567308
\(532\) 4.92170 0.213383
\(533\) −4.97559 −0.215517
\(534\) −5.11579 −0.221382
\(535\) 2.03776 0.0881001
\(536\) −97.3918 −4.20668
\(537\) 6.43287 0.277599
\(538\) −59.0285 −2.54490
\(539\) 5.22560 0.225082
\(540\) −34.8514 −1.49977
\(541\) −12.2018 −0.524598 −0.262299 0.964987i \(-0.584481\pi\)
−0.262299 + 0.964987i \(0.584481\pi\)
\(542\) −20.8262 −0.894563
\(543\) 5.27529 0.226384
\(544\) −40.7374 −1.74660
\(545\) 6.86157 0.293917
\(546\) −1.09840 −0.0470070
\(547\) −38.1604 −1.63162 −0.815811 0.578319i \(-0.803709\pi\)
−0.815811 + 0.578319i \(0.803709\pi\)
\(548\) 11.2510 0.480618
\(549\) −2.02620 −0.0864762
\(550\) 17.5053 0.746430
\(551\) −4.38173 −0.186668
\(552\) −5.90924 −0.251514
\(553\) −2.00030 −0.0850615
\(554\) 64.0959 2.72318
\(555\) −7.88736 −0.334800
\(556\) 66.8574 2.83539
\(557\) −11.5485 −0.489328 −0.244664 0.969608i \(-0.578678\pi\)
−0.244664 + 0.969608i \(0.578678\pi\)
\(558\) −5.65693 −0.239477
\(559\) −11.3315 −0.479273
\(560\) 32.0807 1.35566
\(561\) −2.01825 −0.0852108
\(562\) −12.6638 −0.534189
\(563\) 42.2857 1.78213 0.891066 0.453874i \(-0.149958\pi\)
0.891066 + 0.453874i \(0.149958\pi\)
\(564\) −19.7227 −0.830477
\(565\) −32.7115 −1.37618
\(566\) 23.0757 0.969946
\(567\) 9.05709 0.380362
\(568\) −24.3004 −1.01962
\(569\) 20.4765 0.858418 0.429209 0.903205i \(-0.358792\pi\)
0.429209 + 0.903205i \(0.358792\pi\)
\(570\) −3.07389 −0.128751
\(571\) 5.52746 0.231317 0.115658 0.993289i \(-0.463102\pi\)
0.115658 + 0.993289i \(0.463102\pi\)
\(572\) −4.23991 −0.177280
\(573\) 5.15409 0.215315
\(574\) 14.8320 0.619077
\(575\) 17.8366 0.743839
\(576\) −5.58590 −0.232746
\(577\) 37.9539 1.58004 0.790020 0.613081i \(-0.210070\pi\)
0.790020 + 0.613081i \(0.210070\pi\)
\(578\) −46.3913 −1.92962
\(579\) −2.10634 −0.0875363
\(580\) −76.4774 −3.17555
\(581\) −15.1064 −0.626718
\(582\) 12.5533 0.520351
\(583\) 10.1819 0.421691
\(584\) 78.8151 3.26139
\(585\) −10.0765 −0.416610
\(586\) 11.0410 0.456100
\(587\) 2.11342 0.0872304 0.0436152 0.999048i \(-0.486112\pi\)
0.0436152 + 0.999048i \(0.486112\pi\)
\(588\) −9.54542 −0.393646
\(589\) −0.711256 −0.0293068
\(590\) 41.2026 1.69628
\(591\) 4.99323 0.205394
\(592\) −47.7621 −1.96301
\(593\) 5.79914 0.238142 0.119071 0.992886i \(-0.462008\pi\)
0.119071 + 0.992886i \(0.462008\pi\)
\(594\) −5.12780 −0.210396
\(595\) 24.2054 0.992323
\(596\) −29.7656 −1.21924
\(597\) −2.31572 −0.0947760
\(598\) −6.20478 −0.253732
\(599\) 14.1315 0.577398 0.288699 0.957420i \(-0.406777\pi\)
0.288699 + 0.957420i \(0.406777\pi\)
\(600\) −18.0271 −0.735952
\(601\) 30.4892 1.24368 0.621840 0.783144i \(-0.286385\pi\)
0.621840 + 0.783144i \(0.286385\pi\)
\(602\) 33.7788 1.37672
\(603\) −42.0592 −1.71278
\(604\) −82.8691 −3.37189
\(605\) −35.6895 −1.45098
\(606\) 9.92175 0.403044
\(607\) −16.7026 −0.677937 −0.338969 0.940798i \(-0.610078\pi\)
−0.338969 + 0.940798i \(0.610078\pi\)
\(608\) −6.35609 −0.257774
\(609\) −2.02964 −0.0822452
\(610\) −6.38618 −0.258569
\(611\) −11.6750 −0.472321
\(612\) −77.7744 −3.14384
\(613\) 22.8210 0.921733 0.460866 0.887470i \(-0.347539\pi\)
0.460866 + 0.887470i \(0.347539\pi\)
\(614\) −81.8289 −3.30235
\(615\) −6.44982 −0.260082
\(616\) 7.12539 0.287090
\(617\) 1.00000 0.0402585
\(618\) 13.9389 0.560707
\(619\) −38.7091 −1.55585 −0.777925 0.628357i \(-0.783728\pi\)
−0.777925 + 0.628357i \(0.783728\pi\)
\(620\) −12.4140 −0.498560
\(621\) −5.22485 −0.209666
\(622\) 75.2427 3.01696
\(623\) 6.28539 0.251819
\(624\) 2.89240 0.115789
\(625\) −7.46927 −0.298771
\(626\) 43.2851 1.73002
\(627\) −0.314900 −0.0125759
\(628\) 60.1375 2.39975
\(629\) −36.0372 −1.43690
\(630\) 30.0375 1.19672
\(631\) −7.20626 −0.286877 −0.143438 0.989659i \(-0.545816\pi\)
−0.143438 + 0.989659i \(0.545816\pi\)
\(632\) 11.4202 0.454272
\(633\) 5.76420 0.229106
\(634\) −66.6147 −2.64561
\(635\) −60.2595 −2.39133
\(636\) −18.5989 −0.737495
\(637\) −5.65048 −0.223880
\(638\) −11.2524 −0.445485
\(639\) −10.4943 −0.415147
\(640\) 30.7894 1.21706
\(641\) −44.6771 −1.76464 −0.882319 0.470652i \(-0.844019\pi\)
−0.882319 + 0.470652i \(0.844019\pi\)
\(642\) −0.547675 −0.0216150
\(643\) 0.207932 0.00820003 0.00410001 0.999992i \(-0.498695\pi\)
0.00410001 + 0.999992i \(0.498695\pi\)
\(644\) 12.8782 0.507473
\(645\) −14.6890 −0.578378
\(646\) −14.0446 −0.552576
\(647\) 0.318867 0.0125360 0.00626799 0.999980i \(-0.498005\pi\)
0.00626799 + 0.999980i \(0.498005\pi\)
\(648\) −51.7092 −2.03133
\(649\) 4.22094 0.165686
\(650\) −18.9287 −0.742443
\(651\) −0.329457 −0.0129125
\(652\) −14.2806 −0.559270
\(653\) 39.8719 1.56031 0.780154 0.625588i \(-0.215141\pi\)
0.780154 + 0.625588i \(0.215141\pi\)
\(654\) −1.84414 −0.0721114
\(655\) −8.94055 −0.349336
\(656\) −39.0571 −1.52492
\(657\) 34.0368 1.32790
\(658\) 34.8028 1.35675
\(659\) −32.0668 −1.24914 −0.624572 0.780967i \(-0.714726\pi\)
−0.624572 + 0.780967i \(0.714726\pi\)
\(660\) −5.49617 −0.213938
\(661\) −1.58993 −0.0618410 −0.0309205 0.999522i \(-0.509844\pi\)
−0.0309205 + 0.999522i \(0.509844\pi\)
\(662\) 21.4978 0.835535
\(663\) 2.18236 0.0847557
\(664\) 86.2461 3.34700
\(665\) 3.77667 0.146453
\(666\) −44.7201 −1.73287
\(667\) −11.4653 −0.443939
\(668\) −21.3589 −0.826402
\(669\) 5.57097 0.215386
\(670\) −132.562 −5.12133
\(671\) −0.654222 −0.0252560
\(672\) −2.94417 −0.113574
\(673\) −11.0307 −0.425201 −0.212601 0.977139i \(-0.568193\pi\)
−0.212601 + 0.977139i \(0.568193\pi\)
\(674\) −86.8115 −3.34385
\(675\) −15.9392 −0.613501
\(676\) 4.58465 0.176333
\(677\) 46.4529 1.78533 0.892665 0.450721i \(-0.148833\pi\)
0.892665 + 0.450721i \(0.148833\pi\)
\(678\) 8.79166 0.337641
\(679\) −15.4233 −0.591892
\(680\) −138.195 −5.29952
\(681\) 4.45660 0.170777
\(682\) −1.82652 −0.0699410
\(683\) 1.68596 0.0645117 0.0322558 0.999480i \(-0.489731\pi\)
0.0322558 + 0.999480i \(0.489731\pi\)
\(684\) −12.1348 −0.463987
\(685\) 8.63343 0.329866
\(686\) 37.7106 1.43980
\(687\) −0.353762 −0.0134968
\(688\) −88.9495 −3.39117
\(689\) −11.0098 −0.419439
\(690\) −8.04320 −0.306200
\(691\) −3.22198 −0.122570 −0.0612849 0.998120i \(-0.519520\pi\)
−0.0612849 + 0.998120i \(0.519520\pi\)
\(692\) 107.591 4.08998
\(693\) 3.07714 0.116891
\(694\) 9.94272 0.377420
\(695\) 51.3030 1.94603
\(696\) 11.5877 0.439232
\(697\) −29.4691 −1.11622
\(698\) −75.8719 −2.87179
\(699\) 7.93050 0.299959
\(700\) 39.2870 1.48491
\(701\) −37.1662 −1.40375 −0.701874 0.712301i \(-0.747653\pi\)
−0.701874 + 0.712301i \(0.747653\pi\)
\(702\) 5.54473 0.209272
\(703\) −5.62274 −0.212066
\(704\) −1.80358 −0.0679751
\(705\) −15.1342 −0.569989
\(706\) −28.2030 −1.06143
\(707\) −12.1901 −0.458457
\(708\) −7.71024 −0.289769
\(709\) 14.5140 0.545083 0.272541 0.962144i \(-0.412136\pi\)
0.272541 + 0.962144i \(0.412136\pi\)
\(710\) −33.0758 −1.24131
\(711\) 4.93189 0.184961
\(712\) −35.8849 −1.34484
\(713\) −1.86109 −0.0696982
\(714\) −6.50551 −0.243463
\(715\) −3.25350 −0.121674
\(716\) 80.0401 2.99124
\(717\) −1.24816 −0.0466132
\(718\) −50.8001 −1.89584
\(719\) 9.33551 0.348156 0.174078 0.984732i \(-0.444306\pi\)
0.174078 + 0.984732i \(0.444306\pi\)
\(720\) −79.0975 −2.94779
\(721\) −17.1258 −0.637797
\(722\) 46.5638 1.73292
\(723\) −9.58326 −0.356405
\(724\) 65.6371 2.43938
\(725\) −34.9768 −1.29901
\(726\) 9.59202 0.355993
\(727\) 26.1027 0.968094 0.484047 0.875042i \(-0.339166\pi\)
0.484047 + 0.875042i \(0.339166\pi\)
\(728\) −7.70474 −0.285557
\(729\) −19.9424 −0.738607
\(730\) 107.277 3.97050
\(731\) −67.1136 −2.48229
\(732\) 1.19505 0.0441702
\(733\) 10.3309 0.381581 0.190790 0.981631i \(-0.438895\pi\)
0.190790 + 0.981631i \(0.438895\pi\)
\(734\) −13.3874 −0.494137
\(735\) −7.32468 −0.270175
\(736\) −16.6315 −0.613044
\(737\) −13.5801 −0.500231
\(738\) −36.5695 −1.34614
\(739\) 35.4105 1.30260 0.651298 0.758822i \(-0.274225\pi\)
0.651298 + 0.758822i \(0.274225\pi\)
\(740\) −98.1375 −3.60761
\(741\) 0.340504 0.0125087
\(742\) 32.8196 1.20485
\(743\) −20.2781 −0.743931 −0.371965 0.928247i \(-0.621316\pi\)
−0.371965 + 0.928247i \(0.621316\pi\)
\(744\) 1.88096 0.0689592
\(745\) −22.8406 −0.836815
\(746\) −87.6175 −3.20790
\(747\) 37.2459 1.36276
\(748\) −25.1119 −0.918181
\(749\) 0.672888 0.0245868
\(750\) −7.90526 −0.288659
\(751\) −22.1270 −0.807425 −0.403713 0.914886i \(-0.632280\pi\)
−0.403713 + 0.914886i \(0.632280\pi\)
\(752\) −91.6459 −3.34198
\(753\) −9.68480 −0.352934
\(754\) 12.1673 0.443106
\(755\) −63.5896 −2.31426
\(756\) −11.5083 −0.418552
\(757\) 4.84322 0.176030 0.0880149 0.996119i \(-0.471948\pi\)
0.0880149 + 0.996119i \(0.471948\pi\)
\(758\) 95.2561 3.45986
\(759\) −0.823974 −0.0299083
\(760\) −21.5619 −0.782134
\(761\) 40.8068 1.47925 0.739623 0.673022i \(-0.235004\pi\)
0.739623 + 0.673022i \(0.235004\pi\)
\(762\) 16.1955 0.586703
\(763\) 2.26575 0.0820258
\(764\) 64.1292 2.32011
\(765\) −59.6802 −2.15774
\(766\) −70.3567 −2.54209
\(767\) −4.56413 −0.164801
\(768\) −9.71226 −0.350461
\(769\) 14.5221 0.523680 0.261840 0.965111i \(-0.415671\pi\)
0.261840 + 0.965111i \(0.415671\pi\)
\(770\) 9.69853 0.349511
\(771\) 4.66464 0.167993
\(772\) −26.2078 −0.943240
\(773\) 33.8195 1.21640 0.608202 0.793782i \(-0.291891\pi\)
0.608202 + 0.793782i \(0.291891\pi\)
\(774\) −83.2842 −2.99359
\(775\) −5.67754 −0.203943
\(776\) 88.0556 3.16101
\(777\) −2.60448 −0.0934353
\(778\) 85.2725 3.05717
\(779\) −4.59795 −0.164739
\(780\) 5.94305 0.212795
\(781\) −3.38840 −0.121247
\(782\) −36.7493 −1.31415
\(783\) 10.2457 0.366151
\(784\) −44.3548 −1.58410
\(785\) 46.1465 1.64704
\(786\) 2.40289 0.0857082
\(787\) 42.2827 1.50722 0.753608 0.657324i \(-0.228312\pi\)
0.753608 + 0.657324i \(0.228312\pi\)
\(788\) 62.1276 2.21320
\(789\) −10.2060 −0.363344
\(790\) 15.5443 0.553043
\(791\) −10.8017 −0.384063
\(792\) −17.5682 −0.624258
\(793\) 0.707416 0.0251211
\(794\) 44.9842 1.59643
\(795\) −14.2719 −0.506171
\(796\) −28.8130 −1.02125
\(797\) 25.3175 0.896791 0.448396 0.893835i \(-0.351996\pi\)
0.448396 + 0.893835i \(0.351996\pi\)
\(798\) −1.01503 −0.0359316
\(799\) −69.1481 −2.44628
\(800\) −50.7369 −1.79382
\(801\) −15.4971 −0.547564
\(802\) −7.39968 −0.261292
\(803\) 10.9898 0.387823
\(804\) 24.8064 0.874853
\(805\) 9.88209 0.348298
\(806\) 1.97503 0.0695674
\(807\) 8.47615 0.298375
\(808\) 69.5965 2.44840
\(809\) 37.4370 1.31621 0.658107 0.752925i \(-0.271357\pi\)
0.658107 + 0.752925i \(0.271357\pi\)
\(810\) −70.3827 −2.47299
\(811\) −28.1335 −0.987900 −0.493950 0.869490i \(-0.664447\pi\)
−0.493950 + 0.869490i \(0.664447\pi\)
\(812\) −25.2536 −0.886226
\(813\) 2.99052 0.104882
\(814\) −14.4393 −0.506097
\(815\) −10.9582 −0.383848
\(816\) 17.1309 0.599702
\(817\) −10.4715 −0.366351
\(818\) 7.24675 0.253377
\(819\) −3.32734 −0.116267
\(820\) −80.2511 −2.80249
\(821\) 20.1736 0.704063 0.352031 0.935988i \(-0.385491\pi\)
0.352031 + 0.935988i \(0.385491\pi\)
\(822\) −2.32035 −0.0809314
\(823\) 5.38928 0.187859 0.0939293 0.995579i \(-0.470057\pi\)
0.0939293 + 0.995579i \(0.470057\pi\)
\(824\) 97.7753 3.40616
\(825\) −2.51366 −0.0875145
\(826\) 13.6055 0.473395
\(827\) −30.1715 −1.04917 −0.524583 0.851360i \(-0.675779\pi\)
−0.524583 + 0.851360i \(0.675779\pi\)
\(828\) −31.7522 −1.10347
\(829\) −39.7778 −1.38154 −0.690771 0.723074i \(-0.742729\pi\)
−0.690771 + 0.723074i \(0.742729\pi\)
\(830\) 117.392 4.07472
\(831\) −9.20380 −0.319276
\(832\) 1.95023 0.0676120
\(833\) −33.4663 −1.15954
\(834\) −13.7884 −0.477452
\(835\) −16.3898 −0.567192
\(836\) −3.91811 −0.135511
\(837\) 1.66311 0.0574855
\(838\) −38.4354 −1.32773
\(839\) 2.80823 0.0969510 0.0484755 0.998824i \(-0.484564\pi\)
0.0484755 + 0.998824i \(0.484564\pi\)
\(840\) −9.98760 −0.344605
\(841\) −6.51704 −0.224726
\(842\) 60.5151 2.08549
\(843\) 1.81844 0.0626305
\(844\) 71.7203 2.46871
\(845\) 3.51803 0.121024
\(846\) −85.8088 −2.95017
\(847\) −11.7850 −0.404938
\(848\) −86.4238 −2.96780
\(849\) −3.31354 −0.113720
\(850\) −112.109 −3.84532
\(851\) −14.7126 −0.504340
\(852\) 6.18948 0.212048
\(853\) 37.2564 1.27563 0.637817 0.770188i \(-0.279837\pi\)
0.637817 + 0.770188i \(0.279837\pi\)
\(854\) −2.10878 −0.0721609
\(855\) −9.31166 −0.318452
\(856\) −3.84169 −0.131306
\(857\) −28.6064 −0.977177 −0.488588 0.872514i \(-0.662488\pi\)
−0.488588 + 0.872514i \(0.662488\pi\)
\(858\) 0.874420 0.0298522
\(859\) −17.6232 −0.601295 −0.300647 0.953735i \(-0.597203\pi\)
−0.300647 + 0.953735i \(0.597203\pi\)
\(860\) −182.766 −6.23226
\(861\) −2.12979 −0.0725832
\(862\) −94.1031 −3.20516
\(863\) 38.2211 1.30106 0.650531 0.759479i \(-0.274546\pi\)
0.650531 + 0.759479i \(0.274546\pi\)
\(864\) 14.8623 0.505624
\(865\) 82.5596 2.80711
\(866\) 34.0947 1.15858
\(867\) 6.66151 0.226237
\(868\) −4.09923 −0.139137
\(869\) 1.59242 0.0540190
\(870\) 15.7723 0.534732
\(871\) 14.6843 0.497559
\(872\) −12.9358 −0.438060
\(873\) 38.0273 1.28703
\(874\) −5.73384 −0.193950
\(875\) 9.71261 0.328346
\(876\) −20.0748 −0.678263
\(877\) −0.655633 −0.0221392 −0.0110696 0.999939i \(-0.503524\pi\)
−0.0110696 + 0.999939i \(0.503524\pi\)
\(878\) 61.8399 2.08700
\(879\) −1.58543 −0.0534751
\(880\) −25.5391 −0.860922
\(881\) −35.9964 −1.21275 −0.606374 0.795180i \(-0.707377\pi\)
−0.606374 + 0.795180i \(0.707377\pi\)
\(882\) −41.5298 −1.39838
\(883\) −16.0251 −0.539287 −0.269644 0.962960i \(-0.586906\pi\)
−0.269644 + 0.962960i \(0.586906\pi\)
\(884\) 27.1537 0.913277
\(885\) −5.91645 −0.198879
\(886\) 48.4806 1.62874
\(887\) −27.4054 −0.920183 −0.460091 0.887872i \(-0.652183\pi\)
−0.460091 + 0.887872i \(0.652183\pi\)
\(888\) 14.8696 0.498993
\(889\) −19.8983 −0.667367
\(890\) −48.8438 −1.63725
\(891\) −7.21024 −0.241552
\(892\) 69.3161 2.32087
\(893\) −10.7889 −0.361037
\(894\) 6.13871 0.205309
\(895\) 61.4188 2.05300
\(896\) 10.1669 0.339654
\(897\) 0.890969 0.0297486
\(898\) −30.5455 −1.01932
\(899\) 3.64950 0.121718
\(900\) −96.8651 −3.22884
\(901\) −65.2079 −2.17239
\(902\) −11.8076 −0.393150
\(903\) −4.85044 −0.161412
\(904\) 61.6694 2.05109
\(905\) 50.3666 1.67424
\(906\) 17.0905 0.567795
\(907\) 7.26434 0.241208 0.120604 0.992701i \(-0.461517\pi\)
0.120604 + 0.992701i \(0.461517\pi\)
\(908\) 55.4507 1.84020
\(909\) 30.0557 0.996884
\(910\) −10.4871 −0.347644
\(911\) −24.7056 −0.818532 −0.409266 0.912415i \(-0.634215\pi\)
−0.409266 + 0.912415i \(0.634215\pi\)
\(912\) 2.67287 0.0885075
\(913\) 12.0260 0.398003
\(914\) −64.0823 −2.11965
\(915\) 0.917018 0.0303157
\(916\) −4.40164 −0.145434
\(917\) −2.95225 −0.0974920
\(918\) 32.8400 1.08388
\(919\) −28.1245 −0.927743 −0.463871 0.885903i \(-0.653540\pi\)
−0.463871 + 0.885903i \(0.653540\pi\)
\(920\) −56.4194 −1.86009
\(921\) 11.7502 0.387181
\(922\) −33.4796 −1.10259
\(923\) 3.66391 0.120599
\(924\) −1.81489 −0.0597054
\(925\) −44.8830 −1.47574
\(926\) 66.3567 2.18062
\(927\) 42.2249 1.38685
\(928\) 32.6135 1.07059
\(929\) −34.8952 −1.14488 −0.572438 0.819948i \(-0.694002\pi\)
−0.572438 + 0.819948i \(0.694002\pi\)
\(930\) 2.56021 0.0839527
\(931\) −5.22161 −0.171132
\(932\) 98.6742 3.23218
\(933\) −10.8044 −0.353720
\(934\) 47.3035 1.54782
\(935\) −19.2696 −0.630183
\(936\) 18.9966 0.620924
\(937\) −48.3688 −1.58014 −0.790070 0.613017i \(-0.789956\pi\)
−0.790070 + 0.613017i \(0.789956\pi\)
\(938\) −43.7733 −1.42925
\(939\) −6.21549 −0.202835
\(940\) −188.306 −6.14186
\(941\) 4.14402 0.135091 0.0675457 0.997716i \(-0.478483\pi\)
0.0675457 + 0.997716i \(0.478483\pi\)
\(942\) −12.4025 −0.404095
\(943\) −12.0311 −0.391786
\(944\) −35.8272 −1.16608
\(945\) −8.83086 −0.287268
\(946\) −26.8909 −0.874299
\(947\) −10.4266 −0.338820 −0.169410 0.985546i \(-0.554186\pi\)
−0.169410 + 0.985546i \(0.554186\pi\)
\(948\) −2.90881 −0.0944738
\(949\) −11.8834 −0.385751
\(950\) −17.4920 −0.567515
\(951\) 9.56549 0.310182
\(952\) −45.6331 −1.47898
\(953\) 49.2698 1.59600 0.798002 0.602654i \(-0.205890\pi\)
0.798002 + 0.602654i \(0.205890\pi\)
\(954\) −80.9193 −2.61986
\(955\) 49.2095 1.59238
\(956\) −15.5300 −0.502277
\(957\) 1.61577 0.0522305
\(958\) −48.5132 −1.56739
\(959\) 2.85084 0.0920584
\(960\) 2.52807 0.0815930
\(961\) −30.4076 −0.980890
\(962\) 15.6133 0.503394
\(963\) −1.65906 −0.0534624
\(964\) −119.239 −3.84042
\(965\) −20.1106 −0.647382
\(966\) −2.65594 −0.0854535
\(967\) 37.8778 1.21807 0.609034 0.793144i \(-0.291557\pi\)
0.609034 + 0.793144i \(0.291557\pi\)
\(968\) 67.2836 2.16258
\(969\) 2.01672 0.0647863
\(970\) 119.854 3.84830
\(971\) −5.80722 −0.186363 −0.0931813 0.995649i \(-0.529704\pi\)
−0.0931813 + 0.995649i \(0.529704\pi\)
\(972\) 42.8902 1.37570
\(973\) 16.9407 0.543095
\(974\) −65.6951 −2.10501
\(975\) 2.71804 0.0870471
\(976\) 5.55303 0.177748
\(977\) 9.44498 0.302172 0.151086 0.988521i \(-0.451723\pi\)
0.151086 + 0.988521i \(0.451723\pi\)
\(978\) 2.94515 0.0941757
\(979\) −5.00373 −0.159920
\(980\) −91.1364 −2.91124
\(981\) −5.58639 −0.178360
\(982\) 70.0702 2.23603
\(983\) 9.33642 0.297786 0.148893 0.988853i \(-0.452429\pi\)
0.148893 + 0.988853i \(0.452429\pi\)
\(984\) 12.1595 0.387632
\(985\) 47.6736 1.51901
\(986\) 72.0635 2.29497
\(987\) −4.99747 −0.159071
\(988\) 4.23668 0.134787
\(989\) −27.3998 −0.871264
\(990\) −23.9125 −0.759988
\(991\) 8.33974 0.264921 0.132460 0.991188i \(-0.457712\pi\)
0.132460 + 0.991188i \(0.457712\pi\)
\(992\) 5.29392 0.168082
\(993\) −3.08695 −0.0979615
\(994\) −10.9220 −0.346423
\(995\) −22.1097 −0.700923
\(996\) −21.9675 −0.696067
\(997\) −12.0083 −0.380308 −0.190154 0.981754i \(-0.560899\pi\)
−0.190154 + 0.981754i \(0.560899\pi\)
\(998\) 25.9198 0.820476
\(999\) 13.1475 0.415968
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 \(a_p\))