Properties

Label 8018.2.a.d.1.8
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(30\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.02842 q^{3}\) \(+1.00000 q^{4}\) \(+2.47134 q^{5}\) \(-2.02842 q^{6}\) \(+1.41486 q^{7}\) \(+1.00000 q^{8}\) \(+1.11447 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.02842 q^{3}\) \(+1.00000 q^{4}\) \(+2.47134 q^{5}\) \(-2.02842 q^{6}\) \(+1.41486 q^{7}\) \(+1.00000 q^{8}\) \(+1.11447 q^{9}\) \(+2.47134 q^{10}\) \(-1.90125 q^{11}\) \(-2.02842 q^{12}\) \(+3.04945 q^{13}\) \(+1.41486 q^{14}\) \(-5.01290 q^{15}\) \(+1.00000 q^{16}\) \(-0.777246 q^{17}\) \(+1.11447 q^{18}\) \(+1.00000 q^{19}\) \(+2.47134 q^{20}\) \(-2.86993 q^{21}\) \(-1.90125 q^{22}\) \(-7.98162 q^{23}\) \(-2.02842 q^{24}\) \(+1.10751 q^{25}\) \(+3.04945 q^{26}\) \(+3.82464 q^{27}\) \(+1.41486 q^{28}\) \(-5.89103 q^{29}\) \(-5.01290 q^{30}\) \(-5.52189 q^{31}\) \(+1.00000 q^{32}\) \(+3.85652 q^{33}\) \(-0.777246 q^{34}\) \(+3.49660 q^{35}\) \(+1.11447 q^{36}\) \(-3.09139 q^{37}\) \(+1.00000 q^{38}\) \(-6.18556 q^{39}\) \(+2.47134 q^{40}\) \(-6.61679 q^{41}\) \(-2.86993 q^{42}\) \(+11.4467 q^{43}\) \(-1.90125 q^{44}\) \(+2.75423 q^{45}\) \(-7.98162 q^{46}\) \(-6.04983 q^{47}\) \(-2.02842 q^{48}\) \(-4.99817 q^{49}\) \(+1.10751 q^{50}\) \(+1.57658 q^{51}\) \(+3.04945 q^{52}\) \(-3.46843 q^{53}\) \(+3.82464 q^{54}\) \(-4.69863 q^{55}\) \(+1.41486 q^{56}\) \(-2.02842 q^{57}\) \(-5.89103 q^{58}\) \(-1.73246 q^{59}\) \(-5.01290 q^{60}\) \(-11.6171 q^{61}\) \(-5.52189 q^{62}\) \(+1.57682 q^{63}\) \(+1.00000 q^{64}\) \(+7.53623 q^{65}\) \(+3.85652 q^{66}\) \(+5.11260 q^{67}\) \(-0.777246 q^{68}\) \(+16.1900 q^{69}\) \(+3.49660 q^{70}\) \(-0.661692 q^{71}\) \(+1.11447 q^{72}\) \(-11.5032 q^{73}\) \(-3.09139 q^{74}\) \(-2.24649 q^{75}\) \(+1.00000 q^{76}\) \(-2.69001 q^{77}\) \(-6.18556 q^{78}\) \(-15.7474 q^{79}\) \(+2.47134 q^{80}\) \(-11.1014 q^{81}\) \(-6.61679 q^{82}\) \(+13.7324 q^{83}\) \(-2.86993 q^{84}\) \(-1.92084 q^{85}\) \(+11.4467 q^{86}\) \(+11.9495 q^{87}\) \(-1.90125 q^{88}\) \(-5.29706 q^{89}\) \(+2.75423 q^{90}\) \(+4.31455 q^{91}\) \(-7.98162 q^{92}\) \(+11.2007 q^{93}\) \(-6.04983 q^{94}\) \(+2.47134 q^{95}\) \(-2.02842 q^{96}\) \(+11.1561 q^{97}\) \(-4.99817 q^{98}\) \(-2.11889 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(30q \) \(\mathstrut +\mathstrut 30q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(30q \) \(\mathstrut +\mathstrut 30q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut -\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 17q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 19q^{13} \) \(\mathstrut -\mathstrut 15q^{14} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 10q^{18} \) \(\mathstrut +\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 14q^{21} \) \(\mathstrut -\mathstrut 17q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 10q^{24} \) \(\mathstrut -\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 19q^{26} \) \(\mathstrut -\mathstrut 37q^{27} \) \(\mathstrut -\mathstrut 15q^{28} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 30q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 18q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 10q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut +\mathstrut 30q^{38} \) \(\mathstrut -\mathstrut 12q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 14q^{42} \) \(\mathstrut -\mathstrut 61q^{43} \) \(\mathstrut -\mathstrut 17q^{44} \) \(\mathstrut -\mathstrut 14q^{45} \) \(\mathstrut -\mathstrut 15q^{46} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut -\mathstrut q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 19q^{52} \) \(\mathstrut -\mathstrut 19q^{53} \) \(\mathstrut -\mathstrut 37q^{54} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 37q^{58} \) \(\mathstrut -\mathstrut 6q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 32q^{61} \) \(\mathstrut -\mathstrut 11q^{62} \) \(\mathstrut -\mathstrut 24q^{63} \) \(\mathstrut +\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 18q^{68} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 10q^{72} \) \(\mathstrut -\mathstrut 58q^{73} \) \(\mathstrut -\mathstrut 46q^{74} \) \(\mathstrut -\mathstrut 42q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut -\mathstrut 32q^{77} \) \(\mathstrut -\mathstrut 42q^{79} \) \(\mathstrut -\mathstrut 12q^{80} \) \(\mathstrut -\mathstrut 38q^{81} \) \(\mathstrut -\mathstrut 28q^{82} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 48q^{85} \) \(\mathstrut -\mathstrut 61q^{86} \) \(\mathstrut -\mathstrut 15q^{87} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut -\mathstrut 39q^{89} \) \(\mathstrut -\mathstrut 14q^{90} \) \(\mathstrut -\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 15q^{92} \) \(\mathstrut -\mathstrut 45q^{93} \) \(\mathstrut -\mathstrut 4q^{94} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut -\mathstrut 10q^{96} \) \(\mathstrut -\mathstrut 33q^{97} \) \(\mathstrut -\mathstrut q^{98} \) \(\mathstrut -\mathstrut 38q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.02842 −1.17111 −0.585553 0.810634i \(-0.699123\pi\)
−0.585553 + 0.810634i \(0.699123\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.47134 1.10522 0.552608 0.833441i \(-0.313633\pi\)
0.552608 + 0.833441i \(0.313633\pi\)
\(6\) −2.02842 −0.828097
\(7\) 1.41486 0.534767 0.267384 0.963590i \(-0.413841\pi\)
0.267384 + 0.963590i \(0.413841\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.11447 0.371490
\(10\) 2.47134 0.781505
\(11\) −1.90125 −0.573248 −0.286624 0.958043i \(-0.592533\pi\)
−0.286624 + 0.958043i \(0.592533\pi\)
\(12\) −2.02842 −0.585553
\(13\) 3.04945 0.845766 0.422883 0.906184i \(-0.361018\pi\)
0.422883 + 0.906184i \(0.361018\pi\)
\(14\) 1.41486 0.378138
\(15\) −5.01290 −1.29432
\(16\) 1.00000 0.250000
\(17\) −0.777246 −0.188510 −0.0942549 0.995548i \(-0.530047\pi\)
−0.0942549 + 0.995548i \(0.530047\pi\)
\(18\) 1.11447 0.262683
\(19\) 1.00000 0.229416
\(20\) 2.47134 0.552608
\(21\) −2.86993 −0.626269
\(22\) −1.90125 −0.405348
\(23\) −7.98162 −1.66428 −0.832141 0.554564i \(-0.812885\pi\)
−0.832141 + 0.554564i \(0.812885\pi\)
\(24\) −2.02842 −0.414049
\(25\) 1.10751 0.221502
\(26\) 3.04945 0.598047
\(27\) 3.82464 0.736052
\(28\) 1.41486 0.267384
\(29\) −5.89103 −1.09394 −0.546969 0.837153i \(-0.684218\pi\)
−0.546969 + 0.837153i \(0.684218\pi\)
\(30\) −5.01290 −0.915226
\(31\) −5.52189 −0.991761 −0.495880 0.868391i \(-0.665155\pi\)
−0.495880 + 0.868391i \(0.665155\pi\)
\(32\) 1.00000 0.176777
\(33\) 3.85652 0.671335
\(34\) −0.777246 −0.133297
\(35\) 3.49660 0.591033
\(36\) 1.11447 0.185745
\(37\) −3.09139 −0.508221 −0.254111 0.967175i \(-0.581783\pi\)
−0.254111 + 0.967175i \(0.581783\pi\)
\(38\) 1.00000 0.162221
\(39\) −6.18556 −0.990482
\(40\) 2.47134 0.390753
\(41\) −6.61679 −1.03337 −0.516684 0.856176i \(-0.672834\pi\)
−0.516684 + 0.856176i \(0.672834\pi\)
\(42\) −2.86993 −0.442839
\(43\) 11.4467 1.74560 0.872799 0.488080i \(-0.162303\pi\)
0.872799 + 0.488080i \(0.162303\pi\)
\(44\) −1.90125 −0.286624
\(45\) 2.75423 0.410577
\(46\) −7.98162 −1.17683
\(47\) −6.04983 −0.882459 −0.441230 0.897394i \(-0.645458\pi\)
−0.441230 + 0.897394i \(0.645458\pi\)
\(48\) −2.02842 −0.292777
\(49\) −4.99817 −0.714024
\(50\) 1.10751 0.156625
\(51\) 1.57658 0.220765
\(52\) 3.04945 0.422883
\(53\) −3.46843 −0.476426 −0.238213 0.971213i \(-0.576562\pi\)
−0.238213 + 0.971213i \(0.576562\pi\)
\(54\) 3.82464 0.520467
\(55\) −4.69863 −0.633563
\(56\) 1.41486 0.189069
\(57\) −2.02842 −0.268670
\(58\) −5.89103 −0.773530
\(59\) −1.73246 −0.225547 −0.112774 0.993621i \(-0.535974\pi\)
−0.112774 + 0.993621i \(0.535974\pi\)
\(60\) −5.01290 −0.647162
\(61\) −11.6171 −1.48742 −0.743709 0.668504i \(-0.766935\pi\)
−0.743709 + 0.668504i \(0.766935\pi\)
\(62\) −5.52189 −0.701281
\(63\) 1.57682 0.198661
\(64\) 1.00000 0.125000
\(65\) 7.53623 0.934754
\(66\) 3.85652 0.474705
\(67\) 5.11260 0.624604 0.312302 0.949983i \(-0.398900\pi\)
0.312302 + 0.949983i \(0.398900\pi\)
\(68\) −0.777246 −0.0942549
\(69\) 16.1900 1.94905
\(70\) 3.49660 0.417924
\(71\) −0.661692 −0.0785284 −0.0392642 0.999229i \(-0.512501\pi\)
−0.0392642 + 0.999229i \(0.512501\pi\)
\(72\) 1.11447 0.131342
\(73\) −11.5032 −1.34635 −0.673173 0.739485i \(-0.735069\pi\)
−0.673173 + 0.739485i \(0.735069\pi\)
\(74\) −3.09139 −0.359367
\(75\) −2.24649 −0.259402
\(76\) 1.00000 0.114708
\(77\) −2.69001 −0.306555
\(78\) −6.18556 −0.700377
\(79\) −15.7474 −1.77172 −0.885858 0.463956i \(-0.846429\pi\)
−0.885858 + 0.463956i \(0.846429\pi\)
\(80\) 2.47134 0.276304
\(81\) −11.1014 −1.23349
\(82\) −6.61679 −0.730702
\(83\) 13.7324 1.50732 0.753661 0.657263i \(-0.228286\pi\)
0.753661 + 0.657263i \(0.228286\pi\)
\(84\) −2.86993 −0.313135
\(85\) −1.92084 −0.208344
\(86\) 11.4467 1.23432
\(87\) 11.9495 1.28112
\(88\) −1.90125 −0.202674
\(89\) −5.29706 −0.561488 −0.280744 0.959783i \(-0.590581\pi\)
−0.280744 + 0.959783i \(0.590581\pi\)
\(90\) 2.75423 0.290321
\(91\) 4.31455 0.452288
\(92\) −7.98162 −0.832141
\(93\) 11.2007 1.16146
\(94\) −6.04983 −0.623993
\(95\) 2.47134 0.253554
\(96\) −2.02842 −0.207024
\(97\) 11.1561 1.13273 0.566364 0.824155i \(-0.308350\pi\)
0.566364 + 0.824155i \(0.308350\pi\)
\(98\) −4.99817 −0.504891
\(99\) −2.11889 −0.212956
\(100\) 1.10751 0.110751
\(101\) −2.64209 −0.262898 −0.131449 0.991323i \(-0.541963\pi\)
−0.131449 + 0.991323i \(0.541963\pi\)
\(102\) 1.57658 0.156104
\(103\) 0.481843 0.0474774 0.0237387 0.999718i \(-0.492443\pi\)
0.0237387 + 0.999718i \(0.492443\pi\)
\(104\) 3.04945 0.299024
\(105\) −7.09256 −0.692163
\(106\) −3.46843 −0.336884
\(107\) 10.6017 1.02490 0.512451 0.858716i \(-0.328738\pi\)
0.512451 + 0.858716i \(0.328738\pi\)
\(108\) 3.82464 0.368026
\(109\) −11.9045 −1.14025 −0.570124 0.821559i \(-0.693105\pi\)
−0.570124 + 0.821559i \(0.693105\pi\)
\(110\) −4.69863 −0.447997
\(111\) 6.27062 0.595181
\(112\) 1.41486 0.133692
\(113\) 3.01625 0.283745 0.141872 0.989885i \(-0.454688\pi\)
0.141872 + 0.989885i \(0.454688\pi\)
\(114\) −2.02842 −0.189979
\(115\) −19.7253 −1.83939
\(116\) −5.89103 −0.546969
\(117\) 3.39852 0.314194
\(118\) −1.73246 −0.159486
\(119\) −1.09970 −0.100809
\(120\) −5.01290 −0.457613
\(121\) −7.38525 −0.671386
\(122\) −11.6171 −1.05176
\(123\) 13.4216 1.21018
\(124\) −5.52189 −0.495880
\(125\) −9.61966 −0.860409
\(126\) 1.57682 0.140474
\(127\) 18.1456 1.61016 0.805079 0.593168i \(-0.202123\pi\)
0.805079 + 0.593168i \(0.202123\pi\)
\(128\) 1.00000 0.0883883
\(129\) −23.2186 −2.04428
\(130\) 7.53623 0.660971
\(131\) 5.03267 0.439706 0.219853 0.975533i \(-0.429442\pi\)
0.219853 + 0.975533i \(0.429442\pi\)
\(132\) 3.85652 0.335667
\(133\) 1.41486 0.122684
\(134\) 5.11260 0.441662
\(135\) 9.45197 0.813496
\(136\) −0.777246 −0.0666483
\(137\) −9.66429 −0.825676 −0.412838 0.910805i \(-0.635462\pi\)
−0.412838 + 0.910805i \(0.635462\pi\)
\(138\) 16.1900 1.37819
\(139\) 6.20866 0.526612 0.263306 0.964712i \(-0.415187\pi\)
0.263306 + 0.964712i \(0.415187\pi\)
\(140\) 3.49660 0.295517
\(141\) 12.2716 1.03345
\(142\) −0.661692 −0.0555280
\(143\) −5.79777 −0.484834
\(144\) 1.11447 0.0928725
\(145\) −14.5587 −1.20904
\(146\) −11.5032 −0.952010
\(147\) 10.1384 0.836198
\(148\) −3.09139 −0.254111
\(149\) 14.0579 1.15167 0.575833 0.817567i \(-0.304678\pi\)
0.575833 + 0.817567i \(0.304678\pi\)
\(150\) −2.24649 −0.183425
\(151\) −8.58786 −0.698870 −0.349435 0.936961i \(-0.613626\pi\)
−0.349435 + 0.936961i \(0.613626\pi\)
\(152\) 1.00000 0.0811107
\(153\) −0.866217 −0.0700295
\(154\) −2.69001 −0.216767
\(155\) −13.6465 −1.09611
\(156\) −6.18556 −0.495241
\(157\) 10.2251 0.816055 0.408027 0.912970i \(-0.366217\pi\)
0.408027 + 0.912970i \(0.366217\pi\)
\(158\) −15.7474 −1.25279
\(159\) 7.03542 0.557945
\(160\) 2.47134 0.195376
\(161\) −11.2929 −0.890004
\(162\) −11.1014 −0.872206
\(163\) −13.0794 −1.02446 −0.512229 0.858849i \(-0.671180\pi\)
−0.512229 + 0.858849i \(0.671180\pi\)
\(164\) −6.61679 −0.516684
\(165\) 9.53077 0.741970
\(166\) 13.7324 1.06584
\(167\) −22.6408 −1.75200 −0.875999 0.482313i \(-0.839797\pi\)
−0.875999 + 0.482313i \(0.839797\pi\)
\(168\) −2.86993 −0.221420
\(169\) −3.70083 −0.284679
\(170\) −1.92084 −0.147321
\(171\) 1.11447 0.0852257
\(172\) 11.4467 0.872799
\(173\) 12.6704 0.963316 0.481658 0.876359i \(-0.340035\pi\)
0.481658 + 0.876359i \(0.340035\pi\)
\(174\) 11.9495 0.905886
\(175\) 1.56697 0.118452
\(176\) −1.90125 −0.143312
\(177\) 3.51415 0.264140
\(178\) −5.29706 −0.397032
\(179\) 24.8335 1.85614 0.928070 0.372405i \(-0.121467\pi\)
0.928070 + 0.372405i \(0.121467\pi\)
\(180\) 2.75423 0.205288
\(181\) −9.34261 −0.694431 −0.347215 0.937785i \(-0.612873\pi\)
−0.347215 + 0.937785i \(0.612873\pi\)
\(182\) 4.31455 0.319816
\(183\) 23.5643 1.74192
\(184\) −7.98162 −0.588413
\(185\) −7.63986 −0.561694
\(186\) 11.2007 0.821274
\(187\) 1.47774 0.108063
\(188\) −6.04983 −0.441230
\(189\) 5.41133 0.393617
\(190\) 2.47134 0.179290
\(191\) 20.9150 1.51335 0.756677 0.653789i \(-0.226822\pi\)
0.756677 + 0.653789i \(0.226822\pi\)
\(192\) −2.02842 −0.146388
\(193\) −19.1158 −1.37599 −0.687993 0.725717i \(-0.741508\pi\)
−0.687993 + 0.725717i \(0.741508\pi\)
\(194\) 11.1561 0.800959
\(195\) −15.2866 −1.09470
\(196\) −4.99817 −0.357012
\(197\) 17.4473 1.24307 0.621534 0.783387i \(-0.286510\pi\)
0.621534 + 0.783387i \(0.286510\pi\)
\(198\) −2.11889 −0.150583
\(199\) −2.95613 −0.209554 −0.104777 0.994496i \(-0.533413\pi\)
−0.104777 + 0.994496i \(0.533413\pi\)
\(200\) 1.10751 0.0783126
\(201\) −10.3705 −0.731478
\(202\) −2.64209 −0.185897
\(203\) −8.33499 −0.585002
\(204\) 1.57658 0.110383
\(205\) −16.3523 −1.14209
\(206\) 0.481843 0.0335716
\(207\) −8.89527 −0.618264
\(208\) 3.04945 0.211442
\(209\) −1.90125 −0.131512
\(210\) −7.09256 −0.489433
\(211\) −1.00000 −0.0688428
\(212\) −3.46843 −0.238213
\(213\) 1.34219 0.0919651
\(214\) 10.6017 0.724716
\(215\) 28.2885 1.92926
\(216\) 3.82464 0.260234
\(217\) −7.81271 −0.530361
\(218\) −11.9045 −0.806277
\(219\) 23.3332 1.57671
\(220\) −4.69863 −0.316782
\(221\) −2.37018 −0.159435
\(222\) 6.27062 0.420857
\(223\) −1.94987 −0.130573 −0.0652866 0.997867i \(-0.520796\pi\)
−0.0652866 + 0.997867i \(0.520796\pi\)
\(224\) 1.41486 0.0945344
\(225\) 1.23428 0.0822856
\(226\) 3.01625 0.200638
\(227\) 10.1743 0.675295 0.337647 0.941273i \(-0.390369\pi\)
0.337647 + 0.941273i \(0.390369\pi\)
\(228\) −2.02842 −0.134335
\(229\) −15.9728 −1.05551 −0.527756 0.849396i \(-0.676966\pi\)
−0.527756 + 0.849396i \(0.676966\pi\)
\(230\) −19.7253 −1.30065
\(231\) 5.45645 0.359008
\(232\) −5.89103 −0.386765
\(233\) 1.97470 0.129367 0.0646835 0.997906i \(-0.479396\pi\)
0.0646835 + 0.997906i \(0.479396\pi\)
\(234\) 3.39852 0.222168
\(235\) −14.9512 −0.975308
\(236\) −1.73246 −0.112774
\(237\) 31.9422 2.07487
\(238\) −1.09970 −0.0712827
\(239\) 4.17581 0.270110 0.135055 0.990838i \(-0.456879\pi\)
0.135055 + 0.990838i \(0.456879\pi\)
\(240\) −5.01290 −0.323581
\(241\) −9.50085 −0.612003 −0.306002 0.952031i \(-0.598991\pi\)
−0.306002 + 0.952031i \(0.598991\pi\)
\(242\) −7.38525 −0.474742
\(243\) 11.0443 0.708490
\(244\) −11.6171 −0.743709
\(245\) −12.3522 −0.789150
\(246\) 13.4216 0.855729
\(247\) 3.04945 0.194032
\(248\) −5.52189 −0.350640
\(249\) −27.8549 −1.76524
\(250\) −9.61966 −0.608401
\(251\) −2.77413 −0.175101 −0.0875507 0.996160i \(-0.527904\pi\)
−0.0875507 + 0.996160i \(0.527904\pi\)
\(252\) 1.57682 0.0993304
\(253\) 15.1750 0.954047
\(254\) 18.1456 1.13855
\(255\) 3.89626 0.243993
\(256\) 1.00000 0.0625000
\(257\) 13.3757 0.834350 0.417175 0.908826i \(-0.363020\pi\)
0.417175 + 0.908826i \(0.363020\pi\)
\(258\) −23.2186 −1.44552
\(259\) −4.37389 −0.271780
\(260\) 7.53623 0.467377
\(261\) −6.56538 −0.406387
\(262\) 5.03267 0.310919
\(263\) 5.46318 0.336874 0.168437 0.985712i \(-0.446128\pi\)
0.168437 + 0.985712i \(0.446128\pi\)
\(264\) 3.85652 0.237353
\(265\) −8.57167 −0.526553
\(266\) 1.41486 0.0867507
\(267\) 10.7446 0.657562
\(268\) 5.11260 0.312302
\(269\) −5.59912 −0.341385 −0.170692 0.985324i \(-0.554600\pi\)
−0.170692 + 0.985324i \(0.554600\pi\)
\(270\) 9.45197 0.575229
\(271\) −6.95593 −0.422543 −0.211271 0.977427i \(-0.567760\pi\)
−0.211271 + 0.977427i \(0.567760\pi\)
\(272\) −0.777246 −0.0471275
\(273\) −8.75171 −0.529678
\(274\) −9.66429 −0.583841
\(275\) −2.10565 −0.126975
\(276\) 16.1900 0.974526
\(277\) 16.3010 0.979430 0.489715 0.871882i \(-0.337101\pi\)
0.489715 + 0.871882i \(0.337101\pi\)
\(278\) 6.20866 0.372371
\(279\) −6.15398 −0.368429
\(280\) 3.49660 0.208962
\(281\) 25.7357 1.53526 0.767632 0.640891i \(-0.221435\pi\)
0.767632 + 0.640891i \(0.221435\pi\)
\(282\) 12.2716 0.730762
\(283\) 0.131593 0.00782241 0.00391121 0.999992i \(-0.498755\pi\)
0.00391121 + 0.999992i \(0.498755\pi\)
\(284\) −0.661692 −0.0392642
\(285\) −5.01290 −0.296939
\(286\) −5.79777 −0.342829
\(287\) −9.36183 −0.552612
\(288\) 1.11447 0.0656708
\(289\) −16.3959 −0.964464
\(290\) −14.5587 −0.854918
\(291\) −22.6291 −1.32654
\(292\) −11.5032 −0.673173
\(293\) 3.62743 0.211917 0.105958 0.994371i \(-0.466209\pi\)
0.105958 + 0.994371i \(0.466209\pi\)
\(294\) 10.1384 0.591281
\(295\) −4.28150 −0.249278
\(296\) −3.09139 −0.179683
\(297\) −7.27159 −0.421941
\(298\) 14.0579 0.814351
\(299\) −24.3396 −1.40759
\(300\) −2.24649 −0.129701
\(301\) 16.1954 0.933489
\(302\) −8.58786 −0.494176
\(303\) 5.35925 0.307881
\(304\) 1.00000 0.0573539
\(305\) −28.7098 −1.64392
\(306\) −0.866217 −0.0495183
\(307\) 0.382256 0.0218165 0.0109082 0.999941i \(-0.496528\pi\)
0.0109082 + 0.999941i \(0.496528\pi\)
\(308\) −2.69001 −0.153277
\(309\) −0.977378 −0.0556011
\(310\) −13.6465 −0.775067
\(311\) 14.8067 0.839613 0.419807 0.907614i \(-0.362098\pi\)
0.419807 + 0.907614i \(0.362098\pi\)
\(312\) −6.18556 −0.350188
\(313\) −18.6361 −1.05337 −0.526686 0.850060i \(-0.676566\pi\)
−0.526686 + 0.850060i \(0.676566\pi\)
\(314\) 10.2251 0.577038
\(315\) 3.89686 0.219563
\(316\) −15.7474 −0.885858
\(317\) 0.143542 0.00806212 0.00403106 0.999992i \(-0.498717\pi\)
0.00403106 + 0.999992i \(0.498717\pi\)
\(318\) 7.03542 0.394527
\(319\) 11.2003 0.627098
\(320\) 2.47134 0.138152
\(321\) −21.5046 −1.20027
\(322\) −11.2929 −0.629328
\(323\) −0.777246 −0.0432471
\(324\) −11.1014 −0.616743
\(325\) 3.37729 0.187339
\(326\) −13.0794 −0.724401
\(327\) 24.1474 1.33535
\(328\) −6.61679 −0.365351
\(329\) −8.55968 −0.471910
\(330\) 9.53077 0.524652
\(331\) −26.5807 −1.46101 −0.730505 0.682908i \(-0.760715\pi\)
−0.730505 + 0.682908i \(0.760715\pi\)
\(332\) 13.7324 0.753661
\(333\) −3.44526 −0.188799
\(334\) −22.6408 −1.23885
\(335\) 12.6350 0.690322
\(336\) −2.86993 −0.156567
\(337\) −8.74594 −0.476422 −0.238211 0.971213i \(-0.576561\pi\)
−0.238211 + 0.971213i \(0.576561\pi\)
\(338\) −3.70083 −0.201299
\(339\) −6.11820 −0.332295
\(340\) −1.92084 −0.104172
\(341\) 10.4985 0.568525
\(342\) 1.11447 0.0602636
\(343\) −16.9757 −0.916604
\(344\) 11.4467 0.617162
\(345\) 40.0110 2.15412
\(346\) 12.6704 0.681167
\(347\) −13.8668 −0.744408 −0.372204 0.928151i \(-0.621398\pi\)
−0.372204 + 0.928151i \(0.621398\pi\)
\(348\) 11.9495 0.640558
\(349\) 7.60207 0.406930 0.203465 0.979082i \(-0.434780\pi\)
0.203465 + 0.979082i \(0.434780\pi\)
\(350\) 1.56697 0.0837581
\(351\) 11.6631 0.622528
\(352\) −1.90125 −0.101337
\(353\) 5.74221 0.305627 0.152813 0.988255i \(-0.451167\pi\)
0.152813 + 0.988255i \(0.451167\pi\)
\(354\) 3.51415 0.186775
\(355\) −1.63526 −0.0867908
\(356\) −5.29706 −0.280744
\(357\) 2.23064 0.118058
\(358\) 24.8335 1.31249
\(359\) −12.4080 −0.654869 −0.327434 0.944874i \(-0.606184\pi\)
−0.327434 + 0.944874i \(0.606184\pi\)
\(360\) 2.75423 0.145161
\(361\) 1.00000 0.0526316
\(362\) −9.34261 −0.491037
\(363\) 14.9804 0.786265
\(364\) 4.31455 0.226144
\(365\) −28.4282 −1.48800
\(366\) 23.5643 1.23173
\(367\) −3.66093 −0.191099 −0.0955495 0.995425i \(-0.530461\pi\)
−0.0955495 + 0.995425i \(0.530461\pi\)
\(368\) −7.98162 −0.416071
\(369\) −7.37421 −0.383886
\(370\) −7.63986 −0.397178
\(371\) −4.90735 −0.254777
\(372\) 11.2007 0.580729
\(373\) −35.5897 −1.84276 −0.921382 0.388658i \(-0.872939\pi\)
−0.921382 + 0.388658i \(0.872939\pi\)
\(374\) 1.47774 0.0764120
\(375\) 19.5127 1.00763
\(376\) −6.04983 −0.311996
\(377\) −17.9644 −0.925215
\(378\) 5.41133 0.278329
\(379\) 33.7772 1.73502 0.867508 0.497423i \(-0.165720\pi\)
0.867508 + 0.497423i \(0.165720\pi\)
\(380\) 2.47134 0.126777
\(381\) −36.8067 −1.88567
\(382\) 20.9150 1.07010
\(383\) 25.0970 1.28240 0.641199 0.767375i \(-0.278437\pi\)
0.641199 + 0.767375i \(0.278437\pi\)
\(384\) −2.02842 −0.103512
\(385\) −6.64791 −0.338809
\(386\) −19.1158 −0.972969
\(387\) 12.7569 0.648472
\(388\) 11.1561 0.566364
\(389\) 14.8264 0.751730 0.375865 0.926674i \(-0.377346\pi\)
0.375865 + 0.926674i \(0.377346\pi\)
\(390\) −15.2866 −0.774067
\(391\) 6.20368 0.313734
\(392\) −4.99817 −0.252446
\(393\) −10.2083 −0.514943
\(394\) 17.4473 0.878981
\(395\) −38.9170 −1.95813
\(396\) −2.11889 −0.106478
\(397\) −17.7690 −0.891801 −0.445900 0.895083i \(-0.647116\pi\)
−0.445900 + 0.895083i \(0.647116\pi\)
\(398\) −2.95613 −0.148177
\(399\) −2.86993 −0.143676
\(400\) 1.10751 0.0553754
\(401\) −8.78872 −0.438888 −0.219444 0.975625i \(-0.570424\pi\)
−0.219444 + 0.975625i \(0.570424\pi\)
\(402\) −10.3705 −0.517233
\(403\) −16.8388 −0.838798
\(404\) −2.64209 −0.131449
\(405\) −27.4352 −1.36327
\(406\) −8.33499 −0.413659
\(407\) 5.87750 0.291337
\(408\) 1.57658 0.0780522
\(409\) 3.01022 0.148846 0.0744229 0.997227i \(-0.476289\pi\)
0.0744229 + 0.997227i \(0.476289\pi\)
\(410\) −16.3523 −0.807583
\(411\) 19.6032 0.966954
\(412\) 0.481843 0.0237387
\(413\) −2.45119 −0.120615
\(414\) −8.89527 −0.437179
\(415\) 33.9373 1.66592
\(416\) 3.04945 0.149512
\(417\) −12.5937 −0.616719
\(418\) −1.90125 −0.0929932
\(419\) −16.5426 −0.808157 −0.404079 0.914724i \(-0.632408\pi\)
−0.404079 + 0.914724i \(0.632408\pi\)
\(420\) −7.09256 −0.346081
\(421\) 0.785599 0.0382877 0.0191439 0.999817i \(-0.493906\pi\)
0.0191439 + 0.999817i \(0.493906\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −6.74236 −0.327825
\(424\) −3.46843 −0.168442
\(425\) −0.860806 −0.0417552
\(426\) 1.34219 0.0650292
\(427\) −16.4366 −0.795422
\(428\) 10.6017 0.512451
\(429\) 11.7603 0.567792
\(430\) 28.2885 1.36419
\(431\) 12.1340 0.584473 0.292237 0.956346i \(-0.405601\pi\)
0.292237 + 0.956346i \(0.405601\pi\)
\(432\) 3.82464 0.184013
\(433\) −18.7692 −0.901990 −0.450995 0.892527i \(-0.648931\pi\)
−0.450995 + 0.892527i \(0.648931\pi\)
\(434\) −7.81271 −0.375022
\(435\) 29.5311 1.41591
\(436\) −11.9045 −0.570124
\(437\) −7.98162 −0.381812
\(438\) 23.3332 1.11490
\(439\) −36.7958 −1.75617 −0.878084 0.478506i \(-0.841179\pi\)
−0.878084 + 0.478506i \(0.841179\pi\)
\(440\) −4.69863 −0.223998
\(441\) −5.57031 −0.265253
\(442\) −2.37018 −0.112738
\(443\) −25.3134 −1.20267 −0.601337 0.798995i \(-0.705365\pi\)
−0.601337 + 0.798995i \(0.705365\pi\)
\(444\) 6.27062 0.297590
\(445\) −13.0908 −0.620565
\(446\) −1.94987 −0.0923292
\(447\) −28.5152 −1.34872
\(448\) 1.41486 0.0668459
\(449\) −7.49329 −0.353630 −0.176815 0.984244i \(-0.556579\pi\)
−0.176815 + 0.984244i \(0.556579\pi\)
\(450\) 1.23428 0.0581847
\(451\) 12.5802 0.592377
\(452\) 3.01625 0.141872
\(453\) 17.4198 0.818451
\(454\) 10.1743 0.477505
\(455\) 10.6627 0.499876
\(456\) −2.02842 −0.0949893
\(457\) 10.7570 0.503193 0.251596 0.967832i \(-0.419044\pi\)
0.251596 + 0.967832i \(0.419044\pi\)
\(458\) −15.9728 −0.746359
\(459\) −2.97268 −0.138753
\(460\) −19.7253 −0.919695
\(461\) −17.7218 −0.825386 −0.412693 0.910870i \(-0.635412\pi\)
−0.412693 + 0.910870i \(0.635412\pi\)
\(462\) 5.45645 0.253857
\(463\) 18.3631 0.853404 0.426702 0.904392i \(-0.359675\pi\)
0.426702 + 0.904392i \(0.359675\pi\)
\(464\) −5.89103 −0.273484
\(465\) 27.6807 1.28366
\(466\) 1.97470 0.0914763
\(467\) −3.64293 −0.168575 −0.0842874 0.996441i \(-0.526861\pi\)
−0.0842874 + 0.996441i \(0.526861\pi\)
\(468\) 3.39852 0.157097
\(469\) 7.23363 0.334018
\(470\) −14.9512 −0.689647
\(471\) −20.7408 −0.955687
\(472\) −1.73246 −0.0797430
\(473\) −21.7629 −1.00066
\(474\) 31.9422 1.46715
\(475\) 1.10751 0.0508159
\(476\) −1.09970 −0.0504045
\(477\) −3.86546 −0.176987
\(478\) 4.17581 0.190997
\(479\) 10.6715 0.487592 0.243796 0.969827i \(-0.421607\pi\)
0.243796 + 0.969827i \(0.421607\pi\)
\(480\) −5.01290 −0.228806
\(481\) −9.42705 −0.429836
\(482\) −9.50085 −0.432752
\(483\) 22.9067 1.04229
\(484\) −7.38525 −0.335693
\(485\) 27.5704 1.25191
\(486\) 11.0443 0.500978
\(487\) 13.0919 0.593249 0.296624 0.954994i \(-0.404139\pi\)
0.296624 + 0.954994i \(0.404139\pi\)
\(488\) −11.6171 −0.525882
\(489\) 26.5305 1.19975
\(490\) −12.3522 −0.558014
\(491\) −13.4801 −0.608350 −0.304175 0.952616i \(-0.598381\pi\)
−0.304175 + 0.952616i \(0.598381\pi\)
\(492\) 13.4216 0.605092
\(493\) 4.57878 0.206218
\(494\) 3.04945 0.137201
\(495\) −5.23648 −0.235362
\(496\) −5.52189 −0.247940
\(497\) −0.936203 −0.0419944
\(498\) −27.8549 −1.24821
\(499\) −29.7634 −1.33239 −0.666197 0.745776i \(-0.732079\pi\)
−0.666197 + 0.745776i \(0.732079\pi\)
\(500\) −9.61966 −0.430204
\(501\) 45.9250 2.05178
\(502\) −2.77413 −0.123815
\(503\) −23.4365 −1.04498 −0.522492 0.852644i \(-0.674997\pi\)
−0.522492 + 0.852644i \(0.674997\pi\)
\(504\) 1.57682 0.0702372
\(505\) −6.52949 −0.290559
\(506\) 15.1750 0.674613
\(507\) 7.50683 0.333390
\(508\) 18.1456 0.805079
\(509\) 20.1337 0.892412 0.446206 0.894930i \(-0.352775\pi\)
0.446206 + 0.894930i \(0.352775\pi\)
\(510\) 3.89626 0.172529
\(511\) −16.2754 −0.719982
\(512\) 1.00000 0.0441942
\(513\) 3.82464 0.168862
\(514\) 13.3757 0.589975
\(515\) 1.19080 0.0524728
\(516\) −23.2186 −1.02214
\(517\) 11.5022 0.505868
\(518\) −4.37389 −0.192178
\(519\) −25.7009 −1.12814
\(520\) 7.53623 0.330485
\(521\) 9.00411 0.394477 0.197239 0.980356i \(-0.436803\pi\)
0.197239 + 0.980356i \(0.436803\pi\)
\(522\) −6.56538 −0.287359
\(523\) 10.0738 0.440495 0.220247 0.975444i \(-0.429314\pi\)
0.220247 + 0.975444i \(0.429314\pi\)
\(524\) 5.03267 0.219853
\(525\) −3.17847 −0.138720
\(526\) 5.46318 0.238206
\(527\) 4.29187 0.186957
\(528\) 3.85652 0.167834
\(529\) 40.7062 1.76983
\(530\) −8.57167 −0.372329
\(531\) −1.93078 −0.0837886
\(532\) 1.41486 0.0613420
\(533\) −20.1776 −0.873988
\(534\) 10.7446 0.464966
\(535\) 26.2003 1.13274
\(536\) 5.11260 0.220831
\(537\) −50.3726 −2.17374
\(538\) −5.59912 −0.241395
\(539\) 9.50276 0.409313
\(540\) 9.45197 0.406748
\(541\) 3.52908 0.151727 0.0758635 0.997118i \(-0.475829\pi\)
0.0758635 + 0.997118i \(0.475829\pi\)
\(542\) −6.95593 −0.298783
\(543\) 18.9507 0.813252
\(544\) −0.777246 −0.0333241
\(545\) −29.4201 −1.26022
\(546\) −8.75171 −0.374539
\(547\) −3.83335 −0.163902 −0.0819512 0.996636i \(-0.526115\pi\)
−0.0819512 + 0.996636i \(0.526115\pi\)
\(548\) −9.66429 −0.412838
\(549\) −12.9469 −0.552561
\(550\) −2.10565 −0.0897852
\(551\) −5.89103 −0.250966
\(552\) 16.1900 0.689094
\(553\) −22.2803 −0.947456
\(554\) 16.3010 0.692562
\(555\) 15.4968 0.657803
\(556\) 6.20866 0.263306
\(557\) −0.553697 −0.0234609 −0.0117304 0.999931i \(-0.503734\pi\)
−0.0117304 + 0.999931i \(0.503734\pi\)
\(558\) −6.15398 −0.260519
\(559\) 34.9060 1.47637
\(560\) 3.49660 0.147758
\(561\) −2.99747 −0.126553
\(562\) 25.7357 1.08559
\(563\) 8.85702 0.373279 0.186640 0.982428i \(-0.440240\pi\)
0.186640 + 0.982428i \(0.440240\pi\)
\(564\) 12.2716 0.516727
\(565\) 7.45416 0.313599
\(566\) 0.131593 0.00553128
\(567\) −15.7069 −0.659628
\(568\) −0.661692 −0.0277640
\(569\) 8.30103 0.347997 0.173999 0.984746i \(-0.444331\pi\)
0.173999 + 0.984746i \(0.444331\pi\)
\(570\) −5.01290 −0.209967
\(571\) −17.5829 −0.735823 −0.367912 0.929861i \(-0.619927\pi\)
−0.367912 + 0.929861i \(0.619927\pi\)
\(572\) −5.79777 −0.242417
\(573\) −42.4242 −1.77230
\(574\) −9.36183 −0.390755
\(575\) −8.83970 −0.368641
\(576\) 1.11447 0.0464362
\(577\) −18.3546 −0.764111 −0.382056 0.924139i \(-0.624784\pi\)
−0.382056 + 0.924139i \(0.624784\pi\)
\(578\) −16.3959 −0.681979
\(579\) 38.7748 1.61143
\(580\) −14.5587 −0.604518
\(581\) 19.4294 0.806067
\(582\) −22.6291 −0.938008
\(583\) 6.59436 0.273110
\(584\) −11.5032 −0.476005
\(585\) 8.39890 0.347252
\(586\) 3.62743 0.149848
\(587\) 15.9962 0.660233 0.330116 0.943940i \(-0.392912\pi\)
0.330116 + 0.943940i \(0.392912\pi\)
\(588\) 10.1384 0.418099
\(589\) −5.52189 −0.227526
\(590\) −4.28150 −0.176266
\(591\) −35.3903 −1.45576
\(592\) −3.09139 −0.127055
\(593\) −28.0311 −1.15110 −0.575550 0.817767i \(-0.695212\pi\)
−0.575550 + 0.817767i \(0.695212\pi\)
\(594\) −7.27159 −0.298357
\(595\) −2.71772 −0.111416
\(596\) 14.0579 0.575833
\(597\) 5.99625 0.245410
\(598\) −24.3396 −0.995319
\(599\) 8.11967 0.331761 0.165880 0.986146i \(-0.446953\pi\)
0.165880 + 0.986146i \(0.446953\pi\)
\(600\) −2.24649 −0.0917124
\(601\) −3.79839 −0.154940 −0.0774698 0.996995i \(-0.524684\pi\)
−0.0774698 + 0.996995i \(0.524684\pi\)
\(602\) 16.1954 0.660076
\(603\) 5.69784 0.232034
\(604\) −8.58786 −0.349435
\(605\) −18.2514 −0.742027
\(606\) 5.35925 0.217705
\(607\) −3.64245 −0.147842 −0.0739212 0.997264i \(-0.523551\pi\)
−0.0739212 + 0.997264i \(0.523551\pi\)
\(608\) 1.00000 0.0405554
\(609\) 16.9068 0.685099
\(610\) −28.7098 −1.16242
\(611\) −18.4487 −0.746354
\(612\) −0.866217 −0.0350148
\(613\) −44.5363 −1.79881 −0.899403 0.437120i \(-0.855998\pi\)
−0.899403 + 0.437120i \(0.855998\pi\)
\(614\) 0.382256 0.0154266
\(615\) 33.1693 1.33751
\(616\) −2.69001 −0.108383
\(617\) −36.8606 −1.48395 −0.741976 0.670426i \(-0.766111\pi\)
−0.741976 + 0.670426i \(0.766111\pi\)
\(618\) −0.977378 −0.0393159
\(619\) −44.3504 −1.78259 −0.891296 0.453421i \(-0.850203\pi\)
−0.891296 + 0.453421i \(0.850203\pi\)
\(620\) −13.6465 −0.548055
\(621\) −30.5268 −1.22500
\(622\) 14.8067 0.593696
\(623\) −7.49461 −0.300265
\(624\) −6.18556 −0.247621
\(625\) −29.3110 −1.17244
\(626\) −18.6361 −0.744847
\(627\) 3.85652 0.154015
\(628\) 10.2251 0.408027
\(629\) 2.40277 0.0958047
\(630\) 3.89686 0.155254
\(631\) −25.8963 −1.03092 −0.515458 0.856915i \(-0.672378\pi\)
−0.515458 + 0.856915i \(0.672378\pi\)
\(632\) −15.7474 −0.626396
\(633\) 2.02842 0.0806223
\(634\) 0.143542 0.00570078
\(635\) 44.8438 1.77957
\(636\) 7.03542 0.278973
\(637\) −15.2417 −0.603897
\(638\) 11.2003 0.443425
\(639\) −0.737436 −0.0291725
\(640\) 2.47134 0.0976882
\(641\) 14.8972 0.588404 0.294202 0.955743i \(-0.404946\pi\)
0.294202 + 0.955743i \(0.404946\pi\)
\(642\) −21.5046 −0.848719
\(643\) 10.8458 0.427717 0.213858 0.976865i \(-0.431397\pi\)
0.213858 + 0.976865i \(0.431397\pi\)
\(644\) −11.2929 −0.445002
\(645\) −57.3809 −2.25937
\(646\) −0.777246 −0.0305803
\(647\) −33.6114 −1.32140 −0.660700 0.750650i \(-0.729741\pi\)
−0.660700 + 0.750650i \(0.729741\pi\)
\(648\) −11.1014 −0.436103
\(649\) 3.29384 0.129295
\(650\) 3.37729 0.132468
\(651\) 15.8474 0.621110
\(652\) −13.0794 −0.512229
\(653\) −9.13589 −0.357515 −0.178757 0.983893i \(-0.557208\pi\)
−0.178757 + 0.983893i \(0.557208\pi\)
\(654\) 24.1474 0.944236
\(655\) 12.4374 0.485970
\(656\) −6.61679 −0.258342
\(657\) −12.8199 −0.500154
\(658\) −8.55968 −0.333691
\(659\) −6.11303 −0.238130 −0.119065 0.992886i \(-0.537990\pi\)
−0.119065 + 0.992886i \(0.537990\pi\)
\(660\) 9.53077 0.370985
\(661\) 33.6797 1.30999 0.654994 0.755634i \(-0.272671\pi\)
0.654994 + 0.755634i \(0.272671\pi\)
\(662\) −26.5807 −1.03309
\(663\) 4.80770 0.186716
\(664\) 13.7324 0.532919
\(665\) 3.49660 0.135592
\(666\) −3.44526 −0.133501
\(667\) 47.0200 1.82062
\(668\) −22.6408 −0.875999
\(669\) 3.95516 0.152915
\(670\) 12.6350 0.488131
\(671\) 22.0870 0.852660
\(672\) −2.86993 −0.110710
\(673\) 20.3592 0.784790 0.392395 0.919797i \(-0.371647\pi\)
0.392395 + 0.919797i \(0.371647\pi\)
\(674\) −8.74594 −0.336881
\(675\) 4.23582 0.163037
\(676\) −3.70083 −0.142340
\(677\) 7.62176 0.292928 0.146464 0.989216i \(-0.453211\pi\)
0.146464 + 0.989216i \(0.453211\pi\)
\(678\) −6.11820 −0.234968
\(679\) 15.7843 0.605746
\(680\) −1.92084 −0.0736607
\(681\) −20.6378 −0.790842
\(682\) 10.4985 0.402008
\(683\) 26.5582 1.01622 0.508111 0.861292i \(-0.330344\pi\)
0.508111 + 0.861292i \(0.330344\pi\)
\(684\) 1.11447 0.0426128
\(685\) −23.8837 −0.912550
\(686\) −16.9757 −0.648137
\(687\) 32.3995 1.23612
\(688\) 11.4467 0.436399
\(689\) −10.5768 −0.402945
\(690\) 40.0110 1.52319
\(691\) −40.5853 −1.54394 −0.771969 0.635660i \(-0.780728\pi\)
−0.771969 + 0.635660i \(0.780728\pi\)
\(692\) 12.6704 0.481658
\(693\) −2.99793 −0.113882
\(694\) −13.8668 −0.526376
\(695\) 15.3437 0.582020
\(696\) 11.9495 0.452943
\(697\) 5.14287 0.194800
\(698\) 7.60207 0.287743
\(699\) −4.00552 −0.151503
\(700\) 1.56697 0.0592259
\(701\) 27.6768 1.04534 0.522670 0.852535i \(-0.324936\pi\)
0.522670 + 0.852535i \(0.324936\pi\)
\(702\) 11.6631 0.440194
\(703\) −3.09139 −0.116594
\(704\) −1.90125 −0.0716560
\(705\) 30.3272 1.14219
\(706\) 5.74221 0.216111
\(707\) −3.73819 −0.140589
\(708\) 3.51415 0.132070
\(709\) 13.7299 0.515639 0.257820 0.966193i \(-0.416996\pi\)
0.257820 + 0.966193i \(0.416996\pi\)
\(710\) −1.63526 −0.0613704
\(711\) −17.5500 −0.658175
\(712\) −5.29706 −0.198516
\(713\) 44.0736 1.65057
\(714\) 2.23064 0.0834796
\(715\) −14.3283 −0.535846
\(716\) 24.8335 0.928070
\(717\) −8.47027 −0.316328
\(718\) −12.4080 −0.463062
\(719\) 11.3179 0.422088 0.211044 0.977477i \(-0.432314\pi\)
0.211044 + 0.977477i \(0.432314\pi\)
\(720\) 2.75423 0.102644
\(721\) 0.681741 0.0253894
\(722\) 1.00000 0.0372161
\(723\) 19.2717 0.716721
\(724\) −9.34261 −0.347215
\(725\) −6.52436 −0.242309
\(726\) 14.9804 0.555973
\(727\) 11.8370 0.439010 0.219505 0.975611i \(-0.429556\pi\)
0.219505 + 0.975611i \(0.429556\pi\)
\(728\) 4.31455 0.159908
\(729\) 10.9017 0.403768
\(730\) −28.4282 −1.05218
\(731\) −8.89686 −0.329062
\(732\) 23.5643 0.870962
\(733\) 27.3043 1.00851 0.504254 0.863555i \(-0.331768\pi\)
0.504254 + 0.863555i \(0.331768\pi\)
\(734\) −3.66093 −0.135127
\(735\) 25.0553 0.924179
\(736\) −7.98162 −0.294206
\(737\) −9.72034 −0.358053
\(738\) −7.37421 −0.271448
\(739\) 35.4056 1.30242 0.651208 0.758899i \(-0.274262\pi\)
0.651208 + 0.758899i \(0.274262\pi\)
\(740\) −7.63986 −0.280847
\(741\) −6.18556 −0.227232
\(742\) −4.90735 −0.180155
\(743\) −7.81352 −0.286650 −0.143325 0.989676i \(-0.545779\pi\)
−0.143325 + 0.989676i \(0.545779\pi\)
\(744\) 11.2007 0.410637
\(745\) 34.7418 1.27284
\(746\) −35.5897 −1.30303
\(747\) 15.3043 0.559955
\(748\) 1.47774 0.0540315
\(749\) 14.9999 0.548084
\(750\) 19.5127 0.712502
\(751\) −28.6632 −1.04593 −0.522967 0.852353i \(-0.675175\pi\)
−0.522967 + 0.852353i \(0.675175\pi\)
\(752\) −6.04983 −0.220615
\(753\) 5.62709 0.205062
\(754\) −17.9644 −0.654226
\(755\) −21.2235 −0.772402
\(756\) 5.41133 0.196808
\(757\) 38.3471 1.39375 0.696875 0.717192i \(-0.254573\pi\)
0.696875 + 0.717192i \(0.254573\pi\)
\(758\) 33.7772 1.22684
\(759\) −30.7813 −1.11729
\(760\) 2.47134 0.0896448
\(761\) 12.5038 0.453264 0.226632 0.973980i \(-0.427228\pi\)
0.226632 + 0.973980i \(0.427228\pi\)
\(762\) −36.8067 −1.33337
\(763\) −16.8433 −0.609768
\(764\) 20.9150 0.756677
\(765\) −2.14072 −0.0773977
\(766\) 25.0970 0.906792
\(767\) −5.28306 −0.190760
\(768\) −2.02842 −0.0731941
\(769\) −42.3418 −1.52688 −0.763442 0.645877i \(-0.776492\pi\)
−0.763442 + 0.645877i \(0.776492\pi\)
\(770\) −6.64791 −0.239574
\(771\) −27.1314 −0.977113
\(772\) −19.1158 −0.687993
\(773\) 21.5922 0.776619 0.388310 0.921529i \(-0.373059\pi\)
0.388310 + 0.921529i \(0.373059\pi\)
\(774\) 12.7569 0.458539
\(775\) −6.11554 −0.219677
\(776\) 11.1561 0.400480
\(777\) 8.87206 0.318283
\(778\) 14.8264 0.531553
\(779\) −6.61679 −0.237071
\(780\) −15.2866 −0.547348
\(781\) 1.25804 0.0450163
\(782\) 6.20368 0.221843
\(783\) −22.5311 −0.805195
\(784\) −4.99817 −0.178506
\(785\) 25.2698 0.901916
\(786\) −10.2083 −0.364119
\(787\) −15.4220 −0.549734 −0.274867 0.961482i \(-0.588634\pi\)
−0.274867 + 0.961482i \(0.588634\pi\)
\(788\) 17.4473 0.621534
\(789\) −11.0816 −0.394516
\(790\) −38.9170 −1.38461
\(791\) 4.26757 0.151737
\(792\) −2.11889 −0.0752913
\(793\) −35.4258 −1.25801
\(794\) −17.7690 −0.630598
\(795\) 17.3869 0.616650
\(796\) −2.95613 −0.104777
\(797\) 30.0978 1.06612 0.533060 0.846078i \(-0.321042\pi\)
0.533060 + 0.846078i \(0.321042\pi\)
\(798\) −2.86993 −0.101594
\(799\) 4.70221 0.166352
\(800\) 1.10751 0.0391563
\(801\) −5.90342 −0.208587
\(802\) −8.78872 −0.310341
\(803\) 21.8704 0.771790
\(804\) −10.3705 −0.365739
\(805\) −27.9085 −0.983646
\(806\) −16.8388 −0.593120
\(807\) 11.3573 0.399798
\(808\) −2.64209 −0.0929483
\(809\) −13.4974 −0.474542 −0.237271 0.971443i \(-0.576253\pi\)
−0.237271 + 0.971443i \(0.576253\pi\)
\(810\) −27.4352 −0.963975
\(811\) 30.4280 1.06847 0.534236 0.845335i \(-0.320599\pi\)
0.534236 + 0.845335i \(0.320599\pi\)
\(812\) −8.33499 −0.292501
\(813\) 14.1095 0.494843
\(814\) 5.87750 0.206006
\(815\) −32.3236 −1.13225
\(816\) 1.57658 0.0551913
\(817\) 11.4467 0.400468
\(818\) 3.01022 0.105250
\(819\) 4.80844 0.168021
\(820\) −16.3523 −0.571047
\(821\) 41.4936 1.44814 0.724069 0.689728i \(-0.242270\pi\)
0.724069 + 0.689728i \(0.242270\pi\)
\(822\) 19.6032 0.683740
\(823\) 25.7677 0.898205 0.449103 0.893480i \(-0.351744\pi\)
0.449103 + 0.893480i \(0.351744\pi\)
\(824\) 0.481843 0.0167858
\(825\) 4.27113 0.148702
\(826\) −2.45119 −0.0852879
\(827\) −42.4322 −1.47551 −0.737756 0.675068i \(-0.764114\pi\)
−0.737756 + 0.675068i \(0.764114\pi\)
\(828\) −8.89527 −0.309132
\(829\) −14.3266 −0.497583 −0.248792 0.968557i \(-0.580033\pi\)
−0.248792 + 0.968557i \(0.580033\pi\)
\(830\) 33.9373 1.17798
\(831\) −33.0651 −1.14702
\(832\) 3.04945 0.105721
\(833\) 3.88480 0.134601
\(834\) −12.5937 −0.436086
\(835\) −55.9531 −1.93634
\(836\) −1.90125 −0.0657561
\(837\) −21.1192 −0.729988
\(838\) −16.5426 −0.571454
\(839\) 5.05886 0.174651 0.0873257 0.996180i \(-0.472168\pi\)
0.0873257 + 0.996180i \(0.472168\pi\)
\(840\) −7.09256 −0.244717
\(841\) 5.70425 0.196698
\(842\) 0.785599 0.0270735
\(843\) −52.2027 −1.79796
\(844\) −1.00000 −0.0344214
\(845\) −9.14601 −0.314632
\(846\) −6.74236 −0.231807
\(847\) −10.4491 −0.359036
\(848\) −3.46843 −0.119106
\(849\) −0.266926 −0.00916087
\(850\) −0.860806 −0.0295254
\(851\) 24.6743 0.845823
\(852\) 1.34219 0.0459826
\(853\) 15.5422 0.532156 0.266078 0.963951i \(-0.414272\pi\)
0.266078 + 0.963951i \(0.414272\pi\)
\(854\) −16.4366 −0.562449
\(855\) 2.75423 0.0941927
\(856\) 10.6017 0.362358
\(857\) −0.110482 −0.00377400 −0.00188700 0.999998i \(-0.500601\pi\)
−0.00188700 + 0.999998i \(0.500601\pi\)
\(858\) 11.7603 0.401490
\(859\) −43.3466 −1.47897 −0.739484 0.673174i \(-0.764930\pi\)
−0.739484 + 0.673174i \(0.764930\pi\)
\(860\) 28.2885 0.964631
\(861\) 18.9897 0.647167
\(862\) 12.1340 0.413285
\(863\) 0.477080 0.0162400 0.00811999 0.999967i \(-0.497415\pi\)
0.00811999 + 0.999967i \(0.497415\pi\)
\(864\) 3.82464 0.130117
\(865\) 31.3129 1.06467
\(866\) −18.7692 −0.637803
\(867\) 33.2577 1.12949
\(868\) −7.81271 −0.265181
\(869\) 29.9397 1.01563
\(870\) 29.5311 1.00120
\(871\) 15.5906 0.528269
\(872\) −11.9045 −0.403139
\(873\) 12.4331 0.420797
\(874\) −7.98162 −0.269982
\(875\) −13.6105 −0.460118
\(876\) 23.3332 0.788357
\(877\) 16.5224 0.557922 0.278961 0.960302i \(-0.410010\pi\)
0.278961 + 0.960302i \(0.410010\pi\)
\(878\) −36.7958 −1.24180
\(879\) −7.35794 −0.248177
\(880\) −4.69863 −0.158391
\(881\) −20.8866 −0.703688 −0.351844 0.936059i \(-0.614445\pi\)
−0.351844 + 0.936059i \(0.614445\pi\)
\(882\) −5.57031 −0.187562
\(883\) −19.5105 −0.656580 −0.328290 0.944577i \(-0.606472\pi\)
−0.328290 + 0.944577i \(0.606472\pi\)
\(884\) −2.37018 −0.0797176
\(885\) 8.68466 0.291932
\(886\) −25.3134 −0.850420
\(887\) 18.4635 0.619944 0.309972 0.950746i \(-0.399680\pi\)
0.309972 + 0.950746i \(0.399680\pi\)
\(888\) 6.27062 0.210428
\(889\) 25.6735 0.861060
\(890\) −13.0908 −0.438806
\(891\) 21.1065 0.707093
\(892\) −1.94987 −0.0652866
\(893\) −6.04983 −0.202450
\(894\) −28.5152 −0.953692
\(895\) 61.3719 2.05144
\(896\) 1.41486 0.0472672
\(897\) 49.3708 1.64844
\(898\) −7.49329 −0.250054
\(899\) 32.5296 1.08492
\(900\) 1.23428 0.0411428
\(901\) 2.69582 0.0898109
\(902\) 12.5802 0.418874
\(903\) −32.8511 −1.09321
\(904\) 3.01625 0.100319
\(905\) −23.0887 −0.767496
\(906\) 17.4198 0.578732
\(907\) 59.4568 1.97423 0.987115 0.160014i \(-0.0511540\pi\)
0.987115 + 0.160014i \(0.0511540\pi\)
\(908\) 10.1743 0.337647
\(909\) −2.94453 −0.0976638
\(910\) 10.6627 0.353466
\(911\) −37.6820 −1.24846 −0.624230 0.781241i \(-0.714587\pi\)
−0.624230 + 0.781241i \(0.714587\pi\)
\(912\) −2.02842 −0.0671676
\(913\) −26.1087 −0.864070
\(914\) 10.7570 0.355811
\(915\) 58.2354 1.92520
\(916\) −15.9728 −0.527756
\(917\) 7.12053 0.235140
\(918\) −2.97268 −0.0981132
\(919\) −41.5015 −1.36901 −0.684505 0.729008i \(-0.739981\pi\)
−0.684505 + 0.729008i \(0.739981\pi\)
\(920\) −19.7253 −0.650323
\(921\) −0.775374 −0.0255494
\(922\) −17.7218 −0.583636
\(923\) −2.01780 −0.0664167
\(924\) 5.45645 0.179504
\(925\) −3.42374 −0.112572
\(926\) 18.3631 0.603448
\(927\) 0.537000 0.0176374
\(928\) −5.89103 −0.193383
\(929\) 26.0963 0.856190 0.428095 0.903734i \(-0.359185\pi\)
0.428095 + 0.903734i \(0.359185\pi\)
\(930\) 27.6807 0.907685
\(931\) −4.99817 −0.163808
\(932\) 1.97470 0.0646835
\(933\) −30.0342 −0.983277
\(934\) −3.64293 −0.119200
\(935\) 3.65199 0.119433
\(936\) 3.39852 0.111084
\(937\) −12.4921 −0.408099 −0.204049 0.978961i \(-0.565410\pi\)
−0.204049 + 0.978961i \(0.565410\pi\)
\(938\) 7.23363 0.236186
\(939\) 37.8017 1.23361
\(940\) −14.9512 −0.487654
\(941\) −8.05821 −0.262690 −0.131345 0.991337i \(-0.541930\pi\)
−0.131345 + 0.991337i \(0.541930\pi\)
\(942\) −20.7408 −0.675773
\(943\) 52.8126 1.71982
\(944\) −1.73246 −0.0563868
\(945\) 13.3732 0.435031
\(946\) −21.7629 −0.707574
\(947\) −24.0892 −0.782793 −0.391397 0.920222i \(-0.628008\pi\)
−0.391397 + 0.920222i \(0.628008\pi\)
\(948\) 31.9422 1.03743
\(949\) −35.0784 −1.13869
\(950\) 1.10751 0.0359323
\(951\) −0.291163 −0.00944160
\(952\) −1.09970 −0.0356413
\(953\) 43.3397 1.40391 0.701956 0.712221i \(-0.252310\pi\)
0.701956 + 0.712221i \(0.252310\pi\)
\(954\) −3.86546 −0.125149
\(955\) 51.6879 1.67258
\(956\) 4.17581 0.135055
\(957\) −22.7189 −0.734398
\(958\) 10.6715 0.344779
\(959\) −13.6736 −0.441544
\(960\) −5.01290 −0.161791
\(961\) −0.508718 −0.0164103
\(962\) −9.42705 −0.303940
\(963\) 11.8152 0.380741
\(964\) −9.50085 −0.306002
\(965\) −47.2416 −1.52076
\(966\) 22.9067 0.737010
\(967\) 21.8390 0.702295 0.351147 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(968\) −7.38525 −0.237371
\(969\) 1.57658 0.0506470
\(970\) 27.5704 0.885233
\(971\) −29.3389 −0.941530 −0.470765 0.882259i \(-0.656022\pi\)
−0.470765 + 0.882259i \(0.656022\pi\)
\(972\) 11.0443 0.354245
\(973\) 8.78440 0.281615
\(974\) 13.0919 0.419490
\(975\) −6.85055 −0.219393
\(976\) −11.6171 −0.371854
\(977\) 5.51365 0.176397 0.0881987 0.996103i \(-0.471889\pi\)
0.0881987 + 0.996103i \(0.471889\pi\)
\(978\) 26.5305 0.848351
\(979\) 10.0710 0.321872
\(980\) −12.3522 −0.394575
\(981\) −13.2673 −0.423591
\(982\) −13.4801 −0.430168
\(983\) −36.3953 −1.16083 −0.580416 0.814320i \(-0.697110\pi\)
−0.580416 + 0.814320i \(0.697110\pi\)
\(984\) 13.4216 0.427865
\(985\) 43.1181 1.37386
\(986\) 4.57878 0.145818
\(987\) 17.3626 0.552657
\(988\) 3.04945 0.0970160
\(989\) −91.3628 −2.90517
\(990\) −5.23648 −0.166426
\(991\) 5.69743 0.180985 0.0904924 0.995897i \(-0.471156\pi\)
0.0904924 + 0.995897i \(0.471156\pi\)
\(992\) −5.52189 −0.175320
\(993\) 53.9168 1.71100
\(994\) −0.936203 −0.0296945
\(995\) −7.30558 −0.231603
\(996\) −27.8549 −0.882618
\(997\) −1.79005 −0.0566916 −0.0283458 0.999598i \(-0.509024\pi\)
−0.0283458 + 0.999598i \(0.509024\pi\)
\(998\) −29.7634 −0.942145
\(999\) −11.8234 −0.374077
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 \(a_p\))