Properties

Label 8018.2.a.j.1.14
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 0
Dimension 47
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: \(0\)
Dimension: \(47\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-1.39823 q^{3}\) \(+1.00000 q^{4}\) \(+0.539425 q^{5}\) \(-1.39823 q^{6}\) \(+5.05784 q^{7}\) \(+1.00000 q^{8}\) \(-1.04494 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-1.39823 q^{3}\) \(+1.00000 q^{4}\) \(+0.539425 q^{5}\) \(-1.39823 q^{6}\) \(+5.05784 q^{7}\) \(+1.00000 q^{8}\) \(-1.04494 q^{9}\) \(+0.539425 q^{10}\) \(-1.12561 q^{11}\) \(-1.39823 q^{12}\) \(-2.68807 q^{13}\) \(+5.05784 q^{14}\) \(-0.754243 q^{15}\) \(+1.00000 q^{16}\) \(-4.30545 q^{17}\) \(-1.04494 q^{18}\) \(-1.00000 q^{19}\) \(+0.539425 q^{20}\) \(-7.07204 q^{21}\) \(-1.12561 q^{22}\) \(+7.92041 q^{23}\) \(-1.39823 q^{24}\) \(-4.70902 q^{25}\) \(-2.68807 q^{26}\) \(+5.65578 q^{27}\) \(+5.05784 q^{28}\) \(-0.281706 q^{29}\) \(-0.754243 q^{30}\) \(-6.56253 q^{31}\) \(+1.00000 q^{32}\) \(+1.57386 q^{33}\) \(-4.30545 q^{34}\) \(+2.72833 q^{35}\) \(-1.04494 q^{36}\) \(+1.71537 q^{37}\) \(-1.00000 q^{38}\) \(+3.75855 q^{39}\) \(+0.539425 q^{40}\) \(+0.408032 q^{41}\) \(-7.07204 q^{42}\) \(+5.34809 q^{43}\) \(-1.12561 q^{44}\) \(-0.563668 q^{45}\) \(+7.92041 q^{46}\) \(-3.58934 q^{47}\) \(-1.39823 q^{48}\) \(+18.5817 q^{49}\) \(-4.70902 q^{50}\) \(+6.02003 q^{51}\) \(-2.68807 q^{52}\) \(-3.58303 q^{53}\) \(+5.65578 q^{54}\) \(-0.607181 q^{55}\) \(+5.05784 q^{56}\) \(+1.39823 q^{57}\) \(-0.281706 q^{58}\) \(+8.94333 q^{59}\) \(-0.754243 q^{60}\) \(+13.1010 q^{61}\) \(-6.56253 q^{62}\) \(-5.28514 q^{63}\) \(+1.00000 q^{64}\) \(-1.45001 q^{65}\) \(+1.57386 q^{66}\) \(+7.49995 q^{67}\) \(-4.30545 q^{68}\) \(-11.0746 q^{69}\) \(+2.72833 q^{70}\) \(+9.98622 q^{71}\) \(-1.04494 q^{72}\) \(-7.18763 q^{73}\) \(+1.71537 q^{74}\) \(+6.58431 q^{75}\) \(-1.00000 q^{76}\) \(-5.69314 q^{77}\) \(+3.75855 q^{78}\) \(+16.4632 q^{79}\) \(+0.539425 q^{80}\) \(-4.77328 q^{81}\) \(+0.408032 q^{82}\) \(+7.00532 q^{83}\) \(-7.07204 q^{84}\) \(-2.32247 q^{85}\) \(+5.34809 q^{86}\) \(+0.393892 q^{87}\) \(-1.12561 q^{88}\) \(-4.37900 q^{89}\) \(-0.563668 q^{90}\) \(-13.5958 q^{91}\) \(+7.92041 q^{92}\) \(+9.17596 q^{93}\) \(-3.58934 q^{94}\) \(-0.539425 q^{95}\) \(-1.39823 q^{96}\) \(+12.0690 q^{97}\) \(+18.5817 q^{98}\) \(+1.17619 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 17q^{11} \) \(\mathstrut +\mathstrut 10q^{12} \) \(\mathstrut +\mathstrut 27q^{13} \) \(\mathstrut +\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 47q^{16} \) \(\mathstrut +\mathstrut 16q^{17} \) \(\mathstrut +\mathstrut 69q^{18} \) \(\mathstrut -\mathstrut 47q^{19} \) \(\mathstrut +\mathstrut 15q^{20} \) \(\mathstrut +\mathstrut 26q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 86q^{25} \) \(\mathstrut +\mathstrut 27q^{26} \) \(\mathstrut +\mathstrut 43q^{27} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 10q^{30} \) \(\mathstrut +\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 47q^{32} \) \(\mathstrut +\mathstrut 18q^{33} \) \(\mathstrut +\mathstrut 16q^{34} \) \(\mathstrut +\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 69q^{36} \) \(\mathstrut +\mathstrut 78q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 53q^{41} \) \(\mathstrut +\mathstrut 26q^{42} \) \(\mathstrut +\mathstrut 47q^{43} \) \(\mathstrut +\mathstrut 17q^{44} \) \(\mathstrut +\mathstrut 23q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 93q^{49} \) \(\mathstrut +\mathstrut 86q^{50} \) \(\mathstrut +\mathstrut 28q^{51} \) \(\mathstrut +\mathstrut 27q^{52} \) \(\mathstrut +\mathstrut 43q^{53} \) \(\mathstrut +\mathstrut 43q^{54} \) \(\mathstrut +\mathstrut 23q^{55} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 58q^{58} \) \(\mathstrut +\mathstrut 3q^{59} \) \(\mathstrut +\mathstrut 10q^{60} \) \(\mathstrut +\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 21q^{62} \) \(\mathstrut -\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 47q^{64} \) \(\mathstrut +\mathstrut 62q^{65} \) \(\mathstrut +\mathstrut 18q^{66} \) \(\mathstrut +\mathstrut 68q^{67} \) \(\mathstrut +\mathstrut 16q^{68} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 69q^{72} \) \(\mathstrut +\mathstrut 35q^{73} \) \(\mathstrut +\mathstrut 78q^{74} \) \(\mathstrut +\mathstrut 22q^{75} \) \(\mathstrut -\mathstrut 47q^{76} \) \(\mathstrut +\mathstrut 26q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut +\mathstrut 15q^{80} \) \(\mathstrut +\mathstrut 123q^{81} \) \(\mathstrut +\mathstrut 53q^{82} \) \(\mathstrut +\mathstrut 23q^{83} \) \(\mathstrut +\mathstrut 26q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut +\mathstrut 47q^{86} \) \(\mathstrut +\mathstrut 39q^{87} \) \(\mathstrut +\mathstrut 17q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut +\mathstrut 23q^{90} \) \(\mathstrut +\mathstrut 49q^{91} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 91q^{93} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut -\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut +\mathstrut 88q^{97} \) \(\mathstrut +\mathstrut 93q^{98} \) \(\mathstrut +\mathstrut 26q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.39823 −0.807271 −0.403635 0.914920i \(-0.632254\pi\)
−0.403635 + 0.914920i \(0.632254\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.539425 0.241238 0.120619 0.992699i \(-0.461512\pi\)
0.120619 + 0.992699i \(0.461512\pi\)
\(6\) −1.39823 −0.570827
\(7\) 5.05784 1.91168 0.955842 0.293883i \(-0.0949475\pi\)
0.955842 + 0.293883i \(0.0949475\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.04494 −0.348314
\(10\) 0.539425 0.170581
\(11\) −1.12561 −0.339383 −0.169692 0.985497i \(-0.554277\pi\)
−0.169692 + 0.985497i \(0.554277\pi\)
\(12\) −1.39823 −0.403635
\(13\) −2.68807 −0.745537 −0.372768 0.927924i \(-0.621591\pi\)
−0.372768 + 0.927924i \(0.621591\pi\)
\(14\) 5.05784 1.35176
\(15\) −0.754243 −0.194745
\(16\) 1.00000 0.250000
\(17\) −4.30545 −1.04423 −0.522113 0.852876i \(-0.674856\pi\)
−0.522113 + 0.852876i \(0.674856\pi\)
\(18\) −1.04494 −0.246295
\(19\) −1.00000 −0.229416
\(20\) 0.539425 0.120619
\(21\) −7.07204 −1.54325
\(22\) −1.12561 −0.239980
\(23\) 7.92041 1.65152 0.825760 0.564022i \(-0.190747\pi\)
0.825760 + 0.564022i \(0.190747\pi\)
\(24\) −1.39823 −0.285413
\(25\) −4.70902 −0.941804
\(26\) −2.68807 −0.527174
\(27\) 5.65578 1.08845
\(28\) 5.05784 0.955842
\(29\) −0.281706 −0.0523116 −0.0261558 0.999658i \(-0.508327\pi\)
−0.0261558 + 0.999658i \(0.508327\pi\)
\(30\) −0.754243 −0.137705
\(31\) −6.56253 −1.17867 −0.589333 0.807890i \(-0.700609\pi\)
−0.589333 + 0.807890i \(0.700609\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.57386 0.273974
\(34\) −4.30545 −0.738379
\(35\) 2.72833 0.461171
\(36\) −1.04494 −0.174157
\(37\) 1.71537 0.282005 0.141003 0.990009i \(-0.454967\pi\)
0.141003 + 0.990009i \(0.454967\pi\)
\(38\) −1.00000 −0.162221
\(39\) 3.75855 0.601850
\(40\) 0.539425 0.0852907
\(41\) 0.408032 0.0637239 0.0318620 0.999492i \(-0.489856\pi\)
0.0318620 + 0.999492i \(0.489856\pi\)
\(42\) −7.07204 −1.09124
\(43\) 5.34809 0.815576 0.407788 0.913077i \(-0.366300\pi\)
0.407788 + 0.913077i \(0.366300\pi\)
\(44\) −1.12561 −0.169692
\(45\) −0.563668 −0.0840266
\(46\) 7.92041 1.16780
\(47\) −3.58934 −0.523559 −0.261780 0.965128i \(-0.584309\pi\)
−0.261780 + 0.965128i \(0.584309\pi\)
\(48\) −1.39823 −0.201818
\(49\) 18.5817 2.65453
\(50\) −4.70902 −0.665956
\(51\) 6.02003 0.842973
\(52\) −2.68807 −0.372768
\(53\) −3.58303 −0.492167 −0.246084 0.969249i \(-0.579144\pi\)
−0.246084 + 0.969249i \(0.579144\pi\)
\(54\) 5.65578 0.769653
\(55\) −0.607181 −0.0818723
\(56\) 5.05784 0.675882
\(57\) 1.39823 0.185201
\(58\) −0.281706 −0.0369899
\(59\) 8.94333 1.16432 0.582161 0.813074i \(-0.302207\pi\)
0.582161 + 0.813074i \(0.302207\pi\)
\(60\) −0.754243 −0.0973724
\(61\) 13.1010 1.67741 0.838703 0.544589i \(-0.183314\pi\)
0.838703 + 0.544589i \(0.183314\pi\)
\(62\) −6.56253 −0.833443
\(63\) −5.28514 −0.665865
\(64\) 1.00000 0.125000
\(65\) −1.45001 −0.179852
\(66\) 1.57386 0.193729
\(67\) 7.49995 0.916265 0.458132 0.888884i \(-0.348519\pi\)
0.458132 + 0.888884i \(0.348519\pi\)
\(68\) −4.30545 −0.522113
\(69\) −11.0746 −1.33322
\(70\) 2.72833 0.326097
\(71\) 9.98622 1.18515 0.592573 0.805517i \(-0.298112\pi\)
0.592573 + 0.805517i \(0.298112\pi\)
\(72\) −1.04494 −0.123147
\(73\) −7.18763 −0.841248 −0.420624 0.907235i \(-0.638189\pi\)
−0.420624 + 0.907235i \(0.638189\pi\)
\(74\) 1.71537 0.199408
\(75\) 6.58431 0.760291
\(76\) −1.00000 −0.114708
\(77\) −5.69314 −0.648793
\(78\) 3.75855 0.425572
\(79\) 16.4632 1.85226 0.926129 0.377206i \(-0.123115\pi\)
0.926129 + 0.377206i \(0.123115\pi\)
\(80\) 0.539425 0.0603096
\(81\) −4.77328 −0.530364
\(82\) 0.408032 0.0450596
\(83\) 7.00532 0.768933 0.384467 0.923139i \(-0.374385\pi\)
0.384467 + 0.923139i \(0.374385\pi\)
\(84\) −7.07204 −0.771623
\(85\) −2.32247 −0.251907
\(86\) 5.34809 0.576699
\(87\) 0.393892 0.0422296
\(88\) −1.12561 −0.119990
\(89\) −4.37900 −0.464173 −0.232086 0.972695i \(-0.574555\pi\)
−0.232086 + 0.972695i \(0.574555\pi\)
\(90\) −0.563668 −0.0594158
\(91\) −13.5958 −1.42523
\(92\) 7.92041 0.825760
\(93\) 9.17596 0.951503
\(94\) −3.58934 −0.370212
\(95\) −0.539425 −0.0553439
\(96\) −1.39823 −0.142707
\(97\) 12.0690 1.22542 0.612709 0.790309i \(-0.290080\pi\)
0.612709 + 0.790309i \(0.290080\pi\)
\(98\) 18.5817 1.87704
\(99\) 1.17619 0.118212
\(100\) −4.70902 −0.470902
\(101\) 1.21217 0.120616 0.0603079 0.998180i \(-0.480792\pi\)
0.0603079 + 0.998180i \(0.480792\pi\)
\(102\) 6.02003 0.596072
\(103\) 17.1286 1.68773 0.843863 0.536558i \(-0.180276\pi\)
0.843863 + 0.536558i \(0.180276\pi\)
\(104\) −2.68807 −0.263587
\(105\) −3.81484 −0.372290
\(106\) −3.58303 −0.348015
\(107\) 5.75691 0.556541 0.278271 0.960503i \(-0.410239\pi\)
0.278271 + 0.960503i \(0.410239\pi\)
\(108\) 5.65578 0.544227
\(109\) 1.63885 0.156973 0.0784865 0.996915i \(-0.474991\pi\)
0.0784865 + 0.996915i \(0.474991\pi\)
\(110\) −0.607181 −0.0578924
\(111\) −2.39849 −0.227655
\(112\) 5.05784 0.477921
\(113\) −2.73876 −0.257641 −0.128821 0.991668i \(-0.541119\pi\)
−0.128821 + 0.991668i \(0.541119\pi\)
\(114\) 1.39823 0.130957
\(115\) 4.27247 0.398410
\(116\) −0.281706 −0.0261558
\(117\) 2.80888 0.259681
\(118\) 8.94333 0.823300
\(119\) −21.7763 −1.99623
\(120\) −0.754243 −0.0688527
\(121\) −9.73301 −0.884819
\(122\) 13.1010 1.18611
\(123\) −0.570524 −0.0514425
\(124\) −6.56253 −0.589333
\(125\) −5.23729 −0.468438
\(126\) −5.28514 −0.470838
\(127\) 15.1724 1.34633 0.673166 0.739492i \(-0.264934\pi\)
0.673166 + 0.739492i \(0.264934\pi\)
\(128\) 1.00000 0.0883883
\(129\) −7.47788 −0.658391
\(130\) −1.45001 −0.127175
\(131\) 17.8014 1.55531 0.777656 0.628690i \(-0.216409\pi\)
0.777656 + 0.628690i \(0.216409\pi\)
\(132\) 1.57386 0.136987
\(133\) −5.05784 −0.438570
\(134\) 7.49995 0.647897
\(135\) 3.05087 0.262577
\(136\) −4.30545 −0.369190
\(137\) −6.31444 −0.539479 −0.269740 0.962933i \(-0.586938\pi\)
−0.269740 + 0.962933i \(0.586938\pi\)
\(138\) −11.0746 −0.942731
\(139\) −4.18766 −0.355193 −0.177596 0.984103i \(-0.556832\pi\)
−0.177596 + 0.984103i \(0.556832\pi\)
\(140\) 2.72833 0.230586
\(141\) 5.01874 0.422654
\(142\) 9.98622 0.838025
\(143\) 3.02571 0.253023
\(144\) −1.04494 −0.0870784
\(145\) −0.151960 −0.0126196
\(146\) −7.18763 −0.594852
\(147\) −25.9816 −2.14293
\(148\) 1.71537 0.141003
\(149\) −13.0258 −1.06712 −0.533558 0.845763i \(-0.679146\pi\)
−0.533558 + 0.845763i \(0.679146\pi\)
\(150\) 6.58431 0.537607
\(151\) −0.626724 −0.0510021 −0.0255010 0.999675i \(-0.508118\pi\)
−0.0255010 + 0.999675i \(0.508118\pi\)
\(152\) −1.00000 −0.0811107
\(153\) 4.49895 0.363718
\(154\) −5.69314 −0.458766
\(155\) −3.54000 −0.284340
\(156\) 3.75855 0.300925
\(157\) −6.57277 −0.524564 −0.262282 0.964991i \(-0.584475\pi\)
−0.262282 + 0.964991i \(0.584475\pi\)
\(158\) 16.4632 1.30974
\(159\) 5.00992 0.397312
\(160\) 0.539425 0.0426453
\(161\) 40.0601 3.15718
\(162\) −4.77328 −0.375024
\(163\) 7.39921 0.579551 0.289776 0.957095i \(-0.406419\pi\)
0.289776 + 0.957095i \(0.406419\pi\)
\(164\) 0.408032 0.0318620
\(165\) 0.848981 0.0660931
\(166\) 7.00532 0.543718
\(167\) −15.1677 −1.17371 −0.586855 0.809692i \(-0.699634\pi\)
−0.586855 + 0.809692i \(0.699634\pi\)
\(168\) −7.07204 −0.545620
\(169\) −5.77428 −0.444175
\(170\) −2.32247 −0.178125
\(171\) 1.04494 0.0799086
\(172\) 5.34809 0.407788
\(173\) −15.7761 −1.19944 −0.599719 0.800211i \(-0.704721\pi\)
−0.599719 + 0.800211i \(0.704721\pi\)
\(174\) 0.393892 0.0298608
\(175\) −23.8175 −1.80043
\(176\) −1.12561 −0.0848458
\(177\) −12.5049 −0.939923
\(178\) −4.37900 −0.328220
\(179\) 0.905811 0.0677035 0.0338518 0.999427i \(-0.489223\pi\)
0.0338518 + 0.999427i \(0.489223\pi\)
\(180\) −0.563668 −0.0420133
\(181\) −16.8041 −1.24904 −0.624518 0.781010i \(-0.714705\pi\)
−0.624518 + 0.781010i \(0.714705\pi\)
\(182\) −13.5958 −1.00779
\(183\) −18.3182 −1.35412
\(184\) 7.92041 0.583900
\(185\) 0.925314 0.0680305
\(186\) 9.17596 0.672814
\(187\) 4.84625 0.354393
\(188\) −3.58934 −0.261780
\(189\) 28.6060 2.08078
\(190\) −0.539425 −0.0391340
\(191\) −9.56666 −0.692219 −0.346109 0.938194i \(-0.612497\pi\)
−0.346109 + 0.938194i \(0.612497\pi\)
\(192\) −1.39823 −0.100909
\(193\) 19.2576 1.38619 0.693097 0.720844i \(-0.256246\pi\)
0.693097 + 0.720844i \(0.256246\pi\)
\(194\) 12.0690 0.866501
\(195\) 2.02746 0.145189
\(196\) 18.5817 1.32727
\(197\) 14.0935 1.00412 0.502060 0.864833i \(-0.332576\pi\)
0.502060 + 0.864833i \(0.332576\pi\)
\(198\) 1.17619 0.0835884
\(199\) 1.07616 0.0762872 0.0381436 0.999272i \(-0.487856\pi\)
0.0381436 + 0.999272i \(0.487856\pi\)
\(200\) −4.70902 −0.332978
\(201\) −10.4867 −0.739674
\(202\) 1.21217 0.0852882
\(203\) −1.42483 −0.100003
\(204\) 6.02003 0.421487
\(205\) 0.220103 0.0153727
\(206\) 17.1286 1.19340
\(207\) −8.27636 −0.575247
\(208\) −2.68807 −0.186384
\(209\) 1.12561 0.0778598
\(210\) −3.81484 −0.263249
\(211\) −1.00000 −0.0688428
\(212\) −3.58303 −0.246084
\(213\) −13.9631 −0.956734
\(214\) 5.75691 0.393534
\(215\) 2.88489 0.196748
\(216\) 5.65578 0.384827
\(217\) −33.1922 −2.25324
\(218\) 1.63885 0.110997
\(219\) 10.0500 0.679115
\(220\) −0.607181 −0.0409361
\(221\) 11.5734 0.778509
\(222\) −2.39849 −0.160976
\(223\) 9.95413 0.666578 0.333289 0.942825i \(-0.391842\pi\)
0.333289 + 0.942825i \(0.391842\pi\)
\(224\) 5.05784 0.337941
\(225\) 4.92065 0.328043
\(226\) −2.73876 −0.182180
\(227\) 25.9588 1.72295 0.861474 0.507801i \(-0.169542\pi\)
0.861474 + 0.507801i \(0.169542\pi\)
\(228\) 1.39823 0.0926003
\(229\) −4.86224 −0.321306 −0.160653 0.987011i \(-0.551360\pi\)
−0.160653 + 0.987011i \(0.551360\pi\)
\(230\) 4.27247 0.281718
\(231\) 7.96034 0.523752
\(232\) −0.281706 −0.0184949
\(233\) 3.48455 0.228280 0.114140 0.993465i \(-0.463589\pi\)
0.114140 + 0.993465i \(0.463589\pi\)
\(234\) 2.80888 0.183622
\(235\) −1.93618 −0.126303
\(236\) 8.94333 0.582161
\(237\) −23.0195 −1.49527
\(238\) −21.7763 −1.41155
\(239\) −23.5249 −1.52170 −0.760848 0.648930i \(-0.775217\pi\)
−0.760848 + 0.648930i \(0.775217\pi\)
\(240\) −0.754243 −0.0486862
\(241\) 14.2840 0.920116 0.460058 0.887889i \(-0.347829\pi\)
0.460058 + 0.887889i \(0.347829\pi\)
\(242\) −9.73301 −0.625662
\(243\) −10.2932 −0.660307
\(244\) 13.1010 0.838703
\(245\) 10.0235 0.640375
\(246\) −0.570524 −0.0363753
\(247\) 2.68807 0.171038
\(248\) −6.56253 −0.416721
\(249\) −9.79507 −0.620738
\(250\) −5.23729 −0.331235
\(251\) −5.37276 −0.339126 −0.169563 0.985519i \(-0.554236\pi\)
−0.169563 + 0.985519i \(0.554236\pi\)
\(252\) −5.28514 −0.332933
\(253\) −8.91526 −0.560498
\(254\) 15.1724 0.952000
\(255\) 3.24736 0.203358
\(256\) 1.00000 0.0625000
\(257\) −2.19233 −0.136754 −0.0683770 0.997660i \(-0.521782\pi\)
−0.0683770 + 0.997660i \(0.521782\pi\)
\(258\) −7.47788 −0.465552
\(259\) 8.67606 0.539104
\(260\) −1.45001 −0.0899260
\(261\) 0.294367 0.0182208
\(262\) 17.8014 1.09977
\(263\) 31.8437 1.96357 0.981785 0.189998i \(-0.0608481\pi\)
0.981785 + 0.189998i \(0.0608481\pi\)
\(264\) 1.57386 0.0968645
\(265\) −1.93278 −0.118730
\(266\) −5.05784 −0.310116
\(267\) 6.12287 0.374713
\(268\) 7.49995 0.458132
\(269\) 17.6913 1.07866 0.539330 0.842095i \(-0.318678\pi\)
0.539330 + 0.842095i \(0.318678\pi\)
\(270\) 3.05087 0.185670
\(271\) 8.78563 0.533689 0.266845 0.963740i \(-0.414019\pi\)
0.266845 + 0.963740i \(0.414019\pi\)
\(272\) −4.30545 −0.261056
\(273\) 19.0101 1.15055
\(274\) −6.31444 −0.381469
\(275\) 5.30050 0.319632
\(276\) −11.0746 −0.666612
\(277\) −21.3490 −1.28274 −0.641368 0.767233i \(-0.721633\pi\)
−0.641368 + 0.767233i \(0.721633\pi\)
\(278\) −4.18766 −0.251159
\(279\) 6.85746 0.410546
\(280\) 2.72833 0.163049
\(281\) 0.534356 0.0318770 0.0159385 0.999873i \(-0.494926\pi\)
0.0159385 + 0.999873i \(0.494926\pi\)
\(282\) 5.01874 0.298862
\(283\) −11.9700 −0.711541 −0.355771 0.934573i \(-0.615782\pi\)
−0.355771 + 0.934573i \(0.615782\pi\)
\(284\) 9.98622 0.592573
\(285\) 0.754243 0.0446775
\(286\) 3.02571 0.178914
\(287\) 2.06376 0.121820
\(288\) −1.04494 −0.0615737
\(289\) 1.53693 0.0904077
\(290\) −0.151960 −0.00892338
\(291\) −16.8752 −0.989244
\(292\) −7.18763 −0.420624
\(293\) −16.8883 −0.986625 −0.493313 0.869852i \(-0.664214\pi\)
−0.493313 + 0.869852i \(0.664214\pi\)
\(294\) −25.9816 −1.51528
\(295\) 4.82426 0.280879
\(296\) 1.71537 0.0997039
\(297\) −6.36618 −0.369403
\(298\) −13.0258 −0.754565
\(299\) −21.2906 −1.23127
\(300\) 6.58431 0.380145
\(301\) 27.0498 1.55912
\(302\) −0.626724 −0.0360639
\(303\) −1.69490 −0.0973696
\(304\) −1.00000 −0.0573539
\(305\) 7.06699 0.404655
\(306\) 4.49895 0.257188
\(307\) −19.8836 −1.13482 −0.567408 0.823437i \(-0.692054\pi\)
−0.567408 + 0.823437i \(0.692054\pi\)
\(308\) −5.69314 −0.324397
\(309\) −23.9497 −1.36245
\(310\) −3.54000 −0.201058
\(311\) 8.70171 0.493428 0.246714 0.969088i \(-0.420649\pi\)
0.246714 + 0.969088i \(0.420649\pi\)
\(312\) 3.75855 0.212786
\(313\) −23.2841 −1.31610 −0.658049 0.752975i \(-0.728618\pi\)
−0.658049 + 0.752975i \(0.728618\pi\)
\(314\) −6.57277 −0.370923
\(315\) −2.85094 −0.160632
\(316\) 16.4632 0.926129
\(317\) −1.08251 −0.0607997 −0.0303998 0.999538i \(-0.509678\pi\)
−0.0303998 + 0.999538i \(0.509678\pi\)
\(318\) 5.00992 0.280942
\(319\) 0.317091 0.0177537
\(320\) 0.539425 0.0301548
\(321\) −8.04951 −0.449280
\(322\) 40.0601 2.23246
\(323\) 4.30545 0.239562
\(324\) −4.77328 −0.265182
\(325\) 12.6582 0.702149
\(326\) 7.39921 0.409804
\(327\) −2.29149 −0.126720
\(328\) 0.408032 0.0225298
\(329\) −18.1543 −1.00088
\(330\) 0.848981 0.0467349
\(331\) 29.4757 1.62013 0.810064 0.586341i \(-0.199432\pi\)
0.810064 + 0.586341i \(0.199432\pi\)
\(332\) 7.00532 0.384467
\(333\) −1.79246 −0.0982262
\(334\) −15.1677 −0.829938
\(335\) 4.04566 0.221038
\(336\) −7.07204 −0.385812
\(337\) −8.97516 −0.488908 −0.244454 0.969661i \(-0.578609\pi\)
−0.244454 + 0.969661i \(0.578609\pi\)
\(338\) −5.77428 −0.314079
\(339\) 3.82943 0.207986
\(340\) −2.32247 −0.125954
\(341\) 7.38683 0.400019
\(342\) 1.04494 0.0565039
\(343\) 58.5785 3.16294
\(344\) 5.34809 0.288350
\(345\) −5.97391 −0.321625
\(346\) −15.7761 −0.848131
\(347\) 26.4970 1.42244 0.711218 0.702971i \(-0.248144\pi\)
0.711218 + 0.702971i \(0.248144\pi\)
\(348\) 0.393892 0.0211148
\(349\) −4.60150 −0.246312 −0.123156 0.992387i \(-0.539302\pi\)
−0.123156 + 0.992387i \(0.539302\pi\)
\(350\) −23.8175 −1.27310
\(351\) −15.2031 −0.811483
\(352\) −1.12561 −0.0599950
\(353\) −3.77583 −0.200967 −0.100484 0.994939i \(-0.532039\pi\)
−0.100484 + 0.994939i \(0.532039\pi\)
\(354\) −12.5049 −0.664626
\(355\) 5.38682 0.285903
\(356\) −4.37900 −0.232086
\(357\) 30.4484 1.61150
\(358\) 0.905811 0.0478736
\(359\) −21.5307 −1.13635 −0.568173 0.822909i \(-0.692350\pi\)
−0.568173 + 0.822909i \(0.692350\pi\)
\(360\) −0.563668 −0.0297079
\(361\) 1.00000 0.0526316
\(362\) −16.8041 −0.883203
\(363\) 13.6090 0.714289
\(364\) −13.5958 −0.712615
\(365\) −3.87719 −0.202941
\(366\) −18.3182 −0.957508
\(367\) −21.8841 −1.14234 −0.571170 0.820832i \(-0.693510\pi\)
−0.571170 + 0.820832i \(0.693510\pi\)
\(368\) 7.92041 0.412880
\(369\) −0.426370 −0.0221959
\(370\) 0.925314 0.0481048
\(371\) −18.1224 −0.940867
\(372\) 9.17596 0.475751
\(373\) 13.7549 0.712203 0.356102 0.934447i \(-0.384106\pi\)
0.356102 + 0.934447i \(0.384106\pi\)
\(374\) 4.84625 0.250593
\(375\) 7.32296 0.378156
\(376\) −3.58934 −0.185106
\(377\) 0.757247 0.0390002
\(378\) 28.6060 1.47133
\(379\) −5.18809 −0.266494 −0.133247 0.991083i \(-0.542540\pi\)
−0.133247 + 0.991083i \(0.542540\pi\)
\(380\) −0.539425 −0.0276719
\(381\) −21.2145 −1.08685
\(382\) −9.56666 −0.489473
\(383\) 32.9761 1.68500 0.842499 0.538697i \(-0.181083\pi\)
0.842499 + 0.538697i \(0.181083\pi\)
\(384\) −1.39823 −0.0713533
\(385\) −3.07102 −0.156514
\(386\) 19.2576 0.980188
\(387\) −5.58844 −0.284076
\(388\) 12.0690 0.612709
\(389\) 11.2758 0.571707 0.285854 0.958273i \(-0.407723\pi\)
0.285854 + 0.958273i \(0.407723\pi\)
\(390\) 2.02746 0.102664
\(391\) −34.1010 −1.72456
\(392\) 18.5817 0.938519
\(393\) −24.8905 −1.25556
\(394\) 14.0935 0.710020
\(395\) 8.88069 0.446836
\(396\) 1.17619 0.0591059
\(397\) −15.9178 −0.798893 −0.399446 0.916757i \(-0.630798\pi\)
−0.399446 + 0.916757i \(0.630798\pi\)
\(398\) 1.07616 0.0539432
\(399\) 7.07204 0.354045
\(400\) −4.70902 −0.235451
\(401\) 30.8843 1.54229 0.771143 0.636662i \(-0.219685\pi\)
0.771143 + 0.636662i \(0.219685\pi\)
\(402\) −10.4867 −0.523028
\(403\) 17.6406 0.878739
\(404\) 1.21217 0.0603079
\(405\) −2.57483 −0.127944
\(406\) −1.42483 −0.0707129
\(407\) −1.93083 −0.0957078
\(408\) 6.02003 0.298036
\(409\) 35.8549 1.77291 0.886455 0.462814i \(-0.153160\pi\)
0.886455 + 0.462814i \(0.153160\pi\)
\(410\) 0.220103 0.0108701
\(411\) 8.82907 0.435506
\(412\) 17.1286 0.843863
\(413\) 45.2339 2.22581
\(414\) −8.27636 −0.406761
\(415\) 3.77885 0.185496
\(416\) −2.68807 −0.131794
\(417\) 5.85533 0.286737
\(418\) 1.12561 0.0550552
\(419\) −25.3099 −1.23647 −0.618234 0.785994i \(-0.712152\pi\)
−0.618234 + 0.785994i \(0.712152\pi\)
\(420\) −3.81484 −0.186145
\(421\) 35.4253 1.72653 0.863263 0.504755i \(-0.168417\pi\)
0.863263 + 0.504755i \(0.168417\pi\)
\(422\) −1.00000 −0.0486792
\(423\) 3.75065 0.182363
\(424\) −3.58303 −0.174007
\(425\) 20.2745 0.983456
\(426\) −13.9631 −0.676513
\(427\) 66.2625 3.20667
\(428\) 5.75691 0.278271
\(429\) −4.23065 −0.204258
\(430\) 2.88489 0.139122
\(431\) 31.1751 1.50165 0.750825 0.660501i \(-0.229656\pi\)
0.750825 + 0.660501i \(0.229656\pi\)
\(432\) 5.65578 0.272114
\(433\) −28.5507 −1.37206 −0.686030 0.727574i \(-0.740648\pi\)
−0.686030 + 0.727574i \(0.740648\pi\)
\(434\) −33.1922 −1.59328
\(435\) 0.212475 0.0101874
\(436\) 1.63885 0.0784865
\(437\) −7.92041 −0.378885
\(438\) 10.0500 0.480207
\(439\) −25.6159 −1.22258 −0.611291 0.791406i \(-0.709350\pi\)
−0.611291 + 0.791406i \(0.709350\pi\)
\(440\) −0.607181 −0.0289462
\(441\) −19.4168 −0.924610
\(442\) 11.5734 0.550489
\(443\) 16.4574 0.781915 0.390957 0.920409i \(-0.372144\pi\)
0.390957 + 0.920409i \(0.372144\pi\)
\(444\) −2.39849 −0.113827
\(445\) −2.36214 −0.111976
\(446\) 9.95413 0.471342
\(447\) 18.2131 0.861452
\(448\) 5.05784 0.238960
\(449\) −6.37899 −0.301043 −0.150522 0.988607i \(-0.548095\pi\)
−0.150522 + 0.988607i \(0.548095\pi\)
\(450\) 4.92065 0.231962
\(451\) −0.459284 −0.0216268
\(452\) −2.73876 −0.128821
\(453\) 0.876307 0.0411725
\(454\) 25.9588 1.21831
\(455\) −7.33393 −0.343820
\(456\) 1.39823 0.0654783
\(457\) −17.7167 −0.828750 −0.414375 0.910106i \(-0.636000\pi\)
−0.414375 + 0.910106i \(0.636000\pi\)
\(458\) −4.86224 −0.227198
\(459\) −24.3507 −1.13659
\(460\) 4.27247 0.199205
\(461\) −11.1057 −0.517242 −0.258621 0.965979i \(-0.583268\pi\)
−0.258621 + 0.965979i \(0.583268\pi\)
\(462\) 7.96034 0.370348
\(463\) −20.2349 −0.940397 −0.470199 0.882561i \(-0.655818\pi\)
−0.470199 + 0.882561i \(0.655818\pi\)
\(464\) −0.281706 −0.0130779
\(465\) 4.94975 0.229539
\(466\) 3.48455 0.161418
\(467\) −33.9185 −1.56956 −0.784781 0.619773i \(-0.787225\pi\)
−0.784781 + 0.619773i \(0.787225\pi\)
\(468\) 2.80888 0.129840
\(469\) 37.9335 1.75161
\(470\) −1.93618 −0.0893094
\(471\) 9.19027 0.423465
\(472\) 8.94333 0.411650
\(473\) −6.01984 −0.276793
\(474\) −23.0195 −1.05732
\(475\) 4.70902 0.216065
\(476\) −21.7763 −0.998114
\(477\) 3.74406 0.171429
\(478\) −23.5249 −1.07600
\(479\) 15.7058 0.717614 0.358807 0.933412i \(-0.383184\pi\)
0.358807 + 0.933412i \(0.383184\pi\)
\(480\) −0.754243 −0.0344263
\(481\) −4.61104 −0.210245
\(482\) 14.2840 0.650620
\(483\) −56.0135 −2.54870
\(484\) −9.73301 −0.442410
\(485\) 6.51031 0.295618
\(486\) −10.2932 −0.466908
\(487\) −17.2930 −0.783618 −0.391809 0.920046i \(-0.628151\pi\)
−0.391809 + 0.920046i \(0.628151\pi\)
\(488\) 13.1010 0.593053
\(489\) −10.3458 −0.467855
\(490\) 10.0235 0.452814
\(491\) 25.0354 1.12983 0.564917 0.825148i \(-0.308908\pi\)
0.564917 + 0.825148i \(0.308908\pi\)
\(492\) −0.570524 −0.0257212
\(493\) 1.21287 0.0546251
\(494\) 2.68807 0.120942
\(495\) 0.634468 0.0285172
\(496\) −6.56253 −0.294667
\(497\) 50.5087 2.26562
\(498\) −9.79507 −0.438928
\(499\) 32.2250 1.44259 0.721295 0.692628i \(-0.243547\pi\)
0.721295 + 0.692628i \(0.243547\pi\)
\(500\) −5.23729 −0.234219
\(501\) 21.2080 0.947501
\(502\) −5.37276 −0.239798
\(503\) −15.4035 −0.686808 −0.343404 0.939188i \(-0.611580\pi\)
−0.343404 + 0.939188i \(0.611580\pi\)
\(504\) −5.28514 −0.235419
\(505\) 0.653877 0.0290971
\(506\) −8.91526 −0.396332
\(507\) 8.07379 0.358570
\(508\) 15.1724 0.673166
\(509\) −29.0628 −1.28818 −0.644092 0.764948i \(-0.722765\pi\)
−0.644092 + 0.764948i \(0.722765\pi\)
\(510\) 3.24736 0.143795
\(511\) −36.3538 −1.60820
\(512\) 1.00000 0.0441942
\(513\) −5.65578 −0.249709
\(514\) −2.19233 −0.0966997
\(515\) 9.23958 0.407144
\(516\) −7.47788 −0.329195
\(517\) 4.04019 0.177687
\(518\) 8.67606 0.381204
\(519\) 22.0587 0.968272
\(520\) −1.45001 −0.0635873
\(521\) −19.6781 −0.862113 −0.431057 0.902325i \(-0.641859\pi\)
−0.431057 + 0.902325i \(0.641859\pi\)
\(522\) 0.294367 0.0128841
\(523\) 28.6016 1.25066 0.625330 0.780360i \(-0.284964\pi\)
0.625330 + 0.780360i \(0.284964\pi\)
\(524\) 17.8014 0.777656
\(525\) 33.3024 1.45344
\(526\) 31.8437 1.38845
\(527\) 28.2547 1.23079
\(528\) 1.57386 0.0684935
\(529\) 39.7329 1.72752
\(530\) −1.93278 −0.0839545
\(531\) −9.34525 −0.405549
\(532\) −5.05784 −0.219285
\(533\) −1.09682 −0.0475085
\(534\) 6.12287 0.264962
\(535\) 3.10542 0.134259
\(536\) 7.49995 0.323948
\(537\) −1.26654 −0.0546551
\(538\) 17.6913 0.762728
\(539\) −20.9157 −0.900904
\(540\) 3.05087 0.131288
\(541\) −17.0969 −0.735052 −0.367526 0.930013i \(-0.619795\pi\)
−0.367526 + 0.930013i \(0.619795\pi\)
\(542\) 8.78563 0.377375
\(543\) 23.4960 1.00831
\(544\) −4.30545 −0.184595
\(545\) 0.884035 0.0378679
\(546\) 19.0101 0.813559
\(547\) −20.2406 −0.865426 −0.432713 0.901532i \(-0.642444\pi\)
−0.432713 + 0.901532i \(0.642444\pi\)
\(548\) −6.31444 −0.269740
\(549\) −13.6897 −0.584264
\(550\) 5.30050 0.226014
\(551\) 0.281706 0.0120011
\(552\) −11.0746 −0.471366
\(553\) 83.2684 3.54093
\(554\) −21.3490 −0.907031
\(555\) −1.29381 −0.0549190
\(556\) −4.18766 −0.177596
\(557\) 11.4566 0.485431 0.242716 0.970097i \(-0.421962\pi\)
0.242716 + 0.970097i \(0.421962\pi\)
\(558\) 6.85746 0.290300
\(559\) −14.3760 −0.608042
\(560\) 2.72833 0.115293
\(561\) −6.77619 −0.286091
\(562\) 0.534356 0.0225405
\(563\) −13.9464 −0.587772 −0.293886 0.955840i \(-0.594949\pi\)
−0.293886 + 0.955840i \(0.594949\pi\)
\(564\) 5.01874 0.211327
\(565\) −1.47736 −0.0621530
\(566\) −11.9700 −0.503136
\(567\) −24.1425 −1.01389
\(568\) 9.98622 0.419013
\(569\) 34.4070 1.44242 0.721208 0.692718i \(-0.243587\pi\)
0.721208 + 0.692718i \(0.243587\pi\)
\(570\) 0.754243 0.0315918
\(571\) 46.0927 1.92892 0.964461 0.264226i \(-0.0851165\pi\)
0.964461 + 0.264226i \(0.0851165\pi\)
\(572\) 3.02571 0.126511
\(573\) 13.3764 0.558808
\(574\) 2.06376 0.0861397
\(575\) −37.2974 −1.55541
\(576\) −1.04494 −0.0435392
\(577\) −20.1814 −0.840162 −0.420081 0.907487i \(-0.637998\pi\)
−0.420081 + 0.907487i \(0.637998\pi\)
\(578\) 1.53693 0.0639279
\(579\) −26.9267 −1.11903
\(580\) −0.151960 −0.00630978
\(581\) 35.4318 1.46996
\(582\) −16.8752 −0.699501
\(583\) 4.03308 0.167033
\(584\) −7.18763 −0.297426
\(585\) 1.51518 0.0626449
\(586\) −16.8883 −0.697649
\(587\) −31.7581 −1.31080 −0.655399 0.755283i \(-0.727499\pi\)
−0.655399 + 0.755283i \(0.727499\pi\)
\(588\) −25.9816 −1.07146
\(589\) 6.56253 0.270405
\(590\) 4.82426 0.198612
\(591\) −19.7060 −0.810597
\(592\) 1.71537 0.0705013
\(593\) 11.8103 0.484992 0.242496 0.970152i \(-0.422034\pi\)
0.242496 + 0.970152i \(0.422034\pi\)
\(594\) −6.36618 −0.261207
\(595\) −11.7467 −0.481567
\(596\) −13.0258 −0.533558
\(597\) −1.50473 −0.0615844
\(598\) −21.2906 −0.870638
\(599\) −16.9161 −0.691173 −0.345586 0.938387i \(-0.612320\pi\)
−0.345586 + 0.938387i \(0.612320\pi\)
\(600\) 6.58431 0.268803
\(601\) 26.4584 1.07926 0.539629 0.841903i \(-0.318564\pi\)
0.539629 + 0.841903i \(0.318564\pi\)
\(602\) 27.0498 1.10247
\(603\) −7.83700 −0.319147
\(604\) −0.626724 −0.0255010
\(605\) −5.25023 −0.213452
\(606\) −1.69490 −0.0688507
\(607\) 32.0869 1.30237 0.651184 0.758920i \(-0.274273\pi\)
0.651184 + 0.758920i \(0.274273\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 1.99224 0.0807296
\(610\) 7.06699 0.286134
\(611\) 9.64840 0.390332
\(612\) 4.49895 0.181859
\(613\) −16.5732 −0.669385 −0.334693 0.942327i \(-0.608632\pi\)
−0.334693 + 0.942327i \(0.608632\pi\)
\(614\) −19.8836 −0.802436
\(615\) −0.307755 −0.0124099
\(616\) −5.69314 −0.229383
\(617\) −46.6098 −1.87644 −0.938220 0.346038i \(-0.887527\pi\)
−0.938220 + 0.346038i \(0.887527\pi\)
\(618\) −23.9497 −0.963399
\(619\) 6.72091 0.270136 0.135068 0.990836i \(-0.456875\pi\)
0.135068 + 0.990836i \(0.456875\pi\)
\(620\) −3.54000 −0.142170
\(621\) 44.7960 1.79760
\(622\) 8.70171 0.348907
\(623\) −22.1483 −0.887352
\(624\) 3.75855 0.150463
\(625\) 20.7200 0.828799
\(626\) −23.2841 −0.930621
\(627\) −1.57386 −0.0628540
\(628\) −6.57277 −0.262282
\(629\) −7.38545 −0.294477
\(630\) −2.85094 −0.113584
\(631\) 18.7172 0.745120 0.372560 0.928008i \(-0.378480\pi\)
0.372560 + 0.928008i \(0.378480\pi\)
\(632\) 16.4632 0.654872
\(633\) 1.39823 0.0555748
\(634\) −1.08251 −0.0429919
\(635\) 8.18437 0.324787
\(636\) 5.00992 0.198656
\(637\) −49.9490 −1.97905
\(638\) 0.317091 0.0125537
\(639\) −10.4350 −0.412803
\(640\) 0.539425 0.0213227
\(641\) −32.6567 −1.28986 −0.644930 0.764241i \(-0.723114\pi\)
−0.644930 + 0.764241i \(0.723114\pi\)
\(642\) −8.04951 −0.317689
\(643\) 23.2928 0.918577 0.459289 0.888287i \(-0.348104\pi\)
0.459289 + 0.888287i \(0.348104\pi\)
\(644\) 40.0601 1.57859
\(645\) −4.03376 −0.158829
\(646\) 4.30545 0.169396
\(647\) −44.0611 −1.73222 −0.866110 0.499854i \(-0.833387\pi\)
−0.866110 + 0.499854i \(0.833387\pi\)
\(648\) −4.77328 −0.187512
\(649\) −10.0667 −0.395151
\(650\) 12.6582 0.496495
\(651\) 46.4105 1.81897
\(652\) 7.39921 0.289776
\(653\) 30.8368 1.20674 0.603368 0.797463i \(-0.293825\pi\)
0.603368 + 0.797463i \(0.293825\pi\)
\(654\) −2.29149 −0.0896043
\(655\) 9.60251 0.375201
\(656\) 0.408032 0.0159310
\(657\) 7.51065 0.293018
\(658\) −18.1543 −0.707728
\(659\) −43.5281 −1.69562 −0.847808 0.530304i \(-0.822078\pi\)
−0.847808 + 0.530304i \(0.822078\pi\)
\(660\) 0.848981 0.0330465
\(661\) 44.1234 1.71620 0.858101 0.513482i \(-0.171645\pi\)
0.858101 + 0.513482i \(0.171645\pi\)
\(662\) 29.4757 1.14560
\(663\) −16.1823 −0.628467
\(664\) 7.00532 0.271859
\(665\) −2.72833 −0.105800
\(666\) −1.79246 −0.0694564
\(667\) −2.23123 −0.0863936
\(668\) −15.1677 −0.586855
\(669\) −13.9182 −0.538109
\(670\) 4.04566 0.156298
\(671\) −14.7465 −0.569283
\(672\) −7.07204 −0.272810
\(673\) 23.0409 0.888163 0.444081 0.895986i \(-0.353530\pi\)
0.444081 + 0.895986i \(0.353530\pi\)
\(674\) −8.97516 −0.345710
\(675\) −26.6332 −1.02511
\(676\) −5.77428 −0.222088
\(677\) 33.9101 1.30327 0.651636 0.758532i \(-0.274083\pi\)
0.651636 + 0.758532i \(0.274083\pi\)
\(678\) 3.82943 0.147069
\(679\) 61.0429 2.34261
\(680\) −2.32247 −0.0890627
\(681\) −36.2965 −1.39089
\(682\) 7.38683 0.282856
\(683\) −37.2066 −1.42367 −0.711836 0.702346i \(-0.752136\pi\)
−0.711836 + 0.702346i \(0.752136\pi\)
\(684\) 1.04494 0.0399543
\(685\) −3.40617 −0.130143
\(686\) 58.5785 2.23654
\(687\) 6.79855 0.259381
\(688\) 5.34809 0.203894
\(689\) 9.63144 0.366929
\(690\) −5.97391 −0.227423
\(691\) 37.3225 1.41982 0.709908 0.704295i \(-0.248737\pi\)
0.709908 + 0.704295i \(0.248737\pi\)
\(692\) −15.7761 −0.599719
\(693\) 5.94899 0.225984
\(694\) 26.4970 1.00581
\(695\) −2.25893 −0.0856861
\(696\) 0.393892 0.0149304
\(697\) −1.75676 −0.0665422
\(698\) −4.60150 −0.174169
\(699\) −4.87221 −0.184284
\(700\) −23.8175 −0.900215
\(701\) 38.9177 1.46990 0.734951 0.678120i \(-0.237205\pi\)
0.734951 + 0.678120i \(0.237205\pi\)
\(702\) −15.2031 −0.573805
\(703\) −1.71537 −0.0646964
\(704\) −1.12561 −0.0424229
\(705\) 2.70724 0.101960
\(706\) −3.77583 −0.142105
\(707\) 6.13097 0.230579
\(708\) −12.5049 −0.469962
\(709\) −41.1852 −1.54674 −0.773371 0.633954i \(-0.781431\pi\)
−0.773371 + 0.633954i \(0.781431\pi\)
\(710\) 5.38682 0.202164
\(711\) −17.2031 −0.645167
\(712\) −4.37900 −0.164110
\(713\) −51.9780 −1.94659
\(714\) 30.4484 1.13950
\(715\) 1.63215 0.0610388
\(716\) 0.905811 0.0338518
\(717\) 32.8933 1.22842
\(718\) −21.5307 −0.803518
\(719\) −18.1056 −0.675226 −0.337613 0.941285i \(-0.609619\pi\)
−0.337613 + 0.941285i \(0.609619\pi\)
\(720\) −0.563668 −0.0210067
\(721\) 86.6334 3.22640
\(722\) 1.00000 0.0372161
\(723\) −19.9724 −0.742783
\(724\) −16.8041 −0.624518
\(725\) 1.32656 0.0492673
\(726\) 13.6090 0.505078
\(727\) −25.9544 −0.962594 −0.481297 0.876557i \(-0.659834\pi\)
−0.481297 + 0.876557i \(0.659834\pi\)
\(728\) −13.5958 −0.503895
\(729\) 28.7121 1.06341
\(730\) −3.87719 −0.143501
\(731\) −23.0259 −0.851645
\(732\) −18.3182 −0.677061
\(733\) 9.40335 0.347321 0.173660 0.984806i \(-0.444441\pi\)
0.173660 + 0.984806i \(0.444441\pi\)
\(734\) −21.8841 −0.807757
\(735\) −14.0151 −0.516956
\(736\) 7.92041 0.291950
\(737\) −8.44199 −0.310965
\(738\) −0.426370 −0.0156949
\(739\) 37.2029 1.36853 0.684266 0.729232i \(-0.260123\pi\)
0.684266 + 0.729232i \(0.260123\pi\)
\(740\) 0.925314 0.0340152
\(741\) −3.75855 −0.138074
\(742\) −18.1224 −0.665294
\(743\) −30.6366 −1.12395 −0.561975 0.827154i \(-0.689958\pi\)
−0.561975 + 0.827154i \(0.689958\pi\)
\(744\) 9.17596 0.336407
\(745\) −7.02646 −0.257430
\(746\) 13.7549 0.503604
\(747\) −7.32014 −0.267830
\(748\) 4.84625 0.177196
\(749\) 29.1175 1.06393
\(750\) 7.32296 0.267397
\(751\) −47.7664 −1.74302 −0.871511 0.490376i \(-0.836860\pi\)
−0.871511 + 0.490376i \(0.836860\pi\)
\(752\) −3.58934 −0.130890
\(753\) 7.51238 0.273766
\(754\) 0.757247 0.0275773
\(755\) −0.338071 −0.0123037
\(756\) 28.6060 1.04039
\(757\) 35.6625 1.29617 0.648087 0.761566i \(-0.275569\pi\)
0.648087 + 0.761566i \(0.275569\pi\)
\(758\) −5.18809 −0.188440
\(759\) 12.4656 0.452474
\(760\) −0.539425 −0.0195670
\(761\) −19.2845 −0.699061 −0.349531 0.936925i \(-0.613659\pi\)
−0.349531 + 0.936925i \(0.613659\pi\)
\(762\) −21.2145 −0.768522
\(763\) 8.28901 0.300082
\(764\) −9.56666 −0.346109
\(765\) 2.42685 0.0877428
\(766\) 32.9761 1.19147
\(767\) −24.0403 −0.868045
\(768\) −1.39823 −0.0504544
\(769\) 33.9307 1.22357 0.611787 0.791023i \(-0.290451\pi\)
0.611787 + 0.791023i \(0.290451\pi\)
\(770\) −3.07102 −0.110672
\(771\) 3.06540 0.110398
\(772\) 19.2576 0.693097
\(773\) 7.83486 0.281801 0.140900 0.990024i \(-0.455000\pi\)
0.140900 + 0.990024i \(0.455000\pi\)
\(774\) −5.58844 −0.200872
\(775\) 30.9031 1.11007
\(776\) 12.0690 0.433251
\(777\) −12.1312 −0.435203
\(778\) 11.2758 0.404258
\(779\) −0.408032 −0.0146193
\(780\) 2.02746 0.0725947
\(781\) −11.2406 −0.402219
\(782\) −34.1010 −1.21945
\(783\) −1.59327 −0.0569388
\(784\) 18.5817 0.663633
\(785\) −3.54552 −0.126545
\(786\) −24.8905 −0.887814
\(787\) 22.4427 0.799994 0.399997 0.916516i \(-0.369011\pi\)
0.399997 + 0.916516i \(0.369011\pi\)
\(788\) 14.0935 0.502060
\(789\) −44.5250 −1.58513
\(790\) 8.88069 0.315961
\(791\) −13.8522 −0.492529
\(792\) 1.17619 0.0417942
\(793\) −35.2163 −1.25057
\(794\) −15.9178 −0.564902
\(795\) 2.70248 0.0958469
\(796\) 1.07616 0.0381436
\(797\) 23.3320 0.826461 0.413230 0.910627i \(-0.364400\pi\)
0.413230 + 0.910627i \(0.364400\pi\)
\(798\) 7.07204 0.250348
\(799\) 15.4537 0.546714
\(800\) −4.70902 −0.166489
\(801\) 4.57580 0.161678
\(802\) 30.8843 1.09056
\(803\) 8.09044 0.285505
\(804\) −10.4867 −0.369837
\(805\) 21.6095 0.761633
\(806\) 17.6406 0.621362
\(807\) −24.7366 −0.870771
\(808\) 1.21217 0.0426441
\(809\) 15.6008 0.548496 0.274248 0.961659i \(-0.411571\pi\)
0.274248 + 0.961659i \(0.411571\pi\)
\(810\) −2.57483 −0.0904702
\(811\) −33.6213 −1.18060 −0.590301 0.807183i \(-0.700991\pi\)
−0.590301 + 0.807183i \(0.700991\pi\)
\(812\) −1.42483 −0.0500016
\(813\) −12.2844 −0.430832
\(814\) −1.93083 −0.0676756
\(815\) 3.99132 0.139810
\(816\) 6.02003 0.210743
\(817\) −5.34809 −0.187106
\(818\) 35.8549 1.25364
\(819\) 14.2068 0.496427
\(820\) 0.220103 0.00768633
\(821\) 44.3042 1.54623 0.773114 0.634268i \(-0.218698\pi\)
0.773114 + 0.634268i \(0.218698\pi\)
\(822\) 8.82907 0.307949
\(823\) 15.8968 0.554128 0.277064 0.960852i \(-0.410639\pi\)
0.277064 + 0.960852i \(0.410639\pi\)
\(824\) 17.1286 0.596701
\(825\) −7.41135 −0.258030
\(826\) 45.2339 1.57389
\(827\) −50.4230 −1.75338 −0.876689 0.481057i \(-0.840253\pi\)
−0.876689 + 0.481057i \(0.840253\pi\)
\(828\) −8.27636 −0.287623
\(829\) −14.0581 −0.488258 −0.244129 0.969743i \(-0.578502\pi\)
−0.244129 + 0.969743i \(0.578502\pi\)
\(830\) 3.77885 0.131166
\(831\) 29.8509 1.03552
\(832\) −2.68807 −0.0931921
\(833\) −80.0028 −2.77193
\(834\) 5.85533 0.202753
\(835\) −8.18183 −0.283144
\(836\) 1.12561 0.0389299
\(837\) −37.1162 −1.28292
\(838\) −25.3099 −0.874315
\(839\) 38.3912 1.32541 0.662706 0.748880i \(-0.269408\pi\)
0.662706 + 0.748880i \(0.269408\pi\)
\(840\) −3.81484 −0.131624
\(841\) −28.9206 −0.997263
\(842\) 35.4253 1.22084
\(843\) −0.747155 −0.0257334
\(844\) −1.00000 −0.0344214
\(845\) −3.11479 −0.107152
\(846\) 3.75065 0.128950
\(847\) −49.2280 −1.69149
\(848\) −3.58303 −0.123042
\(849\) 16.7368 0.574407
\(850\) 20.2745 0.695409
\(851\) 13.5864 0.465737
\(852\) −13.9631 −0.478367
\(853\) −42.4341 −1.45292 −0.726458 0.687211i \(-0.758835\pi\)
−0.726458 + 0.687211i \(0.758835\pi\)
\(854\) 66.2625 2.26746
\(855\) 0.563668 0.0192770
\(856\) 5.75691 0.196767
\(857\) 20.3091 0.693746 0.346873 0.937912i \(-0.387244\pi\)
0.346873 + 0.937912i \(0.387244\pi\)
\(858\) −4.23065 −0.144432
\(859\) 10.8351 0.369690 0.184845 0.982768i \(-0.440822\pi\)
0.184845 + 0.982768i \(0.440822\pi\)
\(860\) 2.88489 0.0983741
\(861\) −2.88562 −0.0983417
\(862\) 31.1751 1.06183
\(863\) 2.34439 0.0798040 0.0399020 0.999204i \(-0.487295\pi\)
0.0399020 + 0.999204i \(0.487295\pi\)
\(864\) 5.65578 0.192413
\(865\) −8.51005 −0.289351
\(866\) −28.5507 −0.970192
\(867\) −2.14899 −0.0729835
\(868\) −33.1922 −1.12662
\(869\) −18.5311 −0.628626
\(870\) 0.212475 0.00720358
\(871\) −20.1604 −0.683109
\(872\) 1.63885 0.0554983
\(873\) −12.6114 −0.426830
\(874\) −7.92041 −0.267912
\(875\) −26.4894 −0.895504
\(876\) 10.0500 0.339558
\(877\) 8.53605 0.288242 0.144121 0.989560i \(-0.453965\pi\)
0.144121 + 0.989560i \(0.453965\pi\)
\(878\) −25.6159 −0.864496
\(879\) 23.6138 0.796474
\(880\) −0.607181 −0.0204681
\(881\) 11.7352 0.395369 0.197685 0.980266i \(-0.436658\pi\)
0.197685 + 0.980266i \(0.436658\pi\)
\(882\) −19.4168 −0.653798
\(883\) −37.5958 −1.26520 −0.632600 0.774479i \(-0.718012\pi\)
−0.632600 + 0.774479i \(0.718012\pi\)
\(884\) 11.5734 0.389254
\(885\) −6.74544 −0.226746
\(886\) 16.4574 0.552897
\(887\) −41.5645 −1.39560 −0.697800 0.716292i \(-0.745838\pi\)
−0.697800 + 0.716292i \(0.745838\pi\)
\(888\) −2.39849 −0.0804880
\(889\) 76.7394 2.57376
\(890\) −2.36214 −0.0791792
\(891\) 5.37283 0.179997
\(892\) 9.95413 0.333289
\(893\) 3.58934 0.120113
\(894\) 18.2131 0.609139
\(895\) 0.488618 0.0163327
\(896\) 5.05784 0.168971
\(897\) 29.7693 0.993967
\(898\) −6.37899 −0.212870
\(899\) 1.84871 0.0616579
\(900\) 4.92065 0.164022
\(901\) 15.4266 0.513934
\(902\) −0.459284 −0.0152925
\(903\) −37.8219 −1.25863
\(904\) −2.73876 −0.0910900
\(905\) −9.06455 −0.301316
\(906\) 0.876307 0.0291133
\(907\) −21.7421 −0.721934 −0.360967 0.932579i \(-0.617553\pi\)
−0.360967 + 0.932579i \(0.617553\pi\)
\(908\) 25.9588 0.861474
\(909\) −1.26665 −0.0420121
\(910\) −7.33393 −0.243118
\(911\) −39.8011 −1.31867 −0.659335 0.751849i \(-0.729162\pi\)
−0.659335 + 0.751849i \(0.729162\pi\)
\(912\) 1.39823 0.0463002
\(913\) −7.88523 −0.260963
\(914\) −17.7167 −0.586015
\(915\) −9.88131 −0.326666
\(916\) −4.86224 −0.160653
\(917\) 90.0364 2.97326
\(918\) −24.3507 −0.803692
\(919\) 36.8996 1.21721 0.608603 0.793475i \(-0.291730\pi\)
0.608603 + 0.793475i \(0.291730\pi\)
\(920\) 4.27247 0.140859
\(921\) 27.8019 0.916104
\(922\) −11.1057 −0.365745
\(923\) −26.8437 −0.883570
\(924\) 7.96034 0.261876
\(925\) −8.07771 −0.265594
\(926\) −20.2349 −0.664961
\(927\) −17.8983 −0.587858
\(928\) −0.281706 −0.00924747
\(929\) −15.8960 −0.521532 −0.260766 0.965402i \(-0.583975\pi\)
−0.260766 + 0.965402i \(0.583975\pi\)
\(930\) 4.94975 0.162309
\(931\) −18.5817 −0.608991
\(932\) 3.48455 0.114140
\(933\) −12.1670 −0.398330
\(934\) −33.9185 −1.10985
\(935\) 2.61419 0.0854931
\(936\) 2.80888 0.0918110
\(937\) 22.0247 0.719515 0.359758 0.933046i \(-0.382859\pi\)
0.359758 + 0.933046i \(0.382859\pi\)
\(938\) 37.9335 1.23857
\(939\) 32.5567 1.06245
\(940\) −1.93618 −0.0631513
\(941\) 14.5777 0.475220 0.237610 0.971361i \(-0.423636\pi\)
0.237610 + 0.971361i \(0.423636\pi\)
\(942\) 9.19027 0.299435
\(943\) 3.23178 0.105241
\(944\) 8.94333 0.291081
\(945\) 15.4308 0.501964
\(946\) −6.01984 −0.195722
\(947\) −18.5352 −0.602314 −0.301157 0.953575i \(-0.597373\pi\)
−0.301157 + 0.953575i \(0.597373\pi\)
\(948\) −23.0195 −0.747637
\(949\) 19.3208 0.627181
\(950\) 4.70902 0.152781
\(951\) 1.51360 0.0490818
\(952\) −21.7763 −0.705774
\(953\) −45.5710 −1.47619 −0.738094 0.674698i \(-0.764274\pi\)
−0.738094 + 0.674698i \(0.764274\pi\)
\(954\) 3.74406 0.121218
\(955\) −5.16050 −0.166990
\(956\) −23.5249 −0.760848
\(957\) −0.443367 −0.0143320
\(958\) 15.7058 0.507430
\(959\) −31.9374 −1.03131
\(960\) −0.754243 −0.0243431
\(961\) 12.0669 0.389254
\(962\) −4.61104 −0.148666
\(963\) −6.01563 −0.193851
\(964\) 14.2840 0.460058
\(965\) 10.3881 0.334403
\(966\) −56.0135 −1.80220
\(967\) −5.76318 −0.185331 −0.0926657 0.995697i \(-0.529539\pi\)
−0.0926657 + 0.995697i \(0.529539\pi\)
\(968\) −9.73301 −0.312831
\(969\) −6.02003 −0.193391
\(970\) 6.51031 0.209033
\(971\) −5.30424 −0.170221 −0.0851106 0.996372i \(-0.527124\pi\)
−0.0851106 + 0.996372i \(0.527124\pi\)
\(972\) −10.2932 −0.330154
\(973\) −21.1805 −0.679016
\(974\) −17.2930 −0.554102
\(975\) −17.6991 −0.566825
\(976\) 13.1010 0.419352
\(977\) −61.5062 −1.96776 −0.983879 0.178834i \(-0.942768\pi\)
−0.983879 + 0.178834i \(0.942768\pi\)
\(978\) −10.3458 −0.330823
\(979\) 4.92903 0.157532
\(980\) 10.0235 0.320188
\(981\) −1.71250 −0.0546758
\(982\) 25.0354 0.798913
\(983\) −9.58788 −0.305806 −0.152903 0.988241i \(-0.548862\pi\)
−0.152903 + 0.988241i \(0.548862\pi\)
\(984\) −0.570524 −0.0181877
\(985\) 7.60239 0.242232
\(986\) 1.21287 0.0386258
\(987\) 25.3840 0.807981
\(988\) 2.68807 0.0855189
\(989\) 42.3590 1.34694
\(990\) 0.634468 0.0201647
\(991\) 11.9546 0.379752 0.189876 0.981808i \(-0.439191\pi\)
0.189876 + 0.981808i \(0.439191\pi\)
\(992\) −6.56253 −0.208361
\(993\) −41.2139 −1.30788
\(994\) 50.5087 1.60204
\(995\) 0.580510 0.0184034
\(996\) −9.79507 −0.310369
\(997\) −36.0288 −1.14104 −0.570522 0.821283i \(-0.693259\pi\)
−0.570522 + 0.821283i \(0.693259\pi\)
\(998\) 32.2250 1.02007
\(999\) 9.70175 0.306950
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 \(a_p\))