Properties

Label 8007.2.a.j.1.7
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 0
Dimension 64
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(0\)
Dimension: \(64\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.37978 q^{2}\) \(-1.00000 q^{3}\) \(+3.66334 q^{4}\) \(+0.734525 q^{5}\) \(+2.37978 q^{6}\) \(+2.72642 q^{7}\) \(-3.95838 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.37978 q^{2}\) \(-1.00000 q^{3}\) \(+3.66334 q^{4}\) \(+0.734525 q^{5}\) \(+2.37978 q^{6}\) \(+2.72642 q^{7}\) \(-3.95838 q^{8}\) \(+1.00000 q^{9}\) \(-1.74801 q^{10}\) \(-6.23656 q^{11}\) \(-3.66334 q^{12}\) \(+2.96601 q^{13}\) \(-6.48826 q^{14}\) \(-0.734525 q^{15}\) \(+2.09338 q^{16}\) \(+1.00000 q^{17}\) \(-2.37978 q^{18}\) \(+0.0641847 q^{19}\) \(+2.69081 q^{20}\) \(-2.72642 q^{21}\) \(+14.8416 q^{22}\) \(+3.60714 q^{23}\) \(+3.95838 q^{24}\) \(-4.46047 q^{25}\) \(-7.05844 q^{26}\) \(-1.00000 q^{27}\) \(+9.98779 q^{28}\) \(+7.19378 q^{29}\) \(+1.74801 q^{30}\) \(+7.92734 q^{31}\) \(+2.93498 q^{32}\) \(+6.23656 q^{33}\) \(-2.37978 q^{34}\) \(+2.00262 q^{35}\) \(+3.66334 q^{36}\) \(+2.69818 q^{37}\) \(-0.152745 q^{38}\) \(-2.96601 q^{39}\) \(-2.90753 q^{40}\) \(+5.63189 q^{41}\) \(+6.48826 q^{42}\) \(-0.575311 q^{43}\) \(-22.8466 q^{44}\) \(+0.734525 q^{45}\) \(-8.58419 q^{46}\) \(-12.2085 q^{47}\) \(-2.09338 q^{48}\) \(+0.433344 q^{49}\) \(+10.6149 q^{50}\) \(-1.00000 q^{51}\) \(+10.8655 q^{52}\) \(-7.23664 q^{53}\) \(+2.37978 q^{54}\) \(-4.58091 q^{55}\) \(-10.7922 q^{56}\) \(-0.0641847 q^{57}\) \(-17.1196 q^{58}\) \(-6.60987 q^{59}\) \(-2.69081 q^{60}\) \(+6.48193 q^{61}\) \(-18.8653 q^{62}\) \(+2.72642 q^{63}\) \(-11.1714 q^{64}\) \(+2.17861 q^{65}\) \(-14.8416 q^{66}\) \(+7.14994 q^{67}\) \(+3.66334 q^{68}\) \(-3.60714 q^{69}\) \(-4.76579 q^{70}\) \(-14.0505 q^{71}\) \(-3.95838 q^{72}\) \(-8.92623 q^{73}\) \(-6.42106 q^{74}\) \(+4.46047 q^{75}\) \(+0.235130 q^{76}\) \(-17.0034 q^{77}\) \(+7.05844 q^{78}\) \(+12.6466 q^{79}\) \(+1.53764 q^{80}\) \(+1.00000 q^{81}\) \(-13.4026 q^{82}\) \(+4.20436 q^{83}\) \(-9.98779 q^{84}\) \(+0.734525 q^{85}\) \(+1.36911 q^{86}\) \(-7.19378 q^{87}\) \(+24.6866 q^{88}\) \(+16.4667 q^{89}\) \(-1.74801 q^{90}\) \(+8.08657 q^{91}\) \(+13.2142 q^{92}\) \(-7.92734 q^{93}\) \(+29.0534 q^{94}\) \(+0.0471453 q^{95}\) \(-2.93498 q^{96}\) \(+14.1044 q^{97}\) \(-1.03126 q^{98}\) \(-6.23656 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 77q^{12} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 103q^{16} \) \(\mathstrut +\mathstrut 64q^{17} \) \(\mathstrut +\mathstrut 5q^{18} \) \(\mathstrut +\mathstrut 26q^{19} \) \(\mathstrut -\mathstrut 24q^{20} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut +\mathstrut 25q^{22} \) \(\mathstrut +\mathstrut 20q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 141q^{25} \) \(\mathstrut +\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 64q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 7q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 3q^{35} \) \(\mathstrut +\mathstrut 77q^{36} \) \(\mathstrut +\mathstrut 50q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut +\mathstrut 28q^{40} \) \(\mathstrut -\mathstrut 9q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 59q^{43} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut -\mathstrut 103q^{48} \) \(\mathstrut +\mathstrut 163q^{49} \) \(\mathstrut +\mathstrut 20q^{50} \) \(\mathstrut -\mathstrut 64q^{51} \) \(\mathstrut +\mathstrut 65q^{52} \) \(\mathstrut +\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 35q^{55} \) \(\mathstrut -\mathstrut 34q^{56} \) \(\mathstrut -\mathstrut 26q^{57} \) \(\mathstrut -\mathstrut 27q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut +\mathstrut 24q^{60} \) \(\mathstrut +\mathstrut 15q^{61} \) \(\mathstrut +\mathstrut 18q^{62} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 152q^{64} \) \(\mathstrut +\mathstrut 49q^{65} \) \(\mathstrut -\mathstrut 25q^{66} \) \(\mathstrut +\mathstrut 56q^{67} \) \(\mathstrut +\mathstrut 77q^{68} \) \(\mathstrut -\mathstrut 20q^{69} \) \(\mathstrut +\mathstrut 28q^{70} \) \(\mathstrut -\mathstrut 18q^{71} \) \(\mathstrut +\mathstrut 18q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut -\mathstrut 76q^{74} \) \(\mathstrut -\mathstrut 141q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 9q^{78} \) \(\mathstrut +\mathstrut 20q^{79} \) \(\mathstrut -\mathstrut 144q^{80} \) \(\mathstrut +\mathstrut 64q^{81} \) \(\mathstrut +\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 3q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 5q^{87} \) \(\mathstrut +\mathstrut 108q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut +\mathstrut 12q^{90} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 42q^{95} \) \(\mathstrut -\mathstrut 31q^{96} \) \(\mathstrut +\mathstrut 72q^{97} \) \(\mathstrut +\mathstrut 18q^{98} \) \(\mathstrut -\mathstrut 7q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.37978 −1.68276 −0.841378 0.540447i \(-0.818255\pi\)
−0.841378 + 0.540447i \(0.818255\pi\)
\(3\) −1.00000 −0.577350
\(4\) 3.66334 1.83167
\(5\) 0.734525 0.328490 0.164245 0.986420i \(-0.447481\pi\)
0.164245 + 0.986420i \(0.447481\pi\)
\(6\) 2.37978 0.971540
\(7\) 2.72642 1.03049 0.515244 0.857043i \(-0.327701\pi\)
0.515244 + 0.857043i \(0.327701\pi\)
\(8\) −3.95838 −1.39950
\(9\) 1.00000 0.333333
\(10\) −1.74801 −0.552768
\(11\) −6.23656 −1.88039 −0.940196 0.340634i \(-0.889358\pi\)
−0.940196 + 0.340634i \(0.889358\pi\)
\(12\) −3.66334 −1.05752
\(13\) 2.96601 0.822622 0.411311 0.911495i \(-0.365071\pi\)
0.411311 + 0.911495i \(0.365071\pi\)
\(14\) −6.48826 −1.73406
\(15\) −0.734525 −0.189654
\(16\) 2.09338 0.523345
\(17\) 1.00000 0.242536
\(18\) −2.37978 −0.560919
\(19\) 0.0641847 0.0147250 0.00736249 0.999973i \(-0.497656\pi\)
0.00736249 + 0.999973i \(0.497656\pi\)
\(20\) 2.69081 0.601684
\(21\) −2.72642 −0.594953
\(22\) 14.8416 3.16424
\(23\) 3.60714 0.752141 0.376070 0.926591i \(-0.377275\pi\)
0.376070 + 0.926591i \(0.377275\pi\)
\(24\) 3.95838 0.808001
\(25\) −4.46047 −0.892095
\(26\) −7.05844 −1.38427
\(27\) −1.00000 −0.192450
\(28\) 9.98779 1.88751
\(29\) 7.19378 1.33585 0.667925 0.744228i \(-0.267183\pi\)
0.667925 + 0.744228i \(0.267183\pi\)
\(30\) 1.74801 0.319141
\(31\) 7.92734 1.42379 0.711896 0.702285i \(-0.247837\pi\)
0.711896 + 0.702285i \(0.247837\pi\)
\(32\) 2.93498 0.518836
\(33\) 6.23656 1.08564
\(34\) −2.37978 −0.408128
\(35\) 2.00262 0.338505
\(36\) 3.66334 0.610557
\(37\) 2.69818 0.443577 0.221789 0.975095i \(-0.428810\pi\)
0.221789 + 0.975095i \(0.428810\pi\)
\(38\) −0.152745 −0.0247786
\(39\) −2.96601 −0.474941
\(40\) −2.90753 −0.459720
\(41\) 5.63189 0.879553 0.439777 0.898107i \(-0.355058\pi\)
0.439777 + 0.898107i \(0.355058\pi\)
\(42\) 6.48826 1.00116
\(43\) −0.575311 −0.0877341 −0.0438670 0.999037i \(-0.513968\pi\)
−0.0438670 + 0.999037i \(0.513968\pi\)
\(44\) −22.8466 −3.44426
\(45\) 0.734525 0.109497
\(46\) −8.58419 −1.26567
\(47\) −12.2085 −1.78079 −0.890394 0.455190i \(-0.849571\pi\)
−0.890394 + 0.455190i \(0.849571\pi\)
\(48\) −2.09338 −0.302153
\(49\) 0.433344 0.0619063
\(50\) 10.6149 1.50118
\(51\) −1.00000 −0.140028
\(52\) 10.8655 1.50677
\(53\) −7.23664 −0.994029 −0.497014 0.867742i \(-0.665570\pi\)
−0.497014 + 0.867742i \(0.665570\pi\)
\(54\) 2.37978 0.323847
\(55\) −4.58091 −0.617689
\(56\) −10.7922 −1.44217
\(57\) −0.0641847 −0.00850147
\(58\) −17.1196 −2.24791
\(59\) −6.60987 −0.860531 −0.430266 0.902702i \(-0.641580\pi\)
−0.430266 + 0.902702i \(0.641580\pi\)
\(60\) −2.69081 −0.347383
\(61\) 6.48193 0.829927 0.414963 0.909838i \(-0.363794\pi\)
0.414963 + 0.909838i \(0.363794\pi\)
\(62\) −18.8653 −2.39590
\(63\) 2.72642 0.343496
\(64\) −11.1714 −1.39642
\(65\) 2.17861 0.270223
\(66\) −14.8416 −1.82688
\(67\) 7.14994 0.873504 0.436752 0.899582i \(-0.356129\pi\)
0.436752 + 0.899582i \(0.356129\pi\)
\(68\) 3.66334 0.444245
\(69\) −3.60714 −0.434249
\(70\) −4.76579 −0.569621
\(71\) −14.0505 −1.66749 −0.833744 0.552151i \(-0.813807\pi\)
−0.833744 + 0.552151i \(0.813807\pi\)
\(72\) −3.95838 −0.466499
\(73\) −8.92623 −1.04474 −0.522368 0.852720i \(-0.674951\pi\)
−0.522368 + 0.852720i \(0.674951\pi\)
\(74\) −6.42106 −0.746433
\(75\) 4.46047 0.515051
\(76\) 0.235130 0.0269713
\(77\) −17.0034 −1.93772
\(78\) 7.05844 0.799211
\(79\) 12.6466 1.42285 0.711427 0.702760i \(-0.248049\pi\)
0.711427 + 0.702760i \(0.248049\pi\)
\(80\) 1.53764 0.171913
\(81\) 1.00000 0.111111
\(82\) −13.4026 −1.48007
\(83\) 4.20436 0.461489 0.230744 0.973014i \(-0.425884\pi\)
0.230744 + 0.973014i \(0.425884\pi\)
\(84\) −9.98779 −1.08976
\(85\) 0.734525 0.0796704
\(86\) 1.36911 0.147635
\(87\) −7.19378 −0.771254
\(88\) 24.6866 2.63161
\(89\) 16.4667 1.74546 0.872732 0.488199i \(-0.162346\pi\)
0.872732 + 0.488199i \(0.162346\pi\)
\(90\) −1.74801 −0.184256
\(91\) 8.08657 0.847703
\(92\) 13.2142 1.37767
\(93\) −7.92734 −0.822027
\(94\) 29.0534 2.99663
\(95\) 0.0471453 0.00483700
\(96\) −2.93498 −0.299550
\(97\) 14.1044 1.43208 0.716042 0.698058i \(-0.245952\pi\)
0.716042 + 0.698058i \(0.245952\pi\)
\(98\) −1.03126 −0.104173
\(99\) −6.23656 −0.626797
\(100\) −16.3402 −1.63402
\(101\) 2.35072 0.233905 0.116953 0.993137i \(-0.462687\pi\)
0.116953 + 0.993137i \(0.462687\pi\)
\(102\) 2.37978 0.235633
\(103\) 5.02849 0.495472 0.247736 0.968828i \(-0.420313\pi\)
0.247736 + 0.968828i \(0.420313\pi\)
\(104\) −11.7406 −1.15126
\(105\) −2.00262 −0.195436
\(106\) 17.2216 1.67271
\(107\) −5.11930 −0.494901 −0.247451 0.968901i \(-0.579593\pi\)
−0.247451 + 0.968901i \(0.579593\pi\)
\(108\) −3.66334 −0.352505
\(109\) 10.6058 1.01585 0.507924 0.861402i \(-0.330413\pi\)
0.507924 + 0.861402i \(0.330413\pi\)
\(110\) 10.9015 1.03942
\(111\) −2.69818 −0.256100
\(112\) 5.70742 0.539301
\(113\) 2.50508 0.235658 0.117829 0.993034i \(-0.462407\pi\)
0.117829 + 0.993034i \(0.462407\pi\)
\(114\) 0.152745 0.0143059
\(115\) 2.64953 0.247070
\(116\) 26.3532 2.44684
\(117\) 2.96601 0.274207
\(118\) 15.7300 1.44806
\(119\) 2.72642 0.249930
\(120\) 2.90753 0.265420
\(121\) 27.8946 2.53587
\(122\) −15.4256 −1.39656
\(123\) −5.63189 −0.507810
\(124\) 29.0405 2.60792
\(125\) −6.94895 −0.621533
\(126\) −6.48826 −0.578020
\(127\) −16.9476 −1.50386 −0.751930 0.659243i \(-0.770877\pi\)
−0.751930 + 0.659243i \(0.770877\pi\)
\(128\) 20.7154 1.83100
\(129\) 0.575311 0.0506533
\(130\) −5.18460 −0.454719
\(131\) −0.998311 −0.0872228 −0.0436114 0.999049i \(-0.513886\pi\)
−0.0436114 + 0.999049i \(0.513886\pi\)
\(132\) 22.8466 1.98854
\(133\) 0.174994 0.0151739
\(134\) −17.0153 −1.46990
\(135\) −0.734525 −0.0632178
\(136\) −3.95838 −0.339428
\(137\) −3.12738 −0.267191 −0.133595 0.991036i \(-0.542652\pi\)
−0.133595 + 0.991036i \(0.542652\pi\)
\(138\) 8.58419 0.730735
\(139\) −0.670797 −0.0568963 −0.0284481 0.999595i \(-0.509057\pi\)
−0.0284481 + 0.999595i \(0.509057\pi\)
\(140\) 7.33628 0.620029
\(141\) 12.2085 1.02814
\(142\) 33.4371 2.80598
\(143\) −18.4977 −1.54685
\(144\) 2.09338 0.174448
\(145\) 5.28401 0.438813
\(146\) 21.2424 1.75804
\(147\) −0.433344 −0.0357416
\(148\) 9.88434 0.812487
\(149\) −18.1619 −1.48788 −0.743941 0.668246i \(-0.767046\pi\)
−0.743941 + 0.668246i \(0.767046\pi\)
\(150\) −10.6149 −0.866706
\(151\) 6.26526 0.509860 0.254930 0.966960i \(-0.417948\pi\)
0.254930 + 0.966960i \(0.417948\pi\)
\(152\) −0.254067 −0.0206076
\(153\) 1.00000 0.0808452
\(154\) 40.4644 3.26072
\(155\) 5.82283 0.467701
\(156\) −10.8655 −0.869936
\(157\) −1.00000 −0.0798087
\(158\) −30.0961 −2.39432
\(159\) 7.23664 0.573903
\(160\) 2.15582 0.170432
\(161\) 9.83457 0.775072
\(162\) −2.37978 −0.186973
\(163\) −8.95837 −0.701674 −0.350837 0.936437i \(-0.614103\pi\)
−0.350837 + 0.936437i \(0.614103\pi\)
\(164\) 20.6315 1.61105
\(165\) 4.58091 0.356623
\(166\) −10.0055 −0.776574
\(167\) 21.1591 1.63734 0.818671 0.574263i \(-0.194711\pi\)
0.818671 + 0.574263i \(0.194711\pi\)
\(168\) 10.7922 0.832635
\(169\) −4.20280 −0.323292
\(170\) −1.74801 −0.134066
\(171\) 0.0641847 0.00490833
\(172\) −2.10756 −0.160700
\(173\) 6.95986 0.529148 0.264574 0.964365i \(-0.414769\pi\)
0.264574 + 0.964365i \(0.414769\pi\)
\(174\) 17.1196 1.29783
\(175\) −12.1611 −0.919293
\(176\) −13.0555 −0.984093
\(177\) 6.60987 0.496828
\(178\) −39.1870 −2.93719
\(179\) 13.7275 1.02604 0.513021 0.858376i \(-0.328526\pi\)
0.513021 + 0.858376i \(0.328526\pi\)
\(180\) 2.69081 0.200561
\(181\) −0.839921 −0.0624308 −0.0312154 0.999513i \(-0.509938\pi\)
−0.0312154 + 0.999513i \(0.509938\pi\)
\(182\) −19.2442 −1.42648
\(183\) −6.48193 −0.479158
\(184\) −14.2784 −1.05262
\(185\) 1.98188 0.145711
\(186\) 18.8653 1.38327
\(187\) −6.23656 −0.456062
\(188\) −44.7238 −3.26182
\(189\) −2.72642 −0.198318
\(190\) −0.112195 −0.00813950
\(191\) 3.44386 0.249189 0.124594 0.992208i \(-0.460237\pi\)
0.124594 + 0.992208i \(0.460237\pi\)
\(192\) 11.1714 0.806223
\(193\) 0.306415 0.0220562 0.0110281 0.999939i \(-0.496490\pi\)
0.0110281 + 0.999939i \(0.496490\pi\)
\(194\) −33.5653 −2.40985
\(195\) −2.17861 −0.156013
\(196\) 1.58749 0.113392
\(197\) −10.4663 −0.745696 −0.372848 0.927892i \(-0.621619\pi\)
−0.372848 + 0.927892i \(0.621619\pi\)
\(198\) 14.8416 1.05475
\(199\) 7.65546 0.542681 0.271341 0.962483i \(-0.412533\pi\)
0.271341 + 0.962483i \(0.412533\pi\)
\(200\) 17.6562 1.24848
\(201\) −7.14994 −0.504318
\(202\) −5.59419 −0.393606
\(203\) 19.6132 1.37658
\(204\) −3.66334 −0.256485
\(205\) 4.13676 0.288924
\(206\) −11.9667 −0.833758
\(207\) 3.60714 0.250714
\(208\) 6.20898 0.430515
\(209\) −0.400291 −0.0276887
\(210\) 4.76579 0.328871
\(211\) 0.111902 0.00770367 0.00385184 0.999993i \(-0.498774\pi\)
0.00385184 + 0.999993i \(0.498774\pi\)
\(212\) −26.5103 −1.82073
\(213\) 14.0505 0.962725
\(214\) 12.1828 0.832798
\(215\) −0.422580 −0.0288197
\(216\) 3.95838 0.269334
\(217\) 21.6132 1.46720
\(218\) −25.2394 −1.70943
\(219\) 8.92623 0.603179
\(220\) −16.7814 −1.13140
\(221\) 2.96601 0.199515
\(222\) 6.42106 0.430953
\(223\) −15.6310 −1.04673 −0.523364 0.852109i \(-0.675323\pi\)
−0.523364 + 0.852109i \(0.675323\pi\)
\(224\) 8.00198 0.534655
\(225\) −4.46047 −0.297365
\(226\) −5.96153 −0.396555
\(227\) 23.1883 1.53906 0.769530 0.638611i \(-0.220491\pi\)
0.769530 + 0.638611i \(0.220491\pi\)
\(228\) −0.235130 −0.0155719
\(229\) −16.1712 −1.06862 −0.534310 0.845289i \(-0.679428\pi\)
−0.534310 + 0.845289i \(0.679428\pi\)
\(230\) −6.30530 −0.415759
\(231\) 17.0034 1.11874
\(232\) −28.4757 −1.86952
\(233\) 25.8962 1.69652 0.848259 0.529581i \(-0.177651\pi\)
0.848259 + 0.529581i \(0.177651\pi\)
\(234\) −7.05844 −0.461424
\(235\) −8.96743 −0.584970
\(236\) −24.2142 −1.57621
\(237\) −12.6466 −0.821485
\(238\) −6.48826 −0.420572
\(239\) −6.26722 −0.405393 −0.202696 0.979242i \(-0.564970\pi\)
−0.202696 + 0.979242i \(0.564970\pi\)
\(240\) −1.53764 −0.0992541
\(241\) −1.72249 −0.110956 −0.0554778 0.998460i \(-0.517668\pi\)
−0.0554778 + 0.998460i \(0.517668\pi\)
\(242\) −66.3830 −4.26726
\(243\) −1.00000 −0.0641500
\(244\) 23.7455 1.52015
\(245\) 0.318302 0.0203356
\(246\) 13.4026 0.854521
\(247\) 0.190372 0.0121131
\(248\) −31.3794 −1.99259
\(249\) −4.20436 −0.266441
\(250\) 16.5370 1.04589
\(251\) −13.7041 −0.864993 −0.432497 0.901636i \(-0.642367\pi\)
−0.432497 + 0.901636i \(0.642367\pi\)
\(252\) 9.98779 0.629172
\(253\) −22.4961 −1.41432
\(254\) 40.3316 2.53063
\(255\) −0.734525 −0.0459977
\(256\) −26.9553 −1.68470
\(257\) −21.6506 −1.35053 −0.675264 0.737576i \(-0.735970\pi\)
−0.675264 + 0.737576i \(0.735970\pi\)
\(258\) −1.36911 −0.0852372
\(259\) 7.35635 0.457101
\(260\) 7.98097 0.494959
\(261\) 7.19378 0.445284
\(262\) 2.37576 0.146775
\(263\) 1.08026 0.0666118 0.0333059 0.999445i \(-0.489396\pi\)
0.0333059 + 0.999445i \(0.489396\pi\)
\(264\) −24.6866 −1.51936
\(265\) −5.31549 −0.326528
\(266\) −0.416447 −0.0255340
\(267\) −16.4667 −1.00774
\(268\) 26.1927 1.59997
\(269\) 7.37209 0.449484 0.224742 0.974418i \(-0.427846\pi\)
0.224742 + 0.974418i \(0.427846\pi\)
\(270\) 1.74801 0.106380
\(271\) 25.2560 1.53419 0.767096 0.641532i \(-0.221701\pi\)
0.767096 + 0.641532i \(0.221701\pi\)
\(272\) 2.09338 0.126930
\(273\) −8.08657 −0.489421
\(274\) 7.44248 0.449617
\(275\) 27.8180 1.67749
\(276\) −13.2142 −0.795400
\(277\) 21.0057 1.26211 0.631055 0.775738i \(-0.282622\pi\)
0.631055 + 0.775738i \(0.282622\pi\)
\(278\) 1.59635 0.0957426
\(279\) 7.92734 0.474598
\(280\) −7.92713 −0.473737
\(281\) −9.78315 −0.583614 −0.291807 0.956477i \(-0.594256\pi\)
−0.291807 + 0.956477i \(0.594256\pi\)
\(282\) −29.0534 −1.73011
\(283\) −26.5537 −1.57845 −0.789226 0.614103i \(-0.789518\pi\)
−0.789226 + 0.614103i \(0.789518\pi\)
\(284\) −51.4718 −3.05429
\(285\) −0.0471453 −0.00279264
\(286\) 44.0203 2.60298
\(287\) 15.3549 0.906370
\(288\) 2.93498 0.172945
\(289\) 1.00000 0.0588235
\(290\) −12.5748 −0.738415
\(291\) −14.1044 −0.826814
\(292\) −32.6998 −1.91361
\(293\) 19.9315 1.16441 0.582205 0.813042i \(-0.302190\pi\)
0.582205 + 0.813042i \(0.302190\pi\)
\(294\) 1.03126 0.0601444
\(295\) −4.85511 −0.282676
\(296\) −10.6804 −0.620786
\(297\) 6.23656 0.361882
\(298\) 43.2213 2.50374
\(299\) 10.6988 0.618728
\(300\) 16.3402 0.943404
\(301\) −1.56854 −0.0904090
\(302\) −14.9099 −0.857970
\(303\) −2.35072 −0.135045
\(304\) 0.134363 0.00770624
\(305\) 4.76114 0.272622
\(306\) −2.37978 −0.136043
\(307\) 8.20924 0.468526 0.234263 0.972173i \(-0.424732\pi\)
0.234263 + 0.972173i \(0.424732\pi\)
\(308\) −62.2894 −3.54927
\(309\) −5.02849 −0.286061
\(310\) −13.8570 −0.787027
\(311\) −27.1860 −1.54158 −0.770790 0.637090i \(-0.780138\pi\)
−0.770790 + 0.637090i \(0.780138\pi\)
\(312\) 11.7406 0.664679
\(313\) 29.5119 1.66811 0.834055 0.551681i \(-0.186013\pi\)
0.834055 + 0.551681i \(0.186013\pi\)
\(314\) 2.37978 0.134299
\(315\) 2.00262 0.112835
\(316\) 46.3288 2.60620
\(317\) −4.77085 −0.267957 −0.133979 0.990984i \(-0.542775\pi\)
−0.133979 + 0.990984i \(0.542775\pi\)
\(318\) −17.2216 −0.965739
\(319\) −44.8644 −2.51192
\(320\) −8.20564 −0.458709
\(321\) 5.11930 0.285731
\(322\) −23.4041 −1.30426
\(323\) 0.0641847 0.00357133
\(324\) 3.66334 0.203519
\(325\) −13.2298 −0.733857
\(326\) 21.3189 1.18075
\(327\) −10.6058 −0.586500
\(328\) −22.2931 −1.23093
\(329\) −33.2854 −1.83508
\(330\) −10.9015 −0.600110
\(331\) −21.6904 −1.19221 −0.596107 0.802905i \(-0.703286\pi\)
−0.596107 + 0.802905i \(0.703286\pi\)
\(332\) 15.4020 0.845295
\(333\) 2.69818 0.147859
\(334\) −50.3540 −2.75525
\(335\) 5.25181 0.286937
\(336\) −5.70742 −0.311365
\(337\) 17.6239 0.960033 0.480017 0.877259i \(-0.340631\pi\)
0.480017 + 0.877259i \(0.340631\pi\)
\(338\) 10.0017 0.544023
\(339\) −2.50508 −0.136057
\(340\) 2.69081 0.145930
\(341\) −49.4393 −2.67729
\(342\) −0.152745 −0.00825952
\(343\) −17.9034 −0.966695
\(344\) 2.27730 0.122784
\(345\) −2.64953 −0.142646
\(346\) −16.5629 −0.890428
\(347\) −15.0512 −0.807993 −0.403996 0.914761i \(-0.632379\pi\)
−0.403996 + 0.914761i \(0.632379\pi\)
\(348\) −26.3532 −1.41268
\(349\) 8.39789 0.449529 0.224764 0.974413i \(-0.427839\pi\)
0.224764 + 0.974413i \(0.427839\pi\)
\(350\) 28.9407 1.54695
\(351\) −2.96601 −0.158314
\(352\) −18.3042 −0.975616
\(353\) 17.1065 0.910488 0.455244 0.890367i \(-0.349552\pi\)
0.455244 + 0.890367i \(0.349552\pi\)
\(354\) −15.7300 −0.836041
\(355\) −10.3204 −0.547753
\(356\) 60.3231 3.19712
\(357\) −2.72642 −0.144297
\(358\) −32.6684 −1.72658
\(359\) 11.5832 0.611340 0.305670 0.952138i \(-0.401120\pi\)
0.305670 + 0.952138i \(0.401120\pi\)
\(360\) −2.90753 −0.153240
\(361\) −18.9959 −0.999783
\(362\) 1.99883 0.105056
\(363\) −27.8946 −1.46409
\(364\) 29.6238 1.55271
\(365\) −6.55654 −0.343185
\(366\) 15.4256 0.806307
\(367\) −6.63303 −0.346241 −0.173121 0.984901i \(-0.555385\pi\)
−0.173121 + 0.984901i \(0.555385\pi\)
\(368\) 7.55111 0.393629
\(369\) 5.63189 0.293184
\(370\) −4.71643 −0.245195
\(371\) −19.7301 −1.02433
\(372\) −29.0405 −1.50568
\(373\) 12.9631 0.671203 0.335602 0.942004i \(-0.391060\pi\)
0.335602 + 0.942004i \(0.391060\pi\)
\(374\) 14.8416 0.767442
\(375\) 6.94895 0.358842
\(376\) 48.3257 2.49221
\(377\) 21.3368 1.09890
\(378\) 6.48826 0.333720
\(379\) 8.54593 0.438975 0.219487 0.975615i \(-0.429562\pi\)
0.219487 + 0.975615i \(0.429562\pi\)
\(380\) 0.172709 0.00885979
\(381\) 16.9476 0.868254
\(382\) −8.19562 −0.419324
\(383\) 20.6986 1.05765 0.528823 0.848732i \(-0.322633\pi\)
0.528823 + 0.848732i \(0.322633\pi\)
\(384\) −20.7154 −1.05713
\(385\) −12.4895 −0.636521
\(386\) −0.729199 −0.0371153
\(387\) −0.575311 −0.0292447
\(388\) 51.6692 2.62310
\(389\) −11.5478 −0.585495 −0.292748 0.956190i \(-0.594570\pi\)
−0.292748 + 0.956190i \(0.594570\pi\)
\(390\) 5.18460 0.262532
\(391\) 3.60714 0.182421
\(392\) −1.71534 −0.0866377
\(393\) 0.998311 0.0503581
\(394\) 24.9076 1.25483
\(395\) 9.28924 0.467392
\(396\) −22.8466 −1.14809
\(397\) −1.61469 −0.0810389 −0.0405195 0.999179i \(-0.512901\pi\)
−0.0405195 + 0.999179i \(0.512901\pi\)
\(398\) −18.2183 −0.913200
\(399\) −0.174994 −0.00876067
\(400\) −9.33746 −0.466873
\(401\) −1.95922 −0.0978388 −0.0489194 0.998803i \(-0.515578\pi\)
−0.0489194 + 0.998803i \(0.515578\pi\)
\(402\) 17.0153 0.848644
\(403\) 23.5126 1.17124
\(404\) 8.61148 0.428437
\(405\) 0.734525 0.0364988
\(406\) −46.6751 −2.31645
\(407\) −16.8273 −0.834100
\(408\) 3.95838 0.195969
\(409\) 20.2309 1.00035 0.500177 0.865923i \(-0.333268\pi\)
0.500177 + 0.865923i \(0.333268\pi\)
\(410\) −9.84457 −0.486189
\(411\) 3.12738 0.154263
\(412\) 18.4211 0.907541
\(413\) −18.0212 −0.886767
\(414\) −8.58419 −0.421890
\(415\) 3.08821 0.151594
\(416\) 8.70518 0.426806
\(417\) 0.670797 0.0328491
\(418\) 0.952605 0.0465934
\(419\) −16.0667 −0.784910 −0.392455 0.919771i \(-0.628374\pi\)
−0.392455 + 0.919771i \(0.628374\pi\)
\(420\) −7.33628 −0.357974
\(421\) −2.14323 −0.104455 −0.0522274 0.998635i \(-0.516632\pi\)
−0.0522274 + 0.998635i \(0.516632\pi\)
\(422\) −0.266302 −0.0129634
\(423\) −12.2085 −0.593596
\(424\) 28.6453 1.39114
\(425\) −4.46047 −0.216365
\(426\) −33.4371 −1.62003
\(427\) 17.6724 0.855230
\(428\) −18.7537 −0.906495
\(429\) 18.4977 0.893076
\(430\) 1.00565 0.0484966
\(431\) −4.74882 −0.228743 −0.114371 0.993438i \(-0.536485\pi\)
−0.114371 + 0.993438i \(0.536485\pi\)
\(432\) −2.09338 −0.100718
\(433\) −5.77068 −0.277321 −0.138661 0.990340i \(-0.544280\pi\)
−0.138661 + 0.990340i \(0.544280\pi\)
\(434\) −51.4347 −2.46894
\(435\) −5.28401 −0.253349
\(436\) 38.8525 1.86070
\(437\) 0.231523 0.0110753
\(438\) −21.2424 −1.01500
\(439\) 34.4854 1.64590 0.822948 0.568116i \(-0.192328\pi\)
0.822948 + 0.568116i \(0.192328\pi\)
\(440\) 18.1330 0.864455
\(441\) 0.433344 0.0206354
\(442\) −7.05844 −0.335736
\(443\) 39.0178 1.85379 0.926896 0.375319i \(-0.122467\pi\)
0.926896 + 0.375319i \(0.122467\pi\)
\(444\) −9.88434 −0.469090
\(445\) 12.0952 0.573367
\(446\) 37.1983 1.76139
\(447\) 18.1619 0.859029
\(448\) −30.4578 −1.43899
\(449\) 6.88449 0.324899 0.162450 0.986717i \(-0.448061\pi\)
0.162450 + 0.986717i \(0.448061\pi\)
\(450\) 10.6149 0.500393
\(451\) −35.1236 −1.65391
\(452\) 9.17696 0.431648
\(453\) −6.26526 −0.294368
\(454\) −55.1829 −2.58986
\(455\) 5.93979 0.278461
\(456\) 0.254067 0.0118978
\(457\) −16.3957 −0.766960 −0.383480 0.923549i \(-0.625275\pi\)
−0.383480 + 0.923549i \(0.625275\pi\)
\(458\) 38.4837 1.79823
\(459\) −1.00000 −0.0466760
\(460\) 9.70615 0.452551
\(461\) −37.8961 −1.76500 −0.882498 0.470316i \(-0.844140\pi\)
−0.882498 + 0.470316i \(0.844140\pi\)
\(462\) −40.4644 −1.88257
\(463\) 15.0192 0.698002 0.349001 0.937122i \(-0.386521\pi\)
0.349001 + 0.937122i \(0.386521\pi\)
\(464\) 15.0593 0.699110
\(465\) −5.82283 −0.270027
\(466\) −61.6273 −2.85483
\(467\) −2.15937 −0.0999238 −0.0499619 0.998751i \(-0.515910\pi\)
−0.0499619 + 0.998751i \(0.515910\pi\)
\(468\) 10.8655 0.502258
\(469\) 19.4937 0.900136
\(470\) 21.3405 0.984363
\(471\) 1.00000 0.0460776
\(472\) 26.1643 1.20431
\(473\) 3.58796 0.164974
\(474\) 30.0961 1.38236
\(475\) −0.286294 −0.0131361
\(476\) 9.98779 0.457790
\(477\) −7.23664 −0.331343
\(478\) 14.9146 0.682178
\(479\) 3.78732 0.173047 0.0865235 0.996250i \(-0.472424\pi\)
0.0865235 + 0.996250i \(0.472424\pi\)
\(480\) −2.15582 −0.0983991
\(481\) 8.00281 0.364897
\(482\) 4.09915 0.186711
\(483\) −9.83457 −0.447488
\(484\) 102.187 4.64489
\(485\) 10.3600 0.470424
\(486\) 2.37978 0.107949
\(487\) −35.2620 −1.59787 −0.798937 0.601415i \(-0.794604\pi\)
−0.798937 + 0.601415i \(0.794604\pi\)
\(488\) −25.6579 −1.16148
\(489\) 8.95837 0.405112
\(490\) −0.757488 −0.0342198
\(491\) 33.8768 1.52884 0.764418 0.644721i \(-0.223026\pi\)
0.764418 + 0.644721i \(0.223026\pi\)
\(492\) −20.6315 −0.930141
\(493\) 7.19378 0.323991
\(494\) −0.453044 −0.0203834
\(495\) −4.58091 −0.205896
\(496\) 16.5949 0.745134
\(497\) −38.3075 −1.71833
\(498\) 10.0055 0.448355
\(499\) −23.1992 −1.03854 −0.519270 0.854610i \(-0.673796\pi\)
−0.519270 + 0.854610i \(0.673796\pi\)
\(500\) −25.4564 −1.13844
\(501\) −21.1591 −0.945320
\(502\) 32.6126 1.45557
\(503\) 4.67068 0.208255 0.104128 0.994564i \(-0.466795\pi\)
0.104128 + 0.994564i \(0.466795\pi\)
\(504\) −10.7922 −0.480722
\(505\) 1.72666 0.0768354
\(506\) 53.5358 2.37996
\(507\) 4.20280 0.186653
\(508\) −62.0850 −2.75458
\(509\) −3.42509 −0.151814 −0.0759072 0.997115i \(-0.524185\pi\)
−0.0759072 + 0.997115i \(0.524185\pi\)
\(510\) 1.74801 0.0774030
\(511\) −24.3366 −1.07659
\(512\) 22.7168 1.00395
\(513\) −0.0641847 −0.00283382
\(514\) 51.5236 2.27261
\(515\) 3.69355 0.162757
\(516\) 2.10756 0.0927801
\(517\) 76.1388 3.34858
\(518\) −17.5065 −0.769190
\(519\) −6.95986 −0.305504
\(520\) −8.62375 −0.378176
\(521\) 23.0456 1.00965 0.504823 0.863223i \(-0.331558\pi\)
0.504823 + 0.863223i \(0.331558\pi\)
\(522\) −17.1196 −0.749304
\(523\) −3.48193 −0.152254 −0.0761271 0.997098i \(-0.524255\pi\)
−0.0761271 + 0.997098i \(0.524255\pi\)
\(524\) −3.65715 −0.159763
\(525\) 12.1611 0.530754
\(526\) −2.57078 −0.112092
\(527\) 7.92734 0.345320
\(528\) 13.0555 0.568166
\(529\) −9.98853 −0.434284
\(530\) 12.6497 0.549467
\(531\) −6.60987 −0.286844
\(532\) 0.641063 0.0277936
\(533\) 16.7042 0.723540
\(534\) 39.1870 1.69579
\(535\) −3.76025 −0.162570
\(536\) −28.3022 −1.22247
\(537\) −13.7275 −0.592386
\(538\) −17.5439 −0.756372
\(539\) −2.70257 −0.116408
\(540\) −2.69081 −0.115794
\(541\) 36.2638 1.55910 0.779552 0.626338i \(-0.215447\pi\)
0.779552 + 0.626338i \(0.215447\pi\)
\(542\) −60.1036 −2.58167
\(543\) 0.839921 0.0360445
\(544\) 2.93498 0.125836
\(545\) 7.79020 0.333695
\(546\) 19.2442 0.823577
\(547\) 5.79785 0.247898 0.123949 0.992289i \(-0.460444\pi\)
0.123949 + 0.992289i \(0.460444\pi\)
\(548\) −11.4567 −0.489405
\(549\) 6.48193 0.276642
\(550\) −66.2006 −2.82280
\(551\) 0.461730 0.0196704
\(552\) 14.2784 0.607730
\(553\) 34.4799 1.46623
\(554\) −49.9889 −2.12382
\(555\) −1.98188 −0.0841260
\(556\) −2.45736 −0.104215
\(557\) 38.5754 1.63449 0.817247 0.576288i \(-0.195499\pi\)
0.817247 + 0.576288i \(0.195499\pi\)
\(558\) −18.8653 −0.798632
\(559\) −1.70638 −0.0721720
\(560\) 4.19224 0.177155
\(561\) 6.23656 0.263308
\(562\) 23.2817 0.982080
\(563\) −21.1826 −0.892740 −0.446370 0.894849i \(-0.647283\pi\)
−0.446370 + 0.894849i \(0.647283\pi\)
\(564\) 44.7238 1.88321
\(565\) 1.84004 0.0774112
\(566\) 63.1918 2.65615
\(567\) 2.72642 0.114499
\(568\) 55.6172 2.33365
\(569\) −0.776453 −0.0325506 −0.0162753 0.999868i \(-0.505181\pi\)
−0.0162753 + 0.999868i \(0.505181\pi\)
\(570\) 0.112195 0.00469934
\(571\) −42.6611 −1.78531 −0.892655 0.450741i \(-0.851160\pi\)
−0.892655 + 0.450741i \(0.851160\pi\)
\(572\) −67.7632 −2.83332
\(573\) −3.44386 −0.143869
\(574\) −36.5412 −1.52520
\(575\) −16.0896 −0.670981
\(576\) −11.1714 −0.465473
\(577\) −6.38700 −0.265894 −0.132947 0.991123i \(-0.542444\pi\)
−0.132947 + 0.991123i \(0.542444\pi\)
\(578\) −2.37978 −0.0989857
\(579\) −0.306415 −0.0127342
\(580\) 19.3571 0.803760
\(581\) 11.4628 0.475559
\(582\) 33.5653 1.39133
\(583\) 45.1317 1.86916
\(584\) 35.3334 1.46211
\(585\) 2.17861 0.0900743
\(586\) −47.4325 −1.95942
\(587\) −0.753975 −0.0311199 −0.0155599 0.999879i \(-0.504953\pi\)
−0.0155599 + 0.999879i \(0.504953\pi\)
\(588\) −1.58749 −0.0654668
\(589\) 0.508814 0.0209653
\(590\) 11.5541 0.475674
\(591\) 10.4663 0.430528
\(592\) 5.64830 0.232144
\(593\) 28.2870 1.16161 0.580803 0.814044i \(-0.302739\pi\)
0.580803 + 0.814044i \(0.302739\pi\)
\(594\) −14.8416 −0.608959
\(595\) 2.00262 0.0820994
\(596\) −66.5332 −2.72531
\(597\) −7.65546 −0.313317
\(598\) −25.4608 −1.04117
\(599\) −22.5470 −0.921244 −0.460622 0.887596i \(-0.652374\pi\)
−0.460622 + 0.887596i \(0.652374\pi\)
\(600\) −17.6562 −0.720813
\(601\) −21.9355 −0.894766 −0.447383 0.894342i \(-0.647644\pi\)
−0.447383 + 0.894342i \(0.647644\pi\)
\(602\) 3.73277 0.152136
\(603\) 7.14994 0.291168
\(604\) 22.9518 0.933895
\(605\) 20.4893 0.833008
\(606\) 5.59419 0.227248
\(607\) 46.9308 1.90486 0.952432 0.304752i \(-0.0985736\pi\)
0.952432 + 0.304752i \(0.0985736\pi\)
\(608\) 0.188381 0.00763986
\(609\) −19.6132 −0.794768
\(610\) −11.3305 −0.458757
\(611\) −36.2104 −1.46492
\(612\) 3.66334 0.148082
\(613\) −15.4681 −0.624752 −0.312376 0.949959i \(-0.601125\pi\)
−0.312376 + 0.949959i \(0.601125\pi\)
\(614\) −19.5362 −0.788416
\(615\) −4.13676 −0.166810
\(616\) 67.3061 2.71184
\(617\) −15.2965 −0.615816 −0.307908 0.951416i \(-0.599629\pi\)
−0.307908 + 0.951416i \(0.599629\pi\)
\(618\) 11.9667 0.481371
\(619\) 1.53191 0.0615726 0.0307863 0.999526i \(-0.490199\pi\)
0.0307863 + 0.999526i \(0.490199\pi\)
\(620\) 21.3310 0.856674
\(621\) −3.60714 −0.144750
\(622\) 64.6967 2.59410
\(623\) 44.8950 1.79868
\(624\) −6.20898 −0.248558
\(625\) 17.1982 0.687927
\(626\) −70.2317 −2.80702
\(627\) 0.400291 0.0159861
\(628\) −3.66334 −0.146183
\(629\) 2.69818 0.107583
\(630\) −4.76579 −0.189874
\(631\) −24.3836 −0.970698 −0.485349 0.874321i \(-0.661307\pi\)
−0.485349 + 0.874321i \(0.661307\pi\)
\(632\) −50.0600 −1.99128
\(633\) −0.111902 −0.00444772
\(634\) 11.3535 0.450907
\(635\) −12.4485 −0.494002
\(636\) 26.5103 1.05120
\(637\) 1.28530 0.0509255
\(638\) 106.767 4.22696
\(639\) −14.0505 −0.555830
\(640\) 15.2160 0.601464
\(641\) −23.4294 −0.925405 −0.462702 0.886514i \(-0.653120\pi\)
−0.462702 + 0.886514i \(0.653120\pi\)
\(642\) −12.1828 −0.480816
\(643\) 11.0157 0.434418 0.217209 0.976125i \(-0.430305\pi\)
0.217209 + 0.976125i \(0.430305\pi\)
\(644\) 36.0274 1.41968
\(645\) 0.422580 0.0166391
\(646\) −0.152745 −0.00600968
\(647\) −32.8575 −1.29176 −0.645880 0.763439i \(-0.723509\pi\)
−0.645880 + 0.763439i \(0.723509\pi\)
\(648\) −3.95838 −0.155500
\(649\) 41.2228 1.61814
\(650\) 31.4840 1.23490
\(651\) −21.6132 −0.847089
\(652\) −32.8176 −1.28524
\(653\) 23.2190 0.908630 0.454315 0.890841i \(-0.349884\pi\)
0.454315 + 0.890841i \(0.349884\pi\)
\(654\) 25.2394 0.986937
\(655\) −0.733284 −0.0286518
\(656\) 11.7897 0.460310
\(657\) −8.92623 −0.348246
\(658\) 79.2118 3.08800
\(659\) −21.7995 −0.849187 −0.424594 0.905384i \(-0.639583\pi\)
−0.424594 + 0.905384i \(0.639583\pi\)
\(660\) 16.7814 0.653216
\(661\) 3.61111 0.140456 0.0702279 0.997531i \(-0.477627\pi\)
0.0702279 + 0.997531i \(0.477627\pi\)
\(662\) 51.6184 2.00621
\(663\) −2.96601 −0.115190
\(664\) −16.6425 −0.645853
\(665\) 0.128538 0.00498447
\(666\) −6.42106 −0.248811
\(667\) 25.9490 1.00475
\(668\) 77.5130 2.99907
\(669\) 15.6310 0.604329
\(670\) −12.4981 −0.482845
\(671\) −40.4249 −1.56059
\(672\) −8.00198 −0.308683
\(673\) 44.4176 1.71217 0.856087 0.516833i \(-0.172889\pi\)
0.856087 + 0.516833i \(0.172889\pi\)
\(674\) −41.9409 −1.61550
\(675\) 4.46047 0.171684
\(676\) −15.3963 −0.592165
\(677\) 47.0903 1.80983 0.904914 0.425594i \(-0.139935\pi\)
0.904914 + 0.425594i \(0.139935\pi\)
\(678\) 5.96153 0.228951
\(679\) 38.4544 1.47575
\(680\) −2.90753 −0.111499
\(681\) −23.1883 −0.888576
\(682\) 117.655 4.50523
\(683\) 27.7821 1.06305 0.531526 0.847042i \(-0.321619\pi\)
0.531526 + 0.847042i \(0.321619\pi\)
\(684\) 0.235130 0.00899043
\(685\) −2.29714 −0.0877693
\(686\) 42.6062 1.62671
\(687\) 16.1712 0.616968
\(688\) −1.20434 −0.0459152
\(689\) −21.4639 −0.817710
\(690\) 6.30530 0.240039
\(691\) −18.2899 −0.695781 −0.347890 0.937535i \(-0.613102\pi\)
−0.347890 + 0.937535i \(0.613102\pi\)
\(692\) 25.4963 0.969225
\(693\) −17.0034 −0.645907
\(694\) 35.8186 1.35966
\(695\) −0.492717 −0.0186898
\(696\) 28.4757 1.07937
\(697\) 5.63189 0.213323
\(698\) −19.9851 −0.756448
\(699\) −25.8962 −0.979485
\(700\) −44.5503 −1.68384
\(701\) 30.5666 1.15448 0.577242 0.816573i \(-0.304129\pi\)
0.577242 + 0.816573i \(0.304129\pi\)
\(702\) 7.05844 0.266404
\(703\) 0.173182 0.00653167
\(704\) 69.6708 2.62582
\(705\) 8.96743 0.337733
\(706\) −40.7097 −1.53213
\(707\) 6.40904 0.241037
\(708\) 24.2142 0.910025
\(709\) −7.79520 −0.292755 −0.146377 0.989229i \(-0.546761\pi\)
−0.146377 + 0.989229i \(0.546761\pi\)
\(710\) 24.5604 0.921734
\(711\) 12.6466 0.474284
\(712\) −65.1814 −2.44277
\(713\) 28.5950 1.07089
\(714\) 6.48826 0.242817
\(715\) −13.5870 −0.508125
\(716\) 50.2885 1.87937
\(717\) 6.26722 0.234054
\(718\) −27.5655 −1.02874
\(719\) 51.3438 1.91480 0.957401 0.288761i \(-0.0932433\pi\)
0.957401 + 0.288761i \(0.0932433\pi\)
\(720\) 1.53764 0.0573044
\(721\) 13.7098 0.510578
\(722\) 45.2060 1.68239
\(723\) 1.72249 0.0640602
\(724\) −3.07692 −0.114353
\(725\) −32.0876 −1.19171
\(726\) 66.3830 2.46370
\(727\) 37.3757 1.38619 0.693093 0.720848i \(-0.256247\pi\)
0.693093 + 0.720848i \(0.256247\pi\)
\(728\) −32.0097 −1.18636
\(729\) 1.00000 0.0370370
\(730\) 15.6031 0.577497
\(731\) −0.575311 −0.0212786
\(732\) −23.7455 −0.877660
\(733\) 26.2548 0.969743 0.484872 0.874585i \(-0.338866\pi\)
0.484872 + 0.874585i \(0.338866\pi\)
\(734\) 15.7851 0.582640
\(735\) −0.318302 −0.0117407
\(736\) 10.5869 0.390238
\(737\) −44.5910 −1.64253
\(738\) −13.4026 −0.493358
\(739\) 33.9499 1.24887 0.624434 0.781077i \(-0.285330\pi\)
0.624434 + 0.781077i \(0.285330\pi\)
\(740\) 7.26029 0.266894
\(741\) −0.190372 −0.00699350
\(742\) 46.9532 1.72371
\(743\) 32.8656 1.20572 0.602862 0.797846i \(-0.294027\pi\)
0.602862 + 0.797846i \(0.294027\pi\)
\(744\) 31.3794 1.15043
\(745\) −13.3404 −0.488753
\(746\) −30.8493 −1.12947
\(747\) 4.20436 0.153830
\(748\) −22.8466 −0.835355
\(749\) −13.9573 −0.509990
\(750\) −16.5370 −0.603844
\(751\) 12.1459 0.443211 0.221605 0.975136i \(-0.428870\pi\)
0.221605 + 0.975136i \(0.428870\pi\)
\(752\) −25.5569 −0.931966
\(753\) 13.7041 0.499404
\(754\) −50.7768 −1.84918
\(755\) 4.60199 0.167484
\(756\) −9.98779 −0.363252
\(757\) −42.7580 −1.55407 −0.777033 0.629459i \(-0.783276\pi\)
−0.777033 + 0.629459i \(0.783276\pi\)
\(758\) −20.3374 −0.738688
\(759\) 22.4961 0.816558
\(760\) −0.186619 −0.00676937
\(761\) 27.6200 1.00122 0.500612 0.865672i \(-0.333108\pi\)
0.500612 + 0.865672i \(0.333108\pi\)
\(762\) −40.3316 −1.46106
\(763\) 28.9157 1.04682
\(764\) 12.6160 0.456432
\(765\) 0.734525 0.0265568
\(766\) −49.2580 −1.77976
\(767\) −19.6049 −0.707892
\(768\) 26.9553 0.972665
\(769\) 18.0964 0.652572 0.326286 0.945271i \(-0.394203\pi\)
0.326286 + 0.945271i \(0.394203\pi\)
\(770\) 29.7221 1.07111
\(771\) 21.6506 0.779728
\(772\) 1.12250 0.0403997
\(773\) −37.1039 −1.33454 −0.667268 0.744818i \(-0.732536\pi\)
−0.667268 + 0.744818i \(0.732536\pi\)
\(774\) 1.36911 0.0492117
\(775\) −35.3597 −1.27016
\(776\) −55.8305 −2.00420
\(777\) −7.35635 −0.263908
\(778\) 27.4811 0.985246
\(779\) 0.361481 0.0129514
\(780\) −7.98097 −0.285765
\(781\) 87.6268 3.13553
\(782\) −8.58419 −0.306970
\(783\) −7.19378 −0.257085
\(784\) 0.907153 0.0323983
\(785\) −0.734525 −0.0262163
\(786\) −2.37576 −0.0847405
\(787\) −49.8328 −1.77635 −0.888173 0.459509i \(-0.848025\pi\)
−0.888173 + 0.459509i \(0.848025\pi\)
\(788\) −38.3418 −1.36587
\(789\) −1.08026 −0.0384584
\(790\) −22.1063 −0.786508
\(791\) 6.82989 0.242843
\(792\) 24.6866 0.877202
\(793\) 19.2255 0.682716
\(794\) 3.84260 0.136369
\(795\) 5.31549 0.188521
\(796\) 28.0446 0.994013
\(797\) 10.9698 0.388572 0.194286 0.980945i \(-0.437761\pi\)
0.194286 + 0.980945i \(0.437761\pi\)
\(798\) 0.416447 0.0147421
\(799\) −12.2085 −0.431905
\(800\) −13.0914 −0.462851
\(801\) 16.4667 0.581822
\(802\) 4.66251 0.164639
\(803\) 55.6690 1.96451
\(804\) −26.1927 −0.923744
\(805\) 7.22373 0.254603
\(806\) −55.9546 −1.97092
\(807\) −7.37209 −0.259510
\(808\) −9.30503 −0.327350
\(809\) −1.91259 −0.0672429 −0.0336215 0.999435i \(-0.510704\pi\)
−0.0336215 + 0.999435i \(0.510704\pi\)
\(810\) −1.74801 −0.0614187
\(811\) 36.0126 1.26457 0.632286 0.774735i \(-0.282117\pi\)
0.632286 + 0.774735i \(0.282117\pi\)
\(812\) 71.8499 2.52144
\(813\) −25.2560 −0.885766
\(814\) 40.0453 1.40359
\(815\) −6.58015 −0.230493
\(816\) −2.09338 −0.0732829
\(817\) −0.0369262 −0.00129188
\(818\) −48.1450 −1.68335
\(819\) 8.08657 0.282568
\(820\) 15.1544 0.529214
\(821\) −29.1493 −1.01732 −0.508659 0.860968i \(-0.669859\pi\)
−0.508659 + 0.860968i \(0.669859\pi\)
\(822\) −7.44248 −0.259586
\(823\) −6.98191 −0.243374 −0.121687 0.992569i \(-0.538830\pi\)
−0.121687 + 0.992569i \(0.538830\pi\)
\(824\) −19.9047 −0.693412
\(825\) −27.8180 −0.968498
\(826\) 42.8865 1.49221
\(827\) 6.65728 0.231496 0.115748 0.993279i \(-0.463073\pi\)
0.115748 + 0.993279i \(0.463073\pi\)
\(828\) 13.2142 0.459225
\(829\) 23.0197 0.799507 0.399753 0.916623i \(-0.369096\pi\)
0.399753 + 0.916623i \(0.369096\pi\)
\(830\) −7.34925 −0.255096
\(831\) −21.0057 −0.728679
\(832\) −33.1343 −1.14873
\(833\) 0.433344 0.0150145
\(834\) −1.59635 −0.0552770
\(835\) 15.5419 0.537850
\(836\) −1.46640 −0.0507166
\(837\) −7.92734 −0.274009
\(838\) 38.2352 1.32081
\(839\) −25.1574 −0.868529 −0.434264 0.900785i \(-0.642992\pi\)
−0.434264 + 0.900785i \(0.642992\pi\)
\(840\) 7.92713 0.273512
\(841\) 22.7504 0.784497
\(842\) 5.10042 0.175772
\(843\) 9.78315 0.336950
\(844\) 0.409936 0.0141106
\(845\) −3.08706 −0.106198
\(846\) 29.0534 0.998878
\(847\) 76.0523 2.61319
\(848\) −15.1490 −0.520220
\(849\) 26.5537 0.911319
\(850\) 10.6149 0.364089
\(851\) 9.73270 0.333633
\(852\) 51.4718 1.76339
\(853\) −4.53789 −0.155374 −0.0776872 0.996978i \(-0.524754\pi\)
−0.0776872 + 0.996978i \(0.524754\pi\)
\(854\) −42.0565 −1.43914
\(855\) 0.0471453 0.00161233
\(856\) 20.2641 0.692613
\(857\) 29.0511 0.992368 0.496184 0.868217i \(-0.334734\pi\)
0.496184 + 0.868217i \(0.334734\pi\)
\(858\) −44.0203 −1.50283
\(859\) −26.8534 −0.916227 −0.458113 0.888894i \(-0.651475\pi\)
−0.458113 + 0.888894i \(0.651475\pi\)
\(860\) −1.54805 −0.0527882
\(861\) −15.3549 −0.523293
\(862\) 11.3011 0.384918
\(863\) 26.7606 0.910941 0.455470 0.890251i \(-0.349471\pi\)
0.455470 + 0.890251i \(0.349471\pi\)
\(864\) −2.93498 −0.0998501
\(865\) 5.11219 0.173820
\(866\) 13.7329 0.466664
\(867\) −1.00000 −0.0339618
\(868\) 79.1766 2.68743
\(869\) −78.8712 −2.67552
\(870\) 12.5748 0.426324
\(871\) 21.2068 0.718564
\(872\) −41.9816 −1.42168
\(873\) 14.1044 0.477361
\(874\) −0.550974 −0.0186370
\(875\) −18.9457 −0.640483
\(876\) 32.6998 1.10482
\(877\) 0.557986 0.0188419 0.00942093 0.999956i \(-0.497001\pi\)
0.00942093 + 0.999956i \(0.497001\pi\)
\(878\) −82.0675 −2.76964
\(879\) −19.9315 −0.672273
\(880\) −9.58957 −0.323264
\(881\) −23.8445 −0.803343 −0.401671 0.915784i \(-0.631571\pi\)
−0.401671 + 0.915784i \(0.631571\pi\)
\(882\) −1.03126 −0.0347244
\(883\) 19.6802 0.662290 0.331145 0.943580i \(-0.392565\pi\)
0.331145 + 0.943580i \(0.392565\pi\)
\(884\) 10.8655 0.365446
\(885\) 4.85511 0.163203
\(886\) −92.8537 −3.11948
\(887\) 7.66179 0.257258 0.128629 0.991693i \(-0.458942\pi\)
0.128629 + 0.991693i \(0.458942\pi\)
\(888\) 10.6804 0.358411
\(889\) −46.2063 −1.54971
\(890\) −28.7839 −0.964837
\(891\) −6.23656 −0.208932
\(892\) −57.2616 −1.91726
\(893\) −0.783597 −0.0262221
\(894\) −43.2213 −1.44554
\(895\) 10.0832 0.337044
\(896\) 56.4788 1.88682
\(897\) −10.6988 −0.357223
\(898\) −16.3836 −0.546726
\(899\) 57.0275 1.90197
\(900\) −16.3402 −0.544674
\(901\) −7.23664 −0.241087
\(902\) 83.5863 2.78312
\(903\) 1.56854 0.0521976
\(904\) −9.91606 −0.329803
\(905\) −0.616943 −0.0205079
\(906\) 14.9099 0.495349
\(907\) −51.6616 −1.71539 −0.857697 0.514156i \(-0.828105\pi\)
−0.857697 + 0.514156i \(0.828105\pi\)
\(908\) 84.9465 2.81905
\(909\) 2.35072 0.0779684
\(910\) −14.1354 −0.468583
\(911\) 1.47121 0.0487434 0.0243717 0.999703i \(-0.492241\pi\)
0.0243717 + 0.999703i \(0.492241\pi\)
\(912\) −0.134363 −0.00444920
\(913\) −26.2208 −0.867780
\(914\) 39.0182 1.29061
\(915\) −4.76114 −0.157398
\(916\) −59.2404 −1.95736
\(917\) −2.72181 −0.0898821
\(918\) 2.37978 0.0785444
\(919\) 31.9780 1.05486 0.527429 0.849599i \(-0.323156\pi\)
0.527429 + 0.849599i \(0.323156\pi\)
\(920\) −10.4879 −0.345775
\(921\) −8.20924 −0.270504
\(922\) 90.1842 2.97006
\(923\) −41.6739 −1.37171
\(924\) 62.2894 2.04917
\(925\) −12.0351 −0.395713
\(926\) −35.7424 −1.17457
\(927\) 5.02849 0.165157
\(928\) 21.1136 0.693088
\(929\) −4.05054 −0.132894 −0.0664469 0.997790i \(-0.521166\pi\)
−0.0664469 + 0.997790i \(0.521166\pi\)
\(930\) 13.8570 0.454390
\(931\) 0.0278141 0.000911569 0
\(932\) 94.8667 3.10746
\(933\) 27.1860 0.890031
\(934\) 5.13882 0.168147
\(935\) −4.58091 −0.149812
\(936\) −11.7406 −0.383753
\(937\) −4.43947 −0.145031 −0.0725156 0.997367i \(-0.523103\pi\)
−0.0725156 + 0.997367i \(0.523103\pi\)
\(938\) −46.3907 −1.51471
\(939\) −29.5119 −0.963084
\(940\) −32.8507 −1.07147
\(941\) −3.99015 −0.130075 −0.0650376 0.997883i \(-0.520717\pi\)
−0.0650376 + 0.997883i \(0.520717\pi\)
\(942\) −2.37978 −0.0775373
\(943\) 20.3150 0.661548
\(944\) −13.8370 −0.450354
\(945\) −2.00262 −0.0651452
\(946\) −8.53854 −0.277612
\(947\) 10.2018 0.331514 0.165757 0.986167i \(-0.446993\pi\)
0.165757 + 0.986167i \(0.446993\pi\)
\(948\) −46.3288 −1.50469
\(949\) −26.4753 −0.859424
\(950\) 0.681316 0.0221048
\(951\) 4.77085 0.154705
\(952\) −10.7922 −0.349777
\(953\) −45.9426 −1.48823 −0.744113 0.668053i \(-0.767128\pi\)
−0.744113 + 0.668053i \(0.767128\pi\)
\(954\) 17.2216 0.557569
\(955\) 2.52960 0.0818559
\(956\) −22.9590 −0.742546
\(957\) 44.8644 1.45026
\(958\) −9.01298 −0.291196
\(959\) −8.52655 −0.275337
\(960\) 8.20564 0.264836
\(961\) 31.8428 1.02719
\(962\) −19.0449 −0.614032
\(963\) −5.11930 −0.164967
\(964\) −6.31008 −0.203234
\(965\) 0.225069 0.00724524
\(966\) 23.4041 0.753014
\(967\) 21.8848 0.703768 0.351884 0.936044i \(-0.385541\pi\)
0.351884 + 0.936044i \(0.385541\pi\)
\(968\) −110.417 −3.54895
\(969\) −0.0641847 −0.00206191
\(970\) −24.6545 −0.791610
\(971\) 16.9456 0.543809 0.271905 0.962324i \(-0.412346\pi\)
0.271905 + 0.962324i \(0.412346\pi\)
\(972\) −3.66334 −0.117502
\(973\) −1.82887 −0.0586310
\(974\) 83.9157 2.68883
\(975\) 13.2298 0.423693
\(976\) 13.5691 0.434338
\(977\) 56.9801 1.82296 0.911478 0.411348i \(-0.134942\pi\)
0.911478 + 0.411348i \(0.134942\pi\)
\(978\) −21.3189 −0.681704
\(979\) −102.695 −3.28216
\(980\) 1.16605 0.0372481
\(981\) 10.6058 0.338616
\(982\) −80.6191 −2.57266
\(983\) 59.0784 1.88431 0.942155 0.335178i \(-0.108797\pi\)
0.942155 + 0.335178i \(0.108797\pi\)
\(984\) 22.2931 0.710680
\(985\) −7.68779 −0.244953
\(986\) −17.1196 −0.545199
\(987\) 33.2854 1.05948
\(988\) 0.697398 0.0221872
\(989\) −2.07523 −0.0659884
\(990\) 10.9015 0.346474
\(991\) −33.3127 −1.05821 −0.529106 0.848556i \(-0.677473\pi\)
−0.529106 + 0.848556i \(0.677473\pi\)
\(992\) 23.2666 0.738715
\(993\) 21.6904 0.688325
\(994\) 91.1634 2.89153
\(995\) 5.62313 0.178265
\(996\) −15.4020 −0.488032
\(997\) 45.0085 1.42543 0.712717 0.701451i \(-0.247464\pi\)
0.712717 + 0.701451i \(0.247464\pi\)
\(998\) 55.2090 1.74761
\(999\) −2.69818 −0.0853665
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 \(a_p\))