Properties

Label 8042.2.a.a.1.6
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 1
Dimension 67
CM No

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Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(1\)
Dimension: \(67\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.60859 q^{3}\) \(+1.00000 q^{4}\) \(+0.145596 q^{5}\) \(-2.60859 q^{6}\) \(+0.982128 q^{7}\) \(+1.00000 q^{8}\) \(+3.80473 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.60859 q^{3}\) \(+1.00000 q^{4}\) \(+0.145596 q^{5}\) \(-2.60859 q^{6}\) \(+0.982128 q^{7}\) \(+1.00000 q^{8}\) \(+3.80473 q^{9}\) \(+0.145596 q^{10}\) \(-4.17910 q^{11}\) \(-2.60859 q^{12}\) \(+2.84300 q^{13}\) \(+0.982128 q^{14}\) \(-0.379799 q^{15}\) \(+1.00000 q^{16}\) \(-1.12150 q^{17}\) \(+3.80473 q^{18}\) \(-4.48714 q^{19}\) \(+0.145596 q^{20}\) \(-2.56197 q^{21}\) \(-4.17910 q^{22}\) \(+6.95573 q^{23}\) \(-2.60859 q^{24}\) \(-4.97880 q^{25}\) \(+2.84300 q^{26}\) \(-2.09920 q^{27}\) \(+0.982128 q^{28}\) \(-7.09928 q^{29}\) \(-0.379799 q^{30}\) \(+5.43800 q^{31}\) \(+1.00000 q^{32}\) \(+10.9015 q^{33}\) \(-1.12150 q^{34}\) \(+0.142994 q^{35}\) \(+3.80473 q^{36}\) \(+11.1763 q^{37}\) \(-4.48714 q^{38}\) \(-7.41622 q^{39}\) \(+0.145596 q^{40}\) \(-0.660816 q^{41}\) \(-2.56197 q^{42}\) \(+7.34193 q^{43}\) \(-4.17910 q^{44}\) \(+0.553952 q^{45}\) \(+6.95573 q^{46}\) \(-9.13043 q^{47}\) \(-2.60859 q^{48}\) \(-6.03542 q^{49}\) \(-4.97880 q^{50}\) \(+2.92552 q^{51}\) \(+2.84300 q^{52}\) \(-2.95851 q^{53}\) \(-2.09920 q^{54}\) \(-0.608459 q^{55}\) \(+0.982128 q^{56}\) \(+11.7051 q^{57}\) \(-7.09928 q^{58}\) \(+14.3274 q^{59}\) \(-0.379799 q^{60}\) \(-9.35855 q^{61}\) \(+5.43800 q^{62}\) \(+3.73673 q^{63}\) \(+1.00000 q^{64}\) \(+0.413929 q^{65}\) \(+10.9015 q^{66}\) \(-3.06041 q^{67}\) \(-1.12150 q^{68}\) \(-18.1446 q^{69}\) \(+0.142994 q^{70}\) \(-6.29243 q^{71}\) \(+3.80473 q^{72}\) \(-13.1900 q^{73}\) \(+11.1763 q^{74}\) \(+12.9876 q^{75}\) \(-4.48714 q^{76}\) \(-4.10441 q^{77}\) \(-7.41622 q^{78}\) \(-7.99316 q^{79}\) \(+0.145596 q^{80}\) \(-5.93823 q^{81}\) \(-0.660816 q^{82}\) \(-5.16337 q^{83}\) \(-2.56197 q^{84}\) \(-0.163285 q^{85}\) \(+7.34193 q^{86}\) \(+18.5191 q^{87}\) \(-4.17910 q^{88}\) \(+11.6929 q^{89}\) \(+0.553952 q^{90}\) \(+2.79219 q^{91}\) \(+6.95573 q^{92}\) \(-14.1855 q^{93}\) \(-9.13043 q^{94}\) \(-0.653309 q^{95}\) \(-2.60859 q^{96}\) \(+8.46759 q^{97}\) \(-6.03542 q^{98}\) \(-15.9003 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut -\mathstrut 11q^{12} \) \(\mathstrut -\mathstrut 51q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 31q^{15} \) \(\mathstrut +\mathstrut 67q^{16} \) \(\mathstrut -\mathstrut 34q^{17} \) \(\mathstrut +\mathstrut 24q^{18} \) \(\mathstrut -\mathstrut 33q^{19} \) \(\mathstrut -\mathstrut 20q^{20} \) \(\mathstrut -\mathstrut 39q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 43q^{23} \) \(\mathstrut -\mathstrut 11q^{24} \) \(\mathstrut -\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut 51q^{26} \) \(\mathstrut -\mathstrut 29q^{27} \) \(\mathstrut -\mathstrut 40q^{28} \) \(\mathstrut -\mathstrut 63q^{29} \) \(\mathstrut -\mathstrut 31q^{30} \) \(\mathstrut -\mathstrut 43q^{31} \) \(\mathstrut +\mathstrut 67q^{32} \) \(\mathstrut -\mathstrut 49q^{33} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut -\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 77q^{37} \) \(\mathstrut -\mathstrut 33q^{38} \) \(\mathstrut -\mathstrut 40q^{39} \) \(\mathstrut -\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 50q^{41} \) \(\mathstrut -\mathstrut 39q^{42} \) \(\mathstrut -\mathstrut 56q^{43} \) \(\mathstrut -\mathstrut 13q^{44} \) \(\mathstrut -\mathstrut 48q^{45} \) \(\mathstrut -\mathstrut 43q^{46} \) \(\mathstrut -\mathstrut 48q^{47} \) \(\mathstrut -\mathstrut 11q^{48} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut -\mathstrut 9q^{50} \) \(\mathstrut -\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut 51q^{52} \) \(\mathstrut -\mathstrut 91q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut -\mathstrut 58q^{55} \) \(\mathstrut -\mathstrut 40q^{56} \) \(\mathstrut -\mathstrut 65q^{57} \) \(\mathstrut -\mathstrut 63q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 31q^{60} \) \(\mathstrut -\mathstrut 45q^{61} \) \(\mathstrut -\mathstrut 43q^{62} \) \(\mathstrut -\mathstrut 67q^{63} \) \(\mathstrut +\mathstrut 67q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 49q^{66} \) \(\mathstrut -\mathstrut 112q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 75q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut -\mathstrut 79q^{73} \) \(\mathstrut -\mathstrut 77q^{74} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 33q^{76} \) \(\mathstrut -\mathstrut 85q^{77} \) \(\mathstrut -\mathstrut 40q^{78} \) \(\mathstrut -\mathstrut 80q^{79} \) \(\mathstrut -\mathstrut 20q^{80} \) \(\mathstrut -\mathstrut 77q^{81} \) \(\mathstrut -\mathstrut 50q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 39q^{84} \) \(\mathstrut -\mathstrut 134q^{85} \) \(\mathstrut -\mathstrut 56q^{86} \) \(\mathstrut -\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 77q^{89} \) \(\mathstrut -\mathstrut 48q^{90} \) \(\mathstrut -\mathstrut 17q^{91} \) \(\mathstrut -\mathstrut 43q^{92} \) \(\mathstrut -\mathstrut 97q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 11q^{96} \) \(\mathstrut -\mathstrut 87q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut -\mathstrut 44q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.60859 −1.50607 −0.753034 0.657981i \(-0.771411\pi\)
−0.753034 + 0.657981i \(0.771411\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.145596 0.0651124 0.0325562 0.999470i \(-0.489635\pi\)
0.0325562 + 0.999470i \(0.489635\pi\)
\(6\) −2.60859 −1.06495
\(7\) 0.982128 0.371210 0.185605 0.982624i \(-0.440576\pi\)
0.185605 + 0.982624i \(0.440576\pi\)
\(8\) 1.00000 0.353553
\(9\) 3.80473 1.26824
\(10\) 0.145596 0.0460414
\(11\) −4.17910 −1.26005 −0.630023 0.776577i \(-0.716954\pi\)
−0.630023 + 0.776577i \(0.716954\pi\)
\(12\) −2.60859 −0.753034
\(13\) 2.84300 0.788507 0.394254 0.919002i \(-0.371003\pi\)
0.394254 + 0.919002i \(0.371003\pi\)
\(14\) 0.982128 0.262485
\(15\) −0.379799 −0.0980637
\(16\) 1.00000 0.250000
\(17\) −1.12150 −0.272003 −0.136001 0.990709i \(-0.543425\pi\)
−0.136001 + 0.990709i \(0.543425\pi\)
\(18\) 3.80473 0.896783
\(19\) −4.48714 −1.02942 −0.514710 0.857364i \(-0.672101\pi\)
−0.514710 + 0.857364i \(0.672101\pi\)
\(20\) 0.145596 0.0325562
\(21\) −2.56197 −0.559067
\(22\) −4.17910 −0.890986
\(23\) 6.95573 1.45037 0.725185 0.688554i \(-0.241754\pi\)
0.725185 + 0.688554i \(0.241754\pi\)
\(24\) −2.60859 −0.532476
\(25\) −4.97880 −0.995760
\(26\) 2.84300 0.557559
\(27\) −2.09920 −0.403991
\(28\) 0.982128 0.185605
\(29\) −7.09928 −1.31830 −0.659152 0.752010i \(-0.729085\pi\)
−0.659152 + 0.752010i \(0.729085\pi\)
\(30\) −0.379799 −0.0693415
\(31\) 5.43800 0.976693 0.488347 0.872650i \(-0.337600\pi\)
0.488347 + 0.872650i \(0.337600\pi\)
\(32\) 1.00000 0.176777
\(33\) 10.9015 1.89771
\(34\) −1.12150 −0.192335
\(35\) 0.142994 0.0241704
\(36\) 3.80473 0.634121
\(37\) 11.1763 1.83738 0.918689 0.394982i \(-0.129249\pi\)
0.918689 + 0.394982i \(0.129249\pi\)
\(38\) −4.48714 −0.727910
\(39\) −7.41622 −1.18755
\(40\) 0.145596 0.0230207
\(41\) −0.660816 −0.103202 −0.0516011 0.998668i \(-0.516432\pi\)
−0.0516011 + 0.998668i \(0.516432\pi\)
\(42\) −2.56197 −0.395320
\(43\) 7.34193 1.11963 0.559817 0.828616i \(-0.310871\pi\)
0.559817 + 0.828616i \(0.310871\pi\)
\(44\) −4.17910 −0.630023
\(45\) 0.553952 0.0825783
\(46\) 6.95573 1.02557
\(47\) −9.13043 −1.33181 −0.665905 0.746036i \(-0.731955\pi\)
−0.665905 + 0.746036i \(0.731955\pi\)
\(48\) −2.60859 −0.376517
\(49\) −6.03542 −0.862203
\(50\) −4.97880 −0.704109
\(51\) 2.92552 0.409655
\(52\) 2.84300 0.394254
\(53\) −2.95851 −0.406382 −0.203191 0.979139i \(-0.565131\pi\)
−0.203191 + 0.979139i \(0.565131\pi\)
\(54\) −2.09920 −0.285665
\(55\) −0.608459 −0.0820446
\(56\) 0.982128 0.131242
\(57\) 11.7051 1.55038
\(58\) −7.09928 −0.932182
\(59\) 14.3274 1.86527 0.932634 0.360823i \(-0.117504\pi\)
0.932634 + 0.360823i \(0.117504\pi\)
\(60\) −0.379799 −0.0490319
\(61\) −9.35855 −1.19824 −0.599120 0.800659i \(-0.704483\pi\)
−0.599120 + 0.800659i \(0.704483\pi\)
\(62\) 5.43800 0.690626
\(63\) 3.73673 0.470784
\(64\) 1.00000 0.125000
\(65\) 0.413929 0.0513416
\(66\) 10.9015 1.34189
\(67\) −3.06041 −0.373889 −0.186944 0.982370i \(-0.559858\pi\)
−0.186944 + 0.982370i \(0.559858\pi\)
\(68\) −1.12150 −0.136001
\(69\) −18.1446 −2.18436
\(70\) 0.142994 0.0170910
\(71\) −6.29243 −0.746774 −0.373387 0.927676i \(-0.621804\pi\)
−0.373387 + 0.927676i \(0.621804\pi\)
\(72\) 3.80473 0.448391
\(73\) −13.1900 −1.54377 −0.771885 0.635762i \(-0.780686\pi\)
−0.771885 + 0.635762i \(0.780686\pi\)
\(74\) 11.1763 1.29922
\(75\) 12.9876 1.49968
\(76\) −4.48714 −0.514710
\(77\) −4.10441 −0.467741
\(78\) −7.41622 −0.839722
\(79\) −7.99316 −0.899301 −0.449651 0.893205i \(-0.648451\pi\)
−0.449651 + 0.893205i \(0.648451\pi\)
\(80\) 0.145596 0.0162781
\(81\) −5.93823 −0.659804
\(82\) −0.660816 −0.0729749
\(83\) −5.16337 −0.566754 −0.283377 0.959009i \(-0.591455\pi\)
−0.283377 + 0.959009i \(0.591455\pi\)
\(84\) −2.56197 −0.279534
\(85\) −0.163285 −0.0177108
\(86\) 7.34193 0.791701
\(87\) 18.5191 1.98546
\(88\) −4.17910 −0.445493
\(89\) 11.6929 1.23944 0.619722 0.784821i \(-0.287245\pi\)
0.619722 + 0.784821i \(0.287245\pi\)
\(90\) 0.553952 0.0583917
\(91\) 2.79219 0.292701
\(92\) 6.95573 0.725185
\(93\) −14.1855 −1.47097
\(94\) −9.13043 −0.941732
\(95\) −0.653309 −0.0670281
\(96\) −2.60859 −0.266238
\(97\) 8.46759 0.859753 0.429877 0.902888i \(-0.358557\pi\)
0.429877 + 0.902888i \(0.358557\pi\)
\(98\) −6.03542 −0.609670
\(99\) −15.9003 −1.59804
\(100\) −4.97880 −0.497880
\(101\) 0.871496 0.0867171 0.0433585 0.999060i \(-0.486194\pi\)
0.0433585 + 0.999060i \(0.486194\pi\)
\(102\) 2.92552 0.289670
\(103\) 9.82432 0.968019 0.484009 0.875063i \(-0.339180\pi\)
0.484009 + 0.875063i \(0.339180\pi\)
\(104\) 2.84300 0.278779
\(105\) −0.373012 −0.0364022
\(106\) −2.95851 −0.287356
\(107\) 7.36675 0.712170 0.356085 0.934453i \(-0.384111\pi\)
0.356085 + 0.934453i \(0.384111\pi\)
\(108\) −2.09920 −0.201996
\(109\) −10.7075 −1.02559 −0.512795 0.858511i \(-0.671390\pi\)
−0.512795 + 0.858511i \(0.671390\pi\)
\(110\) −0.608459 −0.0580143
\(111\) −29.1544 −2.76722
\(112\) 0.982128 0.0928024
\(113\) −0.866005 −0.0814669 −0.0407335 0.999170i \(-0.512969\pi\)
−0.0407335 + 0.999170i \(0.512969\pi\)
\(114\) 11.7051 1.09628
\(115\) 1.01273 0.0944371
\(116\) −7.09928 −0.659152
\(117\) 10.8168 1.00002
\(118\) 14.3274 1.31894
\(119\) −1.10145 −0.100970
\(120\) −0.379799 −0.0346708
\(121\) 6.46485 0.587714
\(122\) −9.35855 −0.847283
\(123\) 1.72380 0.155429
\(124\) 5.43800 0.488347
\(125\) −1.45287 −0.129949
\(126\) 3.73673 0.332894
\(127\) −11.5635 −1.02610 −0.513049 0.858359i \(-0.671484\pi\)
−0.513049 + 0.858359i \(0.671484\pi\)
\(128\) 1.00000 0.0883883
\(129\) −19.1521 −1.68625
\(130\) 0.413929 0.0363040
\(131\) −3.57634 −0.312466 −0.156233 0.987720i \(-0.549935\pi\)
−0.156233 + 0.987720i \(0.549935\pi\)
\(132\) 10.9015 0.948857
\(133\) −4.40695 −0.382131
\(134\) −3.06041 −0.264379
\(135\) −0.305635 −0.0263048
\(136\) −1.12150 −0.0961675
\(137\) 19.3456 1.65281 0.826404 0.563078i \(-0.190383\pi\)
0.826404 + 0.563078i \(0.190383\pi\)
\(138\) −18.1446 −1.54457
\(139\) 8.96056 0.760025 0.380012 0.924981i \(-0.375920\pi\)
0.380012 + 0.924981i \(0.375920\pi\)
\(140\) 0.142994 0.0120852
\(141\) 23.8175 2.00580
\(142\) −6.29243 −0.528049
\(143\) −11.8812 −0.993555
\(144\) 3.80473 0.317061
\(145\) −1.03363 −0.0858379
\(146\) −13.1900 −1.09161
\(147\) 15.7439 1.29854
\(148\) 11.1763 0.918689
\(149\) 1.60782 0.131718 0.0658589 0.997829i \(-0.479021\pi\)
0.0658589 + 0.997829i \(0.479021\pi\)
\(150\) 12.9876 1.06044
\(151\) −21.6866 −1.76483 −0.882415 0.470472i \(-0.844084\pi\)
−0.882415 + 0.470472i \(0.844084\pi\)
\(152\) −4.48714 −0.363955
\(153\) −4.26699 −0.344965
\(154\) −4.10441 −0.330743
\(155\) 0.791749 0.0635948
\(156\) −7.41622 −0.593773
\(157\) −9.50045 −0.758218 −0.379109 0.925352i \(-0.623769\pi\)
−0.379109 + 0.925352i \(0.623769\pi\)
\(158\) −7.99316 −0.635902
\(159\) 7.71752 0.612039
\(160\) 0.145596 0.0115104
\(161\) 6.83142 0.538392
\(162\) −5.93823 −0.466552
\(163\) 22.8072 1.78640 0.893199 0.449661i \(-0.148455\pi\)
0.893199 + 0.449661i \(0.148455\pi\)
\(164\) −0.660816 −0.0516011
\(165\) 1.58722 0.123565
\(166\) −5.16337 −0.400756
\(167\) 19.8803 1.53839 0.769193 0.639017i \(-0.220659\pi\)
0.769193 + 0.639017i \(0.220659\pi\)
\(168\) −2.56197 −0.197660
\(169\) −4.91734 −0.378257
\(170\) −0.163285 −0.0125234
\(171\) −17.0723 −1.30555
\(172\) 7.34193 0.559817
\(173\) 10.6793 0.811929 0.405964 0.913889i \(-0.366936\pi\)
0.405964 + 0.913889i \(0.366936\pi\)
\(174\) 18.5191 1.40393
\(175\) −4.88982 −0.369636
\(176\) −4.17910 −0.315011
\(177\) −37.3743 −2.80922
\(178\) 11.6929 0.876420
\(179\) 6.10198 0.456084 0.228042 0.973651i \(-0.426768\pi\)
0.228042 + 0.973651i \(0.426768\pi\)
\(180\) 0.553952 0.0412892
\(181\) −21.8897 −1.62705 −0.813524 0.581531i \(-0.802454\pi\)
−0.813524 + 0.581531i \(0.802454\pi\)
\(182\) 2.79219 0.206971
\(183\) 24.4126 1.80463
\(184\) 6.95573 0.512783
\(185\) 1.62723 0.119636
\(186\) −14.1855 −1.04013
\(187\) 4.68684 0.342736
\(188\) −9.13043 −0.665905
\(189\) −2.06168 −0.149965
\(190\) −0.653309 −0.0473960
\(191\) −24.0960 −1.74352 −0.871762 0.489929i \(-0.837023\pi\)
−0.871762 + 0.489929i \(0.837023\pi\)
\(192\) −2.60859 −0.188259
\(193\) −19.5552 −1.40761 −0.703807 0.710391i \(-0.748518\pi\)
−0.703807 + 0.710391i \(0.748518\pi\)
\(194\) 8.46759 0.607937
\(195\) −1.07977 −0.0773240
\(196\) −6.03542 −0.431102
\(197\) 4.14320 0.295191 0.147595 0.989048i \(-0.452847\pi\)
0.147595 + 0.989048i \(0.452847\pi\)
\(198\) −15.9003 −1.12999
\(199\) −25.5671 −1.81241 −0.906203 0.422843i \(-0.861032\pi\)
−0.906203 + 0.422843i \(0.861032\pi\)
\(200\) −4.97880 −0.352054
\(201\) 7.98335 0.563102
\(202\) 0.871496 0.0613182
\(203\) −6.97241 −0.489367
\(204\) 2.92552 0.204827
\(205\) −0.0962120 −0.00671974
\(206\) 9.82432 0.684493
\(207\) 26.4647 1.83942
\(208\) 2.84300 0.197127
\(209\) 18.7522 1.29712
\(210\) −0.373012 −0.0257402
\(211\) 21.2399 1.46222 0.731109 0.682260i \(-0.239003\pi\)
0.731109 + 0.682260i \(0.239003\pi\)
\(212\) −2.95851 −0.203191
\(213\) 16.4143 1.12469
\(214\) 7.36675 0.503581
\(215\) 1.06895 0.0729021
\(216\) −2.09920 −0.142832
\(217\) 5.34081 0.362558
\(218\) −10.7075 −0.725202
\(219\) 34.4072 2.32502
\(220\) −0.608459 −0.0410223
\(221\) −3.18842 −0.214476
\(222\) −29.1544 −1.95672
\(223\) 20.5761 1.37787 0.688937 0.724821i \(-0.258078\pi\)
0.688937 + 0.724821i \(0.258078\pi\)
\(224\) 0.982128 0.0656212
\(225\) −18.9430 −1.26287
\(226\) −0.866005 −0.0576058
\(227\) 13.3978 0.889242 0.444621 0.895719i \(-0.353338\pi\)
0.444621 + 0.895719i \(0.353338\pi\)
\(228\) 11.7051 0.775189
\(229\) −19.0055 −1.25592 −0.627960 0.778246i \(-0.716110\pi\)
−0.627960 + 0.778246i \(0.716110\pi\)
\(230\) 1.01273 0.0667771
\(231\) 10.7067 0.704450
\(232\) −7.09928 −0.466091
\(233\) −8.74974 −0.573214 −0.286607 0.958048i \(-0.592527\pi\)
−0.286607 + 0.958048i \(0.592527\pi\)
\(234\) 10.8168 0.707120
\(235\) −1.32935 −0.0867174
\(236\) 14.3274 0.932634
\(237\) 20.8509 1.35441
\(238\) −1.10145 −0.0713966
\(239\) −1.65843 −0.107275 −0.0536375 0.998560i \(-0.517082\pi\)
−0.0536375 + 0.998560i \(0.517082\pi\)
\(240\) −0.379799 −0.0245159
\(241\) −24.4901 −1.57754 −0.788772 0.614686i \(-0.789283\pi\)
−0.788772 + 0.614686i \(0.789283\pi\)
\(242\) 6.46485 0.415576
\(243\) 21.7880 1.39770
\(244\) −9.35855 −0.599120
\(245\) −0.878732 −0.0561401
\(246\) 1.72380 0.109905
\(247\) −12.7570 −0.811705
\(248\) 5.43800 0.345313
\(249\) 13.4691 0.853570
\(250\) −1.45287 −0.0918877
\(251\) −5.75452 −0.363222 −0.181611 0.983370i \(-0.558131\pi\)
−0.181611 + 0.983370i \(0.558131\pi\)
\(252\) 3.73673 0.235392
\(253\) −29.0687 −1.82753
\(254\) −11.5635 −0.725561
\(255\) 0.425943 0.0266736
\(256\) 1.00000 0.0625000
\(257\) −29.9548 −1.86853 −0.934266 0.356578i \(-0.883943\pi\)
−0.934266 + 0.356578i \(0.883943\pi\)
\(258\) −19.1521 −1.19236
\(259\) 10.9766 0.682052
\(260\) 0.413929 0.0256708
\(261\) −27.0108 −1.67193
\(262\) −3.57634 −0.220947
\(263\) 2.00121 0.123400 0.0617001 0.998095i \(-0.480348\pi\)
0.0617001 + 0.998095i \(0.480348\pi\)
\(264\) 10.9015 0.670943
\(265\) −0.430746 −0.0264605
\(266\) −4.40695 −0.270207
\(267\) −30.5019 −1.86669
\(268\) −3.06041 −0.186944
\(269\) −24.9755 −1.52278 −0.761391 0.648293i \(-0.775483\pi\)
−0.761391 + 0.648293i \(0.775483\pi\)
\(270\) −0.305635 −0.0186003
\(271\) 20.3382 1.23545 0.617727 0.786392i \(-0.288053\pi\)
0.617727 + 0.786392i \(0.288053\pi\)
\(272\) −1.12150 −0.0680007
\(273\) −7.28368 −0.440828
\(274\) 19.3456 1.16871
\(275\) 20.8069 1.25470
\(276\) −18.1446 −1.09218
\(277\) −17.4865 −1.05066 −0.525331 0.850898i \(-0.676059\pi\)
−0.525331 + 0.850898i \(0.676059\pi\)
\(278\) 8.96056 0.537419
\(279\) 20.6901 1.23868
\(280\) 0.142994 0.00854551
\(281\) 9.51003 0.567321 0.283660 0.958925i \(-0.408451\pi\)
0.283660 + 0.958925i \(0.408451\pi\)
\(282\) 23.8175 1.41831
\(283\) −14.0463 −0.834967 −0.417483 0.908685i \(-0.637088\pi\)
−0.417483 + 0.908685i \(0.637088\pi\)
\(284\) −6.29243 −0.373387
\(285\) 1.70421 0.100949
\(286\) −11.8812 −0.702549
\(287\) −0.649006 −0.0383096
\(288\) 3.80473 0.224196
\(289\) −15.7422 −0.926015
\(290\) −1.03363 −0.0606966
\(291\) −22.0884 −1.29485
\(292\) −13.1900 −0.771885
\(293\) 17.7409 1.03643 0.518217 0.855249i \(-0.326596\pi\)
0.518217 + 0.855249i \(0.326596\pi\)
\(294\) 15.7439 0.918205
\(295\) 2.08601 0.121452
\(296\) 11.1763 0.649611
\(297\) 8.77276 0.509047
\(298\) 1.60782 0.0931386
\(299\) 19.7752 1.14363
\(300\) 12.9876 0.749842
\(301\) 7.21072 0.415619
\(302\) −21.6866 −1.24792
\(303\) −2.27337 −0.130602
\(304\) −4.48714 −0.257355
\(305\) −1.36257 −0.0780203
\(306\) −4.26699 −0.243927
\(307\) 1.17197 0.0668877 0.0334438 0.999441i \(-0.489353\pi\)
0.0334438 + 0.999441i \(0.489353\pi\)
\(308\) −4.10441 −0.233870
\(309\) −25.6276 −1.45790
\(310\) 0.791749 0.0449683
\(311\) −32.6009 −1.84862 −0.924312 0.381637i \(-0.875361\pi\)
−0.924312 + 0.381637i \(0.875361\pi\)
\(312\) −7.41622 −0.419861
\(313\) −9.02642 −0.510204 −0.255102 0.966914i \(-0.582109\pi\)
−0.255102 + 0.966914i \(0.582109\pi\)
\(314\) −9.50045 −0.536141
\(315\) 0.544052 0.0306539
\(316\) −7.99316 −0.449651
\(317\) 5.36467 0.301310 0.150655 0.988586i \(-0.451862\pi\)
0.150655 + 0.988586i \(0.451862\pi\)
\(318\) 7.71752 0.432777
\(319\) 29.6686 1.66112
\(320\) 0.145596 0.00813905
\(321\) −19.2168 −1.07258
\(322\) 6.83142 0.380700
\(323\) 5.03231 0.280005
\(324\) −5.93823 −0.329902
\(325\) −14.1547 −0.785164
\(326\) 22.8072 1.26317
\(327\) 27.9314 1.54461
\(328\) −0.660816 −0.0364875
\(329\) −8.96726 −0.494381
\(330\) 1.58722 0.0873735
\(331\) −24.3500 −1.33840 −0.669198 0.743084i \(-0.733362\pi\)
−0.669198 + 0.743084i \(0.733362\pi\)
\(332\) −5.16337 −0.283377
\(333\) 42.5229 2.33024
\(334\) 19.8803 1.08780
\(335\) −0.445583 −0.0243448
\(336\) −2.56197 −0.139767
\(337\) 10.3891 0.565929 0.282964 0.959130i \(-0.408682\pi\)
0.282964 + 0.959130i \(0.408682\pi\)
\(338\) −4.91734 −0.267468
\(339\) 2.25905 0.122695
\(340\) −0.163285 −0.00885538
\(341\) −22.7259 −1.23068
\(342\) −17.0723 −0.923167
\(343\) −12.8025 −0.691268
\(344\) 7.34193 0.395851
\(345\) −2.64178 −0.142229
\(346\) 10.6793 0.574120
\(347\) −25.6316 −1.37598 −0.687988 0.725722i \(-0.741506\pi\)
−0.687988 + 0.725722i \(0.741506\pi\)
\(348\) 18.5191 0.992728
\(349\) −0.863826 −0.0462395 −0.0231198 0.999733i \(-0.507360\pi\)
−0.0231198 + 0.999733i \(0.507360\pi\)
\(350\) −4.88982 −0.261372
\(351\) −5.96803 −0.318550
\(352\) −4.17910 −0.222747
\(353\) −23.4397 −1.24757 −0.623783 0.781597i \(-0.714405\pi\)
−0.623783 + 0.781597i \(0.714405\pi\)
\(354\) −37.3743 −1.98642
\(355\) −0.916151 −0.0486242
\(356\) 11.6929 0.619722
\(357\) 2.87324 0.152068
\(358\) 6.10198 0.322500
\(359\) −11.4780 −0.605788 −0.302894 0.953024i \(-0.597953\pi\)
−0.302894 + 0.953024i \(0.597953\pi\)
\(360\) 0.553952 0.0291958
\(361\) 1.13443 0.0597069
\(362\) −21.8897 −1.15050
\(363\) −16.8641 −0.885137
\(364\) 2.79219 0.146351
\(365\) −1.92041 −0.100519
\(366\) 24.4126 1.27607
\(367\) −34.6076 −1.80650 −0.903250 0.429114i \(-0.858826\pi\)
−0.903250 + 0.429114i \(0.858826\pi\)
\(368\) 6.95573 0.362593
\(369\) −2.51422 −0.130885
\(370\) 1.62723 0.0845955
\(371\) −2.90563 −0.150853
\(372\) −14.1855 −0.735483
\(373\) −22.3932 −1.15947 −0.579737 0.814804i \(-0.696845\pi\)
−0.579737 + 0.814804i \(0.696845\pi\)
\(374\) 4.68684 0.242351
\(375\) 3.78994 0.195712
\(376\) −9.13043 −0.470866
\(377\) −20.1833 −1.03949
\(378\) −2.06168 −0.106042
\(379\) −24.4406 −1.25543 −0.627715 0.778443i \(-0.716010\pi\)
−0.627715 + 0.778443i \(0.716010\pi\)
\(380\) −0.653309 −0.0335140
\(381\) 30.1645 1.54537
\(382\) −24.0960 −1.23286
\(383\) 2.87614 0.146964 0.0734820 0.997297i \(-0.476589\pi\)
0.0734820 + 0.997297i \(0.476589\pi\)
\(384\) −2.60859 −0.133119
\(385\) −0.597585 −0.0304557
\(386\) −19.5552 −0.995333
\(387\) 27.9341 1.41997
\(388\) 8.46759 0.429877
\(389\) −25.9085 −1.31361 −0.656807 0.754059i \(-0.728093\pi\)
−0.656807 + 0.754059i \(0.728093\pi\)
\(390\) −1.07977 −0.0546763
\(391\) −7.80083 −0.394505
\(392\) −6.03542 −0.304835
\(393\) 9.32919 0.470595
\(394\) 4.14320 0.208731
\(395\) −1.16377 −0.0585557
\(396\) −15.9003 −0.799021
\(397\) 26.7674 1.34342 0.671710 0.740814i \(-0.265560\pi\)
0.671710 + 0.740814i \(0.265560\pi\)
\(398\) −25.5671 −1.28156
\(399\) 11.4959 0.575515
\(400\) −4.97880 −0.248940
\(401\) −14.4337 −0.720787 −0.360393 0.932800i \(-0.617358\pi\)
−0.360393 + 0.932800i \(0.617358\pi\)
\(402\) 7.98335 0.398173
\(403\) 15.4602 0.770129
\(404\) 0.871496 0.0433585
\(405\) −0.864582 −0.0429614
\(406\) −6.97241 −0.346035
\(407\) −46.7070 −2.31518
\(408\) 2.92552 0.144835
\(409\) −7.13102 −0.352606 −0.176303 0.984336i \(-0.556414\pi\)
−0.176303 + 0.984336i \(0.556414\pi\)
\(410\) −0.0962120 −0.00475157
\(411\) −50.4647 −2.48924
\(412\) 9.82432 0.484009
\(413\) 14.0713 0.692406
\(414\) 26.4647 1.30067
\(415\) −0.751766 −0.0369027
\(416\) 2.84300 0.139390
\(417\) −23.3744 −1.14465
\(418\) 18.7522 0.917200
\(419\) 24.8397 1.21350 0.606749 0.794894i \(-0.292473\pi\)
0.606749 + 0.794894i \(0.292473\pi\)
\(420\) −0.373012 −0.0182011
\(421\) 18.7183 0.912276 0.456138 0.889909i \(-0.349232\pi\)
0.456138 + 0.889909i \(0.349232\pi\)
\(422\) 21.2399 1.03394
\(423\) −34.7388 −1.68906
\(424\) −2.95851 −0.143678
\(425\) 5.58371 0.270850
\(426\) 16.4143 0.795278
\(427\) −9.19130 −0.444798
\(428\) 7.36675 0.356085
\(429\) 30.9931 1.49636
\(430\) 1.06895 0.0515496
\(431\) 9.75181 0.469728 0.234864 0.972028i \(-0.424536\pi\)
0.234864 + 0.972028i \(0.424536\pi\)
\(432\) −2.09920 −0.100998
\(433\) −17.9369 −0.861992 −0.430996 0.902354i \(-0.641838\pi\)
−0.430996 + 0.902354i \(0.641838\pi\)
\(434\) 5.34081 0.256367
\(435\) 2.69630 0.129278
\(436\) −10.7075 −0.512795
\(437\) −31.2113 −1.49304
\(438\) 34.4072 1.64404
\(439\) −33.8196 −1.61412 −0.807062 0.590467i \(-0.798944\pi\)
−0.807062 + 0.590467i \(0.798944\pi\)
\(440\) −0.608459 −0.0290071
\(441\) −22.9631 −1.09348
\(442\) −3.18842 −0.151657
\(443\) 12.6160 0.599404 0.299702 0.954033i \(-0.403113\pi\)
0.299702 + 0.954033i \(0.403113\pi\)
\(444\) −29.1544 −1.38361
\(445\) 1.70244 0.0807032
\(446\) 20.5761 0.974305
\(447\) −4.19414 −0.198376
\(448\) 0.982128 0.0464012
\(449\) −10.6555 −0.502865 −0.251432 0.967875i \(-0.580902\pi\)
−0.251432 + 0.967875i \(0.580902\pi\)
\(450\) −18.9430 −0.892981
\(451\) 2.76161 0.130039
\(452\) −0.866005 −0.0407335
\(453\) 56.5714 2.65795
\(454\) 13.3978 0.628789
\(455\) 0.406532 0.0190585
\(456\) 11.7051 0.548141
\(457\) −3.43555 −0.160708 −0.0803540 0.996766i \(-0.525605\pi\)
−0.0803540 + 0.996766i \(0.525605\pi\)
\(458\) −19.0055 −0.888069
\(459\) 2.35424 0.109887
\(460\) 1.01273 0.0472186
\(461\) 16.5076 0.768837 0.384418 0.923159i \(-0.374402\pi\)
0.384418 + 0.923159i \(0.374402\pi\)
\(462\) 10.7067 0.498121
\(463\) −8.20063 −0.381116 −0.190558 0.981676i \(-0.561030\pi\)
−0.190558 + 0.981676i \(0.561030\pi\)
\(464\) −7.09928 −0.329576
\(465\) −2.06535 −0.0957782
\(466\) −8.74974 −0.405324
\(467\) −37.1932 −1.72110 −0.860548 0.509369i \(-0.829879\pi\)
−0.860548 + 0.509369i \(0.829879\pi\)
\(468\) 10.8168 0.500009
\(469\) −3.00572 −0.138791
\(470\) −1.32935 −0.0613185
\(471\) 24.7827 1.14193
\(472\) 14.3274 0.659472
\(473\) −30.6827 −1.41079
\(474\) 20.8509 0.957712
\(475\) 22.3406 1.02506
\(476\) −1.10145 −0.0504850
\(477\) −11.2563 −0.515391
\(478\) −1.65843 −0.0758549
\(479\) −11.6550 −0.532528 −0.266264 0.963900i \(-0.585789\pi\)
−0.266264 + 0.963900i \(0.585789\pi\)
\(480\) −0.379799 −0.0173354
\(481\) 31.7743 1.44879
\(482\) −24.4901 −1.11549
\(483\) −17.8204 −0.810854
\(484\) 6.46485 0.293857
\(485\) 1.23284 0.0559806
\(486\) 21.7880 0.988324
\(487\) 14.4079 0.652882 0.326441 0.945218i \(-0.394151\pi\)
0.326441 + 0.945218i \(0.394151\pi\)
\(488\) −9.35855 −0.423642
\(489\) −59.4946 −2.69044
\(490\) −0.878732 −0.0396971
\(491\) 28.4748 1.28505 0.642525 0.766265i \(-0.277887\pi\)
0.642525 + 0.766265i \(0.277887\pi\)
\(492\) 1.72380 0.0777147
\(493\) 7.96182 0.358582
\(494\) −12.7570 −0.573962
\(495\) −2.31502 −0.104052
\(496\) 5.43800 0.244173
\(497\) −6.17997 −0.277210
\(498\) 13.4691 0.603565
\(499\) 26.6036 1.19094 0.595469 0.803378i \(-0.296966\pi\)
0.595469 + 0.803378i \(0.296966\pi\)
\(500\) −1.45287 −0.0649744
\(501\) −51.8595 −2.31691
\(502\) −5.75452 −0.256837
\(503\) 42.3254 1.88720 0.943598 0.331092i \(-0.107417\pi\)
0.943598 + 0.331092i \(0.107417\pi\)
\(504\) 3.73673 0.166447
\(505\) 0.126886 0.00564636
\(506\) −29.0687 −1.29226
\(507\) 12.8273 0.569680
\(508\) −11.5635 −0.513049
\(509\) 30.8707 1.36832 0.684160 0.729332i \(-0.260169\pi\)
0.684160 + 0.729332i \(0.260169\pi\)
\(510\) 0.425943 0.0188611
\(511\) −12.9543 −0.573062
\(512\) 1.00000 0.0441942
\(513\) 9.41941 0.415877
\(514\) −29.9548 −1.32125
\(515\) 1.43038 0.0630300
\(516\) −19.1521 −0.843123
\(517\) 38.1570 1.67814
\(518\) 10.9766 0.482284
\(519\) −27.8578 −1.22282
\(520\) 0.413929 0.0181520
\(521\) −22.0811 −0.967389 −0.483695 0.875237i \(-0.660705\pi\)
−0.483695 + 0.875237i \(0.660705\pi\)
\(522\) −27.0108 −1.18223
\(523\) 6.87619 0.300675 0.150338 0.988635i \(-0.451964\pi\)
0.150338 + 0.988635i \(0.451964\pi\)
\(524\) −3.57634 −0.156233
\(525\) 12.7555 0.556697
\(526\) 2.00121 0.0872571
\(527\) −6.09869 −0.265663
\(528\) 10.9015 0.474429
\(529\) 25.3822 1.10357
\(530\) −0.430746 −0.0187104
\(531\) 54.5119 2.36561
\(532\) −4.40695 −0.191065
\(533\) −1.87870 −0.0813756
\(534\) −30.5019 −1.31995
\(535\) 1.07257 0.0463711
\(536\) −3.06041 −0.132190
\(537\) −15.9176 −0.686893
\(538\) −24.9755 −1.07677
\(539\) 25.2226 1.08642
\(540\) −0.305635 −0.0131524
\(541\) −9.52185 −0.409376 −0.204688 0.978827i \(-0.565618\pi\)
−0.204688 + 0.978827i \(0.565618\pi\)
\(542\) 20.3382 0.873599
\(543\) 57.1012 2.45045
\(544\) −1.12150 −0.0480837
\(545\) −1.55896 −0.0667787
\(546\) −7.28368 −0.311713
\(547\) −40.0218 −1.71121 −0.855605 0.517629i \(-0.826815\pi\)
−0.855605 + 0.517629i \(0.826815\pi\)
\(548\) 19.3456 0.826404
\(549\) −35.6067 −1.51966
\(550\) 20.8069 0.887209
\(551\) 31.8555 1.35709
\(552\) −18.1446 −0.772287
\(553\) −7.85031 −0.333829
\(554\) −17.4865 −0.742930
\(555\) −4.24476 −0.180180
\(556\) 8.96056 0.380012
\(557\) 4.90683 0.207909 0.103955 0.994582i \(-0.466850\pi\)
0.103955 + 0.994582i \(0.466850\pi\)
\(558\) 20.6901 0.875882
\(559\) 20.8731 0.882840
\(560\) 0.142994 0.00604259
\(561\) −12.2260 −0.516183
\(562\) 9.51003 0.401156
\(563\) 3.30350 0.139226 0.0696130 0.997574i \(-0.477824\pi\)
0.0696130 + 0.997574i \(0.477824\pi\)
\(564\) 23.8175 1.00290
\(565\) −0.126087 −0.00530451
\(566\) −14.0463 −0.590411
\(567\) −5.83211 −0.244926
\(568\) −6.29243 −0.264024
\(569\) 1.81288 0.0760001 0.0380000 0.999278i \(-0.487901\pi\)
0.0380000 + 0.999278i \(0.487901\pi\)
\(570\) 1.70421 0.0713816
\(571\) −9.18884 −0.384541 −0.192271 0.981342i \(-0.561585\pi\)
−0.192271 + 0.981342i \(0.561585\pi\)
\(572\) −11.8812 −0.496777
\(573\) 62.8565 2.62587
\(574\) −0.649006 −0.0270890
\(575\) −34.6312 −1.44422
\(576\) 3.80473 0.158530
\(577\) 33.7871 1.40658 0.703289 0.710904i \(-0.251714\pi\)
0.703289 + 0.710904i \(0.251714\pi\)
\(578\) −15.7422 −0.654791
\(579\) 51.0114 2.11996
\(580\) −1.03363 −0.0429190
\(581\) −5.07110 −0.210385
\(582\) −22.0884 −0.915595
\(583\) 12.3639 0.512060
\(584\) −13.1900 −0.545805
\(585\) 1.57489 0.0651136
\(586\) 17.7409 0.732869
\(587\) −20.9975 −0.866660 −0.433330 0.901235i \(-0.642662\pi\)
−0.433330 + 0.901235i \(0.642662\pi\)
\(588\) 15.7439 0.649269
\(589\) −24.4011 −1.00543
\(590\) 2.08601 0.0858796
\(591\) −10.8079 −0.444577
\(592\) 11.1763 0.459344
\(593\) 19.0178 0.780967 0.390484 0.920610i \(-0.372308\pi\)
0.390484 + 0.920610i \(0.372308\pi\)
\(594\) 8.77276 0.359951
\(595\) −0.160367 −0.00657440
\(596\) 1.60782 0.0658589
\(597\) 66.6941 2.72961
\(598\) 19.7752 0.808667
\(599\) 17.4150 0.711556 0.355778 0.934570i \(-0.384216\pi\)
0.355778 + 0.934570i \(0.384216\pi\)
\(600\) 12.9876 0.530218
\(601\) −10.8429 −0.442290 −0.221145 0.975241i \(-0.570979\pi\)
−0.221145 + 0.975241i \(0.570979\pi\)
\(602\) 7.21072 0.293887
\(603\) −11.6440 −0.474182
\(604\) −21.6866 −0.882415
\(605\) 0.941255 0.0382675
\(606\) −2.27337 −0.0923495
\(607\) −18.5934 −0.754684 −0.377342 0.926074i \(-0.623162\pi\)
−0.377342 + 0.926074i \(0.623162\pi\)
\(608\) −4.48714 −0.181978
\(609\) 18.1881 0.737020
\(610\) −1.36257 −0.0551687
\(611\) −25.9579 −1.05014
\(612\) −4.26699 −0.172483
\(613\) −18.2150 −0.735697 −0.367849 0.929886i \(-0.619906\pi\)
−0.367849 + 0.929886i \(0.619906\pi\)
\(614\) 1.17197 0.0472967
\(615\) 0.250977 0.0101204
\(616\) −4.10441 −0.165371
\(617\) −19.1359 −0.770381 −0.385191 0.922837i \(-0.625864\pi\)
−0.385191 + 0.922837i \(0.625864\pi\)
\(618\) −25.6276 −1.03089
\(619\) −16.7729 −0.674161 −0.337081 0.941476i \(-0.609439\pi\)
−0.337081 + 0.941476i \(0.609439\pi\)
\(620\) 0.791749 0.0317974
\(621\) −14.6015 −0.585937
\(622\) −32.6009 −1.30718
\(623\) 11.4839 0.460094
\(624\) −7.41622 −0.296886
\(625\) 24.6825 0.987299
\(626\) −9.02642 −0.360768
\(627\) −48.9167 −1.95355
\(628\) −9.50045 −0.379109
\(629\) −12.5342 −0.499772
\(630\) 0.544052 0.0216756
\(631\) −30.8133 −1.22666 −0.613330 0.789827i \(-0.710170\pi\)
−0.613330 + 0.789827i \(0.710170\pi\)
\(632\) −7.99316 −0.317951
\(633\) −55.4063 −2.20220
\(634\) 5.36467 0.213058
\(635\) −1.68360 −0.0668117
\(636\) 7.71752 0.306020
\(637\) −17.1587 −0.679853
\(638\) 29.6686 1.17459
\(639\) −23.9410 −0.947090
\(640\) 0.145596 0.00575518
\(641\) −6.21677 −0.245548 −0.122774 0.992435i \(-0.539179\pi\)
−0.122774 + 0.992435i \(0.539179\pi\)
\(642\) −19.2168 −0.758427
\(643\) 36.3817 1.43475 0.717377 0.696685i \(-0.245342\pi\)
0.717377 + 0.696685i \(0.245342\pi\)
\(644\) 6.83142 0.269196
\(645\) −2.78846 −0.109796
\(646\) 5.03231 0.197994
\(647\) −6.22989 −0.244922 −0.122461 0.992473i \(-0.539079\pi\)
−0.122461 + 0.992473i \(0.539079\pi\)
\(648\) −5.93823 −0.233276
\(649\) −59.8756 −2.35032
\(650\) −14.1547 −0.555195
\(651\) −13.9320 −0.546037
\(652\) 22.8072 0.893199
\(653\) −29.9552 −1.17224 −0.586119 0.810225i \(-0.699345\pi\)
−0.586119 + 0.810225i \(0.699345\pi\)
\(654\) 27.9314 1.09220
\(655\) −0.520700 −0.0203454
\(656\) −0.660816 −0.0258005
\(657\) −50.1843 −1.95787
\(658\) −8.96726 −0.349580
\(659\) 19.0976 0.743936 0.371968 0.928246i \(-0.378683\pi\)
0.371968 + 0.928246i \(0.378683\pi\)
\(660\) 1.58722 0.0617824
\(661\) −1.69913 −0.0660884 −0.0330442 0.999454i \(-0.510520\pi\)
−0.0330442 + 0.999454i \(0.510520\pi\)
\(662\) −24.3500 −0.946389
\(663\) 8.31726 0.323016
\(664\) −5.16337 −0.200378
\(665\) −0.641633 −0.0248815
\(666\) 42.5229 1.64773
\(667\) −49.3807 −1.91203
\(668\) 19.8803 0.769193
\(669\) −53.6744 −2.07517
\(670\) −0.445583 −0.0172144
\(671\) 39.1103 1.50984
\(672\) −2.56197 −0.0988300
\(673\) −5.19469 −0.200241 −0.100120 0.994975i \(-0.531923\pi\)
−0.100120 + 0.994975i \(0.531923\pi\)
\(674\) 10.3891 0.400172
\(675\) 10.4515 0.402279
\(676\) −4.91734 −0.189128
\(677\) 22.3458 0.858819 0.429409 0.903110i \(-0.358722\pi\)
0.429409 + 0.903110i \(0.358722\pi\)
\(678\) 2.25905 0.0867583
\(679\) 8.31626 0.319149
\(680\) −0.163285 −0.00626170
\(681\) −34.9493 −1.33926
\(682\) −22.7259 −0.870220
\(683\) −15.1973 −0.581508 −0.290754 0.956798i \(-0.593906\pi\)
−0.290754 + 0.956798i \(0.593906\pi\)
\(684\) −17.0723 −0.652777
\(685\) 2.81664 0.107618
\(686\) −12.8025 −0.488800
\(687\) 49.5775 1.89150
\(688\) 7.34193 0.279909
\(689\) −8.41104 −0.320435
\(690\) −2.64178 −0.100571
\(691\) −6.18654 −0.235347 −0.117674 0.993052i \(-0.537544\pi\)
−0.117674 + 0.993052i \(0.537544\pi\)
\(692\) 10.6793 0.405964
\(693\) −15.6162 −0.593209
\(694\) −25.6316 −0.972962
\(695\) 1.30462 0.0494870
\(696\) 18.5191 0.701965
\(697\) 0.741102 0.0280713
\(698\) −0.863826 −0.0326963
\(699\) 22.8245 0.863300
\(700\) −4.88982 −0.184818
\(701\) −6.90189 −0.260681 −0.130340 0.991469i \(-0.541607\pi\)
−0.130340 + 0.991469i \(0.541607\pi\)
\(702\) −5.96803 −0.225249
\(703\) −50.1498 −1.89143
\(704\) −4.17910 −0.157506
\(705\) 3.46773 0.130602
\(706\) −23.4397 −0.882163
\(707\) 0.855921 0.0321902
\(708\) −37.3743 −1.40461
\(709\) −13.2084 −0.496052 −0.248026 0.968753i \(-0.579782\pi\)
−0.248026 + 0.968753i \(0.579782\pi\)
\(710\) −0.916151 −0.0343825
\(711\) −30.4118 −1.14053
\(712\) 11.6929 0.438210
\(713\) 37.8253 1.41657
\(714\) 2.87324 0.107528
\(715\) −1.72985 −0.0646927
\(716\) 6.10198 0.228042
\(717\) 4.32616 0.161564
\(718\) −11.4780 −0.428357
\(719\) 15.4681 0.576862 0.288431 0.957501i \(-0.406866\pi\)
0.288431 + 0.957501i \(0.406866\pi\)
\(720\) 0.553952 0.0206446
\(721\) 9.64874 0.359338
\(722\) 1.13443 0.0422191
\(723\) 63.8845 2.37589
\(724\) −21.8897 −0.813524
\(725\) 35.3459 1.31271
\(726\) −16.8641 −0.625887
\(727\) 45.9219 1.70315 0.851574 0.524234i \(-0.175648\pi\)
0.851574 + 0.524234i \(0.175648\pi\)
\(728\) 2.79219 0.103486
\(729\) −39.0212 −1.44523
\(730\) −1.92041 −0.0710774
\(731\) −8.23395 −0.304544
\(732\) 24.4126 0.902315
\(733\) 30.4401 1.12433 0.562165 0.827025i \(-0.309968\pi\)
0.562165 + 0.827025i \(0.309968\pi\)
\(734\) −34.6076 −1.27739
\(735\) 2.29225 0.0845509
\(736\) 6.95573 0.256392
\(737\) 12.7898 0.471117
\(738\) −2.51422 −0.0925499
\(739\) −50.0032 −1.83940 −0.919698 0.392626i \(-0.871567\pi\)
−0.919698 + 0.392626i \(0.871567\pi\)
\(740\) 1.62723 0.0598180
\(741\) 33.2776 1.22248
\(742\) −2.90563 −0.106669
\(743\) 22.1897 0.814060 0.407030 0.913415i \(-0.366564\pi\)
0.407030 + 0.913415i \(0.366564\pi\)
\(744\) −14.1855 −0.520065
\(745\) 0.234092 0.00857647
\(746\) −22.3932 −0.819872
\(747\) −19.6452 −0.718781
\(748\) 4.68684 0.171368
\(749\) 7.23509 0.264365
\(750\) 3.78994 0.138389
\(751\) 9.04184 0.329941 0.164971 0.986298i \(-0.447247\pi\)
0.164971 + 0.986298i \(0.447247\pi\)
\(752\) −9.13043 −0.332953
\(753\) 15.0112 0.547037
\(754\) −20.1833 −0.735032
\(755\) −3.15748 −0.114912
\(756\) −2.06168 −0.0749827
\(757\) 15.8333 0.575470 0.287735 0.957710i \(-0.407098\pi\)
0.287735 + 0.957710i \(0.407098\pi\)
\(758\) −24.4406 −0.887723
\(759\) 75.8282 2.75239
\(760\) −0.653309 −0.0236980
\(761\) −39.2370 −1.42234 −0.711170 0.703020i \(-0.751835\pi\)
−0.711170 + 0.703020i \(0.751835\pi\)
\(762\) 30.1645 1.09274
\(763\) −10.5161 −0.380709
\(764\) −24.0960 −0.871762
\(765\) −0.621255 −0.0224615
\(766\) 2.87614 0.103919
\(767\) 40.7328 1.47078
\(768\) −2.60859 −0.0941293
\(769\) 5.25552 0.189519 0.0947595 0.995500i \(-0.469792\pi\)
0.0947595 + 0.995500i \(0.469792\pi\)
\(770\) −0.597585 −0.0215355
\(771\) 78.1398 2.81414
\(772\) −19.5552 −0.703807
\(773\) −17.2388 −0.620038 −0.310019 0.950730i \(-0.600335\pi\)
−0.310019 + 0.950730i \(0.600335\pi\)
\(774\) 27.9341 1.00407
\(775\) −27.0747 −0.972552
\(776\) 8.46759 0.303969
\(777\) −28.6334 −1.02722
\(778\) −25.9085 −0.928865
\(779\) 2.96517 0.106238
\(780\) −1.07977 −0.0386620
\(781\) 26.2967 0.940969
\(782\) −7.80083 −0.278957
\(783\) 14.9028 0.532583
\(784\) −6.03542 −0.215551
\(785\) −1.38322 −0.0493694
\(786\) 9.32919 0.332761
\(787\) 15.8568 0.565233 0.282616 0.959233i \(-0.408798\pi\)
0.282616 + 0.959233i \(0.408798\pi\)
\(788\) 4.14320 0.147595
\(789\) −5.22034 −0.185849
\(790\) −1.16377 −0.0414051
\(791\) −0.850528 −0.0302413
\(792\) −15.9003 −0.564993
\(793\) −26.6064 −0.944820
\(794\) 26.7674 0.949941
\(795\) 1.12364 0.0398514
\(796\) −25.5671 −0.906203
\(797\) −30.1792 −1.06900 −0.534502 0.845167i \(-0.679501\pi\)
−0.534502 + 0.845167i \(0.679501\pi\)
\(798\) 11.4959 0.406951
\(799\) 10.2397 0.362256
\(800\) −4.97880 −0.176027
\(801\) 44.4883 1.57192
\(802\) −14.4337 −0.509673
\(803\) 55.1222 1.94522
\(804\) 7.98335 0.281551
\(805\) 0.994626 0.0350560
\(806\) 15.4602 0.544564
\(807\) 65.1507 2.29341
\(808\) 0.871496 0.0306591
\(809\) 34.5855 1.21596 0.607981 0.793952i \(-0.291980\pi\)
0.607981 + 0.793952i \(0.291980\pi\)
\(810\) −0.864582 −0.0303783
\(811\) −1.29947 −0.0456307 −0.0228154 0.999740i \(-0.507263\pi\)
−0.0228154 + 0.999740i \(0.507263\pi\)
\(812\) −6.97241 −0.244684
\(813\) −53.0539 −1.86068
\(814\) −46.7070 −1.63708
\(815\) 3.32063 0.116317
\(816\) 2.92552 0.102414
\(817\) −32.9443 −1.15257
\(818\) −7.13102 −0.249330
\(819\) 10.6235 0.371216
\(820\) −0.0962120 −0.00335987
\(821\) −36.5952 −1.27718 −0.638591 0.769546i \(-0.720482\pi\)
−0.638591 + 0.769546i \(0.720482\pi\)
\(822\) −50.4647 −1.76016
\(823\) −11.9860 −0.417805 −0.208903 0.977936i \(-0.566989\pi\)
−0.208903 + 0.977936i \(0.566989\pi\)
\(824\) 9.82432 0.342246
\(825\) −54.2766 −1.88967
\(826\) 14.0713 0.489605
\(827\) −24.9497 −0.867586 −0.433793 0.901013i \(-0.642825\pi\)
−0.433793 + 0.901013i \(0.642825\pi\)
\(828\) 26.4647 0.919711
\(829\) 27.9114 0.969402 0.484701 0.874680i \(-0.338928\pi\)
0.484701 + 0.874680i \(0.338928\pi\)
\(830\) −0.751766 −0.0260942
\(831\) 45.6151 1.58237
\(832\) 2.84300 0.0985634
\(833\) 6.76870 0.234522
\(834\) −23.3744 −0.809389
\(835\) 2.89449 0.100168
\(836\) 18.7522 0.648558
\(837\) −11.4154 −0.394576
\(838\) 24.8397 0.858072
\(839\) 39.6354 1.36836 0.684182 0.729311i \(-0.260159\pi\)
0.684182 + 0.729311i \(0.260159\pi\)
\(840\) −0.373012 −0.0128701
\(841\) 21.3998 0.737925
\(842\) 18.7183 0.645077
\(843\) −24.8077 −0.854424
\(844\) 21.2399 0.731109
\(845\) −0.715943 −0.0246292
\(846\) −34.7388 −1.19434
\(847\) 6.34932 0.218165
\(848\) −2.95851 −0.101596
\(849\) 36.6410 1.25752
\(850\) 5.58371 0.191520
\(851\) 77.7396 2.66488
\(852\) 16.4143 0.562346
\(853\) 32.9854 1.12940 0.564700 0.825296i \(-0.308992\pi\)
0.564700 + 0.825296i \(0.308992\pi\)
\(854\) −9.19130 −0.314520
\(855\) −2.48566 −0.0850078
\(856\) 7.36675 0.251790
\(857\) 42.3009 1.44497 0.722485 0.691386i \(-0.243000\pi\)
0.722485 + 0.691386i \(0.243000\pi\)
\(858\) 30.9931 1.05809
\(859\) −0.398186 −0.0135859 −0.00679297 0.999977i \(-0.502162\pi\)
−0.00679297 + 0.999977i \(0.502162\pi\)
\(860\) 1.06895 0.0364510
\(861\) 1.69299 0.0576969
\(862\) 9.75181 0.332148
\(863\) 14.5331 0.494713 0.247357 0.968925i \(-0.420438\pi\)
0.247357 + 0.968925i \(0.420438\pi\)
\(864\) −2.09920 −0.0714162
\(865\) 1.55485 0.0528666
\(866\) −17.9369 −0.609520
\(867\) 41.0650 1.39464
\(868\) 5.34081 0.181279
\(869\) 33.4042 1.13316
\(870\) 2.69630 0.0914132
\(871\) −8.70076 −0.294814
\(872\) −10.7075 −0.362601
\(873\) 32.2169 1.09038
\(874\) −31.2113 −1.05574
\(875\) −1.42691 −0.0482382
\(876\) 34.4072 1.16251
\(877\) −10.6976 −0.361234 −0.180617 0.983554i \(-0.557809\pi\)
−0.180617 + 0.983554i \(0.557809\pi\)
\(878\) −33.8196 −1.14136
\(879\) −46.2786 −1.56094
\(880\) −0.608459 −0.0205111
\(881\) −5.07855 −0.171101 −0.0855504 0.996334i \(-0.527265\pi\)
−0.0855504 + 0.996334i \(0.527265\pi\)
\(882\) −22.9631 −0.773209
\(883\) −19.9889 −0.672679 −0.336339 0.941741i \(-0.609189\pi\)
−0.336339 + 0.941741i \(0.609189\pi\)
\(884\) −3.18842 −0.107238
\(885\) −5.44154 −0.182915
\(886\) 12.6160 0.423843
\(887\) 57.1958 1.92045 0.960223 0.279234i \(-0.0900806\pi\)
0.960223 + 0.279234i \(0.0900806\pi\)
\(888\) −29.1544 −0.978359
\(889\) −11.3569 −0.380898
\(890\) 1.70244 0.0570658
\(891\) 24.8165 0.831383
\(892\) 20.5761 0.688937
\(893\) 40.9695 1.37099
\(894\) −4.19414 −0.140273
\(895\) 0.888423 0.0296967
\(896\) 0.982128 0.0328106
\(897\) −51.5852 −1.72238
\(898\) −10.6555 −0.355579
\(899\) −38.6059 −1.28758
\(900\) −18.9430 −0.631433
\(901\) 3.31795 0.110537
\(902\) 2.76161 0.0919517
\(903\) −18.8098 −0.625951
\(904\) −0.866005 −0.0288029
\(905\) −3.18705 −0.105941
\(906\) 56.5714 1.87946
\(907\) 1.27533 0.0423466 0.0211733 0.999776i \(-0.493260\pi\)
0.0211733 + 0.999776i \(0.493260\pi\)
\(908\) 13.3978 0.444621
\(909\) 3.31580 0.109978
\(910\) 0.406532 0.0134764
\(911\) −2.03231 −0.0673333 −0.0336666 0.999433i \(-0.510718\pi\)
−0.0336666 + 0.999433i \(0.510718\pi\)
\(912\) 11.7051 0.387595
\(913\) 21.5782 0.714136
\(914\) −3.43555 −0.113638
\(915\) 3.55437 0.117504
\(916\) −19.0055 −0.627960
\(917\) −3.51242 −0.115990
\(918\) 2.35424 0.0777017
\(919\) −45.1493 −1.48934 −0.744669 0.667433i \(-0.767393\pi\)
−0.744669 + 0.667433i \(0.767393\pi\)
\(920\) 1.01273 0.0333886
\(921\) −3.05718 −0.100737
\(922\) 16.5076 0.543650
\(923\) −17.8894 −0.588836
\(924\) 10.7067 0.352225
\(925\) −55.6447 −1.82959
\(926\) −8.20063 −0.269490
\(927\) 37.3788 1.22768
\(928\) −7.09928 −0.233045
\(929\) 11.8446 0.388608 0.194304 0.980941i \(-0.437755\pi\)
0.194304 + 0.980941i \(0.437755\pi\)
\(930\) −2.06535 −0.0677254
\(931\) 27.0818 0.887570
\(932\) −8.74974 −0.286607
\(933\) 85.0422 2.78416
\(934\) −37.1932 −1.21700
\(935\) 0.682384 0.0223163
\(936\) 10.8168 0.353560
\(937\) −30.4979 −0.996322 −0.498161 0.867085i \(-0.665991\pi\)
−0.498161 + 0.867085i \(0.665991\pi\)
\(938\) −3.00572 −0.0981402
\(939\) 23.5462 0.768402
\(940\) −1.32935 −0.0433587
\(941\) 58.3892 1.90343 0.951717 0.306976i \(-0.0993173\pi\)
0.951717 + 0.306976i \(0.0993173\pi\)
\(942\) 24.7827 0.807465
\(943\) −4.59646 −0.149681
\(944\) 14.3274 0.466317
\(945\) −0.300173 −0.00976461
\(946\) −30.6827 −0.997579
\(947\) 61.3679 1.99419 0.997095 0.0761692i \(-0.0242689\pi\)
0.997095 + 0.0761692i \(0.0242689\pi\)
\(948\) 20.8509 0.677205
\(949\) −37.4991 −1.21727
\(950\) 22.3406 0.724824
\(951\) −13.9942 −0.453793
\(952\) −1.10145 −0.0356983
\(953\) −0.00959351 −0.000310764 0 −0.000155382 1.00000i \(-0.500049\pi\)
−0.000155382 1.00000i \(0.500049\pi\)
\(954\) −11.2563 −0.364436
\(955\) −3.50827 −0.113525
\(956\) −1.65843 −0.0536375
\(957\) −77.3931 −2.50176
\(958\) −11.6550 −0.376555
\(959\) 18.9999 0.613538
\(960\) −0.379799 −0.0122580
\(961\) −1.42819 −0.0460706
\(962\) 31.7743 1.02445
\(963\) 28.0285 0.903205
\(964\) −24.4901 −0.788772
\(965\) −2.84715 −0.0916531
\(966\) −17.8204 −0.573361
\(967\) 12.8709 0.413900 0.206950 0.978352i \(-0.433646\pi\)
0.206950 + 0.978352i \(0.433646\pi\)
\(968\) 6.46485 0.207788
\(969\) −13.1272 −0.421707
\(970\) 1.23284 0.0395843
\(971\) −45.7703 −1.46884 −0.734419 0.678696i \(-0.762545\pi\)
−0.734419 + 0.678696i \(0.762545\pi\)
\(972\) 21.7880 0.698850
\(973\) 8.80042 0.282129
\(974\) 14.4079 0.461657
\(975\) 36.9239 1.18251
\(976\) −9.35855 −0.299560
\(977\) 4.55087 0.145595 0.0727977 0.997347i \(-0.476807\pi\)
0.0727977 + 0.997347i \(0.476807\pi\)
\(978\) −59.4946 −1.90243
\(979\) −48.8658 −1.56176
\(980\) −0.878732 −0.0280701
\(981\) −40.7391 −1.30070
\(982\) 28.4748 0.908667
\(983\) 27.1554 0.866123 0.433062 0.901364i \(-0.357433\pi\)
0.433062 + 0.901364i \(0.357433\pi\)
\(984\) 1.72380 0.0549526
\(985\) 0.603232 0.0192206
\(986\) 7.96182 0.253556
\(987\) 23.3919 0.744572
\(988\) −12.7570 −0.405853
\(989\) 51.0685 1.62388
\(990\) −2.31502 −0.0735762
\(991\) 26.3209 0.836110 0.418055 0.908422i \(-0.362712\pi\)
0.418055 + 0.908422i \(0.362712\pi\)
\(992\) 5.43800 0.172657
\(993\) 63.5190 2.01572
\(994\) −6.17997 −0.196017
\(995\) −3.72247 −0.118010
\(996\) 13.4691 0.426785
\(997\) 50.0322 1.58454 0.792268 0.610173i \(-0.208900\pi\)
0.792268 + 0.610173i \(0.208900\pi\)
\(998\) 26.6036 0.842121
\(999\) −23.4614 −0.742285
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 \(a_p\))