Properties

Label 8007.2.a.j.1.6
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 1.6
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.38697 q^{2}\) \(-1.00000 q^{3}\) \(+3.69761 q^{4}\) \(+2.25593 q^{5}\) \(+2.38697 q^{6}\) \(-4.86795 q^{7}\) \(-4.05215 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.38697 q^{2}\) \(-1.00000 q^{3}\) \(+3.69761 q^{4}\) \(+2.25593 q^{5}\) \(+2.38697 q^{6}\) \(-4.86795 q^{7}\) \(-4.05215 q^{8}\) \(+1.00000 q^{9}\) \(-5.38482 q^{10}\) \(+1.03520 q^{11}\) \(-3.69761 q^{12}\) \(-0.688087 q^{13}\) \(+11.6196 q^{14}\) \(-2.25593 q^{15}\) \(+2.27712 q^{16}\) \(+1.00000 q^{17}\) \(-2.38697 q^{18}\) \(-8.17166 q^{19}\) \(+8.34155 q^{20}\) \(+4.86795 q^{21}\) \(-2.47100 q^{22}\) \(+7.38826 q^{23}\) \(+4.05215 q^{24}\) \(+0.0892066 q^{25}\) \(+1.64244 q^{26}\) \(-1.00000 q^{27}\) \(-17.9998 q^{28}\) \(+2.85376 q^{29}\) \(+5.38482 q^{30}\) \(-10.3049 q^{31}\) \(+2.66889 q^{32}\) \(-1.03520 q^{33}\) \(-2.38697 q^{34}\) \(-10.9817 q^{35}\) \(+3.69761 q^{36}\) \(+1.32195 q^{37}\) \(+19.5055 q^{38}\) \(+0.688087 q^{39}\) \(-9.14135 q^{40}\) \(+8.69790 q^{41}\) \(-11.6196 q^{42}\) \(+4.03880 q^{43}\) \(+3.82779 q^{44}\) \(+2.25593 q^{45}\) \(-17.6355 q^{46}\) \(-12.0312 q^{47}\) \(-2.27712 q^{48}\) \(+16.6969 q^{49}\) \(-0.212933 q^{50}\) \(-1.00000 q^{51}\) \(-2.54428 q^{52}\) \(-8.62613 q^{53}\) \(+2.38697 q^{54}\) \(+2.33535 q^{55}\) \(+19.7256 q^{56}\) \(+8.17166 q^{57}\) \(-6.81184 q^{58}\) \(-2.74590 q^{59}\) \(-8.34155 q^{60}\) \(-10.2874 q^{61}\) \(+24.5974 q^{62}\) \(-4.86795 q^{63}\) \(-10.9248 q^{64}\) \(-1.55227 q^{65}\) \(+2.47100 q^{66}\) \(+15.1775 q^{67}\) \(+3.69761 q^{68}\) \(-7.38826 q^{69}\) \(+26.2130 q^{70}\) \(-3.50593 q^{71}\) \(-4.05215 q^{72}\) \(+5.22796 q^{73}\) \(-3.15545 q^{74}\) \(-0.0892066 q^{75}\) \(-30.2156 q^{76}\) \(-5.03932 q^{77}\) \(-1.64244 q^{78}\) \(+4.50555 q^{79}\) \(+5.13702 q^{80}\) \(+1.00000 q^{81}\) \(-20.7616 q^{82}\) \(-7.62159 q^{83}\) \(+17.9998 q^{84}\) \(+2.25593 q^{85}\) \(-9.64049 q^{86}\) \(-2.85376 q^{87}\) \(-4.19480 q^{88}\) \(-3.63646 q^{89}\) \(-5.38482 q^{90}\) \(+3.34957 q^{91}\) \(+27.3189 q^{92}\) \(+10.3049 q^{93}\) \(+28.7180 q^{94}\) \(-18.4347 q^{95}\) \(-2.66889 q^{96}\) \(-4.49489 q^{97}\) \(-39.8550 q^{98}\) \(+1.03520 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 77q^{12} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 103q^{16} \) \(\mathstrut +\mathstrut 64q^{17} \) \(\mathstrut +\mathstrut 5q^{18} \) \(\mathstrut +\mathstrut 26q^{19} \) \(\mathstrut -\mathstrut 24q^{20} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut +\mathstrut 25q^{22} \) \(\mathstrut +\mathstrut 20q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 141q^{25} \) \(\mathstrut +\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 64q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 7q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 3q^{35} \) \(\mathstrut +\mathstrut 77q^{36} \) \(\mathstrut +\mathstrut 50q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut +\mathstrut 28q^{40} \) \(\mathstrut -\mathstrut 9q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 59q^{43} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut -\mathstrut 103q^{48} \) \(\mathstrut +\mathstrut 163q^{49} \) \(\mathstrut +\mathstrut 20q^{50} \) \(\mathstrut -\mathstrut 64q^{51} \) \(\mathstrut +\mathstrut 65q^{52} \) \(\mathstrut +\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 35q^{55} \) \(\mathstrut -\mathstrut 34q^{56} \) \(\mathstrut -\mathstrut 26q^{57} \) \(\mathstrut -\mathstrut 27q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut +\mathstrut 24q^{60} \) \(\mathstrut +\mathstrut 15q^{61} \) \(\mathstrut +\mathstrut 18q^{62} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 152q^{64} \) \(\mathstrut +\mathstrut 49q^{65} \) \(\mathstrut -\mathstrut 25q^{66} \) \(\mathstrut +\mathstrut 56q^{67} \) \(\mathstrut +\mathstrut 77q^{68} \) \(\mathstrut -\mathstrut 20q^{69} \) \(\mathstrut +\mathstrut 28q^{70} \) \(\mathstrut -\mathstrut 18q^{71} \) \(\mathstrut +\mathstrut 18q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut -\mathstrut 76q^{74} \) \(\mathstrut -\mathstrut 141q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 9q^{78} \) \(\mathstrut +\mathstrut 20q^{79} \) \(\mathstrut -\mathstrut 144q^{80} \) \(\mathstrut +\mathstrut 64q^{81} \) \(\mathstrut +\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 3q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 5q^{87} \) \(\mathstrut +\mathstrut 108q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut +\mathstrut 12q^{90} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 42q^{95} \) \(\mathstrut -\mathstrut 31q^{96} \) \(\mathstrut +\mathstrut 72q^{97} \) \(\mathstrut +\mathstrut 18q^{98} \) \(\mathstrut -\mathstrut 7q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.38697 −1.68784 −0.843920 0.536468i \(-0.819758\pi\)
−0.843920 + 0.536468i \(0.819758\pi\)
\(3\) −1.00000 −0.577350
\(4\) 3.69761 1.84881
\(5\) 2.25593 1.00888 0.504441 0.863446i \(-0.331699\pi\)
0.504441 + 0.863446i \(0.331699\pi\)
\(6\) 2.38697 0.974475
\(7\) −4.86795 −1.83991 −0.919956 0.392022i \(-0.871776\pi\)
−0.919956 + 0.392022i \(0.871776\pi\)
\(8\) −4.05215 −1.43265
\(9\) 1.00000 0.333333
\(10\) −5.38482 −1.70283
\(11\) 1.03520 0.312126 0.156063 0.987747i \(-0.450120\pi\)
0.156063 + 0.987747i \(0.450120\pi\)
\(12\) −3.69761 −1.06741
\(13\) −0.688087 −0.190841 −0.0954205 0.995437i \(-0.530420\pi\)
−0.0954205 + 0.995437i \(0.530420\pi\)
\(14\) 11.6196 3.10548
\(15\) −2.25593 −0.582478
\(16\) 2.27712 0.569280
\(17\) 1.00000 0.242536
\(18\) −2.38697 −0.562614
\(19\) −8.17166 −1.87471 −0.937354 0.348379i \(-0.886732\pi\)
−0.937354 + 0.348379i \(0.886732\pi\)
\(20\) 8.34155 1.86523
\(21\) 4.86795 1.06227
\(22\) −2.47100 −0.526819
\(23\) 7.38826 1.54056 0.770280 0.637706i \(-0.220117\pi\)
0.770280 + 0.637706i \(0.220117\pi\)
\(24\) 4.05215 0.827141
\(25\) 0.0892066 0.0178413
\(26\) 1.64244 0.322109
\(27\) −1.00000 −0.192450
\(28\) −17.9998 −3.40164
\(29\) 2.85376 0.529930 0.264965 0.964258i \(-0.414640\pi\)
0.264965 + 0.964258i \(0.414640\pi\)
\(30\) 5.38482 0.983130
\(31\) −10.3049 −1.85081 −0.925406 0.378978i \(-0.876276\pi\)
−0.925406 + 0.378978i \(0.876276\pi\)
\(32\) 2.66889 0.471797
\(33\) −1.03520 −0.180206
\(34\) −2.38697 −0.409362
\(35\) −10.9817 −1.85625
\(36\) 3.69761 0.616269
\(37\) 1.32195 0.217327 0.108664 0.994079i \(-0.465343\pi\)
0.108664 + 0.994079i \(0.465343\pi\)
\(38\) 19.5055 3.16421
\(39\) 0.688087 0.110182
\(40\) −9.14135 −1.44537
\(41\) 8.69790 1.35838 0.679192 0.733961i \(-0.262330\pi\)
0.679192 + 0.733961i \(0.262330\pi\)
\(42\) −11.6196 −1.79295
\(43\) 4.03880 0.615912 0.307956 0.951401i \(-0.400355\pi\)
0.307956 + 0.951401i \(0.400355\pi\)
\(44\) 3.82779 0.577061
\(45\) 2.25593 0.336294
\(46\) −17.6355 −2.60022
\(47\) −12.0312 −1.75493 −0.877464 0.479643i \(-0.840766\pi\)
−0.877464 + 0.479643i \(0.840766\pi\)
\(48\) −2.27712 −0.328674
\(49\) 16.6969 2.38527
\(50\) −0.212933 −0.0301133
\(51\) −1.00000 −0.140028
\(52\) −2.54428 −0.352828
\(53\) −8.62613 −1.18489 −0.592445 0.805611i \(-0.701837\pi\)
−0.592445 + 0.805611i \(0.701837\pi\)
\(54\) 2.38697 0.324825
\(55\) 2.33535 0.314898
\(56\) 19.7256 2.63595
\(57\) 8.17166 1.08236
\(58\) −6.81184 −0.894438
\(59\) −2.74590 −0.357486 −0.178743 0.983896i \(-0.557203\pi\)
−0.178743 + 0.983896i \(0.557203\pi\)
\(60\) −8.34155 −1.07689
\(61\) −10.2874 −1.31717 −0.658586 0.752505i \(-0.728845\pi\)
−0.658586 + 0.752505i \(0.728845\pi\)
\(62\) 24.5974 3.12387
\(63\) −4.86795 −0.613304
\(64\) −10.9248 −1.36560
\(65\) −1.55227 −0.192536
\(66\) 2.47100 0.304159
\(67\) 15.1775 1.85423 0.927114 0.374780i \(-0.122282\pi\)
0.927114 + 0.374780i \(0.122282\pi\)
\(68\) 3.69761 0.448402
\(69\) −7.38826 −0.889443
\(70\) 26.2130 3.13306
\(71\) −3.50593 −0.416078 −0.208039 0.978121i \(-0.566708\pi\)
−0.208039 + 0.978121i \(0.566708\pi\)
\(72\) −4.05215 −0.477550
\(73\) 5.22796 0.611886 0.305943 0.952050i \(-0.401028\pi\)
0.305943 + 0.952050i \(0.401028\pi\)
\(74\) −3.15545 −0.366814
\(75\) −0.0892066 −0.0103007
\(76\) −30.2156 −3.46597
\(77\) −5.03932 −0.574284
\(78\) −1.64244 −0.185970
\(79\) 4.50555 0.506914 0.253457 0.967347i \(-0.418432\pi\)
0.253457 + 0.967347i \(0.418432\pi\)
\(80\) 5.13702 0.574336
\(81\) 1.00000 0.111111
\(82\) −20.7616 −2.29274
\(83\) −7.62159 −0.836578 −0.418289 0.908314i \(-0.637370\pi\)
−0.418289 + 0.908314i \(0.637370\pi\)
\(84\) 17.9998 1.96394
\(85\) 2.25593 0.244690
\(86\) −9.64049 −1.03956
\(87\) −2.85376 −0.305955
\(88\) −4.19480 −0.447168
\(89\) −3.63646 −0.385464 −0.192732 0.981251i \(-0.561735\pi\)
−0.192732 + 0.981251i \(0.561735\pi\)
\(90\) −5.38482 −0.567610
\(91\) 3.34957 0.351131
\(92\) 27.3189 2.84820
\(93\) 10.3049 1.06857
\(94\) 28.7180 2.96204
\(95\) −18.4347 −1.89136
\(96\) −2.66889 −0.272392
\(97\) −4.49489 −0.456387 −0.228194 0.973616i \(-0.573282\pi\)
−0.228194 + 0.973616i \(0.573282\pi\)
\(98\) −39.8550 −4.02596
\(99\) 1.03520 0.104042
\(100\) 0.329852 0.0329852
\(101\) −14.1289 −1.40588 −0.702938 0.711251i \(-0.748129\pi\)
−0.702938 + 0.711251i \(0.748129\pi\)
\(102\) 2.38697 0.236345
\(103\) 2.40939 0.237404 0.118702 0.992930i \(-0.462127\pi\)
0.118702 + 0.992930i \(0.462127\pi\)
\(104\) 2.78823 0.273409
\(105\) 10.9817 1.07171
\(106\) 20.5903 1.99991
\(107\) 7.48379 0.723486 0.361743 0.932278i \(-0.382182\pi\)
0.361743 + 0.932278i \(0.382182\pi\)
\(108\) −3.69761 −0.355803
\(109\) −8.01499 −0.767697 −0.383848 0.923396i \(-0.625401\pi\)
−0.383848 + 0.923396i \(0.625401\pi\)
\(110\) −5.57439 −0.531498
\(111\) −1.32195 −0.125474
\(112\) −11.0849 −1.04742
\(113\) 6.04782 0.568931 0.284465 0.958686i \(-0.408184\pi\)
0.284465 + 0.958686i \(0.408184\pi\)
\(114\) −19.5055 −1.82686
\(115\) 16.6674 1.55424
\(116\) 10.5521 0.979739
\(117\) −0.688087 −0.0636137
\(118\) 6.55437 0.603379
\(119\) −4.86795 −0.446244
\(120\) 9.14135 0.834487
\(121\) −9.92835 −0.902577
\(122\) 24.5558 2.22318
\(123\) −8.69790 −0.784263
\(124\) −38.1035 −3.42179
\(125\) −11.0784 −0.990881
\(126\) 11.6196 1.03516
\(127\) −15.1142 −1.34117 −0.670585 0.741833i \(-0.733957\pi\)
−0.670585 + 0.741833i \(0.733957\pi\)
\(128\) 20.7393 1.83312
\(129\) −4.03880 −0.355597
\(130\) 3.70523 0.324970
\(131\) −3.12398 −0.272943 −0.136471 0.990644i \(-0.543576\pi\)
−0.136471 + 0.990644i \(0.543576\pi\)
\(132\) −3.82779 −0.333166
\(133\) 39.7792 3.44930
\(134\) −36.2282 −3.12964
\(135\) −2.25593 −0.194159
\(136\) −4.05215 −0.347469
\(137\) 14.0665 1.20179 0.600893 0.799329i \(-0.294812\pi\)
0.600893 + 0.799329i \(0.294812\pi\)
\(138\) 17.6355 1.50124
\(139\) 1.39970 0.118721 0.0593603 0.998237i \(-0.481094\pi\)
0.0593603 + 0.998237i \(0.481094\pi\)
\(140\) −40.6062 −3.43185
\(141\) 12.0312 1.01321
\(142\) 8.36855 0.702273
\(143\) −0.712311 −0.0595664
\(144\) 2.27712 0.189760
\(145\) 6.43788 0.534637
\(146\) −12.4790 −1.03277
\(147\) −16.6969 −1.37714
\(148\) 4.88806 0.401796
\(149\) 23.2464 1.90442 0.952208 0.305451i \(-0.0988071\pi\)
0.952208 + 0.305451i \(0.0988071\pi\)
\(150\) 0.212933 0.0173859
\(151\) −18.3008 −1.48930 −0.744650 0.667456i \(-0.767383\pi\)
−0.744650 + 0.667456i \(0.767383\pi\)
\(152\) 33.1128 2.68580
\(153\) 1.00000 0.0808452
\(154\) 12.0287 0.969300
\(155\) −23.2471 −1.86725
\(156\) 2.54428 0.203705
\(157\) −1.00000 −0.0798087
\(158\) −10.7546 −0.855590
\(159\) 8.62613 0.684096
\(160\) 6.02081 0.475987
\(161\) −35.9657 −2.83449
\(162\) −2.38697 −0.187538
\(163\) 23.0881 1.80840 0.904201 0.427107i \(-0.140467\pi\)
0.904201 + 0.427107i \(0.140467\pi\)
\(164\) 32.1615 2.51139
\(165\) −2.33535 −0.181806
\(166\) 18.1925 1.41201
\(167\) −5.92527 −0.458511 −0.229255 0.973366i \(-0.573629\pi\)
−0.229255 + 0.973366i \(0.573629\pi\)
\(168\) −19.7256 −1.52187
\(169\) −12.5265 −0.963580
\(170\) −5.38482 −0.412997
\(171\) −8.17166 −0.624903
\(172\) 14.9339 1.13870
\(173\) 9.10713 0.692402 0.346201 0.938160i \(-0.387472\pi\)
0.346201 + 0.938160i \(0.387472\pi\)
\(174\) 6.81184 0.516404
\(175\) −0.434253 −0.0328265
\(176\) 2.35729 0.177687
\(177\) 2.74590 0.206394
\(178\) 8.68011 0.650602
\(179\) 8.84444 0.661064 0.330532 0.943795i \(-0.392772\pi\)
0.330532 + 0.943795i \(0.392772\pi\)
\(180\) 8.34155 0.621742
\(181\) 4.37866 0.325463 0.162732 0.986670i \(-0.447970\pi\)
0.162732 + 0.986670i \(0.447970\pi\)
\(182\) −7.99532 −0.592653
\(183\) 10.2874 0.760470
\(184\) −29.9383 −2.20708
\(185\) 2.98222 0.219257
\(186\) −24.5974 −1.80357
\(187\) 1.03520 0.0757017
\(188\) −44.4866 −3.24452
\(189\) 4.86795 0.354091
\(190\) 44.0030 3.19231
\(191\) 23.8655 1.72684 0.863422 0.504483i \(-0.168317\pi\)
0.863422 + 0.504483i \(0.168317\pi\)
\(192\) 10.9248 0.788428
\(193\) 25.8382 1.85987 0.929936 0.367722i \(-0.119862\pi\)
0.929936 + 0.367722i \(0.119862\pi\)
\(194\) 10.7292 0.770309
\(195\) 1.55227 0.111161
\(196\) 61.7388 4.40991
\(197\) −11.8190 −0.842072 −0.421036 0.907044i \(-0.638333\pi\)
−0.421036 + 0.907044i \(0.638333\pi\)
\(198\) −2.47100 −0.175606
\(199\) −8.56448 −0.607120 −0.303560 0.952812i \(-0.598175\pi\)
−0.303560 + 0.952812i \(0.598175\pi\)
\(200\) −0.361478 −0.0255604
\(201\) −15.1775 −1.07054
\(202\) 33.7252 2.37290
\(203\) −13.8920 −0.975025
\(204\) −3.69761 −0.258885
\(205\) 19.6218 1.37045
\(206\) −5.75112 −0.400700
\(207\) 7.38826 0.513520
\(208\) −1.56686 −0.108642
\(209\) −8.45934 −0.585145
\(210\) −26.2130 −1.80887
\(211\) −19.5382 −1.34506 −0.672532 0.740068i \(-0.734793\pi\)
−0.672532 + 0.740068i \(0.734793\pi\)
\(212\) −31.8961 −2.19063
\(213\) 3.50593 0.240223
\(214\) −17.8636 −1.22113
\(215\) 9.11125 0.621382
\(216\) 4.05215 0.275714
\(217\) 50.1636 3.40533
\(218\) 19.1315 1.29575
\(219\) −5.22796 −0.353273
\(220\) 8.63521 0.582186
\(221\) −0.688087 −0.0462858
\(222\) 3.15545 0.211780
\(223\) 16.2790 1.09012 0.545060 0.838397i \(-0.316507\pi\)
0.545060 + 0.838397i \(0.316507\pi\)
\(224\) −12.9920 −0.868064
\(225\) 0.0892066 0.00594711
\(226\) −14.4359 −0.960265
\(227\) 1.57421 0.104484 0.0522420 0.998634i \(-0.483363\pi\)
0.0522420 + 0.998634i \(0.483363\pi\)
\(228\) 30.2156 2.00108
\(229\) 1.72625 0.114074 0.0570368 0.998372i \(-0.481835\pi\)
0.0570368 + 0.998372i \(0.481835\pi\)
\(230\) −39.7845 −2.62331
\(231\) 5.03932 0.331563
\(232\) −11.5639 −0.759205
\(233\) 8.90826 0.583600 0.291800 0.956479i \(-0.405746\pi\)
0.291800 + 0.956479i \(0.405746\pi\)
\(234\) 1.64244 0.107370
\(235\) −27.1415 −1.77051
\(236\) −10.1533 −0.660922
\(237\) −4.50555 −0.292667
\(238\) 11.6196 0.753189
\(239\) 12.7409 0.824140 0.412070 0.911152i \(-0.364806\pi\)
0.412070 + 0.911152i \(0.364806\pi\)
\(240\) −5.13702 −0.331593
\(241\) −5.25252 −0.338344 −0.169172 0.985587i \(-0.554109\pi\)
−0.169172 + 0.985587i \(0.554109\pi\)
\(242\) 23.6987 1.52341
\(243\) −1.00000 −0.0641500
\(244\) −38.0390 −2.43520
\(245\) 37.6670 2.40646
\(246\) 20.7616 1.32371
\(247\) 5.62282 0.357771
\(248\) 41.7569 2.65157
\(249\) 7.62159 0.482999
\(250\) 26.4438 1.67245
\(251\) −0.517752 −0.0326802 −0.0163401 0.999866i \(-0.505201\pi\)
−0.0163401 + 0.999866i \(0.505201\pi\)
\(252\) −17.9998 −1.13388
\(253\) 7.64837 0.480849
\(254\) 36.0771 2.26368
\(255\) −2.25593 −0.141272
\(256\) −27.6545 −1.72841
\(257\) 23.9250 1.49240 0.746200 0.665722i \(-0.231876\pi\)
0.746200 + 0.665722i \(0.231876\pi\)
\(258\) 9.64049 0.600191
\(259\) −6.43518 −0.399863
\(260\) −5.73971 −0.355962
\(261\) 2.85376 0.176643
\(262\) 7.45683 0.460684
\(263\) −24.0357 −1.48211 −0.741053 0.671447i \(-0.765673\pi\)
−0.741053 + 0.671447i \(0.765673\pi\)
\(264\) 4.19480 0.258172
\(265\) −19.4599 −1.19541
\(266\) −94.9517 −5.82186
\(267\) 3.63646 0.222548
\(268\) 56.1206 3.42811
\(269\) 1.15181 0.0702268 0.0351134 0.999383i \(-0.488821\pi\)
0.0351134 + 0.999383i \(0.488821\pi\)
\(270\) 5.38482 0.327710
\(271\) 6.73126 0.408895 0.204447 0.978878i \(-0.434460\pi\)
0.204447 + 0.978878i \(0.434460\pi\)
\(272\) 2.27712 0.138071
\(273\) −3.34957 −0.202725
\(274\) −33.5764 −2.02842
\(275\) 0.0923471 0.00556874
\(276\) −27.3189 −1.64441
\(277\) −19.6709 −1.18191 −0.590955 0.806705i \(-0.701249\pi\)
−0.590955 + 0.806705i \(0.701249\pi\)
\(278\) −3.34103 −0.200382
\(279\) −10.3049 −0.616937
\(280\) 44.4996 2.65936
\(281\) 14.5307 0.866831 0.433415 0.901194i \(-0.357308\pi\)
0.433415 + 0.901194i \(0.357308\pi\)
\(282\) −28.7180 −1.71013
\(283\) 1.06397 0.0632463 0.0316232 0.999500i \(-0.489932\pi\)
0.0316232 + 0.999500i \(0.489932\pi\)
\(284\) −12.9636 −0.769247
\(285\) 18.4347 1.09198
\(286\) 1.70026 0.100539
\(287\) −42.3409 −2.49931
\(288\) 2.66889 0.157266
\(289\) 1.00000 0.0588235
\(290\) −15.3670 −0.902382
\(291\) 4.49489 0.263495
\(292\) 19.3310 1.13126
\(293\) −16.5473 −0.966706 −0.483353 0.875426i \(-0.660581\pi\)
−0.483353 + 0.875426i \(0.660581\pi\)
\(294\) 39.8550 2.32439
\(295\) −6.19455 −0.360661
\(296\) −5.35674 −0.311354
\(297\) −1.03520 −0.0600687
\(298\) −55.4883 −3.21435
\(299\) −5.08377 −0.294002
\(300\) −0.329852 −0.0190440
\(301\) −19.6607 −1.13322
\(302\) 43.6834 2.51370
\(303\) 14.1289 0.811683
\(304\) −18.6079 −1.06723
\(305\) −23.2077 −1.32887
\(306\) −2.38697 −0.136454
\(307\) −12.0964 −0.690377 −0.345188 0.938533i \(-0.612185\pi\)
−0.345188 + 0.938533i \(0.612185\pi\)
\(308\) −18.6335 −1.06174
\(309\) −2.40939 −0.137065
\(310\) 55.4900 3.15162
\(311\) −20.6007 −1.16816 −0.584079 0.811697i \(-0.698544\pi\)
−0.584079 + 0.811697i \(0.698544\pi\)
\(312\) −2.78823 −0.157853
\(313\) 19.8787 1.12361 0.561804 0.827270i \(-0.310108\pi\)
0.561804 + 0.827270i \(0.310108\pi\)
\(314\) 2.38697 0.134704
\(315\) −10.9817 −0.618751
\(316\) 16.6598 0.937186
\(317\) 12.4872 0.701351 0.350676 0.936497i \(-0.385952\pi\)
0.350676 + 0.936497i \(0.385952\pi\)
\(318\) −20.5903 −1.15465
\(319\) 2.95423 0.165405
\(320\) −24.6455 −1.37773
\(321\) −7.48379 −0.417705
\(322\) 85.8489 4.78417
\(323\) −8.17166 −0.454683
\(324\) 3.69761 0.205423
\(325\) −0.0613819 −0.00340486
\(326\) −55.1106 −3.05230
\(327\) 8.01499 0.443230
\(328\) −35.2452 −1.94609
\(329\) 58.5671 3.22891
\(330\) 5.57439 0.306860
\(331\) −32.9406 −1.81058 −0.905291 0.424792i \(-0.860347\pi\)
−0.905291 + 0.424792i \(0.860347\pi\)
\(332\) −28.1817 −1.54667
\(333\) 1.32195 0.0724424
\(334\) 14.1434 0.773893
\(335\) 34.2393 1.87070
\(336\) 11.0849 0.604731
\(337\) 30.3454 1.65302 0.826510 0.562922i \(-0.190323\pi\)
0.826510 + 0.562922i \(0.190323\pi\)
\(338\) 29.9004 1.62637
\(339\) −6.04782 −0.328472
\(340\) 8.34155 0.452384
\(341\) −10.6677 −0.577686
\(342\) 19.5055 1.05474
\(343\) −47.2041 −2.54878
\(344\) −16.3658 −0.882387
\(345\) −16.6674 −0.897342
\(346\) −21.7384 −1.16866
\(347\) −4.53769 −0.243596 −0.121798 0.992555i \(-0.538866\pi\)
−0.121798 + 0.992555i \(0.538866\pi\)
\(348\) −10.5521 −0.565653
\(349\) −23.4313 −1.25425 −0.627126 0.778918i \(-0.715769\pi\)
−0.627126 + 0.778918i \(0.715769\pi\)
\(350\) 1.03655 0.0554058
\(351\) 0.688087 0.0367274
\(352\) 2.76284 0.147260
\(353\) −24.5331 −1.30577 −0.652883 0.757458i \(-0.726441\pi\)
−0.652883 + 0.757458i \(0.726441\pi\)
\(354\) −6.55437 −0.348361
\(355\) −7.90913 −0.419773
\(356\) −13.4462 −0.712648
\(357\) 4.86795 0.257639
\(358\) −21.1114 −1.11577
\(359\) −16.6243 −0.877399 −0.438700 0.898634i \(-0.644561\pi\)
−0.438700 + 0.898634i \(0.644561\pi\)
\(360\) −9.14135 −0.481792
\(361\) 47.7760 2.51453
\(362\) −10.4517 −0.549330
\(363\) 9.92835 0.521103
\(364\) 12.3854 0.649173
\(365\) 11.7939 0.617320
\(366\) −24.5558 −1.28355
\(367\) 30.8098 1.60826 0.804129 0.594455i \(-0.202632\pi\)
0.804129 + 0.594455i \(0.202632\pi\)
\(368\) 16.8240 0.877010
\(369\) 8.69790 0.452795
\(370\) −7.11846 −0.370071
\(371\) 41.9915 2.18009
\(372\) 38.1035 1.97557
\(373\) −27.8694 −1.44302 −0.721510 0.692404i \(-0.756552\pi\)
−0.721510 + 0.692404i \(0.756552\pi\)
\(374\) −2.47100 −0.127772
\(375\) 11.0784 0.572086
\(376\) 48.7521 2.51420
\(377\) −1.96364 −0.101132
\(378\) −11.6196 −0.597649
\(379\) 0.141939 0.00729092 0.00364546 0.999993i \(-0.498840\pi\)
0.00364546 + 0.999993i \(0.498840\pi\)
\(380\) −68.1643 −3.49675
\(381\) 15.1142 0.774325
\(382\) −56.9661 −2.91464
\(383\) −18.9612 −0.968872 −0.484436 0.874827i \(-0.660975\pi\)
−0.484436 + 0.874827i \(0.660975\pi\)
\(384\) −20.7393 −1.05835
\(385\) −11.3683 −0.579384
\(386\) −61.6748 −3.13917
\(387\) 4.03880 0.205304
\(388\) −16.6204 −0.843772
\(389\) 14.6757 0.744086 0.372043 0.928216i \(-0.378657\pi\)
0.372043 + 0.928216i \(0.378657\pi\)
\(390\) −3.70523 −0.187622
\(391\) 7.38826 0.373641
\(392\) −67.6584 −3.41727
\(393\) 3.12398 0.157584
\(394\) 28.2117 1.42128
\(395\) 10.1642 0.511416
\(396\) 3.82779 0.192354
\(397\) −6.47396 −0.324919 −0.162459 0.986715i \(-0.551943\pi\)
−0.162459 + 0.986715i \(0.551943\pi\)
\(398\) 20.4431 1.02472
\(399\) −39.7792 −1.99145
\(400\) 0.203134 0.0101567
\(401\) 26.7107 1.33387 0.666934 0.745117i \(-0.267606\pi\)
0.666934 + 0.745117i \(0.267606\pi\)
\(402\) 36.2282 1.80690
\(403\) 7.09066 0.353211
\(404\) −52.2432 −2.59919
\(405\) 2.25593 0.112098
\(406\) 33.1597 1.64569
\(407\) 1.36849 0.0678334
\(408\) 4.05215 0.200611
\(409\) −4.47245 −0.221148 −0.110574 0.993868i \(-0.535269\pi\)
−0.110574 + 0.993868i \(0.535269\pi\)
\(410\) −46.8367 −2.31310
\(411\) −14.0665 −0.693852
\(412\) 8.90898 0.438914
\(413\) 13.3669 0.657742
\(414\) −17.6355 −0.866740
\(415\) −17.1938 −0.844008
\(416\) −1.83643 −0.0900382
\(417\) −1.39970 −0.0685434
\(418\) 20.1922 0.987631
\(419\) −4.70265 −0.229739 −0.114870 0.993381i \(-0.536645\pi\)
−0.114870 + 0.993381i \(0.536645\pi\)
\(420\) 40.6062 1.98138
\(421\) 23.6631 1.15327 0.576633 0.817003i \(-0.304366\pi\)
0.576633 + 0.817003i \(0.304366\pi\)
\(422\) 46.6370 2.27025
\(423\) −12.0312 −0.584976
\(424\) 34.9544 1.69753
\(425\) 0.0892066 0.00432716
\(426\) −8.36855 −0.405458
\(427\) 50.0788 2.42348
\(428\) 27.6722 1.33759
\(429\) 0.712311 0.0343907
\(430\) −21.7482 −1.04879
\(431\) −16.0270 −0.771992 −0.385996 0.922501i \(-0.626142\pi\)
−0.385996 + 0.922501i \(0.626142\pi\)
\(432\) −2.27712 −0.109558
\(433\) 8.77716 0.421803 0.210902 0.977507i \(-0.432360\pi\)
0.210902 + 0.977507i \(0.432360\pi\)
\(434\) −119.739 −5.74765
\(435\) −6.43788 −0.308673
\(436\) −29.6363 −1.41932
\(437\) −60.3744 −2.88810
\(438\) 12.4790 0.596268
\(439\) −32.1966 −1.53666 −0.768330 0.640054i \(-0.778912\pi\)
−0.768330 + 0.640054i \(0.778912\pi\)
\(440\) −9.46317 −0.451139
\(441\) 16.6969 0.795091
\(442\) 1.64244 0.0781230
\(443\) 28.9989 1.37778 0.688890 0.724866i \(-0.258098\pi\)
0.688890 + 0.724866i \(0.258098\pi\)
\(444\) −4.88806 −0.231977
\(445\) −8.20359 −0.388887
\(446\) −38.8574 −1.83995
\(447\) −23.2464 −1.09951
\(448\) 53.1813 2.51258
\(449\) 6.15803 0.290615 0.145308 0.989387i \(-0.453583\pi\)
0.145308 + 0.989387i \(0.453583\pi\)
\(450\) −0.212933 −0.0100378
\(451\) 9.00410 0.423987
\(452\) 22.3625 1.05184
\(453\) 18.3008 0.859847
\(454\) −3.75759 −0.176352
\(455\) 7.55639 0.354249
\(456\) −33.1128 −1.55065
\(457\) −4.17338 −0.195222 −0.0976112 0.995225i \(-0.531120\pi\)
−0.0976112 + 0.995225i \(0.531120\pi\)
\(458\) −4.12050 −0.192538
\(459\) −1.00000 −0.0466760
\(460\) 61.6296 2.87349
\(461\) 13.6076 0.633770 0.316885 0.948464i \(-0.397363\pi\)
0.316885 + 0.948464i \(0.397363\pi\)
\(462\) −12.0287 −0.559626
\(463\) −17.9595 −0.834648 −0.417324 0.908758i \(-0.637032\pi\)
−0.417324 + 0.908758i \(0.637032\pi\)
\(464\) 6.49836 0.301679
\(465\) 23.2471 1.07806
\(466\) −21.2637 −0.985023
\(467\) −20.2696 −0.937963 −0.468982 0.883208i \(-0.655379\pi\)
−0.468982 + 0.883208i \(0.655379\pi\)
\(468\) −2.54428 −0.117609
\(469\) −73.8833 −3.41161
\(470\) 64.7858 2.98835
\(471\) 1.00000 0.0460776
\(472\) 11.1268 0.512152
\(473\) 4.18099 0.192242
\(474\) 10.7546 0.493975
\(475\) −0.728966 −0.0334473
\(476\) −17.9998 −0.825019
\(477\) −8.62613 −0.394963
\(478\) −30.4121 −1.39102
\(479\) 29.2474 1.33635 0.668175 0.744004i \(-0.267076\pi\)
0.668175 + 0.744004i \(0.267076\pi\)
\(480\) −6.02081 −0.274811
\(481\) −0.909616 −0.0414749
\(482\) 12.5376 0.571071
\(483\) 35.9657 1.63650
\(484\) −36.7112 −1.66869
\(485\) −10.1401 −0.460440
\(486\) 2.38697 0.108275
\(487\) −27.1984 −1.23248 −0.616239 0.787559i \(-0.711345\pi\)
−0.616239 + 0.787559i \(0.711345\pi\)
\(488\) 41.6863 1.88705
\(489\) −23.0881 −1.04408
\(490\) −89.9100 −4.06172
\(491\) 18.3532 0.828270 0.414135 0.910215i \(-0.364084\pi\)
0.414135 + 0.910215i \(0.364084\pi\)
\(492\) −32.1615 −1.44995
\(493\) 2.85376 0.128527
\(494\) −13.4215 −0.603861
\(495\) 2.33535 0.104966
\(496\) −23.4654 −1.05363
\(497\) 17.0667 0.765546
\(498\) −18.1925 −0.815225
\(499\) 38.9303 1.74276 0.871381 0.490608i \(-0.163225\pi\)
0.871381 + 0.490608i \(0.163225\pi\)
\(500\) −40.9636 −1.83195
\(501\) 5.92527 0.264721
\(502\) 1.23586 0.0551590
\(503\) −16.4097 −0.731671 −0.365835 0.930680i \(-0.619217\pi\)
−0.365835 + 0.930680i \(0.619217\pi\)
\(504\) 19.7256 0.878650
\(505\) −31.8737 −1.41836
\(506\) −18.2564 −0.811596
\(507\) 12.5265 0.556323
\(508\) −55.8865 −2.47956
\(509\) 29.0100 1.28585 0.642923 0.765931i \(-0.277722\pi\)
0.642923 + 0.765931i \(0.277722\pi\)
\(510\) 5.38482 0.238444
\(511\) −25.4494 −1.12582
\(512\) 24.5318 1.08416
\(513\) 8.17166 0.360788
\(514\) −57.1082 −2.51893
\(515\) 5.43540 0.239512
\(516\) −14.9339 −0.657430
\(517\) −12.4547 −0.547758
\(518\) 15.3606 0.674905
\(519\) −9.10713 −0.399758
\(520\) 6.29005 0.275837
\(521\) −26.2257 −1.14897 −0.574485 0.818515i \(-0.694798\pi\)
−0.574485 + 0.818515i \(0.694798\pi\)
\(522\) −6.81184 −0.298146
\(523\) −15.9597 −0.697868 −0.348934 0.937147i \(-0.613456\pi\)
−0.348934 + 0.937147i \(0.613456\pi\)
\(524\) −11.5513 −0.504619
\(525\) 0.434253 0.0189524
\(526\) 57.3725 2.50156
\(527\) −10.3049 −0.448888
\(528\) −2.35729 −0.102588
\(529\) 31.5865 1.37332
\(530\) 46.4502 2.01767
\(531\) −2.74590 −0.119162
\(532\) 147.088 6.37708
\(533\) −5.98491 −0.259235
\(534\) −8.68011 −0.375625
\(535\) 16.8829 0.729911
\(536\) −61.5015 −2.65646
\(537\) −8.84444 −0.381666
\(538\) −2.74932 −0.118532
\(539\) 17.2847 0.744506
\(540\) −8.34155 −0.358963
\(541\) −18.9157 −0.813251 −0.406626 0.913595i \(-0.633295\pi\)
−0.406626 + 0.913595i \(0.633295\pi\)
\(542\) −16.0673 −0.690150
\(543\) −4.37866 −0.187906
\(544\) 2.66889 0.114428
\(545\) −18.0812 −0.774515
\(546\) 7.99532 0.342168
\(547\) −14.0848 −0.602225 −0.301112 0.953589i \(-0.597358\pi\)
−0.301112 + 0.953589i \(0.597358\pi\)
\(548\) 52.0127 2.22187
\(549\) −10.2874 −0.439058
\(550\) −0.220430 −0.00939915
\(551\) −23.3200 −0.993465
\(552\) 29.9383 1.27426
\(553\) −21.9328 −0.932677
\(554\) 46.9538 1.99488
\(555\) −2.98222 −0.126588
\(556\) 5.17553 0.219492
\(557\) 25.0666 1.06210 0.531052 0.847339i \(-0.321797\pi\)
0.531052 + 0.847339i \(0.321797\pi\)
\(558\) 24.5974 1.04129
\(559\) −2.77905 −0.117541
\(560\) −25.0067 −1.05673
\(561\) −1.03520 −0.0437064
\(562\) −34.6844 −1.46307
\(563\) 20.9268 0.881961 0.440980 0.897517i \(-0.354631\pi\)
0.440980 + 0.897517i \(0.354631\pi\)
\(564\) 44.4866 1.87323
\(565\) 13.6434 0.573984
\(566\) −2.53966 −0.106750
\(567\) −4.86795 −0.204435
\(568\) 14.2066 0.596094
\(569\) −20.2596 −0.849328 −0.424664 0.905351i \(-0.639608\pi\)
−0.424664 + 0.905351i \(0.639608\pi\)
\(570\) −44.0030 −1.84308
\(571\) −11.9229 −0.498958 −0.249479 0.968380i \(-0.580259\pi\)
−0.249479 + 0.968380i \(0.580259\pi\)
\(572\) −2.63385 −0.110127
\(573\) −23.8655 −0.996994
\(574\) 101.066 4.21843
\(575\) 0.659082 0.0274856
\(576\) −10.9248 −0.455199
\(577\) 24.8018 1.03251 0.516256 0.856434i \(-0.327325\pi\)
0.516256 + 0.856434i \(0.327325\pi\)
\(578\) −2.38697 −0.0992848
\(579\) −25.8382 −1.07380
\(580\) 23.8048 0.988440
\(581\) 37.1015 1.53923
\(582\) −10.7292 −0.444738
\(583\) −8.92981 −0.369835
\(584\) −21.1845 −0.876619
\(585\) −1.55227 −0.0641786
\(586\) 39.4980 1.63165
\(587\) −42.9454 −1.77255 −0.886273 0.463163i \(-0.846714\pi\)
−0.886273 + 0.463163i \(0.846714\pi\)
\(588\) −61.7388 −2.54606
\(589\) 84.2080 3.46973
\(590\) 14.7862 0.608738
\(591\) 11.8190 0.486171
\(592\) 3.01024 0.123720
\(593\) 4.33274 0.177924 0.0889621 0.996035i \(-0.471645\pi\)
0.0889621 + 0.996035i \(0.471645\pi\)
\(594\) 2.47100 0.101386
\(595\) −10.9817 −0.450207
\(596\) 85.9560 3.52090
\(597\) 8.56448 0.350521
\(598\) 12.1348 0.496229
\(599\) −2.55928 −0.104569 −0.0522847 0.998632i \(-0.516650\pi\)
−0.0522847 + 0.998632i \(0.516650\pi\)
\(600\) 0.361478 0.0147573
\(601\) 48.9485 1.99665 0.998325 0.0578602i \(-0.0184278\pi\)
0.998325 + 0.0578602i \(0.0184278\pi\)
\(602\) 46.9294 1.91270
\(603\) 15.1775 0.618076
\(604\) −67.6693 −2.75343
\(605\) −22.3976 −0.910593
\(606\) −33.7252 −1.36999
\(607\) 12.1269 0.492217 0.246109 0.969242i \(-0.420848\pi\)
0.246109 + 0.969242i \(0.420848\pi\)
\(608\) −21.8092 −0.884481
\(609\) 13.8920 0.562931
\(610\) 55.3961 2.24292
\(611\) 8.27850 0.334912
\(612\) 3.69761 0.149467
\(613\) 44.0029 1.77726 0.888631 0.458623i \(-0.151657\pi\)
0.888631 + 0.458623i \(0.151657\pi\)
\(614\) 28.8737 1.16525
\(615\) −19.6218 −0.791228
\(616\) 20.4201 0.822749
\(617\) 20.8755 0.840416 0.420208 0.907428i \(-0.361957\pi\)
0.420208 + 0.907428i \(0.361957\pi\)
\(618\) 5.75112 0.231344
\(619\) −0.996380 −0.0400479 −0.0200239 0.999800i \(-0.506374\pi\)
−0.0200239 + 0.999800i \(0.506374\pi\)
\(620\) −85.9586 −3.45218
\(621\) −7.38826 −0.296481
\(622\) 49.1731 1.97166
\(623\) 17.7021 0.709219
\(624\) 1.56686 0.0627245
\(625\) −25.4381 −1.01752
\(626\) −47.4497 −1.89647
\(627\) 8.45934 0.337834
\(628\) −3.69761 −0.147551
\(629\) 1.32195 0.0527096
\(630\) 26.2130 1.04435
\(631\) 8.38733 0.333894 0.166947 0.985966i \(-0.446609\pi\)
0.166947 + 0.985966i \(0.446609\pi\)
\(632\) −18.2572 −0.726231
\(633\) 19.5382 0.776573
\(634\) −29.8065 −1.18377
\(635\) −34.0966 −1.35308
\(636\) 31.8961 1.26476
\(637\) −11.4889 −0.455208
\(638\) −7.05165 −0.279177
\(639\) −3.50593 −0.138693
\(640\) 46.7864 1.84940
\(641\) 35.4979 1.40208 0.701042 0.713120i \(-0.252719\pi\)
0.701042 + 0.713120i \(0.252719\pi\)
\(642\) 17.8636 0.705019
\(643\) 21.1198 0.832883 0.416442 0.909162i \(-0.363277\pi\)
0.416442 + 0.909162i \(0.363277\pi\)
\(644\) −132.987 −5.24043
\(645\) −9.11125 −0.358755
\(646\) 19.5055 0.767433
\(647\) 21.1705 0.832297 0.416148 0.909297i \(-0.363380\pi\)
0.416148 + 0.909297i \(0.363380\pi\)
\(648\) −4.05215 −0.159183
\(649\) −2.84257 −0.111581
\(650\) 0.146517 0.00574686
\(651\) −50.1636 −1.96607
\(652\) 85.3710 3.34339
\(653\) 28.6436 1.12091 0.560456 0.828185i \(-0.310626\pi\)
0.560456 + 0.828185i \(0.310626\pi\)
\(654\) −19.1315 −0.748101
\(655\) −7.04746 −0.275367
\(656\) 19.8062 0.773301
\(657\) 5.22796 0.203962
\(658\) −139.798 −5.44989
\(659\) 5.58343 0.217499 0.108750 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(660\) −8.63521 −0.336125
\(661\) −25.2857 −0.983499 −0.491749 0.870737i \(-0.663642\pi\)
−0.491749 + 0.870737i \(0.663642\pi\)
\(662\) 78.6283 3.05597
\(663\) 0.688087 0.0267231
\(664\) 30.8838 1.19852
\(665\) 89.7390 3.47993
\(666\) −3.15545 −0.122271
\(667\) 21.0844 0.816389
\(668\) −21.9093 −0.847698
\(669\) −16.2790 −0.629381
\(670\) −81.7282 −3.15744
\(671\) −10.6496 −0.411124
\(672\) 12.9920 0.501177
\(673\) −6.22366 −0.239904 −0.119952 0.992780i \(-0.538274\pi\)
−0.119952 + 0.992780i \(0.538274\pi\)
\(674\) −72.4335 −2.79003
\(675\) −0.0892066 −0.00343356
\(676\) −46.3183 −1.78147
\(677\) 24.4292 0.938890 0.469445 0.882962i \(-0.344454\pi\)
0.469445 + 0.882962i \(0.344454\pi\)
\(678\) 14.4359 0.554409
\(679\) 21.8809 0.839712
\(680\) −9.14135 −0.350555
\(681\) −1.57421 −0.0603238
\(682\) 25.4634 0.975042
\(683\) 50.5092 1.93268 0.966340 0.257268i \(-0.0828222\pi\)
0.966340 + 0.257268i \(0.0828222\pi\)
\(684\) −30.2156 −1.15532
\(685\) 31.7331 1.21246
\(686\) 112.675 4.30194
\(687\) −1.72625 −0.0658605
\(688\) 9.19684 0.350626
\(689\) 5.93553 0.226126
\(690\) 39.7845 1.51457
\(691\) 16.7000 0.635298 0.317649 0.948208i \(-0.397107\pi\)
0.317649 + 0.948208i \(0.397107\pi\)
\(692\) 33.6746 1.28012
\(693\) −5.03932 −0.191428
\(694\) 10.8313 0.411151
\(695\) 3.15761 0.119775
\(696\) 11.5639 0.438327
\(697\) 8.69790 0.329456
\(698\) 55.9299 2.11698
\(699\) −8.90826 −0.336941
\(700\) −1.60570 −0.0606898
\(701\) −11.9214 −0.450265 −0.225133 0.974328i \(-0.572282\pi\)
−0.225133 + 0.974328i \(0.572282\pi\)
\(702\) −1.64244 −0.0619900
\(703\) −10.8025 −0.407425
\(704\) −11.3094 −0.426239
\(705\) 27.1415 1.02221
\(706\) 58.5598 2.20393
\(707\) 68.7787 2.58669
\(708\) 10.1533 0.381584
\(709\) −3.68560 −0.138416 −0.0692078 0.997602i \(-0.522047\pi\)
−0.0692078 + 0.997602i \(0.522047\pi\)
\(710\) 18.8788 0.708510
\(711\) 4.50555 0.168971
\(712\) 14.7355 0.552235
\(713\) −76.1352 −2.85129
\(714\) −11.6196 −0.434854
\(715\) −1.60692 −0.0600955
\(716\) 32.7033 1.22218
\(717\) −12.7409 −0.475818
\(718\) 39.6818 1.48091
\(719\) 19.9854 0.745330 0.372665 0.927966i \(-0.378444\pi\)
0.372665 + 0.927966i \(0.378444\pi\)
\(720\) 5.13702 0.191445
\(721\) −11.7288 −0.436802
\(722\) −114.040 −4.24412
\(723\) 5.25252 0.195343
\(724\) 16.1906 0.601718
\(725\) 0.254574 0.00945466
\(726\) −23.6987 −0.879539
\(727\) 48.8817 1.81292 0.906460 0.422291i \(-0.138774\pi\)
0.906460 + 0.422291i \(0.138774\pi\)
\(728\) −13.5730 −0.503048
\(729\) 1.00000 0.0370370
\(730\) −28.1516 −1.04194
\(731\) 4.03880 0.149381
\(732\) 38.0390 1.40596
\(733\) −48.1988 −1.78026 −0.890132 0.455704i \(-0.849388\pi\)
−0.890132 + 0.455704i \(0.849388\pi\)
\(734\) −73.5420 −2.71448
\(735\) −37.6670 −1.38937
\(736\) 19.7184 0.726831
\(737\) 15.7118 0.578752
\(738\) −20.7616 −0.764245
\(739\) 10.8723 0.399944 0.199972 0.979802i \(-0.435915\pi\)
0.199972 + 0.979802i \(0.435915\pi\)
\(740\) 11.0271 0.405364
\(741\) −5.62282 −0.206559
\(742\) −100.232 −3.67965
\(743\) −4.04041 −0.148228 −0.0741141 0.997250i \(-0.523613\pi\)
−0.0741141 + 0.997250i \(0.523613\pi\)
\(744\) −41.7569 −1.53088
\(745\) 52.4421 1.92133
\(746\) 66.5233 2.43559
\(747\) −7.62159 −0.278859
\(748\) 3.82779 0.139958
\(749\) −36.4307 −1.33115
\(750\) −26.4438 −0.965590
\(751\) 50.6975 1.84998 0.924989 0.379993i \(-0.124074\pi\)
0.924989 + 0.379993i \(0.124074\pi\)
\(752\) −27.3964 −0.999045
\(753\) 0.517752 0.0188679
\(754\) 4.68714 0.170696
\(755\) −41.2853 −1.50253
\(756\) 17.9998 0.654646
\(757\) 15.8022 0.574340 0.287170 0.957880i \(-0.407286\pi\)
0.287170 + 0.957880i \(0.407286\pi\)
\(758\) −0.338804 −0.0123059
\(759\) −7.64837 −0.277618
\(760\) 74.7000 2.70965
\(761\) 32.2278 1.16826 0.584129 0.811661i \(-0.301436\pi\)
0.584129 + 0.811661i \(0.301436\pi\)
\(762\) −36.0771 −1.30694
\(763\) 39.0165 1.41249
\(764\) 88.2452 3.19260
\(765\) 2.25593 0.0815632
\(766\) 45.2598 1.63530
\(767\) 1.88942 0.0682229
\(768\) 27.6545 0.997897
\(769\) 0.0266519 0.000961094 0 0.000480547 1.00000i \(-0.499847\pi\)
0.000480547 1.00000i \(0.499847\pi\)
\(770\) 27.1359 0.977909
\(771\) −23.9250 −0.861637
\(772\) 95.5395 3.43854
\(773\) 8.33097 0.299644 0.149822 0.988713i \(-0.452130\pi\)
0.149822 + 0.988713i \(0.452130\pi\)
\(774\) −9.64049 −0.346520
\(775\) −0.919263 −0.0330209
\(776\) 18.2140 0.653844
\(777\) 6.43518 0.230861
\(778\) −35.0303 −1.25590
\(779\) −71.0763 −2.54657
\(780\) 5.73971 0.205515
\(781\) −3.62936 −0.129869
\(782\) −17.6355 −0.630646
\(783\) −2.85376 −0.101985
\(784\) 38.0209 1.35789
\(785\) −2.25593 −0.0805175
\(786\) −7.45683 −0.265976
\(787\) 6.96595 0.248309 0.124155 0.992263i \(-0.460378\pi\)
0.124155 + 0.992263i \(0.460378\pi\)
\(788\) −43.7023 −1.55683
\(789\) 24.0357 0.855694
\(790\) −24.2616 −0.863189
\(791\) −29.4405 −1.04678
\(792\) −4.19480 −0.149056
\(793\) 7.07866 0.251371
\(794\) 15.4531 0.548411
\(795\) 19.4599 0.690172
\(796\) −31.6681 −1.12245
\(797\) −50.1632 −1.77687 −0.888436 0.459001i \(-0.848207\pi\)
−0.888436 + 0.459001i \(0.848207\pi\)
\(798\) 94.9517 3.36125
\(799\) −12.0312 −0.425632
\(800\) 0.238082 0.00841748
\(801\) −3.63646 −0.128488
\(802\) −63.7576 −2.25136
\(803\) 5.41201 0.190986
\(804\) −56.1206 −1.97922
\(805\) −81.1360 −2.85967
\(806\) −16.9252 −0.596164
\(807\) −1.15181 −0.0405455
\(808\) 57.2523 2.01413
\(809\) 22.7875 0.801165 0.400583 0.916261i \(-0.368808\pi\)
0.400583 + 0.916261i \(0.368808\pi\)
\(810\) −5.38482 −0.189203
\(811\) 22.7928 0.800363 0.400181 0.916436i \(-0.368947\pi\)
0.400181 + 0.916436i \(0.368947\pi\)
\(812\) −51.3671 −1.80263
\(813\) −6.73126 −0.236076
\(814\) −3.26654 −0.114492
\(815\) 52.0852 1.82446
\(816\) −2.27712 −0.0797151
\(817\) −33.0037 −1.15465
\(818\) 10.6756 0.373263
\(819\) 3.34957 0.117044
\(820\) 72.5539 2.53369
\(821\) −31.5337 −1.10053 −0.550266 0.834989i \(-0.685474\pi\)
−0.550266 + 0.834989i \(0.685474\pi\)
\(822\) 33.5764 1.17111
\(823\) 48.0071 1.67342 0.836712 0.547643i \(-0.184475\pi\)
0.836712 + 0.547643i \(0.184475\pi\)
\(824\) −9.76319 −0.340117
\(825\) −0.0923471 −0.00321511
\(826\) −31.9063 −1.11016
\(827\) 33.5928 1.16814 0.584068 0.811705i \(-0.301460\pi\)
0.584068 + 0.811705i \(0.301460\pi\)
\(828\) 27.3189 0.949399
\(829\) −44.4695 −1.54449 −0.772245 0.635325i \(-0.780866\pi\)
−0.772245 + 0.635325i \(0.780866\pi\)
\(830\) 41.0409 1.42455
\(831\) 19.6709 0.682376
\(832\) 7.51720 0.260612
\(833\) 16.6969 0.578514
\(834\) 3.34103 0.115690
\(835\) −13.3670 −0.462583
\(836\) −31.2794 −1.08182
\(837\) 10.3049 0.356189
\(838\) 11.2251 0.387763
\(839\) 7.51957 0.259604 0.129802 0.991540i \(-0.458566\pi\)
0.129802 + 0.991540i \(0.458566\pi\)
\(840\) −44.4996 −1.53538
\(841\) −20.8560 −0.719174
\(842\) −56.4829 −1.94653
\(843\) −14.5307 −0.500465
\(844\) −72.2446 −2.48676
\(845\) −28.2590 −0.972137
\(846\) 28.7180 0.987346
\(847\) 48.3307 1.66066
\(848\) −19.6427 −0.674534
\(849\) −1.06397 −0.0365153
\(850\) −0.212933 −0.00730355
\(851\) 9.76691 0.334805
\(852\) 12.9636 0.444125
\(853\) −11.9113 −0.407834 −0.203917 0.978988i \(-0.565367\pi\)
−0.203917 + 0.978988i \(0.565367\pi\)
\(854\) −119.536 −4.09045
\(855\) −18.4347 −0.630452
\(856\) −30.3254 −1.03650
\(857\) −25.0072 −0.854230 −0.427115 0.904197i \(-0.640470\pi\)
−0.427115 + 0.904197i \(0.640470\pi\)
\(858\) −1.70026 −0.0580460
\(859\) 40.2573 1.37356 0.686780 0.726865i \(-0.259023\pi\)
0.686780 + 0.726865i \(0.259023\pi\)
\(860\) 33.6899 1.14882
\(861\) 42.3409 1.44297
\(862\) 38.2558 1.30300
\(863\) 11.4655 0.390291 0.195146 0.980774i \(-0.437482\pi\)
0.195146 + 0.980774i \(0.437482\pi\)
\(864\) −2.66889 −0.0907974
\(865\) 20.5450 0.698551
\(866\) −20.9508 −0.711937
\(867\) −1.00000 −0.0339618
\(868\) 185.486 6.29579
\(869\) 4.66417 0.158221
\(870\) 15.3670 0.520990
\(871\) −10.4434 −0.353863
\(872\) 32.4779 1.09984
\(873\) −4.49489 −0.152129
\(874\) 144.112 4.87465
\(875\) 53.9290 1.82313
\(876\) −19.3310 −0.653133
\(877\) −8.02608 −0.271022 −0.135511 0.990776i \(-0.543268\pi\)
−0.135511 + 0.990776i \(0.543268\pi\)
\(878\) 76.8523 2.59364
\(879\) 16.5473 0.558128
\(880\) 5.31786 0.179265
\(881\) −1.37081 −0.0461836 −0.0230918 0.999733i \(-0.507351\pi\)
−0.0230918 + 0.999733i \(0.507351\pi\)
\(882\) −39.8550 −1.34199
\(883\) 46.8654 1.57715 0.788573 0.614941i \(-0.210820\pi\)
0.788573 + 0.614941i \(0.210820\pi\)
\(884\) −2.54428 −0.0855734
\(885\) 6.19455 0.208228
\(886\) −69.2194 −2.32547
\(887\) 44.6925 1.50063 0.750314 0.661082i \(-0.229902\pi\)
0.750314 + 0.661082i \(0.229902\pi\)
\(888\) 5.35674 0.179760
\(889\) 73.5752 2.46763
\(890\) 19.5817 0.656380
\(891\) 1.03520 0.0346807
\(892\) 60.1933 2.01542
\(893\) 98.3147 3.28998
\(894\) 55.4883 1.85581
\(895\) 19.9524 0.666935
\(896\) −100.958 −3.37277
\(897\) 5.08377 0.169742
\(898\) −14.6990 −0.490512
\(899\) −29.4077 −0.980801
\(900\) 0.329852 0.0109951
\(901\) −8.62613 −0.287378
\(902\) −21.4925 −0.715622
\(903\) 19.6607 0.654267
\(904\) −24.5067 −0.815079
\(905\) 9.87793 0.328354
\(906\) −43.6834 −1.45129
\(907\) 16.8013 0.557877 0.278939 0.960309i \(-0.410017\pi\)
0.278939 + 0.960309i \(0.410017\pi\)
\(908\) 5.82082 0.193171
\(909\) −14.1289 −0.468626
\(910\) −18.0369 −0.597916
\(911\) −25.4071 −0.841774 −0.420887 0.907113i \(-0.638281\pi\)
−0.420887 + 0.907113i \(0.638281\pi\)
\(912\) 18.6079 0.616168
\(913\) −7.88991 −0.261118
\(914\) 9.96172 0.329504
\(915\) 23.2077 0.767224
\(916\) 6.38300 0.210900
\(917\) 15.2073 0.502191
\(918\) 2.38697 0.0787817
\(919\) 3.57057 0.117782 0.0588912 0.998264i \(-0.481244\pi\)
0.0588912 + 0.998264i \(0.481244\pi\)
\(920\) −67.5387 −2.22669
\(921\) 12.0964 0.398589
\(922\) −32.4809 −1.06970
\(923\) 2.41239 0.0794047
\(924\) 18.6335 0.612996
\(925\) 0.117927 0.00387740
\(926\) 42.8687 1.40875
\(927\) 2.40939 0.0791346
\(928\) 7.61637 0.250020
\(929\) −0.00949945 −0.000311667 0 −0.000155833 1.00000i \(-0.500050\pi\)
−0.000155833 1.00000i \(0.500050\pi\)
\(930\) −55.4900 −1.81959
\(931\) −136.442 −4.47169
\(932\) 32.9393 1.07896
\(933\) 20.6007 0.674436
\(934\) 48.3828 1.58313
\(935\) 2.33535 0.0763740
\(936\) 2.78823 0.0911362
\(937\) 11.8867 0.388320 0.194160 0.980970i \(-0.437802\pi\)
0.194160 + 0.980970i \(0.437802\pi\)
\(938\) 176.357 5.75826
\(939\) −19.8787 −0.648715
\(940\) −100.359 −3.27334
\(941\) 1.27612 0.0416005 0.0208002 0.999784i \(-0.493379\pi\)
0.0208002 + 0.999784i \(0.493379\pi\)
\(942\) −2.38697 −0.0777716
\(943\) 64.2624 2.09267
\(944\) −6.25274 −0.203509
\(945\) 10.9817 0.357236
\(946\) −9.97988 −0.324474
\(947\) −14.2844 −0.464180 −0.232090 0.972694i \(-0.574556\pi\)
−0.232090 + 0.972694i \(0.574556\pi\)
\(948\) −16.6598 −0.541085
\(949\) −3.59729 −0.116773
\(950\) 1.74002 0.0564537
\(951\) −12.4872 −0.404925
\(952\) 19.7256 0.639312
\(953\) 1.39435 0.0451674 0.0225837 0.999745i \(-0.492811\pi\)
0.0225837 + 0.999745i \(0.492811\pi\)
\(954\) 20.5903 0.666635
\(955\) 53.8387 1.74218
\(956\) 47.1109 1.52368
\(957\) −2.95423 −0.0954966
\(958\) −69.8127 −2.25555
\(959\) −68.4752 −2.21118
\(960\) 24.6455 0.795431
\(961\) 75.1906 2.42550
\(962\) 2.17122 0.0700031
\(963\) 7.48379 0.241162
\(964\) −19.4218 −0.625533
\(965\) 58.2890 1.87639
\(966\) −85.8489 −2.76214
\(967\) 32.5456 1.04660 0.523298 0.852150i \(-0.324702\pi\)
0.523298 + 0.852150i \(0.324702\pi\)
\(968\) 40.2312 1.29308
\(969\) 8.17166 0.262512
\(970\) 24.2042 0.777150
\(971\) 23.2256 0.745346 0.372673 0.927963i \(-0.378441\pi\)
0.372673 + 0.927963i \(0.378441\pi\)
\(972\) −3.69761 −0.118601
\(973\) −6.81364 −0.218435
\(974\) 64.9218 2.08023
\(975\) 0.0613819 0.00196579
\(976\) −23.4258 −0.749840
\(977\) −50.8529 −1.62693 −0.813465 0.581614i \(-0.802421\pi\)
−0.813465 + 0.581614i \(0.802421\pi\)
\(978\) 55.1106 1.76224
\(979\) −3.76448 −0.120313
\(980\) 139.278 4.44908
\(981\) −8.01499 −0.255899
\(982\) −43.8086 −1.39799
\(983\) 0.196709 0.00627403 0.00313702 0.999995i \(-0.499001\pi\)
0.00313702 + 0.999995i \(0.499001\pi\)
\(984\) 35.2452 1.12358
\(985\) −26.6629 −0.849551
\(986\) −6.81184 −0.216933
\(987\) −58.5671 −1.86421
\(988\) 20.7910 0.661450
\(989\) 29.8398 0.948849
\(990\) −5.57439 −0.177166
\(991\) 42.1068 1.33757 0.668784 0.743457i \(-0.266815\pi\)
0.668784 + 0.743457i \(0.266815\pi\)
\(992\) −27.5026 −0.873207
\(993\) 32.9406 1.04534
\(994\) −40.7377 −1.29212
\(995\) −19.3208 −0.612512
\(996\) 28.1817 0.892971
\(997\) 43.7861 1.38672 0.693360 0.720592i \(-0.256130\pi\)
0.693360 + 0.720592i \(0.256130\pi\)
\(998\) −92.9255 −2.94150
\(999\) −1.32195 −0.0418246
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 \(a_p\))