Properties

Label 8002.2.a.d.1.15
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 1
Dimension 69
CM No

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Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.15867 q^{3}\) \(+1.00000 q^{4}\) \(+0.496482 q^{5}\) \(-2.15867 q^{6}\) \(-0.313465 q^{7}\) \(+1.00000 q^{8}\) \(+1.65985 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.15867 q^{3}\) \(+1.00000 q^{4}\) \(+0.496482 q^{5}\) \(-2.15867 q^{6}\) \(-0.313465 q^{7}\) \(+1.00000 q^{8}\) \(+1.65985 q^{9}\) \(+0.496482 q^{10}\) \(-0.947161 q^{11}\) \(-2.15867 q^{12}\) \(+0.165631 q^{13}\) \(-0.313465 q^{14}\) \(-1.07174 q^{15}\) \(+1.00000 q^{16}\) \(-6.79807 q^{17}\) \(+1.65985 q^{18}\) \(+1.01270 q^{19}\) \(+0.496482 q^{20}\) \(+0.676667 q^{21}\) \(-0.947161 q^{22}\) \(+4.85504 q^{23}\) \(-2.15867 q^{24}\) \(-4.75351 q^{25}\) \(+0.165631 q^{26}\) \(+2.89293 q^{27}\) \(-0.313465 q^{28}\) \(+8.41712 q^{29}\) \(-1.07174 q^{30}\) \(-0.965191 q^{31}\) \(+1.00000 q^{32}\) \(+2.04461 q^{33}\) \(-6.79807 q^{34}\) \(-0.155629 q^{35}\) \(+1.65985 q^{36}\) \(+10.9954 q^{37}\) \(+1.01270 q^{38}\) \(-0.357542 q^{39}\) \(+0.496482 q^{40}\) \(-1.43868 q^{41}\) \(+0.676667 q^{42}\) \(-7.10074 q^{43}\) \(-0.947161 q^{44}\) \(+0.824087 q^{45}\) \(+4.85504 q^{46}\) \(-6.38432 q^{47}\) \(-2.15867 q^{48}\) \(-6.90174 q^{49}\) \(-4.75351 q^{50}\) \(+14.6748 q^{51}\) \(+0.165631 q^{52}\) \(+7.98758 q^{53}\) \(+2.89293 q^{54}\) \(-0.470248 q^{55}\) \(-0.313465 q^{56}\) \(-2.18608 q^{57}\) \(+8.41712 q^{58}\) \(+0.213356 q^{59}\) \(-1.07174 q^{60}\) \(+4.95459 q^{61}\) \(-0.965191 q^{62}\) \(-0.520306 q^{63}\) \(+1.00000 q^{64}\) \(+0.0822325 q^{65}\) \(+2.04461 q^{66}\) \(+8.95755 q^{67}\) \(-6.79807 q^{68}\) \(-10.4804 q^{69}\) \(-0.155629 q^{70}\) \(+0.235117 q^{71}\) \(+1.65985 q^{72}\) \(-13.4876 q^{73}\) \(+10.9954 q^{74}\) \(+10.2612 q^{75}\) \(+1.01270 q^{76}\) \(+0.296902 q^{77}\) \(-0.357542 q^{78}\) \(-12.3178 q^{79}\) \(+0.496482 q^{80}\) \(-11.2244 q^{81}\) \(-1.43868 q^{82}\) \(-3.57389 q^{83}\) \(+0.676667 q^{84}\) \(-3.37511 q^{85}\) \(-7.10074 q^{86}\) \(-18.1698 q^{87}\) \(-0.947161 q^{88}\) \(-2.22111 q^{89}\) \(+0.824087 q^{90}\) \(-0.0519193 q^{91}\) \(+4.85504 q^{92}\) \(+2.08353 q^{93}\) \(-6.38432 q^{94}\) \(+0.502786 q^{95}\) \(-2.15867 q^{96}\) \(-14.0019 q^{97}\) \(-6.90174 q^{98}\) \(-1.57215 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 30q^{11} \) \(\mathstrut -\mathstrut 25q^{12} \) \(\mathstrut -\mathstrut 58q^{13} \) \(\mathstrut -\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 69q^{16} \) \(\mathstrut -\mathstrut 80q^{17} \) \(\mathstrut +\mathstrut 54q^{18} \) \(\mathstrut -\mathstrut 40q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 32q^{21} \) \(\mathstrut -\mathstrut 30q^{22} \) \(\mathstrut -\mathstrut 45q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 42q^{25} \) \(\mathstrut -\mathstrut 58q^{26} \) \(\mathstrut -\mathstrut 76q^{27} \) \(\mathstrut -\mathstrut 19q^{28} \) \(\mathstrut -\mathstrut 44q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 69q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 80q^{34} \) \(\mathstrut -\mathstrut 49q^{35} \) \(\mathstrut +\mathstrut 54q^{36} \) \(\mathstrut -\mathstrut 47q^{37} \) \(\mathstrut -\mathstrut 40q^{38} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 33q^{40} \) \(\mathstrut -\mathstrut 94q^{41} \) \(\mathstrut -\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 30q^{44} \) \(\mathstrut -\mathstrut 89q^{45} \) \(\mathstrut -\mathstrut 45q^{46} \) \(\mathstrut -\mathstrut 85q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut +\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 10q^{51} \) \(\mathstrut -\mathstrut 58q^{52} \) \(\mathstrut -\mathstrut 41q^{53} \) \(\mathstrut -\mathstrut 76q^{54} \) \(\mathstrut -\mathstrut 27q^{55} \) \(\mathstrut -\mathstrut 19q^{56} \) \(\mathstrut -\mathstrut 72q^{57} \) \(\mathstrut -\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 75q^{59} \) \(\mathstrut +\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 98q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 69q^{64} \) \(\mathstrut -\mathstrut 47q^{65} \) \(\mathstrut -\mathstrut 41q^{66} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 80q^{68} \) \(\mathstrut -\mathstrut 74q^{69} \) \(\mathstrut -\mathstrut 49q^{70} \) \(\mathstrut -\mathstrut 22q^{71} \) \(\mathstrut +\mathstrut 54q^{72} \) \(\mathstrut -\mathstrut 129q^{73} \) \(\mathstrut -\mathstrut 47q^{74} \) \(\mathstrut -\mathstrut 106q^{75} \) \(\mathstrut -\mathstrut 40q^{76} \) \(\mathstrut -\mathstrut 108q^{77} \) \(\mathstrut -\mathstrut 14q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 33q^{80} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 94q^{82} \) \(\mathstrut -\mathstrut 111q^{83} \) \(\mathstrut -\mathstrut 32q^{84} \) \(\mathstrut -\mathstrut 67q^{85} \) \(\mathstrut -\mathstrut 10q^{86} \) \(\mathstrut -\mathstrut 38q^{87} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 89q^{90} \) \(\mathstrut -\mathstrut 55q^{91} \) \(\mathstrut -\mathstrut 45q^{92} \) \(\mathstrut -\mathstrut 90q^{93} \) \(\mathstrut -\mathstrut 85q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 25q^{96} \) \(\mathstrut -\mathstrut 98q^{97} \) \(\mathstrut +\mathstrut 32q^{98} \) \(\mathstrut -\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.15867 −1.24631 −0.623154 0.782099i \(-0.714149\pi\)
−0.623154 + 0.782099i \(0.714149\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.496482 0.222033 0.111017 0.993819i \(-0.464589\pi\)
0.111017 + 0.993819i \(0.464589\pi\)
\(6\) −2.15867 −0.881273
\(7\) −0.313465 −0.118479 −0.0592393 0.998244i \(-0.518867\pi\)
−0.0592393 + 0.998244i \(0.518867\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.65985 0.553285
\(10\) 0.496482 0.157001
\(11\) −0.947161 −0.285580 −0.142790 0.989753i \(-0.545607\pi\)
−0.142790 + 0.989753i \(0.545607\pi\)
\(12\) −2.15867 −0.623154
\(13\) 0.165631 0.0459377 0.0229688 0.999736i \(-0.492688\pi\)
0.0229688 + 0.999736i \(0.492688\pi\)
\(14\) −0.313465 −0.0837770
\(15\) −1.07174 −0.276722
\(16\) 1.00000 0.250000
\(17\) −6.79807 −1.64877 −0.824387 0.566027i \(-0.808480\pi\)
−0.824387 + 0.566027i \(0.808480\pi\)
\(18\) 1.65985 0.391231
\(19\) 1.01270 0.232329 0.116164 0.993230i \(-0.462940\pi\)
0.116164 + 0.993230i \(0.462940\pi\)
\(20\) 0.496482 0.111017
\(21\) 0.676667 0.147661
\(22\) −0.947161 −0.201935
\(23\) 4.85504 1.01235 0.506173 0.862432i \(-0.331060\pi\)
0.506173 + 0.862432i \(0.331060\pi\)
\(24\) −2.15867 −0.440637
\(25\) −4.75351 −0.950701
\(26\) 0.165631 0.0324828
\(27\) 2.89293 0.556745
\(28\) −0.313465 −0.0592393
\(29\) 8.41712 1.56302 0.781510 0.623892i \(-0.214450\pi\)
0.781510 + 0.623892i \(0.214450\pi\)
\(30\) −1.07174 −0.195672
\(31\) −0.965191 −0.173353 −0.0866767 0.996236i \(-0.527625\pi\)
−0.0866767 + 0.996236i \(0.527625\pi\)
\(32\) 1.00000 0.176777
\(33\) 2.04461 0.355920
\(34\) −6.79807 −1.16586
\(35\) −0.155629 −0.0263062
\(36\) 1.65985 0.276642
\(37\) 10.9954 1.80764 0.903820 0.427913i \(-0.140751\pi\)
0.903820 + 0.427913i \(0.140751\pi\)
\(38\) 1.01270 0.164281
\(39\) −0.357542 −0.0572525
\(40\) 0.496482 0.0785006
\(41\) −1.43868 −0.224683 −0.112342 0.993670i \(-0.535835\pi\)
−0.112342 + 0.993670i \(0.535835\pi\)
\(42\) 0.676667 0.104412
\(43\) −7.10074 −1.08285 −0.541426 0.840748i \(-0.682115\pi\)
−0.541426 + 0.840748i \(0.682115\pi\)
\(44\) −0.947161 −0.142790
\(45\) 0.824087 0.122848
\(46\) 4.85504 0.715837
\(47\) −6.38432 −0.931249 −0.465624 0.884983i \(-0.654170\pi\)
−0.465624 + 0.884983i \(0.654170\pi\)
\(48\) −2.15867 −0.311577
\(49\) −6.90174 −0.985963
\(50\) −4.75351 −0.672247
\(51\) 14.6748 2.05488
\(52\) 0.165631 0.0229688
\(53\) 7.98758 1.09718 0.548590 0.836092i \(-0.315165\pi\)
0.548590 + 0.836092i \(0.315165\pi\)
\(54\) 2.89293 0.393678
\(55\) −0.470248 −0.0634082
\(56\) −0.313465 −0.0418885
\(57\) −2.18608 −0.289553
\(58\) 8.41712 1.10522
\(59\) 0.213356 0.0277766 0.0138883 0.999904i \(-0.495579\pi\)
0.0138883 + 0.999904i \(0.495579\pi\)
\(60\) −1.07174 −0.138361
\(61\) 4.95459 0.634370 0.317185 0.948364i \(-0.397262\pi\)
0.317185 + 0.948364i \(0.397262\pi\)
\(62\) −0.965191 −0.122579
\(63\) −0.520306 −0.0655523
\(64\) 1.00000 0.125000
\(65\) 0.0822325 0.0101997
\(66\) 2.04461 0.251674
\(67\) 8.95755 1.09434 0.547169 0.837022i \(-0.315705\pi\)
0.547169 + 0.837022i \(0.315705\pi\)
\(68\) −6.79807 −0.824387
\(69\) −10.4804 −1.26170
\(70\) −0.155629 −0.0186013
\(71\) 0.235117 0.0279033 0.0139516 0.999903i \(-0.495559\pi\)
0.0139516 + 0.999903i \(0.495559\pi\)
\(72\) 1.65985 0.195616
\(73\) −13.4876 −1.57861 −0.789305 0.614002i \(-0.789559\pi\)
−0.789305 + 0.614002i \(0.789559\pi\)
\(74\) 10.9954 1.27819
\(75\) 10.2612 1.18487
\(76\) 1.01270 0.116164
\(77\) 0.296902 0.0338351
\(78\) −0.357542 −0.0404836
\(79\) −12.3178 −1.38586 −0.692932 0.721003i \(-0.743682\pi\)
−0.692932 + 0.721003i \(0.743682\pi\)
\(80\) 0.496482 0.0555083
\(81\) −11.2244 −1.24716
\(82\) −1.43868 −0.158875
\(83\) −3.57389 −0.392285 −0.196143 0.980575i \(-0.562842\pi\)
−0.196143 + 0.980575i \(0.562842\pi\)
\(84\) 0.676667 0.0738304
\(85\) −3.37511 −0.366083
\(86\) −7.10074 −0.765692
\(87\) −18.1698 −1.94801
\(88\) −0.947161 −0.100968
\(89\) −2.22111 −0.235438 −0.117719 0.993047i \(-0.537558\pi\)
−0.117719 + 0.993047i \(0.537558\pi\)
\(90\) 0.824087 0.0868664
\(91\) −0.0519193 −0.00544263
\(92\) 4.85504 0.506173
\(93\) 2.08353 0.216052
\(94\) −6.38432 −0.658492
\(95\) 0.502786 0.0515847
\(96\) −2.15867 −0.220318
\(97\) −14.0019 −1.42168 −0.710841 0.703353i \(-0.751685\pi\)
−0.710841 + 0.703353i \(0.751685\pi\)
\(98\) −6.90174 −0.697181
\(99\) −1.57215 −0.158007
\(100\) −4.75351 −0.475351
\(101\) −10.5233 −1.04711 −0.523554 0.851992i \(-0.675394\pi\)
−0.523554 + 0.851992i \(0.675394\pi\)
\(102\) 14.6748 1.45302
\(103\) 7.98345 0.786632 0.393316 0.919403i \(-0.371328\pi\)
0.393316 + 0.919403i \(0.371328\pi\)
\(104\) 0.165631 0.0162414
\(105\) 0.335953 0.0327856
\(106\) 7.98758 0.775823
\(107\) −12.2727 −1.18644 −0.593222 0.805039i \(-0.702144\pi\)
−0.593222 + 0.805039i \(0.702144\pi\)
\(108\) 2.89293 0.278373
\(109\) 6.20572 0.594400 0.297200 0.954815i \(-0.403947\pi\)
0.297200 + 0.954815i \(0.403947\pi\)
\(110\) −0.470248 −0.0448364
\(111\) −23.7355 −2.25288
\(112\) −0.313465 −0.0296196
\(113\) 16.5787 1.55960 0.779798 0.626031i \(-0.215322\pi\)
0.779798 + 0.626031i \(0.215322\pi\)
\(114\) −2.18608 −0.204745
\(115\) 2.41044 0.224775
\(116\) 8.41712 0.781510
\(117\) 0.274922 0.0254166
\(118\) 0.213356 0.0196410
\(119\) 2.13095 0.195344
\(120\) −1.07174 −0.0978360
\(121\) −10.1029 −0.918444
\(122\) 4.95459 0.448567
\(123\) 3.10563 0.280025
\(124\) −0.965191 −0.0866767
\(125\) −4.84244 −0.433121
\(126\) −0.520306 −0.0463525
\(127\) 0.215287 0.0191037 0.00955183 0.999954i \(-0.496960\pi\)
0.00955183 + 0.999954i \(0.496960\pi\)
\(128\) 1.00000 0.0883883
\(129\) 15.3282 1.34957
\(130\) 0.0822325 0.00721227
\(131\) 3.83192 0.334796 0.167398 0.985889i \(-0.446463\pi\)
0.167398 + 0.985889i \(0.446463\pi\)
\(132\) 2.04461 0.177960
\(133\) −0.317445 −0.0275260
\(134\) 8.95755 0.773814
\(135\) 1.43629 0.123616
\(136\) −6.79807 −0.582929
\(137\) −11.8464 −1.01211 −0.506054 0.862502i \(-0.668896\pi\)
−0.506054 + 0.862502i \(0.668896\pi\)
\(138\) −10.4804 −0.892153
\(139\) 23.2156 1.96912 0.984562 0.175039i \(-0.0560050\pi\)
0.984562 + 0.175039i \(0.0560050\pi\)
\(140\) −0.155629 −0.0131531
\(141\) 13.7816 1.16062
\(142\) 0.235117 0.0197306
\(143\) −0.156879 −0.0131189
\(144\) 1.65985 0.138321
\(145\) 4.17895 0.347043
\(146\) −13.4876 −1.11625
\(147\) 14.8986 1.22881
\(148\) 10.9954 0.903820
\(149\) 2.97121 0.243411 0.121705 0.992566i \(-0.461164\pi\)
0.121705 + 0.992566i \(0.461164\pi\)
\(150\) 10.2612 0.837827
\(151\) −9.49867 −0.772991 −0.386495 0.922291i \(-0.626314\pi\)
−0.386495 + 0.922291i \(0.626314\pi\)
\(152\) 1.01270 0.0821406
\(153\) −11.2838 −0.912241
\(154\) 0.296902 0.0239250
\(155\) −0.479200 −0.0384902
\(156\) −0.357542 −0.0286262
\(157\) −13.5598 −1.08219 −0.541097 0.840960i \(-0.681991\pi\)
−0.541097 + 0.840960i \(0.681991\pi\)
\(158\) −12.3178 −0.979954
\(159\) −17.2426 −1.36742
\(160\) 0.496482 0.0392503
\(161\) −1.52188 −0.119941
\(162\) −11.2244 −0.881876
\(163\) 3.12522 0.244786 0.122393 0.992482i \(-0.460943\pi\)
0.122393 + 0.992482i \(0.460943\pi\)
\(164\) −1.43868 −0.112342
\(165\) 1.01511 0.0790262
\(166\) −3.57389 −0.277387
\(167\) 21.3478 1.65194 0.825971 0.563713i \(-0.190627\pi\)
0.825971 + 0.563713i \(0.190627\pi\)
\(168\) 0.676667 0.0522060
\(169\) −12.9726 −0.997890
\(170\) −3.37511 −0.258859
\(171\) 1.68093 0.128544
\(172\) −7.10074 −0.541426
\(173\) −24.8639 −1.89036 −0.945182 0.326544i \(-0.894116\pi\)
−0.945182 + 0.326544i \(0.894116\pi\)
\(174\) −18.1698 −1.37745
\(175\) 1.49006 0.112638
\(176\) −0.947161 −0.0713949
\(177\) −0.460566 −0.0346182
\(178\) −2.22111 −0.166480
\(179\) −3.43967 −0.257093 −0.128547 0.991703i \(-0.541031\pi\)
−0.128547 + 0.991703i \(0.541031\pi\)
\(180\) 0.824087 0.0614238
\(181\) 8.01064 0.595426 0.297713 0.954655i \(-0.403776\pi\)
0.297713 + 0.954655i \(0.403776\pi\)
\(182\) −0.0519193 −0.00384852
\(183\) −10.6953 −0.790621
\(184\) 4.85504 0.357918
\(185\) 5.45904 0.401356
\(186\) 2.08353 0.152772
\(187\) 6.43886 0.470856
\(188\) −6.38432 −0.465624
\(189\) −0.906833 −0.0659624
\(190\) 0.502786 0.0364759
\(191\) −3.09608 −0.224025 −0.112012 0.993707i \(-0.535730\pi\)
−0.112012 + 0.993707i \(0.535730\pi\)
\(192\) −2.15867 −0.155789
\(193\) 12.4919 0.899186 0.449593 0.893233i \(-0.351569\pi\)
0.449593 + 0.893233i \(0.351569\pi\)
\(194\) −14.0019 −1.00528
\(195\) −0.177513 −0.0127120
\(196\) −6.90174 −0.492981
\(197\) 13.3977 0.954546 0.477273 0.878755i \(-0.341625\pi\)
0.477273 + 0.878755i \(0.341625\pi\)
\(198\) −1.57215 −0.111728
\(199\) −12.6721 −0.898304 −0.449152 0.893455i \(-0.648274\pi\)
−0.449152 + 0.893455i \(0.648274\pi\)
\(200\) −4.75351 −0.336124
\(201\) −19.3364 −1.36388
\(202\) −10.5233 −0.740417
\(203\) −2.63847 −0.185184
\(204\) 14.6748 1.02744
\(205\) −0.714276 −0.0498872
\(206\) 7.98345 0.556233
\(207\) 8.05866 0.560115
\(208\) 0.165631 0.0114844
\(209\) −0.959188 −0.0663484
\(210\) 0.335953 0.0231829
\(211\) −12.7324 −0.876537 −0.438269 0.898844i \(-0.644408\pi\)
−0.438269 + 0.898844i \(0.644408\pi\)
\(212\) 7.98758 0.548590
\(213\) −0.507540 −0.0347761
\(214\) −12.2727 −0.838942
\(215\) −3.52539 −0.240429
\(216\) 2.89293 0.196839
\(217\) 0.302553 0.0205387
\(218\) 6.20572 0.420304
\(219\) 29.1154 1.96743
\(220\) −0.470248 −0.0317041
\(221\) −1.12597 −0.0757408
\(222\) −23.7355 −1.59302
\(223\) −29.4755 −1.97382 −0.986911 0.161265i \(-0.948443\pi\)
−0.986911 + 0.161265i \(0.948443\pi\)
\(224\) −0.313465 −0.0209442
\(225\) −7.89012 −0.526008
\(226\) 16.5787 1.10280
\(227\) −12.6452 −0.839294 −0.419647 0.907687i \(-0.637846\pi\)
−0.419647 + 0.907687i \(0.637846\pi\)
\(228\) −2.18608 −0.144777
\(229\) 10.5157 0.694894 0.347447 0.937700i \(-0.387049\pi\)
0.347447 + 0.937700i \(0.387049\pi\)
\(230\) 2.41044 0.158940
\(231\) −0.640912 −0.0421689
\(232\) 8.41712 0.552611
\(233\) 9.57748 0.627442 0.313721 0.949515i \(-0.398424\pi\)
0.313721 + 0.949515i \(0.398424\pi\)
\(234\) 0.274922 0.0179722
\(235\) −3.16970 −0.206768
\(236\) 0.213356 0.0138883
\(237\) 26.5901 1.72721
\(238\) 2.13095 0.138129
\(239\) 8.94706 0.578737 0.289369 0.957218i \(-0.406555\pi\)
0.289369 + 0.957218i \(0.406555\pi\)
\(240\) −1.07174 −0.0691805
\(241\) −12.3296 −0.794219 −0.397109 0.917771i \(-0.629987\pi\)
−0.397109 + 0.917771i \(0.629987\pi\)
\(242\) −10.1029 −0.649438
\(243\) 15.5511 0.997602
\(244\) 4.95459 0.317185
\(245\) −3.42659 −0.218917
\(246\) 3.10563 0.198007
\(247\) 0.167734 0.0106726
\(248\) −0.965191 −0.0612897
\(249\) 7.71484 0.488908
\(250\) −4.84244 −0.306263
\(251\) 13.3033 0.839696 0.419848 0.907594i \(-0.362083\pi\)
0.419848 + 0.907594i \(0.362083\pi\)
\(252\) −0.520306 −0.0327762
\(253\) −4.59850 −0.289106
\(254\) 0.215287 0.0135083
\(255\) 7.28576 0.456252
\(256\) 1.00000 0.0625000
\(257\) −25.7708 −1.60754 −0.803769 0.594942i \(-0.797175\pi\)
−0.803769 + 0.594942i \(0.797175\pi\)
\(258\) 15.3282 0.954289
\(259\) −3.44668 −0.214167
\(260\) 0.0822325 0.00509984
\(261\) 13.9712 0.864795
\(262\) 3.83192 0.236737
\(263\) 8.07327 0.497819 0.248910 0.968527i \(-0.419928\pi\)
0.248910 + 0.968527i \(0.419928\pi\)
\(264\) 2.04461 0.125837
\(265\) 3.96569 0.243610
\(266\) −0.317445 −0.0194638
\(267\) 4.79465 0.293428
\(268\) 8.95755 0.547169
\(269\) −23.8405 −1.45358 −0.726791 0.686859i \(-0.758989\pi\)
−0.726791 + 0.686859i \(0.758989\pi\)
\(270\) 1.43629 0.0874097
\(271\) 2.13690 0.129807 0.0649036 0.997892i \(-0.479326\pi\)
0.0649036 + 0.997892i \(0.479326\pi\)
\(272\) −6.79807 −0.412193
\(273\) 0.112077 0.00678319
\(274\) −11.8464 −0.715668
\(275\) 4.50233 0.271501
\(276\) −10.4804 −0.630848
\(277\) −18.1933 −1.09313 −0.546564 0.837417i \(-0.684064\pi\)
−0.546564 + 0.837417i \(0.684064\pi\)
\(278\) 23.2156 1.39238
\(279\) −1.60208 −0.0959138
\(280\) −0.155629 −0.00930064
\(281\) −17.3775 −1.03665 −0.518327 0.855182i \(-0.673445\pi\)
−0.518327 + 0.855182i \(0.673445\pi\)
\(282\) 13.7816 0.820684
\(283\) −6.93786 −0.412413 −0.206206 0.978509i \(-0.566112\pi\)
−0.206206 + 0.978509i \(0.566112\pi\)
\(284\) 0.235117 0.0139516
\(285\) −1.08535 −0.0642905
\(286\) −0.156879 −0.00927644
\(287\) 0.450974 0.0266202
\(288\) 1.65985 0.0978078
\(289\) 29.2137 1.71845
\(290\) 4.17895 0.245396
\(291\) 30.2256 1.77185
\(292\) −13.4876 −0.789305
\(293\) −33.5837 −1.96198 −0.980990 0.194061i \(-0.937834\pi\)
−0.980990 + 0.194061i \(0.937834\pi\)
\(294\) 14.8986 0.868903
\(295\) 0.105927 0.00616733
\(296\) 10.9954 0.639097
\(297\) −2.74007 −0.158995
\(298\) 2.97121 0.172118
\(299\) 0.804143 0.0465048
\(300\) 10.2612 0.592433
\(301\) 2.22583 0.128295
\(302\) −9.49867 −0.546587
\(303\) 22.7163 1.30502
\(304\) 1.01270 0.0580822
\(305\) 2.45986 0.140851
\(306\) −11.2838 −0.645052
\(307\) 1.47970 0.0844507 0.0422254 0.999108i \(-0.486555\pi\)
0.0422254 + 0.999108i \(0.486555\pi\)
\(308\) 0.296902 0.0169175
\(309\) −17.2336 −0.980386
\(310\) −0.479200 −0.0272167
\(311\) −31.9898 −1.81397 −0.906987 0.421158i \(-0.861624\pi\)
−0.906987 + 0.421158i \(0.861624\pi\)
\(312\) −0.357542 −0.0202418
\(313\) −7.83489 −0.442854 −0.221427 0.975177i \(-0.571072\pi\)
−0.221427 + 0.975177i \(0.571072\pi\)
\(314\) −13.5598 −0.765226
\(315\) −0.258322 −0.0145548
\(316\) −12.3178 −0.692932
\(317\) −13.0466 −0.732772 −0.366386 0.930463i \(-0.619405\pi\)
−0.366386 + 0.930463i \(0.619405\pi\)
\(318\) −17.2426 −0.966914
\(319\) −7.97237 −0.446367
\(320\) 0.496482 0.0277542
\(321\) 26.4926 1.47867
\(322\) −1.52188 −0.0848113
\(323\) −6.88439 −0.383058
\(324\) −11.2244 −0.623580
\(325\) −0.787326 −0.0436730
\(326\) 3.12522 0.173090
\(327\) −13.3961 −0.740806
\(328\) −1.43868 −0.0794376
\(329\) 2.00126 0.110333
\(330\) 1.01511 0.0558799
\(331\) 10.7342 0.590005 0.295003 0.955496i \(-0.404679\pi\)
0.295003 + 0.955496i \(0.404679\pi\)
\(332\) −3.57389 −0.196143
\(333\) 18.2508 1.00014
\(334\) 21.3478 1.16810
\(335\) 4.44726 0.242980
\(336\) 0.676667 0.0369152
\(337\) 12.1708 0.662984 0.331492 0.943458i \(-0.392448\pi\)
0.331492 + 0.943458i \(0.392448\pi\)
\(338\) −12.9726 −0.705615
\(339\) −35.7880 −1.94374
\(340\) −3.37511 −0.183041
\(341\) 0.914191 0.0495062
\(342\) 1.68093 0.0908943
\(343\) 4.35771 0.235294
\(344\) −7.10074 −0.382846
\(345\) −5.20334 −0.280138
\(346\) −24.8639 −1.33669
\(347\) 1.17081 0.0628524 0.0314262 0.999506i \(-0.489995\pi\)
0.0314262 + 0.999506i \(0.489995\pi\)
\(348\) −18.1698 −0.974003
\(349\) 27.3594 1.46451 0.732257 0.681028i \(-0.238467\pi\)
0.732257 + 0.681028i \(0.238467\pi\)
\(350\) 1.49006 0.0796469
\(351\) 0.479158 0.0255756
\(352\) −0.947161 −0.0504838
\(353\) 23.1708 1.23326 0.616629 0.787254i \(-0.288498\pi\)
0.616629 + 0.787254i \(0.288498\pi\)
\(354\) −0.460566 −0.0244788
\(355\) 0.116731 0.00619546
\(356\) −2.22111 −0.117719
\(357\) −4.60003 −0.243459
\(358\) −3.43967 −0.181792
\(359\) 9.50037 0.501410 0.250705 0.968064i \(-0.419338\pi\)
0.250705 + 0.968064i \(0.419338\pi\)
\(360\) 0.824087 0.0434332
\(361\) −17.9744 −0.946023
\(362\) 8.01064 0.421030
\(363\) 21.8088 1.14466
\(364\) −0.0519193 −0.00272131
\(365\) −6.69637 −0.350504
\(366\) −10.6953 −0.559053
\(367\) −26.2152 −1.36842 −0.684212 0.729283i \(-0.739854\pi\)
−0.684212 + 0.729283i \(0.739854\pi\)
\(368\) 4.85504 0.253087
\(369\) −2.38799 −0.124314
\(370\) 5.45904 0.283802
\(371\) −2.50383 −0.129992
\(372\) 2.08353 0.108026
\(373\) −31.0937 −1.60997 −0.804986 0.593293i \(-0.797827\pi\)
−0.804986 + 0.593293i \(0.797827\pi\)
\(374\) 6.43886 0.332946
\(375\) 10.4532 0.539802
\(376\) −6.38432 −0.329246
\(377\) 1.39413 0.0718015
\(378\) −0.906833 −0.0466424
\(379\) 19.5885 1.00619 0.503097 0.864230i \(-0.332194\pi\)
0.503097 + 0.864230i \(0.332194\pi\)
\(380\) 0.502786 0.0257924
\(381\) −0.464734 −0.0238091
\(382\) −3.09608 −0.158409
\(383\) −19.6501 −1.00407 −0.502036 0.864847i \(-0.667415\pi\)
−0.502036 + 0.864847i \(0.667415\pi\)
\(384\) −2.15867 −0.110159
\(385\) 0.147406 0.00751251
\(386\) 12.4919 0.635821
\(387\) −11.7862 −0.599126
\(388\) −14.0019 −0.710841
\(389\) −21.4746 −1.08881 −0.544403 0.838824i \(-0.683244\pi\)
−0.544403 + 0.838824i \(0.683244\pi\)
\(390\) −0.177513 −0.00898871
\(391\) −33.0049 −1.66913
\(392\) −6.90174 −0.348591
\(393\) −8.27185 −0.417259
\(394\) 13.3977 0.674966
\(395\) −6.11558 −0.307708
\(396\) −1.57215 −0.0790034
\(397\) 22.5403 1.13127 0.565633 0.824657i \(-0.308632\pi\)
0.565633 + 0.824657i \(0.308632\pi\)
\(398\) −12.6721 −0.635197
\(399\) 0.685259 0.0343058
\(400\) −4.75351 −0.237675
\(401\) −11.4310 −0.570837 −0.285419 0.958403i \(-0.592133\pi\)
−0.285419 + 0.958403i \(0.592133\pi\)
\(402\) −19.3364 −0.964411
\(403\) −0.159865 −0.00796345
\(404\) −10.5233 −0.523554
\(405\) −5.57273 −0.276911
\(406\) −2.63847 −0.130945
\(407\) −10.4145 −0.516225
\(408\) 14.6748 0.726510
\(409\) 10.8461 0.536307 0.268154 0.963376i \(-0.413587\pi\)
0.268154 + 0.963376i \(0.413587\pi\)
\(410\) −0.714276 −0.0352756
\(411\) 25.5725 1.26140
\(412\) 7.98345 0.393316
\(413\) −0.0668796 −0.00329093
\(414\) 8.05866 0.396061
\(415\) −1.77437 −0.0871003
\(416\) 0.165631 0.00812071
\(417\) −50.1148 −2.45413
\(418\) −0.959188 −0.0469154
\(419\) 17.0512 0.833006 0.416503 0.909134i \(-0.363256\pi\)
0.416503 + 0.909134i \(0.363256\pi\)
\(420\) 0.335953 0.0163928
\(421\) −26.6281 −1.29777 −0.648887 0.760885i \(-0.724765\pi\)
−0.648887 + 0.760885i \(0.724765\pi\)
\(422\) −12.7324 −0.619806
\(423\) −10.5970 −0.515245
\(424\) 7.98758 0.387911
\(425\) 32.3147 1.56749
\(426\) −0.507540 −0.0245904
\(427\) −1.55309 −0.0751592
\(428\) −12.2727 −0.593222
\(429\) 0.338649 0.0163501
\(430\) −3.52539 −0.170009
\(431\) −2.97008 −0.143064 −0.0715319 0.997438i \(-0.522789\pi\)
−0.0715319 + 0.997438i \(0.522789\pi\)
\(432\) 2.89293 0.139186
\(433\) −5.02363 −0.241420 −0.120710 0.992688i \(-0.538517\pi\)
−0.120710 + 0.992688i \(0.538517\pi\)
\(434\) 0.302553 0.0145230
\(435\) −9.02096 −0.432522
\(436\) 6.20572 0.297200
\(437\) 4.91669 0.235197
\(438\) 29.1154 1.39119
\(439\) 9.22859 0.440457 0.220228 0.975448i \(-0.429320\pi\)
0.220228 + 0.975448i \(0.429320\pi\)
\(440\) −0.470248 −0.0224182
\(441\) −11.4559 −0.545518
\(442\) −1.12597 −0.0535568
\(443\) −30.2716 −1.43825 −0.719123 0.694883i \(-0.755456\pi\)
−0.719123 + 0.694883i \(0.755456\pi\)
\(444\) −23.7355 −1.12644
\(445\) −1.10274 −0.0522750
\(446\) −29.4755 −1.39570
\(447\) −6.41386 −0.303365
\(448\) −0.313465 −0.0148098
\(449\) −16.0401 −0.756980 −0.378490 0.925605i \(-0.623557\pi\)
−0.378490 + 0.925605i \(0.623557\pi\)
\(450\) −7.89012 −0.371944
\(451\) 1.36266 0.0641650
\(452\) 16.5787 0.779798
\(453\) 20.5045 0.963385
\(454\) −12.6452 −0.593470
\(455\) −0.0257770 −0.00120844
\(456\) −2.18608 −0.102373
\(457\) 9.06796 0.424181 0.212091 0.977250i \(-0.431973\pi\)
0.212091 + 0.977250i \(0.431973\pi\)
\(458\) 10.5157 0.491365
\(459\) −19.6664 −0.917947
\(460\) 2.41044 0.112387
\(461\) −13.0767 −0.609044 −0.304522 0.952505i \(-0.598497\pi\)
−0.304522 + 0.952505i \(0.598497\pi\)
\(462\) −0.640912 −0.0298179
\(463\) −9.00584 −0.418537 −0.209268 0.977858i \(-0.567108\pi\)
−0.209268 + 0.977858i \(0.567108\pi\)
\(464\) 8.41712 0.390755
\(465\) 1.03443 0.0479707
\(466\) 9.57748 0.443668
\(467\) 7.81614 0.361688 0.180844 0.983512i \(-0.442117\pi\)
0.180844 + 0.983512i \(0.442117\pi\)
\(468\) 0.274922 0.0127083
\(469\) −2.80787 −0.129656
\(470\) −3.16970 −0.146207
\(471\) 29.2712 1.34875
\(472\) 0.213356 0.00982052
\(473\) 6.72554 0.309241
\(474\) 26.5901 1.22133
\(475\) −4.81386 −0.220875
\(476\) 2.13095 0.0976721
\(477\) 13.2582 0.607052
\(478\) 8.94706 0.409229
\(479\) 37.7812 1.72627 0.863134 0.504974i \(-0.168498\pi\)
0.863134 + 0.504974i \(0.168498\pi\)
\(480\) −1.07174 −0.0489180
\(481\) 1.82118 0.0830387
\(482\) −12.3296 −0.561597
\(483\) 3.28524 0.149484
\(484\) −10.1029 −0.459222
\(485\) −6.95170 −0.315661
\(486\) 15.5511 0.705411
\(487\) −15.7752 −0.714841 −0.357420 0.933944i \(-0.616344\pi\)
−0.357420 + 0.933944i \(0.616344\pi\)
\(488\) 4.95459 0.224284
\(489\) −6.74632 −0.305079
\(490\) −3.42659 −0.154797
\(491\) −7.37765 −0.332949 −0.166474 0.986046i \(-0.553238\pi\)
−0.166474 + 0.986046i \(0.553238\pi\)
\(492\) 3.10563 0.140012
\(493\) −57.2202 −2.57707
\(494\) 0.167734 0.00754670
\(495\) −0.780543 −0.0350828
\(496\) −0.965191 −0.0433384
\(497\) −0.0737010 −0.00330594
\(498\) 7.71484 0.345710
\(499\) −13.4031 −0.600007 −0.300003 0.953938i \(-0.596988\pi\)
−0.300003 + 0.953938i \(0.596988\pi\)
\(500\) −4.84244 −0.216560
\(501\) −46.0828 −2.05883
\(502\) 13.3033 0.593755
\(503\) −31.6257 −1.41012 −0.705060 0.709147i \(-0.749080\pi\)
−0.705060 + 0.709147i \(0.749080\pi\)
\(504\) −0.520306 −0.0231763
\(505\) −5.22463 −0.232493
\(506\) −4.59850 −0.204428
\(507\) 28.0035 1.24368
\(508\) 0.215287 0.00955183
\(509\) −16.1894 −0.717582 −0.358791 0.933418i \(-0.616811\pi\)
−0.358791 + 0.933418i \(0.616811\pi\)
\(510\) 7.28576 0.322619
\(511\) 4.22790 0.187031
\(512\) 1.00000 0.0441942
\(513\) 2.92967 0.129348
\(514\) −25.7708 −1.13670
\(515\) 3.96363 0.174659
\(516\) 15.3282 0.674784
\(517\) 6.04698 0.265946
\(518\) −3.44668 −0.151439
\(519\) 53.6728 2.35598
\(520\) 0.0822325 0.00360613
\(521\) 5.48548 0.240323 0.120162 0.992754i \(-0.461659\pi\)
0.120162 + 0.992754i \(0.461659\pi\)
\(522\) 13.9712 0.611502
\(523\) 43.1354 1.88618 0.943090 0.332538i \(-0.107905\pi\)
0.943090 + 0.332538i \(0.107905\pi\)
\(524\) 3.83192 0.167398
\(525\) −3.21654 −0.140381
\(526\) 8.07327 0.352011
\(527\) 6.56143 0.285821
\(528\) 2.04461 0.0889801
\(529\) 0.571423 0.0248445
\(530\) 3.96569 0.172258
\(531\) 0.354140 0.0153684
\(532\) −0.317445 −0.0137630
\(533\) −0.238289 −0.0103214
\(534\) 4.79465 0.207485
\(535\) −6.09315 −0.263430
\(536\) 8.95755 0.386907
\(537\) 7.42512 0.320418
\(538\) −23.8405 −1.02784
\(539\) 6.53706 0.281571
\(540\) 1.43629 0.0618080
\(541\) 14.5612 0.626034 0.313017 0.949748i \(-0.398660\pi\)
0.313017 + 0.949748i \(0.398660\pi\)
\(542\) 2.13690 0.0917875
\(543\) −17.2923 −0.742084
\(544\) −6.79807 −0.291465
\(545\) 3.08102 0.131977
\(546\) 0.112077 0.00479644
\(547\) −24.2392 −1.03639 −0.518197 0.855261i \(-0.673397\pi\)
−0.518197 + 0.855261i \(0.673397\pi\)
\(548\) −11.8464 −0.506054
\(549\) 8.22389 0.350987
\(550\) 4.50233 0.191980
\(551\) 8.52400 0.363135
\(552\) −10.4804 −0.446077
\(553\) 3.86121 0.164195
\(554\) −18.1933 −0.772958
\(555\) −11.7843 −0.500214
\(556\) 23.2156 0.984562
\(557\) −24.3627 −1.03228 −0.516141 0.856504i \(-0.672632\pi\)
−0.516141 + 0.856504i \(0.672632\pi\)
\(558\) −1.60208 −0.0678213
\(559\) −1.17610 −0.0497437
\(560\) −0.155629 −0.00657654
\(561\) −13.8994 −0.586832
\(562\) −17.3775 −0.733026
\(563\) −20.1340 −0.848548 −0.424274 0.905534i \(-0.639471\pi\)
−0.424274 + 0.905534i \(0.639471\pi\)
\(564\) 13.7816 0.580311
\(565\) 8.23104 0.346282
\(566\) −6.93786 −0.291620
\(567\) 3.51847 0.147762
\(568\) 0.235117 0.00986530
\(569\) −22.5303 −0.944519 −0.472260 0.881460i \(-0.656562\pi\)
−0.472260 + 0.881460i \(0.656562\pi\)
\(570\) −1.08535 −0.0454602
\(571\) 33.3064 1.39383 0.696914 0.717155i \(-0.254556\pi\)
0.696914 + 0.717155i \(0.254556\pi\)
\(572\) −0.156879 −0.00655943
\(573\) 6.68342 0.279204
\(574\) 0.450974 0.0188233
\(575\) −23.0785 −0.962439
\(576\) 1.65985 0.0691606
\(577\) −27.7946 −1.15711 −0.578553 0.815645i \(-0.696382\pi\)
−0.578553 + 0.815645i \(0.696382\pi\)
\(578\) 29.2137 1.21513
\(579\) −26.9659 −1.12066
\(580\) 4.17895 0.173521
\(581\) 1.12029 0.0464774
\(582\) 30.2256 1.25289
\(583\) −7.56553 −0.313332
\(584\) −13.4876 −0.558123
\(585\) 0.136494 0.00564333
\(586\) −33.5837 −1.38733
\(587\) −0.857469 −0.0353915 −0.0176958 0.999843i \(-0.505633\pi\)
−0.0176958 + 0.999843i \(0.505633\pi\)
\(588\) 14.8986 0.614407
\(589\) −0.977447 −0.0402750
\(590\) 0.105927 0.00436096
\(591\) −28.9212 −1.18966
\(592\) 10.9954 0.451910
\(593\) 17.7236 0.727822 0.363911 0.931434i \(-0.381441\pi\)
0.363911 + 0.931434i \(0.381441\pi\)
\(594\) −2.74007 −0.112427
\(595\) 1.05798 0.0433729
\(596\) 2.97121 0.121705
\(597\) 27.3549 1.11956
\(598\) 0.804143 0.0328839
\(599\) −36.4639 −1.48987 −0.744937 0.667134i \(-0.767521\pi\)
−0.744937 + 0.667134i \(0.767521\pi\)
\(600\) 10.2612 0.418914
\(601\) −14.5317 −0.592761 −0.296381 0.955070i \(-0.595780\pi\)
−0.296381 + 0.955070i \(0.595780\pi\)
\(602\) 2.22583 0.0907181
\(603\) 14.8682 0.605481
\(604\) −9.49867 −0.386495
\(605\) −5.01590 −0.203925
\(606\) 22.7163 0.922788
\(607\) 19.3202 0.784182 0.392091 0.919926i \(-0.371752\pi\)
0.392091 + 0.919926i \(0.371752\pi\)
\(608\) 1.01270 0.0410703
\(609\) 5.69559 0.230797
\(610\) 2.45986 0.0995969
\(611\) −1.05744 −0.0427794
\(612\) −11.2838 −0.456120
\(613\) −12.8765 −0.520077 −0.260039 0.965598i \(-0.583735\pi\)
−0.260039 + 0.965598i \(0.583735\pi\)
\(614\) 1.47970 0.0597157
\(615\) 1.54189 0.0621748
\(616\) 0.296902 0.0119625
\(617\) −17.9693 −0.723416 −0.361708 0.932291i \(-0.617806\pi\)
−0.361708 + 0.932291i \(0.617806\pi\)
\(618\) −17.2336 −0.693238
\(619\) −31.5851 −1.26951 −0.634756 0.772712i \(-0.718899\pi\)
−0.634756 + 0.772712i \(0.718899\pi\)
\(620\) −0.479200 −0.0192451
\(621\) 14.0453 0.563619
\(622\) −31.9898 −1.28267
\(623\) 0.696241 0.0278943
\(624\) −0.357542 −0.0143131
\(625\) 21.3634 0.854534
\(626\) −7.83489 −0.313145
\(627\) 2.07057 0.0826906
\(628\) −13.5598 −0.541097
\(629\) −74.7478 −2.98039
\(630\) −0.258322 −0.0102918
\(631\) 37.2956 1.48471 0.742356 0.670005i \(-0.233708\pi\)
0.742356 + 0.670005i \(0.233708\pi\)
\(632\) −12.3178 −0.489977
\(633\) 27.4851 1.09244
\(634\) −13.0466 −0.518148
\(635\) 0.106886 0.00424165
\(636\) −17.2426 −0.683712
\(637\) −1.14314 −0.0452928
\(638\) −7.97237 −0.315629
\(639\) 0.390260 0.0154385
\(640\) 0.496482 0.0196252
\(641\) 30.8298 1.21770 0.608851 0.793284i \(-0.291631\pi\)
0.608851 + 0.793284i \(0.291631\pi\)
\(642\) 26.4926 1.04558
\(643\) 21.5872 0.851317 0.425658 0.904884i \(-0.360042\pi\)
0.425658 + 0.904884i \(0.360042\pi\)
\(644\) −1.52188 −0.0599706
\(645\) 7.61014 0.299649
\(646\) −6.88439 −0.270863
\(647\) 14.2129 0.558767 0.279383 0.960180i \(-0.409870\pi\)
0.279383 + 0.960180i \(0.409870\pi\)
\(648\) −11.2244 −0.440938
\(649\) −0.202083 −0.00793244
\(650\) −0.787326 −0.0308815
\(651\) −0.653113 −0.0255975
\(652\) 3.12522 0.122393
\(653\) −25.2831 −0.989402 −0.494701 0.869063i \(-0.664723\pi\)
−0.494701 + 0.869063i \(0.664723\pi\)
\(654\) −13.3961 −0.523829
\(655\) 1.90248 0.0743359
\(656\) −1.43868 −0.0561709
\(657\) −22.3875 −0.873420
\(658\) 2.00126 0.0780172
\(659\) 16.0532 0.625345 0.312672 0.949861i \(-0.398776\pi\)
0.312672 + 0.949861i \(0.398776\pi\)
\(660\) 1.01511 0.0395131
\(661\) 26.0691 1.01397 0.506985 0.861955i \(-0.330760\pi\)
0.506985 + 0.861955i \(0.330760\pi\)
\(662\) 10.7342 0.417197
\(663\) 2.43059 0.0943964
\(664\) −3.57389 −0.138694
\(665\) −0.157606 −0.00611168
\(666\) 18.2508 0.707205
\(667\) 40.8655 1.58232
\(668\) 21.3478 0.825971
\(669\) 63.6278 2.45999
\(670\) 4.44726 0.171813
\(671\) −4.69279 −0.181163
\(672\) 0.676667 0.0261030
\(673\) 2.58440 0.0996212 0.0498106 0.998759i \(-0.484138\pi\)
0.0498106 + 0.998759i \(0.484138\pi\)
\(674\) 12.1708 0.468801
\(675\) −13.7516 −0.529298
\(676\) −12.9726 −0.498945
\(677\) −24.2058 −0.930303 −0.465152 0.885231i \(-0.654000\pi\)
−0.465152 + 0.885231i \(0.654000\pi\)
\(678\) −35.7880 −1.37443
\(679\) 4.38911 0.168439
\(680\) −3.37511 −0.129430
\(681\) 27.2969 1.04602
\(682\) 0.914191 0.0350062
\(683\) 17.5887 0.673011 0.336506 0.941681i \(-0.390755\pi\)
0.336506 + 0.941681i \(0.390755\pi\)
\(684\) 1.68093 0.0642720
\(685\) −5.88153 −0.224722
\(686\) 4.35771 0.166378
\(687\) −22.6998 −0.866053
\(688\) −7.10074 −0.270713
\(689\) 1.32299 0.0504018
\(690\) −5.20334 −0.198088
\(691\) 42.1265 1.60257 0.801284 0.598284i \(-0.204151\pi\)
0.801284 + 0.598284i \(0.204151\pi\)
\(692\) −24.8639 −0.945182
\(693\) 0.492813 0.0187204
\(694\) 1.17081 0.0444434
\(695\) 11.5261 0.437211
\(696\) −18.1698 −0.688724
\(697\) 9.78022 0.370452
\(698\) 27.3594 1.03557
\(699\) −20.6746 −0.781986
\(700\) 1.49006 0.0563188
\(701\) −16.4316 −0.620611 −0.310306 0.950637i \(-0.600431\pi\)
−0.310306 + 0.950637i \(0.600431\pi\)
\(702\) 0.479158 0.0180847
\(703\) 11.1351 0.419967
\(704\) −0.947161 −0.0356975
\(705\) 6.84233 0.257697
\(706\) 23.1708 0.872045
\(707\) 3.29869 0.124060
\(708\) −0.460566 −0.0173091
\(709\) 9.81023 0.368431 0.184215 0.982886i \(-0.441026\pi\)
0.184215 + 0.982886i \(0.441026\pi\)
\(710\) 0.116731 0.00438085
\(711\) −20.4458 −0.766777
\(712\) −2.22111 −0.0832398
\(713\) −4.68604 −0.175494
\(714\) −4.60003 −0.172152
\(715\) −0.0778874 −0.00291282
\(716\) −3.43967 −0.128547
\(717\) −19.3138 −0.721285
\(718\) 9.50037 0.354550
\(719\) −3.25745 −0.121482 −0.0607412 0.998154i \(-0.519346\pi\)
−0.0607412 + 0.998154i \(0.519346\pi\)
\(720\) 0.824087 0.0307119
\(721\) −2.50253 −0.0931990
\(722\) −17.9744 −0.668940
\(723\) 26.6155 0.989842
\(724\) 8.01064 0.297713
\(725\) −40.0108 −1.48597
\(726\) 21.8088 0.809400
\(727\) −42.4730 −1.57524 −0.787618 0.616164i \(-0.788686\pi\)
−0.787618 + 0.616164i \(0.788686\pi\)
\(728\) −0.0519193 −0.00192426
\(729\) 0.103721 0.00384153
\(730\) −6.69637 −0.247844
\(731\) 48.2713 1.78538
\(732\) −10.6953 −0.395310
\(733\) −23.4279 −0.865331 −0.432666 0.901555i \(-0.642427\pi\)
−0.432666 + 0.901555i \(0.642427\pi\)
\(734\) −26.2152 −0.967622
\(735\) 7.39687 0.272838
\(736\) 4.85504 0.178959
\(737\) −8.48424 −0.312521
\(738\) −2.38799 −0.0879032
\(739\) −36.9772 −1.36023 −0.680114 0.733106i \(-0.738070\pi\)
−0.680114 + 0.733106i \(0.738070\pi\)
\(740\) 5.45904 0.200678
\(741\) −0.362082 −0.0133014
\(742\) −2.50383 −0.0919183
\(743\) 29.5559 1.08430 0.542150 0.840282i \(-0.317610\pi\)
0.542150 + 0.840282i \(0.317610\pi\)
\(744\) 2.08353 0.0763859
\(745\) 1.47515 0.0540453
\(746\) −31.0937 −1.13842
\(747\) −5.93213 −0.217045
\(748\) 6.43886 0.235428
\(749\) 3.84705 0.140568
\(750\) 10.4532 0.381698
\(751\) 10.5651 0.385527 0.192764 0.981245i \(-0.438255\pi\)
0.192764 + 0.981245i \(0.438255\pi\)
\(752\) −6.38432 −0.232812
\(753\) −28.7174 −1.04652
\(754\) 1.39413 0.0507713
\(755\) −4.71591 −0.171630
\(756\) −0.906833 −0.0329812
\(757\) 43.1175 1.56713 0.783566 0.621309i \(-0.213399\pi\)
0.783566 + 0.621309i \(0.213399\pi\)
\(758\) 19.5885 0.711487
\(759\) 9.92665 0.360315
\(760\) 0.502786 0.0182380
\(761\) 32.2537 1.16920 0.584598 0.811323i \(-0.301252\pi\)
0.584598 + 0.811323i \(0.301252\pi\)
\(762\) −0.464734 −0.0168355
\(763\) −1.94527 −0.0704236
\(764\) −3.09608 −0.112012
\(765\) −5.60220 −0.202548
\(766\) −19.6501 −0.709986
\(767\) 0.0353383 0.00127599
\(768\) −2.15867 −0.0778943
\(769\) −5.08801 −0.183478 −0.0917391 0.995783i \(-0.529243\pi\)
−0.0917391 + 0.995783i \(0.529243\pi\)
\(770\) 0.147406 0.00531215
\(771\) 55.6306 2.00349
\(772\) 12.4919 0.449593
\(773\) −38.8251 −1.39644 −0.698222 0.715882i \(-0.746025\pi\)
−0.698222 + 0.715882i \(0.746025\pi\)
\(774\) −11.7862 −0.423646
\(775\) 4.58804 0.164807
\(776\) −14.0019 −0.502640
\(777\) 7.44025 0.266918
\(778\) −21.4746 −0.769902
\(779\) −1.45694 −0.0522004
\(780\) −0.177513 −0.00635598
\(781\) −0.222694 −0.00796861
\(782\) −33.0049 −1.18025
\(783\) 24.3502 0.870204
\(784\) −6.90174 −0.246491
\(785\) −6.73221 −0.240283
\(786\) −8.27185 −0.295047
\(787\) −20.7356 −0.739143 −0.369571 0.929202i \(-0.620496\pi\)
−0.369571 + 0.929202i \(0.620496\pi\)
\(788\) 13.3977 0.477273
\(789\) −17.4275 −0.620436
\(790\) −6.11558 −0.217582
\(791\) −5.19685 −0.184779
\(792\) −1.57215 −0.0558639
\(793\) 0.820631 0.0291415
\(794\) 22.5403 0.799926
\(795\) −8.56061 −0.303614
\(796\) −12.6721 −0.449152
\(797\) −47.2442 −1.67348 −0.836738 0.547603i \(-0.815540\pi\)
−0.836738 + 0.547603i \(0.815540\pi\)
\(798\) 0.685259 0.0242579
\(799\) 43.4010 1.53542
\(800\) −4.75351 −0.168062
\(801\) −3.68672 −0.130264
\(802\) −11.4310 −0.403643
\(803\) 12.7750 0.450819
\(804\) −19.3364 −0.681942
\(805\) −0.755587 −0.0266310
\(806\) −0.159865 −0.00563101
\(807\) 51.4638 1.81161
\(808\) −10.5233 −0.370209
\(809\) −14.5940 −0.513098 −0.256549 0.966531i \(-0.582585\pi\)
−0.256549 + 0.966531i \(0.582585\pi\)
\(810\) −5.57273 −0.195806
\(811\) 25.2081 0.885177 0.442589 0.896725i \(-0.354060\pi\)
0.442589 + 0.896725i \(0.354060\pi\)
\(812\) −2.63847 −0.0925922
\(813\) −4.61285 −0.161780
\(814\) −10.4145 −0.365026
\(815\) 1.55161 0.0543507
\(816\) 14.6748 0.513720
\(817\) −7.19090 −0.251578
\(818\) 10.8461 0.379226
\(819\) −0.0861785 −0.00301132
\(820\) −0.714276 −0.0249436
\(821\) 10.3738 0.362048 0.181024 0.983479i \(-0.442059\pi\)
0.181024 + 0.983479i \(0.442059\pi\)
\(822\) 25.5725 0.891943
\(823\) 34.1058 1.18885 0.594427 0.804149i \(-0.297379\pi\)
0.594427 + 0.804149i \(0.297379\pi\)
\(824\) 7.98345 0.278117
\(825\) −9.71905 −0.338374
\(826\) −0.0668796 −0.00232704
\(827\) 36.0318 1.25295 0.626475 0.779442i \(-0.284497\pi\)
0.626475 + 0.779442i \(0.284497\pi\)
\(828\) 8.05866 0.280058
\(829\) 10.9138 0.379054 0.189527 0.981876i \(-0.439305\pi\)
0.189527 + 0.981876i \(0.439305\pi\)
\(830\) −1.77437 −0.0615892
\(831\) 39.2733 1.36237
\(832\) 0.165631 0.00574221
\(833\) 46.9185 1.62563
\(834\) −50.1148 −1.73534
\(835\) 10.5988 0.366786
\(836\) −0.959188 −0.0331742
\(837\) −2.79223 −0.0965137
\(838\) 17.0512 0.589024
\(839\) −12.3669 −0.426952 −0.213476 0.976948i \(-0.568479\pi\)
−0.213476 + 0.976948i \(0.568479\pi\)
\(840\) 0.335953 0.0115915
\(841\) 41.8480 1.44303
\(842\) −26.6281 −0.917665
\(843\) 37.5123 1.29199
\(844\) −12.7324 −0.438269
\(845\) −6.44064 −0.221565
\(846\) −10.5970 −0.364334
\(847\) 3.16690 0.108816
\(848\) 7.98758 0.274295
\(849\) 14.9765 0.513994
\(850\) 32.3147 1.10838
\(851\) 53.3833 1.82996
\(852\) −0.507540 −0.0173880
\(853\) 17.2970 0.592239 0.296119 0.955151i \(-0.404307\pi\)
0.296119 + 0.955151i \(0.404307\pi\)
\(854\) −1.55309 −0.0531456
\(855\) 0.834551 0.0285410
\(856\) −12.2727 −0.419471
\(857\) −36.9891 −1.26352 −0.631762 0.775162i \(-0.717668\pi\)
−0.631762 + 0.775162i \(0.717668\pi\)
\(858\) 0.338649 0.0115613
\(859\) 38.6362 1.31825 0.659126 0.752033i \(-0.270927\pi\)
0.659126 + 0.752033i \(0.270927\pi\)
\(860\) −3.52539 −0.120215
\(861\) −0.973504 −0.0331769
\(862\) −2.97008 −0.101161
\(863\) 11.7063 0.398488 0.199244 0.979950i \(-0.436151\pi\)
0.199244 + 0.979950i \(0.436151\pi\)
\(864\) 2.89293 0.0984196
\(865\) −12.3444 −0.419724
\(866\) −5.02363 −0.170710
\(867\) −63.0628 −2.14172
\(868\) 0.302553 0.0102693
\(869\) 11.6670 0.395775
\(870\) −9.02096 −0.305839
\(871\) 1.48364 0.0502713
\(872\) 6.20572 0.210152
\(873\) −23.2412 −0.786594
\(874\) 4.91669 0.166309
\(875\) 1.51793 0.0513155
\(876\) 29.1154 0.983717
\(877\) −16.6424 −0.561973 −0.280986 0.959712i \(-0.590662\pi\)
−0.280986 + 0.959712i \(0.590662\pi\)
\(878\) 9.22859 0.311450
\(879\) 72.4960 2.44523
\(880\) −0.470248 −0.0158521
\(881\) −2.49252 −0.0839750 −0.0419875 0.999118i \(-0.513369\pi\)
−0.0419875 + 0.999118i \(0.513369\pi\)
\(882\) −11.4559 −0.385739
\(883\) 35.5553 1.19653 0.598266 0.801298i \(-0.295857\pi\)
0.598266 + 0.801298i \(0.295857\pi\)
\(884\) −1.12597 −0.0378704
\(885\) −0.228662 −0.00768640
\(886\) −30.2716 −1.01699
\(887\) 55.1552 1.85193 0.925966 0.377608i \(-0.123253\pi\)
0.925966 + 0.377608i \(0.123253\pi\)
\(888\) −23.7355 −0.796512
\(889\) −0.0674850 −0.00226337
\(890\) −1.10274 −0.0369640
\(891\) 10.6314 0.356164
\(892\) −29.4755 −0.986911
\(893\) −6.46538 −0.216356
\(894\) −6.41386 −0.214511
\(895\) −1.70773 −0.0570833
\(896\) −0.313465 −0.0104721
\(897\) −1.73588 −0.0579593
\(898\) −16.0401 −0.535266
\(899\) −8.12413 −0.270955
\(900\) −7.89012 −0.263004
\(901\) −54.3001 −1.80900
\(902\) 1.36266 0.0453715
\(903\) −4.80483 −0.159895
\(904\) 16.5787 0.551401
\(905\) 3.97713 0.132204
\(906\) 20.5045 0.681216
\(907\) 20.2270 0.671627 0.335813 0.941929i \(-0.390989\pi\)
0.335813 + 0.941929i \(0.390989\pi\)
\(908\) −12.6452 −0.419647
\(909\) −17.4671 −0.579349
\(910\) −0.0257770 −0.000854499 0
\(911\) −2.66666 −0.0883503 −0.0441752 0.999024i \(-0.514066\pi\)
−0.0441752 + 0.999024i \(0.514066\pi\)
\(912\) −2.18608 −0.0723883
\(913\) 3.38505 0.112029
\(914\) 9.06796 0.299941
\(915\) −5.31003 −0.175544
\(916\) 10.5157 0.347447
\(917\) −1.20117 −0.0396662
\(918\) −19.6664 −0.649086
\(919\) 28.9288 0.954274 0.477137 0.878829i \(-0.341675\pi\)
0.477137 + 0.878829i \(0.341675\pi\)
\(920\) 2.41044 0.0794698
\(921\) −3.19417 −0.105252
\(922\) −13.0767 −0.430659
\(923\) 0.0389426 0.00128181
\(924\) −0.640912 −0.0210845
\(925\) −52.2669 −1.71853
\(926\) −9.00584 −0.295950
\(927\) 13.2514 0.435231
\(928\) 8.41712 0.276306
\(929\) −3.62246 −0.118849 −0.0594246 0.998233i \(-0.518927\pi\)
−0.0594246 + 0.998233i \(0.518927\pi\)
\(930\) 1.03443 0.0339204
\(931\) −6.98938 −0.229068
\(932\) 9.57748 0.313721
\(933\) 69.0554 2.26077
\(934\) 7.81614 0.255752
\(935\) 3.19678 0.104546
\(936\) 0.274922 0.00898612
\(937\) 0.0206771 0.000675490 0 0.000337745 1.00000i \(-0.499892\pi\)
0.000337745 1.00000i \(0.499892\pi\)
\(938\) −2.80787 −0.0916804
\(939\) 16.9129 0.551933
\(940\) −3.16970 −0.103384
\(941\) 19.9670 0.650906 0.325453 0.945558i \(-0.394483\pi\)
0.325453 + 0.945558i \(0.394483\pi\)
\(942\) 29.2712 0.953708
\(943\) −6.98483 −0.227457
\(944\) 0.213356 0.00694415
\(945\) −0.450226 −0.0146458
\(946\) 6.72554 0.218666
\(947\) −10.4608 −0.339929 −0.169965 0.985450i \(-0.554365\pi\)
−0.169965 + 0.985450i \(0.554365\pi\)
\(948\) 26.5901 0.863607
\(949\) −2.23397 −0.0725176
\(950\) −4.81386 −0.156182
\(951\) 28.1634 0.913260
\(952\) 2.13095 0.0690646
\(953\) 16.9418 0.548800 0.274400 0.961616i \(-0.411521\pi\)
0.274400 + 0.961616i \(0.411521\pi\)
\(954\) 13.2582 0.429251
\(955\) −1.53715 −0.0497410
\(956\) 8.94706 0.289369
\(957\) 17.2097 0.556311
\(958\) 37.7812 1.22066
\(959\) 3.71343 0.119913
\(960\) −1.07174 −0.0345902
\(961\) −30.0684 −0.969949
\(962\) 1.82118 0.0587173
\(963\) −20.3708 −0.656441
\(964\) −12.3296 −0.397109
\(965\) 6.20199 0.199649
\(966\) 3.28524 0.105701
\(967\) 26.9773 0.867532 0.433766 0.901026i \(-0.357184\pi\)
0.433766 + 0.901026i \(0.357184\pi\)
\(968\) −10.1029 −0.324719
\(969\) 14.8611 0.477408
\(970\) −6.95170 −0.223206
\(971\) 40.7916 1.30906 0.654532 0.756034i \(-0.272866\pi\)
0.654532 + 0.756034i \(0.272866\pi\)
\(972\) 15.5511 0.498801
\(973\) −7.27728 −0.233299
\(974\) −15.7752 −0.505469
\(975\) 1.69958 0.0544300
\(976\) 4.95459 0.158592
\(977\) 38.1376 1.22013 0.610065 0.792351i \(-0.291143\pi\)
0.610065 + 0.792351i \(0.291143\pi\)
\(978\) −6.74632 −0.215723
\(979\) 2.10375 0.0672362
\(980\) −3.42659 −0.109458
\(981\) 10.3006 0.328872
\(982\) −7.37765 −0.235430
\(983\) 56.8439 1.81304 0.906520 0.422163i \(-0.138729\pi\)
0.906520 + 0.422163i \(0.138729\pi\)
\(984\) 3.10563 0.0990037
\(985\) 6.65171 0.211941
\(986\) −57.2202 −1.82226
\(987\) −4.32006 −0.137509
\(988\) 0.167734 0.00533632
\(989\) −34.4744 −1.09622
\(990\) −0.780543 −0.0248073
\(991\) 23.4411 0.744632 0.372316 0.928106i \(-0.378564\pi\)
0.372316 + 0.928106i \(0.378564\pi\)
\(992\) −0.965191 −0.0306448
\(993\) −23.1716 −0.735329
\(994\) −0.0737010 −0.00233765
\(995\) −6.29148 −0.199453
\(996\) 7.71484 0.244454
\(997\) −43.4111 −1.37484 −0.687421 0.726259i \(-0.741257\pi\)
−0.687421 + 0.726259i \(0.741257\pi\)
\(998\) −13.4031 −0.424269
\(999\) 31.8091 1.00640
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 \(a_p\))