Properties

Label 4019.2.a.b.1.20
Level 4019
Weight 2
Character 4019.1
Self dual Yes
Analytic conductor 32.092
Analytic rank 0
Dimension 186
CM No

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Newspace parameters

Level: \( N \) = \( 4019 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0918765724\)
Analytic rank: \(0\)
Dimension: \(186\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 4019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.34165 q^{2}\) \(-0.437788 q^{3}\) \(+3.48332 q^{4}\) \(+0.358726 q^{5}\) \(+1.02515 q^{6}\) \(+3.39349 q^{7}\) \(-3.47342 q^{8}\) \(-2.80834 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.34165 q^{2}\) \(-0.437788 q^{3}\) \(+3.48332 q^{4}\) \(+0.358726 q^{5}\) \(+1.02515 q^{6}\) \(+3.39349 q^{7}\) \(-3.47342 q^{8}\) \(-2.80834 q^{9}\) \(-0.840010 q^{10}\) \(-1.11610 q^{11}\) \(-1.52496 q^{12}\) \(-4.45688 q^{13}\) \(-7.94637 q^{14}\) \(-0.157046 q^{15}\) \(+1.16689 q^{16}\) \(+6.33668 q^{17}\) \(+6.57615 q^{18}\) \(-2.34535 q^{19}\) \(+1.24956 q^{20}\) \(-1.48563 q^{21}\) \(+2.61352 q^{22}\) \(-0.282972 q^{23}\) \(+1.52062 q^{24}\) \(-4.87132 q^{25}\) \(+10.4365 q^{26}\) \(+2.54282 q^{27}\) \(+11.8206 q^{28}\) \(-9.05378 q^{29}\) \(+0.367746 q^{30}\) \(-0.329502 q^{31}\) \(+4.21439 q^{32}\) \(+0.488616 q^{33}\) \(-14.8383 q^{34}\) \(+1.21733 q^{35}\) \(-9.78236 q^{36}\) \(+0.0658927 q^{37}\) \(+5.49199 q^{38}\) \(+1.95117 q^{39}\) \(-1.24601 q^{40}\) \(-10.2733 q^{41}\) \(+3.47882 q^{42}\) \(+7.73519 q^{43}\) \(-3.88774 q^{44}\) \(-1.00742 q^{45}\) \(+0.662621 q^{46}\) \(-11.0036 q^{47}\) \(-0.510852 q^{48}\) \(+4.51580 q^{49}\) \(+11.4069 q^{50}\) \(-2.77412 q^{51}\) \(-15.5248 q^{52}\) \(+1.11064 q^{53}\) \(-5.95439 q^{54}\) \(-0.400374 q^{55}\) \(-11.7870 q^{56}\) \(+1.02676 q^{57}\) \(+21.2008 q^{58}\) \(+14.2019 q^{59}\) \(-0.547041 q^{60}\) \(+6.80698 q^{61}\) \(+0.771579 q^{62}\) \(-9.53009 q^{63}\) \(-12.2024 q^{64}\) \(-1.59880 q^{65}\) \(-1.14417 q^{66}\) \(+11.3700 q^{67}\) \(+22.0727 q^{68}\) \(+0.123882 q^{69}\) \(-2.85057 q^{70}\) \(+5.88288 q^{71}\) \(+9.75456 q^{72}\) \(+8.90981 q^{73}\) \(-0.154298 q^{74}\) \(+2.13260 q^{75}\) \(-8.16961 q^{76}\) \(-3.78749 q^{77}\) \(-4.56895 q^{78}\) \(+8.35937 q^{79}\) \(+0.418595 q^{80}\) \(+7.31181 q^{81}\) \(+24.0564 q^{82}\) \(+6.63373 q^{83}\) \(-5.17493 q^{84}\) \(+2.27313 q^{85}\) \(-18.1131 q^{86}\) \(+3.96363 q^{87}\) \(+3.87669 q^{88}\) \(-7.80016 q^{89}\) \(+2.35904 q^{90}\) \(-15.1244 q^{91}\) \(-0.985682 q^{92}\) \(+0.144252 q^{93}\) \(+25.7667 q^{94}\) \(-0.841337 q^{95}\) \(-1.84501 q^{96}\) \(+19.0062 q^{97}\) \(-10.5744 q^{98}\) \(+3.13440 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut 50q^{10} \) \(\mathstrut +\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 17q^{12} \) \(\mathstrut +\mathstrut 113q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 252q^{16} \) \(\mathstrut +\mathstrut 35q^{17} \) \(\mathstrut +\mathstrut 13q^{18} \) \(\mathstrut +\mathstrut 97q^{19} \) \(\mathstrut +\mathstrut 55q^{20} \) \(\mathstrut +\mathstrut 115q^{21} \) \(\mathstrut +\mathstrut 14q^{22} \) \(\mathstrut +\mathstrut 27q^{23} \) \(\mathstrut +\mathstrut 122q^{24} \) \(\mathstrut +\mathstrut 244q^{25} \) \(\mathstrut +\mathstrut 39q^{26} \) \(\mathstrut +\mathstrut 34q^{27} \) \(\mathstrut +\mathstrut 66q^{28} \) \(\mathstrut +\mathstrut 91q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 135q^{31} \) \(\mathstrut +\mathstrut 21q^{32} \) \(\mathstrut +\mathstrut 32q^{33} \) \(\mathstrut +\mathstrut 58q^{34} \) \(\mathstrut +\mathstrut 17q^{35} \) \(\mathstrut +\mathstrut 273q^{36} \) \(\mathstrut +\mathstrut 133q^{37} \) \(\mathstrut -\mathstrut 3q^{38} \) \(\mathstrut +\mathstrut 55q^{39} \) \(\mathstrut +\mathstrut 142q^{40} \) \(\mathstrut +\mathstrut 97q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 67q^{43} \) \(\mathstrut +\mathstrut 44q^{44} \) \(\mathstrut +\mathstrut 154q^{45} \) \(\mathstrut +\mathstrut 101q^{46} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 312q^{49} \) \(\mathstrut +\mathstrut 21q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut +\mathstrut 193q^{52} \) \(\mathstrut +\mathstrut 22q^{53} \) \(\mathstrut +\mathstrut 141q^{54} \) \(\mathstrut +\mathstrut 88q^{55} \) \(\mathstrut +\mathstrut 28q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 62q^{58} \) \(\mathstrut +\mathstrut 41q^{59} \) \(\mathstrut +\mathstrut q^{60} \) \(\mathstrut +\mathstrut 377q^{61} \) \(\mathstrut +\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 39q^{63} \) \(\mathstrut +\mathstrut 311q^{64} \) \(\mathstrut +\mathstrut 21q^{65} \) \(\mathstrut +\mathstrut 35q^{66} \) \(\mathstrut +\mathstrut 42q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut +\mathstrut 137q^{69} \) \(\mathstrut +\mathstrut 35q^{70} \) \(\mathstrut +\mathstrut 17q^{71} \) \(\mathstrut -\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 213q^{73} \) \(\mathstrut -\mathstrut 9q^{74} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut +\mathstrut 242q^{76} \) \(\mathstrut +\mathstrut 60q^{77} \) \(\mathstrut +\mathstrut 103q^{79} \) \(\mathstrut +\mathstrut 80q^{80} \) \(\mathstrut +\mathstrut 270q^{81} \) \(\mathstrut +\mathstrut 84q^{82} \) \(\mathstrut +\mathstrut 42q^{83} \) \(\mathstrut +\mathstrut 137q^{84} \) \(\mathstrut +\mathstrut 294q^{85} \) \(\mathstrut -\mathstrut 9q^{86} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut +\mathstrut 78q^{89} \) \(\mathstrut +\mathstrut 69q^{90} \) \(\mathstrut +\mathstrut 118q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 51q^{93} \) \(\mathstrut +\mathstrut 93q^{94} \) \(\mathstrut +\mathstrut 10q^{95} \) \(\mathstrut +\mathstrut 260q^{96} \) \(\mathstrut +\mathstrut 142q^{97} \) \(\mathstrut -\mathstrut 31q^{98} \) \(\mathstrut +\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.34165 −1.65580 −0.827898 0.560878i \(-0.810464\pi\)
−0.827898 + 0.560878i \(0.810464\pi\)
\(3\) −0.437788 −0.252757 −0.126378 0.991982i \(-0.540335\pi\)
−0.126378 + 0.991982i \(0.540335\pi\)
\(4\) 3.48332 1.74166
\(5\) 0.358726 0.160427 0.0802135 0.996778i \(-0.474440\pi\)
0.0802135 + 0.996778i \(0.474440\pi\)
\(6\) 1.02515 0.418514
\(7\) 3.39349 1.28262 0.641310 0.767282i \(-0.278391\pi\)
0.641310 + 0.767282i \(0.278391\pi\)
\(8\) −3.47342 −1.22804
\(9\) −2.80834 −0.936114
\(10\) −0.840010 −0.265634
\(11\) −1.11610 −0.336517 −0.168259 0.985743i \(-0.553814\pi\)
−0.168259 + 0.985743i \(0.553814\pi\)
\(12\) −1.52496 −0.440217
\(13\) −4.45688 −1.23612 −0.618059 0.786132i \(-0.712081\pi\)
−0.618059 + 0.786132i \(0.712081\pi\)
\(14\) −7.94637 −2.12376
\(15\) −0.157046 −0.0405490
\(16\) 1.16689 0.291724
\(17\) 6.33668 1.53687 0.768435 0.639928i \(-0.221036\pi\)
0.768435 + 0.639928i \(0.221036\pi\)
\(18\) 6.57615 1.55001
\(19\) −2.34535 −0.538060 −0.269030 0.963132i \(-0.586703\pi\)
−0.269030 + 0.963132i \(0.586703\pi\)
\(20\) 1.24956 0.279410
\(21\) −1.48563 −0.324191
\(22\) 2.61352 0.557204
\(23\) −0.282972 −0.0590037 −0.0295019 0.999565i \(-0.509392\pi\)
−0.0295019 + 0.999565i \(0.509392\pi\)
\(24\) 1.52062 0.310396
\(25\) −4.87132 −0.974263
\(26\) 10.4365 2.04676
\(27\) 2.54282 0.489366
\(28\) 11.8206 2.23389
\(29\) −9.05378 −1.68125 −0.840623 0.541621i \(-0.817811\pi\)
−0.840623 + 0.541621i \(0.817811\pi\)
\(30\) 0.367746 0.0671409
\(31\) −0.329502 −0.0591804 −0.0295902 0.999562i \(-0.509420\pi\)
−0.0295902 + 0.999562i \(0.509420\pi\)
\(32\) 4.21439 0.745006
\(33\) 0.488616 0.0850571
\(34\) −14.8383 −2.54474
\(35\) 1.21733 0.205767
\(36\) −9.78236 −1.63039
\(37\) 0.0658927 0.0108327 0.00541634 0.999985i \(-0.498276\pi\)
0.00541634 + 0.999985i \(0.498276\pi\)
\(38\) 5.49199 0.890918
\(39\) 1.95117 0.312437
\(40\) −1.24601 −0.197011
\(41\) −10.2733 −1.60442 −0.802208 0.597045i \(-0.796342\pi\)
−0.802208 + 0.597045i \(0.796342\pi\)
\(42\) 3.47882 0.536794
\(43\) 7.73519 1.17961 0.589803 0.807547i \(-0.299205\pi\)
0.589803 + 0.807547i \(0.299205\pi\)
\(44\) −3.88774 −0.586099
\(45\) −1.00742 −0.150178
\(46\) 0.662621 0.0976981
\(47\) −11.0036 −1.60505 −0.802524 0.596621i \(-0.796510\pi\)
−0.802524 + 0.596621i \(0.796510\pi\)
\(48\) −0.510852 −0.0737351
\(49\) 4.51580 0.645114
\(50\) 11.4069 1.61318
\(51\) −2.77412 −0.388454
\(52\) −15.5248 −2.15290
\(53\) 1.11064 0.152558 0.0762788 0.997087i \(-0.475696\pi\)
0.0762788 + 0.997087i \(0.475696\pi\)
\(54\) −5.95439 −0.810291
\(55\) −0.400374 −0.0539865
\(56\) −11.7870 −1.57511
\(57\) 1.02676 0.135998
\(58\) 21.2008 2.78380
\(59\) 14.2019 1.84893 0.924466 0.381265i \(-0.124511\pi\)
0.924466 + 0.381265i \(0.124511\pi\)
\(60\) −0.547041 −0.0706227
\(61\) 6.80698 0.871545 0.435772 0.900057i \(-0.356475\pi\)
0.435772 + 0.900057i \(0.356475\pi\)
\(62\) 0.771579 0.0979906
\(63\) −9.53009 −1.20068
\(64\) −12.2024 −1.52530
\(65\) −1.59880 −0.198307
\(66\) −1.14417 −0.140837
\(67\) 11.3700 1.38906 0.694530 0.719463i \(-0.255612\pi\)
0.694530 + 0.719463i \(0.255612\pi\)
\(68\) 22.0727 2.67671
\(69\) 0.123882 0.0149136
\(70\) −2.85057 −0.340708
\(71\) 5.88288 0.698169 0.349085 0.937091i \(-0.386493\pi\)
0.349085 + 0.937091i \(0.386493\pi\)
\(72\) 9.75456 1.14959
\(73\) 8.90981 1.04281 0.521407 0.853308i \(-0.325407\pi\)
0.521407 + 0.853308i \(0.325407\pi\)
\(74\) −0.154298 −0.0179367
\(75\) 2.13260 0.246252
\(76\) −8.16961 −0.937118
\(77\) −3.78749 −0.431624
\(78\) −4.56895 −0.517332
\(79\) 8.35937 0.940503 0.470252 0.882532i \(-0.344163\pi\)
0.470252 + 0.882532i \(0.344163\pi\)
\(80\) 0.418595 0.0468003
\(81\) 7.31181 0.812423
\(82\) 24.0564 2.65659
\(83\) 6.63373 0.728146 0.364073 0.931370i \(-0.381386\pi\)
0.364073 + 0.931370i \(0.381386\pi\)
\(84\) −5.17493 −0.564631
\(85\) 2.27313 0.246555
\(86\) −18.1131 −1.95319
\(87\) 3.96363 0.424946
\(88\) 3.87669 0.413257
\(89\) −7.80016 −0.826816 −0.413408 0.910546i \(-0.635662\pi\)
−0.413408 + 0.910546i \(0.635662\pi\)
\(90\) 2.35904 0.248664
\(91\) −15.1244 −1.58547
\(92\) −0.985682 −0.102764
\(93\) 0.144252 0.0149582
\(94\) 25.7667 2.65763
\(95\) −0.841337 −0.0863194
\(96\) −1.84501 −0.188305
\(97\) 19.0062 1.92979 0.964895 0.262635i \(-0.0845914\pi\)
0.964895 + 0.262635i \(0.0845914\pi\)
\(98\) −10.5744 −1.06818
\(99\) 3.13440 0.315019
\(100\) −16.9684 −1.69684
\(101\) 14.1883 1.41179 0.705894 0.708317i \(-0.250545\pi\)
0.705894 + 0.708317i \(0.250545\pi\)
\(102\) 6.49601 0.643201
\(103\) 0.329243 0.0324413 0.0162206 0.999868i \(-0.494837\pi\)
0.0162206 + 0.999868i \(0.494837\pi\)
\(104\) 15.4806 1.51800
\(105\) −0.532934 −0.0520090
\(106\) −2.60072 −0.252604
\(107\) 3.18162 0.307579 0.153790 0.988104i \(-0.450852\pi\)
0.153790 + 0.988104i \(0.450852\pi\)
\(108\) 8.85747 0.852310
\(109\) 0.00227135 0.000217556 0 0.000108778 1.00000i \(-0.499965\pi\)
0.000108778 1.00000i \(0.499965\pi\)
\(110\) 0.937537 0.0893906
\(111\) −0.0288470 −0.00273804
\(112\) 3.95985 0.374170
\(113\) −14.7948 −1.39178 −0.695889 0.718149i \(-0.744990\pi\)
−0.695889 + 0.718149i \(0.744990\pi\)
\(114\) −2.40432 −0.225186
\(115\) −0.101509 −0.00946579
\(116\) −31.5372 −2.92816
\(117\) 12.5165 1.15715
\(118\) −33.2559 −3.06145
\(119\) 21.5035 1.97122
\(120\) 0.545486 0.0497958
\(121\) −9.75432 −0.886756
\(122\) −15.9396 −1.44310
\(123\) 4.49751 0.405527
\(124\) −1.14776 −0.103072
\(125\) −3.54109 −0.316725
\(126\) 22.3161 1.98808
\(127\) 8.19744 0.727405 0.363703 0.931515i \(-0.381512\pi\)
0.363703 + 0.931515i \(0.381512\pi\)
\(128\) 20.1450 1.78058
\(129\) −3.38637 −0.298153
\(130\) 3.74383 0.328355
\(131\) −16.6557 −1.45522 −0.727609 0.685992i \(-0.759368\pi\)
−0.727609 + 0.685992i \(0.759368\pi\)
\(132\) 1.70201 0.148141
\(133\) −7.95893 −0.690126
\(134\) −26.6244 −2.30000
\(135\) 0.912175 0.0785075
\(136\) −22.0100 −1.88734
\(137\) 2.44283 0.208705 0.104353 0.994540i \(-0.466723\pi\)
0.104353 + 0.994540i \(0.466723\pi\)
\(138\) −0.290087 −0.0246939
\(139\) −3.01871 −0.256044 −0.128022 0.991771i \(-0.540863\pi\)
−0.128022 + 0.991771i \(0.540863\pi\)
\(140\) 4.24037 0.358376
\(141\) 4.81726 0.405687
\(142\) −13.7756 −1.15603
\(143\) 4.97434 0.415975
\(144\) −3.27704 −0.273087
\(145\) −3.24782 −0.269717
\(146\) −20.8636 −1.72669
\(147\) −1.97696 −0.163057
\(148\) 0.229525 0.0188669
\(149\) −17.6155 −1.44312 −0.721558 0.692354i \(-0.756574\pi\)
−0.721558 + 0.692354i \(0.756574\pi\)
\(150\) −4.99381 −0.407743
\(151\) 6.53463 0.531781 0.265890 0.964003i \(-0.414334\pi\)
0.265890 + 0.964003i \(0.414334\pi\)
\(152\) 8.14639 0.660759
\(153\) −17.7956 −1.43869
\(154\) 8.86896 0.714681
\(155\) −0.118201 −0.00949413
\(156\) 6.79655 0.544160
\(157\) 21.0609 1.68084 0.840419 0.541936i \(-0.182309\pi\)
0.840419 + 0.541936i \(0.182309\pi\)
\(158\) −19.5747 −1.55728
\(159\) −0.486223 −0.0385600
\(160\) 1.51181 0.119519
\(161\) −0.960263 −0.0756793
\(162\) −17.1217 −1.34521
\(163\) −8.74516 −0.684974 −0.342487 0.939523i \(-0.611269\pi\)
−0.342487 + 0.939523i \(0.611269\pi\)
\(164\) −35.7851 −2.79435
\(165\) 0.175279 0.0136455
\(166\) −15.5339 −1.20566
\(167\) 3.65416 0.282767 0.141384 0.989955i \(-0.454845\pi\)
0.141384 + 0.989955i \(0.454845\pi\)
\(168\) 5.16022 0.398120
\(169\) 6.86382 0.527986
\(170\) −5.32287 −0.408246
\(171\) 6.58654 0.503685
\(172\) 26.9442 2.05447
\(173\) −23.6903 −1.80114 −0.900571 0.434709i \(-0.856851\pi\)
−0.900571 + 0.434709i \(0.856851\pi\)
\(174\) −9.28144 −0.703624
\(175\) −16.5308 −1.24961
\(176\) −1.30237 −0.0981701
\(177\) −6.21742 −0.467330
\(178\) 18.2653 1.36904
\(179\) 21.3915 1.59887 0.799436 0.600751i \(-0.205132\pi\)
0.799436 + 0.600751i \(0.205132\pi\)
\(180\) −3.50919 −0.261559
\(181\) 12.7464 0.947436 0.473718 0.880677i \(-0.342912\pi\)
0.473718 + 0.880677i \(0.342912\pi\)
\(182\) 35.4161 2.62521
\(183\) −2.98001 −0.220289
\(184\) 0.982881 0.0724589
\(185\) 0.0236374 0.00173786
\(186\) −0.337788 −0.0247678
\(187\) −7.07238 −0.517183
\(188\) −38.3293 −2.79545
\(189\) 8.62905 0.627671
\(190\) 1.97012 0.142927
\(191\) −2.71538 −0.196478 −0.0982389 0.995163i \(-0.531321\pi\)
−0.0982389 + 0.995163i \(0.531321\pi\)
\(192\) 5.34207 0.385530
\(193\) −6.32621 −0.455371 −0.227685 0.973735i \(-0.573116\pi\)
−0.227685 + 0.973735i \(0.573116\pi\)
\(194\) −44.5059 −3.19534
\(195\) 0.699935 0.0501234
\(196\) 15.7300 1.12357
\(197\) 10.2970 0.733632 0.366816 0.930294i \(-0.380448\pi\)
0.366816 + 0.930294i \(0.380448\pi\)
\(198\) −7.33966 −0.521607
\(199\) 11.2383 0.796664 0.398332 0.917241i \(-0.369589\pi\)
0.398332 + 0.917241i \(0.369589\pi\)
\(200\) 16.9201 1.19643
\(201\) −4.97762 −0.351095
\(202\) −33.2240 −2.33763
\(203\) −30.7240 −2.15640
\(204\) −9.66315 −0.676556
\(205\) −3.68529 −0.257392
\(206\) −0.770972 −0.0537161
\(207\) 0.794682 0.0552342
\(208\) −5.20071 −0.360605
\(209\) 2.61765 0.181067
\(210\) 1.24794 0.0861163
\(211\) 28.1377 1.93708 0.968541 0.248855i \(-0.0800543\pi\)
0.968541 + 0.248855i \(0.0800543\pi\)
\(212\) 3.86870 0.265704
\(213\) −2.57545 −0.176467
\(214\) −7.45025 −0.509288
\(215\) 2.77481 0.189241
\(216\) −8.83229 −0.600961
\(217\) −1.11816 −0.0759059
\(218\) −0.00531870 −0.000360228 0
\(219\) −3.90060 −0.263578
\(220\) −1.39463 −0.0940262
\(221\) −28.2418 −1.89975
\(222\) 0.0675496 0.00453363
\(223\) 20.4221 1.36756 0.683782 0.729686i \(-0.260334\pi\)
0.683782 + 0.729686i \(0.260334\pi\)
\(224\) 14.3015 0.955559
\(225\) 13.6803 0.912021
\(226\) 34.6443 2.30450
\(227\) −14.3892 −0.955043 −0.477522 0.878620i \(-0.658465\pi\)
−0.477522 + 0.878620i \(0.658465\pi\)
\(228\) 3.57655 0.236863
\(229\) −13.3730 −0.883715 −0.441857 0.897085i \(-0.645680\pi\)
−0.441857 + 0.897085i \(0.645680\pi\)
\(230\) 0.237699 0.0156734
\(231\) 1.65811 0.109096
\(232\) 31.4476 2.06464
\(233\) 3.15750 0.206855 0.103427 0.994637i \(-0.467019\pi\)
0.103427 + 0.994637i \(0.467019\pi\)
\(234\) −29.3092 −1.91600
\(235\) −3.94729 −0.257493
\(236\) 49.4699 3.22021
\(237\) −3.65963 −0.237719
\(238\) −50.3536 −3.26394
\(239\) 9.95161 0.643716 0.321858 0.946788i \(-0.395693\pi\)
0.321858 + 0.946788i \(0.395693\pi\)
\(240\) −0.183256 −0.0118291
\(241\) −1.63636 −0.105407 −0.0527036 0.998610i \(-0.516784\pi\)
−0.0527036 + 0.998610i \(0.516784\pi\)
\(242\) 22.8412 1.46829
\(243\) −10.8295 −0.694712
\(244\) 23.7109 1.51794
\(245\) 1.61993 0.103494
\(246\) −10.5316 −0.671470
\(247\) 10.4529 0.665105
\(248\) 1.14450 0.0726759
\(249\) −2.90416 −0.184044
\(250\) 8.29200 0.524432
\(251\) 1.02428 0.0646520 0.0323260 0.999477i \(-0.489709\pi\)
0.0323260 + 0.999477i \(0.489709\pi\)
\(252\) −33.1964 −2.09118
\(253\) 0.315825 0.0198558
\(254\) −19.1955 −1.20444
\(255\) −0.995148 −0.0623186
\(256\) −22.7677 −1.42298
\(257\) −6.80941 −0.424759 −0.212380 0.977187i \(-0.568121\pi\)
−0.212380 + 0.977187i \(0.568121\pi\)
\(258\) 7.92970 0.493681
\(259\) 0.223606 0.0138942
\(260\) −5.56913 −0.345383
\(261\) 25.4261 1.57384
\(262\) 39.0019 2.40954
\(263\) 10.4225 0.642678 0.321339 0.946964i \(-0.395867\pi\)
0.321339 + 0.946964i \(0.395867\pi\)
\(264\) −1.69717 −0.104454
\(265\) 0.398414 0.0244744
\(266\) 18.6370 1.14271
\(267\) 3.41482 0.208983
\(268\) 39.6052 2.41927
\(269\) −21.5507 −1.31397 −0.656984 0.753905i \(-0.728168\pi\)
−0.656984 + 0.753905i \(0.728168\pi\)
\(270\) −2.13599 −0.129992
\(271\) 4.26267 0.258939 0.129469 0.991583i \(-0.458673\pi\)
0.129469 + 0.991583i \(0.458673\pi\)
\(272\) 7.39423 0.448341
\(273\) 6.62128 0.400738
\(274\) −5.72026 −0.345573
\(275\) 5.43689 0.327857
\(276\) 0.431520 0.0259744
\(277\) 15.9214 0.956625 0.478313 0.878190i \(-0.341249\pi\)
0.478313 + 0.878190i \(0.341249\pi\)
\(278\) 7.06876 0.423956
\(279\) 0.925355 0.0553996
\(280\) −4.22831 −0.252690
\(281\) 8.00350 0.477449 0.238724 0.971087i \(-0.423271\pi\)
0.238724 + 0.971087i \(0.423271\pi\)
\(282\) −11.2803 −0.671734
\(283\) 2.40190 0.142778 0.0713890 0.997449i \(-0.477257\pi\)
0.0713890 + 0.997449i \(0.477257\pi\)
\(284\) 20.4920 1.21597
\(285\) 0.368327 0.0218178
\(286\) −11.6482 −0.688770
\(287\) −34.8623 −2.05786
\(288\) −11.8354 −0.697410
\(289\) 23.1535 1.36197
\(290\) 7.60527 0.446597
\(291\) −8.32069 −0.487768
\(292\) 31.0357 1.81623
\(293\) −19.5879 −1.14433 −0.572167 0.820137i \(-0.693897\pi\)
−0.572167 + 0.820137i \(0.693897\pi\)
\(294\) 4.62935 0.269989
\(295\) 5.09459 0.296619
\(296\) −0.228873 −0.0133030
\(297\) −2.83805 −0.164680
\(298\) 41.2493 2.38951
\(299\) 1.26117 0.0729355
\(300\) 7.42854 0.428887
\(301\) 26.2493 1.51299
\(302\) −15.3018 −0.880520
\(303\) −6.21146 −0.356839
\(304\) −2.73677 −0.156965
\(305\) 2.44184 0.139819
\(306\) 41.6710 2.38217
\(307\) 11.7220 0.669009 0.334504 0.942394i \(-0.391431\pi\)
0.334504 + 0.942394i \(0.391431\pi\)
\(308\) −13.1930 −0.751743
\(309\) −0.144138 −0.00819975
\(310\) 0.276785 0.0157203
\(311\) 23.6782 1.34267 0.671334 0.741155i \(-0.265721\pi\)
0.671334 + 0.741155i \(0.265721\pi\)
\(312\) −6.77724 −0.383685
\(313\) 18.1630 1.02663 0.513316 0.858200i \(-0.328417\pi\)
0.513316 + 0.858200i \(0.328417\pi\)
\(314\) −49.3171 −2.78313
\(315\) −3.41869 −0.192621
\(316\) 29.1184 1.63804
\(317\) 19.7993 1.11204 0.556019 0.831170i \(-0.312328\pi\)
0.556019 + 0.831170i \(0.312328\pi\)
\(318\) 1.13856 0.0638475
\(319\) 10.1049 0.565768
\(320\) −4.37732 −0.244700
\(321\) −1.39288 −0.0777427
\(322\) 2.24860 0.125310
\(323\) −14.8617 −0.826928
\(324\) 25.4694 1.41497
\(325\) 21.7109 1.20430
\(326\) 20.4781 1.13418
\(327\) −0.000994368 0 −5.49887e−5 0
\(328\) 35.6834 1.97029
\(329\) −37.3408 −2.05867
\(330\) −0.410442 −0.0225941
\(331\) −11.4205 −0.627727 −0.313864 0.949468i \(-0.601623\pi\)
−0.313864 + 0.949468i \(0.601623\pi\)
\(332\) 23.1074 1.26818
\(333\) −0.185049 −0.0101406
\(334\) −8.55676 −0.468205
\(335\) 4.07869 0.222843
\(336\) −1.73357 −0.0945741
\(337\) −11.2706 −0.613949 −0.306974 0.951718i \(-0.599317\pi\)
−0.306974 + 0.951718i \(0.599317\pi\)
\(338\) −16.0727 −0.874237
\(339\) 6.47698 0.351781
\(340\) 7.91804 0.429416
\(341\) 0.367758 0.0199152
\(342\) −15.4234 −0.834001
\(343\) −8.43012 −0.455184
\(344\) −26.8676 −1.44860
\(345\) 0.0444395 0.00239254
\(346\) 55.4745 2.98232
\(347\) −20.1839 −1.08353 −0.541764 0.840531i \(-0.682243\pi\)
−0.541764 + 0.840531i \(0.682243\pi\)
\(348\) 13.8066 0.740112
\(349\) 2.08367 0.111537 0.0557683 0.998444i \(-0.482239\pi\)
0.0557683 + 0.998444i \(0.482239\pi\)
\(350\) 38.7093 2.06910
\(351\) −11.3331 −0.604914
\(352\) −4.70369 −0.250707
\(353\) 9.91563 0.527756 0.263878 0.964556i \(-0.414998\pi\)
0.263878 + 0.964556i \(0.414998\pi\)
\(354\) 14.5590 0.773804
\(355\) 2.11034 0.112005
\(356\) −27.1705 −1.44003
\(357\) −9.41395 −0.498239
\(358\) −50.0913 −2.64741
\(359\) 26.0532 1.37503 0.687517 0.726168i \(-0.258701\pi\)
0.687517 + 0.726168i \(0.258701\pi\)
\(360\) 3.49921 0.184425
\(361\) −13.4993 −0.710491
\(362\) −29.8477 −1.56876
\(363\) 4.27032 0.224134
\(364\) −52.6832 −2.76135
\(365\) 3.19618 0.167296
\(366\) 6.97814 0.364753
\(367\) −6.74178 −0.351918 −0.175959 0.984397i \(-0.556303\pi\)
−0.175959 + 0.984397i \(0.556303\pi\)
\(368\) −0.330198 −0.0172128
\(369\) 28.8509 1.50192
\(370\) −0.0553505 −0.00287754
\(371\) 3.76894 0.195673
\(372\) 0.502477 0.0260522
\(373\) 13.2044 0.683696 0.341848 0.939755i \(-0.388947\pi\)
0.341848 + 0.939755i \(0.388947\pi\)
\(374\) 16.5610 0.856350
\(375\) 1.55025 0.0800544
\(376\) 38.2203 1.97106
\(377\) 40.3517 2.07822
\(378\) −20.2062 −1.03929
\(379\) −2.26102 −0.116141 −0.0580704 0.998312i \(-0.518495\pi\)
−0.0580704 + 0.998312i \(0.518495\pi\)
\(380\) −2.93065 −0.150339
\(381\) −3.58874 −0.183857
\(382\) 6.35846 0.325327
\(383\) −9.86894 −0.504279 −0.252140 0.967691i \(-0.581134\pi\)
−0.252140 + 0.967691i \(0.581134\pi\)
\(384\) −8.81923 −0.450054
\(385\) −1.35867 −0.0692441
\(386\) 14.8138 0.754001
\(387\) −21.7231 −1.10425
\(388\) 66.2049 3.36104
\(389\) 12.8695 0.652507 0.326254 0.945282i \(-0.394214\pi\)
0.326254 + 0.945282i \(0.394214\pi\)
\(390\) −1.63900 −0.0829941
\(391\) −1.79310 −0.0906810
\(392\) −15.6853 −0.792226
\(393\) 7.29167 0.367816
\(394\) −24.1120 −1.21474
\(395\) 2.99872 0.150882
\(396\) 10.9181 0.548656
\(397\) 9.16350 0.459903 0.229951 0.973202i \(-0.426143\pi\)
0.229951 + 0.973202i \(0.426143\pi\)
\(398\) −26.3162 −1.31911
\(399\) 3.48432 0.174434
\(400\) −5.68431 −0.284216
\(401\) −5.55171 −0.277239 −0.138620 0.990346i \(-0.544267\pi\)
−0.138620 + 0.990346i \(0.544267\pi\)
\(402\) 11.6559 0.581341
\(403\) 1.46855 0.0731539
\(404\) 49.4224 2.45886
\(405\) 2.62293 0.130335
\(406\) 71.9447 3.57056
\(407\) −0.0735429 −0.00364539
\(408\) 9.63569 0.477038
\(409\) −11.3015 −0.558824 −0.279412 0.960171i \(-0.590140\pi\)
−0.279412 + 0.960171i \(0.590140\pi\)
\(410\) 8.62965 0.426188
\(411\) −1.06944 −0.0527517
\(412\) 1.14686 0.0565017
\(413\) 48.1941 2.37148
\(414\) −1.86087 −0.0914566
\(415\) 2.37969 0.116814
\(416\) −18.7830 −0.920915
\(417\) 1.32155 0.0647168
\(418\) −6.12962 −0.299809
\(419\) 37.8498 1.84908 0.924541 0.381083i \(-0.124449\pi\)
0.924541 + 0.381083i \(0.124449\pi\)
\(420\) −1.85638 −0.0905821
\(421\) 6.54301 0.318887 0.159443 0.987207i \(-0.449030\pi\)
0.159443 + 0.987207i \(0.449030\pi\)
\(422\) −65.8887 −3.20741
\(423\) 30.9020 1.50251
\(424\) −3.85771 −0.187347
\(425\) −30.8680 −1.49732
\(426\) 6.03080 0.292193
\(427\) 23.0994 1.11786
\(428\) 11.0826 0.535699
\(429\) −2.17770 −0.105141
\(430\) −6.49764 −0.313344
\(431\) 15.1655 0.730496 0.365248 0.930910i \(-0.380984\pi\)
0.365248 + 0.930910i \(0.380984\pi\)
\(432\) 2.96720 0.142760
\(433\) −5.51206 −0.264892 −0.132446 0.991190i \(-0.542283\pi\)
−0.132446 + 0.991190i \(0.542283\pi\)
\(434\) 2.61835 0.125685
\(435\) 1.42186 0.0681728
\(436\) 0.00791184 0.000378908 0
\(437\) 0.663668 0.0317475
\(438\) 9.13385 0.436432
\(439\) −5.86387 −0.279867 −0.139934 0.990161i \(-0.544689\pi\)
−0.139934 + 0.990161i \(0.544689\pi\)
\(440\) 1.39067 0.0662976
\(441\) −12.6819 −0.603900
\(442\) 66.1325 3.14560
\(443\) 12.0408 0.572078 0.286039 0.958218i \(-0.407661\pi\)
0.286039 + 0.958218i \(0.407661\pi\)
\(444\) −0.100483 −0.00476873
\(445\) −2.79812 −0.132644
\(446\) −47.8214 −2.26441
\(447\) 7.71184 0.364757
\(448\) −41.4088 −1.95638
\(449\) −28.5061 −1.34529 −0.672643 0.739967i \(-0.734841\pi\)
−0.672643 + 0.739967i \(0.734841\pi\)
\(450\) −32.0345 −1.51012
\(451\) 11.4660 0.539914
\(452\) −51.5351 −2.42401
\(453\) −2.86078 −0.134411
\(454\) 33.6944 1.58136
\(455\) −5.42551 −0.254352
\(456\) −3.56639 −0.167011
\(457\) −0.275369 −0.0128812 −0.00644060 0.999979i \(-0.502050\pi\)
−0.00644060 + 0.999979i \(0.502050\pi\)
\(458\) 31.3150 1.46325
\(459\) 16.1130 0.752092
\(460\) −0.353590 −0.0164862
\(461\) 27.5656 1.28386 0.641928 0.766765i \(-0.278135\pi\)
0.641928 + 0.766765i \(0.278135\pi\)
\(462\) −3.88272 −0.180641
\(463\) −16.0011 −0.743633 −0.371816 0.928306i \(-0.621265\pi\)
−0.371816 + 0.928306i \(0.621265\pi\)
\(464\) −10.5648 −0.490459
\(465\) 0.0517469 0.00239971
\(466\) −7.39376 −0.342510
\(467\) −6.64048 −0.307285 −0.153642 0.988127i \(-0.549100\pi\)
−0.153642 + 0.988127i \(0.549100\pi\)
\(468\) 43.5989 2.01536
\(469\) 38.5839 1.78164
\(470\) 9.24317 0.426356
\(471\) −9.22018 −0.424844
\(472\) −49.3293 −2.27056
\(473\) −8.63326 −0.396958
\(474\) 8.56957 0.393614
\(475\) 11.4249 0.524212
\(476\) 74.9035 3.43320
\(477\) −3.11905 −0.142811
\(478\) −23.3032 −1.06586
\(479\) 5.90173 0.269657 0.134829 0.990869i \(-0.456952\pi\)
0.134829 + 0.990869i \(0.456952\pi\)
\(480\) −0.661852 −0.0302093
\(481\) −0.293676 −0.0133905
\(482\) 3.83178 0.174533
\(483\) 0.420391 0.0191285
\(484\) −33.9774 −1.54443
\(485\) 6.81802 0.309591
\(486\) 25.3589 1.15030
\(487\) −13.2061 −0.598427 −0.299214 0.954186i \(-0.596724\pi\)
−0.299214 + 0.954186i \(0.596724\pi\)
\(488\) −23.6435 −1.07029
\(489\) 3.82852 0.173132
\(490\) −3.79332 −0.171365
\(491\) 15.9325 0.719026 0.359513 0.933140i \(-0.382943\pi\)
0.359513 + 0.933140i \(0.382943\pi\)
\(492\) 15.6663 0.706291
\(493\) −57.3709 −2.58385
\(494\) −24.4771 −1.10128
\(495\) 1.12439 0.0505375
\(496\) −0.384494 −0.0172643
\(497\) 19.9635 0.895486
\(498\) 6.80054 0.304739
\(499\) −9.87843 −0.442219 −0.221110 0.975249i \(-0.570968\pi\)
−0.221110 + 0.975249i \(0.570968\pi\)
\(500\) −12.3348 −0.551628
\(501\) −1.59975 −0.0714714
\(502\) −2.39851 −0.107051
\(503\) −22.9873 −1.02495 −0.512477 0.858701i \(-0.671272\pi\)
−0.512477 + 0.858701i \(0.671272\pi\)
\(504\) 33.1020 1.47448
\(505\) 5.08971 0.226489
\(506\) −0.739553 −0.0328771
\(507\) −3.00490 −0.133452
\(508\) 28.5543 1.26689
\(509\) 11.6725 0.517373 0.258687 0.965961i \(-0.416710\pi\)
0.258687 + 0.965961i \(0.416710\pi\)
\(510\) 2.33029 0.103187
\(511\) 30.2354 1.33753
\(512\) 13.0240 0.575584
\(513\) −5.96380 −0.263308
\(514\) 15.9453 0.703315
\(515\) 0.118108 0.00520446
\(516\) −11.7958 −0.519282
\(517\) 12.2812 0.540126
\(518\) −0.523608 −0.0230060
\(519\) 10.3713 0.455251
\(520\) 5.55331 0.243529
\(521\) 12.1587 0.532684 0.266342 0.963879i \(-0.414185\pi\)
0.266342 + 0.963879i \(0.414185\pi\)
\(522\) −59.5391 −2.60595
\(523\) 10.2136 0.446607 0.223304 0.974749i \(-0.428316\pi\)
0.223304 + 0.974749i \(0.428316\pi\)
\(524\) −58.0173 −2.53450
\(525\) 7.23697 0.315847
\(526\) −24.4058 −1.06414
\(527\) −2.08795 −0.0909525
\(528\) 0.570163 0.0248132
\(529\) −22.9199 −0.996519
\(530\) −0.932945 −0.0405245
\(531\) −39.8838 −1.73081
\(532\) −27.7235 −1.20197
\(533\) 45.7868 1.98325
\(534\) −7.99630 −0.346034
\(535\) 1.14133 0.0493440
\(536\) −39.4927 −1.70582
\(537\) −9.36492 −0.404126
\(538\) 50.4641 2.17566
\(539\) −5.04009 −0.217092
\(540\) 3.17740 0.136734
\(541\) 12.4937 0.537147 0.268573 0.963259i \(-0.413448\pi\)
0.268573 + 0.963259i \(0.413448\pi\)
\(542\) −9.98168 −0.428750
\(543\) −5.58024 −0.239471
\(544\) 26.7052 1.14498
\(545\) 0.000814791 0 3.49018e−5 0
\(546\) −15.5047 −0.663541
\(547\) −1.80967 −0.0773758 −0.0386879 0.999251i \(-0.512318\pi\)
−0.0386879 + 0.999251i \(0.512318\pi\)
\(548\) 8.50917 0.363494
\(549\) −19.1163 −0.815865
\(550\) −12.7313 −0.542864
\(551\) 21.2343 0.904611
\(552\) −0.430293 −0.0183145
\(553\) 28.3675 1.20631
\(554\) −37.2824 −1.58398
\(555\) −0.0103482 −0.000439255 0
\(556\) −10.5151 −0.445942
\(557\) 11.5872 0.490964 0.245482 0.969401i \(-0.421054\pi\)
0.245482 + 0.969401i \(0.421054\pi\)
\(558\) −2.16686 −0.0917304
\(559\) −34.4749 −1.45813
\(560\) 1.42050 0.0600271
\(561\) 3.09620 0.130722
\(562\) −18.7414 −0.790558
\(563\) −29.6044 −1.24768 −0.623838 0.781553i \(-0.714428\pi\)
−0.623838 + 0.781553i \(0.714428\pi\)
\(564\) 16.7801 0.706569
\(565\) −5.30728 −0.223279
\(566\) −5.62440 −0.236411
\(567\) 24.8126 1.04203
\(568\) −20.4337 −0.857380
\(569\) −5.15781 −0.216227 −0.108113 0.994139i \(-0.534481\pi\)
−0.108113 + 0.994139i \(0.534481\pi\)
\(570\) −0.862493 −0.0361258
\(571\) −28.9582 −1.21186 −0.605932 0.795516i \(-0.707200\pi\)
−0.605932 + 0.795516i \(0.707200\pi\)
\(572\) 17.3272 0.724488
\(573\) 1.18876 0.0496611
\(574\) 81.6353 3.40739
\(575\) 1.37845 0.0574851
\(576\) 34.2685 1.42786
\(577\) 37.8112 1.57410 0.787051 0.616888i \(-0.211607\pi\)
0.787051 + 0.616888i \(0.211607\pi\)
\(578\) −54.2173 −2.25514
\(579\) 2.76954 0.115098
\(580\) −11.3132 −0.469756
\(581\) 22.5115 0.933935
\(582\) 19.4842 0.807644
\(583\) −1.23958 −0.0513383
\(584\) −30.9475 −1.28062
\(585\) 4.48997 0.185638
\(586\) 45.8679 1.89478
\(587\) −11.0475 −0.455981 −0.227990 0.973663i \(-0.573215\pi\)
−0.227990 + 0.973663i \(0.573215\pi\)
\(588\) −6.88640 −0.283990
\(589\) 0.772798 0.0318426
\(590\) −11.9297 −0.491140
\(591\) −4.50791 −0.185430
\(592\) 0.0768898 0.00316015
\(593\) 10.6953 0.439202 0.219601 0.975590i \(-0.429524\pi\)
0.219601 + 0.975590i \(0.429524\pi\)
\(594\) 6.64571 0.272677
\(595\) 7.71385 0.316237
\(596\) −61.3604 −2.51342
\(597\) −4.92000 −0.201362
\(598\) −2.95322 −0.120766
\(599\) 6.57106 0.268486 0.134243 0.990948i \(-0.457140\pi\)
0.134243 + 0.990948i \(0.457140\pi\)
\(600\) −7.40743 −0.302407
\(601\) 41.6967 1.70084 0.850422 0.526100i \(-0.176346\pi\)
0.850422 + 0.526100i \(0.176346\pi\)
\(602\) −61.4667 −2.50520
\(603\) −31.9307 −1.30032
\(604\) 22.7622 0.926182
\(605\) −3.49912 −0.142260
\(606\) 14.5451 0.590853
\(607\) −1.69124 −0.0686454 −0.0343227 0.999411i \(-0.510927\pi\)
−0.0343227 + 0.999411i \(0.510927\pi\)
\(608\) −9.88421 −0.400858
\(609\) 13.4506 0.545044
\(610\) −5.71793 −0.231512
\(611\) 49.0420 1.98403
\(612\) −61.9877 −2.50570
\(613\) −11.0082 −0.444618 −0.222309 0.974976i \(-0.571359\pi\)
−0.222309 + 0.974976i \(0.571359\pi\)
\(614\) −27.4488 −1.10774
\(615\) 1.61337 0.0650575
\(616\) 13.1555 0.530052
\(617\) 21.9853 0.885096 0.442548 0.896745i \(-0.354075\pi\)
0.442548 + 0.896745i \(0.354075\pi\)
\(618\) 0.337522 0.0135771
\(619\) 24.9238 1.00177 0.500887 0.865513i \(-0.333007\pi\)
0.500887 + 0.865513i \(0.333007\pi\)
\(620\) −0.411732 −0.0165356
\(621\) −0.719547 −0.0288744
\(622\) −55.4461 −2.22319
\(623\) −26.4698 −1.06049
\(624\) 2.27681 0.0911453
\(625\) 23.0863 0.923452
\(626\) −42.5313 −1.69989
\(627\) −1.14597 −0.0457658
\(628\) 73.3618 2.92745
\(629\) 0.417540 0.0166484
\(630\) 8.00537 0.318942
\(631\) −19.8290 −0.789382 −0.394691 0.918814i \(-0.629148\pi\)
−0.394691 + 0.918814i \(0.629148\pi\)
\(632\) −29.0356 −1.15498
\(633\) −12.3184 −0.489611
\(634\) −46.3629 −1.84131
\(635\) 2.94063 0.116695
\(636\) −1.69367 −0.0671584
\(637\) −20.1264 −0.797437
\(638\) −23.6622 −0.936797
\(639\) −16.5211 −0.653566
\(640\) 7.22653 0.285654
\(641\) −3.79896 −0.150050 −0.0750250 0.997182i \(-0.523904\pi\)
−0.0750250 + 0.997182i \(0.523904\pi\)
\(642\) 3.26163 0.128726
\(643\) 47.1945 1.86117 0.930585 0.366075i \(-0.119299\pi\)
0.930585 + 0.366075i \(0.119299\pi\)
\(644\) −3.34491 −0.131808
\(645\) −1.21478 −0.0478319
\(646\) 34.8009 1.36922
\(647\) 6.92533 0.272263 0.136131 0.990691i \(-0.456533\pi\)
0.136131 + 0.990691i \(0.456533\pi\)
\(648\) −25.3970 −0.997689
\(649\) −15.8508 −0.622198
\(650\) −50.8393 −1.99408
\(651\) 0.489518 0.0191857
\(652\) −30.4622 −1.19299
\(653\) 32.2940 1.26376 0.631880 0.775066i \(-0.282283\pi\)
0.631880 + 0.775066i \(0.282283\pi\)
\(654\) 0.00232846 9.10501e−5 0
\(655\) −5.97484 −0.233456
\(656\) −11.9878 −0.468046
\(657\) −25.0218 −0.976193
\(658\) 87.4391 3.40873
\(659\) 5.06870 0.197449 0.0987243 0.995115i \(-0.468524\pi\)
0.0987243 + 0.995115i \(0.468524\pi\)
\(660\) 0.610553 0.0237658
\(661\) 13.0491 0.507550 0.253775 0.967263i \(-0.418328\pi\)
0.253775 + 0.967263i \(0.418328\pi\)
\(662\) 26.7428 1.03939
\(663\) 12.3639 0.480175
\(664\) −23.0418 −0.894193
\(665\) −2.85507 −0.110715
\(666\) 0.433320 0.0167908
\(667\) 2.56197 0.0991997
\(668\) 12.7286 0.492485
\(669\) −8.94054 −0.345661
\(670\) −9.55087 −0.368982
\(671\) −7.59728 −0.293290
\(672\) −6.26102 −0.241524
\(673\) −45.0455 −1.73638 −0.868189 0.496234i \(-0.834716\pi\)
−0.868189 + 0.496234i \(0.834716\pi\)
\(674\) 26.3918 1.01657
\(675\) −12.3869 −0.476771
\(676\) 23.9089 0.919573
\(677\) 32.1256 1.23469 0.617344 0.786693i \(-0.288208\pi\)
0.617344 + 0.786693i \(0.288208\pi\)
\(678\) −15.1668 −0.582479
\(679\) 64.4975 2.47519
\(680\) −7.89554 −0.302780
\(681\) 6.29941 0.241394
\(682\) −0.861161 −0.0329756
\(683\) 50.4661 1.93103 0.965515 0.260346i \(-0.0838367\pi\)
0.965515 + 0.260346i \(0.0838367\pi\)
\(684\) 22.9431 0.877250
\(685\) 0.876306 0.0334819
\(686\) 19.7404 0.753691
\(687\) 5.85455 0.223365
\(688\) 9.02615 0.344119
\(689\) −4.94998 −0.188579
\(690\) −0.104062 −0.00396156
\(691\) 48.7678 1.85522 0.927608 0.373556i \(-0.121861\pi\)
0.927608 + 0.373556i \(0.121861\pi\)
\(692\) −82.5211 −3.13698
\(693\) 10.6366 0.404049
\(694\) 47.2636 1.79410
\(695\) −1.08289 −0.0410763
\(696\) −13.7674 −0.521851
\(697\) −65.0984 −2.46578
\(698\) −4.87924 −0.184682
\(699\) −1.38232 −0.0522840
\(700\) −57.5820 −2.17640
\(701\) 22.0662 0.833428 0.416714 0.909038i \(-0.363182\pi\)
0.416714 + 0.909038i \(0.363182\pi\)
\(702\) 26.5381 1.00161
\(703\) −0.154541 −0.00582864
\(704\) 13.6191 0.513290
\(705\) 1.72808 0.0650831
\(706\) −23.2189 −0.873856
\(707\) 48.1479 1.81079
\(708\) −21.6573 −0.813931
\(709\) 24.3535 0.914614 0.457307 0.889309i \(-0.348814\pi\)
0.457307 + 0.889309i \(0.348814\pi\)
\(710\) −4.94168 −0.185458
\(711\) −23.4760 −0.880418
\(712\) 27.0933 1.01536
\(713\) 0.0932399 0.00349186
\(714\) 22.0442 0.824983
\(715\) 1.78442 0.0667336
\(716\) 74.5134 2.78470
\(717\) −4.35669 −0.162704
\(718\) −61.0074 −2.27678
\(719\) 40.9178 1.52598 0.762989 0.646412i \(-0.223731\pi\)
0.762989 + 0.646412i \(0.223731\pi\)
\(720\) −1.17556 −0.0438105
\(721\) 1.11728 0.0416098
\(722\) 31.6107 1.17643
\(723\) 0.716379 0.0266424
\(724\) 44.4000 1.65011
\(725\) 44.1038 1.63798
\(726\) −9.99959 −0.371120
\(727\) 22.8789 0.848531 0.424265 0.905538i \(-0.360532\pi\)
0.424265 + 0.905538i \(0.360532\pi\)
\(728\) 52.5335 1.94702
\(729\) −17.1944 −0.636830
\(730\) −7.48432 −0.277007
\(731\) 49.0154 1.81290
\(732\) −10.3803 −0.383669
\(733\) −37.7703 −1.39508 −0.697538 0.716548i \(-0.745721\pi\)
−0.697538 + 0.716548i \(0.745721\pi\)
\(734\) 15.7869 0.582705
\(735\) −0.709187 −0.0261588
\(736\) −1.19255 −0.0439581
\(737\) −12.6900 −0.467443
\(738\) −67.5586 −2.48687
\(739\) −4.84983 −0.178404 −0.0892019 0.996014i \(-0.528432\pi\)
−0.0892019 + 0.996014i \(0.528432\pi\)
\(740\) 0.0823367 0.00302676
\(741\) −4.57617 −0.168110
\(742\) −8.82553 −0.323995
\(743\) −9.93345 −0.364423 −0.182211 0.983259i \(-0.558326\pi\)
−0.182211 + 0.983259i \(0.558326\pi\)
\(744\) −0.501049 −0.0183693
\(745\) −6.31912 −0.231515
\(746\) −30.9200 −1.13206
\(747\) −18.6298 −0.681628
\(748\) −24.6354 −0.900759
\(749\) 10.7968 0.394507
\(750\) −3.63014 −0.132554
\(751\) 4.98144 0.181775 0.0908876 0.995861i \(-0.471030\pi\)
0.0908876 + 0.995861i \(0.471030\pi\)
\(752\) −12.8401 −0.468230
\(753\) −0.448417 −0.0163412
\(754\) −94.4894 −3.44110
\(755\) 2.34414 0.0853120
\(756\) 30.0578 1.09319
\(757\) 39.4946 1.43545 0.717727 0.696324i \(-0.245182\pi\)
0.717727 + 0.696324i \(0.245182\pi\)
\(758\) 5.29452 0.192306
\(759\) −0.138264 −0.00501868
\(760\) 2.92232 0.106004
\(761\) −16.3169 −0.591488 −0.295744 0.955267i \(-0.595568\pi\)
−0.295744 + 0.955267i \(0.595568\pi\)
\(762\) 8.40357 0.304429
\(763\) 0.00770781 0.000279041 0
\(764\) −9.45854 −0.342198
\(765\) −6.38372 −0.230804
\(766\) 23.1096 0.834984
\(767\) −63.2963 −2.28550
\(768\) 9.96742 0.359668
\(769\) 11.2026 0.403977 0.201989 0.979388i \(-0.435260\pi\)
0.201989 + 0.979388i \(0.435260\pi\)
\(770\) 3.18153 0.114654
\(771\) 2.98108 0.107361
\(772\) −22.0362 −0.793101
\(773\) −44.0784 −1.58539 −0.792695 0.609618i \(-0.791323\pi\)
−0.792695 + 0.609618i \(0.791323\pi\)
\(774\) 50.8678 1.82841
\(775\) 1.60511 0.0576573
\(776\) −66.0167 −2.36986
\(777\) −0.0978921 −0.00351186
\(778\) −30.1358 −1.08042
\(779\) 24.0944 0.863272
\(780\) 2.43810 0.0872979
\(781\) −6.56589 −0.234946
\(782\) 4.19881 0.150149
\(783\) −23.0221 −0.822744
\(784\) 5.26946 0.188195
\(785\) 7.55507 0.269652
\(786\) −17.0745 −0.609029
\(787\) 1.98422 0.0707297 0.0353648 0.999374i \(-0.488741\pi\)
0.0353648 + 0.999374i \(0.488741\pi\)
\(788\) 35.8678 1.27774
\(789\) −4.56284 −0.162441
\(790\) −7.02196 −0.249830
\(791\) −50.2061 −1.78512
\(792\) −10.8871 −0.386856
\(793\) −30.3379 −1.07733
\(794\) −21.4577 −0.761505
\(795\) −0.174421 −0.00618606
\(796\) 39.1467 1.38752
\(797\) −28.2809 −1.00176 −0.500880 0.865517i \(-0.666990\pi\)
−0.500880 + 0.865517i \(0.666990\pi\)
\(798\) −8.15906 −0.288827
\(799\) −69.7266 −2.46675
\(800\) −20.5296 −0.725832
\(801\) 21.9055 0.773994
\(802\) 13.0002 0.459052
\(803\) −9.94425 −0.350925
\(804\) −17.3387 −0.611488
\(805\) −0.344471 −0.0121410
\(806\) −3.43884 −0.121128
\(807\) 9.43461 0.332114
\(808\) −49.2820 −1.73373
\(809\) 16.4780 0.579337 0.289668 0.957127i \(-0.406455\pi\)
0.289668 + 0.957127i \(0.406455\pi\)
\(810\) −6.14199 −0.215808
\(811\) −40.5809 −1.42499 −0.712494 0.701679i \(-0.752434\pi\)
−0.712494 + 0.701679i \(0.752434\pi\)
\(812\) −107.021 −3.75572
\(813\) −1.86614 −0.0654485
\(814\) 0.172212 0.00603602
\(815\) −3.13711 −0.109888
\(816\) −3.23710 −0.113321
\(817\) −18.1417 −0.634699
\(818\) 26.4642 0.925299
\(819\) 42.4745 1.48418
\(820\) −12.8371 −0.448289
\(821\) 50.5083 1.76275 0.881376 0.472416i \(-0.156618\pi\)
0.881376 + 0.472416i \(0.156618\pi\)
\(822\) 2.50426 0.0873460
\(823\) 25.7541 0.897731 0.448865 0.893599i \(-0.351828\pi\)
0.448865 + 0.893599i \(0.351828\pi\)
\(824\) −1.14360 −0.0398392
\(825\) −2.38020 −0.0828680
\(826\) −112.854 −3.92668
\(827\) −10.2641 −0.356917 −0.178459 0.983947i \(-0.557111\pi\)
−0.178459 + 0.983947i \(0.557111\pi\)
\(828\) 2.76813 0.0961993
\(829\) −25.1531 −0.873605 −0.436802 0.899558i \(-0.643889\pi\)
−0.436802 + 0.899558i \(0.643889\pi\)
\(830\) −5.57240 −0.193421
\(831\) −6.97020 −0.241794
\(832\) 54.3847 1.88545
\(833\) 28.6152 0.991456
\(834\) −3.09462 −0.107158
\(835\) 1.31084 0.0453635
\(836\) 9.11812 0.315357
\(837\) −0.837865 −0.0289609
\(838\) −88.6309 −3.06170
\(839\) −14.5706 −0.503034 −0.251517 0.967853i \(-0.580929\pi\)
−0.251517 + 0.967853i \(0.580929\pi\)
\(840\) 1.85110 0.0638692
\(841\) 52.9710 1.82658
\(842\) −15.3214 −0.528011
\(843\) −3.50383 −0.120678
\(844\) 98.0128 3.37374
\(845\) 2.46223 0.0847032
\(846\) −72.3617 −2.48785
\(847\) −33.1012 −1.13737
\(848\) 1.29599 0.0445046
\(849\) −1.05152 −0.0360881
\(850\) 72.2819 2.47925
\(851\) −0.0186458 −0.000639169 0
\(852\) −8.97113 −0.307346
\(853\) −48.1849 −1.64982 −0.824910 0.565263i \(-0.808774\pi\)
−0.824910 + 0.565263i \(0.808774\pi\)
\(854\) −54.0908 −1.85095
\(855\) 2.36276 0.0808048
\(856\) −11.0511 −0.377720
\(857\) −7.96120 −0.271949 −0.135975 0.990712i \(-0.543417\pi\)
−0.135975 + 0.990712i \(0.543417\pi\)
\(858\) 5.09942 0.174091
\(859\) −49.9784 −1.70524 −0.852620 0.522531i \(-0.824988\pi\)
−0.852620 + 0.522531i \(0.824988\pi\)
\(860\) 9.66557 0.329593
\(861\) 15.2623 0.520137
\(862\) −35.5123 −1.20955
\(863\) −20.6894 −0.704274 −0.352137 0.935948i \(-0.614545\pi\)
−0.352137 + 0.935948i \(0.614545\pi\)
\(864\) 10.7164 0.364581
\(865\) −8.49833 −0.288952
\(866\) 12.9073 0.438608
\(867\) −10.1363 −0.344247
\(868\) −3.89493 −0.132202
\(869\) −9.32991 −0.316496
\(870\) −3.32949 −0.112880
\(871\) −50.6746 −1.71704
\(872\) −0.00788935 −0.000267167 0
\(873\) −53.3760 −1.80650
\(874\) −1.55408 −0.0525674
\(875\) −12.0167 −0.406238
\(876\) −13.5871 −0.459064
\(877\) 16.7222 0.564668 0.282334 0.959316i \(-0.408891\pi\)
0.282334 + 0.959316i \(0.408891\pi\)
\(878\) 13.7311 0.463403
\(879\) 8.57532 0.289238
\(880\) −0.467195 −0.0157491
\(881\) −12.6555 −0.426374 −0.213187 0.977011i \(-0.568384\pi\)
−0.213187 + 0.977011i \(0.568384\pi\)
\(882\) 29.6966 0.999936
\(883\) 24.3092 0.818070 0.409035 0.912519i \(-0.365865\pi\)
0.409035 + 0.912519i \(0.365865\pi\)
\(884\) −98.3754 −3.30872
\(885\) −2.23035 −0.0749724
\(886\) −28.1954 −0.947244
\(887\) 38.9644 1.30830 0.654148 0.756367i \(-0.273028\pi\)
0.654148 + 0.756367i \(0.273028\pi\)
\(888\) 0.100198 0.00336242
\(889\) 27.8180 0.932985
\(890\) 6.55222 0.219631
\(891\) −8.16073 −0.273395
\(892\) 71.1368 2.38184
\(893\) 25.8074 0.863612
\(894\) −18.0584 −0.603964
\(895\) 7.67367 0.256502
\(896\) 68.3619 2.28381
\(897\) −0.552126 −0.0184349
\(898\) 66.7513 2.22752
\(899\) 2.98324 0.0994967
\(900\) 47.6530 1.58843
\(901\) 7.03774 0.234461
\(902\) −26.8494 −0.893988
\(903\) −11.4916 −0.382418
\(904\) 51.3886 1.70916
\(905\) 4.57248 0.151994
\(906\) 6.69895 0.222558
\(907\) −31.5800 −1.04860 −0.524299 0.851534i \(-0.675673\pi\)
−0.524299 + 0.851534i \(0.675673\pi\)
\(908\) −50.1222 −1.66336
\(909\) −39.8456 −1.32159
\(910\) 12.7047 0.421155
\(911\) −50.3164 −1.66706 −0.833528 0.552477i \(-0.813683\pi\)
−0.833528 + 0.552477i \(0.813683\pi\)
\(912\) 1.19813 0.0396739
\(913\) −7.40392 −0.245034
\(914\) 0.644817 0.0213287
\(915\) −1.06901 −0.0353403
\(916\) −46.5826 −1.53913
\(917\) −56.5211 −1.86649
\(918\) −37.7311 −1.24531
\(919\) −10.9756 −0.362051 −0.181026 0.983478i \(-0.557942\pi\)
−0.181026 + 0.983478i \(0.557942\pi\)
\(920\) 0.352585 0.0116244
\(921\) −5.13174 −0.169097
\(922\) −64.5489 −2.12581
\(923\) −26.2193 −0.863019
\(924\) 5.77575 0.190008
\(925\) −0.320984 −0.0105539
\(926\) 37.4689 1.23130
\(927\) −0.924627 −0.0303687
\(928\) −38.1562 −1.25254
\(929\) 4.81786 0.158069 0.0790345 0.996872i \(-0.474816\pi\)
0.0790345 + 0.996872i \(0.474816\pi\)
\(930\) −0.121173 −0.00397342
\(931\) −10.5911 −0.347110
\(932\) 10.9986 0.360271
\(933\) −10.3660 −0.339369
\(934\) 15.5497 0.508801
\(935\) −2.53704 −0.0829702
\(936\) −43.4749 −1.42102
\(937\) −48.8481 −1.59580 −0.797900 0.602790i \(-0.794056\pi\)
−0.797900 + 0.602790i \(0.794056\pi\)
\(938\) −90.3499 −2.95003
\(939\) −7.95153 −0.259488
\(940\) −13.7497 −0.448466
\(941\) −53.4332 −1.74187 −0.870937 0.491396i \(-0.836487\pi\)
−0.870937 + 0.491396i \(0.836487\pi\)
\(942\) 21.5904 0.703454
\(943\) 2.90705 0.0946665
\(944\) 16.5721 0.539377
\(945\) 3.09546 0.100695
\(946\) 20.2161 0.657281
\(947\) 38.0769 1.23733 0.618666 0.785654i \(-0.287673\pi\)
0.618666 + 0.785654i \(0.287673\pi\)
\(948\) −12.7477 −0.414025
\(949\) −39.7100 −1.28904
\(950\) −26.7532 −0.867988
\(951\) −8.66787 −0.281075
\(952\) −74.6907 −2.42074
\(953\) −20.0787 −0.650414 −0.325207 0.945643i \(-0.605434\pi\)
−0.325207 + 0.945643i \(0.605434\pi\)
\(954\) 7.30371 0.236466
\(955\) −0.974076 −0.0315204
\(956\) 34.6647 1.12114
\(957\) −4.42382 −0.143002
\(958\) −13.8198 −0.446497
\(959\) 8.28973 0.267689
\(960\) 1.91634 0.0618495
\(961\) −30.8914 −0.996498
\(962\) 0.687686 0.0221719
\(963\) −8.93508 −0.287929
\(964\) −5.69997 −0.183584
\(965\) −2.26937 −0.0730537
\(966\) −0.984409 −0.0316729
\(967\) 13.6347 0.438464 0.219232 0.975673i \(-0.429645\pi\)
0.219232 + 0.975673i \(0.429645\pi\)
\(968\) 33.8809 1.08897
\(969\) 6.50628 0.209012
\(970\) −15.9654 −0.512619
\(971\) −30.7116 −0.985581 −0.492790 0.870148i \(-0.664023\pi\)
−0.492790 + 0.870148i \(0.664023\pi\)
\(972\) −37.7226 −1.20995
\(973\) −10.2440 −0.328407
\(974\) 30.9241 0.990873
\(975\) −9.50476 −0.304396
\(976\) 7.94303 0.254250
\(977\) −30.2357 −0.967327 −0.483663 0.875254i \(-0.660694\pi\)
−0.483663 + 0.875254i \(0.660694\pi\)
\(978\) −8.96506 −0.286671
\(979\) 8.70578 0.278238
\(980\) 5.64275 0.180251
\(981\) −0.00637872 −0.000203657 0
\(982\) −37.3084 −1.19056
\(983\) −12.2019 −0.389181 −0.194591 0.980885i \(-0.562338\pi\)
−0.194591 + 0.980885i \(0.562338\pi\)
\(984\) −15.6218 −0.498004
\(985\) 3.69380 0.117694
\(986\) 134.343 4.27834
\(987\) 16.3473 0.520342
\(988\) 36.4110 1.15839
\(989\) −2.18884 −0.0696011
\(990\) −2.63292 −0.0836798
\(991\) −32.1730 −1.02201 −0.511005 0.859578i \(-0.670726\pi\)
−0.511005 + 0.859578i \(0.670726\pi\)
\(992\) −1.38865 −0.0440897
\(993\) 4.99975 0.158662
\(994\) −46.7475 −1.48274
\(995\) 4.03148 0.127806
\(996\) −10.1161 −0.320542
\(997\) 34.1417 1.08128 0.540640 0.841254i \(-0.318182\pi\)
0.540640 + 0.841254i \(0.318182\pi\)
\(998\) 23.1318 0.732225
\(999\) 0.167553 0.00530115
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 \(a_p\))