Properties

Label 4031.2.a.c.1.4
Level 4031
Weight 2
Character 4031.1
Self dual Yes
Analytic conductor 32.188
Analytic rank 1
Dimension 61
CM No

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Newspace parameters

Level: \( N \) = \( 4031 = 29 \cdot 139 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4031.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1876970548\)
Analytic rank: \(1\)
Dimension: \(61\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 4031.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.49843 q^{2}\) \(-0.867725 q^{3}\) \(+4.24214 q^{4}\) \(+3.27534 q^{5}\) \(+2.16795 q^{6}\) \(+1.98132 q^{7}\) \(-5.60183 q^{8}\) \(-2.24705 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.49843 q^{2}\) \(-0.867725 q^{3}\) \(+4.24214 q^{4}\) \(+3.27534 q^{5}\) \(+2.16795 q^{6}\) \(+1.98132 q^{7}\) \(-5.60183 q^{8}\) \(-2.24705 q^{9}\) \(-8.18321 q^{10}\) \(+2.44571 q^{11}\) \(-3.68101 q^{12}\) \(-4.07719 q^{13}\) \(-4.95018 q^{14}\) \(-2.84210 q^{15}\) \(+5.51149 q^{16}\) \(-3.48151 q^{17}\) \(+5.61410 q^{18}\) \(+1.20918 q^{19}\) \(+13.8945 q^{20}\) \(-1.71924 q^{21}\) \(-6.11044 q^{22}\) \(-5.75094 q^{23}\) \(+4.86085 q^{24}\) \(+5.72787 q^{25}\) \(+10.1866 q^{26}\) \(+4.55300 q^{27}\) \(+8.40502 q^{28}\) \(-1.00000 q^{29}\) \(+7.10077 q^{30}\) \(-2.86533 q^{31}\) \(-2.56639 q^{32}\) \(-2.12221 q^{33}\) \(+8.69829 q^{34}\) \(+6.48949 q^{35}\) \(-9.53232 q^{36}\) \(+11.8840 q^{37}\) \(-3.02104 q^{38}\) \(+3.53788 q^{39}\) \(-18.3479 q^{40}\) \(-0.892481 q^{41}\) \(+4.29539 q^{42}\) \(-10.8277 q^{43}\) \(+10.3751 q^{44}\) \(-7.35987 q^{45}\) \(+14.3683 q^{46}\) \(+12.6747 q^{47}\) \(-4.78245 q^{48}\) \(-3.07439 q^{49}\) \(-14.3107 q^{50}\) \(+3.02099 q^{51}\) \(-17.2960 q^{52}\) \(+4.12783 q^{53}\) \(-11.3753 q^{54}\) \(+8.01055 q^{55}\) \(-11.0990 q^{56}\) \(-1.04923 q^{57}\) \(+2.49843 q^{58}\) \(-14.2386 q^{59}\) \(-12.0566 q^{60}\) \(-10.5744 q^{61}\) \(+7.15883 q^{62}\) \(-4.45212 q^{63}\) \(-4.61103 q^{64}\) \(-13.3542 q^{65}\) \(+5.30218 q^{66}\) \(+5.16192 q^{67}\) \(-14.7690 q^{68}\) \(+4.99023 q^{69}\) \(-16.2135 q^{70}\) \(+1.85405 q^{71}\) \(+12.5876 q^{72}\) \(+9.25762 q^{73}\) \(-29.6913 q^{74}\) \(-4.97022 q^{75}\) \(+5.12949 q^{76}\) \(+4.84573 q^{77}\) \(-8.83913 q^{78}\) \(-13.4490 q^{79}\) \(+18.0520 q^{80}\) \(+2.79041 q^{81}\) \(+2.22980 q^{82}\) \(-14.3099 q^{83}\) \(-7.29325 q^{84}\) \(-11.4031 q^{85}\) \(+27.0522 q^{86}\) \(+0.867725 q^{87}\) \(-13.7005 q^{88}\) \(+5.36321 q^{89}\) \(+18.3881 q^{90}\) \(-8.07820 q^{91}\) \(-24.3963 q^{92}\) \(+2.48632 q^{93}\) \(-31.6668 q^{94}\) \(+3.96046 q^{95}\) \(+2.22692 q^{96}\) \(+0.827274 q^{97}\) \(+7.68113 q^{98}\) \(-5.49565 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 11q^{16} \) \(\mathstrut -\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 17q^{18} \) \(\mathstrut -\mathstrut 36q^{19} \) \(\mathstrut -\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 42q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 28q^{24} \) \(\mathstrut -\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut -\mathstrut 10q^{27} \) \(\mathstrut -\mathstrut 25q^{28} \) \(\mathstrut -\mathstrut 61q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 18q^{31} \) \(\mathstrut -\mathstrut 3q^{32} \) \(\mathstrut -\mathstrut 42q^{33} \) \(\mathstrut -\mathstrut 22q^{34} \) \(\mathstrut -\mathstrut 29q^{35} \) \(\mathstrut -\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 30q^{37} \) \(\mathstrut -\mathstrut 27q^{38} \) \(\mathstrut -\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut 22q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 58q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 31q^{45} \) \(\mathstrut -\mathstrut 40q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 37q^{48} \) \(\mathstrut -\mathstrut 37q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 43q^{52} \) \(\mathstrut -\mathstrut 27q^{53} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut -\mathstrut 22q^{56} \) \(\mathstrut -\mathstrut 50q^{57} \) \(\mathstrut +\mathstrut q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 76q^{61} \) \(\mathstrut -\mathstrut 17q^{62} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 60q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 7q^{66} \) \(\mathstrut -\mathstrut 45q^{67} \) \(\mathstrut -\mathstrut 31q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 28q^{71} \) \(\mathstrut -\mathstrut 40q^{72} \) \(\mathstrut -\mathstrut 50q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 35q^{75} \) \(\mathstrut -\mathstrut 100q^{76} \) \(\mathstrut +\mathstrut q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 66q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut -\mathstrut 63q^{81} \) \(\mathstrut -\mathstrut 5q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 62q^{88} \) \(\mathstrut -\mathstrut 30q^{89} \) \(\mathstrut +\mathstrut 50q^{90} \) \(\mathstrut -\mathstrut 52q^{91} \) \(\mathstrut -\mathstrut 53q^{92} \) \(\mathstrut -\mathstrut 42q^{93} \) \(\mathstrut -\mathstrut 92q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut -\mathstrut 47q^{96} \) \(\mathstrut -\mathstrut 34q^{97} \) \(\mathstrut +\mathstrut 36q^{98} \) \(\mathstrut -\mathstrut 29q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.49843 −1.76666 −0.883328 0.468756i \(-0.844702\pi\)
−0.883328 + 0.468756i \(0.844702\pi\)
\(3\) −0.867725 −0.500981 −0.250491 0.968119i \(-0.580592\pi\)
−0.250491 + 0.968119i \(0.580592\pi\)
\(4\) 4.24214 2.12107
\(5\) 3.27534 1.46478 0.732389 0.680886i \(-0.238405\pi\)
0.732389 + 0.680886i \(0.238405\pi\)
\(6\) 2.16795 0.885061
\(7\) 1.98132 0.748867 0.374434 0.927254i \(-0.377837\pi\)
0.374434 + 0.927254i \(0.377837\pi\)
\(8\) −5.60183 −1.98055
\(9\) −2.24705 −0.749018
\(10\) −8.18321 −2.58776
\(11\) 2.44571 0.737410 0.368705 0.929546i \(-0.379801\pi\)
0.368705 + 0.929546i \(0.379801\pi\)
\(12\) −3.68101 −1.06262
\(13\) −4.07719 −1.13081 −0.565404 0.824814i \(-0.691280\pi\)
−0.565404 + 0.824814i \(0.691280\pi\)
\(14\) −4.95018 −1.32299
\(15\) −2.84210 −0.733826
\(16\) 5.51149 1.37787
\(17\) −3.48151 −0.844389 −0.422195 0.906505i \(-0.638740\pi\)
−0.422195 + 0.906505i \(0.638740\pi\)
\(18\) 5.61410 1.32326
\(19\) 1.20918 0.277404 0.138702 0.990334i \(-0.455707\pi\)
0.138702 + 0.990334i \(0.455707\pi\)
\(20\) 13.8945 3.10690
\(21\) −1.71924 −0.375168
\(22\) −6.11044 −1.30275
\(23\) −5.75094 −1.19915 −0.599577 0.800317i \(-0.704664\pi\)
−0.599577 + 0.800317i \(0.704664\pi\)
\(24\) 4.86085 0.992216
\(25\) 5.72787 1.14557
\(26\) 10.1866 1.99775
\(27\) 4.55300 0.876225
\(28\) 8.40502 1.58840
\(29\) −1.00000 −0.185695
\(30\) 7.10077 1.29642
\(31\) −2.86533 −0.514629 −0.257314 0.966328i \(-0.582838\pi\)
−0.257314 + 0.966328i \(0.582838\pi\)
\(32\) −2.56639 −0.453678
\(33\) −2.12221 −0.369429
\(34\) 8.69829 1.49174
\(35\) 6.48949 1.09692
\(36\) −9.53232 −1.58872
\(37\) 11.8840 1.95372 0.976860 0.213881i \(-0.0686106\pi\)
0.976860 + 0.213881i \(0.0686106\pi\)
\(38\) −3.02104 −0.490077
\(39\) 3.53788 0.566514
\(40\) −18.3479 −2.90106
\(41\) −0.892481 −0.139382 −0.0696910 0.997569i \(-0.522201\pi\)
−0.0696910 + 0.997569i \(0.522201\pi\)
\(42\) 4.29539 0.662793
\(43\) −10.8277 −1.65121 −0.825603 0.564252i \(-0.809165\pi\)
−0.825603 + 0.564252i \(0.809165\pi\)
\(44\) 10.3751 1.56410
\(45\) −7.35987 −1.09715
\(46\) 14.3683 2.11849
\(47\) 12.6747 1.84879 0.924396 0.381434i \(-0.124570\pi\)
0.924396 + 0.381434i \(0.124570\pi\)
\(48\) −4.78245 −0.690287
\(49\) −3.07439 −0.439198
\(50\) −14.3107 −2.02384
\(51\) 3.02099 0.423023
\(52\) −17.2960 −2.39852
\(53\) 4.12783 0.567001 0.283500 0.958972i \(-0.408504\pi\)
0.283500 + 0.958972i \(0.408504\pi\)
\(54\) −11.3753 −1.54799
\(55\) 8.01055 1.08014
\(56\) −11.0990 −1.48317
\(57\) −1.04923 −0.138974
\(58\) 2.49843 0.328060
\(59\) −14.2386 −1.85371 −0.926853 0.375425i \(-0.877497\pi\)
−0.926853 + 0.375425i \(0.877497\pi\)
\(60\) −12.0566 −1.55650
\(61\) −10.5744 −1.35392 −0.676958 0.736021i \(-0.736702\pi\)
−0.676958 + 0.736021i \(0.736702\pi\)
\(62\) 7.15883 0.909172
\(63\) −4.45212 −0.560915
\(64\) −4.61103 −0.576379
\(65\) −13.3542 −1.65638
\(66\) 5.30218 0.652653
\(67\) 5.16192 0.630629 0.315315 0.948987i \(-0.397890\pi\)
0.315315 + 0.948987i \(0.397890\pi\)
\(68\) −14.7690 −1.79101
\(69\) 4.99023 0.600753
\(70\) −16.2135 −1.93789
\(71\) 1.85405 0.220035 0.110018 0.993930i \(-0.464909\pi\)
0.110018 + 0.993930i \(0.464909\pi\)
\(72\) 12.5876 1.48346
\(73\) 9.25762 1.08352 0.541761 0.840532i \(-0.317758\pi\)
0.541761 + 0.840532i \(0.317758\pi\)
\(74\) −29.6913 −3.45155
\(75\) −4.97022 −0.573911
\(76\) 5.12949 0.588393
\(77\) 4.84573 0.552222
\(78\) −8.83913 −1.00083
\(79\) −13.4490 −1.51313 −0.756565 0.653918i \(-0.773124\pi\)
−0.756565 + 0.653918i \(0.773124\pi\)
\(80\) 18.0520 2.01828
\(81\) 2.79041 0.310046
\(82\) 2.22980 0.246240
\(83\) −14.3099 −1.57071 −0.785356 0.619044i \(-0.787520\pi\)
−0.785356 + 0.619044i \(0.787520\pi\)
\(84\) −7.29325 −0.795758
\(85\) −11.4031 −1.23684
\(86\) 27.0522 2.91711
\(87\) 0.867725 0.0930299
\(88\) −13.7005 −1.46047
\(89\) 5.36321 0.568499 0.284250 0.958750i \(-0.408256\pi\)
0.284250 + 0.958750i \(0.408256\pi\)
\(90\) 18.3881 1.93828
\(91\) −8.07820 −0.846825
\(92\) −24.3963 −2.54349
\(93\) 2.48632 0.257819
\(94\) −31.6668 −3.26618
\(95\) 3.96046 0.406335
\(96\) 2.22692 0.227284
\(97\) 0.827274 0.0839970 0.0419985 0.999118i \(-0.486628\pi\)
0.0419985 + 0.999118i \(0.486628\pi\)
\(98\) 7.68113 0.775912
\(99\) −5.49565 −0.552333
\(100\) 24.2985 2.42985
\(101\) −10.3918 −1.03403 −0.517013 0.855978i \(-0.672956\pi\)
−0.517013 + 0.855978i \(0.672956\pi\)
\(102\) −7.54772 −0.747336
\(103\) −15.0826 −1.48613 −0.743065 0.669219i \(-0.766629\pi\)
−0.743065 + 0.669219i \(0.766629\pi\)
\(104\) 22.8397 2.23962
\(105\) −5.63109 −0.549538
\(106\) −10.3131 −1.00170
\(107\) 14.5506 1.40666 0.703328 0.710865i \(-0.251696\pi\)
0.703328 + 0.710865i \(0.251696\pi\)
\(108\) 19.3145 1.85854
\(109\) −5.14960 −0.493242 −0.246621 0.969112i \(-0.579320\pi\)
−0.246621 + 0.969112i \(0.579320\pi\)
\(110\) −20.0138 −1.90824
\(111\) −10.3120 −0.978776
\(112\) 10.9200 1.03184
\(113\) −3.54863 −0.333827 −0.166913 0.985972i \(-0.553380\pi\)
−0.166913 + 0.985972i \(0.553380\pi\)
\(114\) 2.62143 0.245519
\(115\) −18.8363 −1.75649
\(116\) −4.24214 −0.393873
\(117\) 9.16166 0.846996
\(118\) 35.5741 3.27486
\(119\) −6.89796 −0.632335
\(120\) 15.9209 1.45338
\(121\) −5.01849 −0.456226
\(122\) 26.4194 2.39190
\(123\) 0.774427 0.0698278
\(124\) −12.1551 −1.09156
\(125\) 2.38403 0.213234
\(126\) 11.1233 0.990943
\(127\) 1.37783 0.122263 0.0611315 0.998130i \(-0.480529\pi\)
0.0611315 + 0.998130i \(0.480529\pi\)
\(128\) 16.6531 1.47194
\(129\) 9.39544 0.827223
\(130\) 33.3645 2.92626
\(131\) 1.85540 0.162107 0.0810537 0.996710i \(-0.474171\pi\)
0.0810537 + 0.996710i \(0.474171\pi\)
\(132\) −9.00270 −0.783584
\(133\) 2.39576 0.207739
\(134\) −12.8967 −1.11410
\(135\) 14.9126 1.28347
\(136\) 19.5028 1.67235
\(137\) −11.5960 −0.990714 −0.495357 0.868689i \(-0.664963\pi\)
−0.495357 + 0.868689i \(0.664963\pi\)
\(138\) −12.4677 −1.06132
\(139\) −1.00000 −0.0848189
\(140\) 27.5293 2.32665
\(141\) −10.9981 −0.926210
\(142\) −4.63221 −0.388727
\(143\) −9.97163 −0.833869
\(144\) −12.3846 −1.03205
\(145\) −3.27534 −0.272002
\(146\) −23.1295 −1.91421
\(147\) 2.66772 0.220030
\(148\) 50.4137 4.14398
\(149\) −5.09836 −0.417674 −0.208837 0.977950i \(-0.566968\pi\)
−0.208837 + 0.977950i \(0.566968\pi\)
\(150\) 12.4177 1.01390
\(151\) −15.5753 −1.26750 −0.633751 0.773537i \(-0.718486\pi\)
−0.633751 + 0.773537i \(0.718486\pi\)
\(152\) −6.77360 −0.549411
\(153\) 7.82313 0.632463
\(154\) −12.1067 −0.975586
\(155\) −9.38495 −0.753817
\(156\) 15.0082 1.20162
\(157\) 16.2350 1.29570 0.647848 0.761770i \(-0.275669\pi\)
0.647848 + 0.761770i \(0.275669\pi\)
\(158\) 33.6014 2.67318
\(159\) −3.58182 −0.284057
\(160\) −8.40580 −0.664537
\(161\) −11.3944 −0.898007
\(162\) −6.97164 −0.547744
\(163\) 6.24534 0.489172 0.244586 0.969628i \(-0.421348\pi\)
0.244586 + 0.969628i \(0.421348\pi\)
\(164\) −3.78603 −0.295639
\(165\) −6.95095 −0.541131
\(166\) 35.7522 2.77491
\(167\) −10.6436 −0.823630 −0.411815 0.911267i \(-0.635105\pi\)
−0.411815 + 0.911267i \(0.635105\pi\)
\(168\) 9.63087 0.743038
\(169\) 3.62346 0.278727
\(170\) 28.4899 2.18507
\(171\) −2.71708 −0.207780
\(172\) −45.9326 −3.50232
\(173\) 16.3574 1.24363 0.621814 0.783165i \(-0.286396\pi\)
0.621814 + 0.783165i \(0.286396\pi\)
\(174\) −2.16795 −0.164352
\(175\) 11.3487 0.857883
\(176\) 13.4795 1.01606
\(177\) 12.3552 0.928671
\(178\) −13.3996 −1.00434
\(179\) 12.7318 0.951619 0.475810 0.879548i \(-0.342155\pi\)
0.475810 + 0.879548i \(0.342155\pi\)
\(180\) −31.2216 −2.32712
\(181\) −9.11335 −0.677390 −0.338695 0.940896i \(-0.609986\pi\)
−0.338695 + 0.940896i \(0.609986\pi\)
\(182\) 20.1828 1.49605
\(183\) 9.17569 0.678287
\(184\) 32.2158 2.37498
\(185\) 38.9242 2.86177
\(186\) −6.21189 −0.455478
\(187\) −8.51476 −0.622661
\(188\) 53.7678 3.92142
\(189\) 9.02093 0.656176
\(190\) −9.89493 −0.717854
\(191\) 8.51043 0.615793 0.307897 0.951420i \(-0.400375\pi\)
0.307897 + 0.951420i \(0.400375\pi\)
\(192\) 4.00111 0.288755
\(193\) −20.3741 −1.46656 −0.733281 0.679926i \(-0.762012\pi\)
−0.733281 + 0.679926i \(0.762012\pi\)
\(194\) −2.06688 −0.148394
\(195\) 11.5878 0.829817
\(196\) −13.0420 −0.931570
\(197\) −5.50200 −0.392001 −0.196001 0.980604i \(-0.562795\pi\)
−0.196001 + 0.980604i \(0.562795\pi\)
\(198\) 13.7305 0.975783
\(199\) 10.0970 0.715759 0.357879 0.933768i \(-0.383500\pi\)
0.357879 + 0.933768i \(0.383500\pi\)
\(200\) −32.0866 −2.26886
\(201\) −4.47913 −0.315933
\(202\) 25.9632 1.82677
\(203\) −1.98132 −0.139061
\(204\) 12.8155 0.897262
\(205\) −2.92318 −0.204164
\(206\) 37.6827 2.62548
\(207\) 12.9227 0.898188
\(208\) −22.4714 −1.55811
\(209\) 2.95730 0.204560
\(210\) 14.0689 0.970845
\(211\) 4.05894 0.279429 0.139714 0.990192i \(-0.455382\pi\)
0.139714 + 0.990192i \(0.455382\pi\)
\(212\) 17.5108 1.20265
\(213\) −1.60881 −0.110234
\(214\) −36.3536 −2.48508
\(215\) −35.4644 −2.41865
\(216\) −25.5051 −1.73540
\(217\) −5.67713 −0.385389
\(218\) 12.8659 0.871388
\(219\) −8.03307 −0.542824
\(220\) 33.9819 2.29106
\(221\) 14.1948 0.954842
\(222\) 25.7639 1.72916
\(223\) 4.19820 0.281132 0.140566 0.990071i \(-0.455108\pi\)
0.140566 + 0.990071i \(0.455108\pi\)
\(224\) −5.08483 −0.339744
\(225\) −12.8708 −0.858056
\(226\) 8.86599 0.589757
\(227\) 19.1394 1.27032 0.635162 0.772379i \(-0.280933\pi\)
0.635162 + 0.772379i \(0.280933\pi\)
\(228\) −4.45099 −0.294774
\(229\) −12.6139 −0.833547 −0.416773 0.909010i \(-0.636839\pi\)
−0.416773 + 0.909010i \(0.636839\pi\)
\(230\) 47.0611 3.10312
\(231\) −4.20476 −0.276653
\(232\) 5.60183 0.367778
\(233\) −4.99031 −0.326926 −0.163463 0.986549i \(-0.552266\pi\)
−0.163463 + 0.986549i \(0.552266\pi\)
\(234\) −22.8897 −1.49635
\(235\) 41.5139 2.70807
\(236\) −60.4021 −3.93184
\(237\) 11.6700 0.758050
\(238\) 17.2341 1.11712
\(239\) −21.3764 −1.38272 −0.691362 0.722509i \(-0.742989\pi\)
−0.691362 + 0.722509i \(0.742989\pi\)
\(240\) −15.6642 −1.01112
\(241\) −2.52755 −0.162814 −0.0814068 0.996681i \(-0.525941\pi\)
−0.0814068 + 0.996681i \(0.525941\pi\)
\(242\) 12.5383 0.805995
\(243\) −16.0803 −1.03155
\(244\) −44.8582 −2.87175
\(245\) −10.0697 −0.643328
\(246\) −1.93485 −0.123362
\(247\) −4.93003 −0.313691
\(248\) 16.0511 1.01925
\(249\) 12.4170 0.786897
\(250\) −5.95634 −0.376712
\(251\) −4.08138 −0.257615 −0.128807 0.991670i \(-0.541115\pi\)
−0.128807 + 0.991670i \(0.541115\pi\)
\(252\) −18.8865 −1.18974
\(253\) −14.0651 −0.884268
\(254\) −3.44242 −0.215997
\(255\) 9.89477 0.619635
\(256\) −32.3845 −2.02403
\(257\) 0.260651 0.0162590 0.00812948 0.999967i \(-0.497412\pi\)
0.00812948 + 0.999967i \(0.497412\pi\)
\(258\) −23.4738 −1.46142
\(259\) 23.5460 1.46308
\(260\) −56.6504 −3.51331
\(261\) 2.24705 0.139089
\(262\) −4.63559 −0.286388
\(263\) −5.47637 −0.337687 −0.168844 0.985643i \(-0.554003\pi\)
−0.168844 + 0.985643i \(0.554003\pi\)
\(264\) 11.8882 0.731670
\(265\) 13.5201 0.830531
\(266\) −5.98563 −0.367003
\(267\) −4.65379 −0.284807
\(268\) 21.8976 1.33761
\(269\) −7.43193 −0.453133 −0.226566 0.973996i \(-0.572750\pi\)
−0.226566 + 0.973996i \(0.572750\pi\)
\(270\) −37.2581 −2.26746
\(271\) 26.7980 1.62786 0.813931 0.580961i \(-0.197323\pi\)
0.813931 + 0.580961i \(0.197323\pi\)
\(272\) −19.1883 −1.16346
\(273\) 7.00965 0.424243
\(274\) 28.9718 1.75025
\(275\) 14.0087 0.844758
\(276\) 21.1693 1.27424
\(277\) −17.4278 −1.04713 −0.523567 0.851984i \(-0.675399\pi\)
−0.523567 + 0.851984i \(0.675399\pi\)
\(278\) 2.49843 0.149846
\(279\) 6.43856 0.385466
\(280\) −36.3530 −2.17251
\(281\) 21.6974 1.29436 0.647180 0.762337i \(-0.275948\pi\)
0.647180 + 0.762337i \(0.275948\pi\)
\(282\) 27.4780 1.63629
\(283\) −21.6764 −1.28853 −0.644263 0.764804i \(-0.722836\pi\)
−0.644263 + 0.764804i \(0.722836\pi\)
\(284\) 7.86515 0.466711
\(285\) −3.43659 −0.203566
\(286\) 24.9134 1.47316
\(287\) −1.76829 −0.104379
\(288\) 5.76681 0.339813
\(289\) −4.87912 −0.287007
\(290\) 8.18321 0.480535
\(291\) −0.717846 −0.0420809
\(292\) 39.2721 2.29823
\(293\) −0.165687 −0.00967954 −0.00483977 0.999988i \(-0.501541\pi\)
−0.00483977 + 0.999988i \(0.501541\pi\)
\(294\) −6.66511 −0.388717
\(295\) −46.6362 −2.71527
\(296\) −66.5722 −3.86943
\(297\) 11.1353 0.646137
\(298\) 12.7379 0.737886
\(299\) 23.4477 1.35601
\(300\) −21.0844 −1.21731
\(301\) −21.4531 −1.23653
\(302\) 38.9138 2.23924
\(303\) 9.01724 0.518027
\(304\) 6.66435 0.382227
\(305\) −34.6349 −1.98319
\(306\) −19.5455 −1.11734
\(307\) −16.0014 −0.913247 −0.456624 0.889660i \(-0.650941\pi\)
−0.456624 + 0.889660i \(0.650941\pi\)
\(308\) 20.5563 1.17130
\(309\) 13.0875 0.744523
\(310\) 23.4476 1.33173
\(311\) −10.2743 −0.582605 −0.291302 0.956631i \(-0.594089\pi\)
−0.291302 + 0.956631i \(0.594089\pi\)
\(312\) −19.8186 −1.12201
\(313\) −24.0710 −1.36057 −0.680287 0.732946i \(-0.738145\pi\)
−0.680287 + 0.732946i \(0.738145\pi\)
\(314\) −40.5620 −2.28905
\(315\) −14.5822 −0.821616
\(316\) −57.0526 −3.20946
\(317\) 8.02767 0.450879 0.225440 0.974257i \(-0.427618\pi\)
0.225440 + 0.974257i \(0.427618\pi\)
\(318\) 8.94892 0.501830
\(319\) −2.44571 −0.136934
\(320\) −15.1027 −0.844268
\(321\) −12.6259 −0.704709
\(322\) 28.4682 1.58647
\(323\) −4.20975 −0.234237
\(324\) 11.8373 0.657629
\(325\) −23.3536 −1.29543
\(326\) −15.6035 −0.864199
\(327\) 4.46843 0.247105
\(328\) 4.99952 0.276053
\(329\) 25.1125 1.38450
\(330\) 17.3664 0.955992
\(331\) 0.821892 0.0451753 0.0225876 0.999745i \(-0.492810\pi\)
0.0225876 + 0.999745i \(0.492810\pi\)
\(332\) −60.7045 −3.33159
\(333\) −26.7040 −1.46337
\(334\) 26.5924 1.45507
\(335\) 16.9071 0.923732
\(336\) −9.47555 −0.516934
\(337\) 8.27780 0.450920 0.225460 0.974252i \(-0.427611\pi\)
0.225460 + 0.974252i \(0.427611\pi\)
\(338\) −9.05295 −0.492415
\(339\) 3.07923 0.167241
\(340\) −48.3737 −2.62343
\(341\) −7.00778 −0.379493
\(342\) 6.78843 0.367076
\(343\) −19.9605 −1.07777
\(344\) 60.6548 3.27029
\(345\) 16.3447 0.879970
\(346\) −40.8677 −2.19706
\(347\) 13.6307 0.731732 0.365866 0.930668i \(-0.380773\pi\)
0.365866 + 0.930668i \(0.380773\pi\)
\(348\) 3.68101 0.197323
\(349\) 24.8994 1.33283 0.666417 0.745579i \(-0.267827\pi\)
0.666417 + 0.745579i \(0.267827\pi\)
\(350\) −28.3540 −1.51558
\(351\) −18.5634 −0.990842
\(352\) −6.27665 −0.334546
\(353\) −8.28003 −0.440702 −0.220351 0.975421i \(-0.570720\pi\)
−0.220351 + 0.975421i \(0.570720\pi\)
\(354\) −30.8685 −1.64064
\(355\) 6.07265 0.322303
\(356\) 22.7515 1.20583
\(357\) 5.98553 0.316788
\(358\) −31.8095 −1.68118
\(359\) 29.7793 1.57169 0.785847 0.618422i \(-0.212228\pi\)
0.785847 + 0.618422i \(0.212228\pi\)
\(360\) 41.2288 2.17295
\(361\) −17.5379 −0.923047
\(362\) 22.7691 1.19671
\(363\) 4.35467 0.228561
\(364\) −34.2689 −1.79618
\(365\) 30.3219 1.58712
\(366\) −22.9248 −1.19830
\(367\) 28.5998 1.49290 0.746450 0.665442i \(-0.231757\pi\)
0.746450 + 0.665442i \(0.231757\pi\)
\(368\) −31.6962 −1.65228
\(369\) 2.00545 0.104400
\(370\) −97.2493 −5.05575
\(371\) 8.17853 0.424608
\(372\) 10.5473 0.546853
\(373\) −30.3035 −1.56905 −0.784527 0.620094i \(-0.787094\pi\)
−0.784527 + 0.620094i \(0.787094\pi\)
\(374\) 21.2735 1.10003
\(375\) −2.06869 −0.106826
\(376\) −71.0014 −3.66162
\(377\) 4.07719 0.209986
\(378\) −22.5381 −1.15924
\(379\) −36.9745 −1.89925 −0.949627 0.313383i \(-0.898538\pi\)
−0.949627 + 0.313383i \(0.898538\pi\)
\(380\) 16.8009 0.861865
\(381\) −1.19558 −0.0612514
\(382\) −21.2627 −1.08789
\(383\) −5.95864 −0.304472 −0.152236 0.988344i \(-0.548647\pi\)
−0.152236 + 0.988344i \(0.548647\pi\)
\(384\) −14.4503 −0.737415
\(385\) 15.8714 0.808883
\(386\) 50.9033 2.59091
\(387\) 24.3304 1.23678
\(388\) 3.50941 0.178164
\(389\) −3.83762 −0.194575 −0.0972876 0.995256i \(-0.531017\pi\)
−0.0972876 + 0.995256i \(0.531017\pi\)
\(390\) −28.9512 −1.46600
\(391\) 20.0219 1.01255
\(392\) 17.2222 0.869852
\(393\) −1.60998 −0.0812127
\(394\) 13.7463 0.692531
\(395\) −44.0501 −2.21640
\(396\) −23.3133 −1.17154
\(397\) −29.3096 −1.47101 −0.735504 0.677520i \(-0.763055\pi\)
−0.735504 + 0.677520i \(0.763055\pi\)
\(398\) −25.2267 −1.26450
\(399\) −2.07886 −0.104073
\(400\) 31.5691 1.57845
\(401\) −9.83092 −0.490933 −0.245466 0.969405i \(-0.578941\pi\)
−0.245466 + 0.969405i \(0.578941\pi\)
\(402\) 11.1908 0.558145
\(403\) 11.6825 0.581947
\(404\) −44.0836 −2.19324
\(405\) 9.13956 0.454148
\(406\) 4.95018 0.245673
\(407\) 29.0649 1.44069
\(408\) −16.9231 −0.837817
\(409\) −34.2641 −1.69425 −0.847126 0.531392i \(-0.821669\pi\)
−0.847126 + 0.531392i \(0.821669\pi\)
\(410\) 7.30335 0.360687
\(411\) 10.0621 0.496329
\(412\) −63.9824 −3.15219
\(413\) −28.2111 −1.38818
\(414\) −32.2864 −1.58679
\(415\) −46.8697 −2.30075
\(416\) 10.4636 0.513022
\(417\) 0.867725 0.0424927
\(418\) −7.38859 −0.361388
\(419\) −8.21977 −0.401562 −0.200781 0.979636i \(-0.564348\pi\)
−0.200781 + 0.979636i \(0.564348\pi\)
\(420\) −23.8879 −1.16561
\(421\) −6.89550 −0.336066 −0.168033 0.985781i \(-0.553742\pi\)
−0.168033 + 0.985781i \(0.553742\pi\)
\(422\) −10.1410 −0.493654
\(423\) −28.4807 −1.38478
\(424\) −23.1234 −1.12297
\(425\) −19.9416 −0.967311
\(426\) 4.01949 0.194745
\(427\) −20.9513 −1.01390
\(428\) 61.7256 2.98362
\(429\) 8.65263 0.417753
\(430\) 88.6052 4.27292
\(431\) 37.6318 1.81266 0.906330 0.422570i \(-0.138872\pi\)
0.906330 + 0.422570i \(0.138872\pi\)
\(432\) 25.0938 1.20733
\(433\) 33.4644 1.60820 0.804099 0.594496i \(-0.202648\pi\)
0.804099 + 0.594496i \(0.202648\pi\)
\(434\) 14.1839 0.680849
\(435\) 2.84210 0.136268
\(436\) −21.8453 −1.04620
\(437\) −6.95389 −0.332650
\(438\) 20.0700 0.958983
\(439\) −15.7301 −0.750758 −0.375379 0.926871i \(-0.622487\pi\)
−0.375379 + 0.926871i \(0.622487\pi\)
\(440\) −44.8737 −2.13927
\(441\) 6.90831 0.328967
\(442\) −35.4646 −1.68688
\(443\) 8.57148 0.407243 0.203622 0.979050i \(-0.434729\pi\)
0.203622 + 0.979050i \(0.434729\pi\)
\(444\) −43.7452 −2.07605
\(445\) 17.5664 0.832725
\(446\) −10.4889 −0.496664
\(447\) 4.42398 0.209247
\(448\) −9.13592 −0.431632
\(449\) 27.2634 1.28664 0.643321 0.765597i \(-0.277556\pi\)
0.643321 + 0.765597i \(0.277556\pi\)
\(450\) 32.1569 1.51589
\(451\) −2.18275 −0.102782
\(452\) −15.0538 −0.708070
\(453\) 13.5151 0.634995
\(454\) −47.8183 −2.24423
\(455\) −26.4589 −1.24041
\(456\) 5.87762 0.275245
\(457\) −40.6977 −1.90376 −0.951878 0.306476i \(-0.900850\pi\)
−0.951878 + 0.306476i \(0.900850\pi\)
\(458\) 31.5148 1.47259
\(459\) −15.8513 −0.739875
\(460\) −79.9063 −3.72565
\(461\) −21.5125 −1.00194 −0.500968 0.865466i \(-0.667023\pi\)
−0.500968 + 0.865466i \(0.667023\pi\)
\(462\) 10.5053 0.488750
\(463\) 0.217725 0.0101185 0.00505927 0.999987i \(-0.498390\pi\)
0.00505927 + 0.999987i \(0.498390\pi\)
\(464\) −5.51149 −0.255864
\(465\) 8.14355 0.377648
\(466\) 12.4679 0.577565
\(467\) −17.7636 −0.822002 −0.411001 0.911635i \(-0.634821\pi\)
−0.411001 + 0.911635i \(0.634821\pi\)
\(468\) 38.8651 1.79654
\(469\) 10.2274 0.472257
\(470\) −103.720 −4.78423
\(471\) −14.0875 −0.649119
\(472\) 79.7621 3.67135
\(473\) −26.4814 −1.21762
\(474\) −29.1567 −1.33921
\(475\) 6.92600 0.317787
\(476\) −29.2621 −1.34123
\(477\) −9.27545 −0.424694
\(478\) 53.4074 2.44280
\(479\) 26.5875 1.21481 0.607406 0.794392i \(-0.292210\pi\)
0.607406 + 0.794392i \(0.292210\pi\)
\(480\) 7.29392 0.332920
\(481\) −48.4533 −2.20928
\(482\) 6.31490 0.287636
\(483\) 9.88723 0.449884
\(484\) −21.2891 −0.967688
\(485\) 2.70961 0.123037
\(486\) 40.1755 1.82240
\(487\) 8.51282 0.385753 0.192876 0.981223i \(-0.438218\pi\)
0.192876 + 0.981223i \(0.438218\pi\)
\(488\) 59.2362 2.68149
\(489\) −5.41923 −0.245066
\(490\) 25.1583 1.13654
\(491\) −34.0259 −1.53557 −0.767783 0.640710i \(-0.778640\pi\)
−0.767783 + 0.640710i \(0.778640\pi\)
\(492\) 3.28523 0.148110
\(493\) 3.48151 0.156799
\(494\) 12.3173 0.554183
\(495\) −18.0001 −0.809046
\(496\) −15.7922 −0.709092
\(497\) 3.67346 0.164777
\(498\) −31.0231 −1.39018
\(499\) −36.9118 −1.65240 −0.826199 0.563379i \(-0.809501\pi\)
−0.826199 + 0.563379i \(0.809501\pi\)
\(500\) 10.1134 0.452285
\(501\) 9.23575 0.412623
\(502\) 10.1970 0.455116
\(503\) 41.0858 1.83193 0.915963 0.401263i \(-0.131429\pi\)
0.915963 + 0.401263i \(0.131429\pi\)
\(504\) 24.9400 1.11092
\(505\) −34.0368 −1.51462
\(506\) 35.1408 1.56220
\(507\) −3.14416 −0.139637
\(508\) 5.84497 0.259328
\(509\) 21.0276 0.932033 0.466016 0.884776i \(-0.345689\pi\)
0.466016 + 0.884776i \(0.345689\pi\)
\(510\) −24.7214 −1.09468
\(511\) 18.3423 0.811414
\(512\) 47.6042 2.10383
\(513\) 5.50537 0.243068
\(514\) −0.651218 −0.0287240
\(515\) −49.4006 −2.17685
\(516\) 39.8568 1.75460
\(517\) 30.9986 1.36332
\(518\) −58.8279 −2.58475
\(519\) −14.1937 −0.623034
\(520\) 74.8079 3.28054
\(521\) 0.563519 0.0246882 0.0123441 0.999924i \(-0.496071\pi\)
0.0123441 + 0.999924i \(0.496071\pi\)
\(522\) −5.61410 −0.245723
\(523\) 43.5957 1.90631 0.953154 0.302486i \(-0.0978167\pi\)
0.953154 + 0.302486i \(0.0978167\pi\)
\(524\) 7.87089 0.343841
\(525\) −9.84757 −0.429783
\(526\) 13.6823 0.596577
\(527\) 9.97567 0.434547
\(528\) −11.6965 −0.509025
\(529\) 10.0733 0.437970
\(530\) −33.7789 −1.46726
\(531\) 31.9949 1.38846
\(532\) 10.1631 0.440628
\(533\) 3.63881 0.157614
\(534\) 11.6272 0.503156
\(535\) 47.6581 2.06044
\(536\) −28.9162 −1.24899
\(537\) −11.0477 −0.476743
\(538\) 18.5682 0.800530
\(539\) −7.51907 −0.323869
\(540\) 63.2615 2.72234
\(541\) 6.76449 0.290828 0.145414 0.989371i \(-0.453549\pi\)
0.145414 + 0.989371i \(0.453549\pi\)
\(542\) −66.9529 −2.87587
\(543\) 7.90788 0.339360
\(544\) 8.93490 0.383080
\(545\) −16.8667 −0.722490
\(546\) −17.5131 −0.749492
\(547\) 6.76551 0.289272 0.144636 0.989485i \(-0.453799\pi\)
0.144636 + 0.989485i \(0.453799\pi\)
\(548\) −49.1919 −2.10138
\(549\) 23.7613 1.01411
\(550\) −34.9998 −1.49240
\(551\) −1.20918 −0.0515126
\(552\) −27.9544 −1.18982
\(553\) −26.6467 −1.13313
\(554\) 43.5421 1.84993
\(555\) −33.7755 −1.43369
\(556\) −4.24214 −0.179907
\(557\) 32.5722 1.38013 0.690065 0.723748i \(-0.257582\pi\)
0.690065 + 0.723748i \(0.257582\pi\)
\(558\) −16.0863 −0.680986
\(559\) 44.1465 1.86720
\(560\) 35.7667 1.51142
\(561\) 7.38847 0.311941
\(562\) −54.2094 −2.28669
\(563\) −8.66575 −0.365218 −0.182609 0.983186i \(-0.558454\pi\)
−0.182609 + 0.983186i \(0.558454\pi\)
\(564\) −46.6556 −1.96456
\(565\) −11.6230 −0.488982
\(566\) 54.1568 2.27638
\(567\) 5.52869 0.232183
\(568\) −10.3861 −0.435790
\(569\) 23.6259 0.990448 0.495224 0.868765i \(-0.335086\pi\)
0.495224 + 0.868765i \(0.335086\pi\)
\(570\) 8.58608 0.359631
\(571\) 18.1019 0.757540 0.378770 0.925491i \(-0.376347\pi\)
0.378770 + 0.925491i \(0.376347\pi\)
\(572\) −42.3011 −1.76870
\(573\) −7.38471 −0.308501
\(574\) 4.41794 0.184401
\(575\) −32.9406 −1.37372
\(576\) 10.3612 0.431718
\(577\) −24.3133 −1.01217 −0.506087 0.862482i \(-0.668909\pi\)
−0.506087 + 0.862482i \(0.668909\pi\)
\(578\) 12.1901 0.507042
\(579\) 17.6791 0.734720
\(580\) −13.8945 −0.576937
\(581\) −28.3524 −1.17626
\(582\) 1.79349 0.0743424
\(583\) 10.0955 0.418112
\(584\) −51.8596 −2.14597
\(585\) 30.0076 1.24066
\(586\) 0.413957 0.0171004
\(587\) 23.5793 0.973222 0.486611 0.873619i \(-0.338233\pi\)
0.486611 + 0.873619i \(0.338233\pi\)
\(588\) 11.3169 0.466699
\(589\) −3.46469 −0.142760
\(590\) 116.517 4.79694
\(591\) 4.77422 0.196385
\(592\) 65.4986 2.69197
\(593\) 36.4052 1.49498 0.747491 0.664272i \(-0.231258\pi\)
0.747491 + 0.664272i \(0.231258\pi\)
\(594\) −27.8208 −1.14150
\(595\) −22.5932 −0.926231
\(596\) −21.6280 −0.885917
\(597\) −8.76143 −0.358582
\(598\) −58.5823 −2.39561
\(599\) −13.3215 −0.544302 −0.272151 0.962255i \(-0.587735\pi\)
−0.272151 + 0.962255i \(0.587735\pi\)
\(600\) 27.8423 1.13666
\(601\) 19.0971 0.778989 0.389494 0.921029i \(-0.372650\pi\)
0.389494 + 0.921029i \(0.372650\pi\)
\(602\) 53.5989 2.18453
\(603\) −11.5991 −0.472353
\(604\) −66.0728 −2.68846
\(605\) −16.4373 −0.668270
\(606\) −22.5289 −0.915175
\(607\) −19.1580 −0.777600 −0.388800 0.921322i \(-0.627110\pi\)
−0.388800 + 0.921322i \(0.627110\pi\)
\(608\) −3.10321 −0.125852
\(609\) 1.71924 0.0696670
\(610\) 86.5328 3.50361
\(611\) −51.6770 −2.09063
\(612\) 33.1868 1.34150
\(613\) −48.1804 −1.94599 −0.972994 0.230830i \(-0.925856\pi\)
−0.972994 + 0.230830i \(0.925856\pi\)
\(614\) 39.9783 1.61339
\(615\) 2.53652 0.102282
\(616\) −27.1450 −1.09370
\(617\) 12.0381 0.484636 0.242318 0.970197i \(-0.422092\pi\)
0.242318 + 0.970197i \(0.422092\pi\)
\(618\) −32.6982 −1.31532
\(619\) −11.6613 −0.468707 −0.234353 0.972151i \(-0.575297\pi\)
−0.234353 + 0.972151i \(0.575297\pi\)
\(620\) −39.8123 −1.59890
\(621\) −26.1840 −1.05073
\(622\) 25.6697 1.02926
\(623\) 10.6262 0.425730
\(624\) 19.4990 0.780583
\(625\) −20.8308 −0.833233
\(626\) 60.1397 2.40367
\(627\) −2.56612 −0.102481
\(628\) 68.8713 2.74826
\(629\) −41.3743 −1.64970
\(630\) 36.4327 1.45151
\(631\) −36.0833 −1.43645 −0.718226 0.695810i \(-0.755046\pi\)
−0.718226 + 0.695810i \(0.755046\pi\)
\(632\) 75.3390 2.99683
\(633\) −3.52204 −0.139988
\(634\) −20.0566 −0.796548
\(635\) 4.51288 0.179088
\(636\) −15.1946 −0.602505
\(637\) 12.5349 0.496649
\(638\) 6.11044 0.241915
\(639\) −4.16615 −0.164810
\(640\) 54.5447 2.15607
\(641\) 30.9032 1.22060 0.610301 0.792170i \(-0.291049\pi\)
0.610301 + 0.792170i \(0.291049\pi\)
\(642\) 31.5449 1.24498
\(643\) 15.7099 0.619539 0.309770 0.950812i \(-0.399748\pi\)
0.309770 + 0.950812i \(0.399748\pi\)
\(644\) −48.3368 −1.90474
\(645\) 30.7733 1.21170
\(646\) 10.5178 0.413816
\(647\) −40.5776 −1.59527 −0.797635 0.603140i \(-0.793916\pi\)
−0.797635 + 0.603140i \(0.793916\pi\)
\(648\) −15.6314 −0.614060
\(649\) −34.8235 −1.36694
\(650\) 58.3473 2.28857
\(651\) 4.92618 0.193072
\(652\) 26.4936 1.03757
\(653\) −7.13315 −0.279142 −0.139571 0.990212i \(-0.544572\pi\)
−0.139571 + 0.990212i \(0.544572\pi\)
\(654\) −11.1641 −0.436549
\(655\) 6.07708 0.237451
\(656\) −4.91889 −0.192051
\(657\) −20.8024 −0.811578
\(658\) −62.7419 −2.44593
\(659\) −28.8769 −1.12488 −0.562442 0.826836i \(-0.690138\pi\)
−0.562442 + 0.826836i \(0.690138\pi\)
\(660\) −29.4869 −1.14778
\(661\) 16.5357 0.643164 0.321582 0.946882i \(-0.395785\pi\)
0.321582 + 0.946882i \(0.395785\pi\)
\(662\) −2.05344 −0.0798091
\(663\) −12.3171 −0.478358
\(664\) 80.1615 3.11087
\(665\) 7.84693 0.304291
\(666\) 66.7181 2.58527
\(667\) 5.75094 0.222677
\(668\) −45.1519 −1.74698
\(669\) −3.64288 −0.140842
\(670\) −42.2411 −1.63192
\(671\) −25.8620 −0.998392
\(672\) 4.41223 0.170205
\(673\) 33.8059 1.30312 0.651562 0.758596i \(-0.274114\pi\)
0.651562 + 0.758596i \(0.274114\pi\)
\(674\) −20.6815 −0.796621
\(675\) 26.0790 1.00378
\(676\) 15.3712 0.591201
\(677\) −31.5729 −1.21344 −0.606722 0.794914i \(-0.707516\pi\)
−0.606722 + 0.794914i \(0.707516\pi\)
\(678\) −7.69323 −0.295457
\(679\) 1.63909 0.0629026
\(680\) 63.8784 2.44962
\(681\) −16.6077 −0.636409
\(682\) 17.5084 0.670433
\(683\) 11.6271 0.444897 0.222449 0.974944i \(-0.428595\pi\)
0.222449 + 0.974944i \(0.428595\pi\)
\(684\) −11.5262 −0.440717
\(685\) −37.9809 −1.45118
\(686\) 49.8700 1.90404
\(687\) 10.9454 0.417591
\(688\) −59.6766 −2.27515
\(689\) −16.8299 −0.641169
\(690\) −40.8361 −1.55460
\(691\) −12.5778 −0.478483 −0.239242 0.970960i \(-0.576899\pi\)
−0.239242 + 0.970960i \(0.576899\pi\)
\(692\) 69.3903 2.63782
\(693\) −10.8886 −0.413624
\(694\) −34.0552 −1.29272
\(695\) −3.27534 −0.124241
\(696\) −4.86085 −0.184250
\(697\) 3.10718 0.117693
\(698\) −62.2094 −2.35466
\(699\) 4.33021 0.163784
\(700\) 48.1429 1.81963
\(701\) −42.5898 −1.60859 −0.804297 0.594228i \(-0.797458\pi\)
−0.804297 + 0.594228i \(0.797458\pi\)
\(702\) 46.3794 1.75048
\(703\) 14.3699 0.541969
\(704\) −11.2773 −0.425028
\(705\) −36.0227 −1.35669
\(706\) 20.6871 0.778568
\(707\) −20.5895 −0.774347
\(708\) 52.4124 1.96978
\(709\) 36.3068 1.36353 0.681765 0.731572i \(-0.261213\pi\)
0.681765 + 0.731572i \(0.261213\pi\)
\(710\) −15.1721 −0.569398
\(711\) 30.2206 1.13336
\(712\) −30.0438 −1.12594
\(713\) 16.4784 0.617119
\(714\) −14.9544 −0.559655
\(715\) −32.6605 −1.22143
\(716\) 54.0101 2.01845
\(717\) 18.5488 0.692719
\(718\) −74.4015 −2.77664
\(719\) 20.0066 0.746119 0.373059 0.927807i \(-0.378309\pi\)
0.373059 + 0.927807i \(0.378309\pi\)
\(720\) −40.5638 −1.51172
\(721\) −29.8834 −1.11291
\(722\) 43.8172 1.63071
\(723\) 2.19322 0.0815666
\(724\) −38.6601 −1.43679
\(725\) −5.72787 −0.212728
\(726\) −10.8798 −0.403788
\(727\) 1.88578 0.0699399 0.0349699 0.999388i \(-0.488866\pi\)
0.0349699 + 0.999388i \(0.488866\pi\)
\(728\) 45.2527 1.67718
\(729\) 5.58204 0.206742
\(730\) −75.7570 −2.80389
\(731\) 37.6966 1.39426
\(732\) 38.9246 1.43869
\(733\) 15.3525 0.567058 0.283529 0.958964i \(-0.408495\pi\)
0.283529 + 0.958964i \(0.408495\pi\)
\(734\) −71.4546 −2.63744
\(735\) 8.73770 0.322295
\(736\) 14.7591 0.544029
\(737\) 12.6246 0.465032
\(738\) −5.01048 −0.184438
\(739\) −29.2378 −1.07553 −0.537764 0.843095i \(-0.680731\pi\)
−0.537764 + 0.843095i \(0.680731\pi\)
\(740\) 165.122 6.07001
\(741\) 4.27791 0.157153
\(742\) −20.4335 −0.750137
\(743\) 24.7869 0.909344 0.454672 0.890659i \(-0.349756\pi\)
0.454672 + 0.890659i \(0.349756\pi\)
\(744\) −13.9279 −0.510623
\(745\) −16.6989 −0.611800
\(746\) 75.7111 2.77198
\(747\) 32.1551 1.17649
\(748\) −36.1208 −1.32071
\(749\) 28.8293 1.05340
\(750\) 5.16846 0.188726
\(751\) 37.8178 1.37999 0.689995 0.723814i \(-0.257613\pi\)
0.689995 + 0.723814i \(0.257613\pi\)
\(752\) 69.8563 2.54740
\(753\) 3.54152 0.129060
\(754\) −10.1866 −0.370973
\(755\) −51.0145 −1.85661
\(756\) 38.2681 1.39180
\(757\) 46.9918 1.70795 0.853974 0.520316i \(-0.174186\pi\)
0.853974 + 0.520316i \(0.174186\pi\)
\(758\) 92.3782 3.35533
\(759\) 12.2047 0.443002
\(760\) −22.1858 −0.804765
\(761\) 40.4662 1.46690 0.733450 0.679744i \(-0.237909\pi\)
0.733450 + 0.679744i \(0.237909\pi\)
\(762\) 2.98707 0.108210
\(763\) −10.2030 −0.369373
\(764\) 36.1025 1.30614
\(765\) 25.6234 0.926417
\(766\) 14.8872 0.537897
\(767\) 58.0534 2.09619
\(768\) 28.1009 1.01400
\(769\) 5.29017 0.190768 0.0953842 0.995441i \(-0.469592\pi\)
0.0953842 + 0.995441i \(0.469592\pi\)
\(770\) −39.6536 −1.42902
\(771\) −0.226173 −0.00814544
\(772\) −86.4300 −3.11068
\(773\) −26.9037 −0.967659 −0.483829 0.875162i \(-0.660754\pi\)
−0.483829 + 0.875162i \(0.660754\pi\)
\(774\) −60.7877 −2.18497
\(775\) −16.4123 −0.589546
\(776\) −4.63425 −0.166360
\(777\) −20.4314 −0.732973
\(778\) 9.58802 0.343747
\(779\) −1.07917 −0.0386651
\(780\) 49.1569 1.76010
\(781\) 4.53448 0.162256
\(782\) −50.0233 −1.78883
\(783\) −4.55300 −0.162711
\(784\) −16.9444 −0.605158
\(785\) 53.1753 1.89791
\(786\) 4.02242 0.143475
\(787\) 7.21154 0.257064 0.128532 0.991705i \(-0.458974\pi\)
0.128532 + 0.991705i \(0.458974\pi\)
\(788\) −23.3403 −0.831462
\(789\) 4.75198 0.169175
\(790\) 110.056 3.91562
\(791\) −7.03095 −0.249992
\(792\) 30.7857 1.09392
\(793\) 43.1139 1.53102
\(794\) 73.2280 2.59876
\(795\) −11.7317 −0.416080
\(796\) 42.8330 1.51818
\(797\) −43.9281 −1.55601 −0.778006 0.628257i \(-0.783769\pi\)
−0.778006 + 0.628257i \(0.783769\pi\)
\(798\) 5.19388 0.183861
\(799\) −44.1270 −1.56110
\(800\) −14.6999 −0.519722
\(801\) −12.0514 −0.425816
\(802\) 24.5619 0.867309
\(803\) 22.6415 0.799000
\(804\) −19.0011 −0.670117
\(805\) −37.3207 −1.31538
\(806\) −29.1879 −1.02810
\(807\) 6.44887 0.227011
\(808\) 58.2132 2.04793
\(809\) −36.5123 −1.28370 −0.641852 0.766829i \(-0.721833\pi\)
−0.641852 + 0.766829i \(0.721833\pi\)
\(810\) −22.8345 −0.802324
\(811\) 9.63388 0.338291 0.169146 0.985591i \(-0.445899\pi\)
0.169146 + 0.985591i \(0.445899\pi\)
\(812\) −8.40502 −0.294959
\(813\) −23.2533 −0.815529
\(814\) −72.6165 −2.54521
\(815\) 20.4556 0.716529
\(816\) 16.6501 0.582871
\(817\) −13.0926 −0.458051
\(818\) 85.6065 2.99316
\(819\) 18.1521 0.634287
\(820\) −12.4005 −0.433046
\(821\) −34.5488 −1.20576 −0.602880 0.797832i \(-0.705980\pi\)
−0.602880 + 0.797832i \(0.705980\pi\)
\(822\) −25.1395 −0.876842
\(823\) 30.1353 1.05045 0.525225 0.850963i \(-0.323981\pi\)
0.525225 + 0.850963i \(0.323981\pi\)
\(824\) 84.4900 2.94335
\(825\) −12.1557 −0.423208
\(826\) 70.4835 2.45243
\(827\) 3.11633 0.108365 0.0541826 0.998531i \(-0.482745\pi\)
0.0541826 + 0.998531i \(0.482745\pi\)
\(828\) 54.8198 1.90512
\(829\) −5.67323 −0.197039 −0.0985197 0.995135i \(-0.531411\pi\)
−0.0985197 + 0.995135i \(0.531411\pi\)
\(830\) 117.101 4.06462
\(831\) 15.1225 0.524594
\(832\) 18.8001 0.651775
\(833\) 10.7035 0.370854
\(834\) −2.16795 −0.0750699
\(835\) −34.8616 −1.20644
\(836\) 12.5453 0.433887
\(837\) −13.0459 −0.450931
\(838\) 20.5365 0.709421
\(839\) −41.1062 −1.41914 −0.709572 0.704633i \(-0.751112\pi\)
−0.709572 + 0.704633i \(0.751112\pi\)
\(840\) 31.5444 1.08839
\(841\) 1.00000 0.0344828
\(842\) 17.2279 0.593713
\(843\) −18.8274 −0.648450
\(844\) 17.2186 0.592688
\(845\) 11.8681 0.408274
\(846\) 71.1569 2.44643
\(847\) −9.94321 −0.341653
\(848\) 22.7505 0.781254
\(849\) 18.8091 0.645527
\(850\) 49.8227 1.70890
\(851\) −68.3442 −2.34281
\(852\) −6.82478 −0.233813
\(853\) −36.7805 −1.25934 −0.629670 0.776862i \(-0.716810\pi\)
−0.629670 + 0.776862i \(0.716810\pi\)
\(854\) 52.3453 1.79122
\(855\) −8.89938 −0.304352
\(856\) −81.5098 −2.78595
\(857\) 49.4753 1.69004 0.845022 0.534732i \(-0.179587\pi\)
0.845022 + 0.534732i \(0.179587\pi\)
\(858\) −21.6180 −0.738025
\(859\) 15.4134 0.525897 0.262948 0.964810i \(-0.415305\pi\)
0.262948 + 0.964810i \(0.415305\pi\)
\(860\) −150.445 −5.13013
\(861\) 1.53439 0.0522917
\(862\) −94.0204 −3.20235
\(863\) 45.7487 1.55730 0.778652 0.627456i \(-0.215904\pi\)
0.778652 + 0.627456i \(0.215904\pi\)
\(864\) −11.6848 −0.397524
\(865\) 53.5760 1.82164
\(866\) −83.6084 −2.84113
\(867\) 4.23373 0.143785
\(868\) −24.0832 −0.817437
\(869\) −32.8924 −1.11580
\(870\) −7.10077 −0.240739
\(871\) −21.0461 −0.713121
\(872\) 28.8472 0.976888
\(873\) −1.85893 −0.0629152
\(874\) 17.3738 0.587678
\(875\) 4.72352 0.159684
\(876\) −34.0774 −1.15137
\(877\) −43.9341 −1.48355 −0.741775 0.670649i \(-0.766016\pi\)
−0.741775 + 0.670649i \(0.766016\pi\)
\(878\) 39.3006 1.32633
\(879\) 0.143771 0.00484927
\(880\) 44.1500 1.48830
\(881\) 1.90035 0.0640244 0.0320122 0.999487i \(-0.489808\pi\)
0.0320122 + 0.999487i \(0.489808\pi\)
\(882\) −17.2599 −0.581172
\(883\) 28.3227 0.953134 0.476567 0.879138i \(-0.341881\pi\)
0.476567 + 0.879138i \(0.341881\pi\)
\(884\) 60.2162 2.02529
\(885\) 40.4674 1.36030
\(886\) −21.4152 −0.719459
\(887\) 15.4350 0.518256 0.259128 0.965843i \(-0.416565\pi\)
0.259128 + 0.965843i \(0.416565\pi\)
\(888\) 57.7664 1.93851
\(889\) 2.72992 0.0915587
\(890\) −43.8883 −1.47114
\(891\) 6.82455 0.228631
\(892\) 17.8094 0.596301
\(893\) 15.3259 0.512862
\(894\) −11.0530 −0.369667
\(895\) 41.7010 1.39391
\(896\) 32.9951 1.10229
\(897\) −20.3461 −0.679337
\(898\) −68.1158 −2.27305
\(899\) 2.86533 0.0955642
\(900\) −54.5999 −1.82000
\(901\) −14.3711 −0.478769
\(902\) 5.45345 0.181580
\(903\) 18.6153 0.619480
\(904\) 19.8788 0.661159
\(905\) −29.8494 −0.992226
\(906\) −33.7665 −1.12182
\(907\) −17.7545 −0.589529 −0.294764 0.955570i \(-0.595241\pi\)
−0.294764 + 0.955570i \(0.595241\pi\)
\(908\) 81.1919 2.69445
\(909\) 23.3510 0.774503
\(910\) 66.1056 2.19138
\(911\) −2.28856 −0.0758234 −0.0379117 0.999281i \(-0.512071\pi\)
−0.0379117 + 0.999281i \(0.512071\pi\)
\(912\) −5.78282 −0.191488
\(913\) −34.9978 −1.15826
\(914\) 101.680 3.36328
\(915\) 30.0535 0.993540
\(916\) −53.5098 −1.76801
\(917\) 3.67614 0.121397
\(918\) 39.6033 1.30710
\(919\) −45.8149 −1.51129 −0.755647 0.654979i \(-0.772678\pi\)
−0.755647 + 0.654979i \(0.772678\pi\)
\(920\) 105.518 3.47882
\(921\) 13.8848 0.457520
\(922\) 53.7474 1.77008
\(923\) −7.55931 −0.248818
\(924\) −17.8372 −0.586800
\(925\) 68.0701 2.23813
\(926\) −0.543971 −0.0178760
\(927\) 33.8914 1.11314
\(928\) 2.56639 0.0842458
\(929\) −4.74983 −0.155837 −0.0779184 0.996960i \(-0.524827\pi\)
−0.0779184 + 0.996960i \(0.524827\pi\)
\(930\) −20.3461 −0.667174
\(931\) −3.71747 −0.121835
\(932\) −21.1696 −0.693433
\(933\) 8.91530 0.291874
\(934\) 44.3811 1.45219
\(935\) −27.8888 −0.912060
\(936\) −51.3221 −1.67751
\(937\) −47.8492 −1.56317 −0.781583 0.623801i \(-0.785588\pi\)
−0.781583 + 0.623801i \(0.785588\pi\)
\(938\) −25.5524 −0.834316
\(939\) 20.8870 0.681622
\(940\) 176.108 5.74401
\(941\) −51.9422 −1.69327 −0.846633 0.532177i \(-0.821374\pi\)
−0.846633 + 0.532177i \(0.821374\pi\)
\(942\) 35.1967 1.14677
\(943\) 5.13260 0.167140
\(944\) −78.4757 −2.55417
\(945\) 29.5466 0.961152
\(946\) 66.1618 2.15111
\(947\) −16.2068 −0.526649 −0.263324 0.964707i \(-0.584819\pi\)
−0.263324 + 0.964707i \(0.584819\pi\)
\(948\) 49.5059 1.60788
\(949\) −37.7451 −1.22526
\(950\) −17.3041 −0.561420
\(951\) −6.96581 −0.225882
\(952\) 38.6412 1.25237
\(953\) −4.96897 −0.160961 −0.0804804 0.996756i \(-0.525645\pi\)
−0.0804804 + 0.996756i \(0.525645\pi\)
\(954\) 23.1741 0.750288
\(955\) 27.8746 0.902001
\(956\) −90.6817 −2.93286
\(957\) 2.12221 0.0686012
\(958\) −66.4269 −2.14615
\(959\) −22.9754 −0.741913
\(960\) 13.1050 0.422962
\(961\) −22.7899 −0.735157
\(962\) 121.057 3.90304
\(963\) −32.6959 −1.05361
\(964\) −10.7222 −0.345339
\(965\) −66.7323 −2.14819
\(966\) −24.7025 −0.794791
\(967\) −25.3463 −0.815082 −0.407541 0.913187i \(-0.633614\pi\)
−0.407541 + 0.913187i \(0.633614\pi\)
\(968\) 28.1127 0.903577
\(969\) 3.65290 0.117348
\(970\) −6.76976 −0.217364
\(971\) 48.9887 1.57212 0.786061 0.618149i \(-0.212117\pi\)
0.786061 + 0.618149i \(0.212117\pi\)
\(972\) −68.2149 −2.18800
\(973\) −1.98132 −0.0635181
\(974\) −21.2687 −0.681492
\(975\) 20.2645 0.648984
\(976\) −58.2808 −1.86552
\(977\) 45.2695 1.44830 0.724150 0.689642i \(-0.242232\pi\)
0.724150 + 0.689642i \(0.242232\pi\)
\(978\) 13.5396 0.432947
\(979\) 13.1169 0.419217
\(980\) −42.7170 −1.36454
\(981\) 11.5714 0.369447
\(982\) 85.0112 2.71282
\(983\) −19.1879 −0.611999 −0.305999 0.952032i \(-0.598991\pi\)
−0.305999 + 0.952032i \(0.598991\pi\)
\(984\) −4.33821 −0.138297
\(985\) −18.0209 −0.574195
\(986\) −8.69829 −0.277010
\(987\) −21.7908 −0.693608
\(988\) −20.9139 −0.665360
\(989\) 62.2693 1.98005
\(990\) 44.9720 1.42931
\(991\) 44.4239 1.41117 0.705586 0.708625i \(-0.250684\pi\)
0.705586 + 0.708625i \(0.250684\pi\)
\(992\) 7.35356 0.233476
\(993\) −0.713176 −0.0226319
\(994\) −9.17788 −0.291105
\(995\) 33.0712 1.04843
\(996\) 52.6748 1.66907
\(997\) −14.5930 −0.462166 −0.231083 0.972934i \(-0.574227\pi\)
−0.231083 + 0.972934i \(0.574227\pi\)
\(998\) 92.2214 2.91922
\(999\) 54.1079 1.71190
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 \(a_p\))