Properties

Label 4019.2.a.b.1.5
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 1.5
Character \(\chi\) = 4019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.72152 q^{2}\) \(-2.92759 q^{3}\) \(+5.40665 q^{4}\) \(-3.58721 q^{5}\) \(+7.96750 q^{6}\) \(-4.23646 q^{7}\) \(-9.27126 q^{8}\) \(+5.57081 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.72152 q^{2}\) \(-2.92759 q^{3}\) \(+5.40665 q^{4}\) \(-3.58721 q^{5}\) \(+7.96750 q^{6}\) \(-4.23646 q^{7}\) \(-9.27126 q^{8}\) \(+5.57081 q^{9}\) \(+9.76265 q^{10}\) \(-0.812006 q^{11}\) \(-15.8285 q^{12}\) \(+5.74531 q^{13}\) \(+11.5296 q^{14}\) \(+10.5019 q^{15}\) \(+14.4186 q^{16}\) \(-4.43616 q^{17}\) \(-15.1610 q^{18}\) \(+4.26293 q^{19}\) \(-19.3948 q^{20}\) \(+12.4026 q^{21}\) \(+2.20989 q^{22}\) \(+6.91630 q^{23}\) \(+27.1425 q^{24}\) \(+7.86806 q^{25}\) \(-15.6360 q^{26}\) \(-7.52628 q^{27}\) \(-22.9050 q^{28}\) \(+2.78340 q^{29}\) \(-28.5811 q^{30}\) \(+9.64726 q^{31}\) \(-20.6979 q^{32}\) \(+2.37722 q^{33}\) \(+12.0731 q^{34}\) \(+15.1970 q^{35}\) \(+30.1194 q^{36}\) \(+8.80524 q^{37}\) \(-11.6016 q^{38}\) \(-16.8199 q^{39}\) \(+33.2579 q^{40}\) \(+3.79424 q^{41}\) \(-33.7539 q^{42}\) \(-8.14223 q^{43}\) \(-4.39023 q^{44}\) \(-19.9836 q^{45}\) \(-18.8228 q^{46}\) \(+2.31756 q^{47}\) \(-42.2118 q^{48}\) \(+10.9476 q^{49}\) \(-21.4131 q^{50}\) \(+12.9873 q^{51}\) \(+31.0629 q^{52}\) \(+1.94360 q^{53}\) \(+20.4829 q^{54}\) \(+2.91283 q^{55}\) \(+39.2773 q^{56}\) \(-12.4801 q^{57}\) \(-7.57507 q^{58}\) \(-0.889207 q^{59}\) \(+56.7801 q^{60}\) \(-2.41942 q^{61}\) \(-26.2552 q^{62}\) \(-23.6005 q^{63}\) \(+27.4925 q^{64}\) \(-20.6096 q^{65}\) \(-6.46965 q^{66}\) \(+0.0402207 q^{67}\) \(-23.9848 q^{68}\) \(-20.2481 q^{69}\) \(-41.3590 q^{70}\) \(-0.981324 q^{71}\) \(-51.6484 q^{72}\) \(+7.25877 q^{73}\) \(-23.9636 q^{74}\) \(-23.0345 q^{75}\) \(+23.0482 q^{76}\) \(+3.44003 q^{77}\) \(+45.7757 q^{78}\) \(+2.14089 q^{79}\) \(-51.7225 q^{80}\) \(+5.32146 q^{81}\) \(-10.3261 q^{82}\) \(+9.08648 q^{83}\) \(+67.0567 q^{84}\) \(+15.9134 q^{85}\) \(+22.1592 q^{86}\) \(-8.14866 q^{87}\) \(+7.52832 q^{88}\) \(+3.14348 q^{89}\) \(+54.3858 q^{90}\) \(-24.3397 q^{91}\) \(+37.3941 q^{92}\) \(-28.2432 q^{93}\) \(-6.30727 q^{94}\) \(-15.2920 q^{95}\) \(+60.5951 q^{96}\) \(+16.7830 q^{97}\) \(-29.7940 q^{98}\) \(-4.52353 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut 50q^{10} \) \(\mathstrut +\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 17q^{12} \) \(\mathstrut +\mathstrut 113q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 252q^{16} \) \(\mathstrut +\mathstrut 35q^{17} \) \(\mathstrut +\mathstrut 13q^{18} \) \(\mathstrut +\mathstrut 97q^{19} \) \(\mathstrut +\mathstrut 55q^{20} \) \(\mathstrut +\mathstrut 115q^{21} \) \(\mathstrut +\mathstrut 14q^{22} \) \(\mathstrut +\mathstrut 27q^{23} \) \(\mathstrut +\mathstrut 122q^{24} \) \(\mathstrut +\mathstrut 244q^{25} \) \(\mathstrut +\mathstrut 39q^{26} \) \(\mathstrut +\mathstrut 34q^{27} \) \(\mathstrut +\mathstrut 66q^{28} \) \(\mathstrut +\mathstrut 91q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 135q^{31} \) \(\mathstrut +\mathstrut 21q^{32} \) \(\mathstrut +\mathstrut 32q^{33} \) \(\mathstrut +\mathstrut 58q^{34} \) \(\mathstrut +\mathstrut 17q^{35} \) \(\mathstrut +\mathstrut 273q^{36} \) \(\mathstrut +\mathstrut 133q^{37} \) \(\mathstrut -\mathstrut 3q^{38} \) \(\mathstrut +\mathstrut 55q^{39} \) \(\mathstrut +\mathstrut 142q^{40} \) \(\mathstrut +\mathstrut 97q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 67q^{43} \) \(\mathstrut +\mathstrut 44q^{44} \) \(\mathstrut +\mathstrut 154q^{45} \) \(\mathstrut +\mathstrut 101q^{46} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 312q^{49} \) \(\mathstrut +\mathstrut 21q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut +\mathstrut 193q^{52} \) \(\mathstrut +\mathstrut 22q^{53} \) \(\mathstrut +\mathstrut 141q^{54} \) \(\mathstrut +\mathstrut 88q^{55} \) \(\mathstrut +\mathstrut 28q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 62q^{58} \) \(\mathstrut +\mathstrut 41q^{59} \) \(\mathstrut +\mathstrut q^{60} \) \(\mathstrut +\mathstrut 377q^{61} \) \(\mathstrut +\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 39q^{63} \) \(\mathstrut +\mathstrut 311q^{64} \) \(\mathstrut +\mathstrut 21q^{65} \) \(\mathstrut +\mathstrut 35q^{66} \) \(\mathstrut +\mathstrut 42q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut +\mathstrut 137q^{69} \) \(\mathstrut +\mathstrut 35q^{70} \) \(\mathstrut +\mathstrut 17q^{71} \) \(\mathstrut -\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 213q^{73} \) \(\mathstrut -\mathstrut 9q^{74} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut +\mathstrut 242q^{76} \) \(\mathstrut +\mathstrut 60q^{77} \) \(\mathstrut +\mathstrut 103q^{79} \) \(\mathstrut +\mathstrut 80q^{80} \) \(\mathstrut +\mathstrut 270q^{81} \) \(\mathstrut +\mathstrut 84q^{82} \) \(\mathstrut +\mathstrut 42q^{83} \) \(\mathstrut +\mathstrut 137q^{84} \) \(\mathstrut +\mathstrut 294q^{85} \) \(\mathstrut -\mathstrut 9q^{86} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut +\mathstrut 78q^{89} \) \(\mathstrut +\mathstrut 69q^{90} \) \(\mathstrut +\mathstrut 118q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 51q^{93} \) \(\mathstrut +\mathstrut 93q^{94} \) \(\mathstrut +\mathstrut 10q^{95} \) \(\mathstrut +\mathstrut 260q^{96} \) \(\mathstrut +\mathstrut 142q^{97} \) \(\mathstrut -\mathstrut 31q^{98} \) \(\mathstrut +\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.72152 −1.92440 −0.962201 0.272339i \(-0.912203\pi\)
−0.962201 + 0.272339i \(0.912203\pi\)
\(3\) −2.92759 −1.69025 −0.845124 0.534571i \(-0.820473\pi\)
−0.845124 + 0.534571i \(0.820473\pi\)
\(4\) 5.40665 2.70333
\(5\) −3.58721 −1.60425 −0.802124 0.597157i \(-0.796297\pi\)
−0.802124 + 0.597157i \(0.796297\pi\)
\(6\) 7.96750 3.25272
\(7\) −4.23646 −1.60123 −0.800615 0.599179i \(-0.795494\pi\)
−0.800615 + 0.599179i \(0.795494\pi\)
\(8\) −9.27126 −3.27789
\(9\) 5.57081 1.85694
\(10\) 9.76265 3.08722
\(11\) −0.812006 −0.244829 −0.122414 0.992479i \(-0.539064\pi\)
−0.122414 + 0.992479i \(0.539064\pi\)
\(12\) −15.8285 −4.56929
\(13\) 5.74531 1.59346 0.796731 0.604334i \(-0.206561\pi\)
0.796731 + 0.604334i \(0.206561\pi\)
\(14\) 11.5296 3.08141
\(15\) 10.5019 2.71158
\(16\) 14.4186 3.60465
\(17\) −4.43616 −1.07593 −0.537964 0.842968i \(-0.680806\pi\)
−0.537964 + 0.842968i \(0.680806\pi\)
\(18\) −15.1610 −3.57349
\(19\) 4.26293 0.977982 0.488991 0.872289i \(-0.337365\pi\)
0.488991 + 0.872289i \(0.337365\pi\)
\(20\) −19.3948 −4.33681
\(21\) 12.4026 2.70647
\(22\) 2.20989 0.471149
\(23\) 6.91630 1.44215 0.721075 0.692858i \(-0.243649\pi\)
0.721075 + 0.692858i \(0.243649\pi\)
\(24\) 27.1425 5.54044
\(25\) 7.86806 1.57361
\(26\) −15.6360 −3.06646
\(27\) −7.52628 −1.44843
\(28\) −22.9050 −4.32865
\(29\) 2.78340 0.516864 0.258432 0.966029i \(-0.416794\pi\)
0.258432 + 0.966029i \(0.416794\pi\)
\(30\) −28.5811 −5.21816
\(31\) 9.64726 1.73270 0.866349 0.499439i \(-0.166460\pi\)
0.866349 + 0.499439i \(0.166460\pi\)
\(32\) −20.6979 −3.65891
\(33\) 2.37722 0.413821
\(34\) 12.0731 2.07052
\(35\) 15.1970 2.56877
\(36\) 30.1194 5.01990
\(37\) 8.80524 1.44757 0.723786 0.690024i \(-0.242400\pi\)
0.723786 + 0.690024i \(0.242400\pi\)
\(38\) −11.6016 −1.88203
\(39\) −16.8199 −2.69334
\(40\) 33.2579 5.25854
\(41\) 3.79424 0.592561 0.296281 0.955101i \(-0.404254\pi\)
0.296281 + 0.955101i \(0.404254\pi\)
\(42\) −33.7539 −5.20835
\(43\) −8.14223 −1.24168 −0.620839 0.783938i \(-0.713208\pi\)
−0.620839 + 0.783938i \(0.713208\pi\)
\(44\) −4.39023 −0.661852
\(45\) −19.9836 −2.97898
\(46\) −18.8228 −2.77528
\(47\) 2.31756 0.338050 0.169025 0.985612i \(-0.445938\pi\)
0.169025 + 0.985612i \(0.445938\pi\)
\(48\) −42.2118 −6.09275
\(49\) 10.9476 1.56394
\(50\) −21.4131 −3.02826
\(51\) 12.9873 1.81858
\(52\) 31.0629 4.30765
\(53\) 1.94360 0.266974 0.133487 0.991051i \(-0.457383\pi\)
0.133487 + 0.991051i \(0.457383\pi\)
\(54\) 20.4829 2.78737
\(55\) 2.91283 0.392766
\(56\) 39.2773 5.24865
\(57\) −12.4801 −1.65303
\(58\) −7.57507 −0.994655
\(59\) −0.889207 −0.115765 −0.0578825 0.998323i \(-0.518435\pi\)
−0.0578825 + 0.998323i \(0.518435\pi\)
\(60\) 56.7801 7.33027
\(61\) −2.41942 −0.309775 −0.154887 0.987932i \(-0.549501\pi\)
−0.154887 + 0.987932i \(0.549501\pi\)
\(62\) −26.2552 −3.33441
\(63\) −23.6005 −2.97338
\(64\) 27.4925 3.43657
\(65\) −20.6096 −2.55631
\(66\) −6.46965 −0.796359
\(67\) 0.0402207 0.00491374 0.00245687 0.999997i \(-0.499218\pi\)
0.00245687 + 0.999997i \(0.499218\pi\)
\(68\) −23.9848 −2.90858
\(69\) −20.2481 −2.43759
\(70\) −41.3590 −4.94335
\(71\) −0.981324 −0.116462 −0.0582309 0.998303i \(-0.518546\pi\)
−0.0582309 + 0.998303i \(0.518546\pi\)
\(72\) −51.6484 −6.08682
\(73\) 7.25877 0.849575 0.424788 0.905293i \(-0.360349\pi\)
0.424788 + 0.905293i \(0.360349\pi\)
\(74\) −23.9636 −2.78571
\(75\) −23.0345 −2.65979
\(76\) 23.0482 2.64381
\(77\) 3.44003 0.392027
\(78\) 45.7757 5.18308
\(79\) 2.14089 0.240869 0.120434 0.992721i \(-0.461571\pi\)
0.120434 + 0.992721i \(0.461571\pi\)
\(80\) −51.7225 −5.78275
\(81\) 5.32146 0.591273
\(82\) −10.3261 −1.14033
\(83\) 9.08648 0.997371 0.498685 0.866783i \(-0.333816\pi\)
0.498685 + 0.866783i \(0.333816\pi\)
\(84\) 67.0567 7.31648
\(85\) 15.9134 1.72606
\(86\) 22.1592 2.38949
\(87\) −8.14866 −0.873628
\(88\) 7.52832 0.802521
\(89\) 3.14348 0.333208 0.166604 0.986024i \(-0.446720\pi\)
0.166604 + 0.986024i \(0.446720\pi\)
\(90\) 54.3858 5.73277
\(91\) −24.3397 −2.55150
\(92\) 37.3941 3.89860
\(93\) −28.2432 −2.92869
\(94\) −6.30727 −0.650545
\(95\) −15.2920 −1.56893
\(96\) 60.5951 6.18446
\(97\) 16.7830 1.70406 0.852030 0.523493i \(-0.175371\pi\)
0.852030 + 0.523493i \(0.175371\pi\)
\(98\) −29.7940 −3.00964
\(99\) −4.52353 −0.454631
\(100\) 42.5399 4.25399
\(101\) 11.6058 1.15482 0.577410 0.816455i \(-0.304064\pi\)
0.577410 + 0.816455i \(0.304064\pi\)
\(102\) −35.3451 −3.49969
\(103\) −4.15549 −0.409452 −0.204726 0.978819i \(-0.565630\pi\)
−0.204726 + 0.978819i \(0.565630\pi\)
\(104\) −53.2663 −5.22319
\(105\) −44.4908 −4.34186
\(106\) −5.28954 −0.513766
\(107\) 18.5577 1.79404 0.897018 0.441994i \(-0.145729\pi\)
0.897018 + 0.441994i \(0.145729\pi\)
\(108\) −40.6920 −3.91559
\(109\) 3.88106 0.371738 0.185869 0.982574i \(-0.440490\pi\)
0.185869 + 0.982574i \(0.440490\pi\)
\(110\) −7.92732 −0.755841
\(111\) −25.7782 −2.44675
\(112\) −61.0837 −5.77187
\(113\) 9.87721 0.929170 0.464585 0.885528i \(-0.346203\pi\)
0.464585 + 0.885528i \(0.346203\pi\)
\(114\) 33.9648 3.18110
\(115\) −24.8102 −2.31356
\(116\) 15.0489 1.39725
\(117\) 32.0060 2.95896
\(118\) 2.41999 0.222778
\(119\) 18.7936 1.72281
\(120\) −97.3658 −8.88824
\(121\) −10.3406 −0.940059
\(122\) 6.58449 0.596132
\(123\) −11.1080 −1.00158
\(124\) 52.1594 4.68405
\(125\) −10.2883 −0.920216
\(126\) 64.2291 5.72198
\(127\) −17.0789 −1.51550 −0.757752 0.652543i \(-0.773702\pi\)
−0.757752 + 0.652543i \(0.773702\pi\)
\(128\) −33.4255 −2.95443
\(129\) 23.8371 2.09874
\(130\) 56.0894 4.91937
\(131\) 20.5294 1.79366 0.896831 0.442373i \(-0.145863\pi\)
0.896831 + 0.442373i \(0.145863\pi\)
\(132\) 12.8528 1.11869
\(133\) −18.0597 −1.56597
\(134\) −0.109461 −0.00945601
\(135\) 26.9983 2.32365
\(136\) 41.1288 3.52677
\(137\) −5.65378 −0.483035 −0.241518 0.970396i \(-0.577645\pi\)
−0.241518 + 0.970396i \(0.577645\pi\)
\(138\) 55.1056 4.69090
\(139\) −10.5136 −0.891750 −0.445875 0.895095i \(-0.647107\pi\)
−0.445875 + 0.895095i \(0.647107\pi\)
\(140\) 82.1652 6.94422
\(141\) −6.78486 −0.571389
\(142\) 2.67069 0.224119
\(143\) −4.66522 −0.390125
\(144\) 80.3232 6.69360
\(145\) −9.98463 −0.829178
\(146\) −19.7549 −1.63492
\(147\) −32.0500 −2.64344
\(148\) 47.6069 3.91326
\(149\) −13.1181 −1.07467 −0.537336 0.843368i \(-0.680569\pi\)
−0.537336 + 0.843368i \(0.680569\pi\)
\(150\) 62.6887 5.11851
\(151\) 19.2207 1.56416 0.782079 0.623179i \(-0.214159\pi\)
0.782079 + 0.623179i \(0.214159\pi\)
\(152\) −39.5227 −3.20572
\(153\) −24.7130 −1.99793
\(154\) −9.36209 −0.754418
\(155\) −34.6067 −2.77968
\(156\) −90.9395 −7.28099
\(157\) −12.8550 −1.02594 −0.512968 0.858407i \(-0.671454\pi\)
−0.512968 + 0.858407i \(0.671454\pi\)
\(158\) −5.82646 −0.463528
\(159\) −5.69008 −0.451252
\(160\) 74.2477 5.86980
\(161\) −29.3006 −2.30921
\(162\) −14.4824 −1.13785
\(163\) −1.47489 −0.115523 −0.0577613 0.998330i \(-0.518396\pi\)
−0.0577613 + 0.998330i \(0.518396\pi\)
\(164\) 20.5142 1.60189
\(165\) −8.52759 −0.663872
\(166\) −24.7290 −1.91934
\(167\) −23.1226 −1.78928 −0.894642 0.446784i \(-0.852569\pi\)
−0.894642 + 0.446784i \(0.852569\pi\)
\(168\) −114.988 −8.87151
\(169\) 20.0086 1.53912
\(170\) −43.3087 −3.32163
\(171\) 23.7479 1.81605
\(172\) −44.0222 −3.35666
\(173\) 16.3115 1.24014 0.620070 0.784546i \(-0.287104\pi\)
0.620070 + 0.784546i \(0.287104\pi\)
\(174\) 22.1767 1.68121
\(175\) −33.3327 −2.51971
\(176\) −11.7080 −0.882522
\(177\) 2.60324 0.195671
\(178\) −8.55503 −0.641227
\(179\) 10.6670 0.797286 0.398643 0.917106i \(-0.369481\pi\)
0.398643 + 0.917106i \(0.369481\pi\)
\(180\) −108.045 −8.05317
\(181\) −13.3600 −0.993038 −0.496519 0.868026i \(-0.665389\pi\)
−0.496519 + 0.868026i \(0.665389\pi\)
\(182\) 66.2410 4.91011
\(183\) 7.08308 0.523596
\(184\) −64.1229 −4.72720
\(185\) −31.5862 −2.32226
\(186\) 76.8645 5.63598
\(187\) 3.60219 0.263418
\(188\) 12.5302 0.913860
\(189\) 31.8847 2.31927
\(190\) 41.6174 3.01925
\(191\) −17.0514 −1.23380 −0.616899 0.787042i \(-0.711611\pi\)
−0.616899 + 0.787042i \(0.711611\pi\)
\(192\) −80.4869 −5.80864
\(193\) 22.5712 1.62471 0.812355 0.583163i \(-0.198185\pi\)
0.812355 + 0.583163i \(0.198185\pi\)
\(194\) −45.6753 −3.27930
\(195\) 60.3366 4.32079
\(196\) 59.1896 4.22783
\(197\) −3.45743 −0.246332 −0.123166 0.992386i \(-0.539305\pi\)
−0.123166 + 0.992386i \(0.539305\pi\)
\(198\) 12.3108 0.874894
\(199\) −23.4836 −1.66471 −0.832354 0.554245i \(-0.813007\pi\)
−0.832354 + 0.554245i \(0.813007\pi\)
\(200\) −72.9469 −5.15812
\(201\) −0.117750 −0.00830543
\(202\) −31.5853 −2.22234
\(203\) −11.7917 −0.827618
\(204\) 70.2178 4.91623
\(205\) −13.6107 −0.950615
\(206\) 11.3092 0.787951
\(207\) 38.5294 2.67798
\(208\) 82.8392 5.74387
\(209\) −3.46152 −0.239438
\(210\) 121.082 8.35548
\(211\) 1.69143 0.116443 0.0582214 0.998304i \(-0.481457\pi\)
0.0582214 + 0.998304i \(0.481457\pi\)
\(212\) 10.5084 0.721718
\(213\) 2.87292 0.196849
\(214\) −50.5050 −3.45245
\(215\) 29.2079 1.99196
\(216\) 69.7781 4.74780
\(217\) −40.8702 −2.77445
\(218\) −10.5624 −0.715374
\(219\) −21.2507 −1.43599
\(220\) 15.7487 1.06178
\(221\) −25.4871 −1.71445
\(222\) 70.1557 4.70854
\(223\) 14.7662 0.988818 0.494409 0.869229i \(-0.335384\pi\)
0.494409 + 0.869229i \(0.335384\pi\)
\(224\) 87.6858 5.85875
\(225\) 43.8314 2.92210
\(226\) −26.8810 −1.78810
\(227\) 13.9001 0.922584 0.461292 0.887248i \(-0.347386\pi\)
0.461292 + 0.887248i \(0.347386\pi\)
\(228\) −67.4757 −4.46868
\(229\) 13.6588 0.902600 0.451300 0.892372i \(-0.350960\pi\)
0.451300 + 0.892372i \(0.350960\pi\)
\(230\) 67.5214 4.45223
\(231\) −10.0710 −0.662623
\(232\) −25.8056 −1.69422
\(233\) 6.02562 0.394751 0.197376 0.980328i \(-0.436758\pi\)
0.197376 + 0.980328i \(0.436758\pi\)
\(234\) −87.1048 −5.69422
\(235\) −8.31356 −0.542317
\(236\) −4.80764 −0.312950
\(237\) −6.26765 −0.407127
\(238\) −51.1471 −3.31538
\(239\) −8.55872 −0.553617 −0.276809 0.960925i \(-0.589277\pi\)
−0.276809 + 0.960925i \(0.589277\pi\)
\(240\) 151.422 9.77428
\(241\) 26.3532 1.69756 0.848781 0.528745i \(-0.177337\pi\)
0.848781 + 0.528745i \(0.177337\pi\)
\(242\) 28.1422 1.80905
\(243\) 6.99975 0.449034
\(244\) −13.0810 −0.837423
\(245\) −39.2712 −2.50894
\(246\) 30.2306 1.92743
\(247\) 24.4918 1.55838
\(248\) −89.4422 −5.67959
\(249\) −26.6015 −1.68580
\(250\) 27.9999 1.77087
\(251\) −28.7461 −1.81444 −0.907219 0.420659i \(-0.861799\pi\)
−0.907219 + 0.420659i \(0.861799\pi\)
\(252\) −127.600 −8.03802
\(253\) −5.61608 −0.353080
\(254\) 46.4804 2.91644
\(255\) −46.5881 −2.91746
\(256\) 35.9831 2.24895
\(257\) −11.0973 −0.692234 −0.346117 0.938191i \(-0.612500\pi\)
−0.346117 + 0.938191i \(0.612500\pi\)
\(258\) −64.8732 −4.03883
\(259\) −37.3030 −2.31790
\(260\) −111.429 −6.91053
\(261\) 15.5058 0.959783
\(262\) −55.8711 −3.45173
\(263\) −2.42736 −0.149678 −0.0748389 0.997196i \(-0.523844\pi\)
−0.0748389 + 0.997196i \(0.523844\pi\)
\(264\) −22.0399 −1.35646
\(265\) −6.97210 −0.428293
\(266\) 49.1498 3.01357
\(267\) −9.20283 −0.563204
\(268\) 0.217459 0.0132834
\(269\) 20.0193 1.22060 0.610300 0.792171i \(-0.291049\pi\)
0.610300 + 0.792171i \(0.291049\pi\)
\(270\) −73.4764 −4.47163
\(271\) 2.02599 0.123070 0.0615350 0.998105i \(-0.480400\pi\)
0.0615350 + 0.998105i \(0.480400\pi\)
\(272\) −63.9632 −3.87834
\(273\) 71.2569 4.31266
\(274\) 15.3869 0.929555
\(275\) −6.38891 −0.385266
\(276\) −109.475 −6.58960
\(277\) 4.70577 0.282742 0.141371 0.989957i \(-0.454849\pi\)
0.141371 + 0.989957i \(0.454849\pi\)
\(278\) 28.6129 1.71609
\(279\) 53.7430 3.21751
\(280\) −140.896 −8.42014
\(281\) 18.4735 1.10204 0.551019 0.834493i \(-0.314239\pi\)
0.551019 + 0.834493i \(0.314239\pi\)
\(282\) 18.4651 1.09958
\(283\) 6.06426 0.360483 0.180241 0.983622i \(-0.442312\pi\)
0.180241 + 0.983622i \(0.442312\pi\)
\(284\) −5.30568 −0.314834
\(285\) 44.7688 2.65187
\(286\) 12.6965 0.750759
\(287\) −16.0741 −0.948827
\(288\) −115.304 −6.79436
\(289\) 2.67956 0.157621
\(290\) 27.1733 1.59567
\(291\) −49.1339 −2.88028
\(292\) 39.2457 2.29668
\(293\) 28.1158 1.64254 0.821272 0.570536i \(-0.193265\pi\)
0.821272 + 0.570536i \(0.193265\pi\)
\(294\) 87.2246 5.08704
\(295\) 3.18977 0.185716
\(296\) −81.6357 −4.74498
\(297\) 6.11138 0.354618
\(298\) 35.7010 2.06810
\(299\) 39.7363 2.29801
\(300\) −124.539 −7.19029
\(301\) 34.4942 1.98821
\(302\) −52.3094 −3.01007
\(303\) −33.9770 −1.95193
\(304\) 61.4654 3.52528
\(305\) 8.67896 0.496956
\(306\) 67.2569 3.84482
\(307\) 5.80774 0.331465 0.165733 0.986171i \(-0.447001\pi\)
0.165733 + 0.986171i \(0.447001\pi\)
\(308\) 18.5990 1.05978
\(309\) 12.1656 0.692076
\(310\) 94.1827 5.34922
\(311\) −3.27688 −0.185815 −0.0929073 0.995675i \(-0.529616\pi\)
−0.0929073 + 0.995675i \(0.529616\pi\)
\(312\) 155.942 8.82848
\(313\) 17.6891 0.999847 0.499924 0.866070i \(-0.333361\pi\)
0.499924 + 0.866070i \(0.333361\pi\)
\(314\) 34.9850 1.97432
\(315\) 84.6598 4.77004
\(316\) 11.5750 0.651147
\(317\) −28.9691 −1.62707 −0.813534 0.581517i \(-0.802459\pi\)
−0.813534 + 0.581517i \(0.802459\pi\)
\(318\) 15.4856 0.868391
\(319\) −2.26014 −0.126543
\(320\) −98.6214 −5.51310
\(321\) −54.3293 −3.03236
\(322\) 79.7421 4.44385
\(323\) −18.9110 −1.05224
\(324\) 28.7713 1.59841
\(325\) 45.2044 2.50749
\(326\) 4.01395 0.222312
\(327\) −11.3622 −0.628330
\(328\) −35.1774 −1.94235
\(329\) −9.81823 −0.541296
\(330\) 23.2080 1.27756
\(331\) −21.1733 −1.16379 −0.581895 0.813264i \(-0.697689\pi\)
−0.581895 + 0.813264i \(0.697689\pi\)
\(332\) 49.1274 2.69622
\(333\) 49.0523 2.68805
\(334\) 62.9287 3.44330
\(335\) −0.144280 −0.00788286
\(336\) 178.828 9.75589
\(337\) 15.7193 0.856283 0.428141 0.903712i \(-0.359169\pi\)
0.428141 + 0.903712i \(0.359169\pi\)
\(338\) −54.4536 −2.96189
\(339\) −28.9165 −1.57053
\(340\) 86.0385 4.66609
\(341\) −7.83363 −0.424215
\(342\) −64.6304 −3.49481
\(343\) −16.7237 −0.902993
\(344\) 75.4888 4.07008
\(345\) 72.6342 3.91050
\(346\) −44.3920 −2.38653
\(347\) 1.71236 0.0919241 0.0459621 0.998943i \(-0.485365\pi\)
0.0459621 + 0.998943i \(0.485365\pi\)
\(348\) −44.0570 −2.36170
\(349\) 30.4210 1.62840 0.814200 0.580584i \(-0.197176\pi\)
0.814200 + 0.580584i \(0.197176\pi\)
\(350\) 90.7155 4.84895
\(351\) −43.2408 −2.30802
\(352\) 16.8068 0.895806
\(353\) 3.10716 0.165378 0.0826888 0.996575i \(-0.473649\pi\)
0.0826888 + 0.996575i \(0.473649\pi\)
\(354\) −7.08476 −0.376551
\(355\) 3.52021 0.186834
\(356\) 16.9957 0.900771
\(357\) −55.0201 −2.91197
\(358\) −29.0303 −1.53430
\(359\) 14.1718 0.747961 0.373981 0.927437i \(-0.377993\pi\)
0.373981 + 0.927437i \(0.377993\pi\)
\(360\) 185.274 9.76477
\(361\) −0.827461 −0.0435506
\(362\) 36.3594 1.91101
\(363\) 30.2732 1.58893
\(364\) −131.597 −6.89753
\(365\) −26.0387 −1.36293
\(366\) −19.2767 −1.00761
\(367\) −11.9927 −0.626015 −0.313007 0.949751i \(-0.601336\pi\)
−0.313007 + 0.949751i \(0.601336\pi\)
\(368\) 99.7234 5.19844
\(369\) 21.1370 1.10035
\(370\) 85.9624 4.46897
\(371\) −8.23398 −0.427487
\(372\) −152.701 −7.91720
\(373\) 23.7254 1.22846 0.614228 0.789128i \(-0.289467\pi\)
0.614228 + 0.789128i \(0.289467\pi\)
\(374\) −9.80342 −0.506923
\(375\) 30.1200 1.55539
\(376\) −21.4867 −1.10809
\(377\) 15.9915 0.823603
\(378\) −86.7748 −4.46322
\(379\) −13.6922 −0.703320 −0.351660 0.936128i \(-0.614383\pi\)
−0.351660 + 0.936128i \(0.614383\pi\)
\(380\) −82.6785 −4.24132
\(381\) 50.0000 2.56158
\(382\) 46.4057 2.37432
\(383\) 27.5624 1.40837 0.704187 0.710014i \(-0.251312\pi\)
0.704187 + 0.710014i \(0.251312\pi\)
\(384\) 97.8564 4.99371
\(385\) −12.3401 −0.628909
\(386\) −61.4279 −3.12660
\(387\) −45.3588 −2.30572
\(388\) 90.7401 4.60663
\(389\) 23.2389 1.17826 0.589129 0.808039i \(-0.299471\pi\)
0.589129 + 0.808039i \(0.299471\pi\)
\(390\) −164.207 −8.31494
\(391\) −30.6819 −1.55165
\(392\) −101.498 −5.12641
\(393\) −60.1018 −3.03173
\(394\) 9.40945 0.474041
\(395\) −7.67981 −0.386413
\(396\) −24.4571 −1.22902
\(397\) −2.53242 −0.127099 −0.0635493 0.997979i \(-0.520242\pi\)
−0.0635493 + 0.997979i \(0.520242\pi\)
\(398\) 63.9110 3.20357
\(399\) 52.8715 2.64688
\(400\) 113.446 5.67232
\(401\) 15.6560 0.781823 0.390912 0.920428i \(-0.372160\pi\)
0.390912 + 0.920428i \(0.372160\pi\)
\(402\) 0.320458 0.0159830
\(403\) 55.4265 2.76099
\(404\) 62.7485 3.12185
\(405\) −19.0892 −0.948549
\(406\) 32.0914 1.59267
\(407\) −7.14990 −0.354407
\(408\) −120.409 −5.96111
\(409\) 10.6639 0.527298 0.263649 0.964619i \(-0.415074\pi\)
0.263649 + 0.964619i \(0.415074\pi\)
\(410\) 37.0419 1.82937
\(411\) 16.5520 0.816449
\(412\) −22.4673 −1.10688
\(413\) 3.76709 0.185366
\(414\) −104.858 −5.15351
\(415\) −32.5951 −1.60003
\(416\) −118.916 −5.83033
\(417\) 30.7795 1.50728
\(418\) 9.42058 0.460776
\(419\) −17.6880 −0.864113 −0.432057 0.901847i \(-0.642212\pi\)
−0.432057 + 0.901847i \(0.642212\pi\)
\(420\) −240.546 −11.7375
\(421\) −5.54481 −0.270238 −0.135119 0.990829i \(-0.543142\pi\)
−0.135119 + 0.990829i \(0.543142\pi\)
\(422\) −4.60325 −0.224083
\(423\) 12.9107 0.627738
\(424\) −18.0196 −0.875111
\(425\) −34.9040 −1.69309
\(426\) −7.81870 −0.378817
\(427\) 10.2498 0.496021
\(428\) 100.335 4.84987
\(429\) 13.6579 0.659408
\(430\) −79.4897 −3.83333
\(431\) −14.7614 −0.711031 −0.355515 0.934670i \(-0.615695\pi\)
−0.355515 + 0.934670i \(0.615695\pi\)
\(432\) −108.518 −5.22109
\(433\) −23.9551 −1.15121 −0.575603 0.817729i \(-0.695233\pi\)
−0.575603 + 0.817729i \(0.695233\pi\)
\(434\) 111.229 5.33916
\(435\) 29.2309 1.40152
\(436\) 20.9836 1.00493
\(437\) 29.4837 1.41040
\(438\) 57.8342 2.76343
\(439\) 17.5216 0.836261 0.418130 0.908387i \(-0.362686\pi\)
0.418130 + 0.908387i \(0.362686\pi\)
\(440\) −27.0056 −1.28744
\(441\) 60.9867 2.90413
\(442\) 69.3637 3.29929
\(443\) −29.6975 −1.41097 −0.705485 0.708724i \(-0.749271\pi\)
−0.705485 + 0.708724i \(0.749271\pi\)
\(444\) −139.374 −6.61438
\(445\) −11.2763 −0.534549
\(446\) −40.1865 −1.90288
\(447\) 38.4043 1.81646
\(448\) −116.471 −5.50273
\(449\) 11.7012 0.552213 0.276106 0.961127i \(-0.410956\pi\)
0.276106 + 0.961127i \(0.410956\pi\)
\(450\) −119.288 −5.62329
\(451\) −3.08095 −0.145076
\(452\) 53.4027 2.51185
\(453\) −56.2704 −2.64381
\(454\) −37.8294 −1.77542
\(455\) 87.3117 4.09324
\(456\) 115.706 5.41845
\(457\) −21.8411 −1.02168 −0.510841 0.859675i \(-0.670666\pi\)
−0.510841 + 0.859675i \(0.670666\pi\)
\(458\) −37.1727 −1.73697
\(459\) 33.3878 1.55841
\(460\) −134.140 −6.25432
\(461\) −4.01641 −0.187063 −0.0935315 0.995616i \(-0.529816\pi\)
−0.0935315 + 0.995616i \(0.529816\pi\)
\(462\) 27.4084 1.27515
\(463\) −19.4102 −0.902070 −0.451035 0.892506i \(-0.648945\pi\)
−0.451035 + 0.892506i \(0.648945\pi\)
\(464\) 40.1327 1.86311
\(465\) 101.314 4.69834
\(466\) −16.3988 −0.759660
\(467\) 19.9888 0.924971 0.462486 0.886627i \(-0.346958\pi\)
0.462486 + 0.886627i \(0.346958\pi\)
\(468\) 173.045 7.99902
\(469\) −0.170393 −0.00786803
\(470\) 22.6255 1.04364
\(471\) 37.6341 1.73409
\(472\) 8.24408 0.379464
\(473\) 6.61154 0.303999
\(474\) 17.0575 0.783477
\(475\) 33.5410 1.53896
\(476\) 101.611 4.65731
\(477\) 10.8274 0.495754
\(478\) 23.2927 1.06538
\(479\) 15.4074 0.703980 0.351990 0.936004i \(-0.385505\pi\)
0.351990 + 0.936004i \(0.385505\pi\)
\(480\) −217.367 −9.92141
\(481\) 50.5888 2.30665
\(482\) −71.7208 −3.26679
\(483\) 85.7803 3.90314
\(484\) −55.9083 −2.54129
\(485\) −60.2043 −2.73373
\(486\) −19.0499 −0.864123
\(487\) −4.73181 −0.214419 −0.107209 0.994236i \(-0.534192\pi\)
−0.107209 + 0.994236i \(0.534192\pi\)
\(488\) 22.4311 1.01541
\(489\) 4.31789 0.195262
\(490\) 106.877 4.82822
\(491\) 0.750374 0.0338639 0.0169320 0.999857i \(-0.494610\pi\)
0.0169320 + 0.999857i \(0.494610\pi\)
\(492\) −60.0571 −2.70758
\(493\) −12.3476 −0.556109
\(494\) −66.6549 −2.99895
\(495\) 16.2268 0.729342
\(496\) 139.100 6.24577
\(497\) 4.15734 0.186482
\(498\) 72.3965 3.24416
\(499\) 41.9809 1.87932 0.939661 0.342107i \(-0.111141\pi\)
0.939661 + 0.342107i \(0.111141\pi\)
\(500\) −55.6254 −2.48764
\(501\) 67.6937 3.02433
\(502\) 78.2330 3.49171
\(503\) 9.47672 0.422546 0.211273 0.977427i \(-0.432239\pi\)
0.211273 + 0.977427i \(0.432239\pi\)
\(504\) 218.806 9.74640
\(505\) −41.6324 −1.85262
\(506\) 15.2842 0.679468
\(507\) −58.5769 −2.60149
\(508\) −92.3395 −4.09690
\(509\) 4.03027 0.178639 0.0893193 0.996003i \(-0.471531\pi\)
0.0893193 + 0.996003i \(0.471531\pi\)
\(510\) 126.790 5.61437
\(511\) −30.7515 −1.36036
\(512\) −31.0776 −1.37345
\(513\) −32.0840 −1.41654
\(514\) 30.2016 1.33214
\(515\) 14.9066 0.656863
\(516\) 128.879 5.67359
\(517\) −1.88187 −0.0827645
\(518\) 101.521 4.46056
\(519\) −47.7535 −2.09614
\(520\) 191.077 8.37929
\(521\) −40.8989 −1.79182 −0.895908 0.444240i \(-0.853474\pi\)
−0.895908 + 0.444240i \(0.853474\pi\)
\(522\) −42.1992 −1.84701
\(523\) 14.2369 0.622535 0.311267 0.950322i \(-0.399247\pi\)
0.311267 + 0.950322i \(0.399247\pi\)
\(524\) 110.995 4.84886
\(525\) 97.5846 4.25894
\(526\) 6.60611 0.288040
\(527\) −42.7968 −1.86426
\(528\) 34.2762 1.49168
\(529\) 24.8353 1.07979
\(530\) 18.9747 0.824208
\(531\) −4.95360 −0.214968
\(532\) −97.6425 −4.23334
\(533\) 21.7991 0.944224
\(534\) 25.0457 1.08383
\(535\) −66.5702 −2.87808
\(536\) −0.372897 −0.0161067
\(537\) −31.2285 −1.34761
\(538\) −54.4829 −2.34892
\(539\) −8.88948 −0.382897
\(540\) 145.971 6.28157
\(541\) 34.2061 1.47064 0.735318 0.677722i \(-0.237033\pi\)
0.735318 + 0.677722i \(0.237033\pi\)
\(542\) −5.51376 −0.236836
\(543\) 39.1125 1.67848
\(544\) 91.8193 3.93672
\(545\) −13.9222 −0.596361
\(546\) −193.927 −8.29930
\(547\) 3.59229 0.153595 0.0767975 0.997047i \(-0.475530\pi\)
0.0767975 + 0.997047i \(0.475530\pi\)
\(548\) −30.5680 −1.30580
\(549\) −13.4781 −0.575232
\(550\) 17.3875 0.741406
\(551\) 11.8654 0.505484
\(552\) 187.726 7.99014
\(553\) −9.06977 −0.385686
\(554\) −12.8068 −0.544110
\(555\) 92.4716 3.92520
\(556\) −56.8432 −2.41069
\(557\) −22.3462 −0.946837 −0.473419 0.880837i \(-0.656980\pi\)
−0.473419 + 0.880837i \(0.656980\pi\)
\(558\) −146.262 −6.19178
\(559\) −46.7796 −1.97857
\(560\) 219.120 9.25951
\(561\) −10.5458 −0.445242
\(562\) −50.2760 −2.12077
\(563\) −35.0493 −1.47715 −0.738576 0.674170i \(-0.764502\pi\)
−0.738576 + 0.674170i \(0.764502\pi\)
\(564\) −36.6834 −1.54465
\(565\) −35.4316 −1.49062
\(566\) −16.5040 −0.693714
\(567\) −22.5441 −0.946765
\(568\) 9.09812 0.381748
\(569\) 15.3310 0.642711 0.321355 0.946959i \(-0.395862\pi\)
0.321355 + 0.946959i \(0.395862\pi\)
\(570\) −121.839 −5.10327
\(571\) −17.4641 −0.730851 −0.365425 0.930841i \(-0.619076\pi\)
−0.365425 + 0.930841i \(0.619076\pi\)
\(572\) −25.2232 −1.05464
\(573\) 49.9197 2.08542
\(574\) 43.7461 1.82593
\(575\) 54.4179 2.26938
\(576\) 153.156 6.38148
\(577\) 11.6577 0.485317 0.242658 0.970112i \(-0.421981\pi\)
0.242658 + 0.970112i \(0.421981\pi\)
\(578\) −7.29246 −0.303326
\(579\) −66.0793 −2.74616
\(580\) −53.9834 −2.24154
\(581\) −38.4945 −1.59702
\(582\) 133.719 5.54282
\(583\) −1.57821 −0.0653630
\(584\) −67.2980 −2.78481
\(585\) −114.812 −4.74690
\(586\) −76.5177 −3.16092
\(587\) 12.9078 0.532761 0.266380 0.963868i \(-0.414172\pi\)
0.266380 + 0.963868i \(0.414172\pi\)
\(588\) −173.283 −7.14608
\(589\) 41.1255 1.69455
\(590\) −8.68102 −0.357392
\(591\) 10.1220 0.416361
\(592\) 126.959 5.21799
\(593\) 38.6077 1.58543 0.792713 0.609595i \(-0.208668\pi\)
0.792713 + 0.609595i \(0.208668\pi\)
\(594\) −16.6322 −0.682428
\(595\) −67.4166 −2.76381
\(596\) −70.9247 −2.90519
\(597\) 68.7504 2.81377
\(598\) −108.143 −4.42230
\(599\) −23.3478 −0.953967 −0.476983 0.878912i \(-0.658270\pi\)
−0.476983 + 0.878912i \(0.658270\pi\)
\(600\) 213.559 8.71850
\(601\) 16.0281 0.653800 0.326900 0.945059i \(-0.393996\pi\)
0.326900 + 0.945059i \(0.393996\pi\)
\(602\) −93.8765 −3.82612
\(603\) 0.224062 0.00912450
\(604\) 103.920 4.22843
\(605\) 37.0940 1.50809
\(606\) 92.4691 3.75630
\(607\) −14.5367 −0.590025 −0.295013 0.955493i \(-0.595324\pi\)
−0.295013 + 0.955493i \(0.595324\pi\)
\(608\) −88.2337 −3.57835
\(609\) 34.5214 1.39888
\(610\) −23.6199 −0.956343
\(611\) 13.3151 0.538670
\(612\) −133.615 −5.40105
\(613\) 17.1730 0.693611 0.346805 0.937937i \(-0.387266\pi\)
0.346805 + 0.937937i \(0.387266\pi\)
\(614\) −15.8059 −0.637873
\(615\) 39.8467 1.60677
\(616\) −31.8934 −1.28502
\(617\) −16.3183 −0.656952 −0.328476 0.944512i \(-0.606535\pi\)
−0.328476 + 0.944512i \(0.606535\pi\)
\(618\) −33.1088 −1.33183
\(619\) 10.2398 0.411571 0.205786 0.978597i \(-0.434025\pi\)
0.205786 + 0.978597i \(0.434025\pi\)
\(620\) −187.106 −7.51438
\(621\) −52.0540 −2.08886
\(622\) 8.91808 0.357582
\(623\) −13.3172 −0.533543
\(624\) −242.520 −9.70856
\(625\) −2.43393 −0.0973574
\(626\) −48.1412 −1.92411
\(627\) 10.1339 0.404710
\(628\) −69.5023 −2.77344
\(629\) −39.0615 −1.55748
\(630\) −230.403 −9.17948
\(631\) −36.7811 −1.46423 −0.732116 0.681180i \(-0.761467\pi\)
−0.732116 + 0.681180i \(0.761467\pi\)
\(632\) −19.8487 −0.789540
\(633\) −4.95182 −0.196817
\(634\) 78.8400 3.13114
\(635\) 61.2654 2.43124
\(636\) −30.7643 −1.21988
\(637\) 62.8971 2.49207
\(638\) 6.15100 0.243520
\(639\) −5.46677 −0.216262
\(640\) 119.904 4.73964
\(641\) −20.5764 −0.812721 −0.406360 0.913713i \(-0.633202\pi\)
−0.406360 + 0.913713i \(0.633202\pi\)
\(642\) 147.858 5.83549
\(643\) −44.2443 −1.74483 −0.872413 0.488770i \(-0.837446\pi\)
−0.872413 + 0.488770i \(0.837446\pi\)
\(644\) −158.418 −6.24255
\(645\) −85.5088 −3.36691
\(646\) 51.4667 2.02493
\(647\) −23.6724 −0.930658 −0.465329 0.885138i \(-0.654064\pi\)
−0.465329 + 0.885138i \(0.654064\pi\)
\(648\) −49.3367 −1.93813
\(649\) 0.722041 0.0283426
\(650\) −123.025 −4.82542
\(651\) 119.651 4.68950
\(652\) −7.97425 −0.312296
\(653\) 30.3736 1.18861 0.594306 0.804239i \(-0.297427\pi\)
0.594306 + 0.804239i \(0.297427\pi\)
\(654\) 30.9224 1.20916
\(655\) −73.6432 −2.87748
\(656\) 54.7076 2.13597
\(657\) 40.4372 1.57761
\(658\) 26.7205 1.04167
\(659\) 48.8388 1.90249 0.951246 0.308434i \(-0.0998050\pi\)
0.951246 + 0.308434i \(0.0998050\pi\)
\(660\) −46.1057 −1.79466
\(661\) −36.0454 −1.40200 −0.701002 0.713159i \(-0.747264\pi\)
−0.701002 + 0.713159i \(0.747264\pi\)
\(662\) 57.6235 2.23960
\(663\) 74.6160 2.89784
\(664\) −84.2431 −3.26927
\(665\) 64.7839 2.51221
\(666\) −133.497 −5.17289
\(667\) 19.2508 0.745395
\(668\) −125.016 −4.83702
\(669\) −43.2294 −1.67135
\(670\) 0.392660 0.0151698
\(671\) 1.96458 0.0758418
\(672\) −256.708 −9.90274
\(673\) −12.3602 −0.476451 −0.238225 0.971210i \(-0.576566\pi\)
−0.238225 + 0.971210i \(0.576566\pi\)
\(674\) −42.7802 −1.64783
\(675\) −59.2172 −2.27927
\(676\) 108.179 4.16074
\(677\) −4.89405 −0.188094 −0.0940469 0.995568i \(-0.529980\pi\)
−0.0940469 + 0.995568i \(0.529980\pi\)
\(678\) 78.6967 3.02233
\(679\) −71.1006 −2.72859
\(680\) −147.538 −5.65781
\(681\) −40.6939 −1.55940
\(682\) 21.3193 0.816360
\(683\) −10.0611 −0.384976 −0.192488 0.981299i \(-0.561656\pi\)
−0.192488 + 0.981299i \(0.561656\pi\)
\(684\) 128.397 4.90938
\(685\) 20.2813 0.774909
\(686\) 45.5137 1.73772
\(687\) −39.9875 −1.52562
\(688\) −117.400 −4.47581
\(689\) 11.1666 0.425413
\(690\) −197.675 −7.52537
\(691\) 21.1330 0.803939 0.401970 0.915653i \(-0.368326\pi\)
0.401970 + 0.915653i \(0.368326\pi\)
\(692\) 88.1906 3.35251
\(693\) 19.1637 0.727969
\(694\) −4.66021 −0.176899
\(695\) 37.7144 1.43059
\(696\) 75.5484 2.86365
\(697\) −16.8319 −0.637553
\(698\) −82.7913 −3.13370
\(699\) −17.6406 −0.667227
\(700\) −180.218 −6.81161
\(701\) −22.3977 −0.845949 −0.422974 0.906142i \(-0.639014\pi\)
−0.422974 + 0.906142i \(0.639014\pi\)
\(702\) 117.680 4.44156
\(703\) 37.5361 1.41570
\(704\) −22.3241 −0.841370
\(705\) 24.3387 0.916649
\(706\) −8.45619 −0.318253
\(707\) −49.1674 −1.84913
\(708\) 14.0748 0.528964
\(709\) −11.1195 −0.417601 −0.208801 0.977958i \(-0.566956\pi\)
−0.208801 + 0.977958i \(0.566956\pi\)
\(710\) −9.58032 −0.359543
\(711\) 11.9265 0.447277
\(712\) −29.1440 −1.09222
\(713\) 66.7234 2.49881
\(714\) 149.738 5.60381
\(715\) 16.7351 0.625858
\(716\) 57.6725 2.15532
\(717\) 25.0564 0.935750
\(718\) −38.5689 −1.43938
\(719\) 29.1072 1.08551 0.542757 0.839890i \(-0.317380\pi\)
0.542757 + 0.839890i \(0.317380\pi\)
\(720\) −288.136 −10.7382
\(721\) 17.6045 0.655627
\(722\) 2.25195 0.0838089
\(723\) −77.1516 −2.86930
\(724\) −72.2327 −2.68451
\(725\) 21.8999 0.813344
\(726\) −82.3891 −3.05774
\(727\) −19.7599 −0.732854 −0.366427 0.930447i \(-0.619419\pi\)
−0.366427 + 0.930447i \(0.619419\pi\)
\(728\) 225.660 8.36352
\(729\) −36.4568 −1.35025
\(730\) 70.8648 2.62282
\(731\) 36.1203 1.33596
\(732\) 38.2957 1.41545
\(733\) −3.19649 −0.118065 −0.0590326 0.998256i \(-0.518802\pi\)
−0.0590326 + 0.998256i \(0.518802\pi\)
\(734\) 32.6384 1.20471
\(735\) 114.970 4.24073
\(736\) −143.153 −5.27669
\(737\) −0.0326594 −0.00120303
\(738\) −57.5247 −2.11751
\(739\) 23.4764 0.863595 0.431797 0.901971i \(-0.357880\pi\)
0.431797 + 0.901971i \(0.357880\pi\)
\(740\) −170.776 −6.27784
\(741\) −71.7021 −2.63404
\(742\) 22.4089 0.822657
\(743\) 22.2324 0.815626 0.407813 0.913065i \(-0.366291\pi\)
0.407813 + 0.913065i \(0.366291\pi\)
\(744\) 261.851 9.59991
\(745\) 47.0572 1.72404
\(746\) −64.5692 −2.36405
\(747\) 50.6190 1.85205
\(748\) 19.4758 0.712106
\(749\) −78.6187 −2.87266
\(750\) −81.9722 −2.99320
\(751\) 53.0732 1.93667 0.968334 0.249659i \(-0.0803184\pi\)
0.968334 + 0.249659i \(0.0803184\pi\)
\(752\) 33.4159 1.21855
\(753\) 84.1569 3.06685
\(754\) −43.5211 −1.58494
\(755\) −68.9486 −2.50930
\(756\) 172.390 6.26975
\(757\) −24.7941 −0.901158 −0.450579 0.892737i \(-0.648782\pi\)
−0.450579 + 0.892737i \(0.648782\pi\)
\(758\) 37.2635 1.35347
\(759\) 16.4416 0.596792
\(760\) 141.776 5.14276
\(761\) −14.2001 −0.514753 −0.257377 0.966311i \(-0.582858\pi\)
−0.257377 + 0.966311i \(0.582858\pi\)
\(762\) −136.076 −4.92951
\(763\) −16.4420 −0.595239
\(764\) −92.1911 −3.33536
\(765\) 88.6507 3.20517
\(766\) −75.0116 −2.71028
\(767\) −5.10877 −0.184467
\(768\) −105.344 −3.80127
\(769\) −53.0620 −1.91346 −0.956732 0.290971i \(-0.906022\pi\)
−0.956732 + 0.290971i \(0.906022\pi\)
\(770\) 33.5838 1.21027
\(771\) 32.4885 1.17005
\(772\) 122.035 4.39212
\(773\) 41.3255 1.48637 0.743187 0.669084i \(-0.233313\pi\)
0.743187 + 0.669084i \(0.233313\pi\)
\(774\) 123.445 4.43713
\(775\) 75.9052 2.72659
\(776\) −155.600 −5.58571
\(777\) 109.208 3.91782
\(778\) −63.2450 −2.26744
\(779\) 16.1746 0.579515
\(780\) 326.219 11.6805
\(781\) 0.796841 0.0285132
\(782\) 83.5012 2.98600
\(783\) −20.9486 −0.748643
\(784\) 157.848 5.63744
\(785\) 46.1134 1.64586
\(786\) 163.568 5.83428
\(787\) 13.6572 0.486826 0.243413 0.969923i \(-0.421733\pi\)
0.243413 + 0.969923i \(0.421733\pi\)
\(788\) −18.6931 −0.665915
\(789\) 7.10634 0.252992
\(790\) 20.9007 0.743614
\(791\) −41.8444 −1.48781
\(792\) 41.9388 1.49023
\(793\) −13.9003 −0.493614
\(794\) 6.89203 0.244589
\(795\) 20.4115 0.723921
\(796\) −126.968 −4.50025
\(797\) 31.8186 1.12707 0.563537 0.826091i \(-0.309440\pi\)
0.563537 + 0.826091i \(0.309440\pi\)
\(798\) −143.891 −5.09367
\(799\) −10.2811 −0.363718
\(800\) −162.852 −5.75770
\(801\) 17.5117 0.618746
\(802\) −42.6081 −1.50454
\(803\) −5.89416 −0.208001
\(804\) −0.636633 −0.0224523
\(805\) 105.107 3.70455
\(806\) −150.844 −5.31325
\(807\) −58.6084 −2.06311
\(808\) −107.600 −3.78537
\(809\) −27.7781 −0.976627 −0.488314 0.872668i \(-0.662388\pi\)
−0.488314 + 0.872668i \(0.662388\pi\)
\(810\) 51.9515 1.82539
\(811\) −22.4548 −0.788496 −0.394248 0.919004i \(-0.628995\pi\)
−0.394248 + 0.919004i \(0.628995\pi\)
\(812\) −63.7539 −2.23732
\(813\) −5.93127 −0.208019
\(814\) 19.4586 0.682023
\(815\) 5.29075 0.185327
\(816\) 187.258 6.55536
\(817\) −34.7097 −1.21434
\(818\) −29.0221 −1.01473
\(819\) −135.592 −4.73797
\(820\) −73.5886 −2.56982
\(821\) −6.25950 −0.218458 −0.109229 0.994017i \(-0.534838\pi\)
−0.109229 + 0.994017i \(0.534838\pi\)
\(822\) −45.0465 −1.57118
\(823\) 45.8724 1.59901 0.799505 0.600659i \(-0.205095\pi\)
0.799505 + 0.600659i \(0.205095\pi\)
\(824\) 38.5266 1.34214
\(825\) 18.7041 0.651194
\(826\) −10.2522 −0.356719
\(827\) −11.2671 −0.391796 −0.195898 0.980624i \(-0.562762\pi\)
−0.195898 + 0.980624i \(0.562762\pi\)
\(828\) 208.315 7.23945
\(829\) −17.4260 −0.605229 −0.302615 0.953113i \(-0.597860\pi\)
−0.302615 + 0.953113i \(0.597860\pi\)
\(830\) 88.7081 3.07910
\(831\) −13.7766 −0.477904
\(832\) 157.953 5.47604
\(833\) −48.5652 −1.68268
\(834\) −83.7668 −2.90061
\(835\) 82.9457 2.87046
\(836\) −18.7152 −0.647280
\(837\) −72.6079 −2.50970
\(838\) 48.1381 1.66290
\(839\) −20.2186 −0.698022 −0.349011 0.937119i \(-0.613482\pi\)
−0.349011 + 0.937119i \(0.613482\pi\)
\(840\) 412.486 14.2321
\(841\) −21.2527 −0.732851
\(842\) 15.0903 0.520046
\(843\) −54.0830 −1.86272
\(844\) 9.14497 0.314783
\(845\) −71.7749 −2.46913
\(846\) −35.1366 −1.20802
\(847\) 43.8077 1.50525
\(848\) 28.0240 0.962348
\(849\) −17.7537 −0.609305
\(850\) 94.9918 3.25819
\(851\) 60.8997 2.08761
\(852\) 15.5329 0.532148
\(853\) 23.9744 0.820867 0.410433 0.911891i \(-0.365377\pi\)
0.410433 + 0.911891i \(0.365377\pi\)
\(854\) −27.8949 −0.954544
\(855\) −85.1888 −2.91339
\(856\) −172.053 −5.88065
\(857\) 18.3770 0.627745 0.313872 0.949465i \(-0.398374\pi\)
0.313872 + 0.949465i \(0.398374\pi\)
\(858\) −37.1701 −1.26897
\(859\) −11.1695 −0.381098 −0.190549 0.981678i \(-0.561027\pi\)
−0.190549 + 0.981678i \(0.561027\pi\)
\(860\) 157.917 5.38492
\(861\) 47.0586 1.60375
\(862\) 40.1733 1.36831
\(863\) −17.4980 −0.595638 −0.297819 0.954622i \(-0.596259\pi\)
−0.297819 + 0.954622i \(0.596259\pi\)
\(864\) 155.778 5.29968
\(865\) −58.5128 −1.98949
\(866\) 65.1941 2.21539
\(867\) −7.84465 −0.266418
\(868\) −220.971 −7.50024
\(869\) −1.73841 −0.0589716
\(870\) −79.5525 −2.69708
\(871\) 0.231080 0.00782986
\(872\) −35.9824 −1.21852
\(873\) 93.4951 3.16433
\(874\) −80.2404 −2.71417
\(875\) 43.5860 1.47348
\(876\) −114.895 −3.88195
\(877\) −7.43542 −0.251076 −0.125538 0.992089i \(-0.540066\pi\)
−0.125538 + 0.992089i \(0.540066\pi\)
\(878\) −47.6853 −1.60930
\(879\) −82.3118 −2.77631
\(880\) 41.9989 1.41578
\(881\) −21.9400 −0.739176 −0.369588 0.929196i \(-0.620501\pi\)
−0.369588 + 0.929196i \(0.620501\pi\)
\(882\) −165.976 −5.58872
\(883\) −20.6143 −0.693727 −0.346863 0.937916i \(-0.612753\pi\)
−0.346863 + 0.937916i \(0.612753\pi\)
\(884\) −137.800 −4.63472
\(885\) −9.33836 −0.313905
\(886\) 80.8222 2.71528
\(887\) −10.1581 −0.341075 −0.170538 0.985351i \(-0.554550\pi\)
−0.170538 + 0.985351i \(0.554550\pi\)
\(888\) 238.996 8.02018
\(889\) 72.3539 2.42667
\(890\) 30.6887 1.02869
\(891\) −4.32106 −0.144761
\(892\) 79.8357 2.67310
\(893\) 9.87957 0.330607
\(894\) −104.518 −3.49561
\(895\) −38.2646 −1.27904
\(896\) 141.606 4.73072
\(897\) −116.332 −3.88420
\(898\) −31.8450 −1.06268
\(899\) 26.8522 0.895570
\(900\) 236.981 7.89938
\(901\) −8.62214 −0.287245
\(902\) 8.38485 0.279185
\(903\) −100.985 −3.36057
\(904\) −91.5743 −3.04571
\(905\) 47.9250 1.59308
\(906\) 153.141 5.08776
\(907\) −8.96702 −0.297745 −0.148873 0.988856i \(-0.547564\pi\)
−0.148873 + 0.988856i \(0.547564\pi\)
\(908\) 75.1532 2.49405
\(909\) 64.6536 2.14442
\(910\) −237.620 −7.87704
\(911\) −38.6670 −1.28109 −0.640547 0.767919i \(-0.721292\pi\)
−0.640547 + 0.767919i \(0.721292\pi\)
\(912\) −179.946 −5.95860
\(913\) −7.37827 −0.244185
\(914\) 59.4409 1.96613
\(915\) −25.4085 −0.839978
\(916\) 73.8485 2.44002
\(917\) −86.9719 −2.87207
\(918\) −90.8655 −2.99901
\(919\) −11.9509 −0.394224 −0.197112 0.980381i \(-0.563156\pi\)
−0.197112 + 0.980381i \(0.563156\pi\)
\(920\) 230.022 7.58360
\(921\) −17.0027 −0.560258
\(922\) 10.9307 0.359984
\(923\) −5.63801 −0.185577
\(924\) −54.4504 −1.79129
\(925\) 69.2801 2.27792
\(926\) 52.8253 1.73595
\(927\) −23.1494 −0.760326
\(928\) −57.6105 −1.89116
\(929\) −26.9891 −0.885483 −0.442741 0.896649i \(-0.645994\pi\)
−0.442741 + 0.896649i \(0.645994\pi\)
\(930\) −275.729 −9.04150
\(931\) 46.6686 1.52950
\(932\) 32.5784 1.06714
\(933\) 9.59337 0.314073
\(934\) −54.3998 −1.78002
\(935\) −12.9218 −0.422588
\(936\) −296.736 −9.69912
\(937\) 1.75980 0.0574903 0.0287451 0.999587i \(-0.490849\pi\)
0.0287451 + 0.999587i \(0.490849\pi\)
\(938\) 0.463728 0.0151413
\(939\) −51.7865 −1.68999
\(940\) −44.9485 −1.46606
\(941\) 29.1840 0.951370 0.475685 0.879616i \(-0.342200\pi\)
0.475685 + 0.879616i \(0.342200\pi\)
\(942\) −102.422 −3.33708
\(943\) 26.2421 0.854562
\(944\) −12.8211 −0.417292
\(945\) −114.377 −3.72069
\(946\) −17.9934 −0.585016
\(947\) 18.9016 0.614220 0.307110 0.951674i \(-0.400638\pi\)
0.307110 + 0.951674i \(0.400638\pi\)
\(948\) −33.8870 −1.10060
\(949\) 41.7039 1.35377
\(950\) −91.2823 −2.96159
\(951\) 84.8099 2.75015
\(952\) −174.241 −5.64717
\(953\) 7.67814 0.248719 0.124360 0.992237i \(-0.460312\pi\)
0.124360 + 0.992237i \(0.460312\pi\)
\(954\) −29.4670 −0.954030
\(955\) 61.1670 1.97932
\(956\) −46.2740 −1.49661
\(957\) 6.61676 0.213889
\(958\) −41.9314 −1.35474
\(959\) 23.9520 0.773451
\(960\) 288.723 9.31851
\(961\) 62.0695 2.00224
\(962\) −137.678 −4.43893
\(963\) 103.381 3.33141
\(964\) 142.483 4.58906
\(965\) −80.9675 −2.60644
\(966\) −233.453 −7.51121
\(967\) 3.75610 0.120788 0.0603941 0.998175i \(-0.480764\pi\)
0.0603941 + 0.998175i \(0.480764\pi\)
\(968\) 95.8709 3.08141
\(969\) 55.3639 1.77854
\(970\) 163.847 5.26081
\(971\) 4.51861 0.145009 0.0725046 0.997368i \(-0.476901\pi\)
0.0725046 + 0.997368i \(0.476901\pi\)
\(972\) 37.8452 1.21389
\(973\) 44.5403 1.42790
\(974\) 12.8777 0.412628
\(975\) −132.340 −4.23828
\(976\) −34.8846 −1.11663
\(977\) −33.4235 −1.06931 −0.534656 0.845070i \(-0.679559\pi\)
−0.534656 + 0.845070i \(0.679559\pi\)
\(978\) −11.7512 −0.375763
\(979\) −2.55252 −0.0815790
\(980\) −212.326 −6.78249
\(981\) 21.6206 0.690294
\(982\) −2.04216 −0.0651678
\(983\) 6.74209 0.215039 0.107520 0.994203i \(-0.465709\pi\)
0.107520 + 0.994203i \(0.465709\pi\)
\(984\) 102.985 3.28305
\(985\) 12.4025 0.395177
\(986\) 33.6042 1.07018
\(987\) 28.7438 0.914924
\(988\) 132.419 4.21280
\(989\) −56.3141 −1.79069
\(990\) −44.1616 −1.40355
\(991\) −36.3277 −1.15399 −0.576994 0.816749i \(-0.695774\pi\)
−0.576994 + 0.816749i \(0.695774\pi\)
\(992\) −199.678 −6.33978
\(993\) 61.9869 1.96709
\(994\) −11.3143 −0.358867
\(995\) 84.2405 2.67060
\(996\) −143.825 −4.55728
\(997\) −16.4234 −0.520133 −0.260067 0.965591i \(-0.583745\pi\)
−0.260067 + 0.965591i \(0.583745\pi\)
\(998\) −114.252 −3.61657
\(999\) −66.2706 −2.09671
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 \(a_p\))