Properties

Label 4019.2.a.b.1.19
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 1.19
Character \(\chi\) = 4019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.39579 q^{2}\) \(+3.13150 q^{3}\) \(+3.73980 q^{4}\) \(+0.529965 q^{5}\) \(-7.50242 q^{6}\) \(-1.46029 q^{7}\) \(-4.16820 q^{8}\) \(+6.80631 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.39579 q^{2}\) \(+3.13150 q^{3}\) \(+3.73980 q^{4}\) \(+0.529965 q^{5}\) \(-7.50242 q^{6}\) \(-1.46029 q^{7}\) \(-4.16820 q^{8}\) \(+6.80631 q^{9}\) \(-1.26968 q^{10}\) \(+4.42489 q^{11}\) \(+11.7112 q^{12}\) \(+6.46275 q^{13}\) \(+3.49855 q^{14}\) \(+1.65959 q^{15}\) \(+2.50652 q^{16}\) \(+1.71135 q^{17}\) \(-16.3065 q^{18}\) \(-1.59807 q^{19}\) \(+1.98197 q^{20}\) \(-4.57291 q^{21}\) \(-10.6011 q^{22}\) \(+5.85306 q^{23}\) \(-13.0527 q^{24}\) \(-4.71914 q^{25}\) \(-15.4834 q^{26}\) \(+11.9195 q^{27}\) \(-5.46120 q^{28}\) \(-6.42396 q^{29}\) \(-3.97602 q^{30}\) \(-2.54140 q^{31}\) \(+2.33130 q^{32}\) \(+13.8565 q^{33}\) \(-4.10004 q^{34}\) \(-0.773904 q^{35}\) \(+25.4543 q^{36}\) \(+7.82017 q^{37}\) \(+3.82864 q^{38}\) \(+20.2381 q^{39}\) \(-2.20900 q^{40}\) \(+12.2992 q^{41}\) \(+10.9557 q^{42}\) \(-2.30731 q^{43}\) \(+16.5482 q^{44}\) \(+3.60711 q^{45}\) \(-14.0227 q^{46}\) \(-1.76939 q^{47}\) \(+7.84919 q^{48}\) \(-4.86755 q^{49}\) \(+11.3061 q^{50}\) \(+5.35911 q^{51}\) \(+24.1694 q^{52}\) \(-0.795921 q^{53}\) \(-28.5566 q^{54}\) \(+2.34504 q^{55}\) \(+6.08679 q^{56}\) \(-5.00436 q^{57}\) \(+15.3904 q^{58}\) \(-14.9641 q^{59}\) \(+6.20653 q^{60}\) \(+12.9958 q^{61}\) \(+6.08866 q^{62}\) \(-9.93920 q^{63}\) \(-10.5984 q^{64}\) \(+3.42503 q^{65}\) \(-33.1974 q^{66}\) \(+12.9765 q^{67}\) \(+6.40012 q^{68}\) \(+18.3289 q^{69}\) \(+1.85411 q^{70}\) \(-9.51351 q^{71}\) \(-28.3701 q^{72}\) \(-0.209957 q^{73}\) \(-18.7355 q^{74}\) \(-14.7780 q^{75}\) \(-5.97647 q^{76}\) \(-6.46162 q^{77}\) \(-48.4862 q^{78}\) \(-5.60830 q^{79}\) \(+1.32837 q^{80}\) \(+16.9070 q^{81}\) \(-29.4663 q^{82}\) \(-6.61460 q^{83}\) \(-17.1018 q^{84}\) \(+0.906958 q^{85}\) \(+5.52782 q^{86}\) \(-20.1166 q^{87}\) \(-18.4438 q^{88}\) \(-9.99098 q^{89}\) \(-8.64187 q^{90}\) \(-9.43749 q^{91}\) \(+21.8893 q^{92}\) \(-7.95841 q^{93}\) \(+4.23909 q^{94}\) \(-0.846921 q^{95}\) \(+7.30048 q^{96}\) \(-5.09962 q^{97}\) \(+11.6616 q^{98}\) \(+30.1172 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut 50q^{10} \) \(\mathstrut +\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 17q^{12} \) \(\mathstrut +\mathstrut 113q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 252q^{16} \) \(\mathstrut +\mathstrut 35q^{17} \) \(\mathstrut +\mathstrut 13q^{18} \) \(\mathstrut +\mathstrut 97q^{19} \) \(\mathstrut +\mathstrut 55q^{20} \) \(\mathstrut +\mathstrut 115q^{21} \) \(\mathstrut +\mathstrut 14q^{22} \) \(\mathstrut +\mathstrut 27q^{23} \) \(\mathstrut +\mathstrut 122q^{24} \) \(\mathstrut +\mathstrut 244q^{25} \) \(\mathstrut +\mathstrut 39q^{26} \) \(\mathstrut +\mathstrut 34q^{27} \) \(\mathstrut +\mathstrut 66q^{28} \) \(\mathstrut +\mathstrut 91q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 135q^{31} \) \(\mathstrut +\mathstrut 21q^{32} \) \(\mathstrut +\mathstrut 32q^{33} \) \(\mathstrut +\mathstrut 58q^{34} \) \(\mathstrut +\mathstrut 17q^{35} \) \(\mathstrut +\mathstrut 273q^{36} \) \(\mathstrut +\mathstrut 133q^{37} \) \(\mathstrut -\mathstrut 3q^{38} \) \(\mathstrut +\mathstrut 55q^{39} \) \(\mathstrut +\mathstrut 142q^{40} \) \(\mathstrut +\mathstrut 97q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 67q^{43} \) \(\mathstrut +\mathstrut 44q^{44} \) \(\mathstrut +\mathstrut 154q^{45} \) \(\mathstrut +\mathstrut 101q^{46} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 312q^{49} \) \(\mathstrut +\mathstrut 21q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut +\mathstrut 193q^{52} \) \(\mathstrut +\mathstrut 22q^{53} \) \(\mathstrut +\mathstrut 141q^{54} \) \(\mathstrut +\mathstrut 88q^{55} \) \(\mathstrut +\mathstrut 28q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 62q^{58} \) \(\mathstrut +\mathstrut 41q^{59} \) \(\mathstrut +\mathstrut q^{60} \) \(\mathstrut +\mathstrut 377q^{61} \) \(\mathstrut +\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 39q^{63} \) \(\mathstrut +\mathstrut 311q^{64} \) \(\mathstrut +\mathstrut 21q^{65} \) \(\mathstrut +\mathstrut 35q^{66} \) \(\mathstrut +\mathstrut 42q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut +\mathstrut 137q^{69} \) \(\mathstrut +\mathstrut 35q^{70} \) \(\mathstrut +\mathstrut 17q^{71} \) \(\mathstrut -\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 213q^{73} \) \(\mathstrut -\mathstrut 9q^{74} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut +\mathstrut 242q^{76} \) \(\mathstrut +\mathstrut 60q^{77} \) \(\mathstrut +\mathstrut 103q^{79} \) \(\mathstrut +\mathstrut 80q^{80} \) \(\mathstrut +\mathstrut 270q^{81} \) \(\mathstrut +\mathstrut 84q^{82} \) \(\mathstrut +\mathstrut 42q^{83} \) \(\mathstrut +\mathstrut 137q^{84} \) \(\mathstrut +\mathstrut 294q^{85} \) \(\mathstrut -\mathstrut 9q^{86} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut +\mathstrut 78q^{89} \) \(\mathstrut +\mathstrut 69q^{90} \) \(\mathstrut +\mathstrut 118q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 51q^{93} \) \(\mathstrut +\mathstrut 93q^{94} \) \(\mathstrut +\mathstrut 10q^{95} \) \(\mathstrut +\mathstrut 260q^{96} \) \(\mathstrut +\mathstrut 142q^{97} \) \(\mathstrut -\mathstrut 31q^{98} \) \(\mathstrut +\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.39579 −1.69408 −0.847039 0.531530i \(-0.821617\pi\)
−0.847039 + 0.531530i \(0.821617\pi\)
\(3\) 3.13150 1.80797 0.903987 0.427560i \(-0.140627\pi\)
0.903987 + 0.427560i \(0.140627\pi\)
\(4\) 3.73980 1.86990
\(5\) 0.529965 0.237008 0.118504 0.992954i \(-0.462190\pi\)
0.118504 + 0.992954i \(0.462190\pi\)
\(6\) −7.50242 −3.06285
\(7\) −1.46029 −0.551938 −0.275969 0.961167i \(-0.588999\pi\)
−0.275969 + 0.961167i \(0.588999\pi\)
\(8\) −4.16820 −1.47368
\(9\) 6.80631 2.26877
\(10\) −1.26968 −0.401510
\(11\) 4.42489 1.33415 0.667077 0.744989i \(-0.267545\pi\)
0.667077 + 0.744989i \(0.267545\pi\)
\(12\) 11.7112 3.38073
\(13\) 6.46275 1.79244 0.896222 0.443606i \(-0.146301\pi\)
0.896222 + 0.443606i \(0.146301\pi\)
\(14\) 3.49855 0.935027
\(15\) 1.65959 0.428504
\(16\) 2.50652 0.626631
\(17\) 1.71135 0.415064 0.207532 0.978228i \(-0.433457\pi\)
0.207532 + 0.978228i \(0.433457\pi\)
\(18\) −16.3065 −3.84348
\(19\) −1.59807 −0.366622 −0.183311 0.983055i \(-0.558682\pi\)
−0.183311 + 0.983055i \(0.558682\pi\)
\(20\) 1.98197 0.443181
\(21\) −4.57291 −0.997890
\(22\) −10.6011 −2.26016
\(23\) 5.85306 1.22045 0.610223 0.792229i \(-0.291080\pi\)
0.610223 + 0.792229i \(0.291080\pi\)
\(24\) −13.0527 −2.66438
\(25\) −4.71914 −0.943827
\(26\) −15.4834 −3.03654
\(27\) 11.9195 2.29391
\(28\) −5.46120 −1.03207
\(29\) −6.42396 −1.19290 −0.596450 0.802651i \(-0.703422\pi\)
−0.596450 + 0.802651i \(0.703422\pi\)
\(30\) −3.97602 −0.725919
\(31\) −2.54140 −0.456449 −0.228225 0.973608i \(-0.573292\pi\)
−0.228225 + 0.973608i \(0.573292\pi\)
\(32\) 2.33130 0.412120
\(33\) 13.8565 2.41211
\(34\) −4.10004 −0.703151
\(35\) −0.773904 −0.130814
\(36\) 25.4543 4.24238
\(37\) 7.82017 1.28563 0.642814 0.766022i \(-0.277767\pi\)
0.642814 + 0.766022i \(0.277767\pi\)
\(38\) 3.82864 0.621087
\(39\) 20.2381 3.24069
\(40\) −2.20900 −0.349274
\(41\) 12.2992 1.92081 0.960405 0.278607i \(-0.0898728\pi\)
0.960405 + 0.278607i \(0.0898728\pi\)
\(42\) 10.9557 1.69050
\(43\) −2.30731 −0.351861 −0.175931 0.984403i \(-0.556293\pi\)
−0.175931 + 0.984403i \(0.556293\pi\)
\(44\) 16.5482 2.49474
\(45\) 3.60711 0.537716
\(46\) −14.0227 −2.06753
\(47\) −1.76939 −0.258092 −0.129046 0.991639i \(-0.541192\pi\)
−0.129046 + 0.991639i \(0.541192\pi\)
\(48\) 7.84919 1.13293
\(49\) −4.86755 −0.695364
\(50\) 11.3061 1.59892
\(51\) 5.35911 0.750425
\(52\) 24.1694 3.35169
\(53\) −0.795921 −0.109328 −0.0546641 0.998505i \(-0.517409\pi\)
−0.0546641 + 0.998505i \(0.517409\pi\)
\(54\) −28.5566 −3.88606
\(55\) 2.34504 0.316205
\(56\) 6.08679 0.813381
\(57\) −5.00436 −0.662844
\(58\) 15.3904 2.02086
\(59\) −14.9641 −1.94817 −0.974083 0.226191i \(-0.927373\pi\)
−0.974083 + 0.226191i \(0.927373\pi\)
\(60\) 6.20653 0.801260
\(61\) 12.9958 1.66394 0.831968 0.554824i \(-0.187214\pi\)
0.831968 + 0.554824i \(0.187214\pi\)
\(62\) 6.08866 0.773261
\(63\) −9.93920 −1.25222
\(64\) −10.5984 −1.32479
\(65\) 3.42503 0.424823
\(66\) −33.1974 −4.08631
\(67\) 12.9765 1.58534 0.792668 0.609653i \(-0.208691\pi\)
0.792668 + 0.609653i \(0.208691\pi\)
\(68\) 6.40012 0.776129
\(69\) 18.3289 2.20654
\(70\) 1.85411 0.221608
\(71\) −9.51351 −1.12905 −0.564523 0.825417i \(-0.690940\pi\)
−0.564523 + 0.825417i \(0.690940\pi\)
\(72\) −28.3701 −3.34345
\(73\) −0.209957 −0.0245737 −0.0122868 0.999925i \(-0.503911\pi\)
−0.0122868 + 0.999925i \(0.503911\pi\)
\(74\) −18.7355 −2.17795
\(75\) −14.7780 −1.70642
\(76\) −5.97647 −0.685548
\(77\) −6.46162 −0.736370
\(78\) −48.4862 −5.48999
\(79\) −5.60830 −0.630983 −0.315492 0.948928i \(-0.602169\pi\)
−0.315492 + 0.948928i \(0.602169\pi\)
\(80\) 1.32837 0.148516
\(81\) 16.9070 1.87855
\(82\) −29.4663 −3.25400
\(83\) −6.61460 −0.726047 −0.363023 0.931780i \(-0.618255\pi\)
−0.363023 + 0.931780i \(0.618255\pi\)
\(84\) −17.1018 −1.86596
\(85\) 0.906958 0.0983734
\(86\) 5.52782 0.596080
\(87\) −20.1166 −2.15673
\(88\) −18.4438 −1.96612
\(89\) −9.99098 −1.05904 −0.529521 0.848297i \(-0.677628\pi\)
−0.529521 + 0.848297i \(0.677628\pi\)
\(90\) −8.64187 −0.910933
\(91\) −9.43749 −0.989318
\(92\) 21.8893 2.28212
\(93\) −7.95841 −0.825249
\(94\) 4.23909 0.437228
\(95\) −0.846921 −0.0868923
\(96\) 7.30048 0.745102
\(97\) −5.09962 −0.517788 −0.258894 0.965906i \(-0.583358\pi\)
−0.258894 + 0.965906i \(0.583358\pi\)
\(98\) 11.6616 1.17800
\(99\) 30.1172 3.02689
\(100\) −17.6486 −1.76486
\(101\) −6.38324 −0.635156 −0.317578 0.948232i \(-0.602870\pi\)
−0.317578 + 0.948232i \(0.602870\pi\)
\(102\) −12.8393 −1.27128
\(103\) 1.54634 0.152365 0.0761826 0.997094i \(-0.475727\pi\)
0.0761826 + 0.997094i \(0.475727\pi\)
\(104\) −26.9380 −2.64149
\(105\) −2.42348 −0.236508
\(106\) 1.90686 0.185211
\(107\) 17.1517 1.65812 0.829060 0.559160i \(-0.188876\pi\)
0.829060 + 0.559160i \(0.188876\pi\)
\(108\) 44.5765 4.28938
\(109\) 15.1280 1.44900 0.724499 0.689276i \(-0.242071\pi\)
0.724499 + 0.689276i \(0.242071\pi\)
\(110\) −5.61821 −0.535675
\(111\) 24.4889 2.32438
\(112\) −3.66025 −0.345862
\(113\) −6.23685 −0.586714 −0.293357 0.956003i \(-0.594772\pi\)
−0.293357 + 0.956003i \(0.594772\pi\)
\(114\) 11.9894 1.12291
\(115\) 3.10192 0.289255
\(116\) −24.0243 −2.23060
\(117\) 43.9875 4.06664
\(118\) 35.8509 3.30035
\(119\) −2.49907 −0.229090
\(120\) −6.91750 −0.631478
\(121\) 8.57962 0.779965
\(122\) −31.1351 −2.81884
\(123\) 38.5149 3.47278
\(124\) −9.50435 −0.853515
\(125\) −5.15081 −0.460702
\(126\) 23.8122 2.12136
\(127\) −6.93786 −0.615635 −0.307818 0.951445i \(-0.599599\pi\)
−0.307818 + 0.951445i \(0.599599\pi\)
\(128\) 20.7288 1.83219
\(129\) −7.22534 −0.636156
\(130\) −8.20565 −0.719683
\(131\) −12.7954 −1.11794 −0.558969 0.829188i \(-0.688803\pi\)
−0.558969 + 0.829188i \(0.688803\pi\)
\(132\) 51.8208 4.51042
\(133\) 2.33365 0.202353
\(134\) −31.0890 −2.68568
\(135\) 6.31691 0.543673
\(136\) −7.13326 −0.611672
\(137\) −5.68126 −0.485383 −0.242692 0.970104i \(-0.578030\pi\)
−0.242692 + 0.970104i \(0.578030\pi\)
\(138\) −43.9121 −3.73805
\(139\) −5.61317 −0.476103 −0.238051 0.971253i \(-0.576509\pi\)
−0.238051 + 0.971253i \(0.576509\pi\)
\(140\) −2.89425 −0.244609
\(141\) −5.54085 −0.466624
\(142\) 22.7924 1.91269
\(143\) 28.5969 2.39139
\(144\) 17.0602 1.42168
\(145\) −3.40448 −0.282726
\(146\) 0.503014 0.0416297
\(147\) −15.2427 −1.25720
\(148\) 29.2459 2.40400
\(149\) −8.32032 −0.681627 −0.340814 0.940131i \(-0.610703\pi\)
−0.340814 + 0.940131i \(0.610703\pi\)
\(150\) 35.4049 2.89080
\(151\) −2.37678 −0.193419 −0.0967097 0.995313i \(-0.530832\pi\)
−0.0967097 + 0.995313i \(0.530832\pi\)
\(152\) 6.66108 0.540285
\(153\) 11.6480 0.941685
\(154\) 15.4807 1.24747
\(155\) −1.34686 −0.108182
\(156\) 75.6866 6.05978
\(157\) −19.7733 −1.57808 −0.789042 0.614339i \(-0.789423\pi\)
−0.789042 + 0.614339i \(0.789423\pi\)
\(158\) 13.4363 1.06893
\(159\) −2.49243 −0.197663
\(160\) 1.23551 0.0976756
\(161\) −8.54717 −0.673611
\(162\) −40.5055 −3.18241
\(163\) −15.5566 −1.21848 −0.609242 0.792984i \(-0.708526\pi\)
−0.609242 + 0.792984i \(0.708526\pi\)
\(164\) 45.9965 3.59173
\(165\) 7.34349 0.571690
\(166\) 15.8472 1.22998
\(167\) 6.56436 0.507965 0.253983 0.967209i \(-0.418259\pi\)
0.253983 + 0.967209i \(0.418259\pi\)
\(168\) 19.0608 1.47057
\(169\) 28.7671 2.21285
\(170\) −2.17288 −0.166652
\(171\) −10.8770 −0.831782
\(172\) −8.62888 −0.657946
\(173\) −8.26455 −0.628342 −0.314171 0.949366i \(-0.601727\pi\)
−0.314171 + 0.949366i \(0.601727\pi\)
\(174\) 48.1952 3.65367
\(175\) 6.89131 0.520934
\(176\) 11.0911 0.836022
\(177\) −46.8603 −3.52223
\(178\) 23.9363 1.79410
\(179\) −19.9138 −1.48843 −0.744214 0.667941i \(-0.767176\pi\)
−0.744214 + 0.667941i \(0.767176\pi\)
\(180\) 13.4899 1.00548
\(181\) 19.8840 1.47797 0.738985 0.673722i \(-0.235306\pi\)
0.738985 + 0.673722i \(0.235306\pi\)
\(182\) 22.6102 1.67598
\(183\) 40.6963 3.00835
\(184\) −24.3967 −1.79855
\(185\) 4.14442 0.304704
\(186\) 19.0667 1.39804
\(187\) 7.57254 0.553759
\(188\) −6.61718 −0.482607
\(189\) −17.4059 −1.26609
\(190\) 2.02904 0.147202
\(191\) 5.33729 0.386193 0.193096 0.981180i \(-0.438147\pi\)
0.193096 + 0.981180i \(0.438147\pi\)
\(192\) −33.1888 −2.39519
\(193\) 14.1630 1.01948 0.509738 0.860330i \(-0.329742\pi\)
0.509738 + 0.860330i \(0.329742\pi\)
\(194\) 12.2176 0.877174
\(195\) 10.7255 0.768069
\(196\) −18.2037 −1.30026
\(197\) −8.88875 −0.633297 −0.316649 0.948543i \(-0.602558\pi\)
−0.316649 + 0.948543i \(0.602558\pi\)
\(198\) −72.1544 −5.12779
\(199\) 19.0844 1.35286 0.676429 0.736508i \(-0.263527\pi\)
0.676429 + 0.736508i \(0.263527\pi\)
\(200\) 19.6703 1.39090
\(201\) 40.6361 2.86625
\(202\) 15.2929 1.07600
\(203\) 9.38085 0.658407
\(204\) 20.0420 1.40322
\(205\) 6.51814 0.455247
\(206\) −3.70470 −0.258119
\(207\) 39.8377 2.76891
\(208\) 16.1990 1.12320
\(209\) −7.07128 −0.489130
\(210\) 5.80615 0.400662
\(211\) 10.0373 0.690994 0.345497 0.938420i \(-0.387710\pi\)
0.345497 + 0.938420i \(0.387710\pi\)
\(212\) −2.97659 −0.204433
\(213\) −29.7916 −2.04129
\(214\) −41.0919 −2.80899
\(215\) −1.22279 −0.0833938
\(216\) −49.6828 −3.38049
\(217\) 3.71119 0.251932
\(218\) −36.2434 −2.45472
\(219\) −0.657482 −0.0444285
\(220\) 8.76997 0.591272
\(221\) 11.0600 0.743979
\(222\) −58.6702 −3.93769
\(223\) −1.53730 −0.102945 −0.0514725 0.998674i \(-0.516391\pi\)
−0.0514725 + 0.998674i \(0.516391\pi\)
\(224\) −3.40438 −0.227465
\(225\) −32.1199 −2.14133
\(226\) 14.9422 0.993939
\(227\) 25.0467 1.66240 0.831202 0.555970i \(-0.187653\pi\)
0.831202 + 0.555970i \(0.187653\pi\)
\(228\) −18.7153 −1.23945
\(229\) −10.0343 −0.663086 −0.331543 0.943440i \(-0.607569\pi\)
−0.331543 + 0.943440i \(0.607569\pi\)
\(230\) −7.43154 −0.490021
\(231\) −20.2346 −1.33134
\(232\) 26.7764 1.75795
\(233\) −7.48980 −0.490673 −0.245337 0.969438i \(-0.578898\pi\)
−0.245337 + 0.969438i \(0.578898\pi\)
\(234\) −105.385 −6.88921
\(235\) −0.937716 −0.0611698
\(236\) −55.9630 −3.64288
\(237\) −17.5624 −1.14080
\(238\) 5.98725 0.388096
\(239\) −18.1515 −1.17412 −0.587062 0.809542i \(-0.699716\pi\)
−0.587062 + 0.809542i \(0.699716\pi\)
\(240\) 4.15980 0.268514
\(241\) 22.0854 1.42265 0.711323 0.702866i \(-0.248097\pi\)
0.711323 + 0.702866i \(0.248097\pi\)
\(242\) −20.5550 −1.32132
\(243\) 17.1857 1.10247
\(244\) 48.6016 3.11140
\(245\) −2.57963 −0.164807
\(246\) −92.2737 −5.88315
\(247\) −10.3279 −0.657150
\(248\) 10.5931 0.672661
\(249\) −20.7136 −1.31267
\(250\) 12.3402 0.780465
\(251\) 6.25714 0.394947 0.197473 0.980308i \(-0.436726\pi\)
0.197473 + 0.980308i \(0.436726\pi\)
\(252\) −37.1706 −2.34153
\(253\) 25.8991 1.62826
\(254\) 16.6216 1.04293
\(255\) 2.84014 0.177857
\(256\) −28.4652 −1.77907
\(257\) 2.16060 0.134775 0.0673874 0.997727i \(-0.478534\pi\)
0.0673874 + 0.997727i \(0.478534\pi\)
\(258\) 17.3104 1.07770
\(259\) −11.4197 −0.709587
\(260\) 12.8089 0.794377
\(261\) −43.7235 −2.70642
\(262\) 30.6551 1.89388
\(263\) −0.965852 −0.0595570 −0.0297785 0.999557i \(-0.509480\pi\)
−0.0297785 + 0.999557i \(0.509480\pi\)
\(264\) −57.7569 −3.55469
\(265\) −0.421811 −0.0259116
\(266\) −5.59093 −0.342802
\(267\) −31.2868 −1.91472
\(268\) 48.5297 2.96442
\(269\) −14.7866 −0.901552 −0.450776 0.892637i \(-0.648853\pi\)
−0.450776 + 0.892637i \(0.648853\pi\)
\(270\) −15.1340 −0.921025
\(271\) 14.8258 0.900602 0.450301 0.892877i \(-0.351317\pi\)
0.450301 + 0.892877i \(0.351317\pi\)
\(272\) 4.28955 0.260092
\(273\) −29.5535 −1.78866
\(274\) 13.6111 0.822277
\(275\) −20.8816 −1.25921
\(276\) 68.5464 4.12601
\(277\) 12.8112 0.769748 0.384874 0.922969i \(-0.374245\pi\)
0.384874 + 0.922969i \(0.374245\pi\)
\(278\) 13.4480 0.806555
\(279\) −17.2976 −1.03558
\(280\) 3.22579 0.192778
\(281\) 20.9247 1.24826 0.624131 0.781320i \(-0.285453\pi\)
0.624131 + 0.781320i \(0.285453\pi\)
\(282\) 13.2747 0.790498
\(283\) −20.7712 −1.23472 −0.617360 0.786680i \(-0.711798\pi\)
−0.617360 + 0.786680i \(0.711798\pi\)
\(284\) −35.5787 −2.11121
\(285\) −2.65214 −0.157099
\(286\) −68.5122 −4.05121
\(287\) −17.9604 −1.06017
\(288\) 15.8676 0.935006
\(289\) −14.0713 −0.827722
\(290\) 8.15640 0.478960
\(291\) −15.9695 −0.936148
\(292\) −0.785200 −0.0459503
\(293\) 20.2046 1.18036 0.590182 0.807270i \(-0.299056\pi\)
0.590182 + 0.807270i \(0.299056\pi\)
\(294\) 36.5184 2.12980
\(295\) −7.93048 −0.461730
\(296\) −32.5961 −1.89461
\(297\) 52.7423 3.06042
\(298\) 19.9337 1.15473
\(299\) 37.8268 2.18758
\(300\) −55.2668 −3.19083
\(301\) 3.36934 0.194206
\(302\) 5.69426 0.327668
\(303\) −19.9891 −1.14835
\(304\) −4.00560 −0.229737
\(305\) 6.88730 0.394366
\(306\) −27.9062 −1.59529
\(307\) −32.6732 −1.86476 −0.932379 0.361483i \(-0.882270\pi\)
−0.932379 + 0.361483i \(0.882270\pi\)
\(308\) −24.1652 −1.37694
\(309\) 4.84237 0.275473
\(310\) 3.22678 0.183269
\(311\) −16.3018 −0.924393 −0.462197 0.886778i \(-0.652939\pi\)
−0.462197 + 0.886778i \(0.652939\pi\)
\(312\) −84.3566 −4.77575
\(313\) −17.3529 −0.980843 −0.490422 0.871485i \(-0.663157\pi\)
−0.490422 + 0.871485i \(0.663157\pi\)
\(314\) 47.3727 2.67340
\(315\) −5.26743 −0.296786
\(316\) −20.9739 −1.17988
\(317\) −14.9627 −0.840390 −0.420195 0.907434i \(-0.638038\pi\)
−0.420195 + 0.907434i \(0.638038\pi\)
\(318\) 5.97134 0.334856
\(319\) −28.4253 −1.59151
\(320\) −5.61676 −0.313986
\(321\) 53.7107 2.99784
\(322\) 20.4772 1.14115
\(323\) −2.73486 −0.152172
\(324\) 63.2287 3.51271
\(325\) −30.4986 −1.69176
\(326\) 37.2702 2.06421
\(327\) 47.3733 2.61975
\(328\) −51.2655 −2.83066
\(329\) 2.58383 0.142451
\(330\) −17.5934 −0.968487
\(331\) 25.2940 1.39028 0.695141 0.718874i \(-0.255342\pi\)
0.695141 + 0.718874i \(0.255342\pi\)
\(332\) −24.7373 −1.35764
\(333\) 53.2265 2.91680
\(334\) −15.7268 −0.860533
\(335\) 6.87711 0.375737
\(336\) −11.4621 −0.625309
\(337\) 22.1697 1.20766 0.603831 0.797112i \(-0.293640\pi\)
0.603831 + 0.797112i \(0.293640\pi\)
\(338\) −68.9199 −3.74875
\(339\) −19.5307 −1.06076
\(340\) 3.39184 0.183949
\(341\) −11.2454 −0.608973
\(342\) 26.0589 1.40910
\(343\) 17.3301 0.935736
\(344\) 9.61733 0.518531
\(345\) 9.71366 0.522966
\(346\) 19.8001 1.06446
\(347\) −25.0865 −1.34671 −0.673357 0.739318i \(-0.735148\pi\)
−0.673357 + 0.739318i \(0.735148\pi\)
\(348\) −75.2323 −4.03288
\(349\) 19.9923 1.07017 0.535083 0.844800i \(-0.320281\pi\)
0.535083 + 0.844800i \(0.320281\pi\)
\(350\) −16.5101 −0.882504
\(351\) 77.0326 4.11170
\(352\) 10.3157 0.549831
\(353\) −2.44246 −0.129999 −0.0649995 0.997885i \(-0.520705\pi\)
−0.0649995 + 0.997885i \(0.520705\pi\)
\(354\) 112.267 5.96694
\(355\) −5.04183 −0.267593
\(356\) −37.3643 −1.98030
\(357\) −7.82586 −0.414188
\(358\) 47.7093 2.52151
\(359\) −13.4527 −0.710007 −0.355003 0.934865i \(-0.615520\pi\)
−0.355003 + 0.934865i \(0.615520\pi\)
\(360\) −15.0352 −0.792423
\(361\) −16.4462 −0.865588
\(362\) −47.6380 −2.50380
\(363\) 26.8671 1.41016
\(364\) −35.2944 −1.84993
\(365\) −0.111270 −0.00582415
\(366\) −97.4996 −5.09639
\(367\) 7.25487 0.378701 0.189351 0.981910i \(-0.439362\pi\)
0.189351 + 0.981910i \(0.439362\pi\)
\(368\) 14.6708 0.764770
\(369\) 83.7121 4.35788
\(370\) −9.92915 −0.516192
\(371\) 1.16228 0.0603424
\(372\) −29.7629 −1.54313
\(373\) 1.38444 0.0716837 0.0358419 0.999357i \(-0.488589\pi\)
0.0358419 + 0.999357i \(0.488589\pi\)
\(374\) −18.1422 −0.938111
\(375\) −16.1298 −0.832937
\(376\) 7.37518 0.380346
\(377\) −41.5164 −2.13820
\(378\) 41.7009 2.14486
\(379\) 26.1572 1.34360 0.671802 0.740730i \(-0.265520\pi\)
0.671802 + 0.740730i \(0.265520\pi\)
\(380\) −3.16732 −0.162480
\(381\) −21.7259 −1.11305
\(382\) −12.7870 −0.654241
\(383\) −10.8836 −0.556125 −0.278063 0.960563i \(-0.589692\pi\)
−0.278063 + 0.960563i \(0.589692\pi\)
\(384\) 64.9124 3.31254
\(385\) −3.42444 −0.174525
\(386\) −33.9316 −1.72707
\(387\) −15.7043 −0.798292
\(388\) −19.0716 −0.968213
\(389\) 34.1828 1.73314 0.866569 0.499057i \(-0.166320\pi\)
0.866569 + 0.499057i \(0.166320\pi\)
\(390\) −25.6960 −1.30117
\(391\) 10.0166 0.506564
\(392\) 20.2889 1.02475
\(393\) −40.0688 −2.02120
\(394\) 21.2956 1.07286
\(395\) −2.97220 −0.149548
\(396\) 112.632 5.65998
\(397\) 24.3851 1.22386 0.611928 0.790914i \(-0.290394\pi\)
0.611928 + 0.790914i \(0.290394\pi\)
\(398\) −45.7222 −2.29185
\(399\) 7.30782 0.365849
\(400\) −11.8286 −0.591431
\(401\) 10.9896 0.548796 0.274398 0.961616i \(-0.411521\pi\)
0.274398 + 0.961616i \(0.411521\pi\)
\(402\) −97.3554 −4.85565
\(403\) −16.4244 −0.818160
\(404\) −23.8721 −1.18768
\(405\) 8.96010 0.445231
\(406\) −22.4745 −1.11539
\(407\) 34.6034 1.71523
\(408\) −22.3378 −1.10589
\(409\) 10.3479 0.511670 0.255835 0.966720i \(-0.417650\pi\)
0.255835 + 0.966720i \(0.417650\pi\)
\(410\) −15.6161 −0.771224
\(411\) −17.7909 −0.877560
\(412\) 5.78300 0.284908
\(413\) 21.8520 1.07527
\(414\) −95.4428 −4.69076
\(415\) −3.50551 −0.172079
\(416\) 15.0666 0.738702
\(417\) −17.5776 −0.860781
\(418\) 16.9413 0.828625
\(419\) 20.5506 1.00396 0.501982 0.864878i \(-0.332604\pi\)
0.501982 + 0.864878i \(0.332604\pi\)
\(420\) −9.06335 −0.442246
\(421\) 30.2571 1.47464 0.737320 0.675544i \(-0.236091\pi\)
0.737320 + 0.675544i \(0.236091\pi\)
\(422\) −24.0472 −1.17060
\(423\) −12.0430 −0.585552
\(424\) 3.31756 0.161115
\(425\) −8.07611 −0.391749
\(426\) 71.3744 3.45810
\(427\) −18.9776 −0.918390
\(428\) 64.1441 3.10052
\(429\) 89.5514 4.32358
\(430\) 2.92955 0.141276
\(431\) −31.5229 −1.51841 −0.759203 0.650854i \(-0.774411\pi\)
−0.759203 + 0.650854i \(0.774411\pi\)
\(432\) 29.8765 1.43743
\(433\) −10.6414 −0.511393 −0.255696 0.966757i \(-0.582305\pi\)
−0.255696 + 0.966757i \(0.582305\pi\)
\(434\) −8.89122 −0.426792
\(435\) −10.6611 −0.511162
\(436\) 56.5757 2.70948
\(437\) −9.35359 −0.447443
\(438\) 1.57519 0.0752654
\(439\) 3.21336 0.153365 0.0766827 0.997056i \(-0.475567\pi\)
0.0766827 + 0.997056i \(0.475567\pi\)
\(440\) −9.77458 −0.465985
\(441\) −33.1301 −1.57762
\(442\) −26.4975 −1.26036
\(443\) −9.92140 −0.471380 −0.235690 0.971828i \(-0.575735\pi\)
−0.235690 + 0.971828i \(0.575735\pi\)
\(444\) 91.5836 4.34637
\(445\) −5.29487 −0.251001
\(446\) 3.68304 0.174397
\(447\) −26.0551 −1.23236
\(448\) 15.4767 0.731205
\(449\) −17.5137 −0.826525 −0.413262 0.910612i \(-0.635611\pi\)
−0.413262 + 0.910612i \(0.635611\pi\)
\(450\) 76.9525 3.62758
\(451\) 54.4225 2.56266
\(452\) −23.3246 −1.09710
\(453\) −7.44289 −0.349697
\(454\) −60.0065 −2.81624
\(455\) −5.00154 −0.234476
\(456\) 20.8592 0.976821
\(457\) −12.7970 −0.598618 −0.299309 0.954156i \(-0.596756\pi\)
−0.299309 + 0.954156i \(0.596756\pi\)
\(458\) 24.0401 1.12332
\(459\) 20.3984 0.952117
\(460\) 11.6006 0.540879
\(461\) 36.4427 1.69731 0.848653 0.528951i \(-0.177414\pi\)
0.848653 + 0.528951i \(0.177414\pi\)
\(462\) 48.4778 2.25539
\(463\) 3.63225 0.168805 0.0844025 0.996432i \(-0.473102\pi\)
0.0844025 + 0.996432i \(0.473102\pi\)
\(464\) −16.1018 −0.747508
\(465\) −4.21768 −0.195590
\(466\) 17.9440 0.831239
\(467\) −28.4290 −1.31554 −0.657768 0.753221i \(-0.728499\pi\)
−0.657768 + 0.753221i \(0.728499\pi\)
\(468\) 164.505 7.60423
\(469\) −18.9495 −0.875008
\(470\) 2.24657 0.103627
\(471\) −61.9203 −2.85313
\(472\) 62.3736 2.87098
\(473\) −10.2096 −0.469437
\(474\) 42.0758 1.93261
\(475\) 7.54151 0.346028
\(476\) −9.34604 −0.428375
\(477\) −5.41729 −0.248041
\(478\) 43.4872 1.98906
\(479\) 13.5961 0.621219 0.310610 0.950538i \(-0.399467\pi\)
0.310610 + 0.950538i \(0.399467\pi\)
\(480\) 3.86900 0.176595
\(481\) 50.5398 2.30442
\(482\) −52.9119 −2.41007
\(483\) −26.7655 −1.21787
\(484\) 32.0861 1.45846
\(485\) −2.70262 −0.122720
\(486\) −41.1734 −1.86766
\(487\) −19.2412 −0.871904 −0.435952 0.899970i \(-0.643588\pi\)
−0.435952 + 0.899970i \(0.643588\pi\)
\(488\) −54.1689 −2.45211
\(489\) −48.7154 −2.20299
\(490\) 6.18025 0.279195
\(491\) 36.7971 1.66063 0.830315 0.557295i \(-0.188161\pi\)
0.830315 + 0.557295i \(0.188161\pi\)
\(492\) 144.038 6.49375
\(493\) −10.9937 −0.495130
\(494\) 24.7435 1.11326
\(495\) 15.9610 0.717396
\(496\) −6.37009 −0.286025
\(497\) 13.8925 0.623164
\(498\) 49.6255 2.22377
\(499\) −22.3439 −1.00025 −0.500125 0.865953i \(-0.666713\pi\)
−0.500125 + 0.865953i \(0.666713\pi\)
\(500\) −19.2630 −0.861468
\(501\) 20.5563 0.918388
\(502\) −14.9908 −0.669071
\(503\) 28.7700 1.28279 0.641394 0.767211i \(-0.278356\pi\)
0.641394 + 0.767211i \(0.278356\pi\)
\(504\) 41.4286 1.84538
\(505\) −3.38290 −0.150537
\(506\) −62.0488 −2.75841
\(507\) 90.0843 4.00078
\(508\) −25.9462 −1.15118
\(509\) 29.8458 1.32289 0.661446 0.749993i \(-0.269943\pi\)
0.661446 + 0.749993i \(0.269943\pi\)
\(510\) −6.80438 −0.301303
\(511\) 0.306599 0.0135631
\(512\) 26.7389 1.18170
\(513\) −19.0482 −0.840997
\(514\) −5.17635 −0.228319
\(515\) 0.819506 0.0361117
\(516\) −27.0214 −1.18955
\(517\) −7.82935 −0.344335
\(518\) 27.3593 1.20210
\(519\) −25.8805 −1.13603
\(520\) −14.2762 −0.626054
\(521\) −31.4999 −1.38004 −0.690019 0.723792i \(-0.742398\pi\)
−0.690019 + 0.723792i \(0.742398\pi\)
\(522\) 104.752 4.58488
\(523\) 4.27785 0.187057 0.0935286 0.995617i \(-0.470185\pi\)
0.0935286 + 0.995617i \(0.470185\pi\)
\(524\) −47.8523 −2.09044
\(525\) 21.5802 0.941836
\(526\) 2.31398 0.100894
\(527\) −4.34924 −0.189456
\(528\) 34.7318 1.51151
\(529\) 11.2583 0.489490
\(530\) 1.01057 0.0438963
\(531\) −101.851 −4.41994
\(532\) 8.72738 0.378380
\(533\) 79.4865 3.44294
\(534\) 74.9565 3.24369
\(535\) 9.08982 0.392987
\(536\) −54.0888 −2.33628
\(537\) −62.3602 −2.69104
\(538\) 35.4255 1.52730
\(539\) −21.5384 −0.927723
\(540\) 23.6240 1.01662
\(541\) −6.94259 −0.298485 −0.149243 0.988801i \(-0.547684\pi\)
−0.149243 + 0.988801i \(0.547684\pi\)
\(542\) −35.5194 −1.52569
\(543\) 62.2670 2.67213
\(544\) 3.98968 0.171056
\(545\) 8.01730 0.343424
\(546\) 70.8040 3.03013
\(547\) −7.97016 −0.340779 −0.170390 0.985377i \(-0.554503\pi\)
−0.170390 + 0.985377i \(0.554503\pi\)
\(548\) −21.2468 −0.907619
\(549\) 88.4532 3.77509
\(550\) 50.0280 2.13320
\(551\) 10.2659 0.437343
\(552\) −76.3984 −3.25173
\(553\) 8.18975 0.348264
\(554\) −30.6928 −1.30401
\(555\) 12.9783 0.550897
\(556\) −20.9921 −0.890265
\(557\) 39.7466 1.68412 0.842060 0.539385i \(-0.181343\pi\)
0.842060 + 0.539385i \(0.181343\pi\)
\(558\) 41.4413 1.75435
\(559\) −14.9115 −0.630691
\(560\) −1.93981 −0.0819718
\(561\) 23.7134 1.00118
\(562\) −50.1311 −2.11465
\(563\) 16.2836 0.686272 0.343136 0.939286i \(-0.388511\pi\)
0.343136 + 0.939286i \(0.388511\pi\)
\(564\) −20.7217 −0.872541
\(565\) −3.30531 −0.139056
\(566\) 49.7635 2.09171
\(567\) −24.6891 −1.03684
\(568\) 39.6542 1.66385
\(569\) −15.1540 −0.635287 −0.317644 0.948210i \(-0.602892\pi\)
−0.317644 + 0.948210i \(0.602892\pi\)
\(570\) 6.35396 0.266138
\(571\) −40.6365 −1.70058 −0.850292 0.526312i \(-0.823575\pi\)
−0.850292 + 0.526312i \(0.823575\pi\)
\(572\) 106.947 4.47167
\(573\) 16.7137 0.698226
\(574\) 43.0293 1.79601
\(575\) −27.6214 −1.15189
\(576\) −72.1357 −3.00565
\(577\) −20.3499 −0.847176 −0.423588 0.905855i \(-0.639230\pi\)
−0.423588 + 0.905855i \(0.639230\pi\)
\(578\) 33.7118 1.40223
\(579\) 44.3515 1.84319
\(580\) −12.7321 −0.528670
\(581\) 9.65924 0.400733
\(582\) 38.2595 1.58591
\(583\) −3.52186 −0.145861
\(584\) 0.875145 0.0362138
\(585\) 23.3118 0.963826
\(586\) −48.4059 −1.99963
\(587\) −34.2532 −1.41378 −0.706890 0.707324i \(-0.749902\pi\)
−0.706890 + 0.707324i \(0.749902\pi\)
\(588\) −57.0049 −2.35084
\(589\) 4.06134 0.167345
\(590\) 18.9997 0.782207
\(591\) −27.8352 −1.14499
\(592\) 19.6014 0.805614
\(593\) −15.4467 −0.634319 −0.317160 0.948372i \(-0.602729\pi\)
−0.317160 + 0.948372i \(0.602729\pi\)
\(594\) −126.360 −5.18459
\(595\) −1.32442 −0.0542960
\(596\) −31.1164 −1.27458
\(597\) 59.7629 2.44593
\(598\) −90.6251 −3.70594
\(599\) 12.2812 0.501796 0.250898 0.968013i \(-0.419274\pi\)
0.250898 + 0.968013i \(0.419274\pi\)
\(600\) 61.5977 2.51471
\(601\) 6.24490 0.254735 0.127367 0.991856i \(-0.459347\pi\)
0.127367 + 0.991856i \(0.459347\pi\)
\(602\) −8.07223 −0.329000
\(603\) 88.3224 3.59677
\(604\) −8.88868 −0.361675
\(605\) 4.54690 0.184858
\(606\) 47.8898 1.94539
\(607\) −34.3688 −1.39499 −0.697493 0.716592i \(-0.745701\pi\)
−0.697493 + 0.716592i \(0.745701\pi\)
\(608\) −3.72558 −0.151092
\(609\) 29.3762 1.19038
\(610\) −16.5005 −0.668086
\(611\) −11.4351 −0.462616
\(612\) 43.5612 1.76086
\(613\) −42.5856 −1.72002 −0.860009 0.510279i \(-0.829542\pi\)
−0.860009 + 0.510279i \(0.829542\pi\)
\(614\) 78.2781 3.15905
\(615\) 20.4116 0.823074
\(616\) 26.9333 1.08518
\(617\) 30.2193 1.21658 0.608292 0.793713i \(-0.291855\pi\)
0.608292 + 0.793713i \(0.291855\pi\)
\(618\) −11.6013 −0.466672
\(619\) 39.6495 1.59365 0.796824 0.604211i \(-0.206512\pi\)
0.796824 + 0.604211i \(0.206512\pi\)
\(620\) −5.03697 −0.202290
\(621\) 69.7654 2.79959
\(622\) 39.0558 1.56599
\(623\) 14.5897 0.584526
\(624\) 50.7273 2.03072
\(625\) 20.8659 0.834637
\(626\) 41.5739 1.66163
\(627\) −22.1437 −0.884335
\(628\) −73.9484 −2.95086
\(629\) 13.3831 0.533618
\(630\) 12.6196 0.502779
\(631\) −26.1083 −1.03935 −0.519677 0.854363i \(-0.673948\pi\)
−0.519677 + 0.854363i \(0.673948\pi\)
\(632\) 23.3765 0.929868
\(633\) 31.4317 1.24930
\(634\) 35.8475 1.42369
\(635\) −3.67682 −0.145910
\(636\) −9.32120 −0.369610
\(637\) −31.4577 −1.24640
\(638\) 68.1010 2.69614
\(639\) −64.7519 −2.56155
\(640\) 10.9856 0.434242
\(641\) −49.0900 −1.93894 −0.969470 0.245210i \(-0.921143\pi\)
−0.969470 + 0.245210i \(0.921143\pi\)
\(642\) −128.679 −5.07857
\(643\) −6.00524 −0.236824 −0.118412 0.992965i \(-0.537780\pi\)
−0.118412 + 0.992965i \(0.537780\pi\)
\(644\) −31.9647 −1.25959
\(645\) −3.82918 −0.150774
\(646\) 6.55215 0.257791
\(647\) 33.1462 1.30311 0.651555 0.758601i \(-0.274117\pi\)
0.651555 + 0.758601i \(0.274117\pi\)
\(648\) −70.4716 −2.76839
\(649\) −66.2146 −2.59915
\(650\) 73.0682 2.86597
\(651\) 11.6216 0.455486
\(652\) −58.1785 −2.27845
\(653\) −2.85218 −0.111614 −0.0558071 0.998442i \(-0.517773\pi\)
−0.0558071 + 0.998442i \(0.517773\pi\)
\(654\) −113.496 −4.43806
\(655\) −6.78111 −0.264960
\(656\) 30.8282 1.20364
\(657\) −1.42904 −0.0557520
\(658\) −6.19030 −0.241323
\(659\) −30.2362 −1.17784 −0.588918 0.808193i \(-0.700446\pi\)
−0.588918 + 0.808193i \(0.700446\pi\)
\(660\) 27.4632 1.06900
\(661\) 45.7913 1.78107 0.890537 0.454910i \(-0.150329\pi\)
0.890537 + 0.454910i \(0.150329\pi\)
\(662\) −60.5990 −2.35525
\(663\) 34.6346 1.34509
\(664\) 27.5710 1.06996
\(665\) 1.23675 0.0479592
\(666\) −127.520 −4.94128
\(667\) −37.5998 −1.45587
\(668\) 24.5494 0.949845
\(669\) −4.81405 −0.186122
\(670\) −16.4761 −0.636528
\(671\) 57.5047 2.21995
\(672\) −10.6608 −0.411250
\(673\) 14.6444 0.564502 0.282251 0.959341i \(-0.408919\pi\)
0.282251 + 0.959341i \(0.408919\pi\)
\(674\) −53.1140 −2.04587
\(675\) −56.2497 −2.16505
\(676\) 107.583 4.13782
\(677\) −41.9309 −1.61154 −0.805768 0.592232i \(-0.798247\pi\)
−0.805768 + 0.592232i \(0.798247\pi\)
\(678\) 46.7915 1.79702
\(679\) 7.44693 0.285787
\(680\) −3.78038 −0.144971
\(681\) 78.4337 3.00559
\(682\) 26.9416 1.03165
\(683\) 16.6061 0.635414 0.317707 0.948189i \(-0.397087\pi\)
0.317707 + 0.948189i \(0.397087\pi\)
\(684\) −40.6777 −1.55535
\(685\) −3.01087 −0.115040
\(686\) −41.5192 −1.58521
\(687\) −31.4225 −1.19884
\(688\) −5.78332 −0.220487
\(689\) −5.14384 −0.195965
\(690\) −23.2719 −0.885946
\(691\) 13.1873 0.501669 0.250834 0.968030i \(-0.419295\pi\)
0.250834 + 0.968030i \(0.419295\pi\)
\(692\) −30.9078 −1.17494
\(693\) −43.9798 −1.67066
\(694\) 60.1019 2.28144
\(695\) −2.97478 −0.112840
\(696\) 83.8503 3.17834
\(697\) 21.0482 0.797259
\(698\) −47.8974 −1.81294
\(699\) −23.4543 −0.887124
\(700\) 25.7722 0.974096
\(701\) −18.5417 −0.700311 −0.350155 0.936692i \(-0.613871\pi\)
−0.350155 + 0.936692i \(0.613871\pi\)
\(702\) −184.554 −6.96554
\(703\) −12.4972 −0.471340
\(704\) −46.8965 −1.76748
\(705\) −2.93646 −0.110593
\(706\) 5.85162 0.220229
\(707\) 9.32139 0.350567
\(708\) −175.248 −6.58623
\(709\) 21.4816 0.806757 0.403378 0.915033i \(-0.367836\pi\)
0.403378 + 0.915033i \(0.367836\pi\)
\(710\) 12.0792 0.453323
\(711\) −38.1719 −1.43156
\(712\) 41.6444 1.56069
\(713\) −14.8750 −0.557072
\(714\) 18.7491 0.701667
\(715\) 15.1554 0.566779
\(716\) −74.4737 −2.78321
\(717\) −56.8415 −2.12279
\(718\) 32.2298 1.20281
\(719\) 25.9331 0.967140 0.483570 0.875306i \(-0.339340\pi\)
0.483570 + 0.875306i \(0.339340\pi\)
\(720\) 9.04131 0.336950
\(721\) −2.25810 −0.0840962
\(722\) 39.4016 1.46637
\(723\) 69.1605 2.57211
\(724\) 74.3624 2.76366
\(725\) 30.3155 1.12589
\(726\) −64.3679 −2.38892
\(727\) 17.4509 0.647217 0.323608 0.946191i \(-0.395104\pi\)
0.323608 + 0.946191i \(0.395104\pi\)
\(728\) 39.3374 1.45794
\(729\) 3.09635 0.114680
\(730\) 0.266580 0.00986656
\(731\) −3.94862 −0.146045
\(732\) 152.196 5.62533
\(733\) −33.3952 −1.23348 −0.616740 0.787167i \(-0.711547\pi\)
−0.616740 + 0.787167i \(0.711547\pi\)
\(734\) −17.3811 −0.641550
\(735\) −8.07813 −0.297966
\(736\) 13.6452 0.502970
\(737\) 57.4197 2.11508
\(738\) −200.557 −7.38259
\(739\) 50.8204 1.86946 0.934730 0.355359i \(-0.115641\pi\)
0.934730 + 0.355359i \(0.115641\pi\)
\(740\) 15.4993 0.569766
\(741\) −32.3419 −1.18811
\(742\) −2.78457 −0.102225
\(743\) −4.00185 −0.146814 −0.0734068 0.997302i \(-0.523387\pi\)
−0.0734068 + 0.997302i \(0.523387\pi\)
\(744\) 33.1723 1.21615
\(745\) −4.40948 −0.161551
\(746\) −3.31683 −0.121438
\(747\) −45.0210 −1.64723
\(748\) 28.3198 1.03548
\(749\) −25.0465 −0.915180
\(750\) 38.6435 1.41106
\(751\) 49.9720 1.82350 0.911752 0.410742i \(-0.134730\pi\)
0.911752 + 0.410742i \(0.134730\pi\)
\(752\) −4.43502 −0.161729
\(753\) 19.5942 0.714054
\(754\) 99.4646 3.62229
\(755\) −1.25961 −0.0458419
\(756\) −65.0947 −2.36747
\(757\) −52.0610 −1.89219 −0.946094 0.323891i \(-0.895009\pi\)
−0.946094 + 0.323891i \(0.895009\pi\)
\(758\) −62.6671 −2.27617
\(759\) 81.1032 2.94386
\(760\) 3.53014 0.128052
\(761\) −13.7063 −0.496855 −0.248427 0.968651i \(-0.579914\pi\)
−0.248427 + 0.968651i \(0.579914\pi\)
\(762\) 52.0507 1.88560
\(763\) −22.0913 −0.799757
\(764\) 19.9604 0.722142
\(765\) 6.17304 0.223187
\(766\) 26.0748 0.942120
\(767\) −96.7095 −3.49198
\(768\) −89.1387 −3.21652
\(769\) 4.44679 0.160355 0.0801777 0.996781i \(-0.474451\pi\)
0.0801777 + 0.996781i \(0.474451\pi\)
\(770\) 8.20422 0.295660
\(771\) 6.76594 0.243669
\(772\) 52.9669 1.90632
\(773\) 11.0974 0.399144 0.199572 0.979883i \(-0.436045\pi\)
0.199572 + 0.979883i \(0.436045\pi\)
\(774\) 37.6241 1.35237
\(775\) 11.9932 0.430809
\(776\) 21.2563 0.763055
\(777\) −35.7609 −1.28292
\(778\) −81.8948 −2.93607
\(779\) −19.6550 −0.704212
\(780\) 40.1113 1.43621
\(781\) −42.0962 −1.50632
\(782\) −23.9978 −0.858158
\(783\) −76.5703 −2.73640
\(784\) −12.2006 −0.435737
\(785\) −10.4792 −0.374018
\(786\) 95.9964 3.42408
\(787\) −1.88559 −0.0672139 −0.0336069 0.999435i \(-0.510699\pi\)
−0.0336069 + 0.999435i \(0.510699\pi\)
\(788\) −33.2422 −1.18420
\(789\) −3.02457 −0.107678
\(790\) 7.12077 0.253346
\(791\) 9.10762 0.323830
\(792\) −125.534 −4.46067
\(793\) 83.9883 2.98251
\(794\) −58.4217 −2.07331
\(795\) −1.32090 −0.0468475
\(796\) 71.3719 2.52971
\(797\) 5.85623 0.207438 0.103719 0.994607i \(-0.466926\pi\)
0.103719 + 0.994607i \(0.466926\pi\)
\(798\) −17.5080 −0.619776
\(799\) −3.02805 −0.107125
\(800\) −11.0017 −0.388970
\(801\) −68.0017 −2.40272
\(802\) −26.3288 −0.929704
\(803\) −0.929038 −0.0327850
\(804\) 151.971 5.35960
\(805\) −4.52970 −0.159651
\(806\) 39.3495 1.38603
\(807\) −46.3041 −1.62998
\(808\) 26.6066 0.936019
\(809\) −7.49863 −0.263638 −0.131819 0.991274i \(-0.542082\pi\)
−0.131819 + 0.991274i \(0.542082\pi\)
\(810\) −21.4665 −0.754256
\(811\) −31.3364 −1.10037 −0.550185 0.835043i \(-0.685443\pi\)
−0.550185 + 0.835043i \(0.685443\pi\)
\(812\) 35.0825 1.23116
\(813\) 46.4270 1.62826
\(814\) −82.9024 −2.90573
\(815\) −8.24444 −0.288790
\(816\) 13.4327 0.470240
\(817\) 3.68724 0.129000
\(818\) −24.7914 −0.866810
\(819\) −64.2345 −2.24454
\(820\) 24.3766 0.851267
\(821\) −44.4557 −1.55152 −0.775758 0.631031i \(-0.782632\pi\)
−0.775758 + 0.631031i \(0.782632\pi\)
\(822\) 42.6232 1.48666
\(823\) 48.7892 1.70068 0.850342 0.526231i \(-0.176395\pi\)
0.850342 + 0.526231i \(0.176395\pi\)
\(824\) −6.44545 −0.224538
\(825\) −65.3909 −2.27662
\(826\) −52.3528 −1.82159
\(827\) −7.85896 −0.273283 −0.136641 0.990621i \(-0.543631\pi\)
−0.136641 + 0.990621i \(0.543631\pi\)
\(828\) 148.985 5.17760
\(829\) −12.8270 −0.445500 −0.222750 0.974876i \(-0.571503\pi\)
−0.222750 + 0.974876i \(0.571503\pi\)
\(830\) 8.39846 0.291515
\(831\) 40.1182 1.39168
\(832\) −68.4945 −2.37462
\(833\) −8.33009 −0.288621
\(834\) 42.1123 1.45823
\(835\) 3.47888 0.120392
\(836\) −26.4452 −0.914626
\(837\) −30.2922 −1.04705
\(838\) −49.2350 −1.70079
\(839\) 19.3220 0.667070 0.333535 0.942738i \(-0.391758\pi\)
0.333535 + 0.942738i \(0.391758\pi\)
\(840\) 10.1016 0.348537
\(841\) 12.2672 0.423009
\(842\) −72.4896 −2.49816
\(843\) 65.5257 2.25683
\(844\) 37.5374 1.29209
\(845\) 15.2456 0.524464
\(846\) 28.8526 0.991971
\(847\) −12.5287 −0.430493
\(848\) −1.99500 −0.0685084
\(849\) −65.0451 −2.23234
\(850\) 19.3486 0.663653
\(851\) 45.7719 1.56904
\(852\) −111.415 −3.81700
\(853\) 44.8801 1.53667 0.768333 0.640050i \(-0.221086\pi\)
0.768333 + 0.640050i \(0.221086\pi\)
\(854\) 45.4663 1.55582
\(855\) −5.76441 −0.197139
\(856\) −71.4919 −2.44354
\(857\) −11.4945 −0.392645 −0.196323 0.980539i \(-0.562900\pi\)
−0.196323 + 0.980539i \(0.562900\pi\)
\(858\) −214.546 −7.32448
\(859\) −12.2624 −0.418388 −0.209194 0.977874i \(-0.567084\pi\)
−0.209194 + 0.977874i \(0.567084\pi\)
\(860\) −4.57301 −0.155938
\(861\) −56.2430 −1.91676
\(862\) 75.5223 2.57230
\(863\) 14.4831 0.493010 0.246505 0.969142i \(-0.420718\pi\)
0.246505 + 0.969142i \(0.420718\pi\)
\(864\) 27.7879 0.945364
\(865\) −4.37992 −0.148922
\(866\) 25.4945 0.866339
\(867\) −44.0642 −1.49650
\(868\) 13.8791 0.471088
\(869\) −24.8161 −0.841828
\(870\) 25.5418 0.865948
\(871\) 83.8641 2.84163
\(872\) −63.0565 −2.13536
\(873\) −34.7096 −1.17474
\(874\) 22.4092 0.758004
\(875\) 7.52168 0.254279
\(876\) −2.45885 −0.0830770
\(877\) −4.57721 −0.154561 −0.0772807 0.997009i \(-0.524624\pi\)
−0.0772807 + 0.997009i \(0.524624\pi\)
\(878\) −7.69854 −0.259813
\(879\) 63.2707 2.13407
\(880\) 5.87789 0.198144
\(881\) −22.1840 −0.747397 −0.373698 0.927550i \(-0.621910\pi\)
−0.373698 + 0.927550i \(0.621910\pi\)
\(882\) 79.3726 2.67262
\(883\) 17.0892 0.575098 0.287549 0.957766i \(-0.407160\pi\)
0.287549 + 0.957766i \(0.407160\pi\)
\(884\) 41.3624 1.39117
\(885\) −24.8343 −0.834796
\(886\) 23.7696 0.798555
\(887\) −5.99375 −0.201250 −0.100625 0.994924i \(-0.532084\pi\)
−0.100625 + 0.994924i \(0.532084\pi\)
\(888\) −102.075 −3.42540
\(889\) 10.1313 0.339793
\(890\) 12.6854 0.425215
\(891\) 74.8114 2.50627
\(892\) −5.74918 −0.192497
\(893\) 2.82761 0.0946224
\(894\) 62.4226 2.08772
\(895\) −10.5536 −0.352769
\(896\) −30.2701 −1.01125
\(897\) 118.455 3.95509
\(898\) 41.9592 1.40020
\(899\) 16.3259 0.544498
\(900\) −120.122 −4.00407
\(901\) −1.36210 −0.0453782
\(902\) −130.385 −4.34134
\(903\) 10.5511 0.351119
\(904\) 25.9965 0.864629
\(905\) 10.5379 0.350290
\(906\) 17.8316 0.592415
\(907\) −22.8978 −0.760307 −0.380154 0.924923i \(-0.624129\pi\)
−0.380154 + 0.924923i \(0.624129\pi\)
\(908\) 93.6696 3.10853
\(909\) −43.4464 −1.44102
\(910\) 11.9826 0.397221
\(911\) −42.6176 −1.41199 −0.705993 0.708219i \(-0.749499\pi\)
−0.705993 + 0.708219i \(0.749499\pi\)
\(912\) −12.5435 −0.415358
\(913\) −29.2689 −0.968658
\(914\) 30.6589 1.01411
\(915\) 21.5676 0.713003
\(916\) −37.5264 −1.23991
\(917\) 18.6850 0.617033
\(918\) −48.8703 −1.61296
\(919\) −1.50308 −0.0495821 −0.0247910 0.999693i \(-0.507892\pi\)
−0.0247910 + 0.999693i \(0.507892\pi\)
\(920\) −12.9294 −0.426270
\(921\) −102.316 −3.37143
\(922\) −87.3090 −2.87537
\(923\) −61.4834 −2.02375
\(924\) −75.6734 −2.48947
\(925\) −36.9045 −1.21341
\(926\) −8.70211 −0.285969
\(927\) 10.5249 0.345682
\(928\) −14.9762 −0.491617
\(929\) −28.0069 −0.918878 −0.459439 0.888209i \(-0.651950\pi\)
−0.459439 + 0.888209i \(0.651950\pi\)
\(930\) 10.1047 0.331345
\(931\) 7.77868 0.254936
\(932\) −28.0104 −0.917511
\(933\) −51.0493 −1.67128
\(934\) 68.1098 2.22862
\(935\) 4.01318 0.131245
\(936\) −183.349 −5.99294
\(937\) −17.3071 −0.565397 −0.282699 0.959209i \(-0.591230\pi\)
−0.282699 + 0.959209i \(0.591230\pi\)
\(938\) 45.3991 1.48233
\(939\) −54.3406 −1.77334
\(940\) −3.50687 −0.114382
\(941\) 0.476801 0.0155433 0.00777163 0.999970i \(-0.497526\pi\)
0.00777163 + 0.999970i \(0.497526\pi\)
\(942\) 148.348 4.83343
\(943\) 71.9878 2.34425
\(944\) −37.5080 −1.22078
\(945\) −9.22453 −0.300074
\(946\) 24.4600 0.795263
\(947\) 23.5709 0.765950 0.382975 0.923759i \(-0.374899\pi\)
0.382975 + 0.923759i \(0.374899\pi\)
\(948\) −65.6800 −2.13319
\(949\) −1.35690 −0.0440469
\(950\) −18.0679 −0.586199
\(951\) −46.8558 −1.51940
\(952\) 10.4166 0.337605
\(953\) −0.209171 −0.00677570 −0.00338785 0.999994i \(-0.501078\pi\)
−0.00338785 + 0.999994i \(0.501078\pi\)
\(954\) 12.9787 0.420200
\(955\) 2.82858 0.0915306
\(956\) −67.8831 −2.19550
\(957\) −89.0139 −2.87741
\(958\) −32.5733 −1.05239
\(959\) 8.29630 0.267901
\(960\) −17.5889 −0.567679
\(961\) −24.5413 −0.791654
\(962\) −121.083 −3.90386
\(963\) 116.740 3.76189
\(964\) 82.5950 2.66021
\(965\) 7.50590 0.241623
\(966\) 64.1244 2.06317
\(967\) −40.5567 −1.30421 −0.652107 0.758127i \(-0.726115\pi\)
−0.652107 + 0.758127i \(0.726115\pi\)
\(968\) −35.7616 −1.14942
\(969\) −8.56423 −0.275123
\(970\) 6.47491 0.207897
\(971\) −26.1376 −0.838795 −0.419397 0.907803i \(-0.637759\pi\)
−0.419397 + 0.907803i \(0.637759\pi\)
\(972\) 64.2713 2.06150
\(973\) 8.19686 0.262779
\(974\) 46.0980 1.47707
\(975\) −95.5064 −3.05865
\(976\) 32.5742 1.04267
\(977\) 26.7372 0.855400 0.427700 0.903921i \(-0.359324\pi\)
0.427700 + 0.903921i \(0.359324\pi\)
\(978\) 116.712 3.73203
\(979\) −44.2090 −1.41292
\(980\) −9.64732 −0.308172
\(981\) 102.966 3.28744
\(982\) −88.1580 −2.81324
\(983\) −9.80023 −0.312579 −0.156289 0.987711i \(-0.549953\pi\)
−0.156289 + 0.987711i \(0.549953\pi\)
\(984\) −160.538 −5.11777
\(985\) −4.71073 −0.150096
\(986\) 26.3385 0.838788
\(987\) 8.09126 0.257548
\(988\) −38.6244 −1.22881
\(989\) −13.5048 −0.429428
\(990\) −38.2393 −1.21532
\(991\) 29.8744 0.948991 0.474495 0.880258i \(-0.342631\pi\)
0.474495 + 0.880258i \(0.342631\pi\)
\(992\) −5.92478 −0.188112
\(993\) 79.2081 2.51359
\(994\) −33.2835 −1.05569
\(995\) 10.1141 0.320638
\(996\) −77.4650 −2.45457
\(997\) 23.8507 0.755359 0.377680 0.925936i \(-0.376722\pi\)
0.377680 + 0.925936i \(0.376722\pi\)
\(998\) 53.5312 1.69450
\(999\) 93.2124 2.94911
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 \(a_p\))