Properties

Label 8003.2.a.c.1.13
Level 8003
Weight 2
Character 8003.1
Self dual Yes
Analytic conductor 63.904
Analytic rank 0
Dimension 172
CM No

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Newspace parameters

Level: \( N \) = \( 8003 = 53 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9042767376\)
Analytic rank: \(0\)
Dimension: \(172\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.52938 q^{2}\) \(-2.71474 q^{3}\) \(+4.39775 q^{4}\) \(-1.01620 q^{5}\) \(+6.86661 q^{6}\) \(+3.17147 q^{7}\) \(-6.06482 q^{8}\) \(+4.36984 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.52938 q^{2}\) \(-2.71474 q^{3}\) \(+4.39775 q^{4}\) \(-1.01620 q^{5}\) \(+6.86661 q^{6}\) \(+3.17147 q^{7}\) \(-6.06482 q^{8}\) \(+4.36984 q^{9}\) \(+2.57036 q^{10}\) \(-1.72198 q^{11}\) \(-11.9388 q^{12}\) \(-2.04995 q^{13}\) \(-8.02184 q^{14}\) \(+2.75873 q^{15}\) \(+6.54472 q^{16}\) \(+2.02987 q^{17}\) \(-11.0530 q^{18}\) \(+7.44930 q^{19}\) \(-4.46901 q^{20}\) \(-8.60972 q^{21}\) \(+4.35555 q^{22}\) \(+1.64276 q^{23}\) \(+16.4644 q^{24}\) \(-3.96733 q^{25}\) \(+5.18511 q^{26}\) \(-3.71876 q^{27}\) \(+13.9473 q^{28}\) \(-6.77724 q^{29}\) \(-6.97788 q^{30}\) \(+1.15418 q^{31}\) \(-4.42443 q^{32}\) \(+4.67474 q^{33}\) \(-5.13430 q^{34}\) \(-3.22286 q^{35}\) \(+19.2175 q^{36}\) \(+6.28134 q^{37}\) \(-18.8421 q^{38}\) \(+5.56510 q^{39}\) \(+6.16310 q^{40}\) \(-7.21808 q^{41}\) \(+21.7772 q^{42}\) \(-0.235456 q^{43}\) \(-7.57285 q^{44}\) \(-4.44065 q^{45}\) \(-4.15517 q^{46}\) \(-2.65341 q^{47}\) \(-17.7672 q^{48}\) \(+3.05821 q^{49}\) \(+10.0349 q^{50}\) \(-5.51057 q^{51}\) \(-9.01519 q^{52}\) \(-1.00000 q^{53}\) \(+9.40614 q^{54}\) \(+1.74989 q^{55}\) \(-19.2344 q^{56}\) \(-20.2229 q^{57}\) \(+17.1422 q^{58}\) \(-5.75196 q^{59}\) \(+12.1322 q^{60}\) \(+11.7353 q^{61}\) \(-2.91937 q^{62}\) \(+13.8588 q^{63}\) \(-1.89839 q^{64}\) \(+2.08317 q^{65}\) \(-11.8242 q^{66}\) \(+6.26921 q^{67}\) \(+8.92686 q^{68}\) \(-4.45968 q^{69}\) \(+8.15183 q^{70}\) \(+4.36727 q^{71}\) \(-26.5023 q^{72}\) \(-8.97038 q^{73}\) \(-15.8879 q^{74}\) \(+10.7703 q^{75}\) \(+32.7602 q^{76}\) \(-5.46121 q^{77}\) \(-14.0762 q^{78}\) \(-1.76049 q^{79}\) \(-6.65077 q^{80}\) \(-3.01404 q^{81}\) \(+18.2573 q^{82}\) \(+2.45457 q^{83}\) \(-37.8634 q^{84}\) \(-2.06276 q^{85}\) \(+0.595557 q^{86}\) \(+18.3985 q^{87}\) \(+10.4435 q^{88}\) \(+5.38980 q^{89}\) \(+11.2321 q^{90}\) \(-6.50136 q^{91}\) \(+7.22446 q^{92}\) \(-3.13331 q^{93}\) \(+6.71149 q^{94}\) \(-7.57001 q^{95}\) \(+12.0112 q^{96}\) \(+4.45042 q^{97}\) \(-7.73536 q^{98}\) \(-7.52478 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 66q^{12} \) \(\mathstrut +\mathstrut 121q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 212q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 40q^{18} \) \(\mathstrut +\mathstrut 41q^{19} \) \(\mathstrut +\mathstrut 64q^{20} \) \(\mathstrut +\mathstrut 56q^{21} \) \(\mathstrut +\mathstrut 50q^{22} \) \(\mathstrut +\mathstrut 28q^{23} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 231q^{25} \) \(\mathstrut +\mathstrut 38q^{26} \) \(\mathstrut +\mathstrut 100q^{27} \) \(\mathstrut +\mathstrut 80q^{28} \) \(\mathstrut +\mathstrut 26q^{29} \) \(\mathstrut +\mathstrut 55q^{30} \) \(\mathstrut +\mathstrut 66q^{31} \) \(\mathstrut +\mathstrut 65q^{32} \) \(\mathstrut +\mathstrut 99q^{33} \) \(\mathstrut +\mathstrut 81q^{34} \) \(\mathstrut +\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 212q^{36} \) \(\mathstrut +\mathstrut 153q^{37} \) \(\mathstrut +\mathstrut q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 59q^{40} \) \(\mathstrut +\mathstrut 40q^{41} \) \(\mathstrut +\mathstrut 50q^{42} \) \(\mathstrut +\mathstrut 39q^{43} \) \(\mathstrut -\mathstrut 51q^{44} \) \(\mathstrut +\mathstrut 123q^{45} \) \(\mathstrut +\mathstrut 59q^{46} \) \(\mathstrut +\mathstrut 29q^{47} \) \(\mathstrut +\mathstrut 128q^{48} \) \(\mathstrut +\mathstrut 245q^{49} \) \(\mathstrut +\mathstrut 19q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 215q^{52} \) \(\mathstrut -\mathstrut 172q^{53} \) \(\mathstrut +\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut 40q^{55} \) \(\mathstrut +\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 54q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 54q^{60} \) \(\mathstrut +\mathstrut 100q^{61} \) \(\mathstrut -\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 92q^{63} \) \(\mathstrut +\mathstrut 253q^{64} \) \(\mathstrut +\mathstrut 77q^{65} \) \(\mathstrut +\mathstrut 14q^{66} \) \(\mathstrut +\mathstrut 126q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut +\mathstrut 47q^{69} \) \(\mathstrut +\mathstrut 72q^{70} \) \(\mathstrut +\mathstrut 38q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 185q^{73} \) \(\mathstrut +\mathstrut 48q^{74} \) \(\mathstrut +\mathstrut 75q^{75} \) \(\mathstrut +\mathstrut 38q^{76} \) \(\mathstrut +\mathstrut 120q^{77} \) \(\mathstrut +\mathstrut 75q^{78} \) \(\mathstrut +\mathstrut 79q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 232q^{81} \) \(\mathstrut +\mathstrut 110q^{82} \) \(\mathstrut +\mathstrut 90q^{83} \) \(\mathstrut +\mathstrut 158q^{84} \) \(\mathstrut +\mathstrut 115q^{85} \) \(\mathstrut +\mathstrut 68q^{86} \) \(\mathstrut +\mathstrut 61q^{87} \) \(\mathstrut +\mathstrut 15q^{88} \) \(\mathstrut -\mathstrut 36q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 33q^{91} \) \(\mathstrut +\mathstrut 139q^{92} \) \(\mathstrut +\mathstrut 103q^{93} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 45q^{95} \) \(\mathstrut +\mathstrut 34q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut -\mathstrut 36q^{98} \) \(\mathstrut +\mathstrut 27q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.52938 −1.78854 −0.894270 0.447528i \(-0.852305\pi\)
−0.894270 + 0.447528i \(0.852305\pi\)
\(3\) −2.71474 −1.56736 −0.783679 0.621166i \(-0.786659\pi\)
−0.783679 + 0.621166i \(0.786659\pi\)
\(4\) 4.39775 2.19888
\(5\) −1.01620 −0.454460 −0.227230 0.973841i \(-0.572967\pi\)
−0.227230 + 0.973841i \(0.572967\pi\)
\(6\) 6.86661 2.80328
\(7\) 3.17147 1.19870 0.599351 0.800486i \(-0.295425\pi\)
0.599351 + 0.800486i \(0.295425\pi\)
\(8\) −6.06482 −2.14424
\(9\) 4.36984 1.45661
\(10\) 2.57036 0.812821
\(11\) −1.72198 −0.519197 −0.259599 0.965717i \(-0.583590\pi\)
−0.259599 + 0.965717i \(0.583590\pi\)
\(12\) −11.9388 −3.44643
\(13\) −2.04995 −0.568555 −0.284278 0.958742i \(-0.591754\pi\)
−0.284278 + 0.958742i \(0.591754\pi\)
\(14\) −8.02184 −2.14393
\(15\) 2.75873 0.712302
\(16\) 6.54472 1.63618
\(17\) 2.02987 0.492315 0.246158 0.969230i \(-0.420832\pi\)
0.246158 + 0.969230i \(0.420832\pi\)
\(18\) −11.0530 −2.60521
\(19\) 7.44930 1.70899 0.854493 0.519463i \(-0.173868\pi\)
0.854493 + 0.519463i \(0.173868\pi\)
\(20\) −4.46901 −0.999302
\(21\) −8.60972 −1.87880
\(22\) 4.35555 0.928605
\(23\) 1.64276 0.342540 0.171270 0.985224i \(-0.445213\pi\)
0.171270 + 0.985224i \(0.445213\pi\)
\(24\) 16.4644 3.36079
\(25\) −3.96733 −0.793466
\(26\) 5.18511 1.01688
\(27\) −3.71876 −0.715675
\(28\) 13.9473 2.63580
\(29\) −6.77724 −1.25850 −0.629251 0.777202i \(-0.716638\pi\)
−0.629251 + 0.777202i \(0.716638\pi\)
\(30\) −6.97788 −1.27398
\(31\) 1.15418 0.207298 0.103649 0.994614i \(-0.466948\pi\)
0.103649 + 0.994614i \(0.466948\pi\)
\(32\) −4.42443 −0.782136
\(33\) 4.67474 0.813768
\(34\) −5.13430 −0.880526
\(35\) −3.22286 −0.544763
\(36\) 19.2175 3.20291
\(37\) 6.28134 1.03265 0.516323 0.856394i \(-0.327300\pi\)
0.516323 + 0.856394i \(0.327300\pi\)
\(38\) −18.8421 −3.05659
\(39\) 5.56510 0.891129
\(40\) 6.16310 0.974471
\(41\) −7.21808 −1.12727 −0.563637 0.826022i \(-0.690598\pi\)
−0.563637 + 0.826022i \(0.690598\pi\)
\(42\) 21.7772 3.36030
\(43\) −0.235456 −0.0359067 −0.0179534 0.999839i \(-0.505715\pi\)
−0.0179534 + 0.999839i \(0.505715\pi\)
\(44\) −7.57285 −1.14165
\(45\) −4.44065 −0.661973
\(46\) −4.15517 −0.612646
\(47\) −2.65341 −0.387040 −0.193520 0.981096i \(-0.561990\pi\)
−0.193520 + 0.981096i \(0.561990\pi\)
\(48\) −17.7672 −2.56448
\(49\) 3.05821 0.436886
\(50\) 10.0349 1.41915
\(51\) −5.51057 −0.771635
\(52\) −9.01519 −1.25018
\(53\) −1.00000 −0.137361
\(54\) 9.40614 1.28001
\(55\) 1.74989 0.235955
\(56\) −19.2344 −2.57030
\(57\) −20.2229 −2.67859
\(58\) 17.1422 2.25088
\(59\) −5.75196 −0.748841 −0.374421 0.927259i \(-0.622158\pi\)
−0.374421 + 0.927259i \(0.622158\pi\)
\(60\) 12.1322 1.56626
\(61\) 11.7353 1.50255 0.751277 0.659987i \(-0.229438\pi\)
0.751277 + 0.659987i \(0.229438\pi\)
\(62\) −2.91937 −0.370760
\(63\) 13.8588 1.74604
\(64\) −1.89839 −0.237299
\(65\) 2.08317 0.258386
\(66\) −11.8242 −1.45546
\(67\) 6.26921 0.765906 0.382953 0.923768i \(-0.374907\pi\)
0.382953 + 0.923768i \(0.374907\pi\)
\(68\) 8.92686 1.08254
\(69\) −4.45968 −0.536882
\(70\) 8.15183 0.974330
\(71\) 4.36727 0.518300 0.259150 0.965837i \(-0.416558\pi\)
0.259150 + 0.965837i \(0.416558\pi\)
\(72\) −26.5023 −3.12332
\(73\) −8.97038 −1.04990 −0.524952 0.851132i \(-0.675917\pi\)
−0.524952 + 0.851132i \(0.675917\pi\)
\(74\) −15.8879 −1.84693
\(75\) 10.7703 1.24365
\(76\) 32.7602 3.75785
\(77\) −5.46121 −0.622363
\(78\) −14.0762 −1.59382
\(79\) −1.76049 −0.198070 −0.0990351 0.995084i \(-0.531576\pi\)
−0.0990351 + 0.995084i \(0.531576\pi\)
\(80\) −6.65077 −0.743579
\(81\) −3.01404 −0.334893
\(82\) 18.2573 2.01618
\(83\) 2.45457 0.269424 0.134712 0.990885i \(-0.456989\pi\)
0.134712 + 0.990885i \(0.456989\pi\)
\(84\) −37.8634 −4.13124
\(85\) −2.06276 −0.223738
\(86\) 0.595557 0.0642206
\(87\) 18.3985 1.97252
\(88\) 10.4435 1.11328
\(89\) 5.38980 0.571318 0.285659 0.958331i \(-0.407788\pi\)
0.285659 + 0.958331i \(0.407788\pi\)
\(90\) 11.2321 1.18396
\(91\) −6.50136 −0.681528
\(92\) 7.22446 0.753202
\(93\) −3.13331 −0.324910
\(94\) 6.71149 0.692237
\(95\) −7.57001 −0.776666
\(96\) 12.0112 1.22589
\(97\) 4.45042 0.451871 0.225936 0.974142i \(-0.427456\pi\)
0.225936 + 0.974142i \(0.427456\pi\)
\(98\) −7.73536 −0.781389
\(99\) −7.52478 −0.756269
\(100\) −17.4473 −1.74473
\(101\) 3.09905 0.308367 0.154184 0.988042i \(-0.450725\pi\)
0.154184 + 0.988042i \(0.450725\pi\)
\(102\) 13.9383 1.38010
\(103\) 15.9941 1.57595 0.787974 0.615708i \(-0.211130\pi\)
0.787974 + 0.615708i \(0.211130\pi\)
\(104\) 12.4326 1.21912
\(105\) 8.74924 0.853838
\(106\) 2.52938 0.245675
\(107\) 6.28801 0.607885 0.303942 0.952690i \(-0.401697\pi\)
0.303942 + 0.952690i \(0.401697\pi\)
\(108\) −16.3542 −1.57368
\(109\) 3.12327 0.299155 0.149577 0.988750i \(-0.452209\pi\)
0.149577 + 0.988750i \(0.452209\pi\)
\(110\) −4.42612 −0.422014
\(111\) −17.0522 −1.61853
\(112\) 20.7564 1.96129
\(113\) 2.35174 0.221233 0.110616 0.993863i \(-0.464718\pi\)
0.110616 + 0.993863i \(0.464718\pi\)
\(114\) 51.1515 4.79077
\(115\) −1.66938 −0.155671
\(116\) −29.8046 −2.76729
\(117\) −8.95797 −0.828164
\(118\) 14.5489 1.33933
\(119\) 6.43766 0.590139
\(120\) −16.7312 −1.52735
\(121\) −8.03477 −0.730434
\(122\) −29.6831 −2.68738
\(123\) 19.5952 1.76684
\(124\) 5.07582 0.455822
\(125\) 9.11264 0.815059
\(126\) −35.0541 −3.12287
\(127\) 6.48154 0.575143 0.287572 0.957759i \(-0.407152\pi\)
0.287572 + 0.957759i \(0.407152\pi\)
\(128\) 13.6506 1.20655
\(129\) 0.639203 0.0562787
\(130\) −5.26913 −0.462133
\(131\) −1.50294 −0.131312 −0.0656562 0.997842i \(-0.520914\pi\)
−0.0656562 + 0.997842i \(0.520914\pi\)
\(132\) 20.5584 1.78938
\(133\) 23.6252 2.04856
\(134\) −15.8572 −1.36985
\(135\) 3.77902 0.325246
\(136\) −12.3108 −1.05564
\(137\) 4.03923 0.345094 0.172547 0.985001i \(-0.444800\pi\)
0.172547 + 0.985001i \(0.444800\pi\)
\(138\) 11.2802 0.960236
\(139\) −7.51618 −0.637514 −0.318757 0.947836i \(-0.603265\pi\)
−0.318757 + 0.947836i \(0.603265\pi\)
\(140\) −14.1733 −1.19787
\(141\) 7.20334 0.606631
\(142\) −11.0465 −0.927000
\(143\) 3.52999 0.295192
\(144\) 28.5994 2.38328
\(145\) 6.88706 0.571939
\(146\) 22.6895 1.87779
\(147\) −8.30225 −0.684758
\(148\) 27.6238 2.27066
\(149\) 7.81344 0.640102 0.320051 0.947400i \(-0.396300\pi\)
0.320051 + 0.947400i \(0.396300\pi\)
\(150\) −27.2421 −2.22431
\(151\) 1.00000 0.0813788
\(152\) −45.1787 −3.66447
\(153\) 8.87019 0.717113
\(154\) 13.8135 1.11312
\(155\) −1.17289 −0.0942085
\(156\) 24.4739 1.95948
\(157\) −2.02541 −0.161646 −0.0808228 0.996728i \(-0.525755\pi\)
−0.0808228 + 0.996728i \(0.525755\pi\)
\(158\) 4.45293 0.354256
\(159\) 2.71474 0.215293
\(160\) 4.49612 0.355450
\(161\) 5.20997 0.410603
\(162\) 7.62364 0.598970
\(163\) 11.5818 0.907158 0.453579 0.891216i \(-0.350147\pi\)
0.453579 + 0.891216i \(0.350147\pi\)
\(164\) −31.7433 −2.47874
\(165\) −4.75049 −0.369825
\(166\) −6.20853 −0.481876
\(167\) 3.16302 0.244762 0.122381 0.992483i \(-0.460947\pi\)
0.122381 + 0.992483i \(0.460947\pi\)
\(168\) 52.2164 4.02859
\(169\) −8.79769 −0.676745
\(170\) 5.21750 0.400164
\(171\) 32.5522 2.48933
\(172\) −1.03548 −0.0789544
\(173\) −10.8951 −0.828336 −0.414168 0.910200i \(-0.635927\pi\)
−0.414168 + 0.910200i \(0.635927\pi\)
\(174\) −46.5367 −3.52794
\(175\) −12.5823 −0.951129
\(176\) −11.2699 −0.849500
\(177\) 15.6151 1.17370
\(178\) −13.6328 −1.02182
\(179\) 13.6802 1.02250 0.511252 0.859431i \(-0.329182\pi\)
0.511252 + 0.859431i \(0.329182\pi\)
\(180\) −19.5289 −1.45560
\(181\) 6.15797 0.457719 0.228859 0.973460i \(-0.426500\pi\)
0.228859 + 0.973460i \(0.426500\pi\)
\(182\) 16.4444 1.21894
\(183\) −31.8584 −2.35504
\(184\) −9.96306 −0.734487
\(185\) −6.38312 −0.469297
\(186\) 7.92534 0.581114
\(187\) −3.49540 −0.255609
\(188\) −11.6691 −0.851054
\(189\) −11.7939 −0.857881
\(190\) 19.1474 1.38910
\(191\) 17.3418 1.25481 0.627403 0.778695i \(-0.284118\pi\)
0.627403 + 0.778695i \(0.284118\pi\)
\(192\) 5.15364 0.371932
\(193\) −6.26252 −0.450786 −0.225393 0.974268i \(-0.572367\pi\)
−0.225393 + 0.974268i \(0.572367\pi\)
\(194\) −11.2568 −0.808190
\(195\) −5.65528 −0.404983
\(196\) 13.4492 0.960659
\(197\) 9.08386 0.647198 0.323599 0.946194i \(-0.395107\pi\)
0.323599 + 0.946194i \(0.395107\pi\)
\(198\) 19.0330 1.35262
\(199\) −22.8262 −1.61811 −0.809055 0.587733i \(-0.800020\pi\)
−0.809055 + 0.587733i \(0.800020\pi\)
\(200\) 24.0611 1.70138
\(201\) −17.0193 −1.20045
\(202\) −7.83867 −0.551527
\(203\) −21.4938 −1.50857
\(204\) −24.2341 −1.69673
\(205\) 7.33504 0.512302
\(206\) −40.4552 −2.81865
\(207\) 7.17860 0.498947
\(208\) −13.4164 −0.930258
\(209\) −12.8276 −0.887301
\(210\) −22.1301 −1.52712
\(211\) 22.4759 1.54730 0.773651 0.633612i \(-0.218428\pi\)
0.773651 + 0.633612i \(0.218428\pi\)
\(212\) −4.39775 −0.302039
\(213\) −11.8560 −0.812362
\(214\) −15.9047 −1.08723
\(215\) 0.239271 0.0163182
\(216\) 22.5536 1.53458
\(217\) 3.66046 0.248488
\(218\) −7.89993 −0.535051
\(219\) 24.3523 1.64557
\(220\) 7.69557 0.518835
\(221\) −4.16114 −0.279908
\(222\) 43.1315 2.89480
\(223\) −2.25917 −0.151286 −0.0756428 0.997135i \(-0.524101\pi\)
−0.0756428 + 0.997135i \(0.524101\pi\)
\(224\) −14.0319 −0.937548
\(225\) −17.3366 −1.15577
\(226\) −5.94843 −0.395684
\(227\) 14.8801 0.987626 0.493813 0.869568i \(-0.335603\pi\)
0.493813 + 0.869568i \(0.335603\pi\)
\(228\) −88.9355 −5.88990
\(229\) −15.1342 −1.00009 −0.500047 0.865998i \(-0.666684\pi\)
−0.500047 + 0.865998i \(0.666684\pi\)
\(230\) 4.22250 0.278423
\(231\) 14.8258 0.975466
\(232\) 41.1027 2.69853
\(233\) −14.5354 −0.952248 −0.476124 0.879378i \(-0.657959\pi\)
−0.476124 + 0.879378i \(0.657959\pi\)
\(234\) 22.6581 1.48121
\(235\) 2.69641 0.175894
\(236\) −25.2957 −1.64661
\(237\) 4.77927 0.310447
\(238\) −16.2833 −1.05549
\(239\) −14.3070 −0.925445 −0.462723 0.886503i \(-0.653127\pi\)
−0.462723 + 0.886503i \(0.653127\pi\)
\(240\) 18.0551 1.16545
\(241\) −17.5599 −1.13113 −0.565567 0.824703i \(-0.691343\pi\)
−0.565567 + 0.824703i \(0.691343\pi\)
\(242\) 20.3230 1.30641
\(243\) 19.3386 1.24057
\(244\) 51.6091 3.30393
\(245\) −3.10776 −0.198548
\(246\) −49.5638 −3.16007
\(247\) −15.2707 −0.971653
\(248\) −6.99992 −0.444495
\(249\) −6.66353 −0.422284
\(250\) −23.0493 −1.45777
\(251\) −14.3877 −0.908147 −0.454073 0.890964i \(-0.650030\pi\)
−0.454073 + 0.890964i \(0.650030\pi\)
\(252\) 60.9475 3.83933
\(253\) −2.82881 −0.177846
\(254\) −16.3943 −1.02867
\(255\) 5.59987 0.350677
\(256\) −30.7308 −1.92067
\(257\) 26.4230 1.64822 0.824112 0.566427i \(-0.191675\pi\)
0.824112 + 0.566427i \(0.191675\pi\)
\(258\) −1.61679 −0.100657
\(259\) 19.9211 1.23783
\(260\) 9.16128 0.568158
\(261\) −29.6154 −1.83315
\(262\) 3.80150 0.234857
\(263\) −31.3019 −1.93016 −0.965078 0.261961i \(-0.915631\pi\)
−0.965078 + 0.261961i \(0.915631\pi\)
\(264\) −28.3515 −1.74491
\(265\) 1.01620 0.0624249
\(266\) −59.7571 −3.66394
\(267\) −14.6319 −0.895459
\(268\) 27.5704 1.68413
\(269\) 10.2698 0.626164 0.313082 0.949726i \(-0.398639\pi\)
0.313082 + 0.949726i \(0.398639\pi\)
\(270\) −9.55856 −0.581715
\(271\) −11.2224 −0.681715 −0.340858 0.940115i \(-0.610717\pi\)
−0.340858 + 0.940115i \(0.610717\pi\)
\(272\) 13.2849 0.805517
\(273\) 17.6495 1.06820
\(274\) −10.2167 −0.617215
\(275\) 6.83167 0.411965
\(276\) −19.6126 −1.18054
\(277\) 1.47933 0.0888846 0.0444423 0.999012i \(-0.485849\pi\)
0.0444423 + 0.999012i \(0.485849\pi\)
\(278\) 19.0113 1.14022
\(279\) 5.04360 0.301952
\(280\) 19.5461 1.16810
\(281\) −24.5959 −1.46727 −0.733635 0.679544i \(-0.762178\pi\)
−0.733635 + 0.679544i \(0.762178\pi\)
\(282\) −18.2200 −1.08498
\(283\) −15.4686 −0.919515 −0.459757 0.888045i \(-0.652064\pi\)
−0.459757 + 0.888045i \(0.652064\pi\)
\(284\) 19.2062 1.13968
\(285\) 20.5506 1.21731
\(286\) −8.92867 −0.527963
\(287\) −22.8919 −1.35127
\(288\) −19.3340 −1.13927
\(289\) −12.8796 −0.757626
\(290\) −17.4200 −1.02294
\(291\) −12.0817 −0.708244
\(292\) −39.4495 −2.30861
\(293\) −8.77489 −0.512634 −0.256317 0.966593i \(-0.582509\pi\)
−0.256317 + 0.966593i \(0.582509\pi\)
\(294\) 20.9995 1.22472
\(295\) 5.84517 0.340319
\(296\) −38.0952 −2.21424
\(297\) 6.40364 0.371577
\(298\) −19.7631 −1.14485
\(299\) −3.36759 −0.194753
\(300\) 47.3650 2.73462
\(301\) −0.746741 −0.0430414
\(302\) −2.52938 −0.145549
\(303\) −8.41313 −0.483322
\(304\) 48.7536 2.79621
\(305\) −11.9255 −0.682852
\(306\) −22.4361 −1.28258
\(307\) 12.5464 0.716058 0.358029 0.933710i \(-0.383449\pi\)
0.358029 + 0.933710i \(0.383449\pi\)
\(308\) −24.0171 −1.36850
\(309\) −43.4200 −2.47008
\(310\) 2.96667 0.168496
\(311\) 7.12651 0.404107 0.202054 0.979374i \(-0.435238\pi\)
0.202054 + 0.979374i \(0.435238\pi\)
\(312\) −33.7513 −1.91079
\(313\) 13.1008 0.740499 0.370249 0.928932i \(-0.379272\pi\)
0.370249 + 0.928932i \(0.379272\pi\)
\(314\) 5.12304 0.289110
\(315\) −14.0834 −0.793508
\(316\) −7.74218 −0.435532
\(317\) −11.5990 −0.651464 −0.325732 0.945462i \(-0.605611\pi\)
−0.325732 + 0.945462i \(0.605611\pi\)
\(318\) −6.86661 −0.385061
\(319\) 11.6703 0.653410
\(320\) 1.92915 0.107843
\(321\) −17.0703 −0.952773
\(322\) −13.1780 −0.734380
\(323\) 15.1211 0.841360
\(324\) −13.2550 −0.736388
\(325\) 8.13284 0.451129
\(326\) −29.2948 −1.62249
\(327\) −8.47888 −0.468883
\(328\) 43.7764 2.41715
\(329\) −8.41522 −0.463946
\(330\) 12.0158 0.661448
\(331\) −12.7462 −0.700594 −0.350297 0.936639i \(-0.613919\pi\)
−0.350297 + 0.936639i \(0.613919\pi\)
\(332\) 10.7946 0.592430
\(333\) 27.4484 1.50416
\(334\) −8.00046 −0.437766
\(335\) −6.37080 −0.348074
\(336\) −56.3482 −3.07405
\(337\) 9.06122 0.493596 0.246798 0.969067i \(-0.420622\pi\)
0.246798 + 0.969067i \(0.420622\pi\)
\(338\) 22.2527 1.21039
\(339\) −6.38436 −0.346751
\(340\) −9.07151 −0.491972
\(341\) −1.98749 −0.107628
\(342\) −82.3369 −4.45227
\(343\) −12.5013 −0.675005
\(344\) 1.42800 0.0769925
\(345\) 4.53195 0.243992
\(346\) 27.5577 1.48151
\(347\) 17.6582 0.947944 0.473972 0.880540i \(-0.342820\pi\)
0.473972 + 0.880540i \(0.342820\pi\)
\(348\) 80.9119 4.33733
\(349\) −24.4833 −1.31056 −0.655279 0.755387i \(-0.727449\pi\)
−0.655279 + 0.755387i \(0.727449\pi\)
\(350\) 31.8253 1.70113
\(351\) 7.62328 0.406901
\(352\) 7.61879 0.406083
\(353\) −25.2002 −1.34127 −0.670635 0.741787i \(-0.733978\pi\)
−0.670635 + 0.741787i \(0.733978\pi\)
\(354\) −39.4965 −2.09921
\(355\) −4.43804 −0.235547
\(356\) 23.7030 1.25626
\(357\) −17.4766 −0.924960
\(358\) −34.6023 −1.82879
\(359\) 2.44838 0.129220 0.0646102 0.997911i \(-0.479420\pi\)
0.0646102 + 0.997911i \(0.479420\pi\)
\(360\) 26.9317 1.41943
\(361\) 36.4920 1.92063
\(362\) −15.5758 −0.818648
\(363\) 21.8124 1.14485
\(364\) −28.5914 −1.49860
\(365\) 9.11573 0.477139
\(366\) 80.5820 4.21209
\(367\) 13.6426 0.712140 0.356070 0.934459i \(-0.384116\pi\)
0.356070 + 0.934459i \(0.384116\pi\)
\(368\) 10.7514 0.560457
\(369\) −31.5418 −1.64200
\(370\) 16.1453 0.839356
\(371\) −3.17147 −0.164654
\(372\) −13.7795 −0.714436
\(373\) 21.4117 1.10866 0.554328 0.832298i \(-0.312975\pi\)
0.554328 + 0.832298i \(0.312975\pi\)
\(374\) 8.84118 0.457167
\(375\) −24.7385 −1.27749
\(376\) 16.0925 0.829907
\(377\) 13.8930 0.715527
\(378\) 29.8313 1.53435
\(379\) −10.2618 −0.527113 −0.263556 0.964644i \(-0.584896\pi\)
−0.263556 + 0.964644i \(0.584896\pi\)
\(380\) −33.2910 −1.70779
\(381\) −17.5957 −0.901456
\(382\) −43.8639 −2.24427
\(383\) 3.78554 0.193432 0.0967160 0.995312i \(-0.469166\pi\)
0.0967160 + 0.995312i \(0.469166\pi\)
\(384\) −37.0579 −1.89110
\(385\) 5.54971 0.282839
\(386\) 15.8403 0.806249
\(387\) −1.02890 −0.0523022
\(388\) 19.5718 0.993609
\(389\) −20.0779 −1.01799 −0.508995 0.860769i \(-0.669983\pi\)
−0.508995 + 0.860769i \(0.669983\pi\)
\(390\) 14.3043 0.724328
\(391\) 3.33459 0.168638
\(392\) −18.5475 −0.936789
\(393\) 4.08009 0.205814
\(394\) −22.9765 −1.15754
\(395\) 1.78901 0.0900150
\(396\) −33.0921 −1.66294
\(397\) 4.93872 0.247867 0.123934 0.992291i \(-0.460449\pi\)
0.123934 + 0.992291i \(0.460449\pi\)
\(398\) 57.7362 2.89405
\(399\) −64.1364 −3.21084
\(400\) −25.9651 −1.29825
\(401\) −0.931897 −0.0465367 −0.0232684 0.999729i \(-0.507407\pi\)
−0.0232684 + 0.999729i \(0.507407\pi\)
\(402\) 43.0482 2.14705
\(403\) −2.36602 −0.117860
\(404\) 13.6289 0.678061
\(405\) 3.06288 0.152196
\(406\) 54.3659 2.69813
\(407\) −10.8164 −0.536147
\(408\) 33.4206 1.65457
\(409\) 22.9404 1.13433 0.567165 0.823604i \(-0.308040\pi\)
0.567165 + 0.823604i \(0.308040\pi\)
\(410\) −18.5531 −0.916272
\(411\) −10.9655 −0.540887
\(412\) 70.3382 3.46532
\(413\) −18.2422 −0.897638
\(414\) −18.1574 −0.892388
\(415\) −2.49434 −0.122443
\(416\) 9.06988 0.444687
\(417\) 20.4045 0.999213
\(418\) 32.4458 1.58697
\(419\) −18.6195 −0.909624 −0.454812 0.890587i \(-0.650294\pi\)
−0.454812 + 0.890587i \(0.650294\pi\)
\(420\) 38.4770 1.87748
\(421\) 22.7000 1.10633 0.553164 0.833072i \(-0.313420\pi\)
0.553164 + 0.833072i \(0.313420\pi\)
\(422\) −56.8500 −2.76741
\(423\) −11.5950 −0.563768
\(424\) 6.06482 0.294534
\(425\) −8.05316 −0.390635
\(426\) 29.9884 1.45294
\(427\) 37.2182 1.80112
\(428\) 27.6531 1.33666
\(429\) −9.58301 −0.462672
\(430\) −0.605208 −0.0291857
\(431\) −14.4004 −0.693644 −0.346822 0.937931i \(-0.612739\pi\)
−0.346822 + 0.937931i \(0.612739\pi\)
\(432\) −24.3382 −1.17097
\(433\) −24.4765 −1.17627 −0.588133 0.808764i \(-0.700137\pi\)
−0.588133 + 0.808764i \(0.700137\pi\)
\(434\) −9.25868 −0.444431
\(435\) −18.6966 −0.896433
\(436\) 13.7354 0.657805
\(437\) 12.2374 0.585395
\(438\) −61.5961 −2.94318
\(439\) 3.45083 0.164699 0.0823497 0.996603i \(-0.473758\pi\)
0.0823497 + 0.996603i \(0.473758\pi\)
\(440\) −10.6127 −0.505943
\(441\) 13.3639 0.636374
\(442\) 10.5251 0.500627
\(443\) −26.9828 −1.28199 −0.640995 0.767545i \(-0.721478\pi\)
−0.640995 + 0.767545i \(0.721478\pi\)
\(444\) −74.9915 −3.55894
\(445\) −5.47714 −0.259641
\(446\) 5.71431 0.270580
\(447\) −21.2115 −1.00327
\(448\) −6.02068 −0.284450
\(449\) 29.3930 1.38714 0.693571 0.720389i \(-0.256036\pi\)
0.693571 + 0.720389i \(0.256036\pi\)
\(450\) 43.8508 2.06714
\(451\) 12.4294 0.585278
\(452\) 10.3424 0.486464
\(453\) −2.71474 −0.127550
\(454\) −37.6374 −1.76641
\(455\) 6.60671 0.309727
\(456\) 122.649 5.74354
\(457\) 33.8081 1.58148 0.790739 0.612154i \(-0.209697\pi\)
0.790739 + 0.612154i \(0.209697\pi\)
\(458\) 38.2801 1.78871
\(459\) −7.54859 −0.352338
\(460\) −7.34153 −0.342301
\(461\) −40.2491 −1.87459 −0.937294 0.348539i \(-0.886678\pi\)
−0.937294 + 0.348539i \(0.886678\pi\)
\(462\) −37.5000 −1.74466
\(463\) 1.78696 0.0830470 0.0415235 0.999138i \(-0.486779\pi\)
0.0415235 + 0.999138i \(0.486779\pi\)
\(464\) −44.3551 −2.05913
\(465\) 3.18409 0.147659
\(466\) 36.7656 1.70313
\(467\) −21.1120 −0.976946 −0.488473 0.872579i \(-0.662446\pi\)
−0.488473 + 0.872579i \(0.662446\pi\)
\(468\) −39.3949 −1.82103
\(469\) 19.8826 0.918093
\(470\) −6.82024 −0.314594
\(471\) 5.49848 0.253357
\(472\) 34.8846 1.60569
\(473\) 0.405451 0.0186427
\(474\) −12.0886 −0.555247
\(475\) −29.5538 −1.35602
\(476\) 28.3112 1.29764
\(477\) −4.36984 −0.200081
\(478\) 36.1879 1.65520
\(479\) −26.6458 −1.21748 −0.608739 0.793371i \(-0.708324\pi\)
−0.608739 + 0.793371i \(0.708324\pi\)
\(480\) −12.2058 −0.557117
\(481\) −12.8765 −0.587116
\(482\) 44.4157 2.02308
\(483\) −14.1437 −0.643562
\(484\) −35.3350 −1.60613
\(485\) −4.52253 −0.205358
\(486\) −48.9147 −2.21881
\(487\) −2.04352 −0.0926008 −0.0463004 0.998928i \(-0.514743\pi\)
−0.0463004 + 0.998928i \(0.514743\pi\)
\(488\) −71.1727 −3.22184
\(489\) −31.4417 −1.42184
\(490\) 7.86070 0.355110
\(491\) 21.0945 0.951980 0.475990 0.879451i \(-0.342090\pi\)
0.475990 + 0.879451i \(0.342090\pi\)
\(492\) 86.1750 3.88507
\(493\) −13.7569 −0.619579
\(494\) 38.6254 1.73784
\(495\) 7.64672 0.343694
\(496\) 7.55381 0.339176
\(497\) 13.8507 0.621287
\(498\) 16.8546 0.755272
\(499\) 29.4438 1.31809 0.659043 0.752106i \(-0.270962\pi\)
0.659043 + 0.752106i \(0.270962\pi\)
\(500\) 40.0751 1.79221
\(501\) −8.58678 −0.383629
\(502\) 36.3921 1.62426
\(503\) 6.91994 0.308545 0.154272 0.988028i \(-0.450697\pi\)
0.154272 + 0.988028i \(0.450697\pi\)
\(504\) −84.0511 −3.74393
\(505\) −3.14927 −0.140141
\(506\) 7.15513 0.318084
\(507\) 23.8835 1.06070
\(508\) 28.5042 1.26467
\(509\) 27.4112 1.21498 0.607490 0.794327i \(-0.292176\pi\)
0.607490 + 0.794327i \(0.292176\pi\)
\(510\) −14.1642 −0.627201
\(511\) −28.4493 −1.25852
\(512\) 50.4285 2.22864
\(513\) −27.7021 −1.22308
\(514\) −66.8338 −2.94791
\(515\) −16.2533 −0.716206
\(516\) 2.81106 0.123750
\(517\) 4.56913 0.200950
\(518\) −50.3879 −2.21392
\(519\) 29.5773 1.29830
\(520\) −12.6341 −0.554041
\(521\) 45.3683 1.98762 0.993811 0.111080i \(-0.0354311\pi\)
0.993811 + 0.111080i \(0.0354311\pi\)
\(522\) 74.9086 3.27866
\(523\) −18.1937 −0.795556 −0.397778 0.917482i \(-0.630219\pi\)
−0.397778 + 0.917482i \(0.630219\pi\)
\(524\) −6.60955 −0.288740
\(525\) 34.1576 1.49076
\(526\) 79.1743 3.45216
\(527\) 2.34284 0.102056
\(528\) 30.5949 1.33147
\(529\) −20.3013 −0.882667
\(530\) −2.57036 −0.111650
\(531\) −25.1351 −1.09077
\(532\) 103.898 4.50454
\(533\) 14.7967 0.640918
\(534\) 37.0097 1.60157
\(535\) −6.38990 −0.276259
\(536\) −38.0216 −1.64228
\(537\) −37.1382 −1.60263
\(538\) −25.9763 −1.11992
\(539\) −5.26618 −0.226830
\(540\) 16.6192 0.715176
\(541\) −15.2149 −0.654140 −0.327070 0.945000i \(-0.606061\pi\)
−0.327070 + 0.945000i \(0.606061\pi\)
\(542\) 28.3858 1.21928
\(543\) −16.7173 −0.717409
\(544\) −8.98101 −0.385058
\(545\) −3.17388 −0.135954
\(546\) −44.6424 −1.91052
\(547\) 26.3853 1.12815 0.564076 0.825723i \(-0.309233\pi\)
0.564076 + 0.825723i \(0.309233\pi\)
\(548\) 17.7635 0.758820
\(549\) 51.2815 2.18864
\(550\) −17.2799 −0.736817
\(551\) −50.4856 −2.15076
\(552\) 27.0472 1.15120
\(553\) −5.58332 −0.237427
\(554\) −3.74180 −0.158974
\(555\) 17.3285 0.735556
\(556\) −33.0543 −1.40181
\(557\) 30.1573 1.27781 0.638904 0.769287i \(-0.279388\pi\)
0.638904 + 0.769287i \(0.279388\pi\)
\(558\) −12.7572 −0.540054
\(559\) 0.482674 0.0204149
\(560\) −21.0927 −0.891330
\(561\) 9.48911 0.400631
\(562\) 62.2124 2.62427
\(563\) 22.1569 0.933801 0.466901 0.884310i \(-0.345371\pi\)
0.466901 + 0.884310i \(0.345371\pi\)
\(564\) 31.6785 1.33391
\(565\) −2.38985 −0.100542
\(566\) 39.1260 1.64459
\(567\) −9.55892 −0.401437
\(568\) −26.4867 −1.11136
\(569\) −21.0799 −0.883715 −0.441858 0.897085i \(-0.645680\pi\)
−0.441858 + 0.897085i \(0.645680\pi\)
\(570\) −51.9803 −2.17722
\(571\) 28.6673 1.19969 0.599845 0.800116i \(-0.295229\pi\)
0.599845 + 0.800116i \(0.295229\pi\)
\(572\) 15.5240 0.649091
\(573\) −47.0785 −1.96673
\(574\) 57.9023 2.41679
\(575\) −6.51738 −0.271793
\(576\) −8.29565 −0.345652
\(577\) 12.7371 0.530252 0.265126 0.964214i \(-0.414586\pi\)
0.265126 + 0.964214i \(0.414586\pi\)
\(578\) 32.5775 1.35504
\(579\) 17.0011 0.706543
\(580\) 30.2876 1.25762
\(581\) 7.78459 0.322959
\(582\) 30.5593 1.26672
\(583\) 1.72198 0.0713172
\(584\) 54.4037 2.25124
\(585\) 9.10312 0.376368
\(586\) 22.1950 0.916867
\(587\) 29.2069 1.20550 0.602749 0.797931i \(-0.294072\pi\)
0.602749 + 0.797931i \(0.294072\pi\)
\(588\) −36.5112 −1.50570
\(589\) 8.59786 0.354269
\(590\) −14.7846 −0.608674
\(591\) −24.6604 −1.01439
\(592\) 41.1096 1.68959
\(593\) −2.97743 −0.122269 −0.0611343 0.998130i \(-0.519472\pi\)
−0.0611343 + 0.998130i \(0.519472\pi\)
\(594\) −16.1972 −0.664580
\(595\) −6.54198 −0.268195
\(596\) 34.3616 1.40750
\(597\) 61.9674 2.53616
\(598\) 8.51790 0.348323
\(599\) −13.6794 −0.558924 −0.279462 0.960157i \(-0.590156\pi\)
−0.279462 + 0.960157i \(0.590156\pi\)
\(600\) −65.3198 −2.66667
\(601\) 16.9758 0.692457 0.346229 0.938150i \(-0.387462\pi\)
0.346229 + 0.938150i \(0.387462\pi\)
\(602\) 1.88879 0.0769814
\(603\) 27.3954 1.11563
\(604\) 4.39775 0.178942
\(605\) 8.16497 0.331953
\(606\) 21.2800 0.864441
\(607\) −6.88128 −0.279303 −0.139651 0.990201i \(-0.544598\pi\)
−0.139651 + 0.990201i \(0.544598\pi\)
\(608\) −32.9589 −1.33666
\(609\) 58.3501 2.36447
\(610\) 30.1641 1.22131
\(611\) 5.43938 0.220054
\(612\) 39.0089 1.57684
\(613\) 37.1082 1.49879 0.749393 0.662126i \(-0.230346\pi\)
0.749393 + 0.662126i \(0.230346\pi\)
\(614\) −31.7345 −1.28070
\(615\) −19.9128 −0.802960
\(616\) 33.1213 1.33449
\(617\) 12.9883 0.522889 0.261445 0.965219i \(-0.415801\pi\)
0.261445 + 0.965219i \(0.415801\pi\)
\(618\) 109.826 4.41783
\(619\) −1.98564 −0.0798097 −0.0399048 0.999203i \(-0.512705\pi\)
−0.0399048 + 0.999203i \(0.512705\pi\)
\(620\) −5.15807 −0.207153
\(621\) −6.10903 −0.245147
\(622\) −18.0256 −0.722762
\(623\) 17.0936 0.684840
\(624\) 36.4220 1.45805
\(625\) 10.5763 0.423054
\(626\) −33.1368 −1.32441
\(627\) 34.8236 1.39072
\(628\) −8.90727 −0.355439
\(629\) 12.7503 0.508387
\(630\) 35.6222 1.41922
\(631\) −24.8408 −0.988898 −0.494449 0.869207i \(-0.664630\pi\)
−0.494449 + 0.869207i \(0.664630\pi\)
\(632\) 10.6770 0.424710
\(633\) −61.0162 −2.42518
\(634\) 29.3382 1.16517
\(635\) −6.58656 −0.261380
\(636\) 11.9388 0.473403
\(637\) −6.26918 −0.248394
\(638\) −29.5186 −1.16865
\(639\) 19.0843 0.754962
\(640\) −13.8718 −0.548331
\(641\) −26.4597 −1.04510 −0.522548 0.852610i \(-0.675018\pi\)
−0.522548 + 0.852610i \(0.675018\pi\)
\(642\) 43.1773 1.70407
\(643\) 15.6491 0.617142 0.308571 0.951201i \(-0.400149\pi\)
0.308571 + 0.951201i \(0.400149\pi\)
\(644\) 22.9121 0.902865
\(645\) −0.649561 −0.0255764
\(646\) −38.2470 −1.50481
\(647\) 10.7335 0.421979 0.210989 0.977488i \(-0.432331\pi\)
0.210989 + 0.977488i \(0.432331\pi\)
\(648\) 18.2796 0.718090
\(649\) 9.90478 0.388796
\(650\) −20.5710 −0.806862
\(651\) −9.93720 −0.389470
\(652\) 50.9340 1.99473
\(653\) 32.8211 1.28439 0.642194 0.766542i \(-0.278024\pi\)
0.642194 + 0.766542i \(0.278024\pi\)
\(654\) 21.4463 0.838616
\(655\) 1.52729 0.0596763
\(656\) −47.2403 −1.84442
\(657\) −39.1991 −1.52930
\(658\) 21.2853 0.829786
\(659\) 22.8968 0.891934 0.445967 0.895049i \(-0.352860\pi\)
0.445967 + 0.895049i \(0.352860\pi\)
\(660\) −20.8915 −0.813200
\(661\) 7.94221 0.308916 0.154458 0.987999i \(-0.450637\pi\)
0.154458 + 0.987999i \(0.450637\pi\)
\(662\) 32.2399 1.25304
\(663\) 11.2964 0.438717
\(664\) −14.8865 −0.577709
\(665\) −24.0080 −0.930992
\(666\) −69.4274 −2.69026
\(667\) −11.1334 −0.431087
\(668\) 13.9102 0.538200
\(669\) 6.13308 0.237119
\(670\) 16.1141 0.622544
\(671\) −20.2080 −0.780122
\(672\) 38.0931 1.46947
\(673\) 17.3319 0.668097 0.334049 0.942556i \(-0.391585\pi\)
0.334049 + 0.942556i \(0.391585\pi\)
\(674\) −22.9192 −0.882817
\(675\) 14.7535 0.567864
\(676\) −38.6901 −1.48808
\(677\) −5.31753 −0.204369 −0.102185 0.994765i \(-0.532583\pi\)
−0.102185 + 0.994765i \(0.532583\pi\)
\(678\) 16.1485 0.620178
\(679\) 14.1144 0.541659
\(680\) 12.5103 0.479747
\(681\) −40.3956 −1.54796
\(682\) 5.02710 0.192498
\(683\) −27.3281 −1.04568 −0.522840 0.852431i \(-0.675128\pi\)
−0.522840 + 0.852431i \(0.675128\pi\)
\(684\) 143.157 5.47373
\(685\) −4.10468 −0.156832
\(686\) 31.6204 1.20727
\(687\) 41.0854 1.56751
\(688\) −1.54099 −0.0587498
\(689\) 2.04995 0.0780970
\(690\) −11.4630 −0.436389
\(691\) −11.5393 −0.438974 −0.219487 0.975615i \(-0.570438\pi\)
−0.219487 + 0.975615i \(0.570438\pi\)
\(692\) −47.9138 −1.82141
\(693\) −23.8646 −0.906541
\(694\) −44.6644 −1.69544
\(695\) 7.63798 0.289725
\(696\) −111.583 −4.22956
\(697\) −14.6518 −0.554975
\(698\) 61.9274 2.34399
\(699\) 39.4600 1.49251
\(700\) −55.3336 −2.09141
\(701\) 16.5174 0.623855 0.311928 0.950106i \(-0.399025\pi\)
0.311928 + 0.950106i \(0.399025\pi\)
\(702\) −19.2822 −0.727758
\(703\) 46.7916 1.76478
\(704\) 3.26899 0.123205
\(705\) −7.32007 −0.275690
\(706\) 63.7408 2.39892
\(707\) 9.82854 0.369640
\(708\) 68.6713 2.58083
\(709\) 32.5822 1.22365 0.611825 0.790993i \(-0.290436\pi\)
0.611825 + 0.790993i \(0.290436\pi\)
\(710\) 11.2255 0.421285
\(711\) −7.69304 −0.288511
\(712\) −32.6882 −1.22504
\(713\) 1.89605 0.0710076
\(714\) 44.2049 1.65433
\(715\) −3.58719 −0.134153
\(716\) 60.1620 2.24836
\(717\) 38.8400 1.45050
\(718\) −6.19287 −0.231116
\(719\) −23.0005 −0.857773 −0.428887 0.903358i \(-0.641094\pi\)
−0.428887 + 0.903358i \(0.641094\pi\)
\(720\) −29.0628 −1.08311
\(721\) 50.7249 1.88909
\(722\) −92.3021 −3.43513
\(723\) 47.6707 1.77289
\(724\) 27.0812 1.00647
\(725\) 26.8875 0.998578
\(726\) −55.1717 −2.04761
\(727\) 9.33453 0.346199 0.173099 0.984904i \(-0.444622\pi\)
0.173099 + 0.984904i \(0.444622\pi\)
\(728\) 39.4296 1.46136
\(729\) −43.4573 −1.60953
\(730\) −23.0571 −0.853383
\(731\) −0.477945 −0.0176774
\(732\) −140.105 −5.17844
\(733\) −6.28618 −0.232185 −0.116093 0.993238i \(-0.537037\pi\)
−0.116093 + 0.993238i \(0.537037\pi\)
\(734\) −34.5074 −1.27369
\(735\) 8.43678 0.311195
\(736\) −7.26829 −0.267913
\(737\) −10.7955 −0.397656
\(738\) 79.7812 2.93679
\(739\) −4.21019 −0.154874 −0.0774371 0.996997i \(-0.524674\pi\)
−0.0774371 + 0.996997i \(0.524674\pi\)
\(740\) −28.0714 −1.03192
\(741\) 41.4561 1.52293
\(742\) 8.02184 0.294491
\(743\) −27.0743 −0.993259 −0.496630 0.867963i \(-0.665429\pi\)
−0.496630 + 0.867963i \(0.665429\pi\)
\(744\) 19.0030 0.696684
\(745\) −7.94005 −0.290901
\(746\) −54.1583 −1.98288
\(747\) 10.7261 0.392446
\(748\) −15.3719 −0.562052
\(749\) 19.9422 0.728672
\(750\) 62.5730 2.28484
\(751\) −24.8042 −0.905116 −0.452558 0.891735i \(-0.649489\pi\)
−0.452558 + 0.891735i \(0.649489\pi\)
\(752\) −17.3659 −0.633268
\(753\) 39.0591 1.42339
\(754\) −35.1407 −1.27975
\(755\) −1.01620 −0.0369835
\(756\) −51.8667 −1.88637
\(757\) −18.3549 −0.667120 −0.333560 0.942729i \(-0.608250\pi\)
−0.333560 + 0.942729i \(0.608250\pi\)
\(758\) 25.9560 0.942763
\(759\) 7.67949 0.278748
\(760\) 45.9107 1.66536
\(761\) 14.4782 0.524834 0.262417 0.964955i \(-0.415480\pi\)
0.262417 + 0.964955i \(0.415480\pi\)
\(762\) 44.5062 1.61229
\(763\) 9.90535 0.358598
\(764\) 76.2648 2.75916
\(765\) −9.01393 −0.325899
\(766\) −9.57506 −0.345961
\(767\) 11.7913 0.425758
\(768\) 83.4261 3.01038
\(769\) −23.3086 −0.840529 −0.420265 0.907402i \(-0.638063\pi\)
−0.420265 + 0.907402i \(0.638063\pi\)
\(770\) −14.0373 −0.505869
\(771\) −71.7318 −2.58336
\(772\) −27.5410 −0.991222
\(773\) −35.4208 −1.27400 −0.636999 0.770865i \(-0.719824\pi\)
−0.636999 + 0.770865i \(0.719824\pi\)
\(774\) 2.60249 0.0935445
\(775\) −4.57903 −0.164484
\(776\) −26.9910 −0.968920
\(777\) −54.0806 −1.94013
\(778\) 50.7846 1.82072
\(779\) −53.7696 −1.92650
\(780\) −24.8705 −0.890508
\(781\) −7.52037 −0.269100
\(782\) −8.43444 −0.301615
\(783\) 25.2029 0.900678
\(784\) 20.0151 0.714825
\(785\) 2.05824 0.0734616
\(786\) −10.3201 −0.368106
\(787\) 34.9955 1.24745 0.623727 0.781642i \(-0.285618\pi\)
0.623727 + 0.781642i \(0.285618\pi\)
\(788\) 39.9486 1.42311
\(789\) 84.9766 3.02525
\(790\) −4.52509 −0.160995
\(791\) 7.45846 0.265192
\(792\) 45.6365 1.62162
\(793\) −24.0569 −0.854285
\(794\) −12.4919 −0.443320
\(795\) −2.75873 −0.0978422
\(796\) −100.384 −3.55802
\(797\) 17.1187 0.606374 0.303187 0.952931i \(-0.401949\pi\)
0.303187 + 0.952931i \(0.401949\pi\)
\(798\) 162.225 5.74271
\(799\) −5.38608 −0.190546
\(800\) 17.5532 0.620598
\(801\) 23.5525 0.832188
\(802\) 2.35712 0.0832328
\(803\) 15.4468 0.545107
\(804\) −74.8466 −2.63964
\(805\) −5.29439 −0.186603
\(806\) 5.98457 0.210797
\(807\) −27.8800 −0.981423
\(808\) −18.7952 −0.661213
\(809\) −13.0541 −0.458957 −0.229478 0.973314i \(-0.573702\pi\)
−0.229478 + 0.973314i \(0.573702\pi\)
\(810\) −7.74717 −0.272208
\(811\) −19.0442 −0.668731 −0.334366 0.942443i \(-0.608522\pi\)
−0.334366 + 0.942443i \(0.608522\pi\)
\(812\) −94.5243 −3.31715
\(813\) 30.4661 1.06849
\(814\) 27.3587 0.958920
\(815\) −11.7695 −0.412267
\(816\) −36.0652 −1.26253
\(817\) −1.75398 −0.0613641
\(818\) −58.0249 −2.02879
\(819\) −28.4099 −0.992722
\(820\) 32.2577 1.12649
\(821\) −31.1681 −1.08778 −0.543888 0.839158i \(-0.683048\pi\)
−0.543888 + 0.839158i \(0.683048\pi\)
\(822\) 27.7358 0.967397
\(823\) 12.0162 0.418858 0.209429 0.977824i \(-0.432840\pi\)
0.209429 + 0.977824i \(0.432840\pi\)
\(824\) −97.0016 −3.37921
\(825\) −18.5462 −0.645697
\(826\) 46.1413 1.60546
\(827\) −4.69508 −0.163264 −0.0816319 0.996663i \(-0.526013\pi\)
−0.0816319 + 0.996663i \(0.526013\pi\)
\(828\) 31.5697 1.09712
\(829\) 27.0897 0.940865 0.470432 0.882436i \(-0.344098\pi\)
0.470432 + 0.882436i \(0.344098\pi\)
\(830\) 6.30914 0.218993
\(831\) −4.01601 −0.139314
\(832\) 3.89161 0.134917
\(833\) 6.20775 0.215086
\(834\) −51.6107 −1.78713
\(835\) −3.21427 −0.111234
\(836\) −56.4124 −1.95107
\(837\) −4.29213 −0.148358
\(838\) 47.0959 1.62690
\(839\) 1.37006 0.0472997 0.0236499 0.999720i \(-0.492471\pi\)
0.0236499 + 0.999720i \(0.492471\pi\)
\(840\) −53.0626 −1.83083
\(841\) 16.9309 0.583825
\(842\) −57.4168 −1.97871
\(843\) 66.7716 2.29974
\(844\) 98.8433 3.40233
\(845\) 8.94025 0.307554
\(846\) 29.3281 1.00832
\(847\) −25.4820 −0.875573
\(848\) −6.54472 −0.224747
\(849\) 41.9934 1.44121
\(850\) 20.3695 0.698667
\(851\) 10.3187 0.353722
\(852\) −52.1399 −1.78628
\(853\) −31.1102 −1.06519 −0.532597 0.846369i \(-0.678784\pi\)
−0.532597 + 0.846369i \(0.678784\pi\)
\(854\) −94.1389 −3.22137
\(855\) −33.0797 −1.13130
\(856\) −38.1356 −1.30345
\(857\) −18.3794 −0.627830 −0.313915 0.949451i \(-0.601641\pi\)
−0.313915 + 0.949451i \(0.601641\pi\)
\(858\) 24.2391 0.827508
\(859\) −20.7343 −0.707446 −0.353723 0.935350i \(-0.615084\pi\)
−0.353723 + 0.935350i \(0.615084\pi\)
\(860\) 1.05226 0.0358817
\(861\) 62.1457 2.11792
\(862\) 36.4241 1.24061
\(863\) −23.7444 −0.808270 −0.404135 0.914699i \(-0.632427\pi\)
−0.404135 + 0.914699i \(0.632427\pi\)
\(864\) 16.4534 0.559755
\(865\) 11.0716 0.376446
\(866\) 61.9103 2.10380
\(867\) 34.9649 1.18747
\(868\) 16.0978 0.546394
\(869\) 3.03153 0.102837
\(870\) 47.2908 1.60331
\(871\) −12.8516 −0.435459
\(872\) −18.9421 −0.641459
\(873\) 19.4476 0.658201
\(874\) −30.9531 −1.04700
\(875\) 28.9004 0.977013
\(876\) 107.095 3.61841
\(877\) −27.4326 −0.926333 −0.463166 0.886271i \(-0.653287\pi\)
−0.463166 + 0.886271i \(0.653287\pi\)
\(878\) −8.72846 −0.294571
\(879\) 23.8216 0.803482
\(880\) 11.4525 0.386064
\(881\) 0.962467 0.0324263 0.0162132 0.999869i \(-0.494839\pi\)
0.0162132 + 0.999869i \(0.494839\pi\)
\(882\) −33.8022 −1.13818
\(883\) 20.2621 0.681875 0.340938 0.940086i \(-0.389256\pi\)
0.340938 + 0.940086i \(0.389256\pi\)
\(884\) −18.2997 −0.615484
\(885\) −15.8681 −0.533401
\(886\) 68.2496 2.29289
\(887\) 34.3812 1.15441 0.577204 0.816600i \(-0.304144\pi\)
0.577204 + 0.816600i \(0.304144\pi\)
\(888\) 103.419 3.47050
\(889\) 20.5560 0.689425
\(890\) 13.8538 0.464379
\(891\) 5.19012 0.173876
\(892\) −9.93529 −0.332658
\(893\) −19.7661 −0.661446
\(894\) 53.6519 1.79439
\(895\) −13.9019 −0.464688
\(896\) 43.2924 1.44630
\(897\) 9.14214 0.305247
\(898\) −74.3460 −2.48096
\(899\) −7.82218 −0.260884
\(900\) −76.2420 −2.54140
\(901\) −2.02987 −0.0676247
\(902\) −31.4387 −1.04679
\(903\) 2.02721 0.0674614
\(904\) −14.2629 −0.474376
\(905\) −6.25776 −0.208015
\(906\) 6.86661 0.228128
\(907\) −33.9325 −1.12671 −0.563355 0.826215i \(-0.690490\pi\)
−0.563355 + 0.826215i \(0.690490\pi\)
\(908\) 65.4389 2.17167
\(909\) 13.5424 0.449171
\(910\) −16.7109 −0.553960
\(911\) 1.32998 0.0440642 0.0220321 0.999757i \(-0.492986\pi\)
0.0220321 + 0.999757i \(0.492986\pi\)
\(912\) −132.353 −4.38266
\(913\) −4.22673 −0.139884
\(914\) −85.5135 −2.82854
\(915\) 32.3747 1.07027
\(916\) −66.5564 −2.19908
\(917\) −4.76652 −0.157404
\(918\) 19.0932 0.630170
\(919\) 5.26297 0.173609 0.0868047 0.996225i \(-0.472334\pi\)
0.0868047 + 0.996225i \(0.472334\pi\)
\(920\) 10.1245 0.333795
\(921\) −34.0602 −1.12232
\(922\) 101.805 3.35278
\(923\) −8.95271 −0.294682
\(924\) 65.2002 2.14493
\(925\) −24.9201 −0.819369
\(926\) −4.51990 −0.148533
\(927\) 69.8918 2.29555
\(928\) 29.9854 0.984319
\(929\) −3.65409 −0.119887 −0.0599434 0.998202i \(-0.519092\pi\)
−0.0599434 + 0.998202i \(0.519092\pi\)
\(930\) −8.05376 −0.264093
\(931\) 22.7815 0.746633
\(932\) −63.9232 −2.09387
\(933\) −19.3467 −0.633381
\(934\) 53.4002 1.74731
\(935\) 3.55204 0.116164
\(936\) 54.3285 1.77578
\(937\) 26.3386 0.860445 0.430222 0.902723i \(-0.358435\pi\)
0.430222 + 0.902723i \(0.358435\pi\)
\(938\) −50.2906 −1.64205
\(939\) −35.5652 −1.16063
\(940\) 11.8581 0.386770
\(941\) 10.2228 0.333255 0.166627 0.986020i \(-0.446712\pi\)
0.166627 + 0.986020i \(0.446712\pi\)
\(942\) −13.9077 −0.453139
\(943\) −11.8576 −0.386136
\(944\) −37.6450 −1.22524
\(945\) 11.9850 0.389873
\(946\) −1.02554 −0.0333432
\(947\) 37.2758 1.21130 0.605650 0.795731i \(-0.292913\pi\)
0.605650 + 0.795731i \(0.292913\pi\)
\(948\) 21.0180 0.682634
\(949\) 18.3889 0.596928
\(950\) 74.7528 2.42530
\(951\) 31.4883 1.02108
\(952\) −39.0433 −1.26540
\(953\) −9.20020 −0.298024 −0.149012 0.988835i \(-0.547609\pi\)
−0.149012 + 0.988835i \(0.547609\pi\)
\(954\) 11.0530 0.357853
\(955\) −17.6228 −0.570260
\(956\) −62.9188 −2.03494
\(957\) −31.6818 −1.02413
\(958\) 67.3973 2.17751
\(959\) 12.8103 0.413665
\(960\) −5.23715 −0.169028
\(961\) −29.6679 −0.957028
\(962\) 32.5694 1.05008
\(963\) 27.4776 0.885452
\(964\) −77.2241 −2.48722
\(965\) 6.36400 0.204864
\(966\) 35.7748 1.15104
\(967\) 25.9819 0.835521 0.417761 0.908557i \(-0.362815\pi\)
0.417761 + 0.908557i \(0.362815\pi\)
\(968\) 48.7295 1.56622
\(969\) −41.0499 −1.31871
\(970\) 11.4392 0.367290
\(971\) 51.3733 1.64865 0.824324 0.566118i \(-0.191555\pi\)
0.824324 + 0.566118i \(0.191555\pi\)
\(972\) 85.0464 2.72787
\(973\) −23.8373 −0.764190
\(974\) 5.16884 0.165620
\(975\) −22.0786 −0.707081
\(976\) 76.8044 2.45845
\(977\) 52.3252 1.67403 0.837016 0.547179i \(-0.184298\pi\)
0.837016 + 0.547179i \(0.184298\pi\)
\(978\) 79.5279 2.54302
\(979\) −9.28114 −0.296627
\(980\) −13.6672 −0.436582
\(981\) 13.6482 0.435753
\(982\) −53.3559 −1.70265
\(983\) −18.3941 −0.586682 −0.293341 0.956008i \(-0.594767\pi\)
−0.293341 + 0.956008i \(0.594767\pi\)
\(984\) −118.842 −3.78853
\(985\) −9.23106 −0.294126
\(986\) 34.7964 1.10814
\(987\) 22.8452 0.727170
\(988\) −67.1568 −2.13654
\(989\) −0.386798 −0.0122995
\(990\) −19.3414 −0.614711
\(991\) 35.1814 1.11757 0.558787 0.829311i \(-0.311267\pi\)
0.558787 + 0.829311i \(0.311267\pi\)
\(992\) −5.10660 −0.162135
\(993\) 34.6026 1.09808
\(994\) −35.0336 −1.11120
\(995\) 23.1961 0.735367
\(996\) −29.3046 −0.928550
\(997\) −0.242728 −0.00768728 −0.00384364 0.999993i \(-0.501223\pi\)
−0.00384364 + 0.999993i \(0.501223\pi\)
\(998\) −74.4745 −2.35745
\(999\) −23.3588 −0.739039
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 \(a_p\))