Properties

Label 8035.2.a.e.1.11
Level 8035
Weight 2
Character 8035.1
Self dual Yes
Analytic conductor 64.160
Analytic rank 0
Dimension 153
CM No

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Newspace parameters

Level: \( N \) = \( 8035 = 5 \cdot 1607 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8035.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1597980241\)
Analytic rank: \(0\)
Dimension: \(153\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 8035.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.52944 q^{2} -2.42468 q^{3} +4.39805 q^{4} +1.00000 q^{5} +6.13306 q^{6} +0.256968 q^{7} -6.06570 q^{8} +2.87905 q^{9} +O(q^{10})\) \(q-2.52944 q^{2} -2.42468 q^{3} +4.39805 q^{4} +1.00000 q^{5} +6.13306 q^{6} +0.256968 q^{7} -6.06570 q^{8} +2.87905 q^{9} -2.52944 q^{10} +0.560693 q^{11} -10.6638 q^{12} -5.31322 q^{13} -0.649984 q^{14} -2.42468 q^{15} +6.54671 q^{16} -6.32354 q^{17} -7.28238 q^{18} +0.712431 q^{19} +4.39805 q^{20} -0.623064 q^{21} -1.41824 q^{22} +6.12771 q^{23} +14.7074 q^{24} +1.00000 q^{25} +13.4394 q^{26} +0.293257 q^{27} +1.13016 q^{28} -5.89093 q^{29} +6.13306 q^{30} +6.98787 q^{31} -4.42808 q^{32} -1.35950 q^{33} +15.9950 q^{34} +0.256968 q^{35} +12.6622 q^{36} -11.9083 q^{37} -1.80205 q^{38} +12.8828 q^{39} -6.06570 q^{40} +0.740184 q^{41} +1.57600 q^{42} -6.63627 q^{43} +2.46595 q^{44} +2.87905 q^{45} -15.4997 q^{46} -10.2422 q^{47} -15.8736 q^{48} -6.93397 q^{49} -2.52944 q^{50} +15.3325 q^{51} -23.3678 q^{52} -2.83729 q^{53} -0.741775 q^{54} +0.560693 q^{55} -1.55869 q^{56} -1.72742 q^{57} +14.9007 q^{58} +2.23817 q^{59} -10.6638 q^{60} -8.91289 q^{61} -17.6754 q^{62} +0.739824 q^{63} -1.89288 q^{64} -5.31322 q^{65} +3.43877 q^{66} -0.700692 q^{67} -27.8112 q^{68} -14.8577 q^{69} -0.649984 q^{70} -12.3380 q^{71} -17.4635 q^{72} +10.8490 q^{73} +30.1212 q^{74} -2.42468 q^{75} +3.13331 q^{76} +0.144080 q^{77} -32.5863 q^{78} +3.82196 q^{79} +6.54671 q^{80} -9.34821 q^{81} -1.87225 q^{82} +4.20223 q^{83} -2.74026 q^{84} -6.32354 q^{85} +16.7860 q^{86} +14.2836 q^{87} -3.40100 q^{88} +2.98034 q^{89} -7.28238 q^{90} -1.36533 q^{91} +26.9500 q^{92} -16.9433 q^{93} +25.9070 q^{94} +0.712431 q^{95} +10.7367 q^{96} +7.51559 q^{97} +17.5390 q^{98} +1.61427 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153q + 18q^{2} + 7q^{3} + 176q^{4} + 153q^{5} + 19q^{6} + 5q^{7} + 57q^{8} + 206q^{9} + O(q^{10}) \) \( 153q + 18q^{2} + 7q^{3} + 176q^{4} + 153q^{5} + 19q^{6} + 5q^{7} + 57q^{8} + 206q^{9} + 18q^{10} + 38q^{11} + 14q^{12} + 28q^{13} + 53q^{14} + 7q^{15} + 214q^{16} + 50q^{17} + 47q^{18} + 65q^{19} + 176q^{20} + 109q^{21} + 13q^{22} + 52q^{23} + 66q^{24} + 153q^{25} + 36q^{26} + 19q^{27} + 26q^{28} + 172q^{29} + 19q^{30} + 60q^{31} + 107q^{32} + 4q^{33} + 40q^{34} + 5q^{35} + 241q^{36} + 65q^{37} + 29q^{38} + 56q^{39} + 57q^{40} + 152q^{41} - 19q^{42} + 22q^{43} + 97q^{44} + 206q^{45} + 86q^{46} + 37q^{47} - 4q^{48} + 260q^{49} + 18q^{50} + 102q^{51} - 6q^{52} + 169q^{53} + 64q^{54} + 38q^{55} + 146q^{56} + 40q^{57} - 9q^{58} + 64q^{59} + 14q^{60} + 164q^{61} + 12q^{62} + 19q^{63} + 259q^{64} + 28q^{65} + 6q^{66} + 5q^{67} + 112q^{68} + 119q^{69} + 53q^{70} + 100q^{71} + 77q^{72} + 10q^{73} + 98q^{74} + 7q^{75} + 126q^{76} + 80q^{77} - 4q^{78} + 110q^{79} + 214q^{80} + 305q^{81} - 27q^{82} + 36q^{83} + 172q^{84} + 50q^{85} + 44q^{86} + 23q^{87} + 47q^{88} + 143q^{89} + 47q^{90} + 82q^{91} + 130q^{92} + 31q^{93} + 77q^{94} + 65q^{95} + 57q^{96} + 11q^{97} + 29q^{98} + 99q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.52944 −1.78858 −0.894291 0.447487i \(-0.852319\pi\)
−0.894291 + 0.447487i \(0.852319\pi\)
\(3\) −2.42468 −1.39989 −0.699944 0.714198i \(-0.746792\pi\)
−0.699944 + 0.714198i \(0.746792\pi\)
\(4\) 4.39805 2.19902
\(5\) 1.00000 0.447214
\(6\) 6.13306 2.50381
\(7\) 0.256968 0.0971247 0.0485624 0.998820i \(-0.484536\pi\)
0.0485624 + 0.998820i \(0.484536\pi\)
\(8\) −6.06570 −2.14455
\(9\) 2.87905 0.959684
\(10\) −2.52944 −0.799878
\(11\) 0.560693 0.169055 0.0845277 0.996421i \(-0.473062\pi\)
0.0845277 + 0.996421i \(0.473062\pi\)
\(12\) −10.6638 −3.07838
\(13\) −5.31322 −1.47362 −0.736811 0.676099i \(-0.763669\pi\)
−0.736811 + 0.676099i \(0.763669\pi\)
\(14\) −0.649984 −0.173715
\(15\) −2.42468 −0.626049
\(16\) 6.54671 1.63668
\(17\) −6.32354 −1.53368 −0.766842 0.641836i \(-0.778173\pi\)
−0.766842 + 0.641836i \(0.778173\pi\)
\(18\) −7.28238 −1.71647
\(19\) 0.712431 0.163443 0.0817215 0.996655i \(-0.473958\pi\)
0.0817215 + 0.996655i \(0.473958\pi\)
\(20\) 4.39805 0.983433
\(21\) −0.623064 −0.135964
\(22\) −1.41824 −0.302369
\(23\) 6.12771 1.27772 0.638858 0.769324i \(-0.279407\pi\)
0.638858 + 0.769324i \(0.279407\pi\)
\(24\) 14.7074 3.00213
\(25\) 1.00000 0.200000
\(26\) 13.4394 2.63569
\(27\) 0.293257 0.0564374
\(28\) 1.13016 0.213579
\(29\) −5.89093 −1.09392 −0.546959 0.837159i \(-0.684215\pi\)
−0.546959 + 0.837159i \(0.684215\pi\)
\(30\) 6.13306 1.11974
\(31\) 6.98787 1.25506 0.627529 0.778593i \(-0.284066\pi\)
0.627529 + 0.778593i \(0.284066\pi\)
\(32\) −4.42808 −0.782781
\(33\) −1.35950 −0.236658
\(34\) 15.9950 2.74312
\(35\) 0.256968 0.0434355
\(36\) 12.6622 2.11037
\(37\) −11.9083 −1.95771 −0.978854 0.204561i \(-0.934423\pi\)
−0.978854 + 0.204561i \(0.934423\pi\)
\(38\) −1.80205 −0.292331
\(39\) 12.8828 2.06290
\(40\) −6.06570 −0.959071
\(41\) 0.740184 0.115597 0.0577987 0.998328i \(-0.481592\pi\)
0.0577987 + 0.998328i \(0.481592\pi\)
\(42\) 1.57600 0.243182
\(43\) −6.63627 −1.01202 −0.506011 0.862527i \(-0.668880\pi\)
−0.506011 + 0.862527i \(0.668880\pi\)
\(44\) 2.46595 0.371756
\(45\) 2.87905 0.429184
\(46\) −15.4997 −2.28530
\(47\) −10.2422 −1.49398 −0.746991 0.664834i \(-0.768502\pi\)
−0.746991 + 0.664834i \(0.768502\pi\)
\(48\) −15.8736 −2.29116
\(49\) −6.93397 −0.990567
\(50\) −2.52944 −0.357716
\(51\) 15.3325 2.14698
\(52\) −23.3678 −3.24053
\(53\) −2.83729 −0.389731 −0.194866 0.980830i \(-0.562427\pi\)
−0.194866 + 0.980830i \(0.562427\pi\)
\(54\) −0.741775 −0.100943
\(55\) 0.560693 0.0756038
\(56\) −1.55869 −0.208289
\(57\) −1.72742 −0.228802
\(58\) 14.9007 1.95656
\(59\) 2.23817 0.291385 0.145692 0.989330i \(-0.453459\pi\)
0.145692 + 0.989330i \(0.453459\pi\)
\(60\) −10.6638 −1.37669
\(61\) −8.91289 −1.14118 −0.570589 0.821236i \(-0.693285\pi\)
−0.570589 + 0.821236i \(0.693285\pi\)
\(62\) −17.6754 −2.24477
\(63\) 0.739824 0.0932091
\(64\) −1.89288 −0.236609
\(65\) −5.31322 −0.659023
\(66\) 3.43877 0.423283
\(67\) −0.700692 −0.0856031 −0.0428016 0.999084i \(-0.513628\pi\)
−0.0428016 + 0.999084i \(0.513628\pi\)
\(68\) −27.8112 −3.37261
\(69\) −14.8577 −1.78866
\(70\) −0.649984 −0.0776879
\(71\) −12.3380 −1.46425 −0.732125 0.681171i \(-0.761471\pi\)
−0.732125 + 0.681171i \(0.761471\pi\)
\(72\) −17.4635 −2.05809
\(73\) 10.8490 1.26978 0.634890 0.772603i \(-0.281046\pi\)
0.634890 + 0.772603i \(0.281046\pi\)
\(74\) 30.1212 3.50152
\(75\) −2.42468 −0.279977
\(76\) 3.13331 0.359415
\(77\) 0.144080 0.0164195
\(78\) −32.5863 −3.68967
\(79\) 3.82196 0.430005 0.215002 0.976614i \(-0.431024\pi\)
0.215002 + 0.976614i \(0.431024\pi\)
\(80\) 6.54671 0.731944
\(81\) −9.34821 −1.03869
\(82\) −1.87225 −0.206755
\(83\) 4.20223 0.461255 0.230627 0.973042i \(-0.425922\pi\)
0.230627 + 0.973042i \(0.425922\pi\)
\(84\) −2.74026 −0.298987
\(85\) −6.32354 −0.685884
\(86\) 16.7860 1.81008
\(87\) 14.2836 1.53136
\(88\) −3.40100 −0.362547
\(89\) 2.98034 0.315915 0.157958 0.987446i \(-0.449509\pi\)
0.157958 + 0.987446i \(0.449509\pi\)
\(90\) −7.28238 −0.767630
\(91\) −1.36533 −0.143125
\(92\) 26.9500 2.80973
\(93\) −16.9433 −1.75694
\(94\) 25.9070 2.67211
\(95\) 0.712431 0.0730939
\(96\) 10.7367 1.09581
\(97\) 7.51559 0.763093 0.381546 0.924350i \(-0.375392\pi\)
0.381546 + 0.924350i \(0.375392\pi\)
\(98\) 17.5390 1.77171
\(99\) 1.61427 0.162240
\(100\) 4.39805 0.439805
\(101\) 8.33417 0.829281 0.414640 0.909985i \(-0.363907\pi\)
0.414640 + 0.909985i \(0.363907\pi\)
\(102\) −38.7827 −3.84006
\(103\) −7.14407 −0.703926 −0.351963 0.936014i \(-0.614486\pi\)
−0.351963 + 0.936014i \(0.614486\pi\)
\(104\) 32.2284 3.16025
\(105\) −0.623064 −0.0608048
\(106\) 7.17673 0.697066
\(107\) 11.4466 1.10658 0.553291 0.832988i \(-0.313372\pi\)
0.553291 + 0.832988i \(0.313372\pi\)
\(108\) 1.28976 0.124107
\(109\) 4.92878 0.472092 0.236046 0.971742i \(-0.424148\pi\)
0.236046 + 0.971742i \(0.424148\pi\)
\(110\) −1.41824 −0.135224
\(111\) 28.8737 2.74057
\(112\) 1.68229 0.158962
\(113\) 4.70337 0.442456 0.221228 0.975222i \(-0.428993\pi\)
0.221228 + 0.975222i \(0.428993\pi\)
\(114\) 4.36939 0.409230
\(115\) 6.12771 0.571412
\(116\) −25.9086 −2.40555
\(117\) −15.2970 −1.41421
\(118\) −5.66131 −0.521166
\(119\) −1.62495 −0.148959
\(120\) 14.7074 1.34259
\(121\) −10.6856 −0.971420
\(122\) 22.5446 2.04109
\(123\) −1.79471 −0.161823
\(124\) 30.7330 2.75990
\(125\) 1.00000 0.0894427
\(126\) −1.87134 −0.166712
\(127\) 2.40934 0.213794 0.106897 0.994270i \(-0.465908\pi\)
0.106897 + 0.994270i \(0.465908\pi\)
\(128\) 13.6441 1.20598
\(129\) 16.0908 1.41672
\(130\) 13.4394 1.17872
\(131\) −2.66779 −0.233086 −0.116543 0.993186i \(-0.537181\pi\)
−0.116543 + 0.993186i \(0.537181\pi\)
\(132\) −5.97914 −0.520417
\(133\) 0.183072 0.0158744
\(134\) 1.77235 0.153108
\(135\) 0.293257 0.0252396
\(136\) 38.3567 3.28906
\(137\) −15.6485 −1.33694 −0.668469 0.743740i \(-0.733050\pi\)
−0.668469 + 0.743740i \(0.733050\pi\)
\(138\) 37.5816 3.19916
\(139\) −9.47689 −0.803819 −0.401910 0.915679i \(-0.631653\pi\)
−0.401910 + 0.915679i \(0.631653\pi\)
\(140\) 1.13016 0.0955156
\(141\) 24.8341 2.09141
\(142\) 31.2081 2.61893
\(143\) −2.97908 −0.249123
\(144\) 18.8483 1.57069
\(145\) −5.89093 −0.489215
\(146\) −27.4418 −2.27110
\(147\) 16.8126 1.38668
\(148\) −52.3731 −4.30504
\(149\) 5.41227 0.443391 0.221695 0.975116i \(-0.428841\pi\)
0.221695 + 0.975116i \(0.428841\pi\)
\(150\) 6.13306 0.500762
\(151\) −6.02995 −0.490710 −0.245355 0.969433i \(-0.578905\pi\)
−0.245355 + 0.969433i \(0.578905\pi\)
\(152\) −4.32140 −0.350511
\(153\) −18.2058 −1.47185
\(154\) −0.364441 −0.0293675
\(155\) 6.98787 0.561279
\(156\) 56.6593 4.53637
\(157\) −14.8601 −1.18596 −0.592982 0.805216i \(-0.702049\pi\)
−0.592982 + 0.805216i \(0.702049\pi\)
\(158\) −9.66741 −0.769098
\(159\) 6.87950 0.545580
\(160\) −4.42808 −0.350070
\(161\) 1.57463 0.124098
\(162\) 23.6457 1.85778
\(163\) 9.87485 0.773458 0.386729 0.922193i \(-0.373605\pi\)
0.386729 + 0.922193i \(0.373605\pi\)
\(164\) 3.25536 0.254201
\(165\) −1.35950 −0.105837
\(166\) −10.6293 −0.824991
\(167\) 7.76686 0.601018 0.300509 0.953779i \(-0.402843\pi\)
0.300509 + 0.953779i \(0.402843\pi\)
\(168\) 3.77932 0.291581
\(169\) 15.2303 1.17156
\(170\) 15.9950 1.22676
\(171\) 2.05113 0.156854
\(172\) −29.1866 −2.22546
\(173\) 10.9674 0.833834 0.416917 0.908945i \(-0.363111\pi\)
0.416917 + 0.908945i \(0.363111\pi\)
\(174\) −36.1294 −2.73897
\(175\) 0.256968 0.0194249
\(176\) 3.67070 0.276689
\(177\) −5.42684 −0.407906
\(178\) −7.53858 −0.565040
\(179\) 11.0270 0.824200 0.412100 0.911139i \(-0.364796\pi\)
0.412100 + 0.911139i \(0.364796\pi\)
\(180\) 12.6622 0.943785
\(181\) 14.5274 1.07981 0.539907 0.841725i \(-0.318459\pi\)
0.539907 + 0.841725i \(0.318459\pi\)
\(182\) 3.45350 0.255991
\(183\) 21.6109 1.59752
\(184\) −37.1689 −2.74013
\(185\) −11.9083 −0.875514
\(186\) 42.8570 3.14243
\(187\) −3.54557 −0.259277
\(188\) −45.0457 −3.28530
\(189\) 0.0753577 0.00548146
\(190\) −1.80205 −0.130734
\(191\) −26.8149 −1.94026 −0.970130 0.242587i \(-0.922004\pi\)
−0.970130 + 0.242587i \(0.922004\pi\)
\(192\) 4.58961 0.331226
\(193\) −3.11703 −0.224369 −0.112185 0.993687i \(-0.535785\pi\)
−0.112185 + 0.993687i \(0.535785\pi\)
\(194\) −19.0102 −1.36485
\(195\) 12.8828 0.922558
\(196\) −30.4959 −2.17828
\(197\) −15.1781 −1.08139 −0.540697 0.841217i \(-0.681840\pi\)
−0.540697 + 0.841217i \(0.681840\pi\)
\(198\) −4.08318 −0.290179
\(199\) −11.3538 −0.804850 −0.402425 0.915453i \(-0.631833\pi\)
−0.402425 + 0.915453i \(0.631833\pi\)
\(200\) −6.06570 −0.428910
\(201\) 1.69895 0.119835
\(202\) −21.0807 −1.48324
\(203\) −1.51378 −0.106247
\(204\) 67.4332 4.72127
\(205\) 0.740184 0.0516967
\(206\) 18.0705 1.25903
\(207\) 17.6420 1.22620
\(208\) −34.7841 −2.41184
\(209\) 0.399455 0.0276309
\(210\) 1.57600 0.108754
\(211\) 11.1800 0.769665 0.384832 0.922986i \(-0.374259\pi\)
0.384832 + 0.922986i \(0.374259\pi\)
\(212\) −12.4785 −0.857028
\(213\) 29.9156 2.04978
\(214\) −28.9534 −1.97921
\(215\) −6.63627 −0.452590
\(216\) −1.77881 −0.121033
\(217\) 1.79566 0.121897
\(218\) −12.4670 −0.844375
\(219\) −26.3053 −1.77755
\(220\) 2.46595 0.166255
\(221\) 33.5983 2.26007
\(222\) −73.0342 −4.90173
\(223\) −27.4596 −1.83883 −0.919415 0.393289i \(-0.871337\pi\)
−0.919415 + 0.393289i \(0.871337\pi\)
\(224\) −1.13787 −0.0760274
\(225\) 2.87905 0.191937
\(226\) −11.8969 −0.791369
\(227\) 10.5942 0.703164 0.351582 0.936157i \(-0.385644\pi\)
0.351582 + 0.936157i \(0.385644\pi\)
\(228\) −7.59725 −0.503140
\(229\) −10.6220 −0.701923 −0.350962 0.936390i \(-0.614145\pi\)
−0.350962 + 0.936390i \(0.614145\pi\)
\(230\) −15.4997 −1.02202
\(231\) −0.349348 −0.0229854
\(232\) 35.7326 2.34596
\(233\) −6.38347 −0.418195 −0.209097 0.977895i \(-0.567053\pi\)
−0.209097 + 0.977895i \(0.567053\pi\)
\(234\) 38.6929 2.52943
\(235\) −10.2422 −0.668129
\(236\) 9.84357 0.640762
\(237\) −9.26702 −0.601958
\(238\) 4.11020 0.266425
\(239\) −0.689703 −0.0446132 −0.0223066 0.999751i \(-0.507101\pi\)
−0.0223066 + 0.999751i \(0.507101\pi\)
\(240\) −15.8736 −1.02464
\(241\) −16.4419 −1.05911 −0.529557 0.848274i \(-0.677642\pi\)
−0.529557 + 0.848274i \(0.677642\pi\)
\(242\) 27.0286 1.73746
\(243\) 21.7866 1.39761
\(244\) −39.1993 −2.50948
\(245\) −6.93397 −0.442995
\(246\) 4.53960 0.289434
\(247\) −3.78530 −0.240853
\(248\) −42.3863 −2.69153
\(249\) −10.1890 −0.645704
\(250\) −2.52944 −0.159976
\(251\) 13.0815 0.825695 0.412847 0.910800i \(-0.364534\pi\)
0.412847 + 0.910800i \(0.364534\pi\)
\(252\) 3.25378 0.204969
\(253\) 3.43577 0.216005
\(254\) −6.09427 −0.382389
\(255\) 15.3325 0.960161
\(256\) −30.7260 −1.92038
\(257\) −8.24367 −0.514226 −0.257113 0.966381i \(-0.582771\pi\)
−0.257113 + 0.966381i \(0.582771\pi\)
\(258\) −40.7007 −2.53391
\(259\) −3.06004 −0.190142
\(260\) −23.3678 −1.44921
\(261\) −16.9603 −1.04982
\(262\) 6.74800 0.416893
\(263\) 11.3850 0.702031 0.351015 0.936370i \(-0.385836\pi\)
0.351015 + 0.936370i \(0.385836\pi\)
\(264\) 8.24631 0.507526
\(265\) −2.83729 −0.174293
\(266\) −0.463069 −0.0283926
\(267\) −7.22636 −0.442246
\(268\) −3.08167 −0.188243
\(269\) 23.3969 1.42653 0.713267 0.700893i \(-0.247215\pi\)
0.713267 + 0.700893i \(0.247215\pi\)
\(270\) −0.741775 −0.0451430
\(271\) −2.63333 −0.159964 −0.0799818 0.996796i \(-0.525486\pi\)
−0.0799818 + 0.996796i \(0.525486\pi\)
\(272\) −41.3984 −2.51015
\(273\) 3.31047 0.200359
\(274\) 39.5818 2.39122
\(275\) 0.560693 0.0338111
\(276\) −65.3449 −3.93330
\(277\) 23.2174 1.39500 0.697500 0.716585i \(-0.254296\pi\)
0.697500 + 0.716585i \(0.254296\pi\)
\(278\) 23.9712 1.43770
\(279\) 20.1184 1.20446
\(280\) −1.55869 −0.0931496
\(281\) 6.70722 0.400119 0.200060 0.979784i \(-0.435886\pi\)
0.200060 + 0.979784i \(0.435886\pi\)
\(282\) −62.8162 −3.74065
\(283\) −27.8629 −1.65628 −0.828139 0.560523i \(-0.810600\pi\)
−0.828139 + 0.560523i \(0.810600\pi\)
\(284\) −54.2630 −3.21992
\(285\) −1.72742 −0.102323
\(286\) 7.53540 0.445578
\(287\) 0.190204 0.0112274
\(288\) −12.7487 −0.751223
\(289\) 22.9872 1.35219
\(290\) 14.9007 0.875001
\(291\) −18.2229 −1.06824
\(292\) 47.7144 2.79227
\(293\) 19.2210 1.12291 0.561453 0.827509i \(-0.310243\pi\)
0.561453 + 0.827509i \(0.310243\pi\)
\(294\) −42.5265 −2.48019
\(295\) 2.23817 0.130311
\(296\) 72.2320 4.19840
\(297\) 0.164427 0.00954104
\(298\) −13.6900 −0.793040
\(299\) −32.5579 −1.88287
\(300\) −10.6638 −0.615677
\(301\) −1.70531 −0.0982924
\(302\) 15.2524 0.877675
\(303\) −20.2077 −1.16090
\(304\) 4.66408 0.267503
\(305\) −8.91289 −0.510351
\(306\) 46.0504 2.63253
\(307\) −5.71845 −0.326369 −0.163185 0.986596i \(-0.552177\pi\)
−0.163185 + 0.986596i \(0.552177\pi\)
\(308\) 0.633671 0.0361067
\(309\) 17.3220 0.985417
\(310\) −17.6754 −1.00389
\(311\) −19.8674 −1.12657 −0.563287 0.826261i \(-0.690464\pi\)
−0.563287 + 0.826261i \(0.690464\pi\)
\(312\) −78.1434 −4.42400
\(313\) −27.7658 −1.56942 −0.784709 0.619865i \(-0.787187\pi\)
−0.784709 + 0.619865i \(0.787187\pi\)
\(314\) 37.5876 2.12119
\(315\) 0.739824 0.0416844
\(316\) 16.8092 0.945590
\(317\) 10.5408 0.592031 0.296015 0.955183i \(-0.404342\pi\)
0.296015 + 0.955183i \(0.404342\pi\)
\(318\) −17.4013 −0.975814
\(319\) −3.30300 −0.184933
\(320\) −1.89288 −0.105815
\(321\) −27.7542 −1.54909
\(322\) −3.98291 −0.221959
\(323\) −4.50509 −0.250670
\(324\) −41.1139 −2.28410
\(325\) −5.31322 −0.294724
\(326\) −24.9778 −1.38339
\(327\) −11.9507 −0.660875
\(328\) −4.48974 −0.247904
\(329\) −2.63192 −0.145103
\(330\) 3.43877 0.189298
\(331\) 23.1138 1.27045 0.635224 0.772328i \(-0.280908\pi\)
0.635224 + 0.772328i \(0.280908\pi\)
\(332\) 18.4816 1.01431
\(333\) −34.2845 −1.87878
\(334\) −19.6458 −1.07497
\(335\) −0.700692 −0.0382829
\(336\) −4.07902 −0.222529
\(337\) −30.9590 −1.68645 −0.843223 0.537564i \(-0.819345\pi\)
−0.843223 + 0.537564i \(0.819345\pi\)
\(338\) −38.5240 −2.09543
\(339\) −11.4042 −0.619389
\(340\) −27.8112 −1.50828
\(341\) 3.91805 0.212174
\(342\) −5.18820 −0.280545
\(343\) −3.58058 −0.193333
\(344\) 40.2536 2.17033
\(345\) −14.8577 −0.799913
\(346\) −27.7413 −1.49138
\(347\) 19.3837 1.04057 0.520286 0.853992i \(-0.325825\pi\)
0.520286 + 0.853992i \(0.325825\pi\)
\(348\) 62.8199 3.36750
\(349\) 0.0165295 0.000884806 0 0.000442403 1.00000i \(-0.499859\pi\)
0.000442403 1.00000i \(0.499859\pi\)
\(350\) −0.649984 −0.0347431
\(351\) −1.55814 −0.0831673
\(352\) −2.48279 −0.132333
\(353\) −6.58197 −0.350323 −0.175161 0.984540i \(-0.556045\pi\)
−0.175161 + 0.984540i \(0.556045\pi\)
\(354\) 13.7268 0.729573
\(355\) −12.3380 −0.654832
\(356\) 13.1077 0.694705
\(357\) 3.93997 0.208525
\(358\) −27.8922 −1.47415
\(359\) 12.0294 0.634889 0.317444 0.948277i \(-0.397175\pi\)
0.317444 + 0.948277i \(0.397175\pi\)
\(360\) −17.4635 −0.920406
\(361\) −18.4924 −0.973286
\(362\) −36.7462 −1.93133
\(363\) 25.9092 1.35988
\(364\) −6.00476 −0.314735
\(365\) 10.8490 0.567863
\(366\) −54.6633 −2.85730
\(367\) 25.3888 1.32528 0.662641 0.748937i \(-0.269435\pi\)
0.662641 + 0.748937i \(0.269435\pi\)
\(368\) 40.1164 2.09121
\(369\) 2.13103 0.110937
\(370\) 30.1212 1.56593
\(371\) −0.729092 −0.0378525
\(372\) −74.5174 −3.86355
\(373\) −24.3993 −1.26335 −0.631673 0.775235i \(-0.717632\pi\)
−0.631673 + 0.775235i \(0.717632\pi\)
\(374\) 8.96828 0.463739
\(375\) −2.42468 −0.125210
\(376\) 62.1262 3.20392
\(377\) 31.2998 1.61202
\(378\) −0.190612 −0.00980404
\(379\) 4.08624 0.209896 0.104948 0.994478i \(-0.466532\pi\)
0.104948 + 0.994478i \(0.466532\pi\)
\(380\) 3.13331 0.160735
\(381\) −5.84187 −0.299288
\(382\) 67.8266 3.47031
\(383\) −0.228835 −0.0116929 −0.00584645 0.999983i \(-0.501861\pi\)
−0.00584645 + 0.999983i \(0.501861\pi\)
\(384\) −33.0824 −1.68823
\(385\) 0.144080 0.00734300
\(386\) 7.88434 0.401302
\(387\) −19.1062 −0.971222
\(388\) 33.0539 1.67806
\(389\) 21.2474 1.07729 0.538644 0.842534i \(-0.318937\pi\)
0.538644 + 0.842534i \(0.318937\pi\)
\(390\) −32.5863 −1.65007
\(391\) −38.7489 −1.95961
\(392\) 42.0594 2.12432
\(393\) 6.46853 0.326294
\(394\) 38.3920 1.93416
\(395\) 3.82196 0.192304
\(396\) 7.09961 0.356769
\(397\) 30.2025 1.51582 0.757910 0.652359i \(-0.226220\pi\)
0.757910 + 0.652359i \(0.226220\pi\)
\(398\) 28.7187 1.43954
\(399\) −0.443890 −0.0222223
\(400\) 6.54671 0.327335
\(401\) −5.88318 −0.293792 −0.146896 0.989152i \(-0.546928\pi\)
−0.146896 + 0.989152i \(0.546928\pi\)
\(402\) −4.29738 −0.214334
\(403\) −37.1280 −1.84948
\(404\) 36.6540 1.82361
\(405\) −9.34821 −0.464516
\(406\) 3.82901 0.190031
\(407\) −6.67689 −0.330961
\(408\) −93.0026 −4.60431
\(409\) 12.4334 0.614792 0.307396 0.951582i \(-0.400542\pi\)
0.307396 + 0.951582i \(0.400542\pi\)
\(410\) −1.87225 −0.0924638
\(411\) 37.9424 1.87156
\(412\) −31.4199 −1.54795
\(413\) 0.575138 0.0283007
\(414\) −44.6243 −2.19317
\(415\) 4.20223 0.206279
\(416\) 23.5273 1.15352
\(417\) 22.9784 1.12526
\(418\) −1.01040 −0.0494201
\(419\) 0.268305 0.0131076 0.00655378 0.999979i \(-0.497914\pi\)
0.00655378 + 0.999979i \(0.497914\pi\)
\(420\) −2.74026 −0.133711
\(421\) 9.42360 0.459278 0.229639 0.973276i \(-0.426245\pi\)
0.229639 + 0.973276i \(0.426245\pi\)
\(422\) −28.2792 −1.37661
\(423\) −29.4879 −1.43375
\(424\) 17.2101 0.835798
\(425\) −6.32354 −0.306737
\(426\) −75.6696 −3.66621
\(427\) −2.29033 −0.110837
\(428\) 50.3426 2.43340
\(429\) 7.22331 0.348745
\(430\) 16.7860 0.809494
\(431\) −7.08354 −0.341202 −0.170601 0.985340i \(-0.554571\pi\)
−0.170601 + 0.985340i \(0.554571\pi\)
\(432\) 1.91987 0.0923697
\(433\) −9.61195 −0.461921 −0.230961 0.972963i \(-0.574187\pi\)
−0.230961 + 0.972963i \(0.574187\pi\)
\(434\) −4.54200 −0.218023
\(435\) 14.2836 0.684846
\(436\) 21.6770 1.03814
\(437\) 4.36558 0.208834
\(438\) 66.5376 3.17929
\(439\) 0.649770 0.0310118 0.0155059 0.999880i \(-0.495064\pi\)
0.0155059 + 0.999880i \(0.495064\pi\)
\(440\) −3.40100 −0.162136
\(441\) −19.9633 −0.950631
\(442\) −84.9848 −4.04232
\(443\) 7.71222 0.366418 0.183209 0.983074i \(-0.441351\pi\)
0.183209 + 0.983074i \(0.441351\pi\)
\(444\) 126.988 6.02658
\(445\) 2.98034 0.141282
\(446\) 69.4572 3.28890
\(447\) −13.1230 −0.620697
\(448\) −0.486408 −0.0229806
\(449\) −32.4820 −1.53292 −0.766460 0.642292i \(-0.777983\pi\)
−0.766460 + 0.642292i \(0.777983\pi\)
\(450\) −7.28238 −0.343295
\(451\) 0.415016 0.0195424
\(452\) 20.6856 0.972971
\(453\) 14.6207 0.686939
\(454\) −26.7974 −1.25767
\(455\) −1.36533 −0.0640075
\(456\) 10.4780 0.490677
\(457\) 11.1553 0.521825 0.260912 0.965362i \(-0.415977\pi\)
0.260912 + 0.965362i \(0.415977\pi\)
\(458\) 26.8677 1.25545
\(459\) −1.85442 −0.0865571
\(460\) 26.9500 1.25655
\(461\) 29.8157 1.38866 0.694328 0.719659i \(-0.255702\pi\)
0.694328 + 0.719659i \(0.255702\pi\)
\(462\) 0.883652 0.0411112
\(463\) −7.56499 −0.351575 −0.175787 0.984428i \(-0.556247\pi\)
−0.175787 + 0.984428i \(0.556247\pi\)
\(464\) −38.5662 −1.79039
\(465\) −16.9433 −0.785727
\(466\) 16.1466 0.747976
\(467\) −24.9538 −1.15473 −0.577363 0.816488i \(-0.695918\pi\)
−0.577363 + 0.816488i \(0.695918\pi\)
\(468\) −67.2770 −3.10988
\(469\) −0.180055 −0.00831418
\(470\) 25.9070 1.19500
\(471\) 36.0309 1.66022
\(472\) −13.5761 −0.624889
\(473\) −3.72091 −0.171088
\(474\) 23.4403 1.07665
\(475\) 0.712431 0.0326886
\(476\) −7.14659 −0.327563
\(477\) −8.16870 −0.374019
\(478\) 1.74456 0.0797943
\(479\) 37.2881 1.70374 0.851869 0.523756i \(-0.175469\pi\)
0.851869 + 0.523756i \(0.175469\pi\)
\(480\) 10.7367 0.490059
\(481\) 63.2712 2.88492
\(482\) 41.5886 1.89431
\(483\) −3.81796 −0.173723
\(484\) −46.9959 −2.13618
\(485\) 7.51559 0.341265
\(486\) −55.1078 −2.49974
\(487\) −2.90652 −0.131707 −0.0658536 0.997829i \(-0.520977\pi\)
−0.0658536 + 0.997829i \(0.520977\pi\)
\(488\) 54.0629 2.44731
\(489\) −23.9433 −1.08275
\(490\) 17.5390 0.792332
\(491\) 1.75165 0.0790508 0.0395254 0.999219i \(-0.487415\pi\)
0.0395254 + 0.999219i \(0.487415\pi\)
\(492\) −7.89320 −0.355853
\(493\) 37.2515 1.67773
\(494\) 9.57468 0.430785
\(495\) 1.61427 0.0725558
\(496\) 45.7475 2.05412
\(497\) −3.17047 −0.142215
\(498\) 25.7725 1.15489
\(499\) −11.0372 −0.494094 −0.247047 0.969004i \(-0.579460\pi\)
−0.247047 + 0.969004i \(0.579460\pi\)
\(500\) 4.39805 0.196687
\(501\) −18.8321 −0.841357
\(502\) −33.0887 −1.47682
\(503\) −17.5668 −0.783265 −0.391633 0.920122i \(-0.628090\pi\)
−0.391633 + 0.920122i \(0.628090\pi\)
\(504\) −4.48755 −0.199891
\(505\) 8.33417 0.370866
\(506\) −8.69055 −0.386342
\(507\) −36.9285 −1.64005
\(508\) 10.5964 0.470139
\(509\) −35.7059 −1.58264 −0.791318 0.611405i \(-0.790605\pi\)
−0.791318 + 0.611405i \(0.790605\pi\)
\(510\) −38.7827 −1.71733
\(511\) 2.78784 0.123327
\(512\) 50.4314 2.22877
\(513\) 0.208926 0.00922429
\(514\) 20.8518 0.919734
\(515\) −7.14407 −0.314805
\(516\) 70.7681 3.11539
\(517\) −5.74274 −0.252566
\(518\) 7.74018 0.340084
\(519\) −26.5923 −1.16727
\(520\) 32.2284 1.41331
\(521\) −31.5676 −1.38300 −0.691500 0.722376i \(-0.743050\pi\)
−0.691500 + 0.722376i \(0.743050\pi\)
\(522\) 42.9000 1.87768
\(523\) 14.1432 0.618437 0.309219 0.950991i \(-0.399933\pi\)
0.309219 + 0.950991i \(0.399933\pi\)
\(524\) −11.7331 −0.512561
\(525\) −0.623064 −0.0271927
\(526\) −28.7977 −1.25564
\(527\) −44.1881 −1.92486
\(528\) −8.90025 −0.387333
\(529\) 14.5489 0.632560
\(530\) 7.17673 0.311737
\(531\) 6.44381 0.279638
\(532\) 0.805159 0.0349081
\(533\) −3.93276 −0.170347
\(534\) 18.2786 0.790992
\(535\) 11.4466 0.494879
\(536\) 4.25019 0.183580
\(537\) −26.7370 −1.15379
\(538\) −59.1809 −2.55147
\(539\) −3.88783 −0.167461
\(540\) 1.28976 0.0555023
\(541\) −1.17196 −0.0503864 −0.0251932 0.999683i \(-0.508020\pi\)
−0.0251932 + 0.999683i \(0.508020\pi\)
\(542\) 6.66085 0.286108
\(543\) −35.2243 −1.51162
\(544\) 28.0011 1.20054
\(545\) 4.92878 0.211126
\(546\) −8.37363 −0.358358
\(547\) −22.0249 −0.941715 −0.470857 0.882209i \(-0.656055\pi\)
−0.470857 + 0.882209i \(0.656055\pi\)
\(548\) −68.8226 −2.93996
\(549\) −25.6607 −1.09517
\(550\) −1.41824 −0.0604738
\(551\) −4.19688 −0.178793
\(552\) 90.1225 3.83587
\(553\) 0.982122 0.0417641
\(554\) −58.7269 −2.49507
\(555\) 28.8737 1.22562
\(556\) −41.6798 −1.76762
\(557\) −19.3907 −0.821610 −0.410805 0.911723i \(-0.634752\pi\)
−0.410805 + 0.911723i \(0.634752\pi\)
\(558\) −50.8883 −2.15427
\(559\) 35.2599 1.49134
\(560\) 1.68229 0.0710899
\(561\) 8.59685 0.362959
\(562\) −16.9655 −0.715646
\(563\) −0.659476 −0.0277936 −0.0138968 0.999903i \(-0.504424\pi\)
−0.0138968 + 0.999903i \(0.504424\pi\)
\(564\) 109.221 4.59905
\(565\) 4.70337 0.197872
\(566\) 70.4774 2.96239
\(567\) −2.40219 −0.100883
\(568\) 74.8385 3.14016
\(569\) 16.4349 0.688986 0.344493 0.938789i \(-0.388051\pi\)
0.344493 + 0.938789i \(0.388051\pi\)
\(570\) 4.36939 0.183013
\(571\) −25.7096 −1.07591 −0.537957 0.842973i \(-0.680804\pi\)
−0.537957 + 0.842973i \(0.680804\pi\)
\(572\) −13.1021 −0.547828
\(573\) 65.0175 2.71614
\(574\) −0.481108 −0.0200811
\(575\) 6.12771 0.255543
\(576\) −5.44969 −0.227070
\(577\) −1.71956 −0.0715861 −0.0357930 0.999359i \(-0.511396\pi\)
−0.0357930 + 0.999359i \(0.511396\pi\)
\(578\) −58.1446 −2.41850
\(579\) 7.55780 0.314091
\(580\) −25.9086 −1.07580
\(581\) 1.07984 0.0447992
\(582\) 46.0936 1.91064
\(583\) −1.59085 −0.0658862
\(584\) −65.8068 −2.72310
\(585\) −15.2970 −0.632454
\(586\) −48.6184 −2.00841
\(587\) 31.9336 1.31804 0.659020 0.752125i \(-0.270971\pi\)
0.659020 + 0.752125i \(0.270971\pi\)
\(588\) 73.9427 3.04934
\(589\) 4.97838 0.205130
\(590\) −5.66131 −0.233072
\(591\) 36.8020 1.51383
\(592\) −77.9600 −3.20414
\(593\) 33.1485 1.36125 0.680624 0.732633i \(-0.261709\pi\)
0.680624 + 0.732633i \(0.261709\pi\)
\(594\) −0.415908 −0.0170649
\(595\) −1.62495 −0.0666163
\(596\) 23.8034 0.975026
\(597\) 27.5293 1.12670
\(598\) 82.3530 3.36767
\(599\) 41.2813 1.68671 0.843355 0.537358i \(-0.180577\pi\)
0.843355 + 0.537358i \(0.180577\pi\)
\(600\) 14.7074 0.600425
\(601\) −42.9948 −1.75380 −0.876898 0.480677i \(-0.840391\pi\)
−0.876898 + 0.480677i \(0.840391\pi\)
\(602\) 4.31347 0.175804
\(603\) −2.01733 −0.0821520
\(604\) −26.5200 −1.07908
\(605\) −10.6856 −0.434432
\(606\) 51.1140 2.07636
\(607\) 13.2110 0.536216 0.268108 0.963389i \(-0.413602\pi\)
0.268108 + 0.963389i \(0.413602\pi\)
\(608\) −3.15470 −0.127940
\(609\) 3.67043 0.148733
\(610\) 22.5446 0.912804
\(611\) 54.4191 2.20156
\(612\) −80.0700 −3.23664
\(613\) −4.08552 −0.165012 −0.0825062 0.996591i \(-0.526292\pi\)
−0.0825062 + 0.996591i \(0.526292\pi\)
\(614\) 14.4645 0.583738
\(615\) −1.79471 −0.0723696
\(616\) −0.873947 −0.0352123
\(617\) −8.56336 −0.344748 −0.172374 0.985032i \(-0.555144\pi\)
−0.172374 + 0.985032i \(0.555144\pi\)
\(618\) −43.8150 −1.76250
\(619\) 13.6141 0.547196 0.273598 0.961844i \(-0.411786\pi\)
0.273598 + 0.961844i \(0.411786\pi\)
\(620\) 30.7330 1.23426
\(621\) 1.79700 0.0721110
\(622\) 50.2532 2.01497
\(623\) 0.765851 0.0306832
\(624\) 84.3401 3.37631
\(625\) 1.00000 0.0400000
\(626\) 70.2319 2.80703
\(627\) −0.968550 −0.0386802
\(628\) −65.3553 −2.60796
\(629\) 75.3024 3.00250
\(630\) −1.87134 −0.0745559
\(631\) −31.6516 −1.26003 −0.630014 0.776583i \(-0.716951\pi\)
−0.630014 + 0.776583i \(0.716951\pi\)
\(632\) −23.1829 −0.922166
\(633\) −27.1079 −1.07744
\(634\) −26.6623 −1.05890
\(635\) 2.40934 0.0956118
\(636\) 30.2564 1.19974
\(637\) 36.8417 1.45972
\(638\) 8.35474 0.330767
\(639\) −35.5217 −1.40522
\(640\) 13.6441 0.539329
\(641\) −23.7758 −0.939086 −0.469543 0.882910i \(-0.655581\pi\)
−0.469543 + 0.882910i \(0.655581\pi\)
\(642\) 70.2026 2.77067
\(643\) −16.1474 −0.636791 −0.318395 0.947958i \(-0.603144\pi\)
−0.318395 + 0.947958i \(0.603144\pi\)
\(644\) 6.92527 0.272894
\(645\) 16.0908 0.633575
\(646\) 11.3953 0.448343
\(647\) −36.0772 −1.41834 −0.709170 0.705037i \(-0.750930\pi\)
−0.709170 + 0.705037i \(0.750930\pi\)
\(648\) 56.7035 2.22752
\(649\) 1.25493 0.0492602
\(650\) 13.4394 0.527138
\(651\) −4.35389 −0.170642
\(652\) 43.4300 1.70085
\(653\) −26.9875 −1.05610 −0.528050 0.849213i \(-0.677077\pi\)
−0.528050 + 0.849213i \(0.677077\pi\)
\(654\) 30.2285 1.18203
\(655\) −2.66779 −0.104239
\(656\) 4.84577 0.189196
\(657\) 31.2348 1.21859
\(658\) 6.65728 0.259528
\(659\) 12.1382 0.472836 0.236418 0.971651i \(-0.424027\pi\)
0.236418 + 0.971651i \(0.424027\pi\)
\(660\) −5.97914 −0.232738
\(661\) −26.4559 −1.02901 −0.514507 0.857486i \(-0.672025\pi\)
−0.514507 + 0.857486i \(0.672025\pi\)
\(662\) −58.4648 −2.27230
\(663\) −81.4651 −3.16384
\(664\) −25.4895 −0.989183
\(665\) 0.183072 0.00709923
\(666\) 86.7206 3.36035
\(667\) −36.0979 −1.39772
\(668\) 34.1590 1.32165
\(669\) 66.5806 2.57415
\(670\) 1.77235 0.0684720
\(671\) −4.99740 −0.192922
\(672\) 2.75898 0.106430
\(673\) 38.0008 1.46482 0.732412 0.680861i \(-0.238394\pi\)
0.732412 + 0.680861i \(0.238394\pi\)
\(674\) 78.3089 3.01635
\(675\) 0.293257 0.0112875
\(676\) 66.9834 2.57628
\(677\) −16.8012 −0.645722 −0.322861 0.946446i \(-0.604645\pi\)
−0.322861 + 0.946446i \(0.604645\pi\)
\(678\) 28.8461 1.10783
\(679\) 1.93127 0.0741152
\(680\) 38.3567 1.47091
\(681\) −25.6876 −0.984350
\(682\) −9.91045 −0.379491
\(683\) −23.6603 −0.905335 −0.452668 0.891679i \(-0.649528\pi\)
−0.452668 + 0.891679i \(0.649528\pi\)
\(684\) 9.02095 0.344925
\(685\) −15.6485 −0.597897
\(686\) 9.05685 0.345792
\(687\) 25.7550 0.982613
\(688\) −43.4457 −1.65635
\(689\) 15.0751 0.574316
\(690\) 37.5816 1.43071
\(691\) −44.5630 −1.69526 −0.847629 0.530590i \(-0.821970\pi\)
−0.847629 + 0.530590i \(0.821970\pi\)
\(692\) 48.2350 1.83362
\(693\) 0.414814 0.0157575
\(694\) −49.0298 −1.86115
\(695\) −9.47689 −0.359479
\(696\) −86.6400 −3.28408
\(697\) −4.68059 −0.177290
\(698\) −0.0418104 −0.00158255
\(699\) 15.4778 0.585426
\(700\) 1.13016 0.0427159
\(701\) 42.1789 1.59307 0.796537 0.604590i \(-0.206663\pi\)
0.796537 + 0.604590i \(0.206663\pi\)
\(702\) 3.94121 0.148751
\(703\) −8.48383 −0.319974
\(704\) −1.06132 −0.0400001
\(705\) 24.8341 0.935305
\(706\) 16.6487 0.626581
\(707\) 2.14161 0.0805436
\(708\) −23.8675 −0.896995
\(709\) −36.1417 −1.35733 −0.678665 0.734448i \(-0.737441\pi\)
−0.678665 + 0.734448i \(0.737441\pi\)
\(710\) 31.2081 1.17122
\(711\) 11.0036 0.412669
\(712\) −18.0778 −0.677496
\(713\) 42.8196 1.60361
\(714\) −9.96590 −0.372964
\(715\) −2.97908 −0.111411
\(716\) 48.4974 1.81243
\(717\) 1.67231 0.0624534
\(718\) −30.4277 −1.13555
\(719\) −20.6227 −0.769099 −0.384549 0.923104i \(-0.625643\pi\)
−0.384549 + 0.923104i \(0.625643\pi\)
\(720\) 18.8483 0.702436
\(721\) −1.83580 −0.0683686
\(722\) 46.7754 1.74080
\(723\) 39.8662 1.48264
\(724\) 63.8922 2.37454
\(725\) −5.89093 −0.218784
\(726\) −65.5356 −2.43225
\(727\) −27.4176 −1.01686 −0.508431 0.861103i \(-0.669774\pi\)
−0.508431 + 0.861103i \(0.669774\pi\)
\(728\) 8.28166 0.306939
\(729\) −24.7808 −0.917809
\(730\) −27.4418 −1.01567
\(731\) 41.9647 1.55212
\(732\) 95.0456 3.51299
\(733\) 19.8461 0.733034 0.366517 0.930411i \(-0.380550\pi\)
0.366517 + 0.930411i \(0.380550\pi\)
\(734\) −64.2192 −2.37038
\(735\) 16.8126 0.620143
\(736\) −27.1340 −1.00017
\(737\) −0.392873 −0.0144717
\(738\) −5.39030 −0.198420
\(739\) 22.3901 0.823632 0.411816 0.911267i \(-0.364895\pi\)
0.411816 + 0.911267i \(0.364895\pi\)
\(740\) −52.3731 −1.92527
\(741\) 9.17813 0.337167
\(742\) 1.84419 0.0677023
\(743\) 39.2243 1.43900 0.719499 0.694493i \(-0.244371\pi\)
0.719499 + 0.694493i \(0.244371\pi\)
\(744\) 102.773 3.76784
\(745\) 5.41227 0.198290
\(746\) 61.7164 2.25960
\(747\) 12.0984 0.442659
\(748\) −15.5936 −0.570157
\(749\) 2.94140 0.107476
\(750\) 6.13306 0.223948
\(751\) −27.7488 −1.01257 −0.506285 0.862366i \(-0.668982\pi\)
−0.506285 + 0.862366i \(0.668982\pi\)
\(752\) −67.0529 −2.44517
\(753\) −31.7183 −1.15588
\(754\) −79.1708 −2.88323
\(755\) −6.02995 −0.219452
\(756\) 0.331426 0.0120539
\(757\) 13.3443 0.485008 0.242504 0.970150i \(-0.422031\pi\)
0.242504 + 0.970150i \(0.422031\pi\)
\(758\) −10.3359 −0.375416
\(759\) −8.33062 −0.302382
\(760\) −4.32140 −0.156753
\(761\) 3.62843 0.131530 0.0657652 0.997835i \(-0.479051\pi\)
0.0657652 + 0.997835i \(0.479051\pi\)
\(762\) 14.7766 0.535301
\(763\) 1.26654 0.0458518
\(764\) −117.933 −4.26667
\(765\) −18.2058 −0.658232
\(766\) 0.578823 0.0209137
\(767\) −11.8919 −0.429391
\(768\) 74.5007 2.68831
\(769\) 7.27894 0.262485 0.131243 0.991350i \(-0.458103\pi\)
0.131243 + 0.991350i \(0.458103\pi\)
\(770\) −0.364441 −0.0131336
\(771\) 19.9882 0.719858
\(772\) −13.7089 −0.493393
\(773\) 37.3601 1.34375 0.671875 0.740665i \(-0.265489\pi\)
0.671875 + 0.740665i \(0.265489\pi\)
\(774\) 48.3279 1.73711
\(775\) 6.98787 0.251012
\(776\) −45.5873 −1.63649
\(777\) 7.41961 0.266177
\(778\) −53.7440 −1.92682
\(779\) 0.527331 0.0188936
\(780\) 56.6593 2.02873
\(781\) −6.91782 −0.247539
\(782\) 98.0127 3.50493
\(783\) −1.72756 −0.0617379
\(784\) −45.3947 −1.62124
\(785\) −14.8601 −0.530379
\(786\) −16.3617 −0.583603
\(787\) −5.81874 −0.207416 −0.103708 0.994608i \(-0.533071\pi\)
−0.103708 + 0.994608i \(0.533071\pi\)
\(788\) −66.7539 −2.37801
\(789\) −27.6050 −0.982764
\(790\) −9.66741 −0.343951
\(791\) 1.20862 0.0429734
\(792\) −9.79165 −0.347931
\(793\) 47.3561 1.68167
\(794\) −76.3953 −2.71117
\(795\) 6.87950 0.243991
\(796\) −49.9346 −1.76988
\(797\) 32.3175 1.14475 0.572373 0.819993i \(-0.306023\pi\)
0.572373 + 0.819993i \(0.306023\pi\)
\(798\) 1.12279 0.0397464
\(799\) 64.7671 2.29130
\(800\) −4.42808 −0.156556
\(801\) 8.58055 0.303179
\(802\) 14.8811 0.525471
\(803\) 6.08296 0.214663
\(804\) 7.47206 0.263519
\(805\) 1.57463 0.0554983
\(806\) 93.9130 3.30794
\(807\) −56.7299 −1.99699
\(808\) −50.5526 −1.77843
\(809\) −37.6548 −1.32387 −0.661937 0.749560i \(-0.730265\pi\)
−0.661937 + 0.749560i \(0.730265\pi\)
\(810\) 23.6457 0.830825
\(811\) −3.12197 −0.109627 −0.0548137 0.998497i \(-0.517456\pi\)
−0.0548137 + 0.998497i \(0.517456\pi\)
\(812\) −6.65767 −0.233639
\(813\) 6.38498 0.223931
\(814\) 16.8888 0.591950
\(815\) 9.87485 0.345901
\(816\) 100.378 3.51392
\(817\) −4.72789 −0.165408
\(818\) −31.4495 −1.09961
\(819\) −3.93085 −0.137355
\(820\) 3.25536 0.113682
\(821\) 47.2997 1.65077 0.825386 0.564569i \(-0.190958\pi\)
0.825386 + 0.564569i \(0.190958\pi\)
\(822\) −95.9730 −3.34744
\(823\) 16.2203 0.565405 0.282702 0.959208i \(-0.408769\pi\)
0.282702 + 0.959208i \(0.408769\pi\)
\(824\) 43.3338 1.50960
\(825\) −1.35950 −0.0473317
\(826\) −1.45477 −0.0506181
\(827\) 41.1812 1.43201 0.716006 0.698094i \(-0.245968\pi\)
0.716006 + 0.698094i \(0.245968\pi\)
\(828\) 77.5904 2.69645
\(829\) 12.1916 0.423431 0.211716 0.977331i \(-0.432095\pi\)
0.211716 + 0.977331i \(0.432095\pi\)
\(830\) −10.6293 −0.368947
\(831\) −56.2947 −1.95284
\(832\) 10.0573 0.348673
\(833\) 43.8472 1.51922
\(834\) −58.1224 −2.01261
\(835\) 7.76686 0.268783
\(836\) 1.75682 0.0607610
\(837\) 2.04924 0.0708321
\(838\) −0.678660 −0.0234439
\(839\) −19.6117 −0.677072 −0.338536 0.940953i \(-0.609932\pi\)
−0.338536 + 0.940953i \(0.609932\pi\)
\(840\) 3.77932 0.130399
\(841\) 5.70307 0.196658
\(842\) −23.8364 −0.821456
\(843\) −16.2628 −0.560122
\(844\) 49.1703 1.69251
\(845\) 15.2303 0.523937
\(846\) 74.5877 2.56438
\(847\) −2.74586 −0.0943489
\(848\) −18.5749 −0.637864
\(849\) 67.5585 2.31860
\(850\) 15.9950 0.548624
\(851\) −72.9705 −2.50140
\(852\) 131.570 4.50752
\(853\) −4.16124 −0.142478 −0.0712391 0.997459i \(-0.522695\pi\)
−0.0712391 + 0.997459i \(0.522695\pi\)
\(854\) 5.79323 0.198240
\(855\) 2.05113 0.0701471
\(856\) −69.4315 −2.37312
\(857\) 1.45006 0.0495330 0.0247665 0.999693i \(-0.492116\pi\)
0.0247665 + 0.999693i \(0.492116\pi\)
\(858\) −18.2709 −0.623758
\(859\) 7.62894 0.260296 0.130148 0.991495i \(-0.458455\pi\)
0.130148 + 0.991495i \(0.458455\pi\)
\(860\) −29.1866 −0.995256
\(861\) −0.461182 −0.0157170
\(862\) 17.9174 0.610268
\(863\) 30.8038 1.04857 0.524286 0.851542i \(-0.324332\pi\)
0.524286 + 0.851542i \(0.324332\pi\)
\(864\) −1.29857 −0.0441781
\(865\) 10.9674 0.372902
\(866\) 24.3128 0.826183
\(867\) −55.7364 −1.89291
\(868\) 7.89738 0.268055
\(869\) 2.14295 0.0726946
\(870\) −36.1294 −1.22490
\(871\) 3.72293 0.126147
\(872\) −29.8965 −1.01242
\(873\) 21.6378 0.732328
\(874\) −11.0424 −0.373516
\(875\) 0.256968 0.00868710
\(876\) −115.692 −3.90887
\(877\) 42.4825 1.43453 0.717267 0.696799i \(-0.245393\pi\)
0.717267 + 0.696799i \(0.245393\pi\)
\(878\) −1.64355 −0.0554672
\(879\) −46.6048 −1.57194
\(880\) 3.67070 0.123739
\(881\) −25.3391 −0.853695 −0.426848 0.904324i \(-0.640376\pi\)
−0.426848 + 0.904324i \(0.640376\pi\)
\(882\) 50.4958 1.70028
\(883\) 50.6192 1.70347 0.851737 0.523970i \(-0.175550\pi\)
0.851737 + 0.523970i \(0.175550\pi\)
\(884\) 147.767 4.96994
\(885\) −5.42684 −0.182421
\(886\) −19.5076 −0.655369
\(887\) 42.1374 1.41484 0.707418 0.706795i \(-0.249860\pi\)
0.707418 + 0.706795i \(0.249860\pi\)
\(888\) −175.139 −5.87729
\(889\) 0.619123 0.0207647
\(890\) −7.53858 −0.252694
\(891\) −5.24148 −0.175596
\(892\) −120.768 −4.04363
\(893\) −7.29688 −0.244181
\(894\) 33.1938 1.11017
\(895\) 11.0270 0.368593
\(896\) 3.50609 0.117130
\(897\) 78.9423 2.63581
\(898\) 82.1611 2.74175
\(899\) −41.1650 −1.37293
\(900\) 12.6622 0.422073
\(901\) 17.9417 0.597725
\(902\) −1.04976 −0.0349531
\(903\) 4.13482 0.137598
\(904\) −28.5293 −0.948869
\(905\) 14.5274 0.482907
\(906\) −36.9820 −1.22865
\(907\) −19.6576 −0.652721 −0.326360 0.945245i \(-0.605822\pi\)
−0.326360 + 0.945245i \(0.605822\pi\)
\(908\) 46.5939 1.54627
\(909\) 23.9945 0.795848
\(910\) 3.45350 0.114483
\(911\) 31.9613 1.05893 0.529463 0.848333i \(-0.322393\pi\)
0.529463 + 0.848333i \(0.322393\pi\)
\(912\) −11.3089 −0.374475
\(913\) 2.35616 0.0779775
\(914\) −28.2167 −0.933326
\(915\) 21.6109 0.714433
\(916\) −46.7161 −1.54354
\(917\) −0.685536 −0.0226384
\(918\) 4.69064 0.154814
\(919\) 27.0232 0.891413 0.445707 0.895179i \(-0.352952\pi\)
0.445707 + 0.895179i \(0.352952\pi\)
\(920\) −37.1689 −1.22542
\(921\) 13.8654 0.456880
\(922\) −75.4169 −2.48372
\(923\) 65.5544 2.15775
\(924\) −1.53645 −0.0505454
\(925\) −11.9083 −0.391542
\(926\) 19.1352 0.628820
\(927\) −20.5681 −0.675547
\(928\) 26.0855 0.856299
\(929\) 53.0777 1.74142 0.870711 0.491795i \(-0.163659\pi\)
0.870711 + 0.491795i \(0.163659\pi\)
\(930\) 42.8570 1.40534
\(931\) −4.93998 −0.161901
\(932\) −28.0748 −0.919620
\(933\) 48.1719 1.57708
\(934\) 63.1191 2.06532
\(935\) −3.54557 −0.115952
\(936\) 92.7872 3.03285
\(937\) 39.8321 1.30126 0.650629 0.759396i \(-0.274505\pi\)
0.650629 + 0.759396i \(0.274505\pi\)
\(938\) 0.455438 0.0148706
\(939\) 67.3231 2.19701
\(940\) −45.0457 −1.46923
\(941\) 19.4679 0.634634 0.317317 0.948319i \(-0.397218\pi\)
0.317317 + 0.948319i \(0.397218\pi\)
\(942\) −91.1378 −2.96943
\(943\) 4.53564 0.147701
\(944\) 14.6526 0.476903
\(945\) 0.0753577 0.00245138
\(946\) 9.41181 0.306004
\(947\) −22.2190 −0.722020 −0.361010 0.932562i \(-0.617568\pi\)
−0.361010 + 0.932562i \(0.617568\pi\)
\(948\) −40.7568 −1.32372
\(949\) −57.6431 −1.87117
\(950\) −1.80205 −0.0584662
\(951\) −25.5580 −0.828776
\(952\) 9.85644 0.319449
\(953\) 34.6986 1.12400 0.561999 0.827138i \(-0.310032\pi\)
0.561999 + 0.827138i \(0.310032\pi\)
\(954\) 20.6622 0.668963
\(955\) −26.8149 −0.867710
\(956\) −3.03334 −0.0981054
\(957\) 8.00872 0.258885
\(958\) −94.3179 −3.04727
\(959\) −4.02115 −0.129850
\(960\) 4.58961 0.148129
\(961\) 17.8303 0.575170
\(962\) −160.040 −5.15991
\(963\) 32.9553 1.06197
\(964\) −72.3121 −2.32901
\(965\) −3.11703 −0.100341
\(966\) 9.65728 0.310718
\(967\) −12.0819 −0.388527 −0.194264 0.980949i \(-0.562232\pi\)
−0.194264 + 0.980949i \(0.562232\pi\)
\(968\) 64.8158 2.08326
\(969\) 10.9234 0.350910
\(970\) −19.0102 −0.610381
\(971\) −35.3199 −1.13347 −0.566736 0.823900i \(-0.691794\pi\)
−0.566736 + 0.823900i \(0.691794\pi\)
\(972\) 95.8185 3.07338
\(973\) −2.43526 −0.0780707
\(974\) 7.35186 0.235569
\(975\) 12.8828 0.412581
\(976\) −58.3501 −1.86774
\(977\) 47.9789 1.53498 0.767490 0.641061i \(-0.221506\pi\)
0.767490 + 0.641061i \(0.221506\pi\)
\(978\) 60.5631 1.93659
\(979\) 1.67106 0.0534072
\(980\) −30.4959 −0.974156
\(981\) 14.1902 0.453059
\(982\) −4.43068 −0.141389
\(983\) 52.8181 1.68463 0.842317 0.538982i \(-0.181191\pi\)
0.842317 + 0.538982i \(0.181191\pi\)
\(984\) 10.8862 0.347038
\(985\) −15.1781 −0.483614
\(986\) −94.2254 −3.00075
\(987\) 6.38156 0.203127
\(988\) −16.6479 −0.529641
\(989\) −40.6652 −1.29308
\(990\) −4.08318 −0.129772
\(991\) 17.2468 0.547862 0.273931 0.961749i \(-0.411676\pi\)
0.273931 + 0.961749i \(0.411676\pi\)
\(992\) −30.9428 −0.982436
\(993\) −56.0434 −1.77849
\(994\) 8.01949 0.254363
\(995\) −11.3538 −0.359940
\(996\) −44.8119 −1.41992
\(997\) −0.846695 −0.0268151 −0.0134076 0.999910i \(-0.504268\pi\)
−0.0134076 + 0.999910i \(0.504268\pi\)
\(998\) 27.9179 0.883727
\(999\) −3.49219 −0.110488
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 \(a_p\))