Properties

Label 8018.2.a.f.1.9
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 34
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(34\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.09965 q^{3} +1.00000 q^{4} +1.88296 q^{5} +2.09965 q^{6} -4.81740 q^{7} -1.00000 q^{8} +1.40851 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.09965 q^{3} +1.00000 q^{4} +1.88296 q^{5} +2.09965 q^{6} -4.81740 q^{7} -1.00000 q^{8} +1.40851 q^{9} -1.88296 q^{10} -2.76481 q^{11} -2.09965 q^{12} +1.57116 q^{13} +4.81740 q^{14} -3.95354 q^{15} +1.00000 q^{16} -7.15980 q^{17} -1.40851 q^{18} -1.00000 q^{19} +1.88296 q^{20} +10.1148 q^{21} +2.76481 q^{22} -0.301499 q^{23} +2.09965 q^{24} -1.45447 q^{25} -1.57116 q^{26} +3.34156 q^{27} -4.81740 q^{28} +5.33121 q^{29} +3.95354 q^{30} +1.70809 q^{31} -1.00000 q^{32} +5.80512 q^{33} +7.15980 q^{34} -9.07096 q^{35} +1.40851 q^{36} -0.603139 q^{37} +1.00000 q^{38} -3.29888 q^{39} -1.88296 q^{40} +10.5477 q^{41} -10.1148 q^{42} +1.20780 q^{43} -2.76481 q^{44} +2.65216 q^{45} +0.301499 q^{46} -0.389772 q^{47} -2.09965 q^{48} +16.2074 q^{49} +1.45447 q^{50} +15.0330 q^{51} +1.57116 q^{52} +1.22228 q^{53} -3.34156 q^{54} -5.20601 q^{55} +4.81740 q^{56} +2.09965 q^{57} -5.33121 q^{58} +5.27734 q^{59} -3.95354 q^{60} +12.5527 q^{61} -1.70809 q^{62} -6.78536 q^{63} +1.00000 q^{64} +2.95843 q^{65} -5.80512 q^{66} +1.65938 q^{67} -7.15980 q^{68} +0.633041 q^{69} +9.07096 q^{70} +1.20648 q^{71} -1.40851 q^{72} -4.43364 q^{73} +0.603139 q^{74} +3.05388 q^{75} -1.00000 q^{76} +13.3192 q^{77} +3.29888 q^{78} -5.43480 q^{79} +1.88296 q^{80} -11.2416 q^{81} -10.5477 q^{82} -0.714078 q^{83} +10.1148 q^{84} -13.4816 q^{85} -1.20780 q^{86} -11.1937 q^{87} +2.76481 q^{88} -4.35208 q^{89} -2.65216 q^{90} -7.56892 q^{91} -0.301499 q^{92} -3.58638 q^{93} +0.389772 q^{94} -1.88296 q^{95} +2.09965 q^{96} +6.13058 q^{97} -16.2074 q^{98} -3.89426 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 34q^{2} - 10q^{3} + 34q^{4} + 7q^{5} + 10q^{6} - 6q^{7} - 34q^{8} + 38q^{9} + O(q^{10}) \) \( 34q - 34q^{2} - 10q^{3} + 34q^{4} + 7q^{5} + 10q^{6} - 6q^{7} - 34q^{8} + 38q^{9} - 7q^{10} + 4q^{11} - 10q^{12} - 5q^{13} + 6q^{14} - 17q^{15} + 34q^{16} + 8q^{17} - 38q^{18} - 34q^{19} + 7q^{20} - 4q^{22} - 24q^{23} + 10q^{24} + 5q^{25} + 5q^{26} - 31q^{27} - 6q^{28} + 24q^{29} + 17q^{30} - 28q^{31} - 34q^{32} - 16q^{33} - 8q^{34} + 2q^{35} + 38q^{36} - 36q^{37} + 34q^{38} - 9q^{39} - 7q^{40} + 9q^{41} - 24q^{43} + 4q^{44} + 22q^{45} + 24q^{46} - 29q^{47} - 10q^{48} + 22q^{49} - 5q^{50} - 21q^{51} - 5q^{52} - 9q^{53} + 31q^{54} - 28q^{55} + 6q^{56} + 10q^{57} - 24q^{58} - 28q^{59} - 17q^{60} + 23q^{61} + 28q^{62} - 27q^{63} + 34q^{64} - 6q^{65} + 16q^{66} - 51q^{67} + 8q^{68} - 17q^{69} - 2q^{70} - 31q^{71} - 38q^{72} - 26q^{73} + 36q^{74} - 109q^{75} - 34q^{76} - 28q^{77} + 9q^{78} - 36q^{79} + 7q^{80} + 6q^{81} - 9q^{82} - 10q^{83} - 32q^{85} + 24q^{86} - 8q^{87} - 4q^{88} - 34q^{89} - 22q^{90} - 41q^{91} - 24q^{92} - 33q^{93} + 29q^{94} - 7q^{95} + 10q^{96} - 56q^{97} - 22q^{98} - 28q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.09965 −1.21223 −0.606115 0.795377i \(-0.707273\pi\)
−0.606115 + 0.795377i \(0.707273\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.88296 0.842084 0.421042 0.907041i \(-0.361665\pi\)
0.421042 + 0.907041i \(0.361665\pi\)
\(6\) 2.09965 0.857177
\(7\) −4.81740 −1.82081 −0.910403 0.413722i \(-0.864229\pi\)
−0.910403 + 0.413722i \(0.864229\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.40851 0.469504
\(10\) −1.88296 −0.595443
\(11\) −2.76481 −0.833621 −0.416811 0.908993i \(-0.636852\pi\)
−0.416811 + 0.908993i \(0.636852\pi\)
\(12\) −2.09965 −0.606115
\(13\) 1.57116 0.435762 0.217881 0.975975i \(-0.430086\pi\)
0.217881 + 0.975975i \(0.430086\pi\)
\(14\) 4.81740 1.28750
\(15\) −3.95354 −1.02080
\(16\) 1.00000 0.250000
\(17\) −7.15980 −1.73651 −0.868253 0.496121i \(-0.834757\pi\)
−0.868253 + 0.496121i \(0.834757\pi\)
\(18\) −1.40851 −0.331989
\(19\) −1.00000 −0.229416
\(20\) 1.88296 0.421042
\(21\) 10.1148 2.20724
\(22\) 2.76481 0.589459
\(23\) −0.301499 −0.0628669 −0.0314335 0.999506i \(-0.510007\pi\)
−0.0314335 + 0.999506i \(0.510007\pi\)
\(24\) 2.09965 0.428588
\(25\) −1.45447 −0.290895
\(26\) −1.57116 −0.308130
\(27\) 3.34156 0.643084
\(28\) −4.81740 −0.910403
\(29\) 5.33121 0.989981 0.494991 0.868898i \(-0.335172\pi\)
0.494991 + 0.868898i \(0.335172\pi\)
\(30\) 3.95354 0.721815
\(31\) 1.70809 0.306782 0.153391 0.988166i \(-0.450981\pi\)
0.153391 + 0.988166i \(0.450981\pi\)
\(32\) −1.00000 −0.176777
\(33\) 5.80512 1.01054
\(34\) 7.15980 1.22790
\(35\) −9.07096 −1.53327
\(36\) 1.40851 0.234752
\(37\) −0.603139 −0.0991555 −0.0495777 0.998770i \(-0.515788\pi\)
−0.0495777 + 0.998770i \(0.515788\pi\)
\(38\) 1.00000 0.162221
\(39\) −3.29888 −0.528244
\(40\) −1.88296 −0.297722
\(41\) 10.5477 1.64728 0.823639 0.567114i \(-0.191940\pi\)
0.823639 + 0.567114i \(0.191940\pi\)
\(42\) −10.1148 −1.56075
\(43\) 1.20780 0.184188 0.0920940 0.995750i \(-0.470644\pi\)
0.0920940 + 0.995750i \(0.470644\pi\)
\(44\) −2.76481 −0.416811
\(45\) 2.65216 0.395361
\(46\) 0.301499 0.0444536
\(47\) −0.389772 −0.0568541 −0.0284271 0.999596i \(-0.509050\pi\)
−0.0284271 + 0.999596i \(0.509050\pi\)
\(48\) −2.09965 −0.303058
\(49\) 16.2074 2.31534
\(50\) 1.45447 0.205694
\(51\) 15.0330 2.10505
\(52\) 1.57116 0.217881
\(53\) 1.22228 0.167892 0.0839462 0.996470i \(-0.473248\pi\)
0.0839462 + 0.996470i \(0.473248\pi\)
\(54\) −3.34156 −0.454729
\(55\) −5.20601 −0.701979
\(56\) 4.81740 0.643752
\(57\) 2.09965 0.278105
\(58\) −5.33121 −0.700022
\(59\) 5.27734 0.687051 0.343526 0.939143i \(-0.388379\pi\)
0.343526 + 0.939143i \(0.388379\pi\)
\(60\) −3.95354 −0.510400
\(61\) 12.5527 1.60721 0.803605 0.595164i \(-0.202913\pi\)
0.803605 + 0.595164i \(0.202913\pi\)
\(62\) −1.70809 −0.216927
\(63\) −6.78536 −0.854875
\(64\) 1.00000 0.125000
\(65\) 2.95843 0.366948
\(66\) −5.80512 −0.714560
\(67\) 1.65938 0.202725 0.101363 0.994850i \(-0.467680\pi\)
0.101363 + 0.994850i \(0.467680\pi\)
\(68\) −7.15980 −0.868253
\(69\) 0.633041 0.0762092
\(70\) 9.07096 1.08419
\(71\) 1.20648 0.143183 0.0715915 0.997434i \(-0.477192\pi\)
0.0715915 + 0.997434i \(0.477192\pi\)
\(72\) −1.40851 −0.165995
\(73\) −4.43364 −0.518918 −0.259459 0.965754i \(-0.583544\pi\)
−0.259459 + 0.965754i \(0.583544\pi\)
\(74\) 0.603139 0.0701135
\(75\) 3.05388 0.352632
\(76\) −1.00000 −0.114708
\(77\) 13.3192 1.51786
\(78\) 3.29888 0.373525
\(79\) −5.43480 −0.611463 −0.305731 0.952118i \(-0.598901\pi\)
−0.305731 + 0.952118i \(0.598901\pi\)
\(80\) 1.88296 0.210521
\(81\) −11.2416 −1.24907
\(82\) −10.5477 −1.16480
\(83\) −0.714078 −0.0783802 −0.0391901 0.999232i \(-0.512478\pi\)
−0.0391901 + 0.999232i \(0.512478\pi\)
\(84\) 10.1148 1.10362
\(85\) −13.4816 −1.46228
\(86\) −1.20780 −0.130241
\(87\) −11.1937 −1.20009
\(88\) 2.76481 0.294730
\(89\) −4.35208 −0.461320 −0.230660 0.973034i \(-0.574088\pi\)
−0.230660 + 0.973034i \(0.574088\pi\)
\(90\) −2.65216 −0.279563
\(91\) −7.56892 −0.793438
\(92\) −0.301499 −0.0314335
\(93\) −3.58638 −0.371890
\(94\) 0.389772 0.0402019
\(95\) −1.88296 −0.193187
\(96\) 2.09965 0.214294
\(97\) 6.13058 0.622466 0.311233 0.950334i \(-0.399258\pi\)
0.311233 + 0.950334i \(0.399258\pi\)
\(98\) −16.2074 −1.63719
\(99\) −3.89426 −0.391388
\(100\) −1.45447 −0.145447
\(101\) 12.0025 1.19429 0.597146 0.802132i \(-0.296301\pi\)
0.597146 + 0.802132i \(0.296301\pi\)
\(102\) −15.0330 −1.48849
\(103\) −0.0219020 −0.00215807 −0.00107904 0.999999i \(-0.500343\pi\)
−0.00107904 + 0.999999i \(0.500343\pi\)
\(104\) −1.57116 −0.154065
\(105\) 19.0458 1.85868
\(106\) −1.22228 −0.118718
\(107\) −12.4139 −1.20010 −0.600050 0.799962i \(-0.704853\pi\)
−0.600050 + 0.799962i \(0.704853\pi\)
\(108\) 3.34156 0.321542
\(109\) 11.4172 1.09357 0.546785 0.837273i \(-0.315851\pi\)
0.546785 + 0.837273i \(0.315851\pi\)
\(110\) 5.20601 0.496374
\(111\) 1.26638 0.120199
\(112\) −4.81740 −0.455202
\(113\) 13.0848 1.23091 0.615456 0.788171i \(-0.288972\pi\)
0.615456 + 0.788171i \(0.288972\pi\)
\(114\) −2.09965 −0.196650
\(115\) −0.567710 −0.0529392
\(116\) 5.33121 0.494991
\(117\) 2.21300 0.204592
\(118\) −5.27734 −0.485818
\(119\) 34.4916 3.16184
\(120\) 3.95354 0.360907
\(121\) −3.35584 −0.305076
\(122\) −12.5527 −1.13647
\(123\) −22.1465 −1.99688
\(124\) 1.70809 0.153391
\(125\) −12.1535 −1.08704
\(126\) 6.78536 0.604488
\(127\) 11.3371 1.00601 0.503003 0.864284i \(-0.332228\pi\)
0.503003 + 0.864284i \(0.332228\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −2.53595 −0.223278
\(130\) −2.95843 −0.259471
\(131\) −12.1602 −1.06244 −0.531220 0.847234i \(-0.678266\pi\)
−0.531220 + 0.847234i \(0.678266\pi\)
\(132\) 5.80512 0.505271
\(133\) 4.81740 0.417722
\(134\) −1.65938 −0.143348
\(135\) 6.29202 0.541531
\(136\) 7.15980 0.613948
\(137\) 0.297548 0.0254213 0.0127106 0.999919i \(-0.495954\pi\)
0.0127106 + 0.999919i \(0.495954\pi\)
\(138\) −0.633041 −0.0538881
\(139\) −19.9823 −1.69488 −0.847440 0.530891i \(-0.821857\pi\)
−0.847440 + 0.530891i \(0.821857\pi\)
\(140\) −9.07096 −0.766636
\(141\) 0.818383 0.0689203
\(142\) −1.20648 −0.101246
\(143\) −4.34396 −0.363260
\(144\) 1.40851 0.117376
\(145\) 10.0384 0.833647
\(146\) 4.43364 0.366931
\(147\) −34.0297 −2.80672
\(148\) −0.603139 −0.0495777
\(149\) 9.77017 0.800403 0.400202 0.916427i \(-0.368940\pi\)
0.400202 + 0.916427i \(0.368940\pi\)
\(150\) −3.05388 −0.249348
\(151\) 0.836833 0.0681005 0.0340503 0.999420i \(-0.489159\pi\)
0.0340503 + 0.999420i \(0.489159\pi\)
\(152\) 1.00000 0.0811107
\(153\) −10.0847 −0.815296
\(154\) −13.3192 −1.07329
\(155\) 3.21626 0.258336
\(156\) −3.29888 −0.264122
\(157\) 3.32601 0.265444 0.132722 0.991153i \(-0.457628\pi\)
0.132722 + 0.991153i \(0.457628\pi\)
\(158\) 5.43480 0.432369
\(159\) −2.56635 −0.203524
\(160\) −1.88296 −0.148861
\(161\) 1.45244 0.114469
\(162\) 11.2416 0.883226
\(163\) 0.0658499 0.00515776 0.00257888 0.999997i \(-0.499179\pi\)
0.00257888 + 0.999997i \(0.499179\pi\)
\(164\) 10.5477 0.823639
\(165\) 10.9308 0.850960
\(166\) 0.714078 0.0554232
\(167\) 14.1717 1.09664 0.548318 0.836270i \(-0.315268\pi\)
0.548318 + 0.836270i \(0.315268\pi\)
\(168\) −10.1148 −0.780376
\(169\) −10.5315 −0.810112
\(170\) 13.4816 1.03399
\(171\) −1.40851 −0.107712
\(172\) 1.20780 0.0920940
\(173\) −12.7976 −0.972986 −0.486493 0.873685i \(-0.661724\pi\)
−0.486493 + 0.873685i \(0.661724\pi\)
\(174\) 11.1937 0.848589
\(175\) 7.00678 0.529663
\(176\) −2.76481 −0.208405
\(177\) −11.0805 −0.832864
\(178\) 4.35208 0.326202
\(179\) −8.81510 −0.658871 −0.329436 0.944178i \(-0.606858\pi\)
−0.329436 + 0.944178i \(0.606858\pi\)
\(180\) 2.65216 0.197681
\(181\) −0.282612 −0.0210064 −0.0105032 0.999945i \(-0.503343\pi\)
−0.0105032 + 0.999945i \(0.503343\pi\)
\(182\) 7.56892 0.561045
\(183\) −26.3562 −1.94831
\(184\) 0.301499 0.0222268
\(185\) −1.13568 −0.0834972
\(186\) 3.58638 0.262966
\(187\) 19.7955 1.44759
\(188\) −0.389772 −0.0284271
\(189\) −16.0977 −1.17093
\(190\) 1.88296 0.136604
\(191\) 14.5928 1.05590 0.527949 0.849276i \(-0.322961\pi\)
0.527949 + 0.849276i \(0.322961\pi\)
\(192\) −2.09965 −0.151529
\(193\) −10.1633 −0.731571 −0.365786 0.930699i \(-0.619200\pi\)
−0.365786 + 0.930699i \(0.619200\pi\)
\(194\) −6.13058 −0.440150
\(195\) −6.21165 −0.444826
\(196\) 16.2074 1.15767
\(197\) −24.2849 −1.73023 −0.865114 0.501575i \(-0.832754\pi\)
−0.865114 + 0.501575i \(0.832754\pi\)
\(198\) 3.89426 0.276753
\(199\) −15.7566 −1.11696 −0.558480 0.829518i \(-0.688615\pi\)
−0.558480 + 0.829518i \(0.688615\pi\)
\(200\) 1.45447 0.102847
\(201\) −3.48410 −0.245750
\(202\) −12.0025 −0.844493
\(203\) −25.6826 −1.80256
\(204\) 15.0330 1.05252
\(205\) 19.8609 1.38715
\(206\) 0.0219020 0.00152599
\(207\) −0.424665 −0.0295163
\(208\) 1.57116 0.108940
\(209\) 2.76481 0.191246
\(210\) −19.0458 −1.31428
\(211\) −1.00000 −0.0688428
\(212\) 1.22228 0.0839462
\(213\) −2.53318 −0.173571
\(214\) 12.4139 0.848599
\(215\) 2.27424 0.155102
\(216\) −3.34156 −0.227365
\(217\) −8.22855 −0.558590
\(218\) −11.4172 −0.773271
\(219\) 9.30907 0.629049
\(220\) −5.20601 −0.350989
\(221\) −11.2492 −0.756703
\(222\) −1.26638 −0.0849937
\(223\) −15.0757 −1.00954 −0.504771 0.863253i \(-0.668423\pi\)
−0.504771 + 0.863253i \(0.668423\pi\)
\(224\) 4.81740 0.321876
\(225\) −2.04864 −0.136576
\(226\) −13.0848 −0.870386
\(227\) −15.7486 −1.04527 −0.522635 0.852556i \(-0.675051\pi\)
−0.522635 + 0.852556i \(0.675051\pi\)
\(228\) 2.09965 0.139052
\(229\) −19.8095 −1.30905 −0.654524 0.756041i \(-0.727131\pi\)
−0.654524 + 0.756041i \(0.727131\pi\)
\(230\) 0.567710 0.0374337
\(231\) −27.9656 −1.84000
\(232\) −5.33121 −0.350011
\(233\) 23.6366 1.54849 0.774244 0.632887i \(-0.218130\pi\)
0.774244 + 0.632887i \(0.218130\pi\)
\(234\) −2.21300 −0.144668
\(235\) −0.733924 −0.0478759
\(236\) 5.27734 0.343526
\(237\) 11.4111 0.741234
\(238\) −34.4916 −2.23576
\(239\) −9.80051 −0.633942 −0.316971 0.948435i \(-0.602666\pi\)
−0.316971 + 0.948435i \(0.602666\pi\)
\(240\) −3.95354 −0.255200
\(241\) −1.29987 −0.0837317 −0.0418658 0.999123i \(-0.513330\pi\)
−0.0418658 + 0.999123i \(0.513330\pi\)
\(242\) 3.35584 0.215721
\(243\) 13.5787 0.871077
\(244\) 12.5527 0.803605
\(245\) 30.5178 1.94971
\(246\) 22.1465 1.41201
\(247\) −1.57116 −0.0999706
\(248\) −1.70809 −0.108464
\(249\) 1.49931 0.0950149
\(250\) 12.1535 0.768655
\(251\) −6.79093 −0.428640 −0.214320 0.976764i \(-0.568753\pi\)
−0.214320 + 0.976764i \(0.568753\pi\)
\(252\) −6.78536 −0.427438
\(253\) 0.833588 0.0524072
\(254\) −11.3371 −0.711354
\(255\) 28.3066 1.77263
\(256\) 1.00000 0.0625000
\(257\) 3.29483 0.205526 0.102763 0.994706i \(-0.467232\pi\)
0.102763 + 0.994706i \(0.467232\pi\)
\(258\) 2.53595 0.157882
\(259\) 2.90556 0.180543
\(260\) 2.95843 0.183474
\(261\) 7.50907 0.464800
\(262\) 12.1602 0.751258
\(263\) −3.69470 −0.227825 −0.113913 0.993491i \(-0.536338\pi\)
−0.113913 + 0.993491i \(0.536338\pi\)
\(264\) −5.80512 −0.357280
\(265\) 2.30149 0.141380
\(266\) −4.81740 −0.295374
\(267\) 9.13783 0.559226
\(268\) 1.65938 0.101363
\(269\) 7.28892 0.444413 0.222207 0.975000i \(-0.428674\pi\)
0.222207 + 0.975000i \(0.428674\pi\)
\(270\) −6.29202 −0.382920
\(271\) 22.7217 1.38024 0.690122 0.723693i \(-0.257557\pi\)
0.690122 + 0.723693i \(0.257557\pi\)
\(272\) −7.15980 −0.434127
\(273\) 15.8920 0.961830
\(274\) −0.297548 −0.0179755
\(275\) 4.02134 0.242496
\(276\) 0.633041 0.0381046
\(277\) 18.6563 1.12095 0.560474 0.828172i \(-0.310619\pi\)
0.560474 + 0.828172i \(0.310619\pi\)
\(278\) 19.9823 1.19846
\(279\) 2.40586 0.144035
\(280\) 9.07096 0.542094
\(281\) 17.1150 1.02099 0.510497 0.859880i \(-0.329461\pi\)
0.510497 + 0.859880i \(0.329461\pi\)
\(282\) −0.818383 −0.0487340
\(283\) 3.87042 0.230072 0.115036 0.993361i \(-0.463302\pi\)
0.115036 + 0.993361i \(0.463302\pi\)
\(284\) 1.20648 0.0715915
\(285\) 3.95354 0.234188
\(286\) 4.34396 0.256864
\(287\) −50.8126 −2.99938
\(288\) −1.40851 −0.0829973
\(289\) 34.2627 2.01545
\(290\) −10.0384 −0.589477
\(291\) −12.8720 −0.754573
\(292\) −4.43364 −0.259459
\(293\) −12.5471 −0.733012 −0.366506 0.930416i \(-0.619446\pi\)
−0.366506 + 0.930416i \(0.619446\pi\)
\(294\) 34.0297 1.98465
\(295\) 9.93700 0.578555
\(296\) 0.603139 0.0350567
\(297\) −9.23878 −0.536088
\(298\) −9.77017 −0.565970
\(299\) −0.473704 −0.0273950
\(300\) 3.05388 0.176316
\(301\) −5.81846 −0.335371
\(302\) −0.836833 −0.0481543
\(303\) −25.2010 −1.44776
\(304\) −1.00000 −0.0573539
\(305\) 23.6362 1.35340
\(306\) 10.0847 0.576501
\(307\) 12.5847 0.718244 0.359122 0.933291i \(-0.383076\pi\)
0.359122 + 0.933291i \(0.383076\pi\)
\(308\) 13.3192 0.758931
\(309\) 0.0459865 0.00261608
\(310\) −3.21626 −0.182671
\(311\) 20.4985 1.16237 0.581183 0.813773i \(-0.302590\pi\)
0.581183 + 0.813773i \(0.302590\pi\)
\(312\) 3.29888 0.186762
\(313\) −25.9923 −1.46917 −0.734587 0.678515i \(-0.762624\pi\)
−0.734587 + 0.678515i \(0.762624\pi\)
\(314\) −3.32601 −0.187697
\(315\) −12.7765 −0.719877
\(316\) −5.43480 −0.305731
\(317\) −5.82998 −0.327444 −0.163722 0.986506i \(-0.552350\pi\)
−0.163722 + 0.986506i \(0.552350\pi\)
\(318\) 2.56635 0.143914
\(319\) −14.7398 −0.825269
\(320\) 1.88296 0.105260
\(321\) 26.0649 1.45480
\(322\) −1.45244 −0.0809415
\(323\) 7.15980 0.398382
\(324\) −11.2416 −0.624535
\(325\) −2.28521 −0.126761
\(326\) −0.0658499 −0.00364709
\(327\) −23.9721 −1.32566
\(328\) −10.5477 −0.582401
\(329\) 1.87769 0.103520
\(330\) −10.9308 −0.601720
\(331\) 35.7053 1.96254 0.981271 0.192632i \(-0.0617025\pi\)
0.981271 + 0.192632i \(0.0617025\pi\)
\(332\) −0.714078 −0.0391901
\(333\) −0.849528 −0.0465538
\(334\) −14.1717 −0.775438
\(335\) 3.12453 0.170712
\(336\) 10.1148 0.551810
\(337\) 19.4861 1.06148 0.530739 0.847536i \(-0.321915\pi\)
0.530739 + 0.847536i \(0.321915\pi\)
\(338\) 10.5315 0.572835
\(339\) −27.4734 −1.49215
\(340\) −13.4816 −0.731142
\(341\) −4.72254 −0.255740
\(342\) 1.40851 0.0761635
\(343\) −44.3556 −2.39497
\(344\) −1.20780 −0.0651203
\(345\) 1.19199 0.0641746
\(346\) 12.7976 0.688005
\(347\) 10.4246 0.559619 0.279810 0.960055i \(-0.409729\pi\)
0.279810 + 0.960055i \(0.409729\pi\)
\(348\) −11.1937 −0.600043
\(349\) 28.0471 1.50133 0.750663 0.660685i \(-0.229734\pi\)
0.750663 + 0.660685i \(0.229734\pi\)
\(350\) −7.00678 −0.374528
\(351\) 5.25014 0.280232
\(352\) 2.76481 0.147365
\(353\) 4.32987 0.230456 0.115228 0.993339i \(-0.463240\pi\)
0.115228 + 0.993339i \(0.463240\pi\)
\(354\) 11.0805 0.588924
\(355\) 2.27175 0.120572
\(356\) −4.35208 −0.230660
\(357\) −72.4202 −3.83288
\(358\) 8.81510 0.465892
\(359\) 30.3696 1.60285 0.801424 0.598097i \(-0.204076\pi\)
0.801424 + 0.598097i \(0.204076\pi\)
\(360\) −2.65216 −0.139781
\(361\) 1.00000 0.0526316
\(362\) 0.282612 0.0148538
\(363\) 7.04606 0.369823
\(364\) −7.56892 −0.396719
\(365\) −8.34835 −0.436973
\(366\) 26.3562 1.37766
\(367\) 2.72398 0.142190 0.0710952 0.997470i \(-0.477351\pi\)
0.0710952 + 0.997470i \(0.477351\pi\)
\(368\) −0.301499 −0.0157167
\(369\) 14.8566 0.773403
\(370\) 1.13568 0.0590414
\(371\) −5.88819 −0.305700
\(372\) −3.58638 −0.185945
\(373\) −12.8019 −0.662857 −0.331428 0.943480i \(-0.607530\pi\)
−0.331428 + 0.943480i \(0.607530\pi\)
\(374\) −19.7955 −1.02360
\(375\) 25.5180 1.31775
\(376\) 0.389772 0.0201010
\(377\) 8.37619 0.431396
\(378\) 16.0977 0.827974
\(379\) −11.3225 −0.581599 −0.290799 0.956784i \(-0.593921\pi\)
−0.290799 + 0.956784i \(0.593921\pi\)
\(380\) −1.88296 −0.0965936
\(381\) −23.8039 −1.21951
\(382\) −14.5928 −0.746633
\(383\) −30.3805 −1.55237 −0.776184 0.630506i \(-0.782847\pi\)
−0.776184 + 0.630506i \(0.782847\pi\)
\(384\) 2.09965 0.107147
\(385\) 25.0795 1.27817
\(386\) 10.1633 0.517299
\(387\) 1.70120 0.0864769
\(388\) 6.13058 0.311233
\(389\) −26.6564 −1.35153 −0.675767 0.737115i \(-0.736188\pi\)
−0.675767 + 0.737115i \(0.736188\pi\)
\(390\) 6.21165 0.314539
\(391\) 2.15867 0.109169
\(392\) −16.2074 −0.818595
\(393\) 25.5321 1.28792
\(394\) 24.2849 1.22346
\(395\) −10.2335 −0.514903
\(396\) −3.89426 −0.195694
\(397\) 33.4711 1.67987 0.839933 0.542690i \(-0.182594\pi\)
0.839933 + 0.542690i \(0.182594\pi\)
\(398\) 15.7566 0.789809
\(399\) −10.1148 −0.506375
\(400\) −1.45447 −0.0727237
\(401\) −13.1479 −0.656575 −0.328288 0.944578i \(-0.606471\pi\)
−0.328288 + 0.944578i \(0.606471\pi\)
\(402\) 3.48410 0.173771
\(403\) 2.68368 0.133684
\(404\) 12.0025 0.597146
\(405\) −21.1675 −1.05182
\(406\) 25.6826 1.27461
\(407\) 1.66756 0.0826581
\(408\) −15.0330 −0.744246
\(409\) −28.0181 −1.38541 −0.692703 0.721223i \(-0.743580\pi\)
−0.692703 + 0.721223i \(0.743580\pi\)
\(410\) −19.8609 −0.980861
\(411\) −0.624746 −0.0308164
\(412\) −0.0219020 −0.00107904
\(413\) −25.4231 −1.25099
\(414\) 0.424665 0.0208711
\(415\) −1.34458 −0.0660027
\(416\) −1.57116 −0.0770325
\(417\) 41.9558 2.05459
\(418\) −2.76481 −0.135231
\(419\) 6.36647 0.311022 0.155511 0.987834i \(-0.450298\pi\)
0.155511 + 0.987834i \(0.450298\pi\)
\(420\) 19.0458 0.929340
\(421\) 34.1193 1.66287 0.831437 0.555619i \(-0.187519\pi\)
0.831437 + 0.555619i \(0.187519\pi\)
\(422\) 1.00000 0.0486792
\(423\) −0.548998 −0.0266932
\(424\) −1.22228 −0.0593590
\(425\) 10.4137 0.505141
\(426\) 2.53318 0.122733
\(427\) −60.4714 −2.92642
\(428\) −12.4139 −0.600050
\(429\) 9.12078 0.440355
\(430\) −2.27424 −0.109673
\(431\) 3.08569 0.148632 0.0743161 0.997235i \(-0.476323\pi\)
0.0743161 + 0.997235i \(0.476323\pi\)
\(432\) 3.34156 0.160771
\(433\) −25.2198 −1.21199 −0.605993 0.795470i \(-0.707224\pi\)
−0.605993 + 0.795470i \(0.707224\pi\)
\(434\) 8.22855 0.394983
\(435\) −21.0772 −1.01057
\(436\) 11.4172 0.546785
\(437\) 0.301499 0.0144227
\(438\) −9.30907 −0.444805
\(439\) 32.3903 1.54591 0.772953 0.634463i \(-0.218779\pi\)
0.772953 + 0.634463i \(0.218779\pi\)
\(440\) 5.20601 0.248187
\(441\) 22.8282 1.08706
\(442\) 11.2492 0.535070
\(443\) −35.3050 −1.67739 −0.838695 0.544602i \(-0.816681\pi\)
−0.838695 + 0.544602i \(0.816681\pi\)
\(444\) 1.26638 0.0600997
\(445\) −8.19478 −0.388470
\(446\) 15.0757 0.713854
\(447\) −20.5139 −0.970273
\(448\) −4.81740 −0.227601
\(449\) −8.73012 −0.412000 −0.206000 0.978552i \(-0.566045\pi\)
−0.206000 + 0.978552i \(0.566045\pi\)
\(450\) 2.04864 0.0965739
\(451\) −29.1624 −1.37321
\(452\) 13.0848 0.615456
\(453\) −1.75705 −0.0825535
\(454\) 15.7486 0.739118
\(455\) −14.2519 −0.668141
\(456\) −2.09965 −0.0983249
\(457\) 24.2227 1.13309 0.566546 0.824030i \(-0.308279\pi\)
0.566546 + 0.824030i \(0.308279\pi\)
\(458\) 19.8095 0.925637
\(459\) −23.9249 −1.11672
\(460\) −0.567710 −0.0264696
\(461\) −20.5729 −0.958178 −0.479089 0.877766i \(-0.659033\pi\)
−0.479089 + 0.877766i \(0.659033\pi\)
\(462\) 27.9656 1.30108
\(463\) −15.5761 −0.723884 −0.361942 0.932201i \(-0.617886\pi\)
−0.361942 + 0.932201i \(0.617886\pi\)
\(464\) 5.33121 0.247495
\(465\) −6.75300 −0.313163
\(466\) −23.6366 −1.09495
\(467\) 23.7314 1.09816 0.549080 0.835770i \(-0.314978\pi\)
0.549080 + 0.835770i \(0.314978\pi\)
\(468\) 2.21300 0.102296
\(469\) −7.99388 −0.369123
\(470\) 0.733924 0.0338534
\(471\) −6.98343 −0.321780
\(472\) −5.27734 −0.242909
\(473\) −3.33934 −0.153543
\(474\) −11.4111 −0.524131
\(475\) 1.45447 0.0667358
\(476\) 34.4916 1.58092
\(477\) 1.72159 0.0788261
\(478\) 9.80051 0.448265
\(479\) 9.61382 0.439267 0.219633 0.975582i \(-0.429514\pi\)
0.219633 + 0.975582i \(0.429514\pi\)
\(480\) 3.95354 0.180454
\(481\) −0.947629 −0.0432082
\(482\) 1.29987 0.0592072
\(483\) −3.04962 −0.138762
\(484\) −3.35584 −0.152538
\(485\) 11.5436 0.524169
\(486\) −13.5787 −0.615944
\(487\) −19.2611 −0.872805 −0.436403 0.899752i \(-0.643748\pi\)
−0.436403 + 0.899752i \(0.643748\pi\)
\(488\) −12.5527 −0.568234
\(489\) −0.138261 −0.00625240
\(490\) −30.5178 −1.37865
\(491\) 0.102718 0.00463559 0.00231780 0.999997i \(-0.499262\pi\)
0.00231780 + 0.999997i \(0.499262\pi\)
\(492\) −22.1465 −0.998441
\(493\) −38.1704 −1.71911
\(494\) 1.57116 0.0706899
\(495\) −7.33273 −0.329582
\(496\) 1.70809 0.0766954
\(497\) −5.81211 −0.260709
\(498\) −1.49931 −0.0671857
\(499\) −2.23133 −0.0998879 −0.0499439 0.998752i \(-0.515904\pi\)
−0.0499439 + 0.998752i \(0.515904\pi\)
\(500\) −12.1535 −0.543521
\(501\) −29.7554 −1.32938
\(502\) 6.79093 0.303094
\(503\) 5.29184 0.235951 0.117976 0.993016i \(-0.462359\pi\)
0.117976 + 0.993016i \(0.462359\pi\)
\(504\) 6.78536 0.302244
\(505\) 22.6002 1.00569
\(506\) −0.833588 −0.0370575
\(507\) 22.1123 0.982042
\(508\) 11.3371 0.503003
\(509\) −28.1957 −1.24975 −0.624877 0.780723i \(-0.714851\pi\)
−0.624877 + 0.780723i \(0.714851\pi\)
\(510\) −28.3066 −1.25344
\(511\) 21.3586 0.944850
\(512\) −1.00000 −0.0441942
\(513\) −3.34156 −0.147534
\(514\) −3.29483 −0.145329
\(515\) −0.0412406 −0.00181728
\(516\) −2.53595 −0.111639
\(517\) 1.07765 0.0473948
\(518\) −2.90556 −0.127663
\(519\) 26.8705 1.17948
\(520\) −2.95843 −0.129736
\(521\) −24.0808 −1.05500 −0.527499 0.849556i \(-0.676870\pi\)
−0.527499 + 0.849556i \(0.676870\pi\)
\(522\) −7.50907 −0.328663
\(523\) 31.5915 1.38140 0.690701 0.723141i \(-0.257302\pi\)
0.690701 + 0.723141i \(0.257302\pi\)
\(524\) −12.1602 −0.531220
\(525\) −14.7118 −0.642074
\(526\) 3.69470 0.161097
\(527\) −12.2296 −0.532728
\(528\) 5.80512 0.252635
\(529\) −22.9091 −0.996048
\(530\) −2.30149 −0.0999704
\(531\) 7.43319 0.322573
\(532\) 4.81740 0.208861
\(533\) 16.5722 0.717821
\(534\) −9.13783 −0.395432
\(535\) −23.3749 −1.01059
\(536\) −1.65938 −0.0716742
\(537\) 18.5086 0.798704
\(538\) −7.28892 −0.314248
\(539\) −44.8102 −1.93011
\(540\) 6.29202 0.270765
\(541\) −25.7606 −1.10753 −0.553767 0.832672i \(-0.686810\pi\)
−0.553767 + 0.832672i \(0.686810\pi\)
\(542\) −22.7217 −0.975980
\(543\) 0.593385 0.0254646
\(544\) 7.15980 0.306974
\(545\) 21.4981 0.920878
\(546\) −15.8920 −0.680117
\(547\) −22.5017 −0.962102 −0.481051 0.876693i \(-0.659745\pi\)
−0.481051 + 0.876693i \(0.659745\pi\)
\(548\) 0.297548 0.0127106
\(549\) 17.6806 0.754590
\(550\) −4.02134 −0.171471
\(551\) −5.33121 −0.227117
\(552\) −0.633041 −0.0269440
\(553\) 26.1816 1.11336
\(554\) −18.6563 −0.792631
\(555\) 2.38454 0.101218
\(556\) −19.9823 −0.847440
\(557\) 4.47645 0.189673 0.0948367 0.995493i \(-0.469767\pi\)
0.0948367 + 0.995493i \(0.469767\pi\)
\(558\) −2.40586 −0.101848
\(559\) 1.89765 0.0802621
\(560\) −9.07096 −0.383318
\(561\) −41.5635 −1.75481
\(562\) −17.1150 −0.721952
\(563\) 11.6876 0.492573 0.246287 0.969197i \(-0.420790\pi\)
0.246287 + 0.969197i \(0.420790\pi\)
\(564\) 0.818383 0.0344602
\(565\) 24.6381 1.03653
\(566\) −3.87042 −0.162686
\(567\) 54.1554 2.27431
\(568\) −1.20648 −0.0506229
\(569\) 22.9851 0.963585 0.481793 0.876285i \(-0.339986\pi\)
0.481793 + 0.876285i \(0.339986\pi\)
\(570\) −3.95354 −0.165596
\(571\) −44.7367 −1.87217 −0.936087 0.351770i \(-0.885580\pi\)
−0.936087 + 0.351770i \(0.885580\pi\)
\(572\) −4.34396 −0.181630
\(573\) −30.6397 −1.27999
\(574\) 50.8126 2.12088
\(575\) 0.438523 0.0182877
\(576\) 1.40851 0.0586879
\(577\) −16.6457 −0.692968 −0.346484 0.938056i \(-0.612624\pi\)
−0.346484 + 0.938056i \(0.612624\pi\)
\(578\) −34.2627 −1.42514
\(579\) 21.3394 0.886833
\(580\) 10.0384 0.416824
\(581\) 3.44000 0.142715
\(582\) 12.8720 0.533563
\(583\) −3.37936 −0.139959
\(584\) 4.43364 0.183465
\(585\) 4.16698 0.172283
\(586\) 12.5471 0.518318
\(587\) −28.3542 −1.17030 −0.585152 0.810923i \(-0.698965\pi\)
−0.585152 + 0.810923i \(0.698965\pi\)
\(588\) −34.0297 −1.40336
\(589\) −1.70809 −0.0703805
\(590\) −9.93700 −0.409100
\(591\) 50.9897 2.09744
\(592\) −0.603139 −0.0247889
\(593\) 14.8584 0.610162 0.305081 0.952326i \(-0.401317\pi\)
0.305081 + 0.952326i \(0.401317\pi\)
\(594\) 9.23878 0.379072
\(595\) 64.9462 2.66254
\(596\) 9.77017 0.400202
\(597\) 33.0834 1.35401
\(598\) 0.473704 0.0193712
\(599\) −23.1526 −0.945991 −0.472995 0.881065i \(-0.656827\pi\)
−0.472995 + 0.881065i \(0.656827\pi\)
\(600\) −3.05388 −0.124674
\(601\) −39.2724 −1.60196 −0.800978 0.598694i \(-0.795687\pi\)
−0.800978 + 0.598694i \(0.795687\pi\)
\(602\) 5.81846 0.237143
\(603\) 2.33725 0.0951802
\(604\) 0.836833 0.0340503
\(605\) −6.31889 −0.256900
\(606\) 25.2010 1.02372
\(607\) 19.8278 0.804787 0.402394 0.915467i \(-0.368178\pi\)
0.402394 + 0.915467i \(0.368178\pi\)
\(608\) 1.00000 0.0405554
\(609\) 53.9243 2.18512
\(610\) −23.6362 −0.957002
\(611\) −0.612395 −0.0247749
\(612\) −10.0847 −0.407648
\(613\) 0.610244 0.0246475 0.0123238 0.999924i \(-0.496077\pi\)
0.0123238 + 0.999924i \(0.496077\pi\)
\(614\) −12.5847 −0.507875
\(615\) −41.7009 −1.68154
\(616\) −13.3192 −0.536646
\(617\) 16.8365 0.677811 0.338906 0.940820i \(-0.389943\pi\)
0.338906 + 0.940820i \(0.389943\pi\)
\(618\) −0.0459865 −0.00184985
\(619\) −41.7701 −1.67888 −0.839440 0.543452i \(-0.817117\pi\)
−0.839440 + 0.543452i \(0.817117\pi\)
\(620\) 3.21626 0.129168
\(621\) −1.00748 −0.0404287
\(622\) −20.4985 −0.821916
\(623\) 20.9657 0.839974
\(624\) −3.29888 −0.132061
\(625\) −15.6121 −0.624486
\(626\) 25.9923 1.03886
\(627\) −5.80512 −0.231834
\(628\) 3.32601 0.132722
\(629\) 4.31835 0.172184
\(630\) 12.7765 0.509030
\(631\) 23.5367 0.936981 0.468490 0.883469i \(-0.344798\pi\)
0.468490 + 0.883469i \(0.344798\pi\)
\(632\) 5.43480 0.216185
\(633\) 2.09965 0.0834534
\(634\) 5.82998 0.231538
\(635\) 21.3473 0.847142
\(636\) −2.56635 −0.101762
\(637\) 25.4644 1.00894
\(638\) 14.7398 0.583553
\(639\) 1.69934 0.0672250
\(640\) −1.88296 −0.0744304
\(641\) −1.66834 −0.0658955 −0.0329477 0.999457i \(-0.510489\pi\)
−0.0329477 + 0.999457i \(0.510489\pi\)
\(642\) −26.0649 −1.02870
\(643\) −20.3749 −0.803508 −0.401754 0.915748i \(-0.631599\pi\)
−0.401754 + 0.915748i \(0.631599\pi\)
\(644\) 1.45244 0.0572343
\(645\) −4.77509 −0.188019
\(646\) −7.15980 −0.281699
\(647\) −10.9925 −0.432161 −0.216080 0.976376i \(-0.569327\pi\)
−0.216080 + 0.976376i \(0.569327\pi\)
\(648\) 11.2416 0.441613
\(649\) −14.5908 −0.572740
\(650\) 2.28521 0.0896334
\(651\) 17.2770 0.677140
\(652\) 0.0658499 0.00257888
\(653\) 5.40621 0.211561 0.105781 0.994389i \(-0.466266\pi\)
0.105781 + 0.994389i \(0.466266\pi\)
\(654\) 23.9721 0.937383
\(655\) −22.8971 −0.894663
\(656\) 10.5477 0.411820
\(657\) −6.24483 −0.243634
\(658\) −1.87769 −0.0731999
\(659\) −37.1232 −1.44611 −0.723057 0.690789i \(-0.757263\pi\)
−0.723057 + 0.690789i \(0.757263\pi\)
\(660\) 10.9308 0.425480
\(661\) 31.7345 1.23433 0.617165 0.786834i \(-0.288281\pi\)
0.617165 + 0.786834i \(0.288281\pi\)
\(662\) −35.7053 −1.38773
\(663\) 23.6193 0.917299
\(664\) 0.714078 0.0277116
\(665\) 9.07096 0.351757
\(666\) 0.849528 0.0329185
\(667\) −1.60736 −0.0622371
\(668\) 14.1717 0.548318
\(669\) 31.6536 1.22380
\(670\) −3.12453 −0.120711
\(671\) −34.7058 −1.33980
\(672\) −10.1148 −0.390188
\(673\) −0.335039 −0.0129148 −0.00645739 0.999979i \(-0.502055\pi\)
−0.00645739 + 0.999979i \(0.502055\pi\)
\(674\) −19.4861 −0.750578
\(675\) −4.86022 −0.187070
\(676\) −10.5315 −0.405056
\(677\) −5.46449 −0.210017 −0.105009 0.994471i \(-0.533487\pi\)
−0.105009 + 0.994471i \(0.533487\pi\)
\(678\) 27.4734 1.05511
\(679\) −29.5335 −1.13339
\(680\) 13.4816 0.516995
\(681\) 33.0664 1.26711
\(682\) 4.72254 0.180835
\(683\) −50.9442 −1.94933 −0.974664 0.223675i \(-0.928195\pi\)
−0.974664 + 0.223675i \(0.928195\pi\)
\(684\) −1.40851 −0.0538558
\(685\) 0.560270 0.0214068
\(686\) 44.3556 1.69350
\(687\) 41.5929 1.58687
\(688\) 1.20780 0.0460470
\(689\) 1.92039 0.0731611
\(690\) −1.19199 −0.0453783
\(691\) −47.8213 −1.81921 −0.909605 0.415475i \(-0.863615\pi\)
−0.909605 + 0.415475i \(0.863615\pi\)
\(692\) −12.7976 −0.486493
\(693\) 18.7602 0.712642
\(694\) −10.4246 −0.395711
\(695\) −37.6259 −1.42723
\(696\) 11.1937 0.424294
\(697\) −75.5196 −2.86051
\(698\) −28.0471 −1.06160
\(699\) −49.6286 −1.87713
\(700\) 7.00678 0.264832
\(701\) 30.3783 1.14737 0.573687 0.819074i \(-0.305513\pi\)
0.573687 + 0.819074i \(0.305513\pi\)
\(702\) −5.25014 −0.198154
\(703\) 0.603139 0.0227478
\(704\) −2.76481 −0.104203
\(705\) 1.54098 0.0580367
\(706\) −4.32987 −0.162957
\(707\) −57.8208 −2.17458
\(708\) −11.0805 −0.416432
\(709\) 20.5173 0.770544 0.385272 0.922803i \(-0.374108\pi\)
0.385272 + 0.922803i \(0.374108\pi\)
\(710\) −2.27175 −0.0852574
\(711\) −7.65497 −0.287084
\(712\) 4.35208 0.163101
\(713\) −0.514987 −0.0192864
\(714\) 72.4202 2.71026
\(715\) −8.17949 −0.305896
\(716\) −8.81510 −0.329436
\(717\) 20.5776 0.768484
\(718\) −30.3696 −1.13338
\(719\) 20.1800 0.752588 0.376294 0.926500i \(-0.377198\pi\)
0.376294 + 0.926500i \(0.377198\pi\)
\(720\) 2.65216 0.0988403
\(721\) 0.105511 0.00392943
\(722\) −1.00000 −0.0372161
\(723\) 2.72926 0.101502
\(724\) −0.282612 −0.0105032
\(725\) −7.75411 −0.287980
\(726\) −7.04606 −0.261504
\(727\) −11.1353 −0.412987 −0.206494 0.978448i \(-0.566205\pi\)
−0.206494 + 0.978448i \(0.566205\pi\)
\(728\) 7.56892 0.280523
\(729\) 5.21434 0.193124
\(730\) 8.34835 0.308986
\(731\) −8.64761 −0.319843
\(732\) −26.3562 −0.974154
\(733\) −41.5712 −1.53547 −0.767734 0.640769i \(-0.778616\pi\)
−0.767734 + 0.640769i \(0.778616\pi\)
\(734\) −2.72398 −0.100544
\(735\) −64.0765 −2.36350
\(736\) 0.301499 0.0111134
\(737\) −4.58786 −0.168996
\(738\) −14.8566 −0.546878
\(739\) 0.761430 0.0280096 0.0140048 0.999902i \(-0.495542\pi\)
0.0140048 + 0.999902i \(0.495542\pi\)
\(740\) −1.13568 −0.0417486
\(741\) 3.29888 0.121187
\(742\) 5.88819 0.216162
\(743\) 1.01856 0.0373672 0.0186836 0.999825i \(-0.494052\pi\)
0.0186836 + 0.999825i \(0.494052\pi\)
\(744\) 3.58638 0.131483
\(745\) 18.3968 0.674007
\(746\) 12.8019 0.468710
\(747\) −1.00579 −0.0367998
\(748\) 19.7955 0.723794
\(749\) 59.8029 2.18515
\(750\) −25.5180 −0.931787
\(751\) 1.28981 0.0470660 0.0235330 0.999723i \(-0.492509\pi\)
0.0235330 + 0.999723i \(0.492509\pi\)
\(752\) −0.389772 −0.0142135
\(753\) 14.2585 0.519610
\(754\) −8.37619 −0.305043
\(755\) 1.57572 0.0573463
\(756\) −16.0977 −0.585466
\(757\) −6.34545 −0.230629 −0.115315 0.993329i \(-0.536788\pi\)
−0.115315 + 0.993329i \(0.536788\pi\)
\(758\) 11.3225 0.411252
\(759\) −1.75024 −0.0635296
\(760\) 1.88296 0.0683020
\(761\) 9.26100 0.335711 0.167855 0.985812i \(-0.446316\pi\)
0.167855 + 0.985812i \(0.446316\pi\)
\(762\) 23.8039 0.862325
\(763\) −55.0013 −1.99118
\(764\) 14.5928 0.527949
\(765\) −18.9890 −0.686548
\(766\) 30.3805 1.09769
\(767\) 8.29155 0.299391
\(768\) −2.09965 −0.0757644
\(769\) −36.5070 −1.31647 −0.658237 0.752811i \(-0.728698\pi\)
−0.658237 + 0.752811i \(0.728698\pi\)
\(770\) −25.0795 −0.903801
\(771\) −6.91797 −0.249145
\(772\) −10.1633 −0.365786
\(773\) −42.6475 −1.53392 −0.766961 0.641693i \(-0.778232\pi\)
−0.766961 + 0.641693i \(0.778232\pi\)
\(774\) −1.70120 −0.0611484
\(775\) −2.48437 −0.0892412
\(776\) −6.13058 −0.220075
\(777\) −6.10065 −0.218860
\(778\) 26.6564 0.955680
\(779\) −10.5477 −0.377912
\(780\) −6.21165 −0.222413
\(781\) −3.33569 −0.119360
\(782\) −2.15867 −0.0771940
\(783\) 17.8146 0.636641
\(784\) 16.2074 0.578834
\(785\) 6.26272 0.223526
\(786\) −25.5321 −0.910698
\(787\) 24.8932 0.887347 0.443674 0.896188i \(-0.353675\pi\)
0.443674 + 0.896188i \(0.353675\pi\)
\(788\) −24.2849 −0.865114
\(789\) 7.75756 0.276177
\(790\) 10.2335 0.364091
\(791\) −63.0346 −2.24125
\(792\) 3.89426 0.138377
\(793\) 19.7223 0.700360
\(794\) −33.4711 −1.18784
\(795\) −4.83232 −0.171385
\(796\) −15.7566 −0.558480
\(797\) 34.7978 1.23260 0.616301 0.787510i \(-0.288630\pi\)
0.616301 + 0.787510i \(0.288630\pi\)
\(798\) 10.1148 0.358061
\(799\) 2.79069 0.0987275
\(800\) 1.45447 0.0514234
\(801\) −6.12995 −0.216591
\(802\) 13.1479 0.464269
\(803\) 12.2582 0.432581
\(804\) −3.48410 −0.122875
\(805\) 2.73489 0.0963921
\(806\) −2.68368 −0.0945287
\(807\) −15.3041 −0.538731
\(808\) −12.0025 −0.422246
\(809\) −22.5330 −0.792219 −0.396110 0.918203i \(-0.629640\pi\)
−0.396110 + 0.918203i \(0.629640\pi\)
\(810\) 21.1675 0.743750
\(811\) −34.8520 −1.22382 −0.611910 0.790928i \(-0.709598\pi\)
−0.611910 + 0.790928i \(0.709598\pi\)
\(812\) −25.6826 −0.901282
\(813\) −47.7075 −1.67318
\(814\) −1.66756 −0.0584481
\(815\) 0.123993 0.00434327
\(816\) 15.0330 0.526262
\(817\) −1.20780 −0.0422556
\(818\) 28.0181 0.979630
\(819\) −10.6609 −0.372522
\(820\) 19.8609 0.693573
\(821\) 44.5870 1.55610 0.778049 0.628203i \(-0.216209\pi\)
0.778049 + 0.628203i \(0.216209\pi\)
\(822\) 0.624746 0.0217905
\(823\) 0.516472 0.0180031 0.00900153 0.999959i \(-0.497135\pi\)
0.00900153 + 0.999959i \(0.497135\pi\)
\(824\) 0.0219020 0.000762993 0
\(825\) −8.44339 −0.293961
\(826\) 25.4231 0.884582
\(827\) 19.0151 0.661218 0.330609 0.943768i \(-0.392746\pi\)
0.330609 + 0.943768i \(0.392746\pi\)
\(828\) −0.424665 −0.0147581
\(829\) −3.86305 −0.134169 −0.0670846 0.997747i \(-0.521370\pi\)
−0.0670846 + 0.997747i \(0.521370\pi\)
\(830\) 1.34458 0.0466710
\(831\) −39.1716 −1.35885
\(832\) 1.57116 0.0544702
\(833\) −116.041 −4.02060
\(834\) −41.9558 −1.45281
\(835\) 26.6846 0.923459
\(836\) 2.76481 0.0956229
\(837\) 5.70768 0.197286
\(838\) −6.36647 −0.219926
\(839\) 17.1653 0.592610 0.296305 0.955093i \(-0.404245\pi\)
0.296305 + 0.955093i \(0.404245\pi\)
\(840\) −19.0458 −0.657142
\(841\) −0.578191 −0.0199376
\(842\) −34.1193 −1.17583
\(843\) −35.9354 −1.23768
\(844\) −1.00000 −0.0344214
\(845\) −19.8303 −0.682182
\(846\) 0.548998 0.0188749
\(847\) 16.1664 0.555484
\(848\) 1.22228 0.0419731
\(849\) −8.12650 −0.278901
\(850\) −10.4137 −0.357188
\(851\) 0.181846 0.00623360
\(852\) −2.53318 −0.0867855
\(853\) 2.00624 0.0686923 0.0343462 0.999410i \(-0.489065\pi\)
0.0343462 + 0.999410i \(0.489065\pi\)
\(854\) 60.4714 2.06929
\(855\) −2.65216 −0.0907021
\(856\) 12.4139 0.424300
\(857\) 19.6955 0.672786 0.336393 0.941722i \(-0.390793\pi\)
0.336393 + 0.941722i \(0.390793\pi\)
\(858\) −9.12078 −0.311378
\(859\) −39.1665 −1.33634 −0.668172 0.744007i \(-0.732923\pi\)
−0.668172 + 0.744007i \(0.732923\pi\)
\(860\) 2.27424 0.0775508
\(861\) 106.689 3.63593
\(862\) −3.08569 −0.105099
\(863\) −7.20329 −0.245203 −0.122601 0.992456i \(-0.539124\pi\)
−0.122601 + 0.992456i \(0.539124\pi\)
\(864\) −3.34156 −0.113682
\(865\) −24.0974 −0.819336
\(866\) 25.2198 0.857004
\(867\) −71.9396 −2.44320
\(868\) −8.22855 −0.279295
\(869\) 15.0262 0.509728
\(870\) 21.0772 0.714583
\(871\) 2.60715 0.0883399
\(872\) −11.4172 −0.386635
\(873\) 8.63499 0.292250
\(874\) −0.301499 −0.0101984
\(875\) 58.5483 1.97929
\(876\) 9.30907 0.314524
\(877\) −36.1355 −1.22021 −0.610104 0.792321i \(-0.708872\pi\)
−0.610104 + 0.792321i \(0.708872\pi\)
\(878\) −32.3903 −1.09312
\(879\) 26.3446 0.888580
\(880\) −5.20601 −0.175495
\(881\) 8.11551 0.273418 0.136709 0.990611i \(-0.456347\pi\)
0.136709 + 0.990611i \(0.456347\pi\)
\(882\) −22.8282 −0.768667
\(883\) −49.1371 −1.65360 −0.826798 0.562500i \(-0.809840\pi\)
−0.826798 + 0.562500i \(0.809840\pi\)
\(884\) −11.2492 −0.378352
\(885\) −20.8642 −0.701342
\(886\) 35.3050 1.18609
\(887\) −1.70519 −0.0572545 −0.0286273 0.999590i \(-0.509114\pi\)
−0.0286273 + 0.999590i \(0.509114\pi\)
\(888\) −1.26638 −0.0424969
\(889\) −54.6155 −1.83174
\(890\) 8.19478 0.274690
\(891\) 31.0809 1.04125
\(892\) −15.0757 −0.504771
\(893\) 0.389772 0.0130432
\(894\) 20.5139 0.686087
\(895\) −16.5984 −0.554825
\(896\) 4.81740 0.160938
\(897\) 0.994611 0.0332091
\(898\) 8.73012 0.291328
\(899\) 9.10618 0.303708
\(900\) −2.04864 −0.0682881
\(901\) −8.75125 −0.291546
\(902\) 29.1624 0.971003
\(903\) 12.2167 0.406547
\(904\) −13.0848 −0.435193
\(905\) −0.532146 −0.0176891
\(906\) 1.75705 0.0583742
\(907\) 37.3227 1.23928 0.619639 0.784887i \(-0.287279\pi\)
0.619639 + 0.784887i \(0.287279\pi\)
\(908\) −15.7486 −0.522635
\(909\) 16.9056 0.560725
\(910\) 14.2519 0.472447
\(911\) −21.9240 −0.726373 −0.363186 0.931716i \(-0.618311\pi\)
−0.363186 + 0.931716i \(0.618311\pi\)
\(912\) 2.09965 0.0695262
\(913\) 1.97429 0.0653394
\(914\) −24.2227 −0.801217
\(915\) −49.6276 −1.64064
\(916\) −19.8095 −0.654524
\(917\) 58.5804 1.93450
\(918\) 23.9249 0.789640
\(919\) −7.93458 −0.261738 −0.130869 0.991400i \(-0.541777\pi\)
−0.130869 + 0.991400i \(0.541777\pi\)
\(920\) 0.567710 0.0187168
\(921\) −26.4233 −0.870678
\(922\) 20.5729 0.677534
\(923\) 1.89558 0.0623937
\(924\) −27.9656 −0.920000
\(925\) 0.877250 0.0288438
\(926\) 15.5761 0.511864
\(927\) −0.0308492 −0.00101322
\(928\) −5.33121 −0.175006
\(929\) 29.3169 0.961857 0.480928 0.876760i \(-0.340300\pi\)
0.480928 + 0.876760i \(0.340300\pi\)
\(930\) 6.75300 0.221440
\(931\) −16.2074 −0.531175
\(932\) 23.6366 0.774244
\(933\) −43.0397 −1.40906
\(934\) −23.7314 −0.776516
\(935\) 37.2740 1.21899
\(936\) −2.21300 −0.0723341
\(937\) 25.7349 0.840723 0.420362 0.907357i \(-0.361903\pi\)
0.420362 + 0.907357i \(0.361903\pi\)
\(938\) 7.99388 0.261010
\(939\) 54.5747 1.78098
\(940\) −0.733924 −0.0239380
\(941\) 8.03342 0.261882 0.130941 0.991390i \(-0.458200\pi\)
0.130941 + 0.991390i \(0.458200\pi\)
\(942\) 6.98343 0.227532
\(943\) −3.18013 −0.103559
\(944\) 5.27734 0.171763
\(945\) −30.3112 −0.986023
\(946\) 3.33934 0.108571
\(947\) −20.7320 −0.673699 −0.336849 0.941559i \(-0.609361\pi\)
−0.336849 + 0.941559i \(0.609361\pi\)
\(948\) 11.4111 0.370617
\(949\) −6.96597 −0.226125
\(950\) −1.45447 −0.0471894
\(951\) 12.2409 0.396938
\(952\) −34.4916 −1.11788
\(953\) −14.5358 −0.470862 −0.235431 0.971891i \(-0.575650\pi\)
−0.235431 + 0.971891i \(0.575650\pi\)
\(954\) −1.72159 −0.0557385
\(955\) 27.4776 0.889155
\(956\) −9.80051 −0.316971
\(957\) 30.9483 1.00042
\(958\) −9.61382 −0.310609
\(959\) −1.43341 −0.0462872
\(960\) −3.95354 −0.127600
\(961\) −28.0824 −0.905885
\(962\) 0.947629 0.0305528
\(963\) −17.4852 −0.563452
\(964\) −1.29987 −0.0418658
\(965\) −19.1371 −0.616044
\(966\) 3.04962 0.0981198
\(967\) 21.0905 0.678225 0.339112 0.940746i \(-0.389873\pi\)
0.339112 + 0.940746i \(0.389873\pi\)
\(968\) 3.35584 0.107861
\(969\) −15.0330 −0.482931
\(970\) −11.5436 −0.370643
\(971\) 50.2581 1.61286 0.806430 0.591329i \(-0.201397\pi\)
0.806430 + 0.591329i \(0.201397\pi\)
\(972\) 13.5787 0.435538
\(973\) 96.2630 3.08605
\(974\) 19.2611 0.617166
\(975\) 4.79814 0.153663
\(976\) 12.5527 0.401802
\(977\) 36.1532 1.15664 0.578322 0.815808i \(-0.303708\pi\)
0.578322 + 0.815808i \(0.303708\pi\)
\(978\) 0.138261 0.00442111
\(979\) 12.0327 0.384566
\(980\) 30.5178 0.974854
\(981\) 16.0813 0.513435
\(982\) −0.102718 −0.00327786
\(983\) −13.1095 −0.418128 −0.209064 0.977902i \(-0.567042\pi\)
−0.209064 + 0.977902i \(0.567042\pi\)
\(984\) 22.1465 0.706004
\(985\) −45.7274 −1.45700
\(986\) 38.1704 1.21559
\(987\) −3.94248 −0.125491
\(988\) −1.57116 −0.0499853
\(989\) −0.364151 −0.0115793
\(990\) 7.33273 0.233049
\(991\) −50.6783 −1.60985 −0.804924 0.593378i \(-0.797794\pi\)
−0.804924 + 0.593378i \(0.797794\pi\)
\(992\) −1.70809 −0.0542319
\(993\) −74.9685 −2.37905
\(994\) 5.81211 0.184349
\(995\) −29.6691 −0.940573
\(996\) 1.49931 0.0475074
\(997\) 45.4307 1.43880 0.719402 0.694594i \(-0.244416\pi\)
0.719402 + 0.694594i \(0.244416\pi\)
\(998\) 2.23133 0.0706314
\(999\) −2.01543 −0.0637653
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 \(a_p\))