Properties

Label 619.2.a.b.1.9
Level 619
Weight 2
Character 619.1
Self dual Yes
Analytic conductor 4.943
Analytic rank 0
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 619.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(4.94273988512\)
Analytic rank: \(0\)
Dimension: \(30\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 619.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.26926 q^{2} +3.28637 q^{3} -0.388969 q^{4} +2.23550 q^{5} -4.17127 q^{6} +3.15236 q^{7} +3.03223 q^{8} +7.80023 q^{9} +O(q^{10})\) \(q-1.26926 q^{2} +3.28637 q^{3} -0.388969 q^{4} +2.23550 q^{5} -4.17127 q^{6} +3.15236 q^{7} +3.03223 q^{8} +7.80023 q^{9} -2.83744 q^{10} +1.25447 q^{11} -1.27830 q^{12} +0.135766 q^{13} -4.00118 q^{14} +7.34667 q^{15} -3.07076 q^{16} -8.12408 q^{17} -9.90055 q^{18} -6.16785 q^{19} -0.869540 q^{20} +10.3598 q^{21} -1.59226 q^{22} -6.32062 q^{23} +9.96504 q^{24} -0.00254610 q^{25} -0.172323 q^{26} +15.7753 q^{27} -1.22617 q^{28} +4.55365 q^{29} -9.32487 q^{30} -6.49824 q^{31} -2.16685 q^{32} +4.12266 q^{33} +10.3116 q^{34} +7.04710 q^{35} -3.03405 q^{36} -6.68758 q^{37} +7.82863 q^{38} +0.446177 q^{39} +6.77855 q^{40} +2.34133 q^{41} -13.1493 q^{42} +8.30502 q^{43} -0.487951 q^{44} +17.4374 q^{45} +8.02253 q^{46} -1.40000 q^{47} -10.0917 q^{48} +2.93738 q^{49} +0.00323167 q^{50} -26.6987 q^{51} -0.0528087 q^{52} -6.60727 q^{53} -20.0230 q^{54} +2.80437 q^{55} +9.55869 q^{56} -20.2698 q^{57} -5.77978 q^{58} +1.32957 q^{59} -2.85763 q^{60} -0.790192 q^{61} +8.24798 q^{62} +24.5891 q^{63} +8.89184 q^{64} +0.303504 q^{65} -5.23274 q^{66} -13.9783 q^{67} +3.16002 q^{68} -20.7719 q^{69} -8.94463 q^{70} +3.99597 q^{71} +23.6521 q^{72} +10.2597 q^{73} +8.48831 q^{74} -0.00836742 q^{75} +2.39910 q^{76} +3.95455 q^{77} -0.566316 q^{78} +3.82418 q^{79} -6.86469 q^{80} +28.4429 q^{81} -2.97177 q^{82} +10.1725 q^{83} -4.02965 q^{84} -18.1614 q^{85} -10.5413 q^{86} +14.9650 q^{87} +3.80385 q^{88} +3.94368 q^{89} -22.1327 q^{90} +0.427983 q^{91} +2.45852 q^{92} -21.3556 q^{93} +1.77697 q^{94} -13.7882 q^{95} -7.12108 q^{96} -1.33017 q^{97} -3.72831 q^{98} +9.78517 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + O(q^{10}) \) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + 5q^{10} + 23q^{11} - 6q^{12} + 9q^{13} + 7q^{14} - 2q^{15} + 35q^{16} + 4q^{17} + 10q^{18} - q^{19} + 29q^{20} + 30q^{21} + 4q^{23} + 4q^{24} + 35q^{25} + q^{26} - 5q^{27} - 13q^{28} + 90q^{29} - 31q^{30} + 2q^{31} + 43q^{32} - 6q^{33} - 9q^{34} + 9q^{35} + 33q^{36} + 19q^{37} + 5q^{38} + 32q^{39} - 12q^{40} + 59q^{41} - 25q^{42} - 4q^{43} + 52q^{44} + 30q^{45} - q^{46} + 4q^{47} - 44q^{48} + 30q^{49} + 31q^{50} - 12q^{52} + 34q^{53} - 28q^{54} - 17q^{55} + 2q^{56} - 8q^{57} + 6q^{58} + 13q^{59} - 64q^{60} + 16q^{61} + 28q^{62} - 40q^{63} + 37q^{64} + 31q^{65} - 59q^{66} - 11q^{67} - 52q^{68} + 6q^{69} - 40q^{70} + 42q^{71} + 6q^{72} - 4q^{73} + 16q^{74} - 52q^{75} - 42q^{76} + 29q^{77} - 56q^{78} + 3q^{79} + 21q^{80} + 30q^{81} - 43q^{82} - 11q^{83} - 36q^{84} + 19q^{85} - 11q^{86} - 20q^{87} - 47q^{88} + 58q^{89} - 33q^{90} - 39q^{91} - 7q^{92} - 15q^{93} - 46q^{94} + 23q^{95} - 70q^{96} - 9q^{97} - 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.26926 −0.897505 −0.448753 0.893656i \(-0.648132\pi\)
−0.448753 + 0.893656i \(0.648132\pi\)
\(3\) 3.28637 1.89739 0.948693 0.316198i \(-0.102406\pi\)
0.948693 + 0.316198i \(0.102406\pi\)
\(4\) −0.388969 −0.194485
\(5\) 2.23550 0.999745 0.499873 0.866099i \(-0.333380\pi\)
0.499873 + 0.866099i \(0.333380\pi\)
\(6\) −4.17127 −1.70291
\(7\) 3.15236 1.19148 0.595740 0.803177i \(-0.296859\pi\)
0.595740 + 0.803177i \(0.296859\pi\)
\(8\) 3.03223 1.07206
\(9\) 7.80023 2.60008
\(10\) −2.83744 −0.897277
\(11\) 1.25447 0.378238 0.189119 0.981954i \(-0.439437\pi\)
0.189119 + 0.981954i \(0.439437\pi\)
\(12\) −1.27830 −0.369012
\(13\) 0.135766 0.0376547 0.0188273 0.999823i \(-0.494007\pi\)
0.0188273 + 0.999823i \(0.494007\pi\)
\(14\) −4.00118 −1.06936
\(15\) 7.34667 1.89690
\(16\) −3.07076 −0.767691
\(17\) −8.12408 −1.97038 −0.985189 0.171471i \(-0.945148\pi\)
−0.985189 + 0.171471i \(0.945148\pi\)
\(18\) −9.90055 −2.33358
\(19\) −6.16785 −1.41500 −0.707501 0.706713i \(-0.750177\pi\)
−0.707501 + 0.706713i \(0.750177\pi\)
\(20\) −0.869540 −0.194435
\(21\) 10.3598 2.26070
\(22\) −1.59226 −0.339470
\(23\) −6.32062 −1.31794 −0.658970 0.752169i \(-0.729007\pi\)
−0.658970 + 0.752169i \(0.729007\pi\)
\(24\) 9.96504 2.03410
\(25\) −0.00254610 −0.000509220 0
\(26\) −0.172323 −0.0337952
\(27\) 15.7753 3.03596
\(28\) −1.22617 −0.231725
\(29\) 4.55365 0.845591 0.422796 0.906225i \(-0.361049\pi\)
0.422796 + 0.906225i \(0.361049\pi\)
\(30\) −9.32487 −1.70248
\(31\) −6.49824 −1.16712 −0.583559 0.812071i \(-0.698340\pi\)
−0.583559 + 0.812071i \(0.698340\pi\)
\(32\) −2.16685 −0.383049
\(33\) 4.12266 0.717663
\(34\) 10.3116 1.76842
\(35\) 7.04710 1.19118
\(36\) −3.03405 −0.505675
\(37\) −6.68758 −1.09943 −0.549716 0.835352i \(-0.685264\pi\)
−0.549716 + 0.835352i \(0.685264\pi\)
\(38\) 7.82863 1.26997
\(39\) 0.446177 0.0714454
\(40\) 6.77855 1.07178
\(41\) 2.34133 0.365655 0.182827 0.983145i \(-0.441475\pi\)
0.182827 + 0.983145i \(0.441475\pi\)
\(42\) −13.1493 −2.02899
\(43\) 8.30502 1.26650 0.633252 0.773946i \(-0.281720\pi\)
0.633252 + 0.773946i \(0.281720\pi\)
\(44\) −0.487951 −0.0735614
\(45\) 17.4374 2.59941
\(46\) 8.02253 1.18286
\(47\) −1.40000 −0.204211 −0.102106 0.994774i \(-0.532558\pi\)
−0.102106 + 0.994774i \(0.532558\pi\)
\(48\) −10.0917 −1.45661
\(49\) 2.93738 0.419626
\(50\) 0.00323167 0.000457027 0
\(51\) −26.6987 −3.73857
\(52\) −0.0528087 −0.00732325
\(53\) −6.60727 −0.907579 −0.453789 0.891109i \(-0.649928\pi\)
−0.453789 + 0.891109i \(0.649928\pi\)
\(54\) −20.0230 −2.72479
\(55\) 2.80437 0.378141
\(56\) 9.55869 1.27733
\(57\) −20.2698 −2.68480
\(58\) −5.77978 −0.758922
\(59\) 1.32957 0.173096 0.0865479 0.996248i \(-0.472416\pi\)
0.0865479 + 0.996248i \(0.472416\pi\)
\(60\) −2.85763 −0.368918
\(61\) −0.790192 −0.101174 −0.0505869 0.998720i \(-0.516109\pi\)
−0.0505869 + 0.998720i \(0.516109\pi\)
\(62\) 8.24798 1.04749
\(63\) 24.5891 3.09794
\(64\) 8.89184 1.11148
\(65\) 0.303504 0.0376451
\(66\) −5.23274 −0.644106
\(67\) −13.9783 −1.70772 −0.853859 0.520504i \(-0.825744\pi\)
−0.853859 + 0.520504i \(0.825744\pi\)
\(68\) 3.16002 0.383208
\(69\) −20.7719 −2.50064
\(70\) −8.94463 −1.06909
\(71\) 3.99597 0.474234 0.237117 0.971481i \(-0.423797\pi\)
0.237117 + 0.971481i \(0.423797\pi\)
\(72\) 23.6521 2.78743
\(73\) 10.2597 1.20080 0.600402 0.799698i \(-0.295007\pi\)
0.600402 + 0.799698i \(0.295007\pi\)
\(74\) 8.48831 0.986746
\(75\) −0.00836742 −0.000966187 0
\(76\) 2.39910 0.275196
\(77\) 3.95455 0.450663
\(78\) −0.566316 −0.0641226
\(79\) 3.82418 0.430254 0.215127 0.976586i \(-0.430983\pi\)
0.215127 + 0.976586i \(0.430983\pi\)
\(80\) −6.86469 −0.767496
\(81\) 28.4429 3.16032
\(82\) −2.97177 −0.328177
\(83\) 10.1725 1.11658 0.558290 0.829646i \(-0.311458\pi\)
0.558290 + 0.829646i \(0.311458\pi\)
\(84\) −4.02965 −0.439671
\(85\) −18.1614 −1.96988
\(86\) −10.5413 −1.13669
\(87\) 14.9650 1.60441
\(88\) 3.80385 0.405492
\(89\) 3.94368 0.418029 0.209014 0.977913i \(-0.432974\pi\)
0.209014 + 0.977913i \(0.432974\pi\)
\(90\) −22.1327 −2.33299
\(91\) 0.427983 0.0448648
\(92\) 2.45852 0.256319
\(93\) −21.3556 −2.21447
\(94\) 1.77697 0.183280
\(95\) −13.7882 −1.41464
\(96\) −7.12108 −0.726792
\(97\) −1.33017 −0.135058 −0.0675289 0.997717i \(-0.521511\pi\)
−0.0675289 + 0.997717i \(0.521511\pi\)
\(98\) −3.72831 −0.376616
\(99\) 9.78517 0.983446
\(100\) 0.000990354 0 9.90354e−5 0
\(101\) 5.50958 0.548224 0.274112 0.961698i \(-0.411616\pi\)
0.274112 + 0.961698i \(0.411616\pi\)
\(102\) 33.8877 3.35538
\(103\) 1.52947 0.150703 0.0753513 0.997157i \(-0.475992\pi\)
0.0753513 + 0.997157i \(0.475992\pi\)
\(104\) 0.411673 0.0403679
\(105\) 23.1594 2.26012
\(106\) 8.38637 0.814557
\(107\) 5.64779 0.545992 0.272996 0.962015i \(-0.411985\pi\)
0.272996 + 0.962015i \(0.411985\pi\)
\(108\) −6.13611 −0.590448
\(109\) 1.60661 0.153885 0.0769425 0.997036i \(-0.475484\pi\)
0.0769425 + 0.997036i \(0.475484\pi\)
\(110\) −3.55949 −0.339384
\(111\) −21.9779 −2.08605
\(112\) −9.68016 −0.914689
\(113\) 9.78658 0.920644 0.460322 0.887752i \(-0.347734\pi\)
0.460322 + 0.887752i \(0.347734\pi\)
\(114\) 25.7278 2.40963
\(115\) −14.1297 −1.31760
\(116\) −1.77123 −0.164454
\(117\) 1.05900 0.0979050
\(118\) −1.68758 −0.155354
\(119\) −25.6100 −2.34767
\(120\) 22.2768 2.03359
\(121\) −9.42630 −0.856936
\(122\) 1.00296 0.0908040
\(123\) 7.69448 0.693788
\(124\) 2.52761 0.226986
\(125\) −11.1832 −1.00025
\(126\) −31.2101 −2.78042
\(127\) 15.0100 1.33193 0.665963 0.745985i \(-0.268021\pi\)
0.665963 + 0.745985i \(0.268021\pi\)
\(128\) −6.95238 −0.614510
\(129\) 27.2934 2.40305
\(130\) −0.385227 −0.0337866
\(131\) 5.04366 0.440667 0.220333 0.975425i \(-0.429285\pi\)
0.220333 + 0.975425i \(0.429285\pi\)
\(132\) −1.60359 −0.139574
\(133\) −19.4433 −1.68595
\(134\) 17.7421 1.53269
\(135\) 35.2657 3.03519
\(136\) −24.6341 −2.11236
\(137\) 13.3492 1.14050 0.570248 0.821472i \(-0.306847\pi\)
0.570248 + 0.821472i \(0.306847\pi\)
\(138\) 26.3650 2.24434
\(139\) −21.2420 −1.80172 −0.900860 0.434109i \(-0.857063\pi\)
−0.900860 + 0.434109i \(0.857063\pi\)
\(140\) −2.74110 −0.231666
\(141\) −4.60092 −0.387467
\(142\) −5.07194 −0.425628
\(143\) 0.170314 0.0142424
\(144\) −23.9527 −1.99605
\(145\) 10.1797 0.845376
\(146\) −13.0222 −1.07773
\(147\) 9.65331 0.796192
\(148\) 2.60126 0.213823
\(149\) 17.7657 1.45542 0.727710 0.685885i \(-0.240585\pi\)
0.727710 + 0.685885i \(0.240585\pi\)
\(150\) 0.0106205 0.000867158 0
\(151\) −15.6478 −1.27340 −0.636700 0.771112i \(-0.719701\pi\)
−0.636700 + 0.771112i \(0.719701\pi\)
\(152\) −18.7023 −1.51696
\(153\) −63.3696 −5.12313
\(154\) −5.01937 −0.404472
\(155\) −14.5268 −1.16682
\(156\) −0.173549 −0.0138950
\(157\) −2.59421 −0.207041 −0.103520 0.994627i \(-0.533011\pi\)
−0.103520 + 0.994627i \(0.533011\pi\)
\(158\) −4.85389 −0.386155
\(159\) −21.7139 −1.72203
\(160\) −4.84400 −0.382952
\(161\) −19.9249 −1.57030
\(162\) −36.1015 −2.83640
\(163\) −9.09160 −0.712109 −0.356055 0.934465i \(-0.615878\pi\)
−0.356055 + 0.934465i \(0.615878\pi\)
\(164\) −0.910706 −0.0711142
\(165\) 9.21620 0.717480
\(166\) −12.9116 −1.00214
\(167\) 19.6332 1.51926 0.759630 0.650355i \(-0.225380\pi\)
0.759630 + 0.650355i \(0.225380\pi\)
\(168\) 31.4134 2.42360
\(169\) −12.9816 −0.998582
\(170\) 23.0516 1.76797
\(171\) −48.1106 −3.67911
\(172\) −3.23040 −0.246315
\(173\) 22.9069 1.74158 0.870789 0.491657i \(-0.163609\pi\)
0.870789 + 0.491657i \(0.163609\pi\)
\(174\) −18.9945 −1.43997
\(175\) −0.00802622 −0.000606726 0
\(176\) −3.85219 −0.290370
\(177\) 4.36947 0.328430
\(178\) −5.00557 −0.375183
\(179\) 14.5618 1.08840 0.544200 0.838955i \(-0.316833\pi\)
0.544200 + 0.838955i \(0.316833\pi\)
\(180\) −6.78261 −0.505546
\(181\) −22.9942 −1.70915 −0.854574 0.519329i \(-0.826182\pi\)
−0.854574 + 0.519329i \(0.826182\pi\)
\(182\) −0.543223 −0.0402664
\(183\) −2.59686 −0.191966
\(184\) −19.1656 −1.41290
\(185\) −14.9501 −1.09915
\(186\) 27.1059 1.98750
\(187\) −10.1914 −0.745271
\(188\) 0.544557 0.0397159
\(189\) 49.7295 3.61729
\(190\) 17.5009 1.26965
\(191\) 5.03712 0.364473 0.182236 0.983255i \(-0.441666\pi\)
0.182236 + 0.983255i \(0.441666\pi\)
\(192\) 29.2219 2.10891
\(193\) −12.2667 −0.882977 −0.441488 0.897267i \(-0.645549\pi\)
−0.441488 + 0.897267i \(0.645549\pi\)
\(194\) 1.68833 0.121215
\(195\) 0.997427 0.0714272
\(196\) −1.14255 −0.0816107
\(197\) 6.88657 0.490648 0.245324 0.969441i \(-0.421106\pi\)
0.245324 + 0.969441i \(0.421106\pi\)
\(198\) −12.4200 −0.882648
\(199\) 20.5642 1.45776 0.728879 0.684643i \(-0.240042\pi\)
0.728879 + 0.684643i \(0.240042\pi\)
\(200\) −0.00772036 −0.000545912 0
\(201\) −45.9378 −3.24020
\(202\) −6.99311 −0.492034
\(203\) 14.3547 1.00751
\(204\) 10.3850 0.727094
\(205\) 5.23405 0.365562
\(206\) −1.94130 −0.135256
\(207\) −49.3022 −3.42674
\(208\) −0.416905 −0.0289071
\(209\) −7.73739 −0.535207
\(210\) −29.3954 −2.02847
\(211\) 22.9563 1.58038 0.790189 0.612863i \(-0.209982\pi\)
0.790189 + 0.612863i \(0.209982\pi\)
\(212\) 2.57003 0.176510
\(213\) 13.1322 0.899806
\(214\) −7.16853 −0.490031
\(215\) 18.5659 1.26618
\(216\) 47.8344 3.25472
\(217\) −20.4848 −1.39060
\(218\) −2.03921 −0.138113
\(219\) 33.7171 2.27839
\(220\) −1.09081 −0.0735426
\(221\) −1.10297 −0.0741939
\(222\) 27.8957 1.87224
\(223\) 18.1325 1.21424 0.607122 0.794608i \(-0.292324\pi\)
0.607122 + 0.794608i \(0.292324\pi\)
\(224\) −6.83070 −0.456396
\(225\) −0.0198602 −0.00132401
\(226\) −12.4218 −0.826283
\(227\) −15.4466 −1.02523 −0.512613 0.858620i \(-0.671322\pi\)
−0.512613 + 0.858620i \(0.671322\pi\)
\(228\) 7.88434 0.522153
\(229\) 8.39998 0.555086 0.277543 0.960713i \(-0.410480\pi\)
0.277543 + 0.960713i \(0.410480\pi\)
\(230\) 17.9344 1.18256
\(231\) 12.9961 0.855081
\(232\) 13.8077 0.906521
\(233\) −23.5411 −1.54223 −0.771114 0.636698i \(-0.780300\pi\)
−0.771114 + 0.636698i \(0.780300\pi\)
\(234\) −1.34416 −0.0878702
\(235\) −3.12970 −0.204159
\(236\) −0.517163 −0.0336645
\(237\) 12.5677 0.816358
\(238\) 32.5059 2.10704
\(239\) 12.4408 0.804726 0.402363 0.915480i \(-0.368189\pi\)
0.402363 + 0.915480i \(0.368189\pi\)
\(240\) −22.5599 −1.45624
\(241\) −6.68701 −0.430748 −0.215374 0.976532i \(-0.569097\pi\)
−0.215374 + 0.976532i \(0.569097\pi\)
\(242\) 11.9645 0.769105
\(243\) 46.1478 2.96038
\(244\) 0.307360 0.0196767
\(245\) 6.56651 0.419519
\(246\) −9.76633 −0.622679
\(247\) −0.837383 −0.0532814
\(248\) −19.7042 −1.25122
\(249\) 33.4307 2.11858
\(250\) 14.1944 0.897733
\(251\) −21.8312 −1.37797 −0.688985 0.724775i \(-0.741944\pi\)
−0.688985 + 0.724775i \(0.741944\pi\)
\(252\) −9.56441 −0.602501
\(253\) −7.92903 −0.498494
\(254\) −19.0517 −1.19541
\(255\) −59.6850 −3.73762
\(256\) −8.95927 −0.559954
\(257\) 12.5522 0.782985 0.391492 0.920181i \(-0.371959\pi\)
0.391492 + 0.920181i \(0.371959\pi\)
\(258\) −34.6425 −2.15675
\(259\) −21.0817 −1.30995
\(260\) −0.118054 −0.00732139
\(261\) 35.5195 2.19860
\(262\) −6.40174 −0.395501
\(263\) 0.979178 0.0603787 0.0301893 0.999544i \(-0.490389\pi\)
0.0301893 + 0.999544i \(0.490389\pi\)
\(264\) 12.5009 0.769375
\(265\) −14.7706 −0.907348
\(266\) 24.6787 1.51315
\(267\) 12.9604 0.793162
\(268\) 5.43712 0.332125
\(269\) 3.51069 0.214050 0.107025 0.994256i \(-0.465867\pi\)
0.107025 + 0.994256i \(0.465867\pi\)
\(270\) −44.7615 −2.72410
\(271\) 15.7189 0.954852 0.477426 0.878672i \(-0.341570\pi\)
0.477426 + 0.878672i \(0.341570\pi\)
\(272\) 24.9471 1.51264
\(273\) 1.40651 0.0851258
\(274\) −16.9436 −1.02360
\(275\) −0.00319401 −0.000192606 0
\(276\) 8.07962 0.486336
\(277\) 14.9778 0.899928 0.449964 0.893047i \(-0.351437\pi\)
0.449964 + 0.893047i \(0.351437\pi\)
\(278\) 26.9617 1.61705
\(279\) −50.6877 −3.03459
\(280\) 21.3684 1.27701
\(281\) 2.81144 0.167716 0.0838581 0.996478i \(-0.473276\pi\)
0.0838581 + 0.996478i \(0.473276\pi\)
\(282\) 5.83978 0.347754
\(283\) 6.77763 0.402888 0.201444 0.979500i \(-0.435437\pi\)
0.201444 + 0.979500i \(0.435437\pi\)
\(284\) −1.55431 −0.0922313
\(285\) −45.3132 −2.68412
\(286\) −0.216174 −0.0127826
\(287\) 7.38072 0.435670
\(288\) −16.9019 −0.995957
\(289\) 49.0006 2.88239
\(290\) −12.9207 −0.758729
\(291\) −4.37141 −0.256257
\(292\) −3.99070 −0.233538
\(293\) −24.1517 −1.41096 −0.705480 0.708730i \(-0.749268\pi\)
−0.705480 + 0.708730i \(0.749268\pi\)
\(294\) −12.2526 −0.714586
\(295\) 2.97226 0.173052
\(296\) −20.2783 −1.17865
\(297\) 19.7897 1.14831
\(298\) −22.5493 −1.30625
\(299\) −0.858123 −0.0496266
\(300\) 0.00325467 0.000187908 0
\(301\) 26.1804 1.50901
\(302\) 19.8612 1.14288
\(303\) 18.1065 1.04019
\(304\) 18.9400 1.08628
\(305\) −1.76647 −0.101148
\(306\) 80.4328 4.59804
\(307\) −30.1751 −1.72218 −0.861091 0.508451i \(-0.830218\pi\)
−0.861091 + 0.508451i \(0.830218\pi\)
\(308\) −1.53820 −0.0876469
\(309\) 5.02639 0.285941
\(310\) 18.4383 1.04723
\(311\) −4.94459 −0.280382 −0.140191 0.990124i \(-0.544772\pi\)
−0.140191 + 0.990124i \(0.544772\pi\)
\(312\) 1.35291 0.0765935
\(313\) −10.3780 −0.586597 −0.293298 0.956021i \(-0.594753\pi\)
−0.293298 + 0.956021i \(0.594753\pi\)
\(314\) 3.29274 0.185820
\(315\) 54.9690 3.09715
\(316\) −1.48749 −0.0836777
\(317\) 31.6647 1.77847 0.889234 0.457452i \(-0.151238\pi\)
0.889234 + 0.457452i \(0.151238\pi\)
\(318\) 27.5607 1.54553
\(319\) 5.71242 0.319834
\(320\) 19.8777 1.11120
\(321\) 18.5607 1.03596
\(322\) 25.2899 1.40935
\(323\) 50.1081 2.78809
\(324\) −11.0634 −0.614633
\(325\) −0.000345673 0 −1.91745e−5 0
\(326\) 11.5396 0.639122
\(327\) 5.27990 0.291979
\(328\) 7.09946 0.392002
\(329\) −4.41331 −0.243314
\(330\) −11.6978 −0.643942
\(331\) −0.416237 −0.0228785 −0.0114392 0.999935i \(-0.503641\pi\)
−0.0114392 + 0.999935i \(0.503641\pi\)
\(332\) −3.95680 −0.217157
\(333\) −52.1647 −2.85861
\(334\) −24.9197 −1.36354
\(335\) −31.2484 −1.70728
\(336\) −31.8126 −1.73552
\(337\) 3.16020 0.172147 0.0860734 0.996289i \(-0.472568\pi\)
0.0860734 + 0.996289i \(0.472568\pi\)
\(338\) 16.4770 0.896233
\(339\) 32.1623 1.74682
\(340\) 7.06421 0.383111
\(341\) −8.15186 −0.441448
\(342\) 61.0651 3.30202
\(343\) −12.8068 −0.691505
\(344\) 25.1827 1.35776
\(345\) −46.4355 −2.50000
\(346\) −29.0749 −1.56307
\(347\) −16.0145 −0.859705 −0.429852 0.902899i \(-0.641434\pi\)
−0.429852 + 0.902899i \(0.641434\pi\)
\(348\) −5.82091 −0.312034
\(349\) 20.4410 1.09418 0.547092 0.837073i \(-0.315735\pi\)
0.547092 + 0.837073i \(0.315735\pi\)
\(350\) 0.0101874 0.000544539 0
\(351\) 2.14175 0.114318
\(352\) −2.71826 −0.144884
\(353\) −16.6502 −0.886203 −0.443101 0.896472i \(-0.646122\pi\)
−0.443101 + 0.896472i \(0.646122\pi\)
\(354\) −5.54602 −0.294767
\(355\) 8.93298 0.474114
\(356\) −1.53397 −0.0813002
\(357\) −84.1640 −4.45443
\(358\) −18.4828 −0.976845
\(359\) −9.22457 −0.486854 −0.243427 0.969919i \(-0.578272\pi\)
−0.243427 + 0.969919i \(0.578272\pi\)
\(360\) 52.8742 2.78672
\(361\) 19.0423 1.00223
\(362\) 29.1858 1.53397
\(363\) −30.9783 −1.62594
\(364\) −0.166472 −0.00872551
\(365\) 22.9355 1.20050
\(366\) 3.29611 0.172290
\(367\) −11.5531 −0.603065 −0.301532 0.953456i \(-0.597498\pi\)
−0.301532 + 0.953456i \(0.597498\pi\)
\(368\) 19.4091 1.01177
\(369\) 18.2629 0.950730
\(370\) 18.9756 0.986494
\(371\) −20.8285 −1.08136
\(372\) 8.30667 0.430681
\(373\) −3.24606 −0.168075 −0.0840374 0.996463i \(-0.526782\pi\)
−0.0840374 + 0.996463i \(0.526782\pi\)
\(374\) 12.9356 0.668885
\(375\) −36.7521 −1.89787
\(376\) −4.24513 −0.218926
\(377\) 0.618230 0.0318404
\(378\) −63.1199 −3.24653
\(379\) −17.9204 −0.920511 −0.460255 0.887787i \(-0.652242\pi\)
−0.460255 + 0.887787i \(0.652242\pi\)
\(380\) 5.36319 0.275126
\(381\) 49.3285 2.52718
\(382\) −6.39343 −0.327116
\(383\) 17.2961 0.883787 0.441894 0.897067i \(-0.354307\pi\)
0.441894 + 0.897067i \(0.354307\pi\)
\(384\) −22.8481 −1.16596
\(385\) 8.84039 0.450548
\(386\) 15.5697 0.792476
\(387\) 64.7810 3.29300
\(388\) 0.517393 0.0262667
\(389\) 2.85574 0.144792 0.0723958 0.997376i \(-0.476936\pi\)
0.0723958 + 0.997376i \(0.476936\pi\)
\(390\) −1.26600 −0.0641063
\(391\) 51.3492 2.59684
\(392\) 8.90681 0.449862
\(393\) 16.5753 0.836115
\(394\) −8.74088 −0.440359
\(395\) 8.54895 0.430144
\(396\) −3.80613 −0.191265
\(397\) −8.98102 −0.450745 −0.225372 0.974273i \(-0.572360\pi\)
−0.225372 + 0.974273i \(0.572360\pi\)
\(398\) −26.1014 −1.30834
\(399\) −63.8978 −3.19889
\(400\) 0.00781847 0.000390924 0
\(401\) −16.8972 −0.843808 −0.421904 0.906640i \(-0.638638\pi\)
−0.421904 + 0.906640i \(0.638638\pi\)
\(402\) 58.3072 2.90810
\(403\) −0.882238 −0.0439474
\(404\) −2.14306 −0.106621
\(405\) 63.5840 3.15951
\(406\) −18.2200 −0.904241
\(407\) −8.38938 −0.415846
\(408\) −80.9567 −4.00796
\(409\) 8.59043 0.424769 0.212385 0.977186i \(-0.431877\pi\)
0.212385 + 0.977186i \(0.431877\pi\)
\(410\) −6.64338 −0.328093
\(411\) 43.8703 2.16396
\(412\) −0.594915 −0.0293093
\(413\) 4.19130 0.206240
\(414\) 62.5775 3.07552
\(415\) 22.7407 1.11629
\(416\) −0.294185 −0.0144236
\(417\) −69.8090 −3.41856
\(418\) 9.82079 0.480351
\(419\) 19.9974 0.976939 0.488470 0.872581i \(-0.337555\pi\)
0.488470 + 0.872581i \(0.337555\pi\)
\(420\) −9.00828 −0.439559
\(421\) 31.6643 1.54322 0.771612 0.636093i \(-0.219451\pi\)
0.771612 + 0.636093i \(0.219451\pi\)
\(422\) −29.1376 −1.41840
\(423\) −10.9203 −0.530964
\(424\) −20.0348 −0.972975
\(425\) 0.0206847 0.00100336
\(426\) −16.6683 −0.807580
\(427\) −2.49097 −0.120547
\(428\) −2.19682 −0.106187
\(429\) 0.559716 0.0270233
\(430\) −23.5650 −1.13640
\(431\) 1.14278 0.0550459 0.0275229 0.999621i \(-0.491238\pi\)
0.0275229 + 0.999621i \(0.491238\pi\)
\(432\) −48.4423 −2.33068
\(433\) 8.47597 0.407329 0.203665 0.979041i \(-0.434715\pi\)
0.203665 + 0.979041i \(0.434715\pi\)
\(434\) 26.0006 1.24807
\(435\) 33.4542 1.60400
\(436\) −0.624920 −0.0299282
\(437\) 38.9846 1.86489
\(438\) −42.7959 −2.04487
\(439\) −16.3741 −0.781495 −0.390747 0.920498i \(-0.627783\pi\)
−0.390747 + 0.920498i \(0.627783\pi\)
\(440\) 8.50350 0.405389
\(441\) 22.9122 1.09106
\(442\) 1.39996 0.0665894
\(443\) −37.0812 −1.76178 −0.880891 0.473319i \(-0.843056\pi\)
−0.880891 + 0.473319i \(0.843056\pi\)
\(444\) 8.54871 0.405704
\(445\) 8.81608 0.417922
\(446\) −23.0150 −1.08979
\(447\) 58.3845 2.76149
\(448\) 28.0303 1.32431
\(449\) −5.57097 −0.262910 −0.131455 0.991322i \(-0.541965\pi\)
−0.131455 + 0.991322i \(0.541965\pi\)
\(450\) 0.0252078 0.00118831
\(451\) 2.93714 0.138304
\(452\) −3.80668 −0.179051
\(453\) −51.4245 −2.41613
\(454\) 19.6058 0.920145
\(455\) 0.956755 0.0448534
\(456\) −61.4628 −2.87826
\(457\) 2.80831 0.131367 0.0656835 0.997841i \(-0.479077\pi\)
0.0656835 + 0.997841i \(0.479077\pi\)
\(458\) −10.6618 −0.498193
\(459\) −128.160 −5.98199
\(460\) 5.49603 0.256254
\(461\) −31.1869 −1.45252 −0.726258 0.687422i \(-0.758742\pi\)
−0.726258 + 0.687422i \(0.758742\pi\)
\(462\) −16.4955 −0.767440
\(463\) −6.96104 −0.323507 −0.161753 0.986831i \(-0.551715\pi\)
−0.161753 + 0.986831i \(0.551715\pi\)
\(464\) −13.9832 −0.649153
\(465\) −47.7404 −2.21391
\(466\) 29.8798 1.38416
\(467\) −18.5088 −0.856486 −0.428243 0.903664i \(-0.640867\pi\)
−0.428243 + 0.903664i \(0.640867\pi\)
\(468\) −0.411920 −0.0190410
\(469\) −44.0646 −2.03471
\(470\) 3.97241 0.183234
\(471\) −8.52555 −0.392836
\(472\) 4.03158 0.185568
\(473\) 10.4184 0.479039
\(474\) −15.9517 −0.732685
\(475\) 0.0157040 0.000720547 0
\(476\) 9.96151 0.456585
\(477\) −51.5382 −2.35977
\(478\) −15.7906 −0.722245
\(479\) −1.25874 −0.0575134 −0.0287567 0.999586i \(-0.509155\pi\)
−0.0287567 + 0.999586i \(0.509155\pi\)
\(480\) −15.9192 −0.726607
\(481\) −0.907945 −0.0413987
\(482\) 8.48758 0.386599
\(483\) −65.4805 −2.97946
\(484\) 3.66654 0.166661
\(485\) −2.97358 −0.135023
\(486\) −58.5737 −2.65696
\(487\) −3.77174 −0.170914 −0.0854569 0.996342i \(-0.527235\pi\)
−0.0854569 + 0.996342i \(0.527235\pi\)
\(488\) −2.39605 −0.108464
\(489\) −29.8784 −1.35115
\(490\) −8.33463 −0.376520
\(491\) −22.3555 −1.00889 −0.504444 0.863444i \(-0.668302\pi\)
−0.504444 + 0.863444i \(0.668302\pi\)
\(492\) −2.99292 −0.134931
\(493\) −36.9942 −1.66613
\(494\) 1.06286 0.0478203
\(495\) 21.8747 0.983196
\(496\) 19.9546 0.895986
\(497\) 12.5967 0.565041
\(498\) −42.4323 −1.90144
\(499\) 9.42498 0.421920 0.210960 0.977495i \(-0.432341\pi\)
0.210960 + 0.977495i \(0.432341\pi\)
\(500\) 4.34991 0.194534
\(501\) 64.5219 2.88262
\(502\) 27.7095 1.23674
\(503\) 3.30752 0.147475 0.0737374 0.997278i \(-0.476507\pi\)
0.0737374 + 0.997278i \(0.476507\pi\)
\(504\) 74.5599 3.32116
\(505\) 12.3167 0.548084
\(506\) 10.0640 0.447401
\(507\) −42.6622 −1.89470
\(508\) −5.83844 −0.259039
\(509\) 25.6399 1.13647 0.568234 0.822867i \(-0.307627\pi\)
0.568234 + 0.822867i \(0.307627\pi\)
\(510\) 75.7560 3.35453
\(511\) 32.3422 1.43074
\(512\) 25.2764 1.11707
\(513\) −97.2997 −4.29589
\(514\) −15.9321 −0.702733
\(515\) 3.41912 0.150664
\(516\) −10.6163 −0.467355
\(517\) −1.75626 −0.0772403
\(518\) 26.7582 1.17569
\(519\) 75.2805 3.30445
\(520\) 0.920295 0.0403576
\(521\) 20.6442 0.904440 0.452220 0.891907i \(-0.350632\pi\)
0.452220 + 0.891907i \(0.350632\pi\)
\(522\) −45.0836 −1.97326
\(523\) −42.7270 −1.86832 −0.934160 0.356854i \(-0.883849\pi\)
−0.934160 + 0.356854i \(0.883849\pi\)
\(524\) −1.96183 −0.0857029
\(525\) −0.0263771 −0.00115119
\(526\) −1.24283 −0.0541902
\(527\) 52.7922 2.29966
\(528\) −12.6597 −0.550943
\(529\) 16.9502 0.736964
\(530\) 18.7477 0.814349
\(531\) 10.3710 0.450062
\(532\) 7.56284 0.327890
\(533\) 0.317873 0.0137686
\(534\) −16.4501 −0.711867
\(535\) 12.6256 0.545853
\(536\) −42.3854 −1.83077
\(537\) 47.8555 2.06512
\(538\) −4.45599 −0.192111
\(539\) 3.68486 0.158718
\(540\) −13.7173 −0.590297
\(541\) 31.4119 1.35050 0.675252 0.737587i \(-0.264035\pi\)
0.675252 + 0.737587i \(0.264035\pi\)
\(542\) −19.9514 −0.856985
\(543\) −75.5676 −3.24292
\(544\) 17.6037 0.754752
\(545\) 3.59157 0.153846
\(546\) −1.78523 −0.0764009
\(547\) −42.7247 −1.82678 −0.913388 0.407090i \(-0.866543\pi\)
−0.913388 + 0.407090i \(0.866543\pi\)
\(548\) −5.19241 −0.221809
\(549\) −6.16368 −0.263059
\(550\) 0.00405404 0.000172865 0
\(551\) −28.0862 −1.19651
\(552\) −62.9852 −2.68083
\(553\) 12.0552 0.512639
\(554\) −19.0108 −0.807690
\(555\) −49.1315 −2.08552
\(556\) 8.26247 0.350407
\(557\) −1.38156 −0.0585384 −0.0292692 0.999572i \(-0.509318\pi\)
−0.0292692 + 0.999572i \(0.509318\pi\)
\(558\) 64.3361 2.72356
\(559\) 1.12754 0.0476898
\(560\) −21.6400 −0.914456
\(561\) −33.4928 −1.41407
\(562\) −3.56845 −0.150526
\(563\) 11.1393 0.469466 0.234733 0.972060i \(-0.424578\pi\)
0.234733 + 0.972060i \(0.424578\pi\)
\(564\) 1.78962 0.0753564
\(565\) 21.8779 0.920410
\(566\) −8.60260 −0.361594
\(567\) 89.6621 3.76546
\(568\) 12.1167 0.508406
\(569\) −0.706950 −0.0296369 −0.0148184 0.999890i \(-0.504717\pi\)
−0.0148184 + 0.999890i \(0.504717\pi\)
\(570\) 57.5144 2.40901
\(571\) 9.42652 0.394488 0.197244 0.980354i \(-0.436801\pi\)
0.197244 + 0.980354i \(0.436801\pi\)
\(572\) −0.0662470 −0.00276993
\(573\) 16.5538 0.691546
\(574\) −9.36809 −0.391016
\(575\) 0.0160929 0.000671121 0
\(576\) 69.3584 2.88993
\(577\) 24.1338 1.00470 0.502351 0.864664i \(-0.332469\pi\)
0.502351 + 0.864664i \(0.332469\pi\)
\(578\) −62.1947 −2.58696
\(579\) −40.3129 −1.67535
\(580\) −3.95958 −0.164413
\(581\) 32.0675 1.33038
\(582\) 5.54848 0.229992
\(583\) −8.28864 −0.343280
\(584\) 31.1097 1.28733
\(585\) 2.36740 0.0978800
\(586\) 30.6549 1.26634
\(587\) 4.16144 0.171761 0.0858806 0.996305i \(-0.472630\pi\)
0.0858806 + 0.996305i \(0.472630\pi\)
\(588\) −3.75484 −0.154847
\(589\) 40.0801 1.65147
\(590\) −3.77259 −0.155315
\(591\) 22.6318 0.930949
\(592\) 20.5360 0.844024
\(593\) 24.6273 1.01132 0.505661 0.862732i \(-0.331249\pi\)
0.505661 + 0.862732i \(0.331249\pi\)
\(594\) −25.1183 −1.03062
\(595\) −57.2512 −2.34707
\(596\) −6.91029 −0.283057
\(597\) 67.5816 2.76593
\(598\) 1.08919 0.0445401
\(599\) 33.4440 1.36648 0.683242 0.730192i \(-0.260569\pi\)
0.683242 + 0.730192i \(0.260569\pi\)
\(600\) −0.0253720 −0.00103581
\(601\) 12.8439 0.523913 0.261957 0.965080i \(-0.415632\pi\)
0.261957 + 0.965080i \(0.415632\pi\)
\(602\) −33.2299 −1.35435
\(603\) −109.034 −4.44020
\(604\) 6.08651 0.247657
\(605\) −21.0725 −0.856718
\(606\) −22.9819 −0.933578
\(607\) −42.2651 −1.71549 −0.857743 0.514079i \(-0.828134\pi\)
−0.857743 + 0.514079i \(0.828134\pi\)
\(608\) 13.3648 0.542015
\(609\) 47.1750 1.91163
\(610\) 2.24212 0.0907808
\(611\) −0.190072 −0.00768950
\(612\) 24.6488 0.996370
\(613\) 36.6595 1.48066 0.740332 0.672241i \(-0.234668\pi\)
0.740332 + 0.672241i \(0.234668\pi\)
\(614\) 38.3001 1.54567
\(615\) 17.2010 0.693612
\(616\) 11.9911 0.483136
\(617\) 30.6911 1.23558 0.617788 0.786345i \(-0.288029\pi\)
0.617788 + 0.786345i \(0.288029\pi\)
\(618\) −6.37981 −0.256634
\(619\) 1.00000 0.0401934
\(620\) 5.65048 0.226929
\(621\) −99.7097 −4.00121
\(622\) 6.27599 0.251644
\(623\) 12.4319 0.498073
\(624\) −1.37010 −0.0548480
\(625\) −24.9873 −0.999491
\(626\) 13.1724 0.526474
\(627\) −25.4279 −1.01549
\(628\) 1.00907 0.0402662
\(629\) 54.3304 2.16630
\(630\) −69.7701 −2.77971
\(631\) −42.3028 −1.68405 −0.842023 0.539441i \(-0.818635\pi\)
−0.842023 + 0.539441i \(0.818635\pi\)
\(632\) 11.5958 0.461256
\(633\) 75.4430 2.99859
\(634\) −40.1909 −1.59618
\(635\) 33.5549 1.33159
\(636\) 8.44605 0.334908
\(637\) 0.398796 0.0158009
\(638\) −7.25057 −0.287053
\(639\) 31.1695 1.23305
\(640\) −15.5420 −0.614353
\(641\) −33.3721 −1.31812 −0.659060 0.752090i \(-0.729046\pi\)
−0.659060 + 0.752090i \(0.729046\pi\)
\(642\) −23.5585 −0.929778
\(643\) 14.1215 0.556898 0.278449 0.960451i \(-0.410180\pi\)
0.278449 + 0.960451i \(0.410180\pi\)
\(644\) 7.75016 0.305399
\(645\) 61.0143 2.40243
\(646\) −63.6004 −2.50232
\(647\) −10.6702 −0.419489 −0.209744 0.977756i \(-0.567263\pi\)
−0.209744 + 0.977756i \(0.567263\pi\)
\(648\) 86.2453 3.38804
\(649\) 1.66791 0.0654714
\(650\) 0.000438751 0 1.72092e−5 0
\(651\) −67.3206 −2.63850
\(652\) 3.53635 0.138494
\(653\) −3.01908 −0.118146 −0.0590728 0.998254i \(-0.518814\pi\)
−0.0590728 + 0.998254i \(0.518814\pi\)
\(654\) −6.70159 −0.262053
\(655\) 11.2751 0.440555
\(656\) −7.18968 −0.280710
\(657\) 80.0278 3.12218
\(658\) 5.60165 0.218375
\(659\) −45.8116 −1.78456 −0.892282 0.451478i \(-0.850897\pi\)
−0.892282 + 0.451478i \(0.850897\pi\)
\(660\) −3.58482 −0.139539
\(661\) −8.99557 −0.349887 −0.174944 0.984578i \(-0.555974\pi\)
−0.174944 + 0.984578i \(0.555974\pi\)
\(662\) 0.528315 0.0205335
\(663\) −3.62477 −0.140775
\(664\) 30.8454 1.19704
\(665\) −43.4654 −1.68552
\(666\) 66.2107 2.56561
\(667\) −28.7819 −1.11444
\(668\) −7.63670 −0.295473
\(669\) 59.5902 2.30389
\(670\) 39.6625 1.53230
\(671\) −0.991274 −0.0382677
\(672\) −22.4482 −0.865959
\(673\) 32.1945 1.24101 0.620504 0.784203i \(-0.286928\pi\)
0.620504 + 0.784203i \(0.286928\pi\)
\(674\) −4.01112 −0.154503
\(675\) −0.0401655 −0.00154597
\(676\) 5.04943 0.194209
\(677\) −11.3483 −0.436149 −0.218075 0.975932i \(-0.569978\pi\)
−0.218075 + 0.975932i \(0.569978\pi\)
\(678\) −40.8225 −1.56778
\(679\) −4.19316 −0.160919
\(680\) −55.0695 −2.11182
\(681\) −50.7632 −1.94525
\(682\) 10.3469 0.396202
\(683\) −42.2406 −1.61629 −0.808147 0.588981i \(-0.799529\pi\)
−0.808147 + 0.588981i \(0.799529\pi\)
\(684\) 18.7135 0.715530
\(685\) 29.8420 1.14021
\(686\) 16.2553 0.620629
\(687\) 27.6054 1.05321
\(688\) −25.5028 −0.972284
\(689\) −0.897042 −0.0341746
\(690\) 58.9389 2.24377
\(691\) 28.2401 1.07431 0.537153 0.843485i \(-0.319500\pi\)
0.537153 + 0.843485i \(0.319500\pi\)
\(692\) −8.91007 −0.338710
\(693\) 30.8464 1.17176
\(694\) 20.3267 0.771589
\(695\) −47.4864 −1.80126
\(696\) 45.3773 1.72002
\(697\) −19.0212 −0.720478
\(698\) −25.9451 −0.982035
\(699\) −77.3647 −2.92620
\(700\) 0.00312195 0.000117999 0
\(701\) 28.3274 1.06991 0.534956 0.844880i \(-0.320328\pi\)
0.534956 + 0.844880i \(0.320328\pi\)
\(702\) −2.71844 −0.102601
\(703\) 41.2480 1.55570
\(704\) 11.1546 0.420403
\(705\) −10.2854 −0.387369
\(706\) 21.1335 0.795371
\(707\) 17.3682 0.653198
\(708\) −1.69959 −0.0638745
\(709\) −38.8780 −1.46009 −0.730047 0.683397i \(-0.760502\pi\)
−0.730047 + 0.683397i \(0.760502\pi\)
\(710\) −11.3383 −0.425519
\(711\) 29.8295 1.11869
\(712\) 11.9581 0.448150
\(713\) 41.0729 1.53819
\(714\) 106.826 3.99788
\(715\) 0.380738 0.0142388
\(716\) −5.66409 −0.211677
\(717\) 40.8849 1.52688
\(718\) 11.7084 0.436954
\(719\) −50.6095 −1.88741 −0.943707 0.330781i \(-0.892688\pi\)
−0.943707 + 0.330781i \(0.892688\pi\)
\(720\) −53.5461 −1.99555
\(721\) 4.82143 0.179559
\(722\) −24.1698 −0.899505
\(723\) −21.9760 −0.817296
\(724\) 8.94405 0.332403
\(725\) −0.0115940 −0.000430592 0
\(726\) 39.3196 1.45929
\(727\) −8.08112 −0.299712 −0.149856 0.988708i \(-0.547881\pi\)
−0.149856 + 0.988708i \(0.547881\pi\)
\(728\) 1.29774 0.0480976
\(729\) 66.3301 2.45667
\(730\) −29.1112 −1.07745
\(731\) −67.4706 −2.49549
\(732\) 1.01010 0.0373344
\(733\) 2.64000 0.0975107 0.0487553 0.998811i \(-0.484475\pi\)
0.0487553 + 0.998811i \(0.484475\pi\)
\(734\) 14.6639 0.541254
\(735\) 21.5800 0.795989
\(736\) 13.6958 0.504836
\(737\) −17.5354 −0.645923
\(738\) −23.1805 −0.853285
\(739\) 29.1750 1.07322 0.536609 0.843831i \(-0.319705\pi\)
0.536609 + 0.843831i \(0.319705\pi\)
\(740\) 5.81512 0.213768
\(741\) −2.75195 −0.101095
\(742\) 26.4369 0.970528
\(743\) −0.618734 −0.0226991 −0.0113496 0.999936i \(-0.503613\pi\)
−0.0113496 + 0.999936i \(0.503613\pi\)
\(744\) −64.7552 −2.37404
\(745\) 39.7151 1.45505
\(746\) 4.12011 0.150848
\(747\) 79.3480 2.90319
\(748\) 3.96415 0.144944
\(749\) 17.8039 0.650539
\(750\) 46.6481 1.70335
\(751\) −13.7705 −0.502492 −0.251246 0.967923i \(-0.580840\pi\)
−0.251246 + 0.967923i \(0.580840\pi\)
\(752\) 4.29907 0.156771
\(753\) −71.7453 −2.61454
\(754\) −0.784697 −0.0285770
\(755\) −34.9806 −1.27308
\(756\) −19.3432 −0.703507
\(757\) −28.0140 −1.01819 −0.509093 0.860711i \(-0.670019\pi\)
−0.509093 + 0.860711i \(0.670019\pi\)
\(758\) 22.7458 0.826163
\(759\) −26.0577 −0.945836
\(760\) −41.8091 −1.51657
\(761\) −10.7431 −0.389436 −0.194718 0.980859i \(-0.562379\pi\)
−0.194718 + 0.980859i \(0.562379\pi\)
\(762\) −62.6109 −2.26815
\(763\) 5.06460 0.183351
\(764\) −1.95928 −0.0708844
\(765\) −141.663 −5.12183
\(766\) −21.9533 −0.793204
\(767\) 0.180511 0.00651787
\(768\) −29.4435 −1.06245
\(769\) −25.7299 −0.927844 −0.463922 0.885876i \(-0.653558\pi\)
−0.463922 + 0.885876i \(0.653558\pi\)
\(770\) −11.2208 −0.404369
\(771\) 41.2512 1.48562
\(772\) 4.77137 0.171725
\(773\) −21.8741 −0.786755 −0.393378 0.919377i \(-0.628694\pi\)
−0.393378 + 0.919377i \(0.628694\pi\)
\(774\) −82.2242 −2.95549
\(775\) 0.0165452 0.000594320 0
\(776\) −4.03337 −0.144790
\(777\) −69.2822 −2.48548
\(778\) −3.62468 −0.129951
\(779\) −14.4410 −0.517402
\(780\) −0.387968 −0.0138915
\(781\) 5.01283 0.179373
\(782\) −65.1756 −2.33068
\(783\) 71.8352 2.56718
\(784\) −9.02000 −0.322143
\(785\) −5.79936 −0.206988
\(786\) −21.0385 −0.750418
\(787\) −19.6488 −0.700403 −0.350201 0.936674i \(-0.613887\pi\)
−0.350201 + 0.936674i \(0.613887\pi\)
\(788\) −2.67866 −0.0954234
\(789\) 3.21794 0.114562
\(790\) −10.8509 −0.386057
\(791\) 30.8508 1.09693
\(792\) 29.6709 1.05431
\(793\) −0.107281 −0.00380966
\(794\) 11.3993 0.404546
\(795\) −48.5415 −1.72159
\(796\) −7.99884 −0.283511
\(797\) −34.3265 −1.21591 −0.607953 0.793973i \(-0.708009\pi\)
−0.607953 + 0.793973i \(0.708009\pi\)
\(798\) 81.1032 2.87102
\(799\) 11.3737 0.402373
\(800\) 0.00551703 0.000195056 0
\(801\) 30.7616 1.08691
\(802\) 21.4471 0.757322
\(803\) 12.8705 0.454189
\(804\) 17.8684 0.630169
\(805\) −44.5420 −1.56990
\(806\) 1.11979 0.0394430
\(807\) 11.5374 0.406136
\(808\) 16.7063 0.587727
\(809\) 11.7599 0.413455 0.206728 0.978399i \(-0.433719\pi\)
0.206728 + 0.978399i \(0.433719\pi\)
\(810\) −80.7048 −2.83568
\(811\) 1.74718 0.0613519 0.0306759 0.999529i \(-0.490234\pi\)
0.0306759 + 0.999529i \(0.490234\pi\)
\(812\) −5.58355 −0.195944
\(813\) 51.6580 1.81172
\(814\) 10.6483 0.373224
\(815\) −20.3243 −0.711928
\(816\) 81.9855 2.87007
\(817\) −51.2241 −1.79210
\(818\) −10.9035 −0.381233
\(819\) 3.33836 0.116652
\(820\) −2.03588 −0.0710961
\(821\) 37.6222 1.31303 0.656513 0.754315i \(-0.272031\pi\)
0.656513 + 0.754315i \(0.272031\pi\)
\(822\) −55.6830 −1.94217
\(823\) 13.0158 0.453701 0.226850 0.973930i \(-0.427157\pi\)
0.226850 + 0.973930i \(0.427157\pi\)
\(824\) 4.63769 0.161562
\(825\) −0.0104967 −0.000365448 0
\(826\) −5.31986 −0.185102
\(827\) −31.8318 −1.10690 −0.553451 0.832882i \(-0.686689\pi\)
−0.553451 + 0.832882i \(0.686689\pi\)
\(828\) 19.1770 0.666448
\(829\) −33.8447 −1.17548 −0.587738 0.809051i \(-0.699981\pi\)
−0.587738 + 0.809051i \(0.699981\pi\)
\(830\) −28.8639 −1.00188
\(831\) 49.2226 1.70751
\(832\) 1.20721 0.0418524
\(833\) −23.8635 −0.826821
\(834\) 88.6060 3.06817
\(835\) 43.8899 1.51887
\(836\) 3.00961 0.104089
\(837\) −102.512 −3.54332
\(838\) −25.3820 −0.876808
\(839\) 6.06404 0.209354 0.104677 0.994506i \(-0.466619\pi\)
0.104677 + 0.994506i \(0.466619\pi\)
\(840\) 70.2246 2.42298
\(841\) −8.26429 −0.284976
\(842\) −40.1904 −1.38505
\(843\) 9.23942 0.318222
\(844\) −8.92930 −0.307359
\(845\) −29.0203 −0.998328
\(846\) 13.8608 0.476543
\(847\) −29.7151 −1.02102
\(848\) 20.2894 0.696740
\(849\) 22.2738 0.764435
\(850\) −0.0262544 −0.000900517 0
\(851\) 42.2696 1.44898
\(852\) −5.10803 −0.174998
\(853\) 52.5673 1.79987 0.899935 0.436025i \(-0.143614\pi\)
0.899935 + 0.436025i \(0.143614\pi\)
\(854\) 3.16170 0.108191
\(855\) −107.551 −3.67817
\(856\) 17.1254 0.585334
\(857\) −5.55207 −0.189655 −0.0948275 0.995494i \(-0.530230\pi\)
−0.0948275 + 0.995494i \(0.530230\pi\)
\(858\) −0.710427 −0.0242536
\(859\) −23.7264 −0.809535 −0.404767 0.914420i \(-0.632647\pi\)
−0.404767 + 0.914420i \(0.632647\pi\)
\(860\) −7.22155 −0.246253
\(861\) 24.2558 0.826635
\(862\) −1.45049 −0.0494040
\(863\) 12.9344 0.440293 0.220147 0.975467i \(-0.429346\pi\)
0.220147 + 0.975467i \(0.429346\pi\)
\(864\) −34.1828 −1.16292
\(865\) 51.2083 1.74113
\(866\) −10.7582 −0.365580
\(867\) 161.034 5.46901
\(868\) 7.96795 0.270450
\(869\) 4.79733 0.162738
\(870\) −42.4622 −1.43960
\(871\) −1.89777 −0.0643035
\(872\) 4.87160 0.164973
\(873\) −10.3756 −0.351160
\(874\) −49.4817 −1.67374
\(875\) −35.2534 −1.19178
\(876\) −13.1149 −0.443112
\(877\) 35.5216 1.19948 0.599739 0.800195i \(-0.295271\pi\)
0.599739 + 0.800195i \(0.295271\pi\)
\(878\) 20.7831 0.701396
\(879\) −79.3715 −2.67714
\(880\) −8.61156 −0.290296
\(881\) −15.8118 −0.532715 −0.266357 0.963874i \(-0.585820\pi\)
−0.266357 + 0.963874i \(0.585820\pi\)
\(882\) −29.0817 −0.979230
\(883\) −41.6550 −1.40180 −0.700902 0.713258i \(-0.747219\pi\)
−0.700902 + 0.713258i \(0.747219\pi\)
\(884\) 0.429022 0.0144296
\(885\) 9.76795 0.328346
\(886\) 47.0659 1.58121
\(887\) −10.6948 −0.359095 −0.179548 0.983749i \(-0.557463\pi\)
−0.179548 + 0.983749i \(0.557463\pi\)
\(888\) −66.6420 −2.23636
\(889\) 47.3171 1.58696
\(890\) −11.1899 −0.375088
\(891\) 35.6808 1.19535
\(892\) −7.05300 −0.236152
\(893\) 8.63499 0.288959
\(894\) −74.1054 −2.47845
\(895\) 32.5529 1.08812
\(896\) −21.9164 −0.732176
\(897\) −2.82011 −0.0941608
\(898\) 7.07104 0.235964
\(899\) −29.5907 −0.986904
\(900\) 0.00772499 0.000257500 0
\(901\) 53.6780 1.78827
\(902\) −3.72800 −0.124129
\(903\) 86.0385 2.86318
\(904\) 29.6752 0.986982
\(905\) −51.4036 −1.70871
\(906\) 65.2712 2.16849
\(907\) 7.55510 0.250863 0.125431 0.992102i \(-0.459969\pi\)
0.125431 + 0.992102i \(0.459969\pi\)
\(908\) 6.00824 0.199391
\(909\) 42.9760 1.42542
\(910\) −1.21437 −0.0402561
\(911\) 1.47199 0.0487692 0.0243846 0.999703i \(-0.492237\pi\)
0.0243846 + 0.999703i \(0.492237\pi\)
\(912\) 62.2439 2.06110
\(913\) 12.7611 0.422332
\(914\) −3.56448 −0.117903
\(915\) −5.80529 −0.191917
\(916\) −3.26733 −0.107956
\(917\) 15.8994 0.525046
\(918\) 162.669 5.36887
\(919\) −26.5075 −0.874400 −0.437200 0.899364i \(-0.644030\pi\)
−0.437200 + 0.899364i \(0.644030\pi\)
\(920\) −42.8446 −1.41255
\(921\) −99.1664 −3.26764
\(922\) 39.5844 1.30364
\(923\) 0.542516 0.0178571
\(924\) −5.05508 −0.166300
\(925\) 0.0170272 0.000559852 0
\(926\) 8.83540 0.290349
\(927\) 11.9302 0.391838
\(928\) −9.86709 −0.323903
\(929\) −6.34088 −0.208037 −0.104019 0.994575i \(-0.533170\pi\)
−0.104019 + 0.994575i \(0.533170\pi\)
\(930\) 60.5952 1.98700
\(931\) −18.1173 −0.593771
\(932\) 9.15675 0.299939
\(933\) −16.2498 −0.531993
\(934\) 23.4926 0.768700
\(935\) −22.7829 −0.745081
\(936\) 3.21115 0.104960
\(937\) −24.0482 −0.785620 −0.392810 0.919620i \(-0.628497\pi\)
−0.392810 + 0.919620i \(0.628497\pi\)
\(938\) 55.9296 1.82616
\(939\) −34.1058 −1.11300
\(940\) 1.21736 0.0397058
\(941\) −18.1223 −0.590771 −0.295385 0.955378i \(-0.595448\pi\)
−0.295385 + 0.955378i \(0.595448\pi\)
\(942\) 10.8212 0.352573
\(943\) −14.7987 −0.481911
\(944\) −4.08281 −0.132884
\(945\) 111.170 3.61637
\(946\) −13.2237 −0.429940
\(947\) −20.1977 −0.656336 −0.328168 0.944619i \(-0.606431\pi\)
−0.328168 + 0.944619i \(0.606431\pi\)
\(948\) −4.88844 −0.158769
\(949\) 1.39291 0.0452159
\(950\) −0.0199325 −0.000646694 0
\(951\) 104.062 3.37444
\(952\) −77.6555 −2.51683
\(953\) 32.2900 1.04598 0.522988 0.852340i \(-0.324817\pi\)
0.522988 + 0.852340i \(0.324817\pi\)
\(954\) 65.4156 2.11791
\(955\) 11.2605 0.364380
\(956\) −4.83907 −0.156507
\(957\) 18.7731 0.606849
\(958\) 1.59767 0.0516185
\(959\) 42.0814 1.35888
\(960\) 65.3254 2.10837
\(961\) 11.2271 0.362164
\(962\) 1.15242 0.0371556
\(963\) 44.0540 1.41962
\(964\) 2.60104 0.0837739
\(965\) −27.4222 −0.882752
\(966\) 83.1120 2.67408
\(967\) −17.9586 −0.577508 −0.288754 0.957403i \(-0.593241\pi\)
−0.288754 + 0.957403i \(0.593241\pi\)
\(968\) −28.5827 −0.918684
\(969\) 164.674 5.29008
\(970\) 3.77426 0.121184
\(971\) 23.0632 0.740134 0.370067 0.929005i \(-0.379335\pi\)
0.370067 + 0.929005i \(0.379335\pi\)
\(972\) −17.9501 −0.575748
\(973\) −66.9624 −2.14671
\(974\) 4.78733 0.153396
\(975\) −0.00113601 −3.63814e−5 0
\(976\) 2.42649 0.0776702
\(977\) −22.2539 −0.711966 −0.355983 0.934492i \(-0.615854\pi\)
−0.355983 + 0.934492i \(0.615854\pi\)
\(978\) 37.9235 1.21266
\(979\) 4.94723 0.158114
\(980\) −2.55417 −0.0815899
\(981\) 12.5319 0.400112
\(982\) 28.3750 0.905482
\(983\) −34.9063 −1.11334 −0.556669 0.830735i \(-0.687921\pi\)
−0.556669 + 0.830735i \(0.687921\pi\)
\(984\) 23.3315 0.743780
\(985\) 15.3949 0.490523
\(986\) 46.9554 1.49536
\(987\) −14.5038 −0.461660
\(988\) 0.325716 0.0103624
\(989\) −52.4928 −1.66917
\(990\) −27.7648 −0.882423
\(991\) −19.4547 −0.617999 −0.309000 0.951062i \(-0.599994\pi\)
−0.309000 + 0.951062i \(0.599994\pi\)
\(992\) 14.0807 0.447064
\(993\) −1.36791 −0.0434093
\(994\) −15.9886 −0.507127
\(995\) 45.9712 1.45739
\(996\) −13.0035 −0.412032
\(997\) −58.4225 −1.85026 −0.925129 0.379652i \(-0.876044\pi\)
−0.925129 + 0.379652i \(0.876044\pi\)
\(998\) −11.9628 −0.378676
\(999\) −105.499 −3.33783
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 \(a_p\))