Properties

Label 8018.2.a.f.1.27
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 1.27
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.61503 q^{3} +1.00000 q^{4} -2.67661 q^{5} -1.61503 q^{6} -0.794060 q^{7} -1.00000 q^{8} -0.391676 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.61503 q^{3} +1.00000 q^{4} -2.67661 q^{5} -1.61503 q^{6} -0.794060 q^{7} -1.00000 q^{8} -0.391676 q^{9} +2.67661 q^{10} -2.37029 q^{11} +1.61503 q^{12} -0.106159 q^{13} +0.794060 q^{14} -4.32281 q^{15} +1.00000 q^{16} +2.83751 q^{17} +0.391676 q^{18} -1.00000 q^{19} -2.67661 q^{20} -1.28243 q^{21} +2.37029 q^{22} +6.31079 q^{23} -1.61503 q^{24} +2.16424 q^{25} +0.106159 q^{26} -5.47766 q^{27} -0.794060 q^{28} +1.48726 q^{29} +4.32281 q^{30} +7.04611 q^{31} -1.00000 q^{32} -3.82810 q^{33} -2.83751 q^{34} +2.12539 q^{35} -0.391676 q^{36} +8.75364 q^{37} +1.00000 q^{38} -0.171450 q^{39} +2.67661 q^{40} -9.87170 q^{41} +1.28243 q^{42} +0.390722 q^{43} -2.37029 q^{44} +1.04836 q^{45} -6.31079 q^{46} +10.5003 q^{47} +1.61503 q^{48} -6.36947 q^{49} -2.16424 q^{50} +4.58267 q^{51} -0.106159 q^{52} -3.80976 q^{53} +5.47766 q^{54} +6.34435 q^{55} +0.794060 q^{56} -1.61503 q^{57} -1.48726 q^{58} +7.62248 q^{59} -4.32281 q^{60} -7.41888 q^{61} -7.04611 q^{62} +0.311015 q^{63} +1.00000 q^{64} +0.284145 q^{65} +3.82810 q^{66} -7.63201 q^{67} +2.83751 q^{68} +10.1921 q^{69} -2.12539 q^{70} +5.42396 q^{71} +0.391676 q^{72} -4.28900 q^{73} -8.75364 q^{74} +3.49531 q^{75} -1.00000 q^{76} +1.88216 q^{77} +0.171450 q^{78} +11.6390 q^{79} -2.67661 q^{80} -7.67156 q^{81} +9.87170 q^{82} +11.4882 q^{83} -1.28243 q^{84} -7.59491 q^{85} -0.390722 q^{86} +2.40198 q^{87} +2.37029 q^{88} -3.26256 q^{89} -1.04836 q^{90} +0.0842964 q^{91} +6.31079 q^{92} +11.3797 q^{93} -10.5003 q^{94} +2.67661 q^{95} -1.61503 q^{96} -9.02393 q^{97} +6.36947 q^{98} +0.928388 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 34q^{2} - 10q^{3} + 34q^{4} + 7q^{5} + 10q^{6} - 6q^{7} - 34q^{8} + 38q^{9} + O(q^{10}) \) \( 34q - 34q^{2} - 10q^{3} + 34q^{4} + 7q^{5} + 10q^{6} - 6q^{7} - 34q^{8} + 38q^{9} - 7q^{10} + 4q^{11} - 10q^{12} - 5q^{13} + 6q^{14} - 17q^{15} + 34q^{16} + 8q^{17} - 38q^{18} - 34q^{19} + 7q^{20} - 4q^{22} - 24q^{23} + 10q^{24} + 5q^{25} + 5q^{26} - 31q^{27} - 6q^{28} + 24q^{29} + 17q^{30} - 28q^{31} - 34q^{32} - 16q^{33} - 8q^{34} + 2q^{35} + 38q^{36} - 36q^{37} + 34q^{38} - 9q^{39} - 7q^{40} + 9q^{41} - 24q^{43} + 4q^{44} + 22q^{45} + 24q^{46} - 29q^{47} - 10q^{48} + 22q^{49} - 5q^{50} - 21q^{51} - 5q^{52} - 9q^{53} + 31q^{54} - 28q^{55} + 6q^{56} + 10q^{57} - 24q^{58} - 28q^{59} - 17q^{60} + 23q^{61} + 28q^{62} - 27q^{63} + 34q^{64} - 6q^{65} + 16q^{66} - 51q^{67} + 8q^{68} - 17q^{69} - 2q^{70} - 31q^{71} - 38q^{72} - 26q^{73} + 36q^{74} - 109q^{75} - 34q^{76} - 28q^{77} + 9q^{78} - 36q^{79} + 7q^{80} + 6q^{81} - 9q^{82} - 10q^{83} - 32q^{85} + 24q^{86} - 8q^{87} - 4q^{88} - 34q^{89} - 22q^{90} - 41q^{91} - 24q^{92} - 33q^{93} + 29q^{94} - 7q^{95} + 10q^{96} - 56q^{97} - 22q^{98} - 28q^{99} + O(q^{100}) \)

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
\(3\) 1.61503 0.932438 0.466219 0.884669i \(-0.345616\pi\)
0.466219 + 0.884669i \(0.345616\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.67661 −1.19702 −0.598508 0.801117i \(-0.704240\pi\)
−0.598508 + 0.801117i \(0.704240\pi\)
\(6\) −1.61503 −0.659333
\(7\) −0.794060 −0.300127 −0.150063 0.988676i \(-0.547948\pi\)
−0.150063 + 0.988676i \(0.547948\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.391676 −0.130559
\(10\) 2.67661 0.846418
\(11\) −2.37029 −0.714670 −0.357335 0.933976i \(-0.616315\pi\)
−0.357335 + 0.933976i \(0.616315\pi\)
\(12\) 1.61503 0.466219
\(13\) −0.106159 −0.0294431 −0.0147216 0.999892i \(-0.504686\pi\)
−0.0147216 + 0.999892i \(0.504686\pi\)
\(14\) 0.794060 0.212222
\(15\) −4.32281 −1.11614
\(16\) 1.00000 0.250000
\(17\) 2.83751 0.688198 0.344099 0.938933i \(-0.388184\pi\)
0.344099 + 0.938933i \(0.388184\pi\)
\(18\) 0.391676 0.0923190
\(19\) −1.00000 −0.229416
\(20\) −2.67661 −0.598508
\(21\) −1.28243 −0.279850
\(22\) 2.37029 0.505348
\(23\) 6.31079 1.31589 0.657945 0.753066i \(-0.271426\pi\)
0.657945 + 0.753066i \(0.271426\pi\)
\(24\) −1.61503 −0.329667
\(25\) 2.16424 0.432848
\(26\) 0.106159 0.0208194
\(27\) −5.47766 −1.05418
\(28\) −0.794060 −0.150063
\(29\) 1.48726 0.276178 0.138089 0.990420i \(-0.455904\pi\)
0.138089 + 0.990420i \(0.455904\pi\)
\(30\) 4.32281 0.789233
\(31\) 7.04611 1.26552 0.632760 0.774348i \(-0.281922\pi\)
0.632760 + 0.774348i \(0.281922\pi\)
\(32\) −1.00000 −0.176777
\(33\) −3.82810 −0.666386
\(34\) −2.83751 −0.486629
\(35\) 2.12539 0.359256
\(36\) −0.391676 −0.0652794
\(37\) 8.75364 1.43909 0.719545 0.694446i \(-0.244350\pi\)
0.719545 + 0.694446i \(0.244350\pi\)
\(38\) 1.00000 0.162221
\(39\) −0.171450 −0.0274539
\(40\) 2.67661 0.423209
\(41\) −9.87170 −1.54170 −0.770851 0.637016i \(-0.780168\pi\)
−0.770851 + 0.637016i \(0.780168\pi\)
\(42\) 1.28243 0.197884
\(43\) 0.390722 0.0595846 0.0297923 0.999556i \(-0.490515\pi\)
0.0297923 + 0.999556i \(0.490515\pi\)
\(44\) −2.37029 −0.357335
\(45\) 1.04836 0.156281
\(46\) −6.31079 −0.930475
\(47\) 10.5003 1.53163 0.765813 0.643063i \(-0.222337\pi\)
0.765813 + 0.643063i \(0.222337\pi\)
\(48\) 1.61503 0.233110
\(49\) −6.36947 −0.909924
\(50\) −2.16424 −0.306070
\(51\) 4.58267 0.641702
\(52\) −0.106159 −0.0147216
\(53\) −3.80976 −0.523310 −0.261655 0.965161i \(-0.584268\pi\)
−0.261655 + 0.965161i \(0.584268\pi\)
\(54\) 5.47766 0.745415
\(55\) 6.34435 0.855472
\(56\) 0.794060 0.106111
\(57\) −1.61503 −0.213916
\(58\) −1.48726 −0.195287
\(59\) 7.62248 0.992362 0.496181 0.868219i \(-0.334735\pi\)
0.496181 + 0.868219i \(0.334735\pi\)
\(60\) −4.32281 −0.558072
\(61\) −7.41888 −0.949890 −0.474945 0.880016i \(-0.657532\pi\)
−0.474945 + 0.880016i \(0.657532\pi\)
\(62\) −7.04611 −0.894857
\(63\) 0.311015 0.0391842
\(64\) 1.00000 0.125000
\(65\) 0.284145 0.0352439
\(66\) 3.82810 0.471206
\(67\) −7.63201 −0.932399 −0.466199 0.884680i \(-0.654377\pi\)
−0.466199 + 0.884680i \(0.654377\pi\)
\(68\) 2.83751 0.344099
\(69\) 10.1921 1.22699
\(70\) −2.12539 −0.254033
\(71\) 5.42396 0.643706 0.321853 0.946790i \(-0.395694\pi\)
0.321853 + 0.946790i \(0.395694\pi\)
\(72\) 0.391676 0.0461595
\(73\) −4.28900 −0.501989 −0.250995 0.967989i \(-0.580758\pi\)
−0.250995 + 0.967989i \(0.580758\pi\)
\(74\) −8.75364 −1.01759
\(75\) 3.49531 0.403604
\(76\) −1.00000 −0.114708
\(77\) 1.88216 0.214492
\(78\) 0.171450 0.0194128
\(79\) 11.6390 1.30949 0.654747 0.755848i \(-0.272775\pi\)
0.654747 + 0.755848i \(0.272775\pi\)
\(80\) −2.67661 −0.299254
\(81\) −7.67156 −0.852396
\(82\) 9.87170 1.09015
\(83\) 11.4882 1.26099 0.630497 0.776192i \(-0.282851\pi\)
0.630497 + 0.776192i \(0.282851\pi\)
\(84\) −1.28243 −0.139925
\(85\) −7.59491 −0.823784
\(86\) −0.390722 −0.0421327
\(87\) 2.40198 0.257519
\(88\) 2.37029 0.252674
\(89\) −3.26256 −0.345831 −0.172915 0.984937i \(-0.555319\pi\)
−0.172915 + 0.984937i \(0.555319\pi\)
\(90\) −1.04836 −0.110507
\(91\) 0.0842964 0.00883667
\(92\) 6.31079 0.657945
\(93\) 11.3797 1.18002
\(94\) −10.5003 −1.08302
\(95\) 2.67661 0.274614
\(96\) −1.61503 −0.164833
\(97\) −9.02393 −0.916241 −0.458121 0.888890i \(-0.651477\pi\)
−0.458121 + 0.888890i \(0.651477\pi\)
\(98\) 6.36947 0.643413
\(99\) 0.928388 0.0933065
\(100\) 2.16424 0.216424
\(101\) −7.20520 −0.716944 −0.358472 0.933540i \(-0.616702\pi\)
−0.358472 + 0.933540i \(0.616702\pi\)
\(102\) −4.58267 −0.453752
\(103\) −15.6889 −1.54587 −0.772935 0.634485i \(-0.781212\pi\)
−0.772935 + 0.634485i \(0.781212\pi\)
\(104\) 0.106159 0.0104097
\(105\) 3.43257 0.334985
\(106\) 3.80976 0.370036
\(107\) −3.36029 −0.324851 −0.162426 0.986721i \(-0.551932\pi\)
−0.162426 + 0.986721i \(0.551932\pi\)
\(108\) −5.47766 −0.527088
\(109\) −14.4527 −1.38431 −0.692156 0.721748i \(-0.743339\pi\)
−0.692156 + 0.721748i \(0.743339\pi\)
\(110\) −6.34435 −0.604910
\(111\) 14.1374 1.34186
\(112\) −0.794060 −0.0750317
\(113\) 12.5063 1.17649 0.588247 0.808681i \(-0.299818\pi\)
0.588247 + 0.808681i \(0.299818\pi\)
\(114\) 1.61503 0.151261
\(115\) −16.8915 −1.57514
\(116\) 1.48726 0.138089
\(117\) 0.0415799 0.00384406
\(118\) −7.62248 −0.701706
\(119\) −2.25316 −0.206547
\(120\) 4.32281 0.394616
\(121\) −5.38171 −0.489246
\(122\) 7.41888 0.671674
\(123\) −15.9431 −1.43754
\(124\) 7.04611 0.632760
\(125\) 7.59022 0.678890
\(126\) −0.311015 −0.0277074
\(127\) −10.7502 −0.953923 −0.476961 0.878924i \(-0.658262\pi\)
−0.476961 + 0.878924i \(0.658262\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0.631029 0.0555590
\(130\) −0.284145 −0.0249212
\(131\) −2.08313 −0.182004 −0.0910022 0.995851i \(-0.529007\pi\)
−0.0910022 + 0.995851i \(0.529007\pi\)
\(132\) −3.82810 −0.333193
\(133\) 0.794060 0.0688538
\(134\) 7.63201 0.659305
\(135\) 14.6616 1.26187
\(136\) −2.83751 −0.243315
\(137\) 9.49257 0.811005 0.405503 0.914094i \(-0.367096\pi\)
0.405503 + 0.914094i \(0.367096\pi\)
\(138\) −10.1921 −0.867610
\(139\) 19.3394 1.64035 0.820174 0.572113i \(-0.193876\pi\)
0.820174 + 0.572113i \(0.193876\pi\)
\(140\) 2.12539 0.179628
\(141\) 16.9583 1.42815
\(142\) −5.42396 −0.455169
\(143\) 0.251627 0.0210421
\(144\) −0.391676 −0.0326397
\(145\) −3.98083 −0.330590
\(146\) 4.28900 0.354960
\(147\) −10.2869 −0.848448
\(148\) 8.75364 0.719545
\(149\) 3.91892 0.321051 0.160525 0.987032i \(-0.448681\pi\)
0.160525 + 0.987032i \(0.448681\pi\)
\(150\) −3.49531 −0.285391
\(151\) −6.72199 −0.547028 −0.273514 0.961868i \(-0.588186\pi\)
−0.273514 + 0.961868i \(0.588186\pi\)
\(152\) 1.00000 0.0811107
\(153\) −1.11139 −0.0898503
\(154\) −1.88216 −0.151668
\(155\) −18.8597 −1.51485
\(156\) −0.171450 −0.0137270
\(157\) −14.1050 −1.12570 −0.562851 0.826558i \(-0.690296\pi\)
−0.562851 + 0.826558i \(0.690296\pi\)
\(158\) −11.6390 −0.925952
\(159\) −6.15287 −0.487954
\(160\) 2.67661 0.211605
\(161\) −5.01115 −0.394934
\(162\) 7.67156 0.602735
\(163\) −10.7606 −0.842837 −0.421419 0.906866i \(-0.638468\pi\)
−0.421419 + 0.906866i \(0.638468\pi\)
\(164\) −9.87170 −0.770851
\(165\) 10.2463 0.797675
\(166\) −11.4882 −0.891657
\(167\) −7.42266 −0.574383 −0.287192 0.957873i \(-0.592722\pi\)
−0.287192 + 0.957873i \(0.592722\pi\)
\(168\) 1.28243 0.0989418
\(169\) −12.9887 −0.999133
\(170\) 7.59491 0.582503
\(171\) 0.391676 0.0299522
\(172\) 0.390722 0.0297923
\(173\) 1.08260 0.0823088 0.0411544 0.999153i \(-0.486896\pi\)
0.0411544 + 0.999153i \(0.486896\pi\)
\(174\) −2.40198 −0.182093
\(175\) −1.71854 −0.129909
\(176\) −2.37029 −0.178668
\(177\) 12.3105 0.925317
\(178\) 3.26256 0.244539
\(179\) −21.7524 −1.62585 −0.812926 0.582367i \(-0.802127\pi\)
−0.812926 + 0.582367i \(0.802127\pi\)
\(180\) 1.04836 0.0781405
\(181\) 8.99403 0.668521 0.334261 0.942481i \(-0.391513\pi\)
0.334261 + 0.942481i \(0.391513\pi\)
\(182\) −0.0842964 −0.00624847
\(183\) −11.9817 −0.885714
\(184\) −6.31079 −0.465237
\(185\) −23.4301 −1.72261
\(186\) −11.3797 −0.834399
\(187\) −6.72574 −0.491835
\(188\) 10.5003 0.765813
\(189\) 4.34959 0.316386
\(190\) −2.67661 −0.194182
\(191\) −19.0289 −1.37688 −0.688442 0.725291i \(-0.741705\pi\)
−0.688442 + 0.725291i \(0.741705\pi\)
\(192\) 1.61503 0.116555
\(193\) 4.55152 0.327626 0.163813 0.986491i \(-0.447621\pi\)
0.163813 + 0.986491i \(0.447621\pi\)
\(194\) 9.02393 0.647880
\(195\) 0.458904 0.0328628
\(196\) −6.36947 −0.454962
\(197\) 6.67082 0.475277 0.237638 0.971354i \(-0.423627\pi\)
0.237638 + 0.971354i \(0.423627\pi\)
\(198\) −0.928388 −0.0659776
\(199\) −0.869939 −0.0616683 −0.0308342 0.999525i \(-0.509816\pi\)
−0.0308342 + 0.999525i \(0.509816\pi\)
\(200\) −2.16424 −0.153035
\(201\) −12.3259 −0.869404
\(202\) 7.20520 0.506956
\(203\) −1.18098 −0.0828884
\(204\) 4.58267 0.320851
\(205\) 26.4227 1.84544
\(206\) 15.6889 1.09310
\(207\) −2.47179 −0.171801
\(208\) −0.106159 −0.00736078
\(209\) 2.37029 0.163957
\(210\) −3.43257 −0.236870
\(211\) −1.00000 −0.0688428
\(212\) −3.80976 −0.261655
\(213\) 8.75987 0.600216
\(214\) 3.36029 0.229705
\(215\) −1.04581 −0.0713237
\(216\) 5.47766 0.372708
\(217\) −5.59504 −0.379816
\(218\) 14.4527 0.978857
\(219\) −6.92686 −0.468074
\(220\) 6.34435 0.427736
\(221\) −0.301227 −0.0202627
\(222\) −14.1374 −0.948840
\(223\) −1.07002 −0.0716541 −0.0358271 0.999358i \(-0.511407\pi\)
−0.0358271 + 0.999358i \(0.511407\pi\)
\(224\) 0.794060 0.0530554
\(225\) −0.847682 −0.0565121
\(226\) −12.5063 −0.831907
\(227\) 20.7730 1.37875 0.689377 0.724402i \(-0.257884\pi\)
0.689377 + 0.724402i \(0.257884\pi\)
\(228\) −1.61503 −0.106958
\(229\) −14.6149 −0.965781 −0.482890 0.875681i \(-0.660413\pi\)
−0.482890 + 0.875681i \(0.660413\pi\)
\(230\) 16.8915 1.11379
\(231\) 3.03974 0.200000
\(232\) −1.48726 −0.0976437
\(233\) 24.6342 1.61384 0.806919 0.590662i \(-0.201133\pi\)
0.806919 + 0.590662i \(0.201133\pi\)
\(234\) −0.0415799 −0.00271816
\(235\) −28.1052 −1.83338
\(236\) 7.62248 0.496181
\(237\) 18.7974 1.22102
\(238\) 2.25316 0.146050
\(239\) 4.79226 0.309986 0.154993 0.987916i \(-0.450465\pi\)
0.154993 + 0.987916i \(0.450465\pi\)
\(240\) −4.32281 −0.279036
\(241\) −24.6089 −1.58520 −0.792600 0.609742i \(-0.791273\pi\)
−0.792600 + 0.609742i \(0.791273\pi\)
\(242\) 5.38171 0.345949
\(243\) 4.04318 0.259370
\(244\) −7.41888 −0.474945
\(245\) 17.0486 1.08919
\(246\) 15.9431 1.01650
\(247\) 0.106159 0.00675472
\(248\) −7.04611 −0.447429
\(249\) 18.5538 1.17580
\(250\) −7.59022 −0.480048
\(251\) −7.69995 −0.486017 −0.243008 0.970024i \(-0.578134\pi\)
−0.243008 + 0.970024i \(0.578134\pi\)
\(252\) 0.311015 0.0195921
\(253\) −14.9584 −0.940427
\(254\) 10.7502 0.674525
\(255\) −12.2660 −0.768128
\(256\) 1.00000 0.0625000
\(257\) −19.9583 −1.24497 −0.622483 0.782633i \(-0.713876\pi\)
−0.622483 + 0.782633i \(0.713876\pi\)
\(258\) −0.631029 −0.0392861
\(259\) −6.95092 −0.431909
\(260\) 0.284145 0.0176220
\(261\) −0.582526 −0.0360575
\(262\) 2.08313 0.128696
\(263\) −13.1179 −0.808883 −0.404441 0.914564i \(-0.632534\pi\)
−0.404441 + 0.914564i \(0.632534\pi\)
\(264\) 3.82810 0.235603
\(265\) 10.1972 0.626411
\(266\) −0.794060 −0.0486870
\(267\) −5.26913 −0.322466
\(268\) −7.63201 −0.466199
\(269\) −20.2656 −1.23562 −0.617808 0.786329i \(-0.711979\pi\)
−0.617808 + 0.786329i \(0.711979\pi\)
\(270\) −14.6616 −0.892274
\(271\) −20.3477 −1.23603 −0.618017 0.786165i \(-0.712064\pi\)
−0.618017 + 0.786165i \(0.712064\pi\)
\(272\) 2.83751 0.172049
\(273\) 0.136141 0.00823965
\(274\) −9.49257 −0.573467
\(275\) −5.12988 −0.309344
\(276\) 10.1921 0.613493
\(277\) 2.99857 0.180166 0.0900832 0.995934i \(-0.471287\pi\)
0.0900832 + 0.995934i \(0.471287\pi\)
\(278\) −19.3394 −1.15990
\(279\) −2.75980 −0.165225
\(280\) −2.12539 −0.127016
\(281\) −21.8688 −1.30458 −0.652291 0.757968i \(-0.726192\pi\)
−0.652291 + 0.757968i \(0.726192\pi\)
\(282\) −16.9583 −1.00985
\(283\) 13.9374 0.828492 0.414246 0.910165i \(-0.364045\pi\)
0.414246 + 0.910165i \(0.364045\pi\)
\(284\) 5.42396 0.321853
\(285\) 4.32281 0.256061
\(286\) −0.251627 −0.0148790
\(287\) 7.83873 0.462706
\(288\) 0.391676 0.0230798
\(289\) −8.94852 −0.526384
\(290\) 3.98083 0.233762
\(291\) −14.5739 −0.854338
\(292\) −4.28900 −0.250995
\(293\) 2.82622 0.165110 0.0825548 0.996587i \(-0.473692\pi\)
0.0825548 + 0.996587i \(0.473692\pi\)
\(294\) 10.2869 0.599943
\(295\) −20.4024 −1.18787
\(296\) −8.75364 −0.508795
\(297\) 12.9837 0.753388
\(298\) −3.91892 −0.227017
\(299\) −0.669945 −0.0387439
\(300\) 3.49531 0.201802
\(301\) −0.310257 −0.0178829
\(302\) 6.72199 0.386807
\(303\) −11.6366 −0.668506
\(304\) −1.00000 −0.0573539
\(305\) 19.8574 1.13703
\(306\) 1.11139 0.0635337
\(307\) 4.32725 0.246969 0.123485 0.992346i \(-0.460593\pi\)
0.123485 + 0.992346i \(0.460593\pi\)
\(308\) 1.88216 0.107246
\(309\) −25.3380 −1.44143
\(310\) 18.8597 1.07116
\(311\) −8.72764 −0.494899 −0.247450 0.968901i \(-0.579592\pi\)
−0.247450 + 0.968901i \(0.579592\pi\)
\(312\) 0.171450 0.00970642
\(313\) −11.6611 −0.659127 −0.329563 0.944133i \(-0.606902\pi\)
−0.329563 + 0.944133i \(0.606902\pi\)
\(314\) 14.1050 0.795992
\(315\) −0.832465 −0.0469041
\(316\) 11.6390 0.654747
\(317\) −14.8110 −0.831868 −0.415934 0.909395i \(-0.636545\pi\)
−0.415934 + 0.909395i \(0.636545\pi\)
\(318\) 6.15287 0.345036
\(319\) −3.52525 −0.197376
\(320\) −2.67661 −0.149627
\(321\) −5.42697 −0.302904
\(322\) 5.01115 0.279260
\(323\) −2.83751 −0.157883
\(324\) −7.67156 −0.426198
\(325\) −0.229753 −0.0127444
\(326\) 10.7606 0.595976
\(327\) −23.3415 −1.29079
\(328\) 9.87170 0.545074
\(329\) −8.33788 −0.459682
\(330\) −10.2463 −0.564041
\(331\) 22.1664 1.21838 0.609189 0.793025i \(-0.291495\pi\)
0.609189 + 0.793025i \(0.291495\pi\)
\(332\) 11.4882 0.630497
\(333\) −3.42860 −0.187886
\(334\) 7.42266 0.406150
\(335\) 20.4279 1.11610
\(336\) −1.28243 −0.0699624
\(337\) −22.9888 −1.25228 −0.626139 0.779711i \(-0.715366\pi\)
−0.626139 + 0.779711i \(0.715366\pi\)
\(338\) 12.9887 0.706494
\(339\) 20.1981 1.09701
\(340\) −7.59491 −0.411892
\(341\) −16.7014 −0.904429
\(342\) −0.391676 −0.0211794
\(343\) 10.6162 0.573219
\(344\) −0.390722 −0.0210663
\(345\) −27.2803 −1.46872
\(346\) −1.08260 −0.0582011
\(347\) 13.0404 0.700046 0.350023 0.936741i \(-0.386174\pi\)
0.350023 + 0.936741i \(0.386174\pi\)
\(348\) 2.40198 0.128760
\(349\) 0.138800 0.00742977 0.00371489 0.999993i \(-0.498818\pi\)
0.00371489 + 0.999993i \(0.498818\pi\)
\(350\) 1.71854 0.0918597
\(351\) 0.581502 0.0310383
\(352\) 2.37029 0.126337
\(353\) −2.97942 −0.158579 −0.0792894 0.996852i \(-0.525265\pi\)
−0.0792894 + 0.996852i \(0.525265\pi\)
\(354\) −12.3105 −0.654298
\(355\) −14.5178 −0.770527
\(356\) −3.26256 −0.172915
\(357\) −3.63892 −0.192592
\(358\) 21.7524 1.14965
\(359\) −11.5898 −0.611688 −0.305844 0.952082i \(-0.598939\pi\)
−0.305844 + 0.952082i \(0.598939\pi\)
\(360\) −1.04836 −0.0552537
\(361\) 1.00000 0.0526316
\(362\) −8.99403 −0.472716
\(363\) −8.69163 −0.456192
\(364\) 0.0842964 0.00441833
\(365\) 11.4800 0.600889
\(366\) 11.9817 0.626294
\(367\) −13.4180 −0.700413 −0.350206 0.936673i \(-0.613889\pi\)
−0.350206 + 0.936673i \(0.613889\pi\)
\(368\) 6.31079 0.328972
\(369\) 3.86651 0.201283
\(370\) 23.4301 1.21807
\(371\) 3.02518 0.157059
\(372\) 11.3797 0.590009
\(373\) 2.65714 0.137582 0.0687908 0.997631i \(-0.478086\pi\)
0.0687908 + 0.997631i \(0.478086\pi\)
\(374\) 6.72574 0.347780
\(375\) 12.2584 0.633023
\(376\) −10.5003 −0.541512
\(377\) −0.157886 −0.00813155
\(378\) −4.34959 −0.223719
\(379\) 4.12094 0.211678 0.105839 0.994383i \(-0.466247\pi\)
0.105839 + 0.994383i \(0.466247\pi\)
\(380\) 2.67661 0.137307
\(381\) −17.3618 −0.889474
\(382\) 19.0289 0.973605
\(383\) 12.3040 0.628707 0.314354 0.949306i \(-0.398212\pi\)
0.314354 + 0.949306i \(0.398212\pi\)
\(384\) −1.61503 −0.0824167
\(385\) −5.03780 −0.256750
\(386\) −4.55152 −0.231666
\(387\) −0.153037 −0.00777929
\(388\) −9.02393 −0.458121
\(389\) −19.0985 −0.968331 −0.484166 0.874976i \(-0.660877\pi\)
−0.484166 + 0.874976i \(0.660877\pi\)
\(390\) −0.458904 −0.0232375
\(391\) 17.9069 0.905593
\(392\) 6.36947 0.321707
\(393\) −3.36433 −0.169708
\(394\) −6.67082 −0.336071
\(395\) −31.1531 −1.56748
\(396\) 0.928388 0.0466532
\(397\) 4.79234 0.240521 0.120260 0.992742i \(-0.461627\pi\)
0.120260 + 0.992742i \(0.461627\pi\)
\(398\) 0.869939 0.0436061
\(399\) 1.28243 0.0642019
\(400\) 2.16424 0.108212
\(401\) −5.86810 −0.293039 −0.146520 0.989208i \(-0.546807\pi\)
−0.146520 + 0.989208i \(0.546807\pi\)
\(402\) 12.3259 0.614762
\(403\) −0.748006 −0.0372609
\(404\) −7.20520 −0.358472
\(405\) 20.5338 1.02033
\(406\) 1.18098 0.0586110
\(407\) −20.7487 −1.02847
\(408\) −4.58267 −0.226876
\(409\) 4.48311 0.221676 0.110838 0.993839i \(-0.464647\pi\)
0.110838 + 0.993839i \(0.464647\pi\)
\(410\) −26.4227 −1.30492
\(411\) 15.3308 0.756212
\(412\) −15.6889 −0.772935
\(413\) −6.05271 −0.297834
\(414\) 2.47179 0.121482
\(415\) −30.7494 −1.50943
\(416\) 0.106159 0.00520486
\(417\) 31.2338 1.52952
\(418\) −2.37029 −0.115935
\(419\) −4.09844 −0.200222 −0.100111 0.994976i \(-0.531920\pi\)
−0.100111 + 0.994976i \(0.531920\pi\)
\(420\) 3.43257 0.167492
\(421\) −37.7803 −1.84130 −0.920650 0.390388i \(-0.872341\pi\)
−0.920650 + 0.390388i \(0.872341\pi\)
\(422\) 1.00000 0.0486792
\(423\) −4.11272 −0.199967
\(424\) 3.80976 0.185018
\(425\) 6.14106 0.297885
\(426\) −8.75987 −0.424417
\(427\) 5.89104 0.285087
\(428\) −3.36029 −0.162426
\(429\) 0.406386 0.0196205
\(430\) 1.04581 0.0504335
\(431\) −9.13044 −0.439798 −0.219899 0.975523i \(-0.570573\pi\)
−0.219899 + 0.975523i \(0.570573\pi\)
\(432\) −5.47766 −0.263544
\(433\) 30.4415 1.46293 0.731463 0.681881i \(-0.238838\pi\)
0.731463 + 0.681881i \(0.238838\pi\)
\(434\) 5.59504 0.268570
\(435\) −6.42916 −0.308255
\(436\) −14.4527 −0.692156
\(437\) −6.31079 −0.301886
\(438\) 6.92686 0.330978
\(439\) 23.2548 1.10989 0.554947 0.831886i \(-0.312739\pi\)
0.554947 + 0.831886i \(0.312739\pi\)
\(440\) −6.34435 −0.302455
\(441\) 2.49477 0.118799
\(442\) 0.301227 0.0143279
\(443\) −19.8758 −0.944328 −0.472164 0.881511i \(-0.656527\pi\)
−0.472164 + 0.881511i \(0.656527\pi\)
\(444\) 14.1374 0.670931
\(445\) 8.73260 0.413965
\(446\) 1.07002 0.0506671
\(447\) 6.32918 0.299360
\(448\) −0.794060 −0.0375158
\(449\) −19.1037 −0.901559 −0.450779 0.892635i \(-0.648854\pi\)
−0.450779 + 0.892635i \(0.648854\pi\)
\(450\) 0.847682 0.0399601
\(451\) 23.3988 1.10181
\(452\) 12.5063 0.588247
\(453\) −10.8562 −0.510069
\(454\) −20.7730 −0.974927
\(455\) −0.225629 −0.0105776
\(456\) 1.61503 0.0756307
\(457\) 17.7529 0.830444 0.415222 0.909720i \(-0.363704\pi\)
0.415222 + 0.909720i \(0.363704\pi\)
\(458\) 14.6149 0.682910
\(459\) −15.5429 −0.725482
\(460\) −16.8915 −0.787571
\(461\) −4.12105 −0.191936 −0.0959682 0.995384i \(-0.530595\pi\)
−0.0959682 + 0.995384i \(0.530595\pi\)
\(462\) −3.03974 −0.141421
\(463\) −22.8859 −1.06360 −0.531799 0.846871i \(-0.678484\pi\)
−0.531799 + 0.846871i \(0.678484\pi\)
\(464\) 1.48726 0.0690445
\(465\) −30.4590 −1.41250
\(466\) −24.6342 −1.14116
\(467\) −15.3207 −0.708956 −0.354478 0.935064i \(-0.615341\pi\)
−0.354478 + 0.935064i \(0.615341\pi\)
\(468\) 0.0415799 0.00192203
\(469\) 6.06028 0.279838
\(470\) 28.1052 1.29640
\(471\) −22.7800 −1.04965
\(472\) −7.62248 −0.350853
\(473\) −0.926127 −0.0425833
\(474\) −18.7974 −0.863393
\(475\) −2.16424 −0.0993022
\(476\) −2.25316 −0.103273
\(477\) 1.49219 0.0683227
\(478\) −4.79226 −0.219193
\(479\) 18.8974 0.863445 0.431722 0.902007i \(-0.357906\pi\)
0.431722 + 0.902007i \(0.357906\pi\)
\(480\) 4.32281 0.197308
\(481\) −0.929276 −0.0423713
\(482\) 24.6089 1.12091
\(483\) −8.09315 −0.368251
\(484\) −5.38171 −0.244623
\(485\) 24.1535 1.09676
\(486\) −4.04318 −0.183402
\(487\) 37.3467 1.69234 0.846171 0.532911i \(-0.178902\pi\)
0.846171 + 0.532911i \(0.178902\pi\)
\(488\) 7.41888 0.335837
\(489\) −17.3787 −0.785894
\(490\) −17.0486 −0.770176
\(491\) 38.7616 1.74929 0.874644 0.484765i \(-0.161095\pi\)
0.874644 + 0.484765i \(0.161095\pi\)
\(492\) −15.9431 −0.718771
\(493\) 4.22013 0.190065
\(494\) −0.106159 −0.00477631
\(495\) −2.48493 −0.111689
\(496\) 7.04611 0.316380
\(497\) −4.30696 −0.193193
\(498\) −18.5538 −0.831415
\(499\) −1.81417 −0.0812136 −0.0406068 0.999175i \(-0.512929\pi\)
−0.0406068 + 0.999175i \(0.512929\pi\)
\(500\) 7.59022 0.339445
\(501\) −11.9878 −0.535577
\(502\) 7.69995 0.343666
\(503\) −25.6164 −1.14218 −0.571090 0.820887i \(-0.693479\pi\)
−0.571090 + 0.820887i \(0.693479\pi\)
\(504\) −0.311015 −0.0138537
\(505\) 19.2855 0.858194
\(506\) 14.9584 0.664983
\(507\) −20.9772 −0.931630
\(508\) −10.7502 −0.476961
\(509\) −18.0158 −0.798534 −0.399267 0.916835i \(-0.630735\pi\)
−0.399267 + 0.916835i \(0.630735\pi\)
\(510\) 12.2660 0.543148
\(511\) 3.40572 0.150660
\(512\) −1.00000 −0.0441942
\(513\) 5.47766 0.241845
\(514\) 19.9583 0.880324
\(515\) 41.9930 1.85043
\(516\) 0.631029 0.0277795
\(517\) −24.8888 −1.09461
\(518\) 6.95092 0.305406
\(519\) 1.74844 0.0767479
\(520\) −0.284145 −0.0124606
\(521\) −2.00623 −0.0878946 −0.0439473 0.999034i \(-0.513993\pi\)
−0.0439473 + 0.999034i \(0.513993\pi\)
\(522\) 0.582526 0.0254965
\(523\) 3.17511 0.138838 0.0694189 0.997588i \(-0.477885\pi\)
0.0694189 + 0.997588i \(0.477885\pi\)
\(524\) −2.08313 −0.0910022
\(525\) −2.77549 −0.121132
\(526\) 13.1179 0.571966
\(527\) 19.9934 0.870928
\(528\) −3.82810 −0.166596
\(529\) 16.8260 0.731566
\(530\) −10.1972 −0.442939
\(531\) −2.98555 −0.129562
\(532\) 0.794060 0.0344269
\(533\) 1.04797 0.0453925
\(534\) 5.26913 0.228018
\(535\) 8.99418 0.388852
\(536\) 7.63201 0.329653
\(537\) −35.1308 −1.51601
\(538\) 20.2656 0.873712
\(539\) 15.0975 0.650296
\(540\) 14.6616 0.630933
\(541\) −22.2056 −0.954692 −0.477346 0.878715i \(-0.658401\pi\)
−0.477346 + 0.878715i \(0.658401\pi\)
\(542\) 20.3477 0.874008
\(543\) 14.5256 0.623355
\(544\) −2.83751 −0.121657
\(545\) 38.6841 1.65705
\(546\) −0.136141 −0.00582631
\(547\) 10.9701 0.469047 0.234524 0.972110i \(-0.424647\pi\)
0.234524 + 0.972110i \(0.424647\pi\)
\(548\) 9.49257 0.405503
\(549\) 2.90580 0.124016
\(550\) 5.12988 0.218739
\(551\) −1.48726 −0.0633596
\(552\) −10.1921 −0.433805
\(553\) −9.24209 −0.393014
\(554\) −2.99857 −0.127397
\(555\) −37.8403 −1.60623
\(556\) 19.3394 0.820174
\(557\) 36.7934 1.55899 0.779494 0.626410i \(-0.215476\pi\)
0.779494 + 0.626410i \(0.215476\pi\)
\(558\) 2.75980 0.116831
\(559\) −0.0414786 −0.00175436
\(560\) 2.12539 0.0898141
\(561\) −10.8623 −0.458605
\(562\) 21.8688 0.922479
\(563\) 43.6752 1.84069 0.920346 0.391105i \(-0.127907\pi\)
0.920346 + 0.391105i \(0.127907\pi\)
\(564\) 16.9583 0.714074
\(565\) −33.4745 −1.40828
\(566\) −13.9374 −0.585832
\(567\) 6.09168 0.255827
\(568\) −5.42396 −0.227584
\(569\) −46.6241 −1.95458 −0.977291 0.211900i \(-0.932035\pi\)
−0.977291 + 0.211900i \(0.932035\pi\)
\(570\) −4.32281 −0.181062
\(571\) −1.34834 −0.0564262 −0.0282131 0.999602i \(-0.508982\pi\)
−0.0282131 + 0.999602i \(0.508982\pi\)
\(572\) 0.251627 0.0105211
\(573\) −30.7323 −1.28386
\(574\) −7.83873 −0.327182
\(575\) 13.6581 0.569581
\(576\) −0.391676 −0.0163198
\(577\) −41.9159 −1.74498 −0.872492 0.488629i \(-0.837497\pi\)
−0.872492 + 0.488629i \(0.837497\pi\)
\(578\) 8.94852 0.372209
\(579\) 7.35085 0.305491
\(580\) −3.98083 −0.165295
\(581\) −9.12232 −0.378458
\(582\) 14.5739 0.604108
\(583\) 9.03024 0.373994
\(584\) 4.28900 0.177480
\(585\) −0.111293 −0.00460140
\(586\) −2.82622 −0.116750
\(587\) −16.1647 −0.667187 −0.333593 0.942717i \(-0.608261\pi\)
−0.333593 + 0.942717i \(0.608261\pi\)
\(588\) −10.2869 −0.424224
\(589\) −7.04611 −0.290330
\(590\) 20.4024 0.839954
\(591\) 10.7736 0.443166
\(592\) 8.75364 0.359773
\(593\) −0.634611 −0.0260603 −0.0130302 0.999915i \(-0.504148\pi\)
−0.0130302 + 0.999915i \(0.504148\pi\)
\(594\) −12.9837 −0.532726
\(595\) 6.03082 0.247240
\(596\) 3.91892 0.160525
\(597\) −1.40498 −0.0575019
\(598\) 0.669945 0.0273961
\(599\) 10.4365 0.426422 0.213211 0.977006i \(-0.431608\pi\)
0.213211 + 0.977006i \(0.431608\pi\)
\(600\) −3.49531 −0.142696
\(601\) 4.34276 0.177145 0.0885725 0.996070i \(-0.471770\pi\)
0.0885725 + 0.996070i \(0.471770\pi\)
\(602\) 0.310257 0.0126451
\(603\) 2.98928 0.121733
\(604\) −6.72199 −0.273514
\(605\) 14.4047 0.585636
\(606\) 11.6366 0.472705
\(607\) −34.2146 −1.38873 −0.694364 0.719624i \(-0.744314\pi\)
−0.694364 + 0.719624i \(0.744314\pi\)
\(608\) 1.00000 0.0405554
\(609\) −1.90732 −0.0772883
\(610\) −19.8574 −0.804004
\(611\) −1.11470 −0.0450959
\(612\) −1.11139 −0.0449251
\(613\) 9.27916 0.374782 0.187391 0.982285i \(-0.439997\pi\)
0.187391 + 0.982285i \(0.439997\pi\)
\(614\) −4.32725 −0.174634
\(615\) 42.6735 1.72076
\(616\) −1.88216 −0.0758342
\(617\) 16.2739 0.655161 0.327581 0.944823i \(-0.393767\pi\)
0.327581 + 0.944823i \(0.393767\pi\)
\(618\) 25.3380 1.01924
\(619\) −3.72705 −0.149803 −0.0749014 0.997191i \(-0.523864\pi\)
−0.0749014 + 0.997191i \(0.523864\pi\)
\(620\) −18.8597 −0.757424
\(621\) −34.5683 −1.38718
\(622\) 8.72764 0.349947
\(623\) 2.59067 0.103793
\(624\) −0.171450 −0.00686348
\(625\) −31.1373 −1.24549
\(626\) 11.6611 0.466073
\(627\) 3.82810 0.152879
\(628\) −14.1050 −0.562851
\(629\) 24.8386 0.990379
\(630\) 0.832465 0.0331662
\(631\) 0.275452 0.0109656 0.00548279 0.999985i \(-0.498255\pi\)
0.00548279 + 0.999985i \(0.498255\pi\)
\(632\) −11.6390 −0.462976
\(633\) −1.61503 −0.0641917
\(634\) 14.8110 0.588219
\(635\) 28.7740 1.14186
\(636\) −6.15287 −0.243977
\(637\) 0.676175 0.0267910
\(638\) 3.52525 0.139566
\(639\) −2.12444 −0.0840415
\(640\) 2.67661 0.105802
\(641\) 32.5471 1.28553 0.642767 0.766061i \(-0.277786\pi\)
0.642767 + 0.766061i \(0.277786\pi\)
\(642\) 5.42697 0.214185
\(643\) −9.13382 −0.360203 −0.180101 0.983648i \(-0.557643\pi\)
−0.180101 + 0.983648i \(0.557643\pi\)
\(644\) −5.01115 −0.197467
\(645\) −1.68902 −0.0665050
\(646\) 2.83751 0.111640
\(647\) 3.01368 0.118480 0.0592401 0.998244i \(-0.481132\pi\)
0.0592401 + 0.998244i \(0.481132\pi\)
\(648\) 7.67156 0.301367
\(649\) −18.0675 −0.709212
\(650\) 0.229753 0.00901166
\(651\) −9.03616 −0.354155
\(652\) −10.7606 −0.421419
\(653\) 46.0687 1.80281 0.901404 0.432979i \(-0.142537\pi\)
0.901404 + 0.432979i \(0.142537\pi\)
\(654\) 23.3415 0.912724
\(655\) 5.57574 0.217862
\(656\) −9.87170 −0.385425
\(657\) 1.67990 0.0655391
\(658\) 8.33788 0.325044
\(659\) −19.4963 −0.759466 −0.379733 0.925096i \(-0.623984\pi\)
−0.379733 + 0.925096i \(0.623984\pi\)
\(660\) 10.2463 0.398837
\(661\) 36.1688 1.40680 0.703402 0.710793i \(-0.251664\pi\)
0.703402 + 0.710793i \(0.251664\pi\)
\(662\) −22.1664 −0.861523
\(663\) −0.486490 −0.0188937
\(664\) −11.4882 −0.445829
\(665\) −2.12539 −0.0824191
\(666\) 3.42860 0.132855
\(667\) 9.38581 0.363420
\(668\) −7.42266 −0.287192
\(669\) −1.72812 −0.0668130
\(670\) −20.4279 −0.789199
\(671\) 17.5849 0.678858
\(672\) 1.28243 0.0494709
\(673\) −10.4373 −0.402330 −0.201165 0.979557i \(-0.564473\pi\)
−0.201165 + 0.979557i \(0.564473\pi\)
\(674\) 22.9888 0.885495
\(675\) −11.8550 −0.456298
\(676\) −12.9887 −0.499567
\(677\) 0.0321498 0.00123562 0.000617810 1.00000i \(-0.499803\pi\)
0.000617810 1.00000i \(0.499803\pi\)
\(678\) −20.1981 −0.775702
\(679\) 7.16554 0.274988
\(680\) 7.59491 0.291252
\(681\) 33.5491 1.28560
\(682\) 16.7014 0.639528
\(683\) −9.61680 −0.367977 −0.183988 0.982928i \(-0.558901\pi\)
−0.183988 + 0.982928i \(0.558901\pi\)
\(684\) 0.391676 0.0149761
\(685\) −25.4079 −0.970787
\(686\) −10.6162 −0.405327
\(687\) −23.6035 −0.900531
\(688\) 0.390722 0.0148962
\(689\) 0.404439 0.0154079
\(690\) 27.2803 1.03854
\(691\) 3.38892 0.128921 0.0644603 0.997920i \(-0.479467\pi\)
0.0644603 + 0.997920i \(0.479467\pi\)
\(692\) 1.08260 0.0411544
\(693\) −0.737196 −0.0280038
\(694\) −13.0404 −0.495007
\(695\) −51.7641 −1.96352
\(696\) −2.40198 −0.0910467
\(697\) −28.0111 −1.06100
\(698\) −0.138800 −0.00525364
\(699\) 39.7849 1.50480
\(700\) −1.71854 −0.0649546
\(701\) 31.5518 1.19169 0.595847 0.803098i \(-0.296816\pi\)
0.595847 + 0.803098i \(0.296816\pi\)
\(702\) −0.581502 −0.0219474
\(703\) −8.75364 −0.330150
\(704\) −2.37029 −0.0893338
\(705\) −45.3908 −1.70952
\(706\) 2.97942 0.112132
\(707\) 5.72136 0.215174
\(708\) 12.3105 0.462658
\(709\) 12.0610 0.452960 0.226480 0.974016i \(-0.427278\pi\)
0.226480 + 0.974016i \(0.427278\pi\)
\(710\) 14.5178 0.544845
\(711\) −4.55873 −0.170966
\(712\) 3.26256 0.122270
\(713\) 44.4665 1.66528
\(714\) 3.63892 0.136183
\(715\) −0.673508 −0.0251878
\(716\) −21.7524 −0.812926
\(717\) 7.73965 0.289042
\(718\) 11.5898 0.432529
\(719\) 15.9690 0.595542 0.297771 0.954637i \(-0.403757\pi\)
0.297771 + 0.954637i \(0.403757\pi\)
\(720\) 1.04836 0.0390703
\(721\) 12.4579 0.463957
\(722\) −1.00000 −0.0372161
\(723\) −39.7442 −1.47810
\(724\) 8.99403 0.334261
\(725\) 3.21880 0.119543
\(726\) 8.69163 0.322577
\(727\) 2.15873 0.0800628 0.0400314 0.999198i \(-0.487254\pi\)
0.0400314 + 0.999198i \(0.487254\pi\)
\(728\) −0.0842964 −0.00312423
\(729\) 29.5445 1.09424
\(730\) −11.4800 −0.424893
\(731\) 1.10868 0.0410060
\(732\) −11.9817 −0.442857
\(733\) −38.2792 −1.41387 −0.706936 0.707277i \(-0.749923\pi\)
−0.706936 + 0.707277i \(0.749923\pi\)
\(734\) 13.4180 0.495267
\(735\) 27.5340 1.01561
\(736\) −6.31079 −0.232619
\(737\) 18.0901 0.666358
\(738\) −3.86651 −0.142328
\(739\) −7.41965 −0.272936 −0.136468 0.990644i \(-0.543575\pi\)
−0.136468 + 0.990644i \(0.543575\pi\)
\(740\) −23.4301 −0.861307
\(741\) 0.171450 0.00629836
\(742\) −3.02518 −0.111058
\(743\) 9.48034 0.347800 0.173900 0.984763i \(-0.444363\pi\)
0.173900 + 0.984763i \(0.444363\pi\)
\(744\) −11.3797 −0.417200
\(745\) −10.4894 −0.384303
\(746\) −2.65714 −0.0972849
\(747\) −4.49966 −0.164634
\(748\) −6.72574 −0.245917
\(749\) 2.66827 0.0974965
\(750\) −12.2584 −0.447615
\(751\) 6.79476 0.247944 0.123972 0.992286i \(-0.460437\pi\)
0.123972 + 0.992286i \(0.460437\pi\)
\(752\) 10.5003 0.382907
\(753\) −12.4357 −0.453180
\(754\) 0.157886 0.00574987
\(755\) 17.9921 0.654801
\(756\) 4.34959 0.158193
\(757\) 8.24416 0.299639 0.149820 0.988713i \(-0.452131\pi\)
0.149820 + 0.988713i \(0.452131\pi\)
\(758\) −4.12094 −0.149679
\(759\) −24.1583 −0.876891
\(760\) −2.67661 −0.0970908
\(761\) 0.585919 0.0212396 0.0106198 0.999944i \(-0.496620\pi\)
0.0106198 + 0.999944i \(0.496620\pi\)
\(762\) 17.3618 0.628953
\(763\) 11.4763 0.415469
\(764\) −19.0289 −0.688442
\(765\) 2.97475 0.107552
\(766\) −12.3040 −0.444563
\(767\) −0.809193 −0.0292183
\(768\) 1.61503 0.0582774
\(769\) −38.7781 −1.39837 −0.699187 0.714939i \(-0.746454\pi\)
−0.699187 + 0.714939i \(0.746454\pi\)
\(770\) 5.03780 0.181550
\(771\) −32.2333 −1.16085
\(772\) 4.55152 0.163813
\(773\) 42.2735 1.52047 0.760235 0.649648i \(-0.225084\pi\)
0.760235 + 0.649648i \(0.225084\pi\)
\(774\) 0.153037 0.00550079
\(775\) 15.2495 0.547778
\(776\) 9.02393 0.323940
\(777\) −11.2260 −0.402729
\(778\) 19.0985 0.684714
\(779\) 9.87170 0.353690
\(780\) 0.458904 0.0164314
\(781\) −12.8564 −0.460038
\(782\) −17.9069 −0.640351
\(783\) −8.14673 −0.291140
\(784\) −6.36947 −0.227481
\(785\) 37.7536 1.34748
\(786\) 3.36433 0.120002
\(787\) 41.0616 1.46369 0.731844 0.681472i \(-0.238660\pi\)
0.731844 + 0.681472i \(0.238660\pi\)
\(788\) 6.67082 0.237638
\(789\) −21.1858 −0.754233
\(790\) 31.1531 1.10838
\(791\) −9.93076 −0.353097
\(792\) −0.928388 −0.0329888
\(793\) 0.787578 0.0279677
\(794\) −4.79234 −0.170074
\(795\) 16.4688 0.584089
\(796\) −0.869939 −0.0308342
\(797\) −35.4097 −1.25428 −0.627138 0.778908i \(-0.715774\pi\)
−0.627138 + 0.778908i \(0.715774\pi\)
\(798\) −1.28243 −0.0453976
\(799\) 29.7947 1.05406
\(800\) −2.16424 −0.0765175
\(801\) 1.27787 0.0451512
\(802\) 5.86810 0.207210
\(803\) 10.1662 0.358757
\(804\) −12.3259 −0.434702
\(805\) 13.4129 0.472742
\(806\) 0.748006 0.0263474
\(807\) −32.7296 −1.15214
\(808\) 7.20520 0.253478
\(809\) 1.87710 0.0659955 0.0329977 0.999455i \(-0.489495\pi\)
0.0329977 + 0.999455i \(0.489495\pi\)
\(810\) −20.5338 −0.721483
\(811\) 12.5240 0.439778 0.219889 0.975525i \(-0.429430\pi\)
0.219889 + 0.975525i \(0.429430\pi\)
\(812\) −1.18098 −0.0414442
\(813\) −32.8622 −1.15253
\(814\) 20.7487 0.727242
\(815\) 28.8020 1.00889
\(816\) 4.58267 0.160426
\(817\) −0.390722 −0.0136696
\(818\) −4.48311 −0.156748
\(819\) −0.0330169 −0.00115370
\(820\) 26.4227 0.922721
\(821\) −26.7749 −0.934449 −0.467224 0.884139i \(-0.654746\pi\)
−0.467224 + 0.884139i \(0.654746\pi\)
\(822\) −15.3308 −0.534723
\(823\) −42.3814 −1.47732 −0.738662 0.674076i \(-0.764542\pi\)
−0.738662 + 0.674076i \(0.764542\pi\)
\(824\) 15.6889 0.546548
\(825\) −8.28492 −0.288444
\(826\) 6.05271 0.210601
\(827\) −3.78946 −0.131772 −0.0658862 0.997827i \(-0.520987\pi\)
−0.0658862 + 0.997827i \(0.520987\pi\)
\(828\) −2.47179 −0.0859005
\(829\) 9.96188 0.345990 0.172995 0.984923i \(-0.444656\pi\)
0.172995 + 0.984923i \(0.444656\pi\)
\(830\) 30.7494 1.06733
\(831\) 4.84277 0.167994
\(832\) −0.106159 −0.00368039
\(833\) −18.0734 −0.626208
\(834\) −31.2338 −1.08154
\(835\) 19.8676 0.687546
\(836\) 2.37029 0.0819783
\(837\) −38.5962 −1.33408
\(838\) 4.09844 0.141578
\(839\) −47.8047 −1.65040 −0.825202 0.564838i \(-0.808938\pi\)
−0.825202 + 0.564838i \(0.808938\pi\)
\(840\) −3.43257 −0.118435
\(841\) −26.7880 −0.923726
\(842\) 37.7803 1.30200
\(843\) −35.3188 −1.21644
\(844\) −1.00000 −0.0344214
\(845\) 34.7658 1.19598
\(846\) 4.11272 0.141398
\(847\) 4.27340 0.146836
\(848\) −3.80976 −0.130828
\(849\) 22.5093 0.772518
\(850\) −6.14106 −0.210637
\(851\) 55.2424 1.89368
\(852\) 8.75987 0.300108
\(853\) −26.2205 −0.897771 −0.448886 0.893589i \(-0.648179\pi\)
−0.448886 + 0.893589i \(0.648179\pi\)
\(854\) −5.89104 −0.201587
\(855\) −1.04836 −0.0358533
\(856\) 3.36029 0.114852
\(857\) 24.5236 0.837710 0.418855 0.908053i \(-0.362432\pi\)
0.418855 + 0.908053i \(0.362432\pi\)
\(858\) −0.406386 −0.0138738
\(859\) 7.86102 0.268215 0.134107 0.990967i \(-0.457183\pi\)
0.134107 + 0.990967i \(0.457183\pi\)
\(860\) −1.04581 −0.0356619
\(861\) 12.6598 0.431444
\(862\) 9.13044 0.310984
\(863\) −8.55689 −0.291280 −0.145640 0.989338i \(-0.546524\pi\)
−0.145640 + 0.989338i \(0.546524\pi\)
\(864\) 5.47766 0.186354
\(865\) −2.89771 −0.0985250
\(866\) −30.4415 −1.03444
\(867\) −14.4521 −0.490820
\(868\) −5.59504 −0.189908
\(869\) −27.5879 −0.935856
\(870\) 6.42916 0.217969
\(871\) 0.810205 0.0274527
\(872\) 14.4527 0.489428
\(873\) 3.53446 0.119623
\(874\) 6.31079 0.213466
\(875\) −6.02709 −0.203753
\(876\) −6.92686 −0.234037
\(877\) 19.3919 0.654817 0.327408 0.944883i \(-0.393825\pi\)
0.327408 + 0.944883i \(0.393825\pi\)
\(878\) −23.2548 −0.784813
\(879\) 4.56443 0.153954
\(880\) 6.34435 0.213868
\(881\) 12.0462 0.405847 0.202924 0.979195i \(-0.434956\pi\)
0.202924 + 0.979195i \(0.434956\pi\)
\(882\) −2.49477 −0.0840033
\(883\) 13.1185 0.441471 0.220736 0.975334i \(-0.429154\pi\)
0.220736 + 0.975334i \(0.429154\pi\)
\(884\) −0.301227 −0.0101314
\(885\) −32.9505 −1.10762
\(886\) 19.8758 0.667741
\(887\) 15.5443 0.521928 0.260964 0.965349i \(-0.415960\pi\)
0.260964 + 0.965349i \(0.415960\pi\)
\(888\) −14.1374 −0.474420
\(889\) 8.53628 0.286298
\(890\) −8.73260 −0.292717
\(891\) 18.1838 0.609182
\(892\) −1.07002 −0.0358271
\(893\) −10.5003 −0.351379
\(894\) −6.32918 −0.211679
\(895\) 58.2227 1.94617
\(896\) 0.794060 0.0265277
\(897\) −1.08198 −0.0361263
\(898\) 19.1037 0.637498
\(899\) 10.4794 0.349509
\(900\) −0.847682 −0.0282561
\(901\) −10.8102 −0.360141
\(902\) −23.3988 −0.779096
\(903\) −0.501075 −0.0166747
\(904\) −12.5063 −0.415953
\(905\) −24.0735 −0.800231
\(906\) 10.8562 0.360674
\(907\) 3.51791 0.116810 0.0584051 0.998293i \(-0.481398\pi\)
0.0584051 + 0.998293i \(0.481398\pi\)
\(908\) 20.7730 0.689377
\(909\) 2.82211 0.0936034
\(910\) 0.225629 0.00747952
\(911\) −23.2310 −0.769678 −0.384839 0.922984i \(-0.625743\pi\)
−0.384839 + 0.922984i \(0.625743\pi\)
\(912\) −1.61503 −0.0534790
\(913\) −27.2304 −0.901195
\(914\) −17.7529 −0.587213
\(915\) 32.0704 1.06021
\(916\) −14.6149 −0.482890
\(917\) 1.65413 0.0546243
\(918\) 15.5429 0.512993
\(919\) 7.71842 0.254607 0.127304 0.991864i \(-0.459368\pi\)
0.127304 + 0.991864i \(0.459368\pi\)
\(920\) 16.8915 0.556897
\(921\) 6.98864 0.230284
\(922\) 4.12105 0.135720
\(923\) −0.575801 −0.0189527
\(924\) 3.03974 0.100000
\(925\) 18.9450 0.622908
\(926\) 22.8859 0.752077
\(927\) 6.14496 0.201827
\(928\) −1.48726 −0.0488219
\(929\) 35.1105 1.15194 0.575968 0.817472i \(-0.304625\pi\)
0.575968 + 0.817472i \(0.304625\pi\)
\(930\) 30.4590 0.998789
\(931\) 6.36947 0.208751
\(932\) 24.6342 0.806919
\(933\) −14.0954 −0.461463
\(934\) 15.3207 0.501308
\(935\) 18.0022 0.588734
\(936\) −0.0415799 −0.00135908
\(937\) −20.7201 −0.676897 −0.338449 0.940985i \(-0.609902\pi\)
−0.338449 + 0.940985i \(0.609902\pi\)
\(938\) −6.06028 −0.197875
\(939\) −18.8331 −0.614595
\(940\) −28.1052 −0.916691
\(941\) 36.0437 1.17499 0.587496 0.809227i \(-0.300114\pi\)
0.587496 + 0.809227i \(0.300114\pi\)
\(942\) 22.7800 0.742213
\(943\) −62.2982 −2.02871
\(944\) 7.62248 0.248091
\(945\) −11.6422 −0.378720
\(946\) 0.926127 0.0301110
\(947\) −4.34265 −0.141117 −0.0705586 0.997508i \(-0.522478\pi\)
−0.0705586 + 0.997508i \(0.522478\pi\)
\(948\) 18.7974 0.610511
\(949\) 0.455314 0.0147801
\(950\) 2.16424 0.0702172
\(951\) −23.9202 −0.775665
\(952\) 2.25316 0.0730252
\(953\) −50.4972 −1.63576 −0.817882 0.575386i \(-0.804852\pi\)
−0.817882 + 0.575386i \(0.804852\pi\)
\(954\) −1.49219 −0.0483115
\(955\) 50.9330 1.64815
\(956\) 4.79226 0.154993
\(957\) −5.69339 −0.184041
\(958\) −18.8974 −0.610547
\(959\) −7.53768 −0.243404
\(960\) −4.32281 −0.139518
\(961\) 18.6477 0.601539
\(962\) 0.929276 0.0299611
\(963\) 1.31615 0.0424122
\(964\) −24.6089 −0.792600
\(965\) −12.1826 −0.392173
\(966\) 8.09315 0.260393
\(967\) −24.0129 −0.772204 −0.386102 0.922456i \(-0.626179\pi\)
−0.386102 + 0.922456i \(0.626179\pi\)
\(968\) 5.38171 0.172975
\(969\) −4.58267 −0.147217
\(970\) −24.1535 −0.775523
\(971\) 17.2446 0.553404 0.276702 0.960956i \(-0.410758\pi\)
0.276702 + 0.960956i \(0.410758\pi\)
\(972\) 4.04318 0.129685
\(973\) −15.3567 −0.492312
\(974\) −37.3467 −1.19667
\(975\) −0.371058 −0.0118834
\(976\) −7.41888 −0.237472
\(977\) 1.95983 0.0627004 0.0313502 0.999508i \(-0.490019\pi\)
0.0313502 + 0.999508i \(0.490019\pi\)
\(978\) 17.3787 0.555711
\(979\) 7.73322 0.247155
\(980\) 17.0486 0.544597
\(981\) 5.66076 0.180734
\(982\) −38.7616 −1.23693
\(983\) 21.9114 0.698865 0.349432 0.936962i \(-0.386374\pi\)
0.349432 + 0.936962i \(0.386374\pi\)
\(984\) 15.9431 0.508248
\(985\) −17.8552 −0.568914
\(986\) −4.22013 −0.134396
\(987\) −13.4659 −0.428625
\(988\) 0.106159 0.00337736
\(989\) 2.46577 0.0784068
\(990\) 2.48493 0.0789763
\(991\) −13.9118 −0.441921 −0.220961 0.975283i \(-0.570919\pi\)
−0.220961 + 0.975283i \(0.570919\pi\)
\(992\) −7.04611 −0.223714
\(993\) 35.7995 1.13606
\(994\) 4.30696 0.136608
\(995\) 2.32849 0.0738180
\(996\) 18.5538 0.587899
\(997\) 35.2080 1.11505 0.557525 0.830160i \(-0.311751\pi\)
0.557525 + 0.830160i \(0.311751\pi\)
\(998\) 1.81417 0.0574267
\(999\) −47.9495 −1.51705
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 \(a_p\))