Properties

Label 8018.2.a.d.1.7
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 30
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: \(30\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.39570 q^{3} +1.00000 q^{4} -3.46674 q^{5} -2.39570 q^{6} -3.11450 q^{7} +1.00000 q^{8} +2.73936 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.39570 q^{3} +1.00000 q^{4} -3.46674 q^{5} -2.39570 q^{6} -3.11450 q^{7} +1.00000 q^{8} +2.73936 q^{9} -3.46674 q^{10} -4.76297 q^{11} -2.39570 q^{12} -3.60047 q^{13} -3.11450 q^{14} +8.30526 q^{15} +1.00000 q^{16} +2.91860 q^{17} +2.73936 q^{18} +1.00000 q^{19} -3.46674 q^{20} +7.46140 q^{21} -4.76297 q^{22} +4.74786 q^{23} -2.39570 q^{24} +7.01829 q^{25} -3.60047 q^{26} +0.624410 q^{27} -3.11450 q^{28} -4.17660 q^{29} +8.30526 q^{30} +6.99380 q^{31} +1.00000 q^{32} +11.4106 q^{33} +2.91860 q^{34} +10.7972 q^{35} +2.73936 q^{36} +0.716100 q^{37} +1.00000 q^{38} +8.62563 q^{39} -3.46674 q^{40} -3.08255 q^{41} +7.46140 q^{42} +0.576373 q^{43} -4.76297 q^{44} -9.49666 q^{45} +4.74786 q^{46} +1.44855 q^{47} -2.39570 q^{48} +2.70013 q^{49} +7.01829 q^{50} -6.99207 q^{51} -3.60047 q^{52} +13.7109 q^{53} +0.624410 q^{54} +16.5120 q^{55} -3.11450 q^{56} -2.39570 q^{57} -4.17660 q^{58} +10.0759 q^{59} +8.30526 q^{60} -1.24194 q^{61} +6.99380 q^{62} -8.53175 q^{63} +1.00000 q^{64} +12.4819 q^{65} +11.4106 q^{66} -0.735972 q^{67} +2.91860 q^{68} -11.3744 q^{69} +10.7972 q^{70} -15.1244 q^{71} +2.73936 q^{72} +5.48450 q^{73} +0.716100 q^{74} -16.8137 q^{75} +1.00000 q^{76} +14.8343 q^{77} +8.62563 q^{78} -3.39442 q^{79} -3.46674 q^{80} -9.71398 q^{81} -3.08255 q^{82} -9.99910 q^{83} +7.46140 q^{84} -10.1180 q^{85} +0.576373 q^{86} +10.0059 q^{87} -4.76297 q^{88} +6.54901 q^{89} -9.49666 q^{90} +11.2137 q^{91} +4.74786 q^{92} -16.7550 q^{93} +1.44855 q^{94} -3.46674 q^{95} -2.39570 q^{96} +3.66525 q^{97} +2.70013 q^{98} -13.0475 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 30q^{2} - 10q^{3} + 30q^{4} - 12q^{5} - 10q^{6} - 15q^{7} + 30q^{8} + 10q^{9} + O(q^{10}) \) \( 30q + 30q^{2} - 10q^{3} + 30q^{4} - 12q^{5} - 10q^{6} - 15q^{7} + 30q^{8} + 10q^{9} - 12q^{10} - 17q^{11} - 10q^{12} - 19q^{13} - 15q^{14} - 8q^{15} + 30q^{16} - 18q^{17} + 10q^{18} + 30q^{19} - 12q^{20} - 14q^{21} - 17q^{22} - 15q^{23} - 10q^{24} - 4q^{25} - 19q^{26} - 37q^{27} - 15q^{28} - 37q^{29} - 8q^{30} - 11q^{31} + 30q^{32} + 6q^{33} - 18q^{34} - 4q^{35} + 10q^{36} - 46q^{37} + 30q^{38} - 12q^{40} - 28q^{41} - 14q^{42} - 61q^{43} - 17q^{44} - 14q^{45} - 15q^{46} - 4q^{47} - 10q^{48} - q^{49} - 4q^{50} - 8q^{51} - 19q^{52} - 19q^{53} - 37q^{54} - 17q^{55} - 15q^{56} - 10q^{57} - 37q^{58} - 6q^{59} - 8q^{60} - 32q^{61} - 11q^{62} - 24q^{63} + 30q^{64} - 24q^{65} + 6q^{66} - 44q^{67} - 18q^{68} - 2q^{69} - 4q^{70} + 10q^{71} + 10q^{72} - 58q^{73} - 46q^{74} - 42q^{75} + 30q^{76} - 32q^{77} - 42q^{79} - 12q^{80} - 38q^{81} - 28q^{82} - 25q^{83} - 14q^{84} - 48q^{85} - 61q^{86} - 15q^{87} - 17q^{88} - 39q^{89} - 14q^{90} - 21q^{91} - 15q^{92} - 45q^{93} - 4q^{94} - 12q^{95} - 10q^{96} - 33q^{97} - q^{98} - 38q^{99} + O(q^{100}) \)

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
\(3\) −2.39570 −1.38316 −0.691578 0.722302i \(-0.743084\pi\)
−0.691578 + 0.722302i \(0.743084\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.46674 −1.55037 −0.775187 0.631732i \(-0.782344\pi\)
−0.775187 + 0.631732i \(0.782344\pi\)
\(6\) −2.39570 −0.978039
\(7\) −3.11450 −1.17717 −0.588586 0.808435i \(-0.700315\pi\)
−0.588586 + 0.808435i \(0.700315\pi\)
\(8\) 1.00000 0.353553
\(9\) 2.73936 0.913121
\(10\) −3.46674 −1.09628
\(11\) −4.76297 −1.43609 −0.718045 0.695997i \(-0.754963\pi\)
−0.718045 + 0.695997i \(0.754963\pi\)
\(12\) −2.39570 −0.691578
\(13\) −3.60047 −0.998590 −0.499295 0.866432i \(-0.666408\pi\)
−0.499295 + 0.866432i \(0.666408\pi\)
\(14\) −3.11450 −0.832386
\(15\) 8.30526 2.14441
\(16\) 1.00000 0.250000
\(17\) 2.91860 0.707864 0.353932 0.935271i \(-0.384844\pi\)
0.353932 + 0.935271i \(0.384844\pi\)
\(18\) 2.73936 0.645674
\(19\) 1.00000 0.229416
\(20\) −3.46674 −0.775187
\(21\) 7.46140 1.62821
\(22\) −4.76297 −1.01547
\(23\) 4.74786 0.989998 0.494999 0.868894i \(-0.335168\pi\)
0.494999 + 0.868894i \(0.335168\pi\)
\(24\) −2.39570 −0.489020
\(25\) 7.01829 1.40366
\(26\) −3.60047 −0.706110
\(27\) 0.624410 0.120168
\(28\) −3.11450 −0.588586
\(29\) −4.17660 −0.775576 −0.387788 0.921749i \(-0.626761\pi\)
−0.387788 + 0.921749i \(0.626761\pi\)
\(30\) 8.30526 1.51633
\(31\) 6.99380 1.25612 0.628062 0.778163i \(-0.283848\pi\)
0.628062 + 0.778163i \(0.283848\pi\)
\(32\) 1.00000 0.176777
\(33\) 11.4106 1.98634
\(34\) 2.91860 0.500535
\(35\) 10.7972 1.82506
\(36\) 2.73936 0.456560
\(37\) 0.716100 0.117726 0.0588630 0.998266i \(-0.481252\pi\)
0.0588630 + 0.998266i \(0.481252\pi\)
\(38\) 1.00000 0.162221
\(39\) 8.62563 1.38121
\(40\) −3.46674 −0.548140
\(41\) −3.08255 −0.481413 −0.240707 0.970598i \(-0.577379\pi\)
−0.240707 + 0.970598i \(0.577379\pi\)
\(42\) 7.46140 1.15132
\(43\) 0.576373 0.0878961 0.0439480 0.999034i \(-0.486006\pi\)
0.0439480 + 0.999034i \(0.486006\pi\)
\(44\) −4.76297 −0.718045
\(45\) −9.49666 −1.41568
\(46\) 4.74786 0.700034
\(47\) 1.44855 0.211293 0.105646 0.994404i \(-0.466309\pi\)
0.105646 + 0.994404i \(0.466309\pi\)
\(48\) −2.39570 −0.345789
\(49\) 2.70013 0.385733
\(50\) 7.01829 0.992536
\(51\) −6.99207 −0.979086
\(52\) −3.60047 −0.499295
\(53\) 13.7109 1.88333 0.941667 0.336545i \(-0.109258\pi\)
0.941667 + 0.336545i \(0.109258\pi\)
\(54\) 0.624410 0.0849715
\(55\) 16.5120 2.22648
\(56\) −3.11450 −0.416193
\(57\) −2.39570 −0.317318
\(58\) −4.17660 −0.548415
\(59\) 10.0759 1.31177 0.655887 0.754859i \(-0.272295\pi\)
0.655887 + 0.754859i \(0.272295\pi\)
\(60\) 8.30526 1.07220
\(61\) −1.24194 −0.159014 −0.0795070 0.996834i \(-0.525335\pi\)
−0.0795070 + 0.996834i \(0.525335\pi\)
\(62\) 6.99380 0.888214
\(63\) −8.53175 −1.07490
\(64\) 1.00000 0.125000
\(65\) 12.4819 1.54819
\(66\) 11.4106 1.40455
\(67\) −0.735972 −0.0899133 −0.0449567 0.998989i \(-0.514315\pi\)
−0.0449567 + 0.998989i \(0.514315\pi\)
\(68\) 2.91860 0.353932
\(69\) −11.3744 −1.36932
\(70\) 10.7972 1.29051
\(71\) −15.1244 −1.79494 −0.897471 0.441074i \(-0.854598\pi\)
−0.897471 + 0.441074i \(0.854598\pi\)
\(72\) 2.73936 0.322837
\(73\) 5.48450 0.641912 0.320956 0.947094i \(-0.395996\pi\)
0.320956 + 0.947094i \(0.395996\pi\)
\(74\) 0.716100 0.0832449
\(75\) −16.8137 −1.94148
\(76\) 1.00000 0.114708
\(77\) 14.8343 1.69052
\(78\) 8.62563 0.976660
\(79\) −3.39442 −0.381902 −0.190951 0.981600i \(-0.561157\pi\)
−0.190951 + 0.981600i \(0.561157\pi\)
\(80\) −3.46674 −0.387593
\(81\) −9.71398 −1.07933
\(82\) −3.08255 −0.340411
\(83\) −9.99910 −1.09754 −0.548772 0.835972i \(-0.684904\pi\)
−0.548772 + 0.835972i \(0.684904\pi\)
\(84\) 7.46140 0.814106
\(85\) −10.1180 −1.09745
\(86\) 0.576373 0.0621519
\(87\) 10.0059 1.07274
\(88\) −4.76297 −0.507734
\(89\) 6.54901 0.694194 0.347097 0.937829i \(-0.387167\pi\)
0.347097 + 0.937829i \(0.387167\pi\)
\(90\) −9.49666 −1.00104
\(91\) 11.2137 1.17551
\(92\) 4.74786 0.494999
\(93\) −16.7550 −1.73742
\(94\) 1.44855 0.149406
\(95\) −3.46674 −0.355680
\(96\) −2.39570 −0.244510
\(97\) 3.66525 0.372150 0.186075 0.982536i \(-0.440423\pi\)
0.186075 + 0.982536i \(0.440423\pi\)
\(98\) 2.70013 0.272754
\(99\) −13.0475 −1.31132
\(100\) 7.01829 0.701829
\(101\) 8.68367 0.864058 0.432029 0.901860i \(-0.357798\pi\)
0.432029 + 0.901860i \(0.357798\pi\)
\(102\) −6.99207 −0.692318
\(103\) −8.26186 −0.814065 −0.407032 0.913414i \(-0.633436\pi\)
−0.407032 + 0.913414i \(0.633436\pi\)
\(104\) −3.60047 −0.353055
\(105\) −25.8668 −2.52434
\(106\) 13.7109 1.33172
\(107\) 2.09800 0.202822 0.101411 0.994845i \(-0.467664\pi\)
0.101411 + 0.994845i \(0.467664\pi\)
\(108\) 0.624410 0.0600839
\(109\) −6.85539 −0.656627 −0.328313 0.944569i \(-0.606480\pi\)
−0.328313 + 0.944569i \(0.606480\pi\)
\(110\) 16.5120 1.57436
\(111\) −1.71556 −0.162833
\(112\) −3.11450 −0.294293
\(113\) −7.58937 −0.713948 −0.356974 0.934114i \(-0.616191\pi\)
−0.356974 + 0.934114i \(0.616191\pi\)
\(114\) −2.39570 −0.224378
\(115\) −16.4596 −1.53487
\(116\) −4.17660 −0.387788
\(117\) −9.86299 −0.911833
\(118\) 10.0759 0.927564
\(119\) −9.08998 −0.833277
\(120\) 8.30526 0.758163
\(121\) 11.6859 1.06235
\(122\) −1.24194 −0.112440
\(123\) 7.38485 0.665870
\(124\) 6.99380 0.628062
\(125\) −6.99687 −0.625819
\(126\) −8.53175 −0.760069
\(127\) 5.20294 0.461687 0.230843 0.972991i \(-0.425852\pi\)
0.230843 + 0.972991i \(0.425852\pi\)
\(128\) 1.00000 0.0883883
\(129\) −1.38082 −0.121574
\(130\) 12.4819 1.09473
\(131\) 1.27464 0.111366 0.0556830 0.998448i \(-0.482266\pi\)
0.0556830 + 0.998448i \(0.482266\pi\)
\(132\) 11.4106 0.993168
\(133\) −3.11450 −0.270062
\(134\) −0.735972 −0.0635783
\(135\) −2.16467 −0.186305
\(136\) 2.91860 0.250268
\(137\) −3.81237 −0.325713 −0.162856 0.986650i \(-0.552071\pi\)
−0.162856 + 0.986650i \(0.552071\pi\)
\(138\) −11.3744 −0.968257
\(139\) 5.87770 0.498540 0.249270 0.968434i \(-0.419809\pi\)
0.249270 + 0.968434i \(0.419809\pi\)
\(140\) 10.7972 0.912528
\(141\) −3.47028 −0.292251
\(142\) −15.1244 −1.26922
\(143\) 17.1489 1.43407
\(144\) 2.73936 0.228280
\(145\) 14.4792 1.20243
\(146\) 5.48450 0.453900
\(147\) −6.46870 −0.533529
\(148\) 0.716100 0.0588630
\(149\) 4.21051 0.344938 0.172469 0.985015i \(-0.444826\pi\)
0.172469 + 0.985015i \(0.444826\pi\)
\(150\) −16.8137 −1.37283
\(151\) 17.5187 1.42565 0.712824 0.701343i \(-0.247416\pi\)
0.712824 + 0.701343i \(0.247416\pi\)
\(152\) 1.00000 0.0811107
\(153\) 7.99509 0.646365
\(154\) 14.8343 1.19538
\(155\) −24.2457 −1.94746
\(156\) 8.62563 0.690603
\(157\) −10.0118 −0.799025 −0.399512 0.916728i \(-0.630821\pi\)
−0.399512 + 0.916728i \(0.630821\pi\)
\(158\) −3.39442 −0.270045
\(159\) −32.8471 −2.60495
\(160\) −3.46674 −0.274070
\(161\) −14.7872 −1.16540
\(162\) −9.71398 −0.763203
\(163\) −6.70898 −0.525488 −0.262744 0.964866i \(-0.584627\pi\)
−0.262744 + 0.964866i \(0.584627\pi\)
\(164\) −3.08255 −0.240707
\(165\) −39.5577 −3.07956
\(166\) −9.99910 −0.776081
\(167\) 4.55028 0.352111 0.176056 0.984380i \(-0.443666\pi\)
0.176056 + 0.984380i \(0.443666\pi\)
\(168\) 7.46140 0.575660
\(169\) −0.0366224 −0.00281711
\(170\) −10.1180 −0.776017
\(171\) 2.73936 0.209484
\(172\) 0.576373 0.0439480
\(173\) −1.75815 −0.133669 −0.0668347 0.997764i \(-0.521290\pi\)
−0.0668347 + 0.997764i \(0.521290\pi\)
\(174\) 10.0059 0.758543
\(175\) −21.8585 −1.65235
\(176\) −4.76297 −0.359022
\(177\) −24.1389 −1.81439
\(178\) 6.54901 0.490869
\(179\) −13.5938 −1.01605 −0.508025 0.861342i \(-0.669624\pi\)
−0.508025 + 0.861342i \(0.669624\pi\)
\(180\) −9.49666 −0.707839
\(181\) −15.0394 −1.11787 −0.558936 0.829211i \(-0.688790\pi\)
−0.558936 + 0.829211i \(0.688790\pi\)
\(182\) 11.2137 0.831213
\(183\) 2.97531 0.219941
\(184\) 4.74786 0.350017
\(185\) −2.48253 −0.182519
\(186\) −16.7550 −1.22854
\(187\) −13.9012 −1.01656
\(188\) 1.44855 0.105646
\(189\) −1.94473 −0.141458
\(190\) −3.46674 −0.251504
\(191\) 16.7799 1.21415 0.607077 0.794643i \(-0.292342\pi\)
0.607077 + 0.794643i \(0.292342\pi\)
\(192\) −2.39570 −0.172895
\(193\) −5.72740 −0.412267 −0.206133 0.978524i \(-0.566088\pi\)
−0.206133 + 0.978524i \(0.566088\pi\)
\(194\) 3.66525 0.263150
\(195\) −29.9028 −2.14139
\(196\) 2.70013 0.192867
\(197\) 4.17820 0.297684 0.148842 0.988861i \(-0.452445\pi\)
0.148842 + 0.988861i \(0.452445\pi\)
\(198\) −13.0475 −0.927245
\(199\) 9.50199 0.673578 0.336789 0.941580i \(-0.390659\pi\)
0.336789 + 0.941580i \(0.390659\pi\)
\(200\) 7.01829 0.496268
\(201\) 1.76317 0.124364
\(202\) 8.68367 0.610981
\(203\) 13.0080 0.912985
\(204\) −6.99207 −0.489543
\(205\) 10.6864 0.746370
\(206\) −8.26186 −0.575631
\(207\) 13.0061 0.903987
\(208\) −3.60047 −0.249648
\(209\) −4.76297 −0.329462
\(210\) −25.8668 −1.78498
\(211\) −1.00000 −0.0688428
\(212\) 13.7109 0.941667
\(213\) 36.2336 2.48268
\(214\) 2.09800 0.143417
\(215\) −1.99814 −0.136272
\(216\) 0.624410 0.0424857
\(217\) −21.7822 −1.47867
\(218\) −6.85539 −0.464305
\(219\) −13.1392 −0.887864
\(220\) 16.5120 1.11324
\(221\) −10.5083 −0.706866
\(222\) −1.71556 −0.115141
\(223\) −0.264142 −0.0176883 −0.00884413 0.999961i \(-0.502815\pi\)
−0.00884413 + 0.999961i \(0.502815\pi\)
\(224\) −3.11450 −0.208097
\(225\) 19.2256 1.28171
\(226\) −7.58937 −0.504837
\(227\) 12.5929 0.835821 0.417910 0.908488i \(-0.362763\pi\)
0.417910 + 0.908488i \(0.362763\pi\)
\(228\) −2.39570 −0.158659
\(229\) 3.05372 0.201796 0.100898 0.994897i \(-0.467828\pi\)
0.100898 + 0.994897i \(0.467828\pi\)
\(230\) −16.4596 −1.08531
\(231\) −35.5385 −2.33826
\(232\) −4.17660 −0.274207
\(233\) −24.2585 −1.58923 −0.794613 0.607117i \(-0.792326\pi\)
−0.794613 + 0.607117i \(0.792326\pi\)
\(234\) −9.86299 −0.644764
\(235\) −5.02174 −0.327582
\(236\) 10.0759 0.655887
\(237\) 8.13199 0.528230
\(238\) −9.08998 −0.589216
\(239\) 16.6046 1.07406 0.537031 0.843562i \(-0.319546\pi\)
0.537031 + 0.843562i \(0.319546\pi\)
\(240\) 8.30526 0.536102
\(241\) 27.3688 1.76298 0.881489 0.472205i \(-0.156542\pi\)
0.881489 + 0.472205i \(0.156542\pi\)
\(242\) 11.6859 0.751198
\(243\) 21.3985 1.37272
\(244\) −1.24194 −0.0795070
\(245\) −9.36065 −0.598030
\(246\) 7.38485 0.470841
\(247\) −3.60047 −0.229092
\(248\) 6.99380 0.444107
\(249\) 23.9548 1.51807
\(250\) −6.99687 −0.442521
\(251\) −0.744054 −0.0469643 −0.0234821 0.999724i \(-0.507475\pi\)
−0.0234821 + 0.999724i \(0.507475\pi\)
\(252\) −8.53175 −0.537450
\(253\) −22.6139 −1.42173
\(254\) 5.20294 0.326462
\(255\) 24.2397 1.51795
\(256\) 1.00000 0.0625000
\(257\) 26.7949 1.67142 0.835710 0.549172i \(-0.185057\pi\)
0.835710 + 0.549172i \(0.185057\pi\)
\(258\) −1.38082 −0.0859658
\(259\) −2.23029 −0.138584
\(260\) 12.4819 0.774094
\(261\) −11.4412 −0.708194
\(262\) 1.27464 0.0787477
\(263\) 2.17017 0.133818 0.0669092 0.997759i \(-0.478686\pi\)
0.0669092 + 0.997759i \(0.478686\pi\)
\(264\) 11.4106 0.702276
\(265\) −47.5321 −2.91987
\(266\) −3.11450 −0.190962
\(267\) −15.6894 −0.960178
\(268\) −0.735972 −0.0449567
\(269\) −15.2664 −0.930811 −0.465406 0.885097i \(-0.654092\pi\)
−0.465406 + 0.885097i \(0.654092\pi\)
\(270\) −2.16467 −0.131737
\(271\) −6.40444 −0.389042 −0.194521 0.980898i \(-0.562315\pi\)
−0.194521 + 0.980898i \(0.562315\pi\)
\(272\) 2.91860 0.176966
\(273\) −26.8646 −1.62592
\(274\) −3.81237 −0.230314
\(275\) −33.4279 −2.01578
\(276\) −11.3744 −0.684661
\(277\) −29.4586 −1.77000 −0.884999 0.465593i \(-0.845841\pi\)
−0.884999 + 0.465593i \(0.845841\pi\)
\(278\) 5.87770 0.352521
\(279\) 19.1586 1.14699
\(280\) 10.7972 0.645255
\(281\) −2.35803 −0.140668 −0.0703342 0.997523i \(-0.522407\pi\)
−0.0703342 + 0.997523i \(0.522407\pi\)
\(282\) −3.47028 −0.206652
\(283\) −10.0881 −0.599673 −0.299837 0.953991i \(-0.596932\pi\)
−0.299837 + 0.953991i \(0.596932\pi\)
\(284\) −15.1244 −0.897471
\(285\) 8.30526 0.491961
\(286\) 17.1489 1.01404
\(287\) 9.60061 0.566706
\(288\) 2.73936 0.161418
\(289\) −8.48179 −0.498929
\(290\) 14.4792 0.850248
\(291\) −8.78083 −0.514742
\(292\) 5.48450 0.320956
\(293\) 11.3310 0.661967 0.330983 0.943637i \(-0.392620\pi\)
0.330983 + 0.943637i \(0.392620\pi\)
\(294\) −6.46870 −0.377262
\(295\) −34.9306 −2.03374
\(296\) 0.716100 0.0416224
\(297\) −2.97405 −0.172572
\(298\) 4.21051 0.243908
\(299\) −17.0945 −0.988602
\(300\) −16.8137 −0.970739
\(301\) −1.79512 −0.103469
\(302\) 17.5187 1.00809
\(303\) −20.8034 −1.19513
\(304\) 1.00000 0.0573539
\(305\) 4.30548 0.246531
\(306\) 7.99509 0.457049
\(307\) −20.0815 −1.14611 −0.573055 0.819517i \(-0.694242\pi\)
−0.573055 + 0.819517i \(0.694242\pi\)
\(308\) 14.8343 0.845262
\(309\) 19.7929 1.12598
\(310\) −24.2457 −1.37706
\(311\) 22.7007 1.28724 0.643619 0.765346i \(-0.277432\pi\)
0.643619 + 0.765346i \(0.277432\pi\)
\(312\) 8.62563 0.488330
\(313\) 19.0345 1.07589 0.537945 0.842980i \(-0.319201\pi\)
0.537945 + 0.842980i \(0.319201\pi\)
\(314\) −10.0118 −0.564996
\(315\) 29.5774 1.66650
\(316\) −3.39442 −0.190951
\(317\) −1.34673 −0.0756400 −0.0378200 0.999285i \(-0.512041\pi\)
−0.0378200 + 0.999285i \(0.512041\pi\)
\(318\) −32.8471 −1.84197
\(319\) 19.8930 1.11380
\(320\) −3.46674 −0.193797
\(321\) −5.02618 −0.280534
\(322\) −14.7872 −0.824060
\(323\) 2.91860 0.162395
\(324\) −9.71398 −0.539666
\(325\) −25.2691 −1.40168
\(326\) −6.70898 −0.371576
\(327\) 16.4234 0.908217
\(328\) −3.08255 −0.170205
\(329\) −4.51151 −0.248728
\(330\) −39.5577 −2.17758
\(331\) −7.28727 −0.400545 −0.200272 0.979740i \(-0.564183\pi\)
−0.200272 + 0.979740i \(0.564183\pi\)
\(332\) −9.99910 −0.548772
\(333\) 1.96166 0.107498
\(334\) 4.55028 0.248980
\(335\) 2.55142 0.139399
\(336\) 7.46140 0.407053
\(337\) −8.73141 −0.475630 −0.237815 0.971310i \(-0.576431\pi\)
−0.237815 + 0.971310i \(0.576431\pi\)
\(338\) −0.0366224 −0.00199199
\(339\) 18.1818 0.987501
\(340\) −10.1180 −0.548727
\(341\) −33.3113 −1.80391
\(342\) 2.73936 0.148128
\(343\) 13.3920 0.723098
\(344\) 0.576373 0.0310760
\(345\) 39.4322 2.12296
\(346\) −1.75815 −0.0945186
\(347\) 18.7884 1.00862 0.504308 0.863524i \(-0.331748\pi\)
0.504308 + 0.863524i \(0.331748\pi\)
\(348\) 10.0059 0.536371
\(349\) 22.0275 1.17910 0.589552 0.807730i \(-0.299304\pi\)
0.589552 + 0.807730i \(0.299304\pi\)
\(350\) −21.8585 −1.16838
\(351\) −2.24817 −0.119998
\(352\) −4.76297 −0.253867
\(353\) −23.7823 −1.26581 −0.632903 0.774231i \(-0.718137\pi\)
−0.632903 + 0.774231i \(0.718137\pi\)
\(354\) −24.1389 −1.28297
\(355\) 52.4325 2.78283
\(356\) 6.54901 0.347097
\(357\) 21.7768 1.15255
\(358\) −13.5938 −0.718456
\(359\) 3.73402 0.197074 0.0985371 0.995133i \(-0.468584\pi\)
0.0985371 + 0.995133i \(0.468584\pi\)
\(360\) −9.49666 −0.500518
\(361\) 1.00000 0.0526316
\(362\) −15.0394 −0.790454
\(363\) −27.9959 −1.46940
\(364\) 11.2137 0.587756
\(365\) −19.0133 −0.995203
\(366\) 2.97531 0.155522
\(367\) 14.5365 0.758799 0.379399 0.925233i \(-0.376131\pi\)
0.379399 + 0.925233i \(0.376131\pi\)
\(368\) 4.74786 0.247499
\(369\) −8.44422 −0.439588
\(370\) −2.48253 −0.129061
\(371\) −42.7026 −2.21701
\(372\) −16.7550 −0.868708
\(373\) 3.93186 0.203584 0.101792 0.994806i \(-0.467542\pi\)
0.101792 + 0.994806i \(0.467542\pi\)
\(374\) −13.9012 −0.718814
\(375\) 16.7624 0.865606
\(376\) 1.44855 0.0747032
\(377\) 15.0377 0.774482
\(378\) −1.94473 −0.100026
\(379\) 11.1988 0.575242 0.287621 0.957744i \(-0.407136\pi\)
0.287621 + 0.957744i \(0.407136\pi\)
\(380\) −3.46674 −0.177840
\(381\) −12.4647 −0.638585
\(382\) 16.7799 0.858536
\(383\) 25.4159 1.29869 0.649346 0.760493i \(-0.275043\pi\)
0.649346 + 0.760493i \(0.275043\pi\)
\(384\) −2.39570 −0.122255
\(385\) −51.4266 −2.62094
\(386\) −5.72740 −0.291517
\(387\) 1.57889 0.0802597
\(388\) 3.66525 0.186075
\(389\) −22.9851 −1.16539 −0.582694 0.812691i \(-0.698002\pi\)
−0.582694 + 0.812691i \(0.698002\pi\)
\(390\) −29.9028 −1.51419
\(391\) 13.8571 0.700784
\(392\) 2.70013 0.136377
\(393\) −3.05366 −0.154037
\(394\) 4.17820 0.210495
\(395\) 11.7676 0.592090
\(396\) −13.0475 −0.655662
\(397\) −26.3767 −1.32381 −0.661904 0.749589i \(-0.730251\pi\)
−0.661904 + 0.749589i \(0.730251\pi\)
\(398\) 9.50199 0.476292
\(399\) 7.46140 0.373537
\(400\) 7.01829 0.350914
\(401\) 14.0205 0.700150 0.350075 0.936722i \(-0.386156\pi\)
0.350075 + 0.936722i \(0.386156\pi\)
\(402\) 1.76317 0.0879387
\(403\) −25.1810 −1.25435
\(404\) 8.68367 0.432029
\(405\) 33.6759 1.67337
\(406\) 13.0080 0.645578
\(407\) −3.41076 −0.169065
\(408\) −6.99207 −0.346159
\(409\) 7.58354 0.374982 0.187491 0.982266i \(-0.439964\pi\)
0.187491 + 0.982266i \(0.439964\pi\)
\(410\) 10.6864 0.527764
\(411\) 9.13328 0.450511
\(412\) −8.26186 −0.407032
\(413\) −31.3815 −1.54418
\(414\) 13.0061 0.639216
\(415\) 34.6643 1.70160
\(416\) −3.60047 −0.176528
\(417\) −14.0812 −0.689559
\(418\) −4.76297 −0.232965
\(419\) −2.08611 −0.101913 −0.0509567 0.998701i \(-0.516227\pi\)
−0.0509567 + 0.998701i \(0.516227\pi\)
\(420\) −25.8668 −1.26217
\(421\) −11.5154 −0.561225 −0.280613 0.959821i \(-0.590538\pi\)
−0.280613 + 0.959821i \(0.590538\pi\)
\(422\) −1.00000 −0.0486792
\(423\) 3.96810 0.192936
\(424\) 13.7109 0.665859
\(425\) 20.4836 0.993598
\(426\) 36.2336 1.75552
\(427\) 3.86802 0.187187
\(428\) 2.09800 0.101411
\(429\) −41.0836 −1.98354
\(430\) −1.99814 −0.0963587
\(431\) −9.52295 −0.458704 −0.229352 0.973343i \(-0.573661\pi\)
−0.229352 + 0.973343i \(0.573661\pi\)
\(432\) 0.624410 0.0300419
\(433\) 1.75745 0.0844574 0.0422287 0.999108i \(-0.486554\pi\)
0.0422287 + 0.999108i \(0.486554\pi\)
\(434\) −21.7822 −1.04558
\(435\) −34.6878 −1.66315
\(436\) −6.85539 −0.328313
\(437\) 4.74786 0.227121
\(438\) −13.1392 −0.627815
\(439\) −14.5340 −0.693668 −0.346834 0.937927i \(-0.612743\pi\)
−0.346834 + 0.937927i \(0.612743\pi\)
\(440\) 16.5120 0.787178
\(441\) 7.39664 0.352221
\(442\) −10.5083 −0.499830
\(443\) −19.7877 −0.940142 −0.470071 0.882629i \(-0.655772\pi\)
−0.470071 + 0.882629i \(0.655772\pi\)
\(444\) −1.71556 −0.0814167
\(445\) −22.7037 −1.07626
\(446\) −0.264142 −0.0125075
\(447\) −10.0871 −0.477103
\(448\) −3.11450 −0.147146
\(449\) −36.7356 −1.73366 −0.866830 0.498603i \(-0.833847\pi\)
−0.866830 + 0.498603i \(0.833847\pi\)
\(450\) 19.2256 0.906305
\(451\) 14.6821 0.691353
\(452\) −7.58937 −0.356974
\(453\) −41.9694 −1.97189
\(454\) 12.5929 0.591014
\(455\) −38.8749 −1.82248
\(456\) −2.39570 −0.112189
\(457\) 21.2778 0.995332 0.497666 0.867369i \(-0.334191\pi\)
0.497666 + 0.867369i \(0.334191\pi\)
\(458\) 3.05372 0.142691
\(459\) 1.82240 0.0850624
\(460\) −16.4596 −0.767433
\(461\) 15.0555 0.701204 0.350602 0.936525i \(-0.385977\pi\)
0.350602 + 0.936525i \(0.385977\pi\)
\(462\) −35.5385 −1.65340
\(463\) 31.3140 1.45529 0.727643 0.685956i \(-0.240616\pi\)
0.727643 + 0.685956i \(0.240616\pi\)
\(464\) −4.17660 −0.193894
\(465\) 58.0853 2.69364
\(466\) −24.2585 −1.12375
\(467\) 3.29466 0.152459 0.0762294 0.997090i \(-0.475712\pi\)
0.0762294 + 0.997090i \(0.475712\pi\)
\(468\) −9.86299 −0.455917
\(469\) 2.29219 0.105843
\(470\) −5.02174 −0.231636
\(471\) 23.9851 1.10518
\(472\) 10.0759 0.463782
\(473\) −2.74525 −0.126227
\(474\) 8.13199 0.373515
\(475\) 7.01829 0.322021
\(476\) −9.08998 −0.416639
\(477\) 37.5591 1.71971
\(478\) 16.6046 0.759477
\(479\) 34.0016 1.55357 0.776786 0.629764i \(-0.216849\pi\)
0.776786 + 0.629764i \(0.216849\pi\)
\(480\) 8.30526 0.379081
\(481\) −2.57829 −0.117560
\(482\) 27.3688 1.24661
\(483\) 35.4257 1.61193
\(484\) 11.6859 0.531177
\(485\) −12.7065 −0.576971
\(486\) 21.3985 0.970657
\(487\) −13.9227 −0.630898 −0.315449 0.948943i \(-0.602155\pi\)
−0.315449 + 0.948943i \(0.602155\pi\)
\(488\) −1.24194 −0.0562199
\(489\) 16.0727 0.726831
\(490\) −9.36065 −0.422871
\(491\) 34.9576 1.57762 0.788808 0.614640i \(-0.210699\pi\)
0.788808 + 0.614640i \(0.210699\pi\)
\(492\) 7.38485 0.332935
\(493\) −12.1898 −0.549002
\(494\) −3.60047 −0.161993
\(495\) 45.2323 2.03304
\(496\) 6.99380 0.314031
\(497\) 47.1051 2.11295
\(498\) 23.9548 1.07344
\(499\) 33.8912 1.51718 0.758590 0.651568i \(-0.225888\pi\)
0.758590 + 0.651568i \(0.225888\pi\)
\(500\) −6.99687 −0.312910
\(501\) −10.9011 −0.487025
\(502\) −0.744054 −0.0332088
\(503\) −34.9088 −1.55651 −0.778253 0.627950i \(-0.783894\pi\)
−0.778253 + 0.627950i \(0.783894\pi\)
\(504\) −8.53175 −0.380034
\(505\) −30.1040 −1.33961
\(506\) −22.6139 −1.00531
\(507\) 0.0877361 0.00389650
\(508\) 5.20294 0.230843
\(509\) 2.61476 0.115897 0.0579486 0.998320i \(-0.481544\pi\)
0.0579486 + 0.998320i \(0.481544\pi\)
\(510\) 24.2397 1.07335
\(511\) −17.0815 −0.755640
\(512\) 1.00000 0.0441942
\(513\) 0.624410 0.0275684
\(514\) 26.7949 1.18187
\(515\) 28.6417 1.26210
\(516\) −1.38082 −0.0607870
\(517\) −6.89940 −0.303435
\(518\) −2.23029 −0.0979935
\(519\) 4.21199 0.184886
\(520\) 12.4819 0.547367
\(521\) −19.1821 −0.840385 −0.420192 0.907435i \(-0.638037\pi\)
−0.420192 + 0.907435i \(0.638037\pi\)
\(522\) −11.4412 −0.500769
\(523\) −21.7511 −0.951107 −0.475554 0.879687i \(-0.657752\pi\)
−0.475554 + 0.879687i \(0.657752\pi\)
\(524\) 1.27464 0.0556830
\(525\) 52.3663 2.28545
\(526\) 2.17017 0.0946238
\(527\) 20.4121 0.889165
\(528\) 11.4106 0.496584
\(529\) −0.457794 −0.0199041
\(530\) −47.5321 −2.06466
\(531\) 27.6016 1.19781
\(532\) −3.11450 −0.135031
\(533\) 11.0986 0.480735
\(534\) −15.6894 −0.678949
\(535\) −7.27324 −0.314449
\(536\) −0.735972 −0.0317892
\(537\) 32.5667 1.40536
\(538\) −15.2664 −0.658183
\(539\) −12.8606 −0.553947
\(540\) −2.16467 −0.0931525
\(541\) −39.8063 −1.71141 −0.855703 0.517468i \(-0.826875\pi\)
−0.855703 + 0.517468i \(0.826875\pi\)
\(542\) −6.40444 −0.275094
\(543\) 36.0299 1.54619
\(544\) 2.91860 0.125134
\(545\) 23.7658 1.01802
\(546\) −26.8646 −1.14970
\(547\) 8.40901 0.359543 0.179772 0.983708i \(-0.442464\pi\)
0.179772 + 0.983708i \(0.442464\pi\)
\(548\) −3.81237 −0.162856
\(549\) −3.40212 −0.145199
\(550\) −33.4279 −1.42537
\(551\) −4.17660 −0.177929
\(552\) −11.3744 −0.484128
\(553\) 10.5719 0.449564
\(554\) −29.4586 −1.25158
\(555\) 5.94739 0.252453
\(556\) 5.87770 0.249270
\(557\) −22.8979 −0.970215 −0.485107 0.874455i \(-0.661219\pi\)
−0.485107 + 0.874455i \(0.661219\pi\)
\(558\) 19.1586 0.811047
\(559\) −2.07521 −0.0877722
\(560\) 10.7972 0.456264
\(561\) 33.3030 1.40606
\(562\) −2.35803 −0.0994676
\(563\) −7.50282 −0.316206 −0.158103 0.987423i \(-0.550538\pi\)
−0.158103 + 0.987423i \(0.550538\pi\)
\(564\) −3.47028 −0.146125
\(565\) 26.3104 1.10689
\(566\) −10.0881 −0.424033
\(567\) 30.2542 1.27056
\(568\) −15.1244 −0.634608
\(569\) −40.2358 −1.68677 −0.843387 0.537307i \(-0.819442\pi\)
−0.843387 + 0.537307i \(0.819442\pi\)
\(570\) 8.30526 0.347869
\(571\) −34.6012 −1.44801 −0.724007 0.689792i \(-0.757702\pi\)
−0.724007 + 0.689792i \(0.757702\pi\)
\(572\) 17.1489 0.717033
\(573\) −40.1996 −1.67936
\(574\) 9.60061 0.400722
\(575\) 33.3219 1.38962
\(576\) 2.73936 0.114140
\(577\) −14.3364 −0.596833 −0.298416 0.954436i \(-0.596458\pi\)
−0.298416 + 0.954436i \(0.596458\pi\)
\(578\) −8.48179 −0.352796
\(579\) 13.7211 0.570229
\(580\) 14.4792 0.601216
\(581\) 31.1422 1.29200
\(582\) −8.78083 −0.363977
\(583\) −65.3045 −2.70464
\(584\) 5.48450 0.226950
\(585\) 34.1924 1.41368
\(586\) 11.3310 0.468081
\(587\) −31.4574 −1.29839 −0.649193 0.760624i \(-0.724893\pi\)
−0.649193 + 0.760624i \(0.724893\pi\)
\(588\) −6.46870 −0.266764
\(589\) 6.99380 0.288175
\(590\) −34.9306 −1.43807
\(591\) −10.0097 −0.411744
\(592\) 0.716100 0.0294315
\(593\) 11.1381 0.457386 0.228693 0.973499i \(-0.426555\pi\)
0.228693 + 0.973499i \(0.426555\pi\)
\(594\) −2.97405 −0.122027
\(595\) 31.5126 1.29189
\(596\) 4.21051 0.172469
\(597\) −22.7639 −0.931663
\(598\) −17.0945 −0.699048
\(599\) 13.2168 0.540025 0.270012 0.962857i \(-0.412972\pi\)
0.270012 + 0.962857i \(0.412972\pi\)
\(600\) −16.8137 −0.686416
\(601\) −22.6203 −0.922702 −0.461351 0.887218i \(-0.652635\pi\)
−0.461351 + 0.887218i \(0.652635\pi\)
\(602\) −1.79512 −0.0731635
\(603\) −2.01609 −0.0821017
\(604\) 17.5187 0.712824
\(605\) −40.5119 −1.64704
\(606\) −20.8034 −0.845082
\(607\) 3.54583 0.143921 0.0719604 0.997407i \(-0.477074\pi\)
0.0719604 + 0.997407i \(0.477074\pi\)
\(608\) 1.00000 0.0405554
\(609\) −31.1633 −1.26280
\(610\) 4.30548 0.174324
\(611\) −5.21546 −0.210995
\(612\) 7.99509 0.323183
\(613\) −22.4850 −0.908159 −0.454080 0.890961i \(-0.650032\pi\)
−0.454080 + 0.890961i \(0.650032\pi\)
\(614\) −20.0815 −0.810422
\(615\) −25.6014 −1.03235
\(616\) 14.8343 0.597691
\(617\) 20.6460 0.831177 0.415588 0.909553i \(-0.363576\pi\)
0.415588 + 0.909553i \(0.363576\pi\)
\(618\) 19.7929 0.796187
\(619\) −23.9668 −0.963306 −0.481653 0.876362i \(-0.659963\pi\)
−0.481653 + 0.876362i \(0.659963\pi\)
\(620\) −24.2457 −0.973731
\(621\) 2.96461 0.118966
\(622\) 22.7007 0.910214
\(623\) −20.3969 −0.817185
\(624\) 8.62563 0.345302
\(625\) −10.8351 −0.433403
\(626\) 19.0345 0.760770
\(627\) 11.4106 0.455697
\(628\) −10.0118 −0.399512
\(629\) 2.09001 0.0833340
\(630\) 29.5774 1.17839
\(631\) 33.5332 1.33494 0.667468 0.744638i \(-0.267378\pi\)
0.667468 + 0.744638i \(0.267378\pi\)
\(632\) −3.39442 −0.135023
\(633\) 2.39570 0.0952204
\(634\) −1.34673 −0.0534856
\(635\) −18.0373 −0.715787
\(636\) −32.8471 −1.30247
\(637\) −9.72174 −0.385189
\(638\) 19.8930 0.787573
\(639\) −41.4313 −1.63900
\(640\) −3.46674 −0.137035
\(641\) 5.40276 0.213396 0.106698 0.994291i \(-0.465972\pi\)
0.106698 + 0.994291i \(0.465972\pi\)
\(642\) −5.02618 −0.198368
\(643\) 8.77311 0.345978 0.172989 0.984924i \(-0.444658\pi\)
0.172989 + 0.984924i \(0.444658\pi\)
\(644\) −14.7872 −0.582699
\(645\) 4.78693 0.188485
\(646\) 2.91860 0.114831
\(647\) 31.4847 1.23779 0.618895 0.785473i \(-0.287581\pi\)
0.618895 + 0.785473i \(0.287581\pi\)
\(648\) −9.71398 −0.381601
\(649\) −47.9913 −1.88382
\(650\) −25.2691 −0.991137
\(651\) 52.1836 2.04524
\(652\) −6.70898 −0.262744
\(653\) −13.0862 −0.512101 −0.256050 0.966663i \(-0.582421\pi\)
−0.256050 + 0.966663i \(0.582421\pi\)
\(654\) 16.4234 0.642207
\(655\) −4.41886 −0.172659
\(656\) −3.08255 −0.120353
\(657\) 15.0240 0.586143
\(658\) −4.51151 −0.175877
\(659\) −41.3855 −1.61215 −0.806074 0.591814i \(-0.798412\pi\)
−0.806074 + 0.591814i \(0.798412\pi\)
\(660\) −39.5577 −1.53978
\(661\) 2.68407 0.104398 0.0521991 0.998637i \(-0.483377\pi\)
0.0521991 + 0.998637i \(0.483377\pi\)
\(662\) −7.28727 −0.283228
\(663\) 25.1747 0.977706
\(664\) −9.99910 −0.388040
\(665\) 10.7972 0.418696
\(666\) 1.96166 0.0760126
\(667\) −19.8299 −0.767818
\(668\) 4.55028 0.176056
\(669\) 0.632804 0.0244656
\(670\) 2.55142 0.0985701
\(671\) 5.91532 0.228358
\(672\) 7.46140 0.287830
\(673\) −29.2692 −1.12825 −0.564123 0.825691i \(-0.690786\pi\)
−0.564123 + 0.825691i \(0.690786\pi\)
\(674\) −8.73141 −0.336322
\(675\) 4.38229 0.168674
\(676\) −0.0366224 −0.00140855
\(677\) −0.312598 −0.0120141 −0.00600707 0.999982i \(-0.501912\pi\)
−0.00600707 + 0.999982i \(0.501912\pi\)
\(678\) 18.1818 0.698269
\(679\) −11.4154 −0.438084
\(680\) −10.1180 −0.388008
\(681\) −30.1688 −1.15607
\(682\) −33.3113 −1.27556
\(683\) −27.8757 −1.06663 −0.533317 0.845915i \(-0.679055\pi\)
−0.533317 + 0.845915i \(0.679055\pi\)
\(684\) 2.73936 0.104742
\(685\) 13.2165 0.504976
\(686\) 13.3920 0.511307
\(687\) −7.31580 −0.279115
\(688\) 0.576373 0.0219740
\(689\) −49.3656 −1.88068
\(690\) 39.4322 1.50116
\(691\) −14.7712 −0.561922 −0.280961 0.959719i \(-0.590653\pi\)
−0.280961 + 0.959719i \(0.590653\pi\)
\(692\) −1.75815 −0.0668347
\(693\) 40.6365 1.54365
\(694\) 18.7884 0.713199
\(695\) −20.3765 −0.772924
\(696\) 10.0059 0.379272
\(697\) −8.99672 −0.340775
\(698\) 22.0275 0.833753
\(699\) 58.1159 2.19815
\(700\) −21.8585 −0.826173
\(701\) 32.3364 1.22133 0.610664 0.791890i \(-0.290903\pi\)
0.610664 + 0.791890i \(0.290903\pi\)
\(702\) −2.24817 −0.0848517
\(703\) 0.716100 0.0270082
\(704\) −4.76297 −0.179511
\(705\) 12.0306 0.453098
\(706\) −23.7823 −0.895060
\(707\) −27.0453 −1.01714
\(708\) −24.1389 −0.907194
\(709\) 19.8481 0.745412 0.372706 0.927949i \(-0.378430\pi\)
0.372706 + 0.927949i \(0.378430\pi\)
\(710\) 52.4325 1.96776
\(711\) −9.29854 −0.348722
\(712\) 6.54901 0.245435
\(713\) 33.2056 1.24356
\(714\) 21.7768 0.814978
\(715\) −59.4509 −2.22334
\(716\) −13.5938 −0.508025
\(717\) −39.7796 −1.48560
\(718\) 3.73402 0.139353
\(719\) 26.7083 0.996050 0.498025 0.867163i \(-0.334059\pi\)
0.498025 + 0.867163i \(0.334059\pi\)
\(720\) −9.49666 −0.353919
\(721\) 25.7316 0.958294
\(722\) 1.00000 0.0372161
\(723\) −65.5673 −2.43847
\(724\) −15.0394 −0.558936
\(725\) −29.3126 −1.08864
\(726\) −27.9959 −1.03902
\(727\) −19.6278 −0.727956 −0.363978 0.931407i \(-0.618582\pi\)
−0.363978 + 0.931407i \(0.618582\pi\)
\(728\) 11.2137 0.415606
\(729\) −22.1224 −0.819349
\(730\) −19.0133 −0.703715
\(731\) 1.68220 0.0622185
\(732\) 2.97531 0.109971
\(733\) −51.2301 −1.89223 −0.946113 0.323836i \(-0.895028\pi\)
−0.946113 + 0.323836i \(0.895028\pi\)
\(734\) 14.5365 0.536552
\(735\) 22.4253 0.827169
\(736\) 4.74786 0.175009
\(737\) 3.50541 0.129124
\(738\) −8.44422 −0.310836
\(739\) 41.3831 1.52230 0.761151 0.648575i \(-0.224635\pi\)
0.761151 + 0.648575i \(0.224635\pi\)
\(740\) −2.48253 −0.0912596
\(741\) 8.62563 0.316870
\(742\) −42.7026 −1.56766
\(743\) −18.8532 −0.691657 −0.345829 0.938298i \(-0.612402\pi\)
−0.345829 + 0.938298i \(0.612402\pi\)
\(744\) −16.7550 −0.614269
\(745\) −14.5967 −0.534783
\(746\) 3.93186 0.143956
\(747\) −27.3911 −1.00219
\(748\) −13.9012 −0.508278
\(749\) −6.53424 −0.238756
\(750\) 16.7624 0.612076
\(751\) −5.65452 −0.206337 −0.103168 0.994664i \(-0.532898\pi\)
−0.103168 + 0.994664i \(0.532898\pi\)
\(752\) 1.44855 0.0528232
\(753\) 1.78253 0.0649589
\(754\) 15.0377 0.547642
\(755\) −60.7326 −2.21029
\(756\) −1.94473 −0.0707291
\(757\) 15.5648 0.565713 0.282856 0.959162i \(-0.408718\pi\)
0.282856 + 0.959162i \(0.408718\pi\)
\(758\) 11.1988 0.406757
\(759\) 54.1761 1.96647
\(760\) −3.46674 −0.125752
\(761\) −20.0597 −0.727165 −0.363583 0.931562i \(-0.618447\pi\)
−0.363583 + 0.931562i \(0.618447\pi\)
\(762\) −12.4647 −0.451547
\(763\) 21.3511 0.772963
\(764\) 16.7799 0.607077
\(765\) −27.7169 −1.00211
\(766\) 25.4159 0.918314
\(767\) −36.2781 −1.30992
\(768\) −2.39570 −0.0864473
\(769\) 33.8449 1.22048 0.610240 0.792217i \(-0.291073\pi\)
0.610240 + 0.792217i \(0.291073\pi\)
\(770\) −51.4266 −1.85329
\(771\) −64.1924 −2.31183
\(772\) −5.72740 −0.206133
\(773\) 3.33000 0.119772 0.0598859 0.998205i \(-0.480926\pi\)
0.0598859 + 0.998205i \(0.480926\pi\)
\(774\) 1.57889 0.0567522
\(775\) 49.0845 1.76317
\(776\) 3.66525 0.131575
\(777\) 5.34311 0.191683
\(778\) −22.9851 −0.824054
\(779\) −3.08255 −0.110444
\(780\) −29.9028 −1.07069
\(781\) 72.0373 2.57770
\(782\) 13.8571 0.495529
\(783\) −2.60791 −0.0931992
\(784\) 2.70013 0.0964333
\(785\) 34.7081 1.23879
\(786\) −3.05366 −0.108920
\(787\) 43.9440 1.56643 0.783217 0.621748i \(-0.213577\pi\)
0.783217 + 0.621748i \(0.213577\pi\)
\(788\) 4.17820 0.148842
\(789\) −5.19906 −0.185092
\(790\) 11.7676 0.418671
\(791\) 23.6371 0.840439
\(792\) −13.0475 −0.463623
\(793\) 4.47156 0.158790
\(794\) −26.3767 −0.936074
\(795\) 113.872 4.03864
\(796\) 9.50199 0.336789
\(797\) −41.4672 −1.46884 −0.734421 0.678694i \(-0.762546\pi\)
−0.734421 + 0.678694i \(0.762546\pi\)
\(798\) 7.46140 0.264131
\(799\) 4.22773 0.149566
\(800\) 7.01829 0.248134
\(801\) 17.9401 0.633883
\(802\) 14.0205 0.495081
\(803\) −26.1225 −0.921843
\(804\) 1.76317 0.0621821
\(805\) 51.2635 1.80680
\(806\) −25.1810 −0.886962
\(807\) 36.5738 1.28746
\(808\) 8.68367 0.305490
\(809\) 46.9593 1.65100 0.825501 0.564401i \(-0.190893\pi\)
0.825501 + 0.564401i \(0.190893\pi\)
\(810\) 33.6759 1.18325
\(811\) 9.54285 0.335095 0.167547 0.985864i \(-0.446415\pi\)
0.167547 + 0.985864i \(0.446415\pi\)
\(812\) 13.0080 0.456493
\(813\) 15.3431 0.538106
\(814\) −3.41076 −0.119547
\(815\) 23.2583 0.814702
\(816\) −6.99207 −0.244772
\(817\) 0.576373 0.0201647
\(818\) 7.58354 0.265152
\(819\) 30.7183 1.07338
\(820\) 10.6864 0.373185
\(821\) 35.7091 1.24626 0.623128 0.782120i \(-0.285861\pi\)
0.623128 + 0.782120i \(0.285861\pi\)
\(822\) 9.13328 0.318560
\(823\) −33.9380 −1.18300 −0.591501 0.806304i \(-0.701465\pi\)
−0.591501 + 0.806304i \(0.701465\pi\)
\(824\) −8.26186 −0.287815
\(825\) 80.0831 2.78814
\(826\) −31.3815 −1.09190
\(827\) −31.2810 −1.08775 −0.543874 0.839167i \(-0.683043\pi\)
−0.543874 + 0.839167i \(0.683043\pi\)
\(828\) 13.0061 0.451994
\(829\) −24.0426 −0.835034 −0.417517 0.908669i \(-0.637100\pi\)
−0.417517 + 0.908669i \(0.637100\pi\)
\(830\) 34.6643 1.20321
\(831\) 70.5739 2.44818
\(832\) −3.60047 −0.124824
\(833\) 7.88060 0.273046
\(834\) −14.0812 −0.487592
\(835\) −15.7746 −0.545904
\(836\) −4.76297 −0.164731
\(837\) 4.36700 0.150946
\(838\) −2.08611 −0.0720636
\(839\) 9.46822 0.326879 0.163440 0.986553i \(-0.447741\pi\)
0.163440 + 0.986553i \(0.447741\pi\)
\(840\) −25.8668 −0.892488
\(841\) −11.5560 −0.398483
\(842\) −11.5154 −0.396846
\(843\) 5.64913 0.194566
\(844\) −1.00000 −0.0344214
\(845\) 0.126960 0.00436756
\(846\) 3.96810 0.136426
\(847\) −36.3957 −1.25057
\(848\) 13.7109 0.470834
\(849\) 24.1679 0.829441
\(850\) 20.4836 0.702580
\(851\) 3.39994 0.116549
\(852\) 36.2336 1.24134
\(853\) −2.30635 −0.0789681 −0.0394840 0.999220i \(-0.512571\pi\)
−0.0394840 + 0.999220i \(0.512571\pi\)
\(854\) 3.86802 0.132361
\(855\) −9.49666 −0.324779
\(856\) 2.09800 0.0717083
\(857\) −45.5345 −1.55543 −0.777714 0.628618i \(-0.783621\pi\)
−0.777714 + 0.628618i \(0.783621\pi\)
\(858\) −41.0836 −1.40257
\(859\) 2.77452 0.0946654 0.0473327 0.998879i \(-0.484928\pi\)
0.0473327 + 0.998879i \(0.484928\pi\)
\(860\) −1.99814 −0.0681359
\(861\) −23.0002 −0.783843
\(862\) −9.52295 −0.324353
\(863\) 3.11531 0.106047 0.0530233 0.998593i \(-0.483114\pi\)
0.0530233 + 0.998593i \(0.483114\pi\)
\(864\) 0.624410 0.0212429
\(865\) 6.09504 0.207238
\(866\) 1.75745 0.0597204
\(867\) 20.3198 0.690096
\(868\) −21.7822 −0.739337
\(869\) 16.1675 0.548445
\(870\) −34.6878 −1.17602
\(871\) 2.64984 0.0897866
\(872\) −6.85539 −0.232153
\(873\) 10.0405 0.339818
\(874\) 4.74786 0.160599
\(875\) 21.7918 0.736697
\(876\) −13.1392 −0.443932
\(877\) −36.4019 −1.22920 −0.614602 0.788837i \(-0.710683\pi\)
−0.614602 + 0.788837i \(0.710683\pi\)
\(878\) −14.5340 −0.490497
\(879\) −27.1457 −0.915603
\(880\) 16.5120 0.556619
\(881\) −10.2607 −0.345692 −0.172846 0.984949i \(-0.555296\pi\)
−0.172846 + 0.984949i \(0.555296\pi\)
\(882\) 7.39664 0.249058
\(883\) −58.1186 −1.95585 −0.977924 0.208962i \(-0.932992\pi\)
−0.977924 + 0.208962i \(0.932992\pi\)
\(884\) −10.5083 −0.353433
\(885\) 83.6831 2.81298
\(886\) −19.7877 −0.664781
\(887\) 45.9652 1.54336 0.771681 0.636010i \(-0.219416\pi\)
0.771681 + 0.636010i \(0.219416\pi\)
\(888\) −1.71556 −0.0575703
\(889\) −16.2046 −0.543484
\(890\) −22.7037 −0.761030
\(891\) 46.2674 1.55002
\(892\) −0.264142 −0.00884413
\(893\) 1.44855 0.0484738
\(894\) −10.0871 −0.337363
\(895\) 47.1263 1.57526
\(896\) −3.11450 −0.104048
\(897\) 40.9533 1.36739
\(898\) −36.7356 −1.22588
\(899\) −29.2103 −0.974219
\(900\) 19.2256 0.640854
\(901\) 40.0165 1.33314
\(902\) 14.6821 0.488860
\(903\) 4.30055 0.143113
\(904\) −7.58937 −0.252419
\(905\) 52.1378 1.73312
\(906\) −41.9694 −1.39434
\(907\) 9.20336 0.305592 0.152796 0.988258i \(-0.451172\pi\)
0.152796 + 0.988258i \(0.451172\pi\)
\(908\) 12.5929 0.417910
\(909\) 23.7877 0.788989
\(910\) −38.8749 −1.28869
\(911\) 47.9069 1.58722 0.793612 0.608424i \(-0.208198\pi\)
0.793612 + 0.608424i \(0.208198\pi\)
\(912\) −2.39570 −0.0793294
\(913\) 47.6254 1.57617
\(914\) 21.2778 0.703806
\(915\) −10.3146 −0.340991
\(916\) 3.05372 0.100898
\(917\) −3.96988 −0.131097
\(918\) 1.82240 0.0601482
\(919\) −2.11610 −0.0698038 −0.0349019 0.999391i \(-0.511112\pi\)
−0.0349019 + 0.999391i \(0.511112\pi\)
\(920\) −16.4596 −0.542657
\(921\) 48.1091 1.58525
\(922\) 15.0555 0.495826
\(923\) 54.4551 1.79241
\(924\) −35.5385 −1.16913
\(925\) 5.02579 0.165247
\(926\) 31.3140 1.02904
\(927\) −22.6322 −0.743339
\(928\) −4.17660 −0.137104
\(929\) 59.1023 1.93908 0.969542 0.244925i \(-0.0787632\pi\)
0.969542 + 0.244925i \(0.0787632\pi\)
\(930\) 58.0853 1.90469
\(931\) 2.70013 0.0884932
\(932\) −24.2585 −0.794613
\(933\) −54.3839 −1.78045
\(934\) 3.29466 0.107805
\(935\) 48.1918 1.57604
\(936\) −9.86299 −0.322382
\(937\) 53.9137 1.76128 0.880642 0.473782i \(-0.157112\pi\)
0.880642 + 0.473782i \(0.157112\pi\)
\(938\) 2.29219 0.0748426
\(939\) −45.6008 −1.48812
\(940\) −5.02174 −0.163791
\(941\) −1.22707 −0.0400013 −0.0200007 0.999800i \(-0.506367\pi\)
−0.0200007 + 0.999800i \(0.506367\pi\)
\(942\) 23.9851 0.781477
\(943\) −14.6355 −0.476598
\(944\) 10.0759 0.327943
\(945\) 6.74186 0.219313
\(946\) −2.74525 −0.0892557
\(947\) 43.1175 1.40113 0.700566 0.713588i \(-0.252931\pi\)
0.700566 + 0.713588i \(0.252931\pi\)
\(948\) 8.13199 0.264115
\(949\) −19.7468 −0.641007
\(950\) 7.01829 0.227703
\(951\) 3.22636 0.104622
\(952\) −9.08998 −0.294608
\(953\) −3.33059 −0.107888 −0.0539442 0.998544i \(-0.517179\pi\)
−0.0539442 + 0.998544i \(0.517179\pi\)
\(954\) 37.5591 1.21602
\(955\) −58.1717 −1.88239
\(956\) 16.6046 0.537031
\(957\) −47.6577 −1.54055
\(958\) 34.0016 1.09854
\(959\) 11.8736 0.383420
\(960\) 8.30526 0.268051
\(961\) 17.9133 0.577848
\(962\) −2.57829 −0.0831275
\(963\) 5.74719 0.185201
\(964\) 27.3688 0.881489
\(965\) 19.8554 0.639168
\(966\) 35.4257 1.13980
\(967\) 33.5724 1.07962 0.539808 0.841788i \(-0.318497\pi\)
0.539808 + 0.841788i \(0.318497\pi\)
\(968\) 11.6859 0.375599
\(969\) −6.99207 −0.224618
\(970\) −12.7065 −0.407980
\(971\) 5.37828 0.172597 0.0862986 0.996269i \(-0.472496\pi\)
0.0862986 + 0.996269i \(0.472496\pi\)
\(972\) 21.3985 0.686358
\(973\) −18.3061 −0.586868
\(974\) −13.9227 −0.446112
\(975\) 60.5372 1.93874
\(976\) −1.24194 −0.0397535
\(977\) 11.7975 0.377434 0.188717 0.982031i \(-0.439567\pi\)
0.188717 + 0.982031i \(0.439567\pi\)
\(978\) 16.0727 0.513947
\(979\) −31.1928 −0.996925
\(980\) −9.36065 −0.299015
\(981\) −18.7794 −0.599580
\(982\) 34.9576 1.11554
\(983\) 57.1198 1.82184 0.910920 0.412584i \(-0.135374\pi\)
0.910920 + 0.412584i \(0.135374\pi\)
\(984\) 7.38485 0.235421
\(985\) −14.4847 −0.461522
\(986\) −12.1898 −0.388203
\(987\) 10.8082 0.344029
\(988\) −3.60047 −0.114546
\(989\) 2.73654 0.0870169
\(990\) 45.2323 1.43758
\(991\) −51.0080 −1.62032 −0.810161 0.586207i \(-0.800621\pi\)
−0.810161 + 0.586207i \(0.800621\pi\)
\(992\) 6.99380 0.222054
\(993\) 17.4581 0.554016
\(994\) 47.1051 1.49408
\(995\) −32.9409 −1.04430
\(996\) 23.9548 0.759037
\(997\) 13.0379 0.412916 0.206458 0.978455i \(-0.433806\pi\)
0.206458 + 0.978455i \(0.433806\pi\)
\(998\) 33.8912 1.07281
\(999\) 0.447140 0.0141469
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 \(a_p\))