Properties

Label 4017.2.a.j.1.12
Level 4017
Weight 2
Character 4017.1
Self dual Yes
Analytic conductor 32.076
Analytic rank 0
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0759064919\)
Analytic rank: \(0\)
Dimension: \(25\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.0371239 q^{2} -1.00000 q^{3} -1.99862 q^{4} +2.55043 q^{5} +0.0371239 q^{6} +1.94695 q^{7} +0.148445 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.0371239 q^{2} -1.00000 q^{3} -1.99862 q^{4} +2.55043 q^{5} +0.0371239 q^{6} +1.94695 q^{7} +0.148445 q^{8} +1.00000 q^{9} -0.0946818 q^{10} +0.0498766 q^{11} +1.99862 q^{12} +1.00000 q^{13} -0.0722783 q^{14} -2.55043 q^{15} +3.99173 q^{16} -4.77817 q^{17} -0.0371239 q^{18} -6.56279 q^{19} -5.09734 q^{20} -1.94695 q^{21} -0.00185162 q^{22} +5.81689 q^{23} -0.148445 q^{24} +1.50467 q^{25} -0.0371239 q^{26} -1.00000 q^{27} -3.89121 q^{28} +7.77905 q^{29} +0.0946818 q^{30} +10.6323 q^{31} -0.445078 q^{32} -0.0498766 q^{33} +0.177384 q^{34} +4.96554 q^{35} -1.99862 q^{36} +6.38869 q^{37} +0.243637 q^{38} -1.00000 q^{39} +0.378597 q^{40} -4.46800 q^{41} +0.0722783 q^{42} -0.323564 q^{43} -0.0996845 q^{44} +2.55043 q^{45} -0.215946 q^{46} -2.86047 q^{47} -3.99173 q^{48} -3.20940 q^{49} -0.0558592 q^{50} +4.77817 q^{51} -1.99862 q^{52} +2.38415 q^{53} +0.0371239 q^{54} +0.127207 q^{55} +0.289014 q^{56} +6.56279 q^{57} -0.288789 q^{58} +5.13046 q^{59} +5.09734 q^{60} -10.4293 q^{61} -0.394712 q^{62} +1.94695 q^{63} -7.96694 q^{64} +2.55043 q^{65} +0.00185162 q^{66} -11.1123 q^{67} +9.54976 q^{68} -5.81689 q^{69} -0.184340 q^{70} +11.4913 q^{71} +0.148445 q^{72} +13.4821 q^{73} -0.237173 q^{74} -1.50467 q^{75} +13.1165 q^{76} +0.0971071 q^{77} +0.0371239 q^{78} +13.8364 q^{79} +10.1806 q^{80} +1.00000 q^{81} +0.165870 q^{82} -16.1941 q^{83} +3.89121 q^{84} -12.1864 q^{85} +0.0120120 q^{86} -7.77905 q^{87} +0.00740391 q^{88} -11.5802 q^{89} -0.0946818 q^{90} +1.94695 q^{91} -11.6258 q^{92} -10.6323 q^{93} +0.106192 q^{94} -16.7379 q^{95} +0.445078 q^{96} +10.5474 q^{97} +0.119146 q^{98} +0.0498766 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0371239 −0.0262506 −0.0131253 0.999914i \(-0.504178\pi\)
−0.0131253 + 0.999914i \(0.504178\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.99862 −0.999311
\(5\) 2.55043 1.14058 0.570292 0.821442i \(-0.306830\pi\)
0.570292 + 0.821442i \(0.306830\pi\)
\(6\) 0.0371239 0.0151558
\(7\) 1.94695 0.735876 0.367938 0.929850i \(-0.380064\pi\)
0.367938 + 0.929850i \(0.380064\pi\)
\(8\) 0.148445 0.0524831
\(9\) 1.00000 0.333333
\(10\) −0.0946818 −0.0299410
\(11\) 0.0498766 0.0150384 0.00751918 0.999972i \(-0.497607\pi\)
0.00751918 + 0.999972i \(0.497607\pi\)
\(12\) 1.99862 0.576952
\(13\) 1.00000 0.277350
\(14\) −0.0722783 −0.0193172
\(15\) −2.55043 −0.658517
\(16\) 3.99173 0.997933
\(17\) −4.77817 −1.15888 −0.579438 0.815016i \(-0.696728\pi\)
−0.579438 + 0.815016i \(0.696728\pi\)
\(18\) −0.0371239 −0.00875019
\(19\) −6.56279 −1.50561 −0.752804 0.658245i \(-0.771299\pi\)
−0.752804 + 0.658245i \(0.771299\pi\)
\(20\) −5.09734 −1.13980
\(21\) −1.94695 −0.424858
\(22\) −0.00185162 −0.000394766 0
\(23\) 5.81689 1.21290 0.606452 0.795120i \(-0.292592\pi\)
0.606452 + 0.795120i \(0.292592\pi\)
\(24\) −0.148445 −0.0303011
\(25\) 1.50467 0.300934
\(26\) −0.0371239 −0.00728060
\(27\) −1.00000 −0.192450
\(28\) −3.89121 −0.735369
\(29\) 7.77905 1.44453 0.722267 0.691614i \(-0.243100\pi\)
0.722267 + 0.691614i \(0.243100\pi\)
\(30\) 0.0946818 0.0172865
\(31\) 10.6323 1.90961 0.954806 0.297228i \(-0.0960623\pi\)
0.954806 + 0.297228i \(0.0960623\pi\)
\(32\) −0.445078 −0.0786794
\(33\) −0.0498766 −0.00868240
\(34\) 0.177384 0.0304212
\(35\) 4.96554 0.839329
\(36\) −1.99862 −0.333104
\(37\) 6.38869 1.05029 0.525147 0.851011i \(-0.324010\pi\)
0.525147 + 0.851011i \(0.324010\pi\)
\(38\) 0.243637 0.0395231
\(39\) −1.00000 −0.160128
\(40\) 0.378597 0.0598614
\(41\) −4.46800 −0.697785 −0.348893 0.937163i \(-0.613442\pi\)
−0.348893 + 0.937163i \(0.613442\pi\)
\(42\) 0.0722783 0.0111528
\(43\) −0.323564 −0.0493431 −0.0246715 0.999696i \(-0.507854\pi\)
−0.0246715 + 0.999696i \(0.507854\pi\)
\(44\) −0.0996845 −0.0150280
\(45\) 2.55043 0.380195
\(46\) −0.215946 −0.0318395
\(47\) −2.86047 −0.417243 −0.208621 0.977996i \(-0.566898\pi\)
−0.208621 + 0.977996i \(0.566898\pi\)
\(48\) −3.99173 −0.576157
\(49\) −3.20940 −0.458486
\(50\) −0.0558592 −0.00789968
\(51\) 4.77817 0.669078
\(52\) −1.99862 −0.277159
\(53\) 2.38415 0.327488 0.163744 0.986503i \(-0.447643\pi\)
0.163744 + 0.986503i \(0.447643\pi\)
\(54\) 0.0371239 0.00505193
\(55\) 0.127207 0.0171525
\(56\) 0.289014 0.0386211
\(57\) 6.56279 0.869263
\(58\) −0.288789 −0.0379199
\(59\) 5.13046 0.667929 0.333964 0.942586i \(-0.391614\pi\)
0.333964 + 0.942586i \(0.391614\pi\)
\(60\) 5.09734 0.658063
\(61\) −10.4293 −1.33533 −0.667666 0.744461i \(-0.732707\pi\)
−0.667666 + 0.744461i \(0.732707\pi\)
\(62\) −0.394712 −0.0501284
\(63\) 1.94695 0.245292
\(64\) −7.96694 −0.995868
\(65\) 2.55043 0.316341
\(66\) 0.00185162 0.000227918 0
\(67\) −11.1123 −1.35759 −0.678793 0.734330i \(-0.737497\pi\)
−0.678793 + 0.734330i \(0.737497\pi\)
\(68\) 9.54976 1.15808
\(69\) −5.81689 −0.700271
\(70\) −0.184340 −0.0220329
\(71\) 11.4913 1.36376 0.681881 0.731463i \(-0.261162\pi\)
0.681881 + 0.731463i \(0.261162\pi\)
\(72\) 0.148445 0.0174944
\(73\) 13.4821 1.57796 0.788981 0.614418i \(-0.210609\pi\)
0.788981 + 0.614418i \(0.210609\pi\)
\(74\) −0.237173 −0.0275708
\(75\) −1.50467 −0.173744
\(76\) 13.1165 1.50457
\(77\) 0.0971071 0.0110664
\(78\) 0.0371239 0.00420346
\(79\) 13.8364 1.55672 0.778360 0.627818i \(-0.216052\pi\)
0.778360 + 0.627818i \(0.216052\pi\)
\(80\) 10.1806 1.13823
\(81\) 1.00000 0.111111
\(82\) 0.165870 0.0183173
\(83\) −16.1941 −1.77753 −0.888766 0.458361i \(-0.848437\pi\)
−0.888766 + 0.458361i \(0.848437\pi\)
\(84\) 3.89121 0.424566
\(85\) −12.1864 −1.32180
\(86\) 0.0120120 0.00129528
\(87\) −7.77905 −0.834002
\(88\) 0.00740391 0.000789260 0
\(89\) −11.5802 −1.22750 −0.613750 0.789500i \(-0.710340\pi\)
−0.613750 + 0.789500i \(0.710340\pi\)
\(90\) −0.0946818 −0.00998034
\(91\) 1.94695 0.204095
\(92\) −11.6258 −1.21207
\(93\) −10.6323 −1.10252
\(94\) 0.106192 0.0109529
\(95\) −16.7379 −1.71727
\(96\) 0.445078 0.0454256
\(97\) 10.5474 1.07093 0.535463 0.844558i \(-0.320137\pi\)
0.535463 + 0.844558i \(0.320137\pi\)
\(98\) 0.119146 0.0120355
\(99\) 0.0498766 0.00501279
\(100\) −3.00726 −0.300726
\(101\) 0.461424 0.0459134 0.0229567 0.999736i \(-0.492692\pi\)
0.0229567 + 0.999736i \(0.492692\pi\)
\(102\) −0.177384 −0.0175637
\(103\) −1.00000 −0.0985329
\(104\) 0.148445 0.0145562
\(105\) −4.96554 −0.484587
\(106\) −0.0885089 −0.00859675
\(107\) 4.61729 0.446370 0.223185 0.974776i \(-0.428355\pi\)
0.223185 + 0.974776i \(0.428355\pi\)
\(108\) 1.99862 0.192317
\(109\) 7.55061 0.723218 0.361609 0.932330i \(-0.382228\pi\)
0.361609 + 0.932330i \(0.382228\pi\)
\(110\) −0.00472241 −0.000450264 0
\(111\) −6.38869 −0.606388
\(112\) 7.77169 0.734356
\(113\) 10.1761 0.957287 0.478643 0.878009i \(-0.341129\pi\)
0.478643 + 0.878009i \(0.341129\pi\)
\(114\) −0.243637 −0.0228187
\(115\) 14.8355 1.38342
\(116\) −15.5474 −1.44354
\(117\) 1.00000 0.0924500
\(118\) −0.190463 −0.0175335
\(119\) −9.30284 −0.852790
\(120\) −0.378597 −0.0345610
\(121\) −10.9975 −0.999774
\(122\) 0.387176 0.0350533
\(123\) 4.46800 0.402866
\(124\) −21.2499 −1.90830
\(125\) −8.91458 −0.797344
\(126\) −0.0722783 −0.00643906
\(127\) 2.86014 0.253796 0.126898 0.991916i \(-0.459498\pi\)
0.126898 + 0.991916i \(0.459498\pi\)
\(128\) 1.18592 0.104822
\(129\) 0.323564 0.0284882
\(130\) −0.0946818 −0.00830414
\(131\) −8.85763 −0.773894 −0.386947 0.922102i \(-0.626470\pi\)
−0.386947 + 0.922102i \(0.626470\pi\)
\(132\) 0.0996845 0.00867642
\(133\) −12.7774 −1.10794
\(134\) 0.412533 0.0356374
\(135\) −2.55043 −0.219506
\(136\) −0.709293 −0.0608214
\(137\) −6.59690 −0.563611 −0.281805 0.959472i \(-0.590933\pi\)
−0.281805 + 0.959472i \(0.590933\pi\)
\(138\) 0.215946 0.0183825
\(139\) −15.4178 −1.30772 −0.653858 0.756617i \(-0.726851\pi\)
−0.653858 + 0.756617i \(0.726851\pi\)
\(140\) −9.92424 −0.838751
\(141\) 2.86047 0.240895
\(142\) −0.426601 −0.0357995
\(143\) 0.0498766 0.00417089
\(144\) 3.99173 0.332644
\(145\) 19.8399 1.64761
\(146\) −0.500509 −0.0414224
\(147\) 3.20940 0.264707
\(148\) −12.7686 −1.04957
\(149\) 0.198567 0.0162672 0.00813361 0.999967i \(-0.497411\pi\)
0.00813361 + 0.999967i \(0.497411\pi\)
\(150\) 0.0558592 0.00456088
\(151\) 21.7587 1.77070 0.885348 0.464929i \(-0.153920\pi\)
0.885348 + 0.464929i \(0.153920\pi\)
\(152\) −0.974210 −0.0790189
\(153\) −4.77817 −0.386292
\(154\) −0.00360500 −0.000290499 0
\(155\) 27.1168 2.17808
\(156\) 1.99862 0.160018
\(157\) 1.35049 0.107781 0.0538904 0.998547i \(-0.482838\pi\)
0.0538904 + 0.998547i \(0.482838\pi\)
\(158\) −0.513663 −0.0408648
\(159\) −2.38415 −0.189075
\(160\) −1.13514 −0.0897405
\(161\) 11.3252 0.892548
\(162\) −0.0371239 −0.00291673
\(163\) 15.3288 1.20064 0.600322 0.799759i \(-0.295039\pi\)
0.600322 + 0.799759i \(0.295039\pi\)
\(164\) 8.92985 0.697304
\(165\) −0.127207 −0.00990302
\(166\) 0.601188 0.0466613
\(167\) 21.7145 1.68032 0.840159 0.542340i \(-0.182462\pi\)
0.840159 + 0.542340i \(0.182462\pi\)
\(168\) −0.289014 −0.0222979
\(169\) 1.00000 0.0769231
\(170\) 0.452406 0.0346979
\(171\) −6.56279 −0.501869
\(172\) 0.646682 0.0493091
\(173\) 7.00246 0.532387 0.266193 0.963920i \(-0.414234\pi\)
0.266193 + 0.963920i \(0.414234\pi\)
\(174\) 0.288789 0.0218930
\(175\) 2.92951 0.221450
\(176\) 0.199094 0.0150073
\(177\) −5.13046 −0.385629
\(178\) 0.429903 0.0322226
\(179\) 11.9163 0.890663 0.445332 0.895366i \(-0.353086\pi\)
0.445332 + 0.895366i \(0.353086\pi\)
\(180\) −5.09734 −0.379933
\(181\) 9.82491 0.730280 0.365140 0.930953i \(-0.381021\pi\)
0.365140 + 0.930953i \(0.381021\pi\)
\(182\) −0.0722783 −0.00535762
\(183\) 10.4293 0.770955
\(184\) 0.863485 0.0636570
\(185\) 16.2939 1.19795
\(186\) 0.394712 0.0289417
\(187\) −0.238319 −0.0174276
\(188\) 5.71700 0.416955
\(189\) −1.94695 −0.141619
\(190\) 0.621377 0.0450794
\(191\) 1.27975 0.0925997 0.0462998 0.998928i \(-0.485257\pi\)
0.0462998 + 0.998928i \(0.485257\pi\)
\(192\) 7.96694 0.574965
\(193\) 14.1365 1.01757 0.508784 0.860894i \(-0.330095\pi\)
0.508784 + 0.860894i \(0.330095\pi\)
\(194\) −0.391561 −0.0281124
\(195\) −2.55043 −0.182640
\(196\) 6.41438 0.458170
\(197\) 17.5154 1.24792 0.623960 0.781457i \(-0.285523\pi\)
0.623960 + 0.781457i \(0.285523\pi\)
\(198\) −0.00185162 −0.000131589 0
\(199\) 0.938390 0.0665207 0.0332604 0.999447i \(-0.489411\pi\)
0.0332604 + 0.999447i \(0.489411\pi\)
\(200\) 0.223360 0.0157939
\(201\) 11.1123 0.783803
\(202\) −0.0171299 −0.00120525
\(203\) 15.1454 1.06300
\(204\) −9.54976 −0.668617
\(205\) −11.3953 −0.795883
\(206\) 0.0371239 0.00258655
\(207\) 5.81689 0.404302
\(208\) 3.99173 0.276777
\(209\) −0.327330 −0.0226419
\(210\) 0.184340 0.0127207
\(211\) 20.4535 1.40808 0.704040 0.710161i \(-0.251378\pi\)
0.704040 + 0.710161i \(0.251378\pi\)
\(212\) −4.76501 −0.327262
\(213\) −11.4913 −0.787368
\(214\) −0.171412 −0.0117175
\(215\) −0.825226 −0.0562799
\(216\) −0.148445 −0.0101004
\(217\) 20.7005 1.40524
\(218\) −0.280308 −0.0189849
\(219\) −13.4821 −0.911036
\(220\) −0.254238 −0.0171407
\(221\) −4.77817 −0.321415
\(222\) 0.237173 0.0159180
\(223\) −10.3658 −0.694143 −0.347071 0.937839i \(-0.612824\pi\)
−0.347071 + 0.937839i \(0.612824\pi\)
\(224\) −0.866543 −0.0578983
\(225\) 1.50467 0.100311
\(226\) −0.377777 −0.0251293
\(227\) 0.475721 0.0315747 0.0157873 0.999875i \(-0.494975\pi\)
0.0157873 + 0.999875i \(0.494975\pi\)
\(228\) −13.1165 −0.868664
\(229\) −8.63360 −0.570525 −0.285262 0.958449i \(-0.592081\pi\)
−0.285262 + 0.958449i \(0.592081\pi\)
\(230\) −0.550753 −0.0363156
\(231\) −0.0971071 −0.00638918
\(232\) 1.15476 0.0758136
\(233\) 17.8265 1.16785 0.583927 0.811806i \(-0.301515\pi\)
0.583927 + 0.811806i \(0.301515\pi\)
\(234\) −0.0371239 −0.00242687
\(235\) −7.29542 −0.475901
\(236\) −10.2538 −0.667468
\(237\) −13.8364 −0.898773
\(238\) 0.345358 0.0223862
\(239\) 18.5128 1.19749 0.598745 0.800940i \(-0.295666\pi\)
0.598745 + 0.800940i \(0.295666\pi\)
\(240\) −10.1806 −0.657156
\(241\) 5.41036 0.348512 0.174256 0.984700i \(-0.444248\pi\)
0.174256 + 0.984700i \(0.444248\pi\)
\(242\) 0.408271 0.0262446
\(243\) −1.00000 −0.0641500
\(244\) 20.8442 1.33441
\(245\) −8.18534 −0.522942
\(246\) −0.165870 −0.0105755
\(247\) −6.56279 −0.417580
\(248\) 1.57830 0.100222
\(249\) 16.1941 1.02626
\(250\) 0.330944 0.0209308
\(251\) −1.25086 −0.0789535 −0.0394768 0.999220i \(-0.512569\pi\)
−0.0394768 + 0.999220i \(0.512569\pi\)
\(252\) −3.89121 −0.245123
\(253\) 0.290127 0.0182401
\(254\) −0.106180 −0.00666230
\(255\) 12.1864 0.763140
\(256\) 15.8899 0.993116
\(257\) −12.8742 −0.803071 −0.401535 0.915844i \(-0.631523\pi\)
−0.401535 + 0.915844i \(0.631523\pi\)
\(258\) −0.0120120 −0.000747833 0
\(259\) 12.4384 0.772887
\(260\) −5.09734 −0.316123
\(261\) 7.77905 0.481511
\(262\) 0.328830 0.0203152
\(263\) 15.6927 0.967651 0.483825 0.875165i \(-0.339247\pi\)
0.483825 + 0.875165i \(0.339247\pi\)
\(264\) −0.00740391 −0.000455679 0
\(265\) 6.08059 0.373528
\(266\) 0.474347 0.0290841
\(267\) 11.5802 0.708697
\(268\) 22.2093 1.35665
\(269\) 23.9752 1.46180 0.730898 0.682486i \(-0.239101\pi\)
0.730898 + 0.682486i \(0.239101\pi\)
\(270\) 0.0946818 0.00576215
\(271\) 6.84031 0.415519 0.207760 0.978180i \(-0.433383\pi\)
0.207760 + 0.978180i \(0.433383\pi\)
\(272\) −19.0732 −1.15648
\(273\) −1.94695 −0.117835
\(274\) 0.244903 0.0147951
\(275\) 0.0750478 0.00452555
\(276\) 11.6258 0.699788
\(277\) −2.42115 −0.145473 −0.0727365 0.997351i \(-0.523173\pi\)
−0.0727365 + 0.997351i \(0.523173\pi\)
\(278\) 0.572368 0.0343283
\(279\) 10.6323 0.636538
\(280\) 0.737107 0.0440506
\(281\) 8.36874 0.499237 0.249619 0.968344i \(-0.419695\pi\)
0.249619 + 0.968344i \(0.419695\pi\)
\(282\) −0.106192 −0.00632364
\(283\) 9.64948 0.573602 0.286801 0.957990i \(-0.407408\pi\)
0.286801 + 0.957990i \(0.407408\pi\)
\(284\) −22.9667 −1.36282
\(285\) 16.7379 0.991468
\(286\) −0.00185162 −0.000109488 0
\(287\) −8.69896 −0.513484
\(288\) −0.445078 −0.0262265
\(289\) 5.83091 0.342995
\(290\) −0.736535 −0.0432508
\(291\) −10.5474 −0.618300
\(292\) −26.9456 −1.57687
\(293\) −13.6847 −0.799470 −0.399735 0.916631i \(-0.630898\pi\)
−0.399735 + 0.916631i \(0.630898\pi\)
\(294\) −0.119146 −0.00694871
\(295\) 13.0848 0.761829
\(296\) 0.948367 0.0551227
\(297\) −0.0498766 −0.00289413
\(298\) −0.00737157 −0.000427024 0
\(299\) 5.81689 0.336399
\(300\) 3.00726 0.173624
\(301\) −0.629962 −0.0363104
\(302\) −0.807768 −0.0464818
\(303\) −0.461424 −0.0265081
\(304\) −26.1969 −1.50250
\(305\) −26.5991 −1.52306
\(306\) 0.177384 0.0101404
\(307\) 4.10802 0.234457 0.117229 0.993105i \(-0.462599\pi\)
0.117229 + 0.993105i \(0.462599\pi\)
\(308\) −0.194080 −0.0110588
\(309\) 1.00000 0.0568880
\(310\) −1.00668 −0.0571757
\(311\) −11.6679 −0.661628 −0.330814 0.943696i \(-0.607323\pi\)
−0.330814 + 0.943696i \(0.607323\pi\)
\(312\) −0.148445 −0.00840402
\(313\) −26.7163 −1.51010 −0.755048 0.655669i \(-0.772387\pi\)
−0.755048 + 0.655669i \(0.772387\pi\)
\(314\) −0.0501354 −0.00282931
\(315\) 4.96554 0.279776
\(316\) −27.6538 −1.55565
\(317\) −8.32549 −0.467606 −0.233803 0.972284i \(-0.575117\pi\)
−0.233803 + 0.972284i \(0.575117\pi\)
\(318\) 0.0885089 0.00496333
\(319\) 0.387993 0.0217234
\(320\) −20.3191 −1.13587
\(321\) −4.61729 −0.257712
\(322\) −0.420435 −0.0234299
\(323\) 31.3581 1.74481
\(324\) −1.99862 −0.111035
\(325\) 1.50467 0.0834640
\(326\) −0.569065 −0.0315176
\(327\) −7.55061 −0.417550
\(328\) −0.663251 −0.0366219
\(329\) −5.56919 −0.307039
\(330\) 0.00472241 0.000259960 0
\(331\) 19.4071 1.06671 0.533355 0.845891i \(-0.320931\pi\)
0.533355 + 0.845891i \(0.320931\pi\)
\(332\) 32.3659 1.77631
\(333\) 6.38869 0.350098
\(334\) −0.806127 −0.0441093
\(335\) −28.3411 −1.54844
\(336\) −7.77169 −0.423980
\(337\) −28.1798 −1.53505 −0.767525 0.641019i \(-0.778512\pi\)
−0.767525 + 0.641019i \(0.778512\pi\)
\(338\) −0.0371239 −0.00201928
\(339\) −10.1761 −0.552690
\(340\) 24.3559 1.32089
\(341\) 0.530302 0.0287175
\(342\) 0.243637 0.0131744
\(343\) −19.8772 −1.07327
\(344\) −0.0480313 −0.00258968
\(345\) −14.8355 −0.798718
\(346\) −0.259959 −0.0139755
\(347\) −3.08745 −0.165743 −0.0828715 0.996560i \(-0.526409\pi\)
−0.0828715 + 0.996560i \(0.526409\pi\)
\(348\) 15.5474 0.833427
\(349\) −21.9241 −1.17357 −0.586784 0.809743i \(-0.699606\pi\)
−0.586784 + 0.809743i \(0.699606\pi\)
\(350\) −0.108755 −0.00581319
\(351\) −1.00000 −0.0533761
\(352\) −0.0221990 −0.00118321
\(353\) 5.91437 0.314790 0.157395 0.987536i \(-0.449690\pi\)
0.157395 + 0.987536i \(0.449690\pi\)
\(354\) 0.190463 0.0101230
\(355\) 29.3076 1.55549
\(356\) 23.1445 1.22665
\(357\) 9.30284 0.492358
\(358\) −0.442378 −0.0233804
\(359\) −2.91048 −0.153609 −0.0768046 0.997046i \(-0.524472\pi\)
−0.0768046 + 0.997046i \(0.524472\pi\)
\(360\) 0.378597 0.0199538
\(361\) 24.0702 1.26685
\(362\) −0.364739 −0.0191703
\(363\) 10.9975 0.577220
\(364\) −3.89121 −0.203955
\(365\) 34.3851 1.79980
\(366\) −0.387176 −0.0202380
\(367\) 16.5755 0.865232 0.432616 0.901578i \(-0.357591\pi\)
0.432616 + 0.901578i \(0.357591\pi\)
\(368\) 23.2195 1.21040
\(369\) −4.46800 −0.232595
\(370\) −0.604893 −0.0314469
\(371\) 4.64181 0.240991
\(372\) 21.2499 1.10176
\(373\) −9.39657 −0.486536 −0.243268 0.969959i \(-0.578219\pi\)
−0.243268 + 0.969959i \(0.578219\pi\)
\(374\) 0.00884734 0.000457485 0
\(375\) 8.91458 0.460347
\(376\) −0.424622 −0.0218982
\(377\) 7.77905 0.400642
\(378\) 0.0722783 0.00371759
\(379\) 1.86986 0.0960482 0.0480241 0.998846i \(-0.484708\pi\)
0.0480241 + 0.998846i \(0.484708\pi\)
\(380\) 33.4527 1.71609
\(381\) −2.86014 −0.146529
\(382\) −0.0475094 −0.00243079
\(383\) −22.6343 −1.15656 −0.578279 0.815839i \(-0.696275\pi\)
−0.578279 + 0.815839i \(0.696275\pi\)
\(384\) −1.18592 −0.0605187
\(385\) 0.247664 0.0126221
\(386\) −0.524802 −0.0267117
\(387\) −0.323564 −0.0164477
\(388\) −21.0803 −1.07019
\(389\) 18.4438 0.935139 0.467570 0.883956i \(-0.345130\pi\)
0.467570 + 0.883956i \(0.345130\pi\)
\(390\) 0.0946818 0.00479440
\(391\) −27.7941 −1.40561
\(392\) −0.476418 −0.0240627
\(393\) 8.85763 0.446808
\(394\) −0.650240 −0.0327586
\(395\) 35.2888 1.77557
\(396\) −0.0996845 −0.00500933
\(397\) −30.4817 −1.52983 −0.764916 0.644130i \(-0.777220\pi\)
−0.764916 + 0.644130i \(0.777220\pi\)
\(398\) −0.0348367 −0.00174621
\(399\) 12.7774 0.639670
\(400\) 6.00623 0.300312
\(401\) 37.7000 1.88265 0.941325 0.337502i \(-0.109582\pi\)
0.941325 + 0.337502i \(0.109582\pi\)
\(402\) −0.412533 −0.0205753
\(403\) 10.6323 0.529631
\(404\) −0.922212 −0.0458818
\(405\) 2.55043 0.126732
\(406\) −0.562257 −0.0279043
\(407\) 0.318646 0.0157947
\(408\) 0.709293 0.0351153
\(409\) −30.4914 −1.50770 −0.753851 0.657045i \(-0.771806\pi\)
−0.753851 + 0.657045i \(0.771806\pi\)
\(410\) 0.423039 0.0208924
\(411\) 6.59690 0.325401
\(412\) 1.99862 0.0984650
\(413\) 9.98872 0.491513
\(414\) −0.215946 −0.0106132
\(415\) −41.3018 −2.02743
\(416\) −0.445078 −0.0218217
\(417\) 15.4178 0.755011
\(418\) 0.0121518 0.000594362 0
\(419\) 26.0498 1.27261 0.636307 0.771436i \(-0.280461\pi\)
0.636307 + 0.771436i \(0.280461\pi\)
\(420\) 9.92424 0.484253
\(421\) 2.11794 0.103222 0.0516111 0.998667i \(-0.483564\pi\)
0.0516111 + 0.998667i \(0.483564\pi\)
\(422\) −0.759316 −0.0369629
\(423\) −2.86047 −0.139081
\(424\) 0.353914 0.0171876
\(425\) −7.18956 −0.348745
\(426\) 0.426601 0.0206689
\(427\) −20.3053 −0.982640
\(428\) −9.22821 −0.446062
\(429\) −0.0498766 −0.00240807
\(430\) 0.0306356 0.00147738
\(431\) 10.1882 0.490747 0.245374 0.969429i \(-0.421089\pi\)
0.245374 + 0.969429i \(0.421089\pi\)
\(432\) −3.99173 −0.192052
\(433\) 34.3380 1.65018 0.825090 0.565001i \(-0.191124\pi\)
0.825090 + 0.565001i \(0.191124\pi\)
\(434\) −0.768483 −0.0368883
\(435\) −19.8399 −0.951250
\(436\) −15.0908 −0.722719
\(437\) −38.1750 −1.82616
\(438\) 0.500509 0.0239152
\(439\) 29.9729 1.43053 0.715263 0.698855i \(-0.246307\pi\)
0.715263 + 0.698855i \(0.246307\pi\)
\(440\) 0.0188831 0.000900218 0
\(441\) −3.20940 −0.152829
\(442\) 0.177384 0.00843732
\(443\) 27.0311 1.28429 0.642144 0.766584i \(-0.278045\pi\)
0.642144 + 0.766584i \(0.278045\pi\)
\(444\) 12.7686 0.605970
\(445\) −29.5345 −1.40007
\(446\) 0.384818 0.0182217
\(447\) −0.198567 −0.00939188
\(448\) −15.5112 −0.732836
\(449\) −13.6059 −0.642102 −0.321051 0.947062i \(-0.604036\pi\)
−0.321051 + 0.947062i \(0.604036\pi\)
\(450\) −0.0558592 −0.00263323
\(451\) −0.222849 −0.0104935
\(452\) −20.3382 −0.956627
\(453\) −21.7587 −1.02231
\(454\) −0.0176606 −0.000828854 0
\(455\) 4.96554 0.232788
\(456\) 0.974210 0.0456216
\(457\) −25.8243 −1.20801 −0.604005 0.796980i \(-0.706429\pi\)
−0.604005 + 0.796980i \(0.706429\pi\)
\(458\) 0.320513 0.0149766
\(459\) 4.77817 0.223026
\(460\) −29.6506 −1.38247
\(461\) −6.48186 −0.301890 −0.150945 0.988542i \(-0.548232\pi\)
−0.150945 + 0.988542i \(0.548232\pi\)
\(462\) 0.00360500 0.000167720 0
\(463\) −1.85098 −0.0860225 −0.0430112 0.999075i \(-0.513695\pi\)
−0.0430112 + 0.999075i \(0.513695\pi\)
\(464\) 31.0519 1.44155
\(465\) −27.1168 −1.25751
\(466\) −0.661791 −0.0306569
\(467\) 7.56847 0.350227 0.175114 0.984548i \(-0.443971\pi\)
0.175114 + 0.984548i \(0.443971\pi\)
\(468\) −1.99862 −0.0923863
\(469\) −21.6351 −0.999016
\(470\) 0.270835 0.0124927
\(471\) −1.35049 −0.0622272
\(472\) 0.761588 0.0350549
\(473\) −0.0161383 −0.000742039 0
\(474\) 0.513663 0.0235933
\(475\) −9.87482 −0.453088
\(476\) 18.5929 0.852202
\(477\) 2.38415 0.109163
\(478\) −0.687266 −0.0314348
\(479\) 1.82057 0.0831841 0.0415921 0.999135i \(-0.486757\pi\)
0.0415921 + 0.999135i \(0.486757\pi\)
\(480\) 1.13514 0.0518117
\(481\) 6.38869 0.291299
\(482\) −0.200854 −0.00914865
\(483\) −11.3252 −0.515313
\(484\) 21.9799 0.999085
\(485\) 26.9004 1.22148
\(486\) 0.0371239 0.00168398
\(487\) −30.2580 −1.37112 −0.685560 0.728016i \(-0.740443\pi\)
−0.685560 + 0.728016i \(0.740443\pi\)
\(488\) −1.54817 −0.0700824
\(489\) −15.3288 −0.693192
\(490\) 0.303872 0.0137275
\(491\) 10.5395 0.475641 0.237821 0.971309i \(-0.423567\pi\)
0.237821 + 0.971309i \(0.423567\pi\)
\(492\) −8.92985 −0.402589
\(493\) −37.1696 −1.67404
\(494\) 0.243637 0.0109617
\(495\) 0.127207 0.00571751
\(496\) 42.4412 1.90567
\(497\) 22.3729 1.00356
\(498\) −0.601188 −0.0269399
\(499\) −13.9722 −0.625482 −0.312741 0.949838i \(-0.601247\pi\)
−0.312741 + 0.949838i \(0.601247\pi\)
\(500\) 17.8169 0.796795
\(501\) −21.7145 −0.970132
\(502\) 0.0464368 0.00207258
\(503\) 12.2658 0.546907 0.273453 0.961885i \(-0.411834\pi\)
0.273453 + 0.961885i \(0.411834\pi\)
\(504\) 0.289014 0.0128737
\(505\) 1.17683 0.0523681
\(506\) −0.0107706 −0.000478813 0
\(507\) −1.00000 −0.0444116
\(508\) −5.71634 −0.253621
\(509\) −1.38145 −0.0612318 −0.0306159 0.999531i \(-0.509747\pi\)
−0.0306159 + 0.999531i \(0.509747\pi\)
\(510\) −0.452406 −0.0200329
\(511\) 26.2489 1.16118
\(512\) −2.96173 −0.130891
\(513\) 6.56279 0.289754
\(514\) 0.477941 0.0210811
\(515\) −2.55043 −0.112385
\(516\) −0.646682 −0.0284686
\(517\) −0.142671 −0.00627465
\(518\) −0.461764 −0.0202887
\(519\) −7.00246 −0.307374
\(520\) 0.378597 0.0166026
\(521\) −32.6388 −1.42993 −0.714966 0.699159i \(-0.753558\pi\)
−0.714966 + 0.699159i \(0.753558\pi\)
\(522\) −0.288789 −0.0126400
\(523\) 8.60655 0.376338 0.188169 0.982137i \(-0.439745\pi\)
0.188169 + 0.982137i \(0.439745\pi\)
\(524\) 17.7030 0.773361
\(525\) −2.92951 −0.127854
\(526\) −0.582573 −0.0254014
\(527\) −50.8028 −2.21301
\(528\) −0.199094 −0.00866446
\(529\) 10.8362 0.471138
\(530\) −0.225735 −0.00980532
\(531\) 5.13046 0.222643
\(532\) 25.5372 1.10718
\(533\) −4.46800 −0.193531
\(534\) −0.429903 −0.0186037
\(535\) 11.7760 0.509123
\(536\) −1.64956 −0.0712503
\(537\) −11.9163 −0.514225
\(538\) −0.890055 −0.0383730
\(539\) −0.160074 −0.00689488
\(540\) 5.09734 0.219354
\(541\) −26.6511 −1.14582 −0.572910 0.819618i \(-0.694186\pi\)
−0.572910 + 0.819618i \(0.694186\pi\)
\(542\) −0.253939 −0.0109076
\(543\) −9.82491 −0.421627
\(544\) 2.12666 0.0911797
\(545\) 19.2573 0.824891
\(546\) 0.0722783 0.00309323
\(547\) 10.3460 0.442361 0.221181 0.975233i \(-0.429009\pi\)
0.221181 + 0.975233i \(0.429009\pi\)
\(548\) 13.1847 0.563222
\(549\) −10.4293 −0.445111
\(550\) −0.00278607 −0.000118798 0
\(551\) −51.0523 −2.17490
\(552\) −0.863485 −0.0367524
\(553\) 26.9388 1.14555
\(554\) 0.0898828 0.00381875
\(555\) −16.2939 −0.691637
\(556\) 30.8143 1.30682
\(557\) 41.1497 1.74357 0.871784 0.489891i \(-0.162964\pi\)
0.871784 + 0.489891i \(0.162964\pi\)
\(558\) −0.394712 −0.0167095
\(559\) −0.323564 −0.0136853
\(560\) 19.8211 0.837595
\(561\) 0.238319 0.0100618
\(562\) −0.310681 −0.0131053
\(563\) 14.2317 0.599796 0.299898 0.953971i \(-0.403047\pi\)
0.299898 + 0.953971i \(0.403047\pi\)
\(564\) −5.71700 −0.240729
\(565\) 25.9534 1.09187
\(566\) −0.358227 −0.0150574
\(567\) 1.94695 0.0817640
\(568\) 1.70581 0.0715744
\(569\) −12.7864 −0.536032 −0.268016 0.963414i \(-0.586368\pi\)
−0.268016 + 0.963414i \(0.586368\pi\)
\(570\) −0.621377 −0.0260266
\(571\) 8.82640 0.369374 0.184687 0.982797i \(-0.440873\pi\)
0.184687 + 0.982797i \(0.440873\pi\)
\(572\) −0.0996845 −0.00416802
\(573\) −1.27975 −0.0534624
\(574\) 0.322940 0.0134792
\(575\) 8.75249 0.365004
\(576\) −7.96694 −0.331956
\(577\) −12.4553 −0.518522 −0.259261 0.965807i \(-0.583479\pi\)
−0.259261 + 0.965807i \(0.583479\pi\)
\(578\) −0.216466 −0.00900381
\(579\) −14.1365 −0.587493
\(580\) −39.6524 −1.64648
\(581\) −31.5290 −1.30804
\(582\) 0.391561 0.0162307
\(583\) 0.118913 0.00492488
\(584\) 2.00135 0.0828163
\(585\) 2.55043 0.105447
\(586\) 0.508031 0.0209866
\(587\) −6.78972 −0.280242 −0.140121 0.990134i \(-0.544749\pi\)
−0.140121 + 0.990134i \(0.544749\pi\)
\(588\) −6.41438 −0.264525
\(589\) −69.7774 −2.87513
\(590\) −0.485761 −0.0199985
\(591\) −17.5154 −0.720486
\(592\) 25.5020 1.04812
\(593\) 6.90788 0.283673 0.141836 0.989890i \(-0.454699\pi\)
0.141836 + 0.989890i \(0.454699\pi\)
\(594\) 0.00185162 7.59727e−5 0
\(595\) −23.7262 −0.972679
\(596\) −0.396860 −0.0162560
\(597\) −0.938390 −0.0384057
\(598\) −0.215946 −0.00883068
\(599\) 18.2094 0.744016 0.372008 0.928229i \(-0.378669\pi\)
0.372008 + 0.928229i \(0.378669\pi\)
\(600\) −0.223360 −0.00911863
\(601\) 12.9665 0.528915 0.264458 0.964397i \(-0.414807\pi\)
0.264458 + 0.964397i \(0.414807\pi\)
\(602\) 0.0233867 0.000953169 0
\(603\) −11.1123 −0.452529
\(604\) −43.4874 −1.76948
\(605\) −28.0483 −1.14033
\(606\) 0.0171299 0.000695854 0
\(607\) 9.83937 0.399368 0.199684 0.979860i \(-0.436008\pi\)
0.199684 + 0.979860i \(0.436008\pi\)
\(608\) 2.92095 0.118460
\(609\) −15.1454 −0.613723
\(610\) 0.987463 0.0399812
\(611\) −2.86047 −0.115722
\(612\) 9.54976 0.386026
\(613\) −21.4508 −0.866389 −0.433194 0.901301i \(-0.642614\pi\)
−0.433194 + 0.901301i \(0.642614\pi\)
\(614\) −0.152506 −0.00615464
\(615\) 11.3953 0.459503
\(616\) 0.0144150 0.000580798 0
\(617\) 47.7367 1.92181 0.960904 0.276882i \(-0.0893013\pi\)
0.960904 + 0.276882i \(0.0893013\pi\)
\(618\) −0.0371239 −0.00149334
\(619\) −29.4694 −1.18447 −0.592237 0.805764i \(-0.701755\pi\)
−0.592237 + 0.805764i \(0.701755\pi\)
\(620\) −54.1963 −2.17657
\(621\) −5.81689 −0.233424
\(622\) 0.433160 0.0173681
\(623\) −22.5460 −0.903288
\(624\) −3.99173 −0.159797
\(625\) −30.2593 −1.21037
\(626\) 0.991815 0.0396409
\(627\) 0.327330 0.0130723
\(628\) −2.69912 −0.107706
\(629\) −30.5263 −1.21716
\(630\) −0.184340 −0.00734430
\(631\) −35.9534 −1.43128 −0.715641 0.698469i \(-0.753865\pi\)
−0.715641 + 0.698469i \(0.753865\pi\)
\(632\) 2.05394 0.0817015
\(633\) −20.4535 −0.812955
\(634\) 0.309075 0.0122749
\(635\) 7.29457 0.289476
\(636\) 4.76501 0.188945
\(637\) −3.20940 −0.127161
\(638\) −0.0144038 −0.000570253 0
\(639\) 11.4913 0.454587
\(640\) 3.02460 0.119558
\(641\) 9.12451 0.360396 0.180198 0.983630i \(-0.442326\pi\)
0.180198 + 0.983630i \(0.442326\pi\)
\(642\) 0.171412 0.00676508
\(643\) −27.9447 −1.10203 −0.551016 0.834495i \(-0.685760\pi\)
−0.551016 + 0.834495i \(0.685760\pi\)
\(644\) −22.6347 −0.891933
\(645\) 0.825226 0.0324932
\(646\) −1.16414 −0.0458024
\(647\) −17.7754 −0.698825 −0.349412 0.936969i \(-0.613619\pi\)
−0.349412 + 0.936969i \(0.613619\pi\)
\(648\) 0.148445 0.00583145
\(649\) 0.255890 0.0100446
\(650\) −0.0558592 −0.00219098
\(651\) −20.7005 −0.811315
\(652\) −30.6365 −1.19982
\(653\) 30.6984 1.20132 0.600662 0.799503i \(-0.294904\pi\)
0.600662 + 0.799503i \(0.294904\pi\)
\(654\) 0.280308 0.0109609
\(655\) −22.5907 −0.882692
\(656\) −17.8351 −0.696343
\(657\) 13.4821 0.525987
\(658\) 0.206750 0.00805996
\(659\) 24.8822 0.969274 0.484637 0.874715i \(-0.338952\pi\)
0.484637 + 0.874715i \(0.338952\pi\)
\(660\) 0.254238 0.00989619
\(661\) 26.4240 1.02777 0.513886 0.857858i \(-0.328205\pi\)
0.513886 + 0.857858i \(0.328205\pi\)
\(662\) −0.720468 −0.0280018
\(663\) 4.77817 0.185569
\(664\) −2.40392 −0.0932904
\(665\) −32.5878 −1.26370
\(666\) −0.237173 −0.00919028
\(667\) 45.2499 1.75208
\(668\) −43.3991 −1.67916
\(669\) 10.3658 0.400763
\(670\) 1.05213 0.0406475
\(671\) −0.520177 −0.0200812
\(672\) 0.866543 0.0334276
\(673\) −23.5149 −0.906433 −0.453217 0.891400i \(-0.649724\pi\)
−0.453217 + 0.891400i \(0.649724\pi\)
\(674\) 1.04614 0.0402960
\(675\) −1.50467 −0.0579147
\(676\) −1.99862 −0.0768701
\(677\) −47.9322 −1.84219 −0.921093 0.389344i \(-0.872702\pi\)
−0.921093 + 0.389344i \(0.872702\pi\)
\(678\) 0.377777 0.0145084
\(679\) 20.5352 0.788070
\(680\) −1.80900 −0.0693720
\(681\) −0.475721 −0.0182297
\(682\) −0.0196869 −0.000753850 0
\(683\) 24.0109 0.918750 0.459375 0.888242i \(-0.348073\pi\)
0.459375 + 0.888242i \(0.348073\pi\)
\(684\) 13.1165 0.501523
\(685\) −16.8249 −0.642846
\(686\) 0.737918 0.0281738
\(687\) 8.63360 0.329393
\(688\) −1.29158 −0.0492411
\(689\) 2.38415 0.0908288
\(690\) 0.550753 0.0209668
\(691\) −17.2194 −0.655058 −0.327529 0.944841i \(-0.606216\pi\)
−0.327529 + 0.944841i \(0.606216\pi\)
\(692\) −13.9953 −0.532020
\(693\) 0.0971071 0.00368879
\(694\) 0.114618 0.00435085
\(695\) −39.3218 −1.49156
\(696\) −1.15476 −0.0437710
\(697\) 21.3489 0.808647
\(698\) 0.813908 0.0308069
\(699\) −17.8265 −0.674261
\(700\) −5.85498 −0.221297
\(701\) 20.8067 0.785860 0.392930 0.919568i \(-0.371461\pi\)
0.392930 + 0.919568i \(0.371461\pi\)
\(702\) 0.0371239 0.00140115
\(703\) −41.9276 −1.58133
\(704\) −0.397364 −0.0149762
\(705\) 7.29542 0.274761
\(706\) −0.219565 −0.00826343
\(707\) 0.898368 0.0337866
\(708\) 10.2538 0.385363
\(709\) 1.89439 0.0711452 0.0355726 0.999367i \(-0.488675\pi\)
0.0355726 + 0.999367i \(0.488675\pi\)
\(710\) −1.08801 −0.0408324
\(711\) 13.8364 0.518907
\(712\) −1.71902 −0.0644230
\(713\) 61.8467 2.31618
\(714\) −0.345358 −0.0129247
\(715\) 0.127207 0.00475726
\(716\) −23.8161 −0.890049
\(717\) −18.5128 −0.691371
\(718\) 0.108048 0.00403233
\(719\) −2.51146 −0.0936616 −0.0468308 0.998903i \(-0.514912\pi\)
−0.0468308 + 0.998903i \(0.514912\pi\)
\(720\) 10.1806 0.379409
\(721\) −1.94695 −0.0725081
\(722\) −0.893581 −0.0332556
\(723\) −5.41036 −0.201214
\(724\) −19.6363 −0.729777
\(725\) 11.7049 0.434709
\(726\) −0.408271 −0.0151524
\(727\) 33.1643 1.23000 0.614998 0.788529i \(-0.289157\pi\)
0.614998 + 0.788529i \(0.289157\pi\)
\(728\) 0.289014 0.0107116
\(729\) 1.00000 0.0370370
\(730\) −1.27651 −0.0472458
\(731\) 1.54604 0.0571825
\(732\) −20.8442 −0.770423
\(733\) 27.2252 1.00559 0.502793 0.864407i \(-0.332306\pi\)
0.502793 + 0.864407i \(0.332306\pi\)
\(734\) −0.615346 −0.0227128
\(735\) 8.18534 0.301921
\(736\) −2.58897 −0.0954306
\(737\) −0.554245 −0.0204159
\(738\) 0.165870 0.00610576
\(739\) −26.2339 −0.965030 −0.482515 0.875888i \(-0.660277\pi\)
−0.482515 + 0.875888i \(0.660277\pi\)
\(740\) −32.5653 −1.19712
\(741\) 6.56279 0.241090
\(742\) −0.172322 −0.00632614
\(743\) 34.4633 1.26434 0.632168 0.774832i \(-0.282165\pi\)
0.632168 + 0.774832i \(0.282165\pi\)
\(744\) −1.57830 −0.0578634
\(745\) 0.506429 0.0185541
\(746\) 0.348838 0.0127719
\(747\) −16.1941 −0.592511
\(748\) 0.476309 0.0174156
\(749\) 8.98961 0.328473
\(750\) −0.330944 −0.0120844
\(751\) 17.3190 0.631978 0.315989 0.948763i \(-0.397664\pi\)
0.315989 + 0.948763i \(0.397664\pi\)
\(752\) −11.4182 −0.416380
\(753\) 1.25086 0.0455838
\(754\) −0.288789 −0.0105171
\(755\) 55.4939 2.01963
\(756\) 3.89121 0.141522
\(757\) −21.0093 −0.763596 −0.381798 0.924246i \(-0.624695\pi\)
−0.381798 + 0.924246i \(0.624695\pi\)
\(758\) −0.0694165 −0.00252132
\(759\) −0.290127 −0.0105309
\(760\) −2.48465 −0.0901277
\(761\) 12.5542 0.455088 0.227544 0.973768i \(-0.426930\pi\)
0.227544 + 0.973768i \(0.426930\pi\)
\(762\) 0.106180 0.00384648
\(763\) 14.7006 0.532199
\(764\) −2.55774 −0.0925358
\(765\) −12.1864 −0.440599
\(766\) 0.840274 0.0303603
\(767\) 5.13046 0.185250
\(768\) −15.8899 −0.573376
\(769\) −32.4897 −1.17161 −0.585805 0.810452i \(-0.699221\pi\)
−0.585805 + 0.810452i \(0.699221\pi\)
\(770\) −0.00919427 −0.000331339 0
\(771\) 12.8742 0.463653
\(772\) −28.2535 −1.01687
\(773\) 34.6872 1.24761 0.623805 0.781580i \(-0.285586\pi\)
0.623805 + 0.781580i \(0.285586\pi\)
\(774\) 0.0120120 0.000431761 0
\(775\) 15.9980 0.574667
\(776\) 1.56570 0.0562055
\(777\) −12.4384 −0.446227
\(778\) −0.684707 −0.0245479
\(779\) 29.3226 1.05059
\(780\) 5.09734 0.182514
\(781\) 0.573145 0.0205087
\(782\) 1.03183 0.0368980
\(783\) −7.77905 −0.278001
\(784\) −12.8111 −0.457538
\(785\) 3.44432 0.122933
\(786\) −0.328830 −0.0117290
\(787\) −17.9722 −0.640640 −0.320320 0.947309i \(-0.603790\pi\)
−0.320320 + 0.947309i \(0.603790\pi\)
\(788\) −35.0066 −1.24706
\(789\) −15.6927 −0.558673
\(790\) −1.31006 −0.0466098
\(791\) 19.8123 0.704445
\(792\) 0.00740391 0.000263087 0
\(793\) −10.4293 −0.370355
\(794\) 1.13160 0.0401590
\(795\) −6.08059 −0.215656
\(796\) −1.87549 −0.0664749
\(797\) −24.2753 −0.859875 −0.429938 0.902859i \(-0.641464\pi\)
−0.429938 + 0.902859i \(0.641464\pi\)
\(798\) −0.474347 −0.0167917
\(799\) 13.6678 0.483533
\(800\) −0.669695 −0.0236773
\(801\) −11.5802 −0.409167
\(802\) −1.39957 −0.0494206
\(803\) 0.672442 0.0237300
\(804\) −22.2093 −0.783263
\(805\) 28.8840 1.01803
\(806\) −0.394712 −0.0139031
\(807\) −23.9752 −0.843969
\(808\) 0.0684959 0.00240968
\(809\) −4.36519 −0.153472 −0.0767360 0.997051i \(-0.524450\pi\)
−0.0767360 + 0.997051i \(0.524450\pi\)
\(810\) −0.0946818 −0.00332678
\(811\) −18.2835 −0.642021 −0.321011 0.947076i \(-0.604023\pi\)
−0.321011 + 0.947076i \(0.604023\pi\)
\(812\) −30.2699 −1.06227
\(813\) −6.84031 −0.239900
\(814\) −0.0118294 −0.000414620 0
\(815\) 39.0949 1.36944
\(816\) 19.0732 0.667695
\(817\) 2.12348 0.0742913
\(818\) 1.13196 0.0395781
\(819\) 1.94695 0.0680318
\(820\) 22.7749 0.795335
\(821\) −37.1048 −1.29497 −0.647483 0.762080i \(-0.724179\pi\)
−0.647483 + 0.762080i \(0.724179\pi\)
\(822\) −0.244903 −0.00854196
\(823\) 44.6479 1.55633 0.778165 0.628060i \(-0.216151\pi\)
0.778165 + 0.628060i \(0.216151\pi\)
\(824\) −0.148445 −0.00517131
\(825\) −0.0750478 −0.00261283
\(826\) −0.370821 −0.0129025
\(827\) −16.5969 −0.577132 −0.288566 0.957460i \(-0.593178\pi\)
−0.288566 + 0.957460i \(0.593178\pi\)
\(828\) −11.6258 −0.404023
\(829\) −9.90980 −0.344182 −0.172091 0.985081i \(-0.555052\pi\)
−0.172091 + 0.985081i \(0.555052\pi\)
\(830\) 1.53329 0.0532211
\(831\) 2.42115 0.0839889
\(832\) −7.96694 −0.276204
\(833\) 15.3351 0.531329
\(834\) −0.572368 −0.0198195
\(835\) 55.3812 1.91654
\(836\) 0.654208 0.0226263
\(837\) −10.6323 −0.367505
\(838\) −0.967070 −0.0334069
\(839\) 33.2864 1.14917 0.574587 0.818443i \(-0.305163\pi\)
0.574587 + 0.818443i \(0.305163\pi\)
\(840\) −0.737107 −0.0254326
\(841\) 31.5137 1.08668
\(842\) −0.0786263 −0.00270964
\(843\) −8.36874 −0.288235
\(844\) −40.8789 −1.40711
\(845\) 2.55043 0.0877373
\(846\) 0.106192 0.00365096
\(847\) −21.4116 −0.735710
\(848\) 9.51688 0.326811
\(849\) −9.64948 −0.331169
\(850\) 0.266905 0.00915476
\(851\) 37.1623 1.27391
\(852\) 22.9667 0.786825
\(853\) 27.5576 0.943554 0.471777 0.881718i \(-0.343613\pi\)
0.471777 + 0.881718i \(0.343613\pi\)
\(854\) 0.753811 0.0257949
\(855\) −16.7379 −0.572424
\(856\) 0.685411 0.0234269
\(857\) −29.9475 −1.02299 −0.511494 0.859287i \(-0.670908\pi\)
−0.511494 + 0.859287i \(0.670908\pi\)
\(858\) 0.00185162 6.32131e−5 0
\(859\) −12.2554 −0.418148 −0.209074 0.977900i \(-0.567045\pi\)
−0.209074 + 0.977900i \(0.567045\pi\)
\(860\) 1.64931 0.0562412
\(861\) 8.69896 0.296460
\(862\) −0.378225 −0.0128824
\(863\) −22.4984 −0.765856 −0.382928 0.923778i \(-0.625084\pi\)
−0.382928 + 0.923778i \(0.625084\pi\)
\(864\) 0.445078 0.0151419
\(865\) 17.8592 0.607232
\(866\) −1.27476 −0.0433182
\(867\) −5.83091 −0.198028
\(868\) −41.3724 −1.40427
\(869\) 0.690114 0.0234105
\(870\) 0.736535 0.0249709
\(871\) −11.1123 −0.376527
\(872\) 1.12085 0.0379567
\(873\) 10.5474 0.356976
\(874\) 1.41721 0.0479377
\(875\) −17.3562 −0.586747
\(876\) 26.9456 0.910409
\(877\) −49.6211 −1.67559 −0.837794 0.545987i \(-0.816155\pi\)
−0.837794 + 0.545987i \(0.816155\pi\)
\(878\) −1.11271 −0.0375522
\(879\) 13.6847 0.461574
\(880\) 0.507775 0.0171171
\(881\) −55.6520 −1.87496 −0.937482 0.348033i \(-0.886850\pi\)
−0.937482 + 0.348033i \(0.886850\pi\)
\(882\) 0.119146 0.00401184
\(883\) −48.1208 −1.61939 −0.809697 0.586849i \(-0.800368\pi\)
−0.809697 + 0.586849i \(0.800368\pi\)
\(884\) 9.54976 0.321193
\(885\) −13.0848 −0.439842
\(886\) −1.00350 −0.0337133
\(887\) −7.92397 −0.266061 −0.133030 0.991112i \(-0.542471\pi\)
−0.133030 + 0.991112i \(0.542471\pi\)
\(888\) −0.948367 −0.0318251
\(889\) 5.56854 0.186763
\(890\) 1.09644 0.0367526
\(891\) 0.0498766 0.00167093
\(892\) 20.7172 0.693664
\(893\) 18.7727 0.628204
\(894\) 0.00737157 0.000246542 0
\(895\) 30.3915 1.01588
\(896\) 2.30892 0.0771357
\(897\) −5.81689 −0.194220
\(898\) 0.505104 0.0168555
\(899\) 82.7090 2.75850
\(900\) −3.00726 −0.100242
\(901\) −11.3919 −0.379518
\(902\) 0.00827303 0.000275462 0
\(903\) 0.629962 0.0209638
\(904\) 1.51059 0.0502414
\(905\) 25.0577 0.832946
\(906\) 0.807768 0.0268363
\(907\) 21.5885 0.716833 0.358417 0.933562i \(-0.383317\pi\)
0.358417 + 0.933562i \(0.383317\pi\)
\(908\) −0.950786 −0.0315529
\(909\) 0.461424 0.0153045
\(910\) −0.184340 −0.00611082
\(911\) −2.11267 −0.0699958 −0.0349979 0.999387i \(-0.511142\pi\)
−0.0349979 + 0.999387i \(0.511142\pi\)
\(912\) 26.1969 0.867466
\(913\) −0.807706 −0.0267312
\(914\) 0.958700 0.0317110
\(915\) 26.5991 0.879339
\(916\) 17.2553 0.570131
\(917\) −17.2453 −0.569491
\(918\) −0.177384 −0.00585456
\(919\) −40.0866 −1.32234 −0.661168 0.750238i \(-0.729939\pi\)
−0.661168 + 0.750238i \(0.729939\pi\)
\(920\) 2.20225 0.0726062
\(921\) −4.10802 −0.135364
\(922\) 0.240632 0.00792479
\(923\) 11.4913 0.378239
\(924\) 0.194080 0.00638477
\(925\) 9.61286 0.316069
\(926\) 0.0687157 0.00225814
\(927\) −1.00000 −0.0328443
\(928\) −3.46229 −0.113655
\(929\) −46.9629 −1.54080 −0.770401 0.637559i \(-0.779944\pi\)
−0.770401 + 0.637559i \(0.779944\pi\)
\(930\) 1.00668 0.0330104
\(931\) 21.0626 0.690300
\(932\) −35.6285 −1.16705
\(933\) 11.6679 0.381991
\(934\) −0.280971 −0.00919367
\(935\) −0.607815 −0.0198777
\(936\) 0.148445 0.00485206
\(937\) 1.48904 0.0486449 0.0243225 0.999704i \(-0.492257\pi\)
0.0243225 + 0.999704i \(0.492257\pi\)
\(938\) 0.803180 0.0262247
\(939\) 26.7163 0.871855
\(940\) 14.5808 0.475573
\(941\) 36.9928 1.20593 0.602966 0.797767i \(-0.293985\pi\)
0.602966 + 0.797767i \(0.293985\pi\)
\(942\) 0.0501354 0.00163350
\(943\) −25.9899 −0.846347
\(944\) 20.4794 0.666548
\(945\) −4.96554 −0.161529
\(946\) 0.000599116 0 1.94790e−5 0
\(947\) −3.01243 −0.0978909 −0.0489454 0.998801i \(-0.515586\pi\)
−0.0489454 + 0.998801i \(0.515586\pi\)
\(948\) 27.6538 0.898154
\(949\) 13.4821 0.437648
\(950\) 0.366592 0.0118938
\(951\) 8.32549 0.269973
\(952\) −1.38096 −0.0447570
\(953\) −52.8784 −1.71290 −0.856449 0.516231i \(-0.827335\pi\)
−0.856449 + 0.516231i \(0.827335\pi\)
\(954\) −0.0885089 −0.00286558
\(955\) 3.26391 0.105618
\(956\) −37.0000 −1.19667
\(957\) −0.387993 −0.0125420
\(958\) −0.0675869 −0.00218363
\(959\) −12.8438 −0.414748
\(960\) 20.3191 0.655796
\(961\) 82.0453 2.64662
\(962\) −0.237173 −0.00764678
\(963\) 4.61729 0.148790
\(964\) −10.8133 −0.348272
\(965\) 36.0541 1.16062
\(966\) 0.420435 0.0135273
\(967\) 23.8672 0.767518 0.383759 0.923433i \(-0.374629\pi\)
0.383759 + 0.923433i \(0.374629\pi\)
\(968\) −1.63252 −0.0524712
\(969\) −31.3581 −1.00737
\(970\) −0.998647 −0.0320646
\(971\) 10.7346 0.344491 0.172245 0.985054i \(-0.444898\pi\)
0.172245 + 0.985054i \(0.444898\pi\)
\(972\) 1.99862 0.0641058
\(973\) −30.0175 −0.962318
\(974\) 1.12330 0.0359927
\(975\) −1.50467 −0.0481880
\(976\) −41.6309 −1.33257
\(977\) 5.66977 0.181392 0.0906960 0.995879i \(-0.471091\pi\)
0.0906960 + 0.995879i \(0.471091\pi\)
\(978\) 0.569065 0.0181967
\(979\) −0.577582 −0.0184596
\(980\) 16.3594 0.522582
\(981\) 7.55061 0.241073
\(982\) −0.391268 −0.0124859
\(983\) 53.1999 1.69681 0.848406 0.529346i \(-0.177563\pi\)
0.848406 + 0.529346i \(0.177563\pi\)
\(984\) 0.663251 0.0211437
\(985\) 44.6717 1.42336
\(986\) 1.37988 0.0439444
\(987\) 5.56919 0.177269
\(988\) 13.1165 0.417293
\(989\) −1.88214 −0.0598484
\(990\) −0.00472241 −0.000150088 0
\(991\) −37.2820 −1.18430 −0.592150 0.805828i \(-0.701721\pi\)
−0.592150 + 0.805828i \(0.701721\pi\)
\(992\) −4.73219 −0.150247
\(993\) −19.4071 −0.615866
\(994\) −0.830568 −0.0263440
\(995\) 2.39329 0.0758725
\(996\) −32.3659 −1.02555
\(997\) −36.5586 −1.15782 −0.578911 0.815391i \(-0.696522\pi\)
−0.578911 + 0.815391i \(0.696522\pi\)
\(998\) 0.518704 0.0164193
\(999\) −6.38869 −0.202129
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 \(a_p\))