Properties

Label 8041.2.a.i.1.19
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 78
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(0\)
Dimension: \(78\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.53655 q^{2} +0.0485562 q^{3} +0.360996 q^{4} -0.584069 q^{5} -0.0746091 q^{6} -1.23435 q^{7} +2.51842 q^{8} -2.99764 q^{9} +O(q^{10})\) \(q-1.53655 q^{2} +0.0485562 q^{3} +0.360996 q^{4} -0.584069 q^{5} -0.0746091 q^{6} -1.23435 q^{7} +2.51842 q^{8} -2.99764 q^{9} +0.897453 q^{10} +1.00000 q^{11} +0.0175286 q^{12} -0.643118 q^{13} +1.89665 q^{14} -0.0283601 q^{15} -4.59167 q^{16} -1.00000 q^{17} +4.60604 q^{18} -5.42219 q^{19} -0.210846 q^{20} -0.0599355 q^{21} -1.53655 q^{22} -9.24603 q^{23} +0.122285 q^{24} -4.65886 q^{25} +0.988185 q^{26} -0.291222 q^{27} -0.445597 q^{28} -8.11165 q^{29} +0.0435769 q^{30} -6.20028 q^{31} +2.01852 q^{32} +0.0485562 q^{33} +1.53655 q^{34} +0.720948 q^{35} -1.08214 q^{36} +5.04229 q^{37} +8.33148 q^{38} -0.0312273 q^{39} -1.47093 q^{40} -4.44113 q^{41} +0.0920941 q^{42} -1.00000 q^{43} +0.360996 q^{44} +1.75083 q^{45} +14.2070 q^{46} -7.15793 q^{47} -0.222954 q^{48} -5.47637 q^{49} +7.15859 q^{50} -0.0485562 q^{51} -0.232163 q^{52} +9.14969 q^{53} +0.447479 q^{54} -0.584069 q^{55} -3.10862 q^{56} -0.263281 q^{57} +12.4640 q^{58} +0.525978 q^{59} -0.0102379 q^{60} -11.6655 q^{61} +9.52706 q^{62} +3.70015 q^{63} +6.08179 q^{64} +0.375625 q^{65} -0.0746091 q^{66} -0.835380 q^{67} -0.360996 q^{68} -0.448952 q^{69} -1.10777 q^{70} +0.263645 q^{71} -7.54931 q^{72} +13.9133 q^{73} -7.74775 q^{74} -0.226216 q^{75} -1.95739 q^{76} -1.23435 q^{77} +0.0479825 q^{78} +0.175797 q^{79} +2.68185 q^{80} +8.97879 q^{81} +6.82404 q^{82} +7.40067 q^{83} -0.0216365 q^{84} +0.584069 q^{85} +1.53655 q^{86} -0.393870 q^{87} +2.51842 q^{88} -10.3951 q^{89} -2.69024 q^{90} +0.793836 q^{91} -3.33778 q^{92} -0.301062 q^{93} +10.9985 q^{94} +3.16693 q^{95} +0.0980114 q^{96} -1.48711 q^{97} +8.41473 q^{98} -2.99764 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + O(q^{10}) \) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + 3q^{10} + 78q^{11} + 31q^{12} - 16q^{13} + 31q^{14} + 38q^{15} + 121q^{16} - 78q^{17} + 11q^{18} + 51q^{20} + 6q^{21} + 7q^{22} + 48q^{23} + 11q^{24} + 101q^{25} + 18q^{26} + 46q^{27} + 27q^{28} + 22q^{29} + 14q^{30} + 56q^{31} + 83q^{32} + 10q^{33} - 7q^{34} + 24q^{35} + 139q^{36} + 53q^{37} + 10q^{38} + 79q^{39} - q^{40} + 23q^{41} + 17q^{42} - 78q^{43} + 91q^{44} + 76q^{45} + 21q^{46} + 57q^{47} + 78q^{48} + 115q^{49} + 58q^{50} - 10q^{51} - 63q^{52} + 22q^{53} - 18q^{54} + 17q^{55} + 111q^{56} - 11q^{57} + 36q^{58} + 71q^{59} + 36q^{60} + 4q^{61} - 5q^{62} + 71q^{63} + 183q^{64} + 47q^{65} + 12q^{66} + 11q^{67} - 91q^{68} + 31q^{69} + 33q^{70} + 159q^{71} + 59q^{72} + 2q^{73} - 4q^{74} + 83q^{75} - 44q^{76} + 11q^{77} + 101q^{78} + 35q^{79} + 85q^{80} + 170q^{81} + 98q^{82} - 32q^{83} + 44q^{84} - 17q^{85} - 7q^{86} - 6q^{87} + 33q^{88} + 50q^{89} - 5q^{90} + 86q^{91} + 106q^{92} + 68q^{93} - q^{94} + 109q^{95} - 50q^{96} + 40q^{97} + 106q^{98} + 102q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.53655 −1.08651 −0.543254 0.839569i \(-0.682808\pi\)
−0.543254 + 0.839569i \(0.682808\pi\)
\(3\) 0.0485562 0.0280339 0.0140170 0.999902i \(-0.495538\pi\)
0.0140170 + 0.999902i \(0.495538\pi\)
\(4\) 0.360996 0.180498
\(5\) −0.584069 −0.261203 −0.130602 0.991435i \(-0.541691\pi\)
−0.130602 + 0.991435i \(0.541691\pi\)
\(6\) −0.0746091 −0.0304590
\(7\) −1.23435 −0.466542 −0.233271 0.972412i \(-0.574943\pi\)
−0.233271 + 0.972412i \(0.574943\pi\)
\(8\) 2.51842 0.890395
\(9\) −2.99764 −0.999214
\(10\) 0.897453 0.283799
\(11\) 1.00000 0.301511
\(12\) 0.0175286 0.00506006
\(13\) −0.643118 −0.178369 −0.0891845 0.996015i \(-0.528426\pi\)
−0.0891845 + 0.996015i \(0.528426\pi\)
\(14\) 1.89665 0.506901
\(15\) −0.0283601 −0.00732255
\(16\) −4.59167 −1.14792
\(17\) −1.00000 −0.242536
\(18\) 4.60604 1.08565
\(19\) −5.42219 −1.24393 −0.621967 0.783043i \(-0.713666\pi\)
−0.621967 + 0.783043i \(0.713666\pi\)
\(20\) −0.210846 −0.0471467
\(21\) −0.0599355 −0.0130790
\(22\) −1.53655 −0.327594
\(23\) −9.24603 −1.92793 −0.963965 0.266028i \(-0.914289\pi\)
−0.963965 + 0.266028i \(0.914289\pi\)
\(24\) 0.122285 0.0249613
\(25\) −4.65886 −0.931773
\(26\) 0.988185 0.193799
\(27\) −0.291222 −0.0560458
\(28\) −0.445597 −0.0842099
\(29\) −8.11165 −1.50629 −0.753147 0.657852i \(-0.771465\pi\)
−0.753147 + 0.657852i \(0.771465\pi\)
\(30\) 0.0435769 0.00795601
\(31\) −6.20028 −1.11360 −0.556802 0.830645i \(-0.687972\pi\)
−0.556802 + 0.830645i \(0.687972\pi\)
\(32\) 2.01852 0.356827
\(33\) 0.0485562 0.00845254
\(34\) 1.53655 0.263517
\(35\) 0.720948 0.121862
\(36\) −1.08214 −0.180356
\(37\) 5.04229 0.828948 0.414474 0.910061i \(-0.363966\pi\)
0.414474 + 0.910061i \(0.363966\pi\)
\(38\) 8.33148 1.35154
\(39\) −0.0312273 −0.00500038
\(40\) −1.47093 −0.232574
\(41\) −4.44113 −0.693588 −0.346794 0.937941i \(-0.612730\pi\)
−0.346794 + 0.937941i \(0.612730\pi\)
\(42\) 0.0920941 0.0142104
\(43\) −1.00000 −0.152499
\(44\) 0.360996 0.0544221
\(45\) 1.75083 0.260998
\(46\) 14.2070 2.09471
\(47\) −7.15793 −1.04409 −0.522046 0.852917i \(-0.674831\pi\)
−0.522046 + 0.852917i \(0.674831\pi\)
\(48\) −0.222954 −0.0321806
\(49\) −5.47637 −0.782338
\(50\) 7.15859 1.01238
\(51\) −0.0485562 −0.00679922
\(52\) −0.232163 −0.0321952
\(53\) 9.14969 1.25681 0.628403 0.777888i \(-0.283709\pi\)
0.628403 + 0.777888i \(0.283709\pi\)
\(54\) 0.447479 0.0608941
\(55\) −0.584069 −0.0787558
\(56\) −3.10862 −0.415407
\(57\) −0.263281 −0.0348724
\(58\) 12.4640 1.63660
\(59\) 0.525978 0.0684766 0.0342383 0.999414i \(-0.489099\pi\)
0.0342383 + 0.999414i \(0.489099\pi\)
\(60\) −0.0102379 −0.00132171
\(61\) −11.6655 −1.49361 −0.746806 0.665042i \(-0.768414\pi\)
−0.746806 + 0.665042i \(0.768414\pi\)
\(62\) 9.52706 1.20994
\(63\) 3.70015 0.466176
\(64\) 6.08179 0.760224
\(65\) 0.375625 0.0465906
\(66\) −0.0746091 −0.00918375
\(67\) −0.835380 −0.102058 −0.0510290 0.998697i \(-0.516250\pi\)
−0.0510290 + 0.998697i \(0.516250\pi\)
\(68\) −0.360996 −0.0437772
\(69\) −0.448952 −0.0540474
\(70\) −1.10777 −0.132404
\(71\) 0.263645 0.0312889 0.0156445 0.999878i \(-0.495020\pi\)
0.0156445 + 0.999878i \(0.495020\pi\)
\(72\) −7.54931 −0.889695
\(73\) 13.9133 1.62843 0.814215 0.580563i \(-0.197168\pi\)
0.814215 + 0.580563i \(0.197168\pi\)
\(74\) −7.74775 −0.900658
\(75\) −0.226216 −0.0261212
\(76\) −1.95739 −0.224528
\(77\) −1.23435 −0.140668
\(78\) 0.0479825 0.00543295
\(79\) 0.175797 0.0197787 0.00988935 0.999951i \(-0.496852\pi\)
0.00988935 + 0.999951i \(0.496852\pi\)
\(80\) 2.68185 0.299840
\(81\) 8.97879 0.997643
\(82\) 6.82404 0.753589
\(83\) 7.40067 0.812329 0.406165 0.913800i \(-0.366866\pi\)
0.406165 + 0.913800i \(0.366866\pi\)
\(84\) −0.0216365 −0.00236073
\(85\) 0.584069 0.0633512
\(86\) 1.53655 0.165691
\(87\) −0.393870 −0.0422273
\(88\) 2.51842 0.268464
\(89\) −10.3951 −1.10188 −0.550940 0.834545i \(-0.685731\pi\)
−0.550940 + 0.834545i \(0.685731\pi\)
\(90\) −2.69024 −0.283576
\(91\) 0.793836 0.0832166
\(92\) −3.33778 −0.347987
\(93\) −0.301062 −0.0312187
\(94\) 10.9985 1.13441
\(95\) 3.16693 0.324920
\(96\) 0.0980114 0.0100032
\(97\) −1.48711 −0.150993 −0.0754967 0.997146i \(-0.524054\pi\)
−0.0754967 + 0.997146i \(0.524054\pi\)
\(98\) 8.41473 0.850016
\(99\) −2.99764 −0.301274
\(100\) −1.68183 −0.168183
\(101\) −6.32102 −0.628965 −0.314482 0.949263i \(-0.601831\pi\)
−0.314482 + 0.949263i \(0.601831\pi\)
\(102\) 0.0746091 0.00738740
\(103\) −4.78599 −0.471578 −0.235789 0.971804i \(-0.575767\pi\)
−0.235789 + 0.971804i \(0.575767\pi\)
\(104\) −1.61964 −0.158819
\(105\) 0.0350065 0.00341628
\(106\) −14.0590 −1.36553
\(107\) 9.13716 0.883323 0.441661 0.897182i \(-0.354389\pi\)
0.441661 + 0.897182i \(0.354389\pi\)
\(108\) −0.105130 −0.0101161
\(109\) 3.94113 0.377492 0.188746 0.982026i \(-0.439558\pi\)
0.188746 + 0.982026i \(0.439558\pi\)
\(110\) 0.897453 0.0855688
\(111\) 0.244834 0.0232386
\(112\) 5.66775 0.535552
\(113\) −8.68162 −0.816698 −0.408349 0.912826i \(-0.633895\pi\)
−0.408349 + 0.912826i \(0.633895\pi\)
\(114\) 0.404545 0.0378891
\(115\) 5.40032 0.503582
\(116\) −2.92827 −0.271883
\(117\) 1.92784 0.178229
\(118\) −0.808194 −0.0744003
\(119\) 1.23435 0.113153
\(120\) −0.0714226 −0.00651997
\(121\) 1.00000 0.0909091
\(122\) 17.9246 1.62282
\(123\) −0.215644 −0.0194440
\(124\) −2.23827 −0.201003
\(125\) 5.64144 0.504586
\(126\) −5.68548 −0.506503
\(127\) 13.6417 1.21050 0.605251 0.796035i \(-0.293073\pi\)
0.605251 + 0.796035i \(0.293073\pi\)
\(128\) −13.3820 −1.18282
\(129\) −0.0485562 −0.00427513
\(130\) −0.577168 −0.0506210
\(131\) −4.29946 −0.375646 −0.187823 0.982203i \(-0.560143\pi\)
−0.187823 + 0.982203i \(0.560143\pi\)
\(132\) 0.0175286 0.00152567
\(133\) 6.69290 0.580348
\(134\) 1.28361 0.110887
\(135\) 0.170094 0.0146394
\(136\) −2.51842 −0.215953
\(137\) −18.4732 −1.57827 −0.789136 0.614219i \(-0.789471\pi\)
−0.789136 + 0.614219i \(0.789471\pi\)
\(138\) 0.689838 0.0587229
\(139\) −21.7475 −1.84460 −0.922299 0.386477i \(-0.873692\pi\)
−0.922299 + 0.386477i \(0.873692\pi\)
\(140\) 0.260259 0.0219959
\(141\) −0.347562 −0.0292700
\(142\) −0.405105 −0.0339957
\(143\) −0.643118 −0.0537803
\(144\) 13.7642 1.14702
\(145\) 4.73776 0.393449
\(146\) −21.3785 −1.76930
\(147\) −0.265911 −0.0219320
\(148\) 1.82025 0.149623
\(149\) −18.4626 −1.51252 −0.756259 0.654272i \(-0.772975\pi\)
−0.756259 + 0.654272i \(0.772975\pi\)
\(150\) 0.347594 0.0283809
\(151\) 1.00422 0.0817220 0.0408610 0.999165i \(-0.486990\pi\)
0.0408610 + 0.999165i \(0.486990\pi\)
\(152\) −13.6553 −1.10759
\(153\) 2.99764 0.242345
\(154\) 1.89665 0.152837
\(155\) 3.62139 0.290877
\(156\) −0.0112729 −0.000902557 0
\(157\) −0.666392 −0.0531839 −0.0265920 0.999646i \(-0.508465\pi\)
−0.0265920 + 0.999646i \(0.508465\pi\)
\(158\) −0.270121 −0.0214897
\(159\) 0.444274 0.0352332
\(160\) −1.17895 −0.0932043
\(161\) 11.4129 0.899461
\(162\) −13.7964 −1.08395
\(163\) −15.0794 −1.18111 −0.590555 0.806997i \(-0.701091\pi\)
−0.590555 + 0.806997i \(0.701091\pi\)
\(164\) −1.60323 −0.125191
\(165\) −0.0283601 −0.00220783
\(166\) −11.3715 −0.882601
\(167\) −0.955468 −0.0739363 −0.0369682 0.999316i \(-0.511770\pi\)
−0.0369682 + 0.999316i \(0.511770\pi\)
\(168\) −0.150943 −0.0116455
\(169\) −12.5864 −0.968185
\(170\) −0.897453 −0.0688315
\(171\) 16.2538 1.24296
\(172\) −0.360996 −0.0275257
\(173\) −14.4563 −1.09909 −0.549544 0.835465i \(-0.685199\pi\)
−0.549544 + 0.835465i \(0.685199\pi\)
\(174\) 0.605203 0.0458803
\(175\) 5.75069 0.434711
\(176\) −4.59167 −0.346110
\(177\) 0.0255395 0.00191967
\(178\) 15.9727 1.19720
\(179\) 6.92508 0.517605 0.258802 0.965930i \(-0.416672\pi\)
0.258802 + 0.965930i \(0.416672\pi\)
\(180\) 0.632042 0.0471096
\(181\) 11.4946 0.854390 0.427195 0.904159i \(-0.359502\pi\)
0.427195 + 0.904159i \(0.359502\pi\)
\(182\) −1.21977 −0.0904155
\(183\) −0.566431 −0.0418718
\(184\) −23.2854 −1.71662
\(185\) −2.94505 −0.216524
\(186\) 0.462597 0.0339193
\(187\) −1.00000 −0.0731272
\(188\) −2.58398 −0.188456
\(189\) 0.359472 0.0261477
\(190\) −4.86616 −0.353028
\(191\) −0.906511 −0.0655928 −0.0327964 0.999462i \(-0.510441\pi\)
−0.0327964 + 0.999462i \(0.510441\pi\)
\(192\) 0.295308 0.0213120
\(193\) −8.49348 −0.611374 −0.305687 0.952132i \(-0.598886\pi\)
−0.305687 + 0.952132i \(0.598886\pi\)
\(194\) 2.28503 0.164055
\(195\) 0.0182389 0.00130612
\(196\) −1.97695 −0.141210
\(197\) 17.9019 1.27545 0.637727 0.770262i \(-0.279875\pi\)
0.637727 + 0.770262i \(0.279875\pi\)
\(198\) 4.60604 0.327337
\(199\) −26.7661 −1.89740 −0.948698 0.316184i \(-0.897598\pi\)
−0.948698 + 0.316184i \(0.897598\pi\)
\(200\) −11.7330 −0.829646
\(201\) −0.0405628 −0.00286108
\(202\) 9.71258 0.683375
\(203\) 10.0126 0.702750
\(204\) −0.0175286 −0.00122724
\(205\) 2.59393 0.181168
\(206\) 7.35393 0.512372
\(207\) 27.7163 1.92642
\(208\) 2.95299 0.204753
\(209\) −5.42219 −0.375060
\(210\) −0.0537893 −0.00371181
\(211\) 23.1076 1.59079 0.795395 0.606091i \(-0.207263\pi\)
0.795395 + 0.606091i \(0.207263\pi\)
\(212\) 3.30300 0.226851
\(213\) 0.0128016 0.000877152 0
\(214\) −14.0397 −0.959736
\(215\) 0.584069 0.0398332
\(216\) −0.733420 −0.0499029
\(217\) 7.65335 0.519543
\(218\) −6.05576 −0.410148
\(219\) 0.675577 0.0456513
\(220\) −0.210846 −0.0142153
\(221\) 0.643118 0.0432608
\(222\) −0.376201 −0.0252490
\(223\) 24.8419 1.66353 0.831767 0.555125i \(-0.187329\pi\)
0.831767 + 0.555125i \(0.187329\pi\)
\(224\) −2.49156 −0.166475
\(225\) 13.9656 0.931040
\(226\) 13.3398 0.887349
\(227\) −10.5292 −0.698850 −0.349425 0.936964i \(-0.613623\pi\)
−0.349425 + 0.936964i \(0.613623\pi\)
\(228\) −0.0950431 −0.00629438
\(229\) −18.4123 −1.21672 −0.608359 0.793662i \(-0.708172\pi\)
−0.608359 + 0.793662i \(0.708172\pi\)
\(230\) −8.29787 −0.547146
\(231\) −0.0599355 −0.00394347
\(232\) −20.4285 −1.34120
\(233\) 0.107721 0.00705702 0.00352851 0.999994i \(-0.498877\pi\)
0.00352851 + 0.999994i \(0.498877\pi\)
\(234\) −2.96223 −0.193647
\(235\) 4.18072 0.272720
\(236\) 0.189876 0.0123599
\(237\) 0.00853602 0.000554474 0
\(238\) −1.89665 −0.122942
\(239\) 7.84106 0.507196 0.253598 0.967310i \(-0.418386\pi\)
0.253598 + 0.967310i \(0.418386\pi\)
\(240\) 0.130220 0.00840570
\(241\) −7.45893 −0.480472 −0.240236 0.970715i \(-0.577225\pi\)
−0.240236 + 0.970715i \(0.577225\pi\)
\(242\) −1.53655 −0.0987734
\(243\) 1.30964 0.0840136
\(244\) −4.21119 −0.269594
\(245\) 3.19858 0.204350
\(246\) 0.331349 0.0211260
\(247\) 3.48711 0.221879
\(248\) −15.6149 −0.991547
\(249\) 0.359348 0.0227728
\(250\) −8.66837 −0.548236
\(251\) 24.0496 1.51800 0.758998 0.651093i \(-0.225689\pi\)
0.758998 + 0.651093i \(0.225689\pi\)
\(252\) 1.33574 0.0841437
\(253\) −9.24603 −0.581293
\(254\) −20.9611 −1.31522
\(255\) 0.0283601 0.00177598
\(256\) 8.39861 0.524913
\(257\) −21.5641 −1.34513 −0.672565 0.740038i \(-0.734807\pi\)
−0.672565 + 0.740038i \(0.734807\pi\)
\(258\) 0.0746091 0.00464496
\(259\) −6.22398 −0.386739
\(260\) 0.135599 0.00840950
\(261\) 24.3158 1.50511
\(262\) 6.60635 0.408142
\(263\) −17.4113 −1.07363 −0.536813 0.843702i \(-0.680372\pi\)
−0.536813 + 0.843702i \(0.680372\pi\)
\(264\) 0.122285 0.00752610
\(265\) −5.34405 −0.328282
\(266\) −10.2840 −0.630552
\(267\) −0.504747 −0.0308900
\(268\) −0.301569 −0.0184212
\(269\) 3.90551 0.238123 0.119061 0.992887i \(-0.462011\pi\)
0.119061 + 0.992887i \(0.462011\pi\)
\(270\) −0.261358 −0.0159058
\(271\) −8.12883 −0.493791 −0.246895 0.969042i \(-0.579410\pi\)
−0.246895 + 0.969042i \(0.579410\pi\)
\(272\) 4.59167 0.278411
\(273\) 0.0385456 0.00233289
\(274\) 28.3851 1.71480
\(275\) −4.65886 −0.280940
\(276\) −0.162070 −0.00975544
\(277\) 21.4082 1.28629 0.643146 0.765744i \(-0.277629\pi\)
0.643146 + 0.765744i \(0.277629\pi\)
\(278\) 33.4162 2.00417
\(279\) 18.5862 1.11273
\(280\) 1.81565 0.108506
\(281\) 14.5081 0.865479 0.432739 0.901519i \(-0.357547\pi\)
0.432739 + 0.901519i \(0.357547\pi\)
\(282\) 0.534047 0.0318020
\(283\) 23.1042 1.37340 0.686702 0.726939i \(-0.259058\pi\)
0.686702 + 0.726939i \(0.259058\pi\)
\(284\) 0.0951748 0.00564759
\(285\) 0.153774 0.00910878
\(286\) 0.988185 0.0584326
\(287\) 5.48193 0.323588
\(288\) −6.05079 −0.356546
\(289\) 1.00000 0.0588235
\(290\) −7.27982 −0.427486
\(291\) −0.0722085 −0.00423294
\(292\) 5.02265 0.293928
\(293\) −11.1265 −0.650019 −0.325010 0.945711i \(-0.605368\pi\)
−0.325010 + 0.945711i \(0.605368\pi\)
\(294\) 0.408587 0.0238293
\(295\) −0.307208 −0.0178863
\(296\) 12.6986 0.738091
\(297\) −0.291222 −0.0168984
\(298\) 28.3688 1.64336
\(299\) 5.94629 0.343883
\(300\) −0.0816632 −0.00471483
\(301\) 1.23435 0.0711470
\(302\) −1.54303 −0.0887916
\(303\) −0.306924 −0.0176323
\(304\) 24.8969 1.42794
\(305\) 6.81345 0.390137
\(306\) −4.60604 −0.263310
\(307\) −20.2711 −1.15693 −0.578466 0.815706i \(-0.696348\pi\)
−0.578466 + 0.815706i \(0.696348\pi\)
\(308\) −0.445597 −0.0253902
\(309\) −0.232389 −0.0132202
\(310\) −5.56446 −0.316040
\(311\) −9.01884 −0.511411 −0.255706 0.966755i \(-0.582308\pi\)
−0.255706 + 0.966755i \(0.582308\pi\)
\(312\) −0.0786435 −0.00445231
\(313\) 10.7103 0.605381 0.302690 0.953089i \(-0.402115\pi\)
0.302690 + 0.953089i \(0.402115\pi\)
\(314\) 1.02395 0.0577847
\(315\) −2.16114 −0.121767
\(316\) 0.0634619 0.00357001
\(317\) 24.1675 1.35738 0.678692 0.734423i \(-0.262547\pi\)
0.678692 + 0.734423i \(0.262547\pi\)
\(318\) −0.682650 −0.0382811
\(319\) −8.11165 −0.454165
\(320\) −3.55218 −0.198573
\(321\) 0.443665 0.0247630
\(322\) −17.5365 −0.977271
\(323\) 5.42219 0.301699
\(324\) 3.24130 0.180072
\(325\) 2.99620 0.166199
\(326\) 23.1703 1.28329
\(327\) 0.191366 0.0105826
\(328\) −11.1846 −0.617568
\(329\) 8.83543 0.487113
\(330\) 0.0435769 0.00239883
\(331\) −24.6210 −1.35329 −0.676646 0.736309i \(-0.736567\pi\)
−0.676646 + 0.736309i \(0.736567\pi\)
\(332\) 2.67161 0.146624
\(333\) −15.1150 −0.828296
\(334\) 1.46813 0.0803324
\(335\) 0.487919 0.0266579
\(336\) 0.275204 0.0150136
\(337\) −4.47958 −0.244018 −0.122009 0.992529i \(-0.538934\pi\)
−0.122009 + 0.992529i \(0.538934\pi\)
\(338\) 19.3397 1.05194
\(339\) −0.421546 −0.0228952
\(340\) 0.210846 0.0114347
\(341\) −6.20028 −0.335764
\(342\) −24.9748 −1.35048
\(343\) 15.4003 0.831536
\(344\) −2.51842 −0.135784
\(345\) 0.262219 0.0141174
\(346\) 22.2128 1.19417
\(347\) 5.22982 0.280752 0.140376 0.990098i \(-0.455169\pi\)
0.140376 + 0.990098i \(0.455169\pi\)
\(348\) −0.142185 −0.00762194
\(349\) 18.2439 0.976573 0.488287 0.872683i \(-0.337622\pi\)
0.488287 + 0.872683i \(0.337622\pi\)
\(350\) −8.83624 −0.472317
\(351\) 0.187290 0.00999683
\(352\) 2.01852 0.107587
\(353\) 10.7747 0.573477 0.286738 0.958009i \(-0.407429\pi\)
0.286738 + 0.958009i \(0.407429\pi\)
\(354\) −0.0392428 −0.00208573
\(355\) −0.153987 −0.00817278
\(356\) −3.75260 −0.198887
\(357\) 0.0599355 0.00317212
\(358\) −10.6407 −0.562381
\(359\) −4.90610 −0.258934 −0.129467 0.991584i \(-0.541327\pi\)
−0.129467 + 0.991584i \(0.541327\pi\)
\(360\) 4.40932 0.232391
\(361\) 10.4001 0.547374
\(362\) −17.6621 −0.928301
\(363\) 0.0485562 0.00254854
\(364\) 0.286571 0.0150204
\(365\) −8.12633 −0.425352
\(366\) 0.870351 0.0454940
\(367\) −28.4388 −1.48450 −0.742248 0.670126i \(-0.766240\pi\)
−0.742248 + 0.670126i \(0.766240\pi\)
\(368\) 42.4547 2.21311
\(369\) 13.3129 0.693043
\(370\) 4.52522 0.235255
\(371\) −11.2940 −0.586353
\(372\) −0.108682 −0.00563490
\(373\) −8.53764 −0.442062 −0.221031 0.975267i \(-0.570942\pi\)
−0.221031 + 0.975267i \(0.570942\pi\)
\(374\) 1.53655 0.0794533
\(375\) 0.273927 0.0141455
\(376\) −18.0267 −0.929654
\(377\) 5.21675 0.268676
\(378\) −0.552347 −0.0284097
\(379\) 20.9665 1.07698 0.538488 0.842633i \(-0.318996\pi\)
0.538488 + 0.842633i \(0.318996\pi\)
\(380\) 1.14325 0.0586474
\(381\) 0.662387 0.0339351
\(382\) 1.39290 0.0712671
\(383\) 9.42317 0.481502 0.240751 0.970587i \(-0.422606\pi\)
0.240751 + 0.970587i \(0.422606\pi\)
\(384\) −0.649780 −0.0331589
\(385\) 0.720948 0.0367429
\(386\) 13.0507 0.664262
\(387\) 2.99764 0.152379
\(388\) −0.536841 −0.0272540
\(389\) −1.74050 −0.0882470 −0.0441235 0.999026i \(-0.514050\pi\)
−0.0441235 + 0.999026i \(0.514050\pi\)
\(390\) −0.0280251 −0.00141910
\(391\) 9.24603 0.467592
\(392\) −13.7918 −0.696590
\(393\) −0.208765 −0.0105308
\(394\) −27.5071 −1.38579
\(395\) −0.102677 −0.00516626
\(396\) −1.08214 −0.0543794
\(397\) 23.1547 1.16210 0.581051 0.813867i \(-0.302642\pi\)
0.581051 + 0.813867i \(0.302642\pi\)
\(398\) 41.1275 2.06153
\(399\) 0.324982 0.0162694
\(400\) 21.3920 1.06960
\(401\) 4.36539 0.217997 0.108999 0.994042i \(-0.465236\pi\)
0.108999 + 0.994042i \(0.465236\pi\)
\(402\) 0.0623270 0.00310859
\(403\) 3.98751 0.198632
\(404\) −2.28186 −0.113527
\(405\) −5.24423 −0.260588
\(406\) −15.3850 −0.763543
\(407\) 5.04229 0.249937
\(408\) −0.122285 −0.00605399
\(409\) −2.94948 −0.145842 −0.0729211 0.997338i \(-0.523232\pi\)
−0.0729211 + 0.997338i \(0.523232\pi\)
\(410\) −3.98571 −0.196840
\(411\) −0.896987 −0.0442451
\(412\) −1.72772 −0.0851187
\(413\) −0.649244 −0.0319472
\(414\) −42.5876 −2.09306
\(415\) −4.32250 −0.212183
\(416\) −1.29814 −0.0636468
\(417\) −1.05597 −0.0517113
\(418\) 8.33148 0.407506
\(419\) −23.0926 −1.12815 −0.564073 0.825725i \(-0.690766\pi\)
−0.564073 + 0.825725i \(0.690766\pi\)
\(420\) 0.0126372 0.000616631 0
\(421\) 13.1345 0.640137 0.320068 0.947394i \(-0.396294\pi\)
0.320068 + 0.947394i \(0.396294\pi\)
\(422\) −35.5060 −1.72841
\(423\) 21.4569 1.04327
\(424\) 23.0427 1.11905
\(425\) 4.65886 0.225988
\(426\) −0.0196703 −0.000953031 0
\(427\) 14.3993 0.696833
\(428\) 3.29848 0.159438
\(429\) −0.0312273 −0.00150767
\(430\) −0.897453 −0.0432790
\(431\) −34.3596 −1.65504 −0.827521 0.561435i \(-0.810250\pi\)
−0.827521 + 0.561435i \(0.810250\pi\)
\(432\) 1.33720 0.0643360
\(433\) −36.5213 −1.75510 −0.877552 0.479482i \(-0.840825\pi\)
−0.877552 + 0.479482i \(0.840825\pi\)
\(434\) −11.7598 −0.564487
\(435\) 0.230047 0.0110299
\(436\) 1.42273 0.0681365
\(437\) 50.1337 2.39822
\(438\) −1.03806 −0.0496004
\(439\) −9.54196 −0.455413 −0.227706 0.973730i \(-0.573123\pi\)
−0.227706 + 0.973730i \(0.573123\pi\)
\(440\) −1.47093 −0.0701238
\(441\) 16.4162 0.781724
\(442\) −0.988185 −0.0470032
\(443\) 13.2121 0.627727 0.313863 0.949468i \(-0.398377\pi\)
0.313863 + 0.949468i \(0.398377\pi\)
\(444\) 0.0883841 0.00419452
\(445\) 6.07147 0.287815
\(446\) −38.1708 −1.80744
\(447\) −0.896475 −0.0424018
\(448\) −7.50709 −0.354676
\(449\) 0.00520906 0.000245831 0 0.000122915 1.00000i \(-0.499961\pi\)
0.000122915 1.00000i \(0.499961\pi\)
\(450\) −21.4589 −1.01158
\(451\) −4.44113 −0.209125
\(452\) −3.13403 −0.147412
\(453\) 0.0487609 0.00229099
\(454\) 16.1787 0.759306
\(455\) −0.463655 −0.0217365
\(456\) −0.663050 −0.0310502
\(457\) −31.5018 −1.47359 −0.736797 0.676114i \(-0.763663\pi\)
−0.736797 + 0.676114i \(0.763663\pi\)
\(458\) 28.2914 1.32197
\(459\) 0.291222 0.0135931
\(460\) 1.94949 0.0908955
\(461\) 0.607061 0.0282737 0.0141368 0.999900i \(-0.495500\pi\)
0.0141368 + 0.999900i \(0.495500\pi\)
\(462\) 0.0920941 0.00428461
\(463\) −37.8214 −1.75771 −0.878854 0.477091i \(-0.841691\pi\)
−0.878854 + 0.477091i \(0.841691\pi\)
\(464\) 37.2460 1.72910
\(465\) 0.175841 0.00815442
\(466\) −0.165519 −0.00766750
\(467\) 26.6899 1.23506 0.617530 0.786547i \(-0.288133\pi\)
0.617530 + 0.786547i \(0.288133\pi\)
\(468\) 0.695941 0.0321699
\(469\) 1.03116 0.0476143
\(470\) −6.42391 −0.296313
\(471\) −0.0323575 −0.00149095
\(472\) 1.32463 0.0609712
\(473\) −1.00000 −0.0459800
\(474\) −0.0131160 −0.000602440 0
\(475\) 25.2612 1.15906
\(476\) 0.445597 0.0204239
\(477\) −27.4275 −1.25582
\(478\) −12.0482 −0.551072
\(479\) 24.3703 1.11351 0.556755 0.830677i \(-0.312046\pi\)
0.556755 + 0.830677i \(0.312046\pi\)
\(480\) −0.0572454 −0.00261288
\(481\) −3.24279 −0.147859
\(482\) 11.4610 0.522036
\(483\) 0.554166 0.0252154
\(484\) 0.360996 0.0164089
\(485\) 0.868576 0.0394400
\(486\) −2.01234 −0.0912814
\(487\) 16.2709 0.737306 0.368653 0.929567i \(-0.379819\pi\)
0.368653 + 0.929567i \(0.379819\pi\)
\(488\) −29.3786 −1.32990
\(489\) −0.732198 −0.0331111
\(490\) −4.91478 −0.222027
\(491\) 32.9265 1.48595 0.742975 0.669319i \(-0.233414\pi\)
0.742975 + 0.669319i \(0.233414\pi\)
\(492\) −0.0778467 −0.00350960
\(493\) 8.11165 0.365330
\(494\) −5.35813 −0.241073
\(495\) 1.75083 0.0786939
\(496\) 28.4697 1.27833
\(497\) −0.325432 −0.0145976
\(498\) −0.552157 −0.0247428
\(499\) −3.77275 −0.168892 −0.0844458 0.996428i \(-0.526912\pi\)
−0.0844458 + 0.996428i \(0.526912\pi\)
\(500\) 2.03654 0.0910766
\(501\) −0.0463939 −0.00207272
\(502\) −36.9534 −1.64931
\(503\) −0.984764 −0.0439084 −0.0219542 0.999759i \(-0.506989\pi\)
−0.0219542 + 0.999759i \(0.506989\pi\)
\(504\) 9.31853 0.415080
\(505\) 3.69191 0.164288
\(506\) 14.2070 0.631579
\(507\) −0.611147 −0.0271420
\(508\) 4.92458 0.218493
\(509\) −23.4354 −1.03876 −0.519378 0.854545i \(-0.673836\pi\)
−0.519378 + 0.854545i \(0.673836\pi\)
\(510\) −0.0435769 −0.00192962
\(511\) −17.1740 −0.759731
\(512\) 13.8591 0.612493
\(513\) 1.57906 0.0697173
\(514\) 33.1343 1.46149
\(515\) 2.79535 0.123178
\(516\) −0.0175286 −0.000771652 0
\(517\) −7.15793 −0.314805
\(518\) 9.56347 0.420195
\(519\) −0.701940 −0.0308118
\(520\) 0.945981 0.0414840
\(521\) −26.1850 −1.14718 −0.573592 0.819141i \(-0.694451\pi\)
−0.573592 + 0.819141i \(0.694451\pi\)
\(522\) −37.3625 −1.63531
\(523\) 20.0920 0.878560 0.439280 0.898350i \(-0.355234\pi\)
0.439280 + 0.898350i \(0.355234\pi\)
\(524\) −1.55209 −0.0678033
\(525\) 0.279231 0.0121867
\(526\) 26.7533 1.16650
\(527\) 6.20028 0.270088
\(528\) −0.222954 −0.00970283
\(529\) 62.4891 2.71692
\(530\) 8.21141 0.356681
\(531\) −1.57670 −0.0684227
\(532\) 2.41611 0.104752
\(533\) 2.85617 0.123715
\(534\) 0.775571 0.0335622
\(535\) −5.33673 −0.230727
\(536\) −2.10384 −0.0908719
\(537\) 0.336255 0.0145105
\(538\) −6.00102 −0.258722
\(539\) −5.47637 −0.235884
\(540\) 0.0614032 0.00264237
\(541\) −8.89476 −0.382415 −0.191208 0.981550i \(-0.561240\pi\)
−0.191208 + 0.981550i \(0.561240\pi\)
\(542\) 12.4904 0.536507
\(543\) 0.558136 0.0239519
\(544\) −2.01852 −0.0865432
\(545\) −2.30189 −0.0986022
\(546\) −0.0592274 −0.00253470
\(547\) −22.9935 −0.983130 −0.491565 0.870841i \(-0.663575\pi\)
−0.491565 + 0.870841i \(0.663575\pi\)
\(548\) −6.66874 −0.284875
\(549\) 34.9690 1.49244
\(550\) 7.15859 0.305243
\(551\) 43.9829 1.87373
\(552\) −1.13065 −0.0481236
\(553\) −0.216996 −0.00922759
\(554\) −32.8948 −1.39757
\(555\) −0.143000 −0.00607001
\(556\) −7.85075 −0.332946
\(557\) −36.7708 −1.55803 −0.779014 0.627006i \(-0.784280\pi\)
−0.779014 + 0.627006i \(0.784280\pi\)
\(558\) −28.5587 −1.20899
\(559\) 0.643118 0.0272010
\(560\) −3.31036 −0.139888
\(561\) −0.0485562 −0.00205004
\(562\) −22.2924 −0.940349
\(563\) −27.5432 −1.16081 −0.580403 0.814330i \(-0.697105\pi\)
−0.580403 + 0.814330i \(0.697105\pi\)
\(564\) −0.125468 −0.00528317
\(565\) 5.07066 0.213324
\(566\) −35.5009 −1.49221
\(567\) −11.0830 −0.465443
\(568\) 0.663969 0.0278595
\(569\) −36.3524 −1.52397 −0.761986 0.647594i \(-0.775775\pi\)
−0.761986 + 0.647594i \(0.775775\pi\)
\(570\) −0.236282 −0.00989676
\(571\) −17.5535 −0.734592 −0.367296 0.930104i \(-0.619716\pi\)
−0.367296 + 0.930104i \(0.619716\pi\)
\(572\) −0.232163 −0.00970722
\(573\) −0.0440167 −0.00183882
\(574\) −8.42328 −0.351581
\(575\) 43.0760 1.79639
\(576\) −18.2310 −0.759626
\(577\) 17.6108 0.733149 0.366574 0.930389i \(-0.380531\pi\)
0.366574 + 0.930389i \(0.380531\pi\)
\(578\) −1.53655 −0.0639122
\(579\) −0.412411 −0.0171392
\(580\) 1.71031 0.0710168
\(581\) −9.13505 −0.378986
\(582\) 0.110952 0.00459912
\(583\) 9.14969 0.378941
\(584\) 35.0395 1.44995
\(585\) −1.12599 −0.0465540
\(586\) 17.0965 0.706251
\(587\) −16.4426 −0.678658 −0.339329 0.940668i \(-0.610200\pi\)
−0.339329 + 0.940668i \(0.610200\pi\)
\(588\) −0.0959929 −0.00395868
\(589\) 33.6191 1.38525
\(590\) 0.472041 0.0194336
\(591\) 0.869245 0.0357560
\(592\) −23.1526 −0.951564
\(593\) 10.3327 0.424315 0.212157 0.977236i \(-0.431951\pi\)
0.212157 + 0.977236i \(0.431951\pi\)
\(594\) 0.447479 0.0183603
\(595\) −0.720948 −0.0295560
\(596\) −6.66493 −0.273006
\(597\) −1.29966 −0.0531914
\(598\) −9.13679 −0.373631
\(599\) 40.2005 1.64255 0.821274 0.570535i \(-0.193264\pi\)
0.821274 + 0.570535i \(0.193264\pi\)
\(600\) −0.569708 −0.0232582
\(601\) −40.1107 −1.63615 −0.818075 0.575112i \(-0.804959\pi\)
−0.818075 + 0.575112i \(0.804959\pi\)
\(602\) −1.89665 −0.0773017
\(603\) 2.50417 0.101978
\(604\) 0.362518 0.0147507
\(605\) −0.584069 −0.0237458
\(606\) 0.471605 0.0191577
\(607\) 1.08336 0.0439720 0.0219860 0.999758i \(-0.493001\pi\)
0.0219860 + 0.999758i \(0.493001\pi\)
\(608\) −10.9448 −0.443869
\(609\) 0.486176 0.0197008
\(610\) −10.4692 −0.423886
\(611\) 4.60340 0.186233
\(612\) 1.08214 0.0437428
\(613\) 10.3660 0.418680 0.209340 0.977843i \(-0.432868\pi\)
0.209340 + 0.977843i \(0.432868\pi\)
\(614\) 31.1476 1.25701
\(615\) 0.125951 0.00507884
\(616\) −3.10862 −0.125250
\(617\) 18.1931 0.732428 0.366214 0.930531i \(-0.380654\pi\)
0.366214 + 0.930531i \(0.380654\pi\)
\(618\) 0.357078 0.0143638
\(619\) −25.4061 −1.02116 −0.510578 0.859832i \(-0.670568\pi\)
−0.510578 + 0.859832i \(0.670568\pi\)
\(620\) 1.30731 0.0525027
\(621\) 2.69265 0.108052
\(622\) 13.8579 0.555652
\(623\) 12.8313 0.514074
\(624\) 0.143386 0.00574003
\(625\) 19.9993 0.799973
\(626\) −16.4569 −0.657751
\(627\) −0.263281 −0.0105144
\(628\) −0.240565 −0.00959958
\(629\) −5.04229 −0.201049
\(630\) 3.32071 0.132300
\(631\) 28.3582 1.12892 0.564461 0.825460i \(-0.309084\pi\)
0.564461 + 0.825460i \(0.309084\pi\)
\(632\) 0.442730 0.0176108
\(633\) 1.12201 0.0445961
\(634\) −37.1347 −1.47481
\(635\) −7.96767 −0.316187
\(636\) 0.160381 0.00635952
\(637\) 3.52195 0.139545
\(638\) 12.4640 0.493453
\(639\) −0.790315 −0.0312644
\(640\) 7.81602 0.308955
\(641\) 6.40696 0.253060 0.126530 0.991963i \(-0.459616\pi\)
0.126530 + 0.991963i \(0.459616\pi\)
\(642\) −0.681715 −0.0269052
\(643\) −7.84093 −0.309216 −0.154608 0.987976i \(-0.549411\pi\)
−0.154608 + 0.987976i \(0.549411\pi\)
\(644\) 4.12000 0.162351
\(645\) 0.0283601 0.00111668
\(646\) −8.33148 −0.327798
\(647\) −20.1715 −0.793023 −0.396512 0.918030i \(-0.629779\pi\)
−0.396512 + 0.918030i \(0.629779\pi\)
\(648\) 22.6123 0.888296
\(649\) 0.525978 0.0206465
\(650\) −4.60382 −0.180577
\(651\) 0.371617 0.0145648
\(652\) −5.44360 −0.213188
\(653\) 34.1642 1.33695 0.668474 0.743735i \(-0.266948\pi\)
0.668474 + 0.743735i \(0.266948\pi\)
\(654\) −0.294044 −0.0114980
\(655\) 2.51118 0.0981200
\(656\) 20.3922 0.796183
\(657\) −41.7071 −1.62715
\(658\) −13.5761 −0.529252
\(659\) 29.7774 1.15996 0.579982 0.814629i \(-0.303060\pi\)
0.579982 + 0.814629i \(0.303060\pi\)
\(660\) −0.0102379 −0.000398509 0
\(661\) 17.9228 0.697117 0.348558 0.937287i \(-0.386671\pi\)
0.348558 + 0.937287i \(0.386671\pi\)
\(662\) 37.8314 1.47036
\(663\) 0.0312273 0.00121277
\(664\) 18.6380 0.723294
\(665\) −3.90911 −0.151589
\(666\) 23.2250 0.899950
\(667\) 75.0005 2.90403
\(668\) −0.344920 −0.0133453
\(669\) 1.20623 0.0466354
\(670\) −0.749714 −0.0289640
\(671\) −11.6655 −0.450341
\(672\) −0.120981 −0.00466694
\(673\) 0.495551 0.0191021 0.00955105 0.999954i \(-0.496960\pi\)
0.00955105 + 0.999954i \(0.496960\pi\)
\(674\) 6.88311 0.265128
\(675\) 1.35677 0.0522219
\(676\) −4.54364 −0.174755
\(677\) 27.5306 1.05809 0.529043 0.848595i \(-0.322551\pi\)
0.529043 + 0.848595i \(0.322551\pi\)
\(678\) 0.647728 0.0248758
\(679\) 1.83562 0.0704448
\(680\) 1.47093 0.0564075
\(681\) −0.511259 −0.0195915
\(682\) 9.52706 0.364810
\(683\) 6.60143 0.252597 0.126298 0.991992i \(-0.459690\pi\)
0.126298 + 0.991992i \(0.459690\pi\)
\(684\) 5.86754 0.224351
\(685\) 10.7896 0.412250
\(686\) −23.6633 −0.903470
\(687\) −0.894029 −0.0341093
\(688\) 4.59167 0.175056
\(689\) −5.88433 −0.224175
\(690\) −0.402913 −0.0153386
\(691\) 10.7782 0.410023 0.205012 0.978760i \(-0.434277\pi\)
0.205012 + 0.978760i \(0.434277\pi\)
\(692\) −5.21865 −0.198383
\(693\) 3.70015 0.140557
\(694\) −8.03590 −0.305039
\(695\) 12.7020 0.481815
\(696\) −0.991930 −0.0375990
\(697\) 4.44113 0.168220
\(698\) −28.0327 −1.06105
\(699\) 0.00523050 0.000197836 0
\(700\) 2.07597 0.0784645
\(701\) 27.9348 1.05508 0.527542 0.849529i \(-0.323114\pi\)
0.527542 + 0.849529i \(0.323114\pi\)
\(702\) −0.287782 −0.0108616
\(703\) −27.3402 −1.03116
\(704\) 6.08179 0.229216
\(705\) 0.203000 0.00764542
\(706\) −16.5558 −0.623087
\(707\) 7.80238 0.293439
\(708\) 0.00921965 0.000346495 0
\(709\) 11.1462 0.418604 0.209302 0.977851i \(-0.432881\pi\)
0.209302 + 0.977851i \(0.432881\pi\)
\(710\) 0.236609 0.00887979
\(711\) −0.526976 −0.0197631
\(712\) −26.1793 −0.981109
\(713\) 57.3280 2.14695
\(714\) −0.0920941 −0.00344654
\(715\) 0.375625 0.0140476
\(716\) 2.49992 0.0934265
\(717\) 0.380732 0.0142187
\(718\) 7.53848 0.281334
\(719\) −23.0778 −0.860657 −0.430328 0.902672i \(-0.641602\pi\)
−0.430328 + 0.902672i \(0.641602\pi\)
\(720\) −8.03924 −0.299605
\(721\) 5.90761 0.220011
\(722\) −15.9803 −0.594726
\(723\) −0.362177 −0.0134695
\(724\) 4.14952 0.154216
\(725\) 37.7910 1.40352
\(726\) −0.0746091 −0.00276900
\(727\) −25.1854 −0.934075 −0.467037 0.884238i \(-0.654679\pi\)
−0.467037 + 0.884238i \(0.654679\pi\)
\(728\) 1.99921 0.0740957
\(729\) −26.8728 −0.995288
\(730\) 12.4865 0.462148
\(731\) 1.00000 0.0369863
\(732\) −0.204479 −0.00755777
\(733\) 0.246073 0.00908893 0.00454446 0.999990i \(-0.498553\pi\)
0.00454446 + 0.999990i \(0.498553\pi\)
\(734\) 43.6978 1.61291
\(735\) 0.155311 0.00572872
\(736\) −18.6633 −0.687937
\(737\) −0.835380 −0.0307716
\(738\) −20.4560 −0.752996
\(739\) −21.0038 −0.772636 −0.386318 0.922366i \(-0.626253\pi\)
−0.386318 + 0.922366i \(0.626253\pi\)
\(740\) −1.06315 −0.0390821
\(741\) 0.169321 0.00622014
\(742\) 17.3538 0.637077
\(743\) 21.5072 0.789022 0.394511 0.918891i \(-0.370914\pi\)
0.394511 + 0.918891i \(0.370914\pi\)
\(744\) −0.758199 −0.0277969
\(745\) 10.7835 0.395075
\(746\) 13.1185 0.480304
\(747\) −22.1846 −0.811691
\(748\) −0.360996 −0.0131993
\(749\) −11.2785 −0.412107
\(750\) −0.420903 −0.0153692
\(751\) −36.5914 −1.33524 −0.667620 0.744502i \(-0.732687\pi\)
−0.667620 + 0.744502i \(0.732687\pi\)
\(752\) 32.8669 1.19853
\(753\) 1.16775 0.0425553
\(754\) −8.01581 −0.291919
\(755\) −0.586532 −0.0213461
\(756\) 0.129768 0.00471961
\(757\) 40.2922 1.46444 0.732222 0.681066i \(-0.238483\pi\)
0.732222 + 0.681066i \(0.238483\pi\)
\(758\) −32.2161 −1.17014
\(759\) −0.448952 −0.0162959
\(760\) 7.97565 0.289307
\(761\) −13.2345 −0.479750 −0.239875 0.970804i \(-0.577107\pi\)
−0.239875 + 0.970804i \(0.577107\pi\)
\(762\) −1.01779 −0.0368707
\(763\) −4.86475 −0.176116
\(764\) −0.327247 −0.0118394
\(765\) −1.75083 −0.0633014
\(766\) −14.4792 −0.523155
\(767\) −0.338266 −0.0122141
\(768\) 0.407804 0.0147154
\(769\) −48.7786 −1.75900 −0.879501 0.475897i \(-0.842123\pi\)
−0.879501 + 0.475897i \(0.842123\pi\)
\(770\) −1.10777 −0.0399214
\(771\) −1.04707 −0.0377092
\(772\) −3.06611 −0.110352
\(773\) 20.8613 0.750330 0.375165 0.926958i \(-0.377586\pi\)
0.375165 + 0.926958i \(0.377586\pi\)
\(774\) −4.60604 −0.165561
\(775\) 28.8863 1.03763
\(776\) −3.74517 −0.134444
\(777\) −0.302212 −0.0108418
\(778\) 2.67437 0.0958810
\(779\) 24.0806 0.862779
\(780\) 0.00658417 0.000235751 0
\(781\) 0.263645 0.00943397
\(782\) −14.2070 −0.508042
\(783\) 2.36229 0.0844215
\(784\) 25.1457 0.898061
\(785\) 0.389219 0.0138918
\(786\) 0.320779 0.0114418
\(787\) −12.4917 −0.445283 −0.222641 0.974900i \(-0.571468\pi\)
−0.222641 + 0.974900i \(0.571468\pi\)
\(788\) 6.46249 0.230217
\(789\) −0.845424 −0.0300979
\(790\) 0.157769 0.00561318
\(791\) 10.7162 0.381024
\(792\) −7.54931 −0.268253
\(793\) 7.50229 0.266414
\(794\) −35.5785 −1.26263
\(795\) −0.259486 −0.00920303
\(796\) −9.66243 −0.342476
\(797\) 48.1209 1.70453 0.852265 0.523111i \(-0.175229\pi\)
0.852265 + 0.523111i \(0.175229\pi\)
\(798\) −0.499351 −0.0176768
\(799\) 7.15793 0.253229
\(800\) −9.40399 −0.332481
\(801\) 31.1609 1.10102
\(802\) −6.70766 −0.236856
\(803\) 13.9133 0.490990
\(804\) −0.0146430 −0.000516419 0
\(805\) −6.66591 −0.234942
\(806\) −6.12703 −0.215815
\(807\) 0.189636 0.00667552
\(808\) −15.9190 −0.560027
\(809\) 1.73362 0.0609508 0.0304754 0.999536i \(-0.490298\pi\)
0.0304754 + 0.999536i \(0.490298\pi\)
\(810\) 8.05804 0.283131
\(811\) 1.05726 0.0371256 0.0185628 0.999828i \(-0.494091\pi\)
0.0185628 + 0.999828i \(0.494091\pi\)
\(812\) 3.61452 0.126845
\(813\) −0.394704 −0.0138429
\(814\) −7.74775 −0.271558
\(815\) 8.80741 0.308510
\(816\) 0.222954 0.00780495
\(817\) 5.42219 0.189698
\(818\) 4.53203 0.158459
\(819\) −2.37964 −0.0831512
\(820\) 0.936396 0.0327004
\(821\) −13.2416 −0.462135 −0.231067 0.972938i \(-0.574222\pi\)
−0.231067 + 0.972938i \(0.574222\pi\)
\(822\) 1.37827 0.0480726
\(823\) −45.7234 −1.59382 −0.796908 0.604100i \(-0.793533\pi\)
−0.796908 + 0.604100i \(0.793533\pi\)
\(824\) −12.0531 −0.419890
\(825\) −0.226216 −0.00787585
\(826\) 0.997598 0.0347109
\(827\) −7.45307 −0.259169 −0.129584 0.991568i \(-0.541364\pi\)
−0.129584 + 0.991568i \(0.541364\pi\)
\(828\) 10.0055 0.347714
\(829\) −17.4547 −0.606226 −0.303113 0.952955i \(-0.598026\pi\)
−0.303113 + 0.952955i \(0.598026\pi\)
\(830\) 6.64175 0.230539
\(831\) 1.03950 0.0360598
\(832\) −3.91131 −0.135600
\(833\) 5.47637 0.189745
\(834\) 1.62256 0.0561847
\(835\) 0.558059 0.0193124
\(836\) −1.95739 −0.0676976
\(837\) 1.80566 0.0624128
\(838\) 35.4829 1.22574
\(839\) −0.0581059 −0.00200604 −0.00100302 0.999999i \(-0.500319\pi\)
−0.00100302 + 0.999999i \(0.500319\pi\)
\(840\) 0.0881609 0.00304184
\(841\) 36.7988 1.26892
\(842\) −20.1819 −0.695513
\(843\) 0.704456 0.0242628
\(844\) 8.34173 0.287134
\(845\) 7.35132 0.252893
\(846\) −32.9697 −1.13352
\(847\) −1.23435 −0.0424129
\(848\) −42.0124 −1.44271
\(849\) 1.12185 0.0385019
\(850\) −7.15859 −0.245538
\(851\) −46.6212 −1.59815
\(852\) 0.00462132 0.000158324 0
\(853\) −54.1779 −1.85502 −0.927509 0.373801i \(-0.878054\pi\)
−0.927509 + 0.373801i \(0.878054\pi\)
\(854\) −22.1254 −0.757114
\(855\) −9.49332 −0.324665
\(856\) 23.0112 0.786506
\(857\) 29.3108 1.00124 0.500619 0.865668i \(-0.333106\pi\)
0.500619 + 0.865668i \(0.333106\pi\)
\(858\) 0.0479825 0.00163809
\(859\) 17.8831 0.610165 0.305082 0.952326i \(-0.401316\pi\)
0.305082 + 0.952326i \(0.401316\pi\)
\(860\) 0.210846 0.00718980
\(861\) 0.266182 0.00907144
\(862\) 52.7953 1.79821
\(863\) −49.5510 −1.68673 −0.843367 0.537337i \(-0.819430\pi\)
−0.843367 + 0.537337i \(0.819430\pi\)
\(864\) −0.587837 −0.0199986
\(865\) 8.44345 0.287086
\(866\) 56.1170 1.90693
\(867\) 0.0485562 0.00164905
\(868\) 2.76282 0.0937764
\(869\) 0.175797 0.00596350
\(870\) −0.353480 −0.0119841
\(871\) 0.537248 0.0182040
\(872\) 9.92541 0.336117
\(873\) 4.45783 0.150875
\(874\) −77.0331 −2.60568
\(875\) −6.96354 −0.235411
\(876\) 0.243880 0.00823996
\(877\) −32.5846 −1.10030 −0.550151 0.835065i \(-0.685430\pi\)
−0.550151 + 0.835065i \(0.685430\pi\)
\(878\) 14.6617 0.494809
\(879\) −0.540262 −0.0182226
\(880\) 2.68185 0.0904052
\(881\) −18.1553 −0.611667 −0.305833 0.952085i \(-0.598935\pi\)
−0.305833 + 0.952085i \(0.598935\pi\)
\(882\) −25.2244 −0.849348
\(883\) −18.1889 −0.612104 −0.306052 0.952015i \(-0.599008\pi\)
−0.306052 + 0.952015i \(0.599008\pi\)
\(884\) 0.232163 0.00780848
\(885\) −0.0149168 −0.000501423 0
\(886\) −20.3011 −0.682029
\(887\) 25.1134 0.843225 0.421613 0.906776i \(-0.361464\pi\)
0.421613 + 0.906776i \(0.361464\pi\)
\(888\) 0.616595 0.0206916
\(889\) −16.8387 −0.564750
\(890\) −9.32913 −0.312713
\(891\) 8.97879 0.300801
\(892\) 8.96781 0.300264
\(893\) 38.8116 1.29878
\(894\) 1.37748 0.0460699
\(895\) −4.04472 −0.135200
\(896\) 16.5182 0.551833
\(897\) 0.288729 0.00964038
\(898\) −0.00800400 −0.000267097 0
\(899\) 50.2945 1.67741
\(900\) 5.04152 0.168051
\(901\) −9.14969 −0.304820
\(902\) 6.82404 0.227216
\(903\) 0.0599355 0.00199453
\(904\) −21.8639 −0.727184
\(905\) −6.71366 −0.223170
\(906\) −0.0749238 −0.00248918
\(907\) 18.7163 0.621466 0.310733 0.950497i \(-0.399426\pi\)
0.310733 + 0.950497i \(0.399426\pi\)
\(908\) −3.80101 −0.126141
\(909\) 18.9481 0.628470
\(910\) 0.712430 0.0236168
\(911\) 14.5867 0.483278 0.241639 0.970366i \(-0.422315\pi\)
0.241639 + 0.970366i \(0.422315\pi\)
\(912\) 1.20890 0.0400306
\(913\) 7.40067 0.244926
\(914\) 48.4042 1.60107
\(915\) 0.330835 0.0109371
\(916\) −6.64675 −0.219615
\(917\) 5.30706 0.175255
\(918\) −0.447479 −0.0147690
\(919\) 14.4411 0.476366 0.238183 0.971220i \(-0.423448\pi\)
0.238183 + 0.971220i \(0.423448\pi\)
\(920\) 13.6003 0.448387
\(921\) −0.984286 −0.0324333
\(922\) −0.932782 −0.0307195
\(923\) −0.169555 −0.00558098
\(924\) −0.0216365 −0.000711787 0
\(925\) −23.4914 −0.772391
\(926\) 58.1145 1.90976
\(927\) 14.3467 0.471207
\(928\) −16.3735 −0.537486
\(929\) 24.5091 0.804118 0.402059 0.915614i \(-0.368295\pi\)
0.402059 + 0.915614i \(0.368295\pi\)
\(930\) −0.270189 −0.00885984
\(931\) 29.6939 0.973178
\(932\) 0.0388867 0.00127378
\(933\) −0.437920 −0.0143369
\(934\) −41.0104 −1.34190
\(935\) 0.584069 0.0191011
\(936\) 4.85510 0.158694
\(937\) −56.8471 −1.85711 −0.928556 0.371192i \(-0.878949\pi\)
−0.928556 + 0.371192i \(0.878949\pi\)
\(938\) −1.58443 −0.0517333
\(939\) 0.520050 0.0169712
\(940\) 1.50922 0.0492254
\(941\) −39.4793 −1.28699 −0.643494 0.765451i \(-0.722516\pi\)
−0.643494 + 0.765451i \(0.722516\pi\)
\(942\) 0.0497189 0.00161993
\(943\) 41.0628 1.33719
\(944\) −2.41512 −0.0786055
\(945\) −0.209956 −0.00682988
\(946\) 1.53655 0.0499577
\(947\) 20.3490 0.661255 0.330628 0.943761i \(-0.392740\pi\)
0.330628 + 0.943761i \(0.392740\pi\)
\(948\) 0.00308147 0.000100081 0
\(949\) −8.94791 −0.290461
\(950\) −38.8152 −1.25933
\(951\) 1.17348 0.0380528
\(952\) 3.10862 0.100751
\(953\) −24.9795 −0.809167 −0.404583 0.914501i \(-0.632583\pi\)
−0.404583 + 0.914501i \(0.632583\pi\)
\(954\) 42.1438 1.36446
\(955\) 0.529465 0.0171331
\(956\) 2.83059 0.0915478
\(957\) −0.393870 −0.0127320
\(958\) −37.4463 −1.20984
\(959\) 22.8025 0.736330
\(960\) −0.172480 −0.00556678
\(961\) 7.44348 0.240112
\(962\) 4.98272 0.160649
\(963\) −27.3899 −0.882628
\(964\) −2.69264 −0.0867241
\(965\) 4.96077 0.159693
\(966\) −0.851505 −0.0273967
\(967\) −28.6863 −0.922489 −0.461244 0.887273i \(-0.652597\pi\)
−0.461244 + 0.887273i \(0.652597\pi\)
\(968\) 2.51842 0.0809450
\(969\) 0.263281 0.00845779
\(970\) −1.33461 −0.0428519
\(971\) 27.6408 0.887035 0.443518 0.896266i \(-0.353730\pi\)
0.443518 + 0.896266i \(0.353730\pi\)
\(972\) 0.472775 0.0151643
\(973\) 26.8441 0.860583
\(974\) −25.0011 −0.801088
\(975\) 0.145484 0.00465922
\(976\) 53.5641 1.71455
\(977\) 22.7559 0.728027 0.364013 0.931394i \(-0.381406\pi\)
0.364013 + 0.931394i \(0.381406\pi\)
\(978\) 1.12506 0.0359755
\(979\) −10.3951 −0.332230
\(980\) 1.15467 0.0368846
\(981\) −11.8141 −0.377195
\(982\) −50.5932 −1.61450
\(983\) −31.8023 −1.01434 −0.507168 0.861847i \(-0.669307\pi\)
−0.507168 + 0.861847i \(0.669307\pi\)
\(984\) −0.543082 −0.0173128
\(985\) −10.4559 −0.333153
\(986\) −12.4640 −0.396934
\(987\) 0.429014 0.0136557
\(988\) 1.25883 0.0400487
\(989\) 9.24603 0.294007
\(990\) −2.69024 −0.0855015
\(991\) 30.4310 0.966672 0.483336 0.875435i \(-0.339425\pi\)
0.483336 + 0.875435i \(0.339425\pi\)
\(992\) −12.5154 −0.397363
\(993\) −1.19550 −0.0379380
\(994\) 0.500043 0.0158604
\(995\) 15.6332 0.495606
\(996\) 0.129723 0.00411043
\(997\) 7.74013 0.245132 0.122566 0.992460i \(-0.460888\pi\)
0.122566 + 0.992460i \(0.460888\pi\)
\(998\) 5.79703 0.183502
\(999\) −1.46843 −0.0464590
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 \(a_p\))