Properties

Label 4017.2.a.j.1.9
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 1.9
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.858580 q^{2} -1.00000 q^{3} -1.26284 q^{4} -4.02605 q^{5} +0.858580 q^{6} +1.69085 q^{7} +2.80141 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.858580 q^{2} -1.00000 q^{3} -1.26284 q^{4} -4.02605 q^{5} +0.858580 q^{6} +1.69085 q^{7} +2.80141 q^{8} +1.00000 q^{9} +3.45668 q^{10} +4.28895 q^{11} +1.26284 q^{12} +1.00000 q^{13} -1.45173 q^{14} +4.02605 q^{15} +0.120444 q^{16} +7.37326 q^{17} -0.858580 q^{18} +0.247701 q^{19} +5.08425 q^{20} -1.69085 q^{21} -3.68241 q^{22} +7.02793 q^{23} -2.80141 q^{24} +11.2091 q^{25} -0.858580 q^{26} -1.00000 q^{27} -2.13527 q^{28} -2.37570 q^{29} -3.45668 q^{30} +7.06841 q^{31} -5.70623 q^{32} -4.28895 q^{33} -6.33054 q^{34} -6.80743 q^{35} -1.26284 q^{36} -0.651425 q^{37} -0.212671 q^{38} -1.00000 q^{39} -11.2786 q^{40} +4.11006 q^{41} +1.45173 q^{42} -4.16005 q^{43} -5.41625 q^{44} -4.02605 q^{45} -6.03404 q^{46} +2.62615 q^{47} -0.120444 q^{48} -4.14104 q^{49} -9.62387 q^{50} -7.37326 q^{51} -1.26284 q^{52} -7.05625 q^{53} +0.858580 q^{54} -17.2675 q^{55} +4.73675 q^{56} -0.247701 q^{57} +2.03973 q^{58} -10.9647 q^{59} -5.08425 q^{60} +9.22303 q^{61} -6.06880 q^{62} +1.69085 q^{63} +4.65837 q^{64} -4.02605 q^{65} +3.68241 q^{66} +0.887929 q^{67} -9.31125 q^{68} -7.02793 q^{69} +5.84472 q^{70} +12.7885 q^{71} +2.80141 q^{72} +8.42670 q^{73} +0.559301 q^{74} -11.2091 q^{75} -0.312806 q^{76} +7.25195 q^{77} +0.858580 q^{78} +5.27331 q^{79} -0.484914 q^{80} +1.00000 q^{81} -3.52881 q^{82} +11.2899 q^{83} +2.13527 q^{84} -29.6851 q^{85} +3.57174 q^{86} +2.37570 q^{87} +12.0151 q^{88} +0.789688 q^{89} +3.45668 q^{90} +1.69085 q^{91} -8.87515 q^{92} -7.06841 q^{93} -2.25476 q^{94} -0.997255 q^{95} +5.70623 q^{96} -14.1860 q^{97} +3.55541 q^{98} +4.28895 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.858580 −0.607108 −0.303554 0.952814i \(-0.598173\pi\)
−0.303554 + 0.952814i \(0.598173\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.26284 −0.631420
\(5\) −4.02605 −1.80050 −0.900251 0.435370i \(-0.856617\pi\)
−0.900251 + 0.435370i \(0.856617\pi\)
\(6\) 0.858580 0.350514
\(7\) 1.69085 0.639080 0.319540 0.947573i \(-0.396472\pi\)
0.319540 + 0.947573i \(0.396472\pi\)
\(8\) 2.80141 0.990448
\(9\) 1.00000 0.333333
\(10\) 3.45668 1.09310
\(11\) 4.28895 1.29317 0.646583 0.762843i \(-0.276197\pi\)
0.646583 + 0.762843i \(0.276197\pi\)
\(12\) 1.26284 0.364550
\(13\) 1.00000 0.277350
\(14\) −1.45173 −0.387991
\(15\) 4.02605 1.03952
\(16\) 0.120444 0.0301110
\(17\) 7.37326 1.78828 0.894139 0.447789i \(-0.147789\pi\)
0.894139 + 0.447789i \(0.147789\pi\)
\(18\) −0.858580 −0.202369
\(19\) 0.247701 0.0568265 0.0284132 0.999596i \(-0.490955\pi\)
0.0284132 + 0.999596i \(0.490955\pi\)
\(20\) 5.08425 1.13687
\(21\) −1.69085 −0.368973
\(22\) −3.68241 −0.785092
\(23\) 7.02793 1.46542 0.732712 0.680539i \(-0.238254\pi\)
0.732712 + 0.680539i \(0.238254\pi\)
\(24\) −2.80141 −0.571835
\(25\) 11.2091 2.24181
\(26\) −0.858580 −0.168381
\(27\) −1.00000 −0.192450
\(28\) −2.13527 −0.403528
\(29\) −2.37570 −0.441157 −0.220579 0.975369i \(-0.570795\pi\)
−0.220579 + 0.975369i \(0.570795\pi\)
\(30\) −3.45668 −0.631101
\(31\) 7.06841 1.26952 0.634762 0.772708i \(-0.281098\pi\)
0.634762 + 0.772708i \(0.281098\pi\)
\(32\) −5.70623 −1.00873
\(33\) −4.28895 −0.746610
\(34\) −6.33054 −1.08568
\(35\) −6.80743 −1.15067
\(36\) −1.26284 −0.210473
\(37\) −0.651425 −0.107094 −0.0535468 0.998565i \(-0.517053\pi\)
−0.0535468 + 0.998565i \(0.517053\pi\)
\(38\) −0.212671 −0.0344998
\(39\) −1.00000 −0.160128
\(40\) −11.2786 −1.78330
\(41\) 4.11006 0.641883 0.320942 0.947099i \(-0.396001\pi\)
0.320942 + 0.947099i \(0.396001\pi\)
\(42\) 1.45173 0.224006
\(43\) −4.16005 −0.634402 −0.317201 0.948358i \(-0.602743\pi\)
−0.317201 + 0.948358i \(0.602743\pi\)
\(44\) −5.41625 −0.816531
\(45\) −4.02605 −0.600168
\(46\) −6.03404 −0.889671
\(47\) 2.62615 0.383064 0.191532 0.981486i \(-0.438654\pi\)
0.191532 + 0.981486i \(0.438654\pi\)
\(48\) −0.120444 −0.0173846
\(49\) −4.14104 −0.591577
\(50\) −9.62387 −1.36102
\(51\) −7.37326 −1.03246
\(52\) −1.26284 −0.175124
\(53\) −7.05625 −0.969250 −0.484625 0.874722i \(-0.661044\pi\)
−0.484625 + 0.874722i \(0.661044\pi\)
\(54\) 0.858580 0.116838
\(55\) −17.2675 −2.32835
\(56\) 4.73675 0.632975
\(57\) −0.247701 −0.0328088
\(58\) 2.03973 0.267830
\(59\) −10.9647 −1.42749 −0.713744 0.700407i \(-0.753002\pi\)
−0.713744 + 0.700407i \(0.753002\pi\)
\(60\) −5.08425 −0.656374
\(61\) 9.22303 1.18089 0.590444 0.807079i \(-0.298953\pi\)
0.590444 + 0.807079i \(0.298953\pi\)
\(62\) −6.06880 −0.770738
\(63\) 1.69085 0.213027
\(64\) 4.65837 0.582296
\(65\) −4.02605 −0.499370
\(66\) 3.68241 0.453273
\(67\) 0.887929 0.108478 0.0542389 0.998528i \(-0.482727\pi\)
0.0542389 + 0.998528i \(0.482727\pi\)
\(68\) −9.31125 −1.12915
\(69\) −7.02793 −0.846063
\(70\) 5.84472 0.698578
\(71\) 12.7885 1.51772 0.758859 0.651254i \(-0.225757\pi\)
0.758859 + 0.651254i \(0.225757\pi\)
\(72\) 2.80141 0.330149
\(73\) 8.42670 0.986271 0.493135 0.869953i \(-0.335851\pi\)
0.493135 + 0.869953i \(0.335851\pi\)
\(74\) 0.559301 0.0650174
\(75\) −11.2091 −1.29431
\(76\) −0.312806 −0.0358814
\(77\) 7.25195 0.826437
\(78\) 0.858580 0.0972151
\(79\) 5.27331 0.593294 0.296647 0.954987i \(-0.404132\pi\)
0.296647 + 0.954987i \(0.404132\pi\)
\(80\) −0.484914 −0.0542150
\(81\) 1.00000 0.111111
\(82\) −3.52881 −0.389692
\(83\) 11.2899 1.23923 0.619613 0.784907i \(-0.287289\pi\)
0.619613 + 0.784907i \(0.287289\pi\)
\(84\) 2.13527 0.232977
\(85\) −29.6851 −3.21980
\(86\) 3.57174 0.385151
\(87\) 2.37570 0.254702
\(88\) 12.0151 1.28081
\(89\) 0.789688 0.0837067 0.0418534 0.999124i \(-0.486674\pi\)
0.0418534 + 0.999124i \(0.486674\pi\)
\(90\) 3.45668 0.364367
\(91\) 1.69085 0.177249
\(92\) −8.87515 −0.925298
\(93\) −7.06841 −0.732960
\(94\) −2.25476 −0.232561
\(95\) −0.997255 −0.102316
\(96\) 5.70623 0.582390
\(97\) −14.1860 −1.44037 −0.720183 0.693784i \(-0.755942\pi\)
−0.720183 + 0.693784i \(0.755942\pi\)
\(98\) 3.55541 0.359151
\(99\) 4.28895 0.431055
\(100\) −14.1552 −1.41552
\(101\) 17.1694 1.70842 0.854211 0.519926i \(-0.174040\pi\)
0.854211 + 0.519926i \(0.174040\pi\)
\(102\) 6.33054 0.626816
\(103\) −1.00000 −0.0985329
\(104\) 2.80141 0.274701
\(105\) 6.80743 0.664337
\(106\) 6.05836 0.588440
\(107\) 0.920374 0.0889759 0.0444879 0.999010i \(-0.485834\pi\)
0.0444879 + 0.999010i \(0.485834\pi\)
\(108\) 1.26284 0.121517
\(109\) −11.6041 −1.11147 −0.555734 0.831360i \(-0.687563\pi\)
−0.555734 + 0.831360i \(0.687563\pi\)
\(110\) 14.8255 1.41356
\(111\) 0.651425 0.0618305
\(112\) 0.203653 0.0192434
\(113\) 13.8477 1.30268 0.651341 0.758785i \(-0.274207\pi\)
0.651341 + 0.758785i \(0.274207\pi\)
\(114\) 0.212671 0.0199185
\(115\) −28.2948 −2.63850
\(116\) 3.00013 0.278556
\(117\) 1.00000 0.0924500
\(118\) 9.41411 0.866639
\(119\) 12.4671 1.14285
\(120\) 11.2786 1.02959
\(121\) 7.39508 0.672280
\(122\) −7.91871 −0.716927
\(123\) −4.11006 −0.370591
\(124\) −8.92627 −0.801602
\(125\) −24.9979 −2.23588
\(126\) −1.45173 −0.129330
\(127\) −15.9315 −1.41369 −0.706845 0.707369i \(-0.749882\pi\)
−0.706845 + 0.707369i \(0.749882\pi\)
\(128\) 7.41288 0.655212
\(129\) 4.16005 0.366272
\(130\) 3.45668 0.303171
\(131\) −11.6337 −1.01644 −0.508219 0.861228i \(-0.669696\pi\)
−0.508219 + 0.861228i \(0.669696\pi\)
\(132\) 5.41625 0.471424
\(133\) 0.418824 0.0363167
\(134\) −0.762358 −0.0658577
\(135\) 4.02605 0.346507
\(136\) 20.6555 1.77120
\(137\) 17.0824 1.45945 0.729723 0.683743i \(-0.239649\pi\)
0.729723 + 0.683743i \(0.239649\pi\)
\(138\) 6.03404 0.513652
\(139\) −16.3737 −1.38880 −0.694401 0.719588i \(-0.744330\pi\)
−0.694401 + 0.719588i \(0.744330\pi\)
\(140\) 8.59669 0.726553
\(141\) −2.62615 −0.221162
\(142\) −10.9800 −0.921419
\(143\) 4.28895 0.358660
\(144\) 0.120444 0.0100370
\(145\) 9.56470 0.794305
\(146\) −7.23500 −0.598773
\(147\) 4.14104 0.341547
\(148\) 0.822646 0.0676211
\(149\) 9.15789 0.750244 0.375122 0.926975i \(-0.377601\pi\)
0.375122 + 0.926975i \(0.377601\pi\)
\(150\) 9.62387 0.785786
\(151\) 10.1681 0.827472 0.413736 0.910397i \(-0.364224\pi\)
0.413736 + 0.910397i \(0.364224\pi\)
\(152\) 0.693912 0.0562837
\(153\) 7.37326 0.596093
\(154\) −6.22638 −0.501736
\(155\) −28.4577 −2.28578
\(156\) 1.26284 0.101108
\(157\) −13.1766 −1.05161 −0.525805 0.850605i \(-0.676236\pi\)
−0.525805 + 0.850605i \(0.676236\pi\)
\(158\) −4.52756 −0.360193
\(159\) 7.05625 0.559597
\(160\) 22.9736 1.81622
\(161\) 11.8831 0.936523
\(162\) −0.858580 −0.0674564
\(163\) 10.3849 0.813407 0.406703 0.913560i \(-0.366678\pi\)
0.406703 + 0.913560i \(0.366678\pi\)
\(164\) −5.19034 −0.405298
\(165\) 17.2675 1.34427
\(166\) −9.69328 −0.752344
\(167\) −7.95912 −0.615895 −0.307948 0.951403i \(-0.599642\pi\)
−0.307948 + 0.951403i \(0.599642\pi\)
\(168\) −4.73675 −0.365449
\(169\) 1.00000 0.0769231
\(170\) 25.4870 1.95477
\(171\) 0.247701 0.0189422
\(172\) 5.25348 0.400574
\(173\) 17.3009 1.31536 0.657682 0.753296i \(-0.271537\pi\)
0.657682 + 0.753296i \(0.271537\pi\)
\(174\) −2.03973 −0.154632
\(175\) 18.9528 1.43270
\(176\) 0.516579 0.0389386
\(177\) 10.9647 0.824161
\(178\) −0.678010 −0.0508190
\(179\) −7.70431 −0.575847 −0.287923 0.957653i \(-0.592965\pi\)
−0.287923 + 0.957653i \(0.592965\pi\)
\(180\) 5.08425 0.378958
\(181\) −23.8049 −1.76940 −0.884702 0.466158i \(-0.845638\pi\)
−0.884702 + 0.466158i \(0.845638\pi\)
\(182\) −1.45173 −0.107609
\(183\) −9.22303 −0.681786
\(184\) 19.6881 1.45143
\(185\) 2.62267 0.192822
\(186\) 6.06880 0.444986
\(187\) 31.6235 2.31254
\(188\) −3.31641 −0.241874
\(189\) −1.69085 −0.122991
\(190\) 0.856224 0.0621170
\(191\) 8.97563 0.649454 0.324727 0.945808i \(-0.394728\pi\)
0.324727 + 0.945808i \(0.394728\pi\)
\(192\) −4.65837 −0.336189
\(193\) −26.9771 −1.94185 −0.970926 0.239379i \(-0.923056\pi\)
−0.970926 + 0.239379i \(0.923056\pi\)
\(194\) 12.1798 0.874457
\(195\) 4.02605 0.288311
\(196\) 5.22947 0.373533
\(197\) −4.08743 −0.291217 −0.145609 0.989342i \(-0.546514\pi\)
−0.145609 + 0.989342i \(0.546514\pi\)
\(198\) −3.68241 −0.261697
\(199\) 11.2881 0.800196 0.400098 0.916472i \(-0.368976\pi\)
0.400098 + 0.916472i \(0.368976\pi\)
\(200\) 31.4011 2.22040
\(201\) −0.887929 −0.0626297
\(202\) −14.7413 −1.03720
\(203\) −4.01695 −0.281935
\(204\) 9.31125 0.651918
\(205\) −16.5473 −1.15571
\(206\) 0.858580 0.0598201
\(207\) 7.02793 0.488475
\(208\) 0.120444 0.00835130
\(209\) 1.06238 0.0734861
\(210\) −5.84472 −0.403324
\(211\) −1.09307 −0.0752500 −0.0376250 0.999292i \(-0.511979\pi\)
−0.0376250 + 0.999292i \(0.511979\pi\)
\(212\) 8.91091 0.612004
\(213\) −12.7885 −0.876255
\(214\) −0.790215 −0.0540180
\(215\) 16.7486 1.14224
\(216\) −2.80141 −0.190612
\(217\) 11.9516 0.811327
\(218\) 9.96303 0.674781
\(219\) −8.42670 −0.569424
\(220\) 21.8061 1.47017
\(221\) 7.37326 0.495979
\(222\) −0.559301 −0.0375378
\(223\) −5.33525 −0.357274 −0.178637 0.983915i \(-0.557169\pi\)
−0.178637 + 0.983915i \(0.557169\pi\)
\(224\) −9.64836 −0.644658
\(225\) 11.2091 0.747270
\(226\) −11.8894 −0.790869
\(227\) −26.6015 −1.76561 −0.882803 0.469744i \(-0.844346\pi\)
−0.882803 + 0.469744i \(0.844346\pi\)
\(228\) 0.312806 0.0207161
\(229\) 22.1490 1.46365 0.731825 0.681492i \(-0.238669\pi\)
0.731825 + 0.681492i \(0.238669\pi\)
\(230\) 24.2933 1.60185
\(231\) −7.25195 −0.477143
\(232\) −6.65532 −0.436943
\(233\) 1.31800 0.0863453 0.0431727 0.999068i \(-0.486253\pi\)
0.0431727 + 0.999068i \(0.486253\pi\)
\(234\) −0.858580 −0.0561272
\(235\) −10.5730 −0.689707
\(236\) 13.8467 0.901344
\(237\) −5.27331 −0.342538
\(238\) −10.7040 −0.693835
\(239\) 25.6984 1.66229 0.831145 0.556056i \(-0.187686\pi\)
0.831145 + 0.556056i \(0.187686\pi\)
\(240\) 0.484914 0.0313011
\(241\) −10.5609 −0.680288 −0.340144 0.940373i \(-0.610476\pi\)
−0.340144 + 0.940373i \(0.610476\pi\)
\(242\) −6.34927 −0.408146
\(243\) −1.00000 −0.0641500
\(244\) −11.6472 −0.745636
\(245\) 16.6720 1.06514
\(246\) 3.52881 0.224989
\(247\) 0.247701 0.0157608
\(248\) 19.8015 1.25740
\(249\) −11.2899 −0.715468
\(250\) 21.4627 1.35742
\(251\) −6.47131 −0.408466 −0.204233 0.978922i \(-0.565470\pi\)
−0.204233 + 0.978922i \(0.565470\pi\)
\(252\) −2.13527 −0.134509
\(253\) 30.1424 1.89504
\(254\) 13.6784 0.858262
\(255\) 29.6851 1.85895
\(256\) −15.6813 −0.980081
\(257\) 5.50697 0.343515 0.171758 0.985139i \(-0.445055\pi\)
0.171758 + 0.985139i \(0.445055\pi\)
\(258\) −3.57174 −0.222367
\(259\) −1.10146 −0.0684414
\(260\) 5.08425 0.315312
\(261\) −2.37570 −0.147052
\(262\) 9.98844 0.617088
\(263\) −15.9892 −0.985938 −0.492969 0.870047i \(-0.664088\pi\)
−0.492969 + 0.870047i \(0.664088\pi\)
\(264\) −12.0151 −0.739478
\(265\) 28.4088 1.74514
\(266\) −0.359594 −0.0220481
\(267\) −0.789688 −0.0483281
\(268\) −1.12131 −0.0684950
\(269\) 19.2576 1.17416 0.587078 0.809531i \(-0.300278\pi\)
0.587078 + 0.809531i \(0.300278\pi\)
\(270\) −3.45668 −0.210367
\(271\) −26.8710 −1.63230 −0.816148 0.577842i \(-0.803895\pi\)
−0.816148 + 0.577842i \(0.803895\pi\)
\(272\) 0.888066 0.0538469
\(273\) −1.69085 −0.102335
\(274\) −14.6666 −0.886041
\(275\) 48.0750 2.89903
\(276\) 8.87515 0.534221
\(277\) −16.4553 −0.988701 −0.494351 0.869263i \(-0.664594\pi\)
−0.494351 + 0.869263i \(0.664594\pi\)
\(278\) 14.0582 0.843153
\(279\) 7.06841 0.423175
\(280\) −19.0704 −1.13967
\(281\) 21.9700 1.31062 0.655309 0.755361i \(-0.272539\pi\)
0.655309 + 0.755361i \(0.272539\pi\)
\(282\) 2.25476 0.134269
\(283\) 25.8394 1.53599 0.767995 0.640456i \(-0.221255\pi\)
0.767995 + 0.640456i \(0.221255\pi\)
\(284\) −16.1499 −0.958318
\(285\) 0.997255 0.0590723
\(286\) −3.68241 −0.217745
\(287\) 6.94948 0.410215
\(288\) −5.70623 −0.336243
\(289\) 37.3650 2.19794
\(290\) −8.21206 −0.482229
\(291\) 14.1860 0.831595
\(292\) −10.6416 −0.622751
\(293\) 25.4574 1.48724 0.743618 0.668605i \(-0.233108\pi\)
0.743618 + 0.668605i \(0.233108\pi\)
\(294\) −3.55541 −0.207356
\(295\) 44.1446 2.57020
\(296\) −1.82491 −0.106071
\(297\) −4.28895 −0.248870
\(298\) −7.86279 −0.455479
\(299\) 7.02793 0.406436
\(300\) 14.1552 0.817253
\(301\) −7.03401 −0.405434
\(302\) −8.73017 −0.502365
\(303\) −17.1694 −0.986358
\(304\) 0.0298341 0.00171110
\(305\) −37.1324 −2.12619
\(306\) −6.33054 −0.361893
\(307\) −3.73983 −0.213443 −0.106722 0.994289i \(-0.534035\pi\)
−0.106722 + 0.994289i \(0.534035\pi\)
\(308\) −9.15805 −0.521829
\(309\) 1.00000 0.0568880
\(310\) 24.4333 1.38772
\(311\) −0.567475 −0.0321786 −0.0160893 0.999871i \(-0.505122\pi\)
−0.0160893 + 0.999871i \(0.505122\pi\)
\(312\) −2.80141 −0.158599
\(313\) −22.0903 −1.24862 −0.624309 0.781177i \(-0.714619\pi\)
−0.624309 + 0.781177i \(0.714619\pi\)
\(314\) 11.3132 0.638441
\(315\) −6.80743 −0.383555
\(316\) −6.65935 −0.374617
\(317\) −7.86061 −0.441496 −0.220748 0.975331i \(-0.570850\pi\)
−0.220748 + 0.975331i \(0.570850\pi\)
\(318\) −6.05836 −0.339736
\(319\) −10.1893 −0.570490
\(320\) −18.7548 −1.04843
\(321\) −0.920374 −0.0513703
\(322\) −10.2026 −0.568571
\(323\) 1.82636 0.101622
\(324\) −1.26284 −0.0701578
\(325\) 11.2091 0.621766
\(326\) −8.91625 −0.493826
\(327\) 11.6041 0.641706
\(328\) 11.5140 0.635752
\(329\) 4.44042 0.244808
\(330\) −14.8255 −0.816119
\(331\) 16.5682 0.910672 0.455336 0.890320i \(-0.349519\pi\)
0.455336 + 0.890320i \(0.349519\pi\)
\(332\) −14.2573 −0.782472
\(333\) −0.651425 −0.0356979
\(334\) 6.83354 0.373915
\(335\) −3.57484 −0.195315
\(336\) −0.203653 −0.0111102
\(337\) 34.0486 1.85475 0.927374 0.374136i \(-0.122061\pi\)
0.927374 + 0.374136i \(0.122061\pi\)
\(338\) −0.858580 −0.0467006
\(339\) −13.8477 −0.752104
\(340\) 37.4875 2.03305
\(341\) 30.3160 1.64171
\(342\) −0.212671 −0.0114999
\(343\) −18.8378 −1.01714
\(344\) −11.6540 −0.628342
\(345\) 28.2948 1.52334
\(346\) −14.8542 −0.798567
\(347\) −30.0388 −1.61256 −0.806282 0.591531i \(-0.798524\pi\)
−0.806282 + 0.591531i \(0.798524\pi\)
\(348\) −3.00013 −0.160824
\(349\) −18.5260 −0.991674 −0.495837 0.868416i \(-0.665139\pi\)
−0.495837 + 0.868416i \(0.665139\pi\)
\(350\) −16.2725 −0.869801
\(351\) −1.00000 −0.0533761
\(352\) −24.4737 −1.30445
\(353\) −2.36822 −0.126048 −0.0630239 0.998012i \(-0.520074\pi\)
−0.0630239 + 0.998012i \(0.520074\pi\)
\(354\) −9.41411 −0.500354
\(355\) −51.4872 −2.73266
\(356\) −0.997249 −0.0528541
\(357\) −12.4671 −0.659826
\(358\) 6.61477 0.349601
\(359\) −26.0752 −1.37620 −0.688098 0.725618i \(-0.741554\pi\)
−0.688098 + 0.725618i \(0.741554\pi\)
\(360\) −11.2786 −0.594435
\(361\) −18.9386 −0.996771
\(362\) 20.4384 1.07422
\(363\) −7.39508 −0.388141
\(364\) −2.13527 −0.111918
\(365\) −33.9263 −1.77578
\(366\) 7.91871 0.413918
\(367\) 14.3303 0.748034 0.374017 0.927422i \(-0.377980\pi\)
0.374017 + 0.927422i \(0.377980\pi\)
\(368\) 0.846473 0.0441254
\(369\) 4.11006 0.213961
\(370\) −2.25177 −0.117064
\(371\) −11.9310 −0.619428
\(372\) 8.92627 0.462805
\(373\) 17.3301 0.897319 0.448660 0.893703i \(-0.351902\pi\)
0.448660 + 0.893703i \(0.351902\pi\)
\(374\) −27.1513 −1.40396
\(375\) 24.9979 1.29089
\(376\) 7.35693 0.379405
\(377\) −2.37570 −0.122355
\(378\) 1.45173 0.0746688
\(379\) 16.5516 0.850197 0.425098 0.905147i \(-0.360240\pi\)
0.425098 + 0.905147i \(0.360240\pi\)
\(380\) 1.25937 0.0646045
\(381\) 15.9315 0.816194
\(382\) −7.70630 −0.394289
\(383\) −17.8751 −0.913373 −0.456686 0.889628i \(-0.650964\pi\)
−0.456686 + 0.889628i \(0.650964\pi\)
\(384\) −7.41288 −0.378287
\(385\) −29.1967 −1.48800
\(386\) 23.1620 1.17891
\(387\) −4.16005 −0.211467
\(388\) 17.9146 0.909475
\(389\) 27.8469 1.41189 0.705947 0.708265i \(-0.250522\pi\)
0.705947 + 0.708265i \(0.250522\pi\)
\(390\) −3.45668 −0.175036
\(391\) 51.8187 2.62059
\(392\) −11.6007 −0.585926
\(393\) 11.6337 0.586841
\(394\) 3.50939 0.176800
\(395\) −21.2306 −1.06823
\(396\) −5.41625 −0.272177
\(397\) 6.50228 0.326340 0.163170 0.986598i \(-0.447828\pi\)
0.163170 + 0.986598i \(0.447828\pi\)
\(398\) −9.69178 −0.485805
\(399\) −0.418824 −0.0209674
\(400\) 1.35006 0.0675032
\(401\) 8.41748 0.420349 0.210175 0.977664i \(-0.432597\pi\)
0.210175 + 0.977664i \(0.432597\pi\)
\(402\) 0.762358 0.0380230
\(403\) 7.06841 0.352102
\(404\) −21.6822 −1.07873
\(405\) −4.02605 −0.200056
\(406\) 3.44888 0.171165
\(407\) −2.79393 −0.138490
\(408\) −20.6555 −1.02260
\(409\) −0.352704 −0.0174401 −0.00872003 0.999962i \(-0.502776\pi\)
−0.00872003 + 0.999962i \(0.502776\pi\)
\(410\) 14.2072 0.701642
\(411\) −17.0824 −0.842611
\(412\) 1.26284 0.0622157
\(413\) −18.5397 −0.912279
\(414\) −6.03404 −0.296557
\(415\) −45.4536 −2.23123
\(416\) −5.70623 −0.279771
\(417\) 16.3737 0.801825
\(418\) −0.912135 −0.0446140
\(419\) −1.00026 −0.0488659 −0.0244330 0.999701i \(-0.507778\pi\)
−0.0244330 + 0.999701i \(0.507778\pi\)
\(420\) −8.59669 −0.419476
\(421\) 8.40125 0.409452 0.204726 0.978819i \(-0.434370\pi\)
0.204726 + 0.978819i \(0.434370\pi\)
\(422\) 0.938488 0.0456849
\(423\) 2.62615 0.127688
\(424\) −19.7674 −0.959992
\(425\) 82.6472 4.00898
\(426\) 10.9800 0.531982
\(427\) 15.5947 0.754682
\(428\) −1.16228 −0.0561812
\(429\) −4.28895 −0.207072
\(430\) −14.3800 −0.693465
\(431\) −17.1273 −0.824995 −0.412498 0.910959i \(-0.635344\pi\)
−0.412498 + 0.910959i \(0.635344\pi\)
\(432\) −0.120444 −0.00579487
\(433\) −18.1040 −0.870023 −0.435012 0.900425i \(-0.643256\pi\)
−0.435012 + 0.900425i \(0.643256\pi\)
\(434\) −10.2614 −0.492563
\(435\) −9.56470 −0.458592
\(436\) 14.6541 0.701803
\(437\) 1.74082 0.0832749
\(438\) 7.23500 0.345702
\(439\) −22.1621 −1.05774 −0.528870 0.848703i \(-0.677384\pi\)
−0.528870 + 0.848703i \(0.677384\pi\)
\(440\) −48.3734 −2.30611
\(441\) −4.14104 −0.197192
\(442\) −6.33054 −0.301113
\(443\) 19.8336 0.942322 0.471161 0.882047i \(-0.343835\pi\)
0.471161 + 0.882047i \(0.343835\pi\)
\(444\) −0.822646 −0.0390410
\(445\) −3.17932 −0.150714
\(446\) 4.58074 0.216904
\(447\) −9.15789 −0.433153
\(448\) 7.87659 0.372134
\(449\) −29.2381 −1.37983 −0.689917 0.723889i \(-0.742353\pi\)
−0.689917 + 0.723889i \(0.742353\pi\)
\(450\) −9.62387 −0.453674
\(451\) 17.6278 0.830062
\(452\) −17.4874 −0.822540
\(453\) −10.1681 −0.477741
\(454\) 22.8396 1.07191
\(455\) −6.80743 −0.319137
\(456\) −0.693912 −0.0324954
\(457\) 23.8289 1.11467 0.557334 0.830289i \(-0.311824\pi\)
0.557334 + 0.830289i \(0.311824\pi\)
\(458\) −19.0167 −0.888594
\(459\) −7.37326 −0.344154
\(460\) 35.7318 1.66600
\(461\) −29.9464 −1.39474 −0.697371 0.716710i \(-0.745647\pi\)
−0.697371 + 0.716710i \(0.745647\pi\)
\(462\) 6.22638 0.289678
\(463\) 7.86033 0.365300 0.182650 0.983178i \(-0.441532\pi\)
0.182650 + 0.983178i \(0.441532\pi\)
\(464\) −0.286140 −0.0132837
\(465\) 28.4577 1.31970
\(466\) −1.13161 −0.0524209
\(467\) 8.61609 0.398705 0.199353 0.979928i \(-0.436116\pi\)
0.199353 + 0.979928i \(0.436116\pi\)
\(468\) −1.26284 −0.0583748
\(469\) 1.50135 0.0693260
\(470\) 9.07778 0.418727
\(471\) 13.1766 0.607148
\(472\) −30.7167 −1.41385
\(473\) −17.8423 −0.820388
\(474\) 4.52756 0.207958
\(475\) 2.77649 0.127394
\(476\) −15.7439 −0.721620
\(477\) −7.05625 −0.323083
\(478\) −22.0641 −1.00919
\(479\) 24.5756 1.12289 0.561444 0.827515i \(-0.310246\pi\)
0.561444 + 0.827515i \(0.310246\pi\)
\(480\) −22.9736 −1.04859
\(481\) −0.651425 −0.0297024
\(482\) 9.06739 0.413008
\(483\) −11.8831 −0.540702
\(484\) −9.33880 −0.424491
\(485\) 57.1133 2.59338
\(486\) 0.858580 0.0389460
\(487\) −11.7752 −0.533586 −0.266793 0.963754i \(-0.585964\pi\)
−0.266793 + 0.963754i \(0.585964\pi\)
\(488\) 25.8375 1.16961
\(489\) −10.3849 −0.469620
\(490\) −14.3143 −0.646652
\(491\) 6.54793 0.295504 0.147752 0.989024i \(-0.452796\pi\)
0.147752 + 0.989024i \(0.452796\pi\)
\(492\) 5.19034 0.233999
\(493\) −17.5167 −0.788912
\(494\) −0.212671 −0.00956852
\(495\) −17.2675 −0.776117
\(496\) 0.851349 0.0382267
\(497\) 21.6234 0.969944
\(498\) 9.69328 0.434366
\(499\) −18.6088 −0.833044 −0.416522 0.909126i \(-0.636751\pi\)
−0.416522 + 0.909126i \(0.636751\pi\)
\(500\) 31.5684 1.41178
\(501\) 7.95912 0.355587
\(502\) 5.55614 0.247983
\(503\) −30.9395 −1.37953 −0.689763 0.724035i \(-0.742285\pi\)
−0.689763 + 0.724035i \(0.742285\pi\)
\(504\) 4.73675 0.210992
\(505\) −69.1250 −3.07602
\(506\) −25.8797 −1.15049
\(507\) −1.00000 −0.0444116
\(508\) 20.1189 0.892632
\(509\) 12.4774 0.553053 0.276526 0.961006i \(-0.410817\pi\)
0.276526 + 0.961006i \(0.410817\pi\)
\(510\) −25.4870 −1.12858
\(511\) 14.2483 0.630306
\(512\) −1.36211 −0.0601973
\(513\) −0.247701 −0.0109363
\(514\) −4.72818 −0.208551
\(515\) 4.02605 0.177409
\(516\) −5.25348 −0.231272
\(517\) 11.2634 0.495365
\(518\) 0.945692 0.0415513
\(519\) −17.3009 −0.759425
\(520\) −11.2786 −0.494600
\(521\) 0.969709 0.0424837 0.0212419 0.999774i \(-0.493238\pi\)
0.0212419 + 0.999774i \(0.493238\pi\)
\(522\) 2.03973 0.0892767
\(523\) 43.8263 1.91639 0.958195 0.286116i \(-0.0923643\pi\)
0.958195 + 0.286116i \(0.0923643\pi\)
\(524\) 14.6915 0.641799
\(525\) −18.9528 −0.827167
\(526\) 13.7280 0.598571
\(527\) 52.1172 2.27026
\(528\) −0.516579 −0.0224812
\(529\) 26.3918 1.14747
\(530\) −24.3912 −1.05949
\(531\) −10.9647 −0.475829
\(532\) −0.528908 −0.0229311
\(533\) 4.11006 0.178026
\(534\) 0.678010 0.0293404
\(535\) −3.70547 −0.160201
\(536\) 2.48745 0.107442
\(537\) 7.70431 0.332465
\(538\) −16.5342 −0.712839
\(539\) −17.7607 −0.765007
\(540\) −5.08425 −0.218791
\(541\) 40.3867 1.73636 0.868179 0.496251i \(-0.165290\pi\)
0.868179 + 0.496251i \(0.165290\pi\)
\(542\) 23.0709 0.990980
\(543\) 23.8049 1.02157
\(544\) −42.0735 −1.80389
\(545\) 46.7185 2.00120
\(546\) 1.45173 0.0621282
\(547\) −16.7888 −0.717837 −0.358918 0.933369i \(-0.616854\pi\)
−0.358918 + 0.933369i \(0.616854\pi\)
\(548\) −21.5723 −0.921523
\(549\) 9.22303 0.393629
\(550\) −41.2763 −1.76003
\(551\) −0.588464 −0.0250694
\(552\) −19.6881 −0.837981
\(553\) 8.91636 0.379162
\(554\) 14.1282 0.600248
\(555\) −2.62267 −0.111326
\(556\) 20.6774 0.876917
\(557\) 20.3733 0.863242 0.431621 0.902055i \(-0.357942\pi\)
0.431621 + 0.902055i \(0.357942\pi\)
\(558\) −6.06880 −0.256913
\(559\) −4.16005 −0.175952
\(560\) −0.819915 −0.0346477
\(561\) −31.6235 −1.33515
\(562\) −18.8630 −0.795686
\(563\) −37.6179 −1.58540 −0.792702 0.609609i \(-0.791326\pi\)
−0.792702 + 0.609609i \(0.791326\pi\)
\(564\) 3.31641 0.139646
\(565\) −55.7515 −2.34548
\(566\) −22.1852 −0.932512
\(567\) 1.69085 0.0710089
\(568\) 35.8259 1.50322
\(569\) −24.7169 −1.03619 −0.518094 0.855324i \(-0.673358\pi\)
−0.518094 + 0.855324i \(0.673358\pi\)
\(570\) −0.856224 −0.0358633
\(571\) −38.4567 −1.60936 −0.804681 0.593708i \(-0.797663\pi\)
−0.804681 + 0.593708i \(0.797663\pi\)
\(572\) −5.41625 −0.226465
\(573\) −8.97563 −0.374962
\(574\) −5.96668 −0.249045
\(575\) 78.7764 3.28520
\(576\) 4.65837 0.194099
\(577\) −18.7365 −0.780013 −0.390006 0.920812i \(-0.627527\pi\)
−0.390006 + 0.920812i \(0.627527\pi\)
\(578\) −32.0808 −1.33439
\(579\) 26.9771 1.12113
\(580\) −12.0787 −0.501540
\(581\) 19.0895 0.791965
\(582\) −12.1798 −0.504868
\(583\) −30.2639 −1.25340
\(584\) 23.6066 0.976850
\(585\) −4.02605 −0.166457
\(586\) −21.8572 −0.902913
\(587\) 32.0935 1.32464 0.662321 0.749220i \(-0.269571\pi\)
0.662321 + 0.749220i \(0.269571\pi\)
\(588\) −5.22947 −0.215660
\(589\) 1.75085 0.0721425
\(590\) −37.9017 −1.56039
\(591\) 4.08743 0.168134
\(592\) −0.0784604 −0.00322470
\(593\) −26.4755 −1.08722 −0.543610 0.839338i \(-0.682943\pi\)
−0.543610 + 0.839338i \(0.682943\pi\)
\(594\) 3.68241 0.151091
\(595\) −50.1929 −2.05771
\(596\) −11.5650 −0.473719
\(597\) −11.2881 −0.461993
\(598\) −6.03404 −0.246750
\(599\) −17.5489 −0.717030 −0.358515 0.933524i \(-0.616717\pi\)
−0.358515 + 0.933524i \(0.616717\pi\)
\(600\) −31.4011 −1.28195
\(601\) −19.2224 −0.784099 −0.392049 0.919944i \(-0.628234\pi\)
−0.392049 + 0.919944i \(0.628234\pi\)
\(602\) 6.03926 0.246142
\(603\) 0.887929 0.0361593
\(604\) −12.8407 −0.522482
\(605\) −29.7729 −1.21044
\(606\) 14.7413 0.598826
\(607\) −3.15030 −0.127867 −0.0639334 0.997954i \(-0.520365\pi\)
−0.0639334 + 0.997954i \(0.520365\pi\)
\(608\) −1.41344 −0.0573225
\(609\) 4.01695 0.162775
\(610\) 31.8811 1.29083
\(611\) 2.62615 0.106243
\(612\) −9.31125 −0.376385
\(613\) 43.6922 1.76471 0.882356 0.470582i \(-0.155956\pi\)
0.882356 + 0.470582i \(0.155956\pi\)
\(614\) 3.21094 0.129583
\(615\) 16.5473 0.667251
\(616\) 20.3157 0.818543
\(617\) 26.2667 1.05746 0.528728 0.848791i \(-0.322669\pi\)
0.528728 + 0.848791i \(0.322669\pi\)
\(618\) −0.858580 −0.0345372
\(619\) 7.58897 0.305027 0.152513 0.988301i \(-0.451263\pi\)
0.152513 + 0.988301i \(0.451263\pi\)
\(620\) 35.9376 1.44329
\(621\) −7.02793 −0.282021
\(622\) 0.487223 0.0195359
\(623\) 1.33524 0.0534953
\(624\) −0.120444 −0.00482163
\(625\) 44.5976 1.78390
\(626\) 18.9663 0.758046
\(627\) −1.06238 −0.0424272
\(628\) 16.6400 0.664008
\(629\) −4.80313 −0.191513
\(630\) 5.84472 0.232859
\(631\) −37.7400 −1.50241 −0.751203 0.660072i \(-0.770526\pi\)
−0.751203 + 0.660072i \(0.770526\pi\)
\(632\) 14.7727 0.587627
\(633\) 1.09307 0.0434456
\(634\) 6.74897 0.268036
\(635\) 64.1409 2.54535
\(636\) −8.91091 −0.353341
\(637\) −4.14104 −0.164074
\(638\) 8.74831 0.346349
\(639\) 12.7885 0.505906
\(640\) −29.8446 −1.17971
\(641\) 1.53065 0.0604570 0.0302285 0.999543i \(-0.490376\pi\)
0.0302285 + 0.999543i \(0.490376\pi\)
\(642\) 0.790215 0.0311873
\(643\) 23.5441 0.928491 0.464245 0.885707i \(-0.346326\pi\)
0.464245 + 0.885707i \(0.346326\pi\)
\(644\) −15.0065 −0.591339
\(645\) −16.7486 −0.659474
\(646\) −1.56808 −0.0616952
\(647\) 5.36402 0.210881 0.105441 0.994426i \(-0.466375\pi\)
0.105441 + 0.994426i \(0.466375\pi\)
\(648\) 2.80141 0.110050
\(649\) −47.0272 −1.84598
\(650\) −9.62387 −0.377479
\(651\) −11.9516 −0.468420
\(652\) −13.1144 −0.513601
\(653\) −12.2900 −0.480943 −0.240471 0.970656i \(-0.577302\pi\)
−0.240471 + 0.970656i \(0.577302\pi\)
\(654\) −9.96303 −0.389585
\(655\) 46.8377 1.83010
\(656\) 0.495032 0.0193278
\(657\) 8.42670 0.328757
\(658\) −3.81246 −0.148625
\(659\) 16.7295 0.651690 0.325845 0.945423i \(-0.394351\pi\)
0.325845 + 0.945423i \(0.394351\pi\)
\(660\) −21.8061 −0.848801
\(661\) 29.0830 1.13120 0.565598 0.824681i \(-0.308645\pi\)
0.565598 + 0.824681i \(0.308645\pi\)
\(662\) −14.2252 −0.552876
\(663\) −7.37326 −0.286354
\(664\) 31.6276 1.22739
\(665\) −1.68621 −0.0653882
\(666\) 0.559301 0.0216725
\(667\) −16.6963 −0.646483
\(668\) 10.0511 0.388889
\(669\) 5.33525 0.206272
\(670\) 3.06929 0.118577
\(671\) 39.5571 1.52708
\(672\) 9.64836 0.372194
\(673\) 31.3705 1.20924 0.604622 0.796512i \(-0.293324\pi\)
0.604622 + 0.796512i \(0.293324\pi\)
\(674\) −29.2335 −1.12603
\(675\) −11.2091 −0.431437
\(676\) −1.26284 −0.0485708
\(677\) −33.5598 −1.28981 −0.644904 0.764264i \(-0.723103\pi\)
−0.644904 + 0.764264i \(0.723103\pi\)
\(678\) 11.8894 0.456608
\(679\) −23.9863 −0.920509
\(680\) −83.1601 −3.18904
\(681\) 26.6015 1.01937
\(682\) −26.0288 −0.996692
\(683\) 25.0836 0.959796 0.479898 0.877324i \(-0.340674\pi\)
0.479898 + 0.877324i \(0.340674\pi\)
\(684\) −0.312806 −0.0119605
\(685\) −68.7744 −2.62774
\(686\) 16.1738 0.617517
\(687\) −22.1490 −0.845039
\(688\) −0.501054 −0.0191025
\(689\) −7.05625 −0.268822
\(690\) −24.2933 −0.924831
\(691\) 7.08459 0.269510 0.134755 0.990879i \(-0.456975\pi\)
0.134755 + 0.990879i \(0.456975\pi\)
\(692\) −21.8483 −0.830547
\(693\) 7.25195 0.275479
\(694\) 25.7907 0.979001
\(695\) 65.9214 2.50054
\(696\) 6.65532 0.252269
\(697\) 30.3045 1.14787
\(698\) 15.9061 0.602053
\(699\) −1.31800 −0.0498515
\(700\) −23.9343 −0.904633
\(701\) −36.3878 −1.37435 −0.687174 0.726493i \(-0.741149\pi\)
−0.687174 + 0.726493i \(0.741149\pi\)
\(702\) 0.858580 0.0324050
\(703\) −0.161359 −0.00608575
\(704\) 19.9795 0.753006
\(705\) 10.5730 0.398203
\(706\) 2.03331 0.0765246
\(707\) 29.0309 1.09182
\(708\) −13.8467 −0.520391
\(709\) −17.7402 −0.666248 −0.333124 0.942883i \(-0.608103\pi\)
−0.333124 + 0.942883i \(0.608103\pi\)
\(710\) 44.2059 1.65902
\(711\) 5.27331 0.197765
\(712\) 2.21224 0.0829071
\(713\) 49.6763 1.86039
\(714\) 10.7040 0.400586
\(715\) −17.2675 −0.645768
\(716\) 9.72930 0.363601
\(717\) −25.6984 −0.959723
\(718\) 22.3876 0.835499
\(719\) 41.9110 1.56302 0.781508 0.623896i \(-0.214451\pi\)
0.781508 + 0.623896i \(0.214451\pi\)
\(720\) −0.484914 −0.0180717
\(721\) −1.69085 −0.0629704
\(722\) 16.2603 0.605147
\(723\) 10.5609 0.392764
\(724\) 30.0618 1.11724
\(725\) −26.6294 −0.988991
\(726\) 6.34927 0.235643
\(727\) 19.2054 0.712290 0.356145 0.934431i \(-0.384091\pi\)
0.356145 + 0.934431i \(0.384091\pi\)
\(728\) 4.73675 0.175556
\(729\) 1.00000 0.0370370
\(730\) 29.1284 1.07809
\(731\) −30.6732 −1.13449
\(732\) 11.6472 0.430493
\(733\) 16.4943 0.609230 0.304615 0.952476i \(-0.401472\pi\)
0.304615 + 0.952476i \(0.401472\pi\)
\(734\) −12.3037 −0.454137
\(735\) −16.6720 −0.614956
\(736\) −40.1030 −1.47822
\(737\) 3.80828 0.140280
\(738\) −3.52881 −0.129897
\(739\) 26.2905 0.967112 0.483556 0.875313i \(-0.339345\pi\)
0.483556 + 0.875313i \(0.339345\pi\)
\(740\) −3.31201 −0.121752
\(741\) −0.247701 −0.00909952
\(742\) 10.2438 0.376060
\(743\) 34.7413 1.27453 0.637267 0.770643i \(-0.280065\pi\)
0.637267 + 0.770643i \(0.280065\pi\)
\(744\) −19.8015 −0.725959
\(745\) −36.8701 −1.35082
\(746\) −14.8793 −0.544770
\(747\) 11.2899 0.413076
\(748\) −39.9355 −1.46018
\(749\) 1.55621 0.0568627
\(750\) −21.4627 −0.783708
\(751\) 8.01149 0.292343 0.146172 0.989259i \(-0.453305\pi\)
0.146172 + 0.989259i \(0.453305\pi\)
\(752\) 0.316305 0.0115345
\(753\) 6.47131 0.235828
\(754\) 2.03973 0.0742827
\(755\) −40.9374 −1.48987
\(756\) 2.13527 0.0776590
\(757\) 41.7228 1.51644 0.758221 0.651998i \(-0.226069\pi\)
0.758221 + 0.651998i \(0.226069\pi\)
\(758\) −14.2108 −0.516161
\(759\) −30.1424 −1.09410
\(760\) −2.79372 −0.101339
\(761\) −33.7882 −1.22482 −0.612411 0.790540i \(-0.709800\pi\)
−0.612411 + 0.790540i \(0.709800\pi\)
\(762\) −13.6784 −0.495518
\(763\) −19.6207 −0.710317
\(764\) −11.3348 −0.410078
\(765\) −29.6851 −1.07327
\(766\) 15.3472 0.554516
\(767\) −10.9647 −0.395914
\(768\) 15.6813 0.565850
\(769\) −37.2396 −1.34289 −0.671447 0.741053i \(-0.734327\pi\)
−0.671447 + 0.741053i \(0.734327\pi\)
\(770\) 25.0677 0.903378
\(771\) −5.50697 −0.198329
\(772\) 34.0677 1.22612
\(773\) −17.3275 −0.623226 −0.311613 0.950209i \(-0.600869\pi\)
−0.311613 + 0.950209i \(0.600869\pi\)
\(774\) 3.57174 0.128384
\(775\) 79.2301 2.84603
\(776\) −39.7407 −1.42661
\(777\) 1.10146 0.0395147
\(778\) −23.9088 −0.857172
\(779\) 1.01806 0.0364759
\(780\) −5.08425 −0.182045
\(781\) 54.8493 1.96266
\(782\) −44.4905 −1.59098
\(783\) 2.37570 0.0849008
\(784\) −0.498764 −0.0178130
\(785\) 53.0498 1.89343
\(786\) −9.98844 −0.356276
\(787\) 22.0824 0.787152 0.393576 0.919292i \(-0.371238\pi\)
0.393576 + 0.919292i \(0.371238\pi\)
\(788\) 5.16177 0.183880
\(789\) 15.9892 0.569231
\(790\) 18.2282 0.648529
\(791\) 23.4143 0.832518
\(792\) 12.0151 0.426938
\(793\) 9.22303 0.327519
\(794\) −5.58273 −0.198124
\(795\) −28.4088 −1.00756
\(796\) −14.2551 −0.505259
\(797\) 6.25171 0.221447 0.110723 0.993851i \(-0.464683\pi\)
0.110723 + 0.993851i \(0.464683\pi\)
\(798\) 0.359594 0.0127295
\(799\) 19.3633 0.685025
\(800\) −63.9614 −2.26138
\(801\) 0.789688 0.0279022
\(802\) −7.22709 −0.255197
\(803\) 36.1417 1.27541
\(804\) 1.12131 0.0395456
\(805\) −47.8421 −1.68621
\(806\) −6.06880 −0.213764
\(807\) −19.2576 −0.677899
\(808\) 48.0986 1.69210
\(809\) 22.0125 0.773917 0.386958 0.922097i \(-0.373526\pi\)
0.386958 + 0.922097i \(0.373526\pi\)
\(810\) 3.45668 0.121456
\(811\) 19.6597 0.690345 0.345173 0.938539i \(-0.387820\pi\)
0.345173 + 0.938539i \(0.387820\pi\)
\(812\) 5.07277 0.178019
\(813\) 26.8710 0.942407
\(814\) 2.39881 0.0840783
\(815\) −41.8100 −1.46454
\(816\) −0.888066 −0.0310885
\(817\) −1.03045 −0.0360508
\(818\) 0.302824 0.0105880
\(819\) 1.69085 0.0590830
\(820\) 20.8966 0.729740
\(821\) 49.6609 1.73318 0.866588 0.499024i \(-0.166308\pi\)
0.866588 + 0.499024i \(0.166308\pi\)
\(822\) 14.6666 0.511556
\(823\) 19.5452 0.681305 0.340652 0.940189i \(-0.389352\pi\)
0.340652 + 0.940189i \(0.389352\pi\)
\(824\) −2.80141 −0.0975917
\(825\) −48.0750 −1.67376
\(826\) 15.9178 0.553852
\(827\) −46.5843 −1.61989 −0.809947 0.586503i \(-0.800504\pi\)
−0.809947 + 0.586503i \(0.800504\pi\)
\(828\) −8.87515 −0.308433
\(829\) 8.03996 0.279239 0.139620 0.990205i \(-0.455412\pi\)
0.139620 + 0.990205i \(0.455412\pi\)
\(830\) 39.0256 1.35460
\(831\) 16.4553 0.570827
\(832\) 4.65837 0.161500
\(833\) −30.5329 −1.05790
\(834\) −14.0582 −0.486794
\(835\) 32.0438 1.10892
\(836\) −1.34161 −0.0464006
\(837\) −7.06841 −0.244320
\(838\) 0.858804 0.0296669
\(839\) 16.3575 0.564725 0.282362 0.959308i \(-0.408882\pi\)
0.282362 + 0.959308i \(0.408882\pi\)
\(840\) 19.0704 0.657991
\(841\) −23.3560 −0.805380
\(842\) −7.21315 −0.248582
\(843\) −21.9700 −0.756685
\(844\) 1.38037 0.0475144
\(845\) −4.02605 −0.138500
\(846\) −2.25476 −0.0775204
\(847\) 12.5039 0.429640
\(848\) −0.849884 −0.0291851
\(849\) −25.8394 −0.886804
\(850\) −70.9593 −2.43388
\(851\) −4.57817 −0.156938
\(852\) 16.1499 0.553285
\(853\) −21.7263 −0.743894 −0.371947 0.928254i \(-0.621310\pi\)
−0.371947 + 0.928254i \(0.621310\pi\)
\(854\) −13.3893 −0.458173
\(855\) −0.997255 −0.0341054
\(856\) 2.57834 0.0881260
\(857\) −22.3367 −0.763008 −0.381504 0.924367i \(-0.624594\pi\)
−0.381504 + 0.924367i \(0.624594\pi\)
\(858\) 3.68241 0.125715
\(859\) −34.4469 −1.17531 −0.587656 0.809111i \(-0.699949\pi\)
−0.587656 + 0.809111i \(0.699949\pi\)
\(860\) −21.1508 −0.721235
\(861\) −6.94948 −0.236837
\(862\) 14.7052 0.500861
\(863\) 19.1394 0.651511 0.325756 0.945454i \(-0.394381\pi\)
0.325756 + 0.945454i \(0.394381\pi\)
\(864\) 5.70623 0.194130
\(865\) −69.6542 −2.36832
\(866\) 15.5437 0.528198
\(867\) −37.3650 −1.26898
\(868\) −15.0929 −0.512288
\(869\) 22.6170 0.767228
\(870\) 8.21206 0.278415
\(871\) 0.887929 0.0300863
\(872\) −32.5078 −1.10085
\(873\) −14.1860 −0.480122
\(874\) −1.49464 −0.0505568
\(875\) −42.2677 −1.42891
\(876\) 10.6416 0.359545
\(877\) 2.28537 0.0771714 0.0385857 0.999255i \(-0.487715\pi\)
0.0385857 + 0.999255i \(0.487715\pi\)
\(878\) 19.0280 0.642162
\(879\) −25.4574 −0.858656
\(880\) −2.07977 −0.0701090
\(881\) −1.52068 −0.0512331 −0.0256166 0.999672i \(-0.508155\pi\)
−0.0256166 + 0.999672i \(0.508155\pi\)
\(882\) 3.55541 0.119717
\(883\) 46.3371 1.55937 0.779683 0.626174i \(-0.215380\pi\)
0.779683 + 0.626174i \(0.215380\pi\)
\(884\) −9.31125 −0.313171
\(885\) −44.1446 −1.48390
\(886\) −17.0287 −0.572091
\(887\) 5.17208 0.173661 0.0868307 0.996223i \(-0.472326\pi\)
0.0868307 + 0.996223i \(0.472326\pi\)
\(888\) 1.82491 0.0612399
\(889\) −26.9377 −0.903461
\(890\) 2.72970 0.0914998
\(891\) 4.28895 0.143685
\(892\) 6.73756 0.225590
\(893\) 0.650500 0.0217682
\(894\) 7.86279 0.262971
\(895\) 31.0179 1.03681
\(896\) 12.5340 0.418733
\(897\) −7.02793 −0.234656
\(898\) 25.1033 0.837708
\(899\) −16.7925 −0.560060
\(900\) −14.1552 −0.471841
\(901\) −52.0276 −1.73329
\(902\) −15.1349 −0.503937
\(903\) 7.03401 0.234077
\(904\) 38.7931 1.29024
\(905\) 95.8396 3.18582
\(906\) 8.73017 0.290040
\(907\) −41.4596 −1.37664 −0.688321 0.725406i \(-0.741652\pi\)
−0.688321 + 0.725406i \(0.741652\pi\)
\(908\) 33.5935 1.11484
\(909\) 17.1694 0.569474
\(910\) 5.84472 0.193751
\(911\) 30.3949 1.00703 0.503514 0.863987i \(-0.332040\pi\)
0.503514 + 0.863987i \(0.332040\pi\)
\(912\) −0.0298341 −0.000987906 0
\(913\) 48.4218 1.60253
\(914\) −20.4590 −0.676724
\(915\) 37.1324 1.22756
\(916\) −27.9707 −0.924178
\(917\) −19.6707 −0.649585
\(918\) 6.33054 0.208939
\(919\) −37.5419 −1.23839 −0.619196 0.785236i \(-0.712541\pi\)
−0.619196 + 0.785236i \(0.712541\pi\)
\(920\) −79.2652 −2.61330
\(921\) 3.73983 0.123231
\(922\) 25.7114 0.846759
\(923\) 12.7885 0.420939
\(924\) 9.15805 0.301278
\(925\) −7.30186 −0.240084
\(926\) −6.74872 −0.221777
\(927\) −1.00000 −0.0328443
\(928\) 13.5563 0.445008
\(929\) 14.7922 0.485318 0.242659 0.970112i \(-0.421980\pi\)
0.242659 + 0.970112i \(0.421980\pi\)
\(930\) −24.4333 −0.801198
\(931\) −1.02574 −0.0336172
\(932\) −1.66443 −0.0545202
\(933\) 0.567475 0.0185783
\(934\) −7.39760 −0.242057
\(935\) −127.318 −4.16374
\(936\) 2.80141 0.0915670
\(937\) −46.8617 −1.53090 −0.765452 0.643493i \(-0.777485\pi\)
−0.765452 + 0.643493i \(0.777485\pi\)
\(938\) −1.28903 −0.0420884
\(939\) 22.0903 0.720890
\(940\) 13.3520 0.435495
\(941\) −10.6042 −0.345686 −0.172843 0.984949i \(-0.555295\pi\)
−0.172843 + 0.984949i \(0.555295\pi\)
\(942\) −11.3132 −0.368604
\(943\) 28.8852 0.940631
\(944\) −1.32064 −0.0429832
\(945\) 6.80743 0.221446
\(946\) 15.3190 0.498064
\(947\) −11.6656 −0.379081 −0.189540 0.981873i \(-0.560700\pi\)
−0.189540 + 0.981873i \(0.560700\pi\)
\(948\) 6.65935 0.216285
\(949\) 8.42670 0.273542
\(950\) −2.38384 −0.0773420
\(951\) 7.86061 0.254898
\(952\) 34.9253 1.13194
\(953\) −38.4317 −1.24492 −0.622462 0.782650i \(-0.713868\pi\)
−0.622462 + 0.782650i \(0.713868\pi\)
\(954\) 6.05836 0.196147
\(955\) −36.1363 −1.16934
\(956\) −32.4529 −1.04960
\(957\) 10.1893 0.329372
\(958\) −21.1001 −0.681714
\(959\) 28.8837 0.932703
\(960\) 18.7548 0.605309
\(961\) 18.9624 0.611690
\(962\) 0.559301 0.0180326
\(963\) 0.920374 0.0296586
\(964\) 13.3367 0.429547
\(965\) 108.611 3.49631
\(966\) 10.2026 0.328264
\(967\) 27.7616 0.892752 0.446376 0.894845i \(-0.352714\pi\)
0.446376 + 0.894845i \(0.352714\pi\)
\(968\) 20.7166 0.665858
\(969\) −1.82636 −0.0586712
\(970\) −49.0364 −1.57446
\(971\) −29.9900 −0.962425 −0.481213 0.876604i \(-0.659804\pi\)
−0.481213 + 0.876604i \(0.659804\pi\)
\(972\) 1.26284 0.0405056
\(973\) −27.6855 −0.887555
\(974\) 10.1100 0.323944
\(975\) −11.2091 −0.358977
\(976\) 1.11086 0.0355578
\(977\) 39.5870 1.26650 0.633250 0.773948i \(-0.281721\pi\)
0.633250 + 0.773948i \(0.281721\pi\)
\(978\) 8.91625 0.285110
\(979\) 3.38693 0.108247
\(980\) −21.0541 −0.672548
\(981\) −11.6041 −0.370489
\(982\) −5.62192 −0.179403
\(983\) −8.39756 −0.267841 −0.133920 0.990992i \(-0.542757\pi\)
−0.133920 + 0.990992i \(0.542757\pi\)
\(984\) −11.5140 −0.367051
\(985\) 16.4562 0.524338
\(986\) 15.0395 0.478955
\(987\) −4.44042 −0.141340
\(988\) −0.312806 −0.00995170
\(989\) −29.2366 −0.929668
\(990\) 14.8255 0.471187
\(991\) −33.1761 −1.05387 −0.526936 0.849905i \(-0.676659\pi\)
−0.526936 + 0.849905i \(0.676659\pi\)
\(992\) −40.3340 −1.28060
\(993\) −16.5682 −0.525777
\(994\) −18.5655 −0.588861
\(995\) −45.4466 −1.44075
\(996\) 14.2573 0.451761
\(997\) 21.9615 0.695527 0.347764 0.937582i \(-0.386941\pi\)
0.347764 + 0.937582i \(0.386941\pi\)
\(998\) 15.9771 0.505747
\(999\) 0.651425 0.0206102
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 \(a_p\))