Properties

Label 4005.2.a.p.1.3
Level 4005
Weight 2
Character 4005.1
Self dual Yes
Analytic conductor 31.980
Analytic rank 1
Dimension 8
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4005 = 3^{2} \cdot 5 \cdot 89 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4005.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9800860095\)
Analytic rank: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.16343\)
Character \(\chi\) = 4005.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.16343 q^{2} -0.646427 q^{4} +1.00000 q^{5} +2.23155 q^{7} +3.07894 q^{8} +O(q^{10})\) \(q-1.16343 q^{2} -0.646427 q^{4} +1.00000 q^{5} +2.23155 q^{7} +3.07894 q^{8} -1.16343 q^{10} -6.24237 q^{11} -4.63493 q^{13} -2.59625 q^{14} -2.28928 q^{16} +2.75732 q^{17} +3.29630 q^{19} -0.646427 q^{20} +7.26257 q^{22} +6.86648 q^{23} +1.00000 q^{25} +5.39242 q^{26} -1.44253 q^{28} -1.22407 q^{29} -5.69744 q^{31} -3.49446 q^{32} -3.20795 q^{34} +2.23155 q^{35} +6.87730 q^{37} -3.83501 q^{38} +3.07894 q^{40} -0.954991 q^{41} -12.5627 q^{43} +4.03524 q^{44} -7.98867 q^{46} +3.00176 q^{47} -2.02020 q^{49} -1.16343 q^{50} +2.99615 q^{52} +10.1149 q^{53} -6.24237 q^{55} +6.87079 q^{56} +1.42412 q^{58} -7.06511 q^{59} -2.99922 q^{61} +6.62858 q^{62} +8.64411 q^{64} -4.63493 q^{65} -10.0152 q^{67} -1.78241 q^{68} -2.59625 q^{70} -9.04184 q^{71} +11.2191 q^{73} -8.00126 q^{74} -2.13082 q^{76} -13.9301 q^{77} +0.814296 q^{79} -2.28928 q^{80} +1.11107 q^{82} -2.94088 q^{83} +2.75732 q^{85} +14.6158 q^{86} -19.2199 q^{88} -1.00000 q^{89} -10.3431 q^{91} -4.43868 q^{92} -3.49234 q^{94} +3.29630 q^{95} +11.5840 q^{97} +2.35036 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - q^{2} + 7q^{4} + 8q^{5} - 6q^{7} - 3q^{8} + O(q^{10}) \) \( 8q - q^{2} + 7q^{4} + 8q^{5} - 6q^{7} - 3q^{8} - q^{10} - 14q^{11} - 7q^{13} - 15q^{14} + 9q^{16} - 17q^{17} + 17q^{19} + 7q^{20} + 2q^{22} + q^{23} + 8q^{25} - 3q^{26} - 29q^{28} - 10q^{29} + q^{31} - 2q^{32} - 16q^{34} - 6q^{35} - 11q^{37} + 30q^{38} - 3q^{40} - 15q^{41} - 5q^{43} - 7q^{44} - 12q^{46} - 12q^{47} + 4q^{49} - q^{50} - 14q^{52} + q^{53} - 14q^{55} - 3q^{56} - 37q^{58} - 26q^{59} + 13q^{61} - 22q^{62} - 15q^{64} - 7q^{65} - 25q^{67} - 23q^{68} - 15q^{70} - 28q^{71} - 17q^{73} + 5q^{74} + 8q^{76} - 7q^{79} + 9q^{80} + 5q^{82} - 44q^{83} - 17q^{85} + 13q^{86} - 66q^{88} - 8q^{89} + 27q^{91} - 15q^{92} - 27q^{94} + 17q^{95} + q^{97} + 34q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.16343 −0.822670 −0.411335 0.911484i \(-0.634937\pi\)
−0.411335 + 0.911484i \(0.634937\pi\)
\(3\) 0 0
\(4\) −0.646427 −0.323214
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 2.23155 0.843445 0.421723 0.906725i \(-0.361426\pi\)
0.421723 + 0.906725i \(0.361426\pi\)
\(8\) 3.07894 1.08857
\(9\) 0 0
\(10\) −1.16343 −0.367909
\(11\) −6.24237 −1.88214 −0.941072 0.338205i \(-0.890180\pi\)
−0.941072 + 0.338205i \(0.890180\pi\)
\(12\) 0 0
\(13\) −4.63493 −1.28550 −0.642749 0.766077i \(-0.722206\pi\)
−0.642749 + 0.766077i \(0.722206\pi\)
\(14\) −2.59625 −0.693877
\(15\) 0 0
\(16\) −2.28928 −0.572319
\(17\) 2.75732 0.668748 0.334374 0.942441i \(-0.391475\pi\)
0.334374 + 0.942441i \(0.391475\pi\)
\(18\) 0 0
\(19\) 3.29630 0.756222 0.378111 0.925760i \(-0.376574\pi\)
0.378111 + 0.925760i \(0.376574\pi\)
\(20\) −0.646427 −0.144546
\(21\) 0 0
\(22\) 7.26257 1.54838
\(23\) 6.86648 1.43176 0.715880 0.698224i \(-0.246026\pi\)
0.715880 + 0.698224i \(0.246026\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 5.39242 1.05754
\(27\) 0 0
\(28\) −1.44253 −0.272613
\(29\) −1.22407 −0.227304 −0.113652 0.993521i \(-0.536255\pi\)
−0.113652 + 0.993521i \(0.536255\pi\)
\(30\) 0 0
\(31\) −5.69744 −1.02329 −0.511645 0.859197i \(-0.670964\pi\)
−0.511645 + 0.859197i \(0.670964\pi\)
\(32\) −3.49446 −0.617738
\(33\) 0 0
\(34\) −3.20795 −0.550159
\(35\) 2.23155 0.377200
\(36\) 0 0
\(37\) 6.87730 1.13062 0.565310 0.824878i \(-0.308756\pi\)
0.565310 + 0.824878i \(0.308756\pi\)
\(38\) −3.83501 −0.622121
\(39\) 0 0
\(40\) 3.07894 0.486823
\(41\) −0.954991 −0.149144 −0.0745722 0.997216i \(-0.523759\pi\)
−0.0745722 + 0.997216i \(0.523759\pi\)
\(42\) 0 0
\(43\) −12.5627 −1.91579 −0.957894 0.287121i \(-0.907302\pi\)
−0.957894 + 0.287121i \(0.907302\pi\)
\(44\) 4.03524 0.608335
\(45\) 0 0
\(46\) −7.98867 −1.17787
\(47\) 3.00176 0.437852 0.218926 0.975741i \(-0.429745\pi\)
0.218926 + 0.975741i \(0.429745\pi\)
\(48\) 0 0
\(49\) −2.02020 −0.288600
\(50\) −1.16343 −0.164534
\(51\) 0 0
\(52\) 2.99615 0.415491
\(53\) 10.1149 1.38939 0.694695 0.719304i \(-0.255539\pi\)
0.694695 + 0.719304i \(0.255539\pi\)
\(54\) 0 0
\(55\) −6.24237 −0.841721
\(56\) 6.87079 0.918148
\(57\) 0 0
\(58\) 1.42412 0.186996
\(59\) −7.06511 −0.919799 −0.459900 0.887971i \(-0.652115\pi\)
−0.459900 + 0.887971i \(0.652115\pi\)
\(60\) 0 0
\(61\) −2.99922 −0.384010 −0.192005 0.981394i \(-0.561499\pi\)
−0.192005 + 0.981394i \(0.561499\pi\)
\(62\) 6.62858 0.841831
\(63\) 0 0
\(64\) 8.64411 1.08051
\(65\) −4.63493 −0.574892
\(66\) 0 0
\(67\) −10.0152 −1.22355 −0.611776 0.791031i \(-0.709545\pi\)
−0.611776 + 0.791031i \(0.709545\pi\)
\(68\) −1.78241 −0.216148
\(69\) 0 0
\(70\) −2.59625 −0.310311
\(71\) −9.04184 −1.07307 −0.536535 0.843878i \(-0.680267\pi\)
−0.536535 + 0.843878i \(0.680267\pi\)
\(72\) 0 0
\(73\) 11.2191 1.31310 0.656548 0.754284i \(-0.272016\pi\)
0.656548 + 0.754284i \(0.272016\pi\)
\(74\) −8.00126 −0.930128
\(75\) 0 0
\(76\) −2.13082 −0.244421
\(77\) −13.9301 −1.58749
\(78\) 0 0
\(79\) 0.814296 0.0916155 0.0458077 0.998950i \(-0.485414\pi\)
0.0458077 + 0.998950i \(0.485414\pi\)
\(80\) −2.28928 −0.255949
\(81\) 0 0
\(82\) 1.11107 0.122697
\(83\) −2.94088 −0.322804 −0.161402 0.986889i \(-0.551601\pi\)
−0.161402 + 0.986889i \(0.551601\pi\)
\(84\) 0 0
\(85\) 2.75732 0.299073
\(86\) 14.6158 1.57606
\(87\) 0 0
\(88\) −19.2199 −2.04884
\(89\) −1.00000 −0.106000
\(90\) 0 0
\(91\) −10.3431 −1.08425
\(92\) −4.43868 −0.462764
\(93\) 0 0
\(94\) −3.49234 −0.360208
\(95\) 3.29630 0.338193
\(96\) 0 0
\(97\) 11.5840 1.17617 0.588086 0.808798i \(-0.299882\pi\)
0.588086 + 0.808798i \(0.299882\pi\)
\(98\) 2.35036 0.237423
\(99\) 0 0
\(100\) −0.646427 −0.0646427
\(101\) −10.8997 −1.08456 −0.542279 0.840199i \(-0.682438\pi\)
−0.542279 + 0.840199i \(0.682438\pi\)
\(102\) 0 0
\(103\) 13.2170 1.30231 0.651153 0.758947i \(-0.274286\pi\)
0.651153 + 0.758947i \(0.274286\pi\)
\(104\) −14.2707 −1.39935
\(105\) 0 0
\(106\) −11.7680 −1.14301
\(107\) 2.56843 0.248299 0.124150 0.992264i \(-0.460380\pi\)
0.124150 + 0.992264i \(0.460380\pi\)
\(108\) 0 0
\(109\) −20.8218 −1.99437 −0.997185 0.0749844i \(-0.976109\pi\)
−0.997185 + 0.0749844i \(0.976109\pi\)
\(110\) 7.26257 0.692459
\(111\) 0 0
\(112\) −5.10863 −0.482720
\(113\) −10.2342 −0.962756 −0.481378 0.876513i \(-0.659864\pi\)
−0.481378 + 0.876513i \(0.659864\pi\)
\(114\) 0 0
\(115\) 6.86648 0.640302
\(116\) 0.791271 0.0734677
\(117\) 0 0
\(118\) 8.21977 0.756691
\(119\) 6.15308 0.564052
\(120\) 0 0
\(121\) 27.9672 2.54247
\(122\) 3.48938 0.315914
\(123\) 0 0
\(124\) 3.68298 0.330742
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −18.9903 −1.68512 −0.842559 0.538605i \(-0.818952\pi\)
−0.842559 + 0.538605i \(0.818952\pi\)
\(128\) −3.06792 −0.271169
\(129\) 0 0
\(130\) 5.39242 0.472947
\(131\) −5.28918 −0.462118 −0.231059 0.972940i \(-0.574219\pi\)
−0.231059 + 0.972940i \(0.574219\pi\)
\(132\) 0 0
\(133\) 7.35584 0.637832
\(134\) 11.6520 1.00658
\(135\) 0 0
\(136\) 8.48961 0.727978
\(137\) 1.36108 0.116285 0.0581425 0.998308i \(-0.481482\pi\)
0.0581425 + 0.998308i \(0.481482\pi\)
\(138\) 0 0
\(139\) −1.45928 −0.123775 −0.0618874 0.998083i \(-0.519712\pi\)
−0.0618874 + 0.998083i \(0.519712\pi\)
\(140\) −1.44253 −0.121916
\(141\) 0 0
\(142\) 10.5196 0.882782
\(143\) 28.9329 2.41949
\(144\) 0 0
\(145\) −1.22407 −0.101653
\(146\) −13.0526 −1.08024
\(147\) 0 0
\(148\) −4.44567 −0.365432
\(149\) −10.1991 −0.835547 −0.417773 0.908551i \(-0.637189\pi\)
−0.417773 + 0.908551i \(0.637189\pi\)
\(150\) 0 0
\(151\) 19.6293 1.59741 0.798703 0.601725i \(-0.205520\pi\)
0.798703 + 0.601725i \(0.205520\pi\)
\(152\) 10.1491 0.823200
\(153\) 0 0
\(154\) 16.2068 1.30598
\(155\) −5.69744 −0.457630
\(156\) 0 0
\(157\) −2.79087 −0.222735 −0.111368 0.993779i \(-0.535523\pi\)
−0.111368 + 0.993779i \(0.535523\pi\)
\(158\) −0.947378 −0.0753693
\(159\) 0 0
\(160\) −3.49446 −0.276261
\(161\) 15.3229 1.20761
\(162\) 0 0
\(163\) 2.22536 0.174303 0.0871517 0.996195i \(-0.472224\pi\)
0.0871517 + 0.996195i \(0.472224\pi\)
\(164\) 0.617332 0.0482055
\(165\) 0 0
\(166\) 3.42151 0.265561
\(167\) −6.89641 −0.533660 −0.266830 0.963744i \(-0.585976\pi\)
−0.266830 + 0.963744i \(0.585976\pi\)
\(168\) 0 0
\(169\) 8.48258 0.652506
\(170\) −3.20795 −0.246039
\(171\) 0 0
\(172\) 8.12085 0.619209
\(173\) −6.88629 −0.523555 −0.261777 0.965128i \(-0.584309\pi\)
−0.261777 + 0.965128i \(0.584309\pi\)
\(174\) 0 0
\(175\) 2.23155 0.168689
\(176\) 14.2905 1.07719
\(177\) 0 0
\(178\) 1.16343 0.0872029
\(179\) 18.4452 1.37866 0.689331 0.724446i \(-0.257904\pi\)
0.689331 + 0.724446i \(0.257904\pi\)
\(180\) 0 0
\(181\) 6.69862 0.497905 0.248952 0.968516i \(-0.419914\pi\)
0.248952 + 0.968516i \(0.419914\pi\)
\(182\) 12.0334 0.891978
\(183\) 0 0
\(184\) 21.1414 1.55857
\(185\) 6.87730 0.505629
\(186\) 0 0
\(187\) −17.2122 −1.25868
\(188\) −1.94042 −0.141520
\(189\) 0 0
\(190\) −3.83501 −0.278221
\(191\) 5.40267 0.390923 0.195462 0.980711i \(-0.437379\pi\)
0.195462 + 0.980711i \(0.437379\pi\)
\(192\) 0 0
\(193\) −1.28529 −0.0925172 −0.0462586 0.998929i \(-0.514730\pi\)
−0.0462586 + 0.998929i \(0.514730\pi\)
\(194\) −13.4771 −0.967602
\(195\) 0 0
\(196\) 1.30591 0.0932794
\(197\) −11.7541 −0.837443 −0.418722 0.908115i \(-0.637522\pi\)
−0.418722 + 0.908115i \(0.637522\pi\)
\(198\) 0 0
\(199\) −14.5646 −1.03246 −0.516230 0.856450i \(-0.672665\pi\)
−0.516230 + 0.856450i \(0.672665\pi\)
\(200\) 3.07894 0.217714
\(201\) 0 0
\(202\) 12.6810 0.892233
\(203\) −2.73157 −0.191718
\(204\) 0 0
\(205\) −0.954991 −0.0666994
\(206\) −15.3770 −1.07137
\(207\) 0 0
\(208\) 10.6106 0.735715
\(209\) −20.5767 −1.42332
\(210\) 0 0
\(211\) 2.66223 0.183276 0.0916379 0.995792i \(-0.470790\pi\)
0.0916379 + 0.995792i \(0.470790\pi\)
\(212\) −6.53856 −0.449070
\(213\) 0 0
\(214\) −2.98819 −0.204268
\(215\) −12.5627 −0.856767
\(216\) 0 0
\(217\) −12.7141 −0.863090
\(218\) 24.2248 1.64071
\(219\) 0 0
\(220\) 4.03524 0.272056
\(221\) −12.7800 −0.859674
\(222\) 0 0
\(223\) 3.03312 0.203113 0.101556 0.994830i \(-0.467618\pi\)
0.101556 + 0.994830i \(0.467618\pi\)
\(224\) −7.79804 −0.521029
\(225\) 0 0
\(226\) 11.9068 0.792031
\(227\) −14.8971 −0.988757 −0.494378 0.869247i \(-0.664604\pi\)
−0.494378 + 0.869247i \(0.664604\pi\)
\(228\) 0 0
\(229\) 11.8049 0.780090 0.390045 0.920796i \(-0.372459\pi\)
0.390045 + 0.920796i \(0.372459\pi\)
\(230\) −7.98867 −0.526758
\(231\) 0 0
\(232\) −3.76883 −0.247436
\(233\) −15.3878 −1.00809 −0.504043 0.863679i \(-0.668155\pi\)
−0.504043 + 0.863679i \(0.668155\pi\)
\(234\) 0 0
\(235\) 3.00176 0.195813
\(236\) 4.56708 0.297292
\(237\) 0 0
\(238\) −7.15869 −0.464029
\(239\) −18.9114 −1.22328 −0.611638 0.791138i \(-0.709489\pi\)
−0.611638 + 0.791138i \(0.709489\pi\)
\(240\) 0 0
\(241\) −18.0672 −1.16381 −0.581905 0.813257i \(-0.697693\pi\)
−0.581905 + 0.813257i \(0.697693\pi\)
\(242\) −32.5379 −2.09161
\(243\) 0 0
\(244\) 1.93877 0.124117
\(245\) −2.02020 −0.129066
\(246\) 0 0
\(247\) −15.2781 −0.972122
\(248\) −17.5421 −1.11392
\(249\) 0 0
\(250\) −1.16343 −0.0735819
\(251\) −1.89277 −0.119471 −0.0597353 0.998214i \(-0.519026\pi\)
−0.0597353 + 0.998214i \(0.519026\pi\)
\(252\) 0 0
\(253\) −42.8631 −2.69478
\(254\) 22.0939 1.38630
\(255\) 0 0
\(256\) −13.7189 −0.857432
\(257\) 6.30045 0.393011 0.196506 0.980503i \(-0.437041\pi\)
0.196506 + 0.980503i \(0.437041\pi\)
\(258\) 0 0
\(259\) 15.3470 0.953617
\(260\) 2.99615 0.185813
\(261\) 0 0
\(262\) 6.15360 0.380171
\(263\) −16.7289 −1.03155 −0.515774 0.856725i \(-0.672496\pi\)
−0.515774 + 0.856725i \(0.672496\pi\)
\(264\) 0 0
\(265\) 10.1149 0.621354
\(266\) −8.55801 −0.524725
\(267\) 0 0
\(268\) 6.47410 0.395469
\(269\) −16.5062 −1.00640 −0.503200 0.864170i \(-0.667844\pi\)
−0.503200 + 0.864170i \(0.667844\pi\)
\(270\) 0 0
\(271\) 4.84164 0.294108 0.147054 0.989128i \(-0.453021\pi\)
0.147054 + 0.989128i \(0.453021\pi\)
\(272\) −6.31226 −0.382737
\(273\) 0 0
\(274\) −1.58352 −0.0956642
\(275\) −6.24237 −0.376429
\(276\) 0 0
\(277\) −24.8548 −1.49338 −0.746690 0.665172i \(-0.768358\pi\)
−0.746690 + 0.665172i \(0.768358\pi\)
\(278\) 1.69778 0.101826
\(279\) 0 0
\(280\) 6.87079 0.410608
\(281\) −4.50358 −0.268661 −0.134330 0.990937i \(-0.542888\pi\)
−0.134330 + 0.990937i \(0.542888\pi\)
\(282\) 0 0
\(283\) 22.3918 1.33106 0.665528 0.746373i \(-0.268206\pi\)
0.665528 + 0.746373i \(0.268206\pi\)
\(284\) 5.84489 0.346831
\(285\) 0 0
\(286\) −33.6615 −1.99045
\(287\) −2.13111 −0.125795
\(288\) 0 0
\(289\) −9.39720 −0.552776
\(290\) 1.42412 0.0836272
\(291\) 0 0
\(292\) −7.25233 −0.424410
\(293\) 11.3874 0.665260 0.332630 0.943057i \(-0.392064\pi\)
0.332630 + 0.943057i \(0.392064\pi\)
\(294\) 0 0
\(295\) −7.06511 −0.411347
\(296\) 21.1748 1.23076
\(297\) 0 0
\(298\) 11.8660 0.687379
\(299\) −31.8256 −1.84052
\(300\) 0 0
\(301\) −28.0342 −1.61586
\(302\) −22.8373 −1.31414
\(303\) 0 0
\(304\) −7.54613 −0.432801
\(305\) −2.99922 −0.171735
\(306\) 0 0
\(307\) −25.3517 −1.44690 −0.723450 0.690377i \(-0.757445\pi\)
−0.723450 + 0.690377i \(0.757445\pi\)
\(308\) 9.00482 0.513097
\(309\) 0 0
\(310\) 6.62858 0.376478
\(311\) −10.7151 −0.607600 −0.303800 0.952736i \(-0.598255\pi\)
−0.303800 + 0.952736i \(0.598255\pi\)
\(312\) 0 0
\(313\) −25.6198 −1.44811 −0.724057 0.689740i \(-0.757725\pi\)
−0.724057 + 0.689740i \(0.757725\pi\)
\(314\) 3.24698 0.183238
\(315\) 0 0
\(316\) −0.526383 −0.0296114
\(317\) −34.3428 −1.92889 −0.964443 0.264292i \(-0.914862\pi\)
−0.964443 + 0.264292i \(0.914862\pi\)
\(318\) 0 0
\(319\) 7.64109 0.427819
\(320\) 8.64411 0.483221
\(321\) 0 0
\(322\) −17.8271 −0.993466
\(323\) 9.08893 0.505722
\(324\) 0 0
\(325\) −4.63493 −0.257100
\(326\) −2.58905 −0.143394
\(327\) 0 0
\(328\) −2.94036 −0.162354
\(329\) 6.69857 0.369304
\(330\) 0 0
\(331\) −20.2047 −1.11055 −0.555276 0.831666i \(-0.687387\pi\)
−0.555276 + 0.831666i \(0.687387\pi\)
\(332\) 1.90107 0.104335
\(333\) 0 0
\(334\) 8.02350 0.439026
\(335\) −10.0152 −0.547189
\(336\) 0 0
\(337\) −13.4799 −0.734299 −0.367149 0.930162i \(-0.619666\pi\)
−0.367149 + 0.930162i \(0.619666\pi\)
\(338\) −9.86890 −0.536797
\(339\) 0 0
\(340\) −1.78241 −0.0966645
\(341\) 35.5655 1.92598
\(342\) 0 0
\(343\) −20.1290 −1.08686
\(344\) −38.6797 −2.08547
\(345\) 0 0
\(346\) 8.01172 0.430713
\(347\) −11.8450 −0.635875 −0.317938 0.948112i \(-0.602990\pi\)
−0.317938 + 0.948112i \(0.602990\pi\)
\(348\) 0 0
\(349\) 5.01356 0.268370 0.134185 0.990956i \(-0.457158\pi\)
0.134185 + 0.990956i \(0.457158\pi\)
\(350\) −2.59625 −0.138775
\(351\) 0 0
\(352\) 21.8137 1.16267
\(353\) 4.72417 0.251442 0.125721 0.992066i \(-0.459876\pi\)
0.125721 + 0.992066i \(0.459876\pi\)
\(354\) 0 0
\(355\) −9.04184 −0.479891
\(356\) 0.646427 0.0342606
\(357\) 0 0
\(358\) −21.4598 −1.13418
\(359\) 21.2719 1.12269 0.561345 0.827582i \(-0.310284\pi\)
0.561345 + 0.827582i \(0.310284\pi\)
\(360\) 0 0
\(361\) −8.13443 −0.428128
\(362\) −7.79339 −0.409611
\(363\) 0 0
\(364\) 6.68604 0.350444
\(365\) 11.2191 0.587234
\(366\) 0 0
\(367\) 17.4395 0.910335 0.455167 0.890406i \(-0.349579\pi\)
0.455167 + 0.890406i \(0.349579\pi\)
\(368\) −15.7193 −0.819424
\(369\) 0 0
\(370\) −8.00126 −0.415966
\(371\) 22.5719 1.17187
\(372\) 0 0
\(373\) 22.9561 1.18862 0.594312 0.804235i \(-0.297424\pi\)
0.594312 + 0.804235i \(0.297424\pi\)
\(374\) 20.0252 1.03548
\(375\) 0 0
\(376\) 9.24223 0.476632
\(377\) 5.67347 0.292199
\(378\) 0 0
\(379\) 7.92479 0.407069 0.203535 0.979068i \(-0.434757\pi\)
0.203535 + 0.979068i \(0.434757\pi\)
\(380\) −2.13082 −0.109309
\(381\) 0 0
\(382\) −6.28563 −0.321601
\(383\) −1.13829 −0.0581641 −0.0290821 0.999577i \(-0.509258\pi\)
−0.0290821 + 0.999577i \(0.509258\pi\)
\(384\) 0 0
\(385\) −13.9301 −0.709945
\(386\) 1.49535 0.0761111
\(387\) 0 0
\(388\) −7.48818 −0.380155
\(389\) 9.12407 0.462609 0.231304 0.972881i \(-0.425701\pi\)
0.231304 + 0.972881i \(0.425701\pi\)
\(390\) 0 0
\(391\) 18.9331 0.957486
\(392\) −6.22007 −0.314161
\(393\) 0 0
\(394\) 13.6751 0.688940
\(395\) 0.814296 0.0409717
\(396\) 0 0
\(397\) −36.7768 −1.84577 −0.922887 0.385072i \(-0.874177\pi\)
−0.922887 + 0.385072i \(0.874177\pi\)
\(398\) 16.9450 0.849374
\(399\) 0 0
\(400\) −2.28928 −0.114464
\(401\) 16.6783 0.832875 0.416437 0.909164i \(-0.363279\pi\)
0.416437 + 0.909164i \(0.363279\pi\)
\(402\) 0 0
\(403\) 26.4072 1.31544
\(404\) 7.04584 0.350544
\(405\) 0 0
\(406\) 3.17799 0.157721
\(407\) −42.9306 −2.12799
\(408\) 0 0
\(409\) −4.71669 −0.233225 −0.116613 0.993177i \(-0.537204\pi\)
−0.116613 + 0.993177i \(0.537204\pi\)
\(410\) 1.11107 0.0548716
\(411\) 0 0
\(412\) −8.54380 −0.420923
\(413\) −15.7661 −0.775800
\(414\) 0 0
\(415\) −2.94088 −0.144362
\(416\) 16.1966 0.794102
\(417\) 0 0
\(418\) 23.9396 1.17092
\(419\) 0.0448056 0.00218890 0.00109445 0.999999i \(-0.499652\pi\)
0.00109445 + 0.999999i \(0.499652\pi\)
\(420\) 0 0
\(421\) 15.1761 0.739639 0.369820 0.929104i \(-0.379420\pi\)
0.369820 + 0.929104i \(0.379420\pi\)
\(422\) −3.09733 −0.150776
\(423\) 0 0
\(424\) 31.1432 1.51245
\(425\) 2.75732 0.133750
\(426\) 0 0
\(427\) −6.69289 −0.323892
\(428\) −1.66030 −0.0802537
\(429\) 0 0
\(430\) 14.6158 0.704836
\(431\) 25.6222 1.23418 0.617089 0.786893i \(-0.288312\pi\)
0.617089 + 0.786893i \(0.288312\pi\)
\(432\) 0 0
\(433\) −0.162207 −0.00779517 −0.00389759 0.999992i \(-0.501241\pi\)
−0.00389759 + 0.999992i \(0.501241\pi\)
\(434\) 14.7920 0.710038
\(435\) 0 0
\(436\) 13.4598 0.644607
\(437\) 22.6339 1.08273
\(438\) 0 0
\(439\) −23.2447 −1.10941 −0.554704 0.832048i \(-0.687168\pi\)
−0.554704 + 0.832048i \(0.687168\pi\)
\(440\) −19.2199 −0.916271
\(441\) 0 0
\(442\) 14.8686 0.707228
\(443\) 40.0330 1.90202 0.951012 0.309153i \(-0.100045\pi\)
0.951012 + 0.309153i \(0.100045\pi\)
\(444\) 0 0
\(445\) −1.00000 −0.0474045
\(446\) −3.52883 −0.167095
\(447\) 0 0
\(448\) 19.2897 0.911355
\(449\) −4.85303 −0.229029 −0.114514 0.993422i \(-0.536531\pi\)
−0.114514 + 0.993422i \(0.536531\pi\)
\(450\) 0 0
\(451\) 5.96140 0.280711
\(452\) 6.61569 0.311176
\(453\) 0 0
\(454\) 17.3318 0.813421
\(455\) −10.3431 −0.484890
\(456\) 0 0
\(457\) 19.5616 0.915054 0.457527 0.889196i \(-0.348735\pi\)
0.457527 + 0.889196i \(0.348735\pi\)
\(458\) −13.7342 −0.641757
\(459\) 0 0
\(460\) −4.43868 −0.206954
\(461\) 16.8856 0.786440 0.393220 0.919444i \(-0.371361\pi\)
0.393220 + 0.919444i \(0.371361\pi\)
\(462\) 0 0
\(463\) −23.2862 −1.08220 −0.541102 0.840957i \(-0.681993\pi\)
−0.541102 + 0.840957i \(0.681993\pi\)
\(464\) 2.80223 0.130090
\(465\) 0 0
\(466\) 17.9026 0.829322
\(467\) −38.4332 −1.77848 −0.889239 0.457443i \(-0.848765\pi\)
−0.889239 + 0.457443i \(0.848765\pi\)
\(468\) 0 0
\(469\) −22.3494 −1.03200
\(470\) −3.49234 −0.161090
\(471\) 0 0
\(472\) −21.7530 −1.00126
\(473\) 78.4208 3.60579
\(474\) 0 0
\(475\) 3.29630 0.151244
\(476\) −3.97752 −0.182309
\(477\) 0 0
\(478\) 22.0021 1.00635
\(479\) −34.0667 −1.55655 −0.778273 0.627926i \(-0.783904\pi\)
−0.778273 + 0.627926i \(0.783904\pi\)
\(480\) 0 0
\(481\) −31.8758 −1.45341
\(482\) 21.0200 0.957432
\(483\) 0 0
\(484\) −18.0787 −0.821761
\(485\) 11.5840 0.526000
\(486\) 0 0
\(487\) −32.0563 −1.45261 −0.726304 0.687374i \(-0.758764\pi\)
−0.726304 + 0.687374i \(0.758764\pi\)
\(488\) −9.23439 −0.418021
\(489\) 0 0
\(490\) 2.35036 0.106179
\(491\) −35.1106 −1.58452 −0.792260 0.610183i \(-0.791096\pi\)
−0.792260 + 0.610183i \(0.791096\pi\)
\(492\) 0 0
\(493\) −3.37515 −0.152009
\(494\) 17.7750 0.799736
\(495\) 0 0
\(496\) 13.0430 0.585649
\(497\) −20.1773 −0.905075
\(498\) 0 0
\(499\) −17.9968 −0.805648 −0.402824 0.915277i \(-0.631971\pi\)
−0.402824 + 0.915277i \(0.631971\pi\)
\(500\) −0.646427 −0.0289091
\(501\) 0 0
\(502\) 2.20211 0.0982849
\(503\) −5.23480 −0.233408 −0.116704 0.993167i \(-0.537233\pi\)
−0.116704 + 0.993167i \(0.537233\pi\)
\(504\) 0 0
\(505\) −10.8997 −0.485029
\(506\) 49.8682 2.21691
\(507\) 0 0
\(508\) 12.2759 0.544653
\(509\) 0.165304 0.00732699 0.00366350 0.999993i \(-0.498834\pi\)
0.00366350 + 0.999993i \(0.498834\pi\)
\(510\) 0 0
\(511\) 25.0359 1.10752
\(512\) 22.0969 0.976552
\(513\) 0 0
\(514\) −7.33014 −0.323319
\(515\) 13.2170 0.582409
\(516\) 0 0
\(517\) −18.7381 −0.824101
\(518\) −17.8552 −0.784512
\(519\) 0 0
\(520\) −14.2707 −0.625810
\(521\) −4.79905 −0.210250 −0.105125 0.994459i \(-0.533524\pi\)
−0.105125 + 0.994459i \(0.533524\pi\)
\(522\) 0 0
\(523\) 20.0143 0.875164 0.437582 0.899179i \(-0.355835\pi\)
0.437582 + 0.899179i \(0.355835\pi\)
\(524\) 3.41907 0.149363
\(525\) 0 0
\(526\) 19.4629 0.848624
\(527\) −15.7097 −0.684323
\(528\) 0 0
\(529\) 24.1485 1.04993
\(530\) −11.7680 −0.511170
\(531\) 0 0
\(532\) −4.75501 −0.206156
\(533\) 4.42631 0.191725
\(534\) 0 0
\(535\) 2.56843 0.111043
\(536\) −30.8362 −1.33192
\(537\) 0 0
\(538\) 19.2038 0.827936
\(539\) 12.6108 0.543187
\(540\) 0 0
\(541\) 34.1351 1.46758 0.733792 0.679374i \(-0.237749\pi\)
0.733792 + 0.679374i \(0.237749\pi\)
\(542\) −5.63291 −0.241954
\(543\) 0 0
\(544\) −9.63533 −0.413111
\(545\) −20.8218 −0.891909
\(546\) 0 0
\(547\) 7.41855 0.317194 0.158597 0.987343i \(-0.449303\pi\)
0.158597 + 0.987343i \(0.449303\pi\)
\(548\) −0.879840 −0.0375849
\(549\) 0 0
\(550\) 7.26257 0.309677
\(551\) −4.03489 −0.171892
\(552\) 0 0
\(553\) 1.81714 0.0772726
\(554\) 28.9168 1.22856
\(555\) 0 0
\(556\) 0.943320 0.0400057
\(557\) 0.699946 0.0296577 0.0148288 0.999890i \(-0.495280\pi\)
0.0148288 + 0.999890i \(0.495280\pi\)
\(558\) 0 0
\(559\) 58.2271 2.46274
\(560\) −5.10863 −0.215879
\(561\) 0 0
\(562\) 5.23960 0.221019
\(563\) −37.4498 −1.57832 −0.789161 0.614186i \(-0.789484\pi\)
−0.789161 + 0.614186i \(0.789484\pi\)
\(564\) 0 0
\(565\) −10.2342 −0.430558
\(566\) −26.0514 −1.09502
\(567\) 0 0
\(568\) −27.8393 −1.16811
\(569\) 16.5455 0.693625 0.346813 0.937934i \(-0.387264\pi\)
0.346813 + 0.937934i \(0.387264\pi\)
\(570\) 0 0
\(571\) −26.1728 −1.09530 −0.547650 0.836708i \(-0.684477\pi\)
−0.547650 + 0.836708i \(0.684477\pi\)
\(572\) −18.7030 −0.782013
\(573\) 0 0
\(574\) 2.47940 0.103488
\(575\) 6.86648 0.286352
\(576\) 0 0
\(577\) 38.9896 1.62316 0.811580 0.584241i \(-0.198608\pi\)
0.811580 + 0.584241i \(0.198608\pi\)
\(578\) 10.9330 0.454753
\(579\) 0 0
\(580\) 0.791271 0.0328558
\(581\) −6.56271 −0.272267
\(582\) 0 0
\(583\) −63.1410 −2.61503
\(584\) 34.5429 1.42939
\(585\) 0 0
\(586\) −13.2485 −0.547289
\(587\) 26.5530 1.09596 0.547979 0.836492i \(-0.315397\pi\)
0.547979 + 0.836492i \(0.315397\pi\)
\(588\) 0 0
\(589\) −18.7805 −0.773835
\(590\) 8.21977 0.338403
\(591\) 0 0
\(592\) −15.7440 −0.647076
\(593\) 17.3600 0.712891 0.356445 0.934316i \(-0.383989\pi\)
0.356445 + 0.934316i \(0.383989\pi\)
\(594\) 0 0
\(595\) 6.15308 0.252252
\(596\) 6.59301 0.270060
\(597\) 0 0
\(598\) 37.0269 1.51414
\(599\) −4.39556 −0.179598 −0.0897989 0.995960i \(-0.528622\pi\)
−0.0897989 + 0.995960i \(0.528622\pi\)
\(600\) 0 0
\(601\) −29.7115 −1.21196 −0.605978 0.795481i \(-0.707218\pi\)
−0.605978 + 0.795481i \(0.707218\pi\)
\(602\) 32.6158 1.32932
\(603\) 0 0
\(604\) −12.6889 −0.516303
\(605\) 27.9672 1.13703
\(606\) 0 0
\(607\) −40.6274 −1.64902 −0.824508 0.565851i \(-0.808548\pi\)
−0.824508 + 0.565851i \(0.808548\pi\)
\(608\) −11.5188 −0.467147
\(609\) 0 0
\(610\) 3.48938 0.141281
\(611\) −13.9130 −0.562858
\(612\) 0 0
\(613\) −13.8543 −0.559571 −0.279785 0.960063i \(-0.590263\pi\)
−0.279785 + 0.960063i \(0.590263\pi\)
\(614\) 29.4950 1.19032
\(615\) 0 0
\(616\) −42.8900 −1.72809
\(617\) 30.0491 1.20973 0.604866 0.796327i \(-0.293227\pi\)
0.604866 + 0.796327i \(0.293227\pi\)
\(618\) 0 0
\(619\) −16.3623 −0.657654 −0.328827 0.944390i \(-0.606653\pi\)
−0.328827 + 0.944390i \(0.606653\pi\)
\(620\) 3.68298 0.147912
\(621\) 0 0
\(622\) 12.4663 0.499854
\(623\) −2.23155 −0.0894050
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 29.8068 1.19132
\(627\) 0 0
\(628\) 1.80409 0.0719911
\(629\) 18.9629 0.756100
\(630\) 0 0
\(631\) 27.8270 1.10778 0.553888 0.832591i \(-0.313144\pi\)
0.553888 + 0.832591i \(0.313144\pi\)
\(632\) 2.50717 0.0997297
\(633\) 0 0
\(634\) 39.9555 1.58684
\(635\) −18.9903 −0.753607
\(636\) 0 0
\(637\) 9.36348 0.370995
\(638\) −8.88988 −0.351954
\(639\) 0 0
\(640\) −3.06792 −0.121270
\(641\) 22.6216 0.893498 0.446749 0.894659i \(-0.352582\pi\)
0.446749 + 0.894659i \(0.352582\pi\)
\(642\) 0 0
\(643\) −9.16994 −0.361627 −0.180814 0.983517i \(-0.557873\pi\)
−0.180814 + 0.983517i \(0.557873\pi\)
\(644\) −9.90512 −0.390316
\(645\) 0 0
\(646\) −10.5744 −0.416042
\(647\) −10.6302 −0.417918 −0.208959 0.977924i \(-0.567007\pi\)
−0.208959 + 0.977924i \(0.567007\pi\)
\(648\) 0 0
\(649\) 44.1030 1.73120
\(650\) 5.39242 0.211508
\(651\) 0 0
\(652\) −1.43853 −0.0563372
\(653\) 6.46716 0.253079 0.126540 0.991962i \(-0.459613\pi\)
0.126540 + 0.991962i \(0.459613\pi\)
\(654\) 0 0
\(655\) −5.28918 −0.206665
\(656\) 2.18624 0.0853583
\(657\) 0 0
\(658\) −7.79333 −0.303816
\(659\) 29.7579 1.15920 0.579601 0.814900i \(-0.303208\pi\)
0.579601 + 0.814900i \(0.303208\pi\)
\(660\) 0 0
\(661\) 34.3396 1.33566 0.667829 0.744315i \(-0.267224\pi\)
0.667829 + 0.744315i \(0.267224\pi\)
\(662\) 23.5068 0.913618
\(663\) 0 0
\(664\) −9.05478 −0.351394
\(665\) 7.35584 0.285247
\(666\) 0 0
\(667\) −8.40504 −0.325444
\(668\) 4.45803 0.172486
\(669\) 0 0
\(670\) 11.6520 0.450156
\(671\) 18.7222 0.722763
\(672\) 0 0
\(673\) 21.0833 0.812700 0.406350 0.913717i \(-0.366801\pi\)
0.406350 + 0.913717i \(0.366801\pi\)
\(674\) 15.6830 0.604086
\(675\) 0 0
\(676\) −5.48337 −0.210899
\(677\) −12.0279 −0.462270 −0.231135 0.972922i \(-0.574244\pi\)
−0.231135 + 0.972922i \(0.574244\pi\)
\(678\) 0 0
\(679\) 25.8501 0.992037
\(680\) 8.48961 0.325562
\(681\) 0 0
\(682\) −41.3781 −1.58445
\(683\) −13.8096 −0.528409 −0.264204 0.964467i \(-0.585109\pi\)
−0.264204 + 0.964467i \(0.585109\pi\)
\(684\) 0 0
\(685\) 1.36108 0.0520042
\(686\) 23.4187 0.894130
\(687\) 0 0
\(688\) 28.7594 1.09644
\(689\) −46.8819 −1.78606
\(690\) 0 0
\(691\) 23.0764 0.877869 0.438935 0.898519i \(-0.355356\pi\)
0.438935 + 0.898519i \(0.355356\pi\)
\(692\) 4.45148 0.169220
\(693\) 0 0
\(694\) 13.7809 0.523116
\(695\) −1.45928 −0.0553538
\(696\) 0 0
\(697\) −2.63321 −0.0997400
\(698\) −5.83293 −0.220780
\(699\) 0 0
\(700\) −1.44253 −0.0545226
\(701\) −2.34166 −0.0884431 −0.0442216 0.999022i \(-0.514081\pi\)
−0.0442216 + 0.999022i \(0.514081\pi\)
\(702\) 0 0
\(703\) 22.6696 0.855000
\(704\) −53.9597 −2.03368
\(705\) 0 0
\(706\) −5.49624 −0.206854
\(707\) −24.3231 −0.914765
\(708\) 0 0
\(709\) −14.8131 −0.556317 −0.278159 0.960535i \(-0.589724\pi\)
−0.278159 + 0.960535i \(0.589724\pi\)
\(710\) 10.5196 0.394792
\(711\) 0 0
\(712\) −3.07894 −0.115388
\(713\) −39.1214 −1.46511
\(714\) 0 0
\(715\) 28.9329 1.08203
\(716\) −11.9235 −0.445603
\(717\) 0 0
\(718\) −24.7484 −0.923603
\(719\) 4.73254 0.176494 0.0882469 0.996099i \(-0.471874\pi\)
0.0882469 + 0.996099i \(0.471874\pi\)
\(720\) 0 0
\(721\) 29.4943 1.09842
\(722\) 9.46386 0.352208
\(723\) 0 0
\(724\) −4.33017 −0.160930
\(725\) −1.22407 −0.0454608
\(726\) 0 0
\(727\) 0.313014 0.0116090 0.00580452 0.999983i \(-0.498152\pi\)
0.00580452 + 0.999983i \(0.498152\pi\)
\(728\) −31.8456 −1.18028
\(729\) 0 0
\(730\) −13.0526 −0.483100
\(731\) −34.6393 −1.28118
\(732\) 0 0
\(733\) 17.4239 0.643566 0.321783 0.946814i \(-0.395718\pi\)
0.321783 + 0.946814i \(0.395718\pi\)
\(734\) −20.2897 −0.748905
\(735\) 0 0
\(736\) −23.9946 −0.884453
\(737\) 62.5186 2.30290
\(738\) 0 0
\(739\) 2.15336 0.0792126 0.0396063 0.999215i \(-0.487390\pi\)
0.0396063 + 0.999215i \(0.487390\pi\)
\(740\) −4.44567 −0.163426
\(741\) 0 0
\(742\) −26.2609 −0.964067
\(743\) 37.1193 1.36177 0.680887 0.732388i \(-0.261594\pi\)
0.680887 + 0.732388i \(0.261594\pi\)
\(744\) 0 0
\(745\) −10.1991 −0.373668
\(746\) −26.7079 −0.977846
\(747\) 0 0
\(748\) 11.1264 0.406823
\(749\) 5.73157 0.209427
\(750\) 0 0
\(751\) −3.42199 −0.124870 −0.0624351 0.998049i \(-0.519887\pi\)
−0.0624351 + 0.998049i \(0.519887\pi\)
\(752\) −6.87186 −0.250591
\(753\) 0 0
\(754\) −6.60070 −0.240383
\(755\) 19.6293 0.714382
\(756\) 0 0
\(757\) −42.7111 −1.55236 −0.776181 0.630510i \(-0.782846\pi\)
−0.776181 + 0.630510i \(0.782846\pi\)
\(758\) −9.21995 −0.334884
\(759\) 0 0
\(760\) 10.1491 0.368146
\(761\) −49.0963 −1.77974 −0.889871 0.456213i \(-0.849206\pi\)
−0.889871 + 0.456213i \(0.849206\pi\)
\(762\) 0 0
\(763\) −46.4649 −1.68214
\(764\) −3.49243 −0.126352
\(765\) 0 0
\(766\) 1.32433 0.0478499
\(767\) 32.7463 1.18240
\(768\) 0 0
\(769\) 33.6377 1.21301 0.606503 0.795081i \(-0.292572\pi\)
0.606503 + 0.795081i \(0.292572\pi\)
\(770\) 16.2068 0.584051
\(771\) 0 0
\(772\) 0.830846 0.0299028
\(773\) −42.5005 −1.52864 −0.764319 0.644838i \(-0.776925\pi\)
−0.764319 + 0.644838i \(0.776925\pi\)
\(774\) 0 0
\(775\) −5.69744 −0.204658
\(776\) 35.6663 1.28034
\(777\) 0 0
\(778\) −10.6152 −0.380575
\(779\) −3.14793 −0.112786
\(780\) 0 0
\(781\) 56.4425 2.01967
\(782\) −22.0273 −0.787695
\(783\) 0 0
\(784\) 4.62480 0.165171
\(785\) −2.79087 −0.0996103
\(786\) 0 0
\(787\) −16.9945 −0.605790 −0.302895 0.953024i \(-0.597953\pi\)
−0.302895 + 0.953024i \(0.597953\pi\)
\(788\) 7.59816 0.270673
\(789\) 0 0
\(790\) −0.947378 −0.0337062
\(791\) −22.8382 −0.812032
\(792\) 0 0
\(793\) 13.9012 0.493644
\(794\) 42.7873 1.51846
\(795\) 0 0
\(796\) 9.41498 0.333705
\(797\) 18.2917 0.647926 0.323963 0.946070i \(-0.394985\pi\)
0.323963 + 0.946070i \(0.394985\pi\)
\(798\) 0 0
\(799\) 8.27681 0.292812
\(800\) −3.49446 −0.123548
\(801\) 0 0
\(802\) −19.4041 −0.685181
\(803\) −70.0337 −2.47144
\(804\) 0 0
\(805\) 15.3229 0.540060
\(806\) −30.7230 −1.08217
\(807\) 0 0
\(808\) −33.5594 −1.18062
\(809\) −10.0297 −0.352626 −0.176313 0.984334i \(-0.556417\pi\)
−0.176313 + 0.984334i \(0.556417\pi\)
\(810\) 0 0
\(811\) −4.44600 −0.156120 −0.0780601 0.996949i \(-0.524873\pi\)
−0.0780601 + 0.996949i \(0.524873\pi\)
\(812\) 1.76576 0.0619660
\(813\) 0 0
\(814\) 49.9468 1.75064
\(815\) 2.22536 0.0779508
\(816\) 0 0
\(817\) −41.4103 −1.44876
\(818\) 5.48754 0.191867
\(819\) 0 0
\(820\) 0.617332 0.0215582
\(821\) 37.9696 1.32515 0.662575 0.748996i \(-0.269464\pi\)
0.662575 + 0.748996i \(0.269464\pi\)
\(822\) 0 0
\(823\) −48.4143 −1.68761 −0.843807 0.536646i \(-0.819691\pi\)
−0.843807 + 0.536646i \(0.819691\pi\)
\(824\) 40.6942 1.41765
\(825\) 0 0
\(826\) 18.3428 0.638228
\(827\) −10.3587 −0.360206 −0.180103 0.983648i \(-0.557643\pi\)
−0.180103 + 0.983648i \(0.557643\pi\)
\(828\) 0 0
\(829\) 6.47084 0.224742 0.112371 0.993666i \(-0.464156\pi\)
0.112371 + 0.993666i \(0.464156\pi\)
\(830\) 3.42151 0.118762
\(831\) 0 0
\(832\) −40.0649 −1.38900
\(833\) −5.57033 −0.193001
\(834\) 0 0
\(835\) −6.89641 −0.238660
\(836\) 13.3013 0.460036
\(837\) 0 0
\(838\) −0.0521283 −0.00180074
\(839\) 0.873216 0.0301468 0.0150734 0.999886i \(-0.495202\pi\)
0.0150734 + 0.999886i \(0.495202\pi\)
\(840\) 0 0
\(841\) −27.5017 −0.948333
\(842\) −17.6564 −0.608479
\(843\) 0 0
\(844\) −1.72094 −0.0592372
\(845\) 8.48258 0.291809
\(846\) 0 0
\(847\) 62.4100 2.14443
\(848\) −23.1558 −0.795175
\(849\) 0 0
\(850\) −3.20795 −0.110032
\(851\) 47.2228 1.61878
\(852\) 0 0
\(853\) −13.2634 −0.454131 −0.227065 0.973880i \(-0.572913\pi\)
−0.227065 + 0.973880i \(0.572913\pi\)
\(854\) 7.78672 0.266456
\(855\) 0 0
\(856\) 7.90803 0.270291
\(857\) 46.9796 1.60479 0.802397 0.596791i \(-0.203558\pi\)
0.802397 + 0.596791i \(0.203558\pi\)
\(858\) 0 0
\(859\) 3.10197 0.105838 0.0529189 0.998599i \(-0.483148\pi\)
0.0529189 + 0.998599i \(0.483148\pi\)
\(860\) 8.12085 0.276919
\(861\) 0 0
\(862\) −29.8097 −1.01532
\(863\) 15.4875 0.527201 0.263601 0.964632i \(-0.415090\pi\)
0.263601 + 0.964632i \(0.415090\pi\)
\(864\) 0 0
\(865\) −6.88629 −0.234141
\(866\) 0.188717 0.00641286
\(867\) 0 0
\(868\) 8.21875 0.278962
\(869\) −5.08314 −0.172434
\(870\) 0 0
\(871\) 46.4198 1.57287
\(872\) −64.1091 −2.17101
\(873\) 0 0
\(874\) −26.3330 −0.890728
\(875\) 2.23155 0.0754400
\(876\) 0 0
\(877\) −18.5712 −0.627103 −0.313552 0.949571i \(-0.601519\pi\)
−0.313552 + 0.949571i \(0.601519\pi\)
\(878\) 27.0436 0.912677
\(879\) 0 0
\(880\) 14.2905 0.481733
\(881\) 57.3001 1.93049 0.965244 0.261350i \(-0.0841677\pi\)
0.965244 + 0.261350i \(0.0841677\pi\)
\(882\) 0 0
\(883\) 21.3909 0.719863 0.359931 0.932979i \(-0.382800\pi\)
0.359931 + 0.932979i \(0.382800\pi\)
\(884\) 8.26132 0.277858
\(885\) 0 0
\(886\) −46.5756 −1.56474
\(887\) −13.1731 −0.442309 −0.221155 0.975239i \(-0.570983\pi\)
−0.221155 + 0.975239i \(0.570983\pi\)
\(888\) 0 0
\(889\) −42.3778 −1.42130
\(890\) 1.16343 0.0389983
\(891\) 0 0
\(892\) −1.96069 −0.0656488
\(893\) 9.89469 0.331113
\(894\) 0 0
\(895\) 18.4452 0.616557
\(896\) −6.84621 −0.228716
\(897\) 0 0
\(898\) 5.64616 0.188415
\(899\) 6.97406 0.232598
\(900\) 0 0
\(901\) 27.8900 0.929152
\(902\) −6.93568 −0.230933
\(903\) 0 0
\(904\) −31.5106 −1.04803
\(905\) 6.69862 0.222670
\(906\) 0 0
\(907\) 31.0645 1.03148 0.515740 0.856745i \(-0.327517\pi\)
0.515740 + 0.856745i \(0.327517\pi\)
\(908\) 9.62991 0.319580
\(909\) 0 0
\(910\) 12.0334 0.398905
\(911\) −49.6807 −1.64600 −0.822998 0.568044i \(-0.807700\pi\)
−0.822998 + 0.568044i \(0.807700\pi\)
\(912\) 0 0
\(913\) 18.3581 0.607563
\(914\) −22.7586 −0.752788
\(915\) 0 0
\(916\) −7.63101 −0.252136
\(917\) −11.8031 −0.389771
\(918\) 0 0
\(919\) −10.1234 −0.333939 −0.166970 0.985962i \(-0.553398\pi\)
−0.166970 + 0.985962i \(0.553398\pi\)
\(920\) 21.1414 0.697013
\(921\) 0 0
\(922\) −19.6452 −0.646981
\(923\) 41.9083 1.37943
\(924\) 0 0
\(925\) 6.87730 0.226124
\(926\) 27.0919 0.890297
\(927\) 0 0
\(928\) 4.27745 0.140414
\(929\) −28.9742 −0.950613 −0.475307 0.879820i \(-0.657663\pi\)
−0.475307 + 0.879820i \(0.657663\pi\)
\(930\) 0 0
\(931\) −6.65917 −0.218246
\(932\) 9.94707 0.325827
\(933\) 0 0
\(934\) 44.7144 1.46310
\(935\) −17.2122 −0.562899
\(936\) 0 0
\(937\) 42.6921 1.39469 0.697345 0.716736i \(-0.254365\pi\)
0.697345 + 0.716736i \(0.254365\pi\)
\(938\) 26.0020 0.848995
\(939\) 0 0
\(940\) −1.94042 −0.0632895
\(941\) 50.1099 1.63354 0.816768 0.576967i \(-0.195764\pi\)
0.816768 + 0.576967i \(0.195764\pi\)
\(942\) 0 0
\(943\) −6.55742 −0.213539
\(944\) 16.1740 0.526419
\(945\) 0 0
\(946\) −91.2372 −2.96638
\(947\) 20.5148 0.666640 0.333320 0.942814i \(-0.391831\pi\)
0.333320 + 0.942814i \(0.391831\pi\)
\(948\) 0 0
\(949\) −51.9997 −1.68798
\(950\) −3.83501 −0.124424
\(951\) 0 0
\(952\) 18.9450 0.614009
\(953\) 14.5669 0.471869 0.235934 0.971769i \(-0.424185\pi\)
0.235934 + 0.971769i \(0.424185\pi\)
\(954\) 0 0
\(955\) 5.40267 0.174826
\(956\) 12.2248 0.395379
\(957\) 0 0
\(958\) 39.6343 1.28052
\(959\) 3.03732 0.0980800
\(960\) 0 0
\(961\) 1.46085 0.0471242
\(962\) 37.0853 1.19568
\(963\) 0 0
\(964\) 11.6791 0.376160
\(965\) −1.28529 −0.0413749
\(966\) 0 0
\(967\) −24.8597 −0.799433 −0.399717 0.916639i \(-0.630891\pi\)
−0.399717 + 0.916639i \(0.630891\pi\)
\(968\) 86.1091 2.76765
\(969\) 0 0
\(970\) −13.4771 −0.432725
\(971\) 33.6301 1.07924 0.539621 0.841908i \(-0.318568\pi\)
0.539621 + 0.841908i \(0.318568\pi\)
\(972\) 0 0
\(973\) −3.25646 −0.104397
\(974\) 37.2953 1.19502
\(975\) 0 0
\(976\) 6.86603 0.219776
\(977\) 10.3812 0.332125 0.166063 0.986115i \(-0.446895\pi\)
0.166063 + 0.986115i \(0.446895\pi\)
\(978\) 0 0
\(979\) 6.24237 0.199507
\(980\) 1.30591 0.0417158
\(981\) 0 0
\(982\) 40.8488 1.30354
\(983\) 47.5089 1.51530 0.757649 0.652663i \(-0.226348\pi\)
0.757649 + 0.652663i \(0.226348\pi\)
\(984\) 0 0
\(985\) −11.7541 −0.374516
\(986\) 3.92675 0.125053
\(987\) 0 0
\(988\) 9.87618 0.314203
\(989\) −86.2613 −2.74295
\(990\) 0 0
\(991\) 1.77873 0.0565033 0.0282517 0.999601i \(-0.491006\pi\)
0.0282517 + 0.999601i \(0.491006\pi\)
\(992\) 19.9095 0.632126
\(993\) 0 0
\(994\) 23.4749 0.744579
\(995\) −14.5646 −0.461730
\(996\) 0 0
\(997\) 38.7428 1.22700 0.613498 0.789696i \(-0.289762\pi\)
0.613498 + 0.789696i \(0.289762\pi\)
\(998\) 20.9381 0.662783
\(999\) 0 0
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 \(a_p\))