Properties

Label 8048.2.a.v.1.16
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.447624 q^{3}\) \(+0.901345 q^{5}\) \(+1.57888 q^{7}\) \(-2.79963 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.447624 q^{3}\) \(+0.901345 q^{5}\) \(+1.57888 q^{7}\) \(-2.79963 q^{9}\) \(-2.73519 q^{11}\) \(-0.127802 q^{13}\) \(+0.403464 q^{15}\) \(-0.965178 q^{17}\) \(-1.08247 q^{19}\) \(+0.706743 q^{21}\) \(-0.734871 q^{23}\) \(-4.18758 q^{25}\) \(-2.59606 q^{27}\) \(+9.81943 q^{29}\) \(+6.56783 q^{31}\) \(-1.22434 q^{33}\) \(+1.42311 q^{35}\) \(-2.91899 q^{37}\) \(-0.0572072 q^{39}\) \(+1.43349 q^{41}\) \(+2.61043 q^{43}\) \(-2.52343 q^{45}\) \(-2.70258 q^{47}\) \(-4.50715 q^{49}\) \(-0.432037 q^{51}\) \(+0.901890 q^{53}\) \(-2.46535 q^{55}\) \(-0.484540 q^{57}\) \(-6.31776 q^{59}\) \(-5.52676 q^{61}\) \(-4.42028 q^{63}\) \(-0.115194 q^{65}\) \(+3.88478 q^{67}\) \(-0.328946 q^{69}\) \(+9.68884 q^{71}\) \(-1.43220 q^{73}\) \(-1.87446 q^{75}\) \(-4.31853 q^{77}\) \(+9.80388 q^{79}\) \(+7.23684 q^{81}\) \(-4.88746 q^{83}\) \(-0.869958 q^{85}\) \(+4.39541 q^{87}\) \(-16.4486 q^{89}\) \(-0.201784 q^{91}\) \(+2.93992 q^{93}\) \(-0.975680 q^{95}\) \(-8.63007 q^{97}\) \(+7.65752 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 31q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 22q^{25} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 26q^{33} \) \(\mathstrut +\mathstrut 13q^{35} \) \(\mathstrut -\mathstrut 67q^{37} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut -\mathstrut 57q^{45} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 20q^{49} \) \(\mathstrut +\mathstrut 11q^{51} \) \(\mathstrut -\mathstrut 58q^{53} \) \(\mathstrut -\mathstrut 15q^{55} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 55q^{61} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 44q^{69} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 5q^{73} \) \(\mathstrut +\mathstrut 25q^{75} \) \(\mathstrut -\mathstrut 50q^{77} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 78q^{85} \) \(\mathstrut +\mathstrut 11q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut +\mathstrut 15q^{91} \) \(\mathstrut -\mathstrut 83q^{93} \) \(\mathstrut +\mathstrut 27q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 70q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 0
\(3\) 0.447624 0.258436 0.129218 0.991616i \(-0.458753\pi\)
0.129218 + 0.991616i \(0.458753\pi\)
\(4\) 0 0
\(5\) 0.901345 0.403094 0.201547 0.979479i \(-0.435403\pi\)
0.201547 + 0.979479i \(0.435403\pi\)
\(6\) 0 0
\(7\) 1.57888 0.596760 0.298380 0.954447i \(-0.403554\pi\)
0.298380 + 0.954447i \(0.403554\pi\)
\(8\) 0 0
\(9\) −2.79963 −0.933211
\(10\) 0 0
\(11\) −2.73519 −0.824690 −0.412345 0.911028i \(-0.635290\pi\)
−0.412345 + 0.911028i \(0.635290\pi\)
\(12\) 0 0
\(13\) −0.127802 −0.0354459 −0.0177229 0.999843i \(-0.505642\pi\)
−0.0177229 + 0.999843i \(0.505642\pi\)
\(14\) 0 0
\(15\) 0.403464 0.104174
\(16\) 0 0
\(17\) −0.965178 −0.234090 −0.117045 0.993127i \(-0.537342\pi\)
−0.117045 + 0.993127i \(0.537342\pi\)
\(18\) 0 0
\(19\) −1.08247 −0.248336 −0.124168 0.992261i \(-0.539626\pi\)
−0.124168 + 0.992261i \(0.539626\pi\)
\(20\) 0 0
\(21\) 0.706743 0.154224
\(22\) 0 0
\(23\) −0.734871 −0.153231 −0.0766156 0.997061i \(-0.524411\pi\)
−0.0766156 + 0.997061i \(0.524411\pi\)
\(24\) 0 0
\(25\) −4.18758 −0.837516
\(26\) 0 0
\(27\) −2.59606 −0.499611
\(28\) 0 0
\(29\) 9.81943 1.82342 0.911711 0.410833i \(-0.134762\pi\)
0.911711 + 0.410833i \(0.134762\pi\)
\(30\) 0 0
\(31\) 6.56783 1.17962 0.589809 0.807543i \(-0.299203\pi\)
0.589809 + 0.807543i \(0.299203\pi\)
\(32\) 0 0
\(33\) −1.22434 −0.213130
\(34\) 0 0
\(35\) 1.42311 0.240550
\(36\) 0 0
\(37\) −2.91899 −0.479879 −0.239939 0.970788i \(-0.577128\pi\)
−0.239939 + 0.970788i \(0.577128\pi\)
\(38\) 0 0
\(39\) −0.0572072 −0.00916049
\(40\) 0 0
\(41\) 1.43349 0.223873 0.111936 0.993715i \(-0.464295\pi\)
0.111936 + 0.993715i \(0.464295\pi\)
\(42\) 0 0
\(43\) 2.61043 0.398087 0.199044 0.979991i \(-0.436216\pi\)
0.199044 + 0.979991i \(0.436216\pi\)
\(44\) 0 0
\(45\) −2.52343 −0.376171
\(46\) 0 0
\(47\) −2.70258 −0.394212 −0.197106 0.980382i \(-0.563154\pi\)
−0.197106 + 0.980382i \(0.563154\pi\)
\(48\) 0 0
\(49\) −4.50715 −0.643878
\(50\) 0 0
\(51\) −0.432037 −0.0604973
\(52\) 0 0
\(53\) 0.901890 0.123884 0.0619421 0.998080i \(-0.480271\pi\)
0.0619421 + 0.998080i \(0.480271\pi\)
\(54\) 0 0
\(55\) −2.46535 −0.332427
\(56\) 0 0
\(57\) −0.484540 −0.0641789
\(58\) 0 0
\(59\) −6.31776 −0.822502 −0.411251 0.911522i \(-0.634908\pi\)
−0.411251 + 0.911522i \(0.634908\pi\)
\(60\) 0 0
\(61\) −5.52676 −0.707629 −0.353815 0.935316i \(-0.615116\pi\)
−0.353815 + 0.935316i \(0.615116\pi\)
\(62\) 0 0
\(63\) −4.42028 −0.556902
\(64\) 0 0
\(65\) −0.115194 −0.0142880
\(66\) 0 0
\(67\) 3.88478 0.474602 0.237301 0.971436i \(-0.423737\pi\)
0.237301 + 0.971436i \(0.423737\pi\)
\(68\) 0 0
\(69\) −0.328946 −0.0396004
\(70\) 0 0
\(71\) 9.68884 1.14985 0.574927 0.818205i \(-0.305031\pi\)
0.574927 + 0.818205i \(0.305031\pi\)
\(72\) 0 0
\(73\) −1.43220 −0.167627 −0.0838134 0.996481i \(-0.526710\pi\)
−0.0838134 + 0.996481i \(0.526710\pi\)
\(74\) 0 0
\(75\) −1.87446 −0.216444
\(76\) 0 0
\(77\) −4.31853 −0.492142
\(78\) 0 0
\(79\) 9.80388 1.10302 0.551511 0.834167i \(-0.314051\pi\)
0.551511 + 0.834167i \(0.314051\pi\)
\(80\) 0 0
\(81\) 7.23684 0.804094
\(82\) 0 0
\(83\) −4.88746 −0.536469 −0.268234 0.963354i \(-0.586440\pi\)
−0.268234 + 0.963354i \(0.586440\pi\)
\(84\) 0 0
\(85\) −0.869958 −0.0943602
\(86\) 0 0
\(87\) 4.39541 0.471237
\(88\) 0 0
\(89\) −16.4486 −1.74355 −0.871776 0.489904i \(-0.837032\pi\)
−0.871776 + 0.489904i \(0.837032\pi\)
\(90\) 0 0
\(91\) −0.201784 −0.0211527
\(92\) 0 0
\(93\) 2.93992 0.304855
\(94\) 0 0
\(95\) −0.975680 −0.100103
\(96\) 0 0
\(97\) −8.63007 −0.876250 −0.438125 0.898914i \(-0.644357\pi\)
−0.438125 + 0.898914i \(0.644357\pi\)
\(98\) 0 0
\(99\) 7.65752 0.769610
\(100\) 0 0
\(101\) 8.46581 0.842380 0.421190 0.906972i \(-0.361613\pi\)
0.421190 + 0.906972i \(0.361613\pi\)
\(102\) 0 0
\(103\) −2.82426 −0.278282 −0.139141 0.990273i \(-0.544434\pi\)
−0.139141 + 0.990273i \(0.544434\pi\)
\(104\) 0 0
\(105\) 0.637019 0.0621667
\(106\) 0 0
\(107\) −15.1261 −1.46230 −0.731148 0.682219i \(-0.761015\pi\)
−0.731148 + 0.682219i \(0.761015\pi\)
\(108\) 0 0
\(109\) −14.9868 −1.43547 −0.717737 0.696315i \(-0.754822\pi\)
−0.717737 + 0.696315i \(0.754822\pi\)
\(110\) 0 0
\(111\) −1.30661 −0.124018
\(112\) 0 0
\(113\) −20.0027 −1.88170 −0.940848 0.338830i \(-0.889969\pi\)
−0.940848 + 0.338830i \(0.889969\pi\)
\(114\) 0 0
\(115\) −0.662372 −0.0617665
\(116\) 0 0
\(117\) 0.357799 0.0330785
\(118\) 0 0
\(119\) −1.52390 −0.139696
\(120\) 0 0
\(121\) −3.51875 −0.319886
\(122\) 0 0
\(123\) 0.641663 0.0578568
\(124\) 0 0
\(125\) −8.28117 −0.740691
\(126\) 0 0
\(127\) −1.02653 −0.0910896 −0.0455448 0.998962i \(-0.514502\pi\)
−0.0455448 + 0.998962i \(0.514502\pi\)
\(128\) 0 0
\(129\) 1.16849 0.102880
\(130\) 0 0
\(131\) 9.10716 0.795696 0.397848 0.917451i \(-0.369757\pi\)
0.397848 + 0.917451i \(0.369757\pi\)
\(132\) 0 0
\(133\) −1.70909 −0.148197
\(134\) 0 0
\(135\) −2.33994 −0.201390
\(136\) 0 0
\(137\) −21.7857 −1.86128 −0.930640 0.365935i \(-0.880749\pi\)
−0.930640 + 0.365935i \(0.880749\pi\)
\(138\) 0 0
\(139\) 0.628032 0.0532689 0.0266345 0.999645i \(-0.491521\pi\)
0.0266345 + 0.999645i \(0.491521\pi\)
\(140\) 0 0
\(141\) −1.20974 −0.101879
\(142\) 0 0
\(143\) 0.349562 0.0292319
\(144\) 0 0
\(145\) 8.85069 0.735009
\(146\) 0 0
\(147\) −2.01751 −0.166401
\(148\) 0 0
\(149\) 10.6024 0.868581 0.434291 0.900773i \(-0.356999\pi\)
0.434291 + 0.900773i \(0.356999\pi\)
\(150\) 0 0
\(151\) −17.4339 −1.41875 −0.709377 0.704829i \(-0.751024\pi\)
−0.709377 + 0.704829i \(0.751024\pi\)
\(152\) 0 0
\(153\) 2.70214 0.218455
\(154\) 0 0
\(155\) 5.91988 0.475496
\(156\) 0 0
\(157\) 0.640002 0.0510778 0.0255389 0.999674i \(-0.491870\pi\)
0.0255389 + 0.999674i \(0.491870\pi\)
\(158\) 0 0
\(159\) 0.403708 0.0320161
\(160\) 0 0
\(161\) −1.16027 −0.0914421
\(162\) 0 0
\(163\) −19.4870 −1.52634 −0.763170 0.646198i \(-0.776358\pi\)
−0.763170 + 0.646198i \(0.776358\pi\)
\(164\) 0 0
\(165\) −1.10355 −0.0859111
\(166\) 0 0
\(167\) −5.58619 −0.432272 −0.216136 0.976363i \(-0.569346\pi\)
−0.216136 + 0.976363i \(0.569346\pi\)
\(168\) 0 0
\(169\) −12.9837 −0.998744
\(170\) 0 0
\(171\) 3.03052 0.231750
\(172\) 0 0
\(173\) −21.2916 −1.61877 −0.809383 0.587281i \(-0.800198\pi\)
−0.809383 + 0.587281i \(0.800198\pi\)
\(174\) 0 0
\(175\) −6.61167 −0.499795
\(176\) 0 0
\(177\) −2.82798 −0.212564
\(178\) 0 0
\(179\) −16.1793 −1.20930 −0.604650 0.796491i \(-0.706687\pi\)
−0.604650 + 0.796491i \(0.706687\pi\)
\(180\) 0 0
\(181\) −21.8341 −1.62291 −0.811456 0.584413i \(-0.801325\pi\)
−0.811456 + 0.584413i \(0.801325\pi\)
\(182\) 0 0
\(183\) −2.47391 −0.182877
\(184\) 0 0
\(185\) −2.63101 −0.193436
\(186\) 0 0
\(187\) 2.63994 0.193052
\(188\) 0 0
\(189\) −4.09885 −0.298148
\(190\) 0 0
\(191\) 17.0262 1.23197 0.615987 0.787757i \(-0.288758\pi\)
0.615987 + 0.787757i \(0.288758\pi\)
\(192\) 0 0
\(193\) −2.80147 −0.201654 −0.100827 0.994904i \(-0.532149\pi\)
−0.100827 + 0.994904i \(0.532149\pi\)
\(194\) 0 0
\(195\) −0.0515634 −0.00369253
\(196\) 0 0
\(197\) 8.21467 0.585271 0.292635 0.956224i \(-0.405468\pi\)
0.292635 + 0.956224i \(0.405468\pi\)
\(198\) 0 0
\(199\) 25.1008 1.77935 0.889674 0.456597i \(-0.150932\pi\)
0.889674 + 0.456597i \(0.150932\pi\)
\(200\) 0 0
\(201\) 1.73892 0.122654
\(202\) 0 0
\(203\) 15.5037 1.08814
\(204\) 0 0
\(205\) 1.29206 0.0902417
\(206\) 0 0
\(207\) 2.05737 0.142997
\(208\) 0 0
\(209\) 2.96076 0.204800
\(210\) 0 0
\(211\) −1.99433 −0.137295 −0.0686476 0.997641i \(-0.521868\pi\)
−0.0686476 + 0.997641i \(0.521868\pi\)
\(212\) 0 0
\(213\) 4.33696 0.297163
\(214\) 0 0
\(215\) 2.35290 0.160466
\(216\) 0 0
\(217\) 10.3698 0.703948
\(218\) 0 0
\(219\) −0.641089 −0.0433208
\(220\) 0 0
\(221\) 0.123352 0.00829753
\(222\) 0 0
\(223\) 22.9920 1.53966 0.769830 0.638249i \(-0.220341\pi\)
0.769830 + 0.638249i \(0.220341\pi\)
\(224\) 0 0
\(225\) 11.7237 0.781579
\(226\) 0 0
\(227\) −24.2522 −1.60967 −0.804836 0.593497i \(-0.797747\pi\)
−0.804836 + 0.593497i \(0.797747\pi\)
\(228\) 0 0
\(229\) 5.04283 0.333240 0.166620 0.986021i \(-0.446715\pi\)
0.166620 + 0.986021i \(0.446715\pi\)
\(230\) 0 0
\(231\) −1.93308 −0.127187
\(232\) 0 0
\(233\) −4.35483 −0.285294 −0.142647 0.989774i \(-0.545561\pi\)
−0.142647 + 0.989774i \(0.545561\pi\)
\(234\) 0 0
\(235\) −2.43596 −0.158904
\(236\) 0 0
\(237\) 4.38845 0.285061
\(238\) 0 0
\(239\) 12.4760 0.807004 0.403502 0.914979i \(-0.367793\pi\)
0.403502 + 0.914979i \(0.367793\pi\)
\(240\) 0 0
\(241\) 8.29161 0.534110 0.267055 0.963681i \(-0.413950\pi\)
0.267055 + 0.963681i \(0.413950\pi\)
\(242\) 0 0
\(243\) 11.0275 0.707418
\(244\) 0 0
\(245\) −4.06249 −0.259543
\(246\) 0 0
\(247\) 0.138342 0.00880249
\(248\) 0 0
\(249\) −2.18775 −0.138643
\(250\) 0 0
\(251\) 17.5576 1.10822 0.554112 0.832442i \(-0.313058\pi\)
0.554112 + 0.832442i \(0.313058\pi\)
\(252\) 0 0
\(253\) 2.01001 0.126368
\(254\) 0 0
\(255\) −0.389414 −0.0243861
\(256\) 0 0
\(257\) 4.60355 0.287162 0.143581 0.989639i \(-0.454138\pi\)
0.143581 + 0.989639i \(0.454138\pi\)
\(258\) 0 0
\(259\) −4.60873 −0.286372
\(260\) 0 0
\(261\) −27.4908 −1.70164
\(262\) 0 0
\(263\) −13.8831 −0.856068 −0.428034 0.903763i \(-0.640794\pi\)
−0.428034 + 0.903763i \(0.640794\pi\)
\(264\) 0 0
\(265\) 0.812914 0.0499369
\(266\) 0 0
\(267\) −7.36281 −0.450597
\(268\) 0 0
\(269\) −2.71959 −0.165816 −0.0829082 0.996557i \(-0.526421\pi\)
−0.0829082 + 0.996557i \(0.526421\pi\)
\(270\) 0 0
\(271\) −6.83383 −0.415126 −0.207563 0.978222i \(-0.566553\pi\)
−0.207563 + 0.978222i \(0.566553\pi\)
\(272\) 0 0
\(273\) −0.0903232 −0.00546661
\(274\) 0 0
\(275\) 11.4538 0.690691
\(276\) 0 0
\(277\) −16.4311 −0.987249 −0.493625 0.869675i \(-0.664328\pi\)
−0.493625 + 0.869675i \(0.664328\pi\)
\(278\) 0 0
\(279\) −18.3875 −1.10083
\(280\) 0 0
\(281\) 15.7034 0.936787 0.468394 0.883520i \(-0.344833\pi\)
0.468394 + 0.883520i \(0.344833\pi\)
\(282\) 0 0
\(283\) −26.5926 −1.58076 −0.790382 0.612615i \(-0.790118\pi\)
−0.790382 + 0.612615i \(0.790118\pi\)
\(284\) 0 0
\(285\) −0.436738 −0.0258701
\(286\) 0 0
\(287\) 2.26330 0.133598
\(288\) 0 0
\(289\) −16.0684 −0.945202
\(290\) 0 0
\(291\) −3.86302 −0.226455
\(292\) 0 0
\(293\) −21.3129 −1.24511 −0.622557 0.782574i \(-0.713906\pi\)
−0.622557 + 0.782574i \(0.713906\pi\)
\(294\) 0 0
\(295\) −5.69448 −0.331545
\(296\) 0 0
\(297\) 7.10070 0.412024
\(298\) 0 0
\(299\) 0.0939179 0.00543141
\(300\) 0 0
\(301\) 4.12155 0.237562
\(302\) 0 0
\(303\) 3.78950 0.217701
\(304\) 0 0
\(305\) −4.98152 −0.285241
\(306\) 0 0
\(307\) 28.3391 1.61740 0.808699 0.588223i \(-0.200172\pi\)
0.808699 + 0.588223i \(0.200172\pi\)
\(308\) 0 0
\(309\) −1.26420 −0.0719181
\(310\) 0 0
\(311\) −12.2327 −0.693655 −0.346827 0.937929i \(-0.612741\pi\)
−0.346827 + 0.937929i \(0.612741\pi\)
\(312\) 0 0
\(313\) 24.4674 1.38298 0.691489 0.722387i \(-0.256955\pi\)
0.691489 + 0.722387i \(0.256955\pi\)
\(314\) 0 0
\(315\) −3.98419 −0.224484
\(316\) 0 0
\(317\) 13.7231 0.770768 0.385384 0.922756i \(-0.374069\pi\)
0.385384 + 0.922756i \(0.374069\pi\)
\(318\) 0 0
\(319\) −26.8580 −1.50376
\(320\) 0 0
\(321\) −6.77081 −0.377910
\(322\) 0 0
\(323\) 1.04478 0.0581330
\(324\) 0 0
\(325\) 0.535181 0.0296865
\(326\) 0 0
\(327\) −6.70844 −0.370978
\(328\) 0 0
\(329\) −4.26704 −0.235250
\(330\) 0 0
\(331\) 32.3649 1.77894 0.889469 0.456996i \(-0.151074\pi\)
0.889469 + 0.456996i \(0.151074\pi\)
\(332\) 0 0
\(333\) 8.17210 0.447828
\(334\) 0 0
\(335\) 3.50153 0.191309
\(336\) 0 0
\(337\) −0.611067 −0.0332869 −0.0166435 0.999861i \(-0.505298\pi\)
−0.0166435 + 0.999861i \(0.505298\pi\)
\(338\) 0 0
\(339\) −8.95369 −0.486297
\(340\) 0 0
\(341\) −17.9643 −0.972819
\(342\) 0 0
\(343\) −18.1684 −0.981000
\(344\) 0 0
\(345\) −0.296493 −0.0159627
\(346\) 0 0
\(347\) 23.0394 1.23682 0.618409 0.785857i \(-0.287778\pi\)
0.618409 + 0.785857i \(0.287778\pi\)
\(348\) 0 0
\(349\) −24.5411 −1.31365 −0.656827 0.754041i \(-0.728102\pi\)
−0.656827 + 0.754041i \(0.728102\pi\)
\(350\) 0 0
\(351\) 0.331781 0.0177092
\(352\) 0 0
\(353\) 34.1596 1.81813 0.909067 0.416651i \(-0.136796\pi\)
0.909067 + 0.416651i \(0.136796\pi\)
\(354\) 0 0
\(355\) 8.73298 0.463498
\(356\) 0 0
\(357\) −0.682133 −0.0361023
\(358\) 0 0
\(359\) 11.9085 0.628507 0.314254 0.949339i \(-0.398246\pi\)
0.314254 + 0.949339i \(0.398246\pi\)
\(360\) 0 0
\(361\) −17.8283 −0.938329
\(362\) 0 0
\(363\) −1.57508 −0.0826700
\(364\) 0 0
\(365\) −1.29091 −0.0675693
\(366\) 0 0
\(367\) −5.95411 −0.310802 −0.155401 0.987851i \(-0.549667\pi\)
−0.155401 + 0.987851i \(0.549667\pi\)
\(368\) 0 0
\(369\) −4.01323 −0.208921
\(370\) 0 0
\(371\) 1.42397 0.0739290
\(372\) 0 0
\(373\) 13.5045 0.699234 0.349617 0.936893i \(-0.386312\pi\)
0.349617 + 0.936893i \(0.386312\pi\)
\(374\) 0 0
\(375\) −3.70685 −0.191421
\(376\) 0 0
\(377\) −1.25494 −0.0646328
\(378\) 0 0
\(379\) −22.3264 −1.14683 −0.573415 0.819265i \(-0.694382\pi\)
−0.573415 + 0.819265i \(0.694382\pi\)
\(380\) 0 0
\(381\) −0.459499 −0.0235408
\(382\) 0 0
\(383\) 19.1315 0.977573 0.488786 0.872403i \(-0.337440\pi\)
0.488786 + 0.872403i \(0.337440\pi\)
\(384\) 0 0
\(385\) −3.89248 −0.198379
\(386\) 0 0
\(387\) −7.30825 −0.371499
\(388\) 0 0
\(389\) 5.32461 0.269969 0.134984 0.990848i \(-0.456902\pi\)
0.134984 + 0.990848i \(0.456902\pi\)
\(390\) 0 0
\(391\) 0.709281 0.0358699
\(392\) 0 0
\(393\) 4.07658 0.205636
\(394\) 0 0
\(395\) 8.83667 0.444621
\(396\) 0 0
\(397\) −13.7991 −0.692558 −0.346279 0.938132i \(-0.612555\pi\)
−0.346279 + 0.938132i \(0.612555\pi\)
\(398\) 0 0
\(399\) −0.765029 −0.0382994
\(400\) 0 0
\(401\) −28.8332 −1.43986 −0.719931 0.694045i \(-0.755827\pi\)
−0.719931 + 0.694045i \(0.755827\pi\)
\(402\) 0 0
\(403\) −0.839382 −0.0418126
\(404\) 0 0
\(405\) 6.52289 0.324125
\(406\) 0 0
\(407\) 7.98398 0.395751
\(408\) 0 0
\(409\) −6.76400 −0.334458 −0.167229 0.985918i \(-0.553482\pi\)
−0.167229 + 0.985918i \(0.553482\pi\)
\(410\) 0 0
\(411\) −9.75182 −0.481022
\(412\) 0 0
\(413\) −9.97496 −0.490836
\(414\) 0 0
\(415\) −4.40529 −0.216247
\(416\) 0 0
\(417\) 0.281122 0.0137666
\(418\) 0 0
\(419\) 35.4135 1.73006 0.865032 0.501717i \(-0.167298\pi\)
0.865032 + 0.501717i \(0.167298\pi\)
\(420\) 0 0
\(421\) 0.422696 0.0206010 0.0103005 0.999947i \(-0.496721\pi\)
0.0103005 + 0.999947i \(0.496721\pi\)
\(422\) 0 0
\(423\) 7.56623 0.367883
\(424\) 0 0
\(425\) 4.04176 0.196054
\(426\) 0 0
\(427\) −8.72608 −0.422284
\(428\) 0 0
\(429\) 0.156473 0.00755456
\(430\) 0 0
\(431\) −13.6898 −0.659415 −0.329707 0.944083i \(-0.606950\pi\)
−0.329707 + 0.944083i \(0.606950\pi\)
\(432\) 0 0
\(433\) 18.9972 0.912946 0.456473 0.889737i \(-0.349112\pi\)
0.456473 + 0.889737i \(0.349112\pi\)
\(434\) 0 0
\(435\) 3.96178 0.189953
\(436\) 0 0
\(437\) 0.795476 0.0380528
\(438\) 0 0
\(439\) −20.6855 −0.987265 −0.493633 0.869671i \(-0.664331\pi\)
−0.493633 + 0.869671i \(0.664331\pi\)
\(440\) 0 0
\(441\) 12.6184 0.600874
\(442\) 0 0
\(443\) −28.7062 −1.36387 −0.681937 0.731411i \(-0.738862\pi\)
−0.681937 + 0.731411i \(0.738862\pi\)
\(444\) 0 0
\(445\) −14.8259 −0.702815
\(446\) 0 0
\(447\) 4.74588 0.224473
\(448\) 0 0
\(449\) 1.92732 0.0909558 0.0454779 0.998965i \(-0.485519\pi\)
0.0454779 + 0.998965i \(0.485519\pi\)
\(450\) 0 0
\(451\) −3.92085 −0.184626
\(452\) 0 0
\(453\) −7.80385 −0.366657
\(454\) 0 0
\(455\) −0.181877 −0.00852650
\(456\) 0 0
\(457\) −33.7613 −1.57929 −0.789645 0.613564i \(-0.789735\pi\)
−0.789645 + 0.613564i \(0.789735\pi\)
\(458\) 0 0
\(459\) 2.50566 0.116954
\(460\) 0 0
\(461\) 24.9746 1.16318 0.581592 0.813480i \(-0.302430\pi\)
0.581592 + 0.813480i \(0.302430\pi\)
\(462\) 0 0
\(463\) 6.36011 0.295579 0.147790 0.989019i \(-0.452784\pi\)
0.147790 + 0.989019i \(0.452784\pi\)
\(464\) 0 0
\(465\) 2.64988 0.122885
\(466\) 0 0
\(467\) 24.4726 1.13245 0.566227 0.824249i \(-0.308402\pi\)
0.566227 + 0.824249i \(0.308402\pi\)
\(468\) 0 0
\(469\) 6.13360 0.283223
\(470\) 0 0
\(471\) 0.286480 0.0132003
\(472\) 0 0
\(473\) −7.14002 −0.328299
\(474\) 0 0
\(475\) 4.53293 0.207985
\(476\) 0 0
\(477\) −2.52496 −0.115610
\(478\) 0 0
\(479\) 18.9355 0.865186 0.432593 0.901589i \(-0.357599\pi\)
0.432593 + 0.901589i \(0.357599\pi\)
\(480\) 0 0
\(481\) 0.373052 0.0170097
\(482\) 0 0
\(483\) −0.519365 −0.0236319
\(484\) 0 0
\(485\) −7.77866 −0.353211
\(486\) 0 0
\(487\) 33.8295 1.53296 0.766481 0.642267i \(-0.222006\pi\)
0.766481 + 0.642267i \(0.222006\pi\)
\(488\) 0 0
\(489\) −8.72285 −0.394461
\(490\) 0 0
\(491\) −12.1072 −0.546390 −0.273195 0.961959i \(-0.588080\pi\)
−0.273195 + 0.961959i \(0.588080\pi\)
\(492\) 0 0
\(493\) −9.47750 −0.426845
\(494\) 0 0
\(495\) 6.90207 0.310225
\(496\) 0 0
\(497\) 15.2975 0.686186
\(498\) 0 0
\(499\) 36.3596 1.62768 0.813839 0.581090i \(-0.197374\pi\)
0.813839 + 0.581090i \(0.197374\pi\)
\(500\) 0 0
\(501\) −2.50051 −0.111715
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 7.63062 0.339558
\(506\) 0 0
\(507\) −5.81180 −0.258111
\(508\) 0 0
\(509\) 41.0203 1.81819 0.909096 0.416587i \(-0.136774\pi\)
0.909096 + 0.416587i \(0.136774\pi\)
\(510\) 0 0
\(511\) −2.26127 −0.100033
\(512\) 0 0
\(513\) 2.81016 0.124071
\(514\) 0 0
\(515\) −2.54563 −0.112174
\(516\) 0 0
\(517\) 7.39207 0.325103
\(518\) 0 0
\(519\) −9.53061 −0.418347
\(520\) 0 0
\(521\) 7.83402 0.343215 0.171607 0.985165i \(-0.445104\pi\)
0.171607 + 0.985165i \(0.445104\pi\)
\(522\) 0 0
\(523\) −40.8245 −1.78513 −0.892565 0.450919i \(-0.851096\pi\)
−0.892565 + 0.450919i \(0.851096\pi\)
\(524\) 0 0
\(525\) −2.95954 −0.129165
\(526\) 0 0
\(527\) −6.33913 −0.276137
\(528\) 0 0
\(529\) −22.4600 −0.976520
\(530\) 0 0
\(531\) 17.6874 0.767568
\(532\) 0 0
\(533\) −0.183202 −0.00793537
\(534\) 0 0
\(535\) −13.6338 −0.589442
\(536\) 0 0
\(537\) −7.24226 −0.312526
\(538\) 0 0
\(539\) 12.3279 0.531000
\(540\) 0 0
\(541\) −23.3073 −1.00206 −0.501030 0.865430i \(-0.667045\pi\)
−0.501030 + 0.865430i \(0.667045\pi\)
\(542\) 0 0
\(543\) −9.77345 −0.419419
\(544\) 0 0
\(545\) −13.5083 −0.578630
\(546\) 0 0
\(547\) 1.00198 0.0428416 0.0214208 0.999771i \(-0.493181\pi\)
0.0214208 + 0.999771i \(0.493181\pi\)
\(548\) 0 0
\(549\) 15.4729 0.660367
\(550\) 0 0
\(551\) −10.6292 −0.452821
\(552\) 0 0
\(553\) 15.4791 0.658239
\(554\) 0 0
\(555\) −1.17771 −0.0499908
\(556\) 0 0
\(557\) −43.2243 −1.83147 −0.915737 0.401778i \(-0.868392\pi\)
−0.915737 + 0.401778i \(0.868392\pi\)
\(558\) 0 0
\(559\) −0.333618 −0.0141105
\(560\) 0 0
\(561\) 1.18170 0.0498915
\(562\) 0 0
\(563\) −43.0714 −1.81524 −0.907621 0.419790i \(-0.862104\pi\)
−0.907621 + 0.419790i \(0.862104\pi\)
\(564\) 0 0
\(565\) −18.0293 −0.758499
\(566\) 0 0
\(567\) 11.4261 0.479850
\(568\) 0 0
\(569\) 45.1586 1.89315 0.946573 0.322491i \(-0.104520\pi\)
0.946573 + 0.322491i \(0.104520\pi\)
\(570\) 0 0
\(571\) −3.24438 −0.135773 −0.0678866 0.997693i \(-0.521626\pi\)
−0.0678866 + 0.997693i \(0.521626\pi\)
\(572\) 0 0
\(573\) 7.62134 0.318386
\(574\) 0 0
\(575\) 3.07733 0.128333
\(576\) 0 0
\(577\) −1.72220 −0.0716960 −0.0358480 0.999357i \(-0.511413\pi\)
−0.0358480 + 0.999357i \(0.511413\pi\)
\(578\) 0 0
\(579\) −1.25400 −0.0521146
\(580\) 0 0
\(581\) −7.71670 −0.320143
\(582\) 0 0
\(583\) −2.46684 −0.102166
\(584\) 0 0
\(585\) 0.322500 0.0133337
\(586\) 0 0
\(587\) 17.8085 0.735036 0.367518 0.930017i \(-0.380208\pi\)
0.367518 + 0.930017i \(0.380208\pi\)
\(588\) 0 0
\(589\) −7.10949 −0.292941
\(590\) 0 0
\(591\) 3.67708 0.151255
\(592\) 0 0
\(593\) 15.2632 0.626783 0.313391 0.949624i \(-0.398535\pi\)
0.313391 + 0.949624i \(0.398535\pi\)
\(594\) 0 0
\(595\) −1.37356 −0.0563104
\(596\) 0 0
\(597\) 11.2357 0.459847
\(598\) 0 0
\(599\) −20.2179 −0.826082 −0.413041 0.910712i \(-0.635533\pi\)
−0.413041 + 0.910712i \(0.635533\pi\)
\(600\) 0 0
\(601\) −23.4812 −0.957818 −0.478909 0.877865i \(-0.658968\pi\)
−0.478909 + 0.877865i \(0.658968\pi\)
\(602\) 0 0
\(603\) −10.8760 −0.442904
\(604\) 0 0
\(605\) −3.17160 −0.128944
\(606\) 0 0
\(607\) −9.16706 −0.372079 −0.186040 0.982542i \(-0.559565\pi\)
−0.186040 + 0.982542i \(0.559565\pi\)
\(608\) 0 0
\(609\) 6.93981 0.281215
\(610\) 0 0
\(611\) 0.345395 0.0139732
\(612\) 0 0
\(613\) 39.4458 1.59320 0.796601 0.604505i \(-0.206629\pi\)
0.796601 + 0.604505i \(0.206629\pi\)
\(614\) 0 0
\(615\) 0.578359 0.0233217
\(616\) 0 0
\(617\) −17.0522 −0.686495 −0.343247 0.939245i \(-0.611527\pi\)
−0.343247 + 0.939245i \(0.611527\pi\)
\(618\) 0 0
\(619\) −35.9531 −1.44508 −0.722538 0.691332i \(-0.757024\pi\)
−0.722538 + 0.691332i \(0.757024\pi\)
\(620\) 0 0
\(621\) 1.90776 0.0765560
\(622\) 0 0
\(623\) −25.9704 −1.04048
\(624\) 0 0
\(625\) 13.4737 0.538948
\(626\) 0 0
\(627\) 1.32531 0.0529277
\(628\) 0 0
\(629\) 2.81734 0.112335
\(630\) 0 0
\(631\) 40.4393 1.60986 0.804932 0.593367i \(-0.202202\pi\)
0.804932 + 0.593367i \(0.202202\pi\)
\(632\) 0 0
\(633\) −0.892710 −0.0354820
\(634\) 0 0
\(635\) −0.925255 −0.0367176
\(636\) 0 0
\(637\) 0.576022 0.0228228
\(638\) 0 0
\(639\) −27.1252 −1.07306
\(640\) 0 0
\(641\) 24.0274 0.949025 0.474512 0.880249i \(-0.342624\pi\)
0.474512 + 0.880249i \(0.342624\pi\)
\(642\) 0 0
\(643\) −5.72714 −0.225856 −0.112928 0.993603i \(-0.536023\pi\)
−0.112928 + 0.993603i \(0.536023\pi\)
\(644\) 0 0
\(645\) 1.05321 0.0414703
\(646\) 0 0
\(647\) −13.3266 −0.523922 −0.261961 0.965079i \(-0.584369\pi\)
−0.261961 + 0.965079i \(0.584369\pi\)
\(648\) 0 0
\(649\) 17.2803 0.678309
\(650\) 0 0
\(651\) 4.64177 0.181925
\(652\) 0 0
\(653\) 3.34007 0.130707 0.0653535 0.997862i \(-0.479182\pi\)
0.0653535 + 0.997862i \(0.479182\pi\)
\(654\) 0 0
\(655\) 8.20869 0.320740
\(656\) 0 0
\(657\) 4.00965 0.156431
\(658\) 0 0
\(659\) 21.8770 0.852207 0.426103 0.904674i \(-0.359886\pi\)
0.426103 + 0.904674i \(0.359886\pi\)
\(660\) 0 0
\(661\) 7.79954 0.303367 0.151683 0.988429i \(-0.451531\pi\)
0.151683 + 0.988429i \(0.451531\pi\)
\(662\) 0 0
\(663\) 0.0552152 0.00214438
\(664\) 0 0
\(665\) −1.54048 −0.0597372
\(666\) 0 0
\(667\) −7.21601 −0.279405
\(668\) 0 0
\(669\) 10.2918 0.397903
\(670\) 0 0
\(671\) 15.1167 0.583575
\(672\) 0 0
\(673\) 17.6284 0.679524 0.339762 0.940511i \(-0.389653\pi\)
0.339762 + 0.940511i \(0.389653\pi\)
\(674\) 0 0
\(675\) 10.8712 0.418432
\(676\) 0 0
\(677\) −27.5792 −1.05995 −0.529977 0.848012i \(-0.677800\pi\)
−0.529977 + 0.848012i \(0.677800\pi\)
\(678\) 0 0
\(679\) −13.6258 −0.522911
\(680\) 0 0
\(681\) −10.8558 −0.415997
\(682\) 0 0
\(683\) 0.636916 0.0243709 0.0121855 0.999926i \(-0.496121\pi\)
0.0121855 + 0.999926i \(0.496121\pi\)
\(684\) 0 0
\(685\) −19.6364 −0.750270
\(686\) 0 0
\(687\) 2.25729 0.0861211
\(688\) 0 0
\(689\) −0.115263 −0.00439118
\(690\) 0 0
\(691\) −51.5685 −1.96176 −0.980878 0.194623i \(-0.937652\pi\)
−0.980878 + 0.194623i \(0.937652\pi\)
\(692\) 0 0
\(693\) 12.0903 0.459272
\(694\) 0 0
\(695\) 0.566073 0.0214724
\(696\) 0 0
\(697\) −1.38357 −0.0524064
\(698\) 0 0
\(699\) −1.94933 −0.0737303
\(700\) 0 0
\(701\) −32.0254 −1.20958 −0.604792 0.796384i \(-0.706744\pi\)
−0.604792 + 0.796384i \(0.706744\pi\)
\(702\) 0 0
\(703\) 3.15972 0.119171
\(704\) 0 0
\(705\) −1.09039 −0.0410666
\(706\) 0 0
\(707\) 13.3665 0.502698
\(708\) 0 0
\(709\) 36.6315 1.37573 0.687863 0.725841i \(-0.258549\pi\)
0.687863 + 0.725841i \(0.258549\pi\)
\(710\) 0 0
\(711\) −27.4473 −1.02935
\(712\) 0 0
\(713\) −4.82651 −0.180754
\(714\) 0 0
\(715\) 0.315076 0.0117832
\(716\) 0 0
\(717\) 5.58455 0.208559
\(718\) 0 0
\(719\) −17.4462 −0.650635 −0.325317 0.945605i \(-0.605471\pi\)
−0.325317 + 0.945605i \(0.605471\pi\)
\(720\) 0 0
\(721\) −4.45915 −0.166068
\(722\) 0 0
\(723\) 3.71153 0.138033
\(724\) 0 0
\(725\) −41.1196 −1.52714
\(726\) 0 0
\(727\) −26.0541 −0.966294 −0.483147 0.875539i \(-0.660506\pi\)
−0.483147 + 0.875539i \(0.660506\pi\)
\(728\) 0 0
\(729\) −16.7743 −0.621271
\(730\) 0 0
\(731\) −2.51953 −0.0931883
\(732\) 0 0
\(733\) −37.0798 −1.36957 −0.684787 0.728743i \(-0.740105\pi\)
−0.684787 + 0.728743i \(0.740105\pi\)
\(734\) 0 0
\(735\) −1.81847 −0.0670752
\(736\) 0 0
\(737\) −10.6256 −0.391400
\(738\) 0 0
\(739\) −37.5384 −1.38087 −0.690436 0.723393i \(-0.742581\pi\)
−0.690436 + 0.723393i \(0.742581\pi\)
\(740\) 0 0
\(741\) 0.0619252 0.00227488
\(742\) 0 0
\(743\) −0.654911 −0.0240263 −0.0120132 0.999928i \(-0.503824\pi\)
−0.0120132 + 0.999928i \(0.503824\pi\)
\(744\) 0 0
\(745\) 9.55640 0.350119
\(746\) 0 0
\(747\) 13.6831 0.500639
\(748\) 0 0
\(749\) −23.8823 −0.872639
\(750\) 0 0
\(751\) −17.0374 −0.621704 −0.310852 0.950458i \(-0.600614\pi\)
−0.310852 + 0.950458i \(0.600614\pi\)
\(752\) 0 0
\(753\) 7.85920 0.286405
\(754\) 0 0
\(755\) −15.7140 −0.571891
\(756\) 0 0
\(757\) 45.7650 1.66336 0.831678 0.555258i \(-0.187381\pi\)
0.831678 + 0.555258i \(0.187381\pi\)
\(758\) 0 0
\(759\) 0.899728 0.0326581
\(760\) 0 0
\(761\) 3.97736 0.144179 0.0720896 0.997398i \(-0.477033\pi\)
0.0720896 + 0.997398i \(0.477033\pi\)
\(762\) 0 0
\(763\) −23.6623 −0.856632
\(764\) 0 0
\(765\) 2.43556 0.0880580
\(766\) 0 0
\(767\) 0.807422 0.0291543
\(768\) 0 0
\(769\) 30.5810 1.10278 0.551389 0.834248i \(-0.314098\pi\)
0.551389 + 0.834248i \(0.314098\pi\)
\(770\) 0 0
\(771\) 2.06066 0.0742129
\(772\) 0 0
\(773\) 38.2675 1.37638 0.688192 0.725528i \(-0.258405\pi\)
0.688192 + 0.725528i \(0.258405\pi\)
\(774\) 0 0
\(775\) −27.5033 −0.987948
\(776\) 0 0
\(777\) −2.06298 −0.0740089
\(778\) 0 0
\(779\) −1.55171 −0.0555957
\(780\) 0 0
\(781\) −26.5008 −0.948273
\(782\) 0 0
\(783\) −25.4918 −0.911001
\(784\) 0 0
\(785\) 0.576863 0.0205891
\(786\) 0 0
\(787\) 23.0437 0.821420 0.410710 0.911766i \(-0.365281\pi\)
0.410710 + 0.911766i \(0.365281\pi\)
\(788\) 0 0
\(789\) −6.21440 −0.221239
\(790\) 0 0
\(791\) −31.5818 −1.12292
\(792\) 0 0
\(793\) 0.706331 0.0250825
\(794\) 0 0
\(795\) 0.363880 0.0129055
\(796\) 0 0
\(797\) 54.3456 1.92502 0.962510 0.271247i \(-0.0874359\pi\)
0.962510 + 0.271247i \(0.0874359\pi\)
\(798\) 0 0
\(799\) 2.60847 0.0922811
\(800\) 0 0
\(801\) 46.0502 1.62710
\(802\) 0 0
\(803\) 3.91735 0.138240
\(804\) 0 0
\(805\) −1.04580 −0.0368597
\(806\) 0 0
\(807\) −1.21735 −0.0428529
\(808\) 0 0
\(809\) 28.0937 0.987720 0.493860 0.869541i \(-0.335585\pi\)
0.493860 + 0.869541i \(0.335585\pi\)
\(810\) 0 0
\(811\) −13.6466 −0.479198 −0.239599 0.970872i \(-0.577016\pi\)
−0.239599 + 0.970872i \(0.577016\pi\)
\(812\) 0 0
\(813\) −3.05899 −0.107283
\(814\) 0 0
\(815\) −17.5645 −0.615258
\(816\) 0 0
\(817\) −2.82572 −0.0988593
\(818\) 0 0
\(819\) 0.564920 0.0197399
\(820\) 0 0
\(821\) −8.16976 −0.285126 −0.142563 0.989786i \(-0.545534\pi\)
−0.142563 + 0.989786i \(0.545534\pi\)
\(822\) 0 0
\(823\) −3.93119 −0.137033 −0.0685163 0.997650i \(-0.521827\pi\)
−0.0685163 + 0.997650i \(0.521827\pi\)
\(824\) 0 0
\(825\) 5.12700 0.178499
\(826\) 0 0
\(827\) −44.6674 −1.55324 −0.776618 0.629972i \(-0.783066\pi\)
−0.776618 + 0.629972i \(0.783066\pi\)
\(828\) 0 0
\(829\) −38.5802 −1.33995 −0.669974 0.742385i \(-0.733695\pi\)
−0.669974 + 0.742385i \(0.733695\pi\)
\(830\) 0 0
\(831\) −7.35496 −0.255141
\(832\) 0 0
\(833\) 4.35020 0.150726
\(834\) 0 0
\(835\) −5.03508 −0.174246
\(836\) 0 0
\(837\) −17.0505 −0.589350
\(838\) 0 0
\(839\) −8.85031 −0.305547 −0.152773 0.988261i \(-0.548820\pi\)
−0.152773 + 0.988261i \(0.548820\pi\)
\(840\) 0 0
\(841\) 67.4211 2.32487
\(842\) 0 0
\(843\) 7.02923 0.242099
\(844\) 0 0
\(845\) −11.7028 −0.402587
\(846\) 0 0
\(847\) −5.55567 −0.190895
\(848\) 0 0
\(849\) −11.9035 −0.408526
\(850\) 0 0
\(851\) 2.14508 0.0735324
\(852\) 0 0
\(853\) −2.45889 −0.0841907 −0.0420953 0.999114i \(-0.513403\pi\)
−0.0420953 + 0.999114i \(0.513403\pi\)
\(854\) 0 0
\(855\) 2.73154 0.0934169
\(856\) 0 0
\(857\) −36.1084 −1.23344 −0.616719 0.787183i \(-0.711539\pi\)
−0.616719 + 0.787183i \(0.711539\pi\)
\(858\) 0 0
\(859\) −31.4366 −1.07260 −0.536301 0.844027i \(-0.680179\pi\)
−0.536301 + 0.844027i \(0.680179\pi\)
\(860\) 0 0
\(861\) 1.01311 0.0345266
\(862\) 0 0
\(863\) 11.2863 0.384189 0.192094 0.981376i \(-0.438472\pi\)
0.192094 + 0.981376i \(0.438472\pi\)
\(864\) 0 0
\(865\) −19.1910 −0.652514
\(866\) 0 0
\(867\) −7.19262 −0.244274
\(868\) 0 0
\(869\) −26.8155 −0.909652
\(870\) 0 0
\(871\) −0.496483 −0.0168227
\(872\) 0 0
\(873\) 24.1610 0.817726
\(874\) 0 0
\(875\) −13.0750 −0.442014
\(876\) 0 0
\(877\) 7.09812 0.239687 0.119843 0.992793i \(-0.461761\pi\)
0.119843 + 0.992793i \(0.461761\pi\)
\(878\) 0 0
\(879\) −9.54018 −0.321782
\(880\) 0 0
\(881\) −2.63729 −0.0888526 −0.0444263 0.999013i \(-0.514146\pi\)
−0.0444263 + 0.999013i \(0.514146\pi\)
\(882\) 0 0
\(883\) −6.24123 −0.210034 −0.105017 0.994470i \(-0.533490\pi\)
−0.105017 + 0.994470i \(0.533490\pi\)
\(884\) 0 0
\(885\) −2.54898 −0.0856832
\(886\) 0 0
\(887\) 24.5186 0.823255 0.411627 0.911352i \(-0.364961\pi\)
0.411627 + 0.911352i \(0.364961\pi\)
\(888\) 0 0
\(889\) −1.62076 −0.0543586
\(890\) 0 0
\(891\) −19.7941 −0.663128
\(892\) 0 0
\(893\) 2.92547 0.0978970
\(894\) 0 0
\(895\) −14.5831 −0.487461
\(896\) 0 0
\(897\) 0.0420399 0.00140367
\(898\) 0 0
\(899\) 64.4923 2.15094
\(900\) 0 0
\(901\) −0.870485 −0.0290001
\(902\) 0 0
\(903\) 1.84491 0.0613946
\(904\) 0 0
\(905\) −19.6800 −0.654185
\(906\) 0 0
\(907\) −12.2547 −0.406911 −0.203456 0.979084i \(-0.565217\pi\)
−0.203456 + 0.979084i \(0.565217\pi\)
\(908\) 0 0
\(909\) −23.7012 −0.786118
\(910\) 0 0
\(911\) −9.26239 −0.306877 −0.153438 0.988158i \(-0.549035\pi\)
−0.153438 + 0.988158i \(0.549035\pi\)
\(912\) 0 0
\(913\) 13.3681 0.442421
\(914\) 0 0
\(915\) −2.22985 −0.0737164
\(916\) 0 0
\(917\) 14.3791 0.474839
\(918\) 0 0
\(919\) −51.4107 −1.69588 −0.847942 0.530090i \(-0.822158\pi\)
−0.847942 + 0.530090i \(0.822158\pi\)
\(920\) 0 0
\(921\) 12.6853 0.417994
\(922\) 0 0
\(923\) −1.23825 −0.0407576
\(924\) 0 0
\(925\) 12.2235 0.401906
\(926\) 0 0
\(927\) 7.90688 0.259696
\(928\) 0 0
\(929\) 1.94174 0.0637065 0.0318532 0.999493i \(-0.489859\pi\)
0.0318532 + 0.999493i \(0.489859\pi\)
\(930\) 0 0
\(931\) 4.87886 0.159898
\(932\) 0 0
\(933\) −5.47567 −0.179265
\(934\) 0 0
\(935\) 2.37950 0.0778180
\(936\) 0 0
\(937\) 33.7004 1.10094 0.550472 0.834854i \(-0.314448\pi\)
0.550472 + 0.834854i \(0.314448\pi\)
\(938\) 0 0
\(939\) 10.9522 0.357411
\(940\) 0 0
\(941\) 19.5026 0.635766 0.317883 0.948130i \(-0.397028\pi\)
0.317883 + 0.948130i \(0.397028\pi\)
\(942\) 0 0
\(943\) −1.05343 −0.0343043
\(944\) 0 0
\(945\) −3.69448 −0.120181
\(946\) 0 0
\(947\) 33.4170 1.08591 0.542954 0.839763i \(-0.317306\pi\)
0.542954 + 0.839763i \(0.317306\pi\)
\(948\) 0 0
\(949\) 0.183038 0.00594168
\(950\) 0 0
\(951\) 6.14280 0.199194
\(952\) 0 0
\(953\) 35.7494 1.15804 0.579019 0.815314i \(-0.303436\pi\)
0.579019 + 0.815314i \(0.303436\pi\)
\(954\) 0 0
\(955\) 15.3465 0.496600
\(956\) 0 0
\(957\) −12.0223 −0.388625
\(958\) 0 0
\(959\) −34.3970 −1.11074
\(960\) 0 0
\(961\) 12.1364 0.391497
\(962\) 0 0
\(963\) 42.3475 1.36463
\(964\) 0 0
\(965\) −2.52509 −0.0812855
\(966\) 0 0
\(967\) −24.9239 −0.801499 −0.400749 0.916188i \(-0.631250\pi\)
−0.400749 + 0.916188i \(0.631250\pi\)
\(968\) 0 0
\(969\) 0.467668 0.0150237
\(970\) 0 0
\(971\) −19.1722 −0.615266 −0.307633 0.951505i \(-0.599537\pi\)
−0.307633 + 0.951505i \(0.599537\pi\)
\(972\) 0 0
\(973\) 0.991585 0.0317887
\(974\) 0 0
\(975\) 0.239560 0.00767205
\(976\) 0 0
\(977\) −15.2149 −0.486768 −0.243384 0.969930i \(-0.578257\pi\)
−0.243384 + 0.969930i \(0.578257\pi\)
\(978\) 0 0
\(979\) 44.9901 1.43789
\(980\) 0 0
\(981\) 41.9575 1.33960
\(982\) 0 0
\(983\) 20.8694 0.665632 0.332816 0.942992i \(-0.392001\pi\)
0.332816 + 0.942992i \(0.392001\pi\)
\(984\) 0 0
\(985\) 7.40425 0.235919
\(986\) 0 0
\(987\) −1.91003 −0.0607970
\(988\) 0 0
\(989\) −1.91833 −0.0609993
\(990\) 0 0
\(991\) 48.6095 1.54413 0.772066 0.635543i \(-0.219224\pi\)
0.772066 + 0.635543i \(0.219224\pi\)
\(992\) 0 0
\(993\) 14.4873 0.459741
\(994\) 0 0
\(995\) 22.6245 0.717244
\(996\) 0 0
\(997\) −38.6835 −1.22512 −0.612559 0.790425i \(-0.709860\pi\)
−0.612559 + 0.790425i \(0.709860\pi\)
\(998\) 0 0
\(999\) 7.57786 0.239753
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 \(a_p\))