Properties

Label 8036.2.a.q.1.4
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 15
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1677830643\)
Analytic rank: \(0\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(1.93225\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.93225 q^{3} -0.475465 q^{5} +0.733587 q^{9} +O(q^{10})\) \(q-1.93225 q^{3} -0.475465 q^{5} +0.733587 q^{9} +0.608408 q^{11} +0.258249 q^{13} +0.918718 q^{15} +6.67585 q^{17} -8.55857 q^{19} -0.540802 q^{23} -4.77393 q^{25} +4.37927 q^{27} +9.17655 q^{29} -3.19512 q^{31} -1.17560 q^{33} +2.11667 q^{37} -0.499002 q^{39} -1.00000 q^{41} -9.45997 q^{43} -0.348795 q^{45} -5.21836 q^{47} -12.8994 q^{51} +11.1314 q^{53} -0.289277 q^{55} +16.5373 q^{57} -6.80041 q^{59} +1.40208 q^{61} -0.122789 q^{65} +15.9998 q^{67} +1.04496 q^{69} +3.72154 q^{71} -9.31128 q^{73} +9.22443 q^{75} +5.46345 q^{79} -10.6626 q^{81} +0.971073 q^{83} -3.17414 q^{85} -17.7314 q^{87} +9.78989 q^{89} +6.17377 q^{93} +4.06930 q^{95} +3.26994 q^{97} +0.446320 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - q^{3} + 3q^{5} + 30q^{9} + O(q^{10}) \) \( 15q - q^{3} + 3q^{5} + 30q^{9} + 9q^{11} + 7q^{13} + 2q^{15} + 3q^{17} + 7q^{19} - q^{23} + 32q^{25} + 11q^{27} + 18q^{29} + 30q^{31} - 16q^{33} + 23q^{37} + 5q^{39} - 15q^{41} + 12q^{43} - 13q^{45} - 16q^{47} + 29q^{51} + 33q^{53} + 37q^{55} + 16q^{57} - 10q^{59} + q^{61} + 16q^{65} + 20q^{67} + 21q^{69} + 5q^{71} - 3q^{73} - 51q^{75} + 25q^{79} + 43q^{81} + 18q^{83} + 36q^{85} - 53q^{87} - 11q^{89} + 65q^{93} - 30q^{95} + 16q^{97} - 18q^{99} + O(q^{100}) \)

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 0
\(3\) −1.93225 −1.11558 −0.557792 0.829981i \(-0.688351\pi\)
−0.557792 + 0.829981i \(0.688351\pi\)
\(4\) 0 0
\(5\) −0.475465 −0.212635 −0.106317 0.994332i \(-0.533906\pi\)
−0.106317 + 0.994332i \(0.533906\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0.733587 0.244529
\(10\) 0 0
\(11\) 0.608408 0.183442 0.0917210 0.995785i \(-0.470763\pi\)
0.0917210 + 0.995785i \(0.470763\pi\)
\(12\) 0 0
\(13\) 0.258249 0.0716255 0.0358127 0.999359i \(-0.488598\pi\)
0.0358127 + 0.999359i \(0.488598\pi\)
\(14\) 0 0
\(15\) 0.918718 0.237212
\(16\) 0 0
\(17\) 6.67585 1.61913 0.809566 0.587029i \(-0.199703\pi\)
0.809566 + 0.587029i \(0.199703\pi\)
\(18\) 0 0
\(19\) −8.55857 −1.96347 −0.981735 0.190252i \(-0.939070\pi\)
−0.981735 + 0.190252i \(0.939070\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.540802 −0.112765 −0.0563825 0.998409i \(-0.517957\pi\)
−0.0563825 + 0.998409i \(0.517957\pi\)
\(24\) 0 0
\(25\) −4.77393 −0.954787
\(26\) 0 0
\(27\) 4.37927 0.842792
\(28\) 0 0
\(29\) 9.17655 1.70404 0.852021 0.523508i \(-0.175377\pi\)
0.852021 + 0.523508i \(0.175377\pi\)
\(30\) 0 0
\(31\) −3.19512 −0.573861 −0.286930 0.957951i \(-0.592635\pi\)
−0.286930 + 0.957951i \(0.592635\pi\)
\(32\) 0 0
\(33\) −1.17560 −0.204645
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.11667 0.347979 0.173989 0.984748i \(-0.444334\pi\)
0.173989 + 0.984748i \(0.444334\pi\)
\(38\) 0 0
\(39\) −0.499002 −0.0799043
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −9.45997 −1.44263 −0.721316 0.692606i \(-0.756462\pi\)
−0.721316 + 0.692606i \(0.756462\pi\)
\(44\) 0 0
\(45\) −0.348795 −0.0519953
\(46\) 0 0
\(47\) −5.21836 −0.761176 −0.380588 0.924745i \(-0.624278\pi\)
−0.380588 + 0.924745i \(0.624278\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −12.8994 −1.80628
\(52\) 0 0
\(53\) 11.1314 1.52901 0.764507 0.644615i \(-0.222982\pi\)
0.764507 + 0.644615i \(0.222982\pi\)
\(54\) 0 0
\(55\) −0.289277 −0.0390061
\(56\) 0 0
\(57\) 16.5373 2.19042
\(58\) 0 0
\(59\) −6.80041 −0.885338 −0.442669 0.896685i \(-0.645968\pi\)
−0.442669 + 0.896685i \(0.645968\pi\)
\(60\) 0 0
\(61\) 1.40208 0.179517 0.0897587 0.995964i \(-0.471390\pi\)
0.0897587 + 0.995964i \(0.471390\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −0.122789 −0.0152301
\(66\) 0 0
\(67\) 15.9998 1.95468 0.977340 0.211674i \(-0.0678915\pi\)
0.977340 + 0.211674i \(0.0678915\pi\)
\(68\) 0 0
\(69\) 1.04496 0.125799
\(70\) 0 0
\(71\) 3.72154 0.441665 0.220833 0.975312i \(-0.429123\pi\)
0.220833 + 0.975312i \(0.429123\pi\)
\(72\) 0 0
\(73\) −9.31128 −1.08980 −0.544902 0.838500i \(-0.683433\pi\)
−0.544902 + 0.838500i \(0.683433\pi\)
\(74\) 0 0
\(75\) 9.22443 1.06515
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 5.46345 0.614686 0.307343 0.951599i \(-0.400560\pi\)
0.307343 + 0.951599i \(0.400560\pi\)
\(80\) 0 0
\(81\) −10.6626 −1.18473
\(82\) 0 0
\(83\) 0.971073 0.106589 0.0532945 0.998579i \(-0.483028\pi\)
0.0532945 + 0.998579i \(0.483028\pi\)
\(84\) 0 0
\(85\) −3.17414 −0.344284
\(86\) 0 0
\(87\) −17.7314 −1.90100
\(88\) 0 0
\(89\) 9.78989 1.03773 0.518863 0.854857i \(-0.326355\pi\)
0.518863 + 0.854857i \(0.326355\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 6.17377 0.640190
\(94\) 0 0
\(95\) 4.06930 0.417502
\(96\) 0 0
\(97\) 3.26994 0.332012 0.166006 0.986125i \(-0.446913\pi\)
0.166006 + 0.986125i \(0.446913\pi\)
\(98\) 0 0
\(99\) 0.446320 0.0448569
\(100\) 0 0
\(101\) −15.3557 −1.52795 −0.763973 0.645248i \(-0.776754\pi\)
−0.763973 + 0.645248i \(0.776754\pi\)
\(102\) 0 0
\(103\) −15.9051 −1.56717 −0.783586 0.621283i \(-0.786612\pi\)
−0.783586 + 0.621283i \(0.786612\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −9.33023 −0.901988 −0.450994 0.892527i \(-0.648930\pi\)
−0.450994 + 0.892527i \(0.648930\pi\)
\(108\) 0 0
\(109\) −13.1284 −1.25747 −0.628736 0.777619i \(-0.716428\pi\)
−0.628736 + 0.777619i \(0.716428\pi\)
\(110\) 0 0
\(111\) −4.08994 −0.388200
\(112\) 0 0
\(113\) −8.66144 −0.814800 −0.407400 0.913250i \(-0.633565\pi\)
−0.407400 + 0.913250i \(0.633565\pi\)
\(114\) 0 0
\(115\) 0.257133 0.0239778
\(116\) 0 0
\(117\) 0.189448 0.0175145
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −10.6298 −0.966349
\(122\) 0 0
\(123\) 1.93225 0.174225
\(124\) 0 0
\(125\) 4.64717 0.415655
\(126\) 0 0
\(127\) 15.3874 1.36541 0.682705 0.730694i \(-0.260803\pi\)
0.682705 + 0.730694i \(0.260803\pi\)
\(128\) 0 0
\(129\) 18.2790 1.60938
\(130\) 0 0
\(131\) −7.68476 −0.671421 −0.335710 0.941965i \(-0.608976\pi\)
−0.335710 + 0.941965i \(0.608976\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −2.08219 −0.179207
\(136\) 0 0
\(137\) 19.5241 1.66805 0.834026 0.551725i \(-0.186030\pi\)
0.834026 + 0.551725i \(0.186030\pi\)
\(138\) 0 0
\(139\) −12.3761 −1.04972 −0.524862 0.851188i \(-0.675883\pi\)
−0.524862 + 0.851188i \(0.675883\pi\)
\(140\) 0 0
\(141\) 10.0832 0.849157
\(142\) 0 0
\(143\) 0.157121 0.0131391
\(144\) 0 0
\(145\) −4.36313 −0.362338
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −5.81485 −0.476371 −0.238186 0.971220i \(-0.576553\pi\)
−0.238186 + 0.971220i \(0.576553\pi\)
\(150\) 0 0
\(151\) 5.96305 0.485266 0.242633 0.970118i \(-0.421989\pi\)
0.242633 + 0.970118i \(0.421989\pi\)
\(152\) 0 0
\(153\) 4.89732 0.395925
\(154\) 0 0
\(155\) 1.51917 0.122023
\(156\) 0 0
\(157\) −15.8012 −1.26108 −0.630538 0.776159i \(-0.717166\pi\)
−0.630538 + 0.776159i \(0.717166\pi\)
\(158\) 0 0
\(159\) −21.5086 −1.70575
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 17.1423 1.34269 0.671345 0.741145i \(-0.265717\pi\)
0.671345 + 0.741145i \(0.265717\pi\)
\(164\) 0 0
\(165\) 0.558956 0.0435146
\(166\) 0 0
\(167\) 14.3673 1.11178 0.555888 0.831257i \(-0.312378\pi\)
0.555888 + 0.831257i \(0.312378\pi\)
\(168\) 0 0
\(169\) −12.9333 −0.994870
\(170\) 0 0
\(171\) −6.27845 −0.480125
\(172\) 0 0
\(173\) 25.2690 1.92116 0.960582 0.277996i \(-0.0896701\pi\)
0.960582 + 0.277996i \(0.0896701\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 13.1401 0.987670
\(178\) 0 0
\(179\) 20.2626 1.51450 0.757250 0.653125i \(-0.226543\pi\)
0.757250 + 0.653125i \(0.226543\pi\)
\(180\) 0 0
\(181\) 8.26666 0.614456 0.307228 0.951636i \(-0.400599\pi\)
0.307228 + 0.951636i \(0.400599\pi\)
\(182\) 0 0
\(183\) −2.70916 −0.200267
\(184\) 0 0
\(185\) −1.00640 −0.0739923
\(186\) 0 0
\(187\) 4.06164 0.297017
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 21.2773 1.53957 0.769786 0.638302i \(-0.220363\pi\)
0.769786 + 0.638302i \(0.220363\pi\)
\(192\) 0 0
\(193\) −10.1778 −0.732615 −0.366307 0.930494i \(-0.619378\pi\)
−0.366307 + 0.930494i \(0.619378\pi\)
\(194\) 0 0
\(195\) 0.237258 0.0169904
\(196\) 0 0
\(197\) 15.0683 1.07357 0.536787 0.843718i \(-0.319638\pi\)
0.536787 + 0.843718i \(0.319638\pi\)
\(198\) 0 0
\(199\) 4.57936 0.324622 0.162311 0.986740i \(-0.448105\pi\)
0.162311 + 0.986740i \(0.448105\pi\)
\(200\) 0 0
\(201\) −30.9155 −2.18061
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0.475465 0.0332080
\(206\) 0 0
\(207\) −0.396725 −0.0275743
\(208\) 0 0
\(209\) −5.20711 −0.360183
\(210\) 0 0
\(211\) −25.2177 −1.73606 −0.868028 0.496515i \(-0.834613\pi\)
−0.868028 + 0.496515i \(0.834613\pi\)
\(212\) 0 0
\(213\) −7.19094 −0.492715
\(214\) 0 0
\(215\) 4.49789 0.306753
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 17.9917 1.21577
\(220\) 0 0
\(221\) 1.72403 0.115971
\(222\) 0 0
\(223\) −9.02063 −0.604066 −0.302033 0.953298i \(-0.597665\pi\)
−0.302033 + 0.953298i \(0.597665\pi\)
\(224\) 0 0
\(225\) −3.50209 −0.233473
\(226\) 0 0
\(227\) 17.7610 1.17884 0.589421 0.807826i \(-0.299356\pi\)
0.589421 + 0.807826i \(0.299356\pi\)
\(228\) 0 0
\(229\) 21.5866 1.42648 0.713242 0.700918i \(-0.247226\pi\)
0.713242 + 0.700918i \(0.247226\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −6.03999 −0.395693 −0.197846 0.980233i \(-0.563395\pi\)
−0.197846 + 0.980233i \(0.563395\pi\)
\(234\) 0 0
\(235\) 2.48115 0.161852
\(236\) 0 0
\(237\) −10.5567 −0.685734
\(238\) 0 0
\(239\) −7.84860 −0.507683 −0.253842 0.967246i \(-0.581694\pi\)
−0.253842 + 0.967246i \(0.581694\pi\)
\(240\) 0 0
\(241\) −26.3385 −1.69661 −0.848306 0.529506i \(-0.822377\pi\)
−0.848306 + 0.529506i \(0.822377\pi\)
\(242\) 0 0
\(243\) 7.46500 0.478880
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −2.21024 −0.140634
\(248\) 0 0
\(249\) −1.87635 −0.118909
\(250\) 0 0
\(251\) −11.7507 −0.741699 −0.370849 0.928693i \(-0.620933\pi\)
−0.370849 + 0.928693i \(0.620933\pi\)
\(252\) 0 0
\(253\) −0.329029 −0.0206858
\(254\) 0 0
\(255\) 6.13322 0.384077
\(256\) 0 0
\(257\) −19.0458 −1.18805 −0.594023 0.804448i \(-0.702461\pi\)
−0.594023 + 0.804448i \(0.702461\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 6.73179 0.416688
\(262\) 0 0
\(263\) −11.7032 −0.721651 −0.360825 0.932633i \(-0.617505\pi\)
−0.360825 + 0.932633i \(0.617505\pi\)
\(264\) 0 0
\(265\) −5.29259 −0.325121
\(266\) 0 0
\(267\) −18.9165 −1.15767
\(268\) 0 0
\(269\) 25.1797 1.53524 0.767618 0.640908i \(-0.221442\pi\)
0.767618 + 0.640908i \(0.221442\pi\)
\(270\) 0 0
\(271\) 13.2398 0.804262 0.402131 0.915582i \(-0.368270\pi\)
0.402131 + 0.915582i \(0.368270\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.90450 −0.175148
\(276\) 0 0
\(277\) 2.96026 0.177865 0.0889323 0.996038i \(-0.471655\pi\)
0.0889323 + 0.996038i \(0.471655\pi\)
\(278\) 0 0
\(279\) −2.34390 −0.140326
\(280\) 0 0
\(281\) 11.8626 0.707666 0.353833 0.935309i \(-0.384878\pi\)
0.353833 + 0.935309i \(0.384878\pi\)
\(282\) 0 0
\(283\) −24.4471 −1.45323 −0.726615 0.687044i \(-0.758908\pi\)
−0.726615 + 0.687044i \(0.758908\pi\)
\(284\) 0 0
\(285\) −7.86291 −0.465759
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 27.5670 1.62159
\(290\) 0 0
\(291\) −6.31834 −0.370388
\(292\) 0 0
\(293\) 31.9974 1.86931 0.934653 0.355561i \(-0.115710\pi\)
0.934653 + 0.355561i \(0.115710\pi\)
\(294\) 0 0
\(295\) 3.23336 0.188254
\(296\) 0 0
\(297\) 2.66439 0.154603
\(298\) 0 0
\(299\) −0.139662 −0.00807685
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 29.6710 1.70455
\(304\) 0 0
\(305\) −0.666639 −0.0381716
\(306\) 0 0
\(307\) −1.37931 −0.0787211 −0.0393606 0.999225i \(-0.512532\pi\)
−0.0393606 + 0.999225i \(0.512532\pi\)
\(308\) 0 0
\(309\) 30.7326 1.74831
\(310\) 0 0
\(311\) 6.57209 0.372669 0.186335 0.982486i \(-0.440339\pi\)
0.186335 + 0.982486i \(0.440339\pi\)
\(312\) 0 0
\(313\) 10.2077 0.576976 0.288488 0.957484i \(-0.406847\pi\)
0.288488 + 0.957484i \(0.406847\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −11.3693 −0.638565 −0.319282 0.947660i \(-0.603442\pi\)
−0.319282 + 0.947660i \(0.603442\pi\)
\(318\) 0 0
\(319\) 5.58309 0.312593
\(320\) 0 0
\(321\) 18.0283 1.00624
\(322\) 0 0
\(323\) −57.1357 −3.17912
\(324\) 0 0
\(325\) −1.23286 −0.0683870
\(326\) 0 0
\(327\) 25.3673 1.40282
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 19.3419 1.06313 0.531564 0.847018i \(-0.321605\pi\)
0.531564 + 0.847018i \(0.321605\pi\)
\(332\) 0 0
\(333\) 1.55276 0.0850909
\(334\) 0 0
\(335\) −7.60733 −0.415633
\(336\) 0 0
\(337\) 13.0087 0.708629 0.354315 0.935126i \(-0.384714\pi\)
0.354315 + 0.935126i \(0.384714\pi\)
\(338\) 0 0
\(339\) 16.7361 0.908978
\(340\) 0 0
\(341\) −1.94394 −0.105270
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −0.496845 −0.0267492
\(346\) 0 0
\(347\) 9.25837 0.497015 0.248508 0.968630i \(-0.420060\pi\)
0.248508 + 0.968630i \(0.420060\pi\)
\(348\) 0 0
\(349\) 3.45465 0.184923 0.0924615 0.995716i \(-0.470527\pi\)
0.0924615 + 0.995716i \(0.470527\pi\)
\(350\) 0 0
\(351\) 1.13094 0.0603653
\(352\) 0 0
\(353\) 7.57050 0.402937 0.201468 0.979495i \(-0.435429\pi\)
0.201468 + 0.979495i \(0.435429\pi\)
\(354\) 0 0
\(355\) −1.76946 −0.0939133
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −15.2984 −0.807419 −0.403710 0.914887i \(-0.632279\pi\)
−0.403710 + 0.914887i \(0.632279\pi\)
\(360\) 0 0
\(361\) 54.2491 2.85522
\(362\) 0 0
\(363\) 20.5395 1.07804
\(364\) 0 0
\(365\) 4.42719 0.231730
\(366\) 0 0
\(367\) −11.1193 −0.580421 −0.290211 0.956963i \(-0.593725\pi\)
−0.290211 + 0.956963i \(0.593725\pi\)
\(368\) 0 0
\(369\) −0.733587 −0.0381890
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 30.7948 1.59449 0.797247 0.603653i \(-0.206289\pi\)
0.797247 + 0.603653i \(0.206289\pi\)
\(374\) 0 0
\(375\) −8.97949 −0.463699
\(376\) 0 0
\(377\) 2.36984 0.122053
\(378\) 0 0
\(379\) 15.7083 0.806881 0.403441 0.915006i \(-0.367814\pi\)
0.403441 + 0.915006i \(0.367814\pi\)
\(380\) 0 0
\(381\) −29.7323 −1.52323
\(382\) 0 0
\(383\) 0.295229 0.0150855 0.00754274 0.999972i \(-0.497599\pi\)
0.00754274 + 0.999972i \(0.497599\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −6.93971 −0.352765
\(388\) 0 0
\(389\) 6.05446 0.306974 0.153487 0.988151i \(-0.450950\pi\)
0.153487 + 0.988151i \(0.450950\pi\)
\(390\) 0 0
\(391\) −3.61031 −0.182581
\(392\) 0 0
\(393\) 14.8489 0.749027
\(394\) 0 0
\(395\) −2.59768 −0.130703
\(396\) 0 0
\(397\) 23.1683 1.16278 0.581392 0.813623i \(-0.302508\pi\)
0.581392 + 0.813623i \(0.302508\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 35.4197 1.76878 0.884388 0.466752i \(-0.154576\pi\)
0.884388 + 0.466752i \(0.154576\pi\)
\(402\) 0 0
\(403\) −0.825137 −0.0411030
\(404\) 0 0
\(405\) 5.06970 0.251916
\(406\) 0 0
\(407\) 1.28780 0.0638339
\(408\) 0 0
\(409\) −20.5932 −1.01827 −0.509135 0.860687i \(-0.670035\pi\)
−0.509135 + 0.860687i \(0.670035\pi\)
\(410\) 0 0
\(411\) −37.7253 −1.86085
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −0.461712 −0.0226645
\(416\) 0 0
\(417\) 23.9136 1.17105
\(418\) 0 0
\(419\) 37.3854 1.82640 0.913198 0.407517i \(-0.133605\pi\)
0.913198 + 0.407517i \(0.133605\pi\)
\(420\) 0 0
\(421\) 9.03447 0.440313 0.220156 0.975465i \(-0.429343\pi\)
0.220156 + 0.975465i \(0.429343\pi\)
\(422\) 0 0
\(423\) −3.82812 −0.186130
\(424\) 0 0
\(425\) −31.8701 −1.54593
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −0.303597 −0.0146578
\(430\) 0 0
\(431\) 5.86857 0.282679 0.141340 0.989961i \(-0.454859\pi\)
0.141340 + 0.989961i \(0.454859\pi\)
\(432\) 0 0
\(433\) 27.3406 1.31391 0.656953 0.753931i \(-0.271845\pi\)
0.656953 + 0.753931i \(0.271845\pi\)
\(434\) 0 0
\(435\) 8.43066 0.404219
\(436\) 0 0
\(437\) 4.62849 0.221411
\(438\) 0 0
\(439\) 30.0278 1.43315 0.716574 0.697512i \(-0.245709\pi\)
0.716574 + 0.697512i \(0.245709\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −7.60397 −0.361276 −0.180638 0.983550i \(-0.557816\pi\)
−0.180638 + 0.983550i \(0.557816\pi\)
\(444\) 0 0
\(445\) −4.65476 −0.220657
\(446\) 0 0
\(447\) 11.2357 0.531432
\(448\) 0 0
\(449\) 0.589677 0.0278286 0.0139143 0.999903i \(-0.495571\pi\)
0.0139143 + 0.999903i \(0.495571\pi\)
\(450\) 0 0
\(451\) −0.608408 −0.0286488
\(452\) 0 0
\(453\) −11.5221 −0.541356
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1.29570 0.0606101 0.0303051 0.999541i \(-0.490352\pi\)
0.0303051 + 0.999541i \(0.490352\pi\)
\(458\) 0 0
\(459\) 29.2354 1.36459
\(460\) 0 0
\(461\) 22.0668 1.02775 0.513876 0.857864i \(-0.328209\pi\)
0.513876 + 0.857864i \(0.328209\pi\)
\(462\) 0 0
\(463\) −20.1079 −0.934493 −0.467246 0.884127i \(-0.654754\pi\)
−0.467246 + 0.884127i \(0.654754\pi\)
\(464\) 0 0
\(465\) −2.93541 −0.136127
\(466\) 0 0
\(467\) 29.8752 1.38246 0.691230 0.722635i \(-0.257069\pi\)
0.691230 + 0.722635i \(0.257069\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 30.5319 1.40684
\(472\) 0 0
\(473\) −5.75552 −0.264639
\(474\) 0 0
\(475\) 40.8580 1.87470
\(476\) 0 0
\(477\) 8.16585 0.373888
\(478\) 0 0
\(479\) −38.5445 −1.76115 −0.880573 0.473911i \(-0.842842\pi\)
−0.880573 + 0.473911i \(0.842842\pi\)
\(480\) 0 0
\(481\) 0.546629 0.0249241
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.55474 −0.0705973
\(486\) 0 0
\(487\) −18.7629 −0.850226 −0.425113 0.905140i \(-0.639766\pi\)
−0.425113 + 0.905140i \(0.639766\pi\)
\(488\) 0 0
\(489\) −33.1232 −1.49788
\(490\) 0 0
\(491\) −1.61032 −0.0726725 −0.0363363 0.999340i \(-0.511569\pi\)
−0.0363363 + 0.999340i \(0.511569\pi\)
\(492\) 0 0
\(493\) 61.2613 2.75907
\(494\) 0 0
\(495\) −0.212210 −0.00953813
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −4.49401 −0.201179 −0.100590 0.994928i \(-0.532073\pi\)
−0.100590 + 0.994928i \(0.532073\pi\)
\(500\) 0 0
\(501\) −27.7613 −1.24028
\(502\) 0 0
\(503\) −0.671350 −0.0299340 −0.0149670 0.999888i \(-0.504764\pi\)
−0.0149670 + 0.999888i \(0.504764\pi\)
\(504\) 0 0
\(505\) 7.30109 0.324894
\(506\) 0 0
\(507\) 24.9904 1.10986
\(508\) 0 0
\(509\) 22.5947 1.00149 0.500745 0.865595i \(-0.333059\pi\)
0.500745 + 0.865595i \(0.333059\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −37.4803 −1.65480
\(514\) 0 0
\(515\) 7.56231 0.333235
\(516\) 0 0
\(517\) −3.17490 −0.139632
\(518\) 0 0
\(519\) −48.8260 −2.14322
\(520\) 0 0
\(521\) −1.35329 −0.0592888 −0.0296444 0.999561i \(-0.509437\pi\)
−0.0296444 + 0.999561i \(0.509437\pi\)
\(522\) 0 0
\(523\) −16.5312 −0.722858 −0.361429 0.932400i \(-0.617711\pi\)
−0.361429 + 0.932400i \(0.617711\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −21.3301 −0.929156
\(528\) 0 0
\(529\) −22.7075 −0.987284
\(530\) 0 0
\(531\) −4.98869 −0.216491
\(532\) 0 0
\(533\) −0.258249 −0.0111860
\(534\) 0 0
\(535\) 4.43620 0.191794
\(536\) 0 0
\(537\) −39.1524 −1.68955
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −6.33057 −0.272172 −0.136086 0.990697i \(-0.543452\pi\)
−0.136086 + 0.990697i \(0.543452\pi\)
\(542\) 0 0
\(543\) −15.9732 −0.685477
\(544\) 0 0
\(545\) 6.24210 0.267382
\(546\) 0 0
\(547\) 28.5272 1.21973 0.609867 0.792503i \(-0.291223\pi\)
0.609867 + 0.792503i \(0.291223\pi\)
\(548\) 0 0
\(549\) 1.02854 0.0438972
\(550\) 0 0
\(551\) −78.5381 −3.34584
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 1.94462 0.0825447
\(556\) 0 0
\(557\) −39.1109 −1.65718 −0.828591 0.559855i \(-0.810857\pi\)
−0.828591 + 0.559855i \(0.810857\pi\)
\(558\) 0 0
\(559\) −2.44303 −0.103329
\(560\) 0 0
\(561\) −7.84811 −0.331347
\(562\) 0 0
\(563\) 29.1984 1.23057 0.615284 0.788306i \(-0.289042\pi\)
0.615284 + 0.788306i \(0.289042\pi\)
\(564\) 0 0
\(565\) 4.11822 0.173255
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 13.3981 0.561679 0.280840 0.959755i \(-0.409387\pi\)
0.280840 + 0.959755i \(0.409387\pi\)
\(570\) 0 0
\(571\) −2.05488 −0.0859941 −0.0429970 0.999075i \(-0.513691\pi\)
−0.0429970 + 0.999075i \(0.513691\pi\)
\(572\) 0 0
\(573\) −41.1131 −1.71752
\(574\) 0 0
\(575\) 2.58175 0.107667
\(576\) 0 0
\(577\) 20.0423 0.834372 0.417186 0.908821i \(-0.363016\pi\)
0.417186 + 0.908821i \(0.363016\pi\)
\(578\) 0 0
\(579\) 19.6661 0.817294
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 6.77243 0.280486
\(584\) 0 0
\(585\) −0.0900761 −0.00372419
\(586\) 0 0
\(587\) 17.2770 0.713098 0.356549 0.934277i \(-0.383953\pi\)
0.356549 + 0.934277i \(0.383953\pi\)
\(588\) 0 0
\(589\) 27.3457 1.12676
\(590\) 0 0
\(591\) −29.1158 −1.19766
\(592\) 0 0
\(593\) −4.43785 −0.182241 −0.0911203 0.995840i \(-0.529045\pi\)
−0.0911203 + 0.995840i \(0.529045\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −8.84846 −0.362144
\(598\) 0 0
\(599\) 36.5564 1.49366 0.746828 0.665017i \(-0.231576\pi\)
0.746828 + 0.665017i \(0.231576\pi\)
\(600\) 0 0
\(601\) 12.7836 0.521453 0.260726 0.965413i \(-0.416038\pi\)
0.260726 + 0.965413i \(0.416038\pi\)
\(602\) 0 0
\(603\) 11.7372 0.477976
\(604\) 0 0
\(605\) 5.05412 0.205479
\(606\) 0 0
\(607\) −15.7778 −0.640401 −0.320200 0.947350i \(-0.603750\pi\)
−0.320200 + 0.947350i \(0.603750\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.34764 −0.0545196
\(612\) 0 0
\(613\) 42.3571 1.71079 0.855394 0.517978i \(-0.173315\pi\)
0.855394 + 0.517978i \(0.173315\pi\)
\(614\) 0 0
\(615\) −0.918718 −0.0370463
\(616\) 0 0
\(617\) −6.74340 −0.271479 −0.135739 0.990745i \(-0.543341\pi\)
−0.135739 + 0.990745i \(0.543341\pi\)
\(618\) 0 0
\(619\) 2.13188 0.0856874 0.0428437 0.999082i \(-0.486358\pi\)
0.0428437 + 0.999082i \(0.486358\pi\)
\(620\) 0 0
\(621\) −2.36832 −0.0950374
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 21.6601 0.866404
\(626\) 0 0
\(627\) 10.0614 0.401815
\(628\) 0 0
\(629\) 14.1306 0.563424
\(630\) 0 0
\(631\) 28.8631 1.14902 0.574511 0.818497i \(-0.305192\pi\)
0.574511 + 0.818497i \(0.305192\pi\)
\(632\) 0 0
\(633\) 48.7268 1.93672
\(634\) 0 0
\(635\) −7.31617 −0.290333
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 2.73007 0.108000
\(640\) 0 0
\(641\) −19.1831 −0.757685 −0.378843 0.925461i \(-0.623678\pi\)
−0.378843 + 0.925461i \(0.623678\pi\)
\(642\) 0 0
\(643\) 32.3924 1.27743 0.638716 0.769442i \(-0.279466\pi\)
0.638716 + 0.769442i \(0.279466\pi\)
\(644\) 0 0
\(645\) −8.69104 −0.342209
\(646\) 0 0
\(647\) 35.4947 1.39544 0.697719 0.716371i \(-0.254198\pi\)
0.697719 + 0.716371i \(0.254198\pi\)
\(648\) 0 0
\(649\) −4.13743 −0.162408
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 39.0785 1.52926 0.764630 0.644469i \(-0.222922\pi\)
0.764630 + 0.644469i \(0.222922\pi\)
\(654\) 0 0
\(655\) 3.65384 0.142767
\(656\) 0 0
\(657\) −6.83063 −0.266488
\(658\) 0 0
\(659\) 19.6445 0.765242 0.382621 0.923905i \(-0.375022\pi\)
0.382621 + 0.923905i \(0.375022\pi\)
\(660\) 0 0
\(661\) 11.5191 0.448041 0.224020 0.974584i \(-0.428082\pi\)
0.224020 + 0.974584i \(0.428082\pi\)
\(662\) 0 0
\(663\) −3.33126 −0.129376
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −4.96269 −0.192156
\(668\) 0 0
\(669\) 17.4301 0.673887
\(670\) 0 0
\(671\) 0.853035 0.0329310
\(672\) 0 0
\(673\) 16.9330 0.652719 0.326359 0.945246i \(-0.394178\pi\)
0.326359 + 0.945246i \(0.394178\pi\)
\(674\) 0 0
\(675\) −20.9064 −0.804686
\(676\) 0 0
\(677\) −26.3909 −1.01429 −0.507143 0.861862i \(-0.669298\pi\)
−0.507143 + 0.861862i \(0.669298\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −34.3188 −1.31510
\(682\) 0 0
\(683\) −26.8163 −1.02610 −0.513049 0.858359i \(-0.671484\pi\)
−0.513049 + 0.858359i \(0.671484\pi\)
\(684\) 0 0
\(685\) −9.28301 −0.354686
\(686\) 0 0
\(687\) −41.7107 −1.59136
\(688\) 0 0
\(689\) 2.87467 0.109516
\(690\) 0 0
\(691\) 30.1588 1.14730 0.573648 0.819102i \(-0.305528\pi\)
0.573648 + 0.819102i \(0.305528\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 5.88439 0.223207
\(696\) 0 0
\(697\) −6.67585 −0.252866
\(698\) 0 0
\(699\) 11.6708 0.441429
\(700\) 0 0
\(701\) −18.1146 −0.684178 −0.342089 0.939668i \(-0.611134\pi\)
−0.342089 + 0.939668i \(0.611134\pi\)
\(702\) 0 0
\(703\) −18.1157 −0.683246
\(704\) 0 0
\(705\) −4.79420 −0.180560
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 37.7306 1.41700 0.708501 0.705709i \(-0.249372\pi\)
0.708501 + 0.705709i \(0.249372\pi\)
\(710\) 0 0
\(711\) 4.00791 0.150308
\(712\) 0 0
\(713\) 1.72793 0.0647114
\(714\) 0 0
\(715\) −0.0747056 −0.00279383
\(716\) 0 0
\(717\) 15.1654 0.566364
\(718\) 0 0
\(719\) −27.6396 −1.03078 −0.515391 0.856955i \(-0.672353\pi\)
−0.515391 + 0.856955i \(0.672353\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 50.8926 1.89271
\(724\) 0 0
\(725\) −43.8082 −1.62700
\(726\) 0 0
\(727\) 36.3955 1.34983 0.674917 0.737894i \(-0.264180\pi\)
0.674917 + 0.737894i \(0.264180\pi\)
\(728\) 0 0
\(729\) 17.5636 0.650504
\(730\) 0 0
\(731\) −63.1533 −2.33581
\(732\) 0 0
\(733\) 18.5815 0.686323 0.343161 0.939276i \(-0.388502\pi\)
0.343161 + 0.939276i \(0.388502\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 9.73438 0.358571
\(738\) 0 0
\(739\) −19.9347 −0.733309 −0.366654 0.930357i \(-0.619497\pi\)
−0.366654 + 0.930357i \(0.619497\pi\)
\(740\) 0 0
\(741\) 4.27074 0.156890
\(742\) 0 0
\(743\) −6.00507 −0.220305 −0.110152 0.993915i \(-0.535134\pi\)
−0.110152 + 0.993915i \(0.535134\pi\)
\(744\) 0 0
\(745\) 2.76476 0.101293
\(746\) 0 0
\(747\) 0.712366 0.0260641
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 15.2815 0.557632 0.278816 0.960345i \(-0.410058\pi\)
0.278816 + 0.960345i \(0.410058\pi\)
\(752\) 0 0
\(753\) 22.7053 0.827428
\(754\) 0 0
\(755\) −2.83523 −0.103184
\(756\) 0 0
\(757\) −34.8279 −1.26584 −0.632921 0.774217i \(-0.718144\pi\)
−0.632921 + 0.774217i \(0.718144\pi\)
\(758\) 0 0
\(759\) 0.635765 0.0230768
\(760\) 0 0
\(761\) −24.2028 −0.877350 −0.438675 0.898646i \(-0.644552\pi\)
−0.438675 + 0.898646i \(0.644552\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −2.32851 −0.0841873
\(766\) 0 0
\(767\) −1.75620 −0.0634128
\(768\) 0 0
\(769\) −8.20909 −0.296027 −0.148014 0.988985i \(-0.547288\pi\)
−0.148014 + 0.988985i \(0.547288\pi\)
\(770\) 0 0
\(771\) 36.8013 1.32537
\(772\) 0 0
\(773\) −6.17621 −0.222143 −0.111071 0.993812i \(-0.535428\pi\)
−0.111071 + 0.993812i \(0.535428\pi\)
\(774\) 0 0
\(775\) 15.2533 0.547914
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 8.55857 0.306643
\(780\) 0 0
\(781\) 2.26421 0.0810199
\(782\) 0 0
\(783\) 40.1866 1.43615
\(784\) 0 0
\(785\) 7.51294 0.268148
\(786\) 0 0
\(787\) −22.0855 −0.787262 −0.393631 0.919269i \(-0.628781\pi\)
−0.393631 + 0.919269i \(0.628781\pi\)
\(788\) 0 0
\(789\) 22.6135 0.805062
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0.362085 0.0128580
\(794\) 0 0
\(795\) 10.2266 0.362701
\(796\) 0 0
\(797\) 27.3116 0.967425 0.483713 0.875227i \(-0.339288\pi\)
0.483713 + 0.875227i \(0.339288\pi\)
\(798\) 0 0
\(799\) −34.8370 −1.23245
\(800\) 0 0
\(801\) 7.18174 0.253754
\(802\) 0 0
\(803\) −5.66506 −0.199916
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −48.6535 −1.71269
\(808\) 0 0
\(809\) 11.5846 0.407294 0.203647 0.979044i \(-0.434721\pi\)
0.203647 + 0.979044i \(0.434721\pi\)
\(810\) 0 0
\(811\) −34.9836 −1.22844 −0.614221 0.789134i \(-0.710530\pi\)
−0.614221 + 0.789134i \(0.710530\pi\)
\(812\) 0 0
\(813\) −25.5826 −0.897222
\(814\) 0 0
\(815\) −8.15058 −0.285502
\(816\) 0 0
\(817\) 80.9638 2.83256
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 23.3594 0.815249 0.407625 0.913150i \(-0.366357\pi\)
0.407625 + 0.913150i \(0.366357\pi\)
\(822\) 0 0
\(823\) 5.52046 0.192431 0.0962156 0.995361i \(-0.469326\pi\)
0.0962156 + 0.995361i \(0.469326\pi\)
\(824\) 0 0
\(825\) 5.61222 0.195392
\(826\) 0 0
\(827\) −33.6872 −1.17142 −0.585710 0.810521i \(-0.699184\pi\)
−0.585710 + 0.810521i \(0.699184\pi\)
\(828\) 0 0
\(829\) 20.9791 0.728635 0.364318 0.931275i \(-0.381302\pi\)
0.364318 + 0.931275i \(0.381302\pi\)
\(830\) 0 0
\(831\) −5.71995 −0.198423
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −6.83117 −0.236402
\(836\) 0 0
\(837\) −13.9923 −0.483645
\(838\) 0 0
\(839\) 42.6347 1.47191 0.735957 0.677029i \(-0.236733\pi\)
0.735957 + 0.677029i \(0.236733\pi\)
\(840\) 0 0
\(841\) 55.2090 1.90376
\(842\) 0 0
\(843\) −22.9216 −0.789461
\(844\) 0 0
\(845\) 6.14934 0.211544
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 47.2379 1.62120
\(850\) 0 0
\(851\) −1.14470 −0.0392398
\(852\) 0 0
\(853\) −5.48928 −0.187949 −0.0939746 0.995575i \(-0.529957\pi\)
−0.0939746 + 0.995575i \(0.529957\pi\)
\(854\) 0 0
\(855\) 2.98519 0.102091
\(856\) 0 0
\(857\) 30.7723 1.05116 0.525581 0.850743i \(-0.323848\pi\)
0.525581 + 0.850743i \(0.323848\pi\)
\(858\) 0 0
\(859\) 12.1640 0.415030 0.207515 0.978232i \(-0.433462\pi\)
0.207515 + 0.978232i \(0.433462\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −0.631149 −0.0214846 −0.0107423 0.999942i \(-0.503419\pi\)
−0.0107423 + 0.999942i \(0.503419\pi\)
\(864\) 0 0
\(865\) −12.0145 −0.408506
\(866\) 0 0
\(867\) −53.2663 −1.80902
\(868\) 0 0
\(869\) 3.32401 0.112759
\(870\) 0 0
\(871\) 4.13192 0.140005
\(872\) 0 0
\(873\) 2.39879 0.0811866
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 6.79128 0.229325 0.114663 0.993404i \(-0.463421\pi\)
0.114663 + 0.993404i \(0.463421\pi\)
\(878\) 0 0
\(879\) −61.8269 −2.08537
\(880\) 0 0
\(881\) −37.5322 −1.26449 −0.632247 0.774767i \(-0.717867\pi\)
−0.632247 + 0.774767i \(0.717867\pi\)
\(882\) 0 0
\(883\) 20.0969 0.676313 0.338157 0.941090i \(-0.390197\pi\)
0.338157 + 0.941090i \(0.390197\pi\)
\(884\) 0 0
\(885\) −6.24766 −0.210013
\(886\) 0 0
\(887\) −23.9581 −0.804433 −0.402217 0.915544i \(-0.631760\pi\)
−0.402217 + 0.915544i \(0.631760\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −6.48722 −0.217330
\(892\) 0 0
\(893\) 44.6617 1.49455
\(894\) 0 0
\(895\) −9.63418 −0.322035
\(896\) 0 0
\(897\) 0.269861 0.00901041
\(898\) 0 0
\(899\) −29.3202 −0.977882
\(900\) 0 0
\(901\) 74.3115 2.47568
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −3.93051 −0.130655
\(906\) 0 0
\(907\) 13.8339 0.459346 0.229673 0.973268i \(-0.426234\pi\)
0.229673 + 0.973268i \(0.426234\pi\)
\(908\) 0 0
\(909\) −11.2647 −0.373627
\(910\) 0 0
\(911\) 11.1585 0.369697 0.184849 0.982767i \(-0.440820\pi\)
0.184849 + 0.982767i \(0.440820\pi\)
\(912\) 0 0
\(913\) 0.590809 0.0195529
\(914\) 0 0
\(915\) 1.28811 0.0425837
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −31.9623 −1.05434 −0.527169 0.849761i \(-0.676746\pi\)
−0.527169 + 0.849761i \(0.676746\pi\)
\(920\) 0 0
\(921\) 2.66516 0.0878201
\(922\) 0 0
\(923\) 0.961084 0.0316345
\(924\) 0 0
\(925\) −10.1049 −0.332245
\(926\) 0 0
\(927\) −11.6677 −0.383219
\(928\) 0 0
\(929\) −21.0007 −0.689011 −0.344505 0.938784i \(-0.611953\pi\)
−0.344505 + 0.938784i \(0.611953\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −12.6989 −0.415744
\(934\) 0 0
\(935\) −1.93117 −0.0631561
\(936\) 0 0
\(937\) 14.6936 0.480019 0.240009 0.970771i \(-0.422850\pi\)
0.240009 + 0.970771i \(0.422850\pi\)
\(938\) 0 0
\(939\) −19.7239 −0.643666
\(940\) 0 0
\(941\) 15.2667 0.497680 0.248840 0.968545i \(-0.419951\pi\)
0.248840 + 0.968545i \(0.419951\pi\)
\(942\) 0 0
\(943\) 0.540802 0.0176109
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −21.8411 −0.709740 −0.354870 0.934916i \(-0.615475\pi\)
−0.354870 + 0.934916i \(0.615475\pi\)
\(948\) 0 0
\(949\) −2.40463 −0.0780576
\(950\) 0 0
\(951\) 21.9684 0.712373
\(952\) 0 0
\(953\) −48.7302 −1.57853 −0.789264 0.614055i \(-0.789537\pi\)
−0.789264 + 0.614055i \(0.789537\pi\)
\(954\) 0 0
\(955\) −10.1166 −0.327366
\(956\) 0 0
\(957\) −10.7879 −0.348724
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −20.7912 −0.670684
\(962\) 0 0
\(963\) −6.84454 −0.220562
\(964\) 0 0
\(965\) 4.83920 0.155779
\(966\) 0 0
\(967\) −25.1717 −0.809467 −0.404734 0.914435i \(-0.632636\pi\)
−0.404734 + 0.914435i \(0.632636\pi\)
\(968\) 0 0
\(969\) 110.401 3.54658
\(970\) 0 0
\(971\) 46.2440 1.48404 0.742020 0.670378i \(-0.233868\pi\)
0.742020 + 0.670378i \(0.233868\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 2.38220 0.0762915
\(976\) 0 0
\(977\) 11.1753 0.357529 0.178765 0.983892i \(-0.442790\pi\)
0.178765 + 0.983892i \(0.442790\pi\)
\(978\) 0 0
\(979\) 5.95625 0.190363
\(980\) 0 0
\(981\) −9.63082 −0.307489
\(982\) 0 0
\(983\) −17.8140 −0.568179 −0.284090 0.958798i \(-0.591691\pi\)
−0.284090 + 0.958798i \(0.591691\pi\)
\(984\) 0 0
\(985\) −7.16447 −0.228279
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 5.11597 0.162678
\(990\) 0 0
\(991\) −4.45574 −0.141541 −0.0707706 0.997493i \(-0.522546\pi\)
−0.0707706 + 0.997493i \(0.522546\pi\)
\(992\) 0 0
\(993\) −37.3734 −1.18601
\(994\) 0 0
\(995\) −2.17733 −0.0690259
\(996\) 0 0
\(997\) −34.9717 −1.10756 −0.553782 0.832662i \(-0.686816\pi\)
−0.553782 + 0.832662i \(0.686816\pi\)
\(998\) 0 0
\(999\) 9.26949 0.293274
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 \(a_p\))