Properties

Label 4032.2.j.e.2591.9
Level 4032
Weight 2
Character 4032.2591
Analytic conductor 32.196
Analytic rank 0
Dimension 16
CM No
Inner twists 8

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Newspace parameters

Level: \( N \) = \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4032.j (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(32.195682095\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: 16.0.162447943996702457856.1
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{18} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2591.9
Root \(-0.825348 + 1.14839i\)
Character \(\chi\) = 4032.2591
Dual form 4032.2.j.e.2591.12

$q$-expansion

\(f(q)\) \(=\) \(q+0.646084 q^{5} -1.00000i q^{7} +O(q^{10})\) \(q+0.646084 q^{5} -1.00000i q^{7} +3.09557i q^{11} -0.913701i q^{13} -6.77590i q^{17} -5.29150 q^{19} +2.53326 q^{23} -4.58258 q^{25} -9.93280 q^{29} +9.16515i q^{31} -0.646084i q^{35} +7.84190i q^{37} +9.01400i q^{41} +12.2197 q^{43} -5.65685 q^{47} -1.00000 q^{49} -1.15732 q^{53} +2.00000i q^{55} +6.92820i q^{61} -0.590327i q^{65} +7.84190 q^{67} -5.36169 q^{71} -0.417424 q^{73} +3.09557 q^{77} -10.7477i q^{79} +15.9891i q^{83} -4.37780i q^{85} -9.01400i q^{89} -0.913701 q^{91} -3.41875 q^{95} -11.5826 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q - 16q^{49} - 80q^{73} - 112q^{97} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(1793\) \(3781\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(-1\)

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 0
\(4\) 0 0
\(5\) 0.646084 0.288937 0.144469 0.989509i \(-0.453853\pi\)
0.144469 + 0.989509i \(0.453853\pi\)
\(6\) 0 0
\(7\) − 1.00000i − 0.377964i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 3.09557i 0.933351i 0.884429 + 0.466675i \(0.154548\pi\)
−0.884429 + 0.466675i \(0.845452\pi\)
\(12\) 0 0
\(13\) − 0.913701i − 0.253415i −0.991940 0.126707i \(-0.959559\pi\)
0.991940 0.126707i \(-0.0404409\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) − 6.77590i − 1.64340i −0.569922 0.821699i \(-0.693026\pi\)
0.569922 0.821699i \(-0.306974\pi\)
\(18\) 0 0
\(19\) −5.29150 −1.21395 −0.606977 0.794719i \(-0.707618\pi\)
−0.606977 + 0.794719i \(0.707618\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.53326 0.528222 0.264111 0.964492i \(-0.414921\pi\)
0.264111 + 0.964492i \(0.414921\pi\)
\(24\) 0 0
\(25\) −4.58258 −0.916515
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −9.93280 −1.84448 −0.922238 0.386623i \(-0.873641\pi\)
−0.922238 + 0.386623i \(0.873641\pi\)
\(30\) 0 0
\(31\) 9.16515i 1.64611i 0.567962 + 0.823055i \(0.307732\pi\)
−0.567962 + 0.823055i \(0.692268\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) − 0.646084i − 0.109208i
\(36\) 0 0
\(37\) 7.84190i 1.28920i 0.764520 + 0.644601i \(0.222976\pi\)
−0.764520 + 0.644601i \(0.777024\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 9.01400i 1.40775i 0.710323 + 0.703875i \(0.248549\pi\)
−0.710323 + 0.703875i \(0.751451\pi\)
\(42\) 0 0
\(43\) 12.2197 1.86349 0.931744 0.363116i \(-0.118287\pi\)
0.931744 + 0.363116i \(0.118287\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5.65685 −0.825137 −0.412568 0.910927i \(-0.635368\pi\)
−0.412568 + 0.910927i \(0.635368\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1.15732 −0.158970 −0.0794852 0.996836i \(-0.525328\pi\)
−0.0794852 + 0.996836i \(0.525328\pi\)
\(54\) 0 0
\(55\) 2.00000i 0.269680i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 6.92820i 0.887066i 0.896258 + 0.443533i \(0.146275\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) − 0.590327i − 0.0732211i
\(66\) 0 0
\(67\) 7.84190 0.958041 0.479021 0.877804i \(-0.340992\pi\)
0.479021 + 0.877804i \(0.340992\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −5.36169 −0.636316 −0.318158 0.948038i \(-0.603064\pi\)
−0.318158 + 0.948038i \(0.603064\pi\)
\(72\) 0 0
\(73\) −0.417424 −0.0488558 −0.0244279 0.999702i \(-0.507776\pi\)
−0.0244279 + 0.999702i \(0.507776\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.09557 0.352773
\(78\) 0 0
\(79\) − 10.7477i − 1.20921i −0.796524 0.604607i \(-0.793330\pi\)
0.796524 0.604607i \(-0.206670\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 15.9891i 1.75503i 0.479547 + 0.877516i \(0.340801\pi\)
−0.479547 + 0.877516i \(0.659199\pi\)
\(84\) 0 0
\(85\) − 4.37780i − 0.474839i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) − 9.01400i − 0.955483i −0.878501 0.477741i \(-0.841456\pi\)
0.878501 0.477741i \(-0.158544\pi\)
\(90\) 0 0
\(91\) −0.913701 −0.0957818
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −3.41875 −0.350757
\(96\) 0 0
\(97\) −11.5826 −1.17603 −0.588016 0.808849i \(-0.700091\pi\)
−0.588016 + 0.808849i \(0.700091\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −14.0509 −1.39811 −0.699056 0.715067i \(-0.746396\pi\)
−0.699056 + 0.715067i \(0.746396\pi\)
\(102\) 0 0
\(103\) − 2.00000i − 0.197066i −0.995134 0.0985329i \(-0.968585\pi\)
0.995134 0.0985329i \(-0.0314150\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.70239i 0.647944i 0.946067 + 0.323972i \(0.105018\pi\)
−0.946067 + 0.323972i \(0.894982\pi\)
\(108\) 0 0
\(109\) − 5.29150i − 0.506834i −0.967357 0.253417i \(-0.918446\pi\)
0.967357 0.253417i \(-0.0815545\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) − 9.89949i − 0.931266i −0.884978 0.465633i \(-0.845827\pi\)
0.884978 0.465633i \(-0.154173\pi\)
\(114\) 0 0
\(115\) 1.63670 0.152623
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −6.77590 −0.621146
\(120\) 0 0
\(121\) 1.41742 0.128857
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −6.19115 −0.553753
\(126\) 0 0
\(127\) 4.41742i 0.391983i 0.980606 + 0.195992i \(0.0627925\pi\)
−0.980606 + 0.195992i \(0.937207\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 11.0901i 0.968949i 0.874805 + 0.484474i \(0.160989\pi\)
−0.874805 + 0.484474i \(0.839011\pi\)
\(132\) 0 0
\(133\) 5.29150i 0.458831i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) − 5.89041i − 0.503252i −0.967825 0.251626i \(-0.919035\pi\)
0.967825 0.251626i \(-0.0809653\pi\)
\(138\) 0 0
\(139\) −1.82740 −0.154998 −0.0774991 0.996992i \(-0.524693\pi\)
−0.0774991 + 0.996992i \(0.524693\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2.82843 0.236525
\(144\) 0 0
\(145\) −6.41742 −0.532938
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −19.7308 −1.61641 −0.808204 0.588903i \(-0.799560\pi\)
−0.808204 + 0.588903i \(0.799560\pi\)
\(150\) 0 0
\(151\) 23.1652i 1.88515i 0.333990 + 0.942577i \(0.391605\pi\)
−0.333990 + 0.942577i \(0.608395\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 5.92146i 0.475623i
\(156\) 0 0
\(157\) 15.6838i 1.25170i 0.779942 + 0.625852i \(0.215249\pi\)
−0.779942 + 0.625852i \(0.784751\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) − 2.53326i − 0.199649i
\(162\) 0 0
\(163\) 13.3241 1.04362 0.521812 0.853060i \(-0.325256\pi\)
0.521812 + 0.853060i \(0.325256\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −7.89495 −0.610930 −0.305465 0.952203i \(-0.598812\pi\)
−0.305465 + 0.952203i \(0.598812\pi\)
\(168\) 0 0
\(169\) 12.1652 0.935781
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −7.85971 −0.597562 −0.298781 0.954322i \(-0.596580\pi\)
−0.298781 + 0.954322i \(0.596580\pi\)
\(174\) 0 0
\(175\) 4.58258i 0.346410i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 11.6014i 0.867127i 0.901123 + 0.433563i \(0.142744\pi\)
−0.901123 + 0.433563i \(0.857256\pi\)
\(180\) 0 0
\(181\) 9.66930i 0.718714i 0.933200 + 0.359357i \(0.117004\pi\)
−0.933200 + 0.359357i \(0.882996\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 5.06653i 0.372498i
\(186\) 0 0
\(187\) 20.9753 1.53387
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −20.5613 −1.48776 −0.743881 0.668312i \(-0.767017\pi\)
−0.743881 + 0.668312i \(0.767017\pi\)
\(192\) 0 0
\(193\) 6.74773 0.485712 0.242856 0.970062i \(-0.421916\pi\)
0.242856 + 0.970062i \(0.421916\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 24.8994 1.77401 0.887006 0.461759i \(-0.152781\pi\)
0.887006 + 0.461759i \(0.152781\pi\)
\(198\) 0 0
\(199\) − 19.1652i − 1.35858i −0.733869 0.679291i \(-0.762288\pi\)
0.733869 0.679291i \(-0.237712\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 9.93280i 0.697146i
\(204\) 0 0
\(205\) 5.82380i 0.406752i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) − 16.3802i − 1.13304i
\(210\) 0 0
\(211\) −0.190700 −0.0131284 −0.00656418 0.999978i \(-0.502089\pi\)
−0.00656418 + 0.999978i \(0.502089\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 7.89495 0.538431
\(216\) 0 0
\(217\) 9.16515 0.622171
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −6.19115 −0.416462
\(222\) 0 0
\(223\) 20.0000i 1.33930i 0.742677 + 0.669650i \(0.233556\pi\)
−0.742677 + 0.669650i \(0.766444\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) − 11.0901i − 0.736078i −0.929810 0.368039i \(-0.880029\pi\)
0.929810 0.368039i \(-0.119971\pi\)
\(228\) 0 0
\(229\) 11.4967i 0.759724i 0.925043 + 0.379862i \(0.124028\pi\)
−0.925043 + 0.379862i \(0.875972\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) − 7.07107i − 0.463241i −0.972806 0.231621i \(-0.925597\pi\)
0.972806 0.231621i \(-0.0744028\pi\)
\(234\) 0 0
\(235\) −3.65480 −0.238413
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −5.95202 −0.385004 −0.192502 0.981297i \(-0.561660\pi\)
−0.192502 + 0.981297i \(0.561660\pi\)
\(240\) 0 0
\(241\) −20.4174 −1.31520 −0.657601 0.753366i \(-0.728429\pi\)
−0.657601 + 0.753366i \(0.728429\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −0.646084 −0.0412768
\(246\) 0 0
\(247\) 4.83485i 0.307634i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.02248i 0.0645381i 0.999479 + 0.0322691i \(0.0102733\pi\)
−0.999479 + 0.0322691i \(0.989727\pi\)
\(252\) 0 0
\(253\) 7.84190i 0.493016i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) − 10.1947i − 0.635925i −0.948103 0.317963i \(-0.897001\pi\)
0.948103 0.317963i \(-0.102999\pi\)
\(258\) 0 0
\(259\) 7.84190 0.487272
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.94294 0.119807 0.0599033 0.998204i \(-0.480921\pi\)
0.0599033 + 0.998204i \(0.480921\pi\)
\(264\) 0 0
\(265\) −0.747727 −0.0459325
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −25.1410 −1.53287 −0.766436 0.642320i \(-0.777972\pi\)
−0.766436 + 0.642320i \(0.777972\pi\)
\(270\) 0 0
\(271\) 5.16515i 0.313761i 0.987618 + 0.156880i \(0.0501437\pi\)
−0.987618 + 0.156880i \(0.949856\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) − 14.1857i − 0.855430i
\(276\) 0 0
\(277\) 14.9608i 0.898908i 0.893304 + 0.449454i \(0.148381\pi\)
−0.893304 + 0.449454i \(0.851619\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 20.6229i 1.23026i 0.788427 + 0.615129i \(0.210896\pi\)
−0.788427 + 0.615129i \(0.789104\pi\)
\(282\) 0 0
\(283\) −17.3205 −1.02960 −0.514799 0.857311i \(-0.672133\pi\)
−0.514799 + 0.857311i \(0.672133\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 9.01400 0.532080
\(288\) 0 0
\(289\) −28.9129 −1.70076
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −14.3205 −0.836615 −0.418308 0.908305i \(-0.637377\pi\)
−0.418308 + 0.908305i \(0.637377\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) − 2.31464i − 0.133859i
\(300\) 0 0
\(301\) − 12.2197i − 0.704332i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 4.47620i 0.256306i
\(306\) 0 0
\(307\) 22.8027 1.30142 0.650710 0.759327i \(-0.274471\pi\)
0.650710 + 0.759327i \(0.274471\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 4.47620 0.253822 0.126911 0.991914i \(-0.459494\pi\)
0.126911 + 0.991914i \(0.459494\pi\)
\(312\) 0 0
\(313\) 9.16515 0.518045 0.259022 0.965871i \(-0.416600\pi\)
0.259022 + 0.965871i \(0.416600\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0.134846 0.00757368 0.00378684 0.999993i \(-0.498795\pi\)
0.00378684 + 0.999993i \(0.498795\pi\)
\(318\) 0 0
\(319\) − 30.7477i − 1.72154i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 35.8547i 1.99501i
\(324\) 0 0
\(325\) 4.18710i 0.232259i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 5.65685i 0.311872i
\(330\) 0 0
\(331\) −8.94630 −0.491733 −0.245867 0.969304i \(-0.579073\pi\)
−0.245867 + 0.969304i \(0.579073\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 5.06653 0.276814
\(336\) 0 0
\(337\) −22.3303 −1.21641 −0.608205 0.793780i \(-0.708110\pi\)
−0.608205 + 0.793780i \(0.708110\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −28.3714 −1.53640
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 31.4670i 1.68924i 0.535370 + 0.844618i \(0.320172\pi\)
−0.535370 + 0.844618i \(0.679828\pi\)
\(348\) 0 0
\(349\) − 21.1660i − 1.13299i −0.824065 0.566495i \(-0.808299\pi\)
0.824065 0.566495i \(-0.191701\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) − 34.4698i − 1.83464i −0.398145 0.917322i \(-0.630346\pi\)
0.398145 0.917322i \(-0.369654\pi\)
\(354\) 0 0
\(355\) −3.46410 −0.183855
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −4.18104 −0.220667 −0.110333 0.993895i \(-0.535192\pi\)
−0.110333 + 0.993895i \(0.535192\pi\)
\(360\) 0 0
\(361\) 9.00000 0.473684
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −0.269691 −0.0141163
\(366\) 0 0
\(367\) − 0.834849i − 0.0435787i −0.999763 0.0217894i \(-0.993064\pi\)
0.999763 0.0217894i \(-0.00693632\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.15732i 0.0600852i
\(372\) 0 0
\(373\) − 21.1660i − 1.09593i −0.836500 0.547967i \(-0.815402\pi\)
0.836500 0.547967i \(-0.184598\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 9.07561i 0.467418i
\(378\) 0 0
\(379\) 2.01810 0.103663 0.0518315 0.998656i \(-0.483494\pi\)
0.0518315 + 0.998656i \(0.483494\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −9.07561 −0.463742 −0.231871 0.972747i \(-0.574485\pi\)
−0.231871 + 0.972747i \(0.574485\pi\)
\(384\) 0 0
\(385\) 2.00000 0.101929
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 23.3376 1.18326 0.591631 0.806209i \(-0.298484\pi\)
0.591631 + 0.806209i \(0.298484\pi\)
\(390\) 0 0
\(391\) − 17.1652i − 0.868079i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) − 6.94393i − 0.349387i
\(396\) 0 0
\(397\) − 8.75560i − 0.439431i −0.975564 0.219716i \(-0.929487\pi\)
0.975564 0.219716i \(-0.0705129\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) − 32.5269i − 1.62432i −0.583437 0.812158i \(-0.698293\pi\)
0.583437 0.812158i \(-0.301707\pi\)
\(402\) 0 0
\(403\) 8.37420 0.417149
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −24.2752 −1.20328
\(408\) 0 0
\(409\) 7.58258 0.374934 0.187467 0.982271i \(-0.439972\pi\)
0.187467 + 0.982271i \(0.439972\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 10.3303i 0.507095i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) − 19.8656i − 0.970499i −0.874376 0.485249i \(-0.838729\pi\)
0.874376 0.485249i \(-0.161271\pi\)
\(420\) 0 0
\(421\) 11.3060i 0.551021i 0.961298 + 0.275510i \(0.0888469\pi\)
−0.961298 + 0.275510i \(0.911153\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 31.0511i 1.50620i
\(426\) 0 0
\(427\) 6.92820 0.335279
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −17.7328 −0.854161 −0.427081 0.904214i \(-0.640458\pi\)
−0.427081 + 0.904214i \(0.640458\pi\)
\(432\) 0 0
\(433\) 21.1652 1.01713 0.508566 0.861023i \(-0.330176\pi\)
0.508566 + 0.861023i \(0.330176\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −13.4048 −0.641237
\(438\) 0 0
\(439\) 18.3303i 0.874858i 0.899253 + 0.437429i \(0.144111\pi\)
−0.899253 + 0.437429i \(0.855889\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) − 22.9612i − 1.09092i −0.838137 0.545459i \(-0.816355\pi\)
0.838137 0.545459i \(-0.183645\pi\)
\(444\) 0 0
\(445\) − 5.82380i − 0.276075i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 9.89949i 0.467186i 0.972334 + 0.233593i \(0.0750483\pi\)
−0.972334 + 0.233593i \(0.924952\pi\)
\(450\) 0 0
\(451\) −27.9035 −1.31393
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −0.590327 −0.0276750
\(456\) 0 0
\(457\) −3.16515 −0.148060 −0.0740298 0.997256i \(-0.523586\pi\)
−0.0740298 + 0.997256i \(0.523586\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 31.6018 1.47184 0.735922 0.677067i \(-0.236749\pi\)
0.735922 + 0.677067i \(0.236749\pi\)
\(462\) 0 0
\(463\) 11.5826i 0.538288i 0.963100 + 0.269144i \(0.0867407\pi\)
−0.963100 + 0.269144i \(0.913259\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 33.5401i − 1.55205i −0.630703 0.776025i \(-0.717233\pi\)
0.630703 0.776025i \(-0.282767\pi\)
\(468\) 0 0
\(469\) − 7.84190i − 0.362105i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 37.8270i 1.73929i
\(474\) 0 0
\(475\) 24.2487 1.11261
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 35.5889 1.62610 0.813049 0.582195i \(-0.197806\pi\)
0.813049 + 0.582195i \(0.197806\pi\)
\(480\) 0 0
\(481\) 7.16515 0.326703
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −7.48331 −0.339800
\(486\) 0 0
\(487\) 22.3303i 1.01188i 0.862568 + 0.505941i \(0.168855\pi\)
−0.862568 + 0.505941i \(0.831145\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 16.5003i 0.744650i 0.928102 + 0.372325i \(0.121439\pi\)
−0.928102 + 0.372325i \(0.878561\pi\)
\(492\) 0 0
\(493\) 67.3037i 3.03121i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 5.36169i 0.240505i
\(498\) 0 0
\(499\) −22.4213 −1.00372 −0.501858 0.864950i \(-0.667350\pi\)
−0.501858 + 0.864950i \(0.667350\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −27.6939 −1.23481 −0.617406 0.786645i \(-0.711816\pi\)
−0.617406 + 0.786645i \(0.711816\pi\)
\(504\) 0 0
\(505\) −9.07803 −0.403967
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 24.1185 1.06903 0.534517 0.845158i \(-0.320494\pi\)
0.534517 + 0.845158i \(0.320494\pi\)
\(510\) 0 0
\(511\) 0.417424i 0.0184658i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) − 1.29217i − 0.0569397i
\(516\) 0 0
\(517\) − 17.5112i − 0.770142i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) − 13.4902i − 0.591017i −0.955340 0.295508i \(-0.904511\pi\)
0.955340 0.295508i \(-0.0954890\pi\)
\(522\) 0 0
\(523\) −40.5046 −1.77114 −0.885572 0.464503i \(-0.846233\pi\)
−0.885572 + 0.464503i \(0.846233\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 62.1022 2.70521
\(528\) 0 0
\(529\) −16.5826 −0.720982
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 8.23610 0.356745
\(534\) 0 0
\(535\) 4.33030i 0.187215i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) − 3.09557i − 0.133336i
\(540\) 0 0
\(541\) 16.7882i 0.721781i 0.932608 + 0.360891i \(0.117527\pi\)
−0.932608 + 0.360891i \(0.882473\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) − 3.41875i − 0.146443i
\(546\) 0 0
\(547\) 7.46050 0.318988 0.159494 0.987199i \(-0.449014\pi\)
0.159494 + 0.987199i \(0.449014\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 52.5595 2.23911
\(552\) 0 0
\(553\) −10.7477 −0.457040
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 11.9778 0.507514 0.253757 0.967268i \(-0.418334\pi\)
0.253757 + 0.967268i \(0.418334\pi\)
\(558\) 0 0
\(559\) − 11.1652i − 0.472236i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) − 14.4272i − 0.608036i −0.952666 0.304018i \(-0.901672\pi\)
0.952666 0.304018i \(-0.0983283\pi\)
\(564\) 0 0
\(565\) − 6.39590i − 0.269078i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 34.1747i 1.43268i 0.697753 + 0.716339i \(0.254183\pi\)
−0.697753 + 0.716339i \(0.745817\pi\)
\(570\) 0 0
\(571\) 34.4901 1.44337 0.721683 0.692223i \(-0.243369\pi\)
0.721683 + 0.692223i \(0.243369\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −11.6089 −0.484123
\(576\) 0 0
\(577\) 5.16515 0.215028 0.107514 0.994204i \(-0.465711\pi\)
0.107514 + 0.994204i \(0.465711\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 15.9891 0.663340
\(582\) 0 0
\(583\) − 3.58258i − 0.148375i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 28.6411i 1.18214i 0.806619 + 0.591072i \(0.201295\pi\)
−0.806619 + 0.591072i \(0.798705\pi\)
\(588\) 0 0
\(589\) − 48.4974i − 1.99830i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) − 31.6414i − 1.29936i −0.760209 0.649679i \(-0.774903\pi\)
0.760209 0.649679i \(-0.225097\pi\)
\(594\) 0 0
\(595\) −4.37780 −0.179472
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −27.3988 −1.11948 −0.559742 0.828667i \(-0.689100\pi\)
−0.559742 + 0.828667i \(0.689100\pi\)
\(600\) 0 0
\(601\) 25.1652 1.02651 0.513254 0.858237i \(-0.328440\pi\)
0.513254 + 0.858237i \(0.328440\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0.915775 0.0372315
\(606\) 0 0
\(607\) − 14.3303i − 0.581649i −0.956776 0.290825i \(-0.906070\pi\)
0.956776 0.290825i \(-0.0939296\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 5.16867i 0.209102i
\(612\) 0 0
\(613\) − 41.9506i − 1.69437i −0.531298 0.847185i \(-0.678296\pi\)
0.531298 0.847185i \(-0.321704\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 11.0801i 0.446070i 0.974810 + 0.223035i \(0.0715964\pi\)
−0.974810 + 0.223035i \(0.928404\pi\)
\(618\) 0 0
\(619\) 0.381401 0.0153298 0.00766490 0.999971i \(-0.497560\pi\)
0.00766490 + 0.999971i \(0.497560\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −9.01400 −0.361138
\(624\) 0 0
\(625\) 18.9129 0.756515
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 53.1360 2.11867
\(630\) 0 0
\(631\) − 13.9129i − 0.553863i −0.960890 0.276931i \(-0.910682\pi\)
0.960890 0.276931i \(-0.0893175\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 2.85403i 0.113259i
\(636\) 0 0
\(637\) 0.913701i 0.0362021i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) − 38.0606i − 1.50330i −0.659561 0.751651i \(-0.729258\pi\)
0.659561 0.751651i \(-0.270742\pi\)
\(642\) 0 0
\(643\) −20.5939 −0.812145 −0.406072 0.913841i \(-0.633102\pi\)
−0.406072 + 0.913841i \(0.633102\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 20.3893 0.801587 0.400793 0.916168i \(-0.368735\pi\)
0.400793 + 0.916168i \(0.368735\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −37.0120 −1.44839 −0.724196 0.689594i \(-0.757789\pi\)
−0.724196 + 0.689594i \(0.757789\pi\)
\(654\) 0 0
\(655\) 7.16515i 0.279966i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 2.07310i 0.0807564i 0.999184 + 0.0403782i \(0.0128563\pi\)
−0.999184 + 0.0403782i \(0.987144\pi\)
\(660\) 0 0
\(661\) − 12.4104i − 0.482709i −0.970437 0.241354i \(-0.922408\pi\)
0.970437 0.241354i \(-0.0775916\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 3.41875i 0.132574i
\(666\) 0 0
\(667\) −25.1624 −0.974292
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −21.4468 −0.827943
\(672\) 0 0
\(673\) 5.91288 0.227925 0.113962 0.993485i \(-0.463646\pi\)
0.113962 + 0.993485i \(0.463646\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −16.9049 −0.649707 −0.324854 0.945764i \(-0.605315\pi\)
−0.324854 + 0.945764i \(0.605315\pi\)
\(678\) 0 0
\(679\) 11.5826i 0.444498i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) − 36.9053i − 1.41214i −0.708140 0.706072i \(-0.750466\pi\)
0.708140 0.706072i \(-0.249534\pi\)
\(684\) 0 0
\(685\) − 3.80570i − 0.145408i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.05745i 0.0402855i
\(690\) 0 0
\(691\) 16.0652 0.611149 0.305575 0.952168i \(-0.401151\pi\)
0.305575 + 0.952168i \(0.401151\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.18065 −0.0447848
\(696\) 0 0
\(697\) 61.0780 2.31350
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 30.8209 1.16409 0.582044 0.813157i \(-0.302253\pi\)
0.582044 + 0.813157i \(0.302253\pi\)
\(702\) 0 0
\(703\) − 41.4955i − 1.56503i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 14.0509i 0.528437i
\(708\) 0 0
\(709\) 29.7309i 1.11657i 0.829650 + 0.558284i \(0.188540\pi\)
−0.829650 + 0.558284i \(0.811460\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 23.2177i 0.869511i
\(714\) 0 0
\(715\) 1.82740 0.0683409
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −22.5042 −0.839265 −0.419633 0.907694i \(-0.637841\pi\)
−0.419633 + 0.907694i \(0.637841\pi\)
\(720\) 0 0
\(721\) −2.00000 −0.0744839
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 45.5178 1.69049
\(726\) 0 0
\(727\) − 19.4955i − 0.723046i −0.932363 0.361523i \(-0.882257\pi\)
0.932363 0.361523i \(-0.117743\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) − 82.7996i − 3.06245i
\(732\) 0 0
\(733\) − 2.35970i − 0.0871575i −0.999050 0.0435788i \(-0.986124\pi\)
0.999050 0.0435788i \(-0.0138759\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 24.2752i 0.894188i
\(738\) 0 0
\(739\) −7.84190 −0.288469 −0.144235 0.989544i \(-0.546072\pi\)
−0.144235 + 0.989544i \(0.546072\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 43.1887 1.58444 0.792220 0.610236i \(-0.208925\pi\)
0.792220 + 0.610236i \(0.208925\pi\)
\(744\) 0 0
\(745\) −12.7477 −0.467041
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 6.70239 0.244900
\(750\) 0 0
\(751\) − 35.1652i − 1.28319i −0.767042 0.641597i \(-0.778272\pi\)
0.767042 0.641597i \(-0.221728\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 14.9666i 0.544691i
\(756\) 0 0
\(757\) − 41.7599i − 1.51779i −0.651213 0.758895i \(-0.725740\pi\)
0.651213 0.758895i \(-0.274260\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) − 5.00492i − 0.181428i −0.995877 0.0907142i \(-0.971085\pi\)
0.995877 0.0907142i \(-0.0289150\pi\)
\(762\) 0 0
\(763\) −5.29150 −0.191565
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −47.3212 −1.70203 −0.851013 0.525144i \(-0.824011\pi\)
−0.851013 + 0.525144i \(0.824011\pi\)
\(774\) 0 0
\(775\) − 42.0000i − 1.50868i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) − 47.6976i − 1.70894i
\(780\) 0 0
\(781\) − 16.5975i − 0.593906i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 10.1331i 0.361664i
\(786\) 0 0
\(787\) −53.9796 −1.92417 −0.962083 0.272757i \(-0.912064\pi\)
−0.962083 + 0.272757i \(0.912064\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −9.89949 −0.351986
\(792\) 0 0
\(793\) 6.33030 0.224796
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.39887 0.0495505 0.0247752 0.999693i \(-0.492113\pi\)
0.0247752 + 0.999693i \(0.492113\pi\)
\(798\) 0 0
\(799\) 38.3303i 1.35603i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) − 1.29217i − 0.0455996i
\(804\) 0 0
\(805\) − 1.63670i − 0.0576861i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 47.7265i 1.67797i 0.544151 + 0.838987i \(0.316852\pi\)
−0.544151 + 0.838987i \(0.683148\pi\)
\(810\) 0 0
\(811\) −5.48220 −0.192506 −0.0962531 0.995357i \(-0.530686\pi\)
−0.0962531 + 0.995357i \(0.530686\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 8.60849 0.301542
\(816\) 0 0
\(817\) −64.6606 −2.26219
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 3.74166 0.130585 0.0652924 0.997866i \(-0.479202\pi\)
0.0652924 + 0.997866i \(0.479202\pi\)
\(822\) 0 0
\(823\) − 1.91288i − 0.0666788i −0.999444 0.0333394i \(-0.989386\pi\)
0.999444 0.0333394i \(-0.0106142\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 30.7142i − 1.06804i −0.845473 0.534018i \(-0.820681\pi\)
0.845473 0.534018i \(-0.179319\pi\)
\(828\) 0 0
\(829\) − 30.8353i − 1.07095i −0.844550 0.535477i \(-0.820132\pi\)
0.844550 0.535477i \(-0.179868\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 6.77590i 0.234771i
\(834\) 0 0
\(835\) −5.10080 −0.176521
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 39.0077 1.34669 0.673347 0.739327i \(-0.264856\pi\)
0.673347 + 0.739327i \(0.264856\pi\)
\(840\) 0 0
\(841\) 69.6606 2.40209
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 7.85971 0.270382
\(846\) 0 0
\(847\) − 1.41742i − 0.0487033i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 19.8656i 0.680984i
\(852\) 0 0
\(853\) 35.0224i 1.19914i 0.800321 + 0.599572i \(0.204663\pi\)
−0.800321 + 0.599572i \(0.795337\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) − 13.0231i − 0.444860i −0.974949 0.222430i \(-0.928601\pi\)
0.974949 0.222430i \(-0.0713989\pi\)
\(858\) 0 0
\(859\) −48.6881 −1.66122 −0.830609 0.556857i \(-0.812007\pi\)
−0.830609 + 0.556857i \(0.812007\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 16.6754 0.567637 0.283819 0.958878i \(-0.408399\pi\)
0.283819 + 0.958878i \(0.408399\pi\)
\(864\) 0 0
\(865\) −5.07803 −0.172658
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 33.2704 1.12862
\(870\) 0 0
\(871\) − 7.16515i − 0.242782i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 6.19115i 0.209299i
\(876\) 0 0
\(877\) 7.30960i 0.246828i 0.992355 + 0.123414i \(0.0393843\pi\)
−0.992355 + 0.123414i \(0.960616\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 18.0896i 0.609455i 0.952440 + 0.304727i \(0.0985653\pi\)
−0.952440 + 0.304727i \(0.901435\pi\)
\(882\) 0 0
\(883\) 24.2487 0.816034 0.408017 0.912974i \(-0.366220\pi\)
0.408017 + 0.912974i \(0.366220\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −22.5042 −0.755617 −0.377809 0.925884i \(-0.623322\pi\)
−0.377809 + 0.925884i \(0.623322\pi\)
\(888\) 0 0
\(889\) 4.41742 0.148156
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 29.9333 1.00168
\(894\) 0 0
\(895\) 7.49545i 0.250545i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) − 91.0357i − 3.03621i
\(900\) 0 0
\(901\) 7.84190i 0.261252i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 6.24718i 0.207663i
\(906\) 0 0
\(907\) 13.6657 0.453762 0.226881 0.973922i \(-0.427147\pi\)
0.226881 + 0.973922i \(0.427147\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 13.2566 0.439212 0.219606 0.975589i \(-0.429523\pi\)
0.219606 + 0.975589i \(0.429523\pi\)
\(912\) 0 0
\(913\) −49.4955 −1.63806
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 11.0901 0.366228
\(918\) 0 0
\(919\) − 12.8348i − 0.423383i −0.977337 0.211691i \(-0.932103\pi\)
0.977337 0.211691i \(-0.0678971\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 4.89898i 0.161252i
\(924\) 0 0
\(925\) − 35.9361i − 1.18157i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) − 1.11905i − 0.0367148i −0.999831 0.0183574i \(-0.994156\pi\)
0.999831 0.0183574i \(-0.00584368\pi\)
\(930\) 0 0
\(931\) 5.29150 0.173422
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 13.5518 0.443192
\(936\) 0 0
\(937\) 39.4955 1.29026 0.645130 0.764073i \(-0.276803\pi\)
0.645130 + 0.764073i \(0.276803\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −12.7587 −0.415921 −0.207961 0.978137i \(-0.566683\pi\)
−0.207961 + 0.978137i \(0.566683\pi\)
\(942\) 0 0
\(943\) 22.8348i 0.743605i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 2.34279i 0.0761304i 0.999275 + 0.0380652i \(0.0121195\pi\)
−0.999275 + 0.0380652i \(0.987881\pi\)
\(948\) 0 0
\(949\) 0.381401i 0.0123808i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 27.4604i 0.889529i 0.895648 + 0.444765i \(0.146713\pi\)
−0.895648 + 0.444765i \(0.853287\pi\)
\(954\) 0 0
\(955\) −13.2843 −0.429870
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −5.89041 −0.190211
\(960\) 0 0
\(961\) −53.0000 −1.70968
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 4.35960 0.140340
\(966\) 0 0
\(967\) 13.0780i 0.420561i 0.977641 + 0.210281i \(0.0674377\pi\)
−0.977641 + 0.210281i \(0.932562\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) − 9.52827i − 0.305777i −0.988243 0.152888i \(-0.951143\pi\)
0.988243 0.152888i \(-0.0488575\pi\)
\(972\) 0 0
\(973\) 1.82740i 0.0585838i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 6.01362i 0.192393i 0.995362 + 0.0961964i \(0.0306677\pi\)
−0.995362 + 0.0961964i \(0.969332\pi\)
\(978\) 0 0
\(979\) 27.9035 0.891800
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −27.5707 −0.879370 −0.439685 0.898152i \(-0.644910\pi\)
−0.439685 + 0.898152i \(0.644910\pi\)
\(984\) 0 0
\(985\) 16.0871 0.512578
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 30.9557 0.984335
\(990\) 0 0
\(991\) 20.0000i 0.635321i 0.948205 + 0.317660i \(0.102897\pi\)
−0.948205 + 0.317660i \(0.897103\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) − 12.3823i − 0.392545i
\(996\) 0 0
\(997\) 6.54680i 0.207339i 0.994612 + 0.103670i \(0.0330585\pi\)
−0.994612 + 0.103670i \(0.966942\pi\)
\(998\) 0 0
\(999\) 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 \(a_p\))