Properties

Label 4032.2.j.b.2591.1
Level 4032
Weight 2
Character 4032.2591
Analytic conductor 32.196
Analytic rank 0
Dimension 4
CM No
Inner twists 4

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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: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2\cdot 3^{2} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2591.1
Root \(0.707107 + 0.707107i\)
Character \(\chi\) = 4032.2591
Dual form 4032.2.j.b.2591.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{7} +O(q^{10})\) \(q-1.00000i q^{7} -4.24264i q^{11} -6.00000i q^{13} -4.24264 q^{23} -5.00000 q^{25} -4.24264 q^{29} -4.00000i q^{31} +6.00000i q^{37} +8.48528i q^{41} -6.00000 q^{43} -8.48528 q^{47} -1.00000 q^{49} +12.7279 q^{53} +8.48528i q^{59} +6.00000i q^{61} +12.0000 q^{67} -4.24264 q^{71} -2.00000 q^{73} -4.24264 q^{77} -10.0000i q^{79} +16.9706i q^{83} +8.48528i q^{89} -6.00000 q^{91} -10.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + O(q^{10}) \) \( 4q - 20q^{25} - 24q^{43} - 4q^{49} + 48q^{67} - 8q^{73} - 24q^{91} - 40q^{97} + O(q^{100}) \)

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 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) − 1.00000i − 0.377964i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) − 4.24264i − 1.27920i −0.768706 0.639602i \(-0.779099\pi\)
0.768706 0.639602i \(-0.220901\pi\)
\(12\) 0 0
\(13\) − 6.00000i − 1.66410i −0.554700 0.832050i \(-0.687167\pi\)
0.554700 0.832050i \(-0.312833\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.24264 −0.884652 −0.442326 0.896854i \(-0.645847\pi\)
−0.442326 + 0.896854i \(0.645847\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4.24264 −0.787839 −0.393919 0.919145i \(-0.628881\pi\)
−0.393919 + 0.919145i \(0.628881\pi\)
\(30\) 0 0
\(31\) − 4.00000i − 0.718421i −0.933257 0.359211i \(-0.883046\pi\)
0.933257 0.359211i \(-0.116954\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 6.00000i 0.986394i 0.869918 + 0.493197i \(0.164172\pi\)
−0.869918 + 0.493197i \(0.835828\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 8.48528i 1.32518i 0.748983 + 0.662589i \(0.230542\pi\)
−0.748983 + 0.662589i \(0.769458\pi\)
\(42\) 0 0
\(43\) −6.00000 −0.914991 −0.457496 0.889212i \(-0.651253\pi\)
−0.457496 + 0.889212i \(0.651253\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −8.48528 −1.23771 −0.618853 0.785507i \(-0.712402\pi\)
−0.618853 + 0.785507i \(0.712402\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 12.7279 1.74831 0.874157 0.485643i \(-0.161414\pi\)
0.874157 + 0.485643i \(0.161414\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 8.48528i 1.10469i 0.833616 + 0.552345i \(0.186267\pi\)
−0.833616 + 0.552345i \(0.813733\pi\)
\(60\) 0 0
\(61\) 6.00000i 0.768221i 0.923287 + 0.384111i \(0.125492\pi\)
−0.923287 + 0.384111i \(0.874508\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 12.0000 1.46603 0.733017 0.680211i \(-0.238112\pi\)
0.733017 + 0.680211i \(0.238112\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −4.24264 −0.503509 −0.251754 0.967791i \(-0.581008\pi\)
−0.251754 + 0.967791i \(0.581008\pi\)
\(72\) 0 0
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −4.24264 −0.483494
\(78\) 0 0
\(79\) − 10.0000i − 1.12509i −0.826767 0.562544i \(-0.809823\pi\)
0.826767 0.562544i \(-0.190177\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 16.9706i 1.86276i 0.364047 + 0.931381i \(0.381395\pi\)
−0.364047 + 0.931381i \(0.618605\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 8.48528i 0.899438i 0.893170 + 0.449719i \(0.148476\pi\)
−0.893170 + 0.449719i \(0.851524\pi\)
\(90\) 0 0
\(91\) −6.00000 −0.628971
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −8.48528 −0.844317 −0.422159 0.906522i \(-0.638727\pi\)
−0.422159 + 0.906522i \(0.638727\pi\)
\(102\) 0 0
\(103\) − 4.00000i − 0.394132i −0.980390 0.197066i \(-0.936859\pi\)
0.980390 0.197066i \(-0.0631413\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) − 12.7279i − 1.23045i −0.788350 0.615227i \(-0.789064\pi\)
0.788350 0.615227i \(-0.210936\pi\)
\(108\) 0 0
\(109\) 6.00000i 0.574696i 0.957826 + 0.287348i \(0.0927736\pi\)
−0.957826 + 0.287348i \(0.907226\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 12.7279i 1.19734i 0.800995 + 0.598671i \(0.204304\pi\)
−0.800995 + 0.598671i \(0.795696\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) − 2.00000i − 0.177471i −0.996055 0.0887357i \(-0.971717\pi\)
0.996055 0.0887357i \(-0.0282826\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) − 16.9706i − 1.48272i −0.671105 0.741362i \(-0.734180\pi\)
0.671105 0.741362i \(-0.265820\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 21.2132i 1.81237i 0.422885 + 0.906183i \(0.361017\pi\)
−0.422885 + 0.906183i \(0.638983\pi\)
\(138\) 0 0
\(139\) 12.0000 1.01783 0.508913 0.860818i \(-0.330047\pi\)
0.508913 + 0.860818i \(0.330047\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −25.4558 −2.12872
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −4.24264 −0.347571 −0.173785 0.984784i \(-0.555600\pi\)
−0.173785 + 0.984784i \(0.555600\pi\)
\(150\) 0 0
\(151\) − 8.00000i − 0.651031i −0.945537 0.325515i \(-0.894462\pi\)
0.945537 0.325515i \(-0.105538\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) − 18.0000i − 1.43656i −0.695756 0.718278i \(-0.744931\pi\)
0.695756 0.718278i \(-0.255069\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 4.24264i 0.334367i
\(162\) 0 0
\(163\) −12.0000 −0.939913 −0.469956 0.882690i \(-0.655730\pi\)
−0.469956 + 0.882690i \(0.655730\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −8.48528 −0.656611 −0.328305 0.944572i \(-0.606478\pi\)
−0.328305 + 0.944572i \(0.606478\pi\)
\(168\) 0 0
\(169\) −23.0000 −1.76923
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 8.48528 0.645124 0.322562 0.946548i \(-0.395456\pi\)
0.322562 + 0.946548i \(0.395456\pi\)
\(174\) 0 0
\(175\) 5.00000i 0.377964i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) − 4.24264i − 0.317110i −0.987350 0.158555i \(-0.949317\pi\)
0.987350 0.158555i \(-0.0506835\pi\)
\(180\) 0 0
\(181\) − 18.0000i − 1.33793i −0.743294 0.668965i \(-0.766738\pi\)
0.743294 0.668965i \(-0.233262\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −12.7279 −0.920960 −0.460480 0.887670i \(-0.652323\pi\)
−0.460480 + 0.887670i \(0.652323\pi\)
\(192\) 0 0
\(193\) −4.00000 −0.287926 −0.143963 0.989583i \(-0.545985\pi\)
−0.143963 + 0.989583i \(0.545985\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −4.24264 −0.302276 −0.151138 0.988513i \(-0.548294\pi\)
−0.151138 + 0.988513i \(0.548294\pi\)
\(198\) 0 0
\(199\) − 16.0000i − 1.13421i −0.823646 0.567105i \(-0.808063\pi\)
0.823646 0.567105i \(-0.191937\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 4.24264i 0.297775i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −6.00000 −0.413057 −0.206529 0.978441i \(-0.566217\pi\)
−0.206529 + 0.978441i \(0.566217\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −4.00000 −0.271538
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) − 8.00000i − 0.535720i −0.963458 0.267860i \(-0.913684\pi\)
0.963458 0.267860i \(-0.0863164\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) − 8.48528i − 0.563188i −0.959534 0.281594i \(-0.909137\pi\)
0.959534 0.281594i \(-0.0908631\pi\)
\(228\) 0 0
\(229\) 6.00000i 0.396491i 0.980152 + 0.198246i \(0.0635244\pi\)
−0.980152 + 0.198246i \(0.936476\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 12.7279i 0.833834i 0.908945 + 0.416917i \(0.136889\pi\)
−0.908945 + 0.416917i \(0.863111\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 4.24264 0.274434 0.137217 0.990541i \(-0.456184\pi\)
0.137217 + 0.990541i \(0.456184\pi\)
\(240\) 0 0
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) − 8.48528i − 0.535586i −0.963476 0.267793i \(-0.913706\pi\)
0.963476 0.267793i \(-0.0862944\pi\)
\(252\) 0 0
\(253\) 18.0000i 1.13165i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) − 8.48528i − 0.529297i −0.964345 0.264649i \(-0.914744\pi\)
0.964345 0.264649i \(-0.0852560\pi\)
\(258\) 0 0
\(259\) 6.00000 0.372822
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −12.7279 −0.784837 −0.392419 0.919787i \(-0.628362\pi\)
−0.392419 + 0.919787i \(0.628362\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 16.9706 1.03471 0.517357 0.855770i \(-0.326916\pi\)
0.517357 + 0.855770i \(0.326916\pi\)
\(270\) 0 0
\(271\) − 20.0000i − 1.21491i −0.794353 0.607457i \(-0.792190\pi\)
0.794353 0.607457i \(-0.207810\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 21.2132i 1.27920i
\(276\) 0 0
\(277\) − 12.0000i − 0.721010i −0.932757 0.360505i \(-0.882604\pi\)
0.932757 0.360505i \(-0.117396\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 29.6985i 1.77166i 0.464007 + 0.885832i \(0.346411\pi\)
−0.464007 + 0.885832i \(0.653589\pi\)
\(282\) 0 0
\(283\) −12.0000 −0.713326 −0.356663 0.934233i \(-0.616086\pi\)
−0.356663 + 0.934233i \(0.616086\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 8.48528 0.500870
\(288\) 0 0
\(289\) 17.0000 1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 8.48528 0.495715 0.247858 0.968796i \(-0.420273\pi\)
0.247858 + 0.968796i \(0.420273\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 25.4558i 1.47215i
\(300\) 0 0
\(301\) 6.00000i 0.345834i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −12.0000 −0.684876 −0.342438 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −25.4558 −1.44347 −0.721734 0.692170i \(-0.756655\pi\)
−0.721734 + 0.692170i \(0.756655\pi\)
\(312\) 0 0
\(313\) −26.0000 −1.46961 −0.734803 0.678280i \(-0.762726\pi\)
−0.734803 + 0.678280i \(0.762726\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4.24264 0.238290 0.119145 0.992877i \(-0.461985\pi\)
0.119145 + 0.992877i \(0.461985\pi\)
\(318\) 0 0
\(319\) 18.0000i 1.00781i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 30.0000i 1.66410i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 8.48528i 0.467809i
\(330\) 0 0
\(331\) 18.0000 0.989369 0.494685 0.869072i \(-0.335284\pi\)
0.494685 + 0.869072i \(0.335284\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −4.00000 −0.217894 −0.108947 0.994048i \(-0.534748\pi\)
−0.108947 + 0.994048i \(0.534748\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −16.9706 −0.919007
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 21.2132i 1.13878i 0.822066 + 0.569392i \(0.192821\pi\)
−0.822066 + 0.569392i \(0.807179\pi\)
\(348\) 0 0
\(349\) 30.0000i 1.60586i 0.596071 + 0.802932i \(0.296728\pi\)
−0.596071 + 0.802932i \(0.703272\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) − 33.9411i − 1.80650i −0.429111 0.903252i \(-0.641173\pi\)
0.429111 0.903252i \(-0.358827\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −21.2132 −1.11959 −0.559795 0.828631i \(-0.689120\pi\)
−0.559795 + 0.828631i \(0.689120\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) − 28.0000i − 1.46159i −0.682598 0.730794i \(-0.739150\pi\)
0.682598 0.730794i \(-0.260850\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) − 12.7279i − 0.660801i
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 25.4558i 1.31104i
\(378\) 0 0
\(379\) 30.0000 1.54100 0.770498 0.637442i \(-0.220007\pi\)
0.770498 + 0.637442i \(0.220007\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −16.9706 −0.867155 −0.433578 0.901116i \(-0.642749\pi\)
−0.433578 + 0.901116i \(0.642749\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −29.6985 −1.50577 −0.752886 0.658150i \(-0.771339\pi\)
−0.752886 + 0.658150i \(0.771339\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) − 30.0000i − 1.50566i −0.658217 0.752828i \(-0.728689\pi\)
0.658217 0.752828i \(-0.271311\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) − 21.2132i − 1.05934i −0.848205 0.529668i \(-0.822316\pi\)
0.848205 0.529668i \(-0.177684\pi\)
\(402\) 0 0
\(403\) −24.0000 −1.19553
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 25.4558 1.26180
\(408\) 0 0
\(409\) 22.0000 1.08783 0.543915 0.839140i \(-0.316941\pi\)
0.543915 + 0.839140i \(0.316941\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 8.48528 0.417533
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) − 25.4558i − 1.24360i −0.783176 0.621800i \(-0.786402\pi\)
0.783176 0.621800i \(-0.213598\pi\)
\(420\) 0 0
\(421\) − 36.0000i − 1.75453i −0.480004 0.877266i \(-0.659365\pi\)
0.480004 0.877266i \(-0.340635\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 6.00000 0.290360
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 29.6985 1.43053 0.715263 0.698856i \(-0.246307\pi\)
0.715263 + 0.698856i \(0.246307\pi\)
\(432\) 0 0
\(433\) −2.00000 −0.0961139 −0.0480569 0.998845i \(-0.515303\pi\)
−0.0480569 + 0.998845i \(0.515303\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 8.00000i 0.381819i 0.981608 + 0.190910i \(0.0611437\pi\)
−0.981608 + 0.190910i \(0.938856\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) − 21.2132i − 1.00787i −0.863742 0.503935i \(-0.831885\pi\)
0.863742 0.503935i \(-0.168115\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) − 12.7279i − 0.600668i −0.953834 0.300334i \(-0.902902\pi\)
0.953834 0.300334i \(-0.0970981\pi\)
\(450\) 0 0
\(451\) 36.0000 1.69517
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −8.00000 −0.374224 −0.187112 0.982339i \(-0.559913\pi\)
−0.187112 + 0.982339i \(0.559913\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −8.48528 −0.395199 −0.197599 0.980283i \(-0.563315\pi\)
−0.197599 + 0.980283i \(0.563315\pi\)
\(462\) 0 0
\(463\) 22.0000i 1.02243i 0.859454 + 0.511213i \(0.170804\pi\)
−0.859454 + 0.511213i \(0.829196\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 8.48528i 0.392652i 0.980539 + 0.196326i \(0.0629011\pi\)
−0.980539 + 0.196326i \(0.937099\pi\)
\(468\) 0 0
\(469\) − 12.0000i − 0.554109i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 25.4558i 1.17046i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −8.48528 −0.387702 −0.193851 0.981031i \(-0.562098\pi\)
−0.193851 + 0.981031i \(0.562098\pi\)
\(480\) 0 0
\(481\) 36.0000 1.64146
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 16.0000i 0.725029i 0.931978 + 0.362515i \(0.118082\pi\)
−0.931978 + 0.362515i \(0.881918\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) − 12.7279i − 0.574403i −0.957870 0.287202i \(-0.907275\pi\)
0.957870 0.287202i \(-0.0927249\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 4.24264i 0.190308i
\(498\) 0 0
\(499\) −6.00000 −0.268597 −0.134298 0.990941i \(-0.542878\pi\)
−0.134298 + 0.990941i \(0.542878\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 33.9411 1.51336 0.756680 0.653785i \(-0.226820\pi\)
0.756680 + 0.653785i \(0.226820\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −16.9706 −0.752207 −0.376103 0.926578i \(-0.622736\pi\)
−0.376103 + 0.926578i \(0.622736\pi\)
\(510\) 0 0
\(511\) 2.00000i 0.0884748i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 36.0000i 1.58328i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) − 16.9706i − 0.743494i −0.928334 0.371747i \(-0.878759\pi\)
0.928334 0.371747i \(-0.121241\pi\)
\(522\) 0 0
\(523\) −24.0000 −1.04945 −0.524723 0.851273i \(-0.675831\pi\)
−0.524723 + 0.851273i \(0.675831\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −5.00000 −0.217391
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 50.9117 2.20523
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 4.24264i 0.182743i
\(540\) 0 0
\(541\) − 36.0000i − 1.54776i −0.633332 0.773880i \(-0.718313\pi\)
0.633332 0.773880i \(-0.281687\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −12.0000 −0.513083 −0.256541 0.966533i \(-0.582583\pi\)
−0.256541 + 0.966533i \(0.582583\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −10.0000 −0.425243
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −29.6985 −1.25837 −0.629183 0.777258i \(-0.716610\pi\)
−0.629183 + 0.777258i \(0.716610\pi\)
\(558\) 0 0
\(559\) 36.0000i 1.52264i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) − 25.4558i − 1.07284i −0.843952 0.536418i \(-0.819777\pi\)
0.843952 0.536418i \(-0.180223\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) − 29.6985i − 1.24503i −0.782610 0.622513i \(-0.786112\pi\)
0.782610 0.622513i \(-0.213888\pi\)
\(570\) 0 0
\(571\) −36.0000 −1.50655 −0.753277 0.657704i \(-0.771528\pi\)
−0.753277 + 0.657704i \(0.771528\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 21.2132 0.884652
\(576\) 0 0
\(577\) 34.0000 1.41544 0.707719 0.706494i \(-0.249724\pi\)
0.707719 + 0.706494i \(0.249724\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 16.9706 0.704058
\(582\) 0 0
\(583\) − 54.0000i − 2.23645i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 25.4558i − 1.05068i −0.850894 0.525338i \(-0.823939\pi\)
0.850894 0.525338i \(-0.176061\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) − 16.9706i − 0.696897i −0.937328 0.348449i \(-0.886709\pi\)
0.937328 0.348449i \(-0.113291\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 38.1838 1.56015 0.780073 0.625688i \(-0.215182\pi\)
0.780073 + 0.625688i \(0.215182\pi\)
\(600\) 0 0
\(601\) −46.0000 −1.87638 −0.938190 0.346122i \(-0.887498\pi\)
−0.938190 + 0.346122i \(0.887498\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 4.00000i 0.162355i 0.996700 + 0.0811775i \(0.0258681\pi\)
−0.996700 + 0.0811775i \(0.974132\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 50.9117i 2.05967i
\(612\) 0 0
\(613\) − 12.0000i − 0.484675i −0.970192 0.242338i \(-0.922086\pi\)
0.970192 0.242338i \(-0.0779142\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 21.2132i 0.854011i 0.904249 + 0.427006i \(0.140432\pi\)
−0.904249 + 0.427006i \(0.859568\pi\)
\(618\) 0 0
\(619\) −12.0000 −0.482321 −0.241160 0.970485i \(-0.577528\pi\)
−0.241160 + 0.970485i \(0.577528\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 8.48528 0.339956
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 34.0000i 1.35352i 0.736204 + 0.676759i \(0.236616\pi\)
−0.736204 + 0.676759i \(0.763384\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 6.00000i 0.237729i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 4.24264i 0.167574i 0.996484 + 0.0837871i \(0.0267016\pi\)
−0.996484 + 0.0837871i \(0.973298\pi\)
\(642\) 0 0
\(643\) −12.0000 −0.473234 −0.236617 0.971603i \(-0.576039\pi\)
−0.236617 + 0.971603i \(0.576039\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −42.4264 −1.66795 −0.833977 0.551799i \(-0.813942\pi\)
−0.833977 + 0.551799i \(0.813942\pi\)
\(648\) 0 0
\(649\) 36.0000 1.41312
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 12.7279 0.498082 0.249041 0.968493i \(-0.419885\pi\)
0.249041 + 0.968493i \(0.419885\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 21.2132i 0.826349i 0.910652 + 0.413175i \(0.135580\pi\)
−0.910652 + 0.413175i \(0.864420\pi\)
\(660\) 0 0
\(661\) 18.0000i 0.700119i 0.936727 + 0.350059i \(0.113839\pi\)
−0.936727 + 0.350059i \(0.886161\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 18.0000 0.696963
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 25.4558 0.982712
\(672\) 0 0
\(673\) −8.00000 −0.308377 −0.154189 0.988041i \(-0.549276\pi\)
−0.154189 + 0.988041i \(0.549276\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 42.4264 1.63058 0.815290 0.579053i \(-0.196578\pi\)
0.815290 + 0.579053i \(0.196578\pi\)
\(678\) 0 0
\(679\) 10.0000i 0.383765i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 21.2132i 0.811701i 0.913940 + 0.405850i \(0.133025\pi\)
−0.913940 + 0.405850i \(0.866975\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) − 76.3675i − 2.90937i
\(690\) 0 0
\(691\) 48.0000 1.82601 0.913003 0.407953i \(-0.133757\pi\)
0.913003 + 0.407953i \(0.133757\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −12.7279 −0.480727 −0.240363 0.970683i \(-0.577267\pi\)
−0.240363 + 0.970683i \(0.577267\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 8.48528i 0.319122i
\(708\) 0 0
\(709\) 6.00000i 0.225335i 0.993633 + 0.112667i \(0.0359394\pi\)
−0.993633 + 0.112667i \(0.964061\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 16.9706i 0.635553i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −16.9706 −0.632895 −0.316448 0.948610i \(-0.602490\pi\)
−0.316448 + 0.948610i \(0.602490\pi\)
\(720\) 0 0
\(721\) −4.00000 −0.148968
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 21.2132 0.787839
\(726\) 0 0
\(727\) 28.0000i 1.03846i 0.854634 + 0.519231i \(0.173782\pi\)
−0.854634 + 0.519231i \(0.826218\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 6.00000i 0.221615i 0.993842 + 0.110808i \(0.0353437\pi\)
−0.993842 + 0.110808i \(0.964656\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 50.9117i − 1.87536i
\(738\) 0 0
\(739\) 12.0000 0.441427 0.220714 0.975339i \(-0.429161\pi\)
0.220714 + 0.975339i \(0.429161\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 29.6985 1.08953 0.544766 0.838588i \(-0.316619\pi\)
0.544766 + 0.838588i \(0.316619\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −12.7279 −0.465068
\(750\) 0 0
\(751\) 32.0000i 1.16770i 0.811863 + 0.583848i \(0.198454\pi\)
−0.811863 + 0.583848i \(0.801546\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 42.0000i 1.52652i 0.646094 + 0.763258i \(0.276401\pi\)
−0.646094 + 0.763258i \(0.723599\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) − 8.48528i − 0.307591i −0.988103 0.153796i \(-0.950850\pi\)
0.988103 0.153796i \(-0.0491497\pi\)
\(762\) 0 0
\(763\) 6.00000 0.217215
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 50.9117 1.83831
\(768\) 0 0
\(769\) 50.0000 1.80305 0.901523 0.432731i \(-0.142450\pi\)
0.901523 + 0.432731i \(0.142450\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −25.4558 −0.915583 −0.457792 0.889060i \(-0.651359\pi\)
−0.457792 + 0.889060i \(0.651359\pi\)
\(774\) 0 0
\(775\) 20.0000i 0.718421i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 18.0000i 0.644091i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −24.0000 −0.855508 −0.427754 0.903895i \(-0.640695\pi\)
−0.427754 + 0.903895i \(0.640695\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 12.7279 0.452553
\(792\) 0 0
\(793\) 36.0000 1.27840
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −8.48528 −0.300564 −0.150282 0.988643i \(-0.548018\pi\)
−0.150282 + 0.988643i \(0.548018\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 8.48528i 0.299439i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 4.24264i 0.149163i 0.997215 + 0.0745817i \(0.0237621\pi\)
−0.997215 + 0.0745817i \(0.976238\pi\)
\(810\) 0 0
\(811\) −36.0000 −1.26413 −0.632065 0.774915i \(-0.717793\pi\)
−0.632065 + 0.774915i \(0.717793\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −29.6985 −1.03648 −0.518242 0.855234i \(-0.673413\pi\)
−0.518242 + 0.855234i \(0.673413\pi\)
\(822\) 0 0
\(823\) 22.0000i 0.766872i 0.923567 + 0.383436i \(0.125259\pi\)
−0.923567 + 0.383436i \(0.874741\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 4.24264i − 0.147531i −0.997276 0.0737655i \(-0.976498\pi\)
0.997276 0.0737655i \(-0.0235016\pi\)
\(828\) 0 0
\(829\) − 18.0000i − 0.625166i −0.949890 0.312583i \(-0.898806\pi\)
0.949890 0.312583i \(-0.101194\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 25.4558 0.878833 0.439417 0.898283i \(-0.355185\pi\)
0.439417 + 0.898283i \(0.355185\pi\)
\(840\) 0 0
\(841\) −11.0000 −0.379310
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 7.00000i 0.240523i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) − 25.4558i − 0.872615i
\(852\) 0 0
\(853\) − 18.0000i − 0.616308i −0.951336 0.308154i \(-0.900289\pi\)
0.951336 0.308154i \(-0.0997113\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) − 42.4264i − 1.44926i −0.689139 0.724629i \(-0.742011\pi\)
0.689139 0.724629i \(-0.257989\pi\)
\(858\) 0 0
\(859\) 12.0000 0.409435 0.204717 0.978821i \(-0.434372\pi\)
0.204717 + 0.978821i \(0.434372\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 4.24264 0.144421 0.0722106 0.997389i \(-0.476995\pi\)
0.0722106 + 0.997389i \(0.476995\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −42.4264 −1.43922
\(870\) 0 0
\(871\) − 72.0000i − 2.43963i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 12.0000i 0.405211i 0.979260 + 0.202606i \(0.0649409\pi\)
−0.979260 + 0.202606i \(0.935059\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) − 33.9411i − 1.14351i −0.820426 0.571753i \(-0.806264\pi\)
0.820426 0.571753i \(-0.193736\pi\)
\(882\) 0 0
\(883\) 54.0000 1.81724 0.908622 0.417619i \(-0.137135\pi\)
0.908622 + 0.417619i \(0.137135\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 42.4264 1.42454 0.712270 0.701906i \(-0.247667\pi\)
0.712270 + 0.701906i \(0.247667\pi\)
\(888\) 0 0
\(889\) −2.00000 −0.0670778
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 16.9706i 0.566000i
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 30.0000 0.996134 0.498067 0.867139i \(-0.334043\pi\)
0.498067 + 0.867139i \(0.334043\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 4.24264 0.140565 0.0702825 0.997527i \(-0.477610\pi\)
0.0702825 + 0.997527i \(0.477610\pi\)
\(912\) 0 0
\(913\) 72.0000 2.38285
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −16.9706 −0.560417
\(918\) 0 0
\(919\) 16.0000i 0.527791i 0.964551 + 0.263896i \(0.0850075\pi\)
−0.964551 + 0.263896i \(0.914993\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 25.4558i 0.837889i
\(924\) 0 0
\(925\) − 30.0000i − 0.986394i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) − 59.3970i − 1.94875i −0.224927 0.974376i \(-0.572214\pi\)
0.224927 0.974376i \(-0.427786\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −2.00000 −0.0653372 −0.0326686 0.999466i \(-0.510401\pi\)
−0.0326686 + 0.999466i \(0.510401\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 33.9411 1.10645 0.553225 0.833032i \(-0.313397\pi\)
0.553225 + 0.833032i \(0.313397\pi\)
\(942\) 0 0
\(943\) − 36.0000i − 1.17232i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) − 55.1543i − 1.79227i −0.443777 0.896137i \(-0.646362\pi\)
0.443777 0.896137i \(-0.353638\pi\)
\(948\) 0 0
\(949\) 12.0000i 0.389536i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 46.6690i 1.51176i 0.654711 + 0.755879i \(0.272790\pi\)
−0.654711 + 0.755879i \(0.727210\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 21.2132 0.685010
\(960\) 0 0
\(961\) 15.0000 0.483871
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 50.0000i 1.60789i 0.594703 + 0.803946i \(0.297270\pi\)
−0.594703 + 0.803946i \(0.702730\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) − 50.9117i − 1.63383i −0.576755 0.816917i \(-0.695681\pi\)
0.576755 0.816917i \(-0.304319\pi\)
\(972\) 0 0
\(973\) − 12.0000i − 0.384702i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) − 4.24264i − 0.135734i −0.997694 0.0678671i \(-0.978381\pi\)
0.997694 0.0678671i \(-0.0216194\pi\)
\(978\) 0 0
\(979\) 36.0000 1.15056
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −50.9117 −1.62383 −0.811915 0.583775i \(-0.801575\pi\)
−0.811915 + 0.583775i \(0.801575\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 25.4558 0.809449
\(990\) 0 0
\(991\) 56.0000i 1.77890i 0.457034 + 0.889449i \(0.348912\pi\)
−0.457034 + 0.889449i \(0.651088\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) − 42.0000i − 1.33015i −0.746775 0.665077i \(-0.768399\pi\)
0.746775 0.665077i \(-0.231601\pi\)
\(998\) 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 \(a_p\))