Properties

Label 8036.2.a.p.1.1
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 10
CM No
Inner twists 1

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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: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.96176\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.96176 q^{3} +4.34462 q^{5} +5.77201 q^{9} +O(q^{10})\) \(q-2.96176 q^{3} +4.34462 q^{5} +5.77201 q^{9} -0.777317 q^{11} -0.473242 q^{13} -12.8677 q^{15} +1.81112 q^{17} +6.26526 q^{19} +5.33938 q^{23} +13.8757 q^{25} -8.21003 q^{27} +4.40596 q^{29} -5.82118 q^{31} +2.30222 q^{33} -8.34567 q^{37} +1.40163 q^{39} +1.00000 q^{41} -6.18004 q^{43} +25.0772 q^{45} +6.01779 q^{47} -5.36410 q^{51} +11.5946 q^{53} -3.37714 q^{55} -18.5562 q^{57} -0.805651 q^{59} +11.1497 q^{61} -2.05606 q^{65} -11.2115 q^{67} -15.8140 q^{69} -1.94934 q^{71} +0.839620 q^{73} -41.0965 q^{75} +7.38355 q^{79} +7.00008 q^{81} +9.38726 q^{83} +7.86863 q^{85} -13.0494 q^{87} -1.70669 q^{89} +17.2409 q^{93} +27.2202 q^{95} +14.6859 q^{97} -4.48668 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{3} + 4q^{5} + 10q^{9} + O(q^{10}) \) \( 10q + 2q^{3} + 4q^{5} + 10q^{9} + 6q^{13} - 4q^{15} + 12q^{17} + 8q^{19} + 4q^{23} + 16q^{25} + 8q^{27} + 2q^{29} + 8q^{31} - 6q^{33} - 2q^{37} - 2q^{39} + 10q^{41} - 2q^{43} + 44q^{45} - 14q^{47} + 14q^{51} + 8q^{53} + 8q^{55} - 10q^{57} + 24q^{59} + 14q^{61} + 2q^{65} - 8q^{67} + 16q^{69} + 10q^{71} + 44q^{73} - 50q^{75} + 10q^{79} - 14q^{81} + 20q^{83} + 8q^{85} + 20q^{87} + 6q^{89} + 8q^{93} + 4q^{95} + 46q^{97} + 2q^{99} + O(q^{100}) \)

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
\(3\) −2.96176 −1.70997 −0.854986 0.518651i \(-0.826434\pi\)
−0.854986 + 0.518651i \(0.826434\pi\)
\(4\) 0 0
\(5\) 4.34462 1.94297 0.971486 0.237095i \(-0.0761954\pi\)
0.971486 + 0.237095i \(0.0761954\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 5.77201 1.92400
\(10\) 0 0
\(11\) −0.777317 −0.234370 −0.117185 0.993110i \(-0.537387\pi\)
−0.117185 + 0.993110i \(0.537387\pi\)
\(12\) 0 0
\(13\) −0.473242 −0.131254 −0.0656269 0.997844i \(-0.520905\pi\)
−0.0656269 + 0.997844i \(0.520905\pi\)
\(14\) 0 0
\(15\) −12.8677 −3.32243
\(16\) 0 0
\(17\) 1.81112 0.439261 0.219631 0.975583i \(-0.429515\pi\)
0.219631 + 0.975583i \(0.429515\pi\)
\(18\) 0 0
\(19\) 6.26526 1.43735 0.718675 0.695346i \(-0.244749\pi\)
0.718675 + 0.695346i \(0.244749\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 5.33938 1.11334 0.556669 0.830734i \(-0.312079\pi\)
0.556669 + 0.830734i \(0.312079\pi\)
\(24\) 0 0
\(25\) 13.8757 2.77514
\(26\) 0 0
\(27\) −8.21003 −1.58002
\(28\) 0 0
\(29\) 4.40596 0.818166 0.409083 0.912497i \(-0.365849\pi\)
0.409083 + 0.912497i \(0.365849\pi\)
\(30\) 0 0
\(31\) −5.82118 −1.04551 −0.522757 0.852482i \(-0.675097\pi\)
−0.522757 + 0.852482i \(0.675097\pi\)
\(32\) 0 0
\(33\) 2.30222 0.400766
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −8.34567 −1.37202 −0.686010 0.727592i \(-0.740639\pi\)
−0.686010 + 0.727592i \(0.740639\pi\)
\(38\) 0 0
\(39\) 1.40163 0.224440
\(40\) 0 0
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −6.18004 −0.942448 −0.471224 0.882014i \(-0.656188\pi\)
−0.471224 + 0.882014i \(0.656188\pi\)
\(44\) 0 0
\(45\) 25.0772 3.73829
\(46\) 0 0
\(47\) 6.01779 0.877785 0.438893 0.898540i \(-0.355371\pi\)
0.438893 + 0.898540i \(0.355371\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −5.36410 −0.751124
\(52\) 0 0
\(53\) 11.5946 1.59263 0.796317 0.604879i \(-0.206779\pi\)
0.796317 + 0.604879i \(0.206779\pi\)
\(54\) 0 0
\(55\) −3.37714 −0.455374
\(56\) 0 0
\(57\) −18.5562 −2.45783
\(58\) 0 0
\(59\) −0.805651 −0.104887 −0.0524434 0.998624i \(-0.516701\pi\)
−0.0524434 + 0.998624i \(0.516701\pi\)
\(60\) 0 0
\(61\) 11.1497 1.42757 0.713787 0.700363i \(-0.246979\pi\)
0.713787 + 0.700363i \(0.246979\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −2.05606 −0.255023
\(66\) 0 0
\(67\) −11.2115 −1.36970 −0.684852 0.728682i \(-0.740133\pi\)
−0.684852 + 0.728682i \(0.740133\pi\)
\(68\) 0 0
\(69\) −15.8140 −1.90378
\(70\) 0 0
\(71\) −1.94934 −0.231344 −0.115672 0.993287i \(-0.536902\pi\)
−0.115672 + 0.993287i \(0.536902\pi\)
\(72\) 0 0
\(73\) 0.839620 0.0982701 0.0491351 0.998792i \(-0.484354\pi\)
0.0491351 + 0.998792i \(0.484354\pi\)
\(74\) 0 0
\(75\) −41.0965 −4.74542
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 7.38355 0.830714 0.415357 0.909659i \(-0.363657\pi\)
0.415357 + 0.909659i \(0.363657\pi\)
\(80\) 0 0
\(81\) 7.00008 0.777787
\(82\) 0 0
\(83\) 9.38726 1.03039 0.515193 0.857074i \(-0.327720\pi\)
0.515193 + 0.857074i \(0.327720\pi\)
\(84\) 0 0
\(85\) 7.86863 0.853473
\(86\) 0 0
\(87\) −13.0494 −1.39904
\(88\) 0 0
\(89\) −1.70669 −0.180909 −0.0904543 0.995901i \(-0.528832\pi\)
−0.0904543 + 0.995901i \(0.528832\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 17.2409 1.78780
\(94\) 0 0
\(95\) 27.2202 2.79273
\(96\) 0 0
\(97\) 14.6859 1.49113 0.745566 0.666432i \(-0.232179\pi\)
0.745566 + 0.666432i \(0.232179\pi\)
\(98\) 0 0
\(99\) −4.48668 −0.450928
\(100\) 0 0
\(101\) 15.9881 1.59087 0.795437 0.606036i \(-0.207241\pi\)
0.795437 + 0.606036i \(0.207241\pi\)
\(102\) 0 0
\(103\) −7.25045 −0.714408 −0.357204 0.934026i \(-0.616270\pi\)
−0.357204 + 0.934026i \(0.616270\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0.674596 0.0652156 0.0326078 0.999468i \(-0.489619\pi\)
0.0326078 + 0.999468i \(0.489619\pi\)
\(108\) 0 0
\(109\) 8.73633 0.836788 0.418394 0.908266i \(-0.362593\pi\)
0.418394 + 0.908266i \(0.362593\pi\)
\(110\) 0 0
\(111\) 24.7179 2.34612
\(112\) 0 0
\(113\) −12.9348 −1.21681 −0.608403 0.793629i \(-0.708189\pi\)
−0.608403 + 0.793629i \(0.708189\pi\)
\(114\) 0 0
\(115\) 23.1976 2.16319
\(116\) 0 0
\(117\) −2.73156 −0.252533
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −10.3958 −0.945071
\(122\) 0 0
\(123\) −2.96176 −0.267053
\(124\) 0 0
\(125\) 38.5616 3.44906
\(126\) 0 0
\(127\) −1.94499 −0.172590 −0.0862948 0.996270i \(-0.527503\pi\)
−0.0862948 + 0.996270i \(0.527503\pi\)
\(128\) 0 0
\(129\) 18.3038 1.61156
\(130\) 0 0
\(131\) 2.79149 0.243894 0.121947 0.992537i \(-0.461086\pi\)
0.121947 + 0.992537i \(0.461086\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −35.6694 −3.06994
\(136\) 0 0
\(137\) −8.57721 −0.732800 −0.366400 0.930457i \(-0.619410\pi\)
−0.366400 + 0.930457i \(0.619410\pi\)
\(138\) 0 0
\(139\) −9.19507 −0.779916 −0.389958 0.920833i \(-0.627510\pi\)
−0.389958 + 0.920833i \(0.627510\pi\)
\(140\) 0 0
\(141\) −17.8232 −1.50099
\(142\) 0 0
\(143\) 0.367859 0.0307619
\(144\) 0 0
\(145\) 19.1422 1.58967
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −16.9177 −1.38595 −0.692976 0.720961i \(-0.743701\pi\)
−0.692976 + 0.720961i \(0.743701\pi\)
\(150\) 0 0
\(151\) −3.66377 −0.298153 −0.149077 0.988826i \(-0.547630\pi\)
−0.149077 + 0.988826i \(0.547630\pi\)
\(152\) 0 0
\(153\) 10.4538 0.845140
\(154\) 0 0
\(155\) −25.2908 −2.03141
\(156\) 0 0
\(157\) 1.32423 0.105685 0.0528425 0.998603i \(-0.483172\pi\)
0.0528425 + 0.998603i \(0.483172\pi\)
\(158\) 0 0
\(159\) −34.3403 −2.72336
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −5.50753 −0.431383 −0.215691 0.976462i \(-0.569201\pi\)
−0.215691 + 0.976462i \(0.569201\pi\)
\(164\) 0 0
\(165\) 10.0023 0.778677
\(166\) 0 0
\(167\) 23.2282 1.79745 0.898724 0.438514i \(-0.144495\pi\)
0.898724 + 0.438514i \(0.144495\pi\)
\(168\) 0 0
\(169\) −12.7760 −0.982772
\(170\) 0 0
\(171\) 36.1632 2.76547
\(172\) 0 0
\(173\) −21.8761 −1.66321 −0.831606 0.555366i \(-0.812578\pi\)
−0.831606 + 0.555366i \(0.812578\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 2.38614 0.179354
\(178\) 0 0
\(179\) −14.6814 −1.09734 −0.548670 0.836039i \(-0.684866\pi\)
−0.548670 + 0.836039i \(0.684866\pi\)
\(180\) 0 0
\(181\) 4.97537 0.369816 0.184908 0.982756i \(-0.440801\pi\)
0.184908 + 0.982756i \(0.440801\pi\)
\(182\) 0 0
\(183\) −33.0227 −2.44111
\(184\) 0 0
\(185\) −36.2588 −2.66580
\(186\) 0 0
\(187\) −1.40781 −0.102950
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 21.3511 1.54491 0.772457 0.635067i \(-0.219027\pi\)
0.772457 + 0.635067i \(0.219027\pi\)
\(192\) 0 0
\(193\) −12.5624 −0.904265 −0.452132 0.891951i \(-0.649337\pi\)
−0.452132 + 0.891951i \(0.649337\pi\)
\(194\) 0 0
\(195\) 6.08954 0.436081
\(196\) 0 0
\(197\) 20.7339 1.47723 0.738614 0.674128i \(-0.235480\pi\)
0.738614 + 0.674128i \(0.235480\pi\)
\(198\) 0 0
\(199\) −15.4142 −1.09268 −0.546341 0.837563i \(-0.683980\pi\)
−0.546341 + 0.837563i \(0.683980\pi\)
\(200\) 0 0
\(201\) 33.2058 2.34216
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 4.34462 0.303441
\(206\) 0 0
\(207\) 30.8190 2.14207
\(208\) 0 0
\(209\) −4.87009 −0.336871
\(210\) 0 0
\(211\) −20.4010 −1.40446 −0.702232 0.711948i \(-0.747813\pi\)
−0.702232 + 0.711948i \(0.747813\pi\)
\(212\) 0 0
\(213\) 5.77346 0.395591
\(214\) 0 0
\(215\) −26.8499 −1.83115
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −2.48675 −0.168039
\(220\) 0 0
\(221\) −0.857099 −0.0576547
\(222\) 0 0
\(223\) −27.8030 −1.86182 −0.930912 0.365242i \(-0.880986\pi\)
−0.930912 + 0.365242i \(0.880986\pi\)
\(224\) 0 0
\(225\) 80.0908 5.33939
\(226\) 0 0
\(227\) −10.3315 −0.685727 −0.342864 0.939385i \(-0.611397\pi\)
−0.342864 + 0.939385i \(0.611397\pi\)
\(228\) 0 0
\(229\) 28.5063 1.88375 0.941874 0.335965i \(-0.109063\pi\)
0.941874 + 0.335965i \(0.109063\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.50991 0.0989176 0.0494588 0.998776i \(-0.484250\pi\)
0.0494588 + 0.998776i \(0.484250\pi\)
\(234\) 0 0
\(235\) 26.1450 1.70551
\(236\) 0 0
\(237\) −21.8683 −1.42050
\(238\) 0 0
\(239\) −7.04433 −0.455660 −0.227830 0.973701i \(-0.573163\pi\)
−0.227830 + 0.973701i \(0.573163\pi\)
\(240\) 0 0
\(241\) −15.1907 −0.978521 −0.489261 0.872138i \(-0.662733\pi\)
−0.489261 + 0.872138i \(0.662733\pi\)
\(242\) 0 0
\(243\) 3.89753 0.250027
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −2.96499 −0.188658
\(248\) 0 0
\(249\) −27.8028 −1.76193
\(250\) 0 0
\(251\) 26.7280 1.68705 0.843527 0.537086i \(-0.180475\pi\)
0.843527 + 0.537086i \(0.180475\pi\)
\(252\) 0 0
\(253\) −4.15039 −0.260933
\(254\) 0 0
\(255\) −23.3050 −1.45941
\(256\) 0 0
\(257\) 1.40136 0.0874142 0.0437071 0.999044i \(-0.486083\pi\)
0.0437071 + 0.999044i \(0.486083\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 25.4312 1.57415
\(262\) 0 0
\(263\) 7.49483 0.462151 0.231075 0.972936i \(-0.425776\pi\)
0.231075 + 0.972936i \(0.425776\pi\)
\(264\) 0 0
\(265\) 50.3739 3.09445
\(266\) 0 0
\(267\) 5.05480 0.309349
\(268\) 0 0
\(269\) −1.15251 −0.0702696 −0.0351348 0.999383i \(-0.511186\pi\)
−0.0351348 + 0.999383i \(0.511186\pi\)
\(270\) 0 0
\(271\) 22.5833 1.37183 0.685917 0.727679i \(-0.259401\pi\)
0.685917 + 0.727679i \(0.259401\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −10.7858 −0.650410
\(276\) 0 0
\(277\) −27.5147 −1.65320 −0.826599 0.562792i \(-0.809727\pi\)
−0.826599 + 0.562792i \(0.809727\pi\)
\(278\) 0 0
\(279\) −33.5999 −2.01157
\(280\) 0 0
\(281\) 24.8737 1.48384 0.741919 0.670489i \(-0.233916\pi\)
0.741919 + 0.670489i \(0.233916\pi\)
\(282\) 0 0
\(283\) 20.3751 1.21117 0.605587 0.795779i \(-0.292938\pi\)
0.605587 + 0.795779i \(0.292938\pi\)
\(284\) 0 0
\(285\) −80.6196 −4.77549
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −13.7198 −0.807050
\(290\) 0 0
\(291\) −43.4962 −2.54979
\(292\) 0 0
\(293\) −30.9980 −1.81092 −0.905461 0.424430i \(-0.860475\pi\)
−0.905461 + 0.424430i \(0.860475\pi\)
\(294\) 0 0
\(295\) −3.50025 −0.203792
\(296\) 0 0
\(297\) 6.38179 0.370309
\(298\) 0 0
\(299\) −2.52682 −0.146130
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −47.3529 −2.72035
\(304\) 0 0
\(305\) 48.4412 2.77374
\(306\) 0 0
\(307\) −10.1771 −0.580836 −0.290418 0.956900i \(-0.593794\pi\)
−0.290418 + 0.956900i \(0.593794\pi\)
\(308\) 0 0
\(309\) 21.4741 1.22162
\(310\) 0 0
\(311\) 3.14919 0.178574 0.0892872 0.996006i \(-0.471541\pi\)
0.0892872 + 0.996006i \(0.471541\pi\)
\(312\) 0 0
\(313\) −8.17767 −0.462229 −0.231115 0.972927i \(-0.574237\pi\)
−0.231115 + 0.972927i \(0.574237\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −8.92361 −0.501200 −0.250600 0.968091i \(-0.580628\pi\)
−0.250600 + 0.968091i \(0.580628\pi\)
\(318\) 0 0
\(319\) −3.42482 −0.191753
\(320\) 0 0
\(321\) −1.99799 −0.111517
\(322\) 0 0
\(323\) 11.3471 0.631372
\(324\) 0 0
\(325\) −6.56658 −0.364248
\(326\) 0 0
\(327\) −25.8749 −1.43088
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 22.5865 1.24147 0.620733 0.784022i \(-0.286835\pi\)
0.620733 + 0.784022i \(0.286835\pi\)
\(332\) 0 0
\(333\) −48.1713 −2.63977
\(334\) 0 0
\(335\) −48.7098 −2.66130
\(336\) 0 0
\(337\) 23.3958 1.27445 0.637226 0.770677i \(-0.280082\pi\)
0.637226 + 0.770677i \(0.280082\pi\)
\(338\) 0 0
\(339\) 38.3098 2.08070
\(340\) 0 0
\(341\) 4.52490 0.245037
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −68.7056 −3.69899
\(346\) 0 0
\(347\) −6.89527 −0.370157 −0.185079 0.982724i \(-0.559254\pi\)
−0.185079 + 0.982724i \(0.559254\pi\)
\(348\) 0 0
\(349\) 16.7273 0.895390 0.447695 0.894186i \(-0.352245\pi\)
0.447695 + 0.894186i \(0.352245\pi\)
\(350\) 0 0
\(351\) 3.88533 0.207384
\(352\) 0 0
\(353\) −5.57591 −0.296776 −0.148388 0.988929i \(-0.547408\pi\)
−0.148388 + 0.988929i \(0.547408\pi\)
\(354\) 0 0
\(355\) −8.46912 −0.449494
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −6.55920 −0.346181 −0.173091 0.984906i \(-0.555375\pi\)
−0.173091 + 0.984906i \(0.555375\pi\)
\(360\) 0 0
\(361\) 20.2535 1.06598
\(362\) 0 0
\(363\) 30.7898 1.61604
\(364\) 0 0
\(365\) 3.64783 0.190936
\(366\) 0 0
\(367\) 13.8404 0.722464 0.361232 0.932476i \(-0.382356\pi\)
0.361232 + 0.932476i \(0.382356\pi\)
\(368\) 0 0
\(369\) 5.77201 0.300479
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 23.6114 1.22255 0.611277 0.791417i \(-0.290656\pi\)
0.611277 + 0.791417i \(0.290656\pi\)
\(374\) 0 0
\(375\) −114.210 −5.89779
\(376\) 0 0
\(377\) −2.08509 −0.107387
\(378\) 0 0
\(379\) −28.5591 −1.46698 −0.733490 0.679700i \(-0.762110\pi\)
−0.733490 + 0.679700i \(0.762110\pi\)
\(380\) 0 0
\(381\) 5.76058 0.295123
\(382\) 0 0
\(383\) 4.45484 0.227632 0.113816 0.993502i \(-0.463693\pi\)
0.113816 + 0.993502i \(0.463693\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −35.6713 −1.81327
\(388\) 0 0
\(389\) 31.2216 1.58300 0.791499 0.611171i \(-0.209301\pi\)
0.791499 + 0.611171i \(0.209301\pi\)
\(390\) 0 0
\(391\) 9.67026 0.489046
\(392\) 0 0
\(393\) −8.26773 −0.417052
\(394\) 0 0
\(395\) 32.0787 1.61405
\(396\) 0 0
\(397\) −3.26537 −0.163884 −0.0819420 0.996637i \(-0.526112\pi\)
−0.0819420 + 0.996637i \(0.526112\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 16.6650 0.832209 0.416104 0.909317i \(-0.363395\pi\)
0.416104 + 0.909317i \(0.363395\pi\)
\(402\) 0 0
\(403\) 2.75483 0.137228
\(404\) 0 0
\(405\) 30.4127 1.51122
\(406\) 0 0
\(407\) 6.48723 0.321560
\(408\) 0 0
\(409\) −16.0203 −0.792151 −0.396075 0.918218i \(-0.629628\pi\)
−0.396075 + 0.918218i \(0.629628\pi\)
\(410\) 0 0
\(411\) 25.4036 1.25307
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 40.7841 2.00201
\(416\) 0 0
\(417\) 27.2336 1.33363
\(418\) 0 0
\(419\) 8.46285 0.413437 0.206719 0.978400i \(-0.433722\pi\)
0.206719 + 0.978400i \(0.433722\pi\)
\(420\) 0 0
\(421\) −15.6972 −0.765033 −0.382517 0.923949i \(-0.624943\pi\)
−0.382517 + 0.923949i \(0.624943\pi\)
\(422\) 0 0
\(423\) 34.7348 1.68886
\(424\) 0 0
\(425\) 25.1306 1.21901
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −1.08951 −0.0526020
\(430\) 0 0
\(431\) 24.8406 1.19653 0.598265 0.801298i \(-0.295857\pi\)
0.598265 + 0.801298i \(0.295857\pi\)
\(432\) 0 0
\(433\) −0.240670 −0.0115658 −0.00578292 0.999983i \(-0.501841\pi\)
−0.00578292 + 0.999983i \(0.501841\pi\)
\(434\) 0 0
\(435\) −56.6946 −2.71830
\(436\) 0 0
\(437\) 33.4526 1.60026
\(438\) 0 0
\(439\) 26.0884 1.24513 0.622566 0.782567i \(-0.286090\pi\)
0.622566 + 0.782567i \(0.286090\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −26.6254 −1.26501 −0.632505 0.774556i \(-0.717973\pi\)
−0.632505 + 0.774556i \(0.717973\pi\)
\(444\) 0 0
\(445\) −7.41491 −0.351501
\(446\) 0 0
\(447\) 50.1061 2.36994
\(448\) 0 0
\(449\) 13.5727 0.640537 0.320269 0.947327i \(-0.396227\pi\)
0.320269 + 0.947327i \(0.396227\pi\)
\(450\) 0 0
\(451\) −0.777317 −0.0366024
\(452\) 0 0
\(453\) 10.8512 0.509834
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −15.1675 −0.709503 −0.354752 0.934961i \(-0.615435\pi\)
−0.354752 + 0.934961i \(0.615435\pi\)
\(458\) 0 0
\(459\) −14.8693 −0.694042
\(460\) 0 0
\(461\) −30.0225 −1.39829 −0.699144 0.714981i \(-0.746436\pi\)
−0.699144 + 0.714981i \(0.746436\pi\)
\(462\) 0 0
\(463\) 18.4379 0.856881 0.428441 0.903570i \(-0.359063\pi\)
0.428441 + 0.903570i \(0.359063\pi\)
\(464\) 0 0
\(465\) 74.9052 3.47365
\(466\) 0 0
\(467\) 14.9313 0.690940 0.345470 0.938430i \(-0.387719\pi\)
0.345470 + 0.938430i \(0.387719\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −3.92205 −0.180718
\(472\) 0 0
\(473\) 4.80385 0.220881
\(474\) 0 0
\(475\) 86.9350 3.98885
\(476\) 0 0
\(477\) 66.9239 3.06423
\(478\) 0 0
\(479\) 1.88129 0.0859585 0.0429792 0.999076i \(-0.486315\pi\)
0.0429792 + 0.999076i \(0.486315\pi\)
\(480\) 0 0
\(481\) 3.94952 0.180083
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 63.8048 2.89723
\(486\) 0 0
\(487\) −34.5885 −1.56736 −0.783678 0.621167i \(-0.786659\pi\)
−0.783678 + 0.621167i \(0.786659\pi\)
\(488\) 0 0
\(489\) 16.3120 0.737653
\(490\) 0 0
\(491\) 10.3562 0.467367 0.233684 0.972313i \(-0.424922\pi\)
0.233684 + 0.972313i \(0.424922\pi\)
\(492\) 0 0
\(493\) 7.97972 0.359389
\(494\) 0 0
\(495\) −19.4929 −0.876141
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 12.6775 0.567523 0.283761 0.958895i \(-0.408418\pi\)
0.283761 + 0.958895i \(0.408418\pi\)
\(500\) 0 0
\(501\) −68.7962 −3.07359
\(502\) 0 0
\(503\) 9.37790 0.418140 0.209070 0.977901i \(-0.432956\pi\)
0.209070 + 0.977901i \(0.432956\pi\)
\(504\) 0 0
\(505\) 69.4622 3.09103
\(506\) 0 0
\(507\) 37.8395 1.68051
\(508\) 0 0
\(509\) 15.4818 0.686217 0.343109 0.939296i \(-0.388520\pi\)
0.343109 + 0.939296i \(0.388520\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −51.4380 −2.27104
\(514\) 0 0
\(515\) −31.5004 −1.38808
\(516\) 0 0
\(517\) −4.67773 −0.205726
\(518\) 0 0
\(519\) 64.7918 2.84405
\(520\) 0 0
\(521\) 9.75537 0.427391 0.213695 0.976900i \(-0.431450\pi\)
0.213695 + 0.976900i \(0.431450\pi\)
\(522\) 0 0
\(523\) −18.1546 −0.793847 −0.396923 0.917852i \(-0.629922\pi\)
−0.396923 + 0.917852i \(0.629922\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −10.5429 −0.459254
\(528\) 0 0
\(529\) 5.50900 0.239522
\(530\) 0 0
\(531\) −4.65023 −0.201803
\(532\) 0 0
\(533\) −0.473242 −0.0204984
\(534\) 0 0
\(535\) 2.93086 0.126712
\(536\) 0 0
\(537\) 43.4828 1.87642
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 17.1428 0.737026 0.368513 0.929623i \(-0.379867\pi\)
0.368513 + 0.929623i \(0.379867\pi\)
\(542\) 0 0
\(543\) −14.7358 −0.632376
\(544\) 0 0
\(545\) 37.9560 1.62586
\(546\) 0 0
\(547\) −8.67181 −0.370780 −0.185390 0.982665i \(-0.559355\pi\)
−0.185390 + 0.982665i \(0.559355\pi\)
\(548\) 0 0
\(549\) 64.3562 2.74666
\(550\) 0 0
\(551\) 27.6045 1.17599
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 107.390 4.55844
\(556\) 0 0
\(557\) 32.3112 1.36907 0.684534 0.728981i \(-0.260006\pi\)
0.684534 + 0.728981i \(0.260006\pi\)
\(558\) 0 0
\(559\) 2.92466 0.123700
\(560\) 0 0
\(561\) 4.16960 0.176041
\(562\) 0 0
\(563\) 8.65741 0.364866 0.182433 0.983218i \(-0.441603\pi\)
0.182433 + 0.983218i \(0.441603\pi\)
\(564\) 0 0
\(565\) −56.1968 −2.36422
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −0.0695216 −0.00291450 −0.00145725 0.999999i \(-0.500464\pi\)
−0.00145725 + 0.999999i \(0.500464\pi\)
\(570\) 0 0
\(571\) 22.9988 0.962471 0.481235 0.876591i \(-0.340188\pi\)
0.481235 + 0.876591i \(0.340188\pi\)
\(572\) 0 0
\(573\) −63.2369 −2.64176
\(574\) 0 0
\(575\) 74.0878 3.08967
\(576\) 0 0
\(577\) 11.4503 0.476684 0.238342 0.971181i \(-0.423396\pi\)
0.238342 + 0.971181i \(0.423396\pi\)
\(578\) 0 0
\(579\) 37.2069 1.54627
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −9.01264 −0.373265
\(584\) 0 0
\(585\) −11.8676 −0.490664
\(586\) 0 0
\(587\) −31.3990 −1.29598 −0.647988 0.761650i \(-0.724389\pi\)
−0.647988 + 0.761650i \(0.724389\pi\)
\(588\) 0 0
\(589\) −36.4712 −1.50277
\(590\) 0 0
\(591\) −61.4088 −2.52602
\(592\) 0 0
\(593\) −34.2830 −1.40784 −0.703918 0.710282i \(-0.748568\pi\)
−0.703918 + 0.710282i \(0.748568\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 45.6531 1.86846
\(598\) 0 0
\(599\) 16.7968 0.686299 0.343149 0.939281i \(-0.388506\pi\)
0.343149 + 0.939281i \(0.388506\pi\)
\(600\) 0 0
\(601\) 33.3700 1.36119 0.680595 0.732660i \(-0.261722\pi\)
0.680595 + 0.732660i \(0.261722\pi\)
\(602\) 0 0
\(603\) −64.7130 −2.63532
\(604\) 0 0
\(605\) −45.1657 −1.83625
\(606\) 0 0
\(607\) −34.0401 −1.38165 −0.690823 0.723024i \(-0.742752\pi\)
−0.690823 + 0.723024i \(0.742752\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2.84787 −0.115213
\(612\) 0 0
\(613\) −3.96034 −0.159957 −0.0799784 0.996797i \(-0.525485\pi\)
−0.0799784 + 0.996797i \(0.525485\pi\)
\(614\) 0 0
\(615\) −12.8677 −0.518876
\(616\) 0 0
\(617\) −7.50998 −0.302340 −0.151170 0.988508i \(-0.548304\pi\)
−0.151170 + 0.988508i \(0.548304\pi\)
\(618\) 0 0
\(619\) 15.4020 0.619060 0.309530 0.950890i \(-0.399828\pi\)
0.309530 + 0.950890i \(0.399828\pi\)
\(620\) 0 0
\(621\) −43.8365 −1.75910
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 98.1569 3.92628
\(626\) 0 0
\(627\) 14.4240 0.576041
\(628\) 0 0
\(629\) −15.1150 −0.602675
\(630\) 0 0
\(631\) −45.3178 −1.80407 −0.902037 0.431659i \(-0.857928\pi\)
−0.902037 + 0.431659i \(0.857928\pi\)
\(632\) 0 0
\(633\) 60.4229 2.40159
\(634\) 0 0
\(635\) −8.45022 −0.335337
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −11.2516 −0.445106
\(640\) 0 0
\(641\) 0.421364 0.0166429 0.00832145 0.999965i \(-0.497351\pi\)
0.00832145 + 0.999965i \(0.497351\pi\)
\(642\) 0 0
\(643\) 34.4259 1.35763 0.678813 0.734311i \(-0.262495\pi\)
0.678813 + 0.734311i \(0.262495\pi\)
\(644\) 0 0
\(645\) 79.5230 3.13122
\(646\) 0 0
\(647\) 45.0852 1.77248 0.886241 0.463225i \(-0.153308\pi\)
0.886241 + 0.463225i \(0.153308\pi\)
\(648\) 0 0
\(649\) 0.626246 0.0245823
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3.66039 −0.143242 −0.0716211 0.997432i \(-0.522817\pi\)
−0.0716211 + 0.997432i \(0.522817\pi\)
\(654\) 0 0
\(655\) 12.1280 0.473879
\(656\) 0 0
\(657\) 4.84630 0.189072
\(658\) 0 0
\(659\) 46.9835 1.83022 0.915110 0.403205i \(-0.132104\pi\)
0.915110 + 0.403205i \(0.132104\pi\)
\(660\) 0 0
\(661\) −5.14381 −0.200071 −0.100035 0.994984i \(-0.531896\pi\)
−0.100035 + 0.994984i \(0.531896\pi\)
\(662\) 0 0
\(663\) 2.53852 0.0985879
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 23.5251 0.910896
\(668\) 0 0
\(669\) 82.3457 3.18367
\(670\) 0 0
\(671\) −8.66685 −0.334580
\(672\) 0 0
\(673\) 37.2378 1.43541 0.717705 0.696347i \(-0.245193\pi\)
0.717705 + 0.696347i \(0.245193\pi\)
\(674\) 0 0
\(675\) −113.920 −4.38478
\(676\) 0 0
\(677\) 38.8501 1.49313 0.746566 0.665312i \(-0.231701\pi\)
0.746566 + 0.665312i \(0.231701\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 30.5995 1.17257
\(682\) 0 0
\(683\) 39.8187 1.52362 0.761810 0.647800i \(-0.224311\pi\)
0.761810 + 0.647800i \(0.224311\pi\)
\(684\) 0 0
\(685\) −37.2647 −1.42381
\(686\) 0 0
\(687\) −84.4287 −3.22116
\(688\) 0 0
\(689\) −5.48703 −0.209039
\(690\) 0 0
\(691\) 0.932852 0.0354874 0.0177437 0.999843i \(-0.494352\pi\)
0.0177437 + 0.999843i \(0.494352\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −39.9491 −1.51535
\(696\) 0 0
\(697\) 1.81112 0.0686011
\(698\) 0 0
\(699\) −4.47199 −0.169146
\(700\) 0 0
\(701\) −5.45593 −0.206068 −0.103034 0.994678i \(-0.532855\pi\)
−0.103034 + 0.994678i \(0.532855\pi\)
\(702\) 0 0
\(703\) −52.2878 −1.97207
\(704\) 0 0
\(705\) −77.4352 −2.91638
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −45.0496 −1.69187 −0.845936 0.533285i \(-0.820957\pi\)
−0.845936 + 0.533285i \(0.820957\pi\)
\(710\) 0 0
\(711\) 42.6179 1.59830
\(712\) 0 0
\(713\) −31.0815 −1.16401
\(714\) 0 0
\(715\) 1.59821 0.0597696
\(716\) 0 0
\(717\) 20.8636 0.779165
\(718\) 0 0
\(719\) −28.8202 −1.07481 −0.537406 0.843324i \(-0.680596\pi\)
−0.537406 + 0.843324i \(0.680596\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 44.9913 1.67324
\(724\) 0 0
\(725\) 61.1358 2.27053
\(726\) 0 0
\(727\) 30.8265 1.14329 0.571645 0.820501i \(-0.306306\pi\)
0.571645 + 0.820501i \(0.306306\pi\)
\(728\) 0 0
\(729\) −32.5438 −1.20533
\(730\) 0 0
\(731\) −11.1928 −0.413981
\(732\) 0 0
\(733\) 53.0576 1.95973 0.979863 0.199669i \(-0.0639867\pi\)
0.979863 + 0.199669i \(0.0639867\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 8.71489 0.321017
\(738\) 0 0
\(739\) 15.2346 0.560415 0.280208 0.959939i \(-0.409597\pi\)
0.280208 + 0.959939i \(0.409597\pi\)
\(740\) 0 0
\(741\) 8.78158 0.322599
\(742\) 0 0
\(743\) 8.89696 0.326398 0.163199 0.986593i \(-0.447819\pi\)
0.163199 + 0.986593i \(0.447819\pi\)
\(744\) 0 0
\(745\) −73.5009 −2.69287
\(746\) 0 0
\(747\) 54.1834 1.98247
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −27.8216 −1.01523 −0.507613 0.861585i \(-0.669472\pi\)
−0.507613 + 0.861585i \(0.669472\pi\)
\(752\) 0 0
\(753\) −79.1618 −2.88482
\(754\) 0 0
\(755\) −15.9177 −0.579303
\(756\) 0 0
\(757\) −29.2295 −1.06236 −0.531182 0.847258i \(-0.678252\pi\)
−0.531182 + 0.847258i \(0.678252\pi\)
\(758\) 0 0
\(759\) 12.2925 0.446188
\(760\) 0 0
\(761\) −29.5761 −1.07213 −0.536066 0.844176i \(-0.680090\pi\)
−0.536066 + 0.844176i \(0.680090\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 45.4178 1.64208
\(766\) 0 0
\(767\) 0.381268 0.0137668
\(768\) 0 0
\(769\) −6.48266 −0.233771 −0.116885 0.993145i \(-0.537291\pi\)
−0.116885 + 0.993145i \(0.537291\pi\)
\(770\) 0 0
\(771\) −4.15048 −0.149476
\(772\) 0 0
\(773\) 18.5208 0.666146 0.333073 0.942901i \(-0.391914\pi\)
0.333073 + 0.942901i \(0.391914\pi\)
\(774\) 0 0
\(775\) −80.7730 −2.90145
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 6.26526 0.224476
\(780\) 0 0
\(781\) 1.51525 0.0542199
\(782\) 0 0
\(783\) −36.1730 −1.29272
\(784\) 0 0
\(785\) 5.75327 0.205343
\(786\) 0 0
\(787\) −48.6346 −1.73364 −0.866818 0.498624i \(-0.833839\pi\)
−0.866818 + 0.498624i \(0.833839\pi\)
\(788\) 0 0
\(789\) −22.1979 −0.790265
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −5.27651 −0.187374
\(794\) 0 0
\(795\) −149.195 −5.29141
\(796\) 0 0
\(797\) −8.70523 −0.308355 −0.154178 0.988043i \(-0.549273\pi\)
−0.154178 + 0.988043i \(0.549273\pi\)
\(798\) 0 0
\(799\) 10.8989 0.385577
\(800\) 0 0
\(801\) −9.85103 −0.348069
\(802\) 0 0
\(803\) −0.652651 −0.0230315
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 3.41345 0.120159
\(808\) 0 0
\(809\) 8.34063 0.293241 0.146620 0.989193i \(-0.453160\pi\)
0.146620 + 0.989193i \(0.453160\pi\)
\(810\) 0 0
\(811\) 27.3542 0.960537 0.480269 0.877121i \(-0.340539\pi\)
0.480269 + 0.877121i \(0.340539\pi\)
\(812\) 0 0
\(813\) −66.8861 −2.34580
\(814\) 0 0
\(815\) −23.9281 −0.838165
\(816\) 0 0
\(817\) −38.7196 −1.35463
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 5.23089 0.182559 0.0912797 0.995825i \(-0.470904\pi\)
0.0912797 + 0.995825i \(0.470904\pi\)
\(822\) 0 0
\(823\) 23.8963 0.832973 0.416487 0.909142i \(-0.363261\pi\)
0.416487 + 0.909142i \(0.363261\pi\)
\(824\) 0 0
\(825\) 31.9450 1.11218
\(826\) 0 0
\(827\) 54.4579 1.89369 0.946843 0.321696i \(-0.104253\pi\)
0.946843 + 0.321696i \(0.104253\pi\)
\(828\) 0 0
\(829\) 48.6163 1.68851 0.844257 0.535939i \(-0.180042\pi\)
0.844257 + 0.535939i \(0.180042\pi\)
\(830\) 0 0
\(831\) 81.4919 2.82692
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 100.917 3.49239
\(836\) 0 0
\(837\) 47.7920 1.65193
\(838\) 0 0
\(839\) −13.5147 −0.466579 −0.233290 0.972407i \(-0.574949\pi\)
−0.233290 + 0.972407i \(0.574949\pi\)
\(840\) 0 0
\(841\) −9.58753 −0.330604
\(842\) 0 0
\(843\) −73.6698 −2.53732
\(844\) 0 0
\(845\) −55.5070 −1.90950
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −60.3461 −2.07107
\(850\) 0 0
\(851\) −44.5607 −1.52752
\(852\) 0 0
\(853\) −23.0117 −0.787906 −0.393953 0.919131i \(-0.628893\pi\)
−0.393953 + 0.919131i \(0.628893\pi\)
\(854\) 0 0
\(855\) 157.115 5.37323
\(856\) 0 0
\(857\) −32.1888 −1.09955 −0.549775 0.835313i \(-0.685287\pi\)
−0.549775 + 0.835313i \(0.685287\pi\)
\(858\) 0 0
\(859\) 6.42212 0.219120 0.109560 0.993980i \(-0.465056\pi\)
0.109560 + 0.993980i \(0.465056\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 48.5039 1.65109 0.825546 0.564335i \(-0.190868\pi\)
0.825546 + 0.564335i \(0.190868\pi\)
\(864\) 0 0
\(865\) −95.0435 −3.23157
\(866\) 0 0
\(867\) 40.6349 1.38003
\(868\) 0 0
\(869\) −5.73935 −0.194694
\(870\) 0 0
\(871\) 5.30576 0.179779
\(872\) 0 0
\(873\) 84.7674 2.86894
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −7.65826 −0.258601 −0.129300 0.991605i \(-0.541273\pi\)
−0.129300 + 0.991605i \(0.541273\pi\)
\(878\) 0 0
\(879\) 91.8085 3.09663
\(880\) 0 0
\(881\) 5.90364 0.198899 0.0994493 0.995043i \(-0.468292\pi\)
0.0994493 + 0.995043i \(0.468292\pi\)
\(882\) 0 0
\(883\) −52.0445 −1.75144 −0.875718 0.482823i \(-0.839611\pi\)
−0.875718 + 0.482823i \(0.839611\pi\)
\(884\) 0 0
\(885\) 10.3669 0.348479
\(886\) 0 0
\(887\) 43.2210 1.45122 0.725609 0.688107i \(-0.241558\pi\)
0.725609 + 0.688107i \(0.241558\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −5.44128 −0.182290
\(892\) 0 0
\(893\) 37.7031 1.26168
\(894\) 0 0
\(895\) −63.7852 −2.13210
\(896\) 0 0
\(897\) 7.48383 0.249878
\(898\) 0 0
\(899\) −25.6479 −0.855404
\(900\) 0 0
\(901\) 20.9991 0.699583
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 21.6161 0.718543
\(906\) 0 0
\(907\) −38.9644 −1.29379 −0.646896 0.762578i \(-0.723933\pi\)
−0.646896 + 0.762578i \(0.723933\pi\)
\(908\) 0 0
\(909\) 92.2835 3.06085
\(910\) 0 0
\(911\) −6.96047 −0.230611 −0.115305 0.993330i \(-0.536785\pi\)
−0.115305 + 0.993330i \(0.536785\pi\)
\(912\) 0 0
\(913\) −7.29688 −0.241491
\(914\) 0 0
\(915\) −143.471 −4.74301
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 44.8592 1.47977 0.739885 0.672734i \(-0.234880\pi\)
0.739885 + 0.672734i \(0.234880\pi\)
\(920\) 0 0
\(921\) 30.1420 0.993213
\(922\) 0 0
\(923\) 0.922508 0.0303647
\(924\) 0 0
\(925\) −115.802 −3.80755
\(926\) 0 0
\(927\) −41.8497 −1.37452
\(928\) 0 0
\(929\) 18.4043 0.603825 0.301912 0.953336i \(-0.402375\pi\)
0.301912 + 0.953336i \(0.402375\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −9.32715 −0.305357
\(934\) 0 0
\(935\) −6.11641 −0.200028
\(936\) 0 0
\(937\) −54.0819 −1.76678 −0.883389 0.468640i \(-0.844744\pi\)
−0.883389 + 0.468640i \(0.844744\pi\)
\(938\) 0 0
\(939\) 24.2203 0.790399
\(940\) 0 0
\(941\) 33.4289 1.08975 0.544876 0.838517i \(-0.316577\pi\)
0.544876 + 0.838517i \(0.316577\pi\)
\(942\) 0 0
\(943\) 5.33938 0.173874
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 40.2312 1.30734 0.653670 0.756780i \(-0.273229\pi\)
0.653670 + 0.756780i \(0.273229\pi\)
\(948\) 0 0
\(949\) −0.397344 −0.0128983
\(950\) 0 0
\(951\) 26.4296 0.857038
\(952\) 0 0
\(953\) −27.9614 −0.905758 −0.452879 0.891572i \(-0.649603\pi\)
−0.452879 + 0.891572i \(0.649603\pi\)
\(954\) 0 0
\(955\) 92.7626 3.00173
\(956\) 0 0
\(957\) 10.1435 0.327893
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 2.88610 0.0930999
\(962\) 0 0
\(963\) 3.89378 0.125475
\(964\) 0 0
\(965\) −54.5791 −1.75696
\(966\) 0 0
\(967\) −29.5335 −0.949735 −0.474867 0.880057i \(-0.657504\pi\)
−0.474867 + 0.880057i \(0.657504\pi\)
\(968\) 0 0
\(969\) −33.6075 −1.07963
\(970\) 0 0
\(971\) −30.8254 −0.989234 −0.494617 0.869111i \(-0.664692\pi\)
−0.494617 + 0.869111i \(0.664692\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 19.4486 0.622854
\(976\) 0 0
\(977\) 10.3591 0.331416 0.165708 0.986175i \(-0.447009\pi\)
0.165708 + 0.986175i \(0.447009\pi\)
\(978\) 0 0
\(979\) 1.32664 0.0423995
\(980\) 0 0
\(981\) 50.4262 1.60998
\(982\) 0 0
\(983\) 40.3298 1.28632 0.643160 0.765732i \(-0.277623\pi\)
0.643160 + 0.765732i \(0.277623\pi\)
\(984\) 0 0
\(985\) 90.0809 2.87022
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −32.9976 −1.04926
\(990\) 0 0
\(991\) 9.26788 0.294404 0.147202 0.989106i \(-0.452973\pi\)
0.147202 + 0.989106i \(0.452973\pi\)
\(992\) 0 0
\(993\) −66.8957 −2.12287
\(994\) 0 0
\(995\) −66.9688 −2.12305
\(996\) 0 0
\(997\) −59.5037 −1.88450 −0.942251 0.334908i \(-0.891295\pi\)
−0.942251 + 0.334908i \(0.891295\pi\)
\(998\) 0 0
\(999\) 68.5182 2.16782
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 \(a_p\))