Properties

Label 8036.2.a.p.1.6
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 1.6
Root \(0.729469\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.729469 q^{3} -3.02160 q^{5} -2.46788 q^{9} +O(q^{10})\) \(q+0.729469 q^{3} -3.02160 q^{5} -2.46788 q^{9} -2.63548 q^{11} +0.419531 q^{13} -2.20416 q^{15} -4.48814 q^{17} +4.82614 q^{19} +0.672994 q^{23} +4.13008 q^{25} -3.98864 q^{27} -7.40739 q^{29} -3.91525 q^{31} -1.92250 q^{33} -2.78938 q^{37} +0.306035 q^{39} +1.00000 q^{41} +9.85531 q^{43} +7.45694 q^{45} -12.2186 q^{47} -3.27396 q^{51} -12.6009 q^{53} +7.96337 q^{55} +3.52052 q^{57} +8.17437 q^{59} -5.69538 q^{61} -1.26766 q^{65} -4.13105 q^{67} +0.490928 q^{69} +16.7449 q^{71} +11.9924 q^{73} +3.01276 q^{75} -5.02996 q^{79} +4.49403 q^{81} +4.57801 q^{83} +13.5614 q^{85} -5.40346 q^{87} -12.8020 q^{89} -2.85605 q^{93} -14.5827 q^{95} +4.57826 q^{97} +6.50404 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{3} + 4q^{5} + 10q^{9} + O(q^{10}) \) \( 10q + 2q^{3} + 4q^{5} + 10q^{9} + 6q^{13} - 4q^{15} + 12q^{17} + 8q^{19} + 4q^{23} + 16q^{25} + 8q^{27} + 2q^{29} + 8q^{31} - 6q^{33} - 2q^{37} - 2q^{39} + 10q^{41} - 2q^{43} + 44q^{45} - 14q^{47} + 14q^{51} + 8q^{53} + 8q^{55} - 10q^{57} + 24q^{59} + 14q^{61} + 2q^{65} - 8q^{67} + 16q^{69} + 10q^{71} + 44q^{73} - 50q^{75} + 10q^{79} - 14q^{81} + 20q^{83} + 8q^{85} + 20q^{87} + 6q^{89} + 8q^{93} + 4q^{95} + 46q^{97} + 2q^{99} + O(q^{100}) \)

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
\(3\) 0.729469 0.421159 0.210580 0.977577i \(-0.432465\pi\)
0.210580 + 0.977577i \(0.432465\pi\)
\(4\) 0 0
\(5\) −3.02160 −1.35130 −0.675651 0.737222i \(-0.736137\pi\)
−0.675651 + 0.737222i \(0.736137\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −2.46788 −0.822625
\(10\) 0 0
\(11\) −2.63548 −0.794627 −0.397314 0.917683i \(-0.630057\pi\)
−0.397314 + 0.917683i \(0.630057\pi\)
\(12\) 0 0
\(13\) 0.419531 0.116357 0.0581785 0.998306i \(-0.481471\pi\)
0.0581785 + 0.998306i \(0.481471\pi\)
\(14\) 0 0
\(15\) −2.20416 −0.569113
\(16\) 0 0
\(17\) −4.48814 −1.08853 −0.544267 0.838912i \(-0.683192\pi\)
−0.544267 + 0.838912i \(0.683192\pi\)
\(18\) 0 0
\(19\) 4.82614 1.10719 0.553596 0.832785i \(-0.313255\pi\)
0.553596 + 0.832785i \(0.313255\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.672994 0.140329 0.0701644 0.997535i \(-0.477648\pi\)
0.0701644 + 0.997535i \(0.477648\pi\)
\(24\) 0 0
\(25\) 4.13008 0.826016
\(26\) 0 0
\(27\) −3.98864 −0.767615
\(28\) 0 0
\(29\) −7.40739 −1.37552 −0.687759 0.725939i \(-0.741405\pi\)
−0.687759 + 0.725939i \(0.741405\pi\)
\(30\) 0 0
\(31\) −3.91525 −0.703200 −0.351600 0.936150i \(-0.614362\pi\)
−0.351600 + 0.936150i \(0.614362\pi\)
\(32\) 0 0
\(33\) −1.92250 −0.334664
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2.78938 −0.458572 −0.229286 0.973359i \(-0.573639\pi\)
−0.229286 + 0.973359i \(0.573639\pi\)
\(38\) 0 0
\(39\) 0.306035 0.0490048
\(40\) 0 0
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 9.85531 1.50292 0.751460 0.659779i \(-0.229350\pi\)
0.751460 + 0.659779i \(0.229350\pi\)
\(44\) 0 0
\(45\) 7.45694 1.11161
\(46\) 0 0
\(47\) −12.2186 −1.78227 −0.891134 0.453741i \(-0.850089\pi\)
−0.891134 + 0.453741i \(0.850089\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −3.27396 −0.458446
\(52\) 0 0
\(53\) −12.6009 −1.73087 −0.865434 0.501023i \(-0.832957\pi\)
−0.865434 + 0.501023i \(0.832957\pi\)
\(54\) 0 0
\(55\) 7.96337 1.07378
\(56\) 0 0
\(57\) 3.52052 0.466304
\(58\) 0 0
\(59\) 8.17437 1.06421 0.532106 0.846678i \(-0.321401\pi\)
0.532106 + 0.846678i \(0.321401\pi\)
\(60\) 0 0
\(61\) −5.69538 −0.729218 −0.364609 0.931161i \(-0.618797\pi\)
−0.364609 + 0.931161i \(0.618797\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.26766 −0.157233
\(66\) 0 0
\(67\) −4.13105 −0.504688 −0.252344 0.967638i \(-0.581201\pi\)
−0.252344 + 0.967638i \(0.581201\pi\)
\(68\) 0 0
\(69\) 0.490928 0.0591008
\(70\) 0 0
\(71\) 16.7449 1.98726 0.993629 0.112696i \(-0.0359487\pi\)
0.993629 + 0.112696i \(0.0359487\pi\)
\(72\) 0 0
\(73\) 11.9924 1.40360 0.701800 0.712374i \(-0.252380\pi\)
0.701800 + 0.712374i \(0.252380\pi\)
\(74\) 0 0
\(75\) 3.01276 0.347884
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −5.02996 −0.565915 −0.282957 0.959132i \(-0.591316\pi\)
−0.282957 + 0.959132i \(0.591316\pi\)
\(80\) 0 0
\(81\) 4.49403 0.499337
\(82\) 0 0
\(83\) 4.57801 0.502502 0.251251 0.967922i \(-0.419158\pi\)
0.251251 + 0.967922i \(0.419158\pi\)
\(84\) 0 0
\(85\) 13.5614 1.47094
\(86\) 0 0
\(87\) −5.40346 −0.579312
\(88\) 0 0
\(89\) −12.8020 −1.35701 −0.678504 0.734596i \(-0.737372\pi\)
−0.678504 + 0.734596i \(0.737372\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −2.85605 −0.296159
\(94\) 0 0
\(95\) −14.5827 −1.49615
\(96\) 0 0
\(97\) 4.57826 0.464852 0.232426 0.972614i \(-0.425334\pi\)
0.232426 + 0.972614i \(0.425334\pi\)
\(98\) 0 0
\(99\) 6.50404 0.653680
\(100\) 0 0
\(101\) 7.02429 0.698943 0.349472 0.936947i \(-0.386361\pi\)
0.349472 + 0.936947i \(0.386361\pi\)
\(102\) 0 0
\(103\) 5.94473 0.585752 0.292876 0.956150i \(-0.405388\pi\)
0.292876 + 0.956150i \(0.405388\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −6.94944 −0.671828 −0.335914 0.941893i \(-0.609045\pi\)
−0.335914 + 0.941893i \(0.609045\pi\)
\(108\) 0 0
\(109\) −18.6652 −1.78780 −0.893900 0.448267i \(-0.852042\pi\)
−0.893900 + 0.448267i \(0.852042\pi\)
\(110\) 0 0
\(111\) −2.03477 −0.193132
\(112\) 0 0
\(113\) −15.0598 −1.41671 −0.708355 0.705857i \(-0.750562\pi\)
−0.708355 + 0.705857i \(0.750562\pi\)
\(114\) 0 0
\(115\) −2.03352 −0.189627
\(116\) 0 0
\(117\) −1.03535 −0.0957181
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −4.05424 −0.368568
\(122\) 0 0
\(123\) 0.729469 0.0657740
\(124\) 0 0
\(125\) 2.62855 0.235105
\(126\) 0 0
\(127\) 3.79505 0.336756 0.168378 0.985722i \(-0.446147\pi\)
0.168378 + 0.985722i \(0.446147\pi\)
\(128\) 0 0
\(129\) 7.18914 0.632968
\(130\) 0 0
\(131\) −0.172315 −0.0150552 −0.00752761 0.999972i \(-0.502396\pi\)
−0.00752761 + 0.999972i \(0.502396\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 12.0521 1.03728
\(136\) 0 0
\(137\) 1.94598 0.166256 0.0831282 0.996539i \(-0.473509\pi\)
0.0831282 + 0.996539i \(0.473509\pi\)
\(138\) 0 0
\(139\) 16.5097 1.40033 0.700166 0.713980i \(-0.253109\pi\)
0.700166 + 0.713980i \(0.253109\pi\)
\(140\) 0 0
\(141\) −8.91310 −0.750618
\(142\) 0 0
\(143\) −1.10567 −0.0924604
\(144\) 0 0
\(145\) 22.3822 1.85874
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2.14372 −0.175620 −0.0878101 0.996137i \(-0.527987\pi\)
−0.0878101 + 0.996137i \(0.527987\pi\)
\(150\) 0 0
\(151\) 13.6070 1.10732 0.553659 0.832743i \(-0.313231\pi\)
0.553659 + 0.832743i \(0.313231\pi\)
\(152\) 0 0
\(153\) 11.0762 0.895455
\(154\) 0 0
\(155\) 11.8303 0.950235
\(156\) 0 0
\(157\) 16.6320 1.32738 0.663690 0.748008i \(-0.268990\pi\)
0.663690 + 0.748008i \(0.268990\pi\)
\(158\) 0 0
\(159\) −9.19197 −0.728971
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2.94527 0.230691 0.115346 0.993325i \(-0.463202\pi\)
0.115346 + 0.993325i \(0.463202\pi\)
\(164\) 0 0
\(165\) 5.80903 0.452233
\(166\) 0 0
\(167\) 16.6880 1.29136 0.645678 0.763610i \(-0.276575\pi\)
0.645678 + 0.763610i \(0.276575\pi\)
\(168\) 0 0
\(169\) −12.8240 −0.986461
\(170\) 0 0
\(171\) −11.9103 −0.910804
\(172\) 0 0
\(173\) 20.1557 1.53241 0.766203 0.642598i \(-0.222144\pi\)
0.766203 + 0.642598i \(0.222144\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 5.96295 0.448203
\(178\) 0 0
\(179\) −19.3960 −1.44972 −0.724861 0.688895i \(-0.758096\pi\)
−0.724861 + 0.688895i \(0.758096\pi\)
\(180\) 0 0
\(181\) 1.65214 0.122802 0.0614012 0.998113i \(-0.480443\pi\)
0.0614012 + 0.998113i \(0.480443\pi\)
\(182\) 0 0
\(183\) −4.15460 −0.307117
\(184\) 0 0
\(185\) 8.42841 0.619669
\(186\) 0 0
\(187\) 11.8284 0.864979
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 23.4468 1.69655 0.848274 0.529557i \(-0.177642\pi\)
0.848274 + 0.529557i \(0.177642\pi\)
\(192\) 0 0
\(193\) 16.2357 1.16867 0.584334 0.811513i \(-0.301356\pi\)
0.584334 + 0.811513i \(0.301356\pi\)
\(194\) 0 0
\(195\) −0.924715 −0.0662202
\(196\) 0 0
\(197\) −15.0901 −1.07512 −0.537561 0.843225i \(-0.680654\pi\)
−0.537561 + 0.843225i \(0.680654\pi\)
\(198\) 0 0
\(199\) 10.9859 0.778772 0.389386 0.921075i \(-0.372687\pi\)
0.389386 + 0.921075i \(0.372687\pi\)
\(200\) 0 0
\(201\) −3.01347 −0.212554
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −3.02160 −0.211038
\(206\) 0 0
\(207\) −1.66086 −0.115438
\(208\) 0 0
\(209\) −12.7192 −0.879805
\(210\) 0 0
\(211\) 23.7238 1.63321 0.816606 0.577196i \(-0.195853\pi\)
0.816606 + 0.577196i \(0.195853\pi\)
\(212\) 0 0
\(213\) 12.2149 0.836952
\(214\) 0 0
\(215\) −29.7788 −2.03090
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 8.74805 0.591139
\(220\) 0 0
\(221\) −1.88291 −0.126658
\(222\) 0 0
\(223\) −21.5235 −1.44132 −0.720659 0.693290i \(-0.756161\pi\)
−0.720659 + 0.693290i \(0.756161\pi\)
\(224\) 0 0
\(225\) −10.1925 −0.679501
\(226\) 0 0
\(227\) 4.57776 0.303837 0.151918 0.988393i \(-0.451455\pi\)
0.151918 + 0.988393i \(0.451455\pi\)
\(228\) 0 0
\(229\) −4.92402 −0.325389 −0.162694 0.986677i \(-0.552018\pi\)
−0.162694 + 0.986677i \(0.552018\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −17.6354 −1.15534 −0.577668 0.816272i \(-0.696037\pi\)
−0.577668 + 0.816272i \(0.696037\pi\)
\(234\) 0 0
\(235\) 36.9198 2.40838
\(236\) 0 0
\(237\) −3.66920 −0.238340
\(238\) 0 0
\(239\) 0.532642 0.0344538 0.0172269 0.999852i \(-0.494516\pi\)
0.0172269 + 0.999852i \(0.494516\pi\)
\(240\) 0 0
\(241\) 10.4604 0.673814 0.336907 0.941538i \(-0.390619\pi\)
0.336907 + 0.941538i \(0.390619\pi\)
\(242\) 0 0
\(243\) 15.2442 0.977915
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.02471 0.128830
\(248\) 0 0
\(249\) 3.33952 0.211633
\(250\) 0 0
\(251\) 24.4434 1.54286 0.771428 0.636317i \(-0.219543\pi\)
0.771428 + 0.636317i \(0.219543\pi\)
\(252\) 0 0
\(253\) −1.77366 −0.111509
\(254\) 0 0
\(255\) 9.89260 0.619499
\(256\) 0 0
\(257\) −13.1025 −0.817309 −0.408655 0.912689i \(-0.634002\pi\)
−0.408655 + 0.912689i \(0.634002\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 18.2805 1.13153
\(262\) 0 0
\(263\) 4.37037 0.269489 0.134744 0.990880i \(-0.456979\pi\)
0.134744 + 0.990880i \(0.456979\pi\)
\(264\) 0 0
\(265\) 38.0749 2.33892
\(266\) 0 0
\(267\) −9.33866 −0.571517
\(268\) 0 0
\(269\) 21.3721 1.30308 0.651540 0.758615i \(-0.274123\pi\)
0.651540 + 0.758615i \(0.274123\pi\)
\(270\) 0 0
\(271\) −16.3061 −0.990526 −0.495263 0.868743i \(-0.664928\pi\)
−0.495263 + 0.868743i \(0.664928\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −10.8847 −0.656375
\(276\) 0 0
\(277\) −19.3362 −1.16180 −0.580901 0.813974i \(-0.697300\pi\)
−0.580901 + 0.813974i \(0.697300\pi\)
\(278\) 0 0
\(279\) 9.66235 0.578470
\(280\) 0 0
\(281\) 24.9338 1.48743 0.743714 0.668498i \(-0.233062\pi\)
0.743714 + 0.668498i \(0.233062\pi\)
\(282\) 0 0
\(283\) 3.46955 0.206243 0.103122 0.994669i \(-0.467117\pi\)
0.103122 + 0.994669i \(0.467117\pi\)
\(284\) 0 0
\(285\) −10.6376 −0.630117
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 3.14340 0.184906
\(290\) 0 0
\(291\) 3.33970 0.195777
\(292\) 0 0
\(293\) −17.5746 −1.02672 −0.513359 0.858174i \(-0.671599\pi\)
−0.513359 + 0.858174i \(0.671599\pi\)
\(294\) 0 0
\(295\) −24.6997 −1.43807
\(296\) 0 0
\(297\) 10.5120 0.609968
\(298\) 0 0
\(299\) 0.282342 0.0163282
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 5.12400 0.294366
\(304\) 0 0
\(305\) 17.2092 0.985393
\(306\) 0 0
\(307\) 18.7869 1.07222 0.536112 0.844147i \(-0.319892\pi\)
0.536112 + 0.844147i \(0.319892\pi\)
\(308\) 0 0
\(309\) 4.33650 0.246695
\(310\) 0 0
\(311\) 24.4618 1.38710 0.693550 0.720408i \(-0.256046\pi\)
0.693550 + 0.720408i \(0.256046\pi\)
\(312\) 0 0
\(313\) 18.0320 1.01923 0.509613 0.860404i \(-0.329789\pi\)
0.509613 + 0.860404i \(0.329789\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.26355 0.183299 0.0916496 0.995791i \(-0.470786\pi\)
0.0916496 + 0.995791i \(0.470786\pi\)
\(318\) 0 0
\(319\) 19.5220 1.09302
\(320\) 0 0
\(321\) −5.06940 −0.282946
\(322\) 0 0
\(323\) −21.6604 −1.20522
\(324\) 0 0
\(325\) 1.73270 0.0961127
\(326\) 0 0
\(327\) −13.6157 −0.752948
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 10.1594 0.558411 0.279206 0.960231i \(-0.409929\pi\)
0.279206 + 0.960231i \(0.409929\pi\)
\(332\) 0 0
\(333\) 6.88385 0.377233
\(334\) 0 0
\(335\) 12.4824 0.681985
\(336\) 0 0
\(337\) 13.3482 0.727124 0.363562 0.931570i \(-0.381561\pi\)
0.363562 + 0.931570i \(0.381561\pi\)
\(338\) 0 0
\(339\) −10.9857 −0.596660
\(340\) 0 0
\(341\) 10.3186 0.558782
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −1.48339 −0.0798630
\(346\) 0 0
\(347\) −6.32015 −0.339283 −0.169642 0.985506i \(-0.554261\pi\)
−0.169642 + 0.985506i \(0.554261\pi\)
\(348\) 0 0
\(349\) −8.29144 −0.443831 −0.221915 0.975066i \(-0.571231\pi\)
−0.221915 + 0.975066i \(0.571231\pi\)
\(350\) 0 0
\(351\) −1.67336 −0.0893173
\(352\) 0 0
\(353\) −30.3657 −1.61620 −0.808102 0.589043i \(-0.799505\pi\)
−0.808102 + 0.589043i \(0.799505\pi\)
\(354\) 0 0
\(355\) −50.5966 −2.68539
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 32.3876 1.70935 0.854675 0.519163i \(-0.173756\pi\)
0.854675 + 0.519163i \(0.173756\pi\)
\(360\) 0 0
\(361\) 4.29162 0.225875
\(362\) 0 0
\(363\) −2.95744 −0.155226
\(364\) 0 0
\(365\) −36.2361 −1.89669
\(366\) 0 0
\(367\) 16.0161 0.836031 0.418016 0.908440i \(-0.362726\pi\)
0.418016 + 0.908440i \(0.362726\pi\)
\(368\) 0 0
\(369\) −2.46788 −0.128472
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 9.50112 0.491949 0.245975 0.969276i \(-0.420892\pi\)
0.245975 + 0.969276i \(0.420892\pi\)
\(374\) 0 0
\(375\) 1.91745 0.0990166
\(376\) 0 0
\(377\) −3.10763 −0.160051
\(378\) 0 0
\(379\) 8.18315 0.420340 0.210170 0.977665i \(-0.432598\pi\)
0.210170 + 0.977665i \(0.432598\pi\)
\(380\) 0 0
\(381\) 2.76837 0.141828
\(382\) 0 0
\(383\) 17.5295 0.895713 0.447857 0.894105i \(-0.352188\pi\)
0.447857 + 0.894105i \(0.352188\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −24.3217 −1.23634
\(388\) 0 0
\(389\) −17.9349 −0.909336 −0.454668 0.890661i \(-0.650242\pi\)
−0.454668 + 0.890661i \(0.650242\pi\)
\(390\) 0 0
\(391\) −3.02049 −0.152753
\(392\) 0 0
\(393\) −0.125698 −0.00634064
\(394\) 0 0
\(395\) 15.1985 0.764722
\(396\) 0 0
\(397\) −25.4109 −1.27534 −0.637668 0.770311i \(-0.720101\pi\)
−0.637668 + 0.770311i \(0.720101\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2.64011 0.131841 0.0659204 0.997825i \(-0.479002\pi\)
0.0659204 + 0.997825i \(0.479002\pi\)
\(402\) 0 0
\(403\) −1.64257 −0.0818222
\(404\) 0 0
\(405\) −13.5792 −0.674755
\(406\) 0 0
\(407\) 7.35137 0.364394
\(408\) 0 0
\(409\) −26.1419 −1.29263 −0.646317 0.763069i \(-0.723692\pi\)
−0.646317 + 0.763069i \(0.723692\pi\)
\(410\) 0 0
\(411\) 1.41953 0.0700204
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −13.8329 −0.679032
\(416\) 0 0
\(417\) 12.0433 0.589763
\(418\) 0 0
\(419\) 2.11337 0.103245 0.0516224 0.998667i \(-0.483561\pi\)
0.0516224 + 0.998667i \(0.483561\pi\)
\(420\) 0 0
\(421\) 13.5523 0.660500 0.330250 0.943894i \(-0.392867\pi\)
0.330250 + 0.943894i \(0.392867\pi\)
\(422\) 0 0
\(423\) 30.1540 1.46614
\(424\) 0 0
\(425\) −18.5364 −0.899146
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −0.806549 −0.0389405
\(430\) 0 0
\(431\) −13.8099 −0.665200 −0.332600 0.943068i \(-0.607926\pi\)
−0.332600 + 0.943068i \(0.607926\pi\)
\(432\) 0 0
\(433\) 2.72356 0.130886 0.0654429 0.997856i \(-0.479154\pi\)
0.0654429 + 0.997856i \(0.479154\pi\)
\(434\) 0 0
\(435\) 16.3271 0.782825
\(436\) 0 0
\(437\) 3.24796 0.155371
\(438\) 0 0
\(439\) 12.3395 0.588931 0.294465 0.955662i \(-0.404858\pi\)
0.294465 + 0.955662i \(0.404858\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −5.66457 −0.269132 −0.134566 0.990905i \(-0.542964\pi\)
−0.134566 + 0.990905i \(0.542964\pi\)
\(444\) 0 0
\(445\) 38.6825 1.83373
\(446\) 0 0
\(447\) −1.56378 −0.0739640
\(448\) 0 0
\(449\) −23.6028 −1.11388 −0.556942 0.830552i \(-0.688025\pi\)
−0.556942 + 0.830552i \(0.688025\pi\)
\(450\) 0 0
\(451\) −2.63548 −0.124100
\(452\) 0 0
\(453\) 9.92585 0.466357
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 13.8068 0.645854 0.322927 0.946424i \(-0.395333\pi\)
0.322927 + 0.946424i \(0.395333\pi\)
\(458\) 0 0
\(459\) 17.9016 0.835575
\(460\) 0 0
\(461\) 7.33393 0.341575 0.170788 0.985308i \(-0.445369\pi\)
0.170788 + 0.985308i \(0.445369\pi\)
\(462\) 0 0
\(463\) −32.3928 −1.50542 −0.752710 0.658352i \(-0.771254\pi\)
−0.752710 + 0.658352i \(0.771254\pi\)
\(464\) 0 0
\(465\) 8.62986 0.400200
\(466\) 0 0
\(467\) −0.471234 −0.0218061 −0.0109030 0.999941i \(-0.503471\pi\)
−0.0109030 + 0.999941i \(0.503471\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 12.1325 0.559038
\(472\) 0 0
\(473\) −25.9735 −1.19426
\(474\) 0 0
\(475\) 19.9323 0.914558
\(476\) 0 0
\(477\) 31.0975 1.42386
\(478\) 0 0
\(479\) −37.2215 −1.70069 −0.850346 0.526224i \(-0.823607\pi\)
−0.850346 + 0.526224i \(0.823607\pi\)
\(480\) 0 0
\(481\) −1.17023 −0.0533580
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −13.8337 −0.628155
\(486\) 0 0
\(487\) −38.3423 −1.73745 −0.868727 0.495292i \(-0.835061\pi\)
−0.868727 + 0.495292i \(0.835061\pi\)
\(488\) 0 0
\(489\) 2.14848 0.0971578
\(490\) 0 0
\(491\) 0.220444 0.00994850 0.00497425 0.999988i \(-0.498417\pi\)
0.00497425 + 0.999988i \(0.498417\pi\)
\(492\) 0 0
\(493\) 33.2454 1.49730
\(494\) 0 0
\(495\) −19.6526 −0.883319
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −1.31343 −0.0587971 −0.0293985 0.999568i \(-0.509359\pi\)
−0.0293985 + 0.999568i \(0.509359\pi\)
\(500\) 0 0
\(501\) 12.1734 0.543866
\(502\) 0 0
\(503\) 24.5426 1.09430 0.547151 0.837034i \(-0.315712\pi\)
0.547151 + 0.837034i \(0.315712\pi\)
\(504\) 0 0
\(505\) −21.2246 −0.944483
\(506\) 0 0
\(507\) −9.35470 −0.415457
\(508\) 0 0
\(509\) −13.1233 −0.581679 −0.290839 0.956772i \(-0.593934\pi\)
−0.290839 + 0.956772i \(0.593934\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −19.2498 −0.849897
\(514\) 0 0
\(515\) −17.9626 −0.791528
\(516\) 0 0
\(517\) 32.2019 1.41624
\(518\) 0 0
\(519\) 14.7029 0.645387
\(520\) 0 0
\(521\) 31.6139 1.38503 0.692515 0.721403i \(-0.256503\pi\)
0.692515 + 0.721403i \(0.256503\pi\)
\(522\) 0 0
\(523\) −2.75542 −0.120486 −0.0602431 0.998184i \(-0.519188\pi\)
−0.0602431 + 0.998184i \(0.519188\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 17.5722 0.765457
\(528\) 0 0
\(529\) −22.5471 −0.980308
\(530\) 0 0
\(531\) −20.1733 −0.875448
\(532\) 0 0
\(533\) 0.419531 0.0181719
\(534\) 0 0
\(535\) 20.9984 0.907842
\(536\) 0 0
\(537\) −14.1487 −0.610564
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −7.02547 −0.302049 −0.151024 0.988530i \(-0.548257\pi\)
−0.151024 + 0.988530i \(0.548257\pi\)
\(542\) 0 0
\(543\) 1.20518 0.0517193
\(544\) 0 0
\(545\) 56.3987 2.41586
\(546\) 0 0
\(547\) 13.3015 0.568732 0.284366 0.958716i \(-0.408217\pi\)
0.284366 + 0.958716i \(0.408217\pi\)
\(548\) 0 0
\(549\) 14.0555 0.599873
\(550\) 0 0
\(551\) −35.7491 −1.52296
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 6.14826 0.260979
\(556\) 0 0
\(557\) 38.9873 1.65194 0.825972 0.563711i \(-0.190627\pi\)
0.825972 + 0.563711i \(0.190627\pi\)
\(558\) 0 0
\(559\) 4.13461 0.174875
\(560\) 0 0
\(561\) 8.62845 0.364294
\(562\) 0 0
\(563\) −5.28994 −0.222945 −0.111472 0.993768i \(-0.535557\pi\)
−0.111472 + 0.993768i \(0.535557\pi\)
\(564\) 0 0
\(565\) 45.5048 1.91440
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 39.3456 1.64945 0.824726 0.565533i \(-0.191329\pi\)
0.824726 + 0.565533i \(0.191329\pi\)
\(570\) 0 0
\(571\) 15.8773 0.664446 0.332223 0.943201i \(-0.392201\pi\)
0.332223 + 0.943201i \(0.392201\pi\)
\(572\) 0 0
\(573\) 17.1037 0.714517
\(574\) 0 0
\(575\) 2.77952 0.115914
\(576\) 0 0
\(577\) 8.01458 0.333651 0.166826 0.985986i \(-0.446648\pi\)
0.166826 + 0.985986i \(0.446648\pi\)
\(578\) 0 0
\(579\) 11.8434 0.492195
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 33.2094 1.37539
\(584\) 0 0
\(585\) 3.12842 0.129344
\(586\) 0 0
\(587\) 6.48213 0.267546 0.133773 0.991012i \(-0.457291\pi\)
0.133773 + 0.991012i \(0.457291\pi\)
\(588\) 0 0
\(589\) −18.8955 −0.778577
\(590\) 0 0
\(591\) −11.0077 −0.452798
\(592\) 0 0
\(593\) 7.02097 0.288317 0.144158 0.989555i \(-0.453953\pi\)
0.144158 + 0.989555i \(0.453953\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 8.01390 0.327987
\(598\) 0 0
\(599\) −14.5721 −0.595399 −0.297699 0.954660i \(-0.596219\pi\)
−0.297699 + 0.954660i \(0.596219\pi\)
\(600\) 0 0
\(601\) −7.94938 −0.324262 −0.162131 0.986769i \(-0.551837\pi\)
−0.162131 + 0.986769i \(0.551837\pi\)
\(602\) 0 0
\(603\) 10.1949 0.415169
\(604\) 0 0
\(605\) 12.2503 0.498046
\(606\) 0 0
\(607\) −5.44728 −0.221098 −0.110549 0.993871i \(-0.535261\pi\)
−0.110549 + 0.993871i \(0.535261\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −5.12609 −0.207379
\(612\) 0 0
\(613\) 30.9589 1.25042 0.625209 0.780458i \(-0.285014\pi\)
0.625209 + 0.780458i \(0.285014\pi\)
\(614\) 0 0
\(615\) −2.20416 −0.0888805
\(616\) 0 0
\(617\) −27.7514 −1.11723 −0.558615 0.829427i \(-0.688667\pi\)
−0.558615 + 0.829427i \(0.688667\pi\)
\(618\) 0 0
\(619\) 13.2653 0.533176 0.266588 0.963811i \(-0.414104\pi\)
0.266588 + 0.963811i \(0.414104\pi\)
\(620\) 0 0
\(621\) −2.68433 −0.107719
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −28.5928 −1.14371
\(626\) 0 0
\(627\) −9.27826 −0.370538
\(628\) 0 0
\(629\) 12.5191 0.499171
\(630\) 0 0
\(631\) −25.6466 −1.02097 −0.510487 0.859885i \(-0.670535\pi\)
−0.510487 + 0.859885i \(0.670535\pi\)
\(632\) 0 0
\(633\) 17.3057 0.687842
\(634\) 0 0
\(635\) −11.4671 −0.455059
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −41.3244 −1.63477
\(640\) 0 0
\(641\) −1.47574 −0.0582884 −0.0291442 0.999575i \(-0.509278\pi\)
−0.0291442 + 0.999575i \(0.509278\pi\)
\(642\) 0 0
\(643\) 13.4628 0.530922 0.265461 0.964122i \(-0.414476\pi\)
0.265461 + 0.964122i \(0.414476\pi\)
\(644\) 0 0
\(645\) −21.7227 −0.855331
\(646\) 0 0
\(647\) 43.7466 1.71986 0.859929 0.510414i \(-0.170508\pi\)
0.859929 + 0.510414i \(0.170508\pi\)
\(648\) 0 0
\(649\) −21.5434 −0.845652
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −42.6172 −1.66774 −0.833869 0.551962i \(-0.813879\pi\)
−0.833869 + 0.551962i \(0.813879\pi\)
\(654\) 0 0
\(655\) 0.520667 0.0203441
\(656\) 0 0
\(657\) −29.5956 −1.15464
\(658\) 0 0
\(659\) 13.4790 0.525068 0.262534 0.964923i \(-0.415442\pi\)
0.262534 + 0.964923i \(0.415442\pi\)
\(660\) 0 0
\(661\) −26.6145 −1.03518 −0.517592 0.855628i \(-0.673171\pi\)
−0.517592 + 0.855628i \(0.673171\pi\)
\(662\) 0 0
\(663\) −1.37353 −0.0533434
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −4.98512 −0.193025
\(668\) 0 0
\(669\) −15.7007 −0.607024
\(670\) 0 0
\(671\) 15.0100 0.579456
\(672\) 0 0
\(673\) 34.8109 1.34186 0.670930 0.741521i \(-0.265895\pi\)
0.670930 + 0.741521i \(0.265895\pi\)
\(674\) 0 0
\(675\) −16.4734 −0.634062
\(676\) 0 0
\(677\) 14.2444 0.547455 0.273728 0.961807i \(-0.411743\pi\)
0.273728 + 0.961807i \(0.411743\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 3.33933 0.127964
\(682\) 0 0
\(683\) 29.2620 1.11968 0.559839 0.828601i \(-0.310863\pi\)
0.559839 + 0.828601i \(0.310863\pi\)
\(684\) 0 0
\(685\) −5.87998 −0.224663
\(686\) 0 0
\(687\) −3.59192 −0.137040
\(688\) 0 0
\(689\) −5.28647 −0.201398
\(690\) 0 0
\(691\) −8.59879 −0.327113 −0.163557 0.986534i \(-0.552297\pi\)
−0.163557 + 0.986534i \(0.552297\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −49.8857 −1.89227
\(696\) 0 0
\(697\) −4.48814 −0.170000
\(698\) 0 0
\(699\) −12.8645 −0.486580
\(700\) 0 0
\(701\) −15.1495 −0.572188 −0.286094 0.958201i \(-0.592357\pi\)
−0.286094 + 0.958201i \(0.592357\pi\)
\(702\) 0 0
\(703\) −13.4620 −0.507727
\(704\) 0 0
\(705\) 26.9318 1.01431
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −15.4893 −0.581713 −0.290857 0.956767i \(-0.593940\pi\)
−0.290857 + 0.956767i \(0.593940\pi\)
\(710\) 0 0
\(711\) 12.4133 0.465536
\(712\) 0 0
\(713\) −2.63494 −0.0986792
\(714\) 0 0
\(715\) 3.34088 0.124942
\(716\) 0 0
\(717\) 0.388546 0.0145105
\(718\) 0 0
\(719\) 44.8745 1.67353 0.836767 0.547559i \(-0.184443\pi\)
0.836767 + 0.547559i \(0.184443\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 7.63054 0.283783
\(724\) 0 0
\(725\) −30.5931 −1.13620
\(726\) 0 0
\(727\) 19.9602 0.740284 0.370142 0.928975i \(-0.379309\pi\)
0.370142 + 0.928975i \(0.379309\pi\)
\(728\) 0 0
\(729\) −2.36194 −0.0874791
\(730\) 0 0
\(731\) −44.2320 −1.63598
\(732\) 0 0
\(733\) −10.0255 −0.370299 −0.185150 0.982710i \(-0.559277\pi\)
−0.185150 + 0.982710i \(0.559277\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 10.8873 0.401039
\(738\) 0 0
\(739\) 14.4879 0.532947 0.266474 0.963842i \(-0.414141\pi\)
0.266474 + 0.963842i \(0.414141\pi\)
\(740\) 0 0
\(741\) 1.47697 0.0542577
\(742\) 0 0
\(743\) −19.2464 −0.706081 −0.353041 0.935608i \(-0.614852\pi\)
−0.353041 + 0.935608i \(0.614852\pi\)
\(744\) 0 0
\(745\) 6.47746 0.237316
\(746\) 0 0
\(747\) −11.2980 −0.413371
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −17.3680 −0.633766 −0.316883 0.948465i \(-0.602636\pi\)
−0.316883 + 0.948465i \(0.602636\pi\)
\(752\) 0 0
\(753\) 17.8307 0.649787
\(754\) 0 0
\(755\) −41.1148 −1.49632
\(756\) 0 0
\(757\) −8.55997 −0.311117 −0.155559 0.987827i \(-0.549718\pi\)
−0.155559 + 0.987827i \(0.549718\pi\)
\(758\) 0 0
\(759\) −1.29383 −0.0469631
\(760\) 0 0
\(761\) 22.8820 0.829474 0.414737 0.909941i \(-0.363874\pi\)
0.414737 + 0.909941i \(0.363874\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −33.4678 −1.21003
\(766\) 0 0
\(767\) 3.42940 0.123829
\(768\) 0 0
\(769\) −42.5966 −1.53607 −0.768036 0.640407i \(-0.778766\pi\)
−0.768036 + 0.640407i \(0.778766\pi\)
\(770\) 0 0
\(771\) −9.55784 −0.344217
\(772\) 0 0
\(773\) −39.0856 −1.40581 −0.702906 0.711282i \(-0.748115\pi\)
−0.702906 + 0.711282i \(0.748115\pi\)
\(774\) 0 0
\(775\) −16.1703 −0.580854
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4.82614 0.172914
\(780\) 0 0
\(781\) −44.1310 −1.57913
\(782\) 0 0
\(783\) 29.5454 1.05587
\(784\) 0 0
\(785\) −50.2553 −1.79369
\(786\) 0 0
\(787\) 5.56896 0.198512 0.0992561 0.995062i \(-0.468354\pi\)
0.0992561 + 0.995062i \(0.468354\pi\)
\(788\) 0 0
\(789\) 3.18805 0.113498
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −2.38939 −0.0848496
\(794\) 0 0
\(795\) 27.7745 0.985059
\(796\) 0 0
\(797\) −22.0942 −0.782616 −0.391308 0.920260i \(-0.627977\pi\)
−0.391308 + 0.920260i \(0.627977\pi\)
\(798\) 0 0
\(799\) 54.8388 1.94006
\(800\) 0 0
\(801\) 31.5937 1.11631
\(802\) 0 0
\(803\) −31.6056 −1.11534
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 15.5903 0.548804
\(808\) 0 0
\(809\) −15.2610 −0.536548 −0.268274 0.963343i \(-0.586453\pi\)
−0.268274 + 0.963343i \(0.586453\pi\)
\(810\) 0 0
\(811\) −25.3582 −0.890446 −0.445223 0.895420i \(-0.646876\pi\)
−0.445223 + 0.895420i \(0.646876\pi\)
\(812\) 0 0
\(813\) −11.8948 −0.417169
\(814\) 0 0
\(815\) −8.89944 −0.311734
\(816\) 0 0
\(817\) 47.5631 1.66402
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 17.2829 0.603178 0.301589 0.953438i \(-0.402483\pi\)
0.301589 + 0.953438i \(0.402483\pi\)
\(822\) 0 0
\(823\) −40.8641 −1.42443 −0.712216 0.701960i \(-0.752308\pi\)
−0.712216 + 0.701960i \(0.752308\pi\)
\(824\) 0 0
\(825\) −7.94008 −0.276438
\(826\) 0 0
\(827\) 13.5665 0.471755 0.235877 0.971783i \(-0.424204\pi\)
0.235877 + 0.971783i \(0.424204\pi\)
\(828\) 0 0
\(829\) −10.0661 −0.349609 −0.174805 0.984603i \(-0.555929\pi\)
−0.174805 + 0.984603i \(0.555929\pi\)
\(830\) 0 0
\(831\) −14.1052 −0.489303
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −50.4245 −1.74501
\(836\) 0 0
\(837\) 15.6165 0.539787
\(838\) 0 0
\(839\) −44.4731 −1.53538 −0.767691 0.640820i \(-0.778595\pi\)
−0.767691 + 0.640820i \(0.778595\pi\)
\(840\) 0 0
\(841\) 25.8694 0.892048
\(842\) 0 0
\(843\) 18.1885 0.626444
\(844\) 0 0
\(845\) 38.7490 1.33301
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 2.53093 0.0868612
\(850\) 0 0
\(851\) −1.87724 −0.0643509
\(852\) 0 0
\(853\) 41.7118 1.42818 0.714092 0.700051i \(-0.246840\pi\)
0.714092 + 0.700051i \(0.246840\pi\)
\(854\) 0 0
\(855\) 35.9882 1.23077
\(856\) 0 0
\(857\) 32.3777 1.10600 0.553000 0.833181i \(-0.313483\pi\)
0.553000 + 0.833181i \(0.313483\pi\)
\(858\) 0 0
\(859\) 10.3027 0.351525 0.175762 0.984433i \(-0.443761\pi\)
0.175762 + 0.984433i \(0.443761\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −11.4435 −0.389543 −0.194771 0.980849i \(-0.562396\pi\)
−0.194771 + 0.980849i \(0.562396\pi\)
\(864\) 0 0
\(865\) −60.9024 −2.07074
\(866\) 0 0
\(867\) 2.29301 0.0778748
\(868\) 0 0
\(869\) 13.2564 0.449691
\(870\) 0 0
\(871\) −1.73310 −0.0587239
\(872\) 0 0
\(873\) −11.2986 −0.382399
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −41.8720 −1.41392 −0.706959 0.707255i \(-0.749933\pi\)
−0.706959 + 0.707255i \(0.749933\pi\)
\(878\) 0 0
\(879\) −12.8201 −0.432411
\(880\) 0 0
\(881\) −10.7494 −0.362158 −0.181079 0.983469i \(-0.557959\pi\)
−0.181079 + 0.983469i \(0.557959\pi\)
\(882\) 0 0
\(883\) 16.8468 0.566940 0.283470 0.958981i \(-0.408514\pi\)
0.283470 + 0.958981i \(0.408514\pi\)
\(884\) 0 0
\(885\) −18.0177 −0.605657
\(886\) 0 0
\(887\) −29.6898 −0.996887 −0.498444 0.866922i \(-0.666095\pi\)
−0.498444 + 0.866922i \(0.666095\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −11.8439 −0.396787
\(892\) 0 0
\(893\) −58.9687 −1.97331
\(894\) 0 0
\(895\) 58.6069 1.95901
\(896\) 0 0
\(897\) 0.205959 0.00687679
\(898\) 0 0
\(899\) 29.0018 0.967263
\(900\) 0 0
\(901\) 56.5546 1.88411
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −4.99210 −0.165943
\(906\) 0 0
\(907\) −18.9752 −0.630060 −0.315030 0.949082i \(-0.602015\pi\)
−0.315030 + 0.949082i \(0.602015\pi\)
\(908\) 0 0
\(909\) −17.3351 −0.574968
\(910\) 0 0
\(911\) −29.1631 −0.966216 −0.483108 0.875561i \(-0.660492\pi\)
−0.483108 + 0.875561i \(0.660492\pi\)
\(912\) 0 0
\(913\) −12.0653 −0.399302
\(914\) 0 0
\(915\) 12.5535 0.415007
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −14.2264 −0.469286 −0.234643 0.972082i \(-0.575392\pi\)
−0.234643 + 0.972082i \(0.575392\pi\)
\(920\) 0 0
\(921\) 13.7045 0.451577
\(922\) 0 0
\(923\) 7.02502 0.231231
\(924\) 0 0
\(925\) −11.5204 −0.378788
\(926\) 0 0
\(927\) −14.6709 −0.481854
\(928\) 0 0
\(929\) 9.29313 0.304898 0.152449 0.988311i \(-0.451284\pi\)
0.152449 + 0.988311i \(0.451284\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 17.8441 0.584190
\(934\) 0 0
\(935\) −35.7407 −1.16885
\(936\) 0 0
\(937\) 40.4919 1.32281 0.661406 0.750028i \(-0.269960\pi\)
0.661406 + 0.750028i \(0.269960\pi\)
\(938\) 0 0
\(939\) 13.1537 0.429256
\(940\) 0 0
\(941\) 40.7076 1.32703 0.663515 0.748163i \(-0.269064\pi\)
0.663515 + 0.748163i \(0.269064\pi\)
\(942\) 0 0
\(943\) 0.672994 0.0219157
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 27.0839 0.880107 0.440054 0.897972i \(-0.354959\pi\)
0.440054 + 0.897972i \(0.354959\pi\)
\(948\) 0 0
\(949\) 5.03117 0.163319
\(950\) 0 0
\(951\) 2.38066 0.0771981
\(952\) 0 0
\(953\) 54.2939 1.75875 0.879376 0.476128i \(-0.157960\pi\)
0.879376 + 0.476128i \(0.157960\pi\)
\(954\) 0 0
\(955\) −70.8468 −2.29255
\(956\) 0 0
\(957\) 14.2407 0.460337
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −15.6708 −0.505510
\(962\) 0 0
\(963\) 17.1503 0.552662
\(964\) 0 0
\(965\) −49.0577 −1.57922
\(966\) 0 0
\(967\) −11.2843 −0.362878 −0.181439 0.983402i \(-0.558075\pi\)
−0.181439 + 0.983402i \(0.558075\pi\)
\(968\) 0 0
\(969\) −15.8006 −0.507588
\(970\) 0 0
\(971\) −54.7201 −1.75605 −0.878025 0.478614i \(-0.841139\pi\)
−0.878025 + 0.478614i \(0.841139\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 1.26395 0.0404787
\(976\) 0 0
\(977\) −45.2859 −1.44882 −0.724412 0.689368i \(-0.757889\pi\)
−0.724412 + 0.689368i \(0.757889\pi\)
\(978\) 0 0
\(979\) 33.7394 1.07832
\(980\) 0 0
\(981\) 46.0633 1.47069
\(982\) 0 0
\(983\) 24.0163 0.766000 0.383000 0.923748i \(-0.374891\pi\)
0.383000 + 0.923748i \(0.374891\pi\)
\(984\) 0 0
\(985\) 45.5962 1.45282
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 6.63256 0.210903
\(990\) 0 0
\(991\) 19.1437 0.608119 0.304060 0.952653i \(-0.401658\pi\)
0.304060 + 0.952653i \(0.401658\pi\)
\(992\) 0 0
\(993\) 7.41097 0.235180
\(994\) 0 0
\(995\) −33.1951 −1.05236
\(996\) 0 0
\(997\) 1.60423 0.0508066 0.0254033 0.999677i \(-0.491913\pi\)
0.0254033 + 0.999677i \(0.491913\pi\)
\(998\) 0 0
\(999\) 11.1259 0.352007
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 \(a_p\))