Properties

Label 8036.2.a.q.1.1
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 15
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: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.42372\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.42372 q^{3} +2.35740 q^{5} +8.72183 q^{9} +O(q^{10})\) \(q-3.42372 q^{3} +2.35740 q^{5} +8.72183 q^{9} -0.142921 q^{11} -2.89147 q^{13} -8.07106 q^{15} -1.39444 q^{17} -7.23396 q^{19} -4.70073 q^{23} +0.557331 q^{25} -19.5899 q^{27} +2.50126 q^{29} -2.29868 q^{31} +0.489322 q^{33} -8.95769 q^{37} +9.89958 q^{39} -1.00000 q^{41} +10.0638 q^{43} +20.5608 q^{45} -0.577516 q^{47} +4.77417 q^{51} -2.67866 q^{53} -0.336922 q^{55} +24.7670 q^{57} -5.00779 q^{59} +10.1819 q^{61} -6.81635 q^{65} +4.81589 q^{67} +16.0940 q^{69} -10.7912 q^{71} -2.06872 q^{73} -1.90814 q^{75} +2.74538 q^{79} +40.9048 q^{81} +8.58858 q^{83} -3.28725 q^{85} -8.56361 q^{87} +11.3580 q^{89} +7.87002 q^{93} -17.0533 q^{95} -4.73305 q^{97} -1.24653 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - q^{3} + 3q^{5} + 30q^{9} + O(q^{10}) \) \( 15q - q^{3} + 3q^{5} + 30q^{9} + 9q^{11} + 7q^{13} + 2q^{15} + 3q^{17} + 7q^{19} - q^{23} + 32q^{25} + 11q^{27} + 18q^{29} + 30q^{31} - 16q^{33} + 23q^{37} + 5q^{39} - 15q^{41} + 12q^{43} - 13q^{45} - 16q^{47} + 29q^{51} + 33q^{53} + 37q^{55} + 16q^{57} - 10q^{59} + q^{61} + 16q^{65} + 20q^{67} + 21q^{69} + 5q^{71} - 3q^{73} - 51q^{75} + 25q^{79} + 43q^{81} + 18q^{83} + 36q^{85} - 53q^{87} - 11q^{89} + 65q^{93} - 30q^{95} + 16q^{97} - 18q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −3.42372 −1.97668 −0.988341 0.152254i \(-0.951347\pi\)
−0.988341 + 0.152254i \(0.951347\pi\)
\(4\) 0 0
\(5\) 2.35740 1.05426 0.527130 0.849784i \(-0.323268\pi\)
0.527130 + 0.849784i \(0.323268\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 8.72183 2.90728
\(10\) 0 0
\(11\) −0.142921 −0.0430924 −0.0215462 0.999768i \(-0.506859\pi\)
−0.0215462 + 0.999768i \(0.506859\pi\)
\(12\) 0 0
\(13\) −2.89147 −0.801950 −0.400975 0.916089i \(-0.631329\pi\)
−0.400975 + 0.916089i \(0.631329\pi\)
\(14\) 0 0
\(15\) −8.07106 −2.08394
\(16\) 0 0
\(17\) −1.39444 −0.338202 −0.169101 0.985599i \(-0.554086\pi\)
−0.169101 + 0.985599i \(0.554086\pi\)
\(18\) 0 0
\(19\) −7.23396 −1.65958 −0.829792 0.558073i \(-0.811541\pi\)
−0.829792 + 0.558073i \(0.811541\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.70073 −0.980170 −0.490085 0.871675i \(-0.663034\pi\)
−0.490085 + 0.871675i \(0.663034\pi\)
\(24\) 0 0
\(25\) 0.557331 0.111466
\(26\) 0 0
\(27\) −19.5899 −3.77008
\(28\) 0 0
\(29\) 2.50126 0.464473 0.232236 0.972659i \(-0.425396\pi\)
0.232236 + 0.972659i \(0.425396\pi\)
\(30\) 0 0
\(31\) −2.29868 −0.412855 −0.206427 0.978462i \(-0.566184\pi\)
−0.206427 + 0.978462i \(0.566184\pi\)
\(32\) 0 0
\(33\) 0.489322 0.0851799
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −8.95769 −1.47263 −0.736317 0.676636i \(-0.763437\pi\)
−0.736317 + 0.676636i \(0.763437\pi\)
\(38\) 0 0
\(39\) 9.89958 1.58520
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 10.0638 1.53471 0.767355 0.641223i \(-0.221573\pi\)
0.767355 + 0.641223i \(0.221573\pi\)
\(44\) 0 0
\(45\) 20.5608 3.06503
\(46\) 0 0
\(47\) −0.577516 −0.0842393 −0.0421197 0.999113i \(-0.513411\pi\)
−0.0421197 + 0.999113i \(0.513411\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 4.77417 0.668517
\(52\) 0 0
\(53\) −2.67866 −0.367942 −0.183971 0.982932i \(-0.558895\pi\)
−0.183971 + 0.982932i \(0.558895\pi\)
\(54\) 0 0
\(55\) −0.336922 −0.0454306
\(56\) 0 0
\(57\) 24.7670 3.28047
\(58\) 0 0
\(59\) −5.00779 −0.651959 −0.325979 0.945377i \(-0.605694\pi\)
−0.325979 + 0.945377i \(0.605694\pi\)
\(60\) 0 0
\(61\) 10.1819 1.30366 0.651832 0.758364i \(-0.274001\pi\)
0.651832 + 0.758364i \(0.274001\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −6.81635 −0.845465
\(66\) 0 0
\(67\) 4.81589 0.588354 0.294177 0.955751i \(-0.404954\pi\)
0.294177 + 0.955751i \(0.404954\pi\)
\(68\) 0 0
\(69\) 16.0940 1.93749
\(70\) 0 0
\(71\) −10.7912 −1.28068 −0.640339 0.768092i \(-0.721206\pi\)
−0.640339 + 0.768092i \(0.721206\pi\)
\(72\) 0 0
\(73\) −2.06872 −0.242125 −0.121063 0.992645i \(-0.538630\pi\)
−0.121063 + 0.992645i \(0.538630\pi\)
\(74\) 0 0
\(75\) −1.90814 −0.220333
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 2.74538 0.308880 0.154440 0.988002i \(-0.450643\pi\)
0.154440 + 0.988002i \(0.450643\pi\)
\(80\) 0 0
\(81\) 40.9048 4.54497
\(82\) 0 0
\(83\) 8.58858 0.942720 0.471360 0.881941i \(-0.343763\pi\)
0.471360 + 0.881941i \(0.343763\pi\)
\(84\) 0 0
\(85\) −3.28725 −0.356553
\(86\) 0 0
\(87\) −8.56361 −0.918116
\(88\) 0 0
\(89\) 11.3580 1.20394 0.601970 0.798518i \(-0.294383\pi\)
0.601970 + 0.798518i \(0.294383\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 7.87002 0.816083
\(94\) 0 0
\(95\) −17.0533 −1.74963
\(96\) 0 0
\(97\) −4.73305 −0.480568 −0.240284 0.970703i \(-0.577241\pi\)
−0.240284 + 0.970703i \(0.577241\pi\)
\(98\) 0 0
\(99\) −1.24653 −0.125281
\(100\) 0 0
\(101\) 7.85182 0.781285 0.390643 0.920542i \(-0.372253\pi\)
0.390643 + 0.920542i \(0.372253\pi\)
\(102\) 0 0
\(103\) −15.3743 −1.51488 −0.757438 0.652907i \(-0.773549\pi\)
−0.757438 + 0.652907i \(0.773549\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 17.8820 1.72872 0.864361 0.502871i \(-0.167723\pi\)
0.864361 + 0.502871i \(0.167723\pi\)
\(108\) 0 0
\(109\) 12.7126 1.21764 0.608822 0.793307i \(-0.291642\pi\)
0.608822 + 0.793307i \(0.291642\pi\)
\(110\) 0 0
\(111\) 30.6686 2.91093
\(112\) 0 0
\(113\) 8.71167 0.819525 0.409763 0.912192i \(-0.365612\pi\)
0.409763 + 0.912192i \(0.365612\pi\)
\(114\) 0 0
\(115\) −11.0815 −1.03336
\(116\) 0 0
\(117\) −25.2189 −2.33149
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −10.9796 −0.998143
\(122\) 0 0
\(123\) 3.42372 0.308706
\(124\) 0 0
\(125\) −10.4731 −0.936746
\(126\) 0 0
\(127\) −5.87321 −0.521163 −0.260581 0.965452i \(-0.583914\pi\)
−0.260581 + 0.965452i \(0.583914\pi\)
\(128\) 0 0
\(129\) −34.4555 −3.03363
\(130\) 0 0
\(131\) 11.1197 0.971533 0.485766 0.874089i \(-0.338541\pi\)
0.485766 + 0.874089i \(0.338541\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −46.1812 −3.97465
\(136\) 0 0
\(137\) 11.7117 1.00060 0.500298 0.865853i \(-0.333224\pi\)
0.500298 + 0.865853i \(0.333224\pi\)
\(138\) 0 0
\(139\) 6.11570 0.518727 0.259364 0.965780i \(-0.416487\pi\)
0.259364 + 0.965780i \(0.416487\pi\)
\(140\) 0 0
\(141\) 1.97725 0.166514
\(142\) 0 0
\(143\) 0.413253 0.0345579
\(144\) 0 0
\(145\) 5.89648 0.489676
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 15.0820 1.23557 0.617784 0.786348i \(-0.288031\pi\)
0.617784 + 0.786348i \(0.288031\pi\)
\(150\) 0 0
\(151\) 15.2951 1.24470 0.622349 0.782740i \(-0.286178\pi\)
0.622349 + 0.782740i \(0.286178\pi\)
\(152\) 0 0
\(153\) −12.1621 −0.983245
\(154\) 0 0
\(155\) −5.41890 −0.435256
\(156\) 0 0
\(157\) −13.0031 −1.03776 −0.518881 0.854847i \(-0.673651\pi\)
−0.518881 + 0.854847i \(0.673651\pi\)
\(158\) 0 0
\(159\) 9.17096 0.727304
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −0.252349 −0.0197655 −0.00988275 0.999951i \(-0.503146\pi\)
−0.00988275 + 0.999951i \(0.503146\pi\)
\(164\) 0 0
\(165\) 1.15353 0.0898019
\(166\) 0 0
\(167\) −21.3675 −1.65347 −0.826733 0.562595i \(-0.809803\pi\)
−0.826733 + 0.562595i \(0.809803\pi\)
\(168\) 0 0
\(169\) −4.63939 −0.356876
\(170\) 0 0
\(171\) −63.0933 −4.82487
\(172\) 0 0
\(173\) 1.58550 0.120543 0.0602715 0.998182i \(-0.480803\pi\)
0.0602715 + 0.998182i \(0.480803\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 17.1452 1.28872
\(178\) 0 0
\(179\) −16.9472 −1.26670 −0.633348 0.773867i \(-0.718320\pi\)
−0.633348 + 0.773867i \(0.718320\pi\)
\(180\) 0 0
\(181\) 18.3755 1.36584 0.682920 0.730493i \(-0.260710\pi\)
0.682920 + 0.730493i \(0.260710\pi\)
\(182\) 0 0
\(183\) −34.8601 −2.57693
\(184\) 0 0
\(185\) −21.1168 −1.55254
\(186\) 0 0
\(187\) 0.199295 0.0145739
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −25.5422 −1.84817 −0.924083 0.382191i \(-0.875170\pi\)
−0.924083 + 0.382191i \(0.875170\pi\)
\(192\) 0 0
\(193\) −4.00444 −0.288246 −0.144123 0.989560i \(-0.546036\pi\)
−0.144123 + 0.989560i \(0.546036\pi\)
\(194\) 0 0
\(195\) 23.3373 1.67122
\(196\) 0 0
\(197\) 12.0879 0.861228 0.430614 0.902536i \(-0.358297\pi\)
0.430614 + 0.902536i \(0.358297\pi\)
\(198\) 0 0
\(199\) −19.5784 −1.38788 −0.693939 0.720034i \(-0.744126\pi\)
−0.693939 + 0.720034i \(0.744126\pi\)
\(200\) 0 0
\(201\) −16.4882 −1.16299
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −2.35740 −0.164648
\(206\) 0 0
\(207\) −40.9990 −2.84963
\(208\) 0 0
\(209\) 1.03389 0.0715154
\(210\) 0 0
\(211\) 14.0250 0.965521 0.482761 0.875752i \(-0.339634\pi\)
0.482761 + 0.875752i \(0.339634\pi\)
\(212\) 0 0
\(213\) 36.9460 2.53149
\(214\) 0 0
\(215\) 23.7243 1.61798
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 7.08271 0.478605
\(220\) 0 0
\(221\) 4.03199 0.271221
\(222\) 0 0
\(223\) −14.7762 −0.989486 −0.494743 0.869039i \(-0.664738\pi\)
−0.494743 + 0.869039i \(0.664738\pi\)
\(224\) 0 0
\(225\) 4.86095 0.324063
\(226\) 0 0
\(227\) −18.2506 −1.21134 −0.605668 0.795718i \(-0.707094\pi\)
−0.605668 + 0.795718i \(0.707094\pi\)
\(228\) 0 0
\(229\) −5.92817 −0.391745 −0.195872 0.980629i \(-0.562754\pi\)
−0.195872 + 0.980629i \(0.562754\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 8.39823 0.550187 0.275093 0.961418i \(-0.411291\pi\)
0.275093 + 0.961418i \(0.411291\pi\)
\(234\) 0 0
\(235\) −1.36144 −0.0888102
\(236\) 0 0
\(237\) −9.39941 −0.610557
\(238\) 0 0
\(239\) 27.2326 1.76153 0.880766 0.473552i \(-0.157028\pi\)
0.880766 + 0.473552i \(0.157028\pi\)
\(240\) 0 0
\(241\) 0.162129 0.0104437 0.00522183 0.999986i \(-0.498338\pi\)
0.00522183 + 0.999986i \(0.498338\pi\)
\(242\) 0 0
\(243\) −81.2766 −5.21389
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 20.9168 1.33090
\(248\) 0 0
\(249\) −29.4049 −1.86346
\(250\) 0 0
\(251\) 27.1939 1.71646 0.858232 0.513261i \(-0.171563\pi\)
0.858232 + 0.513261i \(0.171563\pi\)
\(252\) 0 0
\(253\) 0.671834 0.0422379
\(254\) 0 0
\(255\) 11.2546 0.704792
\(256\) 0 0
\(257\) 22.0781 1.37719 0.688597 0.725144i \(-0.258227\pi\)
0.688597 + 0.725144i \(0.258227\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 21.8156 1.35035
\(262\) 0 0
\(263\) 15.3850 0.948679 0.474339 0.880342i \(-0.342687\pi\)
0.474339 + 0.880342i \(0.342687\pi\)
\(264\) 0 0
\(265\) −6.31466 −0.387907
\(266\) 0 0
\(267\) −38.8864 −2.37981
\(268\) 0 0
\(269\) 20.7321 1.26406 0.632028 0.774946i \(-0.282223\pi\)
0.632028 + 0.774946i \(0.282223\pi\)
\(270\) 0 0
\(271\) 12.7232 0.772880 0.386440 0.922315i \(-0.373705\pi\)
0.386440 + 0.922315i \(0.373705\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.0796545 −0.00480334
\(276\) 0 0
\(277\) 12.0748 0.725502 0.362751 0.931886i \(-0.381838\pi\)
0.362751 + 0.931886i \(0.381838\pi\)
\(278\) 0 0
\(279\) −20.0487 −1.20028
\(280\) 0 0
\(281\) 0.165786 0.00988995 0.00494497 0.999988i \(-0.498426\pi\)
0.00494497 + 0.999988i \(0.498426\pi\)
\(282\) 0 0
\(283\) 8.94687 0.531836 0.265918 0.963996i \(-0.414325\pi\)
0.265918 + 0.963996i \(0.414325\pi\)
\(284\) 0 0
\(285\) 58.3857 3.45847
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −15.0555 −0.885620
\(290\) 0 0
\(291\) 16.2046 0.949931
\(292\) 0 0
\(293\) 17.2016 1.00493 0.502465 0.864597i \(-0.332427\pi\)
0.502465 + 0.864597i \(0.332427\pi\)
\(294\) 0 0
\(295\) −11.8054 −0.687334
\(296\) 0 0
\(297\) 2.79981 0.162462
\(298\) 0 0
\(299\) 13.5920 0.786048
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −26.8824 −1.54435
\(304\) 0 0
\(305\) 24.0029 1.37440
\(306\) 0 0
\(307\) 33.1945 1.89451 0.947256 0.320478i \(-0.103843\pi\)
0.947256 + 0.320478i \(0.103843\pi\)
\(308\) 0 0
\(309\) 52.6373 2.99443
\(310\) 0 0
\(311\) 10.9294 0.619748 0.309874 0.950778i \(-0.399713\pi\)
0.309874 + 0.950778i \(0.399713\pi\)
\(312\) 0 0
\(313\) −10.5812 −0.598087 −0.299043 0.954240i \(-0.596667\pi\)
−0.299043 + 0.954240i \(0.596667\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −30.9547 −1.73859 −0.869295 0.494294i \(-0.835427\pi\)
−0.869295 + 0.494294i \(0.835427\pi\)
\(318\) 0 0
\(319\) −0.357484 −0.0200152
\(320\) 0 0
\(321\) −61.2230 −3.41714
\(322\) 0 0
\(323\) 10.0873 0.561274
\(324\) 0 0
\(325\) −1.61151 −0.0893904
\(326\) 0 0
\(327\) −43.5242 −2.40690
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −25.2861 −1.38985 −0.694925 0.719082i \(-0.744563\pi\)
−0.694925 + 0.719082i \(0.744563\pi\)
\(332\) 0 0
\(333\) −78.1274 −4.28135
\(334\) 0 0
\(335\) 11.3530 0.620279
\(336\) 0 0
\(337\) 5.87859 0.320227 0.160114 0.987099i \(-0.448814\pi\)
0.160114 + 0.987099i \(0.448814\pi\)
\(338\) 0 0
\(339\) −29.8263 −1.61994
\(340\) 0 0
\(341\) 0.328530 0.0177909
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 37.9399 2.04262
\(346\) 0 0
\(347\) 7.35540 0.394858 0.197429 0.980317i \(-0.436741\pi\)
0.197429 + 0.980317i \(0.436741\pi\)
\(348\) 0 0
\(349\) −4.99991 −0.267639 −0.133820 0.991006i \(-0.542724\pi\)
−0.133820 + 0.991006i \(0.542724\pi\)
\(350\) 0 0
\(351\) 56.6436 3.02341
\(352\) 0 0
\(353\) 8.91487 0.474491 0.237245 0.971450i \(-0.423755\pi\)
0.237245 + 0.971450i \(0.423755\pi\)
\(354\) 0 0
\(355\) −25.4391 −1.35017
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 17.4212 0.919457 0.459728 0.888060i \(-0.347947\pi\)
0.459728 + 0.888060i \(0.347947\pi\)
\(360\) 0 0
\(361\) 33.3302 1.75422
\(362\) 0 0
\(363\) 37.5909 1.97301
\(364\) 0 0
\(365\) −4.87680 −0.255263
\(366\) 0 0
\(367\) 0.663350 0.0346266 0.0173133 0.999850i \(-0.494489\pi\)
0.0173133 + 0.999850i \(0.494489\pi\)
\(368\) 0 0
\(369\) −8.72183 −0.454040
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −17.3767 −0.899733 −0.449866 0.893096i \(-0.648528\pi\)
−0.449866 + 0.893096i \(0.648528\pi\)
\(374\) 0 0
\(375\) 35.8571 1.85165
\(376\) 0 0
\(377\) −7.23233 −0.372484
\(378\) 0 0
\(379\) 18.2083 0.935297 0.467648 0.883915i \(-0.345101\pi\)
0.467648 + 0.883915i \(0.345101\pi\)
\(380\) 0 0
\(381\) 20.1082 1.03017
\(382\) 0 0
\(383\) −2.90905 −0.148645 −0.0743227 0.997234i \(-0.523679\pi\)
−0.0743227 + 0.997234i \(0.523679\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 87.7744 4.46182
\(388\) 0 0
\(389\) −18.3040 −0.928049 −0.464024 0.885822i \(-0.653595\pi\)
−0.464024 + 0.885822i \(0.653595\pi\)
\(390\) 0 0
\(391\) 6.55489 0.331495
\(392\) 0 0
\(393\) −38.0707 −1.92041
\(394\) 0 0
\(395\) 6.47196 0.325640
\(396\) 0 0
\(397\) −23.3639 −1.17260 −0.586300 0.810094i \(-0.699416\pi\)
−0.586300 + 0.810094i \(0.699416\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3.02683 0.151153 0.0755764 0.997140i \(-0.475920\pi\)
0.0755764 + 0.997140i \(0.475920\pi\)
\(402\) 0 0
\(403\) 6.64656 0.331089
\(404\) 0 0
\(405\) 96.4289 4.79159
\(406\) 0 0
\(407\) 1.28024 0.0634593
\(408\) 0 0
\(409\) −7.53066 −0.372367 −0.186184 0.982515i \(-0.559612\pi\)
−0.186184 + 0.982515i \(0.559612\pi\)
\(410\) 0 0
\(411\) −40.0975 −1.97786
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 20.2467 0.993872
\(416\) 0 0
\(417\) −20.9384 −1.02536
\(418\) 0 0
\(419\) 40.5782 1.98238 0.991188 0.132463i \(-0.0422886\pi\)
0.991188 + 0.132463i \(0.0422886\pi\)
\(420\) 0 0
\(421\) 8.44073 0.411376 0.205688 0.978618i \(-0.434057\pi\)
0.205688 + 0.978618i \(0.434057\pi\)
\(422\) 0 0
\(423\) −5.03699 −0.244907
\(424\) 0 0
\(425\) −0.777166 −0.0376981
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −1.41486 −0.0683100
\(430\) 0 0
\(431\) 16.4807 0.793845 0.396923 0.917852i \(-0.370078\pi\)
0.396923 + 0.917852i \(0.370078\pi\)
\(432\) 0 0
\(433\) −8.61281 −0.413905 −0.206953 0.978351i \(-0.566355\pi\)
−0.206953 + 0.978351i \(0.566355\pi\)
\(434\) 0 0
\(435\) −20.1879 −0.967933
\(436\) 0 0
\(437\) 34.0049 1.62668
\(438\) 0 0
\(439\) −32.4539 −1.54894 −0.774470 0.632610i \(-0.781984\pi\)
−0.774470 + 0.632610i \(0.781984\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 32.8043 1.55858 0.779290 0.626664i \(-0.215580\pi\)
0.779290 + 0.626664i \(0.215580\pi\)
\(444\) 0 0
\(445\) 26.7752 1.26927
\(446\) 0 0
\(447\) −51.6365 −2.44232
\(448\) 0 0
\(449\) 4.28694 0.202313 0.101157 0.994871i \(-0.467746\pi\)
0.101157 + 0.994871i \(0.467746\pi\)
\(450\) 0 0
\(451\) 0.142921 0.00672990
\(452\) 0 0
\(453\) −52.3661 −2.46037
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 10.1645 0.475474 0.237737 0.971330i \(-0.423594\pi\)
0.237737 + 0.971330i \(0.423594\pi\)
\(458\) 0 0
\(459\) 27.3170 1.27505
\(460\) 0 0
\(461\) −26.9754 −1.25637 −0.628184 0.778065i \(-0.716201\pi\)
−0.628184 + 0.778065i \(0.716201\pi\)
\(462\) 0 0
\(463\) −26.2945 −1.22201 −0.611005 0.791627i \(-0.709234\pi\)
−0.611005 + 0.791627i \(0.709234\pi\)
\(464\) 0 0
\(465\) 18.5528 0.860364
\(466\) 0 0
\(467\) 26.2776 1.21598 0.607990 0.793945i \(-0.291976\pi\)
0.607990 + 0.793945i \(0.291976\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 44.5190 2.05133
\(472\) 0 0
\(473\) −1.43833 −0.0661343
\(474\) 0 0
\(475\) −4.03171 −0.184988
\(476\) 0 0
\(477\) −23.3628 −1.06971
\(478\) 0 0
\(479\) 10.5456 0.481839 0.240919 0.970545i \(-0.422551\pi\)
0.240919 + 0.970545i \(0.422551\pi\)
\(480\) 0 0
\(481\) 25.9009 1.18098
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −11.1577 −0.506644
\(486\) 0 0
\(487\) 41.8841 1.89795 0.948974 0.315354i \(-0.102123\pi\)
0.948974 + 0.315354i \(0.102123\pi\)
\(488\) 0 0
\(489\) 0.863971 0.0390701
\(490\) 0 0
\(491\) −9.42364 −0.425283 −0.212641 0.977130i \(-0.568207\pi\)
−0.212641 + 0.977130i \(0.568207\pi\)
\(492\) 0 0
\(493\) −3.48786 −0.157085
\(494\) 0 0
\(495\) −2.93858 −0.132079
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 39.6921 1.77686 0.888430 0.459011i \(-0.151796\pi\)
0.888430 + 0.459011i \(0.151796\pi\)
\(500\) 0 0
\(501\) 73.1562 3.26838
\(502\) 0 0
\(503\) −14.7881 −0.659371 −0.329685 0.944091i \(-0.606943\pi\)
−0.329685 + 0.944091i \(0.606943\pi\)
\(504\) 0 0
\(505\) 18.5099 0.823678
\(506\) 0 0
\(507\) 15.8840 0.705431
\(508\) 0 0
\(509\) −3.37315 −0.149512 −0.0747561 0.997202i \(-0.523818\pi\)
−0.0747561 + 0.997202i \(0.523818\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 141.713 6.25676
\(514\) 0 0
\(515\) −36.2434 −1.59708
\(516\) 0 0
\(517\) 0.0825392 0.00363007
\(518\) 0 0
\(519\) −5.42829 −0.238275
\(520\) 0 0
\(521\) 34.0110 1.49005 0.745025 0.667037i \(-0.232438\pi\)
0.745025 + 0.667037i \(0.232438\pi\)
\(522\) 0 0
\(523\) 32.9876 1.44245 0.721223 0.692703i \(-0.243580\pi\)
0.721223 + 0.692703i \(0.243580\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 3.20537 0.139628
\(528\) 0 0
\(529\) −0.903114 −0.0392658
\(530\) 0 0
\(531\) −43.6771 −1.89542
\(532\) 0 0
\(533\) 2.89147 0.125244
\(534\) 0 0
\(535\) 42.1551 1.82253
\(536\) 0 0
\(537\) 58.0225 2.50386
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −11.0357 −0.474460 −0.237230 0.971453i \(-0.576240\pi\)
−0.237230 + 0.971453i \(0.576240\pi\)
\(542\) 0 0
\(543\) −62.9125 −2.69983
\(544\) 0 0
\(545\) 29.9686 1.28371
\(546\) 0 0
\(547\) −1.82860 −0.0781851 −0.0390926 0.999236i \(-0.512447\pi\)
−0.0390926 + 0.999236i \(0.512447\pi\)
\(548\) 0 0
\(549\) 88.8051 3.79011
\(550\) 0 0
\(551\) −18.0940 −0.770832
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 72.2981 3.06888
\(556\) 0 0
\(557\) −33.4105 −1.41565 −0.707825 0.706388i \(-0.750323\pi\)
−0.707825 + 0.706388i \(0.750323\pi\)
\(558\) 0 0
\(559\) −29.0991 −1.23076
\(560\) 0 0
\(561\) −0.682330 −0.0288080
\(562\) 0 0
\(563\) −15.0651 −0.634919 −0.317459 0.948272i \(-0.602830\pi\)
−0.317459 + 0.948272i \(0.602830\pi\)
\(564\) 0 0
\(565\) 20.5369 0.863993
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −39.0813 −1.63837 −0.819186 0.573528i \(-0.805574\pi\)
−0.819186 + 0.573528i \(0.805574\pi\)
\(570\) 0 0
\(571\) 7.81585 0.327083 0.163542 0.986536i \(-0.447708\pi\)
0.163542 + 0.986536i \(0.447708\pi\)
\(572\) 0 0
\(573\) 87.4491 3.65324
\(574\) 0 0
\(575\) −2.61987 −0.109256
\(576\) 0 0
\(577\) 6.42279 0.267384 0.133692 0.991023i \(-0.457317\pi\)
0.133692 + 0.991023i \(0.457317\pi\)
\(578\) 0 0
\(579\) 13.7100 0.569770
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0.382837 0.0158555
\(584\) 0 0
\(585\) −59.4510 −2.45800
\(586\) 0 0
\(587\) −8.49043 −0.350438 −0.175219 0.984530i \(-0.556063\pi\)
−0.175219 + 0.984530i \(0.556063\pi\)
\(588\) 0 0
\(589\) 16.6285 0.685167
\(590\) 0 0
\(591\) −41.3856 −1.70237
\(592\) 0 0
\(593\) −5.85832 −0.240572 −0.120286 0.992739i \(-0.538381\pi\)
−0.120286 + 0.992739i \(0.538381\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 67.0310 2.74340
\(598\) 0 0
\(599\) −21.4262 −0.875450 −0.437725 0.899109i \(-0.644216\pi\)
−0.437725 + 0.899109i \(0.644216\pi\)
\(600\) 0 0
\(601\) 40.7091 1.66056 0.830279 0.557347i \(-0.188181\pi\)
0.830279 + 0.557347i \(0.188181\pi\)
\(602\) 0 0
\(603\) 42.0033 1.71051
\(604\) 0 0
\(605\) −25.8832 −1.05230
\(606\) 0 0
\(607\) 31.5300 1.27976 0.639882 0.768474i \(-0.278983\pi\)
0.639882 + 0.768474i \(0.278983\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.66987 0.0675557
\(612\) 0 0
\(613\) −22.5191 −0.909538 −0.454769 0.890609i \(-0.650278\pi\)
−0.454769 + 0.890609i \(0.650278\pi\)
\(614\) 0 0
\(615\) 8.07106 0.325457
\(616\) 0 0
\(617\) 8.08398 0.325449 0.162724 0.986672i \(-0.447972\pi\)
0.162724 + 0.986672i \(0.447972\pi\)
\(618\) 0 0
\(619\) 17.8816 0.718720 0.359360 0.933199i \(-0.382995\pi\)
0.359360 + 0.933199i \(0.382995\pi\)
\(620\) 0 0
\(621\) 92.0869 3.69532
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −27.4760 −1.09904
\(626\) 0 0
\(627\) −3.53973 −0.141363
\(628\) 0 0
\(629\) 12.4910 0.498047
\(630\) 0 0
\(631\) −2.38709 −0.0950284 −0.0475142 0.998871i \(-0.515130\pi\)
−0.0475142 + 0.998871i \(0.515130\pi\)
\(632\) 0 0
\(633\) −48.0176 −1.90853
\(634\) 0 0
\(635\) −13.8455 −0.549442
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −94.1189 −3.72328
\(640\) 0 0
\(641\) 7.11567 0.281052 0.140526 0.990077i \(-0.455121\pi\)
0.140526 + 0.990077i \(0.455121\pi\)
\(642\) 0 0
\(643\) −3.43177 −0.135336 −0.0676679 0.997708i \(-0.521556\pi\)
−0.0676679 + 0.997708i \(0.521556\pi\)
\(644\) 0 0
\(645\) −81.2253 −3.19824
\(646\) 0 0
\(647\) −8.56016 −0.336535 −0.168267 0.985741i \(-0.553817\pi\)
−0.168267 + 0.985741i \(0.553817\pi\)
\(648\) 0 0
\(649\) 0.715719 0.0280944
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −12.3539 −0.483447 −0.241724 0.970345i \(-0.577713\pi\)
−0.241724 + 0.970345i \(0.577713\pi\)
\(654\) 0 0
\(655\) 26.2136 1.02425
\(656\) 0 0
\(657\) −18.0430 −0.703925
\(658\) 0 0
\(659\) −48.6368 −1.89462 −0.947310 0.320320i \(-0.896210\pi\)
−0.947310 + 0.320320i \(0.896210\pi\)
\(660\) 0 0
\(661\) 12.3667 0.481007 0.240504 0.970648i \(-0.422687\pi\)
0.240504 + 0.970648i \(0.422687\pi\)
\(662\) 0 0
\(663\) −13.8044 −0.536117
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −11.7578 −0.455263
\(668\) 0 0
\(669\) 50.5894 1.95590
\(670\) 0 0
\(671\) −1.45521 −0.0561780
\(672\) 0 0
\(673\) −44.1413 −1.70152 −0.850760 0.525554i \(-0.823858\pi\)
−0.850760 + 0.525554i \(0.823858\pi\)
\(674\) 0 0
\(675\) −10.9181 −0.420237
\(676\) 0 0
\(677\) −10.3534 −0.397912 −0.198956 0.980008i \(-0.563755\pi\)
−0.198956 + 0.980008i \(0.563755\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 62.4849 2.39443
\(682\) 0 0
\(683\) −23.0424 −0.881693 −0.440846 0.897583i \(-0.645322\pi\)
−0.440846 + 0.897583i \(0.645322\pi\)
\(684\) 0 0
\(685\) 27.6091 1.05489
\(686\) 0 0
\(687\) 20.2964 0.774355
\(688\) 0 0
\(689\) 7.74526 0.295071
\(690\) 0 0
\(691\) 10.9576 0.416847 0.208423 0.978039i \(-0.433167\pi\)
0.208423 + 0.978039i \(0.433167\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 14.4172 0.546874
\(696\) 0 0
\(697\) 1.39444 0.0528182
\(698\) 0 0
\(699\) −28.7532 −1.08754
\(700\) 0 0
\(701\) 3.05919 0.115544 0.0577721 0.998330i \(-0.481600\pi\)
0.0577721 + 0.998330i \(0.481600\pi\)
\(702\) 0 0
\(703\) 64.7995 2.44396
\(704\) 0 0
\(705\) 4.66117 0.175550
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −24.2009 −0.908884 −0.454442 0.890776i \(-0.650161\pi\)
−0.454442 + 0.890776i \(0.650161\pi\)
\(710\) 0 0
\(711\) 23.9448 0.897998
\(712\) 0 0
\(713\) 10.8055 0.404668
\(714\) 0 0
\(715\) 0.974201 0.0364331
\(716\) 0 0
\(717\) −93.2368 −3.48199
\(718\) 0 0
\(719\) 0.874589 0.0326167 0.0163083 0.999867i \(-0.494809\pi\)
0.0163083 + 0.999867i \(0.494809\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −0.555084 −0.0206438
\(724\) 0 0
\(725\) 1.39403 0.0517731
\(726\) 0 0
\(727\) 21.7602 0.807040 0.403520 0.914971i \(-0.367787\pi\)
0.403520 + 0.914971i \(0.367787\pi\)
\(728\) 0 0
\(729\) 155.554 5.76124
\(730\) 0 0
\(731\) −14.0333 −0.519041
\(732\) 0 0
\(733\) 9.33091 0.344645 0.172323 0.985041i \(-0.444873\pi\)
0.172323 + 0.985041i \(0.444873\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.688293 −0.0253536
\(738\) 0 0
\(739\) 35.0351 1.28879 0.644394 0.764693i \(-0.277110\pi\)
0.644394 + 0.764693i \(0.277110\pi\)
\(740\) 0 0
\(741\) −71.6131 −2.63077
\(742\) 0 0
\(743\) −30.6618 −1.12487 −0.562436 0.826841i \(-0.690136\pi\)
−0.562436 + 0.826841i \(0.690136\pi\)
\(744\) 0 0
\(745\) 35.5543 1.30261
\(746\) 0 0
\(747\) 74.9081 2.74075
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −3.72070 −0.135770 −0.0678851 0.997693i \(-0.521625\pi\)
−0.0678851 + 0.997693i \(0.521625\pi\)
\(752\) 0 0
\(753\) −93.1042 −3.39291
\(754\) 0 0
\(755\) 36.0567 1.31224
\(756\) 0 0
\(757\) 32.8896 1.19539 0.597697 0.801722i \(-0.296082\pi\)
0.597697 + 0.801722i \(0.296082\pi\)
\(758\) 0 0
\(759\) −2.30017 −0.0834909
\(760\) 0 0
\(761\) 1.06473 0.0385963 0.0192982 0.999814i \(-0.493857\pi\)
0.0192982 + 0.999814i \(0.493857\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −28.6709 −1.03660
\(766\) 0 0
\(767\) 14.4799 0.522838
\(768\) 0 0
\(769\) 51.5858 1.86023 0.930116 0.367267i \(-0.119706\pi\)
0.930116 + 0.367267i \(0.119706\pi\)
\(770\) 0 0
\(771\) −75.5891 −2.72228
\(772\) 0 0
\(773\) 36.3187 1.30629 0.653147 0.757231i \(-0.273449\pi\)
0.653147 + 0.757231i \(0.273449\pi\)
\(774\) 0 0
\(775\) −1.28112 −0.0460194
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 7.23396 0.259183
\(780\) 0 0
\(781\) 1.54229 0.0551875
\(782\) 0 0
\(783\) −48.9995 −1.75110
\(784\) 0 0
\(785\) −30.6535 −1.09407
\(786\) 0 0
\(787\) −9.90378 −0.353032 −0.176516 0.984298i \(-0.556483\pi\)
−0.176516 + 0.984298i \(0.556483\pi\)
\(788\) 0 0
\(789\) −52.6738 −1.87524
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −29.4408 −1.04547
\(794\) 0 0
\(795\) 21.6196 0.766768
\(796\) 0 0
\(797\) 7.09187 0.251207 0.125603 0.992081i \(-0.459913\pi\)
0.125603 + 0.992081i \(0.459913\pi\)
\(798\) 0 0
\(799\) 0.805312 0.0284899
\(800\) 0 0
\(801\) 99.0621 3.50019
\(802\) 0 0
\(803\) 0.295664 0.0104338
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −70.9806 −2.49864
\(808\) 0 0
\(809\) 37.8692 1.33141 0.665706 0.746214i \(-0.268131\pi\)
0.665706 + 0.746214i \(0.268131\pi\)
\(810\) 0 0
\(811\) −27.2005 −0.955140 −0.477570 0.878594i \(-0.658482\pi\)
−0.477570 + 0.878594i \(0.658482\pi\)
\(812\) 0 0
\(813\) −43.5607 −1.52774
\(814\) 0 0
\(815\) −0.594887 −0.0208380
\(816\) 0 0
\(817\) −72.8009 −2.54698
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 11.1330 0.388545 0.194272 0.980948i \(-0.437765\pi\)
0.194272 + 0.980948i \(0.437765\pi\)
\(822\) 0 0
\(823\) −46.5787 −1.62363 −0.811815 0.583915i \(-0.801520\pi\)
−0.811815 + 0.583915i \(0.801520\pi\)
\(824\) 0 0
\(825\) 0.272714 0.00949469
\(826\) 0 0
\(827\) −22.1049 −0.768662 −0.384331 0.923195i \(-0.625568\pi\)
−0.384331 + 0.923195i \(0.625568\pi\)
\(828\) 0 0
\(829\) −0.0353550 −0.00122793 −0.000613965 1.00000i \(-0.500195\pi\)
−0.000613965 1.00000i \(0.500195\pi\)
\(830\) 0 0
\(831\) −41.3405 −1.43409
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −50.3717 −1.74318
\(836\) 0 0
\(837\) 45.0309 1.55649
\(838\) 0 0
\(839\) 19.0702 0.658375 0.329188 0.944265i \(-0.393225\pi\)
0.329188 + 0.944265i \(0.393225\pi\)
\(840\) 0 0
\(841\) −22.7437 −0.784265
\(842\) 0 0
\(843\) −0.567603 −0.0195493
\(844\) 0 0
\(845\) −10.9369 −0.376241
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −30.6315 −1.05127
\(850\) 0 0
\(851\) 42.1077 1.44343
\(852\) 0 0
\(853\) 33.9594 1.16275 0.581373 0.813637i \(-0.302516\pi\)
0.581373 + 0.813637i \(0.302516\pi\)
\(854\) 0 0
\(855\) −148.736 −5.08667
\(856\) 0 0
\(857\) 8.30473 0.283684 0.141842 0.989889i \(-0.454697\pi\)
0.141842 + 0.989889i \(0.454697\pi\)
\(858\) 0 0
\(859\) 47.3641 1.61604 0.808021 0.589154i \(-0.200539\pi\)
0.808021 + 0.589154i \(0.200539\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 6.83698 0.232733 0.116367 0.993206i \(-0.462875\pi\)
0.116367 + 0.993206i \(0.462875\pi\)
\(864\) 0 0
\(865\) 3.73765 0.127084
\(866\) 0 0
\(867\) 51.5459 1.75059
\(868\) 0 0
\(869\) −0.392373 −0.0133104
\(870\) 0 0
\(871\) −13.9250 −0.471831
\(872\) 0 0
\(873\) −41.2808 −1.39714
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −41.9935 −1.41802 −0.709011 0.705198i \(-0.750858\pi\)
−0.709011 + 0.705198i \(0.750858\pi\)
\(878\) 0 0
\(879\) −58.8935 −1.98643
\(880\) 0 0
\(881\) −26.1100 −0.879670 −0.439835 0.898079i \(-0.644963\pi\)
−0.439835 + 0.898079i \(0.644963\pi\)
\(882\) 0 0
\(883\) −24.5630 −0.826611 −0.413305 0.910593i \(-0.635626\pi\)
−0.413305 + 0.910593i \(0.635626\pi\)
\(884\) 0 0
\(885\) 40.4182 1.35864
\(886\) 0 0
\(887\) 48.1527 1.61681 0.808405 0.588626i \(-0.200331\pi\)
0.808405 + 0.588626i \(0.200331\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −5.84616 −0.195854
\(892\) 0 0
\(893\) 4.17772 0.139802
\(894\) 0 0
\(895\) −39.9514 −1.33543
\(896\) 0 0
\(897\) −46.5353 −1.55377
\(898\) 0 0
\(899\) −5.74960 −0.191760
\(900\) 0 0
\(901\) 3.73523 0.124439
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 43.3184 1.43995
\(906\) 0 0
\(907\) 47.0075 1.56086 0.780429 0.625244i \(-0.215001\pi\)
0.780429 + 0.625244i \(0.215001\pi\)
\(908\) 0 0
\(909\) 68.4822 2.27141
\(910\) 0 0
\(911\) 9.28031 0.307470 0.153735 0.988112i \(-0.450870\pi\)
0.153735 + 0.988112i \(0.450870\pi\)
\(912\) 0 0
\(913\) −1.22749 −0.0406240
\(914\) 0 0
\(915\) −82.1791 −2.71676
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 22.9220 0.756126 0.378063 0.925780i \(-0.376590\pi\)
0.378063 + 0.925780i \(0.376590\pi\)
\(920\) 0 0
\(921\) −113.649 −3.74485
\(922\) 0 0
\(923\) 31.2024 1.02704
\(924\) 0 0
\(925\) −4.99240 −0.164149
\(926\) 0 0
\(927\) −134.092 −4.40416
\(928\) 0 0
\(929\) −6.33924 −0.207984 −0.103992 0.994578i \(-0.533162\pi\)
−0.103992 + 0.994578i \(0.533162\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −37.4191 −1.22505
\(934\) 0 0
\(935\) 0.469818 0.0153647
\(936\) 0 0
\(937\) −37.6996 −1.23159 −0.615797 0.787905i \(-0.711166\pi\)
−0.615797 + 0.787905i \(0.711166\pi\)
\(938\) 0 0
\(939\) 36.2271 1.18223
\(940\) 0 0
\(941\) 4.58289 0.149398 0.0746990 0.997206i \(-0.476200\pi\)
0.0746990 + 0.997206i \(0.476200\pi\)
\(942\) 0 0
\(943\) 4.70073 0.153077
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −29.8988 −0.971581 −0.485791 0.874075i \(-0.661468\pi\)
−0.485791 + 0.874075i \(0.661468\pi\)
\(948\) 0 0
\(949\) 5.98164 0.194172
\(950\) 0 0
\(951\) 105.980 3.43664
\(952\) 0 0
\(953\) 14.5225 0.470429 0.235214 0.971944i \(-0.424421\pi\)
0.235214 + 0.971944i \(0.424421\pi\)
\(954\) 0 0
\(955\) −60.2131 −1.94845
\(956\) 0 0
\(957\) 1.22392 0.0395638
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −25.7161 −0.829551
\(962\) 0 0
\(963\) 155.964 5.02587
\(964\) 0 0
\(965\) −9.44006 −0.303886
\(966\) 0 0
\(967\) −11.0380 −0.354957 −0.177479 0.984125i \(-0.556794\pi\)
−0.177479 + 0.984125i \(0.556794\pi\)
\(968\) 0 0
\(969\) −34.5361 −1.10946
\(970\) 0 0
\(971\) −30.7755 −0.987633 −0.493817 0.869566i \(-0.664399\pi\)
−0.493817 + 0.869566i \(0.664399\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 5.51734 0.176696
\(976\) 0 0
\(977\) −31.3186 −1.00197 −0.500985 0.865456i \(-0.667029\pi\)
−0.500985 + 0.865456i \(0.667029\pi\)
\(978\) 0 0
\(979\) −1.62329 −0.0518807
\(980\) 0 0
\(981\) 110.877 3.54003
\(982\) 0 0
\(983\) −2.27332 −0.0725075 −0.0362538 0.999343i \(-0.511542\pi\)
−0.0362538 + 0.999343i \(0.511542\pi\)
\(984\) 0 0
\(985\) 28.4960 0.907959
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −47.3071 −1.50428
\(990\) 0 0
\(991\) −1.16054 −0.0368658 −0.0184329 0.999830i \(-0.505868\pi\)
−0.0184329 + 0.999830i \(0.505868\pi\)
\(992\) 0 0
\(993\) 86.5724 2.74729
\(994\) 0 0
\(995\) −46.1542 −1.46319
\(996\) 0 0
\(997\) 1.53162 0.0485069 0.0242534 0.999706i \(-0.492279\pi\)
0.0242534 + 0.999706i \(0.492279\pi\)
\(998\) 0 0
\(999\) 175.480 5.55195
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 \(a_p\))