Properties

Label 6004.2.a.d.1.1
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 0
Dimension 8
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9421813736\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{29}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.49694\)
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.49694 q^{5}\) \(+4.08498 q^{7}\) \(-3.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.49694 q^{5}\) \(+4.08498 q^{7}\) \(-3.00000 q^{9}\) \(-6.35071 q^{11}\) \(-3.31501 q^{13}\) \(-0.507955 q^{17}\) \(+1.00000 q^{19}\) \(+3.01491 q^{23}\) \(+1.23472 q^{25}\) \(+4.18318 q^{29}\) \(-9.86256 q^{31}\) \(-10.2000 q^{35}\) \(-9.92158 q^{37}\) \(+0.808619 q^{41}\) \(-5.39678 q^{43}\) \(+7.49082 q^{45}\) \(+10.4997 q^{47}\) \(+9.68707 q^{49}\) \(+10.9310 q^{53}\) \(+15.8574 q^{55}\) \(+3.91423 q^{59}\) \(-8.02958 q^{61}\) \(-12.2549 q^{63}\) \(+8.27740 q^{65}\) \(+5.98899 q^{67}\) \(+10.8922 q^{71}\) \(+0.522948 q^{73}\) \(-25.9425 q^{77}\) \(+1.00000 q^{79}\) \(+9.00000 q^{81}\) \(+2.67212 q^{83}\) \(+1.26833 q^{85}\) \(+1.13711 q^{89}\) \(-13.5418 q^{91}\) \(-2.49694 q^{95}\) \(-7.68703 q^{97}\) \(+19.0521 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(8q \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 7q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 10q^{23} \) \(\mathstrut +\mathstrut 6q^{25} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 3q^{31} \) \(\mathstrut -\mathstrut 11q^{35} \) \(\mathstrut -\mathstrut 15q^{37} \) \(\mathstrut -\mathstrut 5q^{41} \) \(\mathstrut +\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 12q^{45} \) \(\mathstrut +\mathstrut 18q^{47} \) \(\mathstrut +\mathstrut 31q^{49} \) \(\mathstrut +\mathstrut 9q^{53} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut +\mathstrut 8q^{59} \) \(\mathstrut +\mathstrut 13q^{61} \) \(\mathstrut -\mathstrut 3q^{63} \) \(\mathstrut +\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 21q^{67} \) \(\mathstrut +\mathstrut 44q^{71} \) \(\mathstrut -\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 72q^{81} \) \(\mathstrut -\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 9q^{85} \) \(\mathstrut -\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 48q^{91} \) \(\mathstrut +\mathstrut 4q^{95} \) \(\mathstrut -\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 21q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 0 0
\(5\) −2.49694 −1.11667 −0.558333 0.829617i \(-0.688559\pi\)
−0.558333 + 0.829617i \(0.688559\pi\)
\(6\) 0 0
\(7\) 4.08498 1.54398 0.771989 0.635636i \(-0.219262\pi\)
0.771989 + 0.635636i \(0.219262\pi\)
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) −6.35071 −1.91481 −0.957406 0.288746i \(-0.906762\pi\)
−0.957406 + 0.288746i \(0.906762\pi\)
\(12\) 0 0
\(13\) −3.31501 −0.919420 −0.459710 0.888069i \(-0.652047\pi\)
−0.459710 + 0.888069i \(0.652047\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.507955 −0.123197 −0.0615986 0.998101i \(-0.519620\pi\)
−0.0615986 + 0.998101i \(0.519620\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.01491 0.628652 0.314326 0.949315i \(-0.398221\pi\)
0.314326 + 0.949315i \(0.398221\pi\)
\(24\) 0 0
\(25\) 1.23472 0.246943
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4.18318 0.776796 0.388398 0.921492i \(-0.373029\pi\)
0.388398 + 0.921492i \(0.373029\pi\)
\(30\) 0 0
\(31\) −9.86256 −1.77137 −0.885684 0.464288i \(-0.846310\pi\)
−0.885684 + 0.464288i \(0.846310\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −10.2000 −1.72411
\(36\) 0 0
\(37\) −9.92158 −1.63110 −0.815549 0.578688i \(-0.803565\pi\)
−0.815549 + 0.578688i \(0.803565\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0.808619 0.126285 0.0631425 0.998005i \(-0.479888\pi\)
0.0631425 + 0.998005i \(0.479888\pi\)
\(42\) 0 0
\(43\) −5.39678 −0.823001 −0.411501 0.911409i \(-0.634995\pi\)
−0.411501 + 0.911409i \(0.634995\pi\)
\(44\) 0 0
\(45\) 7.49082 1.11667
\(46\) 0 0
\(47\) 10.4997 1.53154 0.765771 0.643114i \(-0.222358\pi\)
0.765771 + 0.643114i \(0.222358\pi\)
\(48\) 0 0
\(49\) 9.68707 1.38387
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 10.9310 1.50149 0.750744 0.660593i \(-0.229695\pi\)
0.750744 + 0.660593i \(0.229695\pi\)
\(54\) 0 0
\(55\) 15.8574 2.13820
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 3.91423 0.509589 0.254795 0.966995i \(-0.417992\pi\)
0.254795 + 0.966995i \(0.417992\pi\)
\(60\) 0 0
\(61\) −8.02958 −1.02808 −0.514041 0.857766i \(-0.671852\pi\)
−0.514041 + 0.857766i \(0.671852\pi\)
\(62\) 0 0
\(63\) −12.2549 −1.54398
\(64\) 0 0
\(65\) 8.27740 1.02668
\(66\) 0 0
\(67\) 5.98899 0.731671 0.365836 0.930679i \(-0.380783\pi\)
0.365836 + 0.930679i \(0.380783\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 10.8922 1.29267 0.646333 0.763055i \(-0.276302\pi\)
0.646333 + 0.763055i \(0.276302\pi\)
\(72\) 0 0
\(73\) 0.522948 0.0612064 0.0306032 0.999532i \(-0.490257\pi\)
0.0306032 + 0.999532i \(0.490257\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −25.9425 −2.95643
\(78\) 0 0
\(79\) 1.00000 0.112509
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 2.67212 0.293303 0.146651 0.989188i \(-0.453150\pi\)
0.146651 + 0.989188i \(0.453150\pi\)
\(84\) 0 0
\(85\) 1.26833 0.137570
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1.13711 0.120533 0.0602665 0.998182i \(-0.480805\pi\)
0.0602665 + 0.998182i \(0.480805\pi\)
\(90\) 0 0
\(91\) −13.5418 −1.41956
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.49694 −0.256181
\(96\) 0 0
\(97\) −7.68703 −0.780499 −0.390250 0.920709i \(-0.627611\pi\)
−0.390250 + 0.920709i \(0.627611\pi\)
\(98\) 0 0
\(99\) 19.0521 1.91481
\(100\) 0 0
\(101\) −13.8526 −1.37838 −0.689191 0.724580i \(-0.742034\pi\)
−0.689191 + 0.724580i \(0.742034\pi\)
\(102\) 0 0
\(103\) 18.4443 1.81737 0.908687 0.417479i \(-0.137086\pi\)
0.908687 + 0.417479i \(0.137086\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.86782 −0.180569 −0.0902847 0.995916i \(-0.528778\pi\)
−0.0902847 + 0.995916i \(0.528778\pi\)
\(108\) 0 0
\(109\) −14.4363 −1.38275 −0.691375 0.722496i \(-0.742995\pi\)
−0.691375 + 0.722496i \(0.742995\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −9.76762 −0.918860 −0.459430 0.888214i \(-0.651946\pi\)
−0.459430 + 0.888214i \(0.651946\pi\)
\(114\) 0 0
\(115\) −7.52806 −0.701995
\(116\) 0 0
\(117\) 9.94504 0.919420
\(118\) 0 0
\(119\) −2.07499 −0.190214
\(120\) 0 0
\(121\) 29.3315 2.66650
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 9.40169 0.840913
\(126\) 0 0
\(127\) 3.81406 0.338443 0.169221 0.985578i \(-0.445875\pi\)
0.169221 + 0.985578i \(0.445875\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 9.45543 0.826125 0.413062 0.910703i \(-0.364459\pi\)
0.413062 + 0.910703i \(0.364459\pi\)
\(132\) 0 0
\(133\) 4.08498 0.354213
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1.54392 −0.131906 −0.0659531 0.997823i \(-0.521009\pi\)
−0.0659531 + 0.997823i \(0.521009\pi\)
\(138\) 0 0
\(139\) 12.4177 1.05325 0.526626 0.850097i \(-0.323457\pi\)
0.526626 + 0.850097i \(0.323457\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 21.0527 1.76052
\(144\) 0 0
\(145\) −10.4451 −0.867422
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3.47555 −0.284728 −0.142364 0.989814i \(-0.545470\pi\)
−0.142364 + 0.989814i \(0.545470\pi\)
\(150\) 0 0
\(151\) 8.06919 0.656662 0.328331 0.944563i \(-0.393514\pi\)
0.328331 + 0.944563i \(0.393514\pi\)
\(152\) 0 0
\(153\) 1.52386 0.123197
\(154\) 0 0
\(155\) 24.6262 1.97803
\(156\) 0 0
\(157\) 1.40571 0.112188 0.0560939 0.998425i \(-0.482135\pi\)
0.0560939 + 0.998425i \(0.482135\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 12.3159 0.970625
\(162\) 0 0
\(163\) 19.5229 1.52915 0.764574 0.644535i \(-0.222949\pi\)
0.764574 + 0.644535i \(0.222949\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 4.18980 0.324217 0.162108 0.986773i \(-0.448171\pi\)
0.162108 + 0.986773i \(0.448171\pi\)
\(168\) 0 0
\(169\) −2.01068 −0.154668
\(170\) 0 0
\(171\) −3.00000 −0.229416
\(172\) 0 0
\(173\) 6.27868 0.477359 0.238680 0.971098i \(-0.423285\pi\)
0.238680 + 0.971098i \(0.423285\pi\)
\(174\) 0 0
\(175\) 5.04379 0.381275
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 8.07119 0.603269 0.301635 0.953424i \(-0.402468\pi\)
0.301635 + 0.953424i \(0.402468\pi\)
\(180\) 0 0
\(181\) −19.5445 −1.45273 −0.726366 0.687309i \(-0.758792\pi\)
−0.726366 + 0.687309i \(0.758792\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 24.7736 1.82139
\(186\) 0 0
\(187\) 3.22587 0.235899
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 11.6953 0.846241 0.423120 0.906073i \(-0.360935\pi\)
0.423120 + 0.906073i \(0.360935\pi\)
\(192\) 0 0
\(193\) 16.8686 1.21423 0.607114 0.794615i \(-0.292327\pi\)
0.607114 + 0.794615i \(0.292327\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −14.2840 −1.01770 −0.508848 0.860856i \(-0.669928\pi\)
−0.508848 + 0.860856i \(0.669928\pi\)
\(198\) 0 0
\(199\) −22.2835 −1.57964 −0.789819 0.613340i \(-0.789826\pi\)
−0.789819 + 0.613340i \(0.789826\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 17.0882 1.19936
\(204\) 0 0
\(205\) −2.01907 −0.141018
\(206\) 0 0
\(207\) −9.04473 −0.628652
\(208\) 0 0
\(209\) −6.35071 −0.439288
\(210\) 0 0
\(211\) −9.30639 −0.640678 −0.320339 0.947303i \(-0.603797\pi\)
−0.320339 + 0.947303i \(0.603797\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 13.4754 0.919018
\(216\) 0 0
\(217\) −40.2884 −2.73495
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1.68388 0.113270
\(222\) 0 0
\(223\) −22.1136 −1.48083 −0.740417 0.672147i \(-0.765372\pi\)
−0.740417 + 0.672147i \(0.765372\pi\)
\(224\) 0 0
\(225\) −3.70415 −0.246943
\(226\) 0 0
\(227\) 13.8498 0.919245 0.459623 0.888114i \(-0.347985\pi\)
0.459623 + 0.888114i \(0.347985\pi\)
\(228\) 0 0
\(229\) 8.86364 0.585726 0.292863 0.956154i \(-0.405392\pi\)
0.292863 + 0.956154i \(0.405392\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 17.1016 1.12036 0.560181 0.828370i \(-0.310732\pi\)
0.560181 + 0.828370i \(0.310732\pi\)
\(234\) 0 0
\(235\) −26.2172 −1.71022
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −7.83880 −0.507050 −0.253525 0.967329i \(-0.581590\pi\)
−0.253525 + 0.967329i \(0.581590\pi\)
\(240\) 0 0
\(241\) 26.6217 1.71486 0.857428 0.514604i \(-0.172061\pi\)
0.857428 + 0.514604i \(0.172061\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −24.1881 −1.54532
\(246\) 0 0
\(247\) −3.31501 −0.210929
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −27.1053 −1.71087 −0.855435 0.517911i \(-0.826710\pi\)
−0.855435 + 0.517911i \(0.826710\pi\)
\(252\) 0 0
\(253\) −19.1468 −1.20375
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −3.93317 −0.245345 −0.122672 0.992447i \(-0.539146\pi\)
−0.122672 + 0.992447i \(0.539146\pi\)
\(258\) 0 0
\(259\) −40.5295 −2.51838
\(260\) 0 0
\(261\) −12.5495 −0.776796
\(262\) 0 0
\(263\) 16.3410 1.00763 0.503814 0.863812i \(-0.331930\pi\)
0.503814 + 0.863812i \(0.331930\pi\)
\(264\) 0 0
\(265\) −27.2941 −1.67666
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 19.4203 1.18408 0.592040 0.805909i \(-0.298323\pi\)
0.592040 + 0.805909i \(0.298323\pi\)
\(270\) 0 0
\(271\) −0.275233 −0.0167192 −0.00835960 0.999965i \(-0.502661\pi\)
−0.00835960 + 0.999965i \(0.502661\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −7.84132 −0.472850
\(276\) 0 0
\(277\) −1.03924 −0.0624416 −0.0312208 0.999513i \(-0.509940\pi\)
−0.0312208 + 0.999513i \(0.509940\pi\)
\(278\) 0 0
\(279\) 29.5877 1.77137
\(280\) 0 0
\(281\) −4.68166 −0.279284 −0.139642 0.990202i \(-0.544595\pi\)
−0.139642 + 0.990202i \(0.544595\pi\)
\(282\) 0 0
\(283\) 15.4508 0.918456 0.459228 0.888319i \(-0.348126\pi\)
0.459228 + 0.888319i \(0.348126\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3.30319 0.194981
\(288\) 0 0
\(289\) −16.7420 −0.984822
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.14756 0.0670413 0.0335206 0.999438i \(-0.489328\pi\)
0.0335206 + 0.999438i \(0.489328\pi\)
\(294\) 0 0
\(295\) −9.77360 −0.569041
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −9.99447 −0.577995
\(300\) 0 0
\(301\) −22.0457 −1.27070
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 20.0494 1.14802
\(306\) 0 0
\(307\) 7.35748 0.419914 0.209957 0.977711i \(-0.432668\pi\)
0.209957 + 0.977711i \(0.432668\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −16.0968 −0.912766 −0.456383 0.889783i \(-0.650855\pi\)
−0.456383 + 0.889783i \(0.650855\pi\)
\(312\) 0 0
\(313\) 13.1282 0.742050 0.371025 0.928623i \(-0.379006\pi\)
0.371025 + 0.928623i \(0.379006\pi\)
\(314\) 0 0
\(315\) 30.5999 1.72411
\(316\) 0 0
\(317\) 10.3176 0.579493 0.289747 0.957103i \(-0.406429\pi\)
0.289747 + 0.957103i \(0.406429\pi\)
\(318\) 0 0
\(319\) −26.5661 −1.48742
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −0.507955 −0.0282634
\(324\) 0 0
\(325\) −4.09310 −0.227044
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 42.8912 2.36467
\(330\) 0 0
\(331\) −22.0219 −1.21044 −0.605218 0.796060i \(-0.706914\pi\)
−0.605218 + 0.796060i \(0.706914\pi\)
\(332\) 0 0
\(333\) 29.7648 1.63110
\(334\) 0 0
\(335\) −14.9541 −0.817032
\(336\) 0 0
\(337\) 16.8706 0.918998 0.459499 0.888178i \(-0.348029\pi\)
0.459499 + 0.888178i \(0.348029\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 62.6343 3.39184
\(342\) 0 0
\(343\) 10.9767 0.592683
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 22.0736 1.18497 0.592485 0.805581i \(-0.298147\pi\)
0.592485 + 0.805581i \(0.298147\pi\)
\(348\) 0 0
\(349\) 13.6558 0.730977 0.365489 0.930816i \(-0.380902\pi\)
0.365489 + 0.930816i \(0.380902\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 22.4971 1.19740 0.598699 0.800974i \(-0.295684\pi\)
0.598699 + 0.800974i \(0.295684\pi\)
\(354\) 0 0
\(355\) −27.1972 −1.44348
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 20.1036 1.06103 0.530515 0.847676i \(-0.321999\pi\)
0.530515 + 0.847676i \(0.321999\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1.30577 −0.0683471
\(366\) 0 0
\(367\) −8.85917 −0.462445 −0.231222 0.972901i \(-0.574273\pi\)
−0.231222 + 0.972901i \(0.574273\pi\)
\(368\) 0 0
\(369\) −2.42586 −0.126285
\(370\) 0 0
\(371\) 44.6529 2.31827
\(372\) 0 0
\(373\) 9.74466 0.504559 0.252280 0.967654i \(-0.418820\pi\)
0.252280 + 0.967654i \(0.418820\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −13.8673 −0.714202
\(378\) 0 0
\(379\) 12.5084 0.642513 0.321256 0.946992i \(-0.395895\pi\)
0.321256 + 0.946992i \(0.395895\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −14.3826 −0.734917 −0.367459 0.930040i \(-0.619772\pi\)
−0.367459 + 0.930040i \(0.619772\pi\)
\(384\) 0 0
\(385\) 64.7770 3.30134
\(386\) 0 0
\(387\) 16.1903 0.823001
\(388\) 0 0
\(389\) −35.3344 −1.79152 −0.895762 0.444533i \(-0.853370\pi\)
−0.895762 + 0.444533i \(0.853370\pi\)
\(390\) 0 0
\(391\) −1.53144 −0.0774482
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2.49694 −0.125635
\(396\) 0 0
\(397\) 25.2423 1.26687 0.633436 0.773795i \(-0.281644\pi\)
0.633436 + 0.773795i \(0.281644\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −15.7168 −0.784858 −0.392429 0.919782i \(-0.628365\pi\)
−0.392429 + 0.919782i \(0.628365\pi\)
\(402\) 0 0
\(403\) 32.6945 1.62863
\(404\) 0 0
\(405\) −22.4725 −1.11667
\(406\) 0 0
\(407\) 63.0091 3.12325
\(408\) 0 0
\(409\) −33.0241 −1.63294 −0.816468 0.577390i \(-0.804071\pi\)
−0.816468 + 0.577390i \(0.804071\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 15.9896 0.786795
\(414\) 0 0
\(415\) −6.67212 −0.327521
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 18.6339 0.910326 0.455163 0.890408i \(-0.349581\pi\)
0.455163 + 0.890408i \(0.349581\pi\)
\(420\) 0 0
\(421\) 36.6986 1.78858 0.894289 0.447489i \(-0.147682\pi\)
0.894289 + 0.447489i \(0.147682\pi\)
\(422\) 0 0
\(423\) −31.4992 −1.53154
\(424\) 0 0
\(425\) −0.627180 −0.0304227
\(426\) 0 0
\(427\) −32.8007 −1.58734
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 15.0376 0.724336 0.362168 0.932113i \(-0.382037\pi\)
0.362168 + 0.932113i \(0.382037\pi\)
\(432\) 0 0
\(433\) −14.3826 −0.691183 −0.345591 0.938385i \(-0.612322\pi\)
−0.345591 + 0.938385i \(0.612322\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3.01491 0.144223
\(438\) 0 0
\(439\) −3.78244 −0.180526 −0.0902629 0.995918i \(-0.528771\pi\)
−0.0902629 + 0.995918i \(0.528771\pi\)
\(440\) 0 0
\(441\) −29.0612 −1.38387
\(442\) 0 0
\(443\) −7.93406 −0.376958 −0.188479 0.982077i \(-0.560356\pi\)
−0.188479 + 0.982077i \(0.560356\pi\)
\(444\) 0 0
\(445\) −2.83929 −0.134595
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −31.2329 −1.47397 −0.736987 0.675907i \(-0.763752\pi\)
−0.736987 + 0.675907i \(0.763752\pi\)
\(450\) 0 0
\(451\) −5.13530 −0.241812
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 33.8130 1.58518
\(456\) 0 0
\(457\) 10.1402 0.474337 0.237168 0.971469i \(-0.423781\pi\)
0.237168 + 0.971469i \(0.423781\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −10.6407 −0.495587 −0.247793 0.968813i \(-0.579705\pi\)
−0.247793 + 0.968813i \(0.579705\pi\)
\(462\) 0 0
\(463\) −9.36515 −0.435235 −0.217618 0.976034i \(-0.569829\pi\)
−0.217618 + 0.976034i \(0.569829\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 16.2947 0.754029 0.377015 0.926207i \(-0.376951\pi\)
0.377015 + 0.926207i \(0.376951\pi\)
\(468\) 0 0
\(469\) 24.4649 1.12968
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 34.2734 1.57589
\(474\) 0 0
\(475\) 1.23472 0.0566526
\(476\) 0 0
\(477\) −32.7930 −1.50149
\(478\) 0 0
\(479\) 2.19942 0.100494 0.0502470 0.998737i \(-0.483999\pi\)
0.0502470 + 0.998737i \(0.483999\pi\)
\(480\) 0 0
\(481\) 32.8902 1.49966
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 19.1941 0.871557
\(486\) 0 0
\(487\) 15.0675 0.682772 0.341386 0.939923i \(-0.389104\pi\)
0.341386 + 0.939923i \(0.389104\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −42.8717 −1.93477 −0.967386 0.253306i \(-0.918482\pi\)
−0.967386 + 0.253306i \(0.918482\pi\)
\(492\) 0 0
\(493\) −2.12486 −0.0956990
\(494\) 0 0
\(495\) −47.5721 −2.13820
\(496\) 0 0
\(497\) 44.4944 1.99585
\(498\) 0 0
\(499\) 0.649143 0.0290596 0.0145298 0.999894i \(-0.495375\pi\)
0.0145298 + 0.999894i \(0.495375\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 30.7477 1.37097 0.685485 0.728086i \(-0.259590\pi\)
0.685485 + 0.728086i \(0.259590\pi\)
\(504\) 0 0
\(505\) 34.5890 1.53919
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −29.8935 −1.32501 −0.662504 0.749059i \(-0.730506\pi\)
−0.662504 + 0.749059i \(0.730506\pi\)
\(510\) 0 0
\(511\) 2.13623 0.0945013
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −46.0544 −2.02940
\(516\) 0 0
\(517\) −66.6807 −2.93261
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 17.1825 0.752778 0.376389 0.926462i \(-0.377166\pi\)
0.376389 + 0.926462i \(0.377166\pi\)
\(522\) 0 0
\(523\) 4.53100 0.198127 0.0990634 0.995081i \(-0.468415\pi\)
0.0990634 + 0.995081i \(0.468415\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 5.00974 0.218227
\(528\) 0 0
\(529\) −13.9103 −0.604796
\(530\) 0 0
\(531\) −11.7427 −0.509589
\(532\) 0 0
\(533\) −2.68058 −0.116109
\(534\) 0 0
\(535\) 4.66385 0.201636
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −61.5198 −2.64985
\(540\) 0 0
\(541\) −13.3847 −0.575452 −0.287726 0.957713i \(-0.592899\pi\)
−0.287726 + 0.957713i \(0.592899\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 36.0467 1.54407
\(546\) 0 0
\(547\) −20.8240 −0.890370 −0.445185 0.895439i \(-0.646862\pi\)
−0.445185 + 0.895439i \(0.646862\pi\)
\(548\) 0 0
\(549\) 24.0887 1.02808
\(550\) 0 0
\(551\) 4.18318 0.178209
\(552\) 0 0
\(553\) 4.08498 0.173711
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 4.50324 0.190809 0.0954043 0.995439i \(-0.469586\pi\)
0.0954043 + 0.995439i \(0.469586\pi\)
\(558\) 0 0
\(559\) 17.8904 0.756684
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 39.8178 1.67812 0.839060 0.544039i \(-0.183106\pi\)
0.839060 + 0.544039i \(0.183106\pi\)
\(564\) 0 0
\(565\) 24.3892 1.02606
\(566\) 0 0
\(567\) 36.7648 1.54398
\(568\) 0 0
\(569\) 33.5776 1.40765 0.703824 0.710375i \(-0.251474\pi\)
0.703824 + 0.710375i \(0.251474\pi\)
\(570\) 0 0
\(571\) −12.4471 −0.520897 −0.260448 0.965488i \(-0.583870\pi\)
−0.260448 + 0.965488i \(0.583870\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 3.72256 0.155241
\(576\) 0 0
\(577\) 46.5869 1.93944 0.969718 0.244226i \(-0.0785338\pi\)
0.969718 + 0.244226i \(0.0785338\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 10.9155 0.452853
\(582\) 0 0
\(583\) −69.4196 −2.87507
\(584\) 0 0
\(585\) −24.8322 −1.02668
\(586\) 0 0
\(587\) 24.6035 1.01549 0.507747 0.861506i \(-0.330479\pi\)
0.507747 + 0.861506i \(0.330479\pi\)
\(588\) 0 0
\(589\) −9.86256 −0.406380
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −12.4433 −0.510983 −0.255492 0.966811i \(-0.582237\pi\)
−0.255492 + 0.966811i \(0.582237\pi\)
\(594\) 0 0
\(595\) 5.18112 0.212405
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 34.5515 1.41174 0.705868 0.708343i \(-0.250557\pi\)
0.705868 + 0.708343i \(0.250557\pi\)
\(600\) 0 0
\(601\) 21.0978 0.860598 0.430299 0.902686i \(-0.358408\pi\)
0.430299 + 0.902686i \(0.358408\pi\)
\(602\) 0 0
\(603\) −17.9670 −0.731671
\(604\) 0 0
\(605\) −73.2391 −2.97759
\(606\) 0 0
\(607\) 5.07158 0.205849 0.102925 0.994689i \(-0.467180\pi\)
0.102925 + 0.994689i \(0.467180\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −34.8067 −1.40813
\(612\) 0 0
\(613\) 29.0490 1.17328 0.586639 0.809848i \(-0.300451\pi\)
0.586639 + 0.809848i \(0.300451\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 43.5495 1.75324 0.876619 0.481185i \(-0.159793\pi\)
0.876619 + 0.481185i \(0.159793\pi\)
\(618\) 0 0
\(619\) 4.92370 0.197900 0.0989502 0.995092i \(-0.468452\pi\)
0.0989502 + 0.995092i \(0.468452\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 4.64506 0.186100
\(624\) 0 0
\(625\) −29.6491 −1.18596
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 5.03972 0.200947
\(630\) 0 0
\(631\) 26.1776 1.04211 0.521057 0.853522i \(-0.325538\pi\)
0.521057 + 0.853522i \(0.325538\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −9.52347 −0.377927
\(636\) 0 0
\(637\) −32.1128 −1.27236
\(638\) 0 0
\(639\) −32.6766 −1.29267
\(640\) 0 0
\(641\) 17.8659 0.705662 0.352831 0.935687i \(-0.385219\pi\)
0.352831 + 0.935687i \(0.385219\pi\)
\(642\) 0 0
\(643\) 25.7348 1.01488 0.507440 0.861687i \(-0.330592\pi\)
0.507440 + 0.861687i \(0.330592\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 39.7509 1.56277 0.781384 0.624050i \(-0.214514\pi\)
0.781384 + 0.624050i \(0.214514\pi\)
\(648\) 0 0
\(649\) −24.8581 −0.975767
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 10.7376 0.420197 0.210098 0.977680i \(-0.432622\pi\)
0.210098 + 0.977680i \(0.432622\pi\)
\(654\) 0 0
\(655\) −23.6097 −0.922506
\(656\) 0 0
\(657\) −1.56884 −0.0612064
\(658\) 0 0
\(659\) −20.5265 −0.799599 −0.399800 0.916603i \(-0.630920\pi\)
−0.399800 + 0.916603i \(0.630920\pi\)
\(660\) 0 0
\(661\) 1.06218 0.0413139 0.0206569 0.999787i \(-0.493424\pi\)
0.0206569 + 0.999787i \(0.493424\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −10.2000 −0.395537
\(666\) 0 0
\(667\) 12.6119 0.488335
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 50.9935 1.96858
\(672\) 0 0
\(673\) −32.4033 −1.24906 −0.624528 0.781003i \(-0.714709\pi\)
−0.624528 + 0.781003i \(0.714709\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 15.7933 0.606985 0.303493 0.952834i \(-0.401847\pi\)
0.303493 + 0.952834i \(0.401847\pi\)
\(678\) 0 0
\(679\) −31.4014 −1.20507
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 11.8814 0.454630 0.227315 0.973821i \(-0.427005\pi\)
0.227315 + 0.973821i \(0.427005\pi\)
\(684\) 0 0
\(685\) 3.85509 0.147295
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −36.2364 −1.38050
\(690\) 0 0
\(691\) 16.6715 0.634215 0.317107 0.948390i \(-0.397288\pi\)
0.317107 + 0.948390i \(0.397288\pi\)
\(692\) 0 0
\(693\) 77.8276 2.95643
\(694\) 0 0
\(695\) −31.0062 −1.17613
\(696\) 0 0
\(697\) −0.410742 −0.0155580
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 30.2071 1.14090 0.570452 0.821331i \(-0.306768\pi\)
0.570452 + 0.821331i \(0.306768\pi\)
\(702\) 0 0
\(703\) −9.92158 −0.374200
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −56.5874 −2.12819
\(708\) 0 0
\(709\) −20.2327 −0.759856 −0.379928 0.925016i \(-0.624051\pi\)
−0.379928 + 0.925016i \(0.624051\pi\)
\(710\) 0 0
\(711\) −3.00000 −0.112509
\(712\) 0 0
\(713\) −29.7348 −1.11358
\(714\) 0 0
\(715\) −52.5674 −1.96591
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 4.53276 0.169043 0.0845217 0.996422i \(-0.473064\pi\)
0.0845217 + 0.996422i \(0.473064\pi\)
\(720\) 0 0
\(721\) 75.3447 2.80598
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 5.16503 0.191824
\(726\) 0 0
\(727\) 6.68674 0.247997 0.123999 0.992282i \(-0.460428\pi\)
0.123999 + 0.992282i \(0.460428\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 2.74132 0.101391
\(732\) 0 0
\(733\) −16.5459 −0.611137 −0.305569 0.952170i \(-0.598847\pi\)
−0.305569 + 0.952170i \(0.598847\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −38.0343 −1.40101
\(738\) 0 0
\(739\) −29.1937 −1.07391 −0.536954 0.843611i \(-0.680425\pi\)
−0.536954 + 0.843611i \(0.680425\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −40.0213 −1.46824 −0.734120 0.679019i \(-0.762405\pi\)
−0.734120 + 0.679019i \(0.762405\pi\)
\(744\) 0 0
\(745\) 8.67824 0.317946
\(746\) 0 0
\(747\) −8.01635 −0.293303
\(748\) 0 0
\(749\) −7.63003 −0.278795
\(750\) 0 0
\(751\) −42.7899 −1.56143 −0.780714 0.624889i \(-0.785144\pi\)
−0.780714 + 0.624889i \(0.785144\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −20.1483 −0.733272
\(756\) 0 0
\(757\) −27.4786 −0.998728 −0.499364 0.866392i \(-0.666433\pi\)
−0.499364 + 0.866392i \(0.666433\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −43.8375 −1.58911 −0.794554 0.607194i \(-0.792295\pi\)
−0.794554 + 0.607194i \(0.792295\pi\)
\(762\) 0 0
\(763\) −58.9721 −2.13493
\(764\) 0 0
\(765\) −3.80500 −0.137570
\(766\) 0 0
\(767\) −12.9757 −0.468526
\(768\) 0 0
\(769\) 11.1742 0.402953 0.201477 0.979493i \(-0.435426\pi\)
0.201477 + 0.979493i \(0.435426\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −4.44411 −0.159843 −0.0799217 0.996801i \(-0.525467\pi\)
−0.0799217 + 0.996801i \(0.525467\pi\)
\(774\) 0 0
\(775\) −12.1775 −0.437427
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0.808619 0.0289718
\(780\) 0 0
\(781\) −69.1732 −2.47521
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −3.50997 −0.125276
\(786\) 0 0
\(787\) 7.75749 0.276525 0.138262 0.990396i \(-0.455848\pi\)
0.138262 + 0.990396i \(0.455848\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −39.9005 −1.41870
\(792\) 0 0
\(793\) 26.6182 0.945239
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −18.9100 −0.669827 −0.334914 0.942249i \(-0.608707\pi\)
−0.334914 + 0.942249i \(0.608707\pi\)
\(798\) 0 0
\(799\) −5.33338 −0.188682
\(800\) 0 0
\(801\) −3.41132 −0.120533
\(802\) 0 0
\(803\) −3.32109 −0.117199
\(804\) 0 0
\(805\) −30.7520 −1.08386
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 36.4443 1.28131 0.640656 0.767828i \(-0.278663\pi\)
0.640656 + 0.767828i \(0.278663\pi\)
\(810\) 0 0
\(811\) 17.8752 0.627683 0.313842 0.949475i \(-0.398384\pi\)
0.313842 + 0.949475i \(0.398384\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −48.7474 −1.70755
\(816\) 0 0
\(817\) −5.39678 −0.188809
\(818\) 0 0
\(819\) 40.6253 1.41956
\(820\) 0 0
\(821\) 36.8018 1.28439 0.642196 0.766541i \(-0.278024\pi\)
0.642196 + 0.766541i \(0.278024\pi\)
\(822\) 0 0
\(823\) 40.9718 1.42819 0.714094 0.700049i \(-0.246839\pi\)
0.714094 + 0.700049i \(0.246839\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −22.7841 −0.792280 −0.396140 0.918190i \(-0.629650\pi\)
−0.396140 + 0.918190i \(0.629650\pi\)
\(828\) 0 0
\(829\) −23.7852 −0.826094 −0.413047 0.910710i \(-0.635536\pi\)
−0.413047 + 0.910710i \(0.635536\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −4.92060 −0.170489
\(834\) 0 0
\(835\) −10.4617 −0.362042
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −7.31748 −0.252627 −0.126314 0.991990i \(-0.540315\pi\)
−0.126314 + 0.991990i \(0.540315\pi\)
\(840\) 0 0
\(841\) −11.5010 −0.396588
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 5.02055 0.172712
\(846\) 0 0
\(847\) 119.819 4.11702
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −29.9127 −1.02539
\(852\) 0 0
\(853\) 39.0182 1.33596 0.667978 0.744181i \(-0.267160\pi\)
0.667978 + 0.744181i \(0.267160\pi\)
\(854\) 0 0
\(855\) 7.49082 0.256181
\(856\) 0 0
\(857\) −48.8249 −1.66783 −0.833913 0.551896i \(-0.813905\pi\)
−0.833913 + 0.551896i \(0.813905\pi\)
\(858\) 0 0
\(859\) −53.3762 −1.82117 −0.910585 0.413321i \(-0.864369\pi\)
−0.910585 + 0.413321i \(0.864369\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 39.8660 1.35705 0.678527 0.734576i \(-0.262619\pi\)
0.678527 + 0.734576i \(0.262619\pi\)
\(864\) 0 0
\(865\) −15.6775 −0.533051
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −6.35071 −0.215433
\(870\) 0 0
\(871\) −19.8536 −0.672713
\(872\) 0 0
\(873\) 23.0611 0.780499
\(874\) 0 0
\(875\) 38.4057 1.29835
\(876\) 0 0
\(877\) 9.76924 0.329884 0.164942 0.986303i \(-0.447256\pi\)
0.164942 + 0.986303i \(0.447256\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −23.6011 −0.795143 −0.397571 0.917571i \(-0.630147\pi\)
−0.397571 + 0.917571i \(0.630147\pi\)
\(882\) 0 0
\(883\) −41.9877 −1.41300 −0.706500 0.707714i \(-0.749727\pi\)
−0.706500 + 0.707714i \(0.749727\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −5.94041 −0.199459 −0.0997297 0.995015i \(-0.531798\pi\)
−0.0997297 + 0.995015i \(0.531798\pi\)
\(888\) 0 0
\(889\) 15.5803 0.522548
\(890\) 0 0
\(891\) −57.1564 −1.91481
\(892\) 0 0
\(893\) 10.4997 0.351360
\(894\) 0 0
\(895\) −20.1533 −0.673650
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −41.2568 −1.37599
\(900\) 0 0
\(901\) −5.55245 −0.184979
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 48.8015 1.62222
\(906\) 0 0
\(907\) −13.5655 −0.450435 −0.225217 0.974309i \(-0.572309\pi\)
−0.225217 + 0.974309i \(0.572309\pi\)
\(908\) 0 0
\(909\) 41.5577 1.37838
\(910\) 0 0
\(911\) −1.33021 −0.0440719 −0.0220359 0.999757i \(-0.507015\pi\)
−0.0220359 + 0.999757i \(0.507015\pi\)
\(912\) 0 0
\(913\) −16.9698 −0.561619
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 38.6253 1.27552
\(918\) 0 0
\(919\) 18.3273 0.604560 0.302280 0.953219i \(-0.402252\pi\)
0.302280 + 0.953219i \(0.402252\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −36.1078 −1.18850
\(924\) 0 0
\(925\) −12.2503 −0.402789
\(926\) 0 0
\(927\) −55.3330 −1.81737
\(928\) 0 0
\(929\) −8.23053 −0.270035 −0.135017 0.990843i \(-0.543109\pi\)
−0.135017 + 0.990843i \(0.543109\pi\)
\(930\) 0 0
\(931\) 9.68707 0.317481
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −8.05482 −0.263421
\(936\) 0 0
\(937\) −27.9085 −0.911732 −0.455866 0.890048i \(-0.650670\pi\)
−0.455866 + 0.890048i \(0.650670\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −8.93387 −0.291236 −0.145618 0.989341i \(-0.546517\pi\)
−0.145618 + 0.989341i \(0.546517\pi\)
\(942\) 0 0
\(943\) 2.43791 0.0793894
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −20.6474 −0.670951 −0.335476 0.942049i \(-0.608897\pi\)
−0.335476 + 0.942049i \(0.608897\pi\)
\(948\) 0 0
\(949\) −1.73358 −0.0562744
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −50.3712 −1.63168 −0.815841 0.578276i \(-0.803726\pi\)
−0.815841 + 0.578276i \(0.803726\pi\)
\(954\) 0 0
\(955\) −29.2024 −0.944968
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −6.30690 −0.203660
\(960\) 0 0
\(961\) 66.2702 2.13775
\(962\) 0 0
\(963\) 5.60347 0.180569
\(964\) 0 0
\(965\) −42.1199 −1.35589
\(966\) 0 0
\(967\) −53.8709 −1.73237 −0.866186 0.499722i \(-0.833436\pi\)
−0.866186 + 0.499722i \(0.833436\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −27.1904 −0.872580 −0.436290 0.899806i \(-0.643708\pi\)
−0.436290 + 0.899806i \(0.643708\pi\)
\(972\) 0 0
\(973\) 50.7259 1.62620
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 42.6281 1.36379 0.681897 0.731448i \(-0.261155\pi\)
0.681897 + 0.731448i \(0.261155\pi\)
\(978\) 0 0
\(979\) −7.22143 −0.230798
\(980\) 0 0
\(981\) 43.3090 1.38275
\(982\) 0 0
\(983\) −6.33641 −0.202100 −0.101050 0.994881i \(-0.532220\pi\)
−0.101050 + 0.994881i \(0.532220\pi\)
\(984\) 0 0
\(985\) 35.6664 1.13643
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −16.2708 −0.517382
\(990\) 0 0
\(991\) −1.49187 −0.0473907 −0.0236954 0.999719i \(-0.507543\pi\)
−0.0236954 + 0.999719i \(0.507543\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 55.6407 1.76393
\(996\) 0 0
\(997\) −43.9745 −1.39268 −0.696342 0.717710i \(-0.745190\pi\)
−0.696342 + 0.717710i \(0.745190\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))