Properties

Label 8016.2.a.bg.1.3
Level 8016
Weight 2
Character 8016.1
Self dual Yes
Analytic conductor 64.008
Analytic rank 0
Dimension 13
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8016.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0080822603\)
Analytic rank: \(0\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-3.05600\)
Character \(\chi\) = 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(-3.05600 q^{5}\) \(-2.59989 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(-3.05600 q^{5}\) \(-2.59989 q^{7}\) \(+1.00000 q^{9}\) \(-4.72064 q^{11}\) \(+6.74051 q^{13}\) \(+3.05600 q^{15}\) \(-3.13623 q^{17}\) \(-2.68764 q^{19}\) \(+2.59989 q^{21}\) \(-6.99219 q^{23}\) \(+4.33912 q^{25}\) \(-1.00000 q^{27}\) \(-7.69073 q^{29}\) \(-4.05540 q^{31}\) \(+4.72064 q^{33}\) \(+7.94526 q^{35}\) \(+0.127532 q^{37}\) \(-6.74051 q^{39}\) \(-8.00281 q^{41}\) \(+10.7440 q^{43}\) \(-3.05600 q^{45}\) \(-1.96112 q^{47}\) \(-0.240573 q^{49}\) \(+3.13623 q^{51}\) \(-7.56814 q^{53}\) \(+14.4263 q^{55}\) \(+2.68764 q^{57}\) \(-10.2078 q^{59}\) \(+2.45141 q^{61}\) \(-2.59989 q^{63}\) \(-20.5990 q^{65}\) \(-14.1052 q^{67}\) \(+6.99219 q^{69}\) \(+3.69140 q^{71}\) \(+4.93617 q^{73}\) \(-4.33912 q^{75}\) \(+12.2731 q^{77}\) \(-9.15118 q^{79}\) \(+1.00000 q^{81}\) \(-7.82320 q^{83}\) \(+9.58433 q^{85}\) \(+7.69073 q^{87}\) \(+5.37710 q^{89}\) \(-17.5246 q^{91}\) \(+4.05540 q^{93}\) \(+8.21342 q^{95}\) \(-10.3975 q^{97}\) \(-4.72064 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 15q^{17} \) \(\mathstrut -\mathstrut 14q^{19} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 9q^{23} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 3q^{29} \) \(\mathstrut +\mathstrut 17q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 12q^{39} \) \(\mathstrut +\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 6q^{47} \) \(\mathstrut +\mathstrut 26q^{49} \) \(\mathstrut -\mathstrut 15q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 7q^{55} \) \(\mathstrut +\mathstrut 14q^{57} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut -\mathstrut q^{63} \) \(\mathstrut +\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 3q^{67} \) \(\mathstrut +\mathstrut 9q^{69} \) \(\mathstrut -\mathstrut 17q^{71} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 37q^{75} \) \(\mathstrut +\mathstrut 30q^{77} \) \(\mathstrut -\mathstrut 10q^{79} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 25q^{85} \) \(\mathstrut +\mathstrut 3q^{87} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 29q^{91} \) \(\mathstrut -\mathstrut 17q^{93} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 38q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) −3.05600 −1.36668 −0.683342 0.730098i \(-0.739474\pi\)
−0.683342 + 0.730098i \(0.739474\pi\)
\(6\) 0 0
\(7\) −2.59989 −0.982666 −0.491333 0.870972i \(-0.663490\pi\)
−0.491333 + 0.870972i \(0.663490\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −4.72064 −1.42333 −0.711663 0.702521i \(-0.752058\pi\)
−0.711663 + 0.702521i \(0.752058\pi\)
\(12\) 0 0
\(13\) 6.74051 1.86948 0.934740 0.355332i \(-0.115632\pi\)
0.934740 + 0.355332i \(0.115632\pi\)
\(14\) 0 0
\(15\) 3.05600 0.789055
\(16\) 0 0
\(17\) −3.13623 −0.760649 −0.380324 0.924853i \(-0.624188\pi\)
−0.380324 + 0.924853i \(0.624188\pi\)
\(18\) 0 0
\(19\) −2.68764 −0.616587 −0.308293 0.951291i \(-0.599758\pi\)
−0.308293 + 0.951291i \(0.599758\pi\)
\(20\) 0 0
\(21\) 2.59989 0.567342
\(22\) 0 0
\(23\) −6.99219 −1.45797 −0.728986 0.684528i \(-0.760008\pi\)
−0.728986 + 0.684528i \(0.760008\pi\)
\(24\) 0 0
\(25\) 4.33912 0.867825
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −7.69073 −1.42813 −0.714067 0.700078i \(-0.753149\pi\)
−0.714067 + 0.700078i \(0.753149\pi\)
\(30\) 0 0
\(31\) −4.05540 −0.728372 −0.364186 0.931326i \(-0.618653\pi\)
−0.364186 + 0.931326i \(0.618653\pi\)
\(32\) 0 0
\(33\) 4.72064 0.821757
\(34\) 0 0
\(35\) 7.94526 1.34299
\(36\) 0 0
\(37\) 0.127532 0.0209662 0.0104831 0.999945i \(-0.496663\pi\)
0.0104831 + 0.999945i \(0.496663\pi\)
\(38\) 0 0
\(39\) −6.74051 −1.07935
\(40\) 0 0
\(41\) −8.00281 −1.24983 −0.624914 0.780693i \(-0.714866\pi\)
−0.624914 + 0.780693i \(0.714866\pi\)
\(42\) 0 0
\(43\) 10.7440 1.63844 0.819221 0.573479i \(-0.194406\pi\)
0.819221 + 0.573479i \(0.194406\pi\)
\(44\) 0 0
\(45\) −3.05600 −0.455561
\(46\) 0 0
\(47\) −1.96112 −0.286059 −0.143030 0.989718i \(-0.545684\pi\)
−0.143030 + 0.989718i \(0.545684\pi\)
\(48\) 0 0
\(49\) −0.240573 −0.0343676
\(50\) 0 0
\(51\) 3.13623 0.439161
\(52\) 0 0
\(53\) −7.56814 −1.03956 −0.519782 0.854299i \(-0.673987\pi\)
−0.519782 + 0.854299i \(0.673987\pi\)
\(54\) 0 0
\(55\) 14.4263 1.94524
\(56\) 0 0
\(57\) 2.68764 0.355986
\(58\) 0 0
\(59\) −10.2078 −1.32895 −0.664474 0.747311i \(-0.731344\pi\)
−0.664474 + 0.747311i \(0.731344\pi\)
\(60\) 0 0
\(61\) 2.45141 0.313871 0.156936 0.987609i \(-0.449838\pi\)
0.156936 + 0.987609i \(0.449838\pi\)
\(62\) 0 0
\(63\) −2.59989 −0.327555
\(64\) 0 0
\(65\) −20.5990 −2.55499
\(66\) 0 0
\(67\) −14.1052 −1.72323 −0.861614 0.507564i \(-0.830546\pi\)
−0.861614 + 0.507564i \(0.830546\pi\)
\(68\) 0 0
\(69\) 6.99219 0.841761
\(70\) 0 0
\(71\) 3.69140 0.438088 0.219044 0.975715i \(-0.429706\pi\)
0.219044 + 0.975715i \(0.429706\pi\)
\(72\) 0 0
\(73\) 4.93617 0.577735 0.288867 0.957369i \(-0.406721\pi\)
0.288867 + 0.957369i \(0.406721\pi\)
\(74\) 0 0
\(75\) −4.33912 −0.501039
\(76\) 0 0
\(77\) 12.2731 1.39865
\(78\) 0 0
\(79\) −9.15118 −1.02959 −0.514794 0.857314i \(-0.672132\pi\)
−0.514794 + 0.857314i \(0.672132\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −7.82320 −0.858708 −0.429354 0.903136i \(-0.641259\pi\)
−0.429354 + 0.903136i \(0.641259\pi\)
\(84\) 0 0
\(85\) 9.58433 1.03957
\(86\) 0 0
\(87\) 7.69073 0.824533
\(88\) 0 0
\(89\) 5.37710 0.569971 0.284986 0.958532i \(-0.408011\pi\)
0.284986 + 0.958532i \(0.408011\pi\)
\(90\) 0 0
\(91\) −17.5246 −1.83707
\(92\) 0 0
\(93\) 4.05540 0.420526
\(94\) 0 0
\(95\) 8.21342 0.842679
\(96\) 0 0
\(97\) −10.3975 −1.05571 −0.527854 0.849335i \(-0.677003\pi\)
−0.527854 + 0.849335i \(0.677003\pi\)
\(98\) 0 0
\(99\) −4.72064 −0.474442
\(100\) 0 0
\(101\) −10.9764 −1.09219 −0.546094 0.837724i \(-0.683886\pi\)
−0.546094 + 0.837724i \(0.683886\pi\)
\(102\) 0 0
\(103\) 2.67179 0.263260 0.131630 0.991299i \(-0.457979\pi\)
0.131630 + 0.991299i \(0.457979\pi\)
\(104\) 0 0
\(105\) −7.94526 −0.775378
\(106\) 0 0
\(107\) 3.57525 0.345633 0.172816 0.984954i \(-0.444713\pi\)
0.172816 + 0.984954i \(0.444713\pi\)
\(108\) 0 0
\(109\) −6.87869 −0.658859 −0.329429 0.944180i \(-0.606856\pi\)
−0.329429 + 0.944180i \(0.606856\pi\)
\(110\) 0 0
\(111\) −0.127532 −0.0121048
\(112\) 0 0
\(113\) 8.92908 0.839977 0.419989 0.907529i \(-0.362034\pi\)
0.419989 + 0.907529i \(0.362034\pi\)
\(114\) 0 0
\(115\) 21.3681 1.99259
\(116\) 0 0
\(117\) 6.74051 0.623160
\(118\) 0 0
\(119\) 8.15386 0.747463
\(120\) 0 0
\(121\) 11.2844 1.02586
\(122\) 0 0
\(123\) 8.00281 0.721589
\(124\) 0 0
\(125\) 2.01963 0.180642
\(126\) 0 0
\(127\) −3.06592 −0.272057 −0.136028 0.990705i \(-0.543434\pi\)
−0.136028 + 0.990705i \(0.543434\pi\)
\(128\) 0 0
\(129\) −10.7440 −0.945954
\(130\) 0 0
\(131\) −16.5982 −1.45019 −0.725097 0.688647i \(-0.758205\pi\)
−0.725097 + 0.688647i \(0.758205\pi\)
\(132\) 0 0
\(133\) 6.98756 0.605899
\(134\) 0 0
\(135\) 3.05600 0.263018
\(136\) 0 0
\(137\) 0.703806 0.0601302 0.0300651 0.999548i \(-0.490429\pi\)
0.0300651 + 0.999548i \(0.490429\pi\)
\(138\) 0 0
\(139\) −14.7166 −1.24825 −0.624124 0.781326i \(-0.714544\pi\)
−0.624124 + 0.781326i \(0.714544\pi\)
\(140\) 0 0
\(141\) 1.96112 0.165156
\(142\) 0 0
\(143\) −31.8195 −2.66088
\(144\) 0 0
\(145\) 23.5029 1.95181
\(146\) 0 0
\(147\) 0.240573 0.0198421
\(148\) 0 0
\(149\) −10.3086 −0.844509 −0.422255 0.906477i \(-0.638761\pi\)
−0.422255 + 0.906477i \(0.638761\pi\)
\(150\) 0 0
\(151\) −9.20583 −0.749160 −0.374580 0.927195i \(-0.622213\pi\)
−0.374580 + 0.927195i \(0.622213\pi\)
\(152\) 0 0
\(153\) −3.13623 −0.253550
\(154\) 0 0
\(155\) 12.3933 0.995454
\(156\) 0 0
\(157\) −20.9456 −1.67164 −0.835820 0.549004i \(-0.815007\pi\)
−0.835820 + 0.549004i \(0.815007\pi\)
\(158\) 0 0
\(159\) 7.56814 0.600192
\(160\) 0 0
\(161\) 18.1789 1.43270
\(162\) 0 0
\(163\) −16.4063 −1.28504 −0.642521 0.766268i \(-0.722111\pi\)
−0.642521 + 0.766268i \(0.722111\pi\)
\(164\) 0 0
\(165\) −14.4263 −1.12308
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) 32.4344 2.49496
\(170\) 0 0
\(171\) −2.68764 −0.205529
\(172\) 0 0
\(173\) −4.45025 −0.338346 −0.169173 0.985586i \(-0.554110\pi\)
−0.169173 + 0.985586i \(0.554110\pi\)
\(174\) 0 0
\(175\) −11.2812 −0.852782
\(176\) 0 0
\(177\) 10.2078 0.767269
\(178\) 0 0
\(179\) −17.7672 −1.32798 −0.663992 0.747740i \(-0.731139\pi\)
−0.663992 + 0.747740i \(0.731139\pi\)
\(180\) 0 0
\(181\) −15.0026 −1.11514 −0.557568 0.830132i \(-0.688265\pi\)
−0.557568 + 0.830132i \(0.688265\pi\)
\(182\) 0 0
\(183\) −2.45141 −0.181214
\(184\) 0 0
\(185\) −0.389739 −0.0286542
\(186\) 0 0
\(187\) 14.8050 1.08265
\(188\) 0 0
\(189\) 2.59989 0.189114
\(190\) 0 0
\(191\) 20.2983 1.46873 0.734367 0.678753i \(-0.237479\pi\)
0.734367 + 0.678753i \(0.237479\pi\)
\(192\) 0 0
\(193\) −0.976343 −0.0702787 −0.0351394 0.999382i \(-0.511188\pi\)
−0.0351394 + 0.999382i \(0.511188\pi\)
\(194\) 0 0
\(195\) 20.5990 1.47512
\(196\) 0 0
\(197\) 22.3449 1.59201 0.796003 0.605293i \(-0.206944\pi\)
0.796003 + 0.605293i \(0.206944\pi\)
\(198\) 0 0
\(199\) −9.41395 −0.667337 −0.333669 0.942690i \(-0.608287\pi\)
−0.333669 + 0.942690i \(0.608287\pi\)
\(200\) 0 0
\(201\) 14.1052 0.994906
\(202\) 0 0
\(203\) 19.9951 1.40338
\(204\) 0 0
\(205\) 24.4566 1.70812
\(206\) 0 0
\(207\) −6.99219 −0.485991
\(208\) 0 0
\(209\) 12.6874 0.877604
\(210\) 0 0
\(211\) −18.5125 −1.27445 −0.637227 0.770676i \(-0.719919\pi\)
−0.637227 + 0.770676i \(0.719919\pi\)
\(212\) 0 0
\(213\) −3.69140 −0.252930
\(214\) 0 0
\(215\) −32.8336 −2.23923
\(216\) 0 0
\(217\) 10.5436 0.715746
\(218\) 0 0
\(219\) −4.93617 −0.333555
\(220\) 0 0
\(221\) −21.1398 −1.42202
\(222\) 0 0
\(223\) 20.0821 1.34480 0.672400 0.740188i \(-0.265264\pi\)
0.672400 + 0.740188i \(0.265264\pi\)
\(224\) 0 0
\(225\) 4.33912 0.289275
\(226\) 0 0
\(227\) −3.07801 −0.204295 −0.102147 0.994769i \(-0.532571\pi\)
−0.102147 + 0.994769i \(0.532571\pi\)
\(228\) 0 0
\(229\) 19.3435 1.27825 0.639127 0.769101i \(-0.279296\pi\)
0.639127 + 0.769101i \(0.279296\pi\)
\(230\) 0 0
\(231\) −12.2731 −0.807513
\(232\) 0 0
\(233\) −7.27948 −0.476895 −0.238447 0.971155i \(-0.576638\pi\)
−0.238447 + 0.971155i \(0.576638\pi\)
\(234\) 0 0
\(235\) 5.99319 0.390953
\(236\) 0 0
\(237\) 9.15118 0.594433
\(238\) 0 0
\(239\) 16.2464 1.05089 0.525446 0.850827i \(-0.323898\pi\)
0.525446 + 0.850827i \(0.323898\pi\)
\(240\) 0 0
\(241\) 24.4511 1.57504 0.787518 0.616292i \(-0.211366\pi\)
0.787518 + 0.616292i \(0.211366\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 0.735191 0.0469697
\(246\) 0 0
\(247\) −18.1160 −1.15270
\(248\) 0 0
\(249\) 7.82320 0.495775
\(250\) 0 0
\(251\) 28.1202 1.77493 0.887465 0.460874i \(-0.152464\pi\)
0.887465 + 0.460874i \(0.152464\pi\)
\(252\) 0 0
\(253\) 33.0076 2.07517
\(254\) 0 0
\(255\) −9.58433 −0.600194
\(256\) 0 0
\(257\) −18.2270 −1.13697 −0.568485 0.822694i \(-0.692470\pi\)
−0.568485 + 0.822694i \(0.692470\pi\)
\(258\) 0 0
\(259\) −0.331570 −0.0206028
\(260\) 0 0
\(261\) −7.69073 −0.476044
\(262\) 0 0
\(263\) 5.53367 0.341220 0.170610 0.985339i \(-0.445426\pi\)
0.170610 + 0.985339i \(0.445426\pi\)
\(264\) 0 0
\(265\) 23.1282 1.42076
\(266\) 0 0
\(267\) −5.37710 −0.329073
\(268\) 0 0
\(269\) −18.1791 −1.10840 −0.554199 0.832385i \(-0.686975\pi\)
−0.554199 + 0.832385i \(0.686975\pi\)
\(270\) 0 0
\(271\) 30.0438 1.82503 0.912516 0.409040i \(-0.134136\pi\)
0.912516 + 0.409040i \(0.134136\pi\)
\(272\) 0 0
\(273\) 17.5246 1.06064
\(274\) 0 0
\(275\) −20.4834 −1.23520
\(276\) 0 0
\(277\) −20.0646 −1.20557 −0.602783 0.797905i \(-0.705942\pi\)
−0.602783 + 0.797905i \(0.705942\pi\)
\(278\) 0 0
\(279\) −4.05540 −0.242791
\(280\) 0 0
\(281\) 20.1320 1.20097 0.600486 0.799635i \(-0.294974\pi\)
0.600486 + 0.799635i \(0.294974\pi\)
\(282\) 0 0
\(283\) 25.1003 1.49206 0.746028 0.665914i \(-0.231958\pi\)
0.746028 + 0.665914i \(0.231958\pi\)
\(284\) 0 0
\(285\) −8.21342 −0.486521
\(286\) 0 0
\(287\) 20.8064 1.22816
\(288\) 0 0
\(289\) −7.16403 −0.421414
\(290\) 0 0
\(291\) 10.3975 0.609513
\(292\) 0 0
\(293\) 29.6784 1.73383 0.866914 0.498457i \(-0.166100\pi\)
0.866914 + 0.498457i \(0.166100\pi\)
\(294\) 0 0
\(295\) 31.1952 1.81625
\(296\) 0 0
\(297\) 4.72064 0.273919
\(298\) 0 0
\(299\) −47.1309 −2.72565
\(300\) 0 0
\(301\) −27.9332 −1.61004
\(302\) 0 0
\(303\) 10.9764 0.630575
\(304\) 0 0
\(305\) −7.49151 −0.428963
\(306\) 0 0
\(307\) −22.0239 −1.25697 −0.628487 0.777820i \(-0.716325\pi\)
−0.628487 + 0.777820i \(0.716325\pi\)
\(308\) 0 0
\(309\) −2.67179 −0.151993
\(310\) 0 0
\(311\) 26.7334 1.51591 0.757956 0.652305i \(-0.226198\pi\)
0.757956 + 0.652305i \(0.226198\pi\)
\(312\) 0 0
\(313\) 24.6867 1.39538 0.697688 0.716402i \(-0.254212\pi\)
0.697688 + 0.716402i \(0.254212\pi\)
\(314\) 0 0
\(315\) 7.94526 0.447665
\(316\) 0 0
\(317\) 29.6092 1.66302 0.831509 0.555511i \(-0.187477\pi\)
0.831509 + 0.555511i \(0.187477\pi\)
\(318\) 0 0
\(319\) 36.3052 2.03270
\(320\) 0 0
\(321\) −3.57525 −0.199551
\(322\) 0 0
\(323\) 8.42906 0.469006
\(324\) 0 0
\(325\) 29.2479 1.62238
\(326\) 0 0
\(327\) 6.87869 0.380392
\(328\) 0 0
\(329\) 5.09871 0.281101
\(330\) 0 0
\(331\) 6.19998 0.340781 0.170391 0.985377i \(-0.445497\pi\)
0.170391 + 0.985377i \(0.445497\pi\)
\(332\) 0 0
\(333\) 0.127532 0.00698874
\(334\) 0 0
\(335\) 43.1056 2.35511
\(336\) 0 0
\(337\) −13.1055 −0.713904 −0.356952 0.934123i \(-0.616184\pi\)
−0.356952 + 0.934123i \(0.616184\pi\)
\(338\) 0 0
\(339\) −8.92908 −0.484961
\(340\) 0 0
\(341\) 19.1441 1.03671
\(342\) 0 0
\(343\) 18.8247 1.01644
\(344\) 0 0
\(345\) −21.3681 −1.15042
\(346\) 0 0
\(347\) 32.6932 1.75506 0.877530 0.479521i \(-0.159190\pi\)
0.877530 + 0.479521i \(0.159190\pi\)
\(348\) 0 0
\(349\) −6.07122 −0.324985 −0.162492 0.986710i \(-0.551953\pi\)
−0.162492 + 0.986710i \(0.551953\pi\)
\(350\) 0 0
\(351\) −6.74051 −0.359782
\(352\) 0 0
\(353\) 20.1820 1.07418 0.537091 0.843525i \(-0.319523\pi\)
0.537091 + 0.843525i \(0.319523\pi\)
\(354\) 0 0
\(355\) −11.2809 −0.598728
\(356\) 0 0
\(357\) −8.15386 −0.431548
\(358\) 0 0
\(359\) −25.8863 −1.36623 −0.683113 0.730313i \(-0.739374\pi\)
−0.683113 + 0.730313i \(0.739374\pi\)
\(360\) 0 0
\(361\) −11.7766 −0.619821
\(362\) 0 0
\(363\) −11.2844 −0.592278
\(364\) 0 0
\(365\) −15.0849 −0.789581
\(366\) 0 0
\(367\) 4.18304 0.218353 0.109176 0.994022i \(-0.465179\pi\)
0.109176 + 0.994022i \(0.465179\pi\)
\(368\) 0 0
\(369\) −8.00281 −0.416609
\(370\) 0 0
\(371\) 19.6763 1.02154
\(372\) 0 0
\(373\) 6.51126 0.337140 0.168570 0.985690i \(-0.446085\pi\)
0.168570 + 0.985690i \(0.446085\pi\)
\(374\) 0 0
\(375\) −2.01963 −0.104293
\(376\) 0 0
\(377\) −51.8394 −2.66987
\(378\) 0 0
\(379\) −16.9299 −0.869631 −0.434815 0.900520i \(-0.643186\pi\)
−0.434815 + 0.900520i \(0.643186\pi\)
\(380\) 0 0
\(381\) 3.06592 0.157072
\(382\) 0 0
\(383\) 26.0508 1.33113 0.665566 0.746339i \(-0.268190\pi\)
0.665566 + 0.746339i \(0.268190\pi\)
\(384\) 0 0
\(385\) −37.5067 −1.91152
\(386\) 0 0
\(387\) 10.7440 0.546147
\(388\) 0 0
\(389\) 32.2295 1.63410 0.817049 0.576568i \(-0.195608\pi\)
0.817049 + 0.576568i \(0.195608\pi\)
\(390\) 0 0
\(391\) 21.9292 1.10900
\(392\) 0 0
\(393\) 16.5982 0.837270
\(394\) 0 0
\(395\) 27.9660 1.40712
\(396\) 0 0
\(397\) −18.5553 −0.931263 −0.465632 0.884979i \(-0.654173\pi\)
−0.465632 + 0.884979i \(0.654173\pi\)
\(398\) 0 0
\(399\) −6.98756 −0.349816
\(400\) 0 0
\(401\) −10.1254 −0.505640 −0.252820 0.967513i \(-0.581358\pi\)
−0.252820 + 0.967513i \(0.581358\pi\)
\(402\) 0 0
\(403\) −27.3355 −1.36168
\(404\) 0 0
\(405\) −3.05600 −0.151854
\(406\) 0 0
\(407\) −0.602035 −0.0298417
\(408\) 0 0
\(409\) −32.8568 −1.62467 −0.812333 0.583194i \(-0.801803\pi\)
−0.812333 + 0.583194i \(0.801803\pi\)
\(410\) 0 0
\(411\) −0.703806 −0.0347162
\(412\) 0 0
\(413\) 26.5393 1.30591
\(414\) 0 0
\(415\) 23.9077 1.17358
\(416\) 0 0
\(417\) 14.7166 0.720676
\(418\) 0 0
\(419\) −25.3416 −1.23802 −0.619010 0.785383i \(-0.712466\pi\)
−0.619010 + 0.785383i \(0.712466\pi\)
\(420\) 0 0
\(421\) 1.17825 0.0574242 0.0287121 0.999588i \(-0.490859\pi\)
0.0287121 + 0.999588i \(0.490859\pi\)
\(422\) 0 0
\(423\) −1.96112 −0.0953531
\(424\) 0 0
\(425\) −13.6085 −0.660110
\(426\) 0 0
\(427\) −6.37340 −0.308431
\(428\) 0 0
\(429\) 31.8195 1.53626
\(430\) 0 0
\(431\) 18.3794 0.885307 0.442653 0.896693i \(-0.354037\pi\)
0.442653 + 0.896693i \(0.354037\pi\)
\(432\) 0 0
\(433\) −24.5067 −1.17772 −0.588859 0.808236i \(-0.700423\pi\)
−0.588859 + 0.808236i \(0.700423\pi\)
\(434\) 0 0
\(435\) −23.5029 −1.12688
\(436\) 0 0
\(437\) 18.7925 0.898967
\(438\) 0 0
\(439\) −10.5405 −0.503070 −0.251535 0.967848i \(-0.580935\pi\)
−0.251535 + 0.967848i \(0.580935\pi\)
\(440\) 0 0
\(441\) −0.240573 −0.0114559
\(442\) 0 0
\(443\) 13.1918 0.626760 0.313380 0.949628i \(-0.398539\pi\)
0.313380 + 0.949628i \(0.398539\pi\)
\(444\) 0 0
\(445\) −16.4324 −0.778970
\(446\) 0 0
\(447\) 10.3086 0.487578
\(448\) 0 0
\(449\) 13.6895 0.646046 0.323023 0.946391i \(-0.395301\pi\)
0.323023 + 0.946391i \(0.395301\pi\)
\(450\) 0 0
\(451\) 37.7783 1.77891
\(452\) 0 0
\(453\) 9.20583 0.432528
\(454\) 0 0
\(455\) 53.5551 2.51070
\(456\) 0 0
\(457\) 14.7356 0.689303 0.344651 0.938731i \(-0.387997\pi\)
0.344651 + 0.938731i \(0.387997\pi\)
\(458\) 0 0
\(459\) 3.13623 0.146387
\(460\) 0 0
\(461\) −22.8198 −1.06283 −0.531413 0.847113i \(-0.678339\pi\)
−0.531413 + 0.847113i \(0.678339\pi\)
\(462\) 0 0
\(463\) −8.50925 −0.395458 −0.197729 0.980257i \(-0.563357\pi\)
−0.197729 + 0.980257i \(0.563357\pi\)
\(464\) 0 0
\(465\) −12.3933 −0.574726
\(466\) 0 0
\(467\) 6.22222 0.287930 0.143965 0.989583i \(-0.454015\pi\)
0.143965 + 0.989583i \(0.454015\pi\)
\(468\) 0 0
\(469\) 36.6720 1.69336
\(470\) 0 0
\(471\) 20.9456 0.965122
\(472\) 0 0
\(473\) −50.7184 −2.33204
\(474\) 0 0
\(475\) −11.6620 −0.535089
\(476\) 0 0
\(477\) −7.56814 −0.346521
\(478\) 0 0
\(479\) −40.6592 −1.85777 −0.928884 0.370372i \(-0.879230\pi\)
−0.928884 + 0.370372i \(0.879230\pi\)
\(480\) 0 0
\(481\) 0.859634 0.0391959
\(482\) 0 0
\(483\) −18.1789 −0.827170
\(484\) 0 0
\(485\) 31.7748 1.44282
\(486\) 0 0
\(487\) 25.3758 1.14989 0.574944 0.818193i \(-0.305024\pi\)
0.574944 + 0.818193i \(0.305024\pi\)
\(488\) 0 0
\(489\) 16.4063 0.741919
\(490\) 0 0
\(491\) −2.83989 −0.128162 −0.0640812 0.997945i \(-0.520412\pi\)
−0.0640812 + 0.997945i \(0.520412\pi\)
\(492\) 0 0
\(493\) 24.1199 1.08631
\(494\) 0 0
\(495\) 14.4263 0.648412
\(496\) 0 0
\(497\) −9.59722 −0.430494
\(498\) 0 0
\(499\) −11.3425 −0.507759 −0.253879 0.967236i \(-0.581707\pi\)
−0.253879 + 0.967236i \(0.581707\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) −23.7022 −1.05683 −0.528415 0.848986i \(-0.677214\pi\)
−0.528415 + 0.848986i \(0.677214\pi\)
\(504\) 0 0
\(505\) 33.5437 1.49268
\(506\) 0 0
\(507\) −32.4344 −1.44046
\(508\) 0 0
\(509\) 1.62782 0.0721517 0.0360758 0.999349i \(-0.488514\pi\)
0.0360758 + 0.999349i \(0.488514\pi\)
\(510\) 0 0
\(511\) −12.8335 −0.567720
\(512\) 0 0
\(513\) 2.68764 0.118662
\(514\) 0 0
\(515\) −8.16500 −0.359793
\(516\) 0 0
\(517\) 9.25775 0.407156
\(518\) 0 0
\(519\) 4.45025 0.195344
\(520\) 0 0
\(521\) 5.03728 0.220687 0.110344 0.993893i \(-0.464805\pi\)
0.110344 + 0.993893i \(0.464805\pi\)
\(522\) 0 0
\(523\) −24.7066 −1.08034 −0.540172 0.841555i \(-0.681641\pi\)
−0.540172 + 0.841555i \(0.681641\pi\)
\(524\) 0 0
\(525\) 11.2812 0.492354
\(526\) 0 0
\(527\) 12.7187 0.554035
\(528\) 0 0
\(529\) 25.8908 1.12568
\(530\) 0 0
\(531\) −10.2078 −0.442983
\(532\) 0 0
\(533\) −53.9430 −2.33653
\(534\) 0 0
\(535\) −10.9260 −0.472370
\(536\) 0 0
\(537\) 17.7672 0.766712
\(538\) 0 0
\(539\) 1.13566 0.0489163
\(540\) 0 0
\(541\) 2.18767 0.0940552 0.0470276 0.998894i \(-0.485025\pi\)
0.0470276 + 0.998894i \(0.485025\pi\)
\(542\) 0 0
\(543\) 15.0026 0.643824
\(544\) 0 0
\(545\) 21.0213 0.900451
\(546\) 0 0
\(547\) −15.8845 −0.679172 −0.339586 0.940575i \(-0.610287\pi\)
−0.339586 + 0.940575i \(0.610287\pi\)
\(548\) 0 0
\(549\) 2.45141 0.104624
\(550\) 0 0
\(551\) 20.6699 0.880568
\(552\) 0 0
\(553\) 23.7921 1.01174
\(554\) 0 0
\(555\) 0.389739 0.0165435
\(556\) 0 0
\(557\) 1.88069 0.0796873 0.0398436 0.999206i \(-0.487314\pi\)
0.0398436 + 0.999206i \(0.487314\pi\)
\(558\) 0 0
\(559\) 72.4199 3.06303
\(560\) 0 0
\(561\) −14.8050 −0.625069
\(562\) 0 0
\(563\) −19.8631 −0.837131 −0.418565 0.908187i \(-0.637467\pi\)
−0.418565 + 0.908187i \(0.637467\pi\)
\(564\) 0 0
\(565\) −27.2873 −1.14798
\(566\) 0 0
\(567\) −2.59989 −0.109185
\(568\) 0 0
\(569\) −21.6129 −0.906058 −0.453029 0.891496i \(-0.649657\pi\)
−0.453029 + 0.891496i \(0.649657\pi\)
\(570\) 0 0
\(571\) −8.15758 −0.341384 −0.170692 0.985324i \(-0.554600\pi\)
−0.170692 + 0.985324i \(0.554600\pi\)
\(572\) 0 0
\(573\) −20.2983 −0.847974
\(574\) 0 0
\(575\) −30.3400 −1.26527
\(576\) 0 0
\(577\) −14.3812 −0.598698 −0.299349 0.954144i \(-0.596769\pi\)
−0.299349 + 0.954144i \(0.596769\pi\)
\(578\) 0 0
\(579\) 0.976343 0.0405754
\(580\) 0 0
\(581\) 20.3395 0.843823
\(582\) 0 0
\(583\) 35.7264 1.47964
\(584\) 0 0
\(585\) −20.5990 −0.851663
\(586\) 0 0
\(587\) −16.4163 −0.677573 −0.338786 0.940863i \(-0.610016\pi\)
−0.338786 + 0.940863i \(0.610016\pi\)
\(588\) 0 0
\(589\) 10.8995 0.449104
\(590\) 0 0
\(591\) −22.3449 −0.919145
\(592\) 0 0
\(593\) −26.4055 −1.08434 −0.542171 0.840268i \(-0.682398\pi\)
−0.542171 + 0.840268i \(0.682398\pi\)
\(594\) 0 0
\(595\) −24.9182 −1.02155
\(596\) 0 0
\(597\) 9.41395 0.385287
\(598\) 0 0
\(599\) 4.34234 0.177423 0.0887116 0.996057i \(-0.471725\pi\)
0.0887116 + 0.996057i \(0.471725\pi\)
\(600\) 0 0
\(601\) 21.5387 0.878583 0.439292 0.898344i \(-0.355229\pi\)
0.439292 + 0.898344i \(0.355229\pi\)
\(602\) 0 0
\(603\) −14.1052 −0.574409
\(604\) 0 0
\(605\) −34.4852 −1.40202
\(606\) 0 0
\(607\) 6.25626 0.253934 0.126967 0.991907i \(-0.459476\pi\)
0.126967 + 0.991907i \(0.459476\pi\)
\(608\) 0 0
\(609\) −19.9951 −0.810241
\(610\) 0 0
\(611\) −13.2190 −0.534782
\(612\) 0 0
\(613\) −32.0598 −1.29488 −0.647441 0.762116i \(-0.724161\pi\)
−0.647441 + 0.762116i \(0.724161\pi\)
\(614\) 0 0
\(615\) −24.4566 −0.986184
\(616\) 0 0
\(617\) −32.0392 −1.28985 −0.644925 0.764246i \(-0.723111\pi\)
−0.644925 + 0.764246i \(0.723111\pi\)
\(618\) 0 0
\(619\) −20.7106 −0.832428 −0.416214 0.909267i \(-0.636643\pi\)
−0.416214 + 0.909267i \(0.636643\pi\)
\(620\) 0 0
\(621\) 6.99219 0.280587
\(622\) 0 0
\(623\) −13.9799 −0.560091
\(624\) 0 0
\(625\) −27.8676 −1.11470
\(626\) 0 0
\(627\) −12.6874 −0.506685
\(628\) 0 0
\(629\) −0.399972 −0.0159479
\(630\) 0 0
\(631\) −26.6970 −1.06279 −0.531395 0.847124i \(-0.678332\pi\)
−0.531395 + 0.847124i \(0.678332\pi\)
\(632\) 0 0
\(633\) 18.5125 0.735806
\(634\) 0 0
\(635\) 9.36946 0.371816
\(636\) 0 0
\(637\) −1.62159 −0.0642496
\(638\) 0 0
\(639\) 3.69140 0.146029
\(640\) 0 0
\(641\) 12.0039 0.474125 0.237062 0.971494i \(-0.423815\pi\)
0.237062 + 0.971494i \(0.423815\pi\)
\(642\) 0 0
\(643\) −33.8943 −1.33666 −0.668331 0.743864i \(-0.732991\pi\)
−0.668331 + 0.743864i \(0.732991\pi\)
\(644\) 0 0
\(645\) 32.8336 1.29282
\(646\) 0 0
\(647\) −17.6487 −0.693842 −0.346921 0.937894i \(-0.612773\pi\)
−0.346921 + 0.937894i \(0.612773\pi\)
\(648\) 0 0
\(649\) 48.1875 1.89153
\(650\) 0 0
\(651\) −10.5436 −0.413236
\(652\) 0 0
\(653\) −12.4535 −0.487344 −0.243672 0.969858i \(-0.578352\pi\)
−0.243672 + 0.969858i \(0.578352\pi\)
\(654\) 0 0
\(655\) 50.7242 1.98196
\(656\) 0 0
\(657\) 4.93617 0.192578
\(658\) 0 0
\(659\) 23.0086 0.896290 0.448145 0.893961i \(-0.352085\pi\)
0.448145 + 0.893961i \(0.352085\pi\)
\(660\) 0 0
\(661\) −3.59936 −0.139999 −0.0699994 0.997547i \(-0.522300\pi\)
−0.0699994 + 0.997547i \(0.522300\pi\)
\(662\) 0 0
\(663\) 21.1398 0.821002
\(664\) 0 0
\(665\) −21.3540 −0.828072
\(666\) 0 0
\(667\) 53.7751 2.08218
\(668\) 0 0
\(669\) −20.0821 −0.776420
\(670\) 0 0
\(671\) −11.5722 −0.446741
\(672\) 0 0
\(673\) −38.0723 −1.46758 −0.733791 0.679376i \(-0.762251\pi\)
−0.733791 + 0.679376i \(0.762251\pi\)
\(674\) 0 0
\(675\) −4.33912 −0.167013
\(676\) 0 0
\(677\) 27.9008 1.07232 0.536158 0.844118i \(-0.319875\pi\)
0.536158 + 0.844118i \(0.319875\pi\)
\(678\) 0 0
\(679\) 27.0324 1.03741
\(680\) 0 0
\(681\) 3.07801 0.117950
\(682\) 0 0
\(683\) 14.7556 0.564608 0.282304 0.959325i \(-0.408901\pi\)
0.282304 + 0.959325i \(0.408901\pi\)
\(684\) 0 0
\(685\) −2.15083 −0.0821790
\(686\) 0 0
\(687\) −19.3435 −0.738000
\(688\) 0 0
\(689\) −51.0131 −1.94344
\(690\) 0 0
\(691\) 26.6875 1.01524 0.507619 0.861581i \(-0.330526\pi\)
0.507619 + 0.861581i \(0.330526\pi\)
\(692\) 0 0
\(693\) 12.2731 0.466218
\(694\) 0 0
\(695\) 44.9739 1.70596
\(696\) 0 0
\(697\) 25.0987 0.950680
\(698\) 0 0
\(699\) 7.27948 0.275335
\(700\) 0 0
\(701\) 7.51451 0.283819 0.141910 0.989880i \(-0.454676\pi\)
0.141910 + 0.989880i \(0.454676\pi\)
\(702\) 0 0
\(703\) −0.342761 −0.0129275
\(704\) 0 0
\(705\) −5.99319 −0.225717
\(706\) 0 0
\(707\) 28.5373 1.07326
\(708\) 0 0
\(709\) −42.9604 −1.61341 −0.806706 0.590953i \(-0.798752\pi\)
−0.806706 + 0.590953i \(0.798752\pi\)
\(710\) 0 0
\(711\) −9.15118 −0.343196
\(712\) 0 0
\(713\) 28.3561 1.06195
\(714\) 0 0
\(715\) 97.2403 3.63658
\(716\) 0 0
\(717\) −16.2464 −0.606733
\(718\) 0 0
\(719\) −2.20012 −0.0820506 −0.0410253 0.999158i \(-0.513062\pi\)
−0.0410253 + 0.999158i \(0.513062\pi\)
\(720\) 0 0
\(721\) −6.94637 −0.258696
\(722\) 0 0
\(723\) −24.4511 −0.909347
\(724\) 0 0
\(725\) −33.3710 −1.23937
\(726\) 0 0
\(727\) 10.7783 0.399746 0.199873 0.979822i \(-0.435947\pi\)
0.199873 + 0.979822i \(0.435947\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −33.6956 −1.24628
\(732\) 0 0
\(733\) 46.4940 1.71730 0.858648 0.512565i \(-0.171305\pi\)
0.858648 + 0.512565i \(0.171305\pi\)
\(734\) 0 0
\(735\) −0.735191 −0.0271179
\(736\) 0 0
\(737\) 66.5857 2.45271
\(738\) 0 0
\(739\) 20.9324 0.770011 0.385006 0.922914i \(-0.374199\pi\)
0.385006 + 0.922914i \(0.374199\pi\)
\(740\) 0 0
\(741\) 18.1160 0.665510
\(742\) 0 0
\(743\) 23.1270 0.848446 0.424223 0.905558i \(-0.360547\pi\)
0.424223 + 0.905558i \(0.360547\pi\)
\(744\) 0 0
\(745\) 31.5029 1.15418
\(746\) 0 0
\(747\) −7.82320 −0.286236
\(748\) 0 0
\(749\) −9.29526 −0.339641
\(750\) 0 0
\(751\) 17.0814 0.623311 0.311655 0.950195i \(-0.399117\pi\)
0.311655 + 0.950195i \(0.399117\pi\)
\(752\) 0 0
\(753\) −28.1202 −1.02476
\(754\) 0 0
\(755\) 28.1330 1.02387
\(756\) 0 0
\(757\) 9.85466 0.358174 0.179087 0.983833i \(-0.442686\pi\)
0.179087 + 0.983833i \(0.442686\pi\)
\(758\) 0 0
\(759\) −33.0076 −1.19810
\(760\) 0 0
\(761\) 28.6740 1.03943 0.519716 0.854339i \(-0.326038\pi\)
0.519716 + 0.854339i \(0.326038\pi\)
\(762\) 0 0
\(763\) 17.8838 0.647438
\(764\) 0 0
\(765\) 9.58433 0.346522
\(766\) 0 0
\(767\) −68.8061 −2.48444
\(768\) 0 0
\(769\) −34.9620 −1.26076 −0.630381 0.776286i \(-0.717101\pi\)
−0.630381 + 0.776286i \(0.717101\pi\)
\(770\) 0 0
\(771\) 18.2270 0.656430
\(772\) 0 0
\(773\) −8.10284 −0.291439 −0.145720 0.989326i \(-0.546550\pi\)
−0.145720 + 0.989326i \(0.546550\pi\)
\(774\) 0 0
\(775\) −17.5969 −0.632099
\(776\) 0 0
\(777\) 0.331570 0.0118950
\(778\) 0 0
\(779\) 21.5086 0.770627
\(780\) 0 0
\(781\) −17.4257 −0.623542
\(782\) 0 0
\(783\) 7.69073 0.274844
\(784\) 0 0
\(785\) 64.0097 2.28460
\(786\) 0 0
\(787\) −37.6200 −1.34101 −0.670504 0.741906i \(-0.733922\pi\)
−0.670504 + 0.741906i \(0.733922\pi\)
\(788\) 0 0
\(789\) −5.53367 −0.197004
\(790\) 0 0
\(791\) −23.2146 −0.825417
\(792\) 0 0
\(793\) 16.5238 0.586776
\(794\) 0 0
\(795\) −23.1282 −0.820273
\(796\) 0 0
\(797\) −29.2219 −1.03509 −0.517546 0.855655i \(-0.673154\pi\)
−0.517546 + 0.855655i \(0.673154\pi\)
\(798\) 0 0
\(799\) 6.15054 0.217591
\(800\) 0 0
\(801\) 5.37710 0.189990
\(802\) 0 0
\(803\) −23.3019 −0.822304
\(804\) 0 0
\(805\) −55.5548 −1.95805
\(806\) 0 0
\(807\) 18.1791 0.639933
\(808\) 0 0
\(809\) −27.9431 −0.982427 −0.491213 0.871039i \(-0.663446\pi\)
−0.491213 + 0.871039i \(0.663446\pi\)
\(810\) 0 0
\(811\) 46.9869 1.64993 0.824967 0.565181i \(-0.191194\pi\)
0.824967 + 0.565181i \(0.191194\pi\)
\(812\) 0 0
\(813\) −30.0438 −1.05368
\(814\) 0 0
\(815\) 50.1377 1.75625
\(816\) 0 0
\(817\) −28.8759 −1.01024
\(818\) 0 0
\(819\) −17.5246 −0.612358
\(820\) 0 0
\(821\) −6.11204 −0.213312 −0.106656 0.994296i \(-0.534014\pi\)
−0.106656 + 0.994296i \(0.534014\pi\)
\(822\) 0 0
\(823\) −23.3315 −0.813285 −0.406643 0.913587i \(-0.633301\pi\)
−0.406643 + 0.913587i \(0.633301\pi\)
\(824\) 0 0
\(825\) 20.4834 0.713142
\(826\) 0 0
\(827\) −47.3352 −1.64601 −0.823003 0.568037i \(-0.807703\pi\)
−0.823003 + 0.568037i \(0.807703\pi\)
\(828\) 0 0
\(829\) 37.7216 1.31012 0.655062 0.755575i \(-0.272642\pi\)
0.655062 + 0.755575i \(0.272642\pi\)
\(830\) 0 0
\(831\) 20.0646 0.696034
\(832\) 0 0
\(833\) 0.754494 0.0261417
\(834\) 0 0
\(835\) −3.05600 −0.105757
\(836\) 0 0
\(837\) 4.05540 0.140175
\(838\) 0 0
\(839\) 38.0910 1.31505 0.657524 0.753434i \(-0.271604\pi\)
0.657524 + 0.753434i \(0.271604\pi\)
\(840\) 0 0
\(841\) 30.1474 1.03956
\(842\) 0 0
\(843\) −20.1320 −0.693382
\(844\) 0 0
\(845\) −99.1196 −3.40982
\(846\) 0 0
\(847\) −29.3382 −1.00807
\(848\) 0 0
\(849\) −25.1003 −0.861439
\(850\) 0 0
\(851\) −0.891732 −0.0305682
\(852\) 0 0
\(853\) 51.7150 1.77069 0.885343 0.464938i \(-0.153923\pi\)
0.885343 + 0.464938i \(0.153923\pi\)
\(854\) 0 0
\(855\) 8.21342 0.280893
\(856\) 0 0
\(857\) −1.25379 −0.0428287 −0.0214143 0.999771i \(-0.506817\pi\)
−0.0214143 + 0.999771i \(0.506817\pi\)
\(858\) 0 0
\(859\) −48.8539 −1.66687 −0.833436 0.552616i \(-0.813630\pi\)
−0.833436 + 0.552616i \(0.813630\pi\)
\(860\) 0 0
\(861\) −20.8064 −0.709081
\(862\) 0 0
\(863\) −17.6303 −0.600143 −0.300072 0.953917i \(-0.597011\pi\)
−0.300072 + 0.953917i \(0.597011\pi\)
\(864\) 0 0
\(865\) 13.5999 0.462412
\(866\) 0 0
\(867\) 7.16403 0.243303
\(868\) 0 0
\(869\) 43.1994 1.46544
\(870\) 0 0
\(871\) −95.0764 −3.22154
\(872\) 0 0
\(873\) −10.3975 −0.351903
\(874\) 0 0
\(875\) −5.25083 −0.177510
\(876\) 0 0
\(877\) −1.77076 −0.0597945 −0.0298972 0.999553i \(-0.509518\pi\)
−0.0298972 + 0.999553i \(0.509518\pi\)
\(878\) 0 0
\(879\) −29.6784 −1.00103
\(880\) 0 0
\(881\) −43.8943 −1.47884 −0.739419 0.673246i \(-0.764900\pi\)
−0.739419 + 0.673246i \(0.764900\pi\)
\(882\) 0 0
\(883\) −17.5616 −0.590996 −0.295498 0.955343i \(-0.595486\pi\)
−0.295498 + 0.955343i \(0.595486\pi\)
\(884\) 0 0
\(885\) −31.1952 −1.04861
\(886\) 0 0
\(887\) −14.0970 −0.473332 −0.236666 0.971591i \(-0.576055\pi\)
−0.236666 + 0.971591i \(0.576055\pi\)
\(888\) 0 0
\(889\) 7.97106 0.267341
\(890\) 0 0
\(891\) −4.72064 −0.158147
\(892\) 0 0
\(893\) 5.27079 0.176380
\(894\) 0 0
\(895\) 54.2966 1.81493
\(896\) 0 0
\(897\) 47.1309 1.57366
\(898\) 0 0
\(899\) 31.1890 1.04021
\(900\) 0 0
\(901\) 23.7355 0.790743
\(902\) 0 0
\(903\) 27.9332 0.929557
\(904\) 0 0
\(905\) 45.8479 1.52404
\(906\) 0 0
\(907\) −12.8504 −0.426692 −0.213346 0.976977i \(-0.568436\pi\)
−0.213346 + 0.976977i \(0.568436\pi\)
\(908\) 0 0
\(909\) −10.9764 −0.364063
\(910\) 0 0
\(911\) −18.4133 −0.610060 −0.305030 0.952343i \(-0.598667\pi\)
−0.305030 + 0.952343i \(0.598667\pi\)
\(912\) 0 0
\(913\) 36.9305 1.22222
\(914\) 0 0
\(915\) 7.49151 0.247662
\(916\) 0 0
\(917\) 43.1536 1.42506
\(918\) 0 0
\(919\) 43.6473 1.43979 0.719895 0.694082i \(-0.244190\pi\)
0.719895 + 0.694082i \(0.244190\pi\)
\(920\) 0 0
\(921\) 22.0239 0.725714
\(922\) 0 0
\(923\) 24.8819 0.818997
\(924\) 0 0
\(925\) 0.553379 0.0181950
\(926\) 0 0
\(927\) 2.67179 0.0877533
\(928\) 0 0
\(929\) −6.48680 −0.212825 −0.106412 0.994322i \(-0.533936\pi\)
−0.106412 + 0.994322i \(0.533936\pi\)
\(930\) 0 0
\(931\) 0.646574 0.0211906
\(932\) 0 0
\(933\) −26.7334 −0.875213
\(934\) 0 0
\(935\) −45.2441 −1.47964
\(936\) 0 0
\(937\) 15.5535 0.508110 0.254055 0.967190i \(-0.418236\pi\)
0.254055 + 0.967190i \(0.418236\pi\)
\(938\) 0 0
\(939\) −24.6867 −0.805620
\(940\) 0 0
\(941\) 47.2420 1.54004 0.770022 0.638017i \(-0.220245\pi\)
0.770022 + 0.638017i \(0.220245\pi\)
\(942\) 0 0
\(943\) 55.9572 1.82222
\(944\) 0 0
\(945\) −7.94526 −0.258459
\(946\) 0 0
\(947\) 31.0655 1.00949 0.504747 0.863268i \(-0.331586\pi\)
0.504747 + 0.863268i \(0.331586\pi\)
\(948\) 0 0
\(949\) 33.2723 1.08006
\(950\) 0 0
\(951\) −29.6092 −0.960144
\(952\) 0 0
\(953\) −8.77668 −0.284304 −0.142152 0.989845i \(-0.545402\pi\)
−0.142152 + 0.989845i \(0.545402\pi\)
\(954\) 0 0
\(955\) −62.0316 −2.00730
\(956\) 0 0
\(957\) −36.3052 −1.17358
\(958\) 0 0
\(959\) −1.82982 −0.0590879
\(960\) 0 0
\(961\) −14.5537 −0.469475
\(962\) 0 0
\(963\) 3.57525 0.115211
\(964\) 0 0
\(965\) 2.98370 0.0960488
\(966\) 0 0
\(967\) 23.9661 0.770697 0.385348 0.922771i \(-0.374081\pi\)
0.385348 + 0.922771i \(0.374081\pi\)
\(968\) 0 0
\(969\) −8.42906 −0.270781
\(970\) 0 0
\(971\) 18.9528 0.608223 0.304112 0.952636i \(-0.401640\pi\)
0.304112 + 0.952636i \(0.401640\pi\)
\(972\) 0 0
\(973\) 38.2616 1.22661
\(974\) 0 0
\(975\) −29.2479 −0.936683
\(976\) 0 0
\(977\) −46.2775 −1.48055 −0.740274 0.672305i \(-0.765304\pi\)
−0.740274 + 0.672305i \(0.765304\pi\)
\(978\) 0 0
\(979\) −25.3833 −0.811254
\(980\) 0 0
\(981\) −6.87869 −0.219620
\(982\) 0 0
\(983\) 7.63097 0.243390 0.121695 0.992568i \(-0.461167\pi\)
0.121695 + 0.992568i \(0.461167\pi\)
\(984\) 0 0
\(985\) −68.2859 −2.17577
\(986\) 0 0
\(987\) −5.09871 −0.162294
\(988\) 0 0
\(989\) −75.1239 −2.38880
\(990\) 0 0
\(991\) −5.91696 −0.187959 −0.0939793 0.995574i \(-0.529959\pi\)
−0.0939793 + 0.995574i \(0.529959\pi\)
\(992\) 0 0
\(993\) −6.19998 −0.196750
\(994\) 0 0
\(995\) 28.7690 0.912039
\(996\) 0 0
\(997\) −3.25299 −0.103023 −0.0515117 0.998672i \(-0.516404\pi\)
−0.0515117 + 0.998672i \(0.516404\pi\)
\(998\) 0 0
\(999\) −0.127532 −0.00403495
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 \(a_p\))