Properties

Label 8048.2.a.v.1.28
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.28
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+3.02746 q^{3}\) \(-1.92479 q^{5}\) \(-4.18734 q^{7}\) \(+6.16549 q^{9}\) \(+O(q^{10})\) \(q\)\(+3.02746 q^{3}\) \(-1.92479 q^{5}\) \(-4.18734 q^{7}\) \(+6.16549 q^{9}\) \(+1.99884 q^{11}\) \(+1.74693 q^{13}\) \(-5.82721 q^{15}\) \(-2.18205 q^{17}\) \(+1.78148 q^{19}\) \(-12.6770 q^{21}\) \(+3.66792 q^{23}\) \(-1.29519 q^{25}\) \(+9.58339 q^{27}\) \(-4.48076 q^{29}\) \(-10.3311 q^{31}\) \(+6.05140 q^{33}\) \(+8.05974 q^{35}\) \(+1.81048 q^{37}\) \(+5.28874 q^{39}\) \(-5.92703 q^{41}\) \(-3.30352 q^{43}\) \(-11.8673 q^{45}\) \(-0.751293 q^{47}\) \(+10.5338 q^{49}\) \(-6.60606 q^{51}\) \(-1.29824 q^{53}\) \(-3.84734 q^{55}\) \(+5.39334 q^{57}\) \(+2.89024 q^{59}\) \(-0.765430 q^{61}\) \(-25.8170 q^{63}\) \(-3.36246 q^{65}\) \(+0.202708 q^{67}\) \(+11.1045 q^{69}\) \(-10.7293 q^{71}\) \(+11.3425 q^{73}\) \(-3.92114 q^{75}\) \(-8.36982 q^{77}\) \(+0.211446 q^{79}\) \(+10.5168 q^{81}\) \(+9.33406 q^{83}\) \(+4.19998 q^{85}\) \(-13.5653 q^{87}\) \(+0.912638 q^{89}\) \(-7.31497 q^{91}\) \(-31.2769 q^{93}\) \(-3.42896 q^{95}\) \(-7.66341 q^{97}\) \(+12.3238 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 31q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 22q^{25} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 26q^{33} \) \(\mathstrut +\mathstrut 13q^{35} \) \(\mathstrut -\mathstrut 67q^{37} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut -\mathstrut 57q^{45} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 20q^{49} \) \(\mathstrut +\mathstrut 11q^{51} \) \(\mathstrut -\mathstrut 58q^{53} \) \(\mathstrut -\mathstrut 15q^{55} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 55q^{61} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 44q^{69} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 5q^{73} \) \(\mathstrut +\mathstrut 25q^{75} \) \(\mathstrut -\mathstrut 50q^{77} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 78q^{85} \) \(\mathstrut +\mathstrut 11q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut +\mathstrut 15q^{91} \) \(\mathstrut -\mathstrut 83q^{93} \) \(\mathstrut +\mathstrut 27q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 70q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 3.02746 1.74790 0.873951 0.486013i \(-0.161549\pi\)
0.873951 + 0.486013i \(0.161549\pi\)
\(4\) 0 0
\(5\) −1.92479 −0.860791 −0.430396 0.902640i \(-0.641626\pi\)
−0.430396 + 0.902640i \(0.641626\pi\)
\(6\) 0 0
\(7\) −4.18734 −1.58266 −0.791332 0.611386i \(-0.790612\pi\)
−0.791332 + 0.611386i \(0.790612\pi\)
\(8\) 0 0
\(9\) 6.16549 2.05516
\(10\) 0 0
\(11\) 1.99884 0.602673 0.301337 0.953518i \(-0.402567\pi\)
0.301337 + 0.953518i \(0.402567\pi\)
\(12\) 0 0
\(13\) 1.74693 0.484510 0.242255 0.970213i \(-0.422113\pi\)
0.242255 + 0.970213i \(0.422113\pi\)
\(14\) 0 0
\(15\) −5.82721 −1.50458
\(16\) 0 0
\(17\) −2.18205 −0.529225 −0.264612 0.964355i \(-0.585244\pi\)
−0.264612 + 0.964355i \(0.585244\pi\)
\(18\) 0 0
\(19\) 1.78148 0.408698 0.204349 0.978898i \(-0.434492\pi\)
0.204349 + 0.978898i \(0.434492\pi\)
\(20\) 0 0
\(21\) −12.6770 −2.76634
\(22\) 0 0
\(23\) 3.66792 0.764814 0.382407 0.923994i \(-0.375095\pi\)
0.382407 + 0.923994i \(0.375095\pi\)
\(24\) 0 0
\(25\) −1.29519 −0.259038
\(26\) 0 0
\(27\) 9.58339 1.84432
\(28\) 0 0
\(29\) −4.48076 −0.832057 −0.416029 0.909352i \(-0.636578\pi\)
−0.416029 + 0.909352i \(0.636578\pi\)
\(30\) 0 0
\(31\) −10.3311 −1.85552 −0.927759 0.373179i \(-0.878268\pi\)
−0.927759 + 0.373179i \(0.878268\pi\)
\(32\) 0 0
\(33\) 6.05140 1.05341
\(34\) 0 0
\(35\) 8.05974 1.36234
\(36\) 0 0
\(37\) 1.81048 0.297642 0.148821 0.988864i \(-0.452452\pi\)
0.148821 + 0.988864i \(0.452452\pi\)
\(38\) 0 0
\(39\) 5.28874 0.846877
\(40\) 0 0
\(41\) −5.92703 −0.925647 −0.462824 0.886450i \(-0.653164\pi\)
−0.462824 + 0.886450i \(0.653164\pi\)
\(42\) 0 0
\(43\) −3.30352 −0.503782 −0.251891 0.967756i \(-0.581052\pi\)
−0.251891 + 0.967756i \(0.581052\pi\)
\(44\) 0 0
\(45\) −11.8673 −1.76907
\(46\) 0 0
\(47\) −0.751293 −0.109587 −0.0547937 0.998498i \(-0.517450\pi\)
−0.0547937 + 0.998498i \(0.517450\pi\)
\(48\) 0 0
\(49\) 10.5338 1.50483
\(50\) 0 0
\(51\) −6.60606 −0.925033
\(52\) 0 0
\(53\) −1.29824 −0.178326 −0.0891632 0.996017i \(-0.528419\pi\)
−0.0891632 + 0.996017i \(0.528419\pi\)
\(54\) 0 0
\(55\) −3.84734 −0.518776
\(56\) 0 0
\(57\) 5.39334 0.714365
\(58\) 0 0
\(59\) 2.89024 0.376277 0.188139 0.982142i \(-0.439755\pi\)
0.188139 + 0.982142i \(0.439755\pi\)
\(60\) 0 0
\(61\) −0.765430 −0.0980033 −0.0490017 0.998799i \(-0.515604\pi\)
−0.0490017 + 0.998799i \(0.515604\pi\)
\(62\) 0 0
\(63\) −25.8170 −3.25264
\(64\) 0 0
\(65\) −3.36246 −0.417062
\(66\) 0 0
\(67\) 0.202708 0.0247647 0.0123823 0.999923i \(-0.496058\pi\)
0.0123823 + 0.999923i \(0.496058\pi\)
\(68\) 0 0
\(69\) 11.1045 1.33682
\(70\) 0 0
\(71\) −10.7293 −1.27333 −0.636667 0.771139i \(-0.719687\pi\)
−0.636667 + 0.771139i \(0.719687\pi\)
\(72\) 0 0
\(73\) 11.3425 1.32754 0.663768 0.747938i \(-0.268956\pi\)
0.663768 + 0.747938i \(0.268956\pi\)
\(74\) 0 0
\(75\) −3.92114 −0.452774
\(76\) 0 0
\(77\) −8.36982 −0.953830
\(78\) 0 0
\(79\) 0.211446 0.0237896 0.0118948 0.999929i \(-0.496214\pi\)
0.0118948 + 0.999929i \(0.496214\pi\)
\(80\) 0 0
\(81\) 10.5168 1.16853
\(82\) 0 0
\(83\) 9.33406 1.02455 0.512273 0.858823i \(-0.328804\pi\)
0.512273 + 0.858823i \(0.328804\pi\)
\(84\) 0 0
\(85\) 4.19998 0.455552
\(86\) 0 0
\(87\) −13.5653 −1.45435
\(88\) 0 0
\(89\) 0.912638 0.0967394 0.0483697 0.998830i \(-0.484597\pi\)
0.0483697 + 0.998830i \(0.484597\pi\)
\(90\) 0 0
\(91\) −7.31497 −0.766817
\(92\) 0 0
\(93\) −31.2769 −3.24327
\(94\) 0 0
\(95\) −3.42896 −0.351804
\(96\) 0 0
\(97\) −7.66341 −0.778101 −0.389051 0.921216i \(-0.627197\pi\)
−0.389051 + 0.921216i \(0.627197\pi\)
\(98\) 0 0
\(99\) 12.3238 1.23859
\(100\) 0 0
\(101\) 3.38623 0.336943 0.168471 0.985707i \(-0.446117\pi\)
0.168471 + 0.985707i \(0.446117\pi\)
\(102\) 0 0
\(103\) −8.59859 −0.847244 −0.423622 0.905839i \(-0.639241\pi\)
−0.423622 + 0.905839i \(0.639241\pi\)
\(104\) 0 0
\(105\) 24.4005 2.38124
\(106\) 0 0
\(107\) −7.86354 −0.760197 −0.380099 0.924946i \(-0.624110\pi\)
−0.380099 + 0.924946i \(0.624110\pi\)
\(108\) 0 0
\(109\) −0.237337 −0.0227328 −0.0113664 0.999935i \(-0.503618\pi\)
−0.0113664 + 0.999935i \(0.503618\pi\)
\(110\) 0 0
\(111\) 5.48116 0.520248
\(112\) 0 0
\(113\) −18.5081 −1.74110 −0.870549 0.492082i \(-0.836236\pi\)
−0.870549 + 0.492082i \(0.836236\pi\)
\(114\) 0 0
\(115\) −7.05997 −0.658345
\(116\) 0 0
\(117\) 10.7707 0.995748
\(118\) 0 0
\(119\) 9.13697 0.837585
\(120\) 0 0
\(121\) −7.00463 −0.636785
\(122\) 0 0
\(123\) −17.9438 −1.61794
\(124\) 0 0
\(125\) 12.1169 1.08377
\(126\) 0 0
\(127\) −12.2050 −1.08302 −0.541508 0.840696i \(-0.682146\pi\)
−0.541508 + 0.840696i \(0.682146\pi\)
\(128\) 0 0
\(129\) −10.0013 −0.880562
\(130\) 0 0
\(131\) −20.6911 −1.80779 −0.903896 0.427753i \(-0.859305\pi\)
−0.903896 + 0.427753i \(0.859305\pi\)
\(132\) 0 0
\(133\) −7.45964 −0.646833
\(134\) 0 0
\(135\) −18.4460 −1.58758
\(136\) 0 0
\(137\) −15.3166 −1.30858 −0.654292 0.756242i \(-0.727033\pi\)
−0.654292 + 0.756242i \(0.727033\pi\)
\(138\) 0 0
\(139\) 12.8022 1.08587 0.542935 0.839775i \(-0.317313\pi\)
0.542935 + 0.839775i \(0.317313\pi\)
\(140\) 0 0
\(141\) −2.27451 −0.191548
\(142\) 0 0
\(143\) 3.49183 0.292001
\(144\) 0 0
\(145\) 8.62452 0.716227
\(146\) 0 0
\(147\) 31.8906 2.63029
\(148\) 0 0
\(149\) 12.0920 0.990619 0.495309 0.868717i \(-0.335055\pi\)
0.495309 + 0.868717i \(0.335055\pi\)
\(150\) 0 0
\(151\) 7.09209 0.577146 0.288573 0.957458i \(-0.406819\pi\)
0.288573 + 0.957458i \(0.406819\pi\)
\(152\) 0 0
\(153\) −13.4534 −1.08764
\(154\) 0 0
\(155\) 19.8852 1.59721
\(156\) 0 0
\(157\) −17.1026 −1.36494 −0.682469 0.730915i \(-0.739094\pi\)
−0.682469 + 0.730915i \(0.739094\pi\)
\(158\) 0 0
\(159\) −3.93035 −0.311697
\(160\) 0 0
\(161\) −15.3588 −1.21044
\(162\) 0 0
\(163\) 9.56130 0.748899 0.374449 0.927247i \(-0.377832\pi\)
0.374449 + 0.927247i \(0.377832\pi\)
\(164\) 0 0
\(165\) −11.6477 −0.906770
\(166\) 0 0
\(167\) −8.74744 −0.676897 −0.338449 0.940985i \(-0.609902\pi\)
−0.338449 + 0.940985i \(0.609902\pi\)
\(168\) 0 0
\(169\) −9.94825 −0.765250
\(170\) 0 0
\(171\) 10.9837 0.839942
\(172\) 0 0
\(173\) −9.59340 −0.729373 −0.364686 0.931130i \(-0.618824\pi\)
−0.364686 + 0.931130i \(0.618824\pi\)
\(174\) 0 0
\(175\) 5.42341 0.409971
\(176\) 0 0
\(177\) 8.75008 0.657696
\(178\) 0 0
\(179\) 17.2593 1.29002 0.645009 0.764175i \(-0.276853\pi\)
0.645009 + 0.764175i \(0.276853\pi\)
\(180\) 0 0
\(181\) −17.4707 −1.29859 −0.649293 0.760538i \(-0.724935\pi\)
−0.649293 + 0.760538i \(0.724935\pi\)
\(182\) 0 0
\(183\) −2.31731 −0.171300
\(184\) 0 0
\(185\) −3.48480 −0.256207
\(186\) 0 0
\(187\) −4.36157 −0.318949
\(188\) 0 0
\(189\) −40.1289 −2.91895
\(190\) 0 0
\(191\) −0.0970807 −0.00702451 −0.00351225 0.999994i \(-0.501118\pi\)
−0.00351225 + 0.999994i \(0.501118\pi\)
\(192\) 0 0
\(193\) 3.31384 0.238536 0.119268 0.992862i \(-0.461945\pi\)
0.119268 + 0.992862i \(0.461945\pi\)
\(194\) 0 0
\(195\) −10.1797 −0.728984
\(196\) 0 0
\(197\) −0.444125 −0.0316426 −0.0158213 0.999875i \(-0.505036\pi\)
−0.0158213 + 0.999875i \(0.505036\pi\)
\(198\) 0 0
\(199\) 17.3971 1.23325 0.616623 0.787259i \(-0.288500\pi\)
0.616623 + 0.787259i \(0.288500\pi\)
\(200\) 0 0
\(201\) 0.613688 0.0432862
\(202\) 0 0
\(203\) 18.7625 1.31687
\(204\) 0 0
\(205\) 11.4083 0.796789
\(206\) 0 0
\(207\) 22.6145 1.57182
\(208\) 0 0
\(209\) 3.56089 0.246312
\(210\) 0 0
\(211\) −1.95704 −0.134728 −0.0673641 0.997728i \(-0.521459\pi\)
−0.0673641 + 0.997728i \(0.521459\pi\)
\(212\) 0 0
\(213\) −32.4825 −2.22566
\(214\) 0 0
\(215\) 6.35857 0.433651
\(216\) 0 0
\(217\) 43.2598 2.93666
\(218\) 0 0
\(219\) 34.3388 2.32040
\(220\) 0 0
\(221\) −3.81188 −0.256415
\(222\) 0 0
\(223\) 14.3677 0.962130 0.481065 0.876685i \(-0.340250\pi\)
0.481065 + 0.876685i \(0.340250\pi\)
\(224\) 0 0
\(225\) −7.98550 −0.532366
\(226\) 0 0
\(227\) −14.4923 −0.961886 −0.480943 0.876752i \(-0.659706\pi\)
−0.480943 + 0.876752i \(0.659706\pi\)
\(228\) 0 0
\(229\) 1.66945 0.110320 0.0551602 0.998478i \(-0.482433\pi\)
0.0551602 + 0.998478i \(0.482433\pi\)
\(230\) 0 0
\(231\) −25.3393 −1.66720
\(232\) 0 0
\(233\) −14.5719 −0.954638 −0.477319 0.878730i \(-0.658391\pi\)
−0.477319 + 0.878730i \(0.658391\pi\)
\(234\) 0 0
\(235\) 1.44608 0.0943318
\(236\) 0 0
\(237\) 0.640144 0.0415818
\(238\) 0 0
\(239\) −11.4900 −0.743229 −0.371614 0.928387i \(-0.621196\pi\)
−0.371614 + 0.928387i \(0.621196\pi\)
\(240\) 0 0
\(241\) −22.8075 −1.46916 −0.734579 0.678523i \(-0.762620\pi\)
−0.734579 + 0.678523i \(0.762620\pi\)
\(242\) 0 0
\(243\) 3.08902 0.198160
\(244\) 0 0
\(245\) −20.2753 −1.29534
\(246\) 0 0
\(247\) 3.11211 0.198019
\(248\) 0 0
\(249\) 28.2584 1.79081
\(250\) 0 0
\(251\) 20.6236 1.30175 0.650874 0.759185i \(-0.274402\pi\)
0.650874 + 0.759185i \(0.274402\pi\)
\(252\) 0 0
\(253\) 7.33159 0.460933
\(254\) 0 0
\(255\) 12.7153 0.796260
\(256\) 0 0
\(257\) −7.15484 −0.446307 −0.223153 0.974783i \(-0.571635\pi\)
−0.223153 + 0.974783i \(0.571635\pi\)
\(258\) 0 0
\(259\) −7.58110 −0.471067
\(260\) 0 0
\(261\) −27.6261 −1.71001
\(262\) 0 0
\(263\) 5.18369 0.319640 0.159820 0.987146i \(-0.448909\pi\)
0.159820 + 0.987146i \(0.448909\pi\)
\(264\) 0 0
\(265\) 2.49883 0.153502
\(266\) 0 0
\(267\) 2.76297 0.169091
\(268\) 0 0
\(269\) −3.72454 −0.227089 −0.113545 0.993533i \(-0.536220\pi\)
−0.113545 + 0.993533i \(0.536220\pi\)
\(270\) 0 0
\(271\) −19.9464 −1.21166 −0.605829 0.795595i \(-0.707158\pi\)
−0.605829 + 0.795595i \(0.707158\pi\)
\(272\) 0 0
\(273\) −22.1457 −1.34032
\(274\) 0 0
\(275\) −2.58888 −0.156116
\(276\) 0 0
\(277\) 7.64942 0.459609 0.229805 0.973237i \(-0.426191\pi\)
0.229805 + 0.973237i \(0.426191\pi\)
\(278\) 0 0
\(279\) −63.6963 −3.81339
\(280\) 0 0
\(281\) 7.39477 0.441135 0.220568 0.975372i \(-0.429209\pi\)
0.220568 + 0.975372i \(0.429209\pi\)
\(282\) 0 0
\(283\) 2.75281 0.163637 0.0818187 0.996647i \(-0.473927\pi\)
0.0818187 + 0.996647i \(0.473927\pi\)
\(284\) 0 0
\(285\) −10.3810 −0.614919
\(286\) 0 0
\(287\) 24.8185 1.46499
\(288\) 0 0
\(289\) −12.2387 −0.719921
\(290\) 0 0
\(291\) −23.2006 −1.36004
\(292\) 0 0
\(293\) 17.1629 1.00267 0.501333 0.865255i \(-0.332843\pi\)
0.501333 + 0.865255i \(0.332843\pi\)
\(294\) 0 0
\(295\) −5.56310 −0.323896
\(296\) 0 0
\(297\) 19.1557 1.11152
\(298\) 0 0
\(299\) 6.40759 0.370560
\(300\) 0 0
\(301\) 13.8330 0.797318
\(302\) 0 0
\(303\) 10.2517 0.588943
\(304\) 0 0
\(305\) 1.47329 0.0843604
\(306\) 0 0
\(307\) 20.0008 1.14150 0.570752 0.821122i \(-0.306652\pi\)
0.570752 + 0.821122i \(0.306652\pi\)
\(308\) 0 0
\(309\) −26.0318 −1.48090
\(310\) 0 0
\(311\) −20.4690 −1.16069 −0.580344 0.814371i \(-0.697082\pi\)
−0.580344 + 0.814371i \(0.697082\pi\)
\(312\) 0 0
\(313\) −29.0165 −1.64011 −0.820054 0.572286i \(-0.806057\pi\)
−0.820054 + 0.572286i \(0.806057\pi\)
\(314\) 0 0
\(315\) 49.6922 2.79984
\(316\) 0 0
\(317\) −28.4199 −1.59622 −0.798109 0.602513i \(-0.794166\pi\)
−0.798109 + 0.602513i \(0.794166\pi\)
\(318\) 0 0
\(319\) −8.95634 −0.501459
\(320\) 0 0
\(321\) −23.8065 −1.32875
\(322\) 0 0
\(323\) −3.88727 −0.216293
\(324\) 0 0
\(325\) −2.26261 −0.125507
\(326\) 0 0
\(327\) −0.718528 −0.0397347
\(328\) 0 0
\(329\) 3.14592 0.173440
\(330\) 0 0
\(331\) 19.6047 1.07757 0.538785 0.842443i \(-0.318883\pi\)
0.538785 + 0.842443i \(0.318883\pi\)
\(332\) 0 0
\(333\) 11.1625 0.611702
\(334\) 0 0
\(335\) −0.390169 −0.0213172
\(336\) 0 0
\(337\) −0.371952 −0.0202615 −0.0101308 0.999949i \(-0.503225\pi\)
−0.0101308 + 0.999949i \(0.503225\pi\)
\(338\) 0 0
\(339\) −56.0325 −3.04327
\(340\) 0 0
\(341\) −20.6502 −1.11827
\(342\) 0 0
\(343\) −14.7972 −0.798973
\(344\) 0 0
\(345\) −21.3737 −1.15072
\(346\) 0 0
\(347\) −18.8832 −1.01370 −0.506851 0.862034i \(-0.669191\pi\)
−0.506851 + 0.862034i \(0.669191\pi\)
\(348\) 0 0
\(349\) 8.11925 0.434614 0.217307 0.976103i \(-0.430273\pi\)
0.217307 + 0.976103i \(0.430273\pi\)
\(350\) 0 0
\(351\) 16.7415 0.893593
\(352\) 0 0
\(353\) 24.8693 1.32366 0.661830 0.749654i \(-0.269780\pi\)
0.661830 + 0.749654i \(0.269780\pi\)
\(354\) 0 0
\(355\) 20.6516 1.09607
\(356\) 0 0
\(357\) 27.6618 1.46402
\(358\) 0 0
\(359\) 9.58819 0.506045 0.253023 0.967460i \(-0.418575\pi\)
0.253023 + 0.967460i \(0.418575\pi\)
\(360\) 0 0
\(361\) −15.8263 −0.832966
\(362\) 0 0
\(363\) −21.2062 −1.11304
\(364\) 0 0
\(365\) −21.8319 −1.14273
\(366\) 0 0
\(367\) −22.1854 −1.15807 −0.579035 0.815302i \(-0.696571\pi\)
−0.579035 + 0.815302i \(0.696571\pi\)
\(368\) 0 0
\(369\) −36.5431 −1.90236
\(370\) 0 0
\(371\) 5.43615 0.282231
\(372\) 0 0
\(373\) −11.0914 −0.574289 −0.287145 0.957887i \(-0.592706\pi\)
−0.287145 + 0.957887i \(0.592706\pi\)
\(374\) 0 0
\(375\) 36.6834 1.89432
\(376\) 0 0
\(377\) −7.82756 −0.403140
\(378\) 0 0
\(379\) 23.1111 1.18714 0.593570 0.804782i \(-0.297718\pi\)
0.593570 + 0.804782i \(0.297718\pi\)
\(380\) 0 0
\(381\) −36.9500 −1.89301
\(382\) 0 0
\(383\) 10.3570 0.529218 0.264609 0.964356i \(-0.414757\pi\)
0.264609 + 0.964356i \(0.414757\pi\)
\(384\) 0 0
\(385\) 16.1101 0.821048
\(386\) 0 0
\(387\) −20.3678 −1.03535
\(388\) 0 0
\(389\) 0.405843 0.0205770 0.0102885 0.999947i \(-0.496725\pi\)
0.0102885 + 0.999947i \(0.496725\pi\)
\(390\) 0 0
\(391\) −8.00358 −0.404759
\(392\) 0 0
\(393\) −62.6415 −3.15984
\(394\) 0 0
\(395\) −0.406989 −0.0204778
\(396\) 0 0
\(397\) 17.1489 0.860677 0.430338 0.902668i \(-0.358394\pi\)
0.430338 + 0.902668i \(0.358394\pi\)
\(398\) 0 0
\(399\) −22.5837 −1.13060
\(400\) 0 0
\(401\) −22.6203 −1.12960 −0.564802 0.825227i \(-0.691047\pi\)
−0.564802 + 0.825227i \(0.691047\pi\)
\(402\) 0 0
\(403\) −18.0477 −0.899018
\(404\) 0 0
\(405\) −20.2426 −1.00586
\(406\) 0 0
\(407\) 3.61887 0.179381
\(408\) 0 0
\(409\) −31.4398 −1.55460 −0.777299 0.629131i \(-0.783411\pi\)
−0.777299 + 0.629131i \(0.783411\pi\)
\(410\) 0 0
\(411\) −46.3703 −2.28728
\(412\) 0 0
\(413\) −12.1024 −0.595521
\(414\) 0 0
\(415\) −17.9661 −0.881920
\(416\) 0 0
\(417\) 38.7581 1.89799
\(418\) 0 0
\(419\) −8.70623 −0.425327 −0.212664 0.977125i \(-0.568214\pi\)
−0.212664 + 0.977125i \(0.568214\pi\)
\(420\) 0 0
\(421\) 10.1795 0.496120 0.248060 0.968745i \(-0.420207\pi\)
0.248060 + 0.968745i \(0.420207\pi\)
\(422\) 0 0
\(423\) −4.63209 −0.225220
\(424\) 0 0
\(425\) 2.82617 0.137090
\(426\) 0 0
\(427\) 3.20511 0.155106
\(428\) 0 0
\(429\) 10.5714 0.510390
\(430\) 0 0
\(431\) 39.7010 1.91233 0.956164 0.292832i \(-0.0945978\pi\)
0.956164 + 0.292832i \(0.0945978\pi\)
\(432\) 0 0
\(433\) 2.99144 0.143760 0.0718798 0.997413i \(-0.477100\pi\)
0.0718798 + 0.997413i \(0.477100\pi\)
\(434\) 0 0
\(435\) 26.1104 1.25190
\(436\) 0 0
\(437\) 6.53431 0.312578
\(438\) 0 0
\(439\) −19.9125 −0.950373 −0.475187 0.879885i \(-0.657619\pi\)
−0.475187 + 0.879885i \(0.657619\pi\)
\(440\) 0 0
\(441\) 64.9460 3.09267
\(442\) 0 0
\(443\) 20.0397 0.952117 0.476058 0.879414i \(-0.342065\pi\)
0.476058 + 0.879414i \(0.342065\pi\)
\(444\) 0 0
\(445\) −1.75663 −0.0832724
\(446\) 0 0
\(447\) 36.6081 1.73151
\(448\) 0 0
\(449\) −10.2247 −0.482533 −0.241267 0.970459i \(-0.577563\pi\)
−0.241267 + 0.970459i \(0.577563\pi\)
\(450\) 0 0
\(451\) −11.8472 −0.557863
\(452\) 0 0
\(453\) 21.4710 1.00880
\(454\) 0 0
\(455\) 14.0798 0.660069
\(456\) 0 0
\(457\) 21.8282 1.02108 0.510541 0.859854i \(-0.329445\pi\)
0.510541 + 0.859854i \(0.329445\pi\)
\(458\) 0 0
\(459\) −20.9114 −0.976061
\(460\) 0 0
\(461\) −29.6711 −1.38192 −0.690961 0.722892i \(-0.742812\pi\)
−0.690961 + 0.722892i \(0.742812\pi\)
\(462\) 0 0
\(463\) 22.7523 1.05739 0.528695 0.848812i \(-0.322681\pi\)
0.528695 + 0.848812i \(0.322681\pi\)
\(464\) 0 0
\(465\) 60.2014 2.79177
\(466\) 0 0
\(467\) −30.5638 −1.41432 −0.707162 0.707052i \(-0.750025\pi\)
−0.707162 + 0.707052i \(0.750025\pi\)
\(468\) 0 0
\(469\) −0.848805 −0.0391942
\(470\) 0 0
\(471\) −51.7774 −2.38578
\(472\) 0 0
\(473\) −6.60321 −0.303616
\(474\) 0 0
\(475\) −2.30735 −0.105869
\(476\) 0 0
\(477\) −8.00427 −0.366490
\(478\) 0 0
\(479\) −5.93081 −0.270986 −0.135493 0.990778i \(-0.543262\pi\)
−0.135493 + 0.990778i \(0.543262\pi\)
\(480\) 0 0
\(481\) 3.16278 0.144210
\(482\) 0 0
\(483\) −46.4982 −2.11574
\(484\) 0 0
\(485\) 14.7504 0.669783
\(486\) 0 0
\(487\) −9.77824 −0.443094 −0.221547 0.975150i \(-0.571111\pi\)
−0.221547 + 0.975150i \(0.571111\pi\)
\(488\) 0 0
\(489\) 28.9464 1.30900
\(490\) 0 0
\(491\) 23.2607 1.04974 0.524870 0.851183i \(-0.324114\pi\)
0.524870 + 0.851183i \(0.324114\pi\)
\(492\) 0 0
\(493\) 9.77725 0.440345
\(494\) 0 0
\(495\) −23.7208 −1.06617
\(496\) 0 0
\(497\) 44.9272 2.01526
\(498\) 0 0
\(499\) −4.32957 −0.193818 −0.0969091 0.995293i \(-0.530896\pi\)
−0.0969091 + 0.995293i \(0.530896\pi\)
\(500\) 0 0
\(501\) −26.4825 −1.18315
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −6.51778 −0.290037
\(506\) 0 0
\(507\) −30.1179 −1.33758
\(508\) 0 0
\(509\) 31.2848 1.38668 0.693338 0.720612i \(-0.256139\pi\)
0.693338 + 0.720612i \(0.256139\pi\)
\(510\) 0 0
\(511\) −47.4948 −2.10105
\(512\) 0 0
\(513\) 17.0726 0.753772
\(514\) 0 0
\(515\) 16.5505 0.729300
\(516\) 0 0
\(517\) −1.50172 −0.0660454
\(518\) 0 0
\(519\) −29.0436 −1.27487
\(520\) 0 0
\(521\) −14.1680 −0.620710 −0.310355 0.950621i \(-0.600448\pi\)
−0.310355 + 0.950621i \(0.600448\pi\)
\(522\) 0 0
\(523\) −1.46629 −0.0641163 −0.0320582 0.999486i \(-0.510206\pi\)
−0.0320582 + 0.999486i \(0.510206\pi\)
\(524\) 0 0
\(525\) 16.4191 0.716590
\(526\) 0 0
\(527\) 22.5429 0.981986
\(528\) 0 0
\(529\) −9.54636 −0.415059
\(530\) 0 0
\(531\) 17.8198 0.773312
\(532\) 0 0
\(533\) −10.3541 −0.448485
\(534\) 0 0
\(535\) 15.1356 0.654371
\(536\) 0 0
\(537\) 52.2517 2.25483
\(538\) 0 0
\(539\) 21.0554 0.906920
\(540\) 0 0
\(541\) −35.6990 −1.53482 −0.767410 0.641157i \(-0.778455\pi\)
−0.767410 + 0.641157i \(0.778455\pi\)
\(542\) 0 0
\(543\) −52.8918 −2.26980
\(544\) 0 0
\(545\) 0.456824 0.0195682
\(546\) 0 0
\(547\) −7.60742 −0.325270 −0.162635 0.986686i \(-0.551999\pi\)
−0.162635 + 0.986686i \(0.551999\pi\)
\(548\) 0 0
\(549\) −4.71925 −0.201413
\(550\) 0 0
\(551\) −7.98237 −0.340060
\(552\) 0 0
\(553\) −0.885397 −0.0376509
\(554\) 0 0
\(555\) −10.5501 −0.447825
\(556\) 0 0
\(557\) 9.75762 0.413444 0.206722 0.978400i \(-0.433721\pi\)
0.206722 + 0.978400i \(0.433721\pi\)
\(558\) 0 0
\(559\) −5.77100 −0.244087
\(560\) 0 0
\(561\) −13.2045 −0.557493
\(562\) 0 0
\(563\) 25.2165 1.06275 0.531374 0.847137i \(-0.321676\pi\)
0.531374 + 0.847137i \(0.321676\pi\)
\(564\) 0 0
\(565\) 35.6242 1.49872
\(566\) 0 0
\(567\) −44.0374 −1.84940
\(568\) 0 0
\(569\) 40.0890 1.68062 0.840310 0.542106i \(-0.182373\pi\)
0.840310 + 0.542106i \(0.182373\pi\)
\(570\) 0 0
\(571\) 19.0147 0.795741 0.397871 0.917441i \(-0.369749\pi\)
0.397871 + 0.917441i \(0.369749\pi\)
\(572\) 0 0
\(573\) −0.293907 −0.0122782
\(574\) 0 0
\(575\) −4.75066 −0.198116
\(576\) 0 0
\(577\) 31.2490 1.30091 0.650456 0.759544i \(-0.274578\pi\)
0.650456 + 0.759544i \(0.274578\pi\)
\(578\) 0 0
\(579\) 10.0325 0.416937
\(580\) 0 0
\(581\) −39.0848 −1.62151
\(582\) 0 0
\(583\) −2.59497 −0.107473
\(584\) 0 0
\(585\) −20.7312 −0.857131
\(586\) 0 0
\(587\) 7.54656 0.311480 0.155740 0.987798i \(-0.450224\pi\)
0.155740 + 0.987798i \(0.450224\pi\)
\(588\) 0 0
\(589\) −18.4046 −0.758348
\(590\) 0 0
\(591\) −1.34457 −0.0553082
\(592\) 0 0
\(593\) 31.8797 1.30914 0.654570 0.756001i \(-0.272850\pi\)
0.654570 + 0.756001i \(0.272850\pi\)
\(594\) 0 0
\(595\) −17.5867 −0.720986
\(596\) 0 0
\(597\) 52.6689 2.15559
\(598\) 0 0
\(599\) 26.6431 1.08861 0.544303 0.838889i \(-0.316794\pi\)
0.544303 + 0.838889i \(0.316794\pi\)
\(600\) 0 0
\(601\) −10.2262 −0.417134 −0.208567 0.978008i \(-0.566880\pi\)
−0.208567 + 0.978008i \(0.566880\pi\)
\(602\) 0 0
\(603\) 1.24979 0.0508955
\(604\) 0 0
\(605\) 13.4824 0.548139
\(606\) 0 0
\(607\) −11.0198 −0.447281 −0.223640 0.974672i \(-0.571794\pi\)
−0.223640 + 0.974672i \(0.571794\pi\)
\(608\) 0 0
\(609\) 56.8026 2.30176
\(610\) 0 0
\(611\) −1.31245 −0.0530962
\(612\) 0 0
\(613\) 22.9207 0.925759 0.462880 0.886421i \(-0.346816\pi\)
0.462880 + 0.886421i \(0.346816\pi\)
\(614\) 0 0
\(615\) 34.5381 1.39271
\(616\) 0 0
\(617\) −29.0044 −1.16767 −0.583836 0.811871i \(-0.698449\pi\)
−0.583836 + 0.811871i \(0.698449\pi\)
\(618\) 0 0
\(619\) 38.2556 1.53762 0.768812 0.639475i \(-0.220848\pi\)
0.768812 + 0.639475i \(0.220848\pi\)
\(620\) 0 0
\(621\) 35.1511 1.41057
\(622\) 0 0
\(623\) −3.82152 −0.153106
\(624\) 0 0
\(625\) −16.8465 −0.673861
\(626\) 0 0
\(627\) 10.7804 0.430529
\(628\) 0 0
\(629\) −3.95056 −0.157519
\(630\) 0 0
\(631\) 0.945492 0.0376394 0.0188197 0.999823i \(-0.494009\pi\)
0.0188197 + 0.999823i \(0.494009\pi\)
\(632\) 0 0
\(633\) −5.92485 −0.235492
\(634\) 0 0
\(635\) 23.4920 0.932250
\(636\) 0 0
\(637\) 18.4018 0.729104
\(638\) 0 0
\(639\) −66.1514 −2.61691
\(640\) 0 0
\(641\) 19.8943 0.785777 0.392888 0.919586i \(-0.371476\pi\)
0.392888 + 0.919586i \(0.371476\pi\)
\(642\) 0 0
\(643\) −1.15954 −0.0457279 −0.0228639 0.999739i \(-0.507278\pi\)
−0.0228639 + 0.999739i \(0.507278\pi\)
\(644\) 0 0
\(645\) 19.2503 0.757980
\(646\) 0 0
\(647\) 24.4790 0.962368 0.481184 0.876620i \(-0.340207\pi\)
0.481184 + 0.876620i \(0.340207\pi\)
\(648\) 0 0
\(649\) 5.77713 0.226772
\(650\) 0 0
\(651\) 130.967 5.13300
\(652\) 0 0
\(653\) −1.56713 −0.0613267 −0.0306633 0.999530i \(-0.509762\pi\)
−0.0306633 + 0.999530i \(0.509762\pi\)
\(654\) 0 0
\(655\) 39.8260 1.55613
\(656\) 0 0
\(657\) 69.9319 2.72830
\(658\) 0 0
\(659\) 28.4072 1.10659 0.553295 0.832986i \(-0.313370\pi\)
0.553295 + 0.832986i \(0.313370\pi\)
\(660\) 0 0
\(661\) 27.5261 1.07064 0.535321 0.844648i \(-0.320190\pi\)
0.535321 + 0.844648i \(0.320190\pi\)
\(662\) 0 0
\(663\) −11.5403 −0.448188
\(664\) 0 0
\(665\) 14.3582 0.556788
\(666\) 0 0
\(667\) −16.4351 −0.636369
\(668\) 0 0
\(669\) 43.4975 1.68171
\(670\) 0 0
\(671\) −1.52997 −0.0590640
\(672\) 0 0
\(673\) −34.7101 −1.33797 −0.668987 0.743274i \(-0.733272\pi\)
−0.668987 + 0.743274i \(0.733272\pi\)
\(674\) 0 0
\(675\) −12.4123 −0.477751
\(676\) 0 0
\(677\) 11.6423 0.447451 0.223725 0.974652i \(-0.428178\pi\)
0.223725 + 0.974652i \(0.428178\pi\)
\(678\) 0 0
\(679\) 32.0893 1.23147
\(680\) 0 0
\(681\) −43.8747 −1.68128
\(682\) 0 0
\(683\) 39.9131 1.52723 0.763617 0.645669i \(-0.223422\pi\)
0.763617 + 0.645669i \(0.223422\pi\)
\(684\) 0 0
\(685\) 29.4812 1.12642
\(686\) 0 0
\(687\) 5.05419 0.192829
\(688\) 0 0
\(689\) −2.26792 −0.0864010
\(690\) 0 0
\(691\) 7.60823 0.289431 0.144715 0.989473i \(-0.453773\pi\)
0.144715 + 0.989473i \(0.453773\pi\)
\(692\) 0 0
\(693\) −51.6041 −1.96028
\(694\) 0 0
\(695\) −24.6415 −0.934707
\(696\) 0 0
\(697\) 12.9331 0.489875
\(698\) 0 0
\(699\) −44.1159 −1.66862
\(700\) 0 0
\(701\) 4.18523 0.158074 0.0790370 0.996872i \(-0.474815\pi\)
0.0790370 + 0.996872i \(0.474815\pi\)
\(702\) 0 0
\(703\) 3.22533 0.121646
\(704\) 0 0
\(705\) 4.37794 0.164883
\(706\) 0 0
\(707\) −14.1793 −0.533268
\(708\) 0 0
\(709\) −26.2363 −0.985326 −0.492663 0.870220i \(-0.663976\pi\)
−0.492663 + 0.870220i \(0.663976\pi\)
\(710\) 0 0
\(711\) 1.30367 0.0488914
\(712\) 0 0
\(713\) −37.8936 −1.41913
\(714\) 0 0
\(715\) −6.72103 −0.251352
\(716\) 0 0
\(717\) −34.7856 −1.29909
\(718\) 0 0
\(719\) −36.3421 −1.35533 −0.677665 0.735371i \(-0.737008\pi\)
−0.677665 + 0.735371i \(0.737008\pi\)
\(720\) 0 0
\(721\) 36.0052 1.34090
\(722\) 0 0
\(723\) −69.0486 −2.56795
\(724\) 0 0
\(725\) 5.80345 0.215535
\(726\) 0 0
\(727\) 24.2159 0.898120 0.449060 0.893502i \(-0.351759\pi\)
0.449060 + 0.893502i \(0.351759\pi\)
\(728\) 0 0
\(729\) −22.1986 −0.822169
\(730\) 0 0
\(731\) 7.20844 0.266614
\(732\) 0 0
\(733\) 21.8245 0.806107 0.403053 0.915176i \(-0.367949\pi\)
0.403053 + 0.915176i \(0.367949\pi\)
\(734\) 0 0
\(735\) −61.3826 −2.26413
\(736\) 0 0
\(737\) 0.405180 0.0149250
\(738\) 0 0
\(739\) −44.5321 −1.63814 −0.819069 0.573695i \(-0.805510\pi\)
−0.819069 + 0.573695i \(0.805510\pi\)
\(740\) 0 0
\(741\) 9.42176 0.346117
\(742\) 0 0
\(743\) 28.1627 1.03319 0.516594 0.856230i \(-0.327200\pi\)
0.516594 + 0.856230i \(0.327200\pi\)
\(744\) 0 0
\(745\) −23.2746 −0.852716
\(746\) 0 0
\(747\) 57.5490 2.10561
\(748\) 0 0
\(749\) 32.9273 1.20314
\(750\) 0 0
\(751\) 45.0726 1.64472 0.822361 0.568966i \(-0.192656\pi\)
0.822361 + 0.568966i \(0.192656\pi\)
\(752\) 0 0
\(753\) 62.4370 2.27533
\(754\) 0 0
\(755\) −13.6508 −0.496803
\(756\) 0 0
\(757\) −15.2957 −0.555932 −0.277966 0.960591i \(-0.589660\pi\)
−0.277966 + 0.960591i \(0.589660\pi\)
\(758\) 0 0
\(759\) 22.1961 0.805666
\(760\) 0 0
\(761\) 13.2795 0.481382 0.240691 0.970602i \(-0.422626\pi\)
0.240691 + 0.970602i \(0.422626\pi\)
\(762\) 0 0
\(763\) 0.993811 0.0359784
\(764\) 0 0
\(765\) 25.8949 0.936234
\(766\) 0 0
\(767\) 5.04904 0.182310
\(768\) 0 0
\(769\) 0.214114 0.00772116 0.00386058 0.999993i \(-0.498771\pi\)
0.00386058 + 0.999993i \(0.498771\pi\)
\(770\) 0 0
\(771\) −21.6610 −0.780101
\(772\) 0 0
\(773\) −0.552400 −0.0198684 −0.00993422 0.999951i \(-0.503162\pi\)
−0.00993422 + 0.999951i \(0.503162\pi\)
\(774\) 0 0
\(775\) 13.3808 0.480651
\(776\) 0 0
\(777\) −22.9515 −0.823379
\(778\) 0 0
\(779\) −10.5589 −0.378311
\(780\) 0 0
\(781\) −21.4462 −0.767404
\(782\) 0 0
\(783\) −42.9409 −1.53458
\(784\) 0 0
\(785\) 32.9189 1.17493
\(786\) 0 0
\(787\) −11.5564 −0.411940 −0.205970 0.978558i \(-0.566035\pi\)
−0.205970 + 0.978558i \(0.566035\pi\)
\(788\) 0 0
\(789\) 15.6934 0.558699
\(790\) 0 0
\(791\) 77.4998 2.75557
\(792\) 0 0
\(793\) −1.33715 −0.0474836
\(794\) 0 0
\(795\) 7.56510 0.268306
\(796\) 0 0
\(797\) 27.2766 0.966188 0.483094 0.875569i \(-0.339513\pi\)
0.483094 + 0.875569i \(0.339513\pi\)
\(798\) 0 0
\(799\) 1.63936 0.0579963
\(800\) 0 0
\(801\) 5.62686 0.198815
\(802\) 0 0
\(803\) 22.6718 0.800071
\(804\) 0 0
\(805\) 29.5625 1.04194
\(806\) 0 0
\(807\) −11.2759 −0.396930
\(808\) 0 0
\(809\) −28.5509 −1.00380 −0.501898 0.864927i \(-0.667365\pi\)
−0.501898 + 0.864927i \(0.667365\pi\)
\(810\) 0 0
\(811\) 54.7477 1.92245 0.961226 0.275762i \(-0.0889301\pi\)
0.961226 + 0.275762i \(0.0889301\pi\)
\(812\) 0 0
\(813\) −60.3869 −2.11786
\(814\) 0 0
\(815\) −18.4035 −0.644645
\(816\) 0 0
\(817\) −5.88514 −0.205895
\(818\) 0 0
\(819\) −45.1004 −1.57593
\(820\) 0 0
\(821\) 19.5798 0.683339 0.341670 0.939820i \(-0.389008\pi\)
0.341670 + 0.939820i \(0.389008\pi\)
\(822\) 0 0
\(823\) 25.8671 0.901669 0.450834 0.892608i \(-0.351126\pi\)
0.450834 + 0.892608i \(0.351126\pi\)
\(824\) 0 0
\(825\) −7.83773 −0.272875
\(826\) 0 0
\(827\) −24.0220 −0.835327 −0.417663 0.908602i \(-0.637151\pi\)
−0.417663 + 0.908602i \(0.637151\pi\)
\(828\) 0 0
\(829\) −13.2092 −0.458774 −0.229387 0.973335i \(-0.573672\pi\)
−0.229387 + 0.973335i \(0.573672\pi\)
\(830\) 0 0
\(831\) 23.1583 0.803352
\(832\) 0 0
\(833\) −22.9853 −0.796392
\(834\) 0 0
\(835\) 16.8370 0.582667
\(836\) 0 0
\(837\) −99.0068 −3.42218
\(838\) 0 0
\(839\) 11.8939 0.410625 0.205312 0.978697i \(-0.434179\pi\)
0.205312 + 0.978697i \(0.434179\pi\)
\(840\) 0 0
\(841\) −8.92275 −0.307681
\(842\) 0 0
\(843\) 22.3874 0.771062
\(844\) 0 0
\(845\) 19.1483 0.658720
\(846\) 0 0
\(847\) 29.3308 1.00782
\(848\) 0 0
\(849\) 8.33400 0.286022
\(850\) 0 0
\(851\) 6.64071 0.227641
\(852\) 0 0
\(853\) 39.5243 1.35329 0.676643 0.736311i \(-0.263434\pi\)
0.676643 + 0.736311i \(0.263434\pi\)
\(854\) 0 0
\(855\) −21.1412 −0.723015
\(856\) 0 0
\(857\) 43.0691 1.47121 0.735606 0.677410i \(-0.236898\pi\)
0.735606 + 0.677410i \(0.236898\pi\)
\(858\) 0 0
\(859\) 24.2573 0.827648 0.413824 0.910357i \(-0.364193\pi\)
0.413824 + 0.910357i \(0.364193\pi\)
\(860\) 0 0
\(861\) 75.1369 2.56066
\(862\) 0 0
\(863\) 14.7300 0.501415 0.250707 0.968063i \(-0.419337\pi\)
0.250707 + 0.968063i \(0.419337\pi\)
\(864\) 0 0
\(865\) 18.4653 0.627838
\(866\) 0 0
\(867\) −37.0520 −1.25835
\(868\) 0 0
\(869\) 0.422647 0.0143373
\(870\) 0 0
\(871\) 0.354115 0.0119987
\(872\) 0 0
\(873\) −47.2487 −1.59912
\(874\) 0 0
\(875\) −50.7376 −1.71524
\(876\) 0 0
\(877\) −25.8480 −0.872825 −0.436413 0.899747i \(-0.643751\pi\)
−0.436413 + 0.899747i \(0.643751\pi\)
\(878\) 0 0
\(879\) 51.9598 1.75256
\(880\) 0 0
\(881\) −45.7809 −1.54240 −0.771199 0.636595i \(-0.780342\pi\)
−0.771199 + 0.636595i \(0.780342\pi\)
\(882\) 0 0
\(883\) 29.1017 0.979351 0.489675 0.871905i \(-0.337115\pi\)
0.489675 + 0.871905i \(0.337115\pi\)
\(884\) 0 0
\(885\) −16.8420 −0.566139
\(886\) 0 0
\(887\) 32.1311 1.07886 0.539428 0.842031i \(-0.318640\pi\)
0.539428 + 0.842031i \(0.318640\pi\)
\(888\) 0 0
\(889\) 51.1063 1.71405
\(890\) 0 0
\(891\) 21.0214 0.704244
\(892\) 0 0
\(893\) −1.33841 −0.0447882
\(894\) 0 0
\(895\) −33.2204 −1.11044
\(896\) 0 0
\(897\) 19.3987 0.647703
\(898\) 0 0
\(899\) 46.2912 1.54390
\(900\) 0 0
\(901\) 2.83282 0.0943748
\(902\) 0 0
\(903\) 41.8787 1.39363
\(904\) 0 0
\(905\) 33.6274 1.11781
\(906\) 0 0
\(907\) −16.9899 −0.564139 −0.282070 0.959394i \(-0.591021\pi\)
−0.282070 + 0.959394i \(0.591021\pi\)
\(908\) 0 0
\(909\) 20.8778 0.692473
\(910\) 0 0
\(911\) 42.6649 1.41355 0.706776 0.707438i \(-0.250149\pi\)
0.706776 + 0.707438i \(0.250149\pi\)
\(912\) 0 0
\(913\) 18.6573 0.617466
\(914\) 0 0
\(915\) 4.46032 0.147454
\(916\) 0 0
\(917\) 86.6407 2.86113
\(918\) 0 0
\(919\) 11.7437 0.387389 0.193694 0.981062i \(-0.437953\pi\)
0.193694 + 0.981062i \(0.437953\pi\)
\(920\) 0 0
\(921\) 60.5515 1.99524
\(922\) 0 0
\(923\) −18.7433 −0.616943
\(924\) 0 0
\(925\) −2.34492 −0.0771006
\(926\) 0 0
\(927\) −53.0145 −1.74122
\(928\) 0 0
\(929\) −58.6215 −1.92331 −0.961655 0.274263i \(-0.911566\pi\)
−0.961655 + 0.274263i \(0.911566\pi\)
\(930\) 0 0
\(931\) 18.7657 0.615021
\(932\) 0 0
\(933\) −61.9689 −2.02877
\(934\) 0 0
\(935\) 8.39509 0.274549
\(936\) 0 0
\(937\) −48.7133 −1.59140 −0.795698 0.605694i \(-0.792895\pi\)
−0.795698 + 0.605694i \(0.792895\pi\)
\(938\) 0 0
\(939\) −87.8461 −2.86675
\(940\) 0 0
\(941\) 52.6479 1.71627 0.858137 0.513421i \(-0.171622\pi\)
0.858137 + 0.513421i \(0.171622\pi\)
\(942\) 0 0
\(943\) −21.7399 −0.707948
\(944\) 0 0
\(945\) 77.2396 2.51260
\(946\) 0 0
\(947\) 21.2551 0.690698 0.345349 0.938474i \(-0.387761\pi\)
0.345349 + 0.938474i \(0.387761\pi\)
\(948\) 0 0
\(949\) 19.8145 0.643205
\(950\) 0 0
\(951\) −86.0399 −2.79003
\(952\) 0 0
\(953\) 8.14389 0.263807 0.131903 0.991263i \(-0.457891\pi\)
0.131903 + 0.991263i \(0.457891\pi\)
\(954\) 0 0
\(955\) 0.186860 0.00604664
\(956\) 0 0
\(957\) −27.1149 −0.876501
\(958\) 0 0
\(959\) 64.1357 2.07105
\(960\) 0 0
\(961\) 75.7314 2.44295
\(962\) 0 0
\(963\) −48.4826 −1.56233
\(964\) 0 0
\(965\) −6.37844 −0.205329
\(966\) 0 0
\(967\) −3.44544 −0.110798 −0.0553990 0.998464i \(-0.517643\pi\)
−0.0553990 + 0.998464i \(0.517643\pi\)
\(968\) 0 0
\(969\) −11.7685 −0.378060
\(970\) 0 0
\(971\) −47.5402 −1.52564 −0.762819 0.646612i \(-0.776185\pi\)
−0.762819 + 0.646612i \(0.776185\pi\)
\(972\) 0 0
\(973\) −53.6072 −1.71857
\(974\) 0 0
\(975\) −6.84994 −0.219374
\(976\) 0 0
\(977\) 56.7589 1.81588 0.907940 0.419101i \(-0.137655\pi\)
0.907940 + 0.419101i \(0.137655\pi\)
\(978\) 0 0
\(979\) 1.82422 0.0583022
\(980\) 0 0
\(981\) −1.46330 −0.0467196
\(982\) 0 0
\(983\) −41.0543 −1.30943 −0.654714 0.755877i \(-0.727211\pi\)
−0.654714 + 0.755877i \(0.727211\pi\)
\(984\) 0 0
\(985\) 0.854847 0.0272377
\(986\) 0 0
\(987\) 9.52413 0.303156
\(988\) 0 0
\(989\) −12.1170 −0.385300
\(990\) 0 0
\(991\) 32.0872 1.01928 0.509642 0.860386i \(-0.329778\pi\)
0.509642 + 0.860386i \(0.329778\pi\)
\(992\) 0 0
\(993\) 59.3523 1.88349
\(994\) 0 0
\(995\) −33.4857 −1.06157
\(996\) 0 0
\(997\) 16.4819 0.521986 0.260993 0.965341i \(-0.415950\pi\)
0.260993 + 0.965341i \(0.415950\pi\)
\(998\) 0 0
\(999\) 17.3506 0.548947
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 \(a_p\))