Properties

Label 51.2.a.a.1.1
Level 51
Weight 2
Character 51.1
Self dual Yes
Analytic conductor 0.407
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 51 = 3 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 51.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.407237050309\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\)
Character \(\chi\) = 51.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} -2.00000 q^{4} +3.00000 q^{5} -4.00000 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -2.00000 q^{4} +3.00000 q^{5} -4.00000 q^{7} +1.00000 q^{9} -3.00000 q^{11} -2.00000 q^{12} -1.00000 q^{13} +3.00000 q^{15} +4.00000 q^{16} -1.00000 q^{17} -1.00000 q^{19} -6.00000 q^{20} -4.00000 q^{21} +9.00000 q^{23} +4.00000 q^{25} +1.00000 q^{27} +8.00000 q^{28} +6.00000 q^{29} +2.00000 q^{31} -3.00000 q^{33} -12.0000 q^{35} -2.00000 q^{36} -4.00000 q^{37} -1.00000 q^{39} -3.00000 q^{41} -7.00000 q^{43} +6.00000 q^{44} +3.00000 q^{45} -6.00000 q^{47} +4.00000 q^{48} +9.00000 q^{49} -1.00000 q^{51} +2.00000 q^{52} -6.00000 q^{53} -9.00000 q^{55} -1.00000 q^{57} +6.00000 q^{59} -6.00000 q^{60} +8.00000 q^{61} -4.00000 q^{63} -8.00000 q^{64} -3.00000 q^{65} -4.00000 q^{67} +2.00000 q^{68} +9.00000 q^{69} +12.0000 q^{71} +2.00000 q^{73} +4.00000 q^{75} +2.00000 q^{76} +12.0000 q^{77} -10.0000 q^{79} +12.0000 q^{80} +1.00000 q^{81} -6.00000 q^{83} +8.00000 q^{84} -3.00000 q^{85} +6.00000 q^{87} +4.00000 q^{91} -18.0000 q^{92} +2.00000 q^{93} -3.00000 q^{95} -16.0000 q^{97} -3.00000 q^{99} +O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(3\) 1.00000 0.577350
\(4\) −2.00000 −1.00000
\(5\) 3.00000 1.34164 0.670820 0.741620i \(-0.265942\pi\)
0.670820 + 0.741620i \(0.265942\pi\)
\(6\) 0 0
\(7\) −4.00000 −1.51186 −0.755929 0.654654i \(-0.772814\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) −2.00000 −0.577350
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 0 0
\(15\) 3.00000 0.774597
\(16\) 4.00000 1.00000
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) −1.00000 −0.229416 −0.114708 0.993399i \(-0.536593\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) −6.00000 −1.34164
\(21\) −4.00000 −0.872872
\(22\) 0 0
\(23\) 9.00000 1.87663 0.938315 0.345782i \(-0.112386\pi\)
0.938315 + 0.345782i \(0.112386\pi\)
\(24\) 0 0
\(25\) 4.00000 0.800000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 8.00000 1.51186
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) 0 0
\(33\) −3.00000 −0.522233
\(34\) 0 0
\(35\) −12.0000 −2.02837
\(36\) −2.00000 −0.333333
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) −3.00000 −0.468521 −0.234261 0.972174i \(-0.575267\pi\)
−0.234261 + 0.972174i \(0.575267\pi\)
\(42\) 0 0
\(43\) −7.00000 −1.06749 −0.533745 0.845645i \(-0.679216\pi\)
−0.533745 + 0.845645i \(0.679216\pi\)
\(44\) 6.00000 0.904534
\(45\) 3.00000 0.447214
\(46\) 0 0
\(47\) −6.00000 −0.875190 −0.437595 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) 4.00000 0.577350
\(49\) 9.00000 1.28571
\(50\) 0 0
\(51\) −1.00000 −0.140028
\(52\) 2.00000 0.277350
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 0 0
\(55\) −9.00000 −1.21356
\(56\) 0 0
\(57\) −1.00000 −0.132453
\(58\) 0 0
\(59\) 6.00000 0.781133 0.390567 0.920575i \(-0.372279\pi\)
0.390567 + 0.920575i \(0.372279\pi\)
\(60\) −6.00000 −0.774597
\(61\) 8.00000 1.02430 0.512148 0.858898i \(-0.328850\pi\)
0.512148 + 0.858898i \(0.328850\pi\)
\(62\) 0 0
\(63\) −4.00000 −0.503953
\(64\) −8.00000 −1.00000
\(65\) −3.00000 −0.372104
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 2.00000 0.242536
\(69\) 9.00000 1.08347
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 0 0
\(75\) 4.00000 0.461880
\(76\) 2.00000 0.229416
\(77\) 12.0000 1.36753
\(78\) 0 0
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 12.0000 1.34164
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 8.00000 0.872872
\(85\) −3.00000 −0.325396
\(86\) 0 0
\(87\) 6.00000 0.643268
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 4.00000 0.419314
\(92\) −18.0000 −1.87663
\(93\) 2.00000 0.207390
\(94\) 0 0
\(95\) −3.00000 −0.307794
\(96\) 0 0
\(97\) −16.0000 −1.62455 −0.812277 0.583272i \(-0.801772\pi\)
−0.812277 + 0.583272i \(0.801772\pi\)
\(98\) 0 0
\(99\) −3.00000 −0.301511
\(100\) −8.00000 −0.800000
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 5.00000 0.492665 0.246332 0.969185i \(-0.420775\pi\)
0.246332 + 0.969185i \(0.420775\pi\)
\(104\) 0 0
\(105\) −12.0000 −1.17108
\(106\) 0 0
\(107\) 9.00000 0.870063 0.435031 0.900415i \(-0.356737\pi\)
0.435031 + 0.900415i \(0.356737\pi\)
\(108\) −2.00000 −0.192450
\(109\) 20.0000 1.91565 0.957826 0.287348i \(-0.0927736\pi\)
0.957826 + 0.287348i \(0.0927736\pi\)
\(110\) 0 0
\(111\) −4.00000 −0.379663
\(112\) −16.0000 −1.51186
\(113\) −9.00000 −0.846649 −0.423324 0.905978i \(-0.639137\pi\)
−0.423324 + 0.905978i \(0.639137\pi\)
\(114\) 0 0
\(115\) 27.0000 2.51776
\(116\) −12.0000 −1.11417
\(117\) −1.00000 −0.0924500
\(118\) 0 0
\(119\) 4.00000 0.366679
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 0 0
\(123\) −3.00000 −0.270501
\(124\) −4.00000 −0.359211
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) −13.0000 −1.15356 −0.576782 0.816898i \(-0.695692\pi\)
−0.576782 + 0.816898i \(0.695692\pi\)
\(128\) 0 0
\(129\) −7.00000 −0.616316
\(130\) 0 0
\(131\) 3.00000 0.262111 0.131056 0.991375i \(-0.458163\pi\)
0.131056 + 0.991375i \(0.458163\pi\)
\(132\) 6.00000 0.522233
\(133\) 4.00000 0.346844
\(134\) 0 0
\(135\) 3.00000 0.258199
\(136\) 0 0
\(137\) −6.00000 −0.512615 −0.256307 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) 0 0
\(139\) 2.00000 0.169638 0.0848189 0.996396i \(-0.472969\pi\)
0.0848189 + 0.996396i \(0.472969\pi\)
\(140\) 24.0000 2.02837
\(141\) −6.00000 −0.505291
\(142\) 0 0
\(143\) 3.00000 0.250873
\(144\) 4.00000 0.333333
\(145\) 18.0000 1.49482
\(146\) 0 0
\(147\) 9.00000 0.742307
\(148\) 8.00000 0.657596
\(149\) −18.0000 −1.47462 −0.737309 0.675556i \(-0.763904\pi\)
−0.737309 + 0.675556i \(0.763904\pi\)
\(150\) 0 0
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 0 0
\(153\) −1.00000 −0.0808452
\(154\) 0 0
\(155\) 6.00000 0.481932
\(156\) 2.00000 0.160128
\(157\) 11.0000 0.877896 0.438948 0.898513i \(-0.355351\pi\)
0.438948 + 0.898513i \(0.355351\pi\)
\(158\) 0 0
\(159\) −6.00000 −0.475831
\(160\) 0 0
\(161\) −36.0000 −2.83720
\(162\) 0 0
\(163\) 2.00000 0.156652 0.0783260 0.996928i \(-0.475042\pi\)
0.0783260 + 0.996928i \(0.475042\pi\)
\(164\) 6.00000 0.468521
\(165\) −9.00000 −0.700649
\(166\) 0 0
\(167\) 21.0000 1.62503 0.812514 0.582941i \(-0.198098\pi\)
0.812514 + 0.582941i \(0.198098\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) −1.00000 −0.0764719
\(172\) 14.0000 1.06749
\(173\) 15.0000 1.14043 0.570214 0.821496i \(-0.306860\pi\)
0.570214 + 0.821496i \(0.306860\pi\)
\(174\) 0 0
\(175\) −16.0000 −1.20949
\(176\) −12.0000 −0.904534
\(177\) 6.00000 0.450988
\(178\) 0 0
\(179\) −6.00000 −0.448461 −0.224231 0.974536i \(-0.571987\pi\)
−0.224231 + 0.974536i \(0.571987\pi\)
\(180\) −6.00000 −0.447214
\(181\) 14.0000 1.04061 0.520306 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 0 0
\(183\) 8.00000 0.591377
\(184\) 0 0
\(185\) −12.0000 −0.882258
\(186\) 0 0
\(187\) 3.00000 0.219382
\(188\) 12.0000 0.875190
\(189\) −4.00000 −0.290957
\(190\) 0 0
\(191\) 18.0000 1.30243 0.651217 0.758891i \(-0.274259\pi\)
0.651217 + 0.758891i \(0.274259\pi\)
\(192\) −8.00000 −0.577350
\(193\) −22.0000 −1.58359 −0.791797 0.610784i \(-0.790854\pi\)
−0.791797 + 0.610784i \(0.790854\pi\)
\(194\) 0 0
\(195\) −3.00000 −0.214834
\(196\) −18.0000 −1.28571
\(197\) 3.00000 0.213741 0.106871 0.994273i \(-0.465917\pi\)
0.106871 + 0.994273i \(0.465917\pi\)
\(198\) 0 0
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) 0 0
\(201\) −4.00000 −0.282138
\(202\) 0 0
\(203\) −24.0000 −1.68447
\(204\) 2.00000 0.140028
\(205\) −9.00000 −0.628587
\(206\) 0 0
\(207\) 9.00000 0.625543
\(208\) −4.00000 −0.277350
\(209\) 3.00000 0.207514
\(210\) 0 0
\(211\) 2.00000 0.137686 0.0688428 0.997628i \(-0.478069\pi\)
0.0688428 + 0.997628i \(0.478069\pi\)
\(212\) 12.0000 0.824163
\(213\) 12.0000 0.822226
\(214\) 0 0
\(215\) −21.0000 −1.43219
\(216\) 0 0
\(217\) −8.00000 −0.543075
\(218\) 0 0
\(219\) 2.00000 0.135147
\(220\) 18.0000 1.21356
\(221\) 1.00000 0.0672673
\(222\) 0 0
\(223\) −1.00000 −0.0669650 −0.0334825 0.999439i \(-0.510660\pi\)
−0.0334825 + 0.999439i \(0.510660\pi\)
\(224\) 0 0
\(225\) 4.00000 0.266667
\(226\) 0 0
\(227\) 3.00000 0.199117 0.0995585 0.995032i \(-0.468257\pi\)
0.0995585 + 0.995032i \(0.468257\pi\)
\(228\) 2.00000 0.132453
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 0 0
\(231\) 12.0000 0.789542
\(232\) 0 0
\(233\) 21.0000 1.37576 0.687878 0.725826i \(-0.258542\pi\)
0.687878 + 0.725826i \(0.258542\pi\)
\(234\) 0 0
\(235\) −18.0000 −1.17419
\(236\) −12.0000 −0.781133
\(237\) −10.0000 −0.649570
\(238\) 0 0
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 12.0000 0.774597
\(241\) 8.00000 0.515325 0.257663 0.966235i \(-0.417048\pi\)
0.257663 + 0.966235i \(0.417048\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) −16.0000 −1.02430
\(245\) 27.0000 1.72497
\(246\) 0 0
\(247\) 1.00000 0.0636285
\(248\) 0 0
\(249\) −6.00000 −0.380235
\(250\) 0 0
\(251\) 24.0000 1.51487 0.757433 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 8.00000 0.503953
\(253\) −27.0000 −1.69748
\(254\) 0 0
\(255\) −3.00000 −0.187867
\(256\) 16.0000 1.00000
\(257\) 12.0000 0.748539 0.374270 0.927320i \(-0.377893\pi\)
0.374270 + 0.927320i \(0.377893\pi\)
\(258\) 0 0
\(259\) 16.0000 0.994192
\(260\) 6.00000 0.372104
\(261\) 6.00000 0.371391
\(262\) 0 0
\(263\) 12.0000 0.739952 0.369976 0.929041i \(-0.379366\pi\)
0.369976 + 0.929041i \(0.379366\pi\)
\(264\) 0 0
\(265\) −18.0000 −1.10573
\(266\) 0 0
\(267\) 0 0
\(268\) 8.00000 0.488678
\(269\) −15.0000 −0.914566 −0.457283 0.889321i \(-0.651177\pi\)
−0.457283 + 0.889321i \(0.651177\pi\)
\(270\) 0 0
\(271\) 11.0000 0.668202 0.334101 0.942537i \(-0.391567\pi\)
0.334101 + 0.942537i \(0.391567\pi\)
\(272\) −4.00000 −0.242536
\(273\) 4.00000 0.242091
\(274\) 0 0
\(275\) −12.0000 −0.723627
\(276\) −18.0000 −1.08347
\(277\) 2.00000 0.120168 0.0600842 0.998193i \(-0.480863\pi\)
0.0600842 + 0.998193i \(0.480863\pi\)
\(278\) 0 0
\(279\) 2.00000 0.119737
\(280\) 0 0
\(281\) 12.0000 0.715860 0.357930 0.933748i \(-0.383483\pi\)
0.357930 + 0.933748i \(0.383483\pi\)
\(282\) 0 0
\(283\) −10.0000 −0.594438 −0.297219 0.954809i \(-0.596059\pi\)
−0.297219 + 0.954809i \(0.596059\pi\)
\(284\) −24.0000 −1.42414
\(285\) −3.00000 −0.177705
\(286\) 0 0
\(287\) 12.0000 0.708338
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) −16.0000 −0.937937
\(292\) −4.00000 −0.234082
\(293\) −24.0000 −1.40209 −0.701047 0.713115i \(-0.747284\pi\)
−0.701047 + 0.713115i \(0.747284\pi\)
\(294\) 0 0
\(295\) 18.0000 1.04800
\(296\) 0 0
\(297\) −3.00000 −0.174078
\(298\) 0 0
\(299\) −9.00000 −0.520483
\(300\) −8.00000 −0.461880
\(301\) 28.0000 1.61389
\(302\) 0 0
\(303\) 0 0
\(304\) −4.00000 −0.229416
\(305\) 24.0000 1.37424
\(306\) 0 0
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) −24.0000 −1.36753
\(309\) 5.00000 0.284440
\(310\) 0 0
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) 0 0
\(313\) −16.0000 −0.904373 −0.452187 0.891923i \(-0.649356\pi\)
−0.452187 + 0.891923i \(0.649356\pi\)
\(314\) 0 0
\(315\) −12.0000 −0.676123
\(316\) 20.0000 1.12509
\(317\) −6.00000 −0.336994 −0.168497 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(318\) 0 0
\(319\) −18.0000 −1.00781
\(320\) −24.0000 −1.34164
\(321\) 9.00000 0.502331
\(322\) 0 0
\(323\) 1.00000 0.0556415
\(324\) −2.00000 −0.111111
\(325\) −4.00000 −0.221880
\(326\) 0 0
\(327\) 20.0000 1.10600
\(328\) 0 0
\(329\) 24.0000 1.32316
\(330\) 0 0
\(331\) −13.0000 −0.714545 −0.357272 0.934000i \(-0.616293\pi\)
−0.357272 + 0.934000i \(0.616293\pi\)
\(332\) 12.0000 0.658586
\(333\) −4.00000 −0.219199
\(334\) 0 0
\(335\) −12.0000 −0.655630
\(336\) −16.0000 −0.872872
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 0 0
\(339\) −9.00000 −0.488813
\(340\) 6.00000 0.325396
\(341\) −6.00000 −0.324918
\(342\) 0 0
\(343\) −8.00000 −0.431959
\(344\) 0 0
\(345\) 27.0000 1.45363
\(346\) 0 0
\(347\) −12.0000 −0.644194 −0.322097 0.946707i \(-0.604388\pi\)
−0.322097 + 0.946707i \(0.604388\pi\)
\(348\) −12.0000 −0.643268
\(349\) −19.0000 −1.01705 −0.508523 0.861048i \(-0.669808\pi\)
−0.508523 + 0.861048i \(0.669808\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) 0 0
\(353\) 6.00000 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 0 0
\(355\) 36.0000 1.91068
\(356\) 0 0
\(357\) 4.00000 0.211702
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) 0 0
\(363\) −2.00000 −0.104973
\(364\) −8.00000 −0.419314
\(365\) 6.00000 0.314054
\(366\) 0 0
\(367\) 8.00000 0.417597 0.208798 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) 36.0000 1.87663
\(369\) −3.00000 −0.156174
\(370\) 0 0
\(371\) 24.0000 1.24602
\(372\) −4.00000 −0.207390
\(373\) −22.0000 −1.13912 −0.569558 0.821951i \(-0.692886\pi\)
−0.569558 + 0.821951i \(0.692886\pi\)
\(374\) 0 0
\(375\) −3.00000 −0.154919
\(376\) 0 0
\(377\) −6.00000 −0.309016
\(378\) 0 0
\(379\) 32.0000 1.64373 0.821865 0.569683i \(-0.192934\pi\)
0.821865 + 0.569683i \(0.192934\pi\)
\(380\) 6.00000 0.307794
\(381\) −13.0000 −0.666010
\(382\) 0 0
\(383\) −12.0000 −0.613171 −0.306586 0.951843i \(-0.599187\pi\)
−0.306586 + 0.951843i \(0.599187\pi\)
\(384\) 0 0
\(385\) 36.0000 1.83473
\(386\) 0 0
\(387\) −7.00000 −0.355830
\(388\) 32.0000 1.62455
\(389\) 36.0000 1.82527 0.912636 0.408773i \(-0.134043\pi\)
0.912636 + 0.408773i \(0.134043\pi\)
\(390\) 0 0
\(391\) −9.00000 −0.455150
\(392\) 0 0
\(393\) 3.00000 0.151330
\(394\) 0 0
\(395\) −30.0000 −1.50946
\(396\) 6.00000 0.301511
\(397\) 20.0000 1.00377 0.501886 0.864934i \(-0.332640\pi\)
0.501886 + 0.864934i \(0.332640\pi\)
\(398\) 0 0
\(399\) 4.00000 0.200250
\(400\) 16.0000 0.800000
\(401\) −15.0000 −0.749064 −0.374532 0.927214i \(-0.622197\pi\)
−0.374532 + 0.927214i \(0.622197\pi\)
\(402\) 0 0
\(403\) −2.00000 −0.0996271
\(404\) 0 0
\(405\) 3.00000 0.149071
\(406\) 0 0
\(407\) 12.0000 0.594818
\(408\) 0 0
\(409\) −19.0000 −0.939490 −0.469745 0.882802i \(-0.655654\pi\)
−0.469745 + 0.882802i \(0.655654\pi\)
\(410\) 0 0
\(411\) −6.00000 −0.295958
\(412\) −10.0000 −0.492665
\(413\) −24.0000 −1.18096
\(414\) 0 0
\(415\) −18.0000 −0.883585
\(416\) 0 0
\(417\) 2.00000 0.0979404
\(418\) 0 0
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 24.0000 1.17108
\(421\) −25.0000 −1.21843 −0.609213 0.793007i \(-0.708514\pi\)
−0.609213 + 0.793007i \(0.708514\pi\)
\(422\) 0 0
\(423\) −6.00000 −0.291730
\(424\) 0 0
\(425\) −4.00000 −0.194029
\(426\) 0 0
\(427\) −32.0000 −1.54859
\(428\) −18.0000 −0.870063
\(429\) 3.00000 0.144841
\(430\) 0 0
\(431\) −24.0000 −1.15604 −0.578020 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 4.00000 0.192450
\(433\) −1.00000 −0.0480569 −0.0240285 0.999711i \(-0.507649\pi\)
−0.0240285 + 0.999711i \(0.507649\pi\)
\(434\) 0 0
\(435\) 18.0000 0.863034
\(436\) −40.0000 −1.91565
\(437\) −9.00000 −0.430528
\(438\) 0 0
\(439\) −28.0000 −1.33637 −0.668184 0.743996i \(-0.732928\pi\)
−0.668184 + 0.743996i \(0.732928\pi\)
\(440\) 0 0
\(441\) 9.00000 0.428571
\(442\) 0 0
\(443\) 6.00000 0.285069 0.142534 0.989790i \(-0.454475\pi\)
0.142534 + 0.989790i \(0.454475\pi\)
\(444\) 8.00000 0.379663
\(445\) 0 0
\(446\) 0 0
\(447\) −18.0000 −0.851371
\(448\) 32.0000 1.51186
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 0 0
\(451\) 9.00000 0.423793
\(452\) 18.0000 0.846649
\(453\) 8.00000 0.375873
\(454\) 0 0
\(455\) 12.0000 0.562569
\(456\) 0 0
\(457\) −19.0000 −0.888783 −0.444391 0.895833i \(-0.646580\pi\)
−0.444391 + 0.895833i \(0.646580\pi\)
\(458\) 0 0
\(459\) −1.00000 −0.0466760
\(460\) −54.0000 −2.51776
\(461\) 30.0000 1.39724 0.698620 0.715493i \(-0.253798\pi\)
0.698620 + 0.715493i \(0.253798\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) 24.0000 1.11417
\(465\) 6.00000 0.278243
\(466\) 0 0
\(467\) 42.0000 1.94353 0.971764 0.235954i \(-0.0758216\pi\)
0.971764 + 0.235954i \(0.0758216\pi\)
\(468\) 2.00000 0.0924500
\(469\) 16.0000 0.738811
\(470\) 0 0
\(471\) 11.0000 0.506853
\(472\) 0 0
\(473\) 21.0000 0.965581
\(474\) 0 0
\(475\) −4.00000 −0.183533
\(476\) −8.00000 −0.366679
\(477\) −6.00000 −0.274721
\(478\) 0 0
\(479\) −27.0000 −1.23366 −0.616831 0.787096i \(-0.711584\pi\)
−0.616831 + 0.787096i \(0.711584\pi\)
\(480\) 0 0
\(481\) 4.00000 0.182384
\(482\) 0 0
\(483\) −36.0000 −1.63806
\(484\) 4.00000 0.181818
\(485\) −48.0000 −2.17957
\(486\) 0 0
\(487\) −22.0000 −0.996915 −0.498458 0.866914i \(-0.666100\pi\)
−0.498458 + 0.866914i \(0.666100\pi\)
\(488\) 0 0
\(489\) 2.00000 0.0904431
\(490\) 0 0
\(491\) −6.00000 −0.270776 −0.135388 0.990793i \(-0.543228\pi\)
−0.135388 + 0.990793i \(0.543228\pi\)
\(492\) 6.00000 0.270501
\(493\) −6.00000 −0.270226
\(494\) 0 0
\(495\) −9.00000 −0.404520
\(496\) 8.00000 0.359211
\(497\) −48.0000 −2.15309
\(498\) 0 0
\(499\) −22.0000 −0.984855 −0.492428 0.870353i \(-0.663890\pi\)
−0.492428 + 0.870353i \(0.663890\pi\)
\(500\) 6.00000 0.268328
\(501\) 21.0000 0.938211
\(502\) 0 0
\(503\) 15.0000 0.668817 0.334408 0.942428i \(-0.391463\pi\)
0.334408 + 0.942428i \(0.391463\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −12.0000 −0.532939
\(508\) 26.0000 1.15356
\(509\) 36.0000 1.59567 0.797836 0.602875i \(-0.205978\pi\)
0.797836 + 0.602875i \(0.205978\pi\)
\(510\) 0 0
\(511\) −8.00000 −0.353899
\(512\) 0 0
\(513\) −1.00000 −0.0441511
\(514\) 0 0
\(515\) 15.0000 0.660979
\(516\) 14.0000 0.616316
\(517\) 18.0000 0.791639
\(518\) 0 0
\(519\) 15.0000 0.658427
\(520\) 0 0
\(521\) 21.0000 0.920027 0.460013 0.887912i \(-0.347845\pi\)
0.460013 + 0.887912i \(0.347845\pi\)
\(522\) 0 0
\(523\) 20.0000 0.874539 0.437269 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(524\) −6.00000 −0.262111
\(525\) −16.0000 −0.698297
\(526\) 0 0
\(527\) −2.00000 −0.0871214
\(528\) −12.0000 −0.522233
\(529\) 58.0000 2.52174
\(530\) 0 0
\(531\) 6.00000 0.260378
\(532\) −8.00000 −0.346844
\(533\) 3.00000 0.129944
\(534\) 0 0
\(535\) 27.0000 1.16731
\(536\) 0 0
\(537\) −6.00000 −0.258919
\(538\) 0 0
\(539\) −27.0000 −1.16297
\(540\) −6.00000 −0.258199
\(541\) −16.0000 −0.687894 −0.343947 0.938989i \(-0.611764\pi\)
−0.343947 + 0.938989i \(0.611764\pi\)
\(542\) 0 0
\(543\) 14.0000 0.600798
\(544\) 0 0
\(545\) 60.0000 2.57012
\(546\) 0 0
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) 12.0000 0.512615
\(549\) 8.00000 0.341432
\(550\) 0 0
\(551\) −6.00000 −0.255609
\(552\) 0 0
\(553\) 40.0000 1.70097
\(554\) 0 0
\(555\) −12.0000 −0.509372
\(556\) −4.00000 −0.169638
\(557\) −30.0000 −1.27114 −0.635570 0.772043i \(-0.719235\pi\)
−0.635570 + 0.772043i \(0.719235\pi\)
\(558\) 0 0
\(559\) 7.00000 0.296068
\(560\) −48.0000 −2.02837
\(561\) 3.00000 0.126660
\(562\) 0 0
\(563\) −30.0000 −1.26435 −0.632175 0.774826i \(-0.717837\pi\)
−0.632175 + 0.774826i \(0.717837\pi\)
\(564\) 12.0000 0.505291
\(565\) −27.0000 −1.13590
\(566\) 0 0
\(567\) −4.00000 −0.167984
\(568\) 0 0
\(569\) −24.0000 −1.00613 −0.503066 0.864248i \(-0.667795\pi\)
−0.503066 + 0.864248i \(0.667795\pi\)
\(570\) 0 0
\(571\) 8.00000 0.334790 0.167395 0.985890i \(-0.446465\pi\)
0.167395 + 0.985890i \(0.446465\pi\)
\(572\) −6.00000 −0.250873
\(573\) 18.0000 0.751961
\(574\) 0 0
\(575\) 36.0000 1.50130
\(576\) −8.00000 −0.333333
\(577\) −7.00000 −0.291414 −0.145707 0.989328i \(-0.546546\pi\)
−0.145707 + 0.989328i \(0.546546\pi\)
\(578\) 0 0
\(579\) −22.0000 −0.914289
\(580\) −36.0000 −1.49482
\(581\) 24.0000 0.995688
\(582\) 0 0
\(583\) 18.0000 0.745484
\(584\) 0 0
\(585\) −3.00000 −0.124035
\(586\) 0 0
\(587\) −36.0000 −1.48588 −0.742940 0.669359i \(-0.766569\pi\)
−0.742940 + 0.669359i \(0.766569\pi\)
\(588\) −18.0000 −0.742307
\(589\) −2.00000 −0.0824086
\(590\) 0 0
\(591\) 3.00000 0.123404
\(592\) −16.0000 −0.657596
\(593\) −18.0000 −0.739171 −0.369586 0.929197i \(-0.620500\pi\)
−0.369586 + 0.929197i \(0.620500\pi\)
\(594\) 0 0
\(595\) 12.0000 0.491952
\(596\) 36.0000 1.47462
\(597\) −16.0000 −0.654836
\(598\) 0 0
\(599\) −6.00000 −0.245153 −0.122577 0.992459i \(-0.539116\pi\)
−0.122577 + 0.992459i \(0.539116\pi\)
\(600\) 0 0
\(601\) 38.0000 1.55005 0.775026 0.631929i \(-0.217737\pi\)
0.775026 + 0.631929i \(0.217737\pi\)
\(602\) 0 0
\(603\) −4.00000 −0.162893
\(604\) −16.0000 −0.651031
\(605\) −6.00000 −0.243935
\(606\) 0 0
\(607\) 38.0000 1.54237 0.771186 0.636610i \(-0.219664\pi\)
0.771186 + 0.636610i \(0.219664\pi\)
\(608\) 0 0
\(609\) −24.0000 −0.972529
\(610\) 0 0
\(611\) 6.00000 0.242734
\(612\) 2.00000 0.0808452
\(613\) 11.0000 0.444286 0.222143 0.975014i \(-0.428695\pi\)
0.222143 + 0.975014i \(0.428695\pi\)
\(614\) 0 0
\(615\) −9.00000 −0.362915
\(616\) 0 0
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) 0 0
\(619\) −10.0000 −0.401934 −0.200967 0.979598i \(-0.564408\pi\)
−0.200967 + 0.979598i \(0.564408\pi\)
\(620\) −12.0000 −0.481932
\(621\) 9.00000 0.361158
\(622\) 0 0
\(623\) 0 0
\(624\) −4.00000 −0.160128
\(625\) −29.0000 −1.16000
\(626\) 0 0
\(627\) 3.00000 0.119808
\(628\) −22.0000 −0.877896
\(629\) 4.00000 0.159490
\(630\) 0 0
\(631\) −37.0000 −1.47295 −0.736473 0.676467i \(-0.763510\pi\)
−0.736473 + 0.676467i \(0.763510\pi\)
\(632\) 0 0
\(633\) 2.00000 0.0794929
\(634\) 0 0
\(635\) −39.0000 −1.54767
\(636\) 12.0000 0.475831
\(637\) −9.00000 −0.356593
\(638\) 0 0
\(639\) 12.0000 0.474713
\(640\) 0 0
\(641\) −33.0000 −1.30342 −0.651711 0.758468i \(-0.725948\pi\)
−0.651711 + 0.758468i \(0.725948\pi\)
\(642\) 0 0
\(643\) 32.0000 1.26196 0.630978 0.775800i \(-0.282654\pi\)
0.630978 + 0.775800i \(0.282654\pi\)
\(644\) 72.0000 2.83720
\(645\) −21.0000 −0.826874
\(646\) 0 0
\(647\) 18.0000 0.707653 0.353827 0.935311i \(-0.384880\pi\)
0.353827 + 0.935311i \(0.384880\pi\)
\(648\) 0 0
\(649\) −18.0000 −0.706562
\(650\) 0 0
\(651\) −8.00000 −0.313545
\(652\) −4.00000 −0.156652
\(653\) 27.0000 1.05659 0.528296 0.849060i \(-0.322831\pi\)
0.528296 + 0.849060i \(0.322831\pi\)
\(654\) 0 0
\(655\) 9.00000 0.351659
\(656\) −12.0000 −0.468521
\(657\) 2.00000 0.0780274
\(658\) 0 0
\(659\) 6.00000 0.233727 0.116863 0.993148i \(-0.462716\pi\)
0.116863 + 0.993148i \(0.462716\pi\)
\(660\) 18.0000 0.700649
\(661\) −31.0000 −1.20576 −0.602880 0.797832i \(-0.705980\pi\)
−0.602880 + 0.797832i \(0.705980\pi\)
\(662\) 0 0
\(663\) 1.00000 0.0388368
\(664\) 0 0
\(665\) 12.0000 0.465340
\(666\) 0 0
\(667\) 54.0000 2.09089
\(668\) −42.0000 −1.62503
\(669\) −1.00000 −0.0386622
\(670\) 0 0
\(671\) −24.0000 −0.926510
\(672\) 0 0
\(673\) −22.0000 −0.848038 −0.424019 0.905653i \(-0.639381\pi\)
−0.424019 + 0.905653i \(0.639381\pi\)
\(674\) 0 0
\(675\) 4.00000 0.153960
\(676\) 24.0000 0.923077
\(677\) −27.0000 −1.03769 −0.518847 0.854867i \(-0.673639\pi\)
−0.518847 + 0.854867i \(0.673639\pi\)
\(678\) 0 0
\(679\) 64.0000 2.45609
\(680\) 0 0
\(681\) 3.00000 0.114960
\(682\) 0 0
\(683\) 3.00000 0.114792 0.0573959 0.998351i \(-0.481720\pi\)
0.0573959 + 0.998351i \(0.481720\pi\)
\(684\) 2.00000 0.0764719
\(685\) −18.0000 −0.687745
\(686\) 0 0
\(687\) 14.0000 0.534133
\(688\) −28.0000 −1.06749
\(689\) 6.00000 0.228582
\(690\) 0 0
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) −30.0000 −1.14043
\(693\) 12.0000 0.455842
\(694\) 0 0
\(695\) 6.00000 0.227593
\(696\) 0 0
\(697\) 3.00000 0.113633
\(698\) 0 0
\(699\) 21.0000 0.794293
\(700\) 32.0000 1.20949
\(701\) 24.0000 0.906467 0.453234 0.891392i \(-0.350270\pi\)
0.453234 + 0.891392i \(0.350270\pi\)
\(702\) 0 0
\(703\) 4.00000 0.150863
\(704\) 24.0000 0.904534
\(705\) −18.0000 −0.677919
\(706\) 0 0
\(707\) 0 0
\(708\) −12.0000 −0.450988
\(709\) 14.0000 0.525781 0.262891 0.964826i \(-0.415324\pi\)
0.262891 + 0.964826i \(0.415324\pi\)
\(710\) 0 0
\(711\) −10.0000 −0.375029
\(712\) 0 0
\(713\) 18.0000 0.674105
\(714\) 0 0
\(715\) 9.00000 0.336581
\(716\) 12.0000 0.448461
\(717\) −12.0000 −0.448148
\(718\) 0 0
\(719\) 3.00000 0.111881 0.0559406 0.998434i \(-0.482184\pi\)
0.0559406 + 0.998434i \(0.482184\pi\)
\(720\) 12.0000 0.447214
\(721\) −20.0000 −0.744839
\(722\) 0 0
\(723\) 8.00000 0.297523
\(724\) −28.0000 −1.04061
\(725\) 24.0000 0.891338
\(726\) 0 0
\(727\) 8.00000 0.296704 0.148352 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 7.00000 0.258904
\(732\) −16.0000 −0.591377
\(733\) 2.00000 0.0738717 0.0369358 0.999318i \(-0.488240\pi\)
0.0369358 + 0.999318i \(0.488240\pi\)
\(734\) 0 0
\(735\) 27.0000 0.995910
\(736\) 0 0
\(737\) 12.0000 0.442026
\(738\) 0 0
\(739\) −1.00000 −0.0367856 −0.0183928 0.999831i \(-0.505855\pi\)
−0.0183928 + 0.999831i \(0.505855\pi\)
\(740\) 24.0000 0.882258
\(741\) 1.00000 0.0367359
\(742\) 0 0
\(743\) 24.0000 0.880475 0.440237 0.897881i \(-0.354894\pi\)
0.440237 + 0.897881i \(0.354894\pi\)
\(744\) 0 0
\(745\) −54.0000 −1.97841
\(746\) 0 0
\(747\) −6.00000 −0.219529
\(748\) −6.00000 −0.219382
\(749\) −36.0000 −1.31541
\(750\) 0 0
\(751\) −46.0000 −1.67856 −0.839282 0.543696i \(-0.817024\pi\)
−0.839282 + 0.543696i \(0.817024\pi\)
\(752\) −24.0000 −0.875190
\(753\) 24.0000 0.874609
\(754\) 0 0
\(755\) 24.0000 0.873449
\(756\) 8.00000 0.290957
\(757\) −43.0000 −1.56286 −0.781431 0.623992i \(-0.785510\pi\)
−0.781431 + 0.623992i \(0.785510\pi\)
\(758\) 0 0
\(759\) −27.0000 −0.980038
\(760\) 0 0
\(761\) 30.0000 1.08750 0.543750 0.839248i \(-0.317004\pi\)
0.543750 + 0.839248i \(0.317004\pi\)
\(762\) 0 0
\(763\) −80.0000 −2.89619
\(764\) −36.0000 −1.30243
\(765\) −3.00000 −0.108465
\(766\) 0 0
\(767\) −6.00000 −0.216647
\(768\) 16.0000 0.577350
\(769\) 41.0000 1.47850 0.739249 0.673432i \(-0.235181\pi\)
0.739249 + 0.673432i \(0.235181\pi\)
\(770\) 0 0
\(771\) 12.0000 0.432169
\(772\) 44.0000 1.58359
\(773\) 24.0000 0.863220 0.431610 0.902060i \(-0.357946\pi\)
0.431610 + 0.902060i \(0.357946\pi\)
\(774\) 0 0
\(775\) 8.00000 0.287368
\(776\) 0 0
\(777\) 16.0000 0.573997
\(778\) 0 0
\(779\) 3.00000 0.107486
\(780\) 6.00000 0.214834
\(781\) −36.0000 −1.28818
\(782\) 0 0
\(783\) 6.00000 0.214423
\(784\) 36.0000 1.28571
\(785\) 33.0000 1.17782
\(786\) 0 0
\(787\) −40.0000 −1.42585 −0.712923 0.701242i \(-0.752629\pi\)
−0.712923 + 0.701242i \(0.752629\pi\)
\(788\) −6.00000 −0.213741
\(789\) 12.0000 0.427211
\(790\) 0 0
\(791\) 36.0000 1.28001
\(792\) 0 0
\(793\) −8.00000 −0.284088
\(794\) 0 0
\(795\) −18.0000 −0.638394
\(796\) 32.0000 1.13421
\(797\) −48.0000 −1.70025 −0.850124 0.526583i \(-0.823473\pi\)
−0.850124 + 0.526583i \(0.823473\pi\)
\(798\) 0 0
\(799\) 6.00000 0.212265
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −6.00000 −0.211735
\(804\) 8.00000 0.282138
\(805\) −108.000 −3.80650
\(806\) 0 0
\(807\) −15.0000 −0.528025
\(808\) 0 0
\(809\) −51.0000 −1.79306 −0.896532 0.442978i \(-0.853922\pi\)
−0.896532 + 0.442978i \(0.853922\pi\)
\(810\) 0 0
\(811\) −10.0000 −0.351147 −0.175574 0.984466i \(-0.556178\pi\)
−0.175574 + 0.984466i \(0.556178\pi\)
\(812\) 48.0000 1.68447
\(813\) 11.0000 0.385787
\(814\) 0 0
\(815\) 6.00000 0.210171
\(816\) −4.00000 −0.140028
\(817\) 7.00000 0.244899
\(818\) 0 0
\(819\) 4.00000 0.139771
\(820\) 18.0000 0.628587
\(821\) −21.0000 −0.732905 −0.366453 0.930437i \(-0.619428\pi\)
−0.366453 + 0.930437i \(0.619428\pi\)
\(822\) 0 0
\(823\) −28.0000 −0.976019 −0.488009 0.872838i \(-0.662277\pi\)
−0.488009 + 0.872838i \(0.662277\pi\)
\(824\) 0 0
\(825\) −12.0000 −0.417786
\(826\) 0 0
\(827\) −21.0000 −0.730242 −0.365121 0.930960i \(-0.618972\pi\)
−0.365121 + 0.930960i \(0.618972\pi\)
\(828\) −18.0000 −0.625543
\(829\) 14.0000 0.486240 0.243120 0.969996i \(-0.421829\pi\)
0.243120 + 0.969996i \(0.421829\pi\)
\(830\) 0 0
\(831\) 2.00000 0.0693792
\(832\) 8.00000 0.277350
\(833\) −9.00000 −0.311832
\(834\) 0 0
\(835\) 63.0000 2.18020
\(836\) −6.00000 −0.207514
\(837\) 2.00000 0.0691301
\(838\) 0 0
\(839\) −57.0000 −1.96786 −0.983929 0.178559i \(-0.942857\pi\)
−0.983929 + 0.178559i \(0.942857\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 0 0
\(843\) 12.0000 0.413302
\(844\) −4.00000 −0.137686
\(845\) −36.0000 −1.23844
\(846\) 0 0
\(847\) 8.00000 0.274883
\(848\) −24.0000 −0.824163
\(849\) −10.0000 −0.343199
\(850\) 0 0
\(851\) −36.0000 −1.23406
\(852\) −24.0000 −0.822226
\(853\) 26.0000 0.890223 0.445112 0.895475i \(-0.353164\pi\)
0.445112 + 0.895475i \(0.353164\pi\)
\(854\) 0 0
\(855\) −3.00000 −0.102598
\(856\) 0 0
\(857\) −18.0000 −0.614868 −0.307434 0.951569i \(-0.599470\pi\)
−0.307434 + 0.951569i \(0.599470\pi\)
\(858\) 0 0
\(859\) 20.0000 0.682391 0.341196 0.939992i \(-0.389168\pi\)
0.341196 + 0.939992i \(0.389168\pi\)
\(860\) 42.0000 1.43219
\(861\) 12.0000 0.408959
\(862\) 0 0
\(863\) 24.0000 0.816970 0.408485 0.912765i \(-0.366057\pi\)
0.408485 + 0.912765i \(0.366057\pi\)
\(864\) 0 0
\(865\) 45.0000 1.53005
\(866\) 0 0
\(867\) 1.00000 0.0339618
\(868\) 16.0000 0.543075
\(869\) 30.0000 1.01768
\(870\) 0 0
\(871\) 4.00000 0.135535
\(872\) 0 0
\(873\) −16.0000 −0.541518
\(874\) 0 0
\(875\) 12.0000 0.405674
\(876\) −4.00000 −0.135147
\(877\) 14.0000 0.472746 0.236373 0.971662i \(-0.424041\pi\)
0.236373 + 0.971662i \(0.424041\pi\)
\(878\) 0 0
\(879\) −24.0000 −0.809500
\(880\) −36.0000 −1.21356
\(881\) 18.0000 0.606435 0.303218 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(882\) 0 0
\(883\) 11.0000 0.370179 0.185090 0.982722i \(-0.440742\pi\)
0.185090 + 0.982722i \(0.440742\pi\)
\(884\) −2.00000 −0.0672673
\(885\) 18.0000 0.605063
\(886\) 0 0
\(887\) 39.0000 1.30949 0.654746 0.755849i \(-0.272776\pi\)
0.654746 + 0.755849i \(0.272776\pi\)
\(888\) 0 0
\(889\) 52.0000 1.74402
\(890\) 0 0
\(891\) −3.00000 −0.100504
\(892\) 2.00000 0.0669650
\(893\) 6.00000 0.200782
\(894\) 0 0
\(895\) −18.0000 −0.601674
\(896\) 0 0
\(897\) −9.00000 −0.300501
\(898\) 0 0
\(899\) 12.0000 0.400222
\(900\) −8.00000 −0.266667
\(901\) 6.00000 0.199889
\(902\) 0 0
\(903\) 28.0000 0.931782
\(904\) 0 0
\(905\) 42.0000 1.39613
\(906\) 0 0
\(907\) 2.00000 0.0664089 0.0332045 0.999449i \(-0.489429\pi\)
0.0332045 + 0.999449i \(0.489429\pi\)
\(908\) −6.00000 −0.199117
\(909\) 0 0
\(910\) 0 0
\(911\) −27.0000 −0.894550 −0.447275 0.894397i \(-0.647605\pi\)
−0.447275 + 0.894397i \(0.647605\pi\)
\(912\) −4.00000 −0.132453
\(913\) 18.0000 0.595713
\(914\) 0 0
\(915\) 24.0000 0.793416
\(916\) −28.0000 −0.925146
\(917\) −12.0000 −0.396275
\(918\) 0 0
\(919\) 11.0000 0.362857 0.181428 0.983404i \(-0.441928\pi\)
0.181428 + 0.983404i \(0.441928\pi\)
\(920\) 0 0
\(921\) 20.0000 0.659022
\(922\) 0 0
\(923\) −12.0000 −0.394985
\(924\) −24.0000 −0.789542
\(925\) −16.0000 −0.526077
\(926\) 0 0
\(927\) 5.00000 0.164222
\(928\) 0 0
\(929\) 15.0000 0.492134 0.246067 0.969253i \(-0.420862\pi\)
0.246067 + 0.969253i \(0.420862\pi\)
\(930\) 0 0
\(931\) −9.00000 −0.294963
\(932\) −42.0000 −1.37576
\(933\) −24.0000 −0.785725
\(934\) 0 0
\(935\) 9.00000 0.294331
\(936\) 0 0
\(937\) −22.0000 −0.718709 −0.359354 0.933201i \(-0.617003\pi\)
−0.359354 + 0.933201i \(0.617003\pi\)
\(938\) 0 0
\(939\) −16.0000 −0.522140
\(940\) 36.0000 1.17419
\(941\) 18.0000 0.586783 0.293392 0.955992i \(-0.405216\pi\)
0.293392 + 0.955992i \(0.405216\pi\)
\(942\) 0 0
\(943\) −27.0000 −0.879241
\(944\) 24.0000 0.781133
\(945\) −12.0000 −0.390360
\(946\) 0 0
\(947\) 36.0000 1.16984 0.584921 0.811090i \(-0.301125\pi\)
0.584921 + 0.811090i \(0.301125\pi\)
\(948\) 20.0000 0.649570
\(949\) −2.00000 −0.0649227
\(950\) 0 0
\(951\) −6.00000 −0.194563
\(952\) 0 0
\(953\) 36.0000 1.16615 0.583077 0.812417i \(-0.301849\pi\)
0.583077 + 0.812417i \(0.301849\pi\)
\(954\) 0 0
\(955\) 54.0000 1.74740
\(956\) 24.0000 0.776215
\(957\) −18.0000 −0.581857
\(958\) 0 0
\(959\) 24.0000 0.775000
\(960\) −24.0000 −0.774597
\(961\) −27.0000 −0.870968
\(962\) 0 0
\(963\) 9.00000 0.290021
\(964\) −16.0000 −0.515325
\(965\) −66.0000 −2.12462
\(966\) 0 0
\(967\) 41.0000 1.31847 0.659236 0.751936i \(-0.270880\pi\)
0.659236 + 0.751936i \(0.270880\pi\)
\(968\) 0 0
\(969\) 1.00000 0.0321246
\(970\) 0 0
\(971\) 6.00000 0.192549 0.0962746 0.995355i \(-0.469307\pi\)
0.0962746 + 0.995355i \(0.469307\pi\)
\(972\) −2.00000 −0.0641500
\(973\) −8.00000 −0.256468
\(974\) 0 0
\(975\) −4.00000 −0.128103
\(976\) 32.0000 1.02430
\(977\) −30.0000 −0.959785 −0.479893 0.877327i \(-0.659324\pi\)
−0.479893 + 0.877327i \(0.659324\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −54.0000 −1.72497
\(981\) 20.0000 0.638551
\(982\) 0 0
\(983\) −9.00000 −0.287055 −0.143528 0.989646i \(-0.545845\pi\)
−0.143528 + 0.989646i \(0.545845\pi\)
\(984\) 0 0
\(985\) 9.00000 0.286764
\(986\) 0 0
\(987\) 24.0000 0.763928
\(988\) −2.00000 −0.0636285
\(989\) −63.0000 −2.00328
\(990\) 0 0
\(991\) −52.0000 −1.65183 −0.825917 0.563791i \(-0.809342\pi\)
−0.825917 + 0.563791i \(0.809342\pi\)
\(992\) 0 0
\(993\) −13.0000 −0.412543
\(994\) 0 0
\(995\) −48.0000 −1.52170
\(996\) 12.0000 0.380235
\(997\) 62.0000 1.96356 0.981780 0.190022i \(-0.0608559\pi\)
0.981780 + 0.190022i \(0.0608559\pi\)
\(998\) 0 0
\(999\) −4.00000 −0.126554
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 \(a_p\))