Properties

Label 4012.2.a.c.1.1
Level 4012
Weight 2
Character 4012.1
Self dual Yes
Analytic conductor 32.036
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4012 = 2^{2} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4012.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0359812909\)
Analytic rank: \(1\)
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 \(\chi\) = 4012.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(-3.00000 q^{5}\) \(+1.00000 q^{7}\) \(-2.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(-3.00000 q^{5}\) \(+1.00000 q^{7}\) \(-2.00000 q^{9}\) \(+2.00000 q^{11}\) \(-2.00000 q^{13}\) \(+3.00000 q^{15}\) \(-1.00000 q^{17}\) \(+1.00000 q^{19}\) \(-1.00000 q^{21}\) \(+8.00000 q^{23}\) \(+4.00000 q^{25}\) \(+5.00000 q^{27}\) \(-1.00000 q^{29}\) \(-2.00000 q^{33}\) \(-3.00000 q^{35}\) \(-2.00000 q^{37}\) \(+2.00000 q^{39}\) \(-7.00000 q^{41}\) \(+8.00000 q^{43}\) \(+6.00000 q^{45}\) \(+8.00000 q^{47}\) \(-6.00000 q^{49}\) \(+1.00000 q^{51}\) \(+3.00000 q^{53}\) \(-6.00000 q^{55}\) \(-1.00000 q^{57}\) \(+1.00000 q^{59}\) \(-2.00000 q^{63}\) \(+6.00000 q^{65}\) \(+14.0000 q^{67}\) \(-8.00000 q^{69}\) \(-8.00000 q^{71}\) \(-10.0000 q^{73}\) \(-4.00000 q^{75}\) \(+2.00000 q^{77}\) \(-5.00000 q^{79}\) \(+1.00000 q^{81}\) \(-6.00000 q^{83}\) \(+3.00000 q^{85}\) \(+1.00000 q^{87}\) \(-2.00000 q^{89}\) \(-2.00000 q^{91}\) \(-3.00000 q^{95}\) \(+8.00000 q^{97}\) \(-4.00000 q^{99}\) \(+O(q^{100})\)

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
\(3\) −1.00000 −0.577350 −0.288675 0.957427i \(-0.593215\pi\)
−0.288675 + 0.957427i \(0.593215\pi\)
\(4\) 0 0
\(5\) −3.00000 −1.34164 −0.670820 0.741620i \(-0.734058\pi\)
−0.670820 + 0.741620i \(0.734058\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964 0.188982 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) 0 0
\(9\) −2.00000 −0.666667
\(10\) 0 0
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 0 0
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 3.00000 0.774597
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) 1.00000 0.229416 0.114708 0.993399i \(-0.463407\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) 0 0
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) 8.00000 1.66812 0.834058 0.551677i \(-0.186012\pi\)
0.834058 + 0.551677i \(0.186012\pi\)
\(24\) 0 0
\(25\) 4.00000 0.800000
\(26\) 0 0
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) −1.00000 −0.185695 −0.0928477 0.995680i \(-0.529597\pi\)
−0.0928477 + 0.995680i \(0.529597\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) −2.00000 −0.348155
\(34\) 0 0
\(35\) −3.00000 −0.507093
\(36\) 0 0
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 0 0
\(39\) 2.00000 0.320256
\(40\) 0 0
\(41\) −7.00000 −1.09322 −0.546608 0.837389i \(-0.684081\pi\)
−0.546608 + 0.837389i \(0.684081\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) 6.00000 0.894427
\(46\) 0 0
\(47\) 8.00000 1.16692 0.583460 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) 0 0
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) 1.00000 0.140028
\(52\) 0 0
\(53\) 3.00000 0.412082 0.206041 0.978543i \(-0.433942\pi\)
0.206041 + 0.978543i \(0.433942\pi\)
\(54\) 0 0
\(55\) −6.00000 −0.809040
\(56\) 0 0
\(57\) −1.00000 −0.132453
\(58\) 0 0
\(59\) 1.00000 0.130189
\(60\) 0 0
\(61\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) 0 0
\(63\) −2.00000 −0.251976
\(64\) 0 0
\(65\) 6.00000 0.744208
\(66\) 0 0
\(67\) 14.0000 1.71037 0.855186 0.518321i \(-0.173443\pi\)
0.855186 + 0.518321i \(0.173443\pi\)
\(68\) 0 0
\(69\) −8.00000 −0.963087
\(70\) 0 0
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) −10.0000 −1.17041 −0.585206 0.810885i \(-0.698986\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 0 0
\(75\) −4.00000 −0.461880
\(76\) 0 0
\(77\) 2.00000 0.227921
\(78\) 0 0
\(79\) −5.00000 −0.562544 −0.281272 0.959628i \(-0.590756\pi\)
−0.281272 + 0.959628i \(0.590756\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0 0
\(85\) 3.00000 0.325396
\(86\) 0 0
\(87\) 1.00000 0.107211
\(88\) 0 0
\(89\) −2.00000 −0.212000 −0.106000 0.994366i \(-0.533804\pi\)
−0.106000 + 0.994366i \(0.533804\pi\)
\(90\) 0 0
\(91\) −2.00000 −0.209657
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −3.00000 −0.307794
\(96\) 0 0
\(97\) 8.00000 0.812277 0.406138 0.913812i \(-0.366875\pi\)
0.406138 + 0.913812i \(0.366875\pi\)
\(98\) 0 0
\(99\) −4.00000 −0.402015
\(100\) 0 0
\(101\) −12.0000 −1.19404 −0.597022 0.802225i \(-0.703650\pi\)
−0.597022 + 0.802225i \(0.703650\pi\)
\(102\) 0 0
\(103\) −6.00000 −0.591198 −0.295599 0.955312i \(-0.595519\pi\)
−0.295599 + 0.955312i \(0.595519\pi\)
\(104\) 0 0
\(105\) 3.00000 0.292770
\(106\) 0 0
\(107\) −13.0000 −1.25676 −0.628379 0.777908i \(-0.716281\pi\)
−0.628379 + 0.777908i \(0.716281\pi\)
\(108\) 0 0
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 0 0
\(111\) 2.00000 0.189832
\(112\) 0 0
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 0 0
\(115\) −24.0000 −2.23801
\(116\) 0 0
\(117\) 4.00000 0.369800
\(118\) 0 0
\(119\) −1.00000 −0.0916698
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) 7.00000 0.631169
\(124\) 0 0
\(125\) 3.00000 0.268328
\(126\) 0 0
\(127\) −3.00000 −0.266207 −0.133103 0.991102i \(-0.542494\pi\)
−0.133103 + 0.991102i \(0.542494\pi\)
\(128\) 0 0
\(129\) −8.00000 −0.704361
\(130\) 0 0
\(131\) −4.00000 −0.349482 −0.174741 0.984614i \(-0.555909\pi\)
−0.174741 + 0.984614i \(0.555909\pi\)
\(132\) 0 0
\(133\) 1.00000 0.0867110
\(134\) 0 0
\(135\) −15.0000 −1.29099
\(136\) 0 0
\(137\) −5.00000 −0.427179 −0.213589 0.976924i \(-0.568515\pi\)
−0.213589 + 0.976924i \(0.568515\pi\)
\(138\) 0 0
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) 0 0
\(141\) −8.00000 −0.673722
\(142\) 0 0
\(143\) −4.00000 −0.334497
\(144\) 0 0
\(145\) 3.00000 0.249136
\(146\) 0 0
\(147\) 6.00000 0.494872
\(148\) 0 0
\(149\) −16.0000 −1.31077 −0.655386 0.755295i \(-0.727494\pi\)
−0.655386 + 0.755295i \(0.727494\pi\)
\(150\) 0 0
\(151\) 12.0000 0.976546 0.488273 0.872691i \(-0.337627\pi\)
0.488273 + 0.872691i \(0.337627\pi\)
\(152\) 0 0
\(153\) 2.00000 0.161690
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −14.0000 −1.11732 −0.558661 0.829396i \(-0.688685\pi\)
−0.558661 + 0.829396i \(0.688685\pi\)
\(158\) 0 0
\(159\) −3.00000 −0.237915
\(160\) 0 0
\(161\) 8.00000 0.630488
\(162\) 0 0
\(163\) 16.0000 1.25322 0.626608 0.779334i \(-0.284443\pi\)
0.626608 + 0.779334i \(0.284443\pi\)
\(164\) 0 0
\(165\) 6.00000 0.467099
\(166\) 0 0
\(167\) 5.00000 0.386912 0.193456 0.981109i \(-0.438030\pi\)
0.193456 + 0.981109i \(0.438030\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) −2.00000 −0.152944
\(172\) 0 0
\(173\) −16.0000 −1.21646 −0.608229 0.793762i \(-0.708120\pi\)
−0.608229 + 0.793762i \(0.708120\pi\)
\(174\) 0 0
\(175\) 4.00000 0.302372
\(176\) 0 0
\(177\) −1.00000 −0.0751646
\(178\) 0 0
\(179\) −6.00000 −0.448461 −0.224231 0.974536i \(-0.571987\pi\)
−0.224231 + 0.974536i \(0.571987\pi\)
\(180\) 0 0
\(181\) 3.00000 0.222988 0.111494 0.993765i \(-0.464436\pi\)
0.111494 + 0.993765i \(0.464436\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 6.00000 0.441129
\(186\) 0 0
\(187\) −2.00000 −0.146254
\(188\) 0 0
\(189\) 5.00000 0.363696
\(190\) 0 0
\(191\) −10.0000 −0.723575 −0.361787 0.932261i \(-0.617833\pi\)
−0.361787 + 0.932261i \(0.617833\pi\)
\(192\) 0 0
\(193\) −11.0000 −0.791797 −0.395899 0.918294i \(-0.629567\pi\)
−0.395899 + 0.918294i \(0.629567\pi\)
\(194\) 0 0
\(195\) −6.00000 −0.429669
\(196\) 0 0
\(197\) 10.0000 0.712470 0.356235 0.934396i \(-0.384060\pi\)
0.356235 + 0.934396i \(0.384060\pi\)
\(198\) 0 0
\(199\) −19.0000 −1.34687 −0.673437 0.739244i \(-0.735183\pi\)
−0.673437 + 0.739244i \(0.735183\pi\)
\(200\) 0 0
\(201\) −14.0000 −0.987484
\(202\) 0 0
\(203\) −1.00000 −0.0701862
\(204\) 0 0
\(205\) 21.0000 1.46670
\(206\) 0 0
\(207\) −16.0000 −1.11208
\(208\) 0 0
\(209\) 2.00000 0.138343
\(210\) 0 0
\(211\) 2.00000 0.137686 0.0688428 0.997628i \(-0.478069\pi\)
0.0688428 + 0.997628i \(0.478069\pi\)
\(212\) 0 0
\(213\) 8.00000 0.548151
\(214\) 0 0
\(215\) −24.0000 −1.63679
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 10.0000 0.675737
\(220\) 0 0
\(221\) 2.00000 0.134535
\(222\) 0 0
\(223\) −24.0000 −1.60716 −0.803579 0.595198i \(-0.797074\pi\)
−0.803579 + 0.595198i \(0.797074\pi\)
\(224\) 0 0
\(225\) −8.00000 −0.533333
\(226\) 0 0
\(227\) −24.0000 −1.59294 −0.796468 0.604681i \(-0.793301\pi\)
−0.796468 + 0.604681i \(0.793301\pi\)
\(228\) 0 0
\(229\) 20.0000 1.32164 0.660819 0.750546i \(-0.270209\pi\)
0.660819 + 0.750546i \(0.270209\pi\)
\(230\) 0 0
\(231\) −2.00000 −0.131590
\(232\) 0 0
\(233\) −14.0000 −0.917170 −0.458585 0.888650i \(-0.651644\pi\)
−0.458585 + 0.888650i \(0.651644\pi\)
\(234\) 0 0
\(235\) −24.0000 −1.56559
\(236\) 0 0
\(237\) 5.00000 0.324785
\(238\) 0 0
\(239\) 7.00000 0.452792 0.226396 0.974035i \(-0.427306\pi\)
0.226396 + 0.974035i \(0.427306\pi\)
\(240\) 0 0
\(241\) −17.0000 −1.09507 −0.547533 0.836784i \(-0.684433\pi\)
−0.547533 + 0.836784i \(0.684433\pi\)
\(242\) 0 0
\(243\) −16.0000 −1.02640
\(244\) 0 0
\(245\) 18.0000 1.14998
\(246\) 0 0
\(247\) −2.00000 −0.127257
\(248\) 0 0
\(249\) 6.00000 0.380235
\(250\) 0 0
\(251\) −9.00000 −0.568075 −0.284037 0.958813i \(-0.591674\pi\)
−0.284037 + 0.958813i \(0.591674\pi\)
\(252\) 0 0
\(253\) 16.0000 1.00591
\(254\) 0 0
\(255\) −3.00000 −0.187867
\(256\) 0 0
\(257\) −23.0000 −1.43470 −0.717350 0.696713i \(-0.754645\pi\)
−0.717350 + 0.696713i \(0.754645\pi\)
\(258\) 0 0
\(259\) −2.00000 −0.124274
\(260\) 0 0
\(261\) 2.00000 0.123797
\(262\) 0 0
\(263\) 3.00000 0.184988 0.0924940 0.995713i \(-0.470516\pi\)
0.0924940 + 0.995713i \(0.470516\pi\)
\(264\) 0 0
\(265\) −9.00000 −0.552866
\(266\) 0 0
\(267\) 2.00000 0.122398
\(268\) 0 0
\(269\) 2.00000 0.121942 0.0609711 0.998140i \(-0.480580\pi\)
0.0609711 + 0.998140i \(0.480580\pi\)
\(270\) 0 0
\(271\) −3.00000 −0.182237 −0.0911185 0.995840i \(-0.529044\pi\)
−0.0911185 + 0.995840i \(0.529044\pi\)
\(272\) 0 0
\(273\) 2.00000 0.121046
\(274\) 0 0
\(275\) 8.00000 0.482418
\(276\) 0 0
\(277\) −23.0000 −1.38194 −0.690968 0.722885i \(-0.742815\pi\)
−0.690968 + 0.722885i \(0.742815\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −17.0000 −1.01413 −0.507067 0.861906i \(-0.669271\pi\)
−0.507067 + 0.861906i \(0.669271\pi\)
\(282\) 0 0
\(283\) 18.0000 1.06999 0.534994 0.844856i \(-0.320314\pi\)
0.534994 + 0.844856i \(0.320314\pi\)
\(284\) 0 0
\(285\) 3.00000 0.177705
\(286\) 0 0
\(287\) −7.00000 −0.413197
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) −8.00000 −0.468968
\(292\) 0 0
\(293\) −23.0000 −1.34367 −0.671837 0.740699i \(-0.734495\pi\)
−0.671837 + 0.740699i \(0.734495\pi\)
\(294\) 0 0
\(295\) −3.00000 −0.174667
\(296\) 0 0
\(297\) 10.0000 0.580259
\(298\) 0 0
\(299\) −16.0000 −0.925304
\(300\) 0 0
\(301\) 8.00000 0.461112
\(302\) 0 0
\(303\) 12.0000 0.689382
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 11.0000 0.627803 0.313902 0.949456i \(-0.398364\pi\)
0.313902 + 0.949456i \(0.398364\pi\)
\(308\) 0 0
\(309\) 6.00000 0.341328
\(310\) 0 0
\(311\) 21.0000 1.19080 0.595400 0.803429i \(-0.296993\pi\)
0.595400 + 0.803429i \(0.296993\pi\)
\(312\) 0 0
\(313\) −16.0000 −0.904373 −0.452187 0.891923i \(-0.649356\pi\)
−0.452187 + 0.891923i \(0.649356\pi\)
\(314\) 0 0
\(315\) 6.00000 0.338062
\(316\) 0 0
\(317\) 18.0000 1.01098 0.505490 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) 0 0
\(319\) −2.00000 −0.111979
\(320\) 0 0
\(321\) 13.0000 0.725589
\(322\) 0 0
\(323\) −1.00000 −0.0556415
\(324\) 0 0
\(325\) −8.00000 −0.443760
\(326\) 0 0
\(327\) −2.00000 −0.110600
\(328\) 0 0
\(329\) 8.00000 0.441054
\(330\) 0 0
\(331\) 17.0000 0.934405 0.467202 0.884150i \(-0.345262\pi\)
0.467202 + 0.884150i \(0.345262\pi\)
\(332\) 0 0
\(333\) 4.00000 0.219199
\(334\) 0 0
\(335\) −42.0000 −2.29471
\(336\) 0 0
\(337\) 20.0000 1.08947 0.544735 0.838608i \(-0.316630\pi\)
0.544735 + 0.838608i \(0.316630\pi\)
\(338\) 0 0
\(339\) −2.00000 −0.108625
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −13.0000 −0.701934
\(344\) 0 0
\(345\) 24.0000 1.29212
\(346\) 0 0
\(347\) −22.0000 −1.18102 −0.590511 0.807030i \(-0.701074\pi\)
−0.590511 + 0.807030i \(0.701074\pi\)
\(348\) 0 0
\(349\) 6.00000 0.321173 0.160586 0.987022i \(-0.448662\pi\)
0.160586 + 0.987022i \(0.448662\pi\)
\(350\) 0 0
\(351\) −10.0000 −0.533761
\(352\) 0 0
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 0 0
\(355\) 24.0000 1.27379
\(356\) 0 0
\(357\) 1.00000 0.0529256
\(358\) 0 0
\(359\) −15.0000 −0.791670 −0.395835 0.918322i \(-0.629545\pi\)
−0.395835 + 0.918322i \(0.629545\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) 0 0
\(363\) 7.00000 0.367405
\(364\) 0 0
\(365\) 30.0000 1.57027
\(366\) 0 0
\(367\) 18.0000 0.939592 0.469796 0.882775i \(-0.344327\pi\)
0.469796 + 0.882775i \(0.344327\pi\)
\(368\) 0 0
\(369\) 14.0000 0.728811
\(370\) 0 0
\(371\) 3.00000 0.155752
\(372\) 0 0
\(373\) 34.0000 1.76045 0.880227 0.474554i \(-0.157390\pi\)
0.880227 + 0.474554i \(0.157390\pi\)
\(374\) 0 0
\(375\) −3.00000 −0.154919
\(376\) 0 0
\(377\) 2.00000 0.103005
\(378\) 0 0
\(379\) 25.0000 1.28416 0.642082 0.766636i \(-0.278071\pi\)
0.642082 + 0.766636i \(0.278071\pi\)
\(380\) 0 0
\(381\) 3.00000 0.153695
\(382\) 0 0
\(383\) −16.0000 −0.817562 −0.408781 0.912633i \(-0.634046\pi\)
−0.408781 + 0.912633i \(0.634046\pi\)
\(384\) 0 0
\(385\) −6.00000 −0.305788
\(386\) 0 0
\(387\) −16.0000 −0.813326
\(388\) 0 0
\(389\) 38.0000 1.92668 0.963338 0.268290i \(-0.0864585\pi\)
0.963338 + 0.268290i \(0.0864585\pi\)
\(390\) 0 0
\(391\) −8.00000 −0.404577
\(392\) 0 0
\(393\) 4.00000 0.201773
\(394\) 0 0
\(395\) 15.0000 0.754732
\(396\) 0 0
\(397\) −4.00000 −0.200754 −0.100377 0.994949i \(-0.532005\pi\)
−0.100377 + 0.994949i \(0.532005\pi\)
\(398\) 0 0
\(399\) −1.00000 −0.0500626
\(400\) 0 0
\(401\) 14.0000 0.699127 0.349563 0.936913i \(-0.386330\pi\)
0.349563 + 0.936913i \(0.386330\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −3.00000 −0.149071
\(406\) 0 0
\(407\) −4.00000 −0.198273
\(408\) 0 0
\(409\) −6.00000 −0.296681 −0.148340 0.988936i \(-0.547393\pi\)
−0.148340 + 0.988936i \(0.547393\pi\)
\(410\) 0 0
\(411\) 5.00000 0.246632
\(412\) 0 0
\(413\) 1.00000 0.0492068
\(414\) 0 0
\(415\) 18.0000 0.883585
\(416\) 0 0
\(417\) −20.0000 −0.979404
\(418\) 0 0
\(419\) −14.0000 −0.683945 −0.341972 0.939710i \(-0.611095\pi\)
−0.341972 + 0.939710i \(0.611095\pi\)
\(420\) 0 0
\(421\) −36.0000 −1.75453 −0.877266 0.480004i \(-0.840635\pi\)
−0.877266 + 0.480004i \(0.840635\pi\)
\(422\) 0 0
\(423\) −16.0000 −0.777947
\(424\) 0 0
\(425\) −4.00000 −0.194029
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 4.00000 0.193122
\(430\) 0 0
\(431\) −16.0000 −0.770693 −0.385346 0.922772i \(-0.625918\pi\)
−0.385346 + 0.922772i \(0.625918\pi\)
\(432\) 0 0
\(433\) 11.0000 0.528626 0.264313 0.964437i \(-0.414855\pi\)
0.264313 + 0.964437i \(0.414855\pi\)
\(434\) 0 0
\(435\) −3.00000 −0.143839
\(436\) 0 0
\(437\) 8.00000 0.382692
\(438\) 0 0
\(439\) 20.0000 0.954548 0.477274 0.878755i \(-0.341625\pi\)
0.477274 + 0.878755i \(0.341625\pi\)
\(440\) 0 0
\(441\) 12.0000 0.571429
\(442\) 0 0
\(443\) −40.0000 −1.90046 −0.950229 0.311553i \(-0.899151\pi\)
−0.950229 + 0.311553i \(0.899151\pi\)
\(444\) 0 0
\(445\) 6.00000 0.284427
\(446\) 0 0
\(447\) 16.0000 0.756774
\(448\) 0 0
\(449\) −1.00000 −0.0471929 −0.0235965 0.999722i \(-0.507512\pi\)
−0.0235965 + 0.999722i \(0.507512\pi\)
\(450\) 0 0
\(451\) −14.0000 −0.659234
\(452\) 0 0
\(453\) −12.0000 −0.563809
\(454\) 0 0
\(455\) 6.00000 0.281284
\(456\) 0 0
\(457\) 2.00000 0.0935561 0.0467780 0.998905i \(-0.485105\pi\)
0.0467780 + 0.998905i \(0.485105\pi\)
\(458\) 0 0
\(459\) −5.00000 −0.233380
\(460\) 0 0
\(461\) 2.00000 0.0931493 0.0465746 0.998915i \(-0.485169\pi\)
0.0465746 + 0.998915i \(0.485169\pi\)
\(462\) 0 0
\(463\) −28.0000 −1.30127 −0.650635 0.759390i \(-0.725497\pi\)
−0.650635 + 0.759390i \(0.725497\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −38.0000 −1.75843 −0.879215 0.476425i \(-0.841932\pi\)
−0.879215 + 0.476425i \(0.841932\pi\)
\(468\) 0 0
\(469\) 14.0000 0.646460
\(470\) 0 0
\(471\) 14.0000 0.645086
\(472\) 0 0
\(473\) 16.0000 0.735681
\(474\) 0 0
\(475\) 4.00000 0.183533
\(476\) 0 0
\(477\) −6.00000 −0.274721
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 4.00000 0.182384
\(482\) 0 0
\(483\) −8.00000 −0.364013
\(484\) 0 0
\(485\) −24.0000 −1.08978
\(486\) 0 0
\(487\) 9.00000 0.407829 0.203914 0.978989i \(-0.434634\pi\)
0.203914 + 0.978989i \(0.434634\pi\)
\(488\) 0 0
\(489\) −16.0000 −0.723545
\(490\) 0 0
\(491\) 15.0000 0.676941 0.338470 0.940977i \(-0.390091\pi\)
0.338470 + 0.940977i \(0.390091\pi\)
\(492\) 0 0
\(493\) 1.00000 0.0450377
\(494\) 0 0
\(495\) 12.0000 0.539360
\(496\) 0 0
\(497\) −8.00000 −0.358849
\(498\) 0 0
\(499\) −13.0000 −0.581960 −0.290980 0.956729i \(-0.593981\pi\)
−0.290980 + 0.956729i \(0.593981\pi\)
\(500\) 0 0
\(501\) −5.00000 −0.223384
\(502\) 0 0
\(503\) 8.00000 0.356702 0.178351 0.983967i \(-0.442924\pi\)
0.178351 + 0.983967i \(0.442924\pi\)
\(504\) 0 0
\(505\) 36.0000 1.60198
\(506\) 0 0
\(507\) 9.00000 0.399704
\(508\) 0 0
\(509\) −18.0000 −0.797836 −0.398918 0.916987i \(-0.630614\pi\)
−0.398918 + 0.916987i \(0.630614\pi\)
\(510\) 0 0
\(511\) −10.0000 −0.442374
\(512\) 0 0
\(513\) 5.00000 0.220755
\(514\) 0 0
\(515\) 18.0000 0.793175
\(516\) 0 0
\(517\) 16.0000 0.703679
\(518\) 0 0
\(519\) 16.0000 0.702322
\(520\) 0 0
\(521\) 6.00000 0.262865 0.131432 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) 0 0
\(523\) −41.0000 −1.79280 −0.896402 0.443241i \(-0.853829\pi\)
−0.896402 + 0.443241i \(0.853829\pi\)
\(524\) 0 0
\(525\) −4.00000 −0.174574
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 41.0000 1.78261
\(530\) 0 0
\(531\) −2.00000 −0.0867926
\(532\) 0 0
\(533\) 14.0000 0.606407
\(534\) 0 0
\(535\) 39.0000 1.68612
\(536\) 0 0
\(537\) 6.00000 0.258919
\(538\) 0 0
\(539\) −12.0000 −0.516877
\(540\) 0 0
\(541\) 32.0000 1.37579 0.687894 0.725811i \(-0.258536\pi\)
0.687894 + 0.725811i \(0.258536\pi\)
\(542\) 0 0
\(543\) −3.00000 −0.128742
\(544\) 0 0
\(545\) −6.00000 −0.257012
\(546\) 0 0
\(547\) 40.0000 1.71028 0.855138 0.518400i \(-0.173472\pi\)
0.855138 + 0.518400i \(0.173472\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.00000 −0.0426014
\(552\) 0 0
\(553\) −5.00000 −0.212622
\(554\) 0 0
\(555\) −6.00000 −0.254686
\(556\) 0 0
\(557\) 19.0000 0.805056 0.402528 0.915408i \(-0.368132\pi\)
0.402528 + 0.915408i \(0.368132\pi\)
\(558\) 0 0
\(559\) −16.0000 −0.676728
\(560\) 0 0
\(561\) 2.00000 0.0844401
\(562\) 0 0
\(563\) 12.0000 0.505740 0.252870 0.967500i \(-0.418626\pi\)
0.252870 + 0.967500i \(0.418626\pi\)
\(564\) 0 0
\(565\) −6.00000 −0.252422
\(566\) 0 0
\(567\) 1.00000 0.0419961
\(568\) 0 0
\(569\) −14.0000 −0.586911 −0.293455 0.955973i \(-0.594805\pi\)
−0.293455 + 0.955973i \(0.594805\pi\)
\(570\) 0 0
\(571\) 36.0000 1.50655 0.753277 0.657704i \(-0.228472\pi\)
0.753277 + 0.657704i \(0.228472\pi\)
\(572\) 0 0
\(573\) 10.0000 0.417756
\(574\) 0 0
\(575\) 32.0000 1.33449
\(576\) 0 0
\(577\) 25.0000 1.04076 0.520382 0.853934i \(-0.325790\pi\)
0.520382 + 0.853934i \(0.325790\pi\)
\(578\) 0 0
\(579\) 11.0000 0.457144
\(580\) 0 0
\(581\) −6.00000 −0.248922
\(582\) 0 0
\(583\) 6.00000 0.248495
\(584\) 0 0
\(585\) −12.0000 −0.496139
\(586\) 0 0
\(587\) −30.0000 −1.23823 −0.619116 0.785299i \(-0.712509\pi\)
−0.619116 + 0.785299i \(0.712509\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) −10.0000 −0.411345
\(592\) 0 0
\(593\) −23.0000 −0.944497 −0.472248 0.881466i \(-0.656557\pi\)
−0.472248 + 0.881466i \(0.656557\pi\)
\(594\) 0 0
\(595\) 3.00000 0.122988
\(596\) 0 0
\(597\) 19.0000 0.777618
\(598\) 0 0
\(599\) 45.0000 1.83865 0.919325 0.393499i \(-0.128735\pi\)
0.919325 + 0.393499i \(0.128735\pi\)
\(600\) 0 0
\(601\) −8.00000 −0.326327 −0.163163 0.986599i \(-0.552170\pi\)
−0.163163 + 0.986599i \(0.552170\pi\)
\(602\) 0 0
\(603\) −28.0000 −1.14025
\(604\) 0 0
\(605\) 21.0000 0.853771
\(606\) 0 0
\(607\) 29.0000 1.17707 0.588537 0.808470i \(-0.299704\pi\)
0.588537 + 0.808470i \(0.299704\pi\)
\(608\) 0 0
\(609\) 1.00000 0.0405220
\(610\) 0 0
\(611\) −16.0000 −0.647291
\(612\) 0 0
\(613\) 34.0000 1.37325 0.686624 0.727013i \(-0.259092\pi\)
0.686624 + 0.727013i \(0.259092\pi\)
\(614\) 0 0
\(615\) −21.0000 −0.846802
\(616\) 0 0
\(617\) −17.0000 −0.684394 −0.342197 0.939628i \(-0.611171\pi\)
−0.342197 + 0.939628i \(0.611171\pi\)
\(618\) 0 0
\(619\) −11.0000 −0.442127 −0.221064 0.975259i \(-0.570953\pi\)
−0.221064 + 0.975259i \(0.570953\pi\)
\(620\) 0 0
\(621\) 40.0000 1.60514
\(622\) 0 0
\(623\) −2.00000 −0.0801283
\(624\) 0 0
\(625\) −29.0000 −1.16000
\(626\) 0 0
\(627\) −2.00000 −0.0798723
\(628\) 0 0
\(629\) 2.00000 0.0797452
\(630\) 0 0
\(631\) −20.0000 −0.796187 −0.398094 0.917345i \(-0.630328\pi\)
−0.398094 + 0.917345i \(0.630328\pi\)
\(632\) 0 0
\(633\) −2.00000 −0.0794929
\(634\) 0 0
\(635\) 9.00000 0.357154
\(636\) 0 0
\(637\) 12.0000 0.475457
\(638\) 0 0
\(639\) 16.0000 0.632950
\(640\) 0 0
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) 0 0
\(643\) −17.0000 −0.670415 −0.335207 0.942144i \(-0.608806\pi\)
−0.335207 + 0.942144i \(0.608806\pi\)
\(644\) 0 0
\(645\) 24.0000 0.944999
\(646\) 0 0
\(647\) −21.0000 −0.825595 −0.412798 0.910823i \(-0.635448\pi\)
−0.412798 + 0.910823i \(0.635448\pi\)
\(648\) 0 0
\(649\) 2.00000 0.0785069
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −31.0000 −1.21312 −0.606562 0.795036i \(-0.707452\pi\)
−0.606562 + 0.795036i \(0.707452\pi\)
\(654\) 0 0
\(655\) 12.0000 0.468879
\(656\) 0 0
\(657\) 20.0000 0.780274
\(658\) 0 0
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0 0
\(661\) 23.0000 0.894596 0.447298 0.894385i \(-0.352386\pi\)
0.447298 + 0.894385i \(0.352386\pi\)
\(662\) 0 0
\(663\) −2.00000 −0.0776736
\(664\) 0 0
\(665\) −3.00000 −0.116335
\(666\) 0 0
\(667\) −8.00000 −0.309761
\(668\) 0 0
\(669\) 24.0000 0.927894
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −38.0000 −1.46479 −0.732396 0.680879i \(-0.761598\pi\)
−0.732396 + 0.680879i \(0.761598\pi\)
\(674\) 0 0
\(675\) 20.0000 0.769800
\(676\) 0 0
\(677\) 2.00000 0.0768662 0.0384331 0.999261i \(-0.487763\pi\)
0.0384331 + 0.999261i \(0.487763\pi\)
\(678\) 0 0
\(679\) 8.00000 0.307012
\(680\) 0 0
\(681\) 24.0000 0.919682
\(682\) 0 0
\(683\) −4.00000 −0.153056 −0.0765279 0.997067i \(-0.524383\pi\)
−0.0765279 + 0.997067i \(0.524383\pi\)
\(684\) 0 0
\(685\) 15.0000 0.573121
\(686\) 0 0
\(687\) −20.0000 −0.763048
\(688\) 0 0
\(689\) −6.00000 −0.228582
\(690\) 0 0
\(691\) 16.0000 0.608669 0.304334 0.952565i \(-0.401566\pi\)
0.304334 + 0.952565i \(0.401566\pi\)
\(692\) 0 0
\(693\) −4.00000 −0.151947
\(694\) 0 0
\(695\) −60.0000 −2.27593
\(696\) 0 0
\(697\) 7.00000 0.265144
\(698\) 0 0
\(699\) 14.0000 0.529529
\(700\) 0 0
\(701\) 36.0000 1.35970 0.679851 0.733351i \(-0.262045\pi\)
0.679851 + 0.733351i \(0.262045\pi\)
\(702\) 0 0
\(703\) −2.00000 −0.0754314
\(704\) 0 0
\(705\) 24.0000 0.903892
\(706\) 0 0
\(707\) −12.0000 −0.451306
\(708\) 0 0
\(709\) −45.0000 −1.69001 −0.845005 0.534758i \(-0.820403\pi\)
−0.845005 + 0.534758i \(0.820403\pi\)
\(710\) 0 0
\(711\) 10.0000 0.375029
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 12.0000 0.448775
\(716\) 0 0
\(717\) −7.00000 −0.261420
\(718\) 0 0
\(719\) 28.0000 1.04422 0.522112 0.852877i \(-0.325144\pi\)
0.522112 + 0.852877i \(0.325144\pi\)
\(720\) 0 0
\(721\) −6.00000 −0.223452
\(722\) 0 0
\(723\) 17.0000 0.632237
\(724\) 0 0
\(725\) −4.00000 −0.148556
\(726\) 0 0
\(727\) 8.00000 0.296704 0.148352 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −8.00000 −0.295891
\(732\) 0 0
\(733\) −14.0000 −0.517102 −0.258551 0.965998i \(-0.583245\pi\)
−0.258551 + 0.965998i \(0.583245\pi\)
\(734\) 0 0
\(735\) −18.0000 −0.663940
\(736\) 0 0
\(737\) 28.0000 1.03139
\(738\) 0 0
\(739\) 42.0000 1.54499 0.772497 0.635018i \(-0.219007\pi\)
0.772497 + 0.635018i \(0.219007\pi\)
\(740\) 0 0
\(741\) 2.00000 0.0734718
\(742\) 0 0
\(743\) −36.0000 −1.32071 −0.660356 0.750953i \(-0.729595\pi\)
−0.660356 + 0.750953i \(0.729595\pi\)
\(744\) 0 0
\(745\) 48.0000 1.75858
\(746\) 0 0
\(747\) 12.0000 0.439057
\(748\) 0 0
\(749\) −13.0000 −0.475010
\(750\) 0 0
\(751\) −2.00000 −0.0729810 −0.0364905 0.999334i \(-0.511618\pi\)
−0.0364905 + 0.999334i \(0.511618\pi\)
\(752\) 0 0
\(753\) 9.00000 0.327978
\(754\) 0 0
\(755\) −36.0000 −1.31017
\(756\) 0 0
\(757\) −35.0000 −1.27210 −0.636048 0.771649i \(-0.719432\pi\)
−0.636048 + 0.771649i \(0.719432\pi\)
\(758\) 0 0
\(759\) −16.0000 −0.580763
\(760\) 0 0
\(761\) 1.00000 0.0362500 0.0181250 0.999836i \(-0.494230\pi\)
0.0181250 + 0.999836i \(0.494230\pi\)
\(762\) 0 0
\(763\) 2.00000 0.0724049
\(764\) 0 0
\(765\) −6.00000 −0.216930
\(766\) 0 0
\(767\) −2.00000 −0.0722158
\(768\) 0 0
\(769\) 12.0000 0.432731 0.216366 0.976312i \(-0.430580\pi\)
0.216366 + 0.976312i \(0.430580\pi\)
\(770\) 0 0
\(771\) 23.0000 0.828325
\(772\) 0 0
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 2.00000 0.0717496
\(778\) 0 0
\(779\) −7.00000 −0.250801
\(780\) 0 0
\(781\) −16.0000 −0.572525
\(782\) 0 0
\(783\) −5.00000 −0.178685
\(784\) 0 0
\(785\) 42.0000 1.49904
\(786\) 0 0
\(787\) 52.0000 1.85360 0.926800 0.375555i \(-0.122548\pi\)
0.926800 + 0.375555i \(0.122548\pi\)
\(788\) 0 0
\(789\) −3.00000 −0.106803
\(790\) 0 0
\(791\) 2.00000 0.0711118
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 9.00000 0.319197
\(796\) 0 0
\(797\) 44.0000 1.55856 0.779280 0.626676i \(-0.215585\pi\)
0.779280 + 0.626676i \(0.215585\pi\)
\(798\) 0 0
\(799\) −8.00000 −0.283020
\(800\) 0 0
\(801\) 4.00000 0.141333
\(802\) 0 0
\(803\) −20.0000 −0.705785
\(804\) 0 0
\(805\) −24.0000 −0.845889
\(806\) 0 0
\(807\) −2.00000 −0.0704033
\(808\) 0 0
\(809\) 6.00000 0.210949 0.105474 0.994422i \(-0.466364\pi\)
0.105474 + 0.994422i \(0.466364\pi\)
\(810\) 0 0
\(811\) −10.0000 −0.351147 −0.175574 0.984466i \(-0.556178\pi\)
−0.175574 + 0.984466i \(0.556178\pi\)
\(812\) 0 0
\(813\) 3.00000 0.105215
\(814\) 0 0
\(815\) −48.0000 −1.68137
\(816\) 0 0
\(817\) 8.00000 0.279885
\(818\) 0 0
\(819\) 4.00000 0.139771
\(820\) 0 0
\(821\) 4.00000 0.139601 0.0698005 0.997561i \(-0.477764\pi\)
0.0698005 + 0.997561i \(0.477764\pi\)
\(822\) 0 0
\(823\) 4.00000 0.139431 0.0697156 0.997567i \(-0.477791\pi\)
0.0697156 + 0.997567i \(0.477791\pi\)
\(824\) 0 0
\(825\) −8.00000 −0.278524
\(826\) 0 0
\(827\) −12.0000 −0.417281 −0.208640 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) 0 0
\(829\) −11.0000 −0.382046 −0.191023 0.981586i \(-0.561180\pi\)
−0.191023 + 0.981586i \(0.561180\pi\)
\(830\) 0 0
\(831\) 23.0000 0.797861
\(832\) 0 0
\(833\) 6.00000 0.207888
\(834\) 0 0
\(835\) −15.0000 −0.519096
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 8.00000 0.276191 0.138095 0.990419i \(-0.455902\pi\)
0.138095 + 0.990419i \(0.455902\pi\)
\(840\) 0 0
\(841\) −28.0000 −0.965517
\(842\) 0 0
\(843\) 17.0000 0.585511
\(844\) 0 0
\(845\) 27.0000 0.928828
\(846\) 0 0
\(847\) −7.00000 −0.240523
\(848\) 0 0
\(849\) −18.0000 −0.617758
\(850\) 0 0
\(851\) −16.0000 −0.548473
\(852\) 0 0
\(853\) −37.0000 −1.26686 −0.633428 0.773802i \(-0.718353\pi\)
−0.633428 + 0.773802i \(0.718353\pi\)
\(854\) 0 0
\(855\) 6.00000 0.205196
\(856\) 0 0
\(857\) 18.0000 0.614868 0.307434 0.951569i \(-0.400530\pi\)
0.307434 + 0.951569i \(0.400530\pi\)
\(858\) 0 0
\(859\) −44.0000 −1.50126 −0.750630 0.660722i \(-0.770250\pi\)
−0.750630 + 0.660722i \(0.770250\pi\)
\(860\) 0 0
\(861\) 7.00000 0.238559
\(862\) 0 0
\(863\) −14.0000 −0.476566 −0.238283 0.971196i \(-0.576585\pi\)
−0.238283 + 0.971196i \(0.576585\pi\)
\(864\) 0 0
\(865\) 48.0000 1.63205
\(866\) 0 0
\(867\) −1.00000 −0.0339618
\(868\) 0 0
\(869\) −10.0000 −0.339227
\(870\) 0 0
\(871\) −28.0000 −0.948744
\(872\) 0 0
\(873\) −16.0000 −0.541518
\(874\) 0 0
\(875\) 3.00000 0.101419
\(876\) 0 0
\(877\) 23.0000 0.776655 0.388327 0.921521i \(-0.373053\pi\)
0.388327 + 0.921521i \(0.373053\pi\)
\(878\) 0 0
\(879\) 23.0000 0.775771
\(880\) 0 0
\(881\) −46.0000 −1.54978 −0.774890 0.632096i \(-0.782195\pi\)
−0.774890 + 0.632096i \(0.782195\pi\)
\(882\) 0 0
\(883\) −33.0000 −1.11054 −0.555269 0.831671i \(-0.687385\pi\)
−0.555269 + 0.831671i \(0.687385\pi\)
\(884\) 0 0
\(885\) 3.00000 0.100844
\(886\) 0 0
\(887\) 30.0000 1.00730 0.503651 0.863907i \(-0.331990\pi\)
0.503651 + 0.863907i \(0.331990\pi\)
\(888\) 0 0
\(889\) −3.00000 −0.100617
\(890\) 0 0
\(891\) 2.00000 0.0670025
\(892\) 0 0
\(893\) 8.00000 0.267710
\(894\) 0 0
\(895\) 18.0000 0.601674
\(896\) 0 0
\(897\) 16.0000 0.534224
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) −3.00000 −0.0999445
\(902\) 0 0
\(903\) −8.00000 −0.266223
\(904\) 0 0
\(905\) −9.00000 −0.299170
\(906\) 0 0
\(907\) 3.00000 0.0996134 0.0498067 0.998759i \(-0.484139\pi\)
0.0498067 + 0.998759i \(0.484139\pi\)
\(908\) 0 0
\(909\) 24.0000 0.796030
\(910\) 0 0
\(911\) 9.00000 0.298183 0.149092 0.988823i \(-0.452365\pi\)
0.149092 + 0.988823i \(0.452365\pi\)
\(912\) 0 0
\(913\) −12.0000 −0.397142
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −4.00000 −0.132092
\(918\) 0 0
\(919\) 22.0000 0.725713 0.362857 0.931845i \(-0.381802\pi\)
0.362857 + 0.931845i \(0.381802\pi\)
\(920\) 0 0
\(921\) −11.0000 −0.362462
\(922\) 0 0
\(923\) 16.0000 0.526646
\(924\) 0 0
\(925\) −8.00000 −0.263038
\(926\) 0 0
\(927\) 12.0000 0.394132
\(928\) 0 0
\(929\) 22.0000 0.721797 0.360898 0.932605i \(-0.382470\pi\)
0.360898 + 0.932605i \(0.382470\pi\)
\(930\) 0 0
\(931\) −6.00000 −0.196642
\(932\) 0 0
\(933\) −21.0000 −0.687509
\(934\) 0 0
\(935\) 6.00000 0.196221
\(936\) 0 0
\(937\) 44.0000 1.43742 0.718709 0.695311i \(-0.244734\pi\)
0.718709 + 0.695311i \(0.244734\pi\)
\(938\) 0 0
\(939\) 16.0000 0.522140
\(940\) 0 0
\(941\) −18.0000 −0.586783 −0.293392 0.955992i \(-0.594784\pi\)
−0.293392 + 0.955992i \(0.594784\pi\)
\(942\) 0 0
\(943\) −56.0000 −1.82361
\(944\) 0 0
\(945\) −15.0000 −0.487950
\(946\) 0 0
\(947\) 19.0000 0.617417 0.308709 0.951157i \(-0.400103\pi\)
0.308709 + 0.951157i \(0.400103\pi\)
\(948\) 0 0
\(949\) 20.0000 0.649227
\(950\) 0 0
\(951\) −18.0000 −0.583690
\(952\) 0 0
\(953\) 22.0000 0.712650 0.356325 0.934362i \(-0.384030\pi\)
0.356325 + 0.934362i \(0.384030\pi\)
\(954\) 0 0
\(955\) 30.0000 0.970777
\(956\) 0 0
\(957\) 2.00000 0.0646508
\(958\) 0 0
\(959\) −5.00000 −0.161458
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) 26.0000 0.837838
\(964\) 0 0
\(965\) 33.0000 1.06231
\(966\) 0 0
\(967\) −54.0000 −1.73652 −0.868261 0.496107i \(-0.834762\pi\)
−0.868261 + 0.496107i \(0.834762\pi\)
\(968\) 0 0
\(969\) 1.00000 0.0321246
\(970\) 0 0
\(971\) −21.0000 −0.673922 −0.336961 0.941519i \(-0.609399\pi\)
−0.336961 + 0.941519i \(0.609399\pi\)
\(972\) 0 0
\(973\) 20.0000 0.641171
\(974\) 0 0
\(975\) 8.00000 0.256205
\(976\) 0 0
\(977\) −6.00000 −0.191957 −0.0959785 0.995383i \(-0.530598\pi\)
−0.0959785 + 0.995383i \(0.530598\pi\)
\(978\) 0 0
\(979\) −4.00000 −0.127841
\(980\) 0 0
\(981\) −4.00000 −0.127710
\(982\) 0 0
\(983\) 6.00000 0.191370 0.0956851 0.995412i \(-0.469496\pi\)
0.0956851 + 0.995412i \(0.469496\pi\)
\(984\) 0 0
\(985\) −30.0000 −0.955879
\(986\) 0 0
\(987\) −8.00000 −0.254643
\(988\) 0 0
\(989\) 64.0000 2.03508
\(990\) 0 0
\(991\) 20.0000 0.635321 0.317660 0.948205i \(-0.397103\pi\)
0.317660 + 0.948205i \(0.397103\pi\)
\(992\) 0 0
\(993\) −17.0000 −0.539479
\(994\) 0 0
\(995\) 57.0000 1.80702
\(996\) 0 0
\(997\) 35.0000 1.10846 0.554231 0.832363i \(-0.313013\pi\)
0.554231 + 0.832363i \(0.313013\pi\)
\(998\) 0 0
\(999\) −10.0000 −0.316386
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 \(a_p\))