Properties

Label 4030.2.a.a.1.1
Level 4030
Weight 2
Character 4030.1
Self dual Yes
Analytic conductor 32.180
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4030.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1797120146\)
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 \(\chi\) = 4030.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+1.00000 q^{5}\) \(-1.00000 q^{8}\) \(-3.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+1.00000 q^{5}\) \(-1.00000 q^{8}\) \(-3.00000 q^{9}\) \(-1.00000 q^{10}\) \(-2.00000 q^{11}\) \(+1.00000 q^{13}\) \(+1.00000 q^{16}\) \(+4.00000 q^{17}\) \(+3.00000 q^{18}\) \(+4.00000 q^{19}\) \(+1.00000 q^{20}\) \(+2.00000 q^{22}\) \(-2.00000 q^{23}\) \(+1.00000 q^{25}\) \(-1.00000 q^{26}\) \(+1.00000 q^{31}\) \(-1.00000 q^{32}\) \(-4.00000 q^{34}\) \(-3.00000 q^{36}\) \(+2.00000 q^{37}\) \(-4.00000 q^{38}\) \(-1.00000 q^{40}\) \(+6.00000 q^{41}\) \(-8.00000 q^{43}\) \(-2.00000 q^{44}\) \(-3.00000 q^{45}\) \(+2.00000 q^{46}\) \(-12.0000 q^{47}\) \(-7.00000 q^{49}\) \(-1.00000 q^{50}\) \(+1.00000 q^{52}\) \(+10.0000 q^{53}\) \(-2.00000 q^{55}\) \(+12.0000 q^{59}\) \(-4.00000 q^{61}\) \(-1.00000 q^{62}\) \(+1.00000 q^{64}\) \(+1.00000 q^{65}\) \(+4.00000 q^{67}\) \(+4.00000 q^{68}\) \(+3.00000 q^{72}\) \(-2.00000 q^{74}\) \(+4.00000 q^{76}\) \(-4.00000 q^{79}\) \(+1.00000 q^{80}\) \(+9.00000 q^{81}\) \(-6.00000 q^{82}\) \(+4.00000 q^{83}\) \(+4.00000 q^{85}\) \(+8.00000 q^{86}\) \(+2.00000 q^{88}\) \(+6.00000 q^{89}\) \(+3.00000 q^{90}\) \(-2.00000 q^{92}\) \(+12.0000 q^{94}\) \(+4.00000 q^{95}\) \(+2.00000 q^{97}\) \(+7.00000 q^{98}\) \(+6.00000 q^{99}\) \(+O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) −1.00000 −0.353553
\(9\) −3.00000 −1.00000
\(10\) −1.00000 −0.316228
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 4.00000 0.970143 0.485071 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) 3.00000 0.707107
\(19\) 4.00000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) 2.00000 0.426401
\(23\) −2.00000 −0.417029 −0.208514 0.978019i \(-0.566863\pi\)
−0.208514 + 0.978019i \(0.566863\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −1.00000 −0.196116
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 1.00000 0.179605
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −4.00000 −0.685994
\(35\) 0 0
\(36\) −3.00000 −0.500000
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −4.00000 −0.648886
\(39\) 0 0
\(40\) −1.00000 −0.158114
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) −2.00000 −0.301511
\(45\) −3.00000 −0.447214
\(46\) 2.00000 0.294884
\(47\) −12.0000 −1.75038 −0.875190 0.483779i \(-0.839264\pi\)
−0.875190 + 0.483779i \(0.839264\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) 1.00000 0.138675
\(53\) 10.0000 1.37361 0.686803 0.726844i \(-0.259014\pi\)
0.686803 + 0.726844i \(0.259014\pi\)
\(54\) 0 0
\(55\) −2.00000 −0.269680
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 12.0000 1.56227 0.781133 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) 0 0
\(61\) −4.00000 −0.512148 −0.256074 0.966657i \(-0.582429\pi\)
−0.256074 + 0.966657i \(0.582429\pi\)
\(62\) −1.00000 −0.127000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) 4.00000 0.488678 0.244339 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) 4.00000 0.485071
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 3.00000 0.353553
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) −2.00000 −0.232495
\(75\) 0 0
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) 0 0
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 1.00000 0.111803
\(81\) 9.00000 1.00000
\(82\) −6.00000 −0.662589
\(83\) 4.00000 0.439057 0.219529 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 0 0
\(85\) 4.00000 0.433861
\(86\) 8.00000 0.862662
\(87\) 0 0
\(88\) 2.00000 0.213201
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 3.00000 0.316228
\(91\) 0 0
\(92\) −2.00000 −0.208514
\(93\) 0 0
\(94\) 12.0000 1.23771
\(95\) 4.00000 0.410391
\(96\) 0 0
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 7.00000 0.707107
\(99\) 6.00000 0.603023
\(100\) 1.00000 0.100000
\(101\) 10.0000 0.995037 0.497519 0.867453i \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) 0 0
\(103\) −4.00000 −0.394132 −0.197066 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) −10.0000 −0.971286
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) −6.00000 −0.574696 −0.287348 0.957826i \(-0.592774\pi\)
−0.287348 + 0.957826i \(0.592774\pi\)
\(110\) 2.00000 0.190693
\(111\) 0 0
\(112\) 0 0
\(113\) 14.0000 1.31701 0.658505 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) 0 0
\(115\) −2.00000 −0.186501
\(116\) 0 0
\(117\) −3.00000 −0.277350
\(118\) −12.0000 −1.10469
\(119\) 0 0
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 4.00000 0.362143
\(123\) 0 0
\(124\) 1.00000 0.0898027
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 18.0000 1.59724 0.798621 0.601834i \(-0.205563\pi\)
0.798621 + 0.601834i \(0.205563\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) −1.00000 −0.0877058
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) −4.00000 −0.342997
\(137\) 12.0000 1.02523 0.512615 0.858619i \(-0.328677\pi\)
0.512615 + 0.858619i \(0.328677\pi\)
\(138\) 0 0
\(139\) 22.0000 1.86602 0.933008 0.359856i \(-0.117174\pi\)
0.933008 + 0.359856i \(0.117174\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2.00000 −0.167248
\(144\) −3.00000 −0.250000
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 2.00000 0.164399
\(149\) −18.0000 −1.47462 −0.737309 0.675556i \(-0.763904\pi\)
−0.737309 + 0.675556i \(0.763904\pi\)
\(150\) 0 0
\(151\) −12.0000 −0.976546 −0.488273 0.872691i \(-0.662373\pi\)
−0.488273 + 0.872691i \(0.662373\pi\)
\(152\) −4.00000 −0.324443
\(153\) −12.0000 −0.970143
\(154\) 0 0
\(155\) 1.00000 0.0803219
\(156\) 0 0
\(157\) 10.0000 0.798087 0.399043 0.916932i \(-0.369342\pi\)
0.399043 + 0.916932i \(0.369342\pi\)
\(158\) 4.00000 0.318223
\(159\) 0 0
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) −9.00000 −0.707107
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) −4.00000 −0.310460
\(167\) 6.00000 0.464294 0.232147 0.972681i \(-0.425425\pi\)
0.232147 + 0.972681i \(0.425425\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −4.00000 −0.306786
\(171\) −12.0000 −0.917663
\(172\) −8.00000 −0.609994
\(173\) 2.00000 0.152057 0.0760286 0.997106i \(-0.475776\pi\)
0.0760286 + 0.997106i \(0.475776\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −2.00000 −0.150756
\(177\) 0 0
\(178\) −6.00000 −0.449719
\(179\) −10.0000 −0.747435 −0.373718 0.927543i \(-0.621917\pi\)
−0.373718 + 0.927543i \(0.621917\pi\)
\(180\) −3.00000 −0.223607
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 2.00000 0.147442
\(185\) 2.00000 0.147043
\(186\) 0 0
\(187\) −8.00000 −0.585018
\(188\) −12.0000 −0.875190
\(189\) 0 0
\(190\) −4.00000 −0.290191
\(191\) −8.00000 −0.578860 −0.289430 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) 0 0
\(193\) 10.0000 0.719816 0.359908 0.932988i \(-0.382808\pi\)
0.359908 + 0.932988i \(0.382808\pi\)
\(194\) −2.00000 −0.143592
\(195\) 0 0
\(196\) −7.00000 −0.500000
\(197\) 22.0000 1.56744 0.783718 0.621117i \(-0.213321\pi\)
0.783718 + 0.621117i \(0.213321\pi\)
\(198\) −6.00000 −0.426401
\(199\) 20.0000 1.41776 0.708881 0.705328i \(-0.249200\pi\)
0.708881 + 0.705328i \(0.249200\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 0 0
\(202\) −10.0000 −0.703598
\(203\) 0 0
\(204\) 0 0
\(205\) 6.00000 0.419058
\(206\) 4.00000 0.278693
\(207\) 6.00000 0.417029
\(208\) 1.00000 0.0693375
\(209\) −8.00000 −0.553372
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) 10.0000 0.686803
\(213\) 0 0
\(214\) −12.0000 −0.820303
\(215\) −8.00000 −0.545595
\(216\) 0 0
\(217\) 0 0
\(218\) 6.00000 0.406371
\(219\) 0 0
\(220\) −2.00000 −0.134840
\(221\) 4.00000 0.269069
\(222\) 0 0
\(223\) 2.00000 0.133930 0.0669650 0.997755i \(-0.478668\pi\)
0.0669650 + 0.997755i \(0.478668\pi\)
\(224\) 0 0
\(225\) −3.00000 −0.200000
\(226\) −14.0000 −0.931266
\(227\) 4.00000 0.265489 0.132745 0.991150i \(-0.457621\pi\)
0.132745 + 0.991150i \(0.457621\pi\)
\(228\) 0 0
\(229\) −12.0000 −0.792982 −0.396491 0.918039i \(-0.629772\pi\)
−0.396491 + 0.918039i \(0.629772\pi\)
\(230\) 2.00000 0.131876
\(231\) 0 0
\(232\) 0 0
\(233\) −2.00000 −0.131024 −0.0655122 0.997852i \(-0.520868\pi\)
−0.0655122 + 0.997852i \(0.520868\pi\)
\(234\) 3.00000 0.196116
\(235\) −12.0000 −0.782794
\(236\) 12.0000 0.781133
\(237\) 0 0
\(238\) 0 0
\(239\) −16.0000 −1.03495 −0.517477 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) 0 0
\(241\) −22.0000 −1.41714 −0.708572 0.705638i \(-0.750660\pi\)
−0.708572 + 0.705638i \(0.750660\pi\)
\(242\) 7.00000 0.449977
\(243\) 0 0
\(244\) −4.00000 −0.256074
\(245\) −7.00000 −0.447214
\(246\) 0 0
\(247\) 4.00000 0.254514
\(248\) −1.00000 −0.0635001
\(249\) 0 0
\(250\) −1.00000 −0.0632456
\(251\) −6.00000 −0.378717 −0.189358 0.981908i \(-0.560641\pi\)
−0.189358 + 0.981908i \(0.560641\pi\)
\(252\) 0 0
\(253\) 4.00000 0.251478
\(254\) −18.0000 −1.12942
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 1.00000 0.0620174
\(261\) 0 0
\(262\) 0 0
\(263\) −18.0000 −1.10993 −0.554964 0.831875i \(-0.687268\pi\)
−0.554964 + 0.831875i \(0.687268\pi\)
\(264\) 0 0
\(265\) 10.0000 0.614295
\(266\) 0 0
\(267\) 0 0
\(268\) 4.00000 0.244339
\(269\) 24.0000 1.46331 0.731653 0.681677i \(-0.238749\pi\)
0.731653 + 0.681677i \(0.238749\pi\)
\(270\) 0 0
\(271\) 24.0000 1.45790 0.728948 0.684569i \(-0.240010\pi\)
0.728948 + 0.684569i \(0.240010\pi\)
\(272\) 4.00000 0.242536
\(273\) 0 0
\(274\) −12.0000 −0.724947
\(275\) −2.00000 −0.120605
\(276\) 0 0
\(277\) 2.00000 0.120168 0.0600842 0.998193i \(-0.480863\pi\)
0.0600842 + 0.998193i \(0.480863\pi\)
\(278\) −22.0000 −1.31947
\(279\) −3.00000 −0.179605
\(280\) 0 0
\(281\) −26.0000 −1.55103 −0.775515 0.631329i \(-0.782510\pi\)
−0.775515 + 0.631329i \(0.782510\pi\)
\(282\) 0 0
\(283\) −12.0000 −0.713326 −0.356663 0.934233i \(-0.616086\pi\)
−0.356663 + 0.934233i \(0.616086\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 2.00000 0.118262
\(287\) 0 0
\(288\) 3.00000 0.176777
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 22.0000 1.28525 0.642627 0.766179i \(-0.277845\pi\)
0.642627 + 0.766179i \(0.277845\pi\)
\(294\) 0 0
\(295\) 12.0000 0.698667
\(296\) −2.00000 −0.116248
\(297\) 0 0
\(298\) 18.0000 1.04271
\(299\) −2.00000 −0.115663
\(300\) 0 0
\(301\) 0 0
\(302\) 12.0000 0.690522
\(303\) 0 0
\(304\) 4.00000 0.229416
\(305\) −4.00000 −0.229039
\(306\) 12.0000 0.685994
\(307\) 12.0000 0.684876 0.342438 0.939540i \(-0.388747\pi\)
0.342438 + 0.939540i \(0.388747\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −1.00000 −0.0567962
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) 28.0000 1.58265 0.791327 0.611393i \(-0.209391\pi\)
0.791327 + 0.611393i \(0.209391\pi\)
\(314\) −10.0000 −0.564333
\(315\) 0 0
\(316\) −4.00000 −0.225018
\(317\) 34.0000 1.90963 0.954815 0.297200i \(-0.0960529\pi\)
0.954815 + 0.297200i \(0.0960529\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 1.00000 0.0559017
\(321\) 0 0
\(322\) 0 0
\(323\) 16.0000 0.890264
\(324\) 9.00000 0.500000
\(325\) 1.00000 0.0554700
\(326\) −4.00000 −0.221540
\(327\) 0 0
\(328\) −6.00000 −0.331295
\(329\) 0 0
\(330\) 0 0
\(331\) −30.0000 −1.64895 −0.824475 0.565899i \(-0.808529\pi\)
−0.824475 + 0.565899i \(0.808529\pi\)
\(332\) 4.00000 0.219529
\(333\) −6.00000 −0.328798
\(334\) −6.00000 −0.328305
\(335\) 4.00000 0.218543
\(336\) 0 0
\(337\) 24.0000 1.30736 0.653682 0.756770i \(-0.273224\pi\)
0.653682 + 0.756770i \(0.273224\pi\)
\(338\) −1.00000 −0.0543928
\(339\) 0 0
\(340\) 4.00000 0.216930
\(341\) −2.00000 −0.108306
\(342\) 12.0000 0.648886
\(343\) 0 0
\(344\) 8.00000 0.431331
\(345\) 0 0
\(346\) −2.00000 −0.107521
\(347\) 28.0000 1.50312 0.751559 0.659665i \(-0.229302\pi\)
0.751559 + 0.659665i \(0.229302\pi\)
\(348\) 0 0
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 2.00000 0.106600
\(353\) 36.0000 1.91609 0.958043 0.286623i \(-0.0925328\pi\)
0.958043 + 0.286623i \(0.0925328\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) 10.0000 0.528516
\(359\) 32.0000 1.68890 0.844448 0.535638i \(-0.179929\pi\)
0.844448 + 0.535638i \(0.179929\pi\)
\(360\) 3.00000 0.158114
\(361\) −3.00000 −0.157895
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −14.0000 −0.730794 −0.365397 0.930852i \(-0.619067\pi\)
−0.365397 + 0.930852i \(0.619067\pi\)
\(368\) −2.00000 −0.104257
\(369\) −18.0000 −0.937043
\(370\) −2.00000 −0.103975
\(371\) 0 0
\(372\) 0 0
\(373\) −10.0000 −0.517780 −0.258890 0.965907i \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) 8.00000 0.413670
\(375\) 0 0
\(376\) 12.0000 0.618853
\(377\) 0 0
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 4.00000 0.205196
\(381\) 0 0
\(382\) 8.00000 0.409316
\(383\) 6.00000 0.306586 0.153293 0.988181i \(-0.451012\pi\)
0.153293 + 0.988181i \(0.451012\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −10.0000 −0.508987
\(387\) 24.0000 1.21999
\(388\) 2.00000 0.101535
\(389\) −20.0000 −1.01404 −0.507020 0.861934i \(-0.669253\pi\)
−0.507020 + 0.861934i \(0.669253\pi\)
\(390\) 0 0
\(391\) −8.00000 −0.404577
\(392\) 7.00000 0.353553
\(393\) 0 0
\(394\) −22.0000 −1.10834
\(395\) −4.00000 −0.201262
\(396\) 6.00000 0.301511
\(397\) 2.00000 0.100377 0.0501886 0.998740i \(-0.484018\pi\)
0.0501886 + 0.998740i \(0.484018\pi\)
\(398\) −20.0000 −1.00251
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) −2.00000 −0.0998752 −0.0499376 0.998752i \(-0.515902\pi\)
−0.0499376 + 0.998752i \(0.515902\pi\)
\(402\) 0 0
\(403\) 1.00000 0.0498135
\(404\) 10.0000 0.497519
\(405\) 9.00000 0.447214
\(406\) 0 0
\(407\) −4.00000 −0.198273
\(408\) 0 0
\(409\) −2.00000 −0.0988936 −0.0494468 0.998777i \(-0.515746\pi\)
−0.0494468 + 0.998777i \(0.515746\pi\)
\(410\) −6.00000 −0.296319
\(411\) 0 0
\(412\) −4.00000 −0.197066
\(413\) 0 0
\(414\) −6.00000 −0.294884
\(415\) 4.00000 0.196352
\(416\) −1.00000 −0.0490290
\(417\) 0 0
\(418\) 8.00000 0.391293
\(419\) 32.0000 1.56330 0.781651 0.623716i \(-0.214378\pi\)
0.781651 + 0.623716i \(0.214378\pi\)
\(420\) 0 0
\(421\) 38.0000 1.85201 0.926003 0.377515i \(-0.123221\pi\)
0.926003 + 0.377515i \(0.123221\pi\)
\(422\) −12.0000 −0.584151
\(423\) 36.0000 1.75038
\(424\) −10.0000 −0.485643
\(425\) 4.00000 0.194029
\(426\) 0 0
\(427\) 0 0
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) 8.00000 0.385794
\(431\) −8.00000 −0.385346 −0.192673 0.981263i \(-0.561716\pi\)
−0.192673 + 0.981263i \(0.561716\pi\)
\(432\) 0 0
\(433\) −4.00000 −0.192228 −0.0961139 0.995370i \(-0.530641\pi\)
−0.0961139 + 0.995370i \(0.530641\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −6.00000 −0.287348
\(437\) −8.00000 −0.382692
\(438\) 0 0
\(439\) 16.0000 0.763638 0.381819 0.924237i \(-0.375298\pi\)
0.381819 + 0.924237i \(0.375298\pi\)
\(440\) 2.00000 0.0953463
\(441\) 21.0000 1.00000
\(442\) −4.00000 −0.190261
\(443\) −36.0000 −1.71041 −0.855206 0.518289i \(-0.826569\pi\)
−0.855206 + 0.518289i \(0.826569\pi\)
\(444\) 0 0
\(445\) 6.00000 0.284427
\(446\) −2.00000 −0.0947027
\(447\) 0 0
\(448\) 0 0
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 3.00000 0.141421
\(451\) −12.0000 −0.565058
\(452\) 14.0000 0.658505
\(453\) 0 0
\(454\) −4.00000 −0.187729
\(455\) 0 0
\(456\) 0 0
\(457\) −4.00000 −0.187112 −0.0935561 0.995614i \(-0.529823\pi\)
−0.0935561 + 0.995614i \(0.529823\pi\)
\(458\) 12.0000 0.560723
\(459\) 0 0
\(460\) −2.00000 −0.0932505
\(461\) −36.0000 −1.67669 −0.838344 0.545142i \(-0.816476\pi\)
−0.838344 + 0.545142i \(0.816476\pi\)
\(462\) 0 0
\(463\) −30.0000 −1.39422 −0.697109 0.716965i \(-0.745531\pi\)
−0.697109 + 0.716965i \(0.745531\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 2.00000 0.0926482
\(467\) −20.0000 −0.925490 −0.462745 0.886492i \(-0.653135\pi\)
−0.462745 + 0.886492i \(0.653135\pi\)
\(468\) −3.00000 −0.138675
\(469\) 0 0
\(470\) 12.0000 0.553519
\(471\) 0 0
\(472\) −12.0000 −0.552345
\(473\) 16.0000 0.735681
\(474\) 0 0
\(475\) 4.00000 0.183533
\(476\) 0 0
\(477\) −30.0000 −1.37361
\(478\) 16.0000 0.731823
\(479\) −40.0000 −1.82765 −0.913823 0.406112i \(-0.866884\pi\)
−0.913823 + 0.406112i \(0.866884\pi\)
\(480\) 0 0
\(481\) 2.00000 0.0911922
\(482\) 22.0000 1.00207
\(483\) 0 0
\(484\) −7.00000 −0.318182
\(485\) 2.00000 0.0908153
\(486\) 0 0
\(487\) −2.00000 −0.0906287 −0.0453143 0.998973i \(-0.514429\pi\)
−0.0453143 + 0.998973i \(0.514429\pi\)
\(488\) 4.00000 0.181071
\(489\) 0 0
\(490\) 7.00000 0.316228
\(491\) −18.0000 −0.812329 −0.406164 0.913800i \(-0.633134\pi\)
−0.406164 + 0.913800i \(0.633134\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −4.00000 −0.179969
\(495\) 6.00000 0.269680
\(496\) 1.00000 0.0449013
\(497\) 0 0
\(498\) 0 0
\(499\) −2.00000 −0.0895323 −0.0447661 0.998997i \(-0.514254\pi\)
−0.0447661 + 0.998997i \(0.514254\pi\)
\(500\) 1.00000 0.0447214
\(501\) 0 0
\(502\) 6.00000 0.267793
\(503\) −36.0000 −1.60516 −0.802580 0.596544i \(-0.796540\pi\)
−0.802580 + 0.596544i \(0.796540\pi\)
\(504\) 0 0
\(505\) 10.0000 0.444994
\(506\) −4.00000 −0.177822
\(507\) 0 0
\(508\) 18.0000 0.798621
\(509\) 40.0000 1.77297 0.886484 0.462758i \(-0.153140\pi\)
0.886484 + 0.462758i \(0.153140\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −6.00000 −0.264649
\(515\) −4.00000 −0.176261
\(516\) 0 0
\(517\) 24.0000 1.05552
\(518\) 0 0
\(519\) 0 0
\(520\) −1.00000 −0.0438529
\(521\) 22.0000 0.963837 0.481919 0.876216i \(-0.339940\pi\)
0.481919 + 0.876216i \(0.339940\pi\)
\(522\) 0 0
\(523\) 32.0000 1.39926 0.699631 0.714504i \(-0.253348\pi\)
0.699631 + 0.714504i \(0.253348\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 18.0000 0.784837
\(527\) 4.00000 0.174243
\(528\) 0 0
\(529\) −19.0000 −0.826087
\(530\) −10.0000 −0.434372
\(531\) −36.0000 −1.56227
\(532\) 0 0
\(533\) 6.00000 0.259889
\(534\) 0 0
\(535\) 12.0000 0.518805
\(536\) −4.00000 −0.172774
\(537\) 0 0
\(538\) −24.0000 −1.03471
\(539\) 14.0000 0.603023
\(540\) 0 0
\(541\) −38.0000 −1.63375 −0.816874 0.576816i \(-0.804295\pi\)
−0.816874 + 0.576816i \(0.804295\pi\)
\(542\) −24.0000 −1.03089
\(543\) 0 0
\(544\) −4.00000 −0.171499
\(545\) −6.00000 −0.257012
\(546\) 0 0
\(547\) 4.00000 0.171028 0.0855138 0.996337i \(-0.472747\pi\)
0.0855138 + 0.996337i \(0.472747\pi\)
\(548\) 12.0000 0.512615
\(549\) 12.0000 0.512148
\(550\) 2.00000 0.0852803
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) −2.00000 −0.0849719
\(555\) 0 0
\(556\) 22.0000 0.933008
\(557\) 6.00000 0.254228 0.127114 0.991888i \(-0.459429\pi\)
0.127114 + 0.991888i \(0.459429\pi\)
\(558\) 3.00000 0.127000
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) 26.0000 1.09674
\(563\) −12.0000 −0.505740 −0.252870 0.967500i \(-0.581374\pi\)
−0.252870 + 0.967500i \(0.581374\pi\)
\(564\) 0 0
\(565\) 14.0000 0.588984
\(566\) 12.0000 0.504398
\(567\) 0 0
\(568\) 0 0
\(569\) −10.0000 −0.419222 −0.209611 0.977785i \(-0.567220\pi\)
−0.209611 + 0.977785i \(0.567220\pi\)
\(570\) 0 0
\(571\) −38.0000 −1.59025 −0.795125 0.606445i \(-0.792595\pi\)
−0.795125 + 0.606445i \(0.792595\pi\)
\(572\) −2.00000 −0.0836242
\(573\) 0 0
\(574\) 0 0
\(575\) −2.00000 −0.0834058
\(576\) −3.00000 −0.125000
\(577\) −26.0000 −1.08239 −0.541197 0.840896i \(-0.682029\pi\)
−0.541197 + 0.840896i \(0.682029\pi\)
\(578\) 1.00000 0.0415945
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −20.0000 −0.828315
\(584\) 0 0
\(585\) −3.00000 −0.124035
\(586\) −22.0000 −0.908812
\(587\) 20.0000 0.825488 0.412744 0.910847i \(-0.364570\pi\)
0.412744 + 0.910847i \(0.364570\pi\)
\(588\) 0 0
\(589\) 4.00000 0.164817
\(590\) −12.0000 −0.494032
\(591\) 0 0
\(592\) 2.00000 0.0821995
\(593\) 30.0000 1.23195 0.615976 0.787765i \(-0.288762\pi\)
0.615976 + 0.787765i \(0.288762\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −18.0000 −0.737309
\(597\) 0 0
\(598\) 2.00000 0.0817861
\(599\) 32.0000 1.30748 0.653742 0.756717i \(-0.273198\pi\)
0.653742 + 0.756717i \(0.273198\pi\)
\(600\) 0 0
\(601\) 14.0000 0.571072 0.285536 0.958368i \(-0.407828\pi\)
0.285536 + 0.958368i \(0.407828\pi\)
\(602\) 0 0
\(603\) −12.0000 −0.488678
\(604\) −12.0000 −0.488273
\(605\) −7.00000 −0.284590
\(606\) 0 0
\(607\) 40.0000 1.62355 0.811775 0.583970i \(-0.198502\pi\)
0.811775 + 0.583970i \(0.198502\pi\)
\(608\) −4.00000 −0.162221
\(609\) 0 0
\(610\) 4.00000 0.161955
\(611\) −12.0000 −0.485468
\(612\) −12.0000 −0.485071
\(613\) −22.0000 −0.888572 −0.444286 0.895885i \(-0.646543\pi\)
−0.444286 + 0.895885i \(0.646543\pi\)
\(614\) −12.0000 −0.484281
\(615\) 0 0
\(616\) 0 0
\(617\) −18.0000 −0.724653 −0.362326 0.932051i \(-0.618017\pi\)
−0.362326 + 0.932051i \(0.618017\pi\)
\(618\) 0 0
\(619\) −14.0000 −0.562708 −0.281354 0.959604i \(-0.590783\pi\)
−0.281354 + 0.959604i \(0.590783\pi\)
\(620\) 1.00000 0.0401610
\(621\) 0 0
\(622\) −24.0000 −0.962312
\(623\) 0 0
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −28.0000 −1.11911
\(627\) 0 0
\(628\) 10.0000 0.399043
\(629\) 8.00000 0.318981
\(630\) 0 0
\(631\) −48.0000 −1.91085 −0.955425 0.295234i \(-0.904602\pi\)
−0.955425 + 0.295234i \(0.904602\pi\)
\(632\) 4.00000 0.159111
\(633\) 0 0
\(634\) −34.0000 −1.35031
\(635\) 18.0000 0.714308
\(636\) 0 0
\(637\) −7.00000 −0.277350
\(638\) 0 0
\(639\) 0 0
\(640\) −1.00000 −0.0395285
\(641\) 42.0000 1.65890 0.829450 0.558581i \(-0.188654\pi\)
0.829450 + 0.558581i \(0.188654\pi\)
\(642\) 0 0
\(643\) −8.00000 −0.315489 −0.157745 0.987480i \(-0.550422\pi\)
−0.157745 + 0.987480i \(0.550422\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −16.0000 −0.629512
\(647\) 18.0000 0.707653 0.353827 0.935311i \(-0.384880\pi\)
0.353827 + 0.935311i \(0.384880\pi\)
\(648\) −9.00000 −0.353553
\(649\) −24.0000 −0.942082
\(650\) −1.00000 −0.0392232
\(651\) 0 0
\(652\) 4.00000 0.156652
\(653\) −34.0000 −1.33052 −0.665261 0.746611i \(-0.731680\pi\)
−0.665261 + 0.746611i \(0.731680\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 6.00000 0.234261
\(657\) 0 0
\(658\) 0 0
\(659\) 48.0000 1.86981 0.934907 0.354892i \(-0.115482\pi\)
0.934907 + 0.354892i \(0.115482\pi\)
\(660\) 0 0
\(661\) −30.0000 −1.16686 −0.583432 0.812162i \(-0.698291\pi\)
−0.583432 + 0.812162i \(0.698291\pi\)
\(662\) 30.0000 1.16598
\(663\) 0 0
\(664\) −4.00000 −0.155230
\(665\) 0 0
\(666\) 6.00000 0.232495
\(667\) 0 0
\(668\) 6.00000 0.232147
\(669\) 0 0
\(670\) −4.00000 −0.154533
\(671\) 8.00000 0.308837
\(672\) 0 0
\(673\) −16.0000 −0.616755 −0.308377 0.951264i \(-0.599786\pi\)
−0.308377 + 0.951264i \(0.599786\pi\)
\(674\) −24.0000 −0.924445
\(675\) 0 0
\(676\) 1.00000 0.0384615
\(677\) 46.0000 1.76792 0.883962 0.467559i \(-0.154866\pi\)
0.883962 + 0.467559i \(0.154866\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −4.00000 −0.153393
\(681\) 0 0
\(682\) 2.00000 0.0765840
\(683\) −12.0000 −0.459167 −0.229584 0.973289i \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) −12.0000 −0.458831
\(685\) 12.0000 0.458496
\(686\) 0 0
\(687\) 0 0
\(688\) −8.00000 −0.304997
\(689\) 10.0000 0.380970
\(690\) 0 0
\(691\) 32.0000 1.21734 0.608669 0.793424i \(-0.291704\pi\)
0.608669 + 0.793424i \(0.291704\pi\)
\(692\) 2.00000 0.0760286
\(693\) 0 0
\(694\) −28.0000 −1.06287
\(695\) 22.0000 0.834508
\(696\) 0 0
\(697\) 24.0000 0.909065
\(698\) −14.0000 −0.529908
\(699\) 0 0
\(700\) 0 0
\(701\) 14.0000 0.528773 0.264386 0.964417i \(-0.414831\pi\)
0.264386 + 0.964417i \(0.414831\pi\)
\(702\) 0 0
\(703\) 8.00000 0.301726
\(704\) −2.00000 −0.0753778
\(705\) 0 0
\(706\) −36.0000 −1.35488
\(707\) 0 0
\(708\) 0 0
\(709\) −16.0000 −0.600893 −0.300446 0.953799i \(-0.597136\pi\)
−0.300446 + 0.953799i \(0.597136\pi\)
\(710\) 0 0
\(711\) 12.0000 0.450035
\(712\) −6.00000 −0.224860
\(713\) −2.00000 −0.0749006
\(714\) 0 0
\(715\) −2.00000 −0.0747958
\(716\) −10.0000 −0.373718
\(717\) 0 0
\(718\) −32.0000 −1.19423
\(719\) −36.0000 −1.34257 −0.671287 0.741198i \(-0.734258\pi\)
−0.671287 + 0.741198i \(0.734258\pi\)
\(720\) −3.00000 −0.111803
\(721\) 0 0
\(722\) 3.00000 0.111648
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 16.0000 0.593407 0.296704 0.954970i \(-0.404113\pi\)
0.296704 + 0.954970i \(0.404113\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −32.0000 −1.18356
\(732\) 0 0
\(733\) −30.0000 −1.10808 −0.554038 0.832492i \(-0.686914\pi\)
−0.554038 + 0.832492i \(0.686914\pi\)
\(734\) 14.0000 0.516749
\(735\) 0 0
\(736\) 2.00000 0.0737210
\(737\) −8.00000 −0.294684
\(738\) 18.0000 0.662589
\(739\) 10.0000 0.367856 0.183928 0.982940i \(-0.441119\pi\)
0.183928 + 0.982940i \(0.441119\pi\)
\(740\) 2.00000 0.0735215
\(741\) 0 0
\(742\) 0 0
\(743\) −22.0000 −0.807102 −0.403551 0.914957i \(-0.632224\pi\)
−0.403551 + 0.914957i \(0.632224\pi\)
\(744\) 0 0
\(745\) −18.0000 −0.659469
\(746\) 10.0000 0.366126
\(747\) −12.0000 −0.439057
\(748\) −8.00000 −0.292509
\(749\) 0 0
\(750\) 0 0
\(751\) 8.00000 0.291924 0.145962 0.989290i \(-0.453372\pi\)
0.145962 + 0.989290i \(0.453372\pi\)
\(752\) −12.0000 −0.437595
\(753\) 0 0
\(754\) 0 0
\(755\) −12.0000 −0.436725
\(756\) 0 0
\(757\) 34.0000 1.23575 0.617876 0.786276i \(-0.287994\pi\)
0.617876 + 0.786276i \(0.287994\pi\)
\(758\) 20.0000 0.726433
\(759\) 0 0
\(760\) −4.00000 −0.145095
\(761\) 22.0000 0.797499 0.398750 0.917060i \(-0.369444\pi\)
0.398750 + 0.917060i \(0.369444\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −8.00000 −0.289430
\(765\) −12.0000 −0.433861
\(766\) −6.00000 −0.216789
\(767\) 12.0000 0.433295
\(768\) 0 0
\(769\) −26.0000 −0.937584 −0.468792 0.883309i \(-0.655311\pi\)
−0.468792 + 0.883309i \(0.655311\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 10.0000 0.359908
\(773\) 2.00000 0.0719350 0.0359675 0.999353i \(-0.488549\pi\)
0.0359675 + 0.999353i \(0.488549\pi\)
\(774\) −24.0000 −0.862662
\(775\) 1.00000 0.0359211
\(776\) −2.00000 −0.0717958
\(777\) 0 0
\(778\) 20.0000 0.717035
\(779\) 24.0000 0.859889
\(780\) 0 0
\(781\) 0 0
\(782\) 8.00000 0.286079
\(783\) 0 0
\(784\) −7.00000 −0.250000
\(785\) 10.0000 0.356915
\(786\) 0 0
\(787\) 12.0000 0.427754 0.213877 0.976861i \(-0.431391\pi\)
0.213877 + 0.976861i \(0.431391\pi\)
\(788\) 22.0000 0.783718
\(789\) 0 0
\(790\) 4.00000 0.142314
\(791\) 0 0
\(792\) −6.00000 −0.213201
\(793\) −4.00000 −0.142044
\(794\) −2.00000 −0.0709773
\(795\) 0 0
\(796\) 20.0000 0.708881
\(797\) 10.0000 0.354218 0.177109 0.984191i \(-0.443325\pi\)
0.177109 + 0.984191i \(0.443325\pi\)
\(798\) 0 0
\(799\) −48.0000 −1.69812
\(800\) −1.00000 −0.0353553
\(801\) −18.0000 −0.635999
\(802\) 2.00000 0.0706225
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) −1.00000 −0.0352235
\(807\) 0 0
\(808\) −10.0000 −0.351799
\(809\) −14.0000 −0.492214 −0.246107 0.969243i \(-0.579151\pi\)
−0.246107 + 0.969243i \(0.579151\pi\)
\(810\) −9.00000 −0.316228
\(811\) 20.0000 0.702295 0.351147 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 4.00000 0.140200
\(815\) 4.00000 0.140114
\(816\) 0 0
\(817\) −32.0000 −1.11954
\(818\) 2.00000 0.0699284
\(819\) 0 0
\(820\) 6.00000 0.209529
\(821\) 36.0000 1.25641 0.628204 0.778048i \(-0.283790\pi\)
0.628204 + 0.778048i \(0.283790\pi\)
\(822\) 0 0
\(823\) 2.00000 0.0697156 0.0348578 0.999392i \(-0.488902\pi\)
0.0348578 + 0.999392i \(0.488902\pi\)
\(824\) 4.00000 0.139347
\(825\) 0 0
\(826\) 0 0
\(827\) −36.0000 −1.25184 −0.625921 0.779886i \(-0.715277\pi\)
−0.625921 + 0.779886i \(0.715277\pi\)
\(828\) 6.00000 0.208514
\(829\) 32.0000 1.11141 0.555703 0.831381i \(-0.312449\pi\)
0.555703 + 0.831381i \(0.312449\pi\)
\(830\) −4.00000 −0.138842
\(831\) 0 0
\(832\) 1.00000 0.0346688
\(833\) −28.0000 −0.970143
\(834\) 0 0
\(835\) 6.00000 0.207639
\(836\) −8.00000 −0.276686
\(837\) 0 0
\(838\) −32.0000 −1.10542
\(839\) −48.0000 −1.65714 −0.828572 0.559883i \(-0.810846\pi\)
−0.828572 + 0.559883i \(0.810846\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) −38.0000 −1.30957
\(843\) 0 0
\(844\) 12.0000 0.413057
\(845\) 1.00000 0.0344010
\(846\) −36.0000 −1.23771
\(847\) 0 0
\(848\) 10.0000 0.343401
\(849\) 0 0
\(850\) −4.00000 −0.137199
\(851\) −4.00000 −0.137118
\(852\) 0 0
\(853\) −42.0000 −1.43805 −0.719026 0.694983i \(-0.755412\pi\)
−0.719026 + 0.694983i \(0.755412\pi\)
\(854\) 0 0
\(855\) −12.0000 −0.410391
\(856\) −12.0000 −0.410152
\(857\) 6.00000 0.204956 0.102478 0.994735i \(-0.467323\pi\)
0.102478 + 0.994735i \(0.467323\pi\)
\(858\) 0 0
\(859\) −14.0000 −0.477674 −0.238837 0.971060i \(-0.576766\pi\)
−0.238837 + 0.971060i \(0.576766\pi\)
\(860\) −8.00000 −0.272798
\(861\) 0 0
\(862\) 8.00000 0.272481
\(863\) −18.0000 −0.612727 −0.306364 0.951915i \(-0.599112\pi\)
−0.306364 + 0.951915i \(0.599112\pi\)
\(864\) 0 0
\(865\) 2.00000 0.0680020
\(866\) 4.00000 0.135926
\(867\) 0 0
\(868\) 0 0
\(869\) 8.00000 0.271381
\(870\) 0 0
\(871\) 4.00000 0.135535
\(872\) 6.00000 0.203186
\(873\) −6.00000 −0.203069
\(874\) 8.00000 0.270604
\(875\) 0 0
\(876\) 0 0
\(877\) −22.0000 −0.742887 −0.371444 0.928456i \(-0.621137\pi\)
−0.371444 + 0.928456i \(0.621137\pi\)
\(878\) −16.0000 −0.539974
\(879\) 0 0
\(880\) −2.00000 −0.0674200
\(881\) 14.0000 0.471672 0.235836 0.971793i \(-0.424217\pi\)
0.235836 + 0.971793i \(0.424217\pi\)
\(882\) −21.0000 −0.707107
\(883\) −16.0000 −0.538443 −0.269221 0.963078i \(-0.586766\pi\)
−0.269221 + 0.963078i \(0.586766\pi\)
\(884\) 4.00000 0.134535
\(885\) 0 0
\(886\) 36.0000 1.20944
\(887\) 8.00000 0.268614 0.134307 0.990940i \(-0.457119\pi\)
0.134307 + 0.990940i \(0.457119\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −6.00000 −0.201120
\(891\) −18.0000 −0.603023
\(892\) 2.00000 0.0669650
\(893\) −48.0000 −1.60626
\(894\) 0 0
\(895\) −10.0000 −0.334263
\(896\) 0 0
\(897\) 0 0
\(898\) −30.0000 −1.00111
\(899\) 0 0
\(900\) −3.00000 −0.100000
\(901\) 40.0000 1.33259
\(902\) 12.0000 0.399556
\(903\) 0 0
\(904\) −14.0000 −0.465633
\(905\) 0 0
\(906\) 0 0
\(907\) −36.0000 −1.19536 −0.597680 0.801735i \(-0.703911\pi\)
−0.597680 + 0.801735i \(0.703911\pi\)
\(908\) 4.00000 0.132745
\(909\) −30.0000 −0.995037
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) −8.00000 −0.264761
\(914\) 4.00000 0.132308
\(915\) 0 0
\(916\) −12.0000 −0.396491
\(917\) 0 0
\(918\) 0 0
\(919\) −48.0000 −1.58337 −0.791687 0.610927i \(-0.790797\pi\)
−0.791687 + 0.610927i \(0.790797\pi\)
\(920\) 2.00000 0.0659380
\(921\) 0 0
\(922\) 36.0000 1.18560
\(923\) 0 0
\(924\) 0 0
\(925\) 2.00000 0.0657596
\(926\) 30.0000 0.985861
\(927\) 12.0000 0.394132
\(928\) 0 0
\(929\) 54.0000 1.77168 0.885841 0.463988i \(-0.153582\pi\)
0.885841 + 0.463988i \(0.153582\pi\)
\(930\) 0 0
\(931\) −28.0000 −0.917663
\(932\) −2.00000 −0.0655122
\(933\) 0 0
\(934\) 20.0000 0.654420
\(935\) −8.00000 −0.261628
\(936\) 3.00000 0.0980581
\(937\) −2.00000 −0.0653372 −0.0326686 0.999466i \(-0.510401\pi\)
−0.0326686 + 0.999466i \(0.510401\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −12.0000 −0.391397
\(941\) −24.0000 −0.782378 −0.391189 0.920310i \(-0.627936\pi\)
−0.391189 + 0.920310i \(0.627936\pi\)
\(942\) 0 0
\(943\) −12.0000 −0.390774
\(944\) 12.0000 0.390567
\(945\) 0 0
\(946\) −16.0000 −0.520205
\(947\) −48.0000 −1.55979 −0.779895 0.625910i \(-0.784728\pi\)
−0.779895 + 0.625910i \(0.784728\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) −4.00000 −0.129777
\(951\) 0 0
\(952\) 0 0
\(953\) −24.0000 −0.777436 −0.388718 0.921357i \(-0.627082\pi\)
−0.388718 + 0.921357i \(0.627082\pi\)
\(954\) 30.0000 0.971286
\(955\) −8.00000 −0.258874
\(956\) −16.0000 −0.517477
\(957\) 0 0
\(958\) 40.0000 1.29234
\(959\) 0 0
\(960\) 0 0
\(961\) 1.00000 0.0322581
\(962\) −2.00000 −0.0644826
\(963\) −36.0000 −1.16008
\(964\) −22.0000 −0.708572
\(965\) 10.0000 0.321911
\(966\) 0 0
\(967\) −50.0000 −1.60789 −0.803946 0.594703i \(-0.797270\pi\)
−0.803946 + 0.594703i \(0.797270\pi\)
\(968\) 7.00000 0.224989
\(969\) 0 0
\(970\) −2.00000 −0.0642161
\(971\) 28.0000 0.898563 0.449281 0.893390i \(-0.351680\pi\)
0.449281 + 0.893390i \(0.351680\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 2.00000 0.0640841
\(975\) 0 0
\(976\) −4.00000 −0.128037
\(977\) 54.0000 1.72761 0.863807 0.503824i \(-0.168074\pi\)
0.863807 + 0.503824i \(0.168074\pi\)
\(978\) 0 0
\(979\) −12.0000 −0.383522
\(980\) −7.00000 −0.223607
\(981\) 18.0000 0.574696
\(982\) 18.0000 0.574403
\(983\) −6.00000 −0.191370 −0.0956851 0.995412i \(-0.530504\pi\)
−0.0956851 + 0.995412i \(0.530504\pi\)
\(984\) 0 0
\(985\) 22.0000 0.700978
\(986\) 0 0
\(987\) 0 0
\(988\) 4.00000 0.127257
\(989\) 16.0000 0.508770
\(990\) −6.00000 −0.190693
\(991\) −20.0000 −0.635321 −0.317660 0.948205i \(-0.602897\pi\)
−0.317660 + 0.948205i \(0.602897\pi\)
\(992\) −1.00000 −0.0317500
\(993\) 0 0
\(994\) 0 0
\(995\) 20.0000 0.634043
\(996\) 0 0
\(997\) 38.0000 1.20347 0.601736 0.798695i \(-0.294476\pi\)
0.601736 + 0.798695i \(0.294476\pi\)
\(998\) 2.00000 0.0633089
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))