Properties

Label 17.2.a.a.1.1
Level 17
Weight 2
Character 17.1
Self dual Yes
Analytic conductor 0.136
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(0.135745683436\)
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 \(\chi\) = 17.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-1.00000 q^{4}\) \(-2.00000 q^{5}\) \(+4.00000 q^{7}\) \(+3.00000 q^{8}\) \(-3.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-1.00000 q^{4}\) \(-2.00000 q^{5}\) \(+4.00000 q^{7}\) \(+3.00000 q^{8}\) \(-3.00000 q^{9}\) \(+2.00000 q^{10}\) \(-2.00000 q^{13}\) \(-4.00000 q^{14}\) \(-1.00000 q^{16}\) \(+1.00000 q^{17}\) \(+3.00000 q^{18}\) \(-4.00000 q^{19}\) \(+2.00000 q^{20}\) \(+4.00000 q^{23}\) \(-1.00000 q^{25}\) \(+2.00000 q^{26}\) \(-4.00000 q^{28}\) \(+6.00000 q^{29}\) \(+4.00000 q^{31}\) \(-5.00000 q^{32}\) \(-1.00000 q^{34}\) \(-8.00000 q^{35}\) \(+3.00000 q^{36}\) \(-2.00000 q^{37}\) \(+4.00000 q^{38}\) \(-6.00000 q^{40}\) \(-6.00000 q^{41}\) \(+4.00000 q^{43}\) \(+6.00000 q^{45}\) \(-4.00000 q^{46}\) \(+9.00000 q^{49}\) \(+1.00000 q^{50}\) \(+2.00000 q^{52}\) \(+6.00000 q^{53}\) \(+12.0000 q^{56}\) \(-6.00000 q^{58}\) \(-12.0000 q^{59}\) \(-10.0000 q^{61}\) \(-4.00000 q^{62}\) \(-12.0000 q^{63}\) \(+7.00000 q^{64}\) \(+4.00000 q^{65}\) \(+4.00000 q^{67}\) \(-1.00000 q^{68}\) \(+8.00000 q^{70}\) \(-4.00000 q^{71}\) \(-9.00000 q^{72}\) \(-6.00000 q^{73}\) \(+2.00000 q^{74}\) \(+4.00000 q^{76}\) \(+12.0000 q^{79}\) \(+2.00000 q^{80}\) \(+9.00000 q^{81}\) \(+6.00000 q^{82}\) \(-4.00000 q^{83}\) \(-2.00000 q^{85}\) \(-4.00000 q^{86}\) \(+10.0000 q^{89}\) \(-6.00000 q^{90}\) \(-8.00000 q^{91}\) \(-4.00000 q^{92}\) \(+8.00000 q^{95}\) \(+2.00000 q^{97}\) \(-9.00000 q^{98}\) \(+O(q^{100})\)

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 −0.353553 0.935414i \(-0.615027\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) −1.00000 −0.500000
\(5\) −2.00000 −0.894427 −0.447214 0.894427i \(-0.647584\pi\)
−0.447214 + 0.894427i \(0.647584\pi\)
\(6\) 0 0
\(7\) 4.00000 1.51186 0.755929 0.654654i \(-0.227186\pi\)
0.755929 + 0.654654i \(0.227186\pi\)
\(8\) 3.00000 1.06066
\(9\) −3.00000 −1.00000
\(10\) 2.00000 0.632456
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) −4.00000 −1.06904
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 1.00000 0.242536
\(18\) 3.00000 0.707107
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) 2.00000 0.447214
\(21\) 0 0
\(22\) 0 0
\(23\) 4.00000 0.834058 0.417029 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 2.00000 0.392232
\(27\) 0 0
\(28\) −4.00000 −0.755929
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) −5.00000 −0.883883
\(33\) 0 0
\(34\) −1.00000 −0.171499
\(35\) −8.00000 −1.35225
\(36\) 3.00000 0.500000
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 4.00000 0.648886
\(39\) 0 0
\(40\) −6.00000 −0.948683
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) 6.00000 0.894427
\(46\) −4.00000 −0.589768
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 9.00000 1.28571
\(50\) 1.00000 0.141421
\(51\) 0 0
\(52\) 2.00000 0.277350
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 12.0000 1.60357
\(57\) 0 0
\(58\) −6.00000 −0.787839
\(59\) −12.0000 −1.56227 −0.781133 0.624364i \(-0.785358\pi\)
−0.781133 + 0.624364i \(0.785358\pi\)
\(60\) 0 0
\(61\) −10.0000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) −4.00000 −0.508001
\(63\) −12.0000 −1.51186
\(64\) 7.00000 0.875000
\(65\) 4.00000 0.496139
\(66\) 0 0
\(67\) 4.00000 0.488678 0.244339 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) −1.00000 −0.121268
\(69\) 0 0
\(70\) 8.00000 0.956183
\(71\) −4.00000 −0.474713 −0.237356 0.971423i \(-0.576281\pi\)
−0.237356 + 0.971423i \(0.576281\pi\)
\(72\) −9.00000 −1.06066
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) 2.00000 0.232495
\(75\) 0 0
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) 0 0
\(79\) 12.0000 1.35011 0.675053 0.737769i \(-0.264121\pi\)
0.675053 + 0.737769i \(0.264121\pi\)
\(80\) 2.00000 0.223607
\(81\) 9.00000 1.00000
\(82\) 6.00000 0.662589
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) −2.00000 −0.216930
\(86\) −4.00000 −0.431331
\(87\) 0 0
\(88\) 0 0
\(89\) 10.0000 1.06000 0.529999 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) −6.00000 −0.632456
\(91\) −8.00000 −0.838628
\(92\) −4.00000 −0.417029
\(93\) 0 0
\(94\) 0 0
\(95\) 8.00000 0.820783
\(96\) 0 0
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) −9.00000 −0.909137
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) −10.0000 −0.995037 −0.497519 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) −6.00000 −0.588348
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 8.00000 0.773389 0.386695 0.922208i \(-0.373617\pi\)
0.386695 + 0.922208i \(0.373617\pi\)
\(108\) 0 0
\(109\) 6.00000 0.574696 0.287348 0.957826i \(-0.407226\pi\)
0.287348 + 0.957826i \(0.407226\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −4.00000 −0.377964
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) 0 0
\(115\) −8.00000 −0.746004
\(116\) −6.00000 −0.557086
\(117\) 6.00000 0.554700
\(118\) 12.0000 1.10469
\(119\) 4.00000 0.366679
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 10.0000 0.905357
\(123\) 0 0
\(124\) −4.00000 −0.359211
\(125\) 12.0000 1.07331
\(126\) 12.0000 1.06904
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 3.00000 0.265165
\(129\) 0 0
\(130\) −4.00000 −0.350823
\(131\) 16.0000 1.39793 0.698963 0.715158i \(-0.253645\pi\)
0.698963 + 0.715158i \(0.253645\pi\)
\(132\) 0 0
\(133\) −16.0000 −1.38738
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) 3.00000 0.257248
\(137\) −6.00000 −0.512615 −0.256307 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) 0 0
\(139\) −8.00000 −0.678551 −0.339276 0.940687i \(-0.610182\pi\)
−0.339276 + 0.940687i \(0.610182\pi\)
\(140\) 8.00000 0.676123
\(141\) 0 0
\(142\) 4.00000 0.335673
\(143\) 0 0
\(144\) 3.00000 0.250000
\(145\) −12.0000 −0.996546
\(146\) 6.00000 0.496564
\(147\) 0 0
\(148\) 2.00000 0.164399
\(149\) −10.0000 −0.819232 −0.409616 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) 0 0
\(151\) −16.0000 −1.30206 −0.651031 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) −12.0000 −0.973329
\(153\) −3.00000 −0.242536
\(154\) 0 0
\(155\) −8.00000 −0.642575
\(156\) 0 0
\(157\) −2.00000 −0.159617 −0.0798087 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) −12.0000 −0.954669
\(159\) 0 0
\(160\) 10.0000 0.790569
\(161\) 16.0000 1.26098
\(162\) −9.00000 −0.707107
\(163\) 24.0000 1.87983 0.939913 0.341415i \(-0.110906\pi\)
0.939913 + 0.341415i \(0.110906\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) 4.00000 0.310460
\(167\) −4.00000 −0.309529 −0.154765 0.987951i \(-0.549462\pi\)
−0.154765 + 0.987951i \(0.549462\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 2.00000 0.153393
\(171\) 12.0000 0.917663
\(172\) −4.00000 −0.304997
\(173\) 22.0000 1.67263 0.836315 0.548250i \(-0.184706\pi\)
0.836315 + 0.548250i \(0.184706\pi\)
\(174\) 0 0
\(175\) −4.00000 −0.302372
\(176\) 0 0
\(177\) 0 0
\(178\) −10.0000 −0.749532
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) −6.00000 −0.447214
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 8.00000 0.592999
\(183\) 0 0
\(184\) 12.0000 0.884652
\(185\) 4.00000 0.294086
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) −8.00000 −0.580381
\(191\) −16.0000 −1.15772 −0.578860 0.815427i \(-0.696502\pi\)
−0.578860 + 0.815427i \(0.696502\pi\)
\(192\) 0 0
\(193\) 2.00000 0.143963 0.0719816 0.997406i \(-0.477068\pi\)
0.0719816 + 0.997406i \(0.477068\pi\)
\(194\) −2.00000 −0.143592
\(195\) 0 0
\(196\) −9.00000 −0.642857
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) −20.0000 −1.41776 −0.708881 0.705328i \(-0.750800\pi\)
−0.708881 + 0.705328i \(0.750800\pi\)
\(200\) −3.00000 −0.212132
\(201\) 0 0
\(202\) 10.0000 0.703598
\(203\) 24.0000 1.68447
\(204\) 0 0
\(205\) 12.0000 0.838116
\(206\) −8.00000 −0.557386
\(207\) −12.0000 −0.834058
\(208\) 2.00000 0.138675
\(209\) 0 0
\(210\) 0 0
\(211\) 8.00000 0.550743 0.275371 0.961338i \(-0.411199\pi\)
0.275371 + 0.961338i \(0.411199\pi\)
\(212\) −6.00000 −0.412082
\(213\) 0 0
\(214\) −8.00000 −0.546869
\(215\) −8.00000 −0.545595
\(216\) 0 0
\(217\) 16.0000 1.08615
\(218\) −6.00000 −0.406371
\(219\) 0 0
\(220\) 0 0
\(221\) −2.00000 −0.134535
\(222\) 0 0
\(223\) 24.0000 1.60716 0.803579 0.595198i \(-0.202926\pi\)
0.803579 + 0.595198i \(0.202926\pi\)
\(224\) −20.0000 −1.33631
\(225\) 3.00000 0.200000
\(226\) 14.0000 0.931266
\(227\) −24.0000 −1.59294 −0.796468 0.604681i \(-0.793301\pi\)
−0.796468 + 0.604681i \(0.793301\pi\)
\(228\) 0 0
\(229\) 6.00000 0.396491 0.198246 0.980152i \(-0.436476\pi\)
0.198246 + 0.980152i \(0.436476\pi\)
\(230\) 8.00000 0.527504
\(231\) 0 0
\(232\) 18.0000 1.18176
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) −6.00000 −0.392232
\(235\) 0 0
\(236\) 12.0000 0.781133
\(237\) 0 0
\(238\) −4.00000 −0.259281
\(239\) −16.0000 −1.03495 −0.517477 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) 0 0
\(241\) 18.0000 1.15948 0.579741 0.814801i \(-0.303154\pi\)
0.579741 + 0.814801i \(0.303154\pi\)
\(242\) 11.0000 0.707107
\(243\) 0 0
\(244\) 10.0000 0.640184
\(245\) −18.0000 −1.14998
\(246\) 0 0
\(247\) 8.00000 0.509028
\(248\) 12.0000 0.762001
\(249\) 0 0
\(250\) −12.0000 −0.758947
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 12.0000 0.755929
\(253\) 0 0
\(254\) −8.00000 −0.501965
\(255\) 0 0
\(256\) −17.0000 −1.06250
\(257\) 18.0000 1.12281 0.561405 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) 0 0
\(259\) −8.00000 −0.497096
\(260\) −4.00000 −0.248069
\(261\) −18.0000 −1.11417
\(262\) −16.0000 −0.988483
\(263\) −16.0000 −0.986602 −0.493301 0.869859i \(-0.664210\pi\)
−0.493301 + 0.869859i \(0.664210\pi\)
\(264\) 0 0
\(265\) −12.0000 −0.737154
\(266\) 16.0000 0.981023
\(267\) 0 0
\(268\) −4.00000 −0.244339
\(269\) 22.0000 1.34136 0.670682 0.741745i \(-0.266002\pi\)
0.670682 + 0.741745i \(0.266002\pi\)
\(270\) 0 0
\(271\) −16.0000 −0.971931 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) −1.00000 −0.0606339
\(273\) 0 0
\(274\) 6.00000 0.362473
\(275\) 0 0
\(276\) 0 0
\(277\) 14.0000 0.841178 0.420589 0.907251i \(-0.361823\pi\)
0.420589 + 0.907251i \(0.361823\pi\)
\(278\) 8.00000 0.479808
\(279\) −12.0000 −0.718421
\(280\) −24.0000 −1.43427
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) 0 0
\(283\) −16.0000 −0.951101 −0.475551 0.879688i \(-0.657751\pi\)
−0.475551 + 0.879688i \(0.657751\pi\)
\(284\) 4.00000 0.237356
\(285\) 0 0
\(286\) 0 0
\(287\) −24.0000 −1.41668
\(288\) 15.0000 0.883883
\(289\) 1.00000 0.0588235
\(290\) 12.0000 0.704664
\(291\) 0 0
\(292\) 6.00000 0.351123
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 0 0
\(295\) 24.0000 1.39733
\(296\) −6.00000 −0.348743
\(297\) 0 0
\(298\) 10.0000 0.579284
\(299\) −8.00000 −0.462652
\(300\) 0 0
\(301\) 16.0000 0.922225
\(302\) 16.0000 0.920697
\(303\) 0 0
\(304\) 4.00000 0.229416
\(305\) 20.0000 1.14520
\(306\) 3.00000 0.171499
\(307\) −12.0000 −0.684876 −0.342438 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 8.00000 0.454369
\(311\) 28.0000 1.58773 0.793867 0.608091i \(-0.208065\pi\)
0.793867 + 0.608091i \(0.208065\pi\)
\(312\) 0 0
\(313\) −22.0000 −1.24351 −0.621757 0.783210i \(-0.713581\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(314\) 2.00000 0.112867
\(315\) 24.0000 1.35225
\(316\) −12.0000 −0.675053
\(317\) −10.0000 −0.561656 −0.280828 0.959758i \(-0.590609\pi\)
−0.280828 + 0.959758i \(0.590609\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −14.0000 −0.782624
\(321\) 0 0
\(322\) −16.0000 −0.891645
\(323\) −4.00000 −0.222566
\(324\) −9.00000 −0.500000
\(325\) 2.00000 0.110940
\(326\) −24.0000 −1.32924
\(327\) 0 0
\(328\) −18.0000 −0.993884
\(329\) 0 0
\(330\) 0 0
\(331\) 4.00000 0.219860 0.109930 0.993939i \(-0.464937\pi\)
0.109930 + 0.993939i \(0.464937\pi\)
\(332\) 4.00000 0.219529
\(333\) 6.00000 0.328798
\(334\) 4.00000 0.218870
\(335\) −8.00000 −0.437087
\(336\) 0 0
\(337\) −14.0000 −0.762629 −0.381314 0.924445i \(-0.624528\pi\)
−0.381314 + 0.924445i \(0.624528\pi\)
\(338\) 9.00000 0.489535
\(339\) 0 0
\(340\) 2.00000 0.108465
\(341\) 0 0
\(342\) −12.0000 −0.648886
\(343\) 8.00000 0.431959
\(344\) 12.0000 0.646997
\(345\) 0 0
\(346\) −22.0000 −1.18273
\(347\) 32.0000 1.71785 0.858925 0.512101i \(-0.171133\pi\)
0.858925 + 0.512101i \(0.171133\pi\)
\(348\) 0 0
\(349\) −18.0000 −0.963518 −0.481759 0.876304i \(-0.660002\pi\)
−0.481759 + 0.876304i \(0.660002\pi\)
\(350\) 4.00000 0.213809
\(351\) 0 0
\(352\) 0 0
\(353\) −30.0000 −1.59674 −0.798369 0.602168i \(-0.794304\pi\)
−0.798369 + 0.602168i \(0.794304\pi\)
\(354\) 0 0
\(355\) 8.00000 0.424596
\(356\) −10.0000 −0.529999
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 18.0000 0.948683
\(361\) −3.00000 −0.157895
\(362\) 2.00000 0.105118
\(363\) 0 0
\(364\) 8.00000 0.419314
\(365\) 12.0000 0.628109
\(366\) 0 0
\(367\) 28.0000 1.46159 0.730794 0.682598i \(-0.239150\pi\)
0.730794 + 0.682598i \(0.239150\pi\)
\(368\) −4.00000 −0.208514
\(369\) 18.0000 0.937043
\(370\) −4.00000 −0.207950
\(371\) 24.0000 1.24602
\(372\) 0 0
\(373\) 6.00000 0.310668 0.155334 0.987862i \(-0.450355\pi\)
0.155334 + 0.987862i \(0.450355\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) −8.00000 −0.410932 −0.205466 0.978664i \(-0.565871\pi\)
−0.205466 + 0.978664i \(0.565871\pi\)
\(380\) −8.00000 −0.410391
\(381\) 0 0
\(382\) 16.0000 0.818631
\(383\) −24.0000 −1.22634 −0.613171 0.789950i \(-0.710106\pi\)
−0.613171 + 0.789950i \(0.710106\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −2.00000 −0.101797
\(387\) −12.0000 −0.609994
\(388\) −2.00000 −0.101535
\(389\) 6.00000 0.304212 0.152106 0.988364i \(-0.451394\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(390\) 0 0
\(391\) 4.00000 0.202289
\(392\) 27.0000 1.36371
\(393\) 0 0
\(394\) 18.0000 0.906827
\(395\) −24.0000 −1.20757
\(396\) 0 0
\(397\) 6.00000 0.301131 0.150566 0.988600i \(-0.451890\pi\)
0.150566 + 0.988600i \(0.451890\pi\)
\(398\) 20.0000 1.00251
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) −14.0000 −0.699127 −0.349563 0.936913i \(-0.613670\pi\)
−0.349563 + 0.936913i \(0.613670\pi\)
\(402\) 0 0
\(403\) −8.00000 −0.398508
\(404\) 10.0000 0.497519
\(405\) −18.0000 −0.894427
\(406\) −24.0000 −1.19110
\(407\) 0 0
\(408\) 0 0
\(409\) 26.0000 1.28562 0.642809 0.766027i \(-0.277769\pi\)
0.642809 + 0.766027i \(0.277769\pi\)
\(410\) −12.0000 −0.592638
\(411\) 0 0
\(412\) −8.00000 −0.394132
\(413\) −48.0000 −2.36193
\(414\) 12.0000 0.589768
\(415\) 8.00000 0.392705
\(416\) 10.0000 0.490290
\(417\) 0 0
\(418\) 0 0
\(419\) 8.00000 0.390826 0.195413 0.980721i \(-0.437395\pi\)
0.195413 + 0.980721i \(0.437395\pi\)
\(420\) 0 0
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) −8.00000 −0.389434
\(423\) 0 0
\(424\) 18.0000 0.874157
\(425\) −1.00000 −0.0485071
\(426\) 0 0
\(427\) −40.0000 −1.93574
\(428\) −8.00000 −0.386695
\(429\) 0 0
\(430\) 8.00000 0.385794
\(431\) 12.0000 0.578020 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) 0 0
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) −16.0000 −0.768025
\(435\) 0 0
\(436\) −6.00000 −0.287348
\(437\) −16.0000 −0.765384
\(438\) 0 0
\(439\) −20.0000 −0.954548 −0.477274 0.878755i \(-0.658375\pi\)
−0.477274 + 0.878755i \(0.658375\pi\)
\(440\) 0 0
\(441\) −27.0000 −1.28571
\(442\) 2.00000 0.0951303
\(443\) 28.0000 1.33032 0.665160 0.746701i \(-0.268363\pi\)
0.665160 + 0.746701i \(0.268363\pi\)
\(444\) 0 0
\(445\) −20.0000 −0.948091
\(446\) −24.0000 −1.13643
\(447\) 0 0
\(448\) 28.0000 1.32288
\(449\) 34.0000 1.60456 0.802280 0.596948i \(-0.203620\pi\)
0.802280 + 0.596948i \(0.203620\pi\)
\(450\) −3.00000 −0.141421
\(451\) 0 0
\(452\) 14.0000 0.658505
\(453\) 0 0
\(454\) 24.0000 1.12638
\(455\) 16.0000 0.750092
\(456\) 0 0
\(457\) −6.00000 −0.280668 −0.140334 0.990104i \(-0.544818\pi\)
−0.140334 + 0.990104i \(0.544818\pi\)
\(458\) −6.00000 −0.280362
\(459\) 0 0
\(460\) 8.00000 0.373002
\(461\) −2.00000 −0.0931493 −0.0465746 0.998915i \(-0.514831\pi\)
−0.0465746 + 0.998915i \(0.514831\pi\)
\(462\) 0 0
\(463\) 32.0000 1.48717 0.743583 0.668644i \(-0.233125\pi\)
0.743583 + 0.668644i \(0.233125\pi\)
\(464\) −6.00000 −0.278543
\(465\) 0 0
\(466\) 6.00000 0.277945
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) −6.00000 −0.277350
\(469\) 16.0000 0.738811
\(470\) 0 0
\(471\) 0 0
\(472\) −36.0000 −1.65703
\(473\) 0 0
\(474\) 0 0
\(475\) 4.00000 0.183533
\(476\) −4.00000 −0.183340
\(477\) −18.0000 −0.824163
\(478\) 16.0000 0.731823
\(479\) 36.0000 1.64488 0.822441 0.568850i \(-0.192612\pi\)
0.822441 + 0.568850i \(0.192612\pi\)
\(480\) 0 0
\(481\) 4.00000 0.182384
\(482\) −18.0000 −0.819878
\(483\) 0 0
\(484\) 11.0000 0.500000
\(485\) −4.00000 −0.181631
\(486\) 0 0
\(487\) 20.0000 0.906287 0.453143 0.891438i \(-0.350303\pi\)
0.453143 + 0.891438i \(0.350303\pi\)
\(488\) −30.0000 −1.35804
\(489\) 0 0
\(490\) 18.0000 0.813157
\(491\) 20.0000 0.902587 0.451294 0.892375i \(-0.350963\pi\)
0.451294 + 0.892375i \(0.350963\pi\)
\(492\) 0 0
\(493\) 6.00000 0.270226
\(494\) −8.00000 −0.359937
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) −16.0000 −0.717698
\(498\) 0 0
\(499\) −40.0000 −1.79065 −0.895323 0.445418i \(-0.853055\pi\)
−0.895323 + 0.445418i \(0.853055\pi\)
\(500\) −12.0000 −0.536656
\(501\) 0 0
\(502\) −12.0000 −0.535586
\(503\) −12.0000 −0.535054 −0.267527 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) −36.0000 −1.60357
\(505\) 20.0000 0.889988
\(506\) 0 0
\(507\) 0 0
\(508\) −8.00000 −0.354943
\(509\) −2.00000 −0.0886484 −0.0443242 0.999017i \(-0.514113\pi\)
−0.0443242 + 0.999017i \(0.514113\pi\)
\(510\) 0 0
\(511\) −24.0000 −1.06170
\(512\) 11.0000 0.486136
\(513\) 0 0
\(514\) −18.0000 −0.793946
\(515\) −16.0000 −0.705044
\(516\) 0 0
\(517\) 0 0
\(518\) 8.00000 0.351500
\(519\) 0 0
\(520\) 12.0000 0.526235
\(521\) 26.0000 1.13908 0.569540 0.821963i \(-0.307121\pi\)
0.569540 + 0.821963i \(0.307121\pi\)
\(522\) 18.0000 0.787839
\(523\) −36.0000 −1.57417 −0.787085 0.616844i \(-0.788411\pi\)
−0.787085 + 0.616844i \(0.788411\pi\)
\(524\) −16.0000 −0.698963
\(525\) 0 0
\(526\) 16.0000 0.697633
\(527\) 4.00000 0.174243
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 12.0000 0.521247
\(531\) 36.0000 1.56227
\(532\) 16.0000 0.693688
\(533\) 12.0000 0.519778
\(534\) 0 0
\(535\) −16.0000 −0.691740
\(536\) 12.0000 0.518321
\(537\) 0 0
\(538\) −22.0000 −0.948487
\(539\) 0 0
\(540\) 0 0
\(541\) 6.00000 0.257960 0.128980 0.991647i \(-0.458830\pi\)
0.128980 + 0.991647i \(0.458830\pi\)
\(542\) 16.0000 0.687259
\(543\) 0 0
\(544\) −5.00000 −0.214373
\(545\) −12.0000 −0.514024
\(546\) 0 0
\(547\) −32.0000 −1.36822 −0.684111 0.729378i \(-0.739809\pi\)
−0.684111 + 0.729378i \(0.739809\pi\)
\(548\) 6.00000 0.256307
\(549\) 30.0000 1.28037
\(550\) 0 0
\(551\) −24.0000 −1.02243
\(552\) 0 0
\(553\) 48.0000 2.04117
\(554\) −14.0000 −0.594803
\(555\) 0 0
\(556\) 8.00000 0.339276
\(557\) 30.0000 1.27114 0.635570 0.772043i \(-0.280765\pi\)
0.635570 + 0.772043i \(0.280765\pi\)
\(558\) 12.0000 0.508001
\(559\) −8.00000 −0.338364
\(560\) 8.00000 0.338062
\(561\) 0 0
\(562\) 6.00000 0.253095
\(563\) −4.00000 −0.168580 −0.0842900 0.996441i \(-0.526862\pi\)
−0.0842900 + 0.996441i \(0.526862\pi\)
\(564\) 0 0
\(565\) 28.0000 1.17797
\(566\) 16.0000 0.672530
\(567\) 36.0000 1.51186
\(568\) −12.0000 −0.503509
\(569\) −38.0000 −1.59304 −0.796521 0.604610i \(-0.793329\pi\)
−0.796521 + 0.604610i \(0.793329\pi\)
\(570\) 0 0
\(571\) −32.0000 −1.33916 −0.669579 0.742741i \(-0.733526\pi\)
−0.669579 + 0.742741i \(0.733526\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 24.0000 1.00174
\(575\) −4.00000 −0.166812
\(576\) −21.0000 −0.875000
\(577\) −14.0000 −0.582828 −0.291414 0.956597i \(-0.594126\pi\)
−0.291414 + 0.956597i \(0.594126\pi\)
\(578\) −1.00000 −0.0415945
\(579\) 0 0
\(580\) 12.0000 0.498273
\(581\) −16.0000 −0.663792
\(582\) 0 0
\(583\) 0 0
\(584\) −18.0000 −0.744845
\(585\) −12.0000 −0.496139
\(586\) −6.00000 −0.247858
\(587\) 4.00000 0.165098 0.0825488 0.996587i \(-0.473694\pi\)
0.0825488 + 0.996587i \(0.473694\pi\)
\(588\) 0 0
\(589\) −16.0000 −0.659269
\(590\) −24.0000 −0.988064
\(591\) 0 0
\(592\) 2.00000 0.0821995
\(593\) 18.0000 0.739171 0.369586 0.929197i \(-0.379500\pi\)
0.369586 + 0.929197i \(0.379500\pi\)
\(594\) 0 0
\(595\) −8.00000 −0.327968
\(596\) 10.0000 0.409616
\(597\) 0 0
\(598\) 8.00000 0.327144
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) −16.0000 −0.652111
\(603\) −12.0000 −0.488678
\(604\) 16.0000 0.651031
\(605\) 22.0000 0.894427
\(606\) 0 0
\(607\) 20.0000 0.811775 0.405887 0.913923i \(-0.366962\pi\)
0.405887 + 0.913923i \(0.366962\pi\)
\(608\) 20.0000 0.811107
\(609\) 0 0
\(610\) −20.0000 −0.809776
\(611\) 0 0
\(612\) 3.00000 0.121268
\(613\) −26.0000 −1.05013 −0.525065 0.851062i \(-0.675959\pi\)
−0.525065 + 0.851062i \(0.675959\pi\)
\(614\) 12.0000 0.484281
\(615\) 0 0
\(616\) 0 0
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) 0 0
\(619\) −48.0000 −1.92928 −0.964641 0.263566i \(-0.915101\pi\)
−0.964641 + 0.263566i \(0.915101\pi\)
\(620\) 8.00000 0.321288
\(621\) 0 0
\(622\) −28.0000 −1.12270
\(623\) 40.0000 1.60257
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) 22.0000 0.879297
\(627\) 0 0
\(628\) 2.00000 0.0798087
\(629\) −2.00000 −0.0797452
\(630\) −24.0000 −0.956183
\(631\) 16.0000 0.636950 0.318475 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) 36.0000 1.43200
\(633\) 0 0
\(634\) 10.0000 0.397151
\(635\) −16.0000 −0.634941
\(636\) 0 0
\(637\) −18.0000 −0.713186
\(638\) 0 0
\(639\) 12.0000 0.474713
\(640\) −6.00000 −0.237171
\(641\) −30.0000 −1.18493 −0.592464 0.805597i \(-0.701845\pi\)
−0.592464 + 0.805597i \(0.701845\pi\)
\(642\) 0 0
\(643\) 32.0000 1.26196 0.630978 0.775800i \(-0.282654\pi\)
0.630978 + 0.775800i \(0.282654\pi\)
\(644\) −16.0000 −0.630488
\(645\) 0 0
\(646\) 4.00000 0.157378
\(647\) 8.00000 0.314512 0.157256 0.987558i \(-0.449735\pi\)
0.157256 + 0.987558i \(0.449735\pi\)
\(648\) 27.0000 1.06066
\(649\) 0 0
\(650\) −2.00000 −0.0784465
\(651\) 0 0
\(652\) −24.0000 −0.939913
\(653\) 6.00000 0.234798 0.117399 0.993085i \(-0.462544\pi\)
0.117399 + 0.993085i \(0.462544\pi\)
\(654\) 0 0
\(655\) −32.0000 −1.25034
\(656\) 6.00000 0.234261
\(657\) 18.0000 0.702247
\(658\) 0 0
\(659\) 4.00000 0.155818 0.0779089 0.996960i \(-0.475176\pi\)
0.0779089 + 0.996960i \(0.475176\pi\)
\(660\) 0 0
\(661\) 38.0000 1.47803 0.739014 0.673690i \(-0.235292\pi\)
0.739014 + 0.673690i \(0.235292\pi\)
\(662\) −4.00000 −0.155464
\(663\) 0 0
\(664\) −12.0000 −0.465690
\(665\) 32.0000 1.24091
\(666\) −6.00000 −0.232495
\(667\) 24.0000 0.929284
\(668\) 4.00000 0.154765
\(669\) 0 0
\(670\) 8.00000 0.309067
\(671\) 0 0
\(672\) 0 0
\(673\) 2.00000 0.0770943 0.0385472 0.999257i \(-0.487727\pi\)
0.0385472 + 0.999257i \(0.487727\pi\)
\(674\) 14.0000 0.539260
\(675\) 0 0
\(676\) 9.00000 0.346154
\(677\) 30.0000 1.15299 0.576497 0.817099i \(-0.304419\pi\)
0.576497 + 0.817099i \(0.304419\pi\)
\(678\) 0 0
\(679\) 8.00000 0.307012
\(680\) −6.00000 −0.230089
\(681\) 0 0
\(682\) 0 0
\(683\) −40.0000 −1.53056 −0.765279 0.643699i \(-0.777399\pi\)
−0.765279 + 0.643699i \(0.777399\pi\)
\(684\) −12.0000 −0.458831
\(685\) 12.0000 0.458496
\(686\) −8.00000 −0.305441
\(687\) 0 0
\(688\) −4.00000 −0.152499
\(689\) −12.0000 −0.457164
\(690\) 0 0
\(691\) −8.00000 −0.304334 −0.152167 0.988355i \(-0.548625\pi\)
−0.152167 + 0.988355i \(0.548625\pi\)
\(692\) −22.0000 −0.836315
\(693\) 0 0
\(694\) −32.0000 −1.21470
\(695\) 16.0000 0.606915
\(696\) 0 0
\(697\) −6.00000 −0.227266
\(698\) 18.0000 0.681310
\(699\) 0 0
\(700\) 4.00000 0.151186
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 0 0
\(703\) 8.00000 0.301726
\(704\) 0 0
\(705\) 0 0
\(706\) 30.0000 1.12906
\(707\) −40.0000 −1.50435
\(708\) 0 0
\(709\) −34.0000 −1.27690 −0.638448 0.769665i \(-0.720423\pi\)
−0.638448 + 0.769665i \(0.720423\pi\)
\(710\) −8.00000 −0.300235
\(711\) −36.0000 −1.35011
\(712\) 30.0000 1.12430
\(713\) 16.0000 0.599205
\(714\) 0 0
\(715\) 0 0
\(716\) −12.0000 −0.448461
\(717\) 0 0
\(718\) 0 0
\(719\) 4.00000 0.149175 0.0745874 0.997214i \(-0.476236\pi\)
0.0745874 + 0.997214i \(0.476236\pi\)
\(720\) −6.00000 −0.223607
\(721\) 32.0000 1.19174
\(722\) 3.00000 0.111648
\(723\) 0 0
\(724\) 2.00000 0.0743294
\(725\) −6.00000 −0.222834
\(726\) 0 0
\(727\) 40.0000 1.48352 0.741759 0.670667i \(-0.233992\pi\)
0.741759 + 0.670667i \(0.233992\pi\)
\(728\) −24.0000 −0.889499
\(729\) −27.0000 −1.00000
\(730\) −12.0000 −0.444140
\(731\) 4.00000 0.147945
\(732\) 0 0
\(733\) −50.0000 −1.84679 −0.923396 0.383849i \(-0.874598\pi\)
−0.923396 + 0.383849i \(0.874598\pi\)
\(734\) −28.0000 −1.03350
\(735\) 0 0
\(736\) −20.0000 −0.737210
\(737\) 0 0
\(738\) −18.0000 −0.662589
\(739\) 28.0000 1.03000 0.514998 0.857191i \(-0.327793\pi\)
0.514998 + 0.857191i \(0.327793\pi\)
\(740\) −4.00000 −0.147043
\(741\) 0 0
\(742\) −24.0000 −0.881068
\(743\) 12.0000 0.440237 0.220119 0.975473i \(-0.429356\pi\)
0.220119 + 0.975473i \(0.429356\pi\)
\(744\) 0 0
\(745\) 20.0000 0.732743
\(746\) −6.00000 −0.219676
\(747\) 12.0000 0.439057
\(748\) 0 0
\(749\) 32.0000 1.16925
\(750\) 0 0
\(751\) 20.0000 0.729810 0.364905 0.931045i \(-0.381101\pi\)
0.364905 + 0.931045i \(0.381101\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 12.0000 0.437014
\(755\) 32.0000 1.16460
\(756\) 0 0
\(757\) 22.0000 0.799604 0.399802 0.916602i \(-0.369079\pi\)
0.399802 + 0.916602i \(0.369079\pi\)
\(758\) 8.00000 0.290573
\(759\) 0 0
\(760\) 24.0000 0.870572
\(761\) −22.0000 −0.797499 −0.398750 0.917060i \(-0.630556\pi\)
−0.398750 + 0.917060i \(0.630556\pi\)
\(762\) 0 0
\(763\) 24.0000 0.868858
\(764\) 16.0000 0.578860
\(765\) 6.00000 0.216930
\(766\) 24.0000 0.867155
\(767\) 24.0000 0.866590
\(768\) 0 0
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −2.00000 −0.0719816
\(773\) −26.0000 −0.935155 −0.467578 0.883952i \(-0.654873\pi\)
−0.467578 + 0.883952i \(0.654873\pi\)
\(774\) 12.0000 0.431331
\(775\) −4.00000 −0.143684
\(776\) 6.00000 0.215387
\(777\) 0 0
\(778\) −6.00000 −0.215110
\(779\) 24.0000 0.859889
\(780\) 0 0
\(781\) 0 0
\(782\) −4.00000 −0.143040
\(783\) 0 0
\(784\) −9.00000 −0.321429
\(785\) 4.00000 0.142766
\(786\) 0 0
\(787\) −32.0000 −1.14068 −0.570338 0.821410i \(-0.693188\pi\)
−0.570338 + 0.821410i \(0.693188\pi\)
\(788\) 18.0000 0.641223
\(789\) 0 0
\(790\) 24.0000 0.853882
\(791\) −56.0000 −1.99113
\(792\) 0 0
\(793\) 20.0000 0.710221
\(794\) −6.00000 −0.212932
\(795\) 0 0
\(796\) 20.0000 0.708881
\(797\) −50.0000 −1.77109 −0.885545 0.464553i \(-0.846215\pi\)
−0.885545 + 0.464553i \(0.846215\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 5.00000 0.176777
\(801\) −30.0000 −1.06000
\(802\) 14.0000 0.494357
\(803\) 0 0
\(804\) 0 0
\(805\) −32.0000 −1.12785
\(806\) 8.00000 0.281788
\(807\) 0 0
\(808\) −30.0000 −1.05540
\(809\) 26.0000 0.914111 0.457056 0.889438i \(-0.348904\pi\)
0.457056 + 0.889438i \(0.348904\pi\)
\(810\) 18.0000 0.632456
\(811\) 40.0000 1.40459 0.702295 0.711886i \(-0.252159\pi\)
0.702295 + 0.711886i \(0.252159\pi\)
\(812\) −24.0000 −0.842235
\(813\) 0 0
\(814\) 0 0
\(815\) −48.0000 −1.68137
\(816\) 0 0
\(817\) −16.0000 −0.559769
\(818\) −26.0000 −0.909069
\(819\) 24.0000 0.838628
\(820\) −12.0000 −0.419058
\(821\) −18.0000 −0.628204 −0.314102 0.949389i \(-0.601703\pi\)
−0.314102 + 0.949389i \(0.601703\pi\)
\(822\) 0 0
\(823\) 20.0000 0.697156 0.348578 0.937280i \(-0.386665\pi\)
0.348578 + 0.937280i \(0.386665\pi\)
\(824\) 24.0000 0.836080
\(825\) 0 0
\(826\) 48.0000 1.67013
\(827\) −48.0000 −1.66912 −0.834562 0.550914i \(-0.814279\pi\)
−0.834562 + 0.550914i \(0.814279\pi\)
\(828\) 12.0000 0.417029
\(829\) −34.0000 −1.18087 −0.590434 0.807086i \(-0.701044\pi\)
−0.590434 + 0.807086i \(0.701044\pi\)
\(830\) −8.00000 −0.277684
\(831\) 0 0
\(832\) −14.0000 −0.485363
\(833\) 9.00000 0.311832
\(834\) 0 0
\(835\) 8.00000 0.276851
\(836\) 0 0
\(837\) 0 0
\(838\) −8.00000 −0.276355
\(839\) 20.0000 0.690477 0.345238 0.938515i \(-0.387798\pi\)
0.345238 + 0.938515i \(0.387798\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) −22.0000 −0.758170
\(843\) 0 0
\(844\) −8.00000 −0.275371
\(845\) 18.0000 0.619219
\(846\) 0 0
\(847\) −44.0000 −1.51186
\(848\) −6.00000 −0.206041
\(849\) 0 0
\(850\) 1.00000 0.0342997
\(851\) −8.00000 −0.274236
\(852\) 0 0
\(853\) 14.0000 0.479351 0.239675 0.970853i \(-0.422959\pi\)
0.239675 + 0.970853i \(0.422959\pi\)
\(854\) 40.0000 1.36877
\(855\) −24.0000 −0.820783
\(856\) 24.0000 0.820303
\(857\) 10.0000 0.341593 0.170797 0.985306i \(-0.445366\pi\)
0.170797 + 0.985306i \(0.445366\pi\)
\(858\) 0 0
\(859\) 52.0000 1.77422 0.887109 0.461561i \(-0.152710\pi\)
0.887109 + 0.461561i \(0.152710\pi\)
\(860\) 8.00000 0.272798
\(861\) 0 0
\(862\) −12.0000 −0.408722
\(863\) 16.0000 0.544646 0.272323 0.962206i \(-0.412208\pi\)
0.272323 + 0.962206i \(0.412208\pi\)
\(864\) 0 0
\(865\) −44.0000 −1.49604
\(866\) −2.00000 −0.0679628
\(867\) 0 0
\(868\) −16.0000 −0.543075
\(869\) 0 0
\(870\) 0 0
\(871\) −8.00000 −0.271070
\(872\) 18.0000 0.609557
\(873\) −6.00000 −0.203069
\(874\) 16.0000 0.541208
\(875\) 48.0000 1.62270
\(876\) 0 0
\(877\) 6.00000 0.202606 0.101303 0.994856i \(-0.467699\pi\)
0.101303 + 0.994856i \(0.467699\pi\)
\(878\) 20.0000 0.674967
\(879\) 0 0
\(880\) 0 0
\(881\) −46.0000 −1.54978 −0.774890 0.632096i \(-0.782195\pi\)
−0.774890 + 0.632096i \(0.782195\pi\)
\(882\) 27.0000 0.909137
\(883\) −12.0000 −0.403832 −0.201916 0.979403i \(-0.564717\pi\)
−0.201916 + 0.979403i \(0.564717\pi\)
\(884\) 2.00000 0.0672673
\(885\) 0 0
\(886\) −28.0000 −0.940678
\(887\) 12.0000 0.402921 0.201460 0.979497i \(-0.435431\pi\)
0.201460 + 0.979497i \(0.435431\pi\)
\(888\) 0 0
\(889\) 32.0000 1.07325
\(890\) 20.0000 0.670402
\(891\) 0 0
\(892\) −24.0000 −0.803579
\(893\) 0 0
\(894\) 0 0
\(895\) −24.0000 −0.802232
\(896\) 12.0000 0.400892
\(897\) 0 0
\(898\) −34.0000 −1.13459
\(899\) 24.0000 0.800445
\(900\) −3.00000 −0.100000
\(901\) 6.00000 0.199889
\(902\) 0 0
\(903\) 0 0
\(904\) −42.0000 −1.39690
\(905\) 4.00000 0.132964
\(906\) 0 0
\(907\) 32.0000 1.06254 0.531271 0.847202i \(-0.321714\pi\)
0.531271 + 0.847202i \(0.321714\pi\)
\(908\) 24.0000 0.796468
\(909\) 30.0000 0.995037
\(910\) −16.0000 −0.530395
\(911\) −4.00000 −0.132526 −0.0662630 0.997802i \(-0.521108\pi\)
−0.0662630 + 0.997802i \(0.521108\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 6.00000 0.198462
\(915\) 0 0
\(916\) −6.00000 −0.198246
\(917\) 64.0000 2.11347
\(918\) 0 0
\(919\) 24.0000 0.791687 0.395843 0.918318i \(-0.370452\pi\)
0.395843 + 0.918318i \(0.370452\pi\)
\(920\) −24.0000 −0.791257
\(921\) 0 0
\(922\) 2.00000 0.0658665
\(923\) 8.00000 0.263323
\(924\) 0 0
\(925\) 2.00000 0.0657596
\(926\) −32.0000 −1.05159
\(927\) −24.0000 −0.788263
\(928\) −30.0000 −0.984798
\(929\) −30.0000 −0.984268 −0.492134 0.870519i \(-0.663783\pi\)
−0.492134 + 0.870519i \(0.663783\pi\)
\(930\) 0 0
\(931\) −36.0000 −1.17985
\(932\) 6.00000 0.196537
\(933\) 0 0
\(934\) −12.0000 −0.392652
\(935\) 0 0
\(936\) 18.0000 0.588348
\(937\) 10.0000 0.326686 0.163343 0.986569i \(-0.447772\pi\)
0.163343 + 0.986569i \(0.447772\pi\)
\(938\) −16.0000 −0.522419
\(939\) 0 0
\(940\) 0 0
\(941\) 6.00000 0.195594 0.0977972 0.995206i \(-0.468820\pi\)
0.0977972 + 0.995206i \(0.468820\pi\)
\(942\) 0 0
\(943\) −24.0000 −0.781548
\(944\) 12.0000 0.390567
\(945\) 0 0
\(946\) 0 0
\(947\) 32.0000 1.03986 0.519930 0.854209i \(-0.325958\pi\)
0.519930 + 0.854209i \(0.325958\pi\)
\(948\) 0 0
\(949\) 12.0000 0.389536
\(950\) −4.00000 −0.129777
\(951\) 0 0
\(952\) 12.0000 0.388922
\(953\) −22.0000 −0.712650 −0.356325 0.934362i \(-0.615970\pi\)
−0.356325 + 0.934362i \(0.615970\pi\)
\(954\) 18.0000 0.582772
\(955\) 32.0000 1.03550
\(956\) 16.0000 0.517477
\(957\) 0 0
\(958\) −36.0000 −1.16311
\(959\) −24.0000 −0.775000
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) −4.00000 −0.128965
\(963\) −24.0000 −0.773389
\(964\) −18.0000 −0.579741
\(965\) −4.00000 −0.128765
\(966\) 0 0
\(967\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) −33.0000 −1.06066
\(969\) 0 0
\(970\) 4.00000 0.128432
\(971\) −12.0000 −0.385098 −0.192549 0.981287i \(-0.561675\pi\)
−0.192549 + 0.981287i \(0.561675\pi\)
\(972\) 0 0
\(973\) −32.0000 −1.02587
\(974\) −20.0000 −0.640841
\(975\) 0 0
\(976\) 10.0000 0.320092
\(977\) 18.0000 0.575871 0.287936 0.957650i \(-0.407031\pi\)
0.287936 + 0.957650i \(0.407031\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 18.0000 0.574989
\(981\) −18.0000 −0.574696
\(982\) −20.0000 −0.638226
\(983\) 12.0000 0.382741 0.191370 0.981518i \(-0.438707\pi\)
0.191370 + 0.981518i \(0.438707\pi\)
\(984\) 0 0
\(985\) 36.0000 1.14706
\(986\) −6.00000 −0.191079
\(987\) 0 0
\(988\) −8.00000 −0.254514
\(989\) 16.0000 0.508770
\(990\) 0 0
\(991\) −12.0000 −0.381193 −0.190596 0.981669i \(-0.561042\pi\)
−0.190596 + 0.981669i \(0.561042\pi\)
\(992\) −20.0000 −0.635001
\(993\) 0 0
\(994\) 16.0000 0.507489
\(995\) 40.0000 1.26809
\(996\) 0 0
\(997\) 46.0000 1.45683 0.728417 0.685134i \(-0.240256\pi\)
0.728417 + 0.685134i \(0.240256\pi\)
\(998\) 40.0000 1.26618
\(999\) 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 \(a_p\))