Properties

Label 11.2.a.a.1.1
Level 11
Weight 2
Character 11.1
Self dual Yes
Analytic conductor 0.088
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 11.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.0878354422234\)
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 \(\chi\) = 11.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.00000 q^{2}\) \(-1.00000 q^{3}\) \(+2.00000 q^{4}\) \(+1.00000 q^{5}\) \(+2.00000 q^{6}\) \(-2.00000 q^{7}\) \(-2.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.00000 q^{2}\) \(-1.00000 q^{3}\) \(+2.00000 q^{4}\) \(+1.00000 q^{5}\) \(+2.00000 q^{6}\) \(-2.00000 q^{7}\) \(-2.00000 q^{9}\) \(-2.00000 q^{10}\) \(+1.00000 q^{11}\) \(-2.00000 q^{12}\) \(+4.00000 q^{13}\) \(+4.00000 q^{14}\) \(-1.00000 q^{15}\) \(-4.00000 q^{16}\) \(-2.00000 q^{17}\) \(+4.00000 q^{18}\) \(+2.00000 q^{20}\) \(+2.00000 q^{21}\) \(-2.00000 q^{22}\) \(-1.00000 q^{23}\) \(-4.00000 q^{25}\) \(-8.00000 q^{26}\) \(+5.00000 q^{27}\) \(-4.00000 q^{28}\) \(+2.00000 q^{30}\) \(+7.00000 q^{31}\) \(+8.00000 q^{32}\) \(-1.00000 q^{33}\) \(+4.00000 q^{34}\) \(-2.00000 q^{35}\) \(-4.00000 q^{36}\) \(+3.00000 q^{37}\) \(-4.00000 q^{39}\) \(-8.00000 q^{41}\) \(-4.00000 q^{42}\) \(-6.00000 q^{43}\) \(+2.00000 q^{44}\) \(-2.00000 q^{45}\) \(+2.00000 q^{46}\) \(+8.00000 q^{47}\) \(+4.00000 q^{48}\) \(-3.00000 q^{49}\) \(+8.00000 q^{50}\) \(+2.00000 q^{51}\) \(+8.00000 q^{52}\) \(-6.00000 q^{53}\) \(-10.0000 q^{54}\) \(+1.00000 q^{55}\) \(+5.00000 q^{59}\) \(-2.00000 q^{60}\) \(+12.0000 q^{61}\) \(-14.0000 q^{62}\) \(+4.00000 q^{63}\) \(-8.00000 q^{64}\) \(+4.00000 q^{65}\) \(+2.00000 q^{66}\) \(-7.00000 q^{67}\) \(-4.00000 q^{68}\) \(+1.00000 q^{69}\) \(+4.00000 q^{70}\) \(-3.00000 q^{71}\) \(+4.00000 q^{73}\) \(-6.00000 q^{74}\) \(+4.00000 q^{75}\) \(-2.00000 q^{77}\) \(+8.00000 q^{78}\) \(-10.0000 q^{79}\) \(-4.00000 q^{80}\) \(+1.00000 q^{81}\) \(+16.0000 q^{82}\) \(-6.00000 q^{83}\) \(+4.00000 q^{84}\) \(-2.00000 q^{85}\) \(+12.0000 q^{86}\) \(+15.0000 q^{89}\) \(+4.00000 q^{90}\) \(-8.00000 q^{91}\) \(-2.00000 q^{92}\) \(-7.00000 q^{93}\) \(-16.0000 q^{94}\) \(-8.00000 q^{96}\) \(-7.00000 q^{97}\) \(+6.00000 q^{98}\) \(-2.00000 q^{99}\) \(+O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(3\) −1.00000 −0.577350 −0.288675 0.957427i \(-0.593215\pi\)
−0.288675 + 0.957427i \(0.593215\pi\)
\(4\) 2.00000 1.00000
\(5\) 1.00000 0.447214 0.223607 0.974679i \(-0.428217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) 2.00000 0.816497
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 0 0
\(9\) −2.00000 −0.666667
\(10\) −2.00000 −0.632456
\(11\) 1.00000 0.301511
\(12\) −2.00000 −0.577350
\(13\) 4.00000 1.10940 0.554700 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 4.00000 1.06904
\(15\) −1.00000 −0.258199
\(16\) −4.00000 −1.00000
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 4.00000 0.942809
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 2.00000 0.447214
\(21\) 2.00000 0.436436
\(22\) −2.00000 −0.426401
\(23\) −1.00000 −0.208514 −0.104257 0.994550i \(-0.533247\pi\)
−0.104257 + 0.994550i \(0.533247\pi\)
\(24\) 0 0
\(25\) −4.00000 −0.800000
\(26\) −8.00000 −1.56893
\(27\) 5.00000 0.962250
\(28\) −4.00000 −0.755929
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 2.00000 0.365148
\(31\) 7.00000 1.25724 0.628619 0.777714i \(-0.283621\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) 8.00000 1.41421
\(33\) −1.00000 −0.174078
\(34\) 4.00000 0.685994
\(35\) −2.00000 −0.338062
\(36\) −4.00000 −0.666667
\(37\) 3.00000 0.493197 0.246598 0.969118i \(-0.420687\pi\)
0.246598 + 0.969118i \(0.420687\pi\)
\(38\) 0 0
\(39\) −4.00000 −0.640513
\(40\) 0 0
\(41\) −8.00000 −1.24939 −0.624695 0.780869i \(-0.714777\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(42\) −4.00000 −0.617213
\(43\) −6.00000 −0.914991 −0.457496 0.889212i \(-0.651253\pi\)
−0.457496 + 0.889212i \(0.651253\pi\)
\(44\) 2.00000 0.301511
\(45\) −2.00000 −0.298142
\(46\) 2.00000 0.294884
\(47\) 8.00000 1.16692 0.583460 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) 4.00000 0.577350
\(49\) −3.00000 −0.428571
\(50\) 8.00000 1.13137
\(51\) 2.00000 0.280056
\(52\) 8.00000 1.10940
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) −10.0000 −1.36083
\(55\) 1.00000 0.134840
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 5.00000 0.650945 0.325472 0.945552i \(-0.394477\pi\)
0.325472 + 0.945552i \(0.394477\pi\)
\(60\) −2.00000 −0.258199
\(61\) 12.0000 1.53644 0.768221 0.640184i \(-0.221142\pi\)
0.768221 + 0.640184i \(0.221142\pi\)
\(62\) −14.0000 −1.77800
\(63\) 4.00000 0.503953
\(64\) −8.00000 −1.00000
\(65\) 4.00000 0.496139
\(66\) 2.00000 0.246183
\(67\) −7.00000 −0.855186 −0.427593 0.903971i \(-0.640638\pi\)
−0.427593 + 0.903971i \(0.640638\pi\)
\(68\) −4.00000 −0.485071
\(69\) 1.00000 0.120386
\(70\) 4.00000 0.478091
\(71\) −3.00000 −0.356034 −0.178017 0.984027i \(-0.556968\pi\)
−0.178017 + 0.984027i \(0.556968\pi\)
\(72\) 0 0
\(73\) 4.00000 0.468165 0.234082 0.972217i \(-0.424791\pi\)
0.234082 + 0.972217i \(0.424791\pi\)
\(74\) −6.00000 −0.697486
\(75\) 4.00000 0.461880
\(76\) 0 0
\(77\) −2.00000 −0.227921
\(78\) 8.00000 0.905822
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) −4.00000 −0.447214
\(81\) 1.00000 0.111111
\(82\) 16.0000 1.76690
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 4.00000 0.436436
\(85\) −2.00000 −0.216930
\(86\) 12.0000 1.29399
\(87\) 0 0
\(88\) 0 0
\(89\) 15.0000 1.59000 0.794998 0.606612i \(-0.207472\pi\)
0.794998 + 0.606612i \(0.207472\pi\)
\(90\) 4.00000 0.421637
\(91\) −8.00000 −0.838628
\(92\) −2.00000 −0.208514
\(93\) −7.00000 −0.725866
\(94\) −16.0000 −1.65027
\(95\) 0 0
\(96\) −8.00000 −0.816497
\(97\) −7.00000 −0.710742 −0.355371 0.934725i \(-0.615646\pi\)
−0.355371 + 0.934725i \(0.615646\pi\)
\(98\) 6.00000 0.606092
\(99\) −2.00000 −0.201008
\(100\) −8.00000 −0.800000
\(101\) 2.00000 0.199007 0.0995037 0.995037i \(-0.468274\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) −4.00000 −0.396059
\(103\) −16.0000 −1.57653 −0.788263 0.615338i \(-0.789020\pi\)
−0.788263 + 0.615338i \(0.789020\pi\)
\(104\) 0 0
\(105\) 2.00000 0.195180
\(106\) 12.0000 1.16554
\(107\) 18.0000 1.74013 0.870063 0.492941i \(-0.164078\pi\)
0.870063 + 0.492941i \(0.164078\pi\)
\(108\) 10.0000 0.962250
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) −2.00000 −0.190693
\(111\) −3.00000 −0.284747
\(112\) 8.00000 0.755929
\(113\) 9.00000 0.846649 0.423324 0.905978i \(-0.360863\pi\)
0.423324 + 0.905978i \(0.360863\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) −8.00000 −0.739600
\(118\) −10.0000 −0.920575
\(119\) 4.00000 0.366679
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −24.0000 −2.17286
\(123\) 8.00000 0.721336
\(124\) 14.0000 1.25724
\(125\) −9.00000 −0.804984
\(126\) −8.00000 −0.712697
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0 0
\(129\) 6.00000 0.528271
\(130\) −8.00000 −0.701646
\(131\) −18.0000 −1.57267 −0.786334 0.617802i \(-0.788023\pi\)
−0.786334 + 0.617802i \(0.788023\pi\)
\(132\) −2.00000 −0.174078
\(133\) 0 0
\(134\) 14.0000 1.20942
\(135\) 5.00000 0.430331
\(136\) 0 0
\(137\) −7.00000 −0.598050 −0.299025 0.954245i \(-0.596661\pi\)
−0.299025 + 0.954245i \(0.596661\pi\)
\(138\) −2.00000 −0.170251
\(139\) 10.0000 0.848189 0.424094 0.905618i \(-0.360592\pi\)
0.424094 + 0.905618i \(0.360592\pi\)
\(140\) −4.00000 −0.338062
\(141\) −8.00000 −0.673722
\(142\) 6.00000 0.503509
\(143\) 4.00000 0.334497
\(144\) 8.00000 0.666667
\(145\) 0 0
\(146\) −8.00000 −0.662085
\(147\) 3.00000 0.247436
\(148\) 6.00000 0.493197
\(149\) −10.0000 −0.819232 −0.409616 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) −8.00000 −0.653197
\(151\) 2.00000 0.162758 0.0813788 0.996683i \(-0.474068\pi\)
0.0813788 + 0.996683i \(0.474068\pi\)
\(152\) 0 0
\(153\) 4.00000 0.323381
\(154\) 4.00000 0.322329
\(155\) 7.00000 0.562254
\(156\) −8.00000 −0.640513
\(157\) −7.00000 −0.558661 −0.279330 0.960195i \(-0.590112\pi\)
−0.279330 + 0.960195i \(0.590112\pi\)
\(158\) 20.0000 1.59111
\(159\) 6.00000 0.475831
\(160\) 8.00000 0.632456
\(161\) 2.00000 0.157622
\(162\) −2.00000 −0.157135
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) −16.0000 −1.24939
\(165\) −1.00000 −0.0778499
\(166\) 12.0000 0.931381
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 4.00000 0.306786
\(171\) 0 0
\(172\) −12.0000 −0.914991
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 0 0
\(175\) 8.00000 0.604743
\(176\) −4.00000 −0.301511
\(177\) −5.00000 −0.375823
\(178\) −30.0000 −2.24860
\(179\) −15.0000 −1.12115 −0.560576 0.828103i \(-0.689420\pi\)
−0.560576 + 0.828103i \(0.689420\pi\)
\(180\) −4.00000 −0.298142
\(181\) 7.00000 0.520306 0.260153 0.965567i \(-0.416227\pi\)
0.260153 + 0.965567i \(0.416227\pi\)
\(182\) 16.0000 1.18600
\(183\) −12.0000 −0.887066
\(184\) 0 0
\(185\) 3.00000 0.220564
\(186\) 14.0000 1.02653
\(187\) −2.00000 −0.146254
\(188\) 16.0000 1.16692
\(189\) −10.0000 −0.727393
\(190\) 0 0
\(191\) 17.0000 1.23008 0.615038 0.788497i \(-0.289140\pi\)
0.615038 + 0.788497i \(0.289140\pi\)
\(192\) 8.00000 0.577350
\(193\) 4.00000 0.287926 0.143963 0.989583i \(-0.454015\pi\)
0.143963 + 0.989583i \(0.454015\pi\)
\(194\) 14.0000 1.00514
\(195\) −4.00000 −0.286446
\(196\) −6.00000 −0.428571
\(197\) −2.00000 −0.142494 −0.0712470 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) 4.00000 0.284268
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 7.00000 0.493742
\(202\) −4.00000 −0.281439
\(203\) 0 0
\(204\) 4.00000 0.280056
\(205\) −8.00000 −0.558744
\(206\) 32.0000 2.22955
\(207\) 2.00000 0.139010
\(208\) −16.0000 −1.10940
\(209\) 0 0
\(210\) −4.00000 −0.276026
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) −12.0000 −0.824163
\(213\) 3.00000 0.205557
\(214\) −36.0000 −2.46091
\(215\) −6.00000 −0.409197
\(216\) 0 0
\(217\) −14.0000 −0.950382
\(218\) −20.0000 −1.35457
\(219\) −4.00000 −0.270295
\(220\) 2.00000 0.134840
\(221\) −8.00000 −0.538138
\(222\) 6.00000 0.402694
\(223\) 19.0000 1.27233 0.636167 0.771551i \(-0.280519\pi\)
0.636167 + 0.771551i \(0.280519\pi\)
\(224\) −16.0000 −1.06904
\(225\) 8.00000 0.533333
\(226\) −18.0000 −1.19734
\(227\) 18.0000 1.19470 0.597351 0.801980i \(-0.296220\pi\)
0.597351 + 0.801980i \(0.296220\pi\)
\(228\) 0 0
\(229\) 15.0000 0.991228 0.495614 0.868543i \(-0.334943\pi\)
0.495614 + 0.868543i \(0.334943\pi\)
\(230\) 2.00000 0.131876
\(231\) 2.00000 0.131590
\(232\) 0 0
\(233\) 24.0000 1.57229 0.786146 0.618041i \(-0.212073\pi\)
0.786146 + 0.618041i \(0.212073\pi\)
\(234\) 16.0000 1.04595
\(235\) 8.00000 0.521862
\(236\) 10.0000 0.650945
\(237\) 10.0000 0.649570
\(238\) −8.00000 −0.518563
\(239\) −30.0000 −1.94054 −0.970269 0.242028i \(-0.922188\pi\)
−0.970269 + 0.242028i \(0.922188\pi\)
\(240\) 4.00000 0.258199
\(241\) −8.00000 −0.515325 −0.257663 0.966235i \(-0.582952\pi\)
−0.257663 + 0.966235i \(0.582952\pi\)
\(242\) −2.00000 −0.128565
\(243\) −16.0000 −1.02640
\(244\) 24.0000 1.53644
\(245\) −3.00000 −0.191663
\(246\) −16.0000 −1.02012
\(247\) 0 0
\(248\) 0 0
\(249\) 6.00000 0.380235
\(250\) 18.0000 1.13842
\(251\) −23.0000 −1.45175 −0.725874 0.687828i \(-0.758564\pi\)
−0.725874 + 0.687828i \(0.758564\pi\)
\(252\) 8.00000 0.503953
\(253\) −1.00000 −0.0628695
\(254\) −16.0000 −1.00393
\(255\) 2.00000 0.125245
\(256\) 16.0000 1.00000
\(257\) −2.00000 −0.124757 −0.0623783 0.998053i \(-0.519869\pi\)
−0.0623783 + 0.998053i \(0.519869\pi\)
\(258\) −12.0000 −0.747087
\(259\) −6.00000 −0.372822
\(260\) 8.00000 0.496139
\(261\) 0 0
\(262\) 36.0000 2.22409
\(263\) 14.0000 0.863277 0.431638 0.902047i \(-0.357936\pi\)
0.431638 + 0.902047i \(0.357936\pi\)
\(264\) 0 0
\(265\) −6.00000 −0.368577
\(266\) 0 0
\(267\) −15.0000 −0.917985
\(268\) −14.0000 −0.855186
\(269\) 10.0000 0.609711 0.304855 0.952399i \(-0.401392\pi\)
0.304855 + 0.952399i \(0.401392\pi\)
\(270\) −10.0000 −0.608581
\(271\) −28.0000 −1.70088 −0.850439 0.526073i \(-0.823664\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) 8.00000 0.485071
\(273\) 8.00000 0.484182
\(274\) 14.0000 0.845771
\(275\) −4.00000 −0.241209
\(276\) 2.00000 0.120386
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) −20.0000 −1.19952
\(279\) −14.0000 −0.838158
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 16.0000 0.952786
\(283\) 4.00000 0.237775 0.118888 0.992908i \(-0.462067\pi\)
0.118888 + 0.992908i \(0.462067\pi\)
\(284\) −6.00000 −0.356034
\(285\) 0 0
\(286\) −8.00000 −0.473050
\(287\) 16.0000 0.944450
\(288\) −16.0000 −0.942809
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 7.00000 0.410347
\(292\) 8.00000 0.468165
\(293\) 24.0000 1.40209 0.701047 0.713115i \(-0.252716\pi\)
0.701047 + 0.713115i \(0.252716\pi\)
\(294\) −6.00000 −0.349927
\(295\) 5.00000 0.291111
\(296\) 0 0
\(297\) 5.00000 0.290129
\(298\) 20.0000 1.15857
\(299\) −4.00000 −0.231326
\(300\) 8.00000 0.461880
\(301\) 12.0000 0.691669
\(302\) −4.00000 −0.230174
\(303\) −2.00000 −0.114897
\(304\) 0 0
\(305\) 12.0000 0.687118
\(306\) −8.00000 −0.457330
\(307\) 8.00000 0.456584 0.228292 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) −4.00000 −0.227921
\(309\) 16.0000 0.910208
\(310\) −14.0000 −0.795147
\(311\) 12.0000 0.680458 0.340229 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) 0 0
\(313\) −1.00000 −0.0565233 −0.0282617 0.999601i \(-0.508997\pi\)
−0.0282617 + 0.999601i \(0.508997\pi\)
\(314\) 14.0000 0.790066
\(315\) 4.00000 0.225374
\(316\) −20.0000 −1.12509
\(317\) 13.0000 0.730153 0.365076 0.930978i \(-0.381043\pi\)
0.365076 + 0.930978i \(0.381043\pi\)
\(318\) −12.0000 −0.672927
\(319\) 0 0
\(320\) −8.00000 −0.447214
\(321\) −18.0000 −1.00466
\(322\) −4.00000 −0.222911
\(323\) 0 0
\(324\) 2.00000 0.111111
\(325\) −16.0000 −0.887520
\(326\) −8.00000 −0.443079
\(327\) −10.0000 −0.553001
\(328\) 0 0
\(329\) −16.0000 −0.882109
\(330\) 2.00000 0.110096
\(331\) 7.00000 0.384755 0.192377 0.981321i \(-0.438380\pi\)
0.192377 + 0.981321i \(0.438380\pi\)
\(332\) −12.0000 −0.658586
\(333\) −6.00000 −0.328798
\(334\) 24.0000 1.31322
\(335\) −7.00000 −0.382451
\(336\) −8.00000 −0.436436
\(337\) −22.0000 −1.19842 −0.599208 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) −6.00000 −0.326357
\(339\) −9.00000 −0.488813
\(340\) −4.00000 −0.216930
\(341\) 7.00000 0.379071
\(342\) 0 0
\(343\) 20.0000 1.07990
\(344\) 0 0
\(345\) 1.00000 0.0538382
\(346\) 12.0000 0.645124
\(347\) 28.0000 1.50312 0.751559 0.659665i \(-0.229302\pi\)
0.751559 + 0.659665i \(0.229302\pi\)
\(348\) 0 0
\(349\) 30.0000 1.60586 0.802932 0.596071i \(-0.203272\pi\)
0.802932 + 0.596071i \(0.203272\pi\)
\(350\) −16.0000 −0.855236
\(351\) 20.0000 1.06752
\(352\) 8.00000 0.426401
\(353\) −21.0000 −1.11772 −0.558859 0.829263i \(-0.688761\pi\)
−0.558859 + 0.829263i \(0.688761\pi\)
\(354\) 10.0000 0.531494
\(355\) −3.00000 −0.159223
\(356\) 30.0000 1.59000
\(357\) −4.00000 −0.211702
\(358\) 30.0000 1.58555
\(359\) −20.0000 −1.05556 −0.527780 0.849381i \(-0.676975\pi\)
−0.527780 + 0.849381i \(0.676975\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) −14.0000 −0.735824
\(363\) −1.00000 −0.0524864
\(364\) −16.0000 −0.838628
\(365\) 4.00000 0.209370
\(366\) 24.0000 1.25450
\(367\) −17.0000 −0.887393 −0.443696 0.896177i \(-0.646333\pi\)
−0.443696 + 0.896177i \(0.646333\pi\)
\(368\) 4.00000 0.208514
\(369\) 16.0000 0.832927
\(370\) −6.00000 −0.311925
\(371\) 12.0000 0.623009
\(372\) −14.0000 −0.725866
\(373\) −26.0000 −1.34623 −0.673114 0.739538i \(-0.735044\pi\)
−0.673114 + 0.739538i \(0.735044\pi\)
\(374\) 4.00000 0.206835
\(375\) 9.00000 0.464758
\(376\) 0 0
\(377\) 0 0
\(378\) 20.0000 1.02869
\(379\) −5.00000 −0.256833 −0.128416 0.991720i \(-0.540989\pi\)
−0.128416 + 0.991720i \(0.540989\pi\)
\(380\) 0 0
\(381\) −8.00000 −0.409852
\(382\) −34.0000 −1.73959
\(383\) −1.00000 −0.0510976 −0.0255488 0.999674i \(-0.508133\pi\)
−0.0255488 + 0.999674i \(0.508133\pi\)
\(384\) 0 0
\(385\) −2.00000 −0.101929
\(386\) −8.00000 −0.407189
\(387\) 12.0000 0.609994
\(388\) −14.0000 −0.710742
\(389\) −15.0000 −0.760530 −0.380265 0.924878i \(-0.624167\pi\)
−0.380265 + 0.924878i \(0.624167\pi\)
\(390\) 8.00000 0.405096
\(391\) 2.00000 0.101144
\(392\) 0 0
\(393\) 18.0000 0.907980
\(394\) 4.00000 0.201517
\(395\) −10.0000 −0.503155
\(396\) −4.00000 −0.201008
\(397\) −2.00000 −0.100377 −0.0501886 0.998740i \(-0.515982\pi\)
−0.0501886 + 0.998740i \(0.515982\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 16.0000 0.800000
\(401\) 2.00000 0.0998752 0.0499376 0.998752i \(-0.484098\pi\)
0.0499376 + 0.998752i \(0.484098\pi\)
\(402\) −14.0000 −0.698257
\(403\) 28.0000 1.39478
\(404\) 4.00000 0.199007
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 3.00000 0.148704
\(408\) 0 0
\(409\) −30.0000 −1.48340 −0.741702 0.670729i \(-0.765981\pi\)
−0.741702 + 0.670729i \(0.765981\pi\)
\(410\) 16.0000 0.790184
\(411\) 7.00000 0.345285
\(412\) −32.0000 −1.57653
\(413\) −10.0000 −0.492068
\(414\) −4.00000 −0.196589
\(415\) −6.00000 −0.294528
\(416\) 32.0000 1.56893
\(417\) −10.0000 −0.489702
\(418\) 0 0
\(419\) 20.0000 0.977064 0.488532 0.872546i \(-0.337533\pi\)
0.488532 + 0.872546i \(0.337533\pi\)
\(420\) 4.00000 0.195180
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) −24.0000 −1.16830
\(423\) −16.0000 −0.777947
\(424\) 0 0
\(425\) 8.00000 0.388057
\(426\) −6.00000 −0.290701
\(427\) −24.0000 −1.16144
\(428\) 36.0000 1.74013
\(429\) −4.00000 −0.193122
\(430\) 12.0000 0.578691
\(431\) −18.0000 −0.867029 −0.433515 0.901146i \(-0.642727\pi\)
−0.433515 + 0.901146i \(0.642727\pi\)
\(432\) −20.0000 −0.962250
\(433\) −11.0000 −0.528626 −0.264313 0.964437i \(-0.585145\pi\)
−0.264313 + 0.964437i \(0.585145\pi\)
\(434\) 28.0000 1.34404
\(435\) 0 0
\(436\) 20.0000 0.957826
\(437\) 0 0
\(438\) 8.00000 0.382255
\(439\) 40.0000 1.90910 0.954548 0.298057i \(-0.0963387\pi\)
0.954548 + 0.298057i \(0.0963387\pi\)
\(440\) 0 0
\(441\) 6.00000 0.285714
\(442\) 16.0000 0.761042
\(443\) −11.0000 −0.522626 −0.261313 0.965254i \(-0.584155\pi\)
−0.261313 + 0.965254i \(0.584155\pi\)
\(444\) −6.00000 −0.284747
\(445\) 15.0000 0.711068
\(446\) −38.0000 −1.79935
\(447\) 10.0000 0.472984
\(448\) 16.0000 0.755929
\(449\) 35.0000 1.65175 0.825876 0.563852i \(-0.190681\pi\)
0.825876 + 0.563852i \(0.190681\pi\)
\(450\) −16.0000 −0.754247
\(451\) −8.00000 −0.376705
\(452\) 18.0000 0.846649
\(453\) −2.00000 −0.0939682
\(454\) −36.0000 −1.68956
\(455\) −8.00000 −0.375046
\(456\) 0 0
\(457\) −12.0000 −0.561336 −0.280668 0.959805i \(-0.590556\pi\)
−0.280668 + 0.959805i \(0.590556\pi\)
\(458\) −30.0000 −1.40181
\(459\) −10.0000 −0.466760
\(460\) −2.00000 −0.0932505
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) −4.00000 −0.186097
\(463\) −11.0000 −0.511213 −0.255607 0.966781i \(-0.582275\pi\)
−0.255607 + 0.966781i \(0.582275\pi\)
\(464\) 0 0
\(465\) −7.00000 −0.324617
\(466\) −48.0000 −2.22356
\(467\) −27.0000 −1.24941 −0.624705 0.780860i \(-0.714781\pi\)
−0.624705 + 0.780860i \(0.714781\pi\)
\(468\) −16.0000 −0.739600
\(469\) 14.0000 0.646460
\(470\) −16.0000 −0.738025
\(471\) 7.00000 0.322543
\(472\) 0 0
\(473\) −6.00000 −0.275880
\(474\) −20.0000 −0.918630
\(475\) 0 0
\(476\) 8.00000 0.366679
\(477\) 12.0000 0.549442
\(478\) 60.0000 2.74434
\(479\) 20.0000 0.913823 0.456912 0.889512i \(-0.348956\pi\)
0.456912 + 0.889512i \(0.348956\pi\)
\(480\) −8.00000 −0.365148
\(481\) 12.0000 0.547153
\(482\) 16.0000 0.728780
\(483\) −2.00000 −0.0910032
\(484\) 2.00000 0.0909091
\(485\) −7.00000 −0.317854
\(486\) 32.0000 1.45155
\(487\) 23.0000 1.04223 0.521115 0.853487i \(-0.325516\pi\)
0.521115 + 0.853487i \(0.325516\pi\)
\(488\) 0 0
\(489\) −4.00000 −0.180886
\(490\) 6.00000 0.271052
\(491\) −8.00000 −0.361035 −0.180517 0.983572i \(-0.557777\pi\)
−0.180517 + 0.983572i \(0.557777\pi\)
\(492\) 16.0000 0.721336
\(493\) 0 0
\(494\) 0 0
\(495\) −2.00000 −0.0898933
\(496\) −28.0000 −1.25724
\(497\) 6.00000 0.269137
\(498\) −12.0000 −0.537733
\(499\) 20.0000 0.895323 0.447661 0.894203i \(-0.352257\pi\)
0.447661 + 0.894203i \(0.352257\pi\)
\(500\) −18.0000 −0.804984
\(501\) 12.0000 0.536120
\(502\) 46.0000 2.05308
\(503\) −26.0000 −1.15928 −0.579641 0.814872i \(-0.696807\pi\)
−0.579641 + 0.814872i \(0.696807\pi\)
\(504\) 0 0
\(505\) 2.00000 0.0889988
\(506\) 2.00000 0.0889108
\(507\) −3.00000 −0.133235
\(508\) 16.0000 0.709885
\(509\) 15.0000 0.664863 0.332432 0.943127i \(-0.392131\pi\)
0.332432 + 0.943127i \(0.392131\pi\)
\(510\) −4.00000 −0.177123
\(511\) −8.00000 −0.353899
\(512\) −32.0000 −1.41421
\(513\) 0 0
\(514\) 4.00000 0.176432
\(515\) −16.0000 −0.705044
\(516\) 12.0000 0.528271
\(517\) 8.00000 0.351840
\(518\) 12.0000 0.527250
\(519\) 6.00000 0.263371
\(520\) 0 0
\(521\) −3.00000 −0.131432 −0.0657162 0.997838i \(-0.520933\pi\)
−0.0657162 + 0.997838i \(0.520933\pi\)
\(522\) 0 0
\(523\) −16.0000 −0.699631 −0.349816 0.936819i \(-0.613756\pi\)
−0.349816 + 0.936819i \(0.613756\pi\)
\(524\) −36.0000 −1.57267
\(525\) −8.00000 −0.349149
\(526\) −28.0000 −1.22086
\(527\) −14.0000 −0.609850
\(528\) 4.00000 0.174078
\(529\) −22.0000 −0.956522
\(530\) 12.0000 0.521247
\(531\) −10.0000 −0.433963
\(532\) 0 0
\(533\) −32.0000 −1.38607
\(534\) 30.0000 1.29823
\(535\) 18.0000 0.778208
\(536\) 0 0
\(537\) 15.0000 0.647298
\(538\) −20.0000 −0.862261
\(539\) −3.00000 −0.129219
\(540\) 10.0000 0.430331
\(541\) −8.00000 −0.343947 −0.171973 0.985102i \(-0.555014\pi\)
−0.171973 + 0.985102i \(0.555014\pi\)
\(542\) 56.0000 2.40541
\(543\) −7.00000 −0.300399
\(544\) −16.0000 −0.685994
\(545\) 10.0000 0.428353
\(546\) −16.0000 −0.684737
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) −14.0000 −0.598050
\(549\) −24.0000 −1.02430
\(550\) 8.00000 0.341121
\(551\) 0 0
\(552\) 0 0
\(553\) 20.0000 0.850487
\(554\) 4.00000 0.169944
\(555\) −3.00000 −0.127343
\(556\) 20.0000 0.848189
\(557\) −2.00000 −0.0847427 −0.0423714 0.999102i \(-0.513491\pi\)
−0.0423714 + 0.999102i \(0.513491\pi\)
\(558\) 28.0000 1.18533
\(559\) −24.0000 −1.01509
\(560\) 8.00000 0.338062
\(561\) 2.00000 0.0844401
\(562\) 36.0000 1.51857
\(563\) 4.00000 0.168580 0.0842900 0.996441i \(-0.473138\pi\)
0.0842900 + 0.996441i \(0.473138\pi\)
\(564\) −16.0000 −0.673722
\(565\) 9.00000 0.378633
\(566\) −8.00000 −0.336265
\(567\) −2.00000 −0.0839921
\(568\) 0 0
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) −28.0000 −1.17176 −0.585882 0.810397i \(-0.699252\pi\)
−0.585882 + 0.810397i \(0.699252\pi\)
\(572\) 8.00000 0.334497
\(573\) −17.0000 −0.710185
\(574\) −32.0000 −1.33565
\(575\) 4.00000 0.166812
\(576\) 16.0000 0.666667
\(577\) 33.0000 1.37381 0.686904 0.726748i \(-0.258969\pi\)
0.686904 + 0.726748i \(0.258969\pi\)
\(578\) 26.0000 1.08146
\(579\) −4.00000 −0.166234
\(580\) 0 0
\(581\) 12.0000 0.497844
\(582\) −14.0000 −0.580319
\(583\) −6.00000 −0.248495
\(584\) 0 0
\(585\) −8.00000 −0.330759
\(586\) −48.0000 −1.98286
\(587\) 28.0000 1.15568 0.577842 0.816149i \(-0.303895\pi\)
0.577842 + 0.816149i \(0.303895\pi\)
\(588\) 6.00000 0.247436
\(589\) 0 0
\(590\) −10.0000 −0.411693
\(591\) 2.00000 0.0822690
\(592\) −12.0000 −0.493197
\(593\) 44.0000 1.80686 0.903432 0.428732i \(-0.141040\pi\)
0.903432 + 0.428732i \(0.141040\pi\)
\(594\) −10.0000 −0.410305
\(595\) 4.00000 0.163984
\(596\) −20.0000 −0.819232
\(597\) 0 0
\(598\) 8.00000 0.327144
\(599\) 40.0000 1.63436 0.817178 0.576386i \(-0.195537\pi\)
0.817178 + 0.576386i \(0.195537\pi\)
\(600\) 0 0
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) −24.0000 −0.978167
\(603\) 14.0000 0.570124
\(604\) 4.00000 0.162758
\(605\) 1.00000 0.0406558
\(606\) 4.00000 0.162489
\(607\) −22.0000 −0.892952 −0.446476 0.894795i \(-0.647321\pi\)
−0.446476 + 0.894795i \(0.647321\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −24.0000 −0.971732
\(611\) 32.0000 1.29458
\(612\) 8.00000 0.323381
\(613\) −16.0000 −0.646234 −0.323117 0.946359i \(-0.604731\pi\)
−0.323117 + 0.946359i \(0.604731\pi\)
\(614\) −16.0000 −0.645707
\(615\) 8.00000 0.322591
\(616\) 0 0
\(617\) 18.0000 0.724653 0.362326 0.932051i \(-0.381983\pi\)
0.362326 + 0.932051i \(0.381983\pi\)
\(618\) −32.0000 −1.28723
\(619\) −25.0000 −1.00483 −0.502417 0.864625i \(-0.667556\pi\)
−0.502417 + 0.864625i \(0.667556\pi\)
\(620\) 14.0000 0.562254
\(621\) −5.00000 −0.200643
\(622\) −24.0000 −0.962312
\(623\) −30.0000 −1.20192
\(624\) 16.0000 0.640513
\(625\) 11.0000 0.440000
\(626\) 2.00000 0.0799361
\(627\) 0 0
\(628\) −14.0000 −0.558661
\(629\) −6.00000 −0.239236
\(630\) −8.00000 −0.318728
\(631\) 7.00000 0.278666 0.139333 0.990246i \(-0.455504\pi\)
0.139333 + 0.990246i \(0.455504\pi\)
\(632\) 0 0
\(633\) −12.0000 −0.476957
\(634\) −26.0000 −1.03259
\(635\) 8.00000 0.317470
\(636\) 12.0000 0.475831
\(637\) −12.0000 −0.475457
\(638\) 0 0
\(639\) 6.00000 0.237356
\(640\) 0 0
\(641\) −33.0000 −1.30342 −0.651711 0.758468i \(-0.725948\pi\)
−0.651711 + 0.758468i \(0.725948\pi\)
\(642\) 36.0000 1.42081
\(643\) 29.0000 1.14365 0.571824 0.820376i \(-0.306236\pi\)
0.571824 + 0.820376i \(0.306236\pi\)
\(644\) 4.00000 0.157622
\(645\) 6.00000 0.236250
\(646\) 0 0
\(647\) −7.00000 −0.275198 −0.137599 0.990488i \(-0.543939\pi\)
−0.137599 + 0.990488i \(0.543939\pi\)
\(648\) 0 0
\(649\) 5.00000 0.196267
\(650\) 32.0000 1.25514
\(651\) 14.0000 0.548703
\(652\) 8.00000 0.313304
\(653\) −41.0000 −1.60445 −0.802227 0.597019i \(-0.796352\pi\)
−0.802227 + 0.597019i \(0.796352\pi\)
\(654\) 20.0000 0.782062
\(655\) −18.0000 −0.703318
\(656\) 32.0000 1.24939
\(657\) −8.00000 −0.312110
\(658\) 32.0000 1.24749
\(659\) 10.0000 0.389545 0.194772 0.980848i \(-0.437603\pi\)
0.194772 + 0.980848i \(0.437603\pi\)
\(660\) −2.00000 −0.0778499
\(661\) 37.0000 1.43913 0.719567 0.694423i \(-0.244340\pi\)
0.719567 + 0.694423i \(0.244340\pi\)
\(662\) −14.0000 −0.544125
\(663\) 8.00000 0.310694
\(664\) 0 0
\(665\) 0 0
\(666\) 12.0000 0.464991
\(667\) 0 0
\(668\) −24.0000 −0.928588
\(669\) −19.0000 −0.734582
\(670\) 14.0000 0.540867
\(671\) 12.0000 0.463255
\(672\) 16.0000 0.617213
\(673\) 14.0000 0.539660 0.269830 0.962908i \(-0.413032\pi\)
0.269830 + 0.962908i \(0.413032\pi\)
\(674\) 44.0000 1.69482
\(675\) −20.0000 −0.769800
\(676\) 6.00000 0.230769
\(677\) −42.0000 −1.61419 −0.807096 0.590421i \(-0.798962\pi\)
−0.807096 + 0.590421i \(0.798962\pi\)
\(678\) 18.0000 0.691286
\(679\) 14.0000 0.537271
\(680\) 0 0
\(681\) −18.0000 −0.689761
\(682\) −14.0000 −0.536088
\(683\) −16.0000 −0.612223 −0.306111 0.951996i \(-0.599028\pi\)
−0.306111 + 0.951996i \(0.599028\pi\)
\(684\) 0 0
\(685\) −7.00000 −0.267456
\(686\) −40.0000 −1.52721
\(687\) −15.0000 −0.572286
\(688\) 24.0000 0.914991
\(689\) −24.0000 −0.914327
\(690\) −2.00000 −0.0761387
\(691\) 17.0000 0.646710 0.323355 0.946278i \(-0.395189\pi\)
0.323355 + 0.946278i \(0.395189\pi\)
\(692\) −12.0000 −0.456172
\(693\) 4.00000 0.151947
\(694\) −56.0000 −2.12573
\(695\) 10.0000 0.379322
\(696\) 0 0
\(697\) 16.0000 0.606043
\(698\) −60.0000 −2.27103
\(699\) −24.0000 −0.907763
\(700\) 16.0000 0.604743
\(701\) 2.00000 0.0755390 0.0377695 0.999286i \(-0.487975\pi\)
0.0377695 + 0.999286i \(0.487975\pi\)
\(702\) −40.0000 −1.50970
\(703\) 0 0
\(704\) −8.00000 −0.301511
\(705\) −8.00000 −0.301297
\(706\) 42.0000 1.58069
\(707\) −4.00000 −0.150435
\(708\) −10.0000 −0.375823
\(709\) −25.0000 −0.938895 −0.469447 0.882960i \(-0.655547\pi\)
−0.469447 + 0.882960i \(0.655547\pi\)
\(710\) 6.00000 0.225176
\(711\) 20.0000 0.750059
\(712\) 0 0
\(713\) −7.00000 −0.262152
\(714\) 8.00000 0.299392
\(715\) 4.00000 0.149592
\(716\) −30.0000 −1.12115
\(717\) 30.0000 1.12037
\(718\) 40.0000 1.49279
\(719\) 15.0000 0.559406 0.279703 0.960087i \(-0.409764\pi\)
0.279703 + 0.960087i \(0.409764\pi\)
\(720\) 8.00000 0.298142
\(721\) 32.0000 1.19174
\(722\) 38.0000 1.41421
\(723\) 8.00000 0.297523
\(724\) 14.0000 0.520306
\(725\) 0 0
\(726\) 2.00000 0.0742270
\(727\) 3.00000 0.111264 0.0556319 0.998451i \(-0.482283\pi\)
0.0556319 + 0.998451i \(0.482283\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) −8.00000 −0.296093
\(731\) 12.0000 0.443836
\(732\) −24.0000 −0.887066
\(733\) −36.0000 −1.32969 −0.664845 0.746981i \(-0.731502\pi\)
−0.664845 + 0.746981i \(0.731502\pi\)
\(734\) 34.0000 1.25496
\(735\) 3.00000 0.110657
\(736\) −8.00000 −0.294884
\(737\) −7.00000 −0.257848
\(738\) −32.0000 −1.17794
\(739\) 50.0000 1.83928 0.919640 0.392763i \(-0.128481\pi\)
0.919640 + 0.392763i \(0.128481\pi\)
\(740\) 6.00000 0.220564
\(741\) 0 0
\(742\) −24.0000 −0.881068
\(743\) 4.00000 0.146746 0.0733729 0.997305i \(-0.476624\pi\)
0.0733729 + 0.997305i \(0.476624\pi\)
\(744\) 0 0
\(745\) −10.0000 −0.366372
\(746\) 52.0000 1.90386
\(747\) 12.0000 0.439057
\(748\) −4.00000 −0.146254
\(749\) −36.0000 −1.31541
\(750\) −18.0000 −0.657267
\(751\) −23.0000 −0.839282 −0.419641 0.907690i \(-0.637844\pi\)
−0.419641 + 0.907690i \(0.637844\pi\)
\(752\) −32.0000 −1.16692
\(753\) 23.0000 0.838167
\(754\) 0 0
\(755\) 2.00000 0.0727875
\(756\) −20.0000 −0.727393
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) 10.0000 0.363216
\(759\) 1.00000 0.0362977
\(760\) 0 0
\(761\) 12.0000 0.435000 0.217500 0.976060i \(-0.430210\pi\)
0.217500 + 0.976060i \(0.430210\pi\)
\(762\) 16.0000 0.579619
\(763\) −20.0000 −0.724049
\(764\) 34.0000 1.23008
\(765\) 4.00000 0.144620
\(766\) 2.00000 0.0722629
\(767\) 20.0000 0.722158
\(768\) −16.0000 −0.577350
\(769\) 20.0000 0.721218 0.360609 0.932717i \(-0.382569\pi\)
0.360609 + 0.932717i \(0.382569\pi\)
\(770\) 4.00000 0.144150
\(771\) 2.00000 0.0720282
\(772\) 8.00000 0.287926
\(773\) −6.00000 −0.215805 −0.107903 0.994161i \(-0.534413\pi\)
−0.107903 + 0.994161i \(0.534413\pi\)
\(774\) −24.0000 −0.862662
\(775\) −28.0000 −1.00579
\(776\) 0 0
\(777\) 6.00000 0.215249
\(778\) 30.0000 1.07555
\(779\) 0 0
\(780\) −8.00000 −0.286446
\(781\) −3.00000 −0.107348
\(782\) −4.00000 −0.143040
\(783\) 0 0
\(784\) 12.0000 0.428571
\(785\) −7.00000 −0.249841
\(786\) −36.0000 −1.28408
\(787\) −32.0000 −1.14068 −0.570338 0.821410i \(-0.693188\pi\)
−0.570338 + 0.821410i \(0.693188\pi\)
\(788\) −4.00000 −0.142494
\(789\) −14.0000 −0.498413
\(790\) 20.0000 0.711568
\(791\) −18.0000 −0.640006
\(792\) 0 0
\(793\) 48.0000 1.70453
\(794\) 4.00000 0.141955
\(795\) 6.00000 0.212798
\(796\) 0 0
\(797\) 53.0000 1.87736 0.938678 0.344795i \(-0.112051\pi\)
0.938678 + 0.344795i \(0.112051\pi\)
\(798\) 0 0
\(799\) −16.0000 −0.566039
\(800\) −32.0000 −1.13137
\(801\) −30.0000 −1.06000
\(802\) −4.00000 −0.141245
\(803\) 4.00000 0.141157
\(804\) 14.0000 0.493742
\(805\) 2.00000 0.0704907
\(806\) −56.0000 −1.97252
\(807\) −10.0000 −0.352017
\(808\) 0 0
\(809\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(810\) −2.00000 −0.0702728
\(811\) −38.0000 −1.33436 −0.667180 0.744896i \(-0.732499\pi\)
−0.667180 + 0.744896i \(0.732499\pi\)
\(812\) 0 0
\(813\) 28.0000 0.982003
\(814\) −6.00000 −0.210300
\(815\) 4.00000 0.140114
\(816\) −8.00000 −0.280056
\(817\) 0 0
\(818\) 60.0000 2.09785
\(819\) 16.0000 0.559085
\(820\) −16.0000 −0.558744
\(821\) 22.0000 0.767805 0.383903 0.923374i \(-0.374580\pi\)
0.383903 + 0.923374i \(0.374580\pi\)
\(822\) −14.0000 −0.488306
\(823\) 39.0000 1.35945 0.679727 0.733465i \(-0.262098\pi\)
0.679727 + 0.733465i \(0.262098\pi\)
\(824\) 0 0
\(825\) 4.00000 0.139262
\(826\) 20.0000 0.695889
\(827\) −52.0000 −1.80822 −0.904109 0.427303i \(-0.859464\pi\)
−0.904109 + 0.427303i \(0.859464\pi\)
\(828\) 4.00000 0.139010
\(829\) 25.0000 0.868286 0.434143 0.900844i \(-0.357051\pi\)
0.434143 + 0.900844i \(0.357051\pi\)
\(830\) 12.0000 0.416526
\(831\) 2.00000 0.0693792
\(832\) −32.0000 −1.10940
\(833\) 6.00000 0.207888
\(834\) 20.0000 0.692543
\(835\) −12.0000 −0.415277
\(836\) 0 0
\(837\) 35.0000 1.20978
\(838\) −40.0000 −1.38178
\(839\) −5.00000 −0.172619 −0.0863096 0.996268i \(-0.527507\pi\)
−0.0863096 + 0.996268i \(0.527507\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) −44.0000 −1.51634
\(843\) 18.0000 0.619953
\(844\) 24.0000 0.826114
\(845\) 3.00000 0.103203
\(846\) 32.0000 1.10018
\(847\) −2.00000 −0.0687208
\(848\) 24.0000 0.824163
\(849\) −4.00000 −0.137280
\(850\) −16.0000 −0.548795
\(851\) −3.00000 −0.102839
\(852\) 6.00000 0.205557
\(853\) 14.0000 0.479351 0.239675 0.970853i \(-0.422959\pi\)
0.239675 + 0.970853i \(0.422959\pi\)
\(854\) 48.0000 1.64253
\(855\) 0 0
\(856\) 0 0
\(857\) 8.00000 0.273275 0.136637 0.990621i \(-0.456370\pi\)
0.136637 + 0.990621i \(0.456370\pi\)
\(858\) 8.00000 0.273115
\(859\) −15.0000 −0.511793 −0.255897 0.966704i \(-0.582371\pi\)
−0.255897 + 0.966704i \(0.582371\pi\)
\(860\) −12.0000 −0.409197
\(861\) −16.0000 −0.545279
\(862\) 36.0000 1.22616
\(863\) 24.0000 0.816970 0.408485 0.912765i \(-0.366057\pi\)
0.408485 + 0.912765i \(0.366057\pi\)
\(864\) 40.0000 1.36083
\(865\) −6.00000 −0.204006
\(866\) 22.0000 0.747590
\(867\) 13.0000 0.441503
\(868\) −28.0000 −0.950382
\(869\) −10.0000 −0.339227
\(870\) 0 0
\(871\) −28.0000 −0.948744
\(872\) 0 0
\(873\) 14.0000 0.473828
\(874\) 0 0
\(875\) 18.0000 0.608511
\(876\) −8.00000 −0.270295
\(877\) −12.0000 −0.405211 −0.202606 0.979260i \(-0.564941\pi\)
−0.202606 + 0.979260i \(0.564941\pi\)
\(878\) −80.0000 −2.69987
\(879\) −24.0000 −0.809500
\(880\) −4.00000 −0.134840
\(881\) −43.0000 −1.44871 −0.724353 0.689429i \(-0.757862\pi\)
−0.724353 + 0.689429i \(0.757862\pi\)
\(882\) −12.0000 −0.404061
\(883\) 4.00000 0.134611 0.0673054 0.997732i \(-0.478560\pi\)
0.0673054 + 0.997732i \(0.478560\pi\)
\(884\) −16.0000 −0.538138
\(885\) −5.00000 −0.168073
\(886\) 22.0000 0.739104
\(887\) −22.0000 −0.738688 −0.369344 0.929293i \(-0.620418\pi\)
−0.369344 + 0.929293i \(0.620418\pi\)
\(888\) 0 0
\(889\) −16.0000 −0.536623
\(890\) −30.0000 −1.00560
\(891\) 1.00000 0.0335013
\(892\) 38.0000 1.27233
\(893\) 0 0
\(894\) −20.0000 −0.668900
\(895\) −15.0000 −0.501395
\(896\) 0 0
\(897\) 4.00000 0.133556
\(898\) −70.0000 −2.33593
\(899\) 0 0
\(900\) 16.0000 0.533333
\(901\) 12.0000 0.399778
\(902\) 16.0000 0.532742
\(903\) −12.0000 −0.399335
\(904\) 0 0
\(905\) 7.00000 0.232688
\(906\) 4.00000 0.132891
\(907\) −12.0000 −0.398453 −0.199227 0.979953i \(-0.563843\pi\)
−0.199227 + 0.979953i \(0.563843\pi\)
\(908\) 36.0000 1.19470
\(909\) −4.00000 −0.132672
\(910\) 16.0000 0.530395
\(911\) 12.0000 0.397578 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) 0 0
\(913\) −6.00000 −0.198571
\(914\) 24.0000 0.793849
\(915\) −12.0000 −0.396708
\(916\) 30.0000 0.991228
\(917\) 36.0000 1.18882
\(918\) 20.0000 0.660098
\(919\) 10.0000 0.329870 0.164935 0.986304i \(-0.447259\pi\)
0.164935 + 0.986304i \(0.447259\pi\)
\(920\) 0 0
\(921\) −8.00000 −0.263609
\(922\) −24.0000 −0.790398
\(923\) −12.0000 −0.394985
\(924\) 4.00000 0.131590
\(925\) −12.0000 −0.394558
\(926\) 22.0000 0.722965
\(927\) 32.0000 1.05102
\(928\) 0 0
\(929\) −30.0000 −0.984268 −0.492134 0.870519i \(-0.663783\pi\)
−0.492134 + 0.870519i \(0.663783\pi\)
\(930\) 14.0000 0.459078
\(931\) 0 0
\(932\) 48.0000 1.57229
\(933\) −12.0000 −0.392862
\(934\) 54.0000 1.76693
\(935\) −2.00000 −0.0654070
\(936\) 0 0
\(937\) 8.00000 0.261349 0.130674 0.991425i \(-0.458286\pi\)
0.130674 + 0.991425i \(0.458286\pi\)
\(938\) −28.0000 −0.914232
\(939\) 1.00000 0.0326338
\(940\) 16.0000 0.521862
\(941\) 42.0000 1.36916 0.684580 0.728937i \(-0.259985\pi\)
0.684580 + 0.728937i \(0.259985\pi\)
\(942\) −14.0000 −0.456145
\(943\) 8.00000 0.260516
\(944\) −20.0000 −0.650945
\(945\) −10.0000 −0.325300
\(946\) 12.0000 0.390154
\(947\) −27.0000 −0.877382 −0.438691 0.898638i \(-0.644558\pi\)
−0.438691 + 0.898638i \(0.644558\pi\)
\(948\) 20.0000 0.649570
\(949\) 16.0000 0.519382
\(950\) 0 0
\(951\) −13.0000 −0.421554
\(952\) 0 0
\(953\) 34.0000 1.10137 0.550684 0.834714i \(-0.314367\pi\)
0.550684 + 0.834714i \(0.314367\pi\)
\(954\) −24.0000 −0.777029
\(955\) 17.0000 0.550107
\(956\) −60.0000 −1.94054
\(957\) 0 0
\(958\) −40.0000 −1.29234
\(959\) 14.0000 0.452084
\(960\) 8.00000 0.258199
\(961\) 18.0000 0.580645
\(962\) −24.0000 −0.773791
\(963\) −36.0000 −1.16008
\(964\) −16.0000 −0.515325
\(965\) 4.00000 0.128765
\(966\) 4.00000 0.128698
\(967\) −32.0000 −1.02905 −0.514525 0.857475i \(-0.672032\pi\)
−0.514525 + 0.857475i \(0.672032\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 14.0000 0.449513
\(971\) 47.0000 1.50830 0.754151 0.656701i \(-0.228049\pi\)
0.754151 + 0.656701i \(0.228049\pi\)
\(972\) −32.0000 −1.02640
\(973\) −20.0000 −0.641171
\(974\) −46.0000 −1.47394
\(975\) 16.0000 0.512410
\(976\) −48.0000 −1.53644
\(977\) −27.0000 −0.863807 −0.431903 0.901920i \(-0.642158\pi\)
−0.431903 + 0.901920i \(0.642158\pi\)
\(978\) 8.00000 0.255812
\(979\) 15.0000 0.479402
\(980\) −6.00000 −0.191663
\(981\) −20.0000 −0.638551
\(982\) 16.0000 0.510581
\(983\) 39.0000 1.24391 0.621953 0.783054i \(-0.286339\pi\)
0.621953 + 0.783054i \(0.286339\pi\)
\(984\) 0 0
\(985\) −2.00000 −0.0637253
\(986\) 0 0
\(987\) 16.0000 0.509286
\(988\) 0 0
\(989\) 6.00000 0.190789
\(990\) 4.00000 0.127128
\(991\) −8.00000 −0.254128 −0.127064 0.991894i \(-0.540555\pi\)
−0.127064 + 0.991894i \(0.540555\pi\)
\(992\) 56.0000 1.77800
\(993\) −7.00000 −0.222138
\(994\) −12.0000 −0.380617
\(995\) 0 0
\(996\) 12.0000 0.380235
\(997\) 38.0000 1.20347 0.601736 0.798695i \(-0.294476\pi\)
0.601736 + 0.798695i \(0.294476\pi\)
\(998\) −40.0000 −1.26618
\(999\) 15.0000 0.474579
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 \(a_p\))