Properties

Label 4026.2.a.e.1.1
Level 4026
Weight 2
Character 4026.1
Self dual Yes
Analytic conductor 32.148
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1477718538\)
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 \(\chi\) = 4026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+4.00000 q^{5}\) \(-1.00000 q^{6}\) \(+4.00000 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+4.00000 q^{5}\) \(-1.00000 q^{6}\) \(+4.00000 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(-4.00000 q^{10}\) \(-1.00000 q^{11}\) \(+1.00000 q^{12}\) \(+6.00000 q^{13}\) \(-4.00000 q^{14}\) \(+4.00000 q^{15}\) \(+1.00000 q^{16}\) \(-6.00000 q^{17}\) \(-1.00000 q^{18}\) \(+4.00000 q^{20}\) \(+4.00000 q^{21}\) \(+1.00000 q^{22}\) \(-4.00000 q^{23}\) \(-1.00000 q^{24}\) \(+11.0000 q^{25}\) \(-6.00000 q^{26}\) \(+1.00000 q^{27}\) \(+4.00000 q^{28}\) \(-6.00000 q^{29}\) \(-4.00000 q^{30}\) \(-6.00000 q^{31}\) \(-1.00000 q^{32}\) \(-1.00000 q^{33}\) \(+6.00000 q^{34}\) \(+16.0000 q^{35}\) \(+1.00000 q^{36}\) \(+6.00000 q^{39}\) \(-4.00000 q^{40}\) \(+12.0000 q^{41}\) \(-4.00000 q^{42}\) \(+10.0000 q^{43}\) \(-1.00000 q^{44}\) \(+4.00000 q^{45}\) \(+4.00000 q^{46}\) \(-6.00000 q^{47}\) \(+1.00000 q^{48}\) \(+9.00000 q^{49}\) \(-11.0000 q^{50}\) \(-6.00000 q^{51}\) \(+6.00000 q^{52}\) \(-14.0000 q^{53}\) \(-1.00000 q^{54}\) \(-4.00000 q^{55}\) \(-4.00000 q^{56}\) \(+6.00000 q^{58}\) \(+12.0000 q^{59}\) \(+4.00000 q^{60}\) \(-1.00000 q^{61}\) \(+6.00000 q^{62}\) \(+4.00000 q^{63}\) \(+1.00000 q^{64}\) \(+24.0000 q^{65}\) \(+1.00000 q^{66}\) \(+4.00000 q^{67}\) \(-6.00000 q^{68}\) \(-4.00000 q^{69}\) \(-16.0000 q^{70}\) \(+8.00000 q^{71}\) \(-1.00000 q^{72}\) \(-6.00000 q^{73}\) \(+11.0000 q^{75}\) \(-4.00000 q^{77}\) \(-6.00000 q^{78}\) \(+4.00000 q^{79}\) \(+4.00000 q^{80}\) \(+1.00000 q^{81}\) \(-12.0000 q^{82}\) \(+6.00000 q^{83}\) \(+4.00000 q^{84}\) \(-24.0000 q^{85}\) \(-10.0000 q^{86}\) \(-6.00000 q^{87}\) \(+1.00000 q^{88}\) \(-6.00000 q^{89}\) \(-4.00000 q^{90}\) \(+24.0000 q^{91}\) \(-4.00000 q^{92}\) \(-6.00000 q^{93}\) \(+6.00000 q^{94}\) \(-1.00000 q^{96}\) \(+2.00000 q^{97}\) \(-9.00000 q^{98}\) \(-1.00000 q^{99}\) \(+O(q^{100})\)

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
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 4.00000 1.78885 0.894427 0.447214i \(-0.147584\pi\)
0.894427 + 0.447214i \(0.147584\pi\)
\(6\) −1.00000 −0.408248
\(7\) 4.00000 1.51186 0.755929 0.654654i \(-0.227186\pi\)
0.755929 + 0.654654i \(0.227186\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −4.00000 −1.26491
\(11\) −1.00000 −0.301511
\(12\) 1.00000 0.288675
\(13\) 6.00000 1.66410 0.832050 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) −4.00000 −1.06904
\(15\) 4.00000 1.03280
\(16\) 1.00000 0.250000
\(17\) −6.00000 −1.45521 −0.727607 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) −1.00000 −0.235702
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 4.00000 0.894427
\(21\) 4.00000 0.872872
\(22\) 1.00000 0.213201
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) −1.00000 −0.204124
\(25\) 11.0000 2.20000
\(26\) −6.00000 −1.17670
\(27\) 1.00000 0.192450
\(28\) 4.00000 0.755929
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) −4.00000 −0.730297
\(31\) −6.00000 −1.07763 −0.538816 0.842424i \(-0.681128\pi\)
−0.538816 + 0.842424i \(0.681128\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.00000 −0.174078
\(34\) 6.00000 1.02899
\(35\) 16.0000 2.70449
\(36\) 1.00000 0.166667
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0 0
\(39\) 6.00000 0.960769
\(40\) −4.00000 −0.632456
\(41\) 12.0000 1.87409 0.937043 0.349215i \(-0.113552\pi\)
0.937043 + 0.349215i \(0.113552\pi\)
\(42\) −4.00000 −0.617213
\(43\) 10.0000 1.52499 0.762493 0.646997i \(-0.223975\pi\)
0.762493 + 0.646997i \(0.223975\pi\)
\(44\) −1.00000 −0.150756
\(45\) 4.00000 0.596285
\(46\) 4.00000 0.589768
\(47\) −6.00000 −0.875190 −0.437595 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) 1.00000 0.144338
\(49\) 9.00000 1.28571
\(50\) −11.0000 −1.55563
\(51\) −6.00000 −0.840168
\(52\) 6.00000 0.832050
\(53\) −14.0000 −1.92305 −0.961524 0.274721i \(-0.911414\pi\)
−0.961524 + 0.274721i \(0.911414\pi\)
\(54\) −1.00000 −0.136083
\(55\) −4.00000 −0.539360
\(56\) −4.00000 −0.534522
\(57\) 0 0
\(58\) 6.00000 0.787839
\(59\) 12.0000 1.56227 0.781133 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) 4.00000 0.516398
\(61\) −1.00000 −0.128037
\(62\) 6.00000 0.762001
\(63\) 4.00000 0.503953
\(64\) 1.00000 0.125000
\(65\) 24.0000 2.97683
\(66\) 1.00000 0.123091
\(67\) 4.00000 0.488678 0.244339 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) −6.00000 −0.727607
\(69\) −4.00000 −0.481543
\(70\) −16.0000 −1.91237
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) −1.00000 −0.117851
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) 0 0
\(75\) 11.0000 1.27017
\(76\) 0 0
\(77\) −4.00000 −0.455842
\(78\) −6.00000 −0.679366
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 4.00000 0.447214
\(81\) 1.00000 0.111111
\(82\) −12.0000 −1.32518
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 4.00000 0.436436
\(85\) −24.0000 −2.60317
\(86\) −10.0000 −1.07833
\(87\) −6.00000 −0.643268
\(88\) 1.00000 0.106600
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) −4.00000 −0.421637
\(91\) 24.0000 2.51588
\(92\) −4.00000 −0.417029
\(93\) −6.00000 −0.622171
\(94\) 6.00000 0.618853
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) −9.00000 −0.909137
\(99\) −1.00000 −0.100504
\(100\) 11.0000 1.10000
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 6.00000 0.594089
\(103\) 4.00000 0.394132 0.197066 0.980390i \(-0.436859\pi\)
0.197066 + 0.980390i \(0.436859\pi\)
\(104\) −6.00000 −0.588348
\(105\) 16.0000 1.56144
\(106\) 14.0000 1.35980
\(107\) 6.00000 0.580042 0.290021 0.957020i \(-0.406338\pi\)
0.290021 + 0.957020i \(0.406338\pi\)
\(108\) 1.00000 0.0962250
\(109\) −14.0000 −1.34096 −0.670478 0.741929i \(-0.733911\pi\)
−0.670478 + 0.741929i \(0.733911\pi\)
\(110\) 4.00000 0.381385
\(111\) 0 0
\(112\) 4.00000 0.377964
\(113\) −2.00000 −0.188144 −0.0940721 0.995565i \(-0.529988\pi\)
−0.0940721 + 0.995565i \(0.529988\pi\)
\(114\) 0 0
\(115\) −16.0000 −1.49201
\(116\) −6.00000 −0.557086
\(117\) 6.00000 0.554700
\(118\) −12.0000 −1.10469
\(119\) −24.0000 −2.20008
\(120\) −4.00000 −0.365148
\(121\) 1.00000 0.0909091
\(122\) 1.00000 0.0905357
\(123\) 12.0000 1.08200
\(124\) −6.00000 −0.538816
\(125\) 24.0000 2.14663
\(126\) −4.00000 −0.356348
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 10.0000 0.880451
\(130\) −24.0000 −2.10494
\(131\) 2.00000 0.174741 0.0873704 0.996176i \(-0.472154\pi\)
0.0873704 + 0.996176i \(0.472154\pi\)
\(132\) −1.00000 −0.0870388
\(133\) 0 0
\(134\) −4.00000 −0.345547
\(135\) 4.00000 0.344265
\(136\) 6.00000 0.514496
\(137\) 2.00000 0.170872 0.0854358 0.996344i \(-0.472772\pi\)
0.0854358 + 0.996344i \(0.472772\pi\)
\(138\) 4.00000 0.340503
\(139\) 2.00000 0.169638 0.0848189 0.996396i \(-0.472969\pi\)
0.0848189 + 0.996396i \(0.472969\pi\)
\(140\) 16.0000 1.35225
\(141\) −6.00000 −0.505291
\(142\) −8.00000 −0.671345
\(143\) −6.00000 −0.501745
\(144\) 1.00000 0.0833333
\(145\) −24.0000 −1.99309
\(146\) 6.00000 0.496564
\(147\) 9.00000 0.742307
\(148\) 0 0
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) −11.0000 −0.898146
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) −6.00000 −0.485071
\(154\) 4.00000 0.322329
\(155\) −24.0000 −1.92773
\(156\) 6.00000 0.480384
\(157\) −20.0000 −1.59617 −0.798087 0.602542i \(-0.794154\pi\)
−0.798087 + 0.602542i \(0.794154\pi\)
\(158\) −4.00000 −0.318223
\(159\) −14.0000 −1.11027
\(160\) −4.00000 −0.316228
\(161\) −16.0000 −1.26098
\(162\) −1.00000 −0.0785674
\(163\) 20.0000 1.56652 0.783260 0.621694i \(-0.213555\pi\)
0.783260 + 0.621694i \(0.213555\pi\)
\(164\) 12.0000 0.937043
\(165\) −4.00000 −0.311400
\(166\) −6.00000 −0.465690
\(167\) 8.00000 0.619059 0.309529 0.950890i \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) −4.00000 −0.308607
\(169\) 23.0000 1.76923
\(170\) 24.0000 1.84072
\(171\) 0 0
\(172\) 10.0000 0.762493
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 6.00000 0.454859
\(175\) 44.0000 3.32609
\(176\) −1.00000 −0.0753778
\(177\) 12.0000 0.901975
\(178\) 6.00000 0.449719
\(179\) −24.0000 −1.79384 −0.896922 0.442189i \(-0.854202\pi\)
−0.896922 + 0.442189i \(0.854202\pi\)
\(180\) 4.00000 0.298142
\(181\) −12.0000 −0.891953 −0.445976 0.895045i \(-0.647144\pi\)
−0.445976 + 0.895045i \(0.647144\pi\)
\(182\) −24.0000 −1.77900
\(183\) −1.00000 −0.0739221
\(184\) 4.00000 0.294884
\(185\) 0 0
\(186\) 6.00000 0.439941
\(187\) 6.00000 0.438763
\(188\) −6.00000 −0.437595
\(189\) 4.00000 0.290957
\(190\) 0 0
\(191\) −8.00000 −0.578860 −0.289430 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) 1.00000 0.0721688
\(193\) −24.0000 −1.72756 −0.863779 0.503871i \(-0.831909\pi\)
−0.863779 + 0.503871i \(0.831909\pi\)
\(194\) −2.00000 −0.143592
\(195\) 24.0000 1.71868
\(196\) 9.00000 0.642857
\(197\) −10.0000 −0.712470 −0.356235 0.934396i \(-0.615940\pi\)
−0.356235 + 0.934396i \(0.615940\pi\)
\(198\) 1.00000 0.0710669
\(199\) −28.0000 −1.98487 −0.992434 0.122782i \(-0.960818\pi\)
−0.992434 + 0.122782i \(0.960818\pi\)
\(200\) −11.0000 −0.777817
\(201\) 4.00000 0.282138
\(202\) −6.00000 −0.422159
\(203\) −24.0000 −1.68447
\(204\) −6.00000 −0.420084
\(205\) 48.0000 3.35247
\(206\) −4.00000 −0.278693
\(207\) −4.00000 −0.278019
\(208\) 6.00000 0.416025
\(209\) 0 0
\(210\) −16.0000 −1.10410
\(211\) −18.0000 −1.23917 −0.619586 0.784929i \(-0.712699\pi\)
−0.619586 + 0.784929i \(0.712699\pi\)
\(212\) −14.0000 −0.961524
\(213\) 8.00000 0.548151
\(214\) −6.00000 −0.410152
\(215\) 40.0000 2.72798
\(216\) −1.00000 −0.0680414
\(217\) −24.0000 −1.62923
\(218\) 14.0000 0.948200
\(219\) −6.00000 −0.405442
\(220\) −4.00000 −0.269680
\(221\) −36.0000 −2.42162
\(222\) 0 0
\(223\) −14.0000 −0.937509 −0.468755 0.883328i \(-0.655297\pi\)
−0.468755 + 0.883328i \(0.655297\pi\)
\(224\) −4.00000 −0.267261
\(225\) 11.0000 0.733333
\(226\) 2.00000 0.133038
\(227\) 8.00000 0.530979 0.265489 0.964114i \(-0.414466\pi\)
0.265489 + 0.964114i \(0.414466\pi\)
\(228\) 0 0
\(229\) −30.0000 −1.98246 −0.991228 0.132164i \(-0.957808\pi\)
−0.991228 + 0.132164i \(0.957808\pi\)
\(230\) 16.0000 1.05501
\(231\) −4.00000 −0.263181
\(232\) 6.00000 0.393919
\(233\) −10.0000 −0.655122 −0.327561 0.944830i \(-0.606227\pi\)
−0.327561 + 0.944830i \(0.606227\pi\)
\(234\) −6.00000 −0.392232
\(235\) −24.0000 −1.56559
\(236\) 12.0000 0.781133
\(237\) 4.00000 0.259828
\(238\) 24.0000 1.55569
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) 4.00000 0.258199
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 1.00000 0.0641500
\(244\) −1.00000 −0.0640184
\(245\) 36.0000 2.29996
\(246\) −12.0000 −0.765092
\(247\) 0 0
\(248\) 6.00000 0.381000
\(249\) 6.00000 0.380235
\(250\) −24.0000 −1.51789
\(251\) −28.0000 −1.76734 −0.883672 0.468106i \(-0.844936\pi\)
−0.883672 + 0.468106i \(0.844936\pi\)
\(252\) 4.00000 0.251976
\(253\) 4.00000 0.251478
\(254\) 0 0
\(255\) −24.0000 −1.50294
\(256\) 1.00000 0.0625000
\(257\) 26.0000 1.62184 0.810918 0.585160i \(-0.198968\pi\)
0.810918 + 0.585160i \(0.198968\pi\)
\(258\) −10.0000 −0.622573
\(259\) 0 0
\(260\) 24.0000 1.48842
\(261\) −6.00000 −0.371391
\(262\) −2.00000 −0.123560
\(263\) 12.0000 0.739952 0.369976 0.929041i \(-0.379366\pi\)
0.369976 + 0.929041i \(0.379366\pi\)
\(264\) 1.00000 0.0615457
\(265\) −56.0000 −3.44005
\(266\) 0 0
\(267\) −6.00000 −0.367194
\(268\) 4.00000 0.244339
\(269\) −28.0000 −1.70719 −0.853595 0.520937i \(-0.825583\pi\)
−0.853595 + 0.520937i \(0.825583\pi\)
\(270\) −4.00000 −0.243432
\(271\) 16.0000 0.971931 0.485965 0.873978i \(-0.338468\pi\)
0.485965 + 0.873978i \(0.338468\pi\)
\(272\) −6.00000 −0.363803
\(273\) 24.0000 1.45255
\(274\) −2.00000 −0.120824
\(275\) −11.0000 −0.663325
\(276\) −4.00000 −0.240772
\(277\) 30.0000 1.80253 0.901263 0.433273i \(-0.142641\pi\)
0.901263 + 0.433273i \(0.142641\pi\)
\(278\) −2.00000 −0.119952
\(279\) −6.00000 −0.359211
\(280\) −16.0000 −0.956183
\(281\) 2.00000 0.119310 0.0596550 0.998219i \(-0.481000\pi\)
0.0596550 + 0.998219i \(0.481000\pi\)
\(282\) 6.00000 0.357295
\(283\) 24.0000 1.42665 0.713326 0.700832i \(-0.247188\pi\)
0.713326 + 0.700832i \(0.247188\pi\)
\(284\) 8.00000 0.474713
\(285\) 0 0
\(286\) 6.00000 0.354787
\(287\) 48.0000 2.83335
\(288\) −1.00000 −0.0589256
\(289\) 19.0000 1.11765
\(290\) 24.0000 1.40933
\(291\) 2.00000 0.117242
\(292\) −6.00000 −0.351123
\(293\) 2.00000 0.116841 0.0584206 0.998292i \(-0.481394\pi\)
0.0584206 + 0.998292i \(0.481394\pi\)
\(294\) −9.00000 −0.524891
\(295\) 48.0000 2.79467
\(296\) 0 0
\(297\) −1.00000 −0.0580259
\(298\) −6.00000 −0.347571
\(299\) −24.0000 −1.38796
\(300\) 11.0000 0.635085
\(301\) 40.0000 2.30556
\(302\) 0 0
\(303\) 6.00000 0.344691
\(304\) 0 0
\(305\) −4.00000 −0.229039
\(306\) 6.00000 0.342997
\(307\) 10.0000 0.570730 0.285365 0.958419i \(-0.407885\pi\)
0.285365 + 0.958419i \(0.407885\pi\)
\(308\) −4.00000 −0.227921
\(309\) 4.00000 0.227552
\(310\) 24.0000 1.36311
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) −6.00000 −0.339683
\(313\) 22.0000 1.24351 0.621757 0.783210i \(-0.286419\pi\)
0.621757 + 0.783210i \(0.286419\pi\)
\(314\) 20.0000 1.12867
\(315\) 16.0000 0.901498
\(316\) 4.00000 0.225018
\(317\) −12.0000 −0.673987 −0.336994 0.941507i \(-0.609410\pi\)
−0.336994 + 0.941507i \(0.609410\pi\)
\(318\) 14.0000 0.785081
\(319\) 6.00000 0.335936
\(320\) 4.00000 0.223607
\(321\) 6.00000 0.334887
\(322\) 16.0000 0.891645
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 66.0000 3.66102
\(326\) −20.0000 −1.10770
\(327\) −14.0000 −0.774202
\(328\) −12.0000 −0.662589
\(329\) −24.0000 −1.32316
\(330\) 4.00000 0.220193
\(331\) 20.0000 1.09930 0.549650 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) 6.00000 0.329293
\(333\) 0 0
\(334\) −8.00000 −0.437741
\(335\) 16.0000 0.874173
\(336\) 4.00000 0.218218
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) −23.0000 −1.25104
\(339\) −2.00000 −0.108625
\(340\) −24.0000 −1.30158
\(341\) 6.00000 0.324918
\(342\) 0 0
\(343\) 8.00000 0.431959
\(344\) −10.0000 −0.539164
\(345\) −16.0000 −0.861411
\(346\) −6.00000 −0.322562
\(347\) 2.00000 0.107366 0.0536828 0.998558i \(-0.482904\pi\)
0.0536828 + 0.998558i \(0.482904\pi\)
\(348\) −6.00000 −0.321634
\(349\) 22.0000 1.17763 0.588817 0.808267i \(-0.299594\pi\)
0.588817 + 0.808267i \(0.299594\pi\)
\(350\) −44.0000 −2.35190
\(351\) 6.00000 0.320256
\(352\) 1.00000 0.0533002
\(353\) −30.0000 −1.59674 −0.798369 0.602168i \(-0.794304\pi\)
−0.798369 + 0.602168i \(0.794304\pi\)
\(354\) −12.0000 −0.637793
\(355\) 32.0000 1.69838
\(356\) −6.00000 −0.317999
\(357\) −24.0000 −1.27021
\(358\) 24.0000 1.26844
\(359\) 16.0000 0.844448 0.422224 0.906492i \(-0.361250\pi\)
0.422224 + 0.906492i \(0.361250\pi\)
\(360\) −4.00000 −0.210819
\(361\) −19.0000 −1.00000
\(362\) 12.0000 0.630706
\(363\) 1.00000 0.0524864
\(364\) 24.0000 1.25794
\(365\) −24.0000 −1.25622
\(366\) 1.00000 0.0522708
\(367\) −12.0000 −0.626395 −0.313197 0.949688i \(-0.601400\pi\)
−0.313197 + 0.949688i \(0.601400\pi\)
\(368\) −4.00000 −0.208514
\(369\) 12.0000 0.624695
\(370\) 0 0
\(371\) −56.0000 −2.90738
\(372\) −6.00000 −0.311086
\(373\) −34.0000 −1.76045 −0.880227 0.474554i \(-0.842610\pi\)
−0.880227 + 0.474554i \(0.842610\pi\)
\(374\) −6.00000 −0.310253
\(375\) 24.0000 1.23935
\(376\) 6.00000 0.309426
\(377\) −36.0000 −1.85409
\(378\) −4.00000 −0.205738
\(379\) −4.00000 −0.205466 −0.102733 0.994709i \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 8.00000 0.409316
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −16.0000 −0.815436
\(386\) 24.0000 1.22157
\(387\) 10.0000 0.508329
\(388\) 2.00000 0.101535
\(389\) −10.0000 −0.507020 −0.253510 0.967333i \(-0.581585\pi\)
−0.253510 + 0.967333i \(0.581585\pi\)
\(390\) −24.0000 −1.21529
\(391\) 24.0000 1.21373
\(392\) −9.00000 −0.454569
\(393\) 2.00000 0.100887
\(394\) 10.0000 0.503793
\(395\) 16.0000 0.805047
\(396\) −1.00000 −0.0502519
\(397\) −8.00000 −0.401508 −0.200754 0.979642i \(-0.564339\pi\)
−0.200754 + 0.979642i \(0.564339\pi\)
\(398\) 28.0000 1.40351
\(399\) 0 0
\(400\) 11.0000 0.550000
\(401\) 6.00000 0.299626 0.149813 0.988714i \(-0.452133\pi\)
0.149813 + 0.988714i \(0.452133\pi\)
\(402\) −4.00000 −0.199502
\(403\) −36.0000 −1.79329
\(404\) 6.00000 0.298511
\(405\) 4.00000 0.198762
\(406\) 24.0000 1.19110
\(407\) 0 0
\(408\) 6.00000 0.297044
\(409\) 32.0000 1.58230 0.791149 0.611623i \(-0.209483\pi\)
0.791149 + 0.611623i \(0.209483\pi\)
\(410\) −48.0000 −2.37055
\(411\) 2.00000 0.0986527
\(412\) 4.00000 0.197066
\(413\) 48.0000 2.36193
\(414\) 4.00000 0.196589
\(415\) 24.0000 1.17811
\(416\) −6.00000 −0.294174
\(417\) 2.00000 0.0979404
\(418\) 0 0
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 16.0000 0.780720
\(421\) 20.0000 0.974740 0.487370 0.873195i \(-0.337956\pi\)
0.487370 + 0.873195i \(0.337956\pi\)
\(422\) 18.0000 0.876226
\(423\) −6.00000 −0.291730
\(424\) 14.0000 0.679900
\(425\) −66.0000 −3.20147
\(426\) −8.00000 −0.387601
\(427\) −4.00000 −0.193574
\(428\) 6.00000 0.290021
\(429\) −6.00000 −0.289683
\(430\) −40.0000 −1.92897
\(431\) 20.0000 0.963366 0.481683 0.876346i \(-0.340026\pi\)
0.481683 + 0.876346i \(0.340026\pi\)
\(432\) 1.00000 0.0481125
\(433\) 10.0000 0.480569 0.240285 0.970702i \(-0.422759\pi\)
0.240285 + 0.970702i \(0.422759\pi\)
\(434\) 24.0000 1.15204
\(435\) −24.0000 −1.15071
\(436\) −14.0000 −0.670478
\(437\) 0 0
\(438\) 6.00000 0.286691
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 4.00000 0.190693
\(441\) 9.00000 0.428571
\(442\) 36.0000 1.71235
\(443\) 12.0000 0.570137 0.285069 0.958507i \(-0.407984\pi\)
0.285069 + 0.958507i \(0.407984\pi\)
\(444\) 0 0
\(445\) −24.0000 −1.13771
\(446\) 14.0000 0.662919
\(447\) 6.00000 0.283790
\(448\) 4.00000 0.188982
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) −11.0000 −0.518545
\(451\) −12.0000 −0.565058
\(452\) −2.00000 −0.0940721
\(453\) 0 0
\(454\) −8.00000 −0.375459
\(455\) 96.0000 4.50055
\(456\) 0 0
\(457\) −4.00000 −0.187112 −0.0935561 0.995614i \(-0.529823\pi\)
−0.0935561 + 0.995614i \(0.529823\pi\)
\(458\) 30.0000 1.40181
\(459\) −6.00000 −0.280056
\(460\) −16.0000 −0.746004
\(461\) −34.0000 −1.58354 −0.791769 0.610821i \(-0.790840\pi\)
−0.791769 + 0.610821i \(0.790840\pi\)
\(462\) 4.00000 0.186097
\(463\) 4.00000 0.185896 0.0929479 0.995671i \(-0.470371\pi\)
0.0929479 + 0.995671i \(0.470371\pi\)
\(464\) −6.00000 −0.278543
\(465\) −24.0000 −1.11297
\(466\) 10.0000 0.463241
\(467\) −20.0000 −0.925490 −0.462745 0.886492i \(-0.653135\pi\)
−0.462745 + 0.886492i \(0.653135\pi\)
\(468\) 6.00000 0.277350
\(469\) 16.0000 0.738811
\(470\) 24.0000 1.10704
\(471\) −20.0000 −0.921551
\(472\) −12.0000 −0.552345
\(473\) −10.0000 −0.459800
\(474\) −4.00000 −0.183726
\(475\) 0 0
\(476\) −24.0000 −1.10004
\(477\) −14.0000 −0.641016
\(478\) 24.0000 1.09773
\(479\) 28.0000 1.27935 0.639676 0.768644i \(-0.279068\pi\)
0.639676 + 0.768644i \(0.279068\pi\)
\(480\) −4.00000 −0.182574
\(481\) 0 0
\(482\) −10.0000 −0.455488
\(483\) −16.0000 −0.728025
\(484\) 1.00000 0.0454545
\(485\) 8.00000 0.363261
\(486\) −1.00000 −0.0453609
\(487\) −20.0000 −0.906287 −0.453143 0.891438i \(-0.649697\pi\)
−0.453143 + 0.891438i \(0.649697\pi\)
\(488\) 1.00000 0.0452679
\(489\) 20.0000 0.904431
\(490\) −36.0000 −1.62631
\(491\) −14.0000 −0.631811 −0.315906 0.948791i \(-0.602308\pi\)
−0.315906 + 0.948791i \(0.602308\pi\)
\(492\) 12.0000 0.541002
\(493\) 36.0000 1.62136
\(494\) 0 0
\(495\) −4.00000 −0.179787
\(496\) −6.00000 −0.269408
\(497\) 32.0000 1.43540
\(498\) −6.00000 −0.268866
\(499\) −16.0000 −0.716258 −0.358129 0.933672i \(-0.616585\pi\)
−0.358129 + 0.933672i \(0.616585\pi\)
\(500\) 24.0000 1.07331
\(501\) 8.00000 0.357414
\(502\) 28.0000 1.24970
\(503\) −20.0000 −0.891756 −0.445878 0.895094i \(-0.647108\pi\)
−0.445878 + 0.895094i \(0.647108\pi\)
\(504\) −4.00000 −0.178174
\(505\) 24.0000 1.06799
\(506\) −4.00000 −0.177822
\(507\) 23.0000 1.02147
\(508\) 0 0
\(509\) 2.00000 0.0886484 0.0443242 0.999017i \(-0.485887\pi\)
0.0443242 + 0.999017i \(0.485887\pi\)
\(510\) 24.0000 1.06274
\(511\) −24.0000 −1.06170
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −26.0000 −1.14681
\(515\) 16.0000 0.705044
\(516\) 10.0000 0.440225
\(517\) 6.00000 0.263880
\(518\) 0 0
\(519\) 6.00000 0.263371
\(520\) −24.0000 −1.05247
\(521\) 10.0000 0.438108 0.219054 0.975713i \(-0.429703\pi\)
0.219054 + 0.975713i \(0.429703\pi\)
\(522\) 6.00000 0.262613
\(523\) 22.0000 0.961993 0.480996 0.876723i \(-0.340275\pi\)
0.480996 + 0.876723i \(0.340275\pi\)
\(524\) 2.00000 0.0873704
\(525\) 44.0000 1.92032
\(526\) −12.0000 −0.523225
\(527\) 36.0000 1.56818
\(528\) −1.00000 −0.0435194
\(529\) −7.00000 −0.304348
\(530\) 56.0000 2.43248
\(531\) 12.0000 0.520756
\(532\) 0 0
\(533\) 72.0000 3.11867
\(534\) 6.00000 0.259645
\(535\) 24.0000 1.03761
\(536\) −4.00000 −0.172774
\(537\) −24.0000 −1.03568
\(538\) 28.0000 1.20717
\(539\) −9.00000 −0.387657
\(540\) 4.00000 0.172133
\(541\) −6.00000 −0.257960 −0.128980 0.991647i \(-0.541170\pi\)
−0.128980 + 0.991647i \(0.541170\pi\)
\(542\) −16.0000 −0.687259
\(543\) −12.0000 −0.514969
\(544\) 6.00000 0.257248
\(545\) −56.0000 −2.39878
\(546\) −24.0000 −1.02711
\(547\) −38.0000 −1.62476 −0.812381 0.583127i \(-0.801829\pi\)
−0.812381 + 0.583127i \(0.801829\pi\)
\(548\) 2.00000 0.0854358
\(549\) −1.00000 −0.0426790
\(550\) 11.0000 0.469042
\(551\) 0 0
\(552\) 4.00000 0.170251
\(553\) 16.0000 0.680389
\(554\) −30.0000 −1.27458
\(555\) 0 0
\(556\) 2.00000 0.0848189
\(557\) −22.0000 −0.932170 −0.466085 0.884740i \(-0.654336\pi\)
−0.466085 + 0.884740i \(0.654336\pi\)
\(558\) 6.00000 0.254000
\(559\) 60.0000 2.53773
\(560\) 16.0000 0.676123
\(561\) 6.00000 0.253320
\(562\) −2.00000 −0.0843649
\(563\) −14.0000 −0.590030 −0.295015 0.955493i \(-0.595325\pi\)
−0.295015 + 0.955493i \(0.595325\pi\)
\(564\) −6.00000 −0.252646
\(565\) −8.00000 −0.336563
\(566\) −24.0000 −1.00880
\(567\) 4.00000 0.167984
\(568\) −8.00000 −0.335673
\(569\) −24.0000 −1.00613 −0.503066 0.864248i \(-0.667795\pi\)
−0.503066 + 0.864248i \(0.667795\pi\)
\(570\) 0 0
\(571\) −12.0000 −0.502184 −0.251092 0.967963i \(-0.580790\pi\)
−0.251092 + 0.967963i \(0.580790\pi\)
\(572\) −6.00000 −0.250873
\(573\) −8.00000 −0.334205
\(574\) −48.0000 −2.00348
\(575\) −44.0000 −1.83493
\(576\) 1.00000 0.0416667
\(577\) 14.0000 0.582828 0.291414 0.956597i \(-0.405874\pi\)
0.291414 + 0.956597i \(0.405874\pi\)
\(578\) −19.0000 −0.790296
\(579\) −24.0000 −0.997406
\(580\) −24.0000 −0.996546
\(581\) 24.0000 0.995688
\(582\) −2.00000 −0.0829027
\(583\) 14.0000 0.579821
\(584\) 6.00000 0.248282
\(585\) 24.0000 0.992278
\(586\) −2.00000 −0.0826192
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 9.00000 0.371154
\(589\) 0 0
\(590\) −48.0000 −1.97613
\(591\) −10.0000 −0.411345
\(592\) 0 0
\(593\) 18.0000 0.739171 0.369586 0.929197i \(-0.379500\pi\)
0.369586 + 0.929197i \(0.379500\pi\)
\(594\) 1.00000 0.0410305
\(595\) −96.0000 −3.93562
\(596\) 6.00000 0.245770
\(597\) −28.0000 −1.14596
\(598\) 24.0000 0.981433
\(599\) 12.0000 0.490307 0.245153 0.969484i \(-0.421162\pi\)
0.245153 + 0.969484i \(0.421162\pi\)
\(600\) −11.0000 −0.449073
\(601\) −2.00000 −0.0815817 −0.0407909 0.999168i \(-0.512988\pi\)
−0.0407909 + 0.999168i \(0.512988\pi\)
\(602\) −40.0000 −1.63028
\(603\) 4.00000 0.162893
\(604\) 0 0
\(605\) 4.00000 0.162623
\(606\) −6.00000 −0.243733
\(607\) −48.0000 −1.94826 −0.974130 0.225989i \(-0.927439\pi\)
−0.974130 + 0.225989i \(0.927439\pi\)
\(608\) 0 0
\(609\) −24.0000 −0.972529
\(610\) 4.00000 0.161955
\(611\) −36.0000 −1.45640
\(612\) −6.00000 −0.242536
\(613\) −22.0000 −0.888572 −0.444286 0.895885i \(-0.646543\pi\)
−0.444286 + 0.895885i \(0.646543\pi\)
\(614\) −10.0000 −0.403567
\(615\) 48.0000 1.93555
\(616\) 4.00000 0.161165
\(617\) 34.0000 1.36879 0.684394 0.729112i \(-0.260067\pi\)
0.684394 + 0.729112i \(0.260067\pi\)
\(618\) −4.00000 −0.160904
\(619\) 20.0000 0.803868 0.401934 0.915669i \(-0.368338\pi\)
0.401934 + 0.915669i \(0.368338\pi\)
\(620\) −24.0000 −0.963863
\(621\) −4.00000 −0.160514
\(622\) 0 0
\(623\) −24.0000 −0.961540
\(624\) 6.00000 0.240192
\(625\) 41.0000 1.64000
\(626\) −22.0000 −0.879297
\(627\) 0 0
\(628\) −20.0000 −0.798087
\(629\) 0 0
\(630\) −16.0000 −0.637455
\(631\) 34.0000 1.35352 0.676759 0.736204i \(-0.263384\pi\)
0.676759 + 0.736204i \(0.263384\pi\)
\(632\) −4.00000 −0.159111
\(633\) −18.0000 −0.715436
\(634\) 12.0000 0.476581
\(635\) 0 0
\(636\) −14.0000 −0.555136
\(637\) 54.0000 2.13956
\(638\) −6.00000 −0.237542
\(639\) 8.00000 0.316475
\(640\) −4.00000 −0.158114
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) −6.00000 −0.236801
\(643\) 4.00000 0.157745 0.0788723 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) −16.0000 −0.630488
\(645\) 40.0000 1.57500
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −12.0000 −0.471041
\(650\) −66.0000 −2.58873
\(651\) −24.0000 −0.940634
\(652\) 20.0000 0.783260
\(653\) −46.0000 −1.80012 −0.900060 0.435767i \(-0.856477\pi\)
−0.900060 + 0.435767i \(0.856477\pi\)
\(654\) 14.0000 0.547443
\(655\) 8.00000 0.312586
\(656\) 12.0000 0.468521
\(657\) −6.00000 −0.234082
\(658\) 24.0000 0.935617
\(659\) 50.0000 1.94772 0.973862 0.227142i \(-0.0729380\pi\)
0.973862 + 0.227142i \(0.0729380\pi\)
\(660\) −4.00000 −0.155700
\(661\) 32.0000 1.24466 0.622328 0.782757i \(-0.286187\pi\)
0.622328 + 0.782757i \(0.286187\pi\)
\(662\) −20.0000 −0.777322
\(663\) −36.0000 −1.39812
\(664\) −6.00000 −0.232845
\(665\) 0 0
\(666\) 0 0
\(667\) 24.0000 0.929284
\(668\) 8.00000 0.309529
\(669\) −14.0000 −0.541271
\(670\) −16.0000 −0.618134
\(671\) 1.00000 0.0386046
\(672\) −4.00000 −0.154303
\(673\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(674\) 0 0
\(675\) 11.0000 0.423390
\(676\) 23.0000 0.884615
\(677\) 6.00000 0.230599 0.115299 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) 2.00000 0.0768095
\(679\) 8.00000 0.307012
\(680\) 24.0000 0.920358
\(681\) 8.00000 0.306561
\(682\) −6.00000 −0.229752
\(683\) 8.00000 0.306111 0.153056 0.988218i \(-0.451089\pi\)
0.153056 + 0.988218i \(0.451089\pi\)
\(684\) 0 0
\(685\) 8.00000 0.305664
\(686\) −8.00000 −0.305441
\(687\) −30.0000 −1.14457
\(688\) 10.0000 0.381246
\(689\) −84.0000 −3.20015
\(690\) 16.0000 0.609110
\(691\) −44.0000 −1.67384 −0.836919 0.547326i \(-0.815646\pi\)
−0.836919 + 0.547326i \(0.815646\pi\)
\(692\) 6.00000 0.228086
\(693\) −4.00000 −0.151947
\(694\) −2.00000 −0.0759190
\(695\) 8.00000 0.303457
\(696\) 6.00000 0.227429
\(697\) −72.0000 −2.72719
\(698\) −22.0000 −0.832712
\(699\) −10.0000 −0.378235
\(700\) 44.0000 1.66304
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) −6.00000 −0.226455
\(703\) 0 0
\(704\) −1.00000 −0.0376889
\(705\) −24.0000 −0.903892
\(706\) 30.0000 1.12906
\(707\) 24.0000 0.902613
\(708\) 12.0000 0.450988
\(709\) −4.00000 −0.150223 −0.0751116 0.997175i \(-0.523931\pi\)
−0.0751116 + 0.997175i \(0.523931\pi\)
\(710\) −32.0000 −1.20094
\(711\) 4.00000 0.150012
\(712\) 6.00000 0.224860
\(713\) 24.0000 0.898807
\(714\) 24.0000 0.898177
\(715\) −24.0000 −0.897549
\(716\) −24.0000 −0.896922
\(717\) −24.0000 −0.896296
\(718\) −16.0000 −0.597115
\(719\) −42.0000 −1.56634 −0.783168 0.621810i \(-0.786397\pi\)
−0.783168 + 0.621810i \(0.786397\pi\)
\(720\) 4.00000 0.149071
\(721\) 16.0000 0.595871
\(722\) 19.0000 0.707107
\(723\) 10.0000 0.371904
\(724\) −12.0000 −0.445976
\(725\) −66.0000 −2.45118
\(726\) −1.00000 −0.0371135
\(727\) 20.0000 0.741759 0.370879 0.928681i \(-0.379056\pi\)
0.370879 + 0.928681i \(0.379056\pi\)
\(728\) −24.0000 −0.889499
\(729\) 1.00000 0.0370370
\(730\) 24.0000 0.888280
\(731\) −60.0000 −2.21918
\(732\) −1.00000 −0.0369611
\(733\) −26.0000 −0.960332 −0.480166 0.877178i \(-0.659424\pi\)
−0.480166 + 0.877178i \(0.659424\pi\)
\(734\) 12.0000 0.442928
\(735\) 36.0000 1.32788
\(736\) 4.00000 0.147442
\(737\) −4.00000 −0.147342
\(738\) −12.0000 −0.441726
\(739\) 30.0000 1.10357 0.551784 0.833987i \(-0.313947\pi\)
0.551784 + 0.833987i \(0.313947\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 56.0000 2.05582
\(743\) −8.00000 −0.293492 −0.146746 0.989174i \(-0.546880\pi\)
−0.146746 + 0.989174i \(0.546880\pi\)
\(744\) 6.00000 0.219971
\(745\) 24.0000 0.879292
\(746\) 34.0000 1.24483
\(747\) 6.00000 0.219529
\(748\) 6.00000 0.219382
\(749\) 24.0000 0.876941
\(750\) −24.0000 −0.876356
\(751\) 28.0000 1.02173 0.510867 0.859660i \(-0.329324\pi\)
0.510867 + 0.859660i \(0.329324\pi\)
\(752\) −6.00000 −0.218797
\(753\) −28.0000 −1.02038
\(754\) 36.0000 1.31104
\(755\) 0 0
\(756\) 4.00000 0.145479
\(757\) −34.0000 −1.23575 −0.617876 0.786276i \(-0.712006\pi\)
−0.617876 + 0.786276i \(0.712006\pi\)
\(758\) 4.00000 0.145287
\(759\) 4.00000 0.145191
\(760\) 0 0
\(761\) 30.0000 1.08750 0.543750 0.839248i \(-0.317004\pi\)
0.543750 + 0.839248i \(0.317004\pi\)
\(762\) 0 0
\(763\) −56.0000 −2.02734
\(764\) −8.00000 −0.289430
\(765\) −24.0000 −0.867722
\(766\) 0 0
\(767\) 72.0000 2.59977
\(768\) 1.00000 0.0360844
\(769\) −36.0000 −1.29819 −0.649097 0.760706i \(-0.724853\pi\)
−0.649097 + 0.760706i \(0.724853\pi\)
\(770\) 16.0000 0.576600
\(771\) 26.0000 0.936367
\(772\) −24.0000 −0.863779
\(773\) −24.0000 −0.863220 −0.431610 0.902060i \(-0.642054\pi\)
−0.431610 + 0.902060i \(0.642054\pi\)
\(774\) −10.0000 −0.359443
\(775\) −66.0000 −2.37079
\(776\) −2.00000 −0.0717958
\(777\) 0 0
\(778\) 10.0000 0.358517
\(779\) 0 0
\(780\) 24.0000 0.859338
\(781\) −8.00000 −0.286263
\(782\) −24.0000 −0.858238
\(783\) −6.00000 −0.214423
\(784\) 9.00000 0.321429
\(785\) −80.0000 −2.85532
\(786\) −2.00000 −0.0713376
\(787\) −2.00000 −0.0712923 −0.0356462 0.999364i \(-0.511349\pi\)
−0.0356462 + 0.999364i \(0.511349\pi\)
\(788\) −10.0000 −0.356235
\(789\) 12.0000 0.427211
\(790\) −16.0000 −0.569254
\(791\) −8.00000 −0.284447
\(792\) 1.00000 0.0355335
\(793\) −6.00000 −0.213066
\(794\) 8.00000 0.283909
\(795\) −56.0000 −1.98612
\(796\) −28.0000 −0.992434
\(797\) 36.0000 1.27519 0.637593 0.770374i \(-0.279930\pi\)
0.637593 + 0.770374i \(0.279930\pi\)
\(798\) 0 0
\(799\) 36.0000 1.27359
\(800\) −11.0000 −0.388909
\(801\) −6.00000 −0.212000
\(802\) −6.00000 −0.211867
\(803\) 6.00000 0.211735
\(804\) 4.00000 0.141069
\(805\) −64.0000 −2.25570
\(806\) 36.0000 1.26805
\(807\) −28.0000 −0.985647
\(808\) −6.00000 −0.211079
\(809\) −16.0000 −0.562530 −0.281265 0.959630i \(-0.590754\pi\)
−0.281265 + 0.959630i \(0.590754\pi\)
\(810\) −4.00000 −0.140546
\(811\) 50.0000 1.75574 0.877869 0.478901i \(-0.158965\pi\)
0.877869 + 0.478901i \(0.158965\pi\)
\(812\) −24.0000 −0.842235
\(813\) 16.0000 0.561144
\(814\) 0 0
\(815\) 80.0000 2.80228
\(816\) −6.00000 −0.210042
\(817\) 0 0
\(818\) −32.0000 −1.11885
\(819\) 24.0000 0.838628
\(820\) 48.0000 1.67623
\(821\) 22.0000 0.767805 0.383903 0.923374i \(-0.374580\pi\)
0.383903 + 0.923374i \(0.374580\pi\)
\(822\) −2.00000 −0.0697580
\(823\) −50.0000 −1.74289 −0.871445 0.490493i \(-0.836817\pi\)
−0.871445 + 0.490493i \(0.836817\pi\)
\(824\) −4.00000 −0.139347
\(825\) −11.0000 −0.382971
\(826\) −48.0000 −1.67013
\(827\) 10.0000 0.347734 0.173867 0.984769i \(-0.444374\pi\)
0.173867 + 0.984769i \(0.444374\pi\)
\(828\) −4.00000 −0.139010
\(829\) −34.0000 −1.18087 −0.590434 0.807086i \(-0.701044\pi\)
−0.590434 + 0.807086i \(0.701044\pi\)
\(830\) −24.0000 −0.833052
\(831\) 30.0000 1.04069
\(832\) 6.00000 0.208013
\(833\) −54.0000 −1.87099
\(834\) −2.00000 −0.0692543
\(835\) 32.0000 1.10741
\(836\) 0 0
\(837\) −6.00000 −0.207390
\(838\) −12.0000 −0.414533
\(839\) −42.0000 −1.45000 −0.725001 0.688748i \(-0.758161\pi\)
−0.725001 + 0.688748i \(0.758161\pi\)
\(840\) −16.0000 −0.552052
\(841\) 7.00000 0.241379
\(842\) −20.0000 −0.689246
\(843\) 2.00000 0.0688837
\(844\) −18.0000 −0.619586
\(845\) 92.0000 3.16490
\(846\) 6.00000 0.206284
\(847\) 4.00000 0.137442
\(848\) −14.0000 −0.480762
\(849\) 24.0000 0.823678
\(850\) 66.0000 2.26378
\(851\) 0 0
\(852\) 8.00000 0.274075
\(853\) −6.00000 −0.205436 −0.102718 0.994711i \(-0.532754\pi\)
−0.102718 + 0.994711i \(0.532754\pi\)
\(854\) 4.00000 0.136877
\(855\) 0 0
\(856\) −6.00000 −0.205076
\(857\) −56.0000 −1.91292 −0.956462 0.291858i \(-0.905727\pi\)
−0.956462 + 0.291858i \(0.905727\pi\)
\(858\) 6.00000 0.204837
\(859\) 20.0000 0.682391 0.341196 0.939992i \(-0.389168\pi\)
0.341196 + 0.939992i \(0.389168\pi\)
\(860\) 40.0000 1.36399
\(861\) 48.0000 1.63584
\(862\) −20.0000 −0.681203
\(863\) 46.0000 1.56586 0.782929 0.622111i \(-0.213725\pi\)
0.782929 + 0.622111i \(0.213725\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 24.0000 0.816024
\(866\) −10.0000 −0.339814
\(867\) 19.0000 0.645274
\(868\) −24.0000 −0.814613
\(869\) −4.00000 −0.135691
\(870\) 24.0000 0.813676
\(871\) 24.0000 0.813209
\(872\) 14.0000 0.474100
\(873\) 2.00000 0.0676897
\(874\) 0 0
\(875\) 96.0000 3.24539
\(876\) −6.00000 −0.202721
\(877\) −10.0000 −0.337676 −0.168838 0.985644i \(-0.554001\pi\)
−0.168838 + 0.985644i \(0.554001\pi\)
\(878\) 0 0
\(879\) 2.00000 0.0674583
\(880\) −4.00000 −0.134840
\(881\) 14.0000 0.471672 0.235836 0.971793i \(-0.424217\pi\)
0.235836 + 0.971793i \(0.424217\pi\)
\(882\) −9.00000 −0.303046
\(883\) 16.0000 0.538443 0.269221 0.963078i \(-0.413234\pi\)
0.269221 + 0.963078i \(0.413234\pi\)
\(884\) −36.0000 −1.21081
\(885\) 48.0000 1.61350
\(886\) −12.0000 −0.403148
\(887\) −16.0000 −0.537227 −0.268614 0.963248i \(-0.586566\pi\)
−0.268614 + 0.963248i \(0.586566\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 24.0000 0.804482
\(891\) −1.00000 −0.0335013
\(892\) −14.0000 −0.468755
\(893\) 0 0
\(894\) −6.00000 −0.200670
\(895\) −96.0000 −3.20893
\(896\) −4.00000 −0.133631
\(897\) −24.0000 −0.801337
\(898\) −30.0000 −1.00111
\(899\) 36.0000 1.20067
\(900\) 11.0000 0.366667
\(901\) 84.0000 2.79845
\(902\) 12.0000 0.399556
\(903\) 40.0000 1.33112
\(904\) 2.00000 0.0665190
\(905\) −48.0000 −1.59557
\(906\) 0 0
\(907\) −4.00000 −0.132818 −0.0664089 0.997792i \(-0.521154\pi\)
−0.0664089 + 0.997792i \(0.521154\pi\)
\(908\) 8.00000 0.265489
\(909\) 6.00000 0.199007
\(910\) −96.0000 −3.18237
\(911\) 58.0000 1.92163 0.960813 0.277198i \(-0.0894057\pi\)
0.960813 + 0.277198i \(0.0894057\pi\)
\(912\) 0 0
\(913\) −6.00000 −0.198571
\(914\) 4.00000 0.132308
\(915\) −4.00000 −0.132236
\(916\) −30.0000 −0.991228
\(917\) 8.00000 0.264183
\(918\) 6.00000 0.198030
\(919\) −16.0000 −0.527791 −0.263896 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) 16.0000 0.527504
\(921\) 10.0000 0.329511
\(922\) 34.0000 1.11973
\(923\) 48.0000 1.57994
\(924\) −4.00000 −0.131590
\(925\) 0 0
\(926\) −4.00000 −0.131448
\(927\) 4.00000 0.131377
\(928\) 6.00000 0.196960
\(929\) 34.0000 1.11550 0.557752 0.830008i \(-0.311664\pi\)
0.557752 + 0.830008i \(0.311664\pi\)
\(930\) 24.0000 0.786991
\(931\) 0 0
\(932\) −10.0000 −0.327561
\(933\) 0 0
\(934\) 20.0000 0.654420
\(935\) 24.0000 0.784884
\(936\) −6.00000 −0.196116
\(937\) 26.0000 0.849383 0.424691 0.905338i \(-0.360383\pi\)
0.424691 + 0.905338i \(0.360383\pi\)
\(938\) −16.0000 −0.522419
\(939\) 22.0000 0.717943
\(940\) −24.0000 −0.782794
\(941\) −10.0000 −0.325991 −0.162995 0.986627i \(-0.552116\pi\)
−0.162995 + 0.986627i \(0.552116\pi\)
\(942\) 20.0000 0.651635
\(943\) −48.0000 −1.56310
\(944\) 12.0000 0.390567
\(945\) 16.0000 0.520480
\(946\) 10.0000 0.325128
\(947\) 4.00000 0.129983 0.0649913 0.997886i \(-0.479298\pi\)
0.0649913 + 0.997886i \(0.479298\pi\)
\(948\) 4.00000 0.129914
\(949\) −36.0000 −1.16861
\(950\) 0 0
\(951\) −12.0000 −0.389127
\(952\) 24.0000 0.777844
\(953\) −14.0000 −0.453504 −0.226752 0.973952i \(-0.572811\pi\)
−0.226752 + 0.973952i \(0.572811\pi\)
\(954\) 14.0000 0.453267
\(955\) −32.0000 −1.03550
\(956\) −24.0000 −0.776215
\(957\) 6.00000 0.193952
\(958\) −28.0000 −0.904639
\(959\) 8.00000 0.258333
\(960\) 4.00000 0.129099
\(961\) 5.00000 0.161290
\(962\) 0 0
\(963\) 6.00000 0.193347
\(964\) 10.0000 0.322078
\(965\) −96.0000 −3.09035
\(966\) 16.0000 0.514792
\(967\) 24.0000 0.771788 0.385894 0.922543i \(-0.373893\pi\)
0.385894 + 0.922543i \(0.373893\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 0 0
\(970\) −8.00000 −0.256865
\(971\) −40.0000 −1.28366 −0.641831 0.766846i \(-0.721825\pi\)
−0.641831 + 0.766846i \(0.721825\pi\)
\(972\) 1.00000 0.0320750
\(973\) 8.00000 0.256468
\(974\) 20.0000 0.640841
\(975\) 66.0000 2.11369
\(976\) −1.00000 −0.0320092
\(977\) 18.0000 0.575871 0.287936 0.957650i \(-0.407031\pi\)
0.287936 + 0.957650i \(0.407031\pi\)
\(978\) −20.0000 −0.639529
\(979\) 6.00000 0.191761
\(980\) 36.0000 1.14998
\(981\) −14.0000 −0.446986
\(982\) 14.0000 0.446758
\(983\) −24.0000 −0.765481 −0.382741 0.923856i \(-0.625020\pi\)
−0.382741 + 0.923856i \(0.625020\pi\)
\(984\) −12.0000 −0.382546
\(985\) −40.0000 −1.27451
\(986\) −36.0000 −1.14647
\(987\) −24.0000 −0.763928
\(988\) 0 0
\(989\) −40.0000 −1.27193
\(990\) 4.00000 0.127128
\(991\) −40.0000 −1.27064 −0.635321 0.772248i \(-0.719132\pi\)
−0.635321 + 0.772248i \(0.719132\pi\)
\(992\) 6.00000 0.190500
\(993\) 20.0000 0.634681
\(994\) −32.0000 −1.01498
\(995\) −112.000 −3.55064
\(996\) 6.00000 0.190117
\(997\) −10.0000 −0.316703 −0.158352 0.987383i \(-0.550618\pi\)
−0.158352 + 0.987383i \(0.550618\pi\)
\(998\) 16.0000 0.506471
\(999\) 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 \(a_p\))