Properties

Label 38.2.a.b.1.1
Level 38
Weight 2
Character 38.1
Self dual Yes
Analytic conductor 0.303
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 38 = 2 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 38.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.303431527681\)
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 \(\chi\) = 38.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-4.00000 q^{5}\) \(-1.00000 q^{6}\) \(+3.00000 q^{7}\) \(+1.00000 q^{8}\) \(-2.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-4.00000 q^{5}\) \(-1.00000 q^{6}\) \(+3.00000 q^{7}\) \(+1.00000 q^{8}\) \(-2.00000 q^{9}\) \(-4.00000 q^{10}\) \(+2.00000 q^{11}\) \(-1.00000 q^{12}\) \(-1.00000 q^{13}\) \(+3.00000 q^{14}\) \(+4.00000 q^{15}\) \(+1.00000 q^{16}\) \(+3.00000 q^{17}\) \(-2.00000 q^{18}\) \(-1.00000 q^{19}\) \(-4.00000 q^{20}\) \(-3.00000 q^{21}\) \(+2.00000 q^{22}\) \(-1.00000 q^{23}\) \(-1.00000 q^{24}\) \(+11.0000 q^{25}\) \(-1.00000 q^{26}\) \(+5.00000 q^{27}\) \(+3.00000 q^{28}\) \(-5.00000 q^{29}\) \(+4.00000 q^{30}\) \(-8.00000 q^{31}\) \(+1.00000 q^{32}\) \(-2.00000 q^{33}\) \(+3.00000 q^{34}\) \(-12.0000 q^{35}\) \(-2.00000 q^{36}\) \(-2.00000 q^{37}\) \(-1.00000 q^{38}\) \(+1.00000 q^{39}\) \(-4.00000 q^{40}\) \(-8.00000 q^{41}\) \(-3.00000 q^{42}\) \(+4.00000 q^{43}\) \(+2.00000 q^{44}\) \(+8.00000 q^{45}\) \(-1.00000 q^{46}\) \(+8.00000 q^{47}\) \(-1.00000 q^{48}\) \(+2.00000 q^{49}\) \(+11.0000 q^{50}\) \(-3.00000 q^{51}\) \(-1.00000 q^{52}\) \(-1.00000 q^{53}\) \(+5.00000 q^{54}\) \(-8.00000 q^{55}\) \(+3.00000 q^{56}\) \(+1.00000 q^{57}\) \(-5.00000 q^{58}\) \(+15.0000 q^{59}\) \(+4.00000 q^{60}\) \(+2.00000 q^{61}\) \(-8.00000 q^{62}\) \(-6.00000 q^{63}\) \(+1.00000 q^{64}\) \(+4.00000 q^{65}\) \(-2.00000 q^{66}\) \(+3.00000 q^{67}\) \(+3.00000 q^{68}\) \(+1.00000 q^{69}\) \(-12.0000 q^{70}\) \(+2.00000 q^{71}\) \(-2.00000 q^{72}\) \(+9.00000 q^{73}\) \(-2.00000 q^{74}\) \(-11.0000 q^{75}\) \(-1.00000 q^{76}\) \(+6.00000 q^{77}\) \(+1.00000 q^{78}\) \(-10.0000 q^{79}\) \(-4.00000 q^{80}\) \(+1.00000 q^{81}\) \(-8.00000 q^{82}\) \(-6.00000 q^{83}\) \(-3.00000 q^{84}\) \(-12.0000 q^{85}\) \(+4.00000 q^{86}\) \(+5.00000 q^{87}\) \(+2.00000 q^{88}\) \(+8.00000 q^{90}\) \(-3.00000 q^{91}\) \(-1.00000 q^{92}\) \(+8.00000 q^{93}\) \(+8.00000 q^{94}\) \(+4.00000 q^{95}\) \(-1.00000 q^{96}\) \(-2.00000 q^{97}\) \(+2.00000 q^{98}\) \(-4.00000 q^{99}\) \(+O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.00000 −0.577350 −0.288675 0.957427i \(-0.593215\pi\)
−0.288675 + 0.957427i \(0.593215\pi\)
\(4\) 1.00000 0.500000
\(5\) −4.00000 −1.78885 −0.894427 0.447214i \(-0.852416\pi\)
−0.894427 + 0.447214i \(0.852416\pi\)
\(6\) −1.00000 −0.408248
\(7\) 3.00000 1.13389 0.566947 0.823754i \(-0.308125\pi\)
0.566947 + 0.823754i \(0.308125\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.00000 −0.666667
\(10\) −4.00000 −1.26491
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) −1.00000 −0.288675
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 3.00000 0.801784
\(15\) 4.00000 1.03280
\(16\) 1.00000 0.250000
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) −2.00000 −0.471405
\(19\) −1.00000 −0.229416
\(20\) −4.00000 −0.894427
\(21\) −3.00000 −0.654654
\(22\) 2.00000 0.426401
\(23\) −1.00000 −0.208514 −0.104257 0.994550i \(-0.533247\pi\)
−0.104257 + 0.994550i \(0.533247\pi\)
\(24\) −1.00000 −0.204124
\(25\) 11.0000 2.20000
\(26\) −1.00000 −0.196116
\(27\) 5.00000 0.962250
\(28\) 3.00000 0.566947
\(29\) −5.00000 −0.928477 −0.464238 0.885710i \(-0.653672\pi\)
−0.464238 + 0.885710i \(0.653672\pi\)
\(30\) 4.00000 0.730297
\(31\) −8.00000 −1.43684 −0.718421 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) 1.00000 0.176777
\(33\) −2.00000 −0.348155
\(34\) 3.00000 0.514496
\(35\) −12.0000 −2.02837
\(36\) −2.00000 −0.333333
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) −1.00000 −0.162221
\(39\) 1.00000 0.160128
\(40\) −4.00000 −0.632456
\(41\) −8.00000 −1.24939 −0.624695 0.780869i \(-0.714777\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(42\) −3.00000 −0.462910
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 2.00000 0.301511
\(45\) 8.00000 1.19257
\(46\) −1.00000 −0.147442
\(47\) 8.00000 1.16692 0.583460 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) −1.00000 −0.144338
\(49\) 2.00000 0.285714
\(50\) 11.0000 1.55563
\(51\) −3.00000 −0.420084
\(52\) −1.00000 −0.138675
\(53\) −1.00000 −0.137361 −0.0686803 0.997639i \(-0.521879\pi\)
−0.0686803 + 0.997639i \(0.521879\pi\)
\(54\) 5.00000 0.680414
\(55\) −8.00000 −1.07872
\(56\) 3.00000 0.400892
\(57\) 1.00000 0.132453
\(58\) −5.00000 −0.656532
\(59\) 15.0000 1.95283 0.976417 0.215894i \(-0.0692665\pi\)
0.976417 + 0.215894i \(0.0692665\pi\)
\(60\) 4.00000 0.516398
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) −8.00000 −1.01600
\(63\) −6.00000 −0.755929
\(64\) 1.00000 0.125000
\(65\) 4.00000 0.496139
\(66\) −2.00000 −0.246183
\(67\) 3.00000 0.366508 0.183254 0.983066i \(-0.441337\pi\)
0.183254 + 0.983066i \(0.441337\pi\)
\(68\) 3.00000 0.363803
\(69\) 1.00000 0.120386
\(70\) −12.0000 −1.43427
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) −2.00000 −0.235702
\(73\) 9.00000 1.05337 0.526685 0.850060i \(-0.323435\pi\)
0.526685 + 0.850060i \(0.323435\pi\)
\(74\) −2.00000 −0.232495
\(75\) −11.0000 −1.27017
\(76\) −1.00000 −0.114708
\(77\) 6.00000 0.683763
\(78\) 1.00000 0.113228
\(79\) −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
\(82\) −8.00000 −0.883452
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) −3.00000 −0.327327
\(85\) −12.0000 −1.30158
\(86\) 4.00000 0.431331
\(87\) 5.00000 0.536056
\(88\) 2.00000 0.213201
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 8.00000 0.843274
\(91\) −3.00000 −0.314485
\(92\) −1.00000 −0.104257
\(93\) 8.00000 0.829561
\(94\) 8.00000 0.825137
\(95\) 4.00000 0.410391
\(96\) −1.00000 −0.102062
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 2.00000 0.202031
\(99\) −4.00000 −0.402015
\(100\) 11.0000 1.10000
\(101\) 2.00000 0.199007 0.0995037 0.995037i \(-0.468274\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) −3.00000 −0.297044
\(103\) −6.00000 −0.591198 −0.295599 0.955312i \(-0.595519\pi\)
−0.295599 + 0.955312i \(0.595519\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 12.0000 1.17108
\(106\) −1.00000 −0.0971286
\(107\) −7.00000 −0.676716 −0.338358 0.941018i \(-0.609871\pi\)
−0.338358 + 0.941018i \(0.609871\pi\)
\(108\) 5.00000 0.481125
\(109\) −15.0000 −1.43674 −0.718370 0.695662i \(-0.755111\pi\)
−0.718370 + 0.695662i \(0.755111\pi\)
\(110\) −8.00000 −0.762770
\(111\) 2.00000 0.189832
\(112\) 3.00000 0.283473
\(113\) 14.0000 1.31701 0.658505 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) 1.00000 0.0936586
\(115\) 4.00000 0.373002
\(116\) −5.00000 −0.464238
\(117\) 2.00000 0.184900
\(118\) 15.0000 1.38086
\(119\) 9.00000 0.825029
\(120\) 4.00000 0.365148
\(121\) −7.00000 −0.636364
\(122\) 2.00000 0.181071
\(123\) 8.00000 0.721336
\(124\) −8.00000 −0.718421
\(125\) −24.0000 −2.14663
\(126\) −6.00000 −0.534522
\(127\) 18.0000 1.59724 0.798621 0.601834i \(-0.205563\pi\)
0.798621 + 0.601834i \(0.205563\pi\)
\(128\) 1.00000 0.0883883
\(129\) −4.00000 −0.352180
\(130\) 4.00000 0.350823
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) −2.00000 −0.174078
\(133\) −3.00000 −0.260133
\(134\) 3.00000 0.259161
\(135\) −20.0000 −1.72133
\(136\) 3.00000 0.257248
\(137\) −17.0000 −1.45241 −0.726204 0.687479i \(-0.758717\pi\)
−0.726204 + 0.687479i \(0.758717\pi\)
\(138\) 1.00000 0.0851257
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) −12.0000 −1.01419
\(141\) −8.00000 −0.673722
\(142\) 2.00000 0.167836
\(143\) −2.00000 −0.167248
\(144\) −2.00000 −0.166667
\(145\) 20.0000 1.66091
\(146\) 9.00000 0.744845
\(147\) −2.00000 −0.164957
\(148\) −2.00000 −0.164399
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) −11.0000 −0.898146
\(151\) 2.00000 0.162758 0.0813788 0.996683i \(-0.474068\pi\)
0.0813788 + 0.996683i \(0.474068\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −6.00000 −0.485071
\(154\) 6.00000 0.483494
\(155\) 32.0000 2.57030
\(156\) 1.00000 0.0800641
\(157\) −2.00000 −0.159617 −0.0798087 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) −10.0000 −0.795557
\(159\) 1.00000 0.0793052
\(160\) −4.00000 −0.316228
\(161\) −3.00000 −0.236433
\(162\) 1.00000 0.0785674
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) −8.00000 −0.624695
\(165\) 8.00000 0.622799
\(166\) −6.00000 −0.465690
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) −3.00000 −0.231455
\(169\) −12.0000 −0.923077
\(170\) −12.0000 −0.920358
\(171\) 2.00000 0.152944
\(172\) 4.00000 0.304997
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 5.00000 0.379049
\(175\) 33.0000 2.49457
\(176\) 2.00000 0.150756
\(177\) −15.0000 −1.12747
\(178\) 0 0
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 8.00000 0.596285
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) −3.00000 −0.222375
\(183\) −2.00000 −0.147844
\(184\) −1.00000 −0.0737210
\(185\) 8.00000 0.588172
\(186\) 8.00000 0.586588
\(187\) 6.00000 0.438763
\(188\) 8.00000 0.583460
\(189\) 15.0000 1.09109
\(190\) 4.00000 0.290191
\(191\) 7.00000 0.506502 0.253251 0.967401i \(-0.418500\pi\)
0.253251 + 0.967401i \(0.418500\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −6.00000 −0.431889 −0.215945 0.976406i \(-0.569283\pi\)
−0.215945 + 0.976406i \(0.569283\pi\)
\(194\) −2.00000 −0.143592
\(195\) −4.00000 −0.286446
\(196\) 2.00000 0.142857
\(197\) 8.00000 0.569976 0.284988 0.958531i \(-0.408010\pi\)
0.284988 + 0.958531i \(0.408010\pi\)
\(198\) −4.00000 −0.284268
\(199\) −25.0000 −1.77220 −0.886102 0.463491i \(-0.846597\pi\)
−0.886102 + 0.463491i \(0.846597\pi\)
\(200\) 11.0000 0.777817
\(201\) −3.00000 −0.211604
\(202\) 2.00000 0.140720
\(203\) −15.0000 −1.05279
\(204\) −3.00000 −0.210042
\(205\) 32.0000 2.23498
\(206\) −6.00000 −0.418040
\(207\) 2.00000 0.139010
\(208\) −1.00000 −0.0693375
\(209\) −2.00000 −0.138343
\(210\) 12.0000 0.828079
\(211\) 27.0000 1.85876 0.929378 0.369129i \(-0.120344\pi\)
0.929378 + 0.369129i \(0.120344\pi\)
\(212\) −1.00000 −0.0686803
\(213\) −2.00000 −0.137038
\(214\) −7.00000 −0.478510
\(215\) −16.0000 −1.09119
\(216\) 5.00000 0.340207
\(217\) −24.0000 −1.62923
\(218\) −15.0000 −1.01593
\(219\) −9.00000 −0.608164
\(220\) −8.00000 −0.539360
\(221\) −3.00000 −0.201802
\(222\) 2.00000 0.134231
\(223\) 14.0000 0.937509 0.468755 0.883328i \(-0.344703\pi\)
0.468755 + 0.883328i \(0.344703\pi\)
\(224\) 3.00000 0.200446
\(225\) −22.0000 −1.46667
\(226\) 14.0000 0.931266
\(227\) −17.0000 −1.12833 −0.564165 0.825662i \(-0.690802\pi\)
−0.564165 + 0.825662i \(0.690802\pi\)
\(228\) 1.00000 0.0662266
\(229\) −10.0000 −0.660819 −0.330409 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) 4.00000 0.263752
\(231\) −6.00000 −0.394771
\(232\) −5.00000 −0.328266
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 2.00000 0.130744
\(235\) −32.0000 −2.08745
\(236\) 15.0000 0.976417
\(237\) 10.0000 0.649570
\(238\) 9.00000 0.583383
\(239\) 15.0000 0.970269 0.485135 0.874439i \(-0.338771\pi\)
0.485135 + 0.874439i \(0.338771\pi\)
\(240\) 4.00000 0.258199
\(241\) −8.00000 −0.515325 −0.257663 0.966235i \(-0.582952\pi\)
−0.257663 + 0.966235i \(0.582952\pi\)
\(242\) −7.00000 −0.449977
\(243\) −16.0000 −1.02640
\(244\) 2.00000 0.128037
\(245\) −8.00000 −0.511101
\(246\) 8.00000 0.510061
\(247\) 1.00000 0.0636285
\(248\) −8.00000 −0.508001
\(249\) 6.00000 0.380235
\(250\) −24.0000 −1.51789
\(251\) 2.00000 0.126239 0.0631194 0.998006i \(-0.479895\pi\)
0.0631194 + 0.998006i \(0.479895\pi\)
\(252\) −6.00000 −0.377964
\(253\) −2.00000 −0.125739
\(254\) 18.0000 1.12942
\(255\) 12.0000 0.751469
\(256\) 1.00000 0.0625000
\(257\) 8.00000 0.499026 0.249513 0.968371i \(-0.419729\pi\)
0.249513 + 0.968371i \(0.419729\pi\)
\(258\) −4.00000 −0.249029
\(259\) −6.00000 −0.372822
\(260\) 4.00000 0.248069
\(261\) 10.0000 0.618984
\(262\) 12.0000 0.741362
\(263\) 24.0000 1.47990 0.739952 0.672660i \(-0.234848\pi\)
0.739952 + 0.672660i \(0.234848\pi\)
\(264\) −2.00000 −0.123091
\(265\) 4.00000 0.245718
\(266\) −3.00000 −0.183942
\(267\) 0 0
\(268\) 3.00000 0.183254
\(269\) 30.0000 1.82913 0.914566 0.404436i \(-0.132532\pi\)
0.914566 + 0.404436i \(0.132532\pi\)
\(270\) −20.0000 −1.21716
\(271\) 7.00000 0.425220 0.212610 0.977137i \(-0.431804\pi\)
0.212610 + 0.977137i \(0.431804\pi\)
\(272\) 3.00000 0.181902
\(273\) 3.00000 0.181568
\(274\) −17.0000 −1.02701
\(275\) 22.0000 1.32665
\(276\) 1.00000 0.0601929
\(277\) 28.0000 1.68236 0.841178 0.540758i \(-0.181862\pi\)
0.841178 + 0.540758i \(0.181862\pi\)
\(278\) 0 0
\(279\) 16.0000 0.957895
\(280\) −12.0000 −0.717137
\(281\) −8.00000 −0.477240 −0.238620 0.971113i \(-0.576695\pi\)
−0.238620 + 0.971113i \(0.576695\pi\)
\(282\) −8.00000 −0.476393
\(283\) −6.00000 −0.356663 −0.178331 0.983970i \(-0.557070\pi\)
−0.178331 + 0.983970i \(0.557070\pi\)
\(284\) 2.00000 0.118678
\(285\) −4.00000 −0.236940
\(286\) −2.00000 −0.118262
\(287\) −24.0000 −1.41668
\(288\) −2.00000 −0.117851
\(289\) −8.00000 −0.470588
\(290\) 20.0000 1.17444
\(291\) 2.00000 0.117242
\(292\) 9.00000 0.526685
\(293\) 9.00000 0.525786 0.262893 0.964825i \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(294\) −2.00000 −0.116642
\(295\) −60.0000 −3.49334
\(296\) −2.00000 −0.116248
\(297\) 10.0000 0.580259
\(298\) 0 0
\(299\) 1.00000 0.0578315
\(300\) −11.0000 −0.635085
\(301\) 12.0000 0.691669
\(302\) 2.00000 0.115087
\(303\) −2.00000 −0.114897
\(304\) −1.00000 −0.0573539
\(305\) −8.00000 −0.458079
\(306\) −6.00000 −0.342997
\(307\) −12.0000 −0.684876 −0.342438 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) 6.00000 0.341882
\(309\) 6.00000 0.341328
\(310\) 32.0000 1.81748
\(311\) 7.00000 0.396934 0.198467 0.980108i \(-0.436404\pi\)
0.198467 + 0.980108i \(0.436404\pi\)
\(312\) 1.00000 0.0566139
\(313\) 29.0000 1.63918 0.819588 0.572953i \(-0.194202\pi\)
0.819588 + 0.572953i \(0.194202\pi\)
\(314\) −2.00000 −0.112867
\(315\) 24.0000 1.35225
\(316\) −10.0000 −0.562544
\(317\) −27.0000 −1.51647 −0.758236 0.651981i \(-0.773938\pi\)
−0.758236 + 0.651981i \(0.773938\pi\)
\(318\) 1.00000 0.0560772
\(319\) −10.0000 −0.559893
\(320\) −4.00000 −0.223607
\(321\) 7.00000 0.390702
\(322\) −3.00000 −0.167183
\(323\) −3.00000 −0.166924
\(324\) 1.00000 0.0555556
\(325\) −11.0000 −0.610170
\(326\) −16.0000 −0.886158
\(327\) 15.0000 0.829502
\(328\) −8.00000 −0.441726
\(329\) 24.0000 1.32316
\(330\) 8.00000 0.440386
\(331\) 17.0000 0.934405 0.467202 0.884150i \(-0.345262\pi\)
0.467202 + 0.884150i \(0.345262\pi\)
\(332\) −6.00000 −0.329293
\(333\) 4.00000 0.219199
\(334\) −12.0000 −0.656611
\(335\) −12.0000 −0.655630
\(336\) −3.00000 −0.163663
\(337\) −32.0000 −1.74315 −0.871576 0.490261i \(-0.836901\pi\)
−0.871576 + 0.490261i \(0.836901\pi\)
\(338\) −12.0000 −0.652714
\(339\) −14.0000 −0.760376
\(340\) −12.0000 −0.650791
\(341\) −16.0000 −0.866449
\(342\) 2.00000 0.108148
\(343\) −15.0000 −0.809924
\(344\) 4.00000 0.215666
\(345\) −4.00000 −0.215353
\(346\) −6.00000 −0.322562
\(347\) −2.00000 −0.107366 −0.0536828 0.998558i \(-0.517096\pi\)
−0.0536828 + 0.998558i \(0.517096\pi\)
\(348\) 5.00000 0.268028
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 33.0000 1.76392
\(351\) −5.00000 −0.266880
\(352\) 2.00000 0.106600
\(353\) 9.00000 0.479022 0.239511 0.970894i \(-0.423013\pi\)
0.239511 + 0.970894i \(0.423013\pi\)
\(354\) −15.0000 −0.797241
\(355\) −8.00000 −0.424596
\(356\) 0 0
\(357\) −9.00000 −0.476331
\(358\) 0 0
\(359\) −15.0000 −0.791670 −0.395835 0.918322i \(-0.629545\pi\)
−0.395835 + 0.918322i \(0.629545\pi\)
\(360\) 8.00000 0.421637
\(361\) 1.00000 0.0526316
\(362\) 22.0000 1.15629
\(363\) 7.00000 0.367405
\(364\) −3.00000 −0.157243
\(365\) −36.0000 −1.88433
\(366\) −2.00000 −0.104542
\(367\) 28.0000 1.46159 0.730794 0.682598i \(-0.239150\pi\)
0.730794 + 0.682598i \(0.239150\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 16.0000 0.832927
\(370\) 8.00000 0.415900
\(371\) −3.00000 −0.155752
\(372\) 8.00000 0.414781
\(373\) 29.0000 1.50156 0.750782 0.660551i \(-0.229677\pi\)
0.750782 + 0.660551i \(0.229677\pi\)
\(374\) 6.00000 0.310253
\(375\) 24.0000 1.23935
\(376\) 8.00000 0.412568
\(377\) 5.00000 0.257513
\(378\) 15.0000 0.771517
\(379\) 15.0000 0.770498 0.385249 0.922813i \(-0.374116\pi\)
0.385249 + 0.922813i \(0.374116\pi\)
\(380\) 4.00000 0.205196
\(381\) −18.0000 −0.922168
\(382\) 7.00000 0.358151
\(383\) −26.0000 −1.32854 −0.664269 0.747494i \(-0.731257\pi\)
−0.664269 + 0.747494i \(0.731257\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −24.0000 −1.22315
\(386\) −6.00000 −0.305392
\(387\) −8.00000 −0.406663
\(388\) −2.00000 −0.101535
\(389\) −30.0000 −1.52106 −0.760530 0.649303i \(-0.775061\pi\)
−0.760530 + 0.649303i \(0.775061\pi\)
\(390\) −4.00000 −0.202548
\(391\) −3.00000 −0.151717
\(392\) 2.00000 0.101015
\(393\) −12.0000 −0.605320
\(394\) 8.00000 0.403034
\(395\) 40.0000 2.01262
\(396\) −4.00000 −0.201008
\(397\) 8.00000 0.401508 0.200754 0.979642i \(-0.435661\pi\)
0.200754 + 0.979642i \(0.435661\pi\)
\(398\) −25.0000 −1.25314
\(399\) 3.00000 0.150188
\(400\) 11.0000 0.550000
\(401\) −8.00000 −0.399501 −0.199750 0.979847i \(-0.564013\pi\)
−0.199750 + 0.979847i \(0.564013\pi\)
\(402\) −3.00000 −0.149626
\(403\) 8.00000 0.398508
\(404\) 2.00000 0.0995037
\(405\) −4.00000 −0.198762
\(406\) −15.0000 −0.744438
\(407\) −4.00000 −0.198273
\(408\) −3.00000 −0.148522
\(409\) −20.0000 −0.988936 −0.494468 0.869196i \(-0.664637\pi\)
−0.494468 + 0.869196i \(0.664637\pi\)
\(410\) 32.0000 1.58037
\(411\) 17.0000 0.838548
\(412\) −6.00000 −0.295599
\(413\) 45.0000 2.21431
\(414\) 2.00000 0.0982946
\(415\) 24.0000 1.17811
\(416\) −1.00000 −0.0490290
\(417\) 0 0
\(418\) −2.00000 −0.0978232
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 12.0000 0.585540
\(421\) −13.0000 −0.633581 −0.316791 0.948495i \(-0.602605\pi\)
−0.316791 + 0.948495i \(0.602605\pi\)
\(422\) 27.0000 1.31434
\(423\) −16.0000 −0.777947
\(424\) −1.00000 −0.0485643
\(425\) 33.0000 1.60074
\(426\) −2.00000 −0.0969003
\(427\) 6.00000 0.290360
\(428\) −7.00000 −0.338358
\(429\) 2.00000 0.0965609
\(430\) −16.0000 −0.771589
\(431\) −18.0000 −0.867029 −0.433515 0.901146i \(-0.642727\pi\)
−0.433515 + 0.901146i \(0.642727\pi\)
\(432\) 5.00000 0.240563
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) −24.0000 −1.15204
\(435\) −20.0000 −0.958927
\(436\) −15.0000 −0.718370
\(437\) 1.00000 0.0478365
\(438\) −9.00000 −0.430037
\(439\) 20.0000 0.954548 0.477274 0.878755i \(-0.341625\pi\)
0.477274 + 0.878755i \(0.341625\pi\)
\(440\) −8.00000 −0.381385
\(441\) −4.00000 −0.190476
\(442\) −3.00000 −0.142695
\(443\) −26.0000 −1.23530 −0.617649 0.786454i \(-0.711915\pi\)
−0.617649 + 0.786454i \(0.711915\pi\)
\(444\) 2.00000 0.0949158
\(445\) 0 0
\(446\) 14.0000 0.662919
\(447\) 0 0
\(448\) 3.00000 0.141737
\(449\) 10.0000 0.471929 0.235965 0.971762i \(-0.424175\pi\)
0.235965 + 0.971762i \(0.424175\pi\)
\(450\) −22.0000 −1.03709
\(451\) −16.0000 −0.753411
\(452\) 14.0000 0.658505
\(453\) −2.00000 −0.0939682
\(454\) −17.0000 −0.797850
\(455\) 12.0000 0.562569
\(456\) 1.00000 0.0468293
\(457\) −7.00000 −0.327446 −0.163723 0.986506i \(-0.552350\pi\)
−0.163723 + 0.986506i \(0.552350\pi\)
\(458\) −10.0000 −0.467269
\(459\) 15.0000 0.700140
\(460\) 4.00000 0.186501
\(461\) −28.0000 −1.30409 −0.652045 0.758180i \(-0.726089\pi\)
−0.652045 + 0.758180i \(0.726089\pi\)
\(462\) −6.00000 −0.279145
\(463\) 4.00000 0.185896 0.0929479 0.995671i \(-0.470371\pi\)
0.0929479 + 0.995671i \(0.470371\pi\)
\(464\) −5.00000 −0.232119
\(465\) −32.0000 −1.48396
\(466\) −6.00000 −0.277945
\(467\) −2.00000 −0.0925490 −0.0462745 0.998929i \(-0.514735\pi\)
−0.0462745 + 0.998929i \(0.514735\pi\)
\(468\) 2.00000 0.0924500
\(469\) 9.00000 0.415581
\(470\) −32.0000 −1.47605
\(471\) 2.00000 0.0921551
\(472\) 15.0000 0.690431
\(473\) 8.00000 0.367840
\(474\) 10.0000 0.459315
\(475\) −11.0000 −0.504715
\(476\) 9.00000 0.412514
\(477\) 2.00000 0.0915737
\(478\) 15.0000 0.686084
\(479\) −20.0000 −0.913823 −0.456912 0.889512i \(-0.651044\pi\)
−0.456912 + 0.889512i \(0.651044\pi\)
\(480\) 4.00000 0.182574
\(481\) 2.00000 0.0911922
\(482\) −8.00000 −0.364390
\(483\) 3.00000 0.136505
\(484\) −7.00000 −0.318182
\(485\) 8.00000 0.363261
\(486\) −16.0000 −0.725775
\(487\) −2.00000 −0.0906287 −0.0453143 0.998973i \(-0.514429\pi\)
−0.0453143 + 0.998973i \(0.514429\pi\)
\(488\) 2.00000 0.0905357
\(489\) 16.0000 0.723545
\(490\) −8.00000 −0.361403
\(491\) −28.0000 −1.26362 −0.631811 0.775122i \(-0.717688\pi\)
−0.631811 + 0.775122i \(0.717688\pi\)
\(492\) 8.00000 0.360668
\(493\) −15.0000 −0.675566
\(494\) 1.00000 0.0449921
\(495\) 16.0000 0.719147
\(496\) −8.00000 −0.359211
\(497\) 6.00000 0.269137
\(498\) 6.00000 0.268866
\(499\) 40.0000 1.79065 0.895323 0.445418i \(-0.146945\pi\)
0.895323 + 0.445418i \(0.146945\pi\)
\(500\) −24.0000 −1.07331
\(501\) 12.0000 0.536120
\(502\) 2.00000 0.0892644
\(503\) 39.0000 1.73892 0.869462 0.494000i \(-0.164466\pi\)
0.869462 + 0.494000i \(0.164466\pi\)
\(504\) −6.00000 −0.267261
\(505\) −8.00000 −0.355995
\(506\) −2.00000 −0.0889108
\(507\) 12.0000 0.532939
\(508\) 18.0000 0.798621
\(509\) −30.0000 −1.32973 −0.664863 0.746965i \(-0.731510\pi\)
−0.664863 + 0.746965i \(0.731510\pi\)
\(510\) 12.0000 0.531369
\(511\) 27.0000 1.19441
\(512\) 1.00000 0.0441942
\(513\) −5.00000 −0.220755
\(514\) 8.00000 0.352865
\(515\) 24.0000 1.05757
\(516\) −4.00000 −0.176090
\(517\) 16.0000 0.703679
\(518\) −6.00000 −0.263625
\(519\) 6.00000 0.263371
\(520\) 4.00000 0.175412
\(521\) −28.0000 −1.22670 −0.613351 0.789810i \(-0.710179\pi\)
−0.613351 + 0.789810i \(0.710179\pi\)
\(522\) 10.0000 0.437688
\(523\) 29.0000 1.26808 0.634041 0.773300i \(-0.281395\pi\)
0.634041 + 0.773300i \(0.281395\pi\)
\(524\) 12.0000 0.524222
\(525\) −33.0000 −1.44024
\(526\) 24.0000 1.04645
\(527\) −24.0000 −1.04546
\(528\) −2.00000 −0.0870388
\(529\) −22.0000 −0.956522
\(530\) 4.00000 0.173749
\(531\) −30.0000 −1.30189
\(532\) −3.00000 −0.130066
\(533\) 8.00000 0.346518
\(534\) 0 0
\(535\) 28.0000 1.21055
\(536\) 3.00000 0.129580
\(537\) 0 0
\(538\) 30.0000 1.29339
\(539\) 4.00000 0.172292
\(540\) −20.0000 −0.860663
\(541\) 2.00000 0.0859867 0.0429934 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) 7.00000 0.300676
\(543\) −22.0000 −0.944110
\(544\) 3.00000 0.128624
\(545\) 60.0000 2.57012
\(546\) 3.00000 0.128388
\(547\) 28.0000 1.19719 0.598597 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) −17.0000 −0.726204
\(549\) −4.00000 −0.170716
\(550\) 22.0000 0.938083
\(551\) 5.00000 0.213007
\(552\) 1.00000 0.0425628
\(553\) −30.0000 −1.27573
\(554\) 28.0000 1.18961
\(555\) −8.00000 −0.339581
\(556\) 0 0
\(557\) 28.0000 1.18640 0.593199 0.805056i \(-0.297865\pi\)
0.593199 + 0.805056i \(0.297865\pi\)
\(558\) 16.0000 0.677334
\(559\) −4.00000 −0.169182
\(560\) −12.0000 −0.507093
\(561\) −6.00000 −0.253320
\(562\) −8.00000 −0.337460
\(563\) −36.0000 −1.51722 −0.758610 0.651546i \(-0.774121\pi\)
−0.758610 + 0.651546i \(0.774121\pi\)
\(564\) −8.00000 −0.336861
\(565\) −56.0000 −2.35594
\(566\) −6.00000 −0.252199
\(567\) 3.00000 0.125988
\(568\) 2.00000 0.0839181
\(569\) 40.0000 1.67689 0.838444 0.544988i \(-0.183466\pi\)
0.838444 + 0.544988i \(0.183466\pi\)
\(570\) −4.00000 −0.167542
\(571\) −28.0000 −1.17176 −0.585882 0.810397i \(-0.699252\pi\)
−0.585882 + 0.810397i \(0.699252\pi\)
\(572\) −2.00000 −0.0836242
\(573\) −7.00000 −0.292429
\(574\) −24.0000 −1.00174
\(575\) −11.0000 −0.458732
\(576\) −2.00000 −0.0833333
\(577\) −37.0000 −1.54033 −0.770165 0.637845i \(-0.779826\pi\)
−0.770165 + 0.637845i \(0.779826\pi\)
\(578\) −8.00000 −0.332756
\(579\) 6.00000 0.249351
\(580\) 20.0000 0.830455
\(581\) −18.0000 −0.746766
\(582\) 2.00000 0.0829027
\(583\) −2.00000 −0.0828315
\(584\) 9.00000 0.372423
\(585\) −8.00000 −0.330759
\(586\) 9.00000 0.371787
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) −2.00000 −0.0824786
\(589\) 8.00000 0.329634
\(590\) −60.0000 −2.47016
\(591\) −8.00000 −0.329076
\(592\) −2.00000 −0.0821995
\(593\) 34.0000 1.39621 0.698106 0.715994i \(-0.254026\pi\)
0.698106 + 0.715994i \(0.254026\pi\)
\(594\) 10.0000 0.410305
\(595\) −36.0000 −1.47586
\(596\) 0 0
\(597\) 25.0000 1.02318
\(598\) 1.00000 0.0408930
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) −11.0000 −0.449073
\(601\) −8.00000 −0.326327 −0.163163 0.986599i \(-0.552170\pi\)
−0.163163 + 0.986599i \(0.552170\pi\)
\(602\) 12.0000 0.489083
\(603\) −6.00000 −0.244339
\(604\) 2.00000 0.0813788
\(605\) 28.0000 1.13836
\(606\) −2.00000 −0.0812444
\(607\) −22.0000 −0.892952 −0.446476 0.894795i \(-0.647321\pi\)
−0.446476 + 0.894795i \(0.647321\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 15.0000 0.607831
\(610\) −8.00000 −0.323911
\(611\) −8.00000 −0.323645
\(612\) −6.00000 −0.242536
\(613\) 34.0000 1.37325 0.686624 0.727013i \(-0.259092\pi\)
0.686624 + 0.727013i \(0.259092\pi\)
\(614\) −12.0000 −0.484281
\(615\) −32.0000 −1.29036
\(616\) 6.00000 0.241747
\(617\) 18.0000 0.724653 0.362326 0.932051i \(-0.381983\pi\)
0.362326 + 0.932051i \(0.381983\pi\)
\(618\) 6.00000 0.241355
\(619\) 10.0000 0.401934 0.200967 0.979598i \(-0.435592\pi\)
0.200967 + 0.979598i \(0.435592\pi\)
\(620\) 32.0000 1.28515
\(621\) −5.00000 −0.200643
\(622\) 7.00000 0.280674
\(623\) 0 0
\(624\) 1.00000 0.0400320
\(625\) 41.0000 1.64000
\(626\) 29.0000 1.15907
\(627\) 2.00000 0.0798723
\(628\) −2.00000 −0.0798087
\(629\) −6.00000 −0.239236
\(630\) 24.0000 0.956183
\(631\) 32.0000 1.27390 0.636950 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) −10.0000 −0.397779
\(633\) −27.0000 −1.07315
\(634\) −27.0000 −1.07231
\(635\) −72.0000 −2.85723
\(636\) 1.00000 0.0396526
\(637\) −2.00000 −0.0792429
\(638\) −10.0000 −0.395904
\(639\) −4.00000 −0.158238
\(640\) −4.00000 −0.158114
\(641\) 42.0000 1.65890 0.829450 0.558581i \(-0.188654\pi\)
0.829450 + 0.558581i \(0.188654\pi\)
\(642\) 7.00000 0.276268
\(643\) −26.0000 −1.02534 −0.512670 0.858586i \(-0.671344\pi\)
−0.512670 + 0.858586i \(0.671344\pi\)
\(644\) −3.00000 −0.118217
\(645\) 16.0000 0.629999
\(646\) −3.00000 −0.118033
\(647\) 23.0000 0.904223 0.452112 0.891961i \(-0.350671\pi\)
0.452112 + 0.891961i \(0.350671\pi\)
\(648\) 1.00000 0.0392837
\(649\) 30.0000 1.17760
\(650\) −11.0000 −0.431455
\(651\) 24.0000 0.940634
\(652\) −16.0000 −0.626608
\(653\) −36.0000 −1.40879 −0.704394 0.709809i \(-0.748781\pi\)
−0.704394 + 0.709809i \(0.748781\pi\)
\(654\) 15.0000 0.586546
\(655\) −48.0000 −1.87552
\(656\) −8.00000 −0.312348
\(657\) −18.0000 −0.702247
\(658\) 24.0000 0.935617
\(659\) 5.00000 0.194772 0.0973862 0.995247i \(-0.468952\pi\)
0.0973862 + 0.995247i \(0.468952\pi\)
\(660\) 8.00000 0.311400
\(661\) −23.0000 −0.894596 −0.447298 0.894385i \(-0.647614\pi\)
−0.447298 + 0.894385i \(0.647614\pi\)
\(662\) 17.0000 0.660724
\(663\) 3.00000 0.116510
\(664\) −6.00000 −0.232845
\(665\) 12.0000 0.465340
\(666\) 4.00000 0.154997
\(667\) 5.00000 0.193601
\(668\) −12.0000 −0.464294
\(669\) −14.0000 −0.541271
\(670\) −12.0000 −0.463600
\(671\) 4.00000 0.154418
\(672\) −3.00000 −0.115728
\(673\) 44.0000 1.69608 0.848038 0.529936i \(-0.177784\pi\)
0.848038 + 0.529936i \(0.177784\pi\)
\(674\) −32.0000 −1.23259
\(675\) 55.0000 2.11695
\(676\) −12.0000 −0.461538
\(677\) 13.0000 0.499631 0.249815 0.968294i \(-0.419630\pi\)
0.249815 + 0.968294i \(0.419630\pi\)
\(678\) −14.0000 −0.537667
\(679\) −6.00000 −0.230259
\(680\) −12.0000 −0.460179
\(681\) 17.0000 0.651441
\(682\) −16.0000 −0.612672
\(683\) 4.00000 0.153056 0.0765279 0.997067i \(-0.475617\pi\)
0.0765279 + 0.997067i \(0.475617\pi\)
\(684\) 2.00000 0.0764719
\(685\) 68.0000 2.59815
\(686\) −15.0000 −0.572703
\(687\) 10.0000 0.381524
\(688\) 4.00000 0.152499
\(689\) 1.00000 0.0380970
\(690\) −4.00000 −0.152277
\(691\) 42.0000 1.59776 0.798878 0.601494i \(-0.205427\pi\)
0.798878 + 0.601494i \(0.205427\pi\)
\(692\) −6.00000 −0.228086
\(693\) −12.0000 −0.455842
\(694\) −2.00000 −0.0759190
\(695\) 0 0
\(696\) 5.00000 0.189525
\(697\) −24.0000 −0.909065
\(698\) 10.0000 0.378506
\(699\) 6.00000 0.226941
\(700\) 33.0000 1.24728
\(701\) −28.0000 −1.05755 −0.528773 0.848763i \(-0.677348\pi\)
−0.528773 + 0.848763i \(0.677348\pi\)
\(702\) −5.00000 −0.188713
\(703\) 2.00000 0.0754314
\(704\) 2.00000 0.0753778
\(705\) 32.0000 1.20519
\(706\) 9.00000 0.338719
\(707\) 6.00000 0.225653
\(708\) −15.0000 −0.563735
\(709\) −30.0000 −1.12667 −0.563337 0.826227i \(-0.690483\pi\)
−0.563337 + 0.826227i \(0.690483\pi\)
\(710\) −8.00000 −0.300235
\(711\) 20.0000 0.750059
\(712\) 0 0
\(713\) 8.00000 0.299602
\(714\) −9.00000 −0.336817
\(715\) 8.00000 0.299183
\(716\) 0 0
\(717\) −15.0000 −0.560185
\(718\) −15.0000 −0.559795
\(719\) −5.00000 −0.186469 −0.0932343 0.995644i \(-0.529721\pi\)
−0.0932343 + 0.995644i \(0.529721\pi\)
\(720\) 8.00000 0.298142
\(721\) −18.0000 −0.670355
\(722\) 1.00000 0.0372161
\(723\) 8.00000 0.297523
\(724\) 22.0000 0.817624
\(725\) −55.0000 −2.04265
\(726\) 7.00000 0.259794
\(727\) −17.0000 −0.630495 −0.315248 0.949009i \(-0.602088\pi\)
−0.315248 + 0.949009i \(0.602088\pi\)
\(728\) −3.00000 −0.111187
\(729\) 13.0000 0.481481
\(730\) −36.0000 −1.33242
\(731\) 12.0000 0.443836
\(732\) −2.00000 −0.0739221
\(733\) −36.0000 −1.32969 −0.664845 0.746981i \(-0.731502\pi\)
−0.664845 + 0.746981i \(0.731502\pi\)
\(734\) 28.0000 1.03350
\(735\) 8.00000 0.295084
\(736\) −1.00000 −0.0368605
\(737\) 6.00000 0.221013
\(738\) 16.0000 0.588968
\(739\) −40.0000 −1.47142 −0.735712 0.677295i \(-0.763152\pi\)
−0.735712 + 0.677295i \(0.763152\pi\)
\(740\) 8.00000 0.294086
\(741\) −1.00000 −0.0367359
\(742\) −3.00000 −0.110133
\(743\) −16.0000 −0.586983 −0.293492 0.955962i \(-0.594817\pi\)
−0.293492 + 0.955962i \(0.594817\pi\)
\(744\) 8.00000 0.293294
\(745\) 0 0
\(746\) 29.0000 1.06177
\(747\) 12.0000 0.439057
\(748\) 6.00000 0.219382
\(749\) −21.0000 −0.767323
\(750\) 24.0000 0.876356
\(751\) 32.0000 1.16770 0.583848 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) 8.00000 0.291730
\(753\) −2.00000 −0.0728841
\(754\) 5.00000 0.182089
\(755\) −8.00000 −0.291150
\(756\) 15.0000 0.545545
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) 15.0000 0.544825
\(759\) 2.00000 0.0725954
\(760\) 4.00000 0.145095
\(761\) 27.0000 0.978749 0.489375 0.872074i \(-0.337225\pi\)
0.489375 + 0.872074i \(0.337225\pi\)
\(762\) −18.0000 −0.652071
\(763\) −45.0000 −1.62911
\(764\) 7.00000 0.253251
\(765\) 24.0000 0.867722
\(766\) −26.0000 −0.939418
\(767\) −15.0000 −0.541619
\(768\) −1.00000 −0.0360844
\(769\) −35.0000 −1.26213 −0.631066 0.775729i \(-0.717382\pi\)
−0.631066 + 0.775729i \(0.717382\pi\)
\(770\) −24.0000 −0.864900
\(771\) −8.00000 −0.288113
\(772\) −6.00000 −0.215945
\(773\) 9.00000 0.323708 0.161854 0.986815i \(-0.448253\pi\)
0.161854 + 0.986815i \(0.448253\pi\)
\(774\) −8.00000 −0.287554
\(775\) −88.0000 −3.16105
\(776\) −2.00000 −0.0717958
\(777\) 6.00000 0.215249
\(778\) −30.0000 −1.07555
\(779\) 8.00000 0.286630
\(780\) −4.00000 −0.143223
\(781\) 4.00000 0.143131
\(782\) −3.00000 −0.107280
\(783\) −25.0000 −0.893427
\(784\) 2.00000 0.0714286
\(785\) 8.00000 0.285532
\(786\) −12.0000 −0.428026
\(787\) −17.0000 −0.605985 −0.302992 0.952993i \(-0.597986\pi\)
−0.302992 + 0.952993i \(0.597986\pi\)
\(788\) 8.00000 0.284988
\(789\) −24.0000 −0.854423
\(790\) 40.0000 1.42314
\(791\) 42.0000 1.49335
\(792\) −4.00000 −0.142134
\(793\) −2.00000 −0.0710221
\(794\) 8.00000 0.283909
\(795\) −4.00000 −0.141865
\(796\) −25.0000 −0.886102
\(797\) 3.00000 0.106265 0.0531327 0.998587i \(-0.483079\pi\)
0.0531327 + 0.998587i \(0.483079\pi\)
\(798\) 3.00000 0.106199
\(799\) 24.0000 0.849059
\(800\) 11.0000 0.388909
\(801\) 0 0
\(802\) −8.00000 −0.282490
\(803\) 18.0000 0.635206
\(804\) −3.00000 −0.105802
\(805\) 12.0000 0.422944
\(806\) 8.00000 0.281788
\(807\) −30.0000 −1.05605
\(808\) 2.00000 0.0703598
\(809\) −15.0000 −0.527372 −0.263686 0.964609i \(-0.584938\pi\)
−0.263686 + 0.964609i \(0.584938\pi\)
\(810\) −4.00000 −0.140546
\(811\) −3.00000 −0.105344 −0.0526721 0.998612i \(-0.516774\pi\)
−0.0526721 + 0.998612i \(0.516774\pi\)
\(812\) −15.0000 −0.526397
\(813\) −7.00000 −0.245501
\(814\) −4.00000 −0.140200
\(815\) 64.0000 2.24182
\(816\) −3.00000 −0.105021
\(817\) −4.00000 −0.139942
\(818\) −20.0000 −0.699284
\(819\) 6.00000 0.209657
\(820\) 32.0000 1.11749
\(821\) 12.0000 0.418803 0.209401 0.977830i \(-0.432848\pi\)
0.209401 + 0.977830i \(0.432848\pi\)
\(822\) 17.0000 0.592943
\(823\) 29.0000 1.01088 0.505438 0.862863i \(-0.331331\pi\)
0.505438 + 0.862863i \(0.331331\pi\)
\(824\) −6.00000 −0.209020
\(825\) −22.0000 −0.765942
\(826\) 45.0000 1.56575
\(827\) 23.0000 0.799788 0.399894 0.916561i \(-0.369047\pi\)
0.399894 + 0.916561i \(0.369047\pi\)
\(828\) 2.00000 0.0695048
\(829\) −15.0000 −0.520972 −0.260486 0.965478i \(-0.583883\pi\)
−0.260486 + 0.965478i \(0.583883\pi\)
\(830\) 24.0000 0.833052
\(831\) −28.0000 −0.971309
\(832\) −1.00000 −0.0346688
\(833\) 6.00000 0.207888
\(834\) 0 0
\(835\) 48.0000 1.66111
\(836\) −2.00000 −0.0691714
\(837\) −40.0000 −1.38260
\(838\) 0 0
\(839\) 20.0000 0.690477 0.345238 0.938515i \(-0.387798\pi\)
0.345238 + 0.938515i \(0.387798\pi\)
\(840\) 12.0000 0.414039
\(841\) −4.00000 −0.137931
\(842\) −13.0000 −0.448010
\(843\) 8.00000 0.275535
\(844\) 27.0000 0.929378
\(845\) 48.0000 1.65125
\(846\) −16.0000 −0.550091
\(847\) −21.0000 −0.721569
\(848\) −1.00000 −0.0343401
\(849\) 6.00000 0.205919
\(850\) 33.0000 1.13189
\(851\) 2.00000 0.0685591
\(852\) −2.00000 −0.0685189
\(853\) −6.00000 −0.205436 −0.102718 0.994711i \(-0.532754\pi\)
−0.102718 + 0.994711i \(0.532754\pi\)
\(854\) 6.00000 0.205316
\(855\) −8.00000 −0.273594
\(856\) −7.00000 −0.239255
\(857\) −12.0000 −0.409912 −0.204956 0.978771i \(-0.565705\pi\)
−0.204956 + 0.978771i \(0.565705\pi\)
\(858\) 2.00000 0.0682789
\(859\) −50.0000 −1.70598 −0.852989 0.521929i \(-0.825213\pi\)
−0.852989 + 0.521929i \(0.825213\pi\)
\(860\) −16.0000 −0.545595
\(861\) 24.0000 0.817918
\(862\) −18.0000 −0.613082
\(863\) 54.0000 1.83818 0.919091 0.394046i \(-0.128925\pi\)
0.919091 + 0.394046i \(0.128925\pi\)
\(864\) 5.00000 0.170103
\(865\) 24.0000 0.816024
\(866\) 14.0000 0.475739
\(867\) 8.00000 0.271694
\(868\) −24.0000 −0.814613
\(869\) −20.0000 −0.678454
\(870\) −20.0000 −0.678064
\(871\) −3.00000 −0.101651
\(872\) −15.0000 −0.507964
\(873\) 4.00000 0.135379
\(874\) 1.00000 0.0338255
\(875\) −72.0000 −2.43404
\(876\) −9.00000 −0.304082
\(877\) 13.0000 0.438979 0.219489 0.975615i \(-0.429561\pi\)
0.219489 + 0.975615i \(0.429561\pi\)
\(878\) 20.0000 0.674967
\(879\) −9.00000 −0.303562
\(880\) −8.00000 −0.269680
\(881\) −18.0000 −0.606435 −0.303218 0.952921i \(-0.598061\pi\)
−0.303218 + 0.952921i \(0.598061\pi\)
\(882\) −4.00000 −0.134687
\(883\) 34.0000 1.14419 0.572096 0.820187i \(-0.306131\pi\)
0.572096 + 0.820187i \(0.306131\pi\)
\(884\) −3.00000 −0.100901
\(885\) 60.0000 2.01688
\(886\) −26.0000 −0.873487
\(887\) −2.00000 −0.0671534 −0.0335767 0.999436i \(-0.510690\pi\)
−0.0335767 + 0.999436i \(0.510690\pi\)
\(888\) 2.00000 0.0671156
\(889\) 54.0000 1.81110
\(890\) 0 0
\(891\) 2.00000 0.0670025
\(892\) 14.0000 0.468755
\(893\) −8.00000 −0.267710
\(894\) 0 0
\(895\) 0 0
\(896\) 3.00000 0.100223
\(897\) −1.00000 −0.0333890
\(898\) 10.0000 0.333704
\(899\) 40.0000 1.33407
\(900\) −22.0000 −0.733333
\(901\) −3.00000 −0.0999445
\(902\) −16.0000 −0.532742
\(903\) −12.0000 −0.399335
\(904\) 14.0000 0.465633
\(905\) −88.0000 −2.92522
\(906\) −2.00000 −0.0664455
\(907\) 53.0000 1.75984 0.879918 0.475125i \(-0.157597\pi\)
0.879918 + 0.475125i \(0.157597\pi\)
\(908\) −17.0000 −0.564165
\(909\) −4.00000 −0.132672
\(910\) 12.0000 0.397796
\(911\) 12.0000 0.397578 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) 1.00000 0.0331133
\(913\) −12.0000 −0.397142
\(914\) −7.00000 −0.231539
\(915\) 8.00000 0.264472
\(916\) −10.0000 −0.330409
\(917\) 36.0000 1.18882
\(918\) 15.0000 0.495074
\(919\) 5.00000 0.164935 0.0824674 0.996594i \(-0.473720\pi\)
0.0824674 + 0.996594i \(0.473720\pi\)
\(920\) 4.00000 0.131876
\(921\) 12.0000 0.395413
\(922\) −28.0000 −0.922131
\(923\) −2.00000 −0.0658308
\(924\) −6.00000 −0.197386
\(925\) −22.0000 −0.723356
\(926\) 4.00000 0.131448
\(927\) 12.0000 0.394132
\(928\) −5.00000 −0.164133
\(929\) −55.0000 −1.80449 −0.902246 0.431222i \(-0.858082\pi\)
−0.902246 + 0.431222i \(0.858082\pi\)
\(930\) −32.0000 −1.04932
\(931\) −2.00000 −0.0655474
\(932\) −6.00000 −0.196537
\(933\) −7.00000 −0.229170
\(934\) −2.00000 −0.0654420
\(935\) −24.0000 −0.784884
\(936\) 2.00000 0.0653720
\(937\) −7.00000 −0.228680 −0.114340 0.993442i \(-0.536475\pi\)
−0.114340 + 0.993442i \(0.536475\pi\)
\(938\) 9.00000 0.293860
\(939\) −29.0000 −0.946379
\(940\) −32.0000 −1.04372
\(941\) 7.00000 0.228193 0.114097 0.993470i \(-0.463603\pi\)
0.114097 + 0.993470i \(0.463603\pi\)
\(942\) 2.00000 0.0651635
\(943\) 8.00000 0.260516
\(944\) 15.0000 0.488208
\(945\) −60.0000 −1.95180
\(946\) 8.00000 0.260102
\(947\) −12.0000 −0.389948 −0.194974 0.980808i \(-0.562462\pi\)
−0.194974 + 0.980808i \(0.562462\pi\)
\(948\) 10.0000 0.324785
\(949\) −9.00000 −0.292152
\(950\) −11.0000 −0.356887
\(951\) 27.0000 0.875535
\(952\) 9.00000 0.291692
\(953\) −46.0000 −1.49009 −0.745043 0.667016i \(-0.767571\pi\)
−0.745043 + 0.667016i \(0.767571\pi\)
\(954\) 2.00000 0.0647524
\(955\) −28.0000 −0.906059
\(956\) 15.0000 0.485135
\(957\) 10.0000 0.323254
\(958\) −20.0000 −0.646171
\(959\) −51.0000 −1.64688
\(960\) 4.00000 0.129099
\(961\) 33.0000 1.06452
\(962\) 2.00000 0.0644826
\(963\) 14.0000 0.451144
\(964\) −8.00000 −0.257663
\(965\) 24.0000 0.772587
\(966\) 3.00000 0.0965234
\(967\) 48.0000 1.54358 0.771788 0.635880i \(-0.219363\pi\)
0.771788 + 0.635880i \(0.219363\pi\)
\(968\) −7.00000 −0.224989
\(969\) 3.00000 0.0963739
\(970\) 8.00000 0.256865
\(971\) −28.0000 −0.898563 −0.449281 0.893390i \(-0.648320\pi\)
−0.449281 + 0.893390i \(0.648320\pi\)
\(972\) −16.0000 −0.513200
\(973\) 0 0
\(974\) −2.00000 −0.0640841
\(975\) 11.0000 0.352282
\(976\) 2.00000 0.0640184
\(977\) 8.00000 0.255943 0.127971 0.991778i \(-0.459153\pi\)
0.127971 + 0.991778i \(0.459153\pi\)
\(978\) 16.0000 0.511624
\(979\) 0 0
\(980\) −8.00000 −0.255551
\(981\) 30.0000 0.957826
\(982\) −28.0000 −0.893516
\(983\) −6.00000 −0.191370 −0.0956851 0.995412i \(-0.530504\pi\)
−0.0956851 + 0.995412i \(0.530504\pi\)
\(984\) 8.00000 0.255031
\(985\) −32.0000 −1.01960
\(986\) −15.0000 −0.477697
\(987\) −24.0000 −0.763928
\(988\) 1.00000 0.0318142
\(989\) −4.00000 −0.127193
\(990\) 16.0000 0.508513
\(991\) −8.00000 −0.254128 −0.127064 0.991894i \(-0.540555\pi\)
−0.127064 + 0.991894i \(0.540555\pi\)
\(992\) −8.00000 −0.254000
\(993\) −17.0000 −0.539479
\(994\) 6.00000 0.190308
\(995\) 100.000 3.17021
\(996\) 6.00000 0.190117
\(997\) 28.0000 0.886769 0.443384 0.896332i \(-0.353778\pi\)
0.443384 + 0.896332i \(0.353778\pi\)
\(998\) 40.0000 1.26618
\(999\) −10.0000 −0.316386
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))