Properties

Label 46.2.a.a.1.1
Level 46
Weight 2
Character 46.1
Self dual Yes
Analytic conductor 0.367
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 46 = 2 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 46.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.367311849298\)
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 \(\chi\) = 46.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+4.00000 q^{5}\) \(-4.00000 q^{7}\) \(-1.00000 q^{8}\) \(-3.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+4.00000 q^{5}\) \(-4.00000 q^{7}\) \(-1.00000 q^{8}\) \(-3.00000 q^{9}\) \(-4.00000 q^{10}\) \(+2.00000 q^{11}\) \(-2.00000 q^{13}\) \(+4.00000 q^{14}\) \(+1.00000 q^{16}\) \(-2.00000 q^{17}\) \(+3.00000 q^{18}\) \(-2.00000 q^{19}\) \(+4.00000 q^{20}\) \(-2.00000 q^{22}\) \(+1.00000 q^{23}\) \(+11.0000 q^{25}\) \(+2.00000 q^{26}\) \(-4.00000 q^{28}\) \(+2.00000 q^{29}\) \(-1.00000 q^{32}\) \(+2.00000 q^{34}\) \(-16.0000 q^{35}\) \(-3.00000 q^{36}\) \(-4.00000 q^{37}\) \(+2.00000 q^{38}\) \(-4.00000 q^{40}\) \(+6.00000 q^{41}\) \(+10.0000 q^{43}\) \(+2.00000 q^{44}\) \(-12.0000 q^{45}\) \(-1.00000 q^{46}\) \(+9.00000 q^{49}\) \(-11.0000 q^{50}\) \(-2.00000 q^{52}\) \(-4.00000 q^{53}\) \(+8.00000 q^{55}\) \(+4.00000 q^{56}\) \(-2.00000 q^{58}\) \(+12.0000 q^{59}\) \(-8.00000 q^{61}\) \(+12.0000 q^{63}\) \(+1.00000 q^{64}\) \(-8.00000 q^{65}\) \(-10.0000 q^{67}\) \(-2.00000 q^{68}\) \(+16.0000 q^{70}\) \(+3.00000 q^{72}\) \(+6.00000 q^{73}\) \(+4.00000 q^{74}\) \(-2.00000 q^{76}\) \(-8.00000 q^{77}\) \(-12.0000 q^{79}\) \(+4.00000 q^{80}\) \(+9.00000 q^{81}\) \(-6.00000 q^{82}\) \(+14.0000 q^{83}\) \(-8.00000 q^{85}\) \(-10.0000 q^{86}\) \(-2.00000 q^{88}\) \(-6.00000 q^{89}\) \(+12.0000 q^{90}\) \(+8.00000 q^{91}\) \(+1.00000 q^{92}\) \(-8.00000 q^{95}\) \(+6.00000 q^{97}\) \(-9.00000 q^{98}\) \(-6.00000 q^{99}\) \(+O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 1.00000 0.500000
\(5\) 4.00000 1.78885 0.894427 0.447214i \(-0.147584\pi\)
0.894427 + 0.447214i \(0.147584\pi\)
\(6\) 0 0
\(7\) −4.00000 −1.51186 −0.755929 0.654654i \(-0.772814\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) −1.00000 −0.353553
\(9\) −3.00000 −1.00000
\(10\) −4.00000 −1.26491
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 0 0
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 4.00000 1.06904
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 3.00000 0.707107
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) 4.00000 0.894427
\(21\) 0 0
\(22\) −2.00000 −0.426401
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 11.0000 2.20000
\(26\) 2.00000 0.392232
\(27\) 0 0
\(28\) −4.00000 −0.755929
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 2.00000 0.342997
\(35\) −16.0000 −2.70449
\(36\) −3.00000 −0.500000
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 2.00000 0.324443
\(39\) 0 0
\(40\) −4.00000 −0.632456
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) 10.0000 1.52499 0.762493 0.646997i \(-0.223975\pi\)
0.762493 + 0.646997i \(0.223975\pi\)
\(44\) 2.00000 0.301511
\(45\) −12.0000 −1.78885
\(46\) −1.00000 −0.147442
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 9.00000 1.28571
\(50\) −11.0000 −1.55563
\(51\) 0 0
\(52\) −2.00000 −0.277350
\(53\) −4.00000 −0.549442 −0.274721 0.961524i \(-0.588586\pi\)
−0.274721 + 0.961524i \(0.588586\pi\)
\(54\) 0 0
\(55\) 8.00000 1.07872
\(56\) 4.00000 0.534522
\(57\) 0 0
\(58\) −2.00000 −0.262613
\(59\) 12.0000 1.56227 0.781133 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) 0 0
\(61\) −8.00000 −1.02430 −0.512148 0.858898i \(-0.671150\pi\)
−0.512148 + 0.858898i \(0.671150\pi\)
\(62\) 0 0
\(63\) 12.0000 1.51186
\(64\) 1.00000 0.125000
\(65\) −8.00000 −0.992278
\(66\) 0 0
\(67\) −10.0000 −1.22169 −0.610847 0.791748i \(-0.709171\pi\)
−0.610847 + 0.791748i \(0.709171\pi\)
\(68\) −2.00000 −0.242536
\(69\) 0 0
\(70\) 16.0000 1.91237
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 3.00000 0.353553
\(73\) 6.00000 0.702247 0.351123 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) 4.00000 0.464991
\(75\) 0 0
\(76\) −2.00000 −0.229416
\(77\) −8.00000 −0.911685
\(78\) 0 0
\(79\) −12.0000 −1.35011 −0.675053 0.737769i \(-0.735879\pi\)
−0.675053 + 0.737769i \(0.735879\pi\)
\(80\) 4.00000 0.447214
\(81\) 9.00000 1.00000
\(82\) −6.00000 −0.662589
\(83\) 14.0000 1.53670 0.768350 0.640030i \(-0.221078\pi\)
0.768350 + 0.640030i \(0.221078\pi\)
\(84\) 0 0
\(85\) −8.00000 −0.867722
\(86\) −10.0000 −1.07833
\(87\) 0 0
\(88\) −2.00000 −0.213201
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 12.0000 1.26491
\(91\) 8.00000 0.838628
\(92\) 1.00000 0.104257
\(93\) 0 0
\(94\) 0 0
\(95\) −8.00000 −0.820783
\(96\) 0 0
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) −9.00000 −0.909137
\(99\) −6.00000 −0.603023
\(100\) 11.0000 1.10000
\(101\) −10.0000 −0.995037 −0.497519 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) 0 0
\(103\) −8.00000 −0.788263 −0.394132 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(104\) 2.00000 0.196116
\(105\) 0 0
\(106\) 4.00000 0.388514
\(107\) −10.0000 −0.966736 −0.483368 0.875417i \(-0.660587\pi\)
−0.483368 + 0.875417i \(0.660587\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) −8.00000 −0.762770
\(111\) 0 0
\(112\) −4.00000 −0.377964
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) 0 0
\(115\) 4.00000 0.373002
\(116\) 2.00000 0.185695
\(117\) 6.00000 0.554700
\(118\) −12.0000 −1.10469
\(119\) 8.00000 0.733359
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 8.00000 0.724286
\(123\) 0 0
\(124\) 0 0
\(125\) 24.0000 2.14663
\(126\) −12.0000 −1.06904
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 8.00000 0.701646
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) 8.00000 0.693688
\(134\) 10.0000 0.863868
\(135\) 0 0
\(136\) 2.00000 0.171499
\(137\) 6.00000 0.512615 0.256307 0.966595i \(-0.417494\pi\)
0.256307 + 0.966595i \(0.417494\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) −16.0000 −1.35225
\(141\) 0 0
\(142\) 0 0
\(143\) −4.00000 −0.334497
\(144\) −3.00000 −0.250000
\(145\) 8.00000 0.664364
\(146\) −6.00000 −0.496564
\(147\) 0 0
\(148\) −4.00000 −0.328798
\(149\) −4.00000 −0.327693 −0.163846 0.986486i \(-0.552390\pi\)
−0.163846 + 0.986486i \(0.552390\pi\)
\(150\) 0 0
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 2.00000 0.162221
\(153\) 6.00000 0.485071
\(154\) 8.00000 0.644658
\(155\) 0 0
\(156\) 0 0
\(157\) 12.0000 0.957704 0.478852 0.877896i \(-0.341053\pi\)
0.478852 + 0.877896i \(0.341053\pi\)
\(158\) 12.0000 0.954669
\(159\) 0 0
\(160\) −4.00000 −0.316228
\(161\) −4.00000 −0.315244
\(162\) −9.00000 −0.707107
\(163\) −8.00000 −0.626608 −0.313304 0.949653i \(-0.601436\pi\)
−0.313304 + 0.949653i \(0.601436\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) −14.0000 −1.08661
\(167\) 16.0000 1.23812 0.619059 0.785345i \(-0.287514\pi\)
0.619059 + 0.785345i \(0.287514\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 8.00000 0.613572
\(171\) 6.00000 0.458831
\(172\) 10.0000 0.762493
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 0 0
\(175\) −44.0000 −3.32609
\(176\) 2.00000 0.150756
\(177\) 0 0
\(178\) 6.00000 0.449719
\(179\) −16.0000 −1.19590 −0.597948 0.801535i \(-0.704017\pi\)
−0.597948 + 0.801535i \(0.704017\pi\)
\(180\) −12.0000 −0.894427
\(181\) −24.0000 −1.78391 −0.891953 0.452128i \(-0.850665\pi\)
−0.891953 + 0.452128i \(0.850665\pi\)
\(182\) −8.00000 −0.592999
\(183\) 0 0
\(184\) −1.00000 −0.0737210
\(185\) −16.0000 −1.17634
\(186\) 0 0
\(187\) −4.00000 −0.292509
\(188\) 0 0
\(189\) 0 0
\(190\) 8.00000 0.580381
\(191\) 20.0000 1.44715 0.723575 0.690246i \(-0.242498\pi\)
0.723575 + 0.690246i \(0.242498\pi\)
\(192\) 0 0
\(193\) 26.0000 1.87152 0.935760 0.352636i \(-0.114715\pi\)
0.935760 + 0.352636i \(0.114715\pi\)
\(194\) −6.00000 −0.430775
\(195\) 0 0
\(196\) 9.00000 0.642857
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 6.00000 0.426401
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) −11.0000 −0.777817
\(201\) 0 0
\(202\) 10.0000 0.703598
\(203\) −8.00000 −0.561490
\(204\) 0 0
\(205\) 24.0000 1.67623
\(206\) 8.00000 0.557386
\(207\) −3.00000 −0.208514
\(208\) −2.00000 −0.138675
\(209\) −4.00000 −0.276686
\(210\) 0 0
\(211\) −20.0000 −1.37686 −0.688428 0.725304i \(-0.741699\pi\)
−0.688428 + 0.725304i \(0.741699\pi\)
\(212\) −4.00000 −0.274721
\(213\) 0 0
\(214\) 10.0000 0.683586
\(215\) 40.0000 2.72798
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 8.00000 0.539360
\(221\) 4.00000 0.269069
\(222\) 0 0
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) 4.00000 0.267261
\(225\) −33.0000 −2.20000
\(226\) 14.0000 0.931266
\(227\) −6.00000 −0.398234 −0.199117 0.979976i \(-0.563807\pi\)
−0.199117 + 0.979976i \(0.563807\pi\)
\(228\) 0 0
\(229\) 8.00000 0.528655 0.264327 0.964433i \(-0.414850\pi\)
0.264327 + 0.964433i \(0.414850\pi\)
\(230\) −4.00000 −0.263752
\(231\) 0 0
\(232\) −2.00000 −0.131306
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) −6.00000 −0.392232
\(235\) 0 0
\(236\) 12.0000 0.781133
\(237\) 0 0
\(238\) −8.00000 −0.518563
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) 0 0
\(241\) 22.0000 1.41714 0.708572 0.705638i \(-0.249340\pi\)
0.708572 + 0.705638i \(0.249340\pi\)
\(242\) 7.00000 0.449977
\(243\) 0 0
\(244\) −8.00000 −0.512148
\(245\) 36.0000 2.29996
\(246\) 0 0
\(247\) 4.00000 0.254514
\(248\) 0 0
\(249\) 0 0
\(250\) −24.0000 −1.51789
\(251\) 14.0000 0.883672 0.441836 0.897096i \(-0.354327\pi\)
0.441836 + 0.897096i \(0.354327\pi\)
\(252\) 12.0000 0.755929
\(253\) 2.00000 0.125739
\(254\) −16.0000 −1.00393
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 22.0000 1.37232 0.686161 0.727450i \(-0.259294\pi\)
0.686161 + 0.727450i \(0.259294\pi\)
\(258\) 0 0
\(259\) 16.0000 0.994192
\(260\) −8.00000 −0.496139
\(261\) −6.00000 −0.371391
\(262\) −12.0000 −0.741362
\(263\) −16.0000 −0.986602 −0.493301 0.869859i \(-0.664210\pi\)
−0.493301 + 0.869859i \(0.664210\pi\)
\(264\) 0 0
\(265\) −16.0000 −0.982872
\(266\) −8.00000 −0.490511
\(267\) 0 0
\(268\) −10.0000 −0.610847
\(269\) −14.0000 −0.853595 −0.426798 0.904347i \(-0.640358\pi\)
−0.426798 + 0.904347i \(0.640358\pi\)
\(270\) 0 0
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) −2.00000 −0.121268
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) 22.0000 1.32665
\(276\) 0 0
\(277\) −14.0000 −0.841178 −0.420589 0.907251i \(-0.638177\pi\)
−0.420589 + 0.907251i \(0.638177\pi\)
\(278\) 4.00000 0.239904
\(279\) 0 0
\(280\) 16.0000 0.956183
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) 0 0
\(283\) −14.0000 −0.832214 −0.416107 0.909316i \(-0.636606\pi\)
−0.416107 + 0.909316i \(0.636606\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 4.00000 0.236525
\(287\) −24.0000 −1.41668
\(288\) 3.00000 0.176777
\(289\) −13.0000 −0.764706
\(290\) −8.00000 −0.469776
\(291\) 0 0
\(292\) 6.00000 0.351123
\(293\) 4.00000 0.233682 0.116841 0.993151i \(-0.462723\pi\)
0.116841 + 0.993151i \(0.462723\pi\)
\(294\) 0 0
\(295\) 48.0000 2.79467
\(296\) 4.00000 0.232495
\(297\) 0 0
\(298\) 4.00000 0.231714
\(299\) −2.00000 −0.115663
\(300\) 0 0
\(301\) −40.0000 −2.30556
\(302\) 8.00000 0.460348
\(303\) 0 0
\(304\) −2.00000 −0.114708
\(305\) −32.0000 −1.83231
\(306\) −6.00000 −0.342997
\(307\) −16.0000 −0.913168 −0.456584 0.889680i \(-0.650927\pi\)
−0.456584 + 0.889680i \(0.650927\pi\)
\(308\) −8.00000 −0.455842
\(309\) 0 0
\(310\) 0 0
\(311\) 32.0000 1.81455 0.907277 0.420534i \(-0.138157\pi\)
0.907277 + 0.420534i \(0.138157\pi\)
\(312\) 0 0
\(313\) 22.0000 1.24351 0.621757 0.783210i \(-0.286419\pi\)
0.621757 + 0.783210i \(0.286419\pi\)
\(314\) −12.0000 −0.677199
\(315\) 48.0000 2.70449
\(316\) −12.0000 −0.675053
\(317\) 2.00000 0.112331 0.0561656 0.998421i \(-0.482113\pi\)
0.0561656 + 0.998421i \(0.482113\pi\)
\(318\) 0 0
\(319\) 4.00000 0.223957
\(320\) 4.00000 0.223607
\(321\) 0 0
\(322\) 4.00000 0.222911
\(323\) 4.00000 0.222566
\(324\) 9.00000 0.500000
\(325\) −22.0000 −1.22034
\(326\) 8.00000 0.443079
\(327\) 0 0
\(328\) −6.00000 −0.331295
\(329\) 0 0
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) 14.0000 0.768350
\(333\) 12.0000 0.657596
\(334\) −16.0000 −0.875481
\(335\) −40.0000 −2.18543
\(336\) 0 0
\(337\) 10.0000 0.544735 0.272367 0.962193i \(-0.412193\pi\)
0.272367 + 0.962193i \(0.412193\pi\)
\(338\) 9.00000 0.489535
\(339\) 0 0
\(340\) −8.00000 −0.433861
\(341\) 0 0
\(342\) −6.00000 −0.324443
\(343\) −8.00000 −0.431959
\(344\) −10.0000 −0.539164
\(345\) 0 0
\(346\) 6.00000 0.322562
\(347\) 8.00000 0.429463 0.214731 0.976673i \(-0.431112\pi\)
0.214731 + 0.976673i \(0.431112\pi\)
\(348\) 0 0
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 44.0000 2.35190
\(351\) 0 0
\(352\) −2.00000 −0.106600
\(353\) 2.00000 0.106449 0.0532246 0.998583i \(-0.483050\pi\)
0.0532246 + 0.998583i \(0.483050\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) 16.0000 0.845626
\(359\) −12.0000 −0.633336 −0.316668 0.948536i \(-0.602564\pi\)
−0.316668 + 0.948536i \(0.602564\pi\)
\(360\) 12.0000 0.632456
\(361\) −15.0000 −0.789474
\(362\) 24.0000 1.26141
\(363\) 0 0
\(364\) 8.00000 0.419314
\(365\) 24.0000 1.25622
\(366\) 0 0
\(367\) 12.0000 0.626395 0.313197 0.949688i \(-0.398600\pi\)
0.313197 + 0.949688i \(0.398600\pi\)
\(368\) 1.00000 0.0521286
\(369\) −18.0000 −0.937043
\(370\) 16.0000 0.831800
\(371\) 16.0000 0.830679
\(372\) 0 0
\(373\) −4.00000 −0.207112 −0.103556 0.994624i \(-0.533022\pi\)
−0.103556 + 0.994624i \(0.533022\pi\)
\(374\) 4.00000 0.206835
\(375\) 0 0
\(376\) 0 0
\(377\) −4.00000 −0.206010
\(378\) 0 0
\(379\) 22.0000 1.13006 0.565032 0.825069i \(-0.308864\pi\)
0.565032 + 0.825069i \(0.308864\pi\)
\(380\) −8.00000 −0.410391
\(381\) 0 0
\(382\) −20.0000 −1.02329
\(383\) −24.0000 −1.22634 −0.613171 0.789950i \(-0.710106\pi\)
−0.613171 + 0.789950i \(0.710106\pi\)
\(384\) 0 0
\(385\) −32.0000 −1.63087
\(386\) −26.0000 −1.32337
\(387\) −30.0000 −1.52499
\(388\) 6.00000 0.304604
\(389\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 0 0
\(391\) −2.00000 −0.101144
\(392\) −9.00000 −0.454569
\(393\) 0 0
\(394\) −18.0000 −0.906827
\(395\) −48.0000 −2.41514
\(396\) −6.00000 −0.301511
\(397\) 14.0000 0.702640 0.351320 0.936255i \(-0.385733\pi\)
0.351320 + 0.936255i \(0.385733\pi\)
\(398\) 4.00000 0.200502
\(399\) 0 0
\(400\) 11.0000 0.550000
\(401\) −18.0000 −0.898877 −0.449439 0.893311i \(-0.648376\pi\)
−0.449439 + 0.893311i \(0.648376\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −10.0000 −0.497519
\(405\) 36.0000 1.78885
\(406\) 8.00000 0.397033
\(407\) −8.00000 −0.396545
\(408\) 0 0
\(409\) 34.0000 1.68119 0.840596 0.541663i \(-0.182205\pi\)
0.840596 + 0.541663i \(0.182205\pi\)
\(410\) −24.0000 −1.18528
\(411\) 0 0
\(412\) −8.00000 −0.394132
\(413\) −48.0000 −2.36193
\(414\) 3.00000 0.147442
\(415\) 56.0000 2.74893
\(416\) 2.00000 0.0980581
\(417\) 0 0
\(418\) 4.00000 0.195646
\(419\) −18.0000 −0.879358 −0.439679 0.898155i \(-0.644908\pi\)
−0.439679 + 0.898155i \(0.644908\pi\)
\(420\) 0 0
\(421\) 28.0000 1.36464 0.682318 0.731055i \(-0.260972\pi\)
0.682318 + 0.731055i \(0.260972\pi\)
\(422\) 20.0000 0.973585
\(423\) 0 0
\(424\) 4.00000 0.194257
\(425\) −22.0000 −1.06716
\(426\) 0 0
\(427\) 32.0000 1.54859
\(428\) −10.0000 −0.483368
\(429\) 0 0
\(430\) −40.0000 −1.92897
\(431\) −12.0000 −0.578020 −0.289010 0.957326i \(-0.593326\pi\)
−0.289010 + 0.957326i \(0.593326\pi\)
\(432\) 0 0
\(433\) −26.0000 −1.24948 −0.624740 0.780833i \(-0.714795\pi\)
−0.624740 + 0.780833i \(0.714795\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.00000 −0.0956730
\(438\) 0 0
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) −8.00000 −0.381385
\(441\) −27.0000 −1.28571
\(442\) −4.00000 −0.190261
\(443\) 8.00000 0.380091 0.190046 0.981775i \(-0.439136\pi\)
0.190046 + 0.981775i \(0.439136\pi\)
\(444\) 0 0
\(445\) −24.0000 −1.13771
\(446\) 16.0000 0.757622
\(447\) 0 0
\(448\) −4.00000 −0.188982
\(449\) 14.0000 0.660701 0.330350 0.943858i \(-0.392833\pi\)
0.330350 + 0.943858i \(0.392833\pi\)
\(450\) 33.0000 1.55563
\(451\) 12.0000 0.565058
\(452\) −14.0000 −0.658505
\(453\) 0 0
\(454\) 6.00000 0.281594
\(455\) 32.0000 1.50018
\(456\) 0 0
\(457\) −10.0000 −0.467780 −0.233890 0.972263i \(-0.575146\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) −8.00000 −0.373815
\(459\) 0 0
\(460\) 4.00000 0.186501
\(461\) 18.0000 0.838344 0.419172 0.907907i \(-0.362320\pi\)
0.419172 + 0.907907i \(0.362320\pi\)
\(462\) 0 0
\(463\) 40.0000 1.85896 0.929479 0.368875i \(-0.120257\pi\)
0.929479 + 0.368875i \(0.120257\pi\)
\(464\) 2.00000 0.0928477
\(465\) 0 0
\(466\) 6.00000 0.277945
\(467\) −2.00000 −0.0925490 −0.0462745 0.998929i \(-0.514735\pi\)
−0.0462745 + 0.998929i \(0.514735\pi\)
\(468\) 6.00000 0.277350
\(469\) 40.0000 1.84703
\(470\) 0 0
\(471\) 0 0
\(472\) −12.0000 −0.552345
\(473\) 20.0000 0.919601
\(474\) 0 0
\(475\) −22.0000 −1.00943
\(476\) 8.00000 0.366679
\(477\) 12.0000 0.549442
\(478\) 24.0000 1.09773
\(479\) −8.00000 −0.365529 −0.182765 0.983157i \(-0.558505\pi\)
−0.182765 + 0.983157i \(0.558505\pi\)
\(480\) 0 0
\(481\) 8.00000 0.364769
\(482\) −22.0000 −1.00207
\(483\) 0 0
\(484\) −7.00000 −0.318182
\(485\) 24.0000 1.08978
\(486\) 0 0
\(487\) −8.00000 −0.362515 −0.181257 0.983436i \(-0.558017\pi\)
−0.181257 + 0.983436i \(0.558017\pi\)
\(488\) 8.00000 0.362143
\(489\) 0 0
\(490\) −36.0000 −1.62631
\(491\) 24.0000 1.08310 0.541552 0.840667i \(-0.317837\pi\)
0.541552 + 0.840667i \(0.317837\pi\)
\(492\) 0 0
\(493\) −4.00000 −0.180151
\(494\) −4.00000 −0.179969
\(495\) −24.0000 −1.07872
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 16.0000 0.716258 0.358129 0.933672i \(-0.383415\pi\)
0.358129 + 0.933672i \(0.383415\pi\)
\(500\) 24.0000 1.07331
\(501\) 0 0
\(502\) −14.0000 −0.624851
\(503\) 12.0000 0.535054 0.267527 0.963550i \(-0.413794\pi\)
0.267527 + 0.963550i \(0.413794\pi\)
\(504\) −12.0000 −0.534522
\(505\) −40.0000 −1.77998
\(506\) −2.00000 −0.0889108
\(507\) 0 0
\(508\) 16.0000 0.709885
\(509\) 18.0000 0.797836 0.398918 0.916987i \(-0.369386\pi\)
0.398918 + 0.916987i \(0.369386\pi\)
\(510\) 0 0
\(511\) −24.0000 −1.06170
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −22.0000 −0.970378
\(515\) −32.0000 −1.41009
\(516\) 0 0
\(517\) 0 0
\(518\) −16.0000 −0.703000
\(519\) 0 0
\(520\) 8.00000 0.350823
\(521\) 38.0000 1.66481 0.832405 0.554168i \(-0.186963\pi\)
0.832405 + 0.554168i \(0.186963\pi\)
\(522\) 6.00000 0.262613
\(523\) −34.0000 −1.48672 −0.743358 0.668894i \(-0.766768\pi\)
−0.743358 + 0.668894i \(0.766768\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) 16.0000 0.697633
\(527\) 0 0
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 16.0000 0.694996
\(531\) −36.0000 −1.56227
\(532\) 8.00000 0.346844
\(533\) −12.0000 −0.519778
\(534\) 0 0
\(535\) −40.0000 −1.72935
\(536\) 10.0000 0.431934
\(537\) 0 0
\(538\) 14.0000 0.603583
\(539\) 18.0000 0.775315
\(540\) 0 0
\(541\) −6.00000 −0.257960 −0.128980 0.991647i \(-0.541170\pi\)
−0.128980 + 0.991647i \(0.541170\pi\)
\(542\) −8.00000 −0.343629
\(543\) 0 0
\(544\) 2.00000 0.0857493
\(545\) 0 0
\(546\) 0 0
\(547\) −36.0000 −1.53925 −0.769624 0.638497i \(-0.779557\pi\)
−0.769624 + 0.638497i \(0.779557\pi\)
\(548\) 6.00000 0.256307
\(549\) 24.0000 1.02430
\(550\) −22.0000 −0.938083
\(551\) −4.00000 −0.170406
\(552\) 0 0
\(553\) 48.0000 2.04117
\(554\) 14.0000 0.594803
\(555\) 0 0
\(556\) −4.00000 −0.169638
\(557\) 16.0000 0.677942 0.338971 0.940797i \(-0.389921\pi\)
0.338971 + 0.940797i \(0.389921\pi\)
\(558\) 0 0
\(559\) −20.0000 −0.845910
\(560\) −16.0000 −0.676123
\(561\) 0 0
\(562\) 6.00000 0.253095
\(563\) −14.0000 −0.590030 −0.295015 0.955493i \(-0.595325\pi\)
−0.295015 + 0.955493i \(0.595325\pi\)
\(564\) 0 0
\(565\) −56.0000 −2.35594
\(566\) 14.0000 0.588464
\(567\) −36.0000 −1.51186
\(568\) 0 0
\(569\) 14.0000 0.586911 0.293455 0.955973i \(-0.405195\pi\)
0.293455 + 0.955973i \(0.405195\pi\)
\(570\) 0 0
\(571\) 14.0000 0.585882 0.292941 0.956131i \(-0.405366\pi\)
0.292941 + 0.956131i \(0.405366\pi\)
\(572\) −4.00000 −0.167248
\(573\) 0 0
\(574\) 24.0000 1.00174
\(575\) 11.0000 0.458732
\(576\) −3.00000 −0.125000
\(577\) 30.0000 1.24892 0.624458 0.781058i \(-0.285320\pi\)
0.624458 + 0.781058i \(0.285320\pi\)
\(578\) 13.0000 0.540729
\(579\) 0 0
\(580\) 8.00000 0.332182
\(581\) −56.0000 −2.32327
\(582\) 0 0
\(583\) −8.00000 −0.331326
\(584\) −6.00000 −0.248282
\(585\) 24.0000 0.992278
\(586\) −4.00000 −0.165238
\(587\) −28.0000 −1.15568 −0.577842 0.816149i \(-0.696105\pi\)
−0.577842 + 0.816149i \(0.696105\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −48.0000 −1.97613
\(591\) 0 0
\(592\) −4.00000 −0.164399
\(593\) 6.00000 0.246390 0.123195 0.992382i \(-0.460686\pi\)
0.123195 + 0.992382i \(0.460686\pi\)
\(594\) 0 0
\(595\) 32.0000 1.31187
\(596\) −4.00000 −0.163846
\(597\) 0 0
\(598\) 2.00000 0.0817861
\(599\) 16.0000 0.653742 0.326871 0.945069i \(-0.394006\pi\)
0.326871 + 0.945069i \(0.394006\pi\)
\(600\) 0 0
\(601\) −26.0000 −1.06056 −0.530281 0.847822i \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) 40.0000 1.63028
\(603\) 30.0000 1.22169
\(604\) −8.00000 −0.325515
\(605\) −28.0000 −1.13836
\(606\) 0 0
\(607\) 32.0000 1.29884 0.649420 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) 2.00000 0.0811107
\(609\) 0 0
\(610\) 32.0000 1.29564
\(611\) 0 0
\(612\) 6.00000 0.242536
\(613\) −16.0000 −0.646234 −0.323117 0.946359i \(-0.604731\pi\)
−0.323117 + 0.946359i \(0.604731\pi\)
\(614\) 16.0000 0.645707
\(615\) 0 0
\(616\) 8.00000 0.322329
\(617\) 18.0000 0.724653 0.362326 0.932051i \(-0.381983\pi\)
0.362326 + 0.932051i \(0.381983\pi\)
\(618\) 0 0
\(619\) −14.0000 −0.562708 −0.281354 0.959604i \(-0.590783\pi\)
−0.281354 + 0.959604i \(0.590783\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −32.0000 −1.28308
\(623\) 24.0000 0.961540
\(624\) 0 0
\(625\) 41.0000 1.64000
\(626\) −22.0000 −0.879297
\(627\) 0 0
\(628\) 12.0000 0.478852
\(629\) 8.00000 0.318981
\(630\) −48.0000 −1.91237
\(631\) −40.0000 −1.59237 −0.796187 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) 12.0000 0.477334
\(633\) 0 0
\(634\) −2.00000 −0.0794301
\(635\) 64.0000 2.53976
\(636\) 0 0
\(637\) −18.0000 −0.713186
\(638\) −4.00000 −0.158362
\(639\) 0 0
\(640\) −4.00000 −0.158114
\(641\) 14.0000 0.552967 0.276483 0.961019i \(-0.410831\pi\)
0.276483 + 0.961019i \(0.410831\pi\)
\(642\) 0 0
\(643\) 10.0000 0.394362 0.197181 0.980367i \(-0.436821\pi\)
0.197181 + 0.980367i \(0.436821\pi\)
\(644\) −4.00000 −0.157622
\(645\) 0 0
\(646\) −4.00000 −0.157378
\(647\) −40.0000 −1.57256 −0.786281 0.617869i \(-0.787996\pi\)
−0.786281 + 0.617869i \(0.787996\pi\)
\(648\) −9.00000 −0.353553
\(649\) 24.0000 0.942082
\(650\) 22.0000 0.862911
\(651\) 0 0
\(652\) −8.00000 −0.313304
\(653\) −42.0000 −1.64359 −0.821794 0.569785i \(-0.807026\pi\)
−0.821794 + 0.569785i \(0.807026\pi\)
\(654\) 0 0
\(655\) 48.0000 1.87552
\(656\) 6.00000 0.234261
\(657\) −18.0000 −0.702247
\(658\) 0 0
\(659\) 30.0000 1.16863 0.584317 0.811525i \(-0.301362\pi\)
0.584317 + 0.811525i \(0.301362\pi\)
\(660\) 0 0
\(661\) −24.0000 −0.933492 −0.466746 0.884391i \(-0.654574\pi\)
−0.466746 + 0.884391i \(0.654574\pi\)
\(662\) 4.00000 0.155464
\(663\) 0 0
\(664\) −14.0000 −0.543305
\(665\) 32.0000 1.24091
\(666\) −12.0000 −0.464991
\(667\) 2.00000 0.0774403
\(668\) 16.0000 0.619059
\(669\) 0 0
\(670\) 40.0000 1.54533
\(671\) −16.0000 −0.617673
\(672\) 0 0
\(673\) −2.00000 −0.0770943 −0.0385472 0.999257i \(-0.512273\pi\)
−0.0385472 + 0.999257i \(0.512273\pi\)
\(674\) −10.0000 −0.385186
\(675\) 0 0
\(676\) −9.00000 −0.346154
\(677\) −12.0000 −0.461197 −0.230599 0.973049i \(-0.574068\pi\)
−0.230599 + 0.973049i \(0.574068\pi\)
\(678\) 0 0
\(679\) −24.0000 −0.921035
\(680\) 8.00000 0.306786
\(681\) 0 0
\(682\) 0 0
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 6.00000 0.229416
\(685\) 24.0000 0.916993
\(686\) 8.00000 0.305441
\(687\) 0 0
\(688\) 10.0000 0.381246
\(689\) 8.00000 0.304776
\(690\) 0 0
\(691\) −4.00000 −0.152167 −0.0760836 0.997101i \(-0.524242\pi\)
−0.0760836 + 0.997101i \(0.524242\pi\)
\(692\) −6.00000 −0.228086
\(693\) 24.0000 0.911685
\(694\) −8.00000 −0.303676
\(695\) −16.0000 −0.606915
\(696\) 0 0
\(697\) −12.0000 −0.454532
\(698\) −26.0000 −0.984115
\(699\) 0 0
\(700\) −44.0000 −1.66304
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 8.00000 0.301726
\(704\) 2.00000 0.0753778
\(705\) 0 0
\(706\) −2.00000 −0.0752710
\(707\) 40.0000 1.50435
\(708\) 0 0
\(709\) −28.0000 −1.05156 −0.525781 0.850620i \(-0.676227\pi\)
−0.525781 + 0.850620i \(0.676227\pi\)
\(710\) 0 0
\(711\) 36.0000 1.35011
\(712\) 6.00000 0.224860
\(713\) 0 0
\(714\) 0 0
\(715\) −16.0000 −0.598366
\(716\) −16.0000 −0.597948
\(717\) 0 0
\(718\) 12.0000 0.447836
\(719\) 48.0000 1.79010 0.895049 0.445968i \(-0.147140\pi\)
0.895049 + 0.445968i \(0.147140\pi\)
\(720\) −12.0000 −0.447214
\(721\) 32.0000 1.19174
\(722\) 15.0000 0.558242
\(723\) 0 0
\(724\) −24.0000 −0.891953
\(725\) 22.0000 0.817059
\(726\) 0 0
\(727\) −36.0000 −1.33517 −0.667583 0.744535i \(-0.732671\pi\)
−0.667583 + 0.744535i \(0.732671\pi\)
\(728\) −8.00000 −0.296500
\(729\) −27.0000 −1.00000
\(730\) −24.0000 −0.888280
\(731\) −20.0000 −0.739727
\(732\) 0 0
\(733\) −44.0000 −1.62518 −0.812589 0.582838i \(-0.801942\pi\)
−0.812589 + 0.582838i \(0.801942\pi\)
\(734\) −12.0000 −0.442928
\(735\) 0 0
\(736\) −1.00000 −0.0368605
\(737\) −20.0000 −0.736709
\(738\) 18.0000 0.662589
\(739\) −32.0000 −1.17714 −0.588570 0.808447i \(-0.700309\pi\)
−0.588570 + 0.808447i \(0.700309\pi\)
\(740\) −16.0000 −0.588172
\(741\) 0 0
\(742\) −16.0000 −0.587378
\(743\) −24.0000 −0.880475 −0.440237 0.897881i \(-0.645106\pi\)
−0.440237 + 0.897881i \(0.645106\pi\)
\(744\) 0 0
\(745\) −16.0000 −0.586195
\(746\) 4.00000 0.146450
\(747\) −42.0000 −1.53670
\(748\) −4.00000 −0.146254
\(749\) 40.0000 1.46157
\(750\) 0 0
\(751\) 48.0000 1.75154 0.875772 0.482724i \(-0.160353\pi\)
0.875772 + 0.482724i \(0.160353\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 4.00000 0.145671
\(755\) −32.0000 −1.16460
\(756\) 0 0
\(757\) −48.0000 −1.74459 −0.872295 0.488980i \(-0.837369\pi\)
−0.872295 + 0.488980i \(0.837369\pi\)
\(758\) −22.0000 −0.799076
\(759\) 0 0
\(760\) 8.00000 0.290191
\(761\) −30.0000 −1.08750 −0.543750 0.839248i \(-0.682996\pi\)
−0.543750 + 0.839248i \(0.682996\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 20.0000 0.723575
\(765\) 24.0000 0.867722
\(766\) 24.0000 0.867155
\(767\) −24.0000 −0.866590
\(768\) 0 0
\(769\) 22.0000 0.793340 0.396670 0.917961i \(-0.370166\pi\)
0.396670 + 0.917961i \(0.370166\pi\)
\(770\) 32.0000 1.15320
\(771\) 0 0
\(772\) 26.0000 0.935760
\(773\) −40.0000 −1.43870 −0.719350 0.694648i \(-0.755560\pi\)
−0.719350 + 0.694648i \(0.755560\pi\)
\(774\) 30.0000 1.07833
\(775\) 0 0
\(776\) −6.00000 −0.215387
\(777\) 0 0
\(778\) 0 0
\(779\) −12.0000 −0.429945
\(780\) 0 0
\(781\) 0 0
\(782\) 2.00000 0.0715199
\(783\) 0 0
\(784\) 9.00000 0.321429
\(785\) 48.0000 1.71319
\(786\) 0 0
\(787\) 18.0000 0.641631 0.320815 0.947142i \(-0.396043\pi\)
0.320815 + 0.947142i \(0.396043\pi\)
\(788\) 18.0000 0.641223
\(789\) 0 0
\(790\) 48.0000 1.70776
\(791\) 56.0000 1.99113
\(792\) 6.00000 0.213201
\(793\) 16.0000 0.568177
\(794\) −14.0000 −0.496841
\(795\) 0 0
\(796\) −4.00000 −0.141776
\(797\) 8.00000 0.283375 0.141687 0.989911i \(-0.454747\pi\)
0.141687 + 0.989911i \(0.454747\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −11.0000 −0.388909
\(801\) 18.0000 0.635999
\(802\) 18.0000 0.635602
\(803\) 12.0000 0.423471
\(804\) 0 0
\(805\) −16.0000 −0.563926
\(806\) 0 0
\(807\) 0 0
\(808\) 10.0000 0.351799
\(809\) −30.0000 −1.05474 −0.527372 0.849635i \(-0.676823\pi\)
−0.527372 + 0.849635i \(0.676823\pi\)
\(810\) −36.0000 −1.26491
\(811\) 20.0000 0.702295 0.351147 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) −8.00000 −0.280745
\(813\) 0 0
\(814\) 8.00000 0.280400
\(815\) −32.0000 −1.12091
\(816\) 0 0
\(817\) −20.0000 −0.699711
\(818\) −34.0000 −1.18878
\(819\) −24.0000 −0.838628
\(820\) 24.0000 0.838116
\(821\) 30.0000 1.04701 0.523504 0.852023i \(-0.324625\pi\)
0.523504 + 0.852023i \(0.324625\pi\)
\(822\) 0 0
\(823\) 24.0000 0.836587 0.418294 0.908312i \(-0.362628\pi\)
0.418294 + 0.908312i \(0.362628\pi\)
\(824\) 8.00000 0.278693
\(825\) 0 0
\(826\) 48.0000 1.67013
\(827\) 6.00000 0.208640 0.104320 0.994544i \(-0.466733\pi\)
0.104320 + 0.994544i \(0.466733\pi\)
\(828\) −3.00000 −0.104257
\(829\) −30.0000 −1.04194 −0.520972 0.853574i \(-0.674430\pi\)
−0.520972 + 0.853574i \(0.674430\pi\)
\(830\) −56.0000 −1.94379
\(831\) 0 0
\(832\) −2.00000 −0.0693375
\(833\) −18.0000 −0.623663
\(834\) 0 0
\(835\) 64.0000 2.21481
\(836\) −4.00000 −0.138343
\(837\) 0 0
\(838\) 18.0000 0.621800
\(839\) 24.0000 0.828572 0.414286 0.910147i \(-0.364031\pi\)
0.414286 + 0.910147i \(0.364031\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) −28.0000 −0.964944
\(843\) 0 0
\(844\) −20.0000 −0.688428
\(845\) −36.0000 −1.23844
\(846\) 0 0
\(847\) 28.0000 0.962091
\(848\) −4.00000 −0.137361
\(849\) 0 0
\(850\) 22.0000 0.754594
\(851\) −4.00000 −0.137118
\(852\) 0 0
\(853\) 46.0000 1.57501 0.787505 0.616308i \(-0.211372\pi\)
0.787505 + 0.616308i \(0.211372\pi\)
\(854\) −32.0000 −1.09502
\(855\) 24.0000 0.820783
\(856\) 10.0000 0.341793
\(857\) 42.0000 1.43469 0.717346 0.696717i \(-0.245357\pi\)
0.717346 + 0.696717i \(0.245357\pi\)
\(858\) 0 0
\(859\) 40.0000 1.36478 0.682391 0.730987i \(-0.260940\pi\)
0.682391 + 0.730987i \(0.260940\pi\)
\(860\) 40.0000 1.36399
\(861\) 0 0
\(862\) 12.0000 0.408722
\(863\) −8.00000 −0.272323 −0.136162 0.990687i \(-0.543477\pi\)
−0.136162 + 0.990687i \(0.543477\pi\)
\(864\) 0 0
\(865\) −24.0000 −0.816024
\(866\) 26.0000 0.883516
\(867\) 0 0
\(868\) 0 0
\(869\) −24.0000 −0.814144
\(870\) 0 0
\(871\) 20.0000 0.677674
\(872\) 0 0
\(873\) −18.0000 −0.609208
\(874\) 2.00000 0.0676510
\(875\) −96.0000 −3.24539
\(876\) 0 0
\(877\) 18.0000 0.607817 0.303908 0.952701i \(-0.401708\pi\)
0.303908 + 0.952701i \(0.401708\pi\)
\(878\) −8.00000 −0.269987
\(879\) 0 0
\(880\) 8.00000 0.269680
\(881\) 18.0000 0.606435 0.303218 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(882\) 27.0000 0.909137
\(883\) −36.0000 −1.21150 −0.605748 0.795656i \(-0.707126\pi\)
−0.605748 + 0.795656i \(0.707126\pi\)
\(884\) 4.00000 0.134535
\(885\) 0 0
\(886\) −8.00000 −0.268765
\(887\) 24.0000 0.805841 0.402921 0.915235i \(-0.367995\pi\)
0.402921 + 0.915235i \(0.367995\pi\)
\(888\) 0 0
\(889\) −64.0000 −2.14649
\(890\) 24.0000 0.804482
\(891\) 18.0000 0.603023
\(892\) −16.0000 −0.535720
\(893\) 0 0
\(894\) 0 0
\(895\) −64.0000 −2.13928
\(896\) 4.00000 0.133631
\(897\) 0 0
\(898\) −14.0000 −0.467186
\(899\) 0 0
\(900\) −33.0000 −1.10000
\(901\) 8.00000 0.266519
\(902\) −12.0000 −0.399556
\(903\) 0 0
\(904\) 14.0000 0.465633
\(905\) −96.0000 −3.19115
\(906\) 0 0
\(907\) 10.0000 0.332045 0.166022 0.986122i \(-0.446908\pi\)
0.166022 + 0.986122i \(0.446908\pi\)
\(908\) −6.00000 −0.199117
\(909\) 30.0000 0.995037
\(910\) −32.0000 −1.06079
\(911\) 20.0000 0.662630 0.331315 0.943520i \(-0.392508\pi\)
0.331315 + 0.943520i \(0.392508\pi\)
\(912\) 0 0
\(913\) 28.0000 0.926665
\(914\) 10.0000 0.330771
\(915\) 0 0
\(916\) 8.00000 0.264327
\(917\) −48.0000 −1.58510
\(918\) 0 0
\(919\) −4.00000 −0.131948 −0.0659739 0.997821i \(-0.521015\pi\)
−0.0659739 + 0.997821i \(0.521015\pi\)
\(920\) −4.00000 −0.131876
\(921\) 0 0
\(922\) −18.0000 −0.592798
\(923\) 0 0
\(924\) 0 0
\(925\) −44.0000 −1.44671
\(926\) −40.0000 −1.31448
\(927\) 24.0000 0.788263
\(928\) −2.00000 −0.0656532
\(929\) −18.0000 −0.590561 −0.295280 0.955411i \(-0.595413\pi\)
−0.295280 + 0.955411i \(0.595413\pi\)
\(930\) 0 0
\(931\) −18.0000 −0.589926
\(932\) −6.00000 −0.196537
\(933\) 0 0
\(934\) 2.00000 0.0654420
\(935\) −16.0000 −0.523256
\(936\) −6.00000 −0.196116
\(937\) 58.0000 1.89478 0.947389 0.320085i \(-0.103712\pi\)
0.947389 + 0.320085i \(0.103712\pi\)
\(938\) −40.0000 −1.30605
\(939\) 0 0
\(940\) 0 0
\(941\) 36.0000 1.17357 0.586783 0.809744i \(-0.300394\pi\)
0.586783 + 0.809744i \(0.300394\pi\)
\(942\) 0 0
\(943\) 6.00000 0.195387
\(944\) 12.0000 0.390567
\(945\) 0 0
\(946\) −20.0000 −0.650256
\(947\) 48.0000 1.55979 0.779895 0.625910i \(-0.215272\pi\)
0.779895 + 0.625910i \(0.215272\pi\)
\(948\) 0 0
\(949\) −12.0000 −0.389536
\(950\) 22.0000 0.713774
\(951\) 0 0
\(952\) −8.00000 −0.259281
\(953\) 46.0000 1.49009 0.745043 0.667016i \(-0.232429\pi\)
0.745043 + 0.667016i \(0.232429\pi\)
\(954\) −12.0000 −0.388514
\(955\) 80.0000 2.58874
\(956\) −24.0000 −0.776215
\(957\) 0 0
\(958\) 8.00000 0.258468
\(959\) −24.0000 −0.775000
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) −8.00000 −0.257930
\(963\) 30.0000 0.966736
\(964\) 22.0000 0.708572
\(965\) 104.000 3.34788
\(966\) 0 0
\(967\) −16.0000 −0.514525 −0.257263 0.966342i \(-0.582821\pi\)
−0.257263 + 0.966342i \(0.582821\pi\)
\(968\) 7.00000 0.224989
\(969\) 0 0
\(970\) −24.0000 −0.770594
\(971\) −38.0000 −1.21948 −0.609739 0.792602i \(-0.708726\pi\)
−0.609739 + 0.792602i \(0.708726\pi\)
\(972\) 0 0
\(973\) 16.0000 0.512936
\(974\) 8.00000 0.256337
\(975\) 0 0
\(976\) −8.00000 −0.256074
\(977\) 6.00000 0.191957 0.0959785 0.995383i \(-0.469402\pi\)
0.0959785 + 0.995383i \(0.469402\pi\)
\(978\) 0 0
\(979\) −12.0000 −0.383522
\(980\) 36.0000 1.14998
\(981\) 0 0
\(982\) −24.0000 −0.765871
\(983\) −36.0000 −1.14822 −0.574111 0.818778i \(-0.694652\pi\)
−0.574111 + 0.818778i \(0.694652\pi\)
\(984\) 0 0
\(985\) 72.0000 2.29411
\(986\) 4.00000 0.127386
\(987\) 0 0
\(988\) 4.00000 0.127257
\(989\) 10.0000 0.317982
\(990\) 24.0000 0.762770
\(991\) −56.0000 −1.77890 −0.889449 0.457034i \(-0.848912\pi\)
−0.889449 + 0.457034i \(0.848912\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −16.0000 −0.507234
\(996\) 0 0
\(997\) 10.0000 0.316703 0.158352 0.987383i \(-0.449382\pi\)
0.158352 + 0.987383i \(0.449382\pi\)
\(998\) −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 \(a_p\))