Properties

Label 4018.2.a.f.1.1
Level 4018
Weight 2
Character 4018.1
Self dual Yes
Analytic conductor 32.084
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0838915322\)
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 \(\chi\) = 4018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+3.00000 q^{5}\) \(+1.00000 q^{6}\) \(-1.00000 q^{8}\) \(-2.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+3.00000 q^{5}\) \(+1.00000 q^{6}\) \(-1.00000 q^{8}\) \(-2.00000 q^{9}\) \(-3.00000 q^{10}\) \(-1.00000 q^{12}\) \(-2.00000 q^{13}\) \(-3.00000 q^{15}\) \(+1.00000 q^{16}\) \(+3.00000 q^{17}\) \(+2.00000 q^{18}\) \(+4.00000 q^{19}\) \(+3.00000 q^{20}\) \(-6.00000 q^{23}\) \(+1.00000 q^{24}\) \(+4.00000 q^{25}\) \(+2.00000 q^{26}\) \(+5.00000 q^{27}\) \(-3.00000 q^{29}\) \(+3.00000 q^{30}\) \(+1.00000 q^{31}\) \(-1.00000 q^{32}\) \(-3.00000 q^{34}\) \(-2.00000 q^{36}\) \(-4.00000 q^{37}\) \(-4.00000 q^{38}\) \(+2.00000 q^{39}\) \(-3.00000 q^{40}\) \(-1.00000 q^{41}\) \(-1.00000 q^{43}\) \(-6.00000 q^{45}\) \(+6.00000 q^{46}\) \(+6.00000 q^{47}\) \(-1.00000 q^{48}\) \(-4.00000 q^{50}\) \(-3.00000 q^{51}\) \(-2.00000 q^{52}\) \(+9.00000 q^{53}\) \(-5.00000 q^{54}\) \(-4.00000 q^{57}\) \(+3.00000 q^{58}\) \(+6.00000 q^{59}\) \(-3.00000 q^{60}\) \(+1.00000 q^{61}\) \(-1.00000 q^{62}\) \(+1.00000 q^{64}\) \(-6.00000 q^{65}\) \(+8.00000 q^{67}\) \(+3.00000 q^{68}\) \(+6.00000 q^{69}\) \(+3.00000 q^{71}\) \(+2.00000 q^{72}\) \(+10.0000 q^{73}\) \(+4.00000 q^{74}\) \(-4.00000 q^{75}\) \(+4.00000 q^{76}\) \(-2.00000 q^{78}\) \(-1.00000 q^{79}\) \(+3.00000 q^{80}\) \(+1.00000 q^{81}\) \(+1.00000 q^{82}\) \(+12.0000 q^{83}\) \(+9.00000 q^{85}\) \(+1.00000 q^{86}\) \(+3.00000 q^{87}\) \(-3.00000 q^{89}\) \(+6.00000 q^{90}\) \(-6.00000 q^{92}\) \(-1.00000 q^{93}\) \(-6.00000 q^{94}\) \(+12.0000 q^{95}\) \(+1.00000 q^{96}\) \(+1.00000 q^{97}\) \(+O(q^{100})\)

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
\(5\) 3.00000 1.34164 0.670820 0.741620i \(-0.265942\pi\)
0.670820 + 0.741620i \(0.265942\pi\)
\(6\) 1.00000 0.408248
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) −2.00000 −0.666667
\(10\) −3.00000 −0.948683
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) −1.00000 −0.288675
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) −3.00000 −0.774597
\(16\) 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
\(19\) 4.00000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 3.00000 0.670820
\(21\) 0 0
\(22\) 0 0
\(23\) −6.00000 −1.25109 −0.625543 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) 1.00000 0.204124
\(25\) 4.00000 0.800000
\(26\) 2.00000 0.392232
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) −3.00000 −0.557086 −0.278543 0.960424i \(-0.589851\pi\)
−0.278543 + 0.960424i \(0.589851\pi\)
\(30\) 3.00000 0.547723
\(31\) 1.00000 0.179605 0.0898027 0.995960i \(-0.471376\pi\)
0.0898027 + 0.995960i \(0.471376\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −3.00000 −0.514496
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) −4.00000 −0.648886
\(39\) 2.00000 0.320256
\(40\) −3.00000 −0.474342
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) 0 0
\(45\) −6.00000 −0.894427
\(46\) 6.00000 0.884652
\(47\) 6.00000 0.875190 0.437595 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) −4.00000 −0.565685
\(51\) −3.00000 −0.420084
\(52\) −2.00000 −0.277350
\(53\) 9.00000 1.23625 0.618123 0.786082i \(-0.287894\pi\)
0.618123 + 0.786082i \(0.287894\pi\)
\(54\) −5.00000 −0.680414
\(55\) 0 0
\(56\) 0 0
\(57\) −4.00000 −0.529813
\(58\) 3.00000 0.393919
\(59\) 6.00000 0.781133 0.390567 0.920575i \(-0.372279\pi\)
0.390567 + 0.920575i \(0.372279\pi\)
\(60\) −3.00000 −0.387298
\(61\) 1.00000 0.128037 0.0640184 0.997949i \(-0.479608\pi\)
0.0640184 + 0.997949i \(0.479608\pi\)
\(62\) −1.00000 −0.127000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −6.00000 −0.744208
\(66\) 0 0
\(67\) 8.00000 0.977356 0.488678 0.872464i \(-0.337479\pi\)
0.488678 + 0.872464i \(0.337479\pi\)
\(68\) 3.00000 0.363803
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) 3.00000 0.356034 0.178017 0.984027i \(-0.443032\pi\)
0.178017 + 0.984027i \(0.443032\pi\)
\(72\) 2.00000 0.235702
\(73\) 10.0000 1.17041 0.585206 0.810885i \(-0.301014\pi\)
0.585206 + 0.810885i \(0.301014\pi\)
\(74\) 4.00000 0.464991
\(75\) −4.00000 −0.461880
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) −2.00000 −0.226455
\(79\) −1.00000 −0.112509 −0.0562544 0.998416i \(-0.517916\pi\)
−0.0562544 + 0.998416i \(0.517916\pi\)
\(80\) 3.00000 0.335410
\(81\) 1.00000 0.111111
\(82\) 1.00000 0.110432
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) 9.00000 0.976187
\(86\) 1.00000 0.107833
\(87\) 3.00000 0.321634
\(88\) 0 0
\(89\) −3.00000 −0.317999 −0.159000 0.987279i \(-0.550827\pi\)
−0.159000 + 0.987279i \(0.550827\pi\)
\(90\) 6.00000 0.632456
\(91\) 0 0
\(92\) −6.00000 −0.625543
\(93\) −1.00000 −0.103695
\(94\) −6.00000 −0.618853
\(95\) 12.0000 1.23117
\(96\) 1.00000 0.102062
\(97\) 1.00000 0.101535 0.0507673 0.998711i \(-0.483833\pi\)
0.0507673 + 0.998711i \(0.483833\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 4.00000 0.400000
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 3.00000 0.297044
\(103\) −11.0000 −1.08386 −0.541931 0.840423i \(-0.682307\pi\)
−0.541931 + 0.840423i \(0.682307\pi\)
\(104\) 2.00000 0.196116
\(105\) 0 0
\(106\) −9.00000 −0.874157
\(107\) 3.00000 0.290021 0.145010 0.989430i \(-0.453678\pi\)
0.145010 + 0.989430i \(0.453678\pi\)
\(108\) 5.00000 0.481125
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 0 0
\(111\) 4.00000 0.379663
\(112\) 0 0
\(113\) 9.00000 0.846649 0.423324 0.905978i \(-0.360863\pi\)
0.423324 + 0.905978i \(0.360863\pi\)
\(114\) 4.00000 0.374634
\(115\) −18.0000 −1.67851
\(116\) −3.00000 −0.278543
\(117\) 4.00000 0.369800
\(118\) −6.00000 −0.552345
\(119\) 0 0
\(120\) 3.00000 0.273861
\(121\) −11.0000 −1.00000
\(122\) −1.00000 −0.0905357
\(123\) 1.00000 0.0901670
\(124\) 1.00000 0.0898027
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) 14.0000 1.24230 0.621150 0.783692i \(-0.286666\pi\)
0.621150 + 0.783692i \(0.286666\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.00000 0.0880451
\(130\) 6.00000 0.526235
\(131\) −18.0000 −1.57267 −0.786334 0.617802i \(-0.788023\pi\)
−0.786334 + 0.617802i \(0.788023\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) 15.0000 1.29099
\(136\) −3.00000 −0.257248
\(137\) −6.00000 −0.512615 −0.256307 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) −6.00000 −0.510754
\(139\) 10.0000 0.848189 0.424094 0.905618i \(-0.360592\pi\)
0.424094 + 0.905618i \(0.360592\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) −3.00000 −0.251754
\(143\) 0 0
\(144\) −2.00000 −0.166667
\(145\) −9.00000 −0.747409
\(146\) −10.0000 −0.827606
\(147\) 0 0
\(148\) −4.00000 −0.328798
\(149\) −3.00000 −0.245770 −0.122885 0.992421i \(-0.539215\pi\)
−0.122885 + 0.992421i \(0.539215\pi\)
\(150\) 4.00000 0.326599
\(151\) 17.0000 1.38344 0.691720 0.722166i \(-0.256853\pi\)
0.691720 + 0.722166i \(0.256853\pi\)
\(152\) −4.00000 −0.324443
\(153\) −6.00000 −0.485071
\(154\) 0 0
\(155\) 3.00000 0.240966
\(156\) 2.00000 0.160128
\(157\) 4.00000 0.319235 0.159617 0.987179i \(-0.448974\pi\)
0.159617 + 0.987179i \(0.448974\pi\)
\(158\) 1.00000 0.0795557
\(159\) −9.00000 −0.713746
\(160\) −3.00000 −0.237171
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) 20.0000 1.56652 0.783260 0.621694i \(-0.213555\pi\)
0.783260 + 0.621694i \(0.213555\pi\)
\(164\) −1.00000 −0.0780869
\(165\) 0 0
\(166\) −12.0000 −0.931381
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) −9.00000 −0.690268
\(171\) −8.00000 −0.611775
\(172\) −1.00000 −0.0762493
\(173\) −21.0000 −1.59660 −0.798300 0.602260i \(-0.794267\pi\)
−0.798300 + 0.602260i \(0.794267\pi\)
\(174\) −3.00000 −0.227429
\(175\) 0 0
\(176\) 0 0
\(177\) −6.00000 −0.450988
\(178\) 3.00000 0.224860
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) −6.00000 −0.447214
\(181\) −8.00000 −0.594635 −0.297318 0.954779i \(-0.596092\pi\)
−0.297318 + 0.954779i \(0.596092\pi\)
\(182\) 0 0
\(183\) −1.00000 −0.0739221
\(184\) 6.00000 0.442326
\(185\) −12.0000 −0.882258
\(186\) 1.00000 0.0733236
\(187\) 0 0
\(188\) 6.00000 0.437595
\(189\) 0 0
\(190\) −12.0000 −0.870572
\(191\) 3.00000 0.217072 0.108536 0.994092i \(-0.465384\pi\)
0.108536 + 0.994092i \(0.465384\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −16.0000 −1.15171 −0.575853 0.817554i \(-0.695330\pi\)
−0.575853 + 0.817554i \(0.695330\pi\)
\(194\) −1.00000 −0.0717958
\(195\) 6.00000 0.429669
\(196\) 0 0
\(197\) 24.0000 1.70993 0.854965 0.518686i \(-0.173579\pi\)
0.854965 + 0.518686i \(0.173579\pi\)
\(198\) 0 0
\(199\) 16.0000 1.13421 0.567105 0.823646i \(-0.308063\pi\)
0.567105 + 0.823646i \(0.308063\pi\)
\(200\) −4.00000 −0.282843
\(201\) −8.00000 −0.564276
\(202\) −6.00000 −0.422159
\(203\) 0 0
\(204\) −3.00000 −0.210042
\(205\) −3.00000 −0.209529
\(206\) 11.0000 0.766406
\(207\) 12.0000 0.834058
\(208\) −2.00000 −0.138675
\(209\) 0 0
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 9.00000 0.618123
\(213\) −3.00000 −0.205557
\(214\) −3.00000 −0.205076
\(215\) −3.00000 −0.204598
\(216\) −5.00000 −0.340207
\(217\) 0 0
\(218\) −2.00000 −0.135457
\(219\) −10.0000 −0.675737
\(220\) 0 0
\(221\) −6.00000 −0.403604
\(222\) −4.00000 −0.268462
\(223\) 1.00000 0.0669650 0.0334825 0.999439i \(-0.489340\pi\)
0.0334825 + 0.999439i \(0.489340\pi\)
\(224\) 0 0
\(225\) −8.00000 −0.533333
\(226\) −9.00000 −0.598671
\(227\) 15.0000 0.995585 0.497792 0.867296i \(-0.334144\pi\)
0.497792 + 0.867296i \(0.334144\pi\)
\(228\) −4.00000 −0.264906
\(229\) 16.0000 1.05731 0.528655 0.848837i \(-0.322697\pi\)
0.528655 + 0.848837i \(0.322697\pi\)
\(230\) 18.0000 1.18688
\(231\) 0 0
\(232\) 3.00000 0.196960
\(233\) −24.0000 −1.57229 −0.786146 0.618041i \(-0.787927\pi\)
−0.786146 + 0.618041i \(0.787927\pi\)
\(234\) −4.00000 −0.261488
\(235\) 18.0000 1.17419
\(236\) 6.00000 0.390567
\(237\) 1.00000 0.0649570
\(238\) 0 0
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) −3.00000 −0.193649
\(241\) 28.0000 1.80364 0.901819 0.432113i \(-0.142232\pi\)
0.901819 + 0.432113i \(0.142232\pi\)
\(242\) 11.0000 0.707107
\(243\) −16.0000 −1.02640
\(244\) 1.00000 0.0640184
\(245\) 0 0
\(246\) −1.00000 −0.0637577
\(247\) −8.00000 −0.509028
\(248\) −1.00000 −0.0635001
\(249\) −12.0000 −0.760469
\(250\) 3.00000 0.189737
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −14.0000 −0.878438
\(255\) −9.00000 −0.563602
\(256\) 1.00000 0.0625000
\(257\) 27.0000 1.68421 0.842107 0.539311i \(-0.181315\pi\)
0.842107 + 0.539311i \(0.181315\pi\)
\(258\) −1.00000 −0.0622573
\(259\) 0 0
\(260\) −6.00000 −0.372104
\(261\) 6.00000 0.371391
\(262\) 18.0000 1.11204
\(263\) 24.0000 1.47990 0.739952 0.672660i \(-0.234848\pi\)
0.739952 + 0.672660i \(0.234848\pi\)
\(264\) 0 0
\(265\) 27.0000 1.65860
\(266\) 0 0
\(267\) 3.00000 0.183597
\(268\) 8.00000 0.488678
\(269\) 6.00000 0.365826 0.182913 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) −15.0000 −0.912871
\(271\) 16.0000 0.971931 0.485965 0.873978i \(-0.338468\pi\)
0.485965 + 0.873978i \(0.338468\pi\)
\(272\) 3.00000 0.181902
\(273\) 0 0
\(274\) 6.00000 0.362473
\(275\) 0 0
\(276\) 6.00000 0.361158
\(277\) 8.00000 0.480673 0.240337 0.970690i \(-0.422742\pi\)
0.240337 + 0.970690i \(0.422742\pi\)
\(278\) −10.0000 −0.599760
\(279\) −2.00000 −0.119737
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 6.00000 0.357295
\(283\) −8.00000 −0.475551 −0.237775 0.971320i \(-0.576418\pi\)
−0.237775 + 0.971320i \(0.576418\pi\)
\(284\) 3.00000 0.178017
\(285\) −12.0000 −0.710819
\(286\) 0 0
\(287\) 0 0
\(288\) 2.00000 0.117851
\(289\) −8.00000 −0.470588
\(290\) 9.00000 0.528498
\(291\) −1.00000 −0.0586210
\(292\) 10.0000 0.585206
\(293\) 24.0000 1.40209 0.701047 0.713115i \(-0.252716\pi\)
0.701047 + 0.713115i \(0.252716\pi\)
\(294\) 0 0
\(295\) 18.0000 1.04800
\(296\) 4.00000 0.232495
\(297\) 0 0
\(298\) 3.00000 0.173785
\(299\) 12.0000 0.693978
\(300\) −4.00000 −0.230940
\(301\) 0 0
\(302\) −17.0000 −0.978240
\(303\) −6.00000 −0.344691
\(304\) 4.00000 0.229416
\(305\) 3.00000 0.171780
\(306\) 6.00000 0.342997
\(307\) −8.00000 −0.456584 −0.228292 0.973593i \(-0.573314\pi\)
−0.228292 + 0.973593i \(0.573314\pi\)
\(308\) 0 0
\(309\) 11.0000 0.625768
\(310\) −3.00000 −0.170389
\(311\) −6.00000 −0.340229 −0.170114 0.985424i \(-0.554414\pi\)
−0.170114 + 0.985424i \(0.554414\pi\)
\(312\) −2.00000 −0.113228
\(313\) −14.0000 −0.791327 −0.395663 0.918396i \(-0.629485\pi\)
−0.395663 + 0.918396i \(0.629485\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) −1.00000 −0.0562544
\(317\) 30.0000 1.68497 0.842484 0.538721i \(-0.181092\pi\)
0.842484 + 0.538721i \(0.181092\pi\)
\(318\) 9.00000 0.504695
\(319\) 0 0
\(320\) 3.00000 0.167705
\(321\) −3.00000 −0.167444
\(322\) 0 0
\(323\) 12.0000 0.667698
\(324\) 1.00000 0.0555556
\(325\) −8.00000 −0.443760
\(326\) −20.0000 −1.10770
\(327\) −2.00000 −0.110600
\(328\) 1.00000 0.0552158
\(329\) 0 0
\(330\) 0 0
\(331\) 2.00000 0.109930 0.0549650 0.998488i \(-0.482495\pi\)
0.0549650 + 0.998488i \(0.482495\pi\)
\(332\) 12.0000 0.658586
\(333\) 8.00000 0.438397
\(334\) 0 0
\(335\) 24.0000 1.31126
\(336\) 0 0
\(337\) −19.0000 −1.03500 −0.517498 0.855684i \(-0.673136\pi\)
−0.517498 + 0.855684i \(0.673136\pi\)
\(338\) 9.00000 0.489535
\(339\) −9.00000 −0.488813
\(340\) 9.00000 0.488094
\(341\) 0 0
\(342\) 8.00000 0.432590
\(343\) 0 0
\(344\) 1.00000 0.0539164
\(345\) 18.0000 0.969087
\(346\) 21.0000 1.12897
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 3.00000 0.160817
\(349\) −26.0000 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 0 0
\(351\) −10.0000 −0.533761
\(352\) 0 0
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 6.00000 0.318896
\(355\) 9.00000 0.477670
\(356\) −3.00000 −0.159000
\(357\) 0 0
\(358\) 0 0
\(359\) 36.0000 1.90001 0.950004 0.312239i \(-0.101079\pi\)
0.950004 + 0.312239i \(0.101079\pi\)
\(360\) 6.00000 0.316228
\(361\) −3.00000 −0.157895
\(362\) 8.00000 0.420471
\(363\) 11.0000 0.577350
\(364\) 0 0
\(365\) 30.0000 1.57027
\(366\) 1.00000 0.0522708
\(367\) 7.00000 0.365397 0.182699 0.983169i \(-0.441517\pi\)
0.182699 + 0.983169i \(0.441517\pi\)
\(368\) −6.00000 −0.312772
\(369\) 2.00000 0.104116
\(370\) 12.0000 0.623850
\(371\) 0 0
\(372\) −1.00000 −0.0518476
\(373\) 32.0000 1.65690 0.828449 0.560065i \(-0.189224\pi\)
0.828449 + 0.560065i \(0.189224\pi\)
\(374\) 0 0
\(375\) 3.00000 0.154919
\(376\) −6.00000 −0.309426
\(377\) 6.00000 0.309016
\(378\) 0 0
\(379\) −7.00000 −0.359566 −0.179783 0.983706i \(-0.557540\pi\)
−0.179783 + 0.983706i \(0.557540\pi\)
\(380\) 12.0000 0.615587
\(381\) −14.0000 −0.717242
\(382\) −3.00000 −0.153493
\(383\) 24.0000 1.22634 0.613171 0.789950i \(-0.289894\pi\)
0.613171 + 0.789950i \(0.289894\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 16.0000 0.814379
\(387\) 2.00000 0.101666
\(388\) 1.00000 0.0507673
\(389\) −36.0000 −1.82527 −0.912636 0.408773i \(-0.865957\pi\)
−0.912636 + 0.408773i \(0.865957\pi\)
\(390\) −6.00000 −0.303822
\(391\) −18.0000 −0.910299
\(392\) 0 0
\(393\) 18.0000 0.907980
\(394\) −24.0000 −1.20910
\(395\) −3.00000 −0.150946
\(396\) 0 0
\(397\) 22.0000 1.10415 0.552074 0.833795i \(-0.313837\pi\)
0.552074 + 0.833795i \(0.313837\pi\)
\(398\) −16.0000 −0.802008
\(399\) 0 0
\(400\) 4.00000 0.200000
\(401\) 3.00000 0.149813 0.0749064 0.997191i \(-0.476134\pi\)
0.0749064 + 0.997191i \(0.476134\pi\)
\(402\) 8.00000 0.399004
\(403\) −2.00000 −0.0996271
\(404\) 6.00000 0.298511
\(405\) 3.00000 0.149071
\(406\) 0 0
\(407\) 0 0
\(408\) 3.00000 0.148522
\(409\) 28.0000 1.38451 0.692255 0.721653i \(-0.256617\pi\)
0.692255 + 0.721653i \(0.256617\pi\)
\(410\) 3.00000 0.148159
\(411\) 6.00000 0.295958
\(412\) −11.0000 −0.541931
\(413\) 0 0
\(414\) −12.0000 −0.589768
\(415\) 36.0000 1.76717
\(416\) 2.00000 0.0980581
\(417\) −10.0000 −0.489702
\(418\) 0 0
\(419\) 30.0000 1.46560 0.732798 0.680446i \(-0.238214\pi\)
0.732798 + 0.680446i \(0.238214\pi\)
\(420\) 0 0
\(421\) 11.0000 0.536107 0.268054 0.963404i \(-0.413620\pi\)
0.268054 + 0.963404i \(0.413620\pi\)
\(422\) 4.00000 0.194717
\(423\) −12.0000 −0.583460
\(424\) −9.00000 −0.437079
\(425\) 12.0000 0.582086
\(426\) 3.00000 0.145350
\(427\) 0 0
\(428\) 3.00000 0.145010
\(429\) 0 0
\(430\) 3.00000 0.144673
\(431\) 12.0000 0.578020 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) 5.00000 0.240563
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) 9.00000 0.431517
\(436\) 2.00000 0.0957826
\(437\) −24.0000 −1.14808
\(438\) 10.0000 0.477818
\(439\) 28.0000 1.33637 0.668184 0.743996i \(-0.267072\pi\)
0.668184 + 0.743996i \(0.267072\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 6.00000 0.285391
\(443\) 15.0000 0.712672 0.356336 0.934358i \(-0.384026\pi\)
0.356336 + 0.934358i \(0.384026\pi\)
\(444\) 4.00000 0.189832
\(445\) −9.00000 −0.426641
\(446\) −1.00000 −0.0473514
\(447\) 3.00000 0.141895
\(448\) 0 0
\(449\) 15.0000 0.707894 0.353947 0.935266i \(-0.384839\pi\)
0.353947 + 0.935266i \(0.384839\pi\)
\(450\) 8.00000 0.377124
\(451\) 0 0
\(452\) 9.00000 0.423324
\(453\) −17.0000 −0.798730
\(454\) −15.0000 −0.703985
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) −34.0000 −1.59045 −0.795226 0.606313i \(-0.792648\pi\)
−0.795226 + 0.606313i \(0.792648\pi\)
\(458\) −16.0000 −0.747631
\(459\) 15.0000 0.700140
\(460\) −18.0000 −0.839254
\(461\) 15.0000 0.698620 0.349310 0.937007i \(-0.386416\pi\)
0.349310 + 0.937007i \(0.386416\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) −3.00000 −0.139272
\(465\) −3.00000 −0.139122
\(466\) 24.0000 1.11178
\(467\) 24.0000 1.11059 0.555294 0.831654i \(-0.312606\pi\)
0.555294 + 0.831654i \(0.312606\pi\)
\(468\) 4.00000 0.184900
\(469\) 0 0
\(470\) −18.0000 −0.830278
\(471\) −4.00000 −0.184310
\(472\) −6.00000 −0.276172
\(473\) 0 0
\(474\) −1.00000 −0.0459315
\(475\) 16.0000 0.734130
\(476\) 0 0
\(477\) −18.0000 −0.824163
\(478\) 24.0000 1.09773
\(479\) −6.00000 −0.274147 −0.137073 0.990561i \(-0.543770\pi\)
−0.137073 + 0.990561i \(0.543770\pi\)
\(480\) 3.00000 0.136931
\(481\) 8.00000 0.364769
\(482\) −28.0000 −1.27537
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) 3.00000 0.136223
\(486\) 16.0000 0.725775
\(487\) 2.00000 0.0906287 0.0453143 0.998973i \(-0.485571\pi\)
0.0453143 + 0.998973i \(0.485571\pi\)
\(488\) −1.00000 −0.0452679
\(489\) −20.0000 −0.904431
\(490\) 0 0
\(491\) −3.00000 −0.135388 −0.0676941 0.997706i \(-0.521564\pi\)
−0.0676941 + 0.997706i \(0.521564\pi\)
\(492\) 1.00000 0.0450835
\(493\) −9.00000 −0.405340
\(494\) 8.00000 0.359937
\(495\) 0 0
\(496\) 1.00000 0.0449013
\(497\) 0 0
\(498\) 12.0000 0.537733
\(499\) −34.0000 −1.52205 −0.761025 0.648723i \(-0.775303\pi\)
−0.761025 + 0.648723i \(0.775303\pi\)
\(500\) −3.00000 −0.134164
\(501\) 0 0
\(502\) −12.0000 −0.535586
\(503\) −30.0000 −1.33763 −0.668817 0.743427i \(-0.733199\pi\)
−0.668817 + 0.743427i \(0.733199\pi\)
\(504\) 0 0
\(505\) 18.0000 0.800989
\(506\) 0 0
\(507\) 9.00000 0.399704
\(508\) 14.0000 0.621150
\(509\) 6.00000 0.265945 0.132973 0.991120i \(-0.457548\pi\)
0.132973 + 0.991120i \(0.457548\pi\)
\(510\) 9.00000 0.398527
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 20.0000 0.883022
\(514\) −27.0000 −1.19092
\(515\) −33.0000 −1.45415
\(516\) 1.00000 0.0440225
\(517\) 0 0
\(518\) 0 0
\(519\) 21.0000 0.921798
\(520\) 6.00000 0.263117
\(521\) −18.0000 −0.788594 −0.394297 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) −6.00000 −0.262613
\(523\) −38.0000 −1.66162 −0.830812 0.556553i \(-0.812124\pi\)
−0.830812 + 0.556553i \(0.812124\pi\)
\(524\) −18.0000 −0.786334
\(525\) 0 0
\(526\) −24.0000 −1.04645
\(527\) 3.00000 0.130682
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) −27.0000 −1.17281
\(531\) −12.0000 −0.520756
\(532\) 0 0
\(533\) 2.00000 0.0866296
\(534\) −3.00000 −0.129823
\(535\) 9.00000 0.389104
\(536\) −8.00000 −0.345547
\(537\) 0 0
\(538\) −6.00000 −0.258678
\(539\) 0 0
\(540\) 15.0000 0.645497
\(541\) −28.0000 −1.20381 −0.601907 0.798566i \(-0.705592\pi\)
−0.601907 + 0.798566i \(0.705592\pi\)
\(542\) −16.0000 −0.687259
\(543\) 8.00000 0.343313
\(544\) −3.00000 −0.128624
\(545\) 6.00000 0.257012
\(546\) 0 0
\(547\) 44.0000 1.88130 0.940652 0.339372i \(-0.110215\pi\)
0.940652 + 0.339372i \(0.110215\pi\)
\(548\) −6.00000 −0.256307
\(549\) −2.00000 −0.0853579
\(550\) 0 0
\(551\) −12.0000 −0.511217
\(552\) −6.00000 −0.255377
\(553\) 0 0
\(554\) −8.00000 −0.339887
\(555\) 12.0000 0.509372
\(556\) 10.0000 0.424094
\(557\) −9.00000 −0.381342 −0.190671 0.981654i \(-0.561066\pi\)
−0.190671 + 0.981654i \(0.561066\pi\)
\(558\) 2.00000 0.0846668
\(559\) 2.00000 0.0845910
\(560\) 0 0
\(561\) 0 0
\(562\) 18.0000 0.759284
\(563\) −12.0000 −0.505740 −0.252870 0.967500i \(-0.581374\pi\)
−0.252870 + 0.967500i \(0.581374\pi\)
\(564\) −6.00000 −0.252646
\(565\) 27.0000 1.13590
\(566\) 8.00000 0.336265
\(567\) 0 0
\(568\) −3.00000 −0.125877
\(569\) −21.0000 −0.880366 −0.440183 0.897908i \(-0.645086\pi\)
−0.440183 + 0.897908i \(0.645086\pi\)
\(570\) 12.0000 0.502625
\(571\) −10.0000 −0.418487 −0.209243 0.977864i \(-0.567100\pi\)
−0.209243 + 0.977864i \(0.567100\pi\)
\(572\) 0 0
\(573\) −3.00000 −0.125327
\(574\) 0 0
\(575\) −24.0000 −1.00087
\(576\) −2.00000 −0.0833333
\(577\) −2.00000 −0.0832611 −0.0416305 0.999133i \(-0.513255\pi\)
−0.0416305 + 0.999133i \(0.513255\pi\)
\(578\) 8.00000 0.332756
\(579\) 16.0000 0.664937
\(580\) −9.00000 −0.373705
\(581\) 0 0
\(582\) 1.00000 0.0414513
\(583\) 0 0
\(584\) −10.0000 −0.413803
\(585\) 12.0000 0.496139
\(586\) −24.0000 −0.991431
\(587\) 33.0000 1.36206 0.681028 0.732257i \(-0.261533\pi\)
0.681028 + 0.732257i \(0.261533\pi\)
\(588\) 0 0
\(589\) 4.00000 0.164817
\(590\) −18.0000 −0.741048
\(591\) −24.0000 −0.987228
\(592\) −4.00000 −0.164399
\(593\) 39.0000 1.60154 0.800769 0.598973i \(-0.204424\pi\)
0.800769 + 0.598973i \(0.204424\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −3.00000 −0.122885
\(597\) −16.0000 −0.654836
\(598\) −12.0000 −0.490716
\(599\) 30.0000 1.22577 0.612883 0.790173i \(-0.290010\pi\)
0.612883 + 0.790173i \(0.290010\pi\)
\(600\) 4.00000 0.163299
\(601\) −29.0000 −1.18293 −0.591467 0.806329i \(-0.701451\pi\)
−0.591467 + 0.806329i \(0.701451\pi\)
\(602\) 0 0
\(603\) −16.0000 −0.651570
\(604\) 17.0000 0.691720
\(605\) −33.0000 −1.34164
\(606\) 6.00000 0.243733
\(607\) 25.0000 1.01472 0.507359 0.861735i \(-0.330622\pi\)
0.507359 + 0.861735i \(0.330622\pi\)
\(608\) −4.00000 −0.162221
\(609\) 0 0
\(610\) −3.00000 −0.121466
\(611\) −12.0000 −0.485468
\(612\) −6.00000 −0.242536
\(613\) −16.0000 −0.646234 −0.323117 0.946359i \(-0.604731\pi\)
−0.323117 + 0.946359i \(0.604731\pi\)
\(614\) 8.00000 0.322854
\(615\) 3.00000 0.120972
\(616\) 0 0
\(617\) −18.0000 −0.724653 −0.362326 0.932051i \(-0.618017\pi\)
−0.362326 + 0.932051i \(0.618017\pi\)
\(618\) −11.0000 −0.442485
\(619\) 4.00000 0.160774 0.0803868 0.996764i \(-0.474384\pi\)
0.0803868 + 0.996764i \(0.474384\pi\)
\(620\) 3.00000 0.120483
\(621\) −30.0000 −1.20386
\(622\) 6.00000 0.240578
\(623\) 0 0
\(624\) 2.00000 0.0800641
\(625\) −29.0000 −1.16000
\(626\) 14.0000 0.559553
\(627\) 0 0
\(628\) 4.00000 0.159617
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) −34.0000 −1.35352 −0.676759 0.736204i \(-0.736616\pi\)
−0.676759 + 0.736204i \(0.736616\pi\)
\(632\) 1.00000 0.0397779
\(633\) 4.00000 0.158986
\(634\) −30.0000 −1.19145
\(635\) 42.0000 1.66672
\(636\) −9.00000 −0.356873
\(637\) 0 0
\(638\) 0 0
\(639\) −6.00000 −0.237356
\(640\) −3.00000 −0.118585
\(641\) 18.0000 0.710957 0.355479 0.934684i \(-0.384318\pi\)
0.355479 + 0.934684i \(0.384318\pi\)
\(642\) 3.00000 0.118401
\(643\) −29.0000 −1.14365 −0.571824 0.820376i \(-0.693764\pi\)
−0.571824 + 0.820376i \(0.693764\pi\)
\(644\) 0 0
\(645\) 3.00000 0.118125
\(646\) −12.0000 −0.472134
\(647\) 45.0000 1.76913 0.884566 0.466415i \(-0.154454\pi\)
0.884566 + 0.466415i \(0.154454\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 0 0
\(650\) 8.00000 0.313786
\(651\) 0 0
\(652\) 20.0000 0.783260
\(653\) 21.0000 0.821794 0.410897 0.911682i \(-0.365216\pi\)
0.410897 + 0.911682i \(0.365216\pi\)
\(654\) 2.00000 0.0782062
\(655\) −54.0000 −2.10995
\(656\) −1.00000 −0.0390434
\(657\) −20.0000 −0.780274
\(658\) 0 0
\(659\) 42.0000 1.63609 0.818044 0.575156i \(-0.195059\pi\)
0.818044 + 0.575156i \(0.195059\pi\)
\(660\) 0 0
\(661\) 10.0000 0.388955 0.194477 0.980907i \(-0.437699\pi\)
0.194477 + 0.980907i \(0.437699\pi\)
\(662\) −2.00000 −0.0777322
\(663\) 6.00000 0.233021
\(664\) −12.0000 −0.465690
\(665\) 0 0
\(666\) −8.00000 −0.309994
\(667\) 18.0000 0.696963
\(668\) 0 0
\(669\) −1.00000 −0.0386622
\(670\) −24.0000 −0.927201
\(671\) 0 0
\(672\) 0 0
\(673\) 8.00000 0.308377 0.154189 0.988041i \(-0.450724\pi\)
0.154189 + 0.988041i \(0.450724\pi\)
\(674\) 19.0000 0.731853
\(675\) 20.0000 0.769800
\(676\) −9.00000 −0.346154
\(677\) 6.00000 0.230599 0.115299 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) 9.00000 0.345643
\(679\) 0 0
\(680\) −9.00000 −0.345134
\(681\) −15.0000 −0.574801
\(682\) 0 0
\(683\) 24.0000 0.918334 0.459167 0.888350i \(-0.348148\pi\)
0.459167 + 0.888350i \(0.348148\pi\)
\(684\) −8.00000 −0.305888
\(685\) −18.0000 −0.687745
\(686\) 0 0
\(687\) −16.0000 −0.610438
\(688\) −1.00000 −0.0381246
\(689\) −18.0000 −0.685745
\(690\) −18.0000 −0.685248
\(691\) −5.00000 −0.190209 −0.0951045 0.995467i \(-0.530319\pi\)
−0.0951045 + 0.995467i \(0.530319\pi\)
\(692\) −21.0000 −0.798300
\(693\) 0 0
\(694\) 0 0
\(695\) 30.0000 1.13796
\(696\) −3.00000 −0.113715
\(697\) −3.00000 −0.113633
\(698\) 26.0000 0.984115
\(699\) 24.0000 0.907763
\(700\) 0 0
\(701\) 42.0000 1.58632 0.793159 0.609015i \(-0.208435\pi\)
0.793159 + 0.609015i \(0.208435\pi\)
\(702\) 10.0000 0.377426
\(703\) −16.0000 −0.603451
\(704\) 0 0
\(705\) −18.0000 −0.677919
\(706\) 6.00000 0.225813
\(707\) 0 0
\(708\) −6.00000 −0.225494
\(709\) −19.0000 −0.713560 −0.356780 0.934188i \(-0.616125\pi\)
−0.356780 + 0.934188i \(0.616125\pi\)
\(710\) −9.00000 −0.337764
\(711\) 2.00000 0.0750059
\(712\) 3.00000 0.112430
\(713\) −6.00000 −0.224702
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 24.0000 0.896296
\(718\) −36.0000 −1.34351
\(719\) 6.00000 0.223762 0.111881 0.993722i \(-0.464312\pi\)
0.111881 + 0.993722i \(0.464312\pi\)
\(720\) −6.00000 −0.223607
\(721\) 0 0
\(722\) 3.00000 0.111648
\(723\) −28.0000 −1.04133
\(724\) −8.00000 −0.297318
\(725\) −12.0000 −0.445669
\(726\) −11.0000 −0.408248
\(727\) −44.0000 −1.63187 −0.815935 0.578144i \(-0.803777\pi\)
−0.815935 + 0.578144i \(0.803777\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) −30.0000 −1.11035
\(731\) −3.00000 −0.110959
\(732\) −1.00000 −0.0369611
\(733\) 25.0000 0.923396 0.461698 0.887037i \(-0.347240\pi\)
0.461698 + 0.887037i \(0.347240\pi\)
\(734\) −7.00000 −0.258375
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) 0 0
\(738\) −2.00000 −0.0736210
\(739\) −37.0000 −1.36107 −0.680534 0.732717i \(-0.738252\pi\)
−0.680534 + 0.732717i \(0.738252\pi\)
\(740\) −12.0000 −0.441129
\(741\) 8.00000 0.293887
\(742\) 0 0
\(743\) 42.0000 1.54083 0.770415 0.637542i \(-0.220049\pi\)
0.770415 + 0.637542i \(0.220049\pi\)
\(744\) 1.00000 0.0366618
\(745\) −9.00000 −0.329734
\(746\) −32.0000 −1.17160
\(747\) −24.0000 −0.878114
\(748\) 0 0
\(749\) 0 0
\(750\) −3.00000 −0.109545
\(751\) −40.0000 −1.45962 −0.729810 0.683650i \(-0.760392\pi\)
−0.729810 + 0.683650i \(0.760392\pi\)
\(752\) 6.00000 0.218797
\(753\) −12.0000 −0.437304
\(754\) −6.00000 −0.218507
\(755\) 51.0000 1.85608
\(756\) 0 0
\(757\) −43.0000 −1.56286 −0.781431 0.623992i \(-0.785510\pi\)
−0.781431 + 0.623992i \(0.785510\pi\)
\(758\) 7.00000 0.254251
\(759\) 0 0
\(760\) −12.0000 −0.435286
\(761\) −6.00000 −0.217500 −0.108750 0.994069i \(-0.534685\pi\)
−0.108750 + 0.994069i \(0.534685\pi\)
\(762\) 14.0000 0.507166
\(763\) 0 0
\(764\) 3.00000 0.108536
\(765\) −18.0000 −0.650791
\(766\) −24.0000 −0.867155
\(767\) −12.0000 −0.433295
\(768\) −1.00000 −0.0360844
\(769\) −2.00000 −0.0721218 −0.0360609 0.999350i \(-0.511481\pi\)
−0.0360609 + 0.999350i \(0.511481\pi\)
\(770\) 0 0
\(771\) −27.0000 −0.972381
\(772\) −16.0000 −0.575853
\(773\) −18.0000 −0.647415 −0.323708 0.946157i \(-0.604929\pi\)
−0.323708 + 0.946157i \(0.604929\pi\)
\(774\) −2.00000 −0.0718885
\(775\) 4.00000 0.143684
\(776\) −1.00000 −0.0358979
\(777\) 0 0
\(778\) 36.0000 1.29066
\(779\) −4.00000 −0.143315
\(780\) 6.00000 0.214834
\(781\) 0 0
\(782\) 18.0000 0.643679
\(783\) −15.0000 −0.536056
\(784\) 0 0
\(785\) 12.0000 0.428298
\(786\) −18.0000 −0.642039
\(787\) 4.00000 0.142585 0.0712923 0.997455i \(-0.477288\pi\)
0.0712923 + 0.997455i \(0.477288\pi\)
\(788\) 24.0000 0.854965
\(789\) −24.0000 −0.854423
\(790\) 3.00000 0.106735
\(791\) 0 0
\(792\) 0 0
\(793\) −2.00000 −0.0710221
\(794\) −22.0000 −0.780751
\(795\) −27.0000 −0.957591
\(796\) 16.0000 0.567105
\(797\) −51.0000 −1.80651 −0.903256 0.429101i \(-0.858830\pi\)
−0.903256 + 0.429101i \(0.858830\pi\)
\(798\) 0 0
\(799\) 18.0000 0.636794
\(800\) −4.00000 −0.141421
\(801\) 6.00000 0.212000
\(802\) −3.00000 −0.105934
\(803\) 0 0
\(804\) −8.00000 −0.282138
\(805\) 0 0
\(806\) 2.00000 0.0704470
\(807\) −6.00000 −0.211210
\(808\) −6.00000 −0.211079
\(809\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(810\) −3.00000 −0.105409
\(811\) −2.00000 −0.0702295 −0.0351147 0.999383i \(-0.511180\pi\)
−0.0351147 + 0.999383i \(0.511180\pi\)
\(812\) 0 0
\(813\) −16.0000 −0.561144
\(814\) 0 0
\(815\) 60.0000 2.10171
\(816\) −3.00000 −0.105021
\(817\) −4.00000 −0.139942
\(818\) −28.0000 −0.978997
\(819\) 0 0
\(820\) −3.00000 −0.104765
\(821\) −24.0000 −0.837606 −0.418803 0.908077i \(-0.637550\pi\)
−0.418803 + 0.908077i \(0.637550\pi\)
\(822\) −6.00000 −0.209274
\(823\) 23.0000 0.801730 0.400865 0.916137i \(-0.368710\pi\)
0.400865 + 0.916137i \(0.368710\pi\)
\(824\) 11.0000 0.383203
\(825\) 0 0
\(826\) 0 0
\(827\) 30.0000 1.04320 0.521601 0.853189i \(-0.325335\pi\)
0.521601 + 0.853189i \(0.325335\pi\)
\(828\) 12.0000 0.417029
\(829\) −41.0000 −1.42399 −0.711994 0.702185i \(-0.752208\pi\)
−0.711994 + 0.702185i \(0.752208\pi\)
\(830\) −36.0000 −1.24958
\(831\) −8.00000 −0.277517
\(832\) −2.00000 −0.0693375
\(833\) 0 0
\(834\) 10.0000 0.346272
\(835\) 0 0
\(836\) 0 0
\(837\) 5.00000 0.172825
\(838\) −30.0000 −1.03633
\(839\) 12.0000 0.414286 0.207143 0.978311i \(-0.433583\pi\)
0.207143 + 0.978311i \(0.433583\pi\)
\(840\) 0 0
\(841\) −20.0000 −0.689655
\(842\) −11.0000 −0.379085
\(843\) 18.0000 0.619953
\(844\) −4.00000 −0.137686
\(845\) −27.0000 −0.928828
\(846\) 12.0000 0.412568
\(847\) 0 0
\(848\) 9.00000 0.309061
\(849\) 8.00000 0.274559
\(850\) −12.0000 −0.411597
\(851\) 24.0000 0.822709
\(852\) −3.00000 −0.102778
\(853\) 19.0000 0.650548 0.325274 0.945620i \(-0.394544\pi\)
0.325274 + 0.945620i \(0.394544\pi\)
\(854\) 0 0
\(855\) −24.0000 −0.820783
\(856\) −3.00000 −0.102538
\(857\) −42.0000 −1.43469 −0.717346 0.696717i \(-0.754643\pi\)
−0.717346 + 0.696717i \(0.754643\pi\)
\(858\) 0 0
\(859\) −14.0000 −0.477674 −0.238837 0.971060i \(-0.576766\pi\)
−0.238837 + 0.971060i \(0.576766\pi\)
\(860\) −3.00000 −0.102299
\(861\) 0 0
\(862\) −12.0000 −0.408722
\(863\) −30.0000 −1.02121 −0.510606 0.859815i \(-0.670579\pi\)
−0.510606 + 0.859815i \(0.670579\pi\)
\(864\) −5.00000 −0.170103
\(865\) −63.0000 −2.14206
\(866\) 14.0000 0.475739
\(867\) 8.00000 0.271694
\(868\) 0 0
\(869\) 0 0
\(870\) −9.00000 −0.305129
\(871\) −16.0000 −0.542139
\(872\) −2.00000 −0.0677285
\(873\) −2.00000 −0.0676897
\(874\) 24.0000 0.811812
\(875\) 0 0
\(876\) −10.0000 −0.337869
\(877\) 32.0000 1.08056 0.540282 0.841484i \(-0.318318\pi\)
0.540282 + 0.841484i \(0.318318\pi\)
\(878\) −28.0000 −0.944954
\(879\) −24.0000 −0.809500
\(880\) 0 0
\(881\) 12.0000 0.404290 0.202145 0.979356i \(-0.435209\pi\)
0.202145 + 0.979356i \(0.435209\pi\)
\(882\) 0 0
\(883\) 8.00000 0.269221 0.134611 0.990899i \(-0.457022\pi\)
0.134611 + 0.990899i \(0.457022\pi\)
\(884\) −6.00000 −0.201802
\(885\) −18.0000 −0.605063
\(886\) −15.0000 −0.503935
\(887\) −30.0000 −1.00730 −0.503651 0.863907i \(-0.668010\pi\)
−0.503651 + 0.863907i \(0.668010\pi\)
\(888\) −4.00000 −0.134231
\(889\) 0 0
\(890\) 9.00000 0.301681
\(891\) 0 0
\(892\) 1.00000 0.0334825
\(893\) 24.0000 0.803129
\(894\) −3.00000 −0.100335
\(895\) 0 0
\(896\) 0 0
\(897\) −12.0000 −0.400668
\(898\) −15.0000 −0.500556
\(899\) −3.00000 −0.100056
\(900\) −8.00000 −0.266667
\(901\) 27.0000 0.899500
\(902\) 0 0
\(903\) 0 0
\(904\) −9.00000 −0.299336
\(905\) −24.0000 −0.797787
\(906\) 17.0000 0.564787
\(907\) −13.0000 −0.431658 −0.215829 0.976431i \(-0.569245\pi\)
−0.215829 + 0.976431i \(0.569245\pi\)
\(908\) 15.0000 0.497792
\(909\) −12.0000 −0.398015
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) −4.00000 −0.132453
\(913\) 0 0
\(914\) 34.0000 1.12462
\(915\) −3.00000 −0.0991769
\(916\) 16.0000 0.528655
\(917\) 0 0
\(918\) −15.0000 −0.495074
\(919\) 5.00000 0.164935 0.0824674 0.996594i \(-0.473720\pi\)
0.0824674 + 0.996594i \(0.473720\pi\)
\(920\) 18.0000 0.593442
\(921\) 8.00000 0.263609
\(922\) −15.0000 −0.493999
\(923\) −6.00000 −0.197492
\(924\) 0 0
\(925\) −16.0000 −0.526077
\(926\) 16.0000 0.525793
\(927\) 22.0000 0.722575
\(928\) 3.00000 0.0984798
\(929\) −6.00000 −0.196854 −0.0984268 0.995144i \(-0.531381\pi\)
−0.0984268 + 0.995144i \(0.531381\pi\)
\(930\) 3.00000 0.0983739
\(931\) 0 0
\(932\) −24.0000 −0.786146
\(933\) 6.00000 0.196431
\(934\) −24.0000 −0.785304
\(935\) 0 0
\(936\) −4.00000 −0.130744
\(937\) −47.0000 −1.53542 −0.767712 0.640796i \(-0.778605\pi\)
−0.767712 + 0.640796i \(0.778605\pi\)
\(938\) 0 0
\(939\) 14.0000 0.456873
\(940\) 18.0000 0.587095
\(941\) 6.00000 0.195594 0.0977972 0.995206i \(-0.468820\pi\)
0.0977972 + 0.995206i \(0.468820\pi\)
\(942\) 4.00000 0.130327
\(943\) 6.00000 0.195387
\(944\) 6.00000 0.195283
\(945\) 0 0
\(946\) 0 0
\(947\) 36.0000 1.16984 0.584921 0.811090i \(-0.301125\pi\)
0.584921 + 0.811090i \(0.301125\pi\)
\(948\) 1.00000 0.0324785
\(949\) −20.0000 −0.649227
\(950\) −16.0000 −0.519109
\(951\) −30.0000 −0.972817
\(952\) 0 0
\(953\) 6.00000 0.194359 0.0971795 0.995267i \(-0.469018\pi\)
0.0971795 + 0.995267i \(0.469018\pi\)
\(954\) 18.0000 0.582772
\(955\) 9.00000 0.291233
\(956\) −24.0000 −0.776215
\(957\) 0 0
\(958\) 6.00000 0.193851
\(959\) 0 0
\(960\) −3.00000 −0.0968246
\(961\) −30.0000 −0.967742
\(962\) −8.00000 −0.257930
\(963\) −6.00000 −0.193347
\(964\) 28.0000 0.901819
\(965\) −48.0000 −1.54517
\(966\) 0 0
\(967\) −49.0000 −1.57573 −0.787867 0.615846i \(-0.788815\pi\)
−0.787867 + 0.615846i \(0.788815\pi\)
\(968\) 11.0000 0.353553
\(969\) −12.0000 −0.385496
\(970\) −3.00000 −0.0963242
\(971\) −45.0000 −1.44412 −0.722059 0.691831i \(-0.756804\pi\)
−0.722059 + 0.691831i \(0.756804\pi\)
\(972\) −16.0000 −0.513200
\(973\) 0 0
\(974\) −2.00000 −0.0640841
\(975\) 8.00000 0.256205
\(976\) 1.00000 0.0320092
\(977\) −42.0000 −1.34370 −0.671850 0.740688i \(-0.734500\pi\)
−0.671850 + 0.740688i \(0.734500\pi\)
\(978\) 20.0000 0.639529
\(979\) 0 0
\(980\) 0 0
\(981\) −4.00000 −0.127710
\(982\) 3.00000 0.0957338
\(983\) 33.0000 1.05254 0.526268 0.850319i \(-0.323591\pi\)
0.526268 + 0.850319i \(0.323591\pi\)
\(984\) −1.00000 −0.0318788
\(985\) 72.0000 2.29411
\(986\) 9.00000 0.286618
\(987\) 0 0
\(988\) −8.00000 −0.254514
\(989\) 6.00000 0.190789
\(990\) 0 0
\(991\) −40.0000 −1.27064 −0.635321 0.772248i \(-0.719132\pi\)
−0.635321 + 0.772248i \(0.719132\pi\)
\(992\) −1.00000 −0.0317500
\(993\) −2.00000 −0.0634681
\(994\) 0 0
\(995\) 48.0000 1.52170
\(996\) −12.0000 −0.380235
\(997\) 58.0000 1.83688 0.918439 0.395562i \(-0.129450\pi\)
0.918439 + 0.395562i \(0.129450\pi\)
\(998\) 34.0000 1.07625
\(999\) −20.0000 −0.632772
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 \(a_p\))