Properties

Label 4002.2.a.r.1.1
Level 4002
Weight 2
Character 4002.1
Self dual Yes
Analytic conductor 31.956
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9561308889\)
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 \(\chi\) = 4002.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+3.00000 q^{5}\) \(+1.00000 q^{6}\) \(+1.00000 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+3.00000 q^{5}\) \(+1.00000 q^{6}\) \(+1.00000 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+3.00000 q^{10}\) \(+1.00000 q^{12}\) \(-2.00000 q^{13}\) \(+1.00000 q^{14}\) \(+3.00000 q^{15}\) \(+1.00000 q^{16}\) \(+1.00000 q^{17}\) \(+1.00000 q^{18}\) \(-1.00000 q^{19}\) \(+3.00000 q^{20}\) \(+1.00000 q^{21}\) \(-1.00000 q^{23}\) \(+1.00000 q^{24}\) \(+4.00000 q^{25}\) \(-2.00000 q^{26}\) \(+1.00000 q^{27}\) \(+1.00000 q^{28}\) \(+1.00000 q^{29}\) \(+3.00000 q^{30}\) \(+10.0000 q^{31}\) \(+1.00000 q^{32}\) \(+1.00000 q^{34}\) \(+3.00000 q^{35}\) \(+1.00000 q^{36}\) \(+5.00000 q^{37}\) \(-1.00000 q^{38}\) \(-2.00000 q^{39}\) \(+3.00000 q^{40}\) \(+7.00000 q^{41}\) \(+1.00000 q^{42}\) \(-11.0000 q^{43}\) \(+3.00000 q^{45}\) \(-1.00000 q^{46}\) \(-13.0000 q^{47}\) \(+1.00000 q^{48}\) \(-6.00000 q^{49}\) \(+4.00000 q^{50}\) \(+1.00000 q^{51}\) \(-2.00000 q^{52}\) \(+10.0000 q^{53}\) \(+1.00000 q^{54}\) \(+1.00000 q^{56}\) \(-1.00000 q^{57}\) \(+1.00000 q^{58}\) \(-3.00000 q^{59}\) \(+3.00000 q^{60}\) \(+10.0000 q^{61}\) \(+10.0000 q^{62}\) \(+1.00000 q^{63}\) \(+1.00000 q^{64}\) \(-6.00000 q^{65}\) \(-4.00000 q^{67}\) \(+1.00000 q^{68}\) \(-1.00000 q^{69}\) \(+3.00000 q^{70}\) \(+10.0000 q^{71}\) \(+1.00000 q^{72}\) \(+10.0000 q^{73}\) \(+5.00000 q^{74}\) \(+4.00000 q^{75}\) \(-1.00000 q^{76}\) \(-2.00000 q^{78}\) \(+4.00000 q^{79}\) \(+3.00000 q^{80}\) \(+1.00000 q^{81}\) \(+7.00000 q^{82}\) \(+8.00000 q^{83}\) \(+1.00000 q^{84}\) \(+3.00000 q^{85}\) \(-11.0000 q^{86}\) \(+1.00000 q^{87}\) \(-6.00000 q^{89}\) \(+3.00000 q^{90}\) \(-2.00000 q^{91}\) \(-1.00000 q^{92}\) \(+10.0000 q^{93}\) \(-13.0000 q^{94}\) \(-3.00000 q^{95}\) \(+1.00000 q^{96}\) \(-6.00000 q^{98}\) \(+O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 3.00000 1.34164 0.670820 0.741620i \(-0.265942\pi\)
0.670820 + 0.741620i \(0.265942\pi\)
\(6\) 1.00000 0.408248
\(7\) 1.00000 0.377964 0.188982 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 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 \(0.589456\pi\)
\(14\) 1.00000 0.267261
\(15\) 3.00000 0.774597
\(16\) 1.00000 0.250000
\(17\) 1.00000 0.242536 0.121268 0.992620i \(-0.461304\pi\)
0.121268 + 0.992620i \(0.461304\pi\)
\(18\) 1.00000 0.235702
\(19\) −1.00000 −0.229416 −0.114708 0.993399i \(-0.536593\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) 3.00000 0.670820
\(21\) 1.00000 0.218218
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 1.00000 0.204124
\(25\) 4.00000 0.800000
\(26\) −2.00000 −0.392232
\(27\) 1.00000 0.192450
\(28\) 1.00000 0.188982
\(29\) 1.00000 0.185695
\(30\) 3.00000 0.547723
\(31\) 10.0000 1.79605 0.898027 0.439941i \(-0.145001\pi\)
0.898027 + 0.439941i \(0.145001\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 1.00000 0.171499
\(35\) 3.00000 0.507093
\(36\) 1.00000 0.166667
\(37\) 5.00000 0.821995 0.410997 0.911636i \(-0.365181\pi\)
0.410997 + 0.911636i \(0.365181\pi\)
\(38\) −1.00000 −0.162221
\(39\) −2.00000 −0.320256
\(40\) 3.00000 0.474342
\(41\) 7.00000 1.09322 0.546608 0.837389i \(-0.315919\pi\)
0.546608 + 0.837389i \(0.315919\pi\)
\(42\) 1.00000 0.154303
\(43\) −11.0000 −1.67748 −0.838742 0.544529i \(-0.816708\pi\)
−0.838742 + 0.544529i \(0.816708\pi\)
\(44\) 0 0
\(45\) 3.00000 0.447214
\(46\) −1.00000 −0.147442
\(47\) −13.0000 −1.89624 −0.948122 0.317905i \(-0.897021\pi\)
−0.948122 + 0.317905i \(0.897021\pi\)
\(48\) 1.00000 0.144338
\(49\) −6.00000 −0.857143
\(50\) 4.00000 0.565685
\(51\) 1.00000 0.140028
\(52\) −2.00000 −0.277350
\(53\) 10.0000 1.37361 0.686803 0.726844i \(-0.259014\pi\)
0.686803 + 0.726844i \(0.259014\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) −1.00000 −0.132453
\(58\) 1.00000 0.131306
\(59\) −3.00000 −0.390567 −0.195283 0.980747i \(-0.562563\pi\)
−0.195283 + 0.980747i \(0.562563\pi\)
\(60\) 3.00000 0.387298
\(61\) 10.0000 1.28037 0.640184 0.768221i \(-0.278858\pi\)
0.640184 + 0.768221i \(0.278858\pi\)
\(62\) 10.0000 1.27000
\(63\) 1.00000 0.125988
\(64\) 1.00000 0.125000
\(65\) −6.00000 −0.744208
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 1.00000 0.121268
\(69\) −1.00000 −0.120386
\(70\) 3.00000 0.358569
\(71\) 10.0000 1.18678 0.593391 0.804914i \(-0.297789\pi\)
0.593391 + 0.804914i \(0.297789\pi\)
\(72\) 1.00000 0.117851
\(73\) 10.0000 1.17041 0.585206 0.810885i \(-0.301014\pi\)
0.585206 + 0.810885i \(0.301014\pi\)
\(74\) 5.00000 0.581238
\(75\) 4.00000 0.461880
\(76\) −1.00000 −0.114708
\(77\) 0 0
\(78\) −2.00000 −0.226455
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 3.00000 0.335410
\(81\) 1.00000 0.111111
\(82\) 7.00000 0.773021
\(83\) 8.00000 0.878114 0.439057 0.898459i \(-0.355313\pi\)
0.439057 + 0.898459i \(0.355313\pi\)
\(84\) 1.00000 0.109109
\(85\) 3.00000 0.325396
\(86\) −11.0000 −1.18616
\(87\) 1.00000 0.107211
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 3.00000 0.316228
\(91\) −2.00000 −0.209657
\(92\) −1.00000 −0.104257
\(93\) 10.0000 1.03695
\(94\) −13.0000 −1.34085
\(95\) −3.00000 −0.307794
\(96\) 1.00000 0.102062
\(97\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) −6.00000 −0.606092
\(99\) 0 0
\(100\) 4.00000 0.400000
\(101\) −10.0000 −0.995037 −0.497519 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) 1.00000 0.0990148
\(103\) 7.00000 0.689730 0.344865 0.938652i \(-0.387925\pi\)
0.344865 + 0.938652i \(0.387925\pi\)
\(104\) −2.00000 −0.196116
\(105\) 3.00000 0.292770
\(106\) 10.0000 0.971286
\(107\) −5.00000 −0.483368 −0.241684 0.970355i \(-0.577700\pi\)
−0.241684 + 0.970355i \(0.577700\pi\)
\(108\) 1.00000 0.0962250
\(109\) −4.00000 −0.383131 −0.191565 0.981480i \(-0.561356\pi\)
−0.191565 + 0.981480i \(0.561356\pi\)
\(110\) 0 0
\(111\) 5.00000 0.474579
\(112\) 1.00000 0.0944911
\(113\) −9.00000 −0.846649 −0.423324 0.905978i \(-0.639137\pi\)
−0.423324 + 0.905978i \(0.639137\pi\)
\(114\) −1.00000 −0.0936586
\(115\) −3.00000 −0.279751
\(116\) 1.00000 0.0928477
\(117\) −2.00000 −0.184900
\(118\) −3.00000 −0.276172
\(119\) 1.00000 0.0916698
\(120\) 3.00000 0.273861
\(121\) −11.0000 −1.00000
\(122\) 10.0000 0.905357
\(123\) 7.00000 0.631169
\(124\) 10.0000 0.898027
\(125\) −3.00000 −0.268328
\(126\) 1.00000 0.0890871
\(127\) −2.00000 −0.177471 −0.0887357 0.996055i \(-0.528283\pi\)
−0.0887357 + 0.996055i \(0.528283\pi\)
\(128\) 1.00000 0.0883883
\(129\) −11.0000 −0.968496
\(130\) −6.00000 −0.526235
\(131\) −14.0000 −1.22319 −0.611593 0.791173i \(-0.709471\pi\)
−0.611593 + 0.791173i \(0.709471\pi\)
\(132\) 0 0
\(133\) −1.00000 −0.0867110
\(134\) −4.00000 −0.345547
\(135\) 3.00000 0.258199
\(136\) 1.00000 0.0857493
\(137\) −18.0000 −1.53784 −0.768922 0.639343i \(-0.779207\pi\)
−0.768922 + 0.639343i \(0.779207\pi\)
\(138\) −1.00000 −0.0851257
\(139\) −18.0000 −1.52674 −0.763370 0.645961i \(-0.776457\pi\)
−0.763370 + 0.645961i \(0.776457\pi\)
\(140\) 3.00000 0.253546
\(141\) −13.0000 −1.09480
\(142\) 10.0000 0.839181
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 3.00000 0.249136
\(146\) 10.0000 0.827606
\(147\) −6.00000 −0.494872
\(148\) 5.00000 0.410997
\(149\) −11.0000 −0.901155 −0.450578 0.892737i \(-0.648782\pi\)
−0.450578 + 0.892737i \(0.648782\pi\)
\(150\) 4.00000 0.326599
\(151\) −1.00000 −0.0813788 −0.0406894 0.999172i \(-0.512955\pi\)
−0.0406894 + 0.999172i \(0.512955\pi\)
\(152\) −1.00000 −0.0811107
\(153\) 1.00000 0.0808452
\(154\) 0 0
\(155\) 30.0000 2.40966
\(156\) −2.00000 −0.160128
\(157\) −7.00000 −0.558661 −0.279330 0.960195i \(-0.590112\pi\)
−0.279330 + 0.960195i \(0.590112\pi\)
\(158\) 4.00000 0.318223
\(159\) 10.0000 0.793052
\(160\) 3.00000 0.237171
\(161\) −1.00000 −0.0788110
\(162\) 1.00000 0.0785674
\(163\) 11.0000 0.861586 0.430793 0.902451i \(-0.358234\pi\)
0.430793 + 0.902451i \(0.358234\pi\)
\(164\) 7.00000 0.546608
\(165\) 0 0
\(166\) 8.00000 0.620920
\(167\) −10.0000 −0.773823 −0.386912 0.922117i \(-0.626458\pi\)
−0.386912 + 0.922117i \(0.626458\pi\)
\(168\) 1.00000 0.0771517
\(169\) −9.00000 −0.692308
\(170\) 3.00000 0.230089
\(171\) −1.00000 −0.0764719
\(172\) −11.0000 −0.838742
\(173\) 23.0000 1.74866 0.874329 0.485334i \(-0.161302\pi\)
0.874329 + 0.485334i \(0.161302\pi\)
\(174\) 1.00000 0.0758098
\(175\) 4.00000 0.302372
\(176\) 0 0
\(177\) −3.00000 −0.225494
\(178\) −6.00000 −0.449719
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 3.00000 0.223607
\(181\) −6.00000 −0.445976 −0.222988 0.974821i \(-0.571581\pi\)
−0.222988 + 0.974821i \(0.571581\pi\)
\(182\) −2.00000 −0.148250
\(183\) 10.0000 0.739221
\(184\) −1.00000 −0.0737210
\(185\) 15.0000 1.10282
\(186\) 10.0000 0.733236
\(187\) 0 0
\(188\) −13.0000 −0.948122
\(189\) 1.00000 0.0727393
\(190\) −3.00000 −0.217643
\(191\) −5.00000 −0.361787 −0.180894 0.983503i \(-0.557899\pi\)
−0.180894 + 0.983503i \(0.557899\pi\)
\(192\) 1.00000 0.0721688
\(193\) 12.0000 0.863779 0.431889 0.901927i \(-0.357847\pi\)
0.431889 + 0.901927i \(0.357847\pi\)
\(194\) 0 0
\(195\) −6.00000 −0.429669
\(196\) −6.00000 −0.428571
\(197\) 1.00000 0.0712470 0.0356235 0.999365i \(-0.488658\pi\)
0.0356235 + 0.999365i \(0.488658\pi\)
\(198\) 0 0
\(199\) 4.00000 0.283552 0.141776 0.989899i \(-0.454719\pi\)
0.141776 + 0.989899i \(0.454719\pi\)
\(200\) 4.00000 0.282843
\(201\) −4.00000 −0.282138
\(202\) −10.0000 −0.703598
\(203\) 1.00000 0.0701862
\(204\) 1.00000 0.0700140
\(205\) 21.0000 1.46670
\(206\) 7.00000 0.487713
\(207\) −1.00000 −0.0695048
\(208\) −2.00000 −0.138675
\(209\) 0 0
\(210\) 3.00000 0.207020
\(211\) −23.0000 −1.58339 −0.791693 0.610920i \(-0.790800\pi\)
−0.791693 + 0.610920i \(0.790800\pi\)
\(212\) 10.0000 0.686803
\(213\) 10.0000 0.685189
\(214\) −5.00000 −0.341793
\(215\) −33.0000 −2.25058
\(216\) 1.00000 0.0680414
\(217\) 10.0000 0.678844
\(218\) −4.00000 −0.270914
\(219\) 10.0000 0.675737
\(220\) 0 0
\(221\) −2.00000 −0.134535
\(222\) 5.00000 0.335578
\(223\) −8.00000 −0.535720 −0.267860 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 1.00000 0.0668153
\(225\) 4.00000 0.266667
\(226\) −9.00000 −0.598671
\(227\) 11.0000 0.730096 0.365048 0.930989i \(-0.381053\pi\)
0.365048 + 0.930989i \(0.381053\pi\)
\(228\) −1.00000 −0.0662266
\(229\) −17.0000 −1.12339 −0.561696 0.827344i \(-0.689851\pi\)
−0.561696 + 0.827344i \(0.689851\pi\)
\(230\) −3.00000 −0.197814
\(231\) 0 0
\(232\) 1.00000 0.0656532
\(233\) −4.00000 −0.262049 −0.131024 0.991379i \(-0.541827\pi\)
−0.131024 + 0.991379i \(0.541827\pi\)
\(234\) −2.00000 −0.130744
\(235\) −39.0000 −2.54408
\(236\) −3.00000 −0.195283
\(237\) 4.00000 0.259828
\(238\) 1.00000 0.0648204
\(239\) −10.0000 −0.646846 −0.323423 0.946254i \(-0.604834\pi\)
−0.323423 + 0.946254i \(0.604834\pi\)
\(240\) 3.00000 0.193649
\(241\) 15.0000 0.966235 0.483117 0.875556i \(-0.339504\pi\)
0.483117 + 0.875556i \(0.339504\pi\)
\(242\) −11.0000 −0.707107
\(243\) 1.00000 0.0641500
\(244\) 10.0000 0.640184
\(245\) −18.0000 −1.14998
\(246\) 7.00000 0.446304
\(247\) 2.00000 0.127257
\(248\) 10.0000 0.635001
\(249\) 8.00000 0.506979
\(250\) −3.00000 −0.189737
\(251\) 4.00000 0.252478 0.126239 0.992000i \(-0.459709\pi\)
0.126239 + 0.992000i \(0.459709\pi\)
\(252\) 1.00000 0.0629941
\(253\) 0 0
\(254\) −2.00000 −0.125491
\(255\) 3.00000 0.187867
\(256\) 1.00000 0.0625000
\(257\) 10.0000 0.623783 0.311891 0.950118i \(-0.399037\pi\)
0.311891 + 0.950118i \(0.399037\pi\)
\(258\) −11.0000 −0.684830
\(259\) 5.00000 0.310685
\(260\) −6.00000 −0.372104
\(261\) 1.00000 0.0618984
\(262\) −14.0000 −0.864923
\(263\) 21.0000 1.29492 0.647458 0.762101i \(-0.275832\pi\)
0.647458 + 0.762101i \(0.275832\pi\)
\(264\) 0 0
\(265\) 30.0000 1.84289
\(266\) −1.00000 −0.0613139
\(267\) −6.00000 −0.367194
\(268\) −4.00000 −0.244339
\(269\) 32.0000 1.95107 0.975537 0.219834i \(-0.0705517\pi\)
0.975537 + 0.219834i \(0.0705517\pi\)
\(270\) 3.00000 0.182574
\(271\) −12.0000 −0.728948 −0.364474 0.931214i \(-0.618751\pi\)
−0.364474 + 0.931214i \(0.618751\pi\)
\(272\) 1.00000 0.0606339
\(273\) −2.00000 −0.121046
\(274\) −18.0000 −1.08742
\(275\) 0 0
\(276\) −1.00000 −0.0601929
\(277\) 8.00000 0.480673 0.240337 0.970690i \(-0.422742\pi\)
0.240337 + 0.970690i \(0.422742\pi\)
\(278\) −18.0000 −1.07957
\(279\) 10.0000 0.598684
\(280\) 3.00000 0.179284
\(281\) −30.0000 −1.78965 −0.894825 0.446417i \(-0.852700\pi\)
−0.894825 + 0.446417i \(0.852700\pi\)
\(282\) −13.0000 −0.774139
\(283\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) 10.0000 0.593391
\(285\) −3.00000 −0.177705
\(286\) 0 0
\(287\) 7.00000 0.413197
\(288\) 1.00000 0.0589256
\(289\) −16.0000 −0.941176
\(290\) 3.00000 0.176166
\(291\) 0 0
\(292\) 10.0000 0.585206
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) −6.00000 −0.349927
\(295\) −9.00000 −0.524000
\(296\) 5.00000 0.290619
\(297\) 0 0
\(298\) −11.0000 −0.637213
\(299\) 2.00000 0.115663
\(300\) 4.00000 0.230940
\(301\) −11.0000 −0.634029
\(302\) −1.00000 −0.0575435
\(303\) −10.0000 −0.574485
\(304\) −1.00000 −0.0573539
\(305\) 30.0000 1.71780
\(306\) 1.00000 0.0571662
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 0 0
\(309\) 7.00000 0.398216
\(310\) 30.0000 1.70389
\(311\) −21.0000 −1.19080 −0.595400 0.803429i \(-0.703007\pi\)
−0.595400 + 0.803429i \(0.703007\pi\)
\(312\) −2.00000 −0.113228
\(313\) −19.0000 −1.07394 −0.536972 0.843600i \(-0.680432\pi\)
−0.536972 + 0.843600i \(0.680432\pi\)
\(314\) −7.00000 −0.395033
\(315\) 3.00000 0.169031
\(316\) 4.00000 0.225018
\(317\) −30.0000 −1.68497 −0.842484 0.538721i \(-0.818908\pi\)
−0.842484 + 0.538721i \(0.818908\pi\)
\(318\) 10.0000 0.560772
\(319\) 0 0
\(320\) 3.00000 0.167705
\(321\) −5.00000 −0.279073
\(322\) −1.00000 −0.0557278
\(323\) −1.00000 −0.0556415
\(324\) 1.00000 0.0555556
\(325\) −8.00000 −0.443760
\(326\) 11.0000 0.609234
\(327\) −4.00000 −0.221201
\(328\) 7.00000 0.386510
\(329\) −13.0000 −0.716713
\(330\) 0 0
\(331\) 11.0000 0.604615 0.302307 0.953211i \(-0.402243\pi\)
0.302307 + 0.953211i \(0.402243\pi\)
\(332\) 8.00000 0.439057
\(333\) 5.00000 0.273998
\(334\) −10.0000 −0.547176
\(335\) −12.0000 −0.655630
\(336\) 1.00000 0.0545545
\(337\) 30.0000 1.63420 0.817102 0.576493i \(-0.195579\pi\)
0.817102 + 0.576493i \(0.195579\pi\)
\(338\) −9.00000 −0.489535
\(339\) −9.00000 −0.488813
\(340\) 3.00000 0.162698
\(341\) 0 0
\(342\) −1.00000 −0.0540738
\(343\) −13.0000 −0.701934
\(344\) −11.0000 −0.593080
\(345\) −3.00000 −0.161515
\(346\) 23.0000 1.23649
\(347\) 23.0000 1.23470 0.617352 0.786687i \(-0.288205\pi\)
0.617352 + 0.786687i \(0.288205\pi\)
\(348\) 1.00000 0.0536056
\(349\) 30.0000 1.60586 0.802932 0.596071i \(-0.203272\pi\)
0.802932 + 0.596071i \(0.203272\pi\)
\(350\) 4.00000 0.213809
\(351\) −2.00000 −0.106752
\(352\) 0 0
\(353\) 34.0000 1.80964 0.904819 0.425797i \(-0.140006\pi\)
0.904819 + 0.425797i \(0.140006\pi\)
\(354\) −3.00000 −0.159448
\(355\) 30.0000 1.59223
\(356\) −6.00000 −0.317999
\(357\) 1.00000 0.0529256
\(358\) 12.0000 0.634220
\(359\) 17.0000 0.897226 0.448613 0.893726i \(-0.351918\pi\)
0.448613 + 0.893726i \(0.351918\pi\)
\(360\) 3.00000 0.158114
\(361\) −18.0000 −0.947368
\(362\) −6.00000 −0.315353
\(363\) −11.0000 −0.577350
\(364\) −2.00000 −0.104828
\(365\) 30.0000 1.57027
\(366\) 10.0000 0.522708
\(367\) −32.0000 −1.67039 −0.835193 0.549957i \(-0.814644\pi\)
−0.835193 + 0.549957i \(0.814644\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 7.00000 0.364405
\(370\) 15.0000 0.779813
\(371\) 10.0000 0.519174
\(372\) 10.0000 0.518476
\(373\) 36.0000 1.86401 0.932005 0.362446i \(-0.118058\pi\)
0.932005 + 0.362446i \(0.118058\pi\)
\(374\) 0 0
\(375\) −3.00000 −0.154919
\(376\) −13.0000 −0.670424
\(377\) −2.00000 −0.103005
\(378\) 1.00000 0.0514344
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) −3.00000 −0.153897
\(381\) −2.00000 −0.102463
\(382\) −5.00000 −0.255822
\(383\) −24.0000 −1.22634 −0.613171 0.789950i \(-0.710106\pi\)
−0.613171 + 0.789950i \(0.710106\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 12.0000 0.610784
\(387\) −11.0000 −0.559161
\(388\) 0 0
\(389\) −4.00000 −0.202808 −0.101404 0.994845i \(-0.532333\pi\)
−0.101404 + 0.994845i \(0.532333\pi\)
\(390\) −6.00000 −0.303822
\(391\) −1.00000 −0.0505722
\(392\) −6.00000 −0.303046
\(393\) −14.0000 −0.706207
\(394\) 1.00000 0.0503793
\(395\) 12.0000 0.603786
\(396\) 0 0
\(397\) −20.0000 −1.00377 −0.501886 0.864934i \(-0.667360\pi\)
−0.501886 + 0.864934i \(0.667360\pi\)
\(398\) 4.00000 0.200502
\(399\) −1.00000 −0.0500626
\(400\) 4.00000 0.200000
\(401\) −10.0000 −0.499376 −0.249688 0.968326i \(-0.580328\pi\)
−0.249688 + 0.968326i \(0.580328\pi\)
\(402\) −4.00000 −0.199502
\(403\) −20.0000 −0.996271
\(404\) −10.0000 −0.497519
\(405\) 3.00000 0.149071
\(406\) 1.00000 0.0496292
\(407\) 0 0
\(408\) 1.00000 0.0495074
\(409\) −6.00000 −0.296681 −0.148340 0.988936i \(-0.547393\pi\)
−0.148340 + 0.988936i \(0.547393\pi\)
\(410\) 21.0000 1.03712
\(411\) −18.0000 −0.887875
\(412\) 7.00000 0.344865
\(413\) −3.00000 −0.147620
\(414\) −1.00000 −0.0491473
\(415\) 24.0000 1.17811
\(416\) −2.00000 −0.0980581
\(417\) −18.0000 −0.881464
\(418\) 0 0
\(419\) −3.00000 −0.146560 −0.0732798 0.997311i \(-0.523347\pi\)
−0.0732798 + 0.997311i \(0.523347\pi\)
\(420\) 3.00000 0.146385
\(421\) 26.0000 1.26716 0.633581 0.773676i \(-0.281584\pi\)
0.633581 + 0.773676i \(0.281584\pi\)
\(422\) −23.0000 −1.11962
\(423\) −13.0000 −0.632082
\(424\) 10.0000 0.485643
\(425\) 4.00000 0.194029
\(426\) 10.0000 0.484502
\(427\) 10.0000 0.483934
\(428\) −5.00000 −0.241684
\(429\) 0 0
\(430\) −33.0000 −1.59140
\(431\) 14.0000 0.674356 0.337178 0.941441i \(-0.390528\pi\)
0.337178 + 0.941441i \(0.390528\pi\)
\(432\) 1.00000 0.0481125
\(433\) 12.0000 0.576683 0.288342 0.957528i \(-0.406896\pi\)
0.288342 + 0.957528i \(0.406896\pi\)
\(434\) 10.0000 0.480015
\(435\) 3.00000 0.143839
\(436\) −4.00000 −0.191565
\(437\) 1.00000 0.0478365
\(438\) 10.0000 0.477818
\(439\) −19.0000 −0.906821 −0.453410 0.891302i \(-0.649793\pi\)
−0.453410 + 0.891302i \(0.649793\pi\)
\(440\) 0 0
\(441\) −6.00000 −0.285714
\(442\) −2.00000 −0.0951303
\(443\) −24.0000 −1.14027 −0.570137 0.821549i \(-0.693110\pi\)
−0.570137 + 0.821549i \(0.693110\pi\)
\(444\) 5.00000 0.237289
\(445\) −18.0000 −0.853282
\(446\) −8.00000 −0.378811
\(447\) −11.0000 −0.520282
\(448\) 1.00000 0.0472456
\(449\) 15.0000 0.707894 0.353947 0.935266i \(-0.384839\pi\)
0.353947 + 0.935266i \(0.384839\pi\)
\(450\) 4.00000 0.188562
\(451\) 0 0
\(452\) −9.00000 −0.423324
\(453\) −1.00000 −0.0469841
\(454\) 11.0000 0.516256
\(455\) −6.00000 −0.281284
\(456\) −1.00000 −0.0468293
\(457\) −7.00000 −0.327446 −0.163723 0.986506i \(-0.552350\pi\)
−0.163723 + 0.986506i \(0.552350\pi\)
\(458\) −17.0000 −0.794358
\(459\) 1.00000 0.0466760
\(460\) −3.00000 −0.139876
\(461\) 22.0000 1.02464 0.512321 0.858794i \(-0.328786\pi\)
0.512321 + 0.858794i \(0.328786\pi\)
\(462\) 0 0
\(463\) −24.0000 −1.11537 −0.557687 0.830051i \(-0.688311\pi\)
−0.557687 + 0.830051i \(0.688311\pi\)
\(464\) 1.00000 0.0464238
\(465\) 30.0000 1.39122
\(466\) −4.00000 −0.185296
\(467\) −22.0000 −1.01804 −0.509019 0.860755i \(-0.669992\pi\)
−0.509019 + 0.860755i \(0.669992\pi\)
\(468\) −2.00000 −0.0924500
\(469\) −4.00000 −0.184703
\(470\) −39.0000 −1.79894
\(471\) −7.00000 −0.322543
\(472\) −3.00000 −0.138086
\(473\) 0 0
\(474\) 4.00000 0.183726
\(475\) −4.00000 −0.183533
\(476\) 1.00000 0.0458349
\(477\) 10.0000 0.457869
\(478\) −10.0000 −0.457389
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 3.00000 0.136931
\(481\) −10.0000 −0.455961
\(482\) 15.0000 0.683231
\(483\) −1.00000 −0.0455016
\(484\) −11.0000 −0.500000
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) 25.0000 1.13286 0.566429 0.824110i \(-0.308325\pi\)
0.566429 + 0.824110i \(0.308325\pi\)
\(488\) 10.0000 0.452679
\(489\) 11.0000 0.497437
\(490\) −18.0000 −0.813157
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 7.00000 0.315584
\(493\) 1.00000 0.0450377
\(494\) 2.00000 0.0899843
\(495\) 0 0
\(496\) 10.0000 0.449013
\(497\) 10.0000 0.448561
\(498\) 8.00000 0.358489
\(499\) −24.0000 −1.07439 −0.537194 0.843459i \(-0.680516\pi\)
−0.537194 + 0.843459i \(0.680516\pi\)
\(500\) −3.00000 −0.134164
\(501\) −10.0000 −0.446767
\(502\) 4.00000 0.178529
\(503\) 11.0000 0.490466 0.245233 0.969464i \(-0.421136\pi\)
0.245233 + 0.969464i \(0.421136\pi\)
\(504\) 1.00000 0.0445435
\(505\) −30.0000 −1.33498
\(506\) 0 0
\(507\) −9.00000 −0.399704
\(508\) −2.00000 −0.0887357
\(509\) 31.0000 1.37405 0.687025 0.726633i \(-0.258916\pi\)
0.687025 + 0.726633i \(0.258916\pi\)
\(510\) 3.00000 0.132842
\(511\) 10.0000 0.442374
\(512\) 1.00000 0.0441942
\(513\) −1.00000 −0.0441511
\(514\) 10.0000 0.441081
\(515\) 21.0000 0.925371
\(516\) −11.0000 −0.484248
\(517\) 0 0
\(518\) 5.00000 0.219687
\(519\) 23.0000 1.00959
\(520\) −6.00000 −0.263117
\(521\) −28.0000 −1.22670 −0.613351 0.789810i \(-0.710179\pi\)
−0.613351 + 0.789810i \(0.710179\pi\)
\(522\) 1.00000 0.0437688
\(523\) −6.00000 −0.262362 −0.131181 0.991358i \(-0.541877\pi\)
−0.131181 + 0.991358i \(0.541877\pi\)
\(524\) −14.0000 −0.611593
\(525\) 4.00000 0.174574
\(526\) 21.0000 0.915644
\(527\) 10.0000 0.435607
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 30.0000 1.30312
\(531\) −3.00000 −0.130189
\(532\) −1.00000 −0.0433555
\(533\) −14.0000 −0.606407
\(534\) −6.00000 −0.259645
\(535\) −15.0000 −0.648507
\(536\) −4.00000 −0.172774
\(537\) 12.0000 0.517838
\(538\) 32.0000 1.37962
\(539\) 0 0
\(540\) 3.00000 0.129099
\(541\) −45.0000 −1.93470 −0.967351 0.253442i \(-0.918437\pi\)
−0.967351 + 0.253442i \(0.918437\pi\)
\(542\) −12.0000 −0.515444
\(543\) −6.00000 −0.257485
\(544\) 1.00000 0.0428746
\(545\) −12.0000 −0.514024
\(546\) −2.00000 −0.0855921
\(547\) −38.0000 −1.62476 −0.812381 0.583127i \(-0.801829\pi\)
−0.812381 + 0.583127i \(0.801829\pi\)
\(548\) −18.0000 −0.768922
\(549\) 10.0000 0.426790
\(550\) 0 0
\(551\) −1.00000 −0.0426014
\(552\) −1.00000 −0.0425628
\(553\) 4.00000 0.170097
\(554\) 8.00000 0.339887
\(555\) 15.0000 0.636715
\(556\) −18.0000 −0.763370
\(557\) 3.00000 0.127114 0.0635570 0.997978i \(-0.479756\pi\)
0.0635570 + 0.997978i \(0.479756\pi\)
\(558\) 10.0000 0.423334
\(559\) 22.0000 0.930501
\(560\) 3.00000 0.126773
\(561\) 0 0
\(562\) −30.0000 −1.26547
\(563\) 30.0000 1.26435 0.632175 0.774826i \(-0.282163\pi\)
0.632175 + 0.774826i \(0.282163\pi\)
\(564\) −13.0000 −0.547399
\(565\) −27.0000 −1.13590
\(566\) 0 0
\(567\) 1.00000 0.0419961
\(568\) 10.0000 0.419591
\(569\) 43.0000 1.80265 0.901327 0.433140i \(-0.142594\pi\)
0.901327 + 0.433140i \(0.142594\pi\)
\(570\) −3.00000 −0.125656
\(571\) 36.0000 1.50655 0.753277 0.657704i \(-0.228472\pi\)
0.753277 + 0.657704i \(0.228472\pi\)
\(572\) 0 0
\(573\) −5.00000 −0.208878
\(574\) 7.00000 0.292174
\(575\) −4.00000 −0.166812
\(576\) 1.00000 0.0416667
\(577\) −2.00000 −0.0832611 −0.0416305 0.999133i \(-0.513255\pi\)
−0.0416305 + 0.999133i \(0.513255\pi\)
\(578\) −16.0000 −0.665512
\(579\) 12.0000 0.498703
\(580\) 3.00000 0.124568
\(581\) 8.00000 0.331896
\(582\) 0 0
\(583\) 0 0
\(584\) 10.0000 0.413803
\(585\) −6.00000 −0.248069
\(586\) −6.00000 −0.247858
\(587\) −5.00000 −0.206372 −0.103186 0.994662i \(-0.532904\pi\)
−0.103186 + 0.994662i \(0.532904\pi\)
\(588\) −6.00000 −0.247436
\(589\) −10.0000 −0.412043
\(590\) −9.00000 −0.370524
\(591\) 1.00000 0.0411345
\(592\) 5.00000 0.205499
\(593\) 24.0000 0.985562 0.492781 0.870153i \(-0.335980\pi\)
0.492781 + 0.870153i \(0.335980\pi\)
\(594\) 0 0
\(595\) 3.00000 0.122988
\(596\) −11.0000 −0.450578
\(597\) 4.00000 0.163709
\(598\) 2.00000 0.0817861
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) 4.00000 0.163299
\(601\) −20.0000 −0.815817 −0.407909 0.913023i \(-0.633742\pi\)
−0.407909 + 0.913023i \(0.633742\pi\)
\(602\) −11.0000 −0.448327
\(603\) −4.00000 −0.162893
\(604\) −1.00000 −0.0406894
\(605\) −33.0000 −1.34164
\(606\) −10.0000 −0.406222
\(607\) −14.0000 −0.568242 −0.284121 0.958788i \(-0.591702\pi\)
−0.284121 + 0.958788i \(0.591702\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 1.00000 0.0405220
\(610\) 30.0000 1.21466
\(611\) 26.0000 1.05185
\(612\) 1.00000 0.0404226
\(613\) −38.0000 −1.53481 −0.767403 0.641165i \(-0.778451\pi\)
−0.767403 + 0.641165i \(0.778451\pi\)
\(614\) 20.0000 0.807134
\(615\) 21.0000 0.846802
\(616\) 0 0
\(617\) 15.0000 0.603877 0.301939 0.953327i \(-0.402366\pi\)
0.301939 + 0.953327i \(0.402366\pi\)
\(618\) 7.00000 0.281581
\(619\) −35.0000 −1.40677 −0.703384 0.710810i \(-0.748329\pi\)
−0.703384 + 0.710810i \(0.748329\pi\)
\(620\) 30.0000 1.20483
\(621\) −1.00000 −0.0401286
\(622\) −21.0000 −0.842023
\(623\) −6.00000 −0.240385
\(624\) −2.00000 −0.0800641
\(625\) −29.0000 −1.16000
\(626\) −19.0000 −0.759393
\(627\) 0 0
\(628\) −7.00000 −0.279330
\(629\) 5.00000 0.199363
\(630\) 3.00000 0.119523
\(631\) −33.0000 −1.31371 −0.656855 0.754017i \(-0.728113\pi\)
−0.656855 + 0.754017i \(0.728113\pi\)
\(632\) 4.00000 0.159111
\(633\) −23.0000 −0.914168
\(634\) −30.0000 −1.19145
\(635\) −6.00000 −0.238103
\(636\) 10.0000 0.396526
\(637\) 12.0000 0.475457
\(638\) 0 0
\(639\) 10.0000 0.395594
\(640\) 3.00000 0.118585
\(641\) 7.00000 0.276483 0.138242 0.990399i \(-0.455855\pi\)
0.138242 + 0.990399i \(0.455855\pi\)
\(642\) −5.00000 −0.197334
\(643\) −2.00000 −0.0788723 −0.0394362 0.999222i \(-0.512556\pi\)
−0.0394362 + 0.999222i \(0.512556\pi\)
\(644\) −1.00000 −0.0394055
\(645\) −33.0000 −1.29937
\(646\) −1.00000 −0.0393445
\(647\) −28.0000 −1.10079 −0.550397 0.834903i \(-0.685524\pi\)
−0.550397 + 0.834903i \(0.685524\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) −8.00000 −0.313786
\(651\) 10.0000 0.391931
\(652\) 11.0000 0.430793
\(653\) −18.0000 −0.704394 −0.352197 0.935926i \(-0.614565\pi\)
−0.352197 + 0.935926i \(0.614565\pi\)
\(654\) −4.00000 −0.156412
\(655\) −42.0000 −1.64108
\(656\) 7.00000 0.273304
\(657\) 10.0000 0.390137
\(658\) −13.0000 −0.506793
\(659\) −4.00000 −0.155818 −0.0779089 0.996960i \(-0.524824\pi\)
−0.0779089 + 0.996960i \(0.524824\pi\)
\(660\) 0 0
\(661\) 36.0000 1.40024 0.700119 0.714026i \(-0.253130\pi\)
0.700119 + 0.714026i \(0.253130\pi\)
\(662\) 11.0000 0.427527
\(663\) −2.00000 −0.0776736
\(664\) 8.00000 0.310460
\(665\) −3.00000 −0.116335
\(666\) 5.00000 0.193746
\(667\) −1.00000 −0.0387202
\(668\) −10.0000 −0.386912
\(669\) −8.00000 −0.309298
\(670\) −12.0000 −0.463600
\(671\) 0 0
\(672\) 1.00000 0.0385758
\(673\) 27.0000 1.04077 0.520387 0.853931i \(-0.325788\pi\)
0.520387 + 0.853931i \(0.325788\pi\)
\(674\) 30.0000 1.15556
\(675\) 4.00000 0.153960
\(676\) −9.00000 −0.346154
\(677\) 26.0000 0.999261 0.499631 0.866239i \(-0.333469\pi\)
0.499631 + 0.866239i \(0.333469\pi\)
\(678\) −9.00000 −0.345643
\(679\) 0 0
\(680\) 3.00000 0.115045
\(681\) 11.0000 0.421521
\(682\) 0 0
\(683\) 33.0000 1.26271 0.631355 0.775494i \(-0.282499\pi\)
0.631355 + 0.775494i \(0.282499\pi\)
\(684\) −1.00000 −0.0382360
\(685\) −54.0000 −2.06323
\(686\) −13.0000 −0.496342
\(687\) −17.0000 −0.648590
\(688\) −11.0000 −0.419371
\(689\) −20.0000 −0.761939
\(690\) −3.00000 −0.114208
\(691\) 22.0000 0.836919 0.418460 0.908235i \(-0.362570\pi\)
0.418460 + 0.908235i \(0.362570\pi\)
\(692\) 23.0000 0.874329
\(693\) 0 0
\(694\) 23.0000 0.873068
\(695\) −54.0000 −2.04834
\(696\) 1.00000 0.0379049
\(697\) 7.00000 0.265144
\(698\) 30.0000 1.13552
\(699\) −4.00000 −0.151294
\(700\) 4.00000 0.151186
\(701\) 51.0000 1.92624 0.963122 0.269066i \(-0.0867150\pi\)
0.963122 + 0.269066i \(0.0867150\pi\)
\(702\) −2.00000 −0.0754851
\(703\) −5.00000 −0.188579
\(704\) 0 0
\(705\) −39.0000 −1.46882
\(706\) 34.0000 1.27961
\(707\) −10.0000 −0.376089
\(708\) −3.00000 −0.112747
\(709\) 20.0000 0.751116 0.375558 0.926799i \(-0.377451\pi\)
0.375558 + 0.926799i \(0.377451\pi\)
\(710\) 30.0000 1.12588
\(711\) 4.00000 0.150012
\(712\) −6.00000 −0.224860
\(713\) −10.0000 −0.374503
\(714\) 1.00000 0.0374241
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) −10.0000 −0.373457
\(718\) 17.0000 0.634434
\(719\) −30.0000 −1.11881 −0.559406 0.828894i \(-0.688971\pi\)
−0.559406 + 0.828894i \(0.688971\pi\)
\(720\) 3.00000 0.111803
\(721\) 7.00000 0.260694
\(722\) −18.0000 −0.669891
\(723\) 15.0000 0.557856
\(724\) −6.00000 −0.222988
\(725\) 4.00000 0.148556
\(726\) −11.0000 −0.408248
\(727\) 14.0000 0.519231 0.259616 0.965712i \(-0.416404\pi\)
0.259616 + 0.965712i \(0.416404\pi\)
\(728\) −2.00000 −0.0741249
\(729\) 1.00000 0.0370370
\(730\) 30.0000 1.11035
\(731\) −11.0000 −0.406850
\(732\) 10.0000 0.369611
\(733\) 6.00000 0.221615 0.110808 0.993842i \(-0.464656\pi\)
0.110808 + 0.993842i \(0.464656\pi\)
\(734\) −32.0000 −1.18114
\(735\) −18.0000 −0.663940
\(736\) −1.00000 −0.0368605
\(737\) 0 0
\(738\) 7.00000 0.257674
\(739\) −4.00000 −0.147142 −0.0735712 0.997290i \(-0.523440\pi\)
−0.0735712 + 0.997290i \(0.523440\pi\)
\(740\) 15.0000 0.551411
\(741\) 2.00000 0.0734718
\(742\) 10.0000 0.367112
\(743\) 11.0000 0.403551 0.201775 0.979432i \(-0.435329\pi\)
0.201775 + 0.979432i \(0.435329\pi\)
\(744\) 10.0000 0.366618
\(745\) −33.0000 −1.20903
\(746\) 36.0000 1.31805
\(747\) 8.00000 0.292705
\(748\) 0 0
\(749\) −5.00000 −0.182696
\(750\) −3.00000 −0.109545
\(751\) −26.0000 −0.948753 −0.474377 0.880322i \(-0.657327\pi\)
−0.474377 + 0.880322i \(0.657327\pi\)
\(752\) −13.0000 −0.474061
\(753\) 4.00000 0.145768
\(754\) −2.00000 −0.0728357
\(755\) −3.00000 −0.109181
\(756\) 1.00000 0.0363696
\(757\) 47.0000 1.70824 0.854122 0.520073i \(-0.174095\pi\)
0.854122 + 0.520073i \(0.174095\pi\)
\(758\) −20.0000 −0.726433
\(759\) 0 0
\(760\) −3.00000 −0.108821
\(761\) −42.0000 −1.52250 −0.761249 0.648459i \(-0.775414\pi\)
−0.761249 + 0.648459i \(0.775414\pi\)
\(762\) −2.00000 −0.0724524
\(763\) −4.00000 −0.144810
\(764\) −5.00000 −0.180894
\(765\) 3.00000 0.108465
\(766\) −24.0000 −0.867155
\(767\) 6.00000 0.216647
\(768\) 1.00000 0.0360844
\(769\) −44.0000 −1.58668 −0.793340 0.608778i \(-0.791660\pi\)
−0.793340 + 0.608778i \(0.791660\pi\)
\(770\) 0 0
\(771\) 10.0000 0.360141
\(772\) 12.0000 0.431889
\(773\) −4.00000 −0.143870 −0.0719350 0.997409i \(-0.522917\pi\)
−0.0719350 + 0.997409i \(0.522917\pi\)
\(774\) −11.0000 −0.395387
\(775\) 40.0000 1.43684
\(776\) 0 0
\(777\) 5.00000 0.179374
\(778\) −4.00000 −0.143407
\(779\) −7.00000 −0.250801
\(780\) −6.00000 −0.214834
\(781\) 0 0
\(782\) −1.00000 −0.0357599
\(783\) 1.00000 0.0357371
\(784\) −6.00000 −0.214286
\(785\) −21.0000 −0.749522
\(786\) −14.0000 −0.499363
\(787\) −42.0000 −1.49714 −0.748569 0.663057i \(-0.769259\pi\)
−0.748569 + 0.663057i \(0.769259\pi\)
\(788\) 1.00000 0.0356235
\(789\) 21.0000 0.747620
\(790\) 12.0000 0.426941
\(791\) −9.00000 −0.320003
\(792\) 0 0
\(793\) −20.0000 −0.710221
\(794\) −20.0000 −0.709773
\(795\) 30.0000 1.06399
\(796\) 4.00000 0.141776
\(797\) 18.0000 0.637593 0.318796 0.947823i \(-0.396721\pi\)
0.318796 + 0.947823i \(0.396721\pi\)
\(798\) −1.00000 −0.0353996
\(799\) −13.0000 −0.459907
\(800\) 4.00000 0.141421
\(801\) −6.00000 −0.212000
\(802\) −10.0000 −0.353112
\(803\) 0 0
\(804\) −4.00000 −0.141069
\(805\) −3.00000 −0.105736
\(806\) −20.0000 −0.704470
\(807\) 32.0000 1.12645
\(808\) −10.0000 −0.351799
\(809\) −22.0000 −0.773479 −0.386739 0.922189i \(-0.626399\pi\)
−0.386739 + 0.922189i \(0.626399\pi\)
\(810\) 3.00000 0.105409
\(811\) −44.0000 −1.54505 −0.772524 0.634985i \(-0.781006\pi\)
−0.772524 + 0.634985i \(0.781006\pi\)
\(812\) 1.00000 0.0350931
\(813\) −12.0000 −0.420858
\(814\) 0 0
\(815\) 33.0000 1.15594
\(816\) 1.00000 0.0350070
\(817\) 11.0000 0.384841
\(818\) −6.00000 −0.209785
\(819\) −2.00000 −0.0698857
\(820\) 21.0000 0.733352
\(821\) 22.0000 0.767805 0.383903 0.923374i \(-0.374580\pi\)
0.383903 + 0.923374i \(0.374580\pi\)
\(822\) −18.0000 −0.627822
\(823\) −4.00000 −0.139431 −0.0697156 0.997567i \(-0.522209\pi\)
−0.0697156 + 0.997567i \(0.522209\pi\)
\(824\) 7.00000 0.243857
\(825\) 0 0
\(826\) −3.00000 −0.104383
\(827\) −48.0000 −1.66912 −0.834562 0.550914i \(-0.814279\pi\)
−0.834562 + 0.550914i \(0.814279\pi\)
\(828\) −1.00000 −0.0347524
\(829\) 11.0000 0.382046 0.191023 0.981586i \(-0.438820\pi\)
0.191023 + 0.981586i \(0.438820\pi\)
\(830\) 24.0000 0.833052
\(831\) 8.00000 0.277517
\(832\) −2.00000 −0.0693375
\(833\) −6.00000 −0.207888
\(834\) −18.0000 −0.623289
\(835\) −30.0000 −1.03819
\(836\) 0 0
\(837\) 10.0000 0.345651
\(838\) −3.00000 −0.103633
\(839\) 13.0000 0.448810 0.224405 0.974496i \(-0.427956\pi\)
0.224405 + 0.974496i \(0.427956\pi\)
\(840\) 3.00000 0.103510
\(841\) 1.00000 0.0344828
\(842\) 26.0000 0.896019
\(843\) −30.0000 −1.03325
\(844\) −23.0000 −0.791693
\(845\) −27.0000 −0.928828
\(846\) −13.0000 −0.446949
\(847\) −11.0000 −0.377964
\(848\) 10.0000 0.343401
\(849\) 0 0
\(850\) 4.00000 0.137199
\(851\) −5.00000 −0.171398
\(852\) 10.0000 0.342594
\(853\) −51.0000 −1.74621 −0.873103 0.487535i \(-0.837896\pi\)
−0.873103 + 0.487535i \(0.837896\pi\)
\(854\) 10.0000 0.342193
\(855\) −3.00000 −0.102598
\(856\) −5.00000 −0.170896
\(857\) 12.0000 0.409912 0.204956 0.978771i \(-0.434295\pi\)
0.204956 + 0.978771i \(0.434295\pi\)
\(858\) 0 0
\(859\) 19.0000 0.648272 0.324136 0.946011i \(-0.394927\pi\)
0.324136 + 0.946011i \(0.394927\pi\)
\(860\) −33.0000 −1.12529
\(861\) 7.00000 0.238559
\(862\) 14.0000 0.476842
\(863\) −22.0000 −0.748889 −0.374444 0.927249i \(-0.622167\pi\)
−0.374444 + 0.927249i \(0.622167\pi\)
\(864\) 1.00000 0.0340207
\(865\) 69.0000 2.34607
\(866\) 12.0000 0.407777
\(867\) −16.0000 −0.543388
\(868\) 10.0000 0.339422
\(869\) 0 0
\(870\) 3.00000 0.101710
\(871\) 8.00000 0.271070
\(872\) −4.00000 −0.135457
\(873\) 0 0
\(874\) 1.00000 0.0338255
\(875\) −3.00000 −0.101419
\(876\) 10.0000 0.337869
\(877\) −18.0000 −0.607817 −0.303908 0.952701i \(-0.598292\pi\)
−0.303908 + 0.952701i \(0.598292\pi\)
\(878\) −19.0000 −0.641219
\(879\) −6.00000 −0.202375
\(880\) 0 0
\(881\) 50.0000 1.68454 0.842271 0.539054i \(-0.181218\pi\)
0.842271 + 0.539054i \(0.181218\pi\)
\(882\) −6.00000 −0.202031
\(883\) −42.0000 −1.41341 −0.706706 0.707507i \(-0.749820\pi\)
−0.706706 + 0.707507i \(0.749820\pi\)
\(884\) −2.00000 −0.0672673
\(885\) −9.00000 −0.302532
\(886\) −24.0000 −0.806296
\(887\) 20.0000 0.671534 0.335767 0.941945i \(-0.391004\pi\)
0.335767 + 0.941945i \(0.391004\pi\)
\(888\) 5.00000 0.167789
\(889\) −2.00000 −0.0670778
\(890\) −18.0000 −0.603361
\(891\) 0 0
\(892\) −8.00000 −0.267860
\(893\) 13.0000 0.435028
\(894\) −11.0000 −0.367895
\(895\) 36.0000 1.20335
\(896\) 1.00000 0.0334077
\(897\) 2.00000 0.0667781
\(898\) 15.0000 0.500556
\(899\) 10.0000 0.333519
\(900\) 4.00000 0.133333
\(901\) 10.0000 0.333148
\(902\) 0 0
\(903\) −11.0000 −0.366057
\(904\) −9.00000 −0.299336
\(905\) −18.0000 −0.598340
\(906\) −1.00000 −0.0332228
\(907\) −28.0000 −0.929725 −0.464862 0.885383i \(-0.653896\pi\)
−0.464862 + 0.885383i \(0.653896\pi\)
\(908\) 11.0000 0.365048
\(909\) −10.0000 −0.331679
\(910\) −6.00000 −0.198898
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) −1.00000 −0.0331133
\(913\) 0 0
\(914\) −7.00000 −0.231539
\(915\) 30.0000 0.991769
\(916\) −17.0000 −0.561696
\(917\) −14.0000 −0.462321
\(918\) 1.00000 0.0330049
\(919\) −11.0000 −0.362857 −0.181428 0.983404i \(-0.558072\pi\)
−0.181428 + 0.983404i \(0.558072\pi\)
\(920\) −3.00000 −0.0989071
\(921\) 20.0000 0.659022
\(922\) 22.0000 0.724531
\(923\) −20.0000 −0.658308
\(924\) 0 0
\(925\) 20.0000 0.657596
\(926\) −24.0000 −0.788689
\(927\) 7.00000 0.229910
\(928\) 1.00000 0.0328266
\(929\) −30.0000 −0.984268 −0.492134 0.870519i \(-0.663783\pi\)
−0.492134 + 0.870519i \(0.663783\pi\)
\(930\) 30.0000 0.983739
\(931\) 6.00000 0.196642
\(932\) −4.00000 −0.131024
\(933\) −21.0000 −0.687509
\(934\) −22.0000 −0.719862
\(935\) 0 0
\(936\) −2.00000 −0.0653720
\(937\) 17.0000 0.555366 0.277683 0.960673i \(-0.410434\pi\)
0.277683 + 0.960673i \(0.410434\pi\)
\(938\) −4.00000 −0.130605
\(939\) −19.0000 −0.620042
\(940\) −39.0000 −1.27204
\(941\) −50.0000 −1.62995 −0.814977 0.579494i \(-0.803250\pi\)
−0.814977 + 0.579494i \(0.803250\pi\)
\(942\) −7.00000 −0.228072
\(943\) −7.00000 −0.227951
\(944\) −3.00000 −0.0976417
\(945\) 3.00000 0.0975900
\(946\) 0 0
\(947\) 26.0000 0.844886 0.422443 0.906389i \(-0.361173\pi\)
0.422443 + 0.906389i \(0.361173\pi\)
\(948\) 4.00000 0.129914
\(949\) −20.0000 −0.649227
\(950\) −4.00000 −0.129777
\(951\) −30.0000 −0.972817
\(952\) 1.00000 0.0324102
\(953\) 56.0000 1.81402 0.907009 0.421111i \(-0.138360\pi\)
0.907009 + 0.421111i \(0.138360\pi\)
\(954\) 10.0000 0.323762
\(955\) −15.0000 −0.485389
\(956\) −10.0000 −0.323423
\(957\) 0 0
\(958\) 0 0
\(959\) −18.0000 −0.581250
\(960\) 3.00000 0.0968246
\(961\) 69.0000 2.22581
\(962\) −10.0000 −0.322413
\(963\) −5.00000 −0.161123
\(964\) 15.0000 0.483117
\(965\) 36.0000 1.15888
\(966\) −1.00000 −0.0321745
\(967\) −6.00000 −0.192947 −0.0964735 0.995336i \(-0.530756\pi\)
−0.0964735 + 0.995336i \(0.530756\pi\)
\(968\) −11.0000 −0.353553
\(969\) −1.00000 −0.0321246
\(970\) 0 0
\(971\) 24.0000 0.770197 0.385098 0.922876i \(-0.374168\pi\)
0.385098 + 0.922876i \(0.374168\pi\)
\(972\) 1.00000 0.0320750
\(973\) −18.0000 −0.577054
\(974\) 25.0000 0.801052
\(975\) −8.00000 −0.256205
\(976\) 10.0000 0.320092
\(977\) −42.0000 −1.34370 −0.671850 0.740688i \(-0.734500\pi\)
−0.671850 + 0.740688i \(0.734500\pi\)
\(978\) 11.0000 0.351741
\(979\) 0 0
\(980\) −18.0000 −0.574989
\(981\) −4.00000 −0.127710
\(982\) 0 0
\(983\) 8.00000 0.255160 0.127580 0.991828i \(-0.459279\pi\)
0.127580 + 0.991828i \(0.459279\pi\)
\(984\) 7.00000 0.223152
\(985\) 3.00000 0.0955879
\(986\) 1.00000 0.0318465
\(987\) −13.0000 −0.413795
\(988\) 2.00000 0.0636285
\(989\) 11.0000 0.349780
\(990\) 0 0
\(991\) −35.0000 −1.11181 −0.555906 0.831245i \(-0.687628\pi\)
−0.555906 + 0.831245i \(0.687628\pi\)
\(992\) 10.0000 0.317500
\(993\) 11.0000 0.349074
\(994\) 10.0000 0.317181
\(995\) 12.0000 0.380426
\(996\) 8.00000 0.253490
\(997\) 21.0000 0.665077 0.332538 0.943090i \(-0.392095\pi\)
0.332538 + 0.943090i \(0.392095\pi\)
\(998\) −24.0000 −0.759707
\(999\) 5.00000 0.158193
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 \(a_p\))