Properties

Label 18.4.a.a.1.1
Level 18
Weight 4
Character 18.1
Self dual Yes
Analytic conductor 1.062
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 18.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.0620343801\)
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 \(\chi\) = 18.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} +4.00000 q^{4} -6.00000 q^{5} -16.0000 q^{7} +8.00000 q^{8} +O(q^{10})\) \(q+2.00000 q^{2} +4.00000 q^{4} -6.00000 q^{5} -16.0000 q^{7} +8.00000 q^{8} -12.0000 q^{10} -12.0000 q^{11} +38.0000 q^{13} -32.0000 q^{14} +16.0000 q^{16} +126.000 q^{17} +20.0000 q^{19} -24.0000 q^{20} -24.0000 q^{22} -168.000 q^{23} -89.0000 q^{25} +76.0000 q^{26} -64.0000 q^{28} -30.0000 q^{29} -88.0000 q^{31} +32.0000 q^{32} +252.000 q^{34} +96.0000 q^{35} +254.000 q^{37} +40.0000 q^{38} -48.0000 q^{40} -42.0000 q^{41} -52.0000 q^{43} -48.0000 q^{44} -336.000 q^{46} +96.0000 q^{47} -87.0000 q^{49} -178.000 q^{50} +152.000 q^{52} -198.000 q^{53} +72.0000 q^{55} -128.000 q^{56} -60.0000 q^{58} +660.000 q^{59} -538.000 q^{61} -176.000 q^{62} +64.0000 q^{64} -228.000 q^{65} +884.000 q^{67} +504.000 q^{68} +192.000 q^{70} -792.000 q^{71} +218.000 q^{73} +508.000 q^{74} +80.0000 q^{76} +192.000 q^{77} -520.000 q^{79} -96.0000 q^{80} -84.0000 q^{82} +492.000 q^{83} -756.000 q^{85} -104.000 q^{86} -96.0000 q^{88} -810.000 q^{89} -608.000 q^{91} -672.000 q^{92} +192.000 q^{94} -120.000 q^{95} +1154.00 q^{97} -174.000 q^{98} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 0.707107
\(3\) 0 0
\(4\) 4.00000 0.500000
\(5\) −6.00000 −0.536656 −0.268328 0.963328i \(-0.586471\pi\)
−0.268328 + 0.963328i \(0.586471\pi\)
\(6\) 0 0
\(7\) −16.0000 −0.863919 −0.431959 0.901893i \(-0.642178\pi\)
−0.431959 + 0.901893i \(0.642178\pi\)
\(8\) 8.00000 0.353553
\(9\) 0 0
\(10\) −12.0000 −0.379473
\(11\) −12.0000 −0.328921 −0.164461 0.986384i \(-0.552588\pi\)
−0.164461 + 0.986384i \(0.552588\pi\)
\(12\) 0 0
\(13\) 38.0000 0.810716 0.405358 0.914158i \(-0.367147\pi\)
0.405358 + 0.914158i \(0.367147\pi\)
\(14\) −32.0000 −0.610883
\(15\) 0 0
\(16\) 16.0000 0.250000
\(17\) 126.000 1.79762 0.898808 0.438342i \(-0.144434\pi\)
0.898808 + 0.438342i \(0.144434\pi\)
\(18\) 0 0
\(19\) 20.0000 0.241490 0.120745 0.992684i \(-0.461472\pi\)
0.120745 + 0.992684i \(0.461472\pi\)
\(20\) −24.0000 −0.268328
\(21\) 0 0
\(22\) −24.0000 −0.232583
\(23\) −168.000 −1.52306 −0.761531 0.648129i \(-0.775552\pi\)
−0.761531 + 0.648129i \(0.775552\pi\)
\(24\) 0 0
\(25\) −89.0000 −0.712000
\(26\) 76.0000 0.573263
\(27\) 0 0
\(28\) −64.0000 −0.431959
\(29\) −30.0000 −0.192099 −0.0960493 0.995377i \(-0.530621\pi\)
−0.0960493 + 0.995377i \(0.530621\pi\)
\(30\) 0 0
\(31\) −88.0000 −0.509847 −0.254924 0.966961i \(-0.582050\pi\)
−0.254924 + 0.966961i \(0.582050\pi\)
\(32\) 32.0000 0.176777
\(33\) 0 0
\(34\) 252.000 1.27111
\(35\) 96.0000 0.463627
\(36\) 0 0
\(37\) 254.000 1.12858 0.564288 0.825578i \(-0.309151\pi\)
0.564288 + 0.825578i \(0.309151\pi\)
\(38\) 40.0000 0.170759
\(39\) 0 0
\(40\) −48.0000 −0.189737
\(41\) −42.0000 −0.159983 −0.0799914 0.996796i \(-0.525489\pi\)
−0.0799914 + 0.996796i \(0.525489\pi\)
\(42\) 0 0
\(43\) −52.0000 −0.184417 −0.0922084 0.995740i \(-0.529393\pi\)
−0.0922084 + 0.995740i \(0.529393\pi\)
\(44\) −48.0000 −0.164461
\(45\) 0 0
\(46\) −336.000 −1.07697
\(47\) 96.0000 0.297937 0.148969 0.988842i \(-0.452405\pi\)
0.148969 + 0.988842i \(0.452405\pi\)
\(48\) 0 0
\(49\) −87.0000 −0.253644
\(50\) −178.000 −0.503460
\(51\) 0 0
\(52\) 152.000 0.405358
\(53\) −198.000 −0.513158 −0.256579 0.966523i \(-0.582595\pi\)
−0.256579 + 0.966523i \(0.582595\pi\)
\(54\) 0 0
\(55\) 72.0000 0.176518
\(56\) −128.000 −0.305441
\(57\) 0 0
\(58\) −60.0000 −0.135834
\(59\) 660.000 1.45635 0.728175 0.685391i \(-0.240369\pi\)
0.728175 + 0.685391i \(0.240369\pi\)
\(60\) 0 0
\(61\) −538.000 −1.12924 −0.564622 0.825350i \(-0.690978\pi\)
−0.564622 + 0.825350i \(0.690978\pi\)
\(62\) −176.000 −0.360516
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −228.000 −0.435076
\(66\) 0 0
\(67\) 884.000 1.61191 0.805954 0.591979i \(-0.201653\pi\)
0.805954 + 0.591979i \(0.201653\pi\)
\(68\) 504.000 0.898808
\(69\) 0 0
\(70\) 192.000 0.327834
\(71\) −792.000 −1.32385 −0.661923 0.749572i \(-0.730260\pi\)
−0.661923 + 0.749572i \(0.730260\pi\)
\(72\) 0 0
\(73\) 218.000 0.349520 0.174760 0.984611i \(-0.444085\pi\)
0.174760 + 0.984611i \(0.444085\pi\)
\(74\) 508.000 0.798024
\(75\) 0 0
\(76\) 80.0000 0.120745
\(77\) 192.000 0.284161
\(78\) 0 0
\(79\) −520.000 −0.740564 −0.370282 0.928919i \(-0.620739\pi\)
−0.370282 + 0.928919i \(0.620739\pi\)
\(80\) −96.0000 −0.134164
\(81\) 0 0
\(82\) −84.0000 −0.113125
\(83\) 492.000 0.650651 0.325325 0.945602i \(-0.394526\pi\)
0.325325 + 0.945602i \(0.394526\pi\)
\(84\) 0 0
\(85\) −756.000 −0.964703
\(86\) −104.000 −0.130402
\(87\) 0 0
\(88\) −96.0000 −0.116291
\(89\) −810.000 −0.964717 −0.482359 0.875974i \(-0.660220\pi\)
−0.482359 + 0.875974i \(0.660220\pi\)
\(90\) 0 0
\(91\) −608.000 −0.700393
\(92\) −672.000 −0.761531
\(93\) 0 0
\(94\) 192.000 0.210673
\(95\) −120.000 −0.129597
\(96\) 0 0
\(97\) 1154.00 1.20795 0.603974 0.797004i \(-0.293583\pi\)
0.603974 + 0.797004i \(0.293583\pi\)
\(98\) −174.000 −0.179354
\(99\) 0 0
\(100\) −356.000 −0.356000
\(101\) 618.000 0.608845 0.304422 0.952537i \(-0.401537\pi\)
0.304422 + 0.952537i \(0.401537\pi\)
\(102\) 0 0
\(103\) 128.000 0.122449 0.0612243 0.998124i \(-0.480499\pi\)
0.0612243 + 0.998124i \(0.480499\pi\)
\(104\) 304.000 0.286631
\(105\) 0 0
\(106\) −396.000 −0.362858
\(107\) 1476.00 1.33355 0.666777 0.745257i \(-0.267673\pi\)
0.666777 + 0.745257i \(0.267673\pi\)
\(108\) 0 0
\(109\) 1190.00 1.04570 0.522850 0.852425i \(-0.324869\pi\)
0.522850 + 0.852425i \(0.324869\pi\)
\(110\) 144.000 0.124817
\(111\) 0 0
\(112\) −256.000 −0.215980
\(113\) 462.000 0.384613 0.192307 0.981335i \(-0.438403\pi\)
0.192307 + 0.981335i \(0.438403\pi\)
\(114\) 0 0
\(115\) 1008.00 0.817361
\(116\) −120.000 −0.0960493
\(117\) 0 0
\(118\) 1320.00 1.02980
\(119\) −2016.00 −1.55300
\(120\) 0 0
\(121\) −1187.00 −0.891811
\(122\) −1076.00 −0.798496
\(123\) 0 0
\(124\) −352.000 −0.254924
\(125\) 1284.00 0.918756
\(126\) 0 0
\(127\) −2536.00 −1.77192 −0.885959 0.463763i \(-0.846499\pi\)
−0.885959 + 0.463763i \(0.846499\pi\)
\(128\) 128.000 0.0883883
\(129\) 0 0
\(130\) −456.000 −0.307645
\(131\) −2292.00 −1.52865 −0.764324 0.644832i \(-0.776927\pi\)
−0.764324 + 0.644832i \(0.776927\pi\)
\(132\) 0 0
\(133\) −320.000 −0.208628
\(134\) 1768.00 1.13979
\(135\) 0 0
\(136\) 1008.00 0.635554
\(137\) 726.000 0.452747 0.226374 0.974041i \(-0.427313\pi\)
0.226374 + 0.974041i \(0.427313\pi\)
\(138\) 0 0
\(139\) 380.000 0.231879 0.115939 0.993256i \(-0.463012\pi\)
0.115939 + 0.993256i \(0.463012\pi\)
\(140\) 384.000 0.231814
\(141\) 0 0
\(142\) −1584.00 −0.936101
\(143\) −456.000 −0.266662
\(144\) 0 0
\(145\) 180.000 0.103091
\(146\) 436.000 0.247148
\(147\) 0 0
\(148\) 1016.00 0.564288
\(149\) −1590.00 −0.874214 −0.437107 0.899410i \(-0.643997\pi\)
−0.437107 + 0.899410i \(0.643997\pi\)
\(150\) 0 0
\(151\) 2432.00 1.31068 0.655342 0.755332i \(-0.272524\pi\)
0.655342 + 0.755332i \(0.272524\pi\)
\(152\) 160.000 0.0853797
\(153\) 0 0
\(154\) 384.000 0.200932
\(155\) 528.000 0.273613
\(156\) 0 0
\(157\) 614.000 0.312118 0.156059 0.987748i \(-0.450121\pi\)
0.156059 + 0.987748i \(0.450121\pi\)
\(158\) −1040.00 −0.523658
\(159\) 0 0
\(160\) −192.000 −0.0948683
\(161\) 2688.00 1.31580
\(162\) 0 0
\(163\) −1852.00 −0.889938 −0.444969 0.895546i \(-0.646785\pi\)
−0.444969 + 0.895546i \(0.646785\pi\)
\(164\) −168.000 −0.0799914
\(165\) 0 0
\(166\) 984.000 0.460080
\(167\) 2136.00 0.989752 0.494876 0.868964i \(-0.335213\pi\)
0.494876 + 0.868964i \(0.335213\pi\)
\(168\) 0 0
\(169\) −753.000 −0.342740
\(170\) −1512.00 −0.682148
\(171\) 0 0
\(172\) −208.000 −0.0922084
\(173\) −1758.00 −0.772591 −0.386296 0.922375i \(-0.626246\pi\)
−0.386296 + 0.922375i \(0.626246\pi\)
\(174\) 0 0
\(175\) 1424.00 0.615110
\(176\) −192.000 −0.0822304
\(177\) 0 0
\(178\) −1620.00 −0.682158
\(179\) 540.000 0.225483 0.112742 0.993624i \(-0.464037\pi\)
0.112742 + 0.993624i \(0.464037\pi\)
\(180\) 0 0
\(181\) 1982.00 0.813928 0.406964 0.913444i \(-0.366588\pi\)
0.406964 + 0.913444i \(0.366588\pi\)
\(182\) −1216.00 −0.495252
\(183\) 0 0
\(184\) −1344.00 −0.538484
\(185\) −1524.00 −0.605658
\(186\) 0 0
\(187\) −1512.00 −0.591275
\(188\) 384.000 0.148969
\(189\) 0 0
\(190\) −240.000 −0.0916391
\(191\) 2688.00 1.01831 0.509154 0.860675i \(-0.329958\pi\)
0.509154 + 0.860675i \(0.329958\pi\)
\(192\) 0 0
\(193\) −2302.00 −0.858557 −0.429279 0.903172i \(-0.641232\pi\)
−0.429279 + 0.903172i \(0.641232\pi\)
\(194\) 2308.00 0.854148
\(195\) 0 0
\(196\) −348.000 −0.126822
\(197\) −4374.00 −1.58190 −0.790951 0.611880i \(-0.790414\pi\)
−0.790951 + 0.611880i \(0.790414\pi\)
\(198\) 0 0
\(199\) −1600.00 −0.569955 −0.284977 0.958534i \(-0.591986\pi\)
−0.284977 + 0.958534i \(0.591986\pi\)
\(200\) −712.000 −0.251730
\(201\) 0 0
\(202\) 1236.00 0.430518
\(203\) 480.000 0.165958
\(204\) 0 0
\(205\) 252.000 0.0858558
\(206\) 256.000 0.0865843
\(207\) 0 0
\(208\) 608.000 0.202679
\(209\) −240.000 −0.0794313
\(210\) 0 0
\(211\) 3332.00 1.08713 0.543565 0.839367i \(-0.317074\pi\)
0.543565 + 0.839367i \(0.317074\pi\)
\(212\) −792.000 −0.256579
\(213\) 0 0
\(214\) 2952.00 0.942965
\(215\) 312.000 0.0989685
\(216\) 0 0
\(217\) 1408.00 0.440467
\(218\) 2380.00 0.739422
\(219\) 0 0
\(220\) 288.000 0.0882589
\(221\) 4788.00 1.45736
\(222\) 0 0
\(223\) 2648.00 0.795171 0.397586 0.917565i \(-0.369848\pi\)
0.397586 + 0.917565i \(0.369848\pi\)
\(224\) −512.000 −0.152721
\(225\) 0 0
\(226\) 924.000 0.271963
\(227\) −2244.00 −0.656121 −0.328061 0.944657i \(-0.606395\pi\)
−0.328061 + 0.944657i \(0.606395\pi\)
\(228\) 0 0
\(229\) −5650.00 −1.63040 −0.815202 0.579177i \(-0.803374\pi\)
−0.815202 + 0.579177i \(0.803374\pi\)
\(230\) 2016.00 0.577961
\(231\) 0 0
\(232\) −240.000 −0.0679171
\(233\) −4698.00 −1.32093 −0.660464 0.750858i \(-0.729640\pi\)
−0.660464 + 0.750858i \(0.729640\pi\)
\(234\) 0 0
\(235\) −576.000 −0.159890
\(236\) 2640.00 0.728175
\(237\) 0 0
\(238\) −4032.00 −1.09813
\(239\) 1200.00 0.324776 0.162388 0.986727i \(-0.448080\pi\)
0.162388 + 0.986727i \(0.448080\pi\)
\(240\) 0 0
\(241\) −718.000 −0.191911 −0.0959553 0.995386i \(-0.530591\pi\)
−0.0959553 + 0.995386i \(0.530591\pi\)
\(242\) −2374.00 −0.630605
\(243\) 0 0
\(244\) −2152.00 −0.564622
\(245\) 522.000 0.136120
\(246\) 0 0
\(247\) 760.000 0.195780
\(248\) −704.000 −0.180258
\(249\) 0 0
\(250\) 2568.00 0.649658
\(251\) −6012.00 −1.51185 −0.755924 0.654659i \(-0.772812\pi\)
−0.755924 + 0.654659i \(0.772812\pi\)
\(252\) 0 0
\(253\) 2016.00 0.500968
\(254\) −5072.00 −1.25294
\(255\) 0 0
\(256\) 256.000 0.0625000
\(257\) 2046.00 0.496599 0.248300 0.968683i \(-0.420128\pi\)
0.248300 + 0.968683i \(0.420128\pi\)
\(258\) 0 0
\(259\) −4064.00 −0.974999
\(260\) −912.000 −0.217538
\(261\) 0 0
\(262\) −4584.00 −1.08092
\(263\) 6072.00 1.42363 0.711817 0.702365i \(-0.247873\pi\)
0.711817 + 0.702365i \(0.247873\pi\)
\(264\) 0 0
\(265\) 1188.00 0.275390
\(266\) −640.000 −0.147522
\(267\) 0 0
\(268\) 3536.00 0.805954
\(269\) 6930.00 1.57074 0.785371 0.619025i \(-0.212472\pi\)
0.785371 + 0.619025i \(0.212472\pi\)
\(270\) 0 0
\(271\) 1352.00 0.303056 0.151528 0.988453i \(-0.451581\pi\)
0.151528 + 0.988453i \(0.451581\pi\)
\(272\) 2016.00 0.449404
\(273\) 0 0
\(274\) 1452.00 0.320141
\(275\) 1068.00 0.234192
\(276\) 0 0
\(277\) −1186.00 −0.257256 −0.128628 0.991693i \(-0.541057\pi\)
−0.128628 + 0.991693i \(0.541057\pi\)
\(278\) 760.000 0.163963
\(279\) 0 0
\(280\) 768.000 0.163917
\(281\) −2442.00 −0.518425 −0.259213 0.965820i \(-0.583463\pi\)
−0.259213 + 0.965820i \(0.583463\pi\)
\(282\) 0 0
\(283\) 2828.00 0.594018 0.297009 0.954875i \(-0.404011\pi\)
0.297009 + 0.954875i \(0.404011\pi\)
\(284\) −3168.00 −0.661923
\(285\) 0 0
\(286\) −912.000 −0.188558
\(287\) 672.000 0.138212
\(288\) 0 0
\(289\) 10963.0 2.23143
\(290\) 360.000 0.0728963
\(291\) 0 0
\(292\) 872.000 0.174760
\(293\) −4758.00 −0.948687 −0.474344 0.880340i \(-0.657315\pi\)
−0.474344 + 0.880340i \(0.657315\pi\)
\(294\) 0 0
\(295\) −3960.00 −0.781560
\(296\) 2032.00 0.399012
\(297\) 0 0
\(298\) −3180.00 −0.618163
\(299\) −6384.00 −1.23477
\(300\) 0 0
\(301\) 832.000 0.159321
\(302\) 4864.00 0.926794
\(303\) 0 0
\(304\) 320.000 0.0603726
\(305\) 3228.00 0.606016
\(306\) 0 0
\(307\) −8476.00 −1.57574 −0.787868 0.615844i \(-0.788815\pi\)
−0.787868 + 0.615844i \(0.788815\pi\)
\(308\) 768.000 0.142081
\(309\) 0 0
\(310\) 1056.00 0.193473
\(311\) −4632.00 −0.844555 −0.422278 0.906467i \(-0.638769\pi\)
−0.422278 + 0.906467i \(0.638769\pi\)
\(312\) 0 0
\(313\) −4822.00 −0.870785 −0.435392 0.900241i \(-0.643390\pi\)
−0.435392 + 0.900241i \(0.643390\pi\)
\(314\) 1228.00 0.220701
\(315\) 0 0
\(316\) −2080.00 −0.370282
\(317\) 3426.00 0.607014 0.303507 0.952829i \(-0.401842\pi\)
0.303507 + 0.952829i \(0.401842\pi\)
\(318\) 0 0
\(319\) 360.000 0.0631854
\(320\) −384.000 −0.0670820
\(321\) 0 0
\(322\) 5376.00 0.930412
\(323\) 2520.00 0.434107
\(324\) 0 0
\(325\) −3382.00 −0.577230
\(326\) −3704.00 −0.629281
\(327\) 0 0
\(328\) −336.000 −0.0565625
\(329\) −1536.00 −0.257393
\(330\) 0 0
\(331\) −2788.00 −0.462968 −0.231484 0.972839i \(-0.574358\pi\)
−0.231484 + 0.972839i \(0.574358\pi\)
\(332\) 1968.00 0.325325
\(333\) 0 0
\(334\) 4272.00 0.699861
\(335\) −5304.00 −0.865040
\(336\) 0 0
\(337\) 434.000 0.0701528 0.0350764 0.999385i \(-0.488833\pi\)
0.0350764 + 0.999385i \(0.488833\pi\)
\(338\) −1506.00 −0.242354
\(339\) 0 0
\(340\) −3024.00 −0.482351
\(341\) 1056.00 0.167700
\(342\) 0 0
\(343\) 6880.00 1.08305
\(344\) −416.000 −0.0652012
\(345\) 0 0
\(346\) −3516.00 −0.546304
\(347\) −6684.00 −1.03405 −0.517026 0.855970i \(-0.672961\pi\)
−0.517026 + 0.855970i \(0.672961\pi\)
\(348\) 0 0
\(349\) 2630.00 0.403383 0.201692 0.979449i \(-0.435356\pi\)
0.201692 + 0.979449i \(0.435356\pi\)
\(350\) 2848.00 0.434949
\(351\) 0 0
\(352\) −384.000 −0.0581456
\(353\) 7422.00 1.11907 0.559537 0.828805i \(-0.310979\pi\)
0.559537 + 0.828805i \(0.310979\pi\)
\(354\) 0 0
\(355\) 4752.00 0.710451
\(356\) −3240.00 −0.482359
\(357\) 0 0
\(358\) 1080.00 0.159441
\(359\) 10440.0 1.53482 0.767412 0.641154i \(-0.221544\pi\)
0.767412 + 0.641154i \(0.221544\pi\)
\(360\) 0 0
\(361\) −6459.00 −0.941682
\(362\) 3964.00 0.575534
\(363\) 0 0
\(364\) −2432.00 −0.350196
\(365\) −1308.00 −0.187572
\(366\) 0 0
\(367\) 10424.0 1.48264 0.741319 0.671153i \(-0.234200\pi\)
0.741319 + 0.671153i \(0.234200\pi\)
\(368\) −2688.00 −0.380765
\(369\) 0 0
\(370\) −3048.00 −0.428265
\(371\) 3168.00 0.443327
\(372\) 0 0
\(373\) 3278.00 0.455036 0.227518 0.973774i \(-0.426939\pi\)
0.227518 + 0.973774i \(0.426939\pi\)
\(374\) −3024.00 −0.418094
\(375\) 0 0
\(376\) 768.000 0.105337
\(377\) −1140.00 −0.155737
\(378\) 0 0
\(379\) 6140.00 0.832165 0.416083 0.909327i \(-0.363403\pi\)
0.416083 + 0.909327i \(0.363403\pi\)
\(380\) −480.000 −0.0647986
\(381\) 0 0
\(382\) 5376.00 0.720053
\(383\) 3072.00 0.409848 0.204924 0.978778i \(-0.434305\pi\)
0.204924 + 0.978778i \(0.434305\pi\)
\(384\) 0 0
\(385\) −1152.00 −0.152497
\(386\) −4604.00 −0.607092
\(387\) 0 0
\(388\) 4616.00 0.603974
\(389\) −6150.00 −0.801587 −0.400794 0.916168i \(-0.631266\pi\)
−0.400794 + 0.916168i \(0.631266\pi\)
\(390\) 0 0
\(391\) −21168.0 −2.73788
\(392\) −696.000 −0.0896768
\(393\) 0 0
\(394\) −8748.00 −1.11857
\(395\) 3120.00 0.397428
\(396\) 0 0
\(397\) −106.000 −0.0134005 −0.00670024 0.999978i \(-0.502133\pi\)
−0.00670024 + 0.999978i \(0.502133\pi\)
\(398\) −3200.00 −0.403019
\(399\) 0 0
\(400\) −1424.00 −0.178000
\(401\) 1758.00 0.218929 0.109464 0.993991i \(-0.465086\pi\)
0.109464 + 0.993991i \(0.465086\pi\)
\(402\) 0 0
\(403\) −3344.00 −0.413341
\(404\) 2472.00 0.304422
\(405\) 0 0
\(406\) 960.000 0.117350
\(407\) −3048.00 −0.371213
\(408\) 0 0
\(409\) −3670.00 −0.443691 −0.221846 0.975082i \(-0.571208\pi\)
−0.221846 + 0.975082i \(0.571208\pi\)
\(410\) 504.000 0.0607092
\(411\) 0 0
\(412\) 512.000 0.0612243
\(413\) −10560.0 −1.25817
\(414\) 0 0
\(415\) −2952.00 −0.349176
\(416\) 1216.00 0.143316
\(417\) 0 0
\(418\) −480.000 −0.0561664
\(419\) 9660.00 1.12631 0.563153 0.826353i \(-0.309588\pi\)
0.563153 + 0.826353i \(0.309588\pi\)
\(420\) 0 0
\(421\) 8462.00 0.979602 0.489801 0.871834i \(-0.337069\pi\)
0.489801 + 0.871834i \(0.337069\pi\)
\(422\) 6664.00 0.768717
\(423\) 0 0
\(424\) −1584.00 −0.181429
\(425\) −11214.0 −1.27990
\(426\) 0 0
\(427\) 8608.00 0.975575
\(428\) 5904.00 0.666777
\(429\) 0 0
\(430\) 624.000 0.0699813
\(431\) −9792.00 −1.09435 −0.547174 0.837019i \(-0.684296\pi\)
−0.547174 + 0.837019i \(0.684296\pi\)
\(432\) 0 0
\(433\) −7342.00 −0.814859 −0.407430 0.913237i \(-0.633575\pi\)
−0.407430 + 0.913237i \(0.633575\pi\)
\(434\) 2816.00 0.311457
\(435\) 0 0
\(436\) 4760.00 0.522850
\(437\) −3360.00 −0.367805
\(438\) 0 0
\(439\) 10640.0 1.15676 0.578382 0.815766i \(-0.303684\pi\)
0.578382 + 0.815766i \(0.303684\pi\)
\(440\) 576.000 0.0624085
\(441\) 0 0
\(442\) 9576.00 1.03051
\(443\) 17412.0 1.86742 0.933712 0.358024i \(-0.116549\pi\)
0.933712 + 0.358024i \(0.116549\pi\)
\(444\) 0 0
\(445\) 4860.00 0.517722
\(446\) 5296.00 0.562271
\(447\) 0 0
\(448\) −1024.00 −0.107990
\(449\) 1710.00 0.179732 0.0898662 0.995954i \(-0.471356\pi\)
0.0898662 + 0.995954i \(0.471356\pi\)
\(450\) 0 0
\(451\) 504.000 0.0526218
\(452\) 1848.00 0.192307
\(453\) 0 0
\(454\) −4488.00 −0.463948
\(455\) 3648.00 0.375870
\(456\) 0 0
\(457\) −646.000 −0.0661239 −0.0330619 0.999453i \(-0.510526\pi\)
−0.0330619 + 0.999453i \(0.510526\pi\)
\(458\) −11300.0 −1.15287
\(459\) 0 0
\(460\) 4032.00 0.408680
\(461\) 6018.00 0.607996 0.303998 0.952673i \(-0.401678\pi\)
0.303998 + 0.952673i \(0.401678\pi\)
\(462\) 0 0
\(463\) −6712.00 −0.673722 −0.336861 0.941554i \(-0.609365\pi\)
−0.336861 + 0.941554i \(0.609365\pi\)
\(464\) −480.000 −0.0480247
\(465\) 0 0
\(466\) −9396.00 −0.934037
\(467\) −5364.00 −0.531512 −0.265756 0.964040i \(-0.585622\pi\)
−0.265756 + 0.964040i \(0.585622\pi\)
\(468\) 0 0
\(469\) −14144.0 −1.39256
\(470\) −1152.00 −0.113059
\(471\) 0 0
\(472\) 5280.00 0.514898
\(473\) 624.000 0.0606587
\(474\) 0 0
\(475\) −1780.00 −0.171941
\(476\) −8064.00 −0.776498
\(477\) 0 0
\(478\) 2400.00 0.229652
\(479\) −9840.00 −0.938624 −0.469312 0.883032i \(-0.655498\pi\)
−0.469312 + 0.883032i \(0.655498\pi\)
\(480\) 0 0
\(481\) 9652.00 0.914955
\(482\) −1436.00 −0.135701
\(483\) 0 0
\(484\) −4748.00 −0.445905
\(485\) −6924.00 −0.648253
\(486\) 0 0
\(487\) 1424.00 0.132500 0.0662501 0.997803i \(-0.478896\pi\)
0.0662501 + 0.997803i \(0.478896\pi\)
\(488\) −4304.00 −0.399248
\(489\) 0 0
\(490\) 1044.00 0.0962513
\(491\) 4548.00 0.418021 0.209011 0.977913i \(-0.432976\pi\)
0.209011 + 0.977913i \(0.432976\pi\)
\(492\) 0 0
\(493\) −3780.00 −0.345320
\(494\) 1520.00 0.138437
\(495\) 0 0
\(496\) −1408.00 −0.127462
\(497\) 12672.0 1.14370
\(498\) 0 0
\(499\) 6500.00 0.583126 0.291563 0.956552i \(-0.405825\pi\)
0.291563 + 0.956552i \(0.405825\pi\)
\(500\) 5136.00 0.459378
\(501\) 0 0
\(502\) −12024.0 −1.06904
\(503\) −12168.0 −1.07862 −0.539308 0.842108i \(-0.681314\pi\)
−0.539308 + 0.842108i \(0.681314\pi\)
\(504\) 0 0
\(505\) −3708.00 −0.326740
\(506\) 4032.00 0.354238
\(507\) 0 0
\(508\) −10144.0 −0.885959
\(509\) 21090.0 1.83654 0.918269 0.395957i \(-0.129587\pi\)
0.918269 + 0.395957i \(0.129587\pi\)
\(510\) 0 0
\(511\) −3488.00 −0.301957
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) 4092.00 0.351149
\(515\) −768.000 −0.0657129
\(516\) 0 0
\(517\) −1152.00 −0.0979979
\(518\) −8128.00 −0.689428
\(519\) 0 0
\(520\) −1824.00 −0.153822
\(521\) 5238.00 0.440462 0.220231 0.975448i \(-0.429319\pi\)
0.220231 + 0.975448i \(0.429319\pi\)
\(522\) 0 0
\(523\) 8588.00 0.718025 0.359012 0.933333i \(-0.383114\pi\)
0.359012 + 0.933333i \(0.383114\pi\)
\(524\) −9168.00 −0.764324
\(525\) 0 0
\(526\) 12144.0 1.00666
\(527\) −11088.0 −0.916510
\(528\) 0 0
\(529\) 16057.0 1.31972
\(530\) 2376.00 0.194730
\(531\) 0 0
\(532\) −1280.00 −0.104314
\(533\) −1596.00 −0.129701
\(534\) 0 0
\(535\) −8856.00 −0.715660
\(536\) 7072.00 0.569895
\(537\) 0 0
\(538\) 13860.0 1.11068
\(539\) 1044.00 0.0834291
\(540\) 0 0
\(541\) 3062.00 0.243338 0.121669 0.992571i \(-0.461175\pi\)
0.121669 + 0.992571i \(0.461175\pi\)
\(542\) 2704.00 0.214293
\(543\) 0 0
\(544\) 4032.00 0.317777
\(545\) −7140.00 −0.561182
\(546\) 0 0
\(547\) −8476.00 −0.662537 −0.331268 0.943537i \(-0.607477\pi\)
−0.331268 + 0.943537i \(0.607477\pi\)
\(548\) 2904.00 0.226374
\(549\) 0 0
\(550\) 2136.00 0.165599
\(551\) −600.000 −0.0463899
\(552\) 0 0
\(553\) 8320.00 0.639787
\(554\) −2372.00 −0.181907
\(555\) 0 0
\(556\) 1520.00 0.115939
\(557\) 12546.0 0.954383 0.477191 0.878799i \(-0.341655\pi\)
0.477191 + 0.878799i \(0.341655\pi\)
\(558\) 0 0
\(559\) −1976.00 −0.149510
\(560\) 1536.00 0.115907
\(561\) 0 0
\(562\) −4884.00 −0.366582
\(563\) 12.0000 0.000898294 0 0.000449147 1.00000i \(-0.499857\pi\)
0.000449147 1.00000i \(0.499857\pi\)
\(564\) 0 0
\(565\) −2772.00 −0.206405
\(566\) 5656.00 0.420034
\(567\) 0 0
\(568\) −6336.00 −0.468050
\(569\) −19290.0 −1.42123 −0.710614 0.703582i \(-0.751583\pi\)
−0.710614 + 0.703582i \(0.751583\pi\)
\(570\) 0 0
\(571\) −12148.0 −0.890329 −0.445165 0.895449i \(-0.646855\pi\)
−0.445165 + 0.895449i \(0.646855\pi\)
\(572\) −1824.00 −0.133331
\(573\) 0 0
\(574\) 1344.00 0.0977308
\(575\) 14952.0 1.08442
\(576\) 0 0
\(577\) −10366.0 −0.747907 −0.373953 0.927447i \(-0.621998\pi\)
−0.373953 + 0.927447i \(0.621998\pi\)
\(578\) 21926.0 1.57786
\(579\) 0 0
\(580\) 720.000 0.0515455
\(581\) −7872.00 −0.562109
\(582\) 0 0
\(583\) 2376.00 0.168789
\(584\) 1744.00 0.123574
\(585\) 0 0
\(586\) −9516.00 −0.670823
\(587\) −7644.00 −0.537482 −0.268741 0.963213i \(-0.586607\pi\)
−0.268741 + 0.963213i \(0.586607\pi\)
\(588\) 0 0
\(589\) −1760.00 −0.123123
\(590\) −7920.00 −0.552646
\(591\) 0 0
\(592\) 4064.00 0.282144
\(593\) −8658.00 −0.599564 −0.299782 0.954008i \(-0.596914\pi\)
−0.299782 + 0.954008i \(0.596914\pi\)
\(594\) 0 0
\(595\) 12096.0 0.833425
\(596\) −6360.00 −0.437107
\(597\) 0 0
\(598\) −12768.0 −0.873114
\(599\) −25800.0 −1.75987 −0.879933 0.475098i \(-0.842413\pi\)
−0.879933 + 0.475098i \(0.842413\pi\)
\(600\) 0 0
\(601\) 16202.0 1.09966 0.549828 0.835278i \(-0.314693\pi\)
0.549828 + 0.835278i \(0.314693\pi\)
\(602\) 1664.00 0.112657
\(603\) 0 0
\(604\) 9728.00 0.655342
\(605\) 7122.00 0.478596
\(606\) 0 0
\(607\) −24136.0 −1.61392 −0.806960 0.590605i \(-0.798889\pi\)
−0.806960 + 0.590605i \(0.798889\pi\)
\(608\) 640.000 0.0426898
\(609\) 0 0
\(610\) 6456.00 0.428518
\(611\) 3648.00 0.241542
\(612\) 0 0
\(613\) −4642.00 −0.305854 −0.152927 0.988237i \(-0.548870\pi\)
−0.152927 + 0.988237i \(0.548870\pi\)
\(614\) −16952.0 −1.11421
\(615\) 0 0
\(616\) 1536.00 0.100466
\(617\) 6726.00 0.438863 0.219432 0.975628i \(-0.429580\pi\)
0.219432 + 0.975628i \(0.429580\pi\)
\(618\) 0 0
\(619\) −21220.0 −1.37787 −0.688937 0.724821i \(-0.741922\pi\)
−0.688937 + 0.724821i \(0.741922\pi\)
\(620\) 2112.00 0.136806
\(621\) 0 0
\(622\) −9264.00 −0.597191
\(623\) 12960.0 0.833437
\(624\) 0 0
\(625\) 3421.00 0.218944
\(626\) −9644.00 −0.615738
\(627\) 0 0
\(628\) 2456.00 0.156059
\(629\) 32004.0 2.02875
\(630\) 0 0
\(631\) 29792.0 1.87956 0.939779 0.341783i \(-0.111031\pi\)
0.939779 + 0.341783i \(0.111031\pi\)
\(632\) −4160.00 −0.261829
\(633\) 0 0
\(634\) 6852.00 0.429223
\(635\) 15216.0 0.950911
\(636\) 0 0
\(637\) −3306.00 −0.205633
\(638\) 720.000 0.0446788
\(639\) 0 0
\(640\) −768.000 −0.0474342
\(641\) 10158.0 0.625923 0.312962 0.949766i \(-0.398679\pi\)
0.312962 + 0.949766i \(0.398679\pi\)
\(642\) 0 0
\(643\) 29828.0 1.82940 0.914698 0.404138i \(-0.132429\pi\)
0.914698 + 0.404138i \(0.132429\pi\)
\(644\) 10752.0 0.657901
\(645\) 0 0
\(646\) 5040.00 0.306960
\(647\) −1944.00 −0.118124 −0.0590622 0.998254i \(-0.518811\pi\)
−0.0590622 + 0.998254i \(0.518811\pi\)
\(648\) 0 0
\(649\) −7920.00 −0.479025
\(650\) −6764.00 −0.408163
\(651\) 0 0
\(652\) −7408.00 −0.444969
\(653\) −26718.0 −1.60116 −0.800579 0.599227i \(-0.795475\pi\)
−0.800579 + 0.599227i \(0.795475\pi\)
\(654\) 0 0
\(655\) 13752.0 0.820359
\(656\) −672.000 −0.0399957
\(657\) 0 0
\(658\) −3072.00 −0.182005
\(659\) −4260.00 −0.251815 −0.125907 0.992042i \(-0.540184\pi\)
−0.125907 + 0.992042i \(0.540184\pi\)
\(660\) 0 0
\(661\) 22862.0 1.34528 0.672639 0.739971i \(-0.265161\pi\)
0.672639 + 0.739971i \(0.265161\pi\)
\(662\) −5576.00 −0.327368
\(663\) 0 0
\(664\) 3936.00 0.230040
\(665\) 1920.00 0.111962
\(666\) 0 0
\(667\) 5040.00 0.292578
\(668\) 8544.00 0.494876
\(669\) 0 0
\(670\) −10608.0 −0.611676
\(671\) 6456.00 0.371432
\(672\) 0 0
\(673\) −32542.0 −1.86390 −0.931948 0.362592i \(-0.881892\pi\)
−0.931948 + 0.362592i \(0.881892\pi\)
\(674\) 868.000 0.0496055
\(675\) 0 0
\(676\) −3012.00 −0.171370
\(677\) −14214.0 −0.806925 −0.403463 0.914996i \(-0.632193\pi\)
−0.403463 + 0.914996i \(0.632193\pi\)
\(678\) 0 0
\(679\) −18464.0 −1.04357
\(680\) −6048.00 −0.341074
\(681\) 0 0
\(682\) 2112.00 0.118582
\(683\) 7092.00 0.397317 0.198659 0.980069i \(-0.436341\pi\)
0.198659 + 0.980069i \(0.436341\pi\)
\(684\) 0 0
\(685\) −4356.00 −0.242970
\(686\) 13760.0 0.765830
\(687\) 0 0
\(688\) −832.000 −0.0461042
\(689\) −7524.00 −0.416026
\(690\) 0 0
\(691\) −13228.0 −0.728244 −0.364122 0.931351i \(-0.618631\pi\)
−0.364122 + 0.931351i \(0.618631\pi\)
\(692\) −7032.00 −0.386296
\(693\) 0 0
\(694\) −13368.0 −0.731185
\(695\) −2280.00 −0.124439
\(696\) 0 0
\(697\) −5292.00 −0.287588
\(698\) 5260.00 0.285235
\(699\) 0 0
\(700\) 5696.00 0.307555
\(701\) −28062.0 −1.51196 −0.755982 0.654592i \(-0.772840\pi\)
−0.755982 + 0.654592i \(0.772840\pi\)
\(702\) 0 0
\(703\) 5080.00 0.272540
\(704\) −768.000 −0.0411152
\(705\) 0 0
\(706\) 14844.0 0.791305
\(707\) −9888.00 −0.525992
\(708\) 0 0
\(709\) −27250.0 −1.44343 −0.721717 0.692188i \(-0.756647\pi\)
−0.721717 + 0.692188i \(0.756647\pi\)
\(710\) 9504.00 0.502364
\(711\) 0 0
\(712\) −6480.00 −0.341079
\(713\) 14784.0 0.776529
\(714\) 0 0
\(715\) 2736.00 0.143106
\(716\) 2160.00 0.112742
\(717\) 0 0
\(718\) 20880.0 1.08529
\(719\) 14400.0 0.746912 0.373456 0.927648i \(-0.378173\pi\)
0.373456 + 0.927648i \(0.378173\pi\)
\(720\) 0 0
\(721\) −2048.00 −0.105786
\(722\) −12918.0 −0.665870
\(723\) 0 0
\(724\) 7928.00 0.406964
\(725\) 2670.00 0.136774
\(726\) 0 0
\(727\) 17984.0 0.917455 0.458727 0.888577i \(-0.348305\pi\)
0.458727 + 0.888577i \(0.348305\pi\)
\(728\) −4864.00 −0.247626
\(729\) 0 0
\(730\) −2616.00 −0.132634
\(731\) −6552.00 −0.331511
\(732\) 0 0
\(733\) 16598.0 0.836373 0.418186 0.908361i \(-0.362666\pi\)
0.418186 + 0.908361i \(0.362666\pi\)
\(734\) 20848.0 1.04838
\(735\) 0 0
\(736\) −5376.00 −0.269242
\(737\) −10608.0 −0.530191
\(738\) 0 0
\(739\) 1460.00 0.0726752 0.0363376 0.999340i \(-0.488431\pi\)
0.0363376 + 0.999340i \(0.488431\pi\)
\(740\) −6096.00 −0.302829
\(741\) 0 0
\(742\) 6336.00 0.313480
\(743\) 30072.0 1.48484 0.742419 0.669936i \(-0.233678\pi\)
0.742419 + 0.669936i \(0.233678\pi\)
\(744\) 0 0
\(745\) 9540.00 0.469152
\(746\) 6556.00 0.321759
\(747\) 0 0
\(748\) −6048.00 −0.295637
\(749\) −23616.0 −1.15208
\(750\) 0 0
\(751\) −18088.0 −0.878882 −0.439441 0.898271i \(-0.644823\pi\)
−0.439441 + 0.898271i \(0.644823\pi\)
\(752\) 1536.00 0.0744843
\(753\) 0 0
\(754\) −2280.00 −0.110123
\(755\) −14592.0 −0.703387
\(756\) 0 0
\(757\) 24734.0 1.18755 0.593773 0.804633i \(-0.297638\pi\)
0.593773 + 0.804633i \(0.297638\pi\)
\(758\) 12280.0 0.588430
\(759\) 0 0
\(760\) −960.000 −0.0458196
\(761\) 22278.0 1.06120 0.530602 0.847621i \(-0.321966\pi\)
0.530602 + 0.847621i \(0.321966\pi\)
\(762\) 0 0
\(763\) −19040.0 −0.903400
\(764\) 10752.0 0.509154
\(765\) 0 0
\(766\) 6144.00 0.289806
\(767\) 25080.0 1.18069
\(768\) 0 0
\(769\) 16130.0 0.756388 0.378194 0.925726i \(-0.376545\pi\)
0.378194 + 0.925726i \(0.376545\pi\)
\(770\) −2304.00 −0.107832
\(771\) 0 0
\(772\) −9208.00 −0.429279
\(773\) −29718.0 −1.38277 −0.691386 0.722486i \(-0.742999\pi\)
−0.691386 + 0.722486i \(0.742999\pi\)
\(774\) 0 0
\(775\) 7832.00 0.363011
\(776\) 9232.00 0.427074
\(777\) 0 0
\(778\) −12300.0 −0.566808
\(779\) −840.000 −0.0386343
\(780\) 0 0
\(781\) 9504.00 0.435442
\(782\) −42336.0 −1.93597
\(783\) 0 0
\(784\) −1392.00 −0.0634111
\(785\) −3684.00 −0.167500
\(786\) 0 0
\(787\) 9524.00 0.431377 0.215689 0.976462i \(-0.430800\pi\)
0.215689 + 0.976462i \(0.430800\pi\)
\(788\) −17496.0 −0.790951
\(789\) 0 0
\(790\) 6240.00 0.281024
\(791\) −7392.00 −0.332275
\(792\) 0 0
\(793\) −20444.0 −0.915495
\(794\) −212.000 −0.00947556
\(795\) 0 0
\(796\) −6400.00 −0.284977
\(797\) 33906.0 1.50692 0.753458 0.657496i \(-0.228384\pi\)
0.753458 + 0.657496i \(0.228384\pi\)
\(798\) 0 0
\(799\) 12096.0 0.535577
\(800\) −2848.00 −0.125865
\(801\) 0 0
\(802\) 3516.00 0.154806
\(803\) −2616.00 −0.114965
\(804\) 0 0
\(805\) −16128.0 −0.706133
\(806\) −6688.00 −0.292276
\(807\) 0 0
\(808\) 4944.00 0.215259
\(809\) 630.000 0.0273790 0.0136895 0.999906i \(-0.495642\pi\)
0.0136895 + 0.999906i \(0.495642\pi\)
\(810\) 0 0
\(811\) −20788.0 −0.900081 −0.450040 0.893008i \(-0.648590\pi\)
−0.450040 + 0.893008i \(0.648590\pi\)
\(812\) 1920.00 0.0829788
\(813\) 0 0
\(814\) −6096.00 −0.262487
\(815\) 11112.0 0.477591
\(816\) 0 0
\(817\) −1040.00 −0.0445349
\(818\) −7340.00 −0.313737
\(819\) 0 0
\(820\) 1008.00 0.0429279
\(821\) 43098.0 1.83207 0.916036 0.401097i \(-0.131371\pi\)
0.916036 + 0.401097i \(0.131371\pi\)
\(822\) 0 0
\(823\) −14272.0 −0.604484 −0.302242 0.953231i \(-0.597735\pi\)
−0.302242 + 0.953231i \(0.597735\pi\)
\(824\) 1024.00 0.0432921
\(825\) 0 0
\(826\) −21120.0 −0.889660
\(827\) −13644.0 −0.573698 −0.286849 0.957976i \(-0.592608\pi\)
−0.286849 + 0.957976i \(0.592608\pi\)
\(828\) 0 0
\(829\) −2410.00 −0.100968 −0.0504842 0.998725i \(-0.516076\pi\)
−0.0504842 + 0.998725i \(0.516076\pi\)
\(830\) −5904.00 −0.246905
\(831\) 0 0
\(832\) 2432.00 0.101339
\(833\) −10962.0 −0.455955
\(834\) 0 0
\(835\) −12816.0 −0.531157
\(836\) −960.000 −0.0397157
\(837\) 0 0
\(838\) 19320.0 0.796418
\(839\) −23160.0 −0.953006 −0.476503 0.879173i \(-0.658096\pi\)
−0.476503 + 0.879173i \(0.658096\pi\)
\(840\) 0 0
\(841\) −23489.0 −0.963098
\(842\) 16924.0 0.692684
\(843\) 0 0
\(844\) 13328.0 0.543565
\(845\) 4518.00 0.183934
\(846\) 0 0
\(847\) 18992.0 0.770452
\(848\) −3168.00 −0.128290
\(849\) 0 0
\(850\) −22428.0 −0.905028
\(851\) −42672.0 −1.71889
\(852\) 0 0
\(853\) 32078.0 1.28761 0.643804 0.765190i \(-0.277355\pi\)
0.643804 + 0.765190i \(0.277355\pi\)
\(854\) 17216.0 0.689835
\(855\) 0 0
\(856\) 11808.0 0.471483
\(857\) 14406.0 0.574212 0.287106 0.957899i \(-0.407307\pi\)
0.287106 + 0.957899i \(0.407307\pi\)
\(858\) 0 0
\(859\) 30620.0 1.21623 0.608115 0.793849i \(-0.291926\pi\)
0.608115 + 0.793849i \(0.291926\pi\)
\(860\) 1248.00 0.0494842
\(861\) 0 0
\(862\) −19584.0 −0.773821
\(863\) −17568.0 −0.692957 −0.346478 0.938058i \(-0.612623\pi\)
−0.346478 + 0.938058i \(0.612623\pi\)
\(864\) 0 0
\(865\) 10548.0 0.414616
\(866\) −14684.0 −0.576192
\(867\) 0 0
\(868\) 5632.00 0.220233
\(869\) 6240.00 0.243587
\(870\) 0 0
\(871\) 33592.0 1.30680
\(872\) 9520.00 0.369711
\(873\) 0 0
\(874\) −6720.00 −0.260077
\(875\) −20544.0 −0.793730
\(876\) 0 0
\(877\) −21706.0 −0.835758 −0.417879 0.908503i \(-0.637226\pi\)
−0.417879 + 0.908503i \(0.637226\pi\)
\(878\) 21280.0 0.817956
\(879\) 0 0
\(880\) 1152.00 0.0441294
\(881\) 14958.0 0.572018 0.286009 0.958227i \(-0.407671\pi\)
0.286009 + 0.958227i \(0.407671\pi\)
\(882\) 0 0
\(883\) −32812.0 −1.25052 −0.625261 0.780415i \(-0.715008\pi\)
−0.625261 + 0.780415i \(0.715008\pi\)
\(884\) 19152.0 0.728678
\(885\) 0 0
\(886\) 34824.0 1.32047
\(887\) 38856.0 1.47086 0.735432 0.677598i \(-0.236979\pi\)
0.735432 + 0.677598i \(0.236979\pi\)
\(888\) 0 0
\(889\) 40576.0 1.53079
\(890\) 9720.00 0.366084
\(891\) 0 0
\(892\) 10592.0 0.397586
\(893\) 1920.00 0.0719489
\(894\) 0 0
\(895\) −3240.00 −0.121007
\(896\) −2048.00 −0.0763604
\(897\) 0 0
\(898\) 3420.00 0.127090
\(899\) 2640.00 0.0979410
\(900\) 0 0
\(901\) −24948.0 −0.922462
\(902\) 1008.00 0.0372092
\(903\) 0 0
\(904\) 3696.00 0.135981
\(905\) −11892.0 −0.436799
\(906\) 0 0
\(907\) −28276.0 −1.03516 −0.517579 0.855635i \(-0.673167\pi\)
−0.517579 + 0.855635i \(0.673167\pi\)
\(908\) −8976.00 −0.328061
\(909\) 0 0
\(910\) 7296.00 0.265780
\(911\) −8112.00 −0.295019 −0.147510 0.989061i \(-0.547126\pi\)
−0.147510 + 0.989061i \(0.547126\pi\)
\(912\) 0 0
\(913\) −5904.00 −0.214013
\(914\) −1292.00 −0.0467566
\(915\) 0 0
\(916\) −22600.0 −0.815202
\(917\) 36672.0 1.32063
\(918\) 0 0
\(919\) −26080.0 −0.936126 −0.468063 0.883695i \(-0.655048\pi\)
−0.468063 + 0.883695i \(0.655048\pi\)
\(920\) 8064.00 0.288981
\(921\) 0 0
\(922\) 12036.0 0.429918
\(923\) −30096.0 −1.07326
\(924\) 0 0
\(925\) −22606.0 −0.803547
\(926\) −13424.0 −0.476393
\(927\) 0 0
\(928\) −960.000 −0.0339586
\(929\) −49170.0 −1.73651 −0.868254 0.496120i \(-0.834757\pi\)
−0.868254 + 0.496120i \(0.834757\pi\)
\(930\) 0 0
\(931\) −1740.00 −0.0612526
\(932\) −18792.0 −0.660464
\(933\) 0 0
\(934\) −10728.0 −0.375836
\(935\) 9072.00 0.317311
\(936\) 0 0
\(937\) 48314.0 1.68447 0.842236 0.539110i \(-0.181239\pi\)
0.842236 + 0.539110i \(0.181239\pi\)
\(938\) −28288.0 −0.984687
\(939\) 0 0
\(940\) −2304.00 −0.0799449
\(941\) −34782.0 −1.20495 −0.602477 0.798137i \(-0.705819\pi\)
−0.602477 + 0.798137i \(0.705819\pi\)
\(942\) 0 0
\(943\) 7056.00 0.243664
\(944\) 10560.0 0.364088
\(945\) 0 0
\(946\) 1248.00 0.0428922
\(947\) 25116.0 0.861838 0.430919 0.902391i \(-0.358190\pi\)
0.430919 + 0.902391i \(0.358190\pi\)
\(948\) 0 0
\(949\) 8284.00 0.283361
\(950\) −3560.00 −0.121581
\(951\) 0 0
\(952\) −16128.0 −0.549067
\(953\) 15462.0 0.525565 0.262782 0.964855i \(-0.415360\pi\)
0.262782 + 0.964855i \(0.415360\pi\)
\(954\) 0 0
\(955\) −16128.0 −0.546481
\(956\) 4800.00 0.162388
\(957\) 0 0
\(958\) −19680.0 −0.663708
\(959\) −11616.0 −0.391137
\(960\) 0 0
\(961\) −22047.0 −0.740056
\(962\) 19304.0 0.646971
\(963\) 0 0
\(964\) −2872.00 −0.0959553
\(965\) 13812.0 0.460750
\(966\) 0 0
\(967\) −736.000 −0.0244759 −0.0122379 0.999925i \(-0.503896\pi\)
−0.0122379 + 0.999925i \(0.503896\pi\)
\(968\) −9496.00 −0.315303
\(969\) 0 0
\(970\) −13848.0 −0.458384
\(971\) 29268.0 0.967307 0.483653 0.875260i \(-0.339310\pi\)
0.483653 + 0.875260i \(0.339310\pi\)
\(972\) 0 0
\(973\) −6080.00 −0.200325
\(974\) 2848.00 0.0936918
\(975\) 0 0
\(976\) −8608.00 −0.282311
\(977\) −16674.0 −0.546007 −0.273003 0.962013i \(-0.588017\pi\)
−0.273003 + 0.962013i \(0.588017\pi\)
\(978\) 0 0
\(979\) 9720.00 0.317316
\(980\) 2088.00 0.0680599
\(981\) 0 0
\(982\) 9096.00 0.295586
\(983\) 31272.0 1.01467 0.507336 0.861749i \(-0.330630\pi\)
0.507336 + 0.861749i \(0.330630\pi\)
\(984\) 0 0
\(985\) 26244.0 0.848937
\(986\) −7560.00 −0.244178
\(987\) 0 0
\(988\) 3040.00 0.0978900
\(989\) 8736.00 0.280878
\(990\) 0 0
\(991\) −15928.0 −0.510565 −0.255282 0.966867i \(-0.582168\pi\)
−0.255282 + 0.966867i \(0.582168\pi\)
\(992\) −2816.00 −0.0901291
\(993\) 0 0
\(994\) 25344.0 0.808715
\(995\) 9600.00 0.305870
\(996\) 0 0
\(997\) 42014.0 1.33460 0.667300 0.744789i \(-0.267450\pi\)
0.667300 + 0.744789i \(0.267450\pi\)
\(998\) 13000.0 0.412332
\(999\) 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 \(a_p\))