Properties

Label 6027.2.a.b.1.1
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
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 \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} -3.00000 q^{5} +1.00000 q^{6} +3.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} -3.00000 q^{5} +1.00000 q^{6} +3.00000 q^{8} +1.00000 q^{9} +3.00000 q^{10} -6.00000 q^{11} +1.00000 q^{12} +7.00000 q^{13} +3.00000 q^{15} -1.00000 q^{16} +6.00000 q^{17} -1.00000 q^{18} +6.00000 q^{19} +3.00000 q^{20} +6.00000 q^{22} +5.00000 q^{23} -3.00000 q^{24} +4.00000 q^{25} -7.00000 q^{26} -1.00000 q^{27} +3.00000 q^{29} -3.00000 q^{30} -5.00000 q^{32} +6.00000 q^{33} -6.00000 q^{34} -1.00000 q^{36} +1.00000 q^{37} -6.00000 q^{38} -7.00000 q^{39} -9.00000 q^{40} -1.00000 q^{41} +6.00000 q^{43} +6.00000 q^{44} -3.00000 q^{45} -5.00000 q^{46} +5.00000 q^{47} +1.00000 q^{48} -4.00000 q^{50} -6.00000 q^{51} -7.00000 q^{52} -9.00000 q^{53} +1.00000 q^{54} +18.0000 q^{55} -6.00000 q^{57} -3.00000 q^{58} +8.00000 q^{59} -3.00000 q^{60} +2.00000 q^{61} +7.00000 q^{64} -21.0000 q^{65} -6.00000 q^{66} +9.00000 q^{67} -6.00000 q^{68} -5.00000 q^{69} -10.0000 q^{71} +3.00000 q^{72} -4.00000 q^{73} -1.00000 q^{74} -4.00000 q^{75} -6.00000 q^{76} +7.00000 q^{78} +9.00000 q^{79} +3.00000 q^{80} +1.00000 q^{81} +1.00000 q^{82} +2.00000 q^{83} -18.0000 q^{85} -6.00000 q^{86} -3.00000 q^{87} -18.0000 q^{88} -16.0000 q^{89} +3.00000 q^{90} -5.00000 q^{92} -5.00000 q^{94} -18.0000 q^{95} +5.00000 q^{96} -13.0000 q^{97} -6.00000 q^{99} +O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107 −0.353553 0.935414i \(-0.615027\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.00000 −0.500000
\(5\) −3.00000 −1.34164 −0.670820 0.741620i \(-0.734058\pi\)
−0.670820 + 0.741620i \(0.734058\pi\)
\(6\) 1.00000 0.408248
\(7\) 0 0
\(8\) 3.00000 1.06066
\(9\) 1.00000 0.333333
\(10\) 3.00000 0.948683
\(11\) −6.00000 −1.80907 −0.904534 0.426401i \(-0.859781\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) 1.00000 0.288675
\(13\) 7.00000 1.94145 0.970725 0.240192i \(-0.0772105\pi\)
0.970725 + 0.240192i \(0.0772105\pi\)
\(14\) 0 0
\(15\) 3.00000 0.774597
\(16\) −1.00000 −0.250000
\(17\) 6.00000 1.45521 0.727607 0.685994i \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) −1.00000 −0.235702
\(19\) 6.00000 1.37649 0.688247 0.725476i \(-0.258380\pi\)
0.688247 + 0.725476i \(0.258380\pi\)
\(20\) 3.00000 0.670820
\(21\) 0 0
\(22\) 6.00000 1.27920
\(23\) 5.00000 1.04257 0.521286 0.853382i \(-0.325452\pi\)
0.521286 + 0.853382i \(0.325452\pi\)
\(24\) −3.00000 −0.612372
\(25\) 4.00000 0.800000
\(26\) −7.00000 −1.37281
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 3.00000 0.557086 0.278543 0.960424i \(-0.410149\pi\)
0.278543 + 0.960424i \(0.410149\pi\)
\(30\) −3.00000 −0.547723
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −5.00000 −0.883883
\(33\) 6.00000 1.04447
\(34\) −6.00000 −1.02899
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 1.00000 0.164399 0.0821995 0.996616i \(-0.473806\pi\)
0.0821995 + 0.996616i \(0.473806\pi\)
\(38\) −6.00000 −0.973329
\(39\) −7.00000 −1.12090
\(40\) −9.00000 −1.42302
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 6.00000 0.914991 0.457496 0.889212i \(-0.348747\pi\)
0.457496 + 0.889212i \(0.348747\pi\)
\(44\) 6.00000 0.904534
\(45\) −3.00000 −0.447214
\(46\) −5.00000 −0.737210
\(47\) 5.00000 0.729325 0.364662 0.931140i \(-0.381184\pi\)
0.364662 + 0.931140i \(0.381184\pi\)
\(48\) 1.00000 0.144338
\(49\) 0 0
\(50\) −4.00000 −0.565685
\(51\) −6.00000 −0.840168
\(52\) −7.00000 −0.970725
\(53\) −9.00000 −1.23625 −0.618123 0.786082i \(-0.712106\pi\)
−0.618123 + 0.786082i \(0.712106\pi\)
\(54\) 1.00000 0.136083
\(55\) 18.0000 2.42712
\(56\) 0 0
\(57\) −6.00000 −0.794719
\(58\) −3.00000 −0.393919
\(59\) 8.00000 1.04151 0.520756 0.853706i \(-0.325650\pi\)
0.520756 + 0.853706i \(0.325650\pi\)
\(60\) −3.00000 −0.387298
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) −21.0000 −2.60473
\(66\) −6.00000 −0.738549
\(67\) 9.00000 1.09952 0.549762 0.835321i \(-0.314718\pi\)
0.549762 + 0.835321i \(0.314718\pi\)
\(68\) −6.00000 −0.727607
\(69\) −5.00000 −0.601929
\(70\) 0 0
\(71\) −10.0000 −1.18678 −0.593391 0.804914i \(-0.702211\pi\)
−0.593391 + 0.804914i \(0.702211\pi\)
\(72\) 3.00000 0.353553
\(73\) −4.00000 −0.468165 −0.234082 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) −1.00000 −0.116248
\(75\) −4.00000 −0.461880
\(76\) −6.00000 −0.688247
\(77\) 0 0
\(78\) 7.00000 0.792594
\(79\) 9.00000 1.01258 0.506290 0.862364i \(-0.331017\pi\)
0.506290 + 0.862364i \(0.331017\pi\)
\(80\) 3.00000 0.335410
\(81\) 1.00000 0.111111
\(82\) 1.00000 0.110432
\(83\) 2.00000 0.219529 0.109764 0.993958i \(-0.464990\pi\)
0.109764 + 0.993958i \(0.464990\pi\)
\(84\) 0 0
\(85\) −18.0000 −1.95237
\(86\) −6.00000 −0.646997
\(87\) −3.00000 −0.321634
\(88\) −18.0000 −1.91881
\(89\) −16.0000 −1.69600 −0.847998 0.529999i \(-0.822192\pi\)
−0.847998 + 0.529999i \(0.822192\pi\)
\(90\) 3.00000 0.316228
\(91\) 0 0
\(92\) −5.00000 −0.521286
\(93\) 0 0
\(94\) −5.00000 −0.515711
\(95\) −18.0000 −1.84676
\(96\) 5.00000 0.510310
\(97\) −13.0000 −1.31995 −0.659975 0.751288i \(-0.729433\pi\)
−0.659975 + 0.751288i \(0.729433\pi\)
\(98\) 0 0
\(99\) −6.00000 −0.603023
\(100\) −4.00000 −0.400000
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 6.00000 0.594089
\(103\) 7.00000 0.689730 0.344865 0.938652i \(-0.387925\pi\)
0.344865 + 0.938652i \(0.387925\pi\)
\(104\) 21.0000 2.05922
\(105\) 0 0
\(106\) 9.00000 0.874157
\(107\) −11.0000 −1.06341 −0.531705 0.846930i \(-0.678449\pi\)
−0.531705 + 0.846930i \(0.678449\pi\)
\(108\) 1.00000 0.0962250
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) −18.0000 −1.71623
\(111\) −1.00000 −0.0949158
\(112\) 0 0
\(113\) −4.00000 −0.376288 −0.188144 0.982141i \(-0.560247\pi\)
−0.188144 + 0.982141i \(0.560247\pi\)
\(114\) 6.00000 0.561951
\(115\) −15.0000 −1.39876
\(116\) −3.00000 −0.278543
\(117\) 7.00000 0.647150
\(118\) −8.00000 −0.736460
\(119\) 0 0
\(120\) 9.00000 0.821584
\(121\) 25.0000 2.27273
\(122\) −2.00000 −0.181071
\(123\) 1.00000 0.0901670
\(124\) 0 0
\(125\) 3.00000 0.268328
\(126\) 0 0
\(127\) −20.0000 −1.77471 −0.887357 0.461084i \(-0.847461\pi\)
−0.887357 + 0.461084i \(0.847461\pi\)
\(128\) 3.00000 0.265165
\(129\) −6.00000 −0.528271
\(130\) 21.0000 1.84182
\(131\) 6.00000 0.524222 0.262111 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) −6.00000 −0.522233
\(133\) 0 0
\(134\) −9.00000 −0.777482
\(135\) 3.00000 0.258199
\(136\) 18.0000 1.54349
\(137\) 19.0000 1.62328 0.811640 0.584158i \(-0.198575\pi\)
0.811640 + 0.584158i \(0.198575\pi\)
\(138\) 5.00000 0.425628
\(139\) 13.0000 1.10265 0.551323 0.834292i \(-0.314123\pi\)
0.551323 + 0.834292i \(0.314123\pi\)
\(140\) 0 0
\(141\) −5.00000 −0.421076
\(142\) 10.0000 0.839181
\(143\) −42.0000 −3.51222
\(144\) −1.00000 −0.0833333
\(145\) −9.00000 −0.747409
\(146\) 4.00000 0.331042
\(147\) 0 0
\(148\) −1.00000 −0.0821995
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 4.00000 0.326599
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 18.0000 1.45999
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) 0 0
\(156\) 7.00000 0.560449
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) −9.00000 −0.716002
\(159\) 9.00000 0.713746
\(160\) 15.0000 1.18585
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 1.00000 0.0780869
\(165\) −18.0000 −1.40130
\(166\) −2.00000 −0.155230
\(167\) 23.0000 1.77979 0.889897 0.456162i \(-0.150776\pi\)
0.889897 + 0.456162i \(0.150776\pi\)
\(168\) 0 0
\(169\) 36.0000 2.76923
\(170\) 18.0000 1.38054
\(171\) 6.00000 0.458831
\(172\) −6.00000 −0.457496
\(173\) −15.0000 −1.14043 −0.570214 0.821496i \(-0.693140\pi\)
−0.570214 + 0.821496i \(0.693140\pi\)
\(174\) 3.00000 0.227429
\(175\) 0 0
\(176\) 6.00000 0.452267
\(177\) −8.00000 −0.601317
\(178\) 16.0000 1.19925
\(179\) 6.00000 0.448461 0.224231 0.974536i \(-0.428013\pi\)
0.224231 + 0.974536i \(0.428013\pi\)
\(180\) 3.00000 0.223607
\(181\) 6.00000 0.445976 0.222988 0.974821i \(-0.428419\pi\)
0.222988 + 0.974821i \(0.428419\pi\)
\(182\) 0 0
\(183\) −2.00000 −0.147844
\(184\) 15.0000 1.10581
\(185\) −3.00000 −0.220564
\(186\) 0 0
\(187\) −36.0000 −2.63258
\(188\) −5.00000 −0.364662
\(189\) 0 0
\(190\) 18.0000 1.30586
\(191\) −18.0000 −1.30243 −0.651217 0.758891i \(-0.725741\pi\)
−0.651217 + 0.758891i \(0.725741\pi\)
\(192\) −7.00000 −0.505181
\(193\) 2.00000 0.143963 0.0719816 0.997406i \(-0.477068\pi\)
0.0719816 + 0.997406i \(0.477068\pi\)
\(194\) 13.0000 0.933346
\(195\) 21.0000 1.50384
\(196\) 0 0
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 6.00000 0.426401
\(199\) 6.00000 0.425329 0.212664 0.977125i \(-0.431786\pi\)
0.212664 + 0.977125i \(0.431786\pi\)
\(200\) 12.0000 0.848528
\(201\) −9.00000 −0.634811
\(202\) −6.00000 −0.422159
\(203\) 0 0
\(204\) 6.00000 0.420084
\(205\) 3.00000 0.209529
\(206\) −7.00000 −0.487713
\(207\) 5.00000 0.347524
\(208\) −7.00000 −0.485363
\(209\) −36.0000 −2.49017
\(210\) 0 0
\(211\) −21.0000 −1.44570 −0.722850 0.691005i \(-0.757168\pi\)
−0.722850 + 0.691005i \(0.757168\pi\)
\(212\) 9.00000 0.618123
\(213\) 10.0000 0.685189
\(214\) 11.0000 0.751945
\(215\) −18.0000 −1.22759
\(216\) −3.00000 −0.204124
\(217\) 0 0
\(218\) −2.00000 −0.135457
\(219\) 4.00000 0.270295
\(220\) −18.0000 −1.21356
\(221\) 42.0000 2.82523
\(222\) 1.00000 0.0671156
\(223\) −11.0000 −0.736614 −0.368307 0.929704i \(-0.620063\pi\)
−0.368307 + 0.929704i \(0.620063\pi\)
\(224\) 0 0
\(225\) 4.00000 0.266667
\(226\) 4.00000 0.266076
\(227\) 7.00000 0.464606 0.232303 0.972643i \(-0.425374\pi\)
0.232303 + 0.972643i \(0.425374\pi\)
\(228\) 6.00000 0.397360
\(229\) 5.00000 0.330409 0.165205 0.986259i \(-0.447172\pi\)
0.165205 + 0.986259i \(0.447172\pi\)
\(230\) 15.0000 0.989071
\(231\) 0 0
\(232\) 9.00000 0.590879
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) −7.00000 −0.457604
\(235\) −15.0000 −0.978492
\(236\) −8.00000 −0.520756
\(237\) −9.00000 −0.584613
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) −3.00000 −0.193649
\(241\) 18.0000 1.15948 0.579741 0.814801i \(-0.303154\pi\)
0.579741 + 0.814801i \(0.303154\pi\)
\(242\) −25.0000 −1.60706
\(243\) −1.00000 −0.0641500
\(244\) −2.00000 −0.128037
\(245\) 0 0
\(246\) −1.00000 −0.0637577
\(247\) 42.0000 2.67240
\(248\) 0 0
\(249\) −2.00000 −0.126745
\(250\) −3.00000 −0.189737
\(251\) 10.0000 0.631194 0.315597 0.948893i \(-0.397795\pi\)
0.315597 + 0.948893i \(0.397795\pi\)
\(252\) 0 0
\(253\) −30.0000 −1.88608
\(254\) 20.0000 1.25491
\(255\) 18.0000 1.12720
\(256\) −17.0000 −1.06250
\(257\) −16.0000 −0.998053 −0.499026 0.866587i \(-0.666309\pi\)
−0.499026 + 0.866587i \(0.666309\pi\)
\(258\) 6.00000 0.373544
\(259\) 0 0
\(260\) 21.0000 1.30236
\(261\) 3.00000 0.185695
\(262\) −6.00000 −0.370681
\(263\) −14.0000 −0.863277 −0.431638 0.902047i \(-0.642064\pi\)
−0.431638 + 0.902047i \(0.642064\pi\)
\(264\) 18.0000 1.10782
\(265\) 27.0000 1.65860
\(266\) 0 0
\(267\) 16.0000 0.979184
\(268\) −9.00000 −0.549762
\(269\) 9.00000 0.548740 0.274370 0.961624i \(-0.411531\pi\)
0.274370 + 0.961624i \(0.411531\pi\)
\(270\) −3.00000 −0.182574
\(271\) −31.0000 −1.88312 −0.941558 0.336851i \(-0.890638\pi\)
−0.941558 + 0.336851i \(0.890638\pi\)
\(272\) −6.00000 −0.363803
\(273\) 0 0
\(274\) −19.0000 −1.14783
\(275\) −24.0000 −1.44725
\(276\) 5.00000 0.300965
\(277\) −3.00000 −0.180253 −0.0901263 0.995930i \(-0.528727\pi\)
−0.0901263 + 0.995930i \(0.528727\pi\)
\(278\) −13.0000 −0.779688
\(279\) 0 0
\(280\) 0 0
\(281\) 3.00000 0.178965 0.0894825 0.995988i \(-0.471479\pi\)
0.0894825 + 0.995988i \(0.471479\pi\)
\(282\) 5.00000 0.297746
\(283\) −20.0000 −1.18888 −0.594438 0.804141i \(-0.702626\pi\)
−0.594438 + 0.804141i \(0.702626\pi\)
\(284\) 10.0000 0.593391
\(285\) 18.0000 1.06623
\(286\) 42.0000 2.48351
\(287\) 0 0
\(288\) −5.00000 −0.294628
\(289\) 19.0000 1.11765
\(290\) 9.00000 0.528498
\(291\) 13.0000 0.762073
\(292\) 4.00000 0.234082
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 0 0
\(295\) −24.0000 −1.39733
\(296\) 3.00000 0.174371
\(297\) 6.00000 0.348155
\(298\) −6.00000 −0.347571
\(299\) 35.0000 2.02410
\(300\) 4.00000 0.230940
\(301\) 0 0
\(302\) −8.00000 −0.460348
\(303\) −6.00000 −0.344691
\(304\) −6.00000 −0.344124
\(305\) −6.00000 −0.343559
\(306\) −6.00000 −0.342997
\(307\) −9.00000 −0.513657 −0.256829 0.966457i \(-0.582678\pi\)
−0.256829 + 0.966457i \(0.582678\pi\)
\(308\) 0 0
\(309\) −7.00000 −0.398216
\(310\) 0 0
\(311\) −21.0000 −1.19080 −0.595400 0.803429i \(-0.703007\pi\)
−0.595400 + 0.803429i \(0.703007\pi\)
\(312\) −21.0000 −1.18889
\(313\) 9.00000 0.508710 0.254355 0.967111i \(-0.418137\pi\)
0.254355 + 0.967111i \(0.418137\pi\)
\(314\) −2.00000 −0.112867
\(315\) 0 0
\(316\) −9.00000 −0.506290
\(317\) 27.0000 1.51647 0.758236 0.651981i \(-0.226062\pi\)
0.758236 + 0.651981i \(0.226062\pi\)
\(318\) −9.00000 −0.504695
\(319\) −18.0000 −1.00781
\(320\) −21.0000 −1.17394
\(321\) 11.0000 0.613960
\(322\) 0 0
\(323\) 36.0000 2.00309
\(324\) −1.00000 −0.0555556
\(325\) 28.0000 1.55316
\(326\) 16.0000 0.886158
\(327\) −2.00000 −0.110600
\(328\) −3.00000 −0.165647
\(329\) 0 0
\(330\) 18.0000 0.990867
\(331\) −19.0000 −1.04433 −0.522167 0.852843i \(-0.674876\pi\)
−0.522167 + 0.852843i \(0.674876\pi\)
\(332\) −2.00000 −0.109764
\(333\) 1.00000 0.0547997
\(334\) −23.0000 −1.25850
\(335\) −27.0000 −1.47517
\(336\) 0 0
\(337\) 11.0000 0.599208 0.299604 0.954064i \(-0.403145\pi\)
0.299604 + 0.954064i \(0.403145\pi\)
\(338\) −36.0000 −1.95814
\(339\) 4.00000 0.217250
\(340\) 18.0000 0.976187
\(341\) 0 0
\(342\) −6.00000 −0.324443
\(343\) 0 0
\(344\) 18.0000 0.970495
\(345\) 15.0000 0.807573
\(346\) 15.0000 0.806405
\(347\) −18.0000 −0.966291 −0.483145 0.875540i \(-0.660506\pi\)
−0.483145 + 0.875540i \(0.660506\pi\)
\(348\) 3.00000 0.160817
\(349\) 12.0000 0.642345 0.321173 0.947021i \(-0.395923\pi\)
0.321173 + 0.947021i \(0.395923\pi\)
\(350\) 0 0
\(351\) −7.00000 −0.373632
\(352\) 30.0000 1.59901
\(353\) 30.0000 1.59674 0.798369 0.602168i \(-0.205696\pi\)
0.798369 + 0.602168i \(0.205696\pi\)
\(354\) 8.00000 0.425195
\(355\) 30.0000 1.59223
\(356\) 16.0000 0.847998
\(357\) 0 0
\(358\) −6.00000 −0.317110
\(359\) −33.0000 −1.74167 −0.870837 0.491572i \(-0.836422\pi\)
−0.870837 + 0.491572i \(0.836422\pi\)
\(360\) −9.00000 −0.474342
\(361\) 17.0000 0.894737
\(362\) −6.00000 −0.315353
\(363\) −25.0000 −1.31216
\(364\) 0 0
\(365\) 12.0000 0.628109
\(366\) 2.00000 0.104542
\(367\) −25.0000 −1.30499 −0.652495 0.757793i \(-0.726278\pi\)
−0.652495 + 0.757793i \(0.726278\pi\)
\(368\) −5.00000 −0.260643
\(369\) −1.00000 −0.0520579
\(370\) 3.00000 0.155963
\(371\) 0 0
\(372\) 0 0
\(373\) 25.0000 1.29445 0.647225 0.762299i \(-0.275929\pi\)
0.647225 + 0.762299i \(0.275929\pi\)
\(374\) 36.0000 1.86152
\(375\) −3.00000 −0.154919
\(376\) 15.0000 0.773566
\(377\) 21.0000 1.08156
\(378\) 0 0
\(379\) 22.0000 1.13006 0.565032 0.825069i \(-0.308864\pi\)
0.565032 + 0.825069i \(0.308864\pi\)
\(380\) 18.0000 0.923381
\(381\) 20.0000 1.02463
\(382\) 18.0000 0.920960
\(383\) 15.0000 0.766464 0.383232 0.923652i \(-0.374811\pi\)
0.383232 + 0.923652i \(0.374811\pi\)
\(384\) −3.00000 −0.153093
\(385\) 0 0
\(386\) −2.00000 −0.101797
\(387\) 6.00000 0.304997
\(388\) 13.0000 0.659975
\(389\) −14.0000 −0.709828 −0.354914 0.934899i \(-0.615490\pi\)
−0.354914 + 0.934899i \(0.615490\pi\)
\(390\) −21.0000 −1.06338
\(391\) 30.0000 1.51717
\(392\) 0 0
\(393\) −6.00000 −0.302660
\(394\) −2.00000 −0.100759
\(395\) −27.0000 −1.35852
\(396\) 6.00000 0.301511
\(397\) −2.00000 −0.100377 −0.0501886 0.998740i \(-0.515982\pi\)
−0.0501886 + 0.998740i \(0.515982\pi\)
\(398\) −6.00000 −0.300753
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) −20.0000 −0.998752 −0.499376 0.866385i \(-0.666437\pi\)
−0.499376 + 0.866385i \(0.666437\pi\)
\(402\) 9.00000 0.448879
\(403\) 0 0
\(404\) −6.00000 −0.298511
\(405\) −3.00000 −0.149071
\(406\) 0 0
\(407\) −6.00000 −0.297409
\(408\) −18.0000 −0.891133
\(409\) 32.0000 1.58230 0.791149 0.611623i \(-0.209483\pi\)
0.791149 + 0.611623i \(0.209483\pi\)
\(410\) −3.00000 −0.148159
\(411\) −19.0000 −0.937201
\(412\) −7.00000 −0.344865
\(413\) 0 0
\(414\) −5.00000 −0.245737
\(415\) −6.00000 −0.294528
\(416\) −35.0000 −1.71602
\(417\) −13.0000 −0.636613
\(418\) 36.0000 1.76082
\(419\) 22.0000 1.07477 0.537385 0.843337i \(-0.319412\pi\)
0.537385 + 0.843337i \(0.319412\pi\)
\(420\) 0 0
\(421\) −2.00000 −0.0974740 −0.0487370 0.998812i \(-0.515520\pi\)
−0.0487370 + 0.998812i \(0.515520\pi\)
\(422\) 21.0000 1.02226
\(423\) 5.00000 0.243108
\(424\) −27.0000 −1.31124
\(425\) 24.0000 1.16417
\(426\) −10.0000 −0.484502
\(427\) 0 0
\(428\) 11.0000 0.531705
\(429\) 42.0000 2.02778
\(430\) 18.0000 0.868037
\(431\) −24.0000 −1.15604 −0.578020 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 1.00000 0.0481125
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 0 0
\(435\) 9.00000 0.431517
\(436\) −2.00000 −0.0957826
\(437\) 30.0000 1.43509
\(438\) −4.00000 −0.191127
\(439\) 4.00000 0.190910 0.0954548 0.995434i \(-0.469569\pi\)
0.0954548 + 0.995434i \(0.469569\pi\)
\(440\) 54.0000 2.57435
\(441\) 0 0
\(442\) −42.0000 −1.99774
\(443\) −24.0000 −1.14027 −0.570137 0.821549i \(-0.693110\pi\)
−0.570137 + 0.821549i \(0.693110\pi\)
\(444\) 1.00000 0.0474579
\(445\) 48.0000 2.27542
\(446\) 11.0000 0.520865
\(447\) −6.00000 −0.283790
\(448\) 0 0
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) −4.00000 −0.188562
\(451\) 6.00000 0.282529
\(452\) 4.00000 0.188144
\(453\) −8.00000 −0.375873
\(454\) −7.00000 −0.328526
\(455\) 0 0
\(456\) −18.0000 −0.842927
\(457\) 20.0000 0.935561 0.467780 0.883845i \(-0.345054\pi\)
0.467780 + 0.883845i \(0.345054\pi\)
\(458\) −5.00000 −0.233635
\(459\) −6.00000 −0.280056
\(460\) 15.0000 0.699379
\(461\) −15.0000 −0.698620 −0.349310 0.937007i \(-0.613584\pi\)
−0.349310 + 0.937007i \(0.613584\pi\)
\(462\) 0 0
\(463\) 1.00000 0.0464739 0.0232370 0.999730i \(-0.492603\pi\)
0.0232370 + 0.999730i \(0.492603\pi\)
\(464\) −3.00000 −0.139272
\(465\) 0 0
\(466\) 6.00000 0.277945
\(467\) −6.00000 −0.277647 −0.138823 0.990317i \(-0.544332\pi\)
−0.138823 + 0.990317i \(0.544332\pi\)
\(468\) −7.00000 −0.323575
\(469\) 0 0
\(470\) 15.0000 0.691898
\(471\) −2.00000 −0.0921551
\(472\) 24.0000 1.10469
\(473\) −36.0000 −1.65528
\(474\) 9.00000 0.413384
\(475\) 24.0000 1.10120
\(476\) 0 0
\(477\) −9.00000 −0.412082
\(478\) −24.0000 −1.09773
\(479\) −24.0000 −1.09659 −0.548294 0.836286i \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) −15.0000 −0.684653
\(481\) 7.00000 0.319173
\(482\) −18.0000 −0.819878
\(483\) 0 0
\(484\) −25.0000 −1.13636
\(485\) 39.0000 1.77090
\(486\) 1.00000 0.0453609
\(487\) 32.0000 1.45006 0.725029 0.688718i \(-0.241826\pi\)
0.725029 + 0.688718i \(0.241826\pi\)
\(488\) 6.00000 0.271607
\(489\) 16.0000 0.723545
\(490\) 0 0
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) −1.00000 −0.0450835
\(493\) 18.0000 0.810679
\(494\) −42.0000 −1.88967
\(495\) 18.0000 0.809040
\(496\) 0 0
\(497\) 0 0
\(498\) 2.00000 0.0896221
\(499\) 24.0000 1.07439 0.537194 0.843459i \(-0.319484\pi\)
0.537194 + 0.843459i \(0.319484\pi\)
\(500\) −3.00000 −0.134164
\(501\) −23.0000 −1.02756
\(502\) −10.0000 −0.446322
\(503\) 21.0000 0.936344 0.468172 0.883637i \(-0.344913\pi\)
0.468172 + 0.883637i \(0.344913\pi\)
\(504\) 0 0
\(505\) −18.0000 −0.800989
\(506\) 30.0000 1.33366
\(507\) −36.0000 −1.59882
\(508\) 20.0000 0.887357
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) −18.0000 −0.797053
\(511\) 0 0
\(512\) 11.0000 0.486136
\(513\) −6.00000 −0.264906
\(514\) 16.0000 0.705730
\(515\) −21.0000 −0.925371
\(516\) 6.00000 0.264135
\(517\) −30.0000 −1.31940
\(518\) 0 0
\(519\) 15.0000 0.658427
\(520\) −63.0000 −2.76273
\(521\) 42.0000 1.84005 0.920027 0.391856i \(-0.128167\pi\)
0.920027 + 0.391856i \(0.128167\pi\)
\(522\) −3.00000 −0.131306
\(523\) 20.0000 0.874539 0.437269 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(524\) −6.00000 −0.262111
\(525\) 0 0
\(526\) 14.0000 0.610429
\(527\) 0 0
\(528\) −6.00000 −0.261116
\(529\) 2.00000 0.0869565
\(530\) −27.0000 −1.17281
\(531\) 8.00000 0.347170
\(532\) 0 0
\(533\) −7.00000 −0.303204
\(534\) −16.0000 −0.692388
\(535\) 33.0000 1.42671
\(536\) 27.0000 1.16622
\(537\) −6.00000 −0.258919
\(538\) −9.00000 −0.388018
\(539\) 0 0
\(540\) −3.00000 −0.129099
\(541\) −9.00000 −0.386940 −0.193470 0.981106i \(-0.561974\pi\)
−0.193470 + 0.981106i \(0.561974\pi\)
\(542\) 31.0000 1.33156
\(543\) −6.00000 −0.257485
\(544\) −30.0000 −1.28624
\(545\) −6.00000 −0.257012
\(546\) 0 0
\(547\) 9.00000 0.384812 0.192406 0.981315i \(-0.438371\pi\)
0.192406 + 0.981315i \(0.438371\pi\)
\(548\) −19.0000 −0.811640
\(549\) 2.00000 0.0853579
\(550\) 24.0000 1.02336
\(551\) 18.0000 0.766826
\(552\) −15.0000 −0.638442
\(553\) 0 0
\(554\) 3.00000 0.127458
\(555\) 3.00000 0.127343
\(556\) −13.0000 −0.551323
\(557\) 18.0000 0.762684 0.381342 0.924434i \(-0.375462\pi\)
0.381342 + 0.924434i \(0.375462\pi\)
\(558\) 0 0
\(559\) 42.0000 1.77641
\(560\) 0 0
\(561\) 36.0000 1.51992
\(562\) −3.00000 −0.126547
\(563\) −19.0000 −0.800755 −0.400377 0.916350i \(-0.631121\pi\)
−0.400377 + 0.916350i \(0.631121\pi\)
\(564\) 5.00000 0.210538
\(565\) 12.0000 0.504844
\(566\) 20.0000 0.840663
\(567\) 0 0
\(568\) −30.0000 −1.25877
\(569\) −20.0000 −0.838444 −0.419222 0.907884i \(-0.637697\pi\)
−0.419222 + 0.907884i \(0.637697\pi\)
\(570\) −18.0000 −0.753937
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 42.0000 1.75611
\(573\) 18.0000 0.751961
\(574\) 0 0
\(575\) 20.0000 0.834058
\(576\) 7.00000 0.291667
\(577\) −14.0000 −0.582828 −0.291414 0.956597i \(-0.594126\pi\)
−0.291414 + 0.956597i \(0.594126\pi\)
\(578\) −19.0000 −0.790296
\(579\) −2.00000 −0.0831172
\(580\) 9.00000 0.373705
\(581\) 0 0
\(582\) −13.0000 −0.538867
\(583\) 54.0000 2.23645
\(584\) −12.0000 −0.496564
\(585\) −21.0000 −0.868243
\(586\) −6.00000 −0.247858
\(587\) −28.0000 −1.15568 −0.577842 0.816149i \(-0.696105\pi\)
−0.577842 + 0.816149i \(0.696105\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 24.0000 0.988064
\(591\) −2.00000 −0.0822690
\(592\) −1.00000 −0.0410997
\(593\) 36.0000 1.47834 0.739171 0.673517i \(-0.235217\pi\)
0.739171 + 0.673517i \(0.235217\pi\)
\(594\) −6.00000 −0.246183
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) −6.00000 −0.245564
\(598\) −35.0000 −1.43126
\(599\) 3.00000 0.122577 0.0612883 0.998120i \(-0.480479\pi\)
0.0612883 + 0.998120i \(0.480479\pi\)
\(600\) −12.0000 −0.489898
\(601\) −39.0000 −1.59084 −0.795422 0.606057i \(-0.792751\pi\)
−0.795422 + 0.606057i \(0.792751\pi\)
\(602\) 0 0
\(603\) 9.00000 0.366508
\(604\) −8.00000 −0.325515
\(605\) −75.0000 −3.04918
\(606\) 6.00000 0.243733
\(607\) −24.0000 −0.974130 −0.487065 0.873366i \(-0.661933\pi\)
−0.487065 + 0.873366i \(0.661933\pi\)
\(608\) −30.0000 −1.21666
\(609\) 0 0
\(610\) 6.00000 0.242933
\(611\) 35.0000 1.41595
\(612\) −6.00000 −0.242536
\(613\) 19.0000 0.767403 0.383701 0.923457i \(-0.374649\pi\)
0.383701 + 0.923457i \(0.374649\pi\)
\(614\) 9.00000 0.363210
\(615\) −3.00000 −0.120972
\(616\) 0 0
\(617\) 4.00000 0.161034 0.0805170 0.996753i \(-0.474343\pi\)
0.0805170 + 0.996753i \(0.474343\pi\)
\(618\) 7.00000 0.281581
\(619\) 35.0000 1.40677 0.703384 0.710810i \(-0.251671\pi\)
0.703384 + 0.710810i \(0.251671\pi\)
\(620\) 0 0
\(621\) −5.00000 −0.200643
\(622\) 21.0000 0.842023
\(623\) 0 0
\(624\) 7.00000 0.280224
\(625\) −29.0000 −1.16000
\(626\) −9.00000 −0.359712
\(627\) 36.0000 1.43770
\(628\) −2.00000 −0.0798087
\(629\) 6.00000 0.239236
\(630\) 0 0
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) 27.0000 1.07400
\(633\) 21.0000 0.834675
\(634\) −27.0000 −1.07231
\(635\) 60.0000 2.38103
\(636\) −9.00000 −0.356873
\(637\) 0 0
\(638\) 18.0000 0.712627
\(639\) −10.0000 −0.395594
\(640\) −9.00000 −0.355756
\(641\) 18.0000 0.710957 0.355479 0.934684i \(-0.384318\pi\)
0.355479 + 0.934684i \(0.384318\pi\)
\(642\) −11.0000 −0.434135
\(643\) −40.0000 −1.57745 −0.788723 0.614749i \(-0.789257\pi\)
−0.788723 + 0.614749i \(0.789257\pi\)
\(644\) 0 0
\(645\) 18.0000 0.708749
\(646\) −36.0000 −1.41640
\(647\) −10.0000 −0.393141 −0.196570 0.980490i \(-0.562980\pi\)
−0.196570 + 0.980490i \(0.562980\pi\)
\(648\) 3.00000 0.117851
\(649\) −48.0000 −1.88416
\(650\) −28.0000 −1.09825
\(651\) 0 0
\(652\) 16.0000 0.626608
\(653\) −18.0000 −0.704394 −0.352197 0.935926i \(-0.614565\pi\)
−0.352197 + 0.935926i \(0.614565\pi\)
\(654\) 2.00000 0.0782062
\(655\) −18.0000 −0.703318
\(656\) 1.00000 0.0390434
\(657\) −4.00000 −0.156055
\(658\) 0 0
\(659\) −38.0000 −1.48027 −0.740135 0.672458i \(-0.765238\pi\)
−0.740135 + 0.672458i \(0.765238\pi\)
\(660\) 18.0000 0.700649
\(661\) 28.0000 1.08907 0.544537 0.838737i \(-0.316705\pi\)
0.544537 + 0.838737i \(0.316705\pi\)
\(662\) 19.0000 0.738456
\(663\) −42.0000 −1.63114
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) −1.00000 −0.0387492
\(667\) 15.0000 0.580802
\(668\) −23.0000 −0.889897
\(669\) 11.0000 0.425285
\(670\) 27.0000 1.04310
\(671\) −12.0000 −0.463255
\(672\) 0 0
\(673\) 34.0000 1.31060 0.655302 0.755367i \(-0.272541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) −11.0000 −0.423704
\(675\) −4.00000 −0.153960
\(676\) −36.0000 −1.38462
\(677\) −22.0000 −0.845529 −0.422764 0.906240i \(-0.638940\pi\)
−0.422764 + 0.906240i \(0.638940\pi\)
\(678\) −4.00000 −0.153619
\(679\) 0 0
\(680\) −54.0000 −2.07081
\(681\) −7.00000 −0.268241
\(682\) 0 0
\(683\) 8.00000 0.306111 0.153056 0.988218i \(-0.451089\pi\)
0.153056 + 0.988218i \(0.451089\pi\)
\(684\) −6.00000 −0.229416
\(685\) −57.0000 −2.17786
\(686\) 0 0
\(687\) −5.00000 −0.190762
\(688\) −6.00000 −0.228748
\(689\) −63.0000 −2.40011
\(690\) −15.0000 −0.571040
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) 15.0000 0.570214
\(693\) 0 0
\(694\) 18.0000 0.683271
\(695\) −39.0000 −1.47935
\(696\) −9.00000 −0.341144
\(697\) −6.00000 −0.227266
\(698\) −12.0000 −0.454207
\(699\) 6.00000 0.226941
\(700\) 0 0
\(701\) 40.0000 1.51078 0.755390 0.655276i \(-0.227448\pi\)
0.755390 + 0.655276i \(0.227448\pi\)
\(702\) 7.00000 0.264198
\(703\) 6.00000 0.226294
\(704\) −42.0000 −1.58293
\(705\) 15.0000 0.564933
\(706\) −30.0000 −1.12906
\(707\) 0 0
\(708\) 8.00000 0.300658
\(709\) 26.0000 0.976450 0.488225 0.872718i \(-0.337644\pi\)
0.488225 + 0.872718i \(0.337644\pi\)
\(710\) −30.0000 −1.12588
\(711\) 9.00000 0.337526
\(712\) −48.0000 −1.79888
\(713\) 0 0
\(714\) 0 0
\(715\) 126.000 4.71213
\(716\) −6.00000 −0.224231
\(717\) −24.0000 −0.896296
\(718\) 33.0000 1.23155
\(719\) −12.0000 −0.447524 −0.223762 0.974644i \(-0.571834\pi\)
−0.223762 + 0.974644i \(0.571834\pi\)
\(720\) 3.00000 0.111803
\(721\) 0 0
\(722\) −17.0000 −0.632674
\(723\) −18.0000 −0.669427
\(724\) −6.00000 −0.222988
\(725\) 12.0000 0.445669
\(726\) 25.0000 0.927837
\(727\) 20.0000 0.741759 0.370879 0.928681i \(-0.379056\pi\)
0.370879 + 0.928681i \(0.379056\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −12.0000 −0.444140
\(731\) 36.0000 1.33151
\(732\) 2.00000 0.0739221
\(733\) 28.0000 1.03420 0.517102 0.855924i \(-0.327011\pi\)
0.517102 + 0.855924i \(0.327011\pi\)
\(734\) 25.0000 0.922767
\(735\) 0 0
\(736\) −25.0000 −0.921512
\(737\) −54.0000 −1.98912
\(738\) 1.00000 0.0368105
\(739\) −34.0000 −1.25071 −0.625355 0.780340i \(-0.715046\pi\)
−0.625355 + 0.780340i \(0.715046\pi\)
\(740\) 3.00000 0.110282
\(741\) −42.0000 −1.54291
\(742\) 0 0
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) −18.0000 −0.659469
\(746\) −25.0000 −0.915315
\(747\) 2.00000 0.0731762
\(748\) 36.0000 1.31629
\(749\) 0 0
\(750\) 3.00000 0.109545
\(751\) −37.0000 −1.35015 −0.675075 0.737749i \(-0.735889\pi\)
−0.675075 + 0.737749i \(0.735889\pi\)
\(752\) −5.00000 −0.182331
\(753\) −10.0000 −0.364420
\(754\) −21.0000 −0.764775
\(755\) −24.0000 −0.873449
\(756\) 0 0
\(757\) −30.0000 −1.09037 −0.545184 0.838316i \(-0.683540\pi\)
−0.545184 + 0.838316i \(0.683540\pi\)
\(758\) −22.0000 −0.799076
\(759\) 30.0000 1.08893
\(760\) −54.0000 −1.95879
\(761\) 47.0000 1.70375 0.851874 0.523746i \(-0.175466\pi\)
0.851874 + 0.523746i \(0.175466\pi\)
\(762\) −20.0000 −0.724524
\(763\) 0 0
\(764\) 18.0000 0.651217
\(765\) −18.0000 −0.650791
\(766\) −15.0000 −0.541972
\(767\) 56.0000 2.02204
\(768\) 17.0000 0.613435
\(769\) −32.0000 −1.15395 −0.576975 0.816762i \(-0.695767\pi\)
−0.576975 + 0.816762i \(0.695767\pi\)
\(770\) 0 0
\(771\) 16.0000 0.576226
\(772\) −2.00000 −0.0719816
\(773\) 16.0000 0.575480 0.287740 0.957709i \(-0.407096\pi\)
0.287740 + 0.957709i \(0.407096\pi\)
\(774\) −6.00000 −0.215666
\(775\) 0 0
\(776\) −39.0000 −1.40002
\(777\) 0 0
\(778\) 14.0000 0.501924
\(779\) −6.00000 −0.214972
\(780\) −21.0000 −0.751921
\(781\) 60.0000 2.14697
\(782\) −30.0000 −1.07280
\(783\) −3.00000 −0.107211
\(784\) 0 0
\(785\) −6.00000 −0.214149
\(786\) 6.00000 0.214013
\(787\) 39.0000 1.39020 0.695100 0.718913i \(-0.255360\pi\)
0.695100 + 0.718913i \(0.255360\pi\)
\(788\) −2.00000 −0.0712470
\(789\) 14.0000 0.498413
\(790\) 27.0000 0.960617
\(791\) 0 0
\(792\) −18.0000 −0.639602
\(793\) 14.0000 0.497155
\(794\) 2.00000 0.0709773
\(795\) −27.0000 −0.957591
\(796\) −6.00000 −0.212664
\(797\) −14.0000 −0.495905 −0.247953 0.968772i \(-0.579758\pi\)
−0.247953 + 0.968772i \(0.579758\pi\)
\(798\) 0 0
\(799\) 30.0000 1.06132
\(800\) −20.0000 −0.707107
\(801\) −16.0000 −0.565332
\(802\) 20.0000 0.706225
\(803\) 24.0000 0.846942
\(804\) 9.00000 0.317406
\(805\) 0 0
\(806\) 0 0
\(807\) −9.00000 −0.316815
\(808\) 18.0000 0.633238
\(809\) −13.0000 −0.457056 −0.228528 0.973537i \(-0.573391\pi\)
−0.228528 + 0.973537i \(0.573391\pi\)
\(810\) 3.00000 0.105409
\(811\) 41.0000 1.43970 0.719852 0.694127i \(-0.244209\pi\)
0.719852 + 0.694127i \(0.244209\pi\)
\(812\) 0 0
\(813\) 31.0000 1.08722
\(814\) 6.00000 0.210300
\(815\) 48.0000 1.68137
\(816\) 6.00000 0.210042
\(817\) 36.0000 1.25948
\(818\) −32.0000 −1.11885
\(819\) 0 0
\(820\) −3.00000 −0.104765
\(821\) 18.0000 0.628204 0.314102 0.949389i \(-0.398297\pi\)
0.314102 + 0.949389i \(0.398297\pi\)
\(822\) 19.0000 0.662701
\(823\) 24.0000 0.836587 0.418294 0.908312i \(-0.362628\pi\)
0.418294 + 0.908312i \(0.362628\pi\)
\(824\) 21.0000 0.731570
\(825\) 24.0000 0.835573
\(826\) 0 0
\(827\) −32.0000 −1.11275 −0.556375 0.830932i \(-0.687808\pi\)
−0.556375 + 0.830932i \(0.687808\pi\)
\(828\) −5.00000 −0.173762
\(829\) 6.00000 0.208389 0.104194 0.994557i \(-0.466774\pi\)
0.104194 + 0.994557i \(0.466774\pi\)
\(830\) 6.00000 0.208263
\(831\) 3.00000 0.104069
\(832\) 49.0000 1.69877
\(833\) 0 0
\(834\) 13.0000 0.450153
\(835\) −69.0000 −2.38784
\(836\) 36.0000 1.24509
\(837\) 0 0
\(838\) −22.0000 −0.759977
\(839\) −27.0000 −0.932144 −0.466072 0.884747i \(-0.654331\pi\)
−0.466072 + 0.884747i \(0.654331\pi\)
\(840\) 0 0
\(841\) −20.0000 −0.689655
\(842\) 2.00000 0.0689246
\(843\) −3.00000 −0.103325
\(844\) 21.0000 0.722850
\(845\) −108.000 −3.71531
\(846\) −5.00000 −0.171904
\(847\) 0 0
\(848\) 9.00000 0.309061
\(849\) 20.0000 0.686398
\(850\) −24.0000 −0.823193
\(851\) 5.00000 0.171398
\(852\) −10.0000 −0.342594
\(853\) −30.0000 −1.02718 −0.513590 0.858036i \(-0.671685\pi\)
−0.513590 + 0.858036i \(0.671685\pi\)
\(854\) 0 0
\(855\) −18.0000 −0.615587
\(856\) −33.0000 −1.12792
\(857\) −21.0000 −0.717346 −0.358673 0.933463i \(-0.616771\pi\)
−0.358673 + 0.933463i \(0.616771\pi\)
\(858\) −42.0000 −1.43386
\(859\) 11.0000 0.375315 0.187658 0.982235i \(-0.439910\pi\)
0.187658 + 0.982235i \(0.439910\pi\)
\(860\) 18.0000 0.613795
\(861\) 0 0
\(862\) 24.0000 0.817443
\(863\) 11.0000 0.374444 0.187222 0.982318i \(-0.440052\pi\)
0.187222 + 0.982318i \(0.440052\pi\)
\(864\) 5.00000 0.170103
\(865\) 45.0000 1.53005
\(866\) −14.0000 −0.475739
\(867\) −19.0000 −0.645274
\(868\) 0 0
\(869\) −54.0000 −1.83182
\(870\) −9.00000 −0.305129
\(871\) 63.0000 2.13467
\(872\) 6.00000 0.203186
\(873\) −13.0000 −0.439983
\(874\) −30.0000 −1.01477
\(875\) 0 0
\(876\) −4.00000 −0.135147
\(877\) 26.0000 0.877958 0.438979 0.898497i \(-0.355340\pi\)
0.438979 + 0.898497i \(0.355340\pi\)
\(878\) −4.00000 −0.134993
\(879\) −6.00000 −0.202375
\(880\) −18.0000 −0.606780
\(881\) 41.0000 1.38133 0.690663 0.723177i \(-0.257319\pi\)
0.690663 + 0.723177i \(0.257319\pi\)
\(882\) 0 0
\(883\) −13.0000 −0.437485 −0.218742 0.975783i \(-0.570195\pi\)
−0.218742 + 0.975783i \(0.570195\pi\)
\(884\) −42.0000 −1.41261
\(885\) 24.0000 0.806751
\(886\) 24.0000 0.806296
\(887\) −33.0000 −1.10803 −0.554016 0.832506i \(-0.686905\pi\)
−0.554016 + 0.832506i \(0.686905\pi\)
\(888\) −3.00000 −0.100673
\(889\) 0 0
\(890\) −48.0000 −1.60896
\(891\) −6.00000 −0.201008
\(892\) 11.0000 0.368307
\(893\) 30.0000 1.00391
\(894\) 6.00000 0.200670
\(895\) −18.0000 −0.601674
\(896\) 0 0
\(897\) −35.0000 −1.16862
\(898\) 0 0
\(899\) 0 0
\(900\) −4.00000 −0.133333
\(901\) −54.0000 −1.79900
\(902\) −6.00000 −0.199778
\(903\) 0 0
\(904\) −12.0000 −0.399114
\(905\) −18.0000 −0.598340
\(906\) 8.00000 0.265782
\(907\) 26.0000 0.863316 0.431658 0.902037i \(-0.357929\pi\)
0.431658 + 0.902037i \(0.357929\pi\)
\(908\) −7.00000 −0.232303
\(909\) 6.00000 0.199007
\(910\) 0 0
\(911\) −24.0000 −0.795155 −0.397578 0.917568i \(-0.630149\pi\)
−0.397578 + 0.917568i \(0.630149\pi\)
\(912\) 6.00000 0.198680
\(913\) −12.0000 −0.397142
\(914\) −20.0000 −0.661541
\(915\) 6.00000 0.198354
\(916\) −5.00000 −0.165205
\(917\) 0 0
\(918\) 6.00000 0.198030
\(919\) −47.0000 −1.55039 −0.775193 0.631724i \(-0.782348\pi\)
−0.775193 + 0.631724i \(0.782348\pi\)
\(920\) −45.0000 −1.48361
\(921\) 9.00000 0.296560
\(922\) 15.0000 0.493999
\(923\) −70.0000 −2.30408
\(924\) 0 0
\(925\) 4.00000 0.131519
\(926\) −1.00000 −0.0328620
\(927\) 7.00000 0.229910
\(928\) −15.0000 −0.492399
\(929\) −36.0000 −1.18112 −0.590561 0.806993i \(-0.701093\pi\)
−0.590561 + 0.806993i \(0.701093\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 6.00000 0.196537
\(933\) 21.0000 0.687509
\(934\) 6.00000 0.196326
\(935\) 108.000 3.53198
\(936\) 21.0000 0.686406
\(937\) −22.0000 −0.718709 −0.359354 0.933201i \(-0.617003\pi\)
−0.359354 + 0.933201i \(0.617003\pi\)
\(938\) 0 0
\(939\) −9.00000 −0.293704
\(940\) 15.0000 0.489246
\(941\) 47.0000 1.53216 0.766078 0.642747i \(-0.222206\pi\)
0.766078 + 0.642747i \(0.222206\pi\)
\(942\) 2.00000 0.0651635
\(943\) −5.00000 −0.162822
\(944\) −8.00000 −0.260378
\(945\) 0 0
\(946\) 36.0000 1.17046
\(947\) 59.0000 1.91724 0.958621 0.284685i \(-0.0918889\pi\)
0.958621 + 0.284685i \(0.0918889\pi\)
\(948\) 9.00000 0.292306
\(949\) −28.0000 −0.908918
\(950\) −24.0000 −0.778663
\(951\) −27.0000 −0.875535
\(952\) 0 0
\(953\) −34.0000 −1.10137 −0.550684 0.834714i \(-0.685633\pi\)
−0.550684 + 0.834714i \(0.685633\pi\)
\(954\) 9.00000 0.291386
\(955\) 54.0000 1.74740
\(956\) −24.0000 −0.776215
\(957\) 18.0000 0.581857
\(958\) 24.0000 0.775405
\(959\) 0 0
\(960\) 21.0000 0.677772
\(961\) −31.0000 −1.00000
\(962\) −7.00000 −0.225689
\(963\) −11.0000 −0.354470
\(964\) −18.0000 −0.579741
\(965\) −6.00000 −0.193147
\(966\) 0 0
\(967\) −5.00000 −0.160789 −0.0803946 0.996763i \(-0.525618\pi\)
−0.0803946 + 0.996763i \(0.525618\pi\)
\(968\) 75.0000 2.41059
\(969\) −36.0000 −1.15649
\(970\) −39.0000 −1.25221
\(971\) −27.0000 −0.866471 −0.433236 0.901281i \(-0.642628\pi\)
−0.433236 + 0.901281i \(0.642628\pi\)
\(972\) 1.00000 0.0320750
\(973\) 0 0
\(974\) −32.0000 −1.02535
\(975\) −28.0000 −0.896718
\(976\) −2.00000 −0.0640184
\(977\) −10.0000 −0.319928 −0.159964 0.987123i \(-0.551138\pi\)
−0.159964 + 0.987123i \(0.551138\pi\)
\(978\) −16.0000 −0.511624
\(979\) 96.0000 3.06817
\(980\) 0 0
\(981\) 2.00000 0.0638551
\(982\) 0 0
\(983\) −4.00000 −0.127580 −0.0637901 0.997963i \(-0.520319\pi\)
−0.0637901 + 0.997963i \(0.520319\pi\)
\(984\) 3.00000 0.0956365
\(985\) −6.00000 −0.191176
\(986\) −18.0000 −0.573237
\(987\) 0 0
\(988\) −42.0000 −1.33620
\(989\) 30.0000 0.953945
\(990\) −18.0000 −0.572078
\(991\) −61.0000 −1.93773 −0.968864 0.247592i \(-0.920361\pi\)
−0.968864 + 0.247592i \(0.920361\pi\)
\(992\) 0 0
\(993\) 19.0000 0.602947
\(994\) 0 0
\(995\) −18.0000 −0.570638
\(996\) 2.00000 0.0633724
\(997\) −9.00000 −0.285033 −0.142516 0.989792i \(-0.545519\pi\)
−0.142516 + 0.989792i \(0.545519\pi\)
\(998\) −24.0000 −0.759707
\(999\) −1.00000 −0.0316386
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 \(a_p\))