Properties

Label 6008.2.a.e.1.12
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(50\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.56448 q^{3}\) \(+2.55356 q^{5}\) \(-2.27627 q^{7}\) \(-0.552416 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.56448 q^{3}\) \(+2.55356 q^{5}\) \(-2.27627 q^{7}\) \(-0.552416 q^{9}\) \(-5.49177 q^{11}\) \(+6.01599 q^{13}\) \(-3.99498 q^{15}\) \(-3.09065 q^{17}\) \(-4.77783 q^{19}\) \(+3.56117 q^{21}\) \(+7.81673 q^{23}\) \(+1.52067 q^{25}\) \(+5.55767 q^{27}\) \(+10.1573 q^{29}\) \(-9.04284 q^{31}\) \(+8.59175 q^{33}\) \(-5.81260 q^{35}\) \(-7.43029 q^{37}\) \(-9.41186 q^{39}\) \(+2.58217 q^{41}\) \(-8.81318 q^{43}\) \(-1.41063 q^{45}\) \(-0.566299 q^{47}\) \(-1.81858 q^{49}\) \(+4.83525 q^{51}\) \(-1.06014 q^{53}\) \(-14.0236 q^{55}\) \(+7.47480 q^{57}\) \(+8.80752 q^{59}\) \(-3.65742 q^{61}\) \(+1.25745 q^{63}\) \(+15.3622 q^{65}\) \(-9.02674 q^{67}\) \(-12.2291 q^{69}\) \(+13.2238 q^{71}\) \(-4.91442 q^{73}\) \(-2.37905 q^{75}\) \(+12.5008 q^{77}\) \(+8.48091 q^{79}\) \(-7.03759 q^{81}\) \(+9.36299 q^{83}\) \(-7.89217 q^{85}\) \(-15.8909 q^{87}\) \(+6.37020 q^{89}\) \(-13.6940 q^{91}\) \(+14.1473 q^{93}\) \(-12.2005 q^{95}\) \(+2.29917 q^{97}\) \(+3.03374 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(50q \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 23q^{5} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 56q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(50q \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 23q^{5} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 56q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 36q^{13} \) \(\mathstrut +\mathstrut 5q^{15} \) \(\mathstrut +\mathstrut 14q^{17} \) \(\mathstrut +\mathstrut 9q^{19} \) \(\mathstrut +\mathstrut 30q^{21} \) \(\mathstrut +\mathstrut 3q^{23} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut +\mathstrut 24q^{27} \) \(\mathstrut +\mathstrut 61q^{29} \) \(\mathstrut +\mathstrut 27q^{31} \) \(\mathstrut +\mathstrut 24q^{33} \) \(\mathstrut -\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 56q^{37} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 19q^{43} \) \(\mathstrut +\mathstrut 76q^{45} \) \(\mathstrut +\mathstrut 3q^{47} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut q^{51} \) \(\mathstrut +\mathstrut 56q^{53} \) \(\mathstrut +\mathstrut 7q^{55} \) \(\mathstrut +\mathstrut 35q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut +\mathstrut 67q^{61} \) \(\mathstrut +\mathstrut 25q^{63} \) \(\mathstrut +\mathstrut 27q^{65} \) \(\mathstrut +\mathstrut 46q^{67} \) \(\mathstrut +\mathstrut 68q^{69} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut +\mathstrut 62q^{73} \) \(\mathstrut +\mathstrut 27q^{75} \) \(\mathstrut +\mathstrut 71q^{77} \) \(\mathstrut +\mathstrut 7q^{79} \) \(\mathstrut +\mathstrut 74q^{81} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut +\mathstrut 72q^{85} \) \(\mathstrut +\mathstrut 25q^{87} \) \(\mathstrut +\mathstrut 19q^{89} \) \(\mathstrut +\mathstrut 45q^{91} \) \(\mathstrut +\mathstrut 72q^{93} \) \(\mathstrut -\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 81q^{97} \) \(\mathstrut +\mathstrut 16q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.56448 −0.903251 −0.451625 0.892208i \(-0.649156\pi\)
−0.451625 + 0.892208i \(0.649156\pi\)
\(4\) 0 0
\(5\) 2.55356 1.14199 0.570993 0.820955i \(-0.306558\pi\)
0.570993 + 0.820955i \(0.306558\pi\)
\(6\) 0 0
\(7\) −2.27627 −0.860350 −0.430175 0.902745i \(-0.641548\pi\)
−0.430175 + 0.902745i \(0.641548\pi\)
\(8\) 0 0
\(9\) −0.552416 −0.184139
\(10\) 0 0
\(11\) −5.49177 −1.65583 −0.827916 0.560852i \(-0.810474\pi\)
−0.827916 + 0.560852i \(0.810474\pi\)
\(12\) 0 0
\(13\) 6.01599 1.66853 0.834267 0.551360i \(-0.185891\pi\)
0.834267 + 0.551360i \(0.185891\pi\)
\(14\) 0 0
\(15\) −3.99498 −1.03150
\(16\) 0 0
\(17\) −3.09065 −0.749594 −0.374797 0.927107i \(-0.622288\pi\)
−0.374797 + 0.927107i \(0.622288\pi\)
\(18\) 0 0
\(19\) −4.77783 −1.09611 −0.548055 0.836442i \(-0.684631\pi\)
−0.548055 + 0.836442i \(0.684631\pi\)
\(20\) 0 0
\(21\) 3.56117 0.777112
\(22\) 0 0
\(23\) 7.81673 1.62990 0.814951 0.579530i \(-0.196764\pi\)
0.814951 + 0.579530i \(0.196764\pi\)
\(24\) 0 0
\(25\) 1.52067 0.304134
\(26\) 0 0
\(27\) 5.55767 1.06957
\(28\) 0 0
\(29\) 10.1573 1.88617 0.943083 0.332559i \(-0.107912\pi\)
0.943083 + 0.332559i \(0.107912\pi\)
\(30\) 0 0
\(31\) −9.04284 −1.62414 −0.812071 0.583559i \(-0.801660\pi\)
−0.812071 + 0.583559i \(0.801660\pi\)
\(32\) 0 0
\(33\) 8.59175 1.49563
\(34\) 0 0
\(35\) −5.81260 −0.982508
\(36\) 0 0
\(37\) −7.43029 −1.22153 −0.610766 0.791811i \(-0.709138\pi\)
−0.610766 + 0.791811i \(0.709138\pi\)
\(38\) 0 0
\(39\) −9.41186 −1.50710
\(40\) 0 0
\(41\) 2.58217 0.403268 0.201634 0.979461i \(-0.435375\pi\)
0.201634 + 0.979461i \(0.435375\pi\)
\(42\) 0 0
\(43\) −8.81318 −1.34400 −0.671998 0.740553i \(-0.734564\pi\)
−0.671998 + 0.740553i \(0.734564\pi\)
\(44\) 0 0
\(45\) −1.41063 −0.210284
\(46\) 0 0
\(47\) −0.566299 −0.0826032 −0.0413016 0.999147i \(-0.513150\pi\)
−0.0413016 + 0.999147i \(0.513150\pi\)
\(48\) 0 0
\(49\) −1.81858 −0.259798
\(50\) 0 0
\(51\) 4.83525 0.677071
\(52\) 0 0
\(53\) −1.06014 −0.145621 −0.0728107 0.997346i \(-0.523197\pi\)
−0.0728107 + 0.997346i \(0.523197\pi\)
\(54\) 0 0
\(55\) −14.0236 −1.89094
\(56\) 0 0
\(57\) 7.47480 0.990061
\(58\) 0 0
\(59\) 8.80752 1.14664 0.573321 0.819331i \(-0.305655\pi\)
0.573321 + 0.819331i \(0.305655\pi\)
\(60\) 0 0
\(61\) −3.65742 −0.468284 −0.234142 0.972202i \(-0.575228\pi\)
−0.234142 + 0.972202i \(0.575228\pi\)
\(62\) 0 0
\(63\) 1.25745 0.158424
\(64\) 0 0
\(65\) 15.3622 1.90544
\(66\) 0 0
\(67\) −9.02674 −1.10279 −0.551396 0.834244i \(-0.685905\pi\)
−0.551396 + 0.834244i \(0.685905\pi\)
\(68\) 0 0
\(69\) −12.2291 −1.47221
\(70\) 0 0
\(71\) 13.2238 1.56938 0.784690 0.619888i \(-0.212822\pi\)
0.784690 + 0.619888i \(0.212822\pi\)
\(72\) 0 0
\(73\) −4.91442 −0.575189 −0.287595 0.957752i \(-0.592856\pi\)
−0.287595 + 0.957752i \(0.592856\pi\)
\(74\) 0 0
\(75\) −2.37905 −0.274709
\(76\) 0 0
\(77\) 12.5008 1.42460
\(78\) 0 0
\(79\) 8.48091 0.954176 0.477088 0.878855i \(-0.341692\pi\)
0.477088 + 0.878855i \(0.341692\pi\)
\(80\) 0 0
\(81\) −7.03759 −0.781954
\(82\) 0 0
\(83\) 9.36299 1.02772 0.513861 0.857874i \(-0.328215\pi\)
0.513861 + 0.857874i \(0.328215\pi\)
\(84\) 0 0
\(85\) −7.89217 −0.856026
\(86\) 0 0
\(87\) −15.8909 −1.70368
\(88\) 0 0
\(89\) 6.37020 0.675240 0.337620 0.941283i \(-0.390378\pi\)
0.337620 + 0.941283i \(0.390378\pi\)
\(90\) 0 0
\(91\) −13.6940 −1.43552
\(92\) 0 0
\(93\) 14.1473 1.46701
\(94\) 0 0
\(95\) −12.2005 −1.25174
\(96\) 0 0
\(97\) 2.29917 0.233445 0.116723 0.993165i \(-0.462761\pi\)
0.116723 + 0.993165i \(0.462761\pi\)
\(98\) 0 0
\(99\) 3.03374 0.304902
\(100\) 0 0
\(101\) 2.68211 0.266879 0.133440 0.991057i \(-0.457398\pi\)
0.133440 + 0.991057i \(0.457398\pi\)
\(102\) 0 0
\(103\) 14.4548 1.42427 0.712136 0.702041i \(-0.247728\pi\)
0.712136 + 0.702041i \(0.247728\pi\)
\(104\) 0 0
\(105\) 9.09367 0.887451
\(106\) 0 0
\(107\) −8.08142 −0.781261 −0.390630 0.920548i \(-0.627743\pi\)
−0.390630 + 0.920548i \(0.627743\pi\)
\(108\) 0 0
\(109\) −9.27715 −0.888590 −0.444295 0.895881i \(-0.646546\pi\)
−0.444295 + 0.895881i \(0.646546\pi\)
\(110\) 0 0
\(111\) 11.6245 1.10335
\(112\) 0 0
\(113\) 14.2851 1.34383 0.671914 0.740629i \(-0.265472\pi\)
0.671914 + 0.740629i \(0.265472\pi\)
\(114\) 0 0
\(115\) 19.9605 1.86133
\(116\) 0 0
\(117\) −3.32332 −0.307241
\(118\) 0 0
\(119\) 7.03517 0.644913
\(120\) 0 0
\(121\) 19.1596 1.74178
\(122\) 0 0
\(123\) −4.03975 −0.364252
\(124\) 0 0
\(125\) −8.88468 −0.794670
\(126\) 0 0
\(127\) −11.2935 −1.00213 −0.501067 0.865408i \(-0.667059\pi\)
−0.501067 + 0.865408i \(0.667059\pi\)
\(128\) 0 0
\(129\) 13.7880 1.21397
\(130\) 0 0
\(131\) 5.50771 0.481211 0.240606 0.970623i \(-0.422654\pi\)
0.240606 + 0.970623i \(0.422654\pi\)
\(132\) 0 0
\(133\) 10.8756 0.943038
\(134\) 0 0
\(135\) 14.1918 1.22144
\(136\) 0 0
\(137\) 1.08824 0.0929750 0.0464875 0.998919i \(-0.485197\pi\)
0.0464875 + 0.998919i \(0.485197\pi\)
\(138\) 0 0
\(139\) 14.2837 1.21153 0.605763 0.795645i \(-0.292868\pi\)
0.605763 + 0.795645i \(0.292868\pi\)
\(140\) 0 0
\(141\) 0.885961 0.0746114
\(142\) 0 0
\(143\) −33.0384 −2.76281
\(144\) 0 0
\(145\) 25.9373 2.15398
\(146\) 0 0
\(147\) 2.84513 0.234662
\(148\) 0 0
\(149\) 11.8921 0.974236 0.487118 0.873336i \(-0.338048\pi\)
0.487118 + 0.873336i \(0.338048\pi\)
\(150\) 0 0
\(151\) 21.4887 1.74873 0.874364 0.485271i \(-0.161279\pi\)
0.874364 + 0.485271i \(0.161279\pi\)
\(152\) 0 0
\(153\) 1.70733 0.138029
\(154\) 0 0
\(155\) −23.0914 −1.85475
\(156\) 0 0
\(157\) −8.32223 −0.664186 −0.332093 0.943247i \(-0.607755\pi\)
−0.332093 + 0.943247i \(0.607755\pi\)
\(158\) 0 0
\(159\) 1.65856 0.131533
\(160\) 0 0
\(161\) −17.7930 −1.40229
\(162\) 0 0
\(163\) 17.2778 1.35330 0.676649 0.736305i \(-0.263431\pi\)
0.676649 + 0.736305i \(0.263431\pi\)
\(164\) 0 0
\(165\) 21.9395 1.70799
\(166\) 0 0
\(167\) −14.0757 −1.08921 −0.544605 0.838693i \(-0.683320\pi\)
−0.544605 + 0.838693i \(0.683320\pi\)
\(168\) 0 0
\(169\) 23.1921 1.78401
\(170\) 0 0
\(171\) 2.63935 0.201836
\(172\) 0 0
\(173\) 11.8755 0.902878 0.451439 0.892302i \(-0.350911\pi\)
0.451439 + 0.892302i \(0.350911\pi\)
\(174\) 0 0
\(175\) −3.46145 −0.261661
\(176\) 0 0
\(177\) −13.7792 −1.03570
\(178\) 0 0
\(179\) −7.48192 −0.559225 −0.279612 0.960113i \(-0.590206\pi\)
−0.279612 + 0.960113i \(0.590206\pi\)
\(180\) 0 0
\(181\) −17.3704 −1.29113 −0.645566 0.763705i \(-0.723378\pi\)
−0.645566 + 0.763705i \(0.723378\pi\)
\(182\) 0 0
\(183\) 5.72194 0.422978
\(184\) 0 0
\(185\) −18.9737 −1.39497
\(186\) 0 0
\(187\) 16.9732 1.24120
\(188\) 0 0
\(189\) −12.6508 −0.920208
\(190\) 0 0
\(191\) −23.6065 −1.70810 −0.854052 0.520188i \(-0.825862\pi\)
−0.854052 + 0.520188i \(0.825862\pi\)
\(192\) 0 0
\(193\) −8.95160 −0.644350 −0.322175 0.946680i \(-0.604414\pi\)
−0.322175 + 0.946680i \(0.604414\pi\)
\(194\) 0 0
\(195\) −24.0338 −1.72109
\(196\) 0 0
\(197\) −10.6082 −0.755804 −0.377902 0.925846i \(-0.623354\pi\)
−0.377902 + 0.925846i \(0.623354\pi\)
\(198\) 0 0
\(199\) 0.0364639 0.00258486 0.00129243 0.999999i \(-0.499589\pi\)
0.00129243 + 0.999999i \(0.499589\pi\)
\(200\) 0 0
\(201\) 14.1221 0.996098
\(202\) 0 0
\(203\) −23.1208 −1.62276
\(204\) 0 0
\(205\) 6.59373 0.460526
\(206\) 0 0
\(207\) −4.31808 −0.300128
\(208\) 0 0
\(209\) 26.2388 1.81497
\(210\) 0 0
\(211\) 17.4829 1.20357 0.601785 0.798658i \(-0.294456\pi\)
0.601785 + 0.798658i \(0.294456\pi\)
\(212\) 0 0
\(213\) −20.6884 −1.41754
\(214\) 0 0
\(215\) −22.5050 −1.53483
\(216\) 0 0
\(217\) 20.5840 1.39733
\(218\) 0 0
\(219\) 7.68849 0.519540
\(220\) 0 0
\(221\) −18.5933 −1.25072
\(222\) 0 0
\(223\) −4.30580 −0.288338 −0.144169 0.989553i \(-0.546051\pi\)
−0.144169 + 0.989553i \(0.546051\pi\)
\(224\) 0 0
\(225\) −0.840041 −0.0560027
\(226\) 0 0
\(227\) 24.6948 1.63905 0.819527 0.573040i \(-0.194236\pi\)
0.819527 + 0.573040i \(0.194236\pi\)
\(228\) 0 0
\(229\) 3.17703 0.209944 0.104972 0.994475i \(-0.466525\pi\)
0.104972 + 0.994475i \(0.466525\pi\)
\(230\) 0 0
\(231\) −19.5572 −1.28677
\(232\) 0 0
\(233\) −21.6926 −1.42113 −0.710566 0.703631i \(-0.751561\pi\)
−0.710566 + 0.703631i \(0.751561\pi\)
\(234\) 0 0
\(235\) −1.44608 −0.0943318
\(236\) 0 0
\(237\) −13.2682 −0.861860
\(238\) 0 0
\(239\) 23.5169 1.52118 0.760590 0.649232i \(-0.224910\pi\)
0.760590 + 0.649232i \(0.224910\pi\)
\(240\) 0 0
\(241\) 20.0100 1.28896 0.644479 0.764622i \(-0.277074\pi\)
0.644479 + 0.764622i \(0.277074\pi\)
\(242\) 0 0
\(243\) −5.66286 −0.363273
\(244\) 0 0
\(245\) −4.64386 −0.296685
\(246\) 0 0
\(247\) −28.7434 −1.82890
\(248\) 0 0
\(249\) −14.6482 −0.928290
\(250\) 0 0
\(251\) −11.7447 −0.741321 −0.370660 0.928769i \(-0.620869\pi\)
−0.370660 + 0.928769i \(0.620869\pi\)
\(252\) 0 0
\(253\) −42.9277 −2.69884
\(254\) 0 0
\(255\) 12.3471 0.773206
\(256\) 0 0
\(257\) 15.4256 0.962223 0.481112 0.876659i \(-0.340233\pi\)
0.481112 + 0.876659i \(0.340233\pi\)
\(258\) 0 0
\(259\) 16.9134 1.05095
\(260\) 0 0
\(261\) −5.61106 −0.347316
\(262\) 0 0
\(263\) 27.0951 1.67076 0.835379 0.549675i \(-0.185248\pi\)
0.835379 + 0.549675i \(0.185248\pi\)
\(264\) 0 0
\(265\) −2.70713 −0.166298
\(266\) 0 0
\(267\) −9.96603 −0.609911
\(268\) 0 0
\(269\) 16.5457 1.00881 0.504405 0.863467i \(-0.331712\pi\)
0.504405 + 0.863467i \(0.331712\pi\)
\(270\) 0 0
\(271\) 16.8104 1.02116 0.510578 0.859831i \(-0.329431\pi\)
0.510578 + 0.859831i \(0.329431\pi\)
\(272\) 0 0
\(273\) 21.4240 1.29664
\(274\) 0 0
\(275\) −8.35116 −0.503594
\(276\) 0 0
\(277\) 18.1850 1.09263 0.546317 0.837579i \(-0.316030\pi\)
0.546317 + 0.837579i \(0.316030\pi\)
\(278\) 0 0
\(279\) 4.99540 0.299067
\(280\) 0 0
\(281\) −5.34514 −0.318865 −0.159432 0.987209i \(-0.550966\pi\)
−0.159432 + 0.987209i \(0.550966\pi\)
\(282\) 0 0
\(283\) 13.2256 0.786181 0.393091 0.919500i \(-0.371406\pi\)
0.393091 + 0.919500i \(0.371406\pi\)
\(284\) 0 0
\(285\) 19.0873 1.13064
\(286\) 0 0
\(287\) −5.87773 −0.346951
\(288\) 0 0
\(289\) −7.44785 −0.438109
\(290\) 0 0
\(291\) −3.59700 −0.210860
\(292\) 0 0
\(293\) 25.4840 1.48879 0.744394 0.667740i \(-0.232738\pi\)
0.744394 + 0.667740i \(0.232738\pi\)
\(294\) 0 0
\(295\) 22.4905 1.30945
\(296\) 0 0
\(297\) −30.5215 −1.77103
\(298\) 0 0
\(299\) 47.0254 2.71955
\(300\) 0 0
\(301\) 20.0612 1.15631
\(302\) 0 0
\(303\) −4.19609 −0.241059
\(304\) 0 0
\(305\) −9.33943 −0.534774
\(306\) 0 0
\(307\) 18.6615 1.06507 0.532534 0.846409i \(-0.321240\pi\)
0.532534 + 0.846409i \(0.321240\pi\)
\(308\) 0 0
\(309\) −22.6142 −1.28647
\(310\) 0 0
\(311\) −7.32284 −0.415240 −0.207620 0.978210i \(-0.566572\pi\)
−0.207620 + 0.978210i \(0.566572\pi\)
\(312\) 0 0
\(313\) 17.7322 1.00228 0.501140 0.865366i \(-0.332914\pi\)
0.501140 + 0.865366i \(0.332914\pi\)
\(314\) 0 0
\(315\) 3.21097 0.180918
\(316\) 0 0
\(317\) −17.9485 −1.00809 −0.504044 0.863678i \(-0.668155\pi\)
−0.504044 + 0.863678i \(0.668155\pi\)
\(318\) 0 0
\(319\) −55.7816 −3.12317
\(320\) 0 0
\(321\) 12.6432 0.705674
\(322\) 0 0
\(323\) 14.7666 0.821637
\(324\) 0 0
\(325\) 9.14832 0.507457
\(326\) 0 0
\(327\) 14.5139 0.802619
\(328\) 0 0
\(329\) 1.28905 0.0710677
\(330\) 0 0
\(331\) 12.1753 0.669215 0.334608 0.942358i \(-0.391396\pi\)
0.334608 + 0.942358i \(0.391396\pi\)
\(332\) 0 0
\(333\) 4.10461 0.224931
\(334\) 0 0
\(335\) −23.0503 −1.25937
\(336\) 0 0
\(337\) −21.9786 −1.19725 −0.598625 0.801029i \(-0.704286\pi\)
−0.598625 + 0.801029i \(0.704286\pi\)
\(338\) 0 0
\(339\) −22.3487 −1.21381
\(340\) 0 0
\(341\) 49.6612 2.68931
\(342\) 0 0
\(343\) 20.0735 1.08387
\(344\) 0 0
\(345\) −31.2277 −1.68124
\(346\) 0 0
\(347\) 9.90242 0.531590 0.265795 0.964030i \(-0.414366\pi\)
0.265795 + 0.964030i \(0.414366\pi\)
\(348\) 0 0
\(349\) −16.2225 −0.868372 −0.434186 0.900823i \(-0.642964\pi\)
−0.434186 + 0.900823i \(0.642964\pi\)
\(350\) 0 0
\(351\) 33.4349 1.78462
\(352\) 0 0
\(353\) 5.91781 0.314973 0.157487 0.987521i \(-0.449661\pi\)
0.157487 + 0.987521i \(0.449661\pi\)
\(354\) 0 0
\(355\) 33.7678 1.79221
\(356\) 0 0
\(357\) −11.0064 −0.582518
\(358\) 0 0
\(359\) 8.38475 0.442530 0.221265 0.975214i \(-0.428981\pi\)
0.221265 + 0.975214i \(0.428981\pi\)
\(360\) 0 0
\(361\) 3.82766 0.201456
\(362\) 0 0
\(363\) −29.9747 −1.57326
\(364\) 0 0
\(365\) −12.5493 −0.656858
\(366\) 0 0
\(367\) −8.25170 −0.430735 −0.215368 0.976533i \(-0.569095\pi\)
−0.215368 + 0.976533i \(0.569095\pi\)
\(368\) 0 0
\(369\) −1.42643 −0.0742571
\(370\) 0 0
\(371\) 2.41317 0.125285
\(372\) 0 0
\(373\) 36.1508 1.87182 0.935910 0.352240i \(-0.114580\pi\)
0.935910 + 0.352240i \(0.114580\pi\)
\(374\) 0 0
\(375\) 13.8999 0.717786
\(376\) 0 0
\(377\) 61.1062 3.14713
\(378\) 0 0
\(379\) −2.69390 −0.138376 −0.0691881 0.997604i \(-0.522041\pi\)
−0.0691881 + 0.997604i \(0.522041\pi\)
\(380\) 0 0
\(381\) 17.6684 0.905179
\(382\) 0 0
\(383\) 5.32147 0.271914 0.135957 0.990715i \(-0.456589\pi\)
0.135957 + 0.990715i \(0.456589\pi\)
\(384\) 0 0
\(385\) 31.9215 1.62687
\(386\) 0 0
\(387\) 4.86854 0.247482
\(388\) 0 0
\(389\) 14.5183 0.736109 0.368054 0.929804i \(-0.380024\pi\)
0.368054 + 0.929804i \(0.380024\pi\)
\(390\) 0 0
\(391\) −24.1588 −1.22176
\(392\) 0 0
\(393\) −8.61669 −0.434654
\(394\) 0 0
\(395\) 21.6565 1.08966
\(396\) 0 0
\(397\) −10.6123 −0.532615 −0.266307 0.963888i \(-0.585804\pi\)
−0.266307 + 0.963888i \(0.585804\pi\)
\(398\) 0 0
\(399\) −17.0147 −0.851800
\(400\) 0 0
\(401\) 29.0551 1.45094 0.725472 0.688252i \(-0.241622\pi\)
0.725472 + 0.688252i \(0.241622\pi\)
\(402\) 0 0
\(403\) −54.4016 −2.70994
\(404\) 0 0
\(405\) −17.9709 −0.892982
\(406\) 0 0
\(407\) 40.8055 2.02265
\(408\) 0 0
\(409\) −16.4481 −0.813306 −0.406653 0.913583i \(-0.633304\pi\)
−0.406653 + 0.913583i \(0.633304\pi\)
\(410\) 0 0
\(411\) −1.70253 −0.0839797
\(412\) 0 0
\(413\) −20.0483 −0.986513
\(414\) 0 0
\(415\) 23.9090 1.17364
\(416\) 0 0
\(417\) −22.3465 −1.09431
\(418\) 0 0
\(419\) −24.1151 −1.17810 −0.589050 0.808097i \(-0.700498\pi\)
−0.589050 + 0.808097i \(0.700498\pi\)
\(420\) 0 0
\(421\) 16.6029 0.809178 0.404589 0.914499i \(-0.367415\pi\)
0.404589 + 0.914499i \(0.367415\pi\)
\(422\) 0 0
\(423\) 0.312832 0.0152104
\(424\) 0 0
\(425\) −4.69986 −0.227977
\(426\) 0 0
\(427\) 8.32528 0.402888
\(428\) 0 0
\(429\) 51.6878 2.49551
\(430\) 0 0
\(431\) −23.7608 −1.14452 −0.572259 0.820073i \(-0.693933\pi\)
−0.572259 + 0.820073i \(0.693933\pi\)
\(432\) 0 0
\(433\) 38.1369 1.83274 0.916371 0.400331i \(-0.131105\pi\)
0.916371 + 0.400331i \(0.131105\pi\)
\(434\) 0 0
\(435\) −40.5783 −1.94558
\(436\) 0 0
\(437\) −37.3470 −1.78655
\(438\) 0 0
\(439\) −25.9263 −1.23740 −0.618698 0.785629i \(-0.712340\pi\)
−0.618698 + 0.785629i \(0.712340\pi\)
\(440\) 0 0
\(441\) 1.00461 0.0478387
\(442\) 0 0
\(443\) 36.6056 1.73919 0.869593 0.493770i \(-0.164381\pi\)
0.869593 + 0.493770i \(0.164381\pi\)
\(444\) 0 0
\(445\) 16.2667 0.771115
\(446\) 0 0
\(447\) −18.6049 −0.879979
\(448\) 0 0
\(449\) −15.3170 −0.722853 −0.361427 0.932401i \(-0.617710\pi\)
−0.361427 + 0.932401i \(0.617710\pi\)
\(450\) 0 0
\(451\) −14.1807 −0.667743
\(452\) 0 0
\(453\) −33.6186 −1.57954
\(454\) 0 0
\(455\) −34.9685 −1.63935
\(456\) 0 0
\(457\) −22.8122 −1.06711 −0.533554 0.845766i \(-0.679144\pi\)
−0.533554 + 0.845766i \(0.679144\pi\)
\(458\) 0 0
\(459\) −17.1768 −0.801746
\(460\) 0 0
\(461\) −2.66668 −0.124200 −0.0620998 0.998070i \(-0.519780\pi\)
−0.0620998 + 0.998070i \(0.519780\pi\)
\(462\) 0 0
\(463\) 29.1229 1.35346 0.676728 0.736233i \(-0.263397\pi\)
0.676728 + 0.736233i \(0.263397\pi\)
\(464\) 0 0
\(465\) 36.1260 1.67530
\(466\) 0 0
\(467\) −17.7065 −0.819360 −0.409680 0.912229i \(-0.634360\pi\)
−0.409680 + 0.912229i \(0.634360\pi\)
\(468\) 0 0
\(469\) 20.5473 0.948788
\(470\) 0 0
\(471\) 13.0199 0.599926
\(472\) 0 0
\(473\) 48.4000 2.22543
\(474\) 0 0
\(475\) −7.26549 −0.333364
\(476\) 0 0
\(477\) 0.585638 0.0268145
\(478\) 0 0
\(479\) 6.16540 0.281704 0.140852 0.990031i \(-0.455016\pi\)
0.140852 + 0.990031i \(0.455016\pi\)
\(480\) 0 0
\(481\) −44.7005 −2.03817
\(482\) 0 0
\(483\) 27.8367 1.26662
\(484\) 0 0
\(485\) 5.87107 0.266592
\(486\) 0 0
\(487\) 24.3662 1.10414 0.552068 0.833799i \(-0.313839\pi\)
0.552068 + 0.833799i \(0.313839\pi\)
\(488\) 0 0
\(489\) −27.0306 −1.22237
\(490\) 0 0
\(491\) −35.3305 −1.59444 −0.797221 0.603687i \(-0.793698\pi\)
−0.797221 + 0.603687i \(0.793698\pi\)
\(492\) 0 0
\(493\) −31.3927 −1.41386
\(494\) 0 0
\(495\) 7.74684 0.348195
\(496\) 0 0
\(497\) −30.1010 −1.35022
\(498\) 0 0
\(499\) 41.6013 1.86233 0.931164 0.364599i \(-0.118794\pi\)
0.931164 + 0.364599i \(0.118794\pi\)
\(500\) 0 0
\(501\) 22.0211 0.983829
\(502\) 0 0
\(503\) −9.93154 −0.442826 −0.221413 0.975180i \(-0.571067\pi\)
−0.221413 + 0.975180i \(0.571067\pi\)
\(504\) 0 0
\(505\) 6.84892 0.304773
\(506\) 0 0
\(507\) −36.2835 −1.61140
\(508\) 0 0
\(509\) 3.05956 0.135612 0.0678062 0.997699i \(-0.478400\pi\)
0.0678062 + 0.997699i \(0.478400\pi\)
\(510\) 0 0
\(511\) 11.1866 0.494864
\(512\) 0 0
\(513\) −26.5536 −1.17237
\(514\) 0 0
\(515\) 36.9112 1.62650
\(516\) 0 0
\(517\) 3.10999 0.136777
\(518\) 0 0
\(519\) −18.5789 −0.815525
\(520\) 0 0
\(521\) −2.80372 −0.122833 −0.0614165 0.998112i \(-0.519562\pi\)
−0.0614165 + 0.998112i \(0.519562\pi\)
\(522\) 0 0
\(523\) −37.3390 −1.63272 −0.816361 0.577542i \(-0.804012\pi\)
−0.816361 + 0.577542i \(0.804012\pi\)
\(524\) 0 0
\(525\) 5.41536 0.236346
\(526\) 0 0
\(527\) 27.9483 1.21745
\(528\) 0 0
\(529\) 38.1013 1.65658
\(530\) 0 0
\(531\) −4.86541 −0.211141
\(532\) 0 0
\(533\) 15.5343 0.672866
\(534\) 0 0
\(535\) −20.6364 −0.892189
\(536\) 0 0
\(537\) 11.7053 0.505120
\(538\) 0 0
\(539\) 9.98724 0.430181
\(540\) 0 0
\(541\) 36.3964 1.56480 0.782401 0.622775i \(-0.213995\pi\)
0.782401 + 0.622775i \(0.213995\pi\)
\(542\) 0 0
\(543\) 27.1756 1.16622
\(544\) 0 0
\(545\) −23.6898 −1.01476
\(546\) 0 0
\(547\) −8.59960 −0.367692 −0.183846 0.982955i \(-0.558855\pi\)
−0.183846 + 0.982955i \(0.558855\pi\)
\(548\) 0 0
\(549\) 2.02041 0.0862292
\(550\) 0 0
\(551\) −48.5299 −2.06744
\(552\) 0 0
\(553\) −19.3049 −0.820926
\(554\) 0 0
\(555\) 29.6839 1.26001
\(556\) 0 0
\(557\) 3.66173 0.155152 0.0775762 0.996986i \(-0.475282\pi\)
0.0775762 + 0.996986i \(0.475282\pi\)
\(558\) 0 0
\(559\) −53.0199 −2.24250
\(560\) 0 0
\(561\) −26.5541 −1.12112
\(562\) 0 0
\(563\) −15.5423 −0.655030 −0.327515 0.944846i \(-0.606211\pi\)
−0.327515 + 0.944846i \(0.606211\pi\)
\(564\) 0 0
\(565\) 36.4778 1.53463
\(566\) 0 0
\(567\) 16.0195 0.672755
\(568\) 0 0
\(569\) −2.81949 −0.118199 −0.0590996 0.998252i \(-0.518823\pi\)
−0.0590996 + 0.998252i \(0.518823\pi\)
\(570\) 0 0
\(571\) −10.7280 −0.448951 −0.224476 0.974480i \(-0.572067\pi\)
−0.224476 + 0.974480i \(0.572067\pi\)
\(572\) 0 0
\(573\) 36.9317 1.54285
\(574\) 0 0
\(575\) 11.8867 0.495708
\(576\) 0 0
\(577\) −24.1374 −1.00485 −0.502426 0.864620i \(-0.667559\pi\)
−0.502426 + 0.864620i \(0.667559\pi\)
\(578\) 0 0
\(579\) 14.0046 0.582010
\(580\) 0 0
\(581\) −21.3127 −0.884201
\(582\) 0 0
\(583\) 5.82205 0.241125
\(584\) 0 0
\(585\) −8.48631 −0.350866
\(586\) 0 0
\(587\) −17.7835 −0.734003 −0.367001 0.930220i \(-0.619616\pi\)
−0.367001 + 0.930220i \(0.619616\pi\)
\(588\) 0 0
\(589\) 43.2051 1.78024
\(590\) 0 0
\(591\) 16.5963 0.682680
\(592\) 0 0
\(593\) 25.5882 1.05078 0.525391 0.850861i \(-0.323919\pi\)
0.525391 + 0.850861i \(0.323919\pi\)
\(594\) 0 0
\(595\) 17.9647 0.736482
\(596\) 0 0
\(597\) −0.0570469 −0.00233478
\(598\) 0 0
\(599\) 31.3014 1.27894 0.639470 0.768816i \(-0.279154\pi\)
0.639470 + 0.768816i \(0.279154\pi\)
\(600\) 0 0
\(601\) 16.0565 0.654959 0.327479 0.944858i \(-0.393801\pi\)
0.327479 + 0.944858i \(0.393801\pi\)
\(602\) 0 0
\(603\) 4.98651 0.203067
\(604\) 0 0
\(605\) 48.9251 1.98909
\(606\) 0 0
\(607\) 11.0513 0.448559 0.224280 0.974525i \(-0.427997\pi\)
0.224280 + 0.974525i \(0.427997\pi\)
\(608\) 0 0
\(609\) 36.1719 1.46576
\(610\) 0 0
\(611\) −3.40685 −0.137826
\(612\) 0 0
\(613\) 42.1688 1.70318 0.851592 0.524206i \(-0.175638\pi\)
0.851592 + 0.524206i \(0.175638\pi\)
\(614\) 0 0
\(615\) −10.3157 −0.415971
\(616\) 0 0
\(617\) 2.95948 0.119144 0.0595722 0.998224i \(-0.481026\pi\)
0.0595722 + 0.998224i \(0.481026\pi\)
\(618\) 0 0
\(619\) 37.7567 1.51757 0.758785 0.651341i \(-0.225793\pi\)
0.758785 + 0.651341i \(0.225793\pi\)
\(620\) 0 0
\(621\) 43.4428 1.74330
\(622\) 0 0
\(623\) −14.5003 −0.580943
\(624\) 0 0
\(625\) −30.2909 −1.21164
\(626\) 0 0
\(627\) −41.0499 −1.63938
\(628\) 0 0
\(629\) 22.9645 0.915653
\(630\) 0 0
\(631\) −34.0356 −1.35493 −0.677467 0.735553i \(-0.736922\pi\)
−0.677467 + 0.735553i \(0.736922\pi\)
\(632\) 0 0
\(633\) −27.3515 −1.08713
\(634\) 0 0
\(635\) −28.8386 −1.14442
\(636\) 0 0
\(637\) −10.9406 −0.433481
\(638\) 0 0
\(639\) −7.30505 −0.288983
\(640\) 0 0
\(641\) 28.6175 1.13032 0.565162 0.824980i \(-0.308814\pi\)
0.565162 + 0.824980i \(0.308814\pi\)
\(642\) 0 0
\(643\) 1.34506 0.0530441 0.0265221 0.999648i \(-0.491557\pi\)
0.0265221 + 0.999648i \(0.491557\pi\)
\(644\) 0 0
\(645\) 35.2085 1.38633
\(646\) 0 0
\(647\) 23.5858 0.927253 0.463627 0.886031i \(-0.346548\pi\)
0.463627 + 0.886031i \(0.346548\pi\)
\(648\) 0 0
\(649\) −48.3689 −1.89865
\(650\) 0 0
\(651\) −32.2031 −1.26214
\(652\) 0 0
\(653\) 21.5890 0.844843 0.422421 0.906400i \(-0.361180\pi\)
0.422421 + 0.906400i \(0.361180\pi\)
\(654\) 0 0
\(655\) 14.0643 0.549537
\(656\) 0 0
\(657\) 2.71480 0.105915
\(658\) 0 0
\(659\) −34.5852 −1.34725 −0.673624 0.739074i \(-0.735263\pi\)
−0.673624 + 0.739074i \(0.735263\pi\)
\(660\) 0 0
\(661\) −31.8437 −1.23858 −0.619289 0.785163i \(-0.712579\pi\)
−0.619289 + 0.785163i \(0.712579\pi\)
\(662\) 0 0
\(663\) 29.0888 1.12972
\(664\) 0 0
\(665\) 27.7716 1.07694
\(666\) 0 0
\(667\) 79.3970 3.07426
\(668\) 0 0
\(669\) 6.73632 0.260441
\(670\) 0 0
\(671\) 20.0857 0.775400
\(672\) 0 0
\(673\) 22.8096 0.879244 0.439622 0.898183i \(-0.355112\pi\)
0.439622 + 0.898183i \(0.355112\pi\)
\(674\) 0 0
\(675\) 8.45137 0.325293
\(676\) 0 0
\(677\) −50.5440 −1.94256 −0.971282 0.237933i \(-0.923530\pi\)
−0.971282 + 0.237933i \(0.923530\pi\)
\(678\) 0 0
\(679\) −5.23354 −0.200845
\(680\) 0 0
\(681\) −38.6345 −1.48048
\(682\) 0 0
\(683\) 24.4105 0.934042 0.467021 0.884246i \(-0.345327\pi\)
0.467021 + 0.884246i \(0.345327\pi\)
\(684\) 0 0
\(685\) 2.77890 0.106176
\(686\) 0 0
\(687\) −4.97039 −0.189632
\(688\) 0 0
\(689\) −6.37779 −0.242974
\(690\) 0 0
\(691\) 12.2365 0.465499 0.232749 0.972537i \(-0.425228\pi\)
0.232749 + 0.972537i \(0.425228\pi\)
\(692\) 0 0
\(693\) −6.90562 −0.262323
\(694\) 0 0
\(695\) 36.4743 1.38355
\(696\) 0 0
\(697\) −7.98061 −0.302287
\(698\) 0 0
\(699\) 33.9376 1.28364
\(700\) 0 0
\(701\) 17.3991 0.657154 0.328577 0.944477i \(-0.393431\pi\)
0.328577 + 0.944477i \(0.393431\pi\)
\(702\) 0 0
\(703\) 35.5007 1.33893
\(704\) 0 0
\(705\) 2.26235 0.0852052
\(706\) 0 0
\(707\) −6.10520 −0.229610
\(708\) 0 0
\(709\) −20.9379 −0.786340 −0.393170 0.919466i \(-0.628622\pi\)
−0.393170 + 0.919466i \(0.628622\pi\)
\(710\) 0 0
\(711\) −4.68498 −0.175701
\(712\) 0 0
\(713\) −70.6854 −2.64719
\(714\) 0 0
\(715\) −84.3656 −3.15509
\(716\) 0 0
\(717\) −36.7916 −1.37401
\(718\) 0 0
\(719\) −7.43750 −0.277372 −0.138686 0.990336i \(-0.544288\pi\)
−0.138686 + 0.990336i \(0.544288\pi\)
\(720\) 0 0
\(721\) −32.9030 −1.22537
\(722\) 0 0
\(723\) −31.3052 −1.16425
\(724\) 0 0
\(725\) 15.4459 0.573646
\(726\) 0 0
\(727\) −38.7866 −1.43852 −0.719258 0.694743i \(-0.755518\pi\)
−0.719258 + 0.694743i \(0.755518\pi\)
\(728\) 0 0
\(729\) 29.9722 1.11008
\(730\) 0 0
\(731\) 27.2385 1.00745
\(732\) 0 0
\(733\) 11.3860 0.420551 0.210275 0.977642i \(-0.432564\pi\)
0.210275 + 0.977642i \(0.432564\pi\)
\(734\) 0 0
\(735\) 7.26521 0.267981
\(736\) 0 0
\(737\) 49.5728 1.82604
\(738\) 0 0
\(739\) 47.8046 1.75852 0.879261 0.476341i \(-0.158037\pi\)
0.879261 + 0.476341i \(0.158037\pi\)
\(740\) 0 0
\(741\) 44.9683 1.65195
\(742\) 0 0
\(743\) −21.8896 −0.803050 −0.401525 0.915848i \(-0.631520\pi\)
−0.401525 + 0.915848i \(0.631520\pi\)
\(744\) 0 0
\(745\) 30.3671 1.11256
\(746\) 0 0
\(747\) −5.17226 −0.189243
\(748\) 0 0
\(749\) 18.3955 0.672158
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 18.3743 0.669598
\(754\) 0 0
\(755\) 54.8727 1.99702
\(756\) 0 0
\(757\) −16.1892 −0.588405 −0.294203 0.955743i \(-0.595054\pi\)
−0.294203 + 0.955743i \(0.595054\pi\)
\(758\) 0 0
\(759\) 67.1594 2.43773
\(760\) 0 0
\(761\) −37.8360 −1.37155 −0.685777 0.727812i \(-0.740537\pi\)
−0.685777 + 0.727812i \(0.740537\pi\)
\(762\) 0 0
\(763\) 21.1173 0.764498
\(764\) 0 0
\(765\) 4.35976 0.157627
\(766\) 0 0
\(767\) 52.9859 1.91321
\(768\) 0 0
\(769\) 24.5357 0.884780 0.442390 0.896823i \(-0.354131\pi\)
0.442390 + 0.896823i \(0.354131\pi\)
\(770\) 0 0
\(771\) −24.1330 −0.869129
\(772\) 0 0
\(773\) −21.0097 −0.755665 −0.377832 0.925874i \(-0.623330\pi\)
−0.377832 + 0.925874i \(0.623330\pi\)
\(774\) 0 0
\(775\) −13.7511 −0.493956
\(776\) 0 0
\(777\) −26.4605 −0.949267
\(778\) 0 0
\(779\) −12.3372 −0.442026
\(780\) 0 0
\(781\) −72.6223 −2.59863
\(782\) 0 0
\(783\) 56.4510 2.01739
\(784\) 0 0
\(785\) −21.2513 −0.758492
\(786\) 0 0
\(787\) 19.5428 0.696627 0.348313 0.937378i \(-0.386754\pi\)
0.348313 + 0.937378i \(0.386754\pi\)
\(788\) 0 0
\(789\) −42.3897 −1.50911
\(790\) 0 0
\(791\) −32.5168 −1.15616
\(792\) 0 0
\(793\) −22.0030 −0.781348
\(794\) 0 0
\(795\) 4.23524 0.150208
\(796\) 0 0
\(797\) −7.92622 −0.280761 −0.140381 0.990098i \(-0.544833\pi\)
−0.140381 + 0.990098i \(0.544833\pi\)
\(798\) 0 0
\(799\) 1.75023 0.0619189
\(800\) 0 0
\(801\) −3.51900 −0.124338
\(802\) 0 0
\(803\) 26.9889 0.952417
\(804\) 0 0
\(805\) −45.4355 −1.60139
\(806\) 0 0
\(807\) −25.8854 −0.911208
\(808\) 0 0
\(809\) −25.9461 −0.912217 −0.456109 0.889924i \(-0.650757\pi\)
−0.456109 + 0.889924i \(0.650757\pi\)
\(810\) 0 0
\(811\) 5.78971 0.203304 0.101652 0.994820i \(-0.467587\pi\)
0.101652 + 0.994820i \(0.467587\pi\)
\(812\) 0 0
\(813\) −26.2994 −0.922360
\(814\) 0 0
\(815\) 44.1198 1.54545
\(816\) 0 0
\(817\) 42.1079 1.47317
\(818\) 0 0
\(819\) 7.56479 0.264335
\(820\) 0 0
\(821\) 18.1110 0.632078 0.316039 0.948746i \(-0.397647\pi\)
0.316039 + 0.948746i \(0.397647\pi\)
\(822\) 0 0
\(823\) 4.49904 0.156827 0.0784134 0.996921i \(-0.475015\pi\)
0.0784134 + 0.996921i \(0.475015\pi\)
\(824\) 0 0
\(825\) 13.0652 0.454872
\(826\) 0 0
\(827\) 4.90543 0.170579 0.0852893 0.996356i \(-0.472819\pi\)
0.0852893 + 0.996356i \(0.472819\pi\)
\(828\) 0 0
\(829\) 7.64569 0.265546 0.132773 0.991146i \(-0.457612\pi\)
0.132773 + 0.991146i \(0.457612\pi\)
\(830\) 0 0
\(831\) −28.4501 −0.986921
\(832\) 0 0
\(833\) 5.62061 0.194743
\(834\) 0 0
\(835\) −35.9431 −1.24386
\(836\) 0 0
\(837\) −50.2571 −1.73714
\(838\) 0 0
\(839\) 8.47301 0.292521 0.146260 0.989246i \(-0.453276\pi\)
0.146260 + 0.989246i \(0.453276\pi\)
\(840\) 0 0
\(841\) 74.1709 2.55762
\(842\) 0 0
\(843\) 8.36235 0.288015
\(844\) 0 0
\(845\) 59.2224 2.03731
\(846\) 0 0
\(847\) −43.6124 −1.49854
\(848\) 0 0
\(849\) −20.6912 −0.710118
\(850\) 0 0
\(851\) −58.0806 −1.99098
\(852\) 0 0
\(853\) −29.2668 −1.00208 −0.501038 0.865425i \(-0.667048\pi\)
−0.501038 + 0.865425i \(0.667048\pi\)
\(854\) 0 0
\(855\) 6.73973 0.230494
\(856\) 0 0
\(857\) −52.7586 −1.80220 −0.901100 0.433611i \(-0.857239\pi\)
−0.901100 + 0.433611i \(0.857239\pi\)
\(858\) 0 0
\(859\) 36.8393 1.25694 0.628470 0.777834i \(-0.283681\pi\)
0.628470 + 0.777834i \(0.283681\pi\)
\(860\) 0 0
\(861\) 9.19557 0.313384
\(862\) 0 0
\(863\) −33.6032 −1.14387 −0.571933 0.820300i \(-0.693806\pi\)
−0.571933 + 0.820300i \(0.693806\pi\)
\(864\) 0 0
\(865\) 30.3248 1.03107
\(866\) 0 0
\(867\) 11.6520 0.395722
\(868\) 0 0
\(869\) −46.5752 −1.57996
\(870\) 0 0
\(871\) −54.3048 −1.84005
\(872\) 0 0
\(873\) −1.27010 −0.0429863
\(874\) 0 0
\(875\) 20.2240 0.683695
\(876\) 0 0
\(877\) −18.8712 −0.637235 −0.318617 0.947883i \(-0.603218\pi\)
−0.318617 + 0.947883i \(0.603218\pi\)
\(878\) 0 0
\(879\) −39.8690 −1.34475
\(880\) 0 0
\(881\) 4.46039 0.150274 0.0751372 0.997173i \(-0.476061\pi\)
0.0751372 + 0.997173i \(0.476061\pi\)
\(882\) 0 0
\(883\) −7.48181 −0.251783 −0.125891 0.992044i \(-0.540179\pi\)
−0.125891 + 0.992044i \(0.540179\pi\)
\(884\) 0 0
\(885\) −35.1859 −1.18276
\(886\) 0 0
\(887\) −14.1865 −0.476336 −0.238168 0.971224i \(-0.576547\pi\)
−0.238168 + 0.971224i \(0.576547\pi\)
\(888\) 0 0
\(889\) 25.7071 0.862187
\(890\) 0 0
\(891\) 38.6488 1.29479
\(892\) 0 0
\(893\) 2.70568 0.0905422
\(894\) 0 0
\(895\) −19.1055 −0.638627
\(896\) 0 0
\(897\) −73.5700 −2.45643
\(898\) 0 0
\(899\) −91.8509 −3.06340
\(900\) 0 0
\(901\) 3.27653 0.109157
\(902\) 0 0
\(903\) −31.3852 −1.04444
\(904\) 0 0
\(905\) −44.3563 −1.47445
\(906\) 0 0
\(907\) 45.2858 1.50369 0.751846 0.659339i \(-0.229164\pi\)
0.751846 + 0.659339i \(0.229164\pi\)
\(908\) 0 0
\(909\) −1.48164 −0.0491428
\(910\) 0 0
\(911\) −16.8228 −0.557364 −0.278682 0.960383i \(-0.589898\pi\)
−0.278682 + 0.960383i \(0.589898\pi\)
\(912\) 0 0
\(913\) −51.4194 −1.70173
\(914\) 0 0
\(915\) 14.6113 0.483035
\(916\) 0 0
\(917\) −12.5371 −0.414010
\(918\) 0 0
\(919\) 7.21545 0.238016 0.119008 0.992893i \(-0.462029\pi\)
0.119008 + 0.992893i \(0.462029\pi\)
\(920\) 0 0
\(921\) −29.1954 −0.962022
\(922\) 0 0
\(923\) 79.5544 2.61856
\(924\) 0 0
\(925\) −11.2990 −0.371509
\(926\) 0 0
\(927\) −7.98505 −0.262263
\(928\) 0 0
\(929\) 3.64130 0.119467 0.0597335 0.998214i \(-0.480975\pi\)
0.0597335 + 0.998214i \(0.480975\pi\)
\(930\) 0 0
\(931\) 8.68888 0.284767
\(932\) 0 0
\(933\) 11.4564 0.375066
\(934\) 0 0
\(935\) 43.3420 1.41744
\(936\) 0 0
\(937\) 1.63208 0.0533176 0.0266588 0.999645i \(-0.491513\pi\)
0.0266588 + 0.999645i \(0.491513\pi\)
\(938\) 0 0
\(939\) −27.7415 −0.905311
\(940\) 0 0
\(941\) 40.4765 1.31950 0.659748 0.751487i \(-0.270663\pi\)
0.659748 + 0.751487i \(0.270663\pi\)
\(942\) 0 0
\(943\) 20.1842 0.657287
\(944\) 0 0
\(945\) −32.3045 −1.05087
\(946\) 0 0
\(947\) −25.1006 −0.815660 −0.407830 0.913058i \(-0.633714\pi\)
−0.407830 + 0.913058i \(0.633714\pi\)
\(948\) 0 0
\(949\) −29.5651 −0.959723
\(950\) 0 0
\(951\) 28.0800 0.910557
\(952\) 0 0
\(953\) 52.1992 1.69090 0.845448 0.534057i \(-0.179333\pi\)
0.845448 + 0.534057i \(0.179333\pi\)
\(954\) 0 0
\(955\) −60.2805 −1.95063
\(956\) 0 0
\(957\) 87.2690 2.82101
\(958\) 0 0
\(959\) −2.47714 −0.0799911
\(960\) 0 0
\(961\) 50.7729 1.63784
\(962\) 0 0
\(963\) 4.46430 0.143860
\(964\) 0 0
\(965\) −22.8584 −0.735839
\(966\) 0 0
\(967\) −49.1898 −1.58184 −0.790919 0.611920i \(-0.790397\pi\)
−0.790919 + 0.611920i \(0.790397\pi\)
\(968\) 0 0
\(969\) −23.1020 −0.742144
\(970\) 0 0
\(971\) −40.0516 −1.28532 −0.642658 0.766153i \(-0.722169\pi\)
−0.642658 + 0.766153i \(0.722169\pi\)
\(972\) 0 0
\(973\) −32.5136 −1.04234
\(974\) 0 0
\(975\) −14.3123 −0.458361
\(976\) 0 0
\(977\) 34.2087 1.09443 0.547217 0.836991i \(-0.315687\pi\)
0.547217 + 0.836991i \(0.315687\pi\)
\(978\) 0 0
\(979\) −34.9837 −1.11808
\(980\) 0 0
\(981\) 5.12484 0.163624
\(982\) 0 0
\(983\) −6.33309 −0.201994 −0.100997 0.994887i \(-0.532203\pi\)
−0.100997 + 0.994887i \(0.532203\pi\)
\(984\) 0 0
\(985\) −27.0887 −0.863118
\(986\) 0 0
\(987\) −2.01669 −0.0641919
\(988\) 0 0
\(989\) −68.8902 −2.19058
\(990\) 0 0
\(991\) −48.6422 −1.54517 −0.772585 0.634911i \(-0.781037\pi\)
−0.772585 + 0.634911i \(0.781037\pi\)
\(992\) 0 0
\(993\) −19.0480 −0.604469
\(994\) 0 0
\(995\) 0.0931128 0.00295187
\(996\) 0 0
\(997\) 8.37412 0.265211 0.132606 0.991169i \(-0.457666\pi\)
0.132606 + 0.991169i \(0.457666\pi\)
\(998\) 0 0
\(999\) −41.2951 −1.30652
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 \(a_p\))