Properties

Label 8001.2.a.u.1.3
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 18
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(0\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2\cdot 5 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.90615\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.90615 q^{2} +1.63341 q^{4} -1.97979 q^{5} +1.00000 q^{7} +0.698768 q^{8} +O(q^{10})\) \(q-1.90615 q^{2} +1.63341 q^{4} -1.97979 q^{5} +1.00000 q^{7} +0.698768 q^{8} +3.77379 q^{10} +5.17880 q^{11} -1.58823 q^{13} -1.90615 q^{14} -4.59879 q^{16} +8.13644 q^{17} +4.36350 q^{19} -3.23382 q^{20} -9.87159 q^{22} +7.89668 q^{23} -1.08042 q^{25} +3.02741 q^{26} +1.63341 q^{28} -2.09112 q^{29} -0.621893 q^{31} +7.36845 q^{32} -15.5093 q^{34} -1.97979 q^{35} +0.803128 q^{37} -8.31749 q^{38} -1.38342 q^{40} +2.54636 q^{41} +11.6823 q^{43} +8.45913 q^{44} -15.0523 q^{46} +10.9388 q^{47} +1.00000 q^{49} +2.05944 q^{50} -2.59424 q^{52} +11.9325 q^{53} -10.2530 q^{55} +0.698768 q^{56} +3.98599 q^{58} -5.22205 q^{59} +5.63485 q^{61} +1.18542 q^{62} -4.84781 q^{64} +3.14437 q^{65} +7.63507 q^{67} +13.2902 q^{68} +3.77379 q^{70} +2.26392 q^{71} +3.81158 q^{73} -1.53088 q^{74} +7.12740 q^{76} +5.17880 q^{77} +12.3567 q^{79} +9.10465 q^{80} -4.85374 q^{82} +1.82793 q^{83} -16.1085 q^{85} -22.2682 q^{86} +3.61878 q^{88} -11.2636 q^{89} -1.58823 q^{91} +12.8986 q^{92} -20.8510 q^{94} -8.63883 q^{95} -14.9449 q^{97} -1.90615 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q + 6q^{2} + 22q^{4} + 10q^{5} + 18q^{7} + 21q^{8} + O(q^{10}) \) \( 18q + 6q^{2} + 22q^{4} + 10q^{5} + 18q^{7} + 21q^{8} - 4q^{10} + 9q^{11} - 25q^{13} + 6q^{14} + 34q^{16} + 17q^{17} - 5q^{19} + 21q^{20} + 5q^{22} + 14q^{23} + 28q^{25} + 8q^{26} + 22q^{28} + 17q^{29} + 5q^{31} + 53q^{32} - 19q^{34} + 10q^{35} - 15q^{37} + 22q^{38} - q^{40} + 17q^{41} + q^{43} + 33q^{44} + 10q^{46} + 31q^{47} + 18q^{49} + 35q^{50} - 70q^{52} + 35q^{53} + 4q^{55} + 21q^{56} + 3q^{58} + 46q^{59} - 5q^{61} + 10q^{62} + 63q^{64} + 12q^{65} + 6q^{67} + 56q^{68} - 4q^{70} + 22q^{71} - 16q^{73} - 18q^{74} + 32q^{76} + 9q^{77} + 46q^{79} + 30q^{80} - 12q^{82} + 46q^{83} + 4q^{85} - 18q^{86} + 30q^{88} + 42q^{89} - 25q^{91} + 48q^{92} + 3q^{94} + 2q^{95} - 35q^{97} + 6q^{98} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.90615 −1.34785 −0.673926 0.738798i \(-0.735394\pi\)
−0.673926 + 0.738798i \(0.735394\pi\)
\(3\) 0 0
\(4\) 1.63341 0.816707
\(5\) −1.97979 −0.885391 −0.442695 0.896672i \(-0.645978\pi\)
−0.442695 + 0.896672i \(0.645978\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0.698768 0.247052
\(9\) 0 0
\(10\) 3.77379 1.19338
\(11\) 5.17880 1.56147 0.780734 0.624863i \(-0.214845\pi\)
0.780734 + 0.624863i \(0.214845\pi\)
\(12\) 0 0
\(13\) −1.58823 −0.440497 −0.220248 0.975444i \(-0.570687\pi\)
−0.220248 + 0.975444i \(0.570687\pi\)
\(14\) −1.90615 −0.509440
\(15\) 0 0
\(16\) −4.59879 −1.14970
\(17\) 8.13644 1.97338 0.986688 0.162624i \(-0.0519957\pi\)
0.986688 + 0.162624i \(0.0519957\pi\)
\(18\) 0 0
\(19\) 4.36350 1.00106 0.500528 0.865721i \(-0.333139\pi\)
0.500528 + 0.865721i \(0.333139\pi\)
\(20\) −3.23382 −0.723105
\(21\) 0 0
\(22\) −9.87159 −2.10463
\(23\) 7.89668 1.64657 0.823286 0.567627i \(-0.192138\pi\)
0.823286 + 0.567627i \(0.192138\pi\)
\(24\) 0 0
\(25\) −1.08042 −0.216084
\(26\) 3.02741 0.593725
\(27\) 0 0
\(28\) 1.63341 0.308686
\(29\) −2.09112 −0.388311 −0.194155 0.980971i \(-0.562197\pi\)
−0.194155 + 0.980971i \(0.562197\pi\)
\(30\) 0 0
\(31\) −0.621893 −0.111695 −0.0558476 0.998439i \(-0.517786\pi\)
−0.0558476 + 0.998439i \(0.517786\pi\)
\(32\) 7.36845 1.30257
\(33\) 0 0
\(34\) −15.5093 −2.65982
\(35\) −1.97979 −0.334646
\(36\) 0 0
\(37\) 0.803128 0.132033 0.0660167 0.997819i \(-0.478971\pi\)
0.0660167 + 0.997819i \(0.478971\pi\)
\(38\) −8.31749 −1.34927
\(39\) 0 0
\(40\) −1.38342 −0.218737
\(41\) 2.54636 0.397674 0.198837 0.980033i \(-0.436284\pi\)
0.198837 + 0.980033i \(0.436284\pi\)
\(42\) 0 0
\(43\) 11.6823 1.78153 0.890764 0.454467i \(-0.150170\pi\)
0.890764 + 0.454467i \(0.150170\pi\)
\(44\) 8.45913 1.27526
\(45\) 0 0
\(46\) −15.0523 −2.21934
\(47\) 10.9388 1.59559 0.797794 0.602930i \(-0.206000\pi\)
0.797794 + 0.602930i \(0.206000\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 2.05944 0.291249
\(51\) 0 0
\(52\) −2.59424 −0.359757
\(53\) 11.9325 1.63905 0.819524 0.573045i \(-0.194238\pi\)
0.819524 + 0.573045i \(0.194238\pi\)
\(54\) 0 0
\(55\) −10.2530 −1.38251
\(56\) 0.698768 0.0933768
\(57\) 0 0
\(58\) 3.98599 0.523386
\(59\) −5.22205 −0.679853 −0.339927 0.940452i \(-0.610402\pi\)
−0.339927 + 0.940452i \(0.610402\pi\)
\(60\) 0 0
\(61\) 5.63485 0.721469 0.360735 0.932669i \(-0.382526\pi\)
0.360735 + 0.932669i \(0.382526\pi\)
\(62\) 1.18542 0.150549
\(63\) 0 0
\(64\) −4.84781 −0.605976
\(65\) 3.14437 0.390011
\(66\) 0 0
\(67\) 7.63507 0.932772 0.466386 0.884581i \(-0.345556\pi\)
0.466386 + 0.884581i \(0.345556\pi\)
\(68\) 13.2902 1.61167
\(69\) 0 0
\(70\) 3.77379 0.451054
\(71\) 2.26392 0.268678 0.134339 0.990935i \(-0.457109\pi\)
0.134339 + 0.990935i \(0.457109\pi\)
\(72\) 0 0
\(73\) 3.81158 0.446112 0.223056 0.974806i \(-0.428397\pi\)
0.223056 + 0.974806i \(0.428397\pi\)
\(74\) −1.53088 −0.177962
\(75\) 0 0
\(76\) 7.12740 0.817569
\(77\) 5.17880 0.590180
\(78\) 0 0
\(79\) 12.3567 1.39024 0.695120 0.718893i \(-0.255351\pi\)
0.695120 + 0.718893i \(0.255351\pi\)
\(80\) 9.10465 1.01793
\(81\) 0 0
\(82\) −4.85374 −0.536006
\(83\) 1.82793 0.200642 0.100321 0.994955i \(-0.468013\pi\)
0.100321 + 0.994955i \(0.468013\pi\)
\(84\) 0 0
\(85\) −16.1085 −1.74721
\(86\) −22.2682 −2.40124
\(87\) 0 0
\(88\) 3.61878 0.385763
\(89\) −11.2636 −1.19394 −0.596971 0.802263i \(-0.703629\pi\)
−0.596971 + 0.802263i \(0.703629\pi\)
\(90\) 0 0
\(91\) −1.58823 −0.166492
\(92\) 12.8986 1.34477
\(93\) 0 0
\(94\) −20.8510 −2.15062
\(95\) −8.63883 −0.886325
\(96\) 0 0
\(97\) −14.9449 −1.51743 −0.758713 0.651425i \(-0.774172\pi\)
−0.758713 + 0.651425i \(0.774172\pi\)
\(98\) −1.90615 −0.192550
\(99\) 0 0
\(100\) −1.76477 −0.176477
\(101\) 6.73317 0.669975 0.334988 0.942223i \(-0.391268\pi\)
0.334988 + 0.942223i \(0.391268\pi\)
\(102\) 0 0
\(103\) −7.36518 −0.725713 −0.362856 0.931845i \(-0.618198\pi\)
−0.362856 + 0.931845i \(0.618198\pi\)
\(104\) −1.10981 −0.108825
\(105\) 0 0
\(106\) −22.7451 −2.20920
\(107\) −2.36070 −0.228218 −0.114109 0.993468i \(-0.536401\pi\)
−0.114109 + 0.993468i \(0.536401\pi\)
\(108\) 0 0
\(109\) 14.6315 1.40144 0.700720 0.713436i \(-0.252862\pi\)
0.700720 + 0.713436i \(0.252862\pi\)
\(110\) 19.5437 1.86342
\(111\) 0 0
\(112\) −4.59879 −0.434544
\(113\) −5.00346 −0.470686 −0.235343 0.971912i \(-0.575621\pi\)
−0.235343 + 0.971912i \(0.575621\pi\)
\(114\) 0 0
\(115\) −15.6338 −1.45786
\(116\) −3.41566 −0.317136
\(117\) 0 0
\(118\) 9.95402 0.916342
\(119\) 8.13644 0.745866
\(120\) 0 0
\(121\) 15.8200 1.43818
\(122\) −10.7409 −0.972434
\(123\) 0 0
\(124\) −1.01581 −0.0912223
\(125\) 12.0380 1.07671
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) −5.49624 −0.485803
\(129\) 0 0
\(130\) −5.99365 −0.525678
\(131\) −7.45485 −0.651334 −0.325667 0.945485i \(-0.605589\pi\)
−0.325667 + 0.945485i \(0.605589\pi\)
\(132\) 0 0
\(133\) 4.36350 0.378363
\(134\) −14.5536 −1.25724
\(135\) 0 0
\(136\) 5.68548 0.487526
\(137\) 18.5476 1.58463 0.792315 0.610112i \(-0.208876\pi\)
0.792315 + 0.610112i \(0.208876\pi\)
\(138\) 0 0
\(139\) −16.7225 −1.41838 −0.709192 0.705015i \(-0.750940\pi\)
−0.709192 + 0.705015i \(0.750940\pi\)
\(140\) −3.23382 −0.273308
\(141\) 0 0
\(142\) −4.31538 −0.362138
\(143\) −8.22515 −0.687821
\(144\) 0 0
\(145\) 4.13998 0.343807
\(146\) −7.26546 −0.601294
\(147\) 0 0
\(148\) 1.31184 0.107833
\(149\) −7.51285 −0.615477 −0.307739 0.951471i \(-0.599572\pi\)
−0.307739 + 0.951471i \(0.599572\pi\)
\(150\) 0 0
\(151\) −18.1145 −1.47414 −0.737069 0.675817i \(-0.763791\pi\)
−0.737069 + 0.675817i \(0.763791\pi\)
\(152\) 3.04907 0.247312
\(153\) 0 0
\(154\) −9.87159 −0.795475
\(155\) 1.23122 0.0988939
\(156\) 0 0
\(157\) −13.3027 −1.06167 −0.530837 0.847474i \(-0.678122\pi\)
−0.530837 + 0.847474i \(0.678122\pi\)
\(158\) −23.5538 −1.87384
\(159\) 0 0
\(160\) −14.5880 −1.15328
\(161\) 7.89668 0.622346
\(162\) 0 0
\(163\) −6.37885 −0.499630 −0.249815 0.968294i \(-0.580370\pi\)
−0.249815 + 0.968294i \(0.580370\pi\)
\(164\) 4.15925 0.324783
\(165\) 0 0
\(166\) −3.48432 −0.270435
\(167\) −4.71885 −0.365156 −0.182578 0.983191i \(-0.558444\pi\)
−0.182578 + 0.983191i \(0.558444\pi\)
\(168\) 0 0
\(169\) −10.4775 −0.805963
\(170\) 30.7052 2.35498
\(171\) 0 0
\(172\) 19.0820 1.45499
\(173\) 12.6074 0.958521 0.479261 0.877673i \(-0.340905\pi\)
0.479261 + 0.877673i \(0.340905\pi\)
\(174\) 0 0
\(175\) −1.08042 −0.0816719
\(176\) −23.8162 −1.79521
\(177\) 0 0
\(178\) 21.4702 1.60926
\(179\) −19.5887 −1.46413 −0.732064 0.681235i \(-0.761443\pi\)
−0.732064 + 0.681235i \(0.761443\pi\)
\(180\) 0 0
\(181\) −12.2615 −0.911393 −0.455696 0.890135i \(-0.650610\pi\)
−0.455696 + 0.890135i \(0.650610\pi\)
\(182\) 3.02741 0.224407
\(183\) 0 0
\(184\) 5.51795 0.406788
\(185\) −1.59003 −0.116901
\(186\) 0 0
\(187\) 42.1370 3.08136
\(188\) 17.8676 1.30313
\(189\) 0 0
\(190\) 16.4669 1.19464
\(191\) 8.08753 0.585193 0.292597 0.956236i \(-0.405481\pi\)
0.292597 + 0.956236i \(0.405481\pi\)
\(192\) 0 0
\(193\) −6.91124 −0.497482 −0.248741 0.968570i \(-0.580017\pi\)
−0.248741 + 0.968570i \(0.580017\pi\)
\(194\) 28.4873 2.04527
\(195\) 0 0
\(196\) 1.63341 0.116672
\(197\) 23.8478 1.69908 0.849542 0.527521i \(-0.176878\pi\)
0.849542 + 0.527521i \(0.176878\pi\)
\(198\) 0 0
\(199\) −24.6886 −1.75013 −0.875064 0.484008i \(-0.839181\pi\)
−0.875064 + 0.484008i \(0.839181\pi\)
\(200\) −0.754961 −0.0533838
\(201\) 0 0
\(202\) −12.8344 −0.903028
\(203\) −2.09112 −0.146768
\(204\) 0 0
\(205\) −5.04126 −0.352097
\(206\) 14.0392 0.978154
\(207\) 0 0
\(208\) 7.30394 0.506437
\(209\) 22.5977 1.56312
\(210\) 0 0
\(211\) 20.8302 1.43401 0.717004 0.697069i \(-0.245513\pi\)
0.717004 + 0.697069i \(0.245513\pi\)
\(212\) 19.4906 1.33862
\(213\) 0 0
\(214\) 4.49985 0.307604
\(215\) −23.1285 −1.57735
\(216\) 0 0
\(217\) −0.621893 −0.0422168
\(218\) −27.8898 −1.88893
\(219\) 0 0
\(220\) −16.7473 −1.12911
\(221\) −12.9226 −0.869265
\(222\) 0 0
\(223\) −0.589818 −0.0394971 −0.0197486 0.999805i \(-0.506287\pi\)
−0.0197486 + 0.999805i \(0.506287\pi\)
\(224\) 7.36845 0.492325
\(225\) 0 0
\(226\) 9.53735 0.634415
\(227\) −26.8903 −1.78477 −0.892385 0.451275i \(-0.850969\pi\)
−0.892385 + 0.451275i \(0.850969\pi\)
\(228\) 0 0
\(229\) 4.08930 0.270228 0.135114 0.990830i \(-0.456860\pi\)
0.135114 + 0.990830i \(0.456860\pi\)
\(230\) 29.8004 1.96498
\(231\) 0 0
\(232\) −1.46121 −0.0959329
\(233\) −17.8233 −1.16764 −0.583822 0.811881i \(-0.698444\pi\)
−0.583822 + 0.811881i \(0.698444\pi\)
\(234\) 0 0
\(235\) −21.6566 −1.41272
\(236\) −8.52977 −0.555241
\(237\) 0 0
\(238\) −15.5093 −1.00532
\(239\) −12.7795 −0.826639 −0.413319 0.910586i \(-0.635631\pi\)
−0.413319 + 0.910586i \(0.635631\pi\)
\(240\) 0 0
\(241\) 0.622612 0.0401060 0.0200530 0.999799i \(-0.493617\pi\)
0.0200530 + 0.999799i \(0.493617\pi\)
\(242\) −30.1554 −1.93846
\(243\) 0 0
\(244\) 9.20405 0.589229
\(245\) −1.97979 −0.126484
\(246\) 0 0
\(247\) −6.93025 −0.440961
\(248\) −0.434558 −0.0275945
\(249\) 0 0
\(250\) −22.9462 −1.45125
\(251\) −4.77595 −0.301455 −0.150728 0.988575i \(-0.548162\pi\)
−0.150728 + 0.988575i \(0.548162\pi\)
\(252\) 0 0
\(253\) 40.8954 2.57107
\(254\) −1.90615 −0.119603
\(255\) 0 0
\(256\) 20.1723 1.26077
\(257\) 9.29252 0.579651 0.289826 0.957079i \(-0.406403\pi\)
0.289826 + 0.957079i \(0.406403\pi\)
\(258\) 0 0
\(259\) 0.803128 0.0499040
\(260\) 5.13606 0.318525
\(261\) 0 0
\(262\) 14.2101 0.877902
\(263\) −13.5268 −0.834101 −0.417050 0.908883i \(-0.636936\pi\)
−0.417050 + 0.908883i \(0.636936\pi\)
\(264\) 0 0
\(265\) −23.6238 −1.45120
\(266\) −8.31749 −0.509978
\(267\) 0 0
\(268\) 12.4712 0.761802
\(269\) 4.24141 0.258603 0.129302 0.991605i \(-0.458726\pi\)
0.129302 + 0.991605i \(0.458726\pi\)
\(270\) 0 0
\(271\) −0.865289 −0.0525626 −0.0262813 0.999655i \(-0.508367\pi\)
−0.0262813 + 0.999655i \(0.508367\pi\)
\(272\) −37.4177 −2.26878
\(273\) 0 0
\(274\) −35.3546 −2.13585
\(275\) −5.59527 −0.337408
\(276\) 0 0
\(277\) −31.0536 −1.86583 −0.932914 0.360100i \(-0.882743\pi\)
−0.932914 + 0.360100i \(0.882743\pi\)
\(278\) 31.8756 1.91177
\(279\) 0 0
\(280\) −1.38342 −0.0826749
\(281\) −30.2059 −1.80194 −0.900968 0.433886i \(-0.857142\pi\)
−0.900968 + 0.433886i \(0.857142\pi\)
\(282\) 0 0
\(283\) −17.4665 −1.03827 −0.519137 0.854691i \(-0.673747\pi\)
−0.519137 + 0.854691i \(0.673747\pi\)
\(284\) 3.69792 0.219431
\(285\) 0 0
\(286\) 15.6784 0.927082
\(287\) 2.54636 0.150307
\(288\) 0 0
\(289\) 49.2016 2.89421
\(290\) −7.89144 −0.463401
\(291\) 0 0
\(292\) 6.22590 0.364343
\(293\) 19.7297 1.15262 0.576312 0.817230i \(-0.304491\pi\)
0.576312 + 0.817230i \(0.304491\pi\)
\(294\) 0 0
\(295\) 10.3386 0.601935
\(296\) 0.561200 0.0326191
\(297\) 0 0
\(298\) 14.3206 0.829572
\(299\) −12.5418 −0.725309
\(300\) 0 0
\(301\) 11.6823 0.673354
\(302\) 34.5290 1.98692
\(303\) 0 0
\(304\) −20.0668 −1.15091
\(305\) −11.1558 −0.638782
\(306\) 0 0
\(307\) 12.1755 0.694894 0.347447 0.937700i \(-0.387049\pi\)
0.347447 + 0.937700i \(0.387049\pi\)
\(308\) 8.45913 0.482004
\(309\) 0 0
\(310\) −2.34689 −0.133294
\(311\) 33.0092 1.87178 0.935890 0.352293i \(-0.114598\pi\)
0.935890 + 0.352293i \(0.114598\pi\)
\(312\) 0 0
\(313\) 34.5663 1.95380 0.976902 0.213686i \(-0.0685469\pi\)
0.976902 + 0.213686i \(0.0685469\pi\)
\(314\) 25.3570 1.43098
\(315\) 0 0
\(316\) 20.1837 1.13542
\(317\) −34.6280 −1.94490 −0.972452 0.233104i \(-0.925112\pi\)
−0.972452 + 0.233104i \(0.925112\pi\)
\(318\) 0 0
\(319\) −10.8295 −0.606335
\(320\) 9.59766 0.536526
\(321\) 0 0
\(322\) −15.0523 −0.838831
\(323\) 35.5033 1.97546
\(324\) 0 0
\(325\) 1.71596 0.0951841
\(326\) 12.1591 0.673428
\(327\) 0 0
\(328\) 1.77931 0.0982460
\(329\) 10.9388 0.603076
\(330\) 0 0
\(331\) 27.6892 1.52194 0.760968 0.648789i \(-0.224724\pi\)
0.760968 + 0.648789i \(0.224724\pi\)
\(332\) 2.98577 0.163865
\(333\) 0 0
\(334\) 8.99484 0.492176
\(335\) −15.1159 −0.825868
\(336\) 0 0
\(337\) −27.9563 −1.52288 −0.761440 0.648236i \(-0.775507\pi\)
−0.761440 + 0.648236i \(0.775507\pi\)
\(338\) 19.9717 1.08632
\(339\) 0 0
\(340\) −26.3118 −1.42696
\(341\) −3.22066 −0.174409
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 8.16318 0.440129
\(345\) 0 0
\(346\) −24.0316 −1.29195
\(347\) −30.4685 −1.63563 −0.817816 0.575480i \(-0.804815\pi\)
−0.817816 + 0.575480i \(0.804815\pi\)
\(348\) 0 0
\(349\) 8.92375 0.477677 0.238839 0.971059i \(-0.423233\pi\)
0.238839 + 0.971059i \(0.423233\pi\)
\(350\) 2.05944 0.110082
\(351\) 0 0
\(352\) 38.1598 2.03392
\(353\) 7.92953 0.422046 0.211023 0.977481i \(-0.432320\pi\)
0.211023 + 0.977481i \(0.432320\pi\)
\(354\) 0 0
\(355\) −4.48210 −0.237885
\(356\) −18.3982 −0.975101
\(357\) 0 0
\(358\) 37.3390 1.97343
\(359\) 29.9988 1.58328 0.791639 0.610989i \(-0.209228\pi\)
0.791639 + 0.610989i \(0.209228\pi\)
\(360\) 0 0
\(361\) 0.0401162 0.00211138
\(362\) 23.3723 1.22842
\(363\) 0 0
\(364\) −2.59424 −0.135975
\(365\) −7.54615 −0.394984
\(366\) 0 0
\(367\) 3.24810 0.169549 0.0847747 0.996400i \(-0.472983\pi\)
0.0847747 + 0.996400i \(0.472983\pi\)
\(368\) −36.3152 −1.89306
\(369\) 0 0
\(370\) 3.03084 0.157566
\(371\) 11.9325 0.619502
\(372\) 0 0
\(373\) −14.4551 −0.748459 −0.374230 0.927336i \(-0.622093\pi\)
−0.374230 + 0.927336i \(0.622093\pi\)
\(374\) −80.3196 −4.15323
\(375\) 0 0
\(376\) 7.64368 0.394193
\(377\) 3.32118 0.171050
\(378\) 0 0
\(379\) 9.92309 0.509715 0.254857 0.966979i \(-0.417971\pi\)
0.254857 + 0.966979i \(0.417971\pi\)
\(380\) −14.1108 −0.723868
\(381\) 0 0
\(382\) −15.4161 −0.788754
\(383\) 11.7627 0.601048 0.300524 0.953774i \(-0.402838\pi\)
0.300524 + 0.953774i \(0.402838\pi\)
\(384\) 0 0
\(385\) −10.2530 −0.522539
\(386\) 13.1739 0.670533
\(387\) 0 0
\(388\) −24.4113 −1.23929
\(389\) −5.27688 −0.267548 −0.133774 0.991012i \(-0.542710\pi\)
−0.133774 + 0.991012i \(0.542710\pi\)
\(390\) 0 0
\(391\) 64.2509 3.24931
\(392\) 0.698768 0.0352931
\(393\) 0 0
\(394\) −45.4575 −2.29012
\(395\) −24.4638 −1.23091
\(396\) 0 0
\(397\) 7.83225 0.393089 0.196545 0.980495i \(-0.437028\pi\)
0.196545 + 0.980495i \(0.437028\pi\)
\(398\) 47.0602 2.35891
\(399\) 0 0
\(400\) 4.96861 0.248431
\(401\) 5.22847 0.261097 0.130549 0.991442i \(-0.458326\pi\)
0.130549 + 0.991442i \(0.458326\pi\)
\(402\) 0 0
\(403\) 0.987710 0.0492014
\(404\) 10.9981 0.547174
\(405\) 0 0
\(406\) 3.98599 0.197821
\(407\) 4.15925 0.206166
\(408\) 0 0
\(409\) 8.44012 0.417337 0.208668 0.977986i \(-0.433087\pi\)
0.208668 + 0.977986i \(0.433087\pi\)
\(410\) 9.60940 0.474575
\(411\) 0 0
\(412\) −12.0304 −0.592695
\(413\) −5.22205 −0.256960
\(414\) 0 0
\(415\) −3.61893 −0.177646
\(416\) −11.7028 −0.573778
\(417\) 0 0
\(418\) −43.0747 −2.10685
\(419\) −11.7497 −0.574008 −0.287004 0.957929i \(-0.592659\pi\)
−0.287004 + 0.957929i \(0.592659\pi\)
\(420\) 0 0
\(421\) −15.2927 −0.745319 −0.372659 0.927968i \(-0.621554\pi\)
−0.372659 + 0.927968i \(0.621554\pi\)
\(422\) −39.7055 −1.93283
\(423\) 0 0
\(424\) 8.33801 0.404930
\(425\) −8.79075 −0.426414
\(426\) 0 0
\(427\) 5.63485 0.272690
\(428\) −3.85600 −0.186387
\(429\) 0 0
\(430\) 44.0863 2.12603
\(431\) −23.8777 −1.15015 −0.575074 0.818102i \(-0.695027\pi\)
−0.575074 + 0.818102i \(0.695027\pi\)
\(432\) 0 0
\(433\) −38.8940 −1.86913 −0.934563 0.355797i \(-0.884209\pi\)
−0.934563 + 0.355797i \(0.884209\pi\)
\(434\) 1.18542 0.0569021
\(435\) 0 0
\(436\) 23.8992 1.14457
\(437\) 34.4572 1.64831
\(438\) 0 0
\(439\) 2.95880 0.141216 0.0706080 0.997504i \(-0.477506\pi\)
0.0706080 + 0.997504i \(0.477506\pi\)
\(440\) −7.16444 −0.341551
\(441\) 0 0
\(442\) 24.6324 1.17164
\(443\) −10.8531 −0.515646 −0.257823 0.966192i \(-0.583005\pi\)
−0.257823 + 0.966192i \(0.583005\pi\)
\(444\) 0 0
\(445\) 22.2996 1.05710
\(446\) 1.12428 0.0532363
\(447\) 0 0
\(448\) −4.84781 −0.229037
\(449\) 19.8143 0.935097 0.467548 0.883967i \(-0.345137\pi\)
0.467548 + 0.883967i \(0.345137\pi\)
\(450\) 0 0
\(451\) 13.1871 0.620955
\(452\) −8.17272 −0.384412
\(453\) 0 0
\(454\) 51.2569 2.40561
\(455\) 3.14437 0.147410
\(456\) 0 0
\(457\) −26.1030 −1.22105 −0.610523 0.791998i \(-0.709041\pi\)
−0.610523 + 0.791998i \(0.709041\pi\)
\(458\) −7.79482 −0.364228
\(459\) 0 0
\(460\) −25.5365 −1.19064
\(461\) 10.0670 0.468867 0.234434 0.972132i \(-0.424676\pi\)
0.234434 + 0.972132i \(0.424676\pi\)
\(462\) 0 0
\(463\) −13.8067 −0.641650 −0.320825 0.947138i \(-0.603960\pi\)
−0.320825 + 0.947138i \(0.603960\pi\)
\(464\) 9.61661 0.446440
\(465\) 0 0
\(466\) 33.9740 1.57381
\(467\) 23.7068 1.09702 0.548510 0.836144i \(-0.315195\pi\)
0.548510 + 0.836144i \(0.315195\pi\)
\(468\) 0 0
\(469\) 7.63507 0.352555
\(470\) 41.2807 1.90414
\(471\) 0 0
\(472\) −3.64900 −0.167959
\(473\) 60.5001 2.78180
\(474\) 0 0
\(475\) −4.71440 −0.216312
\(476\) 13.2902 0.609154
\(477\) 0 0
\(478\) 24.3597 1.11419
\(479\) 0.638921 0.0291930 0.0145965 0.999893i \(-0.495354\pi\)
0.0145965 + 0.999893i \(0.495354\pi\)
\(480\) 0 0
\(481\) −1.27556 −0.0581603
\(482\) −1.18679 −0.0540569
\(483\) 0 0
\(484\) 25.8406 1.17457
\(485\) 29.5879 1.34352
\(486\) 0 0
\(487\) 15.9657 0.723473 0.361736 0.932280i \(-0.382184\pi\)
0.361736 + 0.932280i \(0.382184\pi\)
\(488\) 3.93745 0.178240
\(489\) 0 0
\(490\) 3.77379 0.170482
\(491\) −2.20827 −0.0996578 −0.0498289 0.998758i \(-0.515868\pi\)
−0.0498289 + 0.998758i \(0.515868\pi\)
\(492\) 0 0
\(493\) −17.0143 −0.766284
\(494\) 13.2101 0.594351
\(495\) 0 0
\(496\) 2.85995 0.128416
\(497\) 2.26392 0.101551
\(498\) 0 0
\(499\) −43.3268 −1.93957 −0.969787 0.243955i \(-0.921555\pi\)
−0.969787 + 0.243955i \(0.921555\pi\)
\(500\) 19.6630 0.879356
\(501\) 0 0
\(502\) 9.10368 0.406317
\(503\) −30.7833 −1.37256 −0.686279 0.727338i \(-0.740757\pi\)
−0.686279 + 0.727338i \(0.740757\pi\)
\(504\) 0 0
\(505\) −13.3303 −0.593190
\(506\) −77.9528 −3.46542
\(507\) 0 0
\(508\) 1.63341 0.0724710
\(509\) −12.3751 −0.548517 −0.274258 0.961656i \(-0.588432\pi\)
−0.274258 + 0.961656i \(0.588432\pi\)
\(510\) 0 0
\(511\) 3.81158 0.168615
\(512\) −27.4590 −1.21353
\(513\) 0 0
\(514\) −17.7129 −0.781285
\(515\) 14.5815 0.642539
\(516\) 0 0
\(517\) 56.6499 2.49146
\(518\) −1.53088 −0.0672632
\(519\) 0 0
\(520\) 2.19719 0.0963530
\(521\) −16.4426 −0.720362 −0.360181 0.932882i \(-0.617285\pi\)
−0.360181 + 0.932882i \(0.617285\pi\)
\(522\) 0 0
\(523\) −35.5760 −1.55563 −0.777815 0.628493i \(-0.783672\pi\)
−0.777815 + 0.628493i \(0.783672\pi\)
\(524\) −12.1769 −0.531949
\(525\) 0 0
\(526\) 25.7842 1.12424
\(527\) −5.05999 −0.220417
\(528\) 0 0
\(529\) 39.3576 1.71120
\(530\) 45.0305 1.95600
\(531\) 0 0
\(532\) 7.12740 0.309012
\(533\) −4.04421 −0.175174
\(534\) 0 0
\(535\) 4.67370 0.202062
\(536\) 5.33514 0.230443
\(537\) 0 0
\(538\) −8.08478 −0.348559
\(539\) 5.17880 0.223067
\(540\) 0 0
\(541\) 9.04038 0.388676 0.194338 0.980935i \(-0.437744\pi\)
0.194338 + 0.980935i \(0.437744\pi\)
\(542\) 1.64937 0.0708466
\(543\) 0 0
\(544\) 59.9529 2.57046
\(545\) −28.9673 −1.24082
\(546\) 0 0
\(547\) 39.9287 1.70723 0.853614 0.520906i \(-0.174406\pi\)
0.853614 + 0.520906i \(0.174406\pi\)
\(548\) 30.2960 1.29418
\(549\) 0 0
\(550\) 10.6654 0.454776
\(551\) −9.12459 −0.388721
\(552\) 0 0
\(553\) 12.3567 0.525462
\(554\) 59.1928 2.51486
\(555\) 0 0
\(556\) −27.3148 −1.15841
\(557\) 11.8703 0.502961 0.251481 0.967862i \(-0.419082\pi\)
0.251481 + 0.967862i \(0.419082\pi\)
\(558\) 0 0
\(559\) −18.5541 −0.784757
\(560\) 9.10465 0.384742
\(561\) 0 0
\(562\) 57.5771 2.42874
\(563\) −32.5540 −1.37199 −0.685993 0.727608i \(-0.740632\pi\)
−0.685993 + 0.727608i \(0.740632\pi\)
\(564\) 0 0
\(565\) 9.90581 0.416741
\(566\) 33.2937 1.39944
\(567\) 0 0
\(568\) 1.58195 0.0663773
\(569\) 28.7488 1.20521 0.602607 0.798038i \(-0.294129\pi\)
0.602607 + 0.798038i \(0.294129\pi\)
\(570\) 0 0
\(571\) 4.04241 0.169169 0.0845847 0.996416i \(-0.473044\pi\)
0.0845847 + 0.996416i \(0.473044\pi\)
\(572\) −13.4351 −0.561749
\(573\) 0 0
\(574\) −4.85374 −0.202591
\(575\) −8.53172 −0.355797
\(576\) 0 0
\(577\) 7.23459 0.301180 0.150590 0.988596i \(-0.451883\pi\)
0.150590 + 0.988596i \(0.451883\pi\)
\(578\) −93.7858 −3.90097
\(579\) 0 0
\(580\) 6.76231 0.280790
\(581\) 1.82793 0.0758354
\(582\) 0 0
\(583\) 61.7958 2.55932
\(584\) 2.66341 0.110213
\(585\) 0 0
\(586\) −37.6079 −1.55357
\(587\) 16.9970 0.701543 0.350771 0.936461i \(-0.385919\pi\)
0.350771 + 0.936461i \(0.385919\pi\)
\(588\) 0 0
\(589\) −2.71363 −0.111813
\(590\) −19.7069 −0.811320
\(591\) 0 0
\(592\) −3.69342 −0.151798
\(593\) 30.9750 1.27199 0.635996 0.771692i \(-0.280590\pi\)
0.635996 + 0.771692i \(0.280590\pi\)
\(594\) 0 0
\(595\) −16.1085 −0.660383
\(596\) −12.2716 −0.502665
\(597\) 0 0
\(598\) 23.9065 0.977610
\(599\) 17.4383 0.712511 0.356256 0.934389i \(-0.384053\pi\)
0.356256 + 0.934389i \(0.384053\pi\)
\(600\) 0 0
\(601\) −0.0703960 −0.00287151 −0.00143576 0.999999i \(-0.500457\pi\)
−0.00143576 + 0.999999i \(0.500457\pi\)
\(602\) −22.2682 −0.907582
\(603\) 0 0
\(604\) −29.5885 −1.20394
\(605\) −31.3204 −1.27335
\(606\) 0 0
\(607\) 23.9613 0.972558 0.486279 0.873804i \(-0.338354\pi\)
0.486279 + 0.873804i \(0.338354\pi\)
\(608\) 32.1522 1.30394
\(609\) 0 0
\(610\) 21.2647 0.860984
\(611\) −17.3734 −0.702851
\(612\) 0 0
\(613\) −27.5676 −1.11344 −0.556722 0.830699i \(-0.687941\pi\)
−0.556722 + 0.830699i \(0.687941\pi\)
\(614\) −23.2084 −0.936615
\(615\) 0 0
\(616\) 3.61878 0.145805
\(617\) −1.96872 −0.0792576 −0.0396288 0.999214i \(-0.512618\pi\)
−0.0396288 + 0.999214i \(0.512618\pi\)
\(618\) 0 0
\(619\) −10.3570 −0.416282 −0.208141 0.978099i \(-0.566741\pi\)
−0.208141 + 0.978099i \(0.566741\pi\)
\(620\) 2.01109 0.0807673
\(621\) 0 0
\(622\) −62.9205 −2.52288
\(623\) −11.2636 −0.451268
\(624\) 0 0
\(625\) −18.4306 −0.737224
\(626\) −65.8887 −2.63344
\(627\) 0 0
\(628\) −21.7289 −0.867077
\(629\) 6.53461 0.260552
\(630\) 0 0
\(631\) 0.137455 0.00547200 0.00273600 0.999996i \(-0.499129\pi\)
0.00273600 + 0.999996i \(0.499129\pi\)
\(632\) 8.63448 0.343461
\(633\) 0 0
\(634\) 66.0063 2.62144
\(635\) −1.97979 −0.0785657
\(636\) 0 0
\(637\) −1.58823 −0.0629281
\(638\) 20.6427 0.817251
\(639\) 0 0
\(640\) 10.8814 0.430126
\(641\) 23.6488 0.934072 0.467036 0.884238i \(-0.345322\pi\)
0.467036 + 0.884238i \(0.345322\pi\)
\(642\) 0 0
\(643\) −13.2588 −0.522878 −0.261439 0.965220i \(-0.584197\pi\)
−0.261439 + 0.965220i \(0.584197\pi\)
\(644\) 12.8986 0.508274
\(645\) 0 0
\(646\) −67.6747 −2.66263
\(647\) −41.9389 −1.64879 −0.824394 0.566016i \(-0.808484\pi\)
−0.824394 + 0.566016i \(0.808484\pi\)
\(648\) 0 0
\(649\) −27.0440 −1.06157
\(650\) −3.27087 −0.128294
\(651\) 0 0
\(652\) −10.4193 −0.408051
\(653\) −6.75287 −0.264260 −0.132130 0.991232i \(-0.542182\pi\)
−0.132130 + 0.991232i \(0.542182\pi\)
\(654\) 0 0
\(655\) 14.7591 0.576685
\(656\) −11.7101 −0.457204
\(657\) 0 0
\(658\) −20.8510 −0.812857
\(659\) 22.6213 0.881202 0.440601 0.897703i \(-0.354765\pi\)
0.440601 + 0.897703i \(0.354765\pi\)
\(660\) 0 0
\(661\) 17.5296 0.681822 0.340911 0.940095i \(-0.389264\pi\)
0.340911 + 0.940095i \(0.389264\pi\)
\(662\) −52.7798 −2.05135
\(663\) 0 0
\(664\) 1.27730 0.0495689
\(665\) −8.63883 −0.334999
\(666\) 0 0
\(667\) −16.5129 −0.639382
\(668\) −7.70784 −0.298225
\(669\) 0 0
\(670\) 28.8131 1.11315
\(671\) 29.1818 1.12655
\(672\) 0 0
\(673\) 32.0213 1.23433 0.617165 0.786834i \(-0.288281\pi\)
0.617165 + 0.786834i \(0.288281\pi\)
\(674\) 53.2890 2.05262
\(675\) 0 0
\(676\) −17.1141 −0.658236
\(677\) 1.28783 0.0494953 0.0247476 0.999694i \(-0.492122\pi\)
0.0247476 + 0.999694i \(0.492122\pi\)
\(678\) 0 0
\(679\) −14.9449 −0.573533
\(680\) −11.2561 −0.431651
\(681\) 0 0
\(682\) 6.13907 0.235077
\(683\) 3.44389 0.131777 0.0658883 0.997827i \(-0.479012\pi\)
0.0658883 + 0.997827i \(0.479012\pi\)
\(684\) 0 0
\(685\) −36.7205 −1.40302
\(686\) −1.90615 −0.0727772
\(687\) 0 0
\(688\) −53.7242 −2.04822
\(689\) −18.9515 −0.721995
\(690\) 0 0
\(691\) −29.4991 −1.12220 −0.561100 0.827748i \(-0.689622\pi\)
−0.561100 + 0.827748i \(0.689622\pi\)
\(692\) 20.5931 0.782831
\(693\) 0 0
\(694\) 58.0775 2.20459
\(695\) 33.1071 1.25582
\(696\) 0 0
\(697\) 20.7183 0.784760
\(698\) −17.0100 −0.643839
\(699\) 0 0
\(700\) −1.76477 −0.0667020
\(701\) 16.7240 0.631658 0.315829 0.948816i \(-0.397717\pi\)
0.315829 + 0.948816i \(0.397717\pi\)
\(702\) 0 0
\(703\) 3.50445 0.132173
\(704\) −25.1059 −0.946213
\(705\) 0 0
\(706\) −15.1149 −0.568856
\(707\) 6.73317 0.253227
\(708\) 0 0
\(709\) −39.6390 −1.48867 −0.744337 0.667804i \(-0.767234\pi\)
−0.744337 + 0.667804i \(0.767234\pi\)
\(710\) 8.54355 0.320634
\(711\) 0 0
\(712\) −7.87066 −0.294965
\(713\) −4.91089 −0.183914
\(714\) 0 0
\(715\) 16.2841 0.608991
\(716\) −31.9965 −1.19576
\(717\) 0 0
\(718\) −57.1823 −2.13403
\(719\) −22.3146 −0.832194 −0.416097 0.909320i \(-0.636602\pi\)
−0.416097 + 0.909320i \(0.636602\pi\)
\(720\) 0 0
\(721\) −7.36518 −0.274294
\(722\) −0.0764676 −0.00284583
\(723\) 0 0
\(724\) −20.0282 −0.744341
\(725\) 2.25928 0.0839076
\(726\) 0 0
\(727\) −43.5620 −1.61563 −0.807813 0.589439i \(-0.799349\pi\)
−0.807813 + 0.589439i \(0.799349\pi\)
\(728\) −1.10981 −0.0411321
\(729\) 0 0
\(730\) 14.3841 0.532380
\(731\) 95.0520 3.51562
\(732\) 0 0
\(733\) −41.1695 −1.52063 −0.760315 0.649554i \(-0.774956\pi\)
−0.760315 + 0.649554i \(0.774956\pi\)
\(734\) −6.19137 −0.228528
\(735\) 0 0
\(736\) 58.1863 2.14478
\(737\) 39.5405 1.45649
\(738\) 0 0
\(739\) 8.29123 0.304998 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(740\) −2.59718 −0.0954741
\(741\) 0 0
\(742\) −22.7451 −0.834997
\(743\) −13.1999 −0.484256 −0.242128 0.970244i \(-0.577845\pi\)
−0.242128 + 0.970244i \(0.577845\pi\)
\(744\) 0 0
\(745\) 14.8739 0.544938
\(746\) 27.5537 1.00881
\(747\) 0 0
\(748\) 68.8272 2.51657
\(749\) −2.36070 −0.0862581
\(750\) 0 0
\(751\) −10.2608 −0.374421 −0.187210 0.982320i \(-0.559945\pi\)
−0.187210 + 0.982320i \(0.559945\pi\)
\(752\) −50.3052 −1.83444
\(753\) 0 0
\(754\) −6.33068 −0.230550
\(755\) 35.8630 1.30519
\(756\) 0 0
\(757\) 18.2390 0.662909 0.331455 0.943471i \(-0.392461\pi\)
0.331455 + 0.943471i \(0.392461\pi\)
\(758\) −18.9149 −0.687021
\(759\) 0 0
\(760\) −6.03653 −0.218968
\(761\) 7.43533 0.269530 0.134765 0.990878i \(-0.456972\pi\)
0.134765 + 0.990878i \(0.456972\pi\)
\(762\) 0 0
\(763\) 14.6315 0.529694
\(764\) 13.2103 0.477931
\(765\) 0 0
\(766\) −22.4216 −0.810124
\(767\) 8.29383 0.299473
\(768\) 0 0
\(769\) 10.0750 0.363313 0.181657 0.983362i \(-0.441854\pi\)
0.181657 + 0.983362i \(0.441854\pi\)
\(770\) 19.5437 0.704306
\(771\) 0 0
\(772\) −11.2889 −0.406297
\(773\) 10.0743 0.362346 0.181173 0.983451i \(-0.442011\pi\)
0.181173 + 0.983451i \(0.442011\pi\)
\(774\) 0 0
\(775\) 0.671904 0.0241355
\(776\) −10.4430 −0.374883
\(777\) 0 0
\(778\) 10.0585 0.360616
\(779\) 11.1110 0.398094
\(780\) 0 0
\(781\) 11.7244 0.419532
\(782\) −122.472 −4.37959
\(783\) 0 0
\(784\) −4.59879 −0.164242
\(785\) 26.3367 0.939996
\(786\) 0 0
\(787\) −11.6451 −0.415103 −0.207551 0.978224i \(-0.566549\pi\)
−0.207551 + 0.978224i \(0.566549\pi\)
\(788\) 38.9533 1.38765
\(789\) 0 0
\(790\) 46.6317 1.65908
\(791\) −5.00346 −0.177902
\(792\) 0 0
\(793\) −8.94946 −0.317805
\(794\) −14.9295 −0.529827
\(795\) 0 0
\(796\) −40.3267 −1.42934
\(797\) 2.79683 0.0990688 0.0495344 0.998772i \(-0.484226\pi\)
0.0495344 + 0.998772i \(0.484226\pi\)
\(798\) 0 0
\(799\) 89.0029 3.14870
\(800\) −7.96100 −0.281464
\(801\) 0 0
\(802\) −9.96625 −0.351920
\(803\) 19.7394 0.696590
\(804\) 0 0
\(805\) −15.6338 −0.551019
\(806\) −1.88273 −0.0663162
\(807\) 0 0
\(808\) 4.70492 0.165519
\(809\) −7.01169 −0.246518 −0.123259 0.992375i \(-0.539335\pi\)
−0.123259 + 0.992375i \(0.539335\pi\)
\(810\) 0 0
\(811\) −45.4030 −1.59431 −0.797157 0.603772i \(-0.793664\pi\)
−0.797157 + 0.603772i \(0.793664\pi\)
\(812\) −3.41566 −0.119866
\(813\) 0 0
\(814\) −7.92815 −0.277882
\(815\) 12.6288 0.442368
\(816\) 0 0
\(817\) 50.9755 1.78341
\(818\) −16.0881 −0.562509
\(819\) 0 0
\(820\) −8.23446 −0.287560
\(821\) −1.36322 −0.0475767 −0.0237883 0.999717i \(-0.507573\pi\)
−0.0237883 + 0.999717i \(0.507573\pi\)
\(822\) 0 0
\(823\) 34.3554 1.19755 0.598777 0.800916i \(-0.295654\pi\)
0.598777 + 0.800916i \(0.295654\pi\)
\(824\) −5.14655 −0.179289
\(825\) 0 0
\(826\) 9.95402 0.346345
\(827\) −23.6447 −0.822208 −0.411104 0.911588i \(-0.634857\pi\)
−0.411104 + 0.911588i \(0.634857\pi\)
\(828\) 0 0
\(829\) −42.8712 −1.48898 −0.744489 0.667635i \(-0.767307\pi\)
−0.744489 + 0.667635i \(0.767307\pi\)
\(830\) 6.89823 0.239441
\(831\) 0 0
\(832\) 7.69945 0.266930
\(833\) 8.13644 0.281911
\(834\) 0 0
\(835\) 9.34235 0.323305
\(836\) 36.9114 1.27661
\(837\) 0 0
\(838\) 22.3966 0.773679
\(839\) 7.78248 0.268681 0.134340 0.990935i \(-0.457108\pi\)
0.134340 + 0.990935i \(0.457108\pi\)
\(840\) 0 0
\(841\) −24.6272 −0.849215
\(842\) 29.1501 1.00458
\(843\) 0 0
\(844\) 34.0243 1.17116
\(845\) 20.7433 0.713592
\(846\) 0 0
\(847\) 15.8200 0.543582
\(848\) −54.8748 −1.88441
\(849\) 0 0
\(850\) 16.7565 0.574744
\(851\) 6.34205 0.217403
\(852\) 0 0
\(853\) 32.6778 1.11887 0.559433 0.828876i \(-0.311019\pi\)
0.559433 + 0.828876i \(0.311019\pi\)
\(854\) −10.7409 −0.367546
\(855\) 0 0
\(856\) −1.64958 −0.0563815
\(857\) 1.01476 0.0346634 0.0173317 0.999850i \(-0.494483\pi\)
0.0173317 + 0.999850i \(0.494483\pi\)
\(858\) 0 0
\(859\) −30.0846 −1.02647 −0.513237 0.858247i \(-0.671554\pi\)
−0.513237 + 0.858247i \(0.671554\pi\)
\(860\) −37.7784 −1.28823
\(861\) 0 0
\(862\) 45.5145 1.55023
\(863\) −28.5365 −0.971393 −0.485696 0.874128i \(-0.661434\pi\)
−0.485696 + 0.874128i \(0.661434\pi\)
\(864\) 0 0
\(865\) −24.9600 −0.848666
\(866\) 74.1379 2.51931
\(867\) 0 0
\(868\) −1.01581 −0.0344788
\(869\) 63.9931 2.17082
\(870\) 0 0
\(871\) −12.1263 −0.410883
\(872\) 10.2240 0.346228
\(873\) 0 0
\(874\) −65.6806 −2.22168
\(875\) 12.0380 0.406958
\(876\) 0 0
\(877\) −4.59332 −0.155105 −0.0775527 0.996988i \(-0.524711\pi\)
−0.0775527 + 0.996988i \(0.524711\pi\)
\(878\) −5.63993 −0.190338
\(879\) 0 0
\(880\) 47.1512 1.58947
\(881\) 32.7435 1.10316 0.551578 0.834123i \(-0.314026\pi\)
0.551578 + 0.834123i \(0.314026\pi\)
\(882\) 0 0
\(883\) 41.4437 1.39469 0.697346 0.716735i \(-0.254364\pi\)
0.697346 + 0.716735i \(0.254364\pi\)
\(884\) −21.1079 −0.709935
\(885\) 0 0
\(886\) 20.6876 0.695015
\(887\) −29.0254 −0.974578 −0.487289 0.873241i \(-0.662014\pi\)
−0.487289 + 0.873241i \(0.662014\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) −42.5065 −1.42482
\(891\) 0 0
\(892\) −0.963418 −0.0322576
\(893\) 47.7314 1.59727
\(894\) 0 0
\(895\) 38.7816 1.29633
\(896\) −5.49624 −0.183616
\(897\) 0 0
\(898\) −37.7691 −1.26037
\(899\) 1.30045 0.0433725
\(900\) 0 0
\(901\) 97.0877 3.23446
\(902\) −25.1366 −0.836956
\(903\) 0 0
\(904\) −3.49625 −0.116284
\(905\) 24.2753 0.806939
\(906\) 0 0
\(907\) −55.9269 −1.85702 −0.928512 0.371303i \(-0.878911\pi\)
−0.928512 + 0.371303i \(0.878911\pi\)
\(908\) −43.9229 −1.45763
\(909\) 0 0
\(910\) −5.99365 −0.198688
\(911\) 44.3323 1.46880 0.734398 0.678719i \(-0.237465\pi\)
0.734398 + 0.678719i \(0.237465\pi\)
\(912\) 0 0
\(913\) 9.46650 0.313296
\(914\) 49.7562 1.64579
\(915\) 0 0
\(916\) 6.67952 0.220697
\(917\) −7.45485 −0.246181
\(918\) 0 0
\(919\) 19.7427 0.651250 0.325625 0.945499i \(-0.394425\pi\)
0.325625 + 0.945499i \(0.394425\pi\)
\(920\) −10.9244 −0.360167
\(921\) 0 0
\(922\) −19.1892 −0.631964
\(923\) −3.59563 −0.118352
\(924\) 0 0
\(925\) −0.867714 −0.0285303
\(926\) 26.3176 0.864850
\(927\) 0 0
\(928\) −15.4083 −0.505802
\(929\) 24.0010 0.787449 0.393724 0.919229i \(-0.371186\pi\)
0.393724 + 0.919229i \(0.371186\pi\)
\(930\) 0 0
\(931\) 4.36350 0.143008
\(932\) −29.1129 −0.953624
\(933\) 0 0
\(934\) −45.1888 −1.47862
\(935\) −83.4226 −2.72821
\(936\) 0 0
\(937\) −39.2507 −1.28226 −0.641132 0.767431i \(-0.721535\pi\)
−0.641132 + 0.767431i \(0.721535\pi\)
\(938\) −14.5536 −0.475192
\(939\) 0 0
\(940\) −35.3742 −1.15378
\(941\) 2.24962 0.0733355 0.0366677 0.999328i \(-0.488326\pi\)
0.0366677 + 0.999328i \(0.488326\pi\)
\(942\) 0 0
\(943\) 20.1078 0.654799
\(944\) 24.0151 0.781625
\(945\) 0 0
\(946\) −115.322 −3.74946
\(947\) 46.7613 1.51954 0.759769 0.650193i \(-0.225312\pi\)
0.759769 + 0.650193i \(0.225312\pi\)
\(948\) 0 0
\(949\) −6.05368 −0.196511
\(950\) 8.98636 0.291556
\(951\) 0 0
\(952\) 5.68548 0.184267
\(953\) 9.10879 0.295063 0.147531 0.989057i \(-0.452867\pi\)
0.147531 + 0.989057i \(0.452867\pi\)
\(954\) 0 0
\(955\) −16.0116 −0.518124
\(956\) −20.8743 −0.675122
\(957\) 0 0
\(958\) −1.21788 −0.0393479
\(959\) 18.5476 0.598934
\(960\) 0 0
\(961\) −30.6132 −0.987524
\(962\) 2.43140 0.0783915
\(963\) 0 0
\(964\) 1.01698 0.0327548
\(965\) 13.6828 0.440466
\(966\) 0 0
\(967\) −0.219150 −0.00704739 −0.00352370 0.999994i \(-0.501122\pi\)
−0.00352370 + 0.999994i \(0.501122\pi\)
\(968\) 11.0545 0.355306
\(969\) 0 0
\(970\) −56.3989 −1.81086
\(971\) 21.5646 0.692041 0.346020 0.938227i \(-0.387533\pi\)
0.346020 + 0.938227i \(0.387533\pi\)
\(972\) 0 0
\(973\) −16.7225 −0.536099
\(974\) −30.4330 −0.975135
\(975\) 0 0
\(976\) −25.9135 −0.829471
\(977\) −29.3741 −0.939760 −0.469880 0.882730i \(-0.655703\pi\)
−0.469880 + 0.882730i \(0.655703\pi\)
\(978\) 0 0
\(979\) −58.3321 −1.86430
\(980\) −3.23382 −0.103301
\(981\) 0 0
\(982\) 4.20930 0.134324
\(983\) 10.1660 0.324246 0.162123 0.986771i \(-0.448166\pi\)
0.162123 + 0.986771i \(0.448166\pi\)
\(984\) 0 0
\(985\) −47.2137 −1.50435
\(986\) 32.4318 1.03284
\(987\) 0 0
\(988\) −11.3200 −0.360136
\(989\) 92.2511 2.93341
\(990\) 0 0
\(991\) 35.1411 1.11629 0.558147 0.829742i \(-0.311512\pi\)
0.558147 + 0.829742i \(0.311512\pi\)
\(992\) −4.58238 −0.145491
\(993\) 0 0
\(994\) −4.31538 −0.136875
\(995\) 48.8783 1.54955
\(996\) 0 0
\(997\) 2.96104 0.0937769 0.0468885 0.998900i \(-0.485069\pi\)
0.0468885 + 0.998900i \(0.485069\pi\)
\(998\) 82.5874 2.61426
\(999\) 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 \(a_p\))