Properties

Label 8043.2.a.t.1.12
Level 8043
Weight 2
Character 8043.1
Self dual Yes
Analytic conductor 64.224
Analytic rank 0
Dimension 52
CM No

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Newspace parameters

Level: \( N \) = \( 8043 = 3 \cdot 7 \cdot 383 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8043.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2236783457\)
Analytic rank: \(0\)
Dimension: \(52\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 8043.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.77779 q^{2} -1.00000 q^{3} +1.16053 q^{4} +3.56820 q^{5} +1.77779 q^{6} +1.00000 q^{7} +1.49240 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.77779 q^{2} -1.00000 q^{3} +1.16053 q^{4} +3.56820 q^{5} +1.77779 q^{6} +1.00000 q^{7} +1.49240 q^{8} +1.00000 q^{9} -6.34350 q^{10} +5.16426 q^{11} -1.16053 q^{12} +2.64380 q^{13} -1.77779 q^{14} -3.56820 q^{15} -4.97423 q^{16} +5.04956 q^{17} -1.77779 q^{18} -5.59180 q^{19} +4.14100 q^{20} -1.00000 q^{21} -9.18096 q^{22} -3.54738 q^{23} -1.49240 q^{24} +7.73206 q^{25} -4.70011 q^{26} -1.00000 q^{27} +1.16053 q^{28} +9.81363 q^{29} +6.34350 q^{30} -2.67330 q^{31} +5.85833 q^{32} -5.16426 q^{33} -8.97704 q^{34} +3.56820 q^{35} +1.16053 q^{36} -5.45641 q^{37} +9.94104 q^{38} -2.64380 q^{39} +5.32518 q^{40} -11.2201 q^{41} +1.77779 q^{42} -3.36590 q^{43} +5.99327 q^{44} +3.56820 q^{45} +6.30648 q^{46} +9.80452 q^{47} +4.97423 q^{48} +1.00000 q^{49} -13.7460 q^{50} -5.04956 q^{51} +3.06820 q^{52} -6.98261 q^{53} +1.77779 q^{54} +18.4271 q^{55} +1.49240 q^{56} +5.59180 q^{57} -17.4466 q^{58} +2.82993 q^{59} -4.14100 q^{60} -3.17822 q^{61} +4.75256 q^{62} +1.00000 q^{63} -0.466399 q^{64} +9.43360 q^{65} +9.18096 q^{66} -5.16188 q^{67} +5.86016 q^{68} +3.54738 q^{69} -6.34350 q^{70} +15.3563 q^{71} +1.49240 q^{72} -12.2590 q^{73} +9.70034 q^{74} -7.73206 q^{75} -6.48945 q^{76} +5.16426 q^{77} +4.70011 q^{78} -4.35170 q^{79} -17.7491 q^{80} +1.00000 q^{81} +19.9470 q^{82} +10.3624 q^{83} -1.16053 q^{84} +18.0178 q^{85} +5.98386 q^{86} -9.81363 q^{87} +7.70714 q^{88} +10.7515 q^{89} -6.34350 q^{90} +2.64380 q^{91} -4.11683 q^{92} +2.67330 q^{93} -17.4303 q^{94} -19.9527 q^{95} -5.85833 q^{96} +2.13548 q^{97} -1.77779 q^{98} +5.16426 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 3q^{2} - 52q^{3} + 61q^{4} - 7q^{5} - 3q^{6} + 52q^{7} + 24q^{8} + 52q^{9} + O(q^{10}) \) \( 52q + 3q^{2} - 52q^{3} + 61q^{4} - 7q^{5} - 3q^{6} + 52q^{7} + 24q^{8} + 52q^{9} - 2q^{10} + 9q^{11} - 61q^{12} + 44q^{13} + 3q^{14} + 7q^{15} + 95q^{16} - 6q^{17} + 3q^{18} + 7q^{19} - 21q^{20} - 52q^{21} + 19q^{22} - 4q^{23} - 24q^{24} + 83q^{25} - 5q^{26} - 52q^{27} + 61q^{28} + 31q^{29} + 2q^{30} + 11q^{31} + 71q^{32} - 9q^{33} + 17q^{34} - 7q^{35} + 61q^{36} + 71q^{37} - 8q^{38} - 44q^{39} + 20q^{40} - 25q^{41} - 3q^{42} + 75q^{43} + 14q^{44} - 7q^{45} + 36q^{46} - 20q^{47} - 95q^{48} + 52q^{49} + 26q^{50} + 6q^{51} + 88q^{52} + 70q^{53} - 3q^{54} + 12q^{55} + 24q^{56} - 7q^{57} + 48q^{58} - 27q^{59} + 21q^{60} + 59q^{61} - 23q^{62} + 52q^{63} + 138q^{64} + 44q^{65} - 19q^{66} + 65q^{67} - 8q^{68} + 4q^{69} - 2q^{70} - 11q^{71} + 24q^{72} + 34q^{73} + 38q^{74} - 83q^{75} + 31q^{76} + 9q^{77} + 5q^{78} + 74q^{79} - 5q^{80} + 52q^{81} + 51q^{82} - 30q^{83} - 61q^{84} + 70q^{85} + 29q^{86} - 31q^{87} + 90q^{88} - q^{89} - 2q^{90} + 44q^{91} + 34q^{92} - 11q^{93} + 27q^{94} + 9q^{95} - 71q^{96} + 73q^{97} + 3q^{98} + 9q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.77779 −1.25709 −0.628543 0.777775i \(-0.716348\pi\)
−0.628543 + 0.777775i \(0.716348\pi\)
\(3\) −1.00000 −0.577350
\(4\) 1.16053 0.580265
\(5\) 3.56820 1.59575 0.797874 0.602824i \(-0.205958\pi\)
0.797874 + 0.602824i \(0.205958\pi\)
\(6\) 1.77779 0.725779
\(7\) 1.00000 0.377964
\(8\) 1.49240 0.527643
\(9\) 1.00000 0.333333
\(10\) −6.34350 −2.00599
\(11\) 5.16426 1.55708 0.778541 0.627593i \(-0.215960\pi\)
0.778541 + 0.627593i \(0.215960\pi\)
\(12\) −1.16053 −0.335016
\(13\) 2.64380 0.733257 0.366629 0.930367i \(-0.380512\pi\)
0.366629 + 0.930367i \(0.380512\pi\)
\(14\) −1.77779 −0.475134
\(15\) −3.56820 −0.921306
\(16\) −4.97423 −1.24356
\(17\) 5.04956 1.22470 0.612349 0.790588i \(-0.290225\pi\)
0.612349 + 0.790588i \(0.290225\pi\)
\(18\) −1.77779 −0.419029
\(19\) −5.59180 −1.28285 −0.641424 0.767187i \(-0.721656\pi\)
−0.641424 + 0.767187i \(0.721656\pi\)
\(20\) 4.14100 0.925956
\(21\) −1.00000 −0.218218
\(22\) −9.18096 −1.95739
\(23\) −3.54738 −0.739679 −0.369839 0.929096i \(-0.620587\pi\)
−0.369839 + 0.929096i \(0.620587\pi\)
\(24\) −1.49240 −0.304635
\(25\) 7.73206 1.54641
\(26\) −4.70011 −0.921768
\(27\) −1.00000 −0.192450
\(28\) 1.16053 0.219319
\(29\) 9.81363 1.82235 0.911173 0.412025i \(-0.135178\pi\)
0.911173 + 0.412025i \(0.135178\pi\)
\(30\) 6.34350 1.15816
\(31\) −2.67330 −0.480139 −0.240069 0.970756i \(-0.577170\pi\)
−0.240069 + 0.970756i \(0.577170\pi\)
\(32\) 5.85833 1.03562
\(33\) −5.16426 −0.898982
\(34\) −8.97704 −1.53955
\(35\) 3.56820 0.603136
\(36\) 1.16053 0.193422
\(37\) −5.45641 −0.897028 −0.448514 0.893776i \(-0.648047\pi\)
−0.448514 + 0.893776i \(0.648047\pi\)
\(38\) 9.94104 1.61265
\(39\) −2.64380 −0.423346
\(40\) 5.32518 0.841986
\(41\) −11.2201 −1.75229 −0.876143 0.482052i \(-0.839892\pi\)
−0.876143 + 0.482052i \(0.839892\pi\)
\(42\) 1.77779 0.274319
\(43\) −3.36590 −0.513296 −0.256648 0.966505i \(-0.582618\pi\)
−0.256648 + 0.966505i \(0.582618\pi\)
\(44\) 5.99327 0.903520
\(45\) 3.56820 0.531916
\(46\) 6.30648 0.929840
\(47\) 9.80452 1.43014 0.715068 0.699055i \(-0.246396\pi\)
0.715068 + 0.699055i \(0.246396\pi\)
\(48\) 4.97423 0.717968
\(49\) 1.00000 0.142857
\(50\) −13.7460 −1.94397
\(51\) −5.04956 −0.707079
\(52\) 3.06820 0.425483
\(53\) −6.98261 −0.959135 −0.479567 0.877505i \(-0.659206\pi\)
−0.479567 + 0.877505i \(0.659206\pi\)
\(54\) 1.77779 0.241926
\(55\) 18.4271 2.48471
\(56\) 1.49240 0.199430
\(57\) 5.59180 0.740652
\(58\) −17.4466 −2.29084
\(59\) 2.82993 0.368426 0.184213 0.982886i \(-0.441026\pi\)
0.184213 + 0.982886i \(0.441026\pi\)
\(60\) −4.14100 −0.534601
\(61\) −3.17822 −0.406930 −0.203465 0.979082i \(-0.565220\pi\)
−0.203465 + 0.979082i \(0.565220\pi\)
\(62\) 4.75256 0.603575
\(63\) 1.00000 0.125988
\(64\) −0.466399 −0.0582998
\(65\) 9.43360 1.17009
\(66\) 9.18096 1.13010
\(67\) −5.16188 −0.630624 −0.315312 0.948988i \(-0.602109\pi\)
−0.315312 + 0.948988i \(0.602109\pi\)
\(68\) 5.86016 0.710649
\(69\) 3.54738 0.427054
\(70\) −6.34350 −0.758194
\(71\) 15.3563 1.82246 0.911229 0.411900i \(-0.135135\pi\)
0.911229 + 0.411900i \(0.135135\pi\)
\(72\) 1.49240 0.175881
\(73\) −12.2590 −1.43481 −0.717406 0.696656i \(-0.754671\pi\)
−0.717406 + 0.696656i \(0.754671\pi\)
\(74\) 9.70034 1.12764
\(75\) −7.73206 −0.892821
\(76\) −6.48945 −0.744391
\(77\) 5.16426 0.588522
\(78\) 4.70011 0.532183
\(79\) −4.35170 −0.489605 −0.244802 0.969573i \(-0.578723\pi\)
−0.244802 + 0.969573i \(0.578723\pi\)
\(80\) −17.7491 −1.98440
\(81\) 1.00000 0.111111
\(82\) 19.9470 2.20277
\(83\) 10.3624 1.13742 0.568709 0.822539i \(-0.307443\pi\)
0.568709 + 0.822539i \(0.307443\pi\)
\(84\) −1.16053 −0.126624
\(85\) 18.0178 1.95431
\(86\) 5.98386 0.645257
\(87\) −9.81363 −1.05213
\(88\) 7.70714 0.821584
\(89\) 10.7515 1.13965 0.569827 0.821765i \(-0.307010\pi\)
0.569827 + 0.821765i \(0.307010\pi\)
\(90\) −6.34350 −0.668664
\(91\) 2.64380 0.277145
\(92\) −4.11683 −0.429210
\(93\) 2.67330 0.277208
\(94\) −17.4303 −1.79780
\(95\) −19.9527 −2.04710
\(96\) −5.85833 −0.597913
\(97\) 2.13548 0.216825 0.108412 0.994106i \(-0.465423\pi\)
0.108412 + 0.994106i \(0.465423\pi\)
\(98\) −1.77779 −0.179584
\(99\) 5.16426 0.519028
\(100\) 8.97328 0.897328
\(101\) 12.6656 1.26027 0.630137 0.776484i \(-0.282999\pi\)
0.630137 + 0.776484i \(0.282999\pi\)
\(102\) 8.97704 0.888859
\(103\) 11.6109 1.14405 0.572026 0.820236i \(-0.306158\pi\)
0.572026 + 0.820236i \(0.306158\pi\)
\(104\) 3.94560 0.386898
\(105\) −3.56820 −0.348221
\(106\) 12.4136 1.20571
\(107\) 4.66636 0.451114 0.225557 0.974230i \(-0.427580\pi\)
0.225557 + 0.974230i \(0.427580\pi\)
\(108\) −1.16053 −0.111672
\(109\) 12.1226 1.16114 0.580569 0.814211i \(-0.302830\pi\)
0.580569 + 0.814211i \(0.302830\pi\)
\(110\) −32.7595 −3.12350
\(111\) 5.45641 0.517899
\(112\) −4.97423 −0.470021
\(113\) 1.28147 0.120551 0.0602754 0.998182i \(-0.480802\pi\)
0.0602754 + 0.998182i \(0.480802\pi\)
\(114\) −9.94104 −0.931064
\(115\) −12.6577 −1.18034
\(116\) 11.3890 1.05744
\(117\) 2.64380 0.244419
\(118\) −5.03102 −0.463143
\(119\) 5.04956 0.462892
\(120\) −5.32518 −0.486121
\(121\) 15.6696 1.42451
\(122\) 5.65021 0.511546
\(123\) 11.2201 1.01168
\(124\) −3.10244 −0.278608
\(125\) 9.74853 0.871935
\(126\) −1.77779 −0.158378
\(127\) 3.66781 0.325465 0.162733 0.986670i \(-0.447969\pi\)
0.162733 + 0.986670i \(0.447969\pi\)
\(128\) −10.8875 −0.962327
\(129\) 3.36590 0.296351
\(130\) −16.7709 −1.47091
\(131\) −17.1864 −1.50159 −0.750793 0.660537i \(-0.770329\pi\)
−0.750793 + 0.660537i \(0.770329\pi\)
\(132\) −5.99327 −0.521648
\(133\) −5.59180 −0.484871
\(134\) 9.17673 0.792749
\(135\) −3.56820 −0.307102
\(136\) 7.53596 0.646203
\(137\) 16.7456 1.43067 0.715337 0.698779i \(-0.246273\pi\)
0.715337 + 0.698779i \(0.246273\pi\)
\(138\) −6.30648 −0.536843
\(139\) −12.6400 −1.07211 −0.536056 0.844183i \(-0.680086\pi\)
−0.536056 + 0.844183i \(0.680086\pi\)
\(140\) 4.14100 0.349979
\(141\) −9.80452 −0.825689
\(142\) −27.3002 −2.29099
\(143\) 13.6533 1.14174
\(144\) −4.97423 −0.414519
\(145\) 35.0170 2.90800
\(146\) 21.7940 1.80368
\(147\) −1.00000 −0.0824786
\(148\) −6.33232 −0.520514
\(149\) 8.12880 0.665937 0.332969 0.942938i \(-0.391950\pi\)
0.332969 + 0.942938i \(0.391950\pi\)
\(150\) 13.7460 1.12235
\(151\) −4.23418 −0.344573 −0.172286 0.985047i \(-0.555115\pi\)
−0.172286 + 0.985047i \(0.555115\pi\)
\(152\) −8.34521 −0.676886
\(153\) 5.04956 0.408232
\(154\) −9.18096 −0.739823
\(155\) −9.53887 −0.766180
\(156\) −3.06820 −0.245653
\(157\) 13.2965 1.06117 0.530587 0.847631i \(-0.321972\pi\)
0.530587 + 0.847631i \(0.321972\pi\)
\(158\) 7.73640 0.615475
\(159\) 6.98261 0.553757
\(160\) 20.9037 1.65258
\(161\) −3.54738 −0.279572
\(162\) −1.77779 −0.139676
\(163\) 1.02659 0.0804084 0.0402042 0.999191i \(-0.487199\pi\)
0.0402042 + 0.999191i \(0.487199\pi\)
\(164\) −13.0213 −1.01679
\(165\) −18.4271 −1.43455
\(166\) −18.4221 −1.42983
\(167\) −0.549046 −0.0424865 −0.0212432 0.999774i \(-0.506762\pi\)
−0.0212432 + 0.999774i \(0.506762\pi\)
\(168\) −1.49240 −0.115141
\(169\) −6.01034 −0.462334
\(170\) −32.0319 −2.45673
\(171\) −5.59180 −0.427616
\(172\) −3.90623 −0.297847
\(173\) 5.50542 0.418569 0.209285 0.977855i \(-0.432886\pi\)
0.209285 + 0.977855i \(0.432886\pi\)
\(174\) 17.4466 1.32262
\(175\) 7.73206 0.584489
\(176\) −25.6882 −1.93632
\(177\) −2.82993 −0.212711
\(178\) −19.1138 −1.43264
\(179\) 16.4288 1.22795 0.613974 0.789326i \(-0.289570\pi\)
0.613974 + 0.789326i \(0.289570\pi\)
\(180\) 4.14100 0.308652
\(181\) 8.02365 0.596393 0.298197 0.954504i \(-0.403615\pi\)
0.298197 + 0.954504i \(0.403615\pi\)
\(182\) −4.70011 −0.348395
\(183\) 3.17822 0.234941
\(184\) −5.29411 −0.390287
\(185\) −19.4696 −1.43143
\(186\) −4.75256 −0.348474
\(187\) 26.0772 1.90695
\(188\) 11.3784 0.829857
\(189\) −1.00000 −0.0727393
\(190\) 35.4716 2.57338
\(191\) −25.7675 −1.86447 −0.932234 0.361856i \(-0.882143\pi\)
−0.932234 + 0.361856i \(0.882143\pi\)
\(192\) 0.466399 0.0336594
\(193\) 21.8665 1.57398 0.786991 0.616964i \(-0.211638\pi\)
0.786991 + 0.616964i \(0.211638\pi\)
\(194\) −3.79642 −0.272567
\(195\) −9.43360 −0.675554
\(196\) 1.16053 0.0828950
\(197\) 11.0476 0.787107 0.393553 0.919302i \(-0.371246\pi\)
0.393553 + 0.919302i \(0.371246\pi\)
\(198\) −9.18096 −0.652462
\(199\) −2.43275 −0.172453 −0.0862264 0.996276i \(-0.527481\pi\)
−0.0862264 + 0.996276i \(0.527481\pi\)
\(200\) 11.5393 0.815954
\(201\) 5.16188 0.364091
\(202\) −22.5167 −1.58427
\(203\) 9.81363 0.688782
\(204\) −5.86016 −0.410293
\(205\) −40.0356 −2.79621
\(206\) −20.6416 −1.43817
\(207\) −3.54738 −0.246560
\(208\) −13.1509 −0.911848
\(209\) −28.8775 −1.99750
\(210\) 6.34350 0.437743
\(211\) 14.1449 0.973778 0.486889 0.873464i \(-0.338132\pi\)
0.486889 + 0.873464i \(0.338132\pi\)
\(212\) −8.10352 −0.556552
\(213\) −15.3563 −1.05220
\(214\) −8.29579 −0.567089
\(215\) −12.0102 −0.819091
\(216\) −1.49240 −0.101545
\(217\) −2.67330 −0.181475
\(218\) −21.5515 −1.45965
\(219\) 12.2590 0.828389
\(220\) 21.3852 1.44179
\(221\) 13.3500 0.898018
\(222\) −9.70034 −0.651044
\(223\) −22.0031 −1.47344 −0.736718 0.676200i \(-0.763625\pi\)
−0.736718 + 0.676200i \(0.763625\pi\)
\(224\) 5.85833 0.391426
\(225\) 7.73206 0.515471
\(226\) −2.27819 −0.151543
\(227\) −5.19944 −0.345099 −0.172549 0.985001i \(-0.555200\pi\)
−0.172549 + 0.985001i \(0.555200\pi\)
\(228\) 6.48945 0.429774
\(229\) 4.65236 0.307437 0.153718 0.988115i \(-0.450875\pi\)
0.153718 + 0.988115i \(0.450875\pi\)
\(230\) 22.5028 1.48379
\(231\) −5.16426 −0.339783
\(232\) 14.6459 0.961548
\(233\) −1.65730 −0.108573 −0.0542867 0.998525i \(-0.517289\pi\)
−0.0542867 + 0.998525i \(0.517289\pi\)
\(234\) −4.70011 −0.307256
\(235\) 34.9845 2.28214
\(236\) 3.28422 0.213785
\(237\) 4.35170 0.282673
\(238\) −8.97704 −0.581895
\(239\) −19.8635 −1.28486 −0.642431 0.766344i \(-0.722074\pi\)
−0.642431 + 0.766344i \(0.722074\pi\)
\(240\) 17.7491 1.14570
\(241\) 1.30808 0.0842606 0.0421303 0.999112i \(-0.486586\pi\)
0.0421303 + 0.999112i \(0.486586\pi\)
\(242\) −27.8572 −1.79073
\(243\) −1.00000 −0.0641500
\(244\) −3.68842 −0.236127
\(245\) 3.56820 0.227964
\(246\) −19.9470 −1.27177
\(247\) −14.7836 −0.940657
\(248\) −3.98963 −0.253342
\(249\) −10.3624 −0.656688
\(250\) −17.3308 −1.09610
\(251\) 2.76424 0.174477 0.0872387 0.996187i \(-0.472196\pi\)
0.0872387 + 0.996187i \(0.472196\pi\)
\(252\) 1.16053 0.0731065
\(253\) −18.3196 −1.15174
\(254\) −6.52058 −0.409138
\(255\) −18.0178 −1.12832
\(256\) 20.2884 1.26803
\(257\) −11.5308 −0.719270 −0.359635 0.933093i \(-0.617099\pi\)
−0.359635 + 0.933093i \(0.617099\pi\)
\(258\) −5.98386 −0.372539
\(259\) −5.45641 −0.339045
\(260\) 10.9480 0.678964
\(261\) 9.81363 0.607449
\(262\) 30.5538 1.88762
\(263\) 18.6024 1.14708 0.573538 0.819179i \(-0.305571\pi\)
0.573538 + 0.819179i \(0.305571\pi\)
\(264\) −7.70714 −0.474342
\(265\) −24.9153 −1.53054
\(266\) 9.94104 0.609524
\(267\) −10.7515 −0.657979
\(268\) −5.99052 −0.365929
\(269\) 4.15629 0.253414 0.126707 0.991940i \(-0.459559\pi\)
0.126707 + 0.991940i \(0.459559\pi\)
\(270\) 6.34350 0.386053
\(271\) 23.7689 1.44386 0.721930 0.691966i \(-0.243255\pi\)
0.721930 + 0.691966i \(0.243255\pi\)
\(272\) −25.1177 −1.52298
\(273\) −2.64380 −0.160010
\(274\) −29.7702 −1.79848
\(275\) 39.9303 2.40789
\(276\) 4.11683 0.247804
\(277\) −17.1397 −1.02982 −0.514912 0.857243i \(-0.672175\pi\)
−0.514912 + 0.857243i \(0.672175\pi\)
\(278\) 22.4713 1.34774
\(279\) −2.67330 −0.160046
\(280\) 5.32518 0.318241
\(281\) 7.18469 0.428603 0.214301 0.976768i \(-0.431253\pi\)
0.214301 + 0.976768i \(0.431253\pi\)
\(282\) 17.4303 1.03796
\(283\) −1.70929 −0.101607 −0.0508035 0.998709i \(-0.516178\pi\)
−0.0508035 + 0.998709i \(0.516178\pi\)
\(284\) 17.8214 1.05751
\(285\) 19.9527 1.18189
\(286\) −24.2726 −1.43527
\(287\) −11.2201 −0.662302
\(288\) 5.85833 0.345205
\(289\) 8.49801 0.499883
\(290\) −62.2528 −3.65561
\(291\) −2.13548 −0.125184
\(292\) −14.2270 −0.832570
\(293\) 2.03527 0.118902 0.0594509 0.998231i \(-0.481065\pi\)
0.0594509 + 0.998231i \(0.481065\pi\)
\(294\) 1.77779 0.103683
\(295\) 10.0978 0.587915
\(296\) −8.14315 −0.473311
\(297\) −5.16426 −0.299661
\(298\) −14.4513 −0.837140
\(299\) −9.37854 −0.542375
\(300\) −8.97328 −0.518073
\(301\) −3.36590 −0.194008
\(302\) 7.52748 0.433158
\(303\) −12.6656 −0.727620
\(304\) 27.8149 1.59529
\(305\) −11.3405 −0.649357
\(306\) −8.97704 −0.513183
\(307\) −4.42991 −0.252828 −0.126414 0.991978i \(-0.540347\pi\)
−0.126414 + 0.991978i \(0.540347\pi\)
\(308\) 5.99327 0.341499
\(309\) −11.6109 −0.660519
\(310\) 16.9581 0.963154
\(311\) −18.8365 −1.06812 −0.534059 0.845447i \(-0.679334\pi\)
−0.534059 + 0.845447i \(0.679334\pi\)
\(312\) −3.94560 −0.223376
\(313\) −12.1668 −0.687711 −0.343855 0.939023i \(-0.611733\pi\)
−0.343855 + 0.939023i \(0.611733\pi\)
\(314\) −23.6383 −1.33399
\(315\) 3.56820 0.201045
\(316\) −5.05028 −0.284100
\(317\) 5.28744 0.296972 0.148486 0.988914i \(-0.452560\pi\)
0.148486 + 0.988914i \(0.452560\pi\)
\(318\) −12.4136 −0.696120
\(319\) 50.6801 2.83754
\(320\) −1.66420 −0.0930318
\(321\) −4.66636 −0.260451
\(322\) 6.30648 0.351446
\(323\) −28.2361 −1.57110
\(324\) 1.16053 0.0644739
\(325\) 20.4420 1.13392
\(326\) −1.82505 −0.101080
\(327\) −12.1226 −0.670384
\(328\) −16.7449 −0.924581
\(329\) 9.80452 0.540540
\(330\) 32.7595 1.80335
\(331\) 28.6932 1.57712 0.788560 0.614958i \(-0.210827\pi\)
0.788560 + 0.614958i \(0.210827\pi\)
\(332\) 12.0258 0.660003
\(333\) −5.45641 −0.299009
\(334\) 0.976087 0.0534091
\(335\) −18.4186 −1.00632
\(336\) 4.97423 0.271367
\(337\) 30.3775 1.65477 0.827384 0.561637i \(-0.189828\pi\)
0.827384 + 0.561637i \(0.189828\pi\)
\(338\) 10.6851 0.581193
\(339\) −1.28147 −0.0696001
\(340\) 20.9102 1.13402
\(341\) −13.8056 −0.747616
\(342\) 9.94104 0.537550
\(343\) 1.00000 0.0539949
\(344\) −5.02328 −0.270837
\(345\) 12.6577 0.681470
\(346\) −9.78746 −0.526177
\(347\) −19.7778 −1.06173 −0.530863 0.847458i \(-0.678132\pi\)
−0.530863 + 0.847458i \(0.678132\pi\)
\(348\) −11.3890 −0.610515
\(349\) 6.77139 0.362464 0.181232 0.983440i \(-0.441991\pi\)
0.181232 + 0.983440i \(0.441991\pi\)
\(350\) −13.7460 −0.734752
\(351\) −2.64380 −0.141115
\(352\) 30.2539 1.61254
\(353\) 8.51251 0.453075 0.226538 0.974002i \(-0.427259\pi\)
0.226538 + 0.974002i \(0.427259\pi\)
\(354\) 5.03102 0.267396
\(355\) 54.7944 2.90818
\(356\) 12.4774 0.661301
\(357\) −5.04956 −0.267251
\(358\) −29.2070 −1.54364
\(359\) −32.2581 −1.70251 −0.851257 0.524748i \(-0.824159\pi\)
−0.851257 + 0.524748i \(0.824159\pi\)
\(360\) 5.32518 0.280662
\(361\) 12.2683 0.645698
\(362\) −14.2643 −0.749717
\(363\) −15.6696 −0.822439
\(364\) 3.06820 0.160818
\(365\) −43.7427 −2.28960
\(366\) −5.65021 −0.295341
\(367\) 0.942900 0.0492190 0.0246095 0.999697i \(-0.492166\pi\)
0.0246095 + 0.999697i \(0.492166\pi\)
\(368\) 17.6455 0.919833
\(369\) −11.2201 −0.584095
\(370\) 34.6128 1.79943
\(371\) −6.98261 −0.362519
\(372\) 3.10244 0.160854
\(373\) −5.26452 −0.272586 −0.136293 0.990669i \(-0.543519\pi\)
−0.136293 + 0.990669i \(0.543519\pi\)
\(374\) −46.3597 −2.39721
\(375\) −9.74853 −0.503412
\(376\) 14.6323 0.754601
\(377\) 25.9453 1.33625
\(378\) 1.77779 0.0914395
\(379\) −24.6145 −1.26436 −0.632182 0.774820i \(-0.717840\pi\)
−0.632182 + 0.774820i \(0.717840\pi\)
\(380\) −23.1557 −1.18786
\(381\) −3.66781 −0.187907
\(382\) 45.8091 2.34380
\(383\) −1.00000 −0.0510976
\(384\) 10.8875 0.555600
\(385\) 18.4271 0.939133
\(386\) −38.8739 −1.97863
\(387\) −3.36590 −0.171099
\(388\) 2.47828 0.125816
\(389\) 22.9733 1.16479 0.582397 0.812905i \(-0.302115\pi\)
0.582397 + 0.812905i \(0.302115\pi\)
\(390\) 16.7709 0.849230
\(391\) −17.9127 −0.905883
\(392\) 1.49240 0.0753776
\(393\) 17.1864 0.866941
\(394\) −19.6402 −0.989460
\(395\) −15.5277 −0.781286
\(396\) 5.99327 0.301173
\(397\) −15.0916 −0.757428 −0.378714 0.925514i \(-0.623634\pi\)
−0.378714 + 0.925514i \(0.623634\pi\)
\(398\) 4.32491 0.216788
\(399\) 5.59180 0.279940
\(400\) −38.4610 −1.92305
\(401\) 3.73872 0.186703 0.0933514 0.995633i \(-0.470242\pi\)
0.0933514 + 0.995633i \(0.470242\pi\)
\(402\) −9.17673 −0.457694
\(403\) −7.06766 −0.352065
\(404\) 14.6988 0.731293
\(405\) 3.56820 0.177305
\(406\) −17.4466 −0.865858
\(407\) −28.1783 −1.39675
\(408\) −7.53596 −0.373086
\(409\) −1.09450 −0.0541194 −0.0270597 0.999634i \(-0.508614\pi\)
−0.0270597 + 0.999634i \(0.508614\pi\)
\(410\) 71.1748 3.51507
\(411\) −16.7456 −0.826001
\(412\) 13.4747 0.663853
\(413\) 2.82993 0.139252
\(414\) 6.30648 0.309947
\(415\) 36.9750 1.81503
\(416\) 15.4882 0.759373
\(417\) 12.6400 0.618984
\(418\) 51.3381 2.51103
\(419\) −17.0939 −0.835093 −0.417547 0.908656i \(-0.637110\pi\)
−0.417547 + 0.908656i \(0.637110\pi\)
\(420\) −4.14100 −0.202060
\(421\) −24.3624 −1.18735 −0.593676 0.804704i \(-0.702324\pi\)
−0.593676 + 0.804704i \(0.702324\pi\)
\(422\) −25.1467 −1.22412
\(423\) 9.80452 0.476712
\(424\) −10.4208 −0.506081
\(425\) 39.0435 1.89389
\(426\) 27.3002 1.32270
\(427\) −3.17822 −0.153805
\(428\) 5.41544 0.261765
\(429\) −13.6533 −0.659185
\(430\) 21.3516 1.02967
\(431\) 37.8944 1.82531 0.912654 0.408734i \(-0.134030\pi\)
0.912654 + 0.408734i \(0.134030\pi\)
\(432\) 4.97423 0.239323
\(433\) 32.8122 1.57685 0.788426 0.615130i \(-0.210896\pi\)
0.788426 + 0.615130i \(0.210896\pi\)
\(434\) 4.75256 0.228130
\(435\) −35.0170 −1.67894
\(436\) 14.0687 0.673768
\(437\) 19.8362 0.948895
\(438\) −21.7940 −1.04136
\(439\) 10.5354 0.502825 0.251413 0.967880i \(-0.419105\pi\)
0.251413 + 0.967880i \(0.419105\pi\)
\(440\) 27.5006 1.31104
\(441\) 1.00000 0.0476190
\(442\) −23.7335 −1.12889
\(443\) 21.9001 1.04050 0.520252 0.854013i \(-0.325838\pi\)
0.520252 + 0.854013i \(0.325838\pi\)
\(444\) 6.33232 0.300519
\(445\) 38.3634 1.81860
\(446\) 39.1168 1.85224
\(447\) −8.12880 −0.384479
\(448\) −0.466399 −0.0220353
\(449\) 19.9363 0.940852 0.470426 0.882440i \(-0.344100\pi\)
0.470426 + 0.882440i \(0.344100\pi\)
\(450\) −13.7460 −0.647991
\(451\) −57.9435 −2.72845
\(452\) 1.48719 0.0699514
\(453\) 4.23418 0.198939
\(454\) 9.24349 0.433819
\(455\) 9.43360 0.442254
\(456\) 8.34521 0.390800
\(457\) −9.61335 −0.449694 −0.224847 0.974394i \(-0.572188\pi\)
−0.224847 + 0.974394i \(0.572188\pi\)
\(458\) −8.27091 −0.386474
\(459\) −5.04956 −0.235693
\(460\) −14.6897 −0.684910
\(461\) −14.5863 −0.679350 −0.339675 0.940543i \(-0.610317\pi\)
−0.339675 + 0.940543i \(0.610317\pi\)
\(462\) 9.18096 0.427137
\(463\) −42.3415 −1.96778 −0.983888 0.178786i \(-0.942783\pi\)
−0.983888 + 0.178786i \(0.942783\pi\)
\(464\) −48.8153 −2.26619
\(465\) 9.53887 0.442354
\(466\) 2.94633 0.136486
\(467\) −32.6293 −1.50990 −0.754952 0.655780i \(-0.772340\pi\)
−0.754952 + 0.655780i \(0.772340\pi\)
\(468\) 3.06820 0.141828
\(469\) −5.16188 −0.238354
\(470\) −62.1950 −2.86884
\(471\) −13.2965 −0.612669
\(472\) 4.22339 0.194397
\(473\) −17.3824 −0.799244
\(474\) −7.73640 −0.355345
\(475\) −43.2361 −1.98381
\(476\) 5.86016 0.268600
\(477\) −6.98261 −0.319712
\(478\) 35.3131 1.61518
\(479\) 25.8706 1.18206 0.591028 0.806651i \(-0.298722\pi\)
0.591028 + 0.806651i \(0.298722\pi\)
\(480\) −20.9037 −0.954118
\(481\) −14.4256 −0.657753
\(482\) −2.32548 −0.105923
\(483\) 3.54738 0.161411
\(484\) 18.1850 0.826591
\(485\) 7.61981 0.345998
\(486\) 1.77779 0.0806421
\(487\) −19.8336 −0.898746 −0.449373 0.893344i \(-0.648353\pi\)
−0.449373 + 0.893344i \(0.648353\pi\)
\(488\) −4.74318 −0.214714
\(489\) −1.02659 −0.0464238
\(490\) −6.34350 −0.286570
\(491\) −13.2526 −0.598082 −0.299041 0.954240i \(-0.596667\pi\)
−0.299041 + 0.954240i \(0.596667\pi\)
\(492\) 13.0213 0.587044
\(493\) 49.5545 2.23182
\(494\) 26.2821 1.18249
\(495\) 18.4271 0.828237
\(496\) 13.2976 0.597080
\(497\) 15.3563 0.688824
\(498\) 18.4221 0.825513
\(499\) −37.2234 −1.66635 −0.833175 0.553010i \(-0.813479\pi\)
−0.833175 + 0.553010i \(0.813479\pi\)
\(500\) 11.3135 0.505953
\(501\) 0.549046 0.0245296
\(502\) −4.91424 −0.219333
\(503\) −37.1974 −1.65855 −0.829274 0.558842i \(-0.811246\pi\)
−0.829274 + 0.558842i \(0.811246\pi\)
\(504\) 1.49240 0.0664768
\(505\) 45.1934 2.01108
\(506\) 32.5683 1.44784
\(507\) 6.01034 0.266928
\(508\) 4.25660 0.188856
\(509\) 7.35668 0.326079 0.163039 0.986620i \(-0.447870\pi\)
0.163039 + 0.986620i \(0.447870\pi\)
\(510\) 32.0319 1.41840
\(511\) −12.2590 −0.542308
\(512\) −14.2936 −0.631693
\(513\) 5.59180 0.246884
\(514\) 20.4993 0.904184
\(515\) 41.4299 1.82562
\(516\) 3.90623 0.171962
\(517\) 50.6331 2.22684
\(518\) 9.70034 0.426208
\(519\) −5.50542 −0.241661
\(520\) 14.0787 0.617392
\(521\) 21.2458 0.930794 0.465397 0.885102i \(-0.345912\pi\)
0.465397 + 0.885102i \(0.345912\pi\)
\(522\) −17.4466 −0.763615
\(523\) 20.3002 0.887666 0.443833 0.896109i \(-0.353618\pi\)
0.443833 + 0.896109i \(0.353618\pi\)
\(524\) −19.9454 −0.871318
\(525\) −7.73206 −0.337455
\(526\) −33.0712 −1.44197
\(527\) −13.4990 −0.588024
\(528\) 25.6882 1.11794
\(529\) −10.4161 −0.452875
\(530\) 44.2942 1.92402
\(531\) 2.82993 0.122809
\(532\) −6.48945 −0.281353
\(533\) −29.6637 −1.28488
\(534\) 19.1138 0.827136
\(535\) 16.6505 0.719864
\(536\) −7.70360 −0.332745
\(537\) −16.4288 −0.708956
\(538\) −7.38901 −0.318563
\(539\) 5.16426 0.222440
\(540\) −4.14100 −0.178200
\(541\) −10.4628 −0.449830 −0.224915 0.974378i \(-0.572210\pi\)
−0.224915 + 0.974378i \(0.572210\pi\)
\(542\) −42.2561 −1.81506
\(543\) −8.02365 −0.344328
\(544\) 29.5819 1.26832
\(545\) 43.2560 1.85289
\(546\) 4.70011 0.201146
\(547\) 4.64212 0.198483 0.0992414 0.995063i \(-0.468358\pi\)
0.0992414 + 0.995063i \(0.468358\pi\)
\(548\) 19.4338 0.830170
\(549\) −3.17822 −0.135643
\(550\) −70.9877 −3.02693
\(551\) −54.8759 −2.33779
\(552\) 5.29411 0.225332
\(553\) −4.35170 −0.185053
\(554\) 30.4707 1.29458
\(555\) 19.4696 0.826437
\(556\) −14.6691 −0.622109
\(557\) −9.39100 −0.397909 −0.198955 0.980009i \(-0.563755\pi\)
−0.198955 + 0.980009i \(0.563755\pi\)
\(558\) 4.75256 0.201192
\(559\) −8.89877 −0.376378
\(560\) −17.7491 −0.750034
\(561\) −26.0772 −1.10098
\(562\) −12.7729 −0.538791
\(563\) 40.5858 1.71049 0.855244 0.518225i \(-0.173407\pi\)
0.855244 + 0.518225i \(0.173407\pi\)
\(564\) −11.3784 −0.479118
\(565\) 4.57255 0.192369
\(566\) 3.03876 0.127729
\(567\) 1.00000 0.0419961
\(568\) 22.9178 0.961608
\(569\) 30.7513 1.28916 0.644580 0.764537i \(-0.277032\pi\)
0.644580 + 0.764537i \(0.277032\pi\)
\(570\) −35.4716 −1.48574
\(571\) −7.72106 −0.323116 −0.161558 0.986863i \(-0.551652\pi\)
−0.161558 + 0.986863i \(0.551652\pi\)
\(572\) 15.8450 0.662513
\(573\) 25.7675 1.07645
\(574\) 19.9470 0.832570
\(575\) −27.4285 −1.14385
\(576\) −0.466399 −0.0194333
\(577\) −1.62087 −0.0674777 −0.0337389 0.999431i \(-0.510741\pi\)
−0.0337389 + 0.999431i \(0.510741\pi\)
\(578\) −15.1077 −0.628396
\(579\) −21.8665 −0.908739
\(580\) 40.6383 1.68741
\(581\) 10.3624 0.429903
\(582\) 3.79642 0.157367
\(583\) −36.0600 −1.49345
\(584\) −18.2954 −0.757069
\(585\) 9.43360 0.390031
\(586\) −3.61828 −0.149470
\(587\) −4.34958 −0.179526 −0.0897632 0.995963i \(-0.528611\pi\)
−0.0897632 + 0.995963i \(0.528611\pi\)
\(588\) −1.16053 −0.0478594
\(589\) 14.9486 0.615945
\(590\) −17.9517 −0.739060
\(591\) −11.0476 −0.454436
\(592\) 27.1414 1.11551
\(593\) −3.98308 −0.163565 −0.0817827 0.996650i \(-0.526061\pi\)
−0.0817827 + 0.996650i \(0.526061\pi\)
\(594\) 9.18096 0.376699
\(595\) 18.0178 0.738659
\(596\) 9.43371 0.386420
\(597\) 2.43275 0.0995657
\(598\) 16.6731 0.681812
\(599\) 5.98169 0.244405 0.122203 0.992505i \(-0.461004\pi\)
0.122203 + 0.992505i \(0.461004\pi\)
\(600\) −11.5393 −0.471091
\(601\) 23.9260 0.975963 0.487982 0.872854i \(-0.337733\pi\)
0.487982 + 0.872854i \(0.337733\pi\)
\(602\) 5.98386 0.243884
\(603\) −5.16188 −0.210208
\(604\) −4.91389 −0.199944
\(605\) 55.9122 2.27315
\(606\) 22.5167 0.914680
\(607\) −28.8160 −1.16961 −0.584803 0.811176i \(-0.698828\pi\)
−0.584803 + 0.811176i \(0.698828\pi\)
\(608\) −32.7586 −1.32854
\(609\) −9.81363 −0.397668
\(610\) 20.1611 0.816298
\(611\) 25.9212 1.04866
\(612\) 5.86016 0.236883
\(613\) −29.8068 −1.20388 −0.601942 0.798540i \(-0.705606\pi\)
−0.601942 + 0.798540i \(0.705606\pi\)
\(614\) 7.87544 0.317827
\(615\) 40.0356 1.61439
\(616\) 7.70714 0.310530
\(617\) −31.0774 −1.25113 −0.625564 0.780173i \(-0.715131\pi\)
−0.625564 + 0.780173i \(0.715131\pi\)
\(618\) 20.6416 0.830329
\(619\) 20.5262 0.825017 0.412508 0.910954i \(-0.364653\pi\)
0.412508 + 0.910954i \(0.364653\pi\)
\(620\) −11.0701 −0.444587
\(621\) 3.54738 0.142351
\(622\) 33.4873 1.34272
\(623\) 10.7515 0.430748
\(624\) 13.1509 0.526456
\(625\) −3.87556 −0.155023
\(626\) 21.6301 0.864512
\(627\) 28.8775 1.15326
\(628\) 15.4309 0.615762
\(629\) −27.5524 −1.09859
\(630\) −6.34350 −0.252731
\(631\) 16.5800 0.660040 0.330020 0.943974i \(-0.392944\pi\)
0.330020 + 0.943974i \(0.392944\pi\)
\(632\) −6.49448 −0.258337
\(633\) −14.1449 −0.562211
\(634\) −9.39995 −0.373320
\(635\) 13.0875 0.519360
\(636\) 8.10352 0.321326
\(637\) 2.64380 0.104751
\(638\) −90.0985 −3.56703
\(639\) 15.3563 0.607486
\(640\) −38.8488 −1.53563
\(641\) −36.5145 −1.44224 −0.721118 0.692812i \(-0.756372\pi\)
−0.721118 + 0.692812i \(0.756372\pi\)
\(642\) 8.29579 0.327409
\(643\) 25.1649 0.992408 0.496204 0.868206i \(-0.334727\pi\)
0.496204 + 0.868206i \(0.334727\pi\)
\(644\) −4.11683 −0.162226
\(645\) 12.0102 0.472902
\(646\) 50.1978 1.97501
\(647\) −20.5297 −0.807107 −0.403553 0.914956i \(-0.632225\pi\)
−0.403553 + 0.914956i \(0.632225\pi\)
\(648\) 1.49240 0.0586270
\(649\) 14.6145 0.573670
\(650\) −36.3415 −1.42543
\(651\) 2.67330 0.104775
\(652\) 1.19138 0.0466582
\(653\) 31.8731 1.24729 0.623646 0.781707i \(-0.285651\pi\)
0.623646 + 0.781707i \(0.285651\pi\)
\(654\) 21.5515 0.842730
\(655\) −61.3247 −2.39615
\(656\) 55.8114 2.17907
\(657\) −12.2590 −0.478270
\(658\) −17.4303 −0.679506
\(659\) 22.5572 0.878704 0.439352 0.898315i \(-0.355208\pi\)
0.439352 + 0.898315i \(0.355208\pi\)
\(660\) −21.3852 −0.832418
\(661\) −33.1690 −1.29012 −0.645062 0.764131i \(-0.723168\pi\)
−0.645062 + 0.764131i \(0.723168\pi\)
\(662\) −51.0104 −1.98257
\(663\) −13.3500 −0.518471
\(664\) 15.4648 0.600151
\(665\) −19.9527 −0.773732
\(666\) 9.70034 0.375880
\(667\) −34.8126 −1.34795
\(668\) −0.637184 −0.0246534
\(669\) 22.0031 0.850689
\(670\) 32.7444 1.26503
\(671\) −16.4132 −0.633623
\(672\) −5.85833 −0.225990
\(673\) 32.8484 1.26621 0.633107 0.774064i \(-0.281779\pi\)
0.633107 + 0.774064i \(0.281779\pi\)
\(674\) −54.0048 −2.08019
\(675\) −7.73206 −0.297607
\(676\) −6.97517 −0.268276
\(677\) −28.2666 −1.08637 −0.543186 0.839612i \(-0.682782\pi\)
−0.543186 + 0.839612i \(0.682782\pi\)
\(678\) 2.27819 0.0874933
\(679\) 2.13548 0.0819520
\(680\) 26.8898 1.03118
\(681\) 5.19944 0.199243
\(682\) 24.5434 0.939817
\(683\) 36.2892 1.38857 0.694283 0.719702i \(-0.255722\pi\)
0.694283 + 0.719702i \(0.255722\pi\)
\(684\) −6.48945 −0.248130
\(685\) 59.7517 2.28300
\(686\) −1.77779 −0.0678763
\(687\) −4.65236 −0.177499
\(688\) 16.7428 0.638313
\(689\) −18.4606 −0.703293
\(690\) −22.5028 −0.856667
\(691\) −25.4549 −0.968348 −0.484174 0.874972i \(-0.660880\pi\)
−0.484174 + 0.874972i \(0.660880\pi\)
\(692\) 6.38920 0.242881
\(693\) 5.16426 0.196174
\(694\) 35.1607 1.33468
\(695\) −45.1021 −1.71082
\(696\) −14.6459 −0.555150
\(697\) −56.6565 −2.14602
\(698\) −12.0381 −0.455649
\(699\) 1.65730 0.0626849
\(700\) 8.97328 0.339158
\(701\) 6.77285 0.255807 0.127904 0.991787i \(-0.459175\pi\)
0.127904 + 0.991787i \(0.459175\pi\)
\(702\) 4.70011 0.177394
\(703\) 30.5112 1.15075
\(704\) −2.40860 −0.0907776
\(705\) −34.9845 −1.31759
\(706\) −15.1334 −0.569555
\(707\) 12.6656 0.476339
\(708\) −3.28422 −0.123429
\(709\) 0.0602769 0.00226375 0.00113187 0.999999i \(-0.499640\pi\)
0.00113187 + 0.999999i \(0.499640\pi\)
\(710\) −97.4128 −3.65584
\(711\) −4.35170 −0.163202
\(712\) 16.0455 0.601330
\(713\) 9.48320 0.355148
\(714\) 8.97704 0.335957
\(715\) 48.7176 1.82193
\(716\) 19.0661 0.712535
\(717\) 19.8635 0.741815
\(718\) 57.3480 2.14021
\(719\) −24.0018 −0.895117 −0.447558 0.894255i \(-0.647706\pi\)
−0.447558 + 0.894255i \(0.647706\pi\)
\(720\) −17.7491 −0.661468
\(721\) 11.6109 0.432411
\(722\) −21.8104 −0.811697
\(723\) −1.30808 −0.0486479
\(724\) 9.31168 0.346066
\(725\) 75.8796 2.81810
\(726\) 27.8572 1.03388
\(727\) 49.9055 1.85089 0.925446 0.378879i \(-0.123690\pi\)
0.925446 + 0.378879i \(0.123690\pi\)
\(728\) 3.94560 0.146234
\(729\) 1.00000 0.0370370
\(730\) 77.7652 2.87822
\(731\) −16.9963 −0.628632
\(732\) 3.68842 0.136328
\(733\) 25.7436 0.950861 0.475430 0.879753i \(-0.342292\pi\)
0.475430 + 0.879753i \(0.342292\pi\)
\(734\) −1.67628 −0.0618725
\(735\) −3.56820 −0.131615
\(736\) −20.7817 −0.766023
\(737\) −26.6573 −0.981934
\(738\) 19.9470 0.734258
\(739\) 33.6369 1.23735 0.618676 0.785646i \(-0.287669\pi\)
0.618676 + 0.785646i \(0.287669\pi\)
\(740\) −22.5950 −0.830609
\(741\) 14.7836 0.543089
\(742\) 12.4136 0.455717
\(743\) −13.6689 −0.501464 −0.250732 0.968057i \(-0.580671\pi\)
−0.250732 + 0.968057i \(0.580671\pi\)
\(744\) 3.98963 0.146267
\(745\) 29.0052 1.06267
\(746\) 9.35919 0.342664
\(747\) 10.3624 0.379139
\(748\) 30.2634 1.10654
\(749\) 4.66636 0.170505
\(750\) 17.3308 0.632832
\(751\) −4.88749 −0.178347 −0.0891735 0.996016i \(-0.528423\pi\)
−0.0891735 + 0.996016i \(0.528423\pi\)
\(752\) −48.7699 −1.77846
\(753\) −2.76424 −0.100735
\(754\) −46.1252 −1.67978
\(755\) −15.1084 −0.549852
\(756\) −1.16053 −0.0422081
\(757\) 33.4597 1.21611 0.608057 0.793893i \(-0.291949\pi\)
0.608057 + 0.793893i \(0.291949\pi\)
\(758\) 43.7594 1.58941
\(759\) 18.3196 0.664958
\(760\) −29.7774 −1.08014
\(761\) −11.2136 −0.406492 −0.203246 0.979128i \(-0.565149\pi\)
−0.203246 + 0.979128i \(0.565149\pi\)
\(762\) 6.52058 0.236216
\(763\) 12.1226 0.438869
\(764\) −29.9039 −1.08189
\(765\) 18.0178 0.651436
\(766\) 1.77779 0.0642341
\(767\) 7.48177 0.270151
\(768\) −20.2884 −0.732096
\(769\) 34.2687 1.23576 0.617880 0.786272i \(-0.287992\pi\)
0.617880 + 0.786272i \(0.287992\pi\)
\(770\) −32.7595 −1.18057
\(771\) 11.5308 0.415271
\(772\) 25.3767 0.913327
\(773\) 26.5659 0.955510 0.477755 0.878493i \(-0.341451\pi\)
0.477755 + 0.878493i \(0.341451\pi\)
\(774\) 5.98386 0.215086
\(775\) −20.6701 −0.742492
\(776\) 3.18698 0.114406
\(777\) 5.45641 0.195748
\(778\) −40.8417 −1.46424
\(779\) 62.7406 2.24791
\(780\) −10.9480 −0.392000
\(781\) 79.3039 2.83772
\(782\) 31.8449 1.13877
\(783\) −9.81363 −0.350711
\(784\) −4.97423 −0.177651
\(785\) 47.4445 1.69337
\(786\) −30.5538 −1.08982
\(787\) −3.72281 −0.132704 −0.0663519 0.997796i \(-0.521136\pi\)
−0.0663519 + 0.997796i \(0.521136\pi\)
\(788\) 12.8210 0.456730
\(789\) −18.6024 −0.662265
\(790\) 27.6050 0.982143
\(791\) 1.28147 0.0455639
\(792\) 7.70714 0.273861
\(793\) −8.40258 −0.298384
\(794\) 26.8297 0.952152
\(795\) 24.9153 0.883656
\(796\) −2.82327 −0.100068
\(797\) 29.1112 1.03117 0.515587 0.856838i \(-0.327574\pi\)
0.515587 + 0.856838i \(0.327574\pi\)
\(798\) −9.94104 −0.351909
\(799\) 49.5084 1.75148
\(800\) 45.2969 1.60149
\(801\) 10.7515 0.379884
\(802\) −6.64665 −0.234702
\(803\) −63.3088 −2.23412
\(804\) 5.99052 0.211269
\(805\) −12.6577 −0.446127
\(806\) 12.5648 0.442576
\(807\) −4.15629 −0.146308
\(808\) 18.9021 0.664975
\(809\) 42.0568 1.47864 0.739319 0.673355i \(-0.235148\pi\)
0.739319 + 0.673355i \(0.235148\pi\)
\(810\) −6.34350 −0.222888
\(811\) −38.5695 −1.35436 −0.677180 0.735817i \(-0.736798\pi\)
−0.677180 + 0.735817i \(0.736798\pi\)
\(812\) 11.3890 0.399676
\(813\) −23.7689 −0.833613
\(814\) 50.0951 1.75583
\(815\) 3.66307 0.128312
\(816\) 25.1177 0.879294
\(817\) 18.8215 0.658480
\(818\) 1.94579 0.0680328
\(819\) 2.64380 0.0923818
\(820\) −46.4625 −1.62254
\(821\) −22.3203 −0.778983 −0.389491 0.921030i \(-0.627349\pi\)
−0.389491 + 0.921030i \(0.627349\pi\)
\(822\) 29.7702 1.03835
\(823\) 1.82260 0.0635319 0.0317660 0.999495i \(-0.489887\pi\)
0.0317660 + 0.999495i \(0.489887\pi\)
\(824\) 17.3280 0.603651
\(825\) −39.9303 −1.39020
\(826\) −5.03102 −0.175052
\(827\) 40.9423 1.42370 0.711852 0.702329i \(-0.247857\pi\)
0.711852 + 0.702329i \(0.247857\pi\)
\(828\) −4.11683 −0.143070
\(829\) −17.8541 −0.620098 −0.310049 0.950721i \(-0.600345\pi\)
−0.310049 + 0.950721i \(0.600345\pi\)
\(830\) −65.7337 −2.28165
\(831\) 17.1397 0.594569
\(832\) −1.23306 −0.0427488
\(833\) 5.04956 0.174957
\(834\) −22.4713 −0.778116
\(835\) −1.95911 −0.0677977
\(836\) −33.5132 −1.15908
\(837\) 2.67330 0.0924027
\(838\) 30.3894 1.04978
\(839\) 9.12909 0.315171 0.157586 0.987505i \(-0.449629\pi\)
0.157586 + 0.987505i \(0.449629\pi\)
\(840\) −5.32518 −0.183736
\(841\) 67.3074 2.32094
\(842\) 43.3112 1.49260
\(843\) −7.18469 −0.247454
\(844\) 16.4156 0.565049
\(845\) −21.4461 −0.737768
\(846\) −17.4303 −0.599268
\(847\) 15.6696 0.538413
\(848\) 34.7331 1.19274
\(849\) 1.70929 0.0586628
\(850\) −69.4110 −2.38078
\(851\) 19.3559 0.663513
\(852\) −17.8214 −0.610553
\(853\) −26.0818 −0.893022 −0.446511 0.894778i \(-0.647334\pi\)
−0.446511 + 0.894778i \(0.647334\pi\)
\(854\) 5.65021 0.193346
\(855\) −19.9527 −0.682367
\(856\) 6.96407 0.238027
\(857\) 45.0053 1.53735 0.768676 0.639639i \(-0.220916\pi\)
0.768676 + 0.639639i \(0.220916\pi\)
\(858\) 24.2726 0.828652
\(859\) 9.13913 0.311823 0.155912 0.987771i \(-0.450169\pi\)
0.155912 + 0.987771i \(0.450169\pi\)
\(860\) −13.9382 −0.475289
\(861\) 11.2201 0.382380
\(862\) −67.3681 −2.29457
\(863\) 48.3617 1.64625 0.823126 0.567859i \(-0.192228\pi\)
0.823126 + 0.567859i \(0.192228\pi\)
\(864\) −5.85833 −0.199304
\(865\) 19.6444 0.667931
\(866\) −58.3331 −1.98224
\(867\) −8.49801 −0.288608
\(868\) −3.10244 −0.105304
\(869\) −22.4733 −0.762355
\(870\) 62.2528 2.11057
\(871\) −13.6470 −0.462410
\(872\) 18.0918 0.612667
\(873\) 2.13548 0.0722749
\(874\) −35.2646 −1.19284
\(875\) 9.74853 0.329561
\(876\) 14.2270 0.480685
\(877\) 47.4991 1.60393 0.801965 0.597371i \(-0.203788\pi\)
0.801965 + 0.597371i \(0.203788\pi\)
\(878\) −18.7296 −0.632095
\(879\) −2.03527 −0.0686480
\(880\) −91.6607 −3.08988
\(881\) −51.9485 −1.75019 −0.875095 0.483950i \(-0.839202\pi\)
−0.875095 + 0.483950i \(0.839202\pi\)
\(882\) −1.77779 −0.0598612
\(883\) −8.06942 −0.271558 −0.135779 0.990739i \(-0.543354\pi\)
−0.135779 + 0.990739i \(0.543354\pi\)
\(884\) 15.4931 0.521088
\(885\) −10.0978 −0.339433
\(886\) −38.9337 −1.30800
\(887\) −39.1341 −1.31399 −0.656997 0.753893i \(-0.728173\pi\)
−0.656997 + 0.753893i \(0.728173\pi\)
\(888\) 8.14315 0.273266
\(889\) 3.66781 0.123014
\(890\) −68.2020 −2.28614
\(891\) 5.16426 0.173009
\(892\) −25.5352 −0.854983
\(893\) −54.8249 −1.83465
\(894\) 14.4513 0.483323
\(895\) 58.6213 1.95949
\(896\) −10.8875 −0.363726
\(897\) 9.37854 0.313140
\(898\) −35.4425 −1.18273
\(899\) −26.2348 −0.874979
\(900\) 8.97328 0.299109
\(901\) −35.2591 −1.17465
\(902\) 103.011 3.42990
\(903\) 3.36590 0.112010
\(904\) 1.91247 0.0636079
\(905\) 28.6300 0.951693
\(906\) −7.52748 −0.250084
\(907\) 46.8084 1.55425 0.777123 0.629348i \(-0.216678\pi\)
0.777123 + 0.629348i \(0.216678\pi\)
\(908\) −6.03410 −0.200249
\(909\) 12.6656 0.420091
\(910\) −16.7709 −0.555951
\(911\) −35.1859 −1.16576 −0.582881 0.812557i \(-0.698075\pi\)
−0.582881 + 0.812557i \(0.698075\pi\)
\(912\) −27.8149 −0.921044
\(913\) 53.5139 1.77105
\(914\) 17.0905 0.565304
\(915\) 11.3405 0.374907
\(916\) 5.39920 0.178395
\(917\) −17.1864 −0.567546
\(918\) 8.97704 0.296286
\(919\) 36.1632 1.19291 0.596457 0.802645i \(-0.296575\pi\)
0.596457 + 0.802645i \(0.296575\pi\)
\(920\) −18.8904 −0.622799
\(921\) 4.42991 0.145971
\(922\) 25.9313 0.854001
\(923\) 40.5990 1.33633
\(924\) −5.99327 −0.197164
\(925\) −42.1893 −1.38717
\(926\) 75.2742 2.47366
\(927\) 11.6109 0.381351
\(928\) 57.4914 1.88725
\(929\) 0.489260 0.0160521 0.00802606 0.999968i \(-0.497445\pi\)
0.00802606 + 0.999968i \(0.497445\pi\)
\(930\) −16.9581 −0.556077
\(931\) −5.59180 −0.183264
\(932\) −1.92335 −0.0630013
\(933\) 18.8365 0.616679
\(934\) 58.0080 1.89808
\(935\) 93.0487 3.04302
\(936\) 3.94560 0.128966
\(937\) 1.33237 0.0435267 0.0217633 0.999763i \(-0.493072\pi\)
0.0217633 + 0.999763i \(0.493072\pi\)
\(938\) 9.17673 0.299631
\(939\) 12.1668 0.397050
\(940\) 40.6005 1.32424
\(941\) 29.0206 0.946046 0.473023 0.881050i \(-0.343163\pi\)
0.473023 + 0.881050i \(0.343163\pi\)
\(942\) 23.6383 0.770177
\(943\) 39.8019 1.29613
\(944\) −14.0767 −0.458159
\(945\) −3.56820 −0.116074
\(946\) 30.9022 1.00472
\(947\) 12.0354 0.391098 0.195549 0.980694i \(-0.437351\pi\)
0.195549 + 0.980694i \(0.437351\pi\)
\(948\) 5.05028 0.164025
\(949\) −32.4104 −1.05209
\(950\) 76.8647 2.49382
\(951\) −5.28744 −0.171457
\(952\) 7.53596 0.244242
\(953\) 36.9603 1.19726 0.598631 0.801025i \(-0.295712\pi\)
0.598631 + 0.801025i \(0.295712\pi\)
\(954\) 12.4136 0.401905
\(955\) −91.9435 −2.97522
\(956\) −23.0522 −0.745560
\(957\) −50.6801 −1.63826
\(958\) −45.9924 −1.48595
\(959\) 16.7456 0.540744
\(960\) 1.66420 0.0537119
\(961\) −23.8535 −0.769467
\(962\) 25.6457 0.826851
\(963\) 4.66636 0.150371
\(964\) 1.51806 0.0488935
\(965\) 78.0239 2.51168
\(966\) −6.30648 −0.202908
\(967\) −34.0293 −1.09431 −0.547154 0.837032i \(-0.684289\pi\)
−0.547154 + 0.837032i \(0.684289\pi\)
\(968\) 23.3853 0.751631
\(969\) 28.2361 0.907075
\(970\) −13.5464 −0.434949
\(971\) −7.01562 −0.225142 −0.112571 0.993644i \(-0.535909\pi\)
−0.112571 + 0.993644i \(0.535909\pi\)
\(972\) −1.16053 −0.0372240
\(973\) −12.6400 −0.405220
\(974\) 35.2599 1.12980
\(975\) −20.4420 −0.654668
\(976\) 15.8092 0.506041
\(977\) 26.3046 0.841557 0.420779 0.907163i \(-0.361757\pi\)
0.420779 + 0.907163i \(0.361757\pi\)
\(978\) 1.82505 0.0583587
\(979\) 55.5234 1.77453
\(980\) 4.14100 0.132279
\(981\) 12.1226 0.387046
\(982\) 23.5603 0.751841
\(983\) 21.3138 0.679805 0.339902 0.940461i \(-0.389606\pi\)
0.339902 + 0.940461i \(0.389606\pi\)
\(984\) 16.7449 0.533807
\(985\) 39.4199 1.25602
\(986\) −88.0973 −2.80559
\(987\) −9.80452 −0.312081
\(988\) −17.1568 −0.545830
\(989\) 11.9401 0.379674
\(990\) −32.7595 −1.04117
\(991\) 4.29404 0.136405 0.0682023 0.997672i \(-0.478274\pi\)
0.0682023 + 0.997672i \(0.478274\pi\)
\(992\) −15.6611 −0.497239
\(993\) −28.6932 −0.910550
\(994\) −27.3002 −0.865911
\(995\) −8.68053 −0.275191
\(996\) −12.0258 −0.381053
\(997\) −9.54370 −0.302252 −0.151126 0.988515i \(-0.548290\pi\)
−0.151126 + 0.988515i \(0.548290\pi\)
\(998\) 66.1753 2.09474
\(999\) 5.45641 0.172633
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 \(a_p\))