Properties

Label 4005.2.a.p.1.8
Level 4005
Weight 2
Character 4005.1
Self dual Yes
Analytic conductor 31.980
Analytic rank 1
Dimension 8
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4005 = 3^{2} \cdot 5 \cdot 89 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4005.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9800860095\)
Analytic rank: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(-2.50065\)
Character \(\chi\) = 4005.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.50065 q^{2} +4.25326 q^{4} +1.00000 q^{5} -4.89614 q^{7} +5.63461 q^{8} +O(q^{10})\) \(q+2.50065 q^{2} +4.25326 q^{4} +1.00000 q^{5} -4.89614 q^{7} +5.63461 q^{8} +2.50065 q^{10} -5.13396 q^{11} +0.293733 q^{13} -12.2435 q^{14} +5.58369 q^{16} -4.78896 q^{17} +4.79227 q^{19} +4.25326 q^{20} -12.8382 q^{22} -5.18988 q^{23} +1.00000 q^{25} +0.734525 q^{26} -20.8246 q^{28} -8.87657 q^{29} -6.58148 q^{31} +2.69363 q^{32} -11.9755 q^{34} -4.89614 q^{35} +0.840228 q^{37} +11.9838 q^{38} +5.63461 q^{40} +2.51195 q^{41} +9.39183 q^{43} -21.8361 q^{44} -12.9781 q^{46} -8.06738 q^{47} +16.9722 q^{49} +2.50065 q^{50} +1.24932 q^{52} +11.4348 q^{53} -5.13396 q^{55} -27.5879 q^{56} -22.1972 q^{58} -1.04378 q^{59} +6.77868 q^{61} -16.4580 q^{62} -4.43155 q^{64} +0.293733 q^{65} -14.0551 q^{67} -20.3687 q^{68} -12.2435 q^{70} -2.08800 q^{71} +6.37951 q^{73} +2.10112 q^{74} +20.3827 q^{76} +25.1366 q^{77} +0.566895 q^{79} +5.58369 q^{80} +6.28152 q^{82} -6.12572 q^{83} -4.78896 q^{85} +23.4857 q^{86} -28.9279 q^{88} -1.00000 q^{89} -1.43816 q^{91} -22.0739 q^{92} -20.1737 q^{94} +4.79227 q^{95} -3.68712 q^{97} +42.4416 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - q^{2} + 7q^{4} + 8q^{5} - 6q^{7} - 3q^{8} + O(q^{10}) \) \( 8q - q^{2} + 7q^{4} + 8q^{5} - 6q^{7} - 3q^{8} - q^{10} - 14q^{11} - 7q^{13} - 15q^{14} + 9q^{16} - 17q^{17} + 17q^{19} + 7q^{20} + 2q^{22} + q^{23} + 8q^{25} - 3q^{26} - 29q^{28} - 10q^{29} + q^{31} - 2q^{32} - 16q^{34} - 6q^{35} - 11q^{37} + 30q^{38} - 3q^{40} - 15q^{41} - 5q^{43} - 7q^{44} - 12q^{46} - 12q^{47} + 4q^{49} - q^{50} - 14q^{52} + q^{53} - 14q^{55} - 3q^{56} - 37q^{58} - 26q^{59} + 13q^{61} - 22q^{62} - 15q^{64} - 7q^{65} - 25q^{67} - 23q^{68} - 15q^{70} - 28q^{71} - 17q^{73} + 5q^{74} + 8q^{76} - 7q^{79} + 9q^{80} + 5q^{82} - 44q^{83} - 17q^{85} + 13q^{86} - 66q^{88} - 8q^{89} + 27q^{91} - 15q^{92} - 27q^{94} + 17q^{95} + q^{97} + 34q^{98} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.50065 1.76823 0.884114 0.467272i \(-0.154763\pi\)
0.884114 + 0.467272i \(0.154763\pi\)
\(3\) 0 0
\(4\) 4.25326 2.12663
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −4.89614 −1.85057 −0.925284 0.379275i \(-0.876173\pi\)
−0.925284 + 0.379275i \(0.876173\pi\)
\(8\) 5.63461 1.99214
\(9\) 0 0
\(10\) 2.50065 0.790775
\(11\) −5.13396 −1.54795 −0.773974 0.633218i \(-0.781734\pi\)
−0.773974 + 0.633218i \(0.781734\pi\)
\(12\) 0 0
\(13\) 0.293733 0.0814670 0.0407335 0.999170i \(-0.487031\pi\)
0.0407335 + 0.999170i \(0.487031\pi\)
\(14\) −12.2435 −3.27223
\(15\) 0 0
\(16\) 5.58369 1.39592
\(17\) −4.78896 −1.16149 −0.580747 0.814084i \(-0.697240\pi\)
−0.580747 + 0.814084i \(0.697240\pi\)
\(18\) 0 0
\(19\) 4.79227 1.09942 0.549711 0.835355i \(-0.314738\pi\)
0.549711 + 0.835355i \(0.314738\pi\)
\(20\) 4.25326 0.951057
\(21\) 0 0
\(22\) −12.8382 −2.73712
\(23\) −5.18988 −1.08216 −0.541082 0.840970i \(-0.681985\pi\)
−0.541082 + 0.840970i \(0.681985\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0.734525 0.144052
\(27\) 0 0
\(28\) −20.8246 −3.93547
\(29\) −8.87657 −1.64834 −0.824169 0.566344i \(-0.808357\pi\)
−0.824169 + 0.566344i \(0.808357\pi\)
\(30\) 0 0
\(31\) −6.58148 −1.18207 −0.591034 0.806646i \(-0.701280\pi\)
−0.591034 + 0.806646i \(0.701280\pi\)
\(32\) 2.69363 0.476171
\(33\) 0 0
\(34\) −11.9755 −2.05379
\(35\) −4.89614 −0.827599
\(36\) 0 0
\(37\) 0.840228 0.138133 0.0690663 0.997612i \(-0.477998\pi\)
0.0690663 + 0.997612i \(0.477998\pi\)
\(38\) 11.9838 1.94403
\(39\) 0 0
\(40\) 5.63461 0.890910
\(41\) 2.51195 0.392301 0.196150 0.980574i \(-0.437156\pi\)
0.196150 + 0.980574i \(0.437156\pi\)
\(42\) 0 0
\(43\) 9.39183 1.43224 0.716120 0.697977i \(-0.245916\pi\)
0.716120 + 0.697977i \(0.245916\pi\)
\(44\) −21.8361 −3.29191
\(45\) 0 0
\(46\) −12.9781 −1.91351
\(47\) −8.06738 −1.17675 −0.588374 0.808589i \(-0.700232\pi\)
−0.588374 + 0.808589i \(0.700232\pi\)
\(48\) 0 0
\(49\) 16.9722 2.42460
\(50\) 2.50065 0.353646
\(51\) 0 0
\(52\) 1.24932 0.173250
\(53\) 11.4348 1.57070 0.785348 0.619055i \(-0.212484\pi\)
0.785348 + 0.619055i \(0.212484\pi\)
\(54\) 0 0
\(55\) −5.13396 −0.692263
\(56\) −27.5879 −3.68658
\(57\) 0 0
\(58\) −22.1972 −2.91464
\(59\) −1.04378 −0.135888 −0.0679441 0.997689i \(-0.521644\pi\)
−0.0679441 + 0.997689i \(0.521644\pi\)
\(60\) 0 0
\(61\) 6.77868 0.867921 0.433961 0.900932i \(-0.357116\pi\)
0.433961 + 0.900932i \(0.357116\pi\)
\(62\) −16.4580 −2.09017
\(63\) 0 0
\(64\) −4.43155 −0.553943
\(65\) 0.293733 0.0364331
\(66\) 0 0
\(67\) −14.0551 −1.71710 −0.858551 0.512727i \(-0.828635\pi\)
−0.858551 + 0.512727i \(0.828635\pi\)
\(68\) −20.3687 −2.47007
\(69\) 0 0
\(70\) −12.2435 −1.46338
\(71\) −2.08800 −0.247800 −0.123900 0.992295i \(-0.539540\pi\)
−0.123900 + 0.992295i \(0.539540\pi\)
\(72\) 0 0
\(73\) 6.37951 0.746665 0.373332 0.927698i \(-0.378215\pi\)
0.373332 + 0.927698i \(0.378215\pi\)
\(74\) 2.10112 0.244250
\(75\) 0 0
\(76\) 20.3827 2.33806
\(77\) 25.1366 2.86458
\(78\) 0 0
\(79\) 0.566895 0.0637807 0.0318903 0.999491i \(-0.489847\pi\)
0.0318903 + 0.999491i \(0.489847\pi\)
\(80\) 5.58369 0.624275
\(81\) 0 0
\(82\) 6.28152 0.693677
\(83\) −6.12572 −0.672385 −0.336192 0.941793i \(-0.609139\pi\)
−0.336192 + 0.941793i \(0.609139\pi\)
\(84\) 0 0
\(85\) −4.78896 −0.519436
\(86\) 23.4857 2.53253
\(87\) 0 0
\(88\) −28.9279 −3.08372
\(89\) −1.00000 −0.106000
\(90\) 0 0
\(91\) −1.43816 −0.150760
\(92\) −22.0739 −2.30136
\(93\) 0 0
\(94\) −20.1737 −2.08076
\(95\) 4.79227 0.491676
\(96\) 0 0
\(97\) −3.68712 −0.374370 −0.187185 0.982325i \(-0.559936\pi\)
−0.187185 + 0.982325i \(0.559936\pi\)
\(98\) 42.4416 4.28725
\(99\) 0 0
\(100\) 4.25326 0.425326
\(101\) 6.79147 0.675777 0.337888 0.941186i \(-0.390287\pi\)
0.337888 + 0.941186i \(0.390287\pi\)
\(102\) 0 0
\(103\) 10.1620 1.00129 0.500646 0.865652i \(-0.333096\pi\)
0.500646 + 0.865652i \(0.333096\pi\)
\(104\) 1.65507 0.162293
\(105\) 0 0
\(106\) 28.5945 2.77735
\(107\) −7.95873 −0.769399 −0.384700 0.923042i \(-0.625695\pi\)
−0.384700 + 0.923042i \(0.625695\pi\)
\(108\) 0 0
\(109\) −3.91220 −0.374721 −0.187360 0.982291i \(-0.559993\pi\)
−0.187360 + 0.982291i \(0.559993\pi\)
\(110\) −12.8382 −1.22408
\(111\) 0 0
\(112\) −27.3385 −2.58325
\(113\) 8.18970 0.770423 0.385211 0.922828i \(-0.374129\pi\)
0.385211 + 0.922828i \(0.374129\pi\)
\(114\) 0 0
\(115\) −5.18988 −0.483958
\(116\) −37.7543 −3.50540
\(117\) 0 0
\(118\) −2.61012 −0.240281
\(119\) 23.4475 2.14942
\(120\) 0 0
\(121\) 15.3576 1.39614
\(122\) 16.9511 1.53468
\(123\) 0 0
\(124\) −27.9927 −2.51382
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −2.03100 −0.180222 −0.0901110 0.995932i \(-0.528722\pi\)
−0.0901110 + 0.995932i \(0.528722\pi\)
\(128\) −16.4690 −1.45567
\(129\) 0 0
\(130\) 0.734525 0.0644221
\(131\) −9.71902 −0.849155 −0.424578 0.905392i \(-0.639577\pi\)
−0.424578 + 0.905392i \(0.639577\pi\)
\(132\) 0 0
\(133\) −23.4636 −2.03455
\(134\) −35.1469 −3.03623
\(135\) 0 0
\(136\) −26.9840 −2.31386
\(137\) −21.4520 −1.83277 −0.916386 0.400296i \(-0.868907\pi\)
−0.916386 + 0.400296i \(0.868907\pi\)
\(138\) 0 0
\(139\) −0.595475 −0.0505075 −0.0252538 0.999681i \(-0.508039\pi\)
−0.0252538 + 0.999681i \(0.508039\pi\)
\(140\) −20.8246 −1.76000
\(141\) 0 0
\(142\) −5.22136 −0.438166
\(143\) −1.50802 −0.126107
\(144\) 0 0
\(145\) −8.87657 −0.737159
\(146\) 15.9529 1.32027
\(147\) 0 0
\(148\) 3.57371 0.293757
\(149\) 16.4598 1.34844 0.674220 0.738531i \(-0.264480\pi\)
0.674220 + 0.738531i \(0.264480\pi\)
\(150\) 0 0
\(151\) 1.01236 0.0823849 0.0411924 0.999151i \(-0.486884\pi\)
0.0411924 + 0.999151i \(0.486884\pi\)
\(152\) 27.0026 2.19020
\(153\) 0 0
\(154\) 62.8579 5.06523
\(155\) −6.58148 −0.528637
\(156\) 0 0
\(157\) −3.66401 −0.292420 −0.146210 0.989254i \(-0.546707\pi\)
−0.146210 + 0.989254i \(0.546707\pi\)
\(158\) 1.41761 0.112779
\(159\) 0 0
\(160\) 2.69363 0.212950
\(161\) 25.4104 2.00262
\(162\) 0 0
\(163\) −0.396340 −0.0310437 −0.0155219 0.999880i \(-0.504941\pi\)
−0.0155219 + 0.999880i \(0.504941\pi\)
\(164\) 10.6840 0.834279
\(165\) 0 0
\(166\) −15.3183 −1.18893
\(167\) 8.91272 0.689687 0.344843 0.938660i \(-0.387932\pi\)
0.344843 + 0.938660i \(0.387932\pi\)
\(168\) 0 0
\(169\) −12.9137 −0.993363
\(170\) −11.9755 −0.918481
\(171\) 0 0
\(172\) 39.9459 3.04584
\(173\) −20.4096 −1.55171 −0.775855 0.630911i \(-0.782681\pi\)
−0.775855 + 0.630911i \(0.782681\pi\)
\(174\) 0 0
\(175\) −4.89614 −0.370114
\(176\) −28.6664 −2.16081
\(177\) 0 0
\(178\) −2.50065 −0.187432
\(179\) 3.85954 0.288476 0.144238 0.989543i \(-0.453927\pi\)
0.144238 + 0.989543i \(0.453927\pi\)
\(180\) 0 0
\(181\) −4.85674 −0.360998 −0.180499 0.983575i \(-0.557771\pi\)
−0.180499 + 0.983575i \(0.557771\pi\)
\(182\) −3.59634 −0.266578
\(183\) 0 0
\(184\) −29.2429 −2.15582
\(185\) 0.840228 0.0617748
\(186\) 0 0
\(187\) 24.5864 1.79793
\(188\) −34.3126 −2.50251
\(189\) 0 0
\(190\) 11.9838 0.869395
\(191\) −7.44680 −0.538831 −0.269416 0.963024i \(-0.586831\pi\)
−0.269416 + 0.963024i \(0.586831\pi\)
\(192\) 0 0
\(193\) −7.68593 −0.553245 −0.276623 0.960979i \(-0.589215\pi\)
−0.276623 + 0.960979i \(0.589215\pi\)
\(194\) −9.22021 −0.661972
\(195\) 0 0
\(196\) 72.1872 5.15623
\(197\) 26.9802 1.92226 0.961131 0.276092i \(-0.0890395\pi\)
0.961131 + 0.276092i \(0.0890395\pi\)
\(198\) 0 0
\(199\) 5.24242 0.371625 0.185813 0.982585i \(-0.440508\pi\)
0.185813 + 0.982585i \(0.440508\pi\)
\(200\) 5.63461 0.398427
\(201\) 0 0
\(202\) 16.9831 1.19493
\(203\) 43.4609 3.05036
\(204\) 0 0
\(205\) 2.51195 0.175442
\(206\) 25.4116 1.77051
\(207\) 0 0
\(208\) 1.64012 0.113722
\(209\) −24.6033 −1.70185
\(210\) 0 0
\(211\) −0.509470 −0.0350734 −0.0175367 0.999846i \(-0.505582\pi\)
−0.0175367 + 0.999846i \(0.505582\pi\)
\(212\) 48.6353 3.34029
\(213\) 0 0
\(214\) −19.9020 −1.36047
\(215\) 9.39183 0.640518
\(216\) 0 0
\(217\) 32.2239 2.18750
\(218\) −9.78305 −0.662592
\(219\) 0 0
\(220\) −21.8361 −1.47219
\(221\) −1.40668 −0.0946235
\(222\) 0 0
\(223\) 11.1310 0.745384 0.372692 0.927955i \(-0.378435\pi\)
0.372692 + 0.927955i \(0.378435\pi\)
\(224\) −13.1884 −0.881186
\(225\) 0 0
\(226\) 20.4796 1.36228
\(227\) 1.50278 0.0997427 0.0498713 0.998756i \(-0.484119\pi\)
0.0498713 + 0.998756i \(0.484119\pi\)
\(228\) 0 0
\(229\) −8.07817 −0.533820 −0.266910 0.963721i \(-0.586003\pi\)
−0.266910 + 0.963721i \(0.586003\pi\)
\(230\) −12.9781 −0.855749
\(231\) 0 0
\(232\) −50.0160 −3.28371
\(233\) −9.45410 −0.619359 −0.309679 0.950841i \(-0.600222\pi\)
−0.309679 + 0.950841i \(0.600222\pi\)
\(234\) 0 0
\(235\) −8.06738 −0.526258
\(236\) −4.43945 −0.288984
\(237\) 0 0
\(238\) 58.6339 3.80067
\(239\) 9.38903 0.607326 0.303663 0.952780i \(-0.401790\pi\)
0.303663 + 0.952780i \(0.401790\pi\)
\(240\) 0 0
\(241\) −1.14337 −0.0736510 −0.0368255 0.999322i \(-0.511725\pi\)
−0.0368255 + 0.999322i \(0.511725\pi\)
\(242\) 38.4039 2.46870
\(243\) 0 0
\(244\) 28.8315 1.84575
\(245\) 16.9722 1.08431
\(246\) 0 0
\(247\) 1.40765 0.0895665
\(248\) −37.0841 −2.35484
\(249\) 0 0
\(250\) 2.50065 0.158155
\(251\) 16.7613 1.05796 0.528981 0.848634i \(-0.322574\pi\)
0.528981 + 0.848634i \(0.322574\pi\)
\(252\) 0 0
\(253\) 26.6446 1.67513
\(254\) −5.07882 −0.318674
\(255\) 0 0
\(256\) −32.3202 −2.02001
\(257\) −17.2697 −1.07725 −0.538626 0.842545i \(-0.681056\pi\)
−0.538626 + 0.842545i \(0.681056\pi\)
\(258\) 0 0
\(259\) −4.11387 −0.255624
\(260\) 1.24932 0.0774798
\(261\) 0 0
\(262\) −24.3039 −1.50150
\(263\) −27.3161 −1.68438 −0.842192 0.539177i \(-0.818735\pi\)
−0.842192 + 0.539177i \(0.818735\pi\)
\(264\) 0 0
\(265\) 11.4348 0.702437
\(266\) −58.6743 −3.59755
\(267\) 0 0
\(268\) −59.7799 −3.65164
\(269\) 8.56066 0.521953 0.260976 0.965345i \(-0.415956\pi\)
0.260976 + 0.965345i \(0.415956\pi\)
\(270\) 0 0
\(271\) −6.04443 −0.367173 −0.183587 0.983004i \(-0.558771\pi\)
−0.183587 + 0.983004i \(0.558771\pi\)
\(272\) −26.7401 −1.62136
\(273\) 0 0
\(274\) −53.6441 −3.24076
\(275\) −5.13396 −0.309590
\(276\) 0 0
\(277\) 1.06300 0.0638694 0.0319347 0.999490i \(-0.489833\pi\)
0.0319347 + 0.999490i \(0.489833\pi\)
\(278\) −1.48908 −0.0893088
\(279\) 0 0
\(280\) −27.5879 −1.64869
\(281\) 0.545199 0.0325239 0.0162619 0.999868i \(-0.494823\pi\)
0.0162619 + 0.999868i \(0.494823\pi\)
\(282\) 0 0
\(283\) 14.1051 0.838461 0.419230 0.907880i \(-0.362300\pi\)
0.419230 + 0.907880i \(0.362300\pi\)
\(284\) −8.88079 −0.526978
\(285\) 0 0
\(286\) −3.77102 −0.222985
\(287\) −12.2989 −0.725980
\(288\) 0 0
\(289\) 5.93418 0.349069
\(290\) −22.1972 −1.30346
\(291\) 0 0
\(292\) 27.1337 1.58788
\(293\) 17.0930 0.998586 0.499293 0.866433i \(-0.333593\pi\)
0.499293 + 0.866433i \(0.333593\pi\)
\(294\) 0 0
\(295\) −1.04378 −0.0607711
\(296\) 4.73436 0.275179
\(297\) 0 0
\(298\) 41.1602 2.38435
\(299\) −1.52444 −0.0881606
\(300\) 0 0
\(301\) −45.9837 −2.65046
\(302\) 2.53157 0.145675
\(303\) 0 0
\(304\) 26.7585 1.53471
\(305\) 6.77868 0.388146
\(306\) 0 0
\(307\) −0.280920 −0.0160329 −0.00801646 0.999968i \(-0.502552\pi\)
−0.00801646 + 0.999968i \(0.502552\pi\)
\(308\) 106.912 6.09190
\(309\) 0 0
\(310\) −16.4580 −0.934751
\(311\) 12.9003 0.731507 0.365753 0.930712i \(-0.380811\pi\)
0.365753 + 0.930712i \(0.380811\pi\)
\(312\) 0 0
\(313\) −3.04911 −0.172346 −0.0861729 0.996280i \(-0.527464\pi\)
−0.0861729 + 0.996280i \(0.527464\pi\)
\(314\) −9.16241 −0.517065
\(315\) 0 0
\(316\) 2.41115 0.135638
\(317\) −1.96859 −0.110567 −0.0552835 0.998471i \(-0.517606\pi\)
−0.0552835 + 0.998471i \(0.517606\pi\)
\(318\) 0 0
\(319\) 45.5720 2.55154
\(320\) −4.43155 −0.247731
\(321\) 0 0
\(322\) 63.5425 3.54108
\(323\) −22.9500 −1.27697
\(324\) 0 0
\(325\) 0.293733 0.0162934
\(326\) −0.991107 −0.0548923
\(327\) 0 0
\(328\) 14.1539 0.781517
\(329\) 39.4990 2.17765
\(330\) 0 0
\(331\) 19.6542 1.08029 0.540147 0.841571i \(-0.318369\pi\)
0.540147 + 0.841571i \(0.318369\pi\)
\(332\) −26.0543 −1.42991
\(333\) 0 0
\(334\) 22.2876 1.21952
\(335\) −14.0551 −0.767912
\(336\) 0 0
\(337\) −19.5743 −1.06628 −0.533140 0.846027i \(-0.678988\pi\)
−0.533140 + 0.846027i \(0.678988\pi\)
\(338\) −32.2927 −1.75649
\(339\) 0 0
\(340\) −20.3687 −1.10465
\(341\) 33.7891 1.82978
\(342\) 0 0
\(343\) −48.8254 −2.63632
\(344\) 52.9193 2.85322
\(345\) 0 0
\(346\) −51.0372 −2.74378
\(347\) −13.2711 −0.712431 −0.356215 0.934404i \(-0.615933\pi\)
−0.356215 + 0.934404i \(0.615933\pi\)
\(348\) 0 0
\(349\) 25.7299 1.37729 0.688646 0.725097i \(-0.258205\pi\)
0.688646 + 0.725097i \(0.258205\pi\)
\(350\) −12.2435 −0.654445
\(351\) 0 0
\(352\) −13.8290 −0.737088
\(353\) −33.4472 −1.78022 −0.890108 0.455750i \(-0.849371\pi\)
−0.890108 + 0.455750i \(0.849371\pi\)
\(354\) 0 0
\(355\) −2.08800 −0.110819
\(356\) −4.25326 −0.225422
\(357\) 0 0
\(358\) 9.65137 0.510091
\(359\) −2.49760 −0.131818 −0.0659090 0.997826i \(-0.520995\pi\)
−0.0659090 + 0.997826i \(0.520995\pi\)
\(360\) 0 0
\(361\) 3.96581 0.208727
\(362\) −12.1450 −0.638327
\(363\) 0 0
\(364\) −6.11687 −0.320611
\(365\) 6.37951 0.333919
\(366\) 0 0
\(367\) −31.2573 −1.63162 −0.815810 0.578320i \(-0.803708\pi\)
−0.815810 + 0.578320i \(0.803708\pi\)
\(368\) −28.9786 −1.51062
\(369\) 0 0
\(370\) 2.10112 0.109232
\(371\) −55.9866 −2.90668
\(372\) 0 0
\(373\) −35.2179 −1.82351 −0.911757 0.410730i \(-0.865274\pi\)
−0.911757 + 0.410730i \(0.865274\pi\)
\(374\) 61.4819 3.17915
\(375\) 0 0
\(376\) −45.4566 −2.34424
\(377\) −2.60735 −0.134285
\(378\) 0 0
\(379\) −3.50658 −0.180121 −0.0900605 0.995936i \(-0.528706\pi\)
−0.0900605 + 0.995936i \(0.528706\pi\)
\(380\) 20.3827 1.04561
\(381\) 0 0
\(382\) −18.6218 −0.952776
\(383\) −21.9576 −1.12198 −0.560991 0.827822i \(-0.689580\pi\)
−0.560991 + 0.827822i \(0.689580\pi\)
\(384\) 0 0
\(385\) 25.1366 1.28108
\(386\) −19.2198 −0.978263
\(387\) 0 0
\(388\) −15.6823 −0.796147
\(389\) 13.3115 0.674918 0.337459 0.941340i \(-0.390433\pi\)
0.337459 + 0.941340i \(0.390433\pi\)
\(390\) 0 0
\(391\) 24.8541 1.25693
\(392\) 95.6318 4.83014
\(393\) 0 0
\(394\) 67.4682 3.39900
\(395\) 0.566895 0.0285236
\(396\) 0 0
\(397\) 17.8358 0.895155 0.447578 0.894245i \(-0.352287\pi\)
0.447578 + 0.894245i \(0.352287\pi\)
\(398\) 13.1095 0.657118
\(399\) 0 0
\(400\) 5.58369 0.279184
\(401\) 3.19387 0.159494 0.0797471 0.996815i \(-0.474589\pi\)
0.0797471 + 0.996815i \(0.474589\pi\)
\(402\) 0 0
\(403\) −1.93320 −0.0962996
\(404\) 28.8859 1.43713
\(405\) 0 0
\(406\) 108.681 5.39373
\(407\) −4.31370 −0.213822
\(408\) 0 0
\(409\) −24.5244 −1.21266 −0.606328 0.795215i \(-0.707358\pi\)
−0.606328 + 0.795215i \(0.707358\pi\)
\(410\) 6.28152 0.310222
\(411\) 0 0
\(412\) 43.2216 2.12938
\(413\) 5.11048 0.251470
\(414\) 0 0
\(415\) −6.12572 −0.300700
\(416\) 0.791209 0.0387922
\(417\) 0 0
\(418\) −61.5243 −3.00925
\(419\) −4.89589 −0.239180 −0.119590 0.992823i \(-0.538158\pi\)
−0.119590 + 0.992823i \(0.538158\pi\)
\(420\) 0 0
\(421\) 4.48965 0.218812 0.109406 0.993997i \(-0.465105\pi\)
0.109406 + 0.993997i \(0.465105\pi\)
\(422\) −1.27401 −0.0620177
\(423\) 0 0
\(424\) 64.4309 3.12904
\(425\) −4.78896 −0.232299
\(426\) 0 0
\(427\) −33.1894 −1.60615
\(428\) −33.8505 −1.63623
\(429\) 0 0
\(430\) 23.4857 1.13258
\(431\) −35.8073 −1.72477 −0.862387 0.506249i \(-0.831032\pi\)
−0.862387 + 0.506249i \(0.831032\pi\)
\(432\) 0 0
\(433\) −18.7569 −0.901399 −0.450700 0.892676i \(-0.648825\pi\)
−0.450700 + 0.892676i \(0.648825\pi\)
\(434\) 80.5807 3.86800
\(435\) 0 0
\(436\) −16.6396 −0.796892
\(437\) −24.8713 −1.18975
\(438\) 0 0
\(439\) 31.4002 1.49865 0.749325 0.662202i \(-0.230378\pi\)
0.749325 + 0.662202i \(0.230378\pi\)
\(440\) −28.9279 −1.37908
\(441\) 0 0
\(442\) −3.51761 −0.167316
\(443\) 25.6079 1.21667 0.608334 0.793681i \(-0.291838\pi\)
0.608334 + 0.793681i \(0.291838\pi\)
\(444\) 0 0
\(445\) −1.00000 −0.0474045
\(446\) 27.8347 1.31801
\(447\) 0 0
\(448\) 21.6975 1.02511
\(449\) 21.3542 1.00777 0.503883 0.863772i \(-0.331904\pi\)
0.503883 + 0.863772i \(0.331904\pi\)
\(450\) 0 0
\(451\) −12.8963 −0.607261
\(452\) 34.8329 1.63840
\(453\) 0 0
\(454\) 3.75792 0.176368
\(455\) −1.43816 −0.0674220
\(456\) 0 0
\(457\) −27.2671 −1.27550 −0.637750 0.770243i \(-0.720135\pi\)
−0.637750 + 0.770243i \(0.720135\pi\)
\(458\) −20.2007 −0.943916
\(459\) 0 0
\(460\) −22.0739 −1.02920
\(461\) 18.9331 0.881801 0.440900 0.897556i \(-0.354659\pi\)
0.440900 + 0.897556i \(0.354659\pi\)
\(462\) 0 0
\(463\) 30.1659 1.40193 0.700965 0.713196i \(-0.252753\pi\)
0.700965 + 0.713196i \(0.252753\pi\)
\(464\) −49.5640 −2.30095
\(465\) 0 0
\(466\) −23.6414 −1.09517
\(467\) −34.1721 −1.58130 −0.790649 0.612270i \(-0.790257\pi\)
−0.790649 + 0.612270i \(0.790257\pi\)
\(468\) 0 0
\(469\) 68.8157 3.17762
\(470\) −20.1737 −0.930544
\(471\) 0 0
\(472\) −5.88128 −0.270708
\(473\) −48.2173 −2.21703
\(474\) 0 0
\(475\) 4.79227 0.219884
\(476\) 99.7281 4.57103
\(477\) 0 0
\(478\) 23.4787 1.07389
\(479\) −19.0555 −0.870666 −0.435333 0.900269i \(-0.643369\pi\)
−0.435333 + 0.900269i \(0.643369\pi\)
\(480\) 0 0
\(481\) 0.246803 0.0112532
\(482\) −2.85917 −0.130232
\(483\) 0 0
\(484\) 65.3196 2.96907
\(485\) −3.68712 −0.167424
\(486\) 0 0
\(487\) 25.7093 1.16500 0.582501 0.812830i \(-0.302074\pi\)
0.582501 + 0.812830i \(0.302074\pi\)
\(488\) 38.1952 1.72902
\(489\) 0 0
\(490\) 42.4416 1.91732
\(491\) −21.1649 −0.955158 −0.477579 0.878589i \(-0.658486\pi\)
−0.477579 + 0.878589i \(0.658486\pi\)
\(492\) 0 0
\(493\) 42.5096 1.91454
\(494\) 3.52004 0.158374
\(495\) 0 0
\(496\) −36.7489 −1.65008
\(497\) 10.2231 0.458570
\(498\) 0 0
\(499\) 25.0315 1.12056 0.560281 0.828302i \(-0.310693\pi\)
0.560281 + 0.828302i \(0.310693\pi\)
\(500\) 4.25326 0.190211
\(501\) 0 0
\(502\) 41.9141 1.87072
\(503\) −5.82665 −0.259797 −0.129899 0.991527i \(-0.541465\pi\)
−0.129899 + 0.991527i \(0.541465\pi\)
\(504\) 0 0
\(505\) 6.79147 0.302217
\(506\) 66.6289 2.96202
\(507\) 0 0
\(508\) −8.63836 −0.383265
\(509\) 13.7961 0.611503 0.305752 0.952111i \(-0.401092\pi\)
0.305752 + 0.952111i \(0.401092\pi\)
\(510\) 0 0
\(511\) −31.2350 −1.38175
\(512\) −47.8834 −2.11617
\(513\) 0 0
\(514\) −43.1854 −1.90483
\(515\) 10.1620 0.447792
\(516\) 0 0
\(517\) 41.4176 1.82154
\(518\) −10.2874 −0.452001
\(519\) 0 0
\(520\) 1.65507 0.0725798
\(521\) −34.4027 −1.50721 −0.753604 0.657329i \(-0.771686\pi\)
−0.753604 + 0.657329i \(0.771686\pi\)
\(522\) 0 0
\(523\) −25.0955 −1.09735 −0.548674 0.836036i \(-0.684867\pi\)
−0.548674 + 0.836036i \(0.684867\pi\)
\(524\) −41.3375 −1.80584
\(525\) 0 0
\(526\) −68.3081 −2.97838
\(527\) 31.5185 1.37297
\(528\) 0 0
\(529\) 3.93481 0.171079
\(530\) 28.5945 1.24207
\(531\) 0 0
\(532\) −99.7968 −4.32674
\(533\) 0.737844 0.0319596
\(534\) 0 0
\(535\) −7.95873 −0.344086
\(536\) −79.1950 −3.42070
\(537\) 0 0
\(538\) 21.4072 0.922931
\(539\) −87.1347 −3.75316
\(540\) 0 0
\(541\) 16.2525 0.698750 0.349375 0.936983i \(-0.386394\pi\)
0.349375 + 0.936983i \(0.386394\pi\)
\(542\) −15.1150 −0.649246
\(543\) 0 0
\(544\) −12.8997 −0.553070
\(545\) −3.91220 −0.167580
\(546\) 0 0
\(547\) 17.3751 0.742905 0.371452 0.928452i \(-0.378860\pi\)
0.371452 + 0.928452i \(0.378860\pi\)
\(548\) −91.2411 −3.89762
\(549\) 0 0
\(550\) −12.8382 −0.547425
\(551\) −42.5389 −1.81222
\(552\) 0 0
\(553\) −2.77560 −0.118030
\(554\) 2.65819 0.112936
\(555\) 0 0
\(556\) −2.53271 −0.107411
\(557\) 43.3855 1.83830 0.919152 0.393904i \(-0.128876\pi\)
0.919152 + 0.393904i \(0.128876\pi\)
\(558\) 0 0
\(559\) 2.75869 0.116680
\(560\) −27.3385 −1.15526
\(561\) 0 0
\(562\) 1.36335 0.0575096
\(563\) −14.5950 −0.615108 −0.307554 0.951531i \(-0.599510\pi\)
−0.307554 + 0.951531i \(0.599510\pi\)
\(564\) 0 0
\(565\) 8.18970 0.344543
\(566\) 35.2719 1.48259
\(567\) 0 0
\(568\) −11.7651 −0.493651
\(569\) 25.4644 1.06752 0.533762 0.845635i \(-0.320778\pi\)
0.533762 + 0.845635i \(0.320778\pi\)
\(570\) 0 0
\(571\) 3.34046 0.139794 0.0698969 0.997554i \(-0.477733\pi\)
0.0698969 + 0.997554i \(0.477733\pi\)
\(572\) −6.41398 −0.268182
\(573\) 0 0
\(574\) −30.7552 −1.28370
\(575\) −5.18988 −0.216433
\(576\) 0 0
\(577\) −28.9214 −1.20401 −0.602007 0.798491i \(-0.705632\pi\)
−0.602007 + 0.798491i \(0.705632\pi\)
\(578\) 14.8393 0.617234
\(579\) 0 0
\(580\) −37.7543 −1.56766
\(581\) 29.9924 1.24429
\(582\) 0 0
\(583\) −58.7060 −2.43135
\(584\) 35.9460 1.48746
\(585\) 0 0
\(586\) 42.7437 1.76573
\(587\) −16.5407 −0.682706 −0.341353 0.939935i \(-0.610885\pi\)
−0.341353 + 0.939935i \(0.610885\pi\)
\(588\) 0 0
\(589\) −31.5402 −1.29959
\(590\) −2.61012 −0.107457
\(591\) 0 0
\(592\) 4.69157 0.192822
\(593\) 27.0667 1.11150 0.555748 0.831351i \(-0.312432\pi\)
0.555748 + 0.831351i \(0.312432\pi\)
\(594\) 0 0
\(595\) 23.4475 0.961252
\(596\) 70.0078 2.86763
\(597\) 0 0
\(598\) −3.81209 −0.155888
\(599\) −7.11352 −0.290651 −0.145325 0.989384i \(-0.546423\pi\)
−0.145325 + 0.989384i \(0.546423\pi\)
\(600\) 0 0
\(601\) −42.8950 −1.74972 −0.874861 0.484374i \(-0.839047\pi\)
−0.874861 + 0.484374i \(0.839047\pi\)
\(602\) −114.989 −4.68661
\(603\) 0 0
\(604\) 4.30584 0.175202
\(605\) 15.3576 0.624373
\(606\) 0 0
\(607\) −27.9087 −1.13278 −0.566390 0.824137i \(-0.691660\pi\)
−0.566390 + 0.824137i \(0.691660\pi\)
\(608\) 12.9086 0.523512
\(609\) 0 0
\(610\) 16.9511 0.686331
\(611\) −2.36966 −0.0958662
\(612\) 0 0
\(613\) 11.2291 0.453538 0.226769 0.973949i \(-0.427184\pi\)
0.226769 + 0.973949i \(0.427184\pi\)
\(614\) −0.702482 −0.0283499
\(615\) 0 0
\(616\) 141.635 5.70664
\(617\) 29.7394 1.19726 0.598631 0.801025i \(-0.295712\pi\)
0.598631 + 0.801025i \(0.295712\pi\)
\(618\) 0 0
\(619\) −47.0184 −1.88983 −0.944915 0.327315i \(-0.893856\pi\)
−0.944915 + 0.327315i \(0.893856\pi\)
\(620\) −27.9927 −1.12422
\(621\) 0 0
\(622\) 32.2591 1.29347
\(623\) 4.89614 0.196160
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −7.62476 −0.304747
\(627\) 0 0
\(628\) −15.5840 −0.621869
\(629\) −4.02382 −0.160440
\(630\) 0 0
\(631\) −4.61993 −0.183917 −0.0919583 0.995763i \(-0.529313\pi\)
−0.0919583 + 0.995763i \(0.529313\pi\)
\(632\) 3.19423 0.127060
\(633\) 0 0
\(634\) −4.92276 −0.195508
\(635\) −2.03100 −0.0805978
\(636\) 0 0
\(637\) 4.98531 0.197525
\(638\) 113.960 4.51170
\(639\) 0 0
\(640\) −16.4690 −0.650995
\(641\) 0.763355 0.0301507 0.0150754 0.999886i \(-0.495201\pi\)
0.0150754 + 0.999886i \(0.495201\pi\)
\(642\) 0 0
\(643\) −24.5483 −0.968091 −0.484046 0.875043i \(-0.660833\pi\)
−0.484046 + 0.875043i \(0.660833\pi\)
\(644\) 108.077 4.25882
\(645\) 0 0
\(646\) −57.3899 −2.25798
\(647\) 20.9739 0.824567 0.412284 0.911056i \(-0.364731\pi\)
0.412284 + 0.911056i \(0.364731\pi\)
\(648\) 0 0
\(649\) 5.35871 0.210348
\(650\) 0.734525 0.0288104
\(651\) 0 0
\(652\) −1.68573 −0.0660185
\(653\) 0.521815 0.0204202 0.0102101 0.999948i \(-0.496750\pi\)
0.0102101 + 0.999948i \(0.496750\pi\)
\(654\) 0 0
\(655\) −9.71902 −0.379754
\(656\) 14.0260 0.547621
\(657\) 0 0
\(658\) 98.7733 3.85059
\(659\) −1.63679 −0.0637603 −0.0318802 0.999492i \(-0.510149\pi\)
−0.0318802 + 0.999492i \(0.510149\pi\)
\(660\) 0 0
\(661\) 25.0711 0.975151 0.487576 0.873081i \(-0.337881\pi\)
0.487576 + 0.873081i \(0.337881\pi\)
\(662\) 49.1484 1.91021
\(663\) 0 0
\(664\) −34.5161 −1.33948
\(665\) −23.4636 −0.909880
\(666\) 0 0
\(667\) 46.0683 1.78377
\(668\) 37.9081 1.46671
\(669\) 0 0
\(670\) −35.1469 −1.35784
\(671\) −34.8015 −1.34350
\(672\) 0 0
\(673\) −33.2875 −1.28314 −0.641569 0.767065i \(-0.721716\pi\)
−0.641569 + 0.767065i \(0.721716\pi\)
\(674\) −48.9485 −1.88542
\(675\) 0 0
\(676\) −54.9254 −2.11251
\(677\) −17.5066 −0.672834 −0.336417 0.941713i \(-0.609215\pi\)
−0.336417 + 0.941713i \(0.609215\pi\)
\(678\) 0 0
\(679\) 18.0527 0.692798
\(680\) −26.9840 −1.03479
\(681\) 0 0
\(682\) 84.4947 3.23547
\(683\) 46.2972 1.77151 0.885757 0.464150i \(-0.153640\pi\)
0.885757 + 0.464150i \(0.153640\pi\)
\(684\) 0 0
\(685\) −21.4520 −0.819640
\(686\) −122.095 −4.66162
\(687\) 0 0
\(688\) 52.4410 1.99930
\(689\) 3.35879 0.127960
\(690\) 0 0
\(691\) 4.46210 0.169746 0.0848732 0.996392i \(-0.472951\pi\)
0.0848732 + 0.996392i \(0.472951\pi\)
\(692\) −86.8071 −3.29991
\(693\) 0 0
\(694\) −33.1864 −1.25974
\(695\) −0.595475 −0.0225877
\(696\) 0 0
\(697\) −12.0296 −0.455655
\(698\) 64.3416 2.43537
\(699\) 0 0
\(700\) −20.8246 −0.787094
\(701\) 5.13544 0.193963 0.0969815 0.995286i \(-0.469081\pi\)
0.0969815 + 0.995286i \(0.469081\pi\)
\(702\) 0 0
\(703\) 4.02659 0.151866
\(704\) 22.7514 0.857475
\(705\) 0 0
\(706\) −83.6398 −3.14783
\(707\) −33.2520 −1.25057
\(708\) 0 0
\(709\) 4.95502 0.186090 0.0930449 0.995662i \(-0.470340\pi\)
0.0930449 + 0.995662i \(0.470340\pi\)
\(710\) −5.22136 −0.195954
\(711\) 0 0
\(712\) −5.63461 −0.211166
\(713\) 34.1571 1.27919
\(714\) 0 0
\(715\) −1.50802 −0.0563966
\(716\) 16.4156 0.613481
\(717\) 0 0
\(718\) −6.24562 −0.233084
\(719\) 32.2241 1.20176 0.600878 0.799341i \(-0.294818\pi\)
0.600878 + 0.799341i \(0.294818\pi\)
\(720\) 0 0
\(721\) −49.7546 −1.85296
\(722\) 9.91712 0.369077
\(723\) 0 0
\(724\) −20.6570 −0.767710
\(725\) −8.87657 −0.329668
\(726\) 0 0
\(727\) −31.3167 −1.16147 −0.580735 0.814093i \(-0.697235\pi\)
−0.580735 + 0.814093i \(0.697235\pi\)
\(728\) −8.10348 −0.300335
\(729\) 0 0
\(730\) 15.9529 0.590444
\(731\) −44.9771 −1.66354
\(732\) 0 0
\(733\) −1.84406 −0.0681118 −0.0340559 0.999420i \(-0.510842\pi\)
−0.0340559 + 0.999420i \(0.510842\pi\)
\(734\) −78.1637 −2.88508
\(735\) 0 0
\(736\) −13.9796 −0.515295
\(737\) 72.1583 2.65799
\(738\) 0 0
\(739\) 23.1432 0.851338 0.425669 0.904879i \(-0.360039\pi\)
0.425669 + 0.904879i \(0.360039\pi\)
\(740\) 3.57371 0.131372
\(741\) 0 0
\(742\) −140.003 −5.13967
\(743\) 2.13174 0.0782059 0.0391029 0.999235i \(-0.487550\pi\)
0.0391029 + 0.999235i \(0.487550\pi\)
\(744\) 0 0
\(745\) 16.4598 0.603041
\(746\) −88.0677 −3.22439
\(747\) 0 0
\(748\) 104.572 3.82354
\(749\) 38.9671 1.42383
\(750\) 0 0
\(751\) 9.83764 0.358981 0.179490 0.983760i \(-0.442555\pi\)
0.179490 + 0.983760i \(0.442555\pi\)
\(752\) −45.0457 −1.64265
\(753\) 0 0
\(754\) −6.52006 −0.237447
\(755\) 1.01236 0.0368436
\(756\) 0 0
\(757\) −38.2109 −1.38880 −0.694400 0.719590i \(-0.744330\pi\)
−0.694400 + 0.719590i \(0.744330\pi\)
\(758\) −8.76874 −0.318495
\(759\) 0 0
\(760\) 27.0026 0.979486
\(761\) 5.67543 0.205734 0.102867 0.994695i \(-0.467198\pi\)
0.102867 + 0.994695i \(0.467198\pi\)
\(762\) 0 0
\(763\) 19.1547 0.693446
\(764\) −31.6731 −1.14589
\(765\) 0 0
\(766\) −54.9083 −1.98392
\(767\) −0.306592 −0.0110704
\(768\) 0 0
\(769\) 19.1784 0.691590 0.345795 0.938310i \(-0.387609\pi\)
0.345795 + 0.938310i \(0.387609\pi\)
\(770\) 62.8579 2.26524
\(771\) 0 0
\(772\) −32.6902 −1.17655
\(773\) −26.8742 −0.966598 −0.483299 0.875455i \(-0.660562\pi\)
−0.483299 + 0.875455i \(0.660562\pi\)
\(774\) 0 0
\(775\) −6.58148 −0.236414
\(776\) −20.7755 −0.745797
\(777\) 0 0
\(778\) 33.2873 1.19341
\(779\) 12.0379 0.431304
\(780\) 0 0
\(781\) 10.7197 0.383581
\(782\) 62.1515 2.22253
\(783\) 0 0
\(784\) 94.7675 3.38455
\(785\) −3.66401 −0.130774
\(786\) 0 0
\(787\) 11.4331 0.407546 0.203773 0.979018i \(-0.434680\pi\)
0.203773 + 0.979018i \(0.434680\pi\)
\(788\) 114.754 4.08794
\(789\) 0 0
\(790\) 1.41761 0.0504362
\(791\) −40.0980 −1.42572
\(792\) 0 0
\(793\) 1.99113 0.0707069
\(794\) 44.6012 1.58284
\(795\) 0 0
\(796\) 22.2974 0.790309
\(797\) 38.2874 1.35621 0.678105 0.734965i \(-0.262801\pi\)
0.678105 + 0.734965i \(0.262801\pi\)
\(798\) 0 0
\(799\) 38.6344 1.36679
\(800\) 2.69363 0.0952342
\(801\) 0 0
\(802\) 7.98676 0.282022
\(803\) −32.7521 −1.15580
\(804\) 0 0
\(805\) 25.4104 0.895598
\(806\) −4.83426 −0.170280
\(807\) 0 0
\(808\) 38.2673 1.34624
\(809\) 4.98203 0.175159 0.0875794 0.996158i \(-0.472087\pi\)
0.0875794 + 0.996158i \(0.472087\pi\)
\(810\) 0 0
\(811\) 2.56566 0.0900924 0.0450462 0.998985i \(-0.485656\pi\)
0.0450462 + 0.998985i \(0.485656\pi\)
\(812\) 184.851 6.48699
\(813\) 0 0
\(814\) −10.7871 −0.378086
\(815\) −0.396340 −0.0138832
\(816\) 0 0
\(817\) 45.0082 1.57464
\(818\) −61.3271 −2.14425
\(819\) 0 0
\(820\) 10.6840 0.373101
\(821\) −7.39548 −0.258104 −0.129052 0.991638i \(-0.541193\pi\)
−0.129052 + 0.991638i \(0.541193\pi\)
\(822\) 0 0
\(823\) 14.2404 0.496389 0.248195 0.968710i \(-0.420163\pi\)
0.248195 + 0.968710i \(0.420163\pi\)
\(824\) 57.2590 1.99471
\(825\) 0 0
\(826\) 12.7795 0.444657
\(827\) 22.1225 0.769273 0.384637 0.923068i \(-0.374327\pi\)
0.384637 + 0.923068i \(0.374327\pi\)
\(828\) 0 0
\(829\) 43.2604 1.50250 0.751248 0.660021i \(-0.229452\pi\)
0.751248 + 0.660021i \(0.229452\pi\)
\(830\) −15.3183 −0.531706
\(831\) 0 0
\(832\) −1.30169 −0.0451281
\(833\) −81.2793 −2.81616
\(834\) 0 0
\(835\) 8.91272 0.308437
\(836\) −104.644 −3.61920
\(837\) 0 0
\(838\) −12.2429 −0.422925
\(839\) 6.71522 0.231835 0.115917 0.993259i \(-0.463019\pi\)
0.115917 + 0.993259i \(0.463019\pi\)
\(840\) 0 0
\(841\) 49.7935 1.71702
\(842\) 11.2271 0.386910
\(843\) 0 0
\(844\) −2.16691 −0.0745880
\(845\) −12.9137 −0.444245
\(846\) 0 0
\(847\) −75.1928 −2.58365
\(848\) 63.8486 2.19257
\(849\) 0 0
\(850\) −11.9755 −0.410757
\(851\) −4.36068 −0.149482
\(852\) 0 0
\(853\) −3.93209 −0.134632 −0.0673160 0.997732i \(-0.521444\pi\)
−0.0673160 + 0.997732i \(0.521444\pi\)
\(854\) −82.9951 −2.84003
\(855\) 0 0
\(856\) −44.8443 −1.53275
\(857\) 4.62748 0.158072 0.0790358 0.996872i \(-0.474816\pi\)
0.0790358 + 0.996872i \(0.474816\pi\)
\(858\) 0 0
\(859\) −19.7777 −0.674805 −0.337403 0.941360i \(-0.609548\pi\)
−0.337403 + 0.941360i \(0.609548\pi\)
\(860\) 39.9459 1.36214
\(861\) 0 0
\(862\) −89.5415 −3.04979
\(863\) −8.03916 −0.273656 −0.136828 0.990595i \(-0.543691\pi\)
−0.136828 + 0.990595i \(0.543691\pi\)
\(864\) 0 0
\(865\) −20.4096 −0.693946
\(866\) −46.9045 −1.59388
\(867\) 0 0
\(868\) 137.056 4.65200
\(869\) −2.91042 −0.0987292
\(870\) 0 0
\(871\) −4.12845 −0.139887
\(872\) −22.0437 −0.746495
\(873\) 0 0
\(874\) −62.1944 −2.10376
\(875\) −4.89614 −0.165520
\(876\) 0 0
\(877\) 55.5811 1.87684 0.938420 0.345496i \(-0.112289\pi\)
0.938420 + 0.345496i \(0.112289\pi\)
\(878\) 78.5210 2.64996
\(879\) 0 0
\(880\) −28.6664 −0.966345
\(881\) −44.8890 −1.51235 −0.756174 0.654370i \(-0.772934\pi\)
−0.756174 + 0.654370i \(0.772934\pi\)
\(882\) 0 0
\(883\) −13.5457 −0.455848 −0.227924 0.973679i \(-0.573194\pi\)
−0.227924 + 0.973679i \(0.573194\pi\)
\(884\) −5.98297 −0.201229
\(885\) 0 0
\(886\) 64.0364 2.15135
\(887\) −36.1333 −1.21324 −0.606619 0.794992i \(-0.707475\pi\)
−0.606619 + 0.794992i \(0.707475\pi\)
\(888\) 0 0
\(889\) 9.94406 0.333513
\(890\) −2.50065 −0.0838220
\(891\) 0 0
\(892\) 47.3429 1.58516
\(893\) −38.6610 −1.29374
\(894\) 0 0
\(895\) 3.85954 0.129010
\(896\) 80.6346 2.69381
\(897\) 0 0
\(898\) 53.3994 1.78196
\(899\) 58.4210 1.94845
\(900\) 0 0
\(901\) −54.7610 −1.82435
\(902\) −32.2491 −1.07378
\(903\) 0 0
\(904\) 46.1458 1.53479
\(905\) −4.85674 −0.161443
\(906\) 0 0
\(907\) −41.6649 −1.38346 −0.691730 0.722156i \(-0.743151\pi\)
−0.691730 + 0.722156i \(0.743151\pi\)
\(908\) 6.39169 0.212116
\(909\) 0 0
\(910\) −3.59634 −0.119217
\(911\) 55.3548 1.83399 0.916993 0.398903i \(-0.130609\pi\)
0.916993 + 0.398903i \(0.130609\pi\)
\(912\) 0 0
\(913\) 31.4492 1.04082
\(914\) −68.1855 −2.25537
\(915\) 0 0
\(916\) −34.3585 −1.13524
\(917\) 47.5857 1.57142
\(918\) 0 0
\(919\) 9.44714 0.311633 0.155816 0.987786i \(-0.450199\pi\)
0.155816 + 0.987786i \(0.450199\pi\)
\(920\) −29.2429 −0.964111
\(921\) 0 0
\(922\) 47.3450 1.55922
\(923\) −0.613315 −0.0201875
\(924\) 0 0
\(925\) 0.840228 0.0276265
\(926\) 75.4345 2.47893
\(927\) 0 0
\(928\) −23.9102 −0.784890
\(929\) 23.0801 0.757234 0.378617 0.925553i \(-0.376400\pi\)
0.378617 + 0.925553i \(0.376400\pi\)
\(930\) 0 0
\(931\) 81.3353 2.66566
\(932\) −40.2107 −1.31715
\(933\) 0 0
\(934\) −85.4526 −2.79609
\(935\) 24.5864 0.804060
\(936\) 0 0
\(937\) 31.4855 1.02859 0.514293 0.857615i \(-0.328054\pi\)
0.514293 + 0.857615i \(0.328054\pi\)
\(938\) 172.084 5.61875
\(939\) 0 0
\(940\) −34.3126 −1.11916
\(941\) −16.7640 −0.546492 −0.273246 0.961944i \(-0.588097\pi\)
−0.273246 + 0.961944i \(0.588097\pi\)
\(942\) 0 0
\(943\) −13.0367 −0.424534
\(944\) −5.82812 −0.189689
\(945\) 0 0
\(946\) −120.575 −3.92022
\(947\) 59.7924 1.94299 0.971497 0.237053i \(-0.0761816\pi\)
0.971497 + 0.237053i \(0.0761816\pi\)
\(948\) 0 0
\(949\) 1.87387 0.0608285
\(950\) 11.9838 0.388805
\(951\) 0 0
\(952\) 132.117 4.28195
\(953\) −17.8565 −0.578428 −0.289214 0.957264i \(-0.593394\pi\)
−0.289214 + 0.957264i \(0.593394\pi\)
\(954\) 0 0
\(955\) −7.44680 −0.240973
\(956\) 39.9340 1.29156
\(957\) 0 0
\(958\) −47.6511 −1.53954
\(959\) 105.032 3.39167
\(960\) 0 0
\(961\) 12.3159 0.397287
\(962\) 0.617168 0.0198983
\(963\) 0 0
\(964\) −4.86305 −0.156628
\(965\) −7.68593 −0.247419
\(966\) 0 0
\(967\) −31.9918 −1.02879 −0.514393 0.857554i \(-0.671983\pi\)
−0.514393 + 0.857554i \(0.671983\pi\)
\(968\) 86.5339 2.78130
\(969\) 0 0
\(970\) −9.22021 −0.296043
\(971\) −13.8839 −0.445555 −0.222778 0.974869i \(-0.571512\pi\)
−0.222778 + 0.974869i \(0.571512\pi\)
\(972\) 0 0
\(973\) 2.91553 0.0934676
\(974\) 64.2901 2.05999
\(975\) 0 0
\(976\) 37.8500 1.21155
\(977\) −5.04704 −0.161469 −0.0807346 0.996736i \(-0.525727\pi\)
−0.0807346 + 0.996736i \(0.525727\pi\)
\(978\) 0 0
\(979\) 5.13396 0.164082
\(980\) 72.1872 2.30593
\(981\) 0 0
\(982\) −52.9260 −1.68894
\(983\) 26.6803 0.850971 0.425485 0.904965i \(-0.360103\pi\)
0.425485 + 0.904965i \(0.360103\pi\)
\(984\) 0 0
\(985\) 26.9802 0.859662
\(986\) 106.302 3.38533
\(987\) 0 0
\(988\) 5.98709 0.190475
\(989\) −48.7424 −1.54992
\(990\) 0 0
\(991\) −37.2339 −1.18277 −0.591386 0.806388i \(-0.701419\pi\)
−0.591386 + 0.806388i \(0.701419\pi\)
\(992\) −17.7281 −0.562867
\(993\) 0 0
\(994\) 25.5645 0.810857
\(995\) 5.24242 0.166196
\(996\) 0 0
\(997\) −15.6534 −0.495748 −0.247874 0.968792i \(-0.579732\pi\)
−0.247874 + 0.968792i \(0.579732\pi\)
\(998\) 62.5950 1.98141
\(999\) 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 \(a_p\))