Properties

Label 8048.2.a.v.1.7
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.67525 q^{3}\) \(-2.92493 q^{5}\) \(+1.65914 q^{7}\) \(-0.193522 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.67525 q^{3}\) \(-2.92493 q^{5}\) \(+1.65914 q^{7}\) \(-0.193522 q^{9}\) \(-5.49209 q^{11}\) \(-4.79504 q^{13}\) \(+4.90001 q^{15}\) \(+5.49743 q^{17}\) \(+0.255062 q^{19}\) \(-2.77948 q^{21}\) \(-3.87181 q^{23}\) \(+3.55524 q^{25}\) \(+5.34996 q^{27}\) \(+2.98739 q^{29}\) \(+5.08489 q^{31}\) \(+9.20064 q^{33}\) \(-4.85288 q^{35}\) \(-0.611446 q^{37}\) \(+8.03291 q^{39}\) \(+3.44582 q^{41}\) \(+3.26488 q^{43}\) \(+0.566040 q^{45}\) \(+2.23291 q^{47}\) \(-4.24725 q^{49}\) \(-9.20959 q^{51}\) \(-1.60340 q^{53}\) \(+16.0640 q^{55}\) \(-0.427293 q^{57}\) \(+8.61014 q^{59}\) \(-2.48498 q^{61}\) \(-0.321081 q^{63}\) \(+14.0252 q^{65}\) \(+8.51103 q^{67}\) \(+6.48626 q^{69}\) \(+15.2777 q^{71}\) \(-0.465430 q^{73}\) \(-5.95594 q^{75}\) \(-9.11215 q^{77}\) \(+0.500221 q^{79}\) \(-8.38198 q^{81}\) \(-8.22195 q^{83}\) \(-16.0796 q^{85}\) \(-5.00465 q^{87}\) \(-0.0767541 q^{89}\) \(-7.95565 q^{91}\) \(-8.51849 q^{93}\) \(-0.746039 q^{95}\) \(-13.7565 q^{97}\) \(+1.06284 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 31q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 22q^{25} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 26q^{33} \) \(\mathstrut +\mathstrut 13q^{35} \) \(\mathstrut -\mathstrut 67q^{37} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut -\mathstrut 57q^{45} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 20q^{49} \) \(\mathstrut +\mathstrut 11q^{51} \) \(\mathstrut -\mathstrut 58q^{53} \) \(\mathstrut -\mathstrut 15q^{55} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 55q^{61} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 44q^{69} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 5q^{73} \) \(\mathstrut +\mathstrut 25q^{75} \) \(\mathstrut -\mathstrut 50q^{77} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 78q^{85} \) \(\mathstrut +\mathstrut 11q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut +\mathstrut 15q^{91} \) \(\mathstrut -\mathstrut 83q^{93} \) \(\mathstrut +\mathstrut 27q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 70q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.67525 −0.967209 −0.483604 0.875287i \(-0.660673\pi\)
−0.483604 + 0.875287i \(0.660673\pi\)
\(4\) 0 0
\(5\) −2.92493 −1.30807 −0.654035 0.756464i \(-0.726925\pi\)
−0.654035 + 0.756464i \(0.726925\pi\)
\(6\) 0 0
\(7\) 1.65914 0.627097 0.313548 0.949572i \(-0.398482\pi\)
0.313548 + 0.949572i \(0.398482\pi\)
\(8\) 0 0
\(9\) −0.193522 −0.0645075
\(10\) 0 0
\(11\) −5.49209 −1.65593 −0.827963 0.560782i \(-0.810500\pi\)
−0.827963 + 0.560782i \(0.810500\pi\)
\(12\) 0 0
\(13\) −4.79504 −1.32990 −0.664952 0.746886i \(-0.731548\pi\)
−0.664952 + 0.746886i \(0.731548\pi\)
\(14\) 0 0
\(15\) 4.90001 1.26518
\(16\) 0 0
\(17\) 5.49743 1.33332 0.666661 0.745361i \(-0.267723\pi\)
0.666661 + 0.745361i \(0.267723\pi\)
\(18\) 0 0
\(19\) 0.255062 0.0585152 0.0292576 0.999572i \(-0.490686\pi\)
0.0292576 + 0.999572i \(0.490686\pi\)
\(20\) 0 0
\(21\) −2.77948 −0.606533
\(22\) 0 0
\(23\) −3.87181 −0.807328 −0.403664 0.914907i \(-0.632263\pi\)
−0.403664 + 0.914907i \(0.632263\pi\)
\(24\) 0 0
\(25\) 3.55524 0.711049
\(26\) 0 0
\(27\) 5.34996 1.02960
\(28\) 0 0
\(29\) 2.98739 0.554745 0.277373 0.960762i \(-0.410536\pi\)
0.277373 + 0.960762i \(0.410536\pi\)
\(30\) 0 0
\(31\) 5.08489 0.913273 0.456637 0.889653i \(-0.349054\pi\)
0.456637 + 0.889653i \(0.349054\pi\)
\(32\) 0 0
\(33\) 9.20064 1.60163
\(34\) 0 0
\(35\) −4.85288 −0.820287
\(36\) 0 0
\(37\) −0.611446 −0.100521 −0.0502605 0.998736i \(-0.516005\pi\)
−0.0502605 + 0.998736i \(0.516005\pi\)
\(38\) 0 0
\(39\) 8.03291 1.28629
\(40\) 0 0
\(41\) 3.44582 0.538147 0.269073 0.963120i \(-0.413283\pi\)
0.269073 + 0.963120i \(0.413283\pi\)
\(42\) 0 0
\(43\) 3.26488 0.497890 0.248945 0.968518i \(-0.419916\pi\)
0.248945 + 0.968518i \(0.419916\pi\)
\(44\) 0 0
\(45\) 0.566040 0.0843803
\(46\) 0 0
\(47\) 2.23291 0.325703 0.162852 0.986651i \(-0.447931\pi\)
0.162852 + 0.986651i \(0.447931\pi\)
\(48\) 0 0
\(49\) −4.24725 −0.606750
\(50\) 0 0
\(51\) −9.20959 −1.28960
\(52\) 0 0
\(53\) −1.60340 −0.220244 −0.110122 0.993918i \(-0.535124\pi\)
−0.110122 + 0.993918i \(0.535124\pi\)
\(54\) 0 0
\(55\) 16.0640 2.16607
\(56\) 0 0
\(57\) −0.427293 −0.0565964
\(58\) 0 0
\(59\) 8.61014 1.12094 0.560472 0.828173i \(-0.310620\pi\)
0.560472 + 0.828173i \(0.310620\pi\)
\(60\) 0 0
\(61\) −2.48498 −0.318169 −0.159084 0.987265i \(-0.550854\pi\)
−0.159084 + 0.987265i \(0.550854\pi\)
\(62\) 0 0
\(63\) −0.321081 −0.0404524
\(64\) 0 0
\(65\) 14.0252 1.73961
\(66\) 0 0
\(67\) 8.51103 1.03979 0.519894 0.854231i \(-0.325972\pi\)
0.519894 + 0.854231i \(0.325972\pi\)
\(68\) 0 0
\(69\) 6.48626 0.780854
\(70\) 0 0
\(71\) 15.2777 1.81313 0.906563 0.422070i \(-0.138696\pi\)
0.906563 + 0.422070i \(0.138696\pi\)
\(72\) 0 0
\(73\) −0.465430 −0.0544744 −0.0272372 0.999629i \(-0.508671\pi\)
−0.0272372 + 0.999629i \(0.508671\pi\)
\(74\) 0 0
\(75\) −5.95594 −0.687733
\(76\) 0 0
\(77\) −9.11215 −1.03843
\(78\) 0 0
\(79\) 0.500221 0.0562793 0.0281396 0.999604i \(-0.491042\pi\)
0.0281396 + 0.999604i \(0.491042\pi\)
\(80\) 0 0
\(81\) −8.38198 −0.931331
\(82\) 0 0
\(83\) −8.22195 −0.902477 −0.451238 0.892404i \(-0.649018\pi\)
−0.451238 + 0.892404i \(0.649018\pi\)
\(84\) 0 0
\(85\) −16.0796 −1.74408
\(86\) 0 0
\(87\) −5.00465 −0.536554
\(88\) 0 0
\(89\) −0.0767541 −0.00813591 −0.00406796 0.999992i \(-0.501295\pi\)
−0.00406796 + 0.999992i \(0.501295\pi\)
\(90\) 0 0
\(91\) −7.95565 −0.833978
\(92\) 0 0
\(93\) −8.51849 −0.883326
\(94\) 0 0
\(95\) −0.746039 −0.0765420
\(96\) 0 0
\(97\) −13.7565 −1.39676 −0.698378 0.715729i \(-0.746095\pi\)
−0.698378 + 0.715729i \(0.746095\pi\)
\(98\) 0 0
\(99\) 1.06284 0.106820
\(100\) 0 0
\(101\) −3.96776 −0.394807 −0.197404 0.980322i \(-0.563251\pi\)
−0.197404 + 0.980322i \(0.563251\pi\)
\(102\) 0 0
\(103\) −4.48119 −0.441545 −0.220772 0.975325i \(-0.570858\pi\)
−0.220772 + 0.975325i \(0.570858\pi\)
\(104\) 0 0
\(105\) 8.12981 0.793388
\(106\) 0 0
\(107\) 12.9807 1.25489 0.627445 0.778661i \(-0.284101\pi\)
0.627445 + 0.778661i \(0.284101\pi\)
\(108\) 0 0
\(109\) −10.9753 −1.05125 −0.525623 0.850718i \(-0.676168\pi\)
−0.525623 + 0.850718i \(0.676168\pi\)
\(110\) 0 0
\(111\) 1.02433 0.0972249
\(112\) 0 0
\(113\) 10.8044 1.01639 0.508195 0.861242i \(-0.330313\pi\)
0.508195 + 0.861242i \(0.330313\pi\)
\(114\) 0 0
\(115\) 11.3248 1.05604
\(116\) 0 0
\(117\) 0.927947 0.0857887
\(118\) 0 0
\(119\) 9.12101 0.836122
\(120\) 0 0
\(121\) 19.1630 1.74209
\(122\) 0 0
\(123\) −5.77263 −0.520500
\(124\) 0 0
\(125\) 4.22582 0.377969
\(126\) 0 0
\(127\) 10.4196 0.924591 0.462295 0.886726i \(-0.347026\pi\)
0.462295 + 0.886726i \(0.347026\pi\)
\(128\) 0 0
\(129\) −5.46951 −0.481564
\(130\) 0 0
\(131\) 7.12290 0.622330 0.311165 0.950356i \(-0.399281\pi\)
0.311165 + 0.950356i \(0.399281\pi\)
\(132\) 0 0
\(133\) 0.423184 0.0366947
\(134\) 0 0
\(135\) −15.6483 −1.34679
\(136\) 0 0
\(137\) −0.131855 −0.0112651 −0.00563257 0.999984i \(-0.501793\pi\)
−0.00563257 + 0.999984i \(0.501793\pi\)
\(138\) 0 0
\(139\) −13.6936 −1.16148 −0.580739 0.814090i \(-0.697236\pi\)
−0.580739 + 0.814090i \(0.697236\pi\)
\(140\) 0 0
\(141\) −3.74069 −0.315023
\(142\) 0 0
\(143\) 26.3348 2.20222
\(144\) 0 0
\(145\) −8.73793 −0.725646
\(146\) 0 0
\(147\) 7.11522 0.586854
\(148\) 0 0
\(149\) −14.9476 −1.22456 −0.612278 0.790642i \(-0.709747\pi\)
−0.612278 + 0.790642i \(0.709747\pi\)
\(150\) 0 0
\(151\) −12.2637 −0.998006 −0.499003 0.866600i \(-0.666300\pi\)
−0.499003 + 0.866600i \(0.666300\pi\)
\(152\) 0 0
\(153\) −1.06388 −0.0860092
\(154\) 0 0
\(155\) −14.8730 −1.19463
\(156\) 0 0
\(157\) −15.1623 −1.21009 −0.605043 0.796193i \(-0.706844\pi\)
−0.605043 + 0.796193i \(0.706844\pi\)
\(158\) 0 0
\(159\) 2.68611 0.213022
\(160\) 0 0
\(161\) −6.42388 −0.506272
\(162\) 0 0
\(163\) 20.8649 1.63426 0.817131 0.576453i \(-0.195563\pi\)
0.817131 + 0.576453i \(0.195563\pi\)
\(164\) 0 0
\(165\) −26.9113 −2.09504
\(166\) 0 0
\(167\) −5.55081 −0.429535 −0.214767 0.976665i \(-0.568899\pi\)
−0.214767 + 0.976665i \(0.568899\pi\)
\(168\) 0 0
\(169\) 9.99239 0.768645
\(170\) 0 0
\(171\) −0.0493601 −0.00377466
\(172\) 0 0
\(173\) 15.6414 1.18919 0.594596 0.804024i \(-0.297312\pi\)
0.594596 + 0.804024i \(0.297312\pi\)
\(174\) 0 0
\(175\) 5.89865 0.445896
\(176\) 0 0
\(177\) −14.4242 −1.08419
\(178\) 0 0
\(179\) 14.1615 1.05848 0.529239 0.848473i \(-0.322478\pi\)
0.529239 + 0.848473i \(0.322478\pi\)
\(180\) 0 0
\(181\) −4.64577 −0.345318 −0.172659 0.984982i \(-0.555236\pi\)
−0.172659 + 0.984982i \(0.555236\pi\)
\(182\) 0 0
\(183\) 4.16297 0.307736
\(184\) 0 0
\(185\) 1.78844 0.131489
\(186\) 0 0
\(187\) −30.1924 −2.20788
\(188\) 0 0
\(189\) 8.87635 0.645659
\(190\) 0 0
\(191\) −0.862120 −0.0623808 −0.0311904 0.999513i \(-0.509930\pi\)
−0.0311904 + 0.999513i \(0.509930\pi\)
\(192\) 0 0
\(193\) −14.7217 −1.05969 −0.529845 0.848094i \(-0.677750\pi\)
−0.529845 + 0.848094i \(0.677750\pi\)
\(194\) 0 0
\(195\) −23.4957 −1.68256
\(196\) 0 0
\(197\) −4.83919 −0.344778 −0.172389 0.985029i \(-0.555149\pi\)
−0.172389 + 0.985029i \(0.555149\pi\)
\(198\) 0 0
\(199\) −1.37690 −0.0976057 −0.0488028 0.998808i \(-0.515541\pi\)
−0.0488028 + 0.998808i \(0.515541\pi\)
\(200\) 0 0
\(201\) −14.2581 −1.00569
\(202\) 0 0
\(203\) 4.95651 0.347879
\(204\) 0 0
\(205\) −10.0788 −0.703934
\(206\) 0 0
\(207\) 0.749281 0.0520786
\(208\) 0 0
\(209\) −1.40082 −0.0968968
\(210\) 0 0
\(211\) −6.30875 −0.434313 −0.217156 0.976137i \(-0.569678\pi\)
−0.217156 + 0.976137i \(0.569678\pi\)
\(212\) 0 0
\(213\) −25.5940 −1.75367
\(214\) 0 0
\(215\) −9.54958 −0.651276
\(216\) 0 0
\(217\) 8.43656 0.572711
\(218\) 0 0
\(219\) 0.779713 0.0526881
\(220\) 0 0
\(221\) −26.3604 −1.77319
\(222\) 0 0
\(223\) 3.09863 0.207500 0.103750 0.994603i \(-0.466916\pi\)
0.103750 + 0.994603i \(0.466916\pi\)
\(224\) 0 0
\(225\) −0.688019 −0.0458679
\(226\) 0 0
\(227\) −11.8291 −0.785126 −0.392563 0.919725i \(-0.628411\pi\)
−0.392563 + 0.919725i \(0.628411\pi\)
\(228\) 0 0
\(229\) 2.41943 0.159880 0.0799402 0.996800i \(-0.474527\pi\)
0.0799402 + 0.996800i \(0.474527\pi\)
\(230\) 0 0
\(231\) 15.2652 1.00437
\(232\) 0 0
\(233\) 11.4383 0.749346 0.374673 0.927157i \(-0.377755\pi\)
0.374673 + 0.927157i \(0.377755\pi\)
\(234\) 0 0
\(235\) −6.53111 −0.426043
\(236\) 0 0
\(237\) −0.837998 −0.0544338
\(238\) 0 0
\(239\) 13.0091 0.841489 0.420745 0.907179i \(-0.361769\pi\)
0.420745 + 0.907179i \(0.361769\pi\)
\(240\) 0 0
\(241\) −8.03111 −0.517329 −0.258665 0.965967i \(-0.583282\pi\)
−0.258665 + 0.965967i \(0.583282\pi\)
\(242\) 0 0
\(243\) −2.00794 −0.128809
\(244\) 0 0
\(245\) 12.4229 0.793672
\(246\) 0 0
\(247\) −1.22303 −0.0778196
\(248\) 0 0
\(249\) 13.7739 0.872883
\(250\) 0 0
\(251\) 1.45532 0.0918591 0.0459296 0.998945i \(-0.485375\pi\)
0.0459296 + 0.998945i \(0.485375\pi\)
\(252\) 0 0
\(253\) 21.2643 1.33687
\(254\) 0 0
\(255\) 26.9375 1.68689
\(256\) 0 0
\(257\) 5.18126 0.323198 0.161599 0.986857i \(-0.448335\pi\)
0.161599 + 0.986857i \(0.448335\pi\)
\(258\) 0 0
\(259\) −1.01448 −0.0630364
\(260\) 0 0
\(261\) −0.578128 −0.0357852
\(262\) 0 0
\(263\) 22.3406 1.37758 0.688789 0.724962i \(-0.258143\pi\)
0.688789 + 0.724962i \(0.258143\pi\)
\(264\) 0 0
\(265\) 4.68985 0.288095
\(266\) 0 0
\(267\) 0.128583 0.00786913
\(268\) 0 0
\(269\) 3.64979 0.222532 0.111266 0.993791i \(-0.464510\pi\)
0.111266 + 0.993791i \(0.464510\pi\)
\(270\) 0 0
\(271\) 8.57494 0.520891 0.260445 0.965489i \(-0.416131\pi\)
0.260445 + 0.965489i \(0.416131\pi\)
\(272\) 0 0
\(273\) 13.3277 0.806631
\(274\) 0 0
\(275\) −19.5257 −1.17744
\(276\) 0 0
\(277\) −3.48305 −0.209276 −0.104638 0.994510i \(-0.533368\pi\)
−0.104638 + 0.994510i \(0.533368\pi\)
\(278\) 0 0
\(279\) −0.984040 −0.0589129
\(280\) 0 0
\(281\) −4.26109 −0.254196 −0.127098 0.991890i \(-0.540566\pi\)
−0.127098 + 0.991890i \(0.540566\pi\)
\(282\) 0 0
\(283\) −5.98973 −0.356052 −0.178026 0.984026i \(-0.556971\pi\)
−0.178026 + 0.984026i \(0.556971\pi\)
\(284\) 0 0
\(285\) 1.24981 0.0740321
\(286\) 0 0
\(287\) 5.71710 0.337470
\(288\) 0 0
\(289\) 13.2217 0.777748
\(290\) 0 0
\(291\) 23.0456 1.35095
\(292\) 0 0
\(293\) 28.1934 1.64708 0.823539 0.567259i \(-0.191996\pi\)
0.823539 + 0.567259i \(0.191996\pi\)
\(294\) 0 0
\(295\) −25.1841 −1.46627
\(296\) 0 0
\(297\) −29.3825 −1.70494
\(298\) 0 0
\(299\) 18.5655 1.07367
\(300\) 0 0
\(301\) 5.41691 0.312225
\(302\) 0 0
\(303\) 6.64701 0.381861
\(304\) 0 0
\(305\) 7.26840 0.416187
\(306\) 0 0
\(307\) −13.9513 −0.796243 −0.398121 0.917333i \(-0.630338\pi\)
−0.398121 + 0.917333i \(0.630338\pi\)
\(308\) 0 0
\(309\) 7.50713 0.427066
\(310\) 0 0
\(311\) −22.7146 −1.28803 −0.644014 0.765014i \(-0.722732\pi\)
−0.644014 + 0.765014i \(0.722732\pi\)
\(312\) 0 0
\(313\) −28.6935 −1.62185 −0.810927 0.585147i \(-0.801037\pi\)
−0.810927 + 0.585147i \(0.801037\pi\)
\(314\) 0 0
\(315\) 0.939141 0.0529146
\(316\) 0 0
\(317\) −17.8556 −1.00287 −0.501434 0.865196i \(-0.667194\pi\)
−0.501434 + 0.865196i \(0.667194\pi\)
\(318\) 0 0
\(319\) −16.4070 −0.918617
\(320\) 0 0
\(321\) −21.7459 −1.21374
\(322\) 0 0
\(323\) 1.40218 0.0780196
\(324\) 0 0
\(325\) −17.0475 −0.945627
\(326\) 0 0
\(327\) 18.3865 1.01677
\(328\) 0 0
\(329\) 3.70471 0.204247
\(330\) 0 0
\(331\) −14.0693 −0.773320 −0.386660 0.922222i \(-0.626371\pi\)
−0.386660 + 0.922222i \(0.626371\pi\)
\(332\) 0 0
\(333\) 0.118328 0.00648436
\(334\) 0 0
\(335\) −24.8942 −1.36012
\(336\) 0 0
\(337\) 20.5736 1.12072 0.560359 0.828250i \(-0.310663\pi\)
0.560359 + 0.828250i \(0.310663\pi\)
\(338\) 0 0
\(339\) −18.1001 −0.983061
\(340\) 0 0
\(341\) −27.9267 −1.51231
\(342\) 0 0
\(343\) −18.6608 −1.00759
\(344\) 0 0
\(345\) −18.9719 −1.02141
\(346\) 0 0
\(347\) −34.1486 −1.83319 −0.916596 0.399815i \(-0.869074\pi\)
−0.916596 + 0.399815i \(0.869074\pi\)
\(348\) 0 0
\(349\) 30.4760 1.63134 0.815672 0.578515i \(-0.196367\pi\)
0.815672 + 0.578515i \(0.196367\pi\)
\(350\) 0 0
\(351\) −25.6533 −1.36927
\(352\) 0 0
\(353\) 4.48599 0.238765 0.119383 0.992848i \(-0.461908\pi\)
0.119383 + 0.992848i \(0.461908\pi\)
\(354\) 0 0
\(355\) −44.6862 −2.37170
\(356\) 0 0
\(357\) −15.2800 −0.808704
\(358\) 0 0
\(359\) 16.7300 0.882976 0.441488 0.897267i \(-0.354451\pi\)
0.441488 + 0.897267i \(0.354451\pi\)
\(360\) 0 0
\(361\) −18.9349 −0.996576
\(362\) 0 0
\(363\) −32.1029 −1.68497
\(364\) 0 0
\(365\) 1.36135 0.0712564
\(366\) 0 0
\(367\) 19.8684 1.03712 0.518562 0.855040i \(-0.326467\pi\)
0.518562 + 0.855040i \(0.326467\pi\)
\(368\) 0 0
\(369\) −0.666843 −0.0347145
\(370\) 0 0
\(371\) −2.66027 −0.138114
\(372\) 0 0
\(373\) −7.63562 −0.395357 −0.197679 0.980267i \(-0.563340\pi\)
−0.197679 + 0.980267i \(0.563340\pi\)
\(374\) 0 0
\(375\) −7.07932 −0.365574
\(376\) 0 0
\(377\) −14.3247 −0.737758
\(378\) 0 0
\(379\) 27.4902 1.41208 0.706039 0.708173i \(-0.250480\pi\)
0.706039 + 0.708173i \(0.250480\pi\)
\(380\) 0 0
\(381\) −17.4555 −0.894272
\(382\) 0 0
\(383\) −5.09662 −0.260425 −0.130213 0.991486i \(-0.541566\pi\)
−0.130213 + 0.991486i \(0.541566\pi\)
\(384\) 0 0
\(385\) 26.6524 1.35833
\(386\) 0 0
\(387\) −0.631828 −0.0321176
\(388\) 0 0
\(389\) −20.8271 −1.05597 −0.527987 0.849252i \(-0.677053\pi\)
−0.527987 + 0.849252i \(0.677053\pi\)
\(390\) 0 0
\(391\) −21.2850 −1.07643
\(392\) 0 0
\(393\) −11.9327 −0.601923
\(394\) 0 0
\(395\) −1.46311 −0.0736173
\(396\) 0 0
\(397\) 34.1090 1.71188 0.855942 0.517073i \(-0.172978\pi\)
0.855942 + 0.517073i \(0.172978\pi\)
\(398\) 0 0
\(399\) −0.708940 −0.0354914
\(400\) 0 0
\(401\) 23.5003 1.17355 0.586774 0.809751i \(-0.300398\pi\)
0.586774 + 0.809751i \(0.300398\pi\)
\(402\) 0 0
\(403\) −24.3822 −1.21457
\(404\) 0 0
\(405\) 24.5168 1.21825
\(406\) 0 0
\(407\) 3.35811 0.166456
\(408\) 0 0
\(409\) 33.5861 1.66073 0.830363 0.557222i \(-0.188133\pi\)
0.830363 + 0.557222i \(0.188133\pi\)
\(410\) 0 0
\(411\) 0.220891 0.0108957
\(412\) 0 0
\(413\) 14.2854 0.702940
\(414\) 0 0
\(415\) 24.0487 1.18050
\(416\) 0 0
\(417\) 22.9403 1.12339
\(418\) 0 0
\(419\) 16.7632 0.818938 0.409469 0.912324i \(-0.365714\pi\)
0.409469 + 0.912324i \(0.365714\pi\)
\(420\) 0 0
\(421\) −17.2099 −0.838760 −0.419380 0.907811i \(-0.637753\pi\)
−0.419380 + 0.907811i \(0.637753\pi\)
\(422\) 0 0
\(423\) −0.432118 −0.0210103
\(424\) 0 0
\(425\) 19.5447 0.948057
\(426\) 0 0
\(427\) −4.12293 −0.199523
\(428\) 0 0
\(429\) −44.1174 −2.13001
\(430\) 0 0
\(431\) −12.1118 −0.583404 −0.291702 0.956509i \(-0.594222\pi\)
−0.291702 + 0.956509i \(0.594222\pi\)
\(432\) 0 0
\(433\) 23.2582 1.11772 0.558860 0.829262i \(-0.311239\pi\)
0.558860 + 0.829262i \(0.311239\pi\)
\(434\) 0 0
\(435\) 14.6383 0.701851
\(436\) 0 0
\(437\) −0.987550 −0.0472409
\(438\) 0 0
\(439\) −33.9160 −1.61872 −0.809362 0.587310i \(-0.800187\pi\)
−0.809362 + 0.587310i \(0.800187\pi\)
\(440\) 0 0
\(441\) 0.821938 0.0391399
\(442\) 0 0
\(443\) −15.8855 −0.754742 −0.377371 0.926062i \(-0.623172\pi\)
−0.377371 + 0.926062i \(0.623172\pi\)
\(444\) 0 0
\(445\) 0.224501 0.0106423
\(446\) 0 0
\(447\) 25.0411 1.18440
\(448\) 0 0
\(449\) −28.1366 −1.32785 −0.663924 0.747800i \(-0.731110\pi\)
−0.663924 + 0.747800i \(0.731110\pi\)
\(450\) 0 0
\(451\) −18.9247 −0.891131
\(452\) 0 0
\(453\) 20.5448 0.965280
\(454\) 0 0
\(455\) 23.2698 1.09090
\(456\) 0 0
\(457\) −24.8513 −1.16249 −0.581247 0.813727i \(-0.697435\pi\)
−0.581247 + 0.813727i \(0.697435\pi\)
\(458\) 0 0
\(459\) 29.4110 1.37279
\(460\) 0 0
\(461\) −23.0225 −1.07226 −0.536132 0.844134i \(-0.680115\pi\)
−0.536132 + 0.844134i \(0.680115\pi\)
\(462\) 0 0
\(463\) −25.1625 −1.16940 −0.584700 0.811250i \(-0.698788\pi\)
−0.584700 + 0.811250i \(0.698788\pi\)
\(464\) 0 0
\(465\) 24.9160 1.15545
\(466\) 0 0
\(467\) −17.8394 −0.825511 −0.412755 0.910842i \(-0.635434\pi\)
−0.412755 + 0.910842i \(0.635434\pi\)
\(468\) 0 0
\(469\) 14.1210 0.652047
\(470\) 0 0
\(471\) 25.4008 1.17041
\(472\) 0 0
\(473\) −17.9310 −0.824470
\(474\) 0 0
\(475\) 0.906807 0.0416071
\(476\) 0 0
\(477\) 0.310294 0.0142074
\(478\) 0 0
\(479\) −35.7755 −1.63463 −0.817313 0.576194i \(-0.804537\pi\)
−0.817313 + 0.576194i \(0.804537\pi\)
\(480\) 0 0
\(481\) 2.93191 0.133683
\(482\) 0 0
\(483\) 10.7616 0.489671
\(484\) 0 0
\(485\) 40.2367 1.82706
\(486\) 0 0
\(487\) −17.8250 −0.807726 −0.403863 0.914819i \(-0.632333\pi\)
−0.403863 + 0.914819i \(0.632333\pi\)
\(488\) 0 0
\(489\) −34.9539 −1.58067
\(490\) 0 0
\(491\) 26.0616 1.17614 0.588072 0.808808i \(-0.299887\pi\)
0.588072 + 0.808808i \(0.299887\pi\)
\(492\) 0 0
\(493\) 16.4230 0.739654
\(494\) 0 0
\(495\) −3.10874 −0.139728
\(496\) 0 0
\(497\) 25.3478 1.13701
\(498\) 0 0
\(499\) 13.3714 0.598588 0.299294 0.954161i \(-0.403249\pi\)
0.299294 + 0.954161i \(0.403249\pi\)
\(500\) 0 0
\(501\) 9.29902 0.415450
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 11.6054 0.516436
\(506\) 0 0
\(507\) −16.7398 −0.743440
\(508\) 0 0
\(509\) 1.40210 0.0621471 0.0310736 0.999517i \(-0.490107\pi\)
0.0310736 + 0.999517i \(0.490107\pi\)
\(510\) 0 0
\(511\) −0.772214 −0.0341607
\(512\) 0 0
\(513\) 1.36457 0.0602473
\(514\) 0 0
\(515\) 13.1072 0.577572
\(516\) 0 0
\(517\) −12.2633 −0.539341
\(518\) 0 0
\(519\) −26.2033 −1.15020
\(520\) 0 0
\(521\) −26.2278 −1.14906 −0.574531 0.818483i \(-0.694816\pi\)
−0.574531 + 0.818483i \(0.694816\pi\)
\(522\) 0 0
\(523\) −13.9265 −0.608965 −0.304482 0.952518i \(-0.598483\pi\)
−0.304482 + 0.952518i \(0.598483\pi\)
\(524\) 0 0
\(525\) −9.88175 −0.431275
\(526\) 0 0
\(527\) 27.9538 1.21769
\(528\) 0 0
\(529\) −8.00911 −0.348222
\(530\) 0 0
\(531\) −1.66625 −0.0723093
\(532\) 0 0
\(533\) −16.5228 −0.715684
\(534\) 0 0
\(535\) −37.9676 −1.64148
\(536\) 0 0
\(537\) −23.7241 −1.02377
\(538\) 0 0
\(539\) 23.3263 1.00473
\(540\) 0 0
\(541\) −13.0315 −0.560266 −0.280133 0.959961i \(-0.590379\pi\)
−0.280133 + 0.959961i \(0.590379\pi\)
\(542\) 0 0
\(543\) 7.78285 0.333994
\(544\) 0 0
\(545\) 32.1021 1.37510
\(546\) 0 0
\(547\) −11.4973 −0.491590 −0.245795 0.969322i \(-0.579049\pi\)
−0.245795 + 0.969322i \(0.579049\pi\)
\(548\) 0 0
\(549\) 0.480899 0.0205243
\(550\) 0 0
\(551\) 0.761970 0.0324610
\(552\) 0 0
\(553\) 0.829938 0.0352925
\(554\) 0 0
\(555\) −2.99609 −0.127177
\(556\) 0 0
\(557\) −16.4495 −0.696988 −0.348494 0.937311i \(-0.613307\pi\)
−0.348494 + 0.937311i \(0.613307\pi\)
\(558\) 0 0
\(559\) −15.6552 −0.662146
\(560\) 0 0
\(561\) 50.5799 2.13548
\(562\) 0 0
\(563\) 23.3455 0.983898 0.491949 0.870624i \(-0.336285\pi\)
0.491949 + 0.870624i \(0.336285\pi\)
\(564\) 0 0
\(565\) −31.6021 −1.32951
\(566\) 0 0
\(567\) −13.9069 −0.584035
\(568\) 0 0
\(569\) −33.4867 −1.40383 −0.701917 0.712258i \(-0.747672\pi\)
−0.701917 + 0.712258i \(0.747672\pi\)
\(570\) 0 0
\(571\) −3.50020 −0.146479 −0.0732393 0.997314i \(-0.523334\pi\)
−0.0732393 + 0.997314i \(0.523334\pi\)
\(572\) 0 0
\(573\) 1.44427 0.0603353
\(574\) 0 0
\(575\) −13.7652 −0.574049
\(576\) 0 0
\(577\) −47.1850 −1.96434 −0.982169 0.188003i \(-0.939799\pi\)
−0.982169 + 0.188003i \(0.939799\pi\)
\(578\) 0 0
\(579\) 24.6626 1.02494
\(580\) 0 0
\(581\) −13.6414 −0.565940
\(582\) 0 0
\(583\) 8.80602 0.364708
\(584\) 0 0
\(585\) −2.71418 −0.112218
\(586\) 0 0
\(587\) 24.5496 1.01327 0.506636 0.862160i \(-0.330889\pi\)
0.506636 + 0.862160i \(0.330889\pi\)
\(588\) 0 0
\(589\) 1.29696 0.0534404
\(590\) 0 0
\(591\) 8.10688 0.333472
\(592\) 0 0
\(593\) −13.6091 −0.558858 −0.279429 0.960166i \(-0.590145\pi\)
−0.279429 + 0.960166i \(0.590145\pi\)
\(594\) 0 0
\(595\) −26.6784 −1.09371
\(596\) 0 0
\(597\) 2.30665 0.0944050
\(598\) 0 0
\(599\) −6.59210 −0.269346 −0.134673 0.990890i \(-0.542998\pi\)
−0.134673 + 0.990890i \(0.542998\pi\)
\(600\) 0 0
\(601\) 16.8678 0.688054 0.344027 0.938960i \(-0.388209\pi\)
0.344027 + 0.938960i \(0.388209\pi\)
\(602\) 0 0
\(603\) −1.64707 −0.0670740
\(604\) 0 0
\(605\) −56.0506 −2.27878
\(606\) 0 0
\(607\) 23.4907 0.953460 0.476730 0.879050i \(-0.341822\pi\)
0.476730 + 0.879050i \(0.341822\pi\)
\(608\) 0 0
\(609\) −8.30342 −0.336471
\(610\) 0 0
\(611\) −10.7069 −0.433154
\(612\) 0 0
\(613\) −39.7929 −1.60722 −0.803611 0.595155i \(-0.797091\pi\)
−0.803611 + 0.595155i \(0.797091\pi\)
\(614\) 0 0
\(615\) 16.8846 0.680851
\(616\) 0 0
\(617\) 5.90322 0.237655 0.118827 0.992915i \(-0.462086\pi\)
0.118827 + 0.992915i \(0.462086\pi\)
\(618\) 0 0
\(619\) 33.4915 1.34614 0.673069 0.739579i \(-0.264976\pi\)
0.673069 + 0.739579i \(0.264976\pi\)
\(620\) 0 0
\(621\) −20.7140 −0.831225
\(622\) 0 0
\(623\) −0.127346 −0.00510200
\(624\) 0 0
\(625\) −30.1365 −1.20546
\(626\) 0 0
\(627\) 2.34673 0.0937194
\(628\) 0 0
\(629\) −3.36138 −0.134027
\(630\) 0 0
\(631\) −23.7313 −0.944729 −0.472364 0.881403i \(-0.656599\pi\)
−0.472364 + 0.881403i \(0.656599\pi\)
\(632\) 0 0
\(633\) 10.5688 0.420071
\(634\) 0 0
\(635\) −30.4767 −1.20943
\(636\) 0 0
\(637\) 20.3657 0.806919
\(638\) 0 0
\(639\) −2.95657 −0.116960
\(640\) 0 0
\(641\) −16.7510 −0.661626 −0.330813 0.943696i \(-0.607323\pi\)
−0.330813 + 0.943696i \(0.607323\pi\)
\(642\) 0 0
\(643\) −8.80580 −0.347267 −0.173633 0.984810i \(-0.555551\pi\)
−0.173633 + 0.984810i \(0.555551\pi\)
\(644\) 0 0
\(645\) 15.9980 0.629919
\(646\) 0 0
\(647\) −28.3986 −1.11646 −0.558232 0.829685i \(-0.688520\pi\)
−0.558232 + 0.829685i \(0.688520\pi\)
\(648\) 0 0
\(649\) −47.2876 −1.85620
\(650\) 0 0
\(651\) −14.1334 −0.553931
\(652\) 0 0
\(653\) −1.81491 −0.0710230 −0.0355115 0.999369i \(-0.511306\pi\)
−0.0355115 + 0.999369i \(0.511306\pi\)
\(654\) 0 0
\(655\) −20.8340 −0.814052
\(656\) 0 0
\(657\) 0.0900711 0.00351401
\(658\) 0 0
\(659\) −3.09694 −0.120640 −0.0603199 0.998179i \(-0.519212\pi\)
−0.0603199 + 0.998179i \(0.519212\pi\)
\(660\) 0 0
\(661\) −32.2197 −1.25320 −0.626601 0.779340i \(-0.715554\pi\)
−0.626601 + 0.779340i \(0.715554\pi\)
\(662\) 0 0
\(663\) 44.1603 1.71505
\(664\) 0 0
\(665\) −1.23778 −0.0479992
\(666\) 0 0
\(667\) −11.5666 −0.447861
\(668\) 0 0
\(669\) −5.19099 −0.200695
\(670\) 0 0
\(671\) 13.6477 0.526864
\(672\) 0 0
\(673\) 29.9648 1.15506 0.577528 0.816371i \(-0.304017\pi\)
0.577528 + 0.816371i \(0.304017\pi\)
\(674\) 0 0
\(675\) 19.0204 0.732096
\(676\) 0 0
\(677\) −29.5307 −1.13496 −0.567479 0.823388i \(-0.692081\pi\)
−0.567479 + 0.823388i \(0.692081\pi\)
\(678\) 0 0
\(679\) −22.8239 −0.875901
\(680\) 0 0
\(681\) 19.8168 0.759380
\(682\) 0 0
\(683\) 35.7975 1.36975 0.684876 0.728659i \(-0.259856\pi\)
0.684876 + 0.728659i \(0.259856\pi\)
\(684\) 0 0
\(685\) 0.385668 0.0147356
\(686\) 0 0
\(687\) −4.05316 −0.154638
\(688\) 0 0
\(689\) 7.68837 0.292904
\(690\) 0 0
\(691\) 4.39357 0.167139 0.0835695 0.996502i \(-0.473368\pi\)
0.0835695 + 0.996502i \(0.473368\pi\)
\(692\) 0 0
\(693\) 1.76340 0.0669862
\(694\) 0 0
\(695\) 40.0530 1.51930
\(696\) 0 0
\(697\) 18.9432 0.717523
\(698\) 0 0
\(699\) −19.1620 −0.724774
\(700\) 0 0
\(701\) −17.1846 −0.649052 −0.324526 0.945877i \(-0.605205\pi\)
−0.324526 + 0.945877i \(0.605205\pi\)
\(702\) 0 0
\(703\) −0.155956 −0.00588201
\(704\) 0 0
\(705\) 10.9413 0.412072
\(706\) 0 0
\(707\) −6.58308 −0.247582
\(708\) 0 0
\(709\) 9.98499 0.374994 0.187497 0.982265i \(-0.439962\pi\)
0.187497 + 0.982265i \(0.439962\pi\)
\(710\) 0 0
\(711\) −0.0968040 −0.00363043
\(712\) 0 0
\(713\) −19.6877 −0.737311
\(714\) 0 0
\(715\) −77.0275 −2.88066
\(716\) 0 0
\(717\) −21.7936 −0.813896
\(718\) 0 0
\(719\) −30.3013 −1.13005 −0.565024 0.825075i \(-0.691133\pi\)
−0.565024 + 0.825075i \(0.691133\pi\)
\(720\) 0 0
\(721\) −7.43493 −0.276891
\(722\) 0 0
\(723\) 13.4542 0.500365
\(724\) 0 0
\(725\) 10.6209 0.394451
\(726\) 0 0
\(727\) −39.0522 −1.44837 −0.724183 0.689608i \(-0.757783\pi\)
−0.724183 + 0.689608i \(0.757783\pi\)
\(728\) 0 0
\(729\) 28.5097 1.05592
\(730\) 0 0
\(731\) 17.9485 0.663848
\(732\) 0 0
\(733\) 51.5101 1.90257 0.951285 0.308312i \(-0.0997640\pi\)
0.951285 + 0.308312i \(0.0997640\pi\)
\(734\) 0 0
\(735\) −20.8116 −0.767646
\(736\) 0 0
\(737\) −46.7433 −1.72181
\(738\) 0 0
\(739\) 22.6626 0.833659 0.416829 0.908985i \(-0.363141\pi\)
0.416829 + 0.908985i \(0.363141\pi\)
\(740\) 0 0
\(741\) 2.04889 0.0752678
\(742\) 0 0
\(743\) 13.2455 0.485929 0.242965 0.970035i \(-0.421880\pi\)
0.242965 + 0.970035i \(0.421880\pi\)
\(744\) 0 0
\(745\) 43.7208 1.60181
\(746\) 0 0
\(747\) 1.59113 0.0582165
\(748\) 0 0
\(749\) 21.5368 0.786937
\(750\) 0 0
\(751\) −31.6069 −1.15335 −0.576677 0.816972i \(-0.695651\pi\)
−0.576677 + 0.816972i \(0.695651\pi\)
\(752\) 0 0
\(753\) −2.43804 −0.0888470
\(754\) 0 0
\(755\) 35.8705 1.30546
\(756\) 0 0
\(757\) −13.6152 −0.494852 −0.247426 0.968907i \(-0.579585\pi\)
−0.247426 + 0.968907i \(0.579585\pi\)
\(758\) 0 0
\(759\) −35.6231 −1.29304
\(760\) 0 0
\(761\) −8.24166 −0.298760 −0.149380 0.988780i \(-0.547728\pi\)
−0.149380 + 0.988780i \(0.547728\pi\)
\(762\) 0 0
\(763\) −18.2096 −0.659233
\(764\) 0 0
\(765\) 3.11177 0.112506
\(766\) 0 0
\(767\) −41.2859 −1.49075
\(768\) 0 0
\(769\) 11.2334 0.405088 0.202544 0.979273i \(-0.435079\pi\)
0.202544 + 0.979273i \(0.435079\pi\)
\(770\) 0 0
\(771\) −8.67993 −0.312600
\(772\) 0 0
\(773\) 42.3532 1.52334 0.761669 0.647966i \(-0.224380\pi\)
0.761669 + 0.647966i \(0.224380\pi\)
\(774\) 0 0
\(775\) 18.0780 0.649382
\(776\) 0 0
\(777\) 1.69950 0.0609694
\(778\) 0 0
\(779\) 0.878897 0.0314898
\(780\) 0 0
\(781\) −83.9063 −3.00240
\(782\) 0 0
\(783\) 15.9824 0.571166
\(784\) 0 0
\(785\) 44.3488 1.58288
\(786\) 0 0
\(787\) 32.3707 1.15389 0.576945 0.816783i \(-0.304245\pi\)
0.576945 + 0.816783i \(0.304245\pi\)
\(788\) 0 0
\(789\) −37.4261 −1.33241
\(790\) 0 0
\(791\) 17.9260 0.637375
\(792\) 0 0
\(793\) 11.9156 0.423134
\(794\) 0 0
\(795\) −7.85669 −0.278648
\(796\) 0 0
\(797\) 15.7618 0.558313 0.279157 0.960246i \(-0.409945\pi\)
0.279157 + 0.960246i \(0.409945\pi\)
\(798\) 0 0
\(799\) 12.2753 0.434267
\(800\) 0 0
\(801\) 0.0148536 0.000524827 0
\(802\) 0 0
\(803\) 2.55618 0.0902056
\(804\) 0 0
\(805\) 18.7894 0.662240
\(806\) 0 0
\(807\) −6.11433 −0.215234
\(808\) 0 0
\(809\) 2.61862 0.0920658 0.0460329 0.998940i \(-0.485342\pi\)
0.0460329 + 0.998940i \(0.485342\pi\)
\(810\) 0 0
\(811\) −46.5376 −1.63416 −0.817078 0.576527i \(-0.804408\pi\)
−0.817078 + 0.576527i \(0.804408\pi\)
\(812\) 0 0
\(813\) −14.3652 −0.503810
\(814\) 0 0
\(815\) −61.0283 −2.13773
\(816\) 0 0
\(817\) 0.832747 0.0291341
\(818\) 0 0
\(819\) 1.53960 0.0537978
\(820\) 0 0
\(821\) −12.8542 −0.448616 −0.224308 0.974518i \(-0.572012\pi\)
−0.224308 + 0.974518i \(0.572012\pi\)
\(822\) 0 0
\(823\) −43.1243 −1.50322 −0.751609 0.659609i \(-0.770722\pi\)
−0.751609 + 0.659609i \(0.770722\pi\)
\(824\) 0 0
\(825\) 32.7105 1.13883
\(826\) 0 0
\(827\) 40.1984 1.39783 0.698917 0.715203i \(-0.253666\pi\)
0.698917 + 0.715203i \(0.253666\pi\)
\(828\) 0 0
\(829\) 17.0860 0.593422 0.296711 0.954967i \(-0.404110\pi\)
0.296711 + 0.954967i \(0.404110\pi\)
\(830\) 0 0
\(831\) 5.83500 0.202414
\(832\) 0 0
\(833\) −23.3489 −0.808993
\(834\) 0 0
\(835\) 16.2358 0.561862
\(836\) 0 0
\(837\) 27.2040 0.940307
\(838\) 0 0
\(839\) 24.8422 0.857648 0.428824 0.903388i \(-0.358928\pi\)
0.428824 + 0.903388i \(0.358928\pi\)
\(840\) 0 0
\(841\) −20.0755 −0.692258
\(842\) 0 0
\(843\) 7.13842 0.245860
\(844\) 0 0
\(845\) −29.2271 −1.00544
\(846\) 0 0
\(847\) 31.7942 1.09246
\(848\) 0 0
\(849\) 10.0343 0.344377
\(850\) 0 0
\(851\) 2.36740 0.0811534
\(852\) 0 0
\(853\) 24.0326 0.822862 0.411431 0.911441i \(-0.365029\pi\)
0.411431 + 0.911441i \(0.365029\pi\)
\(854\) 0 0
\(855\) 0.144375 0.00493753
\(856\) 0 0
\(857\) 3.56986 0.121944 0.0609720 0.998139i \(-0.480580\pi\)
0.0609720 + 0.998139i \(0.480580\pi\)
\(858\) 0 0
\(859\) 20.5639 0.701630 0.350815 0.936445i \(-0.385905\pi\)
0.350815 + 0.936445i \(0.385905\pi\)
\(860\) 0 0
\(861\) −9.57761 −0.326404
\(862\) 0 0
\(863\) 45.2368 1.53988 0.769939 0.638118i \(-0.220287\pi\)
0.769939 + 0.638118i \(0.220287\pi\)
\(864\) 0 0
\(865\) −45.7500 −1.55555
\(866\) 0 0
\(867\) −22.1497 −0.752245
\(868\) 0 0
\(869\) −2.74726 −0.0931943
\(870\) 0 0
\(871\) −40.8107 −1.38282
\(872\) 0 0
\(873\) 2.66218 0.0901012
\(874\) 0 0
\(875\) 7.01123 0.237023
\(876\) 0 0
\(877\) −23.4083 −0.790443 −0.395222 0.918586i \(-0.629332\pi\)
−0.395222 + 0.918586i \(0.629332\pi\)
\(878\) 0 0
\(879\) −47.2312 −1.59307
\(880\) 0 0
\(881\) 17.1411 0.577499 0.288749 0.957405i \(-0.406761\pi\)
0.288749 + 0.957405i \(0.406761\pi\)
\(882\) 0 0
\(883\) −34.4628 −1.15977 −0.579883 0.814700i \(-0.696902\pi\)
−0.579883 + 0.814700i \(0.696902\pi\)
\(884\) 0 0
\(885\) 42.1898 1.41819
\(886\) 0 0
\(887\) −0.775217 −0.0260293 −0.0130146 0.999915i \(-0.504143\pi\)
−0.0130146 + 0.999915i \(0.504143\pi\)
\(888\) 0 0
\(889\) 17.2876 0.579808
\(890\) 0 0
\(891\) 46.0346 1.54222
\(892\) 0 0
\(893\) 0.569529 0.0190586
\(894\) 0 0
\(895\) −41.4214 −1.38456
\(896\) 0 0
\(897\) −31.1019 −1.03846
\(898\) 0 0
\(899\) 15.1906 0.506634
\(900\) 0 0
\(901\) −8.81459 −0.293656
\(902\) 0 0
\(903\) −9.07470 −0.301987
\(904\) 0 0
\(905\) 13.5886 0.451700
\(906\) 0 0
\(907\) −29.1042 −0.966389 −0.483194 0.875513i \(-0.660524\pi\)
−0.483194 + 0.875513i \(0.660524\pi\)
\(908\) 0 0
\(909\) 0.767851 0.0254680
\(910\) 0 0
\(911\) 42.0173 1.39210 0.696048 0.717995i \(-0.254940\pi\)
0.696048 + 0.717995i \(0.254940\pi\)
\(912\) 0 0
\(913\) 45.1557 1.49443
\(914\) 0 0
\(915\) −12.1764 −0.402540
\(916\) 0 0
\(917\) 11.8179 0.390261
\(918\) 0 0
\(919\) 4.95872 0.163573 0.0817865 0.996650i \(-0.473937\pi\)
0.0817865 + 0.996650i \(0.473937\pi\)
\(920\) 0 0
\(921\) 23.3720 0.770133
\(922\) 0 0
\(923\) −73.2570 −2.41128
\(924\) 0 0
\(925\) −2.17384 −0.0714754
\(926\) 0 0
\(927\) 0.867210 0.0284829
\(928\) 0 0
\(929\) −28.2747 −0.927663 −0.463832 0.885923i \(-0.653526\pi\)
−0.463832 + 0.885923i \(0.653526\pi\)
\(930\) 0 0
\(931\) −1.08331 −0.0355041
\(932\) 0 0
\(933\) 38.0528 1.24579
\(934\) 0 0
\(935\) 88.3107 2.88807
\(936\) 0 0
\(937\) 58.6513 1.91605 0.958027 0.286677i \(-0.0925505\pi\)
0.958027 + 0.286677i \(0.0925505\pi\)
\(938\) 0 0
\(939\) 48.0690 1.56867
\(940\) 0 0
\(941\) 35.5220 1.15798 0.578991 0.815334i \(-0.303446\pi\)
0.578991 + 0.815334i \(0.303446\pi\)
\(942\) 0 0
\(943\) −13.3416 −0.434461
\(944\) 0 0
\(945\) −25.9627 −0.844568
\(946\) 0 0
\(947\) −7.64695 −0.248492 −0.124246 0.992251i \(-0.539651\pi\)
−0.124246 + 0.992251i \(0.539651\pi\)
\(948\) 0 0
\(949\) 2.23175 0.0724458
\(950\) 0 0
\(951\) 29.9126 0.969982
\(952\) 0 0
\(953\) 41.2516 1.33627 0.668135 0.744040i \(-0.267093\pi\)
0.668135 + 0.744040i \(0.267093\pi\)
\(954\) 0 0
\(955\) 2.52165 0.0815985
\(956\) 0 0
\(957\) 27.4859 0.888495
\(958\) 0 0
\(959\) −0.218766 −0.00706433
\(960\) 0 0
\(961\) −5.14388 −0.165932
\(962\) 0 0
\(963\) −2.51205 −0.0809497
\(964\) 0 0
\(965\) 43.0600 1.38615
\(966\) 0 0
\(967\) −44.2579 −1.42324 −0.711620 0.702565i \(-0.752038\pi\)
−0.711620 + 0.702565i \(0.752038\pi\)
\(968\) 0 0
\(969\) −2.34901 −0.0754612
\(970\) 0 0
\(971\) 9.32573 0.299277 0.149638 0.988741i \(-0.452189\pi\)
0.149638 + 0.988741i \(0.452189\pi\)
\(972\) 0 0
\(973\) −22.7197 −0.728359
\(974\) 0 0
\(975\) 28.5590 0.914618
\(976\) 0 0
\(977\) 27.6771 0.885470 0.442735 0.896653i \(-0.354008\pi\)
0.442735 + 0.896653i \(0.354008\pi\)
\(978\) 0 0
\(979\) 0.421540 0.0134725
\(980\) 0 0
\(981\) 2.12397 0.0678132
\(982\) 0 0
\(983\) −58.9984 −1.88176 −0.940878 0.338744i \(-0.889998\pi\)
−0.940878 + 0.338744i \(0.889998\pi\)
\(984\) 0 0
\(985\) 14.1543 0.450994
\(986\) 0 0
\(987\) −6.20633 −0.197550
\(988\) 0 0
\(989\) −12.6410 −0.401960
\(990\) 0 0
\(991\) 24.7333 0.785679 0.392839 0.919607i \(-0.371493\pi\)
0.392839 + 0.919607i \(0.371493\pi\)
\(992\) 0 0
\(993\) 23.5697 0.747961
\(994\) 0 0
\(995\) 4.02733 0.127675
\(996\) 0 0
\(997\) −47.7695 −1.51287 −0.756437 0.654066i \(-0.773062\pi\)
−0.756437 + 0.654066i \(0.773062\pi\)
\(998\) 0 0
\(999\) −3.27121 −0.103497
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 \(a_p\))