Properties

Label 8016.2.a.bg.1.8
Level 8016
Weight 2
Character 8016.1
Self dual Yes
Analytic conductor 64.008
Analytic rank 0
Dimension 13
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8016.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0080822603\)
Analytic rank: \(0\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(1.25667\)
Character \(\chi\) = 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(+1.25667 q^{5}\) \(+4.55521 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(+1.25667 q^{5}\) \(+4.55521 q^{7}\) \(+1.00000 q^{9}\) \(+5.23461 q^{11}\) \(-1.93555 q^{13}\) \(-1.25667 q^{15}\) \(+7.59670 q^{17}\) \(+4.42731 q^{19}\) \(-4.55521 q^{21}\) \(-6.61071 q^{23}\) \(-3.42078 q^{25}\) \(-1.00000 q^{27}\) \(+3.73263 q^{29}\) \(+1.27190 q^{31}\) \(-5.23461 q^{33}\) \(+5.72440 q^{35}\) \(+6.87153 q^{37}\) \(+1.93555 q^{39}\) \(+8.71632 q^{41}\) \(-5.25563 q^{43}\) \(+1.25667 q^{45}\) \(+6.55882 q^{47}\) \(+13.7500 q^{49}\) \(-7.59670 q^{51}\) \(+3.93979 q^{53}\) \(+6.57819 q^{55}\) \(-4.42731 q^{57}\) \(-12.3546 q^{59}\) \(-0.282357 q^{61}\) \(+4.55521 q^{63}\) \(-2.43235 q^{65}\) \(+8.25155 q^{67}\) \(+6.61071 q^{69}\) \(+1.66362 q^{71}\) \(-3.89727 q^{73}\) \(+3.42078 q^{75}\) \(+23.8448 q^{77}\) \(-6.21505 q^{79}\) \(+1.00000 q^{81}\) \(-14.1118 q^{83}\) \(+9.54655 q^{85}\) \(-3.73263 q^{87}\) \(-6.93566 q^{89}\) \(-8.81684 q^{91}\) \(-1.27190 q^{93}\) \(+5.56367 q^{95}\) \(-3.11931 q^{97}\) \(+5.23461 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 15q^{17} \) \(\mathstrut -\mathstrut 14q^{19} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 9q^{23} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 3q^{29} \) \(\mathstrut +\mathstrut 17q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 12q^{39} \) \(\mathstrut +\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 6q^{47} \) \(\mathstrut +\mathstrut 26q^{49} \) \(\mathstrut -\mathstrut 15q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 7q^{55} \) \(\mathstrut +\mathstrut 14q^{57} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut -\mathstrut q^{63} \) \(\mathstrut +\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 3q^{67} \) \(\mathstrut +\mathstrut 9q^{69} \) \(\mathstrut -\mathstrut 17q^{71} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 37q^{75} \) \(\mathstrut +\mathstrut 30q^{77} \) \(\mathstrut -\mathstrut 10q^{79} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 25q^{85} \) \(\mathstrut +\mathstrut 3q^{87} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 29q^{91} \) \(\mathstrut -\mathstrut 17q^{93} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 38q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 1.25667 0.562000 0.281000 0.959708i \(-0.409334\pi\)
0.281000 + 0.959708i \(0.409334\pi\)
\(6\) 0 0
\(7\) 4.55521 1.72171 0.860854 0.508852i \(-0.169930\pi\)
0.860854 + 0.508852i \(0.169930\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 5.23461 1.57829 0.789147 0.614204i \(-0.210523\pi\)
0.789147 + 0.614204i \(0.210523\pi\)
\(12\) 0 0
\(13\) −1.93555 −0.536825 −0.268412 0.963304i \(-0.586499\pi\)
−0.268412 + 0.963304i \(0.586499\pi\)
\(14\) 0 0
\(15\) −1.25667 −0.324471
\(16\) 0 0
\(17\) 7.59670 1.84247 0.921235 0.389007i \(-0.127182\pi\)
0.921235 + 0.389007i \(0.127182\pi\)
\(18\) 0 0
\(19\) 4.42731 1.01569 0.507847 0.861447i \(-0.330442\pi\)
0.507847 + 0.861447i \(0.330442\pi\)
\(20\) 0 0
\(21\) −4.55521 −0.994029
\(22\) 0 0
\(23\) −6.61071 −1.37843 −0.689214 0.724558i \(-0.742044\pi\)
−0.689214 + 0.724558i \(0.742044\pi\)
\(24\) 0 0
\(25\) −3.42078 −0.684156
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 3.73263 0.693132 0.346566 0.938026i \(-0.387348\pi\)
0.346566 + 0.938026i \(0.387348\pi\)
\(30\) 0 0
\(31\) 1.27190 0.228440 0.114220 0.993455i \(-0.463563\pi\)
0.114220 + 0.993455i \(0.463563\pi\)
\(32\) 0 0
\(33\) −5.23461 −0.911229
\(34\) 0 0
\(35\) 5.72440 0.967601
\(36\) 0 0
\(37\) 6.87153 1.12967 0.564836 0.825203i \(-0.308939\pi\)
0.564836 + 0.825203i \(0.308939\pi\)
\(38\) 0 0
\(39\) 1.93555 0.309936
\(40\) 0 0
\(41\) 8.71632 1.36126 0.680631 0.732627i \(-0.261706\pi\)
0.680631 + 0.732627i \(0.261706\pi\)
\(42\) 0 0
\(43\) −5.25563 −0.801476 −0.400738 0.916193i \(-0.631246\pi\)
−0.400738 + 0.916193i \(0.631246\pi\)
\(44\) 0 0
\(45\) 1.25667 0.187333
\(46\) 0 0
\(47\) 6.55882 0.956702 0.478351 0.878169i \(-0.341235\pi\)
0.478351 + 0.878169i \(0.341235\pi\)
\(48\) 0 0
\(49\) 13.7500 1.96428
\(50\) 0 0
\(51\) −7.59670 −1.06375
\(52\) 0 0
\(53\) 3.93979 0.541172 0.270586 0.962696i \(-0.412783\pi\)
0.270586 + 0.962696i \(0.412783\pi\)
\(54\) 0 0
\(55\) 6.57819 0.887002
\(56\) 0 0
\(57\) −4.42731 −0.586411
\(58\) 0 0
\(59\) −12.3546 −1.60844 −0.804218 0.594335i \(-0.797416\pi\)
−0.804218 + 0.594335i \(0.797416\pi\)
\(60\) 0 0
\(61\) −0.282357 −0.0361522 −0.0180761 0.999837i \(-0.505754\pi\)
−0.0180761 + 0.999837i \(0.505754\pi\)
\(62\) 0 0
\(63\) 4.55521 0.573903
\(64\) 0 0
\(65\) −2.43235 −0.301696
\(66\) 0 0
\(67\) 8.25155 1.00809 0.504043 0.863678i \(-0.331845\pi\)
0.504043 + 0.863678i \(0.331845\pi\)
\(68\) 0 0
\(69\) 6.61071 0.795836
\(70\) 0 0
\(71\) 1.66362 0.197435 0.0987175 0.995115i \(-0.468526\pi\)
0.0987175 + 0.995115i \(0.468526\pi\)
\(72\) 0 0
\(73\) −3.89727 −0.456141 −0.228071 0.973645i \(-0.573242\pi\)
−0.228071 + 0.973645i \(0.573242\pi\)
\(74\) 0 0
\(75\) 3.42078 0.394997
\(76\) 0 0
\(77\) 23.8448 2.71736
\(78\) 0 0
\(79\) −6.21505 −0.699248 −0.349624 0.936890i \(-0.613691\pi\)
−0.349624 + 0.936890i \(0.613691\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −14.1118 −1.54898 −0.774488 0.632588i \(-0.781993\pi\)
−0.774488 + 0.632588i \(0.781993\pi\)
\(84\) 0 0
\(85\) 9.54655 1.03547
\(86\) 0 0
\(87\) −3.73263 −0.400180
\(88\) 0 0
\(89\) −6.93566 −0.735178 −0.367589 0.929988i \(-0.619817\pi\)
−0.367589 + 0.929988i \(0.619817\pi\)
\(90\) 0 0
\(91\) −8.81684 −0.924256
\(92\) 0 0
\(93\) −1.27190 −0.131890
\(94\) 0 0
\(95\) 5.56367 0.570820
\(96\) 0 0
\(97\) −3.11931 −0.316718 −0.158359 0.987382i \(-0.550620\pi\)
−0.158359 + 0.987382i \(0.550620\pi\)
\(98\) 0 0
\(99\) 5.23461 0.526098
\(100\) 0 0
\(101\) 11.8680 1.18091 0.590457 0.807069i \(-0.298948\pi\)
0.590457 + 0.807069i \(0.298948\pi\)
\(102\) 0 0
\(103\) 2.31747 0.228347 0.114174 0.993461i \(-0.463578\pi\)
0.114174 + 0.993461i \(0.463578\pi\)
\(104\) 0 0
\(105\) −5.72440 −0.558645
\(106\) 0 0
\(107\) 1.55158 0.149997 0.0749985 0.997184i \(-0.476105\pi\)
0.0749985 + 0.997184i \(0.476105\pi\)
\(108\) 0 0
\(109\) 5.37197 0.514541 0.257271 0.966339i \(-0.417177\pi\)
0.257271 + 0.966339i \(0.417177\pi\)
\(110\) 0 0
\(111\) −6.87153 −0.652217
\(112\) 0 0
\(113\) 17.3036 1.62779 0.813893 0.581014i \(-0.197344\pi\)
0.813893 + 0.581014i \(0.197344\pi\)
\(114\) 0 0
\(115\) −8.30748 −0.774677
\(116\) 0 0
\(117\) −1.93555 −0.178942
\(118\) 0 0
\(119\) 34.6046 3.17220
\(120\) 0 0
\(121\) 16.4012 1.49101
\(122\) 0 0
\(123\) −8.71632 −0.785925
\(124\) 0 0
\(125\) −10.5821 −0.946496
\(126\) 0 0
\(127\) −7.88097 −0.699323 −0.349662 0.936876i \(-0.613703\pi\)
−0.349662 + 0.936876i \(0.613703\pi\)
\(128\) 0 0
\(129\) 5.25563 0.462732
\(130\) 0 0
\(131\) −20.2297 −1.76748 −0.883739 0.467979i \(-0.844982\pi\)
−0.883739 + 0.467979i \(0.844982\pi\)
\(132\) 0 0
\(133\) 20.1673 1.74873
\(134\) 0 0
\(135\) −1.25667 −0.108157
\(136\) 0 0
\(137\) −3.73853 −0.319404 −0.159702 0.987165i \(-0.551053\pi\)
−0.159702 + 0.987165i \(0.551053\pi\)
\(138\) 0 0
\(139\) −13.1822 −1.11810 −0.559049 0.829135i \(-0.688833\pi\)
−0.559049 + 0.829135i \(0.688833\pi\)
\(140\) 0 0
\(141\) −6.55882 −0.552352
\(142\) 0 0
\(143\) −10.1318 −0.847268
\(144\) 0 0
\(145\) 4.69069 0.389540
\(146\) 0 0
\(147\) −13.7500 −1.13408
\(148\) 0 0
\(149\) −16.0892 −1.31808 −0.659040 0.752108i \(-0.729037\pi\)
−0.659040 + 0.752108i \(0.729037\pi\)
\(150\) 0 0
\(151\) −19.2676 −1.56797 −0.783987 0.620778i \(-0.786817\pi\)
−0.783987 + 0.620778i \(0.786817\pi\)
\(152\) 0 0
\(153\) 7.59670 0.614156
\(154\) 0 0
\(155\) 1.59836 0.128383
\(156\) 0 0
\(157\) −8.92368 −0.712187 −0.356094 0.934450i \(-0.615892\pi\)
−0.356094 + 0.934450i \(0.615892\pi\)
\(158\) 0 0
\(159\) −3.93979 −0.312446
\(160\) 0 0
\(161\) −30.1132 −2.37325
\(162\) 0 0
\(163\) 2.94760 0.230874 0.115437 0.993315i \(-0.463173\pi\)
0.115437 + 0.993315i \(0.463173\pi\)
\(164\) 0 0
\(165\) −6.57819 −0.512111
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) −9.25365 −0.711819
\(170\) 0 0
\(171\) 4.42731 0.338564
\(172\) 0 0
\(173\) −12.5486 −0.954055 −0.477028 0.878888i \(-0.658286\pi\)
−0.477028 + 0.878888i \(0.658286\pi\)
\(174\) 0 0
\(175\) −15.5824 −1.17792
\(176\) 0 0
\(177\) 12.3546 0.928631
\(178\) 0 0
\(179\) −3.07676 −0.229968 −0.114984 0.993367i \(-0.536682\pi\)
−0.114984 + 0.993367i \(0.536682\pi\)
\(180\) 0 0
\(181\) 2.50830 0.186440 0.0932201 0.995646i \(-0.470284\pi\)
0.0932201 + 0.995646i \(0.470284\pi\)
\(182\) 0 0
\(183\) 0.282357 0.0208725
\(184\) 0 0
\(185\) 8.63525 0.634877
\(186\) 0 0
\(187\) 39.7658 2.90796
\(188\) 0 0
\(189\) −4.55521 −0.331343
\(190\) 0 0
\(191\) 3.30849 0.239394 0.119697 0.992810i \(-0.461808\pi\)
0.119697 + 0.992810i \(0.461808\pi\)
\(192\) 0 0
\(193\) −18.4096 −1.32515 −0.662577 0.748994i \(-0.730537\pi\)
−0.662577 + 0.748994i \(0.730537\pi\)
\(194\) 0 0
\(195\) 2.43235 0.174184
\(196\) 0 0
\(197\) −13.0745 −0.931520 −0.465760 0.884911i \(-0.654219\pi\)
−0.465760 + 0.884911i \(0.654219\pi\)
\(198\) 0 0
\(199\) 18.8563 1.33669 0.668343 0.743853i \(-0.267004\pi\)
0.668343 + 0.743853i \(0.267004\pi\)
\(200\) 0 0
\(201\) −8.25155 −0.582019
\(202\) 0 0
\(203\) 17.0029 1.19337
\(204\) 0 0
\(205\) 10.9536 0.765029
\(206\) 0 0
\(207\) −6.61071 −0.459476
\(208\) 0 0
\(209\) 23.1752 1.60306
\(210\) 0 0
\(211\) −7.39616 −0.509173 −0.254586 0.967050i \(-0.581939\pi\)
−0.254586 + 0.967050i \(0.581939\pi\)
\(212\) 0 0
\(213\) −1.66362 −0.113989
\(214\) 0 0
\(215\) −6.60460 −0.450430
\(216\) 0 0
\(217\) 5.79377 0.393307
\(218\) 0 0
\(219\) 3.89727 0.263353
\(220\) 0 0
\(221\) −14.7038 −0.989083
\(222\) 0 0
\(223\) 1.81997 0.121874 0.0609371 0.998142i \(-0.480591\pi\)
0.0609371 + 0.998142i \(0.480591\pi\)
\(224\) 0 0
\(225\) −3.42078 −0.228052
\(226\) 0 0
\(227\) −21.8780 −1.45209 −0.726045 0.687647i \(-0.758644\pi\)
−0.726045 + 0.687647i \(0.758644\pi\)
\(228\) 0 0
\(229\) 1.04962 0.0693609 0.0346804 0.999398i \(-0.488959\pi\)
0.0346804 + 0.999398i \(0.488959\pi\)
\(230\) 0 0
\(231\) −23.8448 −1.56887
\(232\) 0 0
\(233\) −17.9898 −1.17855 −0.589274 0.807933i \(-0.700586\pi\)
−0.589274 + 0.807933i \(0.700586\pi\)
\(234\) 0 0
\(235\) 8.24227 0.537667
\(236\) 0 0
\(237\) 6.21505 0.403711
\(238\) 0 0
\(239\) 27.1655 1.75719 0.878596 0.477565i \(-0.158481\pi\)
0.878596 + 0.477565i \(0.158481\pi\)
\(240\) 0 0
\(241\) 21.7168 1.39890 0.699451 0.714680i \(-0.253428\pi\)
0.699451 + 0.714680i \(0.253428\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 17.2792 1.10393
\(246\) 0 0
\(247\) −8.56927 −0.545249
\(248\) 0 0
\(249\) 14.1118 0.894302
\(250\) 0 0
\(251\) −30.4390 −1.92130 −0.960648 0.277770i \(-0.910405\pi\)
−0.960648 + 0.277770i \(0.910405\pi\)
\(252\) 0 0
\(253\) −34.6045 −2.17557
\(254\) 0 0
\(255\) −9.54655 −0.597828
\(256\) 0 0
\(257\) −23.0748 −1.43937 −0.719684 0.694301i \(-0.755714\pi\)
−0.719684 + 0.694301i \(0.755714\pi\)
\(258\) 0 0
\(259\) 31.3013 1.94497
\(260\) 0 0
\(261\) 3.73263 0.231044
\(262\) 0 0
\(263\) −21.5164 −1.32676 −0.663379 0.748284i \(-0.730878\pi\)
−0.663379 + 0.748284i \(0.730878\pi\)
\(264\) 0 0
\(265\) 4.95102 0.304139
\(266\) 0 0
\(267\) 6.93566 0.424455
\(268\) 0 0
\(269\) 16.2955 0.993554 0.496777 0.867878i \(-0.334517\pi\)
0.496777 + 0.867878i \(0.334517\pi\)
\(270\) 0 0
\(271\) 25.9830 1.57835 0.789177 0.614166i \(-0.210507\pi\)
0.789177 + 0.614166i \(0.210507\pi\)
\(272\) 0 0
\(273\) 8.81684 0.533619
\(274\) 0 0
\(275\) −17.9064 −1.07980
\(276\) 0 0
\(277\) −8.26377 −0.496522 −0.248261 0.968693i \(-0.579859\pi\)
−0.248261 + 0.968693i \(0.579859\pi\)
\(278\) 0 0
\(279\) 1.27190 0.0761466
\(280\) 0 0
\(281\) −0.956330 −0.0570499 −0.0285249 0.999593i \(-0.509081\pi\)
−0.0285249 + 0.999593i \(0.509081\pi\)
\(282\) 0 0
\(283\) −7.81438 −0.464517 −0.232258 0.972654i \(-0.574611\pi\)
−0.232258 + 0.972654i \(0.574611\pi\)
\(284\) 0 0
\(285\) −5.56367 −0.329563
\(286\) 0 0
\(287\) 39.7047 2.34369
\(288\) 0 0
\(289\) 40.7098 2.39469
\(290\) 0 0
\(291\) 3.11931 0.182857
\(292\) 0 0
\(293\) −18.0569 −1.05490 −0.527448 0.849587i \(-0.676851\pi\)
−0.527448 + 0.849587i \(0.676851\pi\)
\(294\) 0 0
\(295\) −15.5257 −0.903942
\(296\) 0 0
\(297\) −5.23461 −0.303743
\(298\) 0 0
\(299\) 12.7954 0.739974
\(300\) 0 0
\(301\) −23.9405 −1.37991
\(302\) 0 0
\(303\) −11.8680 −0.681801
\(304\) 0 0
\(305\) −0.354830 −0.0203175
\(306\) 0 0
\(307\) 26.9495 1.53809 0.769046 0.639193i \(-0.220732\pi\)
0.769046 + 0.639193i \(0.220732\pi\)
\(308\) 0 0
\(309\) −2.31747 −0.131836
\(310\) 0 0
\(311\) 7.51738 0.426272 0.213136 0.977023i \(-0.431632\pi\)
0.213136 + 0.977023i \(0.431632\pi\)
\(312\) 0 0
\(313\) 24.9480 1.41015 0.705073 0.709135i \(-0.250914\pi\)
0.705073 + 0.709135i \(0.250914\pi\)
\(314\) 0 0
\(315\) 5.72440 0.322534
\(316\) 0 0
\(317\) 28.0071 1.57303 0.786517 0.617569i \(-0.211882\pi\)
0.786517 + 0.617569i \(0.211882\pi\)
\(318\) 0 0
\(319\) 19.5389 1.09397
\(320\) 0 0
\(321\) −1.55158 −0.0866008
\(322\) 0 0
\(323\) 33.6329 1.87138
\(324\) 0 0
\(325\) 6.62108 0.367272
\(326\) 0 0
\(327\) −5.37197 −0.297071
\(328\) 0 0
\(329\) 29.8768 1.64716
\(330\) 0 0
\(331\) −7.36380 −0.404751 −0.202375 0.979308i \(-0.564866\pi\)
−0.202375 + 0.979308i \(0.564866\pi\)
\(332\) 0 0
\(333\) 6.87153 0.376558
\(334\) 0 0
\(335\) 10.3695 0.566545
\(336\) 0 0
\(337\) 12.2355 0.666512 0.333256 0.942836i \(-0.391853\pi\)
0.333256 + 0.942836i \(0.391853\pi\)
\(338\) 0 0
\(339\) −17.3036 −0.939803
\(340\) 0 0
\(341\) 6.65789 0.360545
\(342\) 0 0
\(343\) 30.7475 1.66021
\(344\) 0 0
\(345\) 8.30748 0.447260
\(346\) 0 0
\(347\) −19.3771 −1.04022 −0.520109 0.854100i \(-0.674109\pi\)
−0.520109 + 0.854100i \(0.674109\pi\)
\(348\) 0 0
\(349\) −7.13099 −0.381713 −0.190857 0.981618i \(-0.561127\pi\)
−0.190857 + 0.981618i \(0.561127\pi\)
\(350\) 0 0
\(351\) 1.93555 0.103312
\(352\) 0 0
\(353\) 10.7743 0.573457 0.286729 0.958012i \(-0.407432\pi\)
0.286729 + 0.958012i \(0.407432\pi\)
\(354\) 0 0
\(355\) 2.09062 0.110959
\(356\) 0 0
\(357\) −34.6046 −1.83147
\(358\) 0 0
\(359\) 21.8570 1.15357 0.576784 0.816896i \(-0.304307\pi\)
0.576784 + 0.816896i \(0.304307\pi\)
\(360\) 0 0
\(361\) 0.601031 0.0316332
\(362\) 0 0
\(363\) −16.4012 −0.860838
\(364\) 0 0
\(365\) −4.89759 −0.256352
\(366\) 0 0
\(367\) 0.0341568 0.00178297 0.000891485 1.00000i \(-0.499716\pi\)
0.000891485 1.00000i \(0.499716\pi\)
\(368\) 0 0
\(369\) 8.71632 0.453754
\(370\) 0 0
\(371\) 17.9466 0.931740
\(372\) 0 0
\(373\) −4.34690 −0.225074 −0.112537 0.993648i \(-0.535898\pi\)
−0.112537 + 0.993648i \(0.535898\pi\)
\(374\) 0 0
\(375\) 10.5821 0.546460
\(376\) 0 0
\(377\) −7.22469 −0.372090
\(378\) 0 0
\(379\) −32.2351 −1.65581 −0.827904 0.560870i \(-0.810467\pi\)
−0.827904 + 0.560870i \(0.810467\pi\)
\(380\) 0 0
\(381\) 7.88097 0.403754
\(382\) 0 0
\(383\) −23.6117 −1.20650 −0.603250 0.797552i \(-0.706128\pi\)
−0.603250 + 0.797552i \(0.706128\pi\)
\(384\) 0 0
\(385\) 29.9650 1.52716
\(386\) 0 0
\(387\) −5.25563 −0.267159
\(388\) 0 0
\(389\) −31.0376 −1.57367 −0.786834 0.617164i \(-0.788281\pi\)
−0.786834 + 0.617164i \(0.788281\pi\)
\(390\) 0 0
\(391\) −50.2195 −2.53971
\(392\) 0 0
\(393\) 20.2297 1.02045
\(394\) 0 0
\(395\) −7.81028 −0.392978
\(396\) 0 0
\(397\) 3.95462 0.198476 0.0992382 0.995064i \(-0.468359\pi\)
0.0992382 + 0.995064i \(0.468359\pi\)
\(398\) 0 0
\(399\) −20.1673 −1.00963
\(400\) 0 0
\(401\) 19.9560 0.996556 0.498278 0.867017i \(-0.333966\pi\)
0.498278 + 0.867017i \(0.333966\pi\)
\(402\) 0 0
\(403\) −2.46182 −0.122632
\(404\) 0 0
\(405\) 1.25667 0.0624445
\(406\) 0 0
\(407\) 35.9698 1.78296
\(408\) 0 0
\(409\) 38.6158 1.90943 0.954714 0.297524i \(-0.0961607\pi\)
0.954714 + 0.297524i \(0.0961607\pi\)
\(410\) 0 0
\(411\) 3.73853 0.184408
\(412\) 0 0
\(413\) −56.2780 −2.76926
\(414\) 0 0
\(415\) −17.7340 −0.870526
\(416\) 0 0
\(417\) 13.1822 0.645534
\(418\) 0 0
\(419\) −4.87110 −0.237969 −0.118984 0.992896i \(-0.537964\pi\)
−0.118984 + 0.992896i \(0.537964\pi\)
\(420\) 0 0
\(421\) 10.1671 0.495512 0.247756 0.968822i \(-0.420307\pi\)
0.247756 + 0.968822i \(0.420307\pi\)
\(422\) 0 0
\(423\) 6.55882 0.318901
\(424\) 0 0
\(425\) −25.9866 −1.26054
\(426\) 0 0
\(427\) −1.28620 −0.0622435
\(428\) 0 0
\(429\) 10.1318 0.489170
\(430\) 0 0
\(431\) 34.5825 1.66578 0.832890 0.553438i \(-0.186685\pi\)
0.832890 + 0.553438i \(0.186685\pi\)
\(432\) 0 0
\(433\) −30.2208 −1.45232 −0.726160 0.687526i \(-0.758697\pi\)
−0.726160 + 0.687526i \(0.758697\pi\)
\(434\) 0 0
\(435\) −4.69069 −0.224901
\(436\) 0 0
\(437\) −29.2676 −1.40006
\(438\) 0 0
\(439\) −3.35552 −0.160150 −0.0800751 0.996789i \(-0.525516\pi\)
−0.0800751 + 0.996789i \(0.525516\pi\)
\(440\) 0 0
\(441\) 13.7500 0.654760
\(442\) 0 0
\(443\) −24.9007 −1.18307 −0.591533 0.806281i \(-0.701477\pi\)
−0.591533 + 0.806281i \(0.701477\pi\)
\(444\) 0 0
\(445\) −8.71584 −0.413170
\(446\) 0 0
\(447\) 16.0892 0.760993
\(448\) 0 0
\(449\) 23.2157 1.09562 0.547808 0.836604i \(-0.315463\pi\)
0.547808 + 0.836604i \(0.315463\pi\)
\(450\) 0 0
\(451\) 45.6266 2.14847
\(452\) 0 0
\(453\) 19.2676 0.905270
\(454\) 0 0
\(455\) −11.0799 −0.519432
\(456\) 0 0
\(457\) −1.56399 −0.0731602 −0.0365801 0.999331i \(-0.511646\pi\)
−0.0365801 + 0.999331i \(0.511646\pi\)
\(458\) 0 0
\(459\) −7.59670 −0.354583
\(460\) 0 0
\(461\) −19.9153 −0.927550 −0.463775 0.885953i \(-0.653505\pi\)
−0.463775 + 0.885953i \(0.653505\pi\)
\(462\) 0 0
\(463\) −26.9153 −1.25086 −0.625431 0.780280i \(-0.715077\pi\)
−0.625431 + 0.780280i \(0.715077\pi\)
\(464\) 0 0
\(465\) −1.59836 −0.0741221
\(466\) 0 0
\(467\) 39.6163 1.83322 0.916611 0.399780i \(-0.130913\pi\)
0.916611 + 0.399780i \(0.130913\pi\)
\(468\) 0 0
\(469\) 37.5875 1.73563
\(470\) 0 0
\(471\) 8.92368 0.411182
\(472\) 0 0
\(473\) −27.5112 −1.26497
\(474\) 0 0
\(475\) −15.1448 −0.694892
\(476\) 0 0
\(477\) 3.93979 0.180391
\(478\) 0 0
\(479\) −38.0876 −1.74027 −0.870134 0.492815i \(-0.835968\pi\)
−0.870134 + 0.492815i \(0.835968\pi\)
\(480\) 0 0
\(481\) −13.3002 −0.606436
\(482\) 0 0
\(483\) 30.1132 1.37020
\(484\) 0 0
\(485\) −3.91994 −0.177995
\(486\) 0 0
\(487\) 4.70083 0.213015 0.106508 0.994312i \(-0.466033\pi\)
0.106508 + 0.994312i \(0.466033\pi\)
\(488\) 0 0
\(489\) −2.94760 −0.133295
\(490\) 0 0
\(491\) −26.9587 −1.21663 −0.608315 0.793696i \(-0.708154\pi\)
−0.608315 + 0.793696i \(0.708154\pi\)
\(492\) 0 0
\(493\) 28.3556 1.27707
\(494\) 0 0
\(495\) 6.57819 0.295667
\(496\) 0 0
\(497\) 7.57813 0.339926
\(498\) 0 0
\(499\) 29.4450 1.31814 0.659069 0.752082i \(-0.270950\pi\)
0.659069 + 0.752082i \(0.270950\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) −27.2438 −1.21474 −0.607371 0.794418i \(-0.707776\pi\)
−0.607371 + 0.794418i \(0.707776\pi\)
\(504\) 0 0
\(505\) 14.9142 0.663674
\(506\) 0 0
\(507\) 9.25365 0.410969
\(508\) 0 0
\(509\) 5.63468 0.249753 0.124876 0.992172i \(-0.460147\pi\)
0.124876 + 0.992172i \(0.460147\pi\)
\(510\) 0 0
\(511\) −17.7529 −0.785342
\(512\) 0 0
\(513\) −4.42731 −0.195470
\(514\) 0 0
\(515\) 2.91230 0.128331
\(516\) 0 0
\(517\) 34.3329 1.50996
\(518\) 0 0
\(519\) 12.5486 0.550824
\(520\) 0 0
\(521\) −6.45179 −0.282658 −0.141329 0.989963i \(-0.545138\pi\)
−0.141329 + 0.989963i \(0.545138\pi\)
\(522\) 0 0
\(523\) −4.82181 −0.210843 −0.105422 0.994428i \(-0.533619\pi\)
−0.105422 + 0.994428i \(0.533619\pi\)
\(524\) 0 0
\(525\) 15.5824 0.680070
\(526\) 0 0
\(527\) 9.66222 0.420893
\(528\) 0 0
\(529\) 20.7015 0.900063
\(530\) 0 0
\(531\) −12.3546 −0.536145
\(532\) 0 0
\(533\) −16.8709 −0.730759
\(534\) 0 0
\(535\) 1.94983 0.0842984
\(536\) 0 0
\(537\) 3.07676 0.132772
\(538\) 0 0
\(539\) 71.9757 3.10021
\(540\) 0 0
\(541\) 35.7479 1.53692 0.768461 0.639896i \(-0.221023\pi\)
0.768461 + 0.639896i \(0.221023\pi\)
\(542\) 0 0
\(543\) −2.50830 −0.107641
\(544\) 0 0
\(545\) 6.75080 0.289172
\(546\) 0 0
\(547\) −2.22907 −0.0953084 −0.0476542 0.998864i \(-0.515175\pi\)
−0.0476542 + 0.998864i \(0.515175\pi\)
\(548\) 0 0
\(549\) −0.282357 −0.0120507
\(550\) 0 0
\(551\) 16.5255 0.704009
\(552\) 0 0
\(553\) −28.3109 −1.20390
\(554\) 0 0
\(555\) −8.63525 −0.366546
\(556\) 0 0
\(557\) 14.8215 0.628008 0.314004 0.949422i \(-0.398330\pi\)
0.314004 + 0.949422i \(0.398330\pi\)
\(558\) 0 0
\(559\) 10.1725 0.430252
\(560\) 0 0
\(561\) −39.7658 −1.67891
\(562\) 0 0
\(563\) 21.1799 0.892627 0.446314 0.894877i \(-0.352737\pi\)
0.446314 + 0.894877i \(0.352737\pi\)
\(564\) 0 0
\(565\) 21.7449 0.914817
\(566\) 0 0
\(567\) 4.55521 0.191301
\(568\) 0 0
\(569\) −7.59884 −0.318560 −0.159280 0.987233i \(-0.550917\pi\)
−0.159280 + 0.987233i \(0.550917\pi\)
\(570\) 0 0
\(571\) 10.3154 0.431688 0.215844 0.976428i \(-0.430750\pi\)
0.215844 + 0.976428i \(0.430750\pi\)
\(572\) 0 0
\(573\) −3.30849 −0.138214
\(574\) 0 0
\(575\) 22.6138 0.943059
\(576\) 0 0
\(577\) 16.2672 0.677211 0.338605 0.940928i \(-0.390045\pi\)
0.338605 + 0.940928i \(0.390045\pi\)
\(578\) 0 0
\(579\) 18.4096 0.765078
\(580\) 0 0
\(581\) −64.2825 −2.66689
\(582\) 0 0
\(583\) 20.6233 0.854129
\(584\) 0 0
\(585\) −2.43235 −0.100565
\(586\) 0 0
\(587\) 26.5861 1.09733 0.548664 0.836043i \(-0.315137\pi\)
0.548664 + 0.836043i \(0.315137\pi\)
\(588\) 0 0
\(589\) 5.63108 0.232025
\(590\) 0 0
\(591\) 13.0745 0.537813
\(592\) 0 0
\(593\) 11.4438 0.469939 0.234969 0.972003i \(-0.424501\pi\)
0.234969 + 0.972003i \(0.424501\pi\)
\(594\) 0 0
\(595\) 43.4866 1.78277
\(596\) 0 0
\(597\) −18.8563 −0.771736
\(598\) 0 0
\(599\) −17.6317 −0.720410 −0.360205 0.932873i \(-0.617293\pi\)
−0.360205 + 0.932873i \(0.617293\pi\)
\(600\) 0 0
\(601\) −5.54770 −0.226295 −0.113148 0.993578i \(-0.536093\pi\)
−0.113148 + 0.993578i \(0.536093\pi\)
\(602\) 0 0
\(603\) 8.25155 0.336029
\(604\) 0 0
\(605\) 20.6109 0.837951
\(606\) 0 0
\(607\) −21.5641 −0.875259 −0.437630 0.899155i \(-0.644182\pi\)
−0.437630 + 0.899155i \(0.644182\pi\)
\(608\) 0 0
\(609\) −17.0029 −0.688993
\(610\) 0 0
\(611\) −12.6949 −0.513581
\(612\) 0 0
\(613\) 47.5125 1.91901 0.959506 0.281687i \(-0.0908939\pi\)
0.959506 + 0.281687i \(0.0908939\pi\)
\(614\) 0 0
\(615\) −10.9536 −0.441690
\(616\) 0 0
\(617\) −3.79509 −0.152785 −0.0763923 0.997078i \(-0.524340\pi\)
−0.0763923 + 0.997078i \(0.524340\pi\)
\(618\) 0 0
\(619\) −10.0986 −0.405898 −0.202949 0.979189i \(-0.565053\pi\)
−0.202949 + 0.979189i \(0.565053\pi\)
\(620\) 0 0
\(621\) 6.61071 0.265279
\(622\) 0 0
\(623\) −31.5934 −1.26576
\(624\) 0 0
\(625\) 3.80561 0.152224
\(626\) 0 0
\(627\) −23.1752 −0.925529
\(628\) 0 0
\(629\) 52.2009 2.08139
\(630\) 0 0
\(631\) 30.5310 1.21542 0.607709 0.794160i \(-0.292089\pi\)
0.607709 + 0.794160i \(0.292089\pi\)
\(632\) 0 0
\(633\) 7.39616 0.293971
\(634\) 0 0
\(635\) −9.90379 −0.393020
\(636\) 0 0
\(637\) −26.6137 −1.05447
\(638\) 0 0
\(639\) 1.66362 0.0658117
\(640\) 0 0
\(641\) −3.23785 −0.127887 −0.0639437 0.997954i \(-0.520368\pi\)
−0.0639437 + 0.997954i \(0.520368\pi\)
\(642\) 0 0
\(643\) 30.2108 1.19140 0.595698 0.803209i \(-0.296876\pi\)
0.595698 + 0.803209i \(0.296876\pi\)
\(644\) 0 0
\(645\) 6.60460 0.260056
\(646\) 0 0
\(647\) 31.9382 1.25562 0.627810 0.778367i \(-0.283952\pi\)
0.627810 + 0.778367i \(0.283952\pi\)
\(648\) 0 0
\(649\) −64.6717 −2.53859
\(650\) 0 0
\(651\) −5.79377 −0.227076
\(652\) 0 0
\(653\) −21.2765 −0.832613 −0.416307 0.909224i \(-0.636676\pi\)
−0.416307 + 0.909224i \(0.636676\pi\)
\(654\) 0 0
\(655\) −25.4221 −0.993324
\(656\) 0 0
\(657\) −3.89727 −0.152047
\(658\) 0 0
\(659\) 20.4493 0.796593 0.398297 0.917257i \(-0.369601\pi\)
0.398297 + 0.917257i \(0.369601\pi\)
\(660\) 0 0
\(661\) 22.9118 0.891165 0.445582 0.895241i \(-0.352997\pi\)
0.445582 + 0.895241i \(0.352997\pi\)
\(662\) 0 0
\(663\) 14.7038 0.571047
\(664\) 0 0
\(665\) 25.3437 0.982786
\(666\) 0 0
\(667\) −24.6753 −0.955432
\(668\) 0 0
\(669\) −1.81997 −0.0703641
\(670\) 0 0
\(671\) −1.47803 −0.0570588
\(672\) 0 0
\(673\) 29.8721 1.15149 0.575743 0.817630i \(-0.304713\pi\)
0.575743 + 0.817630i \(0.304713\pi\)
\(674\) 0 0
\(675\) 3.42078 0.131666
\(676\) 0 0
\(677\) −10.0786 −0.387353 −0.193676 0.981065i \(-0.562041\pi\)
−0.193676 + 0.981065i \(0.562041\pi\)
\(678\) 0 0
\(679\) −14.2091 −0.545295
\(680\) 0 0
\(681\) 21.8780 0.838365
\(682\) 0 0
\(683\) −17.1938 −0.657901 −0.328951 0.944347i \(-0.606695\pi\)
−0.328951 + 0.944347i \(0.606695\pi\)
\(684\) 0 0
\(685\) −4.69810 −0.179505
\(686\) 0 0
\(687\) −1.04962 −0.0400455
\(688\) 0 0
\(689\) −7.62566 −0.290515
\(690\) 0 0
\(691\) −4.30843 −0.163900 −0.0819502 0.996636i \(-0.526115\pi\)
−0.0819502 + 0.996636i \(0.526115\pi\)
\(692\) 0 0
\(693\) 23.8448 0.905788
\(694\) 0 0
\(695\) −16.5657 −0.628371
\(696\) 0 0
\(697\) 66.2153 2.50808
\(698\) 0 0
\(699\) 17.9898 0.680435
\(700\) 0 0
\(701\) −20.4059 −0.770720 −0.385360 0.922766i \(-0.625923\pi\)
−0.385360 + 0.922766i \(0.625923\pi\)
\(702\) 0 0
\(703\) 30.4224 1.14740
\(704\) 0 0
\(705\) −8.24227 −0.310422
\(706\) 0 0
\(707\) 54.0614 2.03319
\(708\) 0 0
\(709\) −8.65515 −0.325051 −0.162525 0.986704i \(-0.551964\pi\)
−0.162525 + 0.986704i \(0.551964\pi\)
\(710\) 0 0
\(711\) −6.21505 −0.233083
\(712\) 0 0
\(713\) −8.40815 −0.314888
\(714\) 0 0
\(715\) −12.7324 −0.476165
\(716\) 0 0
\(717\) −27.1655 −1.01452
\(718\) 0 0
\(719\) 37.7603 1.40822 0.704111 0.710090i \(-0.251346\pi\)
0.704111 + 0.710090i \(0.251346\pi\)
\(720\) 0 0
\(721\) 10.5566 0.393148
\(722\) 0 0
\(723\) −21.7168 −0.807657
\(724\) 0 0
\(725\) −12.7685 −0.474210
\(726\) 0 0
\(727\) −50.5464 −1.87466 −0.937332 0.348438i \(-0.886712\pi\)
−0.937332 + 0.348438i \(0.886712\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −39.9254 −1.47669
\(732\) 0 0
\(733\) 45.7422 1.68953 0.844763 0.535140i \(-0.179741\pi\)
0.844763 + 0.535140i \(0.179741\pi\)
\(734\) 0 0
\(735\) −17.2792 −0.637352
\(736\) 0 0
\(737\) 43.1936 1.59106
\(738\) 0 0
\(739\) −9.01671 −0.331685 −0.165842 0.986152i \(-0.553034\pi\)
−0.165842 + 0.986152i \(0.553034\pi\)
\(740\) 0 0
\(741\) 8.56927 0.314800
\(742\) 0 0
\(743\) −24.8707 −0.912416 −0.456208 0.889873i \(-0.650793\pi\)
−0.456208 + 0.889873i \(0.650793\pi\)
\(744\) 0 0
\(745\) −20.2188 −0.740761
\(746\) 0 0
\(747\) −14.1118 −0.516326
\(748\) 0 0
\(749\) 7.06778 0.258251
\(750\) 0 0
\(751\) 50.0545 1.82652 0.913258 0.407382i \(-0.133558\pi\)
0.913258 + 0.407382i \(0.133558\pi\)
\(752\) 0 0
\(753\) 30.4390 1.10926
\(754\) 0 0
\(755\) −24.2130 −0.881201
\(756\) 0 0
\(757\) 6.17487 0.224430 0.112215 0.993684i \(-0.464206\pi\)
0.112215 + 0.993684i \(0.464206\pi\)
\(758\) 0 0
\(759\) 34.6045 1.25606
\(760\) 0 0
\(761\) −29.9236 −1.08473 −0.542365 0.840143i \(-0.682471\pi\)
−0.542365 + 0.840143i \(0.682471\pi\)
\(762\) 0 0
\(763\) 24.4705 0.885890
\(764\) 0 0
\(765\) 9.54655 0.345156
\(766\) 0 0
\(767\) 23.9130 0.863448
\(768\) 0 0
\(769\) −18.6073 −0.670995 −0.335497 0.942041i \(-0.608904\pi\)
−0.335497 + 0.942041i \(0.608904\pi\)
\(770\) 0 0
\(771\) 23.0748 0.831020
\(772\) 0 0
\(773\) 29.9797 1.07830 0.539148 0.842211i \(-0.318746\pi\)
0.539148 + 0.842211i \(0.318746\pi\)
\(774\) 0 0
\(775\) −4.35088 −0.156288
\(776\) 0 0
\(777\) −31.3013 −1.12293
\(778\) 0 0
\(779\) 38.5898 1.38262
\(780\) 0 0
\(781\) 8.70839 0.311611
\(782\) 0 0
\(783\) −3.73263 −0.133393
\(784\) 0 0
\(785\) −11.2141 −0.400250
\(786\) 0 0
\(787\) −37.9894 −1.35417 −0.677087 0.735903i \(-0.736758\pi\)
−0.677087 + 0.735903i \(0.736758\pi\)
\(788\) 0 0
\(789\) 21.5164 0.766004
\(790\) 0 0
\(791\) 78.8216 2.80257
\(792\) 0 0
\(793\) 0.546517 0.0194074
\(794\) 0 0
\(795\) −4.95102 −0.175595
\(796\) 0 0
\(797\) 22.2033 0.786483 0.393242 0.919435i \(-0.371354\pi\)
0.393242 + 0.919435i \(0.371354\pi\)
\(798\) 0 0
\(799\) 49.8253 1.76269
\(800\) 0 0
\(801\) −6.93566 −0.245059
\(802\) 0 0
\(803\) −20.4007 −0.719925
\(804\) 0 0
\(805\) −37.8424 −1.33377
\(806\) 0 0
\(807\) −16.2955 −0.573629
\(808\) 0 0
\(809\) −15.6829 −0.551380 −0.275690 0.961247i \(-0.588906\pi\)
−0.275690 + 0.961247i \(0.588906\pi\)
\(810\) 0 0
\(811\) −14.4336 −0.506834 −0.253417 0.967357i \(-0.581554\pi\)
−0.253417 + 0.967357i \(0.581554\pi\)
\(812\) 0 0
\(813\) −25.9830 −0.911263
\(814\) 0 0
\(815\) 3.70417 0.129751
\(816\) 0 0
\(817\) −23.2683 −0.814054
\(818\) 0 0
\(819\) −8.81684 −0.308085
\(820\) 0 0
\(821\) 9.25042 0.322842 0.161421 0.986886i \(-0.448392\pi\)
0.161421 + 0.986886i \(0.448392\pi\)
\(822\) 0 0
\(823\) 15.7006 0.547290 0.273645 0.961831i \(-0.411771\pi\)
0.273645 + 0.961831i \(0.411771\pi\)
\(824\) 0 0
\(825\) 17.9064 0.623422
\(826\) 0 0
\(827\) −30.4073 −1.05737 −0.528683 0.848819i \(-0.677314\pi\)
−0.528683 + 0.848819i \(0.677314\pi\)
\(828\) 0 0
\(829\) −38.7371 −1.34539 −0.672697 0.739918i \(-0.734864\pi\)
−0.672697 + 0.739918i \(0.734864\pi\)
\(830\) 0 0
\(831\) 8.26377 0.286667
\(832\) 0 0
\(833\) 104.454 3.61913
\(834\) 0 0
\(835\) 1.25667 0.0434889
\(836\) 0 0
\(837\) −1.27190 −0.0439632
\(838\) 0 0
\(839\) 32.4743 1.12114 0.560568 0.828108i \(-0.310583\pi\)
0.560568 + 0.828108i \(0.310583\pi\)
\(840\) 0 0
\(841\) −15.0675 −0.519568
\(842\) 0 0
\(843\) 0.956330 0.0329378
\(844\) 0 0
\(845\) −11.6288 −0.400043
\(846\) 0 0
\(847\) 74.7108 2.56709
\(848\) 0 0
\(849\) 7.81438 0.268189
\(850\) 0 0
\(851\) −45.4257 −1.55717
\(852\) 0 0
\(853\) −21.3706 −0.731716 −0.365858 0.930671i \(-0.619224\pi\)
−0.365858 + 0.930671i \(0.619224\pi\)
\(854\) 0 0
\(855\) 5.56367 0.190273
\(856\) 0 0
\(857\) −38.7853 −1.32488 −0.662440 0.749115i \(-0.730479\pi\)
−0.662440 + 0.749115i \(0.730479\pi\)
\(858\) 0 0
\(859\) −41.2770 −1.40835 −0.704176 0.710025i \(-0.748683\pi\)
−0.704176 + 0.710025i \(0.748683\pi\)
\(860\) 0 0
\(861\) −39.7047 −1.35313
\(862\) 0 0
\(863\) −3.03297 −0.103244 −0.0516218 0.998667i \(-0.516439\pi\)
−0.0516218 + 0.998667i \(0.516439\pi\)
\(864\) 0 0
\(865\) −15.7695 −0.536179
\(866\) 0 0
\(867\) −40.7098 −1.38258
\(868\) 0 0
\(869\) −32.5334 −1.10362
\(870\) 0 0
\(871\) −15.9713 −0.541166
\(872\) 0 0
\(873\) −3.11931 −0.105573
\(874\) 0 0
\(875\) −48.2039 −1.62959
\(876\) 0 0
\(877\) 26.2512 0.886439 0.443220 0.896413i \(-0.353836\pi\)
0.443220 + 0.896413i \(0.353836\pi\)
\(878\) 0 0
\(879\) 18.0569 0.609045
\(880\) 0 0
\(881\) 3.69895 0.124621 0.0623104 0.998057i \(-0.480153\pi\)
0.0623104 + 0.998057i \(0.480153\pi\)
\(882\) 0 0
\(883\) 47.7365 1.60646 0.803230 0.595669i \(-0.203113\pi\)
0.803230 + 0.595669i \(0.203113\pi\)
\(884\) 0 0
\(885\) 15.5257 0.521891
\(886\) 0 0
\(887\) −1.04390 −0.0350508 −0.0175254 0.999846i \(-0.505579\pi\)
−0.0175254 + 0.999846i \(0.505579\pi\)
\(888\) 0 0
\(889\) −35.8995 −1.20403
\(890\) 0 0
\(891\) 5.23461 0.175366
\(892\) 0 0
\(893\) 29.0379 0.971716
\(894\) 0 0
\(895\) −3.86647 −0.129242
\(896\) 0 0
\(897\) −12.7954 −0.427224
\(898\) 0 0
\(899\) 4.74752 0.158339
\(900\) 0 0
\(901\) 29.9294 0.997093
\(902\) 0 0
\(903\) 23.9405 0.796690
\(904\) 0 0
\(905\) 3.15210 0.104779
\(906\) 0 0
\(907\) 15.2974 0.507943 0.253971 0.967212i \(-0.418263\pi\)
0.253971 + 0.967212i \(0.418263\pi\)
\(908\) 0 0
\(909\) 11.8680 0.393638
\(910\) 0 0
\(911\) 33.8233 1.12062 0.560308 0.828285i \(-0.310683\pi\)
0.560308 + 0.828285i \(0.310683\pi\)
\(912\) 0 0
\(913\) −73.8701 −2.44474
\(914\) 0 0
\(915\) 0.354830 0.0117303
\(916\) 0 0
\(917\) −92.1507 −3.04308
\(918\) 0 0
\(919\) 18.1404 0.598396 0.299198 0.954191i \(-0.403281\pi\)
0.299198 + 0.954191i \(0.403281\pi\)
\(920\) 0 0
\(921\) −26.9495 −0.888018
\(922\) 0 0
\(923\) −3.22001 −0.105988
\(924\) 0 0
\(925\) −23.5060 −0.772872
\(926\) 0 0
\(927\) 2.31747 0.0761158
\(928\) 0 0
\(929\) −49.9152 −1.63767 −0.818833 0.574032i \(-0.805378\pi\)
−0.818833 + 0.574032i \(0.805378\pi\)
\(930\) 0 0
\(931\) 60.8753 1.99511
\(932\) 0 0
\(933\) −7.51738 −0.246108
\(934\) 0 0
\(935\) 49.9725 1.63427
\(936\) 0 0
\(937\) −45.2081 −1.47689 −0.738443 0.674316i \(-0.764438\pi\)
−0.738443 + 0.674316i \(0.764438\pi\)
\(938\) 0 0
\(939\) −24.9480 −0.814148
\(940\) 0 0
\(941\) 0.416944 0.0135920 0.00679599 0.999977i \(-0.497837\pi\)
0.00679599 + 0.999977i \(0.497837\pi\)
\(942\) 0 0
\(943\) −57.6211 −1.87640
\(944\) 0 0
\(945\) −5.72440 −0.186215
\(946\) 0 0
\(947\) 40.5028 1.31616 0.658082 0.752946i \(-0.271368\pi\)
0.658082 + 0.752946i \(0.271368\pi\)
\(948\) 0 0
\(949\) 7.54336 0.244868
\(950\) 0 0
\(951\) −28.0071 −0.908192
\(952\) 0 0
\(953\) 46.8908 1.51894 0.759470 0.650542i \(-0.225458\pi\)
0.759470 + 0.650542i \(0.225458\pi\)
\(954\) 0 0
\(955\) 4.15768 0.134539
\(956\) 0 0
\(957\) −19.5389 −0.631602
\(958\) 0 0
\(959\) −17.0298 −0.549920
\(960\) 0 0
\(961\) −29.3823 −0.947815
\(962\) 0 0
\(963\) 1.55158 0.0499990
\(964\) 0 0
\(965\) −23.1349 −0.744737
\(966\) 0 0
\(967\) 28.5237 0.917262 0.458631 0.888627i \(-0.348340\pi\)
0.458631 + 0.888627i \(0.348340\pi\)
\(968\) 0 0
\(969\) −33.6329 −1.08044
\(970\) 0 0
\(971\) −32.4613 −1.04173 −0.520867 0.853638i \(-0.674391\pi\)
−0.520867 + 0.853638i \(0.674391\pi\)
\(972\) 0 0
\(973\) −60.0476 −1.92504
\(974\) 0 0
\(975\) −6.62108 −0.212044
\(976\) 0 0
\(977\) 29.7999 0.953382 0.476691 0.879071i \(-0.341836\pi\)
0.476691 + 0.879071i \(0.341836\pi\)
\(978\) 0 0
\(979\) −36.3055 −1.16033
\(980\) 0 0
\(981\) 5.37197 0.171514
\(982\) 0 0
\(983\) 17.3606 0.553717 0.276859 0.960911i \(-0.410707\pi\)
0.276859 + 0.960911i \(0.410707\pi\)
\(984\) 0 0
\(985\) −16.4304 −0.523515
\(986\) 0 0
\(987\) −29.8768 −0.950989
\(988\) 0 0
\(989\) 34.7434 1.10478
\(990\) 0 0
\(991\) 6.60573 0.209838 0.104919 0.994481i \(-0.466542\pi\)
0.104919 + 0.994481i \(0.466542\pi\)
\(992\) 0 0
\(993\) 7.36380 0.233683
\(994\) 0 0
\(995\) 23.6961 0.751218
\(996\) 0 0
\(997\) 0.907767 0.0287493 0.0143746 0.999897i \(-0.495424\pi\)
0.0143746 + 0.999897i \(0.495424\pi\)
\(998\) 0 0
\(999\) −6.87153 −0.217406
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 \(a_p\))