Properties

Label 8016.2.a.bf.1.12
Level 8016
Weight 2
Character 8016.1
Self dual Yes
Analytic conductor 64.008
Analytic rank 1
Dimension 12
CM No
Inner twists 1

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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: \(1\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
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 1.12
Root \(3.77676\)
Character \(\chi\) = 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(+3.77676 q^{5}\) \(+1.75359 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(+3.77676 q^{5}\) \(+1.75359 q^{7}\) \(+1.00000 q^{9}\) \(-2.41460 q^{11}\) \(-1.58092 q^{13}\) \(-3.77676 q^{15}\) \(+0.811189 q^{17}\) \(-3.41955 q^{19}\) \(-1.75359 q^{21}\) \(-6.93574 q^{23}\) \(+9.26390 q^{25}\) \(-1.00000 q^{27}\) \(-0.520367 q^{29}\) \(+3.53773 q^{31}\) \(+2.41460 q^{33}\) \(+6.62290 q^{35}\) \(-9.20908 q^{37}\) \(+1.58092 q^{39}\) \(-3.31600 q^{41}\) \(-6.00002 q^{43}\) \(+3.77676 q^{45}\) \(-12.4567 q^{47}\) \(-3.92491 q^{49}\) \(-0.811189 q^{51}\) \(+12.1117 q^{53}\) \(-9.11937 q^{55}\) \(+3.41955 q^{57}\) \(+10.0728 q^{59}\) \(-13.5319 q^{61}\) \(+1.75359 q^{63}\) \(-5.97076 q^{65}\) \(+14.1817 q^{67}\) \(+6.93574 q^{69}\) \(-11.5259 q^{71}\) \(+3.71440 q^{73}\) \(-9.26390 q^{75}\) \(-4.23423 q^{77}\) \(-12.9098 q^{79}\) \(+1.00000 q^{81}\) \(-13.0558 q^{83}\) \(+3.06367 q^{85}\) \(+0.520367 q^{87}\) \(+0.129594 q^{89}\) \(-2.77230 q^{91}\) \(-3.53773 q^{93}\) \(-12.9148 q^{95}\) \(-11.6438 q^{97}\) \(-2.41460 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut -\mathstrut q^{11} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 11q^{21} \) \(\mathstrut -\mathstrut 7q^{23} \) \(\mathstrut +\mathstrut 18q^{25} \) \(\mathstrut -\mathstrut 12q^{27} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 33q^{31} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut -\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 4q^{45} \) \(\mathstrut -\mathstrut 18q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 20q^{53} \) \(\mathstrut -\mathstrut 39q^{55} \) \(\mathstrut +\mathstrut 12q^{57} \) \(\mathstrut -\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 10q^{61} \) \(\mathstrut -\mathstrut 11q^{63} \) \(\mathstrut -\mathstrut 9q^{67} \) \(\mathstrut +\mathstrut 7q^{69} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 18q^{75} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut -\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 12q^{81} \) \(\mathstrut -\mathstrut 26q^{83} \) \(\mathstrut +\mathstrut 15q^{85} \) \(\mathstrut -\mathstrut 5q^{87} \) \(\mathstrut -\mathstrut 15q^{89} \) \(\mathstrut -\mathstrut 11q^{91} \) \(\mathstrut +\mathstrut 33q^{93} \) \(\mathstrut -\mathstrut 3q^{95} \) \(\mathstrut +\mathstrut 8q^{97} \) \(\mathstrut -\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 3.77676 1.68902 0.844509 0.535542i \(-0.179892\pi\)
0.844509 + 0.535542i \(0.179892\pi\)
\(6\) 0 0
\(7\) 1.75359 0.662796 0.331398 0.943491i \(-0.392480\pi\)
0.331398 + 0.943491i \(0.392480\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −2.41460 −0.728030 −0.364015 0.931393i \(-0.618594\pi\)
−0.364015 + 0.931393i \(0.618594\pi\)
\(12\) 0 0
\(13\) −1.58092 −0.438469 −0.219235 0.975672i \(-0.570356\pi\)
−0.219235 + 0.975672i \(0.570356\pi\)
\(14\) 0 0
\(15\) −3.77676 −0.975155
\(16\) 0 0
\(17\) 0.811189 0.196742 0.0983712 0.995150i \(-0.468637\pi\)
0.0983712 + 0.995150i \(0.468637\pi\)
\(18\) 0 0
\(19\) −3.41955 −0.784498 −0.392249 0.919859i \(-0.628303\pi\)
−0.392249 + 0.919859i \(0.628303\pi\)
\(20\) 0 0
\(21\) −1.75359 −0.382665
\(22\) 0 0
\(23\) −6.93574 −1.44620 −0.723101 0.690742i \(-0.757284\pi\)
−0.723101 + 0.690742i \(0.757284\pi\)
\(24\) 0 0
\(25\) 9.26390 1.85278
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −0.520367 −0.0966297 −0.0483149 0.998832i \(-0.515385\pi\)
−0.0483149 + 0.998832i \(0.515385\pi\)
\(30\) 0 0
\(31\) 3.53773 0.635394 0.317697 0.948192i \(-0.397090\pi\)
0.317697 + 0.948192i \(0.397090\pi\)
\(32\) 0 0
\(33\) 2.41460 0.420328
\(34\) 0 0
\(35\) 6.62290 1.11947
\(36\) 0 0
\(37\) −9.20908 −1.51396 −0.756982 0.653436i \(-0.773327\pi\)
−0.756982 + 0.653436i \(0.773327\pi\)
\(38\) 0 0
\(39\) 1.58092 0.253150
\(40\) 0 0
\(41\) −3.31600 −0.517873 −0.258936 0.965894i \(-0.583372\pi\)
−0.258936 + 0.965894i \(0.583372\pi\)
\(42\) 0 0
\(43\) −6.00002 −0.914995 −0.457498 0.889211i \(-0.651254\pi\)
−0.457498 + 0.889211i \(0.651254\pi\)
\(44\) 0 0
\(45\) 3.77676 0.563006
\(46\) 0 0
\(47\) −12.4567 −1.81699 −0.908496 0.417893i \(-0.862769\pi\)
−0.908496 + 0.417893i \(0.862769\pi\)
\(48\) 0 0
\(49\) −3.92491 −0.560701
\(50\) 0 0
\(51\) −0.811189 −0.113589
\(52\) 0 0
\(53\) 12.1117 1.66368 0.831838 0.555019i \(-0.187289\pi\)
0.831838 + 0.555019i \(0.187289\pi\)
\(54\) 0 0
\(55\) −9.11937 −1.22966
\(56\) 0 0
\(57\) 3.41955 0.452930
\(58\) 0 0
\(59\) 10.0728 1.31137 0.655683 0.755036i \(-0.272381\pi\)
0.655683 + 0.755036i \(0.272381\pi\)
\(60\) 0 0
\(61\) −13.5319 −1.73258 −0.866289 0.499544i \(-0.833501\pi\)
−0.866289 + 0.499544i \(0.833501\pi\)
\(62\) 0 0
\(63\) 1.75359 0.220932
\(64\) 0 0
\(65\) −5.97076 −0.740582
\(66\) 0 0
\(67\) 14.1817 1.73257 0.866286 0.499548i \(-0.166500\pi\)
0.866286 + 0.499548i \(0.166500\pi\)
\(68\) 0 0
\(69\) 6.93574 0.834965
\(70\) 0 0
\(71\) −11.5259 −1.36787 −0.683934 0.729544i \(-0.739732\pi\)
−0.683934 + 0.729544i \(0.739732\pi\)
\(72\) 0 0
\(73\) 3.71440 0.434738 0.217369 0.976089i \(-0.430252\pi\)
0.217369 + 0.976089i \(0.430252\pi\)
\(74\) 0 0
\(75\) −9.26390 −1.06970
\(76\) 0 0
\(77\) −4.23423 −0.482536
\(78\) 0 0
\(79\) −12.9098 −1.45246 −0.726232 0.687450i \(-0.758730\pi\)
−0.726232 + 0.687450i \(0.758730\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −13.0558 −1.43306 −0.716532 0.697554i \(-0.754272\pi\)
−0.716532 + 0.697554i \(0.754272\pi\)
\(84\) 0 0
\(85\) 3.06367 0.332301
\(86\) 0 0
\(87\) 0.520367 0.0557892
\(88\) 0 0
\(89\) 0.129594 0.0137369 0.00686844 0.999976i \(-0.497814\pi\)
0.00686844 + 0.999976i \(0.497814\pi\)
\(90\) 0 0
\(91\) −2.77230 −0.290616
\(92\) 0 0
\(93\) −3.53773 −0.366845
\(94\) 0 0
\(95\) −12.9148 −1.32503
\(96\) 0 0
\(97\) −11.6438 −1.18225 −0.591123 0.806582i \(-0.701315\pi\)
−0.591123 + 0.806582i \(0.701315\pi\)
\(98\) 0 0
\(99\) −2.41460 −0.242677
\(100\) 0 0
\(101\) 9.16093 0.911547 0.455773 0.890096i \(-0.349363\pi\)
0.455773 + 0.890096i \(0.349363\pi\)
\(102\) 0 0
\(103\) 2.06620 0.203589 0.101794 0.994805i \(-0.467542\pi\)
0.101794 + 0.994805i \(0.467542\pi\)
\(104\) 0 0
\(105\) −6.62290 −0.646329
\(106\) 0 0
\(107\) −3.49830 −0.338194 −0.169097 0.985599i \(-0.554085\pi\)
−0.169097 + 0.985599i \(0.554085\pi\)
\(108\) 0 0
\(109\) 8.78182 0.841146 0.420573 0.907259i \(-0.361829\pi\)
0.420573 + 0.907259i \(0.361829\pi\)
\(110\) 0 0
\(111\) 9.20908 0.874087
\(112\) 0 0
\(113\) −0.230019 −0.0216384 −0.0108192 0.999941i \(-0.503444\pi\)
−0.0108192 + 0.999941i \(0.503444\pi\)
\(114\) 0 0
\(115\) −26.1946 −2.44266
\(116\) 0 0
\(117\) −1.58092 −0.146156
\(118\) 0 0
\(119\) 1.42250 0.130400
\(120\) 0 0
\(121\) −5.16969 −0.469972
\(122\) 0 0
\(123\) 3.31600 0.298994
\(124\) 0 0
\(125\) 16.1037 1.44036
\(126\) 0 0
\(127\) 11.4655 1.01740 0.508698 0.860945i \(-0.330127\pi\)
0.508698 + 0.860945i \(0.330127\pi\)
\(128\) 0 0
\(129\) 6.00002 0.528273
\(130\) 0 0
\(131\) −18.3513 −1.60336 −0.801680 0.597754i \(-0.796060\pi\)
−0.801680 + 0.597754i \(0.796060\pi\)
\(132\) 0 0
\(133\) −5.99650 −0.519962
\(134\) 0 0
\(135\) −3.77676 −0.325052
\(136\) 0 0
\(137\) −16.8506 −1.43964 −0.719822 0.694159i \(-0.755776\pi\)
−0.719822 + 0.694159i \(0.755776\pi\)
\(138\) 0 0
\(139\) −11.9744 −1.01566 −0.507830 0.861458i \(-0.669552\pi\)
−0.507830 + 0.861458i \(0.669552\pi\)
\(140\) 0 0
\(141\) 12.4567 1.04904
\(142\) 0 0
\(143\) 3.81730 0.319219
\(144\) 0 0
\(145\) −1.96530 −0.163209
\(146\) 0 0
\(147\) 3.92491 0.323721
\(148\) 0 0
\(149\) 8.00922 0.656141 0.328071 0.944653i \(-0.393602\pi\)
0.328071 + 0.944653i \(0.393602\pi\)
\(150\) 0 0
\(151\) −11.3118 −0.920545 −0.460272 0.887778i \(-0.652248\pi\)
−0.460272 + 0.887778i \(0.652248\pi\)
\(152\) 0 0
\(153\) 0.811189 0.0655808
\(154\) 0 0
\(155\) 13.3611 1.07319
\(156\) 0 0
\(157\) −16.7028 −1.33303 −0.666514 0.745492i \(-0.732215\pi\)
−0.666514 + 0.745492i \(0.732215\pi\)
\(158\) 0 0
\(159\) −12.1117 −0.960523
\(160\) 0 0
\(161\) −12.1625 −0.958537
\(162\) 0 0
\(163\) 15.1384 1.18573 0.592864 0.805302i \(-0.297997\pi\)
0.592864 + 0.805302i \(0.297997\pi\)
\(164\) 0 0
\(165\) 9.11937 0.709942
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) −10.5007 −0.807745
\(170\) 0 0
\(171\) −3.41955 −0.261499
\(172\) 0 0
\(173\) −19.6112 −1.49101 −0.745507 0.666498i \(-0.767792\pi\)
−0.745507 + 0.666498i \(0.767792\pi\)
\(174\) 0 0
\(175\) 16.2451 1.22802
\(176\) 0 0
\(177\) −10.0728 −0.757117
\(178\) 0 0
\(179\) 9.58562 0.716463 0.358231 0.933633i \(-0.383380\pi\)
0.358231 + 0.933633i \(0.383380\pi\)
\(180\) 0 0
\(181\) 11.6532 0.866176 0.433088 0.901352i \(-0.357424\pi\)
0.433088 + 0.901352i \(0.357424\pi\)
\(182\) 0 0
\(183\) 13.5319 1.00030
\(184\) 0 0
\(185\) −34.7805 −2.55711
\(186\) 0 0
\(187\) −1.95870 −0.143234
\(188\) 0 0
\(189\) −1.75359 −0.127555
\(190\) 0 0
\(191\) 4.42341 0.320067 0.160034 0.987112i \(-0.448840\pi\)
0.160034 + 0.987112i \(0.448840\pi\)
\(192\) 0 0
\(193\) 18.6988 1.34597 0.672983 0.739658i \(-0.265013\pi\)
0.672983 + 0.739658i \(0.265013\pi\)
\(194\) 0 0
\(195\) 5.97076 0.427575
\(196\) 0 0
\(197\) 13.0189 0.927557 0.463778 0.885951i \(-0.346493\pi\)
0.463778 + 0.885951i \(0.346493\pi\)
\(198\) 0 0
\(199\) −1.19991 −0.0850596 −0.0425298 0.999095i \(-0.513542\pi\)
−0.0425298 + 0.999095i \(0.513542\pi\)
\(200\) 0 0
\(201\) −14.1817 −1.00030
\(202\) 0 0
\(203\) −0.912512 −0.0640458
\(204\) 0 0
\(205\) −12.5237 −0.874696
\(206\) 0 0
\(207\) −6.93574 −0.482067
\(208\) 0 0
\(209\) 8.25685 0.571139
\(210\) 0 0
\(211\) 0.264859 0.0182336 0.00911681 0.999958i \(-0.497098\pi\)
0.00911681 + 0.999958i \(0.497098\pi\)
\(212\) 0 0
\(213\) 11.5259 0.789739
\(214\) 0 0
\(215\) −22.6606 −1.54544
\(216\) 0 0
\(217\) 6.20373 0.421137
\(218\) 0 0
\(219\) −3.71440 −0.250996
\(220\) 0 0
\(221\) −1.28243 −0.0862654
\(222\) 0 0
\(223\) 10.3649 0.694086 0.347043 0.937849i \(-0.387186\pi\)
0.347043 + 0.937849i \(0.387186\pi\)
\(224\) 0 0
\(225\) 9.26390 0.617594
\(226\) 0 0
\(227\) 8.46824 0.562057 0.281028 0.959699i \(-0.409324\pi\)
0.281028 + 0.959699i \(0.409324\pi\)
\(228\) 0 0
\(229\) 0.0378672 0.00250233 0.00125117 0.999999i \(-0.499602\pi\)
0.00125117 + 0.999999i \(0.499602\pi\)
\(230\) 0 0
\(231\) 4.23423 0.278592
\(232\) 0 0
\(233\) 1.89120 0.123896 0.0619482 0.998079i \(-0.480269\pi\)
0.0619482 + 0.998079i \(0.480269\pi\)
\(234\) 0 0
\(235\) −47.0458 −3.06893
\(236\) 0 0
\(237\) 12.9098 0.838580
\(238\) 0 0
\(239\) 18.5619 1.20067 0.600334 0.799749i \(-0.295034\pi\)
0.600334 + 0.799749i \(0.295034\pi\)
\(240\) 0 0
\(241\) 28.3402 1.82555 0.912776 0.408462i \(-0.133935\pi\)
0.912776 + 0.408462i \(0.133935\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −14.8234 −0.947035
\(246\) 0 0
\(247\) 5.40604 0.343978
\(248\) 0 0
\(249\) 13.0558 0.827380
\(250\) 0 0
\(251\) 13.7155 0.865717 0.432858 0.901462i \(-0.357505\pi\)
0.432858 + 0.901462i \(0.357505\pi\)
\(252\) 0 0
\(253\) 16.7471 1.05288
\(254\) 0 0
\(255\) −3.06367 −0.191854
\(256\) 0 0
\(257\) 24.7495 1.54383 0.771917 0.635724i \(-0.219298\pi\)
0.771917 + 0.635724i \(0.219298\pi\)
\(258\) 0 0
\(259\) −16.1490 −1.00345
\(260\) 0 0
\(261\) −0.520367 −0.0322099
\(262\) 0 0
\(263\) 6.68918 0.412472 0.206236 0.978502i \(-0.433879\pi\)
0.206236 + 0.978502i \(0.433879\pi\)
\(264\) 0 0
\(265\) 45.7431 2.80998
\(266\) 0 0
\(267\) −0.129594 −0.00793099
\(268\) 0 0
\(269\) −13.4921 −0.822628 −0.411314 0.911494i \(-0.634930\pi\)
−0.411314 + 0.911494i \(0.634930\pi\)
\(270\) 0 0
\(271\) 23.0913 1.40270 0.701349 0.712818i \(-0.252582\pi\)
0.701349 + 0.712818i \(0.252582\pi\)
\(272\) 0 0
\(273\) 2.77230 0.167787
\(274\) 0 0
\(275\) −22.3687 −1.34888
\(276\) 0 0
\(277\) 10.5004 0.630906 0.315453 0.948941i \(-0.397843\pi\)
0.315453 + 0.948941i \(0.397843\pi\)
\(278\) 0 0
\(279\) 3.53773 0.211798
\(280\) 0 0
\(281\) 7.39023 0.440864 0.220432 0.975402i \(-0.429253\pi\)
0.220432 + 0.975402i \(0.429253\pi\)
\(282\) 0 0
\(283\) 10.2756 0.610819 0.305410 0.952221i \(-0.401207\pi\)
0.305410 + 0.952221i \(0.401207\pi\)
\(284\) 0 0
\(285\) 12.9148 0.765007
\(286\) 0 0
\(287\) −5.81492 −0.343244
\(288\) 0 0
\(289\) −16.3420 −0.961292
\(290\) 0 0
\(291\) 11.6438 0.682570
\(292\) 0 0
\(293\) −11.5362 −0.673950 −0.336975 0.941514i \(-0.609404\pi\)
−0.336975 + 0.941514i \(0.609404\pi\)
\(294\) 0 0
\(295\) 38.0425 2.21492
\(296\) 0 0
\(297\) 2.41460 0.140109
\(298\) 0 0
\(299\) 10.9649 0.634115
\(300\) 0 0
\(301\) −10.5216 −0.606455
\(302\) 0 0
\(303\) −9.16093 −0.526282
\(304\) 0 0
\(305\) −51.1066 −2.92635
\(306\) 0 0
\(307\) 30.0628 1.71577 0.857887 0.513839i \(-0.171777\pi\)
0.857887 + 0.513839i \(0.171777\pi\)
\(308\) 0 0
\(309\) −2.06620 −0.117542
\(310\) 0 0
\(311\) −3.22673 −0.182971 −0.0914856 0.995806i \(-0.529162\pi\)
−0.0914856 + 0.995806i \(0.529162\pi\)
\(312\) 0 0
\(313\) 17.2220 0.973448 0.486724 0.873556i \(-0.338192\pi\)
0.486724 + 0.873556i \(0.338192\pi\)
\(314\) 0 0
\(315\) 6.62290 0.373158
\(316\) 0 0
\(317\) 8.51767 0.478400 0.239200 0.970970i \(-0.423115\pi\)
0.239200 + 0.970970i \(0.423115\pi\)
\(318\) 0 0
\(319\) 1.25648 0.0703494
\(320\) 0 0
\(321\) 3.49830 0.195256
\(322\) 0 0
\(323\) −2.77390 −0.154344
\(324\) 0 0
\(325\) −14.6455 −0.812387
\(326\) 0 0
\(327\) −8.78182 −0.485636
\(328\) 0 0
\(329\) −21.8439 −1.20430
\(330\) 0 0
\(331\) −15.5876 −0.856770 −0.428385 0.903596i \(-0.640917\pi\)
−0.428385 + 0.903596i \(0.640917\pi\)
\(332\) 0 0
\(333\) −9.20908 −0.504655
\(334\) 0 0
\(335\) 53.5609 2.92635
\(336\) 0 0
\(337\) −24.7917 −1.35049 −0.675246 0.737593i \(-0.735962\pi\)
−0.675246 + 0.737593i \(0.735962\pi\)
\(338\) 0 0
\(339\) 0.230019 0.0124929
\(340\) 0 0
\(341\) −8.54220 −0.462586
\(342\) 0 0
\(343\) −19.1579 −1.03443
\(344\) 0 0
\(345\) 26.1946 1.41027
\(346\) 0 0
\(347\) −20.0028 −1.07380 −0.536902 0.843645i \(-0.680406\pi\)
−0.536902 + 0.843645i \(0.680406\pi\)
\(348\) 0 0
\(349\) 12.8599 0.688374 0.344187 0.938901i \(-0.388155\pi\)
0.344187 + 0.938901i \(0.388155\pi\)
\(350\) 0 0
\(351\) 1.58092 0.0843834
\(352\) 0 0
\(353\) −17.4529 −0.928922 −0.464461 0.885594i \(-0.653752\pi\)
−0.464461 + 0.885594i \(0.653752\pi\)
\(354\) 0 0
\(355\) −43.5304 −2.31035
\(356\) 0 0
\(357\) −1.42250 −0.0752865
\(358\) 0 0
\(359\) 29.6090 1.56270 0.781352 0.624091i \(-0.214531\pi\)
0.781352 + 0.624091i \(0.214531\pi\)
\(360\) 0 0
\(361\) −7.30668 −0.384562
\(362\) 0 0
\(363\) 5.16969 0.271338
\(364\) 0 0
\(365\) 14.0284 0.734281
\(366\) 0 0
\(367\) −30.1359 −1.57308 −0.786540 0.617540i \(-0.788129\pi\)
−0.786540 + 0.617540i \(0.788129\pi\)
\(368\) 0 0
\(369\) −3.31600 −0.172624
\(370\) 0 0
\(371\) 21.2391 1.10268
\(372\) 0 0
\(373\) 10.0710 0.521458 0.260729 0.965412i \(-0.416037\pi\)
0.260729 + 0.965412i \(0.416037\pi\)
\(374\) 0 0
\(375\) −16.1037 −0.831593
\(376\) 0 0
\(377\) 0.822660 0.0423691
\(378\) 0 0
\(379\) 10.7931 0.554407 0.277203 0.960811i \(-0.410592\pi\)
0.277203 + 0.960811i \(0.410592\pi\)
\(380\) 0 0
\(381\) −11.4655 −0.587394
\(382\) 0 0
\(383\) −35.0045 −1.78865 −0.894323 0.447422i \(-0.852342\pi\)
−0.894323 + 0.447422i \(0.852342\pi\)
\(384\) 0 0
\(385\) −15.9917 −0.815011
\(386\) 0 0
\(387\) −6.00002 −0.304998
\(388\) 0 0
\(389\) 12.6554 0.641655 0.320828 0.947138i \(-0.396039\pi\)
0.320828 + 0.947138i \(0.396039\pi\)
\(390\) 0 0
\(391\) −5.62620 −0.284529
\(392\) 0 0
\(393\) 18.3513 0.925700
\(394\) 0 0
\(395\) −48.7571 −2.45324
\(396\) 0 0
\(397\) 23.1156 1.16014 0.580069 0.814567i \(-0.303025\pi\)
0.580069 + 0.814567i \(0.303025\pi\)
\(398\) 0 0
\(399\) 5.99650 0.300200
\(400\) 0 0
\(401\) −11.3533 −0.566956 −0.283478 0.958979i \(-0.591488\pi\)
−0.283478 + 0.958979i \(0.591488\pi\)
\(402\) 0 0
\(403\) −5.59287 −0.278601
\(404\) 0 0
\(405\) 3.77676 0.187669
\(406\) 0 0
\(407\) 22.2363 1.10221
\(408\) 0 0
\(409\) −33.5045 −1.65669 −0.828346 0.560217i \(-0.810718\pi\)
−0.828346 + 0.560217i \(0.810718\pi\)
\(410\) 0 0
\(411\) 16.8506 0.831178
\(412\) 0 0
\(413\) 17.6636 0.869168
\(414\) 0 0
\(415\) −49.3087 −2.42047
\(416\) 0 0
\(417\) 11.9744 0.586391
\(418\) 0 0
\(419\) −26.2541 −1.28260 −0.641299 0.767291i \(-0.721604\pi\)
−0.641299 + 0.767291i \(0.721604\pi\)
\(420\) 0 0
\(421\) −27.5746 −1.34390 −0.671951 0.740596i \(-0.734543\pi\)
−0.671951 + 0.740596i \(0.734543\pi\)
\(422\) 0 0
\(423\) −12.4567 −0.605664
\(424\) 0 0
\(425\) 7.51478 0.364520
\(426\) 0 0
\(427\) −23.7294 −1.14835
\(428\) 0 0
\(429\) −3.81730 −0.184301
\(430\) 0 0
\(431\) 24.4575 1.17808 0.589039 0.808105i \(-0.299507\pi\)
0.589039 + 0.808105i \(0.299507\pi\)
\(432\) 0 0
\(433\) −2.62253 −0.126031 −0.0630153 0.998013i \(-0.520072\pi\)
−0.0630153 + 0.998013i \(0.520072\pi\)
\(434\) 0 0
\(435\) 1.96530 0.0942289
\(436\) 0 0
\(437\) 23.7171 1.13454
\(438\) 0 0
\(439\) −29.1576 −1.39161 −0.695807 0.718228i \(-0.744953\pi\)
−0.695807 + 0.718228i \(0.744953\pi\)
\(440\) 0 0
\(441\) −3.92491 −0.186900
\(442\) 0 0
\(443\) 40.5738 1.92772 0.963859 0.266411i \(-0.0858379\pi\)
0.963859 + 0.266411i \(0.0858379\pi\)
\(444\) 0 0
\(445\) 0.489443 0.0232018
\(446\) 0 0
\(447\) −8.00922 −0.378823
\(448\) 0 0
\(449\) −27.1601 −1.28176 −0.640881 0.767640i \(-0.721431\pi\)
−0.640881 + 0.767640i \(0.721431\pi\)
\(450\) 0 0
\(451\) 8.00683 0.377027
\(452\) 0 0
\(453\) 11.3118 0.531477
\(454\) 0 0
\(455\) −10.4703 −0.490855
\(456\) 0 0
\(457\) −39.8219 −1.86279 −0.931396 0.364007i \(-0.881408\pi\)
−0.931396 + 0.364007i \(0.881408\pi\)
\(458\) 0 0
\(459\) −0.811189 −0.0378631
\(460\) 0 0
\(461\) 29.6135 1.37924 0.689618 0.724173i \(-0.257778\pi\)
0.689618 + 0.724173i \(0.257778\pi\)
\(462\) 0 0
\(463\) −2.07428 −0.0964001 −0.0482000 0.998838i \(-0.515348\pi\)
−0.0482000 + 0.998838i \(0.515348\pi\)
\(464\) 0 0
\(465\) −13.3611 −0.619608
\(466\) 0 0
\(467\) −9.02001 −0.417396 −0.208698 0.977980i \(-0.566923\pi\)
−0.208698 + 0.977980i \(0.566923\pi\)
\(468\) 0 0
\(469\) 24.8690 1.14834
\(470\) 0 0
\(471\) 16.7028 0.769625
\(472\) 0 0
\(473\) 14.4877 0.666144
\(474\) 0 0
\(475\) −31.6784 −1.45350
\(476\) 0 0
\(477\) 12.1117 0.554558
\(478\) 0 0
\(479\) 25.6751 1.17312 0.586562 0.809904i \(-0.300481\pi\)
0.586562 + 0.809904i \(0.300481\pi\)
\(480\) 0 0
\(481\) 14.5588 0.663826
\(482\) 0 0
\(483\) 12.1625 0.553412
\(484\) 0 0
\(485\) −43.9757 −1.99683
\(486\) 0 0
\(487\) −1.17918 −0.0534337 −0.0267169 0.999643i \(-0.508505\pi\)
−0.0267169 + 0.999643i \(0.508505\pi\)
\(488\) 0 0
\(489\) −15.1384 −0.684581
\(490\) 0 0
\(491\) −3.20030 −0.144428 −0.0722138 0.997389i \(-0.523006\pi\)
−0.0722138 + 0.997389i \(0.523006\pi\)
\(492\) 0 0
\(493\) −0.422116 −0.0190112
\(494\) 0 0
\(495\) −9.11937 −0.409885
\(496\) 0 0
\(497\) −20.2117 −0.906617
\(498\) 0 0
\(499\) −30.2627 −1.35475 −0.677373 0.735640i \(-0.736882\pi\)
−0.677373 + 0.735640i \(0.736882\pi\)
\(500\) 0 0
\(501\) 1.00000 0.0446767
\(502\) 0 0
\(503\) −8.41219 −0.375081 −0.187540 0.982257i \(-0.560052\pi\)
−0.187540 + 0.982257i \(0.560052\pi\)
\(504\) 0 0
\(505\) 34.5986 1.53962
\(506\) 0 0
\(507\) 10.5007 0.466352
\(508\) 0 0
\(509\) −31.2162 −1.38363 −0.691816 0.722074i \(-0.743189\pi\)
−0.691816 + 0.722074i \(0.743189\pi\)
\(510\) 0 0
\(511\) 6.51356 0.288143
\(512\) 0 0
\(513\) 3.41955 0.150977
\(514\) 0 0
\(515\) 7.80354 0.343865
\(516\) 0 0
\(517\) 30.0779 1.32283
\(518\) 0 0
\(519\) 19.6112 0.860837
\(520\) 0 0
\(521\) 2.42706 0.106331 0.0531656 0.998586i \(-0.483069\pi\)
0.0531656 + 0.998586i \(0.483069\pi\)
\(522\) 0 0
\(523\) −10.6211 −0.464429 −0.232214 0.972665i \(-0.574597\pi\)
−0.232214 + 0.972665i \(0.574597\pi\)
\(524\) 0 0
\(525\) −16.2451 −0.708995
\(526\) 0 0
\(527\) 2.86977 0.125009
\(528\) 0 0
\(529\) 25.1045 1.09150
\(530\) 0 0
\(531\) 10.0728 0.437122
\(532\) 0 0
\(533\) 5.24235 0.227071
\(534\) 0 0
\(535\) −13.2123 −0.571215
\(536\) 0 0
\(537\) −9.58562 −0.413650
\(538\) 0 0
\(539\) 9.47710 0.408208
\(540\) 0 0
\(541\) −19.6519 −0.844902 −0.422451 0.906386i \(-0.638830\pi\)
−0.422451 + 0.906386i \(0.638830\pi\)
\(542\) 0 0
\(543\) −11.6532 −0.500087
\(544\) 0 0
\(545\) 33.1668 1.42071
\(546\) 0 0
\(547\) −19.2002 −0.820941 −0.410471 0.911874i \(-0.634636\pi\)
−0.410471 + 0.911874i \(0.634636\pi\)
\(548\) 0 0
\(549\) −13.5319 −0.577526
\(550\) 0 0
\(551\) 1.77942 0.0758059
\(552\) 0 0
\(553\) −22.6385 −0.962687
\(554\) 0 0
\(555\) 34.7805 1.47635
\(556\) 0 0
\(557\) 16.0785 0.681268 0.340634 0.940196i \(-0.389358\pi\)
0.340634 + 0.940196i \(0.389358\pi\)
\(558\) 0 0
\(559\) 9.48558 0.401197
\(560\) 0 0
\(561\) 1.95870 0.0826964
\(562\) 0 0
\(563\) −32.0926 −1.35254 −0.676270 0.736654i \(-0.736405\pi\)
−0.676270 + 0.736654i \(0.736405\pi\)
\(564\) 0 0
\(565\) −0.868728 −0.0365476
\(566\) 0 0
\(567\) 1.75359 0.0736440
\(568\) 0 0
\(569\) 11.5180 0.482861 0.241430 0.970418i \(-0.422383\pi\)
0.241430 + 0.970418i \(0.422383\pi\)
\(570\) 0 0
\(571\) 12.7614 0.534050 0.267025 0.963690i \(-0.413959\pi\)
0.267025 + 0.963690i \(0.413959\pi\)
\(572\) 0 0
\(573\) −4.42341 −0.184791
\(574\) 0 0
\(575\) −64.2521 −2.67950
\(576\) 0 0
\(577\) −20.3828 −0.848546 −0.424273 0.905534i \(-0.639470\pi\)
−0.424273 + 0.905534i \(0.639470\pi\)
\(578\) 0 0
\(579\) −18.6988 −0.777094
\(580\) 0 0
\(581\) −22.8946 −0.949829
\(582\) 0 0
\(583\) −29.2450 −1.21121
\(584\) 0 0
\(585\) −5.97076 −0.246861
\(586\) 0 0
\(587\) 41.5389 1.71450 0.857248 0.514904i \(-0.172173\pi\)
0.857248 + 0.514904i \(0.172173\pi\)
\(588\) 0 0
\(589\) −12.0974 −0.498466
\(590\) 0 0
\(591\) −13.0189 −0.535525
\(592\) 0 0
\(593\) 7.55642 0.310305 0.155152 0.987891i \(-0.450413\pi\)
0.155152 + 0.987891i \(0.450413\pi\)
\(594\) 0 0
\(595\) 5.37242 0.220248
\(596\) 0 0
\(597\) 1.19991 0.0491092
\(598\) 0 0
\(599\) −5.56179 −0.227249 −0.113624 0.993524i \(-0.536246\pi\)
−0.113624 + 0.993524i \(0.536246\pi\)
\(600\) 0 0
\(601\) −3.53324 −0.144124 −0.0720619 0.997400i \(-0.522958\pi\)
−0.0720619 + 0.997400i \(0.522958\pi\)
\(602\) 0 0
\(603\) 14.1817 0.577524
\(604\) 0 0
\(605\) −19.5247 −0.793791
\(606\) 0 0
\(607\) −15.0346 −0.610236 −0.305118 0.952314i \(-0.598696\pi\)
−0.305118 + 0.952314i \(0.598696\pi\)
\(608\) 0 0
\(609\) 0.912512 0.0369769
\(610\) 0 0
\(611\) 19.6930 0.796695
\(612\) 0 0
\(613\) −38.2450 −1.54470 −0.772350 0.635197i \(-0.780919\pi\)
−0.772350 + 0.635197i \(0.780919\pi\)
\(614\) 0 0
\(615\) 12.5237 0.505006
\(616\) 0 0
\(617\) 6.92434 0.278764 0.139382 0.990239i \(-0.455488\pi\)
0.139382 + 0.990239i \(0.455488\pi\)
\(618\) 0 0
\(619\) 33.8045 1.35872 0.679359 0.733806i \(-0.262258\pi\)
0.679359 + 0.733806i \(0.262258\pi\)
\(620\) 0 0
\(621\) 6.93574 0.278322
\(622\) 0 0
\(623\) 0.227254 0.00910475
\(624\) 0 0
\(625\) 14.5004 0.580016
\(626\) 0 0
\(627\) −8.25685 −0.329747
\(628\) 0 0
\(629\) −7.47031 −0.297861
\(630\) 0 0
\(631\) −20.7676 −0.826746 −0.413373 0.910562i \(-0.635649\pi\)
−0.413373 + 0.910562i \(0.635649\pi\)
\(632\) 0 0
\(633\) −0.264859 −0.0105272
\(634\) 0 0
\(635\) 43.3023 1.71840
\(636\) 0 0
\(637\) 6.20498 0.245850
\(638\) 0 0
\(639\) −11.5259 −0.455956
\(640\) 0 0
\(641\) −42.4228 −1.67560 −0.837800 0.545977i \(-0.816158\pi\)
−0.837800 + 0.545977i \(0.816158\pi\)
\(642\) 0 0
\(643\) 17.1884 0.677844 0.338922 0.940814i \(-0.389938\pi\)
0.338922 + 0.940814i \(0.389938\pi\)
\(644\) 0 0
\(645\) 22.6606 0.892262
\(646\) 0 0
\(647\) 33.9398 1.33431 0.667155 0.744919i \(-0.267512\pi\)
0.667155 + 0.744919i \(0.267512\pi\)
\(648\) 0 0
\(649\) −24.3218 −0.954714
\(650\) 0 0
\(651\) −6.20373 −0.243143
\(652\) 0 0
\(653\) −3.87635 −0.151693 −0.0758466 0.997119i \(-0.524166\pi\)
−0.0758466 + 0.997119i \(0.524166\pi\)
\(654\) 0 0
\(655\) −69.3084 −2.70810
\(656\) 0 0
\(657\) 3.71440 0.144913
\(658\) 0 0
\(659\) −23.8087 −0.927457 −0.463728 0.885977i \(-0.653489\pi\)
−0.463728 + 0.885977i \(0.653489\pi\)
\(660\) 0 0
\(661\) 3.05094 0.118668 0.0593340 0.998238i \(-0.481102\pi\)
0.0593340 + 0.998238i \(0.481102\pi\)
\(662\) 0 0
\(663\) 1.28243 0.0498054
\(664\) 0 0
\(665\) −22.6473 −0.878226
\(666\) 0 0
\(667\) 3.60913 0.139746
\(668\) 0 0
\(669\) −10.3649 −0.400731
\(670\) 0 0
\(671\) 32.6741 1.26137
\(672\) 0 0
\(673\) −15.3106 −0.590180 −0.295090 0.955469i \(-0.595350\pi\)
−0.295090 + 0.955469i \(0.595350\pi\)
\(674\) 0 0
\(675\) −9.26390 −0.356568
\(676\) 0 0
\(677\) 16.9262 0.650526 0.325263 0.945624i \(-0.394547\pi\)
0.325263 + 0.945624i \(0.394547\pi\)
\(678\) 0 0
\(679\) −20.4184 −0.783588
\(680\) 0 0
\(681\) −8.46824 −0.324504
\(682\) 0 0
\(683\) 1.54551 0.0591372 0.0295686 0.999563i \(-0.490587\pi\)
0.0295686 + 0.999563i \(0.490587\pi\)
\(684\) 0 0
\(685\) −63.6406 −2.43158
\(686\) 0 0
\(687\) −0.0378672 −0.00144472
\(688\) 0 0
\(689\) −19.1477 −0.729470
\(690\) 0 0
\(691\) 30.5564 1.16242 0.581211 0.813753i \(-0.302579\pi\)
0.581211 + 0.813753i \(0.302579\pi\)
\(692\) 0 0
\(693\) −4.23423 −0.160845
\(694\) 0 0
\(695\) −45.2246 −1.71547
\(696\) 0 0
\(697\) −2.68991 −0.101887
\(698\) 0 0
\(699\) −1.89120 −0.0715316
\(700\) 0 0
\(701\) −38.5235 −1.45501 −0.727507 0.686100i \(-0.759321\pi\)
−0.727507 + 0.686100i \(0.759321\pi\)
\(702\) 0 0
\(703\) 31.4909 1.18770
\(704\) 0 0
\(705\) 47.0458 1.77185
\(706\) 0 0
\(707\) 16.0646 0.604170
\(708\) 0 0
\(709\) 19.4274 0.729610 0.364805 0.931084i \(-0.381136\pi\)
0.364805 + 0.931084i \(0.381136\pi\)
\(710\) 0 0
\(711\) −12.9098 −0.484155
\(712\) 0 0
\(713\) −24.5368 −0.918909
\(714\) 0 0
\(715\) 14.4170 0.539166
\(716\) 0 0
\(717\) −18.5619 −0.693206
\(718\) 0 0
\(719\) −2.55899 −0.0954341 −0.0477170 0.998861i \(-0.515195\pi\)
−0.0477170 + 0.998861i \(0.515195\pi\)
\(720\) 0 0
\(721\) 3.62328 0.134938
\(722\) 0 0
\(723\) −28.3402 −1.05398
\(724\) 0 0
\(725\) −4.82063 −0.179034
\(726\) 0 0
\(727\) −20.2028 −0.749282 −0.374641 0.927170i \(-0.622234\pi\)
−0.374641 + 0.927170i \(0.622234\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −4.86716 −0.180018
\(732\) 0 0
\(733\) 16.2646 0.600745 0.300372 0.953822i \(-0.402889\pi\)
0.300372 + 0.953822i \(0.402889\pi\)
\(734\) 0 0
\(735\) 14.8234 0.546771
\(736\) 0 0
\(737\) −34.2432 −1.26137
\(738\) 0 0
\(739\) 47.8478 1.76011 0.880054 0.474873i \(-0.157506\pi\)
0.880054 + 0.474873i \(0.157506\pi\)
\(740\) 0 0
\(741\) −5.40604 −0.198596
\(742\) 0 0
\(743\) 33.1597 1.21651 0.608256 0.793741i \(-0.291870\pi\)
0.608256 + 0.793741i \(0.291870\pi\)
\(744\) 0 0
\(745\) 30.2489 1.10823
\(746\) 0 0
\(747\) −13.0558 −0.477688
\(748\) 0 0
\(749\) −6.13460 −0.224154
\(750\) 0 0
\(751\) −43.8667 −1.60072 −0.800359 0.599521i \(-0.795358\pi\)
−0.800359 + 0.599521i \(0.795358\pi\)
\(752\) 0 0
\(753\) −13.7155 −0.499822
\(754\) 0 0
\(755\) −42.7221 −1.55482
\(756\) 0 0
\(757\) −47.8859 −1.74044 −0.870221 0.492661i \(-0.836024\pi\)
−0.870221 + 0.492661i \(0.836024\pi\)
\(758\) 0 0
\(759\) −16.7471 −0.607880
\(760\) 0 0
\(761\) 14.3472 0.520084 0.260042 0.965597i \(-0.416264\pi\)
0.260042 + 0.965597i \(0.416264\pi\)
\(762\) 0 0
\(763\) 15.3997 0.557508
\(764\) 0 0
\(765\) 3.06367 0.110767
\(766\) 0 0
\(767\) −15.9243 −0.574993
\(768\) 0 0
\(769\) 6.42450 0.231673 0.115837 0.993268i \(-0.463045\pi\)
0.115837 + 0.993268i \(0.463045\pi\)
\(770\) 0 0
\(771\) −24.7495 −0.891332
\(772\) 0 0
\(773\) 4.35272 0.156556 0.0782782 0.996932i \(-0.475058\pi\)
0.0782782 + 0.996932i \(0.475058\pi\)
\(774\) 0 0
\(775\) 32.7732 1.17725
\(776\) 0 0
\(777\) 16.1490 0.579342
\(778\) 0 0
\(779\) 11.3392 0.406270
\(780\) 0 0
\(781\) 27.8304 0.995849
\(782\) 0 0
\(783\) 0.520367 0.0185964
\(784\) 0 0
\(785\) −63.0825 −2.25151
\(786\) 0 0
\(787\) 4.33561 0.154548 0.0772739 0.997010i \(-0.475378\pi\)
0.0772739 + 0.997010i \(0.475378\pi\)
\(788\) 0 0
\(789\) −6.68918 −0.238141
\(790\) 0 0
\(791\) −0.403360 −0.0143418
\(792\) 0 0
\(793\) 21.3928 0.759682
\(794\) 0 0
\(795\) −45.7431 −1.62234
\(796\) 0 0
\(797\) −17.2783 −0.612027 −0.306014 0.952027i \(-0.598995\pi\)
−0.306014 + 0.952027i \(0.598995\pi\)
\(798\) 0 0
\(799\) −10.1047 −0.357479
\(800\) 0 0
\(801\) 0.129594 0.00457896
\(802\) 0 0
\(803\) −8.96881 −0.316503
\(804\) 0 0
\(805\) −45.9347 −1.61899
\(806\) 0 0
\(807\) 13.4921 0.474945
\(808\) 0 0
\(809\) 15.9662 0.561342 0.280671 0.959804i \(-0.409443\pi\)
0.280671 + 0.959804i \(0.409443\pi\)
\(810\) 0 0
\(811\) 49.3014 1.73121 0.865603 0.500731i \(-0.166935\pi\)
0.865603 + 0.500731i \(0.166935\pi\)
\(812\) 0 0
\(813\) −23.0913 −0.809848
\(814\) 0 0
\(815\) 57.1740 2.00272
\(816\) 0 0
\(817\) 20.5174 0.717812
\(818\) 0 0
\(819\) −2.77230 −0.0968719
\(820\) 0 0
\(821\) 38.2189 1.33385 0.666924 0.745126i \(-0.267610\pi\)
0.666924 + 0.745126i \(0.267610\pi\)
\(822\) 0 0
\(823\) 14.4225 0.502736 0.251368 0.967892i \(-0.419119\pi\)
0.251368 + 0.967892i \(0.419119\pi\)
\(824\) 0 0
\(825\) 22.3687 0.778777
\(826\) 0 0
\(827\) 34.6869 1.20618 0.603090 0.797673i \(-0.293936\pi\)
0.603090 + 0.797673i \(0.293936\pi\)
\(828\) 0 0
\(829\) −43.5439 −1.51234 −0.756171 0.654375i \(-0.772932\pi\)
−0.756171 + 0.654375i \(0.772932\pi\)
\(830\) 0 0
\(831\) −10.5004 −0.364254
\(832\) 0 0
\(833\) −3.18385 −0.110314
\(834\) 0 0
\(835\) −3.77676 −0.130700
\(836\) 0 0
\(837\) −3.53773 −0.122282
\(838\) 0 0
\(839\) −13.1785 −0.454974 −0.227487 0.973781i \(-0.573051\pi\)
−0.227487 + 0.973781i \(0.573051\pi\)
\(840\) 0 0
\(841\) −28.7292 −0.990663
\(842\) 0 0
\(843\) −7.39023 −0.254533
\(844\) 0 0
\(845\) −39.6585 −1.36430
\(846\) 0 0
\(847\) −9.06554 −0.311496
\(848\) 0 0
\(849\) −10.2756 −0.352657
\(850\) 0 0
\(851\) 63.8718 2.18950
\(852\) 0 0
\(853\) 13.4897 0.461878 0.230939 0.972968i \(-0.425820\pi\)
0.230939 + 0.972968i \(0.425820\pi\)
\(854\) 0 0
\(855\) −12.9148 −0.441677
\(856\) 0 0
\(857\) 26.7955 0.915317 0.457659 0.889128i \(-0.348688\pi\)
0.457659 + 0.889128i \(0.348688\pi\)
\(858\) 0 0
\(859\) −46.2866 −1.57928 −0.789640 0.613571i \(-0.789732\pi\)
−0.789640 + 0.613571i \(0.789732\pi\)
\(860\) 0 0
\(861\) 5.81492 0.198172
\(862\) 0 0
\(863\) 11.0943 0.377653 0.188827 0.982010i \(-0.439532\pi\)
0.188827 + 0.982010i \(0.439532\pi\)
\(864\) 0 0
\(865\) −74.0668 −2.51835
\(866\) 0 0
\(867\) 16.3420 0.555002
\(868\) 0 0
\(869\) 31.1720 1.05744
\(870\) 0 0
\(871\) −22.4202 −0.759680
\(872\) 0 0
\(873\) −11.6438 −0.394082
\(874\) 0 0
\(875\) 28.2394 0.954666
\(876\) 0 0
\(877\) 3.85241 0.130087 0.0650433 0.997882i \(-0.479281\pi\)
0.0650433 + 0.997882i \(0.479281\pi\)
\(878\) 0 0
\(879\) 11.5362 0.389105
\(880\) 0 0
\(881\) −50.4047 −1.69818 −0.849089 0.528250i \(-0.822849\pi\)
−0.849089 + 0.528250i \(0.822849\pi\)
\(882\) 0 0
\(883\) −0.621522 −0.0209159 −0.0104579 0.999945i \(-0.503329\pi\)
−0.0104579 + 0.999945i \(0.503329\pi\)
\(884\) 0 0
\(885\) −38.0425 −1.27878
\(886\) 0 0
\(887\) −1.37732 −0.0462458 −0.0231229 0.999733i \(-0.507361\pi\)
−0.0231229 + 0.999733i \(0.507361\pi\)
\(888\) 0 0
\(889\) 20.1058 0.674326
\(890\) 0 0
\(891\) −2.41460 −0.0808923
\(892\) 0 0
\(893\) 42.5962 1.42543
\(894\) 0 0
\(895\) 36.2026 1.21012
\(896\) 0 0
\(897\) −10.9649 −0.366106
\(898\) 0 0
\(899\) −1.84092 −0.0613980
\(900\) 0 0
\(901\) 9.82491 0.327315
\(902\) 0 0
\(903\) 10.5216 0.350137
\(904\) 0 0
\(905\) 44.0113 1.46299
\(906\) 0 0
\(907\) −5.57385 −0.185077 −0.0925383 0.995709i \(-0.529498\pi\)
−0.0925383 + 0.995709i \(0.529498\pi\)
\(908\) 0 0
\(909\) 9.16093 0.303849
\(910\) 0 0
\(911\) 53.4020 1.76929 0.884644 0.466267i \(-0.154401\pi\)
0.884644 + 0.466267i \(0.154401\pi\)
\(912\) 0 0
\(913\) 31.5247 1.04331
\(914\) 0 0
\(915\) 51.1066 1.68953
\(916\) 0 0
\(917\) −32.1807 −1.06270
\(918\) 0 0
\(919\) −54.9803 −1.81363 −0.906816 0.421527i \(-0.861494\pi\)
−0.906816 + 0.421527i \(0.861494\pi\)
\(920\) 0 0
\(921\) −30.0628 −0.990602
\(922\) 0 0
\(923\) 18.2215 0.599768
\(924\) 0 0
\(925\) −85.3121 −2.80504
\(926\) 0 0
\(927\) 2.06620 0.0678630
\(928\) 0 0
\(929\) −50.7144 −1.66389 −0.831943 0.554861i \(-0.812772\pi\)
−0.831943 + 0.554861i \(0.812772\pi\)
\(930\) 0 0
\(931\) 13.4214 0.439869
\(932\) 0 0
\(933\) 3.22673 0.105638
\(934\) 0 0
\(935\) −7.39754 −0.241925
\(936\) 0 0
\(937\) 41.1997 1.34594 0.672968 0.739672i \(-0.265019\pi\)
0.672968 + 0.739672i \(0.265019\pi\)
\(938\) 0 0
\(939\) −17.2220 −0.562020
\(940\) 0 0
\(941\) 11.2604 0.367078 0.183539 0.983012i \(-0.441245\pi\)
0.183539 + 0.983012i \(0.441245\pi\)
\(942\) 0 0
\(943\) 22.9989 0.748949
\(944\) 0 0
\(945\) −6.62290 −0.215443
\(946\) 0 0
\(947\) −46.2686 −1.50353 −0.751763 0.659433i \(-0.770796\pi\)
−0.751763 + 0.659433i \(0.770796\pi\)
\(948\) 0 0
\(949\) −5.87219 −0.190619
\(950\) 0 0
\(951\) −8.51767 −0.276204
\(952\) 0 0
\(953\) 6.24795 0.202391 0.101196 0.994867i \(-0.467733\pi\)
0.101196 + 0.994867i \(0.467733\pi\)
\(954\) 0 0
\(955\) 16.7062 0.540599
\(956\) 0 0
\(957\) −1.25648 −0.0406162
\(958\) 0 0
\(959\) −29.5491 −0.954190
\(960\) 0 0
\(961\) −18.4845 −0.596274
\(962\) 0 0
\(963\) −3.49830 −0.112731
\(964\) 0 0
\(965\) 70.6207 2.27336
\(966\) 0 0
\(967\) 6.48597 0.208575 0.104287 0.994547i \(-0.466744\pi\)
0.104287 + 0.994547i \(0.466744\pi\)
\(968\) 0 0
\(969\) 2.77390 0.0891106
\(970\) 0 0
\(971\) 15.0219 0.482077 0.241038 0.970516i \(-0.422512\pi\)
0.241038 + 0.970516i \(0.422512\pi\)
\(972\) 0 0
\(973\) −20.9983 −0.673175
\(974\) 0 0
\(975\) 14.6455 0.469032
\(976\) 0 0
\(977\) 26.0541 0.833543 0.416772 0.909011i \(-0.363161\pi\)
0.416772 + 0.909011i \(0.363161\pi\)
\(978\) 0 0
\(979\) −0.312917 −0.0100009
\(980\) 0 0
\(981\) 8.78182 0.280382
\(982\) 0 0
\(983\) −3.46591 −0.110545 −0.0552727 0.998471i \(-0.517603\pi\)
−0.0552727 + 0.998471i \(0.517603\pi\)
\(984\) 0 0
\(985\) 49.1692 1.56666
\(986\) 0 0
\(987\) 21.8439 0.695300
\(988\) 0 0
\(989\) 41.6146 1.32327
\(990\) 0 0
\(991\) 31.3162 0.994791 0.497395 0.867524i \(-0.334290\pi\)
0.497395 + 0.867524i \(0.334290\pi\)
\(992\) 0 0
\(993\) 15.5876 0.494656
\(994\) 0 0
\(995\) −4.53178 −0.143667
\(996\) 0 0
\(997\) 15.0051 0.475215 0.237607 0.971361i \(-0.423637\pi\)
0.237607 + 0.971361i \(0.423637\pi\)
\(998\) 0 0
\(999\) 9.20908 0.291362
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 \(a_p\))