Properties

Label 6008.2.a.e.1.13
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(50\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.42091 q^{3}\) \(-3.43075 q^{5}\) \(+0.534513 q^{7}\) \(-0.981020 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.42091 q^{3}\) \(-3.43075 q^{5}\) \(+0.534513 q^{7}\) \(-0.981020 q^{9}\) \(+2.02073 q^{11}\) \(-1.33304 q^{13}\) \(+4.87478 q^{15}\) \(-2.74602 q^{17}\) \(-2.29614 q^{19}\) \(-0.759494 q^{21}\) \(-7.13304 q^{23}\) \(+6.77004 q^{25}\) \(+5.65666 q^{27}\) \(-7.32409 q^{29}\) \(+1.25667 q^{31}\) \(-2.87127 q^{33}\) \(-1.83378 q^{35}\) \(-2.73951 q^{37}\) \(+1.89413 q^{39}\) \(-10.4882 q^{41}\) \(+6.16757 q^{43}\) \(+3.36563 q^{45}\) \(+5.32098 q^{47}\) \(-6.71430 q^{49}\) \(+3.90184 q^{51}\) \(+2.73392 q^{53}\) \(-6.93262 q^{55}\) \(+3.26260 q^{57}\) \(+2.37055 q^{59}\) \(-2.88421 q^{61}\) \(-0.524368 q^{63}\) \(+4.57334 q^{65}\) \(-7.96331 q^{67}\) \(+10.1354 q^{69}\) \(-9.75154 q^{71}\) \(+2.03091 q^{73}\) \(-9.61961 q^{75}\) \(+1.08011 q^{77}\) \(+2.43818 q^{79}\) \(-5.09454 q^{81}\) \(-16.3530 q^{83}\) \(+9.42090 q^{85}\) \(+10.4069 q^{87}\) \(-1.73118 q^{89}\) \(-0.712528 q^{91}\) \(-1.78561 q^{93}\) \(+7.87748 q^{95}\) \(-10.8188 q^{97}\) \(-1.98238 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(50q \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 23q^{5} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 56q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(50q \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 23q^{5} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 56q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 36q^{13} \) \(\mathstrut +\mathstrut 5q^{15} \) \(\mathstrut +\mathstrut 14q^{17} \) \(\mathstrut +\mathstrut 9q^{19} \) \(\mathstrut +\mathstrut 30q^{21} \) \(\mathstrut +\mathstrut 3q^{23} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut +\mathstrut 24q^{27} \) \(\mathstrut +\mathstrut 61q^{29} \) \(\mathstrut +\mathstrut 27q^{31} \) \(\mathstrut +\mathstrut 24q^{33} \) \(\mathstrut -\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 56q^{37} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 19q^{43} \) \(\mathstrut +\mathstrut 76q^{45} \) \(\mathstrut +\mathstrut 3q^{47} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut q^{51} \) \(\mathstrut +\mathstrut 56q^{53} \) \(\mathstrut +\mathstrut 7q^{55} \) \(\mathstrut +\mathstrut 35q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut +\mathstrut 67q^{61} \) \(\mathstrut +\mathstrut 25q^{63} \) \(\mathstrut +\mathstrut 27q^{65} \) \(\mathstrut +\mathstrut 46q^{67} \) \(\mathstrut +\mathstrut 68q^{69} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut +\mathstrut 62q^{73} \) \(\mathstrut +\mathstrut 27q^{75} \) \(\mathstrut +\mathstrut 71q^{77} \) \(\mathstrut +\mathstrut 7q^{79} \) \(\mathstrut +\mathstrut 74q^{81} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut +\mathstrut 72q^{85} \) \(\mathstrut +\mathstrut 25q^{87} \) \(\mathstrut +\mathstrut 19q^{89} \) \(\mathstrut +\mathstrut 45q^{91} \) \(\mathstrut +\mathstrut 72q^{93} \) \(\mathstrut -\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 81q^{97} \) \(\mathstrut +\mathstrut 16q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.42091 −0.820362 −0.410181 0.912004i \(-0.634534\pi\)
−0.410181 + 0.912004i \(0.634534\pi\)
\(4\) 0 0
\(5\) −3.43075 −1.53428 −0.767139 0.641481i \(-0.778320\pi\)
−0.767139 + 0.641481i \(0.778320\pi\)
\(6\) 0 0
\(7\) 0.534513 0.202027 0.101013 0.994885i \(-0.467791\pi\)
0.101013 + 0.994885i \(0.467791\pi\)
\(8\) 0 0
\(9\) −0.981020 −0.327007
\(10\) 0 0
\(11\) 2.02073 0.609273 0.304637 0.952469i \(-0.401465\pi\)
0.304637 + 0.952469i \(0.401465\pi\)
\(12\) 0 0
\(13\) −1.33304 −0.369720 −0.184860 0.982765i \(-0.559183\pi\)
−0.184860 + 0.982765i \(0.559183\pi\)
\(14\) 0 0
\(15\) 4.87478 1.25866
\(16\) 0 0
\(17\) −2.74602 −0.666007 −0.333004 0.942926i \(-0.608062\pi\)
−0.333004 + 0.942926i \(0.608062\pi\)
\(18\) 0 0
\(19\) −2.29614 −0.526771 −0.263385 0.964691i \(-0.584839\pi\)
−0.263385 + 0.964691i \(0.584839\pi\)
\(20\) 0 0
\(21\) −0.759494 −0.165735
\(22\) 0 0
\(23\) −7.13304 −1.48734 −0.743671 0.668546i \(-0.766917\pi\)
−0.743671 + 0.668546i \(0.766917\pi\)
\(24\) 0 0
\(25\) 6.77004 1.35401
\(26\) 0 0
\(27\) 5.65666 1.08863
\(28\) 0 0
\(29\) −7.32409 −1.36005 −0.680025 0.733189i \(-0.738031\pi\)
−0.680025 + 0.733189i \(0.738031\pi\)
\(30\) 0 0
\(31\) 1.25667 0.225705 0.112852 0.993612i \(-0.464001\pi\)
0.112852 + 0.993612i \(0.464001\pi\)
\(32\) 0 0
\(33\) −2.87127 −0.499824
\(34\) 0 0
\(35\) −1.83378 −0.309965
\(36\) 0 0
\(37\) −2.73951 −0.450373 −0.225186 0.974316i \(-0.572299\pi\)
−0.225186 + 0.974316i \(0.572299\pi\)
\(38\) 0 0
\(39\) 1.89413 0.303304
\(40\) 0 0
\(41\) −10.4882 −1.63798 −0.818990 0.573808i \(-0.805465\pi\)
−0.818990 + 0.573808i \(0.805465\pi\)
\(42\) 0 0
\(43\) 6.16757 0.940545 0.470273 0.882521i \(-0.344156\pi\)
0.470273 + 0.882521i \(0.344156\pi\)
\(44\) 0 0
\(45\) 3.36563 0.501719
\(46\) 0 0
\(47\) 5.32098 0.776145 0.388072 0.921629i \(-0.373141\pi\)
0.388072 + 0.921629i \(0.373141\pi\)
\(48\) 0 0
\(49\) −6.71430 −0.959185
\(50\) 0 0
\(51\) 3.90184 0.546367
\(52\) 0 0
\(53\) 2.73392 0.375533 0.187766 0.982214i \(-0.439875\pi\)
0.187766 + 0.982214i \(0.439875\pi\)
\(54\) 0 0
\(55\) −6.93262 −0.934794
\(56\) 0 0
\(57\) 3.26260 0.432143
\(58\) 0 0
\(59\) 2.37055 0.308620 0.154310 0.988022i \(-0.450685\pi\)
0.154310 + 0.988022i \(0.450685\pi\)
\(60\) 0 0
\(61\) −2.88421 −0.369285 −0.184642 0.982806i \(-0.559113\pi\)
−0.184642 + 0.982806i \(0.559113\pi\)
\(62\) 0 0
\(63\) −0.524368 −0.0660641
\(64\) 0 0
\(65\) 4.57334 0.567252
\(66\) 0 0
\(67\) −7.96331 −0.972873 −0.486437 0.873716i \(-0.661704\pi\)
−0.486437 + 0.873716i \(0.661704\pi\)
\(68\) 0 0
\(69\) 10.1354 1.22016
\(70\) 0 0
\(71\) −9.75154 −1.15729 −0.578647 0.815578i \(-0.696419\pi\)
−0.578647 + 0.815578i \(0.696419\pi\)
\(72\) 0 0
\(73\) 2.03091 0.237701 0.118850 0.992912i \(-0.462079\pi\)
0.118850 + 0.992912i \(0.462079\pi\)
\(74\) 0 0
\(75\) −9.61961 −1.11078
\(76\) 0 0
\(77\) 1.08011 0.123090
\(78\) 0 0
\(79\) 2.43818 0.274317 0.137158 0.990549i \(-0.456203\pi\)
0.137158 + 0.990549i \(0.456203\pi\)
\(80\) 0 0
\(81\) −5.09454 −0.566060
\(82\) 0 0
\(83\) −16.3530 −1.79497 −0.897485 0.441044i \(-0.854608\pi\)
−0.897485 + 0.441044i \(0.854608\pi\)
\(84\) 0 0
\(85\) 9.42090 1.02184
\(86\) 0 0
\(87\) 10.4069 1.11573
\(88\) 0 0
\(89\) −1.73118 −0.183505 −0.0917524 0.995782i \(-0.529247\pi\)
−0.0917524 + 0.995782i \(0.529247\pi\)
\(90\) 0 0
\(91\) −0.712528 −0.0746933
\(92\) 0 0
\(93\) −1.78561 −0.185159
\(94\) 0 0
\(95\) 7.87748 0.808213
\(96\) 0 0
\(97\) −10.8188 −1.09848 −0.549242 0.835664i \(-0.685083\pi\)
−0.549242 + 0.835664i \(0.685083\pi\)
\(98\) 0 0
\(99\) −1.98238 −0.199236
\(100\) 0 0
\(101\) 18.6266 1.85342 0.926709 0.375779i \(-0.122625\pi\)
0.926709 + 0.375779i \(0.122625\pi\)
\(102\) 0 0
\(103\) −11.2212 −1.10566 −0.552830 0.833294i \(-0.686452\pi\)
−0.552830 + 0.833294i \(0.686452\pi\)
\(104\) 0 0
\(105\) 2.60563 0.254284
\(106\) 0 0
\(107\) −17.3155 −1.67395 −0.836976 0.547240i \(-0.815679\pi\)
−0.836976 + 0.547240i \(0.815679\pi\)
\(108\) 0 0
\(109\) −6.23092 −0.596814 −0.298407 0.954439i \(-0.596455\pi\)
−0.298407 + 0.954439i \(0.596455\pi\)
\(110\) 0 0
\(111\) 3.89259 0.369469
\(112\) 0 0
\(113\) −5.26670 −0.495450 −0.247725 0.968830i \(-0.579683\pi\)
−0.247725 + 0.968830i \(0.579683\pi\)
\(114\) 0 0
\(115\) 24.4717 2.28200
\(116\) 0 0
\(117\) 1.30774 0.120901
\(118\) 0 0
\(119\) −1.46778 −0.134551
\(120\) 0 0
\(121\) −6.91665 −0.628786
\(122\) 0 0
\(123\) 14.9028 1.34374
\(124\) 0 0
\(125\) −6.07258 −0.543148
\(126\) 0 0
\(127\) 3.62744 0.321884 0.160942 0.986964i \(-0.448547\pi\)
0.160942 + 0.986964i \(0.448547\pi\)
\(128\) 0 0
\(129\) −8.76355 −0.771587
\(130\) 0 0
\(131\) −5.36615 −0.468842 −0.234421 0.972135i \(-0.575319\pi\)
−0.234421 + 0.972135i \(0.575319\pi\)
\(132\) 0 0
\(133\) −1.22732 −0.106422
\(134\) 0 0
\(135\) −19.4066 −1.67025
\(136\) 0 0
\(137\) −12.5089 −1.06871 −0.534355 0.845260i \(-0.679445\pi\)
−0.534355 + 0.845260i \(0.679445\pi\)
\(138\) 0 0
\(139\) 11.9616 1.01457 0.507284 0.861779i \(-0.330650\pi\)
0.507284 + 0.861779i \(0.330650\pi\)
\(140\) 0 0
\(141\) −7.56062 −0.636719
\(142\) 0 0
\(143\) −2.69372 −0.225260
\(144\) 0 0
\(145\) 25.1271 2.08669
\(146\) 0 0
\(147\) 9.54040 0.786879
\(148\) 0 0
\(149\) 6.81477 0.558288 0.279144 0.960249i \(-0.409949\pi\)
0.279144 + 0.960249i \(0.409949\pi\)
\(150\) 0 0
\(151\) 11.3242 0.921554 0.460777 0.887516i \(-0.347571\pi\)
0.460777 + 0.887516i \(0.347571\pi\)
\(152\) 0 0
\(153\) 2.69390 0.217789
\(154\) 0 0
\(155\) −4.31132 −0.346294
\(156\) 0 0
\(157\) 4.15016 0.331219 0.165609 0.986191i \(-0.447041\pi\)
0.165609 + 0.986191i \(0.447041\pi\)
\(158\) 0 0
\(159\) −3.88465 −0.308073
\(160\) 0 0
\(161\) −3.81270 −0.300483
\(162\) 0 0
\(163\) 12.0540 0.944139 0.472070 0.881561i \(-0.343507\pi\)
0.472070 + 0.881561i \(0.343507\pi\)
\(164\) 0 0
\(165\) 9.85062 0.766870
\(166\) 0 0
\(167\) 22.9165 1.77334 0.886668 0.462407i \(-0.153014\pi\)
0.886668 + 0.462407i \(0.153014\pi\)
\(168\) 0 0
\(169\) −11.2230 −0.863307
\(170\) 0 0
\(171\) 2.25256 0.172257
\(172\) 0 0
\(173\) −11.2546 −0.855670 −0.427835 0.903857i \(-0.640724\pi\)
−0.427835 + 0.903857i \(0.640724\pi\)
\(174\) 0 0
\(175\) 3.61868 0.273546
\(176\) 0 0
\(177\) −3.36834 −0.253180
\(178\) 0 0
\(179\) −6.42395 −0.480148 −0.240074 0.970755i \(-0.577172\pi\)
−0.240074 + 0.970755i \(0.577172\pi\)
\(180\) 0 0
\(181\) 18.2203 1.35430 0.677150 0.735845i \(-0.263215\pi\)
0.677150 + 0.735845i \(0.263215\pi\)
\(182\) 0 0
\(183\) 4.09819 0.302947
\(184\) 0 0
\(185\) 9.39858 0.690997
\(186\) 0 0
\(187\) −5.54896 −0.405780
\(188\) 0 0
\(189\) 3.02356 0.219932
\(190\) 0 0
\(191\) −24.1949 −1.75068 −0.875341 0.483506i \(-0.839363\pi\)
−0.875341 + 0.483506i \(0.839363\pi\)
\(192\) 0 0
\(193\) 0.721920 0.0519649 0.0259825 0.999662i \(-0.491729\pi\)
0.0259825 + 0.999662i \(0.491729\pi\)
\(194\) 0 0
\(195\) −6.49829 −0.465352
\(196\) 0 0
\(197\) 18.5422 1.32108 0.660538 0.750793i \(-0.270328\pi\)
0.660538 + 0.750793i \(0.270328\pi\)
\(198\) 0 0
\(199\) 16.5856 1.17572 0.587862 0.808961i \(-0.299970\pi\)
0.587862 + 0.808961i \(0.299970\pi\)
\(200\) 0 0
\(201\) 11.3151 0.798108
\(202\) 0 0
\(203\) −3.91482 −0.274767
\(204\) 0 0
\(205\) 35.9823 2.51312
\(206\) 0 0
\(207\) 6.99765 0.486370
\(208\) 0 0
\(209\) −4.63988 −0.320947
\(210\) 0 0
\(211\) 19.2846 1.32761 0.663805 0.747906i \(-0.268941\pi\)
0.663805 + 0.747906i \(0.268941\pi\)
\(212\) 0 0
\(213\) 13.8560 0.949400
\(214\) 0 0
\(215\) −21.1594 −1.44306
\(216\) 0 0
\(217\) 0.671706 0.0455984
\(218\) 0 0
\(219\) −2.88574 −0.195000
\(220\) 0 0
\(221\) 3.66056 0.246236
\(222\) 0 0
\(223\) −6.72788 −0.450532 −0.225266 0.974297i \(-0.572325\pi\)
−0.225266 + 0.974297i \(0.572325\pi\)
\(224\) 0 0
\(225\) −6.64155 −0.442770
\(226\) 0 0
\(227\) −14.8744 −0.987245 −0.493623 0.869676i \(-0.664328\pi\)
−0.493623 + 0.869676i \(0.664328\pi\)
\(228\) 0 0
\(229\) −5.46475 −0.361121 −0.180560 0.983564i \(-0.557791\pi\)
−0.180560 + 0.983564i \(0.557791\pi\)
\(230\) 0 0
\(231\) −1.53473 −0.100978
\(232\) 0 0
\(233\) 3.81016 0.249612 0.124806 0.992181i \(-0.460169\pi\)
0.124806 + 0.992181i \(0.460169\pi\)
\(234\) 0 0
\(235\) −18.2549 −1.19082
\(236\) 0 0
\(237\) −3.46443 −0.225039
\(238\) 0 0
\(239\) 30.7876 1.99148 0.995742 0.0921882i \(-0.0293861\pi\)
0.995742 + 0.0921882i \(0.0293861\pi\)
\(240\) 0 0
\(241\) 17.9658 1.15728 0.578638 0.815585i \(-0.303584\pi\)
0.578638 + 0.815585i \(0.303584\pi\)
\(242\) 0 0
\(243\) −9.73111 −0.624251
\(244\) 0 0
\(245\) 23.0351 1.47166
\(246\) 0 0
\(247\) 3.06085 0.194757
\(248\) 0 0
\(249\) 23.2361 1.47253
\(250\) 0 0
\(251\) −3.04855 −0.192423 −0.0962113 0.995361i \(-0.530672\pi\)
−0.0962113 + 0.995361i \(0.530672\pi\)
\(252\) 0 0
\(253\) −14.4140 −0.906197
\(254\) 0 0
\(255\) −13.3862 −0.838279
\(256\) 0 0
\(257\) 17.3990 1.08532 0.542660 0.839953i \(-0.317417\pi\)
0.542660 + 0.839953i \(0.317417\pi\)
\(258\) 0 0
\(259\) −1.46430 −0.0909874
\(260\) 0 0
\(261\) 7.18508 0.444745
\(262\) 0 0
\(263\) −23.3874 −1.44213 −0.721064 0.692868i \(-0.756347\pi\)
−0.721064 + 0.692868i \(0.756347\pi\)
\(264\) 0 0
\(265\) −9.37940 −0.576172
\(266\) 0 0
\(267\) 2.45985 0.150540
\(268\) 0 0
\(269\) 19.1181 1.16565 0.582825 0.812598i \(-0.301947\pi\)
0.582825 + 0.812598i \(0.301947\pi\)
\(270\) 0 0
\(271\) −7.62607 −0.463251 −0.231625 0.972805i \(-0.574404\pi\)
−0.231625 + 0.972805i \(0.574404\pi\)
\(272\) 0 0
\(273\) 1.01244 0.0612755
\(274\) 0 0
\(275\) 13.6804 0.824961
\(276\) 0 0
\(277\) 29.6187 1.77961 0.889807 0.456336i \(-0.150839\pi\)
0.889807 + 0.456336i \(0.150839\pi\)
\(278\) 0 0
\(279\) −1.23282 −0.0738069
\(280\) 0 0
\(281\) 19.0003 1.13346 0.566731 0.823903i \(-0.308208\pi\)
0.566731 + 0.823903i \(0.308208\pi\)
\(282\) 0 0
\(283\) 18.3732 1.09217 0.546087 0.837729i \(-0.316117\pi\)
0.546087 + 0.837729i \(0.316117\pi\)
\(284\) 0 0
\(285\) −11.1932 −0.663027
\(286\) 0 0
\(287\) −5.60607 −0.330916
\(288\) 0 0
\(289\) −9.45938 −0.556434
\(290\) 0 0
\(291\) 15.3725 0.901154
\(292\) 0 0
\(293\) 29.4043 1.71782 0.858909 0.512129i \(-0.171143\pi\)
0.858909 + 0.512129i \(0.171143\pi\)
\(294\) 0 0
\(295\) −8.13278 −0.473509
\(296\) 0 0
\(297\) 11.4306 0.663270
\(298\) 0 0
\(299\) 9.50865 0.549899
\(300\) 0 0
\(301\) 3.29664 0.190015
\(302\) 0 0
\(303\) −26.4667 −1.52047
\(304\) 0 0
\(305\) 9.89499 0.566585
\(306\) 0 0
\(307\) 25.7169 1.46774 0.733871 0.679289i \(-0.237712\pi\)
0.733871 + 0.679289i \(0.237712\pi\)
\(308\) 0 0
\(309\) 15.9443 0.907041
\(310\) 0 0
\(311\) −30.0912 −1.70631 −0.853156 0.521655i \(-0.825315\pi\)
−0.853156 + 0.521655i \(0.825315\pi\)
\(312\) 0 0
\(313\) 7.10566 0.401636 0.200818 0.979629i \(-0.435640\pi\)
0.200818 + 0.979629i \(0.435640\pi\)
\(314\) 0 0
\(315\) 1.79897 0.101361
\(316\) 0 0
\(317\) 8.94735 0.502533 0.251267 0.967918i \(-0.419153\pi\)
0.251267 + 0.967918i \(0.419153\pi\)
\(318\) 0 0
\(319\) −14.8000 −0.828642
\(320\) 0 0
\(321\) 24.6037 1.37325
\(322\) 0 0
\(323\) 6.30524 0.350833
\(324\) 0 0
\(325\) −9.02476 −0.500603
\(326\) 0 0
\(327\) 8.85357 0.489604
\(328\) 0 0
\(329\) 2.84413 0.156802
\(330\) 0 0
\(331\) −4.50527 −0.247632 −0.123816 0.992305i \(-0.539513\pi\)
−0.123816 + 0.992305i \(0.539513\pi\)
\(332\) 0 0
\(333\) 2.68751 0.147275
\(334\) 0 0
\(335\) 27.3201 1.49266
\(336\) 0 0
\(337\) 30.6487 1.66954 0.834772 0.550596i \(-0.185600\pi\)
0.834772 + 0.550596i \(0.185600\pi\)
\(338\) 0 0
\(339\) 7.48350 0.406448
\(340\) 0 0
\(341\) 2.53939 0.137516
\(342\) 0 0
\(343\) −7.33047 −0.395808
\(344\) 0 0
\(345\) −34.7720 −1.87206
\(346\) 0 0
\(347\) 14.6588 0.786923 0.393462 0.919341i \(-0.371277\pi\)
0.393462 + 0.919341i \(0.371277\pi\)
\(348\) 0 0
\(349\) −27.0146 −1.44606 −0.723030 0.690817i \(-0.757251\pi\)
−0.723030 + 0.690817i \(0.757251\pi\)
\(350\) 0 0
\(351\) −7.54057 −0.402486
\(352\) 0 0
\(353\) 8.73538 0.464938 0.232469 0.972604i \(-0.425320\pi\)
0.232469 + 0.972604i \(0.425320\pi\)
\(354\) 0 0
\(355\) 33.4551 1.77561
\(356\) 0 0
\(357\) 2.08558 0.110381
\(358\) 0 0
\(359\) 1.12674 0.0594669 0.0297334 0.999558i \(-0.490534\pi\)
0.0297334 + 0.999558i \(0.490534\pi\)
\(360\) 0 0
\(361\) −13.7277 −0.722513
\(362\) 0 0
\(363\) 9.82792 0.515832
\(364\) 0 0
\(365\) −6.96756 −0.364699
\(366\) 0 0
\(367\) −30.7255 −1.60386 −0.801928 0.597421i \(-0.796192\pi\)
−0.801928 + 0.597421i \(0.796192\pi\)
\(368\) 0 0
\(369\) 10.2891 0.535630
\(370\) 0 0
\(371\) 1.46132 0.0758677
\(372\) 0 0
\(373\) 4.67812 0.242224 0.121112 0.992639i \(-0.461354\pi\)
0.121112 + 0.992639i \(0.461354\pi\)
\(374\) 0 0
\(375\) 8.62858 0.445578
\(376\) 0 0
\(377\) 9.76332 0.502837
\(378\) 0 0
\(379\) −9.98838 −0.513069 −0.256534 0.966535i \(-0.582581\pi\)
−0.256534 + 0.966535i \(0.582581\pi\)
\(380\) 0 0
\(381\) −5.15426 −0.264061
\(382\) 0 0
\(383\) −11.5330 −0.589310 −0.294655 0.955604i \(-0.595205\pi\)
−0.294655 + 0.955604i \(0.595205\pi\)
\(384\) 0 0
\(385\) −3.70558 −0.188854
\(386\) 0 0
\(387\) −6.05050 −0.307564
\(388\) 0 0
\(389\) 16.2244 0.822609 0.411304 0.911498i \(-0.365073\pi\)
0.411304 + 0.911498i \(0.365073\pi\)
\(390\) 0 0
\(391\) 19.5875 0.990581
\(392\) 0 0
\(393\) 7.62480 0.384620
\(394\) 0 0
\(395\) −8.36479 −0.420878
\(396\) 0 0
\(397\) 28.9202 1.45147 0.725733 0.687977i \(-0.241501\pi\)
0.725733 + 0.687977i \(0.241501\pi\)
\(398\) 0 0
\(399\) 1.74390 0.0873044
\(400\) 0 0
\(401\) −8.49304 −0.424122 −0.212061 0.977256i \(-0.568018\pi\)
−0.212061 + 0.977256i \(0.568018\pi\)
\(402\) 0 0
\(403\) −1.67519 −0.0834474
\(404\) 0 0
\(405\) 17.4781 0.868494
\(406\) 0 0
\(407\) −5.53581 −0.274400
\(408\) 0 0
\(409\) 24.0666 1.19002 0.595008 0.803720i \(-0.297149\pi\)
0.595008 + 0.803720i \(0.297149\pi\)
\(410\) 0 0
\(411\) 17.7740 0.876729
\(412\) 0 0
\(413\) 1.26709 0.0623495
\(414\) 0 0
\(415\) 56.1029 2.75398
\(416\) 0 0
\(417\) −16.9963 −0.832313
\(418\) 0 0
\(419\) 14.4107 0.704009 0.352004 0.935998i \(-0.385500\pi\)
0.352004 + 0.935998i \(0.385500\pi\)
\(420\) 0 0
\(421\) −25.3454 −1.23526 −0.617630 0.786468i \(-0.711907\pi\)
−0.617630 + 0.786468i \(0.711907\pi\)
\(422\) 0 0
\(423\) −5.21998 −0.253804
\(424\) 0 0
\(425\) −18.5907 −0.901780
\(426\) 0 0
\(427\) −1.54165 −0.0746055
\(428\) 0 0
\(429\) 3.82753 0.184795
\(430\) 0 0
\(431\) −24.8824 −1.19854 −0.599272 0.800546i \(-0.704543\pi\)
−0.599272 + 0.800546i \(0.704543\pi\)
\(432\) 0 0
\(433\) −29.5652 −1.42081 −0.710406 0.703792i \(-0.751489\pi\)
−0.710406 + 0.703792i \(0.751489\pi\)
\(434\) 0 0
\(435\) −35.7033 −1.71184
\(436\) 0 0
\(437\) 16.3785 0.783488
\(438\) 0 0
\(439\) 12.8822 0.614836 0.307418 0.951575i \(-0.400535\pi\)
0.307418 + 0.951575i \(0.400535\pi\)
\(440\) 0 0
\(441\) 6.58686 0.313660
\(442\) 0 0
\(443\) 7.52766 0.357650 0.178825 0.983881i \(-0.442770\pi\)
0.178825 + 0.983881i \(0.442770\pi\)
\(444\) 0 0
\(445\) 5.93925 0.281547
\(446\) 0 0
\(447\) −9.68316 −0.457998
\(448\) 0 0
\(449\) −25.3085 −1.19438 −0.597190 0.802100i \(-0.703716\pi\)
−0.597190 + 0.802100i \(0.703716\pi\)
\(450\) 0 0
\(451\) −21.1938 −0.997977
\(452\) 0 0
\(453\) −16.0907 −0.756007
\(454\) 0 0
\(455\) 2.44451 0.114600
\(456\) 0 0
\(457\) 15.3782 0.719363 0.359682 0.933075i \(-0.382885\pi\)
0.359682 + 0.933075i \(0.382885\pi\)
\(458\) 0 0
\(459\) −15.5333 −0.725033
\(460\) 0 0
\(461\) −17.4478 −0.812624 −0.406312 0.913734i \(-0.633185\pi\)
−0.406312 + 0.913734i \(0.633185\pi\)
\(462\) 0 0
\(463\) −15.6244 −0.726130 −0.363065 0.931764i \(-0.618270\pi\)
−0.363065 + 0.931764i \(0.618270\pi\)
\(464\) 0 0
\(465\) 6.12599 0.284086
\(466\) 0 0
\(467\) −9.57103 −0.442895 −0.221447 0.975172i \(-0.571078\pi\)
−0.221447 + 0.975172i \(0.571078\pi\)
\(468\) 0 0
\(469\) −4.25649 −0.196547
\(470\) 0 0
\(471\) −5.89699 −0.271719
\(472\) 0 0
\(473\) 12.4630 0.573049
\(474\) 0 0
\(475\) −15.5450 −0.713252
\(476\) 0 0
\(477\) −2.68203 −0.122802
\(478\) 0 0
\(479\) 28.0103 1.27982 0.639912 0.768448i \(-0.278971\pi\)
0.639912 + 0.768448i \(0.278971\pi\)
\(480\) 0 0
\(481\) 3.65189 0.166512
\(482\) 0 0
\(483\) 5.41750 0.246505
\(484\) 0 0
\(485\) 37.1166 1.68538
\(486\) 0 0
\(487\) −2.40682 −0.109063 −0.0545317 0.998512i \(-0.517367\pi\)
−0.0545317 + 0.998512i \(0.517367\pi\)
\(488\) 0 0
\(489\) −17.1276 −0.774536
\(490\) 0 0
\(491\) −19.7804 −0.892677 −0.446339 0.894864i \(-0.647272\pi\)
−0.446339 + 0.894864i \(0.647272\pi\)
\(492\) 0 0
\(493\) 20.1121 0.905803
\(494\) 0 0
\(495\) 6.80104 0.305684
\(496\) 0 0
\(497\) −5.21232 −0.233805
\(498\) 0 0
\(499\) 10.4300 0.466911 0.233455 0.972368i \(-0.424997\pi\)
0.233455 + 0.972368i \(0.424997\pi\)
\(500\) 0 0
\(501\) −32.5623 −1.45478
\(502\) 0 0
\(503\) −4.51291 −0.201221 −0.100610 0.994926i \(-0.532080\pi\)
−0.100610 + 0.994926i \(0.532080\pi\)
\(504\) 0 0
\(505\) −63.9033 −2.84366
\(506\) 0 0
\(507\) 15.9469 0.708224
\(508\) 0 0
\(509\) −5.16980 −0.229147 −0.114574 0.993415i \(-0.536550\pi\)
−0.114574 + 0.993415i \(0.536550\pi\)
\(510\) 0 0
\(511\) 1.08555 0.0480219
\(512\) 0 0
\(513\) −12.9885 −0.573456
\(514\) 0 0
\(515\) 38.4972 1.69639
\(516\) 0 0
\(517\) 10.7523 0.472884
\(518\) 0 0
\(519\) 15.9917 0.701959
\(520\) 0 0
\(521\) 1.32701 0.0581373 0.0290687 0.999577i \(-0.490746\pi\)
0.0290687 + 0.999577i \(0.490746\pi\)
\(522\) 0 0
\(523\) −37.7140 −1.64912 −0.824560 0.565774i \(-0.808577\pi\)
−0.824560 + 0.565774i \(0.808577\pi\)
\(524\) 0 0
\(525\) −5.14181 −0.224407
\(526\) 0 0
\(527\) −3.45084 −0.150321
\(528\) 0 0
\(529\) 27.8803 1.21219
\(530\) 0 0
\(531\) −2.32556 −0.100921
\(532\) 0 0
\(533\) 13.9812 0.605593
\(534\) 0 0
\(535\) 59.4051 2.56831
\(536\) 0 0
\(537\) 9.12784 0.393895
\(538\) 0 0
\(539\) −13.5678 −0.584406
\(540\) 0 0
\(541\) 17.5239 0.753410 0.376705 0.926333i \(-0.377057\pi\)
0.376705 + 0.926333i \(0.377057\pi\)
\(542\) 0 0
\(543\) −25.8893 −1.11102
\(544\) 0 0
\(545\) 21.3767 0.915679
\(546\) 0 0
\(547\) −43.4808 −1.85911 −0.929553 0.368689i \(-0.879807\pi\)
−0.929553 + 0.368689i \(0.879807\pi\)
\(548\) 0 0
\(549\) 2.82946 0.120759
\(550\) 0 0
\(551\) 16.8171 0.716434
\(552\) 0 0
\(553\) 1.30324 0.0554194
\(554\) 0 0
\(555\) −13.3545 −0.566868
\(556\) 0 0
\(557\) −16.8982 −0.716000 −0.358000 0.933722i \(-0.616541\pi\)
−0.358000 + 0.933722i \(0.616541\pi\)
\(558\) 0 0
\(559\) −8.22163 −0.347738
\(560\) 0 0
\(561\) 7.88457 0.332887
\(562\) 0 0
\(563\) 10.5645 0.445241 0.222621 0.974905i \(-0.428539\pi\)
0.222621 + 0.974905i \(0.428539\pi\)
\(564\) 0 0
\(565\) 18.0687 0.760158
\(566\) 0 0
\(567\) −2.72310 −0.114359
\(568\) 0 0
\(569\) −38.9609 −1.63333 −0.816663 0.577115i \(-0.804179\pi\)
−0.816663 + 0.577115i \(0.804179\pi\)
\(570\) 0 0
\(571\) 2.89631 0.121207 0.0606034 0.998162i \(-0.480698\pi\)
0.0606034 + 0.998162i \(0.480698\pi\)
\(572\) 0 0
\(573\) 34.3788 1.43619
\(574\) 0 0
\(575\) −48.2910 −2.01387
\(576\) 0 0
\(577\) 10.7421 0.447198 0.223599 0.974681i \(-0.428219\pi\)
0.223599 + 0.974681i \(0.428219\pi\)
\(578\) 0 0
\(579\) −1.02578 −0.0426300
\(580\) 0 0
\(581\) −8.74087 −0.362632
\(582\) 0 0
\(583\) 5.52452 0.228802
\(584\) 0 0
\(585\) −4.48653 −0.185495
\(586\) 0 0
\(587\) 9.34105 0.385546 0.192773 0.981243i \(-0.438252\pi\)
0.192773 + 0.981243i \(0.438252\pi\)
\(588\) 0 0
\(589\) −2.88549 −0.118895
\(590\) 0 0
\(591\) −26.3467 −1.08376
\(592\) 0 0
\(593\) 11.7326 0.481802 0.240901 0.970550i \(-0.422557\pi\)
0.240901 + 0.970550i \(0.422557\pi\)
\(594\) 0 0
\(595\) 5.03559 0.206439
\(596\) 0 0
\(597\) −23.5667 −0.964520
\(598\) 0 0
\(599\) 5.93707 0.242582 0.121291 0.992617i \(-0.461297\pi\)
0.121291 + 0.992617i \(0.461297\pi\)
\(600\) 0 0
\(601\) 29.3099 1.19558 0.597788 0.801654i \(-0.296046\pi\)
0.597788 + 0.801654i \(0.296046\pi\)
\(602\) 0 0
\(603\) 7.81216 0.318136
\(604\) 0 0
\(605\) 23.7293 0.964733
\(606\) 0 0
\(607\) 36.4339 1.47881 0.739403 0.673263i \(-0.235108\pi\)
0.739403 + 0.673263i \(0.235108\pi\)
\(608\) 0 0
\(609\) 5.56260 0.225408
\(610\) 0 0
\(611\) −7.09309 −0.286956
\(612\) 0 0
\(613\) −17.1098 −0.691059 −0.345529 0.938408i \(-0.612301\pi\)
−0.345529 + 0.938408i \(0.612301\pi\)
\(614\) 0 0
\(615\) −51.1276 −2.06166
\(616\) 0 0
\(617\) −23.4037 −0.942197 −0.471098 0.882081i \(-0.656142\pi\)
−0.471098 + 0.882081i \(0.656142\pi\)
\(618\) 0 0
\(619\) −46.2329 −1.85826 −0.929129 0.369755i \(-0.879442\pi\)
−0.929129 + 0.369755i \(0.879442\pi\)
\(620\) 0 0
\(621\) −40.3492 −1.61916
\(622\) 0 0
\(623\) −0.925339 −0.0370729
\(624\) 0 0
\(625\) −13.0167 −0.520669
\(626\) 0 0
\(627\) 6.59285 0.263293
\(628\) 0 0
\(629\) 7.52275 0.299952
\(630\) 0 0
\(631\) −31.1563 −1.24031 −0.620157 0.784478i \(-0.712931\pi\)
−0.620157 + 0.784478i \(0.712931\pi\)
\(632\) 0 0
\(633\) −27.4017 −1.08912
\(634\) 0 0
\(635\) −12.4449 −0.493859
\(636\) 0 0
\(637\) 8.95044 0.354629
\(638\) 0 0
\(639\) 9.56645 0.378443
\(640\) 0 0
\(641\) 22.7425 0.898276 0.449138 0.893463i \(-0.351731\pi\)
0.449138 + 0.893463i \(0.351731\pi\)
\(642\) 0 0
\(643\) 20.9350 0.825596 0.412798 0.910823i \(-0.364551\pi\)
0.412798 + 0.910823i \(0.364551\pi\)
\(644\) 0 0
\(645\) 30.0655 1.18383
\(646\) 0 0
\(647\) 27.4638 1.07971 0.539856 0.841757i \(-0.318479\pi\)
0.539856 + 0.841757i \(0.318479\pi\)
\(648\) 0 0
\(649\) 4.79025 0.188034
\(650\) 0 0
\(651\) −0.954433 −0.0374072
\(652\) 0 0
\(653\) 21.7438 0.850900 0.425450 0.904982i \(-0.360116\pi\)
0.425450 + 0.904982i \(0.360116\pi\)
\(654\) 0 0
\(655\) 18.4099 0.719334
\(656\) 0 0
\(657\) −1.99237 −0.0777296
\(658\) 0 0
\(659\) −18.5840 −0.723931 −0.361966 0.932191i \(-0.617894\pi\)
−0.361966 + 0.932191i \(0.617894\pi\)
\(660\) 0 0
\(661\) 27.0551 1.05232 0.526161 0.850385i \(-0.323631\pi\)
0.526161 + 0.850385i \(0.323631\pi\)
\(662\) 0 0
\(663\) −5.20132 −0.202003
\(664\) 0 0
\(665\) 4.21062 0.163281
\(666\) 0 0
\(667\) 52.2430 2.02286
\(668\) 0 0
\(669\) 9.55971 0.369600
\(670\) 0 0
\(671\) −5.82820 −0.224995
\(672\) 0 0
\(673\) −40.4382 −1.55878 −0.779389 0.626541i \(-0.784470\pi\)
−0.779389 + 0.626541i \(0.784470\pi\)
\(674\) 0 0
\(675\) 38.2959 1.47401
\(676\) 0 0
\(677\) 39.4535 1.51632 0.758161 0.652068i \(-0.226098\pi\)
0.758161 + 0.652068i \(0.226098\pi\)
\(678\) 0 0
\(679\) −5.78279 −0.221923
\(680\) 0 0
\(681\) 21.1351 0.809898
\(682\) 0 0
\(683\) 3.44550 0.131838 0.0659192 0.997825i \(-0.479002\pi\)
0.0659192 + 0.997825i \(0.479002\pi\)
\(684\) 0 0
\(685\) 42.9150 1.63970
\(686\) 0 0
\(687\) 7.76491 0.296250
\(688\) 0 0
\(689\) −3.64443 −0.138842
\(690\) 0 0
\(691\) −19.3908 −0.737659 −0.368830 0.929497i \(-0.620241\pi\)
−0.368830 + 0.929497i \(0.620241\pi\)
\(692\) 0 0
\(693\) −1.05961 −0.0402511
\(694\) 0 0
\(695\) −41.0372 −1.55663
\(696\) 0 0
\(697\) 28.8008 1.09091
\(698\) 0 0
\(699\) −5.41388 −0.204772
\(700\) 0 0
\(701\) −18.6975 −0.706194 −0.353097 0.935587i \(-0.614871\pi\)
−0.353097 + 0.935587i \(0.614871\pi\)
\(702\) 0 0
\(703\) 6.29030 0.237243
\(704\) 0 0
\(705\) 25.9386 0.976904
\(706\) 0 0
\(707\) 9.95617 0.374440
\(708\) 0 0
\(709\) 1.27090 0.0477298 0.0238649 0.999715i \(-0.492403\pi\)
0.0238649 + 0.999715i \(0.492403\pi\)
\(710\) 0 0
\(711\) −2.39190 −0.0897034
\(712\) 0 0
\(713\) −8.96388 −0.335700
\(714\) 0 0
\(715\) 9.24148 0.345612
\(716\) 0 0
\(717\) −43.7463 −1.63374
\(718\) 0 0
\(719\) 9.16395 0.341758 0.170879 0.985292i \(-0.445339\pi\)
0.170879 + 0.985292i \(0.445339\pi\)
\(720\) 0 0
\(721\) −5.99788 −0.223373
\(722\) 0 0
\(723\) −25.5277 −0.949385
\(724\) 0 0
\(725\) −49.5844 −1.84152
\(726\) 0 0
\(727\) 12.0913 0.448440 0.224220 0.974539i \(-0.428017\pi\)
0.224220 + 0.974539i \(0.428017\pi\)
\(728\) 0 0
\(729\) 29.1106 1.07817
\(730\) 0 0
\(731\) −16.9363 −0.626410
\(732\) 0 0
\(733\) 12.0391 0.444673 0.222337 0.974970i \(-0.428632\pi\)
0.222337 + 0.974970i \(0.428632\pi\)
\(734\) 0 0
\(735\) −32.7307 −1.20729
\(736\) 0 0
\(737\) −16.0917 −0.592745
\(738\) 0 0
\(739\) 32.4300 1.19296 0.596478 0.802630i \(-0.296566\pi\)
0.596478 + 0.802630i \(0.296566\pi\)
\(740\) 0 0
\(741\) −4.34919 −0.159772
\(742\) 0 0
\(743\) 21.2839 0.780830 0.390415 0.920639i \(-0.372332\pi\)
0.390415 + 0.920639i \(0.372332\pi\)
\(744\) 0 0
\(745\) −23.3798 −0.856568
\(746\) 0 0
\(747\) 16.0426 0.586967
\(748\) 0 0
\(749\) −9.25535 −0.338183
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 4.33170 0.157856
\(754\) 0 0
\(755\) −38.8506 −1.41392
\(756\) 0 0
\(757\) −31.7941 −1.15558 −0.577788 0.816187i \(-0.696084\pi\)
−0.577788 + 0.816187i \(0.696084\pi\)
\(758\) 0 0
\(759\) 20.4809 0.743410
\(760\) 0 0
\(761\) −44.1947 −1.60206 −0.801029 0.598625i \(-0.795714\pi\)
−0.801029 + 0.598625i \(0.795714\pi\)
\(762\) 0 0
\(763\) −3.33051 −0.120573
\(764\) 0 0
\(765\) −9.24209 −0.334148
\(766\) 0 0
\(767\) −3.16005 −0.114103
\(768\) 0 0
\(769\) 5.10314 0.184024 0.0920120 0.995758i \(-0.470670\pi\)
0.0920120 + 0.995758i \(0.470670\pi\)
\(770\) 0 0
\(771\) −24.7224 −0.890354
\(772\) 0 0
\(773\) −19.8193 −0.712850 −0.356425 0.934324i \(-0.616005\pi\)
−0.356425 + 0.934324i \(0.616005\pi\)
\(774\) 0 0
\(775\) 8.50771 0.305606
\(776\) 0 0
\(777\) 2.08064 0.0746426
\(778\) 0 0
\(779\) 24.0823 0.862840
\(780\) 0 0
\(781\) −19.7052 −0.705108
\(782\) 0 0
\(783\) −41.4299 −1.48058
\(784\) 0 0
\(785\) −14.2382 −0.508181
\(786\) 0 0
\(787\) 26.7823 0.954686 0.477343 0.878717i \(-0.341600\pi\)
0.477343 + 0.878717i \(0.341600\pi\)
\(788\) 0 0
\(789\) 33.2313 1.18307
\(790\) 0 0
\(791\) −2.81512 −0.100094
\(792\) 0 0
\(793\) 3.84477 0.136532
\(794\) 0 0
\(795\) 13.3273 0.472669
\(796\) 0 0
\(797\) 31.3741 1.11133 0.555664 0.831407i \(-0.312464\pi\)
0.555664 + 0.831407i \(0.312464\pi\)
\(798\) 0 0
\(799\) −14.6115 −0.516918
\(800\) 0 0
\(801\) 1.69832 0.0600073
\(802\) 0 0
\(803\) 4.10393 0.144825
\(804\) 0 0
\(805\) 13.0804 0.461024
\(806\) 0 0
\(807\) −27.1650 −0.956255
\(808\) 0 0
\(809\) −36.2157 −1.27328 −0.636638 0.771163i \(-0.719675\pi\)
−0.636638 + 0.771163i \(0.719675\pi\)
\(810\) 0 0
\(811\) −15.2165 −0.534324 −0.267162 0.963652i \(-0.586086\pi\)
−0.267162 + 0.963652i \(0.586086\pi\)
\(812\) 0 0
\(813\) 10.8360 0.380033
\(814\) 0 0
\(815\) −41.3541 −1.44857
\(816\) 0 0
\(817\) −14.1616 −0.495452
\(818\) 0 0
\(819\) 0.699004 0.0244252
\(820\) 0 0
\(821\) 2.00689 0.0700409 0.0350204 0.999387i \(-0.488850\pi\)
0.0350204 + 0.999387i \(0.488850\pi\)
\(822\) 0 0
\(823\) 22.3096 0.777664 0.388832 0.921309i \(-0.372879\pi\)
0.388832 + 0.921309i \(0.372879\pi\)
\(824\) 0 0
\(825\) −19.4386 −0.676767
\(826\) 0 0
\(827\) −41.4512 −1.44140 −0.720700 0.693247i \(-0.756180\pi\)
−0.720700 + 0.693247i \(0.756180\pi\)
\(828\) 0 0
\(829\) −35.4228 −1.23028 −0.615142 0.788417i \(-0.710901\pi\)
−0.615142 + 0.788417i \(0.710901\pi\)
\(830\) 0 0
\(831\) −42.0854 −1.45993
\(832\) 0 0
\(833\) 18.4376 0.638824
\(834\) 0 0
\(835\) −78.6209 −2.72079
\(836\) 0 0
\(837\) 7.10856 0.245708
\(838\) 0 0
\(839\) −45.1507 −1.55878 −0.779388 0.626542i \(-0.784470\pi\)
−0.779388 + 0.626542i \(0.784470\pi\)
\(840\) 0 0
\(841\) 24.6423 0.849735
\(842\) 0 0
\(843\) −26.9977 −0.929850
\(844\) 0 0
\(845\) 38.5033 1.32455
\(846\) 0 0
\(847\) −3.69704 −0.127032
\(848\) 0 0
\(849\) −26.1066 −0.895977
\(850\) 0 0
\(851\) 19.5410 0.669858
\(852\) 0 0
\(853\) 39.6427 1.35734 0.678670 0.734443i \(-0.262557\pi\)
0.678670 + 0.734443i \(0.262557\pi\)
\(854\) 0 0
\(855\) −7.72796 −0.264291
\(856\) 0 0
\(857\) 53.2397 1.81863 0.909317 0.416105i \(-0.136605\pi\)
0.909317 + 0.416105i \(0.136605\pi\)
\(858\) 0 0
\(859\) −32.1333 −1.09637 −0.548186 0.836356i \(-0.684682\pi\)
−0.548186 + 0.836356i \(0.684682\pi\)
\(860\) 0 0
\(861\) 7.96571 0.271471
\(862\) 0 0
\(863\) −27.3278 −0.930248 −0.465124 0.885246i \(-0.653990\pi\)
−0.465124 + 0.885246i \(0.653990\pi\)
\(864\) 0 0
\(865\) 38.6117 1.31284
\(866\) 0 0
\(867\) 13.4409 0.456477
\(868\) 0 0
\(869\) 4.92691 0.167134
\(870\) 0 0
\(871\) 10.6154 0.359690
\(872\) 0 0
\(873\) 10.6135 0.359211
\(874\) 0 0
\(875\) −3.24587 −0.109730
\(876\) 0 0
\(877\) 21.6237 0.730180 0.365090 0.930972i \(-0.381038\pi\)
0.365090 + 0.930972i \(0.381038\pi\)
\(878\) 0 0
\(879\) −41.7808 −1.40923
\(880\) 0 0
\(881\) −51.1335 −1.72273 −0.861366 0.507985i \(-0.830391\pi\)
−0.861366 + 0.507985i \(0.830391\pi\)
\(882\) 0 0
\(883\) 16.9290 0.569708 0.284854 0.958571i \(-0.408055\pi\)
0.284854 + 0.958571i \(0.408055\pi\)
\(884\) 0 0
\(885\) 11.5559 0.388449
\(886\) 0 0
\(887\) −43.8163 −1.47121 −0.735604 0.677412i \(-0.763102\pi\)
−0.735604 + 0.677412i \(0.763102\pi\)
\(888\) 0 0
\(889\) 1.93892 0.0650291
\(890\) 0 0
\(891\) −10.2947 −0.344885
\(892\) 0 0
\(893\) −12.2177 −0.408850
\(894\) 0 0
\(895\) 22.0389 0.736681
\(896\) 0 0
\(897\) −13.5109 −0.451116
\(898\) 0 0
\(899\) −9.20397 −0.306969
\(900\) 0 0
\(901\) −7.50739 −0.250108
\(902\) 0 0
\(903\) −4.68423 −0.155881
\(904\) 0 0
\(905\) −62.5091 −2.07787
\(906\) 0 0
\(907\) 52.2717 1.73565 0.867827 0.496867i \(-0.165516\pi\)
0.867827 + 0.496867i \(0.165516\pi\)
\(908\) 0 0
\(909\) −18.2731 −0.606080
\(910\) 0 0
\(911\) −18.4449 −0.611106 −0.305553 0.952175i \(-0.598841\pi\)
−0.305553 + 0.952175i \(0.598841\pi\)
\(912\) 0 0
\(913\) −33.0449 −1.09363
\(914\) 0 0
\(915\) −14.0599 −0.464805
\(916\) 0 0
\(917\) −2.86827 −0.0947188
\(918\) 0 0
\(919\) −0.355688 −0.0117331 −0.00586653 0.999983i \(-0.501867\pi\)
−0.00586653 + 0.999983i \(0.501867\pi\)
\(920\) 0 0
\(921\) −36.5414 −1.20408
\(922\) 0 0
\(923\) 12.9992 0.427874
\(924\) 0 0
\(925\) −18.5466 −0.609809
\(926\) 0 0
\(927\) 11.0082 0.361558
\(928\) 0 0
\(929\) −8.90560 −0.292183 −0.146092 0.989271i \(-0.546669\pi\)
−0.146092 + 0.989271i \(0.546669\pi\)
\(930\) 0 0
\(931\) 15.4170 0.505271
\(932\) 0 0
\(933\) 42.7568 1.39979
\(934\) 0 0
\(935\) 19.0371 0.622580
\(936\) 0 0
\(937\) 13.8456 0.452316 0.226158 0.974091i \(-0.427384\pi\)
0.226158 + 0.974091i \(0.427384\pi\)
\(938\) 0 0
\(939\) −10.0965 −0.329486
\(940\) 0 0
\(941\) 43.9045 1.43125 0.715623 0.698486i \(-0.246143\pi\)
0.715623 + 0.698486i \(0.246143\pi\)
\(942\) 0 0
\(943\) 74.8127 2.43624
\(944\) 0 0
\(945\) −10.3731 −0.337436
\(946\) 0 0
\(947\) 16.4787 0.535485 0.267742 0.963491i \(-0.413722\pi\)
0.267742 + 0.963491i \(0.413722\pi\)
\(948\) 0 0
\(949\) −2.70730 −0.0878825
\(950\) 0 0
\(951\) −12.7134 −0.412259
\(952\) 0 0
\(953\) 25.5958 0.829129 0.414564 0.910020i \(-0.363934\pi\)
0.414564 + 0.910020i \(0.363934\pi\)
\(954\) 0 0
\(955\) 83.0067 2.68603
\(956\) 0 0
\(957\) 21.0295 0.679786
\(958\) 0 0
\(959\) −6.68618 −0.215908
\(960\) 0 0
\(961\) −29.4208 −0.949057
\(962\) 0 0
\(963\) 16.9868 0.547393
\(964\) 0 0
\(965\) −2.47673 −0.0797286
\(966\) 0 0
\(967\) 13.7793 0.443111 0.221556 0.975148i \(-0.428887\pi\)
0.221556 + 0.975148i \(0.428887\pi\)
\(968\) 0 0
\(969\) −8.95917 −0.287810
\(970\) 0 0
\(971\) 35.7294 1.14661 0.573306 0.819341i \(-0.305661\pi\)
0.573306 + 0.819341i \(0.305661\pi\)
\(972\) 0 0
\(973\) 6.39362 0.204970
\(974\) 0 0
\(975\) 12.8234 0.410676
\(976\) 0 0
\(977\) −40.7899 −1.30498 −0.652492 0.757795i \(-0.726276\pi\)
−0.652492 + 0.757795i \(0.726276\pi\)
\(978\) 0 0
\(979\) −3.49825 −0.111805
\(980\) 0 0
\(981\) 6.11266 0.195162
\(982\) 0 0
\(983\) −27.7071 −0.883719 −0.441860 0.897084i \(-0.645681\pi\)
−0.441860 + 0.897084i \(0.645681\pi\)
\(984\) 0 0
\(985\) −63.6136 −2.02690
\(986\) 0 0
\(987\) −4.04125 −0.128634
\(988\) 0 0
\(989\) −43.9935 −1.39891
\(990\) 0 0
\(991\) −5.84738 −0.185748 −0.0928740 0.995678i \(-0.529605\pi\)
−0.0928740 + 0.995678i \(0.529605\pi\)
\(992\) 0 0
\(993\) 6.40157 0.203148
\(994\) 0 0
\(995\) −56.9012 −1.80389
\(996\) 0 0
\(997\) 12.2585 0.388231 0.194115 0.980979i \(-0.437816\pi\)
0.194115 + 0.980979i \(0.437816\pi\)
\(998\) 0 0
\(999\) −15.4965 −0.490287
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 \(a_p\))