Properties

Label 8048.2.a.v.1.27
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.27
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+2.92644 q^{3}\) \(+0.124991 q^{5}\) \(-2.19824 q^{7}\) \(+5.56407 q^{9}\) \(+O(q^{10})\) \(q\)\(+2.92644 q^{3}\) \(+0.124991 q^{5}\) \(-2.19824 q^{7}\) \(+5.56407 q^{9}\) \(-0.684798 q^{11}\) \(-5.23188 q^{13}\) \(+0.365779 q^{15}\) \(+3.19997 q^{17}\) \(+1.04142 q^{19}\) \(-6.43301 q^{21}\) \(-6.34708 q^{23}\) \(-4.98438 q^{25}\) \(+7.50361 q^{27}\) \(-6.90634 q^{29}\) \(+1.53143 q^{31}\) \(-2.00402 q^{33}\) \(-0.274759 q^{35}\) \(-1.84431 q^{37}\) \(-15.3108 q^{39}\) \(+10.2063 q^{41}\) \(+6.72891 q^{43}\) \(+0.695458 q^{45}\) \(+2.89294 q^{47}\) \(-2.16776 q^{49}\) \(+9.36454 q^{51}\) \(-6.45664 q^{53}\) \(-0.0855935 q^{55}\) \(+3.04766 q^{57}\) \(-3.81560 q^{59}\) \(+9.92318 q^{61}\) \(-12.2311 q^{63}\) \(-0.653937 q^{65}\) \(-10.4558 q^{67}\) \(-18.5744 q^{69}\) \(+2.63957 q^{71}\) \(-16.4537 q^{73}\) \(-14.5865 q^{75}\) \(+1.50535 q^{77}\) \(+0.990261 q^{79}\) \(+5.26667 q^{81}\) \(-12.7822 q^{83}\) \(+0.399967 q^{85}\) \(-20.2110 q^{87}\) \(+1.30655 q^{89}\) \(+11.5009 q^{91}\) \(+4.48164 q^{93}\) \(+0.130168 q^{95}\) \(+12.0738 q^{97}\) \(-3.81026 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 31q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 22q^{25} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 26q^{33} \) \(\mathstrut +\mathstrut 13q^{35} \) \(\mathstrut -\mathstrut 67q^{37} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut -\mathstrut 57q^{45} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 20q^{49} \) \(\mathstrut +\mathstrut 11q^{51} \) \(\mathstrut -\mathstrut 58q^{53} \) \(\mathstrut -\mathstrut 15q^{55} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 55q^{61} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 44q^{69} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 5q^{73} \) \(\mathstrut +\mathstrut 25q^{75} \) \(\mathstrut -\mathstrut 50q^{77} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 78q^{85} \) \(\mathstrut +\mathstrut 11q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut +\mathstrut 15q^{91} \) \(\mathstrut -\mathstrut 83q^{93} \) \(\mathstrut +\mathstrut 27q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 70q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.92644 1.68958 0.844791 0.535096i \(-0.179724\pi\)
0.844791 + 0.535096i \(0.179724\pi\)
\(4\) 0 0
\(5\) 0.124991 0.0558976 0.0279488 0.999609i \(-0.491102\pi\)
0.0279488 + 0.999609i \(0.491102\pi\)
\(6\) 0 0
\(7\) −2.19824 −0.830855 −0.415427 0.909626i \(-0.636368\pi\)
−0.415427 + 0.909626i \(0.636368\pi\)
\(8\) 0 0
\(9\) 5.56407 1.85469
\(10\) 0 0
\(11\) −0.684798 −0.206474 −0.103237 0.994657i \(-0.532920\pi\)
−0.103237 + 0.994657i \(0.532920\pi\)
\(12\) 0 0
\(13\) −5.23188 −1.45106 −0.725531 0.688190i \(-0.758406\pi\)
−0.725531 + 0.688190i \(0.758406\pi\)
\(14\) 0 0
\(15\) 0.365779 0.0944437
\(16\) 0 0
\(17\) 3.19997 0.776107 0.388054 0.921637i \(-0.373148\pi\)
0.388054 + 0.921637i \(0.373148\pi\)
\(18\) 0 0
\(19\) 1.04142 0.238919 0.119459 0.992839i \(-0.461884\pi\)
0.119459 + 0.992839i \(0.461884\pi\)
\(20\) 0 0
\(21\) −6.43301 −1.40380
\(22\) 0 0
\(23\) −6.34708 −1.32346 −0.661729 0.749743i \(-0.730177\pi\)
−0.661729 + 0.749743i \(0.730177\pi\)
\(24\) 0 0
\(25\) −4.98438 −0.996875
\(26\) 0 0
\(27\) 7.50361 1.44407
\(28\) 0 0
\(29\) −6.90634 −1.28247 −0.641237 0.767343i \(-0.721579\pi\)
−0.641237 + 0.767343i \(0.721579\pi\)
\(30\) 0 0
\(31\) 1.53143 0.275053 0.137527 0.990498i \(-0.456085\pi\)
0.137527 + 0.990498i \(0.456085\pi\)
\(32\) 0 0
\(33\) −2.00402 −0.348856
\(34\) 0 0
\(35\) −0.274759 −0.0464428
\(36\) 0 0
\(37\) −1.84431 −0.303202 −0.151601 0.988442i \(-0.548443\pi\)
−0.151601 + 0.988442i \(0.548443\pi\)
\(38\) 0 0
\(39\) −15.3108 −2.45169
\(40\) 0 0
\(41\) 10.2063 1.59395 0.796975 0.604013i \(-0.206432\pi\)
0.796975 + 0.604013i \(0.206432\pi\)
\(42\) 0 0
\(43\) 6.72891 1.02615 0.513074 0.858344i \(-0.328506\pi\)
0.513074 + 0.858344i \(0.328506\pi\)
\(44\) 0 0
\(45\) 0.695458 0.103673
\(46\) 0 0
\(47\) 2.89294 0.421978 0.210989 0.977488i \(-0.432332\pi\)
0.210989 + 0.977488i \(0.432332\pi\)
\(48\) 0 0
\(49\) −2.16776 −0.309680
\(50\) 0 0
\(51\) 9.36454 1.31130
\(52\) 0 0
\(53\) −6.45664 −0.886888 −0.443444 0.896302i \(-0.646244\pi\)
−0.443444 + 0.896302i \(0.646244\pi\)
\(54\) 0 0
\(55\) −0.0855935 −0.0115414
\(56\) 0 0
\(57\) 3.04766 0.403673
\(58\) 0 0
\(59\) −3.81560 −0.496748 −0.248374 0.968664i \(-0.579896\pi\)
−0.248374 + 0.968664i \(0.579896\pi\)
\(60\) 0 0
\(61\) 9.92318 1.27053 0.635267 0.772293i \(-0.280890\pi\)
0.635267 + 0.772293i \(0.280890\pi\)
\(62\) 0 0
\(63\) −12.2311 −1.54098
\(64\) 0 0
\(65\) −0.653937 −0.0811109
\(66\) 0 0
\(67\) −10.4558 −1.27738 −0.638692 0.769462i \(-0.720524\pi\)
−0.638692 + 0.769462i \(0.720524\pi\)
\(68\) 0 0
\(69\) −18.5744 −2.23609
\(70\) 0 0
\(71\) 2.63957 0.313260 0.156630 0.987657i \(-0.449937\pi\)
0.156630 + 0.987657i \(0.449937\pi\)
\(72\) 0 0
\(73\) −16.4537 −1.92575 −0.962877 0.269939i \(-0.912996\pi\)
−0.962877 + 0.269939i \(0.912996\pi\)
\(74\) 0 0
\(75\) −14.5865 −1.68430
\(76\) 0 0
\(77\) 1.50535 0.171550
\(78\) 0 0
\(79\) 0.990261 0.111413 0.0557065 0.998447i \(-0.482259\pi\)
0.0557065 + 0.998447i \(0.482259\pi\)
\(80\) 0 0
\(81\) 5.26667 0.585186
\(82\) 0 0
\(83\) −12.7822 −1.40302 −0.701512 0.712657i \(-0.747491\pi\)
−0.701512 + 0.712657i \(0.747491\pi\)
\(84\) 0 0
\(85\) 0.399967 0.0433825
\(86\) 0 0
\(87\) −20.2110 −2.16685
\(88\) 0 0
\(89\) 1.30655 0.138494 0.0692469 0.997600i \(-0.477940\pi\)
0.0692469 + 0.997600i \(0.477940\pi\)
\(90\) 0 0
\(91\) 11.5009 1.20562
\(92\) 0 0
\(93\) 4.48164 0.464725
\(94\) 0 0
\(95\) 0.130168 0.0133550
\(96\) 0 0
\(97\) 12.0738 1.22591 0.612953 0.790119i \(-0.289981\pi\)
0.612953 + 0.790119i \(0.289981\pi\)
\(98\) 0 0
\(99\) −3.81026 −0.382946
\(100\) 0 0
\(101\) −15.3447 −1.52686 −0.763429 0.645892i \(-0.776486\pi\)
−0.763429 + 0.645892i \(0.776486\pi\)
\(102\) 0 0
\(103\) −14.9224 −1.47034 −0.735172 0.677880i \(-0.762899\pi\)
−0.735172 + 0.677880i \(0.762899\pi\)
\(104\) 0 0
\(105\) −0.804068 −0.0784690
\(106\) 0 0
\(107\) −17.8895 −1.72944 −0.864720 0.502255i \(-0.832504\pi\)
−0.864720 + 0.502255i \(0.832504\pi\)
\(108\) 0 0
\(109\) −4.13401 −0.395967 −0.197983 0.980205i \(-0.563439\pi\)
−0.197983 + 0.980205i \(0.563439\pi\)
\(110\) 0 0
\(111\) −5.39726 −0.512285
\(112\) 0 0
\(113\) 16.5479 1.55670 0.778350 0.627831i \(-0.216057\pi\)
0.778350 + 0.627831i \(0.216057\pi\)
\(114\) 0 0
\(115\) −0.793327 −0.0739781
\(116\) 0 0
\(117\) −29.1105 −2.69127
\(118\) 0 0
\(119\) −7.03429 −0.644832
\(120\) 0 0
\(121\) −10.5311 −0.957368
\(122\) 0 0
\(123\) 29.8680 2.69311
\(124\) 0 0
\(125\) −1.24796 −0.111621
\(126\) 0 0
\(127\) −1.42164 −0.126150 −0.0630752 0.998009i \(-0.520091\pi\)
−0.0630752 + 0.998009i \(0.520091\pi\)
\(128\) 0 0
\(129\) 19.6918 1.73376
\(130\) 0 0
\(131\) 8.96875 0.783603 0.391802 0.920050i \(-0.371852\pi\)
0.391802 + 0.920050i \(0.371852\pi\)
\(132\) 0 0
\(133\) −2.28929 −0.198507
\(134\) 0 0
\(135\) 0.937882 0.0807201
\(136\) 0 0
\(137\) −15.5701 −1.33024 −0.665120 0.746736i \(-0.731620\pi\)
−0.665120 + 0.746736i \(0.731620\pi\)
\(138\) 0 0
\(139\) 12.9396 1.09753 0.548763 0.835978i \(-0.315099\pi\)
0.548763 + 0.835978i \(0.315099\pi\)
\(140\) 0 0
\(141\) 8.46601 0.712967
\(142\) 0 0
\(143\) 3.58278 0.299607
\(144\) 0 0
\(145\) −0.863229 −0.0716873
\(146\) 0 0
\(147\) −6.34383 −0.523231
\(148\) 0 0
\(149\) −23.0629 −1.88939 −0.944695 0.327951i \(-0.893642\pi\)
−0.944695 + 0.327951i \(0.893642\pi\)
\(150\) 0 0
\(151\) −0.534439 −0.0434921 −0.0217460 0.999764i \(-0.506923\pi\)
−0.0217460 + 0.999764i \(0.506923\pi\)
\(152\) 0 0
\(153\) 17.8049 1.43944
\(154\) 0 0
\(155\) 0.191415 0.0153748
\(156\) 0 0
\(157\) −22.6311 −1.80616 −0.903080 0.429472i \(-0.858700\pi\)
−0.903080 + 0.429472i \(0.858700\pi\)
\(158\) 0 0
\(159\) −18.8950 −1.49847
\(160\) 0 0
\(161\) 13.9524 1.09960
\(162\) 0 0
\(163\) −2.19723 −0.172100 −0.0860501 0.996291i \(-0.527425\pi\)
−0.0860501 + 0.996291i \(0.527425\pi\)
\(164\) 0 0
\(165\) −0.250485 −0.0195002
\(166\) 0 0
\(167\) 7.38930 0.571801 0.285901 0.958259i \(-0.407707\pi\)
0.285901 + 0.958259i \(0.407707\pi\)
\(168\) 0 0
\(169\) 14.3725 1.10558
\(170\) 0 0
\(171\) 5.79455 0.443120
\(172\) 0 0
\(173\) −10.8931 −0.828185 −0.414093 0.910235i \(-0.635901\pi\)
−0.414093 + 0.910235i \(0.635901\pi\)
\(174\) 0 0
\(175\) 10.9568 0.828259
\(176\) 0 0
\(177\) −11.1661 −0.839298
\(178\) 0 0
\(179\) 14.2624 1.06602 0.533012 0.846108i \(-0.321060\pi\)
0.533012 + 0.846108i \(0.321060\pi\)
\(180\) 0 0
\(181\) 17.3329 1.28835 0.644173 0.764880i \(-0.277202\pi\)
0.644173 + 0.764880i \(0.277202\pi\)
\(182\) 0 0
\(183\) 29.0396 2.14667
\(184\) 0 0
\(185\) −0.230521 −0.0169483
\(186\) 0 0
\(187\) −2.19133 −0.160246
\(188\) 0 0
\(189\) −16.4947 −1.19981
\(190\) 0 0
\(191\) 5.90903 0.427563 0.213781 0.976882i \(-0.431422\pi\)
0.213781 + 0.976882i \(0.431422\pi\)
\(192\) 0 0
\(193\) −18.2410 −1.31301 −0.656507 0.754320i \(-0.727967\pi\)
−0.656507 + 0.754320i \(0.727967\pi\)
\(194\) 0 0
\(195\) −1.91371 −0.137044
\(196\) 0 0
\(197\) 13.7541 0.979937 0.489968 0.871740i \(-0.337008\pi\)
0.489968 + 0.871740i \(0.337008\pi\)
\(198\) 0 0
\(199\) 15.1280 1.07240 0.536198 0.844092i \(-0.319860\pi\)
0.536198 + 0.844092i \(0.319860\pi\)
\(200\) 0 0
\(201\) −30.5984 −2.15825
\(202\) 0 0
\(203\) 15.1818 1.06555
\(204\) 0 0
\(205\) 1.27569 0.0890980
\(206\) 0 0
\(207\) −35.3156 −2.45460
\(208\) 0 0
\(209\) −0.713164 −0.0493306
\(210\) 0 0
\(211\) 0.0288291 0.00198467 0.000992337 1.00000i \(-0.499684\pi\)
0.000992337 1.00000i \(0.499684\pi\)
\(212\) 0 0
\(213\) 7.72456 0.529278
\(214\) 0 0
\(215\) 0.841052 0.0573593
\(216\) 0 0
\(217\) −3.36644 −0.228529
\(218\) 0 0
\(219\) −48.1507 −3.25372
\(220\) 0 0
\(221\) −16.7419 −1.12618
\(222\) 0 0
\(223\) 19.1423 1.28186 0.640931 0.767599i \(-0.278549\pi\)
0.640931 + 0.767599i \(0.278549\pi\)
\(224\) 0 0
\(225\) −27.7334 −1.84890
\(226\) 0 0
\(227\) −20.2540 −1.34430 −0.672152 0.740413i \(-0.734630\pi\)
−0.672152 + 0.740413i \(0.734630\pi\)
\(228\) 0 0
\(229\) 17.6183 1.16425 0.582125 0.813100i \(-0.302222\pi\)
0.582125 + 0.813100i \(0.302222\pi\)
\(230\) 0 0
\(231\) 4.40531 0.289848
\(232\) 0 0
\(233\) 0.493520 0.0323316 0.0161658 0.999869i \(-0.494854\pi\)
0.0161658 + 0.999869i \(0.494854\pi\)
\(234\) 0 0
\(235\) 0.361591 0.0235876
\(236\) 0 0
\(237\) 2.89794 0.188242
\(238\) 0 0
\(239\) 26.6049 1.72093 0.860463 0.509514i \(-0.170175\pi\)
0.860463 + 0.509514i \(0.170175\pi\)
\(240\) 0 0
\(241\) 3.16066 0.203596 0.101798 0.994805i \(-0.467540\pi\)
0.101798 + 0.994805i \(0.467540\pi\)
\(242\) 0 0
\(243\) −7.09821 −0.455350
\(244\) 0 0
\(245\) −0.270951 −0.0173104
\(246\) 0 0
\(247\) −5.44859 −0.346686
\(248\) 0 0
\(249\) −37.4063 −2.37053
\(250\) 0 0
\(251\) −9.66267 −0.609903 −0.304951 0.952368i \(-0.598640\pi\)
−0.304951 + 0.952368i \(0.598640\pi\)
\(252\) 0 0
\(253\) 4.34647 0.273260
\(254\) 0 0
\(255\) 1.17048 0.0732984
\(256\) 0 0
\(257\) −12.8046 −0.798727 −0.399364 0.916793i \(-0.630769\pi\)
−0.399364 + 0.916793i \(0.630769\pi\)
\(258\) 0 0
\(259\) 4.05422 0.251917
\(260\) 0 0
\(261\) −38.4274 −2.37859
\(262\) 0 0
\(263\) 23.2755 1.43523 0.717613 0.696442i \(-0.245235\pi\)
0.717613 + 0.696442i \(0.245235\pi\)
\(264\) 0 0
\(265\) −0.807022 −0.0495749
\(266\) 0 0
\(267\) 3.82354 0.233997
\(268\) 0 0
\(269\) −6.70921 −0.409068 −0.204534 0.978859i \(-0.565568\pi\)
−0.204534 + 0.978859i \(0.565568\pi\)
\(270\) 0 0
\(271\) −6.11292 −0.371334 −0.185667 0.982613i \(-0.559445\pi\)
−0.185667 + 0.982613i \(0.559445\pi\)
\(272\) 0 0
\(273\) 33.6567 2.03700
\(274\) 0 0
\(275\) 3.41329 0.205829
\(276\) 0 0
\(277\) −11.6950 −0.702683 −0.351341 0.936247i \(-0.614274\pi\)
−0.351341 + 0.936247i \(0.614274\pi\)
\(278\) 0 0
\(279\) 8.52099 0.510138
\(280\) 0 0
\(281\) −22.5841 −1.34725 −0.673627 0.739071i \(-0.735265\pi\)
−0.673627 + 0.739071i \(0.735265\pi\)
\(282\) 0 0
\(283\) 22.4502 1.33453 0.667264 0.744821i \(-0.267465\pi\)
0.667264 + 0.744821i \(0.267465\pi\)
\(284\) 0 0
\(285\) 0.380930 0.0225644
\(286\) 0 0
\(287\) −22.4358 −1.32434
\(288\) 0 0
\(289\) −6.76018 −0.397658
\(290\) 0 0
\(291\) 35.3332 2.07127
\(292\) 0 0
\(293\) −24.8303 −1.45060 −0.725301 0.688432i \(-0.758300\pi\)
−0.725301 + 0.688432i \(0.758300\pi\)
\(294\) 0 0
\(295\) −0.476915 −0.0277671
\(296\) 0 0
\(297\) −5.13846 −0.298163
\(298\) 0 0
\(299\) 33.2071 1.92042
\(300\) 0 0
\(301\) −14.7917 −0.852581
\(302\) 0 0
\(303\) −44.9055 −2.57975
\(304\) 0 0
\(305\) 1.24031 0.0710198
\(306\) 0 0
\(307\) −6.08657 −0.347379 −0.173690 0.984800i \(-0.555569\pi\)
−0.173690 + 0.984800i \(0.555569\pi\)
\(308\) 0 0
\(309\) −43.6695 −2.48427
\(310\) 0 0
\(311\) 23.1084 1.31036 0.655178 0.755475i \(-0.272594\pi\)
0.655178 + 0.755475i \(0.272594\pi\)
\(312\) 0 0
\(313\) 13.6387 0.770902 0.385451 0.922728i \(-0.374046\pi\)
0.385451 + 0.922728i \(0.374046\pi\)
\(314\) 0 0
\(315\) −1.52878 −0.0861370
\(316\) 0 0
\(317\) −3.22419 −0.181089 −0.0905444 0.995892i \(-0.528861\pi\)
−0.0905444 + 0.995892i \(0.528861\pi\)
\(318\) 0 0
\(319\) 4.72945 0.264798
\(320\) 0 0
\(321\) −52.3525 −2.92203
\(322\) 0 0
\(323\) 3.33252 0.185427
\(324\) 0 0
\(325\) 26.0776 1.44653
\(326\) 0 0
\(327\) −12.0980 −0.669018
\(328\) 0 0
\(329\) −6.35935 −0.350602
\(330\) 0 0
\(331\) 29.7151 1.63329 0.816644 0.577142i \(-0.195832\pi\)
0.816644 + 0.577142i \(0.195832\pi\)
\(332\) 0 0
\(333\) −10.2618 −0.562346
\(334\) 0 0
\(335\) −1.30689 −0.0714028
\(336\) 0 0
\(337\) 22.3421 1.21705 0.608526 0.793534i \(-0.291761\pi\)
0.608526 + 0.793534i \(0.291761\pi\)
\(338\) 0 0
\(339\) 48.4266 2.63017
\(340\) 0 0
\(341\) −1.04872 −0.0567914
\(342\) 0 0
\(343\) 20.1529 1.08815
\(344\) 0 0
\(345\) −2.32163 −0.124992
\(346\) 0 0
\(347\) 28.0064 1.50346 0.751730 0.659471i \(-0.229220\pi\)
0.751730 + 0.659471i \(0.229220\pi\)
\(348\) 0 0
\(349\) 16.2555 0.870138 0.435069 0.900397i \(-0.356724\pi\)
0.435069 + 0.900397i \(0.356724\pi\)
\(350\) 0 0
\(351\) −39.2579 −2.09543
\(352\) 0 0
\(353\) −14.7318 −0.784095 −0.392048 0.919945i \(-0.628233\pi\)
−0.392048 + 0.919945i \(0.628233\pi\)
\(354\) 0 0
\(355\) 0.329922 0.0175105
\(356\) 0 0
\(357\) −20.5855 −1.08950
\(358\) 0 0
\(359\) 22.8293 1.20488 0.602441 0.798163i \(-0.294195\pi\)
0.602441 + 0.798163i \(0.294195\pi\)
\(360\) 0 0
\(361\) −17.9154 −0.942918
\(362\) 0 0
\(363\) −30.8185 −1.61755
\(364\) 0 0
\(365\) −2.05656 −0.107645
\(366\) 0 0
\(367\) −21.1688 −1.10500 −0.552501 0.833512i \(-0.686327\pi\)
−0.552501 + 0.833512i \(0.686327\pi\)
\(368\) 0 0
\(369\) 56.7883 2.95628
\(370\) 0 0
\(371\) 14.1932 0.736875
\(372\) 0 0
\(373\) 15.8669 0.821558 0.410779 0.911735i \(-0.365257\pi\)
0.410779 + 0.911735i \(0.365257\pi\)
\(374\) 0 0
\(375\) −3.65207 −0.188592
\(376\) 0 0
\(377\) 36.1331 1.86095
\(378\) 0 0
\(379\) −27.6503 −1.42030 −0.710149 0.704051i \(-0.751373\pi\)
−0.710149 + 0.704051i \(0.751373\pi\)
\(380\) 0 0
\(381\) −4.16036 −0.213141
\(382\) 0 0
\(383\) 2.53070 0.129313 0.0646563 0.997908i \(-0.479405\pi\)
0.0646563 + 0.997908i \(0.479405\pi\)
\(384\) 0 0
\(385\) 0.188155 0.00958925
\(386\) 0 0
\(387\) 37.4401 1.90319
\(388\) 0 0
\(389\) 17.7301 0.898950 0.449475 0.893293i \(-0.351611\pi\)
0.449475 + 0.893293i \(0.351611\pi\)
\(390\) 0 0
\(391\) −20.3105 −1.02715
\(392\) 0 0
\(393\) 26.2465 1.32396
\(394\) 0 0
\(395\) 0.123774 0.00622773
\(396\) 0 0
\(397\) 5.30065 0.266032 0.133016 0.991114i \(-0.457534\pi\)
0.133016 + 0.991114i \(0.457534\pi\)
\(398\) 0 0
\(399\) −6.69948 −0.335394
\(400\) 0 0
\(401\) 8.10636 0.404812 0.202406 0.979302i \(-0.435124\pi\)
0.202406 + 0.979302i \(0.435124\pi\)
\(402\) 0 0
\(403\) −8.01225 −0.399119
\(404\) 0 0
\(405\) 0.658286 0.0327105
\(406\) 0 0
\(407\) 1.26298 0.0626035
\(408\) 0 0
\(409\) −18.8134 −0.930263 −0.465132 0.885241i \(-0.653993\pi\)
−0.465132 + 0.885241i \(0.653993\pi\)
\(410\) 0 0
\(411\) −45.5649 −2.24755
\(412\) 0 0
\(413\) 8.38758 0.412726
\(414\) 0 0
\(415\) −1.59765 −0.0784257
\(416\) 0 0
\(417\) 37.8671 1.85436
\(418\) 0 0
\(419\) −20.7589 −1.01414 −0.507069 0.861906i \(-0.669271\pi\)
−0.507069 + 0.861906i \(0.669271\pi\)
\(420\) 0 0
\(421\) 25.4315 1.23945 0.619727 0.784817i \(-0.287243\pi\)
0.619727 + 0.784817i \(0.287243\pi\)
\(422\) 0 0
\(423\) 16.0965 0.782639
\(424\) 0 0
\(425\) −15.9499 −0.773682
\(426\) 0 0
\(427\) −21.8135 −1.05563
\(428\) 0 0
\(429\) 10.4848 0.506211
\(430\) 0 0
\(431\) −20.4276 −0.983963 −0.491982 0.870606i \(-0.663727\pi\)
−0.491982 + 0.870606i \(0.663727\pi\)
\(432\) 0 0
\(433\) −22.3315 −1.07318 −0.536592 0.843842i \(-0.680289\pi\)
−0.536592 + 0.843842i \(0.680289\pi\)
\(434\) 0 0
\(435\) −2.52619 −0.121122
\(436\) 0 0
\(437\) −6.60999 −0.316199
\(438\) 0 0
\(439\) −10.7157 −0.511432 −0.255716 0.966752i \(-0.582311\pi\)
−0.255716 + 0.966752i \(0.582311\pi\)
\(440\) 0 0
\(441\) −12.0616 −0.574361
\(442\) 0 0
\(443\) −25.4030 −1.20693 −0.603466 0.797388i \(-0.706214\pi\)
−0.603466 + 0.797388i \(0.706214\pi\)
\(444\) 0 0
\(445\) 0.163307 0.00774148
\(446\) 0 0
\(447\) −67.4924 −3.19228
\(448\) 0 0
\(449\) −32.5238 −1.53490 −0.767448 0.641112i \(-0.778474\pi\)
−0.767448 + 0.641112i \(0.778474\pi\)
\(450\) 0 0
\(451\) −6.98922 −0.329110
\(452\) 0 0
\(453\) −1.56401 −0.0734834
\(454\) 0 0
\(455\) 1.43751 0.0673914
\(456\) 0 0
\(457\) −7.75980 −0.362988 −0.181494 0.983392i \(-0.558093\pi\)
−0.181494 + 0.983392i \(0.558093\pi\)
\(458\) 0 0
\(459\) 24.0113 1.12075
\(460\) 0 0
\(461\) 20.1297 0.937532 0.468766 0.883322i \(-0.344699\pi\)
0.468766 + 0.883322i \(0.344699\pi\)
\(462\) 0 0
\(463\) 8.91696 0.414406 0.207203 0.978298i \(-0.433564\pi\)
0.207203 + 0.978298i \(0.433564\pi\)
\(464\) 0 0
\(465\) 0.560165 0.0259770
\(466\) 0 0
\(467\) 21.8796 1.01247 0.506233 0.862397i \(-0.331038\pi\)
0.506233 + 0.862397i \(0.331038\pi\)
\(468\) 0 0
\(469\) 22.9844 1.06132
\(470\) 0 0
\(471\) −66.2287 −3.05166
\(472\) 0 0
\(473\) −4.60794 −0.211873
\(474\) 0 0
\(475\) −5.19084 −0.238172
\(476\) 0 0
\(477\) −35.9252 −1.64490
\(478\) 0 0
\(479\) −22.1664 −1.01281 −0.506404 0.862297i \(-0.669025\pi\)
−0.506404 + 0.862297i \(0.669025\pi\)
\(480\) 0 0
\(481\) 9.64918 0.439965
\(482\) 0 0
\(483\) 40.8308 1.85787
\(484\) 0 0
\(485\) 1.50911 0.0685252
\(486\) 0 0
\(487\) 1.47231 0.0667167 0.0333584 0.999443i \(-0.489380\pi\)
0.0333584 + 0.999443i \(0.489380\pi\)
\(488\) 0 0
\(489\) −6.43007 −0.290778
\(490\) 0 0
\(491\) 32.0435 1.44610 0.723051 0.690795i \(-0.242739\pi\)
0.723051 + 0.690795i \(0.242739\pi\)
\(492\) 0 0
\(493\) −22.1001 −0.995338
\(494\) 0 0
\(495\) −0.476248 −0.0214058
\(496\) 0 0
\(497\) −5.80240 −0.260273
\(498\) 0 0
\(499\) 6.46266 0.289308 0.144654 0.989482i \(-0.453793\pi\)
0.144654 + 0.989482i \(0.453793\pi\)
\(500\) 0 0
\(501\) 21.6244 0.966105
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −1.91795 −0.0853477
\(506\) 0 0
\(507\) 42.0604 1.86797
\(508\) 0 0
\(509\) −21.3454 −0.946119 −0.473059 0.881031i \(-0.656850\pi\)
−0.473059 + 0.881031i \(0.656850\pi\)
\(510\) 0 0
\(511\) 36.1690 1.60002
\(512\) 0 0
\(513\) 7.81443 0.345015
\(514\) 0 0
\(515\) −1.86516 −0.0821888
\(516\) 0 0
\(517\) −1.98108 −0.0871277
\(518\) 0 0
\(519\) −31.8780 −1.39929
\(520\) 0 0
\(521\) 1.25630 0.0550395 0.0275198 0.999621i \(-0.491239\pi\)
0.0275198 + 0.999621i \(0.491239\pi\)
\(522\) 0 0
\(523\) 11.5794 0.506334 0.253167 0.967423i \(-0.418528\pi\)
0.253167 + 0.967423i \(0.418528\pi\)
\(524\) 0 0
\(525\) 32.0646 1.39941
\(526\) 0 0
\(527\) 4.90054 0.213471
\(528\) 0 0
\(529\) 17.2854 0.751540
\(530\) 0 0
\(531\) −21.2303 −0.921315
\(532\) 0 0
\(533\) −53.3979 −2.31292
\(534\) 0 0
\(535\) −2.23602 −0.0966716
\(536\) 0 0
\(537\) 41.7382 1.80114
\(538\) 0 0
\(539\) 1.48448 0.0639411
\(540\) 0 0
\(541\) 13.2144 0.568132 0.284066 0.958805i \(-0.408316\pi\)
0.284066 + 0.958805i \(0.408316\pi\)
\(542\) 0 0
\(543\) 50.7238 2.17677
\(544\) 0 0
\(545\) −0.516714 −0.0221336
\(546\) 0 0
\(547\) 23.8882 1.02139 0.510693 0.859763i \(-0.329389\pi\)
0.510693 + 0.859763i \(0.329389\pi\)
\(548\) 0 0
\(549\) 55.2133 2.35645
\(550\) 0 0
\(551\) −7.19242 −0.306407
\(552\) 0 0
\(553\) −2.17683 −0.0925681
\(554\) 0 0
\(555\) −0.674608 −0.0286355
\(556\) 0 0
\(557\) 31.1120 1.31826 0.659130 0.752029i \(-0.270925\pi\)
0.659130 + 0.752029i \(0.270925\pi\)
\(558\) 0 0
\(559\) −35.2048 −1.48900
\(560\) 0 0
\(561\) −6.41282 −0.270749
\(562\) 0 0
\(563\) 12.1112 0.510424 0.255212 0.966885i \(-0.417855\pi\)
0.255212 + 0.966885i \(0.417855\pi\)
\(564\) 0 0
\(565\) 2.06834 0.0870158
\(566\) 0 0
\(567\) −11.5774 −0.486204
\(568\) 0 0
\(569\) −4.88936 −0.204972 −0.102486 0.994734i \(-0.532680\pi\)
−0.102486 + 0.994734i \(0.532680\pi\)
\(570\) 0 0
\(571\) 16.7597 0.701371 0.350685 0.936493i \(-0.385949\pi\)
0.350685 + 0.936493i \(0.385949\pi\)
\(572\) 0 0
\(573\) 17.2925 0.722403
\(574\) 0 0
\(575\) 31.6362 1.31932
\(576\) 0 0
\(577\) 29.2363 1.21712 0.608561 0.793507i \(-0.291747\pi\)
0.608561 + 0.793507i \(0.291747\pi\)
\(578\) 0 0
\(579\) −53.3812 −2.21845
\(580\) 0 0
\(581\) 28.0982 1.16571
\(582\) 0 0
\(583\) 4.42150 0.183120
\(584\) 0 0
\(585\) −3.63855 −0.150436
\(586\) 0 0
\(587\) −13.2629 −0.547418 −0.273709 0.961812i \(-0.588251\pi\)
−0.273709 + 0.961812i \(0.588251\pi\)
\(588\) 0 0
\(589\) 1.59487 0.0657153
\(590\) 0 0
\(591\) 40.2505 1.65568
\(592\) 0 0
\(593\) 15.9463 0.654834 0.327417 0.944880i \(-0.393822\pi\)
0.327417 + 0.944880i \(0.393822\pi\)
\(594\) 0 0
\(595\) −0.879222 −0.0360446
\(596\) 0 0
\(597\) 44.2713 1.81190
\(598\) 0 0
\(599\) −42.3185 −1.72909 −0.864544 0.502557i \(-0.832393\pi\)
−0.864544 + 0.502557i \(0.832393\pi\)
\(600\) 0 0
\(601\) 4.15062 0.169307 0.0846537 0.996410i \(-0.473022\pi\)
0.0846537 + 0.996410i \(0.473022\pi\)
\(602\) 0 0
\(603\) −58.1771 −2.36915
\(604\) 0 0
\(605\) −1.31629 −0.0535146
\(606\) 0 0
\(607\) −36.4247 −1.47843 −0.739217 0.673467i \(-0.764804\pi\)
−0.739217 + 0.673467i \(0.764804\pi\)
\(608\) 0 0
\(609\) 44.4285 1.80034
\(610\) 0 0
\(611\) −15.1355 −0.612316
\(612\) 0 0
\(613\) −21.3761 −0.863372 −0.431686 0.902024i \(-0.642081\pi\)
−0.431686 + 0.902024i \(0.642081\pi\)
\(614\) 0 0
\(615\) 3.73323 0.150538
\(616\) 0 0
\(617\) 28.7707 1.15826 0.579131 0.815234i \(-0.303392\pi\)
0.579131 + 0.815234i \(0.303392\pi\)
\(618\) 0 0
\(619\) −13.4867 −0.542076 −0.271038 0.962569i \(-0.587367\pi\)
−0.271038 + 0.962569i \(0.587367\pi\)
\(620\) 0 0
\(621\) −47.6260 −1.91117
\(622\) 0 0
\(623\) −2.87210 −0.115068
\(624\) 0 0
\(625\) 24.7659 0.990636
\(626\) 0 0
\(627\) −2.08703 −0.0833481
\(628\) 0 0
\(629\) −5.90173 −0.235317
\(630\) 0 0
\(631\) 32.1866 1.28133 0.640665 0.767821i \(-0.278659\pi\)
0.640665 + 0.767821i \(0.278659\pi\)
\(632\) 0 0
\(633\) 0.0843666 0.00335327
\(634\) 0 0
\(635\) −0.177692 −0.00705150
\(636\) 0 0
\(637\) 11.3415 0.449365
\(638\) 0 0
\(639\) 14.6868 0.580999
\(640\) 0 0
\(641\) −43.8329 −1.73129 −0.865647 0.500655i \(-0.833092\pi\)
−0.865647 + 0.500655i \(0.833092\pi\)
\(642\) 0 0
\(643\) −35.1898 −1.38775 −0.693875 0.720096i \(-0.744098\pi\)
−0.693875 + 0.720096i \(0.744098\pi\)
\(644\) 0 0
\(645\) 2.46129 0.0969132
\(646\) 0 0
\(647\) −0.759380 −0.0298543 −0.0149271 0.999889i \(-0.504752\pi\)
−0.0149271 + 0.999889i \(0.504752\pi\)
\(648\) 0 0
\(649\) 2.61291 0.102566
\(650\) 0 0
\(651\) −9.85171 −0.386119
\(652\) 0 0
\(653\) −19.8143 −0.775395 −0.387698 0.921787i \(-0.626730\pi\)
−0.387698 + 0.921787i \(0.626730\pi\)
\(654\) 0 0
\(655\) 1.12101 0.0438016
\(656\) 0 0
\(657\) −91.5493 −3.57168
\(658\) 0 0
\(659\) 48.9815 1.90805 0.954024 0.299729i \(-0.0968964\pi\)
0.954024 + 0.299729i \(0.0968964\pi\)
\(660\) 0 0
\(661\) −33.7707 −1.31353 −0.656763 0.754097i \(-0.728075\pi\)
−0.656763 + 0.754097i \(0.728075\pi\)
\(662\) 0 0
\(663\) −48.9941 −1.90277
\(664\) 0 0
\(665\) −0.286141 −0.0110961
\(666\) 0 0
\(667\) 43.8351 1.69730
\(668\) 0 0
\(669\) 56.0188 2.16581
\(670\) 0 0
\(671\) −6.79538 −0.262333
\(672\) 0 0
\(673\) 13.3901 0.516149 0.258075 0.966125i \(-0.416912\pi\)
0.258075 + 0.966125i \(0.416912\pi\)
\(674\) 0 0
\(675\) −37.4008 −1.43956
\(676\) 0 0
\(677\) −7.81952 −0.300529 −0.150264 0.988646i \(-0.548012\pi\)
−0.150264 + 0.988646i \(0.548012\pi\)
\(678\) 0 0
\(679\) −26.5410 −1.01855
\(680\) 0 0
\(681\) −59.2722 −2.27131
\(682\) 0 0
\(683\) 3.29209 0.125968 0.0629841 0.998015i \(-0.479938\pi\)
0.0629841 + 0.998015i \(0.479938\pi\)
\(684\) 0 0
\(685\) −1.94612 −0.0743573
\(686\) 0 0
\(687\) 51.5589 1.96710
\(688\) 0 0
\(689\) 33.7804 1.28693
\(690\) 0 0
\(691\) 48.7786 1.85563 0.927813 0.373045i \(-0.121686\pi\)
0.927813 + 0.373045i \(0.121686\pi\)
\(692\) 0 0
\(693\) 8.37586 0.318173
\(694\) 0 0
\(695\) 1.61734 0.0613490
\(696\) 0 0
\(697\) 32.6597 1.23708
\(698\) 0 0
\(699\) 1.44426 0.0546269
\(700\) 0 0
\(701\) −18.1750 −0.686462 −0.343231 0.939251i \(-0.611521\pi\)
−0.343231 + 0.939251i \(0.611521\pi\)
\(702\) 0 0
\(703\) −1.92070 −0.0724406
\(704\) 0 0
\(705\) 1.05817 0.0398532
\(706\) 0 0
\(707\) 33.7313 1.26860
\(708\) 0 0
\(709\) −17.9486 −0.674073 −0.337036 0.941492i \(-0.609425\pi\)
−0.337036 + 0.941492i \(0.609425\pi\)
\(710\) 0 0
\(711\) 5.50988 0.206637
\(712\) 0 0
\(713\) −9.72011 −0.364021
\(714\) 0 0
\(715\) 0.447815 0.0167473
\(716\) 0 0
\(717\) 77.8576 2.90765
\(718\) 0 0
\(719\) 12.2202 0.455736 0.227868 0.973692i \(-0.426825\pi\)
0.227868 + 0.973692i \(0.426825\pi\)
\(720\) 0 0
\(721\) 32.8029 1.22164
\(722\) 0 0
\(723\) 9.24950 0.343993
\(724\) 0 0
\(725\) 34.4238 1.27847
\(726\) 0 0
\(727\) −12.1125 −0.449228 −0.224614 0.974448i \(-0.572112\pi\)
−0.224614 + 0.974448i \(0.572112\pi\)
\(728\) 0 0
\(729\) −36.5725 −1.35454
\(730\) 0 0
\(731\) 21.5323 0.796402
\(732\) 0 0
\(733\) −8.94868 −0.330527 −0.165264 0.986249i \(-0.552847\pi\)
−0.165264 + 0.986249i \(0.552847\pi\)
\(734\) 0 0
\(735\) −0.792922 −0.0292474
\(736\) 0 0
\(737\) 7.16014 0.263747
\(738\) 0 0
\(739\) −20.4727 −0.753100 −0.376550 0.926396i \(-0.622890\pi\)
−0.376550 + 0.926396i \(0.622890\pi\)
\(740\) 0 0
\(741\) −15.9450 −0.585754
\(742\) 0 0
\(743\) 3.47345 0.127429 0.0637143 0.997968i \(-0.479705\pi\)
0.0637143 + 0.997968i \(0.479705\pi\)
\(744\) 0 0
\(745\) −2.88266 −0.105612
\(746\) 0 0
\(747\) −71.1208 −2.60218
\(748\) 0 0
\(749\) 39.3252 1.43691
\(750\) 0 0
\(751\) 17.9585 0.655316 0.327658 0.944796i \(-0.393741\pi\)
0.327658 + 0.944796i \(0.393741\pi\)
\(752\) 0 0
\(753\) −28.2773 −1.03048
\(754\) 0 0
\(755\) −0.0668000 −0.00243110
\(756\) 0 0
\(757\) 27.5553 1.00152 0.500758 0.865588i \(-0.333055\pi\)
0.500758 + 0.865588i \(0.333055\pi\)
\(758\) 0 0
\(759\) 12.7197 0.461696
\(760\) 0 0
\(761\) −15.2016 −0.551059 −0.275529 0.961293i \(-0.588853\pi\)
−0.275529 + 0.961293i \(0.588853\pi\)
\(762\) 0 0
\(763\) 9.08753 0.328991
\(764\) 0 0
\(765\) 2.22545 0.0804612
\(766\) 0 0
\(767\) 19.9627 0.720813
\(768\) 0 0
\(769\) 39.3884 1.42038 0.710190 0.704010i \(-0.248609\pi\)
0.710190 + 0.704010i \(0.248609\pi\)
\(770\) 0 0
\(771\) −37.4719 −1.34952
\(772\) 0 0
\(773\) 2.28513 0.0821903 0.0410952 0.999155i \(-0.486915\pi\)
0.0410952 + 0.999155i \(0.486915\pi\)
\(774\) 0 0
\(775\) −7.63323 −0.274194
\(776\) 0 0
\(777\) 11.8644 0.425634
\(778\) 0 0
\(779\) 10.6290 0.380824
\(780\) 0 0
\(781\) −1.80757 −0.0646801
\(782\) 0 0
\(783\) −51.8225 −1.85198
\(784\) 0 0
\(785\) −2.82868 −0.100960
\(786\) 0 0
\(787\) −51.1008 −1.82155 −0.910773 0.412908i \(-0.864513\pi\)
−0.910773 + 0.412908i \(0.864513\pi\)
\(788\) 0 0
\(789\) 68.1143 2.42493
\(790\) 0 0
\(791\) −36.3763 −1.29339
\(792\) 0 0
\(793\) −51.9169 −1.84362
\(794\) 0 0
\(795\) −2.36170 −0.0837610
\(796\) 0 0
\(797\) −21.7081 −0.768941 −0.384470 0.923137i \(-0.625616\pi\)
−0.384470 + 0.923137i \(0.625616\pi\)
\(798\) 0 0
\(799\) 9.25731 0.327500
\(800\) 0 0
\(801\) 7.26973 0.256863
\(802\) 0 0
\(803\) 11.2674 0.397619
\(804\) 0 0
\(805\) 1.74392 0.0614651
\(806\) 0 0
\(807\) −19.6341 −0.691154
\(808\) 0 0
\(809\) 25.3624 0.891694 0.445847 0.895109i \(-0.352903\pi\)
0.445847 + 0.895109i \(0.352903\pi\)
\(810\) 0 0
\(811\) 20.0122 0.702722 0.351361 0.936240i \(-0.385719\pi\)
0.351361 + 0.936240i \(0.385719\pi\)
\(812\) 0 0
\(813\) −17.8891 −0.627399
\(814\) 0 0
\(815\) −0.274634 −0.00962000
\(816\) 0 0
\(817\) 7.00764 0.245166
\(818\) 0 0
\(819\) 63.9918 2.23605
\(820\) 0 0
\(821\) 10.4190 0.363627 0.181813 0.983333i \(-0.441803\pi\)
0.181813 + 0.983333i \(0.441803\pi\)
\(822\) 0 0
\(823\) −13.6657 −0.476355 −0.238177 0.971222i \(-0.576550\pi\)
−0.238177 + 0.971222i \(0.576550\pi\)
\(824\) 0 0
\(825\) 9.98880 0.347766
\(826\) 0 0
\(827\) 44.3157 1.54101 0.770504 0.637435i \(-0.220005\pi\)
0.770504 + 0.637435i \(0.220005\pi\)
\(828\) 0 0
\(829\) −22.0998 −0.767559 −0.383780 0.923425i \(-0.625378\pi\)
−0.383780 + 0.923425i \(0.625378\pi\)
\(830\) 0 0
\(831\) −34.2247 −1.18724
\(832\) 0 0
\(833\) −6.93678 −0.240345
\(834\) 0 0
\(835\) 0.923595 0.0319623
\(836\) 0 0
\(837\) 11.4913 0.397196
\(838\) 0 0
\(839\) 23.8595 0.823722 0.411861 0.911247i \(-0.364879\pi\)
0.411861 + 0.911247i \(0.364879\pi\)
\(840\) 0 0
\(841\) 18.6975 0.644742
\(842\) 0 0
\(843\) −66.0911 −2.27630
\(844\) 0 0
\(845\) 1.79643 0.0617992
\(846\) 0 0
\(847\) 23.1497 0.795434
\(848\) 0 0
\(849\) 65.6994 2.25480
\(850\) 0 0
\(851\) 11.7060 0.401275
\(852\) 0 0
\(853\) −30.4220 −1.04163 −0.520815 0.853670i \(-0.674372\pi\)
−0.520815 + 0.853670i \(0.674372\pi\)
\(854\) 0 0
\(855\) 0.724266 0.0247694
\(856\) 0 0
\(857\) 4.61527 0.157654 0.0788272 0.996888i \(-0.474882\pi\)
0.0788272 + 0.996888i \(0.474882\pi\)
\(858\) 0 0
\(859\) 8.44274 0.288063 0.144031 0.989573i \(-0.453993\pi\)
0.144031 + 0.989573i \(0.453993\pi\)
\(860\) 0 0
\(861\) −65.6570 −2.23758
\(862\) 0 0
\(863\) 14.4390 0.491509 0.245755 0.969332i \(-0.420964\pi\)
0.245755 + 0.969332i \(0.420964\pi\)
\(864\) 0 0
\(865\) −1.36154 −0.0462936
\(866\) 0 0
\(867\) −19.7833 −0.671875
\(868\) 0 0
\(869\) −0.678129 −0.0230039
\(870\) 0 0
\(871\) 54.7037 1.85356
\(872\) 0 0
\(873\) 67.1793 2.27368
\(874\) 0 0
\(875\) 2.74330 0.0927405
\(876\) 0 0
\(877\) 24.3153 0.821069 0.410535 0.911845i \(-0.365342\pi\)
0.410535 + 0.911845i \(0.365342\pi\)
\(878\) 0 0
\(879\) −72.6645 −2.45091
\(880\) 0 0
\(881\) −27.7217 −0.933966 −0.466983 0.884266i \(-0.654659\pi\)
−0.466983 + 0.884266i \(0.654659\pi\)
\(882\) 0 0
\(883\) 22.8793 0.769948 0.384974 0.922927i \(-0.374210\pi\)
0.384974 + 0.922927i \(0.374210\pi\)
\(884\) 0 0
\(885\) −1.39566 −0.0469147
\(886\) 0 0
\(887\) −9.37976 −0.314942 −0.157471 0.987524i \(-0.550334\pi\)
−0.157471 + 0.987524i \(0.550334\pi\)
\(888\) 0 0
\(889\) 3.12510 0.104813
\(890\) 0 0
\(891\) −3.60661 −0.120826
\(892\) 0 0
\(893\) 3.01277 0.100818
\(894\) 0 0
\(895\) 1.78267 0.0595882
\(896\) 0 0
\(897\) 97.1788 3.24471
\(898\) 0 0
\(899\) −10.5766 −0.352749
\(900\) 0 0
\(901\) −20.6611 −0.688320
\(902\) 0 0
\(903\) −43.2871 −1.44051
\(904\) 0 0
\(905\) 2.16646 0.0720155
\(906\) 0 0
\(907\) −19.4578 −0.646087 −0.323044 0.946384i \(-0.604706\pi\)
−0.323044 + 0.946384i \(0.604706\pi\)
\(908\) 0 0
\(909\) −85.3791 −2.83185
\(910\) 0 0
\(911\) 25.2593 0.836878 0.418439 0.908245i \(-0.362577\pi\)
0.418439 + 0.908245i \(0.362577\pi\)
\(912\) 0 0
\(913\) 8.75320 0.289689
\(914\) 0 0
\(915\) 3.62969 0.119994
\(916\) 0 0
\(917\) −19.7154 −0.651061
\(918\) 0 0
\(919\) 20.9774 0.691982 0.345991 0.938238i \(-0.387543\pi\)
0.345991 + 0.938238i \(0.387543\pi\)
\(920\) 0 0
\(921\) −17.8120 −0.586926
\(922\) 0 0
\(923\) −13.8099 −0.454559
\(924\) 0 0
\(925\) 9.19272 0.302255
\(926\) 0 0
\(927\) −83.0291 −2.72703
\(928\) 0 0
\(929\) 60.5873 1.98780 0.993902 0.110263i \(-0.0351695\pi\)
0.993902 + 0.110263i \(0.0351695\pi\)
\(930\) 0 0
\(931\) −2.25756 −0.0739884
\(932\) 0 0
\(933\) 67.6254 2.21395
\(934\) 0 0
\(935\) −0.273897 −0.00895738
\(936\) 0 0
\(937\) −27.5445 −0.899839 −0.449920 0.893069i \(-0.648547\pi\)
−0.449920 + 0.893069i \(0.648547\pi\)
\(938\) 0 0
\(939\) 39.9128 1.30250
\(940\) 0 0
\(941\) 1.17112 0.0381774 0.0190887 0.999818i \(-0.493924\pi\)
0.0190887 + 0.999818i \(0.493924\pi\)
\(942\) 0 0
\(943\) −64.7799 −2.10952
\(944\) 0 0
\(945\) −2.06169 −0.0670667
\(946\) 0 0
\(947\) 12.8030 0.416040 0.208020 0.978125i \(-0.433298\pi\)
0.208020 + 0.978125i \(0.433298\pi\)
\(948\) 0 0
\(949\) 86.0835 2.79439
\(950\) 0 0
\(951\) −9.43542 −0.305964
\(952\) 0 0
\(953\) 13.5203 0.437966 0.218983 0.975729i \(-0.429726\pi\)
0.218983 + 0.975729i \(0.429726\pi\)
\(954\) 0 0
\(955\) 0.738575 0.0238997
\(956\) 0 0
\(957\) 13.8405 0.447399
\(958\) 0 0
\(959\) 34.2267 1.10524
\(960\) 0 0
\(961\) −28.6547 −0.924346
\(962\) 0 0
\(963\) −99.5382 −3.20757
\(964\) 0 0
\(965\) −2.27996 −0.0733944
\(966\) 0 0
\(967\) 62.1877 1.99982 0.999911 0.0133649i \(-0.00425429\pi\)
0.999911 + 0.0133649i \(0.00425429\pi\)
\(968\) 0 0
\(969\) 9.75244 0.313294
\(970\) 0 0
\(971\) −19.5870 −0.628578 −0.314289 0.949327i \(-0.601766\pi\)
−0.314289 + 0.949327i \(0.601766\pi\)
\(972\) 0 0
\(973\) −28.4443 −0.911884
\(974\) 0 0
\(975\) 76.3147 2.44403
\(976\) 0 0
\(977\) −24.8114 −0.793787 −0.396893 0.917865i \(-0.629912\pi\)
−0.396893 + 0.917865i \(0.629912\pi\)
\(978\) 0 0
\(979\) −0.894722 −0.0285954
\(980\) 0 0
\(981\) −23.0019 −0.734395
\(982\) 0 0
\(983\) −9.40956 −0.300118 −0.150059 0.988677i \(-0.547946\pi\)
−0.150059 + 0.988677i \(0.547946\pi\)
\(984\) 0 0
\(985\) 1.71913 0.0547761
\(986\) 0 0
\(987\) −18.6103 −0.592372
\(988\) 0 0
\(989\) −42.7089 −1.35806
\(990\) 0 0
\(991\) 16.3958 0.520829 0.260414 0.965497i \(-0.416141\pi\)
0.260414 + 0.965497i \(0.416141\pi\)
\(992\) 0 0
\(993\) 86.9594 2.75957
\(994\) 0 0
\(995\) 1.89086 0.0599444
\(996\) 0 0
\(997\) −10.9983 −0.348320 −0.174160 0.984717i \(-0.555721\pi\)
−0.174160 + 0.984717i \(0.555721\pi\)
\(998\) 0 0
\(999\) −13.8389 −0.437845
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 \(a_p\))