Properties

Label 6040.2.a.p.1.5
Level 6040
Weight 2
Character 6040.1
Self dual Yes
Analytic conductor 48.230
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6040 = 2^{3} \cdot 5 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6040.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2296428209\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{7} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(2.34269\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.34269 q^{3}\) \(+1.00000 q^{5}\) \(-1.53409 q^{7}\) \(+2.48818 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.34269 q^{3}\) \(+1.00000 q^{5}\) \(-1.53409 q^{7}\) \(+2.48818 q^{9}\) \(-2.13813 q^{11}\) \(-0.470591 q^{13}\) \(-2.34269 q^{15}\) \(+2.13955 q^{17}\) \(-4.98365 q^{19}\) \(+3.59390 q^{21}\) \(-2.33382 q^{23}\) \(+1.00000 q^{25}\) \(+1.19902 q^{27}\) \(+6.12425 q^{29}\) \(+6.34138 q^{31}\) \(+5.00898 q^{33}\) \(-1.53409 q^{35}\) \(+2.64294 q^{37}\) \(+1.10245 q^{39}\) \(+6.14093 q^{41}\) \(-7.94163 q^{43}\) \(+2.48818 q^{45}\) \(+10.8356 q^{47}\) \(-4.64656 q^{49}\) \(-5.01230 q^{51}\) \(+6.95012 q^{53}\) \(-2.13813 q^{55}\) \(+11.6751 q^{57}\) \(-9.95452 q^{59}\) \(-11.6416 q^{61}\) \(-3.81711 q^{63}\) \(-0.470591 q^{65}\) \(+1.12749 q^{67}\) \(+5.46741 q^{69}\) \(-8.62775 q^{71}\) \(-1.80753 q^{73}\) \(-2.34269 q^{75}\) \(+3.28010 q^{77}\) \(+5.78496 q^{79}\) \(-10.2735 q^{81}\) \(+10.7240 q^{83}\) \(+2.13955 q^{85}\) \(-14.3472 q^{87}\) \(-11.5253 q^{89}\) \(+0.721931 q^{91}\) \(-14.8559 q^{93}\) \(-4.98365 q^{95}\) \(-3.80804 q^{97}\) \(-5.32007 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 18q^{11} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 5q^{15} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 18q^{21} \) \(\mathstrut -\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 19q^{25} \) \(\mathstrut -\mathstrut 35q^{27} \) \(\mathstrut -\mathstrut 35q^{29} \) \(\mathstrut -\mathstrut 26q^{31} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 21q^{43} \) \(\mathstrut +\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 40q^{47} \) \(\mathstrut +\mathstrut 23q^{49} \) \(\mathstrut -\mathstrut 32q^{51} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 18q^{55} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut -\mathstrut 53q^{63} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut -\mathstrut 42q^{67} \) \(\mathstrut -\mathstrut 31q^{69} \) \(\mathstrut -\mathstrut 46q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut -\mathstrut 7q^{89} \) \(\mathstrut -\mathstrut 61q^{91} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut -\mathstrut 27q^{95} \) \(\mathstrut +\mathstrut 39q^{97} \) \(\mathstrut -\mathstrut 52q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.34269 −1.35255 −0.676276 0.736649i \(-0.736407\pi\)
−0.676276 + 0.736649i \(0.736407\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −1.53409 −0.579833 −0.289916 0.957052i \(-0.593628\pi\)
−0.289916 + 0.957052i \(0.593628\pi\)
\(8\) 0 0
\(9\) 2.48818 0.829395
\(10\) 0 0
\(11\) −2.13813 −0.644672 −0.322336 0.946625i \(-0.604468\pi\)
−0.322336 + 0.946625i \(0.604468\pi\)
\(12\) 0 0
\(13\) −0.470591 −0.130518 −0.0652592 0.997868i \(-0.520787\pi\)
−0.0652592 + 0.997868i \(0.520787\pi\)
\(14\) 0 0
\(15\) −2.34269 −0.604879
\(16\) 0 0
\(17\) 2.13955 0.518918 0.259459 0.965754i \(-0.416456\pi\)
0.259459 + 0.965754i \(0.416456\pi\)
\(18\) 0 0
\(19\) −4.98365 −1.14333 −0.571663 0.820488i \(-0.693702\pi\)
−0.571663 + 0.820488i \(0.693702\pi\)
\(20\) 0 0
\(21\) 3.59390 0.784254
\(22\) 0 0
\(23\) −2.33382 −0.486635 −0.243317 0.969947i \(-0.578236\pi\)
−0.243317 + 0.969947i \(0.578236\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 1.19902 0.230752
\(28\) 0 0
\(29\) 6.12425 1.13725 0.568623 0.822599i \(-0.307477\pi\)
0.568623 + 0.822599i \(0.307477\pi\)
\(30\) 0 0
\(31\) 6.34138 1.13894 0.569472 0.822011i \(-0.307148\pi\)
0.569472 + 0.822011i \(0.307148\pi\)
\(32\) 0 0
\(33\) 5.00898 0.871952
\(34\) 0 0
\(35\) −1.53409 −0.259309
\(36\) 0 0
\(37\) 2.64294 0.434497 0.217249 0.976116i \(-0.430292\pi\)
0.217249 + 0.976116i \(0.430292\pi\)
\(38\) 0 0
\(39\) 1.10245 0.176533
\(40\) 0 0
\(41\) 6.14093 0.959052 0.479526 0.877528i \(-0.340809\pi\)
0.479526 + 0.877528i \(0.340809\pi\)
\(42\) 0 0
\(43\) −7.94163 −1.21109 −0.605544 0.795812i \(-0.707044\pi\)
−0.605544 + 0.795812i \(0.707044\pi\)
\(44\) 0 0
\(45\) 2.48818 0.370917
\(46\) 0 0
\(47\) 10.8356 1.58053 0.790267 0.612763i \(-0.209942\pi\)
0.790267 + 0.612763i \(0.209942\pi\)
\(48\) 0 0
\(49\) −4.64656 −0.663794
\(50\) 0 0
\(51\) −5.01230 −0.701863
\(52\) 0 0
\(53\) 6.95012 0.954673 0.477337 0.878721i \(-0.341602\pi\)
0.477337 + 0.878721i \(0.341602\pi\)
\(54\) 0 0
\(55\) −2.13813 −0.288306
\(56\) 0 0
\(57\) 11.6751 1.54641
\(58\) 0 0
\(59\) −9.95452 −1.29597 −0.647984 0.761654i \(-0.724388\pi\)
−0.647984 + 0.761654i \(0.724388\pi\)
\(60\) 0 0
\(61\) −11.6416 −1.49056 −0.745280 0.666752i \(-0.767684\pi\)
−0.745280 + 0.666752i \(0.767684\pi\)
\(62\) 0 0
\(63\) −3.81711 −0.480911
\(64\) 0 0
\(65\) −0.470591 −0.0583696
\(66\) 0 0
\(67\) 1.12749 0.137745 0.0688723 0.997625i \(-0.478060\pi\)
0.0688723 + 0.997625i \(0.478060\pi\)
\(68\) 0 0
\(69\) 5.46741 0.658199
\(70\) 0 0
\(71\) −8.62775 −1.02393 −0.511963 0.859008i \(-0.671081\pi\)
−0.511963 + 0.859008i \(0.671081\pi\)
\(72\) 0 0
\(73\) −1.80753 −0.211555 −0.105778 0.994390i \(-0.533733\pi\)
−0.105778 + 0.994390i \(0.533733\pi\)
\(74\) 0 0
\(75\) −2.34269 −0.270510
\(76\) 0 0
\(77\) 3.28010 0.373802
\(78\) 0 0
\(79\) 5.78496 0.650858 0.325429 0.945566i \(-0.394491\pi\)
0.325429 + 0.945566i \(0.394491\pi\)
\(80\) 0 0
\(81\) −10.2735 −1.14150
\(82\) 0 0
\(83\) 10.7240 1.17711 0.588557 0.808456i \(-0.299696\pi\)
0.588557 + 0.808456i \(0.299696\pi\)
\(84\) 0 0
\(85\) 2.13955 0.232067
\(86\) 0 0
\(87\) −14.3472 −1.53818
\(88\) 0 0
\(89\) −11.5253 −1.22168 −0.610841 0.791753i \(-0.709169\pi\)
−0.610841 + 0.791753i \(0.709169\pi\)
\(90\) 0 0
\(91\) 0.721931 0.0756789
\(92\) 0 0
\(93\) −14.8559 −1.54048
\(94\) 0 0
\(95\) −4.98365 −0.511311
\(96\) 0 0
\(97\) −3.80804 −0.386648 −0.193324 0.981135i \(-0.561927\pi\)
−0.193324 + 0.981135i \(0.561927\pi\)
\(98\) 0 0
\(99\) −5.32007 −0.534687
\(100\) 0 0
\(101\) 16.4634 1.63817 0.819086 0.573671i \(-0.194481\pi\)
0.819086 + 0.573671i \(0.194481\pi\)
\(102\) 0 0
\(103\) 8.93869 0.880755 0.440377 0.897813i \(-0.354845\pi\)
0.440377 + 0.897813i \(0.354845\pi\)
\(104\) 0 0
\(105\) 3.59390 0.350729
\(106\) 0 0
\(107\) −9.36125 −0.904986 −0.452493 0.891768i \(-0.649465\pi\)
−0.452493 + 0.891768i \(0.649465\pi\)
\(108\) 0 0
\(109\) 6.95632 0.666294 0.333147 0.942875i \(-0.391889\pi\)
0.333147 + 0.942875i \(0.391889\pi\)
\(110\) 0 0
\(111\) −6.19159 −0.587680
\(112\) 0 0
\(113\) 7.75915 0.729919 0.364960 0.931023i \(-0.381083\pi\)
0.364960 + 0.931023i \(0.381083\pi\)
\(114\) 0 0
\(115\) −2.33382 −0.217630
\(116\) 0 0
\(117\) −1.17092 −0.108251
\(118\) 0 0
\(119\) −3.28227 −0.300886
\(120\) 0 0
\(121\) −6.42838 −0.584398
\(122\) 0 0
\(123\) −14.3863 −1.29717
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 10.2593 0.910367 0.455184 0.890398i \(-0.349574\pi\)
0.455184 + 0.890398i \(0.349574\pi\)
\(128\) 0 0
\(129\) 18.6048 1.63806
\(130\) 0 0
\(131\) 4.40919 0.385232 0.192616 0.981274i \(-0.438303\pi\)
0.192616 + 0.981274i \(0.438303\pi\)
\(132\) 0 0
\(133\) 7.64538 0.662938
\(134\) 0 0
\(135\) 1.19902 0.103195
\(136\) 0 0
\(137\) 17.3442 1.48181 0.740906 0.671609i \(-0.234396\pi\)
0.740906 + 0.671609i \(0.234396\pi\)
\(138\) 0 0
\(139\) −18.7375 −1.58929 −0.794646 0.607073i \(-0.792344\pi\)
−0.794646 + 0.607073i \(0.792344\pi\)
\(140\) 0 0
\(141\) −25.3844 −2.13775
\(142\) 0 0
\(143\) 1.00619 0.0841415
\(144\) 0 0
\(145\) 6.12425 0.508591
\(146\) 0 0
\(147\) 10.8854 0.897815
\(148\) 0 0
\(149\) −13.3543 −1.09402 −0.547012 0.837125i \(-0.684235\pi\)
−0.547012 + 0.837125i \(0.684235\pi\)
\(150\) 0 0
\(151\) 1.00000 0.0813788
\(152\) 0 0
\(153\) 5.32360 0.430388
\(154\) 0 0
\(155\) 6.34138 0.509352
\(156\) 0 0
\(157\) −2.26259 −0.180574 −0.0902871 0.995916i \(-0.528778\pi\)
−0.0902871 + 0.995916i \(0.528778\pi\)
\(158\) 0 0
\(159\) −16.2820 −1.29124
\(160\) 0 0
\(161\) 3.58030 0.282167
\(162\) 0 0
\(163\) 1.08367 0.0848794 0.0424397 0.999099i \(-0.486487\pi\)
0.0424397 + 0.999099i \(0.486487\pi\)
\(164\) 0 0
\(165\) 5.00898 0.389949
\(166\) 0 0
\(167\) −6.51511 −0.504155 −0.252077 0.967707i \(-0.581114\pi\)
−0.252077 + 0.967707i \(0.581114\pi\)
\(168\) 0 0
\(169\) −12.7785 −0.982965
\(170\) 0 0
\(171\) −12.4002 −0.948269
\(172\) 0 0
\(173\) −3.76879 −0.286536 −0.143268 0.989684i \(-0.545761\pi\)
−0.143268 + 0.989684i \(0.545761\pi\)
\(174\) 0 0
\(175\) −1.53409 −0.115967
\(176\) 0 0
\(177\) 23.3203 1.75286
\(178\) 0 0
\(179\) −2.53535 −0.189501 −0.0947506 0.995501i \(-0.530205\pi\)
−0.0947506 + 0.995501i \(0.530205\pi\)
\(180\) 0 0
\(181\) 5.12147 0.380676 0.190338 0.981719i \(-0.439042\pi\)
0.190338 + 0.981719i \(0.439042\pi\)
\(182\) 0 0
\(183\) 27.2727 2.01606
\(184\) 0 0
\(185\) 2.64294 0.194313
\(186\) 0 0
\(187\) −4.57465 −0.334532
\(188\) 0 0
\(189\) −1.83941 −0.133798
\(190\) 0 0
\(191\) 23.9806 1.73517 0.867587 0.497286i \(-0.165670\pi\)
0.867587 + 0.497286i \(0.165670\pi\)
\(192\) 0 0
\(193\) 18.3581 1.32144 0.660722 0.750631i \(-0.270250\pi\)
0.660722 + 0.750631i \(0.270250\pi\)
\(194\) 0 0
\(195\) 1.10245 0.0789479
\(196\) 0 0
\(197\) −25.3522 −1.80627 −0.903133 0.429360i \(-0.858739\pi\)
−0.903133 + 0.429360i \(0.858739\pi\)
\(198\) 0 0
\(199\) 1.52208 0.107897 0.0539486 0.998544i \(-0.482819\pi\)
0.0539486 + 0.998544i \(0.482819\pi\)
\(200\) 0 0
\(201\) −2.64135 −0.186307
\(202\) 0 0
\(203\) −9.39518 −0.659412
\(204\) 0 0
\(205\) 6.14093 0.428901
\(206\) 0 0
\(207\) −5.80697 −0.403612
\(208\) 0 0
\(209\) 10.6557 0.737070
\(210\) 0 0
\(211\) 5.84374 0.402300 0.201150 0.979560i \(-0.435532\pi\)
0.201150 + 0.979560i \(0.435532\pi\)
\(212\) 0 0
\(213\) 20.2121 1.38491
\(214\) 0 0
\(215\) −7.94163 −0.541615
\(216\) 0 0
\(217\) −9.72826 −0.660398
\(218\) 0 0
\(219\) 4.23447 0.286139
\(220\) 0 0
\(221\) −1.00685 −0.0677283
\(222\) 0 0
\(223\) −26.8074 −1.79515 −0.897577 0.440858i \(-0.854674\pi\)
−0.897577 + 0.440858i \(0.854674\pi\)
\(224\) 0 0
\(225\) 2.48818 0.165879
\(226\) 0 0
\(227\) −7.51585 −0.498844 −0.249422 0.968395i \(-0.580241\pi\)
−0.249422 + 0.968395i \(0.580241\pi\)
\(228\) 0 0
\(229\) −14.7307 −0.973435 −0.486717 0.873559i \(-0.661806\pi\)
−0.486717 + 0.873559i \(0.661806\pi\)
\(230\) 0 0
\(231\) −7.68425 −0.505586
\(232\) 0 0
\(233\) −21.5943 −1.41469 −0.707344 0.706870i \(-0.750107\pi\)
−0.707344 + 0.706870i \(0.750107\pi\)
\(234\) 0 0
\(235\) 10.8356 0.706836
\(236\) 0 0
\(237\) −13.5523 −0.880319
\(238\) 0 0
\(239\) −3.63938 −0.235412 −0.117706 0.993048i \(-0.537554\pi\)
−0.117706 + 0.993048i \(0.537554\pi\)
\(240\) 0 0
\(241\) −13.8607 −0.892844 −0.446422 0.894822i \(-0.647302\pi\)
−0.446422 + 0.894822i \(0.647302\pi\)
\(242\) 0 0
\(243\) 20.4705 1.31318
\(244\) 0 0
\(245\) −4.64656 −0.296858
\(246\) 0 0
\(247\) 2.34526 0.149225
\(248\) 0 0
\(249\) −25.1230 −1.59211
\(250\) 0 0
\(251\) −17.7326 −1.11927 −0.559637 0.828738i \(-0.689059\pi\)
−0.559637 + 0.828738i \(0.689059\pi\)
\(252\) 0 0
\(253\) 4.99002 0.313720
\(254\) 0 0
\(255\) −5.01230 −0.313883
\(256\) 0 0
\(257\) −12.6072 −0.786414 −0.393207 0.919450i \(-0.628634\pi\)
−0.393207 + 0.919450i \(0.628634\pi\)
\(258\) 0 0
\(259\) −4.05452 −0.251936
\(260\) 0 0
\(261\) 15.2383 0.943225
\(262\) 0 0
\(263\) −29.0394 −1.79065 −0.895324 0.445416i \(-0.853056\pi\)
−0.895324 + 0.445416i \(0.853056\pi\)
\(264\) 0 0
\(265\) 6.95012 0.426943
\(266\) 0 0
\(267\) 27.0002 1.65239
\(268\) 0 0
\(269\) 26.8894 1.63947 0.819737 0.572740i \(-0.194119\pi\)
0.819737 + 0.572740i \(0.194119\pi\)
\(270\) 0 0
\(271\) −12.7656 −0.775455 −0.387727 0.921774i \(-0.626740\pi\)
−0.387727 + 0.921774i \(0.626740\pi\)
\(272\) 0 0
\(273\) −1.69126 −0.102360
\(274\) 0 0
\(275\) −2.13813 −0.128934
\(276\) 0 0
\(277\) 29.7716 1.78880 0.894400 0.447269i \(-0.147603\pi\)
0.894400 + 0.447269i \(0.147603\pi\)
\(278\) 0 0
\(279\) 15.7785 0.944635
\(280\) 0 0
\(281\) 11.7299 0.699750 0.349875 0.936796i \(-0.386224\pi\)
0.349875 + 0.936796i \(0.386224\pi\)
\(282\) 0 0
\(283\) −24.8547 −1.47746 −0.738729 0.674002i \(-0.764574\pi\)
−0.738729 + 0.674002i \(0.764574\pi\)
\(284\) 0 0
\(285\) 11.6751 0.691575
\(286\) 0 0
\(287\) −9.42076 −0.556090
\(288\) 0 0
\(289\) −12.4223 −0.730724
\(290\) 0 0
\(291\) 8.92105 0.522961
\(292\) 0 0
\(293\) −22.7840 −1.33105 −0.665526 0.746374i \(-0.731793\pi\)
−0.665526 + 0.746374i \(0.731793\pi\)
\(294\) 0 0
\(295\) −9.95452 −0.579575
\(296\) 0 0
\(297\) −2.56367 −0.148759
\(298\) 0 0
\(299\) 1.09827 0.0635148
\(300\) 0 0
\(301\) 12.1832 0.702229
\(302\) 0 0
\(303\) −38.5687 −2.21571
\(304\) 0 0
\(305\) −11.6416 −0.666599
\(306\) 0 0
\(307\) −17.8743 −1.02014 −0.510070 0.860133i \(-0.670381\pi\)
−0.510070 + 0.860133i \(0.670381\pi\)
\(308\) 0 0
\(309\) −20.9406 −1.19127
\(310\) 0 0
\(311\) −14.3909 −0.816035 −0.408017 0.912974i \(-0.633780\pi\)
−0.408017 + 0.912974i \(0.633780\pi\)
\(312\) 0 0
\(313\) −5.94964 −0.336294 −0.168147 0.985762i \(-0.553778\pi\)
−0.168147 + 0.985762i \(0.553778\pi\)
\(314\) 0 0
\(315\) −3.81711 −0.215070
\(316\) 0 0
\(317\) 21.2783 1.19511 0.597555 0.801828i \(-0.296139\pi\)
0.597555 + 0.801828i \(0.296139\pi\)
\(318\) 0 0
\(319\) −13.0945 −0.733150
\(320\) 0 0
\(321\) 21.9305 1.22404
\(322\) 0 0
\(323\) −10.6628 −0.593293
\(324\) 0 0
\(325\) −0.470591 −0.0261037
\(326\) 0 0
\(327\) −16.2965 −0.901197
\(328\) 0 0
\(329\) −16.6228 −0.916446
\(330\) 0 0
\(331\) 0.843628 0.0463700 0.0231850 0.999731i \(-0.492619\pi\)
0.0231850 + 0.999731i \(0.492619\pi\)
\(332\) 0 0
\(333\) 6.57613 0.360370
\(334\) 0 0
\(335\) 1.12749 0.0616012
\(336\) 0 0
\(337\) 29.7351 1.61977 0.809886 0.586587i \(-0.199529\pi\)
0.809886 + 0.586587i \(0.199529\pi\)
\(338\) 0 0
\(339\) −18.1773 −0.987253
\(340\) 0 0
\(341\) −13.5587 −0.734245
\(342\) 0 0
\(343\) 17.8669 0.964722
\(344\) 0 0
\(345\) 5.46741 0.294355
\(346\) 0 0
\(347\) 5.71094 0.306579 0.153290 0.988181i \(-0.451013\pi\)
0.153290 + 0.988181i \(0.451013\pi\)
\(348\) 0 0
\(349\) −22.9550 −1.22875 −0.614377 0.789013i \(-0.710593\pi\)
−0.614377 + 0.789013i \(0.710593\pi\)
\(350\) 0 0
\(351\) −0.564249 −0.0301174
\(352\) 0 0
\(353\) −28.1580 −1.49870 −0.749349 0.662176i \(-0.769633\pi\)
−0.749349 + 0.662176i \(0.769633\pi\)
\(354\) 0 0
\(355\) −8.62775 −0.457913
\(356\) 0 0
\(357\) 7.68934 0.406963
\(358\) 0 0
\(359\) 8.39658 0.443154 0.221577 0.975143i \(-0.428880\pi\)
0.221577 + 0.975143i \(0.428880\pi\)
\(360\) 0 0
\(361\) 5.83672 0.307196
\(362\) 0 0
\(363\) 15.0597 0.790429
\(364\) 0 0
\(365\) −1.80753 −0.0946104
\(366\) 0 0
\(367\) 17.4444 0.910590 0.455295 0.890341i \(-0.349534\pi\)
0.455295 + 0.890341i \(0.349534\pi\)
\(368\) 0 0
\(369\) 15.2798 0.795433
\(370\) 0 0
\(371\) −10.6621 −0.553551
\(372\) 0 0
\(373\) −8.12399 −0.420644 −0.210322 0.977632i \(-0.567451\pi\)
−0.210322 + 0.977632i \(0.567451\pi\)
\(374\) 0 0
\(375\) −2.34269 −0.120976
\(376\) 0 0
\(377\) −2.88202 −0.148431
\(378\) 0 0
\(379\) −17.4033 −0.893950 −0.446975 0.894547i \(-0.647499\pi\)
−0.446975 + 0.894547i \(0.647499\pi\)
\(380\) 0 0
\(381\) −24.0344 −1.23132
\(382\) 0 0
\(383\) 15.6984 0.802153 0.401076 0.916045i \(-0.368636\pi\)
0.401076 + 0.916045i \(0.368636\pi\)
\(384\) 0 0
\(385\) 3.28010 0.167169
\(386\) 0 0
\(387\) −19.7603 −1.00447
\(388\) 0 0
\(389\) −16.2270 −0.822741 −0.411370 0.911468i \(-0.634950\pi\)
−0.411370 + 0.911468i \(0.634950\pi\)
\(390\) 0 0
\(391\) −4.99333 −0.252524
\(392\) 0 0
\(393\) −10.3293 −0.521047
\(394\) 0 0
\(395\) 5.78496 0.291073
\(396\) 0 0
\(397\) −31.5789 −1.58490 −0.792450 0.609937i \(-0.791195\pi\)
−0.792450 + 0.609937i \(0.791195\pi\)
\(398\) 0 0
\(399\) −17.9107 −0.896658
\(400\) 0 0
\(401\) −2.88267 −0.143954 −0.0719768 0.997406i \(-0.522931\pi\)
−0.0719768 + 0.997406i \(0.522931\pi\)
\(402\) 0 0
\(403\) −2.98419 −0.148653
\(404\) 0 0
\(405\) −10.2735 −0.510494
\(406\) 0 0
\(407\) −5.65097 −0.280108
\(408\) 0 0
\(409\) 17.9093 0.885557 0.442778 0.896631i \(-0.353993\pi\)
0.442778 + 0.896631i \(0.353993\pi\)
\(410\) 0 0
\(411\) −40.6320 −2.00423
\(412\) 0 0
\(413\) 15.2712 0.751445
\(414\) 0 0
\(415\) 10.7240 0.526421
\(416\) 0 0
\(417\) 43.8961 2.14960
\(418\) 0 0
\(419\) 6.13161 0.299549 0.149774 0.988720i \(-0.452145\pi\)
0.149774 + 0.988720i \(0.452145\pi\)
\(420\) 0 0
\(421\) −35.7932 −1.74445 −0.872227 0.489100i \(-0.837325\pi\)
−0.872227 + 0.489100i \(0.837325\pi\)
\(422\) 0 0
\(423\) 26.9610 1.31089
\(424\) 0 0
\(425\) 2.13955 0.103784
\(426\) 0 0
\(427\) 17.8594 0.864276
\(428\) 0 0
\(429\) −2.35718 −0.113806
\(430\) 0 0
\(431\) −32.5146 −1.56617 −0.783087 0.621912i \(-0.786356\pi\)
−0.783087 + 0.621912i \(0.786356\pi\)
\(432\) 0 0
\(433\) 27.5934 1.32606 0.663028 0.748595i \(-0.269271\pi\)
0.663028 + 0.748595i \(0.269271\pi\)
\(434\) 0 0
\(435\) −14.3472 −0.687896
\(436\) 0 0
\(437\) 11.6309 0.556383
\(438\) 0 0
\(439\) 11.1400 0.531685 0.265843 0.964016i \(-0.414350\pi\)
0.265843 + 0.964016i \(0.414350\pi\)
\(440\) 0 0
\(441\) −11.5615 −0.550547
\(442\) 0 0
\(443\) 5.43580 0.258262 0.129131 0.991628i \(-0.458781\pi\)
0.129131 + 0.991628i \(0.458781\pi\)
\(444\) 0 0
\(445\) −11.5253 −0.546353
\(446\) 0 0
\(447\) 31.2849 1.47972
\(448\) 0 0
\(449\) −18.3551 −0.866230 −0.433115 0.901339i \(-0.642586\pi\)
−0.433115 + 0.901339i \(0.642586\pi\)
\(450\) 0 0
\(451\) −13.1301 −0.618274
\(452\) 0 0
\(453\) −2.34269 −0.110069
\(454\) 0 0
\(455\) 0.721931 0.0338446
\(456\) 0 0
\(457\) −9.54149 −0.446332 −0.223166 0.974780i \(-0.571639\pi\)
−0.223166 + 0.974780i \(0.571639\pi\)
\(458\) 0 0
\(459\) 2.56537 0.119741
\(460\) 0 0
\(461\) −32.4864 −1.51304 −0.756521 0.653970i \(-0.773102\pi\)
−0.756521 + 0.653970i \(0.773102\pi\)
\(462\) 0 0
\(463\) −7.99549 −0.371582 −0.185791 0.982589i \(-0.559485\pi\)
−0.185791 + 0.982589i \(0.559485\pi\)
\(464\) 0 0
\(465\) −14.8559 −0.688924
\(466\) 0 0
\(467\) 20.3813 0.943136 0.471568 0.881830i \(-0.343688\pi\)
0.471568 + 0.881830i \(0.343688\pi\)
\(468\) 0 0
\(469\) −1.72967 −0.0798688
\(470\) 0 0
\(471\) 5.30054 0.244236
\(472\) 0 0
\(473\) 16.9803 0.780754
\(474\) 0 0
\(475\) −4.98365 −0.228665
\(476\) 0 0
\(477\) 17.2932 0.791801
\(478\) 0 0
\(479\) 11.9464 0.545845 0.272923 0.962036i \(-0.412010\pi\)
0.272923 + 0.962036i \(0.412010\pi\)
\(480\) 0 0
\(481\) −1.24375 −0.0567099
\(482\) 0 0
\(483\) −8.38752 −0.381645
\(484\) 0 0
\(485\) −3.80804 −0.172914
\(486\) 0 0
\(487\) −18.3090 −0.829661 −0.414830 0.909899i \(-0.636159\pi\)
−0.414830 + 0.909899i \(0.636159\pi\)
\(488\) 0 0
\(489\) −2.53870 −0.114804
\(490\) 0 0
\(491\) −38.3267 −1.72966 −0.864831 0.502063i \(-0.832574\pi\)
−0.864831 + 0.502063i \(0.832574\pi\)
\(492\) 0 0
\(493\) 13.1032 0.590137
\(494\) 0 0
\(495\) −5.32007 −0.239120
\(496\) 0 0
\(497\) 13.2358 0.593706
\(498\) 0 0
\(499\) −26.2404 −1.17468 −0.587340 0.809340i \(-0.699825\pi\)
−0.587340 + 0.809340i \(0.699825\pi\)
\(500\) 0 0
\(501\) 15.2629 0.681895
\(502\) 0 0
\(503\) 14.4877 0.645973 0.322986 0.946404i \(-0.395313\pi\)
0.322986 + 0.946404i \(0.395313\pi\)
\(504\) 0 0
\(505\) 16.4634 0.732613
\(506\) 0 0
\(507\) 29.9361 1.32951
\(508\) 0 0
\(509\) 35.2685 1.56325 0.781624 0.623750i \(-0.214392\pi\)
0.781624 + 0.623750i \(0.214392\pi\)
\(510\) 0 0
\(511\) 2.77292 0.122667
\(512\) 0 0
\(513\) −5.97550 −0.263825
\(514\) 0 0
\(515\) 8.93869 0.393886
\(516\) 0 0
\(517\) −23.1680 −1.01893
\(518\) 0 0
\(519\) 8.82911 0.387555
\(520\) 0 0
\(521\) −32.6900 −1.43217 −0.716087 0.698011i \(-0.754069\pi\)
−0.716087 + 0.698011i \(0.754069\pi\)
\(522\) 0 0
\(523\) 15.0223 0.656880 0.328440 0.944525i \(-0.393477\pi\)
0.328440 + 0.944525i \(0.393477\pi\)
\(524\) 0 0
\(525\) 3.59390 0.156851
\(526\) 0 0
\(527\) 13.5677 0.591019
\(528\) 0 0
\(529\) −17.5533 −0.763187
\(530\) 0 0
\(531\) −24.7687 −1.07487
\(532\) 0 0
\(533\) −2.88987 −0.125174
\(534\) 0 0
\(535\) −9.36125 −0.404722
\(536\) 0 0
\(537\) 5.93954 0.256310
\(538\) 0 0
\(539\) 9.93496 0.427929
\(540\) 0 0
\(541\) 23.3271 1.00291 0.501455 0.865184i \(-0.332798\pi\)
0.501455 + 0.865184i \(0.332798\pi\)
\(542\) 0 0
\(543\) −11.9980 −0.514883
\(544\) 0 0
\(545\) 6.95632 0.297976
\(546\) 0 0
\(547\) −16.2255 −0.693754 −0.346877 0.937911i \(-0.612758\pi\)
−0.346877 + 0.937911i \(0.612758\pi\)
\(548\) 0 0
\(549\) −28.9666 −1.23626
\(550\) 0 0
\(551\) −30.5211 −1.30024
\(552\) 0 0
\(553\) −8.87467 −0.377389
\(554\) 0 0
\(555\) −6.19159 −0.262819
\(556\) 0 0
\(557\) 25.3055 1.07223 0.536115 0.844145i \(-0.319891\pi\)
0.536115 + 0.844145i \(0.319891\pi\)
\(558\) 0 0
\(559\) 3.73726 0.158069
\(560\) 0 0
\(561\) 10.7170 0.452471
\(562\) 0 0
\(563\) 12.4154 0.523248 0.261624 0.965170i \(-0.415742\pi\)
0.261624 + 0.965170i \(0.415742\pi\)
\(564\) 0 0
\(565\) 7.75915 0.326430
\(566\) 0 0
\(567\) 15.7605 0.661879
\(568\) 0 0
\(569\) 46.9428 1.96794 0.983972 0.178322i \(-0.0570669\pi\)
0.983972 + 0.178322i \(0.0570669\pi\)
\(570\) 0 0
\(571\) −26.6173 −1.11390 −0.556950 0.830546i \(-0.688028\pi\)
−0.556950 + 0.830546i \(0.688028\pi\)
\(572\) 0 0
\(573\) −56.1790 −2.34691
\(574\) 0 0
\(575\) −2.33382 −0.0973270
\(576\) 0 0
\(577\) 2.77259 0.115424 0.0577122 0.998333i \(-0.481619\pi\)
0.0577122 + 0.998333i \(0.481619\pi\)
\(578\) 0 0
\(579\) −43.0072 −1.78732
\(580\) 0 0
\(581\) −16.4516 −0.682529
\(582\) 0 0
\(583\) −14.8603 −0.615451
\(584\) 0 0
\(585\) −1.17092 −0.0484115
\(586\) 0 0
\(587\) −42.9921 −1.77447 −0.887237 0.461313i \(-0.847378\pi\)
−0.887237 + 0.461313i \(0.847378\pi\)
\(588\) 0 0
\(589\) −31.6032 −1.30219
\(590\) 0 0
\(591\) 59.3922 2.44307
\(592\) 0 0
\(593\) −11.2655 −0.462617 −0.231308 0.972880i \(-0.574301\pi\)
−0.231308 + 0.972880i \(0.574301\pi\)
\(594\) 0 0
\(595\) −3.28227 −0.134560
\(596\) 0 0
\(597\) −3.56575 −0.145937
\(598\) 0 0
\(599\) −23.8803 −0.975724 −0.487862 0.872921i \(-0.662223\pi\)
−0.487862 + 0.872921i \(0.662223\pi\)
\(600\) 0 0
\(601\) −5.39691 −0.220145 −0.110072 0.993924i \(-0.535108\pi\)
−0.110072 + 0.993924i \(0.535108\pi\)
\(602\) 0 0
\(603\) 2.80540 0.114245
\(604\) 0 0
\(605\) −6.42838 −0.261351
\(606\) 0 0
\(607\) 7.16153 0.290678 0.145339 0.989382i \(-0.453573\pi\)
0.145339 + 0.989382i \(0.453573\pi\)
\(608\) 0 0
\(609\) 22.0100 0.891889
\(610\) 0 0
\(611\) −5.09913 −0.206289
\(612\) 0 0
\(613\) −21.7198 −0.877256 −0.438628 0.898669i \(-0.644535\pi\)
−0.438628 + 0.898669i \(0.644535\pi\)
\(614\) 0 0
\(615\) −14.3863 −0.580111
\(616\) 0 0
\(617\) −17.8005 −0.716622 −0.358311 0.933602i \(-0.616647\pi\)
−0.358311 + 0.933602i \(0.616647\pi\)
\(618\) 0 0
\(619\) 0.0443852 0.00178399 0.000891996 1.00000i \(-0.499716\pi\)
0.000891996 1.00000i \(0.499716\pi\)
\(620\) 0 0
\(621\) −2.79830 −0.112292
\(622\) 0 0
\(623\) 17.6809 0.708372
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −24.9630 −0.996925
\(628\) 0 0
\(629\) 5.65472 0.225468
\(630\) 0 0
\(631\) 14.1559 0.563537 0.281769 0.959482i \(-0.409079\pi\)
0.281769 + 0.959482i \(0.409079\pi\)
\(632\) 0 0
\(633\) −13.6901 −0.544131
\(634\) 0 0
\(635\) 10.2593 0.407129
\(636\) 0 0
\(637\) 2.18663 0.0866373
\(638\) 0 0
\(639\) −21.4674 −0.849239
\(640\) 0 0
\(641\) −27.6008 −1.09017 −0.545083 0.838382i \(-0.683502\pi\)
−0.545083 + 0.838382i \(0.683502\pi\)
\(642\) 0 0
\(643\) 9.08990 0.358471 0.179235 0.983806i \(-0.442638\pi\)
0.179235 + 0.983806i \(0.442638\pi\)
\(644\) 0 0
\(645\) 18.6048 0.732562
\(646\) 0 0
\(647\) 45.8102 1.80099 0.900493 0.434870i \(-0.143206\pi\)
0.900493 + 0.434870i \(0.143206\pi\)
\(648\) 0 0
\(649\) 21.2841 0.835474
\(650\) 0 0
\(651\) 22.7903 0.893222
\(652\) 0 0
\(653\) −25.8298 −1.01080 −0.505398 0.862886i \(-0.668654\pi\)
−0.505398 + 0.862886i \(0.668654\pi\)
\(654\) 0 0
\(655\) 4.40919 0.172281
\(656\) 0 0
\(657\) −4.49747 −0.175463
\(658\) 0 0
\(659\) −33.3393 −1.29871 −0.649357 0.760484i \(-0.724962\pi\)
−0.649357 + 0.760484i \(0.724962\pi\)
\(660\) 0 0
\(661\) −28.2987 −1.10069 −0.550346 0.834937i \(-0.685504\pi\)
−0.550346 + 0.834937i \(0.685504\pi\)
\(662\) 0 0
\(663\) 2.35874 0.0916061
\(664\) 0 0
\(665\) 7.64538 0.296475
\(666\) 0 0
\(667\) −14.2929 −0.553423
\(668\) 0 0
\(669\) 62.8013 2.42804
\(670\) 0 0
\(671\) 24.8914 0.960922
\(672\) 0 0
\(673\) −11.3107 −0.435996 −0.217998 0.975949i \(-0.569953\pi\)
−0.217998 + 0.975949i \(0.569953\pi\)
\(674\) 0 0
\(675\) 1.19902 0.0461504
\(676\) 0 0
\(677\) 47.1099 1.81058 0.905290 0.424795i \(-0.139654\pi\)
0.905290 + 0.424795i \(0.139654\pi\)
\(678\) 0 0
\(679\) 5.84189 0.224191
\(680\) 0 0
\(681\) 17.6073 0.674713
\(682\) 0 0
\(683\) 11.2475 0.430372 0.215186 0.976573i \(-0.430964\pi\)
0.215186 + 0.976573i \(0.430964\pi\)
\(684\) 0 0
\(685\) 17.3442 0.662687
\(686\) 0 0
\(687\) 34.5095 1.31662
\(688\) 0 0
\(689\) −3.27067 −0.124602
\(690\) 0 0
\(691\) 26.7880 1.01906 0.509531 0.860452i \(-0.329819\pi\)
0.509531 + 0.860452i \(0.329819\pi\)
\(692\) 0 0
\(693\) 8.16149 0.310029
\(694\) 0 0
\(695\) −18.7375 −0.710753
\(696\) 0 0
\(697\) 13.1388 0.497669
\(698\) 0 0
\(699\) 50.5886 1.91344
\(700\) 0 0
\(701\) −12.2160 −0.461391 −0.230696 0.973026i \(-0.574100\pi\)
−0.230696 + 0.973026i \(0.574100\pi\)
\(702\) 0 0
\(703\) −13.1715 −0.496772
\(704\) 0 0
\(705\) −25.3844 −0.956032
\(706\) 0 0
\(707\) −25.2564 −0.949866
\(708\) 0 0
\(709\) −10.0659 −0.378034 −0.189017 0.981974i \(-0.560530\pi\)
−0.189017 + 0.981974i \(0.560530\pi\)
\(710\) 0 0
\(711\) 14.3940 0.539819
\(712\) 0 0
\(713\) −14.7996 −0.554250
\(714\) 0 0
\(715\) 1.00619 0.0376292
\(716\) 0 0
\(717\) 8.52593 0.318407
\(718\) 0 0
\(719\) 24.2850 0.905679 0.452840 0.891592i \(-0.350411\pi\)
0.452840 + 0.891592i \(0.350411\pi\)
\(720\) 0 0
\(721\) −13.7128 −0.510691
\(722\) 0 0
\(723\) 32.4712 1.20762
\(724\) 0 0
\(725\) 6.12425 0.227449
\(726\) 0 0
\(727\) 31.7157 1.17627 0.588135 0.808762i \(-0.299862\pi\)
0.588135 + 0.808762i \(0.299862\pi\)
\(728\) 0 0
\(729\) −17.1355 −0.634649
\(730\) 0 0
\(731\) −16.9915 −0.628455
\(732\) 0 0
\(733\) −10.1203 −0.373801 −0.186900 0.982379i \(-0.559844\pi\)
−0.186900 + 0.982379i \(0.559844\pi\)
\(734\) 0 0
\(735\) 10.8854 0.401515
\(736\) 0 0
\(737\) −2.41072 −0.0888000
\(738\) 0 0
\(739\) −45.9129 −1.68893 −0.844467 0.535608i \(-0.820082\pi\)
−0.844467 + 0.535608i \(0.820082\pi\)
\(740\) 0 0
\(741\) −5.49421 −0.201835
\(742\) 0 0
\(743\) −14.0301 −0.514714 −0.257357 0.966316i \(-0.582852\pi\)
−0.257357 + 0.966316i \(0.582852\pi\)
\(744\) 0 0
\(745\) −13.3543 −0.489263
\(746\) 0 0
\(747\) 26.6833 0.976292
\(748\) 0 0
\(749\) 14.3610 0.524741
\(750\) 0 0
\(751\) 7.04609 0.257115 0.128558 0.991702i \(-0.458965\pi\)
0.128558 + 0.991702i \(0.458965\pi\)
\(752\) 0 0
\(753\) 41.5420 1.51388
\(754\) 0 0
\(755\) 1.00000 0.0363937
\(756\) 0 0
\(757\) 15.9434 0.579473 0.289737 0.957106i \(-0.406432\pi\)
0.289737 + 0.957106i \(0.406432\pi\)
\(758\) 0 0
\(759\) −11.6901 −0.424322
\(760\) 0 0
\(761\) 8.02167 0.290785 0.145393 0.989374i \(-0.453555\pi\)
0.145393 + 0.989374i \(0.453555\pi\)
\(762\) 0 0
\(763\) −10.6716 −0.386339
\(764\) 0 0
\(765\) 5.32360 0.192475
\(766\) 0 0
\(767\) 4.68451 0.169148
\(768\) 0 0
\(769\) 9.10965 0.328502 0.164251 0.986419i \(-0.447479\pi\)
0.164251 + 0.986419i \(0.447479\pi\)
\(770\) 0 0
\(771\) 29.5347 1.06367
\(772\) 0 0
\(773\) −43.3037 −1.55753 −0.778763 0.627318i \(-0.784152\pi\)
−0.778763 + 0.627318i \(0.784152\pi\)
\(774\) 0 0
\(775\) 6.34138 0.227789
\(776\) 0 0
\(777\) 9.49848 0.340756
\(778\) 0 0
\(779\) −30.6042 −1.09651
\(780\) 0 0
\(781\) 18.4473 0.660096
\(782\) 0 0
\(783\) 7.34312 0.262422
\(784\) 0 0
\(785\) −2.26259 −0.0807552
\(786\) 0 0
\(787\) −2.73232 −0.0973967 −0.0486984 0.998814i \(-0.515507\pi\)
−0.0486984 + 0.998814i \(0.515507\pi\)
\(788\) 0 0
\(789\) 68.0303 2.42194
\(790\) 0 0
\(791\) −11.9033 −0.423231
\(792\) 0 0
\(793\) 5.47845 0.194546
\(794\) 0 0
\(795\) −16.2820 −0.577462
\(796\) 0 0
\(797\) 51.7344 1.83253 0.916263 0.400577i \(-0.131190\pi\)
0.916263 + 0.400577i \(0.131190\pi\)
\(798\) 0 0
\(799\) 23.1833 0.820167
\(800\) 0 0
\(801\) −28.6771 −1.01326
\(802\) 0 0
\(803\) 3.86474 0.136384
\(804\) 0 0
\(805\) 3.58030 0.126189
\(806\) 0 0
\(807\) −62.9934 −2.21747
\(808\) 0 0
\(809\) −15.1644 −0.533154 −0.266577 0.963814i \(-0.585893\pi\)
−0.266577 + 0.963814i \(0.585893\pi\)
\(810\) 0 0
\(811\) 29.6580 1.04143 0.520716 0.853730i \(-0.325665\pi\)
0.520716 + 0.853730i \(0.325665\pi\)
\(812\) 0 0
\(813\) 29.9058 1.04884
\(814\) 0 0
\(815\) 1.08367 0.0379592
\(816\) 0 0
\(817\) 39.5783 1.38467
\(818\) 0 0
\(819\) 1.79630 0.0627677
\(820\) 0 0
\(821\) −39.9429 −1.39402 −0.697008 0.717063i \(-0.745486\pi\)
−0.697008 + 0.717063i \(0.745486\pi\)
\(822\) 0 0
\(823\) −10.8775 −0.379164 −0.189582 0.981865i \(-0.560713\pi\)
−0.189582 + 0.981865i \(0.560713\pi\)
\(824\) 0 0
\(825\) 5.00898 0.174390
\(826\) 0 0
\(827\) −2.37489 −0.0825831 −0.0412915 0.999147i \(-0.513147\pi\)
−0.0412915 + 0.999147i \(0.513147\pi\)
\(828\) 0 0
\(829\) −21.6713 −0.752677 −0.376338 0.926482i \(-0.622817\pi\)
−0.376338 + 0.926482i \(0.622817\pi\)
\(830\) 0 0
\(831\) −69.7454 −2.41944
\(832\) 0 0
\(833\) −9.94155 −0.344454
\(834\) 0 0
\(835\) −6.51511 −0.225465
\(836\) 0 0
\(837\) 7.60345 0.262814
\(838\) 0 0
\(839\) 27.6715 0.955328 0.477664 0.878543i \(-0.341484\pi\)
0.477664 + 0.878543i \(0.341484\pi\)
\(840\) 0 0
\(841\) 8.50646 0.293326
\(842\) 0 0
\(843\) −27.4796 −0.946447
\(844\) 0 0
\(845\) −12.7785 −0.439595
\(846\) 0 0
\(847\) 9.86174 0.338853
\(848\) 0 0
\(849\) 58.2268 1.99834
\(850\) 0 0
\(851\) −6.16815 −0.211442
\(852\) 0 0
\(853\) −48.6219 −1.66478 −0.832390 0.554190i \(-0.813028\pi\)
−0.832390 + 0.554190i \(0.813028\pi\)
\(854\) 0 0
\(855\) −12.4002 −0.424079
\(856\) 0 0
\(857\) −31.0486 −1.06060 −0.530299 0.847810i \(-0.677920\pi\)
−0.530299 + 0.847810i \(0.677920\pi\)
\(858\) 0 0
\(859\) −17.5514 −0.598847 −0.299424 0.954120i \(-0.596794\pi\)
−0.299424 + 0.954120i \(0.596794\pi\)
\(860\) 0 0
\(861\) 22.0699 0.752140
\(862\) 0 0
\(863\) 15.0347 0.511787 0.255894 0.966705i \(-0.417630\pi\)
0.255894 + 0.966705i \(0.417630\pi\)
\(864\) 0 0
\(865\) −3.76879 −0.128143
\(866\) 0 0
\(867\) 29.1016 0.988342
\(868\) 0 0
\(869\) −12.3690 −0.419590
\(870\) 0 0
\(871\) −0.530585 −0.0179782
\(872\) 0 0
\(873\) −9.47511 −0.320684
\(874\) 0 0
\(875\) −1.53409 −0.0518618
\(876\) 0 0
\(877\) 13.0582 0.440943 0.220472 0.975393i \(-0.429240\pi\)
0.220472 + 0.975393i \(0.429240\pi\)
\(878\) 0 0
\(879\) 53.3757 1.80032
\(880\) 0 0
\(881\) −24.2230 −0.816093 −0.408047 0.912961i \(-0.633790\pi\)
−0.408047 + 0.912961i \(0.633790\pi\)
\(882\) 0 0
\(883\) 36.6556 1.23356 0.616779 0.787136i \(-0.288437\pi\)
0.616779 + 0.787136i \(0.288437\pi\)
\(884\) 0 0
\(885\) 23.3203 0.783904
\(886\) 0 0
\(887\) 45.0955 1.51416 0.757079 0.653324i \(-0.226626\pi\)
0.757079 + 0.653324i \(0.226626\pi\)
\(888\) 0 0
\(889\) −15.7388 −0.527861
\(890\) 0 0
\(891\) 21.9661 0.735892
\(892\) 0 0
\(893\) −54.0008 −1.80707
\(894\) 0 0
\(895\) −2.53535 −0.0847475
\(896\) 0 0
\(897\) −2.57291 −0.0859070
\(898\) 0 0
\(899\) 38.8362 1.29526
\(900\) 0 0
\(901\) 14.8702 0.495397
\(902\) 0 0
\(903\) −28.5415 −0.949800
\(904\) 0 0
\(905\) 5.12147 0.170243
\(906\) 0 0
\(907\) −15.3556 −0.509874 −0.254937 0.966958i \(-0.582055\pi\)
−0.254937 + 0.966958i \(0.582055\pi\)
\(908\) 0 0
\(909\) 40.9640 1.35869
\(910\) 0 0
\(911\) −51.6696 −1.71189 −0.855944 0.517068i \(-0.827023\pi\)
−0.855944 + 0.517068i \(0.827023\pi\)
\(912\) 0 0
\(913\) −22.9294 −0.758852
\(914\) 0 0
\(915\) 27.2727 0.901609
\(916\) 0 0
\(917\) −6.76411 −0.223370
\(918\) 0 0
\(919\) 33.9576 1.12016 0.560080 0.828439i \(-0.310771\pi\)
0.560080 + 0.828439i \(0.310771\pi\)
\(920\) 0 0
\(921\) 41.8739 1.37979
\(922\) 0 0
\(923\) 4.06014 0.133641
\(924\) 0 0
\(925\) 2.64294 0.0868995
\(926\) 0 0
\(927\) 22.2411 0.730494
\(928\) 0 0
\(929\) 59.3695 1.94785 0.973925 0.226872i \(-0.0728497\pi\)
0.973925 + 0.226872i \(0.0728497\pi\)
\(930\) 0 0
\(931\) 23.1568 0.758933
\(932\) 0 0
\(933\) 33.7134 1.10373
\(934\) 0 0
\(935\) −4.57465 −0.149607
\(936\) 0 0
\(937\) 53.0524 1.73315 0.866573 0.499050i \(-0.166317\pi\)
0.866573 + 0.499050i \(0.166317\pi\)
\(938\) 0 0
\(939\) 13.9381 0.454854
\(940\) 0 0
\(941\) −21.4469 −0.699150 −0.349575 0.936908i \(-0.613674\pi\)
−0.349575 + 0.936908i \(0.613674\pi\)
\(942\) 0 0
\(943\) −14.3318 −0.466708
\(944\) 0 0
\(945\) −1.83941 −0.0598361
\(946\) 0 0
\(947\) −34.0827 −1.10754 −0.553770 0.832670i \(-0.686811\pi\)
−0.553770 + 0.832670i \(0.686811\pi\)
\(948\) 0 0
\(949\) 0.850607 0.0276119
\(950\) 0 0
\(951\) −49.8485 −1.61645
\(952\) 0 0
\(953\) −58.1867 −1.88485 −0.942426 0.334416i \(-0.891461\pi\)
−0.942426 + 0.334416i \(0.891461\pi\)
\(954\) 0 0
\(955\) 23.9806 0.775993
\(956\) 0 0
\(957\) 30.6763 0.991623
\(958\) 0 0
\(959\) −26.6076 −0.859204
\(960\) 0 0
\(961\) 9.21304 0.297195
\(962\) 0 0
\(963\) −23.2925 −0.750591
\(964\) 0 0
\(965\) 18.3581 0.590967
\(966\) 0 0
\(967\) −26.3432 −0.847139 −0.423570 0.905864i \(-0.639223\pi\)
−0.423570 + 0.905864i \(0.639223\pi\)
\(968\) 0 0
\(969\) 24.9795 0.802459
\(970\) 0 0
\(971\) 25.5703 0.820588 0.410294 0.911953i \(-0.365426\pi\)
0.410294 + 0.911953i \(0.365426\pi\)
\(972\) 0 0
\(973\) 28.7450 0.921524
\(974\) 0 0
\(975\) 1.10245 0.0353066
\(976\) 0 0
\(977\) −0.109403 −0.00350011 −0.00175006 0.999998i \(-0.500557\pi\)
−0.00175006 + 0.999998i \(0.500557\pi\)
\(978\) 0 0
\(979\) 24.6427 0.787584
\(980\) 0 0
\(981\) 17.3086 0.552621
\(982\) 0 0
\(983\) 16.9658 0.541124 0.270562 0.962703i \(-0.412790\pi\)
0.270562 + 0.962703i \(0.412790\pi\)
\(984\) 0 0
\(985\) −25.3522 −0.807787
\(986\) 0 0
\(987\) 38.9421 1.23954
\(988\) 0 0
\(989\) 18.5343 0.589357
\(990\) 0 0
\(991\) −22.0384 −0.700073 −0.350036 0.936736i \(-0.613831\pi\)
−0.350036 + 0.936736i \(0.613831\pi\)
\(992\) 0 0
\(993\) −1.97636 −0.0627178
\(994\) 0 0
\(995\) 1.52208 0.0482531
\(996\) 0 0
\(997\) 24.7975 0.785346 0.392673 0.919678i \(-0.371550\pi\)
0.392673 + 0.919678i \(0.371550\pi\)
\(998\) 0 0
\(999\) 3.16895 0.100261
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 \(a_p\))