Properties

Label 8024.2.a.y.1.16
Level 8024
Weight 2
Character 8024.1
Self dual Yes
Analytic conductor 64.072
Analytic rank 1
Dimension 23
CM No

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Newspace parameters

Level: \( N \) = \( 8024 = 2^{3} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8024.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0719625819\)
Analytic rank: \(1\)
Dimension: \(23\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 8024.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.04245 q^{3}\) \(-0.295436 q^{5}\) \(+1.92039 q^{7}\) \(-1.91330 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.04245 q^{3}\) \(-0.295436 q^{5}\) \(+1.92039 q^{7}\) \(-1.91330 q^{9}\) \(+3.27908 q^{11}\) \(+3.24353 q^{13}\) \(-0.307977 q^{15}\) \(-1.00000 q^{17}\) \(-1.86258 q^{19}\) \(+2.00190 q^{21}\) \(-2.35457 q^{23}\) \(-4.91272 q^{25}\) \(-5.12186 q^{27}\) \(-1.73309 q^{29}\) \(-0.135282 q^{31}\) \(+3.41826 q^{33}\) \(-0.567352 q^{35}\) \(-10.7188 q^{37}\) \(+3.38121 q^{39}\) \(-11.0877 q^{41}\) \(-6.38228 q^{43}\) \(+0.565259 q^{45}\) \(-6.90334 q^{47}\) \(-3.31212 q^{49}\) \(-1.04245 q^{51}\) \(-1.91282 q^{53}\) \(-0.968758 q^{55}\) \(-1.94164 q^{57}\) \(-1.00000 q^{59}\) \(-2.57248 q^{61}\) \(-3.67428 q^{63}\) \(-0.958256 q^{65}\) \(+1.87229 q^{67}\) \(-2.45451 q^{69}\) \(-0.397381 q^{71}\) \(-2.58042 q^{73}\) \(-5.12125 q^{75}\) \(+6.29709 q^{77}\) \(+6.41241 q^{79}\) \(+0.400638 q^{81}\) \(+8.47271 q^{83}\) \(+0.295436 q^{85}\) \(-1.80666 q^{87}\) \(+1.33110 q^{89}\) \(+6.22883 q^{91}\) \(-0.141025 q^{93}\) \(+0.550274 q^{95}\) \(-4.73893 q^{97}\) \(-6.27386 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 23q^{17} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut -\mathstrut 29q^{23} \) \(\mathstrut +\mathstrut 31q^{25} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 22q^{35} \) \(\mathstrut +\mathstrut 5q^{37} \) \(\mathstrut +\mathstrut 16q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 39q^{47} \) \(\mathstrut +\mathstrut 16q^{49} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 35q^{55} \) \(\mathstrut +\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 23q^{59} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut +\mathstrut 33q^{65} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut -\mathstrut 66q^{69} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut -\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 81q^{75} \) \(\mathstrut -\mathstrut 4q^{77} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut +\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 18q^{91} \) \(\mathstrut -\mathstrut 62q^{93} \) \(\mathstrut -\mathstrut 33q^{95} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.04245 0.601857 0.300929 0.953647i \(-0.402703\pi\)
0.300929 + 0.953647i \(0.402703\pi\)
\(4\) 0 0
\(5\) −0.295436 −0.132123 −0.0660616 0.997816i \(-0.521043\pi\)
−0.0660616 + 0.997816i \(0.521043\pi\)
\(6\) 0 0
\(7\) 1.92039 0.725838 0.362919 0.931821i \(-0.381780\pi\)
0.362919 + 0.931821i \(0.381780\pi\)
\(8\) 0 0
\(9\) −1.91330 −0.637768
\(10\) 0 0
\(11\) 3.27908 0.988678 0.494339 0.869269i \(-0.335410\pi\)
0.494339 + 0.869269i \(0.335410\pi\)
\(12\) 0 0
\(13\) 3.24353 0.899593 0.449796 0.893131i \(-0.351497\pi\)
0.449796 + 0.893131i \(0.351497\pi\)
\(14\) 0 0
\(15\) −0.307977 −0.0795193
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) −1.86258 −0.427305 −0.213652 0.976910i \(-0.568536\pi\)
−0.213652 + 0.976910i \(0.568536\pi\)
\(20\) 0 0
\(21\) 2.00190 0.436851
\(22\) 0 0
\(23\) −2.35457 −0.490961 −0.245481 0.969401i \(-0.578946\pi\)
−0.245481 + 0.969401i \(0.578946\pi\)
\(24\) 0 0
\(25\) −4.91272 −0.982543
\(26\) 0 0
\(27\) −5.12186 −0.985703
\(28\) 0 0
\(29\) −1.73309 −0.321827 −0.160914 0.986969i \(-0.551444\pi\)
−0.160914 + 0.986969i \(0.551444\pi\)
\(30\) 0 0
\(31\) −0.135282 −0.0242974 −0.0121487 0.999926i \(-0.503867\pi\)
−0.0121487 + 0.999926i \(0.503867\pi\)
\(32\) 0 0
\(33\) 3.41826 0.595043
\(34\) 0 0
\(35\) −0.567352 −0.0959000
\(36\) 0 0
\(37\) −10.7188 −1.76215 −0.881077 0.472972i \(-0.843181\pi\)
−0.881077 + 0.472972i \(0.843181\pi\)
\(38\) 0 0
\(39\) 3.38121 0.541427
\(40\) 0 0
\(41\) −11.0877 −1.73161 −0.865804 0.500384i \(-0.833192\pi\)
−0.865804 + 0.500384i \(0.833192\pi\)
\(42\) 0 0
\(43\) −6.38228 −0.973289 −0.486644 0.873600i \(-0.661779\pi\)
−0.486644 + 0.873600i \(0.661779\pi\)
\(44\) 0 0
\(45\) 0.565259 0.0842639
\(46\) 0 0
\(47\) −6.90334 −1.00696 −0.503478 0.864008i \(-0.667946\pi\)
−0.503478 + 0.864008i \(0.667946\pi\)
\(48\) 0 0
\(49\) −3.31212 −0.473159
\(50\) 0 0
\(51\) −1.04245 −0.145972
\(52\) 0 0
\(53\) −1.91282 −0.262746 −0.131373 0.991333i \(-0.541939\pi\)
−0.131373 + 0.991333i \(0.541939\pi\)
\(54\) 0 0
\(55\) −0.968758 −0.130627
\(56\) 0 0
\(57\) −1.94164 −0.257177
\(58\) 0 0
\(59\) −1.00000 −0.130189
\(60\) 0 0
\(61\) −2.57248 −0.329373 −0.164686 0.986346i \(-0.552661\pi\)
−0.164686 + 0.986346i \(0.552661\pi\)
\(62\) 0 0
\(63\) −3.67428 −0.462916
\(64\) 0 0
\(65\) −0.958256 −0.118857
\(66\) 0 0
\(67\) 1.87229 0.228737 0.114369 0.993438i \(-0.463516\pi\)
0.114369 + 0.993438i \(0.463516\pi\)
\(68\) 0 0
\(69\) −2.45451 −0.295489
\(70\) 0 0
\(71\) −0.397381 −0.0471604 −0.0235802 0.999722i \(-0.507507\pi\)
−0.0235802 + 0.999722i \(0.507507\pi\)
\(72\) 0 0
\(73\) −2.58042 −0.302015 −0.151007 0.988533i \(-0.548252\pi\)
−0.151007 + 0.988533i \(0.548252\pi\)
\(74\) 0 0
\(75\) −5.12125 −0.591351
\(76\) 0 0
\(77\) 6.29709 0.717620
\(78\) 0 0
\(79\) 6.41241 0.721452 0.360726 0.932672i \(-0.382529\pi\)
0.360726 + 0.932672i \(0.382529\pi\)
\(80\) 0 0
\(81\) 0.400638 0.0445153
\(82\) 0 0
\(83\) 8.47271 0.930001 0.465000 0.885311i \(-0.346054\pi\)
0.465000 + 0.885311i \(0.346054\pi\)
\(84\) 0 0
\(85\) 0.295436 0.0320446
\(86\) 0 0
\(87\) −1.80666 −0.193694
\(88\) 0 0
\(89\) 1.33110 0.141096 0.0705481 0.997508i \(-0.477525\pi\)
0.0705481 + 0.997508i \(0.477525\pi\)
\(90\) 0 0
\(91\) 6.22883 0.652959
\(92\) 0 0
\(93\) −0.141025 −0.0146236
\(94\) 0 0
\(95\) 0.550274 0.0564569
\(96\) 0 0
\(97\) −4.73893 −0.481165 −0.240583 0.970629i \(-0.577338\pi\)
−0.240583 + 0.970629i \(0.577338\pi\)
\(98\) 0 0
\(99\) −6.27386 −0.630547
\(100\) 0 0
\(101\) 7.18974 0.715406 0.357703 0.933835i \(-0.383560\pi\)
0.357703 + 0.933835i \(0.383560\pi\)
\(102\) 0 0
\(103\) 2.94439 0.290119 0.145060 0.989423i \(-0.453663\pi\)
0.145060 + 0.989423i \(0.453663\pi\)
\(104\) 0 0
\(105\) −0.591435 −0.0577181
\(106\) 0 0
\(107\) −8.91793 −0.862129 −0.431064 0.902321i \(-0.641862\pi\)
−0.431064 + 0.902321i \(0.641862\pi\)
\(108\) 0 0
\(109\) 12.0022 1.14960 0.574801 0.818293i \(-0.305080\pi\)
0.574801 + 0.818293i \(0.305080\pi\)
\(110\) 0 0
\(111\) −11.1738 −1.06057
\(112\) 0 0
\(113\) 4.51709 0.424932 0.212466 0.977168i \(-0.431850\pi\)
0.212466 + 0.977168i \(0.431850\pi\)
\(114\) 0 0
\(115\) 0.695625 0.0648674
\(116\) 0 0
\(117\) −6.20585 −0.573731
\(118\) 0 0
\(119\) −1.92039 −0.176042
\(120\) 0 0
\(121\) −0.247666 −0.0225151
\(122\) 0 0
\(123\) −11.5583 −1.04218
\(124\) 0 0
\(125\) 2.92858 0.261940
\(126\) 0 0
\(127\) 15.1996 1.34874 0.674371 0.738392i \(-0.264415\pi\)
0.674371 + 0.738392i \(0.264415\pi\)
\(128\) 0 0
\(129\) −6.65319 −0.585781
\(130\) 0 0
\(131\) 19.8991 1.73859 0.869294 0.494295i \(-0.164574\pi\)
0.869294 + 0.494295i \(0.164574\pi\)
\(132\) 0 0
\(133\) −3.57687 −0.310154
\(134\) 0 0
\(135\) 1.51318 0.130234
\(136\) 0 0
\(137\) −11.4779 −0.980626 −0.490313 0.871546i \(-0.663118\pi\)
−0.490313 + 0.871546i \(0.663118\pi\)
\(138\) 0 0
\(139\) −2.80625 −0.238023 −0.119012 0.992893i \(-0.537973\pi\)
−0.119012 + 0.992893i \(0.537973\pi\)
\(140\) 0 0
\(141\) −7.19637 −0.606044
\(142\) 0 0
\(143\) 10.6358 0.889408
\(144\) 0 0
\(145\) 0.512018 0.0425208
\(146\) 0 0
\(147\) −3.45271 −0.284774
\(148\) 0 0
\(149\) −22.1082 −1.81118 −0.905588 0.424159i \(-0.860570\pi\)
−0.905588 + 0.424159i \(0.860570\pi\)
\(150\) 0 0
\(151\) −15.7730 −1.28359 −0.641793 0.766878i \(-0.721809\pi\)
−0.641793 + 0.766878i \(0.721809\pi\)
\(152\) 0 0
\(153\) 1.91330 0.154681
\(154\) 0 0
\(155\) 0.0399673 0.00321025
\(156\) 0 0
\(157\) −7.60735 −0.607132 −0.303566 0.952810i \(-0.598177\pi\)
−0.303566 + 0.952810i \(0.598177\pi\)
\(158\) 0 0
\(159\) −1.99402 −0.158136
\(160\) 0 0
\(161\) −4.52168 −0.356358
\(162\) 0 0
\(163\) 17.0102 1.33234 0.666170 0.745800i \(-0.267932\pi\)
0.666170 + 0.745800i \(0.267932\pi\)
\(164\) 0 0
\(165\) −1.00988 −0.0786190
\(166\) 0 0
\(167\) 18.1015 1.40074 0.700369 0.713781i \(-0.253019\pi\)
0.700369 + 0.713781i \(0.253019\pi\)
\(168\) 0 0
\(169\) −2.47953 −0.190733
\(170\) 0 0
\(171\) 3.56368 0.272521
\(172\) 0 0
\(173\) 7.37460 0.560680 0.280340 0.959901i \(-0.409553\pi\)
0.280340 + 0.959901i \(0.409553\pi\)
\(174\) 0 0
\(175\) −9.43432 −0.713167
\(176\) 0 0
\(177\) −1.04245 −0.0783552
\(178\) 0 0
\(179\) −8.25246 −0.616817 −0.308409 0.951254i \(-0.599796\pi\)
−0.308409 + 0.951254i \(0.599796\pi\)
\(180\) 0 0
\(181\) 16.4663 1.22393 0.611965 0.790885i \(-0.290379\pi\)
0.611965 + 0.790885i \(0.290379\pi\)
\(182\) 0 0
\(183\) −2.68168 −0.198235
\(184\) 0 0
\(185\) 3.16671 0.232821
\(186\) 0 0
\(187\) −3.27908 −0.239790
\(188\) 0 0
\(189\) −9.83595 −0.715460
\(190\) 0 0
\(191\) 3.32488 0.240580 0.120290 0.992739i \(-0.461618\pi\)
0.120290 + 0.992739i \(0.461618\pi\)
\(192\) 0 0
\(193\) −0.0533281 −0.00383864 −0.00191932 0.999998i \(-0.500611\pi\)
−0.00191932 + 0.999998i \(0.500611\pi\)
\(194\) 0 0
\(195\) −0.998932 −0.0715350
\(196\) 0 0
\(197\) −4.20202 −0.299382 −0.149691 0.988733i \(-0.547828\pi\)
−0.149691 + 0.988733i \(0.547828\pi\)
\(198\) 0 0
\(199\) −25.7339 −1.82423 −0.912113 0.409938i \(-0.865550\pi\)
−0.912113 + 0.409938i \(0.865550\pi\)
\(200\) 0 0
\(201\) 1.95177 0.137667
\(202\) 0 0
\(203\) −3.32821 −0.233594
\(204\) 0 0
\(205\) 3.27571 0.228785
\(206\) 0 0
\(207\) 4.50500 0.313119
\(208\) 0 0
\(209\) −6.10754 −0.422467
\(210\) 0 0
\(211\) −1.92195 −0.132313 −0.0661563 0.997809i \(-0.521074\pi\)
−0.0661563 + 0.997809i \(0.521074\pi\)
\(212\) 0 0
\(213\) −0.414249 −0.0283838
\(214\) 0 0
\(215\) 1.88556 0.128594
\(216\) 0 0
\(217\) −0.259794 −0.0176360
\(218\) 0 0
\(219\) −2.68995 −0.181770
\(220\) 0 0
\(221\) −3.24353 −0.218183
\(222\) 0 0
\(223\) −4.14063 −0.277277 −0.138638 0.990343i \(-0.544273\pi\)
−0.138638 + 0.990343i \(0.544273\pi\)
\(224\) 0 0
\(225\) 9.39952 0.626634
\(226\) 0 0
\(227\) 25.1528 1.66945 0.834723 0.550670i \(-0.185628\pi\)
0.834723 + 0.550670i \(0.185628\pi\)
\(228\) 0 0
\(229\) 9.46711 0.625604 0.312802 0.949818i \(-0.398732\pi\)
0.312802 + 0.949818i \(0.398732\pi\)
\(230\) 0 0
\(231\) 6.56439 0.431905
\(232\) 0 0
\(233\) −25.8208 −1.69158 −0.845789 0.533517i \(-0.820870\pi\)
−0.845789 + 0.533517i \(0.820870\pi\)
\(234\) 0 0
\(235\) 2.03950 0.133042
\(236\) 0 0
\(237\) 6.68460 0.434211
\(238\) 0 0
\(239\) −4.91227 −0.317748 −0.158874 0.987299i \(-0.550786\pi\)
−0.158874 + 0.987299i \(0.550786\pi\)
\(240\) 0 0
\(241\) −17.3554 −1.11796 −0.558979 0.829182i \(-0.688807\pi\)
−0.558979 + 0.829182i \(0.688807\pi\)
\(242\) 0 0
\(243\) 15.7832 1.01249
\(244\) 0 0
\(245\) 0.978520 0.0625153
\(246\) 0 0
\(247\) −6.04133 −0.384400
\(248\) 0 0
\(249\) 8.83236 0.559728
\(250\) 0 0
\(251\) −28.6676 −1.80948 −0.904740 0.425964i \(-0.859935\pi\)
−0.904740 + 0.425964i \(0.859935\pi\)
\(252\) 0 0
\(253\) −7.72081 −0.485403
\(254\) 0 0
\(255\) 0.307977 0.0192863
\(256\) 0 0
\(257\) 25.0309 1.56138 0.780692 0.624916i \(-0.214867\pi\)
0.780692 + 0.624916i \(0.214867\pi\)
\(258\) 0 0
\(259\) −20.5842 −1.27904
\(260\) 0 0
\(261\) 3.31593 0.205251
\(262\) 0 0
\(263\) −8.93489 −0.550949 −0.275474 0.961308i \(-0.588835\pi\)
−0.275474 + 0.961308i \(0.588835\pi\)
\(264\) 0 0
\(265\) 0.565117 0.0347149
\(266\) 0 0
\(267\) 1.38760 0.0849198
\(268\) 0 0
\(269\) −20.3366 −1.23994 −0.619971 0.784625i \(-0.712856\pi\)
−0.619971 + 0.784625i \(0.712856\pi\)
\(270\) 0 0
\(271\) 3.32063 0.201714 0.100857 0.994901i \(-0.467842\pi\)
0.100857 + 0.994901i \(0.467842\pi\)
\(272\) 0 0
\(273\) 6.49323 0.392988
\(274\) 0 0
\(275\) −16.1092 −0.971419
\(276\) 0 0
\(277\) −0.282261 −0.0169594 −0.00847971 0.999964i \(-0.502699\pi\)
−0.00847971 + 0.999964i \(0.502699\pi\)
\(278\) 0 0
\(279\) 0.258836 0.0154961
\(280\) 0 0
\(281\) 8.86850 0.529050 0.264525 0.964379i \(-0.414785\pi\)
0.264525 + 0.964379i \(0.414785\pi\)
\(282\) 0 0
\(283\) −12.4945 −0.742720 −0.371360 0.928489i \(-0.621108\pi\)
−0.371360 + 0.928489i \(0.621108\pi\)
\(284\) 0 0
\(285\) 0.573631 0.0339790
\(286\) 0 0
\(287\) −21.2927 −1.25687
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) −4.94008 −0.289593
\(292\) 0 0
\(293\) 24.0725 1.40633 0.703165 0.711027i \(-0.251770\pi\)
0.703165 + 0.711027i \(0.251770\pi\)
\(294\) 0 0
\(295\) 0.295436 0.0172010
\(296\) 0 0
\(297\) −16.7950 −0.974543
\(298\) 0 0
\(299\) −7.63711 −0.441665
\(300\) 0 0
\(301\) −12.2564 −0.706450
\(302\) 0 0
\(303\) 7.49492 0.430572
\(304\) 0 0
\(305\) 0.760005 0.0435178
\(306\) 0 0
\(307\) 12.9555 0.739411 0.369706 0.929149i \(-0.379459\pi\)
0.369706 + 0.929149i \(0.379459\pi\)
\(308\) 0 0
\(309\) 3.06937 0.174610
\(310\) 0 0
\(311\) −1.77783 −0.100812 −0.0504059 0.998729i \(-0.516051\pi\)
−0.0504059 + 0.998729i \(0.516051\pi\)
\(312\) 0 0
\(313\) −4.94579 −0.279552 −0.139776 0.990183i \(-0.544638\pi\)
−0.139776 + 0.990183i \(0.544638\pi\)
\(314\) 0 0
\(315\) 1.08552 0.0611619
\(316\) 0 0
\(317\) 11.3554 0.637785 0.318893 0.947791i \(-0.396689\pi\)
0.318893 + 0.947791i \(0.396689\pi\)
\(318\) 0 0
\(319\) −5.68294 −0.318183
\(320\) 0 0
\(321\) −9.29647 −0.518878
\(322\) 0 0
\(323\) 1.86258 0.103637
\(324\) 0 0
\(325\) −15.9345 −0.883889
\(326\) 0 0
\(327\) 12.5117 0.691896
\(328\) 0 0
\(329\) −13.2571 −0.730887
\(330\) 0 0
\(331\) 22.7355 1.24966 0.624828 0.780763i \(-0.285169\pi\)
0.624828 + 0.780763i \(0.285169\pi\)
\(332\) 0 0
\(333\) 20.5083 1.12385
\(334\) 0 0
\(335\) −0.553144 −0.0302215
\(336\) 0 0
\(337\) −30.2203 −1.64620 −0.823102 0.567894i \(-0.807758\pi\)
−0.823102 + 0.567894i \(0.807758\pi\)
\(338\) 0 0
\(339\) 4.70883 0.255749
\(340\) 0 0
\(341\) −0.443600 −0.0240223
\(342\) 0 0
\(343\) −19.8032 −1.06927
\(344\) 0 0
\(345\) 0.725153 0.0390409
\(346\) 0 0
\(347\) −33.4186 −1.79400 −0.897001 0.442029i \(-0.854259\pi\)
−0.897001 + 0.442029i \(0.854259\pi\)
\(348\) 0 0
\(349\) −28.8992 −1.54694 −0.773469 0.633834i \(-0.781480\pi\)
−0.773469 + 0.633834i \(0.781480\pi\)
\(350\) 0 0
\(351\) −16.6129 −0.886731
\(352\) 0 0
\(353\) −5.48377 −0.291871 −0.145936 0.989294i \(-0.546619\pi\)
−0.145936 + 0.989294i \(0.546619\pi\)
\(354\) 0 0
\(355\) 0.117401 0.00623099
\(356\) 0 0
\(357\) −2.00190 −0.105952
\(358\) 0 0
\(359\) 8.53091 0.450244 0.225122 0.974331i \(-0.427722\pi\)
0.225122 + 0.974331i \(0.427722\pi\)
\(360\) 0 0
\(361\) −15.5308 −0.817411
\(362\) 0 0
\(363\) −0.258178 −0.0135508
\(364\) 0 0
\(365\) 0.762349 0.0399032
\(366\) 0 0
\(367\) −24.4809 −1.27789 −0.638946 0.769252i \(-0.720629\pi\)
−0.638946 + 0.769252i \(0.720629\pi\)
\(368\) 0 0
\(369\) 21.2141 1.10436
\(370\) 0 0
\(371\) −3.67336 −0.190711
\(372\) 0 0
\(373\) 13.9489 0.722249 0.361124 0.932518i \(-0.382393\pi\)
0.361124 + 0.932518i \(0.382393\pi\)
\(374\) 0 0
\(375\) 3.05289 0.157651
\(376\) 0 0
\(377\) −5.62133 −0.289513
\(378\) 0 0
\(379\) −7.65161 −0.393037 −0.196518 0.980500i \(-0.562964\pi\)
−0.196518 + 0.980500i \(0.562964\pi\)
\(380\) 0 0
\(381\) 15.8447 0.811751
\(382\) 0 0
\(383\) −13.6379 −0.696866 −0.348433 0.937334i \(-0.613286\pi\)
−0.348433 + 0.937334i \(0.613286\pi\)
\(384\) 0 0
\(385\) −1.86039 −0.0948143
\(386\) 0 0
\(387\) 12.2112 0.620732
\(388\) 0 0
\(389\) 27.2317 1.38070 0.690351 0.723475i \(-0.257456\pi\)
0.690351 + 0.723475i \(0.257456\pi\)
\(390\) 0 0
\(391\) 2.35457 0.119076
\(392\) 0 0
\(393\) 20.7437 1.04638
\(394\) 0 0
\(395\) −1.89446 −0.0953206
\(396\) 0 0
\(397\) −28.1339 −1.41200 −0.705999 0.708213i \(-0.749502\pi\)
−0.705999 + 0.708213i \(0.749502\pi\)
\(398\) 0 0
\(399\) −3.72870 −0.186669
\(400\) 0 0
\(401\) 37.8963 1.89245 0.946227 0.323505i \(-0.104861\pi\)
0.946227 + 0.323505i \(0.104861\pi\)
\(402\) 0 0
\(403\) −0.438791 −0.0218578
\(404\) 0 0
\(405\) −0.118363 −0.00588150
\(406\) 0 0
\(407\) −35.1476 −1.74220
\(408\) 0 0
\(409\) 5.47442 0.270693 0.135346 0.990798i \(-0.456785\pi\)
0.135346 + 0.990798i \(0.456785\pi\)
\(410\) 0 0
\(411\) −11.9651 −0.590197
\(412\) 0 0
\(413\) −1.92039 −0.0944960
\(414\) 0 0
\(415\) −2.50315 −0.122875
\(416\) 0 0
\(417\) −2.92537 −0.143256
\(418\) 0 0
\(419\) −14.8244 −0.724220 −0.362110 0.932135i \(-0.617944\pi\)
−0.362110 + 0.932135i \(0.617944\pi\)
\(420\) 0 0
\(421\) 37.0134 1.80392 0.901961 0.431816i \(-0.142127\pi\)
0.901961 + 0.431816i \(0.142127\pi\)
\(422\) 0 0
\(423\) 13.2082 0.642204
\(424\) 0 0
\(425\) 4.91272 0.238302
\(426\) 0 0
\(427\) −4.94016 −0.239071
\(428\) 0 0
\(429\) 11.0872 0.535297
\(430\) 0 0
\(431\) −11.9219 −0.574258 −0.287129 0.957892i \(-0.592701\pi\)
−0.287129 + 0.957892i \(0.592701\pi\)
\(432\) 0 0
\(433\) 5.68771 0.273334 0.136667 0.990617i \(-0.456361\pi\)
0.136667 + 0.990617i \(0.456361\pi\)
\(434\) 0 0
\(435\) 0.533752 0.0255915
\(436\) 0 0
\(437\) 4.38557 0.209790
\(438\) 0 0
\(439\) 8.38916 0.400393 0.200196 0.979756i \(-0.435842\pi\)
0.200196 + 0.979756i \(0.435842\pi\)
\(440\) 0 0
\(441\) 6.33708 0.301766
\(442\) 0 0
\(443\) −21.7826 −1.03492 −0.517461 0.855707i \(-0.673123\pi\)
−0.517461 + 0.855707i \(0.673123\pi\)
\(444\) 0 0
\(445\) −0.393255 −0.0186421
\(446\) 0 0
\(447\) −23.0467 −1.09007
\(448\) 0 0
\(449\) 35.6040 1.68026 0.840128 0.542388i \(-0.182480\pi\)
0.840128 + 0.542388i \(0.182480\pi\)
\(450\) 0 0
\(451\) −36.3574 −1.71200
\(452\) 0 0
\(453\) −16.4425 −0.772536
\(454\) 0 0
\(455\) −1.84022 −0.0862710
\(456\) 0 0
\(457\) 18.0337 0.843581 0.421790 0.906693i \(-0.361402\pi\)
0.421790 + 0.906693i \(0.361402\pi\)
\(458\) 0 0
\(459\) 5.12186 0.239068
\(460\) 0 0
\(461\) −22.6715 −1.05592 −0.527959 0.849270i \(-0.677042\pi\)
−0.527959 + 0.849270i \(0.677042\pi\)
\(462\) 0 0
\(463\) −37.1967 −1.72868 −0.864338 0.502911i \(-0.832262\pi\)
−0.864338 + 0.502911i \(0.832262\pi\)
\(464\) 0 0
\(465\) 0.0416638 0.00193211
\(466\) 0 0
\(467\) −3.19263 −0.147737 −0.0738687 0.997268i \(-0.523535\pi\)
−0.0738687 + 0.997268i \(0.523535\pi\)
\(468\) 0 0
\(469\) 3.59553 0.166026
\(470\) 0 0
\(471\) −7.93026 −0.365407
\(472\) 0 0
\(473\) −20.9280 −0.962269
\(474\) 0 0
\(475\) 9.15032 0.419846
\(476\) 0 0
\(477\) 3.65981 0.167571
\(478\) 0 0
\(479\) −10.1957 −0.465854 −0.232927 0.972494i \(-0.574830\pi\)
−0.232927 + 0.972494i \(0.574830\pi\)
\(480\) 0 0
\(481\) −34.7666 −1.58522
\(482\) 0 0
\(483\) −4.71362 −0.214477
\(484\) 0 0
\(485\) 1.40005 0.0635731
\(486\) 0 0
\(487\) −6.62628 −0.300266 −0.150133 0.988666i \(-0.547970\pi\)
−0.150133 + 0.988666i \(0.547970\pi\)
\(488\) 0 0
\(489\) 17.7322 0.801879
\(490\) 0 0
\(491\) 14.3148 0.646018 0.323009 0.946396i \(-0.395306\pi\)
0.323009 + 0.946396i \(0.395306\pi\)
\(492\) 0 0
\(493\) 1.73309 0.0780545
\(494\) 0 0
\(495\) 1.85353 0.0833099
\(496\) 0 0
\(497\) −0.763125 −0.0342308
\(498\) 0 0
\(499\) 16.9217 0.757519 0.378760 0.925495i \(-0.376351\pi\)
0.378760 + 0.925495i \(0.376351\pi\)
\(500\) 0 0
\(501\) 18.8699 0.843044
\(502\) 0 0
\(503\) 21.0979 0.940708 0.470354 0.882478i \(-0.344126\pi\)
0.470354 + 0.882478i \(0.344126\pi\)
\(504\) 0 0
\(505\) −2.12411 −0.0945217
\(506\) 0 0
\(507\) −2.58478 −0.114794
\(508\) 0 0
\(509\) 31.1001 1.37849 0.689244 0.724529i \(-0.257943\pi\)
0.689244 + 0.724529i \(0.257943\pi\)
\(510\) 0 0
\(511\) −4.95540 −0.219214
\(512\) 0 0
\(513\) 9.53987 0.421196
\(514\) 0 0
\(515\) −0.869880 −0.0383315
\(516\) 0 0
\(517\) −22.6366 −0.995555
\(518\) 0 0
\(519\) 7.68763 0.337450
\(520\) 0 0
\(521\) 18.5174 0.811263 0.405631 0.914037i \(-0.367052\pi\)
0.405631 + 0.914037i \(0.367052\pi\)
\(522\) 0 0
\(523\) 25.0712 1.09629 0.548144 0.836384i \(-0.315335\pi\)
0.548144 + 0.836384i \(0.315335\pi\)
\(524\) 0 0
\(525\) −9.83478 −0.429225
\(526\) 0 0
\(527\) 0.135282 0.00589298
\(528\) 0 0
\(529\) −17.4560 −0.758957
\(530\) 0 0
\(531\) 1.91330 0.0830303
\(532\) 0 0
\(533\) −35.9633 −1.55774
\(534\) 0 0
\(535\) 2.63468 0.113907
\(536\) 0 0
\(537\) −8.60275 −0.371236
\(538\) 0 0
\(539\) −10.8607 −0.467802
\(540\) 0 0
\(541\) −1.69927 −0.0730575 −0.0365287 0.999333i \(-0.511630\pi\)
−0.0365287 + 0.999333i \(0.511630\pi\)
\(542\) 0 0
\(543\) 17.1653 0.736632
\(544\) 0 0
\(545\) −3.54588 −0.151889
\(546\) 0 0
\(547\) 45.0928 1.92803 0.964015 0.265847i \(-0.0856517\pi\)
0.964015 + 0.265847i \(0.0856517\pi\)
\(548\) 0 0
\(549\) 4.92194 0.210063
\(550\) 0 0
\(551\) 3.22802 0.137518
\(552\) 0 0
\(553\) 12.3143 0.523657
\(554\) 0 0
\(555\) 3.30113 0.140125
\(556\) 0 0
\(557\) 29.7877 1.26214 0.631072 0.775724i \(-0.282615\pi\)
0.631072 + 0.775724i \(0.282615\pi\)
\(558\) 0 0
\(559\) −20.7011 −0.875564
\(560\) 0 0
\(561\) −3.41826 −0.144319
\(562\) 0 0
\(563\) 38.9948 1.64343 0.821717 0.569896i \(-0.193017\pi\)
0.821717 + 0.569896i \(0.193017\pi\)
\(564\) 0 0
\(565\) −1.33451 −0.0561434
\(566\) 0 0
\(567\) 0.769379 0.0323109
\(568\) 0 0
\(569\) 42.4720 1.78052 0.890260 0.455453i \(-0.150523\pi\)
0.890260 + 0.455453i \(0.150523\pi\)
\(570\) 0 0
\(571\) 19.6584 0.822677 0.411338 0.911483i \(-0.365061\pi\)
0.411338 + 0.911483i \(0.365061\pi\)
\(572\) 0 0
\(573\) 3.46601 0.144795
\(574\) 0 0
\(575\) 11.5673 0.482391
\(576\) 0 0
\(577\) −19.4990 −0.811752 −0.405876 0.913928i \(-0.633034\pi\)
−0.405876 + 0.913928i \(0.633034\pi\)
\(578\) 0 0
\(579\) −0.0555917 −0.00231031
\(580\) 0 0
\(581\) 16.2709 0.675030
\(582\) 0 0
\(583\) −6.27228 −0.259771
\(584\) 0 0
\(585\) 1.83343 0.0758032
\(586\) 0 0
\(587\) −18.7187 −0.772603 −0.386302 0.922373i \(-0.626248\pi\)
−0.386302 + 0.922373i \(0.626248\pi\)
\(588\) 0 0
\(589\) 0.251974 0.0103824
\(590\) 0 0
\(591\) −4.38039 −0.180185
\(592\) 0 0
\(593\) 27.2702 1.11985 0.559926 0.828543i \(-0.310830\pi\)
0.559926 + 0.828543i \(0.310830\pi\)
\(594\) 0 0
\(595\) 0.567352 0.0232592
\(596\) 0 0
\(597\) −26.8262 −1.09792
\(598\) 0 0
\(599\) −4.60374 −0.188104 −0.0940520 0.995567i \(-0.529982\pi\)
−0.0940520 + 0.995567i \(0.529982\pi\)
\(600\) 0 0
\(601\) 8.28819 0.338082 0.169041 0.985609i \(-0.445933\pi\)
0.169041 + 0.985609i \(0.445933\pi\)
\(602\) 0 0
\(603\) −3.58227 −0.145881
\(604\) 0 0
\(605\) 0.0731694 0.00297476
\(606\) 0 0
\(607\) 2.69559 0.109410 0.0547052 0.998503i \(-0.482578\pi\)
0.0547052 + 0.998503i \(0.482578\pi\)
\(608\) 0 0
\(609\) −3.46948 −0.140590
\(610\) 0 0
\(611\) −22.3912 −0.905850
\(612\) 0 0
\(613\) 25.9919 1.04980 0.524901 0.851163i \(-0.324102\pi\)
0.524901 + 0.851163i \(0.324102\pi\)
\(614\) 0 0
\(615\) 3.41476 0.137696
\(616\) 0 0
\(617\) −36.7605 −1.47992 −0.739962 0.672649i \(-0.765157\pi\)
−0.739962 + 0.672649i \(0.765157\pi\)
\(618\) 0 0
\(619\) −21.4174 −0.860838 −0.430419 0.902629i \(-0.641634\pi\)
−0.430419 + 0.902629i \(0.641634\pi\)
\(620\) 0 0
\(621\) 12.0598 0.483942
\(622\) 0 0
\(623\) 2.55622 0.102413
\(624\) 0 0
\(625\) 23.6984 0.947935
\(626\) 0 0
\(627\) −6.36679 −0.254265
\(628\) 0 0
\(629\) 10.7188 0.427385
\(630\) 0 0
\(631\) −15.1048 −0.601313 −0.300656 0.953733i \(-0.597206\pi\)
−0.300656 + 0.953733i \(0.597206\pi\)
\(632\) 0 0
\(633\) −2.00353 −0.0796333
\(634\) 0 0
\(635\) −4.49050 −0.178200
\(636\) 0 0
\(637\) −10.7429 −0.425651
\(638\) 0 0
\(639\) 0.760310 0.0300774
\(640\) 0 0
\(641\) 3.33015 0.131533 0.0657664 0.997835i \(-0.479051\pi\)
0.0657664 + 0.997835i \(0.479051\pi\)
\(642\) 0 0
\(643\) 5.29353 0.208757 0.104378 0.994538i \(-0.466715\pi\)
0.104378 + 0.994538i \(0.466715\pi\)
\(644\) 0 0
\(645\) 1.96560 0.0773953
\(646\) 0 0
\(647\) −2.37880 −0.0935202 −0.0467601 0.998906i \(-0.514890\pi\)
−0.0467601 + 0.998906i \(0.514890\pi\)
\(648\) 0 0
\(649\) −3.27908 −0.128715
\(650\) 0 0
\(651\) −0.270822 −0.0106143
\(652\) 0 0
\(653\) −38.7039 −1.51460 −0.757299 0.653068i \(-0.773482\pi\)
−0.757299 + 0.653068i \(0.773482\pi\)
\(654\) 0 0
\(655\) −5.87891 −0.229708
\(656\) 0 0
\(657\) 4.93712 0.192615
\(658\) 0 0
\(659\) 7.52473 0.293122 0.146561 0.989202i \(-0.453180\pi\)
0.146561 + 0.989202i \(0.453180\pi\)
\(660\) 0 0
\(661\) −32.3946 −1.26000 −0.630002 0.776593i \(-0.716946\pi\)
−0.630002 + 0.776593i \(0.716946\pi\)
\(662\) 0 0
\(663\) −3.38121 −0.131315
\(664\) 0 0
\(665\) 1.05674 0.0409785
\(666\) 0 0
\(667\) 4.08068 0.158005
\(668\) 0 0
\(669\) −4.31639 −0.166881
\(670\) 0 0
\(671\) −8.43537 −0.325644
\(672\) 0 0
\(673\) 36.0394 1.38922 0.694608 0.719388i \(-0.255578\pi\)
0.694608 + 0.719388i \(0.255578\pi\)
\(674\) 0 0
\(675\) 25.1623 0.968496
\(676\) 0 0
\(677\) −33.5713 −1.29025 −0.645125 0.764077i \(-0.723195\pi\)
−0.645125 + 0.764077i \(0.723195\pi\)
\(678\) 0 0
\(679\) −9.10057 −0.349248
\(680\) 0 0
\(681\) 26.2204 1.00477
\(682\) 0 0
\(683\) −40.4193 −1.54660 −0.773302 0.634038i \(-0.781396\pi\)
−0.773302 + 0.634038i \(0.781396\pi\)
\(684\) 0 0
\(685\) 3.39100 0.129563
\(686\) 0 0
\(687\) 9.86897 0.376525
\(688\) 0 0
\(689\) −6.20429 −0.236365
\(690\) 0 0
\(691\) −17.5767 −0.668648 −0.334324 0.942458i \(-0.608508\pi\)
−0.334324 + 0.942458i \(0.608508\pi\)
\(692\) 0 0
\(693\) −12.0482 −0.457675
\(694\) 0 0
\(695\) 0.829070 0.0314484
\(696\) 0 0
\(697\) 11.0877 0.419976
\(698\) 0 0
\(699\) −26.9169 −1.01809
\(700\) 0 0
\(701\) −29.1292 −1.10020 −0.550098 0.835100i \(-0.685410\pi\)
−0.550098 + 0.835100i \(0.685410\pi\)
\(702\) 0 0
\(703\) 19.9646 0.752977
\(704\) 0 0
\(705\) 2.12607 0.0800724
\(706\) 0 0
\(707\) 13.8071 0.519268
\(708\) 0 0
\(709\) −7.94810 −0.298497 −0.149249 0.988800i \(-0.547685\pi\)
−0.149249 + 0.988800i \(0.547685\pi\)
\(710\) 0 0
\(711\) −12.2689 −0.460119
\(712\) 0 0
\(713\) 0.318531 0.0119291
\(714\) 0 0
\(715\) −3.14219 −0.117511
\(716\) 0 0
\(717\) −5.12079 −0.191239
\(718\) 0 0
\(719\) 43.7516 1.63166 0.815829 0.578293i \(-0.196281\pi\)
0.815829 + 0.578293i \(0.196281\pi\)
\(720\) 0 0
\(721\) 5.65437 0.210580
\(722\) 0 0
\(723\) −18.0921 −0.672852
\(724\) 0 0
\(725\) 8.51419 0.316209
\(726\) 0 0
\(727\) 2.93621 0.108898 0.0544491 0.998517i \(-0.482660\pi\)
0.0544491 + 0.998517i \(0.482660\pi\)
\(728\) 0 0
\(729\) 15.2513 0.564862
\(730\) 0 0
\(731\) 6.38228 0.236057
\(732\) 0 0
\(733\) 39.0379 1.44190 0.720948 0.692989i \(-0.243706\pi\)
0.720948 + 0.692989i \(0.243706\pi\)
\(734\) 0 0
\(735\) 1.02006 0.0376253
\(736\) 0 0
\(737\) 6.13939 0.226148
\(738\) 0 0
\(739\) −49.4562 −1.81928 −0.909638 0.415402i \(-0.863641\pi\)
−0.909638 + 0.415402i \(0.863641\pi\)
\(740\) 0 0
\(741\) −6.29777 −0.231354
\(742\) 0 0
\(743\) 44.5921 1.63593 0.817963 0.575270i \(-0.195103\pi\)
0.817963 + 0.575270i \(0.195103\pi\)
\(744\) 0 0
\(745\) 6.53157 0.239298
\(746\) 0 0
\(747\) −16.2109 −0.593124
\(748\) 0 0
\(749\) −17.1259 −0.625766
\(750\) 0 0
\(751\) −53.3628 −1.94724 −0.973618 0.228185i \(-0.926721\pi\)
−0.973618 + 0.228185i \(0.926721\pi\)
\(752\) 0 0
\(753\) −29.8844 −1.08905
\(754\) 0 0
\(755\) 4.65991 0.169592
\(756\) 0 0
\(757\) −25.0805 −0.911567 −0.455784 0.890091i \(-0.650641\pi\)
−0.455784 + 0.890091i \(0.650641\pi\)
\(758\) 0 0
\(759\) −8.04854 −0.292143
\(760\) 0 0
\(761\) 48.0543 1.74197 0.870983 0.491313i \(-0.163483\pi\)
0.870983 + 0.491313i \(0.163483\pi\)
\(762\) 0 0
\(763\) 23.0488 0.834424
\(764\) 0 0
\(765\) −0.565259 −0.0204370
\(766\) 0 0
\(767\) −3.24353 −0.117117
\(768\) 0 0
\(769\) 27.2382 0.982235 0.491117 0.871093i \(-0.336589\pi\)
0.491117 + 0.871093i \(0.336589\pi\)
\(770\) 0 0
\(771\) 26.0934 0.939730
\(772\) 0 0
\(773\) 43.9805 1.58187 0.790935 0.611901i \(-0.209595\pi\)
0.790935 + 0.611901i \(0.209595\pi\)
\(774\) 0 0
\(775\) 0.664603 0.0238732
\(776\) 0 0
\(777\) −21.4579 −0.769799
\(778\) 0 0
\(779\) 20.6517 0.739924
\(780\) 0 0
\(781\) −1.30304 −0.0466265
\(782\) 0 0
\(783\) 8.87665 0.317226
\(784\) 0 0
\(785\) 2.24749 0.0802163
\(786\) 0 0
\(787\) −35.3416 −1.25979 −0.629895 0.776680i \(-0.716902\pi\)
−0.629895 + 0.776680i \(0.716902\pi\)
\(788\) 0 0
\(789\) −9.31415 −0.331593
\(790\) 0 0
\(791\) 8.67456 0.308432
\(792\) 0 0
\(793\) −8.34392 −0.296301
\(794\) 0 0
\(795\) 0.589105 0.0208934
\(796\) 0 0
\(797\) −32.1892 −1.14020 −0.570100 0.821575i \(-0.693095\pi\)
−0.570100 + 0.821575i \(0.693095\pi\)
\(798\) 0 0
\(799\) 6.90334 0.244223
\(800\) 0 0
\(801\) −2.54680 −0.0899866
\(802\) 0 0
\(803\) −8.46138 −0.298596
\(804\) 0 0
\(805\) 1.33587 0.0470832
\(806\) 0 0
\(807\) −21.1998 −0.746268
\(808\) 0 0
\(809\) 11.7482 0.413046 0.206523 0.978442i \(-0.433785\pi\)
0.206523 + 0.978442i \(0.433785\pi\)
\(810\) 0 0
\(811\) 19.3126 0.678158 0.339079 0.940758i \(-0.389885\pi\)
0.339079 + 0.940758i \(0.389885\pi\)
\(812\) 0 0
\(813\) 3.46158 0.121403
\(814\) 0 0
\(815\) −5.02543 −0.176033
\(816\) 0 0
\(817\) 11.8875 0.415891
\(818\) 0 0
\(819\) −11.9176 −0.416436
\(820\) 0 0
\(821\) 20.0690 0.700413 0.350206 0.936673i \(-0.386111\pi\)
0.350206 + 0.936673i \(0.386111\pi\)
\(822\) 0 0
\(823\) −45.4430 −1.58404 −0.792022 0.610492i \(-0.790972\pi\)
−0.792022 + 0.610492i \(0.790972\pi\)
\(824\) 0 0
\(825\) −16.7930 −0.584656
\(826\) 0 0
\(827\) −23.5531 −0.819021 −0.409510 0.912305i \(-0.634300\pi\)
−0.409510 + 0.912305i \(0.634300\pi\)
\(828\) 0 0
\(829\) −22.9646 −0.797594 −0.398797 0.917039i \(-0.630572\pi\)
−0.398797 + 0.917039i \(0.630572\pi\)
\(830\) 0 0
\(831\) −0.294242 −0.0102072
\(832\) 0 0
\(833\) 3.31212 0.114758
\(834\) 0 0
\(835\) −5.34785 −0.185070
\(836\) 0 0
\(837\) 0.692896 0.0239500
\(838\) 0 0
\(839\) −27.8817 −0.962584 −0.481292 0.876560i \(-0.659832\pi\)
−0.481292 + 0.876560i \(0.659832\pi\)
\(840\) 0 0
\(841\) −25.9964 −0.896427
\(842\) 0 0
\(843\) 9.24494 0.318413
\(844\) 0 0
\(845\) 0.732542 0.0252002
\(846\) 0 0
\(847\) −0.475614 −0.0163423
\(848\) 0 0
\(849\) −13.0248 −0.447011
\(850\) 0 0
\(851\) 25.2381 0.865150
\(852\) 0 0
\(853\) 0.717295 0.0245597 0.0122799 0.999925i \(-0.496091\pi\)
0.0122799 + 0.999925i \(0.496091\pi\)
\(854\) 0 0
\(855\) −1.05284 −0.0360064
\(856\) 0 0
\(857\) 28.7512 0.982122 0.491061 0.871125i \(-0.336609\pi\)
0.491061 + 0.871125i \(0.336609\pi\)
\(858\) 0 0
\(859\) −41.4002 −1.41256 −0.706278 0.707934i \(-0.749627\pi\)
−0.706278 + 0.707934i \(0.749627\pi\)
\(860\) 0 0
\(861\) −22.1965 −0.756454
\(862\) 0 0
\(863\) 2.13789 0.0727747 0.0363873 0.999338i \(-0.488415\pi\)
0.0363873 + 0.999338i \(0.488415\pi\)
\(864\) 0 0
\(865\) −2.17873 −0.0740789
\(866\) 0 0
\(867\) 1.04245 0.0354034
\(868\) 0 0
\(869\) 21.0268 0.713284
\(870\) 0 0
\(871\) 6.07284 0.205770
\(872\) 0 0
\(873\) 9.06700 0.306872
\(874\) 0 0
\(875\) 5.62400 0.190126
\(876\) 0 0
\(877\) −15.1807 −0.512616 −0.256308 0.966595i \(-0.582506\pi\)
−0.256308 + 0.966595i \(0.582506\pi\)
\(878\) 0 0
\(879\) 25.0943 0.846410
\(880\) 0 0
\(881\) 27.8442 0.938094 0.469047 0.883173i \(-0.344598\pi\)
0.469047 + 0.883173i \(0.344598\pi\)
\(882\) 0 0
\(883\) 43.9197 1.47802 0.739008 0.673697i \(-0.235295\pi\)
0.739008 + 0.673697i \(0.235295\pi\)
\(884\) 0 0
\(885\) 0.307977 0.0103525
\(886\) 0 0
\(887\) 45.9115 1.54156 0.770779 0.637102i \(-0.219867\pi\)
0.770779 + 0.637102i \(0.219867\pi\)
\(888\) 0 0
\(889\) 29.1890 0.978968
\(890\) 0 0
\(891\) 1.31372 0.0440113
\(892\) 0 0
\(893\) 12.8580 0.430277
\(894\) 0 0
\(895\) 2.43808 0.0814959
\(896\) 0 0
\(897\) −7.96129 −0.265820
\(898\) 0 0
\(899\) 0.234456 0.00781956
\(900\) 0 0
\(901\) 1.91282 0.0637253
\(902\) 0 0
\(903\) −12.7767 −0.425182
\(904\) 0 0
\(905\) −4.86474 −0.161710
\(906\) 0 0
\(907\) 19.6154 0.651319 0.325659 0.945487i \(-0.394414\pi\)
0.325659 + 0.945487i \(0.394414\pi\)
\(908\) 0 0
\(909\) −13.7561 −0.456263
\(910\) 0 0
\(911\) −10.3995 −0.344551 −0.172275 0.985049i \(-0.555112\pi\)
−0.172275 + 0.985049i \(0.555112\pi\)
\(912\) 0 0
\(913\) 27.7827 0.919472
\(914\) 0 0
\(915\) 0.792266 0.0261915
\(916\) 0 0
\(917\) 38.2139 1.26193
\(918\) 0 0
\(919\) 37.5471 1.23857 0.619283 0.785168i \(-0.287424\pi\)
0.619283 + 0.785168i \(0.287424\pi\)
\(920\) 0 0
\(921\) 13.5055 0.445020
\(922\) 0 0
\(923\) −1.28892 −0.0424252
\(924\) 0 0
\(925\) 52.6583 1.73139
\(926\) 0 0
\(927\) −5.63351 −0.185029
\(928\) 0 0
\(929\) −50.4230 −1.65432 −0.827162 0.561963i \(-0.810046\pi\)
−0.827162 + 0.561963i \(0.810046\pi\)
\(930\) 0 0
\(931\) 6.16908 0.202183
\(932\) 0 0
\(933\) −1.85330 −0.0606743
\(934\) 0 0
\(935\) 0.968758 0.0316818
\(936\) 0 0
\(937\) −17.8639 −0.583589 −0.291794 0.956481i \(-0.594252\pi\)
−0.291794 + 0.956481i \(0.594252\pi\)
\(938\) 0 0
\(939\) −5.15572 −0.168251
\(940\) 0 0
\(941\) −16.2434 −0.529518 −0.264759 0.964315i \(-0.585292\pi\)
−0.264759 + 0.964315i \(0.585292\pi\)
\(942\) 0 0
\(943\) 26.1067 0.850152
\(944\) 0 0
\(945\) 2.90590 0.0945289
\(946\) 0 0
\(947\) −46.6444 −1.51574 −0.757869 0.652407i \(-0.773759\pi\)
−0.757869 + 0.652407i \(0.773759\pi\)
\(948\) 0 0
\(949\) −8.36966 −0.271691
\(950\) 0 0
\(951\) 11.8375 0.383856
\(952\) 0 0
\(953\) 2.94924 0.0955353 0.0477676 0.998858i \(-0.484789\pi\)
0.0477676 + 0.998858i \(0.484789\pi\)
\(954\) 0 0
\(955\) −0.982290 −0.0317862
\(956\) 0 0
\(957\) −5.92417 −0.191501
\(958\) 0 0
\(959\) −22.0421 −0.711775
\(960\) 0 0
\(961\) −30.9817 −0.999410
\(962\) 0 0
\(963\) 17.0627 0.549838
\(964\) 0 0
\(965\) 0.0157551 0.000507173 0
\(966\) 0 0
\(967\) −22.7304 −0.730959 −0.365480 0.930819i \(-0.619095\pi\)
−0.365480 + 0.930819i \(0.619095\pi\)
\(968\) 0 0
\(969\) 1.94164 0.0623745
\(970\) 0 0
\(971\) 42.2904 1.35716 0.678582 0.734524i \(-0.262595\pi\)
0.678582 + 0.734524i \(0.262595\pi\)
\(972\) 0 0
\(973\) −5.38909 −0.172766
\(974\) 0 0
\(975\) −16.6109 −0.531975
\(976\) 0 0
\(977\) 5.15611 0.164958 0.0824792 0.996593i \(-0.473716\pi\)
0.0824792 + 0.996593i \(0.473716\pi\)
\(978\) 0 0
\(979\) 4.36477 0.139499
\(980\) 0 0
\(981\) −22.9638 −0.733179
\(982\) 0 0
\(983\) −20.0024 −0.637978 −0.318989 0.947758i \(-0.603343\pi\)
−0.318989 + 0.947758i \(0.603343\pi\)
\(984\) 0 0
\(985\) 1.24143 0.0395552
\(986\) 0 0
\(987\) −13.8198 −0.439889
\(988\) 0 0
\(989\) 15.0275 0.477847
\(990\) 0 0
\(991\) −26.2396 −0.833530 −0.416765 0.909014i \(-0.636836\pi\)
−0.416765 + 0.909014i \(0.636836\pi\)
\(992\) 0 0
\(993\) 23.7005 0.752114
\(994\) 0 0
\(995\) 7.60273 0.241023
\(996\) 0 0
\(997\) −14.6227 −0.463107 −0.231553 0.972822i \(-0.574381\pi\)
−0.231553 + 0.972822i \(0.574381\pi\)
\(998\) 0 0
\(999\) 54.9000 1.73696
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 \(a_p\))