Properties

Label 8024.2.a.y.1.3
Level 8024
Weight 2
Character 8024.1
Self dual Yes
Analytic conductor 64.072
Analytic rank 1
Dimension 23
CM No

Related objects

Downloads

Learn more about

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 1.3
Character \(\chi\) = 8024.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.88993 q^{3}\) \(-1.71727 q^{5}\) \(-4.47538 q^{7}\) \(+5.35170 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.88993 q^{3}\) \(-1.71727 q^{5}\) \(-4.47538 q^{7}\) \(+5.35170 q^{9}\) \(-4.06786 q^{11}\) \(-4.73647 q^{13}\) \(+4.96278 q^{15}\) \(-1.00000 q^{17}\) \(-8.07202 q^{19}\) \(+12.9335 q^{21}\) \(+4.47945 q^{23}\) \(-2.05100 q^{25}\) \(-6.79624 q^{27}\) \(-1.34908 q^{29}\) \(+5.63309 q^{31}\) \(+11.7558 q^{33}\) \(+7.68542 q^{35}\) \(+9.06811 q^{37}\) \(+13.6881 q^{39}\) \(+8.49539 q^{41}\) \(+0.753759 q^{43}\) \(-9.19029 q^{45}\) \(-4.24429 q^{47}\) \(+13.0290 q^{49}\) \(+2.88993 q^{51}\) \(-1.55350 q^{53}\) \(+6.98559 q^{55}\) \(+23.3276 q^{57}\) \(-1.00000 q^{59}\) \(-8.96870 q^{61}\) \(-23.9509 q^{63}\) \(+8.13378 q^{65}\) \(+2.40539 q^{67}\) \(-12.9453 q^{69}\) \(-11.9331 q^{71}\) \(+6.99818 q^{73}\) \(+5.92724 q^{75}\) \(+18.2052 q^{77}\) \(-0.499053 q^{79}\) \(+3.58558 q^{81}\) \(-0.659380 q^{83}\) \(+1.71727 q^{85}\) \(+3.89876 q^{87}\) \(-4.70016 q^{89}\) \(+21.1975 q^{91}\) \(-16.2792 q^{93}\) \(+13.8618 q^{95}\) \(+13.0666 q^{97}\) \(-21.7699 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 23q^{17} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut -\mathstrut 29q^{23} \) \(\mathstrut +\mathstrut 31q^{25} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 22q^{35} \) \(\mathstrut +\mathstrut 5q^{37} \) \(\mathstrut +\mathstrut 16q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 39q^{47} \) \(\mathstrut +\mathstrut 16q^{49} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 35q^{55} \) \(\mathstrut +\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 23q^{59} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut +\mathstrut 33q^{65} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut -\mathstrut 66q^{69} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut -\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 81q^{75} \) \(\mathstrut -\mathstrut 4q^{77} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut +\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 18q^{91} \) \(\mathstrut -\mathstrut 62q^{93} \) \(\mathstrut -\mathstrut 33q^{95} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.88993 −1.66850 −0.834251 0.551385i \(-0.814100\pi\)
−0.834251 + 0.551385i \(0.814100\pi\)
\(4\) 0 0
\(5\) −1.71727 −0.767985 −0.383992 0.923336i \(-0.625451\pi\)
−0.383992 + 0.923336i \(0.625451\pi\)
\(6\) 0 0
\(7\) −4.47538 −1.69153 −0.845767 0.533552i \(-0.820857\pi\)
−0.845767 + 0.533552i \(0.820857\pi\)
\(8\) 0 0
\(9\) 5.35170 1.78390
\(10\) 0 0
\(11\) −4.06786 −1.22650 −0.613252 0.789887i \(-0.710139\pi\)
−0.613252 + 0.789887i \(0.710139\pi\)
\(12\) 0 0
\(13\) −4.73647 −1.31366 −0.656830 0.754038i \(-0.728103\pi\)
−0.656830 + 0.754038i \(0.728103\pi\)
\(14\) 0 0
\(15\) 4.96278 1.28138
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) −8.07202 −1.85185 −0.925924 0.377710i \(-0.876712\pi\)
−0.925924 + 0.377710i \(0.876712\pi\)
\(20\) 0 0
\(21\) 12.9335 2.82233
\(22\) 0 0
\(23\) 4.47945 0.934030 0.467015 0.884249i \(-0.345329\pi\)
0.467015 + 0.884249i \(0.345329\pi\)
\(24\) 0 0
\(25\) −2.05100 −0.410199
\(26\) 0 0
\(27\) −6.79624 −1.30794
\(28\) 0 0
\(29\) −1.34908 −0.250519 −0.125259 0.992124i \(-0.539976\pi\)
−0.125259 + 0.992124i \(0.539976\pi\)
\(30\) 0 0
\(31\) 5.63309 1.01173 0.505866 0.862612i \(-0.331173\pi\)
0.505866 + 0.862612i \(0.331173\pi\)
\(32\) 0 0
\(33\) 11.7558 2.04643
\(34\) 0 0
\(35\) 7.68542 1.29907
\(36\) 0 0
\(37\) 9.06811 1.49079 0.745394 0.666624i \(-0.232261\pi\)
0.745394 + 0.666624i \(0.232261\pi\)
\(38\) 0 0
\(39\) 13.6881 2.19185
\(40\) 0 0
\(41\) 8.49539 1.32676 0.663378 0.748284i \(-0.269122\pi\)
0.663378 + 0.748284i \(0.269122\pi\)
\(42\) 0 0
\(43\) 0.753759 0.114947 0.0574736 0.998347i \(-0.481696\pi\)
0.0574736 + 0.998347i \(0.481696\pi\)
\(44\) 0 0
\(45\) −9.19029 −1.37001
\(46\) 0 0
\(47\) −4.24429 −0.619094 −0.309547 0.950884i \(-0.600177\pi\)
−0.309547 + 0.950884i \(0.600177\pi\)
\(48\) 0 0
\(49\) 13.0290 1.86129
\(50\) 0 0
\(51\) 2.88993 0.404671
\(52\) 0 0
\(53\) −1.55350 −0.213390 −0.106695 0.994292i \(-0.534027\pi\)
−0.106695 + 0.994292i \(0.534027\pi\)
\(54\) 0 0
\(55\) 6.98559 0.941937
\(56\) 0 0
\(57\) 23.3276 3.08981
\(58\) 0 0
\(59\) −1.00000 −0.130189
\(60\) 0 0
\(61\) −8.96870 −1.14832 −0.574162 0.818741i \(-0.694672\pi\)
−0.574162 + 0.818741i \(0.694672\pi\)
\(62\) 0 0
\(63\) −23.9509 −3.01753
\(64\) 0 0
\(65\) 8.13378 1.00887
\(66\) 0 0
\(67\) 2.40539 0.293865 0.146933 0.989146i \(-0.453060\pi\)
0.146933 + 0.989146i \(0.453060\pi\)
\(68\) 0 0
\(69\) −12.9453 −1.55843
\(70\) 0 0
\(71\) −11.9331 −1.41620 −0.708100 0.706112i \(-0.750447\pi\)
−0.708100 + 0.706112i \(0.750447\pi\)
\(72\) 0 0
\(73\) 6.99818 0.819075 0.409537 0.912293i \(-0.365690\pi\)
0.409537 + 0.912293i \(0.365690\pi\)
\(74\) 0 0
\(75\) 5.92724 0.684418
\(76\) 0 0
\(77\) 18.2052 2.07468
\(78\) 0 0
\(79\) −0.499053 −0.0561479 −0.0280739 0.999606i \(-0.508937\pi\)
−0.0280739 + 0.999606i \(0.508937\pi\)
\(80\) 0 0
\(81\) 3.58558 0.398397
\(82\) 0 0
\(83\) −0.659380 −0.0723764 −0.0361882 0.999345i \(-0.511522\pi\)
−0.0361882 + 0.999345i \(0.511522\pi\)
\(84\) 0 0
\(85\) 1.71727 0.186264
\(86\) 0 0
\(87\) 3.89876 0.417991
\(88\) 0 0
\(89\) −4.70016 −0.498216 −0.249108 0.968476i \(-0.580137\pi\)
−0.249108 + 0.968476i \(0.580137\pi\)
\(90\) 0 0
\(91\) 21.1975 2.22210
\(92\) 0 0
\(93\) −16.2792 −1.68808
\(94\) 0 0
\(95\) 13.8618 1.42219
\(96\) 0 0
\(97\) 13.0666 1.32671 0.663357 0.748303i \(-0.269131\pi\)
0.663357 + 0.748303i \(0.269131\pi\)
\(98\) 0 0
\(99\) −21.7699 −2.18796
\(100\) 0 0
\(101\) 3.30043 0.328405 0.164203 0.986427i \(-0.447495\pi\)
0.164203 + 0.986427i \(0.447495\pi\)
\(102\) 0 0
\(103\) 9.80224 0.965843 0.482921 0.875664i \(-0.339576\pi\)
0.482921 + 0.875664i \(0.339576\pi\)
\(104\) 0 0
\(105\) −22.2103 −2.16751
\(106\) 0 0
\(107\) −7.77994 −0.752116 −0.376058 0.926596i \(-0.622721\pi\)
−0.376058 + 0.926596i \(0.622721\pi\)
\(108\) 0 0
\(109\) −4.58102 −0.438782 −0.219391 0.975637i \(-0.570407\pi\)
−0.219391 + 0.975637i \(0.570407\pi\)
\(110\) 0 0
\(111\) −26.2062 −2.48738
\(112\) 0 0
\(113\) 16.7672 1.57733 0.788663 0.614826i \(-0.210774\pi\)
0.788663 + 0.614826i \(0.210774\pi\)
\(114\) 0 0
\(115\) −7.69241 −0.717321
\(116\) 0 0
\(117\) −25.3482 −2.34344
\(118\) 0 0
\(119\) 4.47538 0.410257
\(120\) 0 0
\(121\) 5.54745 0.504314
\(122\) 0 0
\(123\) −24.5511 −2.21370
\(124\) 0 0
\(125\) 12.1084 1.08301
\(126\) 0 0
\(127\) −19.1287 −1.69739 −0.848697 0.528879i \(-0.822613\pi\)
−0.848697 + 0.528879i \(0.822613\pi\)
\(128\) 0 0
\(129\) −2.17831 −0.191789
\(130\) 0 0
\(131\) −0.475014 −0.0415021 −0.0207511 0.999785i \(-0.506606\pi\)
−0.0207511 + 0.999785i \(0.506606\pi\)
\(132\) 0 0
\(133\) 36.1254 3.13247
\(134\) 0 0
\(135\) 11.6710 1.00448
\(136\) 0 0
\(137\) −5.28095 −0.451182 −0.225591 0.974222i \(-0.572431\pi\)
−0.225591 + 0.974222i \(0.572431\pi\)
\(138\) 0 0
\(139\) −1.83085 −0.155290 −0.0776452 0.996981i \(-0.524740\pi\)
−0.0776452 + 0.996981i \(0.524740\pi\)
\(140\) 0 0
\(141\) 12.2657 1.03296
\(142\) 0 0
\(143\) 19.2673 1.61121
\(144\) 0 0
\(145\) 2.31674 0.192395
\(146\) 0 0
\(147\) −37.6530 −3.10557
\(148\) 0 0
\(149\) 8.76962 0.718435 0.359218 0.933254i \(-0.383044\pi\)
0.359218 + 0.933254i \(0.383044\pi\)
\(150\) 0 0
\(151\) 14.1799 1.15394 0.576971 0.816765i \(-0.304235\pi\)
0.576971 + 0.816765i \(0.304235\pi\)
\(152\) 0 0
\(153\) −5.35170 −0.432659
\(154\) 0 0
\(155\) −9.67351 −0.776995
\(156\) 0 0
\(157\) 1.82382 0.145556 0.0727782 0.997348i \(-0.476813\pi\)
0.0727782 + 0.997348i \(0.476813\pi\)
\(158\) 0 0
\(159\) 4.48951 0.356041
\(160\) 0 0
\(161\) −20.0472 −1.57994
\(162\) 0 0
\(163\) 10.9175 0.855127 0.427564 0.903985i \(-0.359372\pi\)
0.427564 + 0.903985i \(0.359372\pi\)
\(164\) 0 0
\(165\) −20.1879 −1.57162
\(166\) 0 0
\(167\) 4.30460 0.333100 0.166550 0.986033i \(-0.446737\pi\)
0.166550 + 0.986033i \(0.446737\pi\)
\(168\) 0 0
\(169\) 9.43416 0.725705
\(170\) 0 0
\(171\) −43.1990 −3.30351
\(172\) 0 0
\(173\) −19.3909 −1.47427 −0.737133 0.675748i \(-0.763821\pi\)
−0.737133 + 0.675748i \(0.763821\pi\)
\(174\) 0 0
\(175\) 9.17899 0.693866
\(176\) 0 0
\(177\) 2.88993 0.217220
\(178\) 0 0
\(179\) 1.97367 0.147519 0.0737594 0.997276i \(-0.476500\pi\)
0.0737594 + 0.997276i \(0.476500\pi\)
\(180\) 0 0
\(181\) 10.1504 0.754475 0.377237 0.926117i \(-0.376874\pi\)
0.377237 + 0.926117i \(0.376874\pi\)
\(182\) 0 0
\(183\) 25.9189 1.91598
\(184\) 0 0
\(185\) −15.5724 −1.14490
\(186\) 0 0
\(187\) 4.06786 0.297471
\(188\) 0 0
\(189\) 30.4158 2.21242
\(190\) 0 0
\(191\) −8.66394 −0.626901 −0.313450 0.949605i \(-0.601485\pi\)
−0.313450 + 0.949605i \(0.601485\pi\)
\(192\) 0 0
\(193\) 18.8228 1.35490 0.677449 0.735570i \(-0.263085\pi\)
0.677449 + 0.735570i \(0.263085\pi\)
\(194\) 0 0
\(195\) −23.5061 −1.68330
\(196\) 0 0
\(197\) 14.3221 1.02041 0.510205 0.860053i \(-0.329569\pi\)
0.510205 + 0.860053i \(0.329569\pi\)
\(198\) 0 0
\(199\) 0.793266 0.0562332 0.0281166 0.999605i \(-0.491049\pi\)
0.0281166 + 0.999605i \(0.491049\pi\)
\(200\) 0 0
\(201\) −6.95142 −0.490315
\(202\) 0 0
\(203\) 6.03766 0.423761
\(204\) 0 0
\(205\) −14.5888 −1.01893
\(206\) 0 0
\(207\) 23.9727 1.66622
\(208\) 0 0
\(209\) 32.8358 2.27130
\(210\) 0 0
\(211\) 5.57426 0.383748 0.191874 0.981420i \(-0.438544\pi\)
0.191874 + 0.981420i \(0.438544\pi\)
\(212\) 0 0
\(213\) 34.4859 2.36293
\(214\) 0 0
\(215\) −1.29440 −0.0882776
\(216\) 0 0
\(217\) −25.2102 −1.71138
\(218\) 0 0
\(219\) −20.2243 −1.36663
\(220\) 0 0
\(221\) 4.73647 0.318610
\(222\) 0 0
\(223\) 15.6461 1.04774 0.523869 0.851799i \(-0.324488\pi\)
0.523869 + 0.851799i \(0.324488\pi\)
\(224\) 0 0
\(225\) −10.9763 −0.731754
\(226\) 0 0
\(227\) −3.54310 −0.235164 −0.117582 0.993063i \(-0.537514\pi\)
−0.117582 + 0.993063i \(0.537514\pi\)
\(228\) 0 0
\(229\) 17.2044 1.13690 0.568451 0.822717i \(-0.307543\pi\)
0.568451 + 0.822717i \(0.307543\pi\)
\(230\) 0 0
\(231\) −52.6118 −3.46160
\(232\) 0 0
\(233\) 18.0935 1.18534 0.592672 0.805444i \(-0.298073\pi\)
0.592672 + 0.805444i \(0.298073\pi\)
\(234\) 0 0
\(235\) 7.28858 0.475455
\(236\) 0 0
\(237\) 1.44223 0.0936829
\(238\) 0 0
\(239\) 7.99926 0.517429 0.258714 0.965954i \(-0.416701\pi\)
0.258714 + 0.965954i \(0.416701\pi\)
\(240\) 0 0
\(241\) −30.9463 −1.99343 −0.996715 0.0809913i \(-0.974191\pi\)
−0.996715 + 0.0809913i \(0.974191\pi\)
\(242\) 0 0
\(243\) 10.0267 0.643211
\(244\) 0 0
\(245\) −22.3743 −1.42944
\(246\) 0 0
\(247\) 38.2329 2.43270
\(248\) 0 0
\(249\) 1.90556 0.120760
\(250\) 0 0
\(251\) −4.54671 −0.286986 −0.143493 0.989651i \(-0.545833\pi\)
−0.143493 + 0.989651i \(0.545833\pi\)
\(252\) 0 0
\(253\) −18.2218 −1.14559
\(254\) 0 0
\(255\) −4.96278 −0.310781
\(256\) 0 0
\(257\) 4.76844 0.297447 0.148723 0.988879i \(-0.452484\pi\)
0.148723 + 0.988879i \(0.452484\pi\)
\(258\) 0 0
\(259\) −40.5833 −2.52172
\(260\) 0 0
\(261\) −7.21989 −0.446900
\(262\) 0 0
\(263\) 21.3309 1.31532 0.657661 0.753314i \(-0.271546\pi\)
0.657661 + 0.753314i \(0.271546\pi\)
\(264\) 0 0
\(265\) 2.66778 0.163880
\(266\) 0 0
\(267\) 13.5831 0.831275
\(268\) 0 0
\(269\) −0.652086 −0.0397584 −0.0198792 0.999802i \(-0.506328\pi\)
−0.0198792 + 0.999802i \(0.506328\pi\)
\(270\) 0 0
\(271\) −32.3022 −1.96222 −0.981108 0.193460i \(-0.938029\pi\)
−0.981108 + 0.193460i \(0.938029\pi\)
\(272\) 0 0
\(273\) −61.2593 −3.70758
\(274\) 0 0
\(275\) 8.34316 0.503111
\(276\) 0 0
\(277\) 14.3466 0.862006 0.431003 0.902350i \(-0.358160\pi\)
0.431003 + 0.902350i \(0.358160\pi\)
\(278\) 0 0
\(279\) 30.1466 1.80483
\(280\) 0 0
\(281\) −31.0110 −1.84996 −0.924981 0.380014i \(-0.875919\pi\)
−0.924981 + 0.380014i \(0.875919\pi\)
\(282\) 0 0
\(283\) 6.55374 0.389579 0.194790 0.980845i \(-0.437598\pi\)
0.194790 + 0.980845i \(0.437598\pi\)
\(284\) 0 0
\(285\) −40.0597 −2.37293
\(286\) 0 0
\(287\) −38.0201 −2.24425
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) −37.7616 −2.21363
\(292\) 0 0
\(293\) −23.1873 −1.35462 −0.677308 0.735700i \(-0.736853\pi\)
−0.677308 + 0.735700i \(0.736853\pi\)
\(294\) 0 0
\(295\) 1.71727 0.0999831
\(296\) 0 0
\(297\) 27.6461 1.60419
\(298\) 0 0
\(299\) −21.2168 −1.22700
\(300\) 0 0
\(301\) −3.37336 −0.194437
\(302\) 0 0
\(303\) −9.53801 −0.547944
\(304\) 0 0
\(305\) 15.4017 0.881896
\(306\) 0 0
\(307\) −22.8589 −1.30462 −0.652312 0.757951i \(-0.726201\pi\)
−0.652312 + 0.757951i \(0.726201\pi\)
\(308\) 0 0
\(309\) −28.3278 −1.61151
\(310\) 0 0
\(311\) −34.0184 −1.92901 −0.964504 0.264068i \(-0.914936\pi\)
−0.964504 + 0.264068i \(0.914936\pi\)
\(312\) 0 0
\(313\) −29.0574 −1.64242 −0.821210 0.570626i \(-0.806700\pi\)
−0.821210 + 0.570626i \(0.806700\pi\)
\(314\) 0 0
\(315\) 41.1300 2.31742
\(316\) 0 0
\(317\) 1.33493 0.0749770 0.0374885 0.999297i \(-0.488064\pi\)
0.0374885 + 0.999297i \(0.488064\pi\)
\(318\) 0 0
\(319\) 5.48788 0.307262
\(320\) 0 0
\(321\) 22.4835 1.25491
\(322\) 0 0
\(323\) 8.07202 0.449139
\(324\) 0 0
\(325\) 9.71448 0.538863
\(326\) 0 0
\(327\) 13.2388 0.732109
\(328\) 0 0
\(329\) 18.9948 1.04722
\(330\) 0 0
\(331\) 4.56118 0.250705 0.125353 0.992112i \(-0.459994\pi\)
0.125353 + 0.992112i \(0.459994\pi\)
\(332\) 0 0
\(333\) 48.5298 2.65942
\(334\) 0 0
\(335\) −4.13070 −0.225684
\(336\) 0 0
\(337\) −4.51392 −0.245889 −0.122944 0.992414i \(-0.539234\pi\)
−0.122944 + 0.992414i \(0.539234\pi\)
\(338\) 0 0
\(339\) −48.4560 −2.63177
\(340\) 0 0
\(341\) −22.9146 −1.24089
\(342\) 0 0
\(343\) −26.9822 −1.45690
\(344\) 0 0
\(345\) 22.2305 1.19685
\(346\) 0 0
\(347\) −33.7414 −1.81133 −0.905666 0.423992i \(-0.860628\pi\)
−0.905666 + 0.423992i \(0.860628\pi\)
\(348\) 0 0
\(349\) −14.8975 −0.797445 −0.398722 0.917072i \(-0.630546\pi\)
−0.398722 + 0.917072i \(0.630546\pi\)
\(350\) 0 0
\(351\) 32.1902 1.71819
\(352\) 0 0
\(353\) 7.47350 0.397774 0.198887 0.980022i \(-0.436267\pi\)
0.198887 + 0.980022i \(0.436267\pi\)
\(354\) 0 0
\(355\) 20.4923 1.08762
\(356\) 0 0
\(357\) −12.9335 −0.684515
\(358\) 0 0
\(359\) −14.1124 −0.744824 −0.372412 0.928068i \(-0.621469\pi\)
−0.372412 + 0.928068i \(0.621469\pi\)
\(360\) 0 0
\(361\) 46.1575 2.42934
\(362\) 0 0
\(363\) −16.0317 −0.841448
\(364\) 0 0
\(365\) −12.0177 −0.629037
\(366\) 0 0
\(367\) 28.5518 1.49039 0.745197 0.666845i \(-0.232356\pi\)
0.745197 + 0.666845i \(0.232356\pi\)
\(368\) 0 0
\(369\) 45.4647 2.36680
\(370\) 0 0
\(371\) 6.95251 0.360956
\(372\) 0 0
\(373\) −6.44808 −0.333869 −0.166935 0.985968i \(-0.553387\pi\)
−0.166935 + 0.985968i \(0.553387\pi\)
\(374\) 0 0
\(375\) −34.9925 −1.80701
\(376\) 0 0
\(377\) 6.38990 0.329097
\(378\) 0 0
\(379\) 21.2657 1.09235 0.546174 0.837672i \(-0.316084\pi\)
0.546174 + 0.837672i \(0.316084\pi\)
\(380\) 0 0
\(381\) 55.2805 2.83211
\(382\) 0 0
\(383\) 3.26860 0.167018 0.0835088 0.996507i \(-0.473387\pi\)
0.0835088 + 0.996507i \(0.473387\pi\)
\(384\) 0 0
\(385\) −31.2632 −1.59332
\(386\) 0 0
\(387\) 4.03389 0.205054
\(388\) 0 0
\(389\) 28.4979 1.44490 0.722451 0.691422i \(-0.243015\pi\)
0.722451 + 0.691422i \(0.243015\pi\)
\(390\) 0 0
\(391\) −4.47945 −0.226536
\(392\) 0 0
\(393\) 1.37276 0.0692464
\(394\) 0 0
\(395\) 0.857008 0.0431207
\(396\) 0 0
\(397\) −2.05913 −0.103345 −0.0516724 0.998664i \(-0.516455\pi\)
−0.0516724 + 0.998664i \(0.516455\pi\)
\(398\) 0 0
\(399\) −104.400 −5.22653
\(400\) 0 0
\(401\) −7.52117 −0.375589 −0.187795 0.982208i \(-0.560134\pi\)
−0.187795 + 0.982208i \(0.560134\pi\)
\(402\) 0 0
\(403\) −26.6810 −1.32907
\(404\) 0 0
\(405\) −6.15739 −0.305963
\(406\) 0 0
\(407\) −36.8878 −1.82846
\(408\) 0 0
\(409\) 0.412793 0.0204113 0.0102056 0.999948i \(-0.496751\pi\)
0.0102056 + 0.999948i \(0.496751\pi\)
\(410\) 0 0
\(411\) 15.2616 0.752798
\(412\) 0 0
\(413\) 4.47538 0.220219
\(414\) 0 0
\(415\) 1.13233 0.0555840
\(416\) 0 0
\(417\) 5.29102 0.259102
\(418\) 0 0
\(419\) 2.68136 0.130993 0.0654966 0.997853i \(-0.479137\pi\)
0.0654966 + 0.997853i \(0.479137\pi\)
\(420\) 0 0
\(421\) −5.87045 −0.286108 −0.143054 0.989715i \(-0.545692\pi\)
−0.143054 + 0.989715i \(0.545692\pi\)
\(422\) 0 0
\(423\) −22.7142 −1.10440
\(424\) 0 0
\(425\) 2.05100 0.0994879
\(426\) 0 0
\(427\) 40.1384 1.94243
\(428\) 0 0
\(429\) −55.6811 −2.68831
\(430\) 0 0
\(431\) 6.35986 0.306344 0.153172 0.988200i \(-0.451051\pi\)
0.153172 + 0.988200i \(0.451051\pi\)
\(432\) 0 0
\(433\) −36.1286 −1.73623 −0.868115 0.496364i \(-0.834668\pi\)
−0.868115 + 0.496364i \(0.834668\pi\)
\(434\) 0 0
\(435\) −6.69521 −0.321011
\(436\) 0 0
\(437\) −36.1582 −1.72968
\(438\) 0 0
\(439\) −19.2290 −0.917751 −0.458876 0.888501i \(-0.651748\pi\)
−0.458876 + 0.888501i \(0.651748\pi\)
\(440\) 0 0
\(441\) 69.7274 3.32035
\(442\) 0 0
\(443\) 40.3422 1.91671 0.958357 0.285574i \(-0.0921841\pi\)
0.958357 + 0.285574i \(0.0921841\pi\)
\(444\) 0 0
\(445\) 8.07143 0.382623
\(446\) 0 0
\(447\) −25.3436 −1.19871
\(448\) 0 0
\(449\) −38.1638 −1.80106 −0.900531 0.434791i \(-0.856822\pi\)
−0.900531 + 0.434791i \(0.856822\pi\)
\(450\) 0 0
\(451\) −34.5580 −1.62727
\(452\) 0 0
\(453\) −40.9788 −1.92535
\(454\) 0 0
\(455\) −36.4018 −1.70654
\(456\) 0 0
\(457\) −27.8331 −1.30198 −0.650989 0.759087i \(-0.725646\pi\)
−0.650989 + 0.759087i \(0.725646\pi\)
\(458\) 0 0
\(459\) 6.79624 0.317221
\(460\) 0 0
\(461\) −18.5222 −0.862665 −0.431332 0.902193i \(-0.641956\pi\)
−0.431332 + 0.902193i \(0.641956\pi\)
\(462\) 0 0
\(463\) −9.69466 −0.450549 −0.225275 0.974295i \(-0.572328\pi\)
−0.225275 + 0.974295i \(0.572328\pi\)
\(464\) 0 0
\(465\) 27.9558 1.29642
\(466\) 0 0
\(467\) 18.8171 0.870754 0.435377 0.900248i \(-0.356615\pi\)
0.435377 + 0.900248i \(0.356615\pi\)
\(468\) 0 0
\(469\) −10.7650 −0.497084
\(470\) 0 0
\(471\) −5.27070 −0.242861
\(472\) 0 0
\(473\) −3.06618 −0.140983
\(474\) 0 0
\(475\) 16.5557 0.759627
\(476\) 0 0
\(477\) −8.31387 −0.380666
\(478\) 0 0
\(479\) 24.6563 1.12657 0.563287 0.826261i \(-0.309536\pi\)
0.563287 + 0.826261i \(0.309536\pi\)
\(480\) 0 0
\(481\) −42.9509 −1.95839
\(482\) 0 0
\(483\) 57.9351 2.63614
\(484\) 0 0
\(485\) −22.4389 −1.01890
\(486\) 0 0
\(487\) 42.3588 1.91946 0.959729 0.280927i \(-0.0906418\pi\)
0.959729 + 0.280927i \(0.0906418\pi\)
\(488\) 0 0
\(489\) −31.5509 −1.42678
\(490\) 0 0
\(491\) 7.39626 0.333789 0.166894 0.985975i \(-0.446626\pi\)
0.166894 + 0.985975i \(0.446626\pi\)
\(492\) 0 0
\(493\) 1.34908 0.0607597
\(494\) 0 0
\(495\) 37.3848 1.68032
\(496\) 0 0
\(497\) 53.4052 2.39555
\(498\) 0 0
\(499\) 16.2424 0.727111 0.363555 0.931573i \(-0.381563\pi\)
0.363555 + 0.931573i \(0.381563\pi\)
\(500\) 0 0
\(501\) −12.4400 −0.555778
\(502\) 0 0
\(503\) −28.3872 −1.26572 −0.632862 0.774265i \(-0.718120\pi\)
−0.632862 + 0.774265i \(0.718120\pi\)
\(504\) 0 0
\(505\) −5.66772 −0.252210
\(506\) 0 0
\(507\) −27.2641 −1.21084
\(508\) 0 0
\(509\) 19.1909 0.850621 0.425311 0.905047i \(-0.360165\pi\)
0.425311 + 0.905047i \(0.360165\pi\)
\(510\) 0 0
\(511\) −31.3195 −1.38549
\(512\) 0 0
\(513\) 54.8594 2.42210
\(514\) 0 0
\(515\) −16.8331 −0.741753
\(516\) 0 0
\(517\) 17.2652 0.759322
\(518\) 0 0
\(519\) 56.0384 2.45981
\(520\) 0 0
\(521\) 23.9137 1.04768 0.523840 0.851817i \(-0.324499\pi\)
0.523840 + 0.851817i \(0.324499\pi\)
\(522\) 0 0
\(523\) 30.2824 1.32416 0.662078 0.749435i \(-0.269675\pi\)
0.662078 + 0.749435i \(0.269675\pi\)
\(524\) 0 0
\(525\) −26.5266 −1.15772
\(526\) 0 0
\(527\) −5.63309 −0.245381
\(528\) 0 0
\(529\) −2.93452 −0.127588
\(530\) 0 0
\(531\) −5.35170 −0.232244
\(532\) 0 0
\(533\) −40.2382 −1.74291
\(534\) 0 0
\(535\) 13.3602 0.577613
\(536\) 0 0
\(537\) −5.70376 −0.246135
\(538\) 0 0
\(539\) −53.0002 −2.28288
\(540\) 0 0
\(541\) −38.2312 −1.64369 −0.821844 0.569713i \(-0.807055\pi\)
−0.821844 + 0.569713i \(0.807055\pi\)
\(542\) 0 0
\(543\) −29.3340 −1.25884
\(544\) 0 0
\(545\) 7.86684 0.336978
\(546\) 0 0
\(547\) 19.9692 0.853820 0.426910 0.904294i \(-0.359602\pi\)
0.426910 + 0.904294i \(0.359602\pi\)
\(548\) 0 0
\(549\) −47.9978 −2.04850
\(550\) 0 0
\(551\) 10.8898 0.463922
\(552\) 0 0
\(553\) 2.23345 0.0949761
\(554\) 0 0
\(555\) 45.0031 1.91027
\(556\) 0 0
\(557\) 31.7958 1.34723 0.673616 0.739081i \(-0.264740\pi\)
0.673616 + 0.739081i \(0.264740\pi\)
\(558\) 0 0
\(559\) −3.57016 −0.151002
\(560\) 0 0
\(561\) −11.7558 −0.496331
\(562\) 0 0
\(563\) −33.0314 −1.39211 −0.696053 0.717990i \(-0.745062\pi\)
−0.696053 + 0.717990i \(0.745062\pi\)
\(564\) 0 0
\(565\) −28.7937 −1.21136
\(566\) 0 0
\(567\) −16.0468 −0.673903
\(568\) 0 0
\(569\) 6.22713 0.261055 0.130527 0.991445i \(-0.458333\pi\)
0.130527 + 0.991445i \(0.458333\pi\)
\(570\) 0 0
\(571\) 24.0822 1.00781 0.503905 0.863759i \(-0.331896\pi\)
0.503905 + 0.863759i \(0.331896\pi\)
\(572\) 0 0
\(573\) 25.0382 1.04599
\(574\) 0 0
\(575\) −9.18733 −0.383138
\(576\) 0 0
\(577\) 37.2371 1.55020 0.775100 0.631838i \(-0.217699\pi\)
0.775100 + 0.631838i \(0.217699\pi\)
\(578\) 0 0
\(579\) −54.3967 −2.26065
\(580\) 0 0
\(581\) 2.95098 0.122427
\(582\) 0 0
\(583\) 6.31942 0.261724
\(584\) 0 0
\(585\) 43.5296 1.79973
\(586\) 0 0
\(587\) 5.29699 0.218630 0.109315 0.994007i \(-0.465134\pi\)
0.109315 + 0.994007i \(0.465134\pi\)
\(588\) 0 0
\(589\) −45.4704 −1.87357
\(590\) 0 0
\(591\) −41.3900 −1.70256
\(592\) 0 0
\(593\) −23.7883 −0.976869 −0.488435 0.872601i \(-0.662432\pi\)
−0.488435 + 0.872601i \(0.662432\pi\)
\(594\) 0 0
\(595\) −7.68542 −0.315072
\(596\) 0 0
\(597\) −2.29248 −0.0938251
\(598\) 0 0
\(599\) 17.4922 0.714712 0.357356 0.933968i \(-0.383678\pi\)
0.357356 + 0.933968i \(0.383678\pi\)
\(600\) 0 0
\(601\) 2.56533 0.104642 0.0523210 0.998630i \(-0.483338\pi\)
0.0523210 + 0.998630i \(0.483338\pi\)
\(602\) 0 0
\(603\) 12.8729 0.524226
\(604\) 0 0
\(605\) −9.52645 −0.387305
\(606\) 0 0
\(607\) −25.6850 −1.04252 −0.521261 0.853398i \(-0.674538\pi\)
−0.521261 + 0.853398i \(0.674538\pi\)
\(608\) 0 0
\(609\) −17.4484 −0.707046
\(610\) 0 0
\(611\) 20.1030 0.813280
\(612\) 0 0
\(613\) −43.0772 −1.73987 −0.869935 0.493166i \(-0.835839\pi\)
−0.869935 + 0.493166i \(0.835839\pi\)
\(614\) 0 0
\(615\) 42.1607 1.70008
\(616\) 0 0
\(617\) 38.7902 1.56164 0.780818 0.624758i \(-0.214803\pi\)
0.780818 + 0.624758i \(0.214803\pi\)
\(618\) 0 0
\(619\) −31.9438 −1.28393 −0.641965 0.766734i \(-0.721881\pi\)
−0.641965 + 0.766734i \(0.721881\pi\)
\(620\) 0 0
\(621\) −30.4434 −1.22165
\(622\) 0 0
\(623\) 21.0350 0.842750
\(624\) 0 0
\(625\) −10.5384 −0.421537
\(626\) 0 0
\(627\) −94.8932 −3.78967
\(628\) 0 0
\(629\) −9.06811 −0.361569
\(630\) 0 0
\(631\) 39.2873 1.56400 0.782002 0.623276i \(-0.214199\pi\)
0.782002 + 0.623276i \(0.214199\pi\)
\(632\) 0 0
\(633\) −16.1092 −0.640284
\(634\) 0 0
\(635\) 32.8490 1.30357
\(636\) 0 0
\(637\) −61.7116 −2.44510
\(638\) 0 0
\(639\) −63.8624 −2.52636
\(640\) 0 0
\(641\) 44.5326 1.75893 0.879467 0.475960i \(-0.157899\pi\)
0.879467 + 0.475960i \(0.157899\pi\)
\(642\) 0 0
\(643\) −44.7336 −1.76412 −0.882061 0.471136i \(-0.843844\pi\)
−0.882061 + 0.471136i \(0.843844\pi\)
\(644\) 0 0
\(645\) 3.74074 0.147291
\(646\) 0 0
\(647\) 14.6161 0.574619 0.287310 0.957838i \(-0.407239\pi\)
0.287310 + 0.957838i \(0.407239\pi\)
\(648\) 0 0
\(649\) 4.06786 0.159677
\(650\) 0 0
\(651\) 72.8557 2.85544
\(652\) 0 0
\(653\) 30.9412 1.21082 0.605412 0.795913i \(-0.293009\pi\)
0.605412 + 0.795913i \(0.293009\pi\)
\(654\) 0 0
\(655\) 0.815725 0.0318730
\(656\) 0 0
\(657\) 37.4521 1.46115
\(658\) 0 0
\(659\) −10.2649 −0.399862 −0.199931 0.979810i \(-0.564072\pi\)
−0.199931 + 0.979810i \(0.564072\pi\)
\(660\) 0 0
\(661\) −5.59649 −0.217678 −0.108839 0.994059i \(-0.534713\pi\)
−0.108839 + 0.994059i \(0.534713\pi\)
\(662\) 0 0
\(663\) −13.6881 −0.531601
\(664\) 0 0
\(665\) −62.0369 −2.40569
\(666\) 0 0
\(667\) −6.04316 −0.233992
\(668\) 0 0
\(669\) −45.2160 −1.74815
\(670\) 0 0
\(671\) 36.4834 1.40843
\(672\) 0 0
\(673\) 8.81939 0.339962 0.169981 0.985447i \(-0.445629\pi\)
0.169981 + 0.985447i \(0.445629\pi\)
\(674\) 0 0
\(675\) 13.9391 0.536515
\(676\) 0 0
\(677\) 1.11855 0.0429893 0.0214947 0.999769i \(-0.493158\pi\)
0.0214947 + 0.999769i \(0.493158\pi\)
\(678\) 0 0
\(679\) −58.4781 −2.24418
\(680\) 0 0
\(681\) 10.2393 0.392371
\(682\) 0 0
\(683\) 47.8278 1.83008 0.915041 0.403361i \(-0.132158\pi\)
0.915041 + 0.403361i \(0.132158\pi\)
\(684\) 0 0
\(685\) 9.06879 0.346501
\(686\) 0 0
\(687\) −49.7196 −1.89692
\(688\) 0 0
\(689\) 7.35812 0.280322
\(690\) 0 0
\(691\) −16.4334 −0.625158 −0.312579 0.949892i \(-0.601193\pi\)
−0.312579 + 0.949892i \(0.601193\pi\)
\(692\) 0 0
\(693\) 97.4287 3.70101
\(694\) 0 0
\(695\) 3.14405 0.119261
\(696\) 0 0
\(697\) −8.49539 −0.321786
\(698\) 0 0
\(699\) −52.2889 −1.97775
\(700\) 0 0
\(701\) 2.88149 0.108832 0.0544162 0.998518i \(-0.482670\pi\)
0.0544162 + 0.998518i \(0.482670\pi\)
\(702\) 0 0
\(703\) −73.1980 −2.76071
\(704\) 0 0
\(705\) −21.0635 −0.793297
\(706\) 0 0
\(707\) −14.7707 −0.555508
\(708\) 0 0
\(709\) −21.2223 −0.797020 −0.398510 0.917164i \(-0.630473\pi\)
−0.398510 + 0.917164i \(0.630473\pi\)
\(710\) 0 0
\(711\) −2.67078 −0.100162
\(712\) 0 0
\(713\) 25.2331 0.944988
\(714\) 0 0
\(715\) −33.0871 −1.23739
\(716\) 0 0
\(717\) −23.1173 −0.863331
\(718\) 0 0
\(719\) −29.1647 −1.08766 −0.543830 0.839195i \(-0.683027\pi\)
−0.543830 + 0.839195i \(0.683027\pi\)
\(720\) 0 0
\(721\) −43.8687 −1.63376
\(722\) 0 0
\(723\) 89.4328 3.32604
\(724\) 0 0
\(725\) 2.76697 0.102763
\(726\) 0 0
\(727\) −30.7973 −1.14221 −0.571104 0.820877i \(-0.693485\pi\)
−0.571104 + 0.820877i \(0.693485\pi\)
\(728\) 0 0
\(729\) −39.7331 −1.47160
\(730\) 0 0
\(731\) −0.753759 −0.0278788
\(732\) 0 0
\(733\) 8.40796 0.310555 0.155277 0.987871i \(-0.450373\pi\)
0.155277 + 0.987871i \(0.450373\pi\)
\(734\) 0 0
\(735\) 64.6602 2.38503
\(736\) 0 0
\(737\) −9.78479 −0.360427
\(738\) 0 0
\(739\) 25.7995 0.949049 0.474524 0.880242i \(-0.342620\pi\)
0.474524 + 0.880242i \(0.342620\pi\)
\(740\) 0 0
\(741\) −110.490 −4.05897
\(742\) 0 0
\(743\) 22.8708 0.839047 0.419524 0.907744i \(-0.362197\pi\)
0.419524 + 0.907744i \(0.362197\pi\)
\(744\) 0 0
\(745\) −15.0598 −0.551747
\(746\) 0 0
\(747\) −3.52881 −0.129112
\(748\) 0 0
\(749\) 34.8182 1.27223
\(750\) 0 0
\(751\) 45.5859 1.66345 0.831727 0.555185i \(-0.187353\pi\)
0.831727 + 0.555185i \(0.187353\pi\)
\(752\) 0 0
\(753\) 13.1397 0.478836
\(754\) 0 0
\(755\) −24.3506 −0.886210
\(756\) 0 0
\(757\) 6.92439 0.251671 0.125836 0.992051i \(-0.459839\pi\)
0.125836 + 0.992051i \(0.459839\pi\)
\(758\) 0 0
\(759\) 52.6596 1.91142
\(760\) 0 0
\(761\) 44.3616 1.60811 0.804053 0.594557i \(-0.202673\pi\)
0.804053 + 0.594557i \(0.202673\pi\)
\(762\) 0 0
\(763\) 20.5018 0.742216
\(764\) 0 0
\(765\) 9.19029 0.332276
\(766\) 0 0
\(767\) 4.73647 0.171024
\(768\) 0 0
\(769\) 37.1631 1.34014 0.670069 0.742299i \(-0.266265\pi\)
0.670069 + 0.742299i \(0.266265\pi\)
\(770\) 0 0
\(771\) −13.7805 −0.496291
\(772\) 0 0
\(773\) 14.2175 0.511368 0.255684 0.966760i \(-0.417699\pi\)
0.255684 + 0.966760i \(0.417699\pi\)
\(774\) 0 0
\(775\) −11.5534 −0.415012
\(776\) 0 0
\(777\) 117.283 4.20750
\(778\) 0 0
\(779\) −68.5749 −2.45695
\(780\) 0 0
\(781\) 48.5422 1.73698
\(782\) 0 0
\(783\) 9.16870 0.327663
\(784\) 0 0
\(785\) −3.13198 −0.111785
\(786\) 0 0
\(787\) 34.6933 1.23668 0.618342 0.785909i \(-0.287805\pi\)
0.618342 + 0.785909i \(0.287805\pi\)
\(788\) 0 0
\(789\) −61.6449 −2.19462
\(790\) 0 0
\(791\) −75.0396 −2.66810
\(792\) 0 0
\(793\) 42.4800 1.50851
\(794\) 0 0
\(795\) −7.70969 −0.273434
\(796\) 0 0
\(797\) −21.3133 −0.754956 −0.377478 0.926019i \(-0.623209\pi\)
−0.377478 + 0.926019i \(0.623209\pi\)
\(798\) 0 0
\(799\) 4.24429 0.150152
\(800\) 0 0
\(801\) −25.1538 −0.888768
\(802\) 0 0
\(803\) −28.4676 −1.00460
\(804\) 0 0
\(805\) 34.4265 1.21337
\(806\) 0 0
\(807\) 1.88448 0.0663370
\(808\) 0 0
\(809\) −26.0844 −0.917078 −0.458539 0.888674i \(-0.651627\pi\)
−0.458539 + 0.888674i \(0.651627\pi\)
\(810\) 0 0
\(811\) −0.830328 −0.0291568 −0.0145784 0.999894i \(-0.504641\pi\)
−0.0145784 + 0.999894i \(0.504641\pi\)
\(812\) 0 0
\(813\) 93.3510 3.27396
\(814\) 0 0
\(815\) −18.7483 −0.656725
\(816\) 0 0
\(817\) −6.08435 −0.212865
\(818\) 0 0
\(819\) 113.443 3.96401
\(820\) 0 0
\(821\) −20.1747 −0.704103 −0.352052 0.935981i \(-0.614516\pi\)
−0.352052 + 0.935981i \(0.614516\pi\)
\(822\) 0 0
\(823\) 8.83226 0.307873 0.153937 0.988081i \(-0.450805\pi\)
0.153937 + 0.988081i \(0.450805\pi\)
\(824\) 0 0
\(825\) −24.1111 −0.839442
\(826\) 0 0
\(827\) −20.8546 −0.725186 −0.362593 0.931948i \(-0.618108\pi\)
−0.362593 + 0.931948i \(0.618108\pi\)
\(828\) 0 0
\(829\) −51.3201 −1.78242 −0.891210 0.453591i \(-0.850143\pi\)
−0.891210 + 0.453591i \(0.850143\pi\)
\(830\) 0 0
\(831\) −41.4608 −1.43826
\(832\) 0 0
\(833\) −13.0290 −0.451429
\(834\) 0 0
\(835\) −7.39214 −0.255816
\(836\) 0 0
\(837\) −38.2838 −1.32328
\(838\) 0 0
\(839\) 43.7431 1.51018 0.755089 0.655622i \(-0.227594\pi\)
0.755089 + 0.655622i \(0.227594\pi\)
\(840\) 0 0
\(841\) −27.1800 −0.937240
\(842\) 0 0
\(843\) 89.6196 3.08666
\(844\) 0 0
\(845\) −16.2010 −0.557330
\(846\) 0 0
\(847\) −24.8269 −0.853064
\(848\) 0 0
\(849\) −18.9399 −0.650014
\(850\) 0 0
\(851\) 40.6202 1.39244
\(852\) 0 0
\(853\) −8.69461 −0.297698 −0.148849 0.988860i \(-0.547557\pi\)
−0.148849 + 0.988860i \(0.547557\pi\)
\(854\) 0 0
\(855\) 74.1842 2.53705
\(856\) 0 0
\(857\) 6.50397 0.222171 0.111086 0.993811i \(-0.464567\pi\)
0.111086 + 0.993811i \(0.464567\pi\)
\(858\) 0 0
\(859\) −36.7116 −1.25258 −0.626292 0.779589i \(-0.715428\pi\)
−0.626292 + 0.779589i \(0.715428\pi\)
\(860\) 0 0
\(861\) 109.875 3.74454
\(862\) 0 0
\(863\) 38.9338 1.32532 0.662661 0.748920i \(-0.269427\pi\)
0.662661 + 0.748920i \(0.269427\pi\)
\(864\) 0 0
\(865\) 33.2994 1.13221
\(866\) 0 0
\(867\) −2.88993 −0.0981472
\(868\) 0 0
\(869\) 2.03008 0.0688656
\(870\) 0 0
\(871\) −11.3931 −0.386040
\(872\) 0 0
\(873\) 69.9286 2.36673
\(874\) 0 0
\(875\) −54.1899 −1.83195
\(876\) 0 0
\(877\) 37.9779 1.28242 0.641211 0.767365i \(-0.278432\pi\)
0.641211 + 0.767365i \(0.278432\pi\)
\(878\) 0 0
\(879\) 67.0096 2.26018
\(880\) 0 0
\(881\) 7.62281 0.256819 0.128409 0.991721i \(-0.459013\pi\)
0.128409 + 0.991721i \(0.459013\pi\)
\(882\) 0 0
\(883\) −23.8355 −0.802130 −0.401065 0.916050i \(-0.631360\pi\)
−0.401065 + 0.916050i \(0.631360\pi\)
\(884\) 0 0
\(885\) −4.96278 −0.166822
\(886\) 0 0
\(887\) 18.3128 0.614885 0.307442 0.951567i \(-0.400527\pi\)
0.307442 + 0.951567i \(0.400527\pi\)
\(888\) 0 0
\(889\) 85.6081 2.87120
\(890\) 0 0
\(891\) −14.5856 −0.488636
\(892\) 0 0
\(893\) 34.2600 1.14647
\(894\) 0 0
\(895\) −3.38931 −0.113292
\(896\) 0 0
\(897\) 61.3151 2.04725
\(898\) 0 0
\(899\) −7.59951 −0.253458
\(900\) 0 0
\(901\) 1.55350 0.0517546
\(902\) 0 0
\(903\) 9.74876 0.324419
\(904\) 0 0
\(905\) −17.4310 −0.579425
\(906\) 0 0
\(907\) 6.30660 0.209407 0.104704 0.994503i \(-0.466611\pi\)
0.104704 + 0.994503i \(0.466611\pi\)
\(908\) 0 0
\(909\) 17.6629 0.585841
\(910\) 0 0
\(911\) 14.9693 0.495955 0.247977 0.968766i \(-0.420234\pi\)
0.247977 + 0.968766i \(0.420234\pi\)
\(912\) 0 0
\(913\) 2.68226 0.0887700
\(914\) 0 0
\(915\) −44.5097 −1.47145
\(916\) 0 0
\(917\) 2.12587 0.0702023
\(918\) 0 0
\(919\) −33.7560 −1.11351 −0.556754 0.830678i \(-0.687953\pi\)
−0.556754 + 0.830678i \(0.687953\pi\)
\(920\) 0 0
\(921\) 66.0605 2.17677
\(922\) 0 0
\(923\) 56.5208 1.86041
\(924\) 0 0
\(925\) −18.5987 −0.611520
\(926\) 0 0
\(927\) 52.4586 1.72297
\(928\) 0 0
\(929\) −31.4366 −1.03140 −0.515701 0.856769i \(-0.672468\pi\)
−0.515701 + 0.856769i \(0.672468\pi\)
\(930\) 0 0
\(931\) −105.171 −3.44683
\(932\) 0 0
\(933\) 98.3109 3.21855
\(934\) 0 0
\(935\) −6.98559 −0.228453
\(936\) 0 0
\(937\) 28.8399 0.942159 0.471079 0.882091i \(-0.343865\pi\)
0.471079 + 0.882091i \(0.343865\pi\)
\(938\) 0 0
\(939\) 83.9738 2.74038
\(940\) 0 0
\(941\) 54.4887 1.77628 0.888141 0.459571i \(-0.151997\pi\)
0.888141 + 0.459571i \(0.151997\pi\)
\(942\) 0 0
\(943\) 38.0547 1.23923
\(944\) 0 0
\(945\) −52.2320 −1.69911
\(946\) 0 0
\(947\) 28.4472 0.924408 0.462204 0.886774i \(-0.347059\pi\)
0.462204 + 0.886774i \(0.347059\pi\)
\(948\) 0 0
\(949\) −33.1467 −1.07599
\(950\) 0 0
\(951\) −3.85785 −0.125099
\(952\) 0 0
\(953\) 44.2333 1.43286 0.716429 0.697660i \(-0.245775\pi\)
0.716429 + 0.697660i \(0.245775\pi\)
\(954\) 0 0
\(955\) 14.8783 0.481450
\(956\) 0 0
\(957\) −15.8596 −0.512668
\(958\) 0 0
\(959\) 23.6342 0.763190
\(960\) 0 0
\(961\) 0.731652 0.0236017
\(962\) 0 0
\(963\) −41.6359 −1.34170
\(964\) 0 0
\(965\) −32.3238 −1.04054
\(966\) 0 0
\(967\) −30.3358 −0.975534 −0.487767 0.872974i \(-0.662189\pi\)
−0.487767 + 0.872974i \(0.662189\pi\)
\(968\) 0 0
\(969\) −23.3276 −0.749390
\(970\) 0 0
\(971\) −28.4789 −0.913930 −0.456965 0.889485i \(-0.651064\pi\)
−0.456965 + 0.889485i \(0.651064\pi\)
\(972\) 0 0
\(973\) 8.19374 0.262679
\(974\) 0 0
\(975\) −28.0742 −0.899093
\(976\) 0 0
\(977\) −20.4121 −0.653040 −0.326520 0.945190i \(-0.605876\pi\)
−0.326520 + 0.945190i \(0.605876\pi\)
\(978\) 0 0
\(979\) 19.1196 0.611065
\(980\) 0 0
\(981\) −24.5162 −0.782744
\(982\) 0 0
\(983\) 5.90253 0.188262 0.0941308 0.995560i \(-0.469993\pi\)
0.0941308 + 0.995560i \(0.469993\pi\)
\(984\) 0 0
\(985\) −24.5949 −0.783660
\(986\) 0 0
\(987\) −54.8937 −1.74729
\(988\) 0 0
\(989\) 3.37642 0.107364
\(990\) 0 0
\(991\) −31.7212 −1.00766 −0.503828 0.863804i \(-0.668075\pi\)
−0.503828 + 0.863804i \(0.668075\pi\)
\(992\) 0 0
\(993\) −13.1815 −0.418302
\(994\) 0 0
\(995\) −1.36225 −0.0431862
\(996\) 0 0
\(997\) 25.2297 0.799032 0.399516 0.916726i \(-0.369178\pi\)
0.399516 + 0.916726i \(0.369178\pi\)
\(998\) 0 0
\(999\) −61.6291 −1.94986
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 \(a_p\))