Properties

Label 6040.2.a.p.1.1
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 1.1
Root \(3.33655\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-3.33655 q^{3}\) \(+1.00000 q^{5}\) \(+2.35293 q^{7}\) \(+8.13258 q^{9}\) \(+O(q^{10})\) \(q\)\(-3.33655 q^{3}\) \(+1.00000 q^{5}\) \(+2.35293 q^{7}\) \(+8.13258 q^{9}\) \(-5.41372 q^{11}\) \(+7.10664 q^{13}\) \(-3.33655 q^{15}\) \(-2.30666 q^{17}\) \(+3.33812 q^{19}\) \(-7.85068 q^{21}\) \(-2.59719 q^{23}\) \(+1.00000 q^{25}\) \(-17.1251 q^{27}\) \(-1.45979 q^{29}\) \(+2.14434 q^{31}\) \(+18.0631 q^{33}\) \(+2.35293 q^{35}\) \(-8.97284 q^{37}\) \(-23.7117 q^{39}\) \(+0.901406 q^{41}\) \(-1.97754 q^{43}\) \(+8.13258 q^{45}\) \(-11.7551 q^{47}\) \(-1.46372 q^{49}\) \(+7.69628 q^{51}\) \(+10.0416 q^{53}\) \(-5.41372 q^{55}\) \(-11.1378 q^{57}\) \(-4.21296 q^{59}\) \(-12.2881 q^{61}\) \(+19.1354 q^{63}\) \(+7.10664 q^{65}\) \(+0.385186 q^{67}\) \(+8.66565 q^{69}\) \(-12.4898 q^{71}\) \(-6.72268 q^{73}\) \(-3.33655 q^{75}\) \(-12.7381 q^{77}\) \(+12.8609 q^{79}\) \(+32.7411 q^{81}\) \(+2.69229 q^{83}\) \(-2.30666 q^{85}\) \(+4.87068 q^{87}\) \(+13.4454 q^{89}\) \(+16.7214 q^{91}\) \(-7.15471 q^{93}\) \(+3.33812 q^{95}\) \(+5.95427 q^{97}\) \(-44.0275 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 18q^{11} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 5q^{15} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 18q^{21} \) \(\mathstrut -\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 19q^{25} \) \(\mathstrut -\mathstrut 35q^{27} \) \(\mathstrut -\mathstrut 35q^{29} \) \(\mathstrut -\mathstrut 26q^{31} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 21q^{43} \) \(\mathstrut +\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 40q^{47} \) \(\mathstrut +\mathstrut 23q^{49} \) \(\mathstrut -\mathstrut 32q^{51} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 18q^{55} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut -\mathstrut 53q^{63} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut -\mathstrut 42q^{67} \) \(\mathstrut -\mathstrut 31q^{69} \) \(\mathstrut -\mathstrut 46q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut -\mathstrut 7q^{89} \) \(\mathstrut -\mathstrut 61q^{91} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut -\mathstrut 27q^{95} \) \(\mathstrut +\mathstrut 39q^{97} \) \(\mathstrut -\mathstrut 52q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −3.33655 −1.92636 −0.963180 0.268858i \(-0.913354\pi\)
−0.963180 + 0.268858i \(0.913354\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 2.35293 0.889324 0.444662 0.895698i \(-0.353324\pi\)
0.444662 + 0.895698i \(0.353324\pi\)
\(8\) 0 0
\(9\) 8.13258 2.71086
\(10\) 0 0
\(11\) −5.41372 −1.63230 −0.816148 0.577842i \(-0.803895\pi\)
−0.816148 + 0.577842i \(0.803895\pi\)
\(12\) 0 0
\(13\) 7.10664 1.97103 0.985513 0.169599i \(-0.0542472\pi\)
0.985513 + 0.169599i \(0.0542472\pi\)
\(14\) 0 0
\(15\) −3.33655 −0.861494
\(16\) 0 0
\(17\) −2.30666 −0.559446 −0.279723 0.960081i \(-0.590243\pi\)
−0.279723 + 0.960081i \(0.590243\pi\)
\(18\) 0 0
\(19\) 3.33812 0.765818 0.382909 0.923786i \(-0.374922\pi\)
0.382909 + 0.923786i \(0.374922\pi\)
\(20\) 0 0
\(21\) −7.85068 −1.71316
\(22\) 0 0
\(23\) −2.59719 −0.541551 −0.270775 0.962643i \(-0.587280\pi\)
−0.270775 + 0.962643i \(0.587280\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −17.1251 −3.29573
\(28\) 0 0
\(29\) −1.45979 −0.271077 −0.135538 0.990772i \(-0.543276\pi\)
−0.135538 + 0.990772i \(0.543276\pi\)
\(30\) 0 0
\(31\) 2.14434 0.385135 0.192568 0.981284i \(-0.438319\pi\)
0.192568 + 0.981284i \(0.438319\pi\)
\(32\) 0 0
\(33\) 18.0631 3.14439
\(34\) 0 0
\(35\) 2.35293 0.397718
\(36\) 0 0
\(37\) −8.97284 −1.47513 −0.737563 0.675278i \(-0.764024\pi\)
−0.737563 + 0.675278i \(0.764024\pi\)
\(38\) 0 0
\(39\) −23.7117 −3.79691
\(40\) 0 0
\(41\) 0.901406 0.140776 0.0703880 0.997520i \(-0.477576\pi\)
0.0703880 + 0.997520i \(0.477576\pi\)
\(42\) 0 0
\(43\) −1.97754 −0.301572 −0.150786 0.988566i \(-0.548181\pi\)
−0.150786 + 0.988566i \(0.548181\pi\)
\(44\) 0 0
\(45\) 8.13258 1.21233
\(46\) 0 0
\(47\) −11.7551 −1.71466 −0.857332 0.514764i \(-0.827880\pi\)
−0.857332 + 0.514764i \(0.827880\pi\)
\(48\) 0 0
\(49\) −1.46372 −0.209103
\(50\) 0 0
\(51\) 7.69628 1.07769
\(52\) 0 0
\(53\) 10.0416 1.37932 0.689658 0.724135i \(-0.257761\pi\)
0.689658 + 0.724135i \(0.257761\pi\)
\(54\) 0 0
\(55\) −5.41372 −0.729985
\(56\) 0 0
\(57\) −11.1378 −1.47524
\(58\) 0 0
\(59\) −4.21296 −0.548480 −0.274240 0.961661i \(-0.588426\pi\)
−0.274240 + 0.961661i \(0.588426\pi\)
\(60\) 0 0
\(61\) −12.2881 −1.57333 −0.786664 0.617382i \(-0.788193\pi\)
−0.786664 + 0.617382i \(0.788193\pi\)
\(62\) 0 0
\(63\) 19.1354 2.41083
\(64\) 0 0
\(65\) 7.10664 0.881470
\(66\) 0 0
\(67\) 0.385186 0.0470579 0.0235290 0.999723i \(-0.492510\pi\)
0.0235290 + 0.999723i \(0.492510\pi\)
\(68\) 0 0
\(69\) 8.66565 1.04322
\(70\) 0 0
\(71\) −12.4898 −1.48226 −0.741131 0.671361i \(-0.765710\pi\)
−0.741131 + 0.671361i \(0.765710\pi\)
\(72\) 0 0
\(73\) −6.72268 −0.786830 −0.393415 0.919361i \(-0.628707\pi\)
−0.393415 + 0.919361i \(0.628707\pi\)
\(74\) 0 0
\(75\) −3.33655 −0.385272
\(76\) 0 0
\(77\) −12.7381 −1.45164
\(78\) 0 0
\(79\) 12.8609 1.44697 0.723484 0.690341i \(-0.242540\pi\)
0.723484 + 0.690341i \(0.242540\pi\)
\(80\) 0 0
\(81\) 32.7411 3.63790
\(82\) 0 0
\(83\) 2.69229 0.295517 0.147759 0.989023i \(-0.452794\pi\)
0.147759 + 0.989023i \(0.452794\pi\)
\(84\) 0 0
\(85\) −2.30666 −0.250192
\(86\) 0 0
\(87\) 4.87068 0.522191
\(88\) 0 0
\(89\) 13.4454 1.42521 0.712604 0.701567i \(-0.247516\pi\)
0.712604 + 0.701567i \(0.247516\pi\)
\(90\) 0 0
\(91\) 16.7214 1.75288
\(92\) 0 0
\(93\) −7.15471 −0.741908
\(94\) 0 0
\(95\) 3.33812 0.342484
\(96\) 0 0
\(97\) 5.95427 0.604564 0.302282 0.953218i \(-0.402251\pi\)
0.302282 + 0.953218i \(0.402251\pi\)
\(98\) 0 0
\(99\) −44.0275 −4.42493
\(100\) 0 0
\(101\) −16.3540 −1.62728 −0.813642 0.581366i \(-0.802519\pi\)
−0.813642 + 0.581366i \(0.802519\pi\)
\(102\) 0 0
\(103\) 2.41825 0.238277 0.119139 0.992878i \(-0.461987\pi\)
0.119139 + 0.992878i \(0.461987\pi\)
\(104\) 0 0
\(105\) −7.85068 −0.766148
\(106\) 0 0
\(107\) 7.76217 0.750397 0.375198 0.926944i \(-0.377575\pi\)
0.375198 + 0.926944i \(0.377575\pi\)
\(108\) 0 0
\(109\) −16.4274 −1.57346 −0.786728 0.617300i \(-0.788226\pi\)
−0.786728 + 0.617300i \(0.788226\pi\)
\(110\) 0 0
\(111\) 29.9384 2.84162
\(112\) 0 0
\(113\) −8.40511 −0.790687 −0.395343 0.918533i \(-0.629374\pi\)
−0.395343 + 0.918533i \(0.629374\pi\)
\(114\) 0 0
\(115\) −2.59719 −0.242189
\(116\) 0 0
\(117\) 57.7953 5.34318
\(118\) 0 0
\(119\) −5.42740 −0.497529
\(120\) 0 0
\(121\) 18.3083 1.66439
\(122\) 0 0
\(123\) −3.00759 −0.271185
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 19.2710 1.71002 0.855010 0.518611i \(-0.173551\pi\)
0.855010 + 0.518611i \(0.173551\pi\)
\(128\) 0 0
\(129\) 6.59818 0.580937
\(130\) 0 0
\(131\) −12.3384 −1.07801 −0.539006 0.842302i \(-0.681200\pi\)
−0.539006 + 0.842302i \(0.681200\pi\)
\(132\) 0 0
\(133\) 7.85437 0.681060
\(134\) 0 0
\(135\) −17.1251 −1.47390
\(136\) 0 0
\(137\) 2.09541 0.179023 0.0895116 0.995986i \(-0.471469\pi\)
0.0895116 + 0.995986i \(0.471469\pi\)
\(138\) 0 0
\(139\) −13.5877 −1.15249 −0.576246 0.817276i \(-0.695483\pi\)
−0.576246 + 0.817276i \(0.695483\pi\)
\(140\) 0 0
\(141\) 39.2217 3.30306
\(142\) 0 0
\(143\) −38.4733 −3.21730
\(144\) 0 0
\(145\) −1.45979 −0.121229
\(146\) 0 0
\(147\) 4.88377 0.402807
\(148\) 0 0
\(149\) 7.63807 0.625735 0.312867 0.949797i \(-0.398710\pi\)
0.312867 + 0.949797i \(0.398710\pi\)
\(150\) 0 0
\(151\) 1.00000 0.0813788
\(152\) 0 0
\(153\) −18.7591 −1.51658
\(154\) 0 0
\(155\) 2.14434 0.172238
\(156\) 0 0
\(157\) −3.64551 −0.290943 −0.145472 0.989362i \(-0.546470\pi\)
−0.145472 + 0.989362i \(0.546470\pi\)
\(158\) 0 0
\(159\) −33.5043 −2.65706
\(160\) 0 0
\(161\) −6.11100 −0.481614
\(162\) 0 0
\(163\) 16.2139 1.26997 0.634984 0.772525i \(-0.281007\pi\)
0.634984 + 0.772525i \(0.281007\pi\)
\(164\) 0 0
\(165\) 18.0631 1.40621
\(166\) 0 0
\(167\) 23.8658 1.84679 0.923396 0.383848i \(-0.125401\pi\)
0.923396 + 0.383848i \(0.125401\pi\)
\(168\) 0 0
\(169\) 37.5043 2.88494
\(170\) 0 0
\(171\) 27.1475 2.07602
\(172\) 0 0
\(173\) −12.4529 −0.946773 −0.473387 0.880855i \(-0.656969\pi\)
−0.473387 + 0.880855i \(0.656969\pi\)
\(174\) 0 0
\(175\) 2.35293 0.177865
\(176\) 0 0
\(177\) 14.0567 1.05657
\(178\) 0 0
\(179\) −11.8873 −0.888498 −0.444249 0.895903i \(-0.646529\pi\)
−0.444249 + 0.895903i \(0.646529\pi\)
\(180\) 0 0
\(181\) −7.53084 −0.559763 −0.279881 0.960035i \(-0.590295\pi\)
−0.279881 + 0.960035i \(0.590295\pi\)
\(182\) 0 0
\(183\) 40.9998 3.03079
\(184\) 0 0
\(185\) −8.97284 −0.659696
\(186\) 0 0
\(187\) 12.4876 0.913183
\(188\) 0 0
\(189\) −40.2942 −2.93097
\(190\) 0 0
\(191\) 4.57380 0.330948 0.165474 0.986214i \(-0.447085\pi\)
0.165474 + 0.986214i \(0.447085\pi\)
\(192\) 0 0
\(193\) 5.68019 0.408869 0.204434 0.978880i \(-0.434464\pi\)
0.204434 + 0.978880i \(0.434464\pi\)
\(194\) 0 0
\(195\) −23.7117 −1.69803
\(196\) 0 0
\(197\) 12.8905 0.918408 0.459204 0.888331i \(-0.348135\pi\)
0.459204 + 0.888331i \(0.348135\pi\)
\(198\) 0 0
\(199\) −13.6389 −0.966834 −0.483417 0.875390i \(-0.660605\pi\)
−0.483417 + 0.875390i \(0.660605\pi\)
\(200\) 0 0
\(201\) −1.28519 −0.0906505
\(202\) 0 0
\(203\) −3.43479 −0.241075
\(204\) 0 0
\(205\) 0.901406 0.0629569
\(206\) 0 0
\(207\) −21.1218 −1.46807
\(208\) 0 0
\(209\) −18.0716 −1.25004
\(210\) 0 0
\(211\) −25.3880 −1.74778 −0.873891 0.486122i \(-0.838411\pi\)
−0.873891 + 0.486122i \(0.838411\pi\)
\(212\) 0 0
\(213\) 41.6727 2.85537
\(214\) 0 0
\(215\) −1.97754 −0.134867
\(216\) 0 0
\(217\) 5.04549 0.342510
\(218\) 0 0
\(219\) 22.4306 1.51572
\(220\) 0 0
\(221\) −16.3926 −1.10268
\(222\) 0 0
\(223\) 22.6645 1.51773 0.758864 0.651249i \(-0.225755\pi\)
0.758864 + 0.651249i \(0.225755\pi\)
\(224\) 0 0
\(225\) 8.13258 0.542172
\(226\) 0 0
\(227\) −20.5011 −1.36071 −0.680353 0.732885i \(-0.738173\pi\)
−0.680353 + 0.732885i \(0.738173\pi\)
\(228\) 0 0
\(229\) −7.31552 −0.483423 −0.241712 0.970348i \(-0.577709\pi\)
−0.241712 + 0.970348i \(0.577709\pi\)
\(230\) 0 0
\(231\) 42.5013 2.79638
\(232\) 0 0
\(233\) −9.36300 −0.613390 −0.306695 0.951808i \(-0.599223\pi\)
−0.306695 + 0.951808i \(0.599223\pi\)
\(234\) 0 0
\(235\) −11.7551 −0.766821
\(236\) 0 0
\(237\) −42.9112 −2.78738
\(238\) 0 0
\(239\) −14.1741 −0.916847 −0.458424 0.888734i \(-0.651586\pi\)
−0.458424 + 0.888734i \(0.651586\pi\)
\(240\) 0 0
\(241\) −7.16536 −0.461561 −0.230781 0.973006i \(-0.574128\pi\)
−0.230781 + 0.973006i \(0.574128\pi\)
\(242\) 0 0
\(243\) −57.8671 −3.71218
\(244\) 0 0
\(245\) −1.46372 −0.0935135
\(246\) 0 0
\(247\) 23.7228 1.50945
\(248\) 0 0
\(249\) −8.98296 −0.569272
\(250\) 0 0
\(251\) −8.50114 −0.536587 −0.268294 0.963337i \(-0.586460\pi\)
−0.268294 + 0.963337i \(0.586460\pi\)
\(252\) 0 0
\(253\) 14.0604 0.883972
\(254\) 0 0
\(255\) 7.69628 0.481960
\(256\) 0 0
\(257\) 8.65320 0.539772 0.269886 0.962892i \(-0.413014\pi\)
0.269886 + 0.962892i \(0.413014\pi\)
\(258\) 0 0
\(259\) −21.1125 −1.31187
\(260\) 0 0
\(261\) −11.8719 −0.734851
\(262\) 0 0
\(263\) −14.4377 −0.890268 −0.445134 0.895464i \(-0.646844\pi\)
−0.445134 + 0.895464i \(0.646844\pi\)
\(264\) 0 0
\(265\) 10.0416 0.616849
\(266\) 0 0
\(267\) −44.8612 −2.74546
\(268\) 0 0
\(269\) −17.3952 −1.06061 −0.530303 0.847808i \(-0.677922\pi\)
−0.530303 + 0.847808i \(0.677922\pi\)
\(270\) 0 0
\(271\) 30.2168 1.83554 0.917770 0.397112i \(-0.129987\pi\)
0.917770 + 0.397112i \(0.129987\pi\)
\(272\) 0 0
\(273\) −55.7919 −3.37668
\(274\) 0 0
\(275\) −5.41372 −0.326459
\(276\) 0 0
\(277\) 1.14217 0.0686261 0.0343131 0.999411i \(-0.489076\pi\)
0.0343131 + 0.999411i \(0.489076\pi\)
\(278\) 0 0
\(279\) 17.4390 1.04405
\(280\) 0 0
\(281\) −16.4049 −0.978634 −0.489317 0.872106i \(-0.662754\pi\)
−0.489317 + 0.872106i \(0.662754\pi\)
\(282\) 0 0
\(283\) −10.6711 −0.634328 −0.317164 0.948371i \(-0.602731\pi\)
−0.317164 + 0.948371i \(0.602731\pi\)
\(284\) 0 0
\(285\) −11.1378 −0.659747
\(286\) 0 0
\(287\) 2.12095 0.125195
\(288\) 0 0
\(289\) −11.6793 −0.687020
\(290\) 0 0
\(291\) −19.8667 −1.16461
\(292\) 0 0
\(293\) 6.92639 0.404644 0.202322 0.979319i \(-0.435151\pi\)
0.202322 + 0.979319i \(0.435151\pi\)
\(294\) 0 0
\(295\) −4.21296 −0.245288
\(296\) 0 0
\(297\) 92.7106 5.37961
\(298\) 0 0
\(299\) −18.4573 −1.06741
\(300\) 0 0
\(301\) −4.65302 −0.268196
\(302\) 0 0
\(303\) 54.5660 3.13474
\(304\) 0 0
\(305\) −12.2881 −0.703613
\(306\) 0 0
\(307\) 5.20357 0.296984 0.148492 0.988914i \(-0.452558\pi\)
0.148492 + 0.988914i \(0.452558\pi\)
\(308\) 0 0
\(309\) −8.06862 −0.459008
\(310\) 0 0
\(311\) 6.77414 0.384127 0.192063 0.981383i \(-0.438482\pi\)
0.192063 + 0.981383i \(0.438482\pi\)
\(312\) 0 0
\(313\) 2.80023 0.158278 0.0791391 0.996864i \(-0.474783\pi\)
0.0791391 + 0.996864i \(0.474783\pi\)
\(314\) 0 0
\(315\) 19.1354 1.07816
\(316\) 0 0
\(317\) −19.7137 −1.10723 −0.553616 0.832772i \(-0.686752\pi\)
−0.553616 + 0.832772i \(0.686752\pi\)
\(318\) 0 0
\(319\) 7.90290 0.442478
\(320\) 0 0
\(321\) −25.8989 −1.44553
\(322\) 0 0
\(323\) −7.69990 −0.428434
\(324\) 0 0
\(325\) 7.10664 0.394205
\(326\) 0 0
\(327\) 54.8107 3.03104
\(328\) 0 0
\(329\) −27.6590 −1.52489
\(330\) 0 0
\(331\) 2.82468 0.155258 0.0776291 0.996982i \(-0.475265\pi\)
0.0776291 + 0.996982i \(0.475265\pi\)
\(332\) 0 0
\(333\) −72.9724 −3.99886
\(334\) 0 0
\(335\) 0.385186 0.0210449
\(336\) 0 0
\(337\) −26.5951 −1.44873 −0.724363 0.689419i \(-0.757866\pi\)
−0.724363 + 0.689419i \(0.757866\pi\)
\(338\) 0 0
\(339\) 28.0441 1.52315
\(340\) 0 0
\(341\) −11.6089 −0.628655
\(342\) 0 0
\(343\) −19.9145 −1.07528
\(344\) 0 0
\(345\) 8.66565 0.466543
\(346\) 0 0
\(347\) 1.89543 0.101752 0.0508760 0.998705i \(-0.483799\pi\)
0.0508760 + 0.998705i \(0.483799\pi\)
\(348\) 0 0
\(349\) 11.5730 0.619487 0.309744 0.950820i \(-0.399757\pi\)
0.309744 + 0.950820i \(0.399757\pi\)
\(350\) 0 0
\(351\) −121.702 −6.49598
\(352\) 0 0
\(353\) −30.5809 −1.62766 −0.813829 0.581105i \(-0.802621\pi\)
−0.813829 + 0.581105i \(0.802621\pi\)
\(354\) 0 0
\(355\) −12.4898 −0.662888
\(356\) 0 0
\(357\) 18.1088 0.958420
\(358\) 0 0
\(359\) −3.93418 −0.207638 −0.103819 0.994596i \(-0.533106\pi\)
−0.103819 + 0.994596i \(0.533106\pi\)
\(360\) 0 0
\(361\) −7.85694 −0.413523
\(362\) 0 0
\(363\) −61.0867 −3.20622
\(364\) 0 0
\(365\) −6.72268 −0.351881
\(366\) 0 0
\(367\) −22.7904 −1.18965 −0.594824 0.803856i \(-0.702778\pi\)
−0.594824 + 0.803856i \(0.702778\pi\)
\(368\) 0 0
\(369\) 7.33076 0.381624
\(370\) 0 0
\(371\) 23.6271 1.22666
\(372\) 0 0
\(373\) −30.2646 −1.56704 −0.783520 0.621367i \(-0.786578\pi\)
−0.783520 + 0.621367i \(0.786578\pi\)
\(374\) 0 0
\(375\) −3.33655 −0.172299
\(376\) 0 0
\(377\) −10.3742 −0.534299
\(378\) 0 0
\(379\) 13.9979 0.719025 0.359513 0.933140i \(-0.382943\pi\)
0.359513 + 0.933140i \(0.382943\pi\)
\(380\) 0 0
\(381\) −64.2985 −3.29411
\(382\) 0 0
\(383\) 20.6813 1.05677 0.528384 0.849006i \(-0.322798\pi\)
0.528384 + 0.849006i \(0.322798\pi\)
\(384\) 0 0
\(385\) −12.7381 −0.649194
\(386\) 0 0
\(387\) −16.0825 −0.817521
\(388\) 0 0
\(389\) −8.90209 −0.451354 −0.225677 0.974202i \(-0.572459\pi\)
−0.225677 + 0.974202i \(0.572459\pi\)
\(390\) 0 0
\(391\) 5.99082 0.302969
\(392\) 0 0
\(393\) 41.1678 2.07664
\(394\) 0 0
\(395\) 12.8609 0.647104
\(396\) 0 0
\(397\) 32.1091 1.61151 0.805756 0.592248i \(-0.201759\pi\)
0.805756 + 0.592248i \(0.201759\pi\)
\(398\) 0 0
\(399\) −26.2065 −1.31197
\(400\) 0 0
\(401\) 18.7681 0.937234 0.468617 0.883401i \(-0.344752\pi\)
0.468617 + 0.883401i \(0.344752\pi\)
\(402\) 0 0
\(403\) 15.2391 0.759111
\(404\) 0 0
\(405\) 32.7411 1.62692
\(406\) 0 0
\(407\) 48.5764 2.40784
\(408\) 0 0
\(409\) −19.6949 −0.973849 −0.486924 0.873444i \(-0.661881\pi\)
−0.486924 + 0.873444i \(0.661881\pi\)
\(410\) 0 0
\(411\) −6.99146 −0.344863
\(412\) 0 0
\(413\) −9.91279 −0.487777
\(414\) 0 0
\(415\) 2.69229 0.132159
\(416\) 0 0
\(417\) 45.3360 2.22011
\(418\) 0 0
\(419\) 2.27818 0.111296 0.0556482 0.998450i \(-0.482277\pi\)
0.0556482 + 0.998450i \(0.482277\pi\)
\(420\) 0 0
\(421\) −10.4056 −0.507136 −0.253568 0.967318i \(-0.581604\pi\)
−0.253568 + 0.967318i \(0.581604\pi\)
\(422\) 0 0
\(423\) −95.5997 −4.64822
\(424\) 0 0
\(425\) −2.30666 −0.111889
\(426\) 0 0
\(427\) −28.9130 −1.39920
\(428\) 0 0
\(429\) 128.368 6.19768
\(430\) 0 0
\(431\) −7.99886 −0.385291 −0.192646 0.981268i \(-0.561707\pi\)
−0.192646 + 0.981268i \(0.561707\pi\)
\(432\) 0 0
\(433\) 29.5222 1.41875 0.709374 0.704832i \(-0.248978\pi\)
0.709374 + 0.704832i \(0.248978\pi\)
\(434\) 0 0
\(435\) 4.87068 0.233531
\(436\) 0 0
\(437\) −8.66972 −0.414729
\(438\) 0 0
\(439\) −10.7474 −0.512946 −0.256473 0.966551i \(-0.582560\pi\)
−0.256473 + 0.966551i \(0.582560\pi\)
\(440\) 0 0
\(441\) −11.9038 −0.566848
\(442\) 0 0
\(443\) −4.61008 −0.219031 −0.109516 0.993985i \(-0.534930\pi\)
−0.109516 + 0.993985i \(0.534930\pi\)
\(444\) 0 0
\(445\) 13.4454 0.637372
\(446\) 0 0
\(447\) −25.4848 −1.20539
\(448\) 0 0
\(449\) 41.1548 1.94222 0.971109 0.238638i \(-0.0767008\pi\)
0.971109 + 0.238638i \(0.0767008\pi\)
\(450\) 0 0
\(451\) −4.87996 −0.229788
\(452\) 0 0
\(453\) −3.33655 −0.156765
\(454\) 0 0
\(455\) 16.7214 0.783912
\(456\) 0 0
\(457\) 16.5181 0.772686 0.386343 0.922355i \(-0.373738\pi\)
0.386343 + 0.922355i \(0.373738\pi\)
\(458\) 0 0
\(459\) 39.5018 1.84379
\(460\) 0 0
\(461\) 0.908549 0.0423154 0.0211577 0.999776i \(-0.493265\pi\)
0.0211577 + 0.999776i \(0.493265\pi\)
\(462\) 0 0
\(463\) −39.7878 −1.84910 −0.924548 0.381066i \(-0.875557\pi\)
−0.924548 + 0.381066i \(0.875557\pi\)
\(464\) 0 0
\(465\) −7.15471 −0.331792
\(466\) 0 0
\(467\) −14.1345 −0.654065 −0.327032 0.945013i \(-0.606049\pi\)
−0.327032 + 0.945013i \(0.606049\pi\)
\(468\) 0 0
\(469\) 0.906315 0.0418498
\(470\) 0 0
\(471\) 12.1634 0.560461
\(472\) 0 0
\(473\) 10.7059 0.492256
\(474\) 0 0
\(475\) 3.33812 0.153164
\(476\) 0 0
\(477\) 81.6640 3.73914
\(478\) 0 0
\(479\) −37.5386 −1.71518 −0.857592 0.514331i \(-0.828040\pi\)
−0.857592 + 0.514331i \(0.828040\pi\)
\(480\) 0 0
\(481\) −63.7667 −2.90751
\(482\) 0 0
\(483\) 20.3897 0.927762
\(484\) 0 0
\(485\) 5.95427 0.270369
\(486\) 0 0
\(487\) 15.3571 0.695898 0.347949 0.937513i \(-0.386878\pi\)
0.347949 + 0.937513i \(0.386878\pi\)
\(488\) 0 0
\(489\) −54.0984 −2.44641
\(490\) 0 0
\(491\) −10.8559 −0.489918 −0.244959 0.969533i \(-0.578775\pi\)
−0.244959 + 0.969533i \(0.578775\pi\)
\(492\) 0 0
\(493\) 3.36724 0.151653
\(494\) 0 0
\(495\) −44.0275 −1.97889
\(496\) 0 0
\(497\) −29.3875 −1.31821
\(498\) 0 0
\(499\) −6.90608 −0.309159 −0.154579 0.987980i \(-0.549402\pi\)
−0.154579 + 0.987980i \(0.549402\pi\)
\(500\) 0 0
\(501\) −79.6295 −3.55759
\(502\) 0 0
\(503\) −36.2667 −1.61705 −0.808526 0.588461i \(-0.799734\pi\)
−0.808526 + 0.588461i \(0.799734\pi\)
\(504\) 0 0
\(505\) −16.3540 −0.727744
\(506\) 0 0
\(507\) −125.135 −5.55744
\(508\) 0 0
\(509\) −6.83221 −0.302833 −0.151416 0.988470i \(-0.548383\pi\)
−0.151416 + 0.988470i \(0.548383\pi\)
\(510\) 0 0
\(511\) −15.8180 −0.699747
\(512\) 0 0
\(513\) −57.1658 −2.52393
\(514\) 0 0
\(515\) 2.41825 0.106561
\(516\) 0 0
\(517\) 63.6390 2.79884
\(518\) 0 0
\(519\) 41.5496 1.82383
\(520\) 0 0
\(521\) 19.5686 0.857314 0.428657 0.903467i \(-0.358987\pi\)
0.428657 + 0.903467i \(0.358987\pi\)
\(522\) 0 0
\(523\) 0.236246 0.0103303 0.00516515 0.999987i \(-0.498356\pi\)
0.00516515 + 0.999987i \(0.498356\pi\)
\(524\) 0 0
\(525\) −7.85068 −0.342632
\(526\) 0 0
\(527\) −4.94626 −0.215462
\(528\) 0 0
\(529\) −16.2546 −0.706723
\(530\) 0 0
\(531\) −34.2622 −1.48685
\(532\) 0 0
\(533\) 6.40597 0.277473
\(534\) 0 0
\(535\) 7.76217 0.335588
\(536\) 0 0
\(537\) 39.6626 1.71157
\(538\) 0 0
\(539\) 7.92415 0.341317
\(540\) 0 0
\(541\) −10.1429 −0.436078 −0.218039 0.975940i \(-0.569966\pi\)
−0.218039 + 0.975940i \(0.569966\pi\)
\(542\) 0 0
\(543\) 25.1270 1.07830
\(544\) 0 0
\(545\) −16.4274 −0.703671
\(546\) 0 0
\(547\) −27.6631 −1.18279 −0.591394 0.806383i \(-0.701422\pi\)
−0.591394 + 0.806383i \(0.701422\pi\)
\(548\) 0 0
\(549\) −99.9338 −4.26507
\(550\) 0 0
\(551\) −4.87297 −0.207595
\(552\) 0 0
\(553\) 30.2609 1.28682
\(554\) 0 0
\(555\) 29.9384 1.27081
\(556\) 0 0
\(557\) 39.7970 1.68625 0.843127 0.537715i \(-0.180712\pi\)
0.843127 + 0.537715i \(0.180712\pi\)
\(558\) 0 0
\(559\) −14.0537 −0.594407
\(560\) 0 0
\(561\) −41.6655 −1.75912
\(562\) 0 0
\(563\) 8.13579 0.342883 0.171441 0.985194i \(-0.445158\pi\)
0.171441 + 0.985194i \(0.445158\pi\)
\(564\) 0 0
\(565\) −8.40511 −0.353606
\(566\) 0 0
\(567\) 77.0376 3.23528
\(568\) 0 0
\(569\) −8.78964 −0.368481 −0.184241 0.982881i \(-0.558983\pi\)
−0.184241 + 0.982881i \(0.558983\pi\)
\(570\) 0 0
\(571\) 10.4366 0.436760 0.218380 0.975864i \(-0.429923\pi\)
0.218380 + 0.975864i \(0.429923\pi\)
\(572\) 0 0
\(573\) −15.2607 −0.637525
\(574\) 0 0
\(575\) −2.59719 −0.108310
\(576\) 0 0
\(577\) −16.4780 −0.685988 −0.342994 0.939338i \(-0.611441\pi\)
−0.342994 + 0.939338i \(0.611441\pi\)
\(578\) 0 0
\(579\) −18.9523 −0.787629
\(580\) 0 0
\(581\) 6.33477 0.262810
\(582\) 0 0
\(583\) −54.3623 −2.25145
\(584\) 0 0
\(585\) 57.7953 2.38954
\(586\) 0 0
\(587\) 5.32677 0.219859 0.109930 0.993939i \(-0.464937\pi\)
0.109930 + 0.993939i \(0.464937\pi\)
\(588\) 0 0
\(589\) 7.15807 0.294943
\(590\) 0 0
\(591\) −43.0097 −1.76918
\(592\) 0 0
\(593\) 28.2745 1.16109 0.580547 0.814227i \(-0.302839\pi\)
0.580547 + 0.814227i \(0.302839\pi\)
\(594\) 0 0
\(595\) −5.42740 −0.222502
\(596\) 0 0
\(597\) 45.5068 1.86247
\(598\) 0 0
\(599\) −20.6103 −0.842115 −0.421057 0.907034i \(-0.638341\pi\)
−0.421057 + 0.907034i \(0.638341\pi\)
\(600\) 0 0
\(601\) −33.8576 −1.38108 −0.690541 0.723293i \(-0.742627\pi\)
−0.690541 + 0.723293i \(0.742627\pi\)
\(602\) 0 0
\(603\) 3.13255 0.127567
\(604\) 0 0
\(605\) 18.3083 0.744339
\(606\) 0 0
\(607\) 18.0293 0.731787 0.365893 0.930657i \(-0.380764\pi\)
0.365893 + 0.930657i \(0.380764\pi\)
\(608\) 0 0
\(609\) 11.4604 0.464397
\(610\) 0 0
\(611\) −83.5395 −3.37965
\(612\) 0 0
\(613\) 39.1057 1.57946 0.789731 0.613453i \(-0.210220\pi\)
0.789731 + 0.613453i \(0.210220\pi\)
\(614\) 0 0
\(615\) −3.00759 −0.121278
\(616\) 0 0
\(617\) −27.0518 −1.08907 −0.544533 0.838740i \(-0.683293\pi\)
−0.544533 + 0.838740i \(0.683293\pi\)
\(618\) 0 0
\(619\) −15.3853 −0.618389 −0.309194 0.950999i \(-0.600059\pi\)
−0.309194 + 0.950999i \(0.600059\pi\)
\(620\) 0 0
\(621\) 44.4771 1.78481
\(622\) 0 0
\(623\) 31.6360 1.26747
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 60.2970 2.40803
\(628\) 0 0
\(629\) 20.6973 0.825254
\(630\) 0 0
\(631\) 31.9743 1.27288 0.636439 0.771327i \(-0.280407\pi\)
0.636439 + 0.771327i \(0.280407\pi\)
\(632\) 0 0
\(633\) 84.7084 3.36686
\(634\) 0 0
\(635\) 19.2710 0.764744
\(636\) 0 0
\(637\) −10.4021 −0.412147
\(638\) 0 0
\(639\) −101.574 −4.01820
\(640\) 0 0
\(641\) −13.2599 −0.523736 −0.261868 0.965104i \(-0.584339\pi\)
−0.261868 + 0.965104i \(0.584339\pi\)
\(642\) 0 0
\(643\) 6.66670 0.262909 0.131454 0.991322i \(-0.458035\pi\)
0.131454 + 0.991322i \(0.458035\pi\)
\(644\) 0 0
\(645\) 6.59818 0.259803
\(646\) 0 0
\(647\) 7.25281 0.285138 0.142569 0.989785i \(-0.454464\pi\)
0.142569 + 0.989785i \(0.454464\pi\)
\(648\) 0 0
\(649\) 22.8077 0.895282
\(650\) 0 0
\(651\) −16.8345 −0.659797
\(652\) 0 0
\(653\) 36.3764 1.42352 0.711760 0.702423i \(-0.247898\pi\)
0.711760 + 0.702423i \(0.247898\pi\)
\(654\) 0 0
\(655\) −12.3384 −0.482102
\(656\) 0 0
\(657\) −54.6728 −2.13299
\(658\) 0 0
\(659\) −31.2710 −1.21815 −0.609073 0.793114i \(-0.708458\pi\)
−0.609073 + 0.793114i \(0.708458\pi\)
\(660\) 0 0
\(661\) −23.3459 −0.908050 −0.454025 0.890989i \(-0.650012\pi\)
−0.454025 + 0.890989i \(0.650012\pi\)
\(662\) 0 0
\(663\) 54.6947 2.12416
\(664\) 0 0
\(665\) 7.85437 0.304579
\(666\) 0 0
\(667\) 3.79135 0.146802
\(668\) 0 0
\(669\) −75.6214 −2.92369
\(670\) 0 0
\(671\) 66.5242 2.56814
\(672\) 0 0
\(673\) −1.23928 −0.0477706 −0.0238853 0.999715i \(-0.507604\pi\)
−0.0238853 + 0.999715i \(0.507604\pi\)
\(674\) 0 0
\(675\) −17.1251 −0.659146
\(676\) 0 0
\(677\) 28.5718 1.09810 0.549051 0.835789i \(-0.314989\pi\)
0.549051 + 0.835789i \(0.314989\pi\)
\(678\) 0 0
\(679\) 14.0100 0.537654
\(680\) 0 0
\(681\) 68.4030 2.62121
\(682\) 0 0
\(683\) 18.5979 0.711629 0.355814 0.934557i \(-0.384204\pi\)
0.355814 + 0.934557i \(0.384204\pi\)
\(684\) 0 0
\(685\) 2.09541 0.0800616
\(686\) 0 0
\(687\) 24.4086 0.931247
\(688\) 0 0
\(689\) 71.3619 2.71867
\(690\) 0 0
\(691\) 24.8610 0.945759 0.472879 0.881127i \(-0.343215\pi\)
0.472879 + 0.881127i \(0.343215\pi\)
\(692\) 0 0
\(693\) −103.594 −3.93520
\(694\) 0 0
\(695\) −13.5877 −0.515410
\(696\) 0 0
\(697\) −2.07923 −0.0787566
\(698\) 0 0
\(699\) 31.2401 1.18161
\(700\) 0 0
\(701\) −38.5861 −1.45738 −0.728689 0.684845i \(-0.759870\pi\)
−0.728689 + 0.684845i \(0.759870\pi\)
\(702\) 0 0
\(703\) −29.9524 −1.12968
\(704\) 0 0
\(705\) 39.2217 1.47717
\(706\) 0 0
\(707\) −38.4799 −1.44718
\(708\) 0 0
\(709\) −9.89928 −0.371775 −0.185888 0.982571i \(-0.559516\pi\)
−0.185888 + 0.982571i \(0.559516\pi\)
\(710\) 0 0
\(711\) 104.593 3.92253
\(712\) 0 0
\(713\) −5.56925 −0.208570
\(714\) 0 0
\(715\) −38.4733 −1.43882
\(716\) 0 0
\(717\) 47.2927 1.76618
\(718\) 0 0
\(719\) 9.55542 0.356357 0.178179 0.983998i \(-0.442980\pi\)
0.178179 + 0.983998i \(0.442980\pi\)
\(720\) 0 0
\(721\) 5.68998 0.211906
\(722\) 0 0
\(723\) 23.9076 0.889133
\(724\) 0 0
\(725\) −1.45979 −0.0542153
\(726\) 0 0
\(727\) 2.10017 0.0778911 0.0389455 0.999241i \(-0.487600\pi\)
0.0389455 + 0.999241i \(0.487600\pi\)
\(728\) 0 0
\(729\) 94.8533 3.51309
\(730\) 0 0
\(731\) 4.56151 0.168714
\(732\) 0 0
\(733\) −3.35961 −0.124090 −0.0620451 0.998073i \(-0.519762\pi\)
−0.0620451 + 0.998073i \(0.519762\pi\)
\(734\) 0 0
\(735\) 4.88377 0.180141
\(736\) 0 0
\(737\) −2.08529 −0.0768125
\(738\) 0 0
\(739\) −12.1420 −0.446652 −0.223326 0.974744i \(-0.571691\pi\)
−0.223326 + 0.974744i \(0.571691\pi\)
\(740\) 0 0
\(741\) −79.1524 −2.90774
\(742\) 0 0
\(743\) 18.3929 0.674772 0.337386 0.941366i \(-0.390457\pi\)
0.337386 + 0.941366i \(0.390457\pi\)
\(744\) 0 0
\(745\) 7.63807 0.279837
\(746\) 0 0
\(747\) 21.8953 0.801106
\(748\) 0 0
\(749\) 18.2638 0.667346
\(750\) 0 0
\(751\) 30.9814 1.13053 0.565264 0.824910i \(-0.308774\pi\)
0.565264 + 0.824910i \(0.308774\pi\)
\(752\) 0 0
\(753\) 28.3645 1.03366
\(754\) 0 0
\(755\) 1.00000 0.0363937
\(756\) 0 0
\(757\) −45.2346 −1.64408 −0.822040 0.569429i \(-0.807164\pi\)
−0.822040 + 0.569429i \(0.807164\pi\)
\(758\) 0 0
\(759\) −46.9134 −1.70285
\(760\) 0 0
\(761\) −21.2717 −0.771100 −0.385550 0.922687i \(-0.625988\pi\)
−0.385550 + 0.922687i \(0.625988\pi\)
\(762\) 0 0
\(763\) −38.6524 −1.39931
\(764\) 0 0
\(765\) −18.7591 −0.678236
\(766\) 0 0
\(767\) −29.9399 −1.08107
\(768\) 0 0
\(769\) 10.1576 0.366292 0.183146 0.983086i \(-0.441372\pi\)
0.183146 + 0.983086i \(0.441372\pi\)
\(770\) 0 0
\(771\) −28.8719 −1.03980
\(772\) 0 0
\(773\) 20.4688 0.736210 0.368105 0.929784i \(-0.380007\pi\)
0.368105 + 0.929784i \(0.380007\pi\)
\(774\) 0 0
\(775\) 2.14434 0.0770270
\(776\) 0 0
\(777\) 70.4429 2.52712
\(778\) 0 0
\(779\) 3.00900 0.107809
\(780\) 0 0
\(781\) 67.6160 2.41949
\(782\) 0 0
\(783\) 24.9991 0.893396
\(784\) 0 0
\(785\) −3.64551 −0.130114
\(786\) 0 0
\(787\) −4.89209 −0.174384 −0.0871921 0.996192i \(-0.527789\pi\)
−0.0871921 + 0.996192i \(0.527789\pi\)
\(788\) 0 0
\(789\) 48.1722 1.71498
\(790\) 0 0
\(791\) −19.7766 −0.703177
\(792\) 0 0
\(793\) −87.3269 −3.10107
\(794\) 0 0
\(795\) −33.5043 −1.18827
\(796\) 0 0
\(797\) −19.0782 −0.675784 −0.337892 0.941185i \(-0.609714\pi\)
−0.337892 + 0.941185i \(0.609714\pi\)
\(798\) 0 0
\(799\) 27.1151 0.959263
\(800\) 0 0
\(801\) 109.346 3.86354
\(802\) 0 0
\(803\) 36.3947 1.28434
\(804\) 0 0
\(805\) −6.11100 −0.215384
\(806\) 0 0
\(807\) 58.0401 2.04311
\(808\) 0 0
\(809\) 33.6655 1.18362 0.591809 0.806078i \(-0.298414\pi\)
0.591809 + 0.806078i \(0.298414\pi\)
\(810\) 0 0
\(811\) 22.8424 0.802104 0.401052 0.916055i \(-0.368645\pi\)
0.401052 + 0.916055i \(0.368645\pi\)
\(812\) 0 0
\(813\) −100.820 −3.53591
\(814\) 0 0
\(815\) 16.2139 0.567947
\(816\) 0 0
\(817\) −6.60128 −0.230950
\(818\) 0 0
\(819\) 135.988 4.75182
\(820\) 0 0
\(821\) 0.517548 0.0180625 0.00903127 0.999959i \(-0.497125\pi\)
0.00903127 + 0.999959i \(0.497125\pi\)
\(822\) 0 0
\(823\) 9.91645 0.345666 0.172833 0.984951i \(-0.444708\pi\)
0.172833 + 0.984951i \(0.444708\pi\)
\(824\) 0 0
\(825\) 18.0631 0.628878
\(826\) 0 0
\(827\) 52.8207 1.83676 0.918378 0.395704i \(-0.129499\pi\)
0.918378 + 0.395704i \(0.129499\pi\)
\(828\) 0 0
\(829\) 29.5853 1.02754 0.513770 0.857928i \(-0.328248\pi\)
0.513770 + 0.857928i \(0.328248\pi\)
\(830\) 0 0
\(831\) −3.81090 −0.132199
\(832\) 0 0
\(833\) 3.37629 0.116982
\(834\) 0 0
\(835\) 23.8658 0.825911
\(836\) 0 0
\(837\) −36.7221 −1.26930
\(838\) 0 0
\(839\) 9.83903 0.339681 0.169840 0.985472i \(-0.445675\pi\)
0.169840 + 0.985472i \(0.445675\pi\)
\(840\) 0 0
\(841\) −26.8690 −0.926517
\(842\) 0 0
\(843\) 54.7358 1.88520
\(844\) 0 0
\(845\) 37.5043 1.29019
\(846\) 0 0
\(847\) 43.0782 1.48019
\(848\) 0 0
\(849\) 35.6045 1.22194
\(850\) 0 0
\(851\) 23.3041 0.798856
\(852\) 0 0
\(853\) −0.0584971 −0.00200290 −0.00100145 0.999999i \(-0.500319\pi\)
−0.00100145 + 0.999999i \(0.500319\pi\)
\(854\) 0 0
\(855\) 27.1475 0.928427
\(856\) 0 0
\(857\) −53.8637 −1.83995 −0.919974 0.391980i \(-0.871790\pi\)
−0.919974 + 0.391980i \(0.871790\pi\)
\(858\) 0 0
\(859\) −24.7577 −0.844721 −0.422361 0.906428i \(-0.638798\pi\)
−0.422361 + 0.906428i \(0.638798\pi\)
\(860\) 0 0
\(861\) −7.07665 −0.241172
\(862\) 0 0
\(863\) 6.23688 0.212306 0.106153 0.994350i \(-0.466147\pi\)
0.106153 + 0.994350i \(0.466147\pi\)
\(864\) 0 0
\(865\) −12.4529 −0.423410
\(866\) 0 0
\(867\) 38.9687 1.32345
\(868\) 0 0
\(869\) −69.6254 −2.36188
\(870\) 0 0
\(871\) 2.73738 0.0927524
\(872\) 0 0
\(873\) 48.4236 1.63889
\(874\) 0 0
\(875\) 2.35293 0.0795436
\(876\) 0 0
\(877\) −30.8283 −1.04100 −0.520499 0.853862i \(-0.674254\pi\)
−0.520499 + 0.853862i \(0.674254\pi\)
\(878\) 0 0
\(879\) −23.1103 −0.779490
\(880\) 0 0
\(881\) 7.43062 0.250344 0.125172 0.992135i \(-0.460052\pi\)
0.125172 + 0.992135i \(0.460052\pi\)
\(882\) 0 0
\(883\) −29.2605 −0.984695 −0.492347 0.870399i \(-0.663861\pi\)
−0.492347 + 0.870399i \(0.663861\pi\)
\(884\) 0 0
\(885\) 14.0567 0.472512
\(886\) 0 0
\(887\) 38.9733 1.30860 0.654298 0.756237i \(-0.272964\pi\)
0.654298 + 0.756237i \(0.272964\pi\)
\(888\) 0 0
\(889\) 45.3432 1.52076
\(890\) 0 0
\(891\) −177.251 −5.93814
\(892\) 0 0
\(893\) −39.2401 −1.31312
\(894\) 0 0
\(895\) −11.8873 −0.397348
\(896\) 0 0
\(897\) 61.5836 2.05622
\(898\) 0 0
\(899\) −3.13029 −0.104401
\(900\) 0 0
\(901\) −23.1625 −0.771654
\(902\) 0 0
\(903\) 15.5250 0.516641
\(904\) 0 0
\(905\) −7.53084 −0.250334
\(906\) 0 0
\(907\) 13.5692 0.450557 0.225279 0.974294i \(-0.427671\pi\)
0.225279 + 0.974294i \(0.427671\pi\)
\(908\) 0 0
\(909\) −133.000 −4.41134
\(910\) 0 0
\(911\) −22.2093 −0.735827 −0.367913 0.929860i \(-0.619928\pi\)
−0.367913 + 0.929860i \(0.619928\pi\)
\(912\) 0 0
\(913\) −14.5753 −0.482372
\(914\) 0 0
\(915\) 40.9998 1.35541
\(916\) 0 0
\(917\) −29.0314 −0.958703
\(918\) 0 0
\(919\) 6.83245 0.225382 0.112691 0.993630i \(-0.464053\pi\)
0.112691 + 0.993630i \(0.464053\pi\)
\(920\) 0 0
\(921\) −17.3620 −0.572097
\(922\) 0 0
\(923\) −88.7602 −2.92158
\(924\) 0 0
\(925\) −8.97284 −0.295025
\(926\) 0 0
\(927\) 19.6666 0.645937
\(928\) 0 0
\(929\) −28.6125 −0.938745 −0.469372 0.883000i \(-0.655520\pi\)
−0.469372 + 0.883000i \(0.655520\pi\)
\(930\) 0 0
\(931\) −4.88607 −0.160134
\(932\) 0 0
\(933\) −22.6023 −0.739966
\(934\) 0 0
\(935\) 12.4876 0.408388
\(936\) 0 0
\(937\) −4.48793 −0.146614 −0.0733072 0.997309i \(-0.523355\pi\)
−0.0733072 + 0.997309i \(0.523355\pi\)
\(938\) 0 0
\(939\) −9.34311 −0.304901
\(940\) 0 0
\(941\) 54.4634 1.77546 0.887728 0.460369i \(-0.152283\pi\)
0.887728 + 0.460369i \(0.152283\pi\)
\(942\) 0 0
\(943\) −2.34112 −0.0762374
\(944\) 0 0
\(945\) −40.2942 −1.31077
\(946\) 0 0
\(947\) −35.4643 −1.15244 −0.576218 0.817296i \(-0.695472\pi\)
−0.576218 + 0.817296i \(0.695472\pi\)
\(948\) 0 0
\(949\) −47.7757 −1.55086
\(950\) 0 0
\(951\) 65.7758 2.13293
\(952\) 0 0
\(953\) −2.68115 −0.0868511 −0.0434256 0.999057i \(-0.513827\pi\)
−0.0434256 + 0.999057i \(0.513827\pi\)
\(954\) 0 0
\(955\) 4.57380 0.148005
\(956\) 0 0
\(957\) −26.3685 −0.852371
\(958\) 0 0
\(959\) 4.93036 0.159210
\(960\) 0 0
\(961\) −26.4018 −0.851671
\(962\) 0 0
\(963\) 63.1265 2.03422
\(964\) 0 0
\(965\) 5.68019 0.182852
\(966\) 0 0
\(967\) −45.1482 −1.45187 −0.725933 0.687765i \(-0.758592\pi\)
−0.725933 + 0.687765i \(0.758592\pi\)
\(968\) 0 0
\(969\) 25.6911 0.825318
\(970\) 0 0
\(971\) −25.8203 −0.828614 −0.414307 0.910137i \(-0.635976\pi\)
−0.414307 + 0.910137i \(0.635976\pi\)
\(972\) 0 0
\(973\) −31.9709 −1.02494
\(974\) 0 0
\(975\) −23.7117 −0.759381
\(976\) 0 0
\(977\) 14.5484 0.465445 0.232722 0.972543i \(-0.425237\pi\)
0.232722 + 0.972543i \(0.425237\pi\)
\(978\) 0 0
\(979\) −72.7895 −2.32636
\(980\) 0 0
\(981\) −133.597 −4.26542
\(982\) 0 0
\(983\) 33.8003 1.07806 0.539032 0.842285i \(-0.318790\pi\)
0.539032 + 0.842285i \(0.318790\pi\)
\(984\) 0 0
\(985\) 12.8905 0.410725
\(986\) 0 0
\(987\) 92.2858 2.93749
\(988\) 0 0
\(989\) 5.13605 0.163317
\(990\) 0 0
\(991\) 11.5476 0.366822 0.183411 0.983036i \(-0.441286\pi\)
0.183411 + 0.983036i \(0.441286\pi\)
\(992\) 0 0
\(993\) −9.42468 −0.299083
\(994\) 0 0
\(995\) −13.6389 −0.432381
\(996\) 0 0
\(997\) 49.0557 1.55361 0.776804 0.629742i \(-0.216839\pi\)
0.776804 + 0.629742i \(0.216839\pi\)
\(998\) 0 0
\(999\) 153.661 4.86162
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 \(a_p\))