Properties

Label 8036.2.a.t.1.16
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 20
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1677830643\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Root \(2.15119\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+2.15119 q^{3}\) \(-3.75581 q^{5}\) \(+1.62763 q^{9}\) \(+O(q^{10})\) \(q\)\(+2.15119 q^{3}\) \(-3.75581 q^{5}\) \(+1.62763 q^{9}\) \(+4.89580 q^{11}\) \(+1.80162 q^{13}\) \(-8.07948 q^{15}\) \(+4.27358 q^{17}\) \(+5.31507 q^{19}\) \(+0.795860 q^{23}\) \(+9.10613 q^{25}\) \(-2.95223 q^{27}\) \(+0.466132 q^{29}\) \(-2.71538 q^{31}\) \(+10.5318 q^{33}\) \(-10.1055 q^{37}\) \(+3.87562 q^{39}\) \(-1.00000 q^{41}\) \(-3.98724 q^{43}\) \(-6.11308 q^{45}\) \(+2.29800 q^{47}\) \(+9.19329 q^{51}\) \(-1.15028 q^{53}\) \(-18.3877 q^{55}\) \(+11.4338 q^{57}\) \(+6.87226 q^{59}\) \(+8.97900 q^{61}\) \(-6.76653 q^{65}\) \(-3.33631 q^{67}\) \(+1.71205 q^{69}\) \(+0.810480 q^{71}\) \(-2.12535 q^{73}\) \(+19.5890 q^{75}\) \(-6.00504 q^{79}\) \(-11.2337 q^{81}\) \(-4.93699 q^{83}\) \(-16.0507 q^{85}\) \(+1.00274 q^{87}\) \(+13.0344 q^{89}\) \(-5.84130 q^{93}\) \(-19.9624 q^{95}\) \(+12.0806 q^{97}\) \(+7.96856 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 24q^{19} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 20q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 44q^{33} \) \(\mathstrut +\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 40q^{45} \) \(\mathstrut +\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 28q^{57} \) \(\mathstrut +\mathstrut 16q^{59} \) \(\mathstrut +\mathstrut 68q^{61} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 32q^{69} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 48q^{73} \) \(\mathstrut +\mathstrut 60q^{75} \) \(\mathstrut -\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 32q^{81} \) \(\mathstrut -\mathstrut 8q^{83} \) \(\mathstrut -\mathstrut 28q^{85} \) \(\mathstrut +\mathstrut 60q^{89} \) \(\mathstrut -\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 40q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 2.15119 1.24199 0.620996 0.783814i \(-0.286728\pi\)
0.620996 + 0.783814i \(0.286728\pi\)
\(4\) 0 0
\(5\) −3.75581 −1.67965 −0.839825 0.542857i \(-0.817343\pi\)
−0.839825 + 0.542857i \(0.817343\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 1.62763 0.542544
\(10\) 0 0
\(11\) 4.89580 1.47614 0.738069 0.674725i \(-0.235738\pi\)
0.738069 + 0.674725i \(0.235738\pi\)
\(12\) 0 0
\(13\) 1.80162 0.499678 0.249839 0.968287i \(-0.419622\pi\)
0.249839 + 0.968287i \(0.419622\pi\)
\(14\) 0 0
\(15\) −8.07948 −2.08611
\(16\) 0 0
\(17\) 4.27358 1.03649 0.518247 0.855231i \(-0.326585\pi\)
0.518247 + 0.855231i \(0.326585\pi\)
\(18\) 0 0
\(19\) 5.31507 1.21936 0.609681 0.792647i \(-0.291298\pi\)
0.609681 + 0.792647i \(0.291298\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.795860 0.165948 0.0829742 0.996552i \(-0.473558\pi\)
0.0829742 + 0.996552i \(0.473558\pi\)
\(24\) 0 0
\(25\) 9.10613 1.82123
\(26\) 0 0
\(27\) −2.95223 −0.568157
\(28\) 0 0
\(29\) 0.466132 0.0865585 0.0432792 0.999063i \(-0.486219\pi\)
0.0432792 + 0.999063i \(0.486219\pi\)
\(30\) 0 0
\(31\) −2.71538 −0.487696 −0.243848 0.969813i \(-0.578410\pi\)
−0.243848 + 0.969813i \(0.578410\pi\)
\(32\) 0 0
\(33\) 10.5318 1.83335
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −10.1055 −1.66133 −0.830667 0.556769i \(-0.812041\pi\)
−0.830667 + 0.556769i \(0.812041\pi\)
\(38\) 0 0
\(39\) 3.87562 0.620597
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −3.98724 −0.608048 −0.304024 0.952664i \(-0.598330\pi\)
−0.304024 + 0.952664i \(0.598330\pi\)
\(44\) 0 0
\(45\) −6.11308 −0.911284
\(46\) 0 0
\(47\) 2.29800 0.335197 0.167599 0.985855i \(-0.446399\pi\)
0.167599 + 0.985855i \(0.446399\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 9.19329 1.28732
\(52\) 0 0
\(53\) −1.15028 −0.158003 −0.0790015 0.996874i \(-0.525173\pi\)
−0.0790015 + 0.996874i \(0.525173\pi\)
\(54\) 0 0
\(55\) −18.3877 −2.47940
\(56\) 0 0
\(57\) 11.4338 1.51444
\(58\) 0 0
\(59\) 6.87226 0.894692 0.447346 0.894361i \(-0.352369\pi\)
0.447346 + 0.894361i \(0.352369\pi\)
\(60\) 0 0
\(61\) 8.97900 1.14964 0.574821 0.818279i \(-0.305072\pi\)
0.574821 + 0.818279i \(0.305072\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −6.76653 −0.839285
\(66\) 0 0
\(67\) −3.33631 −0.407595 −0.203797 0.979013i \(-0.565328\pi\)
−0.203797 + 0.979013i \(0.565328\pi\)
\(68\) 0 0
\(69\) 1.71205 0.206107
\(70\) 0 0
\(71\) 0.810480 0.0961863 0.0480931 0.998843i \(-0.484686\pi\)
0.0480931 + 0.998843i \(0.484686\pi\)
\(72\) 0 0
\(73\) −2.12535 −0.248753 −0.124376 0.992235i \(-0.539693\pi\)
−0.124376 + 0.992235i \(0.539693\pi\)
\(74\) 0 0
\(75\) 19.5890 2.26195
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −6.00504 −0.675619 −0.337810 0.941214i \(-0.609686\pi\)
−0.337810 + 0.941214i \(0.609686\pi\)
\(80\) 0 0
\(81\) −11.2337 −1.24819
\(82\) 0 0
\(83\) −4.93699 −0.541905 −0.270952 0.962593i \(-0.587339\pi\)
−0.270952 + 0.962593i \(0.587339\pi\)
\(84\) 0 0
\(85\) −16.0507 −1.74095
\(86\) 0 0
\(87\) 1.00274 0.107505
\(88\) 0 0
\(89\) 13.0344 1.38165 0.690824 0.723023i \(-0.257248\pi\)
0.690824 + 0.723023i \(0.257248\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −5.84130 −0.605715
\(94\) 0 0
\(95\) −19.9624 −2.04810
\(96\) 0 0
\(97\) 12.0806 1.22660 0.613298 0.789852i \(-0.289843\pi\)
0.613298 + 0.789852i \(0.289843\pi\)
\(98\) 0 0
\(99\) 7.96856 0.800870
\(100\) 0 0
\(101\) 16.5725 1.64903 0.824513 0.565843i \(-0.191449\pi\)
0.824513 + 0.565843i \(0.191449\pi\)
\(102\) 0 0
\(103\) 3.30586 0.325736 0.162868 0.986648i \(-0.447926\pi\)
0.162868 + 0.986648i \(0.447926\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.64267 0.642171 0.321085 0.947050i \(-0.395952\pi\)
0.321085 + 0.947050i \(0.395952\pi\)
\(108\) 0 0
\(109\) −2.65846 −0.254634 −0.127317 0.991862i \(-0.540637\pi\)
−0.127317 + 0.991862i \(0.540637\pi\)
\(110\) 0 0
\(111\) −21.7389 −2.06336
\(112\) 0 0
\(113\) −4.59350 −0.432120 −0.216060 0.976380i \(-0.569321\pi\)
−0.216060 + 0.976380i \(0.569321\pi\)
\(114\) 0 0
\(115\) −2.98910 −0.278735
\(116\) 0 0
\(117\) 2.93237 0.271098
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 12.9688 1.17899
\(122\) 0 0
\(123\) −2.15119 −0.193967
\(124\) 0 0
\(125\) −15.4218 −1.37937
\(126\) 0 0
\(127\) 15.9912 1.41899 0.709494 0.704711i \(-0.248924\pi\)
0.709494 + 0.704711i \(0.248924\pi\)
\(128\) 0 0
\(129\) −8.57731 −0.755190
\(130\) 0 0
\(131\) 5.20712 0.454948 0.227474 0.973784i \(-0.426953\pi\)
0.227474 + 0.973784i \(0.426953\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 11.0880 0.954304
\(136\) 0 0
\(137\) 4.66661 0.398696 0.199348 0.979929i \(-0.436118\pi\)
0.199348 + 0.979929i \(0.436118\pi\)
\(138\) 0 0
\(139\) 6.46110 0.548023 0.274012 0.961726i \(-0.411649\pi\)
0.274012 + 0.961726i \(0.411649\pi\)
\(140\) 0 0
\(141\) 4.94343 0.416312
\(142\) 0 0
\(143\) 8.82035 0.737595
\(144\) 0 0
\(145\) −1.75070 −0.145388
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −7.41639 −0.607574 −0.303787 0.952740i \(-0.598251\pi\)
−0.303787 + 0.952740i \(0.598251\pi\)
\(150\) 0 0
\(151\) 6.87902 0.559806 0.279903 0.960028i \(-0.409698\pi\)
0.279903 + 0.960028i \(0.409698\pi\)
\(152\) 0 0
\(153\) 6.95581 0.562344
\(154\) 0 0
\(155\) 10.1985 0.819159
\(156\) 0 0
\(157\) −13.9637 −1.11443 −0.557214 0.830369i \(-0.688130\pi\)
−0.557214 + 0.830369i \(0.688130\pi\)
\(158\) 0 0
\(159\) −2.47447 −0.196239
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 21.5670 1.68926 0.844628 0.535353i \(-0.179822\pi\)
0.844628 + 0.535353i \(0.179822\pi\)
\(164\) 0 0
\(165\) −39.5555 −3.07939
\(166\) 0 0
\(167\) −13.2690 −1.02679 −0.513394 0.858153i \(-0.671612\pi\)
−0.513394 + 0.858153i \(0.671612\pi\)
\(168\) 0 0
\(169\) −9.75418 −0.750321
\(170\) 0 0
\(171\) 8.65099 0.661557
\(172\) 0 0
\(173\) −3.58266 −0.272384 −0.136192 0.990682i \(-0.543486\pi\)
−0.136192 + 0.990682i \(0.543486\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 14.7836 1.11120
\(178\) 0 0
\(179\) −0.682622 −0.0510216 −0.0255108 0.999675i \(-0.508121\pi\)
−0.0255108 + 0.999675i \(0.508121\pi\)
\(180\) 0 0
\(181\) 6.20632 0.461312 0.230656 0.973035i \(-0.425913\pi\)
0.230656 + 0.973035i \(0.425913\pi\)
\(182\) 0 0
\(183\) 19.3156 1.42785
\(184\) 0 0
\(185\) 37.9544 2.79046
\(186\) 0 0
\(187\) 20.9226 1.53001
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −15.9415 −1.15349 −0.576745 0.816924i \(-0.695677\pi\)
−0.576745 + 0.816924i \(0.695677\pi\)
\(192\) 0 0
\(193\) 19.9740 1.43776 0.718880 0.695134i \(-0.244655\pi\)
0.718880 + 0.695134i \(0.244655\pi\)
\(194\) 0 0
\(195\) −14.5561 −1.04239
\(196\) 0 0
\(197\) 8.46343 0.602994 0.301497 0.953467i \(-0.402514\pi\)
0.301497 + 0.953467i \(0.402514\pi\)
\(198\) 0 0
\(199\) 26.7937 1.89935 0.949677 0.313231i \(-0.101411\pi\)
0.949677 + 0.313231i \(0.101411\pi\)
\(200\) 0 0
\(201\) −7.17704 −0.506229
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 3.75581 0.262317
\(206\) 0 0
\(207\) 1.29537 0.0900343
\(208\) 0 0
\(209\) 26.0215 1.79995
\(210\) 0 0
\(211\) 9.86401 0.679066 0.339533 0.940594i \(-0.389731\pi\)
0.339533 + 0.940594i \(0.389731\pi\)
\(212\) 0 0
\(213\) 1.74350 0.119463
\(214\) 0 0
\(215\) 14.9753 1.02131
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −4.57203 −0.308949
\(220\) 0 0
\(221\) 7.69934 0.517914
\(222\) 0 0
\(223\) −28.6007 −1.91524 −0.957622 0.288028i \(-0.907000\pi\)
−0.957622 + 0.288028i \(0.907000\pi\)
\(224\) 0 0
\(225\) 14.8214 0.988095
\(226\) 0 0
\(227\) −15.9504 −1.05867 −0.529333 0.848414i \(-0.677558\pi\)
−0.529333 + 0.848414i \(0.677558\pi\)
\(228\) 0 0
\(229\) 20.0736 1.32650 0.663249 0.748399i \(-0.269177\pi\)
0.663249 + 0.748399i \(0.269177\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −28.0841 −1.83985 −0.919926 0.392093i \(-0.871751\pi\)
−0.919926 + 0.392093i \(0.871751\pi\)
\(234\) 0 0
\(235\) −8.63084 −0.563014
\(236\) 0 0
\(237\) −12.9180 −0.839114
\(238\) 0 0
\(239\) 4.35261 0.281547 0.140773 0.990042i \(-0.455041\pi\)
0.140773 + 0.990042i \(0.455041\pi\)
\(240\) 0 0
\(241\) 20.0638 1.29243 0.646213 0.763157i \(-0.276352\pi\)
0.646213 + 0.763157i \(0.276352\pi\)
\(242\) 0 0
\(243\) −15.3092 −0.982085
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 9.57572 0.609289
\(248\) 0 0
\(249\) −10.6204 −0.673041
\(250\) 0 0
\(251\) 14.6468 0.924495 0.462248 0.886751i \(-0.347043\pi\)
0.462248 + 0.886751i \(0.347043\pi\)
\(252\) 0 0
\(253\) 3.89637 0.244963
\(254\) 0 0
\(255\) −34.5283 −2.16224
\(256\) 0 0
\(257\) −31.3870 −1.95787 −0.978935 0.204174i \(-0.934549\pi\)
−0.978935 + 0.204174i \(0.934549\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0.758691 0.0469618
\(262\) 0 0
\(263\) 6.23273 0.384327 0.192163 0.981363i \(-0.438450\pi\)
0.192163 + 0.981363i \(0.438450\pi\)
\(264\) 0 0
\(265\) 4.32024 0.265390
\(266\) 0 0
\(267\) 28.0396 1.71600
\(268\) 0 0
\(269\) −13.7736 −0.839793 −0.419897 0.907572i \(-0.637934\pi\)
−0.419897 + 0.907572i \(0.637934\pi\)
\(270\) 0 0
\(271\) 24.4987 1.48819 0.744096 0.668073i \(-0.232880\pi\)
0.744096 + 0.668073i \(0.232880\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 44.5818 2.68838
\(276\) 0 0
\(277\) 28.3534 1.70359 0.851794 0.523876i \(-0.175515\pi\)
0.851794 + 0.523876i \(0.175515\pi\)
\(278\) 0 0
\(279\) −4.41964 −0.264597
\(280\) 0 0
\(281\) −16.7300 −0.998026 −0.499013 0.866595i \(-0.666304\pi\)
−0.499013 + 0.866595i \(0.666304\pi\)
\(282\) 0 0
\(283\) 0.592314 0.0352094 0.0176047 0.999845i \(-0.494396\pi\)
0.0176047 + 0.999845i \(0.494396\pi\)
\(284\) 0 0
\(285\) −42.9430 −2.54373
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 1.26345 0.0743206
\(290\) 0 0
\(291\) 25.9876 1.52342
\(292\) 0 0
\(293\) 8.47237 0.494961 0.247480 0.968893i \(-0.420397\pi\)
0.247480 + 0.968893i \(0.420397\pi\)
\(294\) 0 0
\(295\) −25.8109 −1.50277
\(296\) 0 0
\(297\) −14.4535 −0.838678
\(298\) 0 0
\(299\) 1.43384 0.0829208
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 35.6507 2.04808
\(304\) 0 0
\(305\) −33.7234 −1.93100
\(306\) 0 0
\(307\) 24.7488 1.41249 0.706245 0.707967i \(-0.250388\pi\)
0.706245 + 0.707967i \(0.250388\pi\)
\(308\) 0 0
\(309\) 7.11154 0.404561
\(310\) 0 0
\(311\) 28.6463 1.62438 0.812190 0.583393i \(-0.198275\pi\)
0.812190 + 0.583393i \(0.198275\pi\)
\(312\) 0 0
\(313\) −7.17226 −0.405400 −0.202700 0.979241i \(-0.564972\pi\)
−0.202700 + 0.979241i \(0.564972\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −31.8823 −1.79069 −0.895343 0.445377i \(-0.853070\pi\)
−0.895343 + 0.445377i \(0.853070\pi\)
\(318\) 0 0
\(319\) 2.28209 0.127772
\(320\) 0 0
\(321\) 14.2897 0.797571
\(322\) 0 0
\(323\) 22.7144 1.26386
\(324\) 0 0
\(325\) 16.4057 0.910027
\(326\) 0 0
\(327\) −5.71886 −0.316254
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 36.1504 1.98700 0.993501 0.113819i \(-0.0363084\pi\)
0.993501 + 0.113819i \(0.0363084\pi\)
\(332\) 0 0
\(333\) −16.4480 −0.901347
\(334\) 0 0
\(335\) 12.5305 0.684617
\(336\) 0 0
\(337\) −6.03769 −0.328894 −0.164447 0.986386i \(-0.552584\pi\)
−0.164447 + 0.986386i \(0.552584\pi\)
\(338\) 0 0
\(339\) −9.88150 −0.536689
\(340\) 0 0
\(341\) −13.2939 −0.719907
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −6.43014 −0.346187
\(346\) 0 0
\(347\) −1.13405 −0.0608790 −0.0304395 0.999537i \(-0.509691\pi\)
−0.0304395 + 0.999537i \(0.509691\pi\)
\(348\) 0 0
\(349\) −30.5719 −1.63648 −0.818239 0.574878i \(-0.805049\pi\)
−0.818239 + 0.574878i \(0.805049\pi\)
\(350\) 0 0
\(351\) −5.31878 −0.283896
\(352\) 0 0
\(353\) −5.97272 −0.317896 −0.158948 0.987287i \(-0.550810\pi\)
−0.158948 + 0.987287i \(0.550810\pi\)
\(354\) 0 0
\(355\) −3.04401 −0.161559
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 18.4602 0.974290 0.487145 0.873321i \(-0.338038\pi\)
0.487145 + 0.873321i \(0.338038\pi\)
\(360\) 0 0
\(361\) 9.25001 0.486843
\(362\) 0 0
\(363\) 27.8985 1.46429
\(364\) 0 0
\(365\) 7.98240 0.417818
\(366\) 0 0
\(367\) −13.6502 −0.712536 −0.356268 0.934384i \(-0.615951\pi\)
−0.356268 + 0.934384i \(0.615951\pi\)
\(368\) 0 0
\(369\) −1.62763 −0.0847311
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 16.5757 0.858255 0.429128 0.903244i \(-0.358821\pi\)
0.429128 + 0.903244i \(0.358821\pi\)
\(374\) 0 0
\(375\) −33.1754 −1.71317
\(376\) 0 0
\(377\) 0.839790 0.0432514
\(378\) 0 0
\(379\) 20.3549 1.04556 0.522781 0.852467i \(-0.324895\pi\)
0.522781 + 0.852467i \(0.324895\pi\)
\(380\) 0 0
\(381\) 34.4001 1.76237
\(382\) 0 0
\(383\) −1.13617 −0.0580554 −0.0290277 0.999579i \(-0.509241\pi\)
−0.0290277 + 0.999579i \(0.509241\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −6.48975 −0.329893
\(388\) 0 0
\(389\) −34.8476 −1.76684 −0.883421 0.468580i \(-0.844766\pi\)
−0.883421 + 0.468580i \(0.844766\pi\)
\(390\) 0 0
\(391\) 3.40117 0.172005
\(392\) 0 0
\(393\) 11.2015 0.565042
\(394\) 0 0
\(395\) 22.5538 1.13480
\(396\) 0 0
\(397\) 35.0264 1.75792 0.878962 0.476892i \(-0.158237\pi\)
0.878962 + 0.476892i \(0.158237\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.52844 0.0763268 0.0381634 0.999272i \(-0.487849\pi\)
0.0381634 + 0.999272i \(0.487849\pi\)
\(402\) 0 0
\(403\) −4.89207 −0.243691
\(404\) 0 0
\(405\) 42.1917 2.09652
\(406\) 0 0
\(407\) −49.4745 −2.45236
\(408\) 0 0
\(409\) 27.0186 1.33599 0.667993 0.744168i \(-0.267154\pi\)
0.667993 + 0.744168i \(0.267154\pi\)
\(410\) 0 0
\(411\) 10.0388 0.495177
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 18.5424 0.910211
\(416\) 0 0
\(417\) 13.8991 0.680640
\(418\) 0 0
\(419\) 30.0427 1.46768 0.733841 0.679321i \(-0.237726\pi\)
0.733841 + 0.679321i \(0.237726\pi\)
\(420\) 0 0
\(421\) 7.97506 0.388681 0.194340 0.980934i \(-0.437743\pi\)
0.194340 + 0.980934i \(0.437743\pi\)
\(422\) 0 0
\(423\) 3.74029 0.181859
\(424\) 0 0
\(425\) 38.9157 1.88769
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 18.9743 0.916087
\(430\) 0 0
\(431\) 10.0717 0.485136 0.242568 0.970134i \(-0.422010\pi\)
0.242568 + 0.970134i \(0.422010\pi\)
\(432\) 0 0
\(433\) 19.6295 0.943332 0.471666 0.881777i \(-0.343653\pi\)
0.471666 + 0.881777i \(0.343653\pi\)
\(434\) 0 0
\(435\) −3.76610 −0.180571
\(436\) 0 0
\(437\) 4.23006 0.202351
\(438\) 0 0
\(439\) −19.3190 −0.922048 −0.461024 0.887388i \(-0.652518\pi\)
−0.461024 + 0.887388i \(0.652518\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −22.5851 −1.07305 −0.536526 0.843884i \(-0.680264\pi\)
−0.536526 + 0.843884i \(0.680264\pi\)
\(444\) 0 0
\(445\) −48.9549 −2.32068
\(446\) 0 0
\(447\) −15.9541 −0.754602
\(448\) 0 0
\(449\) 24.3860 1.15085 0.575424 0.817855i \(-0.304837\pi\)
0.575424 + 0.817855i \(0.304837\pi\)
\(450\) 0 0
\(451\) −4.89580 −0.230534
\(452\) 0 0
\(453\) 14.7981 0.695275
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 25.6503 1.19987 0.599935 0.800049i \(-0.295193\pi\)
0.599935 + 0.800049i \(0.295193\pi\)
\(458\) 0 0
\(459\) −12.6166 −0.588891
\(460\) 0 0
\(461\) −33.4123 −1.55617 −0.778084 0.628161i \(-0.783808\pi\)
−0.778084 + 0.628161i \(0.783808\pi\)
\(462\) 0 0
\(463\) 12.7774 0.593816 0.296908 0.954906i \(-0.404044\pi\)
0.296908 + 0.954906i \(0.404044\pi\)
\(464\) 0 0
\(465\) 21.9388 1.01739
\(466\) 0 0
\(467\) 29.1333 1.34813 0.674063 0.738674i \(-0.264547\pi\)
0.674063 + 0.738674i \(0.264547\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −30.0387 −1.38411
\(472\) 0 0
\(473\) −19.5207 −0.897563
\(474\) 0 0
\(475\) 48.3997 2.22073
\(476\) 0 0
\(477\) −1.87223 −0.0857236
\(478\) 0 0
\(479\) 32.5993 1.48950 0.744751 0.667343i \(-0.232568\pi\)
0.744751 + 0.667343i \(0.232568\pi\)
\(480\) 0 0
\(481\) −18.2062 −0.830133
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −45.3723 −2.06025
\(486\) 0 0
\(487\) −9.16540 −0.415324 −0.207662 0.978201i \(-0.566585\pi\)
−0.207662 + 0.978201i \(0.566585\pi\)
\(488\) 0 0
\(489\) 46.3947 2.09804
\(490\) 0 0
\(491\) 10.8127 0.487970 0.243985 0.969779i \(-0.421545\pi\)
0.243985 + 0.969779i \(0.421545\pi\)
\(492\) 0 0
\(493\) 1.99205 0.0897174
\(494\) 0 0
\(495\) −29.9284 −1.34518
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −41.0860 −1.83926 −0.919632 0.392782i \(-0.871513\pi\)
−0.919632 + 0.392782i \(0.871513\pi\)
\(500\) 0 0
\(501\) −28.5442 −1.27526
\(502\) 0 0
\(503\) 40.6226 1.81127 0.905637 0.424054i \(-0.139393\pi\)
0.905637 + 0.424054i \(0.139393\pi\)
\(504\) 0 0
\(505\) −62.2432 −2.76979
\(506\) 0 0
\(507\) −20.9831 −0.931893
\(508\) 0 0
\(509\) −11.0824 −0.491218 −0.245609 0.969369i \(-0.578988\pi\)
−0.245609 + 0.969369i \(0.578988\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −15.6913 −0.692788
\(514\) 0 0
\(515\) −12.4162 −0.547122
\(516\) 0 0
\(517\) 11.2505 0.494798
\(518\) 0 0
\(519\) −7.70699 −0.338299
\(520\) 0 0
\(521\) −5.97583 −0.261806 −0.130903 0.991395i \(-0.541788\pi\)
−0.130903 + 0.991395i \(0.541788\pi\)
\(522\) 0 0
\(523\) 35.8554 1.56785 0.783925 0.620856i \(-0.213215\pi\)
0.783925 + 0.620856i \(0.213215\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −11.6044 −0.505494
\(528\) 0 0
\(529\) −22.3666 −0.972461
\(530\) 0 0
\(531\) 11.1855 0.485410
\(532\) 0 0
\(533\) −1.80162 −0.0780367
\(534\) 0 0
\(535\) −24.9486 −1.07862
\(536\) 0 0
\(537\) −1.46845 −0.0633684
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 43.4848 1.86956 0.934780 0.355228i \(-0.115597\pi\)
0.934780 + 0.355228i \(0.115597\pi\)
\(542\) 0 0
\(543\) 13.3510 0.572946
\(544\) 0 0
\(545\) 9.98468 0.427697
\(546\) 0 0
\(547\) −20.0946 −0.859183 −0.429592 0.903023i \(-0.641342\pi\)
−0.429592 + 0.903023i \(0.641342\pi\)
\(548\) 0 0
\(549\) 14.6145 0.623732
\(550\) 0 0
\(551\) 2.47752 0.105546
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 81.6472 3.46573
\(556\) 0 0
\(557\) 10.9467 0.463826 0.231913 0.972736i \(-0.425501\pi\)
0.231913 + 0.972736i \(0.425501\pi\)
\(558\) 0 0
\(559\) −7.18347 −0.303828
\(560\) 0 0
\(561\) 45.0085 1.90026
\(562\) 0 0
\(563\) −12.1109 −0.510413 −0.255207 0.966887i \(-0.582144\pi\)
−0.255207 + 0.966887i \(0.582144\pi\)
\(564\) 0 0
\(565\) 17.2523 0.725810
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −31.9522 −1.33950 −0.669752 0.742584i \(-0.733600\pi\)
−0.669752 + 0.742584i \(0.733600\pi\)
\(570\) 0 0
\(571\) −18.7625 −0.785185 −0.392593 0.919712i \(-0.628422\pi\)
−0.392593 + 0.919712i \(0.628422\pi\)
\(572\) 0 0
\(573\) −34.2933 −1.43262
\(574\) 0 0
\(575\) 7.24721 0.302229
\(576\) 0 0
\(577\) −2.53985 −0.105736 −0.0528678 0.998602i \(-0.516836\pi\)
−0.0528678 + 0.998602i \(0.516836\pi\)
\(578\) 0 0
\(579\) 42.9679 1.78569
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −5.63154 −0.233235
\(584\) 0 0
\(585\) −11.0134 −0.455349
\(586\) 0 0
\(587\) −39.3984 −1.62615 −0.813073 0.582162i \(-0.802207\pi\)
−0.813073 + 0.582162i \(0.802207\pi\)
\(588\) 0 0
\(589\) −14.4324 −0.594678
\(590\) 0 0
\(591\) 18.2065 0.748914
\(592\) 0 0
\(593\) 19.8084 0.813434 0.406717 0.913554i \(-0.366674\pi\)
0.406717 + 0.913554i \(0.366674\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 57.6384 2.35898
\(598\) 0 0
\(599\) −8.58948 −0.350957 −0.175478 0.984483i \(-0.556147\pi\)
−0.175478 + 0.984483i \(0.556147\pi\)
\(600\) 0 0
\(601\) 23.9096 0.975295 0.487647 0.873041i \(-0.337855\pi\)
0.487647 + 0.873041i \(0.337855\pi\)
\(602\) 0 0
\(603\) −5.43028 −0.221138
\(604\) 0 0
\(605\) −48.7086 −1.98028
\(606\) 0 0
\(607\) −37.4089 −1.51838 −0.759190 0.650869i \(-0.774405\pi\)
−0.759190 + 0.650869i \(0.774405\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 4.14011 0.167491
\(612\) 0 0
\(613\) −42.5834 −1.71993 −0.859964 0.510355i \(-0.829514\pi\)
−0.859964 + 0.510355i \(0.829514\pi\)
\(614\) 0 0
\(615\) 8.07948 0.325796
\(616\) 0 0
\(617\) −20.0073 −0.805463 −0.402731 0.915318i \(-0.631939\pi\)
−0.402731 + 0.915318i \(0.631939\pi\)
\(618\) 0 0
\(619\) −36.3030 −1.45914 −0.729571 0.683905i \(-0.760280\pi\)
−0.729571 + 0.683905i \(0.760280\pi\)
\(620\) 0 0
\(621\) −2.34956 −0.0942847
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 12.3909 0.495637
\(626\) 0 0
\(627\) 55.9773 2.23552
\(628\) 0 0
\(629\) −43.1866 −1.72196
\(630\) 0 0
\(631\) 38.2166 1.52138 0.760690 0.649115i \(-0.224861\pi\)
0.760690 + 0.649115i \(0.224861\pi\)
\(632\) 0 0
\(633\) 21.2194 0.843395
\(634\) 0 0
\(635\) −60.0599 −2.38340
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 1.31916 0.0521853
\(640\) 0 0
\(641\) 3.65170 0.144233 0.0721167 0.997396i \(-0.477025\pi\)
0.0721167 + 0.997396i \(0.477025\pi\)
\(642\) 0 0
\(643\) −12.9103 −0.509132 −0.254566 0.967055i \(-0.581933\pi\)
−0.254566 + 0.967055i \(0.581933\pi\)
\(644\) 0 0
\(645\) 32.2148 1.26846
\(646\) 0 0
\(647\) 35.5774 1.39869 0.699345 0.714784i \(-0.253475\pi\)
0.699345 + 0.714784i \(0.253475\pi\)
\(648\) 0 0
\(649\) 33.6452 1.32069
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −25.3469 −0.991899 −0.495950 0.868351i \(-0.665180\pi\)
−0.495950 + 0.868351i \(0.665180\pi\)
\(654\) 0 0
\(655\) −19.5570 −0.764153
\(656\) 0 0
\(657\) −3.45928 −0.134959
\(658\) 0 0
\(659\) −14.6083 −0.569059 −0.284530 0.958667i \(-0.591837\pi\)
−0.284530 + 0.958667i \(0.591837\pi\)
\(660\) 0 0
\(661\) −23.5466 −0.915855 −0.457928 0.888989i \(-0.651408\pi\)
−0.457928 + 0.888989i \(0.651408\pi\)
\(662\) 0 0
\(663\) 16.5628 0.643245
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0.370976 0.0143642
\(668\) 0 0
\(669\) −61.5256 −2.37872
\(670\) 0 0
\(671\) 43.9594 1.69703
\(672\) 0 0
\(673\) 17.9476 0.691827 0.345914 0.938266i \(-0.387569\pi\)
0.345914 + 0.938266i \(0.387569\pi\)
\(674\) 0 0
\(675\) −26.8834 −1.03474
\(676\) 0 0
\(677\) −1.41360 −0.0543291 −0.0271645 0.999631i \(-0.508648\pi\)
−0.0271645 + 0.999631i \(0.508648\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −34.3124 −1.31485
\(682\) 0 0
\(683\) −26.7811 −1.02475 −0.512374 0.858762i \(-0.671234\pi\)
−0.512374 + 0.858762i \(0.671234\pi\)
\(684\) 0 0
\(685\) −17.5269 −0.669669
\(686\) 0 0
\(687\) 43.1821 1.64750
\(688\) 0 0
\(689\) −2.07236 −0.0789507
\(690\) 0 0
\(691\) −30.5061 −1.16050 −0.580252 0.814437i \(-0.697046\pi\)
−0.580252 + 0.814437i \(0.697046\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −24.2667 −0.920487
\(696\) 0 0
\(697\) −4.27358 −0.161873
\(698\) 0 0
\(699\) −60.4143 −2.28508
\(700\) 0 0
\(701\) 0.524271 0.0198014 0.00990072 0.999951i \(-0.496848\pi\)
0.00990072 + 0.999951i \(0.496848\pi\)
\(702\) 0 0
\(703\) −53.7115 −2.02577
\(704\) 0 0
\(705\) −18.5666 −0.699259
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −42.2384 −1.58630 −0.793148 0.609029i \(-0.791559\pi\)
−0.793148 + 0.609029i \(0.791559\pi\)
\(710\) 0 0
\(711\) −9.77399 −0.366553
\(712\) 0 0
\(713\) −2.16106 −0.0809324
\(714\) 0 0
\(715\) −33.1276 −1.23890
\(716\) 0 0
\(717\) 9.36330 0.349679
\(718\) 0 0
\(719\) −10.6669 −0.397807 −0.198904 0.980019i \(-0.563738\pi\)
−0.198904 + 0.980019i \(0.563738\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 43.1612 1.60518
\(724\) 0 0
\(725\) 4.24465 0.157643
\(726\) 0 0
\(727\) −23.1863 −0.859931 −0.429965 0.902845i \(-0.641474\pi\)
−0.429965 + 0.902845i \(0.641474\pi\)
\(728\) 0 0
\(729\) 0.768094 0.0284479
\(730\) 0 0
\(731\) −17.0398 −0.630238
\(732\) 0 0
\(733\) −0.143539 −0.00530173 −0.00265086 0.999996i \(-0.500844\pi\)
−0.00265086 + 0.999996i \(0.500844\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −16.3339 −0.601667
\(738\) 0 0
\(739\) 21.0099 0.772863 0.386431 0.922318i \(-0.373708\pi\)
0.386431 + 0.922318i \(0.373708\pi\)
\(740\) 0 0
\(741\) 20.5992 0.756732
\(742\) 0 0
\(743\) 5.99529 0.219946 0.109973 0.993935i \(-0.464924\pi\)
0.109973 + 0.993935i \(0.464924\pi\)
\(744\) 0 0
\(745\) 27.8546 1.02051
\(746\) 0 0
\(747\) −8.03560 −0.294007
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −25.5741 −0.933213 −0.466607 0.884465i \(-0.654524\pi\)
−0.466607 + 0.884465i \(0.654524\pi\)
\(752\) 0 0
\(753\) 31.5080 1.14822
\(754\) 0 0
\(755\) −25.8363 −0.940279
\(756\) 0 0
\(757\) −42.9799 −1.56213 −0.781066 0.624449i \(-0.785324\pi\)
−0.781066 + 0.624449i \(0.785324\pi\)
\(758\) 0 0
\(759\) 8.38185 0.304242
\(760\) 0 0
\(761\) 20.1201 0.729352 0.364676 0.931134i \(-0.381180\pi\)
0.364676 + 0.931134i \(0.381180\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −26.1247 −0.944541
\(766\) 0 0
\(767\) 12.3812 0.447058
\(768\) 0 0
\(769\) 5.03102 0.181423 0.0907116 0.995877i \(-0.471086\pi\)
0.0907116 + 0.995877i \(0.471086\pi\)
\(770\) 0 0
\(771\) −67.5196 −2.43166
\(772\) 0 0
\(773\) 13.5637 0.487851 0.243925 0.969794i \(-0.421565\pi\)
0.243925 + 0.969794i \(0.421565\pi\)
\(774\) 0 0
\(775\) −24.7266 −0.888205
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −5.31507 −0.190432
\(780\) 0 0
\(781\) 3.96795 0.141984
\(782\) 0 0
\(783\) −1.37613 −0.0491788
\(784\) 0 0
\(785\) 52.4452 1.87185
\(786\) 0 0
\(787\) 9.03110 0.321924 0.160962 0.986961i \(-0.448540\pi\)
0.160962 + 0.986961i \(0.448540\pi\)
\(788\) 0 0
\(789\) 13.4078 0.477331
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 16.1767 0.574452
\(794\) 0 0
\(795\) 9.29366 0.329612
\(796\) 0 0
\(797\) −5.18087 −0.183516 −0.0917579 0.995781i \(-0.529249\pi\)
−0.0917579 + 0.995781i \(0.529249\pi\)
\(798\) 0 0
\(799\) 9.82066 0.347430
\(800\) 0 0
\(801\) 21.2153 0.749605
\(802\) 0 0
\(803\) −10.4053 −0.367194
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −29.6297 −1.04302
\(808\) 0 0
\(809\) −44.1674 −1.55284 −0.776421 0.630214i \(-0.782967\pi\)
−0.776421 + 0.630214i \(0.782967\pi\)
\(810\) 0 0
\(811\) −34.6464 −1.21660 −0.608300 0.793707i \(-0.708148\pi\)
−0.608300 + 0.793707i \(0.708148\pi\)
\(812\) 0 0
\(813\) 52.7015 1.84832
\(814\) 0 0
\(815\) −81.0015 −2.83736
\(816\) 0 0
\(817\) −21.1925 −0.741430
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −39.0119 −1.36152 −0.680762 0.732505i \(-0.738351\pi\)
−0.680762 + 0.732505i \(0.738351\pi\)
\(822\) 0 0
\(823\) 18.9152 0.659343 0.329672 0.944096i \(-0.393062\pi\)
0.329672 + 0.944096i \(0.393062\pi\)
\(824\) 0 0
\(825\) 95.9040 3.33895
\(826\) 0 0
\(827\) −18.9323 −0.658339 −0.329169 0.944271i \(-0.606769\pi\)
−0.329169 + 0.944271i \(0.606769\pi\)
\(828\) 0 0
\(829\) −14.3111 −0.497046 −0.248523 0.968626i \(-0.579945\pi\)
−0.248523 + 0.968626i \(0.579945\pi\)
\(830\) 0 0
\(831\) 60.9936 2.11584
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 49.8360 1.72464
\(836\) 0 0
\(837\) 8.01642 0.277088
\(838\) 0 0
\(839\) −51.1176 −1.76478 −0.882388 0.470522i \(-0.844066\pi\)
−0.882388 + 0.470522i \(0.844066\pi\)
\(840\) 0 0
\(841\) −28.7827 −0.992508
\(842\) 0 0
\(843\) −35.9894 −1.23954
\(844\) 0 0
\(845\) 36.6349 1.26028
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 1.27418 0.0437298
\(850\) 0 0
\(851\) −8.04257 −0.275696
\(852\) 0 0
\(853\) 49.6010 1.69831 0.849153 0.528147i \(-0.177113\pi\)
0.849153 + 0.528147i \(0.177113\pi\)
\(854\) 0 0
\(855\) −32.4915 −1.11119
\(856\) 0 0
\(857\) −51.3659 −1.75463 −0.877313 0.479919i \(-0.840666\pi\)
−0.877313 + 0.479919i \(0.840666\pi\)
\(858\) 0 0
\(859\) 40.1818 1.37099 0.685493 0.728080i \(-0.259587\pi\)
0.685493 + 0.728080i \(0.259587\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −18.8413 −0.641367 −0.320683 0.947186i \(-0.603913\pi\)
−0.320683 + 0.947186i \(0.603913\pi\)
\(864\) 0 0
\(865\) 13.4558 0.457511
\(866\) 0 0
\(867\) 2.71792 0.0923056
\(868\) 0 0
\(869\) −29.3994 −0.997308
\(870\) 0 0
\(871\) −6.01075 −0.203666
\(872\) 0 0
\(873\) 19.6627 0.665482
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −6.08184 −0.205369 −0.102685 0.994714i \(-0.532743\pi\)
−0.102685 + 0.994714i \(0.532743\pi\)
\(878\) 0 0
\(879\) 18.2257 0.614738
\(880\) 0 0
\(881\) −38.8074 −1.30745 −0.653727 0.756731i \(-0.726795\pi\)
−0.653727 + 0.756731i \(0.726795\pi\)
\(882\) 0 0
\(883\) −43.4610 −1.46258 −0.731289 0.682068i \(-0.761081\pi\)
−0.731289 + 0.682068i \(0.761081\pi\)
\(884\) 0 0
\(885\) −55.5243 −1.86643
\(886\) 0 0
\(887\) 7.92458 0.266081 0.133041 0.991111i \(-0.457526\pi\)
0.133041 + 0.991111i \(0.457526\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −54.9980 −1.84250
\(892\) 0 0
\(893\) 12.2140 0.408727
\(894\) 0 0
\(895\) 2.56380 0.0856984
\(896\) 0 0
\(897\) 3.08446 0.102987
\(898\) 0 0
\(899\) −1.26572 −0.0422143
\(900\) 0 0
\(901\) −4.91581 −0.163769
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −23.3098 −0.774843
\(906\) 0 0
\(907\) 24.7983 0.823415 0.411707 0.911316i \(-0.364933\pi\)
0.411707 + 0.911316i \(0.364933\pi\)
\(908\) 0 0
\(909\) 26.9739 0.894669
\(910\) 0 0
\(911\) −19.4131 −0.643185 −0.321592 0.946878i \(-0.604218\pi\)
−0.321592 + 0.946878i \(0.604218\pi\)
\(912\) 0 0
\(913\) −24.1705 −0.799927
\(914\) 0 0
\(915\) −72.5456 −2.39828
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 16.6399 0.548898 0.274449 0.961602i \(-0.411505\pi\)
0.274449 + 0.961602i \(0.411505\pi\)
\(920\) 0 0
\(921\) 53.2395 1.75430
\(922\) 0 0
\(923\) 1.46017 0.0480622
\(924\) 0 0
\(925\) −92.0220 −3.02566
\(926\) 0 0
\(927\) 5.38072 0.176726
\(928\) 0 0
\(929\) 40.3751 1.32467 0.662333 0.749210i \(-0.269567\pi\)
0.662333 + 0.749210i \(0.269567\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 61.6236 2.01747
\(934\) 0 0
\(935\) −78.5812 −2.56988
\(936\) 0 0
\(937\) −31.0533 −1.01447 −0.507234 0.861809i \(-0.669332\pi\)
−0.507234 + 0.861809i \(0.669332\pi\)
\(938\) 0 0
\(939\) −15.4289 −0.503504
\(940\) 0 0
\(941\) 38.3305 1.24954 0.624769 0.780810i \(-0.285193\pi\)
0.624769 + 0.780810i \(0.285193\pi\)
\(942\) 0 0
\(943\) −0.795860 −0.0259168
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 4.77100 0.155037 0.0775183 0.996991i \(-0.475300\pi\)
0.0775183 + 0.996991i \(0.475300\pi\)
\(948\) 0 0
\(949\) −3.82906 −0.124297
\(950\) 0 0
\(951\) −68.5849 −2.22402
\(952\) 0 0
\(953\) −6.73083 −0.218033 −0.109016 0.994040i \(-0.534770\pi\)
−0.109016 + 0.994040i \(0.534770\pi\)
\(954\) 0 0
\(955\) 59.8734 1.93746
\(956\) 0 0
\(957\) 4.90921 0.158692
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −23.6267 −0.762152
\(962\) 0 0
\(963\) 10.8118 0.348406
\(964\) 0 0
\(965\) −75.0186 −2.41493
\(966\) 0 0
\(967\) −41.8582 −1.34607 −0.673034 0.739611i \(-0.735009\pi\)
−0.673034 + 0.739611i \(0.735009\pi\)
\(968\) 0 0
\(969\) 48.8630 1.56971
\(970\) 0 0
\(971\) 32.8108 1.05295 0.526475 0.850191i \(-0.323513\pi\)
0.526475 + 0.850191i \(0.323513\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 35.2919 1.13025
\(976\) 0 0
\(977\) 20.6724 0.661368 0.330684 0.943741i \(-0.392720\pi\)
0.330684 + 0.943741i \(0.392720\pi\)
\(978\) 0 0
\(979\) 63.8140 2.03950
\(980\) 0 0
\(981\) −4.32700 −0.138150
\(982\) 0 0
\(983\) −2.71927 −0.0867313 −0.0433657 0.999059i \(-0.513808\pi\)
−0.0433657 + 0.999059i \(0.513808\pi\)
\(984\) 0 0
\(985\) −31.7870 −1.01282
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −3.17328 −0.100905
\(990\) 0 0
\(991\) 8.32195 0.264356 0.132178 0.991226i \(-0.457803\pi\)
0.132178 + 0.991226i \(0.457803\pi\)
\(992\) 0 0
\(993\) 77.7664 2.46784
\(994\) 0 0
\(995\) −100.632 −3.19025
\(996\) 0 0
\(997\) −4.74009 −0.150120 −0.0750600 0.997179i \(-0.523915\pi\)
−0.0750600 + 0.997179i \(0.523915\pi\)
\(998\) 0 0
\(999\) 29.8338 0.943898
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 \(a_p\))