Properties

Label 8046.2.a.l.1.7
Level 8046
Weight 2
Character 8046.1
Self dual Yes
Analytic conductor 64.248
Analytic rank 0
Dimension 12
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8046 = 2 \cdot 3^{3} \cdot 149 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8046.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2476334663\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(1.06735\)
Character \(\chi\) = 8046.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+1.06735 q^{5}\) \(+2.41300 q^{7}\) \(-1.00000 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+1.06735 q^{5}\) \(+2.41300 q^{7}\) \(-1.00000 q^{8}\) \(-1.06735 q^{10}\) \(+2.87774 q^{11}\) \(+6.31805 q^{13}\) \(-2.41300 q^{14}\) \(+1.00000 q^{16}\) \(+5.80297 q^{17}\) \(+2.51725 q^{19}\) \(+1.06735 q^{20}\) \(-2.87774 q^{22}\) \(+4.87648 q^{23}\) \(-3.86076 q^{25}\) \(-6.31805 q^{26}\) \(+2.41300 q^{28}\) \(+5.18081 q^{29}\) \(-7.91286 q^{31}\) \(-1.00000 q^{32}\) \(-5.80297 q^{34}\) \(+2.57552 q^{35}\) \(-4.64638 q^{37}\) \(-2.51725 q^{38}\) \(-1.06735 q^{40}\) \(+10.6771 q^{41}\) \(+11.1447 q^{43}\) \(+2.87774 q^{44}\) \(-4.87648 q^{46}\) \(+8.19941 q^{47}\) \(-1.17744 q^{49}\) \(+3.86076 q^{50}\) \(+6.31805 q^{52}\) \(+6.76900 q^{53}\) \(+3.07157 q^{55}\) \(-2.41300 q^{56}\) \(-5.18081 q^{58}\) \(-6.78939 q^{59}\) \(-11.8514 q^{61}\) \(+7.91286 q^{62}\) \(+1.00000 q^{64}\) \(+6.74360 q^{65}\) \(+12.4327 q^{67}\) \(+5.80297 q^{68}\) \(-2.57552 q^{70}\) \(+3.88117 q^{71}\) \(-1.97024 q^{73}\) \(+4.64638 q^{74}\) \(+2.51725 q^{76}\) \(+6.94399 q^{77}\) \(+2.26625 q^{79}\) \(+1.06735 q^{80}\) \(-10.6771 q^{82}\) \(-2.68059 q^{83}\) \(+6.19382 q^{85}\) \(-11.1447 q^{86}\) \(-2.87774 q^{88}\) \(-12.9074 q^{89}\) \(+15.2455 q^{91}\) \(+4.87648 q^{92}\) \(-8.19941 q^{94}\) \(+2.68680 q^{95}\) \(+6.69563 q^{97}\) \(+1.17744 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 12q^{2} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 12q^{2} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut -\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 12q^{16} \) \(\mathstrut +\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 10q^{19} \) \(\mathstrut +\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 10q^{22} \) \(\mathstrut +\mathstrut 15q^{23} \) \(\mathstrut +\mathstrut 7q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 6q^{31} \) \(\mathstrut -\mathstrut 12q^{32} \) \(\mathstrut -\mathstrut 6q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 13q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut -\mathstrut 5q^{40} \) \(\mathstrut +\mathstrut 20q^{41} \) \(\mathstrut -\mathstrut 11q^{43} \) \(\mathstrut +\mathstrut 10q^{44} \) \(\mathstrut -\mathstrut 15q^{46} \) \(\mathstrut +\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 7q^{50} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 4q^{53} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut -\mathstrut 33q^{58} \) \(\mathstrut +\mathstrut 10q^{59} \) \(\mathstrut -\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 6q^{62} \) \(\mathstrut +\mathstrut 12q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 19q^{67} \) \(\mathstrut +\mathstrut 6q^{68} \) \(\mathstrut -\mathstrut 16q^{70} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 2q^{73} \) \(\mathstrut +\mathstrut 13q^{74} \) \(\mathstrut -\mathstrut 10q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut -\mathstrut 15q^{79} \) \(\mathstrut +\mathstrut 5q^{80} \) \(\mathstrut -\mathstrut 20q^{82} \) \(\mathstrut +\mathstrut 18q^{83} \) \(\mathstrut -\mathstrut 25q^{85} \) \(\mathstrut +\mathstrut 11q^{86} \) \(\mathstrut -\mathstrut 10q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut -\mathstrut 3q^{91} \) \(\mathstrut +\mathstrut 15q^{92} \) \(\mathstrut -\mathstrut 15q^{94} \) \(\mathstrut -\mathstrut 3q^{95} \) \(\mathstrut -\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 1.06735 0.477335 0.238668 0.971101i \(-0.423289\pi\)
0.238668 + 0.971101i \(0.423289\pi\)
\(6\) 0 0
\(7\) 2.41300 0.912028 0.456014 0.889973i \(-0.349277\pi\)
0.456014 + 0.889973i \(0.349277\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.06735 −0.337527
\(11\) 2.87774 0.867672 0.433836 0.900992i \(-0.357160\pi\)
0.433836 + 0.900992i \(0.357160\pi\)
\(12\) 0 0
\(13\) 6.31805 1.75231 0.876156 0.482027i \(-0.160099\pi\)
0.876156 + 0.482027i \(0.160099\pi\)
\(14\) −2.41300 −0.644901
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 5.80297 1.40743 0.703714 0.710484i \(-0.251524\pi\)
0.703714 + 0.710484i \(0.251524\pi\)
\(18\) 0 0
\(19\) 2.51725 0.577498 0.288749 0.957405i \(-0.406761\pi\)
0.288749 + 0.957405i \(0.406761\pi\)
\(20\) 1.06735 0.238668
\(21\) 0 0
\(22\) −2.87774 −0.613537
\(23\) 4.87648 1.01682 0.508408 0.861116i \(-0.330234\pi\)
0.508408 + 0.861116i \(0.330234\pi\)
\(24\) 0 0
\(25\) −3.86076 −0.772151
\(26\) −6.31805 −1.23907
\(27\) 0 0
\(28\) 2.41300 0.456014
\(29\) 5.18081 0.962052 0.481026 0.876706i \(-0.340264\pi\)
0.481026 + 0.876706i \(0.340264\pi\)
\(30\) 0 0
\(31\) −7.91286 −1.42119 −0.710596 0.703600i \(-0.751575\pi\)
−0.710596 + 0.703600i \(0.751575\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −5.80297 −0.995201
\(35\) 2.57552 0.435343
\(36\) 0 0
\(37\) −4.64638 −0.763860 −0.381930 0.924191i \(-0.624740\pi\)
−0.381930 + 0.924191i \(0.624740\pi\)
\(38\) −2.51725 −0.408353
\(39\) 0 0
\(40\) −1.06735 −0.168763
\(41\) 10.6771 1.66749 0.833744 0.552152i \(-0.186193\pi\)
0.833744 + 0.552152i \(0.186193\pi\)
\(42\) 0 0
\(43\) 11.1447 1.69955 0.849776 0.527144i \(-0.176737\pi\)
0.849776 + 0.527144i \(0.176737\pi\)
\(44\) 2.87774 0.433836
\(45\) 0 0
\(46\) −4.87648 −0.718998
\(47\) 8.19941 1.19601 0.598004 0.801493i \(-0.295961\pi\)
0.598004 + 0.801493i \(0.295961\pi\)
\(48\) 0 0
\(49\) −1.17744 −0.168206
\(50\) 3.86076 0.545993
\(51\) 0 0
\(52\) 6.31805 0.876156
\(53\) 6.76900 0.929794 0.464897 0.885365i \(-0.346091\pi\)
0.464897 + 0.885365i \(0.346091\pi\)
\(54\) 0 0
\(55\) 3.07157 0.414170
\(56\) −2.41300 −0.322450
\(57\) 0 0
\(58\) −5.18081 −0.680274
\(59\) −6.78939 −0.883903 −0.441951 0.897039i \(-0.645714\pi\)
−0.441951 + 0.897039i \(0.645714\pi\)
\(60\) 0 0
\(61\) −11.8514 −1.51742 −0.758711 0.651428i \(-0.774170\pi\)
−0.758711 + 0.651428i \(0.774170\pi\)
\(62\) 7.91286 1.00493
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 6.74360 0.836440
\(66\) 0 0
\(67\) 12.4327 1.51890 0.759448 0.650568i \(-0.225469\pi\)
0.759448 + 0.650568i \(0.225469\pi\)
\(68\) 5.80297 0.703714
\(69\) 0 0
\(70\) −2.57552 −0.307834
\(71\) 3.88117 0.460610 0.230305 0.973118i \(-0.426028\pi\)
0.230305 + 0.973118i \(0.426028\pi\)
\(72\) 0 0
\(73\) −1.97024 −0.230599 −0.115299 0.993331i \(-0.536783\pi\)
−0.115299 + 0.993331i \(0.536783\pi\)
\(74\) 4.64638 0.540130
\(75\) 0 0
\(76\) 2.51725 0.288749
\(77\) 6.94399 0.791341
\(78\) 0 0
\(79\) 2.26625 0.254973 0.127487 0.991840i \(-0.459309\pi\)
0.127487 + 0.991840i \(0.459309\pi\)
\(80\) 1.06735 0.119334
\(81\) 0 0
\(82\) −10.6771 −1.17909
\(83\) −2.68059 −0.294233 −0.147117 0.989119i \(-0.546999\pi\)
−0.147117 + 0.989119i \(0.546999\pi\)
\(84\) 0 0
\(85\) 6.19382 0.671814
\(86\) −11.1447 −1.20176
\(87\) 0 0
\(88\) −2.87774 −0.306768
\(89\) −12.9074 −1.36818 −0.684091 0.729397i \(-0.739801\pi\)
−0.684091 + 0.729397i \(0.739801\pi\)
\(90\) 0 0
\(91\) 15.2455 1.59816
\(92\) 4.87648 0.508408
\(93\) 0 0
\(94\) −8.19941 −0.845705
\(95\) 2.68680 0.275660
\(96\) 0 0
\(97\) 6.69563 0.679839 0.339919 0.940455i \(-0.389600\pi\)
0.339919 + 0.940455i \(0.389600\pi\)
\(98\) 1.17744 0.118939
\(99\) 0 0
\(100\) −3.86076 −0.386076
\(101\) −9.08647 −0.904137 −0.452069 0.891983i \(-0.649314\pi\)
−0.452069 + 0.891983i \(0.649314\pi\)
\(102\) 0 0
\(103\) −12.3461 −1.21650 −0.608251 0.793745i \(-0.708129\pi\)
−0.608251 + 0.793745i \(0.708129\pi\)
\(104\) −6.31805 −0.619536
\(105\) 0 0
\(106\) −6.76900 −0.657464
\(107\) −4.76521 −0.460670 −0.230335 0.973111i \(-0.573982\pi\)
−0.230335 + 0.973111i \(0.573982\pi\)
\(108\) 0 0
\(109\) −5.74157 −0.549943 −0.274971 0.961452i \(-0.588668\pi\)
−0.274971 + 0.961452i \(0.588668\pi\)
\(110\) −3.07157 −0.292863
\(111\) 0 0
\(112\) 2.41300 0.228007
\(113\) 13.1555 1.23756 0.618781 0.785563i \(-0.287627\pi\)
0.618781 + 0.785563i \(0.287627\pi\)
\(114\) 0 0
\(115\) 5.20493 0.485362
\(116\) 5.18081 0.481026
\(117\) 0 0
\(118\) 6.78939 0.625014
\(119\) 14.0026 1.28361
\(120\) 0 0
\(121\) −2.71860 −0.247145
\(122\) 11.8514 1.07298
\(123\) 0 0
\(124\) −7.91286 −0.710596
\(125\) −9.45756 −0.845910
\(126\) 0 0
\(127\) 3.03628 0.269426 0.134713 0.990885i \(-0.456989\pi\)
0.134713 + 0.990885i \(0.456989\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) −6.74360 −0.591453
\(131\) −20.9274 −1.82843 −0.914217 0.405226i \(-0.867193\pi\)
−0.914217 + 0.405226i \(0.867193\pi\)
\(132\) 0 0
\(133\) 6.07413 0.526694
\(134\) −12.4327 −1.07402
\(135\) 0 0
\(136\) −5.80297 −0.497601
\(137\) −5.40932 −0.462150 −0.231075 0.972936i \(-0.574224\pi\)
−0.231075 + 0.972936i \(0.574224\pi\)
\(138\) 0 0
\(139\) −11.5243 −0.977475 −0.488738 0.872431i \(-0.662542\pi\)
−0.488738 + 0.872431i \(0.662542\pi\)
\(140\) 2.57552 0.217671
\(141\) 0 0
\(142\) −3.88117 −0.325701
\(143\) 18.1817 1.52043
\(144\) 0 0
\(145\) 5.52976 0.459221
\(146\) 1.97024 0.163058
\(147\) 0 0
\(148\) −4.64638 −0.381930
\(149\) 1.00000 0.0819232
\(150\) 0 0
\(151\) −18.4343 −1.50016 −0.750080 0.661347i \(-0.769985\pi\)
−0.750080 + 0.661347i \(0.769985\pi\)
\(152\) −2.51725 −0.204176
\(153\) 0 0
\(154\) −6.94399 −0.559562
\(155\) −8.44582 −0.678385
\(156\) 0 0
\(157\) −18.8174 −1.50179 −0.750896 0.660421i \(-0.770378\pi\)
−0.750896 + 0.660421i \(0.770378\pi\)
\(158\) −2.26625 −0.180293
\(159\) 0 0
\(160\) −1.06735 −0.0843817
\(161\) 11.7669 0.927365
\(162\) 0 0
\(163\) −18.6680 −1.46219 −0.731097 0.682273i \(-0.760991\pi\)
−0.731097 + 0.682273i \(0.760991\pi\)
\(164\) 10.6771 0.833744
\(165\) 0 0
\(166\) 2.68059 0.208054
\(167\) −10.7650 −0.833017 −0.416509 0.909132i \(-0.636746\pi\)
−0.416509 + 0.909132i \(0.636746\pi\)
\(168\) 0 0
\(169\) 26.9178 2.07060
\(170\) −6.19382 −0.475045
\(171\) 0 0
\(172\) 11.1447 0.849776
\(173\) −14.3128 −1.08818 −0.544092 0.839025i \(-0.683126\pi\)
−0.544092 + 0.839025i \(0.683126\pi\)
\(174\) 0 0
\(175\) −9.31600 −0.704223
\(176\) 2.87774 0.216918
\(177\) 0 0
\(178\) 12.9074 0.967451
\(179\) −14.8159 −1.10739 −0.553696 0.832719i \(-0.686783\pi\)
−0.553696 + 0.832719i \(0.686783\pi\)
\(180\) 0 0
\(181\) 12.4854 0.928030 0.464015 0.885827i \(-0.346408\pi\)
0.464015 + 0.885827i \(0.346408\pi\)
\(182\) −15.2455 −1.13007
\(183\) 0 0
\(184\) −4.87648 −0.359499
\(185\) −4.95933 −0.364617
\(186\) 0 0
\(187\) 16.6995 1.22119
\(188\) 8.19941 0.598004
\(189\) 0 0
\(190\) −2.68680 −0.194921
\(191\) 0.208714 0.0151020 0.00755100 0.999971i \(-0.497596\pi\)
0.00755100 + 0.999971i \(0.497596\pi\)
\(192\) 0 0
\(193\) 20.4582 1.47261 0.736307 0.676648i \(-0.236568\pi\)
0.736307 + 0.676648i \(0.236568\pi\)
\(194\) −6.69563 −0.480718
\(195\) 0 0
\(196\) −1.17744 −0.0841028
\(197\) 24.9769 1.77953 0.889765 0.456419i \(-0.150868\pi\)
0.889765 + 0.456419i \(0.150868\pi\)
\(198\) 0 0
\(199\) −18.3928 −1.30383 −0.651916 0.758291i \(-0.726035\pi\)
−0.651916 + 0.758291i \(0.726035\pi\)
\(200\) 3.86076 0.272997
\(201\) 0 0
\(202\) 9.08647 0.639322
\(203\) 12.5013 0.877418
\(204\) 0 0
\(205\) 11.3963 0.795950
\(206\) 12.3461 0.860197
\(207\) 0 0
\(208\) 6.31805 0.438078
\(209\) 7.24401 0.501079
\(210\) 0 0
\(211\) −5.11885 −0.352396 −0.176198 0.984355i \(-0.556380\pi\)
−0.176198 + 0.984355i \(0.556380\pi\)
\(212\) 6.76900 0.464897
\(213\) 0 0
\(214\) 4.76521 0.325743
\(215\) 11.8953 0.811256
\(216\) 0 0
\(217\) −19.0937 −1.29617
\(218\) 5.74157 0.388868
\(219\) 0 0
\(220\) 3.07157 0.207085
\(221\) 36.6635 2.46625
\(222\) 0 0
\(223\) −24.0494 −1.61047 −0.805233 0.592958i \(-0.797960\pi\)
−0.805233 + 0.592958i \(0.797960\pi\)
\(224\) −2.41300 −0.161225
\(225\) 0 0
\(226\) −13.1555 −0.875089
\(227\) 16.4469 1.09162 0.545809 0.837910i \(-0.316223\pi\)
0.545809 + 0.837910i \(0.316223\pi\)
\(228\) 0 0
\(229\) 3.67491 0.242845 0.121423 0.992601i \(-0.461254\pi\)
0.121423 + 0.992601i \(0.461254\pi\)
\(230\) −5.20493 −0.343203
\(231\) 0 0
\(232\) −5.18081 −0.340137
\(233\) −1.22524 −0.0802679 −0.0401340 0.999194i \(-0.512778\pi\)
−0.0401340 + 0.999194i \(0.512778\pi\)
\(234\) 0 0
\(235\) 8.75167 0.570896
\(236\) −6.78939 −0.441951
\(237\) 0 0
\(238\) −14.0026 −0.907651
\(239\) −19.6354 −1.27011 −0.635055 0.772467i \(-0.719022\pi\)
−0.635055 + 0.772467i \(0.719022\pi\)
\(240\) 0 0
\(241\) −21.6153 −1.39237 −0.696183 0.717865i \(-0.745120\pi\)
−0.696183 + 0.717865i \(0.745120\pi\)
\(242\) 2.71860 0.174758
\(243\) 0 0
\(244\) −11.8514 −0.758711
\(245\) −1.25674 −0.0802904
\(246\) 0 0
\(247\) 15.9041 1.01196
\(248\) 7.91286 0.502467
\(249\) 0 0
\(250\) 9.45756 0.598149
\(251\) 22.9313 1.44741 0.723704 0.690110i \(-0.242438\pi\)
0.723704 + 0.690110i \(0.242438\pi\)
\(252\) 0 0
\(253\) 14.0333 0.882263
\(254\) −3.03628 −0.190513
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −13.7438 −0.857313 −0.428656 0.903468i \(-0.641013\pi\)
−0.428656 + 0.903468i \(0.641013\pi\)
\(258\) 0 0
\(259\) −11.2117 −0.696661
\(260\) 6.74360 0.418220
\(261\) 0 0
\(262\) 20.9274 1.29290
\(263\) 3.02740 0.186678 0.0933388 0.995634i \(-0.470246\pi\)
0.0933388 + 0.995634i \(0.470246\pi\)
\(264\) 0 0
\(265\) 7.22492 0.443823
\(266\) −6.07413 −0.372429
\(267\) 0 0
\(268\) 12.4327 0.759448
\(269\) −30.7276 −1.87350 −0.936748 0.350005i \(-0.886180\pi\)
−0.936748 + 0.350005i \(0.886180\pi\)
\(270\) 0 0
\(271\) −12.7435 −0.774111 −0.387056 0.922056i \(-0.626508\pi\)
−0.387056 + 0.922056i \(0.626508\pi\)
\(272\) 5.80297 0.351857
\(273\) 0 0
\(274\) 5.40932 0.326789
\(275\) −11.1103 −0.669974
\(276\) 0 0
\(277\) 10.0878 0.606117 0.303059 0.952972i \(-0.401992\pi\)
0.303059 + 0.952972i \(0.401992\pi\)
\(278\) 11.5243 0.691179
\(279\) 0 0
\(280\) −2.57552 −0.153917
\(281\) 20.1407 1.20149 0.600746 0.799440i \(-0.294870\pi\)
0.600746 + 0.799440i \(0.294870\pi\)
\(282\) 0 0
\(283\) −9.42116 −0.560030 −0.280015 0.959996i \(-0.590339\pi\)
−0.280015 + 0.959996i \(0.590339\pi\)
\(284\) 3.88117 0.230305
\(285\) 0 0
\(286\) −18.1817 −1.07511
\(287\) 25.7639 1.52079
\(288\) 0 0
\(289\) 16.6745 0.980852
\(290\) −5.52976 −0.324718
\(291\) 0 0
\(292\) −1.97024 −0.115299
\(293\) −9.52070 −0.556205 −0.278103 0.960551i \(-0.589706\pi\)
−0.278103 + 0.960551i \(0.589706\pi\)
\(294\) 0 0
\(295\) −7.24668 −0.421918
\(296\) 4.64638 0.270065
\(297\) 0 0
\(298\) −1.00000 −0.0579284
\(299\) 30.8099 1.78178
\(300\) 0 0
\(301\) 26.8922 1.55004
\(302\) 18.4343 1.06077
\(303\) 0 0
\(304\) 2.51725 0.144374
\(305\) −12.6497 −0.724318
\(306\) 0 0
\(307\) 4.01472 0.229132 0.114566 0.993416i \(-0.463452\pi\)
0.114566 + 0.993416i \(0.463452\pi\)
\(308\) 6.94399 0.395670
\(309\) 0 0
\(310\) 8.44582 0.479690
\(311\) 12.5289 0.710450 0.355225 0.934781i \(-0.384404\pi\)
0.355225 + 0.934781i \(0.384404\pi\)
\(312\) 0 0
\(313\) −17.9628 −1.01532 −0.507660 0.861558i \(-0.669489\pi\)
−0.507660 + 0.861558i \(0.669489\pi\)
\(314\) 18.8174 1.06193
\(315\) 0 0
\(316\) 2.26625 0.127487
\(317\) −0.635891 −0.0357152 −0.0178576 0.999841i \(-0.505685\pi\)
−0.0178576 + 0.999841i \(0.505685\pi\)
\(318\) 0 0
\(319\) 14.9090 0.834746
\(320\) 1.06735 0.0596669
\(321\) 0 0
\(322\) −11.7669 −0.655746
\(323\) 14.6076 0.812786
\(324\) 0 0
\(325\) −24.3925 −1.35305
\(326\) 18.6680 1.03393
\(327\) 0 0
\(328\) −10.6771 −0.589546
\(329\) 19.7852 1.09079
\(330\) 0 0
\(331\) −3.11325 −0.171120 −0.0855599 0.996333i \(-0.527268\pi\)
−0.0855599 + 0.996333i \(0.527268\pi\)
\(332\) −2.68059 −0.147117
\(333\) 0 0
\(334\) 10.7650 0.589032
\(335\) 13.2701 0.725022
\(336\) 0 0
\(337\) −33.9883 −1.85146 −0.925731 0.378182i \(-0.876549\pi\)
−0.925731 + 0.378182i \(0.876549\pi\)
\(338\) −26.9178 −1.46413
\(339\) 0 0
\(340\) 6.19382 0.335907
\(341\) −22.7712 −1.23313
\(342\) 0 0
\(343\) −19.7321 −1.06544
\(344\) −11.1447 −0.600882
\(345\) 0 0
\(346\) 14.3128 0.769463
\(347\) −25.5691 −1.37262 −0.686309 0.727310i \(-0.740770\pi\)
−0.686309 + 0.727310i \(0.740770\pi\)
\(348\) 0 0
\(349\) −6.64078 −0.355473 −0.177736 0.984078i \(-0.556877\pi\)
−0.177736 + 0.984078i \(0.556877\pi\)
\(350\) 9.31600 0.497961
\(351\) 0 0
\(352\) −2.87774 −0.153384
\(353\) −4.63793 −0.246852 −0.123426 0.992354i \(-0.539388\pi\)
−0.123426 + 0.992354i \(0.539388\pi\)
\(354\) 0 0
\(355\) 4.14258 0.219866
\(356\) −12.9074 −0.684091
\(357\) 0 0
\(358\) 14.8159 0.783045
\(359\) −14.7744 −0.779761 −0.389881 0.920865i \(-0.627484\pi\)
−0.389881 + 0.920865i \(0.627484\pi\)
\(360\) 0 0
\(361\) −12.6634 −0.666496
\(362\) −12.4854 −0.656216
\(363\) 0 0
\(364\) 15.2455 0.799079
\(365\) −2.10294 −0.110073
\(366\) 0 0
\(367\) 6.92697 0.361585 0.180792 0.983521i \(-0.442134\pi\)
0.180792 + 0.983521i \(0.442134\pi\)
\(368\) 4.87648 0.254204
\(369\) 0 0
\(370\) 4.95933 0.257823
\(371\) 16.3336 0.847998
\(372\) 0 0
\(373\) 7.15412 0.370426 0.185213 0.982698i \(-0.440702\pi\)
0.185213 + 0.982698i \(0.440702\pi\)
\(374\) −16.6995 −0.863508
\(375\) 0 0
\(376\) −8.19941 −0.422853
\(377\) 32.7326 1.68582
\(378\) 0 0
\(379\) 25.6854 1.31937 0.659684 0.751543i \(-0.270690\pi\)
0.659684 + 0.751543i \(0.270690\pi\)
\(380\) 2.68680 0.137830
\(381\) 0 0
\(382\) −0.208714 −0.0106787
\(383\) −23.5765 −1.20471 −0.602353 0.798230i \(-0.705770\pi\)
−0.602353 + 0.798230i \(0.705770\pi\)
\(384\) 0 0
\(385\) 7.41169 0.377735
\(386\) −20.4582 −1.04130
\(387\) 0 0
\(388\) 6.69563 0.339919
\(389\) 16.7592 0.849724 0.424862 0.905258i \(-0.360323\pi\)
0.424862 + 0.905258i \(0.360323\pi\)
\(390\) 0 0
\(391\) 28.2981 1.43110
\(392\) 1.17744 0.0594697
\(393\) 0 0
\(394\) −24.9769 −1.25832
\(395\) 2.41889 0.121708
\(396\) 0 0
\(397\) −5.12235 −0.257083 −0.128542 0.991704i \(-0.541030\pi\)
−0.128542 + 0.991704i \(0.541030\pi\)
\(398\) 18.3928 0.921949
\(399\) 0 0
\(400\) −3.86076 −0.193038
\(401\) −19.0659 −0.952106 −0.476053 0.879417i \(-0.657933\pi\)
−0.476053 + 0.879417i \(0.657933\pi\)
\(402\) 0 0
\(403\) −49.9939 −2.49037
\(404\) −9.08647 −0.452069
\(405\) 0 0
\(406\) −12.5013 −0.620428
\(407\) −13.3711 −0.662780
\(408\) 0 0
\(409\) 15.0451 0.743933 0.371966 0.928246i \(-0.378684\pi\)
0.371966 + 0.928246i \(0.378684\pi\)
\(410\) −11.3963 −0.562822
\(411\) 0 0
\(412\) −12.3461 −0.608251
\(413\) −16.3828 −0.806144
\(414\) 0 0
\(415\) −2.86114 −0.140448
\(416\) −6.31805 −0.309768
\(417\) 0 0
\(418\) −7.24401 −0.354316
\(419\) −12.6427 −0.617637 −0.308818 0.951121i \(-0.599934\pi\)
−0.308818 + 0.951121i \(0.599934\pi\)
\(420\) 0 0
\(421\) −8.70185 −0.424102 −0.212051 0.977259i \(-0.568014\pi\)
−0.212051 + 0.977259i \(0.568014\pi\)
\(422\) 5.11885 0.249182
\(423\) 0 0
\(424\) −6.76900 −0.328732
\(425\) −22.4039 −1.08675
\(426\) 0 0
\(427\) −28.5975 −1.38393
\(428\) −4.76521 −0.230335
\(429\) 0 0
\(430\) −11.8953 −0.573644
\(431\) 13.9905 0.673897 0.336948 0.941523i \(-0.390605\pi\)
0.336948 + 0.941523i \(0.390605\pi\)
\(432\) 0 0
\(433\) 23.4355 1.12624 0.563120 0.826375i \(-0.309601\pi\)
0.563120 + 0.826375i \(0.309601\pi\)
\(434\) 19.0937 0.916528
\(435\) 0 0
\(436\) −5.74157 −0.274971
\(437\) 12.2753 0.587209
\(438\) 0 0
\(439\) −17.3808 −0.829540 −0.414770 0.909926i \(-0.636138\pi\)
−0.414770 + 0.909926i \(0.636138\pi\)
\(440\) −3.07157 −0.146431
\(441\) 0 0
\(442\) −36.6635 −1.74390
\(443\) 14.3666 0.682579 0.341290 0.939958i \(-0.389136\pi\)
0.341290 + 0.939958i \(0.389136\pi\)
\(444\) 0 0
\(445\) −13.7768 −0.653081
\(446\) 24.0494 1.13877
\(447\) 0 0
\(448\) 2.41300 0.114003
\(449\) −4.35069 −0.205322 −0.102661 0.994716i \(-0.532736\pi\)
−0.102661 + 0.994716i \(0.532736\pi\)
\(450\) 0 0
\(451\) 30.7260 1.44683
\(452\) 13.1555 0.618781
\(453\) 0 0
\(454\) −16.4469 −0.771890
\(455\) 16.2723 0.762857
\(456\) 0 0
\(457\) −28.9116 −1.35243 −0.676214 0.736705i \(-0.736380\pi\)
−0.676214 + 0.736705i \(0.736380\pi\)
\(458\) −3.67491 −0.171717
\(459\) 0 0
\(460\) 5.20493 0.242681
\(461\) −3.48477 −0.162302 −0.0811509 0.996702i \(-0.525860\pi\)
−0.0811509 + 0.996702i \(0.525860\pi\)
\(462\) 0 0
\(463\) −17.3353 −0.805640 −0.402820 0.915279i \(-0.631970\pi\)
−0.402820 + 0.915279i \(0.631970\pi\)
\(464\) 5.18081 0.240513
\(465\) 0 0
\(466\) 1.22524 0.0567580
\(467\) 21.8269 1.01003 0.505013 0.863111i \(-0.331488\pi\)
0.505013 + 0.863111i \(0.331488\pi\)
\(468\) 0 0
\(469\) 30.0001 1.38527
\(470\) −8.75167 −0.403685
\(471\) 0 0
\(472\) 6.78939 0.312507
\(473\) 32.0716 1.47465
\(474\) 0 0
\(475\) −9.71850 −0.445916
\(476\) 14.0026 0.641806
\(477\) 0 0
\(478\) 19.6354 0.898103
\(479\) −32.2298 −1.47262 −0.736308 0.676647i \(-0.763433\pi\)
−0.736308 + 0.676647i \(0.763433\pi\)
\(480\) 0 0
\(481\) −29.3561 −1.33852
\(482\) 21.6153 0.984551
\(483\) 0 0
\(484\) −2.71860 −0.123573
\(485\) 7.14661 0.324511
\(486\) 0 0
\(487\) 36.3486 1.64711 0.823556 0.567235i \(-0.191987\pi\)
0.823556 + 0.567235i \(0.191987\pi\)
\(488\) 11.8514 0.536489
\(489\) 0 0
\(490\) 1.25674 0.0567739
\(491\) −6.27108 −0.283010 −0.141505 0.989938i \(-0.545194\pi\)
−0.141505 + 0.989938i \(0.545194\pi\)
\(492\) 0 0
\(493\) 30.0641 1.35402
\(494\) −15.9041 −0.715561
\(495\) 0 0
\(496\) −7.91286 −0.355298
\(497\) 9.36526 0.420089
\(498\) 0 0
\(499\) 31.2490 1.39890 0.699449 0.714683i \(-0.253429\pi\)
0.699449 + 0.714683i \(0.253429\pi\)
\(500\) −9.45756 −0.422955
\(501\) 0 0
\(502\) −22.9313 −1.02347
\(503\) 7.83456 0.349326 0.174663 0.984628i \(-0.444116\pi\)
0.174663 + 0.984628i \(0.444116\pi\)
\(504\) 0 0
\(505\) −9.69847 −0.431576
\(506\) −14.0333 −0.623854
\(507\) 0 0
\(508\) 3.03628 0.134713
\(509\) −13.6569 −0.605331 −0.302665 0.953097i \(-0.597876\pi\)
−0.302665 + 0.953097i \(0.597876\pi\)
\(510\) 0 0
\(511\) −4.75418 −0.210312
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 13.7438 0.606212
\(515\) −13.1777 −0.580679
\(516\) 0 0
\(517\) 23.5958 1.03774
\(518\) 11.2117 0.492614
\(519\) 0 0
\(520\) −6.74360 −0.295726
\(521\) 21.5222 0.942903 0.471452 0.881892i \(-0.343730\pi\)
0.471452 + 0.881892i \(0.343730\pi\)
\(522\) 0 0
\(523\) 17.3077 0.756815 0.378407 0.925639i \(-0.376472\pi\)
0.378407 + 0.925639i \(0.376472\pi\)
\(524\) −20.9274 −0.914217
\(525\) 0 0
\(526\) −3.02740 −0.132001
\(527\) −45.9181 −2.00022
\(528\) 0 0
\(529\) 0.780061 0.0339157
\(530\) −7.22492 −0.313831
\(531\) 0 0
\(532\) 6.07413 0.263347
\(533\) 67.4587 2.92196
\(534\) 0 0
\(535\) −5.08617 −0.219894
\(536\) −12.4327 −0.537011
\(537\) 0 0
\(538\) 30.7276 1.32476
\(539\) −3.38837 −0.145947
\(540\) 0 0
\(541\) 34.3916 1.47861 0.739306 0.673370i \(-0.235154\pi\)
0.739306 + 0.673370i \(0.235154\pi\)
\(542\) 12.7435 0.547379
\(543\) 0 0
\(544\) −5.80297 −0.248800
\(545\) −6.12829 −0.262507
\(546\) 0 0
\(547\) −1.48789 −0.0636177 −0.0318089 0.999494i \(-0.510127\pi\)
−0.0318089 + 0.999494i \(0.510127\pi\)
\(548\) −5.40932 −0.231075
\(549\) 0 0
\(550\) 11.1103 0.473743
\(551\) 13.0414 0.555583
\(552\) 0 0
\(553\) 5.46846 0.232543
\(554\) −10.0878 −0.428590
\(555\) 0 0
\(556\) −11.5243 −0.488738
\(557\) 27.4929 1.16491 0.582457 0.812862i \(-0.302092\pi\)
0.582457 + 0.812862i \(0.302092\pi\)
\(558\) 0 0
\(559\) 70.4128 2.97815
\(560\) 2.57552 0.108836
\(561\) 0 0
\(562\) −20.1407 −0.849584
\(563\) −1.46719 −0.0618345 −0.0309173 0.999522i \(-0.509843\pi\)
−0.0309173 + 0.999522i \(0.509843\pi\)
\(564\) 0 0
\(565\) 14.0415 0.590732
\(566\) 9.42116 0.396001
\(567\) 0 0
\(568\) −3.88117 −0.162850
\(569\) −34.4730 −1.44518 −0.722592 0.691274i \(-0.757050\pi\)
−0.722592 + 0.691274i \(0.757050\pi\)
\(570\) 0 0
\(571\) 46.4755 1.94494 0.972470 0.233028i \(-0.0748633\pi\)
0.972470 + 0.233028i \(0.0748633\pi\)
\(572\) 18.1817 0.760216
\(573\) 0 0
\(574\) −25.7639 −1.07536
\(575\) −18.8269 −0.785136
\(576\) 0 0
\(577\) 11.1971 0.466140 0.233070 0.972460i \(-0.425123\pi\)
0.233070 + 0.972460i \(0.425123\pi\)
\(578\) −16.6745 −0.693567
\(579\) 0 0
\(580\) 5.52976 0.229611
\(581\) −6.46826 −0.268349
\(582\) 0 0
\(583\) 19.4795 0.806756
\(584\) 1.97024 0.0815289
\(585\) 0 0
\(586\) 9.52070 0.393296
\(587\) 13.7039 0.565622 0.282811 0.959176i \(-0.408733\pi\)
0.282811 + 0.959176i \(0.408733\pi\)
\(588\) 0 0
\(589\) −19.9187 −0.820735
\(590\) 7.24668 0.298341
\(591\) 0 0
\(592\) −4.64638 −0.190965
\(593\) 45.7421 1.87840 0.939201 0.343367i \(-0.111568\pi\)
0.939201 + 0.343367i \(0.111568\pi\)
\(594\) 0 0
\(595\) 14.9457 0.612713
\(596\) 1.00000 0.0409616
\(597\) 0 0
\(598\) −30.8099 −1.25991
\(599\) 27.8465 1.13778 0.568889 0.822414i \(-0.307373\pi\)
0.568889 + 0.822414i \(0.307373\pi\)
\(600\) 0 0
\(601\) −7.82327 −0.319118 −0.159559 0.987188i \(-0.551007\pi\)
−0.159559 + 0.987188i \(0.551007\pi\)
\(602\) −26.8922 −1.09604
\(603\) 0 0
\(604\) −18.4343 −0.750080
\(605\) −2.90171 −0.117971
\(606\) 0 0
\(607\) −7.46791 −0.303113 −0.151557 0.988449i \(-0.548429\pi\)
−0.151557 + 0.988449i \(0.548429\pi\)
\(608\) −2.51725 −0.102088
\(609\) 0 0
\(610\) 12.6497 0.512170
\(611\) 51.8043 2.09578
\(612\) 0 0
\(613\) 26.6402 1.07599 0.537993 0.842949i \(-0.319183\pi\)
0.537993 + 0.842949i \(0.319183\pi\)
\(614\) −4.01472 −0.162021
\(615\) 0 0
\(616\) −6.94399 −0.279781
\(617\) −16.0512 −0.646198 −0.323099 0.946365i \(-0.604725\pi\)
−0.323099 + 0.946365i \(0.604725\pi\)
\(618\) 0 0
\(619\) −42.0240 −1.68909 −0.844544 0.535487i \(-0.820128\pi\)
−0.844544 + 0.535487i \(0.820128\pi\)
\(620\) −8.44582 −0.339192
\(621\) 0 0
\(622\) −12.5289 −0.502364
\(623\) −31.1455 −1.24782
\(624\) 0 0
\(625\) 9.20922 0.368369
\(626\) 17.9628 0.717939
\(627\) 0 0
\(628\) −18.8174 −0.750896
\(629\) −26.9628 −1.07508
\(630\) 0 0
\(631\) −23.5755 −0.938524 −0.469262 0.883059i \(-0.655480\pi\)
−0.469262 + 0.883059i \(0.655480\pi\)
\(632\) −2.26625 −0.0901467
\(633\) 0 0
\(634\) 0.635891 0.0252545
\(635\) 3.24079 0.128607
\(636\) 0 0
\(637\) −7.43912 −0.294749
\(638\) −14.9090 −0.590254
\(639\) 0 0
\(640\) −1.06735 −0.0421909
\(641\) −11.1542 −0.440564 −0.220282 0.975436i \(-0.570698\pi\)
−0.220282 + 0.975436i \(0.570698\pi\)
\(642\) 0 0
\(643\) 8.17816 0.322515 0.161258 0.986912i \(-0.448445\pi\)
0.161258 + 0.986912i \(0.448445\pi\)
\(644\) 11.7669 0.463682
\(645\) 0 0
\(646\) −14.6076 −0.574726
\(647\) −2.23055 −0.0876921 −0.0438461 0.999038i \(-0.513961\pi\)
−0.0438461 + 0.999038i \(0.513961\pi\)
\(648\) 0 0
\(649\) −19.5381 −0.766938
\(650\) 24.3925 0.956751
\(651\) 0 0
\(652\) −18.6680 −0.731097
\(653\) 13.8175 0.540721 0.270361 0.962759i \(-0.412857\pi\)
0.270361 + 0.962759i \(0.412857\pi\)
\(654\) 0 0
\(655\) −22.3369 −0.872775
\(656\) 10.6771 0.416872
\(657\) 0 0
\(658\) −19.7852 −0.771306
\(659\) −17.9428 −0.698951 −0.349475 0.936946i \(-0.613640\pi\)
−0.349475 + 0.936946i \(0.613640\pi\)
\(660\) 0 0
\(661\) 6.74759 0.262451 0.131225 0.991353i \(-0.458109\pi\)
0.131225 + 0.991353i \(0.458109\pi\)
\(662\) 3.11325 0.121000
\(663\) 0 0
\(664\) 2.68059 0.104027
\(665\) 6.48324 0.251409
\(666\) 0 0
\(667\) 25.2641 0.978230
\(668\) −10.7650 −0.416509
\(669\) 0 0
\(670\) −13.2701 −0.512668
\(671\) −34.1054 −1.31662
\(672\) 0 0
\(673\) 29.2188 1.12630 0.563152 0.826353i \(-0.309589\pi\)
0.563152 + 0.826353i \(0.309589\pi\)
\(674\) 33.9883 1.30918
\(675\) 0 0
\(676\) 26.9178 1.03530
\(677\) −41.1604 −1.58192 −0.790961 0.611866i \(-0.790419\pi\)
−0.790961 + 0.611866i \(0.790419\pi\)
\(678\) 0 0
\(679\) 16.1566 0.620032
\(680\) −6.19382 −0.237522
\(681\) 0 0
\(682\) 22.7712 0.871953
\(683\) 25.1460 0.962184 0.481092 0.876670i \(-0.340240\pi\)
0.481092 + 0.876670i \(0.340240\pi\)
\(684\) 0 0
\(685\) −5.77366 −0.220600
\(686\) 19.7321 0.753377
\(687\) 0 0
\(688\) 11.1447 0.424888
\(689\) 42.7669 1.62929
\(690\) 0 0
\(691\) 9.33945 0.355290 0.177645 0.984095i \(-0.443152\pi\)
0.177645 + 0.984095i \(0.443152\pi\)
\(692\) −14.3128 −0.544092
\(693\) 0 0
\(694\) 25.5691 0.970588
\(695\) −12.3005 −0.466583
\(696\) 0 0
\(697\) 61.9591 2.34687
\(698\) 6.64078 0.251357
\(699\) 0 0
\(700\) −9.31600 −0.352112
\(701\) 20.7946 0.785400 0.392700 0.919667i \(-0.371541\pi\)
0.392700 + 0.919667i \(0.371541\pi\)
\(702\) 0 0
\(703\) −11.6961 −0.441127
\(704\) 2.87774 0.108459
\(705\) 0 0
\(706\) 4.63793 0.174551
\(707\) −21.9256 −0.824598
\(708\) 0 0
\(709\) −34.3030 −1.28828 −0.644139 0.764909i \(-0.722784\pi\)
−0.644139 + 0.764909i \(0.722784\pi\)
\(710\) −4.14258 −0.155468
\(711\) 0 0
\(712\) 12.9074 0.483725
\(713\) −38.5869 −1.44509
\(714\) 0 0
\(715\) 19.4063 0.725756
\(716\) −14.8159 −0.553696
\(717\) 0 0
\(718\) 14.7744 0.551374
\(719\) 42.1754 1.57288 0.786438 0.617670i \(-0.211923\pi\)
0.786438 + 0.617670i \(0.211923\pi\)
\(720\) 0 0
\(721\) −29.7912 −1.10948
\(722\) 12.6634 0.471284
\(723\) 0 0
\(724\) 12.4854 0.464015
\(725\) −20.0018 −0.742850
\(726\) 0 0
\(727\) −30.1726 −1.11904 −0.559520 0.828817i \(-0.689015\pi\)
−0.559520 + 0.828817i \(0.689015\pi\)
\(728\) −15.2455 −0.565034
\(729\) 0 0
\(730\) 2.10294 0.0778332
\(731\) 64.6724 2.39200
\(732\) 0 0
\(733\) 21.2752 0.785816 0.392908 0.919578i \(-0.371469\pi\)
0.392908 + 0.919578i \(0.371469\pi\)
\(734\) −6.92697 −0.255679
\(735\) 0 0
\(736\) −4.87648 −0.179749
\(737\) 35.7781 1.31790
\(738\) 0 0
\(739\) −27.0373 −0.994583 −0.497292 0.867583i \(-0.665672\pi\)
−0.497292 + 0.867583i \(0.665672\pi\)
\(740\) −4.95933 −0.182309
\(741\) 0 0
\(742\) −16.3336 −0.599625
\(743\) 14.0456 0.515281 0.257641 0.966241i \(-0.417055\pi\)
0.257641 + 0.966241i \(0.417055\pi\)
\(744\) 0 0
\(745\) 1.06735 0.0391048
\(746\) −7.15412 −0.261931
\(747\) 0 0
\(748\) 16.6995 0.610593
\(749\) −11.4984 −0.420144
\(750\) 0 0
\(751\) 35.1905 1.28412 0.642060 0.766655i \(-0.278080\pi\)
0.642060 + 0.766655i \(0.278080\pi\)
\(752\) 8.19941 0.299002
\(753\) 0 0
\(754\) −32.7326 −1.19205
\(755\) −19.6759 −0.716079
\(756\) 0 0
\(757\) 12.0391 0.437567 0.218783 0.975773i \(-0.429791\pi\)
0.218783 + 0.975773i \(0.429791\pi\)
\(758\) −25.6854 −0.932935
\(759\) 0 0
\(760\) −2.68680 −0.0974605
\(761\) −45.8827 −1.66325 −0.831623 0.555341i \(-0.812588\pi\)
−0.831623 + 0.555341i \(0.812588\pi\)
\(762\) 0 0
\(763\) −13.8544 −0.501563
\(764\) 0.208714 0.00755100
\(765\) 0 0
\(766\) 23.5765 0.851855
\(767\) −42.8957 −1.54887
\(768\) 0 0
\(769\) −5.55195 −0.200208 −0.100104 0.994977i \(-0.531918\pi\)
−0.100104 + 0.994977i \(0.531918\pi\)
\(770\) −7.41169 −0.267099
\(771\) 0 0
\(772\) 20.4582 0.736307
\(773\) 10.5156 0.378219 0.189110 0.981956i \(-0.439440\pi\)
0.189110 + 0.981956i \(0.439440\pi\)
\(774\) 0 0
\(775\) 30.5496 1.09738
\(776\) −6.69563 −0.240359
\(777\) 0 0
\(778\) −16.7592 −0.600846
\(779\) 26.8770 0.962970
\(780\) 0 0
\(781\) 11.1690 0.399659
\(782\) −28.2981 −1.01194
\(783\) 0 0
\(784\) −1.17744 −0.0420514
\(785\) −20.0848 −0.716858
\(786\) 0 0
\(787\) −39.3725 −1.40348 −0.701739 0.712434i \(-0.747593\pi\)
−0.701739 + 0.712434i \(0.747593\pi\)
\(788\) 24.9769 0.889765
\(789\) 0 0
\(790\) −2.41889 −0.0860604
\(791\) 31.7441 1.12869
\(792\) 0 0
\(793\) −74.8780 −2.65900
\(794\) 5.12235 0.181785
\(795\) 0 0
\(796\) −18.3928 −0.651916
\(797\) 19.0023 0.673097 0.336549 0.941666i \(-0.390740\pi\)
0.336549 + 0.941666i \(0.390740\pi\)
\(798\) 0 0
\(799\) 47.5810 1.68329
\(800\) 3.86076 0.136498
\(801\) 0 0
\(802\) 19.0659 0.673241
\(803\) −5.66983 −0.200084
\(804\) 0 0
\(805\) 12.5595 0.442664
\(806\) 49.9939 1.76096
\(807\) 0 0
\(808\) 9.08647 0.319661
\(809\) 8.93922 0.314286 0.157143 0.987576i \(-0.449772\pi\)
0.157143 + 0.987576i \(0.449772\pi\)
\(810\) 0 0
\(811\) 5.23231 0.183731 0.0918657 0.995771i \(-0.470717\pi\)
0.0918657 + 0.995771i \(0.470717\pi\)
\(812\) 12.5013 0.438709
\(813\) 0 0
\(814\) 13.3711 0.468656
\(815\) −19.9254 −0.697957
\(816\) 0 0
\(817\) 28.0541 0.981487
\(818\) −15.0451 −0.526040
\(819\) 0 0
\(820\) 11.3963 0.397975
\(821\) 38.6144 1.34765 0.673826 0.738890i \(-0.264650\pi\)
0.673826 + 0.738890i \(0.264650\pi\)
\(822\) 0 0
\(823\) −54.1702 −1.88825 −0.944127 0.329583i \(-0.893092\pi\)
−0.944127 + 0.329583i \(0.893092\pi\)
\(824\) 12.3461 0.430098
\(825\) 0 0
\(826\) 16.3828 0.570030
\(827\) −29.8399 −1.03764 −0.518818 0.854885i \(-0.673628\pi\)
−0.518818 + 0.854885i \(0.673628\pi\)
\(828\) 0 0
\(829\) 29.4296 1.02213 0.511067 0.859541i \(-0.329251\pi\)
0.511067 + 0.859541i \(0.329251\pi\)
\(830\) 2.86114 0.0993116
\(831\) 0 0
\(832\) 6.31805 0.219039
\(833\) −6.83265 −0.236737
\(834\) 0 0
\(835\) −11.4900 −0.397628
\(836\) 7.24401 0.250539
\(837\) 0 0
\(838\) 12.6427 0.436735
\(839\) 6.91988 0.238901 0.119450 0.992840i \(-0.461887\pi\)
0.119450 + 0.992840i \(0.461887\pi\)
\(840\) 0 0
\(841\) −2.15922 −0.0744558
\(842\) 8.70185 0.299885
\(843\) 0 0
\(844\) −5.11885 −0.176198
\(845\) 28.7308 0.988370
\(846\) 0 0
\(847\) −6.55997 −0.225403
\(848\) 6.76900 0.232449
\(849\) 0 0
\(850\) 22.4039 0.768446
\(851\) −22.6580 −0.776705
\(852\) 0 0
\(853\) −30.8776 −1.05723 −0.528614 0.848862i \(-0.677288\pi\)
−0.528614 + 0.848862i \(0.677288\pi\)
\(854\) 28.5975 0.978586
\(855\) 0 0
\(856\) 4.76521 0.162872
\(857\) 24.3599 0.832119 0.416059 0.909337i \(-0.363411\pi\)
0.416059 + 0.909337i \(0.363411\pi\)
\(858\) 0 0
\(859\) 46.2628 1.57847 0.789233 0.614093i \(-0.210478\pi\)
0.789233 + 0.614093i \(0.210478\pi\)
\(860\) 11.8953 0.405628
\(861\) 0 0
\(862\) −13.9905 −0.476517
\(863\) 51.5003 1.75309 0.876546 0.481318i \(-0.159842\pi\)
0.876546 + 0.481318i \(0.159842\pi\)
\(864\) 0 0
\(865\) −15.2769 −0.519429
\(866\) −23.4355 −0.796371
\(867\) 0 0
\(868\) −19.0937 −0.648083
\(869\) 6.52169 0.221233
\(870\) 0 0
\(871\) 78.5504 2.66158
\(872\) 5.74157 0.194434
\(873\) 0 0
\(874\) −12.2753 −0.415220
\(875\) −22.8211 −0.771493
\(876\) 0 0
\(877\) −6.71660 −0.226803 −0.113402 0.993549i \(-0.536175\pi\)
−0.113402 + 0.993549i \(0.536175\pi\)
\(878\) 17.3808 0.586574
\(879\) 0 0
\(880\) 3.07157 0.103543
\(881\) 15.0720 0.507789 0.253894 0.967232i \(-0.418288\pi\)
0.253894 + 0.967232i \(0.418288\pi\)
\(882\) 0 0
\(883\) −1.56028 −0.0525077 −0.0262539 0.999655i \(-0.508358\pi\)
−0.0262539 + 0.999655i \(0.508358\pi\)
\(884\) 36.6635 1.23313
\(885\) 0 0
\(886\) −14.3666 −0.482656
\(887\) −3.52972 −0.118517 −0.0592583 0.998243i \(-0.518874\pi\)
−0.0592583 + 0.998243i \(0.518874\pi\)
\(888\) 0 0
\(889\) 7.32654 0.245724
\(890\) 13.7768 0.461798
\(891\) 0 0
\(892\) −24.0494 −0.805233
\(893\) 20.6400 0.690692
\(894\) 0 0
\(895\) −15.8138 −0.528597
\(896\) −2.41300 −0.0806126
\(897\) 0 0
\(898\) 4.35069 0.145184
\(899\) −40.9950 −1.36726
\(900\) 0 0
\(901\) 39.2803 1.30862
\(902\) −30.7260 −1.02306
\(903\) 0 0
\(904\) −13.1555 −0.437544
\(905\) 13.3263 0.442981
\(906\) 0 0
\(907\) 0.131286 0.00435928 0.00217964 0.999998i \(-0.499306\pi\)
0.00217964 + 0.999998i \(0.499306\pi\)
\(908\) 16.4469 0.545809
\(909\) 0 0
\(910\) −16.2723 −0.539421
\(911\) −0.346696 −0.0114866 −0.00574328 0.999984i \(-0.501828\pi\)
−0.00574328 + 0.999984i \(0.501828\pi\)
\(912\) 0 0
\(913\) −7.71405 −0.255298
\(914\) 28.9116 0.956311
\(915\) 0 0
\(916\) 3.67491 0.121423
\(917\) −50.4977 −1.66758
\(918\) 0 0
\(919\) 52.9227 1.74576 0.872880 0.487935i \(-0.162250\pi\)
0.872880 + 0.487935i \(0.162250\pi\)
\(920\) −5.20493 −0.171601
\(921\) 0 0
\(922\) 3.48477 0.114765
\(923\) 24.5215 0.807133
\(924\) 0 0
\(925\) 17.9385 0.589815
\(926\) 17.3353 0.569673
\(927\) 0 0
\(928\) −5.18081 −0.170068
\(929\) −29.1343 −0.955864 −0.477932 0.878397i \(-0.658613\pi\)
−0.477932 + 0.878397i \(0.658613\pi\)
\(930\) 0 0
\(931\) −2.96391 −0.0971383
\(932\) −1.22524 −0.0401340
\(933\) 0 0
\(934\) −21.8269 −0.714197
\(935\) 17.8242 0.582915
\(936\) 0 0
\(937\) 55.7638 1.82172 0.910862 0.412711i \(-0.135418\pi\)
0.910862 + 0.412711i \(0.135418\pi\)
\(938\) −30.0001 −0.979537
\(939\) 0 0
\(940\) 8.75167 0.285448
\(941\) −43.0006 −1.40178 −0.700889 0.713270i \(-0.747213\pi\)
−0.700889 + 0.713270i \(0.747213\pi\)
\(942\) 0 0
\(943\) 52.0668 1.69553
\(944\) −6.78939 −0.220976
\(945\) 0 0
\(946\) −32.0716 −1.04274
\(947\) −7.81340 −0.253901 −0.126951 0.991909i \(-0.540519\pi\)
−0.126951 + 0.991909i \(0.540519\pi\)
\(948\) 0 0
\(949\) −12.4481 −0.404081
\(950\) 9.71850 0.315310
\(951\) 0 0
\(952\) −14.0026 −0.453826
\(953\) −17.0448 −0.552135 −0.276067 0.961138i \(-0.589031\pi\)
−0.276067 + 0.961138i \(0.589031\pi\)
\(954\) 0 0
\(955\) 0.222771 0.00720871
\(956\) −19.6354 −0.635055
\(957\) 0 0
\(958\) 32.2298 1.04130
\(959\) −13.0527 −0.421493
\(960\) 0 0
\(961\) 31.6134 1.01979
\(962\) 29.3561 0.946477
\(963\) 0 0
\(964\) −21.6153 −0.696183
\(965\) 21.8361 0.702930
\(966\) 0 0
\(967\) 30.5292 0.981753 0.490876 0.871229i \(-0.336677\pi\)
0.490876 + 0.871229i \(0.336677\pi\)
\(968\) 2.71860 0.0873791
\(969\) 0 0
\(970\) −7.14661 −0.229464
\(971\) −41.4714 −1.33088 −0.665440 0.746451i \(-0.731756\pi\)
−0.665440 + 0.746451i \(0.731756\pi\)
\(972\) 0 0
\(973\) −27.8080 −0.891485
\(974\) −36.3486 −1.16468
\(975\) 0 0
\(976\) −11.8514 −0.379355
\(977\) 56.3272 1.80207 0.901033 0.433750i \(-0.142810\pi\)
0.901033 + 0.433750i \(0.142810\pi\)
\(978\) 0 0
\(979\) −37.1442 −1.18713
\(980\) −1.25674 −0.0401452
\(981\) 0 0
\(982\) 6.27108 0.200118
\(983\) 43.9298 1.40114 0.700571 0.713583i \(-0.252929\pi\)
0.700571 + 0.713583i \(0.252929\pi\)
\(984\) 0 0
\(985\) 26.6592 0.849432
\(986\) −30.0641 −0.957436
\(987\) 0 0
\(988\) 15.9041 0.505978
\(989\) 54.3469 1.72813
\(990\) 0 0
\(991\) −39.1494 −1.24362 −0.621810 0.783168i \(-0.713602\pi\)
−0.621810 + 0.783168i \(0.713602\pi\)
\(992\) 7.91286 0.251234
\(993\) 0 0
\(994\) −9.36526 −0.297048
\(995\) −19.6316 −0.622365
\(996\) 0 0
\(997\) −30.2386 −0.957666 −0.478833 0.877906i \(-0.658940\pi\)
−0.478833 + 0.877906i \(0.658940\pi\)
\(998\) −31.2490 −0.989170
\(999\) 0 0
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 \(a_p\))