Properties

Label 6036.2.a.i.1.9
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 0
Dimension 26
CM No

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Newspace parameters

Level: \( N \) = \( 6036 = 2^{2} \cdot 3 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.19770266\)
Analytic rank: \(0\)
Dimension: \(26\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(-1.78585 q^{5}\) \(-2.07926 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(-1.78585 q^{5}\) \(-2.07926 q^{7}\) \(+1.00000 q^{9}\) \(+2.20363 q^{11}\) \(-6.61519 q^{13}\) \(+1.78585 q^{15}\) \(-6.93993 q^{17}\) \(-3.40790 q^{19}\) \(+2.07926 q^{21}\) \(+2.31931 q^{23}\) \(-1.81076 q^{25}\) \(-1.00000 q^{27}\) \(-1.77508 q^{29}\) \(+5.22504 q^{31}\) \(-2.20363 q^{33}\) \(+3.71323 q^{35}\) \(-10.8349 q^{37}\) \(+6.61519 q^{39}\) \(+3.10677 q^{41}\) \(-3.95587 q^{43}\) \(-1.78585 q^{45}\) \(+6.71070 q^{47}\) \(-2.67669 q^{49}\) \(+6.93993 q^{51}\) \(-9.33131 q^{53}\) \(-3.93534 q^{55}\) \(+3.40790 q^{57}\) \(-8.55552 q^{59}\) \(+8.78763 q^{61}\) \(-2.07926 q^{63}\) \(+11.8137 q^{65}\) \(-8.71231 q^{67}\) \(-2.31931 q^{69}\) \(-10.1955 q^{71}\) \(-9.60865 q^{73}\) \(+1.81076 q^{75}\) \(-4.58191 q^{77}\) \(+12.9198 q^{79}\) \(+1.00000 q^{81}\) \(+3.56790 q^{83}\) \(+12.3936 q^{85}\) \(+1.77508 q^{87}\) \(+11.0077 q^{89}\) \(+13.7547 q^{91}\) \(-5.22504 q^{93}\) \(+6.08599 q^{95}\) \(+13.1768 q^{97}\) \(+2.20363 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 13q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 48q^{25} \) \(\mathstrut -\mathstrut 26q^{27} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 19q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 21q^{35} \) \(\mathstrut +\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 13q^{39} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 67q^{49} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut +\mathstrut 20q^{55} \) \(\mathstrut +\mathstrut q^{57} \) \(\mathstrut -\mathstrut 18q^{59} \) \(\mathstrut +\mathstrut 43q^{61} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 41q^{65} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 22q^{69} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 48q^{75} \) \(\mathstrut +\mathstrut 23q^{77} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 26q^{81} \) \(\mathstrut -\mathstrut 19q^{83} \) \(\mathstrut +\mathstrut 29q^{85} \) \(\mathstrut -\mathstrut 6q^{87} \) \(\mathstrut +\mathstrut 49q^{89} \) \(\mathstrut -\mathstrut 13q^{91} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 26q^{95} \) \(\mathstrut +\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) −1.78585 −0.798654 −0.399327 0.916809i \(-0.630756\pi\)
−0.399327 + 0.916809i \(0.630756\pi\)
\(6\) 0 0
\(7\) −2.07926 −0.785885 −0.392942 0.919563i \(-0.628543\pi\)
−0.392942 + 0.919563i \(0.628543\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 2.20363 0.664419 0.332209 0.943206i \(-0.392206\pi\)
0.332209 + 0.943206i \(0.392206\pi\)
\(12\) 0 0
\(13\) −6.61519 −1.83472 −0.917362 0.398055i \(-0.869685\pi\)
−0.917362 + 0.398055i \(0.869685\pi\)
\(14\) 0 0
\(15\) 1.78585 0.461103
\(16\) 0 0
\(17\) −6.93993 −1.68318 −0.841590 0.540117i \(-0.818380\pi\)
−0.841590 + 0.540117i \(0.818380\pi\)
\(18\) 0 0
\(19\) −3.40790 −0.781827 −0.390913 0.920427i \(-0.627841\pi\)
−0.390913 + 0.920427i \(0.627841\pi\)
\(20\) 0 0
\(21\) 2.07926 0.453731
\(22\) 0 0
\(23\) 2.31931 0.483609 0.241804 0.970325i \(-0.422261\pi\)
0.241804 + 0.970325i \(0.422261\pi\)
\(24\) 0 0
\(25\) −1.81076 −0.362151
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −1.77508 −0.329624 −0.164812 0.986325i \(-0.552702\pi\)
−0.164812 + 0.986325i \(0.552702\pi\)
\(30\) 0 0
\(31\) 5.22504 0.938444 0.469222 0.883080i \(-0.344534\pi\)
0.469222 + 0.883080i \(0.344534\pi\)
\(32\) 0 0
\(33\) −2.20363 −0.383602
\(34\) 0 0
\(35\) 3.71323 0.627650
\(36\) 0 0
\(37\) −10.8349 −1.78125 −0.890625 0.454739i \(-0.849732\pi\)
−0.890625 + 0.454739i \(0.849732\pi\)
\(38\) 0 0
\(39\) 6.61519 1.05928
\(40\) 0 0
\(41\) 3.10677 0.485197 0.242598 0.970127i \(-0.422000\pi\)
0.242598 + 0.970127i \(0.422000\pi\)
\(42\) 0 0
\(43\) −3.95587 −0.603264 −0.301632 0.953424i \(-0.597531\pi\)
−0.301632 + 0.953424i \(0.597531\pi\)
\(44\) 0 0
\(45\) −1.78585 −0.266218
\(46\) 0 0
\(47\) 6.71070 0.978857 0.489428 0.872044i \(-0.337205\pi\)
0.489428 + 0.872044i \(0.337205\pi\)
\(48\) 0 0
\(49\) −2.67669 −0.382385
\(50\) 0 0
\(51\) 6.93993 0.971784
\(52\) 0 0
\(53\) −9.33131 −1.28175 −0.640877 0.767644i \(-0.721429\pi\)
−0.640877 + 0.767644i \(0.721429\pi\)
\(54\) 0 0
\(55\) −3.93534 −0.530641
\(56\) 0 0
\(57\) 3.40790 0.451388
\(58\) 0 0
\(59\) −8.55552 −1.11383 −0.556917 0.830568i \(-0.688016\pi\)
−0.556917 + 0.830568i \(0.688016\pi\)
\(60\) 0 0
\(61\) 8.78763 1.12514 0.562571 0.826749i \(-0.309812\pi\)
0.562571 + 0.826749i \(0.309812\pi\)
\(62\) 0 0
\(63\) −2.07926 −0.261962
\(64\) 0 0
\(65\) 11.8137 1.46531
\(66\) 0 0
\(67\) −8.71231 −1.06438 −0.532189 0.846626i \(-0.678630\pi\)
−0.532189 + 0.846626i \(0.678630\pi\)
\(68\) 0 0
\(69\) −2.31931 −0.279212
\(70\) 0 0
\(71\) −10.1955 −1.20998 −0.604989 0.796234i \(-0.706823\pi\)
−0.604989 + 0.796234i \(0.706823\pi\)
\(72\) 0 0
\(73\) −9.60865 −1.12461 −0.562304 0.826931i \(-0.690085\pi\)
−0.562304 + 0.826931i \(0.690085\pi\)
\(74\) 0 0
\(75\) 1.81076 0.209088
\(76\) 0 0
\(77\) −4.58191 −0.522157
\(78\) 0 0
\(79\) 12.9198 1.45359 0.726794 0.686855i \(-0.241009\pi\)
0.726794 + 0.686855i \(0.241009\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 3.56790 0.391628 0.195814 0.980641i \(-0.437265\pi\)
0.195814 + 0.980641i \(0.437265\pi\)
\(84\) 0 0
\(85\) 12.3936 1.34428
\(86\) 0 0
\(87\) 1.77508 0.190309
\(88\) 0 0
\(89\) 11.0077 1.16682 0.583408 0.812179i \(-0.301719\pi\)
0.583408 + 0.812179i \(0.301719\pi\)
\(90\) 0 0
\(91\) 13.7547 1.44188
\(92\) 0 0
\(93\) −5.22504 −0.541811
\(94\) 0 0
\(95\) 6.08599 0.624409
\(96\) 0 0
\(97\) 13.1768 1.33790 0.668950 0.743308i \(-0.266744\pi\)
0.668950 + 0.743308i \(0.266744\pi\)
\(98\) 0 0
\(99\) 2.20363 0.221473
\(100\) 0 0
\(101\) 1.21326 0.120723 0.0603617 0.998177i \(-0.480775\pi\)
0.0603617 + 0.998177i \(0.480775\pi\)
\(102\) 0 0
\(103\) 15.8674 1.56346 0.781728 0.623619i \(-0.214338\pi\)
0.781728 + 0.623619i \(0.214338\pi\)
\(104\) 0 0
\(105\) −3.71323 −0.362374
\(106\) 0 0
\(107\) −17.6627 −1.70751 −0.853757 0.520671i \(-0.825682\pi\)
−0.853757 + 0.520671i \(0.825682\pi\)
\(108\) 0 0
\(109\) −15.2491 −1.46060 −0.730301 0.683126i \(-0.760620\pi\)
−0.730301 + 0.683126i \(0.760620\pi\)
\(110\) 0 0
\(111\) 10.8349 1.02840
\(112\) 0 0
\(113\) 5.21830 0.490896 0.245448 0.969410i \(-0.421065\pi\)
0.245448 + 0.969410i \(0.421065\pi\)
\(114\) 0 0
\(115\) −4.14192 −0.386236
\(116\) 0 0
\(117\) −6.61519 −0.611574
\(118\) 0 0
\(119\) 14.4299 1.32279
\(120\) 0 0
\(121\) −6.14402 −0.558547
\(122\) 0 0
\(123\) −3.10677 −0.280128
\(124\) 0 0
\(125\) 12.1630 1.08789
\(126\) 0 0
\(127\) −14.3938 −1.27724 −0.638620 0.769522i \(-0.720495\pi\)
−0.638620 + 0.769522i \(0.720495\pi\)
\(128\) 0 0
\(129\) 3.95587 0.348295
\(130\) 0 0
\(131\) −10.5082 −0.918110 −0.459055 0.888408i \(-0.651812\pi\)
−0.459055 + 0.888408i \(0.651812\pi\)
\(132\) 0 0
\(133\) 7.08591 0.614426
\(134\) 0 0
\(135\) 1.78585 0.153701
\(136\) 0 0
\(137\) −11.5382 −0.985771 −0.492886 0.870094i \(-0.664058\pi\)
−0.492886 + 0.870094i \(0.664058\pi\)
\(138\) 0 0
\(139\) 15.2200 1.29094 0.645472 0.763784i \(-0.276661\pi\)
0.645472 + 0.763784i \(0.276661\pi\)
\(140\) 0 0
\(141\) −6.71070 −0.565143
\(142\) 0 0
\(143\) −14.5774 −1.21902
\(144\) 0 0
\(145\) 3.17002 0.263256
\(146\) 0 0
\(147\) 2.67669 0.220770
\(148\) 0 0
\(149\) 12.0350 0.985945 0.492973 0.870045i \(-0.335910\pi\)
0.492973 + 0.870045i \(0.335910\pi\)
\(150\) 0 0
\(151\) −15.9197 −1.29553 −0.647763 0.761842i \(-0.724295\pi\)
−0.647763 + 0.761842i \(0.724295\pi\)
\(152\) 0 0
\(153\) −6.93993 −0.561060
\(154\) 0 0
\(155\) −9.33110 −0.749492
\(156\) 0 0
\(157\) −1.08167 −0.0863263 −0.0431632 0.999068i \(-0.513744\pi\)
−0.0431632 + 0.999068i \(0.513744\pi\)
\(158\) 0 0
\(159\) 9.33131 0.740021
\(160\) 0 0
\(161\) −4.82243 −0.380061
\(162\) 0 0
\(163\) 5.26307 0.412235 0.206118 0.978527i \(-0.433917\pi\)
0.206118 + 0.978527i \(0.433917\pi\)
\(164\) 0 0
\(165\) 3.93534 0.306366
\(166\) 0 0
\(167\) −20.0357 −1.55041 −0.775206 0.631708i \(-0.782354\pi\)
−0.775206 + 0.631708i \(0.782354\pi\)
\(168\) 0 0
\(169\) 30.7607 2.36621
\(170\) 0 0
\(171\) −3.40790 −0.260609
\(172\) 0 0
\(173\) 4.63384 0.352305 0.176152 0.984363i \(-0.443635\pi\)
0.176152 + 0.984363i \(0.443635\pi\)
\(174\) 0 0
\(175\) 3.76503 0.284609
\(176\) 0 0
\(177\) 8.55552 0.643072
\(178\) 0 0
\(179\) 19.0524 1.42404 0.712021 0.702158i \(-0.247780\pi\)
0.712021 + 0.702158i \(0.247780\pi\)
\(180\) 0 0
\(181\) 9.45601 0.702860 0.351430 0.936214i \(-0.385696\pi\)
0.351430 + 0.936214i \(0.385696\pi\)
\(182\) 0 0
\(183\) −8.78763 −0.649600
\(184\) 0 0
\(185\) 19.3495 1.42260
\(186\) 0 0
\(187\) −15.2930 −1.11834
\(188\) 0 0
\(189\) 2.07926 0.151244
\(190\) 0 0
\(191\) −7.54585 −0.545999 −0.272999 0.962014i \(-0.588016\pi\)
−0.272999 + 0.962014i \(0.588016\pi\)
\(192\) 0 0
\(193\) 11.5660 0.832541 0.416271 0.909241i \(-0.363337\pi\)
0.416271 + 0.909241i \(0.363337\pi\)
\(194\) 0 0
\(195\) −11.8137 −0.845997
\(196\) 0 0
\(197\) −8.50436 −0.605910 −0.302955 0.953005i \(-0.597973\pi\)
−0.302955 + 0.953005i \(0.597973\pi\)
\(198\) 0 0
\(199\) 5.92204 0.419802 0.209901 0.977723i \(-0.432686\pi\)
0.209901 + 0.977723i \(0.432686\pi\)
\(200\) 0 0
\(201\) 8.71231 0.614519
\(202\) 0 0
\(203\) 3.69085 0.259047
\(204\) 0 0
\(205\) −5.54822 −0.387504
\(206\) 0 0
\(207\) 2.31931 0.161203
\(208\) 0 0
\(209\) −7.50975 −0.519461
\(210\) 0 0
\(211\) −2.66403 −0.183399 −0.0916996 0.995787i \(-0.529230\pi\)
−0.0916996 + 0.995787i \(0.529230\pi\)
\(212\) 0 0
\(213\) 10.1955 0.698581
\(214\) 0 0
\(215\) 7.06457 0.481800
\(216\) 0 0
\(217\) −10.8642 −0.737509
\(218\) 0 0
\(219\) 9.60865 0.649292
\(220\) 0 0
\(221\) 45.9089 3.08817
\(222\) 0 0
\(223\) 11.6207 0.778178 0.389089 0.921200i \(-0.372790\pi\)
0.389089 + 0.921200i \(0.372790\pi\)
\(224\) 0 0
\(225\) −1.81076 −0.120717
\(226\) 0 0
\(227\) −5.73829 −0.380864 −0.190432 0.981700i \(-0.560989\pi\)
−0.190432 + 0.981700i \(0.560989\pi\)
\(228\) 0 0
\(229\) −2.94839 −0.194835 −0.0974177 0.995244i \(-0.531058\pi\)
−0.0974177 + 0.995244i \(0.531058\pi\)
\(230\) 0 0
\(231\) 4.58191 0.301467
\(232\) 0 0
\(233\) 16.0655 1.05249 0.526243 0.850334i \(-0.323600\pi\)
0.526243 + 0.850334i \(0.323600\pi\)
\(234\) 0 0
\(235\) −11.9843 −0.781768
\(236\) 0 0
\(237\) −12.9198 −0.839229
\(238\) 0 0
\(239\) −17.3794 −1.12418 −0.562091 0.827076i \(-0.690003\pi\)
−0.562091 + 0.827076i \(0.690003\pi\)
\(240\) 0 0
\(241\) −20.3416 −1.31031 −0.655157 0.755493i \(-0.727398\pi\)
−0.655157 + 0.755493i \(0.727398\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 4.78016 0.305393
\(246\) 0 0
\(247\) 22.5439 1.43444
\(248\) 0 0
\(249\) −3.56790 −0.226107
\(250\) 0 0
\(251\) −23.3382 −1.47310 −0.736548 0.676386i \(-0.763545\pi\)
−0.736548 + 0.676386i \(0.763545\pi\)
\(252\) 0 0
\(253\) 5.11089 0.321319
\(254\) 0 0
\(255\) −12.3936 −0.776119
\(256\) 0 0
\(257\) 2.27427 0.141865 0.0709326 0.997481i \(-0.477402\pi\)
0.0709326 + 0.997481i \(0.477402\pi\)
\(258\) 0 0
\(259\) 22.5286 1.39986
\(260\) 0 0
\(261\) −1.77508 −0.109875
\(262\) 0 0
\(263\) 14.3925 0.887477 0.443738 0.896156i \(-0.353652\pi\)
0.443738 + 0.896156i \(0.353652\pi\)
\(264\) 0 0
\(265\) 16.6643 1.02368
\(266\) 0 0
\(267\) −11.0077 −0.673661
\(268\) 0 0
\(269\) 12.1315 0.739673 0.369837 0.929097i \(-0.379414\pi\)
0.369837 + 0.929097i \(0.379414\pi\)
\(270\) 0 0
\(271\) −26.5739 −1.61425 −0.807126 0.590380i \(-0.798978\pi\)
−0.807126 + 0.590380i \(0.798978\pi\)
\(272\) 0 0
\(273\) −13.7547 −0.832471
\(274\) 0 0
\(275\) −3.99023 −0.240620
\(276\) 0 0
\(277\) 16.6649 1.00130 0.500649 0.865650i \(-0.333095\pi\)
0.500649 + 0.865650i \(0.333095\pi\)
\(278\) 0 0
\(279\) 5.22504 0.312815
\(280\) 0 0
\(281\) 18.0299 1.07558 0.537788 0.843080i \(-0.319260\pi\)
0.537788 + 0.843080i \(0.319260\pi\)
\(282\) 0 0
\(283\) 22.0846 1.31280 0.656398 0.754415i \(-0.272079\pi\)
0.656398 + 0.754415i \(0.272079\pi\)
\(284\) 0 0
\(285\) −6.08599 −0.360503
\(286\) 0 0
\(287\) −6.45978 −0.381309
\(288\) 0 0
\(289\) 31.1626 1.83309
\(290\) 0 0
\(291\) −13.1768 −0.772436
\(292\) 0 0
\(293\) 2.24011 0.130869 0.0654344 0.997857i \(-0.479157\pi\)
0.0654344 + 0.997857i \(0.479157\pi\)
\(294\) 0 0
\(295\) 15.2788 0.889568
\(296\) 0 0
\(297\) −2.20363 −0.127867
\(298\) 0 0
\(299\) −15.3427 −0.887288
\(300\) 0 0
\(301\) 8.22526 0.474096
\(302\) 0 0
\(303\) −1.21326 −0.0696997
\(304\) 0 0
\(305\) −15.6934 −0.898599
\(306\) 0 0
\(307\) 21.0330 1.20041 0.600207 0.799845i \(-0.295085\pi\)
0.600207 + 0.799845i \(0.295085\pi\)
\(308\) 0 0
\(309\) −15.8674 −0.902662
\(310\) 0 0
\(311\) 23.7129 1.34464 0.672319 0.740262i \(-0.265298\pi\)
0.672319 + 0.740262i \(0.265298\pi\)
\(312\) 0 0
\(313\) 16.7181 0.944963 0.472482 0.881341i \(-0.343358\pi\)
0.472482 + 0.881341i \(0.343358\pi\)
\(314\) 0 0
\(315\) 3.71323 0.209217
\(316\) 0 0
\(317\) −8.17881 −0.459368 −0.229684 0.973265i \(-0.573769\pi\)
−0.229684 + 0.973265i \(0.573769\pi\)
\(318\) 0 0
\(319\) −3.91162 −0.219008
\(320\) 0 0
\(321\) 17.6627 0.985834
\(322\) 0 0
\(323\) 23.6506 1.31595
\(324\) 0 0
\(325\) 11.9785 0.664447
\(326\) 0 0
\(327\) 15.2491 0.843279
\(328\) 0 0
\(329\) −13.9533 −0.769269
\(330\) 0 0
\(331\) 24.5580 1.34983 0.674915 0.737895i \(-0.264180\pi\)
0.674915 + 0.737895i \(0.264180\pi\)
\(332\) 0 0
\(333\) −10.8349 −0.593750
\(334\) 0 0
\(335\) 15.5588 0.850070
\(336\) 0 0
\(337\) −8.14991 −0.443954 −0.221977 0.975052i \(-0.571251\pi\)
−0.221977 + 0.975052i \(0.571251\pi\)
\(338\) 0 0
\(339\) −5.21830 −0.283419
\(340\) 0 0
\(341\) 11.5140 0.623520
\(342\) 0 0
\(343\) 20.1203 1.08640
\(344\) 0 0
\(345\) 4.14192 0.222994
\(346\) 0 0
\(347\) −17.4526 −0.936903 −0.468451 0.883489i \(-0.655188\pi\)
−0.468451 + 0.883489i \(0.655188\pi\)
\(348\) 0 0
\(349\) 28.2331 1.51129 0.755643 0.654984i \(-0.227325\pi\)
0.755643 + 0.654984i \(0.227325\pi\)
\(350\) 0 0
\(351\) 6.61519 0.353093
\(352\) 0 0
\(353\) −32.5433 −1.73211 −0.866053 0.499953i \(-0.833351\pi\)
−0.866053 + 0.499953i \(0.833351\pi\)
\(354\) 0 0
\(355\) 18.2075 0.966354
\(356\) 0 0
\(357\) −14.4299 −0.763710
\(358\) 0 0
\(359\) 10.1755 0.537042 0.268521 0.963274i \(-0.413465\pi\)
0.268521 + 0.963274i \(0.413465\pi\)
\(360\) 0 0
\(361\) −7.38619 −0.388747
\(362\) 0 0
\(363\) 6.14402 0.322478
\(364\) 0 0
\(365\) 17.1596 0.898173
\(366\) 0 0
\(367\) 31.6754 1.65344 0.826721 0.562612i \(-0.190204\pi\)
0.826721 + 0.562612i \(0.190204\pi\)
\(368\) 0 0
\(369\) 3.10677 0.161732
\(370\) 0 0
\(371\) 19.4022 1.00731
\(372\) 0 0
\(373\) 12.9400 0.670009 0.335004 0.942217i \(-0.391262\pi\)
0.335004 + 0.942217i \(0.391262\pi\)
\(374\) 0 0
\(375\) −12.1630 −0.628092
\(376\) 0 0
\(377\) 11.7425 0.604769
\(378\) 0 0
\(379\) 24.8771 1.27785 0.638926 0.769269i \(-0.279379\pi\)
0.638926 + 0.769269i \(0.279379\pi\)
\(380\) 0 0
\(381\) 14.3938 0.737415
\(382\) 0 0
\(383\) −31.0011 −1.58408 −0.792042 0.610467i \(-0.790982\pi\)
−0.792042 + 0.610467i \(0.790982\pi\)
\(384\) 0 0
\(385\) 8.18258 0.417023
\(386\) 0 0
\(387\) −3.95587 −0.201088
\(388\) 0 0
\(389\) −4.84548 −0.245676 −0.122838 0.992427i \(-0.539199\pi\)
−0.122838 + 0.992427i \(0.539199\pi\)
\(390\) 0 0
\(391\) −16.0958 −0.814000
\(392\) 0 0
\(393\) 10.5082 0.530071
\(394\) 0 0
\(395\) −23.0727 −1.16091
\(396\) 0 0
\(397\) 23.9252 1.20077 0.600387 0.799710i \(-0.295013\pi\)
0.600387 + 0.799710i \(0.295013\pi\)
\(398\) 0 0
\(399\) −7.08591 −0.354739
\(400\) 0 0
\(401\) −1.03354 −0.0516125 −0.0258062 0.999667i \(-0.508215\pi\)
−0.0258062 + 0.999667i \(0.508215\pi\)
\(402\) 0 0
\(403\) −34.5646 −1.72179
\(404\) 0 0
\(405\) −1.78585 −0.0887394
\(406\) 0 0
\(407\) −23.8761 −1.18350
\(408\) 0 0
\(409\) −18.6327 −0.921328 −0.460664 0.887575i \(-0.652389\pi\)
−0.460664 + 0.887575i \(0.652389\pi\)
\(410\) 0 0
\(411\) 11.5382 0.569135
\(412\) 0 0
\(413\) 17.7891 0.875345
\(414\) 0 0
\(415\) −6.37172 −0.312775
\(416\) 0 0
\(417\) −15.2200 −0.745327
\(418\) 0 0
\(419\) −8.19130 −0.400171 −0.200086 0.979778i \(-0.564122\pi\)
−0.200086 + 0.979778i \(0.564122\pi\)
\(420\) 0 0
\(421\) −4.27517 −0.208359 −0.104180 0.994559i \(-0.533222\pi\)
−0.104180 + 0.994559i \(0.533222\pi\)
\(422\) 0 0
\(423\) 6.71070 0.326286
\(424\) 0 0
\(425\) 12.5665 0.609566
\(426\) 0 0
\(427\) −18.2717 −0.884231
\(428\) 0 0
\(429\) 14.5774 0.703804
\(430\) 0 0
\(431\) 29.0027 1.39701 0.698506 0.715604i \(-0.253848\pi\)
0.698506 + 0.715604i \(0.253848\pi\)
\(432\) 0 0
\(433\) −0.842181 −0.0404727 −0.0202363 0.999795i \(-0.506442\pi\)
−0.0202363 + 0.999795i \(0.506442\pi\)
\(434\) 0 0
\(435\) −3.17002 −0.151991
\(436\) 0 0
\(437\) −7.90398 −0.378098
\(438\) 0 0
\(439\) −7.92802 −0.378384 −0.189192 0.981940i \(-0.560587\pi\)
−0.189192 + 0.981940i \(0.560587\pi\)
\(440\) 0 0
\(441\) −2.67669 −0.127462
\(442\) 0 0
\(443\) −16.3090 −0.774862 −0.387431 0.921899i \(-0.626637\pi\)
−0.387431 + 0.921899i \(0.626637\pi\)
\(444\) 0 0
\(445\) −19.6581 −0.931882
\(446\) 0 0
\(447\) −12.0350 −0.569236
\(448\) 0 0
\(449\) 12.7992 0.604031 0.302015 0.953303i \(-0.402341\pi\)
0.302015 + 0.953303i \(0.402341\pi\)
\(450\) 0 0
\(451\) 6.84617 0.322374
\(452\) 0 0
\(453\) 15.9197 0.747972
\(454\) 0 0
\(455\) −24.5637 −1.15156
\(456\) 0 0
\(457\) 11.1398 0.521097 0.260548 0.965461i \(-0.416097\pi\)
0.260548 + 0.965461i \(0.416097\pi\)
\(458\) 0 0
\(459\) 6.93993 0.323928
\(460\) 0 0
\(461\) −16.5693 −0.771710 −0.385855 0.922559i \(-0.626094\pi\)
−0.385855 + 0.922559i \(0.626094\pi\)
\(462\) 0 0
\(463\) −30.4349 −1.41443 −0.707215 0.706999i \(-0.750049\pi\)
−0.707215 + 0.706999i \(0.750049\pi\)
\(464\) 0 0
\(465\) 9.33110 0.432720
\(466\) 0 0
\(467\) 16.7129 0.773379 0.386689 0.922210i \(-0.373619\pi\)
0.386689 + 0.922210i \(0.373619\pi\)
\(468\) 0 0
\(469\) 18.1151 0.836478
\(470\) 0 0
\(471\) 1.08167 0.0498405
\(472\) 0 0
\(473\) −8.71726 −0.400820
\(474\) 0 0
\(475\) 6.17089 0.283140
\(476\) 0 0
\(477\) −9.33131 −0.427251
\(478\) 0 0
\(479\) 10.3321 0.472084 0.236042 0.971743i \(-0.424150\pi\)
0.236042 + 0.971743i \(0.424150\pi\)
\(480\) 0 0
\(481\) 71.6750 3.26810
\(482\) 0 0
\(483\) 4.82243 0.219428
\(484\) 0 0
\(485\) −23.5317 −1.06852
\(486\) 0 0
\(487\) 27.3555 1.23959 0.619797 0.784762i \(-0.287215\pi\)
0.619797 + 0.784762i \(0.287215\pi\)
\(488\) 0 0
\(489\) −5.26307 −0.238004
\(490\) 0 0
\(491\) 1.46231 0.0659933 0.0329967 0.999455i \(-0.489495\pi\)
0.0329967 + 0.999455i \(0.489495\pi\)
\(492\) 0 0
\(493\) 12.3189 0.554816
\(494\) 0 0
\(495\) −3.93534 −0.176880
\(496\) 0 0
\(497\) 21.1990 0.950904
\(498\) 0 0
\(499\) −10.0351 −0.449231 −0.224616 0.974447i \(-0.572113\pi\)
−0.224616 + 0.974447i \(0.572113\pi\)
\(500\) 0 0
\(501\) 20.0357 0.895131
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −2.16669 −0.0964163
\(506\) 0 0
\(507\) −30.7607 −1.36613
\(508\) 0 0
\(509\) 14.9267 0.661616 0.330808 0.943698i \(-0.392679\pi\)
0.330808 + 0.943698i \(0.392679\pi\)
\(510\) 0 0
\(511\) 19.9788 0.883812
\(512\) 0 0
\(513\) 3.40790 0.150463
\(514\) 0 0
\(515\) −28.3366 −1.24866
\(516\) 0 0
\(517\) 14.7879 0.650371
\(518\) 0 0
\(519\) −4.63384 −0.203403
\(520\) 0 0
\(521\) 11.4560 0.501896 0.250948 0.968001i \(-0.419258\pi\)
0.250948 + 0.968001i \(0.419258\pi\)
\(522\) 0 0
\(523\) −31.2698 −1.36733 −0.683667 0.729794i \(-0.739616\pi\)
−0.683667 + 0.729794i \(0.739616\pi\)
\(524\) 0 0
\(525\) −3.76503 −0.164319
\(526\) 0 0
\(527\) −36.2614 −1.57957
\(528\) 0 0
\(529\) −17.6208 −0.766122
\(530\) 0 0
\(531\) −8.55552 −0.371278
\(532\) 0 0
\(533\) −20.5519 −0.890201
\(534\) 0 0
\(535\) 31.5428 1.36371
\(536\) 0 0
\(537\) −19.0524 −0.822171
\(538\) 0 0
\(539\) −5.89844 −0.254064
\(540\) 0 0
\(541\) −26.0403 −1.11956 −0.559780 0.828641i \(-0.689114\pi\)
−0.559780 + 0.828641i \(0.689114\pi\)
\(542\) 0 0
\(543\) −9.45601 −0.405796
\(544\) 0 0
\(545\) 27.2326 1.16652
\(546\) 0 0
\(547\) 3.18501 0.136181 0.0680907 0.997679i \(-0.478309\pi\)
0.0680907 + 0.997679i \(0.478309\pi\)
\(548\) 0 0
\(549\) 8.78763 0.375047
\(550\) 0 0
\(551\) 6.04930 0.257709
\(552\) 0 0
\(553\) −26.8635 −1.14235
\(554\) 0 0
\(555\) −19.3495 −0.821340
\(556\) 0 0
\(557\) −43.3455 −1.83661 −0.918304 0.395876i \(-0.870441\pi\)
−0.918304 + 0.395876i \(0.870441\pi\)
\(558\) 0 0
\(559\) 26.1688 1.10682
\(560\) 0 0
\(561\) 15.2930 0.645672
\(562\) 0 0
\(563\) −5.97360 −0.251757 −0.125879 0.992046i \(-0.540175\pi\)
−0.125879 + 0.992046i \(0.540175\pi\)
\(564\) 0 0
\(565\) −9.31907 −0.392056
\(566\) 0 0
\(567\) −2.07926 −0.0873205
\(568\) 0 0
\(569\) −33.9243 −1.42218 −0.711090 0.703101i \(-0.751798\pi\)
−0.711090 + 0.703101i \(0.751798\pi\)
\(570\) 0 0
\(571\) 7.50760 0.314183 0.157092 0.987584i \(-0.449788\pi\)
0.157092 + 0.987584i \(0.449788\pi\)
\(572\) 0 0
\(573\) 7.54585 0.315232
\(574\) 0 0
\(575\) −4.19970 −0.175140
\(576\) 0 0
\(577\) −0.765181 −0.0318549 −0.0159274 0.999873i \(-0.505070\pi\)
−0.0159274 + 0.999873i \(0.505070\pi\)
\(578\) 0 0
\(579\) −11.5660 −0.480668
\(580\) 0 0
\(581\) −7.41858 −0.307775
\(582\) 0 0
\(583\) −20.5627 −0.851622
\(584\) 0 0
\(585\) 11.8137 0.488437
\(586\) 0 0
\(587\) −30.1637 −1.24499 −0.622494 0.782624i \(-0.713881\pi\)
−0.622494 + 0.782624i \(0.713881\pi\)
\(588\) 0 0
\(589\) −17.8064 −0.733701
\(590\) 0 0
\(591\) 8.50436 0.349823
\(592\) 0 0
\(593\) 29.9808 1.23116 0.615581 0.788074i \(-0.288921\pi\)
0.615581 + 0.788074i \(0.288921\pi\)
\(594\) 0 0
\(595\) −25.7695 −1.05645
\(596\) 0 0
\(597\) −5.92204 −0.242373
\(598\) 0 0
\(599\) −13.0064 −0.531428 −0.265714 0.964052i \(-0.585608\pi\)
−0.265714 + 0.964052i \(0.585608\pi\)
\(600\) 0 0
\(601\) −18.3763 −0.749587 −0.374793 0.927108i \(-0.622286\pi\)
−0.374793 + 0.927108i \(0.622286\pi\)
\(602\) 0 0
\(603\) −8.71231 −0.354793
\(604\) 0 0
\(605\) 10.9723 0.446086
\(606\) 0 0
\(607\) −9.30961 −0.377866 −0.188933 0.981990i \(-0.560503\pi\)
−0.188933 + 0.981990i \(0.560503\pi\)
\(608\) 0 0
\(609\) −3.69085 −0.149561
\(610\) 0 0
\(611\) −44.3926 −1.79593
\(612\) 0 0
\(613\) 41.3076 1.66840 0.834200 0.551462i \(-0.185930\pi\)
0.834200 + 0.551462i \(0.185930\pi\)
\(614\) 0 0
\(615\) 5.54822 0.223726
\(616\) 0 0
\(617\) 37.1629 1.49612 0.748062 0.663629i \(-0.230985\pi\)
0.748062 + 0.663629i \(0.230985\pi\)
\(618\) 0 0
\(619\) 1.50754 0.0605932 0.0302966 0.999541i \(-0.490355\pi\)
0.0302966 + 0.999541i \(0.490355\pi\)
\(620\) 0 0
\(621\) −2.31931 −0.0930706
\(622\) 0 0
\(623\) −22.8879 −0.916983
\(624\) 0 0
\(625\) −12.6674 −0.506695
\(626\) 0 0
\(627\) 7.50975 0.299911
\(628\) 0 0
\(629\) 75.1935 2.99816
\(630\) 0 0
\(631\) −31.0906 −1.23770 −0.618849 0.785510i \(-0.712401\pi\)
−0.618849 + 0.785510i \(0.712401\pi\)
\(632\) 0 0
\(633\) 2.66403 0.105886
\(634\) 0 0
\(635\) 25.7050 1.02007
\(636\) 0 0
\(637\) 17.7068 0.701570
\(638\) 0 0
\(639\) −10.1955 −0.403326
\(640\) 0 0
\(641\) −6.14338 −0.242649 −0.121324 0.992613i \(-0.538714\pi\)
−0.121324 + 0.992613i \(0.538714\pi\)
\(642\) 0 0
\(643\) 24.2097 0.954739 0.477369 0.878703i \(-0.341590\pi\)
0.477369 + 0.878703i \(0.341590\pi\)
\(644\) 0 0
\(645\) −7.06457 −0.278167
\(646\) 0 0
\(647\) 35.2774 1.38690 0.693449 0.720506i \(-0.256090\pi\)
0.693449 + 0.720506i \(0.256090\pi\)
\(648\) 0 0
\(649\) −18.8532 −0.740052
\(650\) 0 0
\(651\) 10.8642 0.425801
\(652\) 0 0
\(653\) −37.6040 −1.47156 −0.735780 0.677221i \(-0.763184\pi\)
−0.735780 + 0.677221i \(0.763184\pi\)
\(654\) 0 0
\(655\) 18.7661 0.733253
\(656\) 0 0
\(657\) −9.60865 −0.374869
\(658\) 0 0
\(659\) −45.2872 −1.76414 −0.882070 0.471119i \(-0.843850\pi\)
−0.882070 + 0.471119i \(0.843850\pi\)
\(660\) 0 0
\(661\) 43.3602 1.68652 0.843258 0.537510i \(-0.180635\pi\)
0.843258 + 0.537510i \(0.180635\pi\)
\(662\) 0 0
\(663\) −45.9089 −1.78295
\(664\) 0 0
\(665\) −12.6543 −0.490714
\(666\) 0 0
\(667\) −4.11695 −0.159409
\(668\) 0 0
\(669\) −11.6207 −0.449282
\(670\) 0 0
\(671\) 19.3647 0.747565
\(672\) 0 0
\(673\) −34.4056 −1.32624 −0.663119 0.748514i \(-0.730768\pi\)
−0.663119 + 0.748514i \(0.730768\pi\)
\(674\) 0 0
\(675\) 1.81076 0.0696961
\(676\) 0 0
\(677\) −24.1246 −0.927184 −0.463592 0.886049i \(-0.653440\pi\)
−0.463592 + 0.886049i \(0.653440\pi\)
\(678\) 0 0
\(679\) −27.3979 −1.05143
\(680\) 0 0
\(681\) 5.73829 0.219892
\(682\) 0 0
\(683\) −29.6435 −1.13428 −0.567139 0.823622i \(-0.691950\pi\)
−0.567139 + 0.823622i \(0.691950\pi\)
\(684\) 0 0
\(685\) 20.6054 0.787290
\(686\) 0 0
\(687\) 2.94839 0.112488
\(688\) 0 0
\(689\) 61.7284 2.35166
\(690\) 0 0
\(691\) −34.9279 −1.32872 −0.664359 0.747414i \(-0.731295\pi\)
−0.664359 + 0.747414i \(0.731295\pi\)
\(692\) 0 0
\(693\) −4.58191 −0.174052
\(694\) 0 0
\(695\) −27.1806 −1.03102
\(696\) 0 0
\(697\) −21.5608 −0.816673
\(698\) 0 0
\(699\) −16.0655 −0.607653
\(700\) 0 0
\(701\) 34.2776 1.29465 0.647323 0.762216i \(-0.275889\pi\)
0.647323 + 0.762216i \(0.275889\pi\)
\(702\) 0 0
\(703\) 36.9244 1.39263
\(704\) 0 0
\(705\) 11.9843 0.451354
\(706\) 0 0
\(707\) −2.52267 −0.0948747
\(708\) 0 0
\(709\) −28.3856 −1.06605 −0.533023 0.846101i \(-0.678944\pi\)
−0.533023 + 0.846101i \(0.678944\pi\)
\(710\) 0 0
\(711\) 12.9198 0.484529
\(712\) 0 0
\(713\) 12.1185 0.453840
\(714\) 0 0
\(715\) 26.0330 0.973579
\(716\) 0 0
\(717\) 17.3794 0.649047
\(718\) 0 0
\(719\) 26.1303 0.974495 0.487247 0.873264i \(-0.338001\pi\)
0.487247 + 0.873264i \(0.338001\pi\)
\(720\) 0 0
\(721\) −32.9923 −1.22870
\(722\) 0 0
\(723\) 20.3416 0.756510
\(724\) 0 0
\(725\) 3.21424 0.119374
\(726\) 0 0
\(727\) 24.3997 0.904935 0.452467 0.891781i \(-0.350544\pi\)
0.452467 + 0.891781i \(0.350544\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 27.4534 1.01540
\(732\) 0 0
\(733\) −3.49438 −0.129068 −0.0645340 0.997916i \(-0.520556\pi\)
−0.0645340 + 0.997916i \(0.520556\pi\)
\(734\) 0 0
\(735\) −4.78016 −0.176319
\(736\) 0 0
\(737\) −19.1987 −0.707193
\(738\) 0 0
\(739\) 19.0377 0.700312 0.350156 0.936691i \(-0.386129\pi\)
0.350156 + 0.936691i \(0.386129\pi\)
\(740\) 0 0
\(741\) −22.5439 −0.828172
\(742\) 0 0
\(743\) 23.2950 0.854611 0.427306 0.904107i \(-0.359463\pi\)
0.427306 + 0.904107i \(0.359463\pi\)
\(744\) 0 0
\(745\) −21.4926 −0.787429
\(746\) 0 0
\(747\) 3.56790 0.130543
\(748\) 0 0
\(749\) 36.7252 1.34191
\(750\) 0 0
\(751\) 6.79988 0.248131 0.124066 0.992274i \(-0.460407\pi\)
0.124066 + 0.992274i \(0.460407\pi\)
\(752\) 0 0
\(753\) 23.3382 0.850492
\(754\) 0 0
\(755\) 28.4301 1.03468
\(756\) 0 0
\(757\) −13.7885 −0.501151 −0.250576 0.968097i \(-0.580620\pi\)
−0.250576 + 0.968097i \(0.580620\pi\)
\(758\) 0 0
\(759\) −5.11089 −0.185514
\(760\) 0 0
\(761\) −34.3678 −1.24583 −0.622916 0.782288i \(-0.714052\pi\)
−0.622916 + 0.782288i \(0.714052\pi\)
\(762\) 0 0
\(763\) 31.7068 1.14786
\(764\) 0 0
\(765\) 12.3936 0.448093
\(766\) 0 0
\(767\) 56.5964 2.04358
\(768\) 0 0
\(769\) −5.34192 −0.192635 −0.0963173 0.995351i \(-0.530706\pi\)
−0.0963173 + 0.995351i \(0.530706\pi\)
\(770\) 0 0
\(771\) −2.27427 −0.0819059
\(772\) 0 0
\(773\) −11.7999 −0.424413 −0.212206 0.977225i \(-0.568065\pi\)
−0.212206 + 0.977225i \(0.568065\pi\)
\(774\) 0 0
\(775\) −9.46127 −0.339859
\(776\) 0 0
\(777\) −22.5286 −0.808208
\(778\) 0 0
\(779\) −10.5876 −0.379340
\(780\) 0 0
\(781\) −22.4670 −0.803932
\(782\) 0 0
\(783\) 1.77508 0.0634362
\(784\) 0 0
\(785\) 1.93169 0.0689449
\(786\) 0 0
\(787\) −13.7088 −0.488667 −0.244333 0.969691i \(-0.578569\pi\)
−0.244333 + 0.969691i \(0.578569\pi\)
\(788\) 0 0
\(789\) −14.3925 −0.512385
\(790\) 0 0
\(791\) −10.8502 −0.385788
\(792\) 0 0
\(793\) −58.1318 −2.06432
\(794\) 0 0
\(795\) −16.6643 −0.591021
\(796\) 0 0
\(797\) −26.0602 −0.923099 −0.461549 0.887115i \(-0.652706\pi\)
−0.461549 + 0.887115i \(0.652706\pi\)
\(798\) 0 0
\(799\) −46.5718 −1.64759
\(800\) 0 0
\(801\) 11.0077 0.388939
\(802\) 0 0
\(803\) −21.1739 −0.747211
\(804\) 0 0
\(805\) 8.61212 0.303537
\(806\) 0 0
\(807\) −12.1315 −0.427051
\(808\) 0 0
\(809\) 5.10703 0.179554 0.0897769 0.995962i \(-0.471385\pi\)
0.0897769 + 0.995962i \(0.471385\pi\)
\(810\) 0 0
\(811\) 2.93796 0.103166 0.0515829 0.998669i \(-0.483573\pi\)
0.0515829 + 0.998669i \(0.483573\pi\)
\(812\) 0 0
\(813\) 26.5739 0.931988
\(814\) 0 0
\(815\) −9.39902 −0.329233
\(816\) 0 0
\(817\) 13.4812 0.471648
\(818\) 0 0
\(819\) 13.7547 0.480627
\(820\) 0 0
\(821\) 30.2615 1.05613 0.528066 0.849203i \(-0.322917\pi\)
0.528066 + 0.849203i \(0.322917\pi\)
\(822\) 0 0
\(823\) 41.9510 1.46232 0.731160 0.682206i \(-0.238979\pi\)
0.731160 + 0.682206i \(0.238979\pi\)
\(824\) 0 0
\(825\) 3.99023 0.138922
\(826\) 0 0
\(827\) 14.4416 0.502184 0.251092 0.967963i \(-0.419210\pi\)
0.251092 + 0.967963i \(0.419210\pi\)
\(828\) 0 0
\(829\) −20.8232 −0.723220 −0.361610 0.932330i \(-0.617773\pi\)
−0.361610 + 0.932330i \(0.617773\pi\)
\(830\) 0 0
\(831\) −16.6649 −0.578100
\(832\) 0 0
\(833\) 18.5761 0.643622
\(834\) 0 0
\(835\) 35.7807 1.23824
\(836\) 0 0
\(837\) −5.22504 −0.180604
\(838\) 0 0
\(839\) 25.3513 0.875225 0.437613 0.899164i \(-0.355824\pi\)
0.437613 + 0.899164i \(0.355824\pi\)
\(840\) 0 0
\(841\) −25.8491 −0.891348
\(842\) 0 0
\(843\) −18.0299 −0.620984
\(844\) 0 0
\(845\) −54.9339 −1.88978
\(846\) 0 0
\(847\) 12.7750 0.438954
\(848\) 0 0
\(849\) −22.0846 −0.757943
\(850\) 0 0
\(851\) −25.1295 −0.861428
\(852\) 0 0
\(853\) 35.1216 1.20254 0.601271 0.799045i \(-0.294661\pi\)
0.601271 + 0.799045i \(0.294661\pi\)
\(854\) 0 0
\(855\) 6.08599 0.208136
\(856\) 0 0
\(857\) −50.0517 −1.70973 −0.854867 0.518848i \(-0.826361\pi\)
−0.854867 + 0.518848i \(0.826361\pi\)
\(858\) 0 0
\(859\) −16.8713 −0.575641 −0.287820 0.957684i \(-0.592931\pi\)
−0.287820 + 0.957684i \(0.592931\pi\)
\(860\) 0 0
\(861\) 6.45978 0.220149
\(862\) 0 0
\(863\) 0.616318 0.0209797 0.0104899 0.999945i \(-0.496661\pi\)
0.0104899 + 0.999945i \(0.496661\pi\)
\(864\) 0 0
\(865\) −8.27533 −0.281370
\(866\) 0 0
\(867\) −31.1626 −1.05834
\(868\) 0 0
\(869\) 28.4704 0.965791
\(870\) 0 0
\(871\) 57.6336 1.95284
\(872\) 0 0
\(873\) 13.1768 0.445966
\(874\) 0 0
\(875\) −25.2899 −0.854955
\(876\) 0 0
\(877\) 5.27092 0.177986 0.0889931 0.996032i \(-0.471635\pi\)
0.0889931 + 0.996032i \(0.471635\pi\)
\(878\) 0 0
\(879\) −2.24011 −0.0755571
\(880\) 0 0
\(881\) −19.7534 −0.665508 −0.332754 0.943014i \(-0.607978\pi\)
−0.332754 + 0.943014i \(0.607978\pi\)
\(882\) 0 0
\(883\) −27.3820 −0.921478 −0.460739 0.887536i \(-0.652416\pi\)
−0.460739 + 0.887536i \(0.652416\pi\)
\(884\) 0 0
\(885\) −15.2788 −0.513592
\(886\) 0 0
\(887\) 22.3374 0.750017 0.375008 0.927021i \(-0.377640\pi\)
0.375008 + 0.927021i \(0.377640\pi\)
\(888\) 0 0
\(889\) 29.9283 1.00376
\(890\) 0 0
\(891\) 2.20363 0.0738243
\(892\) 0 0
\(893\) −22.8694 −0.765296
\(894\) 0 0
\(895\) −34.0246 −1.13732
\(896\) 0 0
\(897\) 15.3427 0.512276
\(898\) 0 0
\(899\) −9.27485 −0.309334
\(900\) 0 0
\(901\) 64.7586 2.15742
\(902\) 0 0
\(903\) −8.22526 −0.273720
\(904\) 0 0
\(905\) −16.8870 −0.561342
\(906\) 0 0
\(907\) −44.2716 −1.47002 −0.735008 0.678059i \(-0.762821\pi\)
−0.735008 + 0.678059i \(0.762821\pi\)
\(908\) 0 0
\(909\) 1.21326 0.0402411
\(910\) 0 0
\(911\) −0.801055 −0.0265401 −0.0132701 0.999912i \(-0.504224\pi\)
−0.0132701 + 0.999912i \(0.504224\pi\)
\(912\) 0 0
\(913\) 7.86233 0.260205
\(914\) 0 0
\(915\) 15.6934 0.518806
\(916\) 0 0
\(917\) 21.8493 0.721529
\(918\) 0 0
\(919\) 20.5873 0.679114 0.339557 0.940586i \(-0.389723\pi\)
0.339557 + 0.940586i \(0.389723\pi\)
\(920\) 0 0
\(921\) −21.0330 −0.693059
\(922\) 0 0
\(923\) 67.4449 2.21997
\(924\) 0 0
\(925\) 19.6194 0.645082
\(926\) 0 0
\(927\) 15.8674 0.521152
\(928\) 0 0
\(929\) −3.26242 −0.107036 −0.0535182 0.998567i \(-0.517044\pi\)
−0.0535182 + 0.998567i \(0.517044\pi\)
\(930\) 0 0
\(931\) 9.12192 0.298959
\(932\) 0 0
\(933\) −23.7129 −0.776327
\(934\) 0 0
\(935\) 27.3110 0.893164
\(936\) 0 0
\(937\) −14.1655 −0.462766 −0.231383 0.972863i \(-0.574325\pi\)
−0.231383 + 0.972863i \(0.574325\pi\)
\(938\) 0 0
\(939\) −16.7181 −0.545575
\(940\) 0 0
\(941\) −39.8614 −1.29945 −0.649723 0.760171i \(-0.725115\pi\)
−0.649723 + 0.760171i \(0.725115\pi\)
\(942\) 0 0
\(943\) 7.20556 0.234645
\(944\) 0 0
\(945\) −3.71323 −0.120791
\(946\) 0 0
\(947\) −6.00969 −0.195289 −0.0976444 0.995221i \(-0.531131\pi\)
−0.0976444 + 0.995221i \(0.531131\pi\)
\(948\) 0 0
\(949\) 63.5630 2.06334
\(950\) 0 0
\(951\) 8.17881 0.265216
\(952\) 0 0
\(953\) 7.59841 0.246137 0.123068 0.992398i \(-0.460727\pi\)
0.123068 + 0.992398i \(0.460727\pi\)
\(954\) 0 0
\(955\) 13.4757 0.436064
\(956\) 0 0
\(957\) 3.91162 0.126445
\(958\) 0 0
\(959\) 23.9908 0.774703
\(960\) 0 0
\(961\) −3.69901 −0.119323
\(962\) 0 0
\(963\) −17.6627 −0.569172
\(964\) 0 0
\(965\) −20.6551 −0.664913
\(966\) 0 0
\(967\) −7.25446 −0.233288 −0.116644 0.993174i \(-0.537214\pi\)
−0.116644 + 0.993174i \(0.537214\pi\)
\(968\) 0 0
\(969\) −23.6506 −0.759767
\(970\) 0 0
\(971\) −48.6297 −1.56060 −0.780301 0.625404i \(-0.784934\pi\)
−0.780301 + 0.625404i \(0.784934\pi\)
\(972\) 0 0
\(973\) −31.6463 −1.01453
\(974\) 0 0
\(975\) −11.9785 −0.383619
\(976\) 0 0
\(977\) −4.78591 −0.153115 −0.0765574 0.997065i \(-0.524393\pi\)
−0.0765574 + 0.997065i \(0.524393\pi\)
\(978\) 0 0
\(979\) 24.2569 0.775254
\(980\) 0 0
\(981\) −15.2491 −0.486867
\(982\) 0 0
\(983\) 51.9979 1.65848 0.829238 0.558896i \(-0.188775\pi\)
0.829238 + 0.558896i \(0.188775\pi\)
\(984\) 0 0
\(985\) 15.1875 0.483913
\(986\) 0 0
\(987\) 13.9533 0.444138
\(988\) 0 0
\(989\) −9.17487 −0.291744
\(990\) 0 0
\(991\) −8.61960 −0.273811 −0.136905 0.990584i \(-0.543716\pi\)
−0.136905 + 0.990584i \(0.543716\pi\)
\(992\) 0 0
\(993\) −24.5580 −0.779325
\(994\) 0 0
\(995\) −10.5759 −0.335277
\(996\) 0 0
\(997\) 38.7783 1.22812 0.614060 0.789259i \(-0.289535\pi\)
0.614060 + 0.789259i \(0.289535\pi\)
\(998\) 0 0
\(999\) 10.8349 0.342802
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 \(a_p\))