Properties

Label 8048.2.a.v.1.18
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.667261 q^{3}\) \(+0.307121 q^{5}\) \(-4.25072 q^{7}\) \(-2.55476 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.667261 q^{3}\) \(+0.307121 q^{5}\) \(-4.25072 q^{7}\) \(-2.55476 q^{9}\) \(-0.721001 q^{11}\) \(-4.50964 q^{13}\) \(+0.204930 q^{15}\) \(+7.96970 q^{17}\) \(+6.29804 q^{19}\) \(-2.83634 q^{21}\) \(+4.88211 q^{23}\) \(-4.90568 q^{25}\) \(-3.70648 q^{27}\) \(+7.38483 q^{29}\) \(+8.57254 q^{31}\) \(-0.481096 q^{33}\) \(-1.30549 q^{35}\) \(-0.903054 q^{37}\) \(-3.00911 q^{39}\) \(-9.48154 q^{41}\) \(+1.86056 q^{43}\) \(-0.784621 q^{45}\) \(+0.432654 q^{47}\) \(+11.0686 q^{49}\) \(+5.31787 q^{51}\) \(-13.1315 q^{53}\) \(-0.221434 q^{55}\) \(+4.20244 q^{57}\) \(-3.80194 q^{59}\) \(-6.98011 q^{61}\) \(+10.8596 q^{63}\) \(-1.38501 q^{65}\) \(-4.59763 q^{67}\) \(+3.25764 q^{69}\) \(-1.98521 q^{71}\) \(+3.07898 q^{73}\) \(-3.27337 q^{75}\) \(+3.06477 q^{77}\) \(-1.39903 q^{79}\) \(+5.19110 q^{81}\) \(+8.69377 q^{83}\) \(+2.44766 q^{85}\) \(+4.92761 q^{87}\) \(+3.04116 q^{89}\) \(+19.1692 q^{91}\) \(+5.72013 q^{93}\) \(+1.93426 q^{95}\) \(-5.67187 q^{97}\) \(+1.84199 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 31q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 22q^{25} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 26q^{33} \) \(\mathstrut +\mathstrut 13q^{35} \) \(\mathstrut -\mathstrut 67q^{37} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut -\mathstrut 57q^{45} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 20q^{49} \) \(\mathstrut +\mathstrut 11q^{51} \) \(\mathstrut -\mathstrut 58q^{53} \) \(\mathstrut -\mathstrut 15q^{55} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 55q^{61} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 44q^{69} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 5q^{73} \) \(\mathstrut +\mathstrut 25q^{75} \) \(\mathstrut -\mathstrut 50q^{77} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 78q^{85} \) \(\mathstrut +\mathstrut 11q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut +\mathstrut 15q^{91} \) \(\mathstrut -\mathstrut 83q^{93} \) \(\mathstrut +\mathstrut 27q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 70q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0.667261 0.385244 0.192622 0.981273i \(-0.438301\pi\)
0.192622 + 0.981273i \(0.438301\pi\)
\(4\) 0 0
\(5\) 0.307121 0.137349 0.0686743 0.997639i \(-0.478123\pi\)
0.0686743 + 0.997639i \(0.478123\pi\)
\(6\) 0 0
\(7\) −4.25072 −1.60662 −0.803311 0.595560i \(-0.796930\pi\)
−0.803311 + 0.595560i \(0.796930\pi\)
\(8\) 0 0
\(9\) −2.55476 −0.851587
\(10\) 0 0
\(11\) −0.721001 −0.217390 −0.108695 0.994075i \(-0.534667\pi\)
−0.108695 + 0.994075i \(0.534667\pi\)
\(12\) 0 0
\(13\) −4.50964 −1.25075 −0.625375 0.780325i \(-0.715054\pi\)
−0.625375 + 0.780325i \(0.715054\pi\)
\(14\) 0 0
\(15\) 0.204930 0.0529127
\(16\) 0 0
\(17\) 7.96970 1.93294 0.966468 0.256786i \(-0.0826635\pi\)
0.966468 + 0.256786i \(0.0826635\pi\)
\(18\) 0 0
\(19\) 6.29804 1.44487 0.722435 0.691439i \(-0.243023\pi\)
0.722435 + 0.691439i \(0.243023\pi\)
\(20\) 0 0
\(21\) −2.83634 −0.618941
\(22\) 0 0
\(23\) 4.88211 1.01799 0.508995 0.860769i \(-0.330017\pi\)
0.508995 + 0.860769i \(0.330017\pi\)
\(24\) 0 0
\(25\) −4.90568 −0.981135
\(26\) 0 0
\(27\) −3.70648 −0.713312
\(28\) 0 0
\(29\) 7.38483 1.37133 0.685664 0.727918i \(-0.259512\pi\)
0.685664 + 0.727918i \(0.259512\pi\)
\(30\) 0 0
\(31\) 8.57254 1.53967 0.769837 0.638241i \(-0.220337\pi\)
0.769837 + 0.638241i \(0.220337\pi\)
\(32\) 0 0
\(33\) −0.481096 −0.0837480
\(34\) 0 0
\(35\) −1.30549 −0.220667
\(36\) 0 0
\(37\) −0.903054 −0.148461 −0.0742306 0.997241i \(-0.523650\pi\)
−0.0742306 + 0.997241i \(0.523650\pi\)
\(38\) 0 0
\(39\) −3.00911 −0.481843
\(40\) 0 0
\(41\) −9.48154 −1.48077 −0.740384 0.672184i \(-0.765356\pi\)
−0.740384 + 0.672184i \(0.765356\pi\)
\(42\) 0 0
\(43\) 1.86056 0.283732 0.141866 0.989886i \(-0.454690\pi\)
0.141866 + 0.989886i \(0.454690\pi\)
\(44\) 0 0
\(45\) −0.784621 −0.116964
\(46\) 0 0
\(47\) 0.432654 0.0631090 0.0315545 0.999502i \(-0.489954\pi\)
0.0315545 + 0.999502i \(0.489954\pi\)
\(48\) 0 0
\(49\) 11.0686 1.58123
\(50\) 0 0
\(51\) 5.31787 0.744651
\(52\) 0 0
\(53\) −13.1315 −1.80375 −0.901876 0.431994i \(-0.857810\pi\)
−0.901876 + 0.431994i \(0.857810\pi\)
\(54\) 0 0
\(55\) −0.221434 −0.0298582
\(56\) 0 0
\(57\) 4.20244 0.556627
\(58\) 0 0
\(59\) −3.80194 −0.494971 −0.247485 0.968892i \(-0.579604\pi\)
−0.247485 + 0.968892i \(0.579604\pi\)
\(60\) 0 0
\(61\) −6.98011 −0.893712 −0.446856 0.894606i \(-0.647456\pi\)
−0.446856 + 0.894606i \(0.647456\pi\)
\(62\) 0 0
\(63\) 10.8596 1.36818
\(64\) 0 0
\(65\) −1.38501 −0.171789
\(66\) 0 0
\(67\) −4.59763 −0.561690 −0.280845 0.959753i \(-0.590615\pi\)
−0.280845 + 0.959753i \(0.590615\pi\)
\(68\) 0 0
\(69\) 3.25764 0.392174
\(70\) 0 0
\(71\) −1.98521 −0.235601 −0.117800 0.993037i \(-0.537584\pi\)
−0.117800 + 0.993037i \(0.537584\pi\)
\(72\) 0 0
\(73\) 3.07898 0.360368 0.180184 0.983633i \(-0.442331\pi\)
0.180184 + 0.983633i \(0.442331\pi\)
\(74\) 0 0
\(75\) −3.27337 −0.377976
\(76\) 0 0
\(77\) 3.06477 0.349263
\(78\) 0 0
\(79\) −1.39903 −0.157403 −0.0787014 0.996898i \(-0.525077\pi\)
−0.0787014 + 0.996898i \(0.525077\pi\)
\(80\) 0 0
\(81\) 5.19110 0.576789
\(82\) 0 0
\(83\) 8.69377 0.954265 0.477132 0.878831i \(-0.341676\pi\)
0.477132 + 0.878831i \(0.341676\pi\)
\(84\) 0 0
\(85\) 2.44766 0.265486
\(86\) 0 0
\(87\) 4.92761 0.528296
\(88\) 0 0
\(89\) 3.04116 0.322362 0.161181 0.986925i \(-0.448470\pi\)
0.161181 + 0.986925i \(0.448470\pi\)
\(90\) 0 0
\(91\) 19.1692 2.00948
\(92\) 0 0
\(93\) 5.72013 0.593149
\(94\) 0 0
\(95\) 1.93426 0.198451
\(96\) 0 0
\(97\) −5.67187 −0.575891 −0.287945 0.957647i \(-0.592972\pi\)
−0.287945 + 0.957647i \(0.592972\pi\)
\(98\) 0 0
\(99\) 1.84199 0.185126
\(100\) 0 0
\(101\) 6.91983 0.688548 0.344274 0.938869i \(-0.388125\pi\)
0.344274 + 0.938869i \(0.388125\pi\)
\(102\) 0 0
\(103\) 1.40902 0.138835 0.0694174 0.997588i \(-0.477886\pi\)
0.0694174 + 0.997588i \(0.477886\pi\)
\(104\) 0 0
\(105\) −0.871100 −0.0850106
\(106\) 0 0
\(107\) 3.70772 0.358439 0.179220 0.983809i \(-0.442643\pi\)
0.179220 + 0.983809i \(0.442643\pi\)
\(108\) 0 0
\(109\) −6.48992 −0.621622 −0.310811 0.950472i \(-0.600601\pi\)
−0.310811 + 0.950472i \(0.600601\pi\)
\(110\) 0 0
\(111\) −0.602573 −0.0571937
\(112\) 0 0
\(113\) −10.0417 −0.944645 −0.472322 0.881426i \(-0.656584\pi\)
−0.472322 + 0.881426i \(0.656584\pi\)
\(114\) 0 0
\(115\) 1.49940 0.139820
\(116\) 0 0
\(117\) 11.5211 1.06512
\(118\) 0 0
\(119\) −33.8770 −3.10550
\(120\) 0 0
\(121\) −10.4802 −0.952742
\(122\) 0 0
\(123\) −6.32667 −0.570456
\(124\) 0 0
\(125\) −3.04224 −0.272106
\(126\) 0 0
\(127\) −19.2654 −1.70953 −0.854764 0.519018i \(-0.826298\pi\)
−0.854764 + 0.519018i \(0.826298\pi\)
\(128\) 0 0
\(129\) 1.24148 0.109306
\(130\) 0 0
\(131\) −20.1144 −1.75740 −0.878701 0.477372i \(-0.841589\pi\)
−0.878701 + 0.477372i \(0.841589\pi\)
\(132\) 0 0
\(133\) −26.7712 −2.32136
\(134\) 0 0
\(135\) −1.13834 −0.0979725
\(136\) 0 0
\(137\) 16.4500 1.40542 0.702711 0.711476i \(-0.251973\pi\)
0.702711 + 0.711476i \(0.251973\pi\)
\(138\) 0 0
\(139\) 9.60624 0.814791 0.407395 0.913252i \(-0.366437\pi\)
0.407395 + 0.913252i \(0.366437\pi\)
\(140\) 0 0
\(141\) 0.288693 0.0243124
\(142\) 0 0
\(143\) 3.25145 0.271900
\(144\) 0 0
\(145\) 2.26804 0.188350
\(146\) 0 0
\(147\) 7.38567 0.609160
\(148\) 0 0
\(149\) −22.3862 −1.83395 −0.916974 0.398947i \(-0.869376\pi\)
−0.916974 + 0.398947i \(0.869376\pi\)
\(150\) 0 0
\(151\) −11.8741 −0.966297 −0.483149 0.875538i \(-0.660507\pi\)
−0.483149 + 0.875538i \(0.660507\pi\)
\(152\) 0 0
\(153\) −20.3607 −1.64606
\(154\) 0 0
\(155\) 2.63281 0.211472
\(156\) 0 0
\(157\) −18.8085 −1.50108 −0.750540 0.660825i \(-0.770207\pi\)
−0.750540 + 0.660825i \(0.770207\pi\)
\(158\) 0 0
\(159\) −8.76215 −0.694884
\(160\) 0 0
\(161\) −20.7525 −1.63552
\(162\) 0 0
\(163\) 23.9259 1.87402 0.937012 0.349297i \(-0.113580\pi\)
0.937012 + 0.349297i \(0.113580\pi\)
\(164\) 0 0
\(165\) −0.147755 −0.0115027
\(166\) 0 0
\(167\) −15.9339 −1.23301 −0.616503 0.787353i \(-0.711451\pi\)
−0.616503 + 0.787353i \(0.711451\pi\)
\(168\) 0 0
\(169\) 7.33686 0.564374
\(170\) 0 0
\(171\) −16.0900 −1.23043
\(172\) 0 0
\(173\) −6.77409 −0.515024 −0.257512 0.966275i \(-0.582903\pi\)
−0.257512 + 0.966275i \(0.582903\pi\)
\(174\) 0 0
\(175\) 20.8527 1.57631
\(176\) 0 0
\(177\) −2.53689 −0.190684
\(178\) 0 0
\(179\) 10.7988 0.807142 0.403571 0.914948i \(-0.367769\pi\)
0.403571 + 0.914948i \(0.367769\pi\)
\(180\) 0 0
\(181\) 12.9864 0.965269 0.482635 0.875822i \(-0.339680\pi\)
0.482635 + 0.875822i \(0.339680\pi\)
\(182\) 0 0
\(183\) −4.65756 −0.344297
\(184\) 0 0
\(185\) −0.277347 −0.0203909
\(186\) 0 0
\(187\) −5.74616 −0.420201
\(188\) 0 0
\(189\) 15.7552 1.14602
\(190\) 0 0
\(191\) 13.7261 0.993188 0.496594 0.867983i \(-0.334584\pi\)
0.496594 + 0.867983i \(0.334584\pi\)
\(192\) 0 0
\(193\) 13.4246 0.966324 0.483162 0.875531i \(-0.339488\pi\)
0.483162 + 0.875531i \(0.339488\pi\)
\(194\) 0 0
\(195\) −0.924160 −0.0661805
\(196\) 0 0
\(197\) −8.99175 −0.640635 −0.320318 0.947310i \(-0.603790\pi\)
−0.320318 + 0.947310i \(0.603790\pi\)
\(198\) 0 0
\(199\) −14.5387 −1.03062 −0.515311 0.857003i \(-0.672324\pi\)
−0.515311 + 0.857003i \(0.672324\pi\)
\(200\) 0 0
\(201\) −3.06782 −0.216387
\(202\) 0 0
\(203\) −31.3909 −2.20321
\(204\) 0 0
\(205\) −2.91198 −0.203382
\(206\) 0 0
\(207\) −12.4726 −0.866908
\(208\) 0 0
\(209\) −4.54089 −0.314100
\(210\) 0 0
\(211\) 1.55378 0.106966 0.0534832 0.998569i \(-0.482968\pi\)
0.0534832 + 0.998569i \(0.482968\pi\)
\(212\) 0 0
\(213\) −1.32465 −0.0907636
\(214\) 0 0
\(215\) 0.571416 0.0389702
\(216\) 0 0
\(217\) −36.4395 −2.47367
\(218\) 0 0
\(219\) 2.05449 0.138829
\(220\) 0 0
\(221\) −35.9405 −2.41762
\(222\) 0 0
\(223\) −15.7987 −1.05796 −0.528978 0.848635i \(-0.677425\pi\)
−0.528978 + 0.848635i \(0.677425\pi\)
\(224\) 0 0
\(225\) 12.5328 0.835523
\(226\) 0 0
\(227\) 20.1142 1.33502 0.667512 0.744599i \(-0.267359\pi\)
0.667512 + 0.744599i \(0.267359\pi\)
\(228\) 0 0
\(229\) −0.478210 −0.0316010 −0.0158005 0.999875i \(-0.505030\pi\)
−0.0158005 + 0.999875i \(0.505030\pi\)
\(230\) 0 0
\(231\) 2.04500 0.134551
\(232\) 0 0
\(233\) −26.9502 −1.76557 −0.882783 0.469781i \(-0.844333\pi\)
−0.882783 + 0.469781i \(0.844333\pi\)
\(234\) 0 0
\(235\) 0.132877 0.00866794
\(236\) 0 0
\(237\) −0.933516 −0.0606384
\(238\) 0 0
\(239\) −2.77549 −0.179532 −0.0897659 0.995963i \(-0.528612\pi\)
−0.0897659 + 0.995963i \(0.528612\pi\)
\(240\) 0 0
\(241\) 4.65974 0.300160 0.150080 0.988674i \(-0.452047\pi\)
0.150080 + 0.988674i \(0.452047\pi\)
\(242\) 0 0
\(243\) 14.5833 0.935516
\(244\) 0 0
\(245\) 3.39941 0.217180
\(246\) 0 0
\(247\) −28.4019 −1.80717
\(248\) 0 0
\(249\) 5.80101 0.367624
\(250\) 0 0
\(251\) −20.0865 −1.26785 −0.633926 0.773394i \(-0.718558\pi\)
−0.633926 + 0.773394i \(0.718558\pi\)
\(252\) 0 0
\(253\) −3.52000 −0.221301
\(254\) 0 0
\(255\) 1.63323 0.102277
\(256\) 0 0
\(257\) −12.3177 −0.768358 −0.384179 0.923259i \(-0.625515\pi\)
−0.384179 + 0.923259i \(0.625515\pi\)
\(258\) 0 0
\(259\) 3.83863 0.238521
\(260\) 0 0
\(261\) −18.8665 −1.16781
\(262\) 0 0
\(263\) −5.98111 −0.368811 −0.184406 0.982850i \(-0.559036\pi\)
−0.184406 + 0.982850i \(0.559036\pi\)
\(264\) 0 0
\(265\) −4.03296 −0.247743
\(266\) 0 0
\(267\) 2.02925 0.124188
\(268\) 0 0
\(269\) −17.6549 −1.07644 −0.538218 0.842806i \(-0.680902\pi\)
−0.538218 + 0.842806i \(0.680902\pi\)
\(270\) 0 0
\(271\) 16.3089 0.990694 0.495347 0.868695i \(-0.335041\pi\)
0.495347 + 0.868695i \(0.335041\pi\)
\(272\) 0 0
\(273\) 12.7909 0.774139
\(274\) 0 0
\(275\) 3.53700 0.213289
\(276\) 0 0
\(277\) −8.18714 −0.491917 −0.245959 0.969280i \(-0.579103\pi\)
−0.245959 + 0.969280i \(0.579103\pi\)
\(278\) 0 0
\(279\) −21.9008 −1.31117
\(280\) 0 0
\(281\) −20.6880 −1.23414 −0.617070 0.786908i \(-0.711681\pi\)
−0.617070 + 0.786908i \(0.711681\pi\)
\(282\) 0 0
\(283\) −0.937311 −0.0557174 −0.0278587 0.999612i \(-0.508869\pi\)
−0.0278587 + 0.999612i \(0.508869\pi\)
\(284\) 0 0
\(285\) 1.29066 0.0764520
\(286\) 0 0
\(287\) 40.3034 2.37903
\(288\) 0 0
\(289\) 46.5162 2.73624
\(290\) 0 0
\(291\) −3.78462 −0.221858
\(292\) 0 0
\(293\) −15.9140 −0.929707 −0.464854 0.885387i \(-0.653893\pi\)
−0.464854 + 0.885387i \(0.653893\pi\)
\(294\) 0 0
\(295\) −1.16766 −0.0679836
\(296\) 0 0
\(297\) 2.67237 0.155067
\(298\) 0 0
\(299\) −22.0166 −1.27325
\(300\) 0 0
\(301\) −7.90871 −0.455850
\(302\) 0 0
\(303\) 4.61733 0.265259
\(304\) 0 0
\(305\) −2.14374 −0.122750
\(306\) 0 0
\(307\) −12.1293 −0.692258 −0.346129 0.938187i \(-0.612504\pi\)
−0.346129 + 0.938187i \(0.612504\pi\)
\(308\) 0 0
\(309\) 0.940184 0.0534852
\(310\) 0 0
\(311\) 9.73181 0.551840 0.275920 0.961181i \(-0.411017\pi\)
0.275920 + 0.961181i \(0.411017\pi\)
\(312\) 0 0
\(313\) −8.94322 −0.505501 −0.252750 0.967532i \(-0.581335\pi\)
−0.252750 + 0.967532i \(0.581335\pi\)
\(314\) 0 0
\(315\) 3.33520 0.187917
\(316\) 0 0
\(317\) −31.7836 −1.78515 −0.892573 0.450902i \(-0.851102\pi\)
−0.892573 + 0.450902i \(0.851102\pi\)
\(318\) 0 0
\(319\) −5.32447 −0.298113
\(320\) 0 0
\(321\) 2.47402 0.138086
\(322\) 0 0
\(323\) 50.1935 2.79284
\(324\) 0 0
\(325\) 22.1228 1.22715
\(326\) 0 0
\(327\) −4.33047 −0.239476
\(328\) 0 0
\(329\) −1.83909 −0.101392
\(330\) 0 0
\(331\) −5.60674 −0.308174 −0.154087 0.988057i \(-0.549244\pi\)
−0.154087 + 0.988057i \(0.549244\pi\)
\(332\) 0 0
\(333\) 2.30709 0.126428
\(334\) 0 0
\(335\) −1.41203 −0.0771474
\(336\) 0 0
\(337\) 14.7356 0.802701 0.401350 0.915925i \(-0.368541\pi\)
0.401350 + 0.915925i \(0.368541\pi\)
\(338\) 0 0
\(339\) −6.70044 −0.363918
\(340\) 0 0
\(341\) −6.18081 −0.334710
\(342\) 0 0
\(343\) −17.2946 −0.933821
\(344\) 0 0
\(345\) 1.00049 0.0538646
\(346\) 0 0
\(347\) 21.2441 1.14044 0.570222 0.821491i \(-0.306857\pi\)
0.570222 + 0.821491i \(0.306857\pi\)
\(348\) 0 0
\(349\) 5.58047 0.298716 0.149358 0.988783i \(-0.452279\pi\)
0.149358 + 0.988783i \(0.452279\pi\)
\(350\) 0 0
\(351\) 16.7149 0.892175
\(352\) 0 0
\(353\) −23.5258 −1.25215 −0.626075 0.779763i \(-0.715340\pi\)
−0.626075 + 0.779763i \(0.715340\pi\)
\(354\) 0 0
\(355\) −0.609698 −0.0323594
\(356\) 0 0
\(357\) −22.6048 −1.19637
\(358\) 0 0
\(359\) −3.93140 −0.207492 −0.103746 0.994604i \(-0.533083\pi\)
−0.103746 + 0.994604i \(0.533083\pi\)
\(360\) 0 0
\(361\) 20.6654 1.08765
\(362\) 0 0
\(363\) −6.99300 −0.367038
\(364\) 0 0
\(365\) 0.945621 0.0494960
\(366\) 0 0
\(367\) 33.7574 1.76212 0.881061 0.473003i \(-0.156830\pi\)
0.881061 + 0.473003i \(0.156830\pi\)
\(368\) 0 0
\(369\) 24.2231 1.26100
\(370\) 0 0
\(371\) 55.8184 2.89795
\(372\) 0 0
\(373\) 21.9721 1.13767 0.568836 0.822451i \(-0.307394\pi\)
0.568836 + 0.822451i \(0.307394\pi\)
\(374\) 0 0
\(375\) −2.02997 −0.104827
\(376\) 0 0
\(377\) −33.3029 −1.71519
\(378\) 0 0
\(379\) 36.9373 1.89734 0.948672 0.316262i \(-0.102428\pi\)
0.948672 + 0.316262i \(0.102428\pi\)
\(380\) 0 0
\(381\) −12.8551 −0.658584
\(382\) 0 0
\(383\) −38.3731 −1.96077 −0.980387 0.197084i \(-0.936853\pi\)
−0.980387 + 0.197084i \(0.936853\pi\)
\(384\) 0 0
\(385\) 0.941256 0.0479708
\(386\) 0 0
\(387\) −4.75328 −0.241623
\(388\) 0 0
\(389\) 3.13829 0.159117 0.0795587 0.996830i \(-0.474649\pi\)
0.0795587 + 0.996830i \(0.474649\pi\)
\(390\) 0 0
\(391\) 38.9090 1.96771
\(392\) 0 0
\(393\) −13.4216 −0.677028
\(394\) 0 0
\(395\) −0.429670 −0.0216191
\(396\) 0 0
\(397\) −12.6226 −0.633509 −0.316755 0.948508i \(-0.602593\pi\)
−0.316755 + 0.948508i \(0.602593\pi\)
\(398\) 0 0
\(399\) −17.8634 −0.894289
\(400\) 0 0
\(401\) −13.1940 −0.658874 −0.329437 0.944177i \(-0.606859\pi\)
−0.329437 + 0.944177i \(0.606859\pi\)
\(402\) 0 0
\(403\) −38.6591 −1.92575
\(404\) 0 0
\(405\) 1.59429 0.0792211
\(406\) 0 0
\(407\) 0.651103 0.0322740
\(408\) 0 0
\(409\) 18.6687 0.923110 0.461555 0.887112i \(-0.347292\pi\)
0.461555 + 0.887112i \(0.347292\pi\)
\(410\) 0 0
\(411\) 10.9765 0.541430
\(412\) 0 0
\(413\) 16.1610 0.795231
\(414\) 0 0
\(415\) 2.67004 0.131067
\(416\) 0 0
\(417\) 6.40987 0.313893
\(418\) 0 0
\(419\) −23.8992 −1.16755 −0.583777 0.811914i \(-0.698426\pi\)
−0.583777 + 0.811914i \(0.698426\pi\)
\(420\) 0 0
\(421\) 12.2272 0.595915 0.297958 0.954579i \(-0.403695\pi\)
0.297958 + 0.954579i \(0.403695\pi\)
\(422\) 0 0
\(423\) −1.10533 −0.0537429
\(424\) 0 0
\(425\) −39.0968 −1.89647
\(426\) 0 0
\(427\) 29.6705 1.43586
\(428\) 0 0
\(429\) 2.16957 0.104748
\(430\) 0 0
\(431\) −12.6741 −0.610491 −0.305246 0.952274i \(-0.598739\pi\)
−0.305246 + 0.952274i \(0.598739\pi\)
\(432\) 0 0
\(433\) −34.0284 −1.63530 −0.817651 0.575714i \(-0.804724\pi\)
−0.817651 + 0.575714i \(0.804724\pi\)
\(434\) 0 0
\(435\) 1.51337 0.0725607
\(436\) 0 0
\(437\) 30.7477 1.47086
\(438\) 0 0
\(439\) 24.6920 1.17849 0.589244 0.807956i \(-0.299426\pi\)
0.589244 + 0.807956i \(0.299426\pi\)
\(440\) 0 0
\(441\) −28.2777 −1.34656
\(442\) 0 0
\(443\) 24.5906 1.16833 0.584167 0.811633i \(-0.301421\pi\)
0.584167 + 0.811633i \(0.301421\pi\)
\(444\) 0 0
\(445\) 0.934002 0.0442760
\(446\) 0 0
\(447\) −14.9374 −0.706517
\(448\) 0 0
\(449\) −7.17674 −0.338691 −0.169346 0.985557i \(-0.554165\pi\)
−0.169346 + 0.985557i \(0.554165\pi\)
\(450\) 0 0
\(451\) 6.83620 0.321904
\(452\) 0 0
\(453\) −7.92310 −0.372260
\(454\) 0 0
\(455\) 5.88727 0.275999
\(456\) 0 0
\(457\) 23.1927 1.08491 0.542455 0.840085i \(-0.317495\pi\)
0.542455 + 0.840085i \(0.317495\pi\)
\(458\) 0 0
\(459\) −29.5395 −1.37879
\(460\) 0 0
\(461\) −5.75291 −0.267940 −0.133970 0.990985i \(-0.542773\pi\)
−0.133970 + 0.990985i \(0.542773\pi\)
\(462\) 0 0
\(463\) −19.8464 −0.922342 −0.461171 0.887311i \(-0.652571\pi\)
−0.461171 + 0.887311i \(0.652571\pi\)
\(464\) 0 0
\(465\) 1.75677 0.0814683
\(466\) 0 0
\(467\) 13.3506 0.617792 0.308896 0.951096i \(-0.400040\pi\)
0.308896 + 0.951096i \(0.400040\pi\)
\(468\) 0 0
\(469\) 19.5432 0.902423
\(470\) 0 0
\(471\) −12.5502 −0.578282
\(472\) 0 0
\(473\) −1.34146 −0.0616805
\(474\) 0 0
\(475\) −30.8962 −1.41761
\(476\) 0 0
\(477\) 33.5479 1.53605
\(478\) 0 0
\(479\) 8.17837 0.373679 0.186840 0.982390i \(-0.440176\pi\)
0.186840 + 0.982390i \(0.440176\pi\)
\(480\) 0 0
\(481\) 4.07245 0.185688
\(482\) 0 0
\(483\) −13.8473 −0.630075
\(484\) 0 0
\(485\) −1.74195 −0.0790978
\(486\) 0 0
\(487\) −32.0826 −1.45380 −0.726900 0.686743i \(-0.759040\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(488\) 0 0
\(489\) 15.9649 0.721956
\(490\) 0 0
\(491\) −39.3077 −1.77393 −0.886965 0.461836i \(-0.847191\pi\)
−0.886965 + 0.461836i \(0.847191\pi\)
\(492\) 0 0
\(493\) 58.8549 2.65069
\(494\) 0 0
\(495\) 0.565712 0.0254269
\(496\) 0 0
\(497\) 8.43855 0.378521
\(498\) 0 0
\(499\) 21.2872 0.952947 0.476474 0.879189i \(-0.341915\pi\)
0.476474 + 0.879189i \(0.341915\pi\)
\(500\) 0 0
\(501\) −10.6321 −0.475008
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 2.12522 0.0945712
\(506\) 0 0
\(507\) 4.89560 0.217421
\(508\) 0 0
\(509\) 32.9814 1.46187 0.730937 0.682445i \(-0.239083\pi\)
0.730937 + 0.682445i \(0.239083\pi\)
\(510\) 0 0
\(511\) −13.0879 −0.578975
\(512\) 0 0
\(513\) −23.3436 −1.03064
\(514\) 0 0
\(515\) 0.432739 0.0190688
\(516\) 0 0
\(517\) −0.311944 −0.0137193
\(518\) 0 0
\(519\) −4.52009 −0.198410
\(520\) 0 0
\(521\) 43.6614 1.91284 0.956421 0.291990i \(-0.0943175\pi\)
0.956421 + 0.291990i \(0.0943175\pi\)
\(522\) 0 0
\(523\) −17.6035 −0.769748 −0.384874 0.922969i \(-0.625755\pi\)
−0.384874 + 0.922969i \(0.625755\pi\)
\(524\) 0 0
\(525\) 13.9142 0.607264
\(526\) 0 0
\(527\) 68.3206 2.97609
\(528\) 0 0
\(529\) 0.834992 0.0363040
\(530\) 0 0
\(531\) 9.71306 0.421511
\(532\) 0 0
\(533\) 42.7584 1.85207
\(534\) 0 0
\(535\) 1.13872 0.0492311
\(536\) 0 0
\(537\) 7.20564 0.310946
\(538\) 0 0
\(539\) −7.98049 −0.343744
\(540\) 0 0
\(541\) −12.7313 −0.547361 −0.273681 0.961821i \(-0.588241\pi\)
−0.273681 + 0.961821i \(0.588241\pi\)
\(542\) 0 0
\(543\) 8.66530 0.371864
\(544\) 0 0
\(545\) −1.99319 −0.0853789
\(546\) 0 0
\(547\) −8.99668 −0.384670 −0.192335 0.981329i \(-0.561606\pi\)
−0.192335 + 0.981329i \(0.561606\pi\)
\(548\) 0 0
\(549\) 17.8325 0.761074
\(550\) 0 0
\(551\) 46.5100 1.98139
\(552\) 0 0
\(553\) 5.94687 0.252887
\(554\) 0 0
\(555\) −0.185063 −0.00785548
\(556\) 0 0
\(557\) 15.6045 0.661182 0.330591 0.943774i \(-0.392752\pi\)
0.330591 + 0.943774i \(0.392752\pi\)
\(558\) 0 0
\(559\) −8.39044 −0.354878
\(560\) 0 0
\(561\) −3.83419 −0.161880
\(562\) 0 0
\(563\) −30.8071 −1.29837 −0.649183 0.760632i \(-0.724889\pi\)
−0.649183 + 0.760632i \(0.724889\pi\)
\(564\) 0 0
\(565\) −3.08402 −0.129746
\(566\) 0 0
\(567\) −22.0659 −0.926681
\(568\) 0 0
\(569\) 12.3008 0.515677 0.257838 0.966188i \(-0.416990\pi\)
0.257838 + 0.966188i \(0.416990\pi\)
\(570\) 0 0
\(571\) −35.1173 −1.46961 −0.734807 0.678276i \(-0.762727\pi\)
−0.734807 + 0.678276i \(0.762727\pi\)
\(572\) 0 0
\(573\) 9.15892 0.382619
\(574\) 0 0
\(575\) −23.9501 −0.998786
\(576\) 0 0
\(577\) −15.6086 −0.649796 −0.324898 0.945749i \(-0.605330\pi\)
−0.324898 + 0.945749i \(0.605330\pi\)
\(578\) 0 0
\(579\) 8.95772 0.372270
\(580\) 0 0
\(581\) −36.9548 −1.53314
\(582\) 0 0
\(583\) 9.46783 0.392118
\(584\) 0 0
\(585\) 3.53836 0.146293
\(586\) 0 0
\(587\) −14.0930 −0.581681 −0.290841 0.956771i \(-0.593935\pi\)
−0.290841 + 0.956771i \(0.593935\pi\)
\(588\) 0 0
\(589\) 53.9902 2.22463
\(590\) 0 0
\(591\) −5.99984 −0.246801
\(592\) 0 0
\(593\) −3.74557 −0.153812 −0.0769060 0.997038i \(-0.524504\pi\)
−0.0769060 + 0.997038i \(0.524504\pi\)
\(594\) 0 0
\(595\) −10.4043 −0.426536
\(596\) 0 0
\(597\) −9.70112 −0.397040
\(598\) 0 0
\(599\) −4.31104 −0.176144 −0.0880722 0.996114i \(-0.528071\pi\)
−0.0880722 + 0.996114i \(0.528071\pi\)
\(600\) 0 0
\(601\) −9.45071 −0.385503 −0.192751 0.981248i \(-0.561741\pi\)
−0.192751 + 0.981248i \(0.561741\pi\)
\(602\) 0 0
\(603\) 11.7459 0.478328
\(604\) 0 0
\(605\) −3.21868 −0.130858
\(606\) 0 0
\(607\) −41.0664 −1.66683 −0.833417 0.552645i \(-0.813619\pi\)
−0.833417 + 0.552645i \(0.813619\pi\)
\(608\) 0 0
\(609\) −20.9459 −0.848771
\(610\) 0 0
\(611\) −1.95111 −0.0789336
\(612\) 0 0
\(613\) −6.03276 −0.243661 −0.121831 0.992551i \(-0.538876\pi\)
−0.121831 + 0.992551i \(0.538876\pi\)
\(614\) 0 0
\(615\) −1.94305 −0.0783514
\(616\) 0 0
\(617\) −3.88785 −0.156519 −0.0782595 0.996933i \(-0.524936\pi\)
−0.0782595 + 0.996933i \(0.524936\pi\)
\(618\) 0 0
\(619\) −17.1723 −0.690213 −0.345107 0.938563i \(-0.612157\pi\)
−0.345107 + 0.938563i \(0.612157\pi\)
\(620\) 0 0
\(621\) −18.0954 −0.726145
\(622\) 0 0
\(623\) −12.9271 −0.517913
\(624\) 0 0
\(625\) 23.5940 0.943762
\(626\) 0 0
\(627\) −3.02996 −0.121005
\(628\) 0 0
\(629\) −7.19707 −0.286966
\(630\) 0 0
\(631\) −15.9300 −0.634165 −0.317082 0.948398i \(-0.602703\pi\)
−0.317082 + 0.948398i \(0.602703\pi\)
\(632\) 0 0
\(633\) 1.03677 0.0412081
\(634\) 0 0
\(635\) −5.91681 −0.234801
\(636\) 0 0
\(637\) −49.9155 −1.97773
\(638\) 0 0
\(639\) 5.07173 0.200634
\(640\) 0 0
\(641\) 39.4598 1.55857 0.779284 0.626671i \(-0.215583\pi\)
0.779284 + 0.626671i \(0.215583\pi\)
\(642\) 0 0
\(643\) 18.1011 0.713836 0.356918 0.934136i \(-0.383828\pi\)
0.356918 + 0.934136i \(0.383828\pi\)
\(644\) 0 0
\(645\) 0.381284 0.0150130
\(646\) 0 0
\(647\) 49.6770 1.95301 0.976503 0.215504i \(-0.0691394\pi\)
0.976503 + 0.215504i \(0.0691394\pi\)
\(648\) 0 0
\(649\) 2.74120 0.107602
\(650\) 0 0
\(651\) −24.3147 −0.952967
\(652\) 0 0
\(653\) −4.61404 −0.180561 −0.0902807 0.995916i \(-0.528776\pi\)
−0.0902807 + 0.995916i \(0.528776\pi\)
\(654\) 0 0
\(655\) −6.17755 −0.241377
\(656\) 0 0
\(657\) −7.86607 −0.306885
\(658\) 0 0
\(659\) −20.5534 −0.800646 −0.400323 0.916374i \(-0.631102\pi\)
−0.400323 + 0.916374i \(0.631102\pi\)
\(660\) 0 0
\(661\) 19.5211 0.759282 0.379641 0.925134i \(-0.376047\pi\)
0.379641 + 0.925134i \(0.376047\pi\)
\(662\) 0 0
\(663\) −23.9817 −0.931372
\(664\) 0 0
\(665\) −8.22200 −0.318836
\(666\) 0 0
\(667\) 36.0536 1.39600
\(668\) 0 0
\(669\) −10.5418 −0.407571
\(670\) 0 0
\(671\) 5.03267 0.194284
\(672\) 0 0
\(673\) 40.6149 1.56559 0.782794 0.622281i \(-0.213794\pi\)
0.782794 + 0.622281i \(0.213794\pi\)
\(674\) 0 0
\(675\) 18.1828 0.699856
\(676\) 0 0
\(677\) 18.7650 0.721199 0.360599 0.932721i \(-0.382572\pi\)
0.360599 + 0.932721i \(0.382572\pi\)
\(678\) 0 0
\(679\) 24.1095 0.925238
\(680\) 0 0
\(681\) 13.4214 0.514310
\(682\) 0 0
\(683\) −16.4215 −0.628353 −0.314176 0.949365i \(-0.601728\pi\)
−0.314176 + 0.949365i \(0.601728\pi\)
\(684\) 0 0
\(685\) 5.05215 0.193033
\(686\) 0 0
\(687\) −0.319091 −0.0121741
\(688\) 0 0
\(689\) 59.2184 2.25604
\(690\) 0 0
\(691\) 11.3456 0.431606 0.215803 0.976437i \(-0.430763\pi\)
0.215803 + 0.976437i \(0.430763\pi\)
\(692\) 0 0
\(693\) −7.82977 −0.297428
\(694\) 0 0
\(695\) 2.95028 0.111910
\(696\) 0 0
\(697\) −75.5651 −2.86223
\(698\) 0 0
\(699\) −17.9828 −0.680173
\(700\) 0 0
\(701\) 2.66016 0.100473 0.0502364 0.998737i \(-0.484003\pi\)
0.0502364 + 0.998737i \(0.484003\pi\)
\(702\) 0 0
\(703\) −5.68747 −0.214507
\(704\) 0 0
\(705\) 0.0886637 0.00333927
\(706\) 0 0
\(707\) −29.4142 −1.10624
\(708\) 0 0
\(709\) −39.7288 −1.49205 −0.746024 0.665919i \(-0.768040\pi\)
−0.746024 + 0.665919i \(0.768040\pi\)
\(710\) 0 0
\(711\) 3.57418 0.134042
\(712\) 0 0
\(713\) 41.8521 1.56737
\(714\) 0 0
\(715\) 0.998590 0.0373451
\(716\) 0 0
\(717\) −1.85198 −0.0691635
\(718\) 0 0
\(719\) 12.3195 0.459441 0.229721 0.973257i \(-0.426219\pi\)
0.229721 + 0.973257i \(0.426219\pi\)
\(720\) 0 0
\(721\) −5.98935 −0.223055
\(722\) 0 0
\(723\) 3.10927 0.115635
\(724\) 0 0
\(725\) −36.2276 −1.34546
\(726\) 0 0
\(727\) −25.3154 −0.938897 −0.469449 0.882960i \(-0.655547\pi\)
−0.469449 + 0.882960i \(0.655547\pi\)
\(728\) 0 0
\(729\) −5.84245 −0.216387
\(730\) 0 0
\(731\) 14.8281 0.548436
\(732\) 0 0
\(733\) −28.5561 −1.05474 −0.527372 0.849634i \(-0.676823\pi\)
−0.527372 + 0.849634i \(0.676823\pi\)
\(734\) 0 0
\(735\) 2.26829 0.0836672
\(736\) 0 0
\(737\) 3.31490 0.122106
\(738\) 0 0
\(739\) 24.0882 0.886100 0.443050 0.896497i \(-0.353896\pi\)
0.443050 + 0.896497i \(0.353896\pi\)
\(740\) 0 0
\(741\) −18.9515 −0.696201
\(742\) 0 0
\(743\) 32.2680 1.18380 0.591899 0.806012i \(-0.298378\pi\)
0.591899 + 0.806012i \(0.298378\pi\)
\(744\) 0 0
\(745\) −6.87527 −0.251890
\(746\) 0 0
\(747\) −22.2105 −0.812640
\(748\) 0 0
\(749\) −15.7605 −0.575876
\(750\) 0 0
\(751\) −27.9809 −1.02104 −0.510519 0.859867i \(-0.670547\pi\)
−0.510519 + 0.859867i \(0.670547\pi\)
\(752\) 0 0
\(753\) −13.4030 −0.488432
\(754\) 0 0
\(755\) −3.64677 −0.132720
\(756\) 0 0
\(757\) 8.00964 0.291115 0.145558 0.989350i \(-0.453502\pi\)
0.145558 + 0.989350i \(0.453502\pi\)
\(758\) 0 0
\(759\) −2.34876 −0.0852547
\(760\) 0 0
\(761\) 24.9041 0.902775 0.451387 0.892328i \(-0.350929\pi\)
0.451387 + 0.892328i \(0.350929\pi\)
\(762\) 0 0
\(763\) 27.5868 0.998710
\(764\) 0 0
\(765\) −6.25320 −0.226085
\(766\) 0 0
\(767\) 17.1454 0.619085
\(768\) 0 0
\(769\) −33.8461 −1.22052 −0.610261 0.792200i \(-0.708935\pi\)
−0.610261 + 0.792200i \(0.708935\pi\)
\(770\) 0 0
\(771\) −8.21914 −0.296005
\(772\) 0 0
\(773\) −45.6404 −1.64157 −0.820786 0.571236i \(-0.806464\pi\)
−0.820786 + 0.571236i \(0.806464\pi\)
\(774\) 0 0
\(775\) −42.0541 −1.51063
\(776\) 0 0
\(777\) 2.56137 0.0918886
\(778\) 0 0
\(779\) −59.7152 −2.13952
\(780\) 0 0
\(781\) 1.43133 0.0512172
\(782\) 0 0
\(783\) −27.3717 −0.978185
\(784\) 0 0
\(785\) −5.77648 −0.206171
\(786\) 0 0
\(787\) −42.2047 −1.50444 −0.752218 0.658914i \(-0.771016\pi\)
−0.752218 + 0.658914i \(0.771016\pi\)
\(788\) 0 0
\(789\) −3.99097 −0.142082
\(790\) 0 0
\(791\) 42.6845 1.51769
\(792\) 0 0
\(793\) 31.4778 1.11781
\(794\) 0 0
\(795\) −2.69104 −0.0954414
\(796\) 0 0
\(797\) −24.9132 −0.882471 −0.441236 0.897391i \(-0.645460\pi\)
−0.441236 + 0.897391i \(0.645460\pi\)
\(798\) 0 0
\(799\) 3.44812 0.121986
\(800\) 0 0
\(801\) −7.76943 −0.274519
\(802\) 0 0
\(803\) −2.21995 −0.0783403
\(804\) 0 0
\(805\) −6.37352 −0.224637
\(806\) 0 0
\(807\) −11.7804 −0.414690
\(808\) 0 0
\(809\) −48.3047 −1.69830 −0.849152 0.528148i \(-0.822887\pi\)
−0.849152 + 0.528148i \(0.822887\pi\)
\(810\) 0 0
\(811\) 4.98459 0.175033 0.0875163 0.996163i \(-0.472107\pi\)
0.0875163 + 0.996163i \(0.472107\pi\)
\(812\) 0 0
\(813\) 10.8823 0.381658
\(814\) 0 0
\(815\) 7.34815 0.257395
\(816\) 0 0
\(817\) 11.7179 0.409956
\(818\) 0 0
\(819\) −48.9728 −1.71125
\(820\) 0 0
\(821\) 20.6862 0.721954 0.360977 0.932575i \(-0.382443\pi\)
0.360977 + 0.932575i \(0.382443\pi\)
\(822\) 0 0
\(823\) −12.0734 −0.420853 −0.210427 0.977610i \(-0.567485\pi\)
−0.210427 + 0.977610i \(0.567485\pi\)
\(824\) 0 0
\(825\) 2.36010 0.0821682
\(826\) 0 0
\(827\) −34.2071 −1.18950 −0.594748 0.803912i \(-0.702748\pi\)
−0.594748 + 0.803912i \(0.702748\pi\)
\(828\) 0 0
\(829\) −47.2677 −1.64168 −0.820838 0.571161i \(-0.806493\pi\)
−0.820838 + 0.571161i \(0.806493\pi\)
\(830\) 0 0
\(831\) −5.46296 −0.189508
\(832\) 0 0
\(833\) 88.2137 3.05642
\(834\) 0 0
\(835\) −4.89365 −0.169352
\(836\) 0 0
\(837\) −31.7739 −1.09827
\(838\) 0 0
\(839\) 36.6906 1.26670 0.633350 0.773865i \(-0.281679\pi\)
0.633350 + 0.773865i \(0.281679\pi\)
\(840\) 0 0
\(841\) 25.5357 0.880543
\(842\) 0 0
\(843\) −13.8043 −0.475445
\(844\) 0 0
\(845\) 2.25330 0.0775160
\(846\) 0 0
\(847\) 44.5482 1.53070
\(848\) 0 0
\(849\) −0.625431 −0.0214648
\(850\) 0 0
\(851\) −4.40881 −0.151132
\(852\) 0 0
\(853\) 16.9228 0.579427 0.289713 0.957113i \(-0.406440\pi\)
0.289713 + 0.957113i \(0.406440\pi\)
\(854\) 0 0
\(855\) −4.94158 −0.168998
\(856\) 0 0
\(857\) 32.3955 1.10661 0.553305 0.832979i \(-0.313367\pi\)
0.553305 + 0.832979i \(0.313367\pi\)
\(858\) 0 0
\(859\) −42.2728 −1.44233 −0.721164 0.692764i \(-0.756393\pi\)
−0.721164 + 0.692764i \(0.756393\pi\)
\(860\) 0 0
\(861\) 26.8929 0.916508
\(862\) 0 0
\(863\) 16.5450 0.563198 0.281599 0.959532i \(-0.409135\pi\)
0.281599 + 0.959532i \(0.409135\pi\)
\(864\) 0 0
\(865\) −2.08046 −0.0707379
\(866\) 0 0
\(867\) 31.0384 1.05412
\(868\) 0 0
\(869\) 1.00870 0.0342178
\(870\) 0 0
\(871\) 20.7337 0.702534
\(872\) 0 0
\(873\) 14.4903 0.490421
\(874\) 0 0
\(875\) 12.9317 0.437172
\(876\) 0 0
\(877\) 7.41710 0.250458 0.125229 0.992128i \(-0.460033\pi\)
0.125229 + 0.992128i \(0.460033\pi\)
\(878\) 0 0
\(879\) −10.6188 −0.358164
\(880\) 0 0
\(881\) 36.5860 1.23261 0.616307 0.787506i \(-0.288628\pi\)
0.616307 + 0.787506i \(0.288628\pi\)
\(882\) 0 0
\(883\) −4.76867 −0.160479 −0.0802393 0.996776i \(-0.525568\pi\)
−0.0802393 + 0.996776i \(0.525568\pi\)
\(884\) 0 0
\(885\) −0.779132 −0.0261902
\(886\) 0 0
\(887\) −14.5077 −0.487120 −0.243560 0.969886i \(-0.578315\pi\)
−0.243560 + 0.969886i \(0.578315\pi\)
\(888\) 0 0
\(889\) 81.8918 2.74656
\(890\) 0 0
\(891\) −3.74278 −0.125388
\(892\) 0 0
\(893\) 2.72487 0.0911844
\(894\) 0 0
\(895\) 3.31655 0.110860
\(896\) 0 0
\(897\) −14.6908 −0.490512
\(898\) 0 0
\(899\) 63.3068 2.11140
\(900\) 0 0
\(901\) −104.654 −3.48654
\(902\) 0 0
\(903\) −5.27717 −0.175613
\(904\) 0 0
\(905\) 3.98839 0.132578
\(906\) 0 0
\(907\) −5.98338 −0.198675 −0.0993374 0.995054i \(-0.531672\pi\)
−0.0993374 + 0.995054i \(0.531672\pi\)
\(908\) 0 0
\(909\) −17.6785 −0.586359
\(910\) 0 0
\(911\) −22.6582 −0.750701 −0.375350 0.926883i \(-0.622478\pi\)
−0.375350 + 0.926883i \(0.622478\pi\)
\(912\) 0 0
\(913\) −6.26821 −0.207448
\(914\) 0 0
\(915\) −1.43043 −0.0472887
\(916\) 0 0
\(917\) 85.5006 2.82348
\(918\) 0 0
\(919\) 8.10778 0.267451 0.133726 0.991018i \(-0.457306\pi\)
0.133726 + 0.991018i \(0.457306\pi\)
\(920\) 0 0
\(921\) −8.09344 −0.266688
\(922\) 0 0
\(923\) 8.95256 0.294677
\(924\) 0 0
\(925\) 4.43009 0.145660
\(926\) 0 0
\(927\) −3.59971 −0.118230
\(928\) 0 0
\(929\) 9.57905 0.314278 0.157139 0.987576i \(-0.449773\pi\)
0.157139 + 0.987576i \(0.449773\pi\)
\(930\) 0 0
\(931\) 69.7107 2.28468
\(932\) 0 0
\(933\) 6.49366 0.212593
\(934\) 0 0
\(935\) −1.76477 −0.0577140
\(936\) 0 0
\(937\) 0.196050 0.00640467 0.00320234 0.999995i \(-0.498981\pi\)
0.00320234 + 0.999995i \(0.498981\pi\)
\(938\) 0 0
\(939\) −5.96746 −0.194741
\(940\) 0 0
\(941\) 0.893569 0.0291295 0.0145648 0.999894i \(-0.495364\pi\)
0.0145648 + 0.999894i \(0.495364\pi\)
\(942\) 0 0
\(943\) −46.2899 −1.50741
\(944\) 0 0
\(945\) 4.83875 0.157405
\(946\) 0 0
\(947\) 34.2934 1.11439 0.557193 0.830383i \(-0.311878\pi\)
0.557193 + 0.830383i \(0.311878\pi\)
\(948\) 0 0
\(949\) −13.8851 −0.450730
\(950\) 0 0
\(951\) −21.2080 −0.687716
\(952\) 0 0
\(953\) 14.0568 0.455346 0.227673 0.973738i \(-0.426888\pi\)
0.227673 + 0.973738i \(0.426888\pi\)
\(954\) 0 0
\(955\) 4.21558 0.136413
\(956\) 0 0
\(957\) −3.55281 −0.114846
\(958\) 0 0
\(959\) −69.9245 −2.25798
\(960\) 0 0
\(961\) 42.4885 1.37060
\(962\) 0 0
\(963\) −9.47235 −0.305242
\(964\) 0 0
\(965\) 4.12298 0.132723
\(966\) 0 0
\(967\) −36.9849 −1.18935 −0.594677 0.803965i \(-0.702720\pi\)
−0.594677 + 0.803965i \(0.702720\pi\)
\(968\) 0 0
\(969\) 33.4922 1.07592
\(970\) 0 0
\(971\) 31.2185 1.00185 0.500924 0.865491i \(-0.332993\pi\)
0.500924 + 0.865491i \(0.332993\pi\)
\(972\) 0 0
\(973\) −40.8334 −1.30906
\(974\) 0 0
\(975\) 14.7617 0.472753
\(976\) 0 0
\(977\) 19.1478 0.612593 0.306297 0.951936i \(-0.400910\pi\)
0.306297 + 0.951936i \(0.400910\pi\)
\(978\) 0 0
\(979\) −2.19268 −0.0700782
\(980\) 0 0
\(981\) 16.5802 0.529365
\(982\) 0 0
\(983\) 16.2033 0.516805 0.258402 0.966037i \(-0.416804\pi\)
0.258402 + 0.966037i \(0.416804\pi\)
\(984\) 0 0
\(985\) −2.76155 −0.0879904
\(986\) 0 0
\(987\) −1.22715 −0.0390607
\(988\) 0 0
\(989\) 9.08344 0.288837
\(990\) 0 0
\(991\) 44.9646 1.42835 0.714174 0.699968i \(-0.246802\pi\)
0.714174 + 0.699968i \(0.246802\pi\)
\(992\) 0 0
\(993\) −3.74116 −0.118722
\(994\) 0 0
\(995\) −4.46514 −0.141555
\(996\) 0 0
\(997\) 48.1546 1.52507 0.762536 0.646946i \(-0.223954\pi\)
0.762536 + 0.646946i \(0.223954\pi\)
\(998\) 0 0
\(999\) 3.34715 0.105899
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 \(a_p\))