Properties

Label 8048.2.a.v.1.25
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 1.25
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.25613 q^{3} +2.34171 q^{5} -2.23682 q^{7} +2.09012 q^{9} +O(q^{10})\) \(q+2.25613 q^{3} +2.34171 q^{5} -2.23682 q^{7} +2.09012 q^{9} -4.83651 q^{11} +0.834816 q^{13} +5.28320 q^{15} -5.54113 q^{17} +1.83270 q^{19} -5.04657 q^{21} +7.33684 q^{23} +0.483606 q^{25} -2.05280 q^{27} -3.35529 q^{29} -0.777446 q^{31} -10.9118 q^{33} -5.23799 q^{35} -7.78842 q^{37} +1.88345 q^{39} -9.17412 q^{41} +11.5622 q^{43} +4.89447 q^{45} +1.92508 q^{47} -1.99662 q^{49} -12.5015 q^{51} -2.04619 q^{53} -11.3257 q^{55} +4.13481 q^{57} -0.668827 q^{59} -8.64673 q^{61} -4.67524 q^{63} +1.95490 q^{65} -10.6650 q^{67} +16.5529 q^{69} +3.57854 q^{71} +5.69843 q^{73} +1.09108 q^{75} +10.8184 q^{77} +8.38518 q^{79} -10.9018 q^{81} -13.7104 q^{83} -12.9757 q^{85} -7.56997 q^{87} -8.41401 q^{89} -1.86734 q^{91} -1.75402 q^{93} +4.29165 q^{95} -3.23181 q^{97} -10.1089 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q - 2q^{3} - 12q^{5} + 18q^{9} + O(q^{10}) \) \( 28q - 2q^{3} - 12q^{5} + 18q^{9} + 14q^{11} - 31q^{13} + 2q^{15} - 9q^{17} + 8q^{19} - 28q^{21} + 4q^{23} + 22q^{25} + 4q^{27} - 47q^{29} + 5q^{31} - 26q^{33} + 13q^{35} - 67q^{37} + 9q^{39} - 28q^{41} - 15q^{43} - 57q^{45} + 10q^{47} + 20q^{49} + 11q^{51} - 58q^{53} - 15q^{55} - 31q^{57} + 32q^{59} - 55q^{61} + 16q^{63} - 44q^{65} - 22q^{67} - 44q^{69} + 47q^{71} - 5q^{73} + 25q^{75} - 50q^{77} + 14q^{79} - 28q^{81} + 16q^{83} - 78q^{85} + 11q^{87} - 20q^{89} + 15q^{91} - 83q^{93} + 27q^{95} - 8q^{97} + 70q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.25613 1.30258 0.651289 0.758830i \(-0.274229\pi\)
0.651289 + 0.758830i \(0.274229\pi\)
\(4\) 0 0
\(5\) 2.34171 1.04724 0.523622 0.851951i \(-0.324580\pi\)
0.523622 + 0.851951i \(0.324580\pi\)
\(6\) 0 0
\(7\) −2.23682 −0.845440 −0.422720 0.906260i \(-0.638925\pi\)
−0.422720 + 0.906260i \(0.638925\pi\)
\(8\) 0 0
\(9\) 2.09012 0.696708
\(10\) 0 0
\(11\) −4.83651 −1.45826 −0.729132 0.684374i \(-0.760076\pi\)
−0.729132 + 0.684374i \(0.760076\pi\)
\(12\) 0 0
\(13\) 0.834816 0.231536 0.115768 0.993276i \(-0.463067\pi\)
0.115768 + 0.993276i \(0.463067\pi\)
\(14\) 0 0
\(15\) 5.28320 1.36412
\(16\) 0 0
\(17\) −5.54113 −1.34392 −0.671961 0.740587i \(-0.734548\pi\)
−0.671961 + 0.740587i \(0.734548\pi\)
\(18\) 0 0
\(19\) 1.83270 0.420450 0.210225 0.977653i \(-0.432580\pi\)
0.210225 + 0.977653i \(0.432580\pi\)
\(20\) 0 0
\(21\) −5.04657 −1.10125
\(22\) 0 0
\(23\) 7.33684 1.52984 0.764919 0.644127i \(-0.222779\pi\)
0.764919 + 0.644127i \(0.222779\pi\)
\(24\) 0 0
\(25\) 0.483606 0.0967212
\(26\) 0 0
\(27\) −2.05280 −0.395061
\(28\) 0 0
\(29\) −3.35529 −0.623062 −0.311531 0.950236i \(-0.600842\pi\)
−0.311531 + 0.950236i \(0.600842\pi\)
\(30\) 0 0
\(31\) −0.777446 −0.139633 −0.0698167 0.997560i \(-0.522241\pi\)
−0.0698167 + 0.997560i \(0.522241\pi\)
\(32\) 0 0
\(33\) −10.9118 −1.89950
\(34\) 0 0
\(35\) −5.23799 −0.885383
\(36\) 0 0
\(37\) −7.78842 −1.28041 −0.640204 0.768205i \(-0.721150\pi\)
−0.640204 + 0.768205i \(0.721150\pi\)
\(38\) 0 0
\(39\) 1.88345 0.301594
\(40\) 0 0
\(41\) −9.17412 −1.43276 −0.716379 0.697712i \(-0.754202\pi\)
−0.716379 + 0.697712i \(0.754202\pi\)
\(42\) 0 0
\(43\) 11.5622 1.76321 0.881606 0.471987i \(-0.156463\pi\)
0.881606 + 0.471987i \(0.156463\pi\)
\(44\) 0 0
\(45\) 4.89447 0.729624
\(46\) 0 0
\(47\) 1.92508 0.280801 0.140401 0.990095i \(-0.455161\pi\)
0.140401 + 0.990095i \(0.455161\pi\)
\(48\) 0 0
\(49\) −1.99662 −0.285231
\(50\) 0 0
\(51\) −12.5015 −1.75056
\(52\) 0 0
\(53\) −2.04619 −0.281066 −0.140533 0.990076i \(-0.544882\pi\)
−0.140533 + 0.990076i \(0.544882\pi\)
\(54\) 0 0
\(55\) −11.3257 −1.52716
\(56\) 0 0
\(57\) 4.13481 0.547669
\(58\) 0 0
\(59\) −0.668827 −0.0870739 −0.0435369 0.999052i \(-0.513863\pi\)
−0.0435369 + 0.999052i \(0.513863\pi\)
\(60\) 0 0
\(61\) −8.64673 −1.10710 −0.553550 0.832816i \(-0.686727\pi\)
−0.553550 + 0.832816i \(0.686727\pi\)
\(62\) 0 0
\(63\) −4.67524 −0.589025
\(64\) 0 0
\(65\) 1.95490 0.242475
\(66\) 0 0
\(67\) −10.6650 −1.30294 −0.651470 0.758675i \(-0.725847\pi\)
−0.651470 + 0.758675i \(0.725847\pi\)
\(68\) 0 0
\(69\) 16.5529 1.99273
\(70\) 0 0
\(71\) 3.57854 0.424694 0.212347 0.977194i \(-0.431889\pi\)
0.212347 + 0.977194i \(0.431889\pi\)
\(72\) 0 0
\(73\) 5.69843 0.666951 0.333476 0.942759i \(-0.391779\pi\)
0.333476 + 0.942759i \(0.391779\pi\)
\(74\) 0 0
\(75\) 1.09108 0.125987
\(76\) 0 0
\(77\) 10.8184 1.23287
\(78\) 0 0
\(79\) 8.38518 0.943407 0.471703 0.881757i \(-0.343639\pi\)
0.471703 + 0.881757i \(0.343639\pi\)
\(80\) 0 0
\(81\) −10.9018 −1.21131
\(82\) 0 0
\(83\) −13.7104 −1.50491 −0.752454 0.658644i \(-0.771130\pi\)
−0.752454 + 0.658644i \(0.771130\pi\)
\(84\) 0 0
\(85\) −12.9757 −1.40741
\(86\) 0 0
\(87\) −7.56997 −0.811586
\(88\) 0 0
\(89\) −8.41401 −0.891883 −0.445942 0.895062i \(-0.647131\pi\)
−0.445942 + 0.895062i \(0.647131\pi\)
\(90\) 0 0
\(91\) −1.86734 −0.195750
\(92\) 0 0
\(93\) −1.75402 −0.181883
\(94\) 0 0
\(95\) 4.29165 0.440314
\(96\) 0 0
\(97\) −3.23181 −0.328140 −0.164070 0.986449i \(-0.552462\pi\)
−0.164070 + 0.986449i \(0.552462\pi\)
\(98\) 0 0
\(99\) −10.1089 −1.01598
\(100\) 0 0
\(101\) −9.70274 −0.965459 −0.482730 0.875769i \(-0.660355\pi\)
−0.482730 + 0.875769i \(0.660355\pi\)
\(102\) 0 0
\(103\) −12.2046 −1.20256 −0.601279 0.799039i \(-0.705342\pi\)
−0.601279 + 0.799039i \(0.705342\pi\)
\(104\) 0 0
\(105\) −11.8176 −1.15328
\(106\) 0 0
\(107\) 8.88079 0.858539 0.429269 0.903177i \(-0.358771\pi\)
0.429269 + 0.903177i \(0.358771\pi\)
\(108\) 0 0
\(109\) 6.62270 0.634340 0.317170 0.948369i \(-0.397267\pi\)
0.317170 + 0.948369i \(0.397267\pi\)
\(110\) 0 0
\(111\) −17.5717 −1.66783
\(112\) 0 0
\(113\) 15.3908 1.44784 0.723922 0.689882i \(-0.242338\pi\)
0.723922 + 0.689882i \(0.242338\pi\)
\(114\) 0 0
\(115\) 17.1808 1.60211
\(116\) 0 0
\(117\) 1.74487 0.161313
\(118\) 0 0
\(119\) 12.3945 1.13620
\(120\) 0 0
\(121\) 12.3918 1.12653
\(122\) 0 0
\(123\) −20.6980 −1.86628
\(124\) 0 0
\(125\) −10.5761 −0.945954
\(126\) 0 0
\(127\) −18.6489 −1.65482 −0.827410 0.561598i \(-0.810187\pi\)
−0.827410 + 0.561598i \(0.810187\pi\)
\(128\) 0 0
\(129\) 26.0857 2.29672
\(130\) 0 0
\(131\) 17.6208 1.53954 0.769769 0.638323i \(-0.220371\pi\)
0.769769 + 0.638323i \(0.220371\pi\)
\(132\) 0 0
\(133\) −4.09943 −0.355466
\(134\) 0 0
\(135\) −4.80706 −0.413726
\(136\) 0 0
\(137\) 20.4354 1.74591 0.872957 0.487797i \(-0.162199\pi\)
0.872957 + 0.487797i \(0.162199\pi\)
\(138\) 0 0
\(139\) −3.68318 −0.312404 −0.156202 0.987725i \(-0.549925\pi\)
−0.156202 + 0.987725i \(0.549925\pi\)
\(140\) 0 0
\(141\) 4.34322 0.365765
\(142\) 0 0
\(143\) −4.03760 −0.337641
\(144\) 0 0
\(145\) −7.85711 −0.652498
\(146\) 0 0
\(147\) −4.50463 −0.371535
\(148\) 0 0
\(149\) −5.97233 −0.489272 −0.244636 0.969615i \(-0.578669\pi\)
−0.244636 + 0.969615i \(0.578669\pi\)
\(150\) 0 0
\(151\) 22.4868 1.82995 0.914974 0.403513i \(-0.132211\pi\)
0.914974 + 0.403513i \(0.132211\pi\)
\(152\) 0 0
\(153\) −11.5816 −0.936321
\(154\) 0 0
\(155\) −1.82055 −0.146230
\(156\) 0 0
\(157\) 7.15379 0.570934 0.285467 0.958388i \(-0.407851\pi\)
0.285467 + 0.958388i \(0.407851\pi\)
\(158\) 0 0
\(159\) −4.61648 −0.366111
\(160\) 0 0
\(161\) −16.4112 −1.29339
\(162\) 0 0
\(163\) −19.2023 −1.50404 −0.752020 0.659141i \(-0.770920\pi\)
−0.752020 + 0.659141i \(0.770920\pi\)
\(164\) 0 0
\(165\) −25.5523 −1.98924
\(166\) 0 0
\(167\) 13.7445 1.06358 0.531790 0.846876i \(-0.321519\pi\)
0.531790 + 0.846876i \(0.321519\pi\)
\(168\) 0 0
\(169\) −12.3031 −0.946391
\(170\) 0 0
\(171\) 3.83057 0.292931
\(172\) 0 0
\(173\) −12.6597 −0.962498 −0.481249 0.876584i \(-0.659817\pi\)
−0.481249 + 0.876584i \(0.659817\pi\)
\(174\) 0 0
\(175\) −1.08174 −0.0817720
\(176\) 0 0
\(177\) −1.50896 −0.113420
\(178\) 0 0
\(179\) −26.2307 −1.96057 −0.980287 0.197581i \(-0.936691\pi\)
−0.980287 + 0.197581i \(0.936691\pi\)
\(180\) 0 0
\(181\) −17.1620 −1.27564 −0.637822 0.770184i \(-0.720164\pi\)
−0.637822 + 0.770184i \(0.720164\pi\)
\(182\) 0 0
\(183\) −19.5082 −1.44208
\(184\) 0 0
\(185\) −18.2382 −1.34090
\(186\) 0 0
\(187\) 26.7997 1.95979
\(188\) 0 0
\(189\) 4.59175 0.334001
\(190\) 0 0
\(191\) −17.3138 −1.25278 −0.626390 0.779510i \(-0.715468\pi\)
−0.626390 + 0.779510i \(0.715468\pi\)
\(192\) 0 0
\(193\) −20.5094 −1.47630 −0.738151 0.674636i \(-0.764301\pi\)
−0.738151 + 0.674636i \(0.764301\pi\)
\(194\) 0 0
\(195\) 4.41050 0.315843
\(196\) 0 0
\(197\) 4.84527 0.345211 0.172606 0.984991i \(-0.444781\pi\)
0.172606 + 0.984991i \(0.444781\pi\)
\(198\) 0 0
\(199\) −25.7280 −1.82381 −0.911905 0.410402i \(-0.865388\pi\)
−0.911905 + 0.410402i \(0.865388\pi\)
\(200\) 0 0
\(201\) −24.0617 −1.69718
\(202\) 0 0
\(203\) 7.50519 0.526761
\(204\) 0 0
\(205\) −21.4831 −1.50045
\(206\) 0 0
\(207\) 15.3349 1.06585
\(208\) 0 0
\(209\) −8.86388 −0.613127
\(210\) 0 0
\(211\) 25.8319 1.77834 0.889171 0.457574i \(-0.151282\pi\)
0.889171 + 0.457574i \(0.151282\pi\)
\(212\) 0 0
\(213\) 8.07365 0.553197
\(214\) 0 0
\(215\) 27.0752 1.84651
\(216\) 0 0
\(217\) 1.73901 0.118052
\(218\) 0 0
\(219\) 12.8564 0.868756
\(220\) 0 0
\(221\) −4.62582 −0.311166
\(222\) 0 0
\(223\) −12.2658 −0.821376 −0.410688 0.911776i \(-0.634712\pi\)
−0.410688 + 0.911776i \(0.634712\pi\)
\(224\) 0 0
\(225\) 1.01080 0.0673865
\(226\) 0 0
\(227\) 15.1894 1.00816 0.504078 0.863658i \(-0.331833\pi\)
0.504078 + 0.863658i \(0.331833\pi\)
\(228\) 0 0
\(229\) 2.63534 0.174148 0.0870741 0.996202i \(-0.472248\pi\)
0.0870741 + 0.996202i \(0.472248\pi\)
\(230\) 0 0
\(231\) 24.4078 1.60591
\(232\) 0 0
\(233\) −9.32971 −0.611209 −0.305605 0.952158i \(-0.598859\pi\)
−0.305605 + 0.952158i \(0.598859\pi\)
\(234\) 0 0
\(235\) 4.50797 0.294067
\(236\) 0 0
\(237\) 18.9181 1.22886
\(238\) 0 0
\(239\) 24.0306 1.55441 0.777204 0.629249i \(-0.216637\pi\)
0.777204 + 0.629249i \(0.216637\pi\)
\(240\) 0 0
\(241\) 3.53600 0.227773 0.113887 0.993494i \(-0.463670\pi\)
0.113887 + 0.993494i \(0.463670\pi\)
\(242\) 0 0
\(243\) −18.4374 −1.18276
\(244\) 0 0
\(245\) −4.67550 −0.298706
\(246\) 0 0
\(247\) 1.52997 0.0973495
\(248\) 0 0
\(249\) −30.9324 −1.96026
\(250\) 0 0
\(251\) 13.9214 0.878709 0.439354 0.898314i \(-0.355207\pi\)
0.439354 + 0.898314i \(0.355207\pi\)
\(252\) 0 0
\(253\) −35.4847 −2.23091
\(254\) 0 0
\(255\) −29.2749 −1.83327
\(256\) 0 0
\(257\) 21.9636 1.37005 0.685025 0.728519i \(-0.259791\pi\)
0.685025 + 0.728519i \(0.259791\pi\)
\(258\) 0 0
\(259\) 17.4213 1.08251
\(260\) 0 0
\(261\) −7.01297 −0.434092
\(262\) 0 0
\(263\) −14.8106 −0.913260 −0.456630 0.889657i \(-0.650944\pi\)
−0.456630 + 0.889657i \(0.650944\pi\)
\(264\) 0 0
\(265\) −4.79160 −0.294345
\(266\) 0 0
\(267\) −18.9831 −1.16175
\(268\) 0 0
\(269\) −2.15656 −0.131488 −0.0657438 0.997837i \(-0.520942\pi\)
−0.0657438 + 0.997837i \(0.520942\pi\)
\(270\) 0 0
\(271\) −10.6666 −0.647948 −0.323974 0.946066i \(-0.605019\pi\)
−0.323974 + 0.946066i \(0.605019\pi\)
\(272\) 0 0
\(273\) −4.21296 −0.254980
\(274\) 0 0
\(275\) −2.33897 −0.141045
\(276\) 0 0
\(277\) 9.51598 0.571760 0.285880 0.958265i \(-0.407714\pi\)
0.285880 + 0.958265i \(0.407714\pi\)
\(278\) 0 0
\(279\) −1.62496 −0.0972838
\(280\) 0 0
\(281\) −17.2666 −1.03004 −0.515020 0.857178i \(-0.672216\pi\)
−0.515020 + 0.857178i \(0.672216\pi\)
\(282\) 0 0
\(283\) 19.4806 1.15800 0.579001 0.815327i \(-0.303443\pi\)
0.579001 + 0.815327i \(0.303443\pi\)
\(284\) 0 0
\(285\) 9.68253 0.573544
\(286\) 0 0
\(287\) 20.5209 1.21131
\(288\) 0 0
\(289\) 13.7041 0.806124
\(290\) 0 0
\(291\) −7.29138 −0.427428
\(292\) 0 0
\(293\) 17.4790 1.02113 0.510566 0.859838i \(-0.329436\pi\)
0.510566 + 0.859838i \(0.329436\pi\)
\(294\) 0 0
\(295\) −1.56620 −0.0911876
\(296\) 0 0
\(297\) 9.92838 0.576103
\(298\) 0 0
\(299\) 6.12491 0.354213
\(300\) 0 0
\(301\) −25.8625 −1.49069
\(302\) 0 0
\(303\) −21.8907 −1.25759
\(304\) 0 0
\(305\) −20.2481 −1.15941
\(306\) 0 0
\(307\) 10.1714 0.580513 0.290256 0.956949i \(-0.406259\pi\)
0.290256 + 0.956949i \(0.406259\pi\)
\(308\) 0 0
\(309\) −27.5353 −1.56643
\(310\) 0 0
\(311\) −20.7723 −1.17789 −0.588946 0.808172i \(-0.700457\pi\)
−0.588946 + 0.808172i \(0.700457\pi\)
\(312\) 0 0
\(313\) −9.40277 −0.531476 −0.265738 0.964045i \(-0.585616\pi\)
−0.265738 + 0.964045i \(0.585616\pi\)
\(314\) 0 0
\(315\) −10.9481 −0.616853
\(316\) 0 0
\(317\) 22.6489 1.27209 0.636046 0.771651i \(-0.280569\pi\)
0.636046 + 0.771651i \(0.280569\pi\)
\(318\) 0 0
\(319\) 16.2279 0.908588
\(320\) 0 0
\(321\) 20.0362 1.11831
\(322\) 0 0
\(323\) −10.1552 −0.565052
\(324\) 0 0
\(325\) 0.403722 0.0223945
\(326\) 0 0
\(327\) 14.9417 0.826277
\(328\) 0 0
\(329\) −4.30606 −0.237401
\(330\) 0 0
\(331\) −17.8139 −0.979143 −0.489571 0.871963i \(-0.662847\pi\)
−0.489571 + 0.871963i \(0.662847\pi\)
\(332\) 0 0
\(333\) −16.2788 −0.892071
\(334\) 0 0
\(335\) −24.9744 −1.36450
\(336\) 0 0
\(337\) 4.74895 0.258692 0.129346 0.991600i \(-0.458712\pi\)
0.129346 + 0.991600i \(0.458712\pi\)
\(338\) 0 0
\(339\) 34.7236 1.88593
\(340\) 0 0
\(341\) 3.76013 0.203622
\(342\) 0 0
\(343\) 20.1239 1.08659
\(344\) 0 0
\(345\) 38.7620 2.08688
\(346\) 0 0
\(347\) −14.3445 −0.770050 −0.385025 0.922906i \(-0.625807\pi\)
−0.385025 + 0.922906i \(0.625807\pi\)
\(348\) 0 0
\(349\) 1.44132 0.0771523 0.0385762 0.999256i \(-0.487718\pi\)
0.0385762 + 0.999256i \(0.487718\pi\)
\(350\) 0 0
\(351\) −1.71371 −0.0914710
\(352\) 0 0
\(353\) −4.80296 −0.255636 −0.127818 0.991798i \(-0.540797\pi\)
−0.127818 + 0.991798i \(0.540797\pi\)
\(354\) 0 0
\(355\) 8.37990 0.444759
\(356\) 0 0
\(357\) 27.9637 1.48000
\(358\) 0 0
\(359\) −32.2320 −1.70114 −0.850570 0.525861i \(-0.823743\pi\)
−0.850570 + 0.525861i \(0.823743\pi\)
\(360\) 0 0
\(361\) −15.6412 −0.823222
\(362\) 0 0
\(363\) 27.9576 1.46739
\(364\) 0 0
\(365\) 13.3441 0.698461
\(366\) 0 0
\(367\) 14.3212 0.747559 0.373780 0.927518i \(-0.378062\pi\)
0.373780 + 0.927518i \(0.378062\pi\)
\(368\) 0 0
\(369\) −19.1751 −0.998214
\(370\) 0 0
\(371\) 4.57698 0.237625
\(372\) 0 0
\(373\) 6.84129 0.354228 0.177114 0.984190i \(-0.443324\pi\)
0.177114 + 0.984190i \(0.443324\pi\)
\(374\) 0 0
\(375\) −23.8610 −1.23218
\(376\) 0 0
\(377\) −2.80105 −0.144261
\(378\) 0 0
\(379\) 17.0591 0.876266 0.438133 0.898910i \(-0.355640\pi\)
0.438133 + 0.898910i \(0.355640\pi\)
\(380\) 0 0
\(381\) −42.0743 −2.15553
\(382\) 0 0
\(383\) 17.0812 0.872810 0.436405 0.899750i \(-0.356252\pi\)
0.436405 + 0.899750i \(0.356252\pi\)
\(384\) 0 0
\(385\) 25.3336 1.29112
\(386\) 0 0
\(387\) 24.1663 1.22844
\(388\) 0 0
\(389\) −12.0141 −0.609137 −0.304568 0.952491i \(-0.598512\pi\)
−0.304568 + 0.952491i \(0.598512\pi\)
\(390\) 0 0
\(391\) −40.6544 −2.05598
\(392\) 0 0
\(393\) 39.7549 2.00537
\(394\) 0 0
\(395\) 19.6357 0.987978
\(396\) 0 0
\(397\) −32.1001 −1.61106 −0.805530 0.592555i \(-0.798119\pi\)
−0.805530 + 0.592555i \(0.798119\pi\)
\(398\) 0 0
\(399\) −9.24885 −0.463022
\(400\) 0 0
\(401\) −5.36837 −0.268084 −0.134042 0.990976i \(-0.542796\pi\)
−0.134042 + 0.990976i \(0.542796\pi\)
\(402\) 0 0
\(403\) −0.649024 −0.0323302
\(404\) 0 0
\(405\) −25.5287 −1.26853
\(406\) 0 0
\(407\) 37.6688 1.86717
\(408\) 0 0
\(409\) 29.4937 1.45837 0.729184 0.684318i \(-0.239900\pi\)
0.729184 + 0.684318i \(0.239900\pi\)
\(410\) 0 0
\(411\) 46.1049 2.27419
\(412\) 0 0
\(413\) 1.49605 0.0736158
\(414\) 0 0
\(415\) −32.1057 −1.57601
\(416\) 0 0
\(417\) −8.30974 −0.406930
\(418\) 0 0
\(419\) 28.6861 1.40141 0.700705 0.713451i \(-0.252869\pi\)
0.700705 + 0.713451i \(0.252869\pi\)
\(420\) 0 0
\(421\) 27.8197 1.35585 0.677924 0.735132i \(-0.262880\pi\)
0.677924 + 0.735132i \(0.262880\pi\)
\(422\) 0 0
\(423\) 4.02365 0.195636
\(424\) 0 0
\(425\) −2.67972 −0.129986
\(426\) 0 0
\(427\) 19.3412 0.935987
\(428\) 0 0
\(429\) −9.10934 −0.439803
\(430\) 0 0
\(431\) 21.4518 1.03330 0.516649 0.856197i \(-0.327179\pi\)
0.516649 + 0.856197i \(0.327179\pi\)
\(432\) 0 0
\(433\) 31.3986 1.50892 0.754459 0.656347i \(-0.227899\pi\)
0.754459 + 0.656347i \(0.227899\pi\)
\(434\) 0 0
\(435\) −17.7267 −0.849929
\(436\) 0 0
\(437\) 13.4462 0.643221
\(438\) 0 0
\(439\) −22.7221 −1.08447 −0.542234 0.840228i \(-0.682421\pi\)
−0.542234 + 0.840228i \(0.682421\pi\)
\(440\) 0 0
\(441\) −4.17318 −0.198723
\(442\) 0 0
\(443\) 12.8897 0.612410 0.306205 0.951966i \(-0.400941\pi\)
0.306205 + 0.951966i \(0.400941\pi\)
\(444\) 0 0
\(445\) −19.7032 −0.934020
\(446\) 0 0
\(447\) −13.4744 −0.637315
\(448\) 0 0
\(449\) 29.8866 1.41043 0.705217 0.708991i \(-0.250850\pi\)
0.705217 + 0.708991i \(0.250850\pi\)
\(450\) 0 0
\(451\) 44.3707 2.08934
\(452\) 0 0
\(453\) 50.7331 2.38365
\(454\) 0 0
\(455\) −4.37276 −0.204998
\(456\) 0 0
\(457\) 9.07693 0.424601 0.212301 0.977204i \(-0.431904\pi\)
0.212301 + 0.977204i \(0.431904\pi\)
\(458\) 0 0
\(459\) 11.3748 0.530931
\(460\) 0 0
\(461\) 0.239249 0.0111429 0.00557147 0.999984i \(-0.498227\pi\)
0.00557147 + 0.999984i \(0.498227\pi\)
\(462\) 0 0
\(463\) 11.2908 0.524726 0.262363 0.964969i \(-0.415498\pi\)
0.262363 + 0.964969i \(0.415498\pi\)
\(464\) 0 0
\(465\) −4.10741 −0.190476
\(466\) 0 0
\(467\) −13.9345 −0.644809 −0.322405 0.946602i \(-0.604491\pi\)
−0.322405 + 0.946602i \(0.604491\pi\)
\(468\) 0 0
\(469\) 23.8558 1.10156
\(470\) 0 0
\(471\) 16.1399 0.743686
\(472\) 0 0
\(473\) −55.9205 −2.57123
\(474\) 0 0
\(475\) 0.886305 0.0406665
\(476\) 0 0
\(477\) −4.27680 −0.195821
\(478\) 0 0
\(479\) −39.9989 −1.82760 −0.913798 0.406169i \(-0.866864\pi\)
−0.913798 + 0.406169i \(0.866864\pi\)
\(480\) 0 0
\(481\) −6.50190 −0.296461
\(482\) 0 0
\(483\) −37.0259 −1.68474
\(484\) 0 0
\(485\) −7.56795 −0.343643
\(486\) 0 0
\(487\) 4.91070 0.222525 0.111263 0.993791i \(-0.464511\pi\)
0.111263 + 0.993791i \(0.464511\pi\)
\(488\) 0 0
\(489\) −43.3229 −1.95913
\(490\) 0 0
\(491\) −7.23885 −0.326685 −0.163342 0.986569i \(-0.552228\pi\)
−0.163342 + 0.986569i \(0.552228\pi\)
\(492\) 0 0
\(493\) 18.5921 0.837346
\(494\) 0 0
\(495\) −23.6721 −1.06398
\(496\) 0 0
\(497\) −8.00456 −0.359054
\(498\) 0 0
\(499\) 10.8028 0.483600 0.241800 0.970326i \(-0.422262\pi\)
0.241800 + 0.970326i \(0.422262\pi\)
\(500\) 0 0
\(501\) 31.0094 1.38540
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −22.7210 −1.01107
\(506\) 0 0
\(507\) −27.7574 −1.23275
\(508\) 0 0
\(509\) 11.6925 0.518261 0.259131 0.965842i \(-0.416564\pi\)
0.259131 + 0.965842i \(0.416564\pi\)
\(510\) 0 0
\(511\) −12.7464 −0.563867
\(512\) 0 0
\(513\) −3.76216 −0.166104
\(514\) 0 0
\(515\) −28.5797 −1.25937
\(516\) 0 0
\(517\) −9.31065 −0.409482
\(518\) 0 0
\(519\) −28.5619 −1.25373
\(520\) 0 0
\(521\) 2.55894 0.112109 0.0560546 0.998428i \(-0.482148\pi\)
0.0560546 + 0.998428i \(0.482148\pi\)
\(522\) 0 0
\(523\) −6.24097 −0.272898 −0.136449 0.990647i \(-0.543569\pi\)
−0.136449 + 0.990647i \(0.543569\pi\)
\(524\) 0 0
\(525\) −2.44055 −0.106514
\(526\) 0 0
\(527\) 4.30793 0.187656
\(528\) 0 0
\(529\) 30.8293 1.34040
\(530\) 0 0
\(531\) −1.39793 −0.0606651
\(532\) 0 0
\(533\) −7.65870 −0.331735
\(534\) 0 0
\(535\) 20.7962 0.899100
\(536\) 0 0
\(537\) −59.1798 −2.55380
\(538\) 0 0
\(539\) 9.65666 0.415942
\(540\) 0 0
\(541\) −28.9363 −1.24407 −0.622034 0.782990i \(-0.713693\pi\)
−0.622034 + 0.782990i \(0.713693\pi\)
\(542\) 0 0
\(543\) −38.7198 −1.66162
\(544\) 0 0
\(545\) 15.5084 0.664309
\(546\) 0 0
\(547\) 8.36518 0.357669 0.178835 0.983879i \(-0.442767\pi\)
0.178835 + 0.983879i \(0.442767\pi\)
\(548\) 0 0
\(549\) −18.0727 −0.771326
\(550\) 0 0
\(551\) −6.14924 −0.261966
\(552\) 0 0
\(553\) −18.7562 −0.797594
\(554\) 0 0
\(555\) −41.1478 −1.74663
\(556\) 0 0
\(557\) −9.53757 −0.404120 −0.202060 0.979373i \(-0.564764\pi\)
−0.202060 + 0.979373i \(0.564764\pi\)
\(558\) 0 0
\(559\) 9.65227 0.408247
\(560\) 0 0
\(561\) 60.4637 2.55278
\(562\) 0 0
\(563\) 2.53621 0.106888 0.0534442 0.998571i \(-0.482980\pi\)
0.0534442 + 0.998571i \(0.482980\pi\)
\(564\) 0 0
\(565\) 36.0408 1.51625
\(566\) 0 0
\(567\) 24.3853 1.02409
\(568\) 0 0
\(569\) −31.1709 −1.30675 −0.653375 0.757034i \(-0.726648\pi\)
−0.653375 + 0.757034i \(0.726648\pi\)
\(570\) 0 0
\(571\) 40.4824 1.69413 0.847067 0.531486i \(-0.178366\pi\)
0.847067 + 0.531486i \(0.178366\pi\)
\(572\) 0 0
\(573\) −39.0621 −1.63184
\(574\) 0 0
\(575\) 3.54814 0.147968
\(576\) 0 0
\(577\) 35.8137 1.49094 0.745472 0.666537i \(-0.232224\pi\)
0.745472 + 0.666537i \(0.232224\pi\)
\(578\) 0 0
\(579\) −46.2720 −1.92300
\(580\) 0 0
\(581\) 30.6677 1.27231
\(582\) 0 0
\(583\) 9.89644 0.409869
\(584\) 0 0
\(585\) 4.08598 0.168934
\(586\) 0 0
\(587\) 31.1701 1.28653 0.643264 0.765644i \(-0.277580\pi\)
0.643264 + 0.765644i \(0.277580\pi\)
\(588\) 0 0
\(589\) −1.42483 −0.0587089
\(590\) 0 0
\(591\) 10.9316 0.449665
\(592\) 0 0
\(593\) 22.6221 0.928977 0.464488 0.885579i \(-0.346238\pi\)
0.464488 + 0.885579i \(0.346238\pi\)
\(594\) 0 0
\(595\) 29.0244 1.18988
\(596\) 0 0
\(597\) −58.0457 −2.37565
\(598\) 0 0
\(599\) 27.2164 1.11203 0.556016 0.831172i \(-0.312329\pi\)
0.556016 + 0.831172i \(0.312329\pi\)
\(600\) 0 0
\(601\) 5.31940 0.216983 0.108492 0.994097i \(-0.465398\pi\)
0.108492 + 0.994097i \(0.465398\pi\)
\(602\) 0 0
\(603\) −22.2912 −0.907769
\(604\) 0 0
\(605\) 29.0181 1.17975
\(606\) 0 0
\(607\) −36.9274 −1.49884 −0.749419 0.662096i \(-0.769667\pi\)
−0.749419 + 0.662096i \(0.769667\pi\)
\(608\) 0 0
\(609\) 16.9327 0.686147
\(610\) 0 0
\(611\) 1.60708 0.0650157
\(612\) 0 0
\(613\) −45.7494 −1.84780 −0.923900 0.382634i \(-0.875017\pi\)
−0.923900 + 0.382634i \(0.875017\pi\)
\(614\) 0 0
\(615\) −48.4687 −1.95445
\(616\) 0 0
\(617\) −20.8664 −0.840052 −0.420026 0.907512i \(-0.637979\pi\)
−0.420026 + 0.907512i \(0.637979\pi\)
\(618\) 0 0
\(619\) −1.81322 −0.0728795 −0.0364398 0.999336i \(-0.511602\pi\)
−0.0364398 + 0.999336i \(0.511602\pi\)
\(620\) 0 0
\(621\) −15.0611 −0.604379
\(622\) 0 0
\(623\) 18.8207 0.754034
\(624\) 0 0
\(625\) −27.1842 −1.08737
\(626\) 0 0
\(627\) −19.9981 −0.798646
\(628\) 0 0
\(629\) 43.1566 1.72077
\(630\) 0 0
\(631\) −16.7480 −0.666729 −0.333364 0.942798i \(-0.608184\pi\)
−0.333364 + 0.942798i \(0.608184\pi\)
\(632\) 0 0
\(633\) 58.2802 2.31643
\(634\) 0 0
\(635\) −43.6703 −1.73300
\(636\) 0 0
\(637\) −1.66681 −0.0660413
\(638\) 0 0
\(639\) 7.47959 0.295888
\(640\) 0 0
\(641\) 18.6738 0.737571 0.368786 0.929514i \(-0.379774\pi\)
0.368786 + 0.929514i \(0.379774\pi\)
\(642\) 0 0
\(643\) −5.70773 −0.225091 −0.112545 0.993647i \(-0.535900\pi\)
−0.112545 + 0.993647i \(0.535900\pi\)
\(644\) 0 0
\(645\) 61.0852 2.40523
\(646\) 0 0
\(647\) 21.1702 0.832286 0.416143 0.909299i \(-0.363382\pi\)
0.416143 + 0.909299i \(0.363382\pi\)
\(648\) 0 0
\(649\) 3.23479 0.126977
\(650\) 0 0
\(651\) 3.92343 0.153772
\(652\) 0 0
\(653\) −8.92038 −0.349082 −0.174541 0.984650i \(-0.555844\pi\)
−0.174541 + 0.984650i \(0.555844\pi\)
\(654\) 0 0
\(655\) 41.2628 1.61227
\(656\) 0 0
\(657\) 11.9104 0.464670
\(658\) 0 0
\(659\) −18.1114 −0.705522 −0.352761 0.935714i \(-0.614757\pi\)
−0.352761 + 0.935714i \(0.614757\pi\)
\(660\) 0 0
\(661\) 30.7241 1.19503 0.597515 0.801858i \(-0.296155\pi\)
0.597515 + 0.801858i \(0.296155\pi\)
\(662\) 0 0
\(663\) −10.4365 −0.405318
\(664\) 0 0
\(665\) −9.59968 −0.372259
\(666\) 0 0
\(667\) −24.6172 −0.953183
\(668\) 0 0
\(669\) −27.6732 −1.06991
\(670\) 0 0
\(671\) 41.8200 1.61444
\(672\) 0 0
\(673\) 2.89455 0.111577 0.0557883 0.998443i \(-0.482233\pi\)
0.0557883 + 0.998443i \(0.482233\pi\)
\(674\) 0 0
\(675\) −0.992745 −0.0382108
\(676\) 0 0
\(677\) 27.8588 1.07070 0.535351 0.844630i \(-0.320179\pi\)
0.535351 + 0.844630i \(0.320179\pi\)
\(678\) 0 0
\(679\) 7.22899 0.277423
\(680\) 0 0
\(681\) 34.2692 1.31320
\(682\) 0 0
\(683\) 28.1880 1.07859 0.539293 0.842118i \(-0.318692\pi\)
0.539293 + 0.842118i \(0.318692\pi\)
\(684\) 0 0
\(685\) 47.8538 1.82840
\(686\) 0 0
\(687\) 5.94567 0.226841
\(688\) 0 0
\(689\) −1.70820 −0.0650771
\(690\) 0 0
\(691\) −4.40269 −0.167486 −0.0837432 0.996487i \(-0.526688\pi\)
−0.0837432 + 0.996487i \(0.526688\pi\)
\(692\) 0 0
\(693\) 22.6119 0.858954
\(694\) 0 0
\(695\) −8.62495 −0.327163
\(696\) 0 0
\(697\) 50.8350 1.92551
\(698\) 0 0
\(699\) −21.0490 −0.796148
\(700\) 0 0
\(701\) −25.3240 −0.956475 −0.478238 0.878230i \(-0.658724\pi\)
−0.478238 + 0.878230i \(0.658724\pi\)
\(702\) 0 0
\(703\) −14.2738 −0.538348
\(704\) 0 0
\(705\) 10.1706 0.383046
\(706\) 0 0
\(707\) 21.7033 0.816238
\(708\) 0 0
\(709\) 16.7502 0.629066 0.314533 0.949247i \(-0.398152\pi\)
0.314533 + 0.949247i \(0.398152\pi\)
\(710\) 0 0
\(711\) 17.5261 0.657279
\(712\) 0 0
\(713\) −5.70400 −0.213616
\(714\) 0 0
\(715\) −9.45488 −0.353592
\(716\) 0 0
\(717\) 54.2161 2.02474
\(718\) 0 0
\(719\) 7.99858 0.298297 0.149148 0.988815i \(-0.452347\pi\)
0.149148 + 0.988815i \(0.452347\pi\)
\(720\) 0 0
\(721\) 27.2996 1.01669
\(722\) 0 0
\(723\) 7.97767 0.296693
\(724\) 0 0
\(725\) −1.62264 −0.0602633
\(726\) 0 0
\(727\) −34.6208 −1.28401 −0.642007 0.766699i \(-0.721898\pi\)
−0.642007 + 0.766699i \(0.721898\pi\)
\(728\) 0 0
\(729\) −8.89189 −0.329329
\(730\) 0 0
\(731\) −64.0674 −2.36962
\(732\) 0 0
\(733\) −1.95052 −0.0720441 −0.0360221 0.999351i \(-0.511469\pi\)
−0.0360221 + 0.999351i \(0.511469\pi\)
\(734\) 0 0
\(735\) −10.5485 −0.389088
\(736\) 0 0
\(737\) 51.5815 1.90003
\(738\) 0 0
\(739\) 37.1600 1.36695 0.683476 0.729973i \(-0.260467\pi\)
0.683476 + 0.729973i \(0.260467\pi\)
\(740\) 0 0
\(741\) 3.45181 0.126805
\(742\) 0 0
\(743\) 27.7445 1.01785 0.508924 0.860811i \(-0.330043\pi\)
0.508924 + 0.860811i \(0.330043\pi\)
\(744\) 0 0
\(745\) −13.9855 −0.512388
\(746\) 0 0
\(747\) −28.6564 −1.04848
\(748\) 0 0
\(749\) −19.8648 −0.725843
\(750\) 0 0
\(751\) −47.0130 −1.71553 −0.857764 0.514043i \(-0.828147\pi\)
−0.857764 + 0.514043i \(0.828147\pi\)
\(752\) 0 0
\(753\) 31.4084 1.14459
\(754\) 0 0
\(755\) 52.6575 1.91640
\(756\) 0 0
\(757\) −31.0594 −1.12887 −0.564436 0.825477i \(-0.690906\pi\)
−0.564436 + 0.825477i \(0.690906\pi\)
\(758\) 0 0
\(759\) −80.0582 −2.90593
\(760\) 0 0
\(761\) 9.98902 0.362102 0.181051 0.983474i \(-0.442050\pi\)
0.181051 + 0.983474i \(0.442050\pi\)
\(762\) 0 0
\(763\) −14.8138 −0.536296
\(764\) 0 0
\(765\) −27.1209 −0.980557
\(766\) 0 0
\(767\) −0.558348 −0.0201608
\(768\) 0 0
\(769\) 34.7684 1.25378 0.626890 0.779108i \(-0.284328\pi\)
0.626890 + 0.779108i \(0.284328\pi\)
\(770\) 0 0
\(771\) 49.5527 1.78460
\(772\) 0 0
\(773\) −40.4865 −1.45620 −0.728100 0.685471i \(-0.759596\pi\)
−0.728100 + 0.685471i \(0.759596\pi\)
\(774\) 0 0
\(775\) −0.375978 −0.0135055
\(776\) 0 0
\(777\) 39.3048 1.41005
\(778\) 0 0
\(779\) −16.8134 −0.602403
\(780\) 0 0
\(781\) −17.3076 −0.619316
\(782\) 0 0
\(783\) 6.88773 0.246147
\(784\) 0 0
\(785\) 16.7521 0.597908
\(786\) 0 0
\(787\) 19.3012 0.688013 0.344007 0.938967i \(-0.388216\pi\)
0.344007 + 0.938967i \(0.388216\pi\)
\(788\) 0 0
\(789\) −33.4146 −1.18959
\(790\) 0 0
\(791\) −34.4265 −1.22407
\(792\) 0 0
\(793\) −7.21843 −0.256334
\(794\) 0 0
\(795\) −10.8105 −0.383408
\(796\) 0 0
\(797\) 15.1738 0.537482 0.268741 0.963212i \(-0.413392\pi\)
0.268741 + 0.963212i \(0.413392\pi\)
\(798\) 0 0
\(799\) −10.6671 −0.377375
\(800\) 0 0
\(801\) −17.5863 −0.621383
\(802\) 0 0
\(803\) −27.5605 −0.972590
\(804\) 0 0
\(805\) −38.4303 −1.35449
\(806\) 0 0
\(807\) −4.86547 −0.171273
\(808\) 0 0
\(809\) −19.0124 −0.668440 −0.334220 0.942495i \(-0.608473\pi\)
−0.334220 + 0.942495i \(0.608473\pi\)
\(810\) 0 0
\(811\) −13.9235 −0.488921 −0.244460 0.969659i \(-0.578611\pi\)
−0.244460 + 0.969659i \(0.578611\pi\)
\(812\) 0 0
\(813\) −24.0652 −0.844003
\(814\) 0 0
\(815\) −44.9662 −1.57510
\(816\) 0 0
\(817\) 21.1900 0.741343
\(818\) 0 0
\(819\) −3.90297 −0.136381
\(820\) 0 0
\(821\) −28.6868 −1.00117 −0.500587 0.865686i \(-0.666883\pi\)
−0.500587 + 0.865686i \(0.666883\pi\)
\(822\) 0 0
\(823\) −12.4739 −0.434814 −0.217407 0.976081i \(-0.569760\pi\)
−0.217407 + 0.976081i \(0.569760\pi\)
\(824\) 0 0
\(825\) −5.27701 −0.183722
\(826\) 0 0
\(827\) 47.9770 1.66832 0.834162 0.551519i \(-0.185952\pi\)
0.834162 + 0.551519i \(0.185952\pi\)
\(828\) 0 0
\(829\) 25.2740 0.877802 0.438901 0.898535i \(-0.355368\pi\)
0.438901 + 0.898535i \(0.355368\pi\)
\(830\) 0 0
\(831\) 21.4693 0.744761
\(832\) 0 0
\(833\) 11.0635 0.383328
\(834\) 0 0
\(835\) 32.1856 1.11383
\(836\) 0 0
\(837\) 1.59594 0.0551637
\(838\) 0 0
\(839\) 6.16546 0.212855 0.106428 0.994320i \(-0.466059\pi\)
0.106428 + 0.994320i \(0.466059\pi\)
\(840\) 0 0
\(841\) −17.7420 −0.611794
\(842\) 0 0
\(843\) −38.9557 −1.34171
\(844\) 0 0
\(845\) −28.8103 −0.991103
\(846\) 0 0
\(847\) −27.7184 −0.952415
\(848\) 0 0
\(849\) 43.9508 1.50839
\(850\) 0 0
\(851\) −57.1424 −1.95882
\(852\) 0 0
\(853\) 49.8675 1.70743 0.853715 0.520741i \(-0.174344\pi\)
0.853715 + 0.520741i \(0.174344\pi\)
\(854\) 0 0
\(855\) 8.97009 0.306771
\(856\) 0 0
\(857\) −21.3701 −0.729990 −0.364995 0.931009i \(-0.618929\pi\)
−0.364995 + 0.931009i \(0.618929\pi\)
\(858\) 0 0
\(859\) −14.6587 −0.500149 −0.250075 0.968227i \(-0.580455\pi\)
−0.250075 + 0.968227i \(0.580455\pi\)
\(860\) 0 0
\(861\) 46.2978 1.57783
\(862\) 0 0
\(863\) −47.8017 −1.62719 −0.813594 0.581434i \(-0.802492\pi\)
−0.813594 + 0.581434i \(0.802492\pi\)
\(864\) 0 0
\(865\) −29.6453 −1.00797
\(866\) 0 0
\(867\) 30.9183 1.05004
\(868\) 0 0
\(869\) −40.5550 −1.37574
\(870\) 0 0
\(871\) −8.90333 −0.301678
\(872\) 0 0
\(873\) −6.75488 −0.228618
\(874\) 0 0
\(875\) 23.6568 0.799747
\(876\) 0 0
\(877\) 48.2557 1.62948 0.814740 0.579826i \(-0.196880\pi\)
0.814740 + 0.579826i \(0.196880\pi\)
\(878\) 0 0
\(879\) 39.4349 1.33010
\(880\) 0 0
\(881\) −42.1880 −1.42135 −0.710674 0.703521i \(-0.751610\pi\)
−0.710674 + 0.703521i \(0.751610\pi\)
\(882\) 0 0
\(883\) −13.6532 −0.459468 −0.229734 0.973253i \(-0.573786\pi\)
−0.229734 + 0.973253i \(0.573786\pi\)
\(884\) 0 0
\(885\) −3.53355 −0.118779
\(886\) 0 0
\(887\) −18.4101 −0.618151 −0.309075 0.951038i \(-0.600020\pi\)
−0.309075 + 0.951038i \(0.600020\pi\)
\(888\) 0 0
\(889\) 41.7143 1.39905
\(890\) 0 0
\(891\) 52.7265 1.76640
\(892\) 0 0
\(893\) 3.52809 0.118063
\(894\) 0 0
\(895\) −61.4246 −2.05320
\(896\) 0 0
\(897\) 13.8186 0.461390
\(898\) 0 0
\(899\) 2.60856 0.0870002
\(900\) 0 0
\(901\) 11.3382 0.377731
\(902\) 0 0
\(903\) −58.3492 −1.94174
\(904\) 0 0
\(905\) −40.1885 −1.33591
\(906\) 0 0
\(907\) −56.5302 −1.87705 −0.938527 0.345206i \(-0.887809\pi\)
−0.938527 + 0.345206i \(0.887809\pi\)
\(908\) 0 0
\(909\) −20.2799 −0.672643
\(910\) 0 0
\(911\) 15.5516 0.515247 0.257623 0.966245i \(-0.417061\pi\)
0.257623 + 0.966245i \(0.417061\pi\)
\(912\) 0 0
\(913\) 66.3104 2.19455
\(914\) 0 0
\(915\) −45.6824 −1.51022
\(916\) 0 0
\(917\) −39.4147 −1.30159
\(918\) 0 0
\(919\) 1.04563 0.0344921 0.0172461 0.999851i \(-0.494510\pi\)
0.0172461 + 0.999851i \(0.494510\pi\)
\(920\) 0 0
\(921\) 22.9480 0.756163
\(922\) 0 0
\(923\) 2.98742 0.0983322
\(924\) 0 0
\(925\) −3.76653 −0.123843
\(926\) 0 0
\(927\) −25.5092 −0.837833
\(928\) 0 0
\(929\) 0.796090 0.0261189 0.0130594 0.999915i \(-0.495843\pi\)
0.0130594 + 0.999915i \(0.495843\pi\)
\(930\) 0 0
\(931\) −3.65920 −0.119925
\(932\) 0 0
\(933\) −46.8651 −1.53430
\(934\) 0 0
\(935\) 62.7572 2.05238
\(936\) 0 0
\(937\) −20.3836 −0.665904 −0.332952 0.942944i \(-0.608045\pi\)
−0.332952 + 0.942944i \(0.608045\pi\)
\(938\) 0 0
\(939\) −21.2139 −0.692288
\(940\) 0 0
\(941\) −12.8415 −0.418621 −0.209310 0.977849i \(-0.567122\pi\)
−0.209310 + 0.977849i \(0.567122\pi\)
\(942\) 0 0
\(943\) −67.3091 −2.19189
\(944\) 0 0
\(945\) 10.7525 0.349780
\(946\) 0 0
\(947\) −42.0108 −1.36517 −0.682585 0.730807i \(-0.739144\pi\)
−0.682585 + 0.730807i \(0.739144\pi\)
\(948\) 0 0
\(949\) 4.75714 0.154423
\(950\) 0 0
\(951\) 51.0990 1.65700
\(952\) 0 0
\(953\) −15.5148 −0.502575 −0.251287 0.967913i \(-0.580854\pi\)
−0.251287 + 0.967913i \(0.580854\pi\)
\(954\) 0 0
\(955\) −40.5438 −1.31197
\(956\) 0 0
\(957\) 36.6122 1.18351
\(958\) 0 0
\(959\) −45.7104 −1.47607
\(960\) 0 0
\(961\) −30.3956 −0.980503
\(962\) 0 0
\(963\) 18.5620 0.598151
\(964\) 0 0
\(965\) −48.0272 −1.54605
\(966\) 0 0
\(967\) 29.9778 0.964022 0.482011 0.876165i \(-0.339906\pi\)
0.482011 + 0.876165i \(0.339906\pi\)
\(968\) 0 0
\(969\) −22.9115 −0.736024
\(970\) 0 0
\(971\) −3.14021 −0.100774 −0.0503870 0.998730i \(-0.516045\pi\)
−0.0503870 + 0.998730i \(0.516045\pi\)
\(972\) 0 0
\(973\) 8.23864 0.264119
\(974\) 0 0
\(975\) 0.910850 0.0291705
\(976\) 0 0
\(977\) 14.3894 0.460357 0.230178 0.973148i \(-0.426069\pi\)
0.230178 + 0.973148i \(0.426069\pi\)
\(978\) 0 0
\(979\) 40.6945 1.30060
\(980\) 0 0
\(981\) 13.8423 0.441950
\(982\) 0 0
\(983\) 59.6676 1.90310 0.951550 0.307495i \(-0.0994906\pi\)
0.951550 + 0.307495i \(0.0994906\pi\)
\(984\) 0 0
\(985\) 11.3462 0.361521
\(986\) 0 0
\(987\) −9.71503 −0.309233
\(988\) 0 0
\(989\) 84.8297 2.69743
\(990\) 0 0
\(991\) 42.6315 1.35424 0.677118 0.735875i \(-0.263229\pi\)
0.677118 + 0.735875i \(0.263229\pi\)
\(992\) 0 0
\(993\) −40.1906 −1.27541
\(994\) 0 0
\(995\) −60.2475 −1.90997
\(996\) 0 0
\(997\) 38.5552 1.22105 0.610527 0.791995i \(-0.290958\pi\)
0.610527 + 0.791995i \(0.290958\pi\)
\(998\) 0 0
\(999\) 15.9880 0.505839
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 \(a_p\))