Properties

Label 8036.2.a.q.1.14
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 15
CM No
Inner twists 1

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1677830643\)
Analytic rank: \(0\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Root \(-2.90634\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.90634 q^{3} +0.506103 q^{5} +5.44682 q^{9} +O(q^{10})\) \(q+2.90634 q^{3} +0.506103 q^{5} +5.44682 q^{9} +5.70801 q^{11} +2.51313 q^{13} +1.47091 q^{15} +5.03384 q^{17} +5.78183 q^{19} +1.51894 q^{23} -4.74386 q^{25} +7.11130 q^{27} +6.63143 q^{29} -3.27388 q^{31} +16.5894 q^{33} +9.82938 q^{37} +7.30402 q^{39} -1.00000 q^{41} -8.37684 q^{43} +2.75665 q^{45} -12.2065 q^{47} +14.6300 q^{51} -12.1084 q^{53} +2.88884 q^{55} +16.8040 q^{57} -8.79288 q^{59} -6.07381 q^{61} +1.27190 q^{65} -11.2129 q^{67} +4.41455 q^{69} -5.46228 q^{71} +4.85721 q^{73} -13.7873 q^{75} -2.19722 q^{79} +4.32740 q^{81} +0.906091 q^{83} +2.54764 q^{85} +19.2732 q^{87} -5.03213 q^{89} -9.51501 q^{93} +2.92620 q^{95} -5.21457 q^{97} +31.0905 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - q^{3} + 3q^{5} + 30q^{9} + O(q^{10}) \) \( 15q - q^{3} + 3q^{5} + 30q^{9} + 9q^{11} + 7q^{13} + 2q^{15} + 3q^{17} + 7q^{19} - q^{23} + 32q^{25} + 11q^{27} + 18q^{29} + 30q^{31} - 16q^{33} + 23q^{37} + 5q^{39} - 15q^{41} + 12q^{43} - 13q^{45} - 16q^{47} + 29q^{51} + 33q^{53} + 37q^{55} + 16q^{57} - 10q^{59} + q^{61} + 16q^{65} + 20q^{67} + 21q^{69} + 5q^{71} - 3q^{73} - 51q^{75} + 25q^{79} + 43q^{81} + 18q^{83} + 36q^{85} - 53q^{87} - 11q^{89} + 65q^{93} - 30q^{95} + 16q^{97} - 18q^{99} + O(q^{100}) \)

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
\(3\) 2.90634 1.67798 0.838989 0.544149i \(-0.183147\pi\)
0.838989 + 0.544149i \(0.183147\pi\)
\(4\) 0 0
\(5\) 0.506103 0.226336 0.113168 0.993576i \(-0.463900\pi\)
0.113168 + 0.993576i \(0.463900\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 5.44682 1.81561
\(10\) 0 0
\(11\) 5.70801 1.72103 0.860515 0.509425i \(-0.170142\pi\)
0.860515 + 0.509425i \(0.170142\pi\)
\(12\) 0 0
\(13\) 2.51313 0.697017 0.348509 0.937306i \(-0.386688\pi\)
0.348509 + 0.937306i \(0.386688\pi\)
\(14\) 0 0
\(15\) 1.47091 0.379787
\(16\) 0 0
\(17\) 5.03384 1.22088 0.610442 0.792061i \(-0.290992\pi\)
0.610442 + 0.792061i \(0.290992\pi\)
\(18\) 0 0
\(19\) 5.78183 1.32644 0.663221 0.748423i \(-0.269189\pi\)
0.663221 + 0.748423i \(0.269189\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.51894 0.316720 0.158360 0.987381i \(-0.449379\pi\)
0.158360 + 0.987381i \(0.449379\pi\)
\(24\) 0 0
\(25\) −4.74386 −0.948772
\(26\) 0 0
\(27\) 7.11130 1.36857
\(28\) 0 0
\(29\) 6.63143 1.23143 0.615713 0.787971i \(-0.288868\pi\)
0.615713 + 0.787971i \(0.288868\pi\)
\(30\) 0 0
\(31\) −3.27388 −0.588006 −0.294003 0.955805i \(-0.594988\pi\)
−0.294003 + 0.955805i \(0.594988\pi\)
\(32\) 0 0
\(33\) 16.5894 2.88785
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 9.82938 1.61594 0.807970 0.589224i \(-0.200566\pi\)
0.807970 + 0.589224i \(0.200566\pi\)
\(38\) 0 0
\(39\) 7.30402 1.16958
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −8.37684 −1.27746 −0.638728 0.769433i \(-0.720539\pi\)
−0.638728 + 0.769433i \(0.720539\pi\)
\(44\) 0 0
\(45\) 2.75665 0.410937
\(46\) 0 0
\(47\) −12.2065 −1.78051 −0.890253 0.455466i \(-0.849472\pi\)
−0.890253 + 0.455466i \(0.849472\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 14.6300 2.04862
\(52\) 0 0
\(53\) −12.1084 −1.66321 −0.831606 0.555366i \(-0.812578\pi\)
−0.831606 + 0.555366i \(0.812578\pi\)
\(54\) 0 0
\(55\) 2.88884 0.389531
\(56\) 0 0
\(57\) 16.8040 2.22574
\(58\) 0 0
\(59\) −8.79288 −1.14474 −0.572368 0.819997i \(-0.693975\pi\)
−0.572368 + 0.819997i \(0.693975\pi\)
\(60\) 0 0
\(61\) −6.07381 −0.777672 −0.388836 0.921307i \(-0.627123\pi\)
−0.388836 + 0.921307i \(0.627123\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.27190 0.157760
\(66\) 0 0
\(67\) −11.2129 −1.36987 −0.684935 0.728604i \(-0.740169\pi\)
−0.684935 + 0.728604i \(0.740169\pi\)
\(68\) 0 0
\(69\) 4.41455 0.531449
\(70\) 0 0
\(71\) −5.46228 −0.648254 −0.324127 0.946014i \(-0.605070\pi\)
−0.324127 + 0.946014i \(0.605070\pi\)
\(72\) 0 0
\(73\) 4.85721 0.568494 0.284247 0.958751i \(-0.408256\pi\)
0.284247 + 0.958751i \(0.408256\pi\)
\(74\) 0 0
\(75\) −13.7873 −1.59202
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −2.19722 −0.247207 −0.123603 0.992332i \(-0.539445\pi\)
−0.123603 + 0.992332i \(0.539445\pi\)
\(80\) 0 0
\(81\) 4.32740 0.480822
\(82\) 0 0
\(83\) 0.906091 0.0994564 0.0497282 0.998763i \(-0.484164\pi\)
0.0497282 + 0.998763i \(0.484164\pi\)
\(84\) 0 0
\(85\) 2.54764 0.276330
\(86\) 0 0
\(87\) 19.2732 2.06630
\(88\) 0 0
\(89\) −5.03213 −0.533405 −0.266702 0.963779i \(-0.585934\pi\)
−0.266702 + 0.963779i \(0.585934\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −9.51501 −0.986661
\(94\) 0 0
\(95\) 2.92620 0.300222
\(96\) 0 0
\(97\) −5.21457 −0.529460 −0.264730 0.964323i \(-0.585283\pi\)
−0.264730 + 0.964323i \(0.585283\pi\)
\(98\) 0 0
\(99\) 31.0905 3.12472
\(100\) 0 0
\(101\) −10.1869 −1.01364 −0.506819 0.862052i \(-0.669179\pi\)
−0.506819 + 0.862052i \(0.669179\pi\)
\(102\) 0 0
\(103\) −4.42232 −0.435744 −0.217872 0.975977i \(-0.569912\pi\)
−0.217872 + 0.975977i \(0.569912\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 5.67421 0.548547 0.274273 0.961652i \(-0.411563\pi\)
0.274273 + 0.961652i \(0.411563\pi\)
\(108\) 0 0
\(109\) 6.63092 0.635127 0.317563 0.948237i \(-0.397135\pi\)
0.317563 + 0.948237i \(0.397135\pi\)
\(110\) 0 0
\(111\) 28.5675 2.71151
\(112\) 0 0
\(113\) −15.8269 −1.48887 −0.744436 0.667694i \(-0.767281\pi\)
−0.744436 + 0.667694i \(0.767281\pi\)
\(114\) 0 0
\(115\) 0.768738 0.0716852
\(116\) 0 0
\(117\) 13.6886 1.26551
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 21.5814 1.96195
\(122\) 0 0
\(123\) −2.90634 −0.262056
\(124\) 0 0
\(125\) −4.93139 −0.441077
\(126\) 0 0
\(127\) −17.0228 −1.51053 −0.755266 0.655419i \(-0.772492\pi\)
−0.755266 + 0.655419i \(0.772492\pi\)
\(128\) 0 0
\(129\) −24.3460 −2.14354
\(130\) 0 0
\(131\) 18.6734 1.63150 0.815749 0.578406i \(-0.196325\pi\)
0.815749 + 0.578406i \(0.196325\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 3.59905 0.309757
\(136\) 0 0
\(137\) 6.31324 0.539376 0.269688 0.962948i \(-0.413079\pi\)
0.269688 + 0.962948i \(0.413079\pi\)
\(138\) 0 0
\(139\) 20.3708 1.72783 0.863915 0.503637i \(-0.168005\pi\)
0.863915 + 0.503637i \(0.168005\pi\)
\(140\) 0 0
\(141\) −35.4764 −2.98765
\(142\) 0 0
\(143\) 14.3450 1.19959
\(144\) 0 0
\(145\) 3.35618 0.278716
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 16.5744 1.35783 0.678913 0.734219i \(-0.262451\pi\)
0.678913 + 0.734219i \(0.262451\pi\)
\(150\) 0 0
\(151\) −19.8198 −1.61291 −0.806455 0.591295i \(-0.798617\pi\)
−0.806455 + 0.591295i \(0.798617\pi\)
\(152\) 0 0
\(153\) 27.4184 2.21665
\(154\) 0 0
\(155\) −1.65692 −0.133087
\(156\) 0 0
\(157\) 0.507136 0.0404739 0.0202369 0.999795i \(-0.493558\pi\)
0.0202369 + 0.999795i \(0.493558\pi\)
\(158\) 0 0
\(159\) −35.1910 −2.79083
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −10.5778 −0.828520 −0.414260 0.910159i \(-0.635960\pi\)
−0.414260 + 0.910159i \(0.635960\pi\)
\(164\) 0 0
\(165\) 8.39596 0.653624
\(166\) 0 0
\(167\) −4.40151 −0.340599 −0.170300 0.985392i \(-0.554474\pi\)
−0.170300 + 0.985392i \(0.554474\pi\)
\(168\) 0 0
\(169\) −6.68417 −0.514167
\(170\) 0 0
\(171\) 31.4926 2.40830
\(172\) 0 0
\(173\) 9.58786 0.728951 0.364476 0.931213i \(-0.381248\pi\)
0.364476 + 0.931213i \(0.381248\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −25.5551 −1.92084
\(178\) 0 0
\(179\) 4.38187 0.327516 0.163758 0.986501i \(-0.447638\pi\)
0.163758 + 0.986501i \(0.447638\pi\)
\(180\) 0 0
\(181\) −20.8224 −1.54772 −0.773858 0.633359i \(-0.781676\pi\)
−0.773858 + 0.633359i \(0.781676\pi\)
\(182\) 0 0
\(183\) −17.6526 −1.30492
\(184\) 0 0
\(185\) 4.97467 0.365745
\(186\) 0 0
\(187\) 28.7332 2.10118
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 18.5815 1.34451 0.672254 0.740320i \(-0.265326\pi\)
0.672254 + 0.740320i \(0.265326\pi\)
\(192\) 0 0
\(193\) −4.45059 −0.320361 −0.160180 0.987088i \(-0.551208\pi\)
−0.160180 + 0.987088i \(0.551208\pi\)
\(194\) 0 0
\(195\) 3.69658 0.264718
\(196\) 0 0
\(197\) 2.25530 0.160684 0.0803419 0.996767i \(-0.474399\pi\)
0.0803419 + 0.996767i \(0.474399\pi\)
\(198\) 0 0
\(199\) −0.734053 −0.0520356 −0.0260178 0.999661i \(-0.508283\pi\)
−0.0260178 + 0.999661i \(0.508283\pi\)
\(200\) 0 0
\(201\) −32.5884 −2.29861
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −0.506103 −0.0353477
\(206\) 0 0
\(207\) 8.27338 0.575040
\(208\) 0 0
\(209\) 33.0028 2.28285
\(210\) 0 0
\(211\) −27.9104 −1.92143 −0.960716 0.277532i \(-0.910484\pi\)
−0.960716 + 0.277532i \(0.910484\pi\)
\(212\) 0 0
\(213\) −15.8753 −1.08775
\(214\) 0 0
\(215\) −4.23954 −0.289134
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 14.1167 0.953919
\(220\) 0 0
\(221\) 12.6507 0.850978
\(222\) 0 0
\(223\) −6.10011 −0.408493 −0.204247 0.978919i \(-0.565474\pi\)
−0.204247 + 0.978919i \(0.565474\pi\)
\(224\) 0 0
\(225\) −25.8390 −1.72260
\(226\) 0 0
\(227\) 2.54979 0.169235 0.0846177 0.996413i \(-0.473033\pi\)
0.0846177 + 0.996413i \(0.473033\pi\)
\(228\) 0 0
\(229\) −8.39344 −0.554654 −0.277327 0.960776i \(-0.589449\pi\)
−0.277327 + 0.960776i \(0.589449\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 19.8195 1.29842 0.649209 0.760610i \(-0.275100\pi\)
0.649209 + 0.760610i \(0.275100\pi\)
\(234\) 0 0
\(235\) −6.17776 −0.402993
\(236\) 0 0
\(237\) −6.38587 −0.414807
\(238\) 0 0
\(239\) 25.0248 1.61872 0.809361 0.587312i \(-0.199814\pi\)
0.809361 + 0.587312i \(0.199814\pi\)
\(240\) 0 0
\(241\) 17.7542 1.14365 0.571823 0.820377i \(-0.306236\pi\)
0.571823 + 0.820377i \(0.306236\pi\)
\(242\) 0 0
\(243\) −8.75699 −0.561761
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 14.5305 0.924554
\(248\) 0 0
\(249\) 2.63341 0.166886
\(250\) 0 0
\(251\) 10.7916 0.681158 0.340579 0.940216i \(-0.389377\pi\)
0.340579 + 0.940216i \(0.389377\pi\)
\(252\) 0 0
\(253\) 8.67011 0.545085
\(254\) 0 0
\(255\) 7.40430 0.463676
\(256\) 0 0
\(257\) −1.34062 −0.0836258 −0.0418129 0.999125i \(-0.513313\pi\)
−0.0418129 + 0.999125i \(0.513313\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 36.1202 2.23579
\(262\) 0 0
\(263\) 2.69500 0.166181 0.0830903 0.996542i \(-0.473521\pi\)
0.0830903 + 0.996542i \(0.473521\pi\)
\(264\) 0 0
\(265\) −6.12807 −0.376445
\(266\) 0 0
\(267\) −14.6251 −0.895041
\(268\) 0 0
\(269\) −12.8105 −0.781069 −0.390534 0.920588i \(-0.627710\pi\)
−0.390534 + 0.920588i \(0.627710\pi\)
\(270\) 0 0
\(271\) 9.59766 0.583016 0.291508 0.956568i \(-0.405843\pi\)
0.291508 + 0.956568i \(0.405843\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −27.0780 −1.63287
\(276\) 0 0
\(277\) 16.1317 0.969259 0.484629 0.874720i \(-0.338954\pi\)
0.484629 + 0.874720i \(0.338954\pi\)
\(278\) 0 0
\(279\) −17.8322 −1.06759
\(280\) 0 0
\(281\) 13.9010 0.829261 0.414631 0.909990i \(-0.363911\pi\)
0.414631 + 0.909990i \(0.363911\pi\)
\(282\) 0 0
\(283\) −19.8856 −1.18207 −0.591037 0.806645i \(-0.701281\pi\)
−0.591037 + 0.806645i \(0.701281\pi\)
\(284\) 0 0
\(285\) 8.50454 0.503765
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 8.33950 0.490559
\(290\) 0 0
\(291\) −15.1553 −0.888421
\(292\) 0 0
\(293\) −12.9804 −0.758325 −0.379163 0.925330i \(-0.623788\pi\)
−0.379163 + 0.925330i \(0.623788\pi\)
\(294\) 0 0
\(295\) −4.45010 −0.259095
\(296\) 0 0
\(297\) 40.5914 2.35535
\(298\) 0 0
\(299\) 3.81729 0.220759
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −29.6067 −1.70086
\(304\) 0 0
\(305\) −3.07397 −0.176015
\(306\) 0 0
\(307\) −6.91179 −0.394477 −0.197238 0.980356i \(-0.563197\pi\)
−0.197238 + 0.980356i \(0.563197\pi\)
\(308\) 0 0
\(309\) −12.8528 −0.731169
\(310\) 0 0
\(311\) 0.0462826 0.00262445 0.00131222 0.999999i \(-0.499582\pi\)
0.00131222 + 0.999999i \(0.499582\pi\)
\(312\) 0 0
\(313\) 21.5865 1.22014 0.610071 0.792346i \(-0.291141\pi\)
0.610071 + 0.792346i \(0.291141\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.24013 −0.125818 −0.0629091 0.998019i \(-0.520038\pi\)
−0.0629091 + 0.998019i \(0.520038\pi\)
\(318\) 0 0
\(319\) 37.8523 2.11932
\(320\) 0 0
\(321\) 16.4912 0.920449
\(322\) 0 0
\(323\) 29.1048 1.61943
\(324\) 0 0
\(325\) −11.9219 −0.661310
\(326\) 0 0
\(327\) 19.2717 1.06573
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 27.7385 1.52464 0.762322 0.647198i \(-0.224059\pi\)
0.762322 + 0.647198i \(0.224059\pi\)
\(332\) 0 0
\(333\) 53.5389 2.93391
\(334\) 0 0
\(335\) −5.67486 −0.310051
\(336\) 0 0
\(337\) 14.2599 0.776785 0.388393 0.921494i \(-0.373030\pi\)
0.388393 + 0.921494i \(0.373030\pi\)
\(338\) 0 0
\(339\) −45.9984 −2.49829
\(340\) 0 0
\(341\) −18.6873 −1.01198
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 2.23422 0.120286
\(346\) 0 0
\(347\) 10.4476 0.560857 0.280428 0.959875i \(-0.409523\pi\)
0.280428 + 0.959875i \(0.409523\pi\)
\(348\) 0 0
\(349\) −30.5661 −1.63616 −0.818082 0.575101i \(-0.804963\pi\)
−0.818082 + 0.575101i \(0.804963\pi\)
\(350\) 0 0
\(351\) 17.8716 0.953917
\(352\) 0 0
\(353\) 29.3571 1.56252 0.781261 0.624204i \(-0.214577\pi\)
0.781261 + 0.624204i \(0.214577\pi\)
\(354\) 0 0
\(355\) −2.76448 −0.146723
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −26.5299 −1.40019 −0.700097 0.714047i \(-0.746860\pi\)
−0.700097 + 0.714047i \(0.746860\pi\)
\(360\) 0 0
\(361\) 14.4296 0.759451
\(362\) 0 0
\(363\) 62.7229 3.29210
\(364\) 0 0
\(365\) 2.45825 0.128671
\(366\) 0 0
\(367\) 4.37178 0.228205 0.114103 0.993469i \(-0.463601\pi\)
0.114103 + 0.993469i \(0.463601\pi\)
\(368\) 0 0
\(369\) −5.44682 −0.283550
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 18.8934 0.978261 0.489131 0.872211i \(-0.337314\pi\)
0.489131 + 0.872211i \(0.337314\pi\)
\(374\) 0 0
\(375\) −14.3323 −0.740117
\(376\) 0 0
\(377\) 16.6657 0.858325
\(378\) 0 0
\(379\) 27.5558 1.41545 0.707723 0.706490i \(-0.249722\pi\)
0.707723 + 0.706490i \(0.249722\pi\)
\(380\) 0 0
\(381\) −49.4741 −2.53464
\(382\) 0 0
\(383\) −28.1536 −1.43858 −0.719291 0.694709i \(-0.755533\pi\)
−0.719291 + 0.694709i \(0.755533\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −45.6271 −2.31936
\(388\) 0 0
\(389\) −15.5849 −0.790187 −0.395093 0.918641i \(-0.629288\pi\)
−0.395093 + 0.918641i \(0.629288\pi\)
\(390\) 0 0
\(391\) 7.64608 0.386679
\(392\) 0 0
\(393\) 54.2711 2.73762
\(394\) 0 0
\(395\) −1.11202 −0.0559518
\(396\) 0 0
\(397\) −24.6831 −1.23881 −0.619405 0.785072i \(-0.712626\pi\)
−0.619405 + 0.785072i \(0.712626\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 12.4381 0.621129 0.310564 0.950552i \(-0.399482\pi\)
0.310564 + 0.950552i \(0.399482\pi\)
\(402\) 0 0
\(403\) −8.22769 −0.409850
\(404\) 0 0
\(405\) 2.19011 0.108827
\(406\) 0 0
\(407\) 56.1062 2.78108
\(408\) 0 0
\(409\) −12.7192 −0.628926 −0.314463 0.949270i \(-0.601824\pi\)
−0.314463 + 0.949270i \(0.601824\pi\)
\(410\) 0 0
\(411\) 18.3484 0.905061
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0.458575 0.0225106
\(416\) 0 0
\(417\) 59.2046 2.89926
\(418\) 0 0
\(419\) −3.02761 −0.147908 −0.0739541 0.997262i \(-0.523562\pi\)
−0.0739541 + 0.997262i \(0.523562\pi\)
\(420\) 0 0
\(421\) −2.51515 −0.122581 −0.0612905 0.998120i \(-0.519522\pi\)
−0.0612905 + 0.998120i \(0.519522\pi\)
\(422\) 0 0
\(423\) −66.4868 −3.23270
\(424\) 0 0
\(425\) −23.8798 −1.15834
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 41.6914 2.01288
\(430\) 0 0
\(431\) −16.7281 −0.805763 −0.402882 0.915252i \(-0.631991\pi\)
−0.402882 + 0.915252i \(0.631991\pi\)
\(432\) 0 0
\(433\) −9.24985 −0.444519 −0.222260 0.974988i \(-0.571343\pi\)
−0.222260 + 0.974988i \(0.571343\pi\)
\(434\) 0 0
\(435\) 9.75422 0.467679
\(436\) 0 0
\(437\) 8.78223 0.420111
\(438\) 0 0
\(439\) 29.8582 1.42506 0.712528 0.701644i \(-0.247550\pi\)
0.712528 + 0.701644i \(0.247550\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 28.8087 1.36874 0.684372 0.729133i \(-0.260076\pi\)
0.684372 + 0.729133i \(0.260076\pi\)
\(444\) 0 0
\(445\) −2.54678 −0.120729
\(446\) 0 0
\(447\) 48.1708 2.27840
\(448\) 0 0
\(449\) 8.35246 0.394177 0.197088 0.980386i \(-0.436851\pi\)
0.197088 + 0.980386i \(0.436851\pi\)
\(450\) 0 0
\(451\) −5.70801 −0.268780
\(452\) 0 0
\(453\) −57.6030 −2.70643
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −25.9129 −1.21215 −0.606076 0.795407i \(-0.707257\pi\)
−0.606076 + 0.795407i \(0.707257\pi\)
\(458\) 0 0
\(459\) 35.7971 1.67087
\(460\) 0 0
\(461\) −10.2580 −0.477762 −0.238881 0.971049i \(-0.576781\pi\)
−0.238881 + 0.971049i \(0.576781\pi\)
\(462\) 0 0
\(463\) 6.55147 0.304472 0.152236 0.988344i \(-0.451353\pi\)
0.152236 + 0.988344i \(0.451353\pi\)
\(464\) 0 0
\(465\) −4.81557 −0.223317
\(466\) 0 0
\(467\) −18.4972 −0.855947 −0.427973 0.903791i \(-0.640772\pi\)
−0.427973 + 0.903791i \(0.640772\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 1.47391 0.0679142
\(472\) 0 0
\(473\) −47.8151 −2.19854
\(474\) 0 0
\(475\) −27.4282 −1.25849
\(476\) 0 0
\(477\) −65.9521 −3.01974
\(478\) 0 0
\(479\) 18.1133 0.827620 0.413810 0.910363i \(-0.364198\pi\)
0.413810 + 0.910363i \(0.364198\pi\)
\(480\) 0 0
\(481\) 24.7025 1.12634
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.63911 −0.119836
\(486\) 0 0
\(487\) 14.9867 0.679111 0.339556 0.940586i \(-0.389723\pi\)
0.339556 + 0.940586i \(0.389723\pi\)
\(488\) 0 0
\(489\) −30.7428 −1.39024
\(490\) 0 0
\(491\) 4.81825 0.217445 0.108722 0.994072i \(-0.465324\pi\)
0.108722 + 0.994072i \(0.465324\pi\)
\(492\) 0 0
\(493\) 33.3815 1.50343
\(494\) 0 0
\(495\) 15.7350 0.707235
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 8.21602 0.367800 0.183900 0.982945i \(-0.441128\pi\)
0.183900 + 0.982945i \(0.441128\pi\)
\(500\) 0 0
\(501\) −12.7923 −0.571518
\(502\) 0 0
\(503\) −38.3859 −1.71154 −0.855772 0.517354i \(-0.826917\pi\)
−0.855772 + 0.517354i \(0.826917\pi\)
\(504\) 0 0
\(505\) −5.15564 −0.229423
\(506\) 0 0
\(507\) −19.4265 −0.862760
\(508\) 0 0
\(509\) −30.9633 −1.37242 −0.686211 0.727402i \(-0.740727\pi\)
−0.686211 + 0.727402i \(0.740727\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 41.1163 1.81533
\(514\) 0 0
\(515\) −2.23815 −0.0986246
\(516\) 0 0
\(517\) −69.6750 −3.06430
\(518\) 0 0
\(519\) 27.8656 1.22316
\(520\) 0 0
\(521\) −6.77849 −0.296971 −0.148485 0.988915i \(-0.547440\pi\)
−0.148485 + 0.988915i \(0.547440\pi\)
\(522\) 0 0
\(523\) 20.9055 0.914134 0.457067 0.889432i \(-0.348900\pi\)
0.457067 + 0.889432i \(0.348900\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −16.4802 −0.717887
\(528\) 0 0
\(529\) −20.6928 −0.899688
\(530\) 0 0
\(531\) −47.8933 −2.07839
\(532\) 0 0
\(533\) −2.51313 −0.108856
\(534\) 0 0
\(535\) 2.87173 0.124156
\(536\) 0 0
\(537\) 12.7352 0.549565
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 1.18831 0.0510894 0.0255447 0.999674i \(-0.491868\pi\)
0.0255447 + 0.999674i \(0.491868\pi\)
\(542\) 0 0
\(543\) −60.5170 −2.59703
\(544\) 0 0
\(545\) 3.35593 0.143752
\(546\) 0 0
\(547\) −11.5228 −0.492680 −0.246340 0.969183i \(-0.579228\pi\)
−0.246340 + 0.969183i \(0.579228\pi\)
\(548\) 0 0
\(549\) −33.0830 −1.41195
\(550\) 0 0
\(551\) 38.3418 1.63342
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 14.4581 0.613712
\(556\) 0 0
\(557\) −1.27508 −0.0540268 −0.0270134 0.999635i \(-0.508600\pi\)
−0.0270134 + 0.999635i \(0.508600\pi\)
\(558\) 0 0
\(559\) −21.0521 −0.890409
\(560\) 0 0
\(561\) 83.5085 3.52573
\(562\) 0 0
\(563\) −2.02739 −0.0854443 −0.0427222 0.999087i \(-0.513603\pi\)
−0.0427222 + 0.999087i \(0.513603\pi\)
\(564\) 0 0
\(565\) −8.01005 −0.336985
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 42.7963 1.79411 0.897057 0.441915i \(-0.145701\pi\)
0.897057 + 0.441915i \(0.145701\pi\)
\(570\) 0 0
\(571\) 11.6779 0.488704 0.244352 0.969687i \(-0.421425\pi\)
0.244352 + 0.969687i \(0.421425\pi\)
\(572\) 0 0
\(573\) 54.0041 2.25605
\(574\) 0 0
\(575\) −7.20562 −0.300495
\(576\) 0 0
\(577\) −7.29918 −0.303869 −0.151934 0.988391i \(-0.548550\pi\)
−0.151934 + 0.988391i \(0.548550\pi\)
\(578\) 0 0
\(579\) −12.9349 −0.537558
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −69.1147 −2.86244
\(584\) 0 0
\(585\) 6.92783 0.286430
\(586\) 0 0
\(587\) 5.35476 0.221015 0.110507 0.993875i \(-0.464752\pi\)
0.110507 + 0.993875i \(0.464752\pi\)
\(588\) 0 0
\(589\) −18.9290 −0.779956
\(590\) 0 0
\(591\) 6.55468 0.269624
\(592\) 0 0
\(593\) −31.7874 −1.30535 −0.652675 0.757638i \(-0.726353\pi\)
−0.652675 + 0.757638i \(0.726353\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −2.13341 −0.0873146
\(598\) 0 0
\(599\) −43.7983 −1.78955 −0.894776 0.446516i \(-0.852665\pi\)
−0.894776 + 0.446516i \(0.852665\pi\)
\(600\) 0 0
\(601\) 21.4183 0.873672 0.436836 0.899541i \(-0.356099\pi\)
0.436836 + 0.899541i \(0.356099\pi\)
\(602\) 0 0
\(603\) −61.0745 −2.48714
\(604\) 0 0
\(605\) 10.9224 0.444059
\(606\) 0 0
\(607\) −21.5754 −0.875718 −0.437859 0.899044i \(-0.644263\pi\)
−0.437859 + 0.899044i \(0.644263\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −30.6766 −1.24104
\(612\) 0 0
\(613\) 18.8291 0.760502 0.380251 0.924883i \(-0.375838\pi\)
0.380251 + 0.924883i \(0.375838\pi\)
\(614\) 0 0
\(615\) −1.47091 −0.0593127
\(616\) 0 0
\(617\) −7.74835 −0.311937 −0.155968 0.987762i \(-0.549850\pi\)
−0.155968 + 0.987762i \(0.549850\pi\)
\(618\) 0 0
\(619\) −13.9297 −0.559883 −0.279942 0.960017i \(-0.590315\pi\)
−0.279942 + 0.960017i \(0.590315\pi\)
\(620\) 0 0
\(621\) 10.8016 0.433454
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 21.2235 0.848940
\(626\) 0 0
\(627\) 95.9173 3.83057
\(628\) 0 0
\(629\) 49.4795 1.97288
\(630\) 0 0
\(631\) 16.8581 0.671109 0.335554 0.942021i \(-0.391076\pi\)
0.335554 + 0.942021i \(0.391076\pi\)
\(632\) 0 0
\(633\) −81.1172 −3.22412
\(634\) 0 0
\(635\) −8.61529 −0.341888
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −29.7521 −1.17697
\(640\) 0 0
\(641\) 48.7214 1.92438 0.962189 0.272382i \(-0.0878115\pi\)
0.962189 + 0.272382i \(0.0878115\pi\)
\(642\) 0 0
\(643\) 24.3027 0.958407 0.479203 0.877704i \(-0.340926\pi\)
0.479203 + 0.877704i \(0.340926\pi\)
\(644\) 0 0
\(645\) −12.3216 −0.485161
\(646\) 0 0
\(647\) 7.57912 0.297966 0.148983 0.988840i \(-0.452400\pi\)
0.148983 + 0.988840i \(0.452400\pi\)
\(648\) 0 0
\(649\) −50.1899 −1.97012
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −24.9280 −0.975507 −0.487754 0.872981i \(-0.662184\pi\)
−0.487754 + 0.872981i \(0.662184\pi\)
\(654\) 0 0
\(655\) 9.45063 0.369267
\(656\) 0 0
\(657\) 26.4564 1.03216
\(658\) 0 0
\(659\) −24.3444 −0.948324 −0.474162 0.880438i \(-0.657249\pi\)
−0.474162 + 0.880438i \(0.657249\pi\)
\(660\) 0 0
\(661\) −40.3785 −1.57054 −0.785271 0.619152i \(-0.787477\pi\)
−0.785271 + 0.619152i \(0.787477\pi\)
\(662\) 0 0
\(663\) 36.7672 1.42792
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 10.0727 0.390017
\(668\) 0 0
\(669\) −17.7290 −0.685443
\(670\) 0 0
\(671\) −34.6694 −1.33840
\(672\) 0 0
\(673\) 19.0815 0.735537 0.367769 0.929917i \(-0.380122\pi\)
0.367769 + 0.929917i \(0.380122\pi\)
\(674\) 0 0
\(675\) −33.7350 −1.29846
\(676\) 0 0
\(677\) 9.19086 0.353234 0.176617 0.984280i \(-0.443485\pi\)
0.176617 + 0.984280i \(0.443485\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 7.41056 0.283973
\(682\) 0 0
\(683\) −5.78539 −0.221372 −0.110686 0.993855i \(-0.535305\pi\)
−0.110686 + 0.993855i \(0.535305\pi\)
\(684\) 0 0
\(685\) 3.19515 0.122080
\(686\) 0 0
\(687\) −24.3942 −0.930697
\(688\) 0 0
\(689\) −30.4299 −1.15929
\(690\) 0 0
\(691\) 44.0361 1.67521 0.837607 0.546274i \(-0.183954\pi\)
0.837607 + 0.546274i \(0.183954\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 10.3097 0.391070
\(696\) 0 0
\(697\) −5.03384 −0.190670
\(698\) 0 0
\(699\) 57.6022 2.17871
\(700\) 0 0
\(701\) 36.9512 1.39563 0.697813 0.716280i \(-0.254157\pi\)
0.697813 + 0.716280i \(0.254157\pi\)
\(702\) 0 0
\(703\) 56.8318 2.14345
\(704\) 0 0
\(705\) −17.9547 −0.676212
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 15.6033 0.585995 0.292997 0.956113i \(-0.405347\pi\)
0.292997 + 0.956113i \(0.405347\pi\)
\(710\) 0 0
\(711\) −11.9679 −0.448830
\(712\) 0 0
\(713\) −4.97281 −0.186233
\(714\) 0 0
\(715\) 7.26003 0.271510
\(716\) 0 0
\(717\) 72.7307 2.71618
\(718\) 0 0
\(719\) −0.493177 −0.0183924 −0.00919619 0.999958i \(-0.502927\pi\)
−0.00919619 + 0.999958i \(0.502927\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 51.5997 1.91901
\(724\) 0 0
\(725\) −31.4586 −1.16834
\(726\) 0 0
\(727\) 6.29693 0.233540 0.116770 0.993159i \(-0.462746\pi\)
0.116770 + 0.993159i \(0.462746\pi\)
\(728\) 0 0
\(729\) −38.4330 −1.42344
\(730\) 0 0
\(731\) −42.1676 −1.55963
\(732\) 0 0
\(733\) 5.44142 0.200983 0.100492 0.994938i \(-0.467958\pi\)
0.100492 + 0.994938i \(0.467958\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −64.0032 −2.35759
\(738\) 0 0
\(739\) 9.13823 0.336155 0.168078 0.985774i \(-0.446244\pi\)
0.168078 + 0.985774i \(0.446244\pi\)
\(740\) 0 0
\(741\) 42.2306 1.55138
\(742\) 0 0
\(743\) −13.9354 −0.511239 −0.255619 0.966778i \(-0.582279\pi\)
−0.255619 + 0.966778i \(0.582279\pi\)
\(744\) 0 0
\(745\) 8.38833 0.307325
\(746\) 0 0
\(747\) 4.93532 0.180574
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 14.6521 0.534663 0.267331 0.963605i \(-0.413858\pi\)
0.267331 + 0.963605i \(0.413858\pi\)
\(752\) 0 0
\(753\) 31.3640 1.14297
\(754\) 0 0
\(755\) −10.0308 −0.365060
\(756\) 0 0
\(757\) 45.3236 1.64732 0.823658 0.567087i \(-0.191930\pi\)
0.823658 + 0.567087i \(0.191930\pi\)
\(758\) 0 0
\(759\) 25.1983 0.914640
\(760\) 0 0
\(761\) −27.2630 −0.988283 −0.494141 0.869382i \(-0.664517\pi\)
−0.494141 + 0.869382i \(0.664517\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 13.8765 0.501707
\(766\) 0 0
\(767\) −22.0977 −0.797900
\(768\) 0 0
\(769\) 33.5462 1.20971 0.604853 0.796337i \(-0.293232\pi\)
0.604853 + 0.796337i \(0.293232\pi\)
\(770\) 0 0
\(771\) −3.89631 −0.140322
\(772\) 0 0
\(773\) −17.2586 −0.620749 −0.310375 0.950614i \(-0.600455\pi\)
−0.310375 + 0.950614i \(0.600455\pi\)
\(774\) 0 0
\(775\) 15.5308 0.557884
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −5.78183 −0.207156
\(780\) 0 0
\(781\) −31.1788 −1.11566
\(782\) 0 0
\(783\) 47.1581 1.68529
\(784\) 0 0
\(785\) 0.256663 0.00916069
\(786\) 0 0
\(787\) −51.9158 −1.85060 −0.925299 0.379239i \(-0.876186\pi\)
−0.925299 + 0.379239i \(0.876186\pi\)
\(788\) 0 0
\(789\) 7.83258 0.278847
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −15.2643 −0.542051
\(794\) 0 0
\(795\) −17.8103 −0.631666
\(796\) 0 0
\(797\) −15.8432 −0.561194 −0.280597 0.959826i \(-0.590532\pi\)
−0.280597 + 0.959826i \(0.590532\pi\)
\(798\) 0 0
\(799\) −61.4457 −2.17379
\(800\) 0 0
\(801\) −27.4091 −0.968454
\(802\) 0 0
\(803\) 27.7250 0.978395
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −37.2316 −1.31062
\(808\) 0 0
\(809\) 15.7929 0.555248 0.277624 0.960690i \(-0.410453\pi\)
0.277624 + 0.960690i \(0.410453\pi\)
\(810\) 0 0
\(811\) 1.92918 0.0677427 0.0338714 0.999426i \(-0.489216\pi\)
0.0338714 + 0.999426i \(0.489216\pi\)
\(812\) 0 0
\(813\) 27.8941 0.978288
\(814\) 0 0
\(815\) −5.35347 −0.187524
\(816\) 0 0
\(817\) −48.4335 −1.69447
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −24.6731 −0.861098 −0.430549 0.902567i \(-0.641680\pi\)
−0.430549 + 0.902567i \(0.641680\pi\)
\(822\) 0 0
\(823\) 15.8147 0.551264 0.275632 0.961263i \(-0.411113\pi\)
0.275632 + 0.961263i \(0.411113\pi\)
\(824\) 0 0
\(825\) −78.6980 −2.73991
\(826\) 0 0
\(827\) −23.0722 −0.802300 −0.401150 0.916012i \(-0.631389\pi\)
−0.401150 + 0.916012i \(0.631389\pi\)
\(828\) 0 0
\(829\) −3.20726 −0.111393 −0.0556964 0.998448i \(-0.517738\pi\)
−0.0556964 + 0.998448i \(0.517738\pi\)
\(830\) 0 0
\(831\) 46.8842 1.62639
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −2.22762 −0.0770898
\(836\) 0 0
\(837\) −23.2815 −0.804728
\(838\) 0 0
\(839\) −13.0822 −0.451647 −0.225823 0.974168i \(-0.572507\pi\)
−0.225823 + 0.974168i \(0.572507\pi\)
\(840\) 0 0
\(841\) 14.9759 0.516409
\(842\) 0 0
\(843\) 40.4009 1.39148
\(844\) 0 0
\(845\) −3.38288 −0.116374
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −57.7942 −1.98349
\(850\) 0 0
\(851\) 14.9302 0.511801
\(852\) 0 0
\(853\) 22.4104 0.767317 0.383658 0.923475i \(-0.374664\pi\)
0.383658 + 0.923475i \(0.374664\pi\)
\(854\) 0 0
\(855\) 15.9385 0.545085
\(856\) 0 0
\(857\) 18.4971 0.631849 0.315925 0.948784i \(-0.397685\pi\)
0.315925 + 0.948784i \(0.397685\pi\)
\(858\) 0 0
\(859\) −39.9579 −1.36335 −0.681673 0.731657i \(-0.738747\pi\)
−0.681673 + 0.731657i \(0.738747\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −22.1995 −0.755678 −0.377839 0.925871i \(-0.623333\pi\)
−0.377839 + 0.925871i \(0.623333\pi\)
\(864\) 0 0
\(865\) 4.85244 0.164988
\(866\) 0 0
\(867\) 24.2374 0.823147
\(868\) 0 0
\(869\) −12.5418 −0.425450
\(870\) 0 0
\(871\) −28.1794 −0.954823
\(872\) 0 0
\(873\) −28.4029 −0.961291
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 9.32226 0.314790 0.157395 0.987536i \(-0.449690\pi\)
0.157395 + 0.987536i \(0.449690\pi\)
\(878\) 0 0
\(879\) −37.7256 −1.27245
\(880\) 0 0
\(881\) 17.5285 0.590550 0.295275 0.955412i \(-0.404589\pi\)
0.295275 + 0.955412i \(0.404589\pi\)
\(882\) 0 0
\(883\) 1.47657 0.0496905 0.0248453 0.999691i \(-0.492091\pi\)
0.0248453 + 0.999691i \(0.492091\pi\)
\(884\) 0 0
\(885\) −12.9335 −0.434755
\(886\) 0 0
\(887\) 29.7404 0.998586 0.499293 0.866433i \(-0.333593\pi\)
0.499293 + 0.866433i \(0.333593\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 24.7009 0.827510
\(892\) 0 0
\(893\) −70.5761 −2.36174
\(894\) 0 0
\(895\) 2.21768 0.0741287
\(896\) 0 0
\(897\) 11.0943 0.370429
\(898\) 0 0
\(899\) −21.7105 −0.724086
\(900\) 0 0
\(901\) −60.9515 −2.03059
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −10.5383 −0.350304
\(906\) 0 0
\(907\) −8.67663 −0.288103 −0.144051 0.989570i \(-0.546013\pi\)
−0.144051 + 0.989570i \(0.546013\pi\)
\(908\) 0 0
\(909\) −55.4865 −1.84037
\(910\) 0 0
\(911\) −22.7245 −0.752895 −0.376448 0.926438i \(-0.622855\pi\)
−0.376448 + 0.926438i \(0.622855\pi\)
\(912\) 0 0
\(913\) 5.17198 0.171168
\(914\) 0 0
\(915\) −8.93401 −0.295349
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 26.8906 0.887040 0.443520 0.896265i \(-0.353730\pi\)
0.443520 + 0.896265i \(0.353730\pi\)
\(920\) 0 0
\(921\) −20.0880 −0.661923
\(922\) 0 0
\(923\) −13.7274 −0.451844
\(924\) 0 0
\(925\) −46.6292 −1.53316
\(926\) 0 0
\(927\) −24.0876 −0.791140
\(928\) 0 0
\(929\) −31.7302 −1.04103 −0.520517 0.853851i \(-0.674261\pi\)
−0.520517 + 0.853851i \(0.674261\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0.134513 0.00440376
\(934\) 0 0
\(935\) 14.5419 0.475572
\(936\) 0 0
\(937\) −22.9242 −0.748901 −0.374450 0.927247i \(-0.622169\pi\)
−0.374450 + 0.927247i \(0.622169\pi\)
\(938\) 0 0
\(939\) 62.7378 2.04737
\(940\) 0 0
\(941\) −15.7909 −0.514767 −0.257384 0.966309i \(-0.582860\pi\)
−0.257384 + 0.966309i \(0.582860\pi\)
\(942\) 0 0
\(943\) −1.51894 −0.0494634
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 13.0933 0.425474 0.212737 0.977109i \(-0.431762\pi\)
0.212737 + 0.977109i \(0.431762\pi\)
\(948\) 0 0
\(949\) 12.2068 0.396250
\(950\) 0 0
\(951\) −6.51059 −0.211120
\(952\) 0 0
\(953\) −8.95732 −0.290156 −0.145078 0.989420i \(-0.546343\pi\)
−0.145078 + 0.989420i \(0.546343\pi\)
\(954\) 0 0
\(955\) 9.40414 0.304311
\(956\) 0 0
\(957\) 110.012 3.55617
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −20.2817 −0.654249
\(962\) 0 0
\(963\) 30.9064 0.995946
\(964\) 0 0
\(965\) −2.25246 −0.0725091
\(966\) 0 0
\(967\) 34.9003 1.12232 0.561160 0.827708i \(-0.310355\pi\)
0.561160 + 0.827708i \(0.310355\pi\)
\(968\) 0 0
\(969\) 84.5884 2.71737
\(970\) 0 0
\(971\) 9.18663 0.294813 0.147407 0.989076i \(-0.452907\pi\)
0.147407 + 0.989076i \(0.452907\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −34.6492 −1.10966
\(976\) 0 0
\(977\) −47.9209 −1.53312 −0.766562 0.642170i \(-0.778034\pi\)
−0.766562 + 0.642170i \(0.778034\pi\)
\(978\) 0 0
\(979\) −28.7235 −0.918006
\(980\) 0 0
\(981\) 36.1174 1.15314
\(982\) 0 0
\(983\) 38.6952 1.23419 0.617093 0.786890i \(-0.288310\pi\)
0.617093 + 0.786890i \(0.288310\pi\)
\(984\) 0 0
\(985\) 1.14142 0.0363685
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −12.7239 −0.404596
\(990\) 0 0
\(991\) 43.2144 1.37275 0.686375 0.727248i \(-0.259201\pi\)
0.686375 + 0.727248i \(0.259201\pi\)
\(992\) 0 0
\(993\) 80.6175 2.55832
\(994\) 0 0
\(995\) −0.371506 −0.0117775
\(996\) 0 0
\(997\) −15.9844 −0.506230 −0.253115 0.967436i \(-0.581455\pi\)
−0.253115 + 0.967436i \(0.581455\pi\)
\(998\) 0 0
\(999\) 69.8996 2.21153
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 \(a_p\))