Properties

Label 4028.2.a.d.1.9
Level 4028
Weight 2
Character 4028.1
Self dual Yes
Analytic conductor 32.164
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4028.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1637419342\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(0.383819\)
Character \(\chi\) = 4028.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.383819 q^{3} -4.10226 q^{5} +0.287206 q^{7} -2.85268 q^{9} +O(q^{10})\) \(q-0.383819 q^{3} -4.10226 q^{5} +0.287206 q^{7} -2.85268 q^{9} +0.513939 q^{11} +2.10829 q^{13} +1.57453 q^{15} -1.15435 q^{17} -1.00000 q^{19} -0.110235 q^{21} +8.21568 q^{23} +11.8286 q^{25} +2.24637 q^{27} -0.842400 q^{29} +5.84212 q^{31} -0.197260 q^{33} -1.17820 q^{35} -4.24583 q^{37} -0.809203 q^{39} +3.80488 q^{41} -1.27243 q^{43} +11.7025 q^{45} +5.24622 q^{47} -6.91751 q^{49} +0.443060 q^{51} +1.00000 q^{53} -2.10831 q^{55} +0.383819 q^{57} +3.73857 q^{59} -13.8747 q^{61} -0.819309 q^{63} -8.64876 q^{65} -0.286137 q^{67} -3.15333 q^{69} +3.50584 q^{71} -7.34802 q^{73} -4.54003 q^{75} +0.147607 q^{77} -12.5141 q^{79} +7.69585 q^{81} -9.32244 q^{83} +4.73543 q^{85} +0.323329 q^{87} +2.32232 q^{89} +0.605515 q^{91} -2.24232 q^{93} +4.10226 q^{95} -17.8148 q^{97} -1.46611 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} + O(q^{10}) \) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} - 11q^{11} + q^{13} - 20q^{15} - q^{17} - 19q^{19} - 10q^{21} - 16q^{23} + 21q^{25} - 4q^{27} - 9q^{31} + 7q^{33} - 25q^{37} - 25q^{39} + q^{41} - 41q^{43} - 27q^{45} - 29q^{47} + 14q^{49} - 24q^{51} + 19q^{53} - 28q^{55} + 4q^{57} - 42q^{59} + q^{61} - 41q^{63} + 2q^{65} - 41q^{67} - 25q^{69} - 20q^{73} + 11q^{75} - 19q^{77} - 38q^{79} + 23q^{81} - 36q^{83} - 58q^{85} - 30q^{87} - 25q^{89} - 55q^{91} - 38q^{93} + 2q^{95} - 13q^{97} + q^{99} + O(q^{100}) \)

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
\(3\) −0.383819 −0.221598 −0.110799 0.993843i \(-0.535341\pi\)
−0.110799 + 0.993843i \(0.535341\pi\)
\(4\) 0 0
\(5\) −4.10226 −1.83459 −0.917294 0.398211i \(-0.869631\pi\)
−0.917294 + 0.398211i \(0.869631\pi\)
\(6\) 0 0
\(7\) 0.287206 0.108554 0.0542769 0.998526i \(-0.482715\pi\)
0.0542769 + 0.998526i \(0.482715\pi\)
\(8\) 0 0
\(9\) −2.85268 −0.950894
\(10\) 0 0
\(11\) 0.513939 0.154959 0.0774793 0.996994i \(-0.475313\pi\)
0.0774793 + 0.996994i \(0.475313\pi\)
\(12\) 0 0
\(13\) 2.10829 0.584735 0.292367 0.956306i \(-0.405557\pi\)
0.292367 + 0.956306i \(0.405557\pi\)
\(14\) 0 0
\(15\) 1.57453 0.406541
\(16\) 0 0
\(17\) −1.15435 −0.279970 −0.139985 0.990154i \(-0.544705\pi\)
−0.139985 + 0.990154i \(0.544705\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) −0.110235 −0.0240553
\(22\) 0 0
\(23\) 8.21568 1.71309 0.856544 0.516075i \(-0.172607\pi\)
0.856544 + 0.516075i \(0.172607\pi\)
\(24\) 0 0
\(25\) 11.8286 2.36571
\(26\) 0 0
\(27\) 2.24637 0.432315
\(28\) 0 0
\(29\) −0.842400 −0.156430 −0.0782149 0.996937i \(-0.524922\pi\)
−0.0782149 + 0.996937i \(0.524922\pi\)
\(30\) 0 0
\(31\) 5.84212 1.04928 0.524638 0.851326i \(-0.324201\pi\)
0.524638 + 0.851326i \(0.324201\pi\)
\(32\) 0 0
\(33\) −0.197260 −0.0343385
\(34\) 0 0
\(35\) −1.17820 −0.199151
\(36\) 0 0
\(37\) −4.24583 −0.698011 −0.349005 0.937121i \(-0.613481\pi\)
−0.349005 + 0.937121i \(0.613481\pi\)
\(38\) 0 0
\(39\) −0.809203 −0.129576
\(40\) 0 0
\(41\) 3.80488 0.594222 0.297111 0.954843i \(-0.403977\pi\)
0.297111 + 0.954843i \(0.403977\pi\)
\(42\) 0 0
\(43\) −1.27243 −0.194043 −0.0970215 0.995282i \(-0.530932\pi\)
−0.0970215 + 0.995282i \(0.530932\pi\)
\(44\) 0 0
\(45\) 11.7025 1.74450
\(46\) 0 0
\(47\) 5.24622 0.765240 0.382620 0.923906i \(-0.375022\pi\)
0.382620 + 0.923906i \(0.375022\pi\)
\(48\) 0 0
\(49\) −6.91751 −0.988216
\(50\) 0 0
\(51\) 0.443060 0.0620408
\(52\) 0 0
\(53\) 1.00000 0.137361
\(54\) 0 0
\(55\) −2.10831 −0.284285
\(56\) 0 0
\(57\) 0.383819 0.0508381
\(58\) 0 0
\(59\) 3.73857 0.486721 0.243360 0.969936i \(-0.421750\pi\)
0.243360 + 0.969936i \(0.421750\pi\)
\(60\) 0 0
\(61\) −13.8747 −1.77647 −0.888236 0.459388i \(-0.848069\pi\)
−0.888236 + 0.459388i \(0.848069\pi\)
\(62\) 0 0
\(63\) −0.819309 −0.103223
\(64\) 0 0
\(65\) −8.64876 −1.07275
\(66\) 0 0
\(67\) −0.286137 −0.0349572 −0.0174786 0.999847i \(-0.505564\pi\)
−0.0174786 + 0.999847i \(0.505564\pi\)
\(68\) 0 0
\(69\) −3.15333 −0.379617
\(70\) 0 0
\(71\) 3.50584 0.416066 0.208033 0.978122i \(-0.433294\pi\)
0.208033 + 0.978122i \(0.433294\pi\)
\(72\) 0 0
\(73\) −7.34802 −0.860021 −0.430010 0.902824i \(-0.641490\pi\)
−0.430010 + 0.902824i \(0.641490\pi\)
\(74\) 0 0
\(75\) −4.54003 −0.524237
\(76\) 0 0
\(77\) 0.147607 0.0168213
\(78\) 0 0
\(79\) −12.5141 −1.40794 −0.703970 0.710229i \(-0.748591\pi\)
−0.703970 + 0.710229i \(0.748591\pi\)
\(80\) 0 0
\(81\) 7.69585 0.855094
\(82\) 0 0
\(83\) −9.32244 −1.02327 −0.511635 0.859203i \(-0.670960\pi\)
−0.511635 + 0.859203i \(0.670960\pi\)
\(84\) 0 0
\(85\) 4.73543 0.513629
\(86\) 0 0
\(87\) 0.323329 0.0346645
\(88\) 0 0
\(89\) 2.32232 0.246165 0.123082 0.992396i \(-0.460722\pi\)
0.123082 + 0.992396i \(0.460722\pi\)
\(90\) 0 0
\(91\) 0.605515 0.0634752
\(92\) 0 0
\(93\) −2.24232 −0.232517
\(94\) 0 0
\(95\) 4.10226 0.420883
\(96\) 0 0
\(97\) −17.8148 −1.80882 −0.904409 0.426667i \(-0.859688\pi\)
−0.904409 + 0.426667i \(0.859688\pi\)
\(98\) 0 0
\(99\) −1.46611 −0.147349
\(100\) 0 0
\(101\) −4.30447 −0.428311 −0.214156 0.976800i \(-0.568700\pi\)
−0.214156 + 0.976800i \(0.568700\pi\)
\(102\) 0 0
\(103\) 12.3918 1.22100 0.610502 0.792015i \(-0.290968\pi\)
0.610502 + 0.792015i \(0.290968\pi\)
\(104\) 0 0
\(105\) 0.452214 0.0441316
\(106\) 0 0
\(107\) 12.9490 1.25183 0.625915 0.779891i \(-0.284726\pi\)
0.625915 + 0.779891i \(0.284726\pi\)
\(108\) 0 0
\(109\) −2.92088 −0.279770 −0.139885 0.990168i \(-0.544673\pi\)
−0.139885 + 0.990168i \(0.544673\pi\)
\(110\) 0 0
\(111\) 1.62963 0.154678
\(112\) 0 0
\(113\) −1.71656 −0.161480 −0.0807400 0.996735i \(-0.525728\pi\)
−0.0807400 + 0.996735i \(0.525728\pi\)
\(114\) 0 0
\(115\) −33.7029 −3.14281
\(116\) 0 0
\(117\) −6.01429 −0.556021
\(118\) 0 0
\(119\) −0.331535 −0.0303918
\(120\) 0 0
\(121\) −10.7359 −0.975988
\(122\) 0 0
\(123\) −1.46039 −0.131679
\(124\) 0 0
\(125\) −28.0125 −2.50552
\(126\) 0 0
\(127\) −16.9095 −1.50047 −0.750237 0.661169i \(-0.770061\pi\)
−0.750237 + 0.661169i \(0.770061\pi\)
\(128\) 0 0
\(129\) 0.488381 0.0429996
\(130\) 0 0
\(131\) 22.7062 1.98385 0.991923 0.126840i \(-0.0404833\pi\)
0.991923 + 0.126840i \(0.0404833\pi\)
\(132\) 0 0
\(133\) −0.287206 −0.0249040
\(134\) 0 0
\(135\) −9.21521 −0.793119
\(136\) 0 0
\(137\) 13.8985 1.18743 0.593715 0.804676i \(-0.297661\pi\)
0.593715 + 0.804676i \(0.297661\pi\)
\(138\) 0 0
\(139\) 1.30301 0.110520 0.0552600 0.998472i \(-0.482401\pi\)
0.0552600 + 0.998472i \(0.482401\pi\)
\(140\) 0 0
\(141\) −2.01360 −0.169576
\(142\) 0 0
\(143\) 1.08353 0.0906097
\(144\) 0 0
\(145\) 3.45575 0.286984
\(146\) 0 0
\(147\) 2.65507 0.218987
\(148\) 0 0
\(149\) −5.57766 −0.456939 −0.228470 0.973551i \(-0.573372\pi\)
−0.228470 + 0.973551i \(0.573372\pi\)
\(150\) 0 0
\(151\) −9.20322 −0.748948 −0.374474 0.927237i \(-0.622177\pi\)
−0.374474 + 0.927237i \(0.622177\pi\)
\(152\) 0 0
\(153\) 3.29298 0.266222
\(154\) 0 0
\(155\) −23.9659 −1.92499
\(156\) 0 0
\(157\) 13.4840 1.07614 0.538070 0.842900i \(-0.319154\pi\)
0.538070 + 0.842900i \(0.319154\pi\)
\(158\) 0 0
\(159\) −0.383819 −0.0304388
\(160\) 0 0
\(161\) 2.35960 0.185962
\(162\) 0 0
\(163\) 1.16173 0.0909938 0.0454969 0.998964i \(-0.485513\pi\)
0.0454969 + 0.998964i \(0.485513\pi\)
\(164\) 0 0
\(165\) 0.809212 0.0629970
\(166\) 0 0
\(167\) 21.4507 1.65990 0.829952 0.557835i \(-0.188368\pi\)
0.829952 + 0.557835i \(0.188368\pi\)
\(168\) 0 0
\(169\) −8.55511 −0.658085
\(170\) 0 0
\(171\) 2.85268 0.218150
\(172\) 0 0
\(173\) −7.76575 −0.590419 −0.295209 0.955433i \(-0.595389\pi\)
−0.295209 + 0.955433i \(0.595389\pi\)
\(174\) 0 0
\(175\) 3.39724 0.256807
\(176\) 0 0
\(177\) −1.43494 −0.107856
\(178\) 0 0
\(179\) −24.8470 −1.85715 −0.928575 0.371144i \(-0.878966\pi\)
−0.928575 + 0.371144i \(0.878966\pi\)
\(180\) 0 0
\(181\) −6.81457 −0.506523 −0.253262 0.967398i \(-0.581503\pi\)
−0.253262 + 0.967398i \(0.581503\pi\)
\(182\) 0 0
\(183\) 5.32537 0.393663
\(184\) 0 0
\(185\) 17.4175 1.28056
\(186\) 0 0
\(187\) −0.593264 −0.0433837
\(188\) 0 0
\(189\) 0.645172 0.0469294
\(190\) 0 0
\(191\) 11.0292 0.798045 0.399022 0.916941i \(-0.369350\pi\)
0.399022 + 0.916941i \(0.369350\pi\)
\(192\) 0 0
\(193\) −5.06967 −0.364923 −0.182461 0.983213i \(-0.558406\pi\)
−0.182461 + 0.983213i \(0.558406\pi\)
\(194\) 0 0
\(195\) 3.31956 0.237719
\(196\) 0 0
\(197\) −16.9139 −1.20507 −0.602534 0.798093i \(-0.705842\pi\)
−0.602534 + 0.798093i \(0.705842\pi\)
\(198\) 0 0
\(199\) 0.979105 0.0694069 0.0347035 0.999398i \(-0.488951\pi\)
0.0347035 + 0.999398i \(0.488951\pi\)
\(200\) 0 0
\(201\) 0.109825 0.00774646
\(202\) 0 0
\(203\) −0.241943 −0.0169810
\(204\) 0 0
\(205\) −15.6086 −1.09015
\(206\) 0 0
\(207\) −23.4367 −1.62896
\(208\) 0 0
\(209\) −0.513939 −0.0355499
\(210\) 0 0
\(211\) −21.3914 −1.47265 −0.736324 0.676629i \(-0.763440\pi\)
−0.736324 + 0.676629i \(0.763440\pi\)
\(212\) 0 0
\(213\) −1.34561 −0.0921995
\(214\) 0 0
\(215\) 5.21982 0.355989
\(216\) 0 0
\(217\) 1.67789 0.113903
\(218\) 0 0
\(219\) 2.82031 0.190579
\(220\) 0 0
\(221\) −2.43370 −0.163708
\(222\) 0 0
\(223\) 2.96662 0.198660 0.0993299 0.995055i \(-0.468330\pi\)
0.0993299 + 0.995055i \(0.468330\pi\)
\(224\) 0 0
\(225\) −33.7431 −2.24954
\(226\) 0 0
\(227\) −5.27779 −0.350299 −0.175150 0.984542i \(-0.556041\pi\)
−0.175150 + 0.984542i \(0.556041\pi\)
\(228\) 0 0
\(229\) −18.6077 −1.22963 −0.614816 0.788671i \(-0.710770\pi\)
−0.614816 + 0.788671i \(0.710770\pi\)
\(230\) 0 0
\(231\) −0.0566543 −0.00372758
\(232\) 0 0
\(233\) −16.1633 −1.05889 −0.529447 0.848343i \(-0.677600\pi\)
−0.529447 + 0.848343i \(0.677600\pi\)
\(234\) 0 0
\(235\) −21.5214 −1.40390
\(236\) 0 0
\(237\) 4.80313 0.311997
\(238\) 0 0
\(239\) −6.42425 −0.415550 −0.207775 0.978177i \(-0.566622\pi\)
−0.207775 + 0.978177i \(0.566622\pi\)
\(240\) 0 0
\(241\) 24.1005 1.55245 0.776225 0.630456i \(-0.217132\pi\)
0.776225 + 0.630456i \(0.217132\pi\)
\(242\) 0 0
\(243\) −9.69293 −0.621802
\(244\) 0 0
\(245\) 28.3774 1.81297
\(246\) 0 0
\(247\) −2.10829 −0.134147
\(248\) 0 0
\(249\) 3.57813 0.226755
\(250\) 0 0
\(251\) −0.107684 −0.00679694 −0.00339847 0.999994i \(-0.501082\pi\)
−0.00339847 + 0.999994i \(0.501082\pi\)
\(252\) 0 0
\(253\) 4.22236 0.265458
\(254\) 0 0
\(255\) −1.81755 −0.113819
\(256\) 0 0
\(257\) 20.1942 1.25968 0.629839 0.776726i \(-0.283121\pi\)
0.629839 + 0.776726i \(0.283121\pi\)
\(258\) 0 0
\(259\) −1.21943 −0.0757717
\(260\) 0 0
\(261\) 2.40310 0.148748
\(262\) 0 0
\(263\) −17.0964 −1.05421 −0.527104 0.849801i \(-0.676722\pi\)
−0.527104 + 0.849801i \(0.676722\pi\)
\(264\) 0 0
\(265\) −4.10226 −0.252000
\(266\) 0 0
\(267\) −0.891349 −0.0545497
\(268\) 0 0
\(269\) −17.2783 −1.05348 −0.526739 0.850027i \(-0.676586\pi\)
−0.526739 + 0.850027i \(0.676586\pi\)
\(270\) 0 0
\(271\) −6.40128 −0.388850 −0.194425 0.980917i \(-0.562284\pi\)
−0.194425 + 0.980917i \(0.562284\pi\)
\(272\) 0 0
\(273\) −0.232408 −0.0140660
\(274\) 0 0
\(275\) 6.07916 0.366587
\(276\) 0 0
\(277\) −4.35360 −0.261582 −0.130791 0.991410i \(-0.541752\pi\)
−0.130791 + 0.991410i \(0.541752\pi\)
\(278\) 0 0
\(279\) −16.6657 −0.997750
\(280\) 0 0
\(281\) −10.4250 −0.621902 −0.310951 0.950426i \(-0.600648\pi\)
−0.310951 + 0.950426i \(0.600648\pi\)
\(282\) 0 0
\(283\) 30.4909 1.81249 0.906247 0.422748i \(-0.138934\pi\)
0.906247 + 0.422748i \(0.138934\pi\)
\(284\) 0 0
\(285\) −1.57453 −0.0932669
\(286\) 0 0
\(287\) 1.09279 0.0645051
\(288\) 0 0
\(289\) −15.6675 −0.921617
\(290\) 0 0
\(291\) 6.83766 0.400831
\(292\) 0 0
\(293\) −25.5499 −1.49264 −0.746322 0.665586i \(-0.768182\pi\)
−0.746322 + 0.665586i \(0.768182\pi\)
\(294\) 0 0
\(295\) −15.3366 −0.892931
\(296\) 0 0
\(297\) 1.15450 0.0669908
\(298\) 0 0
\(299\) 17.3210 1.00170
\(300\) 0 0
\(301\) −0.365449 −0.0210641
\(302\) 0 0
\(303\) 1.65214 0.0949130
\(304\) 0 0
\(305\) 56.9176 3.25909
\(306\) 0 0
\(307\) −30.1906 −1.72307 −0.861534 0.507699i \(-0.830496\pi\)
−0.861534 + 0.507699i \(0.830496\pi\)
\(308\) 0 0
\(309\) −4.75623 −0.270572
\(310\) 0 0
\(311\) −1.45973 −0.0827734 −0.0413867 0.999143i \(-0.513178\pi\)
−0.0413867 + 0.999143i \(0.513178\pi\)
\(312\) 0 0
\(313\) 25.4003 1.43571 0.717855 0.696192i \(-0.245124\pi\)
0.717855 + 0.696192i \(0.245124\pi\)
\(314\) 0 0
\(315\) 3.36102 0.189372
\(316\) 0 0
\(317\) 11.5159 0.646797 0.323399 0.946263i \(-0.395175\pi\)
0.323399 + 0.946263i \(0.395175\pi\)
\(318\) 0 0
\(319\) −0.432943 −0.0242401
\(320\) 0 0
\(321\) −4.97009 −0.277403
\(322\) 0 0
\(323\) 1.15435 0.0642295
\(324\) 0 0
\(325\) 24.9380 1.38331
\(326\) 0 0
\(327\) 1.12109 0.0619965
\(328\) 0 0
\(329\) 1.50675 0.0830697
\(330\) 0 0
\(331\) 10.7679 0.591858 0.295929 0.955210i \(-0.404371\pi\)
0.295929 + 0.955210i \(0.404371\pi\)
\(332\) 0 0
\(333\) 12.1120 0.663735
\(334\) 0 0
\(335\) 1.17381 0.0641321
\(336\) 0 0
\(337\) 28.1022 1.53082 0.765412 0.643541i \(-0.222535\pi\)
0.765412 + 0.643541i \(0.222535\pi\)
\(338\) 0 0
\(339\) 0.658847 0.0357837
\(340\) 0 0
\(341\) 3.00249 0.162594
\(342\) 0 0
\(343\) −3.99720 −0.215828
\(344\) 0 0
\(345\) 12.9358 0.696440
\(346\) 0 0
\(347\) 1.65294 0.0887347 0.0443673 0.999015i \(-0.485873\pi\)
0.0443673 + 0.999015i \(0.485873\pi\)
\(348\) 0 0
\(349\) 26.0054 1.39204 0.696018 0.718024i \(-0.254953\pi\)
0.696018 + 0.718024i \(0.254953\pi\)
\(350\) 0 0
\(351\) 4.73601 0.252789
\(352\) 0 0
\(353\) 1.62045 0.0862479 0.0431239 0.999070i \(-0.486269\pi\)
0.0431239 + 0.999070i \(0.486269\pi\)
\(354\) 0 0
\(355\) −14.3819 −0.763310
\(356\) 0 0
\(357\) 0.127250 0.00673477
\(358\) 0 0
\(359\) 20.6462 1.08966 0.544832 0.838545i \(-0.316593\pi\)
0.544832 + 0.838545i \(0.316593\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 4.12063 0.216277
\(364\) 0 0
\(365\) 30.1435 1.57778
\(366\) 0 0
\(367\) −12.5293 −0.654023 −0.327012 0.945020i \(-0.606042\pi\)
−0.327012 + 0.945020i \(0.606042\pi\)
\(368\) 0 0
\(369\) −10.8541 −0.565043
\(370\) 0 0
\(371\) 0.287206 0.0149110
\(372\) 0 0
\(373\) −11.0739 −0.573383 −0.286692 0.958023i \(-0.592556\pi\)
−0.286692 + 0.958023i \(0.592556\pi\)
\(374\) 0 0
\(375\) 10.7517 0.555218
\(376\) 0 0
\(377\) −1.77602 −0.0914699
\(378\) 0 0
\(379\) −19.8531 −1.01979 −0.509893 0.860238i \(-0.670315\pi\)
−0.509893 + 0.860238i \(0.670315\pi\)
\(380\) 0 0
\(381\) 6.49019 0.332502
\(382\) 0 0
\(383\) 1.74220 0.0890222 0.0445111 0.999009i \(-0.485827\pi\)
0.0445111 + 0.999009i \(0.485827\pi\)
\(384\) 0 0
\(385\) −0.605521 −0.0308602
\(386\) 0 0
\(387\) 3.62983 0.184514
\(388\) 0 0
\(389\) −19.4618 −0.986752 −0.493376 0.869816i \(-0.664237\pi\)
−0.493376 + 0.869816i \(0.664237\pi\)
\(390\) 0 0
\(391\) −9.48373 −0.479613
\(392\) 0 0
\(393\) −8.71506 −0.439617
\(394\) 0 0
\(395\) 51.3359 2.58299
\(396\) 0 0
\(397\) 0.208797 0.0104792 0.00523960 0.999986i \(-0.498332\pi\)
0.00523960 + 0.999986i \(0.498332\pi\)
\(398\) 0 0
\(399\) 0.110235 0.00551867
\(400\) 0 0
\(401\) −30.0175 −1.49900 −0.749501 0.662003i \(-0.769707\pi\)
−0.749501 + 0.662003i \(0.769707\pi\)
\(402\) 0 0
\(403\) 12.3169 0.613548
\(404\) 0 0
\(405\) −31.5704 −1.56875
\(406\) 0 0
\(407\) −2.18210 −0.108163
\(408\) 0 0
\(409\) −3.07405 −0.152002 −0.0760009 0.997108i \(-0.524215\pi\)
−0.0760009 + 0.997108i \(0.524215\pi\)
\(410\) 0 0
\(411\) −5.33451 −0.263132
\(412\) 0 0
\(413\) 1.07374 0.0528354
\(414\) 0 0
\(415\) 38.2431 1.87728
\(416\) 0 0
\(417\) −0.500121 −0.0244910
\(418\) 0 0
\(419\) −30.6784 −1.49874 −0.749368 0.662153i \(-0.769643\pi\)
−0.749368 + 0.662153i \(0.769643\pi\)
\(420\) 0 0
\(421\) 19.3709 0.944080 0.472040 0.881577i \(-0.343518\pi\)
0.472040 + 0.881577i \(0.343518\pi\)
\(422\) 0 0
\(423\) −14.9658 −0.727663
\(424\) 0 0
\(425\) −13.6542 −0.662328
\(426\) 0 0
\(427\) −3.98490 −0.192843
\(428\) 0 0
\(429\) −0.415881 −0.0200789
\(430\) 0 0
\(431\) −11.6691 −0.562080 −0.281040 0.959696i \(-0.590679\pi\)
−0.281040 + 0.959696i \(0.590679\pi\)
\(432\) 0 0
\(433\) −12.9461 −0.622152 −0.311076 0.950385i \(-0.600689\pi\)
−0.311076 + 0.950385i \(0.600689\pi\)
\(434\) 0 0
\(435\) −1.32638 −0.0635951
\(436\) 0 0
\(437\) −8.21568 −0.393009
\(438\) 0 0
\(439\) −11.2382 −0.536370 −0.268185 0.963367i \(-0.586424\pi\)
−0.268185 + 0.963367i \(0.586424\pi\)
\(440\) 0 0
\(441\) 19.7335 0.939689
\(442\) 0 0
\(443\) −5.76155 −0.273740 −0.136870 0.990589i \(-0.543704\pi\)
−0.136870 + 0.990589i \(0.543704\pi\)
\(444\) 0 0
\(445\) −9.52675 −0.451611
\(446\) 0 0
\(447\) 2.14081 0.101257
\(448\) 0 0
\(449\) −7.32440 −0.345660 −0.172830 0.984952i \(-0.555291\pi\)
−0.172830 + 0.984952i \(0.555291\pi\)
\(450\) 0 0
\(451\) 1.95548 0.0920798
\(452\) 0 0
\(453\) 3.53237 0.165965
\(454\) 0 0
\(455\) −2.48398 −0.116451
\(456\) 0 0
\(457\) 17.6055 0.823548 0.411774 0.911286i \(-0.364909\pi\)
0.411774 + 0.911286i \(0.364909\pi\)
\(458\) 0 0
\(459\) −2.59309 −0.121035
\(460\) 0 0
\(461\) 17.5982 0.819631 0.409815 0.912168i \(-0.365593\pi\)
0.409815 + 0.912168i \(0.365593\pi\)
\(462\) 0 0
\(463\) −20.5584 −0.955429 −0.477715 0.878515i \(-0.658535\pi\)
−0.477715 + 0.878515i \(0.658535\pi\)
\(464\) 0 0
\(465\) 9.19857 0.426573
\(466\) 0 0
\(467\) 15.7545 0.729032 0.364516 0.931197i \(-0.381234\pi\)
0.364516 + 0.931197i \(0.381234\pi\)
\(468\) 0 0
\(469\) −0.0821805 −0.00379474
\(470\) 0 0
\(471\) −5.17541 −0.238471
\(472\) 0 0
\(473\) −0.653949 −0.0300686
\(474\) 0 0
\(475\) −11.8286 −0.542731
\(476\) 0 0
\(477\) −2.85268 −0.130615
\(478\) 0 0
\(479\) 11.9229 0.544771 0.272385 0.962188i \(-0.412187\pi\)
0.272385 + 0.962188i \(0.412187\pi\)
\(480\) 0 0
\(481\) −8.95146 −0.408151
\(482\) 0 0
\(483\) −0.905658 −0.0412089
\(484\) 0 0
\(485\) 73.0809 3.31843
\(486\) 0 0
\(487\) −33.1036 −1.50007 −0.750033 0.661401i \(-0.769962\pi\)
−0.750033 + 0.661401i \(0.769962\pi\)
\(488\) 0 0
\(489\) −0.445895 −0.0201641
\(490\) 0 0
\(491\) 0.777119 0.0350709 0.0175355 0.999846i \(-0.494418\pi\)
0.0175355 + 0.999846i \(0.494418\pi\)
\(492\) 0 0
\(493\) 0.972421 0.0437956
\(494\) 0 0
\(495\) 6.01435 0.270325
\(496\) 0 0
\(497\) 1.00690 0.0451656
\(498\) 0 0
\(499\) −9.81805 −0.439516 −0.219758 0.975554i \(-0.570527\pi\)
−0.219758 + 0.975554i \(0.570527\pi\)
\(500\) 0 0
\(501\) −8.23318 −0.367831
\(502\) 0 0
\(503\) −3.49990 −0.156053 −0.0780263 0.996951i \(-0.524862\pi\)
−0.0780263 + 0.996951i \(0.524862\pi\)
\(504\) 0 0
\(505\) 17.6581 0.785774
\(506\) 0 0
\(507\) 3.28361 0.145830
\(508\) 0 0
\(509\) −29.5525 −1.30989 −0.654946 0.755676i \(-0.727309\pi\)
−0.654946 + 0.755676i \(0.727309\pi\)
\(510\) 0 0
\(511\) −2.11040 −0.0933585
\(512\) 0 0
\(513\) −2.24637 −0.0991798
\(514\) 0 0
\(515\) −50.8346 −2.24004
\(516\) 0 0
\(517\) 2.69624 0.118581
\(518\) 0 0
\(519\) 2.98064 0.130836
\(520\) 0 0
\(521\) 2.32943 0.102054 0.0510270 0.998697i \(-0.483751\pi\)
0.0510270 + 0.998697i \(0.483751\pi\)
\(522\) 0 0
\(523\) −11.2617 −0.492440 −0.246220 0.969214i \(-0.579189\pi\)
−0.246220 + 0.969214i \(0.579189\pi\)
\(524\) 0 0
\(525\) −1.30392 −0.0569079
\(526\) 0 0
\(527\) −6.74382 −0.293765
\(528\) 0 0
\(529\) 44.4974 1.93467
\(530\) 0 0
\(531\) −10.6650 −0.462820
\(532\) 0 0
\(533\) 8.02179 0.347462
\(534\) 0 0
\(535\) −53.1203 −2.29659
\(536\) 0 0
\(537\) 9.53675 0.411541
\(538\) 0 0
\(539\) −3.55518 −0.153133
\(540\) 0 0
\(541\) 30.8328 1.32561 0.662803 0.748794i \(-0.269367\pi\)
0.662803 + 0.748794i \(0.269367\pi\)
\(542\) 0 0
\(543\) 2.61556 0.112245
\(544\) 0 0
\(545\) 11.9822 0.513263
\(546\) 0 0
\(547\) 10.2865 0.439818 0.219909 0.975520i \(-0.429424\pi\)
0.219909 + 0.975520i \(0.429424\pi\)
\(548\) 0 0
\(549\) 39.5801 1.68924
\(550\) 0 0
\(551\) 0.842400 0.0358874
\(552\) 0 0
\(553\) −3.59412 −0.152837
\(554\) 0 0
\(555\) −6.68518 −0.283770
\(556\) 0 0
\(557\) −29.3582 −1.24395 −0.621974 0.783038i \(-0.713669\pi\)
−0.621974 + 0.783038i \(0.713669\pi\)
\(558\) 0 0
\(559\) −2.68264 −0.113464
\(560\) 0 0
\(561\) 0.227706 0.00961376
\(562\) 0 0
\(563\) −12.1101 −0.510380 −0.255190 0.966891i \(-0.582138\pi\)
−0.255190 + 0.966891i \(0.582138\pi\)
\(564\) 0 0
\(565\) 7.04176 0.296249
\(566\) 0 0
\(567\) 2.21030 0.0928237
\(568\) 0 0
\(569\) 23.2912 0.976417 0.488208 0.872727i \(-0.337651\pi\)
0.488208 + 0.872727i \(0.337651\pi\)
\(570\) 0 0
\(571\) 5.01580 0.209905 0.104952 0.994477i \(-0.466531\pi\)
0.104952 + 0.994477i \(0.466531\pi\)
\(572\) 0 0
\(573\) −4.23322 −0.176845
\(574\) 0 0
\(575\) 97.1796 4.05267
\(576\) 0 0
\(577\) 13.2297 0.550760 0.275380 0.961335i \(-0.411196\pi\)
0.275380 + 0.961335i \(0.411196\pi\)
\(578\) 0 0
\(579\) 1.94584 0.0808662
\(580\) 0 0
\(581\) −2.67746 −0.111080
\(582\) 0 0
\(583\) 0.513939 0.0212852
\(584\) 0 0
\(585\) 24.6722 1.02007
\(586\) 0 0
\(587\) 16.5555 0.683319 0.341659 0.939824i \(-0.389011\pi\)
0.341659 + 0.939824i \(0.389011\pi\)
\(588\) 0 0
\(589\) −5.84212 −0.240720
\(590\) 0 0
\(591\) 6.49189 0.267041
\(592\) 0 0
\(593\) 13.4410 0.551957 0.275979 0.961164i \(-0.410998\pi\)
0.275979 + 0.961164i \(0.410998\pi\)
\(594\) 0 0
\(595\) 1.36005 0.0557564
\(596\) 0 0
\(597\) −0.375799 −0.0153804
\(598\) 0 0
\(599\) −3.22531 −0.131783 −0.0658913 0.997827i \(-0.520989\pi\)
−0.0658913 + 0.997827i \(0.520989\pi\)
\(600\) 0 0
\(601\) −4.21383 −0.171886 −0.0859429 0.996300i \(-0.527390\pi\)
−0.0859429 + 0.996300i \(0.527390\pi\)
\(602\) 0 0
\(603\) 0.816259 0.0332406
\(604\) 0 0
\(605\) 44.0413 1.79053
\(606\) 0 0
\(607\) −17.4099 −0.706646 −0.353323 0.935501i \(-0.614948\pi\)
−0.353323 + 0.935501i \(0.614948\pi\)
\(608\) 0 0
\(609\) 0.0928622 0.00376297
\(610\) 0 0
\(611\) 11.0606 0.447463
\(612\) 0 0
\(613\) 2.92550 0.118160 0.0590800 0.998253i \(-0.481183\pi\)
0.0590800 + 0.998253i \(0.481183\pi\)
\(614\) 0 0
\(615\) 5.99089 0.241576
\(616\) 0 0
\(617\) −13.3011 −0.535484 −0.267742 0.963491i \(-0.586277\pi\)
−0.267742 + 0.963491i \(0.586277\pi\)
\(618\) 0 0
\(619\) −28.7135 −1.15409 −0.577047 0.816711i \(-0.695795\pi\)
−0.577047 + 0.816711i \(0.695795\pi\)
\(620\) 0 0
\(621\) 18.4555 0.740592
\(622\) 0 0
\(623\) 0.666984 0.0267221
\(624\) 0 0
\(625\) 55.7719 2.23088
\(626\) 0 0
\(627\) 0.197260 0.00787780
\(628\) 0 0
\(629\) 4.90116 0.195422
\(630\) 0 0
\(631\) −25.0365 −0.996686 −0.498343 0.866980i \(-0.666058\pi\)
−0.498343 + 0.866980i \(0.666058\pi\)
\(632\) 0 0
\(633\) 8.21045 0.326336
\(634\) 0 0
\(635\) 69.3671 2.75275
\(636\) 0 0
\(637\) −14.5841 −0.577844
\(638\) 0 0
\(639\) −10.0010 −0.395635
\(640\) 0 0
\(641\) −14.9778 −0.591589 −0.295795 0.955252i \(-0.595584\pi\)
−0.295795 + 0.955252i \(0.595584\pi\)
\(642\) 0 0
\(643\) −20.9750 −0.827172 −0.413586 0.910465i \(-0.635724\pi\)
−0.413586 + 0.910465i \(0.635724\pi\)
\(644\) 0 0
\(645\) −2.00347 −0.0788865
\(646\) 0 0
\(647\) −34.5495 −1.35828 −0.679140 0.734009i \(-0.737647\pi\)
−0.679140 + 0.734009i \(0.737647\pi\)
\(648\) 0 0
\(649\) 1.92140 0.0754215
\(650\) 0 0
\(651\) −0.644008 −0.0252406
\(652\) 0 0
\(653\) 27.9690 1.09451 0.547256 0.836965i \(-0.315673\pi\)
0.547256 + 0.836965i \(0.315673\pi\)
\(654\) 0 0
\(655\) −93.1466 −3.63954
\(656\) 0 0
\(657\) 20.9616 0.817789
\(658\) 0 0
\(659\) 20.7208 0.807169 0.403584 0.914942i \(-0.367764\pi\)
0.403584 + 0.914942i \(0.367764\pi\)
\(660\) 0 0
\(661\) 29.5669 1.15002 0.575010 0.818146i \(-0.304998\pi\)
0.575010 + 0.818146i \(0.304998\pi\)
\(662\) 0 0
\(663\) 0.934100 0.0362774
\(664\) 0 0
\(665\) 1.17820 0.0456885
\(666\) 0 0
\(667\) −6.92089 −0.267978
\(668\) 0 0
\(669\) −1.13865 −0.0440226
\(670\) 0 0
\(671\) −7.13075 −0.275279
\(672\) 0 0
\(673\) 31.3600 1.20884 0.604420 0.796666i \(-0.293405\pi\)
0.604420 + 0.796666i \(0.293405\pi\)
\(674\) 0 0
\(675\) 26.5713 1.02273
\(676\) 0 0
\(677\) −43.3889 −1.66757 −0.833785 0.552089i \(-0.813831\pi\)
−0.833785 + 0.552089i \(0.813831\pi\)
\(678\) 0 0
\(679\) −5.11652 −0.196354
\(680\) 0 0
\(681\) 2.02572 0.0776257
\(682\) 0 0
\(683\) 17.2824 0.661292 0.330646 0.943755i \(-0.392733\pi\)
0.330646 + 0.943755i \(0.392733\pi\)
\(684\) 0 0
\(685\) −57.0153 −2.17844
\(686\) 0 0
\(687\) 7.14200 0.272484
\(688\) 0 0
\(689\) 2.10829 0.0803195
\(690\) 0 0
\(691\) −15.1753 −0.577296 −0.288648 0.957435i \(-0.593206\pi\)
−0.288648 + 0.957435i \(0.593206\pi\)
\(692\) 0 0
\(693\) −0.421075 −0.0159953
\(694\) 0 0
\(695\) −5.34530 −0.202759
\(696\) 0 0
\(697\) −4.39215 −0.166364
\(698\) 0 0
\(699\) 6.20379 0.234649
\(700\) 0 0
\(701\) 38.6222 1.45874 0.729370 0.684119i \(-0.239813\pi\)
0.729370 + 0.684119i \(0.239813\pi\)
\(702\) 0 0
\(703\) 4.24583 0.160135
\(704\) 0 0
\(705\) 8.26032 0.311102
\(706\) 0 0
\(707\) −1.23627 −0.0464948
\(708\) 0 0
\(709\) −52.3288 −1.96525 −0.982625 0.185605i \(-0.940576\pi\)
−0.982625 + 0.185605i \(0.940576\pi\)
\(710\) 0 0
\(711\) 35.6986 1.33880
\(712\) 0 0
\(713\) 47.9969 1.79750
\(714\) 0 0
\(715\) −4.44494 −0.166231
\(716\) 0 0
\(717\) 2.46575 0.0920851
\(718\) 0 0
\(719\) 23.4900 0.876029 0.438014 0.898968i \(-0.355682\pi\)
0.438014 + 0.898968i \(0.355682\pi\)
\(720\) 0 0
\(721\) 3.55901 0.132545
\(722\) 0 0
\(723\) −9.25024 −0.344020
\(724\) 0 0
\(725\) −9.96437 −0.370068
\(726\) 0 0
\(727\) −23.7890 −0.882286 −0.441143 0.897437i \(-0.645427\pi\)
−0.441143 + 0.897437i \(0.645427\pi\)
\(728\) 0 0
\(729\) −19.3672 −0.717304
\(730\) 0 0
\(731\) 1.46882 0.0543262
\(732\) 0 0
\(733\) 4.04253 0.149314 0.0746571 0.997209i \(-0.476214\pi\)
0.0746571 + 0.997209i \(0.476214\pi\)
\(734\) 0 0
\(735\) −10.8918 −0.401750
\(736\) 0 0
\(737\) −0.147057 −0.00541692
\(738\) 0 0
\(739\) 48.5927 1.78751 0.893757 0.448552i \(-0.148060\pi\)
0.893757 + 0.448552i \(0.148060\pi\)
\(740\) 0 0
\(741\) 0.809203 0.0297268
\(742\) 0 0
\(743\) −12.7592 −0.468090 −0.234045 0.972226i \(-0.575196\pi\)
−0.234045 + 0.972226i \(0.575196\pi\)
\(744\) 0 0
\(745\) 22.8810 0.838295
\(746\) 0 0
\(747\) 26.5940 0.973022
\(748\) 0 0
\(749\) 3.71905 0.135891
\(750\) 0 0
\(751\) −27.0166 −0.985851 −0.492926 0.870071i \(-0.664073\pi\)
−0.492926 + 0.870071i \(0.664073\pi\)
\(752\) 0 0
\(753\) 0.0413311 0.00150619
\(754\) 0 0
\(755\) 37.7540 1.37401
\(756\) 0 0
\(757\) 22.9827 0.835320 0.417660 0.908603i \(-0.362850\pi\)
0.417660 + 0.908603i \(0.362850\pi\)
\(758\) 0 0
\(759\) −1.62062 −0.0588249
\(760\) 0 0
\(761\) −4.39314 −0.159251 −0.0796256 0.996825i \(-0.525372\pi\)
−0.0796256 + 0.996825i \(0.525372\pi\)
\(762\) 0 0
\(763\) −0.838897 −0.0303701
\(764\) 0 0
\(765\) −13.5087 −0.488407
\(766\) 0 0
\(767\) 7.88200 0.284602
\(768\) 0 0
\(769\) 7.56514 0.272806 0.136403 0.990653i \(-0.456446\pi\)
0.136403 + 0.990653i \(0.456446\pi\)
\(770\) 0 0
\(771\) −7.75091 −0.279142
\(772\) 0 0
\(773\) −39.9962 −1.43856 −0.719282 0.694718i \(-0.755529\pi\)
−0.719282 + 0.694718i \(0.755529\pi\)
\(774\) 0 0
\(775\) 69.1038 2.48228
\(776\) 0 0
\(777\) 0.468041 0.0167909
\(778\) 0 0
\(779\) −3.80488 −0.136324
\(780\) 0 0
\(781\) 1.80179 0.0644730
\(782\) 0 0
\(783\) −1.89234 −0.0676269
\(784\) 0 0
\(785\) −55.3149 −1.97427
\(786\) 0 0
\(787\) 19.1406 0.682289 0.341145 0.940011i \(-0.389185\pi\)
0.341145 + 0.940011i \(0.389185\pi\)
\(788\) 0 0
\(789\) 6.56192 0.233610
\(790\) 0 0
\(791\) −0.493006 −0.0175293
\(792\) 0 0
\(793\) −29.2519 −1.03876
\(794\) 0 0
\(795\) 1.57453 0.0558427
\(796\) 0 0
\(797\) −45.9035 −1.62599 −0.812994 0.582273i \(-0.802164\pi\)
−0.812994 + 0.582273i \(0.802164\pi\)
\(798\) 0 0
\(799\) −6.05595 −0.214244
\(800\) 0 0
\(801\) −6.62483 −0.234077
\(802\) 0 0
\(803\) −3.77644 −0.133268
\(804\) 0 0
\(805\) −9.67968 −0.341164
\(806\) 0 0
\(807\) 6.63175 0.233449
\(808\) 0 0
\(809\) −8.78468 −0.308853 −0.154426 0.988004i \(-0.549353\pi\)
−0.154426 + 0.988004i \(0.549353\pi\)
\(810\) 0 0
\(811\) −23.8294 −0.836763 −0.418382 0.908271i \(-0.637403\pi\)
−0.418382 + 0.908271i \(0.637403\pi\)
\(812\) 0 0
\(813\) 2.45694 0.0861685
\(814\) 0 0
\(815\) −4.76572 −0.166936
\(816\) 0 0
\(817\) 1.27243 0.0445165
\(818\) 0 0
\(819\) −1.72734 −0.0603582
\(820\) 0 0
\(821\) 12.4667 0.435089 0.217545 0.976050i \(-0.430195\pi\)
0.217545 + 0.976050i \(0.430195\pi\)
\(822\) 0 0
\(823\) −18.8253 −0.656207 −0.328104 0.944642i \(-0.606410\pi\)
−0.328104 + 0.944642i \(0.606410\pi\)
\(824\) 0 0
\(825\) −2.33330 −0.0812350
\(826\) 0 0
\(827\) −20.6971 −0.719709 −0.359854 0.933008i \(-0.617174\pi\)
−0.359854 + 0.933008i \(0.617174\pi\)
\(828\) 0 0
\(829\) 19.3184 0.670955 0.335477 0.942048i \(-0.391102\pi\)
0.335477 + 0.942048i \(0.391102\pi\)
\(830\) 0 0
\(831\) 1.67100 0.0579662
\(832\) 0 0
\(833\) 7.98520 0.276671
\(834\) 0 0
\(835\) −87.9963 −3.04524
\(836\) 0 0
\(837\) 13.1236 0.453617
\(838\) 0 0
\(839\) −8.48295 −0.292864 −0.146432 0.989221i \(-0.546779\pi\)
−0.146432 + 0.989221i \(0.546779\pi\)
\(840\) 0 0
\(841\) −28.2904 −0.975530
\(842\) 0 0
\(843\) 4.00131 0.137812
\(844\) 0 0
\(845\) 35.0953 1.20731
\(846\) 0 0
\(847\) −3.08341 −0.105947
\(848\) 0 0
\(849\) −11.7030 −0.401645
\(850\) 0 0
\(851\) −34.8824 −1.19575
\(852\) 0 0
\(853\) 11.3568 0.388851 0.194425 0.980917i \(-0.437716\pi\)
0.194425 + 0.980917i \(0.437716\pi\)
\(854\) 0 0
\(855\) −11.7025 −0.400215
\(856\) 0 0
\(857\) −18.6348 −0.636553 −0.318277 0.947998i \(-0.603104\pi\)
−0.318277 + 0.947998i \(0.603104\pi\)
\(858\) 0 0
\(859\) −33.3031 −1.13629 −0.568144 0.822929i \(-0.692338\pi\)
−0.568144 + 0.822929i \(0.692338\pi\)
\(860\) 0 0
\(861\) −0.419432 −0.0142942
\(862\) 0 0
\(863\) −5.03616 −0.171433 −0.0857165 0.996320i \(-0.527318\pi\)
−0.0857165 + 0.996320i \(0.527318\pi\)
\(864\) 0 0
\(865\) 31.8571 1.08317
\(866\) 0 0
\(867\) 6.01348 0.204229
\(868\) 0 0
\(869\) −6.43147 −0.218173
\(870\) 0 0
\(871\) −0.603261 −0.0204407
\(872\) 0 0
\(873\) 50.8199 1.71999
\(874\) 0 0
\(875\) −8.04537 −0.271983
\(876\) 0 0
\(877\) −56.1751 −1.89690 −0.948450 0.316928i \(-0.897349\pi\)
−0.948450 + 0.316928i \(0.897349\pi\)
\(878\) 0 0
\(879\) 9.80656 0.330767
\(880\) 0 0
\(881\) 39.6428 1.33560 0.667801 0.744340i \(-0.267236\pi\)
0.667801 + 0.744340i \(0.267236\pi\)
\(882\) 0 0
\(883\) 25.5965 0.861390 0.430695 0.902497i \(-0.358268\pi\)
0.430695 + 0.902497i \(0.358268\pi\)
\(884\) 0 0
\(885\) 5.88648 0.197872
\(886\) 0 0
\(887\) −2.94753 −0.0989685 −0.0494843 0.998775i \(-0.515758\pi\)
−0.0494843 + 0.998775i \(0.515758\pi\)
\(888\) 0 0
\(889\) −4.85651 −0.162882
\(890\) 0 0
\(891\) 3.95520 0.132504
\(892\) 0 0
\(893\) −5.24622 −0.175558
\(894\) 0 0
\(895\) 101.929 3.40711
\(896\) 0 0
\(897\) −6.64815 −0.221975
\(898\) 0 0
\(899\) −4.92140 −0.164138
\(900\) 0 0
\(901\) −1.15435 −0.0384568
\(902\) 0 0
\(903\) 0.140266 0.00466777
\(904\) 0 0
\(905\) 27.9552 0.929261
\(906\) 0 0
\(907\) 41.6606 1.38332 0.691659 0.722224i \(-0.256880\pi\)
0.691659 + 0.722224i \(0.256880\pi\)
\(908\) 0 0
\(909\) 12.2793 0.407279
\(910\) 0 0
\(911\) −40.7596 −1.35043 −0.675213 0.737623i \(-0.735948\pi\)
−0.675213 + 0.737623i \(0.735948\pi\)
\(912\) 0 0
\(913\) −4.79117 −0.158565
\(914\) 0 0
\(915\) −21.8461 −0.722209
\(916\) 0 0
\(917\) 6.52135 0.215354
\(918\) 0 0
\(919\) 32.3314 1.06652 0.533258 0.845953i \(-0.320968\pi\)
0.533258 + 0.845953i \(0.320968\pi\)
\(920\) 0 0
\(921\) 11.5877 0.381829
\(922\) 0 0
\(923\) 7.39133 0.243288
\(924\) 0 0
\(925\) −50.2221 −1.65129
\(926\) 0 0
\(927\) −35.3500 −1.16105
\(928\) 0 0
\(929\) 39.0707 1.28187 0.640934 0.767596i \(-0.278547\pi\)
0.640934 + 0.767596i \(0.278547\pi\)
\(930\) 0 0
\(931\) 6.91751 0.226712
\(932\) 0 0
\(933\) 0.560271 0.0183424
\(934\) 0 0
\(935\) 2.43372 0.0795913
\(936\) 0 0
\(937\) 47.3450 1.54669 0.773347 0.633983i \(-0.218581\pi\)
0.773347 + 0.633983i \(0.218581\pi\)
\(938\) 0 0
\(939\) −9.74913 −0.318151
\(940\) 0 0
\(941\) −28.7459 −0.937088 −0.468544 0.883440i \(-0.655221\pi\)
−0.468544 + 0.883440i \(0.655221\pi\)
\(942\) 0 0
\(943\) 31.2597 1.01795
\(944\) 0 0
\(945\) −2.64667 −0.0860961
\(946\) 0 0
\(947\) −31.0986 −1.01057 −0.505284 0.862953i \(-0.668612\pi\)
−0.505284 + 0.862953i \(0.668612\pi\)
\(948\) 0 0
\(949\) −15.4918 −0.502884
\(950\) 0 0
\(951\) −4.42002 −0.143329
\(952\) 0 0
\(953\) 7.70006 0.249429 0.124715 0.992193i \(-0.460198\pi\)
0.124715 + 0.992193i \(0.460198\pi\)
\(954\) 0 0
\(955\) −45.2447 −1.46408
\(956\) 0 0
\(957\) 0.166172 0.00537157
\(958\) 0 0
\(959\) 3.99174 0.128900
\(960\) 0 0
\(961\) 3.13032 0.100978
\(962\) 0 0
\(963\) −36.9395 −1.19036
\(964\) 0 0
\(965\) 20.7971 0.669482
\(966\) 0 0
\(967\) −54.0601 −1.73845 −0.869227 0.494413i \(-0.835383\pi\)
−0.869227 + 0.494413i \(0.835383\pi\)
\(968\) 0 0
\(969\) −0.443060 −0.0142331
\(970\) 0 0
\(971\) −15.7172 −0.504388 −0.252194 0.967677i \(-0.581152\pi\)
−0.252194 + 0.967677i \(0.581152\pi\)
\(972\) 0 0
\(973\) 0.374234 0.0119974
\(974\) 0 0
\(975\) −9.57170 −0.306540
\(976\) 0 0
\(977\) −45.6254 −1.45969 −0.729843 0.683615i \(-0.760407\pi\)
−0.729843 + 0.683615i \(0.760407\pi\)
\(978\) 0 0
\(979\) 1.19353 0.0381454
\(980\) 0 0
\(981\) 8.33236 0.266032
\(982\) 0 0
\(983\) 46.4886 1.48276 0.741379 0.671087i \(-0.234172\pi\)
0.741379 + 0.671087i \(0.234172\pi\)
\(984\) 0 0
\(985\) 69.3854 2.21080
\(986\) 0 0
\(987\) −0.578319 −0.0184081
\(988\) 0 0
\(989\) −10.4538 −0.332413
\(990\) 0 0
\(991\) −4.45801 −0.141613 −0.0708067 0.997490i \(-0.522557\pi\)
−0.0708067 + 0.997490i \(0.522557\pi\)
\(992\) 0 0
\(993\) −4.13293 −0.131155
\(994\) 0 0
\(995\) −4.01655 −0.127333
\(996\) 0 0
\(997\) 6.55199 0.207503 0.103752 0.994603i \(-0.466915\pi\)
0.103752 + 0.994603i \(0.466915\pi\)
\(998\) 0 0
\(999\) −9.53773 −0.301760
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 \(a_p\))