Properties

Label 8048.2.a.v.1.22
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 1.22
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.73728 q^{3}\) \(+2.58604 q^{5}\) \(-2.10260 q^{7}\) \(+0.0181326 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.73728 q^{3}\) \(+2.58604 q^{5}\) \(-2.10260 q^{7}\) \(+0.0181326 q^{9}\) \(+2.62289 q^{11}\) \(+0.715213 q^{13}\) \(+4.49267 q^{15}\) \(-5.38011 q^{17}\) \(-1.38337 q^{19}\) \(-3.65280 q^{21}\) \(-6.72492 q^{23}\) \(+1.68762 q^{25}\) \(-5.18033 q^{27}\) \(-4.19384 q^{29}\) \(+5.92164 q^{31}\) \(+4.55669 q^{33}\) \(-5.43741 q^{35}\) \(-7.49843 q^{37}\) \(+1.24252 q^{39}\) \(-2.29080 q^{41}\) \(-7.41206 q^{43}\) \(+0.0468916 q^{45}\) \(+7.28843 q^{47}\) \(-2.57908 q^{49}\) \(-9.34674 q^{51}\) \(-11.8850 q^{53}\) \(+6.78291 q^{55}\) \(-2.40330 q^{57}\) \(+7.39694 q^{59}\) \(-1.47413 q^{61}\) \(-0.0381255 q^{63}\) \(+1.84957 q^{65}\) \(+4.45942 q^{67}\) \(-11.6831 q^{69}\) \(-8.17012 q^{71}\) \(-9.67286 q^{73}\) \(+2.93186 q^{75}\) \(-5.51489 q^{77}\) \(-9.04789 q^{79}\) \(-9.05407 q^{81}\) \(-4.25798 q^{83}\) \(-13.9132 q^{85}\) \(-7.28586 q^{87}\) \(+9.05608 q^{89}\) \(-1.50381 q^{91}\) \(+10.2875 q^{93}\) \(-3.57746 q^{95}\) \(+8.08527 q^{97}\) \(+0.0475598 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 31q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 22q^{25} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 26q^{33} \) \(\mathstrut +\mathstrut 13q^{35} \) \(\mathstrut -\mathstrut 67q^{37} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut -\mathstrut 57q^{45} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 20q^{49} \) \(\mathstrut +\mathstrut 11q^{51} \) \(\mathstrut -\mathstrut 58q^{53} \) \(\mathstrut -\mathstrut 15q^{55} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 55q^{61} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 44q^{69} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 5q^{73} \) \(\mathstrut +\mathstrut 25q^{75} \) \(\mathstrut -\mathstrut 50q^{77} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 78q^{85} \) \(\mathstrut +\mathstrut 11q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut +\mathstrut 15q^{91} \) \(\mathstrut -\mathstrut 83q^{93} \) \(\mathstrut +\mathstrut 27q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 70q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.73728 1.00302 0.501509 0.865153i \(-0.332779\pi\)
0.501509 + 0.865153i \(0.332779\pi\)
\(4\) 0 0
\(5\) 2.58604 1.15651 0.578257 0.815855i \(-0.303733\pi\)
0.578257 + 0.815855i \(0.303733\pi\)
\(6\) 0 0
\(7\) −2.10260 −0.794708 −0.397354 0.917665i \(-0.630071\pi\)
−0.397354 + 0.917665i \(0.630071\pi\)
\(8\) 0 0
\(9\) 0.0181326 0.00604419
\(10\) 0 0
\(11\) 2.62289 0.790832 0.395416 0.918502i \(-0.370600\pi\)
0.395416 + 0.918502i \(0.370600\pi\)
\(12\) 0 0
\(13\) 0.715213 0.198364 0.0991822 0.995069i \(-0.468377\pi\)
0.0991822 + 0.995069i \(0.468377\pi\)
\(14\) 0 0
\(15\) 4.49267 1.16000
\(16\) 0 0
\(17\) −5.38011 −1.30487 −0.652434 0.757846i \(-0.726252\pi\)
−0.652434 + 0.757846i \(0.726252\pi\)
\(18\) 0 0
\(19\) −1.38337 −0.317367 −0.158684 0.987330i \(-0.550725\pi\)
−0.158684 + 0.987330i \(0.550725\pi\)
\(20\) 0 0
\(21\) −3.65280 −0.797106
\(22\) 0 0
\(23\) −6.72492 −1.40224 −0.701122 0.713041i \(-0.747317\pi\)
−0.701122 + 0.713041i \(0.747317\pi\)
\(24\) 0 0
\(25\) 1.68762 0.337523
\(26\) 0 0
\(27\) −5.18033 −0.996955
\(28\) 0 0
\(29\) −4.19384 −0.778776 −0.389388 0.921074i \(-0.627313\pi\)
−0.389388 + 0.921074i \(0.627313\pi\)
\(30\) 0 0
\(31\) 5.92164 1.06356 0.531779 0.846883i \(-0.321524\pi\)
0.531779 + 0.846883i \(0.321524\pi\)
\(32\) 0 0
\(33\) 4.55669 0.793218
\(34\) 0 0
\(35\) −5.43741 −0.919090
\(36\) 0 0
\(37\) −7.49843 −1.23273 −0.616367 0.787459i \(-0.711396\pi\)
−0.616367 + 0.787459i \(0.711396\pi\)
\(38\) 0 0
\(39\) 1.24252 0.198963
\(40\) 0 0
\(41\) −2.29080 −0.357763 −0.178882 0.983871i \(-0.557248\pi\)
−0.178882 + 0.983871i \(0.557248\pi\)
\(42\) 0 0
\(43\) −7.41206 −1.13033 −0.565164 0.824979i \(-0.691187\pi\)
−0.565164 + 0.824979i \(0.691187\pi\)
\(44\) 0 0
\(45\) 0.0468916 0.00699019
\(46\) 0 0
\(47\) 7.28843 1.06313 0.531564 0.847018i \(-0.321605\pi\)
0.531564 + 0.847018i \(0.321605\pi\)
\(48\) 0 0
\(49\) −2.57908 −0.368440
\(50\) 0 0
\(51\) −9.34674 −1.30881
\(52\) 0 0
\(53\) −11.8850 −1.63253 −0.816266 0.577677i \(-0.803959\pi\)
−0.816266 + 0.577677i \(0.803959\pi\)
\(54\) 0 0
\(55\) 6.78291 0.914608
\(56\) 0 0
\(57\) −2.40330 −0.318325
\(58\) 0 0
\(59\) 7.39694 0.963000 0.481500 0.876446i \(-0.340092\pi\)
0.481500 + 0.876446i \(0.340092\pi\)
\(60\) 0 0
\(61\) −1.47413 −0.188743 −0.0943717 0.995537i \(-0.530084\pi\)
−0.0943717 + 0.995537i \(0.530084\pi\)
\(62\) 0 0
\(63\) −0.0381255 −0.00480337
\(64\) 0 0
\(65\) 1.84957 0.229411
\(66\) 0 0
\(67\) 4.45942 0.544805 0.272402 0.962183i \(-0.412182\pi\)
0.272402 + 0.962183i \(0.412182\pi\)
\(68\) 0 0
\(69\) −11.6831 −1.40648
\(70\) 0 0
\(71\) −8.17012 −0.969615 −0.484807 0.874621i \(-0.661110\pi\)
−0.484807 + 0.874621i \(0.661110\pi\)
\(72\) 0 0
\(73\) −9.67286 −1.13212 −0.566061 0.824363i \(-0.691533\pi\)
−0.566061 + 0.824363i \(0.691533\pi\)
\(74\) 0 0
\(75\) 2.93186 0.338542
\(76\) 0 0
\(77\) −5.51489 −0.628480
\(78\) 0 0
\(79\) −9.04789 −1.01797 −0.508983 0.860776i \(-0.669979\pi\)
−0.508983 + 0.860776i \(0.669979\pi\)
\(80\) 0 0
\(81\) −9.05407 −1.00601
\(82\) 0 0
\(83\) −4.25798 −0.467374 −0.233687 0.972312i \(-0.575079\pi\)
−0.233687 + 0.972312i \(0.575079\pi\)
\(84\) 0 0
\(85\) −13.9132 −1.50910
\(86\) 0 0
\(87\) −7.28586 −0.781126
\(88\) 0 0
\(89\) 9.05608 0.959943 0.479972 0.877284i \(-0.340647\pi\)
0.479972 + 0.877284i \(0.340647\pi\)
\(90\) 0 0
\(91\) −1.50381 −0.157642
\(92\) 0 0
\(93\) 10.2875 1.06677
\(94\) 0 0
\(95\) −3.57746 −0.367039
\(96\) 0 0
\(97\) 8.08527 0.820934 0.410467 0.911875i \(-0.365366\pi\)
0.410467 + 0.911875i \(0.365366\pi\)
\(98\) 0 0
\(99\) 0.0475598 0.00477994
\(100\) 0 0
\(101\) 18.8020 1.87087 0.935436 0.353497i \(-0.115008\pi\)
0.935436 + 0.353497i \(0.115008\pi\)
\(102\) 0 0
\(103\) −1.20257 −0.118492 −0.0592462 0.998243i \(-0.518870\pi\)
−0.0592462 + 0.998243i \(0.518870\pi\)
\(104\) 0 0
\(105\) −9.44629 −0.921863
\(106\) 0 0
\(107\) 16.6032 1.60509 0.802544 0.596593i \(-0.203479\pi\)
0.802544 + 0.596593i \(0.203479\pi\)
\(108\) 0 0
\(109\) 10.9284 1.04675 0.523376 0.852102i \(-0.324672\pi\)
0.523376 + 0.852102i \(0.324672\pi\)
\(110\) 0 0
\(111\) −13.0269 −1.23645
\(112\) 0 0
\(113\) −18.5233 −1.74252 −0.871261 0.490820i \(-0.836697\pi\)
−0.871261 + 0.490820i \(0.836697\pi\)
\(114\) 0 0
\(115\) −17.3909 −1.62171
\(116\) 0 0
\(117\) 0.0129687 0.00119895
\(118\) 0 0
\(119\) 11.3122 1.03699
\(120\) 0 0
\(121\) −4.12043 −0.374585
\(122\) 0 0
\(123\) −3.97976 −0.358843
\(124\) 0 0
\(125\) −8.56597 −0.766163
\(126\) 0 0
\(127\) −10.1838 −0.903668 −0.451834 0.892102i \(-0.649230\pi\)
−0.451834 + 0.892102i \(0.649230\pi\)
\(128\) 0 0
\(129\) −12.8768 −1.13374
\(130\) 0 0
\(131\) 1.75144 0.153024 0.0765121 0.997069i \(-0.475622\pi\)
0.0765121 + 0.997069i \(0.475622\pi\)
\(132\) 0 0
\(133\) 2.90867 0.252214
\(134\) 0 0
\(135\) −13.3966 −1.15299
\(136\) 0 0
\(137\) −15.0405 −1.28499 −0.642496 0.766289i \(-0.722101\pi\)
−0.642496 + 0.766289i \(0.722101\pi\)
\(138\) 0 0
\(139\) 8.98840 0.762386 0.381193 0.924495i \(-0.375513\pi\)
0.381193 + 0.924495i \(0.375513\pi\)
\(140\) 0 0
\(141\) 12.6620 1.06634
\(142\) 0 0
\(143\) 1.87593 0.156873
\(144\) 0 0
\(145\) −10.8454 −0.900665
\(146\) 0 0
\(147\) −4.48057 −0.369551
\(148\) 0 0
\(149\) 18.8981 1.54819 0.774097 0.633067i \(-0.218204\pi\)
0.774097 + 0.633067i \(0.218204\pi\)
\(150\) 0 0
\(151\) −17.6152 −1.43351 −0.716754 0.697326i \(-0.754373\pi\)
−0.716754 + 0.697326i \(0.754373\pi\)
\(152\) 0 0
\(153\) −0.0975552 −0.00788687
\(154\) 0 0
\(155\) 15.3136 1.23002
\(156\) 0 0
\(157\) 21.9626 1.75280 0.876401 0.481582i \(-0.159937\pi\)
0.876401 + 0.481582i \(0.159937\pi\)
\(158\) 0 0
\(159\) −20.6476 −1.63746
\(160\) 0 0
\(161\) 14.1398 1.11437
\(162\) 0 0
\(163\) 21.4671 1.68143 0.840717 0.541474i \(-0.182134\pi\)
0.840717 + 0.541474i \(0.182134\pi\)
\(164\) 0 0
\(165\) 11.7838 0.917368
\(166\) 0 0
\(167\) −2.18943 −0.169423 −0.0847114 0.996406i \(-0.526997\pi\)
−0.0847114 + 0.996406i \(0.526997\pi\)
\(168\) 0 0
\(169\) −12.4885 −0.960652
\(170\) 0 0
\(171\) −0.0250841 −0.00191823
\(172\) 0 0
\(173\) 2.58894 0.196833 0.0984167 0.995145i \(-0.468622\pi\)
0.0984167 + 0.995145i \(0.468622\pi\)
\(174\) 0 0
\(175\) −3.54838 −0.268232
\(176\) 0 0
\(177\) 12.8505 0.965906
\(178\) 0 0
\(179\) 14.8091 1.10688 0.553442 0.832888i \(-0.313314\pi\)
0.553442 + 0.832888i \(0.313314\pi\)
\(180\) 0 0
\(181\) −26.5615 −1.97430 −0.987152 0.159784i \(-0.948920\pi\)
−0.987152 + 0.159784i \(0.948920\pi\)
\(182\) 0 0
\(183\) −2.56098 −0.189313
\(184\) 0 0
\(185\) −19.3913 −1.42567
\(186\) 0 0
\(187\) −14.1115 −1.03193
\(188\) 0 0
\(189\) 10.8922 0.792288
\(190\) 0 0
\(191\) 7.64557 0.553214 0.276607 0.960983i \(-0.410790\pi\)
0.276607 + 0.960983i \(0.410790\pi\)
\(192\) 0 0
\(193\) 18.6737 1.34417 0.672083 0.740476i \(-0.265400\pi\)
0.672083 + 0.740476i \(0.265400\pi\)
\(194\) 0 0
\(195\) 3.21322 0.230103
\(196\) 0 0
\(197\) −23.8450 −1.69889 −0.849443 0.527680i \(-0.823062\pi\)
−0.849443 + 0.527680i \(0.823062\pi\)
\(198\) 0 0
\(199\) 21.5661 1.52878 0.764390 0.644754i \(-0.223040\pi\)
0.764390 + 0.644754i \(0.223040\pi\)
\(200\) 0 0
\(201\) 7.74724 0.546448
\(202\) 0 0
\(203\) 8.81796 0.618899
\(204\) 0 0
\(205\) −5.92411 −0.413758
\(206\) 0 0
\(207\) −0.121940 −0.00847543
\(208\) 0 0
\(209\) −3.62843 −0.250984
\(210\) 0 0
\(211\) 13.1034 0.902078 0.451039 0.892504i \(-0.351054\pi\)
0.451039 + 0.892504i \(0.351054\pi\)
\(212\) 0 0
\(213\) −14.1938 −0.972541
\(214\) 0 0
\(215\) −19.1679 −1.30724
\(216\) 0 0
\(217\) −12.4508 −0.845218
\(218\) 0 0
\(219\) −16.8044 −1.13554
\(220\) 0 0
\(221\) −3.84792 −0.258839
\(222\) 0 0
\(223\) −7.00682 −0.469211 −0.234606 0.972091i \(-0.575380\pi\)
−0.234606 + 0.972091i \(0.575380\pi\)
\(224\) 0 0
\(225\) 0.0306008 0.00204005
\(226\) 0 0
\(227\) 11.6164 0.771006 0.385503 0.922707i \(-0.374028\pi\)
0.385503 + 0.922707i \(0.374028\pi\)
\(228\) 0 0
\(229\) −19.2049 −1.26909 −0.634547 0.772884i \(-0.718813\pi\)
−0.634547 + 0.772884i \(0.718813\pi\)
\(230\) 0 0
\(231\) −9.58090 −0.630377
\(232\) 0 0
\(233\) 2.65846 0.174161 0.0870807 0.996201i \(-0.472246\pi\)
0.0870807 + 0.996201i \(0.472246\pi\)
\(234\) 0 0
\(235\) 18.8482 1.22952
\(236\) 0 0
\(237\) −15.7187 −1.02104
\(238\) 0 0
\(239\) 9.78193 0.632740 0.316370 0.948636i \(-0.397536\pi\)
0.316370 + 0.948636i \(0.397536\pi\)
\(240\) 0 0
\(241\) 14.1847 0.913718 0.456859 0.889539i \(-0.348974\pi\)
0.456859 + 0.889539i \(0.348974\pi\)
\(242\) 0 0
\(243\) −0.188437 −0.0120882
\(244\) 0 0
\(245\) −6.66960 −0.426105
\(246\) 0 0
\(247\) −0.989405 −0.0629543
\(248\) 0 0
\(249\) −7.39730 −0.468785
\(250\) 0 0
\(251\) −7.28945 −0.460106 −0.230053 0.973178i \(-0.573890\pi\)
−0.230053 + 0.973178i \(0.573890\pi\)
\(252\) 0 0
\(253\) −17.6388 −1.10894
\(254\) 0 0
\(255\) −24.1711 −1.51365
\(256\) 0 0
\(257\) −24.3811 −1.52085 −0.760424 0.649427i \(-0.775009\pi\)
−0.760424 + 0.649427i \(0.775009\pi\)
\(258\) 0 0
\(259\) 15.7662 0.979664
\(260\) 0 0
\(261\) −0.0760451 −0.00470707
\(262\) 0 0
\(263\) −10.9637 −0.676052 −0.338026 0.941137i \(-0.609759\pi\)
−0.338026 + 0.941137i \(0.609759\pi\)
\(264\) 0 0
\(265\) −30.7351 −1.88804
\(266\) 0 0
\(267\) 15.7329 0.962840
\(268\) 0 0
\(269\) 6.72724 0.410167 0.205084 0.978744i \(-0.434253\pi\)
0.205084 + 0.978744i \(0.434253\pi\)
\(270\) 0 0
\(271\) 6.57983 0.399696 0.199848 0.979827i \(-0.435955\pi\)
0.199848 + 0.979827i \(0.435955\pi\)
\(272\) 0 0
\(273\) −2.61253 −0.158117
\(274\) 0 0
\(275\) 4.42643 0.266924
\(276\) 0 0
\(277\) 5.65170 0.339577 0.169789 0.985480i \(-0.445691\pi\)
0.169789 + 0.985480i \(0.445691\pi\)
\(278\) 0 0
\(279\) 0.107375 0.00642835
\(280\) 0 0
\(281\) 6.49270 0.387322 0.193661 0.981069i \(-0.437964\pi\)
0.193661 + 0.981069i \(0.437964\pi\)
\(282\) 0 0
\(283\) 15.3968 0.915246 0.457623 0.889146i \(-0.348701\pi\)
0.457623 + 0.889146i \(0.348701\pi\)
\(284\) 0 0
\(285\) −6.21503 −0.368147
\(286\) 0 0
\(287\) 4.81664 0.284317
\(288\) 0 0
\(289\) 11.9456 0.702681
\(290\) 0 0
\(291\) 14.0464 0.823412
\(292\) 0 0
\(293\) −25.3812 −1.48279 −0.741393 0.671071i \(-0.765835\pi\)
−0.741393 + 0.671071i \(0.765835\pi\)
\(294\) 0 0
\(295\) 19.1288 1.11372
\(296\) 0 0
\(297\) −13.5875 −0.788424
\(298\) 0 0
\(299\) −4.80975 −0.278155
\(300\) 0 0
\(301\) 15.5846 0.898281
\(302\) 0 0
\(303\) 32.6643 1.87652
\(304\) 0 0
\(305\) −3.81217 −0.218284
\(306\) 0 0
\(307\) −24.9503 −1.42399 −0.711993 0.702186i \(-0.752207\pi\)
−0.711993 + 0.702186i \(0.752207\pi\)
\(308\) 0 0
\(309\) −2.08919 −0.118850
\(310\) 0 0
\(311\) −9.38125 −0.531962 −0.265981 0.963978i \(-0.585696\pi\)
−0.265981 + 0.963978i \(0.585696\pi\)
\(312\) 0 0
\(313\) −7.27785 −0.411368 −0.205684 0.978618i \(-0.565942\pi\)
−0.205684 + 0.978618i \(0.565942\pi\)
\(314\) 0 0
\(315\) −0.0985943 −0.00555516
\(316\) 0 0
\(317\) 4.69633 0.263772 0.131886 0.991265i \(-0.457897\pi\)
0.131886 + 0.991265i \(0.457897\pi\)
\(318\) 0 0
\(319\) −11.0000 −0.615881
\(320\) 0 0
\(321\) 28.8443 1.60993
\(322\) 0 0
\(323\) 7.44268 0.414122
\(324\) 0 0
\(325\) 1.20700 0.0669525
\(326\) 0 0
\(327\) 18.9857 1.04991
\(328\) 0 0
\(329\) −15.3247 −0.844875
\(330\) 0 0
\(331\) 19.3105 1.06140 0.530700 0.847560i \(-0.321929\pi\)
0.530700 + 0.847560i \(0.321929\pi\)
\(332\) 0 0
\(333\) −0.135966 −0.00745088
\(334\) 0 0
\(335\) 11.5322 0.630074
\(336\) 0 0
\(337\) 17.1916 0.936488 0.468244 0.883599i \(-0.344887\pi\)
0.468244 + 0.883599i \(0.344887\pi\)
\(338\) 0 0
\(339\) −32.1800 −1.74778
\(340\) 0 0
\(341\) 15.5318 0.841096
\(342\) 0 0
\(343\) 20.1410 1.08751
\(344\) 0 0
\(345\) −30.2129 −1.62661
\(346\) 0 0
\(347\) 14.6384 0.785832 0.392916 0.919574i \(-0.371466\pi\)
0.392916 + 0.919574i \(0.371466\pi\)
\(348\) 0 0
\(349\) −9.91051 −0.530497 −0.265249 0.964180i \(-0.585454\pi\)
−0.265249 + 0.964180i \(0.585454\pi\)
\(350\) 0 0
\(351\) −3.70504 −0.197760
\(352\) 0 0
\(353\) −30.7124 −1.63466 −0.817329 0.576171i \(-0.804546\pi\)
−0.817329 + 0.576171i \(0.804546\pi\)
\(354\) 0 0
\(355\) −21.1283 −1.12137
\(356\) 0 0
\(357\) 19.6524 1.04012
\(358\) 0 0
\(359\) −35.5684 −1.87723 −0.938614 0.344968i \(-0.887890\pi\)
−0.938614 + 0.344968i \(0.887890\pi\)
\(360\) 0 0
\(361\) −17.0863 −0.899278
\(362\) 0 0
\(363\) −7.15833 −0.375715
\(364\) 0 0
\(365\) −25.0144 −1.30931
\(366\) 0 0
\(367\) −32.6083 −1.70214 −0.851070 0.525052i \(-0.824046\pi\)
−0.851070 + 0.525052i \(0.824046\pi\)
\(368\) 0 0
\(369\) −0.0415382 −0.00216239
\(370\) 0 0
\(371\) 24.9894 1.29739
\(372\) 0 0
\(373\) 31.6305 1.63777 0.818883 0.573961i \(-0.194594\pi\)
0.818883 + 0.573961i \(0.194594\pi\)
\(374\) 0 0
\(375\) −14.8815 −0.768475
\(376\) 0 0
\(377\) −2.99949 −0.154481
\(378\) 0 0
\(379\) −25.6286 −1.31645 −0.658227 0.752820i \(-0.728693\pi\)
−0.658227 + 0.752820i \(0.728693\pi\)
\(380\) 0 0
\(381\) −17.6921 −0.906394
\(382\) 0 0
\(383\) −29.2140 −1.49276 −0.746382 0.665518i \(-0.768211\pi\)
−0.746382 + 0.665518i \(0.768211\pi\)
\(384\) 0 0
\(385\) −14.2617 −0.726846
\(386\) 0 0
\(387\) −0.134400 −0.00683192
\(388\) 0 0
\(389\) −18.4995 −0.937962 −0.468981 0.883208i \(-0.655379\pi\)
−0.468981 + 0.883208i \(0.655379\pi\)
\(390\) 0 0
\(391\) 36.1808 1.82974
\(392\) 0 0
\(393\) 3.04274 0.153486
\(394\) 0 0
\(395\) −23.3982 −1.17729
\(396\) 0 0
\(397\) −3.21806 −0.161510 −0.0807550 0.996734i \(-0.525733\pi\)
−0.0807550 + 0.996734i \(0.525733\pi\)
\(398\) 0 0
\(399\) 5.05317 0.252975
\(400\) 0 0
\(401\) 28.4986 1.42315 0.711576 0.702609i \(-0.247982\pi\)
0.711576 + 0.702609i \(0.247982\pi\)
\(402\) 0 0
\(403\) 4.23523 0.210972
\(404\) 0 0
\(405\) −23.4142 −1.16346
\(406\) 0 0
\(407\) −19.6676 −0.974886
\(408\) 0 0
\(409\) 9.38723 0.464168 0.232084 0.972696i \(-0.425446\pi\)
0.232084 + 0.972696i \(0.425446\pi\)
\(410\) 0 0
\(411\) −26.1294 −1.28887
\(412\) 0 0
\(413\) −15.5528 −0.765303
\(414\) 0 0
\(415\) −11.0113 −0.540525
\(416\) 0 0
\(417\) 15.6153 0.764687
\(418\) 0 0
\(419\) 24.9405 1.21842 0.609211 0.793008i \(-0.291486\pi\)
0.609211 + 0.793008i \(0.291486\pi\)
\(420\) 0 0
\(421\) −30.2102 −1.47236 −0.736178 0.676788i \(-0.763371\pi\)
−0.736178 + 0.676788i \(0.763371\pi\)
\(422\) 0 0
\(423\) 0.132158 0.00642574
\(424\) 0 0
\(425\) −9.07955 −0.440423
\(426\) 0 0
\(427\) 3.09951 0.149996
\(428\) 0 0
\(429\) 3.25901 0.157346
\(430\) 0 0
\(431\) 36.8695 1.77594 0.887970 0.459902i \(-0.152116\pi\)
0.887970 + 0.459902i \(0.152116\pi\)
\(432\) 0 0
\(433\) −18.5932 −0.893530 −0.446765 0.894651i \(-0.647424\pi\)
−0.446765 + 0.894651i \(0.647424\pi\)
\(434\) 0 0
\(435\) −18.8415 −0.903383
\(436\) 0 0
\(437\) 9.30306 0.445026
\(438\) 0 0
\(439\) 5.25442 0.250780 0.125390 0.992108i \(-0.459982\pi\)
0.125390 + 0.992108i \(0.459982\pi\)
\(440\) 0 0
\(441\) −0.0467653 −0.00222692
\(442\) 0 0
\(443\) −16.1896 −0.769190 −0.384595 0.923085i \(-0.625659\pi\)
−0.384595 + 0.923085i \(0.625659\pi\)
\(444\) 0 0
\(445\) 23.4194 1.11019
\(446\) 0 0
\(447\) 32.8313 1.55287
\(448\) 0 0
\(449\) −0.629326 −0.0296997 −0.0148499 0.999890i \(-0.504727\pi\)
−0.0148499 + 0.999890i \(0.504727\pi\)
\(450\) 0 0
\(451\) −6.00853 −0.282931
\(452\) 0 0
\(453\) −30.6026 −1.43783
\(454\) 0 0
\(455\) −3.88891 −0.182315
\(456\) 0 0
\(457\) 13.6403 0.638066 0.319033 0.947744i \(-0.396642\pi\)
0.319033 + 0.947744i \(0.396642\pi\)
\(458\) 0 0
\(459\) 27.8707 1.30089
\(460\) 0 0
\(461\) 13.8122 0.643298 0.321649 0.946859i \(-0.395763\pi\)
0.321649 + 0.946859i \(0.395763\pi\)
\(462\) 0 0
\(463\) −6.86831 −0.319197 −0.159599 0.987182i \(-0.551020\pi\)
−0.159599 + 0.987182i \(0.551020\pi\)
\(464\) 0 0
\(465\) 26.6040 1.23373
\(466\) 0 0
\(467\) −1.48619 −0.0687728 −0.0343864 0.999409i \(-0.510948\pi\)
−0.0343864 + 0.999409i \(0.510948\pi\)
\(468\) 0 0
\(469\) −9.37637 −0.432960
\(470\) 0 0
\(471\) 38.1550 1.75809
\(472\) 0 0
\(473\) −19.4410 −0.893900
\(474\) 0 0
\(475\) −2.33460 −0.107119
\(476\) 0 0
\(477\) −0.215506 −0.00986733
\(478\) 0 0
\(479\) 0.419481 0.0191666 0.00958329 0.999954i \(-0.496949\pi\)
0.00958329 + 0.999954i \(0.496949\pi\)
\(480\) 0 0
\(481\) −5.36297 −0.244531
\(482\) 0 0
\(483\) 24.5648 1.11774
\(484\) 0 0
\(485\) 20.9088 0.949422
\(486\) 0 0
\(487\) 25.9633 1.17651 0.588255 0.808676i \(-0.299815\pi\)
0.588255 + 0.808676i \(0.299815\pi\)
\(488\) 0 0
\(489\) 37.2943 1.68651
\(490\) 0 0
\(491\) 36.8094 1.66119 0.830594 0.556879i \(-0.188001\pi\)
0.830594 + 0.556879i \(0.188001\pi\)
\(492\) 0 0
\(493\) 22.5633 1.01620
\(494\) 0 0
\(495\) 0.122992 0.00552807
\(496\) 0 0
\(497\) 17.1785 0.770561
\(498\) 0 0
\(499\) −2.13357 −0.0955116 −0.0477558 0.998859i \(-0.515207\pi\)
−0.0477558 + 0.998859i \(0.515207\pi\)
\(500\) 0 0
\(501\) −3.80364 −0.169934
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 48.6228 2.16369
\(506\) 0 0
\(507\) −21.6959 −0.963550
\(508\) 0 0
\(509\) −30.2938 −1.34275 −0.671375 0.741118i \(-0.734296\pi\)
−0.671375 + 0.741118i \(0.734296\pi\)
\(510\) 0 0
\(511\) 20.3381 0.899706
\(512\) 0 0
\(513\) 7.16632 0.316401
\(514\) 0 0
\(515\) −3.10989 −0.137038
\(516\) 0 0
\(517\) 19.1168 0.840755
\(518\) 0 0
\(519\) 4.49771 0.197427
\(520\) 0 0
\(521\) −27.1463 −1.18930 −0.594650 0.803985i \(-0.702709\pi\)
−0.594650 + 0.803985i \(0.702709\pi\)
\(522\) 0 0
\(523\) −21.3731 −0.934580 −0.467290 0.884104i \(-0.654770\pi\)
−0.467290 + 0.884104i \(0.654770\pi\)
\(524\) 0 0
\(525\) −6.16452 −0.269042
\(526\) 0 0
\(527\) −31.8591 −1.38780
\(528\) 0 0
\(529\) 22.2246 0.966287
\(530\) 0 0
\(531\) 0.134126 0.00582056
\(532\) 0 0
\(533\) −1.63841 −0.0709675
\(534\) 0 0
\(535\) 42.9365 1.85631
\(536\) 0 0
\(537\) 25.7275 1.11022
\(538\) 0 0
\(539\) −6.76464 −0.291374
\(540\) 0 0
\(541\) 29.9286 1.28673 0.643366 0.765559i \(-0.277537\pi\)
0.643366 + 0.765559i \(0.277537\pi\)
\(542\) 0 0
\(543\) −46.1448 −1.98026
\(544\) 0 0
\(545\) 28.2613 1.21058
\(546\) 0 0
\(547\) 29.9207 1.27931 0.639657 0.768660i \(-0.279076\pi\)
0.639657 + 0.768660i \(0.279076\pi\)
\(548\) 0 0
\(549\) −0.0267298 −0.00114080
\(550\) 0 0
\(551\) 5.80163 0.247158
\(552\) 0 0
\(553\) 19.0241 0.808986
\(554\) 0 0
\(555\) −33.6880 −1.42998
\(556\) 0 0
\(557\) −13.2317 −0.560644 −0.280322 0.959906i \(-0.590441\pi\)
−0.280322 + 0.959906i \(0.590441\pi\)
\(558\) 0 0
\(559\) −5.30120 −0.224217
\(560\) 0 0
\(561\) −24.5155 −1.03505
\(562\) 0 0
\(563\) −15.4871 −0.652701 −0.326351 0.945249i \(-0.605819\pi\)
−0.326351 + 0.945249i \(0.605819\pi\)
\(564\) 0 0
\(565\) −47.9019 −2.01525
\(566\) 0 0
\(567\) 19.0371 0.799482
\(568\) 0 0
\(569\) 16.7971 0.704170 0.352085 0.935968i \(-0.385473\pi\)
0.352085 + 0.935968i \(0.385473\pi\)
\(570\) 0 0
\(571\) 30.2291 1.26505 0.632525 0.774540i \(-0.282018\pi\)
0.632525 + 0.774540i \(0.282018\pi\)
\(572\) 0 0
\(573\) 13.2825 0.554883
\(574\) 0 0
\(575\) −11.3491 −0.473290
\(576\) 0 0
\(577\) 1.03748 0.0431910 0.0215955 0.999767i \(-0.493125\pi\)
0.0215955 + 0.999767i \(0.493125\pi\)
\(578\) 0 0
\(579\) 32.4415 1.34822
\(580\) 0 0
\(581\) 8.95283 0.371426
\(582\) 0 0
\(583\) −31.1731 −1.29106
\(584\) 0 0
\(585\) 0.0335375 0.00138660
\(586\) 0 0
\(587\) 26.9328 1.11164 0.555818 0.831304i \(-0.312405\pi\)
0.555818 + 0.831304i \(0.312405\pi\)
\(588\) 0 0
\(589\) −8.19183 −0.337538
\(590\) 0 0
\(591\) −41.4254 −1.70401
\(592\) 0 0
\(593\) 8.67227 0.356127 0.178064 0.984019i \(-0.443017\pi\)
0.178064 + 0.984019i \(0.443017\pi\)
\(594\) 0 0
\(595\) 29.2539 1.19929
\(596\) 0 0
\(597\) 37.4663 1.53339
\(598\) 0 0
\(599\) −7.03128 −0.287290 −0.143645 0.989629i \(-0.545882\pi\)
−0.143645 + 0.989629i \(0.545882\pi\)
\(600\) 0 0
\(601\) 16.9913 0.693088 0.346544 0.938034i \(-0.387355\pi\)
0.346544 + 0.938034i \(0.387355\pi\)
\(602\) 0 0
\(603\) 0.0808607 0.00329290
\(604\) 0 0
\(605\) −10.6556 −0.433212
\(606\) 0 0
\(607\) −33.6055 −1.36400 −0.682002 0.731350i \(-0.738890\pi\)
−0.682002 + 0.731350i \(0.738890\pi\)
\(608\) 0 0
\(609\) 15.3192 0.620767
\(610\) 0 0
\(611\) 5.21278 0.210887
\(612\) 0 0
\(613\) −41.5746 −1.67918 −0.839591 0.543219i \(-0.817205\pi\)
−0.839591 + 0.543219i \(0.817205\pi\)
\(614\) 0 0
\(615\) −10.2918 −0.415007
\(616\) 0 0
\(617\) 10.0211 0.403434 0.201717 0.979444i \(-0.435348\pi\)
0.201717 + 0.979444i \(0.435348\pi\)
\(618\) 0 0
\(619\) 10.8542 0.436267 0.218133 0.975919i \(-0.430003\pi\)
0.218133 + 0.975919i \(0.430003\pi\)
\(620\) 0 0
\(621\) 34.8373 1.39797
\(622\) 0 0
\(623\) −19.0413 −0.762874
\(624\) 0 0
\(625\) −30.5900 −1.22360
\(626\) 0 0
\(627\) −6.30360 −0.251741
\(628\) 0 0
\(629\) 40.3424 1.60856
\(630\) 0 0
\(631\) −18.4761 −0.735524 −0.367762 0.929920i \(-0.619876\pi\)
−0.367762 + 0.929920i \(0.619876\pi\)
\(632\) 0 0
\(633\) 22.7643 0.904800
\(634\) 0 0
\(635\) −26.3358 −1.04510
\(636\) 0 0
\(637\) −1.84459 −0.0730853
\(638\) 0 0
\(639\) −0.148145 −0.00586054
\(640\) 0 0
\(641\) 0.947579 0.0374271 0.0187136 0.999825i \(-0.494043\pi\)
0.0187136 + 0.999825i \(0.494043\pi\)
\(642\) 0 0
\(643\) 22.9716 0.905913 0.452956 0.891533i \(-0.350369\pi\)
0.452956 + 0.891533i \(0.350369\pi\)
\(644\) 0 0
\(645\) −33.2999 −1.31118
\(646\) 0 0
\(647\) −29.7014 −1.16768 −0.583842 0.811868i \(-0.698451\pi\)
−0.583842 + 0.811868i \(0.698451\pi\)
\(648\) 0 0
\(649\) 19.4014 0.761571
\(650\) 0 0
\(651\) −21.6306 −0.847768
\(652\) 0 0
\(653\) 42.3223 1.65620 0.828099 0.560581i \(-0.189422\pi\)
0.828099 + 0.560581i \(0.189422\pi\)
\(654\) 0 0
\(655\) 4.52930 0.176974
\(656\) 0 0
\(657\) −0.175394 −0.00684276
\(658\) 0 0
\(659\) −15.9106 −0.619789 −0.309895 0.950771i \(-0.600294\pi\)
−0.309895 + 0.950771i \(0.600294\pi\)
\(660\) 0 0
\(661\) 0.347986 0.0135351 0.00676755 0.999977i \(-0.497846\pi\)
0.00676755 + 0.999977i \(0.497846\pi\)
\(662\) 0 0
\(663\) −6.68491 −0.259620
\(664\) 0 0
\(665\) 7.52195 0.291689
\(666\) 0 0
\(667\) 28.2032 1.09203
\(668\) 0 0
\(669\) −12.1728 −0.470627
\(670\) 0 0
\(671\) −3.86649 −0.149264
\(672\) 0 0
\(673\) 18.8705 0.727406 0.363703 0.931515i \(-0.381512\pi\)
0.363703 + 0.931515i \(0.381512\pi\)
\(674\) 0 0
\(675\) −8.74241 −0.336495
\(676\) 0 0
\(677\) 15.1564 0.582508 0.291254 0.956646i \(-0.405928\pi\)
0.291254 + 0.956646i \(0.405928\pi\)
\(678\) 0 0
\(679\) −17.0001 −0.652403
\(680\) 0 0
\(681\) 20.1809 0.773332
\(682\) 0 0
\(683\) −39.5457 −1.51318 −0.756588 0.653892i \(-0.773135\pi\)
−0.756588 + 0.653892i \(0.773135\pi\)
\(684\) 0 0
\(685\) −38.8953 −1.48611
\(686\) 0 0
\(687\) −33.3642 −1.27292
\(688\) 0 0
\(689\) −8.50031 −0.323836
\(690\) 0 0
\(691\) 33.2527 1.26499 0.632495 0.774564i \(-0.282031\pi\)
0.632495 + 0.774564i \(0.282031\pi\)
\(692\) 0 0
\(693\) −0.0999992 −0.00379866
\(694\) 0 0
\(695\) 23.2444 0.881710
\(696\) 0 0
\(697\) 12.3248 0.466834
\(698\) 0 0
\(699\) 4.61848 0.174687
\(700\) 0 0
\(701\) 38.7601 1.46395 0.731975 0.681331i \(-0.238599\pi\)
0.731975 + 0.681331i \(0.238599\pi\)
\(702\) 0 0
\(703\) 10.3731 0.391229
\(704\) 0 0
\(705\) 32.7445 1.23323
\(706\) 0 0
\(707\) −39.5331 −1.48680
\(708\) 0 0
\(709\) 30.6093 1.14956 0.574778 0.818310i \(-0.305089\pi\)
0.574778 + 0.818310i \(0.305089\pi\)
\(710\) 0 0
\(711\) −0.164061 −0.00615279
\(712\) 0 0
\(713\) −39.8226 −1.49137
\(714\) 0 0
\(715\) 4.85123 0.181426
\(716\) 0 0
\(717\) 16.9939 0.634650
\(718\) 0 0
\(719\) −51.1073 −1.90598 −0.952990 0.303002i \(-0.902011\pi\)
−0.952990 + 0.303002i \(0.902011\pi\)
\(720\) 0 0
\(721\) 2.52851 0.0941668
\(722\) 0 0
\(723\) 24.6428 0.916475
\(724\) 0 0
\(725\) −7.07758 −0.262855
\(726\) 0 0
\(727\) −2.23928 −0.0830505 −0.0415252 0.999137i \(-0.513222\pi\)
−0.0415252 + 0.999137i \(0.513222\pi\)
\(728\) 0 0
\(729\) 26.8348 0.993883
\(730\) 0 0
\(731\) 39.8777 1.47493
\(732\) 0 0
\(733\) 2.66853 0.0985643 0.0492821 0.998785i \(-0.484307\pi\)
0.0492821 + 0.998785i \(0.484307\pi\)
\(734\) 0 0
\(735\) −11.5869 −0.427391
\(736\) 0 0
\(737\) 11.6966 0.430849
\(738\) 0 0
\(739\) −23.9717 −0.881815 −0.440907 0.897553i \(-0.645343\pi\)
−0.440907 + 0.897553i \(0.645343\pi\)
\(740\) 0 0
\(741\) −1.71887 −0.0631443
\(742\) 0 0
\(743\) 6.79980 0.249460 0.124730 0.992191i \(-0.460193\pi\)
0.124730 + 0.992191i \(0.460193\pi\)
\(744\) 0 0
\(745\) 48.8713 1.79051
\(746\) 0 0
\(747\) −0.0772082 −0.00282490
\(748\) 0 0
\(749\) −34.9098 −1.27558
\(750\) 0 0
\(751\) 28.4576 1.03843 0.519217 0.854642i \(-0.326224\pi\)
0.519217 + 0.854642i \(0.326224\pi\)
\(752\) 0 0
\(753\) −12.6638 −0.461495
\(754\) 0 0
\(755\) −45.5538 −1.65787
\(756\) 0 0
\(757\) −25.9573 −0.943434 −0.471717 0.881750i \(-0.656366\pi\)
−0.471717 + 0.881750i \(0.656366\pi\)
\(758\) 0 0
\(759\) −30.6434 −1.11229
\(760\) 0 0
\(761\) −38.7281 −1.40389 −0.701946 0.712230i \(-0.747685\pi\)
−0.701946 + 0.712230i \(0.747685\pi\)
\(762\) 0 0
\(763\) −22.9781 −0.831862
\(764\) 0 0
\(765\) −0.252282 −0.00912127
\(766\) 0 0
\(767\) 5.29039 0.191025
\(768\) 0 0
\(769\) −31.1088 −1.12181 −0.560906 0.827879i \(-0.689547\pi\)
−0.560906 + 0.827879i \(0.689547\pi\)
\(770\) 0 0
\(771\) −42.3567 −1.52544
\(772\) 0 0
\(773\) 38.9856 1.40222 0.701108 0.713055i \(-0.252689\pi\)
0.701108 + 0.713055i \(0.252689\pi\)
\(774\) 0 0
\(775\) 9.99345 0.358975
\(776\) 0 0
\(777\) 27.3903 0.982620
\(778\) 0 0
\(779\) 3.16903 0.113542
\(780\) 0 0
\(781\) −21.4294 −0.766803
\(782\) 0 0
\(783\) 21.7255 0.776405
\(784\) 0 0
\(785\) 56.7961 2.02714
\(786\) 0 0
\(787\) 9.31965 0.332210 0.166105 0.986108i \(-0.446881\pi\)
0.166105 + 0.986108i \(0.446881\pi\)
\(788\) 0 0
\(789\) −19.0470 −0.678092
\(790\) 0 0
\(791\) 38.9470 1.38480
\(792\) 0 0
\(793\) −1.05432 −0.0374399
\(794\) 0 0
\(795\) −53.3954 −1.89374
\(796\) 0 0
\(797\) −6.06555 −0.214853 −0.107426 0.994213i \(-0.534261\pi\)
−0.107426 + 0.994213i \(0.534261\pi\)
\(798\) 0 0
\(799\) −39.2126 −1.38724
\(800\) 0 0
\(801\) 0.164210 0.00580208
\(802\) 0 0
\(803\) −25.3709 −0.895319
\(804\) 0 0
\(805\) 36.5662 1.28879
\(806\) 0 0
\(807\) 11.6871 0.411405
\(808\) 0 0
\(809\) −10.5655 −0.371463 −0.185732 0.982601i \(-0.559466\pi\)
−0.185732 + 0.982601i \(0.559466\pi\)
\(810\) 0 0
\(811\) −29.8315 −1.04752 −0.523762 0.851865i \(-0.675472\pi\)
−0.523762 + 0.851865i \(0.675472\pi\)
\(812\) 0 0
\(813\) 11.4310 0.400902
\(814\) 0 0
\(815\) 55.5149 1.94460
\(816\) 0 0
\(817\) 10.2536 0.358729
\(818\) 0 0
\(819\) −0.0272679 −0.000952817 0
\(820\) 0 0
\(821\) −23.0775 −0.805409 −0.402705 0.915330i \(-0.631930\pi\)
−0.402705 + 0.915330i \(0.631930\pi\)
\(822\) 0 0
\(823\) −5.76982 −0.201123 −0.100562 0.994931i \(-0.532064\pi\)
−0.100562 + 0.994931i \(0.532064\pi\)
\(824\) 0 0
\(825\) 7.68994 0.267730
\(826\) 0 0
\(827\) 6.15648 0.214082 0.107041 0.994255i \(-0.465862\pi\)
0.107041 + 0.994255i \(0.465862\pi\)
\(828\) 0 0
\(829\) −20.9851 −0.728842 −0.364421 0.931234i \(-0.618733\pi\)
−0.364421 + 0.931234i \(0.618733\pi\)
\(830\) 0 0
\(831\) 9.81856 0.340602
\(832\) 0 0
\(833\) 13.8757 0.480765
\(834\) 0 0
\(835\) −5.66195 −0.195940
\(836\) 0 0
\(837\) −30.6761 −1.06032
\(838\) 0 0
\(839\) −32.9640 −1.13804 −0.569022 0.822323i \(-0.692678\pi\)
−0.569022 + 0.822323i \(0.692678\pi\)
\(840\) 0 0
\(841\) −11.4117 −0.393508
\(842\) 0 0
\(843\) 11.2796 0.388491
\(844\) 0 0
\(845\) −32.2957 −1.11101
\(846\) 0 0
\(847\) 8.66361 0.297685
\(848\) 0 0
\(849\) 26.7486 0.918008
\(850\) 0 0
\(851\) 50.4264 1.72859
\(852\) 0 0
\(853\) −46.8181 −1.60302 −0.801511 0.597980i \(-0.795970\pi\)
−0.801511 + 0.597980i \(0.795970\pi\)
\(854\) 0 0
\(855\) −0.0648685 −0.00221846
\(856\) 0 0
\(857\) −21.3371 −0.728861 −0.364430 0.931231i \(-0.618736\pi\)
−0.364430 + 0.931231i \(0.618736\pi\)
\(858\) 0 0
\(859\) 3.48916 0.119049 0.0595243 0.998227i \(-0.481042\pi\)
0.0595243 + 0.998227i \(0.481042\pi\)
\(860\) 0 0
\(861\) 8.36784 0.285175
\(862\) 0 0
\(863\) −37.4202 −1.27380 −0.636900 0.770947i \(-0.719783\pi\)
−0.636900 + 0.770947i \(0.719783\pi\)
\(864\) 0 0
\(865\) 6.69511 0.227641
\(866\) 0 0
\(867\) 20.7528 0.704801
\(868\) 0 0
\(869\) −23.7316 −0.805041
\(870\) 0 0
\(871\) 3.18943 0.108070
\(872\) 0 0
\(873\) 0.146607 0.00496189
\(874\) 0 0
\(875\) 18.0108 0.608876
\(876\) 0 0
\(877\) 27.9015 0.942166 0.471083 0.882089i \(-0.343863\pi\)
0.471083 + 0.882089i \(0.343863\pi\)
\(878\) 0 0
\(879\) −44.0942 −1.48726
\(880\) 0 0
\(881\) −40.3310 −1.35879 −0.679393 0.733775i \(-0.737757\pi\)
−0.679393 + 0.733775i \(0.737757\pi\)
\(882\) 0 0
\(883\) −52.3288 −1.76100 −0.880502 0.474043i \(-0.842794\pi\)
−0.880502 + 0.474043i \(0.842794\pi\)
\(884\) 0 0
\(885\) 33.2320 1.11708
\(886\) 0 0
\(887\) −28.4277 −0.954510 −0.477255 0.878765i \(-0.658368\pi\)
−0.477255 + 0.878765i \(0.658368\pi\)
\(888\) 0 0
\(889\) 21.4125 0.718152
\(890\) 0 0
\(891\) −23.7479 −0.795583
\(892\) 0 0
\(893\) −10.0826 −0.337401
\(894\) 0 0
\(895\) 38.2970 1.28013
\(896\) 0 0
\(897\) −8.35587 −0.278995
\(898\) 0 0
\(899\) −24.8344 −0.828274
\(900\) 0 0
\(901\) 63.9426 2.13024
\(902\) 0 0
\(903\) 27.0747 0.900991
\(904\) 0 0
\(905\) −68.6893 −2.28331
\(906\) 0 0
\(907\) −48.2852 −1.60328 −0.801641 0.597805i \(-0.796040\pi\)
−0.801641 + 0.597805i \(0.796040\pi\)
\(908\) 0 0
\(909\) 0.340929 0.0113079
\(910\) 0 0
\(911\) 19.7120 0.653087 0.326543 0.945182i \(-0.394116\pi\)
0.326543 + 0.945182i \(0.394116\pi\)
\(912\) 0 0
\(913\) −11.1682 −0.369615
\(914\) 0 0
\(915\) −6.62279 −0.218943
\(916\) 0 0
\(917\) −3.68258 −0.121609
\(918\) 0 0
\(919\) −28.4127 −0.937248 −0.468624 0.883398i \(-0.655250\pi\)
−0.468624 + 0.883398i \(0.655250\pi\)
\(920\) 0 0
\(921\) −43.3455 −1.42828
\(922\) 0 0
\(923\) −5.84338 −0.192337
\(924\) 0 0
\(925\) −12.6545 −0.416076
\(926\) 0 0
\(927\) −0.0218056 −0.000716190 0
\(928\) 0 0
\(929\) −53.6116 −1.75894 −0.879470 0.475954i \(-0.842103\pi\)
−0.879470 + 0.475954i \(0.842103\pi\)
\(930\) 0 0
\(931\) 3.56782 0.116931
\(932\) 0 0
\(933\) −16.2978 −0.533567
\(934\) 0 0
\(935\) −36.4928 −1.19344
\(936\) 0 0
\(937\) 37.8601 1.23684 0.618418 0.785849i \(-0.287774\pi\)
0.618418 + 0.785849i \(0.287774\pi\)
\(938\) 0 0
\(939\) −12.6436 −0.412610
\(940\) 0 0
\(941\) −56.8829 −1.85433 −0.927165 0.374652i \(-0.877762\pi\)
−0.927165 + 0.374652i \(0.877762\pi\)
\(942\) 0 0
\(943\) 15.4055 0.501671
\(944\) 0 0
\(945\) 28.1676 0.916292
\(946\) 0 0
\(947\) −0.601397 −0.0195428 −0.00977140 0.999952i \(-0.503110\pi\)
−0.00977140 + 0.999952i \(0.503110\pi\)
\(948\) 0 0
\(949\) −6.91815 −0.224573
\(950\) 0 0
\(951\) 8.15883 0.264568
\(952\) 0 0
\(953\) −11.9862 −0.388270 −0.194135 0.980975i \(-0.562190\pi\)
−0.194135 + 0.980975i \(0.562190\pi\)
\(954\) 0 0
\(955\) 19.7718 0.639799
\(956\) 0 0
\(957\) −19.1100 −0.617740
\(958\) 0 0
\(959\) 31.6240 1.02119
\(960\) 0 0
\(961\) 4.06584 0.131156
\(962\) 0 0
\(963\) 0.301058 0.00970146
\(964\) 0 0
\(965\) 48.2911 1.55455
\(966\) 0 0
\(967\) −40.9121 −1.31564 −0.657822 0.753173i \(-0.728522\pi\)
−0.657822 + 0.753173i \(0.728522\pi\)
\(968\) 0 0
\(969\) 12.9300 0.415372
\(970\) 0 0
\(971\) 55.2770 1.77392 0.886962 0.461842i \(-0.152811\pi\)
0.886962 + 0.461842i \(0.152811\pi\)
\(972\) 0 0
\(973\) −18.8990 −0.605874
\(974\) 0 0
\(975\) 2.09690 0.0671546
\(976\) 0 0
\(977\) 13.0269 0.416767 0.208384 0.978047i \(-0.433180\pi\)
0.208384 + 0.978047i \(0.433180\pi\)
\(978\) 0 0
\(979\) 23.7531 0.759154
\(980\) 0 0
\(981\) 0.198160 0.00632677
\(982\) 0 0
\(983\) −45.8814 −1.46339 −0.731695 0.681632i \(-0.761270\pi\)
−0.731695 + 0.681632i \(0.761270\pi\)
\(984\) 0 0
\(985\) −61.6642 −1.96478
\(986\) 0 0
\(987\) −26.6232 −0.847425
\(988\) 0 0
\(989\) 49.8455 1.58500
\(990\) 0 0
\(991\) −50.5955 −1.60722 −0.803609 0.595158i \(-0.797090\pi\)
−0.803609 + 0.595158i \(0.797090\pi\)
\(992\) 0 0
\(993\) 33.5477 1.06460
\(994\) 0 0
\(995\) 55.7708 1.76805
\(996\) 0 0
\(997\) 42.6441 1.35055 0.675276 0.737565i \(-0.264025\pi\)
0.675276 + 0.737565i \(0.264025\pi\)
\(998\) 0 0
\(999\) 38.8444 1.22898
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 \(a_p\))