Properties

Label 6008.2.a.e.1.36
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(50\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.36
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.83858 q^{3} +4.41353 q^{5} +3.19108 q^{7} +0.380391 q^{9} +O(q^{10})\) \(q+1.83858 q^{3} +4.41353 q^{5} +3.19108 q^{7} +0.380391 q^{9} -5.76845 q^{11} +6.18779 q^{13} +8.11464 q^{15} +2.08881 q^{17} +2.76564 q^{19} +5.86706 q^{21} +0.206321 q^{23} +14.4792 q^{25} -4.81637 q^{27} +3.05541 q^{29} +5.45060 q^{31} -10.6058 q^{33} +14.0839 q^{35} -5.94239 q^{37} +11.3768 q^{39} -4.72190 q^{41} -1.65760 q^{43} +1.67887 q^{45} -6.83514 q^{47} +3.18297 q^{49} +3.84045 q^{51} +8.67166 q^{53} -25.4592 q^{55} +5.08486 q^{57} -10.8182 q^{59} -6.58965 q^{61} +1.21386 q^{63} +27.3100 q^{65} -7.21819 q^{67} +0.379338 q^{69} -16.6430 q^{71} +11.4742 q^{73} +26.6213 q^{75} -18.4076 q^{77} -9.03959 q^{79} -9.99648 q^{81} +6.69813 q^{83} +9.21901 q^{85} +5.61763 q^{87} -7.60669 q^{89} +19.7457 q^{91} +10.0214 q^{93} +12.2062 q^{95} -0.349298 q^{97} -2.19426 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) 1.83858 1.06151 0.530753 0.847526i \(-0.321909\pi\)
0.530753 + 0.847526i \(0.321909\pi\)
\(4\) 0 0
\(5\) 4.41353 1.97379 0.986895 0.161363i \(-0.0515889\pi\)
0.986895 + 0.161363i \(0.0515889\pi\)
\(6\) 0 0
\(7\) 3.19108 1.20611 0.603057 0.797698i \(-0.293949\pi\)
0.603057 + 0.797698i \(0.293949\pi\)
\(8\) 0 0
\(9\) 0.380391 0.126797
\(10\) 0 0
\(11\) −5.76845 −1.73925 −0.869626 0.493711i \(-0.835640\pi\)
−0.869626 + 0.493711i \(0.835640\pi\)
\(12\) 0 0
\(13\) 6.18779 1.71618 0.858092 0.513495i \(-0.171650\pi\)
0.858092 + 0.513495i \(0.171650\pi\)
\(14\) 0 0
\(15\) 8.11464 2.09519
\(16\) 0 0
\(17\) 2.08881 0.506610 0.253305 0.967386i \(-0.418482\pi\)
0.253305 + 0.967386i \(0.418482\pi\)
\(18\) 0 0
\(19\) 2.76564 0.634481 0.317240 0.948345i \(-0.397244\pi\)
0.317240 + 0.948345i \(0.397244\pi\)
\(20\) 0 0
\(21\) 5.86706 1.28030
\(22\) 0 0
\(23\) 0.206321 0.0430209 0.0215104 0.999769i \(-0.493152\pi\)
0.0215104 + 0.999769i \(0.493152\pi\)
\(24\) 0 0
\(25\) 14.4792 2.89585
\(26\) 0 0
\(27\) −4.81637 −0.926911
\(28\) 0 0
\(29\) 3.05541 0.567376 0.283688 0.958917i \(-0.408442\pi\)
0.283688 + 0.958917i \(0.408442\pi\)
\(30\) 0 0
\(31\) 5.45060 0.978957 0.489478 0.872015i \(-0.337187\pi\)
0.489478 + 0.872015i \(0.337187\pi\)
\(32\) 0 0
\(33\) −10.6058 −1.84623
\(34\) 0 0
\(35\) 14.0839 2.38062
\(36\) 0 0
\(37\) −5.94239 −0.976923 −0.488461 0.872586i \(-0.662442\pi\)
−0.488461 + 0.872586i \(0.662442\pi\)
\(38\) 0 0
\(39\) 11.3768 1.82174
\(40\) 0 0
\(41\) −4.72190 −0.737437 −0.368719 0.929541i \(-0.620203\pi\)
−0.368719 + 0.929541i \(0.620203\pi\)
\(42\) 0 0
\(43\) −1.65760 −0.252781 −0.126391 0.991981i \(-0.540339\pi\)
−0.126391 + 0.991981i \(0.540339\pi\)
\(44\) 0 0
\(45\) 1.67887 0.250271
\(46\) 0 0
\(47\) −6.83514 −0.997008 −0.498504 0.866888i \(-0.666117\pi\)
−0.498504 + 0.866888i \(0.666117\pi\)
\(48\) 0 0
\(49\) 3.18297 0.454710
\(50\) 0 0
\(51\) 3.84045 0.537770
\(52\) 0 0
\(53\) 8.67166 1.19114 0.595572 0.803302i \(-0.296925\pi\)
0.595572 + 0.803302i \(0.296925\pi\)
\(54\) 0 0
\(55\) −25.4592 −3.43292
\(56\) 0 0
\(57\) 5.08486 0.673506
\(58\) 0 0
\(59\) −10.8182 −1.40841 −0.704207 0.709995i \(-0.748697\pi\)
−0.704207 + 0.709995i \(0.748697\pi\)
\(60\) 0 0
\(61\) −6.58965 −0.843718 −0.421859 0.906662i \(-0.638622\pi\)
−0.421859 + 0.906662i \(0.638622\pi\)
\(62\) 0 0
\(63\) 1.21386 0.152931
\(64\) 0 0
\(65\) 27.3100 3.38739
\(66\) 0 0
\(67\) −7.21819 −0.881842 −0.440921 0.897546i \(-0.645348\pi\)
−0.440921 + 0.897546i \(0.645348\pi\)
\(68\) 0 0
\(69\) 0.379338 0.0456669
\(70\) 0 0
\(71\) −16.6430 −1.97516 −0.987582 0.157104i \(-0.949784\pi\)
−0.987582 + 0.157104i \(0.949784\pi\)
\(72\) 0 0
\(73\) 11.4742 1.34295 0.671475 0.741028i \(-0.265661\pi\)
0.671475 + 0.741028i \(0.265661\pi\)
\(74\) 0 0
\(75\) 26.6213 3.07396
\(76\) 0 0
\(77\) −18.4076 −2.09774
\(78\) 0 0
\(79\) −9.03959 −1.01703 −0.508517 0.861052i \(-0.669806\pi\)
−0.508517 + 0.861052i \(0.669806\pi\)
\(80\) 0 0
\(81\) −9.99648 −1.11072
\(82\) 0 0
\(83\) 6.69813 0.735215 0.367608 0.929981i \(-0.380177\pi\)
0.367608 + 0.929981i \(0.380177\pi\)
\(84\) 0 0
\(85\) 9.21901 0.999942
\(86\) 0 0
\(87\) 5.61763 0.602273
\(88\) 0 0
\(89\) −7.60669 −0.806308 −0.403154 0.915132i \(-0.632086\pi\)
−0.403154 + 0.915132i \(0.632086\pi\)
\(90\) 0 0
\(91\) 19.7457 2.06991
\(92\) 0 0
\(93\) 10.0214 1.03917
\(94\) 0 0
\(95\) 12.2062 1.25233
\(96\) 0 0
\(97\) −0.349298 −0.0354659 −0.0177329 0.999843i \(-0.505645\pi\)
−0.0177329 + 0.999843i \(0.505645\pi\)
\(98\) 0 0
\(99\) −2.19426 −0.220532
\(100\) 0 0
\(101\) 2.79592 0.278204 0.139102 0.990278i \(-0.455578\pi\)
0.139102 + 0.990278i \(0.455578\pi\)
\(102\) 0 0
\(103\) 11.0391 1.08772 0.543859 0.839176i \(-0.316962\pi\)
0.543859 + 0.839176i \(0.316962\pi\)
\(104\) 0 0
\(105\) 25.8945 2.52704
\(106\) 0 0
\(107\) −3.67417 −0.355196 −0.177598 0.984103i \(-0.556833\pi\)
−0.177598 + 0.984103i \(0.556833\pi\)
\(108\) 0 0
\(109\) −12.6464 −1.21130 −0.605651 0.795730i \(-0.707087\pi\)
−0.605651 + 0.795730i \(0.707087\pi\)
\(110\) 0 0
\(111\) −10.9256 −1.03701
\(112\) 0 0
\(113\) −12.5845 −1.18385 −0.591926 0.805993i \(-0.701632\pi\)
−0.591926 + 0.805993i \(0.701632\pi\)
\(114\) 0 0
\(115\) 0.910603 0.0849141
\(116\) 0 0
\(117\) 2.35378 0.217607
\(118\) 0 0
\(119\) 6.66554 0.611029
\(120\) 0 0
\(121\) 22.2750 2.02500
\(122\) 0 0
\(123\) −8.68161 −0.782795
\(124\) 0 0
\(125\) 41.8369 3.74201
\(126\) 0 0
\(127\) 0.372511 0.0330550 0.0165275 0.999863i \(-0.494739\pi\)
0.0165275 + 0.999863i \(0.494739\pi\)
\(128\) 0 0
\(129\) −3.04763 −0.268329
\(130\) 0 0
\(131\) −4.66689 −0.407748 −0.203874 0.978997i \(-0.565353\pi\)
−0.203874 + 0.978997i \(0.565353\pi\)
\(132\) 0 0
\(133\) 8.82536 0.765256
\(134\) 0 0
\(135\) −21.2572 −1.82953
\(136\) 0 0
\(137\) −4.51917 −0.386099 −0.193049 0.981189i \(-0.561838\pi\)
−0.193049 + 0.981189i \(0.561838\pi\)
\(138\) 0 0
\(139\) 15.4332 1.30902 0.654512 0.756051i \(-0.272874\pi\)
0.654512 + 0.756051i \(0.272874\pi\)
\(140\) 0 0
\(141\) −12.5670 −1.05833
\(142\) 0 0
\(143\) −35.6940 −2.98488
\(144\) 0 0
\(145\) 13.4851 1.11988
\(146\) 0 0
\(147\) 5.85216 0.482678
\(148\) 0 0
\(149\) −18.5931 −1.52321 −0.761603 0.648044i \(-0.775587\pi\)
−0.761603 + 0.648044i \(0.775587\pi\)
\(150\) 0 0
\(151\) −0.643894 −0.0523994 −0.0261997 0.999657i \(-0.508341\pi\)
−0.0261997 + 0.999657i \(0.508341\pi\)
\(152\) 0 0
\(153\) 0.794563 0.0642366
\(154\) 0 0
\(155\) 24.0564 1.93226
\(156\) 0 0
\(157\) 3.85080 0.307327 0.153664 0.988123i \(-0.450893\pi\)
0.153664 + 0.988123i \(0.450893\pi\)
\(158\) 0 0
\(159\) 15.9436 1.26441
\(160\) 0 0
\(161\) 0.658385 0.0518880
\(162\) 0 0
\(163\) 19.1544 1.50029 0.750144 0.661275i \(-0.229984\pi\)
0.750144 + 0.661275i \(0.229984\pi\)
\(164\) 0 0
\(165\) −46.8089 −3.64407
\(166\) 0 0
\(167\) 8.46701 0.655197 0.327598 0.944817i \(-0.393761\pi\)
0.327598 + 0.944817i \(0.393761\pi\)
\(168\) 0 0
\(169\) 25.2888 1.94529
\(170\) 0 0
\(171\) 1.05202 0.0804502
\(172\) 0 0
\(173\) 22.3964 1.70277 0.851384 0.524543i \(-0.175764\pi\)
0.851384 + 0.524543i \(0.175764\pi\)
\(174\) 0 0
\(175\) 46.2044 3.49272
\(176\) 0 0
\(177\) −19.8902 −1.49504
\(178\) 0 0
\(179\) −0.210884 −0.0157622 −0.00788110 0.999969i \(-0.502509\pi\)
−0.00788110 + 0.999969i \(0.502509\pi\)
\(180\) 0 0
\(181\) −3.71607 −0.276214 −0.138107 0.990417i \(-0.544102\pi\)
−0.138107 + 0.990417i \(0.544102\pi\)
\(182\) 0 0
\(183\) −12.1156 −0.895612
\(184\) 0 0
\(185\) −26.2269 −1.92824
\(186\) 0 0
\(187\) −12.0492 −0.881123
\(188\) 0 0
\(189\) −15.3694 −1.11796
\(190\) 0 0
\(191\) 6.88090 0.497884 0.248942 0.968518i \(-0.419917\pi\)
0.248942 + 0.968518i \(0.419917\pi\)
\(192\) 0 0
\(193\) 14.4359 1.03912 0.519558 0.854435i \(-0.326097\pi\)
0.519558 + 0.854435i \(0.326097\pi\)
\(194\) 0 0
\(195\) 50.2117 3.59574
\(196\) 0 0
\(197\) −11.1143 −0.791860 −0.395930 0.918281i \(-0.629578\pi\)
−0.395930 + 0.918281i \(0.629578\pi\)
\(198\) 0 0
\(199\) −19.9596 −1.41490 −0.707450 0.706764i \(-0.750154\pi\)
−0.707450 + 0.706764i \(0.750154\pi\)
\(200\) 0 0
\(201\) −13.2712 −0.936081
\(202\) 0 0
\(203\) 9.75005 0.684320
\(204\) 0 0
\(205\) −20.8403 −1.45555
\(206\) 0 0
\(207\) 0.0784825 0.00545491
\(208\) 0 0
\(209\) −15.9534 −1.10352
\(210\) 0 0
\(211\) 20.1947 1.39026 0.695131 0.718883i \(-0.255346\pi\)
0.695131 + 0.718883i \(0.255346\pi\)
\(212\) 0 0
\(213\) −30.5996 −2.09665
\(214\) 0 0
\(215\) −7.31585 −0.498937
\(216\) 0 0
\(217\) 17.3933 1.18073
\(218\) 0 0
\(219\) 21.0962 1.42555
\(220\) 0 0
\(221\) 12.9251 0.869437
\(222\) 0 0
\(223\) 0.171091 0.0114571 0.00572856 0.999984i \(-0.498177\pi\)
0.00572856 + 0.999984i \(0.498177\pi\)
\(224\) 0 0
\(225\) 5.50777 0.367185
\(226\) 0 0
\(227\) 11.5019 0.763406 0.381703 0.924285i \(-0.375338\pi\)
0.381703 + 0.924285i \(0.375338\pi\)
\(228\) 0 0
\(229\) −6.76731 −0.447196 −0.223598 0.974681i \(-0.571780\pi\)
−0.223598 + 0.974681i \(0.571780\pi\)
\(230\) 0 0
\(231\) −33.8438 −2.22676
\(232\) 0 0
\(233\) 5.74422 0.376316 0.188158 0.982139i \(-0.439748\pi\)
0.188158 + 0.982139i \(0.439748\pi\)
\(234\) 0 0
\(235\) −30.1671 −1.96788
\(236\) 0 0
\(237\) −16.6200 −1.07959
\(238\) 0 0
\(239\) −20.0459 −1.29666 −0.648330 0.761360i \(-0.724532\pi\)
−0.648330 + 0.761360i \(0.724532\pi\)
\(240\) 0 0
\(241\) 18.4927 1.19122 0.595611 0.803273i \(-0.296910\pi\)
0.595611 + 0.803273i \(0.296910\pi\)
\(242\) 0 0
\(243\) −3.93024 −0.252125
\(244\) 0 0
\(245\) 14.0481 0.897502
\(246\) 0 0
\(247\) 17.1132 1.08889
\(248\) 0 0
\(249\) 12.3151 0.780436
\(250\) 0 0
\(251\) −11.6549 −0.735652 −0.367826 0.929895i \(-0.619898\pi\)
−0.367826 + 0.929895i \(0.619898\pi\)
\(252\) 0 0
\(253\) −1.19015 −0.0748241
\(254\) 0 0
\(255\) 16.9499 1.06145
\(256\) 0 0
\(257\) −14.4909 −0.903915 −0.451957 0.892039i \(-0.649274\pi\)
−0.451957 + 0.892039i \(0.649274\pi\)
\(258\) 0 0
\(259\) −18.9626 −1.17828
\(260\) 0 0
\(261\) 1.16225 0.0719415
\(262\) 0 0
\(263\) −24.2691 −1.49650 −0.748248 0.663419i \(-0.769105\pi\)
−0.748248 + 0.663419i \(0.769105\pi\)
\(264\) 0 0
\(265\) 38.2726 2.35107
\(266\) 0 0
\(267\) −13.9855 −0.855902
\(268\) 0 0
\(269\) 24.1915 1.47498 0.737492 0.675356i \(-0.236010\pi\)
0.737492 + 0.675356i \(0.236010\pi\)
\(270\) 0 0
\(271\) 3.85814 0.234365 0.117183 0.993110i \(-0.462614\pi\)
0.117183 + 0.993110i \(0.462614\pi\)
\(272\) 0 0
\(273\) 36.3042 2.19723
\(274\) 0 0
\(275\) −83.5228 −5.03661
\(276\) 0 0
\(277\) −9.92750 −0.596486 −0.298243 0.954490i \(-0.596401\pi\)
−0.298243 + 0.954490i \(0.596401\pi\)
\(278\) 0 0
\(279\) 2.07336 0.124129
\(280\) 0 0
\(281\) 3.73454 0.222784 0.111392 0.993777i \(-0.464469\pi\)
0.111392 + 0.993777i \(0.464469\pi\)
\(282\) 0 0
\(283\) 15.0927 0.897167 0.448584 0.893741i \(-0.351929\pi\)
0.448584 + 0.893741i \(0.351929\pi\)
\(284\) 0 0
\(285\) 22.4422 1.32936
\(286\) 0 0
\(287\) −15.0680 −0.889433
\(288\) 0 0
\(289\) −12.6369 −0.743346
\(290\) 0 0
\(291\) −0.642214 −0.0376473
\(292\) 0 0
\(293\) −9.71078 −0.567310 −0.283655 0.958926i \(-0.591547\pi\)
−0.283655 + 0.958926i \(0.591547\pi\)
\(294\) 0 0
\(295\) −47.7466 −2.77991
\(296\) 0 0
\(297\) 27.7830 1.61213
\(298\) 0 0
\(299\) 1.27667 0.0738317
\(300\) 0 0
\(301\) −5.28952 −0.304883
\(302\) 0 0
\(303\) 5.14052 0.295315
\(304\) 0 0
\(305\) −29.0836 −1.66532
\(306\) 0 0
\(307\) −19.8412 −1.13240 −0.566198 0.824269i \(-0.691586\pi\)
−0.566198 + 0.824269i \(0.691586\pi\)
\(308\) 0 0
\(309\) 20.2964 1.15462
\(310\) 0 0
\(311\) 24.3097 1.37848 0.689238 0.724535i \(-0.257945\pi\)
0.689238 + 0.724535i \(0.257945\pi\)
\(312\) 0 0
\(313\) −32.1551 −1.81751 −0.908757 0.417327i \(-0.862967\pi\)
−0.908757 + 0.417327i \(0.862967\pi\)
\(314\) 0 0
\(315\) 5.35739 0.301855
\(316\) 0 0
\(317\) −22.4920 −1.26328 −0.631639 0.775263i \(-0.717617\pi\)
−0.631639 + 0.775263i \(0.717617\pi\)
\(318\) 0 0
\(319\) −17.6250 −0.986810
\(320\) 0 0
\(321\) −6.75528 −0.377043
\(322\) 0 0
\(323\) 5.77688 0.321434
\(324\) 0 0
\(325\) 89.5945 4.96981
\(326\) 0 0
\(327\) −23.2514 −1.28581
\(328\) 0 0
\(329\) −21.8115 −1.20250
\(330\) 0 0
\(331\) 15.1564 0.833070 0.416535 0.909120i \(-0.363244\pi\)
0.416535 + 0.909120i \(0.363244\pi\)
\(332\) 0 0
\(333\) −2.26043 −0.123871
\(334\) 0 0
\(335\) −31.8577 −1.74057
\(336\) 0 0
\(337\) −7.26897 −0.395966 −0.197983 0.980205i \(-0.563439\pi\)
−0.197983 + 0.980205i \(0.563439\pi\)
\(338\) 0 0
\(339\) −23.1377 −1.25667
\(340\) 0 0
\(341\) −31.4415 −1.70265
\(342\) 0 0
\(343\) −12.1804 −0.657682
\(344\) 0 0
\(345\) 1.67422 0.0901370
\(346\) 0 0
\(347\) 11.7570 0.631149 0.315575 0.948901i \(-0.397803\pi\)
0.315575 + 0.948901i \(0.397803\pi\)
\(348\) 0 0
\(349\) 25.0460 1.34068 0.670341 0.742054i \(-0.266148\pi\)
0.670341 + 0.742054i \(0.266148\pi\)
\(350\) 0 0
\(351\) −29.8027 −1.59075
\(352\) 0 0
\(353\) 22.8400 1.21565 0.607827 0.794070i \(-0.292042\pi\)
0.607827 + 0.794070i \(0.292042\pi\)
\(354\) 0 0
\(355\) −73.4545 −3.89856
\(356\) 0 0
\(357\) 12.2552 0.648612
\(358\) 0 0
\(359\) 1.60511 0.0847142 0.0423571 0.999103i \(-0.486513\pi\)
0.0423571 + 0.999103i \(0.486513\pi\)
\(360\) 0 0
\(361\) −11.3512 −0.597434
\(362\) 0 0
\(363\) 40.9544 2.14955
\(364\) 0 0
\(365\) 50.6416 2.65070
\(366\) 0 0
\(367\) 15.9548 0.832832 0.416416 0.909174i \(-0.363286\pi\)
0.416416 + 0.909174i \(0.363286\pi\)
\(368\) 0 0
\(369\) −1.79617 −0.0935048
\(370\) 0 0
\(371\) 27.6719 1.43666
\(372\) 0 0
\(373\) −20.9920 −1.08693 −0.543463 0.839433i \(-0.682887\pi\)
−0.543463 + 0.839433i \(0.682887\pi\)
\(374\) 0 0
\(375\) 76.9207 3.97217
\(376\) 0 0
\(377\) 18.9062 0.973721
\(378\) 0 0
\(379\) −30.8432 −1.58431 −0.792154 0.610321i \(-0.791040\pi\)
−0.792154 + 0.610321i \(0.791040\pi\)
\(380\) 0 0
\(381\) 0.684892 0.0350881
\(382\) 0 0
\(383\) 32.8983 1.68102 0.840511 0.541794i \(-0.182255\pi\)
0.840511 + 0.541794i \(0.182255\pi\)
\(384\) 0 0
\(385\) −81.2423 −4.14049
\(386\) 0 0
\(387\) −0.630534 −0.0320519
\(388\) 0 0
\(389\) −32.6721 −1.65654 −0.828270 0.560329i \(-0.810675\pi\)
−0.828270 + 0.560329i \(0.810675\pi\)
\(390\) 0 0
\(391\) 0.430964 0.0217948
\(392\) 0 0
\(393\) −8.58047 −0.432827
\(394\) 0 0
\(395\) −39.8965 −2.00741
\(396\) 0 0
\(397\) 19.0413 0.955654 0.477827 0.878454i \(-0.341425\pi\)
0.477827 + 0.878454i \(0.341425\pi\)
\(398\) 0 0
\(399\) 16.2262 0.812324
\(400\) 0 0
\(401\) −27.5683 −1.37670 −0.688348 0.725380i \(-0.741664\pi\)
−0.688348 + 0.725380i \(0.741664\pi\)
\(402\) 0 0
\(403\) 33.7272 1.68007
\(404\) 0 0
\(405\) −44.1197 −2.19233
\(406\) 0 0
\(407\) 34.2784 1.69912
\(408\) 0 0
\(409\) 18.0509 0.892560 0.446280 0.894893i \(-0.352749\pi\)
0.446280 + 0.894893i \(0.352749\pi\)
\(410\) 0 0
\(411\) −8.30887 −0.409847
\(412\) 0 0
\(413\) −34.5218 −1.69871
\(414\) 0 0
\(415\) 29.5624 1.45116
\(416\) 0 0
\(417\) 28.3752 1.38954
\(418\) 0 0
\(419\) 12.1865 0.595349 0.297675 0.954667i \(-0.403789\pi\)
0.297675 + 0.954667i \(0.403789\pi\)
\(420\) 0 0
\(421\) 14.6178 0.712427 0.356214 0.934405i \(-0.384068\pi\)
0.356214 + 0.934405i \(0.384068\pi\)
\(422\) 0 0
\(423\) −2.60002 −0.126417
\(424\) 0 0
\(425\) 30.2444 1.46707
\(426\) 0 0
\(427\) −21.0281 −1.01762
\(428\) 0 0
\(429\) −65.6263 −3.16847
\(430\) 0 0
\(431\) 32.5109 1.56599 0.782997 0.622026i \(-0.213690\pi\)
0.782997 + 0.622026i \(0.213690\pi\)
\(432\) 0 0
\(433\) −16.1939 −0.778229 −0.389115 0.921189i \(-0.627219\pi\)
−0.389115 + 0.921189i \(0.627219\pi\)
\(434\) 0 0
\(435\) 24.7936 1.18876
\(436\) 0 0
\(437\) 0.570608 0.0272959
\(438\) 0 0
\(439\) −10.7643 −0.513750 −0.256875 0.966445i \(-0.582693\pi\)
−0.256875 + 0.966445i \(0.582693\pi\)
\(440\) 0 0
\(441\) 1.21077 0.0576558
\(442\) 0 0
\(443\) −35.1136 −1.66830 −0.834148 0.551541i \(-0.814040\pi\)
−0.834148 + 0.551541i \(0.814040\pi\)
\(444\) 0 0
\(445\) −33.5724 −1.59148
\(446\) 0 0
\(447\) −34.1850 −1.61689
\(448\) 0 0
\(449\) 28.0647 1.32445 0.662227 0.749303i \(-0.269612\pi\)
0.662227 + 0.749303i \(0.269612\pi\)
\(450\) 0 0
\(451\) 27.2380 1.28259
\(452\) 0 0
\(453\) −1.18385 −0.0556223
\(454\) 0 0
\(455\) 87.1483 4.08558
\(456\) 0 0
\(457\) 30.1216 1.40903 0.704515 0.709689i \(-0.251164\pi\)
0.704515 + 0.709689i \(0.251164\pi\)
\(458\) 0 0
\(459\) −10.0605 −0.469583
\(460\) 0 0
\(461\) 25.2291 1.17504 0.587518 0.809211i \(-0.300105\pi\)
0.587518 + 0.809211i \(0.300105\pi\)
\(462\) 0 0
\(463\) 4.67366 0.217203 0.108602 0.994085i \(-0.465363\pi\)
0.108602 + 0.994085i \(0.465363\pi\)
\(464\) 0 0
\(465\) 44.2297 2.05110
\(466\) 0 0
\(467\) −6.59519 −0.305189 −0.152595 0.988289i \(-0.548763\pi\)
−0.152595 + 0.988289i \(0.548763\pi\)
\(468\) 0 0
\(469\) −23.0338 −1.06360
\(470\) 0 0
\(471\) 7.08002 0.326230
\(472\) 0 0
\(473\) 9.56176 0.439650
\(474\) 0 0
\(475\) 40.0443 1.83736
\(476\) 0 0
\(477\) 3.29862 0.151033
\(478\) 0 0
\(479\) −9.33595 −0.426571 −0.213285 0.976990i \(-0.568416\pi\)
−0.213285 + 0.976990i \(0.568416\pi\)
\(480\) 0 0
\(481\) −36.7703 −1.67658
\(482\) 0 0
\(483\) 1.21050 0.0550795
\(484\) 0 0
\(485\) −1.54164 −0.0700022
\(486\) 0 0
\(487\) −15.7194 −0.712316 −0.356158 0.934426i \(-0.615913\pi\)
−0.356158 + 0.934426i \(0.615913\pi\)
\(488\) 0 0
\(489\) 35.2170 1.59257
\(490\) 0 0
\(491\) −15.8117 −0.713571 −0.356786 0.934186i \(-0.616127\pi\)
−0.356786 + 0.934186i \(0.616127\pi\)
\(492\) 0 0
\(493\) 6.38217 0.287438
\(494\) 0 0
\(495\) −9.68445 −0.435284
\(496\) 0 0
\(497\) −53.1092 −2.38227
\(498\) 0 0
\(499\) −15.3430 −0.686847 −0.343424 0.939181i \(-0.611587\pi\)
−0.343424 + 0.939181i \(0.611587\pi\)
\(500\) 0 0
\(501\) 15.5673 0.695496
\(502\) 0 0
\(503\) −13.8434 −0.617248 −0.308624 0.951184i \(-0.599868\pi\)
−0.308624 + 0.951184i \(0.599868\pi\)
\(504\) 0 0
\(505\) 12.3399 0.549116
\(506\) 0 0
\(507\) 46.4955 2.06494
\(508\) 0 0
\(509\) 21.7069 0.962143 0.481072 0.876681i \(-0.340248\pi\)
0.481072 + 0.876681i \(0.340248\pi\)
\(510\) 0 0
\(511\) 36.6149 1.61975
\(512\) 0 0
\(513\) −13.3203 −0.588107
\(514\) 0 0
\(515\) 48.7216 2.14693
\(516\) 0 0
\(517\) 39.4281 1.73405
\(518\) 0 0
\(519\) 41.1777 1.80750
\(520\) 0 0
\(521\) 21.0525 0.922327 0.461163 0.887315i \(-0.347432\pi\)
0.461163 + 0.887315i \(0.347432\pi\)
\(522\) 0 0
\(523\) −22.5116 −0.984362 −0.492181 0.870493i \(-0.663800\pi\)
−0.492181 + 0.870493i \(0.663800\pi\)
\(524\) 0 0
\(525\) 84.9506 3.70755
\(526\) 0 0
\(527\) 11.3853 0.495950
\(528\) 0 0
\(529\) −22.9574 −0.998149
\(530\) 0 0
\(531\) −4.11515 −0.178582
\(532\) 0 0
\(533\) −29.2181 −1.26558
\(534\) 0 0
\(535\) −16.2161 −0.701082
\(536\) 0 0
\(537\) −0.387728 −0.0167317
\(538\) 0 0
\(539\) −18.3608 −0.790855
\(540\) 0 0
\(541\) 36.3683 1.56360 0.781798 0.623531i \(-0.214303\pi\)
0.781798 + 0.623531i \(0.214303\pi\)
\(542\) 0 0
\(543\) −6.83232 −0.293203
\(544\) 0 0
\(545\) −55.8151 −2.39086
\(546\) 0 0
\(547\) 21.5180 0.920042 0.460021 0.887908i \(-0.347842\pi\)
0.460021 + 0.887908i \(0.347842\pi\)
\(548\) 0 0
\(549\) −2.50664 −0.106981
\(550\) 0 0
\(551\) 8.45016 0.359989
\(552\) 0 0
\(553\) −28.8460 −1.22666
\(554\) 0 0
\(555\) −48.2204 −2.04684
\(556\) 0 0
\(557\) −40.1886 −1.70285 −0.851423 0.524480i \(-0.824260\pi\)
−0.851423 + 0.524480i \(0.824260\pi\)
\(558\) 0 0
\(559\) −10.2569 −0.433819
\(560\) 0 0
\(561\) −22.1534 −0.935318
\(562\) 0 0
\(563\) 18.0394 0.760269 0.380135 0.924931i \(-0.375878\pi\)
0.380135 + 0.924931i \(0.375878\pi\)
\(564\) 0 0
\(565\) −55.5421 −2.33667
\(566\) 0 0
\(567\) −31.8995 −1.33965
\(568\) 0 0
\(569\) 34.7862 1.45832 0.729158 0.684346i \(-0.239912\pi\)
0.729158 + 0.684346i \(0.239912\pi\)
\(570\) 0 0
\(571\) −37.7914 −1.58152 −0.790760 0.612127i \(-0.790314\pi\)
−0.790760 + 0.612127i \(0.790314\pi\)
\(572\) 0 0
\(573\) 12.6511 0.528508
\(574\) 0 0
\(575\) 2.98737 0.124582
\(576\) 0 0
\(577\) −23.5036 −0.978468 −0.489234 0.872152i \(-0.662724\pi\)
−0.489234 + 0.872152i \(0.662724\pi\)
\(578\) 0 0
\(579\) 26.5416 1.10303
\(580\) 0 0
\(581\) 21.3742 0.886753
\(582\) 0 0
\(583\) −50.0220 −2.07170
\(584\) 0 0
\(585\) 10.3885 0.429510
\(586\) 0 0
\(587\) 24.9338 1.02913 0.514564 0.857452i \(-0.327954\pi\)
0.514564 + 0.857452i \(0.327954\pi\)
\(588\) 0 0
\(589\) 15.0744 0.621129
\(590\) 0 0
\(591\) −20.4345 −0.840564
\(592\) 0 0
\(593\) −9.20816 −0.378134 −0.189067 0.981964i \(-0.560546\pi\)
−0.189067 + 0.981964i \(0.560546\pi\)
\(594\) 0 0
\(595\) 29.4186 1.20604
\(596\) 0 0
\(597\) −36.6974 −1.50193
\(598\) 0 0
\(599\) 45.7527 1.86941 0.934703 0.355430i \(-0.115665\pi\)
0.934703 + 0.355430i \(0.115665\pi\)
\(600\) 0 0
\(601\) 12.2404 0.499298 0.249649 0.968336i \(-0.419685\pi\)
0.249649 + 0.968336i \(0.419685\pi\)
\(602\) 0 0
\(603\) −2.74573 −0.111815
\(604\) 0 0
\(605\) 98.3113 3.99692
\(606\) 0 0
\(607\) 30.9651 1.25684 0.628418 0.777876i \(-0.283703\pi\)
0.628418 + 0.777876i \(0.283703\pi\)
\(608\) 0 0
\(609\) 17.9263 0.726410
\(610\) 0 0
\(611\) −42.2944 −1.71105
\(612\) 0 0
\(613\) 11.7066 0.472825 0.236412 0.971653i \(-0.424028\pi\)
0.236412 + 0.971653i \(0.424028\pi\)
\(614\) 0 0
\(615\) −38.3166 −1.54507
\(616\) 0 0
\(617\) 34.7155 1.39759 0.698797 0.715320i \(-0.253719\pi\)
0.698797 + 0.715320i \(0.253719\pi\)
\(618\) 0 0
\(619\) −32.9516 −1.32444 −0.662219 0.749311i \(-0.730385\pi\)
−0.662219 + 0.749311i \(0.730385\pi\)
\(620\) 0 0
\(621\) −0.993717 −0.0398765
\(622\) 0 0
\(623\) −24.2735 −0.972499
\(624\) 0 0
\(625\) 112.252 4.49009
\(626\) 0 0
\(627\) −29.3317 −1.17140
\(628\) 0 0
\(629\) −12.4125 −0.494919
\(630\) 0 0
\(631\) −9.20156 −0.366308 −0.183154 0.983084i \(-0.558631\pi\)
−0.183154 + 0.983084i \(0.558631\pi\)
\(632\) 0 0
\(633\) 37.1297 1.47577
\(634\) 0 0
\(635\) 1.64409 0.0652436
\(636\) 0 0
\(637\) 19.6956 0.780366
\(638\) 0 0
\(639\) −6.33085 −0.250445
\(640\) 0 0
\(641\) −2.14001 −0.0845253 −0.0422627 0.999107i \(-0.513457\pi\)
−0.0422627 + 0.999107i \(0.513457\pi\)
\(642\) 0 0
\(643\) 4.33293 0.170874 0.0854370 0.996344i \(-0.472771\pi\)
0.0854370 + 0.996344i \(0.472771\pi\)
\(644\) 0 0
\(645\) −13.4508 −0.529625
\(646\) 0 0
\(647\) 20.7194 0.814562 0.407281 0.913303i \(-0.366477\pi\)
0.407281 + 0.913303i \(0.366477\pi\)
\(648\) 0 0
\(649\) 62.4044 2.44959
\(650\) 0 0
\(651\) 31.9790 1.25336
\(652\) 0 0
\(653\) −2.77847 −0.108730 −0.0543649 0.998521i \(-0.517313\pi\)
−0.0543649 + 0.998521i \(0.517313\pi\)
\(654\) 0 0
\(655\) −20.5975 −0.804809
\(656\) 0 0
\(657\) 4.36467 0.170282
\(658\) 0 0
\(659\) 13.1545 0.512427 0.256213 0.966620i \(-0.417525\pi\)
0.256213 + 0.966620i \(0.417525\pi\)
\(660\) 0 0
\(661\) 6.97313 0.271223 0.135612 0.990762i \(-0.456700\pi\)
0.135612 + 0.990762i \(0.456700\pi\)
\(662\) 0 0
\(663\) 23.7639 0.922913
\(664\) 0 0
\(665\) 38.9510 1.51045
\(666\) 0 0
\(667\) 0.630395 0.0244090
\(668\) 0 0
\(669\) 0.314566 0.0121618
\(670\) 0 0
\(671\) 38.0120 1.46744
\(672\) 0 0
\(673\) 40.1282 1.54683 0.773415 0.633900i \(-0.218547\pi\)
0.773415 + 0.633900i \(0.218547\pi\)
\(674\) 0 0
\(675\) −69.7374 −2.68419
\(676\) 0 0
\(677\) −35.2764 −1.35578 −0.677892 0.735162i \(-0.737106\pi\)
−0.677892 + 0.735162i \(0.737106\pi\)
\(678\) 0 0
\(679\) −1.11464 −0.0427759
\(680\) 0 0
\(681\) 21.1472 0.810361
\(682\) 0 0
\(683\) 35.4466 1.35633 0.678164 0.734910i \(-0.262776\pi\)
0.678164 + 0.734910i \(0.262776\pi\)
\(684\) 0 0
\(685\) −19.9455 −0.762078
\(686\) 0 0
\(687\) −12.4423 −0.474702
\(688\) 0 0
\(689\) 53.6584 2.04422
\(690\) 0 0
\(691\) −4.21985 −0.160531 −0.0802653 0.996774i \(-0.525577\pi\)
−0.0802653 + 0.996774i \(0.525577\pi\)
\(692\) 0 0
\(693\) −7.00207 −0.265986
\(694\) 0 0
\(695\) 68.1147 2.58374
\(696\) 0 0
\(697\) −9.86314 −0.373593
\(698\) 0 0
\(699\) 10.5612 0.399462
\(700\) 0 0
\(701\) −13.8064 −0.521462 −0.260731 0.965411i \(-0.583964\pi\)
−0.260731 + 0.965411i \(0.583964\pi\)
\(702\) 0 0
\(703\) −16.4345 −0.619839
\(704\) 0 0
\(705\) −55.4647 −2.08892
\(706\) 0 0
\(707\) 8.92198 0.335546
\(708\) 0 0
\(709\) 15.0247 0.564263 0.282132 0.959376i \(-0.408958\pi\)
0.282132 + 0.959376i \(0.408958\pi\)
\(710\) 0 0
\(711\) −3.43858 −0.128957
\(712\) 0 0
\(713\) 1.12457 0.0421156
\(714\) 0 0
\(715\) −157.536 −5.89152
\(716\) 0 0
\(717\) −36.8560 −1.37641
\(718\) 0 0
\(719\) −25.3960 −0.947109 −0.473555 0.880764i \(-0.657029\pi\)
−0.473555 + 0.880764i \(0.657029\pi\)
\(720\) 0 0
\(721\) 35.2267 1.31191
\(722\) 0 0
\(723\) 34.0005 1.26449
\(724\) 0 0
\(725\) 44.2400 1.64303
\(726\) 0 0
\(727\) −31.9476 −1.18487 −0.592436 0.805618i \(-0.701834\pi\)
−0.592436 + 0.805618i \(0.701834\pi\)
\(728\) 0 0
\(729\) 22.7633 0.843087
\(730\) 0 0
\(731\) −3.46240 −0.128061
\(732\) 0 0
\(733\) 8.98593 0.331903 0.165952 0.986134i \(-0.446930\pi\)
0.165952 + 0.986134i \(0.446930\pi\)
\(734\) 0 0
\(735\) 25.8287 0.952705
\(736\) 0 0
\(737\) 41.6377 1.53375
\(738\) 0 0
\(739\) −30.3398 −1.11607 −0.558033 0.829819i \(-0.688444\pi\)
−0.558033 + 0.829819i \(0.688444\pi\)
\(740\) 0 0
\(741\) 31.4640 1.15586
\(742\) 0 0
\(743\) −47.5979 −1.74620 −0.873098 0.487545i \(-0.837893\pi\)
−0.873098 + 0.487545i \(0.837893\pi\)
\(744\) 0 0
\(745\) −82.0612 −3.00649
\(746\) 0 0
\(747\) 2.54791 0.0932230
\(748\) 0 0
\(749\) −11.7246 −0.428407
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −21.4286 −0.780900
\(754\) 0 0
\(755\) −2.84185 −0.103425
\(756\) 0 0
\(757\) −16.9916 −0.617571 −0.308786 0.951132i \(-0.599923\pi\)
−0.308786 + 0.951132i \(0.599923\pi\)
\(758\) 0 0
\(759\) −2.18819 −0.0794263
\(760\) 0 0
\(761\) 37.1372 1.34622 0.673112 0.739541i \(-0.264957\pi\)
0.673112 + 0.739541i \(0.264957\pi\)
\(762\) 0 0
\(763\) −40.3555 −1.46097
\(764\) 0 0
\(765\) 3.50683 0.126790
\(766\) 0 0
\(767\) −66.9409 −2.41710
\(768\) 0 0
\(769\) −19.6996 −0.710384 −0.355192 0.934793i \(-0.615585\pi\)
−0.355192 + 0.934793i \(0.615585\pi\)
\(770\) 0 0
\(771\) −26.6427 −0.959512
\(772\) 0 0
\(773\) 32.4048 1.16552 0.582760 0.812644i \(-0.301973\pi\)
0.582760 + 0.812644i \(0.301973\pi\)
\(774\) 0 0
\(775\) 78.9206 2.83491
\(776\) 0 0
\(777\) −34.8644 −1.25075
\(778\) 0 0
\(779\) −13.0591 −0.467890
\(780\) 0 0
\(781\) 96.0044 3.43531
\(782\) 0 0
\(783\) −14.7160 −0.525907
\(784\) 0 0
\(785\) 16.9956 0.606600
\(786\) 0 0
\(787\) −5.04972 −0.180003 −0.0900016 0.995942i \(-0.528687\pi\)
−0.0900016 + 0.995942i \(0.528687\pi\)
\(788\) 0 0
\(789\) −44.6208 −1.58854
\(790\) 0 0
\(791\) −40.1581 −1.42786
\(792\) 0 0
\(793\) −40.7754 −1.44798
\(794\) 0 0
\(795\) 70.3674 2.49568
\(796\) 0 0
\(797\) −53.3119 −1.88840 −0.944202 0.329368i \(-0.893164\pi\)
−0.944202 + 0.329368i \(0.893164\pi\)
\(798\) 0 0
\(799\) −14.2773 −0.505094
\(800\) 0 0
\(801\) −2.89352 −0.102237
\(802\) 0 0
\(803\) −66.1881 −2.33573
\(804\) 0 0
\(805\) 2.90580 0.102416
\(806\) 0 0
\(807\) 44.4782 1.56571
\(808\) 0 0
\(809\) −27.8865 −0.980437 −0.490219 0.871599i \(-0.663083\pi\)
−0.490219 + 0.871599i \(0.663083\pi\)
\(810\) 0 0
\(811\) −38.5146 −1.35243 −0.676214 0.736705i \(-0.736381\pi\)
−0.676214 + 0.736705i \(0.736381\pi\)
\(812\) 0 0
\(813\) 7.09351 0.248780
\(814\) 0 0
\(815\) 84.5385 2.96125
\(816\) 0 0
\(817\) −4.58431 −0.160385
\(818\) 0 0
\(819\) 7.51109 0.262459
\(820\) 0 0
\(821\) −45.0145 −1.57102 −0.785508 0.618851i \(-0.787598\pi\)
−0.785508 + 0.618851i \(0.787598\pi\)
\(822\) 0 0
\(823\) −48.1363 −1.67792 −0.838962 0.544189i \(-0.816837\pi\)
−0.838962 + 0.544189i \(0.816837\pi\)
\(824\) 0 0
\(825\) −153.564 −5.34640
\(826\) 0 0
\(827\) −30.4803 −1.05990 −0.529951 0.848028i \(-0.677790\pi\)
−0.529951 + 0.848028i \(0.677790\pi\)
\(828\) 0 0
\(829\) 13.7029 0.475920 0.237960 0.971275i \(-0.423521\pi\)
0.237960 + 0.971275i \(0.423521\pi\)
\(830\) 0 0
\(831\) −18.2525 −0.633174
\(832\) 0 0
\(833\) 6.64861 0.230361
\(834\) 0 0
\(835\) 37.3694 1.29322
\(836\) 0 0
\(837\) −26.2521 −0.907406
\(838\) 0 0
\(839\) −23.1845 −0.800417 −0.400209 0.916424i \(-0.631062\pi\)
−0.400209 + 0.916424i \(0.631062\pi\)
\(840\) 0 0
\(841\) −19.6645 −0.678085
\(842\) 0 0
\(843\) 6.86627 0.236487
\(844\) 0 0
\(845\) 111.613 3.83959
\(846\) 0 0
\(847\) 71.0812 2.44238
\(848\) 0 0
\(849\) 27.7492 0.952349
\(850\) 0 0
\(851\) −1.22604 −0.0420280
\(852\) 0 0
\(853\) 35.5179 1.21611 0.608055 0.793895i \(-0.291950\pi\)
0.608055 + 0.793895i \(0.291950\pi\)
\(854\) 0 0
\(855\) 4.64313 0.158792
\(856\) 0 0
\(857\) −21.7468 −0.742857 −0.371428 0.928462i \(-0.621132\pi\)
−0.371428 + 0.928462i \(0.621132\pi\)
\(858\) 0 0
\(859\) 24.1470 0.823885 0.411943 0.911210i \(-0.364850\pi\)
0.411943 + 0.911210i \(0.364850\pi\)
\(860\) 0 0
\(861\) −27.7037 −0.944139
\(862\) 0 0
\(863\) −10.1227 −0.344582 −0.172291 0.985046i \(-0.555117\pi\)
−0.172291 + 0.985046i \(0.555117\pi\)
\(864\) 0 0
\(865\) 98.8473 3.36091
\(866\) 0 0
\(867\) −23.2340 −0.789067
\(868\) 0 0
\(869\) 52.1444 1.76888
\(870\) 0 0
\(871\) −44.6646 −1.51340
\(872\) 0 0
\(873\) −0.132870 −0.00449696
\(874\) 0 0
\(875\) 133.505 4.51329
\(876\) 0 0
\(877\) −3.96635 −0.133934 −0.0669671 0.997755i \(-0.521332\pi\)
−0.0669671 + 0.997755i \(0.521332\pi\)
\(878\) 0 0
\(879\) −17.8541 −0.602204
\(880\) 0 0
\(881\) −22.3579 −0.753256 −0.376628 0.926365i \(-0.622916\pi\)
−0.376628 + 0.926365i \(0.622916\pi\)
\(882\) 0 0
\(883\) −9.09669 −0.306128 −0.153064 0.988216i \(-0.548914\pi\)
−0.153064 + 0.988216i \(0.548914\pi\)
\(884\) 0 0
\(885\) −87.7861 −2.95090
\(886\) 0 0
\(887\) −28.3378 −0.951490 −0.475745 0.879583i \(-0.657821\pi\)
−0.475745 + 0.879583i \(0.657821\pi\)
\(888\) 0 0
\(889\) 1.18871 0.0398680
\(890\) 0 0
\(891\) 57.6641 1.93182
\(892\) 0 0
\(893\) −18.9035 −0.632582
\(894\) 0 0
\(895\) −0.930742 −0.0311113
\(896\) 0 0
\(897\) 2.34726 0.0783729
\(898\) 0 0
\(899\) 16.6538 0.555436
\(900\) 0 0
\(901\) 18.1134 0.603446
\(902\) 0 0
\(903\) −9.72522 −0.323635
\(904\) 0 0
\(905\) −16.4010 −0.545188
\(906\) 0 0
\(907\) −53.8586 −1.78835 −0.894173 0.447721i \(-0.852236\pi\)
−0.894173 + 0.447721i \(0.852236\pi\)
\(908\) 0 0
\(909\) 1.06354 0.0352754
\(910\) 0 0
\(911\) −2.36505 −0.0783575 −0.0391788 0.999232i \(-0.512474\pi\)
−0.0391788 + 0.999232i \(0.512474\pi\)
\(912\) 0 0
\(913\) −38.6378 −1.27872
\(914\) 0 0
\(915\) −53.4726 −1.76775
\(916\) 0 0
\(917\) −14.8924 −0.491790
\(918\) 0 0
\(919\) 51.2506 1.69060 0.845300 0.534292i \(-0.179422\pi\)
0.845300 + 0.534292i \(0.179422\pi\)
\(920\) 0 0
\(921\) −36.4797 −1.20205
\(922\) 0 0
\(923\) −102.984 −3.38975
\(924\) 0 0
\(925\) −86.0413 −2.82902
\(926\) 0 0
\(927\) 4.19919 0.137919
\(928\) 0 0
\(929\) −4.90182 −0.160823 −0.0804117 0.996762i \(-0.525624\pi\)
−0.0804117 + 0.996762i \(0.525624\pi\)
\(930\) 0 0
\(931\) 8.80294 0.288505
\(932\) 0 0
\(933\) 44.6954 1.46326
\(934\) 0 0
\(935\) −53.1794 −1.73915
\(936\) 0 0
\(937\) 51.2289 1.67357 0.836787 0.547528i \(-0.184431\pi\)
0.836787 + 0.547528i \(0.184431\pi\)
\(938\) 0 0
\(939\) −59.1198 −1.92930
\(940\) 0 0
\(941\) 1.95788 0.0638252 0.0319126 0.999491i \(-0.489840\pi\)
0.0319126 + 0.999491i \(0.489840\pi\)
\(942\) 0 0
\(943\) −0.974227 −0.0317252
\(944\) 0 0
\(945\) −67.8333 −2.20662
\(946\) 0 0
\(947\) 1.20853 0.0392718 0.0196359 0.999807i \(-0.493749\pi\)
0.0196359 + 0.999807i \(0.493749\pi\)
\(948\) 0 0
\(949\) 70.9997 2.30475
\(950\) 0 0
\(951\) −41.3535 −1.34098
\(952\) 0 0
\(953\) −30.1358 −0.976195 −0.488097 0.872789i \(-0.662309\pi\)
−0.488097 + 0.872789i \(0.662309\pi\)
\(954\) 0 0
\(955\) 30.3690 0.982719
\(956\) 0 0
\(957\) −32.4050 −1.04751
\(958\) 0 0
\(959\) −14.4210 −0.465679
\(960\) 0 0
\(961\) −1.29095 −0.0416437
\(962\) 0 0
\(963\) −1.39762 −0.0450377
\(964\) 0 0
\(965\) 63.7131 2.05100
\(966\) 0 0
\(967\) −25.3222 −0.814307 −0.407153 0.913360i \(-0.633479\pi\)
−0.407153 + 0.913360i \(0.633479\pi\)
\(968\) 0 0
\(969\) 10.6213 0.341205
\(970\) 0 0
\(971\) −7.78253 −0.249753 −0.124877 0.992172i \(-0.539854\pi\)
−0.124877 + 0.992172i \(0.539854\pi\)
\(972\) 0 0
\(973\) 49.2484 1.57883
\(974\) 0 0
\(975\) 164.727 5.27549
\(976\) 0 0
\(977\) −47.6249 −1.52365 −0.761827 0.647780i \(-0.775698\pi\)
−0.761827 + 0.647780i \(0.775698\pi\)
\(978\) 0 0
\(979\) 43.8788 1.40237
\(980\) 0 0
\(981\) −4.81056 −0.153589
\(982\) 0 0
\(983\) −19.8158 −0.632027 −0.316013 0.948755i \(-0.602344\pi\)
−0.316013 + 0.948755i \(0.602344\pi\)
\(984\) 0 0
\(985\) −49.0532 −1.56296
\(986\) 0 0
\(987\) −40.1022 −1.27647
\(988\) 0 0
\(989\) −0.341997 −0.0108749
\(990\) 0 0
\(991\) 19.3883 0.615890 0.307945 0.951404i \(-0.400359\pi\)
0.307945 + 0.951404i \(0.400359\pi\)
\(992\) 0 0
\(993\) 27.8663 0.884310
\(994\) 0 0
\(995\) −88.0924 −2.79272
\(996\) 0 0
\(997\) −36.4954 −1.15582 −0.577910 0.816100i \(-0.696132\pi\)
−0.577910 + 0.816100i \(0.696132\pi\)
\(998\) 0 0
\(999\) 28.6208 0.905520
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 \(a_p\))