Properties

Label 6003.2.a.t.1.2
Level 6003
Weight 2
Character 6003.1
Self dual Yes
Analytic conductor 47.934
Analytic rank 1
Dimension 22
CM No

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Newspace parameters

Level: \( N \) = \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(1\)
Dimension: \(22\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.33095 q^{2} +3.43331 q^{4} +2.03702 q^{5} +4.28183 q^{7} -3.34096 q^{8} +O(q^{10})\) \(q-2.33095 q^{2} +3.43331 q^{4} +2.03702 q^{5} +4.28183 q^{7} -3.34096 q^{8} -4.74817 q^{10} +3.57655 q^{11} -5.73812 q^{13} -9.98070 q^{14} +0.920976 q^{16} -4.13707 q^{17} -8.31788 q^{19} +6.99370 q^{20} -8.33675 q^{22} +1.00000 q^{23} -0.850567 q^{25} +13.3752 q^{26} +14.7008 q^{28} +1.00000 q^{29} +4.54582 q^{31} +4.53517 q^{32} +9.64327 q^{34} +8.72215 q^{35} -9.15659 q^{37} +19.3885 q^{38} -6.80558 q^{40} +3.77238 q^{41} -4.11401 q^{43} +12.2794 q^{44} -2.33095 q^{46} -6.22762 q^{47} +11.3340 q^{49} +1.98263 q^{50} -19.7007 q^{52} -1.32969 q^{53} +7.28549 q^{55} -14.3054 q^{56} -2.33095 q^{58} +12.0838 q^{59} +4.42239 q^{61} -10.5961 q^{62} -12.4132 q^{64} -11.6886 q^{65} -5.73198 q^{67} -14.2038 q^{68} -20.3309 q^{70} -9.12802 q^{71} -11.8581 q^{73} +21.3435 q^{74} -28.5578 q^{76} +15.3142 q^{77} +2.03687 q^{79} +1.87604 q^{80} -8.79321 q^{82} -2.51017 q^{83} -8.42727 q^{85} +9.58952 q^{86} -11.9491 q^{88} -10.0168 q^{89} -24.5696 q^{91} +3.43331 q^{92} +14.5163 q^{94} -16.9436 q^{95} +0.738955 q^{97} -26.4190 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} + O(q^{10}) \) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} - 12q^{10} - 28q^{13} - q^{14} + 3q^{16} - 10q^{17} - 8q^{19} - 11q^{22} + 22q^{23} + 11q^{26} - 21q^{28} + 22q^{29} - 18q^{31} + 5q^{32} - 33q^{34} + 2q^{35} - 28q^{37} + 14q^{38} - 30q^{40} - 10q^{41} - 14q^{43} + 37q^{44} - 3q^{46} - 18q^{47} + 2q^{49} + 7q^{50} - 57q^{52} + 20q^{53} - 42q^{55} - 2q^{56} - 3q^{58} - 20q^{59} - 38q^{61} + 4q^{62} - 24q^{64} + 12q^{65} - 50q^{67} + 11q^{68} - 48q^{70} + 12q^{71} - 46q^{73} - 6q^{74} - 16q^{76} - 14q^{77} - 20q^{79} - 58q^{80} - 42q^{82} + 22q^{83} - 66q^{85} + 22q^{86} - 68q^{88} - 14q^{89} - 16q^{91} + 17q^{92} - 27q^{94} - 20q^{95} - 48q^{97} - 28q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.33095 −1.64823 −0.824114 0.566425i \(-0.808326\pi\)
−0.824114 + 0.566425i \(0.808326\pi\)
\(3\) 0 0
\(4\) 3.43331 1.71665
\(5\) 2.03702 0.910981 0.455491 0.890241i \(-0.349464\pi\)
0.455491 + 0.890241i \(0.349464\pi\)
\(6\) 0 0
\(7\) 4.28183 1.61838 0.809189 0.587548i \(-0.199907\pi\)
0.809189 + 0.587548i \(0.199907\pi\)
\(8\) −3.34096 −1.18121
\(9\) 0 0
\(10\) −4.74817 −1.50150
\(11\) 3.57655 1.07837 0.539186 0.842187i \(-0.318732\pi\)
0.539186 + 0.842187i \(0.318732\pi\)
\(12\) 0 0
\(13\) −5.73812 −1.59147 −0.795734 0.605646i \(-0.792915\pi\)
−0.795734 + 0.605646i \(0.792915\pi\)
\(14\) −9.98070 −2.66746
\(15\) 0 0
\(16\) 0.920976 0.230244
\(17\) −4.13707 −1.00339 −0.501693 0.865046i \(-0.667289\pi\)
−0.501693 + 0.865046i \(0.667289\pi\)
\(18\) 0 0
\(19\) −8.31788 −1.90825 −0.954126 0.299406i \(-0.903212\pi\)
−0.954126 + 0.299406i \(0.903212\pi\)
\(20\) 6.99370 1.56384
\(21\) 0 0
\(22\) −8.33675 −1.77740
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −0.850567 −0.170113
\(26\) 13.3752 2.62310
\(27\) 0 0
\(28\) 14.7008 2.77819
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 4.54582 0.816454 0.408227 0.912880i \(-0.366147\pi\)
0.408227 + 0.912880i \(0.366147\pi\)
\(32\) 4.53517 0.801712
\(33\) 0 0
\(34\) 9.64327 1.65381
\(35\) 8.72215 1.47431
\(36\) 0 0
\(37\) −9.15659 −1.50533 −0.752667 0.658401i \(-0.771233\pi\)
−0.752667 + 0.658401i \(0.771233\pi\)
\(38\) 19.3885 3.14523
\(39\) 0 0
\(40\) −6.80558 −1.07606
\(41\) 3.77238 0.589146 0.294573 0.955629i \(-0.404823\pi\)
0.294573 + 0.955629i \(0.404823\pi\)
\(42\) 0 0
\(43\) −4.11401 −0.627380 −0.313690 0.949525i \(-0.601565\pi\)
−0.313690 + 0.949525i \(0.601565\pi\)
\(44\) 12.2794 1.85119
\(45\) 0 0
\(46\) −2.33095 −0.343679
\(47\) −6.22762 −0.908392 −0.454196 0.890902i \(-0.650073\pi\)
−0.454196 + 0.890902i \(0.650073\pi\)
\(48\) 0 0
\(49\) 11.3340 1.61915
\(50\) 1.98263 0.280386
\(51\) 0 0
\(52\) −19.7007 −2.73200
\(53\) −1.32969 −0.182647 −0.0913237 0.995821i \(-0.529110\pi\)
−0.0913237 + 0.995821i \(0.529110\pi\)
\(54\) 0 0
\(55\) 7.28549 0.982376
\(56\) −14.3054 −1.91164
\(57\) 0 0
\(58\) −2.33095 −0.306068
\(59\) 12.0838 1.57318 0.786591 0.617475i \(-0.211844\pi\)
0.786591 + 0.617475i \(0.211844\pi\)
\(60\) 0 0
\(61\) 4.42239 0.566229 0.283115 0.959086i \(-0.408632\pi\)
0.283115 + 0.959086i \(0.408632\pi\)
\(62\) −10.5961 −1.34570
\(63\) 0 0
\(64\) −12.4132 −1.55165
\(65\) −11.6886 −1.44980
\(66\) 0 0
\(67\) −5.73198 −0.700273 −0.350136 0.936699i \(-0.613865\pi\)
−0.350136 + 0.936699i \(0.613865\pi\)
\(68\) −14.2038 −1.72246
\(69\) 0 0
\(70\) −20.3309 −2.43000
\(71\) −9.12802 −1.08330 −0.541648 0.840605i \(-0.682199\pi\)
−0.541648 + 0.840605i \(0.682199\pi\)
\(72\) 0 0
\(73\) −11.8581 −1.38788 −0.693940 0.720033i \(-0.744127\pi\)
−0.693940 + 0.720033i \(0.744127\pi\)
\(74\) 21.3435 2.48113
\(75\) 0 0
\(76\) −28.5578 −3.27581
\(77\) 15.3142 1.74521
\(78\) 0 0
\(79\) 2.03687 0.229166 0.114583 0.993414i \(-0.463447\pi\)
0.114583 + 0.993414i \(0.463447\pi\)
\(80\) 1.87604 0.209748
\(81\) 0 0
\(82\) −8.79321 −0.971047
\(83\) −2.51017 −0.275527 −0.137764 0.990465i \(-0.543991\pi\)
−0.137764 + 0.990465i \(0.543991\pi\)
\(84\) 0 0
\(85\) −8.42727 −0.914065
\(86\) 9.58952 1.03406
\(87\) 0 0
\(88\) −11.9491 −1.27378
\(89\) −10.0168 −1.06178 −0.530889 0.847441i \(-0.678142\pi\)
−0.530889 + 0.847441i \(0.678142\pi\)
\(90\) 0 0
\(91\) −24.5696 −2.57560
\(92\) 3.43331 0.357947
\(93\) 0 0
\(94\) 14.5163 1.49724
\(95\) −16.9436 −1.73838
\(96\) 0 0
\(97\) 0.738955 0.0750295 0.0375147 0.999296i \(-0.488056\pi\)
0.0375147 + 0.999296i \(0.488056\pi\)
\(98\) −26.4190 −2.66873
\(99\) 0 0
\(100\) −2.92026 −0.292026
\(101\) −14.1605 −1.40902 −0.704509 0.709695i \(-0.748833\pi\)
−0.704509 + 0.709695i \(0.748833\pi\)
\(102\) 0 0
\(103\) −15.3578 −1.51325 −0.756626 0.653848i \(-0.773154\pi\)
−0.756626 + 0.653848i \(0.773154\pi\)
\(104\) 19.1708 1.87985
\(105\) 0 0
\(106\) 3.09944 0.301044
\(107\) −13.1005 −1.26647 −0.633237 0.773958i \(-0.718274\pi\)
−0.633237 + 0.773958i \(0.718274\pi\)
\(108\) 0 0
\(109\) 17.4120 1.66777 0.833883 0.551941i \(-0.186113\pi\)
0.833883 + 0.551941i \(0.186113\pi\)
\(110\) −16.9821 −1.61918
\(111\) 0 0
\(112\) 3.94346 0.372622
\(113\) 13.9526 1.31255 0.656276 0.754521i \(-0.272131\pi\)
0.656276 + 0.754521i \(0.272131\pi\)
\(114\) 0 0
\(115\) 2.03702 0.189953
\(116\) 3.43331 0.318774
\(117\) 0 0
\(118\) −28.1668 −2.59296
\(119\) −17.7142 −1.62386
\(120\) 0 0
\(121\) 1.79173 0.162884
\(122\) −10.3084 −0.933275
\(123\) 0 0
\(124\) 15.6072 1.40157
\(125\) −11.9177 −1.06595
\(126\) 0 0
\(127\) 9.48833 0.841953 0.420976 0.907072i \(-0.361687\pi\)
0.420976 + 0.907072i \(0.361687\pi\)
\(128\) 19.8641 1.75576
\(129\) 0 0
\(130\) 27.2456 2.38959
\(131\) −8.07820 −0.705795 −0.352898 0.935662i \(-0.614804\pi\)
−0.352898 + 0.935662i \(0.614804\pi\)
\(132\) 0 0
\(133\) −35.6157 −3.08827
\(134\) 13.3609 1.15421
\(135\) 0 0
\(136\) 13.8218 1.18521
\(137\) 14.5574 1.24372 0.621861 0.783128i \(-0.286377\pi\)
0.621861 + 0.783128i \(0.286377\pi\)
\(138\) 0 0
\(139\) −16.1942 −1.37358 −0.686788 0.726858i \(-0.740980\pi\)
−0.686788 + 0.726858i \(0.740980\pi\)
\(140\) 29.9458 2.53088
\(141\) 0 0
\(142\) 21.2769 1.78552
\(143\) −20.5227 −1.71619
\(144\) 0 0
\(145\) 2.03702 0.169165
\(146\) 27.6405 2.28754
\(147\) 0 0
\(148\) −31.4374 −2.58414
\(149\) 8.75292 0.717067 0.358533 0.933517i \(-0.383277\pi\)
0.358533 + 0.933517i \(0.383277\pi\)
\(150\) 0 0
\(151\) 20.0492 1.63158 0.815791 0.578347i \(-0.196302\pi\)
0.815791 + 0.578347i \(0.196302\pi\)
\(152\) 27.7897 2.25404
\(153\) 0 0
\(154\) −35.6965 −2.87651
\(155\) 9.25991 0.743774
\(156\) 0 0
\(157\) −9.08819 −0.725316 −0.362658 0.931922i \(-0.618131\pi\)
−0.362658 + 0.931922i \(0.618131\pi\)
\(158\) −4.74783 −0.377717
\(159\) 0 0
\(160\) 9.23821 0.730345
\(161\) 4.28183 0.337455
\(162\) 0 0
\(163\) −11.1959 −0.876933 −0.438467 0.898747i \(-0.644478\pi\)
−0.438467 + 0.898747i \(0.644478\pi\)
\(164\) 12.9517 1.01136
\(165\) 0 0
\(166\) 5.85107 0.454131
\(167\) 11.7353 0.908102 0.454051 0.890976i \(-0.349978\pi\)
0.454051 + 0.890976i \(0.349978\pi\)
\(168\) 0 0
\(169\) 19.9260 1.53277
\(170\) 19.6435 1.50659
\(171\) 0 0
\(172\) −14.1246 −1.07699
\(173\) 20.2443 1.53915 0.769573 0.638558i \(-0.220469\pi\)
0.769573 + 0.638558i \(0.220469\pi\)
\(174\) 0 0
\(175\) −3.64198 −0.275308
\(176\) 3.29392 0.248288
\(177\) 0 0
\(178\) 23.3486 1.75005
\(179\) −8.16709 −0.610437 −0.305219 0.952282i \(-0.598730\pi\)
−0.305219 + 0.952282i \(0.598730\pi\)
\(180\) 0 0
\(181\) 25.1168 1.86692 0.933459 0.358684i \(-0.116774\pi\)
0.933459 + 0.358684i \(0.116774\pi\)
\(182\) 57.2705 4.24517
\(183\) 0 0
\(184\) −3.34096 −0.246299
\(185\) −18.6521 −1.37133
\(186\) 0 0
\(187\) −14.7964 −1.08202
\(188\) −21.3813 −1.55939
\(189\) 0 0
\(190\) 39.4947 2.86525
\(191\) −24.6470 −1.78340 −0.891699 0.452629i \(-0.850486\pi\)
−0.891699 + 0.452629i \(0.850486\pi\)
\(192\) 0 0
\(193\) 1.35264 0.0973648 0.0486824 0.998814i \(-0.484498\pi\)
0.0486824 + 0.998814i \(0.484498\pi\)
\(194\) −1.72246 −0.123666
\(195\) 0 0
\(196\) 38.9132 2.77952
\(197\) −6.03899 −0.430260 −0.215130 0.976585i \(-0.569018\pi\)
−0.215130 + 0.976585i \(0.569018\pi\)
\(198\) 0 0
\(199\) −21.5865 −1.53023 −0.765114 0.643895i \(-0.777317\pi\)
−0.765114 + 0.643895i \(0.777317\pi\)
\(200\) 2.84171 0.200939
\(201\) 0 0
\(202\) 33.0072 2.32238
\(203\) 4.28183 0.300525
\(204\) 0 0
\(205\) 7.68439 0.536701
\(206\) 35.7983 2.49418
\(207\) 0 0
\(208\) −5.28467 −0.366426
\(209\) −29.7493 −2.05780
\(210\) 0 0
\(211\) −16.2713 −1.12016 −0.560081 0.828438i \(-0.689230\pi\)
−0.560081 + 0.828438i \(0.689230\pi\)
\(212\) −4.56524 −0.313542
\(213\) 0 0
\(214\) 30.5366 2.08744
\(215\) −8.38029 −0.571531
\(216\) 0 0
\(217\) 19.4644 1.32133
\(218\) −40.5864 −2.74886
\(219\) 0 0
\(220\) 25.0133 1.68640
\(221\) 23.7390 1.59686
\(222\) 0 0
\(223\) −10.7544 −0.720165 −0.360083 0.932920i \(-0.617252\pi\)
−0.360083 + 0.932920i \(0.617252\pi\)
\(224\) 19.4188 1.29747
\(225\) 0 0
\(226\) −32.5228 −2.16338
\(227\) 8.21789 0.545441 0.272720 0.962093i \(-0.412077\pi\)
0.272720 + 0.962093i \(0.412077\pi\)
\(228\) 0 0
\(229\) −28.0859 −1.85597 −0.927984 0.372620i \(-0.878460\pi\)
−0.927984 + 0.372620i \(0.878460\pi\)
\(230\) −4.74817 −0.313085
\(231\) 0 0
\(232\) −3.34096 −0.219345
\(233\) 3.17124 0.207755 0.103878 0.994590i \(-0.466875\pi\)
0.103878 + 0.994590i \(0.466875\pi\)
\(234\) 0 0
\(235\) −12.6858 −0.827528
\(236\) 41.4875 2.70061
\(237\) 0 0
\(238\) 41.2908 2.67649
\(239\) −17.8380 −1.15384 −0.576921 0.816800i \(-0.695746\pi\)
−0.576921 + 0.816800i \(0.695746\pi\)
\(240\) 0 0
\(241\) −23.9855 −1.54504 −0.772522 0.634988i \(-0.781005\pi\)
−0.772522 + 0.634988i \(0.781005\pi\)
\(242\) −4.17642 −0.268470
\(243\) 0 0
\(244\) 15.1834 0.972019
\(245\) 23.0876 1.47501
\(246\) 0 0
\(247\) 47.7290 3.03692
\(248\) −15.1874 −0.964401
\(249\) 0 0
\(250\) 27.7795 1.75693
\(251\) −10.0692 −0.635564 −0.317782 0.948164i \(-0.602938\pi\)
−0.317782 + 0.948164i \(0.602938\pi\)
\(252\) 0 0
\(253\) 3.57655 0.224856
\(254\) −22.1168 −1.38773
\(255\) 0 0
\(256\) −21.4758 −1.34224
\(257\) −7.58949 −0.473419 −0.236710 0.971580i \(-0.576069\pi\)
−0.236710 + 0.971580i \(0.576069\pi\)
\(258\) 0 0
\(259\) −39.2069 −2.43620
\(260\) −40.1307 −2.48880
\(261\) 0 0
\(262\) 18.8298 1.16331
\(263\) 12.8724 0.793746 0.396873 0.917874i \(-0.370095\pi\)
0.396873 + 0.917874i \(0.370095\pi\)
\(264\) 0 0
\(265\) −2.70861 −0.166388
\(266\) 83.0183 5.09018
\(267\) 0 0
\(268\) −19.6796 −1.20213
\(269\) −16.0869 −0.980835 −0.490417 0.871488i \(-0.663156\pi\)
−0.490417 + 0.871488i \(0.663156\pi\)
\(270\) 0 0
\(271\) −5.79337 −0.351922 −0.175961 0.984397i \(-0.556303\pi\)
−0.175961 + 0.984397i \(0.556303\pi\)
\(272\) −3.81014 −0.231023
\(273\) 0 0
\(274\) −33.9325 −2.04993
\(275\) −3.04210 −0.183445
\(276\) 0 0
\(277\) 4.05254 0.243494 0.121747 0.992561i \(-0.461150\pi\)
0.121747 + 0.992561i \(0.461150\pi\)
\(278\) 37.7478 2.26396
\(279\) 0 0
\(280\) −29.1403 −1.74147
\(281\) 30.6926 1.83096 0.915482 0.402359i \(-0.131810\pi\)
0.915482 + 0.402359i \(0.131810\pi\)
\(282\) 0 0
\(283\) 25.6797 1.52650 0.763250 0.646103i \(-0.223602\pi\)
0.763250 + 0.646103i \(0.223602\pi\)
\(284\) −31.3393 −1.85964
\(285\) 0 0
\(286\) 47.8372 2.82868
\(287\) 16.1527 0.953462
\(288\) 0 0
\(289\) 0.115308 0.00678284
\(290\) −4.74817 −0.278822
\(291\) 0 0
\(292\) −40.7123 −2.38251
\(293\) −16.9783 −0.991886 −0.495943 0.868355i \(-0.665177\pi\)
−0.495943 + 0.868355i \(0.665177\pi\)
\(294\) 0 0
\(295\) 24.6150 1.43314
\(296\) 30.5918 1.77811
\(297\) 0 0
\(298\) −20.4026 −1.18189
\(299\) −5.73812 −0.331844
\(300\) 0 0
\(301\) −17.6155 −1.01534
\(302\) −46.7336 −2.68922
\(303\) 0 0
\(304\) −7.66056 −0.439363
\(305\) 9.00848 0.515824
\(306\) 0 0
\(307\) 5.04995 0.288216 0.144108 0.989562i \(-0.453969\pi\)
0.144108 + 0.989562i \(0.453969\pi\)
\(308\) 52.5783 2.99592
\(309\) 0 0
\(310\) −21.5843 −1.22591
\(311\) 11.5885 0.657124 0.328562 0.944482i \(-0.393436\pi\)
0.328562 + 0.944482i \(0.393436\pi\)
\(312\) 0 0
\(313\) −17.4835 −0.988226 −0.494113 0.869398i \(-0.664507\pi\)
−0.494113 + 0.869398i \(0.664507\pi\)
\(314\) 21.1841 1.19549
\(315\) 0 0
\(316\) 6.99320 0.393398
\(317\) −17.8893 −1.00476 −0.502382 0.864646i \(-0.667543\pi\)
−0.502382 + 0.864646i \(0.667543\pi\)
\(318\) 0 0
\(319\) 3.57655 0.200248
\(320\) −25.2858 −1.41352
\(321\) 0 0
\(322\) −9.98070 −0.556203
\(323\) 34.4116 1.91471
\(324\) 0 0
\(325\) 4.88066 0.270730
\(326\) 26.0971 1.44539
\(327\) 0 0
\(328\) −12.6034 −0.695904
\(329\) −26.6656 −1.47012
\(330\) 0 0
\(331\) −4.66032 −0.256154 −0.128077 0.991764i \(-0.540880\pi\)
−0.128077 + 0.991764i \(0.540880\pi\)
\(332\) −8.61819 −0.472985
\(333\) 0 0
\(334\) −27.3543 −1.49676
\(335\) −11.6761 −0.637935
\(336\) 0 0
\(337\) −7.31254 −0.398339 −0.199170 0.979965i \(-0.563824\pi\)
−0.199170 + 0.979965i \(0.563824\pi\)
\(338\) −46.4464 −2.52635
\(339\) 0 0
\(340\) −28.9334 −1.56913
\(341\) 16.2584 0.880440
\(342\) 0 0
\(343\) 18.5576 1.00202
\(344\) 13.7447 0.741065
\(345\) 0 0
\(346\) −47.1884 −2.53686
\(347\) 27.3907 1.47041 0.735204 0.677846i \(-0.237086\pi\)
0.735204 + 0.677846i \(0.237086\pi\)
\(348\) 0 0
\(349\) 20.2650 1.08476 0.542379 0.840134i \(-0.317524\pi\)
0.542379 + 0.840134i \(0.317524\pi\)
\(350\) 8.48926 0.453770
\(351\) 0 0
\(352\) 16.2203 0.864543
\(353\) −9.51815 −0.506600 −0.253300 0.967388i \(-0.581516\pi\)
−0.253300 + 0.967388i \(0.581516\pi\)
\(354\) 0 0
\(355\) −18.5939 −0.986863
\(356\) −34.3907 −1.82271
\(357\) 0 0
\(358\) 19.0370 1.00614
\(359\) −8.98273 −0.474090 −0.237045 0.971499i \(-0.576179\pi\)
−0.237045 + 0.971499i \(0.576179\pi\)
\(360\) 0 0
\(361\) 50.1871 2.64142
\(362\) −58.5459 −3.07711
\(363\) 0 0
\(364\) −84.3550 −4.42141
\(365\) −24.1550 −1.26433
\(366\) 0 0
\(367\) −25.2777 −1.31949 −0.659744 0.751491i \(-0.729335\pi\)
−0.659744 + 0.751491i \(0.729335\pi\)
\(368\) 0.920976 0.0480092
\(369\) 0 0
\(370\) 43.4771 2.26027
\(371\) −5.69352 −0.295593
\(372\) 0 0
\(373\) 2.48700 0.128772 0.0643859 0.997925i \(-0.479491\pi\)
0.0643859 + 0.997925i \(0.479491\pi\)
\(374\) 34.4897 1.78342
\(375\) 0 0
\(376\) 20.8062 1.07300
\(377\) −5.73812 −0.295528
\(378\) 0 0
\(379\) 32.0311 1.64533 0.822664 0.568528i \(-0.192487\pi\)
0.822664 + 0.568528i \(0.192487\pi\)
\(380\) −58.1727 −2.98420
\(381\) 0 0
\(382\) 57.4509 2.93944
\(383\) 0.611138 0.0312277 0.0156139 0.999878i \(-0.495030\pi\)
0.0156139 + 0.999878i \(0.495030\pi\)
\(384\) 0 0
\(385\) 31.1952 1.58986
\(386\) −3.15292 −0.160479
\(387\) 0 0
\(388\) 2.53706 0.128800
\(389\) −20.0636 −1.01727 −0.508633 0.860984i \(-0.669849\pi\)
−0.508633 + 0.860984i \(0.669849\pi\)
\(390\) 0 0
\(391\) −4.13707 −0.209220
\(392\) −37.8665 −1.91255
\(393\) 0 0
\(394\) 14.0765 0.709166
\(395\) 4.14914 0.208766
\(396\) 0 0
\(397\) 0.630252 0.0316314 0.0158157 0.999875i \(-0.494965\pi\)
0.0158157 + 0.999875i \(0.494965\pi\)
\(398\) 50.3170 2.52216
\(399\) 0 0
\(400\) −0.783352 −0.0391676
\(401\) 23.2037 1.15874 0.579368 0.815066i \(-0.303299\pi\)
0.579368 + 0.815066i \(0.303299\pi\)
\(402\) 0 0
\(403\) −26.0845 −1.29936
\(404\) −48.6172 −2.41879
\(405\) 0 0
\(406\) −9.98070 −0.495334
\(407\) −32.7490 −1.62331
\(408\) 0 0
\(409\) 13.6159 0.673265 0.336632 0.941636i \(-0.390712\pi\)
0.336632 + 0.941636i \(0.390712\pi\)
\(410\) −17.9119 −0.884606
\(411\) 0 0
\(412\) −52.7281 −2.59773
\(413\) 51.7409 2.54600
\(414\) 0 0
\(415\) −5.11326 −0.251000
\(416\) −26.0233 −1.27590
\(417\) 0 0
\(418\) 69.3440 3.39173
\(419\) 29.5393 1.44309 0.721543 0.692369i \(-0.243433\pi\)
0.721543 + 0.692369i \(0.243433\pi\)
\(420\) 0 0
\(421\) 10.1117 0.492816 0.246408 0.969166i \(-0.420750\pi\)
0.246408 + 0.969166i \(0.420750\pi\)
\(422\) 37.9275 1.84628
\(423\) 0 0
\(424\) 4.44245 0.215744
\(425\) 3.51885 0.170689
\(426\) 0 0
\(427\) 18.9359 0.916374
\(428\) −44.9780 −2.17410
\(429\) 0 0
\(430\) 19.5340 0.942013
\(431\) 0.288442 0.0138937 0.00694687 0.999976i \(-0.497789\pi\)
0.00694687 + 0.999976i \(0.497789\pi\)
\(432\) 0 0
\(433\) −12.5475 −0.602993 −0.301496 0.953467i \(-0.597486\pi\)
−0.301496 + 0.953467i \(0.597486\pi\)
\(434\) −45.3705 −2.17785
\(435\) 0 0
\(436\) 59.7807 2.86298
\(437\) −8.31788 −0.397898
\(438\) 0 0
\(439\) 5.33735 0.254738 0.127369 0.991855i \(-0.459347\pi\)
0.127369 + 0.991855i \(0.459347\pi\)
\(440\) −24.3405 −1.16039
\(441\) 0 0
\(442\) −55.3342 −2.63198
\(443\) −22.8067 −1.08358 −0.541790 0.840514i \(-0.682253\pi\)
−0.541790 + 0.840514i \(0.682253\pi\)
\(444\) 0 0
\(445\) −20.4044 −0.967260
\(446\) 25.0678 1.18700
\(447\) 0 0
\(448\) −53.1511 −2.51115
\(449\) −23.8512 −1.12561 −0.562805 0.826590i \(-0.690278\pi\)
−0.562805 + 0.826590i \(0.690278\pi\)
\(450\) 0 0
\(451\) 13.4921 0.635319
\(452\) 47.9036 2.25320
\(453\) 0 0
\(454\) −19.1555 −0.899010
\(455\) −50.0487 −2.34632
\(456\) 0 0
\(457\) 22.1886 1.03794 0.518969 0.854793i \(-0.326316\pi\)
0.518969 + 0.854793i \(0.326316\pi\)
\(458\) 65.4667 3.05906
\(459\) 0 0
\(460\) 6.99370 0.326083
\(461\) 18.8126 0.876192 0.438096 0.898928i \(-0.355653\pi\)
0.438096 + 0.898928i \(0.355653\pi\)
\(462\) 0 0
\(463\) −5.42370 −0.252061 −0.126030 0.992026i \(-0.540224\pi\)
−0.126030 + 0.992026i \(0.540224\pi\)
\(464\) 0.920976 0.0427552
\(465\) 0 0
\(466\) −7.39200 −0.342428
\(467\) 16.8183 0.778257 0.389129 0.921183i \(-0.372776\pi\)
0.389129 + 0.921183i \(0.372776\pi\)
\(468\) 0 0
\(469\) −24.5434 −1.13331
\(470\) 29.5698 1.36395
\(471\) 0 0
\(472\) −40.3716 −1.85825
\(473\) −14.7140 −0.676548
\(474\) 0 0
\(475\) 7.07491 0.324619
\(476\) −60.8183 −2.78760
\(477\) 0 0
\(478\) 41.5793 1.90179
\(479\) 32.8574 1.50129 0.750647 0.660704i \(-0.229742\pi\)
0.750647 + 0.660704i \(0.229742\pi\)
\(480\) 0 0
\(481\) 52.5416 2.39569
\(482\) 55.9090 2.54658
\(483\) 0 0
\(484\) 6.15155 0.279616
\(485\) 1.50526 0.0683504
\(486\) 0 0
\(487\) 2.35263 0.106608 0.0533039 0.998578i \(-0.483025\pi\)
0.0533039 + 0.998578i \(0.483025\pi\)
\(488\) −14.7750 −0.668834
\(489\) 0 0
\(490\) −53.8160 −2.43116
\(491\) 14.0933 0.636023 0.318011 0.948087i \(-0.396985\pi\)
0.318011 + 0.948087i \(0.396985\pi\)
\(492\) 0 0
\(493\) −4.13707 −0.186324
\(494\) −111.254 −5.00554
\(495\) 0 0
\(496\) 4.18659 0.187984
\(497\) −39.0846 −1.75318
\(498\) 0 0
\(499\) −7.21406 −0.322946 −0.161473 0.986877i \(-0.551624\pi\)
−0.161473 + 0.986877i \(0.551624\pi\)
\(500\) −40.9171 −1.82987
\(501\) 0 0
\(502\) 23.4708 1.04755
\(503\) 35.3702 1.57708 0.788541 0.614983i \(-0.210837\pi\)
0.788541 + 0.614983i \(0.210837\pi\)
\(504\) 0 0
\(505\) −28.8451 −1.28359
\(506\) −8.33675 −0.370614
\(507\) 0 0
\(508\) 32.5763 1.44534
\(509\) −7.23766 −0.320803 −0.160402 0.987052i \(-0.551279\pi\)
−0.160402 + 0.987052i \(0.551279\pi\)
\(510\) 0 0
\(511\) −50.7741 −2.24612
\(512\) 10.3307 0.456555
\(513\) 0 0
\(514\) 17.6907 0.780303
\(515\) −31.2841 −1.37854
\(516\) 0 0
\(517\) −22.2734 −0.979584
\(518\) 91.3892 4.01541
\(519\) 0 0
\(520\) 39.0512 1.71251
\(521\) 41.0518 1.79851 0.899256 0.437422i \(-0.144108\pi\)
0.899256 + 0.437422i \(0.144108\pi\)
\(522\) 0 0
\(523\) −29.1248 −1.27354 −0.636770 0.771054i \(-0.719730\pi\)
−0.636770 + 0.771054i \(0.719730\pi\)
\(524\) −27.7349 −1.21161
\(525\) 0 0
\(526\) −30.0048 −1.30827
\(527\) −18.8064 −0.819218
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 6.31361 0.274246
\(531\) 0 0
\(532\) −122.280 −5.30149
\(533\) −21.6464 −0.937608
\(534\) 0 0
\(535\) −26.6859 −1.15373
\(536\) 19.1503 0.827167
\(537\) 0 0
\(538\) 37.4976 1.61664
\(539\) 40.5368 1.74604
\(540\) 0 0
\(541\) 26.1303 1.12343 0.561715 0.827331i \(-0.310142\pi\)
0.561715 + 0.827331i \(0.310142\pi\)
\(542\) 13.5040 0.580048
\(543\) 0 0
\(544\) −18.7623 −0.804427
\(545\) 35.4685 1.51930
\(546\) 0 0
\(547\) −25.3917 −1.08567 −0.542835 0.839839i \(-0.682649\pi\)
−0.542835 + 0.839839i \(0.682649\pi\)
\(548\) 49.9799 2.13504
\(549\) 0 0
\(550\) 7.09097 0.302360
\(551\) −8.31788 −0.354353
\(552\) 0 0
\(553\) 8.72153 0.370877
\(554\) −9.44626 −0.401333
\(555\) 0 0
\(556\) −55.5997 −2.35795
\(557\) −29.2515 −1.23943 −0.619714 0.784828i \(-0.712751\pi\)
−0.619714 + 0.784828i \(0.712751\pi\)
\(558\) 0 0
\(559\) 23.6067 0.998455
\(560\) 8.03289 0.339451
\(561\) 0 0
\(562\) −71.5427 −3.01784
\(563\) −28.7525 −1.21177 −0.605886 0.795551i \(-0.707181\pi\)
−0.605886 + 0.795551i \(0.707181\pi\)
\(564\) 0 0
\(565\) 28.4217 1.19571
\(566\) −59.8580 −2.51602
\(567\) 0 0
\(568\) 30.4963 1.27960
\(569\) −13.9221 −0.583647 −0.291823 0.956472i \(-0.594262\pi\)
−0.291823 + 0.956472i \(0.594262\pi\)
\(570\) 0 0
\(571\) 7.66013 0.320566 0.160283 0.987071i \(-0.448759\pi\)
0.160283 + 0.987071i \(0.448759\pi\)
\(572\) −70.4606 −2.94611
\(573\) 0 0
\(574\) −37.6510 −1.57152
\(575\) −0.850567 −0.0354711
\(576\) 0 0
\(577\) −28.4816 −1.18570 −0.592851 0.805312i \(-0.701998\pi\)
−0.592851 + 0.805312i \(0.701998\pi\)
\(578\) −0.268777 −0.0111797
\(579\) 0 0
\(580\) 6.99370 0.290397
\(581\) −10.7481 −0.445907
\(582\) 0 0
\(583\) −4.75572 −0.196962
\(584\) 39.6172 1.63937
\(585\) 0 0
\(586\) 39.5756 1.63485
\(587\) −28.0018 −1.15576 −0.577879 0.816122i \(-0.696120\pi\)
−0.577879 + 0.816122i \(0.696120\pi\)
\(588\) 0 0
\(589\) −37.8116 −1.55800
\(590\) −57.3761 −2.36214
\(591\) 0 0
\(592\) −8.43300 −0.346594
\(593\) −37.7603 −1.55063 −0.775315 0.631575i \(-0.782409\pi\)
−0.775315 + 0.631575i \(0.782409\pi\)
\(594\) 0 0
\(595\) −36.0841 −1.47930
\(596\) 30.0514 1.23095
\(597\) 0 0
\(598\) 13.3752 0.546954
\(599\) 15.7412 0.643168 0.321584 0.946881i \(-0.395785\pi\)
0.321584 + 0.946881i \(0.395785\pi\)
\(600\) 0 0
\(601\) −17.6070 −0.718204 −0.359102 0.933298i \(-0.616917\pi\)
−0.359102 + 0.933298i \(0.616917\pi\)
\(602\) 41.0607 1.67351
\(603\) 0 0
\(604\) 68.8351 2.80086
\(605\) 3.64978 0.148385
\(606\) 0 0
\(607\) 33.3243 1.35259 0.676297 0.736629i \(-0.263584\pi\)
0.676297 + 0.736629i \(0.263584\pi\)
\(608\) −37.7230 −1.52987
\(609\) 0 0
\(610\) −20.9983 −0.850196
\(611\) 35.7348 1.44568
\(612\) 0 0
\(613\) −19.6103 −0.792053 −0.396027 0.918239i \(-0.629611\pi\)
−0.396027 + 0.918239i \(0.629611\pi\)
\(614\) −11.7712 −0.475046
\(615\) 0 0
\(616\) −51.1640 −2.06146
\(617\) −1.16373 −0.0468500 −0.0234250 0.999726i \(-0.507457\pi\)
−0.0234250 + 0.999726i \(0.507457\pi\)
\(618\) 0 0
\(619\) −21.1267 −0.849154 −0.424577 0.905392i \(-0.639577\pi\)
−0.424577 + 0.905392i \(0.639577\pi\)
\(620\) 31.7921 1.27680
\(621\) 0 0
\(622\) −27.0122 −1.08309
\(623\) −42.8902 −1.71836
\(624\) 0 0
\(625\) −20.0237 −0.800948
\(626\) 40.7531 1.62882
\(627\) 0 0
\(628\) −31.2025 −1.24512
\(629\) 37.8814 1.51043
\(630\) 0 0
\(631\) 22.5717 0.898565 0.449282 0.893390i \(-0.351680\pi\)
0.449282 + 0.893390i \(0.351680\pi\)
\(632\) −6.80510 −0.270692
\(633\) 0 0
\(634\) 41.6990 1.65608
\(635\) 19.3279 0.767003
\(636\) 0 0
\(637\) −65.0361 −2.57682
\(638\) −8.33675 −0.330055
\(639\) 0 0
\(640\) 40.4635 1.59946
\(641\) 1.63884 0.0647303 0.0323651 0.999476i \(-0.489696\pi\)
0.0323651 + 0.999476i \(0.489696\pi\)
\(642\) 0 0
\(643\) −17.0563 −0.672634 −0.336317 0.941749i \(-0.609181\pi\)
−0.336317 + 0.941749i \(0.609181\pi\)
\(644\) 14.7008 0.579293
\(645\) 0 0
\(646\) −80.2115 −3.15588
\(647\) 42.8199 1.68342 0.841712 0.539926i \(-0.181548\pi\)
0.841712 + 0.539926i \(0.181548\pi\)
\(648\) 0 0
\(649\) 43.2185 1.69647
\(650\) −11.3765 −0.446225
\(651\) 0 0
\(652\) −38.4391 −1.50539
\(653\) −13.5203 −0.529091 −0.264545 0.964373i \(-0.585222\pi\)
−0.264545 + 0.964373i \(0.585222\pi\)
\(654\) 0 0
\(655\) −16.4554 −0.642966
\(656\) 3.47427 0.135647
\(657\) 0 0
\(658\) 62.1561 2.42310
\(659\) −3.50630 −0.136586 −0.0682929 0.997665i \(-0.521755\pi\)
−0.0682929 + 0.997665i \(0.521755\pi\)
\(660\) 0 0
\(661\) −24.3043 −0.945328 −0.472664 0.881243i \(-0.656708\pi\)
−0.472664 + 0.881243i \(0.656708\pi\)
\(662\) 10.8629 0.422200
\(663\) 0 0
\(664\) 8.38638 0.325455
\(665\) −72.5498 −2.81336
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) 40.2907 1.55890
\(669\) 0 0
\(670\) 27.2164 1.05146
\(671\) 15.8169 0.610606
\(672\) 0 0
\(673\) −8.49381 −0.327412 −0.163706 0.986509i \(-0.552345\pi\)
−0.163706 + 0.986509i \(0.552345\pi\)
\(674\) 17.0451 0.656553
\(675\) 0 0
\(676\) 68.4120 2.63123
\(677\) −6.22294 −0.239167 −0.119584 0.992824i \(-0.538156\pi\)
−0.119584 + 0.992824i \(0.538156\pi\)
\(678\) 0 0
\(679\) 3.16408 0.121426
\(680\) 28.1551 1.07970
\(681\) 0 0
\(682\) −37.8974 −1.45117
\(683\) −24.5440 −0.939152 −0.469576 0.882892i \(-0.655593\pi\)
−0.469576 + 0.882892i \(0.655593\pi\)
\(684\) 0 0
\(685\) 29.6536 1.13301
\(686\) −43.2568 −1.65155
\(687\) 0 0
\(688\) −3.78890 −0.144450
\(689\) 7.62994 0.290678
\(690\) 0 0
\(691\) −13.7582 −0.523386 −0.261693 0.965151i \(-0.584281\pi\)
−0.261693 + 0.965151i \(0.584281\pi\)
\(692\) 69.5049 2.64218
\(693\) 0 0
\(694\) −63.8462 −2.42357
\(695\) −32.9879 −1.25130
\(696\) 0 0
\(697\) −15.6066 −0.591141
\(698\) −47.2365 −1.78793
\(699\) 0 0
\(700\) −12.5040 −0.472608
\(701\) 38.9004 1.46925 0.734625 0.678474i \(-0.237358\pi\)
0.734625 + 0.678474i \(0.237358\pi\)
\(702\) 0 0
\(703\) 76.1634 2.87256
\(704\) −44.3964 −1.67325
\(705\) 0 0
\(706\) 22.1863 0.834991
\(707\) −60.6326 −2.28032
\(708\) 0 0
\(709\) 49.1600 1.84624 0.923121 0.384510i \(-0.125629\pi\)
0.923121 + 0.384510i \(0.125629\pi\)
\(710\) 43.3414 1.62657
\(711\) 0 0
\(712\) 33.4657 1.25418
\(713\) 4.54582 0.170242
\(714\) 0 0
\(715\) −41.8050 −1.56342
\(716\) −28.0401 −1.04791
\(717\) 0 0
\(718\) 20.9382 0.781408
\(719\) −26.3301 −0.981947 −0.490973 0.871175i \(-0.663359\pi\)
−0.490973 + 0.871175i \(0.663359\pi\)
\(720\) 0 0
\(721\) −65.7596 −2.44901
\(722\) −116.983 −4.35367
\(723\) 0 0
\(724\) 86.2337 3.20485
\(725\) −0.850567 −0.0315893
\(726\) 0 0
\(727\) 30.5986 1.13484 0.567420 0.823428i \(-0.307942\pi\)
0.567420 + 0.823428i \(0.307942\pi\)
\(728\) 82.0861 3.04231
\(729\) 0 0
\(730\) 56.3041 2.08391
\(731\) 17.0199 0.629504
\(732\) 0 0
\(733\) −47.0714 −1.73862 −0.869311 0.494266i \(-0.835437\pi\)
−0.869311 + 0.494266i \(0.835437\pi\)
\(734\) 58.9210 2.17482
\(735\) 0 0
\(736\) 4.53517 0.167169
\(737\) −20.5007 −0.755154
\(738\) 0 0
\(739\) −35.4173 −1.30285 −0.651424 0.758714i \(-0.725828\pi\)
−0.651424 + 0.758714i \(0.725828\pi\)
\(740\) −64.0384 −2.35410
\(741\) 0 0
\(742\) 13.2713 0.487204
\(743\) −11.1959 −0.410738 −0.205369 0.978685i \(-0.565839\pi\)
−0.205369 + 0.978685i \(0.565839\pi\)
\(744\) 0 0
\(745\) 17.8298 0.653234
\(746\) −5.79706 −0.212245
\(747\) 0 0
\(748\) −50.8007 −1.85746
\(749\) −56.0941 −2.04963
\(750\) 0 0
\(751\) −19.4942 −0.711352 −0.355676 0.934609i \(-0.615749\pi\)
−0.355676 + 0.934609i \(0.615749\pi\)
\(752\) −5.73549 −0.209152
\(753\) 0 0
\(754\) 13.3752 0.487097
\(755\) 40.8406 1.48634
\(756\) 0 0
\(757\) 34.4467 1.25199 0.625993 0.779829i \(-0.284694\pi\)
0.625993 + 0.779829i \(0.284694\pi\)
\(758\) −74.6628 −2.71187
\(759\) 0 0
\(760\) 56.6080 2.05339
\(761\) −26.7158 −0.968447 −0.484223 0.874944i \(-0.660898\pi\)
−0.484223 + 0.874944i \(0.660898\pi\)
\(762\) 0 0
\(763\) 74.5551 2.69908
\(764\) −84.6208 −3.06147
\(765\) 0 0
\(766\) −1.42453 −0.0514704
\(767\) −69.3385 −2.50367
\(768\) 0 0
\(769\) 23.6647 0.853372 0.426686 0.904400i \(-0.359681\pi\)
0.426686 + 0.904400i \(0.359681\pi\)
\(770\) −72.7144 −2.62044
\(771\) 0 0
\(772\) 4.64401 0.167142
\(773\) −49.9240 −1.79564 −0.897822 0.440359i \(-0.854851\pi\)
−0.897822 + 0.440359i \(0.854851\pi\)
\(774\) 0 0
\(775\) −3.86653 −0.138890
\(776\) −2.46882 −0.0886253
\(777\) 0 0
\(778\) 46.7672 1.67668
\(779\) −31.3782 −1.12424
\(780\) 0 0
\(781\) −32.6468 −1.16820
\(782\) 9.64327 0.344843
\(783\) 0 0
\(784\) 10.4384 0.372799
\(785\) −18.5128 −0.660749
\(786\) 0 0
\(787\) −7.48300 −0.266740 −0.133370 0.991066i \(-0.542580\pi\)
−0.133370 + 0.991066i \(0.542580\pi\)
\(788\) −20.7337 −0.738607
\(789\) 0 0
\(790\) −9.67141 −0.344093
\(791\) 59.7427 2.12421
\(792\) 0 0
\(793\) −25.3762 −0.901136
\(794\) −1.46908 −0.0521358
\(795\) 0 0
\(796\) −74.1131 −2.62687
\(797\) 36.0709 1.27770 0.638849 0.769332i \(-0.279411\pi\)
0.638849 + 0.769332i \(0.279411\pi\)
\(798\) 0 0
\(799\) 25.7641 0.911468
\(800\) −3.85747 −0.136382
\(801\) 0 0
\(802\) −54.0865 −1.90986
\(803\) −42.4110 −1.49665
\(804\) 0 0
\(805\) 8.72215 0.307415
\(806\) 60.8015 2.14164
\(807\) 0 0
\(808\) 47.3095 1.66434
\(809\) −15.9545 −0.560929 −0.280465 0.959864i \(-0.590489\pi\)
−0.280465 + 0.959864i \(0.590489\pi\)
\(810\) 0 0
\(811\) 36.2089 1.27147 0.635733 0.771909i \(-0.280698\pi\)
0.635733 + 0.771909i \(0.280698\pi\)
\(812\) 14.7008 0.515898
\(813\) 0 0
\(814\) 76.3362 2.67558
\(815\) −22.8063 −0.798870
\(816\) 0 0
\(817\) 34.2198 1.19720
\(818\) −31.7380 −1.10969
\(819\) 0 0
\(820\) 26.3829 0.921330
\(821\) 5.97804 0.208635 0.104317 0.994544i \(-0.466734\pi\)
0.104317 + 0.994544i \(0.466734\pi\)
\(822\) 0 0
\(823\) 21.2654 0.741264 0.370632 0.928780i \(-0.379141\pi\)
0.370632 + 0.928780i \(0.379141\pi\)
\(824\) 51.3098 1.78746
\(825\) 0 0
\(826\) −120.605 −4.19639
\(827\) 35.3932 1.23074 0.615371 0.788237i \(-0.289006\pi\)
0.615371 + 0.788237i \(0.289006\pi\)
\(828\) 0 0
\(829\) 10.3204 0.358444 0.179222 0.983809i \(-0.442642\pi\)
0.179222 + 0.983809i \(0.442642\pi\)
\(830\) 11.9187 0.413705
\(831\) 0 0
\(832\) 71.2283 2.46940
\(833\) −46.8897 −1.62463
\(834\) 0 0
\(835\) 23.9049 0.827264
\(836\) −102.139 −3.53253
\(837\) 0 0
\(838\) −68.8544 −2.37853
\(839\) −23.4456 −0.809433 −0.404717 0.914442i \(-0.632630\pi\)
−0.404717 + 0.914442i \(0.632630\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) −23.5699 −0.812272
\(843\) 0 0
\(844\) −55.8643 −1.92293
\(845\) 40.5896 1.39632
\(846\) 0 0
\(847\) 7.67187 0.263608
\(848\) −1.22462 −0.0420535
\(849\) 0 0
\(850\) −8.20225 −0.281335
\(851\) −9.15659 −0.313884
\(852\) 0 0
\(853\) 23.9444 0.819842 0.409921 0.912121i \(-0.365556\pi\)
0.409921 + 0.912121i \(0.365556\pi\)
\(854\) −44.1386 −1.51039
\(855\) 0 0
\(856\) 43.7682 1.49597
\(857\) 13.0836 0.446927 0.223464 0.974712i \(-0.428264\pi\)
0.223464 + 0.974712i \(0.428264\pi\)
\(858\) 0 0
\(859\) 41.8025 1.42628 0.713141 0.701020i \(-0.247272\pi\)
0.713141 + 0.701020i \(0.247272\pi\)
\(860\) −28.7721 −0.981121
\(861\) 0 0
\(862\) −0.672342 −0.0229000
\(863\) −10.4612 −0.356105 −0.178052 0.984021i \(-0.556980\pi\)
−0.178052 + 0.984021i \(0.556980\pi\)
\(864\) 0 0
\(865\) 41.2380 1.40213
\(866\) 29.2474 0.993869
\(867\) 0 0
\(868\) 66.8273 2.26827
\(869\) 7.28498 0.247126
\(870\) 0 0
\(871\) 32.8908 1.11446
\(872\) −58.1727 −1.96998
\(873\) 0 0
\(874\) 19.3885 0.655826
\(875\) −51.0295 −1.72511
\(876\) 0 0
\(877\) 28.4848 0.961862 0.480931 0.876758i \(-0.340299\pi\)
0.480931 + 0.876758i \(0.340299\pi\)
\(878\) −12.4411 −0.419866
\(879\) 0 0
\(880\) 6.70976 0.226186
\(881\) 38.9665 1.31281 0.656407 0.754407i \(-0.272075\pi\)
0.656407 + 0.754407i \(0.272075\pi\)
\(882\) 0 0
\(883\) 10.6192 0.357365 0.178683 0.983907i \(-0.442816\pi\)
0.178683 + 0.983907i \(0.442816\pi\)
\(884\) 81.5031 2.74125
\(885\) 0 0
\(886\) 53.1612 1.78599
\(887\) 0.468182 0.0157200 0.00786000 0.999969i \(-0.497498\pi\)
0.00786000 + 0.999969i \(0.497498\pi\)
\(888\) 0 0
\(889\) 40.6274 1.36260
\(890\) 47.5615 1.59426
\(891\) 0 0
\(892\) −36.9230 −1.23627
\(893\) 51.8006 1.73344
\(894\) 0 0
\(895\) −16.6365 −0.556097
\(896\) 85.0547 2.84148
\(897\) 0 0
\(898\) 55.5959 1.85526
\(899\) 4.54582 0.151612
\(900\) 0 0
\(901\) 5.50103 0.183266
\(902\) −31.4494 −1.04715
\(903\) 0 0
\(904\) −46.6151 −1.55040
\(905\) 51.1633 1.70073
\(906\) 0 0
\(907\) 11.6922 0.388233 0.194117 0.980978i \(-0.437816\pi\)
0.194117 + 0.980978i \(0.437816\pi\)
\(908\) 28.2145 0.936332
\(909\) 0 0
\(910\) 116.661 3.86727
\(911\) 29.7390 0.985298 0.492649 0.870228i \(-0.336029\pi\)
0.492649 + 0.870228i \(0.336029\pi\)
\(912\) 0 0
\(913\) −8.97776 −0.297121
\(914\) −51.7203 −1.71076
\(915\) 0 0
\(916\) −96.4275 −3.18605
\(917\) −34.5894 −1.14224
\(918\) 0 0
\(919\) −16.8566 −0.556048 −0.278024 0.960574i \(-0.589679\pi\)
−0.278024 + 0.960574i \(0.589679\pi\)
\(920\) −6.80558 −0.224373
\(921\) 0 0
\(922\) −43.8512 −1.44416
\(923\) 52.3776 1.72403
\(924\) 0 0
\(925\) 7.78830 0.256078
\(926\) 12.6423 0.415453
\(927\) 0 0
\(928\) 4.53517 0.148874
\(929\) −24.0401 −0.788730 −0.394365 0.918954i \(-0.629035\pi\)
−0.394365 + 0.918954i \(0.629035\pi\)
\(930\) 0 0
\(931\) −94.2752 −3.08974
\(932\) 10.8878 0.356643
\(933\) 0 0
\(934\) −39.2025 −1.28275
\(935\) −30.1406 −0.985702
\(936\) 0 0
\(937\) 5.39247 0.176164 0.0880821 0.996113i \(-0.471926\pi\)
0.0880821 + 0.996113i \(0.471926\pi\)
\(938\) 57.2092 1.86795
\(939\) 0 0
\(940\) −43.5541 −1.42058
\(941\) 8.82008 0.287527 0.143763 0.989612i \(-0.454080\pi\)
0.143763 + 0.989612i \(0.454080\pi\)
\(942\) 0 0
\(943\) 3.77238 0.122846
\(944\) 11.1289 0.362215
\(945\) 0 0
\(946\) 34.2974 1.11511
\(947\) −9.44632 −0.306964 −0.153482 0.988151i \(-0.549049\pi\)
−0.153482 + 0.988151i \(0.549049\pi\)
\(948\) 0 0
\(949\) 68.0429 2.20877
\(950\) −16.4912 −0.535046
\(951\) 0 0
\(952\) 59.1824 1.91811
\(953\) 52.6988 1.70708 0.853541 0.521025i \(-0.174450\pi\)
0.853541 + 0.521025i \(0.174450\pi\)
\(954\) 0 0
\(955\) −50.2064 −1.62464
\(956\) −61.2432 −1.98075
\(957\) 0 0
\(958\) −76.5888 −2.47447
\(959\) 62.3322 2.01281
\(960\) 0 0
\(961\) −10.3355 −0.333403
\(962\) −122.472 −3.94864
\(963\) 0 0
\(964\) −82.3497 −2.65230
\(965\) 2.75534 0.0886975
\(966\) 0 0
\(967\) −37.7635 −1.21439 −0.607197 0.794552i \(-0.707706\pi\)
−0.607197 + 0.794552i \(0.707706\pi\)
\(968\) −5.98608 −0.192400
\(969\) 0 0
\(970\) −3.50868 −0.112657
\(971\) −10.8940 −0.349605 −0.174803 0.984604i \(-0.555929\pi\)
−0.174803 + 0.984604i \(0.555929\pi\)
\(972\) 0 0
\(973\) −69.3408 −2.22297
\(974\) −5.48385 −0.175714
\(975\) 0 0
\(976\) 4.07292 0.130371
\(977\) −57.4977 −1.83951 −0.919756 0.392489i \(-0.871614\pi\)
−0.919756 + 0.392489i \(0.871614\pi\)
\(978\) 0 0
\(979\) −35.8256 −1.14499
\(980\) 79.2669 2.53209
\(981\) 0 0
\(982\) −32.8508 −1.04831
\(983\) 48.8762 1.55891 0.779454 0.626459i \(-0.215496\pi\)
0.779454 + 0.626459i \(0.215496\pi\)
\(984\) 0 0
\(985\) −12.3015 −0.391959
\(986\) 9.64327 0.307104
\(987\) 0 0
\(988\) 163.868 5.21334
\(989\) −4.11401 −0.130818
\(990\) 0 0
\(991\) 39.1297 1.24300 0.621498 0.783416i \(-0.286524\pi\)
0.621498 + 0.783416i \(0.286524\pi\)
\(992\) 20.6161 0.654561
\(993\) 0 0
\(994\) 91.1040 2.88964
\(995\) −43.9721 −1.39401
\(996\) 0 0
\(997\) 2.04245 0.0646851 0.0323425 0.999477i \(-0.489703\pi\)
0.0323425 + 0.999477i \(0.489703\pi\)
\(998\) 16.8156 0.532288
\(999\) 0 0
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 \(a_p\))