Properties

Label 8001.2.a.z.1.6
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 1
Dimension 32
CM No

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(1\)
Dimension: \(32\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.96743 q^{2}\) \(+1.87078 q^{4}\) \(+2.35101 q^{5}\) \(-1.00000 q^{7}\) \(+0.254227 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.96743 q^{2}\) \(+1.87078 q^{4}\) \(+2.35101 q^{5}\) \(-1.00000 q^{7}\) \(+0.254227 q^{8}\) \(-4.62544 q^{10}\) \(-2.89015 q^{11}\) \(+6.85121 q^{13}\) \(+1.96743 q^{14}\) \(-4.24174 q^{16}\) \(+2.39968 q^{17}\) \(-4.06451 q^{19}\) \(+4.39822 q^{20}\) \(+5.68618 q^{22}\) \(-2.32861 q^{23}\) \(+0.527232 q^{25}\) \(-13.4793 q^{26}\) \(-1.87078 q^{28}\) \(+3.14236 q^{29}\) \(-6.35057 q^{31}\) \(+7.83687 q^{32}\) \(-4.72121 q^{34}\) \(-2.35101 q^{35}\) \(+5.72445 q^{37}\) \(+7.99665 q^{38}\) \(+0.597690 q^{40}\) \(+5.44826 q^{41}\) \(-4.92110 q^{43}\) \(-5.40685 q^{44}\) \(+4.58138 q^{46}\) \(-6.42833 q^{47}\) \(+1.00000 q^{49}\) \(-1.03729 q^{50}\) \(+12.8171 q^{52}\) \(-13.2746 q^{53}\) \(-6.79477 q^{55}\) \(-0.254227 q^{56}\) \(-6.18238 q^{58}\) \(-4.10912 q^{59}\) \(+10.0147 q^{61}\) \(+12.4943 q^{62}\) \(-6.93502 q^{64}\) \(+16.1072 q^{65}\) \(-9.78035 q^{67}\) \(+4.48929 q^{68}\) \(+4.62544 q^{70}\) \(-0.218239 q^{71}\) \(-12.3655 q^{73}\) \(-11.2625 q^{74}\) \(-7.60382 q^{76}\) \(+2.89015 q^{77}\) \(-2.97850 q^{79}\) \(-9.97236 q^{80}\) \(-10.7191 q^{82}\) \(+13.0162 q^{83}\) \(+5.64167 q^{85}\) \(+9.68193 q^{86}\) \(-0.734756 q^{88}\) \(+7.20192 q^{89}\) \(-6.85121 q^{91}\) \(-4.35632 q^{92}\) \(+12.6473 q^{94}\) \(-9.55570 q^{95}\) \(-18.5452 q^{97}\) \(-1.96743 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(32q \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(32q \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut +\mathstrut 18q^{16} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 10q^{22} \) \(\mathstrut +\mathstrut 36q^{25} \) \(\mathstrut -\mathstrut 30q^{28} \) \(\mathstrut -\mathstrut 58q^{31} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut -\mathstrut 34q^{40} \) \(\mathstrut +\mathstrut 6q^{43} \) \(\mathstrut -\mathstrut 36q^{46} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 56q^{52} \) \(\mathstrut -\mathstrut 88q^{55} \) \(\mathstrut -\mathstrut 22q^{58} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut +\mathstrut 20q^{64} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut +\mathstrut 16q^{70} \) \(\mathstrut -\mathstrut 60q^{73} \) \(\mathstrut -\mathstrut 128q^{76} \) \(\mathstrut -\mathstrut 74q^{79} \) \(\mathstrut -\mathstrut 52q^{82} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 64q^{88} \) \(\mathstrut +\mathstrut 14q^{91} \) \(\mathstrut -\mathstrut 58q^{94} \) \(\mathstrut -\mathstrut 44q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.96743 −1.39118 −0.695592 0.718437i \(-0.744858\pi\)
−0.695592 + 0.718437i \(0.744858\pi\)
\(3\) 0 0
\(4\) 1.87078 0.935391
\(5\) 2.35101 1.05140 0.525701 0.850669i \(-0.323803\pi\)
0.525701 + 0.850669i \(0.323803\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0.254227 0.0898829
\(9\) 0 0
\(10\) −4.62544 −1.46269
\(11\) −2.89015 −0.871414 −0.435707 0.900088i \(-0.643502\pi\)
−0.435707 + 0.900088i \(0.643502\pi\)
\(12\) 0 0
\(13\) 6.85121 1.90018 0.950092 0.311970i \(-0.100989\pi\)
0.950092 + 0.311970i \(0.100989\pi\)
\(14\) 1.96743 0.525818
\(15\) 0 0
\(16\) −4.24174 −1.06043
\(17\) 2.39968 0.582009 0.291005 0.956722i \(-0.406011\pi\)
0.291005 + 0.956722i \(0.406011\pi\)
\(18\) 0 0
\(19\) −4.06451 −0.932464 −0.466232 0.884663i \(-0.654389\pi\)
−0.466232 + 0.884663i \(0.654389\pi\)
\(20\) 4.39822 0.983472
\(21\) 0 0
\(22\) 5.68618 1.21230
\(23\) −2.32861 −0.485549 −0.242775 0.970083i \(-0.578058\pi\)
−0.242775 + 0.970083i \(0.578058\pi\)
\(24\) 0 0
\(25\) 0.527232 0.105446
\(26\) −13.4793 −2.64350
\(27\) 0 0
\(28\) −1.87078 −0.353545
\(29\) 3.14236 0.583522 0.291761 0.956491i \(-0.405759\pi\)
0.291761 + 0.956491i \(0.405759\pi\)
\(30\) 0 0
\(31\) −6.35057 −1.14060 −0.570298 0.821438i \(-0.693172\pi\)
−0.570298 + 0.821438i \(0.693172\pi\)
\(32\) 7.83687 1.38538
\(33\) 0 0
\(34\) −4.72121 −0.809681
\(35\) −2.35101 −0.397393
\(36\) 0 0
\(37\) 5.72445 0.941095 0.470547 0.882375i \(-0.344057\pi\)
0.470547 + 0.882375i \(0.344057\pi\)
\(38\) 7.99665 1.29723
\(39\) 0 0
\(40\) 0.597690 0.0945031
\(41\) 5.44826 0.850875 0.425438 0.904988i \(-0.360120\pi\)
0.425438 + 0.904988i \(0.360120\pi\)
\(42\) 0 0
\(43\) −4.92110 −0.750461 −0.375231 0.926931i \(-0.622436\pi\)
−0.375231 + 0.926931i \(0.622436\pi\)
\(44\) −5.40685 −0.815113
\(45\) 0 0
\(46\) 4.58138 0.675488
\(47\) −6.42833 −0.937668 −0.468834 0.883286i \(-0.655326\pi\)
−0.468834 + 0.883286i \(0.655326\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −1.03729 −0.146695
\(51\) 0 0
\(52\) 12.8171 1.77742
\(53\) −13.2746 −1.82340 −0.911702 0.410853i \(-0.865231\pi\)
−0.911702 + 0.410853i \(0.865231\pi\)
\(54\) 0 0
\(55\) −6.79477 −0.916207
\(56\) −0.254227 −0.0339726
\(57\) 0 0
\(58\) −6.18238 −0.811787
\(59\) −4.10912 −0.534962 −0.267481 0.963563i \(-0.586191\pi\)
−0.267481 + 0.963563i \(0.586191\pi\)
\(60\) 0 0
\(61\) 10.0147 1.28225 0.641126 0.767436i \(-0.278468\pi\)
0.641126 + 0.767436i \(0.278468\pi\)
\(62\) 12.4943 1.58678
\(63\) 0 0
\(64\) −6.93502 −0.866877
\(65\) 16.1072 1.99786
\(66\) 0 0
\(67\) −9.78035 −1.19486 −0.597430 0.801921i \(-0.703811\pi\)
−0.597430 + 0.801921i \(0.703811\pi\)
\(68\) 4.48929 0.544406
\(69\) 0 0
\(70\) 4.62544 0.552846
\(71\) −0.218239 −0.0259003 −0.0129501 0.999916i \(-0.504122\pi\)
−0.0129501 + 0.999916i \(0.504122\pi\)
\(72\) 0 0
\(73\) −12.3655 −1.44727 −0.723635 0.690183i \(-0.757530\pi\)
−0.723635 + 0.690183i \(0.757530\pi\)
\(74\) −11.2625 −1.30924
\(75\) 0 0
\(76\) −7.60382 −0.872218
\(77\) 2.89015 0.329364
\(78\) 0 0
\(79\) −2.97850 −0.335107 −0.167553 0.985863i \(-0.553587\pi\)
−0.167553 + 0.985863i \(0.553587\pi\)
\(80\) −9.97236 −1.11494
\(81\) 0 0
\(82\) −10.7191 −1.18372
\(83\) 13.0162 1.42871 0.714355 0.699783i \(-0.246720\pi\)
0.714355 + 0.699783i \(0.246720\pi\)
\(84\) 0 0
\(85\) 5.64167 0.611926
\(86\) 9.68193 1.04403
\(87\) 0 0
\(88\) −0.734756 −0.0783253
\(89\) 7.20192 0.763402 0.381701 0.924286i \(-0.375338\pi\)
0.381701 + 0.924286i \(0.375338\pi\)
\(90\) 0 0
\(91\) −6.85121 −0.718202
\(92\) −4.35632 −0.454178
\(93\) 0 0
\(94\) 12.6473 1.30447
\(95\) −9.55570 −0.980394
\(96\) 0 0
\(97\) −18.5452 −1.88298 −0.941491 0.337039i \(-0.890574\pi\)
−0.941491 + 0.337039i \(0.890574\pi\)
\(98\) −1.96743 −0.198740
\(99\) 0 0
\(100\) 0.986336 0.0986336
\(101\) −4.67088 −0.464770 −0.232385 0.972624i \(-0.574653\pi\)
−0.232385 + 0.972624i \(0.574653\pi\)
\(102\) 0 0
\(103\) −5.40554 −0.532624 −0.266312 0.963887i \(-0.585805\pi\)
−0.266312 + 0.963887i \(0.585805\pi\)
\(104\) 1.74176 0.170794
\(105\) 0 0
\(106\) 26.1168 2.53669
\(107\) 12.5665 1.21485 0.607425 0.794377i \(-0.292203\pi\)
0.607425 + 0.794377i \(0.292203\pi\)
\(108\) 0 0
\(109\) −16.6939 −1.59898 −0.799492 0.600676i \(-0.794898\pi\)
−0.799492 + 0.600676i \(0.794898\pi\)
\(110\) 13.3682 1.27461
\(111\) 0 0
\(112\) 4.24174 0.400807
\(113\) 4.88624 0.459658 0.229829 0.973231i \(-0.426183\pi\)
0.229829 + 0.973231i \(0.426183\pi\)
\(114\) 0 0
\(115\) −5.47458 −0.510507
\(116\) 5.87868 0.545822
\(117\) 0 0
\(118\) 8.08440 0.744230
\(119\) −2.39968 −0.219979
\(120\) 0 0
\(121\) −2.64701 −0.240637
\(122\) −19.7032 −1.78385
\(123\) 0 0
\(124\) −11.8805 −1.06690
\(125\) −10.5155 −0.940536
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) −2.02957 −0.179391
\(129\) 0 0
\(130\) −31.6899 −2.77939
\(131\) 21.4230 1.87173 0.935866 0.352356i \(-0.114619\pi\)
0.935866 + 0.352356i \(0.114619\pi\)
\(132\) 0 0
\(133\) 4.06451 0.352438
\(134\) 19.2422 1.66227
\(135\) 0 0
\(136\) 0.610065 0.0523127
\(137\) −8.73744 −0.746490 −0.373245 0.927733i \(-0.621755\pi\)
−0.373245 + 0.927733i \(0.621755\pi\)
\(138\) 0 0
\(139\) −7.92793 −0.672438 −0.336219 0.941784i \(-0.609148\pi\)
−0.336219 + 0.941784i \(0.609148\pi\)
\(140\) −4.39822 −0.371718
\(141\) 0 0
\(142\) 0.429371 0.0360320
\(143\) −19.8011 −1.65585
\(144\) 0 0
\(145\) 7.38772 0.613517
\(146\) 24.3282 2.01342
\(147\) 0 0
\(148\) 10.7092 0.880291
\(149\) 0.536374 0.0439415 0.0219707 0.999759i \(-0.493006\pi\)
0.0219707 + 0.999759i \(0.493006\pi\)
\(150\) 0 0
\(151\) 12.9566 1.05439 0.527196 0.849744i \(-0.323243\pi\)
0.527196 + 0.849744i \(0.323243\pi\)
\(152\) −1.03331 −0.0838125
\(153\) 0 0
\(154\) −5.68618 −0.458205
\(155\) −14.9302 −1.19923
\(156\) 0 0
\(157\) −1.78766 −0.142671 −0.0713353 0.997452i \(-0.522726\pi\)
−0.0713353 + 0.997452i \(0.522726\pi\)
\(158\) 5.85998 0.466195
\(159\) 0 0
\(160\) 18.4245 1.45659
\(161\) 2.32861 0.183520
\(162\) 0 0
\(163\) −20.0026 −1.56672 −0.783362 0.621566i \(-0.786497\pi\)
−0.783362 + 0.621566i \(0.786497\pi\)
\(164\) 10.1925 0.795901
\(165\) 0 0
\(166\) −25.6084 −1.98760
\(167\) −8.46145 −0.654767 −0.327383 0.944892i \(-0.606167\pi\)
−0.327383 + 0.944892i \(0.606167\pi\)
\(168\) 0 0
\(169\) 33.9391 2.61070
\(170\) −11.0996 −0.851301
\(171\) 0 0
\(172\) −9.20631 −0.701975
\(173\) 17.8933 1.36040 0.680202 0.733024i \(-0.261892\pi\)
0.680202 + 0.733024i \(0.261892\pi\)
\(174\) 0 0
\(175\) −0.527232 −0.0398550
\(176\) 12.2593 0.924078
\(177\) 0 0
\(178\) −14.1693 −1.06203
\(179\) −2.60034 −0.194359 −0.0971793 0.995267i \(-0.530982\pi\)
−0.0971793 + 0.995267i \(0.530982\pi\)
\(180\) 0 0
\(181\) 2.34080 0.173990 0.0869952 0.996209i \(-0.472274\pi\)
0.0869952 + 0.996209i \(0.472274\pi\)
\(182\) 13.4793 0.999151
\(183\) 0 0
\(184\) −0.591997 −0.0436426
\(185\) 13.4582 0.989469
\(186\) 0 0
\(187\) −6.93546 −0.507171
\(188\) −12.0260 −0.877087
\(189\) 0 0
\(190\) 18.8002 1.36391
\(191\) −14.5839 −1.05525 −0.527626 0.849477i \(-0.676918\pi\)
−0.527626 + 0.849477i \(0.676918\pi\)
\(192\) 0 0
\(193\) 4.35927 0.313787 0.156894 0.987615i \(-0.449852\pi\)
0.156894 + 0.987615i \(0.449852\pi\)
\(194\) 36.4864 2.61957
\(195\) 0 0
\(196\) 1.87078 0.133627
\(197\) −21.7166 −1.54724 −0.773620 0.633649i \(-0.781556\pi\)
−0.773620 + 0.633649i \(0.781556\pi\)
\(198\) 0 0
\(199\) −12.8349 −0.909842 −0.454921 0.890532i \(-0.650332\pi\)
−0.454921 + 0.890532i \(0.650332\pi\)
\(200\) 0.134037 0.00947783
\(201\) 0 0
\(202\) 9.18963 0.646580
\(203\) −3.14236 −0.220551
\(204\) 0 0
\(205\) 12.8089 0.894612
\(206\) 10.6350 0.740977
\(207\) 0 0
\(208\) −29.0610 −2.01502
\(209\) 11.7471 0.812562
\(210\) 0 0
\(211\) −16.0684 −1.10619 −0.553097 0.833117i \(-0.686554\pi\)
−0.553097 + 0.833117i \(0.686554\pi\)
\(212\) −24.8338 −1.70560
\(213\) 0 0
\(214\) −24.7237 −1.69008
\(215\) −11.5695 −0.789037
\(216\) 0 0
\(217\) 6.35057 0.431105
\(218\) 32.8441 2.22448
\(219\) 0 0
\(220\) −12.7115 −0.857012
\(221\) 16.4407 1.10592
\(222\) 0 0
\(223\) −21.4097 −1.43370 −0.716848 0.697229i \(-0.754416\pi\)
−0.716848 + 0.697229i \(0.754416\pi\)
\(224\) −7.83687 −0.523623
\(225\) 0 0
\(226\) −9.61333 −0.639469
\(227\) 21.6474 1.43679 0.718395 0.695635i \(-0.244877\pi\)
0.718395 + 0.695635i \(0.244877\pi\)
\(228\) 0 0
\(229\) −24.4516 −1.61580 −0.807902 0.589316i \(-0.799397\pi\)
−0.807902 + 0.589316i \(0.799397\pi\)
\(230\) 10.7709 0.710209
\(231\) 0 0
\(232\) 0.798875 0.0524487
\(233\) 5.42084 0.355131 0.177566 0.984109i \(-0.443178\pi\)
0.177566 + 0.984109i \(0.443178\pi\)
\(234\) 0 0
\(235\) −15.1130 −0.985867
\(236\) −7.68727 −0.500398
\(237\) 0 0
\(238\) 4.72121 0.306031
\(239\) −13.9893 −0.904895 −0.452448 0.891791i \(-0.649449\pi\)
−0.452448 + 0.891791i \(0.649449\pi\)
\(240\) 0 0
\(241\) 9.01626 0.580788 0.290394 0.956907i \(-0.406214\pi\)
0.290394 + 0.956907i \(0.406214\pi\)
\(242\) 5.20780 0.334770
\(243\) 0 0
\(244\) 18.7353 1.19941
\(245\) 2.35101 0.150200
\(246\) 0 0
\(247\) −27.8468 −1.77185
\(248\) −1.61449 −0.102520
\(249\) 0 0
\(250\) 20.6885 1.30846
\(251\) −18.3298 −1.15697 −0.578485 0.815693i \(-0.696356\pi\)
−0.578485 + 0.815693i \(0.696356\pi\)
\(252\) 0 0
\(253\) 6.73005 0.423114
\(254\) 1.96743 0.123448
\(255\) 0 0
\(256\) 17.8631 1.11644
\(257\) −1.18621 −0.0739939 −0.0369970 0.999315i \(-0.511779\pi\)
−0.0369970 + 0.999315i \(0.511779\pi\)
\(258\) 0 0
\(259\) −5.72445 −0.355700
\(260\) 30.1331 1.86878
\(261\) 0 0
\(262\) −42.1482 −2.60392
\(263\) 13.8991 0.857054 0.428527 0.903529i \(-0.359033\pi\)
0.428527 + 0.903529i \(0.359033\pi\)
\(264\) 0 0
\(265\) −31.2086 −1.91713
\(266\) −7.99665 −0.490306
\(267\) 0 0
\(268\) −18.2969 −1.11766
\(269\) 24.4471 1.49057 0.745283 0.666748i \(-0.232314\pi\)
0.745283 + 0.666748i \(0.232314\pi\)
\(270\) 0 0
\(271\) 5.36960 0.326180 0.163090 0.986611i \(-0.447854\pi\)
0.163090 + 0.986611i \(0.447854\pi\)
\(272\) −10.1788 −0.617183
\(273\) 0 0
\(274\) 17.1903 1.03850
\(275\) −1.52378 −0.0918875
\(276\) 0 0
\(277\) −10.2489 −0.615799 −0.307899 0.951419i \(-0.599626\pi\)
−0.307899 + 0.951419i \(0.599626\pi\)
\(278\) 15.5976 0.935485
\(279\) 0 0
\(280\) −0.597690 −0.0357188
\(281\) 22.3072 1.33074 0.665369 0.746515i \(-0.268274\pi\)
0.665369 + 0.746515i \(0.268274\pi\)
\(282\) 0 0
\(283\) 21.7199 1.29111 0.645557 0.763712i \(-0.276625\pi\)
0.645557 + 0.763712i \(0.276625\pi\)
\(284\) −0.408278 −0.0242269
\(285\) 0 0
\(286\) 38.9572 2.30359
\(287\) −5.44826 −0.321601
\(288\) 0 0
\(289\) −11.2415 −0.661266
\(290\) −14.5348 −0.853514
\(291\) 0 0
\(292\) −23.1331 −1.35376
\(293\) −10.2743 −0.600233 −0.300117 0.953902i \(-0.597026\pi\)
−0.300117 + 0.953902i \(0.597026\pi\)
\(294\) 0 0
\(295\) −9.66057 −0.562460
\(296\) 1.45531 0.0845883
\(297\) 0 0
\(298\) −1.05528 −0.0611306
\(299\) −15.9538 −0.922633
\(300\) 0 0
\(301\) 4.92110 0.283648
\(302\) −25.4912 −1.46685
\(303\) 0 0
\(304\) 17.2406 0.988817
\(305\) 23.5446 1.34816
\(306\) 0 0
\(307\) −15.5926 −0.889915 −0.444957 0.895552i \(-0.646781\pi\)
−0.444957 + 0.895552i \(0.646781\pi\)
\(308\) 5.40685 0.308084
\(309\) 0 0
\(310\) 29.3742 1.66834
\(311\) −7.50153 −0.425373 −0.212686 0.977121i \(-0.568221\pi\)
−0.212686 + 0.977121i \(0.568221\pi\)
\(312\) 0 0
\(313\) 28.8638 1.63148 0.815739 0.578420i \(-0.196330\pi\)
0.815739 + 0.578420i \(0.196330\pi\)
\(314\) 3.51709 0.198481
\(315\) 0 0
\(316\) −5.57212 −0.313456
\(317\) −20.0007 −1.12335 −0.561675 0.827358i \(-0.689843\pi\)
−0.561675 + 0.827358i \(0.689843\pi\)
\(318\) 0 0
\(319\) −9.08192 −0.508490
\(320\) −16.3043 −0.911437
\(321\) 0 0
\(322\) −4.58138 −0.255310
\(323\) −9.75355 −0.542702
\(324\) 0 0
\(325\) 3.61218 0.200368
\(326\) 39.3537 2.17960
\(327\) 0 0
\(328\) 1.38510 0.0764792
\(329\) 6.42833 0.354405
\(330\) 0 0
\(331\) −11.3898 −0.626039 −0.313020 0.949747i \(-0.601341\pi\)
−0.313020 + 0.949747i \(0.601341\pi\)
\(332\) 24.3504 1.33640
\(333\) 0 0
\(334\) 16.6473 0.910901
\(335\) −22.9937 −1.25628
\(336\) 0 0
\(337\) 22.2950 1.21448 0.607242 0.794517i \(-0.292276\pi\)
0.607242 + 0.794517i \(0.292276\pi\)
\(338\) −66.7728 −3.63196
\(339\) 0 0
\(340\) 10.5543 0.572390
\(341\) 18.3541 0.993932
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) −1.25108 −0.0674537
\(345\) 0 0
\(346\) −35.2039 −1.89257
\(347\) −15.8395 −0.850306 −0.425153 0.905121i \(-0.639780\pi\)
−0.425153 + 0.905121i \(0.639780\pi\)
\(348\) 0 0
\(349\) 17.2082 0.921133 0.460567 0.887625i \(-0.347646\pi\)
0.460567 + 0.887625i \(0.347646\pi\)
\(350\) 1.03729 0.0554456
\(351\) 0 0
\(352\) −22.6498 −1.20724
\(353\) 7.97989 0.424727 0.212363 0.977191i \(-0.431884\pi\)
0.212363 + 0.977191i \(0.431884\pi\)
\(354\) 0 0
\(355\) −0.513082 −0.0272316
\(356\) 13.4732 0.714079
\(357\) 0 0
\(358\) 5.11599 0.270388
\(359\) 20.0243 1.05684 0.528420 0.848983i \(-0.322784\pi\)
0.528420 + 0.848983i \(0.322784\pi\)
\(360\) 0 0
\(361\) −2.47972 −0.130512
\(362\) −4.60536 −0.242053
\(363\) 0 0
\(364\) −12.8171 −0.671800
\(365\) −29.0713 −1.52166
\(366\) 0 0
\(367\) 27.9152 1.45716 0.728581 0.684960i \(-0.240180\pi\)
0.728581 + 0.684960i \(0.240180\pi\)
\(368\) 9.87736 0.514893
\(369\) 0 0
\(370\) −26.4781 −1.37653
\(371\) 13.2746 0.689182
\(372\) 0 0
\(373\) 8.01565 0.415035 0.207517 0.978231i \(-0.433462\pi\)
0.207517 + 0.978231i \(0.433462\pi\)
\(374\) 13.6450 0.705568
\(375\) 0 0
\(376\) −1.63426 −0.0842804
\(377\) 21.5290 1.10880
\(378\) 0 0
\(379\) −2.39197 −0.122867 −0.0614336 0.998111i \(-0.519567\pi\)
−0.0614336 + 0.998111i \(0.519567\pi\)
\(380\) −17.8766 −0.917052
\(381\) 0 0
\(382\) 28.6927 1.46805
\(383\) 19.5791 1.00045 0.500223 0.865896i \(-0.333251\pi\)
0.500223 + 0.865896i \(0.333251\pi\)
\(384\) 0 0
\(385\) 6.79477 0.346294
\(386\) −8.57657 −0.436536
\(387\) 0 0
\(388\) −34.6941 −1.76132
\(389\) −3.39595 −0.172181 −0.0860907 0.996287i \(-0.527437\pi\)
−0.0860907 + 0.996287i \(0.527437\pi\)
\(390\) 0 0
\(391\) −5.58793 −0.282594
\(392\) 0.254227 0.0128404
\(393\) 0 0
\(394\) 42.7258 2.15250
\(395\) −7.00246 −0.352332
\(396\) 0 0
\(397\) −6.78359 −0.340459 −0.170229 0.985404i \(-0.554451\pi\)
−0.170229 + 0.985404i \(0.554451\pi\)
\(398\) 25.2518 1.26576
\(399\) 0 0
\(400\) −2.23638 −0.111819
\(401\) −33.3109 −1.66347 −0.831734 0.555174i \(-0.812651\pi\)
−0.831734 + 0.555174i \(0.812651\pi\)
\(402\) 0 0
\(403\) −43.5091 −2.16734
\(404\) −8.73820 −0.434742
\(405\) 0 0
\(406\) 6.18238 0.306827
\(407\) −16.5446 −0.820083
\(408\) 0 0
\(409\) 20.2438 1.00099 0.500497 0.865738i \(-0.333151\pi\)
0.500497 + 0.865738i \(0.333151\pi\)
\(410\) −25.2006 −1.24457
\(411\) 0 0
\(412\) −10.1126 −0.498211
\(413\) 4.10912 0.202197
\(414\) 0 0
\(415\) 30.6011 1.50215
\(416\) 53.6921 2.63247
\(417\) 0 0
\(418\) −23.1115 −1.13042
\(419\) 28.0474 1.37020 0.685102 0.728447i \(-0.259758\pi\)
0.685102 + 0.728447i \(0.259758\pi\)
\(420\) 0 0
\(421\) 20.8208 1.01474 0.507372 0.861727i \(-0.330617\pi\)
0.507372 + 0.861727i \(0.330617\pi\)
\(422\) 31.6134 1.53892
\(423\) 0 0
\(424\) −3.37476 −0.163893
\(425\) 1.26519 0.0613708
\(426\) 0 0
\(427\) −10.0147 −0.484646
\(428\) 23.5092 1.13636
\(429\) 0 0
\(430\) 22.7623 1.09769
\(431\) −8.67253 −0.417741 −0.208870 0.977943i \(-0.566979\pi\)
−0.208870 + 0.977943i \(0.566979\pi\)
\(432\) 0 0
\(433\) −3.89886 −0.187367 −0.0936837 0.995602i \(-0.529864\pi\)
−0.0936837 + 0.995602i \(0.529864\pi\)
\(434\) −12.4943 −0.599746
\(435\) 0 0
\(436\) −31.2306 −1.49568
\(437\) 9.46467 0.452757
\(438\) 0 0
\(439\) 8.02937 0.383221 0.191610 0.981471i \(-0.438629\pi\)
0.191610 + 0.981471i \(0.438629\pi\)
\(440\) −1.72742 −0.0823514
\(441\) 0 0
\(442\) −32.3460 −1.53854
\(443\) 12.5240 0.595036 0.297518 0.954716i \(-0.403841\pi\)
0.297518 + 0.954716i \(0.403841\pi\)
\(444\) 0 0
\(445\) 16.9318 0.802643
\(446\) 42.1220 1.99453
\(447\) 0 0
\(448\) 6.93502 0.327649
\(449\) 8.48558 0.400459 0.200230 0.979749i \(-0.435831\pi\)
0.200230 + 0.979749i \(0.435831\pi\)
\(450\) 0 0
\(451\) −15.7463 −0.741465
\(452\) 9.14108 0.429960
\(453\) 0 0
\(454\) −42.5898 −1.99884
\(455\) −16.1072 −0.755119
\(456\) 0 0
\(457\) −24.8695 −1.16335 −0.581673 0.813423i \(-0.697602\pi\)
−0.581673 + 0.813423i \(0.697602\pi\)
\(458\) 48.1067 2.24788
\(459\) 0 0
\(460\) −10.2417 −0.477524
\(461\) 16.4708 0.767121 0.383560 0.923516i \(-0.374698\pi\)
0.383560 + 0.923516i \(0.374698\pi\)
\(462\) 0 0
\(463\) 40.8908 1.90035 0.950177 0.311710i \(-0.100902\pi\)
0.950177 + 0.311710i \(0.100902\pi\)
\(464\) −13.3291 −0.618787
\(465\) 0 0
\(466\) −10.6651 −0.494053
\(467\) 24.6291 1.13970 0.569850 0.821749i \(-0.307001\pi\)
0.569850 + 0.821749i \(0.307001\pi\)
\(468\) 0 0
\(469\) 9.78035 0.451615
\(470\) 29.7339 1.37152
\(471\) 0 0
\(472\) −1.04465 −0.0480839
\(473\) 14.2227 0.653963
\(474\) 0 0
\(475\) −2.14294 −0.0983249
\(476\) −4.48929 −0.205766
\(477\) 0 0
\(478\) 27.5231 1.25888
\(479\) 15.8536 0.724369 0.362184 0.932106i \(-0.382031\pi\)
0.362184 + 0.932106i \(0.382031\pi\)
\(480\) 0 0
\(481\) 39.2194 1.78825
\(482\) −17.7389 −0.807983
\(483\) 0 0
\(484\) −4.95197 −0.225090
\(485\) −43.5999 −1.97977
\(486\) 0 0
\(487\) 10.3699 0.469904 0.234952 0.972007i \(-0.424507\pi\)
0.234952 + 0.972007i \(0.424507\pi\)
\(488\) 2.54601 0.115253
\(489\) 0 0
\(490\) −4.62544 −0.208956
\(491\) −38.5101 −1.73794 −0.868968 0.494869i \(-0.835216\pi\)
−0.868968 + 0.494869i \(0.835216\pi\)
\(492\) 0 0
\(493\) 7.54068 0.339615
\(494\) 54.7867 2.46497
\(495\) 0 0
\(496\) 26.9375 1.20953
\(497\) 0.218239 0.00978937
\(498\) 0 0
\(499\) −19.6920 −0.881536 −0.440768 0.897621i \(-0.645294\pi\)
−0.440768 + 0.897621i \(0.645294\pi\)
\(500\) −19.6722 −0.879768
\(501\) 0 0
\(502\) 36.0627 1.60956
\(503\) 10.8754 0.484909 0.242454 0.970163i \(-0.422047\pi\)
0.242454 + 0.970163i \(0.422047\pi\)
\(504\) 0 0
\(505\) −10.9813 −0.488660
\(506\) −13.2409 −0.588630
\(507\) 0 0
\(508\) −1.87078 −0.0830025
\(509\) 36.5494 1.62002 0.810011 0.586415i \(-0.199461\pi\)
0.810011 + 0.586415i \(0.199461\pi\)
\(510\) 0 0
\(511\) 12.3655 0.547016
\(512\) −31.0852 −1.37379
\(513\) 0 0
\(514\) 2.33379 0.102939
\(515\) −12.7085 −0.560002
\(516\) 0 0
\(517\) 18.5789 0.817098
\(518\) 11.2625 0.494844
\(519\) 0 0
\(520\) 4.09490 0.179573
\(521\) −30.1034 −1.31885 −0.659426 0.751769i \(-0.729201\pi\)
−0.659426 + 0.751769i \(0.729201\pi\)
\(522\) 0 0
\(523\) −33.0254 −1.44410 −0.722049 0.691842i \(-0.756800\pi\)
−0.722049 + 0.691842i \(0.756800\pi\)
\(524\) 40.0777 1.75080
\(525\) 0 0
\(526\) −27.3455 −1.19232
\(527\) −15.2394 −0.663837
\(528\) 0 0
\(529\) −17.5776 −0.764242
\(530\) 61.4008 2.66708
\(531\) 0 0
\(532\) 7.60382 0.329667
\(533\) 37.3272 1.61682
\(534\) 0 0
\(535\) 29.5439 1.27730
\(536\) −2.48643 −0.107397
\(537\) 0 0
\(538\) −48.0980 −2.07365
\(539\) −2.89015 −0.124488
\(540\) 0 0
\(541\) −3.86545 −0.166189 −0.0830943 0.996542i \(-0.526480\pi\)
−0.0830943 + 0.996542i \(0.526480\pi\)
\(542\) −10.5643 −0.453776
\(543\) 0 0
\(544\) 18.8060 0.806301
\(545\) −39.2474 −1.68118
\(546\) 0 0
\(547\) −4.24929 −0.181687 −0.0908433 0.995865i \(-0.528956\pi\)
−0.0908433 + 0.995865i \(0.528956\pi\)
\(548\) −16.3458 −0.698260
\(549\) 0 0
\(550\) 2.99794 0.127832
\(551\) −12.7722 −0.544113
\(552\) 0 0
\(553\) 2.97850 0.126659
\(554\) 20.1641 0.856689
\(555\) 0 0
\(556\) −14.8314 −0.628993
\(557\) −42.3091 −1.79269 −0.896347 0.443352i \(-0.853789\pi\)
−0.896347 + 0.443352i \(0.853789\pi\)
\(558\) 0 0
\(559\) −33.7155 −1.42601
\(560\) 9.97236 0.421409
\(561\) 0 0
\(562\) −43.8879 −1.85130
\(563\) 32.4926 1.36940 0.684701 0.728825i \(-0.259933\pi\)
0.684701 + 0.728825i \(0.259933\pi\)
\(564\) 0 0
\(565\) 11.4876 0.483286
\(566\) −42.7324 −1.79618
\(567\) 0 0
\(568\) −0.0554824 −0.00232799
\(569\) −13.2130 −0.553917 −0.276959 0.960882i \(-0.589327\pi\)
−0.276959 + 0.960882i \(0.589327\pi\)
\(570\) 0 0
\(571\) 11.5633 0.483907 0.241954 0.970288i \(-0.422212\pi\)
0.241954 + 0.970288i \(0.422212\pi\)
\(572\) −37.0435 −1.54887
\(573\) 0 0
\(574\) 10.7191 0.447405
\(575\) −1.22772 −0.0511994
\(576\) 0 0
\(577\) −31.1420 −1.29646 −0.648230 0.761445i \(-0.724490\pi\)
−0.648230 + 0.761445i \(0.724490\pi\)
\(578\) 22.1169 0.919942
\(579\) 0 0
\(580\) 13.8208 0.573878
\(581\) −13.0162 −0.540002
\(582\) 0 0
\(583\) 38.3656 1.58894
\(584\) −3.14364 −0.130085
\(585\) 0 0
\(586\) 20.2141 0.835035
\(587\) −35.5404 −1.46691 −0.733455 0.679738i \(-0.762093\pi\)
−0.733455 + 0.679738i \(0.762093\pi\)
\(588\) 0 0
\(589\) 25.8120 1.06356
\(590\) 19.0065 0.782485
\(591\) 0 0
\(592\) −24.2816 −0.997969
\(593\) −47.0247 −1.93107 −0.965536 0.260271i \(-0.916188\pi\)
−0.965536 + 0.260271i \(0.916188\pi\)
\(594\) 0 0
\(595\) −5.64167 −0.231286
\(596\) 1.00344 0.0411025
\(597\) 0 0
\(598\) 31.3880 1.28355
\(599\) −24.5946 −1.00491 −0.502453 0.864604i \(-0.667569\pi\)
−0.502453 + 0.864604i \(0.667569\pi\)
\(600\) 0 0
\(601\) −35.5297 −1.44929 −0.724643 0.689124i \(-0.757995\pi\)
−0.724643 + 0.689124i \(0.757995\pi\)
\(602\) −9.68193 −0.394606
\(603\) 0 0
\(604\) 24.2390 0.986269
\(605\) −6.22313 −0.253006
\(606\) 0 0
\(607\) 6.31589 0.256354 0.128177 0.991751i \(-0.459087\pi\)
0.128177 + 0.991751i \(0.459087\pi\)
\(608\) −31.8531 −1.29181
\(609\) 0 0
\(610\) −46.3224 −1.87554
\(611\) −44.0419 −1.78174
\(612\) 0 0
\(613\) −44.7009 −1.80545 −0.902727 0.430215i \(-0.858438\pi\)
−0.902727 + 0.430215i \(0.858438\pi\)
\(614\) 30.6773 1.23803
\(615\) 0 0
\(616\) 0.734756 0.0296042
\(617\) −2.00783 −0.0808322 −0.0404161 0.999183i \(-0.512868\pi\)
−0.0404161 + 0.999183i \(0.512868\pi\)
\(618\) 0 0
\(619\) 23.2979 0.936421 0.468211 0.883617i \(-0.344899\pi\)
0.468211 + 0.883617i \(0.344899\pi\)
\(620\) −27.9312 −1.12174
\(621\) 0 0
\(622\) 14.7587 0.591771
\(623\) −7.20192 −0.288539
\(624\) 0 0
\(625\) −27.3582 −1.09433
\(626\) −56.7875 −2.26969
\(627\) 0 0
\(628\) −3.34432 −0.133453
\(629\) 13.7369 0.547725
\(630\) 0 0
\(631\) 38.1985 1.52066 0.760329 0.649538i \(-0.225038\pi\)
0.760329 + 0.649538i \(0.225038\pi\)
\(632\) −0.757215 −0.0301204
\(633\) 0 0
\(634\) 39.3499 1.56279
\(635\) −2.35101 −0.0932969
\(636\) 0 0
\(637\) 6.85121 0.271455
\(638\) 17.8680 0.707403
\(639\) 0 0
\(640\) −4.77154 −0.188612
\(641\) −48.1272 −1.90091 −0.950454 0.310864i \(-0.899382\pi\)
−0.950454 + 0.310864i \(0.899382\pi\)
\(642\) 0 0
\(643\) 26.4929 1.04478 0.522390 0.852707i \(-0.325041\pi\)
0.522390 + 0.852707i \(0.325041\pi\)
\(644\) 4.35632 0.171663
\(645\) 0 0
\(646\) 19.1894 0.754998
\(647\) −22.9476 −0.902164 −0.451082 0.892483i \(-0.648962\pi\)
−0.451082 + 0.892483i \(0.648962\pi\)
\(648\) 0 0
\(649\) 11.8760 0.466173
\(650\) −7.10671 −0.278748
\(651\) 0 0
\(652\) −37.4205 −1.46550
\(653\) −21.4210 −0.838268 −0.419134 0.907924i \(-0.637666\pi\)
−0.419134 + 0.907924i \(0.637666\pi\)
\(654\) 0 0
\(655\) 50.3655 1.96794
\(656\) −23.1101 −0.902298
\(657\) 0 0
\(658\) −12.6473 −0.493043
\(659\) −48.0153 −1.87041 −0.935205 0.354106i \(-0.884785\pi\)
−0.935205 + 0.354106i \(0.884785\pi\)
\(660\) 0 0
\(661\) 13.4557 0.523367 0.261683 0.965154i \(-0.415722\pi\)
0.261683 + 0.965154i \(0.415722\pi\)
\(662\) 22.4086 0.870935
\(663\) 0 0
\(664\) 3.30907 0.128417
\(665\) 9.55570 0.370554
\(666\) 0 0
\(667\) −7.31735 −0.283329
\(668\) −15.8295 −0.612463
\(669\) 0 0
\(670\) 45.2384 1.74771
\(671\) −28.9440 −1.11737
\(672\) 0 0
\(673\) −31.6378 −1.21955 −0.609773 0.792576i \(-0.708739\pi\)
−0.609773 + 0.792576i \(0.708739\pi\)
\(674\) −43.8638 −1.68957
\(675\) 0 0
\(676\) 63.4927 2.44203
\(677\) 9.63313 0.370231 0.185116 0.982717i \(-0.440734\pi\)
0.185116 + 0.982717i \(0.440734\pi\)
\(678\) 0 0
\(679\) 18.5452 0.711700
\(680\) 1.43427 0.0550017
\(681\) 0 0
\(682\) −36.1105 −1.38274
\(683\) 11.6247 0.444808 0.222404 0.974955i \(-0.428610\pi\)
0.222404 + 0.974955i \(0.428610\pi\)
\(684\) 0 0
\(685\) −20.5418 −0.784861
\(686\) 1.96743 0.0751168
\(687\) 0 0
\(688\) 20.8740 0.795815
\(689\) −90.9469 −3.46480
\(690\) 0 0
\(691\) −12.6074 −0.479608 −0.239804 0.970821i \(-0.577083\pi\)
−0.239804 + 0.970821i \(0.577083\pi\)
\(692\) 33.4745 1.27251
\(693\) 0 0
\(694\) 31.1630 1.18293
\(695\) −18.6386 −0.707003
\(696\) 0 0
\(697\) 13.0741 0.495217
\(698\) −33.8559 −1.28147
\(699\) 0 0
\(700\) −0.986336 −0.0372800
\(701\) −8.45875 −0.319483 −0.159741 0.987159i \(-0.551066\pi\)
−0.159741 + 0.987159i \(0.551066\pi\)
\(702\) 0 0
\(703\) −23.2671 −0.877536
\(704\) 20.0433 0.755409
\(705\) 0 0
\(706\) −15.6999 −0.590873
\(707\) 4.67088 0.175667
\(708\) 0 0
\(709\) −28.2276 −1.06011 −0.530056 0.847963i \(-0.677829\pi\)
−0.530056 + 0.847963i \(0.677829\pi\)
\(710\) 1.00945 0.0378841
\(711\) 0 0
\(712\) 1.83092 0.0686168
\(713\) 14.7880 0.553815
\(714\) 0 0
\(715\) −46.5524 −1.74096
\(716\) −4.86467 −0.181801
\(717\) 0 0
\(718\) −39.3964 −1.47026
\(719\) 20.8897 0.779056 0.389528 0.921015i \(-0.372638\pi\)
0.389528 + 0.921015i \(0.372638\pi\)
\(720\) 0 0
\(721\) 5.40554 0.201313
\(722\) 4.87868 0.181566
\(723\) 0 0
\(724\) 4.37913 0.162749
\(725\) 1.65676 0.0615304
\(726\) 0 0
\(727\) −21.4574 −0.795811 −0.397906 0.917426i \(-0.630263\pi\)
−0.397906 + 0.917426i \(0.630263\pi\)
\(728\) −1.74176 −0.0645541
\(729\) 0 0
\(730\) 57.1958 2.11691
\(731\) −11.8091 −0.436775
\(732\) 0 0
\(733\) −48.1668 −1.77908 −0.889540 0.456857i \(-0.848975\pi\)
−0.889540 + 0.456857i \(0.848975\pi\)
\(734\) −54.9212 −2.02718
\(735\) 0 0
\(736\) −18.2490 −0.672668
\(737\) 28.2667 1.04122
\(738\) 0 0
\(739\) 33.3207 1.22572 0.612861 0.790191i \(-0.290019\pi\)
0.612861 + 0.790191i \(0.290019\pi\)
\(740\) 25.1774 0.925540
\(741\) 0 0
\(742\) −26.1168 −0.958778
\(743\) −16.0300 −0.588085 −0.294043 0.955792i \(-0.595001\pi\)
−0.294043 + 0.955792i \(0.595001\pi\)
\(744\) 0 0
\(745\) 1.26102 0.0462002
\(746\) −15.7702 −0.577389
\(747\) 0 0
\(748\) −12.9747 −0.474403
\(749\) −12.5665 −0.459170
\(750\) 0 0
\(751\) −31.2938 −1.14193 −0.570964 0.820975i \(-0.693430\pi\)
−0.570964 + 0.820975i \(0.693430\pi\)
\(752\) 27.2673 0.994336
\(753\) 0 0
\(754\) −42.3568 −1.54254
\(755\) 30.4610 1.10859
\(756\) 0 0
\(757\) 6.16678 0.224136 0.112068 0.993701i \(-0.464253\pi\)
0.112068 + 0.993701i \(0.464253\pi\)
\(758\) 4.70604 0.170931
\(759\) 0 0
\(760\) −2.42932 −0.0881207
\(761\) 42.7410 1.54936 0.774680 0.632353i \(-0.217911\pi\)
0.774680 + 0.632353i \(0.217911\pi\)
\(762\) 0 0
\(763\) 16.6939 0.604359
\(764\) −27.2832 −0.987072
\(765\) 0 0
\(766\) −38.5206 −1.39181
\(767\) −28.1524 −1.01653
\(768\) 0 0
\(769\) 17.4128 0.627923 0.313961 0.949436i \(-0.398344\pi\)
0.313961 + 0.949436i \(0.398344\pi\)
\(770\) −13.3682 −0.481758
\(771\) 0 0
\(772\) 8.15525 0.293514
\(773\) −29.8993 −1.07540 −0.537701 0.843135i \(-0.680707\pi\)
−0.537701 + 0.843135i \(0.680707\pi\)
\(774\) 0 0
\(775\) −3.34823 −0.120272
\(776\) −4.71470 −0.169248
\(777\) 0 0
\(778\) 6.68129 0.239536
\(779\) −22.1445 −0.793410
\(780\) 0 0
\(781\) 0.630746 0.0225699
\(782\) 10.9939 0.393140
\(783\) 0 0
\(784\) −4.24174 −0.151491
\(785\) −4.20279 −0.150004
\(786\) 0 0
\(787\) −25.7598 −0.918238 −0.459119 0.888375i \(-0.651835\pi\)
−0.459119 + 0.888375i \(0.651835\pi\)
\(788\) −40.6269 −1.44728
\(789\) 0 0
\(790\) 13.7769 0.490159
\(791\) −4.88624 −0.173735
\(792\) 0 0
\(793\) 68.6129 2.43651
\(794\) 13.3462 0.473640
\(795\) 0 0
\(796\) −24.0113 −0.851058
\(797\) −23.7025 −0.839584 −0.419792 0.907620i \(-0.637897\pi\)
−0.419792 + 0.907620i \(0.637897\pi\)
\(798\) 0 0
\(799\) −15.4260 −0.545731
\(800\) 4.13185 0.146083
\(801\) 0 0
\(802\) 65.5369 2.31419
\(803\) 35.7381 1.26117
\(804\) 0 0
\(805\) 5.47458 0.192954
\(806\) 85.6011 3.01517
\(807\) 0 0
\(808\) −1.18747 −0.0417749
\(809\) −46.8159 −1.64596 −0.822981 0.568070i \(-0.807690\pi\)
−0.822981 + 0.568070i \(0.807690\pi\)
\(810\) 0 0
\(811\) −21.3447 −0.749515 −0.374758 0.927123i \(-0.622274\pi\)
−0.374758 + 0.927123i \(0.622274\pi\)
\(812\) −5.87868 −0.206301
\(813\) 0 0
\(814\) 32.5503 1.14089
\(815\) −47.0262 −1.64726
\(816\) 0 0
\(817\) 20.0019 0.699778
\(818\) −39.8283 −1.39257
\(819\) 0 0
\(820\) 23.9627 0.836812
\(821\) 25.9217 0.904673 0.452337 0.891847i \(-0.350591\pi\)
0.452337 + 0.891847i \(0.350591\pi\)
\(822\) 0 0
\(823\) 18.6224 0.649137 0.324568 0.945862i \(-0.394781\pi\)
0.324568 + 0.945862i \(0.394781\pi\)
\(824\) −1.37424 −0.0478738
\(825\) 0 0
\(826\) −8.08440 −0.281292
\(827\) −3.32877 −0.115753 −0.0578763 0.998324i \(-0.518433\pi\)
−0.0578763 + 0.998324i \(0.518433\pi\)
\(828\) 0 0
\(829\) 32.9044 1.14282 0.571409 0.820665i \(-0.306397\pi\)
0.571409 + 0.820665i \(0.306397\pi\)
\(830\) −60.2056 −2.08977
\(831\) 0 0
\(832\) −47.5133 −1.64723
\(833\) 2.39968 0.0831441
\(834\) 0 0
\(835\) −19.8929 −0.688423
\(836\) 21.9762 0.760063
\(837\) 0 0
\(838\) −55.1813 −1.90620
\(839\) −32.9296 −1.13686 −0.568428 0.822733i \(-0.692448\pi\)
−0.568428 + 0.822733i \(0.692448\pi\)
\(840\) 0 0
\(841\) −19.1255 −0.659502
\(842\) −40.9635 −1.41170
\(843\) 0 0
\(844\) −30.0605 −1.03472
\(845\) 79.7910 2.74490
\(846\) 0 0
\(847\) 2.64701 0.0909522
\(848\) 56.3073 1.93360
\(849\) 0 0
\(850\) −2.48917 −0.0853780
\(851\) −13.3300 −0.456948
\(852\) 0 0
\(853\) 19.4639 0.666431 0.333215 0.942851i \(-0.391866\pi\)
0.333215 + 0.942851i \(0.391866\pi\)
\(854\) 19.7032 0.674231
\(855\) 0 0
\(856\) 3.19475 0.109194
\(857\) 27.8327 0.950749 0.475374 0.879784i \(-0.342313\pi\)
0.475374 + 0.879784i \(0.342313\pi\)
\(858\) 0 0
\(859\) 50.4371 1.72089 0.860447 0.509541i \(-0.170185\pi\)
0.860447 + 0.509541i \(0.170185\pi\)
\(860\) −21.6441 −0.738058
\(861\) 0 0
\(862\) 17.0626 0.581154
\(863\) 33.6526 1.14555 0.572774 0.819714i \(-0.305867\pi\)
0.572774 + 0.819714i \(0.305867\pi\)
\(864\) 0 0
\(865\) 42.0673 1.43033
\(866\) 7.67074 0.260662
\(867\) 0 0
\(868\) 11.8805 0.403252
\(869\) 8.60831 0.292017
\(870\) 0 0
\(871\) −67.0072 −2.27045
\(872\) −4.24404 −0.143721
\(873\) 0 0
\(874\) −18.6211 −0.629868
\(875\) 10.5155 0.355489
\(876\) 0 0
\(877\) −45.8712 −1.54896 −0.774480 0.632598i \(-0.781989\pi\)
−0.774480 + 0.632598i \(0.781989\pi\)
\(878\) −15.7972 −0.533131
\(879\) 0 0
\(880\) 28.8216 0.971578
\(881\) −46.2258 −1.55739 −0.778694 0.627404i \(-0.784118\pi\)
−0.778694 + 0.627404i \(0.784118\pi\)
\(882\) 0 0
\(883\) 25.5211 0.858854 0.429427 0.903102i \(-0.358716\pi\)
0.429427 + 0.903102i \(0.358716\pi\)
\(884\) 30.7571 1.03447
\(885\) 0 0
\(886\) −24.6402 −0.827803
\(887\) 54.5602 1.83195 0.915976 0.401232i \(-0.131418\pi\)
0.915976 + 0.401232i \(0.131418\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) −33.3121 −1.11662
\(891\) 0 0
\(892\) −40.0528 −1.34107
\(893\) 26.1280 0.874342
\(894\) 0 0
\(895\) −6.11342 −0.204349
\(896\) 2.02957 0.0678033
\(897\) 0 0
\(898\) −16.6948 −0.557112
\(899\) −19.9558 −0.665564
\(900\) 0 0
\(901\) −31.8548 −1.06124
\(902\) 30.9798 1.03151
\(903\) 0 0
\(904\) 1.24221 0.0413154
\(905\) 5.50324 0.182934
\(906\) 0 0
\(907\) 13.5809 0.450947 0.225474 0.974249i \(-0.427607\pi\)
0.225474 + 0.974249i \(0.427607\pi\)
\(908\) 40.4976 1.34396
\(909\) 0 0
\(910\) 31.6899 1.05051
\(911\) −23.8052 −0.788700 −0.394350 0.918960i \(-0.629030\pi\)
−0.394350 + 0.918960i \(0.629030\pi\)
\(912\) 0 0
\(913\) −37.6188 −1.24500
\(914\) 48.9290 1.61843
\(915\) 0 0
\(916\) −45.7435 −1.51141
\(917\) −21.4230 −0.707448
\(918\) 0 0
\(919\) −6.64193 −0.219097 −0.109549 0.993981i \(-0.534941\pi\)
−0.109549 + 0.993981i \(0.534941\pi\)
\(920\) −1.39179 −0.0458859
\(921\) 0 0
\(922\) −32.4051 −1.06721
\(923\) −1.49520 −0.0492152
\(924\) 0 0
\(925\) 3.01812 0.0992351
\(926\) −80.4497 −2.64374
\(927\) 0 0
\(928\) 24.6263 0.808398
\(929\) −18.6804 −0.612883 −0.306441 0.951890i \(-0.599138\pi\)
−0.306441 + 0.951890i \(0.599138\pi\)
\(930\) 0 0
\(931\) −4.06451 −0.133209
\(932\) 10.1412 0.332187
\(933\) 0 0
\(934\) −48.4561 −1.58553
\(935\) −16.3053 −0.533241
\(936\) 0 0
\(937\) 36.7818 1.20161 0.600805 0.799396i \(-0.294847\pi\)
0.600805 + 0.799396i \(0.294847\pi\)
\(938\) −19.2422 −0.628279
\(939\) 0 0
\(940\) −28.2732 −0.922171
\(941\) −5.52071 −0.179970 −0.0899850 0.995943i \(-0.528682\pi\)
−0.0899850 + 0.995943i \(0.528682\pi\)
\(942\) 0 0
\(943\) −12.6869 −0.413142
\(944\) 17.4298 0.567292
\(945\) 0 0
\(946\) −27.9823 −0.909782
\(947\) 50.0953 1.62788 0.813940 0.580949i \(-0.197318\pi\)
0.813940 + 0.580949i \(0.197318\pi\)
\(948\) 0 0
\(949\) −84.7185 −2.75008
\(950\) 4.21609 0.136788
\(951\) 0 0
\(952\) −0.610065 −0.0197723
\(953\) −19.8040 −0.641514 −0.320757 0.947162i \(-0.603937\pi\)
−0.320757 + 0.947162i \(0.603937\pi\)
\(954\) 0 0
\(955\) −34.2868 −1.10949
\(956\) −26.1710 −0.846431
\(957\) 0 0
\(958\) −31.1908 −1.00773
\(959\) 8.73744 0.282147
\(960\) 0 0
\(961\) 9.32975 0.300960
\(962\) −77.1615 −2.48779
\(963\) 0 0
\(964\) 16.8675 0.543264
\(965\) 10.2487 0.329917
\(966\) 0 0
\(967\) 20.7804 0.668253 0.334127 0.942528i \(-0.391559\pi\)
0.334127 + 0.942528i \(0.391559\pi\)
\(968\) −0.672941 −0.0216292
\(969\) 0 0
\(970\) 85.7798 2.75422
\(971\) −32.0142 −1.02739 −0.513693 0.857974i \(-0.671723\pi\)
−0.513693 + 0.857974i \(0.671723\pi\)
\(972\) 0 0
\(973\) 7.92793 0.254158
\(974\) −20.4020 −0.653723
\(975\) 0 0
\(976\) −42.4798 −1.35974
\(977\) −30.7497 −0.983772 −0.491886 0.870660i \(-0.663692\pi\)
−0.491886 + 0.870660i \(0.663692\pi\)
\(978\) 0 0
\(979\) −20.8147 −0.665240
\(980\) 4.39822 0.140496
\(981\) 0 0
\(982\) 75.7659 2.41779
\(983\) −43.4959 −1.38730 −0.693651 0.720311i \(-0.743999\pi\)
−0.693651 + 0.720311i \(0.743999\pi\)
\(984\) 0 0
\(985\) −51.0558 −1.62677
\(986\) −14.8358 −0.472467
\(987\) 0 0
\(988\) −52.0954 −1.65737
\(989\) 11.4593 0.364386
\(990\) 0 0
\(991\) −31.8498 −1.01174 −0.505871 0.862609i \(-0.668829\pi\)
−0.505871 + 0.862609i \(0.668829\pi\)
\(992\) −49.7686 −1.58015
\(993\) 0 0
\(994\) −0.429371 −0.0136188
\(995\) −30.1749 −0.956610
\(996\) 0 0
\(997\) 20.8478 0.660257 0.330129 0.943936i \(-0.392908\pi\)
0.330129 + 0.943936i \(0.392908\pi\)
\(998\) 38.7427 1.22638
\(999\) 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 \(a_p\))