Properties

Label 4012.2.a.g.1.4
Level 4012
Weight 2
Character 4012.1
Self dual Yes
Analytic conductor 32.036
Analytic rank 1
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4012 = 2^{2} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4012.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0359812909\)
Analytic rank: \(1\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(1.85534\)
Character \(\chi\) = 4012.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.85534 q^{3}\) \(-3.75753 q^{5}\) \(-3.33364 q^{7}\) \(+0.442279 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.85534 q^{3}\) \(-3.75753 q^{5}\) \(-3.33364 q^{7}\) \(+0.442279 q^{9}\) \(+2.31567 q^{11}\) \(-1.30252 q^{13}\) \(+6.97149 q^{15}\) \(-1.00000 q^{17}\) \(-1.32303 q^{19}\) \(+6.18503 q^{21}\) \(-2.50661 q^{23}\) \(+9.11905 q^{25}\) \(+4.74544 q^{27}\) \(+6.82690 q^{29}\) \(+7.79295 q^{31}\) \(-4.29635 q^{33}\) \(+12.5263 q^{35}\) \(+2.02635 q^{37}\) \(+2.41661 q^{39}\) \(+6.45582 q^{41}\) \(-4.87421 q^{43}\) \(-1.66188 q^{45}\) \(-7.41036 q^{47}\) \(+4.11316 q^{49}\) \(+1.85534 q^{51}\) \(-0.619651 q^{53}\) \(-8.70120 q^{55}\) \(+2.45467 q^{57}\) \(+1.00000 q^{59}\) \(-1.42317 q^{61}\) \(-1.47440 q^{63}\) \(+4.89425 q^{65}\) \(+0.724862 q^{67}\) \(+4.65060 q^{69}\) \(+8.70782 q^{71}\) \(-10.8925 q^{73}\) \(-16.9189 q^{75}\) \(-7.71961 q^{77}\) \(+14.5916 q^{79}\) \(-10.1312 q^{81}\) \(-1.49687 q^{83}\) \(+3.75753 q^{85}\) \(-12.6662 q^{87}\) \(-6.21141 q^{89}\) \(+4.34213 q^{91}\) \(-14.4586 q^{93}\) \(+4.97134 q^{95}\) \(-4.07138 q^{97}\) \(+1.02417 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 9q^{13} \) \(\mathstrut -\mathstrut 16q^{15} \) \(\mathstrut -\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut 15q^{19} \) \(\mathstrut +\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut -\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 33q^{33} \) \(\mathstrut -\mathstrut 9q^{35} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut -\mathstrut 18q^{41} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 30q^{45} \) \(\mathstrut -\mathstrut 60q^{47} \) \(\mathstrut +\mathstrut 10q^{49} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 41q^{57} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 23q^{63} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 4q^{73} \) \(\mathstrut -\mathstrut 62q^{75} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 48q^{79} \) \(\mathstrut +\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 20q^{83} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 13q^{87} \) \(\mathstrut -\mathstrut 29q^{89} \) \(\mathstrut -\mathstrut 28q^{91} \) \(\mathstrut -\mathstrut 31q^{93} \) \(\mathstrut -\mathstrut 48q^{95} \) \(\mathstrut -\mathstrut 26q^{97} \) \(\mathstrut -\mathstrut 3q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.85534 −1.07118 −0.535590 0.844478i \(-0.679911\pi\)
−0.535590 + 0.844478i \(0.679911\pi\)
\(4\) 0 0
\(5\) −3.75753 −1.68042 −0.840210 0.542261i \(-0.817568\pi\)
−0.840210 + 0.542261i \(0.817568\pi\)
\(6\) 0 0
\(7\) −3.33364 −1.26000 −0.629999 0.776596i \(-0.716945\pi\)
−0.629999 + 0.776596i \(0.716945\pi\)
\(8\) 0 0
\(9\) 0.442279 0.147426
\(10\) 0 0
\(11\) 2.31567 0.698200 0.349100 0.937085i \(-0.386487\pi\)
0.349100 + 0.937085i \(0.386487\pi\)
\(12\) 0 0
\(13\) −1.30252 −0.361253 −0.180627 0.983552i \(-0.557813\pi\)
−0.180627 + 0.983552i \(0.557813\pi\)
\(14\) 0 0
\(15\) 6.97149 1.80003
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) −1.32303 −0.303524 −0.151762 0.988417i \(-0.548495\pi\)
−0.151762 + 0.988417i \(0.548495\pi\)
\(20\) 0 0
\(21\) 6.18503 1.34968
\(22\) 0 0
\(23\) −2.50661 −0.522664 −0.261332 0.965249i \(-0.584162\pi\)
−0.261332 + 0.965249i \(0.584162\pi\)
\(24\) 0 0
\(25\) 9.11905 1.82381
\(26\) 0 0
\(27\) 4.74544 0.913260
\(28\) 0 0
\(29\) 6.82690 1.26772 0.633862 0.773446i \(-0.281469\pi\)
0.633862 + 0.773446i \(0.281469\pi\)
\(30\) 0 0
\(31\) 7.79295 1.39966 0.699828 0.714312i \(-0.253260\pi\)
0.699828 + 0.714312i \(0.253260\pi\)
\(32\) 0 0
\(33\) −4.29635 −0.747898
\(34\) 0 0
\(35\) 12.5263 2.11733
\(36\) 0 0
\(37\) 2.02635 0.333130 0.166565 0.986030i \(-0.446732\pi\)
0.166565 + 0.986030i \(0.446732\pi\)
\(38\) 0 0
\(39\) 2.41661 0.386967
\(40\) 0 0
\(41\) 6.45582 1.00823 0.504115 0.863637i \(-0.331819\pi\)
0.504115 + 0.863637i \(0.331819\pi\)
\(42\) 0 0
\(43\) −4.87421 −0.743310 −0.371655 0.928371i \(-0.621210\pi\)
−0.371655 + 0.928371i \(0.621210\pi\)
\(44\) 0 0
\(45\) −1.66188 −0.247738
\(46\) 0 0
\(47\) −7.41036 −1.08091 −0.540456 0.841372i \(-0.681748\pi\)
−0.540456 + 0.841372i \(0.681748\pi\)
\(48\) 0 0
\(49\) 4.11316 0.587595
\(50\) 0 0
\(51\) 1.85534 0.259799
\(52\) 0 0
\(53\) −0.619651 −0.0851156 −0.0425578 0.999094i \(-0.513551\pi\)
−0.0425578 + 0.999094i \(0.513551\pi\)
\(54\) 0 0
\(55\) −8.70120 −1.17327
\(56\) 0 0
\(57\) 2.45467 0.325129
\(58\) 0 0
\(59\) 1.00000 0.130189
\(60\) 0 0
\(61\) −1.42317 −0.182219 −0.0911093 0.995841i \(-0.529041\pi\)
−0.0911093 + 0.995841i \(0.529041\pi\)
\(62\) 0 0
\(63\) −1.47440 −0.185757
\(64\) 0 0
\(65\) 4.89425 0.607057
\(66\) 0 0
\(67\) 0.724862 0.0885559 0.0442780 0.999019i \(-0.485901\pi\)
0.0442780 + 0.999019i \(0.485901\pi\)
\(68\) 0 0
\(69\) 4.65060 0.559867
\(70\) 0 0
\(71\) 8.70782 1.03343 0.516714 0.856158i \(-0.327155\pi\)
0.516714 + 0.856158i \(0.327155\pi\)
\(72\) 0 0
\(73\) −10.8925 −1.27487 −0.637435 0.770504i \(-0.720005\pi\)
−0.637435 + 0.770504i \(0.720005\pi\)
\(74\) 0 0
\(75\) −16.9189 −1.95363
\(76\) 0 0
\(77\) −7.71961 −0.879731
\(78\) 0 0
\(79\) 14.5916 1.64169 0.820843 0.571154i \(-0.193504\pi\)
0.820843 + 0.571154i \(0.193504\pi\)
\(80\) 0 0
\(81\) −10.1312 −1.12569
\(82\) 0 0
\(83\) −1.49687 −0.164303 −0.0821515 0.996620i \(-0.526179\pi\)
−0.0821515 + 0.996620i \(0.526179\pi\)
\(84\) 0 0
\(85\) 3.75753 0.407562
\(86\) 0 0
\(87\) −12.6662 −1.35796
\(88\) 0 0
\(89\) −6.21141 −0.658408 −0.329204 0.944259i \(-0.606780\pi\)
−0.329204 + 0.944259i \(0.606780\pi\)
\(90\) 0 0
\(91\) 4.34213 0.455179
\(92\) 0 0
\(93\) −14.4586 −1.49928
\(94\) 0 0
\(95\) 4.97134 0.510048
\(96\) 0 0
\(97\) −4.07138 −0.413386 −0.206693 0.978406i \(-0.566270\pi\)
−0.206693 + 0.978406i \(0.566270\pi\)
\(98\) 0 0
\(99\) 1.02417 0.102933
\(100\) 0 0
\(101\) 7.13480 0.709939 0.354970 0.934878i \(-0.384491\pi\)
0.354970 + 0.934878i \(0.384491\pi\)
\(102\) 0 0
\(103\) 3.16352 0.311711 0.155856 0.987780i \(-0.450187\pi\)
0.155856 + 0.987780i \(0.450187\pi\)
\(104\) 0 0
\(105\) −23.2405 −2.26804
\(106\) 0 0
\(107\) −2.34450 −0.226651 −0.113326 0.993558i \(-0.536150\pi\)
−0.113326 + 0.993558i \(0.536150\pi\)
\(108\) 0 0
\(109\) 9.44291 0.904467 0.452234 0.891900i \(-0.350627\pi\)
0.452234 + 0.891900i \(0.350627\pi\)
\(110\) 0 0
\(111\) −3.75956 −0.356842
\(112\) 0 0
\(113\) 4.66821 0.439149 0.219574 0.975596i \(-0.429533\pi\)
0.219574 + 0.975596i \(0.429533\pi\)
\(114\) 0 0
\(115\) 9.41866 0.878294
\(116\) 0 0
\(117\) −0.576077 −0.0532583
\(118\) 0 0
\(119\) 3.33364 0.305594
\(120\) 0 0
\(121\) −5.63768 −0.512517
\(122\) 0 0
\(123\) −11.9777 −1.07999
\(124\) 0 0
\(125\) −15.4775 −1.38435
\(126\) 0 0
\(127\) 12.2936 1.09088 0.545439 0.838151i \(-0.316363\pi\)
0.545439 + 0.838151i \(0.316363\pi\)
\(128\) 0 0
\(129\) 9.04331 0.796219
\(130\) 0 0
\(131\) −14.2561 −1.24557 −0.622783 0.782395i \(-0.713998\pi\)
−0.622783 + 0.782395i \(0.713998\pi\)
\(132\) 0 0
\(133\) 4.41051 0.382440
\(134\) 0 0
\(135\) −17.8311 −1.53466
\(136\) 0 0
\(137\) 6.26542 0.535291 0.267646 0.963517i \(-0.413754\pi\)
0.267646 + 0.963517i \(0.413754\pi\)
\(138\) 0 0
\(139\) −3.32589 −0.282098 −0.141049 0.990003i \(-0.545048\pi\)
−0.141049 + 0.990003i \(0.545048\pi\)
\(140\) 0 0
\(141\) 13.7487 1.15785
\(142\) 0 0
\(143\) −3.01620 −0.252227
\(144\) 0 0
\(145\) −25.6523 −2.13031
\(146\) 0 0
\(147\) −7.63131 −0.629420
\(148\) 0 0
\(149\) 13.0987 1.07309 0.536544 0.843872i \(-0.319729\pi\)
0.536544 + 0.843872i \(0.319729\pi\)
\(150\) 0 0
\(151\) −4.44446 −0.361685 −0.180842 0.983512i \(-0.557882\pi\)
−0.180842 + 0.983512i \(0.557882\pi\)
\(152\) 0 0
\(153\) −0.442279 −0.0357562
\(154\) 0 0
\(155\) −29.2823 −2.35201
\(156\) 0 0
\(157\) 16.6740 1.33073 0.665366 0.746517i \(-0.268275\pi\)
0.665366 + 0.746517i \(0.268275\pi\)
\(158\) 0 0
\(159\) 1.14966 0.0911741
\(160\) 0 0
\(161\) 8.35613 0.658555
\(162\) 0 0
\(163\) −10.2534 −0.803110 −0.401555 0.915835i \(-0.631530\pi\)
−0.401555 + 0.915835i \(0.631530\pi\)
\(164\) 0 0
\(165\) 16.1437 1.25678
\(166\) 0 0
\(167\) −23.1224 −1.78926 −0.894632 0.446804i \(-0.852562\pi\)
−0.894632 + 0.446804i \(0.852562\pi\)
\(168\) 0 0
\(169\) −11.3034 −0.869496
\(170\) 0 0
\(171\) −0.585150 −0.0447475
\(172\) 0 0
\(173\) −24.1860 −1.83883 −0.919413 0.393294i \(-0.871335\pi\)
−0.919413 + 0.393294i \(0.871335\pi\)
\(174\) 0 0
\(175\) −30.3997 −2.29800
\(176\) 0 0
\(177\) −1.85534 −0.139456
\(178\) 0 0
\(179\) −1.42312 −0.106369 −0.0531844 0.998585i \(-0.516937\pi\)
−0.0531844 + 0.998585i \(0.516937\pi\)
\(180\) 0 0
\(181\) −3.43803 −0.255547 −0.127773 0.991803i \(-0.540783\pi\)
−0.127773 + 0.991803i \(0.540783\pi\)
\(182\) 0 0
\(183\) 2.64047 0.195189
\(184\) 0 0
\(185\) −7.61408 −0.559798
\(186\) 0 0
\(187\) −2.31567 −0.169338
\(188\) 0 0
\(189\) −15.8196 −1.15071
\(190\) 0 0
\(191\) −23.7509 −1.71855 −0.859276 0.511512i \(-0.829086\pi\)
−0.859276 + 0.511512i \(0.829086\pi\)
\(192\) 0 0
\(193\) 3.29389 0.237099 0.118550 0.992948i \(-0.462176\pi\)
0.118550 + 0.992948i \(0.462176\pi\)
\(194\) 0 0
\(195\) −9.08050 −0.650268
\(196\) 0 0
\(197\) 13.7650 0.980715 0.490358 0.871521i \(-0.336866\pi\)
0.490358 + 0.871521i \(0.336866\pi\)
\(198\) 0 0
\(199\) 9.49296 0.672938 0.336469 0.941694i \(-0.390767\pi\)
0.336469 + 0.941694i \(0.390767\pi\)
\(200\) 0 0
\(201\) −1.34486 −0.0948593
\(202\) 0 0
\(203\) −22.7584 −1.59733
\(204\) 0 0
\(205\) −24.2579 −1.69425
\(206\) 0 0
\(207\) −1.10862 −0.0770544
\(208\) 0 0
\(209\) −3.06370 −0.211921
\(210\) 0 0
\(211\) 0.313416 0.0215765 0.0107882 0.999942i \(-0.496566\pi\)
0.0107882 + 0.999942i \(0.496566\pi\)
\(212\) 0 0
\(213\) −16.1560 −1.10699
\(214\) 0 0
\(215\) 18.3150 1.24907
\(216\) 0 0
\(217\) −25.9789 −1.76356
\(218\) 0 0
\(219\) 20.2093 1.36562
\(220\) 0 0
\(221\) 1.30252 0.0876168
\(222\) 0 0
\(223\) 2.29570 0.153732 0.0768658 0.997041i \(-0.475509\pi\)
0.0768658 + 0.997041i \(0.475509\pi\)
\(224\) 0 0
\(225\) 4.03317 0.268878
\(226\) 0 0
\(227\) 8.08017 0.536300 0.268150 0.963377i \(-0.413588\pi\)
0.268150 + 0.963377i \(0.413588\pi\)
\(228\) 0 0
\(229\) 16.4214 1.08516 0.542580 0.840004i \(-0.317448\pi\)
0.542580 + 0.840004i \(0.317448\pi\)
\(230\) 0 0
\(231\) 14.3225 0.942350
\(232\) 0 0
\(233\) 6.47619 0.424269 0.212135 0.977240i \(-0.431958\pi\)
0.212135 + 0.977240i \(0.431958\pi\)
\(234\) 0 0
\(235\) 27.8447 1.81639
\(236\) 0 0
\(237\) −27.0724 −1.75854
\(238\) 0 0
\(239\) −20.9063 −1.35232 −0.676158 0.736757i \(-0.736356\pi\)
−0.676158 + 0.736757i \(0.736356\pi\)
\(240\) 0 0
\(241\) 8.60994 0.554615 0.277307 0.960781i \(-0.410558\pi\)
0.277307 + 0.960781i \(0.410558\pi\)
\(242\) 0 0
\(243\) 4.56054 0.292559
\(244\) 0 0
\(245\) −15.4553 −0.987406
\(246\) 0 0
\(247\) 1.72327 0.109649
\(248\) 0 0
\(249\) 2.77720 0.175998
\(250\) 0 0
\(251\) −25.8758 −1.63327 −0.816633 0.577157i \(-0.804162\pi\)
−0.816633 + 0.577157i \(0.804162\pi\)
\(252\) 0 0
\(253\) −5.80447 −0.364924
\(254\) 0 0
\(255\) −6.97149 −0.436572
\(256\) 0 0
\(257\) 11.5391 0.719787 0.359893 0.932993i \(-0.382813\pi\)
0.359893 + 0.932993i \(0.382813\pi\)
\(258\) 0 0
\(259\) −6.75512 −0.419743
\(260\) 0 0
\(261\) 3.01940 0.186896
\(262\) 0 0
\(263\) −10.4215 −0.642615 −0.321308 0.946975i \(-0.604122\pi\)
−0.321308 + 0.946975i \(0.604122\pi\)
\(264\) 0 0
\(265\) 2.32836 0.143030
\(266\) 0 0
\(267\) 11.5243 0.705274
\(268\) 0 0
\(269\) 26.8465 1.63686 0.818429 0.574608i \(-0.194845\pi\)
0.818429 + 0.574608i \(0.194845\pi\)
\(270\) 0 0
\(271\) −12.2274 −0.742761 −0.371381 0.928481i \(-0.621116\pi\)
−0.371381 + 0.928481i \(0.621116\pi\)
\(272\) 0 0
\(273\) −8.05611 −0.487578
\(274\) 0 0
\(275\) 21.1167 1.27338
\(276\) 0 0
\(277\) 29.3809 1.76533 0.882664 0.470004i \(-0.155748\pi\)
0.882664 + 0.470004i \(0.155748\pi\)
\(278\) 0 0
\(279\) 3.44666 0.206346
\(280\) 0 0
\(281\) −2.83346 −0.169030 −0.0845150 0.996422i \(-0.526934\pi\)
−0.0845150 + 0.996422i \(0.526934\pi\)
\(282\) 0 0
\(283\) −17.2973 −1.02822 −0.514109 0.857725i \(-0.671877\pi\)
−0.514109 + 0.857725i \(0.671877\pi\)
\(284\) 0 0
\(285\) −9.22351 −0.546354
\(286\) 0 0
\(287\) −21.5214 −1.27037
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 7.55379 0.442811
\(292\) 0 0
\(293\) 17.7358 1.03614 0.518068 0.855339i \(-0.326651\pi\)
0.518068 + 0.855339i \(0.326651\pi\)
\(294\) 0 0
\(295\) −3.75753 −0.218772
\(296\) 0 0
\(297\) 10.9889 0.637638
\(298\) 0 0
\(299\) 3.26490 0.188814
\(300\) 0 0
\(301\) 16.2489 0.936570
\(302\) 0 0
\(303\) −13.2375 −0.760473
\(304\) 0 0
\(305\) 5.34762 0.306204
\(306\) 0 0
\(307\) −15.9930 −0.912769 −0.456385 0.889783i \(-0.650856\pi\)
−0.456385 + 0.889783i \(0.650856\pi\)
\(308\) 0 0
\(309\) −5.86940 −0.333899
\(310\) 0 0
\(311\) −11.1535 −0.632457 −0.316229 0.948683i \(-0.602417\pi\)
−0.316229 + 0.948683i \(0.602417\pi\)
\(312\) 0 0
\(313\) −10.7340 −0.606721 −0.303361 0.952876i \(-0.598109\pi\)
−0.303361 + 0.952876i \(0.598109\pi\)
\(314\) 0 0
\(315\) 5.54011 0.312150
\(316\) 0 0
\(317\) 4.66865 0.262218 0.131109 0.991368i \(-0.458146\pi\)
0.131109 + 0.991368i \(0.458146\pi\)
\(318\) 0 0
\(319\) 15.8088 0.885125
\(320\) 0 0
\(321\) 4.34984 0.242784
\(322\) 0 0
\(323\) 1.32303 0.0736155
\(324\) 0 0
\(325\) −11.8777 −0.658858
\(326\) 0 0
\(327\) −17.5198 −0.968847
\(328\) 0 0
\(329\) 24.7035 1.36195
\(330\) 0 0
\(331\) 9.03028 0.496349 0.248174 0.968715i \(-0.420169\pi\)
0.248174 + 0.968715i \(0.420169\pi\)
\(332\) 0 0
\(333\) 0.896213 0.0491122
\(334\) 0 0
\(335\) −2.72369 −0.148811
\(336\) 0 0
\(337\) 10.6963 0.582663 0.291331 0.956622i \(-0.405902\pi\)
0.291331 + 0.956622i \(0.405902\pi\)
\(338\) 0 0
\(339\) −8.66111 −0.470407
\(340\) 0 0
\(341\) 18.0459 0.977239
\(342\) 0 0
\(343\) 9.62368 0.519630
\(344\) 0 0
\(345\) −17.4748 −0.940811
\(346\) 0 0
\(347\) 27.6983 1.48692 0.743462 0.668778i \(-0.233182\pi\)
0.743462 + 0.668778i \(0.233182\pi\)
\(348\) 0 0
\(349\) −1.72901 −0.0925519 −0.0462760 0.998929i \(-0.514735\pi\)
−0.0462760 + 0.998929i \(0.514735\pi\)
\(350\) 0 0
\(351\) −6.18102 −0.329918
\(352\) 0 0
\(353\) −5.82177 −0.309862 −0.154931 0.987925i \(-0.549515\pi\)
−0.154931 + 0.987925i \(0.549515\pi\)
\(354\) 0 0
\(355\) −32.7199 −1.73659
\(356\) 0 0
\(357\) −6.18503 −0.327347
\(358\) 0 0
\(359\) −0.912868 −0.0481793 −0.0240897 0.999710i \(-0.507669\pi\)
−0.0240897 + 0.999710i \(0.507669\pi\)
\(360\) 0 0
\(361\) −17.2496 −0.907873
\(362\) 0 0
\(363\) 10.4598 0.548998
\(364\) 0 0
\(365\) 40.9289 2.14232
\(366\) 0 0
\(367\) 3.83714 0.200297 0.100149 0.994972i \(-0.468068\pi\)
0.100149 + 0.994972i \(0.468068\pi\)
\(368\) 0 0
\(369\) 2.85527 0.148640
\(370\) 0 0
\(371\) 2.06569 0.107245
\(372\) 0 0
\(373\) 11.3125 0.585736 0.292868 0.956153i \(-0.405390\pi\)
0.292868 + 0.956153i \(0.405390\pi\)
\(374\) 0 0
\(375\) 28.7160 1.48289
\(376\) 0 0
\(377\) −8.89216 −0.457970
\(378\) 0 0
\(379\) −5.54089 −0.284617 −0.142308 0.989822i \(-0.545452\pi\)
−0.142308 + 0.989822i \(0.545452\pi\)
\(380\) 0 0
\(381\) −22.8087 −1.16853
\(382\) 0 0
\(383\) −5.46082 −0.279035 −0.139517 0.990220i \(-0.544555\pi\)
−0.139517 + 0.990220i \(0.544555\pi\)
\(384\) 0 0
\(385\) 29.0067 1.47832
\(386\) 0 0
\(387\) −2.15576 −0.109584
\(388\) 0 0
\(389\) −6.88390 −0.349028 −0.174514 0.984655i \(-0.555835\pi\)
−0.174514 + 0.984655i \(0.555835\pi\)
\(390\) 0 0
\(391\) 2.50661 0.126765
\(392\) 0 0
\(393\) 26.4500 1.33422
\(394\) 0 0
\(395\) −54.8285 −2.75872
\(396\) 0 0
\(397\) 19.9273 1.00012 0.500060 0.865991i \(-0.333311\pi\)
0.500060 + 0.865991i \(0.333311\pi\)
\(398\) 0 0
\(399\) −8.18300 −0.409662
\(400\) 0 0
\(401\) −16.4500 −0.821473 −0.410736 0.911754i \(-0.634728\pi\)
−0.410736 + 0.911754i \(0.634728\pi\)
\(402\) 0 0
\(403\) −10.1505 −0.505630
\(404\) 0 0
\(405\) 38.0684 1.89163
\(406\) 0 0
\(407\) 4.69235 0.232591
\(408\) 0 0
\(409\) −15.2889 −0.755989 −0.377994 0.925808i \(-0.623386\pi\)
−0.377994 + 0.925808i \(0.623386\pi\)
\(410\) 0 0
\(411\) −11.6245 −0.573393
\(412\) 0 0
\(413\) −3.33364 −0.164038
\(414\) 0 0
\(415\) 5.62455 0.276098
\(416\) 0 0
\(417\) 6.17065 0.302178
\(418\) 0 0
\(419\) −2.72035 −0.132898 −0.0664488 0.997790i \(-0.521167\pi\)
−0.0664488 + 0.997790i \(0.521167\pi\)
\(420\) 0 0
\(421\) 8.86840 0.432219 0.216110 0.976369i \(-0.430663\pi\)
0.216110 + 0.976369i \(0.430663\pi\)
\(422\) 0 0
\(423\) −3.27745 −0.159355
\(424\) 0 0
\(425\) −9.11905 −0.442339
\(426\) 0 0
\(427\) 4.74435 0.229595
\(428\) 0 0
\(429\) 5.59607 0.270181
\(430\) 0 0
\(431\) −18.6159 −0.896698 −0.448349 0.893859i \(-0.647988\pi\)
−0.448349 + 0.893859i \(0.647988\pi\)
\(432\) 0 0
\(433\) 29.6155 1.42323 0.711614 0.702570i \(-0.247964\pi\)
0.711614 + 0.702570i \(0.247964\pi\)
\(434\) 0 0
\(435\) 47.5937 2.28194
\(436\) 0 0
\(437\) 3.31632 0.158641
\(438\) 0 0
\(439\) 3.72431 0.177752 0.0888759 0.996043i \(-0.471673\pi\)
0.0888759 + 0.996043i \(0.471673\pi\)
\(440\) 0 0
\(441\) 1.81917 0.0866270
\(442\) 0 0
\(443\) 5.22885 0.248430 0.124215 0.992255i \(-0.460359\pi\)
0.124215 + 0.992255i \(0.460359\pi\)
\(444\) 0 0
\(445\) 23.3396 1.10640
\(446\) 0 0
\(447\) −24.3025 −1.14947
\(448\) 0 0
\(449\) −27.0624 −1.27716 −0.638578 0.769557i \(-0.720477\pi\)
−0.638578 + 0.769557i \(0.720477\pi\)
\(450\) 0 0
\(451\) 14.9495 0.703946
\(452\) 0 0
\(453\) 8.24597 0.387430
\(454\) 0 0
\(455\) −16.3157 −0.764891
\(456\) 0 0
\(457\) −41.0564 −1.92054 −0.960268 0.279080i \(-0.909971\pi\)
−0.960268 + 0.279080i \(0.909971\pi\)
\(458\) 0 0
\(459\) −4.74544 −0.221498
\(460\) 0 0
\(461\) 3.16975 0.147630 0.0738150 0.997272i \(-0.476483\pi\)
0.0738150 + 0.997272i \(0.476483\pi\)
\(462\) 0 0
\(463\) −21.9669 −1.02089 −0.510445 0.859911i \(-0.670519\pi\)
−0.510445 + 0.859911i \(0.670519\pi\)
\(464\) 0 0
\(465\) 54.3285 2.51942
\(466\) 0 0
\(467\) 4.73251 0.218995 0.109497 0.993987i \(-0.465076\pi\)
0.109497 + 0.993987i \(0.465076\pi\)
\(468\) 0 0
\(469\) −2.41643 −0.111580
\(470\) 0 0
\(471\) −30.9360 −1.42545
\(472\) 0 0
\(473\) −11.2871 −0.518979
\(474\) 0 0
\(475\) −12.0648 −0.553571
\(476\) 0 0
\(477\) −0.274059 −0.0125483
\(478\) 0 0
\(479\) −8.48804 −0.387828 −0.193914 0.981018i \(-0.562118\pi\)
−0.193914 + 0.981018i \(0.562118\pi\)
\(480\) 0 0
\(481\) −2.63936 −0.120344
\(482\) 0 0
\(483\) −15.5034 −0.705431
\(484\) 0 0
\(485\) 15.2983 0.694662
\(486\) 0 0
\(487\) −24.8532 −1.12620 −0.563102 0.826387i \(-0.690392\pi\)
−0.563102 + 0.826387i \(0.690392\pi\)
\(488\) 0 0
\(489\) 19.0236 0.860275
\(490\) 0 0
\(491\) −24.2916 −1.09627 −0.548133 0.836391i \(-0.684661\pi\)
−0.548133 + 0.836391i \(0.684661\pi\)
\(492\) 0 0
\(493\) −6.82690 −0.307468
\(494\) 0 0
\(495\) −3.84836 −0.172971
\(496\) 0 0
\(497\) −29.0288 −1.30212
\(498\) 0 0
\(499\) 28.7278 1.28603 0.643017 0.765852i \(-0.277682\pi\)
0.643017 + 0.765852i \(0.277682\pi\)
\(500\) 0 0
\(501\) 42.8998 1.91662
\(502\) 0 0
\(503\) 15.9124 0.709499 0.354750 0.934961i \(-0.384566\pi\)
0.354750 + 0.934961i \(0.384566\pi\)
\(504\) 0 0
\(505\) −26.8093 −1.19300
\(506\) 0 0
\(507\) 20.9717 0.931387
\(508\) 0 0
\(509\) 19.6646 0.871618 0.435809 0.900039i \(-0.356462\pi\)
0.435809 + 0.900039i \(0.356462\pi\)
\(510\) 0 0
\(511\) 36.3117 1.60633
\(512\) 0 0
\(513\) −6.27837 −0.277197
\(514\) 0 0
\(515\) −11.8870 −0.523805
\(516\) 0 0
\(517\) −17.1599 −0.754693
\(518\) 0 0
\(519\) 44.8732 1.96971
\(520\) 0 0
\(521\) 8.18680 0.358670 0.179335 0.983788i \(-0.442605\pi\)
0.179335 + 0.983788i \(0.442605\pi\)
\(522\) 0 0
\(523\) −19.4485 −0.850423 −0.425211 0.905094i \(-0.639800\pi\)
−0.425211 + 0.905094i \(0.639800\pi\)
\(524\) 0 0
\(525\) 56.4016 2.46157
\(526\) 0 0
\(527\) −7.79295 −0.339466
\(528\) 0 0
\(529\) −16.7169 −0.726823
\(530\) 0 0
\(531\) 0.442279 0.0191933
\(532\) 0 0
\(533\) −8.40882 −0.364226
\(534\) 0 0
\(535\) 8.80953 0.380869
\(536\) 0 0
\(537\) 2.64036 0.113940
\(538\) 0 0
\(539\) 9.52472 0.410259
\(540\) 0 0
\(541\) 21.6221 0.929605 0.464802 0.885414i \(-0.346125\pi\)
0.464802 + 0.885414i \(0.346125\pi\)
\(542\) 0 0
\(543\) 6.37871 0.273737
\(544\) 0 0
\(545\) −35.4821 −1.51988
\(546\) 0 0
\(547\) 30.4016 1.29988 0.649938 0.759987i \(-0.274795\pi\)
0.649938 + 0.759987i \(0.274795\pi\)
\(548\) 0 0
\(549\) −0.629440 −0.0268638
\(550\) 0 0
\(551\) −9.03221 −0.384785
\(552\) 0 0
\(553\) −48.6432 −2.06852
\(554\) 0 0
\(555\) 14.1267 0.599644
\(556\) 0 0
\(557\) −18.4359 −0.781155 −0.390577 0.920570i \(-0.627725\pi\)
−0.390577 + 0.920570i \(0.627725\pi\)
\(558\) 0 0
\(559\) 6.34875 0.268523
\(560\) 0 0
\(561\) 4.29635 0.181392
\(562\) 0 0
\(563\) −21.8813 −0.922188 −0.461094 0.887351i \(-0.652543\pi\)
−0.461094 + 0.887351i \(0.652543\pi\)
\(564\) 0 0
\(565\) −17.5410 −0.737954
\(566\) 0 0
\(567\) 33.7739 1.41837
\(568\) 0 0
\(569\) −4.89113 −0.205047 −0.102523 0.994731i \(-0.532692\pi\)
−0.102523 + 0.994731i \(0.532692\pi\)
\(570\) 0 0
\(571\) 13.9503 0.583804 0.291902 0.956448i \(-0.405712\pi\)
0.291902 + 0.956448i \(0.405712\pi\)
\(572\) 0 0
\(573\) 44.0659 1.84088
\(574\) 0 0
\(575\) −22.8579 −0.953239
\(576\) 0 0
\(577\) 12.1864 0.507326 0.253663 0.967293i \(-0.418365\pi\)
0.253663 + 0.967293i \(0.418365\pi\)
\(578\) 0 0
\(579\) −6.11127 −0.253976
\(580\) 0 0
\(581\) 4.99003 0.207022
\(582\) 0 0
\(583\) −1.43491 −0.0594277
\(584\) 0 0
\(585\) 2.16463 0.0894963
\(586\) 0 0
\(587\) 0.143998 0.00594342 0.00297171 0.999996i \(-0.499054\pi\)
0.00297171 + 0.999996i \(0.499054\pi\)
\(588\) 0 0
\(589\) −10.3103 −0.424830
\(590\) 0 0
\(591\) −25.5387 −1.05052
\(592\) 0 0
\(593\) 14.0804 0.578212 0.289106 0.957297i \(-0.406642\pi\)
0.289106 + 0.957297i \(0.406642\pi\)
\(594\) 0 0
\(595\) −12.5263 −0.513527
\(596\) 0 0
\(597\) −17.6127 −0.720838
\(598\) 0 0
\(599\) −1.99932 −0.0816899 −0.0408450 0.999165i \(-0.513005\pi\)
−0.0408450 + 0.999165i \(0.513005\pi\)
\(600\) 0 0
\(601\) 16.3950 0.668767 0.334383 0.942437i \(-0.391472\pi\)
0.334383 + 0.942437i \(0.391472\pi\)
\(602\) 0 0
\(603\) 0.320591 0.0130555
\(604\) 0 0
\(605\) 21.1838 0.861243
\(606\) 0 0
\(607\) −19.9240 −0.808690 −0.404345 0.914606i \(-0.632501\pi\)
−0.404345 + 0.914606i \(0.632501\pi\)
\(608\) 0 0
\(609\) 42.2246 1.71103
\(610\) 0 0
\(611\) 9.65212 0.390483
\(612\) 0 0
\(613\) −5.07961 −0.205164 −0.102582 0.994725i \(-0.532710\pi\)
−0.102582 + 0.994725i \(0.532710\pi\)
\(614\) 0 0
\(615\) 45.0067 1.81484
\(616\) 0 0
\(617\) 8.85737 0.356584 0.178292 0.983978i \(-0.442943\pi\)
0.178292 + 0.983978i \(0.442943\pi\)
\(618\) 0 0
\(619\) 1.30527 0.0524632 0.0262316 0.999656i \(-0.491649\pi\)
0.0262316 + 0.999656i \(0.491649\pi\)
\(620\) 0 0
\(621\) −11.8949 −0.477328
\(622\) 0 0
\(623\) 20.7066 0.829593
\(624\) 0 0
\(625\) 12.5619 0.502475
\(626\) 0 0
\(627\) 5.68420 0.227005
\(628\) 0 0
\(629\) −2.02635 −0.0807959
\(630\) 0 0
\(631\) 42.8589 1.70619 0.853094 0.521758i \(-0.174723\pi\)
0.853094 + 0.521758i \(0.174723\pi\)
\(632\) 0 0
\(633\) −0.581493 −0.0231123
\(634\) 0 0
\(635\) −46.1935 −1.83313
\(636\) 0 0
\(637\) −5.35747 −0.212271
\(638\) 0 0
\(639\) 3.85129 0.152355
\(640\) 0 0
\(641\) −48.6014 −1.91964 −0.959819 0.280618i \(-0.909460\pi\)
−0.959819 + 0.280618i \(0.909460\pi\)
\(642\) 0 0
\(643\) 44.7479 1.76469 0.882343 0.470607i \(-0.155965\pi\)
0.882343 + 0.470607i \(0.155965\pi\)
\(644\) 0 0
\(645\) −33.9805 −1.33798
\(646\) 0 0
\(647\) −29.6310 −1.16491 −0.582457 0.812861i \(-0.697909\pi\)
−0.582457 + 0.812861i \(0.697909\pi\)
\(648\) 0 0
\(649\) 2.31567 0.0908979
\(650\) 0 0
\(651\) 48.1996 1.88909
\(652\) 0 0
\(653\) −19.7112 −0.771358 −0.385679 0.922633i \(-0.626033\pi\)
−0.385679 + 0.922633i \(0.626033\pi\)
\(654\) 0 0
\(655\) 53.5679 2.09307
\(656\) 0 0
\(657\) −4.81753 −0.187950
\(658\) 0 0
\(659\) −20.8278 −0.811335 −0.405667 0.914021i \(-0.632961\pi\)
−0.405667 + 0.914021i \(0.632961\pi\)
\(660\) 0 0
\(661\) 21.1383 0.822186 0.411093 0.911593i \(-0.365147\pi\)
0.411093 + 0.911593i \(0.365147\pi\)
\(662\) 0 0
\(663\) −2.41661 −0.0938534
\(664\) 0 0
\(665\) −16.5727 −0.642660
\(666\) 0 0
\(667\) −17.1124 −0.662593
\(668\) 0 0
\(669\) −4.25930 −0.164674
\(670\) 0 0
\(671\) −3.29560 −0.127225
\(672\) 0 0
\(673\) 23.1361 0.891832 0.445916 0.895075i \(-0.352878\pi\)
0.445916 + 0.895075i \(0.352878\pi\)
\(674\) 0 0
\(675\) 43.2739 1.66561
\(676\) 0 0
\(677\) −30.5934 −1.17580 −0.587899 0.808934i \(-0.700045\pi\)
−0.587899 + 0.808934i \(0.700045\pi\)
\(678\) 0 0
\(679\) 13.5725 0.520866
\(680\) 0 0
\(681\) −14.9914 −0.574473
\(682\) 0 0
\(683\) 41.8411 1.60100 0.800502 0.599330i \(-0.204566\pi\)
0.800502 + 0.599330i \(0.204566\pi\)
\(684\) 0 0
\(685\) −23.5425 −0.899514
\(686\) 0 0
\(687\) −30.4673 −1.16240
\(688\) 0 0
\(689\) 0.807106 0.0307483
\(690\) 0 0
\(691\) −29.3358 −1.11599 −0.557993 0.829846i \(-0.688428\pi\)
−0.557993 + 0.829846i \(0.688428\pi\)
\(692\) 0 0
\(693\) −3.41422 −0.129696
\(694\) 0 0
\(695\) 12.4971 0.474044
\(696\) 0 0
\(697\) −6.45582 −0.244531
\(698\) 0 0
\(699\) −12.0155 −0.454469
\(700\) 0 0
\(701\) 32.0370 1.21002 0.605010 0.796218i \(-0.293169\pi\)
0.605010 + 0.796218i \(0.293169\pi\)
\(702\) 0 0
\(703\) −2.68093 −0.101113
\(704\) 0 0
\(705\) −51.6613 −1.94568
\(706\) 0 0
\(707\) −23.7849 −0.894522
\(708\) 0 0
\(709\) 42.0818 1.58042 0.790208 0.612839i \(-0.209973\pi\)
0.790208 + 0.612839i \(0.209973\pi\)
\(710\) 0 0
\(711\) 6.45357 0.242028
\(712\) 0 0
\(713\) −19.5339 −0.731549
\(714\) 0 0
\(715\) 11.3335 0.423848
\(716\) 0 0
\(717\) 38.7882 1.44857
\(718\) 0 0
\(719\) 10.8796 0.405742 0.202871 0.979205i \(-0.434973\pi\)
0.202871 + 0.979205i \(0.434973\pi\)
\(720\) 0 0
\(721\) −10.5460 −0.392755
\(722\) 0 0
\(723\) −15.9743 −0.594092
\(724\) 0 0
\(725\) 62.2549 2.31209
\(726\) 0 0
\(727\) 43.9809 1.63116 0.815581 0.578643i \(-0.196417\pi\)
0.815581 + 0.578643i \(0.196417\pi\)
\(728\) 0 0
\(729\) 21.9323 0.812309
\(730\) 0 0
\(731\) 4.87421 0.180279
\(732\) 0 0
\(733\) 5.17663 0.191203 0.0956016 0.995420i \(-0.469523\pi\)
0.0956016 + 0.995420i \(0.469523\pi\)
\(734\) 0 0
\(735\) 28.6749 1.05769
\(736\) 0 0
\(737\) 1.67854 0.0618298
\(738\) 0 0
\(739\) −14.9165 −0.548713 −0.274357 0.961628i \(-0.588465\pi\)
−0.274357 + 0.961628i \(0.588465\pi\)
\(740\) 0 0
\(741\) −3.19725 −0.117454
\(742\) 0 0
\(743\) −26.7072 −0.979792 −0.489896 0.871781i \(-0.662965\pi\)
−0.489896 + 0.871781i \(0.662965\pi\)
\(744\) 0 0
\(745\) −49.2189 −1.80324
\(746\) 0 0
\(747\) −0.662036 −0.0242226
\(748\) 0 0
\(749\) 7.81572 0.285580
\(750\) 0 0
\(751\) −8.17483 −0.298304 −0.149152 0.988814i \(-0.547654\pi\)
−0.149152 + 0.988814i \(0.547654\pi\)
\(752\) 0 0
\(753\) 48.0084 1.74952
\(754\) 0 0
\(755\) 16.7002 0.607782
\(756\) 0 0
\(757\) 17.2068 0.625392 0.312696 0.949853i \(-0.398768\pi\)
0.312696 + 0.949853i \(0.398768\pi\)
\(758\) 0 0
\(759\) 10.7692 0.390899
\(760\) 0 0
\(761\) −24.0300 −0.871086 −0.435543 0.900168i \(-0.643444\pi\)
−0.435543 + 0.900168i \(0.643444\pi\)
\(762\) 0 0
\(763\) −31.4793 −1.13963
\(764\) 0 0
\(765\) 1.66188 0.0600854
\(766\) 0 0
\(767\) −1.30252 −0.0470312
\(768\) 0 0
\(769\) −5.03458 −0.181552 −0.0907758 0.995871i \(-0.528935\pi\)
−0.0907758 + 0.995871i \(0.528935\pi\)
\(770\) 0 0
\(771\) −21.4089 −0.771021
\(772\) 0 0
\(773\) −8.61254 −0.309772 −0.154886 0.987932i \(-0.549501\pi\)
−0.154886 + 0.987932i \(0.549501\pi\)
\(774\) 0 0
\(775\) 71.0643 2.55271
\(776\) 0 0
\(777\) 12.5330 0.449620
\(778\) 0 0
\(779\) −8.54125 −0.306022
\(780\) 0 0
\(781\) 20.1644 0.721540
\(782\) 0 0
\(783\) 32.3966 1.15776
\(784\) 0 0
\(785\) −62.6532 −2.23619
\(786\) 0 0
\(787\) −6.41439 −0.228648 −0.114324 0.993443i \(-0.536470\pi\)
−0.114324 + 0.993443i \(0.536470\pi\)
\(788\) 0 0
\(789\) 19.3354 0.688357
\(790\) 0 0
\(791\) −15.5621 −0.553326
\(792\) 0 0
\(793\) 1.85371 0.0658271
\(794\) 0 0
\(795\) −4.31989 −0.153211
\(796\) 0 0
\(797\) −36.6551 −1.29839 −0.649196 0.760621i \(-0.724894\pi\)
−0.649196 + 0.760621i \(0.724894\pi\)
\(798\) 0 0
\(799\) 7.41036 0.262160
\(800\) 0 0
\(801\) −2.74718 −0.0970668
\(802\) 0 0
\(803\) −25.2234 −0.890115
\(804\) 0 0
\(805\) −31.3984 −1.10665
\(806\) 0 0
\(807\) −49.8093 −1.75337
\(808\) 0 0
\(809\) 6.81501 0.239603 0.119801 0.992798i \(-0.461774\pi\)
0.119801 + 0.992798i \(0.461774\pi\)
\(810\) 0 0
\(811\) −37.5929 −1.32006 −0.660032 0.751237i \(-0.729457\pi\)
−0.660032 + 0.751237i \(0.729457\pi\)
\(812\) 0 0
\(813\) 22.6860 0.795631
\(814\) 0 0
\(815\) 38.5276 1.34956
\(816\) 0 0
\(817\) 6.44874 0.225613
\(818\) 0 0
\(819\) 1.92043 0.0671054
\(820\) 0 0
\(821\) 10.3793 0.362240 0.181120 0.983461i \(-0.442028\pi\)
0.181120 + 0.983461i \(0.442028\pi\)
\(822\) 0 0
\(823\) 2.53711 0.0884382 0.0442191 0.999022i \(-0.485920\pi\)
0.0442191 + 0.999022i \(0.485920\pi\)
\(824\) 0 0
\(825\) −39.1786 −1.36402
\(826\) 0 0
\(827\) 20.8288 0.724289 0.362145 0.932122i \(-0.382045\pi\)
0.362145 + 0.932122i \(0.382045\pi\)
\(828\) 0 0
\(829\) −53.9717 −1.87452 −0.937258 0.348638i \(-0.886644\pi\)
−0.937258 + 0.348638i \(0.886644\pi\)
\(830\) 0 0
\(831\) −54.5115 −1.89098
\(832\) 0 0
\(833\) −4.11316 −0.142513
\(834\) 0 0
\(835\) 86.8831 3.00671
\(836\) 0 0
\(837\) 36.9810 1.27825
\(838\) 0 0
\(839\) −55.8041 −1.92657 −0.963286 0.268478i \(-0.913479\pi\)
−0.963286 + 0.268478i \(0.913479\pi\)
\(840\) 0 0
\(841\) 17.6066 0.607123
\(842\) 0 0
\(843\) 5.25703 0.181062
\(844\) 0 0
\(845\) 42.4731 1.46112
\(846\) 0 0
\(847\) 18.7940 0.645770
\(848\) 0 0
\(849\) 32.0923 1.10141
\(850\) 0 0
\(851\) −5.07926 −0.174115
\(852\) 0 0
\(853\) 6.07550 0.208021 0.104011 0.994576i \(-0.466832\pi\)
0.104011 + 0.994576i \(0.466832\pi\)
\(854\) 0 0
\(855\) 2.19872 0.0751946
\(856\) 0 0
\(857\) −24.8784 −0.849831 −0.424916 0.905233i \(-0.639696\pi\)
−0.424916 + 0.905233i \(0.639696\pi\)
\(858\) 0 0
\(859\) 22.1644 0.756239 0.378119 0.925757i \(-0.376571\pi\)
0.378119 + 0.925757i \(0.376571\pi\)
\(860\) 0 0
\(861\) 39.9294 1.36079
\(862\) 0 0
\(863\) −53.0075 −1.80440 −0.902198 0.431322i \(-0.858047\pi\)
−0.902198 + 0.431322i \(0.858047\pi\)
\(864\) 0 0
\(865\) 90.8796 3.09000
\(866\) 0 0
\(867\) −1.85534 −0.0630106
\(868\) 0 0
\(869\) 33.7894 1.14623
\(870\) 0 0
\(871\) −0.944145 −0.0319911
\(872\) 0 0
\(873\) −1.80069 −0.0609440
\(874\) 0 0
\(875\) 51.5964 1.74428
\(876\) 0 0
\(877\) 11.1445 0.376322 0.188161 0.982138i \(-0.439747\pi\)
0.188161 + 0.982138i \(0.439747\pi\)
\(878\) 0 0
\(879\) −32.9059 −1.10989
\(880\) 0 0
\(881\) 38.7999 1.30720 0.653601 0.756839i \(-0.273257\pi\)
0.653601 + 0.756839i \(0.273257\pi\)
\(882\) 0 0
\(883\) −27.3775 −0.921327 −0.460664 0.887575i \(-0.652389\pi\)
−0.460664 + 0.887575i \(0.652389\pi\)
\(884\) 0 0
\(885\) 6.97149 0.234344
\(886\) 0 0
\(887\) −36.8543 −1.23745 −0.618723 0.785609i \(-0.712350\pi\)
−0.618723 + 0.785609i \(0.712350\pi\)
\(888\) 0 0
\(889\) −40.9823 −1.37450
\(890\) 0 0
\(891\) −23.4606 −0.785958
\(892\) 0 0
\(893\) 9.80414 0.328083
\(894\) 0 0
\(895\) 5.34741 0.178744
\(896\) 0 0
\(897\) −6.05749 −0.202254
\(898\) 0 0
\(899\) 53.2017 1.77438
\(900\) 0 0
\(901\) 0.619651 0.0206436
\(902\) 0 0
\(903\) −30.1472 −1.00323
\(904\) 0 0
\(905\) 12.9185 0.429426
\(906\) 0 0
\(907\) −46.8188 −1.55459 −0.777296 0.629136i \(-0.783409\pi\)
−0.777296 + 0.629136i \(0.783409\pi\)
\(908\) 0 0
\(909\) 3.15558 0.104664
\(910\) 0 0
\(911\) 33.2475 1.10154 0.550770 0.834657i \(-0.314334\pi\)
0.550770 + 0.834657i \(0.314334\pi\)
\(912\) 0 0
\(913\) −3.46626 −0.114716
\(914\) 0 0
\(915\) −9.92164 −0.327999
\(916\) 0 0
\(917\) 47.5249 1.56941
\(918\) 0 0
\(919\) 26.7710 0.883094 0.441547 0.897238i \(-0.354430\pi\)
0.441547 + 0.897238i \(0.354430\pi\)
\(920\) 0 0
\(921\) 29.6724 0.977740
\(922\) 0 0
\(923\) −11.3421 −0.373330
\(924\) 0 0
\(925\) 18.4784 0.607566
\(926\) 0 0
\(927\) 1.39916 0.0459545
\(928\) 0 0
\(929\) −28.5662 −0.937227 −0.468613 0.883403i \(-0.655246\pi\)
−0.468613 + 0.883403i \(0.655246\pi\)
\(930\) 0 0
\(931\) −5.44185 −0.178349
\(932\) 0 0
\(933\) 20.6935 0.677475
\(934\) 0 0
\(935\) 8.70120 0.284560
\(936\) 0 0
\(937\) 45.0107 1.47044 0.735218 0.677831i \(-0.237080\pi\)
0.735218 + 0.677831i \(0.237080\pi\)
\(938\) 0 0
\(939\) 19.9152 0.649907
\(940\) 0 0
\(941\) −10.5546 −0.344069 −0.172035 0.985091i \(-0.555034\pi\)
−0.172035 + 0.985091i \(0.555034\pi\)
\(942\) 0 0
\(943\) −16.1822 −0.526965
\(944\) 0 0
\(945\) 59.4426 1.93367
\(946\) 0 0
\(947\) −46.5326 −1.51211 −0.756053 0.654511i \(-0.772875\pi\)
−0.756053 + 0.654511i \(0.772875\pi\)
\(948\) 0 0
\(949\) 14.1877 0.460551
\(950\) 0 0
\(951\) −8.66193 −0.280882
\(952\) 0 0
\(953\) −32.6950 −1.05910 −0.529548 0.848280i \(-0.677638\pi\)
−0.529548 + 0.848280i \(0.677638\pi\)
\(954\) 0 0
\(955\) 89.2447 2.88789
\(956\) 0 0
\(957\) −29.3307 −0.948128
\(958\) 0 0
\(959\) −20.8867 −0.674466
\(960\) 0 0
\(961\) 29.7301 0.959035
\(962\) 0 0
\(963\) −1.03692 −0.0334144
\(964\) 0 0
\(965\) −12.3769 −0.398426
\(966\) 0 0
\(967\) 31.5525 1.01466 0.507329 0.861752i \(-0.330633\pi\)
0.507329 + 0.861752i \(0.330633\pi\)
\(968\) 0 0
\(969\) −2.45467 −0.0788554
\(970\) 0 0
\(971\) 8.18250 0.262589 0.131294 0.991343i \(-0.458087\pi\)
0.131294 + 0.991343i \(0.458087\pi\)
\(972\) 0 0
\(973\) 11.0873 0.355443
\(974\) 0 0
\(975\) 22.0372 0.705755
\(976\) 0 0
\(977\) 39.0246 1.24851 0.624253 0.781222i \(-0.285403\pi\)
0.624253 + 0.781222i \(0.285403\pi\)
\(978\) 0 0
\(979\) −14.3836 −0.459701
\(980\) 0 0
\(981\) 4.17641 0.133342
\(982\) 0 0
\(983\) −16.6447 −0.530884 −0.265442 0.964127i \(-0.585518\pi\)
−0.265442 + 0.964127i \(0.585518\pi\)
\(984\) 0 0
\(985\) −51.7224 −1.64801
\(986\) 0 0
\(987\) −45.8333 −1.45889
\(988\) 0 0
\(989\) 12.2177 0.388501
\(990\) 0 0
\(991\) 58.9404 1.87230 0.936151 0.351598i \(-0.114361\pi\)
0.936151 + 0.351598i \(0.114361\pi\)
\(992\) 0 0
\(993\) −16.7542 −0.531679
\(994\) 0 0
\(995\) −35.6701 −1.13082
\(996\) 0 0
\(997\) 20.6381 0.653616 0.326808 0.945091i \(-0.394027\pi\)
0.326808 + 0.945091i \(0.394027\pi\)
\(998\) 0 0
\(999\) 9.61591 0.304234
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 \(a_p\))