Properties

Label 4012.2.a.g.1.6
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 1.6
Root \(0.859886\)
Character \(\chi\) = 4012.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.859886 q^{3}\) \(+2.49803 q^{5}\) \(-3.53399 q^{7}\) \(-2.26060 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.859886 q^{3}\) \(+2.49803 q^{5}\) \(-3.53399 q^{7}\) \(-2.26060 q^{9}\) \(+1.54144 q^{11}\) \(+3.17355 q^{13}\) \(-2.14802 q^{15}\) \(-1.00000 q^{17}\) \(+0.523938 q^{19}\) \(+3.03883 q^{21}\) \(-5.23538 q^{23}\) \(+1.24016 q^{25}\) \(+4.52351 q^{27}\) \(+4.96421 q^{29}\) \(+3.14090 q^{31}\) \(-1.32546 q^{33}\) \(-8.82803 q^{35}\) \(-7.80477 q^{37}\) \(-2.72889 q^{39}\) \(-1.58833 q^{41}\) \(-1.96140 q^{43}\) \(-5.64704 q^{45}\) \(+2.57853 q^{47}\) \(+5.48912 q^{49}\) \(+0.859886 q^{51}\) \(+2.58777 q^{53}\) \(+3.85056 q^{55}\) \(-0.450527 q^{57}\) \(+1.00000 q^{59}\) \(+6.54735 q^{61}\) \(+7.98893 q^{63}\) \(+7.92762 q^{65}\) \(-5.68694 q^{67}\) \(+4.50183 q^{69}\) \(-13.9886 q^{71}\) \(-1.37301 q^{73}\) \(-1.06639 q^{75}\) \(-5.44743 q^{77}\) \(-6.64369 q^{79}\) \(+2.89208 q^{81}\) \(-16.8533 q^{83}\) \(-2.49803 q^{85}\) \(-4.26866 q^{87}\) \(+2.73484 q^{89}\) \(-11.2153 q^{91}\) \(-2.70082 q^{93}\) \(+1.30881 q^{95}\) \(+3.59905 q^{97}\) \(-3.48457 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 9q^{13} \) \(\mathstrut -\mathstrut 16q^{15} \) \(\mathstrut -\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut 15q^{19} \) \(\mathstrut +\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut -\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 33q^{33} \) \(\mathstrut -\mathstrut 9q^{35} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut -\mathstrut 18q^{41} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 30q^{45} \) \(\mathstrut -\mathstrut 60q^{47} \) \(\mathstrut +\mathstrut 10q^{49} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 41q^{57} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 23q^{63} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 4q^{73} \) \(\mathstrut -\mathstrut 62q^{75} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 48q^{79} \) \(\mathstrut +\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 20q^{83} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 13q^{87} \) \(\mathstrut -\mathstrut 29q^{89} \) \(\mathstrut -\mathstrut 28q^{91} \) \(\mathstrut -\mathstrut 31q^{93} \) \(\mathstrut -\mathstrut 48q^{95} \) \(\mathstrut -\mathstrut 26q^{97} \) \(\mathstrut -\mathstrut 3q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −0.859886 −0.496455 −0.248228 0.968702i \(-0.579848\pi\)
−0.248228 + 0.968702i \(0.579848\pi\)
\(4\) 0 0
\(5\) 2.49803 1.11715 0.558577 0.829453i \(-0.311348\pi\)
0.558577 + 0.829453i \(0.311348\pi\)
\(6\) 0 0
\(7\) −3.53399 −1.33572 −0.667862 0.744285i \(-0.732790\pi\)
−0.667862 + 0.744285i \(0.732790\pi\)
\(8\) 0 0
\(9\) −2.26060 −0.753532
\(10\) 0 0
\(11\) 1.54144 0.464761 0.232380 0.972625i \(-0.425349\pi\)
0.232380 + 0.972625i \(0.425349\pi\)
\(12\) 0 0
\(13\) 3.17355 0.880184 0.440092 0.897953i \(-0.354946\pi\)
0.440092 + 0.897953i \(0.354946\pi\)
\(14\) 0 0
\(15\) −2.14802 −0.554617
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) 0.523938 0.120200 0.0600998 0.998192i \(-0.480858\pi\)
0.0600998 + 0.998192i \(0.480858\pi\)
\(20\) 0 0
\(21\) 3.03883 0.663128
\(22\) 0 0
\(23\) −5.23538 −1.09165 −0.545826 0.837898i \(-0.683784\pi\)
−0.545826 + 0.837898i \(0.683784\pi\)
\(24\) 0 0
\(25\) 1.24016 0.248031
\(26\) 0 0
\(27\) 4.52351 0.870550
\(28\) 0 0
\(29\) 4.96421 0.921831 0.460916 0.887444i \(-0.347521\pi\)
0.460916 + 0.887444i \(0.347521\pi\)
\(30\) 0 0
\(31\) 3.14090 0.564123 0.282061 0.959396i \(-0.408982\pi\)
0.282061 + 0.959396i \(0.408982\pi\)
\(32\) 0 0
\(33\) −1.32546 −0.230733
\(34\) 0 0
\(35\) −8.82803 −1.49221
\(36\) 0 0
\(37\) −7.80477 −1.28310 −0.641548 0.767083i \(-0.721708\pi\)
−0.641548 + 0.767083i \(0.721708\pi\)
\(38\) 0 0
\(39\) −2.72889 −0.436972
\(40\) 0 0
\(41\) −1.58833 −0.248055 −0.124028 0.992279i \(-0.539581\pi\)
−0.124028 + 0.992279i \(0.539581\pi\)
\(42\) 0 0
\(43\) −1.96140 −0.299111 −0.149556 0.988753i \(-0.547784\pi\)
−0.149556 + 0.988753i \(0.547784\pi\)
\(44\) 0 0
\(45\) −5.64704 −0.841811
\(46\) 0 0
\(47\) 2.57853 0.376117 0.188059 0.982158i \(-0.439780\pi\)
0.188059 + 0.982158i \(0.439780\pi\)
\(48\) 0 0
\(49\) 5.48912 0.784160
\(50\) 0 0
\(51\) 0.859886 0.120408
\(52\) 0 0
\(53\) 2.58777 0.355457 0.177729 0.984080i \(-0.443125\pi\)
0.177729 + 0.984080i \(0.443125\pi\)
\(54\) 0 0
\(55\) 3.85056 0.519209
\(56\) 0 0
\(57\) −0.450527 −0.0596737
\(58\) 0 0
\(59\) 1.00000 0.130189
\(60\) 0 0
\(61\) 6.54735 0.838302 0.419151 0.907917i \(-0.362328\pi\)
0.419151 + 0.907917i \(0.362328\pi\)
\(62\) 0 0
\(63\) 7.98893 1.00651
\(64\) 0 0
\(65\) 7.92762 0.983300
\(66\) 0 0
\(67\) −5.68694 −0.694770 −0.347385 0.937723i \(-0.612930\pi\)
−0.347385 + 0.937723i \(0.612930\pi\)
\(68\) 0 0
\(69\) 4.50183 0.541957
\(70\) 0 0
\(71\) −13.9886 −1.66014 −0.830072 0.557656i \(-0.811701\pi\)
−0.830072 + 0.557656i \(0.811701\pi\)
\(72\) 0 0
\(73\) −1.37301 −0.160699 −0.0803494 0.996767i \(-0.525604\pi\)
−0.0803494 + 0.996767i \(0.525604\pi\)
\(74\) 0 0
\(75\) −1.06639 −0.123137
\(76\) 0 0
\(77\) −5.44743 −0.620792
\(78\) 0 0
\(79\) −6.64369 −0.747474 −0.373737 0.927535i \(-0.621924\pi\)
−0.373737 + 0.927535i \(0.621924\pi\)
\(80\) 0 0
\(81\) 2.89208 0.321343
\(82\) 0 0
\(83\) −16.8533 −1.84990 −0.924948 0.380094i \(-0.875891\pi\)
−0.924948 + 0.380094i \(0.875891\pi\)
\(84\) 0 0
\(85\) −2.49803 −0.270949
\(86\) 0 0
\(87\) −4.26866 −0.457648
\(88\) 0 0
\(89\) 2.73484 0.289893 0.144946 0.989439i \(-0.453699\pi\)
0.144946 + 0.989439i \(0.453699\pi\)
\(90\) 0 0
\(91\) −11.2153 −1.17568
\(92\) 0 0
\(93\) −2.70082 −0.280062
\(94\) 0 0
\(95\) 1.30881 0.134281
\(96\) 0 0
\(97\) 3.59905 0.365428 0.182714 0.983166i \(-0.441512\pi\)
0.182714 + 0.983166i \(0.441512\pi\)
\(98\) 0 0
\(99\) −3.48457 −0.350212
\(100\) 0 0
\(101\) −13.0337 −1.29690 −0.648451 0.761256i \(-0.724583\pi\)
−0.648451 + 0.761256i \(0.724583\pi\)
\(102\) 0 0
\(103\) −8.90735 −0.877667 −0.438834 0.898568i \(-0.644608\pi\)
−0.438834 + 0.898568i \(0.644608\pi\)
\(104\) 0 0
\(105\) 7.59110 0.740815
\(106\) 0 0
\(107\) −9.92583 −0.959566 −0.479783 0.877387i \(-0.659285\pi\)
−0.479783 + 0.877387i \(0.659285\pi\)
\(108\) 0 0
\(109\) 1.21141 0.116032 0.0580161 0.998316i \(-0.481523\pi\)
0.0580161 + 0.998316i \(0.481523\pi\)
\(110\) 0 0
\(111\) 6.71121 0.637000
\(112\) 0 0
\(113\) 8.03970 0.756312 0.378156 0.925742i \(-0.376558\pi\)
0.378156 + 0.925742i \(0.376558\pi\)
\(114\) 0 0
\(115\) −13.0781 −1.21954
\(116\) 0 0
\(117\) −7.17411 −0.663247
\(118\) 0 0
\(119\) 3.53399 0.323961
\(120\) 0 0
\(121\) −8.62397 −0.783997
\(122\) 0 0
\(123\) 1.36578 0.123148
\(124\) 0 0
\(125\) −9.39220 −0.840064
\(126\) 0 0
\(127\) −17.7870 −1.57834 −0.789171 0.614173i \(-0.789490\pi\)
−0.789171 + 0.614173i \(0.789490\pi\)
\(128\) 0 0
\(129\) 1.68658 0.148495
\(130\) 0 0
\(131\) 11.1752 0.976385 0.488192 0.872736i \(-0.337656\pi\)
0.488192 + 0.872736i \(0.337656\pi\)
\(132\) 0 0
\(133\) −1.85159 −0.160554
\(134\) 0 0
\(135\) 11.2999 0.972538
\(136\) 0 0
\(137\) 5.64695 0.482451 0.241226 0.970469i \(-0.422451\pi\)
0.241226 + 0.970469i \(0.422451\pi\)
\(138\) 0 0
\(139\) −4.13706 −0.350901 −0.175450 0.984488i \(-0.556138\pi\)
−0.175450 + 0.984488i \(0.556138\pi\)
\(140\) 0 0
\(141\) −2.21724 −0.186726
\(142\) 0 0
\(143\) 4.89182 0.409075
\(144\) 0 0
\(145\) 12.4008 1.02983
\(146\) 0 0
\(147\) −4.72001 −0.389300
\(148\) 0 0
\(149\) 13.7421 1.12580 0.562898 0.826527i \(-0.309687\pi\)
0.562898 + 0.826527i \(0.309687\pi\)
\(150\) 0 0
\(151\) −0.425241 −0.0346056 −0.0173028 0.999850i \(-0.505508\pi\)
−0.0173028 + 0.999850i \(0.505508\pi\)
\(152\) 0 0
\(153\) 2.26060 0.182758
\(154\) 0 0
\(155\) 7.84607 0.630212
\(156\) 0 0
\(157\) 2.00538 0.160047 0.0800234 0.996793i \(-0.474500\pi\)
0.0800234 + 0.996793i \(0.474500\pi\)
\(158\) 0 0
\(159\) −2.22518 −0.176469
\(160\) 0 0
\(161\) 18.5018 1.45815
\(162\) 0 0
\(163\) −9.86513 −0.772697 −0.386348 0.922353i \(-0.626264\pi\)
−0.386348 + 0.922353i \(0.626264\pi\)
\(164\) 0 0
\(165\) −3.31104 −0.257764
\(166\) 0 0
\(167\) 15.4041 1.19201 0.596003 0.802982i \(-0.296755\pi\)
0.596003 + 0.802982i \(0.296755\pi\)
\(168\) 0 0
\(169\) −2.92860 −0.225277
\(170\) 0 0
\(171\) −1.18441 −0.0905742
\(172\) 0 0
\(173\) −2.50616 −0.190539 −0.0952697 0.995451i \(-0.530371\pi\)
−0.0952697 + 0.995451i \(0.530371\pi\)
\(174\) 0 0
\(175\) −4.38271 −0.331302
\(176\) 0 0
\(177\) −0.859886 −0.0646330
\(178\) 0 0
\(179\) −10.6318 −0.794657 −0.397328 0.917676i \(-0.630063\pi\)
−0.397328 + 0.917676i \(0.630063\pi\)
\(180\) 0 0
\(181\) −4.52625 −0.336434 −0.168217 0.985750i \(-0.553801\pi\)
−0.168217 + 0.985750i \(0.553801\pi\)
\(182\) 0 0
\(183\) −5.62997 −0.416179
\(184\) 0 0
\(185\) −19.4966 −1.43342
\(186\) 0 0
\(187\) −1.54144 −0.112721
\(188\) 0 0
\(189\) −15.9861 −1.16282
\(190\) 0 0
\(191\) −1.62563 −0.117626 −0.0588132 0.998269i \(-0.518732\pi\)
−0.0588132 + 0.998269i \(0.518732\pi\)
\(192\) 0 0
\(193\) 11.2000 0.806193 0.403096 0.915158i \(-0.367934\pi\)
0.403096 + 0.915158i \(0.367934\pi\)
\(194\) 0 0
\(195\) −6.81685 −0.488165
\(196\) 0 0
\(197\) −24.3579 −1.73543 −0.867715 0.497061i \(-0.834412\pi\)
−0.867715 + 0.497061i \(0.834412\pi\)
\(198\) 0 0
\(199\) 10.6308 0.753595 0.376798 0.926296i \(-0.377025\pi\)
0.376798 + 0.926296i \(0.377025\pi\)
\(200\) 0 0
\(201\) 4.89012 0.344922
\(202\) 0 0
\(203\) −17.5435 −1.23131
\(204\) 0 0
\(205\) −3.96769 −0.277116
\(206\) 0 0
\(207\) 11.8351 0.822595
\(208\) 0 0
\(209\) 0.807617 0.0558641
\(210\) 0 0
\(211\) −24.1799 −1.66461 −0.832307 0.554315i \(-0.812980\pi\)
−0.832307 + 0.554315i \(0.812980\pi\)
\(212\) 0 0
\(213\) 12.0286 0.824187
\(214\) 0 0
\(215\) −4.89965 −0.334153
\(216\) 0 0
\(217\) −11.0999 −0.753513
\(218\) 0 0
\(219\) 1.18063 0.0797798
\(220\) 0 0
\(221\) −3.17355 −0.213476
\(222\) 0 0
\(223\) −10.4427 −0.699298 −0.349649 0.936881i \(-0.613699\pi\)
−0.349649 + 0.936881i \(0.613699\pi\)
\(224\) 0 0
\(225\) −2.80349 −0.186900
\(226\) 0 0
\(227\) 10.7140 0.711115 0.355558 0.934654i \(-0.384291\pi\)
0.355558 + 0.934654i \(0.384291\pi\)
\(228\) 0 0
\(229\) −4.09820 −0.270817 −0.135408 0.990790i \(-0.543235\pi\)
−0.135408 + 0.990790i \(0.543235\pi\)
\(230\) 0 0
\(231\) 4.68417 0.308196
\(232\) 0 0
\(233\) −26.4695 −1.73407 −0.867036 0.498245i \(-0.833978\pi\)
−0.867036 + 0.498245i \(0.833978\pi\)
\(234\) 0 0
\(235\) 6.44125 0.420181
\(236\) 0 0
\(237\) 5.71282 0.371087
\(238\) 0 0
\(239\) 12.5621 0.812576 0.406288 0.913745i \(-0.366823\pi\)
0.406288 + 0.913745i \(0.366823\pi\)
\(240\) 0 0
\(241\) 6.48443 0.417699 0.208849 0.977948i \(-0.433028\pi\)
0.208849 + 0.977948i \(0.433028\pi\)
\(242\) 0 0
\(243\) −16.0574 −1.03008
\(244\) 0 0
\(245\) 13.7120 0.876026
\(246\) 0 0
\(247\) 1.66274 0.105798
\(248\) 0 0
\(249\) 14.4920 0.918391
\(250\) 0 0
\(251\) 0.613499 0.0387237 0.0193618 0.999813i \(-0.493837\pi\)
0.0193618 + 0.999813i \(0.493837\pi\)
\(252\) 0 0
\(253\) −8.07001 −0.507357
\(254\) 0 0
\(255\) 2.14802 0.134514
\(256\) 0 0
\(257\) 27.3070 1.70336 0.851681 0.524060i \(-0.175583\pi\)
0.851681 + 0.524060i \(0.175583\pi\)
\(258\) 0 0
\(259\) 27.5820 1.71386
\(260\) 0 0
\(261\) −11.2221 −0.694629
\(262\) 0 0
\(263\) −25.6118 −1.57929 −0.789645 0.613564i \(-0.789735\pi\)
−0.789645 + 0.613564i \(0.789735\pi\)
\(264\) 0 0
\(265\) 6.46432 0.397100
\(266\) 0 0
\(267\) −2.35165 −0.143919
\(268\) 0 0
\(269\) 18.9356 1.15453 0.577263 0.816558i \(-0.304121\pi\)
0.577263 + 0.816558i \(0.304121\pi\)
\(270\) 0 0
\(271\) −22.8234 −1.38642 −0.693212 0.720734i \(-0.743805\pi\)
−0.693212 + 0.720734i \(0.743805\pi\)
\(272\) 0 0
\(273\) 9.64388 0.583674
\(274\) 0 0
\(275\) 1.91162 0.115275
\(276\) 0 0
\(277\) 11.9504 0.718030 0.359015 0.933332i \(-0.383113\pi\)
0.359015 + 0.933332i \(0.383113\pi\)
\(278\) 0 0
\(279\) −7.10031 −0.425085
\(280\) 0 0
\(281\) −8.81255 −0.525713 −0.262856 0.964835i \(-0.584665\pi\)
−0.262856 + 0.964835i \(0.584665\pi\)
\(282\) 0 0
\(283\) −21.4080 −1.27257 −0.636286 0.771453i \(-0.719530\pi\)
−0.636286 + 0.771453i \(0.719530\pi\)
\(284\) 0 0
\(285\) −1.12543 −0.0666647
\(286\) 0 0
\(287\) 5.61314 0.331333
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) −3.09477 −0.181419
\(292\) 0 0
\(293\) 17.9472 1.04849 0.524245 0.851568i \(-0.324348\pi\)
0.524245 + 0.851568i \(0.324348\pi\)
\(294\) 0 0
\(295\) 2.49803 0.145441
\(296\) 0 0
\(297\) 6.97271 0.404598
\(298\) 0 0
\(299\) −16.6147 −0.960855
\(300\) 0 0
\(301\) 6.93159 0.399530
\(302\) 0 0
\(303\) 11.2075 0.643854
\(304\) 0 0
\(305\) 16.3555 0.936511
\(306\) 0 0
\(307\) −3.03015 −0.172940 −0.0864699 0.996254i \(-0.527559\pi\)
−0.0864699 + 0.996254i \(0.527559\pi\)
\(308\) 0 0
\(309\) 7.65930 0.435723
\(310\) 0 0
\(311\) 10.5182 0.596432 0.298216 0.954498i \(-0.403608\pi\)
0.298216 + 0.954498i \(0.403608\pi\)
\(312\) 0 0
\(313\) 10.8453 0.613014 0.306507 0.951868i \(-0.400840\pi\)
0.306507 + 0.951868i \(0.400840\pi\)
\(314\) 0 0
\(315\) 19.9566 1.12443
\(316\) 0 0
\(317\) −28.1582 −1.58152 −0.790760 0.612127i \(-0.790314\pi\)
−0.790760 + 0.612127i \(0.790314\pi\)
\(318\) 0 0
\(319\) 7.65202 0.428431
\(320\) 0 0
\(321\) 8.53508 0.476382
\(322\) 0 0
\(323\) −0.523938 −0.0291527
\(324\) 0 0
\(325\) 3.93570 0.218313
\(326\) 0 0
\(327\) −1.04168 −0.0576048
\(328\) 0 0
\(329\) −9.11251 −0.502389
\(330\) 0 0
\(331\) −14.3683 −0.789751 −0.394875 0.918735i \(-0.629212\pi\)
−0.394875 + 0.918735i \(0.629212\pi\)
\(332\) 0 0
\(333\) 17.6434 0.966854
\(334\) 0 0
\(335\) −14.2061 −0.776164
\(336\) 0 0
\(337\) 0.225511 0.0122843 0.00614217 0.999981i \(-0.498045\pi\)
0.00614217 + 0.999981i \(0.498045\pi\)
\(338\) 0 0
\(339\) −6.91323 −0.375475
\(340\) 0 0
\(341\) 4.84151 0.262182
\(342\) 0 0
\(343\) 5.33945 0.288303
\(344\) 0 0
\(345\) 11.2457 0.605449
\(346\) 0 0
\(347\) −14.8161 −0.795372 −0.397686 0.917522i \(-0.630187\pi\)
−0.397686 + 0.917522i \(0.630187\pi\)
\(348\) 0 0
\(349\) −0.379178 −0.0202969 −0.0101485 0.999949i \(-0.503230\pi\)
−0.0101485 + 0.999949i \(0.503230\pi\)
\(350\) 0 0
\(351\) 14.3556 0.766244
\(352\) 0 0
\(353\) 2.37860 0.126600 0.0633000 0.997995i \(-0.479838\pi\)
0.0633000 + 0.997995i \(0.479838\pi\)
\(354\) 0 0
\(355\) −34.9440 −1.85464
\(356\) 0 0
\(357\) −3.03883 −0.160832
\(358\) 0 0
\(359\) 12.4888 0.659133 0.329566 0.944132i \(-0.393097\pi\)
0.329566 + 0.944132i \(0.393097\pi\)
\(360\) 0 0
\(361\) −18.7255 −0.985552
\(362\) 0 0
\(363\) 7.41563 0.389220
\(364\) 0 0
\(365\) −3.42982 −0.179525
\(366\) 0 0
\(367\) −24.3802 −1.27264 −0.636319 0.771426i \(-0.719544\pi\)
−0.636319 + 0.771426i \(0.719544\pi\)
\(368\) 0 0
\(369\) 3.59057 0.186918
\(370\) 0 0
\(371\) −9.14516 −0.474793
\(372\) 0 0
\(373\) −33.6638 −1.74304 −0.871522 0.490357i \(-0.836867\pi\)
−0.871522 + 0.490357i \(0.836867\pi\)
\(374\) 0 0
\(375\) 8.07622 0.417054
\(376\) 0 0
\(377\) 15.7542 0.811381
\(378\) 0 0
\(379\) −7.27325 −0.373602 −0.186801 0.982398i \(-0.559812\pi\)
−0.186801 + 0.982398i \(0.559812\pi\)
\(380\) 0 0
\(381\) 15.2948 0.783576
\(382\) 0 0
\(383\) 24.0268 1.22771 0.613857 0.789417i \(-0.289617\pi\)
0.613857 + 0.789417i \(0.289617\pi\)
\(384\) 0 0
\(385\) −13.6079 −0.693520
\(386\) 0 0
\(387\) 4.43394 0.225390
\(388\) 0 0
\(389\) 4.37457 0.221799 0.110900 0.993832i \(-0.464627\pi\)
0.110900 + 0.993832i \(0.464627\pi\)
\(390\) 0 0
\(391\) 5.23538 0.264765
\(392\) 0 0
\(393\) −9.60943 −0.484731
\(394\) 0 0
\(395\) −16.5961 −0.835043
\(396\) 0 0
\(397\) −35.7166 −1.79257 −0.896283 0.443482i \(-0.853743\pi\)
−0.896283 + 0.443482i \(0.853743\pi\)
\(398\) 0 0
\(399\) 1.59216 0.0797077
\(400\) 0 0
\(401\) −10.3711 −0.517906 −0.258953 0.965890i \(-0.583378\pi\)
−0.258953 + 0.965890i \(0.583378\pi\)
\(402\) 0 0
\(403\) 9.96781 0.496532
\(404\) 0 0
\(405\) 7.22451 0.358989
\(406\) 0 0
\(407\) −12.0306 −0.596333
\(408\) 0 0
\(409\) 25.6922 1.27040 0.635198 0.772349i \(-0.280918\pi\)
0.635198 + 0.772349i \(0.280918\pi\)
\(410\) 0 0
\(411\) −4.85573 −0.239516
\(412\) 0 0
\(413\) −3.53399 −0.173897
\(414\) 0 0
\(415\) −42.1002 −2.06662
\(416\) 0 0
\(417\) 3.55740 0.174206
\(418\) 0 0
\(419\) 23.3221 1.13936 0.569679 0.821868i \(-0.307068\pi\)
0.569679 + 0.821868i \(0.307068\pi\)
\(420\) 0 0
\(421\) −27.2315 −1.32718 −0.663591 0.748096i \(-0.730968\pi\)
−0.663591 + 0.748096i \(0.730968\pi\)
\(422\) 0 0
\(423\) −5.82902 −0.283417
\(424\) 0 0
\(425\) −1.24016 −0.0601565
\(426\) 0 0
\(427\) −23.1383 −1.11974
\(428\) 0 0
\(429\) −4.20641 −0.203087
\(430\) 0 0
\(431\) −31.6188 −1.52303 −0.761513 0.648150i \(-0.775543\pi\)
−0.761513 + 0.648150i \(0.775543\pi\)
\(432\) 0 0
\(433\) −2.91444 −0.140059 −0.0700295 0.997545i \(-0.522309\pi\)
−0.0700295 + 0.997545i \(0.522309\pi\)
\(434\) 0 0
\(435\) −10.6632 −0.511263
\(436\) 0 0
\(437\) −2.74301 −0.131216
\(438\) 0 0
\(439\) 25.7288 1.22797 0.613985 0.789318i \(-0.289566\pi\)
0.613985 + 0.789318i \(0.289566\pi\)
\(440\) 0 0
\(441\) −12.4087 −0.590889
\(442\) 0 0
\(443\) 9.86400 0.468653 0.234326 0.972158i \(-0.424712\pi\)
0.234326 + 0.972158i \(0.424712\pi\)
\(444\) 0 0
\(445\) 6.83173 0.323855
\(446\) 0 0
\(447\) −11.8166 −0.558907
\(448\) 0 0
\(449\) −4.43929 −0.209503 −0.104751 0.994498i \(-0.533405\pi\)
−0.104751 + 0.994498i \(0.533405\pi\)
\(450\) 0 0
\(451\) −2.44831 −0.115286
\(452\) 0 0
\(453\) 0.365659 0.0171801
\(454\) 0 0
\(455\) −28.0162 −1.31342
\(456\) 0 0
\(457\) −16.8780 −0.789521 −0.394761 0.918784i \(-0.629172\pi\)
−0.394761 + 0.918784i \(0.629172\pi\)
\(458\) 0 0
\(459\) −4.52351 −0.211139
\(460\) 0 0
\(461\) 1.44300 0.0672073 0.0336037 0.999435i \(-0.489302\pi\)
0.0336037 + 0.999435i \(0.489302\pi\)
\(462\) 0 0
\(463\) 13.3709 0.621400 0.310700 0.950508i \(-0.399437\pi\)
0.310700 + 0.950508i \(0.399437\pi\)
\(464\) 0 0
\(465\) −6.74673 −0.312872
\(466\) 0 0
\(467\) 1.24377 0.0575548 0.0287774 0.999586i \(-0.490839\pi\)
0.0287774 + 0.999586i \(0.490839\pi\)
\(468\) 0 0
\(469\) 20.0976 0.928021
\(470\) 0 0
\(471\) −1.72440 −0.0794561
\(472\) 0 0
\(473\) −3.02338 −0.139015
\(474\) 0 0
\(475\) 0.649765 0.0298133
\(476\) 0 0
\(477\) −5.84990 −0.267848
\(478\) 0 0
\(479\) 11.0190 0.503471 0.251735 0.967796i \(-0.418999\pi\)
0.251735 + 0.967796i \(0.418999\pi\)
\(480\) 0 0
\(481\) −24.7688 −1.12936
\(482\) 0 0
\(483\) −15.9094 −0.723905
\(484\) 0 0
\(485\) 8.99054 0.408239
\(486\) 0 0
\(487\) 15.9006 0.720525 0.360262 0.932851i \(-0.382687\pi\)
0.360262 + 0.932851i \(0.382687\pi\)
\(488\) 0 0
\(489\) 8.48289 0.383609
\(490\) 0 0
\(491\) 14.1416 0.638202 0.319101 0.947721i \(-0.396619\pi\)
0.319101 + 0.947721i \(0.396619\pi\)
\(492\) 0 0
\(493\) −4.96421 −0.223577
\(494\) 0 0
\(495\) −8.70456 −0.391241
\(496\) 0 0
\(497\) 49.4357 2.21749
\(498\) 0 0
\(499\) 6.92123 0.309837 0.154918 0.987927i \(-0.450489\pi\)
0.154918 + 0.987927i \(0.450489\pi\)
\(500\) 0 0
\(501\) −13.2458 −0.591778
\(502\) 0 0
\(503\) −13.0842 −0.583396 −0.291698 0.956510i \(-0.594220\pi\)
−0.291698 + 0.956510i \(0.594220\pi\)
\(504\) 0 0
\(505\) −32.5586 −1.44884
\(506\) 0 0
\(507\) 2.51826 0.111840
\(508\) 0 0
\(509\) −16.6478 −0.737903 −0.368951 0.929449i \(-0.620283\pi\)
−0.368951 + 0.929449i \(0.620283\pi\)
\(510\) 0 0
\(511\) 4.85221 0.214649
\(512\) 0 0
\(513\) 2.37004 0.104640
\(514\) 0 0
\(515\) −22.2508 −0.980489
\(516\) 0 0
\(517\) 3.97464 0.174805
\(518\) 0 0
\(519\) 2.15501 0.0945944
\(520\) 0 0
\(521\) 9.64096 0.422378 0.211189 0.977445i \(-0.432266\pi\)
0.211189 + 0.977445i \(0.432266\pi\)
\(522\) 0 0
\(523\) 20.9852 0.917617 0.458809 0.888535i \(-0.348276\pi\)
0.458809 + 0.888535i \(0.348276\pi\)
\(524\) 0 0
\(525\) 3.76863 0.164477
\(526\) 0 0
\(527\) −3.14090 −0.136820
\(528\) 0 0
\(529\) 4.40921 0.191705
\(530\) 0 0
\(531\) −2.26060 −0.0981015
\(532\) 0 0
\(533\) −5.04063 −0.218334
\(534\) 0 0
\(535\) −24.7950 −1.07198
\(536\) 0 0
\(537\) 9.14212 0.394512
\(538\) 0 0
\(539\) 8.46113 0.364447
\(540\) 0 0
\(541\) 22.6895 0.975496 0.487748 0.872984i \(-0.337819\pi\)
0.487748 + 0.872984i \(0.337819\pi\)
\(542\) 0 0
\(543\) 3.89206 0.167024
\(544\) 0 0
\(545\) 3.02614 0.129626
\(546\) 0 0
\(547\) 42.1363 1.80162 0.900808 0.434217i \(-0.142975\pi\)
0.900808 + 0.434217i \(0.142975\pi\)
\(548\) 0 0
\(549\) −14.8009 −0.631687
\(550\) 0 0
\(551\) 2.60094 0.110804
\(552\) 0 0
\(553\) 23.4788 0.998419
\(554\) 0 0
\(555\) 16.7648 0.711627
\(556\) 0 0
\(557\) −10.3277 −0.437601 −0.218800 0.975770i \(-0.570214\pi\)
−0.218800 + 0.975770i \(0.570214\pi\)
\(558\) 0 0
\(559\) −6.22461 −0.263273
\(560\) 0 0
\(561\) 1.32546 0.0559610
\(562\) 0 0
\(563\) −8.23744 −0.347167 −0.173583 0.984819i \(-0.555535\pi\)
−0.173583 + 0.984819i \(0.555535\pi\)
\(564\) 0 0
\(565\) 20.0834 0.844916
\(566\) 0 0
\(567\) −10.2206 −0.429225
\(568\) 0 0
\(569\) −26.6695 −1.11805 −0.559023 0.829152i \(-0.688824\pi\)
−0.559023 + 0.829152i \(0.688824\pi\)
\(570\) 0 0
\(571\) 28.8644 1.20794 0.603968 0.797009i \(-0.293586\pi\)
0.603968 + 0.797009i \(0.293586\pi\)
\(572\) 0 0
\(573\) 1.39785 0.0583962
\(574\) 0 0
\(575\) −6.49270 −0.270764
\(576\) 0 0
\(577\) 28.2153 1.17462 0.587310 0.809362i \(-0.300187\pi\)
0.587310 + 0.809362i \(0.300187\pi\)
\(578\) 0 0
\(579\) −9.63071 −0.400239
\(580\) 0 0
\(581\) 59.5596 2.47095
\(582\) 0 0
\(583\) 3.98888 0.165203
\(584\) 0 0
\(585\) −17.9211 −0.740948
\(586\) 0 0
\(587\) 0.367332 0.0151614 0.00758070 0.999971i \(-0.497587\pi\)
0.00758070 + 0.999971i \(0.497587\pi\)
\(588\) 0 0
\(589\) 1.64564 0.0678073
\(590\) 0 0
\(591\) 20.9450 0.861564
\(592\) 0 0
\(593\) 2.06664 0.0848669 0.0424335 0.999099i \(-0.486489\pi\)
0.0424335 + 0.999099i \(0.486489\pi\)
\(594\) 0 0
\(595\) 8.82803 0.361914
\(596\) 0 0
\(597\) −9.14125 −0.374126
\(598\) 0 0
\(599\) −18.0232 −0.736409 −0.368205 0.929745i \(-0.620027\pi\)
−0.368205 + 0.929745i \(0.620027\pi\)
\(600\) 0 0
\(601\) −2.24935 −0.0917530 −0.0458765 0.998947i \(-0.514608\pi\)
−0.0458765 + 0.998947i \(0.514608\pi\)
\(602\) 0 0
\(603\) 12.8559 0.523531
\(604\) 0 0
\(605\) −21.5429 −0.875845
\(606\) 0 0
\(607\) 39.7027 1.61148 0.805742 0.592266i \(-0.201767\pi\)
0.805742 + 0.592266i \(0.201767\pi\)
\(608\) 0 0
\(609\) 15.0854 0.611292
\(610\) 0 0
\(611\) 8.18309 0.331052
\(612\) 0 0
\(613\) −5.25236 −0.212141 −0.106070 0.994359i \(-0.533827\pi\)
−0.106070 + 0.994359i \(0.533827\pi\)
\(614\) 0 0
\(615\) 3.41176 0.137576
\(616\) 0 0
\(617\) −44.4029 −1.78759 −0.893797 0.448472i \(-0.851968\pi\)
−0.893797 + 0.448472i \(0.851968\pi\)
\(618\) 0 0
\(619\) 21.7679 0.874928 0.437464 0.899236i \(-0.355877\pi\)
0.437464 + 0.899236i \(0.355877\pi\)
\(620\) 0 0
\(621\) −23.6823 −0.950338
\(622\) 0 0
\(623\) −9.66493 −0.387217
\(624\) 0 0
\(625\) −29.6628 −1.18651
\(626\) 0 0
\(627\) −0.694459 −0.0277340
\(628\) 0 0
\(629\) 7.80477 0.311197
\(630\) 0 0
\(631\) −17.2043 −0.684894 −0.342447 0.939537i \(-0.611256\pi\)
−0.342447 + 0.939537i \(0.611256\pi\)
\(632\) 0 0
\(633\) 20.7920 0.826407
\(634\) 0 0
\(635\) −44.4325 −1.76325
\(636\) 0 0
\(637\) 17.4200 0.690205
\(638\) 0 0
\(639\) 31.6226 1.25097
\(640\) 0 0
\(641\) 38.1210 1.50569 0.752844 0.658198i \(-0.228681\pi\)
0.752844 + 0.658198i \(0.228681\pi\)
\(642\) 0 0
\(643\) −23.4962 −0.926598 −0.463299 0.886202i \(-0.653334\pi\)
−0.463299 + 0.886202i \(0.653334\pi\)
\(644\) 0 0
\(645\) 4.21314 0.165892
\(646\) 0 0
\(647\) −6.58999 −0.259079 −0.129540 0.991574i \(-0.541350\pi\)
−0.129540 + 0.991574i \(0.541350\pi\)
\(648\) 0 0
\(649\) 1.54144 0.0605067
\(650\) 0 0
\(651\) 9.54468 0.374085
\(652\) 0 0
\(653\) 34.8504 1.36380 0.681900 0.731445i \(-0.261154\pi\)
0.681900 + 0.731445i \(0.261154\pi\)
\(654\) 0 0
\(655\) 27.9161 1.09077
\(656\) 0 0
\(657\) 3.10382 0.121092
\(658\) 0 0
\(659\) −25.6375 −0.998693 −0.499347 0.866402i \(-0.666427\pi\)
−0.499347 + 0.866402i \(0.666427\pi\)
\(660\) 0 0
\(661\) −31.2665 −1.21613 −0.608064 0.793888i \(-0.708053\pi\)
−0.608064 + 0.793888i \(0.708053\pi\)
\(662\) 0 0
\(663\) 2.72889 0.105981
\(664\) 0 0
\(665\) −4.62534 −0.179363
\(666\) 0 0
\(667\) −25.9895 −1.00632
\(668\) 0 0
\(669\) 8.97957 0.347170
\(670\) 0 0
\(671\) 10.0923 0.389610
\(672\) 0 0
\(673\) −1.99467 −0.0768889 −0.0384445 0.999261i \(-0.512240\pi\)
−0.0384445 + 0.999261i \(0.512240\pi\)
\(674\) 0 0
\(675\) 5.60987 0.215924
\(676\) 0 0
\(677\) −0.331632 −0.0127457 −0.00637283 0.999980i \(-0.502029\pi\)
−0.00637283 + 0.999980i \(0.502029\pi\)
\(678\) 0 0
\(679\) −12.7190 −0.488111
\(680\) 0 0
\(681\) −9.21285 −0.353037
\(682\) 0 0
\(683\) 19.2037 0.734810 0.367405 0.930061i \(-0.380246\pi\)
0.367405 + 0.930061i \(0.380246\pi\)
\(684\) 0 0
\(685\) 14.1063 0.538972
\(686\) 0 0
\(687\) 3.52399 0.134449
\(688\) 0 0
\(689\) 8.21240 0.312868
\(690\) 0 0
\(691\) 30.6610 1.16640 0.583200 0.812329i \(-0.301801\pi\)
0.583200 + 0.812329i \(0.301801\pi\)
\(692\) 0 0
\(693\) 12.3144 0.467787
\(694\) 0 0
\(695\) −10.3345 −0.392010
\(696\) 0 0
\(697\) 1.58833 0.0601622
\(698\) 0 0
\(699\) 22.7607 0.860889
\(700\) 0 0
\(701\) 10.0165 0.378317 0.189158 0.981947i \(-0.439424\pi\)
0.189158 + 0.981947i \(0.439424\pi\)
\(702\) 0 0
\(703\) −4.08921 −0.154228
\(704\) 0 0
\(705\) −5.53874 −0.208601
\(706\) 0 0
\(707\) 46.0610 1.73230
\(708\) 0 0
\(709\) −13.5734 −0.509759 −0.254880 0.966973i \(-0.582036\pi\)
−0.254880 + 0.966973i \(0.582036\pi\)
\(710\) 0 0
\(711\) 15.0187 0.563245
\(712\) 0 0
\(713\) −16.4438 −0.615826
\(714\) 0 0
\(715\) 12.2199 0.456999
\(716\) 0 0
\(717\) −10.8020 −0.403408
\(718\) 0 0
\(719\) 8.75380 0.326461 0.163231 0.986588i \(-0.447809\pi\)
0.163231 + 0.986588i \(0.447809\pi\)
\(720\) 0 0
\(721\) 31.4785 1.17232
\(722\) 0 0
\(723\) −5.57587 −0.207369
\(724\) 0 0
\(725\) 6.15640 0.228643
\(726\) 0 0
\(727\) 18.0212 0.668370 0.334185 0.942508i \(-0.391539\pi\)
0.334185 + 0.942508i \(0.391539\pi\)
\(728\) 0 0
\(729\) 5.13128 0.190048
\(730\) 0 0
\(731\) 1.96140 0.0725452
\(732\) 0 0
\(733\) 23.1797 0.856163 0.428082 0.903740i \(-0.359190\pi\)
0.428082 + 0.903740i \(0.359190\pi\)
\(734\) 0 0
\(735\) −11.7907 −0.434908
\(736\) 0 0
\(737\) −8.76606 −0.322902
\(738\) 0 0
\(739\) 24.3936 0.897335 0.448667 0.893699i \(-0.351899\pi\)
0.448667 + 0.893699i \(0.351899\pi\)
\(740\) 0 0
\(741\) −1.42977 −0.0525238
\(742\) 0 0
\(743\) 26.6662 0.978287 0.489143 0.872203i \(-0.337309\pi\)
0.489143 + 0.872203i \(0.337309\pi\)
\(744\) 0 0
\(745\) 34.3281 1.25769
\(746\) 0 0
\(747\) 38.0986 1.39396
\(748\) 0 0
\(749\) 35.0778 1.28172
\(750\) 0 0
\(751\) 46.7858 1.70724 0.853618 0.520899i \(-0.174403\pi\)
0.853618 + 0.520899i \(0.174403\pi\)
\(752\) 0 0
\(753\) −0.527539 −0.0192246
\(754\) 0 0
\(755\) −1.06226 −0.0386598
\(756\) 0 0
\(757\) −13.8514 −0.503438 −0.251719 0.967800i \(-0.580996\pi\)
−0.251719 + 0.967800i \(0.580996\pi\)
\(758\) 0 0
\(759\) 6.93929 0.251880
\(760\) 0 0
\(761\) 9.87791 0.358074 0.179037 0.983842i \(-0.442702\pi\)
0.179037 + 0.983842i \(0.442702\pi\)
\(762\) 0 0
\(763\) −4.28112 −0.154987
\(764\) 0 0
\(765\) 5.64704 0.204169
\(766\) 0 0
\(767\) 3.17355 0.114590
\(768\) 0 0
\(769\) 5.78278 0.208532 0.104266 0.994549i \(-0.466751\pi\)
0.104266 + 0.994549i \(0.466751\pi\)
\(770\) 0 0
\(771\) −23.4809 −0.845644
\(772\) 0 0
\(773\) 33.2286 1.19515 0.597574 0.801814i \(-0.296131\pi\)
0.597574 + 0.801814i \(0.296131\pi\)
\(774\) 0 0
\(775\) 3.89521 0.139920
\(776\) 0 0
\(777\) −23.7174 −0.850857
\(778\) 0 0
\(779\) −0.832185 −0.0298161
\(780\) 0 0
\(781\) −21.5626 −0.771570
\(782\) 0 0
\(783\) 22.4557 0.802501
\(784\) 0 0
\(785\) 5.00950 0.178797
\(786\) 0 0
\(787\) −27.1882 −0.969155 −0.484577 0.874748i \(-0.661027\pi\)
−0.484577 + 0.874748i \(0.661027\pi\)
\(788\) 0 0
\(789\) 22.0232 0.784047
\(790\) 0 0
\(791\) −28.4123 −1.01022
\(792\) 0 0
\(793\) 20.7783 0.737859
\(794\) 0 0
\(795\) −5.55858 −0.197143
\(796\) 0 0
\(797\) 52.3247 1.85343 0.926717 0.375759i \(-0.122618\pi\)
0.926717 + 0.375759i \(0.122618\pi\)
\(798\) 0 0
\(799\) −2.57853 −0.0912219
\(800\) 0 0
\(801\) −6.18238 −0.218444
\(802\) 0 0
\(803\) −2.11641 −0.0746865
\(804\) 0 0
\(805\) 46.2181 1.62897
\(806\) 0 0
\(807\) −16.2825 −0.573171
\(808\) 0 0
\(809\) 36.9217 1.29810 0.649048 0.760747i \(-0.275167\pi\)
0.649048 + 0.760747i \(0.275167\pi\)
\(810\) 0 0
\(811\) 7.03514 0.247037 0.123519 0.992342i \(-0.460582\pi\)
0.123519 + 0.992342i \(0.460582\pi\)
\(812\) 0 0
\(813\) 19.6255 0.688297
\(814\) 0 0
\(815\) −24.6434 −0.863221
\(816\) 0 0
\(817\) −1.02765 −0.0359531
\(818\) 0 0
\(819\) 25.3533 0.885915
\(820\) 0 0
\(821\) −18.7702 −0.655085 −0.327542 0.944836i \(-0.606220\pi\)
−0.327542 + 0.944836i \(0.606220\pi\)
\(822\) 0 0
\(823\) 52.7145 1.83751 0.918756 0.394825i \(-0.129195\pi\)
0.918756 + 0.394825i \(0.129195\pi\)
\(824\) 0 0
\(825\) −1.64378 −0.0572291
\(826\) 0 0
\(827\) −17.6427 −0.613498 −0.306749 0.951790i \(-0.599241\pi\)
−0.306749 + 0.951790i \(0.599241\pi\)
\(828\) 0 0
\(829\) 34.9409 1.21355 0.606775 0.794874i \(-0.292463\pi\)
0.606775 + 0.794874i \(0.292463\pi\)
\(830\) 0 0
\(831\) −10.2760 −0.356470
\(832\) 0 0
\(833\) −5.48912 −0.190187
\(834\) 0 0
\(835\) 38.4799 1.33165
\(836\) 0 0
\(837\) 14.2079 0.491097
\(838\) 0 0
\(839\) 12.2284 0.422170 0.211085 0.977468i \(-0.432300\pi\)
0.211085 + 0.977468i \(0.432300\pi\)
\(840\) 0 0
\(841\) −4.35659 −0.150227
\(842\) 0 0
\(843\) 7.57779 0.260993
\(844\) 0 0
\(845\) −7.31572 −0.251669
\(846\) 0 0
\(847\) 30.4771 1.04720
\(848\) 0 0
\(849\) 18.4084 0.631775
\(850\) 0 0
\(851\) 40.8609 1.40069
\(852\) 0 0
\(853\) −14.9504 −0.511891 −0.255945 0.966691i \(-0.582387\pi\)
−0.255945 + 0.966691i \(0.582387\pi\)
\(854\) 0 0
\(855\) −2.95870 −0.101185
\(856\) 0 0
\(857\) −28.8802 −0.986530 −0.493265 0.869879i \(-0.664197\pi\)
−0.493265 + 0.869879i \(0.664197\pi\)
\(858\) 0 0
\(859\) 18.3304 0.625424 0.312712 0.949848i \(-0.398763\pi\)
0.312712 + 0.949848i \(0.398763\pi\)
\(860\) 0 0
\(861\) −4.82666 −0.164492
\(862\) 0 0
\(863\) −30.9280 −1.05280 −0.526401 0.850237i \(-0.676459\pi\)
−0.526401 + 0.850237i \(0.676459\pi\)
\(864\) 0 0
\(865\) −6.26045 −0.212862
\(866\) 0 0
\(867\) −0.859886 −0.0292033
\(868\) 0 0
\(869\) −10.2408 −0.347397
\(870\) 0 0
\(871\) −18.0478 −0.611525
\(872\) 0 0
\(873\) −8.13600 −0.275362
\(874\) 0 0
\(875\) 33.1920 1.12209
\(876\) 0 0
\(877\) 42.0300 1.41925 0.709627 0.704578i \(-0.248864\pi\)
0.709627 + 0.704578i \(0.248864\pi\)
\(878\) 0 0
\(879\) −15.4326 −0.520528
\(880\) 0 0
\(881\) −58.8585 −1.98299 −0.991497 0.130127i \(-0.958461\pi\)
−0.991497 + 0.130127i \(0.958461\pi\)
\(882\) 0 0
\(883\) 48.8906 1.64530 0.822650 0.568548i \(-0.192495\pi\)
0.822650 + 0.568548i \(0.192495\pi\)
\(884\) 0 0
\(885\) −2.14802 −0.0722050
\(886\) 0 0
\(887\) 21.3749 0.717698 0.358849 0.933396i \(-0.383169\pi\)
0.358849 + 0.933396i \(0.383169\pi\)
\(888\) 0 0
\(889\) 62.8592 2.10823
\(890\) 0 0
\(891\) 4.45797 0.149347
\(892\) 0 0
\(893\) 1.35099 0.0452092
\(894\) 0 0
\(895\) −26.5585 −0.887753
\(896\) 0 0
\(897\) 14.2868 0.477021
\(898\) 0 0
\(899\) 15.5921 0.520026
\(900\) 0 0
\(901\) −2.58777 −0.0862110
\(902\) 0 0
\(903\) −5.96038 −0.198349
\(904\) 0 0
\(905\) −11.3067 −0.375848
\(906\) 0 0
\(907\) 53.1059 1.76335 0.881676 0.471854i \(-0.156415\pi\)
0.881676 + 0.471854i \(0.156415\pi\)
\(908\) 0 0
\(909\) 29.4639 0.977257
\(910\) 0 0
\(911\) −41.3354 −1.36950 −0.684752 0.728776i \(-0.740090\pi\)
−0.684752 + 0.728776i \(0.740090\pi\)
\(912\) 0 0
\(913\) −25.9784 −0.859759
\(914\) 0 0
\(915\) −14.0638 −0.464936
\(916\) 0 0
\(917\) −39.4932 −1.30418
\(918\) 0 0
\(919\) 21.9600 0.724395 0.362197 0.932101i \(-0.382027\pi\)
0.362197 + 0.932101i \(0.382027\pi\)
\(920\) 0 0
\(921\) 2.60558 0.0858569
\(922\) 0 0
\(923\) −44.3936 −1.46123
\(924\) 0 0
\(925\) −9.67914 −0.318248
\(926\) 0 0
\(927\) 20.1359 0.661350
\(928\) 0 0
\(929\) −9.76489 −0.320376 −0.160188 0.987087i \(-0.551210\pi\)
−0.160188 + 0.987087i \(0.551210\pi\)
\(930\) 0 0
\(931\) 2.87596 0.0942557
\(932\) 0 0
\(933\) −9.04445 −0.296102
\(934\) 0 0
\(935\) −3.85056 −0.125927
\(936\) 0 0
\(937\) 6.07167 0.198353 0.0991765 0.995070i \(-0.468379\pi\)
0.0991765 + 0.995070i \(0.468379\pi\)
\(938\) 0 0
\(939\) −9.32574 −0.304334
\(940\) 0 0
\(941\) −2.95743 −0.0964095 −0.0482048 0.998837i \(-0.515350\pi\)
−0.0482048 + 0.998837i \(0.515350\pi\)
\(942\) 0 0
\(943\) 8.31550 0.270790
\(944\) 0 0
\(945\) −39.9337 −1.29904
\(946\) 0 0
\(947\) −3.09886 −0.100699 −0.0503497 0.998732i \(-0.516034\pi\)
−0.0503497 + 0.998732i \(0.516034\pi\)
\(948\) 0 0
\(949\) −4.35732 −0.141444
\(950\) 0 0
\(951\) 24.2128 0.785154
\(952\) 0 0
\(953\) 16.4416 0.532596 0.266298 0.963891i \(-0.414199\pi\)
0.266298 + 0.963891i \(0.414199\pi\)
\(954\) 0 0
\(955\) −4.06087 −0.131407
\(956\) 0 0
\(957\) −6.57987 −0.212697
\(958\) 0 0
\(959\) −19.9563 −0.644422
\(960\) 0 0
\(961\) −21.1347 −0.681765
\(962\) 0 0
\(963\) 22.4383 0.723064
\(964\) 0 0
\(965\) 27.9779 0.900641
\(966\) 0 0
\(967\) −26.0967 −0.839213 −0.419606 0.907706i \(-0.637832\pi\)
−0.419606 + 0.907706i \(0.637832\pi\)
\(968\) 0 0
\(969\) 0.450527 0.0144730
\(970\) 0 0
\(971\) 14.5210 0.466000 0.233000 0.972477i \(-0.425146\pi\)
0.233000 + 0.972477i \(0.425146\pi\)
\(972\) 0 0
\(973\) 14.6203 0.468706
\(974\) 0 0
\(975\) −3.38425 −0.108383
\(976\) 0 0
\(977\) −39.9161 −1.27703 −0.638515 0.769609i \(-0.720451\pi\)
−0.638515 + 0.769609i \(0.720451\pi\)
\(978\) 0 0
\(979\) 4.21559 0.134731
\(980\) 0 0
\(981\) −2.73851 −0.0874340
\(982\) 0 0
\(983\) −12.7747 −0.407449 −0.203725 0.979028i \(-0.565305\pi\)
−0.203725 + 0.979028i \(0.565305\pi\)
\(984\) 0 0
\(985\) −60.8469 −1.93874
\(986\) 0 0
\(987\) 7.83572 0.249414
\(988\) 0 0
\(989\) 10.2687 0.326526
\(990\) 0 0
\(991\) −31.3208 −0.994939 −0.497470 0.867481i \(-0.665737\pi\)
−0.497470 + 0.867481i \(0.665737\pi\)
\(992\) 0 0
\(993\) 12.3551 0.392076
\(994\) 0 0
\(995\) 26.5560 0.841881
\(996\) 0 0
\(997\) 4.01525 0.127164 0.0635821 0.997977i \(-0.479748\pi\)
0.0635821 + 0.997977i \(0.479748\pi\)
\(998\) 0 0
\(999\) −35.3050 −1.11700
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 \(a_p\))