Properties

Label 4014.2.a.q.1.1
Level 4014
Weight 2
Character 4014.1
Self dual Yes
Analytic conductor 32.052
Analytic rank 1
Dimension 4
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4014 = 2 \cdot 3^{2} \cdot 223 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4014.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0519513713\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: 4.4.10273.1
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.38266\)
Character \(\chi\) = 4014.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{4}\) \(-2.38266 q^{5}\) \(+1.61326 q^{7}\) \(+1.00000 q^{8}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{4}\) \(-2.38266 q^{5}\) \(+1.61326 q^{7}\) \(+1.00000 q^{8}\) \(-2.38266 q^{10}\) \(-1.29442 q^{11}\) \(-6.29035 q^{13}\) \(+1.61326 q^{14}\) \(+1.00000 q^{16}\) \(+6.73683 q^{17}\) \(-4.10296 q^{19}\) \(-2.38266 q^{20}\) \(-1.29442 q^{22}\) \(+8.82507 q^{23}\) \(+0.677084 q^{25}\) \(-6.29035 q^{26}\) \(+1.61326 q^{28}\) \(-3.74090 q^{29}\) \(+2.10296 q^{31}\) \(+1.00000 q^{32}\) \(+6.73683 q^{34}\) \(-3.84386 q^{35}\) \(-9.37859 q^{37}\) \(-4.10296 q^{38}\) \(-2.38266 q^{40}\) \(-8.42180 q^{41}\) \(-3.32292 q^{43}\) \(-1.29442 q^{44}\) \(+8.82507 q^{46}\) \(+1.48970 q^{47}\) \(-4.39738 q^{49}\) \(+0.677084 q^{50}\) \(-6.29035 q^{52}\) \(-7.88889 q^{53}\) \(+3.08417 q^{55}\) \(+1.61326 q^{56}\) \(-3.74090 q^{58}\) \(+11.0704 q^{59}\) \(+4.37859 q^{61}\) \(+2.10296 q^{62}\) \(+1.00000 q^{64}\) \(+14.9878 q^{65}\) \(-3.61734 q^{67}\) \(+6.73683 q^{68}\) \(-3.84386 q^{70}\) \(-2.01472 q^{71}\) \(+7.03507 q^{73}\) \(-9.37859 q^{74}\) \(-4.10296 q^{76}\) \(-2.08824 q^{77}\) \(-16.2716 q^{79}\) \(-2.38266 q^{80}\) \(-8.42180 q^{82}\) \(-4.90361 q^{83}\) \(-16.0516 q^{85}\) \(-3.32292 q^{86}\) \(-1.29442 q^{88}\) \(-18.3704 q^{89}\) \(-10.1480 q^{91}\) \(+8.82507 q^{92}\) \(+1.48970 q^{94}\) \(+9.77597 q^{95}\) \(-15.7613 q^{97}\) \(-4.39738 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(4q \) \(\mathstrut +\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 4q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut +\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 4q^{8} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 5q^{14} \) \(\mathstrut +\mathstrut 4q^{16} \) \(\mathstrut +\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut 7q^{19} \) \(\mathstrut -\mathstrut 2q^{20} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 6q^{25} \) \(\mathstrut -\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 5q^{28} \) \(\mathstrut -\mathstrut 9q^{29} \) \(\mathstrut -\mathstrut q^{31} \) \(\mathstrut +\mathstrut 4q^{32} \) \(\mathstrut +\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 11q^{37} \) \(\mathstrut -\mathstrut 7q^{38} \) \(\mathstrut -\mathstrut 2q^{40} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 22q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 4q^{46} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut -\mathstrut 7q^{49} \) \(\mathstrut -\mathstrut 6q^{50} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 13q^{55} \) \(\mathstrut -\mathstrut 5q^{56} \) \(\mathstrut -\mathstrut 9q^{58} \) \(\mathstrut +\mathstrut 6q^{59} \) \(\mathstrut -\mathstrut 9q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut +\mathstrut 4q^{64} \) \(\mathstrut +\mathstrut 3q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut -\mathstrut 5q^{71} \) \(\mathstrut -\mathstrut 3q^{73} \) \(\mathstrut -\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 7q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut -\mathstrut 29q^{79} \) \(\mathstrut -\mathstrut 2q^{80} \) \(\mathstrut -\mathstrut 14q^{82} \) \(\mathstrut +\mathstrut 12q^{83} \) \(\mathstrut -\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 22q^{86} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 18q^{91} \) \(\mathstrut +\mathstrut 4q^{92} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut -\mathstrut 29q^{97} \) \(\mathstrut -\mathstrut 7q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −2.38266 −1.06556 −0.532780 0.846254i \(-0.678853\pi\)
−0.532780 + 0.846254i \(0.678853\pi\)
\(6\) 0 0
\(7\) 1.61326 0.609756 0.304878 0.952391i \(-0.401384\pi\)
0.304878 + 0.952391i \(0.401384\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −2.38266 −0.753464
\(11\) −1.29442 −0.390283 −0.195141 0.980775i \(-0.562517\pi\)
−0.195141 + 0.980775i \(0.562517\pi\)
\(12\) 0 0
\(13\) −6.29035 −1.74463 −0.872314 0.488946i \(-0.837382\pi\)
−0.872314 + 0.488946i \(0.837382\pi\)
\(14\) 1.61326 0.431163
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 6.73683 1.63392 0.816961 0.576693i \(-0.195657\pi\)
0.816961 + 0.576693i \(0.195657\pi\)
\(18\) 0 0
\(19\) −4.10296 −0.941283 −0.470642 0.882324i \(-0.655978\pi\)
−0.470642 + 0.882324i \(0.655978\pi\)
\(20\) −2.38266 −0.532780
\(21\) 0 0
\(22\) −1.29442 −0.275971
\(23\) 8.82507 1.84016 0.920078 0.391736i \(-0.128125\pi\)
0.920078 + 0.391736i \(0.128125\pi\)
\(24\) 0 0
\(25\) 0.677084 0.135417
\(26\) −6.29035 −1.23364
\(27\) 0 0
\(28\) 1.61326 0.304878
\(29\) −3.74090 −0.694669 −0.347334 0.937741i \(-0.612913\pi\)
−0.347334 + 0.937741i \(0.612913\pi\)
\(30\) 0 0
\(31\) 2.10296 0.377703 0.188851 0.982006i \(-0.439524\pi\)
0.188851 + 0.982006i \(0.439524\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 6.73683 1.15536
\(35\) −3.84386 −0.649732
\(36\) 0 0
\(37\) −9.37859 −1.54183 −0.770915 0.636938i \(-0.780201\pi\)
−0.770915 + 0.636938i \(0.780201\pi\)
\(38\) −4.10296 −0.665588
\(39\) 0 0
\(40\) −2.38266 −0.376732
\(41\) −8.42180 −1.31526 −0.657632 0.753339i \(-0.728442\pi\)
−0.657632 + 0.753339i \(0.728442\pi\)
\(42\) 0 0
\(43\) −3.32292 −0.506740 −0.253370 0.967369i \(-0.581539\pi\)
−0.253370 + 0.967369i \(0.581539\pi\)
\(44\) −1.29442 −0.195141
\(45\) 0 0
\(46\) 8.82507 1.30119
\(47\) 1.48970 0.217294 0.108647 0.994080i \(-0.465348\pi\)
0.108647 + 0.994080i \(0.465348\pi\)
\(48\) 0 0
\(49\) −4.39738 −0.628197
\(50\) 0.677084 0.0957542
\(51\) 0 0
\(52\) −6.29035 −0.872314
\(53\) −7.88889 −1.08362 −0.541812 0.840500i \(-0.682261\pi\)
−0.541812 + 0.840500i \(0.682261\pi\)
\(54\) 0 0
\(55\) 3.08417 0.415869
\(56\) 1.61326 0.215581
\(57\) 0 0
\(58\) −3.74090 −0.491205
\(59\) 11.0704 1.44124 0.720621 0.693329i \(-0.243857\pi\)
0.720621 + 0.693329i \(0.243857\pi\)
\(60\) 0 0
\(61\) 4.37859 0.560621 0.280311 0.959909i \(-0.409563\pi\)
0.280311 + 0.959909i \(0.409563\pi\)
\(62\) 2.10296 0.267076
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 14.9878 1.85901
\(66\) 0 0
\(67\) −3.61734 −0.441928 −0.220964 0.975282i \(-0.570920\pi\)
−0.220964 + 0.975282i \(0.570920\pi\)
\(68\) 6.73683 0.816961
\(69\) 0 0
\(70\) −3.84386 −0.459430
\(71\) −2.01472 −0.239103 −0.119551 0.992828i \(-0.538146\pi\)
−0.119551 + 0.992828i \(0.538146\pi\)
\(72\) 0 0
\(73\) 7.03507 0.823392 0.411696 0.911321i \(-0.364937\pi\)
0.411696 + 0.911321i \(0.364937\pi\)
\(74\) −9.37859 −1.09024
\(75\) 0 0
\(76\) −4.10296 −0.470642
\(77\) −2.08824 −0.237977
\(78\) 0 0
\(79\) −16.2716 −1.83069 −0.915347 0.402667i \(-0.868083\pi\)
−0.915347 + 0.402667i \(0.868083\pi\)
\(80\) −2.38266 −0.266390
\(81\) 0 0
\(82\) −8.42180 −0.930032
\(83\) −4.90361 −0.538241 −0.269121 0.963106i \(-0.586733\pi\)
−0.269121 + 0.963106i \(0.586733\pi\)
\(84\) 0 0
\(85\) −16.0516 −1.74104
\(86\) −3.32292 −0.358319
\(87\) 0 0
\(88\) −1.29442 −0.137986
\(89\) −18.3704 −1.94726 −0.973632 0.228126i \(-0.926740\pi\)
−0.973632 + 0.228126i \(0.926740\pi\)
\(90\) 0 0
\(91\) −10.1480 −1.06380
\(92\) 8.82507 0.920078
\(93\) 0 0
\(94\) 1.48970 0.153650
\(95\) 9.77597 1.00299
\(96\) 0 0
\(97\) −15.7613 −1.60031 −0.800156 0.599791i \(-0.795250\pi\)
−0.800156 + 0.599791i \(0.795250\pi\)
\(98\) −4.39738 −0.444202
\(99\) 0 0
\(100\) 0.677084 0.0677084
\(101\) −2.17267 −0.216189 −0.108094 0.994141i \(-0.534475\pi\)
−0.108094 + 0.994141i \(0.534475\pi\)
\(102\) 0 0
\(103\) 4.33131 0.426776 0.213388 0.976968i \(-0.431550\pi\)
0.213388 + 0.976968i \(0.431550\pi\)
\(104\) −6.29035 −0.616819
\(105\) 0 0
\(106\) −7.88889 −0.766237
\(107\) −13.7531 −1.32956 −0.664782 0.747038i \(-0.731475\pi\)
−0.664782 + 0.747038i \(0.731475\pi\)
\(108\) 0 0
\(109\) 7.03125 0.673472 0.336736 0.941599i \(-0.390677\pi\)
0.336736 + 0.941599i \(0.390677\pi\)
\(110\) 3.08417 0.294064
\(111\) 0 0
\(112\) 1.61326 0.152439
\(113\) −8.71215 −0.819570 −0.409785 0.912182i \(-0.634396\pi\)
−0.409785 + 0.912182i \(0.634396\pi\)
\(114\) 0 0
\(115\) −21.0272 −1.96079
\(116\) −3.74090 −0.347334
\(117\) 0 0
\(118\) 11.0704 1.01911
\(119\) 10.8683 0.996294
\(120\) 0 0
\(121\) −9.32447 −0.847679
\(122\) 4.37859 0.396419
\(123\) 0 0
\(124\) 2.10296 0.188851
\(125\) 10.3001 0.921265
\(126\) 0 0
\(127\) −9.49940 −0.842935 −0.421468 0.906843i \(-0.638485\pi\)
−0.421468 + 0.906843i \(0.638485\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 14.9878 1.31452
\(131\) 14.3460 1.25342 0.626709 0.779253i \(-0.284402\pi\)
0.626709 + 0.779253i \(0.284402\pi\)
\(132\) 0 0
\(133\) −6.61916 −0.573954
\(134\) −3.61734 −0.312490
\(135\) 0 0
\(136\) 6.73683 0.577679
\(137\) 5.10296 0.435975 0.217988 0.975952i \(-0.430051\pi\)
0.217988 + 0.975952i \(0.430051\pi\)
\(138\) 0 0
\(139\) −5.63795 −0.478204 −0.239102 0.970994i \(-0.576853\pi\)
−0.239102 + 0.970994i \(0.576853\pi\)
\(140\) −3.84386 −0.324866
\(141\) 0 0
\(142\) −2.01472 −0.169071
\(143\) 8.14236 0.680898
\(144\) 0 0
\(145\) 8.91332 0.740211
\(146\) 7.03507 0.582226
\(147\) 0 0
\(148\) −9.37859 −0.770915
\(149\) 5.67119 0.464602 0.232301 0.972644i \(-0.425375\pi\)
0.232301 + 0.972644i \(0.425375\pi\)
\(150\) 0 0
\(151\) 12.4343 1.01189 0.505943 0.862567i \(-0.331145\pi\)
0.505943 + 0.862567i \(0.331145\pi\)
\(152\) −4.10296 −0.332794
\(153\) 0 0
\(154\) −2.08824 −0.168275
\(155\) −5.01064 −0.402465
\(156\) 0 0
\(157\) 8.23623 0.657323 0.328661 0.944448i \(-0.393402\pi\)
0.328661 + 0.944448i \(0.393402\pi\)
\(158\) −16.2716 −1.29450
\(159\) 0 0
\(160\) −2.38266 −0.188366
\(161\) 14.2372 1.12205
\(162\) 0 0
\(163\) −7.27000 −0.569430 −0.284715 0.958612i \(-0.591899\pi\)
−0.284715 + 0.958612i \(0.591899\pi\)
\(164\) −8.42180 −0.657632
\(165\) 0 0
\(166\) −4.90361 −0.380594
\(167\) 9.90361 0.766364 0.383182 0.923673i \(-0.374828\pi\)
0.383182 + 0.923673i \(0.374828\pi\)
\(168\) 0 0
\(169\) 26.5685 2.04373
\(170\) −16.0516 −1.23110
\(171\) 0 0
\(172\) −3.32292 −0.253370
\(173\) −23.2252 −1.76578 −0.882890 0.469580i \(-0.844405\pi\)
−0.882890 + 0.469580i \(0.844405\pi\)
\(174\) 0 0
\(175\) 1.09232 0.0825713
\(176\) −1.29442 −0.0975707
\(177\) 0 0
\(178\) −18.3704 −1.37692
\(179\) 21.2499 1.58829 0.794146 0.607727i \(-0.207919\pi\)
0.794146 + 0.607727i \(0.207919\pi\)
\(180\) 0 0
\(181\) −20.7569 −1.54285 −0.771425 0.636320i \(-0.780456\pi\)
−0.771425 + 0.636320i \(0.780456\pi\)
\(182\) −10.1480 −0.752219
\(183\) 0 0
\(184\) 8.82507 0.650593
\(185\) 22.3460 1.64291
\(186\) 0 0
\(187\) −8.72030 −0.637691
\(188\) 1.48970 0.108647
\(189\) 0 0
\(190\) 9.77597 0.709223
\(191\) −19.2018 −1.38940 −0.694698 0.719301i \(-0.744462\pi\)
−0.694698 + 0.719301i \(0.744462\pi\)
\(192\) 0 0
\(193\) 10.2433 0.737331 0.368665 0.929562i \(-0.379815\pi\)
0.368665 + 0.929562i \(0.379815\pi\)
\(194\) −15.7613 −1.13159
\(195\) 0 0
\(196\) −4.39738 −0.314099
\(197\) −9.76507 −0.695732 −0.347866 0.937544i \(-0.613094\pi\)
−0.347866 + 0.937544i \(0.613094\pi\)
\(198\) 0 0
\(199\) −3.06564 −0.217317 −0.108659 0.994079i \(-0.534656\pi\)
−0.108659 + 0.994079i \(0.534656\pi\)
\(200\) 0.677084 0.0478771
\(201\) 0 0
\(202\) −2.17267 −0.152869
\(203\) −6.03507 −0.423579
\(204\) 0 0
\(205\) 20.0663 1.40149
\(206\) 4.33131 0.301776
\(207\) 0 0
\(208\) −6.29035 −0.436157
\(209\) 5.31096 0.367367
\(210\) 0 0
\(211\) 0.240565 0.0165612 0.00828059 0.999966i \(-0.497364\pi\)
0.00828059 + 0.999966i \(0.497364\pi\)
\(212\) −7.88889 −0.541812
\(213\) 0 0
\(214\) −13.7531 −0.940143
\(215\) 7.91739 0.539961
\(216\) 0 0
\(217\) 3.39263 0.230307
\(218\) 7.03125 0.476217
\(219\) 0 0
\(220\) 3.08417 0.207935
\(221\) −42.3770 −2.85059
\(222\) 0 0
\(223\) −1.00000 −0.0669650
\(224\) 1.61326 0.107791
\(225\) 0 0
\(226\) −8.71215 −0.579524
\(227\) 14.8523 0.985779 0.492889 0.870092i \(-0.335941\pi\)
0.492889 + 0.870092i \(0.335941\pi\)
\(228\) 0 0
\(229\) 5.82639 0.385019 0.192509 0.981295i \(-0.438337\pi\)
0.192509 + 0.981295i \(0.438337\pi\)
\(230\) −21.0272 −1.38649
\(231\) 0 0
\(232\) −3.74090 −0.245602
\(233\) −17.0770 −1.11875 −0.559375 0.828915i \(-0.688959\pi\)
−0.559375 + 0.828915i \(0.688959\pi\)
\(234\) 0 0
\(235\) −3.54944 −0.231540
\(236\) 11.0704 0.720621
\(237\) 0 0
\(238\) 10.8683 0.704486
\(239\) 22.0091 1.42365 0.711824 0.702358i \(-0.247869\pi\)
0.711824 + 0.702358i \(0.247869\pi\)
\(240\) 0 0
\(241\) 13.7948 0.888599 0.444299 0.895878i \(-0.353453\pi\)
0.444299 + 0.895878i \(0.353453\pi\)
\(242\) −9.32447 −0.599400
\(243\) 0 0
\(244\) 4.37859 0.280311
\(245\) 10.4775 0.669381
\(246\) 0 0
\(247\) 25.8090 1.64219
\(248\) 2.10296 0.133538
\(249\) 0 0
\(250\) 10.3001 0.651433
\(251\) 12.2127 0.770862 0.385431 0.922737i \(-0.374053\pi\)
0.385431 + 0.922737i \(0.374053\pi\)
\(252\) 0 0
\(253\) −11.4234 −0.718181
\(254\) −9.49940 −0.596045
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 15.2616 0.951992 0.475996 0.879447i \(-0.342088\pi\)
0.475996 + 0.879447i \(0.342088\pi\)
\(258\) 0 0
\(259\) −15.1301 −0.940141
\(260\) 14.9878 0.929503
\(261\) 0 0
\(262\) 14.3460 0.886300
\(263\) −29.3341 −1.80882 −0.904408 0.426669i \(-0.859687\pi\)
−0.904408 + 0.426669i \(0.859687\pi\)
\(264\) 0 0
\(265\) 18.7966 1.15466
\(266\) −6.61916 −0.405846
\(267\) 0 0
\(268\) −3.61734 −0.220964
\(269\) −5.04597 −0.307658 −0.153829 0.988097i \(-0.549161\pi\)
−0.153829 + 0.988097i \(0.549161\pi\)
\(270\) 0 0
\(271\) −17.5932 −1.06871 −0.534354 0.845261i \(-0.679445\pi\)
−0.534354 + 0.845261i \(0.679445\pi\)
\(272\) 6.73683 0.408480
\(273\) 0 0
\(274\) 5.10296 0.308281
\(275\) −0.876432 −0.0528508
\(276\) 0 0
\(277\) −21.1091 −1.26832 −0.634161 0.773201i \(-0.718654\pi\)
−0.634161 + 0.773201i \(0.718654\pi\)
\(278\) −5.63795 −0.338141
\(279\) 0 0
\(280\) −3.84386 −0.229715
\(281\) −24.8464 −1.48221 −0.741105 0.671389i \(-0.765698\pi\)
−0.741105 + 0.671389i \(0.765698\pi\)
\(282\) 0 0
\(283\) 15.2459 0.906277 0.453138 0.891440i \(-0.350304\pi\)
0.453138 + 0.891440i \(0.350304\pi\)
\(284\) −2.01472 −0.119551
\(285\) 0 0
\(286\) 8.14236 0.481468
\(287\) −13.5866 −0.801991
\(288\) 0 0
\(289\) 28.3849 1.66970
\(290\) 8.91332 0.523408
\(291\) 0 0
\(292\) 7.03507 0.411696
\(293\) −16.2334 −0.948363 −0.474181 0.880427i \(-0.657256\pi\)
−0.474181 + 0.880427i \(0.657256\pi\)
\(294\) 0 0
\(295\) −26.3770 −1.53573
\(296\) −9.37859 −0.545119
\(297\) 0 0
\(298\) 5.67119 0.328523
\(299\) −55.5128 −3.21039
\(300\) 0 0
\(301\) −5.36074 −0.308988
\(302\) 12.4343 0.715512
\(303\) 0 0
\(304\) −4.10296 −0.235321
\(305\) −10.4327 −0.597375
\(306\) 0 0
\(307\) 8.09889 0.462228 0.231114 0.972927i \(-0.425763\pi\)
0.231114 + 0.972927i \(0.425763\pi\)
\(308\) −2.08824 −0.118989
\(309\) 0 0
\(310\) −5.01064 −0.284585
\(311\) 23.2534 1.31858 0.659291 0.751888i \(-0.270857\pi\)
0.659291 + 0.751888i \(0.270857\pi\)
\(312\) 0 0
\(313\) 7.91176 0.447199 0.223599 0.974681i \(-0.428219\pi\)
0.223599 + 0.974681i \(0.428219\pi\)
\(314\) 8.23623 0.464797
\(315\) 0 0
\(316\) −16.2716 −0.915347
\(317\) 2.05975 0.115687 0.0578435 0.998326i \(-0.481578\pi\)
0.0578435 + 0.998326i \(0.481578\pi\)
\(318\) 0 0
\(319\) 4.84231 0.271117
\(320\) −2.38266 −0.133195
\(321\) 0 0
\(322\) 14.2372 0.793407
\(323\) −27.6409 −1.53798
\(324\) 0 0
\(325\) −4.25910 −0.236252
\(326\) −7.27000 −0.402648
\(327\) 0 0
\(328\) −8.42180 −0.465016
\(329\) 2.40327 0.132497
\(330\) 0 0
\(331\) 6.59629 0.362565 0.181283 0.983431i \(-0.441975\pi\)
0.181283 + 0.983431i \(0.441975\pi\)
\(332\) −4.90361 −0.269121
\(333\) 0 0
\(334\) 9.90361 0.541902
\(335\) 8.61890 0.470901
\(336\) 0 0
\(337\) 13.5444 0.737812 0.368906 0.929467i \(-0.379732\pi\)
0.368906 + 0.929467i \(0.379732\pi\)
\(338\) 26.5685 1.44513
\(339\) 0 0
\(340\) −16.0516 −0.870520
\(341\) −2.72211 −0.147411
\(342\) 0 0
\(343\) −18.3870 −0.992804
\(344\) −3.32292 −0.179160
\(345\) 0 0
\(346\) −23.2252 −1.24860
\(347\) 11.3204 0.607711 0.303855 0.952718i \(-0.401726\pi\)
0.303855 + 0.952718i \(0.401726\pi\)
\(348\) 0 0
\(349\) −23.1517 −1.23928 −0.619641 0.784886i \(-0.712722\pi\)
−0.619641 + 0.784886i \(0.712722\pi\)
\(350\) 1.09232 0.0583867
\(351\) 0 0
\(352\) −1.29442 −0.0689929
\(353\) 31.6382 1.68393 0.841965 0.539531i \(-0.181399\pi\)
0.841965 + 0.539531i \(0.181399\pi\)
\(354\) 0 0
\(355\) 4.80039 0.254778
\(356\) −18.3704 −0.973632
\(357\) 0 0
\(358\) 21.2499 1.12309
\(359\) 30.8685 1.62918 0.814589 0.580038i \(-0.196962\pi\)
0.814589 + 0.580038i \(0.196962\pi\)
\(360\) 0 0
\(361\) −2.16572 −0.113986
\(362\) −20.7569 −1.09096
\(363\) 0 0
\(364\) −10.1480 −0.531899
\(365\) −16.7622 −0.877373
\(366\) 0 0
\(367\) 18.5835 0.970048 0.485024 0.874501i \(-0.338811\pi\)
0.485024 + 0.874501i \(0.338811\pi\)
\(368\) 8.82507 0.460039
\(369\) 0 0
\(370\) 22.3460 1.16171
\(371\) −12.7269 −0.660746
\(372\) 0 0
\(373\) 4.22351 0.218685 0.109343 0.994004i \(-0.465125\pi\)
0.109343 + 0.994004i \(0.465125\pi\)
\(374\) −8.72030 −0.450916
\(375\) 0 0
\(376\) 1.48970 0.0768252
\(377\) 23.5316 1.21194
\(378\) 0 0
\(379\) 9.04753 0.464740 0.232370 0.972627i \(-0.425352\pi\)
0.232370 + 0.972627i \(0.425352\pi\)
\(380\) 9.77597 0.501497
\(381\) 0 0
\(382\) −19.2018 −0.982452
\(383\) −14.8525 −0.758928 −0.379464 0.925207i \(-0.623892\pi\)
−0.379464 + 0.925207i \(0.623892\pi\)
\(384\) 0 0
\(385\) 4.97558 0.253579
\(386\) 10.2433 0.521371
\(387\) 0 0
\(388\) −15.7613 −0.800156
\(389\) 4.34446 0.220273 0.110137 0.993916i \(-0.464871\pi\)
0.110137 + 0.993916i \(0.464871\pi\)
\(390\) 0 0
\(391\) 59.4530 3.00667
\(392\) −4.39738 −0.222101
\(393\) 0 0
\(394\) −9.76507 −0.491957
\(395\) 38.7696 1.95071
\(396\) 0 0
\(397\) −36.6902 −1.84143 −0.920715 0.390236i \(-0.872393\pi\)
−0.920715 + 0.390236i \(0.872393\pi\)
\(398\) −3.06564 −0.153667
\(399\) 0 0
\(400\) 0.677084 0.0338542
\(401\) −7.96441 −0.397724 −0.198862 0.980028i \(-0.563725\pi\)
−0.198862 + 0.980028i \(0.563725\pi\)
\(402\) 0 0
\(403\) −13.2283 −0.658951
\(404\) −2.17267 −0.108094
\(405\) 0 0
\(406\) −6.03507 −0.299515
\(407\) 12.1398 0.601750
\(408\) 0 0
\(409\) −5.89271 −0.291376 −0.145688 0.989331i \(-0.546540\pi\)
−0.145688 + 0.989331i \(0.546540\pi\)
\(410\) 20.0663 0.991005
\(411\) 0 0
\(412\) 4.33131 0.213388
\(413\) 17.8595 0.878807
\(414\) 0 0
\(415\) 11.6837 0.573528
\(416\) −6.29035 −0.308410
\(417\) 0 0
\(418\) 5.31096 0.259767
\(419\) 12.3962 0.605593 0.302797 0.953055i \(-0.402080\pi\)
0.302797 + 0.953055i \(0.402080\pi\)
\(420\) 0 0
\(421\) −27.5556 −1.34298 −0.671488 0.741015i \(-0.734345\pi\)
−0.671488 + 0.741015i \(0.734345\pi\)
\(422\) 0.240565 0.0117105
\(423\) 0 0
\(424\) −7.88889 −0.383119
\(425\) 4.56140 0.221261
\(426\) 0 0
\(427\) 7.06382 0.341842
\(428\) −13.7531 −0.664782
\(429\) 0 0
\(430\) 7.91739 0.381810
\(431\) −19.1468 −0.922268 −0.461134 0.887330i \(-0.652557\pi\)
−0.461134 + 0.887330i \(0.652557\pi\)
\(432\) 0 0
\(433\) −30.9452 −1.48713 −0.743567 0.668662i \(-0.766868\pi\)
−0.743567 + 0.668662i \(0.766868\pi\)
\(434\) 3.39263 0.162851
\(435\) 0 0
\(436\) 7.03125 0.336736
\(437\) −36.2089 −1.73211
\(438\) 0 0
\(439\) 22.6235 1.07976 0.539880 0.841742i \(-0.318470\pi\)
0.539880 + 0.841742i \(0.318470\pi\)
\(440\) 3.08417 0.147032
\(441\) 0 0
\(442\) −42.3770 −2.01567
\(443\) 0.982585 0.0466840 0.0233420 0.999728i \(-0.492569\pi\)
0.0233420 + 0.999728i \(0.492569\pi\)
\(444\) 0 0
\(445\) 43.7706 2.07492
\(446\) −1.00000 −0.0473514
\(447\) 0 0
\(448\) 1.61326 0.0762195
\(449\) −5.66487 −0.267342 −0.133671 0.991026i \(-0.542676\pi\)
−0.133671 + 0.991026i \(0.542676\pi\)
\(450\) 0 0
\(451\) 10.9014 0.513325
\(452\) −8.71215 −0.409785
\(453\) 0 0
\(454\) 14.8523 0.697051
\(455\) 24.1792 1.13354
\(456\) 0 0
\(457\) −7.75756 −0.362883 −0.181442 0.983402i \(-0.558076\pi\)
−0.181442 + 0.983402i \(0.558076\pi\)
\(458\) 5.82639 0.272249
\(459\) 0 0
\(460\) −21.0272 −0.980397
\(461\) 28.0453 1.30620 0.653099 0.757272i \(-0.273468\pi\)
0.653099 + 0.757272i \(0.273468\pi\)
\(462\) 0 0
\(463\) −2.07628 −0.0964931 −0.0482465 0.998835i \(-0.515363\pi\)
−0.0482465 + 0.998835i \(0.515363\pi\)
\(464\) −3.74090 −0.173667
\(465\) 0 0
\(466\) −17.0770 −0.791075
\(467\) −23.7477 −1.09891 −0.549457 0.835522i \(-0.685165\pi\)
−0.549457 + 0.835522i \(0.685165\pi\)
\(468\) 0 0
\(469\) −5.83572 −0.269468
\(470\) −3.54944 −0.163724
\(471\) 0 0
\(472\) 11.0704 0.509556
\(473\) 4.30125 0.197772
\(474\) 0 0
\(475\) −2.77805 −0.127466
\(476\) 10.8683 0.498147
\(477\) 0 0
\(478\) 22.0091 1.00667
\(479\) 16.7167 0.763807 0.381903 0.924202i \(-0.375269\pi\)
0.381903 + 0.924202i \(0.375269\pi\)
\(480\) 0 0
\(481\) 58.9946 2.68992
\(482\) 13.7948 0.628334
\(483\) 0 0
\(484\) −9.32447 −0.423840
\(485\) 37.5538 1.70523
\(486\) 0 0
\(487\) 6.73683 0.305275 0.152637 0.988282i \(-0.451223\pi\)
0.152637 + 0.988282i \(0.451223\pi\)
\(488\) 4.37859 0.198209
\(489\) 0 0
\(490\) 10.4775 0.473324
\(491\) −17.0566 −0.769754 −0.384877 0.922968i \(-0.625756\pi\)
−0.384877 + 0.922968i \(0.625756\pi\)
\(492\) 0 0
\(493\) −25.2018 −1.13503
\(494\) 25.8090 1.16120
\(495\) 0 0
\(496\) 2.10296 0.0944257
\(497\) −3.25027 −0.145795
\(498\) 0 0
\(499\) 35.2150 1.57644 0.788220 0.615394i \(-0.211003\pi\)
0.788220 + 0.615394i \(0.211003\pi\)
\(500\) 10.3001 0.460632
\(501\) 0 0
\(502\) 12.2127 0.545082
\(503\) 5.47723 0.244218 0.122109 0.992517i \(-0.461034\pi\)
0.122109 + 0.992517i \(0.461034\pi\)
\(504\) 0 0
\(505\) 5.17674 0.230362
\(506\) −11.4234 −0.507830
\(507\) 0 0
\(508\) −9.49940 −0.421468
\(509\) 37.9674 1.68288 0.841438 0.540354i \(-0.181710\pi\)
0.841438 + 0.540354i \(0.181710\pi\)
\(510\) 0 0
\(511\) 11.3494 0.502069
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 15.2616 0.673160
\(515\) −10.3200 −0.454755
\(516\) 0 0
\(517\) −1.92829 −0.0848062
\(518\) −15.1301 −0.664780
\(519\) 0 0
\(520\) 14.9878 0.657258
\(521\) 19.1242 0.837848 0.418924 0.908021i \(-0.362407\pi\)
0.418924 + 0.908021i \(0.362407\pi\)
\(522\) 0 0
\(523\) −43.0530 −1.88258 −0.941289 0.337602i \(-0.890384\pi\)
−0.941289 + 0.337602i \(0.890384\pi\)
\(524\) 14.3460 0.626709
\(525\) 0 0
\(526\) −29.3341 −1.27903
\(527\) 14.1673 0.617137
\(528\) 0 0
\(529\) 54.8819 2.38617
\(530\) 18.7966 0.816471
\(531\) 0 0
\(532\) −6.61916 −0.286977
\(533\) 52.9761 2.29465
\(534\) 0 0
\(535\) 32.7690 1.41673
\(536\) −3.61734 −0.156245
\(537\) 0 0
\(538\) −5.04597 −0.217547
\(539\) 5.69206 0.245174
\(540\) 0 0
\(541\) −19.2809 −0.828950 −0.414475 0.910061i \(-0.636035\pi\)
−0.414475 + 0.910061i \(0.636035\pi\)
\(542\) −17.5932 −0.755691
\(543\) 0 0
\(544\) 6.73683 0.288839
\(545\) −16.7531 −0.717624
\(546\) 0 0
\(547\) 20.1958 0.863509 0.431755 0.901991i \(-0.357895\pi\)
0.431755 + 0.901991i \(0.357895\pi\)
\(548\) 5.10296 0.217988
\(549\) 0 0
\(550\) −0.876432 −0.0373712
\(551\) 15.3488 0.653880
\(552\) 0 0
\(553\) −26.2503 −1.11628
\(554\) −21.1091 −0.896839
\(555\) 0 0
\(556\) −5.63795 −0.239102
\(557\) −15.2462 −0.646002 −0.323001 0.946399i \(-0.604692\pi\)
−0.323001 + 0.946399i \(0.604692\pi\)
\(558\) 0 0
\(559\) 20.9023 0.884073
\(560\) −3.84386 −0.162433
\(561\) 0 0
\(562\) −24.8464 −1.04808
\(563\) 12.8131 0.540008 0.270004 0.962859i \(-0.412975\pi\)
0.270004 + 0.962859i \(0.412975\pi\)
\(564\) 0 0
\(565\) 20.7581 0.873301
\(566\) 15.2459 0.640835
\(567\) 0 0
\(568\) −2.01472 −0.0845356
\(569\) −14.6814 −0.615476 −0.307738 0.951471i \(-0.599572\pi\)
−0.307738 + 0.951471i \(0.599572\pi\)
\(570\) 0 0
\(571\) 10.8880 0.455647 0.227823 0.973702i \(-0.426839\pi\)
0.227823 + 0.973702i \(0.426839\pi\)
\(572\) 8.14236 0.340449
\(573\) 0 0
\(574\) −13.5866 −0.567093
\(575\) 5.97532 0.249188
\(576\) 0 0
\(577\) 26.2349 1.09217 0.546087 0.837729i \(-0.316117\pi\)
0.546087 + 0.837729i \(0.316117\pi\)
\(578\) 28.3849 1.18066
\(579\) 0 0
\(580\) 8.91332 0.370105
\(581\) −7.91082 −0.328196
\(582\) 0 0
\(583\) 10.2116 0.422919
\(584\) 7.03507 0.291113
\(585\) 0 0
\(586\) −16.2334 −0.670594
\(587\) 10.5850 0.436891 0.218445 0.975849i \(-0.429901\pi\)
0.218445 + 0.975849i \(0.429901\pi\)
\(588\) 0 0
\(589\) −8.62836 −0.355525
\(590\) −26.3770 −1.08592
\(591\) 0 0
\(592\) −9.37859 −0.385458
\(593\) 24.4252 1.00302 0.501512 0.865151i \(-0.332777\pi\)
0.501512 + 0.865151i \(0.332777\pi\)
\(594\) 0 0
\(595\) −25.8955 −1.06161
\(596\) 5.67119 0.232301
\(597\) 0 0
\(598\) −55.5128 −2.27009
\(599\) −39.2278 −1.60281 −0.801403 0.598125i \(-0.795913\pi\)
−0.801403 + 0.598125i \(0.795913\pi\)
\(600\) 0 0
\(601\) 34.6552 1.41361 0.706807 0.707407i \(-0.250135\pi\)
0.706807 + 0.707407i \(0.250135\pi\)
\(602\) −5.36074 −0.218487
\(603\) 0 0
\(604\) 12.4343 0.505943
\(605\) 22.2171 0.903253
\(606\) 0 0
\(607\) 1.28853 0.0522998 0.0261499 0.999658i \(-0.491675\pi\)
0.0261499 + 0.999658i \(0.491675\pi\)
\(608\) −4.10296 −0.166397
\(609\) 0 0
\(610\) −10.4327 −0.422408
\(611\) −9.37070 −0.379098
\(612\) 0 0
\(613\) 31.4868 1.27174 0.635870 0.771796i \(-0.280641\pi\)
0.635870 + 0.771796i \(0.280641\pi\)
\(614\) 8.09889 0.326844
\(615\) 0 0
\(616\) −2.08824 −0.0841377
\(617\) 20.5693 0.828088 0.414044 0.910257i \(-0.364116\pi\)
0.414044 + 0.910257i \(0.364116\pi\)
\(618\) 0 0
\(619\) −0.765762 −0.0307786 −0.0153893 0.999882i \(-0.504899\pi\)
−0.0153893 + 0.999882i \(0.504899\pi\)
\(620\) −5.01064 −0.201232
\(621\) 0 0
\(622\) 23.2534 0.932378
\(623\) −29.6364 −1.18736
\(624\) 0 0
\(625\) −27.9270 −1.11708
\(626\) 7.91176 0.316217
\(627\) 0 0
\(628\) 8.23623 0.328661
\(629\) −63.1820 −2.51923
\(630\) 0 0
\(631\) −25.8176 −1.02778 −0.513892 0.857855i \(-0.671797\pi\)
−0.513892 + 0.857855i \(0.671797\pi\)
\(632\) −16.2716 −0.647248
\(633\) 0 0
\(634\) 2.05975 0.0818030
\(635\) 22.6339 0.898198
\(636\) 0 0
\(637\) 27.6611 1.09597
\(638\) 4.84231 0.191709
\(639\) 0 0
\(640\) −2.38266 −0.0941830
\(641\) −23.2933 −0.920029 −0.460015 0.887911i \(-0.652156\pi\)
−0.460015 + 0.887911i \(0.652156\pi\)
\(642\) 0 0
\(643\) −34.0373 −1.34230 −0.671150 0.741321i \(-0.734199\pi\)
−0.671150 + 0.741321i \(0.734199\pi\)
\(644\) 14.2372 0.561023
\(645\) 0 0
\(646\) −27.6409 −1.08752
\(647\) 37.4626 1.47281 0.736404 0.676542i \(-0.236522\pi\)
0.736404 + 0.676542i \(0.236522\pi\)
\(648\) 0 0
\(649\) −14.3297 −0.562492
\(650\) −4.25910 −0.167055
\(651\) 0 0
\(652\) −7.27000 −0.284715
\(653\) −36.2540 −1.41873 −0.709363 0.704843i \(-0.751017\pi\)
−0.709363 + 0.704843i \(0.751017\pi\)
\(654\) 0 0
\(655\) −34.1817 −1.33559
\(656\) −8.42180 −0.328816
\(657\) 0 0
\(658\) 2.40327 0.0936893
\(659\) 20.3589 0.793071 0.396535 0.918019i \(-0.370212\pi\)
0.396535 + 0.918019i \(0.370212\pi\)
\(660\) 0 0
\(661\) 38.1758 1.48487 0.742434 0.669919i \(-0.233671\pi\)
0.742434 + 0.669919i \(0.233671\pi\)
\(662\) 6.59629 0.256372
\(663\) 0 0
\(664\) −4.90361 −0.190297
\(665\) 15.7712 0.611582
\(666\) 0 0
\(667\) −33.0138 −1.27830
\(668\) 9.90361 0.383182
\(669\) 0 0
\(670\) 8.61890 0.332977
\(671\) −5.66774 −0.218801
\(672\) 0 0
\(673\) 20.4071 0.786635 0.393318 0.919403i \(-0.371327\pi\)
0.393318 + 0.919403i \(0.371327\pi\)
\(674\) 13.5444 0.521712
\(675\) 0 0
\(676\) 26.5685 1.02186
\(677\) 34.5293 1.32707 0.663535 0.748145i \(-0.269055\pi\)
0.663535 + 0.748145i \(0.269055\pi\)
\(678\) 0 0
\(679\) −25.4271 −0.975801
\(680\) −16.0516 −0.615551
\(681\) 0 0
\(682\) −2.72211 −0.104235
\(683\) 7.23805 0.276956 0.138478 0.990365i \(-0.455779\pi\)
0.138478 + 0.990365i \(0.455779\pi\)
\(684\) 0 0
\(685\) −12.1586 −0.464558
\(686\) −18.3870 −0.702018
\(687\) 0 0
\(688\) −3.32292 −0.126685
\(689\) 49.6239 1.89052
\(690\) 0 0
\(691\) −26.0593 −0.991343 −0.495671 0.868510i \(-0.665078\pi\)
−0.495671 + 0.868510i \(0.665078\pi\)
\(692\) −23.2252 −0.882890
\(693\) 0 0
\(694\) 11.3204 0.429717
\(695\) 13.4333 0.509555
\(696\) 0 0
\(697\) −56.7363 −2.14904
\(698\) −23.1517 −0.876304
\(699\) 0 0
\(700\) 1.09232 0.0412856
\(701\) 3.75011 0.141640 0.0708198 0.997489i \(-0.477438\pi\)
0.0708198 + 0.997489i \(0.477438\pi\)
\(702\) 0 0
\(703\) 38.4800 1.45130
\(704\) −1.29442 −0.0487853
\(705\) 0 0
\(706\) 31.6382 1.19072
\(707\) −3.50509 −0.131823
\(708\) 0 0
\(709\) −24.7368 −0.929011 −0.464506 0.885570i \(-0.653768\pi\)
−0.464506 + 0.885570i \(0.653768\pi\)
\(710\) 4.80039 0.180156
\(711\) 0 0
\(712\) −18.3704 −0.688461
\(713\) 18.5588 0.695031
\(714\) 0 0
\(715\) −19.4005 −0.725537
\(716\) 21.2499 0.794146
\(717\) 0 0
\(718\) 30.8685 1.15200
\(719\) −23.8382 −0.889015 −0.444508 0.895775i \(-0.646621\pi\)
−0.444508 + 0.895775i \(0.646621\pi\)
\(720\) 0 0
\(721\) 6.98754 0.260229
\(722\) −2.16572 −0.0805999
\(723\) 0 0
\(724\) −20.7569 −0.771425
\(725\) −2.53291 −0.0940698
\(726\) 0 0
\(727\) −21.3209 −0.790749 −0.395375 0.918520i \(-0.629385\pi\)
−0.395375 + 0.918520i \(0.629385\pi\)
\(728\) −10.1480 −0.376110
\(729\) 0 0
\(730\) −16.7622 −0.620397
\(731\) −22.3859 −0.827973
\(732\) 0 0
\(733\) 41.0982 1.51800 0.758998 0.651093i \(-0.225689\pi\)
0.758998 + 0.651093i \(0.225689\pi\)
\(734\) 18.5835 0.685928
\(735\) 0 0
\(736\) 8.82507 0.325297
\(737\) 4.68236 0.172477
\(738\) 0 0
\(739\) −15.0093 −0.552127 −0.276064 0.961139i \(-0.589030\pi\)
−0.276064 + 0.961139i \(0.589030\pi\)
\(740\) 22.3460 0.821456
\(741\) 0 0
\(742\) −12.7269 −0.467218
\(743\) −37.6777 −1.38226 −0.691131 0.722729i \(-0.742887\pi\)
−0.691131 + 0.722729i \(0.742887\pi\)
\(744\) 0 0
\(745\) −13.5125 −0.495061
\(746\) 4.22351 0.154634
\(747\) 0 0
\(748\) −8.72030 −0.318846
\(749\) −22.1874 −0.810710
\(750\) 0 0
\(751\) 0.0365249 0.00133281 0.000666406 1.00000i \(-0.499788\pi\)
0.000666406 1.00000i \(0.499788\pi\)
\(752\) 1.48970 0.0543236
\(753\) 0 0
\(754\) 23.5316 0.856970
\(755\) −29.6267 −1.07822
\(756\) 0 0
\(757\) 9.40958 0.341997 0.170999 0.985271i \(-0.445301\pi\)
0.170999 + 0.985271i \(0.445301\pi\)
\(758\) 9.04753 0.328621
\(759\) 0 0
\(760\) 9.77597 0.354612
\(761\) −4.60658 −0.166988 −0.0834941 0.996508i \(-0.526608\pi\)
−0.0834941 + 0.996508i \(0.526608\pi\)
\(762\) 0 0
\(763\) 11.3433 0.410654
\(764\) −19.2018 −0.694698
\(765\) 0 0
\(766\) −14.8525 −0.536643
\(767\) −69.6366 −2.51443
\(768\) 0 0
\(769\) 53.1560 1.91685 0.958427 0.285337i \(-0.0921055\pi\)
0.958427 + 0.285337i \(0.0921055\pi\)
\(770\) 4.97558 0.179307
\(771\) 0 0
\(772\) 10.2433 0.368665
\(773\) 38.6451 1.38997 0.694984 0.719025i \(-0.255411\pi\)
0.694984 + 0.719025i \(0.255411\pi\)
\(774\) 0 0
\(775\) 1.42388 0.0511473
\(776\) −15.7613 −0.565796
\(777\) 0 0
\(778\) 4.34446 0.155757
\(779\) 34.5543 1.23804
\(780\) 0 0
\(781\) 2.60789 0.0933177
\(782\) 59.4530 2.12604
\(783\) 0 0
\(784\) −4.39738 −0.157049
\(785\) −19.6242 −0.700417
\(786\) 0 0
\(787\) 49.8025 1.77527 0.887634 0.460550i \(-0.152348\pi\)
0.887634 + 0.460550i \(0.152348\pi\)
\(788\) −9.76507 −0.347866
\(789\) 0 0
\(790\) 38.7696 1.37936
\(791\) −14.0550 −0.499738
\(792\) 0 0
\(793\) −27.5429 −0.978075
\(794\) −36.6902 −1.30209
\(795\) 0 0
\(796\) −3.06564 −0.108659
\(797\) 36.2893 1.28543 0.642716 0.766104i \(-0.277807\pi\)
0.642716 + 0.766104i \(0.277807\pi\)
\(798\) 0 0
\(799\) 10.0358 0.355042
\(800\) 0.677084 0.0239385
\(801\) 0 0
\(802\) −7.96441 −0.281233
\(803\) −9.10634 −0.321356
\(804\) 0 0
\(805\) −33.9224 −1.19561
\(806\) −13.2283 −0.465949
\(807\) 0 0
\(808\) −2.17267 −0.0764343
\(809\) 21.1471 0.743493 0.371746 0.928334i \(-0.378759\pi\)
0.371746 + 0.928334i \(0.378759\pi\)
\(810\) 0 0
\(811\) −33.5906 −1.17953 −0.589764 0.807576i \(-0.700779\pi\)
−0.589764 + 0.807576i \(0.700779\pi\)
\(812\) −6.03507 −0.211789
\(813\) 0 0
\(814\) 12.1398 0.425501
\(815\) 17.3220 0.606762
\(816\) 0 0
\(817\) 13.6338 0.476986
\(818\) −5.89271 −0.206034
\(819\) 0 0
\(820\) 20.0663 0.700746
\(821\) 39.7957 1.38888 0.694439 0.719551i \(-0.255652\pi\)
0.694439 + 0.719551i \(0.255652\pi\)
\(822\) 0 0
\(823\) −33.5506 −1.16950 −0.584751 0.811213i \(-0.698808\pi\)
−0.584751 + 0.811213i \(0.698808\pi\)
\(824\) 4.33131 0.150888
\(825\) 0 0
\(826\) 17.8595 0.621410
\(827\) 37.2737 1.29613 0.648066 0.761584i \(-0.275578\pi\)
0.648066 + 0.761584i \(0.275578\pi\)
\(828\) 0 0
\(829\) 1.16245 0.0403734 0.0201867 0.999796i \(-0.493574\pi\)
0.0201867 + 0.999796i \(0.493574\pi\)
\(830\) 11.6837 0.405546
\(831\) 0 0
\(832\) −6.29035 −0.218079
\(833\) −29.6244 −1.02643
\(834\) 0 0
\(835\) −23.5970 −0.816607
\(836\) 5.31096 0.183683
\(837\) 0 0
\(838\) 12.3962 0.428219
\(839\) 19.5397 0.674587 0.337293 0.941400i \(-0.390489\pi\)
0.337293 + 0.941400i \(0.390489\pi\)
\(840\) 0 0
\(841\) −15.0056 −0.517436
\(842\) −27.5556 −0.949628
\(843\) 0 0
\(844\) 0.240565 0.00828059
\(845\) −63.3037 −2.17771
\(846\) 0 0
\(847\) −15.0428 −0.516878
\(848\) −7.88889 −0.270906
\(849\) 0 0
\(850\) 4.56140 0.156455
\(851\) −82.7668 −2.83721
\(852\) 0 0
\(853\) 19.5682 0.670004 0.335002 0.942217i \(-0.391263\pi\)
0.335002 + 0.942217i \(0.391263\pi\)
\(854\) 7.06382 0.241719
\(855\) 0 0
\(856\) −13.7531 −0.470072
\(857\) −25.5547 −0.872932 −0.436466 0.899721i \(-0.643770\pi\)
−0.436466 + 0.899721i \(0.643770\pi\)
\(858\) 0 0
\(859\) −17.9939 −0.613945 −0.306973 0.951718i \(-0.599316\pi\)
−0.306973 + 0.951718i \(0.599316\pi\)
\(860\) 7.91739 0.269981
\(861\) 0 0
\(862\) −19.1468 −0.652142
\(863\) 25.7633 0.876993 0.438497 0.898733i \(-0.355511\pi\)
0.438497 + 0.898733i \(0.355511\pi\)
\(864\) 0 0
\(865\) 55.3379 1.88154
\(866\) −30.9452 −1.05156
\(867\) 0 0
\(868\) 3.39263 0.115153
\(869\) 21.0622 0.714488
\(870\) 0 0
\(871\) 22.7543 0.771000
\(872\) 7.03125 0.238108
\(873\) 0 0
\(874\) −36.2089 −1.22478
\(875\) 16.6167 0.561747
\(876\) 0 0
\(877\) 14.5703 0.492004 0.246002 0.969269i \(-0.420883\pi\)
0.246002 + 0.969269i \(0.420883\pi\)
\(878\) 22.6235 0.763505
\(879\) 0 0
\(880\) 3.08417 0.103967
\(881\) −22.2400 −0.749286 −0.374643 0.927169i \(-0.622235\pi\)
−0.374643 + 0.927169i \(0.622235\pi\)
\(882\) 0 0
\(883\) −36.4675 −1.22723 −0.613615 0.789606i \(-0.710285\pi\)
−0.613615 + 0.789606i \(0.710285\pi\)
\(884\) −42.3770 −1.42529
\(885\) 0 0
\(886\) 0.982585 0.0330106
\(887\) −15.1332 −0.508122 −0.254061 0.967188i \(-0.581766\pi\)
−0.254061 + 0.967188i \(0.581766\pi\)
\(888\) 0 0
\(889\) −15.3250 −0.513985
\(890\) 43.7706 1.46719
\(891\) 0 0
\(892\) −1.00000 −0.0334825
\(893\) −6.11216 −0.204536
\(894\) 0 0
\(895\) −50.6313 −1.69242
\(896\) 1.61326 0.0538954
\(897\) 0 0
\(898\) −5.66487 −0.189039
\(899\) −7.86697 −0.262378
\(900\) 0 0
\(901\) −53.1462 −1.77056
\(902\) 10.9014 0.362975
\(903\) 0 0
\(904\) −8.71215 −0.289762
\(905\) 49.4568 1.64400
\(906\) 0 0
\(907\) 50.7958 1.68665 0.843323 0.537407i \(-0.180596\pi\)
0.843323 + 0.537407i \(0.180596\pi\)
\(908\) 14.8523 0.492889
\(909\) 0 0
\(910\) 24.1792 0.801534
\(911\) −50.6064 −1.67667 −0.838333 0.545159i \(-0.816469\pi\)
−0.838333 + 0.545159i \(0.816469\pi\)
\(912\) 0 0
\(913\) 6.34734 0.210066
\(914\) −7.75756 −0.256597
\(915\) 0 0
\(916\) 5.82639 0.192509
\(917\) 23.1439 0.764279
\(918\) 0 0
\(919\) −1.34015 −0.0442074 −0.0221037 0.999756i \(-0.507036\pi\)
−0.0221037 + 0.999756i \(0.507036\pi\)
\(920\) −21.0272 −0.693246
\(921\) 0 0
\(922\) 28.0453 0.923622
\(923\) 12.6733 0.417146
\(924\) 0 0
\(925\) −6.35010 −0.208790
\(926\) −2.07628 −0.0682309
\(927\) 0 0
\(928\) −3.74090 −0.122801
\(929\) 55.9142 1.83448 0.917242 0.398330i \(-0.130410\pi\)
0.917242 + 0.398330i \(0.130410\pi\)
\(930\) 0 0
\(931\) 18.0423 0.591312
\(932\) −17.0770 −0.559375
\(933\) 0 0
\(934\) −23.7477 −0.777049
\(935\) 20.7775 0.679498
\(936\) 0 0
\(937\) 27.2834 0.891310 0.445655 0.895205i \(-0.352971\pi\)
0.445655 + 0.895205i \(0.352971\pi\)
\(938\) −5.83572 −0.190543
\(939\) 0 0
\(940\) −3.54944 −0.115770
\(941\) −22.9411 −0.747859 −0.373929 0.927457i \(-0.621990\pi\)
−0.373929 + 0.927457i \(0.621990\pi\)
\(942\) 0 0
\(943\) −74.3230 −2.42029
\(944\) 11.0704 0.360311
\(945\) 0 0
\(946\) 4.30125 0.139846
\(947\) −42.6806 −1.38693 −0.693467 0.720488i \(-0.743918\pi\)
−0.693467 + 0.720488i \(0.743918\pi\)
\(948\) 0 0
\(949\) −44.2530 −1.43651
\(950\) −2.77805 −0.0901318
\(951\) 0 0
\(952\) 10.8683 0.352243
\(953\) 26.7188 0.865507 0.432753 0.901512i \(-0.357542\pi\)
0.432753 + 0.901512i \(0.357542\pi\)
\(954\) 0 0
\(955\) 45.7515 1.48048
\(956\) 22.0091 0.711824
\(957\) 0 0
\(958\) 16.7167 0.540093
\(959\) 8.23242 0.265839
\(960\) 0 0
\(961\) −26.5776 −0.857341
\(962\) 58.9946 1.90206
\(963\) 0 0
\(964\) 13.7948 0.444299
\(965\) −24.4064 −0.785669
\(966\) 0 0
\(967\) −55.9573 −1.79946 −0.899732 0.436442i \(-0.856238\pi\)
−0.899732 + 0.436442i \(0.856238\pi\)
\(968\) −9.32447 −0.299700
\(969\) 0 0
\(970\) 37.5538 1.20578
\(971\) 5.50174 0.176559 0.0882796 0.996096i \(-0.471863\pi\)
0.0882796 + 0.996096i \(0.471863\pi\)
\(972\) 0 0
\(973\) −9.09549 −0.291588
\(974\) 6.73683 0.215862
\(975\) 0 0
\(976\) 4.37859 0.140155
\(977\) 15.0995 0.483076 0.241538 0.970391i \(-0.422348\pi\)
0.241538 + 0.970391i \(0.422348\pi\)
\(978\) 0 0
\(979\) 23.7791 0.759983
\(980\) 10.4775 0.334691
\(981\) 0 0
\(982\) −17.0566 −0.544298
\(983\) −48.5862 −1.54966 −0.774830 0.632170i \(-0.782164\pi\)
−0.774830 + 0.632170i \(0.782164\pi\)
\(984\) 0 0
\(985\) 23.2669 0.741344
\(986\) −25.2018 −0.802590
\(987\) 0 0
\(988\) 25.8090 0.821095
\(989\) −29.3250 −0.932480
\(990\) 0 0
\(991\) 33.9605 1.07879 0.539395 0.842053i \(-0.318653\pi\)
0.539395 + 0.842053i \(0.318653\pi\)
\(992\) 2.10296 0.0667690
\(993\) 0 0
\(994\) −3.25027 −0.103092
\(995\) 7.30439 0.231565
\(996\) 0 0
\(997\) 8.69148 0.275262 0.137631 0.990484i \(-0.456051\pi\)
0.137631 + 0.990484i \(0.456051\pi\)
\(998\) 35.2150 1.11471
\(999\) 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 \(a_p\))