Properties

Label 8046.2.a.l.1.9
Level 8046
Weight 2
Character 8046.1
Self dual Yes
Analytic conductor 64.248
Analytic rank 0
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8046 = 2 \cdot 3^{3} \cdot 149 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8046.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2476334663\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(1.53008\)
Character \(\chi\) = 8046.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+1.53008 q^{5}\) \(+5.04291 q^{7}\) \(-1.00000 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+1.53008 q^{5}\) \(+5.04291 q^{7}\) \(-1.00000 q^{8}\) \(-1.53008 q^{10}\) \(+2.19639 q^{11}\) \(-3.71640 q^{13}\) \(-5.04291 q^{14}\) \(+1.00000 q^{16}\) \(+2.18832 q^{17}\) \(+0.428199 q^{19}\) \(+1.53008 q^{20}\) \(-2.19639 q^{22}\) \(+2.68792 q^{23}\) \(-2.65886 q^{25}\) \(+3.71640 q^{26}\) \(+5.04291 q^{28}\) \(+1.03044 q^{29}\) \(+0.812378 q^{31}\) \(-1.00000 q^{32}\) \(-2.18832 q^{34}\) \(+7.71606 q^{35}\) \(-2.71746 q^{37}\) \(-0.428199 q^{38}\) \(-1.53008 q^{40}\) \(+3.18736 q^{41}\) \(-10.6001 q^{43}\) \(+2.19639 q^{44}\) \(-2.68792 q^{46}\) \(+3.13589 q^{47}\) \(+18.4310 q^{49}\) \(+2.65886 q^{50}\) \(-3.71640 q^{52}\) \(-7.68548 q^{53}\) \(+3.36065 q^{55}\) \(-5.04291 q^{56}\) \(-1.03044 q^{58}\) \(+11.9319 q^{59}\) \(+0.845814 q^{61}\) \(-0.812378 q^{62}\) \(+1.00000 q^{64}\) \(-5.68639 q^{65}\) \(-4.18466 q^{67}\) \(+2.18832 q^{68}\) \(-7.71606 q^{70}\) \(+9.74208 q^{71}\) \(-14.1375 q^{73}\) \(+2.71746 q^{74}\) \(+0.428199 q^{76}\) \(+11.0762 q^{77}\) \(+14.8966 q^{79}\) \(+1.53008 q^{80}\) \(-3.18736 q^{82}\) \(-1.50002 q^{83}\) \(+3.34830 q^{85}\) \(+10.6001 q^{86}\) \(-2.19639 q^{88}\) \(+6.94999 q^{89}\) \(-18.7415 q^{91}\) \(+2.68792 q^{92}\) \(-3.13589 q^{94}\) \(+0.655179 q^{95}\) \(-15.0130 q^{97}\) \(-18.4310 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 12q^{2} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 12q^{2} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut -\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 12q^{16} \) \(\mathstrut +\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 10q^{19} \) \(\mathstrut +\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 10q^{22} \) \(\mathstrut +\mathstrut 15q^{23} \) \(\mathstrut +\mathstrut 7q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 6q^{31} \) \(\mathstrut -\mathstrut 12q^{32} \) \(\mathstrut -\mathstrut 6q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 13q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut -\mathstrut 5q^{40} \) \(\mathstrut +\mathstrut 20q^{41} \) \(\mathstrut -\mathstrut 11q^{43} \) \(\mathstrut +\mathstrut 10q^{44} \) \(\mathstrut -\mathstrut 15q^{46} \) \(\mathstrut +\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 7q^{50} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 4q^{53} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut -\mathstrut 33q^{58} \) \(\mathstrut +\mathstrut 10q^{59} \) \(\mathstrut -\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 6q^{62} \) \(\mathstrut +\mathstrut 12q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 19q^{67} \) \(\mathstrut +\mathstrut 6q^{68} \) \(\mathstrut -\mathstrut 16q^{70} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 2q^{73} \) \(\mathstrut +\mathstrut 13q^{74} \) \(\mathstrut -\mathstrut 10q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut -\mathstrut 15q^{79} \) \(\mathstrut +\mathstrut 5q^{80} \) \(\mathstrut -\mathstrut 20q^{82} \) \(\mathstrut +\mathstrut 18q^{83} \) \(\mathstrut -\mathstrut 25q^{85} \) \(\mathstrut +\mathstrut 11q^{86} \) \(\mathstrut -\mathstrut 10q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut -\mathstrut 3q^{91} \) \(\mathstrut +\mathstrut 15q^{92} \) \(\mathstrut -\mathstrut 15q^{94} \) \(\mathstrut -\mathstrut 3q^{95} \) \(\mathstrut -\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 1.53008 0.684272 0.342136 0.939650i \(-0.388850\pi\)
0.342136 + 0.939650i \(0.388850\pi\)
\(6\) 0 0
\(7\) 5.04291 1.90604 0.953021 0.302905i \(-0.0979563\pi\)
0.953021 + 0.302905i \(0.0979563\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.53008 −0.483854
\(11\) 2.19639 0.662237 0.331118 0.943589i \(-0.392574\pi\)
0.331118 + 0.943589i \(0.392574\pi\)
\(12\) 0 0
\(13\) −3.71640 −1.03074 −0.515372 0.856966i \(-0.672346\pi\)
−0.515372 + 0.856966i \(0.672346\pi\)
\(14\) −5.04291 −1.34778
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 2.18832 0.530745 0.265372 0.964146i \(-0.414505\pi\)
0.265372 + 0.964146i \(0.414505\pi\)
\(18\) 0 0
\(19\) 0.428199 0.0982357 0.0491178 0.998793i \(-0.484359\pi\)
0.0491178 + 0.998793i \(0.484359\pi\)
\(20\) 1.53008 0.342136
\(21\) 0 0
\(22\) −2.19639 −0.468272
\(23\) 2.68792 0.560471 0.280235 0.959931i \(-0.409587\pi\)
0.280235 + 0.959931i \(0.409587\pi\)
\(24\) 0 0
\(25\) −2.65886 −0.531772
\(26\) 3.71640 0.728846
\(27\) 0 0
\(28\) 5.04291 0.953021
\(29\) 1.03044 0.191348 0.0956738 0.995413i \(-0.469499\pi\)
0.0956738 + 0.995413i \(0.469499\pi\)
\(30\) 0 0
\(31\) 0.812378 0.145907 0.0729537 0.997335i \(-0.476757\pi\)
0.0729537 + 0.997335i \(0.476757\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −2.18832 −0.375293
\(35\) 7.71606 1.30425
\(36\) 0 0
\(37\) −2.71746 −0.446747 −0.223374 0.974733i \(-0.571707\pi\)
−0.223374 + 0.974733i \(0.571707\pi\)
\(38\) −0.428199 −0.0694631
\(39\) 0 0
\(40\) −1.53008 −0.241927
\(41\) 3.18736 0.497782 0.248891 0.968532i \(-0.419934\pi\)
0.248891 + 0.968532i \(0.419934\pi\)
\(42\) 0 0
\(43\) −10.6001 −1.61649 −0.808247 0.588843i \(-0.799583\pi\)
−0.808247 + 0.588843i \(0.799583\pi\)
\(44\) 2.19639 0.331118
\(45\) 0 0
\(46\) −2.68792 −0.396313
\(47\) 3.13589 0.457416 0.228708 0.973495i \(-0.426550\pi\)
0.228708 + 0.973495i \(0.426550\pi\)
\(48\) 0 0
\(49\) 18.4310 2.63300
\(50\) 2.65886 0.376019
\(51\) 0 0
\(52\) −3.71640 −0.515372
\(53\) −7.68548 −1.05568 −0.527841 0.849343i \(-0.676998\pi\)
−0.527841 + 0.849343i \(0.676998\pi\)
\(54\) 0 0
\(55\) 3.36065 0.453150
\(56\) −5.04291 −0.673888
\(57\) 0 0
\(58\) −1.03044 −0.135303
\(59\) 11.9319 1.55340 0.776701 0.629870i \(-0.216892\pi\)
0.776701 + 0.629870i \(0.216892\pi\)
\(60\) 0 0
\(61\) 0.845814 0.108295 0.0541477 0.998533i \(-0.482756\pi\)
0.0541477 + 0.998533i \(0.482756\pi\)
\(62\) −0.812378 −0.103172
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −5.68639 −0.705310
\(66\) 0 0
\(67\) −4.18466 −0.511237 −0.255619 0.966778i \(-0.582279\pi\)
−0.255619 + 0.966778i \(0.582279\pi\)
\(68\) 2.18832 0.265372
\(69\) 0 0
\(70\) −7.71606 −0.922245
\(71\) 9.74208 1.15617 0.578086 0.815976i \(-0.303800\pi\)
0.578086 + 0.815976i \(0.303800\pi\)
\(72\) 0 0
\(73\) −14.1375 −1.65467 −0.827333 0.561712i \(-0.810143\pi\)
−0.827333 + 0.561712i \(0.810143\pi\)
\(74\) 2.71746 0.315898
\(75\) 0 0
\(76\) 0.428199 0.0491178
\(77\) 11.0762 1.26225
\(78\) 0 0
\(79\) 14.8966 1.67600 0.838000 0.545670i \(-0.183725\pi\)
0.838000 + 0.545670i \(0.183725\pi\)
\(80\) 1.53008 0.171068
\(81\) 0 0
\(82\) −3.18736 −0.351985
\(83\) −1.50002 −0.164649 −0.0823245 0.996606i \(-0.526234\pi\)
−0.0823245 + 0.996606i \(0.526234\pi\)
\(84\) 0 0
\(85\) 3.34830 0.363174
\(86\) 10.6001 1.14303
\(87\) 0 0
\(88\) −2.19639 −0.234136
\(89\) 6.94999 0.736697 0.368348 0.929688i \(-0.379923\pi\)
0.368348 + 0.929688i \(0.379923\pi\)
\(90\) 0 0
\(91\) −18.7415 −1.96464
\(92\) 2.68792 0.280235
\(93\) 0 0
\(94\) −3.13589 −0.323442
\(95\) 0.655179 0.0672199
\(96\) 0 0
\(97\) −15.0130 −1.52434 −0.762168 0.647379i \(-0.775865\pi\)
−0.762168 + 0.647379i \(0.775865\pi\)
\(98\) −18.4310 −1.86181
\(99\) 0 0
\(100\) −2.65886 −0.265886
\(101\) 18.5580 1.84659 0.923293 0.384096i \(-0.125487\pi\)
0.923293 + 0.384096i \(0.125487\pi\)
\(102\) 0 0
\(103\) 17.8293 1.75677 0.878386 0.477952i \(-0.158621\pi\)
0.878386 + 0.477952i \(0.158621\pi\)
\(104\) 3.71640 0.364423
\(105\) 0 0
\(106\) 7.68548 0.746480
\(107\) 16.8615 1.63007 0.815033 0.579414i \(-0.196719\pi\)
0.815033 + 0.579414i \(0.196719\pi\)
\(108\) 0 0
\(109\) 13.4120 1.28464 0.642320 0.766436i \(-0.277972\pi\)
0.642320 + 0.766436i \(0.277972\pi\)
\(110\) −3.36065 −0.320426
\(111\) 0 0
\(112\) 5.04291 0.476510
\(113\) 4.50527 0.423820 0.211910 0.977289i \(-0.432032\pi\)
0.211910 + 0.977289i \(0.432032\pi\)
\(114\) 0 0
\(115\) 4.11274 0.383515
\(116\) 1.03044 0.0956738
\(117\) 0 0
\(118\) −11.9319 −1.09842
\(119\) 11.0355 1.01162
\(120\) 0 0
\(121\) −6.17587 −0.561443
\(122\) −0.845814 −0.0765764
\(123\) 0 0
\(124\) 0.812378 0.0729537
\(125\) −11.7187 −1.04815
\(126\) 0 0
\(127\) 11.1412 0.988619 0.494309 0.869286i \(-0.335421\pi\)
0.494309 + 0.869286i \(0.335421\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 5.68639 0.498729
\(131\) −14.1460 −1.23594 −0.617972 0.786200i \(-0.712046\pi\)
−0.617972 + 0.786200i \(0.712046\pi\)
\(132\) 0 0
\(133\) 2.15937 0.187241
\(134\) 4.18466 0.361499
\(135\) 0 0
\(136\) −2.18832 −0.187647
\(137\) −3.26025 −0.278542 −0.139271 0.990254i \(-0.544476\pi\)
−0.139271 + 0.990254i \(0.544476\pi\)
\(138\) 0 0
\(139\) 18.1889 1.54276 0.771381 0.636374i \(-0.219566\pi\)
0.771381 + 0.636374i \(0.219566\pi\)
\(140\) 7.71606 0.652126
\(141\) 0 0
\(142\) −9.74208 −0.817537
\(143\) −8.16267 −0.682597
\(144\) 0 0
\(145\) 1.57665 0.130934
\(146\) 14.1375 1.17003
\(147\) 0 0
\(148\) −2.71746 −0.223374
\(149\) 1.00000 0.0819232
\(150\) 0 0
\(151\) 13.8103 1.12386 0.561932 0.827183i \(-0.310058\pi\)
0.561932 + 0.827183i \(0.310058\pi\)
\(152\) −0.428199 −0.0347315
\(153\) 0 0
\(154\) −11.0762 −0.892546
\(155\) 1.24300 0.0998403
\(156\) 0 0
\(157\) 15.5334 1.23970 0.619849 0.784721i \(-0.287194\pi\)
0.619849 + 0.784721i \(0.287194\pi\)
\(158\) −14.8966 −1.18511
\(159\) 0 0
\(160\) −1.53008 −0.120963
\(161\) 13.5550 1.06828
\(162\) 0 0
\(163\) −15.8819 −1.24396 −0.621982 0.783031i \(-0.713672\pi\)
−0.621982 + 0.783031i \(0.713672\pi\)
\(164\) 3.18736 0.248891
\(165\) 0 0
\(166\) 1.50002 0.116424
\(167\) −21.1258 −1.63476 −0.817381 0.576097i \(-0.804575\pi\)
−0.817381 + 0.576097i \(0.804575\pi\)
\(168\) 0 0
\(169\) 0.811642 0.0624340
\(170\) −3.34830 −0.256803
\(171\) 0 0
\(172\) −10.6001 −0.808247
\(173\) −12.1765 −0.925765 −0.462882 0.886420i \(-0.653185\pi\)
−0.462882 + 0.886420i \(0.653185\pi\)
\(174\) 0 0
\(175\) −13.4084 −1.01358
\(176\) 2.19639 0.165559
\(177\) 0 0
\(178\) −6.94999 −0.520923
\(179\) 22.3807 1.67281 0.836406 0.548110i \(-0.184652\pi\)
0.836406 + 0.548110i \(0.184652\pi\)
\(180\) 0 0
\(181\) −16.5525 −1.23034 −0.615170 0.788395i \(-0.710913\pi\)
−0.615170 + 0.788395i \(0.710913\pi\)
\(182\) 18.7415 1.38921
\(183\) 0 0
\(184\) −2.68792 −0.198156
\(185\) −4.15793 −0.305697
\(186\) 0 0
\(187\) 4.80640 0.351479
\(188\) 3.13589 0.228708
\(189\) 0 0
\(190\) −0.655179 −0.0475317
\(191\) 20.5627 1.48787 0.743933 0.668254i \(-0.232958\pi\)
0.743933 + 0.668254i \(0.232958\pi\)
\(192\) 0 0
\(193\) 16.6431 1.19800 0.598998 0.800751i \(-0.295566\pi\)
0.598998 + 0.800751i \(0.295566\pi\)
\(194\) 15.0130 1.07787
\(195\) 0 0
\(196\) 18.4310 1.31650
\(197\) 21.4204 1.52614 0.763069 0.646317i \(-0.223691\pi\)
0.763069 + 0.646317i \(0.223691\pi\)
\(198\) 0 0
\(199\) 6.13385 0.434817 0.217409 0.976081i \(-0.430240\pi\)
0.217409 + 0.976081i \(0.430240\pi\)
\(200\) 2.65886 0.188010
\(201\) 0 0
\(202\) −18.5580 −1.30573
\(203\) 5.19641 0.364717
\(204\) 0 0
\(205\) 4.87691 0.340618
\(206\) −17.8293 −1.24223
\(207\) 0 0
\(208\) −3.71640 −0.257686
\(209\) 0.940493 0.0650553
\(210\) 0 0
\(211\) −1.92401 −0.132454 −0.0662272 0.997805i \(-0.521096\pi\)
−0.0662272 + 0.997805i \(0.521096\pi\)
\(212\) −7.68548 −0.527841
\(213\) 0 0
\(214\) −16.8615 −1.15263
\(215\) −16.2189 −1.10612
\(216\) 0 0
\(217\) 4.09675 0.278105
\(218\) −13.4120 −0.908378
\(219\) 0 0
\(220\) 3.36065 0.226575
\(221\) −8.13267 −0.547062
\(222\) 0 0
\(223\) 11.4543 0.767040 0.383520 0.923533i \(-0.374712\pi\)
0.383520 + 0.923533i \(0.374712\pi\)
\(224\) −5.04291 −0.336944
\(225\) 0 0
\(226\) −4.50527 −0.299686
\(227\) −7.54669 −0.500891 −0.250446 0.968131i \(-0.580577\pi\)
−0.250446 + 0.968131i \(0.580577\pi\)
\(228\) 0 0
\(229\) −27.8224 −1.83855 −0.919277 0.393610i \(-0.871226\pi\)
−0.919277 + 0.393610i \(0.871226\pi\)
\(230\) −4.11274 −0.271186
\(231\) 0 0
\(232\) −1.03044 −0.0676516
\(233\) 26.3727 1.72773 0.863867 0.503720i \(-0.168036\pi\)
0.863867 + 0.503720i \(0.168036\pi\)
\(234\) 0 0
\(235\) 4.79816 0.312997
\(236\) 11.9319 0.776701
\(237\) 0 0
\(238\) −11.0355 −0.715325
\(239\) −19.1553 −1.23905 −0.619527 0.784975i \(-0.712676\pi\)
−0.619527 + 0.784975i \(0.712676\pi\)
\(240\) 0 0
\(241\) −18.2493 −1.17554 −0.587772 0.809027i \(-0.699995\pi\)
−0.587772 + 0.809027i \(0.699995\pi\)
\(242\) 6.17587 0.397000
\(243\) 0 0
\(244\) 0.845814 0.0541477
\(245\) 28.2008 1.80169
\(246\) 0 0
\(247\) −1.59136 −0.101256
\(248\) −0.812378 −0.0515860
\(249\) 0 0
\(250\) 11.7187 0.741153
\(251\) −3.34068 −0.210862 −0.105431 0.994427i \(-0.533622\pi\)
−0.105431 + 0.994427i \(0.533622\pi\)
\(252\) 0 0
\(253\) 5.90373 0.371164
\(254\) −11.1412 −0.699059
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −1.84462 −0.115064 −0.0575320 0.998344i \(-0.518323\pi\)
−0.0575320 + 0.998344i \(0.518323\pi\)
\(258\) 0 0
\(259\) −13.7039 −0.851519
\(260\) −5.68639 −0.352655
\(261\) 0 0
\(262\) 14.1460 0.873945
\(263\) 0.236331 0.0145728 0.00728638 0.999973i \(-0.497681\pi\)
0.00728638 + 0.999973i \(0.497681\pi\)
\(264\) 0 0
\(265\) −11.7594 −0.722374
\(266\) −2.15937 −0.132400
\(267\) 0 0
\(268\) −4.18466 −0.255619
\(269\) 0.492739 0.0300428 0.0150214 0.999887i \(-0.495218\pi\)
0.0150214 + 0.999887i \(0.495218\pi\)
\(270\) 0 0
\(271\) 7.28712 0.442661 0.221330 0.975199i \(-0.428960\pi\)
0.221330 + 0.975199i \(0.428960\pi\)
\(272\) 2.18832 0.132686
\(273\) 0 0
\(274\) 3.26025 0.196959
\(275\) −5.83989 −0.352159
\(276\) 0 0
\(277\) −26.1050 −1.56850 −0.784248 0.620447i \(-0.786951\pi\)
−0.784248 + 0.620447i \(0.786951\pi\)
\(278\) −18.1889 −1.09090
\(279\) 0 0
\(280\) −7.71606 −0.461123
\(281\) −26.6711 −1.59106 −0.795531 0.605913i \(-0.792808\pi\)
−0.795531 + 0.605913i \(0.792808\pi\)
\(282\) 0 0
\(283\) 17.0033 1.01074 0.505371 0.862902i \(-0.331356\pi\)
0.505371 + 0.862902i \(0.331356\pi\)
\(284\) 9.74208 0.578086
\(285\) 0 0
\(286\) 8.16267 0.482669
\(287\) 16.0736 0.948793
\(288\) 0 0
\(289\) −12.2113 −0.718310
\(290\) −1.57665 −0.0925842
\(291\) 0 0
\(292\) −14.1375 −0.827333
\(293\) −24.2864 −1.41882 −0.709412 0.704794i \(-0.751040\pi\)
−0.709412 + 0.704794i \(0.751040\pi\)
\(294\) 0 0
\(295\) 18.2568 1.06295
\(296\) 2.71746 0.157949
\(297\) 0 0
\(298\) −1.00000 −0.0579284
\(299\) −9.98941 −0.577702
\(300\) 0 0
\(301\) −53.4552 −3.08111
\(302\) −13.8103 −0.794692
\(303\) 0 0
\(304\) 0.428199 0.0245589
\(305\) 1.29416 0.0741035
\(306\) 0 0
\(307\) 1.13742 0.0649161 0.0324581 0.999473i \(-0.489666\pi\)
0.0324581 + 0.999473i \(0.489666\pi\)
\(308\) 11.0762 0.631125
\(309\) 0 0
\(310\) −1.24300 −0.0705978
\(311\) −0.447203 −0.0253586 −0.0126793 0.999920i \(-0.504036\pi\)
−0.0126793 + 0.999920i \(0.504036\pi\)
\(312\) 0 0
\(313\) 12.9333 0.731031 0.365516 0.930805i \(-0.380893\pi\)
0.365516 + 0.930805i \(0.380893\pi\)
\(314\) −15.5334 −0.876599
\(315\) 0 0
\(316\) 14.8966 0.838000
\(317\) 4.60730 0.258772 0.129386 0.991594i \(-0.458699\pi\)
0.129386 + 0.991594i \(0.458699\pi\)
\(318\) 0 0
\(319\) 2.26324 0.126717
\(320\) 1.53008 0.0855340
\(321\) 0 0
\(322\) −13.5550 −0.755389
\(323\) 0.937036 0.0521381
\(324\) 0 0
\(325\) 9.88138 0.548121
\(326\) 15.8819 0.879616
\(327\) 0 0
\(328\) −3.18736 −0.175992
\(329\) 15.8140 0.871854
\(330\) 0 0
\(331\) −9.54771 −0.524789 −0.262395 0.964961i \(-0.584512\pi\)
−0.262395 + 0.964961i \(0.584512\pi\)
\(332\) −1.50002 −0.0823245
\(333\) 0 0
\(334\) 21.1258 1.15595
\(335\) −6.40286 −0.349825
\(336\) 0 0
\(337\) 1.90607 0.103830 0.0519151 0.998651i \(-0.483467\pi\)
0.0519151 + 0.998651i \(0.483467\pi\)
\(338\) −0.811642 −0.0441475
\(339\) 0 0
\(340\) 3.34830 0.181587
\(341\) 1.78430 0.0966252
\(342\) 0 0
\(343\) 57.6454 3.11256
\(344\) 10.6001 0.571517
\(345\) 0 0
\(346\) 12.1765 0.654615
\(347\) −31.8251 −1.70846 −0.854230 0.519896i \(-0.825971\pi\)
−0.854230 + 0.519896i \(0.825971\pi\)
\(348\) 0 0
\(349\) −14.2839 −0.764602 −0.382301 0.924038i \(-0.624868\pi\)
−0.382301 + 0.924038i \(0.624868\pi\)
\(350\) 13.4084 0.716708
\(351\) 0 0
\(352\) −2.19639 −0.117068
\(353\) −4.35738 −0.231920 −0.115960 0.993254i \(-0.536994\pi\)
−0.115960 + 0.993254i \(0.536994\pi\)
\(354\) 0 0
\(355\) 14.9062 0.791136
\(356\) 6.94999 0.368348
\(357\) 0 0
\(358\) −22.3807 −1.18286
\(359\) −17.6460 −0.931319 −0.465659 0.884964i \(-0.654183\pi\)
−0.465659 + 0.884964i \(0.654183\pi\)
\(360\) 0 0
\(361\) −18.8166 −0.990350
\(362\) 16.5525 0.869981
\(363\) 0 0
\(364\) −18.7415 −0.982321
\(365\) −21.6314 −1.13224
\(366\) 0 0
\(367\) −12.9361 −0.675257 −0.337628 0.941280i \(-0.609625\pi\)
−0.337628 + 0.941280i \(0.609625\pi\)
\(368\) 2.68792 0.140118
\(369\) 0 0
\(370\) 4.15793 0.216160
\(371\) −38.7572 −2.01217
\(372\) 0 0
\(373\) −8.95023 −0.463425 −0.231713 0.972784i \(-0.574433\pi\)
−0.231713 + 0.972784i \(0.574433\pi\)
\(374\) −4.80640 −0.248533
\(375\) 0 0
\(376\) −3.13589 −0.161721
\(377\) −3.82952 −0.197230
\(378\) 0 0
\(379\) −25.4453 −1.30704 −0.653520 0.756910i \(-0.726708\pi\)
−0.653520 + 0.756910i \(0.726708\pi\)
\(380\) 0.655179 0.0336100
\(381\) 0 0
\(382\) −20.5627 −1.05208
\(383\) 20.2374 1.03408 0.517042 0.855960i \(-0.327033\pi\)
0.517042 + 0.855960i \(0.327033\pi\)
\(384\) 0 0
\(385\) 16.9475 0.863723
\(386\) −16.6431 −0.847111
\(387\) 0 0
\(388\) −15.0130 −0.762168
\(389\) 15.5789 0.789880 0.394940 0.918707i \(-0.370765\pi\)
0.394940 + 0.918707i \(0.370765\pi\)
\(390\) 0 0
\(391\) 5.88203 0.297467
\(392\) −18.4310 −0.930904
\(393\) 0 0
\(394\) −21.4204 −1.07914
\(395\) 22.7930 1.14684
\(396\) 0 0
\(397\) −21.5619 −1.08216 −0.541081 0.840970i \(-0.681985\pi\)
−0.541081 + 0.840970i \(0.681985\pi\)
\(398\) −6.13385 −0.307462
\(399\) 0 0
\(400\) −2.65886 −0.132943
\(401\) 20.2428 1.01088 0.505439 0.862862i \(-0.331330\pi\)
0.505439 + 0.862862i \(0.331330\pi\)
\(402\) 0 0
\(403\) −3.01912 −0.150393
\(404\) 18.5580 0.923293
\(405\) 0 0
\(406\) −5.19641 −0.257894
\(407\) −5.96860 −0.295852
\(408\) 0 0
\(409\) 7.78181 0.384786 0.192393 0.981318i \(-0.438375\pi\)
0.192393 + 0.981318i \(0.438375\pi\)
\(410\) −4.87691 −0.240854
\(411\) 0 0
\(412\) 17.8293 0.878386
\(413\) 60.1715 2.96085
\(414\) 0 0
\(415\) −2.29515 −0.112665
\(416\) 3.71640 0.182212
\(417\) 0 0
\(418\) −0.940493 −0.0460010
\(419\) 29.8913 1.46029 0.730143 0.683295i \(-0.239454\pi\)
0.730143 + 0.683295i \(0.239454\pi\)
\(420\) 0 0
\(421\) 3.47305 0.169266 0.0846331 0.996412i \(-0.473028\pi\)
0.0846331 + 0.996412i \(0.473028\pi\)
\(422\) 1.92401 0.0936594
\(423\) 0 0
\(424\) 7.68548 0.373240
\(425\) −5.81843 −0.282235
\(426\) 0 0
\(427\) 4.26536 0.206415
\(428\) 16.8615 0.815033
\(429\) 0 0
\(430\) 16.2189 0.782146
\(431\) 26.4524 1.27416 0.637082 0.770796i \(-0.280141\pi\)
0.637082 + 0.770796i \(0.280141\pi\)
\(432\) 0 0
\(433\) 9.06980 0.435867 0.217933 0.975964i \(-0.430068\pi\)
0.217933 + 0.975964i \(0.430068\pi\)
\(434\) −4.09675 −0.196650
\(435\) 0 0
\(436\) 13.4120 0.642320
\(437\) 1.15097 0.0550582
\(438\) 0 0
\(439\) 14.3151 0.683224 0.341612 0.939841i \(-0.389027\pi\)
0.341612 + 0.939841i \(0.389027\pi\)
\(440\) −3.36065 −0.160213
\(441\) 0 0
\(442\) 8.13267 0.386832
\(443\) 18.3436 0.871529 0.435764 0.900061i \(-0.356478\pi\)
0.435764 + 0.900061i \(0.356478\pi\)
\(444\) 0 0
\(445\) 10.6340 0.504101
\(446\) −11.4543 −0.542379
\(447\) 0 0
\(448\) 5.04291 0.238255
\(449\) 5.91128 0.278971 0.139485 0.990224i \(-0.455455\pi\)
0.139485 + 0.990224i \(0.455455\pi\)
\(450\) 0 0
\(451\) 7.00068 0.329649
\(452\) 4.50527 0.211910
\(453\) 0 0
\(454\) 7.54669 0.354184
\(455\) −28.6760 −1.34435
\(456\) 0 0
\(457\) −4.51467 −0.211187 −0.105594 0.994409i \(-0.533674\pi\)
−0.105594 + 0.994409i \(0.533674\pi\)
\(458\) 27.8224 1.30005
\(459\) 0 0
\(460\) 4.11274 0.191757
\(461\) −17.7809 −0.828140 −0.414070 0.910245i \(-0.635893\pi\)
−0.414070 + 0.910245i \(0.635893\pi\)
\(462\) 0 0
\(463\) −34.2340 −1.59099 −0.795495 0.605960i \(-0.792789\pi\)
−0.795495 + 0.605960i \(0.792789\pi\)
\(464\) 1.03044 0.0478369
\(465\) 0 0
\(466\) −26.3727 −1.22169
\(467\) −2.79934 −0.129538 −0.0647689 0.997900i \(-0.520631\pi\)
−0.0647689 + 0.997900i \(0.520631\pi\)
\(468\) 0 0
\(469\) −21.1029 −0.974440
\(470\) −4.79816 −0.221322
\(471\) 0 0
\(472\) −11.9319 −0.549210
\(473\) −23.2819 −1.07050
\(474\) 0 0
\(475\) −1.13852 −0.0522389
\(476\) 11.0355 0.505811
\(477\) 0 0
\(478\) 19.1553 0.876144
\(479\) −3.83579 −0.175262 −0.0876308 0.996153i \(-0.527930\pi\)
−0.0876308 + 0.996153i \(0.527930\pi\)
\(480\) 0 0
\(481\) 10.0992 0.460482
\(482\) 18.2493 0.831235
\(483\) 0 0
\(484\) −6.17587 −0.280721
\(485\) −22.9710 −1.04306
\(486\) 0 0
\(487\) 26.3377 1.19347 0.596737 0.802437i \(-0.296464\pi\)
0.596737 + 0.802437i \(0.296464\pi\)
\(488\) −0.845814 −0.0382882
\(489\) 0 0
\(490\) −28.2008 −1.27398
\(491\) −22.8728 −1.03224 −0.516119 0.856517i \(-0.672624\pi\)
−0.516119 + 0.856517i \(0.672624\pi\)
\(492\) 0 0
\(493\) 2.25493 0.101557
\(494\) 1.59136 0.0715987
\(495\) 0 0
\(496\) 0.812378 0.0364768
\(497\) 49.1284 2.20371
\(498\) 0 0
\(499\) 3.17734 0.142237 0.0711187 0.997468i \(-0.477343\pi\)
0.0711187 + 0.997468i \(0.477343\pi\)
\(500\) −11.7187 −0.524074
\(501\) 0 0
\(502\) 3.34068 0.149102
\(503\) 31.6477 1.41110 0.705550 0.708660i \(-0.250700\pi\)
0.705550 + 0.708660i \(0.250700\pi\)
\(504\) 0 0
\(505\) 28.3951 1.26357
\(506\) −5.90373 −0.262453
\(507\) 0 0
\(508\) 11.1412 0.494309
\(509\) 23.9531 1.06170 0.530851 0.847465i \(-0.321872\pi\)
0.530851 + 0.847465i \(0.321872\pi\)
\(510\) 0 0
\(511\) −71.2940 −3.15386
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 1.84462 0.0813625
\(515\) 27.2802 1.20211
\(516\) 0 0
\(517\) 6.88763 0.302918
\(518\) 13.7039 0.602115
\(519\) 0 0
\(520\) 5.68639 0.249365
\(521\) −4.11740 −0.180387 −0.0901934 0.995924i \(-0.528749\pi\)
−0.0901934 + 0.995924i \(0.528749\pi\)
\(522\) 0 0
\(523\) 16.4484 0.719238 0.359619 0.933099i \(-0.382907\pi\)
0.359619 + 0.933099i \(0.382907\pi\)
\(524\) −14.1460 −0.617972
\(525\) 0 0
\(526\) −0.236331 −0.0103045
\(527\) 1.77774 0.0774396
\(528\) 0 0
\(529\) −15.7751 −0.685872
\(530\) 11.7594 0.510796
\(531\) 0 0
\(532\) 2.15937 0.0936206
\(533\) −11.8455 −0.513086
\(534\) 0 0
\(535\) 25.7995 1.11541
\(536\) 4.18466 0.180750
\(537\) 0 0
\(538\) −0.492739 −0.0212435
\(539\) 40.4816 1.74367
\(540\) 0 0
\(541\) 19.6792 0.846076 0.423038 0.906112i \(-0.360964\pi\)
0.423038 + 0.906112i \(0.360964\pi\)
\(542\) −7.28712 −0.313009
\(543\) 0 0
\(544\) −2.18832 −0.0938233
\(545\) 20.5215 0.879044
\(546\) 0 0
\(547\) −23.7784 −1.01669 −0.508345 0.861154i \(-0.669742\pi\)
−0.508345 + 0.861154i \(0.669742\pi\)
\(548\) −3.26025 −0.139271
\(549\) 0 0
\(550\) 5.83989 0.249014
\(551\) 0.441233 0.0187972
\(552\) 0 0
\(553\) 75.1224 3.19453
\(554\) 26.1050 1.10909
\(555\) 0 0
\(556\) 18.1889 0.771381
\(557\) 7.29901 0.309269 0.154635 0.987972i \(-0.450580\pi\)
0.154635 + 0.987972i \(0.450580\pi\)
\(558\) 0 0
\(559\) 39.3941 1.66619
\(560\) 7.71606 0.326063
\(561\) 0 0
\(562\) 26.6711 1.12505
\(563\) −2.03753 −0.0858716 −0.0429358 0.999078i \(-0.513671\pi\)
−0.0429358 + 0.999078i \(0.513671\pi\)
\(564\) 0 0
\(565\) 6.89342 0.290008
\(566\) −17.0033 −0.714702
\(567\) 0 0
\(568\) −9.74208 −0.408768
\(569\) 17.2444 0.722921 0.361461 0.932387i \(-0.382278\pi\)
0.361461 + 0.932387i \(0.382278\pi\)
\(570\) 0 0
\(571\) −19.9527 −0.834993 −0.417496 0.908679i \(-0.637092\pi\)
−0.417496 + 0.908679i \(0.637092\pi\)
\(572\) −8.16267 −0.341298
\(573\) 0 0
\(574\) −16.0736 −0.670898
\(575\) −7.14681 −0.298042
\(576\) 0 0
\(577\) 8.77032 0.365113 0.182557 0.983195i \(-0.441563\pi\)
0.182557 + 0.983195i \(0.441563\pi\)
\(578\) 12.2113 0.507922
\(579\) 0 0
\(580\) 1.57665 0.0654669
\(581\) −7.56449 −0.313828
\(582\) 0 0
\(583\) −16.8803 −0.699111
\(584\) 14.1375 0.585013
\(585\) 0 0
\(586\) 24.2864 1.00326
\(587\) −3.84784 −0.158817 −0.0794087 0.996842i \(-0.525303\pi\)
−0.0794087 + 0.996842i \(0.525303\pi\)
\(588\) 0 0
\(589\) 0.347860 0.0143333
\(590\) −18.2568 −0.751619
\(591\) 0 0
\(592\) −2.71746 −0.111687
\(593\) −22.2185 −0.912404 −0.456202 0.889876i \(-0.650790\pi\)
−0.456202 + 0.889876i \(0.650790\pi\)
\(594\) 0 0
\(595\) 16.8852 0.692225
\(596\) 1.00000 0.0409616
\(597\) 0 0
\(598\) 9.98941 0.408497
\(599\) −37.4024 −1.52822 −0.764110 0.645086i \(-0.776822\pi\)
−0.764110 + 0.645086i \(0.776822\pi\)
\(600\) 0 0
\(601\) 20.9418 0.854234 0.427117 0.904196i \(-0.359529\pi\)
0.427117 + 0.904196i \(0.359529\pi\)
\(602\) 53.4552 2.17867
\(603\) 0 0
\(604\) 13.8103 0.561932
\(605\) −9.44957 −0.384180
\(606\) 0 0
\(607\) −8.43905 −0.342531 −0.171265 0.985225i \(-0.554786\pi\)
−0.171265 + 0.985225i \(0.554786\pi\)
\(608\) −0.428199 −0.0173658
\(609\) 0 0
\(610\) −1.29416 −0.0523991
\(611\) −11.6542 −0.471479
\(612\) 0 0
\(613\) −16.8275 −0.679656 −0.339828 0.940488i \(-0.610369\pi\)
−0.339828 + 0.940488i \(0.610369\pi\)
\(614\) −1.13742 −0.0459026
\(615\) 0 0
\(616\) −11.0762 −0.446273
\(617\) −43.7674 −1.76201 −0.881005 0.473108i \(-0.843132\pi\)
−0.881005 + 0.473108i \(0.843132\pi\)
\(618\) 0 0
\(619\) 32.3525 1.30036 0.650178 0.759782i \(-0.274694\pi\)
0.650178 + 0.759782i \(0.274694\pi\)
\(620\) 1.24300 0.0499202
\(621\) 0 0
\(622\) 0.447203 0.0179312
\(623\) 35.0482 1.40418
\(624\) 0 0
\(625\) −4.63619 −0.185448
\(626\) −12.9333 −0.516917
\(627\) 0 0
\(628\) 15.5334 0.619849
\(629\) −5.94666 −0.237109
\(630\) 0 0
\(631\) 5.92934 0.236043 0.118022 0.993011i \(-0.462345\pi\)
0.118022 + 0.993011i \(0.462345\pi\)
\(632\) −14.8966 −0.592556
\(633\) 0 0
\(634\) −4.60730 −0.182979
\(635\) 17.0469 0.676484
\(636\) 0 0
\(637\) −68.4969 −2.71395
\(638\) −2.26324 −0.0896027
\(639\) 0 0
\(640\) −1.53008 −0.0604817
\(641\) 10.6182 0.419394 0.209697 0.977766i \(-0.432752\pi\)
0.209697 + 0.977766i \(0.432752\pi\)
\(642\) 0 0
\(643\) −8.30984 −0.327708 −0.163854 0.986485i \(-0.552393\pi\)
−0.163854 + 0.986485i \(0.552393\pi\)
\(644\) 13.5550 0.534140
\(645\) 0 0
\(646\) −0.937036 −0.0368672
\(647\) 2.82555 0.111084 0.0555419 0.998456i \(-0.482311\pi\)
0.0555419 + 0.998456i \(0.482311\pi\)
\(648\) 0 0
\(649\) 26.2071 1.02872
\(650\) −9.88138 −0.387580
\(651\) 0 0
\(652\) −15.8819 −0.621982
\(653\) −14.4243 −0.564465 −0.282232 0.959346i \(-0.591075\pi\)
−0.282232 + 0.959346i \(0.591075\pi\)
\(654\) 0 0
\(655\) −21.6446 −0.845723
\(656\) 3.18736 0.124445
\(657\) 0 0
\(658\) −15.8140 −0.616494
\(659\) 1.31140 0.0510848 0.0255424 0.999674i \(-0.491869\pi\)
0.0255424 + 0.999674i \(0.491869\pi\)
\(660\) 0 0
\(661\) −0.269664 −0.0104887 −0.00524436 0.999986i \(-0.501669\pi\)
−0.00524436 + 0.999986i \(0.501669\pi\)
\(662\) 9.54771 0.371082
\(663\) 0 0
\(664\) 1.50002 0.0582122
\(665\) 3.30401 0.128124
\(666\) 0 0
\(667\) 2.76974 0.107245
\(668\) −21.1258 −0.817381
\(669\) 0 0
\(670\) 6.40286 0.247364
\(671\) 1.85774 0.0717171
\(672\) 0 0
\(673\) 13.5720 0.523164 0.261582 0.965181i \(-0.415756\pi\)
0.261582 + 0.965181i \(0.415756\pi\)
\(674\) −1.90607 −0.0734191
\(675\) 0 0
\(676\) 0.811642 0.0312170
\(677\) 23.7120 0.911324 0.455662 0.890153i \(-0.349403\pi\)
0.455662 + 0.890153i \(0.349403\pi\)
\(678\) 0 0
\(679\) −75.7091 −2.90545
\(680\) −3.34830 −0.128401
\(681\) 0 0
\(682\) −1.78430 −0.0683243
\(683\) 21.4299 0.819993 0.409997 0.912087i \(-0.365530\pi\)
0.409997 + 0.912087i \(0.365530\pi\)
\(684\) 0 0
\(685\) −4.98844 −0.190598
\(686\) −57.6454 −2.20091
\(687\) 0 0
\(688\) −10.6001 −0.404124
\(689\) 28.5623 1.08814
\(690\) 0 0
\(691\) −25.3951 −0.966076 −0.483038 0.875599i \(-0.660467\pi\)
−0.483038 + 0.875599i \(0.660467\pi\)
\(692\) −12.1765 −0.462882
\(693\) 0 0
\(694\) 31.8251 1.20806
\(695\) 27.8304 1.05567
\(696\) 0 0
\(697\) 6.97495 0.264195
\(698\) 14.2839 0.540655
\(699\) 0 0
\(700\) −13.4084 −0.506789
\(701\) −18.3848 −0.694384 −0.347192 0.937794i \(-0.612865\pi\)
−0.347192 + 0.937794i \(0.612865\pi\)
\(702\) 0 0
\(703\) −1.16361 −0.0438865
\(704\) 2.19639 0.0827796
\(705\) 0 0
\(706\) 4.35738 0.163992
\(707\) 93.5862 3.51967
\(708\) 0 0
\(709\) −0.380764 −0.0142999 −0.00714995 0.999974i \(-0.502276\pi\)
−0.00714995 + 0.999974i \(0.502276\pi\)
\(710\) −14.9062 −0.559418
\(711\) 0 0
\(712\) −6.94999 −0.260462
\(713\) 2.18361 0.0817768
\(714\) 0 0
\(715\) −12.4895 −0.467082
\(716\) 22.3807 0.836406
\(717\) 0 0
\(718\) 17.6460 0.658542
\(719\) 5.68886 0.212159 0.106079 0.994358i \(-0.466170\pi\)
0.106079 + 0.994358i \(0.466170\pi\)
\(720\) 0 0
\(721\) 89.9115 3.34848
\(722\) 18.8166 0.700283
\(723\) 0 0
\(724\) −16.5525 −0.615170
\(725\) −2.73979 −0.101753
\(726\) 0 0
\(727\) −18.4997 −0.686115 −0.343058 0.939314i \(-0.611463\pi\)
−0.343058 + 0.939314i \(0.611463\pi\)
\(728\) 18.7415 0.694606
\(729\) 0 0
\(730\) 21.6314 0.800616
\(731\) −23.1963 −0.857946
\(732\) 0 0
\(733\) −0.985838 −0.0364127 −0.0182064 0.999834i \(-0.505796\pi\)
−0.0182064 + 0.999834i \(0.505796\pi\)
\(734\) 12.9361 0.477479
\(735\) 0 0
\(736\) −2.68792 −0.0990782
\(737\) −9.19114 −0.338560
\(738\) 0 0
\(739\) 14.4601 0.531925 0.265962 0.963983i \(-0.414310\pi\)
0.265962 + 0.963983i \(0.414310\pi\)
\(740\) −4.15793 −0.152848
\(741\) 0 0
\(742\) 38.7572 1.42282
\(743\) 30.5301 1.12004 0.560020 0.828479i \(-0.310793\pi\)
0.560020 + 0.828479i \(0.310793\pi\)
\(744\) 0 0
\(745\) 1.53008 0.0560578
\(746\) 8.95023 0.327691
\(747\) 0 0
\(748\) 4.80640 0.175739
\(749\) 85.0313 3.10698
\(750\) 0 0
\(751\) 39.7575 1.45077 0.725385 0.688343i \(-0.241662\pi\)
0.725385 + 0.688343i \(0.241662\pi\)
\(752\) 3.13589 0.114354
\(753\) 0 0
\(754\) 3.82952 0.139463
\(755\) 21.1308 0.769029
\(756\) 0 0
\(757\) 16.0332 0.582737 0.291369 0.956611i \(-0.405889\pi\)
0.291369 + 0.956611i \(0.405889\pi\)
\(758\) 25.4453 0.924216
\(759\) 0 0
\(760\) −0.655179 −0.0237658
\(761\) 22.2255 0.805674 0.402837 0.915272i \(-0.368024\pi\)
0.402837 + 0.915272i \(0.368024\pi\)
\(762\) 0 0
\(763\) 67.6357 2.44858
\(764\) 20.5627 0.743933
\(765\) 0 0
\(766\) −20.2374 −0.731208
\(767\) −44.3437 −1.60116
\(768\) 0 0
\(769\) −47.0661 −1.69725 −0.848623 0.528998i \(-0.822568\pi\)
−0.848623 + 0.528998i \(0.822568\pi\)
\(770\) −16.9475 −0.610744
\(771\) 0 0
\(772\) 16.6431 0.598998
\(773\) 15.0500 0.541312 0.270656 0.962676i \(-0.412759\pi\)
0.270656 + 0.962676i \(0.412759\pi\)
\(774\) 0 0
\(775\) −2.16000 −0.0775894
\(776\) 15.0130 0.538934
\(777\) 0 0
\(778\) −15.5789 −0.558529
\(779\) 1.36482 0.0488999
\(780\) 0 0
\(781\) 21.3974 0.765659
\(782\) −5.88203 −0.210341
\(783\) 0 0
\(784\) 18.4310 0.658249
\(785\) 23.7673 0.848291
\(786\) 0 0
\(787\) −14.4696 −0.515786 −0.257893 0.966174i \(-0.583028\pi\)
−0.257893 + 0.966174i \(0.583028\pi\)
\(788\) 21.4204 0.763069
\(789\) 0 0
\(790\) −22.7930 −0.810939
\(791\) 22.7197 0.807819
\(792\) 0 0
\(793\) −3.14338 −0.111625
\(794\) 21.5619 0.765204
\(795\) 0 0
\(796\) 6.13385 0.217409
\(797\) −20.3370 −0.720374 −0.360187 0.932880i \(-0.617287\pi\)
−0.360187 + 0.932880i \(0.617287\pi\)
\(798\) 0 0
\(799\) 6.86232 0.242771
\(800\) 2.65886 0.0940048
\(801\) 0 0
\(802\) −20.2428 −0.714799
\(803\) −31.0514 −1.09578
\(804\) 0 0
\(805\) 20.7402 0.730995
\(806\) 3.01912 0.106344
\(807\) 0 0
\(808\) −18.5580 −0.652867
\(809\) −19.2164 −0.675614 −0.337807 0.941215i \(-0.609685\pi\)
−0.337807 + 0.941215i \(0.609685\pi\)
\(810\) 0 0
\(811\) 37.5596 1.31890 0.659448 0.751750i \(-0.270790\pi\)
0.659448 + 0.751750i \(0.270790\pi\)
\(812\) 5.19641 0.182358
\(813\) 0 0
\(814\) 5.96860 0.209199
\(815\) −24.3005 −0.851211
\(816\) 0 0
\(817\) −4.53894 −0.158797
\(818\) −7.78181 −0.272085
\(819\) 0 0
\(820\) 4.87691 0.170309
\(821\) −37.2215 −1.29904 −0.649520 0.760344i \(-0.725030\pi\)
−0.649520 + 0.760344i \(0.725030\pi\)
\(822\) 0 0
\(823\) −4.34491 −0.151454 −0.0757270 0.997129i \(-0.524128\pi\)
−0.0757270 + 0.997129i \(0.524128\pi\)
\(824\) −17.8293 −0.621113
\(825\) 0 0
\(826\) −60.1715 −2.09364
\(827\) 21.0032 0.730355 0.365177 0.930938i \(-0.381008\pi\)
0.365177 + 0.930938i \(0.381008\pi\)
\(828\) 0 0
\(829\) 19.1963 0.666716 0.333358 0.942800i \(-0.391818\pi\)
0.333358 + 0.942800i \(0.391818\pi\)
\(830\) 2.29515 0.0796660
\(831\) 0 0
\(832\) −3.71640 −0.128843
\(833\) 40.3328 1.39745
\(834\) 0 0
\(835\) −32.3241 −1.11862
\(836\) 0.940493 0.0325276
\(837\) 0 0
\(838\) −29.8913 −1.03258
\(839\) −30.8957 −1.06664 −0.533320 0.845914i \(-0.679056\pi\)
−0.533320 + 0.845914i \(0.679056\pi\)
\(840\) 0 0
\(841\) −27.9382 −0.963386
\(842\) −3.47305 −0.119689
\(843\) 0 0
\(844\) −1.92401 −0.0662272
\(845\) 1.24188 0.0427218
\(846\) 0 0
\(847\) −31.1444 −1.07013
\(848\) −7.68548 −0.263921
\(849\) 0 0
\(850\) 5.81843 0.199570
\(851\) −7.30432 −0.250389
\(852\) 0 0
\(853\) 51.8321 1.77470 0.887349 0.461099i \(-0.152545\pi\)
0.887349 + 0.461099i \(0.152545\pi\)
\(854\) −4.26536 −0.145958
\(855\) 0 0
\(856\) −16.8615 −0.576316
\(857\) 38.9753 1.33137 0.665685 0.746233i \(-0.268140\pi\)
0.665685 + 0.746233i \(0.268140\pi\)
\(858\) 0 0
\(859\) −29.0741 −0.991996 −0.495998 0.868324i \(-0.665198\pi\)
−0.495998 + 0.868324i \(0.665198\pi\)
\(860\) −16.2189 −0.553061
\(861\) 0 0
\(862\) −26.4524 −0.900971
\(863\) −43.1294 −1.46814 −0.734071 0.679072i \(-0.762382\pi\)
−0.734071 + 0.679072i \(0.762382\pi\)
\(864\) 0 0
\(865\) −18.6311 −0.633475
\(866\) −9.06980 −0.308204
\(867\) 0 0
\(868\) 4.09675 0.139053
\(869\) 32.7188 1.10991
\(870\) 0 0
\(871\) 15.5519 0.526955
\(872\) −13.4120 −0.454189
\(873\) 0 0
\(874\) −1.15097 −0.0389320
\(875\) −59.0962 −1.99782
\(876\) 0 0
\(877\) 51.7592 1.74778 0.873892 0.486120i \(-0.161588\pi\)
0.873892 + 0.486120i \(0.161588\pi\)
\(878\) −14.3151 −0.483112
\(879\) 0 0
\(880\) 3.36065 0.113288
\(881\) −11.2445 −0.378838 −0.189419 0.981896i \(-0.560660\pi\)
−0.189419 + 0.981896i \(0.560660\pi\)
\(882\) 0 0
\(883\) −35.2347 −1.18574 −0.592872 0.805297i \(-0.702006\pi\)
−0.592872 + 0.805297i \(0.702006\pi\)
\(884\) −8.13267 −0.273531
\(885\) 0 0
\(886\) −18.3436 −0.616264
\(887\) 5.09499 0.171073 0.0855366 0.996335i \(-0.472740\pi\)
0.0855366 + 0.996335i \(0.472740\pi\)
\(888\) 0 0
\(889\) 56.1839 1.88435
\(890\) −10.6340 −0.356453
\(891\) 0 0
\(892\) 11.4543 0.383520
\(893\) 1.34278 0.0449346
\(894\) 0 0
\(895\) 34.2443 1.14466
\(896\) −5.04291 −0.168472
\(897\) 0 0
\(898\) −5.91128 −0.197262
\(899\) 0.837105 0.0279190
\(900\) 0 0
\(901\) −16.8183 −0.560298
\(902\) −7.00068 −0.233097
\(903\) 0 0
\(904\) −4.50527 −0.149843
\(905\) −25.3267 −0.841887
\(906\) 0 0
\(907\) −36.8786 −1.22453 −0.612266 0.790652i \(-0.709742\pi\)
−0.612266 + 0.790652i \(0.709742\pi\)
\(908\) −7.54669 −0.250446
\(909\) 0 0
\(910\) 28.6760 0.950599
\(911\) −33.3860 −1.10613 −0.553064 0.833139i \(-0.686542\pi\)
−0.553064 + 0.833139i \(0.686542\pi\)
\(912\) 0 0
\(913\) −3.29464 −0.109037
\(914\) 4.51467 0.149332
\(915\) 0 0
\(916\) −27.8224 −0.919277
\(917\) −71.3372 −2.35576
\(918\) 0 0
\(919\) 42.0441 1.38691 0.693454 0.720501i \(-0.256088\pi\)
0.693454 + 0.720501i \(0.256088\pi\)
\(920\) −4.11274 −0.135593
\(921\) 0 0
\(922\) 17.7809 0.585583
\(923\) −36.2055 −1.19172
\(924\) 0 0
\(925\) 7.22533 0.237568
\(926\) 34.2340 1.12500
\(927\) 0 0
\(928\) −1.03044 −0.0338258
\(929\) −26.8964 −0.882441 −0.441221 0.897399i \(-0.645454\pi\)
−0.441221 + 0.897399i \(0.645454\pi\)
\(930\) 0 0
\(931\) 7.89213 0.258654
\(932\) 26.3727 0.863867
\(933\) 0 0
\(934\) 2.79934 0.0915971
\(935\) 7.35417 0.240507
\(936\) 0 0
\(937\) −3.40736 −0.111314 −0.0556568 0.998450i \(-0.517725\pi\)
−0.0556568 + 0.998450i \(0.517725\pi\)
\(938\) 21.1029 0.689033
\(939\) 0 0
\(940\) 4.79816 0.156499
\(941\) −31.5304 −1.02786 −0.513931 0.857832i \(-0.671811\pi\)
−0.513931 + 0.857832i \(0.671811\pi\)
\(942\) 0 0
\(943\) 8.56738 0.278992
\(944\) 11.9319 0.388350
\(945\) 0 0
\(946\) 23.2819 0.756959
\(947\) −25.3895 −0.825048 −0.412524 0.910947i \(-0.635353\pi\)
−0.412524 + 0.910947i \(0.635353\pi\)
\(948\) 0 0
\(949\) 52.5405 1.70554
\(950\) 1.13852 0.0369385
\(951\) 0 0
\(952\) −11.0355 −0.357662
\(953\) −28.2057 −0.913673 −0.456837 0.889551i \(-0.651018\pi\)
−0.456837 + 0.889551i \(0.651018\pi\)
\(954\) 0 0
\(955\) 31.4626 1.01811
\(956\) −19.1553 −0.619527
\(957\) 0 0
\(958\) 3.83579 0.123929
\(959\) −16.4411 −0.530912
\(960\) 0 0
\(961\) −30.3400 −0.978711
\(962\) −10.0992 −0.325610
\(963\) 0 0
\(964\) −18.2493 −0.587772
\(965\) 25.4652 0.819755
\(966\) 0 0
\(967\) −16.4498 −0.528991 −0.264495 0.964387i \(-0.585205\pi\)
−0.264495 + 0.964387i \(0.585205\pi\)
\(968\) 6.17587 0.198500
\(969\) 0 0
\(970\) 22.9710 0.737555
\(971\) 45.5948 1.46321 0.731604 0.681730i \(-0.238772\pi\)
0.731604 + 0.681730i \(0.238772\pi\)
\(972\) 0 0
\(973\) 91.7250 2.94057
\(974\) −26.3377 −0.843913
\(975\) 0 0
\(976\) 0.845814 0.0270738
\(977\) −8.73458 −0.279444 −0.139722 0.990191i \(-0.544621\pi\)
−0.139722 + 0.990191i \(0.544621\pi\)
\(978\) 0 0
\(979\) 15.2649 0.487868
\(980\) 28.2008 0.900843
\(981\) 0 0
\(982\) 22.8728 0.729902
\(983\) −43.3752 −1.38345 −0.691726 0.722160i \(-0.743150\pi\)
−0.691726 + 0.722160i \(0.743150\pi\)
\(984\) 0 0
\(985\) 32.7749 1.04429
\(986\) −2.25493 −0.0718115
\(987\) 0 0
\(988\) −1.59136 −0.0506279
\(989\) −28.4922 −0.905998
\(990\) 0 0
\(991\) 7.62311 0.242156 0.121078 0.992643i \(-0.461365\pi\)
0.121078 + 0.992643i \(0.461365\pi\)
\(992\) −0.812378 −0.0257930
\(993\) 0 0
\(994\) −49.1284 −1.55826
\(995\) 9.38528 0.297533
\(996\) 0 0
\(997\) −43.7993 −1.38714 −0.693569 0.720390i \(-0.743963\pi\)
−0.693569 + 0.720390i \(0.743963\pi\)
\(998\) −3.17734 −0.100577
\(999\) 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 \(a_p\))