Properties

Label 6039.2.a.j.1.1
Level 6039
Weight 2
Character 6039.1
Self dual Yes
Analytic conductor 48.222
Analytic rank 0
Dimension 14
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6039 = 3^{2} \cdot 11 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6039.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2216577807\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.57087\)
Character \(\chi\) = 6039.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.57087 q^{2}\) \(+4.60938 q^{4}\) \(-4.00721 q^{5}\) \(+2.04273 q^{7}\) \(-6.70837 q^{8}\) \(+O(q^{10})\) \(q\)\(-2.57087 q^{2}\) \(+4.60938 q^{4}\) \(-4.00721 q^{5}\) \(+2.04273 q^{7}\) \(-6.70837 q^{8}\) \(+10.3020 q^{10}\) \(+1.00000 q^{11}\) \(-4.75237 q^{13}\) \(-5.25159 q^{14}\) \(+8.02760 q^{16}\) \(+0.339679 q^{17}\) \(+4.54116 q^{19}\) \(-18.4707 q^{20}\) \(-2.57087 q^{22}\) \(+4.75749 q^{23}\) \(+11.0577 q^{25}\) \(+12.2177 q^{26}\) \(+9.41571 q^{28}\) \(+4.28494 q^{29}\) \(+1.81765 q^{31}\) \(-7.22118 q^{32}\) \(-0.873272 q^{34}\) \(-8.18565 q^{35}\) \(-2.11204 q^{37}\) \(-11.6747 q^{38}\) \(+26.8819 q^{40}\) \(+10.2585 q^{41}\) \(-9.89546 q^{43}\) \(+4.60938 q^{44}\) \(-12.2309 q^{46}\) \(+5.22451 q^{47}\) \(-2.82726 q^{49}\) \(-28.4280 q^{50}\) \(-21.9055 q^{52}\) \(-9.68455 q^{53}\) \(-4.00721 q^{55}\) \(-13.7034 q^{56}\) \(-11.0160 q^{58}\) \(+2.04679 q^{59}\) \(+1.00000 q^{61}\) \(-4.67295 q^{62}\) \(+2.50953 q^{64}\) \(+19.0437 q^{65}\) \(+5.30981 q^{67}\) \(+1.56571 q^{68}\) \(+21.0442 q^{70}\) \(-11.4906 q^{71}\) \(-4.51365 q^{73}\) \(+5.42978 q^{74}\) \(+20.9319 q^{76}\) \(+2.04273 q^{77}\) \(+5.49270 q^{79}\) \(-32.1683 q^{80}\) \(-26.3733 q^{82}\) \(-14.2207 q^{83}\) \(-1.36117 q^{85}\) \(+25.4399 q^{86}\) \(-6.70837 q^{88}\) \(+6.05470 q^{89}\) \(-9.70780 q^{91}\) \(+21.9291 q^{92}\) \(-13.4315 q^{94}\) \(-18.1974 q^{95}\) \(+13.6004 q^{97}\) \(+7.26851 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut +\mathstrut q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut +\mathstrut 17q^{16} \) \(\mathstrut +\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 22q^{19} \) \(\mathstrut -\mathstrut 23q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 25q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut +\mathstrut 37q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 9q^{31} \) \(\mathstrut -\mathstrut 4q^{32} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 18q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 25q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 36q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut -\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 13q^{52} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 40q^{56} \) \(\mathstrut +\mathstrut 33q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut +\mathstrut 14q^{61} \) \(\mathstrut +\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 6q^{64} \) \(\mathstrut +\mathstrut 61q^{65} \) \(\mathstrut +\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 66q^{68} \) \(\mathstrut +\mathstrut 44q^{70} \) \(\mathstrut +\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 12q^{74} \) \(\mathstrut +\mathstrut 49q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut -\mathstrut 88q^{80} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 32q^{83} \) \(\mathstrut +\mathstrut 2q^{85} \) \(\mathstrut +\mathstrut 14q^{86} \) \(\mathstrut +\mathstrut 21q^{89} \) \(\mathstrut +\mathstrut 45q^{91} \) \(\mathstrut +\mathstrut 14q^{92} \) \(\mathstrut -\mathstrut 31q^{94} \) \(\mathstrut -\mathstrut 23q^{95} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut +\mathstrut 38q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.57087 −1.81788 −0.908940 0.416927i \(-0.863107\pi\)
−0.908940 + 0.416927i \(0.863107\pi\)
\(3\) 0 0
\(4\) 4.60938 2.30469
\(5\) −4.00721 −1.79208 −0.896040 0.443974i \(-0.853568\pi\)
−0.896040 + 0.443974i \(0.853568\pi\)
\(6\) 0 0
\(7\) 2.04273 0.772079 0.386040 0.922482i \(-0.373843\pi\)
0.386040 + 0.922482i \(0.373843\pi\)
\(8\) −6.70837 −2.37177
\(9\) 0 0
\(10\) 10.3020 3.25779
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −4.75237 −1.31807 −0.659035 0.752112i \(-0.729035\pi\)
−0.659035 + 0.752112i \(0.729035\pi\)
\(14\) −5.25159 −1.40355
\(15\) 0 0
\(16\) 8.02760 2.00690
\(17\) 0.339679 0.0823844 0.0411922 0.999151i \(-0.486884\pi\)
0.0411922 + 0.999151i \(0.486884\pi\)
\(18\) 0 0
\(19\) 4.54116 1.04181 0.520907 0.853613i \(-0.325594\pi\)
0.520907 + 0.853613i \(0.325594\pi\)
\(20\) −18.4707 −4.13018
\(21\) 0 0
\(22\) −2.57087 −0.548112
\(23\) 4.75749 0.992006 0.496003 0.868321i \(-0.334800\pi\)
0.496003 + 0.868321i \(0.334800\pi\)
\(24\) 0 0
\(25\) 11.0577 2.21155
\(26\) 12.2177 2.39609
\(27\) 0 0
\(28\) 9.41571 1.77940
\(29\) 4.28494 0.795693 0.397846 0.917452i \(-0.369758\pi\)
0.397846 + 0.917452i \(0.369758\pi\)
\(30\) 0 0
\(31\) 1.81765 0.326460 0.163230 0.986588i \(-0.447809\pi\)
0.163230 + 0.986588i \(0.447809\pi\)
\(32\) −7.22118 −1.27654
\(33\) 0 0
\(34\) −0.873272 −0.149765
\(35\) −8.18565 −1.38363
\(36\) 0 0
\(37\) −2.11204 −0.347217 −0.173609 0.984815i \(-0.555543\pi\)
−0.173609 + 0.984815i \(0.555543\pi\)
\(38\) −11.6747 −1.89389
\(39\) 0 0
\(40\) 26.8819 4.25039
\(41\) 10.2585 1.60211 0.801056 0.598589i \(-0.204272\pi\)
0.801056 + 0.598589i \(0.204272\pi\)
\(42\) 0 0
\(43\) −9.89546 −1.50904 −0.754522 0.656275i \(-0.772131\pi\)
−0.754522 + 0.656275i \(0.772131\pi\)
\(44\) 4.60938 0.694890
\(45\) 0 0
\(46\) −12.2309 −1.80335
\(47\) 5.22451 0.762074 0.381037 0.924560i \(-0.375567\pi\)
0.381037 + 0.924560i \(0.375567\pi\)
\(48\) 0 0
\(49\) −2.82726 −0.403894
\(50\) −28.4280 −4.02033
\(51\) 0 0
\(52\) −21.9055 −3.03774
\(53\) −9.68455 −1.33028 −0.665138 0.746721i \(-0.731627\pi\)
−0.665138 + 0.746721i \(0.731627\pi\)
\(54\) 0 0
\(55\) −4.00721 −0.540332
\(56\) −13.7034 −1.83119
\(57\) 0 0
\(58\) −11.0160 −1.44647
\(59\) 2.04679 0.266469 0.133235 0.991085i \(-0.457464\pi\)
0.133235 + 0.991085i \(0.457464\pi\)
\(60\) 0 0
\(61\) 1.00000 0.128037
\(62\) −4.67295 −0.593465
\(63\) 0 0
\(64\) 2.50953 0.313691
\(65\) 19.0437 2.36209
\(66\) 0 0
\(67\) 5.30981 0.648697 0.324348 0.945938i \(-0.394855\pi\)
0.324348 + 0.945938i \(0.394855\pi\)
\(68\) 1.56571 0.189870
\(69\) 0 0
\(70\) 21.0442 2.51527
\(71\) −11.4906 −1.36368 −0.681841 0.731500i \(-0.738820\pi\)
−0.681841 + 0.731500i \(0.738820\pi\)
\(72\) 0 0
\(73\) −4.51365 −0.528283 −0.264142 0.964484i \(-0.585089\pi\)
−0.264142 + 0.964484i \(0.585089\pi\)
\(74\) 5.42978 0.631199
\(75\) 0 0
\(76\) 20.9319 2.40106
\(77\) 2.04273 0.232791
\(78\) 0 0
\(79\) 5.49270 0.617977 0.308989 0.951066i \(-0.400009\pi\)
0.308989 + 0.951066i \(0.400009\pi\)
\(80\) −32.1683 −3.59652
\(81\) 0 0
\(82\) −26.3733 −2.91245
\(83\) −14.2207 −1.56092 −0.780460 0.625206i \(-0.785015\pi\)
−0.780460 + 0.625206i \(0.785015\pi\)
\(84\) 0 0
\(85\) −1.36117 −0.147639
\(86\) 25.4399 2.74326
\(87\) 0 0
\(88\) −6.70837 −0.715115
\(89\) 6.05470 0.641797 0.320899 0.947114i \(-0.396015\pi\)
0.320899 + 0.947114i \(0.396015\pi\)
\(90\) 0 0
\(91\) −9.70780 −1.01765
\(92\) 21.9291 2.28626
\(93\) 0 0
\(94\) −13.4315 −1.38536
\(95\) −18.1974 −1.86701
\(96\) 0 0
\(97\) 13.6004 1.38092 0.690458 0.723373i \(-0.257409\pi\)
0.690458 + 0.723373i \(0.257409\pi\)
\(98\) 7.26851 0.734231
\(99\) 0 0
\(100\) 50.9693 5.09693
\(101\) 10.2656 1.02147 0.510735 0.859738i \(-0.329373\pi\)
0.510735 + 0.859738i \(0.329373\pi\)
\(102\) 0 0
\(103\) 10.8307 1.06718 0.533590 0.845743i \(-0.320843\pi\)
0.533590 + 0.845743i \(0.320843\pi\)
\(104\) 31.8807 3.12616
\(105\) 0 0
\(106\) 24.8977 2.41828
\(107\) 10.3745 1.00294 0.501471 0.865174i \(-0.332792\pi\)
0.501471 + 0.865174i \(0.332792\pi\)
\(108\) 0 0
\(109\) −15.9251 −1.52534 −0.762672 0.646786i \(-0.776113\pi\)
−0.762672 + 0.646786i \(0.776113\pi\)
\(110\) 10.3020 0.982259
\(111\) 0 0
\(112\) 16.3982 1.54949
\(113\) −4.50235 −0.423546 −0.211773 0.977319i \(-0.567924\pi\)
−0.211773 + 0.977319i \(0.567924\pi\)
\(114\) 0 0
\(115\) −19.0643 −1.77775
\(116\) 19.7509 1.83382
\(117\) 0 0
\(118\) −5.26203 −0.484409
\(119\) 0.693873 0.0636072
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −2.57087 −0.232756
\(123\) 0 0
\(124\) 8.37824 0.752388
\(125\) −24.2746 −2.17119
\(126\) 0 0
\(127\) −12.2578 −1.08770 −0.543852 0.839181i \(-0.683035\pi\)
−0.543852 + 0.839181i \(0.683035\pi\)
\(128\) 7.99069 0.706284
\(129\) 0 0
\(130\) −48.9590 −4.29399
\(131\) −14.1653 −1.23763 −0.618814 0.785538i \(-0.712386\pi\)
−0.618814 + 0.785538i \(0.712386\pi\)
\(132\) 0 0
\(133\) 9.27637 0.804363
\(134\) −13.6508 −1.17925
\(135\) 0 0
\(136\) −2.27870 −0.195397
\(137\) −11.8311 −1.01080 −0.505401 0.862885i \(-0.668655\pi\)
−0.505401 + 0.862885i \(0.668655\pi\)
\(138\) 0 0
\(139\) 21.4652 1.82066 0.910328 0.413887i \(-0.135829\pi\)
0.910328 + 0.413887i \(0.135829\pi\)
\(140\) −37.7307 −3.18883
\(141\) 0 0
\(142\) 29.5408 2.47901
\(143\) −4.75237 −0.397413
\(144\) 0 0
\(145\) −17.1706 −1.42594
\(146\) 11.6040 0.960356
\(147\) 0 0
\(148\) −9.73519 −0.800227
\(149\) −5.71869 −0.468493 −0.234247 0.972177i \(-0.575262\pi\)
−0.234247 + 0.972177i \(0.575262\pi\)
\(150\) 0 0
\(151\) 4.53058 0.368694 0.184347 0.982861i \(-0.440983\pi\)
0.184347 + 0.982861i \(0.440983\pi\)
\(152\) −30.4638 −2.47094
\(153\) 0 0
\(154\) −5.25159 −0.423185
\(155\) −7.28371 −0.585042
\(156\) 0 0
\(157\) −10.4733 −0.835859 −0.417930 0.908479i \(-0.637244\pi\)
−0.417930 + 0.908479i \(0.637244\pi\)
\(158\) −14.1210 −1.12341
\(159\) 0 0
\(160\) 28.9368 2.28766
\(161\) 9.71827 0.765907
\(162\) 0 0
\(163\) 12.0156 0.941136 0.470568 0.882364i \(-0.344049\pi\)
0.470568 + 0.882364i \(0.344049\pi\)
\(164\) 47.2854 3.69237
\(165\) 0 0
\(166\) 36.5595 2.83756
\(167\) −7.72247 −0.597582 −0.298791 0.954318i \(-0.596583\pi\)
−0.298791 + 0.954318i \(0.596583\pi\)
\(168\) 0 0
\(169\) 9.58501 0.737308
\(170\) 3.49938 0.268391
\(171\) 0 0
\(172\) −45.6119 −3.47787
\(173\) −14.5915 −1.10937 −0.554684 0.832061i \(-0.687161\pi\)
−0.554684 + 0.832061i \(0.687161\pi\)
\(174\) 0 0
\(175\) 22.5880 1.70749
\(176\) 8.02760 0.605103
\(177\) 0 0
\(178\) −15.5659 −1.16671
\(179\) 13.1655 0.984037 0.492019 0.870585i \(-0.336259\pi\)
0.492019 + 0.870585i \(0.336259\pi\)
\(180\) 0 0
\(181\) −7.26104 −0.539709 −0.269854 0.962901i \(-0.586976\pi\)
−0.269854 + 0.962901i \(0.586976\pi\)
\(182\) 24.9575 1.84997
\(183\) 0 0
\(184\) −31.9150 −2.35281
\(185\) 8.46339 0.622241
\(186\) 0 0
\(187\) 0.339679 0.0248398
\(188\) 24.0818 1.75634
\(189\) 0 0
\(190\) 46.7832 3.39401
\(191\) −3.04371 −0.220235 −0.110118 0.993919i \(-0.535123\pi\)
−0.110118 + 0.993919i \(0.535123\pi\)
\(192\) 0 0
\(193\) 6.85641 0.493535 0.246768 0.969075i \(-0.420632\pi\)
0.246768 + 0.969075i \(0.420632\pi\)
\(194\) −34.9650 −2.51034
\(195\) 0 0
\(196\) −13.0319 −0.930850
\(197\) 12.1375 0.864763 0.432381 0.901691i \(-0.357673\pi\)
0.432381 + 0.901691i \(0.357673\pi\)
\(198\) 0 0
\(199\) −13.8050 −0.978613 −0.489306 0.872112i \(-0.662750\pi\)
−0.489306 + 0.872112i \(0.662750\pi\)
\(200\) −74.1794 −5.24528
\(201\) 0 0
\(202\) −26.3916 −1.85691
\(203\) 8.75297 0.614338
\(204\) 0 0
\(205\) −41.1081 −2.87111
\(206\) −27.8443 −1.94001
\(207\) 0 0
\(208\) −38.1501 −2.64523
\(209\) 4.54116 0.314119
\(210\) 0 0
\(211\) 13.4936 0.928938 0.464469 0.885589i \(-0.346245\pi\)
0.464469 + 0.885589i \(0.346245\pi\)
\(212\) −44.6398 −3.06587
\(213\) 0 0
\(214\) −26.6715 −1.82323
\(215\) 39.6532 2.70432
\(216\) 0 0
\(217\) 3.71297 0.252053
\(218\) 40.9413 2.77289
\(219\) 0 0
\(220\) −18.4707 −1.24530
\(221\) −1.61428 −0.108588
\(222\) 0 0
\(223\) −3.65818 −0.244970 −0.122485 0.992470i \(-0.539086\pi\)
−0.122485 + 0.992470i \(0.539086\pi\)
\(224\) −14.7509 −0.985588
\(225\) 0 0
\(226\) 11.5750 0.769956
\(227\) 6.72165 0.446131 0.223066 0.974803i \(-0.428394\pi\)
0.223066 + 0.974803i \(0.428394\pi\)
\(228\) 0 0
\(229\) −1.23766 −0.0817871 −0.0408935 0.999164i \(-0.513020\pi\)
−0.0408935 + 0.999164i \(0.513020\pi\)
\(230\) 49.0118 3.23174
\(231\) 0 0
\(232\) −28.7449 −1.88720
\(233\) −12.9299 −0.847065 −0.423532 0.905881i \(-0.639210\pi\)
−0.423532 + 0.905881i \(0.639210\pi\)
\(234\) 0 0
\(235\) −20.9357 −1.36570
\(236\) 9.43442 0.614128
\(237\) 0 0
\(238\) −1.78386 −0.115630
\(239\) 18.5458 1.19963 0.599814 0.800140i \(-0.295241\pi\)
0.599814 + 0.800140i \(0.295241\pi\)
\(240\) 0 0
\(241\) −27.7936 −1.79034 −0.895171 0.445723i \(-0.852947\pi\)
−0.895171 + 0.445723i \(0.852947\pi\)
\(242\) −2.57087 −0.165262
\(243\) 0 0
\(244\) 4.60938 0.295085
\(245\) 11.3294 0.723810
\(246\) 0 0
\(247\) −21.5813 −1.37318
\(248\) −12.1935 −0.774287
\(249\) 0 0
\(250\) 62.4070 3.94696
\(251\) 4.56250 0.287982 0.143991 0.989579i \(-0.454006\pi\)
0.143991 + 0.989579i \(0.454006\pi\)
\(252\) 0 0
\(253\) 4.75749 0.299101
\(254\) 31.5132 1.97732
\(255\) 0 0
\(256\) −25.5621 −1.59763
\(257\) 16.8127 1.04874 0.524372 0.851489i \(-0.324300\pi\)
0.524372 + 0.851489i \(0.324300\pi\)
\(258\) 0 0
\(259\) −4.31433 −0.268079
\(260\) 87.7798 5.44387
\(261\) 0 0
\(262\) 36.4171 2.24986
\(263\) 8.19724 0.505463 0.252732 0.967536i \(-0.418671\pi\)
0.252732 + 0.967536i \(0.418671\pi\)
\(264\) 0 0
\(265\) 38.8081 2.38396
\(266\) −23.8483 −1.46224
\(267\) 0 0
\(268\) 24.4749 1.49504
\(269\) −12.7223 −0.775690 −0.387845 0.921725i \(-0.626780\pi\)
−0.387845 + 0.921725i \(0.626780\pi\)
\(270\) 0 0
\(271\) 28.9215 1.75686 0.878428 0.477875i \(-0.158593\pi\)
0.878428 + 0.477875i \(0.158593\pi\)
\(272\) 2.72681 0.165337
\(273\) 0 0
\(274\) 30.4163 1.83752
\(275\) 11.0577 0.666807
\(276\) 0 0
\(277\) 9.01259 0.541514 0.270757 0.962648i \(-0.412726\pi\)
0.270757 + 0.962648i \(0.412726\pi\)
\(278\) −55.1843 −3.30974
\(279\) 0 0
\(280\) 54.9124 3.28164
\(281\) 20.0391 1.19543 0.597715 0.801708i \(-0.296075\pi\)
0.597715 + 0.801708i \(0.296075\pi\)
\(282\) 0 0
\(283\) 29.2872 1.74094 0.870471 0.492221i \(-0.163815\pi\)
0.870471 + 0.492221i \(0.163815\pi\)
\(284\) −52.9645 −3.14286
\(285\) 0 0
\(286\) 12.2177 0.722449
\(287\) 20.9554 1.23696
\(288\) 0 0
\(289\) −16.8846 −0.993213
\(290\) 44.1435 2.59220
\(291\) 0 0
\(292\) −20.8051 −1.21753
\(293\) −31.2913 −1.82806 −0.914029 0.405649i \(-0.867046\pi\)
−0.914029 + 0.405649i \(0.867046\pi\)
\(294\) 0 0
\(295\) −8.20191 −0.477534
\(296\) 14.1683 0.823518
\(297\) 0 0
\(298\) 14.7020 0.851665
\(299\) −22.6094 −1.30753
\(300\) 0 0
\(301\) −20.2137 −1.16510
\(302\) −11.6475 −0.670241
\(303\) 0 0
\(304\) 36.4547 2.09082
\(305\) −4.00721 −0.229452
\(306\) 0 0
\(307\) 0.203717 0.0116268 0.00581338 0.999983i \(-0.498150\pi\)
0.00581338 + 0.999983i \(0.498150\pi\)
\(308\) 9.41571 0.536510
\(309\) 0 0
\(310\) 18.7255 1.06354
\(311\) 15.4938 0.878573 0.439287 0.898347i \(-0.355231\pi\)
0.439287 + 0.898347i \(0.355231\pi\)
\(312\) 0 0
\(313\) −27.2007 −1.53747 −0.768737 0.639565i \(-0.779114\pi\)
−0.768737 + 0.639565i \(0.779114\pi\)
\(314\) 26.9255 1.51949
\(315\) 0 0
\(316\) 25.3179 1.42425
\(317\) 11.9050 0.668653 0.334327 0.942457i \(-0.391491\pi\)
0.334327 + 0.942457i \(0.391491\pi\)
\(318\) 0 0
\(319\) 4.28494 0.239910
\(320\) −10.0562 −0.562159
\(321\) 0 0
\(322\) −24.9844 −1.39233
\(323\) 1.54254 0.0858292
\(324\) 0 0
\(325\) −52.5505 −2.91497
\(326\) −30.8906 −1.71087
\(327\) 0 0
\(328\) −68.8180 −3.79984
\(329\) 10.6723 0.588381
\(330\) 0 0
\(331\) −5.44265 −0.299155 −0.149577 0.988750i \(-0.547791\pi\)
−0.149577 + 0.988750i \(0.547791\pi\)
\(332\) −65.5483 −3.59743
\(333\) 0 0
\(334\) 19.8535 1.08633
\(335\) −21.2775 −1.16252
\(336\) 0 0
\(337\) 11.5595 0.629687 0.314843 0.949144i \(-0.398048\pi\)
0.314843 + 0.949144i \(0.398048\pi\)
\(338\) −24.6418 −1.34034
\(339\) 0 0
\(340\) −6.27413 −0.340263
\(341\) 1.81765 0.0984314
\(342\) 0 0
\(343\) −20.0744 −1.08392
\(344\) 66.3824 3.57910
\(345\) 0 0
\(346\) 37.5128 2.01670
\(347\) 34.9338 1.87535 0.937673 0.347519i \(-0.112976\pi\)
0.937673 + 0.347519i \(0.112976\pi\)
\(348\) 0 0
\(349\) −16.4637 −0.881281 −0.440641 0.897684i \(-0.645249\pi\)
−0.440641 + 0.897684i \(0.645249\pi\)
\(350\) −58.0708 −3.10401
\(351\) 0 0
\(352\) −7.22118 −0.384890
\(353\) −36.1064 −1.92175 −0.960876 0.276980i \(-0.910667\pi\)
−0.960876 + 0.276980i \(0.910667\pi\)
\(354\) 0 0
\(355\) 46.0452 2.44383
\(356\) 27.9084 1.47914
\(357\) 0 0
\(358\) −33.8469 −1.78886
\(359\) 16.1146 0.850498 0.425249 0.905076i \(-0.360187\pi\)
0.425249 + 0.905076i \(0.360187\pi\)
\(360\) 0 0
\(361\) 1.62217 0.0853773
\(362\) 18.6672 0.981126
\(363\) 0 0
\(364\) −44.7469 −2.34538
\(365\) 18.0872 0.946725
\(366\) 0 0
\(367\) 35.8180 1.86969 0.934843 0.355061i \(-0.115540\pi\)
0.934843 + 0.355061i \(0.115540\pi\)
\(368\) 38.1913 1.99086
\(369\) 0 0
\(370\) −21.7583 −1.13116
\(371\) −19.7829 −1.02708
\(372\) 0 0
\(373\) −18.3914 −0.952273 −0.476137 0.879371i \(-0.657963\pi\)
−0.476137 + 0.879371i \(0.657963\pi\)
\(374\) −0.873272 −0.0451558
\(375\) 0 0
\(376\) −35.0480 −1.80746
\(377\) −20.3636 −1.04878
\(378\) 0 0
\(379\) −5.27053 −0.270729 −0.135364 0.990796i \(-0.543221\pi\)
−0.135364 + 0.990796i \(0.543221\pi\)
\(380\) −83.8787 −4.30289
\(381\) 0 0
\(382\) 7.82499 0.400361
\(383\) −32.5167 −1.66153 −0.830763 0.556626i \(-0.812096\pi\)
−0.830763 + 0.556626i \(0.812096\pi\)
\(384\) 0 0
\(385\) −8.18565 −0.417179
\(386\) −17.6269 −0.897188
\(387\) 0 0
\(388\) 62.6895 3.18258
\(389\) 24.3758 1.23590 0.617950 0.786217i \(-0.287963\pi\)
0.617950 + 0.786217i \(0.287963\pi\)
\(390\) 0 0
\(391\) 1.61602 0.0817258
\(392\) 18.9663 0.957942
\(393\) 0 0
\(394\) −31.2040 −1.57203
\(395\) −22.0104 −1.10746
\(396\) 0 0
\(397\) −18.0276 −0.904779 −0.452390 0.891820i \(-0.649428\pi\)
−0.452390 + 0.891820i \(0.649428\pi\)
\(398\) 35.4909 1.77900
\(399\) 0 0
\(400\) 88.7671 4.43836
\(401\) 29.1981 1.45808 0.729042 0.684469i \(-0.239966\pi\)
0.729042 + 0.684469i \(0.239966\pi\)
\(402\) 0 0
\(403\) −8.63815 −0.430297
\(404\) 47.3182 2.35417
\(405\) 0 0
\(406\) −22.5027 −1.11679
\(407\) −2.11204 −0.104690
\(408\) 0 0
\(409\) 2.63476 0.130280 0.0651401 0.997876i \(-0.479251\pi\)
0.0651401 + 0.997876i \(0.479251\pi\)
\(410\) 105.684 5.21934
\(411\) 0 0
\(412\) 49.9227 2.45952
\(413\) 4.18103 0.205735
\(414\) 0 0
\(415\) 56.9852 2.79729
\(416\) 34.3177 1.68257
\(417\) 0 0
\(418\) −11.6747 −0.571030
\(419\) −32.0724 −1.56684 −0.783420 0.621492i \(-0.786527\pi\)
−0.783420 + 0.621492i \(0.786527\pi\)
\(420\) 0 0
\(421\) 6.02368 0.293576 0.146788 0.989168i \(-0.453106\pi\)
0.146788 + 0.989168i \(0.453106\pi\)
\(422\) −34.6903 −1.68870
\(423\) 0 0
\(424\) 64.9676 3.15510
\(425\) 3.75609 0.182197
\(426\) 0 0
\(427\) 2.04273 0.0988546
\(428\) 47.8200 2.31147
\(429\) 0 0
\(430\) −101.943 −4.91614
\(431\) 19.6288 0.945487 0.472744 0.881200i \(-0.343264\pi\)
0.472744 + 0.881200i \(0.343264\pi\)
\(432\) 0 0
\(433\) 27.8579 1.33876 0.669382 0.742919i \(-0.266559\pi\)
0.669382 + 0.742919i \(0.266559\pi\)
\(434\) −9.54557 −0.458202
\(435\) 0 0
\(436\) −73.4046 −3.51544
\(437\) 21.6046 1.03349
\(438\) 0 0
\(439\) −25.4823 −1.21620 −0.608102 0.793859i \(-0.708069\pi\)
−0.608102 + 0.793859i \(0.708069\pi\)
\(440\) 26.8819 1.28154
\(441\) 0 0
\(442\) 4.15011 0.197401
\(443\) −29.0256 −1.37905 −0.689524 0.724263i \(-0.742180\pi\)
−0.689524 + 0.724263i \(0.742180\pi\)
\(444\) 0 0
\(445\) −24.2625 −1.15015
\(446\) 9.40471 0.445326
\(447\) 0 0
\(448\) 5.12629 0.242194
\(449\) −23.3018 −1.09968 −0.549840 0.835270i \(-0.685311\pi\)
−0.549840 + 0.835270i \(0.685311\pi\)
\(450\) 0 0
\(451\) 10.2585 0.483055
\(452\) −20.7530 −0.976141
\(453\) 0 0
\(454\) −17.2805 −0.811013
\(455\) 38.9012 1.82372
\(456\) 0 0
\(457\) 38.8508 1.81737 0.908683 0.417487i \(-0.137089\pi\)
0.908683 + 0.417487i \(0.137089\pi\)
\(458\) 3.18187 0.148679
\(459\) 0 0
\(460\) −87.8745 −4.09717
\(461\) −2.42547 −0.112965 −0.0564827 0.998404i \(-0.517989\pi\)
−0.0564827 + 0.998404i \(0.517989\pi\)
\(462\) 0 0
\(463\) 37.3362 1.73516 0.867581 0.497295i \(-0.165673\pi\)
0.867581 + 0.497295i \(0.165673\pi\)
\(464\) 34.3978 1.59688
\(465\) 0 0
\(466\) 33.2411 1.53986
\(467\) 7.55898 0.349788 0.174894 0.984587i \(-0.444042\pi\)
0.174894 + 0.984587i \(0.444042\pi\)
\(468\) 0 0
\(469\) 10.8465 0.500845
\(470\) 53.8231 2.48267
\(471\) 0 0
\(472\) −13.7306 −0.632003
\(473\) −9.89546 −0.454994
\(474\) 0 0
\(475\) 50.2150 2.30402
\(476\) 3.19832 0.146595
\(477\) 0 0
\(478\) −47.6788 −2.18078
\(479\) 35.7614 1.63398 0.816990 0.576651i \(-0.195641\pi\)
0.816990 + 0.576651i \(0.195641\pi\)
\(480\) 0 0
\(481\) 10.0372 0.457657
\(482\) 71.4537 3.25463
\(483\) 0 0
\(484\) 4.60938 0.209517
\(485\) −54.4998 −2.47471
\(486\) 0 0
\(487\) −6.39232 −0.289664 −0.144832 0.989456i \(-0.546264\pi\)
−0.144832 + 0.989456i \(0.546264\pi\)
\(488\) −6.70837 −0.303674
\(489\) 0 0
\(490\) −29.1265 −1.31580
\(491\) −16.7893 −0.757691 −0.378846 0.925460i \(-0.623679\pi\)
−0.378846 + 0.925460i \(0.623679\pi\)
\(492\) 0 0
\(493\) 1.45550 0.0655526
\(494\) 55.4827 2.49628
\(495\) 0 0
\(496\) 14.5914 0.655172
\(497\) −23.4722 −1.05287
\(498\) 0 0
\(499\) 2.39493 0.107212 0.0536060 0.998562i \(-0.482929\pi\)
0.0536060 + 0.998562i \(0.482929\pi\)
\(500\) −111.891 −5.00392
\(501\) 0 0
\(502\) −11.7296 −0.523517
\(503\) −2.97796 −0.132781 −0.0663903 0.997794i \(-0.521148\pi\)
−0.0663903 + 0.997794i \(0.521148\pi\)
\(504\) 0 0
\(505\) −41.1366 −1.83055
\(506\) −12.2309 −0.543730
\(507\) 0 0
\(508\) −56.5008 −2.50682
\(509\) 13.6035 0.602964 0.301482 0.953472i \(-0.402519\pi\)
0.301482 + 0.953472i \(0.402519\pi\)
\(510\) 0 0
\(511\) −9.22017 −0.407876
\(512\) 49.7355 2.19802
\(513\) 0 0
\(514\) −43.2232 −1.90649
\(515\) −43.4009 −1.91247
\(516\) 0 0
\(517\) 5.22451 0.229774
\(518\) 11.0916 0.487336
\(519\) 0 0
\(520\) −127.752 −5.60232
\(521\) −4.86305 −0.213054 −0.106527 0.994310i \(-0.533973\pi\)
−0.106527 + 0.994310i \(0.533973\pi\)
\(522\) 0 0
\(523\) 4.06198 0.177618 0.0888091 0.996049i \(-0.471694\pi\)
0.0888091 + 0.996049i \(0.471694\pi\)
\(524\) −65.2932 −2.85234
\(525\) 0 0
\(526\) −21.0740 −0.918872
\(527\) 0.617419 0.0268952
\(528\) 0 0
\(529\) −0.366250 −0.0159239
\(530\) −99.7705 −4.33375
\(531\) 0 0
\(532\) 42.7583 1.85381
\(533\) −48.7523 −2.11170
\(534\) 0 0
\(535\) −41.5729 −1.79735
\(536\) −35.6202 −1.53856
\(537\) 0 0
\(538\) 32.7073 1.41011
\(539\) −2.82726 −0.121779
\(540\) 0 0
\(541\) 43.0563 1.85113 0.925566 0.378585i \(-0.123589\pi\)
0.925566 + 0.378585i \(0.123589\pi\)
\(542\) −74.3534 −3.19375
\(543\) 0 0
\(544\) −2.45289 −0.105167
\(545\) 63.8150 2.73354
\(546\) 0 0
\(547\) 8.25809 0.353090 0.176545 0.984293i \(-0.443508\pi\)
0.176545 + 0.984293i \(0.443508\pi\)
\(548\) −54.5341 −2.32958
\(549\) 0 0
\(550\) −28.4280 −1.21217
\(551\) 19.4586 0.828964
\(552\) 0 0
\(553\) 11.2201 0.477127
\(554\) −23.1702 −0.984408
\(555\) 0 0
\(556\) 98.9413 4.19605
\(557\) 12.2925 0.520852 0.260426 0.965494i \(-0.416137\pi\)
0.260426 + 0.965494i \(0.416137\pi\)
\(558\) 0 0
\(559\) 47.0269 1.98902
\(560\) −65.7111 −2.77680
\(561\) 0 0
\(562\) −51.5179 −2.17315
\(563\) 20.3279 0.856719 0.428359 0.903609i \(-0.359092\pi\)
0.428359 + 0.903609i \(0.359092\pi\)
\(564\) 0 0
\(565\) 18.0419 0.759028
\(566\) −75.2935 −3.16482
\(567\) 0 0
\(568\) 77.0831 3.23434
\(569\) 6.99933 0.293427 0.146714 0.989179i \(-0.453130\pi\)
0.146714 + 0.989179i \(0.453130\pi\)
\(570\) 0 0
\(571\) −28.0828 −1.17523 −0.587615 0.809141i \(-0.699933\pi\)
−0.587615 + 0.809141i \(0.699933\pi\)
\(572\) −21.9055 −0.915913
\(573\) 0 0
\(574\) −53.8736 −2.24864
\(575\) 52.6071 2.19387
\(576\) 0 0
\(577\) −20.0459 −0.834523 −0.417262 0.908786i \(-0.637010\pi\)
−0.417262 + 0.908786i \(0.637010\pi\)
\(578\) 43.4082 1.80554
\(579\) 0 0
\(580\) −79.1460 −3.28636
\(581\) −29.0489 −1.20515
\(582\) 0 0
\(583\) −9.68455 −0.401093
\(584\) 30.2793 1.25296
\(585\) 0 0
\(586\) 80.4459 3.32319
\(587\) 16.2870 0.672235 0.336118 0.941820i \(-0.390886\pi\)
0.336118 + 0.941820i \(0.390886\pi\)
\(588\) 0 0
\(589\) 8.25425 0.340111
\(590\) 21.0861 0.868099
\(591\) 0 0
\(592\) −16.9546 −0.696830
\(593\) 36.0721 1.48130 0.740652 0.671889i \(-0.234517\pi\)
0.740652 + 0.671889i \(0.234517\pi\)
\(594\) 0 0
\(595\) −2.78050 −0.113989
\(596\) −26.3596 −1.07973
\(597\) 0 0
\(598\) 58.1258 2.37694
\(599\) 12.5585 0.513125 0.256563 0.966528i \(-0.417410\pi\)
0.256563 + 0.966528i \(0.417410\pi\)
\(600\) 0 0
\(601\) 35.2090 1.43621 0.718103 0.695936i \(-0.245010\pi\)
0.718103 + 0.695936i \(0.245010\pi\)
\(602\) 51.9669 2.11801
\(603\) 0 0
\(604\) 20.8832 0.849724
\(605\) −4.00721 −0.162916
\(606\) 0 0
\(607\) 1.60580 0.0651773 0.0325886 0.999469i \(-0.489625\pi\)
0.0325886 + 0.999469i \(0.489625\pi\)
\(608\) −32.7926 −1.32991
\(609\) 0 0
\(610\) 10.3020 0.417117
\(611\) −24.8288 −1.00447
\(612\) 0 0
\(613\) −2.16291 −0.0873591 −0.0436796 0.999046i \(-0.513908\pi\)
−0.0436796 + 0.999046i \(0.513908\pi\)
\(614\) −0.523731 −0.0211361
\(615\) 0 0
\(616\) −13.7034 −0.552125
\(617\) 14.6864 0.591253 0.295627 0.955304i \(-0.404472\pi\)
0.295627 + 0.955304i \(0.404472\pi\)
\(618\) 0 0
\(619\) 47.1847 1.89651 0.948257 0.317505i \(-0.102845\pi\)
0.948257 + 0.317505i \(0.102845\pi\)
\(620\) −33.5734 −1.34834
\(621\) 0 0
\(622\) −39.8326 −1.59714
\(623\) 12.3681 0.495518
\(624\) 0 0
\(625\) 41.9849 1.67940
\(626\) 69.9294 2.79494
\(627\) 0 0
\(628\) −48.2753 −1.92639
\(629\) −0.717416 −0.0286053
\(630\) 0 0
\(631\) 44.0652 1.75421 0.877104 0.480300i \(-0.159472\pi\)
0.877104 + 0.480300i \(0.159472\pi\)
\(632\) −36.8471 −1.46570
\(633\) 0 0
\(634\) −30.6063 −1.21553
\(635\) 49.1196 1.94925
\(636\) 0 0
\(637\) 13.4362 0.532360
\(638\) −11.0160 −0.436128
\(639\) 0 0
\(640\) −32.0204 −1.26572
\(641\) 32.9295 1.30064 0.650319 0.759661i \(-0.274635\pi\)
0.650319 + 0.759661i \(0.274635\pi\)
\(642\) 0 0
\(643\) 34.3960 1.35645 0.678223 0.734856i \(-0.262750\pi\)
0.678223 + 0.734856i \(0.262750\pi\)
\(644\) 44.7952 1.76518
\(645\) 0 0
\(646\) −3.96567 −0.156027
\(647\) −40.6293 −1.59730 −0.798652 0.601793i \(-0.794453\pi\)
−0.798652 + 0.601793i \(0.794453\pi\)
\(648\) 0 0
\(649\) 2.04679 0.0803435
\(650\) 135.100 5.29908
\(651\) 0 0
\(652\) 55.3845 2.16903
\(653\) 0.882411 0.0345314 0.0172657 0.999851i \(-0.494504\pi\)
0.0172657 + 0.999851i \(0.494504\pi\)
\(654\) 0 0
\(655\) 56.7633 2.21793
\(656\) 82.3514 3.21528
\(657\) 0 0
\(658\) −27.4370 −1.06961
\(659\) −24.8985 −0.969906 −0.484953 0.874540i \(-0.661163\pi\)
−0.484953 + 0.874540i \(0.661163\pi\)
\(660\) 0 0
\(661\) 40.3972 1.57127 0.785635 0.618690i \(-0.212336\pi\)
0.785635 + 0.618690i \(0.212336\pi\)
\(662\) 13.9923 0.543828
\(663\) 0 0
\(664\) 95.3974 3.70214
\(665\) −37.1724 −1.44148
\(666\) 0 0
\(667\) 20.3856 0.789332
\(668\) −35.5958 −1.37724
\(669\) 0 0
\(670\) 54.7018 2.11331
\(671\) 1.00000 0.0386046
\(672\) 0 0
\(673\) −4.08661 −0.157527 −0.0787636 0.996893i \(-0.525097\pi\)
−0.0787636 + 0.996893i \(0.525097\pi\)
\(674\) −29.7180 −1.14469
\(675\) 0 0
\(676\) 44.1809 1.69927
\(677\) 3.16188 0.121521 0.0607604 0.998152i \(-0.480647\pi\)
0.0607604 + 0.998152i \(0.480647\pi\)
\(678\) 0 0
\(679\) 27.7820 1.06618
\(680\) 9.13121 0.350166
\(681\) 0 0
\(682\) −4.67295 −0.178936
\(683\) 2.84581 0.108892 0.0544459 0.998517i \(-0.482661\pi\)
0.0544459 + 0.998517i \(0.482661\pi\)
\(684\) 0 0
\(685\) 47.4098 1.81144
\(686\) 51.6088 1.97043
\(687\) 0 0
\(688\) −79.4368 −3.02850
\(689\) 46.0246 1.75340
\(690\) 0 0
\(691\) 24.9625 0.949620 0.474810 0.880088i \(-0.342517\pi\)
0.474810 + 0.880088i \(0.342517\pi\)
\(692\) −67.2576 −2.55675
\(693\) 0 0
\(694\) −89.8104 −3.40915
\(695\) −86.0157 −3.26276
\(696\) 0 0
\(697\) 3.48461 0.131989
\(698\) 42.3260 1.60206
\(699\) 0 0
\(700\) 104.116 3.93523
\(701\) −3.42189 −0.129243 −0.0646216 0.997910i \(-0.520584\pi\)
−0.0646216 + 0.997910i \(0.520584\pi\)
\(702\) 0 0
\(703\) −9.59112 −0.361736
\(704\) 2.50953 0.0945815
\(705\) 0 0
\(706\) 92.8250 3.49351
\(707\) 20.9699 0.788655
\(708\) 0 0
\(709\) −52.0319 −1.95410 −0.977050 0.213008i \(-0.931674\pi\)
−0.977050 + 0.213008i \(0.931674\pi\)
\(710\) −118.376 −4.44258
\(711\) 0 0
\(712\) −40.6172 −1.52219
\(713\) 8.64747 0.323850
\(714\) 0 0
\(715\) 19.0437 0.712196
\(716\) 60.6849 2.26790
\(717\) 0 0
\(718\) −41.4287 −1.54610
\(719\) 10.9759 0.409332 0.204666 0.978832i \(-0.434389\pi\)
0.204666 + 0.978832i \(0.434389\pi\)
\(720\) 0 0
\(721\) 22.1242 0.823947
\(722\) −4.17038 −0.155206
\(723\) 0 0
\(724\) −33.4689 −1.24386
\(725\) 47.3817 1.75971
\(726\) 0 0
\(727\) 32.1350 1.19182 0.595911 0.803051i \(-0.296791\pi\)
0.595911 + 0.803051i \(0.296791\pi\)
\(728\) 65.1235 2.41364
\(729\) 0 0
\(730\) −46.4998 −1.72103
\(731\) −3.36128 −0.124322
\(732\) 0 0
\(733\) 17.1024 0.631693 0.315846 0.948810i \(-0.397712\pi\)
0.315846 + 0.948810i \(0.397712\pi\)
\(734\) −92.0835 −3.39887
\(735\) 0 0
\(736\) −34.3547 −1.26633
\(737\) 5.30981 0.195589
\(738\) 0 0
\(739\) 43.8812 1.61420 0.807098 0.590417i \(-0.201037\pi\)
0.807098 + 0.590417i \(0.201037\pi\)
\(740\) 39.0109 1.43407
\(741\) 0 0
\(742\) 50.8593 1.86711
\(743\) 34.0979 1.25093 0.625465 0.780252i \(-0.284909\pi\)
0.625465 + 0.780252i \(0.284909\pi\)
\(744\) 0 0
\(745\) 22.9160 0.839577
\(746\) 47.2820 1.73112
\(747\) 0 0
\(748\) 1.56571 0.0572480
\(749\) 21.1923 0.774351
\(750\) 0 0
\(751\) −0.462726 −0.0168851 −0.00844255 0.999964i \(-0.502687\pi\)
−0.00844255 + 0.999964i \(0.502687\pi\)
\(752\) 41.9403 1.52941
\(753\) 0 0
\(754\) 52.3522 1.90655
\(755\) −18.1550 −0.660728
\(756\) 0 0
\(757\) −15.0488 −0.546957 −0.273479 0.961878i \(-0.588174\pi\)
−0.273479 + 0.961878i \(0.588174\pi\)
\(758\) 13.5498 0.492153
\(759\) 0 0
\(760\) 122.075 4.42812
\(761\) 3.40565 0.123455 0.0617274 0.998093i \(-0.480339\pi\)
0.0617274 + 0.998093i \(0.480339\pi\)
\(762\) 0 0
\(763\) −32.5306 −1.17769
\(764\) −14.0296 −0.507574
\(765\) 0 0
\(766\) 83.5963 3.02046
\(767\) −9.72709 −0.351225
\(768\) 0 0
\(769\) 16.3158 0.588363 0.294182 0.955750i \(-0.404953\pi\)
0.294182 + 0.955750i \(0.404953\pi\)
\(770\) 21.0442 0.758382
\(771\) 0 0
\(772\) 31.6038 1.13744
\(773\) −33.0741 −1.18959 −0.594797 0.803876i \(-0.702768\pi\)
−0.594797 + 0.803876i \(0.702768\pi\)
\(774\) 0 0
\(775\) 20.0991 0.721982
\(776\) −91.2368 −3.27521
\(777\) 0 0
\(778\) −62.6669 −2.24672
\(779\) 46.5857 1.66910
\(780\) 0 0
\(781\) −11.4906 −0.411166
\(782\) −4.15459 −0.148568
\(783\) 0 0
\(784\) −22.6961 −0.810575
\(785\) 41.9687 1.49793
\(786\) 0 0
\(787\) 13.5591 0.483328 0.241664 0.970360i \(-0.422307\pi\)
0.241664 + 0.970360i \(0.422307\pi\)
\(788\) 55.9464 1.99301
\(789\) 0 0
\(790\) 56.5860 2.01324
\(791\) −9.19709 −0.327011
\(792\) 0 0
\(793\) −4.75237 −0.168762
\(794\) 46.3466 1.64478
\(795\) 0 0
\(796\) −63.6326 −2.25540
\(797\) −18.0188 −0.638257 −0.319129 0.947711i \(-0.603390\pi\)
−0.319129 + 0.947711i \(0.603390\pi\)
\(798\) 0 0
\(799\) 1.77466 0.0627829
\(800\) −79.8500 −2.82312
\(801\) 0 0
\(802\) −75.0646 −2.65062
\(803\) −4.51365 −0.159283
\(804\) 0 0
\(805\) −38.9432 −1.37257
\(806\) 22.2076 0.782228
\(807\) 0 0
\(808\) −68.8657 −2.42269
\(809\) −11.1179 −0.390883 −0.195441 0.980715i \(-0.562614\pi\)
−0.195441 + 0.980715i \(0.562614\pi\)
\(810\) 0 0
\(811\) 9.75699 0.342614 0.171307 0.985218i \(-0.445201\pi\)
0.171307 + 0.985218i \(0.445201\pi\)
\(812\) 40.3457 1.41586
\(813\) 0 0
\(814\) 5.42978 0.190314
\(815\) −48.1491 −1.68659
\(816\) 0 0
\(817\) −44.9369 −1.57214
\(818\) −6.77362 −0.236834
\(819\) 0 0
\(820\) −189.483 −6.61702
\(821\) −17.6656 −0.616535 −0.308268 0.951300i \(-0.599749\pi\)
−0.308268 + 0.951300i \(0.599749\pi\)
\(822\) 0 0
\(823\) 45.2415 1.57702 0.788510 0.615022i \(-0.210853\pi\)
0.788510 + 0.615022i \(0.210853\pi\)
\(824\) −72.6563 −2.53110
\(825\) 0 0
\(826\) −10.7489 −0.374002
\(827\) 26.0944 0.907392 0.453696 0.891157i \(-0.350105\pi\)
0.453696 + 0.891157i \(0.350105\pi\)
\(828\) 0 0
\(829\) −36.7769 −1.27732 −0.638658 0.769491i \(-0.720510\pi\)
−0.638658 + 0.769491i \(0.720510\pi\)
\(830\) −146.501 −5.08514
\(831\) 0 0
\(832\) −11.9262 −0.413467
\(833\) −0.960361 −0.0332745
\(834\) 0 0
\(835\) 30.9456 1.07092
\(836\) 20.9319 0.723946
\(837\) 0 0
\(838\) 82.4541 2.84833
\(839\) 5.35112 0.184741 0.0923706 0.995725i \(-0.470556\pi\)
0.0923706 + 0.995725i \(0.470556\pi\)
\(840\) 0 0
\(841\) −10.6393 −0.366873
\(842\) −15.4861 −0.533686
\(843\) 0 0
\(844\) 62.1971 2.14091
\(845\) −38.4092 −1.32131
\(846\) 0 0
\(847\) 2.04273 0.0701890
\(848\) −77.7437 −2.66973
\(849\) 0 0
\(850\) −9.65641 −0.331212
\(851\) −10.0480 −0.344442
\(852\) 0 0
\(853\) 44.6105 1.52744 0.763718 0.645550i \(-0.223372\pi\)
0.763718 + 0.645550i \(0.223372\pi\)
\(854\) −5.25159 −0.179706
\(855\) 0 0
\(856\) −69.5961 −2.37875
\(857\) 7.03968 0.240471 0.120235 0.992745i \(-0.461635\pi\)
0.120235 + 0.992745i \(0.461635\pi\)
\(858\) 0 0
\(859\) 55.9231 1.90807 0.954036 0.299693i \(-0.0968841\pi\)
0.954036 + 0.299693i \(0.0968841\pi\)
\(860\) 182.776 6.23263
\(861\) 0 0
\(862\) −50.4632 −1.71878
\(863\) 47.1465 1.60489 0.802443 0.596729i \(-0.203533\pi\)
0.802443 + 0.596729i \(0.203533\pi\)
\(864\) 0 0
\(865\) 58.4711 1.98808
\(866\) −71.6190 −2.43371
\(867\) 0 0
\(868\) 17.1145 0.580903
\(869\) 5.49270 0.186327
\(870\) 0 0
\(871\) −25.2342 −0.855028
\(872\) 106.831 3.61776
\(873\) 0 0
\(874\) −55.5425 −1.87875
\(875\) −49.5865 −1.67633
\(876\) 0 0
\(877\) −15.8127 −0.533957 −0.266979 0.963702i \(-0.586025\pi\)
−0.266979 + 0.963702i \(0.586025\pi\)
\(878\) 65.5117 2.21091
\(879\) 0 0
\(880\) −32.1683 −1.08439
\(881\) −13.2185 −0.445343 −0.222672 0.974894i \(-0.571478\pi\)
−0.222672 + 0.974894i \(0.571478\pi\)
\(882\) 0 0
\(883\) −31.4226 −1.05746 −0.528728 0.848791i \(-0.677331\pi\)
−0.528728 + 0.848791i \(0.677331\pi\)
\(884\) −7.44083 −0.250262
\(885\) 0 0
\(886\) 74.6211 2.50694
\(887\) 26.4566 0.888326 0.444163 0.895946i \(-0.353501\pi\)
0.444163 + 0.895946i \(0.353501\pi\)
\(888\) 0 0
\(889\) −25.0394 −0.839793
\(890\) 62.3757 2.09084
\(891\) 0 0
\(892\) −16.8619 −0.564579
\(893\) 23.7254 0.793939
\(894\) 0 0
\(895\) −52.7570 −1.76347
\(896\) 16.3228 0.545307
\(897\) 0 0
\(898\) 59.9059 1.99909
\(899\) 7.78852 0.259762
\(900\) 0 0
\(901\) −3.28964 −0.109594
\(902\) −26.3733 −0.878136
\(903\) 0 0
\(904\) 30.2035 1.00455
\(905\) 29.0965 0.967201
\(906\) 0 0
\(907\) −34.1071 −1.13251 −0.566254 0.824231i \(-0.691608\pi\)
−0.566254 + 0.824231i \(0.691608\pi\)
\(908\) 30.9826 1.02819
\(909\) 0 0
\(910\) −100.010 −3.31530
\(911\) −9.45811 −0.313361 −0.156681 0.987649i \(-0.550079\pi\)
−0.156681 + 0.987649i \(0.550079\pi\)
\(912\) 0 0
\(913\) −14.2207 −0.470635
\(914\) −99.8805 −3.30375
\(915\) 0 0
\(916\) −5.70485 −0.188494
\(917\) −28.9359 −0.955546
\(918\) 0 0
\(919\) 21.9708 0.724750 0.362375 0.932032i \(-0.381966\pi\)
0.362375 + 0.932032i \(0.381966\pi\)
\(920\) 127.890 4.21642
\(921\) 0 0
\(922\) 6.23557 0.205357
\(923\) 54.6075 1.79743
\(924\) 0 0
\(925\) −23.3544 −0.767887
\(926\) −95.9867 −3.15432
\(927\) 0 0
\(928\) −30.9423 −1.01573
\(929\) 0.381863 0.0125285 0.00626425 0.999980i \(-0.498006\pi\)
0.00626425 + 0.999980i \(0.498006\pi\)
\(930\) 0 0
\(931\) −12.8390 −0.420782
\(932\) −59.5987 −1.95222
\(933\) 0 0
\(934\) −19.4332 −0.635873
\(935\) −1.36117 −0.0445149
\(936\) 0 0
\(937\) −45.5441 −1.48786 −0.743931 0.668256i \(-0.767041\pi\)
−0.743931 + 0.668256i \(0.767041\pi\)
\(938\) −27.8850 −0.910477
\(939\) 0 0
\(940\) −96.5007 −3.14750
\(941\) 24.7833 0.807911 0.403956 0.914779i \(-0.367635\pi\)
0.403956 + 0.914779i \(0.367635\pi\)
\(942\) 0 0
\(943\) 48.8049 1.58931
\(944\) 16.4308 0.534777
\(945\) 0 0
\(946\) 25.4399 0.827124
\(947\) −3.66692 −0.119159 −0.0595794 0.998224i \(-0.518976\pi\)
−0.0595794 + 0.998224i \(0.518976\pi\)
\(948\) 0 0
\(949\) 21.4505 0.696314
\(950\) −129.096 −4.18844
\(951\) 0 0
\(952\) −4.65476 −0.150862
\(953\) 55.9404 1.81209 0.906044 0.423184i \(-0.139088\pi\)
0.906044 + 0.423184i \(0.139088\pi\)
\(954\) 0 0
\(955\) 12.1968 0.394679
\(956\) 85.4845 2.76477
\(957\) 0 0
\(958\) −91.9380 −2.97038
\(959\) −24.1678 −0.780419
\(960\) 0 0
\(961\) −27.6961 −0.893424
\(962\) −25.8043 −0.831965
\(963\) 0 0
\(964\) −128.111 −4.12618
\(965\) −27.4751 −0.884454
\(966\) 0 0
\(967\) 40.3407 1.29727 0.648634 0.761100i \(-0.275341\pi\)
0.648634 + 0.761100i \(0.275341\pi\)
\(968\) −6.70837 −0.215615
\(969\) 0 0
\(970\) 140.112 4.49873
\(971\) −23.6883 −0.760193 −0.380096 0.924947i \(-0.624109\pi\)
−0.380096 + 0.924947i \(0.624109\pi\)
\(972\) 0 0
\(973\) 43.8476 1.40569
\(974\) 16.4338 0.526574
\(975\) 0 0
\(976\) 8.02760 0.256957
\(977\) −10.2404 −0.327620 −0.163810 0.986492i \(-0.552378\pi\)
−0.163810 + 0.986492i \(0.552378\pi\)
\(978\) 0 0
\(979\) 6.05470 0.193509
\(980\) 52.2215 1.66816
\(981\) 0 0
\(982\) 43.1632 1.37739
\(983\) 26.3822 0.841461 0.420730 0.907186i \(-0.361774\pi\)
0.420730 + 0.907186i \(0.361774\pi\)
\(984\) 0 0
\(985\) −48.6376 −1.54972
\(986\) −3.74191 −0.119167
\(987\) 0 0
\(988\) −99.4763 −3.16476
\(989\) −47.0776 −1.49698
\(990\) 0 0
\(991\) 35.8606 1.13915 0.569575 0.821939i \(-0.307108\pi\)
0.569575 + 0.821939i \(0.307108\pi\)
\(992\) −13.1256 −0.416738
\(993\) 0 0
\(994\) 60.3439 1.91399
\(995\) 55.3197 1.75375
\(996\) 0 0
\(997\) 7.80670 0.247241 0.123620 0.992330i \(-0.460550\pi\)
0.123620 + 0.992330i \(0.460550\pi\)
\(998\) −6.15707 −0.194899
\(999\) 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 \(a_p\))