Properties

Label 6039.2.a.j.1.9
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 1.9
Root \(0.546298\)
Character \(\chi\) = 6039.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.546298 q^{2}\) \(-1.70156 q^{4}\) \(+0.842631 q^{5}\) \(-4.19208 q^{7}\) \(-2.02216 q^{8}\) \(+O(q^{10})\) \(q\)\(+0.546298 q^{2}\) \(-1.70156 q^{4}\) \(+0.842631 q^{5}\) \(-4.19208 q^{7}\) \(-2.02216 q^{8}\) \(+0.460328 q^{10}\) \(+1.00000 q^{11}\) \(-5.95974 q^{13}\) \(-2.29012 q^{14}\) \(+2.29842 q^{16}\) \(-0.386200 q^{17}\) \(-2.95453 q^{19}\) \(-1.43379 q^{20}\) \(+0.546298 q^{22}\) \(+0.974992 q^{23}\) \(-4.28997 q^{25}\) \(-3.25580 q^{26}\) \(+7.13306 q^{28}\) \(+10.0563 q^{29}\) \(-10.6290 q^{31}\) \(+5.29993 q^{32}\) \(-0.210980 q^{34}\) \(-3.53237 q^{35}\) \(-3.16781 q^{37}\) \(-1.61405 q^{38}\) \(-1.70393 q^{40}\) \(+1.29317 q^{41}\) \(-4.99709 q^{43}\) \(-1.70156 q^{44}\) \(+0.532636 q^{46}\) \(-7.87272 q^{47}\) \(+10.5735 q^{49}\) \(-2.34361 q^{50}\) \(+10.1408 q^{52}\) \(-0.370002 q^{53}\) \(+0.842631 q^{55}\) \(+8.47703 q^{56}\) \(+5.49376 q^{58}\) \(-13.7723 q^{59}\) \(+1.00000 q^{61}\) \(-5.80661 q^{62}\) \(-1.70149 q^{64}\) \(-5.02186 q^{65}\) \(+9.80901 q^{67}\) \(+0.657141 q^{68}\) \(-1.92973 q^{70}\) \(+4.36706 q^{71}\) \(-2.06518 q^{73}\) \(-1.73057 q^{74}\) \(+5.02730 q^{76}\) \(-4.19208 q^{77}\) \(-8.67552 q^{79}\) \(+1.93672 q^{80}\) \(+0.706457 q^{82}\) \(+7.09673 q^{83}\) \(-0.325424 q^{85}\) \(-2.72990 q^{86}\) \(-2.02216 q^{88}\) \(+7.42432 q^{89}\) \(+24.9837 q^{91}\) \(-1.65901 q^{92}\) \(-4.30086 q^{94}\) \(-2.48957 q^{95}\) \(-6.00940 q^{97}\) \(+5.77628 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut +\mathstrut q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut +\mathstrut 17q^{16} \) \(\mathstrut +\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 22q^{19} \) \(\mathstrut -\mathstrut 23q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 25q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut +\mathstrut 37q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 9q^{31} \) \(\mathstrut -\mathstrut 4q^{32} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 18q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 25q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 36q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut -\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 13q^{52} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 40q^{56} \) \(\mathstrut +\mathstrut 33q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut +\mathstrut 14q^{61} \) \(\mathstrut +\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 6q^{64} \) \(\mathstrut +\mathstrut 61q^{65} \) \(\mathstrut +\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 66q^{68} \) \(\mathstrut +\mathstrut 44q^{70} \) \(\mathstrut +\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 12q^{74} \) \(\mathstrut +\mathstrut 49q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut -\mathstrut 88q^{80} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 32q^{83} \) \(\mathstrut +\mathstrut 2q^{85} \) \(\mathstrut +\mathstrut 14q^{86} \) \(\mathstrut +\mathstrut 21q^{89} \) \(\mathstrut +\mathstrut 45q^{91} \) \(\mathstrut +\mathstrut 14q^{92} \) \(\mathstrut -\mathstrut 31q^{94} \) \(\mathstrut -\mathstrut 23q^{95} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut +\mathstrut 38q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.546298 0.386291 0.193146 0.981170i \(-0.438131\pi\)
0.193146 + 0.981170i \(0.438131\pi\)
\(3\) 0 0
\(4\) −1.70156 −0.850779
\(5\) 0.842631 0.376836 0.188418 0.982089i \(-0.439664\pi\)
0.188418 + 0.982089i \(0.439664\pi\)
\(6\) 0 0
\(7\) −4.19208 −1.58446 −0.792228 0.610226i \(-0.791079\pi\)
−0.792228 + 0.610226i \(0.791079\pi\)
\(8\) −2.02216 −0.714940
\(9\) 0 0
\(10\) 0.460328 0.145568
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) −5.95974 −1.65293 −0.826467 0.562985i \(-0.809653\pi\)
−0.826467 + 0.562985i \(0.809653\pi\)
\(14\) −2.29012 −0.612061
\(15\) 0 0
\(16\) 2.29842 0.574604
\(17\) −0.386200 −0.0936672 −0.0468336 0.998903i \(-0.514913\pi\)
−0.0468336 + 0.998903i \(0.514913\pi\)
\(18\) 0 0
\(19\) −2.95453 −0.677815 −0.338907 0.940820i \(-0.610057\pi\)
−0.338907 + 0.940820i \(0.610057\pi\)
\(20\) −1.43379 −0.320604
\(21\) 0 0
\(22\) 0.546298 0.116471
\(23\) 0.974992 0.203300 0.101650 0.994820i \(-0.467588\pi\)
0.101650 + 0.994820i \(0.467588\pi\)
\(24\) 0 0
\(25\) −4.28997 −0.857995
\(26\) −3.25580 −0.638514
\(27\) 0 0
\(28\) 7.13306 1.34802
\(29\) 10.0563 1.86741 0.933707 0.358038i \(-0.116554\pi\)
0.933707 + 0.358038i \(0.116554\pi\)
\(30\) 0 0
\(31\) −10.6290 −1.90902 −0.954512 0.298171i \(-0.903623\pi\)
−0.954512 + 0.298171i \(0.903623\pi\)
\(32\) 5.29993 0.936904
\(33\) 0 0
\(34\) −0.210980 −0.0361828
\(35\) −3.53237 −0.597080
\(36\) 0 0
\(37\) −3.16781 −0.520785 −0.260392 0.965503i \(-0.583852\pi\)
−0.260392 + 0.965503i \(0.583852\pi\)
\(38\) −1.61405 −0.261834
\(39\) 0 0
\(40\) −1.70393 −0.269415
\(41\) 1.29317 0.201959 0.100980 0.994888i \(-0.467802\pi\)
0.100980 + 0.994888i \(0.467802\pi\)
\(42\) 0 0
\(43\) −4.99709 −0.762050 −0.381025 0.924565i \(-0.624429\pi\)
−0.381025 + 0.924565i \(0.624429\pi\)
\(44\) −1.70156 −0.256520
\(45\) 0 0
\(46\) 0.532636 0.0785330
\(47\) −7.87272 −1.14835 −0.574177 0.818731i \(-0.694678\pi\)
−0.574177 + 0.818731i \(0.694678\pi\)
\(48\) 0 0
\(49\) 10.5735 1.51050
\(50\) −2.34361 −0.331436
\(51\) 0 0
\(52\) 10.1408 1.40628
\(53\) −0.370002 −0.0508237 −0.0254119 0.999677i \(-0.508090\pi\)
−0.0254119 + 0.999677i \(0.508090\pi\)
\(54\) 0 0
\(55\) 0.842631 0.113620
\(56\) 8.47703 1.13279
\(57\) 0 0
\(58\) 5.49376 0.721366
\(59\) −13.7723 −1.79299 −0.896497 0.443049i \(-0.853897\pi\)
−0.896497 + 0.443049i \(0.853897\pi\)
\(60\) 0 0
\(61\) 1.00000 0.128037
\(62\) −5.80661 −0.737440
\(63\) 0 0
\(64\) −1.70149 −0.212686
\(65\) −5.02186 −0.622885
\(66\) 0 0
\(67\) 9.80901 1.19836 0.599181 0.800614i \(-0.295493\pi\)
0.599181 + 0.800614i \(0.295493\pi\)
\(68\) 0.657141 0.0796901
\(69\) 0 0
\(70\) −1.92973 −0.230647
\(71\) 4.36706 0.518274 0.259137 0.965841i \(-0.416562\pi\)
0.259137 + 0.965841i \(0.416562\pi\)
\(72\) 0 0
\(73\) −2.06518 −0.241711 −0.120855 0.992670i \(-0.538564\pi\)
−0.120855 + 0.992670i \(0.538564\pi\)
\(74\) −1.73057 −0.201175
\(75\) 0 0
\(76\) 5.02730 0.576671
\(77\) −4.19208 −0.477731
\(78\) 0 0
\(79\) −8.67552 −0.976072 −0.488036 0.872823i \(-0.662287\pi\)
−0.488036 + 0.872823i \(0.662287\pi\)
\(80\) 1.93672 0.216531
\(81\) 0 0
\(82\) 0.706457 0.0780151
\(83\) 7.09673 0.778967 0.389483 0.921033i \(-0.372654\pi\)
0.389483 + 0.921033i \(0.372654\pi\)
\(84\) 0 0
\(85\) −0.325424 −0.0352972
\(86\) −2.72990 −0.294373
\(87\) 0 0
\(88\) −2.02216 −0.215562
\(89\) 7.42432 0.786976 0.393488 0.919330i \(-0.371268\pi\)
0.393488 + 0.919330i \(0.371268\pi\)
\(90\) 0 0
\(91\) 24.9837 2.61900
\(92\) −1.65901 −0.172963
\(93\) 0 0
\(94\) −4.30086 −0.443599
\(95\) −2.48957 −0.255425
\(96\) 0 0
\(97\) −6.00940 −0.610162 −0.305081 0.952326i \(-0.598684\pi\)
−0.305081 + 0.952326i \(0.598684\pi\)
\(98\) 5.77628 0.583493
\(99\) 0 0
\(100\) 7.29964 0.729964
\(101\) 18.1851 1.80948 0.904742 0.425961i \(-0.140064\pi\)
0.904742 + 0.425961i \(0.140064\pi\)
\(102\) 0 0
\(103\) 10.9494 1.07887 0.539436 0.842026i \(-0.318637\pi\)
0.539436 + 0.842026i \(0.318637\pi\)
\(104\) 12.0515 1.18175
\(105\) 0 0
\(106\) −0.202132 −0.0196328
\(107\) −2.84318 −0.274860 −0.137430 0.990511i \(-0.543884\pi\)
−0.137430 + 0.990511i \(0.543884\pi\)
\(108\) 0 0
\(109\) 19.4494 1.86291 0.931456 0.363855i \(-0.118540\pi\)
0.931456 + 0.363855i \(0.118540\pi\)
\(110\) 0.460328 0.0438905
\(111\) 0 0
\(112\) −9.63513 −0.910434
\(113\) −8.08952 −0.760998 −0.380499 0.924781i \(-0.624248\pi\)
−0.380499 + 0.924781i \(0.624248\pi\)
\(114\) 0 0
\(115\) 0.821558 0.0766107
\(116\) −17.1114 −1.58876
\(117\) 0 0
\(118\) −7.52376 −0.692618
\(119\) 1.61898 0.148411
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0.546298 0.0494595
\(123\) 0 0
\(124\) 18.0859 1.62416
\(125\) −7.82802 −0.700159
\(126\) 0 0
\(127\) 1.18990 0.105587 0.0527934 0.998605i \(-0.483188\pi\)
0.0527934 + 0.998605i \(0.483188\pi\)
\(128\) −11.5294 −1.01906
\(129\) 0 0
\(130\) −2.74343 −0.240615
\(131\) 0.232276 0.0202940 0.0101470 0.999949i \(-0.496770\pi\)
0.0101470 + 0.999949i \(0.496770\pi\)
\(132\) 0 0
\(133\) 12.3856 1.07397
\(134\) 5.35865 0.462917
\(135\) 0 0
\(136\) 0.780956 0.0669664
\(137\) 13.7946 1.17855 0.589276 0.807932i \(-0.299413\pi\)
0.589276 + 0.807932i \(0.299413\pi\)
\(138\) 0 0
\(139\) 10.2427 0.868777 0.434388 0.900726i \(-0.356965\pi\)
0.434388 + 0.900726i \(0.356965\pi\)
\(140\) 6.01053 0.507983
\(141\) 0 0
\(142\) 2.38572 0.200205
\(143\) −5.95974 −0.498378
\(144\) 0 0
\(145\) 8.47377 0.703709
\(146\) −1.12820 −0.0933708
\(147\) 0 0
\(148\) 5.39021 0.443073
\(149\) 2.70615 0.221697 0.110848 0.993837i \(-0.464643\pi\)
0.110848 + 0.993837i \(0.464643\pi\)
\(150\) 0 0
\(151\) −15.6416 −1.27290 −0.636448 0.771319i \(-0.719597\pi\)
−0.636448 + 0.771319i \(0.719597\pi\)
\(152\) 5.97451 0.484597
\(153\) 0 0
\(154\) −2.29012 −0.184543
\(155\) −8.95632 −0.719389
\(156\) 0 0
\(157\) 3.50083 0.279397 0.139698 0.990194i \(-0.455387\pi\)
0.139698 + 0.990194i \(0.455387\pi\)
\(158\) −4.73942 −0.377048
\(159\) 0 0
\(160\) 4.46589 0.353059
\(161\) −4.08724 −0.322120
\(162\) 0 0
\(163\) 16.8255 1.31788 0.658938 0.752197i \(-0.271006\pi\)
0.658938 + 0.752197i \(0.271006\pi\)
\(164\) −2.20040 −0.171823
\(165\) 0 0
\(166\) 3.87693 0.300908
\(167\) −18.1086 −1.40129 −0.700645 0.713510i \(-0.747104\pi\)
−0.700645 + 0.713510i \(0.747104\pi\)
\(168\) 0 0
\(169\) 22.5185 1.73219
\(170\) −0.177778 −0.0136350
\(171\) 0 0
\(172\) 8.50285 0.648336
\(173\) 9.84724 0.748672 0.374336 0.927293i \(-0.377871\pi\)
0.374336 + 0.927293i \(0.377871\pi\)
\(174\) 0 0
\(175\) 17.9839 1.35945
\(176\) 2.29842 0.173250
\(177\) 0 0
\(178\) 4.05589 0.304002
\(179\) 10.0310 0.749749 0.374875 0.927075i \(-0.377686\pi\)
0.374875 + 0.927075i \(0.377686\pi\)
\(180\) 0 0
\(181\) −13.2298 −0.983362 −0.491681 0.870775i \(-0.663617\pi\)
−0.491681 + 0.870775i \(0.663617\pi\)
\(182\) 13.6485 1.01170
\(183\) 0 0
\(184\) −1.97158 −0.145347
\(185\) −2.66929 −0.196250
\(186\) 0 0
\(187\) −0.386200 −0.0282417
\(188\) 13.3959 0.976996
\(189\) 0 0
\(190\) −1.36005 −0.0986684
\(191\) 26.0670 1.88614 0.943069 0.332596i \(-0.107925\pi\)
0.943069 + 0.332596i \(0.107925\pi\)
\(192\) 0 0
\(193\) −1.64976 −0.118752 −0.0593760 0.998236i \(-0.518911\pi\)
−0.0593760 + 0.998236i \(0.518911\pi\)
\(194\) −3.28292 −0.235700
\(195\) 0 0
\(196\) −17.9914 −1.28510
\(197\) 15.0092 1.06936 0.534681 0.845054i \(-0.320432\pi\)
0.534681 + 0.845054i \(0.320432\pi\)
\(198\) 0 0
\(199\) 0.432727 0.0306752 0.0153376 0.999882i \(-0.495118\pi\)
0.0153376 + 0.999882i \(0.495118\pi\)
\(200\) 8.67499 0.613415
\(201\) 0 0
\(202\) 9.93448 0.698988
\(203\) −42.1569 −2.95883
\(204\) 0 0
\(205\) 1.08967 0.0761055
\(206\) 5.98162 0.416759
\(207\) 0 0
\(208\) −13.6980 −0.949783
\(209\) −2.95453 −0.204369
\(210\) 0 0
\(211\) −5.99457 −0.412683 −0.206342 0.978480i \(-0.566156\pi\)
−0.206342 + 0.978480i \(0.566156\pi\)
\(212\) 0.629580 0.0432398
\(213\) 0 0
\(214\) −1.55322 −0.106176
\(215\) −4.21070 −0.287168
\(216\) 0 0
\(217\) 44.5576 3.02476
\(218\) 10.6252 0.719626
\(219\) 0 0
\(220\) −1.43379 −0.0966658
\(221\) 2.30165 0.154826
\(222\) 0 0
\(223\) 1.20744 0.0808559 0.0404280 0.999182i \(-0.487128\pi\)
0.0404280 + 0.999182i \(0.487128\pi\)
\(224\) −22.2177 −1.48448
\(225\) 0 0
\(226\) −4.41929 −0.293967
\(227\) −3.17333 −0.210621 −0.105311 0.994439i \(-0.533584\pi\)
−0.105311 + 0.994439i \(0.533584\pi\)
\(228\) 0 0
\(229\) −26.1824 −1.73018 −0.865091 0.501614i \(-0.832740\pi\)
−0.865091 + 0.501614i \(0.832740\pi\)
\(230\) 0.448816 0.0295940
\(231\) 0 0
\(232\) −20.3355 −1.33509
\(233\) −15.3586 −1.00617 −0.503087 0.864236i \(-0.667803\pi\)
−0.503087 + 0.864236i \(0.667803\pi\)
\(234\) 0 0
\(235\) −6.63380 −0.432741
\(236\) 23.4343 1.52544
\(237\) 0 0
\(238\) 0.884445 0.0573301
\(239\) 6.48318 0.419362 0.209681 0.977770i \(-0.432757\pi\)
0.209681 + 0.977770i \(0.432757\pi\)
\(240\) 0 0
\(241\) −2.05017 −0.132063 −0.0660315 0.997818i \(-0.521034\pi\)
−0.0660315 + 0.997818i \(0.521034\pi\)
\(242\) 0.546298 0.0351174
\(243\) 0 0
\(244\) −1.70156 −0.108931
\(245\) 8.90955 0.569210
\(246\) 0 0
\(247\) 17.6082 1.12038
\(248\) 21.4935 1.36484
\(249\) 0 0
\(250\) −4.27643 −0.270465
\(251\) −0.403663 −0.0254790 −0.0127395 0.999919i \(-0.504055\pi\)
−0.0127395 + 0.999919i \(0.504055\pi\)
\(252\) 0 0
\(253\) 0.974992 0.0612972
\(254\) 0.650042 0.0407873
\(255\) 0 0
\(256\) −2.89551 −0.180969
\(257\) 3.52100 0.219634 0.109817 0.993952i \(-0.464973\pi\)
0.109817 + 0.993952i \(0.464973\pi\)
\(258\) 0 0
\(259\) 13.2797 0.825160
\(260\) 8.54498 0.529937
\(261\) 0 0
\(262\) 0.126892 0.00783940
\(263\) −25.3122 −1.56082 −0.780408 0.625271i \(-0.784988\pi\)
−0.780408 + 0.625271i \(0.784988\pi\)
\(264\) 0 0
\(265\) −0.311775 −0.0191522
\(266\) 6.76623 0.414864
\(267\) 0 0
\(268\) −16.6906 −1.01954
\(269\) −26.8357 −1.63620 −0.818100 0.575076i \(-0.804972\pi\)
−0.818100 + 0.575076i \(0.804972\pi\)
\(270\) 0 0
\(271\) −8.80885 −0.535099 −0.267550 0.963544i \(-0.586214\pi\)
−0.267550 + 0.963544i \(0.586214\pi\)
\(272\) −0.887648 −0.0538215
\(273\) 0 0
\(274\) 7.53597 0.455264
\(275\) −4.28997 −0.258695
\(276\) 0 0
\(277\) 21.3581 1.28328 0.641641 0.767005i \(-0.278254\pi\)
0.641641 + 0.767005i \(0.278254\pi\)
\(278\) 5.59559 0.335601
\(279\) 0 0
\(280\) 7.14300 0.426876
\(281\) 29.9872 1.78889 0.894444 0.447181i \(-0.147572\pi\)
0.894444 + 0.447181i \(0.147572\pi\)
\(282\) 0 0
\(283\) 10.0912 0.599862 0.299931 0.953961i \(-0.403036\pi\)
0.299931 + 0.953961i \(0.403036\pi\)
\(284\) −7.43080 −0.440937
\(285\) 0 0
\(286\) −3.25580 −0.192519
\(287\) −5.42107 −0.319996
\(288\) 0 0
\(289\) −16.8508 −0.991226
\(290\) 4.62921 0.271837
\(291\) 0 0
\(292\) 3.51402 0.205643
\(293\) 11.7387 0.685783 0.342892 0.939375i \(-0.388594\pi\)
0.342892 + 0.939375i \(0.388594\pi\)
\(294\) 0 0
\(295\) −11.6049 −0.675665
\(296\) 6.40580 0.372330
\(297\) 0 0
\(298\) 1.47837 0.0856395
\(299\) −5.81070 −0.336041
\(300\) 0 0
\(301\) 20.9482 1.20743
\(302\) −8.54499 −0.491709
\(303\) 0 0
\(304\) −6.79073 −0.389475
\(305\) 0.842631 0.0482489
\(306\) 0 0
\(307\) 12.1646 0.694269 0.347135 0.937815i \(-0.387155\pi\)
0.347135 + 0.937815i \(0.387155\pi\)
\(308\) 7.13306 0.406444
\(309\) 0 0
\(310\) −4.89282 −0.277894
\(311\) 10.4238 0.591079 0.295539 0.955331i \(-0.404501\pi\)
0.295539 + 0.955331i \(0.404501\pi\)
\(312\) 0 0
\(313\) −3.70708 −0.209536 −0.104768 0.994497i \(-0.533410\pi\)
−0.104768 + 0.994497i \(0.533410\pi\)
\(314\) 1.91250 0.107928
\(315\) 0 0
\(316\) 14.7619 0.830422
\(317\) 17.7635 0.997696 0.498848 0.866690i \(-0.333757\pi\)
0.498848 + 0.866690i \(0.333757\pi\)
\(318\) 0 0
\(319\) 10.0563 0.563046
\(320\) −1.43373 −0.0801477
\(321\) 0 0
\(322\) −2.23285 −0.124432
\(323\) 1.14104 0.0634890
\(324\) 0 0
\(325\) 25.5671 1.41821
\(326\) 9.19176 0.509084
\(327\) 0 0
\(328\) −2.61499 −0.144389
\(329\) 33.0030 1.81952
\(330\) 0 0
\(331\) 25.2813 1.38959 0.694794 0.719209i \(-0.255496\pi\)
0.694794 + 0.719209i \(0.255496\pi\)
\(332\) −12.0755 −0.662729
\(333\) 0 0
\(334\) −9.89273 −0.541306
\(335\) 8.26538 0.451586
\(336\) 0 0
\(337\) −15.8267 −0.862134 −0.431067 0.902320i \(-0.641863\pi\)
−0.431067 + 0.902320i \(0.641863\pi\)
\(338\) 12.3018 0.669130
\(339\) 0 0
\(340\) 0.553727 0.0300301
\(341\) −10.6290 −0.575593
\(342\) 0 0
\(343\) −14.9804 −0.808863
\(344\) 10.1049 0.544820
\(345\) 0 0
\(346\) 5.37953 0.289205
\(347\) 14.2210 0.763424 0.381712 0.924281i \(-0.375335\pi\)
0.381712 + 0.924281i \(0.375335\pi\)
\(348\) 0 0
\(349\) 20.6858 1.10728 0.553642 0.832755i \(-0.313238\pi\)
0.553642 + 0.832755i \(0.313238\pi\)
\(350\) 9.82457 0.525145
\(351\) 0 0
\(352\) 5.29993 0.282487
\(353\) 13.3604 0.711102 0.355551 0.934657i \(-0.384293\pi\)
0.355551 + 0.934657i \(0.384293\pi\)
\(354\) 0 0
\(355\) 3.67981 0.195304
\(356\) −12.6329 −0.669543
\(357\) 0 0
\(358\) 5.47990 0.289622
\(359\) 10.9660 0.578761 0.289381 0.957214i \(-0.406551\pi\)
0.289381 + 0.957214i \(0.406551\pi\)
\(360\) 0 0
\(361\) −10.2708 −0.540567
\(362\) −7.22741 −0.379864
\(363\) 0 0
\(364\) −42.5112 −2.22819
\(365\) −1.74018 −0.0910854
\(366\) 0 0
\(367\) −18.2275 −0.951468 −0.475734 0.879589i \(-0.657818\pi\)
−0.475734 + 0.879589i \(0.657818\pi\)
\(368\) 2.24094 0.116817
\(369\) 0 0
\(370\) −1.45823 −0.0758098
\(371\) 1.55108 0.0805279
\(372\) 0 0
\(373\) −14.3974 −0.745467 −0.372733 0.927938i \(-0.621579\pi\)
−0.372733 + 0.927938i \(0.621579\pi\)
\(374\) −0.210980 −0.0109095
\(375\) 0 0
\(376\) 15.9199 0.821005
\(377\) −59.9331 −3.08671
\(378\) 0 0
\(379\) 11.1418 0.572316 0.286158 0.958182i \(-0.407622\pi\)
0.286158 + 0.958182i \(0.407622\pi\)
\(380\) 4.23616 0.217310
\(381\) 0 0
\(382\) 14.2403 0.728599
\(383\) 13.6433 0.697140 0.348570 0.937283i \(-0.386667\pi\)
0.348570 + 0.937283i \(0.386667\pi\)
\(384\) 0 0
\(385\) −3.53237 −0.180026
\(386\) −0.901260 −0.0458729
\(387\) 0 0
\(388\) 10.2253 0.519113
\(389\) −23.6998 −1.20163 −0.600814 0.799389i \(-0.705157\pi\)
−0.600814 + 0.799389i \(0.705157\pi\)
\(390\) 0 0
\(391\) −0.376542 −0.0190425
\(392\) −21.3812 −1.07992
\(393\) 0 0
\(394\) 8.19951 0.413086
\(395\) −7.31026 −0.367819
\(396\) 0 0
\(397\) −19.8855 −0.998023 −0.499011 0.866595i \(-0.666303\pi\)
−0.499011 + 0.866595i \(0.666303\pi\)
\(398\) 0.236398 0.0118496
\(399\) 0 0
\(400\) −9.86014 −0.493007
\(401\) 15.1693 0.757517 0.378758 0.925496i \(-0.376351\pi\)
0.378758 + 0.925496i \(0.376351\pi\)
\(402\) 0 0
\(403\) 63.3461 3.15549
\(404\) −30.9430 −1.53947
\(405\) 0 0
\(406\) −23.0302 −1.14297
\(407\) −3.16781 −0.157022
\(408\) 0 0
\(409\) −20.3853 −1.00799 −0.503995 0.863706i \(-0.668137\pi\)
−0.503995 + 0.863706i \(0.668137\pi\)
\(410\) 0.595282 0.0293989
\(411\) 0 0
\(412\) −18.6310 −0.917882
\(413\) 57.7343 2.84092
\(414\) 0 0
\(415\) 5.97992 0.293543
\(416\) −31.5862 −1.54864
\(417\) 0 0
\(418\) −1.61405 −0.0789459
\(419\) −19.1519 −0.935633 −0.467817 0.883826i \(-0.654959\pi\)
−0.467817 + 0.883826i \(0.654959\pi\)
\(420\) 0 0
\(421\) −8.29681 −0.404362 −0.202181 0.979348i \(-0.564803\pi\)
−0.202181 + 0.979348i \(0.564803\pi\)
\(422\) −3.27482 −0.159416
\(423\) 0 0
\(424\) 0.748202 0.0363359
\(425\) 1.65679 0.0803660
\(426\) 0 0
\(427\) −4.19208 −0.202869
\(428\) 4.83783 0.233845
\(429\) 0 0
\(430\) −2.30030 −0.110930
\(431\) 17.6981 0.852485 0.426243 0.904609i \(-0.359837\pi\)
0.426243 + 0.904609i \(0.359837\pi\)
\(432\) 0 0
\(433\) 5.57917 0.268118 0.134059 0.990973i \(-0.457199\pi\)
0.134059 + 0.990973i \(0.457199\pi\)
\(434\) 24.3417 1.16844
\(435\) 0 0
\(436\) −33.0942 −1.58493
\(437\) −2.88064 −0.137800
\(438\) 0 0
\(439\) −6.90623 −0.329616 −0.164808 0.986326i \(-0.552701\pi\)
−0.164808 + 0.986326i \(0.552701\pi\)
\(440\) −1.70393 −0.0812317
\(441\) 0 0
\(442\) 1.25739 0.0598078
\(443\) −8.54914 −0.406182 −0.203091 0.979160i \(-0.565099\pi\)
−0.203091 + 0.979160i \(0.565099\pi\)
\(444\) 0 0
\(445\) 6.25596 0.296561
\(446\) 0.659621 0.0312339
\(447\) 0 0
\(448\) 7.13276 0.336991
\(449\) 22.1028 1.04309 0.521547 0.853223i \(-0.325355\pi\)
0.521547 + 0.853223i \(0.325355\pi\)
\(450\) 0 0
\(451\) 1.29317 0.0608930
\(452\) 13.7648 0.647441
\(453\) 0 0
\(454\) −1.73358 −0.0813611
\(455\) 21.0520 0.986933
\(456\) 0 0
\(457\) −12.2492 −0.572995 −0.286497 0.958081i \(-0.592491\pi\)
−0.286497 + 0.958081i \(0.592491\pi\)
\(458\) −14.3034 −0.668355
\(459\) 0 0
\(460\) −1.39793 −0.0651788
\(461\) 5.51693 0.256949 0.128475 0.991713i \(-0.458992\pi\)
0.128475 + 0.991713i \(0.458992\pi\)
\(462\) 0 0
\(463\) −39.0620 −1.81536 −0.907682 0.419659i \(-0.862150\pi\)
−0.907682 + 0.419659i \(0.862150\pi\)
\(464\) 23.1136 1.07302
\(465\) 0 0
\(466\) −8.39037 −0.388676
\(467\) 15.4534 0.715099 0.357550 0.933894i \(-0.383612\pi\)
0.357550 + 0.933894i \(0.383612\pi\)
\(468\) 0 0
\(469\) −41.1201 −1.89875
\(470\) −3.62403 −0.167164
\(471\) 0 0
\(472\) 27.8496 1.28188
\(473\) −4.99709 −0.229767
\(474\) 0 0
\(475\) 12.6748 0.581561
\(476\) −2.75479 −0.126265
\(477\) 0 0
\(478\) 3.54175 0.161996
\(479\) −19.2183 −0.878106 −0.439053 0.898461i \(-0.644686\pi\)
−0.439053 + 0.898461i \(0.644686\pi\)
\(480\) 0 0
\(481\) 18.8793 0.860823
\(482\) −1.12000 −0.0510148
\(483\) 0 0
\(484\) −1.70156 −0.0773435
\(485\) −5.06370 −0.229931
\(486\) 0 0
\(487\) −5.36667 −0.243187 −0.121594 0.992580i \(-0.538800\pi\)
−0.121594 + 0.992580i \(0.538800\pi\)
\(488\) −2.02216 −0.0915387
\(489\) 0 0
\(490\) 4.86727 0.219881
\(491\) 30.3986 1.37187 0.685936 0.727662i \(-0.259393\pi\)
0.685936 + 0.727662i \(0.259393\pi\)
\(492\) 0 0
\(493\) −3.88375 −0.174915
\(494\) 9.61933 0.432794
\(495\) 0 0
\(496\) −24.4299 −1.09693
\(497\) −18.3070 −0.821182
\(498\) 0 0
\(499\) −17.0924 −0.765160 −0.382580 0.923922i \(-0.624964\pi\)
−0.382580 + 0.923922i \(0.624964\pi\)
\(500\) 13.3198 0.595681
\(501\) 0 0
\(502\) −0.220521 −0.00984231
\(503\) −32.1659 −1.43421 −0.717103 0.696967i \(-0.754532\pi\)
−0.717103 + 0.696967i \(0.754532\pi\)
\(504\) 0 0
\(505\) 15.3233 0.681878
\(506\) 0.532636 0.0236786
\(507\) 0 0
\(508\) −2.02469 −0.0898310
\(509\) −20.2801 −0.898900 −0.449450 0.893306i \(-0.648380\pi\)
−0.449450 + 0.893306i \(0.648380\pi\)
\(510\) 0 0
\(511\) 8.65739 0.382980
\(512\) 21.4770 0.949156
\(513\) 0 0
\(514\) 1.92352 0.0848428
\(515\) 9.22627 0.406558
\(516\) 0 0
\(517\) −7.87272 −0.346242
\(518\) 7.25467 0.318752
\(519\) 0 0
\(520\) 10.1550 0.445325
\(521\) −27.3063 −1.19631 −0.598156 0.801380i \(-0.704100\pi\)
−0.598156 + 0.801380i \(0.704100\pi\)
\(522\) 0 0
\(523\) −23.5138 −1.02819 −0.514093 0.857734i \(-0.671871\pi\)
−0.514093 + 0.857734i \(0.671871\pi\)
\(524\) −0.395230 −0.0172657
\(525\) 0 0
\(526\) −13.8280 −0.602929
\(527\) 4.10492 0.178813
\(528\) 0 0
\(529\) −22.0494 −0.958669
\(530\) −0.170322 −0.00739833
\(531\) 0 0
\(532\) −21.0748 −0.913709
\(533\) −7.70696 −0.333825
\(534\) 0 0
\(535\) −2.39575 −0.103577
\(536\) −19.8353 −0.856757
\(537\) 0 0
\(538\) −14.6603 −0.632050
\(539\) 10.5735 0.455433
\(540\) 0 0
\(541\) 21.3883 0.919556 0.459778 0.888034i \(-0.347929\pi\)
0.459778 + 0.888034i \(0.347929\pi\)
\(542\) −4.81226 −0.206704
\(543\) 0 0
\(544\) −2.04683 −0.0877572
\(545\) 16.3886 0.702012
\(546\) 0 0
\(547\) −18.4841 −0.790322 −0.395161 0.918612i \(-0.629311\pi\)
−0.395161 + 0.918612i \(0.629311\pi\)
\(548\) −23.4723 −1.00269
\(549\) 0 0
\(550\) −2.34361 −0.0999317
\(551\) −29.7117 −1.26576
\(552\) 0 0
\(553\) 36.3684 1.54654
\(554\) 11.6679 0.495721
\(555\) 0 0
\(556\) −17.4286 −0.739137
\(557\) 24.4886 1.03762 0.518808 0.854891i \(-0.326376\pi\)
0.518808 + 0.854891i \(0.326376\pi\)
\(558\) 0 0
\(559\) 29.7814 1.25962
\(560\) −8.11886 −0.343084
\(561\) 0 0
\(562\) 16.3820 0.691032
\(563\) 20.3211 0.856433 0.428216 0.903676i \(-0.359142\pi\)
0.428216 + 0.903676i \(0.359142\pi\)
\(564\) 0 0
\(565\) −6.81648 −0.286771
\(566\) 5.51283 0.231721
\(567\) 0 0
\(568\) −8.83086 −0.370535
\(569\) 24.7529 1.03769 0.518847 0.854867i \(-0.326361\pi\)
0.518847 + 0.854867i \(0.326361\pi\)
\(570\) 0 0
\(571\) 10.7099 0.448195 0.224098 0.974567i \(-0.428057\pi\)
0.224098 + 0.974567i \(0.428057\pi\)
\(572\) 10.1408 0.424010
\(573\) 0 0
\(574\) −2.96152 −0.123612
\(575\) −4.18269 −0.174430
\(576\) 0 0
\(577\) −4.97286 −0.207023 −0.103512 0.994628i \(-0.533008\pi\)
−0.103512 + 0.994628i \(0.533008\pi\)
\(578\) −9.20559 −0.382902
\(579\) 0 0
\(580\) −14.4186 −0.598701
\(581\) −29.7500 −1.23424
\(582\) 0 0
\(583\) −0.370002 −0.0153239
\(584\) 4.17611 0.172809
\(585\) 0 0
\(586\) 6.41284 0.264912
\(587\) −2.13571 −0.0881502 −0.0440751 0.999028i \(-0.514034\pi\)
−0.0440751 + 0.999028i \(0.514034\pi\)
\(588\) 0 0
\(589\) 31.4037 1.29397
\(590\) −6.33975 −0.261003
\(591\) 0 0
\(592\) −7.28094 −0.299245
\(593\) −13.9935 −0.574646 −0.287323 0.957834i \(-0.592765\pi\)
−0.287323 + 0.957834i \(0.592765\pi\)
\(594\) 0 0
\(595\) 1.36420 0.0559268
\(596\) −4.60468 −0.188615
\(597\) 0 0
\(598\) −3.17437 −0.129810
\(599\) 27.2804 1.11465 0.557324 0.830295i \(-0.311828\pi\)
0.557324 + 0.830295i \(0.311828\pi\)
\(600\) 0 0
\(601\) 38.7081 1.57894 0.789468 0.613791i \(-0.210356\pi\)
0.789468 + 0.613791i \(0.210356\pi\)
\(602\) 11.4440 0.466421
\(603\) 0 0
\(604\) 26.6151 1.08295
\(605\) 0.842631 0.0342578
\(606\) 0 0
\(607\) 27.3959 1.11197 0.555983 0.831194i \(-0.312342\pi\)
0.555983 + 0.831194i \(0.312342\pi\)
\(608\) −15.6588 −0.635048
\(609\) 0 0
\(610\) 0.460328 0.0186381
\(611\) 46.9194 1.89815
\(612\) 0 0
\(613\) 8.56875 0.346088 0.173044 0.984914i \(-0.444640\pi\)
0.173044 + 0.984914i \(0.444640\pi\)
\(614\) 6.64549 0.268190
\(615\) 0 0
\(616\) 8.47703 0.341549
\(617\) −45.6108 −1.83622 −0.918112 0.396322i \(-0.870287\pi\)
−0.918112 + 0.396322i \(0.870287\pi\)
\(618\) 0 0
\(619\) 36.2410 1.45665 0.728325 0.685232i \(-0.240299\pi\)
0.728325 + 0.685232i \(0.240299\pi\)
\(620\) 15.2397 0.612041
\(621\) 0 0
\(622\) 5.69450 0.228329
\(623\) −31.1233 −1.24693
\(624\) 0 0
\(625\) 14.8537 0.594150
\(626\) −2.02517 −0.0809421
\(627\) 0 0
\(628\) −5.95686 −0.237705
\(629\) 1.22341 0.0487804
\(630\) 0 0
\(631\) −5.90488 −0.235070 −0.117535 0.993069i \(-0.537499\pi\)
−0.117535 + 0.993069i \(0.537499\pi\)
\(632\) 17.5432 0.697833
\(633\) 0 0
\(634\) 9.70415 0.385401
\(635\) 1.00265 0.0397889
\(636\) 0 0
\(637\) −63.0153 −2.49676
\(638\) 5.49376 0.217500
\(639\) 0 0
\(640\) −9.71501 −0.384020
\(641\) 27.6940 1.09385 0.546923 0.837183i \(-0.315799\pi\)
0.546923 + 0.837183i \(0.315799\pi\)
\(642\) 0 0
\(643\) 39.7962 1.56941 0.784704 0.619871i \(-0.212815\pi\)
0.784704 + 0.619871i \(0.212815\pi\)
\(644\) 6.95467 0.274053
\(645\) 0 0
\(646\) 0.623347 0.0245253
\(647\) −35.8326 −1.40872 −0.704362 0.709841i \(-0.748767\pi\)
−0.704362 + 0.709841i \(0.748767\pi\)
\(648\) 0 0
\(649\) −13.7723 −0.540608
\(650\) 13.9673 0.547842
\(651\) 0 0
\(652\) −28.6296 −1.12122
\(653\) −3.93565 −0.154014 −0.0770070 0.997031i \(-0.524536\pi\)
−0.0770070 + 0.997031i \(0.524536\pi\)
\(654\) 0 0
\(655\) 0.195723 0.00764751
\(656\) 2.97224 0.116047
\(657\) 0 0
\(658\) 18.0295 0.702864
\(659\) 1.14603 0.0446429 0.0223215 0.999751i \(-0.492894\pi\)
0.0223215 + 0.999751i \(0.492894\pi\)
\(660\) 0 0
\(661\) −21.1185 −0.821414 −0.410707 0.911767i \(-0.634718\pi\)
−0.410707 + 0.911767i \(0.634718\pi\)
\(662\) 13.8112 0.536786
\(663\) 0 0
\(664\) −14.3507 −0.556915
\(665\) 10.4365 0.404709
\(666\) 0 0
\(667\) 9.80484 0.379645
\(668\) 30.8129 1.19219
\(669\) 0 0
\(670\) 4.51536 0.174444
\(671\) 1.00000 0.0386046
\(672\) 0 0
\(673\) −50.2053 −1.93527 −0.967636 0.252349i \(-0.918797\pi\)
−0.967636 + 0.252349i \(0.918797\pi\)
\(674\) −8.64609 −0.333035
\(675\) 0 0
\(676\) −38.3165 −1.47371
\(677\) 15.0864 0.579819 0.289910 0.957054i \(-0.406375\pi\)
0.289910 + 0.957054i \(0.406375\pi\)
\(678\) 0 0
\(679\) 25.1918 0.966774
\(680\) 0.658057 0.0252353
\(681\) 0 0
\(682\) −5.80661 −0.222346
\(683\) −48.5108 −1.85621 −0.928107 0.372314i \(-0.878564\pi\)
−0.928107 + 0.372314i \(0.878564\pi\)
\(684\) 0 0
\(685\) 11.6238 0.444121
\(686\) −8.18375 −0.312457
\(687\) 0 0
\(688\) −11.4854 −0.437877
\(689\) 2.20512 0.0840083
\(690\) 0 0
\(691\) −28.3558 −1.07871 −0.539353 0.842080i \(-0.681331\pi\)
−0.539353 + 0.842080i \(0.681331\pi\)
\(692\) −16.7557 −0.636954
\(693\) 0 0
\(694\) 7.76891 0.294904
\(695\) 8.63084 0.327386
\(696\) 0 0
\(697\) −0.499422 −0.0189170
\(698\) 11.3006 0.427734
\(699\) 0 0
\(700\) −30.6006 −1.15660
\(701\) 4.65092 0.175663 0.0878313 0.996135i \(-0.472006\pi\)
0.0878313 + 0.996135i \(0.472006\pi\)
\(702\) 0 0
\(703\) 9.35937 0.352995
\(704\) −1.70149 −0.0641272
\(705\) 0 0
\(706\) 7.29876 0.274692
\(707\) −76.2332 −2.86705
\(708\) 0 0
\(709\) 47.0222 1.76595 0.882977 0.469416i \(-0.155536\pi\)
0.882977 + 0.469416i \(0.155536\pi\)
\(710\) 2.01028 0.0754443
\(711\) 0 0
\(712\) −15.0131 −0.562641
\(713\) −10.3632 −0.388104
\(714\) 0 0
\(715\) −5.02186 −0.187807
\(716\) −17.0683 −0.637871
\(717\) 0 0
\(718\) 5.99069 0.223570
\(719\) −8.60663 −0.320973 −0.160487 0.987038i \(-0.551306\pi\)
−0.160487 + 0.987038i \(0.551306\pi\)
\(720\) 0 0
\(721\) −45.9005 −1.70943
\(722\) −5.61091 −0.208816
\(723\) 0 0
\(724\) 22.5112 0.836624
\(725\) −43.1414 −1.60223
\(726\) 0 0
\(727\) 29.4993 1.09407 0.547034 0.837110i \(-0.315757\pi\)
0.547034 + 0.837110i \(0.315757\pi\)
\(728\) −50.5209 −1.87243
\(729\) 0 0
\(730\) −0.950659 −0.0351855
\(731\) 1.92988 0.0713791
\(732\) 0 0
\(733\) −42.0201 −1.55205 −0.776025 0.630702i \(-0.782767\pi\)
−0.776025 + 0.630702i \(0.782767\pi\)
\(734\) −9.95766 −0.367544
\(735\) 0 0
\(736\) 5.16739 0.190473
\(737\) 9.80901 0.361320
\(738\) 0 0
\(739\) 50.8992 1.87236 0.936179 0.351523i \(-0.114336\pi\)
0.936179 + 0.351523i \(0.114336\pi\)
\(740\) 4.54196 0.166966
\(741\) 0 0
\(742\) 0.847351 0.0311072
\(743\) 4.44260 0.162983 0.0814916 0.996674i \(-0.474032\pi\)
0.0814916 + 0.996674i \(0.474032\pi\)
\(744\) 0 0
\(745\) 2.28029 0.0835433
\(746\) −7.86525 −0.287967
\(747\) 0 0
\(748\) 0.657141 0.0240275
\(749\) 11.9188 0.435504
\(750\) 0 0
\(751\) 3.39662 0.123944 0.0619722 0.998078i \(-0.480261\pi\)
0.0619722 + 0.998078i \(0.480261\pi\)
\(752\) −18.0948 −0.659849
\(753\) 0 0
\(754\) −32.7414 −1.19237
\(755\) −13.1801 −0.479673
\(756\) 0 0
\(757\) 13.8258 0.502508 0.251254 0.967921i \(-0.419157\pi\)
0.251254 + 0.967921i \(0.419157\pi\)
\(758\) 6.08675 0.221081
\(759\) 0 0
\(760\) 5.03431 0.182613
\(761\) 34.7597 1.26004 0.630018 0.776580i \(-0.283047\pi\)
0.630018 + 0.776580i \(0.283047\pi\)
\(762\) 0 0
\(763\) −81.5332 −2.95170
\(764\) −44.3544 −1.60469
\(765\) 0 0
\(766\) 7.45331 0.269299
\(767\) 82.0790 2.96370
\(768\) 0 0
\(769\) −1.09955 −0.0396507 −0.0198254 0.999803i \(-0.506311\pi\)
−0.0198254 + 0.999803i \(0.506311\pi\)
\(770\) −1.92973 −0.0695426
\(771\) 0 0
\(772\) 2.80716 0.101032
\(773\) 13.8425 0.497879 0.248939 0.968519i \(-0.419918\pi\)
0.248939 + 0.968519i \(0.419918\pi\)
\(774\) 0 0
\(775\) 45.5981 1.63793
\(776\) 12.1519 0.436229
\(777\) 0 0
\(778\) −12.9472 −0.464178
\(779\) −3.82071 −0.136891
\(780\) 0 0
\(781\) 4.36706 0.156266
\(782\) −0.205704 −0.00735596
\(783\) 0 0
\(784\) 24.3023 0.867939
\(785\) 2.94991 0.105287
\(786\) 0 0
\(787\) −33.6766 −1.20044 −0.600220 0.799835i \(-0.704920\pi\)
−0.600220 + 0.799835i \(0.704920\pi\)
\(788\) −25.5391 −0.909792
\(789\) 0 0
\(790\) −3.99358 −0.142085
\(791\) 33.9119 1.20577
\(792\) 0 0
\(793\) −5.95974 −0.211637
\(794\) −10.8634 −0.385528
\(795\) 0 0
\(796\) −0.736310 −0.0260978
\(797\) 1.47756 0.0523377 0.0261689 0.999658i \(-0.491669\pi\)
0.0261689 + 0.999658i \(0.491669\pi\)
\(798\) 0 0
\(799\) 3.04044 0.107563
\(800\) −22.7366 −0.803859
\(801\) 0 0
\(802\) 8.28694 0.292622
\(803\) −2.06518 −0.0728786
\(804\) 0 0
\(805\) −3.44403 −0.121386
\(806\) 34.6059 1.21894
\(807\) 0 0
\(808\) −36.7731 −1.29367
\(809\) −26.0611 −0.916260 −0.458130 0.888885i \(-0.651481\pi\)
−0.458130 + 0.888885i \(0.651481\pi\)
\(810\) 0 0
\(811\) 21.1286 0.741925 0.370962 0.928648i \(-0.379028\pi\)
0.370962 + 0.928648i \(0.379028\pi\)
\(812\) 71.7324 2.51731
\(813\) 0 0
\(814\) −1.73057 −0.0606564
\(815\) 14.1777 0.496623
\(816\) 0 0
\(817\) 14.7640 0.516529
\(818\) −11.1365 −0.389378
\(819\) 0 0
\(820\) −1.85413 −0.0647490
\(821\) 46.0338 1.60659 0.803295 0.595582i \(-0.203078\pi\)
0.803295 + 0.595582i \(0.203078\pi\)
\(822\) 0 0
\(823\) −23.0217 −0.802488 −0.401244 0.915971i \(-0.631422\pi\)
−0.401244 + 0.915971i \(0.631422\pi\)
\(824\) −22.1413 −0.771329
\(825\) 0 0
\(826\) 31.5402 1.09742
\(827\) 15.9583 0.554923 0.277461 0.960737i \(-0.410507\pi\)
0.277461 + 0.960737i \(0.410507\pi\)
\(828\) 0 0
\(829\) −36.0118 −1.25074 −0.625370 0.780328i \(-0.715052\pi\)
−0.625370 + 0.780328i \(0.715052\pi\)
\(830\) 3.26682 0.113393
\(831\) 0 0
\(832\) 10.1404 0.351556
\(833\) −4.08348 −0.141484
\(834\) 0 0
\(835\) −15.2589 −0.528056
\(836\) 5.02730 0.173873
\(837\) 0 0
\(838\) −10.4627 −0.361427
\(839\) −34.2082 −1.18100 −0.590499 0.807038i \(-0.701069\pi\)
−0.590499 + 0.807038i \(0.701069\pi\)
\(840\) 0 0
\(841\) 72.1298 2.48723
\(842\) −4.53253 −0.156201
\(843\) 0 0
\(844\) 10.2001 0.351102
\(845\) 18.9748 0.652752
\(846\) 0 0
\(847\) −4.19208 −0.144041
\(848\) −0.850419 −0.0292035
\(849\) 0 0
\(850\) 0.905100 0.0310447
\(851\) −3.08859 −0.105875
\(852\) 0 0
\(853\) 11.3190 0.387554 0.193777 0.981046i \(-0.437926\pi\)
0.193777 + 0.981046i \(0.437926\pi\)
\(854\) −2.29012 −0.0783664
\(855\) 0 0
\(856\) 5.74935 0.196509
\(857\) −43.3860 −1.48204 −0.741019 0.671485i \(-0.765657\pi\)
−0.741019 + 0.671485i \(0.765657\pi\)
\(858\) 0 0
\(859\) −25.6339 −0.874617 −0.437308 0.899312i \(-0.644068\pi\)
−0.437308 + 0.899312i \(0.644068\pi\)
\(860\) 7.16476 0.244316
\(861\) 0 0
\(862\) 9.66842 0.329308
\(863\) −16.0782 −0.547309 −0.273654 0.961828i \(-0.588232\pi\)
−0.273654 + 0.961828i \(0.588232\pi\)
\(864\) 0 0
\(865\) 8.29759 0.282126
\(866\) 3.04789 0.103572
\(867\) 0 0
\(868\) −75.8173 −2.57341
\(869\) −8.67552 −0.294297
\(870\) 0 0
\(871\) −58.4592 −1.98081
\(872\) −39.3296 −1.33187
\(873\) 0 0
\(874\) −1.57369 −0.0532308
\(875\) 32.8156 1.10937
\(876\) 0 0
\(877\) −17.4124 −0.587974 −0.293987 0.955809i \(-0.594982\pi\)
−0.293987 + 0.955809i \(0.594982\pi\)
\(878\) −3.77286 −0.127328
\(879\) 0 0
\(880\) 1.93672 0.0652867
\(881\) 41.4135 1.39526 0.697628 0.716460i \(-0.254239\pi\)
0.697628 + 0.716460i \(0.254239\pi\)
\(882\) 0 0
\(883\) −49.5096 −1.66613 −0.833066 0.553174i \(-0.813416\pi\)
−0.833066 + 0.553174i \(0.813416\pi\)
\(884\) −3.91639 −0.131722
\(885\) 0 0
\(886\) −4.67038 −0.156905
\(887\) 48.4377 1.62638 0.813190 0.581999i \(-0.197729\pi\)
0.813190 + 0.581999i \(0.197729\pi\)
\(888\) 0 0
\(889\) −4.98816 −0.167298
\(890\) 3.41762 0.114559
\(891\) 0 0
\(892\) −2.05452 −0.0687905
\(893\) 23.2602 0.778372
\(894\) 0 0
\(895\) 8.45240 0.282533
\(896\) 48.3320 1.61466
\(897\) 0 0
\(898\) 12.0747 0.402938
\(899\) −106.889 −3.56494
\(900\) 0 0
\(901\) 0.142895 0.00476052
\(902\) 0.706457 0.0235224
\(903\) 0 0
\(904\) 16.3583 0.544068
\(905\) −11.1478 −0.370566
\(906\) 0 0
\(907\) 50.1623 1.66561 0.832807 0.553564i \(-0.186733\pi\)
0.832807 + 0.553564i \(0.186733\pi\)
\(908\) 5.39960 0.179192
\(909\) 0 0
\(910\) 11.5007 0.381244
\(911\) 19.2889 0.639071 0.319536 0.947574i \(-0.396473\pi\)
0.319536 + 0.947574i \(0.396473\pi\)
\(912\) 0 0
\(913\) 7.09673 0.234867
\(914\) −6.69173 −0.221343
\(915\) 0 0
\(916\) 44.5509 1.47200
\(917\) −0.973717 −0.0321550
\(918\) 0 0
\(919\) −43.7882 −1.44444 −0.722220 0.691663i \(-0.756878\pi\)
−0.722220 + 0.691663i \(0.756878\pi\)
\(920\) −1.66132 −0.0547720
\(921\) 0 0
\(922\) 3.01389 0.0992572
\(923\) −26.0265 −0.856673
\(924\) 0 0
\(925\) 13.5898 0.446830
\(926\) −21.3395 −0.701259
\(927\) 0 0
\(928\) 53.2979 1.74959
\(929\) 27.0615 0.887858 0.443929 0.896062i \(-0.353584\pi\)
0.443929 + 0.896062i \(0.353584\pi\)
\(930\) 0 0
\(931\) −31.2397 −1.02384
\(932\) 26.1335 0.856032
\(933\) 0 0
\(934\) 8.44218 0.276237
\(935\) −0.325424 −0.0106425
\(936\) 0 0
\(937\) 2.66965 0.0872137 0.0436068 0.999049i \(-0.486115\pi\)
0.0436068 + 0.999049i \(0.486115\pi\)
\(938\) −22.4639 −0.733471
\(939\) 0 0
\(940\) 11.2878 0.368167
\(941\) 31.2522 1.01879 0.509397 0.860532i \(-0.329868\pi\)
0.509397 + 0.860532i \(0.329868\pi\)
\(942\) 0 0
\(943\) 1.26083 0.0410583
\(944\) −31.6544 −1.03026
\(945\) 0 0
\(946\) −2.72990 −0.0887568
\(947\) 6.67071 0.216769 0.108384 0.994109i \(-0.465432\pi\)
0.108384 + 0.994109i \(0.465432\pi\)
\(948\) 0 0
\(949\) 12.3079 0.399532
\(950\) 6.92424 0.224652
\(951\) 0 0
\(952\) −3.27383 −0.106105
\(953\) −14.3407 −0.464540 −0.232270 0.972651i \(-0.574615\pi\)
−0.232270 + 0.972651i \(0.574615\pi\)
\(954\) 0 0
\(955\) 21.9648 0.710765
\(956\) −11.0315 −0.356785
\(957\) 0 0
\(958\) −10.4989 −0.339205
\(959\) −57.8280 −1.86736
\(960\) 0 0
\(961\) 81.9756 2.64438
\(962\) 10.3137 0.332528
\(963\) 0 0
\(964\) 3.48848 0.112356
\(965\) −1.39014 −0.0447501
\(966\) 0 0
\(967\) 33.8580 1.08880 0.544400 0.838826i \(-0.316757\pi\)
0.544400 + 0.838826i \(0.316757\pi\)
\(968\) −2.02216 −0.0649945
\(969\) 0 0
\(970\) −2.76629 −0.0888203
\(971\) −23.2171 −0.745074 −0.372537 0.928017i \(-0.621512\pi\)
−0.372537 + 0.928017i \(0.621512\pi\)
\(972\) 0 0
\(973\) −42.9383 −1.37654
\(974\) −2.93180 −0.0939411
\(975\) 0 0
\(976\) 2.29842 0.0735705
\(977\) −11.4832 −0.367381 −0.183690 0.982984i \(-0.558804\pi\)
−0.183690 + 0.982984i \(0.558804\pi\)
\(978\) 0 0
\(979\) 7.42432 0.237282
\(980\) −15.1601 −0.484272
\(981\) 0 0
\(982\) 16.6067 0.529942
\(983\) 2.32576 0.0741803 0.0370901 0.999312i \(-0.488191\pi\)
0.0370901 + 0.999312i \(0.488191\pi\)
\(984\) 0 0
\(985\) 12.6472 0.402974
\(986\) −2.12169 −0.0675683
\(987\) 0 0
\(988\) −29.9614 −0.953199
\(989\) −4.87213 −0.154925
\(990\) 0 0
\(991\) −27.4890 −0.873218 −0.436609 0.899651i \(-0.643821\pi\)
−0.436609 + 0.899651i \(0.643821\pi\)
\(992\) −56.3330 −1.78857
\(993\) 0 0
\(994\) −10.0011 −0.317216
\(995\) 0.364629 0.0115595
\(996\) 0 0
\(997\) −0.204845 −0.00648751 −0.00324375 0.999995i \(-0.501033\pi\)
−0.00324375 + 0.999995i \(0.501033\pi\)
\(998\) −9.33754 −0.295575
\(999\) 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 \(a_p\))