Properties

Label 6039.2.a.j.1.4
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 1.4
Root \(-1.69494\)
Character \(\chi\) = 6039.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.69494 q^{2}\) \(+0.872835 q^{4}\) \(-1.13650 q^{5}\) \(+4.14659 q^{7}\) \(+1.91048 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.69494 q^{2}\) \(+0.872835 q^{4}\) \(-1.13650 q^{5}\) \(+4.14659 q^{7}\) \(+1.91048 q^{8}\) \(+1.92630 q^{10}\) \(+1.00000 q^{11}\) \(+2.80864 q^{13}\) \(-7.02824 q^{14}\) \(-4.98383 q^{16}\) \(+0.763911 q^{17}\) \(+3.34950 q^{19}\) \(-0.991974 q^{20}\) \(-1.69494 q^{22}\) \(-3.86313 q^{23}\) \(-3.70838 q^{25}\) \(-4.76049 q^{26}\) \(+3.61929 q^{28}\) \(-2.17513 q^{29}\) \(+6.15568 q^{31}\) \(+4.62635 q^{32}\) \(-1.29479 q^{34}\) \(-4.71258 q^{35}\) \(+3.38312 q^{37}\) \(-5.67721 q^{38}\) \(-2.17125 q^{40}\) \(-1.67214 q^{41}\) \(+5.23257 q^{43}\) \(+0.872835 q^{44}\) \(+6.54779 q^{46}\) \(+12.4466 q^{47}\) \(+10.1942 q^{49}\) \(+6.28549 q^{50}\) \(+2.45148 q^{52}\) \(-4.85562 q^{53}\) \(-1.13650 q^{55}\) \(+7.92198 q^{56}\) \(+3.68672 q^{58}\) \(+11.2371 q^{59}\) \(+1.00000 q^{61}\) \(-10.4335 q^{62}\) \(+2.12626 q^{64}\) \(-3.19201 q^{65}\) \(+3.11299 q^{67}\) \(+0.666769 q^{68}\) \(+7.98757 q^{70}\) \(+0.313422 q^{71}\) \(+4.11415 q^{73}\) \(-5.73420 q^{74}\) \(+2.92356 q^{76}\) \(+4.14659 q^{77}\) \(+0.122521 q^{79}\) \(+5.66410 q^{80}\) \(+2.83418 q^{82}\) \(+2.98302 q^{83}\) \(-0.868182 q^{85}\) \(-8.86891 q^{86}\) \(+1.91048 q^{88}\) \(-12.3890 q^{89}\) \(+11.6463 q^{91}\) \(-3.37187 q^{92}\) \(-21.0963 q^{94}\) \(-3.80669 q^{95}\) \(+0.287224 q^{97}\) \(-17.2786 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut +\mathstrut q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut +\mathstrut 17q^{16} \) \(\mathstrut +\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 22q^{19} \) \(\mathstrut -\mathstrut 23q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 25q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut +\mathstrut 37q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 9q^{31} \) \(\mathstrut -\mathstrut 4q^{32} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 18q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 25q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 36q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut -\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 13q^{52} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 40q^{56} \) \(\mathstrut +\mathstrut 33q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut +\mathstrut 14q^{61} \) \(\mathstrut +\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 6q^{64} \) \(\mathstrut +\mathstrut 61q^{65} \) \(\mathstrut +\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 66q^{68} \) \(\mathstrut +\mathstrut 44q^{70} \) \(\mathstrut +\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 12q^{74} \) \(\mathstrut +\mathstrut 49q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut -\mathstrut 88q^{80} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 32q^{83} \) \(\mathstrut +\mathstrut 2q^{85} \) \(\mathstrut +\mathstrut 14q^{86} \) \(\mathstrut +\mathstrut 21q^{89} \) \(\mathstrut +\mathstrut 45q^{91} \) \(\mathstrut +\mathstrut 14q^{92} \) \(\mathstrut -\mathstrut 31q^{94} \) \(\mathstrut -\mathstrut 23q^{95} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut +\mathstrut 38q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.69494 −1.19851 −0.599253 0.800560i \(-0.704536\pi\)
−0.599253 + 0.800560i \(0.704536\pi\)
\(3\) 0 0
\(4\) 0.872835 0.436418
\(5\) −1.13650 −0.508256 −0.254128 0.967171i \(-0.581789\pi\)
−0.254128 + 0.967171i \(0.581789\pi\)
\(6\) 0 0
\(7\) 4.14659 1.56726 0.783632 0.621225i \(-0.213365\pi\)
0.783632 + 0.621225i \(0.213365\pi\)
\(8\) 1.91048 0.675457
\(9\) 0 0
\(10\) 1.92630 0.609149
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 2.80864 0.778977 0.389488 0.921031i \(-0.372652\pi\)
0.389488 + 0.921031i \(0.372652\pi\)
\(14\) −7.02824 −1.87838
\(15\) 0 0
\(16\) −4.98383 −1.24596
\(17\) 0.763911 0.185276 0.0926379 0.995700i \(-0.470470\pi\)
0.0926379 + 0.995700i \(0.470470\pi\)
\(18\) 0 0
\(19\) 3.34950 0.768428 0.384214 0.923244i \(-0.374473\pi\)
0.384214 + 0.923244i \(0.374473\pi\)
\(20\) −0.991974 −0.221812
\(21\) 0 0
\(22\) −1.69494 −0.361363
\(23\) −3.86313 −0.805518 −0.402759 0.915306i \(-0.631949\pi\)
−0.402759 + 0.915306i \(0.631949\pi\)
\(24\) 0 0
\(25\) −3.70838 −0.741675
\(26\) −4.76049 −0.933609
\(27\) 0 0
\(28\) 3.61929 0.683982
\(29\) −2.17513 −0.403911 −0.201955 0.979395i \(-0.564730\pi\)
−0.201955 + 0.979395i \(0.564730\pi\)
\(30\) 0 0
\(31\) 6.15568 1.10559 0.552796 0.833317i \(-0.313561\pi\)
0.552796 + 0.833317i \(0.313561\pi\)
\(32\) 4.62635 0.817831
\(33\) 0 0
\(34\) −1.29479 −0.222054
\(35\) −4.71258 −0.796572
\(36\) 0 0
\(37\) 3.38312 0.556181 0.278091 0.960555i \(-0.410298\pi\)
0.278091 + 0.960555i \(0.410298\pi\)
\(38\) −5.67721 −0.920965
\(39\) 0 0
\(40\) −2.17125 −0.343305
\(41\) −1.67214 −0.261144 −0.130572 0.991439i \(-0.541681\pi\)
−0.130572 + 0.991439i \(0.541681\pi\)
\(42\) 0 0
\(43\) 5.23257 0.797959 0.398980 0.916960i \(-0.369364\pi\)
0.398980 + 0.916960i \(0.369364\pi\)
\(44\) 0.872835 0.131585
\(45\) 0 0
\(46\) 6.54779 0.965419
\(47\) 12.4466 1.81553 0.907764 0.419481i \(-0.137788\pi\)
0.907764 + 0.419481i \(0.137788\pi\)
\(48\) 0 0
\(49\) 10.1942 1.45632
\(50\) 6.28549 0.888903
\(51\) 0 0
\(52\) 2.45148 0.339959
\(53\) −4.85562 −0.666971 −0.333485 0.942755i \(-0.608225\pi\)
−0.333485 + 0.942755i \(0.608225\pi\)
\(54\) 0 0
\(55\) −1.13650 −0.153245
\(56\) 7.92198 1.05862
\(57\) 0 0
\(58\) 3.68672 0.484090
\(59\) 11.2371 1.46295 0.731473 0.681871i \(-0.238833\pi\)
0.731473 + 0.681871i \(0.238833\pi\)
\(60\) 0 0
\(61\) 1.00000 0.128037
\(62\) −10.4335 −1.32506
\(63\) 0 0
\(64\) 2.12626 0.265782
\(65\) −3.19201 −0.395920
\(66\) 0 0
\(67\) 3.11299 0.380313 0.190156 0.981754i \(-0.439101\pi\)
0.190156 + 0.981754i \(0.439101\pi\)
\(68\) 0.666769 0.0808576
\(69\) 0 0
\(70\) 7.98757 0.954697
\(71\) 0.313422 0.0371964 0.0185982 0.999827i \(-0.494080\pi\)
0.0185982 + 0.999827i \(0.494080\pi\)
\(72\) 0 0
\(73\) 4.11415 0.481525 0.240762 0.970584i \(-0.422603\pi\)
0.240762 + 0.970584i \(0.422603\pi\)
\(74\) −5.73420 −0.666587
\(75\) 0 0
\(76\) 2.92356 0.335355
\(77\) 4.14659 0.472548
\(78\) 0 0
\(79\) 0.122521 0.0137846 0.00689232 0.999976i \(-0.497806\pi\)
0.00689232 + 0.999976i \(0.497806\pi\)
\(80\) 5.66410 0.633266
\(81\) 0 0
\(82\) 2.83418 0.312983
\(83\) 2.98302 0.327430 0.163715 0.986508i \(-0.447652\pi\)
0.163715 + 0.986508i \(0.447652\pi\)
\(84\) 0 0
\(85\) −0.868182 −0.0941676
\(86\) −8.86891 −0.956359
\(87\) 0 0
\(88\) 1.91048 0.203658
\(89\) −12.3890 −1.31323 −0.656617 0.754224i \(-0.728013\pi\)
−0.656617 + 0.754224i \(0.728013\pi\)
\(90\) 0 0
\(91\) 11.6463 1.22086
\(92\) −3.37187 −0.351542
\(93\) 0 0
\(94\) −21.0963 −2.17592
\(95\) −3.80669 −0.390558
\(96\) 0 0
\(97\) 0.287224 0.0291632 0.0145816 0.999894i \(-0.495358\pi\)
0.0145816 + 0.999894i \(0.495358\pi\)
\(98\) −17.2786 −1.74540
\(99\) 0 0
\(100\) −3.23680 −0.323680
\(101\) −8.25985 −0.821886 −0.410943 0.911661i \(-0.634800\pi\)
−0.410943 + 0.911661i \(0.634800\pi\)
\(102\) 0 0
\(103\) 11.1319 1.09686 0.548428 0.836198i \(-0.315226\pi\)
0.548428 + 0.836198i \(0.315226\pi\)
\(104\) 5.36586 0.526165
\(105\) 0 0
\(106\) 8.23000 0.799368
\(107\) −20.5662 −1.98821 −0.994104 0.108435i \(-0.965416\pi\)
−0.994104 + 0.108435i \(0.965416\pi\)
\(108\) 0 0
\(109\) −2.42639 −0.232406 −0.116203 0.993225i \(-0.537072\pi\)
−0.116203 + 0.993225i \(0.537072\pi\)
\(110\) 1.92630 0.183665
\(111\) 0 0
\(112\) −20.6659 −1.95274
\(113\) 0.194417 0.0182892 0.00914462 0.999958i \(-0.497089\pi\)
0.00914462 + 0.999958i \(0.497089\pi\)
\(114\) 0 0
\(115\) 4.39043 0.409410
\(116\) −1.89853 −0.176274
\(117\) 0 0
\(118\) −19.0462 −1.75335
\(119\) 3.16763 0.290376
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −1.69494 −0.153453
\(123\) 0 0
\(124\) 5.37289 0.482500
\(125\) 9.89704 0.885218
\(126\) 0 0
\(127\) −1.09170 −0.0968730 −0.0484365 0.998826i \(-0.515424\pi\)
−0.0484365 + 0.998826i \(0.515424\pi\)
\(128\) −12.8566 −1.13637
\(129\) 0 0
\(130\) 5.41028 0.474513
\(131\) 8.56374 0.748217 0.374109 0.927385i \(-0.377949\pi\)
0.374109 + 0.927385i \(0.377949\pi\)
\(132\) 0 0
\(133\) 13.8890 1.20433
\(134\) −5.27635 −0.455807
\(135\) 0 0
\(136\) 1.45944 0.125146
\(137\) 15.2173 1.30010 0.650049 0.759892i \(-0.274748\pi\)
0.650049 + 0.759892i \(0.274748\pi\)
\(138\) 0 0
\(139\) −7.34342 −0.622861 −0.311430 0.950269i \(-0.600808\pi\)
−0.311430 + 0.950269i \(0.600808\pi\)
\(140\) −4.11331 −0.347638
\(141\) 0 0
\(142\) −0.531233 −0.0445801
\(143\) 2.80864 0.234870
\(144\) 0 0
\(145\) 2.47202 0.205290
\(146\) −6.97325 −0.577111
\(147\) 0 0
\(148\) 2.95291 0.242727
\(149\) −8.97409 −0.735186 −0.367593 0.929987i \(-0.619818\pi\)
−0.367593 + 0.929987i \(0.619818\pi\)
\(150\) 0 0
\(151\) 5.70128 0.463963 0.231982 0.972720i \(-0.425479\pi\)
0.231982 + 0.972720i \(0.425479\pi\)
\(152\) 6.39915 0.519040
\(153\) 0 0
\(154\) −7.02824 −0.566352
\(155\) −6.99590 −0.561924
\(156\) 0 0
\(157\) −0.592821 −0.0473123 −0.0236561 0.999720i \(-0.507531\pi\)
−0.0236561 + 0.999720i \(0.507531\pi\)
\(158\) −0.207665 −0.0165210
\(159\) 0 0
\(160\) −5.25783 −0.415668
\(161\) −16.0188 −1.26246
\(162\) 0 0
\(163\) −20.0035 −1.56680 −0.783398 0.621521i \(-0.786515\pi\)
−0.783398 + 0.621521i \(0.786515\pi\)
\(164\) −1.45950 −0.113968
\(165\) 0 0
\(166\) −5.05606 −0.392426
\(167\) −1.97988 −0.153208 −0.0766038 0.997062i \(-0.524408\pi\)
−0.0766038 + 0.997062i \(0.524408\pi\)
\(168\) 0 0
\(169\) −5.11154 −0.393195
\(170\) 1.47152 0.112860
\(171\) 0 0
\(172\) 4.56717 0.348244
\(173\) 5.75321 0.437408 0.218704 0.975791i \(-0.429817\pi\)
0.218704 + 0.975791i \(0.429817\pi\)
\(174\) 0 0
\(175\) −15.3771 −1.16240
\(176\) −4.98383 −0.375670
\(177\) 0 0
\(178\) 20.9987 1.57392
\(179\) 21.2013 1.58466 0.792329 0.610095i \(-0.208869\pi\)
0.792329 + 0.610095i \(0.208869\pi\)
\(180\) 0 0
\(181\) −18.2793 −1.35869 −0.679345 0.733819i \(-0.737736\pi\)
−0.679345 + 0.733819i \(0.737736\pi\)
\(182\) −19.7398 −1.46321
\(183\) 0 0
\(184\) −7.38044 −0.544093
\(185\) −3.84490 −0.282683
\(186\) 0 0
\(187\) 0.763911 0.0558627
\(188\) 10.8639 0.792328
\(189\) 0 0
\(190\) 6.45213 0.468087
\(191\) 6.81813 0.493342 0.246671 0.969099i \(-0.420663\pi\)
0.246671 + 0.969099i \(0.420663\pi\)
\(192\) 0 0
\(193\) −25.6061 −1.84317 −0.921583 0.388181i \(-0.873104\pi\)
−0.921583 + 0.388181i \(0.873104\pi\)
\(194\) −0.486828 −0.0349522
\(195\) 0 0
\(196\) 8.89787 0.635562
\(197\) 4.60372 0.328002 0.164001 0.986460i \(-0.447560\pi\)
0.164001 + 0.986460i \(0.447560\pi\)
\(198\) 0 0
\(199\) −10.2809 −0.728796 −0.364398 0.931243i \(-0.618725\pi\)
−0.364398 + 0.931243i \(0.618725\pi\)
\(200\) −7.08478 −0.500970
\(201\) 0 0
\(202\) 14.0000 0.985035
\(203\) −9.01936 −0.633035
\(204\) 0 0
\(205\) 1.90038 0.132728
\(206\) −18.8679 −1.31459
\(207\) 0 0
\(208\) −13.9978 −0.970572
\(209\) 3.34950 0.231690
\(210\) 0 0
\(211\) 19.2901 1.32798 0.663991 0.747740i \(-0.268861\pi\)
0.663991 + 0.747740i \(0.268861\pi\)
\(212\) −4.23816 −0.291078
\(213\) 0 0
\(214\) 34.8585 2.38288
\(215\) −5.94680 −0.405568
\(216\) 0 0
\(217\) 25.5251 1.73275
\(218\) 4.11259 0.278540
\(219\) 0 0
\(220\) −0.991974 −0.0668789
\(221\) 2.14555 0.144325
\(222\) 0 0
\(223\) 21.7966 1.45961 0.729803 0.683657i \(-0.239612\pi\)
0.729803 + 0.683657i \(0.239612\pi\)
\(224\) 19.1836 1.28176
\(225\) 0 0
\(226\) −0.329526 −0.0219198
\(227\) 19.0029 1.26127 0.630633 0.776081i \(-0.282795\pi\)
0.630633 + 0.776081i \(0.282795\pi\)
\(228\) 0 0
\(229\) −28.4656 −1.88106 −0.940529 0.339713i \(-0.889670\pi\)
−0.940529 + 0.339713i \(0.889670\pi\)
\(230\) −7.44153 −0.490680
\(231\) 0 0
\(232\) −4.15554 −0.272824
\(233\) 7.38981 0.484123 0.242061 0.970261i \(-0.422176\pi\)
0.242061 + 0.970261i \(0.422176\pi\)
\(234\) 0 0
\(235\) −14.1456 −0.922754
\(236\) 9.80813 0.638455
\(237\) 0 0
\(238\) −5.36895 −0.348017
\(239\) −10.8094 −0.699205 −0.349602 0.936898i \(-0.613683\pi\)
−0.349602 + 0.936898i \(0.613683\pi\)
\(240\) 0 0
\(241\) −26.6577 −1.71718 −0.858588 0.512666i \(-0.828658\pi\)
−0.858588 + 0.512666i \(0.828658\pi\)
\(242\) −1.69494 −0.108955
\(243\) 0 0
\(244\) 0.872835 0.0558775
\(245\) −11.5857 −0.740182
\(246\) 0 0
\(247\) 9.40754 0.598587
\(248\) 11.7603 0.746780
\(249\) 0 0
\(250\) −16.7749 −1.06094
\(251\) −12.8841 −0.813236 −0.406618 0.913598i \(-0.633292\pi\)
−0.406618 + 0.913598i \(0.633292\pi\)
\(252\) 0 0
\(253\) −3.86313 −0.242873
\(254\) 1.85038 0.116103
\(255\) 0 0
\(256\) 17.5387 1.09617
\(257\) 26.0777 1.62668 0.813341 0.581788i \(-0.197647\pi\)
0.813341 + 0.581788i \(0.197647\pi\)
\(258\) 0 0
\(259\) 14.0284 0.871683
\(260\) −2.78610 −0.172786
\(261\) 0 0
\(262\) −14.5151 −0.896743
\(263\) 21.6443 1.33464 0.667322 0.744769i \(-0.267441\pi\)
0.667322 + 0.744769i \(0.267441\pi\)
\(264\) 0 0
\(265\) 5.51839 0.338992
\(266\) −23.5411 −1.44340
\(267\) 0 0
\(268\) 2.71713 0.165975
\(269\) 1.70348 0.103863 0.0519315 0.998651i \(-0.483462\pi\)
0.0519315 + 0.998651i \(0.483462\pi\)
\(270\) 0 0
\(271\) 21.2091 1.28836 0.644180 0.764874i \(-0.277199\pi\)
0.644180 + 0.764874i \(0.277199\pi\)
\(272\) −3.80720 −0.230846
\(273\) 0 0
\(274\) −25.7924 −1.55818
\(275\) −3.70838 −0.223624
\(276\) 0 0
\(277\) −4.64693 −0.279207 −0.139603 0.990207i \(-0.544583\pi\)
−0.139603 + 0.990207i \(0.544583\pi\)
\(278\) 12.4467 0.746503
\(279\) 0 0
\(280\) −9.00330 −0.538050
\(281\) 3.70914 0.221269 0.110634 0.993861i \(-0.464712\pi\)
0.110634 + 0.993861i \(0.464712\pi\)
\(282\) 0 0
\(283\) 1.52229 0.0904910 0.0452455 0.998976i \(-0.485593\pi\)
0.0452455 + 0.998976i \(0.485593\pi\)
\(284\) 0.273566 0.0162331
\(285\) 0 0
\(286\) −4.76049 −0.281494
\(287\) −6.93367 −0.409281
\(288\) 0 0
\(289\) −16.4164 −0.965673
\(290\) −4.18994 −0.246042
\(291\) 0 0
\(292\) 3.59098 0.210146
\(293\) 25.9504 1.51604 0.758018 0.652234i \(-0.226168\pi\)
0.758018 + 0.652234i \(0.226168\pi\)
\(294\) 0 0
\(295\) −12.7709 −0.743551
\(296\) 6.46339 0.375677
\(297\) 0 0
\(298\) 15.2106 0.881125
\(299\) −10.8501 −0.627480
\(300\) 0 0
\(301\) 21.6973 1.25061
\(302\) −9.66335 −0.556063
\(303\) 0 0
\(304\) −16.6933 −0.957428
\(305\) −1.13650 −0.0650756
\(306\) 0 0
\(307\) 12.7503 0.727700 0.363850 0.931458i \(-0.381462\pi\)
0.363850 + 0.931458i \(0.381462\pi\)
\(308\) 3.61929 0.206228
\(309\) 0 0
\(310\) 11.8577 0.673470
\(311\) −2.42241 −0.137362 −0.0686812 0.997639i \(-0.521879\pi\)
−0.0686812 + 0.997639i \(0.521879\pi\)
\(312\) 0 0
\(313\) 1.39019 0.0785779 0.0392890 0.999228i \(-0.487491\pi\)
0.0392890 + 0.999228i \(0.487491\pi\)
\(314\) 1.00480 0.0567040
\(315\) 0 0
\(316\) 0.106940 0.00601586
\(317\) −4.56623 −0.256465 −0.128233 0.991744i \(-0.540930\pi\)
−0.128233 + 0.991744i \(0.540930\pi\)
\(318\) 0 0
\(319\) −2.17513 −0.121784
\(320\) −2.41648 −0.135085
\(321\) 0 0
\(322\) 27.1510 1.51307
\(323\) 2.55872 0.142371
\(324\) 0 0
\(325\) −10.4155 −0.577748
\(326\) 33.9048 1.87781
\(327\) 0 0
\(328\) −3.19459 −0.176391
\(329\) 51.6111 2.84541
\(330\) 0 0
\(331\) 8.68359 0.477293 0.238647 0.971106i \(-0.423296\pi\)
0.238647 + 0.971106i \(0.423296\pi\)
\(332\) 2.60369 0.142896
\(333\) 0 0
\(334\) 3.35579 0.183620
\(335\) −3.53790 −0.193296
\(336\) 0 0
\(337\) −19.3769 −1.05553 −0.527764 0.849391i \(-0.676969\pi\)
−0.527764 + 0.849391i \(0.676969\pi\)
\(338\) 8.66377 0.471247
\(339\) 0 0
\(340\) −0.757780 −0.0410964
\(341\) 6.15568 0.333349
\(342\) 0 0
\(343\) 13.2451 0.715168
\(344\) 9.99673 0.538987
\(345\) 0 0
\(346\) −9.75137 −0.524237
\(347\) −12.5548 −0.673978 −0.336989 0.941509i \(-0.609409\pi\)
−0.336989 + 0.941509i \(0.609409\pi\)
\(348\) 0 0
\(349\) 23.5352 1.25981 0.629907 0.776671i \(-0.283093\pi\)
0.629907 + 0.776671i \(0.283093\pi\)
\(350\) 26.0634 1.39315
\(351\) 0 0
\(352\) 4.62635 0.246585
\(353\) 29.5091 1.57061 0.785306 0.619108i \(-0.212506\pi\)
0.785306 + 0.619108i \(0.212506\pi\)
\(354\) 0 0
\(355\) −0.356203 −0.0189053
\(356\) −10.8136 −0.573118
\(357\) 0 0
\(358\) −35.9350 −1.89922
\(359\) 5.82428 0.307394 0.153697 0.988118i \(-0.450882\pi\)
0.153697 + 0.988118i \(0.450882\pi\)
\(360\) 0 0
\(361\) −7.78086 −0.409519
\(362\) 30.9824 1.62840
\(363\) 0 0
\(364\) 10.1653 0.532806
\(365\) −4.67572 −0.244738
\(366\) 0 0
\(367\) 32.4023 1.69139 0.845693 0.533670i \(-0.179188\pi\)
0.845693 + 0.533670i \(0.179188\pi\)
\(368\) 19.2532 1.00364
\(369\) 0 0
\(370\) 6.51689 0.338797
\(371\) −20.1343 −1.04532
\(372\) 0 0
\(373\) 4.55651 0.235927 0.117964 0.993018i \(-0.462363\pi\)
0.117964 + 0.993018i \(0.462363\pi\)
\(374\) −1.29479 −0.0669518
\(375\) 0 0
\(376\) 23.7791 1.22631
\(377\) −6.10915 −0.314637
\(378\) 0 0
\(379\) −26.0481 −1.33800 −0.669001 0.743262i \(-0.733278\pi\)
−0.669001 + 0.743262i \(0.733278\pi\)
\(380\) −3.32261 −0.170447
\(381\) 0 0
\(382\) −11.5563 −0.591274
\(383\) −9.19798 −0.469995 −0.234997 0.971996i \(-0.575508\pi\)
−0.234997 + 0.971996i \(0.575508\pi\)
\(384\) 0 0
\(385\) −4.71258 −0.240176
\(386\) 43.4009 2.20905
\(387\) 0 0
\(388\) 0.250699 0.0127273
\(389\) −4.77997 −0.242354 −0.121177 0.992631i \(-0.538667\pi\)
−0.121177 + 0.992631i \(0.538667\pi\)
\(390\) 0 0
\(391\) −2.95109 −0.149243
\(392\) 19.4759 0.983679
\(393\) 0 0
\(394\) −7.80306 −0.393112
\(395\) −0.139244 −0.00700613
\(396\) 0 0
\(397\) −0.984062 −0.0493886 −0.0246943 0.999695i \(-0.507861\pi\)
−0.0246943 + 0.999695i \(0.507861\pi\)
\(398\) 17.4256 0.873466
\(399\) 0 0
\(400\) 18.4819 0.924096
\(401\) −18.2690 −0.912312 −0.456156 0.889900i \(-0.650774\pi\)
−0.456156 + 0.889900i \(0.650774\pi\)
\(402\) 0 0
\(403\) 17.2891 0.861231
\(404\) −7.20949 −0.358685
\(405\) 0 0
\(406\) 15.2873 0.758696
\(407\) 3.38312 0.167695
\(408\) 0 0
\(409\) 29.2832 1.44796 0.723981 0.689820i \(-0.242310\pi\)
0.723981 + 0.689820i \(0.242310\pi\)
\(410\) −3.22103 −0.159075
\(411\) 0 0
\(412\) 9.71630 0.478688
\(413\) 46.5956 2.29282
\(414\) 0 0
\(415\) −3.39020 −0.166418
\(416\) 12.9938 0.637071
\(417\) 0 0
\(418\) −5.67721 −0.277681
\(419\) 30.2004 1.47539 0.737694 0.675135i \(-0.235915\pi\)
0.737694 + 0.675135i \(0.235915\pi\)
\(420\) 0 0
\(421\) 26.3462 1.28404 0.642018 0.766689i \(-0.278097\pi\)
0.642018 + 0.766689i \(0.278097\pi\)
\(422\) −32.6956 −1.59160
\(423\) 0 0
\(424\) −9.27657 −0.450510
\(425\) −2.83287 −0.137414
\(426\) 0 0
\(427\) 4.14659 0.200668
\(428\) −17.9509 −0.867689
\(429\) 0 0
\(430\) 10.0795 0.486076
\(431\) −27.7478 −1.33656 −0.668282 0.743908i \(-0.732970\pi\)
−0.668282 + 0.743908i \(0.732970\pi\)
\(432\) 0 0
\(433\) −7.30026 −0.350828 −0.175414 0.984495i \(-0.556126\pi\)
−0.175414 + 0.984495i \(0.556126\pi\)
\(434\) −43.2636 −2.07672
\(435\) 0 0
\(436\) −2.11784 −0.101426
\(437\) −12.9395 −0.618982
\(438\) 0 0
\(439\) 1.66481 0.0794573 0.0397286 0.999211i \(-0.487351\pi\)
0.0397286 + 0.999211i \(0.487351\pi\)
\(440\) −2.17125 −0.103510
\(441\) 0 0
\(442\) −3.63659 −0.172975
\(443\) 2.28757 0.108686 0.0543428 0.998522i \(-0.482694\pi\)
0.0543428 + 0.998522i \(0.482694\pi\)
\(444\) 0 0
\(445\) 14.0801 0.667460
\(446\) −36.9440 −1.74935
\(447\) 0 0
\(448\) 8.81671 0.416551
\(449\) 10.2005 0.481390 0.240695 0.970601i \(-0.422625\pi\)
0.240695 + 0.970601i \(0.422625\pi\)
\(450\) 0 0
\(451\) −1.67214 −0.0787378
\(452\) 0.169694 0.00798174
\(453\) 0 0
\(454\) −32.2088 −1.51163
\(455\) −13.2360 −0.620511
\(456\) 0 0
\(457\) −32.8187 −1.53520 −0.767598 0.640932i \(-0.778548\pi\)
−0.767598 + 0.640932i \(0.778548\pi\)
\(458\) 48.2476 2.25446
\(459\) 0 0
\(460\) 3.83212 0.178674
\(461\) −17.3153 −0.806455 −0.403228 0.915100i \(-0.632112\pi\)
−0.403228 + 0.915100i \(0.632112\pi\)
\(462\) 0 0
\(463\) −28.6210 −1.33013 −0.665066 0.746785i \(-0.731597\pi\)
−0.665066 + 0.746785i \(0.731597\pi\)
\(464\) 10.8405 0.503256
\(465\) 0 0
\(466\) −12.5253 −0.580224
\(467\) 16.1513 0.747393 0.373696 0.927551i \(-0.378090\pi\)
0.373696 + 0.927551i \(0.378090\pi\)
\(468\) 0 0
\(469\) 12.9083 0.596050
\(470\) 23.9759 1.10593
\(471\) 0 0
\(472\) 21.4683 0.988157
\(473\) 5.23257 0.240594
\(474\) 0 0
\(475\) −12.4212 −0.569924
\(476\) 2.76482 0.126725
\(477\) 0 0
\(478\) 18.3214 0.838001
\(479\) −15.7906 −0.721493 −0.360747 0.932664i \(-0.617478\pi\)
−0.360747 + 0.932664i \(0.617478\pi\)
\(480\) 0 0
\(481\) 9.50197 0.433252
\(482\) 45.1834 2.05805
\(483\) 0 0
\(484\) 0.872835 0.0396743
\(485\) −0.326429 −0.0148224
\(486\) 0 0
\(487\) −7.39301 −0.335009 −0.167505 0.985871i \(-0.553571\pi\)
−0.167505 + 0.985871i \(0.553571\pi\)
\(488\) 1.91048 0.0864834
\(489\) 0 0
\(490\) 19.6371 0.887113
\(491\) 23.8693 1.07721 0.538604 0.842559i \(-0.318952\pi\)
0.538604 + 0.842559i \(0.318952\pi\)
\(492\) 0 0
\(493\) −1.66160 −0.0748349
\(494\) −15.9452 −0.717411
\(495\) 0 0
\(496\) −30.6788 −1.37752
\(497\) 1.29963 0.0582965
\(498\) 0 0
\(499\) 25.5180 1.14234 0.571172 0.820830i \(-0.306489\pi\)
0.571172 + 0.820830i \(0.306489\pi\)
\(500\) 8.63848 0.386325
\(501\) 0 0
\(502\) 21.8378 0.974669
\(503\) 0.804971 0.0358919 0.0179459 0.999839i \(-0.494287\pi\)
0.0179459 + 0.999839i \(0.494287\pi\)
\(504\) 0 0
\(505\) 9.38729 0.417729
\(506\) 6.54779 0.291085
\(507\) 0 0
\(508\) −0.952877 −0.0422771
\(509\) −33.1176 −1.46791 −0.733955 0.679198i \(-0.762328\pi\)
−0.733955 + 0.679198i \(0.762328\pi\)
\(510\) 0 0
\(511\) 17.0597 0.754677
\(512\) −4.01391 −0.177391
\(513\) 0 0
\(514\) −44.2002 −1.94959
\(515\) −12.6513 −0.557485
\(516\) 0 0
\(517\) 12.4466 0.547402
\(518\) −23.7774 −1.04472
\(519\) 0 0
\(520\) −6.09827 −0.267427
\(521\) −9.15916 −0.401270 −0.200635 0.979666i \(-0.564301\pi\)
−0.200635 + 0.979666i \(0.564301\pi\)
\(522\) 0 0
\(523\) 21.3574 0.933893 0.466947 0.884285i \(-0.345354\pi\)
0.466947 + 0.884285i \(0.345354\pi\)
\(524\) 7.47473 0.326535
\(525\) 0 0
\(526\) −36.6858 −1.59958
\(527\) 4.70239 0.204839
\(528\) 0 0
\(529\) −8.07623 −0.351141
\(530\) −9.35337 −0.406284
\(531\) 0 0
\(532\) 12.1228 0.525590
\(533\) −4.69643 −0.203425
\(534\) 0 0
\(535\) 23.3734 1.01052
\(536\) 5.94732 0.256885
\(537\) 0 0
\(538\) −2.88731 −0.124481
\(539\) 10.1942 0.439096
\(540\) 0 0
\(541\) −24.7604 −1.06453 −0.532266 0.846577i \(-0.678659\pi\)
−0.532266 + 0.846577i \(0.678659\pi\)
\(542\) −35.9482 −1.54411
\(543\) 0 0
\(544\) 3.53412 0.151524
\(545\) 2.75758 0.118122
\(546\) 0 0
\(547\) 2.04043 0.0872427 0.0436213 0.999048i \(-0.486110\pi\)
0.0436213 + 0.999048i \(0.486110\pi\)
\(548\) 13.2822 0.567386
\(549\) 0 0
\(550\) 6.28549 0.268014
\(551\) −7.28558 −0.310376
\(552\) 0 0
\(553\) 0.508042 0.0216042
\(554\) 7.87628 0.334631
\(555\) 0 0
\(556\) −6.40960 −0.271827
\(557\) 6.92621 0.293473 0.146737 0.989176i \(-0.453123\pi\)
0.146737 + 0.989176i \(0.453123\pi\)
\(558\) 0 0
\(559\) 14.6964 0.621592
\(560\) 23.4867 0.992495
\(561\) 0 0
\(562\) −6.28679 −0.265192
\(563\) −24.0659 −1.01426 −0.507128 0.861871i \(-0.669293\pi\)
−0.507128 + 0.861871i \(0.669293\pi\)
\(564\) 0 0
\(565\) −0.220954 −0.00929562
\(566\) −2.58020 −0.108454
\(567\) 0 0
\(568\) 0.598787 0.0251245
\(569\) 10.8199 0.453594 0.226797 0.973942i \(-0.427175\pi\)
0.226797 + 0.973942i \(0.427175\pi\)
\(570\) 0 0
\(571\) 23.3189 0.975867 0.487933 0.872881i \(-0.337751\pi\)
0.487933 + 0.872881i \(0.337751\pi\)
\(572\) 2.45148 0.102502
\(573\) 0 0
\(574\) 11.7522 0.490526
\(575\) 14.3259 0.597433
\(576\) 0 0
\(577\) 19.0741 0.794066 0.397033 0.917804i \(-0.370040\pi\)
0.397033 + 0.917804i \(0.370040\pi\)
\(578\) 27.8249 1.15737
\(579\) 0 0
\(580\) 2.15767 0.0895923
\(581\) 12.3694 0.513168
\(582\) 0 0
\(583\) −4.85562 −0.201099
\(584\) 7.86001 0.325249
\(585\) 0 0
\(586\) −43.9844 −1.81698
\(587\) 19.9932 0.825206 0.412603 0.910911i \(-0.364620\pi\)
0.412603 + 0.910911i \(0.364620\pi\)
\(588\) 0 0
\(589\) 20.6184 0.849568
\(590\) 21.6460 0.891151
\(591\) 0 0
\(592\) −16.8609 −0.692978
\(593\) −20.8462 −0.856052 −0.428026 0.903766i \(-0.640791\pi\)
−0.428026 + 0.903766i \(0.640791\pi\)
\(594\) 0 0
\(595\) −3.60000 −0.147585
\(596\) −7.83290 −0.320848
\(597\) 0 0
\(598\) 18.3904 0.752039
\(599\) 35.7082 1.45900 0.729498 0.683983i \(-0.239754\pi\)
0.729498 + 0.683983i \(0.239754\pi\)
\(600\) 0 0
\(601\) −25.3646 −1.03464 −0.517322 0.855791i \(-0.673071\pi\)
−0.517322 + 0.855791i \(0.673071\pi\)
\(602\) −36.7758 −1.49887
\(603\) 0 0
\(604\) 4.97628 0.202482
\(605\) −1.13650 −0.0462051
\(606\) 0 0
\(607\) 31.9208 1.29562 0.647812 0.761800i \(-0.275684\pi\)
0.647812 + 0.761800i \(0.275684\pi\)
\(608\) 15.4959 0.628444
\(609\) 0 0
\(610\) 1.92630 0.0779935
\(611\) 34.9581 1.41425
\(612\) 0 0
\(613\) 12.6456 0.510751 0.255376 0.966842i \(-0.417801\pi\)
0.255376 + 0.966842i \(0.417801\pi\)
\(614\) −21.6111 −0.872153
\(615\) 0 0
\(616\) 7.92198 0.319186
\(617\) 11.8467 0.476930 0.238465 0.971151i \(-0.423356\pi\)
0.238465 + 0.971151i \(0.423356\pi\)
\(618\) 0 0
\(619\) 5.81776 0.233835 0.116918 0.993142i \(-0.462699\pi\)
0.116918 + 0.993142i \(0.462699\pi\)
\(620\) −6.10627 −0.245234
\(621\) 0 0
\(622\) 4.10585 0.164630
\(623\) −51.3722 −2.05818
\(624\) 0 0
\(625\) 7.29394 0.291758
\(626\) −2.35629 −0.0941762
\(627\) 0 0
\(628\) −0.517435 −0.0206479
\(629\) 2.58440 0.103047
\(630\) 0 0
\(631\) 28.1087 1.11899 0.559495 0.828834i \(-0.310995\pi\)
0.559495 + 0.828834i \(0.310995\pi\)
\(632\) 0.234073 0.00931093
\(633\) 0 0
\(634\) 7.73951 0.307375
\(635\) 1.24072 0.0492363
\(636\) 0 0
\(637\) 28.6319 1.13444
\(638\) 3.68672 0.145959
\(639\) 0 0
\(640\) 14.6115 0.577568
\(641\) 17.8256 0.704069 0.352034 0.935987i \(-0.385490\pi\)
0.352034 + 0.935987i \(0.385490\pi\)
\(642\) 0 0
\(643\) −21.3216 −0.840842 −0.420421 0.907329i \(-0.638118\pi\)
−0.420421 + 0.907329i \(0.638118\pi\)
\(644\) −13.9818 −0.550960
\(645\) 0 0
\(646\) −4.33689 −0.170633
\(647\) 37.4930 1.47400 0.737000 0.675893i \(-0.236242\pi\)
0.737000 + 0.675893i \(0.236242\pi\)
\(648\) 0 0
\(649\) 11.2371 0.441095
\(650\) 17.6537 0.692435
\(651\) 0 0
\(652\) −17.4598 −0.683777
\(653\) −26.0148 −1.01804 −0.509018 0.860756i \(-0.669991\pi\)
−0.509018 + 0.860756i \(0.669991\pi\)
\(654\) 0 0
\(655\) −9.73266 −0.380286
\(656\) 8.33364 0.325374
\(657\) 0 0
\(658\) −87.4779 −3.41024
\(659\) 1.69718 0.0661127 0.0330564 0.999453i \(-0.489476\pi\)
0.0330564 + 0.999453i \(0.489476\pi\)
\(660\) 0 0
\(661\) 28.7729 1.11914 0.559569 0.828784i \(-0.310967\pi\)
0.559569 + 0.828784i \(0.310967\pi\)
\(662\) −14.7182 −0.572039
\(663\) 0 0
\(664\) 5.69901 0.221165
\(665\) −15.7848 −0.612108
\(666\) 0 0
\(667\) 8.40280 0.325358
\(668\) −1.72811 −0.0668625
\(669\) 0 0
\(670\) 5.99655 0.231667
\(671\) 1.00000 0.0386046
\(672\) 0 0
\(673\) −31.1045 −1.19899 −0.599496 0.800378i \(-0.704632\pi\)
−0.599496 + 0.800378i \(0.704632\pi\)
\(674\) 32.8428 1.26506
\(675\) 0 0
\(676\) −4.46153 −0.171597
\(677\) −24.6673 −0.948043 −0.474021 0.880513i \(-0.657198\pi\)
−0.474021 + 0.880513i \(0.657198\pi\)
\(678\) 0 0
\(679\) 1.19100 0.0457064
\(680\) −1.65865 −0.0636062
\(681\) 0 0
\(682\) −10.4335 −0.399520
\(683\) −42.6506 −1.63198 −0.815990 0.578066i \(-0.803807\pi\)
−0.815990 + 0.578066i \(0.803807\pi\)
\(684\) 0 0
\(685\) −17.2944 −0.660783
\(686\) −22.4497 −0.857133
\(687\) 0 0
\(688\) −26.0782 −0.994223
\(689\) −13.6377 −0.519555
\(690\) 0 0
\(691\) −13.0177 −0.495218 −0.247609 0.968860i \(-0.579645\pi\)
−0.247609 + 0.968860i \(0.579645\pi\)
\(692\) 5.02160 0.190893
\(693\) 0 0
\(694\) 21.2797 0.807767
\(695\) 8.34577 0.316573
\(696\) 0 0
\(697\) −1.27736 −0.0483836
\(698\) −39.8909 −1.50989
\(699\) 0 0
\(700\) −13.4217 −0.507292
\(701\) −28.0409 −1.05909 −0.529545 0.848282i \(-0.677638\pi\)
−0.529545 + 0.848282i \(0.677638\pi\)
\(702\) 0 0
\(703\) 11.3318 0.427385
\(704\) 2.12626 0.0801363
\(705\) 0 0
\(706\) −50.0163 −1.88239
\(707\) −34.2502 −1.28811
\(708\) 0 0
\(709\) −25.5510 −0.959587 −0.479794 0.877381i \(-0.659288\pi\)
−0.479794 + 0.877381i \(0.659288\pi\)
\(710\) 0.603744 0.0226581
\(711\) 0 0
\(712\) −23.6690 −0.887033
\(713\) −23.7802 −0.890575
\(714\) 0 0
\(715\) −3.19201 −0.119374
\(716\) 18.5052 0.691572
\(717\) 0 0
\(718\) −9.87182 −0.368413
\(719\) −29.5599 −1.10240 −0.551200 0.834373i \(-0.685830\pi\)
−0.551200 + 0.834373i \(0.685830\pi\)
\(720\) 0 0
\(721\) 46.1594 1.71906
\(722\) 13.1881 0.490811
\(723\) 0 0
\(724\) −15.9548 −0.592956
\(725\) 8.06619 0.299571
\(726\) 0 0
\(727\) 46.5039 1.72473 0.862367 0.506285i \(-0.168981\pi\)
0.862367 + 0.506285i \(0.168981\pi\)
\(728\) 22.2500 0.824640
\(729\) 0 0
\(730\) 7.92508 0.293320
\(731\) 3.99722 0.147843
\(732\) 0 0
\(733\) 30.3793 1.12209 0.561043 0.827787i \(-0.310400\pi\)
0.561043 + 0.827787i \(0.310400\pi\)
\(734\) −54.9201 −2.02714
\(735\) 0 0
\(736\) −17.8722 −0.658777
\(737\) 3.11299 0.114669
\(738\) 0 0
\(739\) 24.5413 0.902765 0.451382 0.892331i \(-0.350931\pi\)
0.451382 + 0.892331i \(0.350931\pi\)
\(740\) −3.35597 −0.123368
\(741\) 0 0
\(742\) 34.1264 1.25282
\(743\) 24.7861 0.909313 0.454657 0.890667i \(-0.349762\pi\)
0.454657 + 0.890667i \(0.349762\pi\)
\(744\) 0 0
\(745\) 10.1990 0.373663
\(746\) −7.72304 −0.282760
\(747\) 0 0
\(748\) 0.666769 0.0243795
\(749\) −85.2795 −3.11605
\(750\) 0 0
\(751\) 23.7265 0.865793 0.432897 0.901444i \(-0.357491\pi\)
0.432897 + 0.901444i \(0.357491\pi\)
\(752\) −62.0319 −2.26207
\(753\) 0 0
\(754\) 10.3547 0.377095
\(755\) −6.47948 −0.235812
\(756\) 0 0
\(757\) −12.6491 −0.459739 −0.229869 0.973222i \(-0.573830\pi\)
−0.229869 + 0.973222i \(0.573830\pi\)
\(758\) 44.1501 1.60360
\(759\) 0 0
\(760\) −7.27261 −0.263805
\(761\) 14.7959 0.536352 0.268176 0.963370i \(-0.413579\pi\)
0.268176 + 0.963370i \(0.413579\pi\)
\(762\) 0 0
\(763\) −10.0612 −0.364241
\(764\) 5.95110 0.215303
\(765\) 0 0
\(766\) 15.5901 0.563292
\(767\) 31.5610 1.13960
\(768\) 0 0
\(769\) 25.1700 0.907652 0.453826 0.891090i \(-0.350059\pi\)
0.453826 + 0.891090i \(0.350059\pi\)
\(770\) 7.98757 0.287852
\(771\) 0 0
\(772\) −22.3499 −0.804390
\(773\) 23.2571 0.836500 0.418250 0.908332i \(-0.362644\pi\)
0.418250 + 0.908332i \(0.362644\pi\)
\(774\) 0 0
\(775\) −22.8276 −0.819991
\(776\) 0.548736 0.0196985
\(777\) 0 0
\(778\) 8.10178 0.290463
\(779\) −5.60082 −0.200670
\(780\) 0 0
\(781\) 0.313422 0.0112151
\(782\) 5.00193 0.178869
\(783\) 0 0
\(784\) −50.8062 −1.81451
\(785\) 0.673739 0.0240468
\(786\) 0 0
\(787\) 34.9096 1.24439 0.622196 0.782862i \(-0.286241\pi\)
0.622196 + 0.782862i \(0.286241\pi\)
\(788\) 4.01829 0.143146
\(789\) 0 0
\(790\) 0.236011 0.00839689
\(791\) 0.806168 0.0286641
\(792\) 0 0
\(793\) 2.80864 0.0997378
\(794\) 1.66793 0.0591926
\(795\) 0 0
\(796\) −8.97355 −0.318059
\(797\) −24.0098 −0.850472 −0.425236 0.905082i \(-0.639809\pi\)
−0.425236 + 0.905082i \(0.639809\pi\)
\(798\) 0 0
\(799\) 9.50812 0.336373
\(800\) −17.1562 −0.606565
\(801\) 0 0
\(802\) 30.9650 1.09341
\(803\) 4.11415 0.145185
\(804\) 0 0
\(805\) 18.2053 0.641653
\(806\) −29.3040 −1.03219
\(807\) 0 0
\(808\) −15.7803 −0.555149
\(809\) 50.4476 1.77364 0.886822 0.462112i \(-0.152908\pi\)
0.886822 + 0.462112i \(0.152908\pi\)
\(810\) 0 0
\(811\) −31.5727 −1.10867 −0.554334 0.832295i \(-0.687027\pi\)
−0.554334 + 0.832295i \(0.687027\pi\)
\(812\) −7.87241 −0.276268
\(813\) 0 0
\(814\) −5.73420 −0.200984
\(815\) 22.7339 0.796334
\(816\) 0 0
\(817\) 17.5265 0.613174
\(818\) −49.6334 −1.73539
\(819\) 0 0
\(820\) 1.65872 0.0579249
\(821\) −5.36610 −0.187278 −0.0936390 0.995606i \(-0.529850\pi\)
−0.0936390 + 0.995606i \(0.529850\pi\)
\(822\) 0 0
\(823\) −34.2346 −1.19334 −0.596671 0.802486i \(-0.703510\pi\)
−0.596671 + 0.802486i \(0.703510\pi\)
\(824\) 21.2672 0.740880
\(825\) 0 0
\(826\) −78.9770 −2.74796
\(827\) −27.0655 −0.941159 −0.470579 0.882358i \(-0.655955\pi\)
−0.470579 + 0.882358i \(0.655955\pi\)
\(828\) 0 0
\(829\) −8.45949 −0.293810 −0.146905 0.989151i \(-0.546931\pi\)
−0.146905 + 0.989151i \(0.546931\pi\)
\(830\) 5.74619 0.199453
\(831\) 0 0
\(832\) 5.97189 0.207038
\(833\) 7.78748 0.269820
\(834\) 0 0
\(835\) 2.25013 0.0778688
\(836\) 2.92356 0.101113
\(837\) 0 0
\(838\) −51.1881 −1.76826
\(839\) 41.7580 1.44165 0.720824 0.693119i \(-0.243764\pi\)
0.720824 + 0.693119i \(0.243764\pi\)
\(840\) 0 0
\(841\) −24.2688 −0.836856
\(842\) −44.6554 −1.53893
\(843\) 0 0
\(844\) 16.8370 0.579555
\(845\) 5.80924 0.199844
\(846\) 0 0
\(847\) 4.14659 0.142479
\(848\) 24.1996 0.831017
\(849\) 0 0
\(850\) 4.80156 0.164692
\(851\) −13.0694 −0.448014
\(852\) 0 0
\(853\) 6.48751 0.222128 0.111064 0.993813i \(-0.464574\pi\)
0.111064 + 0.993813i \(0.464574\pi\)
\(854\) −7.02824 −0.240501
\(855\) 0 0
\(856\) −39.2913 −1.34295
\(857\) 53.2173 1.81787 0.908933 0.416941i \(-0.136898\pi\)
0.908933 + 0.416941i \(0.136898\pi\)
\(858\) 0 0
\(859\) 54.5457 1.86107 0.930537 0.366198i \(-0.119341\pi\)
0.930537 + 0.366198i \(0.119341\pi\)
\(860\) −5.19057 −0.176997
\(861\) 0 0
\(862\) 47.0310 1.60188
\(863\) −9.97813 −0.339660 −0.169830 0.985473i \(-0.554322\pi\)
−0.169830 + 0.985473i \(0.554322\pi\)
\(864\) 0 0
\(865\) −6.53850 −0.222316
\(866\) 12.3735 0.420469
\(867\) 0 0
\(868\) 22.2792 0.756205
\(869\) 0.122521 0.00415622
\(870\) 0 0
\(871\) 8.74328 0.296255
\(872\) −4.63557 −0.156980
\(873\) 0 0
\(874\) 21.9318 0.741854
\(875\) 41.0390 1.38737
\(876\) 0 0
\(877\) 18.1582 0.613159 0.306580 0.951845i \(-0.400815\pi\)
0.306580 + 0.951845i \(0.400815\pi\)
\(878\) −2.82177 −0.0952300
\(879\) 0 0
\(880\) 5.66410 0.190937
\(881\) 26.6452 0.897700 0.448850 0.893607i \(-0.351834\pi\)
0.448850 + 0.893607i \(0.351834\pi\)
\(882\) 0 0
\(883\) −10.9254 −0.367668 −0.183834 0.982957i \(-0.558851\pi\)
−0.183834 + 0.982957i \(0.558851\pi\)
\(884\) 1.87271 0.0629862
\(885\) 0 0
\(886\) −3.87730 −0.130260
\(887\) 34.3580 1.15363 0.576814 0.816875i \(-0.304296\pi\)
0.576814 + 0.816875i \(0.304296\pi\)
\(888\) 0 0
\(889\) −4.52685 −0.151826
\(890\) −23.8649 −0.799955
\(891\) 0 0
\(892\) 19.0248 0.636998
\(893\) 41.6900 1.39510
\(894\) 0 0
\(895\) −24.0952 −0.805412
\(896\) −53.3110 −1.78099
\(897\) 0 0
\(898\) −17.2892 −0.576949
\(899\) −13.3894 −0.446561
\(900\) 0 0
\(901\) −3.70926 −0.123573
\(902\) 2.83418 0.0943678
\(903\) 0 0
\(904\) 0.371430 0.0123536
\(905\) 20.7743 0.690563
\(906\) 0 0
\(907\) −0.294342 −0.00977345 −0.00488673 0.999988i \(-0.501555\pi\)
−0.00488673 + 0.999988i \(0.501555\pi\)
\(908\) 16.5864 0.550438
\(909\) 0 0
\(910\) 22.4342 0.743687
\(911\) 5.06741 0.167891 0.0839454 0.996470i \(-0.473248\pi\)
0.0839454 + 0.996470i \(0.473248\pi\)
\(912\) 0 0
\(913\) 2.98302 0.0987237
\(914\) 55.6259 1.83994
\(915\) 0 0
\(916\) −24.8458 −0.820927
\(917\) 35.5103 1.17265
\(918\) 0 0
\(919\) −1.35956 −0.0448476 −0.0224238 0.999749i \(-0.507138\pi\)
−0.0224238 + 0.999749i \(0.507138\pi\)
\(920\) 8.38784 0.276539
\(921\) 0 0
\(922\) 29.3485 0.966542
\(923\) 0.880290 0.0289751
\(924\) 0 0
\(925\) −12.5459 −0.412506
\(926\) 48.5110 1.59417
\(927\) 0 0
\(928\) −10.0629 −0.330331
\(929\) −28.0140 −0.919111 −0.459555 0.888149i \(-0.651991\pi\)
−0.459555 + 0.888149i \(0.651991\pi\)
\(930\) 0 0
\(931\) 34.1455 1.11907
\(932\) 6.45009 0.211280
\(933\) 0 0
\(934\) −27.3755 −0.895755
\(935\) −0.868182 −0.0283926
\(936\) 0 0
\(937\) −30.1476 −0.984879 −0.492439 0.870347i \(-0.663895\pi\)
−0.492439 + 0.870347i \(0.663895\pi\)
\(938\) −21.8789 −0.714370
\(939\) 0 0
\(940\) −12.3467 −0.402706
\(941\) 38.8303 1.26583 0.632916 0.774221i \(-0.281858\pi\)
0.632916 + 0.774221i \(0.281858\pi\)
\(942\) 0 0
\(943\) 6.45968 0.210356
\(944\) −56.0038 −1.82277
\(945\) 0 0
\(946\) −8.86891 −0.288353
\(947\) −8.12694 −0.264090 −0.132045 0.991244i \(-0.542154\pi\)
−0.132045 + 0.991244i \(0.542154\pi\)
\(948\) 0 0
\(949\) 11.5552 0.375097
\(950\) 21.0532 0.683057
\(951\) 0 0
\(952\) 6.05169 0.196136
\(953\) 15.8810 0.514436 0.257218 0.966353i \(-0.417194\pi\)
0.257218 + 0.966353i \(0.417194\pi\)
\(954\) 0 0
\(955\) −7.74877 −0.250744
\(956\) −9.43486 −0.305145
\(957\) 0 0
\(958\) 26.7643 0.864714
\(959\) 63.0997 2.03760
\(960\) 0 0
\(961\) 6.89236 0.222334
\(962\) −16.1053 −0.519256
\(963\) 0 0
\(964\) −23.2678 −0.749406
\(965\) 29.1012 0.936801
\(966\) 0 0
\(967\) −12.2586 −0.394209 −0.197104 0.980383i \(-0.563154\pi\)
−0.197104 + 0.980383i \(0.563154\pi\)
\(968\) 1.91048 0.0614052
\(969\) 0 0
\(970\) 0.553278 0.0177647
\(971\) 31.0824 0.997482 0.498741 0.866751i \(-0.333796\pi\)
0.498741 + 0.866751i \(0.333796\pi\)
\(972\) 0 0
\(973\) −30.4502 −0.976187
\(974\) 12.5307 0.401511
\(975\) 0 0
\(976\) −4.98383 −0.159528
\(977\) 33.1624 1.06096 0.530480 0.847697i \(-0.322012\pi\)
0.530480 + 0.847697i \(0.322012\pi\)
\(978\) 0 0
\(979\) −12.3890 −0.395955
\(980\) −10.1124 −0.323029
\(981\) 0 0
\(982\) −40.4572 −1.29104
\(983\) 15.8218 0.504638 0.252319 0.967644i \(-0.418807\pi\)
0.252319 + 0.967644i \(0.418807\pi\)
\(984\) 0 0
\(985\) −5.23212 −0.166709
\(986\) 2.81633 0.0896901
\(987\) 0 0
\(988\) 8.21123 0.261234
\(989\) −20.2141 −0.642771
\(990\) 0 0
\(991\) −0.275528 −0.00875245 −0.00437623 0.999990i \(-0.501393\pi\)
−0.00437623 + 0.999990i \(0.501393\pi\)
\(992\) 28.4783 0.904187
\(993\) 0 0
\(994\) −2.20281 −0.0698687
\(995\) 11.6842 0.370415
\(996\) 0 0
\(997\) 45.5754 1.44339 0.721694 0.692212i \(-0.243364\pi\)
0.721694 + 0.692212i \(0.243364\pi\)
\(998\) −43.2516 −1.36911
\(999\) 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 \(a_p\))