Properties

Label 8048.2.a.p.1.8
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 10
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(-0.858231\)
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.85823 q^{3}\) \(+1.44291 q^{5}\) \(+1.96509 q^{7}\) \(+0.453023 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.85823 q^{3}\) \(+1.44291 q^{5}\) \(+1.96509 q^{7}\) \(+0.453023 q^{9}\) \(-2.85614 q^{11}\) \(-3.84427 q^{13}\) \(+2.68126 q^{15}\) \(+1.30329 q^{17}\) \(-3.53196 q^{19}\) \(+3.65159 q^{21}\) \(-4.20650 q^{23}\) \(-2.91801 q^{25}\) \(-4.73287 q^{27}\) \(-1.10402 q^{29}\) \(+3.53201 q^{31}\) \(-5.30738 q^{33}\) \(+2.83545 q^{35}\) \(-6.61903 q^{37}\) \(-7.14353 q^{39}\) \(+0.671095 q^{41}\) \(+4.32289 q^{43}\) \(+0.653672 q^{45}\) \(+0.378524 q^{47}\) \(-3.13843 q^{49}\) \(+2.42182 q^{51}\) \(-7.13700 q^{53}\) \(-4.12116 q^{55}\) \(-6.56319 q^{57}\) \(+13.8806 q^{59}\) \(-6.51374 q^{61}\) \(+0.890231 q^{63}\) \(-5.54693 q^{65}\) \(+7.55189 q^{67}\) \(-7.81664 q^{69}\) \(-0.0744967 q^{71}\) \(+3.29052 q^{73}\) \(-5.42234 q^{75}\) \(-5.61258 q^{77}\) \(-8.57578 q^{79}\) \(-10.1538 q^{81}\) \(-14.8165 q^{83}\) \(+1.88053 q^{85}\) \(-2.05152 q^{87}\) \(-17.5415 q^{89}\) \(-7.55432 q^{91}\) \(+6.56329 q^{93}\) \(-5.09630 q^{95}\) \(-8.01702 q^{97}\) \(-1.29390 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(10q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(10q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut -\mathstrut 27q^{25} \) \(\mathstrut +\mathstrut 2q^{27} \) \(\mathstrut -\mathstrut 9q^{29} \) \(\mathstrut +\mathstrut 22q^{31} \) \(\mathstrut -\mathstrut 10q^{33} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut -\mathstrut 35q^{37} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 4q^{41} \) \(\mathstrut +\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 7q^{47} \) \(\mathstrut -\mathstrut 27q^{49} \) \(\mathstrut -\mathstrut 9q^{51} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut -\mathstrut 23q^{57} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 4q^{61} \) \(\mathstrut -\mathstrut 10q^{63} \) \(\mathstrut -\mathstrut 16q^{65} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut q^{71} \) \(\mathstrut -\mathstrut 31q^{73} \) \(\mathstrut -\mathstrut 30q^{75} \) \(\mathstrut +\mathstrut 3q^{77} \) \(\mathstrut +\mathstrut 10q^{79} \) \(\mathstrut -\mathstrut 6q^{81} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 25q^{87} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 6q^{93} \) \(\mathstrut -\mathstrut 39q^{95} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 35q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 0
\(3\) 1.85823 1.07285 0.536425 0.843948i \(-0.319774\pi\)
0.536425 + 0.843948i \(0.319774\pi\)
\(4\) 0 0
\(5\) 1.44291 0.645289 0.322644 0.946520i \(-0.395428\pi\)
0.322644 + 0.946520i \(0.395428\pi\)
\(6\) 0 0
\(7\) 1.96509 0.742734 0.371367 0.928486i \(-0.378889\pi\)
0.371367 + 0.928486i \(0.378889\pi\)
\(8\) 0 0
\(9\) 0.453023 0.151008
\(10\) 0 0
\(11\) −2.85614 −0.861160 −0.430580 0.902552i \(-0.641691\pi\)
−0.430580 + 0.902552i \(0.641691\pi\)
\(12\) 0 0
\(13\) −3.84427 −1.06621 −0.533104 0.846050i \(-0.678974\pi\)
−0.533104 + 0.846050i \(0.678974\pi\)
\(14\) 0 0
\(15\) 2.68126 0.692298
\(16\) 0 0
\(17\) 1.30329 0.316095 0.158047 0.987432i \(-0.449480\pi\)
0.158047 + 0.987432i \(0.449480\pi\)
\(18\) 0 0
\(19\) −3.53196 −0.810287 −0.405143 0.914253i \(-0.632778\pi\)
−0.405143 + 0.914253i \(0.632778\pi\)
\(20\) 0 0
\(21\) 3.65159 0.796842
\(22\) 0 0
\(23\) −4.20650 −0.877115 −0.438558 0.898703i \(-0.644510\pi\)
−0.438558 + 0.898703i \(0.644510\pi\)
\(24\) 0 0
\(25\) −2.91801 −0.583602
\(26\) 0 0
\(27\) −4.73287 −0.910842
\(28\) 0 0
\(29\) −1.10402 −0.205011 −0.102506 0.994732i \(-0.532686\pi\)
−0.102506 + 0.994732i \(0.532686\pi\)
\(30\) 0 0
\(31\) 3.53201 0.634368 0.317184 0.948364i \(-0.397263\pi\)
0.317184 + 0.948364i \(0.397263\pi\)
\(32\) 0 0
\(33\) −5.30738 −0.923896
\(34\) 0 0
\(35\) 2.83545 0.479278
\(36\) 0 0
\(37\) −6.61903 −1.08816 −0.544081 0.839033i \(-0.683121\pi\)
−0.544081 + 0.839033i \(0.683121\pi\)
\(38\) 0 0
\(39\) −7.14353 −1.14388
\(40\) 0 0
\(41\) 0.671095 0.104807 0.0524037 0.998626i \(-0.483312\pi\)
0.0524037 + 0.998626i \(0.483312\pi\)
\(42\) 0 0
\(43\) 4.32289 0.659235 0.329617 0.944115i \(-0.393080\pi\)
0.329617 + 0.944115i \(0.393080\pi\)
\(44\) 0 0
\(45\) 0.653672 0.0974436
\(46\) 0 0
\(47\) 0.378524 0.0552134 0.0276067 0.999619i \(-0.491211\pi\)
0.0276067 + 0.999619i \(0.491211\pi\)
\(48\) 0 0
\(49\) −3.13843 −0.448347
\(50\) 0 0
\(51\) 2.42182 0.339122
\(52\) 0 0
\(53\) −7.13700 −0.980342 −0.490171 0.871626i \(-0.663066\pi\)
−0.490171 + 0.871626i \(0.663066\pi\)
\(54\) 0 0
\(55\) −4.12116 −0.555697
\(56\) 0 0
\(57\) −6.56319 −0.869316
\(58\) 0 0
\(59\) 13.8806 1.80709 0.903547 0.428489i \(-0.140954\pi\)
0.903547 + 0.428489i \(0.140954\pi\)
\(60\) 0 0
\(61\) −6.51374 −0.833999 −0.417000 0.908907i \(-0.636918\pi\)
−0.417000 + 0.908907i \(0.636918\pi\)
\(62\) 0 0
\(63\) 0.890231 0.112159
\(64\) 0 0
\(65\) −5.54693 −0.688012
\(66\) 0 0
\(67\) 7.55189 0.922610 0.461305 0.887242i \(-0.347381\pi\)
0.461305 + 0.887242i \(0.347381\pi\)
\(68\) 0 0
\(69\) −7.81664 −0.941013
\(70\) 0 0
\(71\) −0.0744967 −0.00884113 −0.00442057 0.999990i \(-0.501407\pi\)
−0.00442057 + 0.999990i \(0.501407\pi\)
\(72\) 0 0
\(73\) 3.29052 0.385126 0.192563 0.981285i \(-0.438320\pi\)
0.192563 + 0.981285i \(0.438320\pi\)
\(74\) 0 0
\(75\) −5.42234 −0.626118
\(76\) 0 0
\(77\) −5.61258 −0.639612
\(78\) 0 0
\(79\) −8.57578 −0.964850 −0.482425 0.875937i \(-0.660244\pi\)
−0.482425 + 0.875937i \(0.660244\pi\)
\(80\) 0 0
\(81\) −10.1538 −1.12820
\(82\) 0 0
\(83\) −14.8165 −1.62632 −0.813158 0.582042i \(-0.802254\pi\)
−0.813158 + 0.582042i \(0.802254\pi\)
\(84\) 0 0
\(85\) 1.88053 0.203973
\(86\) 0 0
\(87\) −2.05152 −0.219946
\(88\) 0 0
\(89\) −17.5415 −1.85940 −0.929700 0.368318i \(-0.879934\pi\)
−0.929700 + 0.368318i \(0.879934\pi\)
\(90\) 0 0
\(91\) −7.55432 −0.791908
\(92\) 0 0
\(93\) 6.56329 0.680582
\(94\) 0 0
\(95\) −5.09630 −0.522869
\(96\) 0 0
\(97\) −8.01702 −0.814005 −0.407003 0.913427i \(-0.633426\pi\)
−0.407003 + 0.913427i \(0.633426\pi\)
\(98\) 0 0
\(99\) −1.29390 −0.130042
\(100\) 0 0
\(101\) 9.11148 0.906626 0.453313 0.891351i \(-0.350242\pi\)
0.453313 + 0.891351i \(0.350242\pi\)
\(102\) 0 0
\(103\) 15.2943 1.50699 0.753494 0.657455i \(-0.228367\pi\)
0.753494 + 0.657455i \(0.228367\pi\)
\(104\) 0 0
\(105\) 5.26891 0.514193
\(106\) 0 0
\(107\) −3.50420 −0.338764 −0.169382 0.985550i \(-0.554177\pi\)
−0.169382 + 0.985550i \(0.554177\pi\)
\(108\) 0 0
\(109\) 2.49301 0.238787 0.119393 0.992847i \(-0.461905\pi\)
0.119393 + 0.992847i \(0.461905\pi\)
\(110\) 0 0
\(111\) −12.2997 −1.16743
\(112\) 0 0
\(113\) −14.5343 −1.36727 −0.683634 0.729825i \(-0.739601\pi\)
−0.683634 + 0.729825i \(0.739601\pi\)
\(114\) 0 0
\(115\) −6.06959 −0.565993
\(116\) 0 0
\(117\) −1.74154 −0.161006
\(118\) 0 0
\(119\) 2.56109 0.234774
\(120\) 0 0
\(121\) −2.84244 −0.258404
\(122\) 0 0
\(123\) 1.24705 0.112443
\(124\) 0 0
\(125\) −11.4250 −1.02188
\(126\) 0 0
\(127\) −5.52702 −0.490443 −0.245222 0.969467i \(-0.578861\pi\)
−0.245222 + 0.969467i \(0.578861\pi\)
\(128\) 0 0
\(129\) 8.03293 0.707260
\(130\) 0 0
\(131\) 21.2174 1.85377 0.926885 0.375346i \(-0.122476\pi\)
0.926885 + 0.375346i \(0.122476\pi\)
\(132\) 0 0
\(133\) −6.94061 −0.601827
\(134\) 0 0
\(135\) −6.82911 −0.587756
\(136\) 0 0
\(137\) 11.6794 0.997835 0.498917 0.866650i \(-0.333731\pi\)
0.498917 + 0.866650i \(0.333731\pi\)
\(138\) 0 0
\(139\) 10.8676 0.921778 0.460889 0.887458i \(-0.347531\pi\)
0.460889 + 0.887458i \(0.347531\pi\)
\(140\) 0 0
\(141\) 0.703385 0.0592357
\(142\) 0 0
\(143\) 10.9798 0.918175
\(144\) 0 0
\(145\) −1.59300 −0.132292
\(146\) 0 0
\(147\) −5.83192 −0.481009
\(148\) 0 0
\(149\) −7.40209 −0.606403 −0.303202 0.952926i \(-0.598056\pi\)
−0.303202 + 0.952926i \(0.598056\pi\)
\(150\) 0 0
\(151\) −6.09188 −0.495750 −0.247875 0.968792i \(-0.579732\pi\)
−0.247875 + 0.968792i \(0.579732\pi\)
\(152\) 0 0
\(153\) 0.590422 0.0477328
\(154\) 0 0
\(155\) 5.09637 0.409350
\(156\) 0 0
\(157\) 2.22790 0.177806 0.0889028 0.996040i \(-0.471664\pi\)
0.0889028 + 0.996040i \(0.471664\pi\)
\(158\) 0 0
\(159\) −13.2622 −1.05176
\(160\) 0 0
\(161\) −8.26614 −0.651463
\(162\) 0 0
\(163\) 18.7370 1.46759 0.733797 0.679368i \(-0.237746\pi\)
0.733797 + 0.679368i \(0.237746\pi\)
\(164\) 0 0
\(165\) −7.65807 −0.596180
\(166\) 0 0
\(167\) −22.7237 −1.75841 −0.879205 0.476443i \(-0.841926\pi\)
−0.879205 + 0.476443i \(0.841926\pi\)
\(168\) 0 0
\(169\) 1.77838 0.136798
\(170\) 0 0
\(171\) −1.60006 −0.122360
\(172\) 0 0
\(173\) −2.25141 −0.171172 −0.0855859 0.996331i \(-0.527276\pi\)
−0.0855859 + 0.996331i \(0.527276\pi\)
\(174\) 0 0
\(175\) −5.73415 −0.433461
\(176\) 0 0
\(177\) 25.7933 1.93874
\(178\) 0 0
\(179\) −15.8986 −1.18832 −0.594159 0.804348i \(-0.702515\pi\)
−0.594159 + 0.804348i \(0.702515\pi\)
\(180\) 0 0
\(181\) 16.5942 1.23344 0.616718 0.787184i \(-0.288462\pi\)
0.616718 + 0.787184i \(0.288462\pi\)
\(182\) 0 0
\(183\) −12.1040 −0.894756
\(184\) 0 0
\(185\) −9.55066 −0.702179
\(186\) 0 0
\(187\) −3.72239 −0.272208
\(188\) 0 0
\(189\) −9.30051 −0.676513
\(190\) 0 0
\(191\) 2.03640 0.147348 0.0736742 0.997282i \(-0.476527\pi\)
0.0736742 + 0.997282i \(0.476527\pi\)
\(192\) 0 0
\(193\) −15.1384 −1.08968 −0.544841 0.838539i \(-0.683410\pi\)
−0.544841 + 0.838539i \(0.683410\pi\)
\(194\) 0 0
\(195\) −10.3075 −0.738134
\(196\) 0 0
\(197\) −6.01285 −0.428398 −0.214199 0.976790i \(-0.568714\pi\)
−0.214199 + 0.976790i \(0.568714\pi\)
\(198\) 0 0
\(199\) −23.5513 −1.66951 −0.834753 0.550624i \(-0.814390\pi\)
−0.834753 + 0.550624i \(0.814390\pi\)
\(200\) 0 0
\(201\) 14.0332 0.989823
\(202\) 0 0
\(203\) −2.16950 −0.152269
\(204\) 0 0
\(205\) 0.968329 0.0676311
\(206\) 0 0
\(207\) −1.90564 −0.132451
\(208\) 0 0
\(209\) 10.0878 0.697786
\(210\) 0 0
\(211\) −2.35555 −0.162163 −0.0810814 0.996707i \(-0.525837\pi\)
−0.0810814 + 0.996707i \(0.525837\pi\)
\(212\) 0 0
\(213\) −0.138432 −0.00948521
\(214\) 0 0
\(215\) 6.23754 0.425397
\(216\) 0 0
\(217\) 6.94071 0.471166
\(218\) 0 0
\(219\) 6.11455 0.413183
\(220\) 0 0
\(221\) −5.01020 −0.337023
\(222\) 0 0
\(223\) −13.6268 −0.912519 −0.456260 0.889847i \(-0.650811\pi\)
−0.456260 + 0.889847i \(0.650811\pi\)
\(224\) 0 0
\(225\) −1.32193 −0.0881285
\(226\) 0 0
\(227\) −11.9812 −0.795218 −0.397609 0.917555i \(-0.630160\pi\)
−0.397609 + 0.917555i \(0.630160\pi\)
\(228\) 0 0
\(229\) 27.2066 1.79786 0.898932 0.438087i \(-0.144344\pi\)
0.898932 + 0.438087i \(0.144344\pi\)
\(230\) 0 0
\(231\) −10.4295 −0.686208
\(232\) 0 0
\(233\) 14.4504 0.946679 0.473339 0.880880i \(-0.343048\pi\)
0.473339 + 0.880880i \(0.343048\pi\)
\(234\) 0 0
\(235\) 0.546176 0.0356286
\(236\) 0 0
\(237\) −15.9358 −1.03514
\(238\) 0 0
\(239\) 23.9361 1.54830 0.774148 0.633005i \(-0.218179\pi\)
0.774148 + 0.633005i \(0.218179\pi\)
\(240\) 0 0
\(241\) −13.7734 −0.887224 −0.443612 0.896219i \(-0.646303\pi\)
−0.443612 + 0.896219i \(0.646303\pi\)
\(242\) 0 0
\(243\) −4.66957 −0.299553
\(244\) 0 0
\(245\) −4.52847 −0.289313
\(246\) 0 0
\(247\) 13.5778 0.863934
\(248\) 0 0
\(249\) −27.5324 −1.74479
\(250\) 0 0
\(251\) 8.26975 0.521982 0.260991 0.965341i \(-0.415951\pi\)
0.260991 + 0.965341i \(0.415951\pi\)
\(252\) 0 0
\(253\) 12.0144 0.755336
\(254\) 0 0
\(255\) 3.49447 0.218832
\(256\) 0 0
\(257\) −20.1486 −1.25684 −0.628418 0.777876i \(-0.716297\pi\)
−0.628418 + 0.777876i \(0.716297\pi\)
\(258\) 0 0
\(259\) −13.0070 −0.808214
\(260\) 0 0
\(261\) −0.500147 −0.0309583
\(262\) 0 0
\(263\) 27.9229 1.72180 0.860900 0.508774i \(-0.169901\pi\)
0.860900 + 0.508774i \(0.169901\pi\)
\(264\) 0 0
\(265\) −10.2980 −0.632604
\(266\) 0 0
\(267\) −32.5962 −1.99486
\(268\) 0 0
\(269\) 11.6165 0.708269 0.354135 0.935194i \(-0.384775\pi\)
0.354135 + 0.935194i \(0.384775\pi\)
\(270\) 0 0
\(271\) 3.27787 0.199117 0.0995583 0.995032i \(-0.468257\pi\)
0.0995583 + 0.995032i \(0.468257\pi\)
\(272\) 0 0
\(273\) −14.0377 −0.849599
\(274\) 0 0
\(275\) 8.33426 0.502575
\(276\) 0 0
\(277\) 10.1157 0.607795 0.303897 0.952705i \(-0.401712\pi\)
0.303897 + 0.952705i \(0.401712\pi\)
\(278\) 0 0
\(279\) 1.60008 0.0957944
\(280\) 0 0
\(281\) 16.7656 1.00015 0.500077 0.865981i \(-0.333305\pi\)
0.500077 + 0.865981i \(0.333305\pi\)
\(282\) 0 0
\(283\) −15.4382 −0.917705 −0.458852 0.888513i \(-0.651739\pi\)
−0.458852 + 0.888513i \(0.651739\pi\)
\(284\) 0 0
\(285\) −9.47010 −0.560960
\(286\) 0 0
\(287\) 1.31876 0.0778440
\(288\) 0 0
\(289\) −15.3014 −0.900084
\(290\) 0 0
\(291\) −14.8975 −0.873306
\(292\) 0 0
\(293\) −7.52887 −0.439841 −0.219921 0.975518i \(-0.570580\pi\)
−0.219921 + 0.975518i \(0.570580\pi\)
\(294\) 0 0
\(295\) 20.0284 1.16610
\(296\) 0 0
\(297\) 13.5178 0.784380
\(298\) 0 0
\(299\) 16.1709 0.935187
\(300\) 0 0
\(301\) 8.49487 0.489636
\(302\) 0 0
\(303\) 16.9312 0.972674
\(304\) 0 0
\(305\) −9.39874 −0.538170
\(306\) 0 0
\(307\) −17.1932 −0.981265 −0.490632 0.871367i \(-0.663234\pi\)
−0.490632 + 0.871367i \(0.663234\pi\)
\(308\) 0 0
\(309\) 28.4203 1.61677
\(310\) 0 0
\(311\) −10.1595 −0.576094 −0.288047 0.957616i \(-0.593006\pi\)
−0.288047 + 0.957616i \(0.593006\pi\)
\(312\) 0 0
\(313\) 26.6909 1.50866 0.754329 0.656496i \(-0.227962\pi\)
0.754329 + 0.656496i \(0.227962\pi\)
\(314\) 0 0
\(315\) 1.28452 0.0723746
\(316\) 0 0
\(317\) 19.3855 1.08880 0.544398 0.838827i \(-0.316758\pi\)
0.544398 + 0.838827i \(0.316758\pi\)
\(318\) 0 0
\(319\) 3.15324 0.176548
\(320\) 0 0
\(321\) −6.51161 −0.363443
\(322\) 0 0
\(323\) −4.60317 −0.256127
\(324\) 0 0
\(325\) 11.2176 0.622241
\(326\) 0 0
\(327\) 4.63258 0.256182
\(328\) 0 0
\(329\) 0.743833 0.0410088
\(330\) 0 0
\(331\) 26.0579 1.43227 0.716135 0.697962i \(-0.245910\pi\)
0.716135 + 0.697962i \(0.245910\pi\)
\(332\) 0 0
\(333\) −2.99857 −0.164321
\(334\) 0 0
\(335\) 10.8967 0.595350
\(336\) 0 0
\(337\) −11.6240 −0.633199 −0.316600 0.948559i \(-0.602541\pi\)
−0.316600 + 0.948559i \(0.602541\pi\)
\(338\) 0 0
\(339\) −27.0080 −1.46687
\(340\) 0 0
\(341\) −10.0879 −0.546292
\(342\) 0 0
\(343\) −19.9229 −1.07574
\(344\) 0 0
\(345\) −11.2787 −0.607225
\(346\) 0 0
\(347\) −24.5102 −1.31578 −0.657888 0.753115i \(-0.728550\pi\)
−0.657888 + 0.753115i \(0.728550\pi\)
\(348\) 0 0
\(349\) 10.6510 0.570133 0.285066 0.958508i \(-0.407984\pi\)
0.285066 + 0.958508i \(0.407984\pi\)
\(350\) 0 0
\(351\) 18.1944 0.971146
\(352\) 0 0
\(353\) 1.04651 0.0557003 0.0278501 0.999612i \(-0.491134\pi\)
0.0278501 + 0.999612i \(0.491134\pi\)
\(354\) 0 0
\(355\) −0.107492 −0.00570508
\(356\) 0 0
\(357\) 4.75909 0.251878
\(358\) 0 0
\(359\) 24.0194 1.26769 0.633847 0.773459i \(-0.281475\pi\)
0.633847 + 0.773459i \(0.281475\pi\)
\(360\) 0 0
\(361\) −6.52528 −0.343436
\(362\) 0 0
\(363\) −5.28191 −0.277228
\(364\) 0 0
\(365\) 4.74793 0.248518
\(366\) 0 0
\(367\) 18.6963 0.975937 0.487969 0.872861i \(-0.337738\pi\)
0.487969 + 0.872861i \(0.337738\pi\)
\(368\) 0 0
\(369\) 0.304022 0.0158267
\(370\) 0 0
\(371\) −14.0248 −0.728133
\(372\) 0 0
\(373\) −23.3008 −1.20647 −0.603235 0.797564i \(-0.706122\pi\)
−0.603235 + 0.797564i \(0.706122\pi\)
\(374\) 0 0
\(375\) −21.2302 −1.09633
\(376\) 0 0
\(377\) 4.24415 0.218585
\(378\) 0 0
\(379\) 9.79951 0.503367 0.251683 0.967810i \(-0.419016\pi\)
0.251683 + 0.967810i \(0.419016\pi\)
\(380\) 0 0
\(381\) −10.2705 −0.526172
\(382\) 0 0
\(383\) 1.97295 0.100813 0.0504066 0.998729i \(-0.483948\pi\)
0.0504066 + 0.998729i \(0.483948\pi\)
\(384\) 0 0
\(385\) −8.09844 −0.412735
\(386\) 0 0
\(387\) 1.95837 0.0995496
\(388\) 0 0
\(389\) −6.61202 −0.335243 −0.167621 0.985851i \(-0.553609\pi\)
−0.167621 + 0.985851i \(0.553609\pi\)
\(390\) 0 0
\(391\) −5.48230 −0.277252
\(392\) 0 0
\(393\) 39.4268 1.98882
\(394\) 0 0
\(395\) −12.3741 −0.622607
\(396\) 0 0
\(397\) −7.61750 −0.382311 −0.191156 0.981560i \(-0.561224\pi\)
−0.191156 + 0.981560i \(0.561224\pi\)
\(398\) 0 0
\(399\) −12.8973 −0.645670
\(400\) 0 0
\(401\) 25.8162 1.28920 0.644601 0.764519i \(-0.277024\pi\)
0.644601 + 0.764519i \(0.277024\pi\)
\(402\) 0 0
\(403\) −13.5780 −0.676368
\(404\) 0 0
\(405\) −14.6511 −0.728018
\(406\) 0 0
\(407\) 18.9049 0.937081
\(408\) 0 0
\(409\) −13.6924 −0.677044 −0.338522 0.940958i \(-0.609927\pi\)
−0.338522 + 0.940958i \(0.609927\pi\)
\(410\) 0 0
\(411\) 21.7029 1.07053
\(412\) 0 0
\(413\) 27.2765 1.34219
\(414\) 0 0
\(415\) −21.3788 −1.04944
\(416\) 0 0
\(417\) 20.1945 0.988930
\(418\) 0 0
\(419\) −24.0027 −1.17261 −0.586305 0.810091i \(-0.699418\pi\)
−0.586305 + 0.810091i \(0.699418\pi\)
\(420\) 0 0
\(421\) 31.1293 1.51715 0.758573 0.651588i \(-0.225897\pi\)
0.758573 + 0.651588i \(0.225897\pi\)
\(422\) 0 0
\(423\) 0.171480 0.00833765
\(424\) 0 0
\(425\) −3.80302 −0.184474
\(426\) 0 0
\(427\) −12.8001 −0.619439
\(428\) 0 0
\(429\) 20.4030 0.985064
\(430\) 0 0
\(431\) −28.0585 −1.35153 −0.675766 0.737116i \(-0.736187\pi\)
−0.675766 + 0.737116i \(0.736187\pi\)
\(432\) 0 0
\(433\) −20.6011 −0.990026 −0.495013 0.868886i \(-0.664837\pi\)
−0.495013 + 0.868886i \(0.664837\pi\)
\(434\) 0 0
\(435\) −2.96016 −0.141929
\(436\) 0 0
\(437\) 14.8572 0.710715
\(438\) 0 0
\(439\) 36.4050 1.73752 0.868758 0.495238i \(-0.164919\pi\)
0.868758 + 0.495238i \(0.164919\pi\)
\(440\) 0 0
\(441\) −1.42178 −0.0677038
\(442\) 0 0
\(443\) 28.1192 1.33598 0.667992 0.744169i \(-0.267154\pi\)
0.667992 + 0.744169i \(0.267154\pi\)
\(444\) 0 0
\(445\) −25.3109 −1.19985
\(446\) 0 0
\(447\) −13.7548 −0.650580
\(448\) 0 0
\(449\) −12.9493 −0.611116 −0.305558 0.952173i \(-0.598843\pi\)
−0.305558 + 0.952173i \(0.598843\pi\)
\(450\) 0 0
\(451\) −1.91674 −0.0902559
\(452\) 0 0
\(453\) −11.3201 −0.531866
\(454\) 0 0
\(455\) −10.9002 −0.511010
\(456\) 0 0
\(457\) 0.149626 0.00699919 0.00349960 0.999994i \(-0.498886\pi\)
0.00349960 + 0.999994i \(0.498886\pi\)
\(458\) 0 0
\(459\) −6.16832 −0.287912
\(460\) 0 0
\(461\) 38.9917 1.81603 0.908013 0.418942i \(-0.137599\pi\)
0.908013 + 0.418942i \(0.137599\pi\)
\(462\) 0 0
\(463\) 20.1386 0.935918 0.467959 0.883750i \(-0.344989\pi\)
0.467959 + 0.883750i \(0.344989\pi\)
\(464\) 0 0
\(465\) 9.47024 0.439172
\(466\) 0 0
\(467\) −14.8664 −0.687936 −0.343968 0.938981i \(-0.611771\pi\)
−0.343968 + 0.938981i \(0.611771\pi\)
\(468\) 0 0
\(469\) 14.8401 0.685254
\(470\) 0 0
\(471\) 4.13995 0.190759
\(472\) 0 0
\(473\) −12.3468 −0.567707
\(474\) 0 0
\(475\) 10.3063 0.472885
\(476\) 0 0
\(477\) −3.23322 −0.148039
\(478\) 0 0
\(479\) 35.2515 1.61068 0.805342 0.592810i \(-0.201982\pi\)
0.805342 + 0.592810i \(0.201982\pi\)
\(480\) 0 0
\(481\) 25.4453 1.16021
\(482\) 0 0
\(483\) −15.3604 −0.698922
\(484\) 0 0
\(485\) −11.5678 −0.525268
\(486\) 0 0
\(487\) −27.4362 −1.24325 −0.621626 0.783314i \(-0.713528\pi\)
−0.621626 + 0.783314i \(0.713528\pi\)
\(488\) 0 0
\(489\) 34.8177 1.57451
\(490\) 0 0
\(491\) 4.83937 0.218398 0.109199 0.994020i \(-0.465171\pi\)
0.109199 + 0.994020i \(0.465171\pi\)
\(492\) 0 0
\(493\) −1.43886 −0.0648030
\(494\) 0 0
\(495\) −1.86698 −0.0839145
\(496\) 0 0
\(497\) −0.146393 −0.00656661
\(498\) 0 0
\(499\) −16.7739 −0.750904 −0.375452 0.926842i \(-0.622512\pi\)
−0.375452 + 0.926842i \(0.622512\pi\)
\(500\) 0 0
\(501\) −42.2258 −1.88651
\(502\) 0 0
\(503\) 1.00000 0.0445878
\(504\) 0 0
\(505\) 13.1470 0.585036
\(506\) 0 0
\(507\) 3.30464 0.146764
\(508\) 0 0
\(509\) −27.5401 −1.22069 −0.610347 0.792134i \(-0.708970\pi\)
−0.610347 + 0.792134i \(0.708970\pi\)
\(510\) 0 0
\(511\) 6.46617 0.286046
\(512\) 0 0
\(513\) 16.7163 0.738043
\(514\) 0 0
\(515\) 22.0682 0.972443
\(516\) 0 0
\(517\) −1.08112 −0.0475475
\(518\) 0 0
\(519\) −4.18365 −0.183642
\(520\) 0 0
\(521\) 25.7250 1.12703 0.563515 0.826106i \(-0.309449\pi\)
0.563515 + 0.826106i \(0.309449\pi\)
\(522\) 0 0
\(523\) 29.5746 1.29321 0.646605 0.762825i \(-0.276188\pi\)
0.646605 + 0.762825i \(0.276188\pi\)
\(524\) 0 0
\(525\) −10.6554 −0.465039
\(526\) 0 0
\(527\) 4.60324 0.200520
\(528\) 0 0
\(529\) −5.30539 −0.230669
\(530\) 0 0
\(531\) 6.28821 0.272885
\(532\) 0 0
\(533\) −2.57987 −0.111746
\(534\) 0 0
\(535\) −5.05624 −0.218601
\(536\) 0 0
\(537\) −29.5433 −1.27489
\(538\) 0 0
\(539\) 8.96380 0.386098
\(540\) 0 0
\(541\) −13.1889 −0.567035 −0.283517 0.958967i \(-0.591501\pi\)
−0.283517 + 0.958967i \(0.591501\pi\)
\(542\) 0 0
\(543\) 30.8358 1.32329
\(544\) 0 0
\(545\) 3.59718 0.154086
\(546\) 0 0
\(547\) 17.9543 0.767673 0.383836 0.923401i \(-0.374603\pi\)
0.383836 + 0.923401i \(0.374603\pi\)
\(548\) 0 0
\(549\) −2.95088 −0.125940
\(550\) 0 0
\(551\) 3.89935 0.166118
\(552\) 0 0
\(553\) −16.8522 −0.716627
\(554\) 0 0
\(555\) −17.7473 −0.753332
\(556\) 0 0
\(557\) 9.47412 0.401431 0.200716 0.979650i \(-0.435673\pi\)
0.200716 + 0.979650i \(0.435673\pi\)
\(558\) 0 0
\(559\) −16.6183 −0.702881
\(560\) 0 0
\(561\) −6.91706 −0.292039
\(562\) 0 0
\(563\) 33.2995 1.40341 0.701704 0.712469i \(-0.252423\pi\)
0.701704 + 0.712469i \(0.252423\pi\)
\(564\) 0 0
\(565\) −20.9716 −0.882283
\(566\) 0 0
\(567\) −19.9532 −0.837955
\(568\) 0 0
\(569\) −28.8525 −1.20956 −0.604780 0.796393i \(-0.706739\pi\)
−0.604780 + 0.796393i \(0.706739\pi\)
\(570\) 0 0
\(571\) −22.7379 −0.951550 −0.475775 0.879567i \(-0.657832\pi\)
−0.475775 + 0.879567i \(0.657832\pi\)
\(572\) 0 0
\(573\) 3.78409 0.158083
\(574\) 0 0
\(575\) 12.2746 0.511886
\(576\) 0 0
\(577\) −4.60031 −0.191513 −0.0957567 0.995405i \(-0.530527\pi\)
−0.0957567 + 0.995405i \(0.530527\pi\)
\(578\) 0 0
\(579\) −28.1306 −1.16907
\(580\) 0 0
\(581\) −29.1156 −1.20792
\(582\) 0 0
\(583\) 20.3843 0.844231
\(584\) 0 0
\(585\) −2.51289 −0.103895
\(586\) 0 0
\(587\) −32.6537 −1.34776 −0.673881 0.738839i \(-0.735374\pi\)
−0.673881 + 0.738839i \(0.735374\pi\)
\(588\) 0 0
\(589\) −12.4749 −0.514020
\(590\) 0 0
\(591\) −11.1733 −0.459607
\(592\) 0 0
\(593\) −36.4077 −1.49509 −0.747543 0.664214i \(-0.768767\pi\)
−0.747543 + 0.664214i \(0.768767\pi\)
\(594\) 0 0
\(595\) 3.69542 0.151497
\(596\) 0 0
\(597\) −43.7637 −1.79113
\(598\) 0 0
\(599\) 40.2375 1.64406 0.822031 0.569443i \(-0.192841\pi\)
0.822031 + 0.569443i \(0.192841\pi\)
\(600\) 0 0
\(601\) 8.80257 0.359065 0.179532 0.983752i \(-0.442542\pi\)
0.179532 + 0.983752i \(0.442542\pi\)
\(602\) 0 0
\(603\) 3.42118 0.139321
\(604\) 0 0
\(605\) −4.10139 −0.166745
\(606\) 0 0
\(607\) −13.3824 −0.543176 −0.271588 0.962414i \(-0.587549\pi\)
−0.271588 + 0.962414i \(0.587549\pi\)
\(608\) 0 0
\(609\) −4.03143 −0.163362
\(610\) 0 0
\(611\) −1.45515 −0.0588689
\(612\) 0 0
\(613\) −15.6160 −0.630725 −0.315363 0.948971i \(-0.602126\pi\)
−0.315363 + 0.948971i \(0.602126\pi\)
\(614\) 0 0
\(615\) 1.79938 0.0725580
\(616\) 0 0
\(617\) 4.29634 0.172964 0.0864820 0.996253i \(-0.472437\pi\)
0.0864820 + 0.996253i \(0.472437\pi\)
\(618\) 0 0
\(619\) 10.8380 0.435614 0.217807 0.975992i \(-0.430110\pi\)
0.217807 + 0.975992i \(0.430110\pi\)
\(620\) 0 0
\(621\) 19.9088 0.798913
\(622\) 0 0
\(623\) −34.4707 −1.38104
\(624\) 0 0
\(625\) −1.89515 −0.0758062
\(626\) 0 0
\(627\) 18.7454 0.748620
\(628\) 0 0
\(629\) −8.62653 −0.343962
\(630\) 0 0
\(631\) −29.5073 −1.17467 −0.587334 0.809345i \(-0.699822\pi\)
−0.587334 + 0.809345i \(0.699822\pi\)
\(632\) 0 0
\(633\) −4.37716 −0.173976
\(634\) 0 0
\(635\) −7.97499 −0.316478
\(636\) 0 0
\(637\) 12.0649 0.478031
\(638\) 0 0
\(639\) −0.0337487 −0.00133508
\(640\) 0 0
\(641\) 7.72732 0.305211 0.152605 0.988287i \(-0.451234\pi\)
0.152605 + 0.988287i \(0.451234\pi\)
\(642\) 0 0
\(643\) −10.0167 −0.395021 −0.197511 0.980301i \(-0.563286\pi\)
−0.197511 + 0.980301i \(0.563286\pi\)
\(644\) 0 0
\(645\) 11.5908 0.456387
\(646\) 0 0
\(647\) 13.6884 0.538147 0.269074 0.963120i \(-0.413282\pi\)
0.269074 + 0.963120i \(0.413282\pi\)
\(648\) 0 0
\(649\) −39.6449 −1.55620
\(650\) 0 0
\(651\) 12.8974 0.505491
\(652\) 0 0
\(653\) 38.1399 1.49253 0.746264 0.665650i \(-0.231845\pi\)
0.746264 + 0.665650i \(0.231845\pi\)
\(654\) 0 0
\(655\) 30.6147 1.19622
\(656\) 0 0
\(657\) 1.49068 0.0581571
\(658\) 0 0
\(659\) −31.5253 −1.22805 −0.614026 0.789286i \(-0.710451\pi\)
−0.614026 + 0.789286i \(0.710451\pi\)
\(660\) 0 0
\(661\) −30.1122 −1.17123 −0.585614 0.810590i \(-0.699146\pi\)
−0.585614 + 0.810590i \(0.699146\pi\)
\(662\) 0 0
\(663\) −9.31012 −0.361575
\(664\) 0 0
\(665\) −10.0147 −0.388352
\(666\) 0 0
\(667\) 4.64405 0.179818
\(668\) 0 0
\(669\) −25.3218 −0.978996
\(670\) 0 0
\(671\) 18.6042 0.718207
\(672\) 0 0
\(673\) −40.7982 −1.57265 −0.786327 0.617810i \(-0.788020\pi\)
−0.786327 + 0.617810i \(0.788020\pi\)
\(674\) 0 0
\(675\) 13.8106 0.531569
\(676\) 0 0
\(677\) 3.18994 0.122599 0.0612997 0.998119i \(-0.480475\pi\)
0.0612997 + 0.998119i \(0.480475\pi\)
\(678\) 0 0
\(679\) −15.7542 −0.604589
\(680\) 0 0
\(681\) −22.2638 −0.853150
\(682\) 0 0
\(683\) −25.0239 −0.957512 −0.478756 0.877948i \(-0.658912\pi\)
−0.478756 + 0.877948i \(0.658912\pi\)
\(684\) 0 0
\(685\) 16.8523 0.643892
\(686\) 0 0
\(687\) 50.5562 1.92884
\(688\) 0 0
\(689\) 27.4365 1.04525
\(690\) 0 0
\(691\) −36.5349 −1.38985 −0.694927 0.719081i \(-0.744563\pi\)
−0.694927 + 0.719081i \(0.744563\pi\)
\(692\) 0 0
\(693\) −2.54263 −0.0965864
\(694\) 0 0
\(695\) 15.6810 0.594813
\(696\) 0 0
\(697\) 0.874633 0.0331291
\(698\) 0 0
\(699\) 26.8522 1.01564
\(700\) 0 0
\(701\) 40.6252 1.53439 0.767196 0.641413i \(-0.221652\pi\)
0.767196 + 0.641413i \(0.221652\pi\)
\(702\) 0 0
\(703\) 23.3781 0.881723
\(704\) 0 0
\(705\) 1.01492 0.0382241
\(706\) 0 0
\(707\) 17.9049 0.673382
\(708\) 0 0
\(709\) −29.3401 −1.10189 −0.550945 0.834542i \(-0.685733\pi\)
−0.550945 + 0.834542i \(0.685733\pi\)
\(710\) 0 0
\(711\) −3.88503 −0.145700
\(712\) 0 0
\(713\) −14.8574 −0.556414
\(714\) 0 0
\(715\) 15.8428 0.592488
\(716\) 0 0
\(717\) 44.4788 1.66109
\(718\) 0 0
\(719\) 5.69273 0.212303 0.106152 0.994350i \(-0.466147\pi\)
0.106152 + 0.994350i \(0.466147\pi\)
\(720\) 0 0
\(721\) 30.0546 1.11929
\(722\) 0 0
\(723\) −25.5942 −0.951858
\(724\) 0 0
\(725\) 3.22154 0.119645
\(726\) 0 0
\(727\) −31.4072 −1.16483 −0.582414 0.812892i \(-0.697892\pi\)
−0.582414 + 0.812892i \(0.697892\pi\)
\(728\) 0 0
\(729\) 21.7844 0.806829
\(730\) 0 0
\(731\) 5.63399 0.208381
\(732\) 0 0
\(733\) 47.6365 1.75949 0.879747 0.475441i \(-0.157712\pi\)
0.879747 + 0.475441i \(0.157712\pi\)
\(734\) 0 0
\(735\) −8.41494 −0.310390
\(736\) 0 0
\(737\) −21.5693 −0.794515
\(738\) 0 0
\(739\) −9.88794 −0.363734 −0.181867 0.983323i \(-0.558214\pi\)
−0.181867 + 0.983323i \(0.558214\pi\)
\(740\) 0 0
\(741\) 25.2307 0.926871
\(742\) 0 0
\(743\) −17.7935 −0.652782 −0.326391 0.945235i \(-0.605833\pi\)
−0.326391 + 0.945235i \(0.605833\pi\)
\(744\) 0 0
\(745\) −10.6806 −0.391305
\(746\) 0 0
\(747\) −6.71220 −0.245586
\(748\) 0 0
\(749\) −6.88606 −0.251611
\(750\) 0 0
\(751\) 43.7934 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(752\) 0 0
\(753\) 15.3671 0.560009
\(754\) 0 0
\(755\) −8.79003 −0.319902
\(756\) 0 0
\(757\) 0.950190 0.0345353 0.0172676 0.999851i \(-0.494503\pi\)
0.0172676 + 0.999851i \(0.494503\pi\)
\(758\) 0 0
\(759\) 22.3255 0.810363
\(760\) 0 0
\(761\) −5.00434 −0.181407 −0.0907035 0.995878i \(-0.528912\pi\)
−0.0907035 + 0.995878i \(0.528912\pi\)
\(762\) 0 0
\(763\) 4.89898 0.177355
\(764\) 0 0
\(765\) 0.851925 0.0308014
\(766\) 0 0
\(767\) −53.3605 −1.92674
\(768\) 0 0
\(769\) 16.5794 0.597870 0.298935 0.954274i \(-0.403369\pi\)
0.298935 + 0.954274i \(0.403369\pi\)
\(770\) 0 0
\(771\) −37.4408 −1.34840
\(772\) 0 0
\(773\) −30.4696 −1.09592 −0.547958 0.836506i \(-0.684595\pi\)
−0.547958 + 0.836506i \(0.684595\pi\)
\(774\) 0 0
\(775\) −10.3064 −0.370218
\(776\) 0 0
\(777\) −24.1700 −0.867093
\(778\) 0 0
\(779\) −2.37028 −0.0849240
\(780\) 0 0
\(781\) 0.212773 0.00761363
\(782\) 0 0
\(783\) 5.22518 0.186733
\(784\) 0 0
\(785\) 3.21465 0.114736
\(786\) 0 0
\(787\) −29.7903 −1.06191 −0.530954 0.847400i \(-0.678166\pi\)
−0.530954 + 0.847400i \(0.678166\pi\)
\(788\) 0 0
\(789\) 51.8872 1.84723
\(790\) 0 0
\(791\) −28.5611 −1.01552
\(792\) 0 0
\(793\) 25.0406 0.889216
\(794\) 0 0
\(795\) −19.1361 −0.678689
\(796\) 0 0
\(797\) 0.503125 0.0178216 0.00891081 0.999960i \(-0.497164\pi\)
0.00891081 + 0.999960i \(0.497164\pi\)
\(798\) 0 0
\(799\) 0.493327 0.0174527
\(800\) 0 0
\(801\) −7.94673 −0.280784
\(802\) 0 0
\(803\) −9.39820 −0.331655
\(804\) 0 0
\(805\) −11.9273 −0.420382
\(806\) 0 0
\(807\) 21.5861 0.759867
\(808\) 0 0
\(809\) −21.1371 −0.743142 −0.371571 0.928405i \(-0.621181\pi\)
−0.371571 + 0.928405i \(0.621181\pi\)
\(810\) 0 0
\(811\) −15.7238 −0.552139 −0.276069 0.961138i \(-0.589032\pi\)
−0.276069 + 0.961138i \(0.589032\pi\)
\(812\) 0 0
\(813\) 6.09105 0.213622
\(814\) 0 0
\(815\) 27.0358 0.947023
\(816\) 0 0
\(817\) −15.2683 −0.534169
\(818\) 0 0
\(819\) −3.42228 −0.119584
\(820\) 0 0
\(821\) −42.7588 −1.49229 −0.746147 0.665781i \(-0.768098\pi\)
−0.746147 + 0.665781i \(0.768098\pi\)
\(822\) 0 0
\(823\) 33.2920 1.16049 0.580243 0.814444i \(-0.302958\pi\)
0.580243 + 0.814444i \(0.302958\pi\)
\(824\) 0 0
\(825\) 15.4870 0.539188
\(826\) 0 0
\(827\) −14.2343 −0.494975 −0.247487 0.968891i \(-0.579605\pi\)
−0.247487 + 0.968891i \(0.579605\pi\)
\(828\) 0 0
\(829\) −12.3766 −0.429855 −0.214928 0.976630i \(-0.568952\pi\)
−0.214928 + 0.976630i \(0.568952\pi\)
\(830\) 0 0
\(831\) 18.7973 0.652073
\(832\) 0 0
\(833\) −4.09029 −0.141720
\(834\) 0 0
\(835\) −32.7882 −1.13468
\(836\) 0 0
\(837\) −16.7166 −0.577809
\(838\) 0 0
\(839\) −31.6864 −1.09394 −0.546969 0.837153i \(-0.684218\pi\)
−0.546969 + 0.837153i \(0.684218\pi\)
\(840\) 0 0
\(841\) −27.7811 −0.957970
\(842\) 0 0
\(843\) 31.1544 1.07301
\(844\) 0 0
\(845\) 2.56604 0.0882745
\(846\) 0 0
\(847\) −5.58565 −0.191925
\(848\) 0 0
\(849\) −28.6877 −0.984560
\(850\) 0 0
\(851\) 27.8429 0.954443
\(852\) 0 0
\(853\) 30.2234 1.03483 0.517416 0.855734i \(-0.326894\pi\)
0.517416 + 0.855734i \(0.326894\pi\)
\(854\) 0 0
\(855\) −2.30874 −0.0789573
\(856\) 0 0
\(857\) −31.4206 −1.07331 −0.536653 0.843803i \(-0.680312\pi\)
−0.536653 + 0.843803i \(0.680312\pi\)
\(858\) 0 0
\(859\) −27.5866 −0.941244 −0.470622 0.882335i \(-0.655970\pi\)
−0.470622 + 0.882335i \(0.655970\pi\)
\(860\) 0 0
\(861\) 2.45056 0.0835149
\(862\) 0 0
\(863\) −40.3690 −1.37418 −0.687088 0.726574i \(-0.741111\pi\)
−0.687088 + 0.726574i \(0.741111\pi\)
\(864\) 0 0
\(865\) −3.24859 −0.110455
\(866\) 0 0
\(867\) −28.4336 −0.965655
\(868\) 0 0
\(869\) 24.4937 0.830890
\(870\) 0 0
\(871\) −29.0315 −0.983694
\(872\) 0 0
\(873\) −3.63190 −0.122921
\(874\) 0 0
\(875\) −22.4511 −0.758985
\(876\) 0 0
\(877\) −0.330616 −0.0111641 −0.00558205 0.999984i \(-0.501777\pi\)
−0.00558205 + 0.999984i \(0.501777\pi\)
\(878\) 0 0
\(879\) −13.9904 −0.471884
\(880\) 0 0
\(881\) −4.51734 −0.152193 −0.0760965 0.997100i \(-0.524246\pi\)
−0.0760965 + 0.997100i \(0.524246\pi\)
\(882\) 0 0
\(883\) 46.7445 1.57308 0.786539 0.617540i \(-0.211871\pi\)
0.786539 + 0.617540i \(0.211871\pi\)
\(884\) 0 0
\(885\) 37.2174 1.25105
\(886\) 0 0
\(887\) 9.29057 0.311947 0.155973 0.987761i \(-0.450149\pi\)
0.155973 + 0.987761i \(0.450149\pi\)
\(888\) 0 0
\(889\) −10.8611 −0.364269
\(890\) 0 0
\(891\) 29.0008 0.971564
\(892\) 0 0
\(893\) −1.33693 −0.0447387
\(894\) 0 0
\(895\) −22.9403 −0.766808
\(896\) 0 0
\(897\) 30.0492 1.00332
\(898\) 0 0
\(899\) −3.89941 −0.130053
\(900\) 0 0
\(901\) −9.30159 −0.309881
\(902\) 0 0
\(903\) 15.7854 0.525306
\(904\) 0 0
\(905\) 23.9439 0.795923
\(906\) 0 0
\(907\) 24.0423 0.798313 0.399156 0.916883i \(-0.369303\pi\)
0.399156 + 0.916883i \(0.369303\pi\)
\(908\) 0 0
\(909\) 4.12771 0.136908
\(910\) 0 0
\(911\) −6.04735 −0.200358 −0.100179 0.994969i \(-0.531941\pi\)
−0.100179 + 0.994969i \(0.531941\pi\)
\(912\) 0 0
\(913\) 42.3179 1.40052
\(914\) 0 0
\(915\) −17.4650 −0.577376
\(916\) 0 0
\(917\) 41.6940 1.37686
\(918\) 0 0
\(919\) 34.8990 1.15121 0.575606 0.817727i \(-0.304766\pi\)
0.575606 + 0.817727i \(0.304766\pi\)
\(920\) 0 0
\(921\) −31.9488 −1.05275
\(922\) 0 0
\(923\) 0.286385 0.00942648
\(924\) 0 0
\(925\) 19.3144 0.635054
\(926\) 0 0
\(927\) 6.92866 0.227567
\(928\) 0 0
\(929\) 39.8343 1.30692 0.653460 0.756961i \(-0.273317\pi\)
0.653460 + 0.756961i \(0.273317\pi\)
\(930\) 0 0
\(931\) 11.0848 0.363289
\(932\) 0 0
\(933\) −18.8788 −0.618063
\(934\) 0 0
\(935\) −5.37108 −0.175653
\(936\) 0 0
\(937\) 10.6822 0.348971 0.174485 0.984660i \(-0.444174\pi\)
0.174485 + 0.984660i \(0.444174\pi\)
\(938\) 0 0
\(939\) 49.5978 1.61856
\(940\) 0 0
\(941\) −1.40329 −0.0457459 −0.0228729 0.999738i \(-0.507281\pi\)
−0.0228729 + 0.999738i \(0.507281\pi\)
\(942\) 0 0
\(943\) −2.82296 −0.0919281
\(944\) 0 0
\(945\) −13.4198 −0.436546
\(946\) 0 0
\(947\) −9.93625 −0.322885 −0.161442 0.986882i \(-0.551615\pi\)
−0.161442 + 0.986882i \(0.551615\pi\)
\(948\) 0 0
\(949\) −12.6496 −0.410625
\(950\) 0 0
\(951\) 36.0227 1.16812
\(952\) 0 0
\(953\) 11.4560 0.371097 0.185548 0.982635i \(-0.440594\pi\)
0.185548 + 0.982635i \(0.440594\pi\)
\(954\) 0 0
\(955\) 2.93834 0.0950823
\(956\) 0 0
\(957\) 5.85945 0.189409
\(958\) 0 0
\(959\) 22.9510 0.741126
\(960\) 0 0
\(961\) −18.5249 −0.597578
\(962\) 0 0
\(963\) −1.58748 −0.0511560
\(964\) 0 0
\(965\) −21.8433 −0.703160
\(966\) 0 0
\(967\) 32.0337 1.03014 0.515068 0.857150i \(-0.327767\pi\)
0.515068 + 0.857150i \(0.327767\pi\)
\(968\) 0 0
\(969\) −8.55376 −0.274786
\(970\) 0 0
\(971\) 21.7771 0.698859 0.349429 0.936963i \(-0.386375\pi\)
0.349429 + 0.936963i \(0.386375\pi\)
\(972\) 0 0
\(973\) 21.3558 0.684636
\(974\) 0 0
\(975\) 20.8449 0.667572
\(976\) 0 0
\(977\) 48.8640 1.56330 0.781649 0.623719i \(-0.214379\pi\)
0.781649 + 0.623719i \(0.214379\pi\)
\(978\) 0 0
\(979\) 50.1012 1.60124
\(980\) 0 0
\(981\) 1.12939 0.0360586
\(982\) 0 0
\(983\) −43.9288 −1.40111 −0.700555 0.713598i \(-0.747064\pi\)
−0.700555 + 0.713598i \(0.747064\pi\)
\(984\) 0 0
\(985\) −8.67600 −0.276440
\(986\) 0 0
\(987\) 1.38221 0.0439963
\(988\) 0 0
\(989\) −18.1842 −0.578225
\(990\) 0 0
\(991\) −18.0715 −0.574060 −0.287030 0.957922i \(-0.592668\pi\)
−0.287030 + 0.957922i \(0.592668\pi\)
\(992\) 0 0
\(993\) 48.4215 1.53661
\(994\) 0 0
\(995\) −33.9824 −1.07731
\(996\) 0 0
\(997\) −36.5966 −1.15903 −0.579514 0.814963i \(-0.696757\pi\)
−0.579514 + 0.814963i \(0.696757\pi\)
\(998\) 0 0
\(999\) 31.3270 0.991143
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 \(a_p\))