Properties

Label 8048.2.a.v.1.26
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 28
CM No

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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: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.26
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+2.80686 q^{3}\) \(-3.33080 q^{5}\) \(+2.85725 q^{7}\) \(+4.87847 q^{9}\) \(+O(q^{10})\) \(q\)\(+2.80686 q^{3}\) \(-3.33080 q^{5}\) \(+2.85725 q^{7}\) \(+4.87847 q^{9}\) \(+6.16199 q^{11}\) \(-3.18285 q^{13}\) \(-9.34908 q^{15}\) \(-3.44720 q^{17}\) \(-6.59579 q^{19}\) \(+8.01992 q^{21}\) \(-9.22071 q^{23}\) \(+6.09421 q^{25}\) \(+5.27260 q^{27}\) \(+1.40217 q^{29}\) \(-0.702160 q^{31}\) \(+17.2959 q^{33}\) \(-9.51693 q^{35}\) \(-9.54930 q^{37}\) \(-8.93381 q^{39}\) \(-2.82571 q^{41}\) \(-8.28009 q^{43}\) \(-16.2492 q^{45}\) \(-10.2543 q^{47}\) \(+1.16390 q^{49}\) \(-9.67581 q^{51}\) \(-5.03097 q^{53}\) \(-20.5243 q^{55}\) \(-18.5135 q^{57}\) \(+3.57284 q^{59}\) \(+2.46580 q^{61}\) \(+13.9390 q^{63}\) \(+10.6014 q^{65}\) \(-0.271159 q^{67}\) \(-25.8813 q^{69}\) \(+6.18072 q^{71}\) \(+13.2210 q^{73}\) \(+17.1056 q^{75}\) \(+17.6064 q^{77}\) \(+7.67343 q^{79}\) \(+0.164052 q^{81}\) \(-1.85568 q^{83}\) \(+11.4819 q^{85}\) \(+3.93570 q^{87}\) \(-1.46966 q^{89}\) \(-9.09420 q^{91}\) \(-1.97087 q^{93}\) \(+21.9692 q^{95}\) \(-0.763796 q^{97}\) \(+30.0611 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 31q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 22q^{25} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 26q^{33} \) \(\mathstrut +\mathstrut 13q^{35} \) \(\mathstrut -\mathstrut 67q^{37} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut -\mathstrut 57q^{45} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 20q^{49} \) \(\mathstrut +\mathstrut 11q^{51} \) \(\mathstrut -\mathstrut 58q^{53} \) \(\mathstrut -\mathstrut 15q^{55} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 55q^{61} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 44q^{69} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 5q^{73} \) \(\mathstrut +\mathstrut 25q^{75} \) \(\mathstrut -\mathstrut 50q^{77} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 78q^{85} \) \(\mathstrut +\mathstrut 11q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut +\mathstrut 15q^{91} \) \(\mathstrut -\mathstrut 83q^{93} \) \(\mathstrut +\mathstrut 27q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 70q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 2.80686 1.62054 0.810271 0.586055i \(-0.199320\pi\)
0.810271 + 0.586055i \(0.199320\pi\)
\(4\) 0 0
\(5\) −3.33080 −1.48958 −0.744789 0.667300i \(-0.767450\pi\)
−0.744789 + 0.667300i \(0.767450\pi\)
\(6\) 0 0
\(7\) 2.85725 1.07994 0.539970 0.841684i \(-0.318435\pi\)
0.539970 + 0.841684i \(0.318435\pi\)
\(8\) 0 0
\(9\) 4.87847 1.62616
\(10\) 0 0
\(11\) 6.16199 1.85791 0.928955 0.370192i \(-0.120708\pi\)
0.928955 + 0.370192i \(0.120708\pi\)
\(12\) 0 0
\(13\) −3.18285 −0.882763 −0.441381 0.897320i \(-0.645511\pi\)
−0.441381 + 0.897320i \(0.645511\pi\)
\(14\) 0 0
\(15\) −9.34908 −2.41392
\(16\) 0 0
\(17\) −3.44720 −0.836069 −0.418035 0.908431i \(-0.637281\pi\)
−0.418035 + 0.908431i \(0.637281\pi\)
\(18\) 0 0
\(19\) −6.59579 −1.51318 −0.756589 0.653890i \(-0.773136\pi\)
−0.756589 + 0.653890i \(0.773136\pi\)
\(20\) 0 0
\(21\) 8.01992 1.75009
\(22\) 0 0
\(23\) −9.22071 −1.92265 −0.961326 0.275414i \(-0.911185\pi\)
−0.961326 + 0.275414i \(0.911185\pi\)
\(24\) 0 0
\(25\) 6.09421 1.21884
\(26\) 0 0
\(27\) 5.27260 1.01471
\(28\) 0 0
\(29\) 1.40217 0.260377 0.130188 0.991489i \(-0.458442\pi\)
0.130188 + 0.991489i \(0.458442\pi\)
\(30\) 0 0
\(31\) −0.702160 −0.126112 −0.0630558 0.998010i \(-0.520085\pi\)
−0.0630558 + 0.998010i \(0.520085\pi\)
\(32\) 0 0
\(33\) 17.2959 3.01082
\(34\) 0 0
\(35\) −9.51693 −1.60866
\(36\) 0 0
\(37\) −9.54930 −1.56989 −0.784947 0.619562i \(-0.787310\pi\)
−0.784947 + 0.619562i \(0.787310\pi\)
\(38\) 0 0
\(39\) −8.93381 −1.43055
\(40\) 0 0
\(41\) −2.82571 −0.441301 −0.220651 0.975353i \(-0.570818\pi\)
−0.220651 + 0.975353i \(0.570818\pi\)
\(42\) 0 0
\(43\) −8.28009 −1.26270 −0.631351 0.775497i \(-0.717499\pi\)
−0.631351 + 0.775497i \(0.717499\pi\)
\(44\) 0 0
\(45\) −16.2492 −2.42229
\(46\) 0 0
\(47\) −10.2543 −1.49574 −0.747872 0.663842i \(-0.768925\pi\)
−0.747872 + 0.663842i \(0.768925\pi\)
\(48\) 0 0
\(49\) 1.16390 0.166272
\(50\) 0 0
\(51\) −9.67581 −1.35488
\(52\) 0 0
\(53\) −5.03097 −0.691057 −0.345529 0.938408i \(-0.612300\pi\)
−0.345529 + 0.938408i \(0.612300\pi\)
\(54\) 0 0
\(55\) −20.5243 −2.76750
\(56\) 0 0
\(57\) −18.5135 −2.45217
\(58\) 0 0
\(59\) 3.57284 0.465145 0.232572 0.972579i \(-0.425286\pi\)
0.232572 + 0.972579i \(0.425286\pi\)
\(60\) 0 0
\(61\) 2.46580 0.315713 0.157856 0.987462i \(-0.449542\pi\)
0.157856 + 0.987462i \(0.449542\pi\)
\(62\) 0 0
\(63\) 13.9390 1.75615
\(64\) 0 0
\(65\) 10.6014 1.31494
\(66\) 0 0
\(67\) −0.271159 −0.0331273 −0.0165636 0.999863i \(-0.505273\pi\)
−0.0165636 + 0.999863i \(0.505273\pi\)
\(68\) 0 0
\(69\) −25.8813 −3.11574
\(70\) 0 0
\(71\) 6.18072 0.733517 0.366759 0.930316i \(-0.380468\pi\)
0.366759 + 0.930316i \(0.380468\pi\)
\(72\) 0 0
\(73\) 13.2210 1.54740 0.773699 0.633553i \(-0.218404\pi\)
0.773699 + 0.633553i \(0.218404\pi\)
\(74\) 0 0
\(75\) 17.1056 1.97518
\(76\) 0 0
\(77\) 17.6064 2.00643
\(78\) 0 0
\(79\) 7.67343 0.863329 0.431664 0.902034i \(-0.357926\pi\)
0.431664 + 0.902034i \(0.357926\pi\)
\(80\) 0 0
\(81\) 0.164052 0.0182280
\(82\) 0 0
\(83\) −1.85568 −0.203688 −0.101844 0.994800i \(-0.532474\pi\)
−0.101844 + 0.994800i \(0.532474\pi\)
\(84\) 0 0
\(85\) 11.4819 1.24539
\(86\) 0 0
\(87\) 3.93570 0.421952
\(88\) 0 0
\(89\) −1.46966 −0.155784 −0.0778920 0.996962i \(-0.524819\pi\)
−0.0778920 + 0.996962i \(0.524819\pi\)
\(90\) 0 0
\(91\) −9.09420 −0.953331
\(92\) 0 0
\(93\) −1.97087 −0.204369
\(94\) 0 0
\(95\) 21.9692 2.25400
\(96\) 0 0
\(97\) −0.763796 −0.0775518 −0.0387759 0.999248i \(-0.512346\pi\)
−0.0387759 + 0.999248i \(0.512346\pi\)
\(98\) 0 0
\(99\) 30.0611 3.02125
\(100\) 0 0
\(101\) 4.20829 0.418741 0.209370 0.977836i \(-0.432859\pi\)
0.209370 + 0.977836i \(0.432859\pi\)
\(102\) 0 0
\(103\) −15.5406 −1.53126 −0.765632 0.643279i \(-0.777573\pi\)
−0.765632 + 0.643279i \(0.777573\pi\)
\(104\) 0 0
\(105\) −26.7127 −2.60689
\(106\) 0 0
\(107\) −8.77861 −0.848660 −0.424330 0.905508i \(-0.639490\pi\)
−0.424330 + 0.905508i \(0.639490\pi\)
\(108\) 0 0
\(109\) −10.4923 −1.00498 −0.502492 0.864582i \(-0.667583\pi\)
−0.502492 + 0.864582i \(0.667583\pi\)
\(110\) 0 0
\(111\) −26.8036 −2.54408
\(112\) 0 0
\(113\) −9.15796 −0.861509 −0.430754 0.902469i \(-0.641752\pi\)
−0.430754 + 0.902469i \(0.641752\pi\)
\(114\) 0 0
\(115\) 30.7123 2.86394
\(116\) 0 0
\(117\) −15.5274 −1.43551
\(118\) 0 0
\(119\) −9.84953 −0.902905
\(120\) 0 0
\(121\) 26.9701 2.45183
\(122\) 0 0
\(123\) −7.93137 −0.715147
\(124\) 0 0
\(125\) −3.64458 −0.325981
\(126\) 0 0
\(127\) −9.14813 −0.811765 −0.405883 0.913925i \(-0.633036\pi\)
−0.405883 + 0.913925i \(0.633036\pi\)
\(128\) 0 0
\(129\) −23.2411 −2.04626
\(130\) 0 0
\(131\) 8.38571 0.732662 0.366331 0.930485i \(-0.380614\pi\)
0.366331 + 0.930485i \(0.380614\pi\)
\(132\) 0 0
\(133\) −18.8459 −1.63414
\(134\) 0 0
\(135\) −17.5620 −1.51149
\(136\) 0 0
\(137\) 18.8496 1.61043 0.805216 0.592981i \(-0.202049\pi\)
0.805216 + 0.592981i \(0.202049\pi\)
\(138\) 0 0
\(139\) 10.0650 0.853706 0.426853 0.904321i \(-0.359622\pi\)
0.426853 + 0.904321i \(0.359622\pi\)
\(140\) 0 0
\(141\) −28.7824 −2.42392
\(142\) 0 0
\(143\) −19.6127 −1.64009
\(144\) 0 0
\(145\) −4.67035 −0.387852
\(146\) 0 0
\(147\) 3.26692 0.269451
\(148\) 0 0
\(149\) −18.5789 −1.52205 −0.761023 0.648725i \(-0.775303\pi\)
−0.761023 + 0.648725i \(0.775303\pi\)
\(150\) 0 0
\(151\) 6.78604 0.552240 0.276120 0.961123i \(-0.410951\pi\)
0.276120 + 0.961123i \(0.410951\pi\)
\(152\) 0 0
\(153\) −16.8171 −1.35958
\(154\) 0 0
\(155\) 2.33875 0.187853
\(156\) 0 0
\(157\) 19.7470 1.57598 0.787990 0.615688i \(-0.211122\pi\)
0.787990 + 0.615688i \(0.211122\pi\)
\(158\) 0 0
\(159\) −14.1212 −1.11989
\(160\) 0 0
\(161\) −26.3459 −2.07635
\(162\) 0 0
\(163\) −11.4905 −0.900005 −0.450002 0.893027i \(-0.648577\pi\)
−0.450002 + 0.893027i \(0.648577\pi\)
\(164\) 0 0
\(165\) −57.6090 −4.48485
\(166\) 0 0
\(167\) 0.914891 0.0707964 0.0353982 0.999373i \(-0.488730\pi\)
0.0353982 + 0.999373i \(0.488730\pi\)
\(168\) 0 0
\(169\) −2.86949 −0.220730
\(170\) 0 0
\(171\) −32.1774 −2.46067
\(172\) 0 0
\(173\) 24.8348 1.88815 0.944076 0.329727i \(-0.106957\pi\)
0.944076 + 0.329727i \(0.106957\pi\)
\(174\) 0 0
\(175\) 17.4127 1.31628
\(176\) 0 0
\(177\) 10.0285 0.753787
\(178\) 0 0
\(179\) 11.6568 0.871274 0.435637 0.900123i \(-0.356523\pi\)
0.435637 + 0.900123i \(0.356523\pi\)
\(180\) 0 0
\(181\) 17.2535 1.28244 0.641221 0.767356i \(-0.278428\pi\)
0.641221 + 0.767356i \(0.278428\pi\)
\(182\) 0 0
\(183\) 6.92115 0.511626
\(184\) 0 0
\(185\) 31.8068 2.33848
\(186\) 0 0
\(187\) −21.2416 −1.55334
\(188\) 0 0
\(189\) 15.0652 1.09583
\(190\) 0 0
\(191\) 24.5481 1.77624 0.888119 0.459614i \(-0.152012\pi\)
0.888119 + 0.459614i \(0.152012\pi\)
\(192\) 0 0
\(193\) −18.1606 −1.30723 −0.653616 0.756826i \(-0.726749\pi\)
−0.653616 + 0.756826i \(0.726749\pi\)
\(194\) 0 0
\(195\) 29.7567 2.13092
\(196\) 0 0
\(197\) −15.6761 −1.11688 −0.558439 0.829546i \(-0.688600\pi\)
−0.558439 + 0.829546i \(0.688600\pi\)
\(198\) 0 0
\(199\) −9.24717 −0.655514 −0.327757 0.944762i \(-0.606293\pi\)
−0.327757 + 0.944762i \(0.606293\pi\)
\(200\) 0 0
\(201\) −0.761104 −0.0536842
\(202\) 0 0
\(203\) 4.00636 0.281192
\(204\) 0 0
\(205\) 9.41185 0.657352
\(206\) 0 0
\(207\) −44.9830 −3.12653
\(208\) 0 0
\(209\) −40.6432 −2.81135
\(210\) 0 0
\(211\) −11.9897 −0.825403 −0.412702 0.910866i \(-0.635415\pi\)
−0.412702 + 0.910866i \(0.635415\pi\)
\(212\) 0 0
\(213\) 17.3484 1.18870
\(214\) 0 0
\(215\) 27.5793 1.88089
\(216\) 0 0
\(217\) −2.00625 −0.136193
\(218\) 0 0
\(219\) 37.1094 2.50762
\(220\) 0 0
\(221\) 10.9719 0.738051
\(222\) 0 0
\(223\) 8.80822 0.589842 0.294921 0.955522i \(-0.404707\pi\)
0.294921 + 0.955522i \(0.404707\pi\)
\(224\) 0 0
\(225\) 29.7304 1.98203
\(226\) 0 0
\(227\) 12.3011 0.816454 0.408227 0.912881i \(-0.366147\pi\)
0.408227 + 0.912881i \(0.366147\pi\)
\(228\) 0 0
\(229\) 3.49454 0.230926 0.115463 0.993312i \(-0.463165\pi\)
0.115463 + 0.993312i \(0.463165\pi\)
\(230\) 0 0
\(231\) 49.4187 3.25151
\(232\) 0 0
\(233\) −8.16901 −0.535170 −0.267585 0.963534i \(-0.586226\pi\)
−0.267585 + 0.963534i \(0.586226\pi\)
\(234\) 0 0
\(235\) 34.1550 2.22803
\(236\) 0 0
\(237\) 21.5383 1.39906
\(238\) 0 0
\(239\) 16.2842 1.05334 0.526668 0.850071i \(-0.323441\pi\)
0.526668 + 0.850071i \(0.323441\pi\)
\(240\) 0 0
\(241\) 17.2260 1.10963 0.554813 0.831975i \(-0.312790\pi\)
0.554813 + 0.831975i \(0.312790\pi\)
\(242\) 0 0
\(243\) −15.3573 −0.985173
\(244\) 0 0
\(245\) −3.87673 −0.247675
\(246\) 0 0
\(247\) 20.9934 1.33578
\(248\) 0 0
\(249\) −5.20864 −0.330084
\(250\) 0 0
\(251\) 6.70328 0.423107 0.211553 0.977366i \(-0.432148\pi\)
0.211553 + 0.977366i \(0.432148\pi\)
\(252\) 0 0
\(253\) −56.8180 −3.57211
\(254\) 0 0
\(255\) 32.2282 2.01821
\(256\) 0 0
\(257\) 22.3504 1.39418 0.697091 0.716983i \(-0.254477\pi\)
0.697091 + 0.716983i \(0.254477\pi\)
\(258\) 0 0
\(259\) −27.2848 −1.69539
\(260\) 0 0
\(261\) 6.84045 0.423414
\(262\) 0 0
\(263\) 13.2208 0.815229 0.407614 0.913154i \(-0.366361\pi\)
0.407614 + 0.913154i \(0.366361\pi\)
\(264\) 0 0
\(265\) 16.7572 1.02938
\(266\) 0 0
\(267\) −4.12514 −0.252455
\(268\) 0 0
\(269\) −28.2269 −1.72102 −0.860511 0.509431i \(-0.829856\pi\)
−0.860511 + 0.509431i \(0.829856\pi\)
\(270\) 0 0
\(271\) −21.3618 −1.29764 −0.648818 0.760944i \(-0.724736\pi\)
−0.648818 + 0.760944i \(0.724736\pi\)
\(272\) 0 0
\(273\) −25.5262 −1.54491
\(274\) 0 0
\(275\) 37.5524 2.26450
\(276\) 0 0
\(277\) −26.8538 −1.61349 −0.806744 0.590902i \(-0.798772\pi\)
−0.806744 + 0.590902i \(0.798772\pi\)
\(278\) 0 0
\(279\) −3.42547 −0.205077
\(280\) 0 0
\(281\) 25.1142 1.49819 0.749093 0.662465i \(-0.230490\pi\)
0.749093 + 0.662465i \(0.230490\pi\)
\(282\) 0 0
\(283\) −25.7681 −1.53175 −0.765877 0.642987i \(-0.777695\pi\)
−0.765877 + 0.642987i \(0.777695\pi\)
\(284\) 0 0
\(285\) 61.6646 3.65270
\(286\) 0 0
\(287\) −8.07376 −0.476579
\(288\) 0 0
\(289\) −5.11681 −0.300989
\(290\) 0 0
\(291\) −2.14387 −0.125676
\(292\) 0 0
\(293\) 18.2273 1.06485 0.532424 0.846478i \(-0.321281\pi\)
0.532424 + 0.846478i \(0.321281\pi\)
\(294\) 0 0
\(295\) −11.9004 −0.692869
\(296\) 0 0
\(297\) 32.4897 1.88524
\(298\) 0 0
\(299\) 29.3481 1.69724
\(300\) 0 0
\(301\) −23.6583 −1.36364
\(302\) 0 0
\(303\) 11.8121 0.678587
\(304\) 0 0
\(305\) −8.21306 −0.470279
\(306\) 0 0
\(307\) 4.85756 0.277236 0.138618 0.990346i \(-0.455734\pi\)
0.138618 + 0.990346i \(0.455734\pi\)
\(308\) 0 0
\(309\) −43.6204 −2.48148
\(310\) 0 0
\(311\) 17.1372 0.971763 0.485882 0.874025i \(-0.338499\pi\)
0.485882 + 0.874025i \(0.338499\pi\)
\(312\) 0 0
\(313\) 7.12125 0.402517 0.201258 0.979538i \(-0.435497\pi\)
0.201258 + 0.979538i \(0.435497\pi\)
\(314\) 0 0
\(315\) −46.4281 −2.61593
\(316\) 0 0
\(317\) −30.5055 −1.71336 −0.856680 0.515848i \(-0.827477\pi\)
−0.856680 + 0.515848i \(0.827477\pi\)
\(318\) 0 0
\(319\) 8.64017 0.483757
\(320\) 0 0
\(321\) −24.6403 −1.37529
\(322\) 0 0
\(323\) 22.7370 1.26512
\(324\) 0 0
\(325\) −19.3969 −1.07595
\(326\) 0 0
\(327\) −29.4505 −1.62862
\(328\) 0 0
\(329\) −29.2992 −1.61532
\(330\) 0 0
\(331\) 7.25577 0.398813 0.199407 0.979917i \(-0.436099\pi\)
0.199407 + 0.979917i \(0.436099\pi\)
\(332\) 0 0
\(333\) −46.5860 −2.55289
\(334\) 0 0
\(335\) 0.903174 0.0493457
\(336\) 0 0
\(337\) 1.67495 0.0912405 0.0456203 0.998959i \(-0.485474\pi\)
0.0456203 + 0.998959i \(0.485474\pi\)
\(338\) 0 0
\(339\) −25.7051 −1.39611
\(340\) 0 0
\(341\) −4.32670 −0.234304
\(342\) 0 0
\(343\) −16.6752 −0.900377
\(344\) 0 0
\(345\) 86.2052 4.64113
\(346\) 0 0
\(347\) −13.7470 −0.737979 −0.368989 0.929434i \(-0.620296\pi\)
−0.368989 + 0.929434i \(0.620296\pi\)
\(348\) 0 0
\(349\) −18.1465 −0.971360 −0.485680 0.874137i \(-0.661428\pi\)
−0.485680 + 0.874137i \(0.661428\pi\)
\(350\) 0 0
\(351\) −16.7819 −0.895750
\(352\) 0 0
\(353\) −22.2901 −1.18638 −0.593191 0.805061i \(-0.702132\pi\)
−0.593191 + 0.805061i \(0.702132\pi\)
\(354\) 0 0
\(355\) −20.5867 −1.09263
\(356\) 0 0
\(357\) −27.6463 −1.46320
\(358\) 0 0
\(359\) −18.1349 −0.957125 −0.478563 0.878053i \(-0.658842\pi\)
−0.478563 + 0.878053i \(0.658842\pi\)
\(360\) 0 0
\(361\) 24.5045 1.28971
\(362\) 0 0
\(363\) 75.7014 3.97329
\(364\) 0 0
\(365\) −44.0364 −2.30497
\(366\) 0 0
\(367\) 31.0147 1.61896 0.809478 0.587150i \(-0.199750\pi\)
0.809478 + 0.587150i \(0.199750\pi\)
\(368\) 0 0
\(369\) −13.7851 −0.717625
\(370\) 0 0
\(371\) −14.3748 −0.746301
\(372\) 0 0
\(373\) 25.7975 1.33574 0.667871 0.744277i \(-0.267206\pi\)
0.667871 + 0.744277i \(0.267206\pi\)
\(374\) 0 0
\(375\) −10.2298 −0.528265
\(376\) 0 0
\(377\) −4.46290 −0.229851
\(378\) 0 0
\(379\) −7.02969 −0.361091 −0.180545 0.983567i \(-0.557786\pi\)
−0.180545 + 0.983567i \(0.557786\pi\)
\(380\) 0 0
\(381\) −25.6775 −1.31550
\(382\) 0 0
\(383\) −4.24162 −0.216737 −0.108368 0.994111i \(-0.534563\pi\)
−0.108368 + 0.994111i \(0.534563\pi\)
\(384\) 0 0
\(385\) −58.6433 −2.98874
\(386\) 0 0
\(387\) −40.3942 −2.05335
\(388\) 0 0
\(389\) 3.56789 0.180899 0.0904497 0.995901i \(-0.471170\pi\)
0.0904497 + 0.995901i \(0.471170\pi\)
\(390\) 0 0
\(391\) 31.7856 1.60747
\(392\) 0 0
\(393\) 23.5375 1.18731
\(394\) 0 0
\(395\) −25.5586 −1.28599
\(396\) 0 0
\(397\) −16.3759 −0.821883 −0.410941 0.911662i \(-0.634800\pi\)
−0.410941 + 0.911662i \(0.634800\pi\)
\(398\) 0 0
\(399\) −52.8977 −2.64820
\(400\) 0 0
\(401\) 6.06998 0.303120 0.151560 0.988448i \(-0.451570\pi\)
0.151560 + 0.988448i \(0.451570\pi\)
\(402\) 0 0
\(403\) 2.23487 0.111327
\(404\) 0 0
\(405\) −0.546425 −0.0271521
\(406\) 0 0
\(407\) −58.8427 −2.91672
\(408\) 0 0
\(409\) 30.2379 1.49517 0.747584 0.664167i \(-0.231214\pi\)
0.747584 + 0.664167i \(0.231214\pi\)
\(410\) 0 0
\(411\) 52.9083 2.60977
\(412\) 0 0
\(413\) 10.2085 0.502329
\(414\) 0 0
\(415\) 6.18090 0.303408
\(416\) 0 0
\(417\) 28.2512 1.38347
\(418\) 0 0
\(419\) −2.93225 −0.143250 −0.0716249 0.997432i \(-0.522818\pi\)
−0.0716249 + 0.997432i \(0.522818\pi\)
\(420\) 0 0
\(421\) 6.43693 0.313717 0.156858 0.987621i \(-0.449863\pi\)
0.156858 + 0.987621i \(0.449863\pi\)
\(422\) 0 0
\(423\) −50.0253 −2.43231
\(424\) 0 0
\(425\) −21.0080 −1.01904
\(426\) 0 0
\(427\) 7.04541 0.340951
\(428\) 0 0
\(429\) −55.0500 −2.65784
\(430\) 0 0
\(431\) −34.4701 −1.66037 −0.830184 0.557490i \(-0.811765\pi\)
−0.830184 + 0.557490i \(0.811765\pi\)
\(432\) 0 0
\(433\) 4.07058 0.195620 0.0978098 0.995205i \(-0.468816\pi\)
0.0978098 + 0.995205i \(0.468816\pi\)
\(434\) 0 0
\(435\) −13.1090 −0.628530
\(436\) 0 0
\(437\) 60.8179 2.90932
\(438\) 0 0
\(439\) −9.95459 −0.475107 −0.237553 0.971374i \(-0.576345\pi\)
−0.237553 + 0.971374i \(0.576345\pi\)
\(440\) 0 0
\(441\) 5.67807 0.270384
\(442\) 0 0
\(443\) −17.5544 −0.834036 −0.417018 0.908898i \(-0.636925\pi\)
−0.417018 + 0.908898i \(0.636925\pi\)
\(444\) 0 0
\(445\) 4.89515 0.232052
\(446\) 0 0
\(447\) −52.1485 −2.46654
\(448\) 0 0
\(449\) 27.8811 1.31579 0.657896 0.753109i \(-0.271447\pi\)
0.657896 + 0.753109i \(0.271447\pi\)
\(450\) 0 0
\(451\) −17.4120 −0.819898
\(452\) 0 0
\(453\) 19.0475 0.894928
\(454\) 0 0
\(455\) 30.2909 1.42006
\(456\) 0 0
\(457\) −21.1029 −0.987152 −0.493576 0.869703i \(-0.664311\pi\)
−0.493576 + 0.869703i \(0.664311\pi\)
\(458\) 0 0
\(459\) −18.1757 −0.848370
\(460\) 0 0
\(461\) −30.4681 −1.41904 −0.709520 0.704685i \(-0.751088\pi\)
−0.709520 + 0.704685i \(0.751088\pi\)
\(462\) 0 0
\(463\) −31.6310 −1.47002 −0.735008 0.678058i \(-0.762822\pi\)
−0.735008 + 0.678058i \(0.762822\pi\)
\(464\) 0 0
\(465\) 6.56455 0.304424
\(466\) 0 0
\(467\) 2.78847 0.129035 0.0645174 0.997917i \(-0.479449\pi\)
0.0645174 + 0.997917i \(0.479449\pi\)
\(468\) 0 0
\(469\) −0.774769 −0.0357755
\(470\) 0 0
\(471\) 55.4270 2.55394
\(472\) 0 0
\(473\) −51.0219 −2.34599
\(474\) 0 0
\(475\) −40.1961 −1.84432
\(476\) 0 0
\(477\) −24.5435 −1.12377
\(478\) 0 0
\(479\) 0.186867 0.00853819 0.00426910 0.999991i \(-0.498641\pi\)
0.00426910 + 0.999991i \(0.498641\pi\)
\(480\) 0 0
\(481\) 30.3939 1.38584
\(482\) 0 0
\(483\) −73.9493 −3.36481
\(484\) 0 0
\(485\) 2.54405 0.115519
\(486\) 0 0
\(487\) 15.6009 0.706943 0.353472 0.935445i \(-0.385001\pi\)
0.353472 + 0.935445i \(0.385001\pi\)
\(488\) 0 0
\(489\) −32.2522 −1.45850
\(490\) 0 0
\(491\) −35.6367 −1.60826 −0.804130 0.594453i \(-0.797369\pi\)
−0.804130 + 0.594453i \(0.797369\pi\)
\(492\) 0 0
\(493\) −4.83357 −0.217693
\(494\) 0 0
\(495\) −100.127 −4.50039
\(496\) 0 0
\(497\) 17.6599 0.792155
\(498\) 0 0
\(499\) −25.9141 −1.16007 −0.580037 0.814590i \(-0.696962\pi\)
−0.580037 + 0.814590i \(0.696962\pi\)
\(500\) 0 0
\(501\) 2.56797 0.114728
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −14.0170 −0.623747
\(506\) 0 0
\(507\) −8.05426 −0.357702
\(508\) 0 0
\(509\) 43.1469 1.91245 0.956227 0.292627i \(-0.0945293\pi\)
0.956227 + 0.292627i \(0.0945293\pi\)
\(510\) 0 0
\(511\) 37.7757 1.67110
\(512\) 0 0
\(513\) −34.7770 −1.53544
\(514\) 0 0
\(515\) 51.7627 2.28094
\(516\) 0 0
\(517\) −63.1870 −2.77896
\(518\) 0 0
\(519\) 69.7078 3.05983
\(520\) 0 0
\(521\) −22.9789 −1.00673 −0.503363 0.864075i \(-0.667904\pi\)
−0.503363 + 0.864075i \(0.667904\pi\)
\(522\) 0 0
\(523\) 2.68716 0.117501 0.0587506 0.998273i \(-0.481288\pi\)
0.0587506 + 0.998273i \(0.481288\pi\)
\(524\) 0 0
\(525\) 48.8750 2.13308
\(526\) 0 0
\(527\) 2.42049 0.105438
\(528\) 0 0
\(529\) 62.0215 2.69659
\(530\) 0 0
\(531\) 17.4300 0.756398
\(532\) 0 0
\(533\) 8.99379 0.389564
\(534\) 0 0
\(535\) 29.2398 1.26415
\(536\) 0 0
\(537\) 32.7192 1.41194
\(538\) 0 0
\(539\) 7.17197 0.308919
\(540\) 0 0
\(541\) 13.7406 0.590754 0.295377 0.955381i \(-0.404555\pi\)
0.295377 + 0.955381i \(0.404555\pi\)
\(542\) 0 0
\(543\) 48.4281 2.07825
\(544\) 0 0
\(545\) 34.9478 1.49700
\(546\) 0 0
\(547\) −38.1975 −1.63321 −0.816604 0.577199i \(-0.804146\pi\)
−0.816604 + 0.577199i \(0.804146\pi\)
\(548\) 0 0
\(549\) 12.0293 0.513398
\(550\) 0 0
\(551\) −9.24844 −0.393997
\(552\) 0 0
\(553\) 21.9250 0.932344
\(554\) 0 0
\(555\) 89.2772 3.78961
\(556\) 0 0
\(557\) −34.0835 −1.44416 −0.722082 0.691807i \(-0.756815\pi\)
−0.722082 + 0.691807i \(0.756815\pi\)
\(558\) 0 0
\(559\) 26.3543 1.11467
\(560\) 0 0
\(561\) −59.6223 −2.51725
\(562\) 0 0
\(563\) −19.5491 −0.823896 −0.411948 0.911207i \(-0.635151\pi\)
−0.411948 + 0.911207i \(0.635151\pi\)
\(564\) 0 0
\(565\) 30.5033 1.28328
\(566\) 0 0
\(567\) 0.468739 0.0196852
\(568\) 0 0
\(569\) 16.6019 0.695987 0.347994 0.937497i \(-0.386863\pi\)
0.347994 + 0.937497i \(0.386863\pi\)
\(570\) 0 0
\(571\) −13.2433 −0.554213 −0.277107 0.960839i \(-0.589376\pi\)
−0.277107 + 0.960839i \(0.589376\pi\)
\(572\) 0 0
\(573\) 68.9031 2.87847
\(574\) 0 0
\(575\) −56.1929 −2.34341
\(576\) 0 0
\(577\) −24.5290 −1.02116 −0.510578 0.859831i \(-0.670569\pi\)
−0.510578 + 0.859831i \(0.670569\pi\)
\(578\) 0 0
\(579\) −50.9744 −2.11842
\(580\) 0 0
\(581\) −5.30216 −0.219971
\(582\) 0 0
\(583\) −31.0008 −1.28392
\(584\) 0 0
\(585\) 51.7187 2.13830
\(586\) 0 0
\(587\) 28.2759 1.16707 0.583535 0.812088i \(-0.301669\pi\)
0.583535 + 0.812088i \(0.301669\pi\)
\(588\) 0 0
\(589\) 4.63130 0.190829
\(590\) 0 0
\(591\) −44.0007 −1.80995
\(592\) 0 0
\(593\) −15.9323 −0.654260 −0.327130 0.944979i \(-0.606082\pi\)
−0.327130 + 0.944979i \(0.606082\pi\)
\(594\) 0 0
\(595\) 32.8068 1.34495
\(596\) 0 0
\(597\) −25.9555 −1.06229
\(598\) 0 0
\(599\) 40.9491 1.67313 0.836567 0.547865i \(-0.184559\pi\)
0.836567 + 0.547865i \(0.184559\pi\)
\(600\) 0 0
\(601\) −39.2764 −1.60212 −0.801058 0.598587i \(-0.795729\pi\)
−0.801058 + 0.598587i \(0.795729\pi\)
\(602\) 0 0
\(603\) −1.32284 −0.0538701
\(604\) 0 0
\(605\) −89.8320 −3.65219
\(606\) 0 0
\(607\) 4.80079 0.194858 0.0974290 0.995242i \(-0.468938\pi\)
0.0974290 + 0.995242i \(0.468938\pi\)
\(608\) 0 0
\(609\) 11.2453 0.455683
\(610\) 0 0
\(611\) 32.6379 1.32039
\(612\) 0 0
\(613\) 8.56017 0.345742 0.172871 0.984944i \(-0.444696\pi\)
0.172871 + 0.984944i \(0.444696\pi\)
\(614\) 0 0
\(615\) 26.4178 1.06527
\(616\) 0 0
\(617\) −21.4421 −0.863228 −0.431614 0.902058i \(-0.642056\pi\)
−0.431614 + 0.902058i \(0.642056\pi\)
\(618\) 0 0
\(619\) −11.7723 −0.473167 −0.236584 0.971611i \(-0.576028\pi\)
−0.236584 + 0.971611i \(0.576028\pi\)
\(620\) 0 0
\(621\) −48.6171 −1.95094
\(622\) 0 0
\(623\) −4.19920 −0.168238
\(624\) 0 0
\(625\) −18.3317 −0.733268
\(626\) 0 0
\(627\) −114.080 −4.55591
\(628\) 0 0
\(629\) 32.9184 1.31254
\(630\) 0 0
\(631\) 36.7998 1.46498 0.732489 0.680779i \(-0.238359\pi\)
0.732489 + 0.680779i \(0.238359\pi\)
\(632\) 0 0
\(633\) −33.6534 −1.33760
\(634\) 0 0
\(635\) 30.4706 1.20919
\(636\) 0 0
\(637\) −3.70453 −0.146779
\(638\) 0 0
\(639\) 30.1525 1.19281
\(640\) 0 0
\(641\) 35.1857 1.38975 0.694877 0.719129i \(-0.255459\pi\)
0.694877 + 0.719129i \(0.255459\pi\)
\(642\) 0 0
\(643\) −22.3621 −0.881874 −0.440937 0.897538i \(-0.645354\pi\)
−0.440937 + 0.897538i \(0.645354\pi\)
\(644\) 0 0
\(645\) 77.4113 3.04807
\(646\) 0 0
\(647\) 12.3698 0.486308 0.243154 0.969988i \(-0.421818\pi\)
0.243154 + 0.969988i \(0.421818\pi\)
\(648\) 0 0
\(649\) 22.0158 0.864197
\(650\) 0 0
\(651\) −5.63126 −0.220707
\(652\) 0 0
\(653\) 4.19397 0.164123 0.0820613 0.996627i \(-0.473850\pi\)
0.0820613 + 0.996627i \(0.473850\pi\)
\(654\) 0 0
\(655\) −27.9311 −1.09136
\(656\) 0 0
\(657\) 64.4981 2.51631
\(658\) 0 0
\(659\) 18.2209 0.709784 0.354892 0.934907i \(-0.384518\pi\)
0.354892 + 0.934907i \(0.384518\pi\)
\(660\) 0 0
\(661\) −21.2704 −0.827324 −0.413662 0.910430i \(-0.635751\pi\)
−0.413662 + 0.910430i \(0.635751\pi\)
\(662\) 0 0
\(663\) 30.7966 1.19604
\(664\) 0 0
\(665\) 62.7717 2.43418
\(666\) 0 0
\(667\) −12.9290 −0.500614
\(668\) 0 0
\(669\) 24.7235 0.955864
\(670\) 0 0
\(671\) 15.1942 0.586566
\(672\) 0 0
\(673\) −15.5656 −0.600011 −0.300005 0.953938i \(-0.596988\pi\)
−0.300005 + 0.953938i \(0.596988\pi\)
\(674\) 0 0
\(675\) 32.1323 1.23677
\(676\) 0 0
\(677\) −5.63298 −0.216493 −0.108247 0.994124i \(-0.534524\pi\)
−0.108247 + 0.994124i \(0.534524\pi\)
\(678\) 0 0
\(679\) −2.18236 −0.0837513
\(680\) 0 0
\(681\) 34.5275 1.32310
\(682\) 0 0
\(683\) 3.67984 0.140805 0.0704026 0.997519i \(-0.477572\pi\)
0.0704026 + 0.997519i \(0.477572\pi\)
\(684\) 0 0
\(685\) −62.7843 −2.39886
\(686\) 0 0
\(687\) 9.80868 0.374225
\(688\) 0 0
\(689\) 16.0128 0.610040
\(690\) 0 0
\(691\) 6.37801 0.242631 0.121316 0.992614i \(-0.461289\pi\)
0.121316 + 0.992614i \(0.461289\pi\)
\(692\) 0 0
\(693\) 85.8922 3.26277
\(694\) 0 0
\(695\) −33.5246 −1.27166
\(696\) 0 0
\(697\) 9.74078 0.368958
\(698\) 0 0
\(699\) −22.9293 −0.867265
\(700\) 0 0
\(701\) 24.3301 0.918936 0.459468 0.888194i \(-0.348040\pi\)
0.459468 + 0.888194i \(0.348040\pi\)
\(702\) 0 0
\(703\) 62.9852 2.37553
\(704\) 0 0
\(705\) 95.8684 3.61061
\(706\) 0 0
\(707\) 12.0242 0.452215
\(708\) 0 0
\(709\) −18.8738 −0.708822 −0.354411 0.935090i \(-0.615319\pi\)
−0.354411 + 0.935090i \(0.615319\pi\)
\(710\) 0 0
\(711\) 37.4346 1.40391
\(712\) 0 0
\(713\) 6.47441 0.242469
\(714\) 0 0
\(715\) 65.3258 2.44305
\(716\) 0 0
\(717\) 45.7074 1.70697
\(718\) 0 0
\(719\) −45.6619 −1.70290 −0.851450 0.524435i \(-0.824276\pi\)
−0.851450 + 0.524435i \(0.824276\pi\)
\(720\) 0 0
\(721\) −44.4035 −1.65367
\(722\) 0 0
\(723\) 48.3511 1.79820
\(724\) 0 0
\(725\) 8.54513 0.317358
\(726\) 0 0
\(727\) −38.1174 −1.41370 −0.706849 0.707365i \(-0.749884\pi\)
−0.706849 + 0.707365i \(0.749884\pi\)
\(728\) 0 0
\(729\) −43.5981 −1.61474
\(730\) 0 0
\(731\) 28.5431 1.05571
\(732\) 0 0
\(733\) −3.54071 −0.130779 −0.0653895 0.997860i \(-0.520829\pi\)
−0.0653895 + 0.997860i \(0.520829\pi\)
\(734\) 0 0
\(735\) −10.8814 −0.401368
\(736\) 0 0
\(737\) −1.67088 −0.0615475
\(738\) 0 0
\(739\) 19.2057 0.706495 0.353247 0.935530i \(-0.385077\pi\)
0.353247 + 0.935530i \(0.385077\pi\)
\(740\) 0 0
\(741\) 58.9255 2.16468
\(742\) 0 0
\(743\) 6.96467 0.255509 0.127755 0.991806i \(-0.459223\pi\)
0.127755 + 0.991806i \(0.459223\pi\)
\(744\) 0 0
\(745\) 61.8827 2.26721
\(746\) 0 0
\(747\) −9.05289 −0.331228
\(748\) 0 0
\(749\) −25.0827 −0.916503
\(750\) 0 0
\(751\) 12.2850 0.448288 0.224144 0.974556i \(-0.428041\pi\)
0.224144 + 0.974556i \(0.428041\pi\)
\(752\) 0 0
\(753\) 18.8152 0.685663
\(754\) 0 0
\(755\) −22.6029 −0.822604
\(756\) 0 0
\(757\) −13.5894 −0.493915 −0.246958 0.969026i \(-0.579431\pi\)
−0.246958 + 0.969026i \(0.579431\pi\)
\(758\) 0 0
\(759\) −159.480 −5.78876
\(760\) 0 0
\(761\) −39.8241 −1.44362 −0.721811 0.692090i \(-0.756690\pi\)
−0.721811 + 0.692090i \(0.756690\pi\)
\(762\) 0 0
\(763\) −29.9793 −1.08532
\(764\) 0 0
\(765\) 56.0142 2.02520
\(766\) 0 0
\(767\) −11.3718 −0.410612
\(768\) 0 0
\(769\) −27.0475 −0.975358 −0.487679 0.873023i \(-0.662156\pi\)
−0.487679 + 0.873023i \(0.662156\pi\)
\(770\) 0 0
\(771\) 62.7346 2.25933
\(772\) 0 0
\(773\) −15.0712 −0.542073 −0.271036 0.962569i \(-0.587366\pi\)
−0.271036 + 0.962569i \(0.587366\pi\)
\(774\) 0 0
\(775\) −4.27911 −0.153710
\(776\) 0 0
\(777\) −76.5846 −2.74746
\(778\) 0 0
\(779\) 18.6378 0.667768
\(780\) 0 0
\(781\) 38.0856 1.36281
\(782\) 0 0
\(783\) 7.39310 0.264208
\(784\) 0 0
\(785\) −65.7732 −2.34755
\(786\) 0 0
\(787\) 28.1114 1.00206 0.501032 0.865429i \(-0.332954\pi\)
0.501032 + 0.865429i \(0.332954\pi\)
\(788\) 0 0
\(789\) 37.1089 1.32111
\(790\) 0 0
\(791\) −26.1666 −0.930378
\(792\) 0 0
\(793\) −7.84825 −0.278699
\(794\) 0 0
\(795\) 47.0350 1.66816
\(796\) 0 0
\(797\) −13.8844 −0.491810 −0.245905 0.969294i \(-0.579085\pi\)
−0.245905 + 0.969294i \(0.579085\pi\)
\(798\) 0 0
\(799\) 35.3487 1.25055
\(800\) 0 0
\(801\) −7.16971 −0.253329
\(802\) 0 0
\(803\) 81.4675 2.87493
\(804\) 0 0
\(805\) 87.7529 3.09288
\(806\) 0 0
\(807\) −79.2289 −2.78899
\(808\) 0 0
\(809\) 35.5748 1.25074 0.625371 0.780327i \(-0.284948\pi\)
0.625371 + 0.780327i \(0.284948\pi\)
\(810\) 0 0
\(811\) −23.0995 −0.811133 −0.405567 0.914065i \(-0.632926\pi\)
−0.405567 + 0.914065i \(0.632926\pi\)
\(812\) 0 0
\(813\) −59.9595 −2.10287
\(814\) 0 0
\(815\) 38.2725 1.34063
\(816\) 0 0
\(817\) 54.6138 1.91069
\(818\) 0 0
\(819\) −44.3658 −1.55027
\(820\) 0 0
\(821\) −21.0963 −0.736265 −0.368132 0.929773i \(-0.620003\pi\)
−0.368132 + 0.929773i \(0.620003\pi\)
\(822\) 0 0
\(823\) −28.7224 −1.00120 −0.500599 0.865679i \(-0.666887\pi\)
−0.500599 + 0.865679i \(0.666887\pi\)
\(824\) 0 0
\(825\) 105.404 3.66971
\(826\) 0 0
\(827\) 27.4860 0.955782 0.477891 0.878419i \(-0.341401\pi\)
0.477891 + 0.878419i \(0.341401\pi\)
\(828\) 0 0
\(829\) 25.5174 0.886255 0.443127 0.896459i \(-0.353869\pi\)
0.443127 + 0.896459i \(0.353869\pi\)
\(830\) 0 0
\(831\) −75.3748 −2.61472
\(832\) 0 0
\(833\) −4.01221 −0.139015
\(834\) 0 0
\(835\) −3.04731 −0.105457
\(836\) 0 0
\(837\) −3.70221 −0.127967
\(838\) 0 0
\(839\) 15.1427 0.522784 0.261392 0.965233i \(-0.415819\pi\)
0.261392 + 0.965233i \(0.415819\pi\)
\(840\) 0 0
\(841\) −27.0339 −0.932204
\(842\) 0 0
\(843\) 70.4920 2.42787
\(844\) 0 0
\(845\) 9.55769 0.328795
\(846\) 0 0
\(847\) 77.0605 2.64783
\(848\) 0 0
\(849\) −72.3275 −2.48227
\(850\) 0 0
\(851\) 88.0513 3.01836
\(852\) 0 0
\(853\) 11.9554 0.409346 0.204673 0.978830i \(-0.434387\pi\)
0.204673 + 0.978830i \(0.434387\pi\)
\(854\) 0 0
\(855\) 107.176 3.66535
\(856\) 0 0
\(857\) 9.53741 0.325792 0.162896 0.986643i \(-0.447917\pi\)
0.162896 + 0.986643i \(0.447917\pi\)
\(858\) 0 0
\(859\) −21.9007 −0.747243 −0.373621 0.927581i \(-0.621884\pi\)
−0.373621 + 0.927581i \(0.621884\pi\)
\(860\) 0 0
\(861\) −22.6619 −0.772317
\(862\) 0 0
\(863\) 7.82525 0.266375 0.133187 0.991091i \(-0.457479\pi\)
0.133187 + 0.991091i \(0.457479\pi\)
\(864\) 0 0
\(865\) −82.7196 −2.81255
\(866\) 0 0
\(867\) −14.3622 −0.487765
\(868\) 0 0
\(869\) 47.2836 1.60399
\(870\) 0 0
\(871\) 0.863056 0.0292435
\(872\) 0 0
\(873\) −3.72616 −0.126111
\(874\) 0 0
\(875\) −10.4135 −0.352040
\(876\) 0 0
\(877\) 22.9618 0.775365 0.387682 0.921793i \(-0.373276\pi\)
0.387682 + 0.921793i \(0.373276\pi\)
\(878\) 0 0
\(879\) 51.1614 1.72563
\(880\) 0 0
\(881\) 13.0701 0.440343 0.220171 0.975461i \(-0.429338\pi\)
0.220171 + 0.975461i \(0.429338\pi\)
\(882\) 0 0
\(883\) −5.64794 −0.190068 −0.0950341 0.995474i \(-0.530296\pi\)
−0.0950341 + 0.995474i \(0.530296\pi\)
\(884\) 0 0
\(885\) −33.4028 −1.12282
\(886\) 0 0
\(887\) −2.03708 −0.0683985 −0.0341992 0.999415i \(-0.510888\pi\)
−0.0341992 + 0.999415i \(0.510888\pi\)
\(888\) 0 0
\(889\) −26.1385 −0.876658
\(890\) 0 0
\(891\) 1.01089 0.0338661
\(892\) 0 0
\(893\) 67.6353 2.26333
\(894\) 0 0
\(895\) −38.8266 −1.29783
\(896\) 0 0
\(897\) 82.3761 2.75046
\(898\) 0 0
\(899\) −0.984549 −0.0328366
\(900\) 0 0
\(901\) 17.3428 0.577772
\(902\) 0 0
\(903\) −66.4057 −2.20984
\(904\) 0 0
\(905\) −57.4679 −1.91030
\(906\) 0 0
\(907\) −49.0974 −1.63025 −0.815127 0.579282i \(-0.803333\pi\)
−0.815127 + 0.579282i \(0.803333\pi\)
\(908\) 0 0
\(909\) 20.5300 0.680938
\(910\) 0 0
\(911\) 23.9150 0.792340 0.396170 0.918177i \(-0.370339\pi\)
0.396170 + 0.918177i \(0.370339\pi\)
\(912\) 0 0
\(913\) −11.4347 −0.378433
\(914\) 0 0
\(915\) −23.0529 −0.762106
\(916\) 0 0
\(917\) 23.9601 0.791232
\(918\) 0 0
\(919\) 27.0185 0.891260 0.445630 0.895217i \(-0.352980\pi\)
0.445630 + 0.895217i \(0.352980\pi\)
\(920\) 0 0
\(921\) 13.6345 0.449272
\(922\) 0 0
\(923\) −19.6723 −0.647522
\(924\) 0 0
\(925\) −58.1954 −1.91345
\(926\) 0 0
\(927\) −75.8145 −2.49007
\(928\) 0 0
\(929\) 17.8916 0.587003 0.293501 0.955959i \(-0.405179\pi\)
0.293501 + 0.955959i \(0.405179\pi\)
\(930\) 0 0
\(931\) −7.67687 −0.251599
\(932\) 0 0
\(933\) 48.1018 1.57478
\(934\) 0 0
\(935\) 70.7515 2.31382
\(936\) 0 0
\(937\) −18.2903 −0.597519 −0.298760 0.954328i \(-0.596573\pi\)
−0.298760 + 0.954328i \(0.596573\pi\)
\(938\) 0 0
\(939\) 19.9884 0.652295
\(940\) 0 0
\(941\) 16.2134 0.528543 0.264272 0.964448i \(-0.414869\pi\)
0.264272 + 0.964448i \(0.414869\pi\)
\(942\) 0 0
\(943\) 26.0550 0.848469
\(944\) 0 0
\(945\) −50.1790 −1.63232
\(946\) 0 0
\(947\) 6.25401 0.203228 0.101614 0.994824i \(-0.467599\pi\)
0.101614 + 0.994824i \(0.467599\pi\)
\(948\) 0 0
\(949\) −42.0803 −1.36599
\(950\) 0 0
\(951\) −85.6247 −2.77657
\(952\) 0 0
\(953\) −18.2420 −0.590916 −0.295458 0.955356i \(-0.595472\pi\)
−0.295458 + 0.955356i \(0.595472\pi\)
\(954\) 0 0
\(955\) −81.7647 −2.64584
\(956\) 0 0
\(957\) 24.2518 0.783948
\(958\) 0 0
\(959\) 53.8582 1.73917
\(960\) 0 0
\(961\) −30.5070 −0.984096
\(962\) 0 0
\(963\) −42.8262 −1.38005
\(964\) 0 0
\(965\) 60.4894 1.94722
\(966\) 0 0
\(967\) 6.35525 0.204371 0.102186 0.994765i \(-0.467416\pi\)
0.102186 + 0.994765i \(0.467416\pi\)
\(968\) 0 0
\(969\) 63.8197 2.05018
\(970\) 0 0
\(971\) 56.2895 1.80642 0.903208 0.429204i \(-0.141206\pi\)
0.903208 + 0.429204i \(0.141206\pi\)
\(972\) 0 0
\(973\) 28.7584 0.921952
\(974\) 0 0
\(975\) −54.4445 −1.74362
\(976\) 0 0
\(977\) 51.3434 1.64262 0.821310 0.570482i \(-0.193243\pi\)
0.821310 + 0.570482i \(0.193243\pi\)
\(978\) 0 0
\(979\) −9.05606 −0.289433
\(980\) 0 0
\(981\) −51.1865 −1.63426
\(982\) 0 0
\(983\) 13.8340 0.441235 0.220617 0.975360i \(-0.429193\pi\)
0.220617 + 0.975360i \(0.429193\pi\)
\(984\) 0 0
\(985\) 52.2140 1.66368
\(986\) 0 0
\(987\) −82.2387 −2.61769
\(988\) 0 0
\(989\) 76.3484 2.42774
\(990\) 0 0
\(991\) −7.41841 −0.235653 −0.117827 0.993034i \(-0.537593\pi\)
−0.117827 + 0.993034i \(0.537593\pi\)
\(992\) 0 0
\(993\) 20.3659 0.646293
\(994\) 0 0
\(995\) 30.8004 0.976439
\(996\) 0 0
\(997\) −33.9777 −1.07608 −0.538042 0.842918i \(-0.680836\pi\)
−0.538042 + 0.842918i \(0.680836\pi\)
\(998\) 0 0
\(999\) −50.3496 −1.59299
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 \(a_p\))