Properties

Label 4012.2.a.f.1.1
Level 4012
Weight 2
Character 4012.1
Self dual Yes
Analytic conductor 32.036
Analytic rank 1
Dimension 3
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4012 = 2^{2} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4012.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0359812909\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.321.1
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.46050\)
Character \(\chi\) = 4012.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(-3.92101 q^{5}\) \(+1.00000 q^{7}\) \(-2.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(-3.92101 q^{5}\) \(+1.00000 q^{7}\) \(-2.00000 q^{9}\) \(-2.00000 q^{11}\) \(+4.92101 q^{13}\) \(+3.92101 q^{15}\) \(+1.00000 q^{17}\) \(+1.92101 q^{19}\) \(-1.00000 q^{21}\) \(-6.10817 q^{23}\) \(+10.3743 q^{25}\) \(+5.00000 q^{27}\) \(-5.92101 q^{29}\) \(+3.73385 q^{31}\) \(+2.00000 q^{33}\) \(-3.92101 q^{35}\) \(+8.65486 q^{37}\) \(-4.92101 q^{39}\) \(+1.92101 q^{41}\) \(-0.266149 q^{43}\) \(+7.84202 q^{45}\) \(+2.10817 q^{47}\) \(-6.00000 q^{49}\) \(-1.00000 q^{51}\) \(+9.37432 q^{53}\) \(+7.84202 q^{55}\) \(-1.92101 q^{57}\) \(-1.00000 q^{59}\) \(-6.92101 q^{61}\) \(-2.00000 q^{63}\) \(-19.2953 q^{65}\) \(+10.2163 q^{67}\) \(+6.10817 q^{69}\) \(+2.37432 q^{71}\) \(+2.00000 q^{73}\) \(-10.3743 q^{75}\) \(-2.00000 q^{77}\) \(-5.00000 q^{79}\) \(+1.00000 q^{81}\) \(+4.65486 q^{83}\) \(-3.92101 q^{85}\) \(+5.92101 q^{87}\) \(+5.73385 q^{89}\) \(+4.92101 q^{91}\) \(-3.73385 q^{93}\) \(-7.53230 q^{95}\) \(-3.45331 q^{97}\) \(+4.00000 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(3q \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 6q^{9} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 7q^{19} \) \(\mathstrut -\mathstrut 3q^{21} \) \(\mathstrut +\mathstrut 20q^{25} \) \(\mathstrut +\mathstrut 15q^{27} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut q^{35} \) \(\mathstrut +\mathstrut 6q^{37} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut -\mathstrut 7q^{41} \) \(\mathstrut -\mathstrut 8q^{43} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 12q^{47} \) \(\mathstrut -\mathstrut 18q^{49} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 17q^{53} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut +\mathstrut 7q^{57} \) \(\mathstrut -\mathstrut 3q^{59} \) \(\mathstrut -\mathstrut 8q^{61} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 34q^{65} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut -\mathstrut 4q^{71} \) \(\mathstrut +\mathstrut 6q^{73} \) \(\mathstrut -\mathstrut 20q^{75} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut -\mathstrut 15q^{79} \) \(\mathstrut +\mathstrut 3q^{81} \) \(\mathstrut -\mathstrut 6q^{83} \) \(\mathstrut +\mathstrut q^{85} \) \(\mathstrut +\mathstrut 5q^{87} \) \(\mathstrut +\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 2q^{91} \) \(\mathstrut -\mathstrut 4q^{93} \) \(\mathstrut -\mathstrut 37q^{95} \) \(\mathstrut -\mathstrut 12q^{97} \) \(\mathstrut +\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.00000 −0.577350 −0.288675 0.957427i \(-0.593215\pi\)
−0.288675 + 0.957427i \(0.593215\pi\)
\(4\) 0 0
\(5\) −3.92101 −1.75353 −0.876764 0.480920i \(-0.840303\pi\)
−0.876764 + 0.480920i \(0.840303\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964 0.188982 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) 0 0
\(9\) −2.00000 −0.666667
\(10\) 0 0
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) 4.92101 1.36484 0.682421 0.730959i \(-0.260927\pi\)
0.682421 + 0.730959i \(0.260927\pi\)
\(14\) 0 0
\(15\) 3.92101 1.01240
\(16\) 0 0
\(17\) 1.00000 0.242536
\(18\) 0 0
\(19\) 1.92101 0.440710 0.220355 0.975420i \(-0.429278\pi\)
0.220355 + 0.975420i \(0.429278\pi\)
\(20\) 0 0
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) −6.10817 −1.27364 −0.636821 0.771012i \(-0.719751\pi\)
−0.636821 + 0.771012i \(0.719751\pi\)
\(24\) 0 0
\(25\) 10.3743 2.07486
\(26\) 0 0
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) −5.92101 −1.09950 −0.549752 0.835328i \(-0.685278\pi\)
−0.549752 + 0.835328i \(0.685278\pi\)
\(30\) 0 0
\(31\) 3.73385 0.670619 0.335310 0.942108i \(-0.391159\pi\)
0.335310 + 0.942108i \(0.391159\pi\)
\(32\) 0 0
\(33\) 2.00000 0.348155
\(34\) 0 0
\(35\) −3.92101 −0.662772
\(36\) 0 0
\(37\) 8.65486 1.42285 0.711425 0.702762i \(-0.248050\pi\)
0.711425 + 0.702762i \(0.248050\pi\)
\(38\) 0 0
\(39\) −4.92101 −0.787992
\(40\) 0 0
\(41\) 1.92101 0.300011 0.150006 0.988685i \(-0.452071\pi\)
0.150006 + 0.988685i \(0.452071\pi\)
\(42\) 0 0
\(43\) −0.266149 −0.0405873 −0.0202937 0.999794i \(-0.506460\pi\)
−0.0202937 + 0.999794i \(0.506460\pi\)
\(44\) 0 0
\(45\) 7.84202 1.16902
\(46\) 0 0
\(47\) 2.10817 0.307508 0.153754 0.988109i \(-0.450864\pi\)
0.153754 + 0.988109i \(0.450864\pi\)
\(48\) 0 0
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) −1.00000 −0.140028
\(52\) 0 0
\(53\) 9.37432 1.28766 0.643831 0.765168i \(-0.277344\pi\)
0.643831 + 0.765168i \(0.277344\pi\)
\(54\) 0 0
\(55\) 7.84202 1.05742
\(56\) 0 0
\(57\) −1.92101 −0.254444
\(58\) 0 0
\(59\) −1.00000 −0.130189
\(60\) 0 0
\(61\) −6.92101 −0.886144 −0.443072 0.896486i \(-0.646111\pi\)
−0.443072 + 0.896486i \(0.646111\pi\)
\(62\) 0 0
\(63\) −2.00000 −0.251976
\(64\) 0 0
\(65\) −19.2953 −2.39329
\(66\) 0 0
\(67\) 10.2163 1.24812 0.624062 0.781375i \(-0.285481\pi\)
0.624062 + 0.781375i \(0.285481\pi\)
\(68\) 0 0
\(69\) 6.10817 0.735337
\(70\) 0 0
\(71\) 2.37432 0.281780 0.140890 0.990025i \(-0.455004\pi\)
0.140890 + 0.990025i \(0.455004\pi\)
\(72\) 0 0
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 0 0
\(75\) −10.3743 −1.19792
\(76\) 0 0
\(77\) −2.00000 −0.227921
\(78\) 0 0
\(79\) −5.00000 −0.562544 −0.281272 0.959628i \(-0.590756\pi\)
−0.281272 + 0.959628i \(0.590756\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 4.65486 0.510937 0.255469 0.966817i \(-0.417770\pi\)
0.255469 + 0.966817i \(0.417770\pi\)
\(84\) 0 0
\(85\) −3.92101 −0.425293
\(86\) 0 0
\(87\) 5.92101 0.634799
\(88\) 0 0
\(89\) 5.73385 0.607787 0.303893 0.952706i \(-0.401713\pi\)
0.303893 + 0.952706i \(0.401713\pi\)
\(90\) 0 0
\(91\) 4.92101 0.515862
\(92\) 0 0
\(93\) −3.73385 −0.387182
\(94\) 0 0
\(95\) −7.53230 −0.772797
\(96\) 0 0
\(97\) −3.45331 −0.350630 −0.175315 0.984512i \(-0.556094\pi\)
−0.175315 + 0.984512i \(0.556094\pi\)
\(98\) 0 0
\(99\) 4.00000 0.402015
\(100\) 0 0
\(101\) −17.0292 −1.69447 −0.847233 0.531221i \(-0.821733\pi\)
−0.847233 + 0.531221i \(0.821733\pi\)
\(102\) 0 0
\(103\) 9.13735 0.900330 0.450165 0.892946i \(-0.351365\pi\)
0.450165 + 0.892946i \(0.351365\pi\)
\(104\) 0 0
\(105\) 3.92101 0.382651
\(106\) 0 0
\(107\) −6.84202 −0.661443 −0.330721 0.943728i \(-0.607292\pi\)
−0.330721 + 0.943728i \(0.607292\pi\)
\(108\) 0 0
\(109\) −6.21634 −0.595417 −0.297709 0.954657i \(-0.596222\pi\)
−0.297709 + 0.954657i \(0.596222\pi\)
\(110\) 0 0
\(111\) −8.65486 −0.821483
\(112\) 0 0
\(113\) −17.1373 −1.61215 −0.806073 0.591816i \(-0.798411\pi\)
−0.806073 + 0.591816i \(0.798411\pi\)
\(114\) 0 0
\(115\) 23.9502 2.23337
\(116\) 0 0
\(117\) −9.84202 −0.909895
\(118\) 0 0
\(119\) 1.00000 0.0916698
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) −1.92101 −0.173212
\(124\) 0 0
\(125\) −21.0728 −1.88480
\(126\) 0 0
\(127\) −5.76303 −0.511386 −0.255693 0.966758i \(-0.582304\pi\)
−0.255693 + 0.966758i \(0.582304\pi\)
\(128\) 0 0
\(129\) 0.266149 0.0234331
\(130\) 0 0
\(131\) −15.4677 −1.35142 −0.675710 0.737168i \(-0.736163\pi\)
−0.675710 + 0.737168i \(0.736163\pi\)
\(132\) 0 0
\(133\) 1.92101 0.166573
\(134\) 0 0
\(135\) −19.6050 −1.68733
\(136\) 0 0
\(137\) −2.84202 −0.242810 −0.121405 0.992603i \(-0.538740\pi\)
−0.121405 + 0.992603i \(0.538740\pi\)
\(138\) 0 0
\(139\) 2.37432 0.201387 0.100693 0.994917i \(-0.467894\pi\)
0.100693 + 0.994917i \(0.467894\pi\)
\(140\) 0 0
\(141\) −2.10817 −0.177540
\(142\) 0 0
\(143\) −9.84202 −0.823031
\(144\) 0 0
\(145\) 23.2163 1.92801
\(146\) 0 0
\(147\) 6.00000 0.494872
\(148\) 0 0
\(149\) −1.07899 −0.0883943 −0.0441972 0.999023i \(-0.514073\pi\)
−0.0441972 + 0.999023i \(0.514073\pi\)
\(150\) 0 0
\(151\) −8.81284 −0.717179 −0.358589 0.933495i \(-0.616742\pi\)
−0.358589 + 0.933495i \(0.616742\pi\)
\(152\) 0 0
\(153\) −2.00000 −0.161690
\(154\) 0 0
\(155\) −14.6405 −1.17595
\(156\) 0 0
\(157\) −1.45331 −0.115987 −0.0579933 0.998317i \(-0.518470\pi\)
−0.0579933 + 0.998317i \(0.518470\pi\)
\(158\) 0 0
\(159\) −9.37432 −0.743432
\(160\) 0 0
\(161\) −6.10817 −0.481391
\(162\) 0 0
\(163\) −18.0584 −1.41444 −0.707220 0.706994i \(-0.750051\pi\)
−0.707220 + 0.706994i \(0.750051\pi\)
\(164\) 0 0
\(165\) −7.84202 −0.610500
\(166\) 0 0
\(167\) 9.21634 0.713182 0.356591 0.934261i \(-0.383939\pi\)
0.356591 + 0.934261i \(0.383939\pi\)
\(168\) 0 0
\(169\) 11.2163 0.862795
\(170\) 0 0
\(171\) −3.84202 −0.293807
\(172\) 0 0
\(173\) 17.2953 1.31494 0.657470 0.753481i \(-0.271627\pi\)
0.657470 + 0.753481i \(0.271627\pi\)
\(174\) 0 0
\(175\) 10.3743 0.784225
\(176\) 0 0
\(177\) 1.00000 0.0751646
\(178\) 0 0
\(179\) −12.9210 −0.965762 −0.482881 0.875686i \(-0.660410\pi\)
−0.482881 + 0.875686i \(0.660410\pi\)
\(180\) 0 0
\(181\) 2.82763 0.210176 0.105088 0.994463i \(-0.466488\pi\)
0.105088 + 0.994463i \(0.466488\pi\)
\(182\) 0 0
\(183\) 6.92101 0.511616
\(184\) 0 0
\(185\) −33.9358 −2.49501
\(186\) 0 0
\(187\) −2.00000 −0.146254
\(188\) 0 0
\(189\) 5.00000 0.363696
\(190\) 0 0
\(191\) −19.5759 −1.41646 −0.708230 0.705982i \(-0.750506\pi\)
−0.708230 + 0.705982i \(0.750506\pi\)
\(192\) 0 0
\(193\) −13.7630 −0.990685 −0.495342 0.868698i \(-0.664957\pi\)
−0.495342 + 0.868698i \(0.664957\pi\)
\(194\) 0 0
\(195\) 19.2953 1.38177
\(196\) 0 0
\(197\) 16.5907 1.18204 0.591018 0.806659i \(-0.298726\pi\)
0.591018 + 0.806659i \(0.298726\pi\)
\(198\) 0 0
\(199\) −13.3743 −0.948080 −0.474040 0.880503i \(-0.657205\pi\)
−0.474040 + 0.880503i \(0.657205\pi\)
\(200\) 0 0
\(201\) −10.2163 −0.720605
\(202\) 0 0
\(203\) −5.92101 −0.415573
\(204\) 0 0
\(205\) −7.53230 −0.526079
\(206\) 0 0
\(207\) 12.2163 0.849094
\(208\) 0 0
\(209\) −3.84202 −0.265758
\(210\) 0 0
\(211\) 13.9502 0.960371 0.480185 0.877167i \(-0.340569\pi\)
0.480185 + 0.877167i \(0.340569\pi\)
\(212\) 0 0
\(213\) −2.37432 −0.162686
\(214\) 0 0
\(215\) 1.04357 0.0711711
\(216\) 0 0
\(217\) 3.73385 0.253470
\(218\) 0 0
\(219\) −2.00000 −0.135147
\(220\) 0 0
\(221\) 4.92101 0.331023
\(222\) 0 0
\(223\) −19.4677 −1.30365 −0.651827 0.758368i \(-0.725997\pi\)
−0.651827 + 0.758368i \(0.725997\pi\)
\(224\) 0 0
\(225\) −20.7486 −1.38324
\(226\) 0 0
\(227\) 6.97082 0.462670 0.231335 0.972874i \(-0.425691\pi\)
0.231335 + 0.972874i \(0.425691\pi\)
\(228\) 0 0
\(229\) −13.5615 −0.896168 −0.448084 0.893992i \(-0.647893\pi\)
−0.448084 + 0.893992i \(0.647893\pi\)
\(230\) 0 0
\(231\) 2.00000 0.131590
\(232\) 0 0
\(233\) −22.4969 −1.47382 −0.736910 0.675991i \(-0.763716\pi\)
−0.736910 + 0.675991i \(0.763716\pi\)
\(234\) 0 0
\(235\) −8.26615 −0.539224
\(236\) 0 0
\(237\) 5.00000 0.324785
\(238\) 0 0
\(239\) −0.0789903 −0.00510946 −0.00255473 0.999997i \(-0.500813\pi\)
−0.00255473 + 0.999997i \(0.500813\pi\)
\(240\) 0 0
\(241\) −2.23697 −0.144096 −0.0720480 0.997401i \(-0.522953\pi\)
−0.0720480 + 0.997401i \(0.522953\pi\)
\(242\) 0 0
\(243\) −16.0000 −1.02640
\(244\) 0 0
\(245\) 23.5261 1.50302
\(246\) 0 0
\(247\) 9.45331 0.601500
\(248\) 0 0
\(249\) −4.65486 −0.294990
\(250\) 0 0
\(251\) 11.3887 0.718849 0.359425 0.933174i \(-0.382973\pi\)
0.359425 + 0.933174i \(0.382973\pi\)
\(252\) 0 0
\(253\) 12.2163 0.768035
\(254\) 0 0
\(255\) 3.92101 0.245543
\(256\) 0 0
\(257\) 12.4677 0.777714 0.388857 0.921298i \(-0.372870\pi\)
0.388857 + 0.921298i \(0.372870\pi\)
\(258\) 0 0
\(259\) 8.65486 0.537787
\(260\) 0 0
\(261\) 11.8420 0.733003
\(262\) 0 0
\(263\) 3.92101 0.241780 0.120890 0.992666i \(-0.461425\pi\)
0.120890 + 0.992666i \(0.461425\pi\)
\(264\) 0 0
\(265\) −36.7568 −2.25795
\(266\) 0 0
\(267\) −5.73385 −0.350906
\(268\) 0 0
\(269\) 21.4035 1.30499 0.652497 0.757791i \(-0.273721\pi\)
0.652497 + 0.757791i \(0.273721\pi\)
\(270\) 0 0
\(271\) −30.5117 −1.85345 −0.926726 0.375738i \(-0.877389\pi\)
−0.926726 + 0.375738i \(0.877389\pi\)
\(272\) 0 0
\(273\) −4.92101 −0.297833
\(274\) 0 0
\(275\) −20.7486 −1.25119
\(276\) 0 0
\(277\) 13.9210 0.836432 0.418216 0.908348i \(-0.362655\pi\)
0.418216 + 0.908348i \(0.362655\pi\)
\(278\) 0 0
\(279\) −7.46770 −0.447080
\(280\) 0 0
\(281\) 18.1230 1.08112 0.540562 0.841304i \(-0.318212\pi\)
0.540562 + 0.841304i \(0.318212\pi\)
\(282\) 0 0
\(283\) −13.6696 −0.812576 −0.406288 0.913745i \(-0.633177\pi\)
−0.406288 + 0.913745i \(0.633177\pi\)
\(284\) 0 0
\(285\) 7.53230 0.446175
\(286\) 0 0
\(287\) 1.92101 0.113394
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 3.45331 0.202436
\(292\) 0 0
\(293\) 16.9004 0.987330 0.493665 0.869652i \(-0.335657\pi\)
0.493665 + 0.869652i \(0.335657\pi\)
\(294\) 0 0
\(295\) 3.92101 0.228290
\(296\) 0 0
\(297\) −10.0000 −0.580259
\(298\) 0 0
\(299\) −30.0584 −1.73832
\(300\) 0 0
\(301\) −0.266149 −0.0153406
\(302\) 0 0
\(303\) 17.0292 0.978301
\(304\) 0 0
\(305\) 27.1373 1.55388
\(306\) 0 0
\(307\) 17.5467 1.00144 0.500721 0.865609i \(-0.333068\pi\)
0.500721 + 0.865609i \(0.333068\pi\)
\(308\) 0 0
\(309\) −9.13735 −0.519805
\(310\) 0 0
\(311\) −15.0000 −0.850572 −0.425286 0.905059i \(-0.639826\pi\)
−0.425286 + 0.905059i \(0.639826\pi\)
\(312\) 0 0
\(313\) 14.9210 0.843385 0.421693 0.906739i \(-0.361436\pi\)
0.421693 + 0.906739i \(0.361436\pi\)
\(314\) 0 0
\(315\) 7.84202 0.441848
\(316\) 0 0
\(317\) −16.0584 −0.901927 −0.450964 0.892542i \(-0.648920\pi\)
−0.450964 + 0.892542i \(0.648920\pi\)
\(318\) 0 0
\(319\) 11.8420 0.663026
\(320\) 0 0
\(321\) 6.84202 0.381884
\(322\) 0 0
\(323\) 1.92101 0.106888
\(324\) 0 0
\(325\) 51.0521 2.83186
\(326\) 0 0
\(327\) 6.21634 0.343764
\(328\) 0 0
\(329\) 2.10817 0.116227
\(330\) 0 0
\(331\) −18.0790 −0.993711 −0.496856 0.867833i \(-0.665512\pi\)
−0.496856 + 0.867833i \(0.665512\pi\)
\(332\) 0 0
\(333\) −17.3097 −0.948567
\(334\) 0 0
\(335\) −40.0584 −2.18862
\(336\) 0 0
\(337\) −13.3097 −0.725027 −0.362513 0.931979i \(-0.618081\pi\)
−0.362513 + 0.931979i \(0.618081\pi\)
\(338\) 0 0
\(339\) 17.1373 0.930773
\(340\) 0 0
\(341\) −7.46770 −0.404399
\(342\) 0 0
\(343\) −13.0000 −0.701934
\(344\) 0 0
\(345\) −23.9502 −1.28943
\(346\) 0 0
\(347\) 1.93579 0.103919 0.0519594 0.998649i \(-0.483453\pi\)
0.0519594 + 0.998649i \(0.483453\pi\)
\(348\) 0 0
\(349\) 11.0292 0.590378 0.295189 0.955439i \(-0.404617\pi\)
0.295189 + 0.955439i \(0.404617\pi\)
\(350\) 0 0
\(351\) 24.6050 1.31332
\(352\) 0 0
\(353\) 18.4969 0.984490 0.492245 0.870457i \(-0.336176\pi\)
0.492245 + 0.870457i \(0.336176\pi\)
\(354\) 0 0
\(355\) −9.30972 −0.494109
\(356\) 0 0
\(357\) −1.00000 −0.0529256
\(358\) 0 0
\(359\) 4.29533 0.226699 0.113349 0.993555i \(-0.463842\pi\)
0.113349 + 0.993555i \(0.463842\pi\)
\(360\) 0 0
\(361\) −15.3097 −0.805775
\(362\) 0 0
\(363\) 7.00000 0.367405
\(364\) 0 0
\(365\) −7.84202 −0.410470
\(366\) 0 0
\(367\) −21.9358 −1.14504 −0.572520 0.819891i \(-0.694034\pi\)
−0.572520 + 0.819891i \(0.694034\pi\)
\(368\) 0 0
\(369\) −3.84202 −0.200008
\(370\) 0 0
\(371\) 9.37432 0.486690
\(372\) 0 0
\(373\) −8.37432 −0.433606 −0.216803 0.976215i \(-0.569563\pi\)
−0.216803 + 0.976215i \(0.569563\pi\)
\(374\) 0 0
\(375\) 21.0728 1.08819
\(376\) 0 0
\(377\) −29.1373 −1.50065
\(378\) 0 0
\(379\) 4.68404 0.240603 0.120301 0.992737i \(-0.461614\pi\)
0.120301 + 0.992737i \(0.461614\pi\)
\(380\) 0 0
\(381\) 5.76303 0.295249
\(382\) 0 0
\(383\) −22.5907 −1.15433 −0.577164 0.816628i \(-0.695841\pi\)
−0.577164 + 0.816628i \(0.695841\pi\)
\(384\) 0 0
\(385\) 7.84202 0.399666
\(386\) 0 0
\(387\) 0.532298 0.0270582
\(388\) 0 0
\(389\) −9.46770 −0.480032 −0.240016 0.970769i \(-0.577153\pi\)
−0.240016 + 0.970769i \(0.577153\pi\)
\(390\) 0 0
\(391\) −6.10817 −0.308903
\(392\) 0 0
\(393\) 15.4677 0.780242
\(394\) 0 0
\(395\) 19.6050 0.986437
\(396\) 0 0
\(397\) 0.330355 0.0165801 0.00829003 0.999966i \(-0.497361\pi\)
0.00829003 + 0.999966i \(0.497361\pi\)
\(398\) 0 0
\(399\) −1.92101 −0.0961708
\(400\) 0 0
\(401\) −0.704673 −0.0351897 −0.0175948 0.999845i \(-0.505601\pi\)
−0.0175948 + 0.999845i \(0.505601\pi\)
\(402\) 0 0
\(403\) 18.3743 0.915290
\(404\) 0 0
\(405\) −3.92101 −0.194837
\(406\) 0 0
\(407\) −17.3097 −0.858011
\(408\) 0 0
\(409\) 4.70467 0.232631 0.116316 0.993212i \(-0.462892\pi\)
0.116316 + 0.993212i \(0.462892\pi\)
\(410\) 0 0
\(411\) 2.84202 0.140186
\(412\) 0 0
\(413\) −1.00000 −0.0492068
\(414\) 0 0
\(415\) −18.2518 −0.895943
\(416\) 0 0
\(417\) −2.37432 −0.116271
\(418\) 0 0
\(419\) −22.5467 −1.10148 −0.550739 0.834678i \(-0.685654\pi\)
−0.550739 + 0.834678i \(0.685654\pi\)
\(420\) 0 0
\(421\) −10.8568 −0.529128 −0.264564 0.964368i \(-0.585228\pi\)
−0.264564 + 0.964368i \(0.585228\pi\)
\(422\) 0 0
\(423\) −4.21634 −0.205005
\(424\) 0 0
\(425\) 10.3743 0.503228
\(426\) 0 0
\(427\) −6.92101 −0.334931
\(428\) 0 0
\(429\) 9.84202 0.475177
\(430\) 0 0
\(431\) 36.2163 1.74448 0.872240 0.489078i \(-0.162667\pi\)
0.872240 + 0.489078i \(0.162667\pi\)
\(432\) 0 0
\(433\) −20.4677 −0.983615 −0.491807 0.870704i \(-0.663664\pi\)
−0.491807 + 0.870704i \(0.663664\pi\)
\(434\) 0 0
\(435\) −23.2163 −1.11314
\(436\) 0 0
\(437\) −11.7339 −0.561306
\(438\) 0 0
\(439\) −10.3743 −0.495139 −0.247570 0.968870i \(-0.579632\pi\)
−0.247570 + 0.968870i \(0.579632\pi\)
\(440\) 0 0
\(441\) 12.0000 0.571429
\(442\) 0 0
\(443\) 35.4179 1.68275 0.841377 0.540448i \(-0.181745\pi\)
0.841377 + 0.540448i \(0.181745\pi\)
\(444\) 0 0
\(445\) −22.4825 −1.06577
\(446\) 0 0
\(447\) 1.07899 0.0510345
\(448\) 0 0
\(449\) 20.6696 0.975461 0.487730 0.872994i \(-0.337825\pi\)
0.487730 + 0.872994i \(0.337825\pi\)
\(450\) 0 0
\(451\) −3.84202 −0.180914
\(452\) 0 0
\(453\) 8.81284 0.414063
\(454\) 0 0
\(455\) −19.2953 −0.904579
\(456\) 0 0
\(457\) −26.1809 −1.22469 −0.612346 0.790590i \(-0.709774\pi\)
−0.612346 + 0.790590i \(0.709774\pi\)
\(458\) 0 0
\(459\) 5.00000 0.233380
\(460\) 0 0
\(461\) 29.4677 1.37245 0.686224 0.727390i \(-0.259267\pi\)
0.686224 + 0.727390i \(0.259267\pi\)
\(462\) 0 0
\(463\) 37.4762 1.74167 0.870834 0.491576i \(-0.163579\pi\)
0.870834 + 0.491576i \(0.163579\pi\)
\(464\) 0 0
\(465\) 14.6405 0.678935
\(466\) 0 0
\(467\) 0.157981 0.00731047 0.00365523 0.999993i \(-0.498837\pi\)
0.00365523 + 0.999993i \(0.498837\pi\)
\(468\) 0 0
\(469\) 10.2163 0.471747
\(470\) 0 0
\(471\) 1.45331 0.0669649
\(472\) 0 0
\(473\) 0.532298 0.0244751
\(474\) 0 0
\(475\) 19.9292 0.914413
\(476\) 0 0
\(477\) −18.7486 −0.858441
\(478\) 0 0
\(479\) −35.1517 −1.60612 −0.803062 0.595895i \(-0.796797\pi\)
−0.803062 + 0.595895i \(0.796797\pi\)
\(480\) 0 0
\(481\) 42.5907 1.94197
\(482\) 0 0
\(483\) 6.10817 0.277931
\(484\) 0 0
\(485\) 13.5405 0.614840
\(486\) 0 0
\(487\) 17.9650 0.814071 0.407035 0.913412i \(-0.366563\pi\)
0.407035 + 0.913412i \(0.366563\pi\)
\(488\) 0 0
\(489\) 18.0584 0.816627
\(490\) 0 0
\(491\) −21.0728 −0.951000 −0.475500 0.879716i \(-0.657733\pi\)
−0.475500 + 0.879716i \(0.657733\pi\)
\(492\) 0 0
\(493\) −5.92101 −0.266669
\(494\) 0 0
\(495\) −15.6840 −0.704945
\(496\) 0 0
\(497\) 2.37432 0.106503
\(498\) 0 0
\(499\) −9.21634 −0.412580 −0.206290 0.978491i \(-0.566139\pi\)
−0.206290 + 0.978491i \(0.566139\pi\)
\(500\) 0 0
\(501\) −9.21634 −0.411756
\(502\) 0 0
\(503\) −38.1226 −1.69980 −0.849901 0.526943i \(-0.823338\pi\)
−0.849901 + 0.526943i \(0.823338\pi\)
\(504\) 0 0
\(505\) 66.7716 2.97130
\(506\) 0 0
\(507\) −11.2163 −0.498135
\(508\) 0 0
\(509\) −16.6050 −0.736006 −0.368003 0.929825i \(-0.619958\pi\)
−0.368003 + 0.929825i \(0.619958\pi\)
\(510\) 0 0
\(511\) 2.00000 0.0884748
\(512\) 0 0
\(513\) 9.60505 0.424073
\(514\) 0 0
\(515\) −35.8276 −1.57875
\(516\) 0 0
\(517\) −4.21634 −0.185434
\(518\) 0 0
\(519\) −17.2953 −0.759181
\(520\) 0 0
\(521\) 13.4677 0.590031 0.295015 0.955493i \(-0.404675\pi\)
0.295015 + 0.955493i \(0.404675\pi\)
\(522\) 0 0
\(523\) 12.3537 0.540189 0.270094 0.962834i \(-0.412945\pi\)
0.270094 + 0.962834i \(0.412945\pi\)
\(524\) 0 0
\(525\) −10.3743 −0.452772
\(526\) 0 0
\(527\) 3.73385 0.162649
\(528\) 0 0
\(529\) 14.3097 0.622162
\(530\) 0 0
\(531\) 2.00000 0.0867926
\(532\) 0 0
\(533\) 9.45331 0.409468
\(534\) 0 0
\(535\) 26.8276 1.15986
\(536\) 0 0
\(537\) 12.9210 0.557583
\(538\) 0 0
\(539\) 12.0000 0.516877
\(540\) 0 0
\(541\) −7.38910 −0.317682 −0.158841 0.987304i \(-0.550776\pi\)
−0.158841 + 0.987304i \(0.550776\pi\)
\(542\) 0 0
\(543\) −2.82763 −0.121345
\(544\) 0 0
\(545\) 24.3743 1.04408
\(546\) 0 0
\(547\) 4.00000 0.171028 0.0855138 0.996337i \(-0.472747\pi\)
0.0855138 + 0.996337i \(0.472747\pi\)
\(548\) 0 0
\(549\) 13.8420 0.590763
\(550\) 0 0
\(551\) −11.3743 −0.484562
\(552\) 0 0
\(553\) −5.00000 −0.212622
\(554\) 0 0
\(555\) 33.9358 1.44049
\(556\) 0 0
\(557\) 40.5261 1.71714 0.858572 0.512693i \(-0.171352\pi\)
0.858572 + 0.512693i \(0.171352\pi\)
\(558\) 0 0
\(559\) −1.30972 −0.0553953
\(560\) 0 0
\(561\) 2.00000 0.0844401
\(562\) 0 0
\(563\) −7.46770 −0.314726 −0.157363 0.987541i \(-0.550299\pi\)
−0.157363 + 0.987541i \(0.550299\pi\)
\(564\) 0 0
\(565\) 67.1957 2.82694
\(566\) 0 0
\(567\) 1.00000 0.0419961
\(568\) 0 0
\(569\) −1.93579 −0.0811527 −0.0405763 0.999176i \(-0.512919\pi\)
−0.0405763 + 0.999176i \(0.512919\pi\)
\(570\) 0 0
\(571\) 42.5264 1.77968 0.889838 0.456276i \(-0.150817\pi\)
0.889838 + 0.456276i \(0.150817\pi\)
\(572\) 0 0
\(573\) 19.5759 0.817794
\(574\) 0 0
\(575\) −63.3681 −2.64263
\(576\) 0 0
\(577\) 25.0000 1.04076 0.520382 0.853934i \(-0.325790\pi\)
0.520382 + 0.853934i \(0.325790\pi\)
\(578\) 0 0
\(579\) 13.7630 0.571972
\(580\) 0 0
\(581\) 4.65486 0.193116
\(582\) 0 0
\(583\) −18.7486 −0.776489
\(584\) 0 0
\(585\) 38.5907 1.59553
\(586\) 0 0
\(587\) −14.1665 −0.584715 −0.292358 0.956309i \(-0.594440\pi\)
−0.292358 + 0.956309i \(0.594440\pi\)
\(588\) 0 0
\(589\) 7.17276 0.295549
\(590\) 0 0
\(591\) −16.5907 −0.682448
\(592\) 0 0
\(593\) 27.8070 1.14190 0.570948 0.820986i \(-0.306576\pi\)
0.570948 + 0.820986i \(0.306576\pi\)
\(594\) 0 0
\(595\) −3.92101 −0.160746
\(596\) 0 0
\(597\) 13.3743 0.547374
\(598\) 0 0
\(599\) 10.6696 0.435950 0.217975 0.975954i \(-0.430055\pi\)
0.217975 + 0.975954i \(0.430055\pi\)
\(600\) 0 0
\(601\) −41.9587 −1.71153 −0.855766 0.517363i \(-0.826914\pi\)
−0.855766 + 0.517363i \(0.826914\pi\)
\(602\) 0 0
\(603\) −20.4327 −0.832083
\(604\) 0 0
\(605\) 27.4471 1.11588
\(606\) 0 0
\(607\) −27.1167 −1.10063 −0.550317 0.834956i \(-0.685493\pi\)
−0.550317 + 0.834956i \(0.685493\pi\)
\(608\) 0 0
\(609\) 5.92101 0.239931
\(610\) 0 0
\(611\) 10.3743 0.419700
\(612\) 0 0
\(613\) 5.41789 0.218827 0.109413 0.993996i \(-0.465103\pi\)
0.109413 + 0.993996i \(0.465103\pi\)
\(614\) 0 0
\(615\) 7.53230 0.303732
\(616\) 0 0
\(617\) −26.6696 −1.07368 −0.536840 0.843684i \(-0.680382\pi\)
−0.536840 + 0.843684i \(0.680382\pi\)
\(618\) 0 0
\(619\) −9.05836 −0.364086 −0.182043 0.983291i \(-0.558271\pi\)
−0.182043 + 0.983291i \(0.558271\pi\)
\(620\) 0 0
\(621\) −30.5408 −1.22556
\(622\) 0 0
\(623\) 5.73385 0.229722
\(624\) 0 0
\(625\) 30.7549 1.23019
\(626\) 0 0
\(627\) 3.84202 0.153435
\(628\) 0 0
\(629\) 8.65486 0.345092
\(630\) 0 0
\(631\) −28.9650 −1.15308 −0.576539 0.817070i \(-0.695597\pi\)
−0.576539 + 0.817070i \(0.695597\pi\)
\(632\) 0 0
\(633\) −13.9502 −0.554470
\(634\) 0 0
\(635\) 22.5969 0.896730
\(636\) 0 0
\(637\) −29.5261 −1.16987
\(638\) 0 0
\(639\) −4.74863 −0.187853
\(640\) 0 0
\(641\) 19.0934 0.754143 0.377072 0.926184i \(-0.376931\pi\)
0.377072 + 0.926184i \(0.376931\pi\)
\(642\) 0 0
\(643\) −27.4031 −1.08067 −0.540337 0.841449i \(-0.681703\pi\)
−0.540337 + 0.841449i \(0.681703\pi\)
\(644\) 0 0
\(645\) −1.04357 −0.0410906
\(646\) 0 0
\(647\) 15.8214 0.622003 0.311001 0.950409i \(-0.399336\pi\)
0.311001 + 0.950409i \(0.399336\pi\)
\(648\) 0 0
\(649\) 2.00000 0.0785069
\(650\) 0 0
\(651\) −3.73385 −0.146341
\(652\) 0 0
\(653\) 33.2891 1.30270 0.651351 0.758776i \(-0.274202\pi\)
0.651351 + 0.758776i \(0.274202\pi\)
\(654\) 0 0
\(655\) 60.6490 2.36975
\(656\) 0 0
\(657\) −4.00000 −0.156055
\(658\) 0 0
\(659\) −28.9296 −1.12694 −0.563468 0.826138i \(-0.690533\pi\)
−0.563468 + 0.826138i \(0.690533\pi\)
\(660\) 0 0
\(661\) 22.1517 0.861603 0.430801 0.902447i \(-0.358231\pi\)
0.430801 + 0.902447i \(0.358231\pi\)
\(662\) 0 0
\(663\) −4.92101 −0.191116
\(664\) 0 0
\(665\) −7.53230 −0.292090
\(666\) 0 0
\(667\) 36.1665 1.40037
\(668\) 0 0
\(669\) 19.4677 0.752665
\(670\) 0 0
\(671\) 13.8420 0.534365
\(672\) 0 0
\(673\) −34.9152 −1.34588 −0.672940 0.739697i \(-0.734969\pi\)
−0.672940 + 0.739697i \(0.734969\pi\)
\(674\) 0 0
\(675\) 51.8716 1.99654
\(676\) 0 0
\(677\) 0.590654 0.0227007 0.0113503 0.999936i \(-0.496387\pi\)
0.0113503 + 0.999936i \(0.496387\pi\)
\(678\) 0 0
\(679\) −3.45331 −0.132526
\(680\) 0 0
\(681\) −6.97082 −0.267122
\(682\) 0 0
\(683\) −20.2019 −0.773006 −0.386503 0.922288i \(-0.626317\pi\)
−0.386503 + 0.922288i \(0.626317\pi\)
\(684\) 0 0
\(685\) 11.1436 0.425775
\(686\) 0 0
\(687\) 13.5615 0.517403
\(688\) 0 0
\(689\) 46.1311 1.75746
\(690\) 0 0
\(691\) −0.827236 −0.0314695 −0.0157348 0.999876i \(-0.505009\pi\)
−0.0157348 + 0.999876i \(0.505009\pi\)
\(692\) 0 0
\(693\) 4.00000 0.151947
\(694\) 0 0
\(695\) −9.30972 −0.353138
\(696\) 0 0
\(697\) 1.92101 0.0727634
\(698\) 0 0
\(699\) 22.4969 0.850910
\(700\) 0 0
\(701\) 2.98522 0.112750 0.0563750 0.998410i \(-0.482046\pi\)
0.0563750 + 0.998410i \(0.482046\pi\)
\(702\) 0 0
\(703\) 16.6261 0.627064
\(704\) 0 0
\(705\) 8.26615 0.311321
\(706\) 0 0
\(707\) −17.0292 −0.640448
\(708\) 0 0
\(709\) 34.2953 1.28799 0.643994 0.765031i \(-0.277276\pi\)
0.643994 + 0.765031i \(0.277276\pi\)
\(710\) 0 0
\(711\) 10.0000 0.375029
\(712\) 0 0
\(713\) −22.8070 −0.854129
\(714\) 0 0
\(715\) 38.5907 1.44321
\(716\) 0 0
\(717\) 0.0789903 0.00294995
\(718\) 0 0
\(719\) −44.1311 −1.64581 −0.822906 0.568177i \(-0.807649\pi\)
−0.822906 + 0.568177i \(0.807649\pi\)
\(720\) 0 0
\(721\) 9.13735 0.340293
\(722\) 0 0
\(723\) 2.23697 0.0831938
\(724\) 0 0
\(725\) −61.4264 −2.28132
\(726\) 0 0
\(727\) −18.5907 −0.689489 −0.344745 0.938697i \(-0.612034\pi\)
−0.344745 + 0.938697i \(0.612034\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −0.266149 −0.00984387
\(732\) 0 0
\(733\) 5.12295 0.189221 0.0946103 0.995514i \(-0.469840\pi\)
0.0946103 + 0.995514i \(0.469840\pi\)
\(734\) 0 0
\(735\) −23.5261 −0.867772
\(736\) 0 0
\(737\) −20.4327 −0.752647
\(738\) 0 0
\(739\) −51.4120 −1.89122 −0.945611 0.325299i \(-0.894535\pi\)
−0.945611 + 0.325299i \(0.894535\pi\)
\(740\) 0 0
\(741\) −9.45331 −0.347276
\(742\) 0 0
\(743\) −9.06460 −0.332548 −0.166274 0.986080i \(-0.553174\pi\)
−0.166274 + 0.986080i \(0.553174\pi\)
\(744\) 0 0
\(745\) 4.23073 0.155002
\(746\) 0 0
\(747\) −9.30972 −0.340625
\(748\) 0 0
\(749\) −6.84202 −0.250002
\(750\) 0 0
\(751\) −33.4677 −1.22125 −0.610627 0.791918i \(-0.709082\pi\)
−0.610627 + 0.791918i \(0.709082\pi\)
\(752\) 0 0
\(753\) −11.3887 −0.415028
\(754\) 0 0
\(755\) 34.5552 1.25759
\(756\) 0 0
\(757\) −12.9416 −0.470372 −0.235186 0.971950i \(-0.575570\pi\)
−0.235186 + 0.971950i \(0.575570\pi\)
\(758\) 0 0
\(759\) −12.2163 −0.443425
\(760\) 0 0
\(761\) −27.9650 −1.01373 −0.506865 0.862026i \(-0.669196\pi\)
−0.506865 + 0.862026i \(0.669196\pi\)
\(762\) 0 0
\(763\) −6.21634 −0.225047
\(764\) 0 0
\(765\) 7.84202 0.283529
\(766\) 0 0
\(767\) −4.92101 −0.177687
\(768\) 0 0
\(769\) 5.07899 0.183153 0.0915765 0.995798i \(-0.470809\pi\)
0.0915765 + 0.995798i \(0.470809\pi\)
\(770\) 0 0
\(771\) −12.4677 −0.449013
\(772\) 0 0
\(773\) −36.1521 −1.30030 −0.650151 0.759805i \(-0.725294\pi\)
−0.650151 + 0.759805i \(0.725294\pi\)
\(774\) 0 0
\(775\) 38.7362 1.39144
\(776\) 0 0
\(777\) −8.65486 −0.310491
\(778\) 0 0
\(779\) 3.69028 0.132218
\(780\) 0 0
\(781\) −4.74863 −0.169920
\(782\) 0 0
\(783\) −29.6050 −1.05800
\(784\) 0 0
\(785\) 5.69843 0.203386
\(786\) 0 0
\(787\) −34.5907 −1.23302 −0.616512 0.787346i \(-0.711455\pi\)
−0.616512 + 0.787346i \(0.711455\pi\)
\(788\) 0 0
\(789\) −3.92101 −0.139592
\(790\) 0 0
\(791\) −17.1373 −0.609334
\(792\) 0 0
\(793\) −34.0584 −1.20945
\(794\) 0 0
\(795\) 36.7568 1.30363
\(796\) 0 0
\(797\) −26.0728 −0.923544 −0.461772 0.886999i \(-0.652786\pi\)
−0.461772 + 0.886999i \(0.652786\pi\)
\(798\) 0 0
\(799\) 2.10817 0.0745816
\(800\) 0 0
\(801\) −11.4677 −0.405191
\(802\) 0 0
\(803\) −4.00000 −0.141157
\(804\) 0 0
\(805\) 23.9502 0.844133
\(806\) 0 0
\(807\) −21.4035 −0.753439
\(808\) 0 0
\(809\) −11.7778 −0.414086 −0.207043 0.978332i \(-0.566384\pi\)
−0.207043 + 0.978332i \(0.566384\pi\)
\(810\) 0 0
\(811\) 15.5903 0.547448 0.273724 0.961808i \(-0.411744\pi\)
0.273724 + 0.961808i \(0.411744\pi\)
\(812\) 0 0
\(813\) 30.5117 1.07009
\(814\) 0 0
\(815\) 70.8070 2.48026
\(816\) 0 0
\(817\) −0.511275 −0.0178872
\(818\) 0 0
\(819\) −9.84202 −0.343908
\(820\) 0 0
\(821\) 3.71946 0.129810 0.0649050 0.997891i \(-0.479326\pi\)
0.0649050 + 0.997891i \(0.479326\pi\)
\(822\) 0 0
\(823\) 28.5467 0.995075 0.497538 0.867442i \(-0.334238\pi\)
0.497538 + 0.867442i \(0.334238\pi\)
\(824\) 0 0
\(825\) 20.7486 0.722375
\(826\) 0 0
\(827\) 10.0584 0.349763 0.174882 0.984589i \(-0.444046\pi\)
0.174882 + 0.984589i \(0.444046\pi\)
\(828\) 0 0
\(829\) 4.43891 0.154170 0.0770849 0.997025i \(-0.475439\pi\)
0.0770849 + 0.997025i \(0.475439\pi\)
\(830\) 0 0
\(831\) −13.9210 −0.482914
\(832\) 0 0
\(833\) −6.00000 −0.207888
\(834\) 0 0
\(835\) −36.1373 −1.25058
\(836\) 0 0
\(837\) 18.6693 0.645304
\(838\) 0 0
\(839\) −38.8712 −1.34198 −0.670991 0.741465i \(-0.734131\pi\)
−0.670991 + 0.741465i \(0.734131\pi\)
\(840\) 0 0
\(841\) 6.05836 0.208909
\(842\) 0 0
\(843\) −18.1230 −0.624188
\(844\) 0 0
\(845\) −43.9794 −1.51294
\(846\) 0 0
\(847\) −7.00000 −0.240523
\(848\) 0 0
\(849\) 13.6696 0.469141
\(850\) 0 0
\(851\) −52.8653 −1.81220
\(852\) 0 0
\(853\) 48.9148 1.67481 0.837405 0.546583i \(-0.184072\pi\)
0.837405 + 0.546583i \(0.184072\pi\)
\(854\) 0 0
\(855\) 15.0646 0.515198
\(856\) 0 0
\(857\) 15.3595 0.524672 0.262336 0.964977i \(-0.415507\pi\)
0.262336 + 0.964977i \(0.415507\pi\)
\(858\) 0 0
\(859\) −36.3829 −1.24137 −0.620684 0.784061i \(-0.713145\pi\)
−0.620684 + 0.784061i \(0.713145\pi\)
\(860\) 0 0
\(861\) −1.92101 −0.0654678
\(862\) 0 0
\(863\) 40.5907 1.38172 0.690861 0.722988i \(-0.257232\pi\)
0.690861 + 0.722988i \(0.257232\pi\)
\(864\) 0 0
\(865\) −67.8151 −2.30578
\(866\) 0 0
\(867\) −1.00000 −0.0339618
\(868\) 0 0
\(869\) 10.0000 0.339227
\(870\) 0 0
\(871\) 50.2747 1.70349
\(872\) 0 0
\(873\) 6.90662 0.233754
\(874\) 0 0
\(875\) −21.0728 −0.712389
\(876\) 0 0
\(877\) 47.8214 1.61481 0.807407 0.589995i \(-0.200870\pi\)
0.807407 + 0.589995i \(0.200870\pi\)
\(878\) 0 0
\(879\) −16.9004 −0.570036
\(880\) 0 0
\(881\) 26.9296 0.907280 0.453640 0.891185i \(-0.350125\pi\)
0.453640 + 0.891185i \(0.350125\pi\)
\(882\) 0 0
\(883\) −27.2019 −0.915418 −0.457709 0.889102i \(-0.651330\pi\)
−0.457709 + 0.889102i \(0.651330\pi\)
\(884\) 0 0
\(885\) −3.92101 −0.131803
\(886\) 0 0
\(887\) 43.7424 1.46873 0.734363 0.678757i \(-0.237481\pi\)
0.734363 + 0.678757i \(0.237481\pi\)
\(888\) 0 0
\(889\) −5.76303 −0.193286
\(890\) 0 0
\(891\) −2.00000 −0.0670025
\(892\) 0 0
\(893\) 4.04981 0.135522
\(894\) 0 0
\(895\) 50.6634 1.69349
\(896\) 0 0
\(897\) 30.0584 1.00362
\(898\) 0 0
\(899\) −22.1082 −0.737349
\(900\) 0 0
\(901\) 9.37432 0.312304
\(902\) 0 0
\(903\) 0.266149 0.00885688
\(904\) 0 0
\(905\) −11.0871 −0.368549
\(906\) 0 0
\(907\) 42.6840 1.41730 0.708650 0.705560i \(-0.249304\pi\)
0.708650 + 0.705560i \(0.249304\pi\)
\(908\) 0 0
\(909\) 34.0584 1.12964
\(910\) 0 0
\(911\) −57.1751 −1.89429 −0.947147 0.320799i \(-0.896049\pi\)
−0.947147 + 0.320799i \(0.896049\pi\)
\(912\) 0 0
\(913\) −9.30972 −0.308107
\(914\) 0 0
\(915\) −27.1373 −0.897133
\(916\) 0 0
\(917\) −15.4677 −0.510789
\(918\) 0 0
\(919\) 37.9358 1.25139 0.625693 0.780069i \(-0.284816\pi\)
0.625693 + 0.780069i \(0.284816\pi\)
\(920\) 0 0
\(921\) −17.5467 −0.578183
\(922\) 0 0
\(923\) 11.6840 0.384585
\(924\) 0 0
\(925\) 89.7883 2.95222
\(926\) 0 0
\(927\) −18.2747 −0.600220
\(928\) 0 0
\(929\) −12.6903 −0.416355 −0.208177 0.978091i \(-0.566753\pi\)
−0.208177 + 0.978091i \(0.566753\pi\)
\(930\) 0 0
\(931\) −11.5261 −0.377751
\(932\) 0 0
\(933\) 15.0000 0.491078
\(934\) 0 0
\(935\) 7.84202 0.256461
\(936\) 0 0
\(937\) −51.0521 −1.66780 −0.833900 0.551916i \(-0.813897\pi\)
−0.833900 + 0.551916i \(0.813897\pi\)
\(938\) 0 0
\(939\) −14.9210 −0.486929
\(940\) 0 0
\(941\) −11.3241 −0.369156 −0.184578 0.982818i \(-0.559092\pi\)
−0.184578 + 0.982818i \(0.559092\pi\)
\(942\) 0 0
\(943\) −11.7339 −0.382107
\(944\) 0 0
\(945\) −19.6050 −0.637752
\(946\) 0 0
\(947\) 16.5261 0.537025 0.268512 0.963276i \(-0.413468\pi\)
0.268512 + 0.963276i \(0.413468\pi\)
\(948\) 0 0
\(949\) 9.84202 0.319485
\(950\) 0 0
\(951\) 16.0584 0.520728
\(952\) 0 0
\(953\) −1.03503 −0.0335279 −0.0167639 0.999859i \(-0.505336\pi\)
−0.0167639 + 0.999859i \(0.505336\pi\)
\(954\) 0 0
\(955\) 76.7572 2.48380
\(956\) 0 0
\(957\) −11.8420 −0.382798
\(958\) 0 0
\(959\) −2.84202 −0.0917736
\(960\) 0 0
\(961\) −17.0584 −0.550270
\(962\) 0 0
\(963\) 13.6840 0.440962
\(964\) 0 0
\(965\) 53.9650 1.73719
\(966\) 0 0
\(967\) −7.24552 −0.233000 −0.116500 0.993191i \(-0.537168\pi\)
−0.116500 + 0.993191i \(0.537168\pi\)
\(968\) 0 0
\(969\) −1.92101 −0.0617117
\(970\) 0 0
\(971\) 28.6696 0.920053 0.460026 0.887905i \(-0.347840\pi\)
0.460026 + 0.887905i \(0.347840\pi\)
\(972\) 0 0
\(973\) 2.37432 0.0761171
\(974\) 0 0
\(975\) −51.0521 −1.63498
\(976\) 0 0
\(977\) 17.8506 0.571090 0.285545 0.958365i \(-0.407825\pi\)
0.285545 + 0.958365i \(0.407825\pi\)
\(978\) 0 0
\(979\) −11.4677 −0.366509
\(980\) 0 0
\(981\) 12.4327 0.396945
\(982\) 0 0
\(983\) −31.7424 −1.01243 −0.506213 0.862409i \(-0.668955\pi\)
−0.506213 + 0.862409i \(0.668955\pi\)
\(984\) 0 0
\(985\) −65.0521 −2.07273
\(986\) 0 0
\(987\) −2.10817 −0.0671037
\(988\) 0 0
\(989\) 1.62568 0.0516937
\(990\) 0 0
\(991\) 1.12880 0.0358576 0.0179288 0.999839i \(-0.494293\pi\)
0.0179288 + 0.999839i \(0.494293\pi\)
\(992\) 0 0
\(993\) 18.0790 0.573719
\(994\) 0 0
\(995\) 52.4408 1.66249
\(996\) 0 0
\(997\) −60.9731 −1.93104 −0.965519 0.260332i \(-0.916168\pi\)
−0.965519 + 0.260332i \(0.916168\pi\)
\(998\) 0 0
\(999\) 43.2743 1.36914
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 \(a_p\))