Properties

Label 8020.2.a.c.1.19
Level 8020
Weight 2
Character 8020.1
Self dual Yes
Analytic conductor 64.040
Analytic rank 1
Dimension 28
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8020 = 2^{2} \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8020.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0400224211\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 8020.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.28191 q^{3}\) \(-1.00000 q^{5}\) \(-0.791593 q^{7}\) \(-1.35670 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.28191 q^{3}\) \(-1.00000 q^{5}\) \(-0.791593 q^{7}\) \(-1.35670 q^{9}\) \(+5.58550 q^{11}\) \(+0.759032 q^{13}\) \(-1.28191 q^{15}\) \(-7.02370 q^{17}\) \(+4.40429 q^{19}\) \(-1.01475 q^{21}\) \(+3.48752 q^{23}\) \(+1.00000 q^{25}\) \(-5.58491 q^{27}\) \(-4.93092 q^{29}\) \(-5.65417 q^{31}\) \(+7.16013 q^{33}\) \(+0.791593 q^{35}\) \(+2.56419 q^{37}\) \(+0.973013 q^{39}\) \(-1.22911 q^{41}\) \(-6.23743 q^{43}\) \(+1.35670 q^{45}\) \(-6.02172 q^{47}\) \(-6.37338 q^{49}\) \(-9.00378 q^{51}\) \(-8.35453 q^{53}\) \(-5.58550 q^{55}\) \(+5.64592 q^{57}\) \(-9.38937 q^{59}\) \(+12.5580 q^{61}\) \(+1.07395 q^{63}\) \(-0.759032 q^{65}\) \(+6.07506 q^{67}\) \(+4.47069 q^{69}\) \(+3.00385 q^{71}\) \(+13.9513 q^{73}\) \(+1.28191 q^{75}\) \(-4.42144 q^{77}\) \(-8.59616 q^{79}\) \(-3.08927 q^{81}\) \(+6.43565 q^{83}\) \(+7.02370 q^{85}\) \(-6.32101 q^{87}\) \(-18.5424 q^{89}\) \(-0.600844 q^{91}\) \(-7.24815 q^{93}\) \(-4.40429 q^{95}\) \(+2.63228 q^{97}\) \(-7.57784 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 3q^{13} \) \(\mathstrut -\mathstrut 3q^{15} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 3q^{37} \) \(\mathstrut -\mathstrut 19q^{39} \) \(\mathstrut -\mathstrut 30q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 17q^{45} \) \(\mathstrut -\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut -\mathstrut 22q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut -\mathstrut 33q^{61} \) \(\mathstrut -\mathstrut 20q^{63} \) \(\mathstrut -\mathstrut 3q^{65} \) \(\mathstrut +\mathstrut 19q^{67} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut -\mathstrut 42q^{77} \) \(\mathstrut -\mathstrut 29q^{79} \) \(\mathstrut -\mathstrut 36q^{81} \) \(\mathstrut +\mathstrut 14q^{83} \) \(\mathstrut +\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 32q^{87} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 39q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.28191 0.740113 0.370056 0.929009i \(-0.379338\pi\)
0.370056 + 0.929009i \(0.379338\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −0.791593 −0.299194 −0.149597 0.988747i \(-0.547798\pi\)
−0.149597 + 0.988747i \(0.547798\pi\)
\(8\) 0 0
\(9\) −1.35670 −0.452233
\(10\) 0 0
\(11\) 5.58550 1.68409 0.842046 0.539406i \(-0.181351\pi\)
0.842046 + 0.539406i \(0.181351\pi\)
\(12\) 0 0
\(13\) 0.759032 0.210517 0.105259 0.994445i \(-0.466433\pi\)
0.105259 + 0.994445i \(0.466433\pi\)
\(14\) 0 0
\(15\) −1.28191 −0.330989
\(16\) 0 0
\(17\) −7.02370 −1.70350 −0.851749 0.523950i \(-0.824458\pi\)
−0.851749 + 0.523950i \(0.824458\pi\)
\(18\) 0 0
\(19\) 4.40429 1.01041 0.505207 0.862998i \(-0.331416\pi\)
0.505207 + 0.862998i \(0.331416\pi\)
\(20\) 0 0
\(21\) −1.01475 −0.221437
\(22\) 0 0
\(23\) 3.48752 0.727197 0.363599 0.931556i \(-0.381548\pi\)
0.363599 + 0.931556i \(0.381548\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −5.58491 −1.07482
\(28\) 0 0
\(29\) −4.93092 −0.915648 −0.457824 0.889043i \(-0.651371\pi\)
−0.457824 + 0.889043i \(0.651371\pi\)
\(30\) 0 0
\(31\) −5.65417 −1.01552 −0.507759 0.861499i \(-0.669526\pi\)
−0.507759 + 0.861499i \(0.669526\pi\)
\(32\) 0 0
\(33\) 7.16013 1.24642
\(34\) 0 0
\(35\) 0.791593 0.133804
\(36\) 0 0
\(37\) 2.56419 0.421550 0.210775 0.977535i \(-0.432401\pi\)
0.210775 + 0.977535i \(0.432401\pi\)
\(38\) 0 0
\(39\) 0.973013 0.155807
\(40\) 0 0
\(41\) −1.22911 −0.191955 −0.0959774 0.995384i \(-0.530598\pi\)
−0.0959774 + 0.995384i \(0.530598\pi\)
\(42\) 0 0
\(43\) −6.23743 −0.951199 −0.475600 0.879662i \(-0.657769\pi\)
−0.475600 + 0.879662i \(0.657769\pi\)
\(44\) 0 0
\(45\) 1.35670 0.202245
\(46\) 0 0
\(47\) −6.02172 −0.878359 −0.439179 0.898399i \(-0.644731\pi\)
−0.439179 + 0.898399i \(0.644731\pi\)
\(48\) 0 0
\(49\) −6.37338 −0.910483
\(50\) 0 0
\(51\) −9.00378 −1.26078
\(52\) 0 0
\(53\) −8.35453 −1.14758 −0.573792 0.819001i \(-0.694528\pi\)
−0.573792 + 0.819001i \(0.694528\pi\)
\(54\) 0 0
\(55\) −5.58550 −0.753149
\(56\) 0 0
\(57\) 5.64592 0.747820
\(58\) 0 0
\(59\) −9.38937 −1.22239 −0.611196 0.791479i \(-0.709311\pi\)
−0.611196 + 0.791479i \(0.709311\pi\)
\(60\) 0 0
\(61\) 12.5580 1.60788 0.803942 0.594707i \(-0.202732\pi\)
0.803942 + 0.594707i \(0.202732\pi\)
\(62\) 0 0
\(63\) 1.07395 0.135305
\(64\) 0 0
\(65\) −0.759032 −0.0941463
\(66\) 0 0
\(67\) 6.07506 0.742186 0.371093 0.928596i \(-0.378983\pi\)
0.371093 + 0.928596i \(0.378983\pi\)
\(68\) 0 0
\(69\) 4.47069 0.538208
\(70\) 0 0
\(71\) 3.00385 0.356491 0.178246 0.983986i \(-0.442958\pi\)
0.178246 + 0.983986i \(0.442958\pi\)
\(72\) 0 0
\(73\) 13.9513 1.63288 0.816439 0.577431i \(-0.195945\pi\)
0.816439 + 0.577431i \(0.195945\pi\)
\(74\) 0 0
\(75\) 1.28191 0.148023
\(76\) 0 0
\(77\) −4.42144 −0.503870
\(78\) 0 0
\(79\) −8.59616 −0.967144 −0.483572 0.875305i \(-0.660661\pi\)
−0.483572 + 0.875305i \(0.660661\pi\)
\(80\) 0 0
\(81\) −3.08927 −0.343253
\(82\) 0 0
\(83\) 6.43565 0.706405 0.353202 0.935547i \(-0.385093\pi\)
0.353202 + 0.935547i \(0.385093\pi\)
\(84\) 0 0
\(85\) 7.02370 0.761828
\(86\) 0 0
\(87\) −6.32101 −0.677683
\(88\) 0 0
\(89\) −18.5424 −1.96549 −0.982746 0.184961i \(-0.940784\pi\)
−0.982746 + 0.184961i \(0.940784\pi\)
\(90\) 0 0
\(91\) −0.600844 −0.0629856
\(92\) 0 0
\(93\) −7.24815 −0.751598
\(94\) 0 0
\(95\) −4.40429 −0.451871
\(96\) 0 0
\(97\) 2.63228 0.267268 0.133634 0.991031i \(-0.457335\pi\)
0.133634 + 0.991031i \(0.457335\pi\)
\(98\) 0 0
\(99\) −7.57784 −0.761602
\(100\) 0 0
\(101\) 9.89067 0.984159 0.492079 0.870550i \(-0.336237\pi\)
0.492079 + 0.870550i \(0.336237\pi\)
\(102\) 0 0
\(103\) 9.81090 0.966696 0.483348 0.875428i \(-0.339421\pi\)
0.483348 + 0.875428i \(0.339421\pi\)
\(104\) 0 0
\(105\) 1.01475 0.0990298
\(106\) 0 0
\(107\) −9.28328 −0.897449 −0.448724 0.893670i \(-0.648122\pi\)
−0.448724 + 0.893670i \(0.648122\pi\)
\(108\) 0 0
\(109\) 9.20596 0.881772 0.440886 0.897563i \(-0.354664\pi\)
0.440886 + 0.897563i \(0.354664\pi\)
\(110\) 0 0
\(111\) 3.28707 0.311995
\(112\) 0 0
\(113\) −7.17329 −0.674806 −0.337403 0.941360i \(-0.609548\pi\)
−0.337403 + 0.941360i \(0.609548\pi\)
\(114\) 0 0
\(115\) −3.48752 −0.325213
\(116\) 0 0
\(117\) −1.02978 −0.0952029
\(118\) 0 0
\(119\) 5.55991 0.509676
\(120\) 0 0
\(121\) 20.1978 1.83617
\(122\) 0 0
\(123\) −1.57561 −0.142068
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −8.87506 −0.787534 −0.393767 0.919210i \(-0.628828\pi\)
−0.393767 + 0.919210i \(0.628828\pi\)
\(128\) 0 0
\(129\) −7.99584 −0.703995
\(130\) 0 0
\(131\) −12.6250 −1.10306 −0.551528 0.834157i \(-0.685955\pi\)
−0.551528 + 0.834157i \(0.685955\pi\)
\(132\) 0 0
\(133\) −3.48640 −0.302310
\(134\) 0 0
\(135\) 5.58491 0.480672
\(136\) 0 0
\(137\) 21.3741 1.82611 0.913057 0.407831i \(-0.133715\pi\)
0.913057 + 0.407831i \(0.133715\pi\)
\(138\) 0 0
\(139\) −16.4161 −1.39240 −0.696198 0.717850i \(-0.745126\pi\)
−0.696198 + 0.717850i \(0.745126\pi\)
\(140\) 0 0
\(141\) −7.71933 −0.650085
\(142\) 0 0
\(143\) 4.23957 0.354531
\(144\) 0 0
\(145\) 4.93092 0.409490
\(146\) 0 0
\(147\) −8.17012 −0.673860
\(148\) 0 0
\(149\) −3.30611 −0.270847 −0.135424 0.990788i \(-0.543240\pi\)
−0.135424 + 0.990788i \(0.543240\pi\)
\(150\) 0 0
\(151\) −22.1331 −1.80116 −0.900582 0.434687i \(-0.856859\pi\)
−0.900582 + 0.434687i \(0.856859\pi\)
\(152\) 0 0
\(153\) 9.52905 0.770378
\(154\) 0 0
\(155\) 5.65417 0.454154
\(156\) 0 0
\(157\) 0.997668 0.0796226 0.0398113 0.999207i \(-0.487324\pi\)
0.0398113 + 0.999207i \(0.487324\pi\)
\(158\) 0 0
\(159\) −10.7098 −0.849341
\(160\) 0 0
\(161\) −2.76069 −0.217573
\(162\) 0 0
\(163\) −8.31518 −0.651295 −0.325647 0.945491i \(-0.605582\pi\)
−0.325647 + 0.945491i \(0.605582\pi\)
\(164\) 0 0
\(165\) −7.16013 −0.557415
\(166\) 0 0
\(167\) 17.7035 1.36993 0.684967 0.728574i \(-0.259816\pi\)
0.684967 + 0.728574i \(0.259816\pi\)
\(168\) 0 0
\(169\) −12.4239 −0.955682
\(170\) 0 0
\(171\) −5.97529 −0.456942
\(172\) 0 0
\(173\) 4.70744 0.357900 0.178950 0.983858i \(-0.442730\pi\)
0.178950 + 0.983858i \(0.442730\pi\)
\(174\) 0 0
\(175\) −0.791593 −0.0598388
\(176\) 0 0
\(177\) −12.0364 −0.904708
\(178\) 0 0
\(179\) 4.46430 0.333678 0.166839 0.985984i \(-0.446644\pi\)
0.166839 + 0.985984i \(0.446644\pi\)
\(180\) 0 0
\(181\) −4.70629 −0.349816 −0.174908 0.984585i \(-0.555963\pi\)
−0.174908 + 0.984585i \(0.555963\pi\)
\(182\) 0 0
\(183\) 16.0982 1.19002
\(184\) 0 0
\(185\) −2.56419 −0.188523
\(186\) 0 0
\(187\) −39.2309 −2.86885
\(188\) 0 0
\(189\) 4.42097 0.321579
\(190\) 0 0
\(191\) −14.7071 −1.06417 −0.532083 0.846692i \(-0.678591\pi\)
−0.532083 + 0.846692i \(0.678591\pi\)
\(192\) 0 0
\(193\) 10.6718 0.768176 0.384088 0.923297i \(-0.374516\pi\)
0.384088 + 0.923297i \(0.374516\pi\)
\(194\) 0 0
\(195\) −0.973013 −0.0696789
\(196\) 0 0
\(197\) −19.5613 −1.39368 −0.696842 0.717224i \(-0.745412\pi\)
−0.696842 + 0.717224i \(0.745412\pi\)
\(198\) 0 0
\(199\) −13.1618 −0.933013 −0.466507 0.884518i \(-0.654488\pi\)
−0.466507 + 0.884518i \(0.654488\pi\)
\(200\) 0 0
\(201\) 7.78770 0.549302
\(202\) 0 0
\(203\) 3.90328 0.273957
\(204\) 0 0
\(205\) 1.22911 0.0858448
\(206\) 0 0
\(207\) −4.73151 −0.328863
\(208\) 0 0
\(209\) 24.6002 1.70163
\(210\) 0 0
\(211\) 10.1961 0.701929 0.350964 0.936389i \(-0.385854\pi\)
0.350964 + 0.936389i \(0.385854\pi\)
\(212\) 0 0
\(213\) 3.85067 0.263844
\(214\) 0 0
\(215\) 6.23743 0.425389
\(216\) 0 0
\(217\) 4.47580 0.303837
\(218\) 0 0
\(219\) 17.8844 1.20851
\(220\) 0 0
\(221\) −5.33121 −0.358616
\(222\) 0 0
\(223\) −22.3836 −1.49891 −0.749457 0.662053i \(-0.769685\pi\)
−0.749457 + 0.662053i \(0.769685\pi\)
\(224\) 0 0
\(225\) −1.35670 −0.0904466
\(226\) 0 0
\(227\) 9.54471 0.633504 0.316752 0.948508i \(-0.397408\pi\)
0.316752 + 0.948508i \(0.397408\pi\)
\(228\) 0 0
\(229\) −27.6539 −1.82742 −0.913709 0.406369i \(-0.866795\pi\)
−0.913709 + 0.406369i \(0.866795\pi\)
\(230\) 0 0
\(231\) −5.66791 −0.372921
\(232\) 0 0
\(233\) 16.9698 1.11173 0.555866 0.831272i \(-0.312387\pi\)
0.555866 + 0.831272i \(0.312387\pi\)
\(234\) 0 0
\(235\) 6.02172 0.392814
\(236\) 0 0
\(237\) −11.0195 −0.715796
\(238\) 0 0
\(239\) −24.1623 −1.56293 −0.781465 0.623949i \(-0.785527\pi\)
−0.781465 + 0.623949i \(0.785527\pi\)
\(240\) 0 0
\(241\) −21.4656 −1.38272 −0.691361 0.722510i \(-0.742988\pi\)
−0.691361 + 0.722510i \(0.742988\pi\)
\(242\) 0 0
\(243\) 12.7945 0.820771
\(244\) 0 0
\(245\) 6.37338 0.407180
\(246\) 0 0
\(247\) 3.34300 0.212710
\(248\) 0 0
\(249\) 8.24995 0.522819
\(250\) 0 0
\(251\) 13.8183 0.872204 0.436102 0.899897i \(-0.356359\pi\)
0.436102 + 0.899897i \(0.356359\pi\)
\(252\) 0 0
\(253\) 19.4795 1.22467
\(254\) 0 0
\(255\) 9.00378 0.563838
\(256\) 0 0
\(257\) 24.0558 1.50056 0.750279 0.661122i \(-0.229919\pi\)
0.750279 + 0.661122i \(0.229919\pi\)
\(258\) 0 0
\(259\) −2.02979 −0.126125
\(260\) 0 0
\(261\) 6.68977 0.414086
\(262\) 0 0
\(263\) 13.2776 0.818730 0.409365 0.912371i \(-0.365750\pi\)
0.409365 + 0.912371i \(0.365750\pi\)
\(264\) 0 0
\(265\) 8.35453 0.513215
\(266\) 0 0
\(267\) −23.7698 −1.45469
\(268\) 0 0
\(269\) −27.6447 −1.68553 −0.842764 0.538284i \(-0.819073\pi\)
−0.842764 + 0.538284i \(0.819073\pi\)
\(270\) 0 0
\(271\) −4.92757 −0.299329 −0.149664 0.988737i \(-0.547819\pi\)
−0.149664 + 0.988737i \(0.547819\pi\)
\(272\) 0 0
\(273\) −0.770230 −0.0466164
\(274\) 0 0
\(275\) 5.58550 0.336818
\(276\) 0 0
\(277\) −15.7921 −0.948856 −0.474428 0.880294i \(-0.657345\pi\)
−0.474428 + 0.880294i \(0.657345\pi\)
\(278\) 0 0
\(279\) 7.67100 0.459251
\(280\) 0 0
\(281\) −24.3943 −1.45524 −0.727622 0.685978i \(-0.759375\pi\)
−0.727622 + 0.685978i \(0.759375\pi\)
\(282\) 0 0
\(283\) 12.4748 0.741552 0.370776 0.928722i \(-0.379092\pi\)
0.370776 + 0.928722i \(0.379092\pi\)
\(284\) 0 0
\(285\) −5.64592 −0.334435
\(286\) 0 0
\(287\) 0.972955 0.0574317
\(288\) 0 0
\(289\) 32.3324 1.90191
\(290\) 0 0
\(291\) 3.37436 0.197808
\(292\) 0 0
\(293\) −18.4210 −1.07617 −0.538084 0.842891i \(-0.680852\pi\)
−0.538084 + 0.842891i \(0.680852\pi\)
\(294\) 0 0
\(295\) 9.38937 0.546670
\(296\) 0 0
\(297\) −31.1945 −1.81009
\(298\) 0 0
\(299\) 2.64713 0.153088
\(300\) 0 0
\(301\) 4.93751 0.284593
\(302\) 0 0
\(303\) 12.6790 0.728388
\(304\) 0 0
\(305\) −12.5580 −0.719068
\(306\) 0 0
\(307\) −12.4379 −0.709869 −0.354934 0.934891i \(-0.615497\pi\)
−0.354934 + 0.934891i \(0.615497\pi\)
\(308\) 0 0
\(309\) 12.5767 0.715465
\(310\) 0 0
\(311\) −17.5287 −0.993962 −0.496981 0.867761i \(-0.665558\pi\)
−0.496981 + 0.867761i \(0.665558\pi\)
\(312\) 0 0
\(313\) −17.4878 −0.988470 −0.494235 0.869328i \(-0.664552\pi\)
−0.494235 + 0.869328i \(0.664552\pi\)
\(314\) 0 0
\(315\) −1.07395 −0.0605104
\(316\) 0 0
\(317\) −21.1071 −1.18549 −0.592747 0.805389i \(-0.701957\pi\)
−0.592747 + 0.805389i \(0.701957\pi\)
\(318\) 0 0
\(319\) −27.5416 −1.54204
\(320\) 0 0
\(321\) −11.9004 −0.664213
\(322\) 0 0
\(323\) −30.9344 −1.72124
\(324\) 0 0
\(325\) 0.759032 0.0421035
\(326\) 0 0
\(327\) 11.8012 0.652610
\(328\) 0 0
\(329\) 4.76675 0.262800
\(330\) 0 0
\(331\) −0.411971 −0.0226440 −0.0113220 0.999936i \(-0.503604\pi\)
−0.0113220 + 0.999936i \(0.503604\pi\)
\(332\) 0 0
\(333\) −3.47883 −0.190639
\(334\) 0 0
\(335\) −6.07506 −0.331916
\(336\) 0 0
\(337\) −22.8128 −1.24269 −0.621346 0.783537i \(-0.713414\pi\)
−0.621346 + 0.783537i \(0.713414\pi\)
\(338\) 0 0
\(339\) −9.19553 −0.499433
\(340\) 0 0
\(341\) −31.5814 −1.71023
\(342\) 0 0
\(343\) 10.5863 0.571605
\(344\) 0 0
\(345\) −4.47069 −0.240694
\(346\) 0 0
\(347\) −3.05568 −0.164037 −0.0820186 0.996631i \(-0.526137\pi\)
−0.0820186 + 0.996631i \(0.526137\pi\)
\(348\) 0 0
\(349\) 12.7216 0.680973 0.340487 0.940249i \(-0.389408\pi\)
0.340487 + 0.940249i \(0.389408\pi\)
\(350\) 0 0
\(351\) −4.23912 −0.226268
\(352\) 0 0
\(353\) −18.7134 −0.996013 −0.498006 0.867173i \(-0.665934\pi\)
−0.498006 + 0.867173i \(0.665934\pi\)
\(354\) 0 0
\(355\) −3.00385 −0.159428
\(356\) 0 0
\(357\) 7.12733 0.377218
\(358\) 0 0
\(359\) −7.73606 −0.408294 −0.204147 0.978940i \(-0.565442\pi\)
−0.204147 + 0.978940i \(0.565442\pi\)
\(360\) 0 0
\(361\) 0.397772 0.0209354
\(362\) 0 0
\(363\) 25.8919 1.35897
\(364\) 0 0
\(365\) −13.9513 −0.730246
\(366\) 0 0
\(367\) 17.9271 0.935785 0.467893 0.883785i \(-0.345013\pi\)
0.467893 + 0.883785i \(0.345013\pi\)
\(368\) 0 0
\(369\) 1.66753 0.0868082
\(370\) 0 0
\(371\) 6.61339 0.343350
\(372\) 0 0
\(373\) −33.9192 −1.75627 −0.878136 0.478411i \(-0.841213\pi\)
−0.878136 + 0.478411i \(0.841213\pi\)
\(374\) 0 0
\(375\) −1.28191 −0.0661977
\(376\) 0 0
\(377\) −3.74272 −0.192760
\(378\) 0 0
\(379\) 6.55881 0.336903 0.168452 0.985710i \(-0.446123\pi\)
0.168452 + 0.985710i \(0.446123\pi\)
\(380\) 0 0
\(381\) −11.3771 −0.582864
\(382\) 0 0
\(383\) −30.9749 −1.58274 −0.791372 0.611335i \(-0.790633\pi\)
−0.791372 + 0.611335i \(0.790633\pi\)
\(384\) 0 0
\(385\) 4.42144 0.225338
\(386\) 0 0
\(387\) 8.46231 0.430163
\(388\) 0 0
\(389\) −18.9747 −0.962055 −0.481028 0.876705i \(-0.659736\pi\)
−0.481028 + 0.876705i \(0.659736\pi\)
\(390\) 0 0
\(391\) −24.4953 −1.23878
\(392\) 0 0
\(393\) −16.1842 −0.816385
\(394\) 0 0
\(395\) 8.59616 0.432520
\(396\) 0 0
\(397\) −21.4745 −1.07778 −0.538888 0.842378i \(-0.681155\pi\)
−0.538888 + 0.842378i \(0.681155\pi\)
\(398\) 0 0
\(399\) −4.46927 −0.223743
\(400\) 0 0
\(401\) 1.00000 0.0499376
\(402\) 0 0
\(403\) −4.29169 −0.213784
\(404\) 0 0
\(405\) 3.08927 0.153507
\(406\) 0 0
\(407\) 14.3223 0.709929
\(408\) 0 0
\(409\) 34.9821 1.72975 0.864876 0.501986i \(-0.167397\pi\)
0.864876 + 0.501986i \(0.167397\pi\)
\(410\) 0 0
\(411\) 27.3998 1.35153
\(412\) 0 0
\(413\) 7.43256 0.365732
\(414\) 0 0
\(415\) −6.43565 −0.315914
\(416\) 0 0
\(417\) −21.0440 −1.03053
\(418\) 0 0
\(419\) −4.72757 −0.230957 −0.115479 0.993310i \(-0.536840\pi\)
−0.115479 + 0.993310i \(0.536840\pi\)
\(420\) 0 0
\(421\) −0.955720 −0.0465790 −0.0232895 0.999729i \(-0.507414\pi\)
−0.0232895 + 0.999729i \(0.507414\pi\)
\(422\) 0 0
\(423\) 8.16966 0.397223
\(424\) 0 0
\(425\) −7.02370 −0.340700
\(426\) 0 0
\(427\) −9.94081 −0.481069
\(428\) 0 0
\(429\) 5.43476 0.262393
\(430\) 0 0
\(431\) −2.32988 −0.112226 −0.0561132 0.998424i \(-0.517871\pi\)
−0.0561132 + 0.998424i \(0.517871\pi\)
\(432\) 0 0
\(433\) 13.3584 0.641962 0.320981 0.947086i \(-0.395987\pi\)
0.320981 + 0.947086i \(0.395987\pi\)
\(434\) 0 0
\(435\) 6.32101 0.303069
\(436\) 0 0
\(437\) 15.3600 0.734770
\(438\) 0 0
\(439\) 23.0726 1.10119 0.550597 0.834771i \(-0.314400\pi\)
0.550597 + 0.834771i \(0.314400\pi\)
\(440\) 0 0
\(441\) 8.64676 0.411750
\(442\) 0 0
\(443\) 29.7515 1.41354 0.706769 0.707444i \(-0.250152\pi\)
0.706769 + 0.707444i \(0.250152\pi\)
\(444\) 0 0
\(445\) 18.5424 0.878995
\(446\) 0 0
\(447\) −4.23815 −0.200458
\(448\) 0 0
\(449\) 10.5472 0.497752 0.248876 0.968535i \(-0.419939\pi\)
0.248876 + 0.968535i \(0.419939\pi\)
\(450\) 0 0
\(451\) −6.86519 −0.323269
\(452\) 0 0
\(453\) −28.3727 −1.33306
\(454\) 0 0
\(455\) 0.600844 0.0281680
\(456\) 0 0
\(457\) 34.1375 1.59688 0.798442 0.602071i \(-0.205658\pi\)
0.798442 + 0.602071i \(0.205658\pi\)
\(458\) 0 0
\(459\) 39.2267 1.83095
\(460\) 0 0
\(461\) −9.24097 −0.430395 −0.215198 0.976571i \(-0.569040\pi\)
−0.215198 + 0.976571i \(0.569040\pi\)
\(462\) 0 0
\(463\) 34.5872 1.60740 0.803702 0.595032i \(-0.202860\pi\)
0.803702 + 0.595032i \(0.202860\pi\)
\(464\) 0 0
\(465\) 7.24815 0.336125
\(466\) 0 0
\(467\) −10.1999 −0.471995 −0.235998 0.971754i \(-0.575836\pi\)
−0.235998 + 0.971754i \(0.575836\pi\)
\(468\) 0 0
\(469\) −4.80897 −0.222058
\(470\) 0 0
\(471\) 1.27892 0.0589297
\(472\) 0 0
\(473\) −34.8392 −1.60191
\(474\) 0 0
\(475\) 4.40429 0.202083
\(476\) 0 0
\(477\) 11.3346 0.518975
\(478\) 0 0
\(479\) 39.9899 1.82718 0.913592 0.406633i \(-0.133297\pi\)
0.913592 + 0.406633i \(0.133297\pi\)
\(480\) 0 0
\(481\) 1.94630 0.0887437
\(482\) 0 0
\(483\) −3.53897 −0.161029
\(484\) 0 0
\(485\) −2.63228 −0.119526
\(486\) 0 0
\(487\) −12.3277 −0.558621 −0.279310 0.960201i \(-0.590106\pi\)
−0.279310 + 0.960201i \(0.590106\pi\)
\(488\) 0 0
\(489\) −10.6593 −0.482032
\(490\) 0 0
\(491\) −36.2443 −1.63568 −0.817841 0.575445i \(-0.804829\pi\)
−0.817841 + 0.575445i \(0.804829\pi\)
\(492\) 0 0
\(493\) 34.6333 1.55981
\(494\) 0 0
\(495\) 7.57784 0.340599
\(496\) 0 0
\(497\) −2.37782 −0.106660
\(498\) 0 0
\(499\) −5.39149 −0.241356 −0.120678 0.992692i \(-0.538507\pi\)
−0.120678 + 0.992692i \(0.538507\pi\)
\(500\) 0 0
\(501\) 22.6943 1.01391
\(502\) 0 0
\(503\) −18.0782 −0.806066 −0.403033 0.915185i \(-0.632044\pi\)
−0.403033 + 0.915185i \(0.632044\pi\)
\(504\) 0 0
\(505\) −9.89067 −0.440129
\(506\) 0 0
\(507\) −15.9263 −0.707313
\(508\) 0 0
\(509\) 1.14418 0.0507148 0.0253574 0.999678i \(-0.491928\pi\)
0.0253574 + 0.999678i \(0.491928\pi\)
\(510\) 0 0
\(511\) −11.0438 −0.488548
\(512\) 0 0
\(513\) −24.5976 −1.08601
\(514\) 0 0
\(515\) −9.81090 −0.432320
\(516\) 0 0
\(517\) −33.6343 −1.47924
\(518\) 0 0
\(519\) 6.03453 0.264887
\(520\) 0 0
\(521\) 29.4115 1.28854 0.644272 0.764797i \(-0.277161\pi\)
0.644272 + 0.764797i \(0.277161\pi\)
\(522\) 0 0
\(523\) 7.60715 0.332637 0.166319 0.986072i \(-0.446812\pi\)
0.166319 + 0.986072i \(0.446812\pi\)
\(524\) 0 0
\(525\) −1.01475 −0.0442875
\(526\) 0 0
\(527\) 39.7132 1.72993
\(528\) 0 0
\(529\) −10.8372 −0.471184
\(530\) 0 0
\(531\) 12.7385 0.552806
\(532\) 0 0
\(533\) −0.932933 −0.0404098
\(534\) 0 0
\(535\) 9.28328 0.401351
\(536\) 0 0
\(537\) 5.72285 0.246959
\(538\) 0 0
\(539\) −35.5985 −1.53334
\(540\) 0 0
\(541\) −10.6971 −0.459906 −0.229953 0.973202i \(-0.573857\pi\)
−0.229953 + 0.973202i \(0.573857\pi\)
\(542\) 0 0
\(543\) −6.03306 −0.258903
\(544\) 0 0
\(545\) −9.20596 −0.394340
\(546\) 0 0
\(547\) −27.1493 −1.16082 −0.580409 0.814325i \(-0.697107\pi\)
−0.580409 + 0.814325i \(0.697107\pi\)
\(548\) 0 0
\(549\) −17.0374 −0.727138
\(550\) 0 0
\(551\) −21.7172 −0.925184
\(552\) 0 0
\(553\) 6.80466 0.289364
\(554\) 0 0
\(555\) −3.28707 −0.139528
\(556\) 0 0
\(557\) 36.9739 1.56663 0.783317 0.621622i \(-0.213526\pi\)
0.783317 + 0.621622i \(0.213526\pi\)
\(558\) 0 0
\(559\) −4.73441 −0.200244
\(560\) 0 0
\(561\) −50.2906 −2.12327
\(562\) 0 0
\(563\) 15.4559 0.651389 0.325694 0.945475i \(-0.394402\pi\)
0.325694 + 0.945475i \(0.394402\pi\)
\(564\) 0 0
\(565\) 7.17329 0.301782
\(566\) 0 0
\(567\) 2.44545 0.102699
\(568\) 0 0
\(569\) 25.7069 1.07769 0.538845 0.842405i \(-0.318861\pi\)
0.538845 + 0.842405i \(0.318861\pi\)
\(570\) 0 0
\(571\) 26.7020 1.11744 0.558721 0.829356i \(-0.311292\pi\)
0.558721 + 0.829356i \(0.311292\pi\)
\(572\) 0 0
\(573\) −18.8532 −0.787604
\(574\) 0 0
\(575\) 3.48752 0.145439
\(576\) 0 0
\(577\) −0.386790 −0.0161023 −0.00805113 0.999968i \(-0.502563\pi\)
−0.00805113 + 0.999968i \(0.502563\pi\)
\(578\) 0 0
\(579\) 13.6804 0.568537
\(580\) 0 0
\(581\) −5.09442 −0.211352
\(582\) 0 0
\(583\) −46.6643 −1.93264
\(584\) 0 0
\(585\) 1.02978 0.0425760
\(586\) 0 0
\(587\) −6.34300 −0.261803 −0.130902 0.991395i \(-0.541787\pi\)
−0.130902 + 0.991395i \(0.541787\pi\)
\(588\) 0 0
\(589\) −24.9026 −1.02609
\(590\) 0 0
\(591\) −25.0759 −1.03148
\(592\) 0 0
\(593\) 25.4452 1.04491 0.522455 0.852667i \(-0.325016\pi\)
0.522455 + 0.852667i \(0.325016\pi\)
\(594\) 0 0
\(595\) −5.55991 −0.227934
\(596\) 0 0
\(597\) −16.8722 −0.690535
\(598\) 0 0
\(599\) 10.4800 0.428201 0.214101 0.976812i \(-0.431318\pi\)
0.214101 + 0.976812i \(0.431318\pi\)
\(600\) 0 0
\(601\) 44.6484 1.82125 0.910624 0.413236i \(-0.135601\pi\)
0.910624 + 0.413236i \(0.135601\pi\)
\(602\) 0 0
\(603\) −8.24202 −0.335641
\(604\) 0 0
\(605\) −20.1978 −0.821158
\(606\) 0 0
\(607\) −8.66242 −0.351597 −0.175798 0.984426i \(-0.556251\pi\)
−0.175798 + 0.984426i \(0.556251\pi\)
\(608\) 0 0
\(609\) 5.00367 0.202759
\(610\) 0 0
\(611\) −4.57068 −0.184910
\(612\) 0 0
\(613\) 32.7969 1.32465 0.662327 0.749215i \(-0.269569\pi\)
0.662327 + 0.749215i \(0.269569\pi\)
\(614\) 0 0
\(615\) 1.57561 0.0635348
\(616\) 0 0
\(617\) −25.6878 −1.03415 −0.517075 0.855940i \(-0.672979\pi\)
−0.517075 + 0.855940i \(0.672979\pi\)
\(618\) 0 0
\(619\) −18.8144 −0.756216 −0.378108 0.925762i \(-0.623425\pi\)
−0.378108 + 0.925762i \(0.623425\pi\)
\(620\) 0 0
\(621\) −19.4775 −0.781604
\(622\) 0 0
\(623\) 14.6780 0.588063
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 31.5353 1.25940
\(628\) 0 0
\(629\) −18.0101 −0.718110
\(630\) 0 0
\(631\) 13.8709 0.552190 0.276095 0.961130i \(-0.410959\pi\)
0.276095 + 0.961130i \(0.410959\pi\)
\(632\) 0 0
\(633\) 13.0705 0.519506
\(634\) 0 0
\(635\) 8.87506 0.352196
\(636\) 0 0
\(637\) −4.83760 −0.191673
\(638\) 0 0
\(639\) −4.07532 −0.161217
\(640\) 0 0
\(641\) 19.1293 0.755562 0.377781 0.925895i \(-0.376687\pi\)
0.377781 + 0.925895i \(0.376687\pi\)
\(642\) 0 0
\(643\) 22.9557 0.905286 0.452643 0.891692i \(-0.350481\pi\)
0.452643 + 0.891692i \(0.350481\pi\)
\(644\) 0 0
\(645\) 7.99584 0.314836
\(646\) 0 0
\(647\) 36.3306 1.42830 0.714151 0.699992i \(-0.246813\pi\)
0.714151 + 0.699992i \(0.246813\pi\)
\(648\) 0 0
\(649\) −52.4444 −2.05862
\(650\) 0 0
\(651\) 5.73759 0.224874
\(652\) 0 0
\(653\) −3.16730 −0.123946 −0.0619730 0.998078i \(-0.519739\pi\)
−0.0619730 + 0.998078i \(0.519739\pi\)
\(654\) 0 0
\(655\) 12.6250 0.493301
\(656\) 0 0
\(657\) −18.9277 −0.738441
\(658\) 0 0
\(659\) −20.1463 −0.784790 −0.392395 0.919797i \(-0.628353\pi\)
−0.392395 + 0.919797i \(0.628353\pi\)
\(660\) 0 0
\(661\) 37.3936 1.45444 0.727221 0.686404i \(-0.240812\pi\)
0.727221 + 0.686404i \(0.240812\pi\)
\(662\) 0 0
\(663\) −6.83415 −0.265416
\(664\) 0 0
\(665\) 3.48640 0.135197
\(666\) 0 0
\(667\) −17.1967 −0.665857
\(668\) 0 0
\(669\) −28.6938 −1.10937
\(670\) 0 0
\(671\) 70.1426 2.70783
\(672\) 0 0
\(673\) 33.3817 1.28677 0.643384 0.765543i \(-0.277530\pi\)
0.643384 + 0.765543i \(0.277530\pi\)
\(674\) 0 0
\(675\) −5.58491 −0.214963
\(676\) 0 0
\(677\) 7.02763 0.270094 0.135047 0.990839i \(-0.456881\pi\)
0.135047 + 0.990839i \(0.456881\pi\)
\(678\) 0 0
\(679\) −2.08370 −0.0799650
\(680\) 0 0
\(681\) 12.2355 0.468865
\(682\) 0 0
\(683\) −38.4854 −1.47260 −0.736301 0.676655i \(-0.763429\pi\)
−0.736301 + 0.676655i \(0.763429\pi\)
\(684\) 0 0
\(685\) −21.3741 −0.816663
\(686\) 0 0
\(687\) −35.4498 −1.35250
\(688\) 0 0
\(689\) −6.34135 −0.241586
\(690\) 0 0
\(691\) 10.4073 0.395912 0.197956 0.980211i \(-0.436570\pi\)
0.197956 + 0.980211i \(0.436570\pi\)
\(692\) 0 0
\(693\) 5.99857 0.227867
\(694\) 0 0
\(695\) 16.4161 0.622698
\(696\) 0 0
\(697\) 8.63290 0.326994
\(698\) 0 0
\(699\) 21.7539 0.822807
\(700\) 0 0
\(701\) 25.1405 0.949543 0.474772 0.880109i \(-0.342531\pi\)
0.474772 + 0.880109i \(0.342531\pi\)
\(702\) 0 0
\(703\) 11.2934 0.425940
\(704\) 0 0
\(705\) 7.71933 0.290727
\(706\) 0 0
\(707\) −7.82938 −0.294454
\(708\) 0 0
\(709\) 32.9132 1.23608 0.618041 0.786146i \(-0.287927\pi\)
0.618041 + 0.786146i \(0.287927\pi\)
\(710\) 0 0
\(711\) 11.6624 0.437374
\(712\) 0 0
\(713\) −19.7190 −0.738482
\(714\) 0 0
\(715\) −4.23957 −0.158551
\(716\) 0 0
\(717\) −30.9740 −1.15675
\(718\) 0 0
\(719\) −6.27997 −0.234203 −0.117102 0.993120i \(-0.537360\pi\)
−0.117102 + 0.993120i \(0.537360\pi\)
\(720\) 0 0
\(721\) −7.76624 −0.289230
\(722\) 0 0
\(723\) −27.5170 −1.02337
\(724\) 0 0
\(725\) −4.93092 −0.183130
\(726\) 0 0
\(727\) 41.1103 1.52470 0.762348 0.647167i \(-0.224046\pi\)
0.762348 + 0.647167i \(0.224046\pi\)
\(728\) 0 0
\(729\) 25.6693 0.950716
\(730\) 0 0
\(731\) 43.8098 1.62037
\(732\) 0 0
\(733\) 4.73963 0.175062 0.0875311 0.996162i \(-0.472102\pi\)
0.0875311 + 0.996162i \(0.472102\pi\)
\(734\) 0 0
\(735\) 8.17012 0.301359
\(736\) 0 0
\(737\) 33.9322 1.24991
\(738\) 0 0
\(739\) 14.3329 0.527245 0.263622 0.964626i \(-0.415083\pi\)
0.263622 + 0.964626i \(0.415083\pi\)
\(740\) 0 0
\(741\) 4.28543 0.157429
\(742\) 0 0
\(743\) −15.6197 −0.573031 −0.286516 0.958076i \(-0.592497\pi\)
−0.286516 + 0.958076i \(0.592497\pi\)
\(744\) 0 0
\(745\) 3.30611 0.121127
\(746\) 0 0
\(747\) −8.73124 −0.319459
\(748\) 0 0
\(749\) 7.34858 0.268511
\(750\) 0 0
\(751\) 22.9051 0.835819 0.417910 0.908489i \(-0.362763\pi\)
0.417910 + 0.908489i \(0.362763\pi\)
\(752\) 0 0
\(753\) 17.7139 0.645529
\(754\) 0 0
\(755\) 22.1331 0.805505
\(756\) 0 0
\(757\) −41.6277 −1.51298 −0.756492 0.654003i \(-0.773088\pi\)
−0.756492 + 0.654003i \(0.773088\pi\)
\(758\) 0 0
\(759\) 24.9711 0.906392
\(760\) 0 0
\(761\) −12.4121 −0.449938 −0.224969 0.974366i \(-0.572228\pi\)
−0.224969 + 0.974366i \(0.572228\pi\)
\(762\) 0 0
\(763\) −7.28738 −0.263821
\(764\) 0 0
\(765\) −9.52905 −0.344523
\(766\) 0 0
\(767\) −7.12683 −0.257335
\(768\) 0 0
\(769\) 30.2853 1.09212 0.546058 0.837747i \(-0.316128\pi\)
0.546058 + 0.837747i \(0.316128\pi\)
\(770\) 0 0
\(771\) 30.8374 1.11058
\(772\) 0 0
\(773\) −39.6168 −1.42492 −0.712459 0.701714i \(-0.752419\pi\)
−0.712459 + 0.701714i \(0.752419\pi\)
\(774\) 0 0
\(775\) −5.65417 −0.203104
\(776\) 0 0
\(777\) −2.60202 −0.0933469
\(778\) 0 0
\(779\) −5.41336 −0.193954
\(780\) 0 0
\(781\) 16.7780 0.600364
\(782\) 0 0
\(783\) 27.5387 0.984154
\(784\) 0 0
\(785\) −0.997668 −0.0356083
\(786\) 0 0
\(787\) 20.3828 0.726567 0.363283 0.931679i \(-0.381656\pi\)
0.363283 + 0.931679i \(0.381656\pi\)
\(788\) 0 0
\(789\) 17.0207 0.605952
\(790\) 0 0
\(791\) 5.67832 0.201898
\(792\) 0 0
\(793\) 9.53190 0.338488
\(794\) 0 0
\(795\) 10.7098 0.379837
\(796\) 0 0
\(797\) 24.2831 0.860151 0.430076 0.902793i \(-0.358487\pi\)
0.430076 + 0.902793i \(0.358487\pi\)
\(798\) 0 0
\(799\) 42.2948 1.49628
\(800\) 0 0
\(801\) 25.1565 0.888860
\(802\) 0 0
\(803\) 77.9251 2.74992
\(804\) 0 0
\(805\) 2.76069 0.0973016
\(806\) 0 0
\(807\) −35.4381 −1.24748
\(808\) 0 0
\(809\) 47.2630 1.66168 0.830839 0.556513i \(-0.187861\pi\)
0.830839 + 0.556513i \(0.187861\pi\)
\(810\) 0 0
\(811\) 9.23784 0.324385 0.162192 0.986759i \(-0.448144\pi\)
0.162192 + 0.986759i \(0.448144\pi\)
\(812\) 0 0
\(813\) −6.31672 −0.221537
\(814\) 0 0
\(815\) 8.31518 0.291268
\(816\) 0 0
\(817\) −27.4714 −0.961104
\(818\) 0 0
\(819\) 0.815164 0.0284841
\(820\) 0 0
\(821\) −49.8556 −1.73997 −0.869986 0.493076i \(-0.835872\pi\)
−0.869986 + 0.493076i \(0.835872\pi\)
\(822\) 0 0
\(823\) −21.7530 −0.758261 −0.379131 0.925343i \(-0.623777\pi\)
−0.379131 + 0.925343i \(0.623777\pi\)
\(824\) 0 0
\(825\) 7.16013 0.249284
\(826\) 0 0
\(827\) −46.1960 −1.60639 −0.803196 0.595714i \(-0.796869\pi\)
−0.803196 + 0.595714i \(0.796869\pi\)
\(828\) 0 0
\(829\) −50.0599 −1.73865 −0.869326 0.494239i \(-0.835447\pi\)
−0.869326 + 0.494239i \(0.835447\pi\)
\(830\) 0 0
\(831\) −20.2441 −0.702261
\(832\) 0 0
\(833\) 44.7647 1.55101
\(834\) 0 0
\(835\) −17.7035 −0.612653
\(836\) 0 0
\(837\) 31.5780 1.09150
\(838\) 0 0
\(839\) 23.2881 0.803996 0.401998 0.915641i \(-0.368316\pi\)
0.401998 + 0.915641i \(0.368316\pi\)
\(840\) 0 0
\(841\) −4.68605 −0.161588
\(842\) 0 0
\(843\) −31.2714 −1.07705
\(844\) 0 0
\(845\) 12.4239 0.427394
\(846\) 0 0
\(847\) −15.9885 −0.549370
\(848\) 0 0
\(849\) 15.9917 0.548832
\(850\) 0 0
\(851\) 8.94265 0.306550
\(852\) 0 0
\(853\) 5.79715 0.198491 0.0992453 0.995063i \(-0.468357\pi\)
0.0992453 + 0.995063i \(0.468357\pi\)
\(854\) 0 0
\(855\) 5.97529 0.204351
\(856\) 0 0
\(857\) −34.4699 −1.17747 −0.588734 0.808327i \(-0.700373\pi\)
−0.588734 + 0.808327i \(0.700373\pi\)
\(858\) 0 0
\(859\) 7.65715 0.261258 0.130629 0.991431i \(-0.458300\pi\)
0.130629 + 0.991431i \(0.458300\pi\)
\(860\) 0 0
\(861\) 1.24724 0.0425059
\(862\) 0 0
\(863\) −35.3622 −1.20374 −0.601871 0.798593i \(-0.705578\pi\)
−0.601871 + 0.798593i \(0.705578\pi\)
\(864\) 0 0
\(865\) −4.70744 −0.160058
\(866\) 0 0
\(867\) 41.4473 1.40763
\(868\) 0 0
\(869\) −48.0139 −1.62876
\(870\) 0 0
\(871\) 4.61116 0.156243
\(872\) 0 0
\(873\) −3.57122 −0.120867
\(874\) 0 0
\(875\) 0.791593 0.0267607
\(876\) 0 0
\(877\) −5.27554 −0.178142 −0.0890711 0.996025i \(-0.528390\pi\)
−0.0890711 + 0.996025i \(0.528390\pi\)
\(878\) 0 0
\(879\) −23.6142 −0.796486
\(880\) 0 0
\(881\) 28.5257 0.961055 0.480527 0.876980i \(-0.340445\pi\)
0.480527 + 0.876980i \(0.340445\pi\)
\(882\) 0 0
\(883\) −55.0960 −1.85413 −0.927064 0.374903i \(-0.877676\pi\)
−0.927064 + 0.374903i \(0.877676\pi\)
\(884\) 0 0
\(885\) 12.0364 0.404598
\(886\) 0 0
\(887\) −9.25850 −0.310870 −0.155435 0.987846i \(-0.549678\pi\)
−0.155435 + 0.987846i \(0.549678\pi\)
\(888\) 0 0
\(889\) 7.02544 0.235626
\(890\) 0 0
\(891\) −17.2551 −0.578069
\(892\) 0 0
\(893\) −26.5214 −0.887505
\(894\) 0 0
\(895\) −4.46430 −0.149225
\(896\) 0 0
\(897\) 3.39340 0.113302
\(898\) 0 0
\(899\) 27.8802 0.929858
\(900\) 0 0
\(901\) 58.6798 1.95491
\(902\) 0 0
\(903\) 6.32945 0.210631
\(904\) 0 0
\(905\) 4.70629 0.156443
\(906\) 0 0
\(907\) 29.0748 0.965414 0.482707 0.875782i \(-0.339654\pi\)
0.482707 + 0.875782i \(0.339654\pi\)
\(908\) 0 0
\(909\) −13.4187 −0.445069
\(910\) 0 0
\(911\) 10.4138 0.345026 0.172513 0.985007i \(-0.444811\pi\)
0.172513 + 0.985007i \(0.444811\pi\)
\(912\) 0 0
\(913\) 35.9464 1.18965
\(914\) 0 0
\(915\) −16.0982 −0.532191
\(916\) 0 0
\(917\) 9.99389 0.330027
\(918\) 0 0
\(919\) 0.399541 0.0131796 0.00658982 0.999978i \(-0.497902\pi\)
0.00658982 + 0.999978i \(0.497902\pi\)
\(920\) 0 0
\(921\) −15.9443 −0.525383
\(922\) 0 0
\(923\) 2.28002 0.0750476
\(924\) 0 0
\(925\) 2.56419 0.0843100
\(926\) 0 0
\(927\) −13.3104 −0.437172
\(928\) 0 0
\(929\) −3.16684 −0.103901 −0.0519504 0.998650i \(-0.516544\pi\)
−0.0519504 + 0.998650i \(0.516544\pi\)
\(930\) 0 0
\(931\) −28.0702 −0.919964
\(932\) 0 0
\(933\) −22.4703 −0.735644
\(934\) 0 0
\(935\) 39.2309 1.28299
\(936\) 0 0
\(937\) 25.6327 0.837384 0.418692 0.908128i \(-0.362489\pi\)
0.418692 + 0.908128i \(0.362489\pi\)
\(938\) 0 0
\(939\) −22.4179 −0.731579
\(940\) 0 0
\(941\) −0.947081 −0.0308740 −0.0154370 0.999881i \(-0.504914\pi\)
−0.0154370 + 0.999881i \(0.504914\pi\)
\(942\) 0 0
\(943\) −4.28654 −0.139589
\(944\) 0 0
\(945\) −4.42097 −0.143814
\(946\) 0 0
\(947\) 40.1998 1.30632 0.653159 0.757220i \(-0.273443\pi\)
0.653159 + 0.757220i \(0.273443\pi\)
\(948\) 0 0
\(949\) 10.5895 0.343750
\(950\) 0 0
\(951\) −27.0575 −0.877400
\(952\) 0 0
\(953\) 45.6009 1.47716 0.738578 0.674168i \(-0.235497\pi\)
0.738578 + 0.674168i \(0.235497\pi\)
\(954\) 0 0
\(955\) 14.7071 0.475910
\(956\) 0 0
\(957\) −35.3060 −1.14128
\(958\) 0 0
\(959\) −16.9196 −0.546363
\(960\) 0 0
\(961\) 0.969612 0.0312778
\(962\) 0 0
\(963\) 12.5946 0.405856
\(964\) 0 0
\(965\) −10.6718 −0.343539
\(966\) 0 0
\(967\) 37.6396 1.21041 0.605204 0.796071i \(-0.293092\pi\)
0.605204 + 0.796071i \(0.293092\pi\)
\(968\) 0 0
\(969\) −39.6552 −1.27391
\(970\) 0 0
\(971\) −12.5218 −0.401845 −0.200923 0.979607i \(-0.564394\pi\)
−0.200923 + 0.979607i \(0.564394\pi\)
\(972\) 0 0
\(973\) 12.9949 0.416596
\(974\) 0 0
\(975\) 0.973013 0.0311613
\(976\) 0 0
\(977\) 61.2046 1.95811 0.979054 0.203599i \(-0.0652638\pi\)
0.979054 + 0.203599i \(0.0652638\pi\)
\(978\) 0 0
\(979\) −103.569 −3.31007
\(980\) 0 0
\(981\) −12.4897 −0.398766
\(982\) 0 0
\(983\) 30.2931 0.966200 0.483100 0.875565i \(-0.339511\pi\)
0.483100 + 0.875565i \(0.339511\pi\)
\(984\) 0 0
\(985\) 19.5613 0.623275
\(986\) 0 0
\(987\) 6.11057 0.194501
\(988\) 0 0
\(989\) −21.7531 −0.691709
\(990\) 0 0
\(991\) −41.3839 −1.31460 −0.657301 0.753628i \(-0.728302\pi\)
−0.657301 + 0.753628i \(0.728302\pi\)
\(992\) 0 0
\(993\) −0.528111 −0.0167591
\(994\) 0 0
\(995\) 13.1618 0.417256
\(996\) 0 0
\(997\) 7.09602 0.224733 0.112367 0.993667i \(-0.464157\pi\)
0.112367 + 0.993667i \(0.464157\pi\)
\(998\) 0 0
\(999\) −14.3208 −0.453089
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 \(a_p\))