Properties

Label 6004.2.a.g.1.16
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 1
Dimension 27
CM No

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Newspace parameters

Level: \( N \) = \( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9421813736\)
Analytic rank: \(1\)
Dimension: \(27\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.314419 q^{3}\) \(-4.24837 q^{5}\) \(+1.07745 q^{7}\) \(-2.90114 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.314419 q^{3}\) \(-4.24837 q^{5}\) \(+1.07745 q^{7}\) \(-2.90114 q^{9}\) \(+3.34805 q^{11}\) \(-1.31870 q^{13}\) \(-1.33577 q^{15}\) \(-2.75429 q^{17}\) \(+1.00000 q^{19}\) \(+0.338771 q^{21}\) \(+9.53559 q^{23}\) \(+13.0487 q^{25}\) \(-1.85543 q^{27}\) \(-8.28473 q^{29}\) \(+3.02324 q^{31}\) \(+1.05269 q^{33}\) \(-4.57741 q^{35}\) \(+4.48446 q^{37}\) \(-0.414625 q^{39}\) \(-2.36401 q^{41}\) \(-10.5342 q^{43}\) \(+12.3251 q^{45}\) \(-3.65470 q^{47}\) \(-5.83910 q^{49}\) \(-0.866001 q^{51}\) \(+11.8308 q^{53}\) \(-14.2238 q^{55}\) \(+0.314419 q^{57}\) \(+10.9586 q^{59}\) \(+8.61564 q^{61}\) \(-3.12584 q^{63}\) \(+5.60233 q^{65}\) \(+3.47244 q^{67}\) \(+2.99817 q^{69}\) \(-13.6913 q^{71}\) \(+3.96374 q^{73}\) \(+4.10275 q^{75}\) \(+3.60736 q^{77}\) \(-1.00000 q^{79}\) \(+8.12004 q^{81}\) \(+7.24315 q^{83}\) \(+11.7012 q^{85}\) \(-2.60488 q^{87}\) \(+10.4935 q^{89}\) \(-1.42083 q^{91}\) \(+0.950564 q^{93}\) \(-4.24837 q^{95}\) \(-0.407329 q^{97}\) \(-9.71316 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(27q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(27q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut -\mathstrut 11q^{23} \) \(\mathstrut +\mathstrut 13q^{25} \) \(\mathstrut -\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 39q^{29} \) \(\mathstrut -\mathstrut 27q^{31} \) \(\mathstrut -\mathstrut 18q^{33} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut -\mathstrut q^{37} \) \(\mathstrut -\mathstrut 22q^{39} \) \(\mathstrut -\mathstrut 36q^{41} \) \(\mathstrut -\mathstrut 2q^{43} \) \(\mathstrut -\mathstrut 18q^{45} \) \(\mathstrut -\mathstrut 12q^{47} \) \(\mathstrut +\mathstrut 15q^{49} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 28q^{53} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 30q^{59} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 32q^{65} \) \(\mathstrut +\mathstrut 13q^{67} \) \(\mathstrut -\mathstrut 27q^{69} \) \(\mathstrut -\mathstrut 59q^{71} \) \(\mathstrut -\mathstrut 30q^{73} \) \(\mathstrut -\mathstrut 21q^{75} \) \(\mathstrut -\mathstrut 39q^{77} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut -\mathstrut 5q^{81} \) \(\mathstrut +\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 56q^{89} \) \(\mathstrut -\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 38q^{93} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 30q^{97} \) \(\mathstrut +\mathstrut 31q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0.314419 0.181530 0.0907650 0.995872i \(-0.471069\pi\)
0.0907650 + 0.995872i \(0.471069\pi\)
\(4\) 0 0
\(5\) −4.24837 −1.89993 −0.949965 0.312356i \(-0.898882\pi\)
−0.949965 + 0.312356i \(0.898882\pi\)
\(6\) 0 0
\(7\) 1.07745 0.407238 0.203619 0.979050i \(-0.434730\pi\)
0.203619 + 0.979050i \(0.434730\pi\)
\(8\) 0 0
\(9\) −2.90114 −0.967047
\(10\) 0 0
\(11\) 3.34805 1.00947 0.504737 0.863273i \(-0.331589\pi\)
0.504737 + 0.863273i \(0.331589\pi\)
\(12\) 0 0
\(13\) −1.31870 −0.365742 −0.182871 0.983137i \(-0.558539\pi\)
−0.182871 + 0.983137i \(0.558539\pi\)
\(14\) 0 0
\(15\) −1.33577 −0.344894
\(16\) 0 0
\(17\) −2.75429 −0.668013 −0.334006 0.942571i \(-0.608401\pi\)
−0.334006 + 0.942571i \(0.608401\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0.338771 0.0739259
\(22\) 0 0
\(23\) 9.53559 1.98831 0.994154 0.107973i \(-0.0344361\pi\)
0.994154 + 0.107973i \(0.0344361\pi\)
\(24\) 0 0
\(25\) 13.0487 2.60973
\(26\) 0 0
\(27\) −1.85543 −0.357078
\(28\) 0 0
\(29\) −8.28473 −1.53844 −0.769218 0.638986i \(-0.779354\pi\)
−0.769218 + 0.638986i \(0.779354\pi\)
\(30\) 0 0
\(31\) 3.02324 0.542990 0.271495 0.962440i \(-0.412482\pi\)
0.271495 + 0.962440i \(0.412482\pi\)
\(32\) 0 0
\(33\) 1.05269 0.183250
\(34\) 0 0
\(35\) −4.57741 −0.773724
\(36\) 0 0
\(37\) 4.48446 0.737241 0.368620 0.929580i \(-0.379830\pi\)
0.368620 + 0.929580i \(0.379830\pi\)
\(38\) 0 0
\(39\) −0.414625 −0.0663931
\(40\) 0 0
\(41\) −2.36401 −0.369197 −0.184599 0.982814i \(-0.559098\pi\)
−0.184599 + 0.982814i \(0.559098\pi\)
\(42\) 0 0
\(43\) −10.5342 −1.60645 −0.803224 0.595677i \(-0.796884\pi\)
−0.803224 + 0.595677i \(0.796884\pi\)
\(44\) 0 0
\(45\) 12.3251 1.83732
\(46\) 0 0
\(47\) −3.65470 −0.533093 −0.266546 0.963822i \(-0.585883\pi\)
−0.266546 + 0.963822i \(0.585883\pi\)
\(48\) 0 0
\(49\) −5.83910 −0.834157
\(50\) 0 0
\(51\) −0.866001 −0.121264
\(52\) 0 0
\(53\) 11.8308 1.62509 0.812545 0.582899i \(-0.198082\pi\)
0.812545 + 0.582899i \(0.198082\pi\)
\(54\) 0 0
\(55\) −14.2238 −1.91793
\(56\) 0 0
\(57\) 0.314419 0.0416458
\(58\) 0 0
\(59\) 10.9586 1.42669 0.713346 0.700812i \(-0.247179\pi\)
0.713346 + 0.700812i \(0.247179\pi\)
\(60\) 0 0
\(61\) 8.61564 1.10312 0.551560 0.834135i \(-0.314033\pi\)
0.551560 + 0.834135i \(0.314033\pi\)
\(62\) 0 0
\(63\) −3.12584 −0.393818
\(64\) 0 0
\(65\) 5.60233 0.694884
\(66\) 0 0
\(67\) 3.47244 0.424226 0.212113 0.977245i \(-0.431965\pi\)
0.212113 + 0.977245i \(0.431965\pi\)
\(68\) 0 0
\(69\) 2.99817 0.360938
\(70\) 0 0
\(71\) −13.6913 −1.62485 −0.812427 0.583063i \(-0.801854\pi\)
−0.812427 + 0.583063i \(0.801854\pi\)
\(72\) 0 0
\(73\) 3.96374 0.463920 0.231960 0.972725i \(-0.425486\pi\)
0.231960 + 0.972725i \(0.425486\pi\)
\(74\) 0 0
\(75\) 4.10275 0.473745
\(76\) 0 0
\(77\) 3.60736 0.411096
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) 8.12004 0.902226
\(82\) 0 0
\(83\) 7.24315 0.795039 0.397520 0.917594i \(-0.369871\pi\)
0.397520 + 0.917594i \(0.369871\pi\)
\(84\) 0 0
\(85\) 11.7012 1.26918
\(86\) 0 0
\(87\) −2.60488 −0.279272
\(88\) 0 0
\(89\) 10.4935 1.11231 0.556157 0.831077i \(-0.312275\pi\)
0.556157 + 0.831077i \(0.312275\pi\)
\(90\) 0 0
\(91\) −1.42083 −0.148944
\(92\) 0 0
\(93\) 0.950564 0.0985689
\(94\) 0 0
\(95\) −4.24837 −0.435874
\(96\) 0 0
\(97\) −0.407329 −0.0413580 −0.0206790 0.999786i \(-0.506583\pi\)
−0.0206790 + 0.999786i \(0.506583\pi\)
\(98\) 0 0
\(99\) −9.71316 −0.976209
\(100\) 0 0
\(101\) −6.78571 −0.675203 −0.337602 0.941289i \(-0.609616\pi\)
−0.337602 + 0.941289i \(0.609616\pi\)
\(102\) 0 0
\(103\) −8.26293 −0.814170 −0.407085 0.913390i \(-0.633455\pi\)
−0.407085 + 0.913390i \(0.633455\pi\)
\(104\) 0 0
\(105\) −1.43923 −0.140454
\(106\) 0 0
\(107\) −8.99492 −0.869572 −0.434786 0.900534i \(-0.643176\pi\)
−0.434786 + 0.900534i \(0.643176\pi\)
\(108\) 0 0
\(109\) −0.0110714 −0.00106044 −0.000530222 1.00000i \(-0.500169\pi\)
−0.000530222 1.00000i \(0.500169\pi\)
\(110\) 0 0
\(111\) 1.41000 0.133831
\(112\) 0 0
\(113\) −18.8046 −1.76899 −0.884494 0.466552i \(-0.845496\pi\)
−0.884494 + 0.466552i \(0.845496\pi\)
\(114\) 0 0
\(115\) −40.5107 −3.77765
\(116\) 0 0
\(117\) 3.82574 0.353689
\(118\) 0 0
\(119\) −2.96761 −0.272040
\(120\) 0 0
\(121\) 0.209429 0.0190390
\(122\) 0 0
\(123\) −0.743292 −0.0670204
\(124\) 0 0
\(125\) −34.1938 −3.05838
\(126\) 0 0
\(127\) −13.2139 −1.17255 −0.586274 0.810113i \(-0.699406\pi\)
−0.586274 + 0.810113i \(0.699406\pi\)
\(128\) 0 0
\(129\) −3.31215 −0.291619
\(130\) 0 0
\(131\) −7.75832 −0.677847 −0.338924 0.940814i \(-0.610063\pi\)
−0.338924 + 0.940814i \(0.610063\pi\)
\(132\) 0 0
\(133\) 1.07745 0.0934268
\(134\) 0 0
\(135\) 7.88257 0.678423
\(136\) 0 0
\(137\) 0.685371 0.0585552 0.0292776 0.999571i \(-0.490679\pi\)
0.0292776 + 0.999571i \(0.490679\pi\)
\(138\) 0 0
\(139\) 14.6121 1.23938 0.619689 0.784847i \(-0.287259\pi\)
0.619689 + 0.784847i \(0.287259\pi\)
\(140\) 0 0
\(141\) −1.14911 −0.0967724
\(142\) 0 0
\(143\) −4.41507 −0.369207
\(144\) 0 0
\(145\) 35.1966 2.92292
\(146\) 0 0
\(147\) −1.83593 −0.151425
\(148\) 0 0
\(149\) −8.29431 −0.679496 −0.339748 0.940516i \(-0.610342\pi\)
−0.339748 + 0.940516i \(0.610342\pi\)
\(150\) 0 0
\(151\) −2.06269 −0.167859 −0.0839296 0.996472i \(-0.526747\pi\)
−0.0839296 + 0.996472i \(0.526747\pi\)
\(152\) 0 0
\(153\) 7.99057 0.646000
\(154\) 0 0
\(155\) −12.8438 −1.03164
\(156\) 0 0
\(157\) 6.81700 0.544056 0.272028 0.962289i \(-0.412306\pi\)
0.272028 + 0.962289i \(0.412306\pi\)
\(158\) 0 0
\(159\) 3.71984 0.295003
\(160\) 0 0
\(161\) 10.2741 0.809714
\(162\) 0 0
\(163\) 9.99974 0.783240 0.391620 0.920127i \(-0.371915\pi\)
0.391620 + 0.920127i \(0.371915\pi\)
\(164\) 0 0
\(165\) −4.47222 −0.348162
\(166\) 0 0
\(167\) −18.2130 −1.40937 −0.704684 0.709522i \(-0.748911\pi\)
−0.704684 + 0.709522i \(0.748911\pi\)
\(168\) 0 0
\(169\) −11.2610 −0.866233
\(170\) 0 0
\(171\) −2.90114 −0.221856
\(172\) 0 0
\(173\) −13.3723 −1.01668 −0.508339 0.861157i \(-0.669740\pi\)
−0.508339 + 0.861157i \(0.669740\pi\)
\(174\) 0 0
\(175\) 14.0593 1.06278
\(176\) 0 0
\(177\) 3.44560 0.258987
\(178\) 0 0
\(179\) 4.94646 0.369716 0.184858 0.982765i \(-0.440818\pi\)
0.184858 + 0.982765i \(0.440818\pi\)
\(180\) 0 0
\(181\) −5.64794 −0.419808 −0.209904 0.977722i \(-0.567315\pi\)
−0.209904 + 0.977722i \(0.567315\pi\)
\(182\) 0 0
\(183\) 2.70892 0.200249
\(184\) 0 0
\(185\) −19.0517 −1.40071
\(186\) 0 0
\(187\) −9.22149 −0.674342
\(188\) 0 0
\(189\) −1.99914 −0.145416
\(190\) 0 0
\(191\) −16.7721 −1.21358 −0.606792 0.794860i \(-0.707544\pi\)
−0.606792 + 0.794860i \(0.707544\pi\)
\(192\) 0 0
\(193\) −4.49497 −0.323555 −0.161777 0.986827i \(-0.551723\pi\)
−0.161777 + 0.986827i \(0.551723\pi\)
\(194\) 0 0
\(195\) 1.76148 0.126142
\(196\) 0 0
\(197\) −9.26504 −0.660107 −0.330053 0.943962i \(-0.607067\pi\)
−0.330053 + 0.943962i \(0.607067\pi\)
\(198\) 0 0
\(199\) 8.53739 0.605199 0.302600 0.953118i \(-0.402145\pi\)
0.302600 + 0.953118i \(0.402145\pi\)
\(200\) 0 0
\(201\) 1.09180 0.0770098
\(202\) 0 0
\(203\) −8.92639 −0.626510
\(204\) 0 0
\(205\) 10.0432 0.701449
\(206\) 0 0
\(207\) −27.6641 −1.92279
\(208\) 0 0
\(209\) 3.34805 0.231589
\(210\) 0 0
\(211\) −17.2161 −1.18520 −0.592602 0.805496i \(-0.701899\pi\)
−0.592602 + 0.805496i \(0.701899\pi\)
\(212\) 0 0
\(213\) −4.30480 −0.294960
\(214\) 0 0
\(215\) 44.7531 3.05214
\(216\) 0 0
\(217\) 3.25739 0.221126
\(218\) 0 0
\(219\) 1.24627 0.0842154
\(220\) 0 0
\(221\) 3.63208 0.244320
\(222\) 0 0
\(223\) 4.00842 0.268424 0.134212 0.990953i \(-0.457150\pi\)
0.134212 + 0.990953i \(0.457150\pi\)
\(224\) 0 0
\(225\) −37.8560 −2.52374
\(226\) 0 0
\(227\) −24.5845 −1.63173 −0.815865 0.578242i \(-0.803739\pi\)
−0.815865 + 0.578242i \(0.803739\pi\)
\(228\) 0 0
\(229\) 20.1420 1.33102 0.665510 0.746389i \(-0.268214\pi\)
0.665510 + 0.746389i \(0.268214\pi\)
\(230\) 0 0
\(231\) 1.13422 0.0746264
\(232\) 0 0
\(233\) −23.7258 −1.55433 −0.777164 0.629298i \(-0.783342\pi\)
−0.777164 + 0.629298i \(0.783342\pi\)
\(234\) 0 0
\(235\) 15.5265 1.01284
\(236\) 0 0
\(237\) −0.314419 −0.0204237
\(238\) 0 0
\(239\) −11.3938 −0.737001 −0.368501 0.929627i \(-0.620129\pi\)
−0.368501 + 0.929627i \(0.620129\pi\)
\(240\) 0 0
\(241\) 14.3831 0.926497 0.463248 0.886229i \(-0.346684\pi\)
0.463248 + 0.886229i \(0.346684\pi\)
\(242\) 0 0
\(243\) 8.11939 0.520859
\(244\) 0 0
\(245\) 24.8067 1.58484
\(246\) 0 0
\(247\) −1.31870 −0.0839069
\(248\) 0 0
\(249\) 2.27739 0.144324
\(250\) 0 0
\(251\) 2.99892 0.189290 0.0946452 0.995511i \(-0.469828\pi\)
0.0946452 + 0.995511i \(0.469828\pi\)
\(252\) 0 0
\(253\) 31.9256 2.00715
\(254\) 0 0
\(255\) 3.67909 0.230394
\(256\) 0 0
\(257\) −28.2966 −1.76509 −0.882546 0.470226i \(-0.844172\pi\)
−0.882546 + 0.470226i \(0.844172\pi\)
\(258\) 0 0
\(259\) 4.83178 0.300232
\(260\) 0 0
\(261\) 24.0352 1.48774
\(262\) 0 0
\(263\) 15.8279 0.975989 0.487994 0.872847i \(-0.337729\pi\)
0.487994 + 0.872847i \(0.337729\pi\)
\(264\) 0 0
\(265\) −50.2618 −3.08756
\(266\) 0 0
\(267\) 3.29937 0.201918
\(268\) 0 0
\(269\) −1.77829 −0.108424 −0.0542121 0.998529i \(-0.517265\pi\)
−0.0542121 + 0.998529i \(0.517265\pi\)
\(270\) 0 0
\(271\) −24.8403 −1.50894 −0.754470 0.656335i \(-0.772106\pi\)
−0.754470 + 0.656335i \(0.772106\pi\)
\(272\) 0 0
\(273\) −0.446738 −0.0270378
\(274\) 0 0
\(275\) 43.6876 2.63446
\(276\) 0 0
\(277\) −16.9930 −1.02101 −0.510506 0.859874i \(-0.670542\pi\)
−0.510506 + 0.859874i \(0.670542\pi\)
\(278\) 0 0
\(279\) −8.77084 −0.525096
\(280\) 0 0
\(281\) 12.9132 0.770335 0.385168 0.922847i \(-0.374144\pi\)
0.385168 + 0.922847i \(0.374144\pi\)
\(282\) 0 0
\(283\) 21.3522 1.26925 0.634627 0.772818i \(-0.281154\pi\)
0.634627 + 0.772818i \(0.281154\pi\)
\(284\) 0 0
\(285\) −1.33577 −0.0791242
\(286\) 0 0
\(287\) −2.54711 −0.150351
\(288\) 0 0
\(289\) −9.41391 −0.553759
\(290\) 0 0
\(291\) −0.128072 −0.00750772
\(292\) 0 0
\(293\) 9.07884 0.530392 0.265196 0.964195i \(-0.414563\pi\)
0.265196 + 0.964195i \(0.414563\pi\)
\(294\) 0 0
\(295\) −46.5563 −2.71061
\(296\) 0 0
\(297\) −6.21208 −0.360461
\(298\) 0 0
\(299\) −12.5746 −0.727207
\(300\) 0 0
\(301\) −11.3501 −0.654207
\(302\) 0 0
\(303\) −2.13356 −0.122570
\(304\) 0 0
\(305\) −36.6024 −2.09585
\(306\) 0 0
\(307\) −5.74929 −0.328129 −0.164065 0.986450i \(-0.552461\pi\)
−0.164065 + 0.986450i \(0.552461\pi\)
\(308\) 0 0
\(309\) −2.59802 −0.147796
\(310\) 0 0
\(311\) −19.5978 −1.11129 −0.555645 0.831420i \(-0.687529\pi\)
−0.555645 + 0.831420i \(0.687529\pi\)
\(312\) 0 0
\(313\) 29.8598 1.68778 0.843888 0.536520i \(-0.180261\pi\)
0.843888 + 0.536520i \(0.180261\pi\)
\(314\) 0 0
\(315\) 13.2797 0.748227
\(316\) 0 0
\(317\) −27.6863 −1.55502 −0.777509 0.628871i \(-0.783517\pi\)
−0.777509 + 0.628871i \(0.783517\pi\)
\(318\) 0 0
\(319\) −27.7377 −1.55301
\(320\) 0 0
\(321\) −2.82818 −0.157853
\(322\) 0 0
\(323\) −2.75429 −0.153253
\(324\) 0 0
\(325\) −17.2073 −0.954489
\(326\) 0 0
\(327\) −0.00348105 −0.000192502 0
\(328\) 0 0
\(329\) −3.93776 −0.217096
\(330\) 0 0
\(331\) 7.99773 0.439595 0.219797 0.975546i \(-0.429460\pi\)
0.219797 + 0.975546i \(0.429460\pi\)
\(332\) 0 0
\(333\) −13.0100 −0.712946
\(334\) 0 0
\(335\) −14.7522 −0.806000
\(336\) 0 0
\(337\) −9.04060 −0.492473 −0.246237 0.969210i \(-0.579194\pi\)
−0.246237 + 0.969210i \(0.579194\pi\)
\(338\) 0 0
\(339\) −5.91253 −0.321124
\(340\) 0 0
\(341\) 10.1219 0.548134
\(342\) 0 0
\(343\) −13.8335 −0.746939
\(344\) 0 0
\(345\) −12.7374 −0.685756
\(346\) 0 0
\(347\) 2.06873 0.111055 0.0555276 0.998457i \(-0.482316\pi\)
0.0555276 + 0.998457i \(0.482316\pi\)
\(348\) 0 0
\(349\) 18.8973 1.01155 0.505776 0.862665i \(-0.331206\pi\)
0.505776 + 0.862665i \(0.331206\pi\)
\(350\) 0 0
\(351\) 2.44676 0.130598
\(352\) 0 0
\(353\) −8.55918 −0.455559 −0.227779 0.973713i \(-0.573147\pi\)
−0.227779 + 0.973713i \(0.573147\pi\)
\(354\) 0 0
\(355\) 58.1656 3.08711
\(356\) 0 0
\(357\) −0.933073 −0.0493835
\(358\) 0 0
\(359\) −26.0237 −1.37348 −0.686739 0.726904i \(-0.740959\pi\)
−0.686739 + 0.726904i \(0.740959\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0.0658485 0.00345615
\(364\) 0 0
\(365\) −16.8394 −0.881416
\(366\) 0 0
\(367\) −17.8267 −0.930546 −0.465273 0.885167i \(-0.654044\pi\)
−0.465273 + 0.885167i \(0.654044\pi\)
\(368\) 0 0
\(369\) 6.85834 0.357031
\(370\) 0 0
\(371\) 12.7471 0.661798
\(372\) 0 0
\(373\) −26.4967 −1.37195 −0.685974 0.727626i \(-0.740624\pi\)
−0.685974 + 0.727626i \(0.740624\pi\)
\(374\) 0 0
\(375\) −10.7512 −0.555188
\(376\) 0 0
\(377\) 10.9251 0.562670
\(378\) 0 0
\(379\) −15.8384 −0.813565 −0.406782 0.913525i \(-0.633349\pi\)
−0.406782 + 0.913525i \(0.633349\pi\)
\(380\) 0 0
\(381\) −4.15472 −0.212853
\(382\) 0 0
\(383\) 23.2204 1.18651 0.593253 0.805016i \(-0.297843\pi\)
0.593253 + 0.805016i \(0.297843\pi\)
\(384\) 0 0
\(385\) −15.3254 −0.781054
\(386\) 0 0
\(387\) 30.5612 1.55351
\(388\) 0 0
\(389\) 1.64433 0.0833707 0.0416853 0.999131i \(-0.486727\pi\)
0.0416853 + 0.999131i \(0.486727\pi\)
\(390\) 0 0
\(391\) −26.2637 −1.32821
\(392\) 0 0
\(393\) −2.43936 −0.123050
\(394\) 0 0
\(395\) 4.24837 0.213759
\(396\) 0 0
\(397\) 4.35835 0.218739 0.109370 0.994001i \(-0.465117\pi\)
0.109370 + 0.994001i \(0.465117\pi\)
\(398\) 0 0
\(399\) 0.338771 0.0169598
\(400\) 0 0
\(401\) 14.0493 0.701591 0.350795 0.936452i \(-0.385911\pi\)
0.350795 + 0.936452i \(0.385911\pi\)
\(402\) 0 0
\(403\) −3.98675 −0.198594
\(404\) 0 0
\(405\) −34.4969 −1.71417
\(406\) 0 0
\(407\) 15.0142 0.744226
\(408\) 0 0
\(409\) −15.3643 −0.759716 −0.379858 0.925045i \(-0.624027\pi\)
−0.379858 + 0.925045i \(0.624027\pi\)
\(410\) 0 0
\(411\) 0.215494 0.0106295
\(412\) 0 0
\(413\) 11.8074 0.581003
\(414\) 0 0
\(415\) −30.7716 −1.51052
\(416\) 0 0
\(417\) 4.59431 0.224984
\(418\) 0 0
\(419\) −8.62082 −0.421155 −0.210577 0.977577i \(-0.567534\pi\)
−0.210577 + 0.977577i \(0.567534\pi\)
\(420\) 0 0
\(421\) 25.7885 1.25686 0.628428 0.777868i \(-0.283699\pi\)
0.628428 + 0.777868i \(0.283699\pi\)
\(422\) 0 0
\(423\) 10.6028 0.515526
\(424\) 0 0
\(425\) −35.9398 −1.74334
\(426\) 0 0
\(427\) 9.28292 0.449232
\(428\) 0 0
\(429\) −1.38818 −0.0670222
\(430\) 0 0
\(431\) −27.4659 −1.32298 −0.661492 0.749952i \(-0.730076\pi\)
−0.661492 + 0.749952i \(0.730076\pi\)
\(432\) 0 0
\(433\) 38.7008 1.85984 0.929921 0.367759i \(-0.119875\pi\)
0.929921 + 0.367759i \(0.119875\pi\)
\(434\) 0 0
\(435\) 11.0665 0.530598
\(436\) 0 0
\(437\) 9.53559 0.456149
\(438\) 0 0
\(439\) −4.25988 −0.203313 −0.101657 0.994820i \(-0.532414\pi\)
−0.101657 + 0.994820i \(0.532414\pi\)
\(440\) 0 0
\(441\) 16.9401 0.806669
\(442\) 0 0
\(443\) 20.6263 0.979986 0.489993 0.871726i \(-0.336999\pi\)
0.489993 + 0.871726i \(0.336999\pi\)
\(444\) 0 0
\(445\) −44.5805 −2.11332
\(446\) 0 0
\(447\) −2.60789 −0.123349
\(448\) 0 0
\(449\) 12.2174 0.576574 0.288287 0.957544i \(-0.406914\pi\)
0.288287 + 0.957544i \(0.406914\pi\)
\(450\) 0 0
\(451\) −7.91484 −0.372695
\(452\) 0 0
\(453\) −0.648549 −0.0304715
\(454\) 0 0
\(455\) 6.03624 0.282983
\(456\) 0 0
\(457\) 19.4790 0.911189 0.455594 0.890188i \(-0.349427\pi\)
0.455594 + 0.890188i \(0.349427\pi\)
\(458\) 0 0
\(459\) 5.11039 0.238533
\(460\) 0 0
\(461\) 7.25036 0.337683 0.168841 0.985643i \(-0.445997\pi\)
0.168841 + 0.985643i \(0.445997\pi\)
\(462\) 0 0
\(463\) −21.1864 −0.984613 −0.492307 0.870422i \(-0.663846\pi\)
−0.492307 + 0.870422i \(0.663846\pi\)
\(464\) 0 0
\(465\) −4.03835 −0.187274
\(466\) 0 0
\(467\) −4.80986 −0.222574 −0.111287 0.993788i \(-0.535497\pi\)
−0.111287 + 0.993788i \(0.535497\pi\)
\(468\) 0 0
\(469\) 3.74138 0.172761
\(470\) 0 0
\(471\) 2.14340 0.0987624
\(472\) 0 0
\(473\) −35.2690 −1.62167
\(474\) 0 0
\(475\) 13.0487 0.598714
\(476\) 0 0
\(477\) −34.3229 −1.57154
\(478\) 0 0
\(479\) 10.9505 0.500343 0.250171 0.968202i \(-0.419513\pi\)
0.250171 + 0.968202i \(0.419513\pi\)
\(480\) 0 0
\(481\) −5.91366 −0.269640
\(482\) 0 0
\(483\) 3.23038 0.146987
\(484\) 0 0
\(485\) 1.73049 0.0785774
\(486\) 0 0
\(487\) 23.5051 1.06512 0.532559 0.846393i \(-0.321230\pi\)
0.532559 + 0.846393i \(0.321230\pi\)
\(488\) 0 0
\(489\) 3.14411 0.142182
\(490\) 0 0
\(491\) −12.5450 −0.566147 −0.283073 0.959098i \(-0.591354\pi\)
−0.283073 + 0.959098i \(0.591354\pi\)
\(492\) 0 0
\(493\) 22.8185 1.02769
\(494\) 0 0
\(495\) 41.2651 1.85473
\(496\) 0 0
\(497\) −14.7517 −0.661702
\(498\) 0 0
\(499\) 38.5083 1.72387 0.861935 0.507018i \(-0.169252\pi\)
0.861935 + 0.507018i \(0.169252\pi\)
\(500\) 0 0
\(501\) −5.72653 −0.255842
\(502\) 0 0
\(503\) −7.85492 −0.350234 −0.175117 0.984548i \(-0.556030\pi\)
−0.175117 + 0.984548i \(0.556030\pi\)
\(504\) 0 0
\(505\) 28.8282 1.28284
\(506\) 0 0
\(507\) −3.54068 −0.157247
\(508\) 0 0
\(509\) 6.62572 0.293680 0.146840 0.989160i \(-0.453090\pi\)
0.146840 + 0.989160i \(0.453090\pi\)
\(510\) 0 0
\(511\) 4.27073 0.188926
\(512\) 0 0
\(513\) −1.85543 −0.0819193
\(514\) 0 0
\(515\) 35.1040 1.54687
\(516\) 0 0
\(517\) −12.2361 −0.538144
\(518\) 0 0
\(519\) −4.20451 −0.184557
\(520\) 0 0
\(521\) 20.2589 0.887558 0.443779 0.896136i \(-0.353637\pi\)
0.443779 + 0.896136i \(0.353637\pi\)
\(522\) 0 0
\(523\) −0.726892 −0.0317848 −0.0158924 0.999874i \(-0.505059\pi\)
−0.0158924 + 0.999874i \(0.505059\pi\)
\(524\) 0 0
\(525\) 4.42051 0.192927
\(526\) 0 0
\(527\) −8.32686 −0.362724
\(528\) 0 0
\(529\) 67.9274 2.95337
\(530\) 0 0
\(531\) −31.7925 −1.37968
\(532\) 0 0
\(533\) 3.11743 0.135031
\(534\) 0 0
\(535\) 38.2138 1.65213
\(536\) 0 0
\(537\) 1.55526 0.0671145
\(538\) 0 0
\(539\) −19.5496 −0.842061
\(540\) 0 0
\(541\) −45.0818 −1.93822 −0.969109 0.246635i \(-0.920675\pi\)
−0.969109 + 0.246635i \(0.920675\pi\)
\(542\) 0 0
\(543\) −1.77582 −0.0762078
\(544\) 0 0
\(545\) 0.0470353 0.00201477
\(546\) 0 0
\(547\) −27.8385 −1.19029 −0.595144 0.803619i \(-0.702905\pi\)
−0.595144 + 0.803619i \(0.702905\pi\)
\(548\) 0 0
\(549\) −24.9952 −1.06677
\(550\) 0 0
\(551\) −8.28473 −0.352941
\(552\) 0 0
\(553\) −1.07745 −0.0458179
\(554\) 0 0
\(555\) −5.99021 −0.254270
\(556\) 0 0
\(557\) 11.4888 0.486794 0.243397 0.969927i \(-0.421738\pi\)
0.243397 + 0.969927i \(0.421738\pi\)
\(558\) 0 0
\(559\) 13.8914 0.587545
\(560\) 0 0
\(561\) −2.89941 −0.122413
\(562\) 0 0
\(563\) −17.5198 −0.738373 −0.369186 0.929355i \(-0.620364\pi\)
−0.369186 + 0.929355i \(0.620364\pi\)
\(564\) 0 0
\(565\) 79.8889 3.36095
\(566\) 0 0
\(567\) 8.74894 0.367421
\(568\) 0 0
\(569\) −4.35993 −0.182778 −0.0913888 0.995815i \(-0.529131\pi\)
−0.0913888 + 0.995815i \(0.529131\pi\)
\(570\) 0 0
\(571\) 9.34403 0.391035 0.195518 0.980700i \(-0.437361\pi\)
0.195518 + 0.980700i \(0.437361\pi\)
\(572\) 0 0
\(573\) −5.27346 −0.220302
\(574\) 0 0
\(575\) 124.427 5.18895
\(576\) 0 0
\(577\) −11.8087 −0.491601 −0.245800 0.969320i \(-0.579051\pi\)
−0.245800 + 0.969320i \(0.579051\pi\)
\(578\) 0 0
\(579\) −1.41330 −0.0587349
\(580\) 0 0
\(581\) 7.80414 0.323770
\(582\) 0 0
\(583\) 39.6102 1.64049
\(584\) 0 0
\(585\) −16.2532 −0.671985
\(586\) 0 0
\(587\) 23.8366 0.983841 0.491921 0.870640i \(-0.336295\pi\)
0.491921 + 0.870640i \(0.336295\pi\)
\(588\) 0 0
\(589\) 3.02324 0.124570
\(590\) 0 0
\(591\) −2.91311 −0.119829
\(592\) 0 0
\(593\) 24.2587 0.996184 0.498092 0.867124i \(-0.334034\pi\)
0.498092 + 0.867124i \(0.334034\pi\)
\(594\) 0 0
\(595\) 12.6075 0.516857
\(596\) 0 0
\(597\) 2.68432 0.109862
\(598\) 0 0
\(599\) −8.03658 −0.328366 −0.164183 0.986430i \(-0.552499\pi\)
−0.164183 + 0.986430i \(0.552499\pi\)
\(600\) 0 0
\(601\) −30.8023 −1.25645 −0.628227 0.778030i \(-0.716219\pi\)
−0.628227 + 0.778030i \(0.716219\pi\)
\(602\) 0 0
\(603\) −10.0740 −0.410247
\(604\) 0 0
\(605\) −0.889733 −0.0361728
\(606\) 0 0
\(607\) −38.4188 −1.55937 −0.779686 0.626171i \(-0.784621\pi\)
−0.779686 + 0.626171i \(0.784621\pi\)
\(608\) 0 0
\(609\) −2.80663 −0.113730
\(610\) 0 0
\(611\) 4.81946 0.194974
\(612\) 0 0
\(613\) −26.9096 −1.08687 −0.543435 0.839452i \(-0.682876\pi\)
−0.543435 + 0.839452i \(0.682876\pi\)
\(614\) 0 0
\(615\) 3.15778 0.127334
\(616\) 0 0
\(617\) −25.1907 −1.01414 −0.507070 0.861905i \(-0.669271\pi\)
−0.507070 + 0.861905i \(0.669271\pi\)
\(618\) 0 0
\(619\) 23.4438 0.942287 0.471144 0.882056i \(-0.343841\pi\)
0.471144 + 0.882056i \(0.343841\pi\)
\(620\) 0 0
\(621\) −17.6926 −0.709981
\(622\) 0 0
\(623\) 11.3063 0.452977
\(624\) 0 0
\(625\) 80.0245 3.20098
\(626\) 0 0
\(627\) 1.05269 0.0420404
\(628\) 0 0
\(629\) −12.3515 −0.492486
\(630\) 0 0
\(631\) −40.4119 −1.60877 −0.804387 0.594106i \(-0.797506\pi\)
−0.804387 + 0.594106i \(0.797506\pi\)
\(632\) 0 0
\(633\) −5.41307 −0.215150
\(634\) 0 0
\(635\) 56.1377 2.22776
\(636\) 0 0
\(637\) 7.70003 0.305086
\(638\) 0 0
\(639\) 39.7203 1.57131
\(640\) 0 0
\(641\) 9.82300 0.387985 0.193993 0.981003i \(-0.437856\pi\)
0.193993 + 0.981003i \(0.437856\pi\)
\(642\) 0 0
\(643\) 24.2675 0.957019 0.478509 0.878082i \(-0.341177\pi\)
0.478509 + 0.878082i \(0.341177\pi\)
\(644\) 0 0
\(645\) 14.0713 0.554055
\(646\) 0 0
\(647\) −11.9056 −0.468057 −0.234029 0.972230i \(-0.575191\pi\)
−0.234029 + 0.972230i \(0.575191\pi\)
\(648\) 0 0
\(649\) 36.6900 1.44021
\(650\) 0 0
\(651\) 1.02419 0.0401410
\(652\) 0 0
\(653\) −14.9196 −0.583850 −0.291925 0.956441i \(-0.594296\pi\)
−0.291925 + 0.956441i \(0.594296\pi\)
\(654\) 0 0
\(655\) 32.9602 1.28786
\(656\) 0 0
\(657\) −11.4994 −0.448633
\(658\) 0 0
\(659\) −27.6364 −1.07656 −0.538280 0.842766i \(-0.680926\pi\)
−0.538280 + 0.842766i \(0.680926\pi\)
\(660\) 0 0
\(661\) −1.57098 −0.0611040 −0.0305520 0.999533i \(-0.509727\pi\)
−0.0305520 + 0.999533i \(0.509727\pi\)
\(662\) 0 0
\(663\) 1.14200 0.0443514
\(664\) 0 0
\(665\) −4.57741 −0.177504
\(666\) 0 0
\(667\) −78.9998 −3.05888
\(668\) 0 0
\(669\) 1.26032 0.0487269
\(670\) 0 0
\(671\) 28.8456 1.11357
\(672\) 0 0
\(673\) −4.81563 −0.185629 −0.0928145 0.995683i \(-0.529586\pi\)
−0.0928145 + 0.995683i \(0.529586\pi\)
\(674\) 0 0
\(675\) −24.2109 −0.931879
\(676\) 0 0
\(677\) 42.5024 1.63350 0.816751 0.576991i \(-0.195773\pi\)
0.816751 + 0.576991i \(0.195773\pi\)
\(678\) 0 0
\(679\) −0.438877 −0.0168426
\(680\) 0 0
\(681\) −7.72984 −0.296208
\(682\) 0 0
\(683\) 45.0747 1.72473 0.862367 0.506284i \(-0.168981\pi\)
0.862367 + 0.506284i \(0.168981\pi\)
\(684\) 0 0
\(685\) −2.91171 −0.111251
\(686\) 0 0
\(687\) 6.33302 0.241620
\(688\) 0 0
\(689\) −15.6013 −0.594363
\(690\) 0 0
\(691\) 31.6640 1.20456 0.602278 0.798287i \(-0.294260\pi\)
0.602278 + 0.798287i \(0.294260\pi\)
\(692\) 0 0
\(693\) −10.4654 −0.397550
\(694\) 0 0
\(695\) −62.0775 −2.35473
\(696\) 0 0
\(697\) 6.51117 0.246628
\(698\) 0 0
\(699\) −7.45984 −0.282157
\(700\) 0 0
\(701\) −18.6888 −0.705864 −0.352932 0.935649i \(-0.614815\pi\)
−0.352932 + 0.935649i \(0.614815\pi\)
\(702\) 0 0
\(703\) 4.48446 0.169135
\(704\) 0 0
\(705\) 4.88184 0.183861
\(706\) 0 0
\(707\) −7.31126 −0.274968
\(708\) 0 0
\(709\) −34.1332 −1.28190 −0.640950 0.767582i \(-0.721460\pi\)
−0.640950 + 0.767582i \(0.721460\pi\)
\(710\) 0 0
\(711\) 2.90114 0.108801
\(712\) 0 0
\(713\) 28.8284 1.07963
\(714\) 0 0
\(715\) 18.7569 0.701468
\(716\) 0 0
\(717\) −3.58242 −0.133788
\(718\) 0 0
\(719\) −7.44422 −0.277623 −0.138811 0.990319i \(-0.544328\pi\)
−0.138811 + 0.990319i \(0.544328\pi\)
\(720\) 0 0
\(721\) −8.90289 −0.331561
\(722\) 0 0
\(723\) 4.52232 0.168187
\(724\) 0 0
\(725\) −108.105 −4.01491
\(726\) 0 0
\(727\) 10.8040 0.400697 0.200348 0.979725i \(-0.435793\pi\)
0.200348 + 0.979725i \(0.435793\pi\)
\(728\) 0 0
\(729\) −21.8072 −0.807675
\(730\) 0 0
\(731\) 29.0142 1.07313
\(732\) 0 0
\(733\) −27.4847 −1.01517 −0.507584 0.861602i \(-0.669461\pi\)
−0.507584 + 0.861602i \(0.669461\pi\)
\(734\) 0 0
\(735\) 7.79970 0.287696
\(736\) 0 0
\(737\) 11.6259 0.428246
\(738\) 0 0
\(739\) −42.9692 −1.58065 −0.790324 0.612689i \(-0.790088\pi\)
−0.790324 + 0.612689i \(0.790088\pi\)
\(740\) 0 0
\(741\) −0.414625 −0.0152316
\(742\) 0 0
\(743\) −28.5775 −1.04841 −0.524203 0.851593i \(-0.675637\pi\)
−0.524203 + 0.851593i \(0.675637\pi\)
\(744\) 0 0
\(745\) 35.2373 1.29099
\(746\) 0 0
\(747\) −21.0134 −0.768840
\(748\) 0 0
\(749\) −9.69159 −0.354123
\(750\) 0 0
\(751\) 52.7716 1.92566 0.962831 0.270104i \(-0.0870581\pi\)
0.962831 + 0.270104i \(0.0870581\pi\)
\(752\) 0 0
\(753\) 0.942919 0.0343619
\(754\) 0 0
\(755\) 8.76307 0.318921
\(756\) 0 0
\(757\) 12.3684 0.449539 0.224769 0.974412i \(-0.427837\pi\)
0.224769 + 0.974412i \(0.427837\pi\)
\(758\) 0 0
\(759\) 10.0380 0.364357
\(760\) 0 0
\(761\) −34.9719 −1.26773 −0.633865 0.773443i \(-0.718533\pi\)
−0.633865 + 0.773443i \(0.718533\pi\)
\(762\) 0 0
\(763\) −0.0119288 −0.000431853 0
\(764\) 0 0
\(765\) −33.9469 −1.22735
\(766\) 0 0
\(767\) −14.4511 −0.521801
\(768\) 0 0
\(769\) 31.5572 1.13798 0.568991 0.822344i \(-0.307334\pi\)
0.568991 + 0.822344i \(0.307334\pi\)
\(770\) 0 0
\(771\) −8.89699 −0.320417
\(772\) 0 0
\(773\) −21.0149 −0.755855 −0.377927 0.925835i \(-0.623363\pi\)
−0.377927 + 0.925835i \(0.623363\pi\)
\(774\) 0 0
\(775\) 39.4492 1.41706
\(776\) 0 0
\(777\) 1.51921 0.0545012
\(778\) 0 0
\(779\) −2.36401 −0.0846996
\(780\) 0 0
\(781\) −45.8390 −1.64025
\(782\) 0 0
\(783\) 15.3718 0.549342
\(784\) 0 0
\(785\) −28.9611 −1.03367
\(786\) 0 0
\(787\) 9.73925 0.347167 0.173583 0.984819i \(-0.444465\pi\)
0.173583 + 0.984819i \(0.444465\pi\)
\(788\) 0 0
\(789\) 4.97659 0.177171
\(790\) 0 0
\(791\) −20.2610 −0.720399
\(792\) 0 0
\(793\) −11.3614 −0.403457
\(794\) 0 0
\(795\) −15.8033 −0.560484
\(796\) 0 0
\(797\) −48.5600 −1.72008 −0.860041 0.510225i \(-0.829562\pi\)
−0.860041 + 0.510225i \(0.829562\pi\)
\(798\) 0 0
\(799\) 10.0661 0.356113
\(800\) 0 0
\(801\) −30.4433 −1.07566
\(802\) 0 0
\(803\) 13.2708 0.468316
\(804\) 0 0
\(805\) −43.6483 −1.53840
\(806\) 0 0
\(807\) −0.559128 −0.0196822
\(808\) 0 0
\(809\) −42.3081 −1.48747 −0.743736 0.668473i \(-0.766948\pi\)
−0.743736 + 0.668473i \(0.766948\pi\)
\(810\) 0 0
\(811\) 10.2832 0.361093 0.180546 0.983566i \(-0.442213\pi\)
0.180546 + 0.983566i \(0.442213\pi\)
\(812\) 0 0
\(813\) −7.81026 −0.273918
\(814\) 0 0
\(815\) −42.4826 −1.48810
\(816\) 0 0
\(817\) −10.5342 −0.368544
\(818\) 0 0
\(819\) 4.12204 0.144036
\(820\) 0 0
\(821\) −14.5056 −0.506250 −0.253125 0.967434i \(-0.581458\pi\)
−0.253125 + 0.967434i \(0.581458\pi\)
\(822\) 0 0
\(823\) 42.6451 1.48651 0.743257 0.669006i \(-0.233280\pi\)
0.743257 + 0.669006i \(0.233280\pi\)
\(824\) 0 0
\(825\) 13.7362 0.478234
\(826\) 0 0
\(827\) 27.6660 0.962040 0.481020 0.876710i \(-0.340266\pi\)
0.481020 + 0.876710i \(0.340266\pi\)
\(828\) 0 0
\(829\) 40.1502 1.39447 0.697236 0.716841i \(-0.254413\pi\)
0.697236 + 0.716841i \(0.254413\pi\)
\(830\) 0 0
\(831\) −5.34293 −0.185344
\(832\) 0 0
\(833\) 16.0826 0.557228
\(834\) 0 0
\(835\) 77.3758 2.67770
\(836\) 0 0
\(837\) −5.60941 −0.193890
\(838\) 0 0
\(839\) 6.56916 0.226792 0.113396 0.993550i \(-0.463827\pi\)
0.113396 + 0.993550i \(0.463827\pi\)
\(840\) 0 0
\(841\) 39.6368 1.36679
\(842\) 0 0
\(843\) 4.06015 0.139839
\(844\) 0 0
\(845\) 47.8410 1.64578
\(846\) 0 0
\(847\) 0.225649 0.00775341
\(848\) 0 0
\(849\) 6.71353 0.230408
\(850\) 0 0
\(851\) 42.7620 1.46586
\(852\) 0 0
\(853\) −17.4858 −0.598703 −0.299351 0.954143i \(-0.596770\pi\)
−0.299351 + 0.954143i \(0.596770\pi\)
\(854\) 0 0
\(855\) 12.3251 0.421510
\(856\) 0 0
\(857\) −2.76241 −0.0943620 −0.0471810 0.998886i \(-0.515024\pi\)
−0.0471810 + 0.998886i \(0.515024\pi\)
\(858\) 0 0
\(859\) 5.81499 0.198405 0.0992024 0.995067i \(-0.468371\pi\)
0.0992024 + 0.995067i \(0.468371\pi\)
\(860\) 0 0
\(861\) −0.800860 −0.0272932
\(862\) 0 0
\(863\) 5.42653 0.184721 0.0923607 0.995726i \(-0.470559\pi\)
0.0923607 + 0.995726i \(0.470559\pi\)
\(864\) 0 0
\(865\) 56.8105 1.93162
\(866\) 0 0
\(867\) −2.95991 −0.100524
\(868\) 0 0
\(869\) −3.34805 −0.113575
\(870\) 0 0
\(871\) −4.57911 −0.155157
\(872\) 0 0
\(873\) 1.18172 0.0399951
\(874\) 0 0
\(875\) −36.8421 −1.24549
\(876\) 0 0
\(877\) 29.9751 1.01219 0.506093 0.862479i \(-0.331089\pi\)
0.506093 + 0.862479i \(0.331089\pi\)
\(878\) 0 0
\(879\) 2.85456 0.0962820
\(880\) 0 0
\(881\) 23.1094 0.778574 0.389287 0.921116i \(-0.372721\pi\)
0.389287 + 0.921116i \(0.372721\pi\)
\(882\) 0 0
\(883\) −42.2997 −1.42350 −0.711749 0.702434i \(-0.752097\pi\)
−0.711749 + 0.702434i \(0.752097\pi\)
\(884\) 0 0
\(885\) −14.6382 −0.492058
\(886\) 0 0
\(887\) 31.1128 1.04467 0.522333 0.852742i \(-0.325062\pi\)
0.522333 + 0.852742i \(0.325062\pi\)
\(888\) 0 0
\(889\) −14.2374 −0.477506
\(890\) 0 0
\(891\) 27.1863 0.910775
\(892\) 0 0
\(893\) −3.65470 −0.122300
\(894\) 0 0
\(895\) −21.0144 −0.702434
\(896\) 0 0
\(897\) −3.95369 −0.132010
\(898\) 0 0
\(899\) −25.0467 −0.835355
\(900\) 0 0
\(901\) −32.5855 −1.08558
\(902\) 0 0
\(903\) −3.56868 −0.118758
\(904\) 0 0
\(905\) 23.9946 0.797606
\(906\) 0 0
\(907\) 21.1778 0.703196 0.351598 0.936151i \(-0.385638\pi\)
0.351598 + 0.936151i \(0.385638\pi\)
\(908\) 0 0
\(909\) 19.6863 0.652953
\(910\) 0 0
\(911\) −23.3822 −0.774686 −0.387343 0.921936i \(-0.626607\pi\)
−0.387343 + 0.921936i \(0.626607\pi\)
\(912\) 0 0
\(913\) 24.2504 0.802572
\(914\) 0 0
\(915\) −11.5085 −0.380460
\(916\) 0 0
\(917\) −8.35920 −0.276045
\(918\) 0 0
\(919\) −57.9593 −1.91190 −0.955951 0.293526i \(-0.905171\pi\)
−0.955951 + 0.293526i \(0.905171\pi\)
\(920\) 0 0
\(921\) −1.80769 −0.0595654
\(922\) 0 0
\(923\) 18.0547 0.594277
\(924\) 0 0
\(925\) 58.5162 1.92400
\(926\) 0 0
\(927\) 23.9719 0.787341
\(928\) 0 0
\(929\) −23.2594 −0.763116 −0.381558 0.924345i \(-0.624612\pi\)
−0.381558 + 0.924345i \(0.624612\pi\)
\(930\) 0 0
\(931\) −5.83910 −0.191369
\(932\) 0 0
\(933\) −6.16193 −0.201732
\(934\) 0 0
\(935\) 39.1763 1.28120
\(936\) 0 0
\(937\) −11.6400 −0.380263 −0.190132 0.981759i \(-0.560891\pi\)
−0.190132 + 0.981759i \(0.560891\pi\)
\(938\) 0 0
\(939\) 9.38850 0.306382
\(940\) 0 0
\(941\) −31.2134 −1.01753 −0.508764 0.860906i \(-0.669898\pi\)
−0.508764 + 0.860906i \(0.669898\pi\)
\(942\) 0 0
\(943\) −22.5423 −0.734077
\(944\) 0 0
\(945\) 8.49308 0.276280
\(946\) 0 0
\(947\) 18.5160 0.601688 0.300844 0.953673i \(-0.402732\pi\)
0.300844 + 0.953673i \(0.402732\pi\)
\(948\) 0 0
\(949\) −5.22698 −0.169675
\(950\) 0 0
\(951\) −8.70511 −0.282283
\(952\) 0 0
\(953\) −13.1901 −0.427270 −0.213635 0.976913i \(-0.568530\pi\)
−0.213635 + 0.976913i \(0.568530\pi\)
\(954\) 0 0
\(955\) 71.2540 2.30573
\(956\) 0 0
\(957\) −8.72126 −0.281918
\(958\) 0 0
\(959\) 0.738453 0.0238459
\(960\) 0 0
\(961\) −21.8600 −0.705162
\(962\) 0 0
\(963\) 26.0955 0.840917
\(964\) 0 0
\(965\) 19.0963 0.614732
\(966\) 0 0
\(967\) −20.3247 −0.653599 −0.326800 0.945094i \(-0.605970\pi\)
−0.326800 + 0.945094i \(0.605970\pi\)
\(968\) 0 0
\(969\) −0.866001 −0.0278200
\(970\) 0 0
\(971\) −6.42856 −0.206302 −0.103151 0.994666i \(-0.532893\pi\)
−0.103151 + 0.994666i \(0.532893\pi\)
\(972\) 0 0
\(973\) 15.7438 0.504722
\(974\) 0 0
\(975\) −5.41030 −0.173268
\(976\) 0 0
\(977\) 3.52455 0.112760 0.0563802 0.998409i \(-0.482044\pi\)
0.0563802 + 0.998409i \(0.482044\pi\)
\(978\) 0 0
\(979\) 35.1329 1.12285
\(980\) 0 0
\(981\) 0.0321196 0.00102550
\(982\) 0 0
\(983\) −52.7012 −1.68091 −0.840453 0.541885i \(-0.817711\pi\)
−0.840453 + 0.541885i \(0.817711\pi\)
\(984\) 0 0
\(985\) 39.3613 1.25416
\(986\) 0 0
\(987\) −1.23811 −0.0394094
\(988\) 0 0
\(989\) −100.450 −3.19411
\(990\) 0 0
\(991\) 3.68444 0.117040 0.0585200 0.998286i \(-0.481362\pi\)
0.0585200 + 0.998286i \(0.481362\pi\)
\(992\) 0 0
\(993\) 2.51464 0.0797997
\(994\) 0 0
\(995\) −36.2700 −1.14984
\(996\) 0 0
\(997\) 20.5510 0.650855 0.325428 0.945567i \(-0.394492\pi\)
0.325428 + 0.945567i \(0.394492\pi\)
\(998\) 0 0
\(999\) −8.32061 −0.263253
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 \(a_p\))