Properties

Label 6036.2.a.g.1.9
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 1
Dimension 15
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6036 = 2^{2} \cdot 3 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.19770266\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(0.546893\)
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-0.453107 q^{5}\) \(+2.17063 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-0.453107 q^{5}\) \(+2.17063 q^{7}\) \(+1.00000 q^{9}\) \(-5.35442 q^{11}\) \(+2.71175 q^{13}\) \(-0.453107 q^{15}\) \(+6.07839 q^{17}\) \(-2.86135 q^{19}\) \(+2.17063 q^{21}\) \(-5.42982 q^{23}\) \(-4.79469 q^{25}\) \(+1.00000 q^{27}\) \(-7.45567 q^{29}\) \(-5.78314 q^{31}\) \(-5.35442 q^{33}\) \(-0.983530 q^{35}\) \(+1.10695 q^{37}\) \(+2.71175 q^{39}\) \(-6.10245 q^{41}\) \(+6.08829 q^{43}\) \(-0.453107 q^{45}\) \(-3.32792 q^{47}\) \(-2.28835 q^{49}\) \(+6.07839 q^{51}\) \(-5.31676 q^{53}\) \(+2.42613 q^{55}\) \(-2.86135 q^{57}\) \(+1.97520 q^{59}\) \(-14.0797 q^{61}\) \(+2.17063 q^{63}\) \(-1.22872 q^{65}\) \(+3.24688 q^{67}\) \(-5.42982 q^{69}\) \(+3.70398 q^{71}\) \(+2.73959 q^{73}\) \(-4.79469 q^{75}\) \(-11.6225 q^{77}\) \(+2.25178 q^{79}\) \(+1.00000 q^{81}\) \(+0.0721083 q^{83}\) \(-2.75416 q^{85}\) \(-7.45567 q^{87}\) \(-9.49320 q^{89}\) \(+5.88622 q^{91}\) \(-5.78314 q^{93}\) \(+1.29650 q^{95}\) \(-2.29553 q^{97}\) \(-5.35442 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(15q \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(15q \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut +\mathstrut 3q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 32q^{23} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut +\mathstrut 15q^{27} \) \(\mathstrut -\mathstrut 23q^{29} \) \(\mathstrut -\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 5q^{33} \) \(\mathstrut -\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 11q^{45} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 9q^{49} \) \(\mathstrut -\mathstrut 5q^{51} \) \(\mathstrut -\mathstrut 30q^{53} \) \(\mathstrut -\mathstrut 10q^{55} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut -\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut -\mathstrut 32q^{69} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 19q^{73} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut -\mathstrut 39q^{77} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut +\mathstrut 15q^{81} \) \(\mathstrut -\mathstrut 17q^{83} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 23q^{87} \) \(\mathstrut -\mathstrut 23q^{89} \) \(\mathstrut +\mathstrut 4q^{91} \) \(\mathstrut -\mathstrut 13q^{93} \) \(\mathstrut -\mathstrut 30q^{95} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(4\) 0 0
\(5\) −0.453107 −0.202636 −0.101318 0.994854i \(-0.532306\pi\)
−0.101318 + 0.994854i \(0.532306\pi\)
\(6\) 0 0
\(7\) 2.17063 0.820422 0.410211 0.911991i \(-0.365455\pi\)
0.410211 + 0.911991i \(0.365455\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −5.35442 −1.61442 −0.807209 0.590266i \(-0.799023\pi\)
−0.807209 + 0.590266i \(0.799023\pi\)
\(12\) 0 0
\(13\) 2.71175 0.752105 0.376052 0.926598i \(-0.377281\pi\)
0.376052 + 0.926598i \(0.377281\pi\)
\(14\) 0 0
\(15\) −0.453107 −0.116992
\(16\) 0 0
\(17\) 6.07839 1.47423 0.737113 0.675770i \(-0.236189\pi\)
0.737113 + 0.675770i \(0.236189\pi\)
\(18\) 0 0
\(19\) −2.86135 −0.656439 −0.328220 0.944601i \(-0.606449\pi\)
−0.328220 + 0.944601i \(0.606449\pi\)
\(20\) 0 0
\(21\) 2.17063 0.473671
\(22\) 0 0
\(23\) −5.42982 −1.13220 −0.566098 0.824338i \(-0.691547\pi\)
−0.566098 + 0.824338i \(0.691547\pi\)
\(24\) 0 0
\(25\) −4.79469 −0.958939
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −7.45567 −1.38448 −0.692242 0.721666i \(-0.743377\pi\)
−0.692242 + 0.721666i \(0.743377\pi\)
\(30\) 0 0
\(31\) −5.78314 −1.03868 −0.519341 0.854567i \(-0.673823\pi\)
−0.519341 + 0.854567i \(0.673823\pi\)
\(32\) 0 0
\(33\) −5.35442 −0.932084
\(34\) 0 0
\(35\) −0.983530 −0.166247
\(36\) 0 0
\(37\) 1.10695 0.181981 0.0909907 0.995852i \(-0.470997\pi\)
0.0909907 + 0.995852i \(0.470997\pi\)
\(38\) 0 0
\(39\) 2.71175 0.434228
\(40\) 0 0
\(41\) −6.10245 −0.953043 −0.476521 0.879163i \(-0.658103\pi\)
−0.476521 + 0.879163i \(0.658103\pi\)
\(42\) 0 0
\(43\) 6.08829 0.928456 0.464228 0.885716i \(-0.346332\pi\)
0.464228 + 0.885716i \(0.346332\pi\)
\(44\) 0 0
\(45\) −0.453107 −0.0675453
\(46\) 0 0
\(47\) −3.32792 −0.485428 −0.242714 0.970098i \(-0.578038\pi\)
−0.242714 + 0.970098i \(0.578038\pi\)
\(48\) 0 0
\(49\) −2.28835 −0.326907
\(50\) 0 0
\(51\) 6.07839 0.851145
\(52\) 0 0
\(53\) −5.31676 −0.730313 −0.365157 0.930946i \(-0.618985\pi\)
−0.365157 + 0.930946i \(0.618985\pi\)
\(54\) 0 0
\(55\) 2.42613 0.327139
\(56\) 0 0
\(57\) −2.86135 −0.378995
\(58\) 0 0
\(59\) 1.97520 0.257150 0.128575 0.991700i \(-0.458960\pi\)
0.128575 + 0.991700i \(0.458960\pi\)
\(60\) 0 0
\(61\) −14.0797 −1.80272 −0.901360 0.433071i \(-0.857430\pi\)
−0.901360 + 0.433071i \(0.857430\pi\)
\(62\) 0 0
\(63\) 2.17063 0.273474
\(64\) 0 0
\(65\) −1.22872 −0.152403
\(66\) 0 0
\(67\) 3.24688 0.396670 0.198335 0.980134i \(-0.436447\pi\)
0.198335 + 0.980134i \(0.436447\pi\)
\(68\) 0 0
\(69\) −5.42982 −0.653673
\(70\) 0 0
\(71\) 3.70398 0.439581 0.219791 0.975547i \(-0.429463\pi\)
0.219791 + 0.975547i \(0.429463\pi\)
\(72\) 0 0
\(73\) 2.73959 0.320645 0.160322 0.987065i \(-0.448747\pi\)
0.160322 + 0.987065i \(0.448747\pi\)
\(74\) 0 0
\(75\) −4.79469 −0.553644
\(76\) 0 0
\(77\) −11.6225 −1.32450
\(78\) 0 0
\(79\) 2.25178 0.253345 0.126673 0.991945i \(-0.459570\pi\)
0.126673 + 0.991945i \(0.459570\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 0.0721083 0.00791492 0.00395746 0.999992i \(-0.498740\pi\)
0.00395746 + 0.999992i \(0.498740\pi\)
\(84\) 0 0
\(85\) −2.75416 −0.298731
\(86\) 0 0
\(87\) −7.45567 −0.799332
\(88\) 0 0
\(89\) −9.49320 −1.00628 −0.503139 0.864206i \(-0.667821\pi\)
−0.503139 + 0.864206i \(0.667821\pi\)
\(90\) 0 0
\(91\) 5.88622 0.617044
\(92\) 0 0
\(93\) −5.78314 −0.599683
\(94\) 0 0
\(95\) 1.29650 0.133018
\(96\) 0 0
\(97\) −2.29553 −0.233076 −0.116538 0.993186i \(-0.537180\pi\)
−0.116538 + 0.993186i \(0.537180\pi\)
\(98\) 0 0
\(99\) −5.35442 −0.538139
\(100\) 0 0
\(101\) 3.49019 0.347286 0.173643 0.984809i \(-0.444446\pi\)
0.173643 + 0.984809i \(0.444446\pi\)
\(102\) 0 0
\(103\) 14.8256 1.46081 0.730404 0.683016i \(-0.239332\pi\)
0.730404 + 0.683016i \(0.239332\pi\)
\(104\) 0 0
\(105\) −0.983530 −0.0959827
\(106\) 0 0
\(107\) 14.2199 1.37469 0.687345 0.726331i \(-0.258776\pi\)
0.687345 + 0.726331i \(0.258776\pi\)
\(108\) 0 0
\(109\) 15.1497 1.45108 0.725541 0.688179i \(-0.241590\pi\)
0.725541 + 0.688179i \(0.241590\pi\)
\(110\) 0 0
\(111\) 1.10695 0.105067
\(112\) 0 0
\(113\) −14.1496 −1.33108 −0.665540 0.746363i \(-0.731799\pi\)
−0.665540 + 0.746363i \(0.731799\pi\)
\(114\) 0 0
\(115\) 2.46029 0.229423
\(116\) 0 0
\(117\) 2.71175 0.250702
\(118\) 0 0
\(119\) 13.1940 1.20949
\(120\) 0 0
\(121\) 17.6698 1.60634
\(122\) 0 0
\(123\) −6.10245 −0.550240
\(124\) 0 0
\(125\) 4.43805 0.396951
\(126\) 0 0
\(127\) −17.1939 −1.52571 −0.762857 0.646568i \(-0.776204\pi\)
−0.762857 + 0.646568i \(0.776204\pi\)
\(128\) 0 0
\(129\) 6.08829 0.536044
\(130\) 0 0
\(131\) 9.99301 0.873093 0.436547 0.899682i \(-0.356201\pi\)
0.436547 + 0.899682i \(0.356201\pi\)
\(132\) 0 0
\(133\) −6.21095 −0.538557
\(134\) 0 0
\(135\) −0.453107 −0.0389973
\(136\) 0 0
\(137\) −23.0873 −1.97248 −0.986239 0.165328i \(-0.947132\pi\)
−0.986239 + 0.165328i \(0.947132\pi\)
\(138\) 0 0
\(139\) −6.63055 −0.562396 −0.281198 0.959650i \(-0.590732\pi\)
−0.281198 + 0.959650i \(0.590732\pi\)
\(140\) 0 0
\(141\) −3.32792 −0.280262
\(142\) 0 0
\(143\) −14.5199 −1.21421
\(144\) 0 0
\(145\) 3.37822 0.280546
\(146\) 0 0
\(147\) −2.28835 −0.188740
\(148\) 0 0
\(149\) −13.9556 −1.14328 −0.571642 0.820503i \(-0.693693\pi\)
−0.571642 + 0.820503i \(0.693693\pi\)
\(150\) 0 0
\(151\) −1.16809 −0.0950575 −0.0475287 0.998870i \(-0.515135\pi\)
−0.0475287 + 0.998870i \(0.515135\pi\)
\(152\) 0 0
\(153\) 6.07839 0.491409
\(154\) 0 0
\(155\) 2.62038 0.210474
\(156\) 0 0
\(157\) −7.29448 −0.582163 −0.291081 0.956698i \(-0.594015\pi\)
−0.291081 + 0.956698i \(0.594015\pi\)
\(158\) 0 0
\(159\) −5.31676 −0.421647
\(160\) 0 0
\(161\) −11.7861 −0.928878
\(162\) 0 0
\(163\) 10.0146 0.784407 0.392203 0.919879i \(-0.371713\pi\)
0.392203 + 0.919879i \(0.371713\pi\)
\(164\) 0 0
\(165\) 2.42613 0.188874
\(166\) 0 0
\(167\) 12.8988 0.998137 0.499069 0.866562i \(-0.333676\pi\)
0.499069 + 0.866562i \(0.333676\pi\)
\(168\) 0 0
\(169\) −5.64640 −0.434338
\(170\) 0 0
\(171\) −2.86135 −0.218813
\(172\) 0 0
\(173\) −11.0976 −0.843737 −0.421868 0.906657i \(-0.638626\pi\)
−0.421868 + 0.906657i \(0.638626\pi\)
\(174\) 0 0
\(175\) −10.4075 −0.786735
\(176\) 0 0
\(177\) 1.97520 0.148465
\(178\) 0 0
\(179\) −19.9102 −1.48816 −0.744081 0.668090i \(-0.767112\pi\)
−0.744081 + 0.668090i \(0.767112\pi\)
\(180\) 0 0
\(181\) 13.2772 0.986884 0.493442 0.869779i \(-0.335739\pi\)
0.493442 + 0.869779i \(0.335739\pi\)
\(182\) 0 0
\(183\) −14.0797 −1.04080
\(184\) 0 0
\(185\) −0.501567 −0.0368760
\(186\) 0 0
\(187\) −32.5462 −2.38002
\(188\) 0 0
\(189\) 2.17063 0.157890
\(190\) 0 0
\(191\) −9.57891 −0.693105 −0.346553 0.938031i \(-0.612648\pi\)
−0.346553 + 0.938031i \(0.612648\pi\)
\(192\) 0 0
\(193\) −2.29142 −0.164940 −0.0824701 0.996594i \(-0.526281\pi\)
−0.0824701 + 0.996594i \(0.526281\pi\)
\(194\) 0 0
\(195\) −1.22872 −0.0879901
\(196\) 0 0
\(197\) −8.32164 −0.592893 −0.296446 0.955050i \(-0.595802\pi\)
−0.296446 + 0.955050i \(0.595802\pi\)
\(198\) 0 0
\(199\) 24.0433 1.70439 0.852193 0.523227i \(-0.175272\pi\)
0.852193 + 0.523227i \(0.175272\pi\)
\(200\) 0 0
\(201\) 3.24688 0.229017
\(202\) 0 0
\(203\) −16.1835 −1.13586
\(204\) 0 0
\(205\) 2.76507 0.193121
\(206\) 0 0
\(207\) −5.42982 −0.377398
\(208\) 0 0
\(209\) 15.3209 1.05977
\(210\) 0 0
\(211\) 19.3329 1.33093 0.665466 0.746428i \(-0.268233\pi\)
0.665466 + 0.746428i \(0.268233\pi\)
\(212\) 0 0
\(213\) 3.70398 0.253792
\(214\) 0 0
\(215\) −2.75865 −0.188138
\(216\) 0 0
\(217\) −12.5531 −0.852158
\(218\) 0 0
\(219\) 2.73959 0.185124
\(220\) 0 0
\(221\) 16.4831 1.10877
\(222\) 0 0
\(223\) −7.11843 −0.476686 −0.238343 0.971181i \(-0.576604\pi\)
−0.238343 + 0.971181i \(0.576604\pi\)
\(224\) 0 0
\(225\) −4.79469 −0.319646
\(226\) 0 0
\(227\) −8.15200 −0.541068 −0.270534 0.962710i \(-0.587200\pi\)
−0.270534 + 0.962710i \(0.587200\pi\)
\(228\) 0 0
\(229\) −3.40020 −0.224692 −0.112346 0.993669i \(-0.535836\pi\)
−0.112346 + 0.993669i \(0.535836\pi\)
\(230\) 0 0
\(231\) −11.6225 −0.764703
\(232\) 0 0
\(233\) −1.36410 −0.0893651 −0.0446825 0.999001i \(-0.514228\pi\)
−0.0446825 + 0.999001i \(0.514228\pi\)
\(234\) 0 0
\(235\) 1.50791 0.0983650
\(236\) 0 0
\(237\) 2.25178 0.146269
\(238\) 0 0
\(239\) −10.6613 −0.689621 −0.344811 0.938672i \(-0.612057\pi\)
−0.344811 + 0.938672i \(0.612057\pi\)
\(240\) 0 0
\(241\) −2.96872 −0.191232 −0.0956160 0.995418i \(-0.530482\pi\)
−0.0956160 + 0.995418i \(0.530482\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 1.03687 0.0662431
\(246\) 0 0
\(247\) −7.75928 −0.493711
\(248\) 0 0
\(249\) 0.0721083 0.00456968
\(250\) 0 0
\(251\) −0.703338 −0.0443943 −0.0221971 0.999754i \(-0.507066\pi\)
−0.0221971 + 0.999754i \(0.507066\pi\)
\(252\) 0 0
\(253\) 29.0735 1.82784
\(254\) 0 0
\(255\) −2.75416 −0.172472
\(256\) 0 0
\(257\) −10.4602 −0.652487 −0.326243 0.945286i \(-0.605783\pi\)
−0.326243 + 0.945286i \(0.605783\pi\)
\(258\) 0 0
\(259\) 2.40278 0.149302
\(260\) 0 0
\(261\) −7.45567 −0.461495
\(262\) 0 0
\(263\) −12.1467 −0.748996 −0.374498 0.927228i \(-0.622185\pi\)
−0.374498 + 0.927228i \(0.622185\pi\)
\(264\) 0 0
\(265\) 2.40906 0.147988
\(266\) 0 0
\(267\) −9.49320 −0.580974
\(268\) 0 0
\(269\) −0.974897 −0.0594405 −0.0297203 0.999558i \(-0.509462\pi\)
−0.0297203 + 0.999558i \(0.509462\pi\)
\(270\) 0 0
\(271\) 9.06798 0.550841 0.275420 0.961324i \(-0.411183\pi\)
0.275420 + 0.961324i \(0.411183\pi\)
\(272\) 0 0
\(273\) 5.88622 0.356250
\(274\) 0 0
\(275\) 25.6728 1.54813
\(276\) 0 0
\(277\) −14.5217 −0.872526 −0.436263 0.899819i \(-0.643698\pi\)
−0.436263 + 0.899819i \(0.643698\pi\)
\(278\) 0 0
\(279\) −5.78314 −0.346227
\(280\) 0 0
\(281\) 0.623745 0.0372095 0.0186048 0.999827i \(-0.494078\pi\)
0.0186048 + 0.999827i \(0.494078\pi\)
\(282\) 0 0
\(283\) −25.1834 −1.49700 −0.748498 0.663137i \(-0.769225\pi\)
−0.748498 + 0.663137i \(0.769225\pi\)
\(284\) 0 0
\(285\) 1.29650 0.0767980
\(286\) 0 0
\(287\) −13.2462 −0.781897
\(288\) 0 0
\(289\) 19.9468 1.17334
\(290\) 0 0
\(291\) −2.29553 −0.134567
\(292\) 0 0
\(293\) 4.37810 0.255772 0.127886 0.991789i \(-0.459181\pi\)
0.127886 + 0.991789i \(0.459181\pi\)
\(294\) 0 0
\(295\) −0.894980 −0.0521077
\(296\) 0 0
\(297\) −5.35442 −0.310695
\(298\) 0 0
\(299\) −14.7243 −0.851529
\(300\) 0 0
\(301\) 13.2155 0.761726
\(302\) 0 0
\(303\) 3.49019 0.200506
\(304\) 0 0
\(305\) 6.37961 0.365295
\(306\) 0 0
\(307\) 3.46257 0.197619 0.0988096 0.995106i \(-0.468497\pi\)
0.0988096 + 0.995106i \(0.468497\pi\)
\(308\) 0 0
\(309\) 14.8256 0.843398
\(310\) 0 0
\(311\) 6.24430 0.354082 0.177041 0.984203i \(-0.443347\pi\)
0.177041 + 0.984203i \(0.443347\pi\)
\(312\) 0 0
\(313\) 15.9415 0.901066 0.450533 0.892760i \(-0.351234\pi\)
0.450533 + 0.892760i \(0.351234\pi\)
\(314\) 0 0
\(315\) −0.983530 −0.0554156
\(316\) 0 0
\(317\) 11.5258 0.647353 0.323677 0.946168i \(-0.395081\pi\)
0.323677 + 0.946168i \(0.395081\pi\)
\(318\) 0 0
\(319\) 39.9208 2.23513
\(320\) 0 0
\(321\) 14.2199 0.793678
\(322\) 0 0
\(323\) −17.3924 −0.967739
\(324\) 0 0
\(325\) −13.0020 −0.721222
\(326\) 0 0
\(327\) 15.1497 0.837782
\(328\) 0 0
\(329\) −7.22370 −0.398256
\(330\) 0 0
\(331\) 20.7940 1.14294 0.571471 0.820622i \(-0.306373\pi\)
0.571471 + 0.820622i \(0.306373\pi\)
\(332\) 0 0
\(333\) 1.10695 0.0606605
\(334\) 0 0
\(335\) −1.47119 −0.0803795
\(336\) 0 0
\(337\) −8.98189 −0.489275 −0.244637 0.969615i \(-0.578669\pi\)
−0.244637 + 0.969615i \(0.578669\pi\)
\(338\) 0 0
\(339\) −14.1496 −0.768499
\(340\) 0 0
\(341\) 30.9653 1.67687
\(342\) 0 0
\(343\) −20.1616 −1.08862
\(344\) 0 0
\(345\) 2.46029 0.132458
\(346\) 0 0
\(347\) 10.2501 0.550256 0.275128 0.961408i \(-0.411280\pi\)
0.275128 + 0.961408i \(0.411280\pi\)
\(348\) 0 0
\(349\) −2.62046 −0.140270 −0.0701351 0.997538i \(-0.522343\pi\)
−0.0701351 + 0.997538i \(0.522343\pi\)
\(350\) 0 0
\(351\) 2.71175 0.144743
\(352\) 0 0
\(353\) 30.2356 1.60928 0.804640 0.593763i \(-0.202358\pi\)
0.804640 + 0.593763i \(0.202358\pi\)
\(354\) 0 0
\(355\) −1.67830 −0.0890749
\(356\) 0 0
\(357\) 13.1940 0.698298
\(358\) 0 0
\(359\) −2.60842 −0.137667 −0.0688336 0.997628i \(-0.521928\pi\)
−0.0688336 + 0.997628i \(0.521928\pi\)
\(360\) 0 0
\(361\) −10.8127 −0.569088
\(362\) 0 0
\(363\) 17.6698 0.927423
\(364\) 0 0
\(365\) −1.24133 −0.0649741
\(366\) 0 0
\(367\) −12.4100 −0.647798 −0.323899 0.946092i \(-0.604994\pi\)
−0.323899 + 0.946092i \(0.604994\pi\)
\(368\) 0 0
\(369\) −6.10245 −0.317681
\(370\) 0 0
\(371\) −11.5407 −0.599165
\(372\) 0 0
\(373\) −33.2918 −1.72378 −0.861892 0.507091i \(-0.830721\pi\)
−0.861892 + 0.507091i \(0.830721\pi\)
\(374\) 0 0
\(375\) 4.43805 0.229180
\(376\) 0 0
\(377\) −20.2179 −1.04128
\(378\) 0 0
\(379\) −5.23029 −0.268662 −0.134331 0.990937i \(-0.542889\pi\)
−0.134331 + 0.990937i \(0.542889\pi\)
\(380\) 0 0
\(381\) −17.1939 −0.880871
\(382\) 0 0
\(383\) 25.1088 1.28300 0.641501 0.767123i \(-0.278312\pi\)
0.641501 + 0.767123i \(0.278312\pi\)
\(384\) 0 0
\(385\) 5.26623 0.268392
\(386\) 0 0
\(387\) 6.08829 0.309485
\(388\) 0 0
\(389\) 4.58702 0.232571 0.116286 0.993216i \(-0.462901\pi\)
0.116286 + 0.993216i \(0.462901\pi\)
\(390\) 0 0
\(391\) −33.0045 −1.66911
\(392\) 0 0
\(393\) 9.99301 0.504081
\(394\) 0 0
\(395\) −1.02030 −0.0513368
\(396\) 0 0
\(397\) 22.0046 1.10438 0.552189 0.833719i \(-0.313793\pi\)
0.552189 + 0.833719i \(0.313793\pi\)
\(398\) 0 0
\(399\) −6.21095 −0.310936
\(400\) 0 0
\(401\) −37.9076 −1.89302 −0.946508 0.322680i \(-0.895416\pi\)
−0.946508 + 0.322680i \(0.895416\pi\)
\(402\) 0 0
\(403\) −15.6824 −0.781198
\(404\) 0 0
\(405\) −0.453107 −0.0225151
\(406\) 0 0
\(407\) −5.92707 −0.293794
\(408\) 0 0
\(409\) −23.8490 −1.17926 −0.589629 0.807674i \(-0.700726\pi\)
−0.589629 + 0.807674i \(0.700726\pi\)
\(410\) 0 0
\(411\) −23.0873 −1.13881
\(412\) 0 0
\(413\) 4.28744 0.210971
\(414\) 0 0
\(415\) −0.0326728 −0.00160384
\(416\) 0 0
\(417\) −6.63055 −0.324699
\(418\) 0 0
\(419\) −4.22924 −0.206612 −0.103306 0.994650i \(-0.532942\pi\)
−0.103306 + 0.994650i \(0.532942\pi\)
\(420\) 0 0
\(421\) 16.8136 0.819447 0.409723 0.912210i \(-0.365625\pi\)
0.409723 + 0.912210i \(0.365625\pi\)
\(422\) 0 0
\(423\) −3.32792 −0.161809
\(424\) 0 0
\(425\) −29.1440 −1.41369
\(426\) 0 0
\(427\) −30.5618 −1.47899
\(428\) 0 0
\(429\) −14.5199 −0.701025
\(430\) 0 0
\(431\) 20.0376 0.965178 0.482589 0.875847i \(-0.339697\pi\)
0.482589 + 0.875847i \(0.339697\pi\)
\(432\) 0 0
\(433\) 14.9602 0.718942 0.359471 0.933156i \(-0.382957\pi\)
0.359471 + 0.933156i \(0.382957\pi\)
\(434\) 0 0
\(435\) 3.37822 0.161973
\(436\) 0 0
\(437\) 15.5366 0.743217
\(438\) 0 0
\(439\) −32.5369 −1.55290 −0.776452 0.630177i \(-0.782982\pi\)
−0.776452 + 0.630177i \(0.782982\pi\)
\(440\) 0 0
\(441\) −2.28835 −0.108969
\(442\) 0 0
\(443\) 18.7623 0.891425 0.445713 0.895176i \(-0.352950\pi\)
0.445713 + 0.895176i \(0.352950\pi\)
\(444\) 0 0
\(445\) 4.30144 0.203908
\(446\) 0 0
\(447\) −13.9556 −0.660075
\(448\) 0 0
\(449\) 18.3823 0.867514 0.433757 0.901030i \(-0.357188\pi\)
0.433757 + 0.901030i \(0.357188\pi\)
\(450\) 0 0
\(451\) 32.6751 1.53861
\(452\) 0 0
\(453\) −1.16809 −0.0548815
\(454\) 0 0
\(455\) −2.66709 −0.125035
\(456\) 0 0
\(457\) −19.0186 −0.889653 −0.444826 0.895617i \(-0.646735\pi\)
−0.444826 + 0.895617i \(0.646735\pi\)
\(458\) 0 0
\(459\) 6.07839 0.283715
\(460\) 0 0
\(461\) 29.6257 1.37980 0.689902 0.723902i \(-0.257653\pi\)
0.689902 + 0.723902i \(0.257653\pi\)
\(462\) 0 0
\(463\) −0.0705096 −0.00327686 −0.00163843 0.999999i \(-0.500522\pi\)
−0.00163843 + 0.999999i \(0.500522\pi\)
\(464\) 0 0
\(465\) 2.62038 0.121517
\(466\) 0 0
\(467\) 9.88942 0.457628 0.228814 0.973470i \(-0.426515\pi\)
0.228814 + 0.973470i \(0.426515\pi\)
\(468\) 0 0
\(469\) 7.04779 0.325437
\(470\) 0 0
\(471\) −7.29448 −0.336112
\(472\) 0 0
\(473\) −32.5993 −1.49892
\(474\) 0 0
\(475\) 13.7193 0.629485
\(476\) 0 0
\(477\) −5.31676 −0.243438
\(478\) 0 0
\(479\) −29.8615 −1.36441 −0.682203 0.731162i \(-0.738978\pi\)
−0.682203 + 0.731162i \(0.738978\pi\)
\(480\) 0 0
\(481\) 3.00177 0.136869
\(482\) 0 0
\(483\) −11.7861 −0.536288
\(484\) 0 0
\(485\) 1.04012 0.0472296
\(486\) 0 0
\(487\) −5.45499 −0.247189 −0.123595 0.992333i \(-0.539442\pi\)
−0.123595 + 0.992333i \(0.539442\pi\)
\(488\) 0 0
\(489\) 10.0146 0.452877
\(490\) 0 0
\(491\) 21.0330 0.949207 0.474604 0.880200i \(-0.342591\pi\)
0.474604 + 0.880200i \(0.342591\pi\)
\(492\) 0 0
\(493\) −45.3185 −2.04104
\(494\) 0 0
\(495\) 2.42613 0.109046
\(496\) 0 0
\(497\) 8.03998 0.360642
\(498\) 0 0
\(499\) −12.1234 −0.542720 −0.271360 0.962478i \(-0.587473\pi\)
−0.271360 + 0.962478i \(0.587473\pi\)
\(500\) 0 0
\(501\) 12.8988 0.576275
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −1.58143 −0.0703727
\(506\) 0 0
\(507\) −5.64640 −0.250765
\(508\) 0 0
\(509\) 13.8830 0.615355 0.307677 0.951491i \(-0.400448\pi\)
0.307677 + 0.951491i \(0.400448\pi\)
\(510\) 0 0
\(511\) 5.94664 0.263064
\(512\) 0 0
\(513\) −2.86135 −0.126332
\(514\) 0 0
\(515\) −6.71758 −0.296012
\(516\) 0 0
\(517\) 17.8191 0.783683
\(518\) 0 0
\(519\) −11.0976 −0.487132
\(520\) 0 0
\(521\) −26.5791 −1.16445 −0.582226 0.813027i \(-0.697818\pi\)
−0.582226 + 0.813027i \(0.697818\pi\)
\(522\) 0 0
\(523\) −9.81327 −0.429104 −0.214552 0.976713i \(-0.568829\pi\)
−0.214552 + 0.976713i \(0.568829\pi\)
\(524\) 0 0
\(525\) −10.4075 −0.454221
\(526\) 0 0
\(527\) −35.1521 −1.53125
\(528\) 0 0
\(529\) 6.48292 0.281866
\(530\) 0 0
\(531\) 1.97520 0.0857166
\(532\) 0 0
\(533\) −16.5483 −0.716788
\(534\) 0 0
\(535\) −6.44315 −0.278561
\(536\) 0 0
\(537\) −19.9102 −0.859190
\(538\) 0 0
\(539\) 12.2528 0.527765
\(540\) 0 0
\(541\) 0.490807 0.0211015 0.0105507 0.999944i \(-0.496642\pi\)
0.0105507 + 0.999944i \(0.496642\pi\)
\(542\) 0 0
\(543\) 13.2772 0.569778
\(544\) 0 0
\(545\) −6.86446 −0.294041
\(546\) 0 0
\(547\) −42.3002 −1.80863 −0.904314 0.426868i \(-0.859617\pi\)
−0.904314 + 0.426868i \(0.859617\pi\)
\(548\) 0 0
\(549\) −14.0797 −0.600906
\(550\) 0 0
\(551\) 21.3333 0.908829
\(552\) 0 0
\(553\) 4.88779 0.207850
\(554\) 0 0
\(555\) −0.501567 −0.0212903
\(556\) 0 0
\(557\) −13.6538 −0.578531 −0.289265 0.957249i \(-0.593411\pi\)
−0.289265 + 0.957249i \(0.593411\pi\)
\(558\) 0 0
\(559\) 16.5099 0.698296
\(560\) 0 0
\(561\) −32.5462 −1.37410
\(562\) 0 0
\(563\) 31.3148 1.31976 0.659881 0.751370i \(-0.270606\pi\)
0.659881 + 0.751370i \(0.270606\pi\)
\(564\) 0 0
\(565\) 6.41127 0.269724
\(566\) 0 0
\(567\) 2.17063 0.0911580
\(568\) 0 0
\(569\) 22.0677 0.925127 0.462563 0.886586i \(-0.346930\pi\)
0.462563 + 0.886586i \(0.346930\pi\)
\(570\) 0 0
\(571\) 36.6681 1.53451 0.767257 0.641340i \(-0.221621\pi\)
0.767257 + 0.641340i \(0.221621\pi\)
\(572\) 0 0
\(573\) −9.57891 −0.400165
\(574\) 0 0
\(575\) 26.0343 1.08571
\(576\) 0 0
\(577\) 31.2547 1.30115 0.650575 0.759442i \(-0.274528\pi\)
0.650575 + 0.759442i \(0.274528\pi\)
\(578\) 0 0
\(579\) −2.29142 −0.0952282
\(580\) 0 0
\(581\) 0.156521 0.00649357
\(582\) 0 0
\(583\) 28.4682 1.17903
\(584\) 0 0
\(585\) −1.22872 −0.0508011
\(586\) 0 0
\(587\) 18.1818 0.750442 0.375221 0.926935i \(-0.377567\pi\)
0.375221 + 0.926935i \(0.377567\pi\)
\(588\) 0 0
\(589\) 16.5476 0.681831
\(590\) 0 0
\(591\) −8.32164 −0.342307
\(592\) 0 0
\(593\) −37.4236 −1.53680 −0.768402 0.639968i \(-0.778948\pi\)
−0.768402 + 0.639968i \(0.778948\pi\)
\(594\) 0 0
\(595\) −5.97828 −0.245085
\(596\) 0 0
\(597\) 24.0433 0.984028
\(598\) 0 0
\(599\) −20.5507 −0.839678 −0.419839 0.907599i \(-0.637914\pi\)
−0.419839 + 0.907599i \(0.637914\pi\)
\(600\) 0 0
\(601\) 3.59515 0.146649 0.0733247 0.997308i \(-0.476639\pi\)
0.0733247 + 0.997308i \(0.476639\pi\)
\(602\) 0 0
\(603\) 3.24688 0.132223
\(604\) 0 0
\(605\) −8.00631 −0.325503
\(606\) 0 0
\(607\) 4.24278 0.172209 0.0861046 0.996286i \(-0.472558\pi\)
0.0861046 + 0.996286i \(0.472558\pi\)
\(608\) 0 0
\(609\) −16.1835 −0.655790
\(610\) 0 0
\(611\) −9.02451 −0.365092
\(612\) 0 0
\(613\) −26.3003 −1.06226 −0.531130 0.847290i \(-0.678232\pi\)
−0.531130 + 0.847290i \(0.678232\pi\)
\(614\) 0 0
\(615\) 2.76507 0.111498
\(616\) 0 0
\(617\) −18.1905 −0.732322 −0.366161 0.930552i \(-0.619328\pi\)
−0.366161 + 0.930552i \(0.619328\pi\)
\(618\) 0 0
\(619\) 1.89833 0.0763004 0.0381502 0.999272i \(-0.487853\pi\)
0.0381502 + 0.999272i \(0.487853\pi\)
\(620\) 0 0
\(621\) −5.42982 −0.217891
\(622\) 0 0
\(623\) −20.6063 −0.825572
\(624\) 0 0
\(625\) 21.9626 0.878502
\(626\) 0 0
\(627\) 15.3209 0.611857
\(628\) 0 0
\(629\) 6.72847 0.268282
\(630\) 0 0
\(631\) 4.86232 0.193566 0.0967829 0.995306i \(-0.469145\pi\)
0.0967829 + 0.995306i \(0.469145\pi\)
\(632\) 0 0
\(633\) 19.3329 0.768414
\(634\) 0 0
\(635\) 7.79069 0.309164
\(636\) 0 0
\(637\) −6.20544 −0.245869
\(638\) 0 0
\(639\) 3.70398 0.146527
\(640\) 0 0
\(641\) −32.1797 −1.27102 −0.635512 0.772091i \(-0.719211\pi\)
−0.635512 + 0.772091i \(0.719211\pi\)
\(642\) 0 0
\(643\) 20.0389 0.790255 0.395128 0.918626i \(-0.370700\pi\)
0.395128 + 0.918626i \(0.370700\pi\)
\(644\) 0 0
\(645\) −2.75865 −0.108622
\(646\) 0 0
\(647\) −24.7994 −0.974966 −0.487483 0.873132i \(-0.662085\pi\)
−0.487483 + 0.873132i \(0.662085\pi\)
\(648\) 0 0
\(649\) −10.5761 −0.415147
\(650\) 0 0
\(651\) −12.5531 −0.491993
\(652\) 0 0
\(653\) 0.457411 0.0178999 0.00894994 0.999960i \(-0.497151\pi\)
0.00894994 + 0.999960i \(0.497151\pi\)
\(654\) 0 0
\(655\) −4.52791 −0.176920
\(656\) 0 0
\(657\) 2.73959 0.106882
\(658\) 0 0
\(659\) −21.3180 −0.830431 −0.415216 0.909723i \(-0.636294\pi\)
−0.415216 + 0.909723i \(0.636294\pi\)
\(660\) 0 0
\(661\) −12.5620 −0.488606 −0.244303 0.969699i \(-0.578559\pi\)
−0.244303 + 0.969699i \(0.578559\pi\)
\(662\) 0 0
\(663\) 16.4831 0.640150
\(664\) 0 0
\(665\) 2.81423 0.109131
\(666\) 0 0
\(667\) 40.4829 1.56751
\(668\) 0 0
\(669\) −7.11843 −0.275215
\(670\) 0 0
\(671\) 75.3885 2.91034
\(672\) 0 0
\(673\) 19.3809 0.747080 0.373540 0.927614i \(-0.378144\pi\)
0.373540 + 0.927614i \(0.378144\pi\)
\(674\) 0 0
\(675\) −4.79469 −0.184548
\(676\) 0 0
\(677\) 1.26226 0.0485124 0.0242562 0.999706i \(-0.492278\pi\)
0.0242562 + 0.999706i \(0.492278\pi\)
\(678\) 0 0
\(679\) −4.98276 −0.191221
\(680\) 0 0
\(681\) −8.15200 −0.312385
\(682\) 0 0
\(683\) −11.6336 −0.445149 −0.222575 0.974916i \(-0.571446\pi\)
−0.222575 + 0.974916i \(0.571446\pi\)
\(684\) 0 0
\(685\) 10.4610 0.399694
\(686\) 0 0
\(687\) −3.40020 −0.129726
\(688\) 0 0
\(689\) −14.4177 −0.549272
\(690\) 0 0
\(691\) 27.7137 1.05428 0.527139 0.849779i \(-0.323265\pi\)
0.527139 + 0.849779i \(0.323265\pi\)
\(692\) 0 0
\(693\) −11.6225 −0.441501
\(694\) 0 0
\(695\) 3.00435 0.113962
\(696\) 0 0
\(697\) −37.0931 −1.40500
\(698\) 0 0
\(699\) −1.36410 −0.0515949
\(700\) 0 0
\(701\) 18.0567 0.681993 0.340997 0.940065i \(-0.389236\pi\)
0.340997 + 0.940065i \(0.389236\pi\)
\(702\) 0 0
\(703\) −3.16737 −0.119460
\(704\) 0 0
\(705\) 1.50791 0.0567911
\(706\) 0 0
\(707\) 7.57591 0.284922
\(708\) 0 0
\(709\) 9.56909 0.359375 0.179687 0.983724i \(-0.442491\pi\)
0.179687 + 0.983724i \(0.442491\pi\)
\(710\) 0 0
\(711\) 2.25178 0.0844484
\(712\) 0 0
\(713\) 31.4014 1.17599
\(714\) 0 0
\(715\) 6.57905 0.246043
\(716\) 0 0
\(717\) −10.6613 −0.398153
\(718\) 0 0
\(719\) −22.6323 −0.844043 −0.422021 0.906586i \(-0.638679\pi\)
−0.422021 + 0.906586i \(0.638679\pi\)
\(720\) 0 0
\(721\) 32.1809 1.19848
\(722\) 0 0
\(723\) −2.96872 −0.110408
\(724\) 0 0
\(725\) 35.7477 1.32764
\(726\) 0 0
\(727\) 17.2755 0.640714 0.320357 0.947297i \(-0.396197\pi\)
0.320357 + 0.947297i \(0.396197\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 37.0070 1.36875
\(732\) 0 0
\(733\) 1.37565 0.0508107 0.0254053 0.999677i \(-0.491912\pi\)
0.0254053 + 0.999677i \(0.491912\pi\)
\(734\) 0 0
\(735\) 1.03687 0.0382455
\(736\) 0 0
\(737\) −17.3852 −0.640391
\(738\) 0 0
\(739\) 41.6690 1.53282 0.766409 0.642353i \(-0.222042\pi\)
0.766409 + 0.642353i \(0.222042\pi\)
\(740\) 0 0
\(741\) −7.75928 −0.285044
\(742\) 0 0
\(743\) −29.5159 −1.08283 −0.541417 0.840754i \(-0.682112\pi\)
−0.541417 + 0.840754i \(0.682112\pi\)
\(744\) 0 0
\(745\) 6.32337 0.231670
\(746\) 0 0
\(747\) 0.0721083 0.00263831
\(748\) 0 0
\(749\) 30.8662 1.12783
\(750\) 0 0
\(751\) −29.0693 −1.06075 −0.530377 0.847762i \(-0.677950\pi\)
−0.530377 + 0.847762i \(0.677950\pi\)
\(752\) 0 0
\(753\) −0.703338 −0.0256310
\(754\) 0 0
\(755\) 0.529268 0.0192621
\(756\) 0 0
\(757\) 23.1987 0.843172 0.421586 0.906788i \(-0.361474\pi\)
0.421586 + 0.906788i \(0.361474\pi\)
\(758\) 0 0
\(759\) 29.0735 1.05530
\(760\) 0 0
\(761\) −50.9946 −1.84855 −0.924276 0.381725i \(-0.875330\pi\)
−0.924276 + 0.381725i \(0.875330\pi\)
\(762\) 0 0
\(763\) 32.8845 1.19050
\(764\) 0 0
\(765\) −2.75416 −0.0995770
\(766\) 0 0
\(767\) 5.35627 0.193404
\(768\) 0 0
\(769\) 16.3536 0.589726 0.294863 0.955540i \(-0.404726\pi\)
0.294863 + 0.955540i \(0.404726\pi\)
\(770\) 0 0
\(771\) −10.4602 −0.376713
\(772\) 0 0
\(773\) 26.7218 0.961116 0.480558 0.876963i \(-0.340434\pi\)
0.480558 + 0.876963i \(0.340434\pi\)
\(774\) 0 0
\(775\) 27.7284 0.996032
\(776\) 0 0
\(777\) 2.40278 0.0861993
\(778\) 0 0
\(779\) 17.4613 0.625615
\(780\) 0 0
\(781\) −19.8326 −0.709668
\(782\) 0 0
\(783\) −7.45567 −0.266444
\(784\) 0 0
\(785\) 3.30518 0.117967
\(786\) 0 0
\(787\) 33.6769 1.20045 0.600226 0.799831i \(-0.295077\pi\)
0.600226 + 0.799831i \(0.295077\pi\)
\(788\) 0 0
\(789\) −12.1467 −0.432433
\(790\) 0 0
\(791\) −30.7135 −1.09205
\(792\) 0 0
\(793\) −38.1806 −1.35583
\(794\) 0 0
\(795\) 2.40906 0.0854407
\(796\) 0 0
\(797\) −18.1019 −0.641202 −0.320601 0.947214i \(-0.603885\pi\)
−0.320601 + 0.947214i \(0.603885\pi\)
\(798\) 0 0
\(799\) −20.2284 −0.715630
\(800\) 0 0
\(801\) −9.49320 −0.335426
\(802\) 0 0
\(803\) −14.6689 −0.517654
\(804\) 0 0
\(805\) 5.34039 0.188224
\(806\) 0 0
\(807\) −0.974897 −0.0343180
\(808\) 0 0
\(809\) −28.4728 −1.00105 −0.500525 0.865722i \(-0.666859\pi\)
−0.500525 + 0.865722i \(0.666859\pi\)
\(810\) 0 0
\(811\) 45.2550 1.58912 0.794559 0.607187i \(-0.207702\pi\)
0.794559 + 0.607187i \(0.207702\pi\)
\(812\) 0 0
\(813\) 9.06798 0.318028
\(814\) 0 0
\(815\) −4.53770 −0.158949
\(816\) 0 0
\(817\) −17.4208 −0.609475
\(818\) 0 0
\(819\) 5.88622 0.205681
\(820\) 0 0
\(821\) 40.4969 1.41335 0.706676 0.707537i \(-0.250194\pi\)
0.706676 + 0.707537i \(0.250194\pi\)
\(822\) 0 0
\(823\) 15.1873 0.529394 0.264697 0.964332i \(-0.414728\pi\)
0.264697 + 0.964332i \(0.414728\pi\)
\(824\) 0 0
\(825\) 25.6728 0.893812
\(826\) 0 0
\(827\) −27.5058 −0.956471 −0.478236 0.878232i \(-0.658724\pi\)
−0.478236 + 0.878232i \(0.658724\pi\)
\(828\) 0 0
\(829\) −9.42817 −0.327454 −0.163727 0.986506i \(-0.552352\pi\)
−0.163727 + 0.986506i \(0.552352\pi\)
\(830\) 0 0
\(831\) −14.5217 −0.503753
\(832\) 0 0
\(833\) −13.9095 −0.481935
\(834\) 0 0
\(835\) −5.84453 −0.202258
\(836\) 0 0
\(837\) −5.78314 −0.199894
\(838\) 0 0
\(839\) 44.2263 1.52686 0.763431 0.645890i \(-0.223513\pi\)
0.763431 + 0.645890i \(0.223513\pi\)
\(840\) 0 0
\(841\) 26.5871 0.916795
\(842\) 0 0
\(843\) 0.623745 0.0214829
\(844\) 0 0
\(845\) 2.55842 0.0880125
\(846\) 0 0
\(847\) 38.3546 1.31788
\(848\) 0 0
\(849\) −25.1834 −0.864291
\(850\) 0 0
\(851\) −6.01054 −0.206039
\(852\) 0 0
\(853\) −0.974354 −0.0333613 −0.0166806 0.999861i \(-0.505310\pi\)
−0.0166806 + 0.999861i \(0.505310\pi\)
\(854\) 0 0
\(855\) 1.29650 0.0443394
\(856\) 0 0
\(857\) 44.8334 1.53148 0.765740 0.643150i \(-0.222373\pi\)
0.765740 + 0.643150i \(0.222373\pi\)
\(858\) 0 0
\(859\) 50.0429 1.70744 0.853721 0.520730i \(-0.174340\pi\)
0.853721 + 0.520730i \(0.174340\pi\)
\(860\) 0 0
\(861\) −13.2462 −0.451429
\(862\) 0 0
\(863\) −10.7593 −0.366251 −0.183126 0.983090i \(-0.558622\pi\)
−0.183126 + 0.983090i \(0.558622\pi\)
\(864\) 0 0
\(865\) 5.02842 0.170971
\(866\) 0 0
\(867\) 19.9468 0.677429
\(868\) 0 0
\(869\) −12.0570 −0.409005
\(870\) 0 0
\(871\) 8.80474 0.298337
\(872\) 0 0
\(873\) −2.29553 −0.0776921
\(874\) 0 0
\(875\) 9.63337 0.325667
\(876\) 0 0
\(877\) −36.9714 −1.24844 −0.624218 0.781250i \(-0.714582\pi\)
−0.624218 + 0.781250i \(0.714582\pi\)
\(878\) 0 0
\(879\) 4.37810 0.147670
\(880\) 0 0
\(881\) −15.3517 −0.517211 −0.258605 0.965983i \(-0.583263\pi\)
−0.258605 + 0.965983i \(0.583263\pi\)
\(882\) 0 0
\(883\) 12.4942 0.420462 0.210231 0.977652i \(-0.432578\pi\)
0.210231 + 0.977652i \(0.432578\pi\)
\(884\) 0 0
\(885\) −0.894980 −0.0300844
\(886\) 0 0
\(887\) 5.75567 0.193256 0.0966282 0.995321i \(-0.469194\pi\)
0.0966282 + 0.995321i \(0.469194\pi\)
\(888\) 0 0
\(889\) −37.3217 −1.25173
\(890\) 0 0
\(891\) −5.35442 −0.179380
\(892\) 0 0
\(893\) 9.52236 0.318654
\(894\) 0 0
\(895\) 9.02148 0.301555
\(896\) 0 0
\(897\) −14.7243 −0.491631
\(898\) 0 0
\(899\) 43.1172 1.43804
\(900\) 0 0
\(901\) −32.3173 −1.07665
\(902\) 0 0
\(903\) 13.2155 0.439783
\(904\) 0 0
\(905\) −6.01598 −0.199978
\(906\) 0 0
\(907\) 33.4509 1.11072 0.555360 0.831610i \(-0.312581\pi\)
0.555360 + 0.831610i \(0.312581\pi\)
\(908\) 0 0
\(909\) 3.49019 0.115762
\(910\) 0 0
\(911\) −58.2620 −1.93031 −0.965153 0.261686i \(-0.915721\pi\)
−0.965153 + 0.261686i \(0.915721\pi\)
\(912\) 0 0
\(913\) −0.386098 −0.0127780
\(914\) 0 0
\(915\) 6.37961 0.210903
\(916\) 0 0
\(917\) 21.6912 0.716305
\(918\) 0 0
\(919\) −18.9879 −0.626352 −0.313176 0.949695i \(-0.601393\pi\)
−0.313176 + 0.949695i \(0.601393\pi\)
\(920\) 0 0
\(921\) 3.46257 0.114095
\(922\) 0 0
\(923\) 10.0443 0.330611
\(924\) 0 0
\(925\) −5.30749 −0.174509
\(926\) 0 0
\(927\) 14.8256 0.486936
\(928\) 0 0
\(929\) −3.14313 −0.103123 −0.0515614 0.998670i \(-0.516420\pi\)
−0.0515614 + 0.998670i \(0.516420\pi\)
\(930\) 0 0
\(931\) 6.54778 0.214595
\(932\) 0 0
\(933\) 6.24430 0.204429
\(934\) 0 0
\(935\) 14.7469 0.482276
\(936\) 0 0
\(937\) 17.4629 0.570489 0.285244 0.958455i \(-0.407925\pi\)
0.285244 + 0.958455i \(0.407925\pi\)
\(938\) 0 0
\(939\) 15.9415 0.520230
\(940\) 0 0
\(941\) −24.1050 −0.785799 −0.392899 0.919581i \(-0.628528\pi\)
−0.392899 + 0.919581i \(0.628528\pi\)
\(942\) 0 0
\(943\) 33.1352 1.07903
\(944\) 0 0
\(945\) −0.983530 −0.0319942
\(946\) 0 0
\(947\) −3.56033 −0.115695 −0.0578476 0.998325i \(-0.518424\pi\)
−0.0578476 + 0.998325i \(0.518424\pi\)
\(948\) 0 0
\(949\) 7.42909 0.241158
\(950\) 0 0
\(951\) 11.5258 0.373749
\(952\) 0 0
\(953\) 24.2055 0.784092 0.392046 0.919946i \(-0.371767\pi\)
0.392046 + 0.919946i \(0.371767\pi\)
\(954\) 0 0
\(955\) 4.34027 0.140448
\(956\) 0 0
\(957\) 39.9208 1.29046
\(958\) 0 0
\(959\) −50.1140 −1.61826
\(960\) 0 0
\(961\) 2.44466 0.0788600
\(962\) 0 0
\(963\) 14.2199 0.458230
\(964\) 0 0
\(965\) 1.03826 0.0334228
\(966\) 0 0
\(967\) 48.3663 1.55536 0.777678 0.628662i \(-0.216397\pi\)
0.777678 + 0.628662i \(0.216397\pi\)
\(968\) 0 0
\(969\) −17.3924 −0.558725
\(970\) 0 0
\(971\) 38.2827 1.22855 0.614276 0.789092i \(-0.289448\pi\)
0.614276 + 0.789092i \(0.289448\pi\)
\(972\) 0 0
\(973\) −14.3925 −0.461402
\(974\) 0 0
\(975\) −13.0020 −0.416398
\(976\) 0 0
\(977\) −50.3330 −1.61030 −0.805148 0.593073i \(-0.797914\pi\)
−0.805148 + 0.593073i \(0.797914\pi\)
\(978\) 0 0
\(979\) 50.8305 1.62455
\(980\) 0 0
\(981\) 15.1497 0.483694
\(982\) 0 0
\(983\) −41.9070 −1.33663 −0.668313 0.743880i \(-0.732983\pi\)
−0.668313 + 0.743880i \(0.732983\pi\)
\(984\) 0 0
\(985\) 3.77060 0.120141
\(986\) 0 0
\(987\) −7.22370 −0.229933
\(988\) 0 0
\(989\) −33.0583 −1.05119
\(990\) 0 0
\(991\) −30.8646 −0.980447 −0.490224 0.871597i \(-0.663085\pi\)
−0.490224 + 0.871597i \(0.663085\pi\)
\(992\) 0 0
\(993\) 20.7940 0.659878
\(994\) 0 0
\(995\) −10.8942 −0.345370
\(996\) 0 0
\(997\) −38.9030 −1.23207 −0.616035 0.787719i \(-0.711262\pi\)
−0.616035 + 0.787719i \(0.711262\pi\)
\(998\) 0 0
\(999\) 1.10695 0.0350224
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 \(a_p\))