Properties

Label 4012.2.a.g.1.7
Level 4012
Weight 2
Character 4012.1
Self dual Yes
Analytic conductor 32.036
Analytic rank 1
Dimension 12
CM No
Inner twists 1

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0359812909\)
Analytic rank: \(1\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-0.660935\)
Character \(\chi\) = 4012.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.660935 q^{3}\) \(+2.45345 q^{5}\) \(+3.10518 q^{7}\) \(-2.56317 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.660935 q^{3}\) \(+2.45345 q^{5}\) \(+3.10518 q^{7}\) \(-2.56317 q^{9}\) \(-3.33884 q^{11}\) \(-5.08477 q^{13}\) \(+1.62157 q^{15}\) \(-1.00000 q^{17}\) \(-5.38873 q^{19}\) \(+2.05232 q^{21}\) \(-3.60332 q^{23}\) \(+1.01943 q^{25}\) \(-3.67689 q^{27}\) \(-0.718872 q^{29}\) \(+8.53934 q^{31}\) \(-2.20676 q^{33}\) \(+7.61841 q^{35}\) \(+2.73317 q^{37}\) \(-3.36070 q^{39}\) \(-1.77689 q^{41}\) \(-10.0004 q^{43}\) \(-6.28861 q^{45}\) \(-9.54752 q^{47}\) \(+2.64214 q^{49}\) \(-0.660935 q^{51}\) \(-8.25925 q^{53}\) \(-8.19169 q^{55}\) \(-3.56160 q^{57}\) \(+1.00000 q^{59}\) \(+0.304416 q^{61}\) \(-7.95909 q^{63}\) \(-12.4753 q^{65}\) \(+2.16849 q^{67}\) \(-2.38156 q^{69}\) \(-15.4011 q^{71}\) \(-16.3540 q^{73}\) \(+0.673778 q^{75}\) \(-10.3677 q^{77}\) \(+14.7037 q^{79}\) \(+5.25931 q^{81}\) \(+9.25266 q^{83}\) \(-2.45345 q^{85}\) \(-0.475128 q^{87}\) \(+1.00738 q^{89}\) \(-15.7891 q^{91}\) \(+5.64394 q^{93}\) \(-13.2210 q^{95}\) \(+11.7259 q^{97}\) \(+8.55800 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 9q^{13} \) \(\mathstrut -\mathstrut 16q^{15} \) \(\mathstrut -\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut 15q^{19} \) \(\mathstrut +\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut -\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 33q^{33} \) \(\mathstrut -\mathstrut 9q^{35} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut -\mathstrut 18q^{41} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 30q^{45} \) \(\mathstrut -\mathstrut 60q^{47} \) \(\mathstrut +\mathstrut 10q^{49} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 41q^{57} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 23q^{63} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 4q^{73} \) \(\mathstrut -\mathstrut 62q^{75} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 48q^{79} \) \(\mathstrut +\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 20q^{83} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 13q^{87} \) \(\mathstrut -\mathstrut 29q^{89} \) \(\mathstrut -\mathstrut 28q^{91} \) \(\mathstrut -\mathstrut 31q^{93} \) \(\mathstrut -\mathstrut 48q^{95} \) \(\mathstrut -\mathstrut 26q^{97} \) \(\mathstrut -\mathstrut 3q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0.660935 0.381591 0.190795 0.981630i \(-0.438893\pi\)
0.190795 + 0.981630i \(0.438893\pi\)
\(4\) 0 0
\(5\) 2.45345 1.09722 0.548609 0.836079i \(-0.315158\pi\)
0.548609 + 0.836079i \(0.315158\pi\)
\(6\) 0 0
\(7\) 3.10518 1.17365 0.586824 0.809715i \(-0.300378\pi\)
0.586824 + 0.809715i \(0.300378\pi\)
\(8\) 0 0
\(9\) −2.56317 −0.854388
\(10\) 0 0
\(11\) −3.33884 −1.00670 −0.503349 0.864083i \(-0.667899\pi\)
−0.503349 + 0.864083i \(0.667899\pi\)
\(12\) 0 0
\(13\) −5.08477 −1.41026 −0.705131 0.709077i \(-0.749112\pi\)
−0.705131 + 0.709077i \(0.749112\pi\)
\(14\) 0 0
\(15\) 1.62157 0.418688
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) −5.38873 −1.23626 −0.618130 0.786076i \(-0.712109\pi\)
−0.618130 + 0.786076i \(0.712109\pi\)
\(20\) 0 0
\(21\) 2.05232 0.447853
\(22\) 0 0
\(23\) −3.60332 −0.751344 −0.375672 0.926753i \(-0.622588\pi\)
−0.375672 + 0.926753i \(0.622588\pi\)
\(24\) 0 0
\(25\) 1.01943 0.203886
\(26\) 0 0
\(27\) −3.67689 −0.707618
\(28\) 0 0
\(29\) −0.718872 −0.133491 −0.0667456 0.997770i \(-0.521262\pi\)
−0.0667456 + 0.997770i \(0.521262\pi\)
\(30\) 0 0
\(31\) 8.53934 1.53371 0.766855 0.641820i \(-0.221821\pi\)
0.766855 + 0.641820i \(0.221821\pi\)
\(32\) 0 0
\(33\) −2.20676 −0.384147
\(34\) 0 0
\(35\) 7.61841 1.28775
\(36\) 0 0
\(37\) 2.73317 0.449331 0.224665 0.974436i \(-0.427871\pi\)
0.224665 + 0.974436i \(0.427871\pi\)
\(38\) 0 0
\(39\) −3.36070 −0.538143
\(40\) 0 0
\(41\) −1.77689 −0.277503 −0.138752 0.990327i \(-0.544309\pi\)
−0.138752 + 0.990327i \(0.544309\pi\)
\(42\) 0 0
\(43\) −10.0004 −1.52505 −0.762526 0.646958i \(-0.776041\pi\)
−0.762526 + 0.646958i \(0.776041\pi\)
\(44\) 0 0
\(45\) −6.28861 −0.937450
\(46\) 0 0
\(47\) −9.54752 −1.39265 −0.696325 0.717727i \(-0.745183\pi\)
−0.696325 + 0.717727i \(0.745183\pi\)
\(48\) 0 0
\(49\) 2.64214 0.377448
\(50\) 0 0
\(51\) −0.660935 −0.0925494
\(52\) 0 0
\(53\) −8.25925 −1.13450 −0.567248 0.823547i \(-0.691992\pi\)
−0.567248 + 0.823547i \(0.691992\pi\)
\(54\) 0 0
\(55\) −8.19169 −1.10457
\(56\) 0 0
\(57\) −3.56160 −0.471745
\(58\) 0 0
\(59\) 1.00000 0.130189
\(60\) 0 0
\(61\) 0.304416 0.0389765 0.0194882 0.999810i \(-0.493796\pi\)
0.0194882 + 0.999810i \(0.493796\pi\)
\(62\) 0 0
\(63\) −7.95909 −1.00275
\(64\) 0 0
\(65\) −12.4753 −1.54736
\(66\) 0 0
\(67\) 2.16849 0.264923 0.132462 0.991188i \(-0.457712\pi\)
0.132462 + 0.991188i \(0.457712\pi\)
\(68\) 0 0
\(69\) −2.38156 −0.286706
\(70\) 0 0
\(71\) −15.4011 −1.82777 −0.913885 0.405973i \(-0.866933\pi\)
−0.913885 + 0.405973i \(0.866933\pi\)
\(72\) 0 0
\(73\) −16.3540 −1.91410 −0.957048 0.289931i \(-0.906368\pi\)
−0.957048 + 0.289931i \(0.906368\pi\)
\(74\) 0 0
\(75\) 0.673778 0.0778012
\(76\) 0 0
\(77\) −10.3677 −1.18151
\(78\) 0 0
\(79\) 14.7037 1.65429 0.827146 0.561987i \(-0.189963\pi\)
0.827146 + 0.561987i \(0.189963\pi\)
\(80\) 0 0
\(81\) 5.25931 0.584368
\(82\) 0 0
\(83\) 9.25266 1.01561 0.507806 0.861472i \(-0.330457\pi\)
0.507806 + 0.861472i \(0.330457\pi\)
\(84\) 0 0
\(85\) −2.45345 −0.266114
\(86\) 0 0
\(87\) −0.475128 −0.0509390
\(88\) 0 0
\(89\) 1.00738 0.106782 0.0533912 0.998574i \(-0.482997\pi\)
0.0533912 + 0.998574i \(0.482997\pi\)
\(90\) 0 0
\(91\) −15.7891 −1.65515
\(92\) 0 0
\(93\) 5.64394 0.585250
\(94\) 0 0
\(95\) −13.2210 −1.35645
\(96\) 0 0
\(97\) 11.7259 1.19058 0.595292 0.803509i \(-0.297036\pi\)
0.595292 + 0.803509i \(0.297036\pi\)
\(98\) 0 0
\(99\) 8.55800 0.860111
\(100\) 0 0
\(101\) 11.6963 1.16382 0.581910 0.813253i \(-0.302306\pi\)
0.581910 + 0.813253i \(0.302306\pi\)
\(102\) 0 0
\(103\) 8.56606 0.844039 0.422019 0.906587i \(-0.361321\pi\)
0.422019 + 0.906587i \(0.361321\pi\)
\(104\) 0 0
\(105\) 5.03527 0.491392
\(106\) 0 0
\(107\) 9.87146 0.954310 0.477155 0.878819i \(-0.341668\pi\)
0.477155 + 0.878819i \(0.341668\pi\)
\(108\) 0 0
\(109\) −11.1260 −1.06567 −0.532837 0.846218i \(-0.678874\pi\)
−0.532837 + 0.846218i \(0.678874\pi\)
\(110\) 0 0
\(111\) 1.80645 0.171460
\(112\) 0 0
\(113\) 8.91916 0.839044 0.419522 0.907745i \(-0.362198\pi\)
0.419522 + 0.907745i \(0.362198\pi\)
\(114\) 0 0
\(115\) −8.84058 −0.824388
\(116\) 0 0
\(117\) 13.0331 1.20491
\(118\) 0 0
\(119\) −3.10518 −0.284651
\(120\) 0 0
\(121\) 0.147848 0.0134407
\(122\) 0 0
\(123\) −1.17441 −0.105893
\(124\) 0 0
\(125\) −9.76614 −0.873510
\(126\) 0 0
\(127\) −19.2947 −1.71213 −0.856064 0.516871i \(-0.827097\pi\)
−0.856064 + 0.516871i \(0.827097\pi\)
\(128\) 0 0
\(129\) −6.60963 −0.581946
\(130\) 0 0
\(131\) 17.0054 1.48577 0.742885 0.669419i \(-0.233457\pi\)
0.742885 + 0.669419i \(0.233457\pi\)
\(132\) 0 0
\(133\) −16.7330 −1.45093
\(134\) 0 0
\(135\) −9.02108 −0.776411
\(136\) 0 0
\(137\) 5.48969 0.469016 0.234508 0.972114i \(-0.424652\pi\)
0.234508 + 0.972114i \(0.424652\pi\)
\(138\) 0 0
\(139\) 22.8288 1.93631 0.968157 0.250343i \(-0.0805433\pi\)
0.968157 + 0.250343i \(0.0805433\pi\)
\(140\) 0 0
\(141\) −6.31029 −0.531422
\(142\) 0 0
\(143\) 16.9772 1.41971
\(144\) 0 0
\(145\) −1.76372 −0.146469
\(146\) 0 0
\(147\) 1.74628 0.144031
\(148\) 0 0
\(149\) 10.4895 0.859337 0.429668 0.902987i \(-0.358630\pi\)
0.429668 + 0.902987i \(0.358630\pi\)
\(150\) 0 0
\(151\) 4.35434 0.354352 0.177176 0.984179i \(-0.443304\pi\)
0.177176 + 0.984179i \(0.443304\pi\)
\(152\) 0 0
\(153\) 2.56317 0.207220
\(154\) 0 0
\(155\) 20.9509 1.68281
\(156\) 0 0
\(157\) 18.2072 1.45310 0.726548 0.687116i \(-0.241124\pi\)
0.726548 + 0.687116i \(0.241124\pi\)
\(158\) 0 0
\(159\) −5.45883 −0.432913
\(160\) 0 0
\(161\) −11.1890 −0.881813
\(162\) 0 0
\(163\) −13.1400 −1.02920 −0.514602 0.857429i \(-0.672060\pi\)
−0.514602 + 0.857429i \(0.672060\pi\)
\(164\) 0 0
\(165\) −5.41417 −0.421493
\(166\) 0 0
\(167\) −16.2523 −1.25764 −0.628821 0.777550i \(-0.716462\pi\)
−0.628821 + 0.777550i \(0.716462\pi\)
\(168\) 0 0
\(169\) 12.8549 0.988840
\(170\) 0 0
\(171\) 13.8122 1.05625
\(172\) 0 0
\(173\) −9.91123 −0.753537 −0.376768 0.926308i \(-0.622965\pi\)
−0.376768 + 0.926308i \(0.622965\pi\)
\(174\) 0 0
\(175\) 3.16552 0.239291
\(176\) 0 0
\(177\) 0.660935 0.0496789
\(178\) 0 0
\(179\) −8.24666 −0.616384 −0.308192 0.951324i \(-0.599724\pi\)
−0.308192 + 0.951324i \(0.599724\pi\)
\(180\) 0 0
\(181\) 4.93880 0.367098 0.183549 0.983011i \(-0.441241\pi\)
0.183549 + 0.983011i \(0.441241\pi\)
\(182\) 0 0
\(183\) 0.201199 0.0148731
\(184\) 0 0
\(185\) 6.70571 0.493013
\(186\) 0 0
\(187\) 3.33884 0.244160
\(188\) 0 0
\(189\) −11.4174 −0.830494
\(190\) 0 0
\(191\) −8.32799 −0.602592 −0.301296 0.953531i \(-0.597419\pi\)
−0.301296 + 0.953531i \(0.597419\pi\)
\(192\) 0 0
\(193\) −22.4847 −1.61848 −0.809241 0.587477i \(-0.800121\pi\)
−0.809241 + 0.587477i \(0.800121\pi\)
\(194\) 0 0
\(195\) −8.24533 −0.590460
\(196\) 0 0
\(197\) 11.5325 0.821653 0.410827 0.911714i \(-0.365240\pi\)
0.410827 + 0.911714i \(0.365240\pi\)
\(198\) 0 0
\(199\) −21.2531 −1.50659 −0.753296 0.657682i \(-0.771537\pi\)
−0.753296 + 0.657682i \(0.771537\pi\)
\(200\) 0 0
\(201\) 1.43323 0.101092
\(202\) 0 0
\(203\) −2.23223 −0.156672
\(204\) 0 0
\(205\) −4.35951 −0.304482
\(206\) 0 0
\(207\) 9.23590 0.641940
\(208\) 0 0
\(209\) 17.9921 1.24454
\(210\) 0 0
\(211\) 17.2682 1.18879 0.594395 0.804173i \(-0.297392\pi\)
0.594395 + 0.804173i \(0.297392\pi\)
\(212\) 0 0
\(213\) −10.1791 −0.697460
\(214\) 0 0
\(215\) −24.5356 −1.67331
\(216\) 0 0
\(217\) 26.5162 1.80003
\(218\) 0 0
\(219\) −10.8090 −0.730401
\(220\) 0 0
\(221\) 5.08477 0.342039
\(222\) 0 0
\(223\) −4.23045 −0.283292 −0.141646 0.989917i \(-0.545239\pi\)
−0.141646 + 0.989917i \(0.545239\pi\)
\(224\) 0 0
\(225\) −2.61297 −0.174198
\(226\) 0 0
\(227\) −13.2076 −0.876616 −0.438308 0.898825i \(-0.644422\pi\)
−0.438308 + 0.898825i \(0.644422\pi\)
\(228\) 0 0
\(229\) 14.1591 0.935658 0.467829 0.883819i \(-0.345036\pi\)
0.467829 + 0.883819i \(0.345036\pi\)
\(230\) 0 0
\(231\) −6.85237 −0.450853
\(232\) 0 0
\(233\) −2.12997 −0.139539 −0.0697695 0.997563i \(-0.522226\pi\)
−0.0697695 + 0.997563i \(0.522226\pi\)
\(234\) 0 0
\(235\) −23.4244 −1.52804
\(236\) 0 0
\(237\) 9.71817 0.631263
\(238\) 0 0
\(239\) 18.4130 1.19104 0.595520 0.803341i \(-0.296946\pi\)
0.595520 + 0.803341i \(0.296946\pi\)
\(240\) 0 0
\(241\) 1.73250 0.111600 0.0558001 0.998442i \(-0.482229\pi\)
0.0558001 + 0.998442i \(0.482229\pi\)
\(242\) 0 0
\(243\) 14.5067 0.930607
\(244\) 0 0
\(245\) 6.48236 0.414143
\(246\) 0 0
\(247\) 27.4005 1.74345
\(248\) 0 0
\(249\) 6.11540 0.387548
\(250\) 0 0
\(251\) −5.08637 −0.321049 −0.160524 0.987032i \(-0.551319\pi\)
−0.160524 + 0.987032i \(0.551319\pi\)
\(252\) 0 0
\(253\) 12.0309 0.756377
\(254\) 0 0
\(255\) −1.62157 −0.101547
\(256\) 0 0
\(257\) −14.7808 −0.922002 −0.461001 0.887400i \(-0.652509\pi\)
−0.461001 + 0.887400i \(0.652509\pi\)
\(258\) 0 0
\(259\) 8.48699 0.527356
\(260\) 0 0
\(261\) 1.84259 0.114053
\(262\) 0 0
\(263\) −6.68659 −0.412313 −0.206156 0.978519i \(-0.566096\pi\)
−0.206156 + 0.978519i \(0.566096\pi\)
\(264\) 0 0
\(265\) −20.2637 −1.24479
\(266\) 0 0
\(267\) 0.665815 0.0407472
\(268\) 0 0
\(269\) 18.8193 1.14743 0.573715 0.819055i \(-0.305502\pi\)
0.573715 + 0.819055i \(0.305502\pi\)
\(270\) 0 0
\(271\) −14.5928 −0.886448 −0.443224 0.896411i \(-0.646165\pi\)
−0.443224 + 0.896411i \(0.646165\pi\)
\(272\) 0 0
\(273\) −10.4356 −0.631590
\(274\) 0 0
\(275\) −3.40372 −0.205252
\(276\) 0 0
\(277\) 27.8797 1.67513 0.837563 0.546340i \(-0.183979\pi\)
0.837563 + 0.546340i \(0.183979\pi\)
\(278\) 0 0
\(279\) −21.8877 −1.31038
\(280\) 0 0
\(281\) −20.7462 −1.23762 −0.618808 0.785543i \(-0.712384\pi\)
−0.618808 + 0.785543i \(0.712384\pi\)
\(282\) 0 0
\(283\) −17.7038 −1.05238 −0.526191 0.850366i \(-0.676380\pi\)
−0.526191 + 0.850366i \(0.676380\pi\)
\(284\) 0 0
\(285\) −8.73822 −0.517607
\(286\) 0 0
\(287\) −5.51756 −0.325691
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 7.75005 0.454316
\(292\) 0 0
\(293\) −11.6136 −0.678474 −0.339237 0.940701i \(-0.610169\pi\)
−0.339237 + 0.940701i \(0.610169\pi\)
\(294\) 0 0
\(295\) 2.45345 0.142846
\(296\) 0 0
\(297\) 12.2765 0.712357
\(298\) 0 0
\(299\) 18.3221 1.05959
\(300\) 0 0
\(301\) −31.0531 −1.78987
\(302\) 0 0
\(303\) 7.73046 0.444103
\(304\) 0 0
\(305\) 0.746871 0.0427657
\(306\) 0 0
\(307\) 19.2632 1.09941 0.549705 0.835359i \(-0.314740\pi\)
0.549705 + 0.835359i \(0.314740\pi\)
\(308\) 0 0
\(309\) 5.66161 0.322078
\(310\) 0 0
\(311\) −33.7242 −1.91232 −0.956162 0.292837i \(-0.905401\pi\)
−0.956162 + 0.292837i \(0.905401\pi\)
\(312\) 0 0
\(313\) 25.3089 1.43055 0.715273 0.698845i \(-0.246302\pi\)
0.715273 + 0.698845i \(0.246302\pi\)
\(314\) 0 0
\(315\) −19.5272 −1.10024
\(316\) 0 0
\(317\) −17.8815 −1.00433 −0.502164 0.864772i \(-0.667463\pi\)
−0.502164 + 0.864772i \(0.667463\pi\)
\(318\) 0 0
\(319\) 2.40020 0.134385
\(320\) 0 0
\(321\) 6.52439 0.364156
\(322\) 0 0
\(323\) 5.38873 0.299837
\(324\) 0 0
\(325\) −5.18358 −0.287533
\(326\) 0 0
\(327\) −7.35354 −0.406652
\(328\) 0 0
\(329\) −29.6468 −1.63448
\(330\) 0 0
\(331\) 6.11436 0.336076 0.168038 0.985781i \(-0.446257\pi\)
0.168038 + 0.985781i \(0.446257\pi\)
\(332\) 0 0
\(333\) −7.00557 −0.383903
\(334\) 0 0
\(335\) 5.32029 0.290679
\(336\) 0 0
\(337\) 0.478656 0.0260741 0.0130370 0.999915i \(-0.495850\pi\)
0.0130370 + 0.999915i \(0.495850\pi\)
\(338\) 0 0
\(339\) 5.89498 0.320172
\(340\) 0 0
\(341\) −28.5115 −1.54398
\(342\) 0 0
\(343\) −13.5319 −0.730656
\(344\) 0 0
\(345\) −5.84304 −0.314579
\(346\) 0 0
\(347\) 2.47317 0.132767 0.0663834 0.997794i \(-0.478854\pi\)
0.0663834 + 0.997794i \(0.478854\pi\)
\(348\) 0 0
\(349\) 11.5110 0.616168 0.308084 0.951359i \(-0.400312\pi\)
0.308084 + 0.951359i \(0.400312\pi\)
\(350\) 0 0
\(351\) 18.6962 0.997927
\(352\) 0 0
\(353\) 0.0790507 0.00420745 0.00210372 0.999998i \(-0.499330\pi\)
0.00210372 + 0.999998i \(0.499330\pi\)
\(354\) 0 0
\(355\) −37.7858 −2.00546
\(356\) 0 0
\(357\) −2.05232 −0.108620
\(358\) 0 0
\(359\) −16.6318 −0.877795 −0.438897 0.898537i \(-0.644631\pi\)
−0.438897 + 0.898537i \(0.644631\pi\)
\(360\) 0 0
\(361\) 10.0384 0.528337
\(362\) 0 0
\(363\) 0.0977180 0.00512886
\(364\) 0 0
\(365\) −40.1239 −2.10018
\(366\) 0 0
\(367\) −31.0009 −1.61823 −0.809116 0.587649i \(-0.800054\pi\)
−0.809116 + 0.587649i \(0.800054\pi\)
\(368\) 0 0
\(369\) 4.55446 0.237096
\(370\) 0 0
\(371\) −25.6465 −1.33150
\(372\) 0 0
\(373\) 8.28208 0.428830 0.214415 0.976743i \(-0.431216\pi\)
0.214415 + 0.976743i \(0.431216\pi\)
\(374\) 0 0
\(375\) −6.45478 −0.333323
\(376\) 0 0
\(377\) 3.65530 0.188258
\(378\) 0 0
\(379\) −35.2827 −1.81235 −0.906176 0.422900i \(-0.861012\pi\)
−0.906176 + 0.422900i \(0.861012\pi\)
\(380\) 0 0
\(381\) −12.7525 −0.653332
\(382\) 0 0
\(383\) −31.5494 −1.61210 −0.806049 0.591849i \(-0.798398\pi\)
−0.806049 + 0.591849i \(0.798398\pi\)
\(384\) 0 0
\(385\) −25.4367 −1.29637
\(386\) 0 0
\(387\) 25.6328 1.30299
\(388\) 0 0
\(389\) 14.0519 0.712459 0.356230 0.934398i \(-0.384062\pi\)
0.356230 + 0.934398i \(0.384062\pi\)
\(390\) 0 0
\(391\) 3.60332 0.182228
\(392\) 0 0
\(393\) 11.2395 0.566956
\(394\) 0 0
\(395\) 36.0748 1.81512
\(396\) 0 0
\(397\) 3.60826 0.181094 0.0905468 0.995892i \(-0.471139\pi\)
0.0905468 + 0.995892i \(0.471139\pi\)
\(398\) 0 0
\(399\) −11.0594 −0.553663
\(400\) 0 0
\(401\) 15.7980 0.788917 0.394458 0.918914i \(-0.370932\pi\)
0.394458 + 0.918914i \(0.370932\pi\)
\(402\) 0 0
\(403\) −43.4206 −2.16293
\(404\) 0 0
\(405\) 12.9035 0.641179
\(406\) 0 0
\(407\) −9.12562 −0.452340
\(408\) 0 0
\(409\) 1.36757 0.0676221 0.0338111 0.999428i \(-0.489236\pi\)
0.0338111 + 0.999428i \(0.489236\pi\)
\(410\) 0 0
\(411\) 3.62833 0.178972
\(412\) 0 0
\(413\) 3.10518 0.152796
\(414\) 0 0
\(415\) 22.7010 1.11435
\(416\) 0 0
\(417\) 15.0884 0.738880
\(418\) 0 0
\(419\) 14.7484 0.720506 0.360253 0.932855i \(-0.382690\pi\)
0.360253 + 0.932855i \(0.382690\pi\)
\(420\) 0 0
\(421\) −11.9744 −0.583596 −0.291798 0.956480i \(-0.594253\pi\)
−0.291798 + 0.956480i \(0.594253\pi\)
\(422\) 0 0
\(423\) 24.4719 1.18986
\(424\) 0 0
\(425\) −1.01943 −0.0494497
\(426\) 0 0
\(427\) 0.945266 0.0457446
\(428\) 0 0
\(429\) 11.2208 0.541748
\(430\) 0 0
\(431\) −8.85550 −0.426555 −0.213277 0.976992i \(-0.568414\pi\)
−0.213277 + 0.976992i \(0.568414\pi\)
\(432\) 0 0
\(433\) 28.4148 1.36553 0.682764 0.730639i \(-0.260778\pi\)
0.682764 + 0.730639i \(0.260778\pi\)
\(434\) 0 0
\(435\) −1.16570 −0.0558912
\(436\) 0 0
\(437\) 19.4173 0.928856
\(438\) 0 0
\(439\) −27.7491 −1.32439 −0.662196 0.749331i \(-0.730375\pi\)
−0.662196 + 0.749331i \(0.730375\pi\)
\(440\) 0 0
\(441\) −6.77223 −0.322487
\(442\) 0 0
\(443\) 2.18906 0.104005 0.0520026 0.998647i \(-0.483440\pi\)
0.0520026 + 0.998647i \(0.483440\pi\)
\(444\) 0 0
\(445\) 2.47157 0.117164
\(446\) 0 0
\(447\) 6.93290 0.327915
\(448\) 0 0
\(449\) 38.0122 1.79391 0.896953 0.442126i \(-0.145775\pi\)
0.896953 + 0.442126i \(0.145775\pi\)
\(450\) 0 0
\(451\) 5.93275 0.279362
\(452\) 0 0
\(453\) 2.87794 0.135217
\(454\) 0 0
\(455\) −38.7379 −1.81606
\(456\) 0 0
\(457\) 18.1792 0.850388 0.425194 0.905102i \(-0.360206\pi\)
0.425194 + 0.905102i \(0.360206\pi\)
\(458\) 0 0
\(459\) 3.67689 0.171622
\(460\) 0 0
\(461\) 32.6942 1.52272 0.761360 0.648330i \(-0.224532\pi\)
0.761360 + 0.648330i \(0.224532\pi\)
\(462\) 0 0
\(463\) 13.1884 0.612918 0.306459 0.951884i \(-0.400856\pi\)
0.306459 + 0.951884i \(0.400856\pi\)
\(464\) 0 0
\(465\) 13.8472 0.642146
\(466\) 0 0
\(467\) −17.9191 −0.829197 −0.414598 0.910005i \(-0.636078\pi\)
−0.414598 + 0.910005i \(0.636078\pi\)
\(468\) 0 0
\(469\) 6.73355 0.310927
\(470\) 0 0
\(471\) 12.0338 0.554488
\(472\) 0 0
\(473\) 33.3898 1.53527
\(474\) 0 0
\(475\) −5.49345 −0.252057
\(476\) 0 0
\(477\) 21.1698 0.969300
\(478\) 0 0
\(479\) −1.73745 −0.0793863 −0.0396932 0.999212i \(-0.512638\pi\)
−0.0396932 + 0.999212i \(0.512638\pi\)
\(480\) 0 0
\(481\) −13.8976 −0.633674
\(482\) 0 0
\(483\) −7.39517 −0.336492
\(484\) 0 0
\(485\) 28.7689 1.30633
\(486\) 0 0
\(487\) 2.90227 0.131515 0.0657573 0.997836i \(-0.479054\pi\)
0.0657573 + 0.997836i \(0.479054\pi\)
\(488\) 0 0
\(489\) −8.68468 −0.392735
\(490\) 0 0
\(491\) −3.23157 −0.145839 −0.0729193 0.997338i \(-0.523232\pi\)
−0.0729193 + 0.997338i \(0.523232\pi\)
\(492\) 0 0
\(493\) 0.718872 0.0323764
\(494\) 0 0
\(495\) 20.9966 0.943729
\(496\) 0 0
\(497\) −47.8231 −2.14516
\(498\) 0 0
\(499\) −36.2953 −1.62480 −0.812400 0.583100i \(-0.801839\pi\)
−0.812400 + 0.583100i \(0.801839\pi\)
\(500\) 0 0
\(501\) −10.7417 −0.479905
\(502\) 0 0
\(503\) 9.92907 0.442715 0.221358 0.975193i \(-0.428951\pi\)
0.221358 + 0.975193i \(0.428951\pi\)
\(504\) 0 0
\(505\) 28.6962 1.27696
\(506\) 0 0
\(507\) 8.49627 0.377332
\(508\) 0 0
\(509\) −42.3483 −1.87705 −0.938527 0.345206i \(-0.887809\pi\)
−0.938527 + 0.345206i \(0.887809\pi\)
\(510\) 0 0
\(511\) −50.7822 −2.24647
\(512\) 0 0
\(513\) 19.8138 0.874799
\(514\) 0 0
\(515\) 21.0164 0.926094
\(516\) 0 0
\(517\) 31.8776 1.40198
\(518\) 0 0
\(519\) −6.55067 −0.287543
\(520\) 0 0
\(521\) −20.6643 −0.905321 −0.452660 0.891683i \(-0.649525\pi\)
−0.452660 + 0.891683i \(0.649525\pi\)
\(522\) 0 0
\(523\) −17.7628 −0.776711 −0.388356 0.921510i \(-0.626957\pi\)
−0.388356 + 0.921510i \(0.626957\pi\)
\(524\) 0 0
\(525\) 2.09220 0.0913112
\(526\) 0 0
\(527\) −8.53934 −0.371979
\(528\) 0 0
\(529\) −10.0161 −0.435482
\(530\) 0 0
\(531\) −2.56317 −0.111232
\(532\) 0 0
\(533\) 9.03508 0.391353
\(534\) 0 0
\(535\) 24.2192 1.04709
\(536\) 0 0
\(537\) −5.45050 −0.235207
\(538\) 0 0
\(539\) −8.82167 −0.379976
\(540\) 0 0
\(541\) −5.63706 −0.242356 −0.121178 0.992631i \(-0.538667\pi\)
−0.121178 + 0.992631i \(0.538667\pi\)
\(542\) 0 0
\(543\) 3.26423 0.140081
\(544\) 0 0
\(545\) −27.2970 −1.16928
\(546\) 0 0
\(547\) 0.384934 0.0164586 0.00822930 0.999966i \(-0.497381\pi\)
0.00822930 + 0.999966i \(0.497381\pi\)
\(548\) 0 0
\(549\) −0.780269 −0.0333011
\(550\) 0 0
\(551\) 3.87381 0.165030
\(552\) 0 0
\(553\) 45.6575 1.94156
\(554\) 0 0
\(555\) 4.43204 0.188129
\(556\) 0 0
\(557\) 11.5820 0.490743 0.245372 0.969429i \(-0.421090\pi\)
0.245372 + 0.969429i \(0.421090\pi\)
\(558\) 0 0
\(559\) 50.8499 2.15072
\(560\) 0 0
\(561\) 2.20676 0.0931693
\(562\) 0 0
\(563\) 43.6941 1.84149 0.920743 0.390170i \(-0.127584\pi\)
0.920743 + 0.390170i \(0.127584\pi\)
\(564\) 0 0
\(565\) 21.8827 0.920614
\(566\) 0 0
\(567\) 16.3311 0.685842
\(568\) 0 0
\(569\) −12.6480 −0.530233 −0.265116 0.964216i \(-0.585410\pi\)
−0.265116 + 0.964216i \(0.585410\pi\)
\(570\) 0 0
\(571\) −11.7061 −0.489887 −0.244943 0.969537i \(-0.578769\pi\)
−0.244943 + 0.969537i \(0.578769\pi\)
\(572\) 0 0
\(573\) −5.50426 −0.229944
\(574\) 0 0
\(575\) −3.67334 −0.153189
\(576\) 0 0
\(577\) 17.1630 0.714507 0.357253 0.934008i \(-0.383713\pi\)
0.357253 + 0.934008i \(0.383713\pi\)
\(578\) 0 0
\(579\) −14.8609 −0.617598
\(580\) 0 0
\(581\) 28.7312 1.19197
\(582\) 0 0
\(583\) 27.5763 1.14209
\(584\) 0 0
\(585\) 31.9761 1.32205
\(586\) 0 0
\(587\) −1.03040 −0.0425292 −0.0212646 0.999774i \(-0.506769\pi\)
−0.0212646 + 0.999774i \(0.506769\pi\)
\(588\) 0 0
\(589\) −46.0162 −1.89606
\(590\) 0 0
\(591\) 7.62220 0.313535
\(592\) 0 0
\(593\) −12.9978 −0.533754 −0.266877 0.963731i \(-0.585992\pi\)
−0.266877 + 0.963731i \(0.585992\pi\)
\(594\) 0 0
\(595\) −7.61841 −0.312324
\(596\) 0 0
\(597\) −14.0469 −0.574902
\(598\) 0 0
\(599\) −23.3677 −0.954779 −0.477390 0.878692i \(-0.658417\pi\)
−0.477390 + 0.878692i \(0.658417\pi\)
\(600\) 0 0
\(601\) 14.1721 0.578091 0.289045 0.957315i \(-0.406662\pi\)
0.289045 + 0.957315i \(0.406662\pi\)
\(602\) 0 0
\(603\) −5.55820 −0.226347
\(604\) 0 0
\(605\) 0.362738 0.0147474
\(606\) 0 0
\(607\) 20.0134 0.812320 0.406160 0.913802i \(-0.366868\pi\)
0.406160 + 0.913802i \(0.366868\pi\)
\(608\) 0 0
\(609\) −1.47536 −0.0597845
\(610\) 0 0
\(611\) 48.5470 1.96400
\(612\) 0 0
\(613\) 17.1274 0.691770 0.345885 0.938277i \(-0.387579\pi\)
0.345885 + 0.938277i \(0.387579\pi\)
\(614\) 0 0
\(615\) −2.88135 −0.116187
\(616\) 0 0
\(617\) −17.9852 −0.724056 −0.362028 0.932167i \(-0.617915\pi\)
−0.362028 + 0.932167i \(0.617915\pi\)
\(618\) 0 0
\(619\) −28.9080 −1.16191 −0.580955 0.813935i \(-0.697321\pi\)
−0.580955 + 0.813935i \(0.697321\pi\)
\(620\) 0 0
\(621\) 13.2490 0.531664
\(622\) 0 0
\(623\) 3.12811 0.125325
\(624\) 0 0
\(625\) −29.0579 −1.16232
\(626\) 0 0
\(627\) 11.8916 0.474905
\(628\) 0 0
\(629\) −2.73317 −0.108979
\(630\) 0 0
\(631\) 15.7580 0.627317 0.313659 0.949536i \(-0.398445\pi\)
0.313659 + 0.949536i \(0.398445\pi\)
\(632\) 0 0
\(633\) 11.4131 0.453631
\(634\) 0 0
\(635\) −47.3386 −1.87858
\(636\) 0 0
\(637\) −13.4347 −0.532301
\(638\) 0 0
\(639\) 39.4755 1.56163
\(640\) 0 0
\(641\) −2.90815 −0.114865 −0.0574325 0.998349i \(-0.518291\pi\)
−0.0574325 + 0.998349i \(0.518291\pi\)
\(642\) 0 0
\(643\) −1.20261 −0.0474262 −0.0237131 0.999719i \(-0.507549\pi\)
−0.0237131 + 0.999719i \(0.507549\pi\)
\(644\) 0 0
\(645\) −16.2164 −0.638521
\(646\) 0 0
\(647\) 40.5464 1.59404 0.797021 0.603951i \(-0.206408\pi\)
0.797021 + 0.603951i \(0.206408\pi\)
\(648\) 0 0
\(649\) −3.33884 −0.131061
\(650\) 0 0
\(651\) 17.5255 0.686877
\(652\) 0 0
\(653\) −10.4233 −0.407894 −0.203947 0.978982i \(-0.565377\pi\)
−0.203947 + 0.978982i \(0.565377\pi\)
\(654\) 0 0
\(655\) 41.7220 1.63021
\(656\) 0 0
\(657\) 41.9181 1.63538
\(658\) 0 0
\(659\) 0.825957 0.0321747 0.0160874 0.999871i \(-0.494879\pi\)
0.0160874 + 0.999871i \(0.494879\pi\)
\(660\) 0 0
\(661\) 8.75766 0.340634 0.170317 0.985389i \(-0.445521\pi\)
0.170317 + 0.985389i \(0.445521\pi\)
\(662\) 0 0
\(663\) 3.36070 0.130519
\(664\) 0 0
\(665\) −41.0536 −1.59199
\(666\) 0 0
\(667\) 2.59033 0.100298
\(668\) 0 0
\(669\) −2.79605 −0.108102
\(670\) 0 0
\(671\) −1.01640 −0.0392375
\(672\) 0 0
\(673\) −10.1027 −0.389431 −0.194715 0.980860i \(-0.562378\pi\)
−0.194715 + 0.980860i \(0.562378\pi\)
\(674\) 0 0
\(675\) −3.74834 −0.144274
\(676\) 0 0
\(677\) −24.5662 −0.944155 −0.472077 0.881557i \(-0.656496\pi\)
−0.472077 + 0.881557i \(0.656496\pi\)
\(678\) 0 0
\(679\) 36.4110 1.39733
\(680\) 0 0
\(681\) −8.72933 −0.334509
\(682\) 0 0
\(683\) −26.9497 −1.03120 −0.515600 0.856829i \(-0.672431\pi\)
−0.515600 + 0.856829i \(0.672431\pi\)
\(684\) 0 0
\(685\) 13.4687 0.514613
\(686\) 0 0
\(687\) 9.35823 0.357039
\(688\) 0 0
\(689\) 41.9964 1.59994
\(690\) 0 0
\(691\) −4.96807 −0.188994 −0.0944972 0.995525i \(-0.530124\pi\)
−0.0944972 + 0.995525i \(0.530124\pi\)
\(692\) 0 0
\(693\) 26.5741 1.00947
\(694\) 0 0
\(695\) 56.0094 2.12456
\(696\) 0 0
\(697\) 1.77689 0.0673045
\(698\) 0 0
\(699\) −1.40777 −0.0532468
\(700\) 0 0
\(701\) −38.7570 −1.46383 −0.731915 0.681395i \(-0.761373\pi\)
−0.731915 + 0.681395i \(0.761373\pi\)
\(702\) 0 0
\(703\) −14.7283 −0.555489
\(704\) 0 0
\(705\) −15.4820 −0.583086
\(706\) 0 0
\(707\) 36.3190 1.36591
\(708\) 0 0
\(709\) −49.7918 −1.86997 −0.934985 0.354688i \(-0.884587\pi\)
−0.934985 + 0.354688i \(0.884587\pi\)
\(710\) 0 0
\(711\) −37.6879 −1.41341
\(712\) 0 0
\(713\) −30.7700 −1.15234
\(714\) 0 0
\(715\) 41.6529 1.55773
\(716\) 0 0
\(717\) 12.1698 0.454490
\(718\) 0 0
\(719\) −33.5082 −1.24965 −0.624823 0.780766i \(-0.714829\pi\)
−0.624823 + 0.780766i \(0.714829\pi\)
\(720\) 0 0
\(721\) 26.5991 0.990604
\(722\) 0 0
\(723\) 1.14507 0.0425856
\(724\) 0 0
\(725\) −0.732842 −0.0272171
\(726\) 0 0
\(727\) −20.5111 −0.760714 −0.380357 0.924840i \(-0.624199\pi\)
−0.380357 + 0.924840i \(0.624199\pi\)
\(728\) 0 0
\(729\) −6.18993 −0.229257
\(730\) 0 0
\(731\) 10.0004 0.369879
\(732\) 0 0
\(733\) 39.7312 1.46750 0.733752 0.679418i \(-0.237768\pi\)
0.733752 + 0.679418i \(0.237768\pi\)
\(734\) 0 0
\(735\) 4.28442 0.158033
\(736\) 0 0
\(737\) −7.24024 −0.266698
\(738\) 0 0
\(739\) −3.29003 −0.121026 −0.0605128 0.998167i \(-0.519274\pi\)
−0.0605128 + 0.998167i \(0.519274\pi\)
\(740\) 0 0
\(741\) 18.1099 0.665285
\(742\) 0 0
\(743\) −45.6042 −1.67306 −0.836529 0.547923i \(-0.815419\pi\)
−0.836529 + 0.547923i \(0.815419\pi\)
\(744\) 0 0
\(745\) 25.7356 0.942880
\(746\) 0 0
\(747\) −23.7161 −0.867726
\(748\) 0 0
\(749\) 30.6526 1.12002
\(750\) 0 0
\(751\) 26.4517 0.965237 0.482618 0.875831i \(-0.339686\pi\)
0.482618 + 0.875831i \(0.339686\pi\)
\(752\) 0 0
\(753\) −3.36176 −0.122509
\(754\) 0 0
\(755\) 10.6832 0.388801
\(756\) 0 0
\(757\) −48.1468 −1.74992 −0.874962 0.484191i \(-0.839114\pi\)
−0.874962 + 0.484191i \(0.839114\pi\)
\(758\) 0 0
\(759\) 7.95164 0.288626
\(760\) 0 0
\(761\) 20.1841 0.731673 0.365836 0.930679i \(-0.380783\pi\)
0.365836 + 0.930679i \(0.380783\pi\)
\(762\) 0 0
\(763\) −34.5481 −1.25073
\(764\) 0 0
\(765\) 6.28861 0.227365
\(766\) 0 0
\(767\) −5.08477 −0.183601
\(768\) 0 0
\(769\) 10.1158 0.364784 0.182392 0.983226i \(-0.441616\pi\)
0.182392 + 0.983226i \(0.441616\pi\)
\(770\) 0 0
\(771\) −9.76915 −0.351827
\(772\) 0 0
\(773\) −23.0470 −0.828941 −0.414471 0.910063i \(-0.636033\pi\)
−0.414471 + 0.910063i \(0.636033\pi\)
\(774\) 0 0
\(775\) 8.70527 0.312703
\(776\) 0 0
\(777\) 5.60934 0.201234
\(778\) 0 0
\(779\) 9.57517 0.343066
\(780\) 0 0
\(781\) 51.4217 1.84001
\(782\) 0 0
\(783\) 2.64321 0.0944608
\(784\) 0 0
\(785\) 44.6706 1.59436
\(786\) 0 0
\(787\) 34.6384 1.23472 0.617362 0.786679i \(-0.288201\pi\)
0.617362 + 0.786679i \(0.288201\pi\)
\(788\) 0 0
\(789\) −4.41940 −0.157335
\(790\) 0 0
\(791\) 27.6956 0.984742
\(792\) 0 0
\(793\) −1.54789 −0.0549671
\(794\) 0 0
\(795\) −13.3930 −0.475000
\(796\) 0 0
\(797\) 5.95250 0.210848 0.105424 0.994427i \(-0.466380\pi\)
0.105424 + 0.994427i \(0.466380\pi\)
\(798\) 0 0
\(799\) 9.54752 0.337767
\(800\) 0 0
\(801\) −2.58209 −0.0912337
\(802\) 0 0
\(803\) 54.6035 1.92692
\(804\) 0 0
\(805\) −27.4516 −0.967541
\(806\) 0 0
\(807\) 12.4383 0.437849
\(808\) 0 0
\(809\) −51.5140 −1.81114 −0.905568 0.424201i \(-0.860555\pi\)
−0.905568 + 0.424201i \(0.860555\pi\)
\(810\) 0 0
\(811\) −3.18270 −0.111760 −0.0558799 0.998438i \(-0.517796\pi\)
−0.0558799 + 0.998438i \(0.517796\pi\)
\(812\) 0 0
\(813\) −9.64487 −0.338260
\(814\) 0 0
\(815\) −32.2384 −1.12926
\(816\) 0 0
\(817\) 53.8896 1.88536
\(818\) 0 0
\(819\) 40.4702 1.41414
\(820\) 0 0
\(821\) −19.2377 −0.671402 −0.335701 0.941969i \(-0.608973\pi\)
−0.335701 + 0.941969i \(0.608973\pi\)
\(822\) 0 0
\(823\) −54.4984 −1.89969 −0.949847 0.312716i \(-0.898761\pi\)
−0.949847 + 0.312716i \(0.898761\pi\)
\(824\) 0 0
\(825\) −2.24964 −0.0783223
\(826\) 0 0
\(827\) −24.7763 −0.861557 −0.430778 0.902458i \(-0.641761\pi\)
−0.430778 + 0.902458i \(0.641761\pi\)
\(828\) 0 0
\(829\) 52.2277 1.81394 0.906971 0.421192i \(-0.138388\pi\)
0.906971 + 0.421192i \(0.138388\pi\)
\(830\) 0 0
\(831\) 18.4266 0.639213
\(832\) 0 0
\(833\) −2.64214 −0.0915446
\(834\) 0 0
\(835\) −39.8743 −1.37991
\(836\) 0 0
\(837\) −31.3982 −1.08528
\(838\) 0 0
\(839\) 25.0058 0.863296 0.431648 0.902042i \(-0.357932\pi\)
0.431648 + 0.902042i \(0.357932\pi\)
\(840\) 0 0
\(841\) −28.4832 −0.982180
\(842\) 0 0
\(843\) −13.7119 −0.472263
\(844\) 0 0
\(845\) 31.5390 1.08497
\(846\) 0 0
\(847\) 0.459095 0.0157747
\(848\) 0 0
\(849\) −11.7011 −0.401580
\(850\) 0 0
\(851\) −9.84849 −0.337602
\(852\) 0 0
\(853\) 26.9546 0.922908 0.461454 0.887164i \(-0.347328\pi\)
0.461454 + 0.887164i \(0.347328\pi\)
\(854\) 0 0
\(855\) 33.8876 1.15893
\(856\) 0 0
\(857\) −32.0787 −1.09579 −0.547894 0.836548i \(-0.684570\pi\)
−0.547894 + 0.836548i \(0.684570\pi\)
\(858\) 0 0
\(859\) −28.8505 −0.984366 −0.492183 0.870492i \(-0.663801\pi\)
−0.492183 + 0.870492i \(0.663801\pi\)
\(860\) 0 0
\(861\) −3.64675 −0.124281
\(862\) 0 0
\(863\) 7.39512 0.251733 0.125866 0.992047i \(-0.459829\pi\)
0.125866 + 0.992047i \(0.459829\pi\)
\(864\) 0 0
\(865\) −24.3167 −0.826794
\(866\) 0 0
\(867\) 0.660935 0.0224465
\(868\) 0 0
\(869\) −49.0932 −1.66537
\(870\) 0 0
\(871\) −11.0263 −0.373612
\(872\) 0 0
\(873\) −30.0554 −1.01722
\(874\) 0 0
\(875\) −30.3256 −1.02519
\(876\) 0 0
\(877\) −8.74842 −0.295413 −0.147707 0.989031i \(-0.547189\pi\)
−0.147707 + 0.989031i \(0.547189\pi\)
\(878\) 0 0
\(879\) −7.67584 −0.258900
\(880\) 0 0
\(881\) −36.6843 −1.23592 −0.617962 0.786208i \(-0.712041\pi\)
−0.617962 + 0.786208i \(0.712041\pi\)
\(882\) 0 0
\(883\) 12.8854 0.433629 0.216815 0.976213i \(-0.430433\pi\)
0.216815 + 0.976213i \(0.430433\pi\)
\(884\) 0 0
\(885\) 1.62157 0.0545086
\(886\) 0 0
\(887\) −21.6305 −0.726282 −0.363141 0.931734i \(-0.618296\pi\)
−0.363141 + 0.931734i \(0.618296\pi\)
\(888\) 0 0
\(889\) −59.9135 −2.00943
\(890\) 0 0
\(891\) −17.5600 −0.588282
\(892\) 0 0
\(893\) 51.4490 1.72168
\(894\) 0 0
\(895\) −20.2328 −0.676307
\(896\) 0 0
\(897\) 12.1097 0.404331
\(898\) 0 0
\(899\) −6.13869 −0.204737
\(900\) 0 0
\(901\) 8.25925 0.275156
\(902\) 0 0
\(903\) −20.5241 −0.682999
\(904\) 0 0
\(905\) 12.1171 0.402787
\(906\) 0 0
\(907\) 26.5017 0.879975 0.439988 0.898004i \(-0.354983\pi\)
0.439988 + 0.898004i \(0.354983\pi\)
\(908\) 0 0
\(909\) −29.9794 −0.994355
\(910\) 0 0
\(911\) 15.8224 0.524220 0.262110 0.965038i \(-0.415582\pi\)
0.262110 + 0.965038i \(0.415582\pi\)
\(912\) 0 0
\(913\) −30.8931 −1.02241
\(914\) 0 0
\(915\) 0.493633 0.0163190
\(916\) 0 0
\(917\) 52.8049 1.74377
\(918\) 0 0
\(919\) 16.0356 0.528966 0.264483 0.964390i \(-0.414799\pi\)
0.264483 + 0.964390i \(0.414799\pi\)
\(920\) 0 0
\(921\) 12.7317 0.419525
\(922\) 0 0
\(923\) 78.3109 2.57764
\(924\) 0 0
\(925\) 2.78628 0.0916124
\(926\) 0 0
\(927\) −21.9562 −0.721137
\(928\) 0 0
\(929\) 29.6096 0.971461 0.485730 0.874109i \(-0.338554\pi\)
0.485730 + 0.874109i \(0.338554\pi\)
\(930\) 0 0
\(931\) −14.2378 −0.466624
\(932\) 0 0
\(933\) −22.2895 −0.729726
\(934\) 0 0
\(935\) 8.19169 0.267897
\(936\) 0 0
\(937\) 52.4643 1.71393 0.856967 0.515371i \(-0.172346\pi\)
0.856967 + 0.515371i \(0.172346\pi\)
\(938\) 0 0
\(939\) 16.7276 0.545883
\(940\) 0 0
\(941\) −27.4776 −0.895744 −0.447872 0.894098i \(-0.647818\pi\)
−0.447872 + 0.894098i \(0.647818\pi\)
\(942\) 0 0
\(943\) 6.40270 0.208501
\(944\) 0 0
\(945\) −28.0121 −0.911232
\(946\) 0 0
\(947\) 32.6627 1.06139 0.530697 0.847561i \(-0.321930\pi\)
0.530697 + 0.847561i \(0.321930\pi\)
\(948\) 0 0
\(949\) 83.1566 2.69938
\(950\) 0 0
\(951\) −11.8185 −0.383242
\(952\) 0 0
\(953\) 38.0028 1.23103 0.615515 0.788125i \(-0.288948\pi\)
0.615515 + 0.788125i \(0.288948\pi\)
\(954\) 0 0
\(955\) −20.4323 −0.661175
\(956\) 0 0
\(957\) 1.58638 0.0512802
\(958\) 0 0
\(959\) 17.0465 0.550460
\(960\) 0 0
\(961\) 41.9203 1.35227
\(962\) 0 0
\(963\) −25.3022 −0.815351
\(964\) 0 0
\(965\) −55.1651 −1.77583
\(966\) 0 0
\(967\) −53.6660 −1.72578 −0.862891 0.505390i \(-0.831349\pi\)
−0.862891 + 0.505390i \(0.831349\pi\)
\(968\) 0 0
\(969\) 3.56160 0.114415
\(970\) 0 0
\(971\) 20.6172 0.661638 0.330819 0.943694i \(-0.392675\pi\)
0.330819 + 0.943694i \(0.392675\pi\)
\(972\) 0 0
\(973\) 70.8876 2.27255
\(974\) 0 0
\(975\) −3.42601 −0.109720
\(976\) 0 0
\(977\) −17.5439 −0.561279 −0.280640 0.959813i \(-0.590547\pi\)
−0.280640 + 0.959813i \(0.590547\pi\)
\(978\) 0 0
\(979\) −3.36349 −0.107498
\(980\) 0 0
\(981\) 28.5177 0.910500
\(982\) 0 0
\(983\) −20.0456 −0.639354 −0.319677 0.947527i \(-0.603574\pi\)
−0.319677 + 0.947527i \(0.603574\pi\)
\(984\) 0 0
\(985\) 28.2943 0.901532
\(986\) 0 0
\(987\) −19.5946 −0.623702
\(988\) 0 0
\(989\) 36.0348 1.14584
\(990\) 0 0
\(991\) 22.7829 0.723723 0.361862 0.932232i \(-0.382141\pi\)
0.361862 + 0.932232i \(0.382141\pi\)
\(992\) 0 0
\(993\) 4.04119 0.128243
\(994\) 0 0
\(995\) −52.1435 −1.65306
\(996\) 0 0
\(997\) 11.4479 0.362558 0.181279 0.983432i \(-0.441976\pi\)
0.181279 + 0.983432i \(0.441976\pi\)
\(998\) 0 0
\(999\) −10.0496 −0.317954
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 \(a_p\))